[{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1057_C. Tanya and Colored Candies","prompt":"Solve the following coding problem using the programming language python:\n\nThere are n candy boxes in front of Tania. The boxes are arranged in a row from left to right, numbered from 1 to n. The i-th box contains r_i candies, candies have the color c_i (the color can take one of three values \u200b\u200b\u2014 red, green, or blue). All candies inside a single box have the same color (and it is equal to c_i).\n\nInitially, Tanya is next to the box number s. Tanya can move to the neighbor box (that is, with a number that differs by one) or eat candies in the current box. Tanya eats candies instantly, but the movement takes one second.\n\nIf Tanya eats candies from the box, then the box itself remains in place, but there is no more candies in it. In other words, Tanya always eats all the candies from the box and candies in the boxes are not refilled.\n\nIt is known that Tanya cannot eat candies of the same color one after another (that is, the colors of candies in two consecutive boxes from which she eats candies are always different). In addition, Tanya's appetite is constantly growing, so in each next box from which she eats candies, there should be strictly more candies than in the previous one.\n\nNote that for the first box from which Tanya will eat candies, there are no restrictions on the color and number of candies.\n\nTanya wants to eat at least k candies. What is the minimum number of seconds she will need? Remember that she eats candies instantly, and time is spent only on movements.\n\nInput\n\nThe first line contains three integers n, s and k (1 \u2264 n \u2264 50, 1 \u2264 s \u2264 n, 1 \u2264 k \u2264 2000) \u2014 number of the boxes, initial position of Tanya and lower bound on number of candies to eat. The following line contains n integers r_i (1 \u2264 r_i \u2264 50) \u2014 numbers of candies in the boxes. The third line contains sequence of n letters 'R', 'G' and 'B', meaning the colors of candies in the correspondent boxes ('R' for red, 'G' for green, 'B' for blue). Recall that each box contains candies of only one color. The third line contains no spaces.\n\nOutput\n\nPrint minimal number of seconds to eat at least k candies. If solution doesn't exist, print \"-1\".\n\nExamples\n\nInput\n\n5 3 10\n1 2 3 4 5\nRGBRR\n\n\nOutput\n\n4\n\n\nInput\n\n2 1 15\n5 6\nRG\n\n\nOutput\n\n-1\n\nNote\n\nThe sequence of actions of Tanya for the first example:\n\n * move from the box 3 to the box 2; \n * eat candies from the box 2; \n * move from the box 2 to the box 3; \n * eat candy from the box 3; \n * move from the box 3 to the box 4; \n * move from the box 4 to the box 5; \n * eat candies from the box 5. \n\n\n\nSince Tanya eats candy instantly, the required time is four seconds.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nINF = 10e9\nn,s,k = map(int, input().split())\nr = list(map(int, input().split()))\nr.append(0)\ncol = input()\nmat = []\nfor i in range(n+1):\n adj = {}\n for j in range(n):\n if i == n:\n adj[j] = abs((s-1)-j)\n else:\n if col[i] != col[j] and r[i] < r[j]:\n adj[j] = abs(i-j)\n mat.append(adj)\n# print(*mat, sep='\\n')\n\nmem = [{} for i in range(n+1)]\n# print(mem)\n\ndef get(s, k):\n # print(s,k)\n # print(mem)\n if mem[s].get(k):\n return mem[s].get(k)\n if r[s] >= k:\n mem[s][k] = 0\n else:\n mi = None\n for nei in mat[s]:\n ncost = get(nei, k-r[s])\n if ncost is None:\n continue\n curr = ncost + mat[s][nei]\n if mi is None or curr < mi:\n mi = curr\n if mi is not None:\n mem[s][k] = mi\n else:\n mem[s][k] = INF\n return mem[s].get(k)\n\n# print(mem)\n\nans = get(n,k)\nif ans is None or ans >= INF:\n print(-1)\nelse:\n print(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 1 15\\n5 6\\nRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 3 10\\n1 2 3 4 5\\nRGBRR\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '30 28 208\\n3 42 42 47 46 44 5 28 35 28 35 44 25 44 47 3 3 35 28 5 3 42 3 46 25 25 5 47 46 3\\nBGBBGBBBBGRRGGGBRGRGRRGBBRRRRG\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '50 39 2000\\n48 43 26 24 46 37 15 30 39 34 4 14 29 34 8 18 40 8 17 37 15 29 2 23 41 7 12 13 36 11 24 22 26 46 11 31 10 46 11 35 6 41 16 50 11 1 46 20 46 28\\nBGBBBBBBRGGBBBRRRRBBGRGGRBBRBBBRBBBBBRRGBGGRRRBBRB\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 32 600\\n21 21 18 47 16 11 10 46 9 15 27 5 11 42 29 25 16 41 31 8 12 28 1 24 17 40 45 12 33 32 34 2 45 17 49 17 20 42 15 17 8 29 2 20 4 27 50 1 49 1\\nBBRBBGBGBBRBGRRGRGGGBGBRRBBBGGBBBBGBGBRBBGRRGGBRGR\\n', 'output': '185\\n'}, {'type': 'stdin_stdout', 'input': '48 2 259\\n25 31 22 30 30 17 31 50 28 30 46 43 4 6 10 22 50 14 5 46 12 6 46 3 17 12 4 28 25 14 5 5 6 14 22 12 17 43 43 10 4 3 31 3 25 28 50 10\\nBBBBGGRRBRRBBRGGGBGGRGBRBGRGRGRBBRRBRRGBGBGGGRBR\\n', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '1 1 10\\n10\\nR\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '9 1 6\\n1 1 1 3 3 3 2 2 2\\nRGGBRRGBB\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5 3 10\\n1 2 3 4 5\\nRGBRG\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6 1 21\\n6 5 4 3 2 1\\nRGBRGB\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '2 1 10\\n5 5\\nRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 1 10\\n5 6\\nRR\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 2000\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '48 33 357\\n18 37 22 21 4 17 39 32 40 43 29 29 50 21 39 43 11 11 4 50 36 40 32 50 18 32 11 36 29 36 22 21 29 43 49 18 17 29 37 40 17 37 49 4 39 49 22 29\\nGRGGGGBRBRRGGRGBRGBBGRBRRGBBRRBBBGRBBBBGRGGRRBRG\\n', 'output': '63\\n'}, {'type': 'stdin_stdout', 'input': '48 25 323\\n39 37 32 4 4 32 18 44 49 4 12 12 12 22 22 37 38 32 24 45 44 37 18 39 45 22 24 22 45 39 4 22 24 22 12 49 4 29 18 38 29 29 38 44 12 12 49 4\\nRRRRRBRRGBBRGRGGBGGBGBBBRBRGGGGBBRGRBGGGRBRBBRBG\\n', 'output': '64\\n'}, {'type': 'stdin_stdout', 'input': '39 21 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 20 29 21 34 36 39 30 34 21 20 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 29 49 33 41 14 25 46 43 7 47 28 25 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 4 200\\n14 10 50 47 41 9 22 21 42 36 50 10 27 28 39 1 36 12 45 35 17 3 15 25 32 4 34 39 44 34 20 15 18 1 38 25 20 45 24 9 18 15 35 36 12 9 28 4 44 10\\nBGBRRBGBRRRGRGRBRGGGRBRRGBBGGRBRRGGRGGGBRRBRGGBGBG\\n', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '6 1 21\\n4 2 3 5 1 6\\nRGBGRB\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '50 37 500\\n25 43 15 16 29 23 46 18 15 21 33 26 38 25 2 17 48 50 33 31 3 45 40 12 42 29 37 42 7 11 47 16 44 17 27 46 32 23 14 7 27 25 13 32 43 33 36 39 35 7\\nGGBBRGBRRRRBBRGBRRRGGRGGRGGBRRRGBBRRGRGGRBGBGGRGBR\\n', 'output': '86\\n'}, {'type': 'stdin_stdout', 'input': '50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nRRRRRRRRRRRRRRRRRRRRRRRRRGGGGGGGGGGGGGGGGGGGGGGGGG\\n', 'output': '992'}, {'type': 'stdin_stdout', 'input': '50 39 2000\\n48 43 26 24 46 37 15 30 39 34 4 14 29 34 8 18 40 8 17 37 15 29 2 23 41 7 12 13 36 11 24 22 26 46 11 31 1 46 11 35 6 41 16 50 11 1 46 20 46 28\\nBGBBBBBBRGGBBBRRRRBBGRGGRBBRBBBRBBBBBRRGBGGRRRBBRB\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '48 2 259\\n25 31 22 30 30 17 31 50 28 30 46 43 4 6 10 22 50 14 5 46 12 6 46 3 17 12 4 28 25 21 5 5 6 14 22 12 17 43 43 10 4 3 31 3 25 28 50 10\\nBBBBGGRRBRRBBRGGGBGGRGBRBGRGRGRBBRRBRRGBGBGGGRBR\\n', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '9 1 6\\n1 1 2 3 3 3 2 2 2\\nRGGBRRGBB\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 1 10\\n9 5\\nRG\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '48 33 357\\n18 37 22 21 4 17 39 32 40 43 29 29 50 21 39 43 11 11 4 50 36 40 32 50 18 32 11 36 29 36 22 21 29 43 49 18 17 29 37 40 17 37 2 4 39 49 22 29\\nGRGGGGBRBRRGGRGBRGBBGRBRRGBBRRBBBGRBBBBGRGGRRBRG\\n', 'output': '63\\n'}, {'type': 'stdin_stdout', 'input': '39 21 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 10 29 21 34 36 39 30 34 21 20 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '50 37 500\\n25 43 15 16 29 23 46 18 15 21 33 26 38 25 2 17 48 50 33 31 3 23 40 12 42 29 37 42 7 11 47 16 44 17 27 46 32 23 14 7 27 25 13 32 43 33 36 39 35 7\\nGGBBRGBRRRRBBRGBRRRGGRGGRGGBRRRGBBRRGRGGRBGBGGRGBR\\n', 'output': '86\\n'}, {'type': 'stdin_stdout', 'input': '39 36 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 10 29 21 34 36 39 30 34 21 20 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '30 28 208\\n3 42 42 47 46 12 5 28 35 28 35 44 25 44 47 3 3 35 28 5 3 42 3 46 25 25 5 47 46 3\\nBGBBGBBBBGRRGGGBRGRGRRGBBRRRRG\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '9 1 6\\n1 1 1 3 3 6 2 2 2\\nRGGBRRGBB\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5 3 10\\n1 2 4 4 5\\nRGBRG\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '39 21 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 20 44 21 34 36 39 30 34 21 20 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '50 4 200\\n14 10 50 47 41 9 22 21 42 36 50 10 27 28 39 1 36 12 45 35 17 3 15 25 32 4 34 39 44 34 20 15 18 1 38 25 20 3 24 9 18 15 35 36 12 9 28 4 44 10\\nBGBRRBGBRRRGRGRBRGGGRBRRGBBGGRBRRGGRGGGBRRBRGGBGBG\\n', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '6 1 21\\n6 5 4 3 4 1\\nRGBRGB\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 2000\\n1 3 5 7 9 11 13 15 32 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 29 49 23 41 14 25 46 43 7 47 28 25 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 1 21\\n4 2 3 5 1 6\\nRGBRGB\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 11 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nRRRRRRRRRRRRRRRRRRRRRRRRRGGGGGGGGGGGGGGGGGGGGGGGGG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 1 24\\n5 6\\nRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '48 2 259\\n25 31 22 30 30 17 31 50 28 30 46 43 4 6 10 22 50 27 5 46 12 6 46 3 17 12 4 28 25 21 5 5 6 14 22 12 17 43 43 10 4 3 31 3 25 28 50 10\\nBBBBGGRRBRRBBRGGGBGGRGBRBGRGRGRBBRRBRRGBGBGGGRBR\\n', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '9 1 6\\n1 1 2 5 3 3 2 2 2\\nRGGBRRGBB\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '50 50 2000\\n1 3 5 7 9 11 13 15 32 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 29 49 23 15 14 25 46 43 7 47 28 25 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 1 21\\n4 2 3 5 1 6\\nBGRBGR\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 11 44 42 40 38 36 34 32 44 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nRRRRRRRRRRRRRRRRRRRRRRRRRGGGGGGGGGGGGGGGGGGGGGGGGG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '9 1 6\\n1 1 1 5 3 3 2 2 2\\nRGGBRRGBB\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '50 50 2000\\n1 3 5 7 9 11 13 15 32 19 21 32 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '39 36 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 10 29 21 34 36 39 30 34 21 21 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 29 49 23 15 14 25 46 43 7 47 28 50 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 1 21\\n5 2 3 5 1 6\\nBGRBGR\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 11 44 42 40 38 36 34 32 44 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGGGGGGGGGGGGGGGGGGGGGGGGGRRRRRRRRRRRRRRRRRRRRRRRRR\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '9 1 6\\n1 1 1 5 3 1 2 2 2\\nRGGBRRGBB\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '50 50 2000\\n1 3 5 7 9 11 13 15 32 19 21 32 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 1 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 40 49 23 15 14 25 46 43 7 47 28 50 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 1250\\n1 3 5 7 9 11 13 15 17 17 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 11 44 42 40 38 36 34 32 44 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGGGGGGGGGGGGGGGGGGGGGGGGGRRRRRRRRRRRRRRRRRRRRRRRRR\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '9 1 6\\n1 1 1 5 3 1 4 2 2\\nRGGBRRGBB\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '50 50 2000\\n1 3 7 7 9 11 13 15 32 19 21 32 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 1 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 2000\\n1 3 7 7 9 11 13 15 32 19 21 32 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 1 10 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 2000\\n1 3 7 7 9 11 13 15 32 19 21 32 25 10 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 1 10 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 2000\\n1 3 7 7 9 11 13 15 32 19 21 32 25 10 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 1 10 6 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 39 2000\\n48 43 26 24 46 37 15 30 39 34 4 14 29 34 8 18 40 8 17 40 15 29 2 23 41 7 12 13 36 11 24 22 26 46 11 31 10 46 11 35 6 41 16 50 11 1 46 20 46 28\\nBGBBBBBBRGGBBBRRRRBBGRGGRBBRBBBRBBBBBRRGBGGRRRBBRB\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '48 2 259\\n25 31 22 30 30 17 31 50 28 30 46 43 4 6 10 22 50 14 5 46 12 6 46 4 17 12 4 28 25 14 5 5 6 14 22 12 17 43 43 10 4 3 31 3 25 28 50 10\\nBBBBGGRRBRRBBRGGGBGGRGBRBGRGRGRBBRRBRRGBGBGGGRBR\\n', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '1 1 20\\n10\\nR\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 1 16\\n5 5\\nRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 1 10\\n1 6\\nRR\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 2000\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 7 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '48 33 357\\n18 37 22 21 4 17 39 32 40 43 29 29 50 21 39 43 11 11 4 50 36 40 32 50 18 32 11 36 29 36 22 21 29 43 49 18 17 29 37 40 17 43 49 4 39 49 22 29\\nGRGGGGBRBRRGGRGBRGBBGRBRRGBBRRBBBGRBBBBGRGGRRBRG\\n', 'output': '63\\n'}, {'type': 'stdin_stdout', 'input': '50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 31 17 23 48 20 44 46 44 13 4 29 49 33 41 14 25 46 43 7 47 28 25 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 1 21\\n4 2 3 2 1 6\\nRGBGRB\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 1 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nRRRRRRRRRRRRRRRRRRRRRRRRRGGGGGGGGGGGGGGGGGGGGGGGGG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 1 15\\n5 1\\nRG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '50 39 2000\\n48 43 26 24 46 37 15 30 36 34 4 14 29 34 8 18 40 8 17 37 15 29 2 23 41 7 12 13 36 11 24 22 26 46 11 31 1 46 11 35 6 41 16 50 11 1 46 20 46 28\\nBGBBBBBBRGGBBBRRRRBBGRGGRBBRBBBRBBBBBRRGBGGRRRBBRB\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77541","program":"```python\nINF = 10e9\nn,s,k = map(int, input().split())\nr = list(map(int, input().split()))\nr.append(0)\ncol = input()\nmat = []\nfor i in range(n+1):\n adj = {}\n for j in range(n):\n if i == n:\n adj[j] = abs((s-1)-j)\n else:\n if col[i] != col[j] and r[i] < r[j]:\n adj[j] = abs(i-j)\n mat.append(adj)\n# print(*mat, sep='\\n')\n\nmem = [{} for i in range(n+1)]\n# print(mem)\n\ndef get(s, k):\n # print(s,k)\n # print(mem)\n if mem[s].get(k):\n return mem[s].get(k)\n if r[s] >= k:\n mem[s][k] = 0\n else:\n mi = None\n for nei in mat[s]:\n ncost = get(nei, k-r[s])\n if ncost is None:\n continue\n curr = ncost + mat[s][nei]\n if mi is None or curr < mi:\n mi = curr\n if mi is not None:\n mem[s][k] = mi\n else:\n mem[s][k] = INF\n return mem[s].get(k)\n\n# print(mem)\n\nans = get(n,k)\nif ans is None or ans >= INF:\n print(-1)\nelse:\n print(ans)\n\n```","inputs":"2 1 15\n5 6\nRG\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12369},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1080_B. Margarite and the best present","prompt":"Solve the following coding problem using the programming language python:\n\nLittle girl Margarita is a big fan of competitive programming. She especially loves problems about arrays and queries on them.\n\nRecently, she was presented with an array a of the size of 10^9 elements that is filled as follows: \n\n * a_1 = -1 \n * a_2 = 2 \n * a_3 = -3 \n * a_4 = 4 \n * a_5 = -5 \n * And so on ... \n\n\n\nThat is, the value of the i-th element of the array a is calculated using the formula a_i = i \u22c5 (-1)^i.\n\nShe immediately came up with q queries on this array. Each query is described with two numbers: l and r. The answer to a query is the sum of all the elements of the array at positions from l to r inclusive.\n\nMargarita really wants to know the answer to each of the requests. She doesn't want to count all this manually, but unfortunately, she couldn't write the program that solves the problem either. She has turned to you \u2014 the best programmer.\n\nHelp her find the answers!\n\nInput\n\nThe first line contains a single integer q (1 \u2264 q \u2264 10^3) \u2014 the number of the queries.\n\nEach of the next q lines contains two integers l and r (1 \u2264 l \u2264 r \u2264 10^9) \u2014 the descriptions of the queries.\n\nOutput\n\nPrint q lines, each containing one number \u2014 the answer to the query. \n\nExample\n\nInput\n\n\n5\n1 3\n2 5\n5 5\n4 4\n2 3\n\n\nOutput\n\n\n-2\n-2\n-5\n4\n-1\n\nNote\n\nIn the first query, you need to find the sum of the elements of the array from position 1 to position 3. The sum is equal to a_1 + a_2 + a_3 = -1 + 2 -3 = -2.\n\nIn the second query, you need to find the sum of the elements of the array from position 2 to position 5. The sum is equal to a_2 + a_3 + a_4 + a_5 = 2 -3 + 4 - 5 = -2.\n\nIn the third query, you need to find the sum of the elements of the array from position 5 to position 5. The sum is equal to a_5 = -5.\n\nIn the fourth query, you need to find the sum of the elements of the array from position 4 to position 4. The sum is equal to a_4 = 4.\n\nIn the fifth query, you need to find the sum of the elements of the array from position 2 to position 3. The sum is equal to a_2 + a_3 = 2 - 3 = -1.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfor i in range(int(input())):\n a,b=map(int,input().split())\n if (b-a)%2!=0:\n if a%2==0:\n print(-(b-a+1)//2)\n else:\n print((b-a+1)//2)\n else:\n if a%2!=0:\n print((b-a)//2 - b)\n else:\n print(-(b-a)//2 + b)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 3\\n2 5\\n5 5\\n4 4\\n2 3\\n', 'output': '-2\\n-2\\n-5\\n4\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n200000000 1000000000\\n', 'output': '600000000\\n'}, {'type': 'stdin_stdout', 'input': '6\\n617758920 825919887\\n775957146 950878973\\n404173573 553845184\\n25837072 795166931\\n756434592 838258528\\n590139756 977664562\\n', 'output': '-104080484\\n-87460914\\n74835806\\n-384664930\\n797346560\\n783902159\\n'}, {'type': 'stdin_stdout', 'input': '10\\n449347852 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'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77545","program":"```python\nfor i in range(int(input())):\n a,b=map(int,input().split())\n if (b-a)%2!=0:\n if a%2==0:\n print(-(b-a+1)//2)\n else:\n print((b-a+1)//2)\n else:\n if a%2!=0:\n print((b-a)//2 - b)\n else:\n print(-(b-a)//2 + b)\n```","inputs":"5\n1 3\n2 5\n5 5\n4 4\n2 3\n","output":"-2\n-2\n-5\n4\n-1\n","actual_output":"-2\n-2\n-5\n4\n-1\n","execution_success":true,"sample_index":12370},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"10_A. Power Consumption Calculation","prompt":"Solve the following coding problem using the programming language python:\n\nTom is interested in power consumption of his favourite laptop. His laptop has three modes. In normal mode laptop consumes P1 watt per minute. T1 minutes after Tom moved the mouse or touched the keyboard for the last time, a screensaver starts and power consumption changes to P2 watt per minute. Finally, after T2 minutes from the start of the screensaver, laptop switches to the \"sleep\" mode and consumes P3 watt per minute. If Tom moves the mouse or touches the keyboard when the laptop is in the second or in the third mode, it switches to the first (normal) mode. Tom's work with the laptop can be divided into n time periods [l1, r1], [l2, r2], ..., [ln, rn]. During each interval Tom continuously moves the mouse and presses buttons on the keyboard. Between the periods Tom stays away from the laptop. Find out the total amount of power consumed by the laptop during the period [l1, rn].\n\nInput\n\nThe first line contains 6 integer numbers n, P1, P2, P3, T1, T2 (1 \u2264 n \u2264 100, 0 \u2264 P1, P2, P3 \u2264 100, 1 \u2264 T1, T2 \u2264 60). The following n lines contain description of Tom's work. Each i-th of these lines contains two space-separated integers li and ri (0 \u2264 li < ri \u2264 1440, ri < li + 1 for i < n), which stand for the start and the end of the i-th period of work.\n\nOutput\n\nOutput the answer to the problem.\n\nExamples\n\nInput\n\n1 3 2 1 5 10\n0 10\n\n\nOutput\n\n30\n\nInput\n\n2 8 4 2 5 10\n20 30\n50 100\n\n\nOutput\n\n570\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,p1,p2,p3,t1,t2 = map(int,input().split())\n\np=[]\nc=0\nfor j in range(n):\n\n\n l,r = map(int,input().split())\n\n\n if j==0:\n c+= (r-l)*p1\n p.append(r)\n else:\n if l-p[-1]>0:\n if l-p[-1]<=t1:\n c+=(l-p[-1])*p1\n else:\n if t1+t2>=l-p[-1]>t1:\n c+=t1*p1 + ((l-p[-1])-t1)*p2\n elif l-p[-1]> t1+t2:\n c+=t1*p1 + (t2)*p2 + ((l-p[-1])-(t1+t2))*p3\n c+=(r-l)*p1\n p.append(r)\n else:\n c+=(r-l)*p1\n p.append(r)\n\n\nprint(c)\n \n \n \n\n \n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 8 4 2 5 10\\n20 30\\n50 100\\n', 'output': '570\\n'}, {'type': 'stdin_stdout', 'input': '1 3 2 1 5 10\\n0 10\\n', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '30 54 76 95 48 16\\n9 11\\n23 97\\n112 116\\n126 185\\n214 223\\n224 271\\n278 282\\n283 348\\n359 368\\n373 376\\n452 463\\n488 512\\n532 552\\n646 665\\n681 685\\n699 718\\n735 736\\n750 777\\n791 810\\n828 838\\n841 858\\n874 1079\\n1136 1171\\n1197 1203\\n1210 1219\\n1230 1248\\n1280 1292\\n1324 1374\\n1397 1435\\n1438 1439\\n', 'output': '79844\\n'}, {'type': 'stdin_stdout', 'input': '5 41 20 33 43 4\\n46 465\\n598 875\\n967 980\\n1135 1151\\n1194 1245\\n', 'output': '46995\\n'}, {'type': 'stdin_stdout', 'input': '30 100 48 14 9 7\\n26 55\\n75 107\\n145 146\\n158 167\\n197 199\\n201 213\\n222 238\\n257 265\\n271 338\\n357 439\\n454 462\\n463 562\\n633 660\\n670 691\\n696 829\\n844 864\\n880 888\\n891 894\\n895 900\\n950 973\\n1004 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c+=t1*p1 + (t2)*p2 + ((l-p[-1])-(t1+t2))*p3\n c+=(r-l)*p1\n p.append(r)\n else:\n c+=(r-l)*p1\n p.append(r)\n\n\nprint(c)\n \n \n \n\n \n\n```","inputs":"2 8 4 2 5 10\n20 30\n50 100\n","output":"570\n","actual_output":"570\n","execution_success":true,"sample_index":12371},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1148_B. Born This Way","prompt":"Solve the following coding problem using the programming language python:\n\nArkady bought an air ticket from a city A to a city C. Unfortunately, there are no direct flights, but there are a lot of flights from A to a city B, and from B to C.\n\nThere are n flights from A to B, they depart at time moments a_1, a_2, a_3, ..., a_n and arrive at B t_a moments later.\n\nThere are m flights from B to C, they depart at time moments b_1, b_2, b_3, ..., b_m and arrive at C t_b moments later.\n\nThe connection time is negligible, so one can use the i-th flight from A to B and the j-th flight from B to C if and only if b_j \u2265 a_i + t_a.\n\nYou can cancel at most k flights. If you cancel a flight, Arkady can not use it.\n\nArkady wants to be in C as early as possible, while you want him to be in C as late as possible. Find the earliest time Arkady can arrive at C, if you optimally cancel k flights. If you can cancel k or less flights in such a way that it is not possible to reach C at all, print -1.\n\nInput\n\nThe first line contains five integers n, m, t_a, t_b and k (1 \u2264 n, m \u2264 2 \u22c5 10^5, 1 \u2264 k \u2264 n + m, 1 \u2264 t_a, t_b \u2264 10^9) \u2014 the number of flights from A to B, the number of flights from B to C, the flight time from A to B, the flight time from B to C and the number of flights you can cancel, respectively.\n\nThe second line contains n distinct integers in increasing order a_1, a_2, a_3, ..., a_n (1 \u2264 a_1 < a_2 < \u2026 < a_n \u2264 10^9) \u2014 the times the flights from A to B depart.\n\nThe third line contains m distinct integers in increasing order b_1, b_2, b_3, ..., b_m (1 \u2264 b_1 < b_2 < \u2026 < b_m \u2264 10^9) \u2014 the times the flights from B to C depart.\n\nOutput\n\nIf you can cancel k or less flights in such a way that it is not possible to reach C at all, print -1.\n\nOtherwise print the earliest time Arkady can arrive at C if you cancel k flights in such a way that maximizes this time.\n\nExamples\n\nInput\n\n\n4 5 1 1 2\n1 3 5 7\n1 2 3 9 10\n\n\nOutput\n\n\n11\n\n\nInput\n\n\n2 2 4 4 2\n1 10\n10 20\n\n\nOutput\n\n\n-1\n\n\nInput\n\n\n4 3 2 3 1\n1 999999998 999999999 1000000000\n3 4 1000000000\n\n\nOutput\n\n\n1000000003\n\nNote\n\nConsider the first example. The flights from A to B depart at time moments 1, 3, 5, and 7 and arrive at B at time moments 2, 4, 6, 8, respectively. The flights from B to C depart at time moments 1, 2, 3, 9, and 10 and arrive at C at time moments 2, 3, 4, 10, 11, respectively. You can cancel at most two flights. The optimal solution is to cancel the first flight from A to B and the fourth flight from B to C. This way Arkady has to take the second flight from A to B, arrive at B at time moment 4, and take the last flight from B to C arriving at C at time moment 11.\n\nIn the second example you can simply cancel all flights from A to B and you're done.\n\nIn the third example you can cancel only one flight, and the optimal solution is to cancel the first flight from A to B. Note that there is still just enough time to catch the last flight from B to C.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import *\nfrom math import *\nimport array\nimport bisect\n\ncin = lambda : [*map(int, input().split())]\n\ndef upper_bound(a, x):\n l = 0\n r = len(a) - 1\n while l < r:\n m = int((l + r + 1) / 2)\n if a[m] <= x:\n l = m\n else:\n r = m - 1\n return l\n\nif __name__ == '__main__':\n\n n, m, ta, tb, k = cin()\n\n a = array.array('i', cin())\n b = array.array('i', cin())\n if k >= min(n, m):\n print('-1')\n exit()\n\n ans = 0\n try:\n for i in range(k + 1):\n # l = upper_bound(b, a[i] + ta)\n l = bisect.bisect_left(b, a[i] + ta)\n\n l += k - i\n ans = max(ans, b[l] + tb)\n\n print(ans)\n except:\n\n print('-1')\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 2 4 4 2\\n1 10\\n10 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17\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 14 10 4\\n1 2\\n7 12\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1 1 1\\n1\\n12 11 12 13 14\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 12 50 1 4\\n1 0 3 4 5\\n1 2 5 8 5 6 7 8 9 10 100 1000\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 0 1 1\\n1 7\\n2 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 1000000000 1000000000 1\\n806890742 1000000000\\n1 0000000001\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 11 4 5 3\\n1 4 0 4 5 6 7 8 9 10\\n16 17 18 19 20 21 22 23 24 25 26\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '2 0 4 0 2\\n1 10\\n10 20\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 1 1 2 1\\n1 1\\n1 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 3 1 0 4\\n0 2 3 4 5\\n12 100 1000\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 0 1 1\\n1 0\\n3 4\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '2 0 2 0 1\\n3 2\\n5\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 5 17 10 3\\n6 7 5 18 15 16 17 19 12 21\\n2 5 8 16 17\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 10 20 4 3\\n8 9 18 19 24\\n3 6 7 8 2 10 14 15 16 17\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 14 10 4\\n1 1\\n7 12\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1 1 1\\n1\\n12 11 11 13 14\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 12 98 1 4\\n1 0 3 4 5\\n1 2 5 8 5 6 7 8 9 10 100 1000\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 0 2 1\\n1 7\\n2 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 1000000000 1000000000 2\\n806890742 1000000000\\n1 0000000001\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 11 4 5 3\\n1 4 0 4 5 6 7 8 9 10\\n16 17 18 19 20 21 34 23 24 25 26\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '2 0 4 0 2\\n1 10\\n10 29\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 3 1 0 4\\n0 2 3 4 5\\n12 100 1100\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 0 2 1 1\\n3 2\\n5\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 5 17 10 3\\n6 3 5 18 15 16 17 19 12 21\\n2 5 8 16 17\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 10 20 4 3\\n8 9 18 19 24\\n3 6 7 8 2 10 14 15 16 17\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 14 20 4\\n1 1\\n7 12\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1 1 1\\n1\\n12 11 11 3 14\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 12 98 1 4\\n1 0 3 4 5\\n1 2 3 8 5 6 7 8 9 10 100 1000\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 -1 2 1\\n1 7\\n2 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 11 4 5 3\\n1 4 0 4 5 6 7 8 9 10\\n16 17 18 19 20 21 34 23 24 25 43\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '2 0 4 0 3\\n1 10\\n10 29\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 2 1 0 4\\n0 2 3 4 5\\n12 100 1100\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 0 2 1 1\\n3 2\\n6\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 5 17 19 3\\n6 3 5 18 15 16 17 19 12 21\\n2 5 8 16 17\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 10 20 4 3\\n8 9 18 19 24\\n3 6 7 8 2 10 20 15 16 17\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 14 3 4\\n1 1\\n7 12\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1 1 1\\n1\\n12 11 1 3 14\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 12 98 2 4\\n1 0 3 4 5\\n1 2 3 8 5 6 7 8 9 10 100 1000\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 -2 2 1\\n1 7\\n2 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 11 4 5 3\\n1 4 0 4 5 6 7 8 9 10\\n15 17 18 19 20 21 34 23 24 25 43\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '0 0 2 1 1\\n3 2\\n6\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 5 17 19 3\\n6 3 5 18 15 16 34 19 12 21\\n2 5 8 16 17\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 10 20 4 3\\n8 9 18 19 24\\n3 6 7 8 2 10 20 15 16 17\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 14 3 4\\n1 1\\n7 23\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1 1 1\\n1\\n12 11 1 6 14\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77557","program":"```python\nfrom collections import *\nfrom math import *\nimport array\nimport bisect\n\ncin = lambda : [*map(int, input().split())]\n\ndef upper_bound(a, x):\n l = 0\n r = len(a) - 1\n while l < r:\n m = int((l + r + 1) / 2)\n if a[m] <= x:\n l = m\n else:\n r = m - 1\n return l\n\nif __name__ == '__main__':\n\n n, m, ta, tb, k = cin()\n\n a = array.array('i', cin())\n b = array.array('i', cin())\n if k >= min(n, m):\n print('-1')\n exit()\n\n ans = 0\n try:\n for i in range(k + 1):\n # l = upper_bound(b, a[i] + ta)\n l = bisect.bisect_left(b, a[i] + ta)\n\n l += k - i\n ans = max(ans, b[l] + tb)\n\n print(ans)\n except:\n\n print('-1')\n\n```","inputs":"2 2 4 4 2\n1 10\n10 20\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12372},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1169_D. Good Triple","prompt":"Solve the following coding problem using the programming language python:\n\nToad Rash has a binary string s. A binary string consists only of zeros and ones.\n\nLet n be the length of s.\n\nRash needs to find the number of such pairs of integers l, r that 1 \u2264 l \u2264 r \u2264 n and there is at least one pair of integers x, k such that 1 \u2264 x, k \u2264 n, l \u2264 x < x + 2k \u2264 r, and s_x = s_{x+k} = s_{x+2k}.\n\nFind this number of pairs for Rash.\n\nInput\n\nThe first line contains the string s (1 \u2264 |s| \u2264 300 000), consisting of zeros and ones.\n\nOutput\n\nOutput one integer: the number of such pairs of integers l, r that 1 \u2264 l \u2264 r \u2264 n and there is at least one pair of integers x, k such that 1 \u2264 x, k \u2264 n, l \u2264 x < x + 2k \u2264 r, and s_x = s_{x+k} = s_{x+2k}.\n\nExamples\n\nInput\n\n\n010101\n\n\nOutput\n\n\n3\n\n\nInput\n\n\n11001100\n\n\nOutput\n\n\n0\n\nNote\n\nIn the first example, there are three l, r pairs we need to count: 1, 6; 2, 6; and 1, 5.\n\nIn the second example, there are no values x, k for the initial string, so the answer is 0.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom sys import stdin\ns=stdin.readline().strip()\nx=-1\nans=0\nfor i in range(len(s)):\n for j in range(1,10):\n if (i-2*j)>=0 and s[i]==s[i-j] and s[i-j]==s[i-2*j]:\n if (i-2*j)>x:\n ans+=(i-2*j-x)*(len(s)-i)\n x=i-2*j\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '010101\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '11001100\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1001\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0100101110\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '0011\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1011\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1000\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '01\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1010\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0000\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '0010\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '100\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '101\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '001\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1101111000011110111111110101100111111110111100001111011010111001101100010110000001010101101010111000\\n', 'output': '4672\\n'}, {'type': 'stdin_stdout', 'input': '00\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '0001\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1100\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0100101111\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '0111\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1101111000011110111111110101100111111110111100001111011010111001101100010110000001010101101010101000\\n', 'output': '4669\\n'}, {'type': 'stdin_stdout', 'input': '111\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1111\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '010111\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '11000100\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '0100101011\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '0100001011\\n', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '1101111000001110111111110101100011111110111100001111011010111001101100010110000001010101101010101000\\n', 'output': '4675\\n'}, {'type': 'stdin_stdout', 'input': '1101111000001110111111110101100011111110101100001111011010111001101100010110000001010101101010101000\\n', 'output': '4664\\n'}, {'type': 'stdin_stdout', 'input': '011100\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '01001000\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '0110100011\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '1101111000001110111111110101100011011110101100001111011010111001101100010110000001010101101010101000\\n', 'output': '4652\\n'}, {'type': 'stdin_stdout', 'input': '0111100011\\n', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '1101111000001110111111110101100011011110101101001111011010111001101100010110000001010101101010101000\\n', 'output': '4636\\n'}, {'type': 'stdin_stdout', 'input': '0111110011\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '1101111000001110111111110100100011011110101101001111011010111001101100010110000001010101101010101000\\n', 'output': '4633\\n'}, {'type': 'stdin_stdout', 'input': '1101111000001110111111110100100011011110101101001111111010111001101100010110000001010101101010101000\\n', 'output': '4646\\n'}, {'type': 'stdin_stdout', 'input': '011110\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '00111000\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '0111111111\\n', 'output': '35\\n'}, {'type': 'stdin_stdout', 'input': '111110\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '00110000\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '0101111000001110111111110100100011011110101100001111111010111001101100010110000001010101001010101000\\n', 'output': '4662\\n'}, {'type': 'stdin_stdout', 'input': '1111101111\\n', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '0101111000001110111111110100100011011110101100001111111010111001101100010110000001110101001010101000\\n', 'output': '4665\\n'}, {'type': 'stdin_stdout', 'input': '1111111111\\n', 'output': '36\\n'}, {'type': 'stdin_stdout', 'input': '0101111000001110111111110100100011011110101100001111111010111001101100010110100001110101001010101000\\n', 'output': '4655\\n'}, {'type': 'stdin_stdout', 'input': '00000000\\n', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '1111111101\\n', 'output': '33\\n'}, {'type': 'stdin_stdout', 'input': '0111111101\\n', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '0110\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1101\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0101\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0100\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1110\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '011\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '110\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '010\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1101111000001110111111110101100111111110111100001111011010111001101100010110000001010101101010101000\\n', 'output': '4669\\n'}, {'type': 'stdin_stdout', 'input': '010110\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '01000100\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '010100\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '01001100\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '0110101011\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '001100\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '01001010\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '011101\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '01011010\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '011000\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '01111010\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '0111110010\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '011010\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '01111000\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '0111110111\\n', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '0101111000001110111111110100100011011110101101001111111010111001101100010110000001010101101010101000\\n', 'output': '4646\\n'}, {'type': 'stdin_stdout', 'input': '0101111000001110111111110100100011011110101101001111111010111001101100010110000001010101001010101000\\n', 'output': '4646\\n'}, {'type': 'stdin_stdout', 'input': '0111101111\\n', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '110110\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '00110100\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '110111\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '00100000\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '100111\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '0101110000001110111111110100100011011110101100001111111010111001101100010110000001110101001010101000\\n', 'output': '4665\\n'}, {'type': 'stdin_stdout', 'input': '000111\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '00001000\\n', 'output': '15\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 4, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77561","program":"```python\nfrom sys import stdin\ns=stdin.readline().strip()\nx=-1\nans=0\nfor i in range(len(s)):\n for j in range(1,10):\n if (i-2*j)>=0 and s[i]==s[i-j] and s[i-j]==s[i-2*j]:\n if (i-2*j)>x:\n ans+=(i-2*j-x)*(len(s)-i)\n x=i-2*j\nprint(ans)\n\n```","inputs":"010101\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12373},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1187_F. Expected Square Beauty","prompt":"Solve the following coding problem using the programming language python:\n\nLet x be an array of integers x = [x_1, x_2, ..., x_n]. Let's define B(x) as a minimal size of a partition of x into subsegments such that all elements in each subsegment are equal. For example, B([3, 3, 6, 1, 6, 6, 6]) = 4 using next partition: [3, 3\\ |\\ 6\\ |\\ 1\\ |\\ 6, 6, 6].\n\nNow you don't have any exact values of x, but you know that x_i can be any integer value from [l_i, r_i] (l_i \u2264 r_i) uniformly at random. All x_i are independent.\n\nCalculate expected value of (B(x))^2, or E((B(x))^2). It's guaranteed that the expected value can be represented as rational fraction P/Q where (P, Q) = 1, so print the value P \u22c5 Q^{-1} mod 10^9 + 7.\n\nInput\n\nThe first line contains the single integer n (1 \u2264 n \u2264 2 \u22c5 10^5) \u2014 the size of the array x.\n\nThe second line contains n integers l_1, l_2, ..., l_n (1 \u2264 l_i \u2264 10^9).\n\nThe third line contains n integers r_1, r_2, ..., r_n (l_i \u2264 r_i \u2264 10^9).\n\nOutput\n\nPrint the single integer \u2014 E((B(x))^2) as P \u22c5 Q^{-1} mod 10^9 + 7.\n\nExamples\n\nInput\n\n\n3\n1 1 1\n1 2 3\n\n\nOutput\n\n\n166666673\n\n\nInput\n\n\n3\n3 4 5\n4 5 6\n\n\nOutput\n\n\n500000010\n\nNote\n\nLet's describe all possible values of x for the first sample: \n\n * [1, 1, 1]: B(x) = 1, B^2(x) = 1; \n * [1, 1, 2]: B(x) = 2, B^2(x) = 4; \n * [1, 1, 3]: B(x) = 2, B^2(x) = 4; \n * [1, 2, 1]: B(x) = 3, B^2(x) = 9; \n * [1, 2, 2]: B(x) = 2, B^2(x) = 4; \n * [1, 2, 3]: B(x) = 3, B^2(x) = 9; \n\nSo E = 1/6 (1 + 4 + 4 + 9 + 4 + 9) = 31/6 or 31 \u22c5 6^{-1} = 166666673.\n\nAll possible values of x for the second sample: \n\n * [3, 4, 5]: B(x) = 3, B^2(x) = 9; \n * [3, 4, 6]: B(x) = 3, B^2(x) = 9; \n * [3, 5, 5]: B(x) = 2, B^2(x) = 4; \n * [3, 5, 6]: B(x) = 3, B^2(x) = 9; \n * [4, 4, 5]: B(x) = 2, B^2(x) = 4; \n * [4, 4, 6]: B(x) = 2, B^2(x) = 4; \n * [4, 5, 5]: B(x) = 2, B^2(x) = 4; \n * [4, 5, 6]: B(x) = 3, B^2(x) = 9; \n\nSo E = 1/8 (9 + 9 + 4 + 9 + 4 + 4 + 4 + 9) = 52/8 or 13 \u22c5 2^{-1} = 500000010.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nmod = 10 ** 9 + 7\n\ndef pow_(x, y, p) : \n res = 1 \n x = x % p \n \n if x == 0: \n return 0\n \n while y > 0: \n if (y & 1) == 1: \n res = (res * x) % p \n \n y = y >> 1 \n x = (x * x) % p \n \n return res \n \ndef reverse(x, mod):\n return pow_(x, mod-2, mod)\n\ndef prob(l_arr, r_arr):\n l_, r_ = max(l_arr), min(r_arr)\n \n if l_ > r_:\n return 1\n \n p = (r_-l_+1)\n for l, r in zip(l_arr, r_arr):\n p *= reverse(r-l+1 ,mod)\n \n return (1-p) % mod\n\nn = int(input())\nL = list(map(int, input().split()))\nR = list(map(int, input().split()))\n\nEX, EX2 = 0, 0\nP = [0] * n\npre = [0] * n\n\nfor i in range(1, n):\n P[i] = prob(L[i-1: i+1], R[i-1: i+1])\n pre[i] = (pre[i-1] + P[i]) % mod\n \n if i >= 2:\n pA, pB, pAB = 1-P[i-1], 1-P[i], 1-prob(L[i-2: i+1], R[i-2: i+1])\n p_ = 1 - (pA+pB-pAB)\n \n EX2 += 2 * (P[i]*pre[i-2] + p_) % mod\n\nEX = sum(P) % mod\nEX2 += EX\nans = (EX2 + 2*EX + 1) % mod\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 1 1\\n1 2 3\\n', 'output': '166666673\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 4 5\\n4 5 6\\n', 'output': '500000010\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 10 1 3 3 3 9 4 7\\n10 10 10 8 5 9 4 9 9 7\\n', 'output': '35714347\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 6 9 1 3 7 8 5 7 3\\n10 6 10 5 8 7 9 8 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'output': '513888963\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 6 9 1 3 7 8 5 6 3\\n10 6 10 3 8 7 10 8 10 4\\n', 'output': '814814912\\n'}, {'type': 'stdin_stdout', 'input': '10\\n3 6 3 10 2 3 1 1 2 9\\n3 9 6 10 10 9 5 8 10 10\\n', 'output': '35251410\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 7 6 3 7 3 3 9 1 4\\n10 9 13 6 7 10 3 10 8 4\\n', 'output': '273437592\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 2 2 3\\n2 3 2 3 3\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 10 1 3 5 3 5 4 7\\n17 10 10 7 5 9 4 9 9 7\\n', 'output': '28571499\\n'}, {'type': 'stdin_stdout', 'input': '10\\n3 6 3 10 2 3 1 1 2 9\\n3 9 6 10 10 9 5 8 8 10\\n', 'output': '452083425\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 1 9 1 9 5 5 4 7 1\\n8 3 9 2 9 5 10 8 10 2\\n', 'output': '733333431\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 1 9 3 9 4 1 3 8 5\\n10 2 10 14 12 4 10 4 10 7\\n', 'output': '441666763\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 10 1 3 5 3 5 4 7\\n34 10 10 7 5 9 4 9 9 7\\n', 'output': '15506787\\n'}, {'type': 'stdin_stdout', 'input': '10\\n3 6 3 10 2 3 1 1 2 9\\n3 9 6 10 10 9 9 8 8 10\\n', 'output': '811811161\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 1 9 1 9 4 5 4 7 1\\n8 3 9 2 9 5 10 8 10 2\\n', 'output': '466666764\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 1 9 3 9 4 1 3 8 5\\n10 2 10 14 12 4 10 7 10 7\\n', 'output': '21666760\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 2 2 1\\n2 3 2 3 3\\n', 'output': '500000015\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 10 1 3 5 3 5 4 7\\n40 10 10 7 5 9 4 9 9 7\\n', 'output': '749504045\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 1 9 3 9 4 1 3 8 5\\n10 2 10 14 11 4 10 7 10 7\\n', 'output': '35555649\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 10 1 3 5 4 5 4 2\\n40 10 10 7 5 9 4 9 9 7\\n', 'output': '917195846\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 10 1 3 5 4 5 4 1\\n40 10 10 7 5 9 4 9 9 7\\n', 'output': '712726835\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 10 1 3 5 3 5 4 1\\n40 10 10 7 5 9 4 9 9 10\\n', 'output': '397400869\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 10 1 3 3 3 9 4 7\\n10 10 10 15 5 9 4 9 9 7\\n', 'output': '912698480\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 6 9 1 3 7 8 5 7 1\\n10 6 10 5 8 7 9 8 10 4\\n', 'output': '279166759\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 4 5 9 2 6 4 7 5 9\\n7 5 7 10 8 6 4 7 9 9\\n', 'output': '414285804\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 1 9 1 9 5 5 4 7 1\\n8 3 9 2 9 7 9 8 10 2\\n', 'output': '940000098\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 1 9 1 9 5 5 4 7 1\\n8 3 9 2 9 5 9 8 10 2\\n', 'output': '940000098\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 1 9 3 9 4 10 3 8 5\\n10 2 10 14 12 4 10 4 10 7\\n', 'output': '875000103\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 2 2 3\\n2 3 2 3 3\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 10 1 3 5 4 5 4 7\\n40 10 10 7 5 9 4 9 9 7\\n', 'output': '749504045\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 10 1 3 5 3 5 4 1\\n40 10 10 7 5 9 4 9 9 7\\n', 'output': '712726835\\n'}], 'language': 'python'}","metadata":"{'difficulty': 12, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77565","program":"```python\nmod = 10 ** 9 + 7\n\ndef pow_(x, y, p) : \n res = 1 \n x = x % p \n \n if x == 0: \n return 0\n \n while y > 0: \n if (y & 1) == 1: \n res = (res * x) % p \n \n y = y >> 1 \n x = (x * x) % p \n \n return res \n \ndef reverse(x, mod):\n return pow_(x, mod-2, mod)\n\ndef prob(l_arr, r_arr):\n l_, r_ = max(l_arr), min(r_arr)\n \n if l_ > r_:\n return 1\n \n p = (r_-l_+1)\n for l, r in zip(l_arr, r_arr):\n p *= reverse(r-l+1 ,mod)\n \n return (1-p) % mod\n\nn = int(input())\nL = list(map(int, input().split()))\nR = list(map(int, input().split()))\n\nEX, EX2 = 0, 0\nP = [0] * n\npre = [0] * n\n\nfor i in range(1, n):\n P[i] = prob(L[i-1: i+1], R[i-1: i+1])\n pre[i] = (pre[i-1] + P[i]) % mod\n \n if i >= 2:\n pA, pB, pAB = 1-P[i-1], 1-P[i], 1-prob(L[i-2: i+1], R[i-2: i+1])\n p_ = 1 - (pA+pB-pAB)\n \n EX2 += 2 * (P[i]*pre[i-2] + p_) % mod\n\nEX = sum(P) % mod\nEX2 += EX\nans = (EX2 + 2*EX + 1) % mod\nprint(ans)\n```","inputs":"3\n1 1 1\n1 2 3\n","output":"166666673\n","actual_output":"166666673\n","execution_success":true,"sample_index":12374},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1225_A. Forgetting Things","prompt":"Solve the following coding problem using the programming language python:\n\nKolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation a + 1 = b with positive integers a and b, but Kolya forgot the numbers a and b. He does, however, remember that the first (leftmost) digit of a was d_a, and the first (leftmost) digit of b was d_b.\n\nCan you reconstruct any equation a + 1 = b that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.\n\nInput\n\nThe only line contains two space-separated digits d_a and d_b (1 \u2264 d_a, d_b \u2264 9).\n\nOutput\n\nIf there is no equation a + 1 = b with positive integers a and b such that the first digit of a is d_a, and the first digit of b is d_b, print a single number -1.\n\nOtherwise, print any suitable a and b that both are positive and do not exceed 10^9. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding 10^9.\n\nExamples\n\nInput\n\n\n1 2\n\n\nOutput\n\n\n199 200\n\n\nInput\n\n\n4 4\n\n\nOutput\n\n\n412 413\n\n\nInput\n\n\n5 7\n\n\nOutput\n\n\n-1\n\n\nInput\n\n\n6 2\n\n\nOutput\n\n\n-1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na,b = map(int,input().split())\nif(b == a+1):\n print(str(a)+\"9 \"+str(b)+\"0\")\nelif(b == a):\n print(str(a)+\"0 \"+str(a)+\"1\")\nelif(b == 1 and a == 9):\n print(\"99 100\")\nelse:\n print(-1)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 2\\n', 'output': '19 20'}, {'type': 'stdin_stdout', 'input': '5 7\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n', 'output': '40 41\\n'}, {'type': 'stdin_stdout', 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'stdin_stdout', 'input': '10 0\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '4 9\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '51 0\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '3 17\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '0 10\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '-1 7\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '2 -1\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '4 0\\n', 'output': '-1'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_77573","program":"```python\na,b = map(int,input().split())\nif(b == a+1):\n print(str(a)+\"9 \"+str(b)+\"0\")\nelif(b == a):\n print(str(a)+\"0 \"+str(a)+\"1\")\nelif(b == 1 and a == 9):\n print(\"99 100\")\nelse:\n print(-1)\n\n```","inputs":"1 2\n","output":"19 20","actual_output":"19 20\n","execution_success":true,"sample_index":12376},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1249_C2. Good Numbers (hard version)","prompt":"Solve the following coding problem using the programming language python:\n\nThe only difference between easy and hard versions is the maximum value of n.\n\nYou are given a positive integer number n. You really love good numbers so you want to find the smallest good number greater than or equal to n.\n\nThe positive integer is called good if it can be represented as a sum of distinct powers of 3 (i.e. no duplicates of powers of 3 are allowed).\n\nFor example:\n\n * 30 is a good number: 30 = 3^3 + 3^1, \n * 1 is a good number: 1 = 3^0, \n * 12 is a good number: 12 = 3^2 + 3^1, \n * but 2 is not a good number: you can't represent it as a sum of distinct powers of 3 (2 = 3^0 + 3^0), \n * 19 is not a good number: you can't represent it as a sum of distinct powers of 3 (for example, the representations 19 = 3^2 + 3^2 + 3^0 = 3^2 + 3^1 + 3^1 + 3^1 + 3^0 are invalid), \n * 20 is also not a good number: you can't represent it as a sum of distinct powers of 3 (for example, the representation 20 = 3^2 + 3^2 + 3^0 + 3^0 is invalid). \n\n\n\nNote, that there exist other representations of 19 and 20 as sums of powers of 3 but none of them consists of distinct powers of 3.\n\nFor the given positive integer n find such smallest m (n \u2264 m) that m is a good number.\n\nYou have to answer q independent queries.\n\nInput\n\nThe first line of the input contains one integer q (1 \u2264 q \u2264 500) \u2014 the number of queries. Then q queries follow.\n\nThe only line of the query contains one integer n (1 \u2264 n \u2264 10^{18}).\n\nOutput\n\nFor each query, print such smallest integer m (where n \u2264 m) that m is a good number.\n\nExample\n\nInput\n\n\n8\n1\n2\n6\n13\n14\n3620\n10000\n1000000000000000000\n\n\nOutput\n\n\n1\n3\n9\n13\n27\n6561\n19683\n1350851717672992089\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfor _ in range(int(input())):\n n=int(input())\n a=[]\n b=[0]\n for i in range(50):\n a.append(3**i)\n b.append(b[-1]+a[-1])\n if b[-1]> n:\n break\n s=b[i+1]\n a=a[::-1]\n # print(s,a)\n\n for j in a:\n if s-j>=n:\n s-=j\n print(s)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '8\\n1\\n2\\n6\\n13\\n14\\n3620\\n10000\\n1000000000000000000\\n', 'output': '1\\n3\\n9\\n13\\n27\\n6561\\n19683\\n1350851717672992089\\n'}, {'type': 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{'type': 'stdin_stdout', 'input': '1\\n375291682952584523\\n', 'output': '450283905890997363\\n'}, {'type': 'stdin_stdout', 'input': '1\\n195606932\\n', 'output': '387420489\\n'}, {'type': 'stdin_stdout', 'input': '1\\n75903703\\n', 'output': '129140163\\n'}, {'type': 'stdin_stdout', 'input': '1\\n83963471\\n', 'output': '129140163\\n'}, {'type': 'stdin_stdout', 'input': '1\\n81354430\\n', 'output': '129140163\\n'}, {'type': 'stdin_stdout', 'input': '1\\n99645\\n', 'output': '177147\\n'}, {'type': 'stdin_stdout', 'input': '100\\n1\\n8\\n4\\n6\\n5\\n4\\n4\\n6\\n12\\n3\\n9\\n5\\n7\\n8\\n8\\n5\\n9\\n6\\n9\\n4\\n7\\n6\\n4\\n4\\n7\\n1\\n2\\n2\\n5\\n6\\n1\\n5\\n10\\n9\\n10\\n9\\n3\\n1\\n2\\n3\\n2\\n6\\n9\\n2\\n9\\n5\\n7\\n8\\n1\\n5\\n9\\n5\\n1\\n3\\n8\\n4\\n7\\n9\\n3\\n1\\n7\\n1\\n2\\n4\\n7\\n2\\n7\\n1\\n1\\n10\\n8\\n5\\n7\\n12\\n10\\n8\\n1\\n7\\n5\\n10\\n7\\n6\\n6\\n6\\n7\\n4\\n9\\n3\\n4\\n9\\n10\\n7\\n1\\n2\\n6\\n9\\n3\\n8\\n10\\n9\\n', 'output': '1\\n9\\n4\\n9\\n9\\n4\\n4\\n9\\n12\\n3\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n4\\n9\\n9\\n4\\n4\\n9\\n1\\n3\\n3\\n9\\n9\\n1\\n9\\n10\\n9\\n10\\n9\\n3\\n1\\n3\\n3\\n3\\n9\\n9\\n3\\n9\\n9\\n9\\n9\\n1\\n9\\n9\\n9\\n1\\n3\\n9\\n4\\n9\\n9\\n3\\n1\\n9\\n1\\n3\\n4\\n9\\n3\\n9\\n1\\n1\\n10\\n9\\n9\\n9\\n12\\n10\\n9\\n1\\n9\\n9\\n10\\n9\\n9\\n9\\n9\\n9\\n4\\n9\\n3\\n4\\n9\\n10\\n9\\n1\\n3\\n9\\n9\\n3\\n9\\n10\\n9\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77577","program":"```python\nfor _ in range(int(input())):\n n=int(input())\n a=[]\n b=[0]\n for i in range(50):\n a.append(3**i)\n b.append(b[-1]+a[-1])\n if b[-1]> n:\n break\n s=b[i+1]\n a=a[::-1]\n # print(s,a)\n\n for j in a:\n if s-j>=n:\n s-=j\n print(s)\n```","inputs":"8\n1\n2\n6\n13\n14\n3620\n10000\n1000000000000000000\n","output":"1\n3\n9\n13\n27\n6561\n19683\n1350851717672992089\n","actual_output":"1\n3\n9\n13\n27\n6561\n19683\n1350851717672992089\n","execution_success":true,"sample_index":12377},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1267_K. Key Storage","prompt":"Solve the following coding problem using the programming language python:\n\nKarl is developing a key storage service. Each user has a positive integer key.\n\nKarl knows that storing keys in plain text is bad practice. So, instead of storing a key, he decided to store a fingerprint of a key. However, using some existing fingerprint algorithm looked too boring to him, so he invented his own one.\n\nKarl's fingerprint is calculated by the following process: divide the given integer by 2, then divide the result by 3, then divide the result by 4, and so on, until we get a result that equals zero (we are speaking about integer division each time). The fingerprint is defined as the multiset of the remainders of these divisions. \n\nFor example, this is how Karl's fingerprint algorithm is applied to the key 11: 11 divided by 2 has remainder 1 and result 5, then 5 divided by 3 has remainder 2 and result 1, and 1 divided by 4 has remainder 1 and result 0. Thus, the key 11 produces the sequence of remainders [1, 2, 1] and has the fingerprint multiset \\{1, 1, 2\\}.\n\nKsenia wants to prove that Karl's fingerprint algorithm is not very good. For example, she found that both keys 178800 and 123456 produce the fingerprint of \\{0, 0, 0, 0, 2, 3, 3, 4\\}. Thus, users are at risk of fingerprint collision with some commonly used and easy to guess keys like 123456.\n\nKsenia wants to make her words more persuasive. She wants to calculate the number of other keys that have the same fingerprint as the keys in the given list of some commonly used keys. Your task is to help her.\n\nInput\n\nThe first line contains an integer t (1 \u2264 t \u2264 50 000) \u2014 the number of commonly used keys to examine. Each of the next t lines contains one integer k_i (1 \u2264 k_i \u2264 10^{18}) \u2014 the key itself. \n\nOutput\n\nFor each of the keys print one integer \u2014 the number of other keys that have the same fingerprint. \n\nExample\n\nInput\n\n\n3\n1\n11\n123456\n\n\nOutput\n\n\n0\n1\n127\n\nNote\n\nThe other key with the same fingerprint as 11 is 15. 15 produces a sequence of remainders [1, 1, 2]. So both numbers have the fingerprint multiset \\{1, 1, 2\\}.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math as m\nimport collections\nIP = lambda: list(map(int, input().split()))\nINF = 1e9\n\n\nf = [1]\nfor i in range(1, 22):\n f.append(f[-1]*i)\n\ndef solve(arr, n):\n d = collections.Counter(arr)\n tu = 1; mau = 1\n a = [0]*22\n for i in arr:\n # print(i, n)\n a[i] += 1\n for i in range(1, len(a)):\n a[i] += a[i-1]\n # print(a, n)\n for i in range(2, n+2):\n tu *= (a[i-1]-i+2)\n # print(tu, '#####')\n for i in d.values():\n mau *= f[i]\n # print(tu, mau, '####')\n return tu//mau\n\nfor _ in range(int(input())):\n n = IP()[0]\n arr = []; i = 2\n while n:\n arr.append(n%i)\n n//=i\n i+=1\n arr.sort()\n pro = solve(arr, len(arr))\n # print(pro, '****')\n if 0 in arr:\n arr.pop(0)\n tru = solve(arr, len(arr))\n # print(pro, tru)\n pro -= tru\n print(pro - 1)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1\\n11\\n123456\\n', 'output': '0\\n1\\n127\\n'}, {'type': 'stdin_stdout', 'input': '100\\n1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\n10\\n11\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n61\\n62\\n63\\n64\\n65\\n66\\n67\\n68\\n69\\n70\\n71\\n72\\n73\\n74\\n75\\n76\\n77\\n78\\n79\\n80\\n81\\n82\\n83\\n84\\n85\\n86\\n87\\n88\\n89\\n90\\n91\\n92\\n93\\n94\\n95\\n96\\n97\\n98\\n99\\n100\\n', 'output': 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'input': '3\\n6\\n23\\n277039\\n', 'output': '0\\n0\\n11\\n'}], 'language': 'python'}","metadata":"{'difficulty': 17, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_77581","program":"```python\nimport math as m\nimport collections\nIP = lambda: list(map(int, input().split()))\nINF = 1e9\n\n\nf = [1]\nfor i in range(1, 22):\n f.append(f[-1]*i)\n\ndef solve(arr, n):\n d = collections.Counter(arr)\n tu = 1; mau = 1\n a = [0]*22\n for i in arr:\n # print(i, n)\n a[i] += 1\n for i in range(1, len(a)):\n a[i] += a[i-1]\n # print(a, n)\n for i in range(2, n+2):\n tu *= (a[i-1]-i+2)\n # print(tu, '#####')\n for i in d.values():\n mau *= f[i]\n # print(tu, mau, '####')\n return tu//mau\n\nfor _ in range(int(input())):\n n = IP()[0]\n arr = []; i = 2\n while n:\n arr.append(n%i)\n n//=i\n i+=1\n arr.sort()\n pro = solve(arr, len(arr))\n # print(pro, '****')\n if 0 in arr:\n arr.pop(0)\n tru = solve(arr, len(arr))\n # print(pro, tru)\n pro -= tru\n print(pro - 1)\n```","inputs":"3\n1\n11\n123456\n","output":"0\n1\n127\n","actual_output":"0\n1\n127\n","execution_success":true,"sample_index":12378},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1310_A. Recommendations","prompt":"Solve the following coding problem using the programming language python:\n\nVK news recommendation system daily selects interesting publications of one of n disjoint categories for each user. Each publication belongs to exactly one category. For each category i batch algorithm selects a_i publications.\n\nThe latest A/B test suggests that users are reading recommended publications more actively if each category has a different number of publications within daily recommendations. The targeted algorithm can find a single interesting publication of i-th category within t_i seconds. \n\nWhat is the minimum total time necessary to add publications to the result of batch algorithm execution, so all categories have a different number of publications? You can't remove publications recommended by the batch algorithm.\n\nInput\n\nThe first line of input consists of single integer n \u2014 the number of news categories (1 \u2264 n \u2264 200 000).\n\nThe second line of input consists of n integers a_i \u2014 the number of publications of i-th category selected by the batch algorithm (1 \u2264 a_i \u2264 10^9).\n\nThe third line of input consists of n integers t_i \u2014 time it takes for targeted algorithm to find one new publication of category i (1 \u2264 t_i \u2264 10^5).\n\nOutput\n\nPrint one integer \u2014 the minimal required time for the targeted algorithm to get rid of categories with the same size.\n\nExamples\n\nInput\n\n\n5\n3 7 9 7 8\n5 2 5 7 5\n\n\nOutput\n\n\n6\n\n\nInput\n\n\n5\n1 2 3 4 5\n1 1 1 1 1\n\n\nOutput\n\n\n0\n\nNote\n\nIn the first example, it is possible to find three publications of the second type, which will take 6 seconds.\n\nIn the second example, all news categories contain a different number of publications.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport heapq\nn = int(input())\n*a, = map(int, input().split())\n*t, = map(int, input().split())\n\n\ni = 0\n\nsorted_idxs = sorted(range(n), key=lambda o: (a[o], -t[o]))\ncur_val = a[sorted_idxs[0]]\ndupls = []\nans = 0\ns = 0\nfor i, idx in enumerate(sorted_idxs):\n cur_val = a[idx]\n heapq.heappush(dupls, (-t[idx], a[idx]))\n s += t[idx]\n while dupls and (i == len(a) - 1 or cur_val + 1 <= a[sorted_idxs[i + 1]]):\n cur_val += 1\n largest, a_val = heapq.heappop(dupls)\n largest *= -1\n s-= largest\n ans += s\n\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 2 3 4 5\\n1 1 1 1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 7 9 7 8\\n5 2 5 7 5\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n72\\n', 'output': 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512000000}","problem_id":"vfc_77589","program":"```python\nimport heapq\nn = int(input())\n*a, = map(int, input().split())\n*t, = map(int, input().split())\n\n\ni = 0\n\nsorted_idxs = sorted(range(n), key=lambda o: (a[o], -t[o]))\ncur_val = a[sorted_idxs[0]]\ndupls = []\nans = 0\ns = 0\nfor i, idx in enumerate(sorted_idxs):\n cur_val = a[idx]\n heapq.heappush(dupls, (-t[idx], a[idx]))\n s += t[idx]\n while dupls and (i == len(a) - 1 or cur_val + 1 <= a[sorted_idxs[i + 1]]):\n cur_val += 1\n largest, a_val = heapq.heappop(dupls)\n largest *= -1\n s-= largest\n ans += s\n\nprint(ans)\n\n```","inputs":"5\n1 2 3 4 5\n1 1 1 1 1\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12379},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1332_F. Independent Set","prompt":"Solve the following coding problem using the programming language python:\n\nEric is the teacher of graph theory class. Today, Eric teaches independent set and edge-induced subgraph.\n\nGiven a graph G=(V,E), an independent set is a subset of vertices V' \u2282 V such that for every pair u,v \u2208 V', (u,v) not \u2208 E (i.e. no edge in E connects two vertices from V').\n\nAn edge-induced subgraph consists of a subset of edges E' \u2282 E and all the vertices in the original graph that are incident on at least one edge in the subgraph.\n\nGiven E' \u2282 E, denote G[E'] the edge-induced subgraph such that E' is the edge set of the subgraph. Here is an illustration of those definitions:\n\n\n\nIn order to help his students get familiar with those definitions, he leaves the following problem as an exercise:\n\nGiven a tree G=(V,E), calculate the sum of w(H) over all except null edge-induced subgraph H of G, where w(H) is the number of independent sets in H. Formally, calculate \u2211 _{\u2205 not= E' \u2282 E} w(G[E']).\n\nShow Eric that you are smarter than his students by providing the correct answer as quickly as possible. Note that the answer might be large, you should output the answer modulo 998,244,353.\n\nInput\n\nThe first line contains a single integer n (2 \u2264 n \u2264 3 \u22c5 10^5), representing the number of vertices of the graph G.\n\nEach of the following n-1 lines contains two integers u and v (1 \u2264 u,v \u2264 n, u not= v), describing edges of the given tree.\n\nIt is guaranteed that the given edges form a tree.\n\nOutput\n\nOutput one integer, representing the desired value modulo 998,244,353.\n\nExamples\n\nInput\n\n\n2\n2 1\n\n\nOutput\n\n\n3\n\n\nInput\n\n\n3\n1 2\n3 2\n\n\nOutput\n\n\n11\n\nNote\n\nFor the second example, all independent sets are listed below.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nreadline = sys.stdin.readline\n\ndef parorder(Edge, p):\n N = len(Edge)\n par = [0]*N\n par[p] = -1\n stack = [p]\n order = []\n visited = set([p])\n ast = stack.append\n apo = order.append\n while stack:\n vn = stack.pop()\n apo(vn)\n for vf in Edge[vn]:\n if vf in visited:\n continue\n visited.add(vf)\n par[vf] = vn\n ast(vf)\n return par, order\n\ndef getcld(p):\n res = [[] for _ in range(len(p))]\n for i, v in enumerate(p[1:], 1):\n res[v].append(i)\n return res\n\n\nN = int(readline())\nMOD = 998244353\nEdge = [[] for _ in range(N)]\nfor _ in range(N-1):\n a, b = map(int, readline().split())\n a -= 1\n b -= 1\n Edge[a].append(b)\n Edge[b].append(a)\n\nP, L = parorder(Edge, 0)\nC = getcld(P)\n\ndp = [[1, 1, 0, 0, 1] for _ in range(N)]\nfor p in L[::-1]:\n if not C[p]:\n continue\n res = 1\n res2 = 1\n res3 = 1\n for ci in C[p]:\n res = (res*(dp[ci][2] + dp[ci][3] + dp[ci][4])) % MOD\n res2 = (res2*(dp[ci][1] + dp[ci][2] + 2*dp[ci][3] + dp[ci][4])) % MOD\n res3 = (res3*(sum(dp[ci]) + dp[ci][2] + dp[ci][3])) % MOD\n dp[p][0] = res\n dp[p][1] = res\n dp[p][2] = (res2 - res)%MOD\n dp[p][3] = (res3 - res)%MOD\n dp[p][4] = res\nprint((dp[0][2] + dp[0][3] + dp[0][4] - 1) %MOD)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n2 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n3 2\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 8\\n5 10\\n3 4\\n1 6\\n3 9\\n1 7\\n4 8\\n10 8\\n1 8\\n', 'output': '24497\\n'}, {'type': 'stdin_stdout', 'input': '12\\n8 12\\n2 4\\n10 11\\n6 9\\n1 3\\n7 12\\n11 12\\n8 4\\n7 9\\n5 3\\n5 6\\n', 'output': '279335\\n'}, {'type': 'stdin_stdout', 'input': '15\\n1 8\\n11 4\\n1 12\\n1 14\\n12 2\\n4 13\\n4 10\\n4 1\\n1 9\\n15 1\\n1 7\\n1 5\\n4 6\\n4 3\\n', 'output': '3832508\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 3\\n4 1\\n4 2\\n', 'output': '33\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2\\n2 3\\n3 4\\n', 'output': '36\\n'}, {'type': 'stdin_stdout', 'input': '9\\n8 1\\n1 4\\n1 5\\n6 1\\n2 1\\n3 1\\n9 1\\n7 1\\n', 'output': '6815\\n'}, {'type': 'stdin_stdout', 'input': '11\\n1 2\\n7 3\\n1 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6\\n4 10\\n7 2\\n3 5\\n9 8\\n3 7\\n1 7\\n8 1\\n1 4\\n11 8\\n', 'output': '69689\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 3\\n2 9\\n10 1\\n5 7\\n7 8\\n10 6\\n5 9\\n9 4\\n1 9\\n', 'output': '26765\\n'}, {'type': 'stdin_stdout', 'input': '20\\n5 20\\n11 8\\n2 11\\n10 7\\n6 14\\n2 15\\n17 13\\n10 1\\n5 1\\n19 13\\n19 3\\n17 1\\n17 12\\n16 18\\n6 11\\n18 8\\n9 4\\n4 13\\n2 1\\n', 'output': '540214836\\n'}, {'type': 'stdin_stdout', 'input': '11\\n1 2\\n7 3\\n1 6\\n11 3\\n8 1\\n9 1\\n5 1\\n2 4\\n1 3\\n1 10\\n', 'output': '59330\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 3\\n2 6\\n9 1\\n2 7\\n5 8\\n10 6\\n5 9\\n9 3\\n2 9\\n', 'output': '24633\\n'}, {'type': 'stdin_stdout', 'input': '11\\n1 9\\n2 3\\n8 1\\n3 11\\n2 6\\n1 5\\n2 4\\n7 10\\n9 7\\n3 10\\n', 'output': '76442\\n'}, {'type': 'stdin_stdout', 'input': '11\\n1 2\\n7 3\\n1 6\\n11 3\\n8 1\\n9 1\\n5 1\\n3 4\\n1 3\\n5 10\\n', 'output': '56996\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 3\\n2 6\\n10 1\\n5 7\\n5 8\\n10 6\\n5 9\\n9 4\\n1 9\\n', 'output': '27128\\n'}, {'type': 'stdin_stdout', 'input': '11\\n1 6\\n7 10\\n7 2\\n3 5\\n9 8\\n3 7\\n1 7\\n8 1\\n1 4\\n11 8\\n', 'output': '62513\\n'}, {'type': 'stdin_stdout', 'input': '11\\n1 2\\n7 3\\n1 6\\n11 3\\n8 1\\n9 1\\n5 1\\n2 4\\n1 3\\n3 10\\n', 'output': '56996\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 3\\n2 6\\n10 1\\n5 7\\n5 8\\n10 6\\n5 9\\n9 4\\n2 9\\n', 'output': '27074\\n'}], 'language': 'python'}","metadata":"{'difficulty': 12, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_77593","program":"```python\nimport sys\nreadline = sys.stdin.readline\n\ndef parorder(Edge, p):\n N = len(Edge)\n par = [0]*N\n par[p] = -1\n stack = [p]\n order = []\n visited = set([p])\n ast = stack.append\n apo = order.append\n while stack:\n vn = stack.pop()\n apo(vn)\n for vf in Edge[vn]:\n if vf in visited:\n continue\n visited.add(vf)\n par[vf] = vn\n ast(vf)\n return par, order\n\ndef getcld(p):\n res = [[] for _ in range(len(p))]\n for i, v in enumerate(p[1:], 1):\n res[v].append(i)\n return res\n\n\nN = int(readline())\nMOD = 998244353\nEdge = [[] for _ in range(N)]\nfor _ in range(N-1):\n a, b = map(int, readline().split())\n a -= 1\n b -= 1\n Edge[a].append(b)\n Edge[b].append(a)\n\nP, L = parorder(Edge, 0)\nC = getcld(P)\n\ndp = [[1, 1, 0, 0, 1] for _ in range(N)]\nfor p in L[::-1]:\n if not C[p]:\n continue\n res = 1\n res2 = 1\n res3 = 1\n for ci in C[p]:\n res = (res*(dp[ci][2] + dp[ci][3] + dp[ci][4])) % MOD\n res2 = (res2*(dp[ci][1] + dp[ci][2] + 2*dp[ci][3] + dp[ci][4])) % MOD\n res3 = (res3*(sum(dp[ci]) + dp[ci][2] + dp[ci][3])) % MOD\n dp[p][0] = res\n dp[p][1] = res\n dp[p][2] = (res2 - res)%MOD\n dp[p][3] = (res3 - res)%MOD\n dp[p][4] = res\nprint((dp[0][2] + dp[0][3] + dp[0][4] - 1) %MOD)\n```","inputs":"2\n2 1\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12380},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1353_B. Two Arrays And Swaps","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given two arrays a and b both consisting of n positive (greater than zero) integers. You are also given an integer k.\n\nIn one move, you can choose two indices i and j (1 \u2264 i, j \u2264 n) and swap a_i and b_j (i.e. a_i becomes b_j and vice versa). Note that i and j can be equal or different (in particular, swap a_2 with b_2 or swap a_3 and b_9 both are acceptable moves).\n\nYour task is to find the maximum possible sum you can obtain in the array a if you can do no more than (i.e. at most) k such moves (swaps).\n\nYou have to answer t independent test cases.\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 200) \u2014 the number of test cases. Then t test cases follow.\n\nThe first line of the test case contains two integers n and k (1 \u2264 n \u2264 30; 0 \u2264 k \u2264 n) \u2014 the number of elements in a and b and the maximum number of moves you can do. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 30), where a_i is the i-th element of a. The third line of the test case contains n integers b_1, b_2, ..., b_n (1 \u2264 b_i \u2264 30), where b_i is the i-th element of b.\n\nOutput\n\nFor each test case, print the answer \u2014 the maximum possible sum you can obtain in the array a if you can do no more than (i.e. at most) k swaps.\n\nExample\n\nInput\n\n\n5\n2 1\n1 2\n3 4\n5 5\n5 5 6 6 5\n1 2 5 4 3\n5 3\n1 2 3 4 5\n10 9 10 10 9\n4 0\n2 2 4 3\n2 4 2 3\n4 4\n1 2 2 1\n4 4 5 4\n\n\nOutput\n\n\n6\n27\n39\n11\n17\n\nNote\n\nIn the first test case of the example, you can swap a_1 = 1 and b_2 = 4, so a=[4, 2] and b=[3, 1].\n\nIn the second test case of the example, you don't need to swap anything.\n\nIn the third test case of the example, you can swap a_1 = 1 and b_1 = 10, a_3 = 3 and b_3 = 10 and a_2 = 2 and b_4 = 10, so a=[10, 10, 10, 4, 5] and b=[1, 9, 3, 2, 9].\n\nIn the fourth test case of the example, you cannot swap anything.\n\nIn the fifth test case of the example, you can swap arrays a and b, so a=[4, 4, 5, 4] and b=[1, 2, 2, 1].\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef swap_sum(a,b,cnt,k):\n if cnt==k or min(a)>=max(b):\n return sum(a)\n \n \n else:\n i=a.index(min(a))\n j=b.index(max(b))\n a[i],b[j]=b[j],a[i]\n #print(a)\n #print(b)\n return swap_sum(a,b,cnt+1,k)\n\n\nfor ii in range(int(input())):\n n,k=map(int,input().split())\n a=list(map(int,input().split()))\n b=list(map(int,input().split()))\n print(swap_sum(a,b,0,k))\n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 2\\n3 4\\n5 5\\n5 5 6 6 5\\n1 2 5 4 3\\n5 3\\n1 2 3 4 5\\n10 9 10 10 9\\n4 0\\n2 2 4 3\\n2 4 2 3\\n4 4\\n1 2 2 1\\n4 4 5 4\\n', 'output': '6\\n27\\n39\\n11\\n17\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 1\\n1 4 2 23 15 13\\n5 6 4 1 15 24\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 2\\n3 4\\n5 5\\n5 5 6 6 5\\n1 2 5 4 3\\n5 3\\n1 2 3 4 5\\n10 9 10 10 9\\n4 0\\n2 2 4 3\\n2 4 2 5\\n4 4\\n1 2 2 1\\n4 4 5 4\\n', 'output': '6\\n27\\n39\\n11\\n17\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 2\\n3 4\\n5 5\\n5 5 6 6 5\\n1 2 5 4 3\\n5 3\\n1 2 3 4 5\\n10 9 10 10 9\\n4 0\\n2 2 4 3\\n2 4 2 0\\n4 3\\n1 2 2 1\\n4 4 5 4\\n', 'output': '6\\n27\\n39\\n11\\n15\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 1\\n1 4 4 23 15 13\\n5 6 4 1 15 24\\n', 'output': '83\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 2\\n3 4\\n5 5\\n5 5 6 6 5\\n1 2 5 4 3\\n5 3\\n1 2 3 4 5\\n10 9 10 10 9\\n4 1\\n2 2 4 3\\n2 4 2 0\\n4 3\\n1 2 2 1\\n4 4 5 4\\n', 'output': '6\\n27\\n39\\n13\\n15\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 2\\n3 7\\n5 5\\n5 5 6 6 5\\n1 2 5 4 4\\n5 3\\n1 2 3 4 5\\n10 9 10 10 9\\n4 0\\n2 2 4 3\\n2 4 2 5\\n4 4\\n1 2 2 1\\n4 4 5 4\\n', 'output': '9\\n27\\n39\\n11\\n17\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 1\\n1 4 4 23 15 7\\n5 9 4 1 15 24\\n', 'output': '77\\n'}, {'type': 'stdin_stdout', 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256000000}","problem_id":"vfc_77597","program":"```python\ndef swap_sum(a,b,cnt,k):\n if cnt==k or min(a)>=max(b):\n return sum(a)\n \n \n else:\n i=a.index(min(a))\n j=b.index(max(b))\n a[i],b[j]=b[j],a[i]\n #print(a)\n #print(b)\n return swap_sum(a,b,cnt+1,k)\n\n\nfor ii in range(int(input())):\n n,k=map(int,input().split())\n a=list(map(int,input().split()))\n b=list(map(int,input().split()))\n print(swap_sum(a,b,0,k))\n \n```","inputs":"5\n2 1\n1 2\n3 4\n5 5\n5 5 6 6 5\n1 2 5 4 3\n5 3\n1 2 3 4 5\n10 9 10 10 9\n4 0\n2 2 4 3\n2 4 2 3\n4 4\n1 2 2 1\n4 4 5 4\n","output":"6\n27\n39\n11\n17\n","actual_output":"6\n27\n39\n11\n17\n","execution_success":true,"sample_index":12381},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1373_A. Donut Shops","prompt":"Solve the following coding problem using the programming language python:\n\nThere are two rival donut shops.\n\nThe first shop sells donuts at retail: each donut costs a dollars.\n\nThe second shop sells donuts only in bulk: box of b donuts costs c dollars. So if you want to buy x donuts from this shop, then you have to buy the smallest number of boxes such that the total number of donuts in them is greater or equal to x.\n\nYou want to determine two positive integer values: \n\n 1. how many donuts can you buy so that they are strictly cheaper in the first shop than in the second shop? \n 2. how many donuts can you buy so that they are strictly cheaper in the second shop than in the first shop? \n\n\n\nIf any of these values doesn't exist then that value should be equal to -1. If there are multiple possible answers, then print any of them.\n\nThe printed values should be less or equal to 10^9. It can be shown that under the given constraints such values always exist if any values exist at all.\n\nInput\n\nThe first line contains a single integer t (1 \u2264 t \u2264 1000) \u2014 the number of testcases.\n\nEach of the next t lines contains three integers a, b and c (1 \u2264 a \u2264 10^9, 2 \u2264 b \u2264 10^9, 1 \u2264 c \u2264 10^9).\n\nOutput\n\nFor each testcase print two positive integers. For both shops print such x that buying x donuts in this shop is strictly cheaper than buying x donuts in the other shop. x should be greater than 0 and less or equal to 10^9.\n\nIf there is no such x, then print -1. If there are multiple answers, then print any of them.\n\nExample\n\nInput\n\n\n4\n5 10 4\n4 5 20\n2 2 3\n1000000000 1000000000 1000000000\n\n\nOutput\n\n\n-1 20\n8 -1\n1 2\n-1 1000000000\n\nNote\n\nIn the first testcase buying any number of donuts will be cheaper in the second shop. For example, for 3 or 5 donuts you'll have to buy a box of 10 donuts for 4 dollars. 3 or 5 donuts in the first shop would cost you 15 or 25 dollars, respectively, however. For 20 donuts you'll have to buy two boxes for 8 dollars total. Note that 3 and 5 are also valid answers for the second shop, along with many other answers.\n\nIn the second testcase buying any number of donuts will be either cheaper in the first shop or the same price. 8 donuts cost 32 dollars in the first shop and 40 dollars in the second shop (because you have to buy two boxes). 10 donuts will cost 40 dollars in both shops, so 10 is not a valid answer for any of the shops.\n\nIn the third testcase 1 donut costs 2 and 3 dollars, respectively. 2 donuts cost 4 and 3 dollars. Thus, 1 is a valid answer for the first shop and 2 is a valid answer for the second shop.\n\nIn the fourth testcase 10^9 donuts cost 10^{18} dollars in the first shop and 10^9 dollars in the second shop.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\n\n\ndef main():\n t = int(input())\n for _ in range(t):\n A, B, C = [int(x) for x in input().split()]\n\n ans1 = -1\n ans2 = -1\n\n if A < C:\n ans1 = 1\n\n if A * B > C:\n ans2 = B\n\n\n print(ans1, ans2)\n\n \n\nif __name__ == '__main__':\n main()\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n5 10 4\\n4 5 20\\n2 2 3\\n1000000000 1000000000 1000000000\\n', 'output': '-1 10\\n1 -1\\n1 2\\n-1 1000000000\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 10 4\\n4 5 20\\n2 2 3\\n1 100000007 100000008\\n1 100000007 100000009\\n1 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Hopscotch","prompt":"Solve the following coding problem using the programming language python:\n\nSo nearly half of the winter is over and Maria is dreaming about summer. She's fed up with skates and sleds, she was dreaming about Hopscotch all night long. It's a very popular children's game. The game field, the court, looks as is shown in the figure (all blocks are square and are numbered from bottom to top, blocks in the same row are numbered from left to right). Let us describe the hopscotch with numbers that denote the number of squares in the row, staring from the lowest one: 1-1-2-1-2-1-2-(1-2)..., where then the period is repeated (1-2).\n\n\n\nThe coordinate system is defined as shown in the figure. Side of all the squares are equal and have length a.\n\nMaria is a very smart and clever girl, and she is concerned with quite serious issues: if she throws a stone into a point with coordinates (x, y), then will she hit some square? If the answer is positive, you are also required to determine the number of the square.\n\nIt is believed that the stone has fallen into the square if it is located strictly inside it. In other words a stone that has fallen on the square border is not considered a to hit a square.\n\nInput\n\nThe only input line contains three integers: a, x, y, where a (1 \u2264 a \u2264 100) is the side of the square, x and y ( - 106 \u2264 x \u2264 106, 0 \u2264 y \u2264 106) are coordinates of the stone.\n\nOutput\n\nPrint the number of the square, inside which the stone fell. If the stone is on a border of some stone or outside the court, print \"-1\" without the quotes.\n\nExamples\n\nInput\n\n1 0 0\n\n\nOutput\n\n-1\n\n\nInput\n\n3 1 1\n\n\nOutput\n\n1\n\n\nInput\n\n3 0 10\n\n\nOutput\n\n5\n\n\nInput\n\n3 0 7\n\n\nOutput\n\n-1\n\n\nInput\n\n3 4 0\n\n\nOutput\n\n-1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na, x, y = map(int, input().split())\nh = a / 2\nif y % a == 0:\n print('-1')\n exit()\ny //= a\ny += 1\nif y == 1:\n if x > -h and x < h:\n print('1')\n else:\n print('-1')\nelse:\n if y % 2 == 0:\n if x > -h and x < h:\n print(y + (y // 2) - 1)\n else:\n print('-1')\n else:\n if x > -a and x < 0:\n print(y + (y // 2) - 1)\n elif x > 0 and x < a:\n print(y + (y // 2))\n else:\n print('-1')\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 4 0\\n', 'output': '-1\\n'}, {'type': 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'stdin_stdout', 'input': '2 -1 10\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '100 0 1332849\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 4 2\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 -5 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 -2 0\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77609","program":"```python\na, x, y = map(int, input().split())\nh = a / 2\nif y % a == 0:\n print('-1')\n exit()\ny //= a\ny += 1\nif y == 1:\n if x > -h and x < h:\n print('1')\n else:\n print('-1')\nelse:\n if y % 2 == 0:\n if x > -h and x < h:\n print(y + (y // 2) - 1)\n else:\n print('-1')\n else:\n if x > -a and x < 0:\n print(y + (y // 2) - 1)\n elif x > 0 and x < a:\n print(y + (y // 2))\n else:\n print('-1')\n\n```","inputs":"3 4 0\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12383},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1438_B. Valerii Against Everyone","prompt":"Solve the following coding problem using the programming language python:\n\nYou're given an array b of length n. Let's define another array a, also of length n, for which a_i = 2^{b_i} (1 \u2264 i \u2264 n). \n\nValerii says that every two non-intersecting subarrays of a have different sums of elements. You want to determine if he is wrong. More formally, you need to determine if there exist four integers l_1,r_1,l_2,r_2 that satisfy the following conditions: \n\n * 1 \u2264 l_1 \u2264 r_1 < l_2 \u2264 r_2 \u2264 n; \n * a_{l_1}+a_{l_1+1}+\u2026+a_{r_1-1}+a_{r_1} = a_{l_2}+a_{l_2+1}+\u2026+a_{r_2-1}+a_{r_2}. \n\n\n\nIf such four integers exist, you will prove Valerii wrong. Do they exist?\n\nAn array c is a subarray of an array d if c can be obtained from d by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.\n\nInput\n\nEach test contains multiple test cases. The first line contains the number of test cases t (1 \u2264 t \u2264 100). Description of the test cases follows.\n\nThe first line of every test case contains a single integer n (2 \u2264 n \u2264 1000).\n\nThe second line of every test case contains n integers b_1,b_2,\u2026,b_n (0 \u2264 b_i \u2264 10^9). \n\nOutput\n\nFor every test case, if there exist two non-intersecting subarrays in a that have the same sum, output YES on a separate line. Otherwise, output NO on a separate line. \n\nAlso, note that each letter can be in any case. \n\nExample\n\nInput\n\n\n2\n6\n4 3 0 1 2 0\n2\n2 5\n\n\nOutput\n\n\nYES\nNO\n\nNote\n\nIn the first case, a = [16,8,1,2,4,1]. Choosing l_1 = 1, r_1 = 1, l_2 = 2 and r_2 = 6 works because 16 = (8+1+2+4+1).\n\nIn the second case, you can verify that there is no way to select to such subarrays.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\n#from collections import deque\n#from functools import *\n#from fractions import Fraction as f\nfrom copy import *\nfrom bisect import *\t\n#from heapq import *\nfrom math import gcd,ceil,sqrt\nfrom itertools import permutations as prm,product\n \ndef eprint(*args):\n print(*args, file=sys.stderr)\nzz=1\n \n#sys.setrecursionlimit(10**6)\nif zz:\n\tinput=sys.stdin.readline\nelse:\t\n\tsys.stdin=open('input.txt', 'r')\n\tsys.stdout=open('all.txt','w')\ndi=[[-1,0],[1,0],[0,1],[0,-1]]\n\ndef string(s):\n\treturn \"\".join(s)\ndef fori(n):\n\treturn [fi() for i in range(n)]\t\ndef inc(d,c,x=1):\n\td[c]=d[c]+x if c in d else x\ndef bo(i):\n\treturn ord(i)-ord('A')\t\ndef li():\n\treturn [int(xx) for xx in input().split()]\ndef fli():\n\treturn [float(x) for x in input().split()]\t\ndef comp(a,b):\n\tif(a>b):\n\t\treturn 2\n\treturn 2 if a==b else 0\t\t\ndef gi():\t\n\treturn [xx for xx in input().split()]\ndef gtc(tc,ans):\n\tprint(\"Case #\"+str(tc)+\":\",ans)\t\ndef cil(n,m):\n\treturn n//m+int(n%m>0)\t\ndef fi():\n\treturn int(input())\ndef pro(a): \n\treturn reduce(lambda a,b:a*b,a)\t\t\ndef swap(a,i,j): \n\ta[i],a[j]=a[j],a[i]\t\ndef si():\n\treturn list(input().rstrip())\t\ndef mi():\n\treturn \tmap(int,input().split())\t\t\t\ndef gh():\n\tsys.stdout.flush()\ndef isvalid(i,j,n,m):\n\treturn 0<=i0:\n\tt-=1\n\tn=fi()\n\ta=li()\n\tprint(\"YES\" if len(a)>len(set(a)) else \"NO\")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 1 2 0\\n2\\n2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 2 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 2 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n0 3 0 1 2 0\\n2\\n2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 2 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 1 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 2 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 2 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 2 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 2 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 3 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 0 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 2 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 1 2 0\\n2\\n4 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 2 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 4 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 1 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 3 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 1 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n2 2 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 0 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 2 0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 0 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 2 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 1 2 0\\n2\\n4 3\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 0 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 3 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 1 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 3 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 1 2 0\\n2\\n4 6\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n3 0 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 6 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 1 2 0\\n2\\n4 2\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n3 1 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 1 2 0\\n2\\n3 2\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n3 1 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 1 2 0\\n2\\n1 2\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 1 2 0\\n2\\n1 4\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 2 0\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n1 3 0 1 2 0\\n2\\n2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 2 0\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 0 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 4 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 3 0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 0 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 2 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 1 4 0\\n2\\n4 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 0 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 8 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n-1 1 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 1 8\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 4 0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 -1 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 4 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n5 3 0 1 2 0\\n2\\n4 3\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n4 0 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 1 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 1 2 0\\n2\\n4 9\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 6 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 3 0 2 2 0\\n2\\n3 2\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n3 2 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 0 0 1 2 0\\n2\\n1 2\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1 0\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 3 -1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 4 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 4 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 4 0 1 4 0\\n2\\n4 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 1 0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n-1 1 8\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 5 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n5 2 0 1 2 0\\n2\\n4 3\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n4 0 0\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 1 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 10 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n6 3 0 2 2 0\\n2\\n3 2\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1 -1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 4 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 4 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6\\n4 4 0 1 4 0\\n2\\n0 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n0 1 0\\n', 'output': 'YES\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77613","program":"```python\nimport sys\n#from collections import deque\n#from functools import *\n#from fractions import Fraction as f\nfrom copy import *\nfrom bisect import *\t\n#from heapq import *\nfrom math import gcd,ceil,sqrt\nfrom itertools import permutations as prm,product\n \ndef eprint(*args):\n print(*args, file=sys.stderr)\nzz=1\n \n#sys.setrecursionlimit(10**6)\nif zz:\n\tinput=sys.stdin.readline\nelse:\t\n\tsys.stdin=open('input.txt', 'r')\n\tsys.stdout=open('all.txt','w')\ndi=[[-1,0],[1,0],[0,1],[0,-1]]\n\ndef string(s):\n\treturn \"\".join(s)\ndef fori(n):\n\treturn [fi() for i in range(n)]\t\ndef inc(d,c,x=1):\n\td[c]=d[c]+x if c in d else x\ndef bo(i):\n\treturn ord(i)-ord('A')\t\ndef li():\n\treturn [int(xx) for xx in input().split()]\ndef fli():\n\treturn [float(x) for x in input().split()]\t\ndef comp(a,b):\n\tif(a>b):\n\t\treturn 2\n\treturn 2 if a==b else 0\t\t\ndef gi():\t\n\treturn [xx for xx in input().split()]\ndef gtc(tc,ans):\n\tprint(\"Case #\"+str(tc)+\":\",ans)\t\ndef cil(n,m):\n\treturn n//m+int(n%m>0)\t\ndef fi():\n\treturn int(input())\ndef pro(a): \n\treturn reduce(lambda a,b:a*b,a)\t\t\ndef swap(a,i,j): \n\ta[i],a[j]=a[j],a[i]\t\ndef si():\n\treturn list(input().rstrip())\t\ndef mi():\n\treturn \tmap(int,input().split())\t\t\t\ndef gh():\n\tsys.stdout.flush()\ndef isvalid(i,j,n,m):\n\treturn 0<=i0:\n\tt-=1\n\tn=fi()\n\ta=li()\n\tprint(\"YES\" if len(a)>len(set(a)) else \"NO\")\n\n```","inputs":"2\n6\n4 3 0 1 2 0\n2\n2 5\n","output":"YES\nNO\n","actual_output":"YES\nNO\n","execution_success":true,"sample_index":12384},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"148_A. Insomnia cure","prompt":"Solve the following coding problem using the programming language python:\n\n\u00abOne dragon. Two dragon. Three dragon\u00bb, \u2014 the princess was counting. She had trouble falling asleep, and she got bored of counting lambs when she was nine.\n\nHowever, just counting dragons was boring as well, so she entertained herself at best she could. Tonight she imagined that all dragons were here to steal her, and she was fighting them off. Every k-th dragon got punched in the face with a frying pan. Every l-th dragon got his tail shut into the balcony door. Every m-th dragon got his paws trampled with sharp heels. Finally, she threatened every n-th dragon to call her mom, and he withdrew in panic.\n\nHow many imaginary dragons suffered moral or physical damage tonight, if the princess counted a total of d dragons?\n\nInput\n\nInput data contains integer numbers k, l, m, n and d, each number in a separate line (1 \u2264 k, l, m, n \u2264 10, 1 \u2264 d \u2264 105).\n\nOutput\n\nOutput the number of damaged dragons.\n\nExamples\n\nInput\n\n1\n2\n3\n4\n12\n\n\nOutput\n\n12\n\n\nInput\n\n2\n3\n4\n5\n24\n\n\nOutput\n\n17\n\nNote\n\nIn the first case every first dragon got punched with a frying pan. Some of the dragons suffered from other reasons as well, but the pan alone would be enough.\n\nIn the second case dragons 1, 7, 11, 13, 17, 19 and 23 escaped unharmed.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nkill=[]\nfor i in range(4):\n a=int(input())\n kill.append(a)\nd=int(input())\ncount=0\nfor i in range(1,d+1):\n for j in kill:\n if i%j==0:\n count+=1\n break\n else:\n count+=0\n\nprint(count)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n3\\n4\\n5\\n24\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n3\\n4\\n12\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4\\n4\\n3\\n65437\\n', 'output': '32718\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2\\n1\\n8\\n63537\\n', 'output': '63537\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5\\n8\\n9\\n79228\\n', 'output': '29931\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7\\n7\\n7\\n84046\\n', 'output': '36019\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1\\n8\\n7\\n44835\\n', 'output': '44835\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n1\\n1\\n100000\\n', 'output': '100000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n2\\n6\\n49547\\n', 'output': '49547\\n'}, {'type': 'stdin_stdout', 'input': '2\\n7\\n4\\n9\\n56937\\n', 'output': '35246\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n10\\n4\\n39901\\n', 'output': '39901\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2\\n3\\n8\\n21754\\n', 'output': '15539\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n2\\n2\\n1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n5\\n6\\n89535\\n', 'output': '89535\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10\\n1\\n10\\n100\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '2\\n9\\n8\\n1\\n75083\\n', 'output': '75083\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10\\n1\\n10\\n10\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '8\\n7\\n7\\n6\\n69038\\n', 'output': '24656\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4\\n2\\n3\\n54481\\n', 'output': '36320\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n4\\n3\\n60504\\n', 'output': '36302\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n3\\n3\\n87079\\n', 'output': '43539\\n'}, {'type': 'stdin_stdout', 'input': '4\\n9\\n6\\n6\\n1070\\n', 'output': '415\\n'}, {'type': 'stdin_stdout', 'input': '5\\n10\\n9\\n3\\n70149\\n', 'output': '32736\\n'}, {'type': 'stdin_stdout', 'input': '3\\n9\\n3\\n3\\n61082\\n', 'output': '20360\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10\\n10\\n10\\n1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '9\\n10\\n4\\n6\\n52003\\n', 'output': '21956\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1\\n7\\n2\\n62982\\n', 'output': '62982\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n7\\n1\\n58048\\n', 'output': '58048\\n'}, {'type': 'stdin_stdout', 'input': '5\\n8\\n4\\n9\\n5226\\n', 'output': '2438\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2\\n10\\n5\\n81684\\n', 'output': '53678\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4\\n1\\n10\\n59392\\n', 'output': '59392\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1\\n6\\n8\\n99831\\n', 'output': '99831\\n'}, {'type': 'stdin_stdout', 'input': '9\\n7\\n8\\n10\\n42357\\n', 'output': '16540\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n1\\n1\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10\\n10\\n10\\n100000\\n', 'output': '10000\\n'}, {'type': 'stdin_stdout', 'input': '7\\n4\\n8\\n8\\n25829\\n', 'output': '9224\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5\\n2\\n1\\n7682\\n', 'output': '7682\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4\\n9\\n8\\n72628\\n', 'output': '28244\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5\\n5\\n10\\n55592\\n', 'output': '11118\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9\\n8\\n7\\n6\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 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'stdin_stdout', 'input': '2\\n1\\n10\\n2\\n75083\\n', 'output': '75083\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77621","program":"```python\nkill=[]\nfor i in range(4):\n a=int(input())\n kill.append(a)\nd=int(input())\ncount=0\nfor i in range(1,d+1):\n for j in kill:\n if i%j==0:\n count+=1\n break\n else:\n count+=0\n\nprint(count)\n```","inputs":"2\n3\n4\n5\n24\n","output":"17\n","actual_output":"17\n","execution_success":true,"sample_index":12386},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1511_E. Colorings and Dominoes","prompt":"Solve the following coding problem using the programming language python:\n\nYou have a large rectangular board which is divided into n \u00d7 m cells (the board has n rows and m columns). Each cell is either white or black.\n\nYou paint each white cell either red or blue. Obviously, the number of different ways to paint them is 2^w, where w is the number of white cells.\n\nAfter painting the white cells of the board, you want to place the maximum number of dominoes on it, according to the following rules:\n\n * each domino covers two adjacent cells; \n * each cell is covered by at most one domino; \n * if a domino is placed horizontally (it covers two adjacent cells in one of the rows), it should cover only red cells; \n * if a domino is placed vertically (it covers two adjacent cells in one of the columns), it should cover only blue cells. \n\n\n\nLet the value of the board be the maximum number of dominoes you can place. Calculate the sum of values of the board over all 2^w possible ways to paint it. Since it can be huge, print it modulo 998 244 353.\n\nInput\n\nThe first line contains two integers n and m (1 \u2264 n, m \u2264 3 \u22c5 10^5; nm \u2264 3 \u22c5 10^5) \u2014 the number of rows and columns, respectively.\n\nThen n lines follow, each line contains a string of m characters. The j-th character in the i-th string is * if the j-th cell in the i-th row is black; otherwise, that character is o.\n\nOutput\n\nPrint one integer \u2014 the sum of values of the board over all 2^w possible ways to paint it, taken modulo 998 244 353.\n\nExamples\n\nInput\n\n\n3 4\n**oo\noo*o\n**oo\n\n\nOutput\n\n\n144\n\n\nInput\n\n\n3 4\n**oo\noo**\n**oo\n\n\nOutput\n\n\n48\n\n\nInput\n\n\n2 2\noo\no*\n\n\nOutput\n\n\n4\n\n\nInput\n\n\n1 4\noooo\n\n\nOutput\n\n\n9\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nmod = 998244353\nm,n = map(int,input().split())\nmat = [[0]*n for _ in range(m)]\nt = 0\nres = 0\ncom = [0] * (max(m,n) + 2)\ncom[2] = 1\npow2 = 1\nfor i in range(3,max(m,n)+1):\n pow2 = (pow2 << 1) % mod\n com[i] = (com[i-1] + 2*com[i-2] + pow2) % mod\n \nfor i in range(m):\n s = input()\n for j in range(n):\n if s[j] ==\"o\":\n mat[i][j] = 1\n t += 1\n\nfor i in range(m):\n count = 0\n for j in range(n):\n if mat[i][j] == 1:\n count += 1\n else:\n if count >= 2:\n res = (res + pow(2,t-count,mod) * com[count] ) % mod\n count = 0\n if count >= 2:\n res = (res + pow(2,t-count,mod) * com[count] ) % mod\n \n\nfor j in range(n):\n count = 0\n for i in range(m):\n if mat[i][j] == 1:\n count += 1\n else:\n if count >= 2:\n res = (res + pow(2,t-count,mod) * com[count] ) % mod\n count = 0\n if count >= 2:\n res = (res + pow(2,t-count,mod) * com[count] ) % mod \n\nprint(res)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 2\\noo\\no*\\n', 'output': '\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n**oo\\noo*o\\n**oo\\n', 'output': '\\n144\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n**oo\\noo**\\n**oo\\n', 'output': '\\n48\\n'}, {'type': 'stdin_stdout', 'input': '1 4\\noooo\\n', 'output': '\\n9\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\noooo\\no*oo\\n', 'output': '200\\n'}, {'type': 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4\\noooo\\no*oo\\noono\\npo**\\n+ooo\\n', 'output': '200\\n'}, {'type': 'stdin_stdout', 'input': '1 4\\noo**\\non*p\\n**oo\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 4\\noo**\\npo*p\\n+o*n\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\noo**\\no*oo\\n*oo+\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '1 4\\noooo\\noo*o\\nopoo\\noo)*\\nooo)\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1 4\\n*oo*\\noo**\\n*on*\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 4\\noooo\\noo*n\\noooo\\noo**\\n*opo\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\noooo\\no*oo\\noooo\\noo)*\\nno*n\\n', 'output': '200\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_77625","program":"```python\nmod = 998244353\nm,n = map(int,input().split())\nmat = [[0]*n for _ in range(m)]\nt = 0\nres = 0\ncom = [0] * (max(m,n) + 2)\ncom[2] = 1\npow2 = 1\nfor i in range(3,max(m,n)+1):\n pow2 = (pow2 << 1) % mod\n com[i] = (com[i-1] + 2*com[i-2] + pow2) % mod\n \nfor i in range(m):\n s = input()\n for j in range(n):\n if s[j] ==\"o\":\n mat[i][j] = 1\n t += 1\n\nfor i in range(m):\n count = 0\n for j in range(n):\n if mat[i][j] == 1:\n count += 1\n else:\n if count >= 2:\n res = (res + pow(2,t-count,mod) * com[count] ) % mod\n count = 0\n if count >= 2:\n res = (res + pow(2,t-count,mod) * com[count] ) % mod\n \n\nfor j in range(n):\n count = 0\n for i in range(m):\n if mat[i][j] == 1:\n count += 1\n else:\n if count >= 2:\n res = (res + pow(2,t-count,mod) * com[count] ) % mod\n count = 0\n if count >= 2:\n res = (res + pow(2,t-count,mod) * com[count] ) % mod \n\nprint(res)\n\n```","inputs":"2 2\noo\no*\n","output":"\n4\n","actual_output":"4\n","execution_success":true,"sample_index":12387},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1539_C. Stable Groups","prompt":"Solve the following coding problem using the programming language python:\n\nThere are n students numerated from 1 to n. The level of the i-th student is a_i. You need to split the students into stable groups. A group of students is called stable, if in the sorted array of their levels no two neighboring elements differ by more than x.\n\nFor example, if x = 4, then the group with levels [1, 10, 8, 4, 4] is stable (because 4 - 1 \u2264 x, 4 - 4 \u2264 x, 8 - 4 \u2264 x, 10 - 8 \u2264 x), while the group with levels [2, 10, 10, 7] is not stable (7 - 2 = 5 > x).\n\nApart from the n given students, teachers can invite at most k additional students with arbitrary levels (at teachers' choice). Find the minimum number of stable groups teachers can form from all students (including the newly invited).\n\nFor example, if there are two students with levels 1 and 5; x = 2; and k \u2265 1, then you can invite a new student with level 3 and put all the students in one stable group.\n\nInput\n\nThe first line contains three integers n, k, x (1 \u2264 n \u2264 200 000, 0 \u2264 k \u2264 10^{18}, 1 \u2264 x \u2264 10^{18}) \u2014 the initial number of students, the number of students you can additionally invite, and the maximum allowed level difference.\n\nThe second line contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 10^{18}) \u2014 the students levels.\n\nOutput\n\nIn the only line print a single integer: the minimum number of stable groups you can split the students into.\n\nExamples\n\nInput\n\n\n8 2 3\n1 1 5 8 12 13 20 22\n\n\nOutput\n\n\n2\n\nInput\n\n\n13 0 37\n20 20 80 70 70 70 420 5 1 5 1 60 90\n\n\nOutput\n\n\n3\n\nNote\n\nIn the first example you can invite two students with levels 2 and 11. Then you can split the students into two stable groups: \n\n 1. [1, 1, 2, 5, 8, 11, 12, 13], \n 2. [20, 22]. \n\n\n\nIn the second example you are not allowed to invite new students, so you need 3 groups: \n\n 1. [1, 1, 5, 5, 20, 20] \n 2. [60, 70, 70, 70, 80, 90] \n 3. [420] \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,k,x =list(map(int ,input().split()))\narr = list(map(int ,input().split()))\narr.sort()\ngroups =1\nre = []\n\nfor i in range(n-1):\n diff = arr[i+1]-arr[i]\n if diff>x :\n\n if x==0:\n groups+=1\n continue\n if diff%x==0:\n diff = diff//x -1\n else:\n diff =diff//x\n re.append(diff)\n groups+=1\nre.sort()\n\nfor i in range(len(re)):\n k-=re[i]\n if k>=0:\n groups-=1\n else:\n break\n\nprint(groups) \n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '8 2 3\\n1 1 5 8 12 13 20 22\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '13 0 37\\n20 20 80 70 70 70 420 5 1 5 1 60 90\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 899688650294255694 1\\n1 899688650294255696 899688650294255698\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10 2 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1000001000000000100\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '13 0 37\\n20 32 64 70 69 70 420 5 2 5 1 60 90\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '10 2 1\\n1 1 1 5 1 22 2 1 1 4\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '2 145138436564422215 4\\n1 1399927557299809099\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '96 15 21\\n76 26 108 220 384 4 170 198 568 571 2 193 244 359 78 133 107 191 110 135 565 228 109 572 243 138 357 52 293 344 595 105 569 362 639 134 135 356 19 137 194 291 499 104 28 290 197 477 339 50 288 289 160 54 358 640 343 542 566 79 136 385 3 641 171 355 361 169 196 429 242 16 338 80 77 161 81 337 132 570 171 354 543 360 476 473 345 474 292 594 51 342 475 106 53 567\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '80 18 17\\n470 460 387 235 83 21 327 236 160 81 23 158 328 59 386 26 237 794 159 121 466 60 465 119 25 24 101 2 1 27 292 489 3 462 363 182 385 383 57 167 238 29 78 94 491 180 30 384 490 511 492 33 120 22 80 38 58 464 381 161 31 82 52 256 424 469 28 32 34 471 162 55 461 200 382 56 388 79 468 122\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '2 12 3\\n1 37\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 3 1\\n1 1 6 1 1 1 0 2 8 13\\n', 'output': '3'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77629","program":"```python\nn,k,x =list(map(int ,input().split()))\narr = list(map(int ,input().split()))\narr.sort()\ngroups =1\nre = []\n\nfor i in range(n-1):\n diff = arr[i+1]-arr[i]\n if diff>x :\n\n if x==0:\n groups+=1\n continue\n if diff%x==0:\n diff = diff//x -1\n else:\n diff =diff//x\n re.append(diff)\n groups+=1\nre.sort()\n\nfor i in range(len(re)):\n k-=re[i]\n if k>=0:\n groups-=1\n else:\n break\n\nprint(groups) \n\n\n\n```","inputs":"8 2 3\n1 1 5 8 12 13 20 22\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12388},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"187_A. Permutations","prompt":"Solve the following coding problem using the programming language python:\n\nHappy PMP is freshman and he is learning about algorithmic problems. He enjoys playing algorithmic games a lot.\n\nOne of the seniors gave Happy PMP a nice game. He is given two permutations of numbers 1 through n and is asked to convert the first one to the second. In one move he can remove the last number from the permutation of numbers and inserts it back in an arbitrary position. He can either insert last number between any two consecutive numbers, or he can place it at the beginning of the permutation.\n\nHappy PMP has an algorithm that solves the problem. But it is not fast enough. He wants to know the minimum number of moves to convert the first permutation to the second. \n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 2\u00b7105) \u2014 the quantity of the numbers in the both given permutations. \n\nNext line contains n space-separated integers \u2014 the first permutation. Each number between 1 to n will appear in the permutation exactly once. \n\nNext line describe the second permutation in the same format.\n\nOutput\n\nPrint a single integer denoting the minimum number of moves required to convert the first permutation to the second.\n\nExamples\n\nInput\n\n3\n3 2 1\n1 2 3\n\n\nOutput\n\n2\n\n\nInput\n\n5\n1 2 3 4 5\n1 5 2 3 4\n\n\nOutput\n\n1\n\n\nInput\n\n5\n1 5 2 3 4\n1 2 3 4 5\n\n\nOutput\n\n3\n\nNote\n\nIn the first sample, he removes number 1 from end of the list and places it at the beginning. After that he takes number 2 and places it between 1 and 3.\n\nIn the second sample, he removes number 5 and inserts it after 1.\n\nIn the third sample, the sequence of changes are like this: \n\n * 1 5 2 3 4 \n * 1 4 5 2 3 \n * 1 3 4 5 2 \n * 1 2 3 4 5 \n\nSo he needs three moves.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\nfrom math import *\nimport bisect as bs\nn=int(input())\na=[int(x) for x in input().split()]\nb= [int(x) for x in input().split()]\nd={}\nfor i in range(n):\n d[b[i]]=i\n\nc=0\nans=0\nu=[0 for i in range(n)]\nfor i in range(n):\n u[i]=d[a[i]]\n#print(u) \nfor i in range(1,n):\n if u[i] 0), that the equation given in the statement holds.\n\nExamples\n\nInput\n\n2\n\n\nOutput\n\n1\n\n\nInput\n\n110\n\n\nOutput\n\n10\n\n\nInput\n\n4\n\n\nOutput\n\n-1\n\nNote\n\nIn the first test case x = 1 is the minimum root. As s(1) = 1 and 12 + 1\u00b71 - 2 = 0.\n\nIn the second test case x = 10 is the minimum root. As s(10) = 1 + 0 = 1 and 102 + 1\u00b710 - 110 = 0.\n\nIn the third test case the equation has no roots.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# your code goes here\nn=int(input())\ndef s(x):\n return sum(int(i) for i in str(x))\nx=int(n**0.5)\nd=0\nwhile x>=0 and d<=50:\n\tif(x*x+s(x)*x==n):\n\t#\tprint(x)\n\t\tbreak\n\td+=1\n\tx-=1\nif d>50:\n\tx=-1\nprint(x)\t\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '110\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '980100017820000000\\n', 'output': '990000000\\n'}, {'type': 'stdin_stdout', 'input': '902500013300000000\\n', 'output': '950000000\\n'}, {'type': 'stdin_stdout', 'input': '172580744\\n', 'output': '13132\\n'}, {'type': 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'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77645","program":"```python\n# your code goes here\nn=int(input())\ndef s(x):\n return sum(int(i) for i in str(x))\nx=int(n**0.5)\nd=0\nwhile x>=0 and d<=50:\n\tif(x*x+s(x)*x==n):\n\t#\tprint(x)\n\t\tbreak\n\td+=1\n\tx-=1\nif d>50:\n\tx=-1\nprint(x)\t\n```","inputs":"4\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12390},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"259_A. Little Elephant and Chess","prompt":"Solve the following coding problem using the programming language python:\n\nThe Little Elephant loves chess very much. \n\nOne day the Little Elephant and his friend decided to play chess. They've got the chess pieces but the board is a problem. They've got an 8 \u00d7 8 checkered board, each square is painted either black or white. The Little Elephant and his friend know that a proper chessboard doesn't have any side-adjacent cells with the same color and the upper left cell is white. To play chess, they want to make the board they have a proper chessboard. For that the friends can choose any row of the board and cyclically shift the cells of the chosen row, that is, put the last (rightmost) square on the first place in the row and shift the others one position to the right. You can run the described operation multiple times (or not run it at all).\n\nFor example, if the first line of the board looks like that \"BBBBBBWW\" (the white cells of the line are marked with character \"W\", the black cells are marked with character \"B\"), then after one cyclic shift it will look like that \"WBBBBBBW\".\n\nHelp the Little Elephant and his friend to find out whether they can use any number of the described operations to turn the board they have into a proper chessboard.\n\nInput\n\nThe input consists of exactly eight lines. Each line contains exactly eight characters \"W\" or \"B\" without any spaces: the j-th character in the i-th line stands for the color of the j-th cell of the i-th row of the elephants' board. Character \"W\" stands for the white color, character \"B\" stands for the black color.\n\nConsider the rows of the board numbered from 1 to 8 from top to bottom, and the columns \u2014 from 1 to 8 from left to right. The given board can initially be a proper chessboard.\n\nOutput\n\nIn a single line print \"YES\" (without the quotes), if we can make the board a proper chessboard and \"NO\" (without the quotes) otherwise.\n\nExamples\n\nInput\n\nWBWBWBWB\nBWBWBWBW\nBWBWBWBW\nBWBWBWBW\nWBWBWBWB\nWBWBWBWB\nBWBWBWBW\nWBWBWBWB\n\n\nOutput\n\nYES\n\n\nInput\n\nWBWBWBWB\nWBWBWBWB\nBBWBWWWB\nBWBWBWBW\nBWBWBWBW\nBWBWBWWW\nBWBWBWBW\nBWBWBWBW\n\n\nOutput\n\nNO\n\nNote\n\nIn the first sample you should shift the following lines one position to the right: the 3-rd, the 6-th, the 7-th and the 8-th.\n\nIn the second sample there is no way you can achieve the goal.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nflag=True\nfor i in range(8):\n k=input()\n if k!='BWBWBWBW' and k!='WBWBWBWB':\n flag=False\nif (flag):\n print (\"YES\")\nelse:\n print (\"NO\")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'WBWBWBWB\\nBWBWBWBW\\nBWBWBWBW\\nBWBWBWBW\\nWBWBWBWB\\nWBWBWBWB\\nBWBWBWBW\\nWBWBWBWB\\n', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'WBWBWBWB\\nWBWBWBWB\\nBBWBWWWB\\nBWBWBWBW\\nBWBWBWBW\\nBWBWBWWW\\nBWBWBWBW\\nBWBWBWBW\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'BWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\nBWWWBWBW\\nWBWBWBWB\\nWBWBWBWB\\nBWBWBWBW\\nWBWBWBBW\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'BWBWBWBW\\nBWBBBWWB\\nWBWBWBWB\\nBWBWBWBW\\nBWBWBWBW\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'BWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\nBWBWBWBW\\nWBWBWBWB\\nWBWBWBWB\\nWBWBWBWB\\nWBWBWBWB\\n', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'WBWBWBWB\\nWBWBWBWB\\nWWBBWBBB\\nWBWBWBWB\\nWWWWBWWB\\nWBBBBWWW\\nBWBWWWBW\\nWWWBWBBB\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'WBWBWBWB\\nBWBWBWBW\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\nBWBWBWBW\\nBWBWBWBW\\nBWBWBWBW\\n', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'BWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\nWBWBWBWB\\nWBWBWBWB\\nWBWBWBWB\\n', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'BWBWBWBW\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\n', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'WBWBWBWB\\nWBWBWBWB\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\nBWBWBWBW\\n', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'WBWBWBWB\\nWBWBWBWB\\nBWBWBWBW\\nBWBWBWBW\\nBWBWBWBW\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\n', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'WBWBWBWB\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWBW\\nWBWBWBWB\\nWBWBWBWB\\nBWBWBWBW\\nBWBWBWBW\\n', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'BBBBBWWW\\nWBBWBWWB\\nWWWWWBWW\\nBWBWWBWW\\nBBBWWBWW\\nBBBBBWBW\\nWBBBWBWB\\nWBWBWWWB\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 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'WBWBWBWB\\nBWBWBWBW\\nWBWBWBWB\\nBWBWBWCW\\nWBWBWBWB\\nWBWBWBWB\\nBWBBWWBV\\nWBWBWBWB\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'BBBBBWWW\\nWBBWBWWB\\nWWWWWBWW\\nBWBWWBWW\\nBBBWWBWW\\nBBBBBWBW\\nBWBWBBBW\\nWBWCWWWB\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'BBBWWWWW\\nWWWBBBBB\\nBBBWWWWW\\nWWWBBBBB\\nWBWBWBWB\\nWBWBWBBW\\nBWBBBWWW\\nBWBWBWBW\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'WBBBBBBB\\nBBBBBBBW\\nBBBWABBB\\nBBBBBBBW\\nWBBBBBBB\\nBBBBBBBW\\nBBBBBBBW\\nBBBBBBBW\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'BBBBBBBB\\nBBBBBBBB\\nBBBBBBBB\\nBBBABBBB\\nWVWXWWXW\\nWWWWWWWW\\nWWWWWWWW\\nWWWWWWWW\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'WBWBWBBW\\nWAWBWBWB\\nBWBVBWBW\\nWBWBWBWB\\nWBWBWBWB\\nWCWBWBWB\\nWBWBWBWB\\nBWWWBWBW\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'BWBBBBBW\\nBWBWAWBW\\nBVBWBWBW\\nWBWBWBWB\\nWBWBWBWB\\nBBBBBWBB\\nWBBWWBWB\\nBWBWBWBW\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'BWBWBWBW\\nBWBWBWBW\\nBWBWBWBW\\nWBWBWCWB\\nWBWBWBWB\\nBWBWBWBW\\nBWBWBWAW\\nVBBWWBWB\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'WCBWWBWB\\nWBWBWBBB\\nBWBWBWBW\\nBWBWBWBW\\nWBWAWBBW\\nWBWBBBBW\\nBWWWWBWB\\nBCBBBBBW\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'WVWWWWWW\\nBBBBBBBB\\nWWWWWWWW\\nBBBBBBBB\\nWWWWWWWW\\nBBBBBBBA\\nWWWWWWWW\\nBBBBCBBB\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'BBBBABBB\\nBBBBBBBB\\nCBBBBBBB\\nBBBBBBAB\\nBBBBBBBB\\nBBBBBBBB\\nBBBBBBBB\\nBBBBBBBB\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'WBWBWBWB\\nBWWBWWWX\\nXBWBWBWB\\nBWBWBWBW\\nVBWBWBWB\\nWWBBBBBW\\nWBWWBWWW\\nWWBBBBWW\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'WWWWBWWB\\nWBBWWBWB\\nBWBWBWBW\\nWWBWBBBB\\nBBWXBBBB\\nBBBWWBBW\\nWWBWWWWB\\nBWWBBBWW\\n', 'output': 'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77649","program":"```python\nflag=True\nfor i in range(8):\n k=input()\n if k!='BWBWBWBW' and k!='WBWBWBWB':\n flag=False\nif (flag):\n print (\"YES\")\nelse:\n print (\"NO\")\n\n```","inputs":"WBWBWBWB\nBWBWBWBW\nBWBWBWBW\nBWBWBWBW\nWBWBWBWB\nWBWBWBWB\nBWBWBWBW\nWBWBWBWB\n","output":"YES","actual_output":"YES\n","execution_success":true,"sample_index":12391},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"282_A. Bit++","prompt":"Solve the following coding problem using the programming language python:\n\nThe classic programming language of Bitland is Bit++. This language is so peculiar and complicated.\n\nThe language is that peculiar as it has exactly one variable, called x. Also, there are two operations:\n\n * Operation ++ increases the value of variable x by 1. \n * Operation -- decreases the value of variable x by 1. \n\n\n\nA statement in language Bit++ is a sequence, consisting of exactly one operation and one variable x. The statement is written without spaces, that is, it can only contain characters \"+\", \"-\", \"X\". Executing a statement means applying the operation it contains.\n\nA programme in Bit++ is a sequence of statements, each of them needs to be executed. Executing a programme means executing all the statements it contains.\n\nYou're given a programme in language Bit++. The initial value of x is 0. Execute the programme and find its final value (the value of the variable when this programme is executed).\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 150) \u2014 the number of statements in the programme.\n\nNext n lines contain a statement each. Each statement contains exactly one operation (++ or --) and exactly one variable x (denoted as letter \u00abX\u00bb). Thus, there are no empty statements. The operation and the variable can be written in any order.\n\nOutput\n\nPrint a single integer \u2014 the final value of x.\n\nExamples\n\nInput\n\n1\n++X\n\n\nOutput\n\n1\n\n\nInput\n\n2\nX++\n--X\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\ncounter= 0\nfor i in range(n):\n\tif input().find('+') > -1:\n\t\tcounter = counter + 1\n\telse:\n\t\tcounter = counter - 1\nprint(counter)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n++X\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\nX++\\n--X\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '28\\nX--\\n++X\\nX++\\nX++\\nX++\\n--X\\n--X\\nX++\\nX--\\n++X\\nX++\\n--X\\nX--\\nX++\\nX--\\n++X\\n++X\\nX++\\nX++\\nX++\\nX++\\n--X\\n++X\\n--X\\n--X\\n--X\\n--X\\nX++\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n--X\\n--X\\n', 'output': '-2\\n'}, {'type': 'stdin_stdout', 'input': '45\\n--X\\n++X\\nX--\\n++X\\n++X\\nX++\\n--X\\n--X\\n--X\\n--X\\n--X\\n--X\\n--X\\nX++\\n++X\\nX--\\n++X\\n++X\\nX--\\nX++\\nX--\\n--X\\nX--\\n++X\\n++X\\n--X\\n--X\\nX--\\nX--\\n--X\\n++X\\nX--\\n--X\\n++X\\n++X\\n--X\\n--X\\nX--\\n++X\\n++X\\nX++\\nX++\\n++X\\n++X\\nX++\\n', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '87\\n--X\\n++X\\n--X\\nX++\\n--X\\nX--\\n--X\\n++X\\nX--\\n++X\\n--X\\n--X\\nX++\\n--X\\nX--\\nX++\\n++X\\n--X\\n++X\\n++X\\n--X\\n++X\\n--X\\nX--\\n++X\\n++X\\nX--\\nX++\\nX++\\n--X\\n--X\\n++X\\nX--\\n--X\\n++X\\n--X\\nX++\\n--X\\n--X\\nX--\\n++X\\n++X\\n--X\\nX--\\nX--\\nX--\\nX--\\nX--\\nX++\\n--X\\n++X\\n--X\\nX++\\n++X\\nX++\\n++X\\n--X\\nX++\\n++X\\nX--\\n--X\\nX++\\n++X\\nX++\\nX++\\n--X\\n--X\\n++X\\n--X\\nX++\\nX++\\n++X\\nX++\\nX++\\nX++\\nX++\\n--X\\n--X\\n--X\\n--X\\n--X\\n--X\\n--X\\nX--\\n--X\\n++X\\n++X\\n', 'output': '-5\\n'}, {'type': 'stdin_stdout', 'input': '101\\nX++\\nX++\\nX++\\n++X\\n--X\\nX--\\nX++\\nX--\\nX--\\n--X\\n--X\\n++X\\nX++\\n++X\\n++X\\nX--\\n--X\\n++X\\nX++\\nX--\\n++X\\n--X\\n--X\\n--X\\n++X\\n--X\\n++X\\nX++\\nX++\\n++X\\n--X\\nX++\\nX--\\nX++\\n++X\\n++X\\nX--\\nX--\\nX--\\nX++\\nX++\\nX--\\nX--\\nX++\\n++X\\n++X\\n++X\\n--X\\n--X\\n++X\\nX--\\nX--\\n--X\\n++X\\nX--\\n++X\\nX++\\n++X\\nX--\\nX--\\n--X\\n++X\\n--X\\n++X\\n++X\\n--X\\nX++\\n++X\\nX--\\n++X\\nX--\\n++X\\nX++\\nX--\\n++X\\nX++\\n--X\\nX++\\nX++\\n++X\\n--X\\n++X\\n--X\\nX++\\n--X\\nX--\\n--X\\n++X\\n++X\\n++X\\n--X\\nX--\\nX--\\nX--\\nX--\\n--X\\n--X\\n--X\\n++X\\n--X\\n--X\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n++X\\n++X\\n++X\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '77\\n++X\\nX++\\n--X\\nX--\\n--X\\n--X\\nX--\\nX++\\nX--\\nX++\\nX--\\n++X\\n--X\\n--X\\n--X\\n--X\\n++X\\nX--\\nX++\\nX--\\n--X\\nX--\\n--X\\nX--\\n++X\\n--X\\n++X\\n++X\\nX++\\nX++\\nX--\\n--X\\nX--\\nX--\\nX++\\n--X\\n--X\\n++X\\nX--\\nX--\\n++X\\nX++\\nX--\\n++X\\n--X\\nX++\\nX--\\n++X\\n++X\\n++X\\nX--\\nX--\\nX--\\n--X\\n++X\\n++X\\n++X\\nX++\\n--X\\n--X\\n++X\\n--X\\nX--\\nX++\\n++X\\nX++\\n++X\\nX--\\nX++\\nX++\\n--X\\nX++\\nX++\\nX++\\n--X\\nX++\\nX--\\n', 'output': '-5\\n'}, {'type': 'stdin_stdout', 'input': '56\\n--X\\nX--\\n--X\\n--X\\nX--\\nX--\\n--X\\nX++\\n++X\\n--X\\nX++\\nX--\\n--X\\n++X\\n--X\\nX--\\nX--\\n++X\\nX--\\nX--\\n--X\\n++X\\n--X\\n++X\\n--X\\nX++\\n++X\\nX++\\n--X\\n++X\\nX++\\nX++\\n--X\\nX++\\nX--\\n--X\\nX--\\n--X\\nX++\\n++X\\n--X\\n++X\\nX++\\nX--\\n--X\\n--X\\n++X\\nX--\\nX--\\n--X\\nX--\\n--X\\nX++\\n--X\\n++X\\n--X\\n', 'output': '-14\\n'}, {'type': 'stdin_stdout', 'input': '21\\nX--\\n++X\\n--X\\nX--\\n++X\\nX--\\n++X\\nX--\\n--X\\n++X\\nX++\\n++X\\nX++\\n++X\\nX--\\n--X\\nX++\\nX++\\nX--\\n++X\\nX--\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\nX--\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '100\\n--X\\n++X\\nX++\\n++X\\nX--\\n++X\\nX--\\nX++\\n--X\\nX++\\nX--\\nX--\\nX--\\n++X\\nX--\\nX++\\nX++\\n++X\\nX++\\nX++\\nX++\\nX++\\n++X\\nX++\\n++X\\nX--\\n--X\\n++X\\nX--\\n--X\\n++X\\n++X\\nX--\\nX++\\nX++\\nX++\\n++X\\n--X\\n++X\\nX++\\nX--\\n++X\\n++X\\n--X\\n++X\\nX--\\nX--\\nX--\\nX++\\nX--\\nX--\\nX++\\nX++\\n--X\\nX++\\nX++\\n--X\\nX--\\n--X\\n++X\\n--X\\n++X\\n++X\\nX--\\n--X\\n++X\\n++X\\n--X\\n--X\\n++X\\nX++\\nX--\\nX++\\nX--\\nX++\\nX++\\n--X\\nX--\\nX--\\n++X\\nX--\\n--X\\n--X\\nX++\\n--X\\n--X\\nX--\\nX--\\n++X\\n++X\\nX--\\n++X\\nX++\\n--X\\n++X\\n++X\\nX++\\n--X\\n--X\\nX++\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': 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{'type': 'stdin_stdout', 'input': '5\\nX++\\nX--\\n++X\\n--X\\n--X\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '45\\n--X\\n++X\\nX--\\n++X\\n++X\\nX++\\n--X\\n--X\\n--X\\n--X\\n--X\\nX--\\n--X\\nX++\\n++X\\nX--\\n++X\\n++X\\nX--\\nX++\\nX--\\n--X\\n--X\\n++X\\n++X\\nX--\\n--X\\nX--\\nX--\\n--X\\n++X\\nX--\\n--X\\n++X\\n++X\\n--X\\n--X\\nX--\\n++X\\n++X\\nX++\\nX++\\n++X\\n++X\\nX++\\n', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '63\\n--X\\nX--\\n++X\\n--X\\n++X\\nX++\\n--X\\n--X\\n++X\\n--X\\n--X\\nX++\\nX--\\nX--\\n--X\\nX++\\nX--\\nX--\\nX++\\n++X\\nX++\\nX++\\n--X\\n--X\\nX++\\nX--\\nX--\\nX--\\n++X\\nX++\\nX--\\n--X\\nX--\\n++X\\n++X\\nX++\\n++X\\nX++\\nX++\\n--X\\nX--\\n++X\\nX--\\n--X\\nX--\\nX--\\nX--\\n++X\\n++X\\n++X\\n++X\\nX++\\nX++\\n++X\\n--X\\n--X\\n++X\\n++X\\n++X\\nX--\\n++X\\n++X\\nX--\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '28\\nX--\\n++X\\nX++\\nX++\\nX++\\n--X\\n--X\\nX++\\nX--\\n++X\\nX++\\n--X\\nX--\\nX++\\nX--\\n++X\\nX++\\nX++\\nX++\\n++X\\nX++\\n--X\\n++X\\n--X\\nX--\\n--X\\n--X\\nX++\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '45\\n--X\\n++X\\nX--\\n++X\\n++X\\nX++\\nX--\\n--X\\n--X\\n--X\\n--X\\nX--\\n--X\\nX++\\n++X\\nX--\\nX++\\n++X\\nX--\\nX++\\nX--\\n--X\\n--X\\n++X\\n++X\\n--X\\n--X\\nX--\\nX--\\n--X\\n++X\\nX--\\nX--\\n++X\\n++X\\nX--\\n--X\\nX--\\n++X\\n++X\\nX++\\nX++\\n++X\\n++X\\nX++\\n', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '100\\n--X\\n++X\\nX++\\n++X\\nX--\\n++X\\nX--\\nX++\\n--X\\nX++\\nX--\\nX--\\nX--\\n++X\\nX--\\nX++\\nX++\\n++X\\nX++\\n++X\\nX++\\nX++\\n++X\\nX++\\n++X\\nX--\\nX--\\n++X\\nX--\\n--X\\n++X\\n++X\\nX--\\nX++\\nX++\\nX++\\n++X\\n--X\\n++X\\nX++\\nX--\\n++X\\n++X\\n--X\\n++X\\nX--\\nX--\\nX--\\n++X\\nX--\\nX--\\nX++\\nX++\\n--X\\nX++\\nX++\\n--X\\nX--\\n--X\\n++X\\n--X\\n++X\\n++X\\nX--\\n--X\\n++X\\n++X\\n--X\\n--X\\n++X\\nX++\\nX--\\nX++\\nX--\\nX++\\nX++\\n--X\\nX--\\nX--\\nX++\\nX--\\n--X\\n--X\\nX++\\n--X\\n--X\\nX--\\nX--\\n++X\\n++X\\nX--\\n++X\\nX++\\n--X\\n++X\\n++X\\nX++\\n--X\\n--X\\nX++\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '94\\nX++\\nX++\\n++X\\n++X\\nX--\\n--X\\nX++\\n--X\\nX++\\n++X\\nX++\\n++X\\n--X\\n--X\\n++X\\nX++\\n--X\\nX--\\nX--\\n--X\\nX--\\nX--\\n--X\\n++X\\n--X\\nX--\\nX--\\nX++\\n++X\\n--X\\nX--\\n++X\\n--X\\nX--\\nX--\\nX--\\nX++\\nX++\\nX--\\nX++\\nX--\\nX--\\nX--\\n--X\\n--X\\nX--\\nX--\\nX++\\n++X\\nX--\\n++X\\nX++\\n--X\\n--X\\n--X\\n--X\\n++X\\nX--\\n--X\\n--X\\n++X\\nX--\\nX--\\nX++\\n++X\\nX++\\n++X\\n--X\\n--X\\nX--\\n++X\\nX--\\nX--\\n++X\\n++X\\n++X\\n++X\\nX++\\n++X\\n--X\\nX++\\n--X\\n--X\\n++X\\n--X\\nX++\\n++X\\n++X\\n--X\\nX--\\nX--\\nX--\\n++X\\nX++\\n', 'output': '-10\\n'}, {'type': 'stdin_stdout', 'input': '56\\n--X\\nX--\\n--X\\n--X\\nX--\\nX--\\n--X\\nX++\\n++X\\n--X\\nX++\\nX--\\n--X\\nX++\\n--X\\nX--\\nX--\\n++X\\nX--\\nX--\\n--X\\n++X\\n--X\\n++X\\n--X\\nX++\\n++X\\nX++\\n--X\\n++X\\nX++\\nX++\\n--X\\nX++\\nX--\\n--X\\nX--\\n--X\\nX++\\n++X\\n--X\\n++X\\nX++\\nX--\\n--X\\nX--\\n++X\\nX--\\nX--\\nX--\\nX--\\n--X\\nX++\\n--X\\n++X\\n--X\\n', 'output': '-14\\n'}, {'type': 'stdin_stdout', 'input': '63\\n--X\\nX--\\n++X\\n--X\\n++X\\nX++\\n--X\\n--X\\n++X\\n--X\\n--X\\nX++\\nX--\\nX--\\n--X\\nX++\\nX--\\nX--\\nX++\\n++X\\nX++\\nX++\\n--X\\n--X\\n++X\\nX--\\nX--\\nX--\\n++X\\nX++\\nX--\\n--X\\nX--\\n++X\\n++X\\nX++\\n++X\\nX++\\nX++\\n--X\\nX--\\n++X\\nX--\\n--X\\nX--\\nX--\\nX--\\n++X\\n++X\\n++X\\n++X\\nX++\\nX++\\n++X\\n--X\\n--X\\n++X\\n++X\\n++X\\nX--\\n++X\\n++X\\nX--\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '28\\nX--\\n++X\\nX++\\nX++\\nX++\\nX--\\n--X\\nX++\\nX--\\n++X\\nX++\\n--X\\nX--\\nX++\\nX--\\n++X\\nX++\\nX++\\nX++\\n++X\\nX++\\n--X\\n++X\\n--X\\nX--\\n--X\\n--X\\nX++\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '45\\n--X\\n++X\\nX--\\n++X\\n++X\\nX++\\nX--\\n--X\\n--X\\n--X\\n--X\\nX--\\n--X\\nX++\\n++X\\nX--\\nX++\\n++X\\nX--\\nX++\\nX--\\n--X\\n--X\\n++X\\n++X\\n--X\\n--X\\nX--\\nX--\\n--X\\n++X\\nX--\\nX--\\n++X\\n++X\\nX--\\n--X\\n--X\\n++X\\n++X\\nX++\\nX++\\n++X\\n++X\\nX++\\n', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '63\\n--X\\nX--\\n++X\\n--X\\n++X\\nX++\\n--X\\n--X\\n++X\\n--X\\n--X\\nX++\\nX--\\nX--\\n--X\\nX++\\nX--\\nX--\\nX++\\n++X\\nX++\\nX++\\n--X\\n--X\\n++X\\nX--\\nX--\\nX--\\n++X\\nX++\\n--X\\n--X\\nX--\\n++X\\n++X\\nX++\\n++X\\nX++\\nX++\\n--X\\nX--\\n++X\\nX--\\n--X\\nX--\\nX--\\nX--\\n++X\\n++X\\n++X\\n++X\\nX++\\nX++\\n++X\\n--X\\n--X\\n++X\\n++X\\n++X\\nX--\\n++X\\n++X\\nX--\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '45\\n--X\\n++X\\nX--\\n++X\\n++X\\nX++\\n--X\\n--X\\n--X\\n--X\\n--X\\n--X\\n--X\\nX++\\n++X\\nX--\\n++X\\n++X\\nX--\\nX++\\nX--\\n--X\\nX--\\n++X\\n++X\\n--X\\n--X\\nX--\\n--X\\n--X\\n++X\\nX--\\n--X\\n++X\\n++X\\n--X\\n--X\\nX--\\n++X\\n++X\\nX++\\nX++\\n++X\\n++X\\nX++\\n', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '87\\n--X\\n++X\\n--X\\n++X\\n--X\\nX--\\n--X\\n++X\\nX--\\n++X\\n--X\\n--X\\nX++\\n--X\\nX--\\nX++\\n++X\\n--X\\n++X\\n++X\\n--X\\n++X\\n--X\\nX--\\n++X\\n++X\\nX--\\nX++\\nX++\\n--X\\n--X\\n++X\\nX--\\n--X\\n++X\\n--X\\nX++\\n--X\\n--X\\nX--\\n++X\\n++X\\n--X\\nX--\\nX--\\nX--\\nX--\\nX--\\nX++\\n--X\\n++X\\n--X\\nX++\\n++X\\nX++\\n++X\\n--X\\nX++\\n++X\\nX--\\n--X\\nX++\\n++X\\nX++\\nX++\\n--X\\n--X\\n++X\\n--X\\nX++\\nX++\\n++X\\nX++\\nX++\\nX++\\nX++\\n--X\\n--X\\n--X\\n--X\\n--X\\n--X\\n--X\\nX--\\n--X\\n++X\\n++X\\n', 'output': '-5\\n'}, {'type': 'stdin_stdout', 'input': '101\\nX++\\nX++\\nX++\\n++X\\n--X\\nX--\\nX++\\nX--\\nX--\\n--X\\n--X\\n++X\\nX++\\n++X\\n++X\\nX--\\n--X\\n++X\\nX++\\nX--\\n++X\\n--X\\n--X\\n--X\\n++X\\n--X\\n++X\\nX++\\nX++\\n++X\\n--X\\nX++\\nX--\\nX++\\n++X\\n++X\\nX--\\nX--\\nX--\\nX++\\nX++\\nX--\\nX--\\nX++\\n++X\\n++X\\n++X\\n--X\\n--X\\n++X\\nX--\\nX--\\n--X\\n++X\\nX--\\n++X\\nX++\\n++X\\nX--\\nX--\\n--X\\n++X\\n--X\\n++X\\n++X\\n--X\\nX++\\n++X\\nX--\\n++X\\nX--\\n++X\\nX++\\nX--\\n++X\\nX++\\n--X\\nX++\\nX++\\n++X\\n--X\\n++X\\n--X\\nX++\\n--X\\nX--\\n--X\\n++X\\n++X\\n++X\\nX--\\nX--\\nX--\\nX--\\nX--\\n--X\\n--X\\n--X\\n++X\\n--X\\n--X\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '56\\n--X\\nX--\\n--X\\n--X\\nX--\\nX--\\n--X\\nX++\\n++X\\n--X\\nX++\\nX--\\n--X\\n++X\\n--X\\nX--\\nX--\\n++X\\nX--\\nX--\\n--X\\nX++\\n--X\\n++X\\n--X\\nX++\\n++X\\nX++\\n--X\\n++X\\nX++\\nX++\\n--X\\nX++\\nX--\\n--X\\nX--\\n--X\\nX++\\n++X\\n--X\\n++X\\nX++\\nX--\\n--X\\n--X\\n++X\\nX--\\nX--\\n--X\\nX--\\n--X\\nX++\\n--X\\n++X\\n--X\\n', 'output': '-14\\n'}, {'type': 'stdin_stdout', 'input': '21\\nX--\\n++X\\n--X\\nX--\\n++X\\nX--\\n++X\\nX--\\n--X\\n++X\\nX++\\n++X\\nX++\\nX++\\nX--\\n--X\\nX++\\nX++\\nX--\\n++X\\nX--\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100\\n--X\\n++X\\nX++\\n++X\\nX--\\n++X\\nX--\\nX++\\n--X\\nX++\\nX--\\nX--\\nX--\\n++X\\nX--\\nX++\\nX++\\n++X\\nX++\\nX++\\nX++\\nX++\\n++X\\nX++\\n++X\\nX--\\n--X\\n++X\\nX--\\n--X\\n++X\\n++X\\nX--\\nX++\\nX++\\nX++\\n++X\\n--X\\n++X\\nX++\\nX--\\nX++\\n++X\\n--X\\n++X\\nX--\\nX--\\nX--\\nX++\\nX--\\nX--\\nX++\\nX++\\n--X\\nX++\\nX++\\n--X\\nX--\\n--X\\n++X\\n--X\\n++X\\n++X\\nX--\\n--X\\n++X\\n++X\\n--X\\n--X\\n++X\\nX++\\nX--\\nX++\\nX--\\nX++\\nX++\\n--X\\nX--\\nX--\\n++X\\nX--\\n--X\\n--X\\nX++\\n--X\\n--X\\nX--\\nX--\\n++X\\n++X\\nX--\\n++X\\nX++\\n--X\\n++X\\n++X\\nX++\\n--X\\n--X\\nX++\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '59\\nX--\\n--X\\nX++\\n++X\\nX--\\n--X\\n--X\\n++X\\n++X\\n++X\\n++X\\nX++\\n++X\\n++X\\nX++\\n--X\\nX--\\nX++\\n++X\\n--X\\nX++\\n--X\\n++X\\nX++\\n--X\\n--X\\nX++\\nX++\\n--X\\nX++\\nX++\\nX++\\nX--\\nX--\\n--X\\nX++\\nX--\\nX--\\n++X\\nX--\\nX++\\n--X\\nX++\\nX--\\nX--\\nX--\\nX--\\nX++\\n--X\\nX++\\nX++\\nX--\\nX++\\n++X\\nX--\\nX++\\nX--\\nX--\\n++X\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n++X\\nX--\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '28\\nX--\\nX++\\nX++\\nX++\\nX++\\n--X\\n--X\\nX++\\nX--\\n++X\\nX++\\n--X\\nX--\\nX++\\n--X\\n++X\\n++X\\nX++\\nX++\\nX++\\nX++\\n--X\\n++X\\n--X\\n--X\\n--X\\n--X\\nX++\\n', 'output': '4\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77653","program":"```python\nn = int(input())\ncounter= 0\nfor i in range(n):\n\tif input().find('+') > -1:\n\t\tcounter = counter + 1\n\telse:\n\t\tcounter = counter - 1\nprint(counter)\n```","inputs":"1\n++X\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12392},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"331_A1. Oh Sweet Beaverette","prompt":"Solve the following coding problem using the programming language python:\n\n\u2014 Oh my sweet Beaverette, would you fancy a walk along a wonderful woodland belt with me? \n\n\u2014 Of course, my Smart Beaver! Let us enjoy the splendid view together. How about Friday night? \n\nAt this point the Smart Beaver got rushing. Everything should be perfect by Friday, so he needed to prepare the belt to the upcoming walk. He needed to cut down several trees.\n\nLet's consider the woodland belt as a sequence of trees. Each tree i is described by the esthetic appeal ai \u2014 some trees are very esthetically pleasing, others are 'so-so', and some trees are positively ugly!\n\nThe Smart Beaver calculated that he needed the following effects to win the Beaverette's heart: \n\n * The first objective is to please the Beaverette: the sum of esthetic appeal of the remaining trees must be maximum possible; \n * the second objective is to surprise the Beaverette: the esthetic appeal of the first and the last trees in the resulting belt must be the same; \n * and of course, the walk should be successful: there must be at least two trees in the woodland belt left. \n\n\n\nNow help the Smart Beaver! Which trees does he need to cut down to win the Beaverette's heart?\n\nInput\n\nThe first line contains a single integer n \u2014 the initial number of trees in the woodland belt, 2 \u2264 n. The second line contains space-separated integers ai \u2014 the esthetic appeals of each tree. All esthetic appeals do not exceed 109 in their absolute value.\n\n * to get 30 points, you need to solve the problem with constraints: n \u2264 100 (subproblem A1); \n * to get 100 points, you need to solve the problem with constraints: n \u2264 3\u00b7105 (subproblems A1+A2). \n\nOutput\n\nIn the first line print two integers \u2014 the total esthetic appeal of the woodland belt after the Smart Beaver's intervention and the number of the cut down trees k.\n\nIn the next line print k integers \u2014 the numbers of the trees the Beaver needs to cut down. Assume that the trees are numbered from 1 to n from left to right.\n\nIf there are multiple solutions, print any of them. It is guaranteed that at least two trees have equal esthetic appeal.\n\nExamples\n\nInput\n\n5\n1 2 3 1 2\n\n\nOutput\n\n8 1\n1 \n\nInput\n\n5\n1 -2 3 1 -2\n\n\nOutput\n\n5 2\n2 5 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import defaultdict\nn = int(input())\na = list(map(int,input().split()))\nsame = defaultdict(list)\nonly_positive = [max(0,x) for x in a]\npartial_sum = [0 for i in range(n+1)]\nfor i in range(1,n+1):\n partial_sum[i] = partial_sum[i-1]+only_positive[i-1]\nfor i in range(n):\n same[a[i]].append(i)\nbest = -10**18\nbl, br = -1, -1\nfor key in same:\n if len(same[key]) >= 2:\n l, r = same[key][0], same[key][-1]\n cur = key*2 + partial_sum[r]-partial_sum[l+1]\n if cur > best:\n best = cur\n bl, br = l, r\ncut = []\nfor i in range(n):\n if not (a[i] >= 0 and bl <= i and i <= br):\n if i != bl and i != br:\n cut.append(i+1)\nprint(best,len(cut))\nprint(*cut)\n\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 2 3 1 2\\n', 'output': '8 1\\n1 '}, {'type': 'stdin_stdout', 'input': '5\\n1 -2 3 1 -2\\n', 'output': '5 2\\n2 5 '}, {'type': 'stdin_stdout', 'input': '4\\n-1 1 -1 1\\n', 'output': '2 2\\n1 3 '}, {'type': 'stdin_stdout', 'input': '3\\n1 1 1\\n', 'output': '3 0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1000000000 -1000000000\\n', 'output': '-2000000000 0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1000000000 1000000000 1000000000\\n', 'output': '3000000000 0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 0\\n', 'output': '0 1\\n2 '}, {'type': 'stdin_stdout', 'input': '6\\n-1 3 3 5 5 -1\\n', 'output': '14 0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 0\\n', 'output': '0 0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 1 1 -1\\n', 'output': '2 2\\n1 4 '}, {'type': 'stdin_stdout', 'input': '20\\n-808998072 733614990 579897311 -337992089 579897311 120800519 -337992089 -803027570 733614990 -686536765 733614990 -803027570 -803027570 733614990 120800519 -803027570 -686536765 579897311 -808998072 -686536765\\n', 'output': '4215055101 13\\n1 4 7 8 10 12 13 15 16 17 18 19 20 '}, {'type': 'stdin_stdout', 'input': '2\\n-1 -1\\n', 'output': '-2 0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1000000000 -1000000000 -1000000000\\n', 'output': '-2000000000 1\\n2 '}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 -1\\n', 'output': '-2 0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-589330597 -126288833 -126288833 -834860352 -834860352 -834860352 -834860352 -21170405 -834860352 -834860352\\n', 'output': '-252577666 8\\n1 4 5 6 7 8 9 10 '}, {'type': 'stdin_stdout', 'input': '4\\n-1 1 -1 0\\n', 'output': '-1 1\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 1\\n', 'output': '4 0\\n\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0000000000 1000000000 1000000000\\n', 'output': '2000000000 1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n-1 3 3 5 6 -1\\n', 'output': '15 0\\n\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 1 1 -2\\n', 'output': '2 2\\n1 4\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-808998072 733614990 579897311 -337992089 579897311 188021958 -337992089 -803027570 733614990 -686536765 733614990 -803027570 -803027570 733614990 120800519 -803027570 -686536765 579897311 -808998072 -686536765\\n', 'output': '4282276540 13\\n1 4 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-514980621 -1000000000 -1000000000\\n', 'output': '-2000000000 1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 -1 -1\\n', 'output': '-2 1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-589330597 -126288833 -126288833 -834860352 -834860352 -834860352 -534114836 -21170405 -834860352 -834860352\\n', 'output': '-252577666 8\\n1 4 5 6 7 8 9 10\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 1 1 2\\n', 'output': '6 1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 -2 0 1 -2\\n', 'output': '2 2\\n2 5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n', 'output': '5 0\\n\\n'}, {'type': 'stdin_stdout', 'input': '6\\n-1 1 3 5 6 -1\\n', 'output': '13 0\\n\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 -1\\n', 'output': '-2 1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 1 1 2\\n', 'output': '8 0\\n\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 -2 0 1 -2\\n', 'output': '-3 1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n-1 1 3 5 9 -1\\n', 'output': '16 0\\n\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 0 1 2\\n', 'output': '7 0\\n\\n'}, {'type': 'stdin_stdout', 'input': '6\\n-1 2 3 5 9 -1\\n', 'output': '17 0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-398816005 -171989355 -126288833 -834860352 -834860352 -834860352 -534114836 -12858129 -834860352 -834860352\\n', 'output': '-1669720704 8\\n1 2 3 5 6 7 8 9\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 -1 1 2\\n', 'output': '7 1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n-1 2 3 5 1 -1\\n', 'output': '9 0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-398816005 -171989355 -126288833 -834860352 -834860352 -834860352 -534114836 -12858129 -834860352 -1244454938\\n', 'output': '-1669720704 8\\n1 2 3 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-752915012 733614990 579897311 -337992089 731950633 188021958 -794539697 -803027570 733614990 -686536765 733614990 -803027570 -803027570 733614990 120800519 -1309420298 -686536765 579897311 -808998072 -686536765\\n', 'output': '4434329862 13\\n1 4 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 2 -2 1 2\\n', 'output': '5 2\\n1 3\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-752915012 1362050108 579897311 -337992089 731950633 188021958 -794539697 -803027570 733614990 -686536765 733614990 -778182255 -803027570 733614990 120800519 -1309420298 -1298858419 579897311 -808998072 -686536765\\n', 'output': '4401412702 12\\n1 2 4 7 8 10 12 13 16 17 19 20\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-752915012 678909940 171502462 -337992089 731950633 188021958 -794539697 -803027570 733614990 -686536765 733614990 -778182255 -803027570 733614990 120800519 -1309420298 -1298858419 579897311 -808998072 -686536765\\n', 'output': '2200844970 17\\n1 2 3 4 5 6 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-1396591240 678909940 171502462 -337992089 731950633 359848987 -794539697 -406471981 733614990 -686536765 837611790 -778182255 -803027570 733614990 120800519 -1309420298 -1298858419 579897311 -808998072 -686536765\\n', 'output': '2304841770 17\\n1 2 3 4 5 6 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 2\\n', 'output': '2 1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1000000000 1000100000 1000000000\\n', 'output': '3000100000 0\\n\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0000000100 1000000000 1000000000\\n', 'output': '2000000000 1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-752915012 733614990 579897311 -337992089 579897311 188021958 -337992089 -803027570 733614990 -686536765 733614990 -803027570 -803027570 733614990 120800519 -803027570 -686536765 579897311 -808998072 -686536765\\n', 'output': '4282276540 13\\n1 4 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-769642967 -1000000000 -1000000000\\n', 'output': '-2000000000 1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-589330597 -126288833 -126288833 -834860352 -834860352 -834860352 -534114836 -12858129 -834860352 -834860352\\n', 'output': '-252577666 8\\n1 4 5 6 7 8 9 10\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-752915012 733614990 579897311 -337992089 579897311 188021958 -337992089 -803027570 733614990 -686536765 733614990 -803027570 -803027570 733614990 120800519 -1309420298 -686536765 579897311 -808998072 -686536765\\n', 'output': '4282276540 13\\n1 4 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-398816005 -126288833 -126288833 -834860352 -834860352 -834860352 -534114836 -12858129 -834860352 -834860352\\n', 'output': '-252577666 8\\n1 4 5 6 7 8 9 10\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-752915012 733614990 579897311 -337992089 579897311 188021958 -416778599 -803027570 733614990 -686536765 733614990 -803027570 -803027570 733614990 120800519 -1309420298 -686536765 579897311 -808998072 -686536765\\n', 'output': '4282276540 13\\n1 4 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-752915012 733614990 579897311 -337992089 579897311 188021958 -794539697 -803027570 733614990 -686536765 733614990 -803027570 -803027570 733614990 120800519 -1309420298 -686536765 579897311 -808998072 -686536765\\n', 'output': '4282276540 13\\n1 4 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 -2 1 2\\n', 'output': '7 1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-398816005 -171989355 -126288833 -834860352 -1617579493 -834860352 -534114836 -12858129 -834860352 -1244454938\\n', 'output': '-1669720704 8\\n1 2 3 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-752915012 733614990 579897311 -337992089 731950633 188021958 -794539697 -803027570 733614990 -686536765 733614990 -778182255 -803027570 733614990 120800519 -1309420298 -686536765 579897311 -808998072 -686536765\\n', 'output': '4434329862 13\\n1 4 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-398816005 -213092711 -126288833 -834860352 -1617579493 -834860352 -534114836 -12858129 -834860352 -1244454938\\n', 'output': '-1669720704 8\\n1 2 3 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-752915012 733614990 579897311 -337992089 731950633 188021958 -794539697 -803027570 733614990 -686536765 733614990 -778182255 -803027570 733614990 120800519 -1309420298 -1298858419 579897311 -808998072 -686536765\\n', 'output': '4434329862 13\\n1 4 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-398816005 -213092711 -126288833 -834860352 -1617579493 -834860352 -534114836 -21293766 -834860352 -1244454938\\n', 'output': '-1669720704 8\\n1 2 3 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-731409820 -213092711 -126288833 -834860352 -1617579493 -834860352 -534114836 -21293766 -834860352 -1244454938\\n', 'output': '-1669720704 8\\n1 2 3 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-752915012 678909940 579897311 -337992089 731950633 188021958 -794539697 -803027570 733614990 -686536765 733614990 -778182255 -803027570 733614990 120800519 -1309420298 -1298858419 579897311 -808998072 -686536765\\n', 'output': '4401412702 12\\n1 2 4 7 8 10 12 13 16 17 19 20\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-731409820 -213092711 -126288833 -834860352 -1617579493 -834860352 -534114836 -21293766 -834860352 -2020319241\\n', 'output': '-1669720704 8\\n1 2 3 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-731409820 -213092711 -126288833 -834860352 -1617579493 -834860352 -534114836 -21293766 -834860352 -968519492\\n', 'output': '-1669720704 8\\n1 2 3 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-1396591240 678909940 171502462 -337992089 731950633 188021958 -794539697 -803027570 733614990 -686536765 733614990 -778182255 -803027570 733614990 120800519 -1309420298 -1298858419 579897311 -808998072 -686536765\\n', 'output': '2200844970 17\\n1 2 3 4 5 6 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-731409820 -397823802 -126288833 -834860352 -1617579493 -834860352 -534114836 -21293766 -834860352 -968519492\\n', 'output': '-1669720704 8\\n1 2 3 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-1396591240 678909940 171502462 -337992089 731950633 188021958 -794539697 -406471981 733614990 -686536765 733614990 -778182255 -803027570 733614990 120800519 -1309420298 -1298858419 579897311 -808998072 -686536765\\n', 'output': '2200844970 17\\n1 2 3 4 5 6 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-731409820 -397823802 -126288833 -834860352 -1617579493 -74942494 -534114836 -21293766 -834860352 -968519492\\n', 'output': '-1669720704 8\\n1 2 3 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-1396591240 678909940 171502462 -337992089 731950633 359848987 -794539697 -406471981 733614990 -686536765 733614990 -778182255 -803027570 733614990 120800519 -1309420298 -1298858419 579897311 -808998072 -686536765\\n', 'output': '2200844970 17\\n1 2 3 4 5 6 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-1396591240 678909940 171502462 -337992089 731950633 359848987 -794539697 -406471981 733614990 -686536765 837611790 -778182255 -803027570 733614990 120800519 -1309420298 -441945125 579897311 -808998072 -686536765\\n', 'output': '2304841770 17\\n1 2 3 4 5 6 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '20\\n-1396591240 678909940 171502462 -337992089 731950633 359848987 -794539697 -406471981 733614990 -1314489056 837611790 -778182255 -803027570 733614990 120800519 -1309420298 -441945125 579897311 -808998072 -686536765\\n', 'output': '2304841770 17\\n1 2 3 4 5 6 7 8 10 12 13 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 1 -1 2\\n', 'output': '-1 1\\n4\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77661","program":"```python\nfrom collections import defaultdict\nn = int(input())\na = list(map(int,input().split()))\nsame = defaultdict(list)\nonly_positive = [max(0,x) for x in a]\npartial_sum = [0 for i in range(n+1)]\nfor i in range(1,n+1):\n partial_sum[i] = partial_sum[i-1]+only_positive[i-1]\nfor i in range(n):\n same[a[i]].append(i)\nbest = -10**18\nbl, br = -1, -1\nfor key in same:\n if len(same[key]) >= 2:\n l, r = same[key][0], same[key][-1]\n cur = key*2 + partial_sum[r]-partial_sum[l+1]\n if cur > best:\n best = cur\n bl, br = l, r\ncut = []\nfor i in range(n):\n if not (a[i] >= 0 and bl <= i and i <= br):\n if i != bl and i != br:\n cut.append(i+1)\nprint(best,len(cut))\nprint(*cut)\n\n\n\n\n```","inputs":"5\n1 2 3 1 2\n","output":"8 1\n1 ","actual_output":"8 1\n1\n","execution_success":true,"sample_index":12393},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"352_D. Jeff and Furik","prompt":"Solve the following coding problem using the programming language python:\n\nJeff has become friends with Furik. Now these two are going to play one quite amusing game.\n\nAt the beginning of the game Jeff takes a piece of paper and writes down a permutation consisting of n numbers: p1, p2, ..., pn. Then the guys take turns to make moves, Jeff moves first. During his move, Jeff chooses two adjacent permutation elements and then the boy swaps them. During his move, Furic tosses a coin and if the coin shows \"heads\" he chooses a random pair of adjacent elements with indexes i and i + 1, for which an inequality pi > pi + 1 holds, and swaps them. But if the coin shows \"tails\", Furik chooses a random pair of adjacent elements with indexes i and i + 1, for which the inequality pi < pi + 1 holds, and swaps them. If the coin shows \"heads\" or \"tails\" and Furik has multiple ways of adjacent pairs to take, then he uniformly takes one of the pairs. If Furik doesn't have any pair to take, he tosses a coin one more time. The game ends when the permutation is sorted in the increasing order.\n\nJeff wants the game to finish as quickly as possible (that is, he wants both players to make as few moves as possible). Help Jeff find the minimum mathematical expectation of the number of moves in the game if he moves optimally well.\n\nYou can consider that the coin shows the heads (or tails) with the probability of 50 percent.\n\nInput\n\nThe first line contains integer n (1 \u2264 n \u2264 3000). The next line contains n distinct integers p1, p2, ..., pn (1 \u2264 pi \u2264 n) \u2014 the permutation p. The numbers are separated by spaces.\n\nOutput\n\nIn a single line print a single real value \u2014 the answer to the problem. The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.\n\nExamples\n\nInput\n\n2\n1 2\n\n\nOutput\n\n0.000000\n\n\nInput\n\n5\n3 5 2 4 1\n\n\nOutput\n\n13.000000\n\nNote\n\nIn the first test the sequence is already sorted, so the answer is 0.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\nA = [int(i) for i in input().split()]\n\ndef mergesort(l):\n\tl = list(l)\n\tif len(l) <= 1:\n\t\treturn l,0\n\tleft,linv = mergesort(l[:len(l) // 2])\n\tright,rinv = mergesort(l[len(l) // 2:])\n\tlefti = 0\n\trighti = 0\n\ti = 0\n\tnuminversions = 0\n\twhile True:\n\t\tif i >= len(l):\n\t\t\tbreak\n\t\tif lefti >= len(left):\n\t\t\tl[i] = right[righti]\n\t\t\trighti += 1\n\t\telif righti >= len(right):\n\t\t\tl[i] = left[lefti]\n\t\t\tlefti += 1\n\t\t\tnuminversions += len(right)\n\t\telif left[lefti] > right[righti]:\n\t\t\tl[i] = right[righti]\n\t\t\trighti += 1\n\t\telse:\n\t\t\tl[i] = left[lefti]\n\t\t\tlefti += 1\n\t\t\tnuminversions += righti\n\t\ti += 1\n\treturn (l,numinversions + linv + rinv)\n\t\nres = mergesort(A)\n\nn = res[1]\n\nif n % 2 == 0:\n\tprint(2*n)\nelse:\n\tprint(2*n-1)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n3 5 2 4 1\\n', 'output': '13'}, {'type': 'stdin_stdout', 'input': '2\\n1 2\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '9\\n4 1 8 6 7 5 2 9 3\\n', 'output': '33'}, {'type': 'stdin_stdout', 'input': '95\\n68 56 24 89 79 20 74 69 49 59 85 67 95 66 15 34 2 13 92 25 84 77 70 71 17 93 62 81 1 87 76 38 75 31 63 51 35 33 37 11 36 52 23 10 27 90 12 6 45 32 86 26 60 47 91 65 58 80 78 88 50 9 44 4 28 29 22 8 48 7 19 57 14 54 55 83 5 30 72 18 82 94 43 46 41 3 61 53 73 39 40 16 64 42 21\\n', 'output': '5076'}, {'type': 'stdin_stdout', 'input': '2\\n2 1\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '10\\n8 4 1 7 6 10 9 5 3 2\\n', 'output': '53'}, {'type': 'stdin_stdout', 'input': '10\\n3 4 1 5 7 9 8 10 6 2\\n', 'output': '29'}, {'type': 'stdin_stdout', 'input': '13\\n3 1 11 12 4 5 8 10 13 7 9 2 6\\n', 'output': '69'}, {'type': 'stdin_stdout', 'input': '16\\n6 15 3 8 7 11 9 10 2 13 4 14 1 16 5 12\\n', 'output': '108'}, {'type': 'stdin_stdout', 'input': '9\\n1 7 8 5 3 4 6 9 2\\n', 'output': '33'}, {'type': 'stdin_stdout', 'input': '5\\n2 3 4 5 1\\n', 'output': '8'}, {'type': 'stdin_stdout', 'input': '5\\n2 3 5 4 1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 5 1 4 2\\n', 'output': '12\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77665","program":"```python\nn = int(input())\nA = [int(i) for i in input().split()]\n\ndef mergesort(l):\n\tl = list(l)\n\tif len(l) <= 1:\n\t\treturn l,0\n\tleft,linv = mergesort(l[:len(l) // 2])\n\tright,rinv = mergesort(l[len(l) // 2:])\n\tlefti = 0\n\trighti = 0\n\ti = 0\n\tnuminversions = 0\n\twhile True:\n\t\tif i >= len(l):\n\t\t\tbreak\n\t\tif lefti >= len(left):\n\t\t\tl[i] = right[righti]\n\t\t\trighti += 1\n\t\telif righti >= len(right):\n\t\t\tl[i] = left[lefti]\n\t\t\tlefti += 1\n\t\t\tnuminversions += len(right)\n\t\telif left[lefti] > right[righti]:\n\t\t\tl[i] = right[righti]\n\t\t\trighti += 1\n\t\telse:\n\t\t\tl[i] = left[lefti]\n\t\t\tlefti += 1\n\t\t\tnuminversions += righti\n\t\ti += 1\n\treturn (l,numinversions + linv + rinv)\n\t\nres = mergesort(A)\n\nn = res[1]\n\nif n % 2 == 0:\n\tprint(2*n)\nelse:\n\tprint(2*n-1)\n```","inputs":"5\n3 5 2 4 1\n","output":"13","actual_output":"13\n","execution_success":true,"sample_index":12394},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"399_B. Red and Blue Balls","prompt":"Solve the following coding problem using the programming language python:\n\nUser ainta has a stack of n red and blue balls. He can apply a certain operation which changes the colors of the balls inside the stack.\n\n * While the top ball inside the stack is red, pop the ball from the top of the stack. \n * Then replace the blue ball on the top with a red ball. \n * And finally push some blue balls to the stack until the stack has total of n balls inside. \n\n\n\nIf there are no blue balls inside the stack, ainta can't apply this operation. Given the initial state of the stack, ainta wants to know the maximum number of operations he can repeatedly apply.\n\nInput\n\nThe first line contains an integer n (1 \u2264 n \u2264 50) \u2014 the number of balls inside the stack.\n\nThe second line contains a string s (|s| = n) describing the initial state of the stack. The i-th character of the string s denotes the color of the i-th ball (we'll number the balls from top to bottom of the stack). If the character is \"R\", the color is red. If the character is \"B\", the color is blue.\n\nOutput\n\nPrint the maximum number of operations ainta can repeatedly apply.\n\nPlease, do not write the %lld specifier to read or write 64-bit integers in \u0421++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\nExamples\n\nInput\n\n3\nRBR\n\n\nOutput\n\n2\n\n\nInput\n\n4\nRBBR\n\n\nOutput\n\n6\n\n\nInput\n\n5\nRBBRR\n\n\nOutput\n\n6\n\nNote\n\nThe first example is depicted below.\n\nThe explanation how user ainta applies the first operation. He pops out one red ball, changes the color of the ball in the middle from blue to red, and pushes one blue ball.\n\n\n\nThe explanation how user ainta applies the second operation. He will not pop out red balls, he simply changes the color of the ball on the top from blue to red.\n\n\n\nFrom now on, ainta can't apply any operation because there are no blue balls inside the stack. ainta applied two operations, so the answer is 2.\n\nThe second example is depicted below. The blue arrow denotes a single operation.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\ns = list(input())\no = 0\n#s.reverse()\n\n# while s.count(\"B\") > 0:\n# while s[-1] == \"R\":\n# s.pop()\n# s[-1] = \"R\"\n# while len(s) < n:\n# s.append(\"B\")\n# o += 1\n# print(s)\n\ntry:\n index = s.index(\"B\")\n o += pow(2, index)\n while True:\n index = s.index(\"B\", index + 1)\n o += pow(2, index)\nexcept:\n print(o)\n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\nRBBR\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5\\nRBBRR\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\nRBR\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '30\\nRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\nRRB\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\nBR\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\nBB\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\nBRBRRRRRRR\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRRBBBBBBRRBBRRRBRRBBBRRRRRRRRRRRRRRRRRRRRR\\n', 'output': '479001600\\n'}, {'type': 'stdin_stdout', 'input': '3\\nRRR\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRBRRBBRRR\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '32\\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBR\\n', 'output': '2147483647\\n'}, {'type': 'stdin_stdout', 'input': '48\\nRBRBRRRRBRBRRBRRRRRRRBBBRRBRBRRRBBRRRRRRRRRRRRRR\\n', 'output': '13235135754\\n'}, {'type': 'stdin_stdout', 'input': '30\\nRRBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n', 'output': '1073741820\\n'}, {'type': 'stdin_stdout', 'input': '2\\nRB\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\nBBB\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRBRRRRRBRBRRBBBBBBRRRBRRRRRBBBRRBRRRRRBBBRRRRRRRRR\\n', 'output': '1929382195842\\n'}, {'type': 'stdin_stdout', 'input': '3\\nRBB\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '20\\nRRBRBBBBBRRRRRRRRRRR\\n', 'output': '500\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRBBBBBBBBBBBBBBBBRBRRBBBRBBRBBBRRBRBBBBBRBBRBBRBR\\n', 'output': '402373705727996\\n'}, {'type': 'stdin_stdout', 'input': '10\\nBRRRRRRRRR\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20\\nBRBRRRRRRRRRRRRRRRRR\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\nB\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\nBRR\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\nBBR\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '50\\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n', 'output': '1125899906842623\\n'}, {'type': 'stdin_stdout', 'input': '5\\nRBRBR\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '3\\nBRB\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '2\\nRR\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '20\\nRRRBRBBBBBRRRRRRRRRR\\n', 'output': '1000\\n'}, {'type': 'stdin_stdout', 'input': '19\\nRRRRRBRRBRRRRBRBBBB\\n', 'output': '500000\\n'}, {'type': 'stdin_stdout', 'input': '50\\nBRRRBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n', 'output': '1125899906842609\\n'}, {'type': 'stdin_stdout', 'input': '1\\nR\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRBRRRBRRR\\n', 'output': '68\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRBBRRBRR\\n', 'output': '152\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRBBBRRRRRBRRBBBRRRRRBRRRBBBBBBRRBRBRRRRRBR\\n', 'output': '287243393699328\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRBRBBRBBRBBBBBRBRRBBBRBBRBBBRRBRBBBBBBBBBBBBBBBBRR\\n', 'output': '281472004832986\\n'}, {'type': 'stdin_stdout', 'input': '5\\nRRBBR\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRRRBBRRR\\n', 'output': '96\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRBRRRBBR\\n', 'output': '392\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRBBRRRBRRR\\n', 'output': '70\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRRBBBBBBRRRBRRRBRRBBBRRRRBRRRRRRRRRRRRRRRR\\n', 'output': '9068674048\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRRRBBRRB\\n', 'output': '608\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRBBBBBBBBBBBBBBBBRBRRBBBRBBRBBBRRBRBBBBBBRBRBBRBR\\n', 'output': '400174682472444\\n'}, {'type': 'stdin_stdout', 'input': '19\\nBBBBRBRRRRBRRBRRRRR\\n', 'output': '9263\\n'}, {'type': 'stdin_stdout', 'input': '50\\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBRRRB\\n', 'output': '633318697598975\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRBBBRRRRRBRRBBBRRRRRBRRRBBBRBBRRBRBRRBRRBR\\n', 'output': '322393406049792\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRBRRBRBR\\n', 'output': '328\\n'}, {'type': 'stdin_stdout', 'input': '10\\nBRRBBRRRRR\\n', 'output': '25\\n'}, {'type': 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'input': '50\\nRRRBRRRRRRRRRRRRRRRRRBBBRRBRRRBRRRBBBBBBRRRRRRRRRR\\n', 'output': '1083487289352\\n'}, {'type': 'stdin_stdout', 'input': '20\\nRRBRBBBBRRRRRRRRRRRB\\n', 'output': '524532\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRBRRRBRR\\n', 'output': '136\\n'}, {'type': 'stdin_stdout', 'input': '5\\nRRRBB\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRBRRRRRRB\\n', 'output': '516\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRBRBBRBBRBBBBBRBRRBBBRBBRBRBBRBRBBBBBBBBBBBBBBBBRR\\n', 'output': '281472206159578\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRRBBBBBBRRRBRRRBRRBBBRRRRRRRRRRRRRRRRRBRRR\\n', 'output': '70369222917120\\n'}, {'type': 'stdin_stdout', 'input': '5\\nBBRRR\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5\\nRRBRB\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '5\\nRBRRB\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '32\\nRBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n', 'output': '4294967294\\n'}, {'type': 'stdin_stdout', 'input': '30\\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBRR\\n', 'output': '268435455\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRRRRRRRB\\n', 'output': '512\\n'}, {'type': 'stdin_stdout', 'input': '20\\nRRRRRBBBBBRRRRRRRBRR\\n', 'output': '132064\\n'}, {'type': 'stdin_stdout', 'input': '19\\nBBBBRBRRRRBRBRRRRRR\\n', 'output': '5167\\n'}, {'type': 'stdin_stdout', 'input': '4\\nRBRB\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRBRBBRBBRBBBBBRBRRBBBRBBRBBBBRBRBBBBBBBBRBBBBBBBRR\\n', 'output': '280372761640666\\n'}, {'type': 'stdin_stdout', 'input': '10\\nBRRRBBRRRR\\n', 'output': '49\\n'}, {'type': 'stdin_stdout', 'input': '19\\nBBRBRBRRRRBRRBRRRRB\\n', 'output': '271403\\n'}, {'type': 'stdin_stdout', 'input': '10\\nBRRBRRBRRR\\n', 'output': '73\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRBRBRBRRRR\\n', 'output': '42\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRBBBBBBBBBBBBBBRBRBRBBBRRBBBBBBRRBRBBBBBRBBRBBRBR\\n', 'output': '402373959417852\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRBBBBBBBBRBBBBBBBRBRBBRBRBBRBBBRRBRBBBBBRBBBBBRBR\\n', 'output': '419965885479932\\n'}, {'type': 'stdin_stdout', 'input': '5\\nBRRBR\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRBRRRRRRRRRRRRRRRRRRBBRRBRRRBRBRBBBBBBRRRRRRRRRR\\n', 'output': '1087780159496\\n'}, {'type': 'stdin_stdout', 'input': '5\\nBRBRR\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5\\nBRRRB\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '20\\nRRBRRRRRRRBBBBBRRRRR\\n', 'output': '31748\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRBBBBBBBRBBBBBBBBRBRBBBBRBBRBBBRRBRBBBBBRBBRBBRBR\\n', 'output': '402373707824636\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRRBBRRRB\\n', 'output': '560\\n'}, {'type': 'stdin_stdout', 'input': '10\\nBBRRRRBRRR\\n', 'output': '67\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRRBRBRBR\\n', 'output': '336\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRBBBBBBBBBBBBBBRBRBRBBBRRBRBBBBRRBBBBBBBRBBRBBRBR\\n', 'output': '402408184938492\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRRRRRBRB\\n', 'output': '640\\n'}, {'type': 'stdin_stdout', 'input': '20\\nRRRRBBBBBBRRRRRRRRRR\\n', 'output': '1008\\n'}, {'type': 'stdin_stdout', 'input': '20\\nRRRRRRRRRRBBBBBRBRRR\\n', 'output': '97280\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRRRRRRRRBRRRRBBBRRBRRRBRRRBBBBBBRRRRRRRRRR\\n', 'output': '1083487354880\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRRRBRRBB\\n', 'output': '800\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRBRBBRBRBBBBBBRBRRBBBRBBRBBBRRBRBBBBBBBBBBBBBBBBRR\\n', 'output': '281472004833114\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRRBBBRBBRRBBRRRBRRBBBRRRRRRRRRRRRRRBRRRRRR\\n', 'output': '8796572015616\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRRRRBRRB\\n', 'output': '576\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRBRBBRBBRBBBBBRBRRBBBRBBRBRBBRBRBBBBBBBBBBBBBRBBRB\\n', 'output': '809237787492058\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRRBBBBRBRRRBRRRBRRBBBRRRRRBRRRRRRRRRRRBRRR\\n', 'output': '70386402769920\\n'}, {'type': 'stdin_stdout', 'input': '19\\nRBBBRBRRRRBRBRRRRRB\\n', 'output': '267310\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRRBRRBRRB\\n', 'output': '584\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRBRBBRBBRBBBBBRBRRBBBBBBRRBBBRBRBRBBBBBBBBBBBBBBRR\\n', 'output': '281463651876570\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRRBBBBBBRBRBRRRBRRBBRRRRRRRRRRRRRRRRRRBRRR\\n', 'output': '70368954612736\\n'}, {'type': 'stdin_stdout', 'input': '10\\nRRBRRRRRBR\\n', 'output': '260\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRRRRRRRRBRRRRBBBBRBRRRBRRRBBBRBBRRRRRRRRRR\\n', 'output': '946065178624\\n'}, {'type': 'stdin_stdout', 'input': '10\\nBBRRBRRRRR\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRBRRRRRRRRRRRBRRRRRBBBRRBRRRBRRRBRBBBBRRRRRRRRRR\\n', 'output': '1049127583752\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRBRBBRBBRBBBBBRBRRBBBBBBRRBBBRBRBRBBBBRBBBBBBBBBBR\\n', 'output': '562663750680282\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRRRRRRRRRRRRRRRRBRRRRBBBBRRRRRBRRRBBBRBBRRRBRRRRRR\\n', 'output': '9742091091968\\n'}, {'type': 'stdin_stdout', 'input': '50\\nRBBBBBBBBBBRBBBBRBRBRBBBRRBBBBBBRRBRBBBBBRBBRBBRBR\\n', 'output': '402373959415806\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 0, 'nanos': 500000000}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77673","program":"```python\nn = int(input())\ns = list(input())\no = 0\n#s.reverse()\n\n# while s.count(\"B\") > 0:\n# while s[-1] == \"R\":\n# s.pop()\n# s[-1] = \"R\"\n# while len(s) < n:\n# s.append(\"B\")\n# o += 1\n# print(s)\n\ntry:\n index = s.index(\"B\")\n o += pow(2, index)\n while True:\n index = s.index(\"B\", index + 1)\n o += pow(2, index)\nexcept:\n print(o)\n \n```","inputs":"4\nRBBR\n","output":"6\n","actual_output":"6\n","execution_success":true,"sample_index":12395},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"421_C. Online Meeting","prompt":"Solve the following coding problem using the programming language python:\n\nNearly each project of the F company has a whole team of developers working on it. They often are in different rooms of the office in different cities and even countries. To keep in touch and track the results of the project, the F company conducts shared online meetings in a Spyke chat.\n\nOne day the director of the F company got hold of the records of a part of an online meeting of one successful team. The director watched the record and wanted to talk to the team leader. But how can he tell who the leader is? The director logically supposed that the leader is the person who is present at any conversation during a chat meeting. In other words, if at some moment of time at least one person is present on the meeting, then the leader is present on the meeting.\n\nYou are the assistant director. Given the 'user logged on'/'user logged off' messages of the meeting in the chronological order, help the director determine who can be the leader. Note that the director has the record of only a continuous part of the meeting (probably, it's not the whole meeting).\n\nInput\n\nThe first line contains integers n and m (1 \u2264 n, m \u2264 105) \u2014 the number of team participants and the number of messages. Each of the next m lines contains a message in the format:\n\n * '+ id': the record means that the person with number id (1 \u2264 id \u2264 n) has logged on to the meeting. \n * '- id': the record means that the person with number id (1 \u2264 id \u2264 n) has logged off from the meeting. \n\n\n\nAssume that all the people of the team are numbered from 1 to n and the messages are given in the chronological order. It is guaranteed that the given sequence is the correct record of a continuous part of the meeting. It is guaranteed that no two log on/log off events occurred simultaneously.\n\nOutput\n\nIn the first line print integer k (0 \u2264 k \u2264 n) \u2014 how many people can be leaders. In the next line, print k integers in the increasing order \u2014 the numbers of the people who can be leaders.\n\nIf the data is such that no member of the team can be a leader, print a single number 0.\n\nExamples\n\nInput\n\n5 4\n+ 1\n+ 2\n- 2\n- 1\n\n\nOutput\n\n4\n1 3 4 5 \n\nInput\n\n3 2\n+ 1\n- 2\n\n\nOutput\n\n1\n3 \n\nInput\n\n2 4\n+ 1\n- 1\n+ 2\n- 2\n\n\nOutput\n\n0\n\n\nInput\n\n5 6\n+ 1\n- 1\n- 3\n+ 3\n+ 4\n- 4\n\n\nOutput\n\n3\n2 3 5 \n\nInput\n\n2 4\n+ 1\n- 2\n+ 2\n- 1\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#!/Library/Frameworks/Python.framework/Versions/3.6/bin/python3\n'''\nCreated on 13/09/2018\n\n@author: ernesto\n'''\n\nn, m = [int(x) for x in input().strip().split(\" \")]\n\nposibles_jefes = set(range(1, n + 1))\nanteriores = set()\nposteriores = set()\ncontinuos = [True] * (n + 1)\nmencionados = set()\nposibles_jefes_mencionados = set()\nultimo_en_salir = [True] * (n + 1)\nultima_salida_inesperada = None\n\nops = []\n\nif(m > 1):\n for _ in range(0, m):\n s, n_s = [x for x in input().strip().split(\" \")]\n n = int(n_s)\n ops.append((s, n))\n for i in range(0, m):\n op, num = ops[i]\n cont = False\n if op == '+':\n cont = not i or (ops[i - 1][0] == '-' and ops[i - 1][1] == num)\n posteriores.add(num)\n if op == '-':\n cont = i == m - 1 or (ops[i + 1][0] == '+' and ops[i + 1][1] == num)\n if num not in mencionados:\n anteriores.add(num)\n ultima_salida_inesperada = num\n posteriores.discard(num)\n ultimo_en_salir[num] &= not posteriores\n continuos[num] &= cont \n mencionados.add(num)\n# print(\"anteriores {} posteriores {} continuos {} ops {}\".format(anteriores, posteriores, continuos, ops))\n if not anteriores and not posteriores:\n assert ultima_salida_inesperada is None\n if ops[0][0] == '+' and ops[-1][0] == '-' and ops[0][1] == ops[-1][1] and continuos[ops[0][1]] and ultimo_en_salir[ops[0][1]]:\n posibles_jefes_mencionados.add(ops[0][1])\n else:\n if not posteriores:\n assert ultima_salida_inesperada is not None\n posibles_jefes_filtrados = list(filter(lambda x:continuos[x] and ultimo_en_salir[x] and ultima_salida_inesperada == x, anteriores))\n assert len(posibles_jefes_filtrados) <= 1\n if(posibles_jefes_filtrados):\n assert posibles_jefes_filtrados[0] == ops[-1][1]\n posibles_jefes_mencionados.add(ops[-1][1])\n else:\n if not anteriores:\n assert ultima_salida_inesperada is None\n posibles_jefes_filtrados = list(filter(lambda x:continuos[x] and ultimo_en_salir[x], posteriores))\n# print(\"posibles {}\".format(posibles_jefes_filtrados))\n assert len(posibles_jefes_filtrados) <= 1\n if(posibles_jefes_filtrados):\n assert posibles_jefes_filtrados[0] == ops[0][1]\n posibles_jefes_mencionados.add(ops[0][1])\n else:\n assert ultima_salida_inesperada is not None\n# print(\"continuos {}\".format(continuos))\n posibles_jefes_mencionados = set(filter(lambda x:ultimo_en_salir[x] and continuos[x] and ultima_salida_inesperada == x, anteriores & posteriores))\n\n# print(\"posibles jefes menc {}\".format(posibles_jefes_mencionados))\n posibles_jefes -= (mencionados - posibles_jefes_mencionados)\n \nprint(len(posibles_jefes))\nif(len(posibles_jefes)):\n print(\" \".join(map(str, sorted(posibles_jefes))))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 2\\n+ 1\\n- 2\\n', 'output': '1\\n3 \\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n+ 1\\n+ 2\\n- 2\\n- 1\\n', 'output': '4\\n1 3 4 5 \\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n+ 1\\n- 1\\n+ 2\\n- 2\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n+ 1\\n- 2\\n+ 2\\n- 1\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n+ 1\\n- 1\\n- 3\\n+ 3\\n+ 4\\n- 4\\n', 'output': '3\\n2 3 5 \\n'}, {'type': 'stdin_stdout', 'input': '20 50\\n+ 5\\n+ 11\\n- 5\\n+ 6\\n- 16\\n- 13\\n+ 5\\n+ 7\\n- 8\\n- 7\\n- 10\\n+ 10\\n- 20\\n- 19\\n+ 17\\n- 2\\n+ 2\\n+ 19\\n+ 18\\n- 2\\n- 6\\n- 5\\n+ 6\\n+ 4\\n- 14\\n+ 14\\n- 9\\n+ 15\\n- 17\\n- 15\\n+ 2\\n+ 5\\n- 2\\n+ 9\\n- 11\\n+ 2\\n- 19\\n+ 7\\n+ 12\\n+ 16\\n+ 19\\n- 18\\n- 2\\n+ 18\\n- 9\\n- 10\\n+ 9\\n+ 13\\n- 14\\n- 16\\n', 'output': '2\\n1 3 \\n'}, {'type': 'stdin_stdout', 'input': '10 7\\n- 8\\n+ 1\\n+ 2\\n+ 3\\n- 2\\n- 3\\n- 1\\n', 'output': '6\\n4 5 6 7 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n- 2\\n- 3\\n+ 3\\n- 6\\n', 'output': '4\\n1 4 5 7 \\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n+ 2\\n- 2\\n+ 2\\n- 2\\n- 3\\n', 'output': '9\\n1 3 4 5 6 7 8 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '20 1\\n- 16\\n', 'output': '20\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 \\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n- 2\\n+ 1\\n+ 2\\n', 'output': '1\\n3 \\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n- 2\\n+ 1\\n+ 2\\n- 2\\n+ 4\\n', 'output': '2\\n3 5 \\n'}, {'type': 'stdin_stdout', 'input': '10 3\\n+ 1\\n+ 2\\n- 7\\n', 'output': '7\\n3 4 5 6 8 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n- 1\\n- 2\\n+ 3\\n+ 4\\n', 'output': '1\\n5 \\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n+ 1\\n- 1\\n- 2\\n+ 3\\n- 3\\n- 4\\n+ 5\\n- 5\\n- 6\\n+ 6\\n', 'output': '5\\n6 7 8 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n+ 1\\n', 'output': '1\\n1 \\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n+ 1\\n- 1\\n- 2\\n+ 3\\n- 3\\n- 4\\n+ 5\\n- 5\\n- 6\\n+ 6\\n+ 7\\n', 'output': '4\\n6 8 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n+ 1\\n- 1\\n+ 1\\n+ 2\\n', 'output': '4\\n1 3 4 5 \\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n+ 5\\n+ 2\\n+ 3\\n+ 4\\n+ 1\\n', 'output': '1\\n5 \\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n- 1\\n+ 1\\n', 'output': '2\\n1 2 \\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n- 1\\n+ 1\\n- 1\\n+ 2\\n', 'output': '2\\n3 4 \\n'}, {'type': 'stdin_stdout', 'input': '1 20\\n- 1\\n+ 1\\n- 1\\n+ 1\\n- 1\\n+ 1\\n- 1\\n+ 1\\n- 1\\n+ 1\\n- 1\\n+ 1\\n- 1\\n+ 1\\n- 1\\n+ 1\\n- 1\\n+ 1\\n- 1\\n+ 1\\n', 'output': '1\\n1 \\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n+ 2\\n- 1\\n- 3\\n- 2\\n', 'output': '1\\n4 \\n'}, {'type': 'stdin_stdout', 'input': '50 20\\n- 6\\n+ 40\\n- 3\\n- 23\\n+ 31\\n- 27\\n- 40\\n+ 25\\n+ 29\\n- 41\\n- 16\\n+ 23\\n+ 20\\n+ 13\\n- 45\\n+ 40\\n+ 24\\n+ 22\\n- 23\\n+ 17\\n', 'output': '34\\n1 2 4 5 7 8 9 10 11 12 14 15 18 19 21 26 28 30 32 33 34 35 36 37 38 39 42 43 44 46 47 48 49 50 \\n'}, {'type': 'stdin_stdout', 'input': '4 10\\n+ 2\\n- 1\\n- 2\\n- 3\\n+ 3\\n+ 2\\n+ 4\\n- 2\\n+ 2\\n+ 1\\n', 'output': '1\\n3 \\n'}, {'type': 'stdin_stdout', 'input': '10 8\\n+ 1\\n- 1\\n- 4\\n+ 4\\n+ 3\\n+ 7\\n- 7\\n+ 9\\n', 'output': '6\\n2 4 5 6 8 10 \\n'}, {'type': 'stdin_stdout', 'input': '10 8\\n+ 1\\n- 1\\n- 2\\n- 3\\n+ 3\\n+ 7\\n- 7\\n+ 9\\n', 'output': '6\\n3 4 5 6 8 10 \\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n+ 1\\n- 1\\n+ 2\\n', 'output': '3\\n3 4 5 \\n'}, {'type': 'stdin_stdout', 'input': '100 5\\n- 60\\n- 58\\n+ 25\\n- 32\\n+ 86\\n', 'output': '95\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 26 27 28 29 30 31 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 59 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 87 88 89 90 91 92 93 94 95 96 97 98 99 100 \\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n- 5\\n- 6\\n- 3\\n- 1\\n- 2\\n- 4\\n', 'output': '1\\n4 \\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n- 2\\n', 'output': '2\\n1 2 \\n'}, {'type': 'stdin_stdout', 'input': '10 12\\n+ 1\\n- 1\\n- 2\\n+ 3\\n- 3\\n- 4\\n+ 5\\n- 5\\n- 6\\n+ 6\\n+ 7\\n- 7\\n', 'output': '4\\n6 8 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n- 1\\n+ 1\\n+ 2\\n- 2\\n+ 3\\n', 'output': '1\\n1 \\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n+ 1\\n+ 2\\n- 1\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 9\\n+ 1\\n- 1\\n- 2\\n+ 3\\n- 3\\n- 4\\n+ 5\\n- 5\\n- 6\\n', 'output': '5\\n6 7 8 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n+ 2\\n- 2\\n+ 2\\n- 2\\n+ 2\\n- 3\\n', 'output': '8\\n1 4 5 6 7 8 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n+ 2\\n- 1\\n- 2\\n- 3\\n+ 3\\n+ 2\\n+ 4\\n- 2\\n+ 2\\n', 'output': '1\\n3 \\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n+ 1\\n- 1\\n- 2\\n+ 3\\n- 3\\n- 4\\n+ 5\\n- 5\\n- 10\\n+ 6\\n', 'output': '3\\n7 8 9 \\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n+ 2\\n- 1\\n- 3\\n- 2\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '14 3\\n+ 1\\n+ 2\\n- 7\\n', 'output': '11\\n3 4 5 6 8 9 10 11 12 13 14 \\n'}, {'type': 'stdin_stdout', 'input': '8 3\\n+ 1\\n- 1\\n+ 2\\n', 'output': '6\\n3 4 5 6 7 8 \\n'}, {'type': 'stdin_stdout', 'input': '10 12\\n+ 1\\n- 1\\n- 2\\n+ 1\\n- 3\\n- 4\\n+ 5\\n- 5\\n- 6\\n+ 6\\n+ 7\\n- 7\\n', 'output': '3\\n8 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '6 2\\n+ 1\\n- 2\\n', 'output': '4\\n3 4 5 6 \\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n+ 4\\n- 1\\n- 3\\n- 2\\n', 'output': '4\\n5 6 7 8 \\n'}, {'type': 'stdin_stdout', 'input': '6 2\\n+ 1\\n- 4\\n', 'output': '4\\n2 3 5 6 \\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n+ 4\\n- 1\\n- 6\\n- 2\\n', 'output': '4\\n3 5 7 8 \\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n+ 1\\n- 1\\n- 6\\n- 2\\n', 'output': '6\\n2 3 4 5 7 8 \\n'}, {'type': 'stdin_stdout', 'input': '14 4\\n+ 1\\n- 1\\n- 6\\n- 2\\n', 'output': '12\\n2 3 4 5 7 8 9 10 11 12 13 14 \\n'}, {'type': 'stdin_stdout', 'input': '20 50\\n+ 5\\n+ 11\\n- 5\\n+ 6\\n- 16\\n- 13\\n+ 5\\n+ 7\\n- 8\\n- 7\\n- 10\\n+ 10\\n- 20\\n- 19\\n+ 17\\n- 2\\n+ 2\\n+ 19\\n+ 18\\n- 2\\n- 6\\n- 5\\n+ 6\\n+ 4\\n- 14\\n+ 14\\n- 9\\n+ 15\\n- 17\\n- 15\\n+ 2\\n+ 5\\n- 2\\n+ 9\\n- 11\\n+ 2\\n- 19\\n+ 8\\n+ 12\\n+ 16\\n+ 19\\n- 18\\n- 2\\n+ 18\\n- 9\\n- 10\\n+ 9\\n+ 13\\n- 14\\n- 16\\n', 'output': '2\\n1 3 \\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n+ 1\\n- 1\\n- 2\\n+ 3\\n- 3\\n- 4\\n+ 5\\n- 5\\n- 6\\n+ 1\\n', 'output': '4\\n7 8 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n+ 1\\n', 'output': '2\\n1 2 \\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n+ 1\\n- 1\\n- 2\\n+ 3\\n- 3\\n- 4\\n+ 9\\n- 5\\n- 6\\n+ 6\\n+ 7\\n', 'output': '2\\n8 10 \\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n+ 1\\n+ 2\\n- 2\\n', 'output': '1\\n1 \\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n+ 2\\n- 2\\n', 'output': '3\\n1 2 3 \\n'}, {'type': 'stdin_stdout', 'input': '8 3\\n+ 1\\n- 1\\n+ 1\\n', 'output': '8\\n1 2 3 4 5 6 7 8 \\n'}, {'type': 'stdin_stdout', 'input': '6 2\\n+ 1\\n- 1\\n', 'output': '6\\n1 2 3 4 5 6 \\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n+ 1\\n- 2\\n', 'output': '3\\n3 4 5 \\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n+ 1\\n- 3\\n', 'output': '3\\n2 4 5 \\n'}, {'type': 'stdin_stdout', 'input': '10 7\\n- 8\\n+ 1\\n+ 3\\n+ 3\\n- 2\\n- 3\\n- 1\\n', 'output': '6\\n4 5 6 7 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n- 2\\n- 3\\n+ 3\\n- 4\\n', 'output': '4\\n1 5 6 7 \\n'}, {'type': 'stdin_stdout', 'input': '9 3\\n+ 1\\n+ 2\\n- 7\\n', 'output': '6\\n3 4 5 6 8 9 \\n'}, {'type': 'stdin_stdout', 'input': '6 4\\n+ 2\\n- 1\\n- 3\\n- 2\\n', 'output': '3\\n4 5 6 \\n'}, {'type': 'stdin_stdout', 'input': '50 20\\n- 4\\n+ 40\\n- 3\\n- 23\\n+ 31\\n- 27\\n- 40\\n+ 25\\n+ 29\\n- 41\\n- 16\\n+ 23\\n+ 20\\n+ 13\\n- 45\\n+ 40\\n+ 24\\n+ 22\\n- 23\\n+ 17\\n', 'output': '34\\n1 2 5 6 7 8 9 10 11 12 14 15 18 19 21 26 28 30 32 33 34 35 36 37 38 39 42 43 44 46 47 48 49 50 \\n'}, {'type': 'stdin_stdout', 'input': '10 8\\n+ 1\\n- 1\\n- 2\\n- 3\\n+ 3\\n+ 5\\n- 7\\n+ 9\\n', 'output': '4\\n4 6 8 10 \\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n- 1\\n- 2\\n+ 3\\n+ 4\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n+ 4\\n- 1\\n- 3\\n- 2\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n- 2\\n+ 1\\n+ 3\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '8 2\\n+ 1\\n- 2\\n', 'output': '6\\n3 4 5 6 7 8 \\n'}, {'type': 'stdin_stdout', 'input': '20 50\\n+ 5\\n+ 14\\n- 5\\n+ 6\\n- 16\\n- 13\\n+ 5\\n+ 7\\n- 8\\n- 7\\n- 10\\n+ 10\\n- 20\\n- 19\\n+ 17\\n- 2\\n+ 2\\n+ 19\\n+ 18\\n- 2\\n- 6\\n- 5\\n+ 6\\n+ 4\\n- 14\\n+ 14\\n- 9\\n+ 15\\n- 17\\n- 15\\n+ 2\\n+ 5\\n- 2\\n+ 9\\n- 11\\n+ 2\\n- 19\\n+ 8\\n+ 12\\n+ 16\\n+ 19\\n- 18\\n- 2\\n+ 18\\n- 9\\n- 10\\n+ 9\\n+ 13\\n- 14\\n- 16\\n', 'output': '2\\n1 3 \\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n+ 1\\n- 1\\n- 2\\n+ 3\\n- 3\\n- 4\\n+ 5\\n- 1\\n- 6\\n+ 1\\n', 'output': '4\\n7 8 9 10 \\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n+ 2\\n', 'output': '2\\n1 2 \\n'}, {'type': 'stdin_stdout', 'input': '20 50\\n+ 5\\n+ 14\\n- 5\\n+ 6\\n- 16\\n- 13\\n+ 5\\n+ 7\\n- 8\\n- 7\\n- 10\\n+ 10\\n- 20\\n- 19\\n+ 17\\n- 2\\n+ 2\\n+ 19\\n+ 18\\n- 2\\n- 6\\n- 5\\n+ 6\\n+ 4\\n- 14\\n+ 14\\n- 9\\n+ 15\\n- 17\\n- 15\\n+ 2\\n+ 5\\n- 2\\n+ 9\\n- 11\\n+ 2\\n- 19\\n+ 8\\n+ 12\\n+ 16\\n+ 19\\n- 18\\n- 2\\n+ 18\\n- 9\\n- 10\\n+ 9\\n+ 13\\n- 14\\n- 7\\n', 'output': '2\\n1 3 \\n'}, {'type': 'stdin_stdout', 'input': '20 50\\n+ 5\\n+ 14\\n- 5\\n+ 6\\n- 16\\n- 13\\n+ 5\\n+ 7\\n- 8\\n- 7\\n- 10\\n+ 3\\n- 20\\n- 19\\n+ 17\\n- 2\\n+ 2\\n+ 19\\n+ 18\\n- 2\\n- 6\\n- 5\\n+ 6\\n+ 4\\n- 14\\n+ 14\\n- 9\\n+ 15\\n- 17\\n- 15\\n+ 2\\n+ 5\\n- 2\\n+ 9\\n- 11\\n+ 2\\n- 19\\n+ 8\\n+ 12\\n+ 16\\n+ 19\\n- 18\\n- 2\\n+ 18\\n- 9\\n- 10\\n+ 9\\n+ 13\\n- 14\\n- 7\\n', 'output': '1\\n1 \\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n- 3\\n+ 1\\n+ 2\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 9\\n+ 1\\n- 1\\n- 2\\n+ 3\\n- 3\\n- 4\\n+ 3\\n- 5\\n- 6\\n', 'output': '4\\n7 8 9 10 \\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77677","program":"```python\n#!/Library/Frameworks/Python.framework/Versions/3.6/bin/python3\n'''\nCreated on 13/09/2018\n\n@author: ernesto\n'''\n\nn, m = [int(x) for x in input().strip().split(\" \")]\n\nposibles_jefes = set(range(1, n + 1))\nanteriores = set()\nposteriores = set()\ncontinuos = [True] * (n + 1)\nmencionados = set()\nposibles_jefes_mencionados = set()\nultimo_en_salir = [True] * (n + 1)\nultima_salida_inesperada = None\n\nops = []\n\nif(m > 1):\n for _ in range(0, m):\n s, n_s = [x for x in input().strip().split(\" \")]\n n = int(n_s)\n ops.append((s, n))\n for i in range(0, m):\n op, num = ops[i]\n cont = False\n if op == '+':\n cont = not i or (ops[i - 1][0] == '-' and ops[i - 1][1] == num)\n posteriores.add(num)\n if op == '-':\n cont = i == m - 1 or (ops[i + 1][0] == '+' and ops[i + 1][1] == num)\n if num not in mencionados:\n anteriores.add(num)\n ultima_salida_inesperada = num\n posteriores.discard(num)\n ultimo_en_salir[num] &= not posteriores\n continuos[num] &= cont \n mencionados.add(num)\n# print(\"anteriores {} posteriores {} continuos {} ops {}\".format(anteriores, posteriores, continuos, ops))\n if not anteriores and not posteriores:\n assert ultima_salida_inesperada is None\n if ops[0][0] == '+' and ops[-1][0] == '-' and ops[0][1] == ops[-1][1] and continuos[ops[0][1]] and ultimo_en_salir[ops[0][1]]:\n posibles_jefes_mencionados.add(ops[0][1])\n else:\n if not posteriores:\n assert ultima_salida_inesperada is not None\n posibles_jefes_filtrados = list(filter(lambda x:continuos[x] and ultimo_en_salir[x] and ultima_salida_inesperada == x, anteriores))\n assert len(posibles_jefes_filtrados) <= 1\n if(posibles_jefes_filtrados):\n assert posibles_jefes_filtrados[0] == ops[-1][1]\n posibles_jefes_mencionados.add(ops[-1][1])\n else:\n if not anteriores:\n assert ultima_salida_inesperada is None\n posibles_jefes_filtrados = list(filter(lambda x:continuos[x] and ultimo_en_salir[x], posteriores))\n# print(\"posibles {}\".format(posibles_jefes_filtrados))\n assert len(posibles_jefes_filtrados) <= 1\n if(posibles_jefes_filtrados):\n assert posibles_jefes_filtrados[0] == ops[0][1]\n posibles_jefes_mencionados.add(ops[0][1])\n else:\n assert ultima_salida_inesperada is not None\n# print(\"continuos {}\".format(continuos))\n posibles_jefes_mencionados = set(filter(lambda x:ultimo_en_salir[x] and continuos[x] and ultima_salida_inesperada == x, anteriores & posteriores))\n\n# print(\"posibles jefes menc {}\".format(posibles_jefes_mencionados))\n posibles_jefes -= (mencionados - posibles_jefes_mencionados)\n \nprint(len(posibles_jefes))\nif(len(posibles_jefes)):\n print(\" \".join(map(str, sorted(posibles_jefes))))\n\n```","inputs":"3 2\n+ 1\n- 2\n","output":"1\n3 \n","actual_output":"1\n3\n","execution_success":true,"sample_index":12396},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"448_A. Rewards","prompt":"Solve the following coding problem using the programming language python:\n\nBizon the Champion is called the Champion for a reason. \n\nBizon the Champion has recently got a present \u2014 a new glass cupboard with n shelves and he decided to put all his presents there. All the presents can be divided into two types: medals and cups. Bizon the Champion has a1 first prize cups, a2 second prize cups and a3 third prize cups. Besides, he has b1 first prize medals, b2 second prize medals and b3 third prize medals. \n\nNaturally, the rewards in the cupboard must look good, that's why Bizon the Champion decided to follow the rules:\n\n * any shelf cannot contain both cups and medals at the same time; \n * no shelf can contain more than five cups; \n * no shelf can have more than ten medals. \n\n\n\nHelp Bizon the Champion find out if we can put all the rewards so that all the conditions are fulfilled.\n\nInput\n\nThe first line contains integers a1, a2 and a3 (0 \u2264 a1, a2, a3 \u2264 100). The second line contains integers b1, b2 and b3 (0 \u2264 b1, b2, b3 \u2264 100). The third line contains integer n (1 \u2264 n \u2264 100).\n\nThe numbers in the lines are separated by single spaces.\n\nOutput\n\nPrint \"YES\" (without the quotes) if all the rewards can be put on the shelves in the described manner. Otherwise, print \"NO\" (without the quotes).\n\nExamples\n\nInput\n\n1 1 1\n1 1 1\n4\n\n\nOutput\n\nYES\n\n\nInput\n\n1 1 3\n2 3 4\n2\n\n\nOutput\n\nYES\n\n\nInput\n\n1 0 0\n1 0 0\n1\n\n\nOutput\n\nNO\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\na1,a2,a3 = list(map(int,input().split()))\nb1,b2,b3 = list(map(int,input().split()))\nn = int(input())\ns1 = a1+a2+a3\ns2 = b1+b2+b3\ns3 = math.ceil(s1/5)+math.ceil(s2/10)\nif s3 <= n:\n print(\"YES\")\nelse :\n print(\"NO\")\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 0 0\\n1 0 0\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 3\\n2 3 4\\n2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n1 1 1\\n4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '100 100 100\\n100 100 100\\n100\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 10 10\\n0 0 0\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 2 3\\n2 4 6\\n3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0\\n0 0 0\\n1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2\\n2 4 4\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 3 5\\n2 3 5\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '21 61 39\\n63 58 69\\n44\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n0 0 0\\n1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 2 2\\n3 3 5\\n3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 6 6\\n11 11 11\\n7\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '18 95 4\\n7 1 75\\n46\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 10 100\\n100 10 1\\n20\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 0 0\\n15 0 0\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0\\n10 10 10\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 5 5\\n0 0 0\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 2 3\\n2 4 6\\n4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0\\n1 1 1\\n1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '64 27 81\\n72 35 23\\n48\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '99 99 99\\n99 99 99\\n89\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 2 3\\n1 5 5\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n1 1 1\\n15\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '100 100 100\\n100 100 100\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '100 100 100\\n101 100 100\\n100\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 10 10\\n0 1 0\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 2 1\\n2 4 6\\n3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0\\n1 0 0\\n1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2\\n2 4 1\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 3 3\\n2 3 5\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '21 61 39\\n63 58 111\\n44\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 2 2\\n3 5 5\\n3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 6 6\\n11 3 11\\n7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '18 95 4\\n7 1 130\\n46\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 10 110\\n100 10 1\\n20\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 0 0\\n15 0 0\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 1 0\\n10 10 10\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 0 3\\n2 4 6\\n4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '64 27 81\\n72 66 23\\n48\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '99 99 99\\n99 99 99\\n45\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 2 4\\n1 5 5\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n1 0 1\\n15\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '100 100 100\\n100 100 000\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 0 0\\n1 1 0\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 3\\n2 3 0\\n2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '0 1 1\\n1 1 1\\n4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '100 100 000\\n101 100 100\\n100\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 10 13\\n0 1 0\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 2 1\\n2 3 6\\n3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0\\n1 -1 0\\n1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2\\n3 4 1\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 3 3\\n2 3 5\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '21 61 39\\n63 58 110\\n44\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 2 2\\n2 5 5\\n3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 6 6\\n11 3 11\\n7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '18 95 2\\n7 1 130\\n46\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 10 110\\n100 0 1\\n20\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 0 -1\\n15 0 0\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 1 1\\n10 10 10\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 0 3\\n2 3 6\\n4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '64 27 142\\n72 66 23\\n48\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '99 99 99\\n20 99 99\\n45\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 2 4\\n1 10 5\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n1 0 1\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '100 100 000\\n100 100 000\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 0 -1\\n1 1 0\\n1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 1 3\\n2 3 -1\\n2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '0 1 1\\n1 1 1\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '000 100 000\\n101 100 100\\n100\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 0 13\\n0 1 0\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 2 1\\n2 5 6\\n3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0\\n0 -1 0\\n1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2\\n4 4 1\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 3 3\\n2 0 5\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '21 61 20\\n63 58 110\\n44\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 2 2\\n2 5 10\\n3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 6 6\\n11 3 11\\n7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '18 95 2\\n5 1 130\\n46\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 10 010\\n100 0 1\\n20\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 0 -1\\n15 0 0\\n0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 1 1\\n10 10 16\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 0 3\\n1 3 6\\n4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '64 27 142\\n72 74 23\\n48\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '99 99 75\\n20 99 99\\n45\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 4\\n1 10 5\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n0 0 1\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '101 100 000\\n100 100 000\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 0 -1\\n1 1 0\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 4\\n2 3 -1\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 1 1\\n1 1 0\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '000 101 000\\n101 100 100\\n100\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 0 13\\n0 1 0\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1\\n2 5 6\\n3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0\\n1 -1 -1\\n1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 0 2\\n4 4 1\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 3 3\\n2 0 5\\n4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '21 61 20\\n63 58 110\\n83\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 2 2\\n2 9 10\\n3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 6 10\\n11 3 11\\n7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '18 95 2\\n5 1 130\\n85\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 10 010\\n101 0 1\\n20\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 0 -1\\n15 0 1\\n0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1\\n10 10 16\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 0 3\\n1 3 6\\n6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '80 27 142\\n72 74 23\\n48\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '99 99 75\\n20 99 99\\n54\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 4\\n1 10 0\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 0\\n0 0 1\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '101 100 000\\n100 100 000\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 0 -1\\n1 1 0\\n2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 1 4\\n1 3 -1\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 1 1\\n1 1 -1\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '000 101 000\\n101 000 100\\n100\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 0 13\\n0 1 0\\n2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1\\n2 5 6\\n5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 0 2\\n8 4 1\\n1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 3 3\\n2 -1 5\\n4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '21 61 20\\n63 58 110\\n144\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 2 2\\n2 18 10\\n3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 6 3\\n11 3 11\\n7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '18 95 2\\n9 1 130\\n85\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '0 10 010\\n101 0 1\\n20\\n', 'output': 'YES\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77681","program":"```python\nimport math\na1,a2,a3 = list(map(int,input().split()))\nb1,b2,b3 = list(map(int,input().split()))\nn = int(input())\ns1 = a1+a2+a3\ns2 = b1+b2+b3\ns3 = math.ceil(s1/5)+math.ceil(s2/10)\nif s3 <= n:\n print(\"YES\")\nelse :\n print(\"NO\")\n```","inputs":"1 0 0\n1 0 0\n1\n","output":"NO\n","actual_output":"NO\n","execution_success":true,"sample_index":12397},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"46_B. T-shirts from Sponsor","prompt":"Solve the following coding problem using the programming language python:\n\nOne day a well-known sponsor of a well-known contest decided to give every participant of the contest a T-shirt as a present. A natural problem occurred: on the one hand, it is not clear how many T-shirts of what sizes should be ordered, and on the other hand, one doesn't want to order too many T-shirts (and we do not exactly paper the walls with the oversupply). After considerable brain racking and some pre-estimating, the sponsor representatives ordered a certain number of T-shirts of sizes S, M, L, XL and XXL. The T-shirts turned out to bring good luck, that's why on the contest day there built up a line of K participants willing to get one. Every contestant is characterized by his/her desired T-shirt size (so it happens that for all the participants it is also one of the sizes S, M, L, XL and XXL). The participants come up to get a T-shirt one by one and try to choose the most suitable one, choosing it like this. If there is still a T-shirt of the optimal size left, that he/she takes it without further ado. Otherwise the contestant would prefer to choose a T-shirt with the size as close to the optimal one as possible (the distance between neighboring sizes is considered equal to one). If the variant of choice is not unique, the contestant will take a T-shirt of a bigger size (in case he/she grows more). For example, for a person whose optimal size is L the preference list looks like this: L, XL, M, XXL, S. Using the data on how many T-shirts of every size had been ordered by the organizers, on the size of contestants in the line determine who got a T-shirt of what size.\n\nInput\n\nThe first line contains five non-negative integers NS, NM, NL, NXL, NXXL not exceeding 1000 which represent the number of T-shirts of the corresponding sizes. The second line contains an integer K (1 \u2264 K \u2264 1000) which represents the number of participants. The next K lines contain the optimal T-shirt sizes for the contestants. The sizes are given in the order in which the participants stand in the line. It is guaranteed that NS + NM + NL + NXL + NXXL \u2265 K.\n\nOutput\n\nFor each contestant, print a line containing the size of the T-shirt he/she got.\n\nExamples\n\nInput\n\n1 0 2 0 1\n3\nXL\nXXL\nM\n\n\nOutput\n\nXXL\nL\nL\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ni=input\ng=range\nl=list(map(int,i().split()))\nd={'S':0,'M':1,'L':2,'XL':3,'XXL':4}\nr={0:'S',1:'M',2:'L',3:'XL',4:'XXL'}\nn=int(i())\nfor x in g(n):\n s=i()\n if(l[d[s]]):\n l[d[s]]-=1\n res=s\n else:\n f=0\n for _ in g(5):\n if(d[s]+_<5 and l[d[s]+_]):\n f=_\n break\n elif(d[s]-_>-1 and l[d[s]-_]):\n f=-_\n break\n res=r[d[s]+f]\n l[d[s]+f]-=1\n print(res)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 0 2 0 1\\n3\\nXL\\nXXL\\nM\\n', 'output': 'XXL\\nL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '1 0 2 1 1\\n4\\nS\\nXXL\\nL\\nM\\n', 'output': 'S\\nXXL\\nL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '13 0 2 4 41\\n20\\nS\\nXXL\\nXXL\\nL\\nXXL\\nM\\nL\\nM\\nXXL\\nM\\nXXL\\nL\\nXXL\\nXL\\nM\\nXL\\nXL\\nL\\nL\\nM\\n', 'output': 'S\\nXXL\\nXXL\\nL\\nXXL\\nL\\nXL\\nS\\nXXL\\nS\\nXXL\\nXL\\nXXL\\nXL\\nS\\nXL\\nXXL\\nXXL\\nXXL\\nS\\n'}, {'type': 'stdin_stdout', 'input': '1 0 1 1 1\\n3\\nS\\nXXL\\nL\\n', 'output': 'S\\nXXL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '14 3 1 0 2\\n10\\nS\\nXL\\nM\\nXL\\nS\\nXXL\\nL\\nXXL\\nS\\nL\\n', 'output': 'S\\nXXL\\nM\\nXXL\\nS\\nL\\nM\\nM\\nS\\nS\\n'}, {'type': 'stdin_stdout', 'input': '3 1 1 4 1\\n10\\nXL\\nL\\nL\\nXXL\\nXXL\\nXL\\nL\\nXXL\\nS\\nM\\n', 'output': 'XL\\nL\\nXL\\nXXL\\nXL\\nXL\\nM\\nS\\nS\\nS\\n'}, {'type': 'stdin_stdout', 'input': '2 1 0 1 3\\n4\\nXL\\nM\\nS\\nS\\n', 'output': 'XL\\nM\\nS\\nS\\n'}, {'type': 'stdin_stdout', 'input': '44 314 100 272 270\\n10\\nXXL\\nXL\\nXXL\\nXXL\\nS\\nS\\nS\\nS\\nL\\nL\\n', 'output': 'XXL\\nXL\\nXXL\\nXXL\\nS\\nS\\nS\\nS\\nL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '2 22 11 9 6\\n20\\nXL\\nXXL\\nXL\\nL\\nXL\\nXXL\\nXXL\\nL\\nS\\nL\\nXXL\\nXL\\nXXL\\nXXL\\nL\\nM\\nL\\nS\\nS\\nXL\\n', 'output': 'XL\\nXXL\\nXL\\nL\\nXL\\nXXL\\nXXL\\nL\\nS\\nL\\nXXL\\nXL\\nXXL\\nXXL\\nL\\nM\\nL\\nS\\nM\\nXL\\n'}, {'type': 'stdin_stdout', 'input': '2 36 4 48 10\\n50\\nXXL\\nXXL\\nS\\nXXL\\nXL\\nXL\\nS\\nL\\nXXL\\nS\\nXL\\nXL\\nS\\nXXL\\nS\\nS\\nS\\nL\\nM\\nM\\nXXL\\nS\\nS\\nM\\nXXL\\nXL\\nL\\nS\\nM\\nXL\\nXL\\nS\\nXXL\\nM\\nL\\nXXL\\nXL\\nXXL\\nXXL\\nXL\\nL\\nL\\nXXL\\nXL\\nXXL\\nL\\nL\\nL\\nS\\nXL\\n', 'output': 'XXL\\nXXL\\nS\\nXXL\\nXL\\nXL\\nS\\nL\\nXXL\\nM\\nXL\\nXL\\nM\\nXXL\\nM\\nM\\nM\\nL\\nM\\nM\\nXXL\\nM\\nM\\nM\\nXXL\\nXL\\nL\\nM\\nM\\nXL\\nXL\\nM\\nXXL\\nM\\nL\\nXXL\\nXL\\nXXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nM\\nXL\\n'}, {'type': 'stdin_stdout', 'input': '450 65 82 309 94\\n50\\nM\\nXL\\nXL\\nXL\\nM\\nM\\nS\\nXL\\nXXL\\nXL\\nM\\nXL\\nS\\nXXL\\nS\\nXL\\nM\\nXL\\nM\\nS\\nS\\nM\\nXL\\nS\\nL\\nS\\nXL\\nXL\\nL\\nL\\nXL\\nXL\\nXL\\nXXL\\nXXL\\nL\\nXXL\\nM\\nXXL\\nM\\nXXL\\nXL\\nM\\nXL\\nL\\nS\\nXL\\nS\\nM\\nXXL\\n', 'output': 'M\\nXL\\nXL\\nXL\\nM\\nM\\nS\\nXL\\nXXL\\nXL\\nM\\nXL\\nS\\nXXL\\nS\\nXL\\nM\\nXL\\nM\\nS\\nS\\nM\\nXL\\nS\\nL\\nS\\nXL\\nXL\\nL\\nL\\nXL\\nXL\\nXL\\nXXL\\nXXL\\nL\\nXXL\\nM\\nXXL\\nM\\nXXL\\nXL\\nM\\nXL\\nL\\nS\\nXL\\nS\\nM\\nXXL\\n'}, {'type': 'stdin_stdout', 'input': '200 910 49 294 547\\n50\\nXXL\\nL\\nXXL\\nS\\nXL\\nXXL\\nL\\nXXL\\nM\\nM\\nM\\nM\\nXXL\\nS\\nXXL\\nXL\\nL\\nXXL\\nL\\nL\\nXL\\nXL\\nXL\\nXL\\nS\\nXL\\nL\\nXXL\\nM\\nXXL\\nS\\nXXL\\nS\\nXXL\\nS\\nS\\nL\\nS\\nL\\nXL\\nXXL\\nL\\nL\\nS\\nS\\nS\\nS\\nXXL\\nXL\\nXXL\\n', 'output': 'XXL\\nL\\nXXL\\nS\\nXL\\nXXL\\nL\\nXXL\\nM\\nM\\nM\\nM\\nXXL\\nS\\nXXL\\nXL\\nL\\nXXL\\nL\\nL\\nXL\\nXL\\nXL\\nXL\\nS\\nXL\\nL\\nXXL\\nM\\nXXL\\nS\\nXXL\\nS\\nXXL\\nS\\nS\\nL\\nS\\nL\\nXL\\nXXL\\nL\\nL\\nS\\nS\\nS\\nS\\nXXL\\nXL\\nXXL\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0 0 1\\n1\\nS\\n', 'output': 'XXL\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1 1 1\\n2\\nXL\\nM\\n', 'output': 'XL\\nM\\n'}, {'type': 'stdin_stdout', 'input': '302 143 40 63 452\\n100\\nXXL\\nM\\nXL\\nS\\nXXL\\nS\\nL\\nXL\\nXL\\nXL\\nXXL\\nS\\nXXL\\nS\\nXXL\\nXL\\nXL\\nXXL\\nXL\\nXXL\\nM\\nS\\nS\\nS\\nS\\nXXL\\nS\\nL\\nXL\\nXXL\\nXXL\\nS\\nXXL\\nL\\nXXL\\nM\\nS\\nL\\nL\\nXL\\nXL\\nS\\nXL\\nL\\nXL\\nM\\nXL\\nL\\nM\\nS\\nXL\\nXXL\\nXL\\nL\\nXL\\nXL\\nXL\\nM\\nM\\nXL\\nL\\nS\\nS\\nXL\\nS\\nXXL\\nXXL\\nXL\\nS\\nXL\\nXXL\\nS\\nS\\nL\\nL\\nXXL\\nXL\\nL\\nXL\\nM\\nS\\nM\\nM\\nXL\\nXXL\\nS\\nXL\\nXL\\nM\\nXL\\nXXL\\nXXL\\nXL\\nL\\nS\\nM\\nXXL\\nM\\nL\\nXXL\\n', 'output': 'XXL\\nM\\nXL\\nS\\nXXL\\nS\\nL\\nXL\\nXL\\nXL\\nXXL\\nS\\nXXL\\nS\\nXXL\\nXL\\nXL\\nXXL\\nXL\\nXXL\\nM\\nS\\nS\\nS\\nS\\nXXL\\nS\\nL\\nXL\\nXXL\\nXXL\\nS\\nXXL\\nL\\nXXL\\nM\\nS\\nL\\nL\\nXL\\nXL\\nS\\nXL\\nL\\nXL\\nM\\nXL\\nL\\nM\\nS\\nXL\\nXXL\\nXL\\nL\\nXL\\nXL\\nXL\\nM\\nM\\nXL\\nL\\nS\\nS\\nXL\\nS\\nXXL\\nXXL\\nXL\\nS\\nXL\\nXXL\\nS\\nS\\nL\\nL\\nXXL\\nXL\\nL\\nXL\\nM\\nS\\nM\\nM\\nXL\\nXXL\\nS\\nXL\\nXL\\nM\\nXL\\nXXL\\nXXL\\nXL\\nL\\nS\\nM\\nXXL\\nM\\nL\\nXXL\\n'}, {'type': 'stdin_stdout', 'input': '85 80 1 27 7\\n100\\nXXL\\nM\\nM\\nS\\nL\\nL\\nXL\\nM\\nXXL\\nXXL\\nXL\\nL\\nM\\nXL\\nM\\nXL\\nXL\\nS\\nM\\nS\\nXXL\\nXL\\nL\\nM\\nS\\nXL\\nS\\nXL\\nS\\nXL\\nS\\nM\\nXXL\\nL\\nM\\nXL\\nM\\nS\\nL\\nM\\nXXL\\nL\\nXXL\\nS\\nM\\nS\\nM\\nL\\nXXL\\nXXL\\nM\\nS\\nS\\nL\\nXXL\\nM\\nXXL\\nM\\nS\\nM\\nXXL\\nM\\nM\\nXL\\nXXL\\nL\\nXXL\\nXL\\nXXL\\nS\\nL\\nL\\nS\\nS\\nS\\nL\\nM\\nL\\nXXL\\nL\\nL\\nXXL\\nS\\nS\\nS\\nXL\\nXXL\\nXL\\nS\\nL\\nXXL\\nS\\nS\\nM\\nL\\nXXL\\nXL\\nXL\\nL\\nXXL\\n', 'output': 'XXL\\nM\\nM\\nS\\nL\\nXL\\nXL\\nM\\nXXL\\nXXL\\nXL\\nXL\\nM\\nXL\\nM\\nXL\\nXL\\nS\\nM\\nS\\nXXL\\nXL\\nXL\\nM\\nS\\nXL\\nS\\nXL\\nS\\nXL\\nS\\nM\\nXXL\\nXL\\nM\\nXL\\nM\\nS\\nXL\\nM\\nXXL\\nXL\\nXXL\\nS\\nM\\nS\\nM\\nXL\\nXL\\nXL\\nM\\nS\\nS\\nXL\\nXL\\nM\\nXL\\nM\\nS\\nM\\nXL\\nM\\nM\\nXL\\nXL\\nXL\\nXL\\nM\\nM\\nS\\nM\\nM\\nS\\nS\\nS\\nM\\nM\\nM\\nM\\nM\\nM\\nM\\nS\\nS\\nS\\nM\\nM\\nM\\nS\\nM\\nM\\nS\\nS\\nM\\nM\\nM\\nM\\nM\\nM\\nM\\n'}, {'type': 'stdin_stdout', 'input': '1 0 3 0 1\\n5\\nS\\nS\\nS\\nXL\\nL\\n', 'output': 'S\\nL\\nL\\nXXL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '1 0 0 0 1\\n2\\nS\\nL\\n', 'output': 'S\\nXXL\\n'}, {'type': 'stdin_stdout', 'input': '3 17 3 21 16\\n50\\nL\\nXL\\nXXL\\nM\\nXXL\\nXL\\nM\\nS\\nXL\\nXXL\\nXL\\nM\\nS\\nS\\nM\\nS\\nXXL\\nXXL\\nXL\\nM\\nL\\nS\\nXL\\nS\\nM\\nS\\nL\\nXL\\nM\\nXL\\nL\\nXL\\nXL\\nL\\nL\\nM\\nXL\\nS\\nXXL\\nL\\nL\\nM\\nL\\nS\\nM\\nL\\nXXL\\nXL\\nS\\nL\\n', 'output': 'L\\nXL\\nXXL\\nM\\nXXL\\nXL\\nM\\nS\\nXL\\nXXL\\nXL\\nM\\nS\\nS\\nM\\nM\\nXXL\\nXXL\\nXL\\nM\\nL\\nM\\nXL\\nM\\nM\\nM\\nL\\nXL\\nM\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nM\\nXL\\nM\\nXXL\\nXL\\nXL\\nM\\nXL\\nM\\nM\\nXL\\nXXL\\nXL\\nM\\nXL\\n'}, {'type': 'stdin_stdout', 'input': '5 7 2 9 7\\n30\\nS\\nM\\nS\\nXL\\nXXL\\nL\\nXL\\nL\\nL\\nXXL\\nS\\nM\\nXXL\\nXXL\\nS\\nL\\nXL\\nS\\nL\\nXXL\\nXXL\\nS\\nM\\nM\\nM\\nXXL\\nS\\nXXL\\nS\\nL\\n', 'output': 'S\\nM\\nS\\nXL\\nXXL\\nL\\nXL\\nL\\nXL\\nXXL\\nS\\nM\\nXXL\\nXXL\\nS\\nXL\\nXL\\nS\\nXL\\nXXL\\nXXL\\nM\\nM\\nM\\nM\\nXXL\\nM\\nXL\\nXL\\nXL\\n'}, {'type': 'stdin_stdout', 'input': '2 2 0 2 1\\n6\\nS\\nXXL\\nM\\nXL\\nXXL\\nXL\\n', 'output': 'S\\nXXL\\nM\\nXL\\nXL\\nM\\n'}, {'type': 'stdin_stdout', 'input': '1 0 1 0 1\\n1\\nS\\n', 'output': 'S\\n'}, {'type': 'stdin_stdout', 'input': '1 0 2 1 0\\n4\\nS\\nXXL\\nL\\nM\\n', 'output': 'S\\nXL\\nL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '13 0 2 4 41\\n20\\nS\\nXXL\\nXXL\\nM\\nXXL\\nM\\nL\\nM\\nXXL\\nM\\nXXL\\nL\\nXXL\\nXL\\nM\\nXL\\nXL\\nL\\nL\\nM\\n', 'output': 'S\\nXXL\\nXXL\\nL\\nXXL\\nL\\nXL\\nS\\nXXL\\nS\\nXXL\\nXL\\nXXL\\nXL\\nS\\nXL\\nXXL\\nXXL\\nXXL\\nS\\n'}, {'type': 'stdin_stdout', 'input': '14 2 1 0 2\\n10\\nS\\nXL\\nM\\nXL\\nS\\nXXL\\nL\\nXXL\\nS\\nL\\n', 'output': 'S\\nXXL\\nM\\nXXL\\nS\\nL\\nM\\nS\\nS\\nS\\n'}, {'type': 'stdin_stdout', 'input': '2 1 0 2 3\\n4\\nXL\\nM\\nS\\nS\\n', 'output': 'XL\\nM\\nS\\nS\\n'}, {'type': 'stdin_stdout', 'input': '200 910 49 294 547\\n50\\nXXL\\nL\\nXXL\\nS\\nXL\\nXXL\\nL\\nXXL\\nM\\nM\\nM\\nM\\nXXL\\nS\\nXXL\\nXL\\nL\\nXXL\\nL\\nL\\nXL\\nXL\\nXL\\nXL\\nS\\nXL\\nL\\nXXL\\nM\\nXXL\\nS\\nXXL\\nS\\nXXL\\nS\\nS\\nL\\nS\\nM\\nXL\\nXXL\\nL\\nL\\nS\\nS\\nS\\nS\\nXXL\\nXL\\nXXL\\n', 'output': 'XXL\\nL\\nXXL\\nS\\nXL\\nXXL\\nL\\nXXL\\nM\\nM\\nM\\nM\\nXXL\\nS\\nXXL\\nXL\\nL\\nXXL\\nL\\nL\\nXL\\nXL\\nXL\\nXL\\nS\\nXL\\nL\\nXXL\\nM\\nXXL\\nS\\nXXL\\nS\\nXXL\\nS\\nS\\nL\\nS\\nM\\nXL\\nXXL\\nL\\nL\\nS\\nS\\nS\\nS\\nXXL\\nXL\\nXXL\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0 0 2\\n1\\nS\\n', 'output': 'XXL\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1 2 1\\n2\\nXL\\nM\\n', 'output': 'XL\\nM\\n'}, {'type': 'stdin_stdout', 'input': '1 1 0 0 1\\n2\\nS\\nL\\n', 'output': 'S\\nM\\n'}, {'type': 'stdin_stdout', 'input': '2 2 0 3 1\\n6\\nS\\nXXL\\nM\\nXL\\nXXL\\nXL\\n', 'output': 'S\\nXXL\\nM\\nXL\\nXL\\nXL\\n'}, {'type': 'stdin_stdout', 'input': '2 0 2 0 1\\n3\\nXL\\nXXL\\nM\\n', 'output': 'XXL\\nL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '14 2 0 0 2\\n10\\nS\\nXL\\nM\\nXL\\nS\\nXXL\\nL\\nXXL\\nS\\nL\\n', 'output': 'S\\nXXL\\nM\\nXXL\\nS\\nM\\nS\\nS\\nS\\nS\\n'}, {'type': 'stdin_stdout', 'input': '2 2 0 1 1\\n6\\nS\\nXXL\\nM\\nXL\\nXXL\\nXL\\n', 'output': 'S\\nXXL\\nM\\nXL\\nM\\nS\\n'}, {'type': 'stdin_stdout', 'input': '1 0 4 1 1\\n4\\nS\\nXXL\\nL\\nM\\n', 'output': 'S\\nXXL\\nL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '13 0 3 4 41\\n20\\nS\\nXXL\\nXXL\\nL\\nXXL\\nM\\nL\\nM\\nXXL\\nM\\nXXL\\nL\\nXXL\\nXL\\nM\\nXL\\nXL\\nL\\nL\\nM\\n', 'output': 'S\\nXXL\\nXXL\\nL\\nXXL\\nL\\nL\\nS\\nXXL\\nS\\nXXL\\nXL\\nXXL\\nXL\\nS\\nXL\\nXL\\nXXL\\nXXL\\nS\\n'}, {'type': 'stdin_stdout', 'input': '14 3 0 0 2\\n10\\nS\\nXL\\nM\\nXL\\nS\\nXXL\\nL\\nXXL\\nS\\nL\\n', 'output': 'S\\nXXL\\nM\\nXXL\\nS\\nM\\nM\\nS\\nS\\nS\\n'}, {'type': 'stdin_stdout', 'input': '2 1 0 0 3\\n4\\nXL\\nM\\nS\\nS\\n', 'output': 'XXL\\nM\\nS\\nS\\n'}, {'type': 'stdin_stdout', 'input': '44 314 110 272 270\\n10\\nXXL\\nXL\\nXXL\\nXXL\\nS\\nS\\nS\\nS\\nL\\nL\\n', 'output': 'XXL\\nXL\\nXXL\\nXXL\\nS\\nS\\nS\\nS\\nL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '1 36 4 48 10\\n50\\nXXL\\nXXL\\nS\\nXXL\\nXL\\nXL\\nS\\nL\\nXXL\\nS\\nXL\\nXL\\nS\\nXXL\\nS\\nS\\nS\\nL\\nM\\nM\\nXXL\\nS\\nS\\nM\\nXXL\\nXL\\nL\\nS\\nM\\nXL\\nXL\\nS\\nXXL\\nM\\nL\\nXXL\\nXL\\nXXL\\nXXL\\nXL\\nL\\nL\\nXXL\\nXL\\nXXL\\nL\\nL\\nL\\nS\\nXL\\n', 'output': 'XXL\\nXXL\\nS\\nXXL\\nXL\\nXL\\nM\\nL\\nXXL\\nM\\nXL\\nXL\\nM\\nXXL\\nM\\nM\\nM\\nL\\nM\\nM\\nXXL\\nM\\nM\\nM\\nXXL\\nXL\\nL\\nM\\nM\\nXL\\nXL\\nM\\nXXL\\nM\\nL\\nXXL\\nXL\\nXXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nXL\\nM\\nXL\\n'}, {'type': 'stdin_stdout', 'input': '5 7 3 9 7\\n30\\nS\\nM\\nS\\nXL\\nXXL\\nL\\nXL\\nL\\nL\\nXXL\\nS\\nM\\nXXL\\nXXL\\nS\\nL\\nXL\\nS\\nL\\nXXL\\nXXL\\nS\\nM\\nM\\nM\\nXXL\\nS\\nXXL\\nS\\nL\\n', 'output': 'S\\nM\\nS\\nXL\\nXXL\\nL\\nXL\\nL\\nL\\nXXL\\nS\\nM\\nXXL\\nXXL\\nS\\nXL\\nXL\\nS\\nXL\\nXXL\\nXXL\\nM\\nM\\nM\\nM\\nXXL\\nM\\nXL\\nXL\\nXL\\n'}, {'type': 'stdin_stdout', 'input': '1 -1 1 0 1\\n1\\nS\\n', 'output': 'S\\n'}, {'type': 'stdin_stdout', 'input': '1 0 2 0 2\\n3\\nXL\\nXXL\\nM\\n', 'output': 'XXL\\nXXL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '1 0 1 2 2\\n2\\nXL\\nM\\n', 'output': 'XL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '0 1 0 0 1\\n1\\nS\\n', 'output': 'M\\n'}, {'type': 'stdin_stdout', 'input': '302 143 27 63 452\\n100\\nXXL\\nM\\nXL\\nS\\nXXL\\nS\\nL\\nXL\\nXL\\nXL\\nXXL\\nS\\nXXL\\nS\\nXXL\\nXL\\nXL\\nXXL\\nXL\\nXXL\\nM\\nS\\nS\\nS\\nS\\nXXL\\nS\\nL\\nXL\\nXXL\\nXXL\\nS\\nXXL\\nL\\nXXL\\nM\\nS\\nL\\nL\\nXL\\nXL\\nS\\nXL\\nL\\nXL\\nM\\nXL\\nL\\nM\\nS\\nXL\\nXXL\\nXL\\nL\\nXL\\nXL\\nXL\\nM\\nM\\nXL\\nL\\nS\\nS\\nXL\\nS\\nXXL\\nXXL\\nXL\\nS\\nXL\\nXXL\\nS\\nS\\nL\\nL\\nXXL\\nXL\\nL\\nXL\\nM\\nS\\nM\\nM\\nXL\\nXXL\\nS\\nXL\\nXL\\nM\\nXL\\nXXL\\nXXL\\nXL\\nL\\nS\\nM\\nXXL\\nM\\nL\\nXXL\\n', 'output': 'XXL\\nM\\nXL\\nS\\nXXL\\nS\\nL\\nXL\\nXL\\nXL\\nXXL\\nS\\nXXL\\nS\\nXXL\\nXL\\nXL\\nXXL\\nXL\\nXXL\\nM\\nS\\nS\\nS\\nS\\nXXL\\nS\\nL\\nXL\\nXXL\\nXXL\\nS\\nXXL\\nL\\nXXL\\nM\\nS\\nL\\nL\\nXL\\nXL\\nS\\nXL\\nL\\nXL\\nM\\nXL\\nL\\nM\\nS\\nXL\\nXXL\\nXL\\nL\\nXL\\nXL\\nXL\\nM\\nM\\nXL\\nL\\nS\\nS\\nXL\\nS\\nXXL\\nXXL\\nXL\\nS\\nXL\\nXXL\\nS\\nS\\nL\\nL\\nXXL\\nXL\\nL\\nXL\\nM\\nS\\nM\\nM\\nXL\\nXXL\\nS\\nXL\\nXL\\nM\\nXL\\nXXL\\nXXL\\nXL\\nL\\nS\\nM\\nXXL\\nM\\nL\\nXXL\\n'}, {'type': 'stdin_stdout', 'input': '1 0 0 0 1\\n2\\nS\\nM\\n', 'output': 'S\\nXXL\\n'}, {'type': 'stdin_stdout', 'input': '1 0 2 1 1\\n3\\nXL\\nXXL\\nM\\n', 'output': 'XL\\nXXL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '13 0 2 3 41\\n20\\nS\\nXXL\\nXXL\\nM\\nXXL\\nM\\nL\\nM\\nXXL\\nM\\nXXL\\nL\\nXXL\\nXL\\nM\\nXL\\nXL\\nL\\nL\\nM\\n', 'output': 'S\\nXXL\\nXXL\\nL\\nXXL\\nL\\nXL\\nS\\nXXL\\nS\\nXXL\\nXL\\nXXL\\nXL\\nS\\nXXL\\nXXL\\nXXL\\nXXL\\nS\\n'}, {'type': 'stdin_stdout', 'input': '2 1 2 2 0\\n4\\nS\\nXXL\\nL\\nM\\n', 'output': 'S\\nXL\\nL\\nM\\n'}, {'type': 'stdin_stdout', 'input': '14 5 0 0 2\\n10\\nS\\nXL\\nM\\nXL\\nS\\nXXL\\nL\\nXXL\\nS\\nL\\n', 'output': 'S\\nXXL\\nM\\nXXL\\nS\\nM\\nM\\nM\\nS\\nM\\n'}, {'type': 'stdin_stdout', 'input': '1 2 1 0 1\\n2\\nXL\\nM\\n', 'output': 'XXL\\nM\\n'}, {'type': 'stdin_stdout', 'input': '1 0 2 1 0\\n3\\nXL\\nXXL\\nM\\n', 'output': 'XL\\nL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '13 0 2 3 41\\n20\\nS\\nXXL\\nXXL\\nM\\nXXL\\nM\\nL\\nM\\nXXL\\nL\\nXXL\\nL\\nXXL\\nXL\\nM\\nXL\\nXL\\nL\\nL\\nM\\n', 'output': 'S\\nXXL\\nXXL\\nL\\nXXL\\nL\\nXL\\nS\\nXXL\\nXL\\nXXL\\nXL\\nXXL\\nXXL\\nS\\nXXL\\nXXL\\nXXL\\nXXL\\nS\\n'}, {'type': 'stdin_stdout', 'input': '13 0 2 3 41\\n20\\nS\\nXXL\\nXXL\\nM\\nXXL\\nM\\nL\\nL\\nXXL\\nL\\nXXL\\nL\\nXXL\\nXL\\nM\\nXL\\nXL\\nL\\nL\\nM\\n', 'output': 'S\\nXXL\\nXXL\\nL\\nXXL\\nL\\nXL\\nXL\\nXXL\\nXL\\nXXL\\nXXL\\nXXL\\nXXL\\nS\\nXXL\\nXXL\\nXXL\\nXXL\\nS\\n'}, {'type': 'stdin_stdout', 'input': '2 1 1 2 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'stdin_stdout', 'input': '14 10 0 0 2\\n10\\nS\\nXL\\nM\\nXL\\nS\\nXXL\\nL\\nXXL\\nS\\nL\\n', 'output': 'S\\nXXL\\nM\\nXXL\\nS\\nM\\nM\\nM\\nS\\nM\\n'}, {'type': 'stdin_stdout', 'input': '0 1 1 0 2\\n1\\nS\\n', 'output': 'M\\n'}, {'type': 'stdin_stdout', 'input': '0 0 1 1 1\\n2\\nXL\\nM\\n', 'output': 'XL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '6 -1 2 1 2\\n1\\nS\\n', 'output': 'S\\n'}, {'type': 'stdin_stdout', 'input': '2 -1 1 0 2\\n1\\nS\\n', 'output': 'S\\n'}, {'type': 'stdin_stdout', 'input': '2 -2 2 1 3\\n1\\nS\\n', 'output': 'S\\n'}, {'type': 'stdin_stdout', 'input': '1 1 0 0 2\\n1\\nS\\n', 'output': 'S\\n'}, {'type': 'stdin_stdout', 'input': '1 1 2 1 0\\n2\\nXL\\nL\\n', 'output': 'XL\\nL\\n'}, {'type': 'stdin_stdout', 'input': '2 0 2 1 0\\n3\\nXL\\nXXL\\nM\\n', 'output': 'XL\\nL\\nL\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77685","program":"```python\ni=input\ng=range\nl=list(map(int,i().split()))\nd={'S':0,'M':1,'L':2,'XL':3,'XXL':4}\nr={0:'S',1:'M',2:'L',3:'XL',4:'XXL'}\nn=int(i())\nfor x in g(n):\n s=i()\n if(l[d[s]]):\n l[d[s]]-=1\n res=s\n else:\n f=0\n for _ in g(5):\n if(d[s]+_<5 and l[d[s]+_]):\n f=_\n break\n elif(d[s]-_>-1 and l[d[s]-_]):\n f=-_\n break\n res=r[d[s]+f]\n l[d[s]+f]-=1\n print(res)\n```","inputs":"1 0 2 0 1\n3\nXL\nXXL\nM\n","output":"XXL\nL\nL\n","actual_output":"XXL\nL\nL\n","execution_success":true,"sample_index":12398},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"492_C. Vanya and Exams","prompt":"Solve the following coding problem using the programming language python:\n\nVanya wants to pass n exams and get the academic scholarship. He will get the scholarship if the average grade mark for all the exams is at least avg. The exam grade cannot exceed r. Vanya has passed the exams and got grade ai for the i-th exam. To increase the grade for the i-th exam by 1 point, Vanya must write bi essays. He can raise the exam grade multiple times.\n\nWhat is the minimum number of essays that Vanya needs to write to get scholarship?\n\nInput\n\nThe first line contains three integers n, r, avg (1 \u2264 n \u2264 105, 1 \u2264 r \u2264 109, 1 \u2264 avg \u2264 min(r, 106)) \u2014 the number of exams, the maximum grade and the required grade point average, respectively.\n\nEach of the following n lines contains space-separated integers ai and bi (1 \u2264 ai \u2264 r, 1 \u2264 bi \u2264 106).\n\nOutput\n\nIn the first line print the minimum number of essays.\n\nExamples\n\nInput\n\n5 5 4\n5 2\n4 7\n3 1\n3 2\n2 5\n\n\nOutput\n\n4\n\n\nInput\n\n2 5 4\n5 2\n5 2\n\n\nOutput\n\n0\n\nNote\n\nIn the first sample Vanya can write 2 essays for the 3rd exam to raise his grade by 2 points and 2 essays for the 4th exam to raise his grade by 1 point.\n\nIn the second sample, Vanya doesn't need to write any essays as his general point average already is above average.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n\"\"\"*There is no salvation without suffering*\"\"\"\n\"\"\"* Read the damn question carefully*\"\"\"\n\nn, r, avg = map(int, input().split())\nneeded = n * avg\ncurrent = 0\nammo = []\n\nfor i in range(n):\n a, b = map(int, input().split())\n current += a\n if a < r:\n ammo.append([b, r - a])\n\n\nneeded -= current\nwritten = 0\n\nif needed > 0:\n ammo.sort()\n\n while needed > 0:\n x = ammo[0][1]\n if needed >= x:\n written += ammo[0][0] * x\n needed -= x\n ammo.pop(0)\n\n elif 0 < needed <= x:\n written += ammo[0][0] * needed\n break\n\nprint(written)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 5 4\\n5 2\\n5 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 5 4\\n5 2\\n4 7\\n3 1\\n3 2\\n2 5\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1 1000000000 1000000\\n1 1000000\\n', 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8\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77689","program":"```python\n\"\"\"*There is no salvation without suffering*\"\"\"\n\"\"\"* Read the damn question carefully*\"\"\"\n\nn, r, avg = map(int, input().split())\nneeded = n * avg\ncurrent = 0\nammo = []\n\nfor i in range(n):\n a, b = map(int, input().split())\n current += a\n if a < r:\n ammo.append([b, r - a])\n\n\nneeded -= current\nwritten = 0\n\nif needed > 0:\n ammo.sort()\n\n while needed > 0:\n x = ammo[0][1]\n if needed >= x:\n written += ammo[0][0] * x\n needed -= x\n ammo.pop(0)\n\n elif 0 < needed <= x:\n written += ammo[0][0] * needed\n break\n\nprint(written)\n```","inputs":"2 5 4\n5 2\n5 2\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12399},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"543_B. Destroying Roads","prompt":"Solve the following coding problem using the programming language python:\n\nIn some country there are exactly n cities and m bidirectional roads connecting the cities. Cities are numbered with integers from 1 to n. If cities a and b are connected by a road, then in an hour you can go along this road either from city a to city b, or from city b to city a. The road network is such that from any city you can get to any other one by moving along the roads.\n\nYou want to destroy the largest possible number of roads in the country so that the remaining roads would allow you to get from city s1 to city t1 in at most l1 hours and get from city s2 to city t2 in at most l2 hours.\n\nDetermine what maximum number of roads you need to destroy in order to meet the condition of your plan. If it is impossible to reach the desired result, print -1.\n\nInput\n\nThe first line contains two integers n, m (1 \u2264 n \u2264 3000, ) \u2014 the number of cities and roads in the country, respectively. \n\nNext m lines contain the descriptions of the roads as pairs of integers ai, bi (1 \u2264 ai, bi \u2264 n, ai \u2260 bi). It is guaranteed that the roads that are given in the description can transport you from any city to any other one. It is guaranteed that each pair of cities has at most one road between them.\n\nThe last two lines contains three integers each, s1, t1, l1 and s2, t2, l2, respectively (1 \u2264 si, ti \u2264 n, 0 \u2264 li \u2264 n).\n\nOutput\n\nPrint a single number \u2014 the answer to the problem. If the it is impossible to meet the conditions, print -1.\n\nExamples\n\nInput\n\n5 4\n1 2\n2 3\n3 4\n4 5\n1 3 2\n3 5 2\n\n\nOutput\n\n0\n\n\nInput\n\n5 4\n1 2\n2 3\n3 4\n4 5\n1 3 2\n2 4 2\n\n\nOutput\n\n1\n\n\nInput\n\n5 4\n1 2\n2 3\n3 4\n4 5\n1 3 2\n3 5 1\n\n\nOutput\n\n-1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom itertools import combinations_with_replacement \nfrom collections import deque\n\n#sys.stdin = open(\"input_py.txt\",\"r\")\n\nn, m = map(int, input().split())\nG = [ [] for i in range(n)]\n\nfor i in range(m):\n x, y = map(int, input().split())\n x-=1; y-=1\n G[x].append(y)\n G[y].append(x)\n\ndef BFS(s):\n dist = [-1 for i in range(n)]\n dist[s] = 0\n Q = deque()\n Q.append(s)\n while len(Q) > 0:\n v = Q.popleft()\n for to in G[v]:\n if dist[to] < 0:\n dist[to] = dist[v] + 1\n Q.append(to)\n return dist \n\n\nDist = [BFS(i) for i in range(n)]\n\ns1, t1, l1 = map(int, input(). split())\ns2, t2, l2 = map(int, input(). split())\ns1-=1; t1-=1; s2-=1; t2-=1\nif Dist[s1][t1] > l1 or Dist[s2][t2] > l2:\n print(-1)\n exit(0)\n\nrest = Dist[s1][t1] + Dist[s2][t2]\n\nfor i in range(n):\n for j in range(n):\n if Dist[i][s1] + Dist[i][j] + Dist[j][t1] <= l1 and Dist[i][s2] + Dist[i][j] + Dist[j][t2] <= l2 :\n rest = min(rest, Dist[i][j] + Dist[i][s1] + Dist[i][s2] + Dist[j][t1] + Dist[j][t2])\n if Dist[i][s1] + Dist[i][j] + Dist[j][t1] <= l1 and Dist[j][s2] + Dist[i][j] + Dist[i][t2] <= l2 :\n rest = min(rest, Dist[i][j] + Dist[j][t1] + Dist[j][s2] + Dist[i][s1] + Dist[i][t2])\nprint(m-rest)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 4\\n1 2\\n2 3\\n3 4\\n4 5\\n1 3 2\\n3 5 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2\\n2 3\\n3 4\\n4 5\\n1 3 2\\n2 4 2\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2\\n2 3\\n3 4\\n4 5\\n1 3 2\\n3 5 2\\n', 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6\\n3 4\\n4 5\\n5 7\\n4 6\\n3 8\\n8 9\\n9 6\\n1 1 5\\n3 2 3\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n1 2\\n2 7\\n3 4\\n4 5\\n5 7\\n4 6\\n3 8\\n8 9\\n9 6\\n1 1 5\\n3 2 3\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n1 2\\n2 7\\n3 4\\n4 5\\n5 7\\n4 6\\n3 8\\n8 9\\n9 6\\n1 1 5\\n5 2 3\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n1 2\\n1 1 -1\\n1 2 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2\\n2 3\\n3 4\\n3 5\\n2 6\\n1 4 4\\n5 6 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n1 3\\n2 3\\n3 4\\n4 5\\n4 6\\n3 7\\n3 8\\n4 9\\n4 10\\n7 9\\n8 10\\n1 5 3\\n6 2 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n1 2\\n2 3\\n2 4\\n1 5\\n5 7\\n5 6\\n3 8\\n1 9\\n9 6\\n1 7 4\\n3 6 4\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2\\n2 3\\n3 4\\n3 5\\n2 6\\n1 4 3\\n5 4 10\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n1 2\\n1 6\\n2 4\\n4 5\\n5 7\\n5 6\\n3 8\\n8 9\\n9 6\\n1 1 4\\n3 6 3\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n1 3\\n2 3\\n3 4\\n4 5\\n4 6\\n3 7\\n3 10\\n4 9\\n4 1\\n7 9\\n8 10\\n1 1 3\\n6 2 3\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n1 2\\n2 6\\n2 4\\n4 5\\n5 7\\n5 6\\n3 8\\n8 9\\n9 6\\n1 1 7\\n3 6 6\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n1 2\\n2 3\\n2 4\\n4 5\\n5 7\\n5 6\\n4 8\\n8 5\\n9 6\\n1 7 4\\n3 6 3\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n1 3\\n2 3\\n2 4\\n8 5\\n3 6\\n3 7\\n3 8\\n4 9\\n4 10\\n7 9\\n8 10\\n1 1 3\\n6 2 3\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n1 4\\n2 6\\n2 4\\n3 5\\n5 7\\n5 1\\n3 8\\n8 9\\n9 9\\n1 1 7\\n4 2 3\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2\\n2 3\\n3 4\\n4 5\\n1 3 2\\n4 3 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n1 2\\n2 6\\n3 4\\n4 5\\n9 7\\n4 6\\n3 8\\n8 9\\n9 6\\n1 1 5\\n3 2 3\\n', 'output': '6\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77697","program":"```python\nfrom itertools import combinations_with_replacement \nfrom collections import deque\n\n#sys.stdin = open(\"input_py.txt\",\"r\")\n\nn, m = map(int, input().split())\nG = [ [] for i in range(n)]\n\nfor i in range(m):\n x, y = map(int, input().split())\n x-=1; y-=1\n G[x].append(y)\n G[y].append(x)\n\ndef BFS(s):\n dist = [-1 for i in range(n)]\n dist[s] = 0\n Q = deque()\n Q.append(s)\n while len(Q) > 0:\n v = Q.popleft()\n for to in G[v]:\n if dist[to] < 0:\n dist[to] = dist[v] + 1\n Q.append(to)\n return dist \n\n\nDist = [BFS(i) for i in range(n)]\n\ns1, t1, l1 = map(int, input(). split())\ns2, t2, l2 = map(int, input(). split())\ns1-=1; t1-=1; s2-=1; t2-=1\nif Dist[s1][t1] > l1 or Dist[s2][t2] > l2:\n print(-1)\n exit(0)\n\nrest = Dist[s1][t1] + Dist[s2][t2]\n\nfor i in range(n):\n for j in range(n):\n if Dist[i][s1] + Dist[i][j] + Dist[j][t1] <= l1 and Dist[i][s2] + Dist[i][j] + Dist[j][t2] <= l2 :\n rest = min(rest, Dist[i][j] + Dist[i][s1] + Dist[i][s2] + Dist[j][t1] + Dist[j][t2])\n if Dist[i][s1] + Dist[i][j] + Dist[j][t1] <= l1 and Dist[j][s2] + Dist[i][j] + Dist[i][t2] <= l2 :\n rest = min(rest, Dist[i][j] + Dist[j][t1] + Dist[j][s2] + Dist[i][s1] + Dist[i][t2])\nprint(m-rest)\n```","inputs":"5 4\n1 2\n2 3\n3 4\n4 5\n1 3 2\n3 5 1\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12400},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"56_D. Changing a String","prompt":"Solve the following coding problem using the programming language python:\n\nThere is a string s, consisting of capital Latin letters. Let's denote its current length as |s|. During one move it is allowed to apply one of the following operations to it: \n\n * INSERT pos ch \u2014 insert a letter ch in the string s in the position pos (1 \u2264 pos \u2264 |s| + 1, A \u2264 ch \u2264 Z). The letter ch becomes the pos-th symbol of the string s, at that the letters shift aside and the length of the string increases by 1. \n * DELETE pos \u2014 delete a character number pos (1 \u2264 pos \u2264 |s|) from the string s. At that the letters shift together and the length of the string decreases by 1. \n * REPLACE pos ch \u2014 the letter in the position pos of the line s is replaced by ch (1 \u2264 pos \u2264 |s|, A \u2264 ch \u2264 Z). At that the length of the string does not change. \n\n\n\nYour task is to find in which minimal number of moves one can get a t string from an s string. You should also find the sequence of actions leading to the required results.\n\nInput\n\nThe first line contains s, the second line contains t. The lines consist only of capital Latin letters, their lengths are positive numbers from 1 to 1000.\n\nOutput\n\nIn the first line print the number of moves k in the given sequence of operations. The number should be the minimal possible one. Then print k lines containing one operation each. Print the operations in the format, described above. If there are several solutions, print any of them.\n\nExamples\n\nInput\n\nABA\nABBBA\n\n\nOutput\n\n2\nINSERT 3 B\nINSERT 4 B\n\n\nInput\n\nACCEPTED\nWRONGANSWER\n\n\nOutput\n\n10\nREPLACE 1 W\nREPLACE 2 R\nREPLACE 3 O\nREPLACE 4 N\nREPLACE 5 G\nREPLACE 6 A\nINSERT 7 N\nINSERT 8 S\nINSERT 9 W\nREPLACE 11 R\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nfrom array import array # noqa: F401\n\n\ndef input():\n return sys.stdin.buffer.readline().decode('utf-8')\n\n\ns, t = input().rstrip(), input().rstrip()\nn, m = len(s), len(t)\n\ndp = [[10**9] * (m + 2) for _ in range(n + 2)]\ndp[n][m] = 0\nprev = [[(-1, -1)] * (m + 2) for _ in range(n + 2)]\n\nfor i in range(n, -1, -1):\n for j in range(m, -1, -1):\n if i < n and j < m and dp[i][j] > dp[i + 1][j + 1] + (0 if s[i] == t[j] else 1):\n dp[i][j] = dp[i + 1][j + 1] + (0 if s[i] == t[j] else 1)\n prev[i][j] = (i + 1, j + 1)\n if i < n and dp[i][j] > dp[i + 1][j] + 1:\n dp[i][j] = dp[i + 1][j] + 1\n prev[i][j] = (i + 1, j)\n if j < m and dp[i][j] > dp[i][j + 1] + 1:\n dp[i][j] = dp[i][j + 1] + 1\n prev[i][j] = (i, j + 1)\n\ni, j = 0, 0\nans = []\nwhile i < n or j < m:\n ti, tj = prev[i][j]\n if i + 1 == ti and j + 1 == tj:\n if s[i] != t[j]:\n ans.append(f'REPLACE {j+1} {t[j]}')\n elif i + 1 == ti:\n ans.append(f'DELETE {j+1}')\n elif j + 1 == tj:\n ans.append(f'INSERT {j+1} {t[j]}')\n i, j = ti, tj\n\n\nsys.stdout.buffer.write((str(len(ans)) + '\\n' + '\\n'.join(ans)).encode('utf-8'))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'ACCEPTED\\nWRONGANSWER\\n', 'output': '10\\nREPLACE 1 W\\nREPLACE 2 R\\nREPLACE 3 O\\nREPLACE 4 N\\nREPLACE 5 G\\nREPLACE 6 A\\nINSERT 7 N\\nINSERT 8 S\\nINSERT 9 W\\nREPLACE 11 R\\n'}, {'type': 'stdin_stdout', 'input': 'ABA\\nABBBA\\n', 'output': '2\\nINSERT 3 B\\nINSERT 4 B\\n'}, {'type': 'stdin_stdout', 'input': 'V\\nBNBNE\\n', 'output': '5\\nREPLACE 1 B\\nINSERT 2 N\\nINSERT 3 B\\nINSERT 4 N\\nINSERT 5 E\\n'}, {'type': 'stdin_stdout', 'input': 'JOYXNKYPF\\nGDV\\n', 'output': '9\\nDELETE 1\\nDELETE 1\\nDELETE 1\\nDELETE 1\\nDELETE 1\\nDELETE 1\\nREPLACE 1 G\\nREPLACE 2 D\\nREPLACE 3 V\\n'}, {'type': 'stdin_stdout', 'input': 'YWJJBIRAPVSKOZUBVXOEMSCFWLSGNDUUBAOGTFAIOWJIZLVJCUKUYCYSAAHVLGCUAXDGYKJQMNOIFUDWFOSAVKRMAKLEKMPPISHARHVGEWRKUADEQZCJUXDVRQIIGO\\nYWJJBIRAPVSKOZUBVXOEMSCFWLSGNDUUBAOGTFAIOWJIZLVJCUKUYCYSAAHVLGCUAXDGYKJQMNOIFUDWFOSAVKRMAKLEKMPISHARHVGEWRKUADEQZCJUXDVRQIIGO\\n', 'output': '1\\nDELETE 96\\n'}, {'type': 'stdin_stdout', 'input': 'SZDAWSVGK\\nUM\\n', 'output': '9\\nDELETE 1\\nDELETE 1\\nDELETE 1\\nDELETE 1\\nDELETE 1\\nDELETE 1\\nDELETE 1\\nREPLACE 1 U\\nREPLACE 2 M\\n'}, {'type': 'stdin_stdout', 'input': 'UB\\nPWL\\n', 'output': '3\\nREPLACE 1 P\\nREPLACE 2 W\\nINSERT 3 L\\n'}, {'type': 'stdin_stdout', 'input': 'TJHGFKKCDOHRNAXZROCWIYFF\\nZBWUEHEVEOUATECAGLZIQMUDXEMHRSOZMAUJRWLQMPPZOUMXHAMWUGEDIKVKBLVMXWUOFMPAFDPRBCFTEWOULCZWRQHCTBTBXRHHODWBCXWIMNCNEXOSKSUJLISGCLLLXOKRSBNOZTHAJNNLILYFFMSYKOFPTXRNEFBSOUHFOLTIQAINRPXWRQ\\n', 'output': '164\\nINSERT 1 Z\\nINSERT 2 B\\nINSERT 3 W\\nINSERT 4 U\\nINSERT 5 E\\nINSERT 6 H\\nINSERT 7 E\\nINSERT 8 V\\nINSERT 9 E\\nINSERT 10 O\\nINSERT 11 U\\nINSERT 12 A\\nINSERT 14 E\\nINSERT 15 C\\nINSERT 16 A\\nINSERT 17 G\\nINSERT 18 L\\nINSERT 19 Z\\nINSERT 20 I\\nINSERT 21 Q\\nINSERT 22 M\\nINSERT 23 U\\nINSERT 24 D\\nINSERT 25 X\\nINSERT 26 E\\nINSERT 27 M\\nINSERT 28 H\\nINSERT 29 R\\nINSERT 30 S\\nINSERT 31 O\\nINSERT 32 Z\\nINSERT 33 M\\nINSERT 34 A\\nINSERT 35 U\\nINSERT 37 R\\nINSERT 38 W\\nINSERT 39 L\\nINSERT 40 Q\\nINSERT 41 M\\nINSERT 42 P\\nINSERT 43 P\\nINSERT 44 Z\\nINSERT 45 O\\nINSERT 46 U\\nINSERT 47 M\\nINSERT 48 X\\nINSERT 50 A\\nINSERT 51 M\\nINSERT 52 W\\nINSERT 53 U\\nREPLACE 55 E\\nINSERT 56 D\\nINSERT 57 I\\nINSERT 59 V\\nREPLACE 61 B\\nINSERT 62 L\\nINSERT 63 V\\nINSERT 64 M\\nINSERT 65 X\\nINSERT 66 W\\nINSERT 67 U\\nINSERT 68 O\\nINSERT 69 F\\nINSERT 70 M\\nINSERT 71 P\\nINSERT 72 A\\nINSERT 73 F\\nINSERT 75 P\\nINSERT 76 R\\nINSERT 77 B\\nINSERT 78 C\\nINSERT 79 F\\nINSERT 80 T\\nINSERT 81 E\\nINSERT 82 W\\nINSERT 84 U\\nINSERT 85 L\\nINSERT 86 C\\nINSERT 87 Z\\nINSERT 88 W\\nINSERT 89 R\\nINSERT 90 Q\\nINSERT 92 C\\nINSERT 93 T\\nINSERT 94 B\\nINSERT 95 T\\nINSERT 96 B\\nINSERT 97 X\\nINSERT 99 H\\nINSERT 100 H\\nINSERT 101 O\\nINSERT 102 D\\nINSERT 103 W\\nINSERT 104 B\\nINSERT 105 C\\nINSERT 106 X\\nINSERT 107 W\\nINSERT 108 I\\nINSERT 109 M\\nREPLACE 111 C\\nINSERT 112 N\\nINSERT 113 E\\nREPLACE 115 O\\nINSERT 116 S\\nINSERT 117 K\\nINSERT 118 S\\nINSERT 119 U\\nINSERT 120 J\\nINSERT 121 L\\nINSERT 122 I\\nINSERT 123 S\\nINSERT 124 G\\nINSERT 125 C\\nINSERT 126 L\\nINSERT 127 L\\nINSERT 128 L\\nINSERT 129 X\\nINSERT 130 O\\nINSERT 131 K\\nINSERT 133 S\\nINSERT 134 B\\nINSERT 135 N\\nREPLACE 137 Z\\nREPLACE 138 T\\nINSERT 139 H\\nINSERT 140 A\\nINSERT 141 J\\nINSERT 142 N\\nINSERT 143 N\\nINSERT 144 L\\nINSERT 146 L\\nINSERT 150 M\\nINSERT 151 S\\nINSERT 152 Y\\nINSERT 153 K\\nINSERT 154 O\\nINSERT 155 F\\nINSERT 156 P\\nINSERT 157 T\\nINSERT 158 X\\nINSERT 159 R\\nINSERT 160 N\\nINSERT 161 E\\nINSERT 162 F\\nINSERT 163 B\\nINSERT 164 S\\nINSERT 165 O\\nINSERT 166 U\\nINSERT 167 H\\nINSERT 168 F\\nINSERT 169 O\\nINSERT 170 L\\nINSERT 171 T\\nINSERT 172 I\\nINSERT 173 Q\\nINSERT 174 A\\nINSERT 175 I\\nINSERT 176 N\\nINSERT 177 R\\nINSERT 178 P\\nINSERT 179 X\\nINSERT 180 W\\nINSERT 181 R\\nINSERT 182 Q\\n'}, {'type': 'stdin_stdout', 'input': 'BPYEOOTCVXAZPTHUEAIUZURZPHBWOEHGVHSDBYNXLHGOPBPCLPWQWVRYJGILKOOLASFSFYFGIMPVFGRRINJOXENOIMETWXUWCKXYBPBPPYRTMOZSBMBVJENPUSAEUPMQDGAQXUDIFUPOHYXPUWZLJP\\nYRWPQARABPMMBLUZJHDVOUODHRNLMOOVGVJIZDDLXEWCPUFYYPKCDDYGYOLTNHAVURLLEKNOLC\\n', 'output': '123\\nDELETE 1\\nDELETE 1\\nDELETE 2\\nREPLACE 2 R\\nREPLACE 3 W\\nREPLACE 4 P\\nREPLACE 5 Q\\nREPLACE 6 A\\nREPLACE 7 R\\nREPLACE 9 B\\nDELETE 11\\nDELETE 11\\nDELETE 11\\nDELETE 11\\nREPLACE 11 M\\nREPLACE 12 M\\nREPLACE 13 B\\nREPLACE 14 L\\nDELETE 16\\nREPLACE 17 J\\nREPLACE 19 D\\nREPLACE 20 V\\nDELETE 22\\nDELETE 22\\nDELETE 22\\nDELETE 22\\nREPLACE 22 U\\nREPLACE 23 O\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nREPLACE 27 N\\nREPLACE 29 M\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 33\\nDELETE 34\\nDELETE 34\\nDELETE 34\\nREPLACE 34 V\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nREPLACE 37 Z\\nREPLACE 38 D\\nREPLACE 39 D\\nREPLACE 40 L\\nREPLACE 42 E\\nDELETE 45\\nDELETE 45\\nDELETE 45\\nDELETE 45\\nDELETE 46\\nREPLACE 46 U\\nREPLACE 47 F\\nREPLACE 49 Y\\nREPLACE 50 P\\nREPLACE 51 K\\nREPLACE 52 C\\nREPLACE 53 D\\nREPLACE 54 D\\nREPLACE 55 Y\\nREPLACE 56 G\\nREPLACE 57 Y\\nREPLACE 58 O\\nREPLACE 59 L\\nREPLACE 60 T\\nDELETE 62\\nDELETE 62\\nREPLACE 62 H\\nREPLACE 64 V\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nREPLACE 66 R\\nREPLACE 67 L\\nREPLACE 68 L\\nREPLACE 69 E\\nREPLACE 70 K\\nREPLACE 71 N\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 74\\nREPLACE 74 C\\n'}, {'type': 'stdin_stdout', 'input': 'TJHGFKKCDOHRNAXZROCWIYFF\\nZBWUEHEVEOUATECAGLZIQMUDXEMHRSOZMAUJRWLQMPPZOUMXHAMWUGEDIKVKBLVMXWUOFMPAFDPRBCFTEWOULCZWRQHCTBTBXRHHODWBCXWIMNCNEXOSKSUJLISGCLLLXOKRSBNOZTHAJNNLILYFFMSYKOFPTXRNEFBSOUHFOLTIQAINRPXWRQ\\n', 'output': '164\\nINSERT 1 Z\\nINSERT 2 B\\nINSERT 3 W\\nINSERT 4 U\\nINSERT 5 E\\nINSERT 6 H\\nINSERT 7 E\\nINSERT 8 V\\nINSERT 9 E\\nINSERT 10 O\\nINSERT 11 U\\nINSERT 12 A\\nINSERT 14 E\\nINSERT 15 C\\nINSERT 16 A\\nINSERT 17 G\\nINSERT 18 L\\nINSERT 19 Z\\nINSERT 20 I\\nINSERT 21 Q\\nINSERT 22 M\\nINSERT 23 U\\nINSERT 24 D\\nINSERT 25 X\\nINSERT 26 E\\nINSERT 27 M\\nINSERT 28 H\\nINSERT 29 R\\nINSERT 30 S\\nINSERT 31 O\\nINSERT 32 Z\\nINSERT 33 M\\nINSERT 34 A\\nINSERT 35 U\\nINSERT 37 R\\nINSERT 38 W\\nINSERT 39 L\\nINSERT 40 Q\\nINSERT 41 M\\nINSERT 42 P\\nINSERT 43 P\\nINSERT 44 Z\\nINSERT 45 O\\nINSERT 46 U\\nINSERT 47 M\\nINSERT 48 X\\nINSERT 50 A\\nINSERT 51 M\\nINSERT 52 W\\nINSERT 53 U\\nREPLACE 55 E\\nINSERT 56 D\\nINSERT 57 I\\nINSERT 59 V\\nREPLACE 61 B\\nINSERT 62 L\\nINSERT 63 V\\nINSERT 64 M\\nINSERT 65 X\\nINSERT 66 W\\nINSERT 67 U\\nINSERT 68 O\\nINSERT 69 F\\nINSERT 70 M\\nINSERT 71 P\\nINSERT 72 A\\nINSERT 73 F\\nINSERT 75 P\\nINSERT 76 R\\nINSERT 77 B\\nINSERT 78 C\\nINSERT 79 F\\nINSERT 80 T\\nINSERT 81 E\\nINSERT 82 W\\nINSERT 84 U\\nINSERT 85 L\\nINSERT 86 C\\nINSERT 87 Z\\nINSERT 88 W\\nINSERT 89 R\\nINSERT 90 Q\\nINSERT 92 C\\nINSERT 93 T\\nINSERT 94 B\\nINSERT 95 T\\nINSERT 96 B\\nINSERT 97 X\\nINSERT 99 H\\nINSERT 100 H\\nINSERT 101 O\\nINSERT 102 D\\nINSERT 103 W\\nINSERT 104 B\\nINSERT 105 C\\nINSERT 106 X\\nINSERT 107 W\\nINSERT 108 I\\nINSERT 109 M\\nREPLACE 111 C\\nINSERT 112 N\\nINSERT 113 E\\nREPLACE 115 O\\nINSERT 116 S\\nINSERT 117 K\\nINSERT 118 S\\nINSERT 119 U\\nINSERT 120 J\\nINSERT 121 L\\nINSERT 122 I\\nINSERT 123 S\\nINSERT 124 G\\nINSERT 125 C\\nINSERT 126 L\\nINSERT 127 L\\nINSERT 128 L\\nINSERT 129 X\\nINSERT 130 O\\nINSERT 131 K\\nINSERT 133 S\\nINSERT 134 B\\nINSERT 135 N\\nREPLACE 137 Z\\nREPLACE 138 T\\nINSERT 139 H\\nINSERT 140 A\\nINSERT 141 J\\nINSERT 142 N\\nINSERT 143 N\\nINSERT 144 L\\nINSERT 146 L\\nINSERT 150 M\\nINSERT 151 S\\nINSERT 152 Y\\nINSERT 153 K\\nINSERT 154 O\\nINSERT 155 F\\nINSERT 156 P\\nINSERT 157 T\\nINSERT 158 X\\nINSERT 159 R\\nINSERT 160 N\\nINSERT 161 E\\nINSERT 162 F\\nINSERT 163 B\\nINSERT 164 S\\nINSERT 165 O\\nINSERT 166 U\\nINSERT 167 H\\nINSERT 168 F\\nINSERT 169 O\\nINSERT 170 L\\nINSERT 171 T\\nINSERT 172 I\\nINSERT 173 Q\\nINSERT 174 A\\nINSERT 175 I\\nINSERT 176 N\\nINSERT 177 R\\nINSERT 178 P\\nINSERT 179 X\\nINSERT 180 W\\nINSERT 181 R\\nINSERT 182 Q\\n'}, {'type': 'stdin_stdout', 'input': 'GXPLMUNZIRBHFJOOJHOMQNIKHVQSGFYSJLSWJQBUWYWHLQHLZYLPZWBOMPOLOLUGSBMHHLYGEIOUWDKPFIAAIRKYRLXTIFAZOPOLLPSNZHCIZDRTJPCYSCDTXBTMFSGEPRNOHJHNXZFYJPAMSHNOVZZYWCVEXLLOVHGAJBANAXVNTWCYTCUMQPEUUESQZTSDANIMUVJGDJCDLIAZKIAYAUQKPXRYKFRBVQJDRSUQZQZTIHWZDXQND\\nYTJUCSBGESVMVRIDTBJTMPVBCWWDWKBPEBVMGDXGIVLWQXVEETNSDXKTVJPXOPERWSGDPPMKNMWDIGEHFXNUQADIS\\n', 'output': '209\\nREPLACE 1 Y\\nREPLACE 2 T\\nREPLACE 3 J\\nDELETE 4\\nDELETE 4\\nREPLACE 5 C\\nREPLACE 6 S\\nDELETE 7\\nDELETE 7\\nREPLACE 8 G\\nREPLACE 9 E\\nREPLACE 10 S\\nREPLACE 11 V\\nDELETE 12\\nDELETE 12\\nDELETE 12\\nDELETE 12\\nREPLACE 13 V\\nREPLACE 14 R\\nREPLACE 16 D\\nREPLACE 17 T\\nREPLACE 18 B\\nDELETE 19\\nDELETE 19\\nDELETE 19\\nDELETE 19\\nDELETE 19\\nDELETE 19\\nREPLACE 20 T\\nREPLACE 21 M\\nREPLACE 22 P\\nREPLACE 23 V\\nDELETE 24\\nREPLACE 25 C\\nDELETE 27\\nREPLACE 28 D\\nREPLACE 29 W\\nREPLACE 30 K\\nREPLACE 31 B\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nREPLACE 33 E\\nDELETE 34\\nREPLACE 35 V\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nREPLACE 38 D\\nREPLACE 39 X\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 41\\nREPLACE 42 V\\nREPLACE 43 L\\nREPLACE 45 Q\\nREPLACE 46 X\\nREPLACE 47 V\\nREPLACE 48 E\\nREPLACE 49 E\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 53\\nDELETE 54\\nREPLACE 55 K\\nREPLACE 57 V\\nREPLACE 58 J\\nDELETE 59\\nDELETE 59\\nDELETE 59\\nREPLACE 60 X\\nDELETE 61\\nREPLACE 62 P\\nREPLACE 63 E\\nREPLACE 64 R\\nREPLACE 65 W\\nREPLACE 66 S\\nREPLACE 67 G\\nREPLACE 68 D\\nREPLACE 69 P\\nDELETE 70\\nDELETE 71\\nREPLACE 72 K\\nDELETE 73\\nREPLACE 74 M\\nREPLACE 75 W\\nREPLACE 76 D\\nREPLACE 77 I\\nREPLACE 78 G\\nDELETE 79\\nDELETE 79\\nDELETE 79\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nREPLACE 81 F\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 83\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 85\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\n'}, {'type': 'stdin_stdout', 'input': 'A\\nC\\n', 'output': '1\\nREPLACE 1 C\\n'}, {'type': 'stdin_stdout', 'input': 'BPYEOOTCVXAZPTHUEAIUZURZPHBWOEHGVHSDBYNXLHGOPBPCLPWQWVRYJGILKOOLASFSFYFGIMPVFGRRINJOXENOIMETWXUWCKXYBPBPPYRTMOZSBMBVJENPUSAEUPMQDGAQXUDIFUPOHYXPUWZLJP\\nYRWPQARABPMMBLUZJHDVOUODHRNLMOOVGVJIZDDLXEWCPUFYYPKCDDYGYOLTNHAVURLLEKNOLC\\n', 'output': '123\\nDELETE 1\\nDELETE 1\\nDELETE 2\\nREPLACE 2 R\\nREPLACE 3 W\\nREPLACE 4 P\\nREPLACE 5 Q\\nREPLACE 6 A\\nREPLACE 7 R\\nREPLACE 9 B\\nDELETE 11\\nDELETE 11\\nDELETE 11\\nDELETE 11\\nREPLACE 11 M\\nREPLACE 12 M\\nREPLACE 13 B\\nREPLACE 14 L\\nDELETE 16\\nREPLACE 17 J\\nREPLACE 19 D\\nREPLACE 20 V\\nDELETE 22\\nDELETE 22\\nDELETE 22\\nDELETE 22\\nREPLACE 22 U\\nREPLACE 23 O\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nREPLACE 27 N\\nREPLACE 29 M\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 33\\nDELETE 34\\nDELETE 34\\nDELETE 34\\nREPLACE 34 V\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nREPLACE 37 Z\\nREPLACE 38 D\\nREPLACE 39 D\\nREPLACE 40 L\\nREPLACE 42 E\\nDELETE 45\\nDELETE 45\\nDELETE 45\\nDELETE 45\\nDELETE 46\\nREPLACE 46 U\\nREPLACE 47 F\\nREPLACE 49 Y\\nREPLACE 50 P\\nREPLACE 51 K\\nREPLACE 52 C\\nREPLACE 53 D\\nREPLACE 54 D\\nREPLACE 55 Y\\nREPLACE 56 G\\nREPLACE 57 Y\\nREPLACE 58 O\\nREPLACE 59 L\\nREPLACE 60 T\\nDELETE 62\\nDELETE 62\\nREPLACE 62 H\\nREPLACE 64 V\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nDELETE 66\\nREPLACE 66 R\\nREPLACE 67 L\\nREPLACE 68 L\\nREPLACE 69 E\\nREPLACE 70 K\\nREPLACE 71 N\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 74\\nREPLACE 74 C\\n'}, {'type': 'stdin_stdout', 'input': 'Z\\nZ\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'V\\nBNBND\\n', 'output': '5\\nREPLACE 1 B\\nINSERT 2 N\\nINSERT 3 B\\nINSERT 4 N\\nINSERT 5 D\\n'}, {'type': 'stdin_stdout', 'input': 'JOYXNKYPF\\nGDU\\n', 'output': '9\\nREPLACE 1 G\\nREPLACE 2 D\\nREPLACE 3 U\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\n'}, {'type': 'stdin_stdout', 'input': 'YWJJBIRAPVSKOZUBVXOEMSCFWLSGNDUUBAXGTFAIOWJIZLVJCUKUYCYSAAHVLGCUAXDGYKJQMNOIFUDWFOSAVKRMAKLEKMPPISHARHVGEWRKUADEQZCJUODVRQIIGO\\nYWJJBIRAPVSKOZUBVXOEMSCFWLSGNDUUBAOGTFAIOWJIZLVJCUKUYCYSAAHVLGCUAXDGYKJQMNOIFUDWFOSAVKRMAKLEKMPISHARHVGEWRKUADEQZCJUXDVRQIIGO\\n', 'output': '3\\nREPLACE 35 O\\nDELETE 96\\nREPLACE 117 X\\n'}, {'type': 'stdin_stdout', 'input': 'SZDAWSVGK\\nMU\\n', 'output': '9\\nREPLACE 1 M\\nREPLACE 2 U\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\n'}, {'type': 'stdin_stdout', 'input': 'BU\\nPWL\\n', 'output': '3\\nREPLACE 1 P\\nREPLACE 2 W\\nINSERT 3 L\\n'}, {'type': 'stdin_stdout', 'input': 'TJHGFKKCDOHRNAXZROCWIYFF\\nZBWUEHEVEOUATECAGLZIQMUDXEMHRSOZMAUJRWLQNPPZOUMXHAMWUGEDIKVKBLVMXWUOFMPAFDPRBCFTEWOULCZWRQHCTBTBXRHHODWBCXWIMNCNEXOSKSUJLISGCLLLXOKRSBNOZTHAJNNLILYFFMSYKOFPTXRNEFBSOUHFOLTIQAINRPXWRQ\\n', 'output': '164\\nINSERT 1 Z\\nINSERT 2 B\\nINSERT 3 W\\nINSERT 4 U\\nINSERT 5 E\\nINSERT 6 H\\nINSERT 7 E\\nINSERT 8 V\\nINSERT 9 E\\nINSERT 10 O\\nINSERT 11 U\\nINSERT 12 A\\nINSERT 14 E\\nINSERT 15 C\\nINSERT 16 A\\nINSERT 17 G\\nINSERT 18 L\\nINSERT 19 Z\\nINSERT 20 I\\nINSERT 21 Q\\nINSERT 22 M\\nINSERT 23 U\\nINSERT 24 D\\nINSERT 25 X\\nINSERT 26 E\\nINSERT 27 M\\nINSERT 28 H\\nINSERT 29 R\\nINSERT 30 S\\nINSERT 31 O\\nINSERT 32 Z\\nINSERT 33 M\\nINSERT 34 A\\nINSERT 35 U\\nINSERT 37 R\\nINSERT 38 W\\nINSERT 39 L\\nINSERT 40 Q\\nINSERT 41 N\\nINSERT 42 P\\nINSERT 43 P\\nINSERT 44 Z\\nINSERT 45 O\\nINSERT 46 U\\nINSERT 47 M\\nINSERT 48 X\\nINSERT 50 A\\nINSERT 51 M\\nINSERT 52 W\\nINSERT 53 U\\nREPLACE 55 E\\nINSERT 56 D\\nINSERT 57 I\\nINSERT 59 V\\nREPLACE 61 B\\nINSERT 62 L\\nINSERT 63 V\\nINSERT 64 M\\nINSERT 65 X\\nINSERT 66 W\\nINSERT 67 U\\nINSERT 68 O\\nINSERT 69 F\\nINSERT 70 M\\nINSERT 71 P\\nINSERT 72 A\\nINSERT 73 F\\nINSERT 75 P\\nINSERT 76 R\\nINSERT 77 B\\nINSERT 78 C\\nINSERT 79 F\\nINSERT 80 T\\nINSERT 81 E\\nINSERT 82 W\\nINSERT 84 U\\nINSERT 85 L\\nINSERT 86 C\\nINSERT 87 Z\\nINSERT 88 W\\nINSERT 89 R\\nINSERT 90 Q\\nINSERT 92 C\\nINSERT 93 T\\nINSERT 94 B\\nINSERT 95 T\\nINSERT 96 B\\nINSERT 97 X\\nINSERT 99 H\\nINSERT 100 H\\nINSERT 101 O\\nINSERT 102 D\\nINSERT 103 W\\nINSERT 104 B\\nINSERT 105 C\\nINSERT 106 X\\nINSERT 107 W\\nINSERT 108 I\\nINSERT 109 M\\nREPLACE 111 C\\nINSERT 112 N\\nINSERT 113 E\\nREPLACE 115 O\\nINSERT 116 S\\nINSERT 117 K\\nINSERT 118 S\\nINSERT 119 U\\nINSERT 120 J\\nINSERT 121 L\\nINSERT 122 I\\nINSERT 123 S\\nINSERT 124 G\\nINSERT 125 C\\nINSERT 126 L\\nINSERT 127 L\\nINSERT 128 L\\nINSERT 129 X\\nINSERT 130 O\\nINSERT 131 K\\nINSERT 133 S\\nINSERT 134 B\\nINSERT 135 N\\nREPLACE 137 Z\\nREPLACE 138 T\\nINSERT 139 H\\nINSERT 140 A\\nINSERT 141 J\\nINSERT 142 N\\nINSERT 143 N\\nINSERT 144 L\\nINSERT 146 L\\nINSERT 150 M\\nINSERT 151 S\\nINSERT 152 Y\\nINSERT 153 K\\nINSERT 154 O\\nINSERT 155 F\\nINSERT 156 P\\nINSERT 157 T\\nINSERT 158 X\\nINSERT 159 R\\nINSERT 160 N\\nINSERT 161 E\\nINSERT 162 F\\nINSERT 163 B\\nINSERT 164 S\\nINSERT 165 O\\nINSERT 166 U\\nINSERT 167 H\\nINSERT 168 F\\nINSERT 169 O\\nINSERT 170 L\\nINSERT 171 T\\nINSERT 172 I\\nINSERT 173 Q\\nINSERT 174 A\\nINSERT 175 I\\nINSERT 176 N\\nINSERT 177 R\\nINSERT 178 P\\nINSERT 179 X\\nINSERT 180 W\\nINSERT 181 R\\nINSERT 182 Q\\n'}, {'type': 'stdin_stdout', 'input': 'BPYEOOTCVXAEPTHUEAIUZURZPHBWOEHGVHSDBYNXLHGOPBPCLPWQWVRYJGILKOOLASFSFYFGIMPVFGRRINJOXZNOIMETWXUWCKXYBPBPPYRTMOZSBMBVJENPUSAEUPMQDGAQXUDIFUPOHYXPUWZLJP\\nYRWPQARABPMMBLUZJHDVOUODHRNLMOOVGVJIZDDLXEWCPUFYYPKCDDYGYOLTNHAVURLLEKNOLC\\n', 'output': '123\\nDELETE 1\\nDELETE 1\\nREPLACE 2 R\\nREPLACE 3 W\\nREPLACE 4 P\\nREPLACE 5 Q\\nREPLACE 6 A\\nREPLACE 7 R\\nDELETE 8\\nREPLACE 9 B\\nREPLACE 11 M\\nREPLACE 12 M\\nREPLACE 13 B\\nREPLACE 14 L\\nDELETE 15\\nDELETE 15\\nREPLACE 17 J\\nDELETE 18\\nDELETE 18\\nDELETE 18\\nREPLACE 19 D\\nREPLACE 20 V\\nREPLACE 22 U\\nREPLACE 23 O\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nREPLACE 27 N\\nDELETE 28\\nDELETE 28\\nDELETE 28\\nREPLACE 29 M\\nREPLACE 32 V\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 34\\nDELETE 34\\nDELETE 34\\nREPLACE 35 J\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nREPLACE 38 D\\nREPLACE 39 D\\nREPLACE 40 L\\nREPLACE 41 X\\nREPLACE 43 W\\nREPLACE 44 C\\nREPLACE 45 P\\nREPLACE 47 F\\nREPLACE 48 Y\\nDELETE 49\\nDELETE 49\\nREPLACE 50 P\\nREPLACE 51 K\\nREPLACE 52 C\\nREPLACE 53 D\\nREPLACE 54 D\\nREPLACE 56 G\\nREPLACE 57 Y\\nDELETE 58\\nREPLACE 59 L\\nREPLACE 60 T\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nREPLACE 62 H\\nDELETE 63\\nDELETE 63\\nREPLACE 64 V\\nREPLACE 66 R\\nREPLACE 67 L\\nREPLACE 68 L\\nREPLACE 69 E\\nREPLACE 70 K\\nREPLACE 71 N\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nREPLACE 74 C\\nDELETE 75\\n'}, {'type': 'stdin_stdout', 'input': 'TJHGWKKCDOHRNAXZROCFIYFF\\nZBWUEHEVEOUATECAGLZIQMUDXEMHRSOZMAUJRWLQMPPZOUMXHAMWUGEDIKVKBLVMXWUOFMPAFDPRBCFTEWOULCZWRQHCTBTBXRHHODWBCXWIMNCNEXOSKSUJLISGCLLLXOKRSBNOZTHAJNNLILYFFMSYKOFPTXRNEFBSOUHFOLTIQAINRPXWRQ\\n', 'output': '164\\nINSERT 1 Z\\nINSERT 2 B\\nINSERT 3 W\\nINSERT 4 U\\nINSERT 5 E\\nINSERT 6 H\\nINSERT 7 E\\nINSERT 8 V\\nINSERT 9 E\\nINSERT 10 O\\nINSERT 11 U\\nINSERT 12 A\\nINSERT 14 E\\nINSERT 15 C\\nINSERT 16 A\\nINSERT 17 G\\nINSERT 18 L\\nINSERT 19 Z\\nINSERT 20 I\\nINSERT 21 Q\\nINSERT 22 M\\nINSERT 23 U\\nINSERT 24 D\\nINSERT 25 X\\nINSERT 26 E\\nINSERT 27 M\\nINSERT 28 H\\nINSERT 29 R\\nINSERT 30 S\\nINSERT 31 O\\nINSERT 32 Z\\nINSERT 33 M\\nINSERT 34 A\\nINSERT 35 U\\nINSERT 37 R\\nINSERT 38 W\\nINSERT 39 L\\nINSERT 40 Q\\nINSERT 41 M\\nINSERT 42 P\\nINSERT 43 P\\nINSERT 44 Z\\nINSERT 45 O\\nINSERT 46 U\\nINSERT 47 M\\nINSERT 48 X\\nREPLACE 50 A\\nINSERT 51 M\\nINSERT 53 U\\nINSERT 54 G\\nINSERT 55 E\\nINSERT 56 D\\nINSERT 57 I\\nINSERT 59 V\\nREPLACE 61 B\\nINSERT 62 L\\nINSERT 63 V\\nINSERT 64 M\\nINSERT 65 X\\nINSERT 66 W\\nINSERT 67 U\\nINSERT 68 O\\nINSERT 69 F\\nINSERT 70 M\\nINSERT 71 P\\nINSERT 72 A\\nINSERT 73 F\\nINSERT 75 P\\nINSERT 76 R\\nINSERT 77 B\\nINSERT 78 C\\nINSERT 79 F\\nINSERT 80 T\\nINSERT 81 E\\nINSERT 82 W\\nINSERT 84 U\\nINSERT 85 L\\nINSERT 86 C\\nINSERT 87 Z\\nINSERT 88 W\\nINSERT 89 R\\nINSERT 90 Q\\nINSERT 92 C\\nINSERT 93 T\\nINSERT 94 B\\nINSERT 95 T\\nINSERT 96 B\\nINSERT 97 X\\nINSERT 99 H\\nINSERT 100 H\\nINSERT 101 O\\nINSERT 102 D\\nINSERT 103 W\\nINSERT 104 B\\nINSERT 105 C\\nINSERT 106 X\\nINSERT 107 W\\nINSERT 108 I\\nINSERT 109 M\\nREPLACE 111 C\\nINSERT 112 N\\nINSERT 113 E\\nREPLACE 115 O\\nINSERT 116 S\\nINSERT 117 K\\nINSERT 118 S\\nINSERT 119 U\\nINSERT 120 J\\nINSERT 121 L\\nINSERT 122 I\\nINSERT 123 S\\nINSERT 124 G\\nINSERT 125 C\\nINSERT 126 L\\nINSERT 127 L\\nINSERT 128 L\\nINSERT 129 X\\nINSERT 130 O\\nINSERT 131 K\\nINSERT 133 S\\nINSERT 134 B\\nINSERT 135 N\\nREPLACE 137 Z\\nREPLACE 138 T\\nINSERT 139 H\\nINSERT 140 A\\nINSERT 141 J\\nINSERT 142 N\\nINSERT 143 N\\nINSERT 144 L\\nINSERT 146 L\\nINSERT 150 M\\nINSERT 151 S\\nINSERT 152 Y\\nINSERT 153 K\\nINSERT 154 O\\nINSERT 155 F\\nINSERT 156 P\\nINSERT 157 T\\nINSERT 158 X\\nINSERT 159 R\\nINSERT 160 N\\nINSERT 161 E\\nINSERT 162 F\\nINSERT 163 B\\nINSERT 164 S\\nINSERT 165 O\\nINSERT 166 U\\nINSERT 167 H\\nINSERT 168 F\\nINSERT 169 O\\nINSERT 170 L\\nINSERT 171 T\\nINSERT 172 I\\nINSERT 173 Q\\nINSERT 174 A\\nINSERT 175 I\\nINSERT 176 N\\nINSERT 177 R\\nINSERT 178 P\\nINSERT 179 X\\nINSERT 180 W\\nINSERT 181 R\\nINSERT 182 Q\\n'}, {'type': 'stdin_stdout', 'input': 'GXPLMUNZIRBHFJOOJHOMQNIKHVQSGFYSJLSWJQBUWYWHLQHLZYLPZWBOMPOLOLUGSBMHHLYGEIOUWDKPFIAAIRKYRLXTIFAZOPOLLPSNZHCIZDRTJPCYSCDTXBTMFSGEPRNOHJHNXZFYJPAMSHNOVZZYWCVEXLLOVHGAJBANAXVNTWCYTCUMQPEUUESQZTSDANIMUVJGDJCDLIAZKIAYAUQKPXRYKFRBVQJDRSUQZQZTIHWZDXQND\\nYTJUCSBGESVMVRIDTBJTMPVACWWDWKBPEBVMGDXGIVLWQXVEETNSDXKTVJPXOPERWSGDPPMKNMWDIGEHFXNUQADIS\\n', 'output': '210\\nREPLACE 1 Y\\nREPLACE 2 T\\nREPLACE 3 J\\nDELETE 4\\nDELETE 4\\nREPLACE 5 C\\nREPLACE 6 S\\nDELETE 7\\nDELETE 7\\nREPLACE 8 G\\nREPLACE 9 E\\nREPLACE 10 S\\nREPLACE 11 V\\nDELETE 12\\nDELETE 12\\nDELETE 12\\nDELETE 12\\nREPLACE 13 V\\nREPLACE 14 R\\nREPLACE 16 D\\nREPLACE 17 T\\nREPLACE 18 B\\nREPLACE 19 J\\nREPLACE 20 T\\nREPLACE 21 M\\nREPLACE 22 P\\nREPLACE 23 V\\nREPLACE 24 A\\nREPLACE 25 C\\nDELETE 26\\nDELETE 26\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nREPLACE 28 D\\nREPLACE 30 K\\nREPLACE 31 B\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nREPLACE 33 E\\nDELETE 34\\nREPLACE 35 V\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nREPLACE 38 D\\nREPLACE 39 X\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 41\\nREPLACE 42 V\\nREPLACE 43 L\\nREPLACE 45 Q\\nREPLACE 46 X\\nREPLACE 47 V\\nREPLACE 48 E\\nREPLACE 49 E\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 53\\nDELETE 54\\nREPLACE 55 K\\nREPLACE 57 V\\nREPLACE 58 J\\nDELETE 59\\nDELETE 59\\nDELETE 59\\nREPLACE 60 X\\nDELETE 61\\nREPLACE 62 P\\nREPLACE 63 E\\nREPLACE 64 R\\nREPLACE 65 W\\nREPLACE 66 S\\nREPLACE 67 G\\nREPLACE 68 D\\nREPLACE 69 P\\nDELETE 70\\nDELETE 71\\nREPLACE 72 K\\nDELETE 73\\nREPLACE 74 M\\nREPLACE 75 W\\nREPLACE 76 D\\nREPLACE 77 I\\nREPLACE 78 G\\nDELETE 79\\nDELETE 79\\nDELETE 79\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nREPLACE 81 F\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 83\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 85\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\n'}, {'type': 'stdin_stdout', 'input': 'B\\nC\\n', 'output': '1\\nREPLACE 1 C\\n'}, {'type': 'stdin_stdout', 'input': 'BPYEOOTCVXAZPTHUEAIUZTRZPHBWOEHGVHSDBYNXLHGOPBPCLPWQWVRYJGILKOOLASFSFYFGIMPVFGRRINJOXENOIMETWXUWCKXYBPBPPYRTMOZSBMBVJENPUSAEUPMQDGAQXUDIFUPOHYXPUWZLJP\\nYRWPQARABPMMBLUZJHDVOUODHRNLMOOVGVJIZDDLXEWCPUFYYPKCDDYGYOLTNHAVURLLEKNOLC\\n', 'output': '123\\nDELETE 1\\nDELETE 1\\nREPLACE 2 R\\nREPLACE 3 W\\nREPLACE 4 P\\nREPLACE 5 Q\\nREPLACE 6 A\\nREPLACE 7 R\\nDELETE 8\\nREPLACE 9 B\\nREPLACE 11 M\\nREPLACE 12 M\\nREPLACE 13 B\\nREPLACE 14 L\\nDELETE 15\\nDELETE 15\\nREPLACE 17 J\\nDELETE 18\\nDELETE 18\\nDELETE 18\\nREPLACE 19 D\\nREPLACE 20 V\\nREPLACE 22 U\\nREPLACE 23 O\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nREPLACE 27 N\\nDELETE 28\\nDELETE 28\\nDELETE 28\\nREPLACE 29 M\\nREPLACE 32 V\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 34\\nDELETE 34\\nDELETE 34\\nDELETE 35\\nDELETE 35\\nDELETE 35\\nDELETE 35\\nDELETE 35\\nDELETE 35\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nREPLACE 37 Z\\nREPLACE 38 D\\nREPLACE 39 D\\nREPLACE 40 L\\nREPLACE 42 E\\nREPLACE 45 P\\nREPLACE 46 U\\nINSERT 47 F\\nREPLACE 49 Y\\nREPLACE 51 K\\nREPLACE 52 C\\nREPLACE 53 D\\nREPLACE 54 D\\nREPLACE 55 Y\\nREPLACE 56 G\\nREPLACE 57 Y\\nREPLACE 59 L\\nREPLACE 60 T\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nREPLACE 62 H\\nDELETE 63\\nDELETE 63\\nREPLACE 64 V\\nREPLACE 66 R\\nREPLACE 67 L\\nREPLACE 68 L\\nREPLACE 69 E\\nREPLACE 70 K\\nREPLACE 71 N\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nREPLACE 74 C\\nDELETE 75\\n'}, {'type': 'stdin_stdout', 'input': 'Y\\nZ\\n', 'output': '1\\nREPLACE 1 Z\\n'}, {'type': 'stdin_stdout', 'input': 'DETPECCA\\nWRONGANSWER\\n', 'output': '11\\nREPLACE 1 W\\nREPLACE 2 R\\nREPLACE 3 O\\nREPLACE 4 N\\nREPLACE 5 G\\nREPLACE 6 A\\nREPLACE 7 N\\nREPLACE 8 S\\nINSERT 9 W\\nINSERT 10 E\\nINSERT 11 R\\n'}, {'type': 'stdin_stdout', 'input': 'AAA\\nABBBA\\n', 'output': '3\\nREPLACE 2 B\\nINSERT 3 B\\nINSERT 4 B\\n'}, {'type': 'stdin_stdout', 'input': 'YWJJBIRAPVSKOZUBVXOEMSCFWLSGNDUUBAXGTFAIOWJIZLVJCUKUYCYSAAHVLGCUAXDGYKJQMNOIFUDWFOSAVKRMAKLEKMPPISHARHVGEWRKUADEQZCJUODURQIIGO\\nYWJJBIRAPVSKOZUBVXOEMSCFWLSGNDUUBAOGTFAIOWJIZLVJCUKUYCYSAAHVLGCUAXDGYKJQMNOIFUDWFOSAVKRMAKLEKMPISHARHVGEWRKUADEQZCJUXDVRQIIGO\\n', 'output': '4\\nREPLACE 35 O\\nDELETE 96\\nREPLACE 117 X\\nREPLACE 119 V\\n'}, {'type': 'stdin_stdout', 'input': 'BU\\nWPL\\n', 'output': '3\\nREPLACE 1 W\\nREPLACE 2 P\\nINSERT 3 L\\n'}, {'type': 'stdin_stdout', 'input': 'TJHGFKKCDOHRNAYZROCWIYFF\\nZBWUEHEVEOUATECAGLZIQMUDXEMHRSOZMAUJRWLQNPPZOUMXHAMWUGEDIKVKBLVMXWUOFMPAFDPRBCFTEWOULCZWRQHCTBTBXRHHODWBCXWIMNCNEXOSKSUJLISGCLLLXOKRSBNOZTHAJNNLILYFFMSYKOFPTXRNEFBSOUHFOLTIQAINRPXWRQ\\n', 'output': '165\\nINSERT 1 Z\\nINSERT 2 B\\nINSERT 3 W\\nINSERT 4 U\\nINSERT 5 E\\nINSERT 6 H\\nINSERT 7 E\\nINSERT 8 V\\nINSERT 9 E\\nINSERT 10 O\\nINSERT 11 U\\nINSERT 12 A\\nINSERT 14 E\\nINSERT 15 C\\nINSERT 16 A\\nINSERT 17 G\\nINSERT 18 L\\nINSERT 19 Z\\nINSERT 20 I\\nINSERT 21 Q\\nINSERT 22 M\\nINSERT 23 U\\nINSERT 24 D\\nINSERT 25 X\\nINSERT 26 E\\nINSERT 27 M\\nINSERT 28 H\\nINSERT 29 R\\nINSERT 30 S\\nINSERT 31 O\\nINSERT 32 Z\\nINSERT 33 M\\nINSERT 34 A\\nINSERT 35 U\\nINSERT 37 R\\nINSERT 38 W\\nINSERT 39 L\\nINSERT 40 Q\\nINSERT 41 N\\nINSERT 42 P\\nINSERT 43 P\\nINSERT 44 Z\\nINSERT 45 O\\nINSERT 46 U\\nINSERT 47 M\\nINSERT 48 X\\nINSERT 50 A\\nINSERT 51 M\\nINSERT 52 W\\nINSERT 53 U\\nREPLACE 55 E\\nINSERT 56 D\\nINSERT 57 I\\nINSERT 59 V\\nREPLACE 61 B\\nREPLACE 62 L\\nINSERT 63 V\\nINSERT 64 M\\nINSERT 65 X\\nINSERT 66 W\\nINSERT 67 U\\nREPLACE 69 F\\nREPLACE 70 M\\nREPLACE 71 P\\nREPLACE 73 F\\nINSERT 74 D\\nINSERT 75 P\\nINSERT 76 R\\nINSERT 77 B\\nINSERT 78 C\\nINSERT 79 F\\nINSERT 80 T\\nINSERT 81 E\\nINSERT 82 W\\nINSERT 83 O\\nINSERT 84 U\\nINSERT 85 L\\nINSERT 86 C\\nINSERT 88 W\\nINSERT 90 Q\\nINSERT 91 H\\nINSERT 92 C\\nINSERT 93 T\\nINSERT 94 B\\nINSERT 95 T\\nINSERT 96 B\\nINSERT 97 X\\nINSERT 98 R\\nINSERT 99 H\\nINSERT 100 H\\nINSERT 102 D\\nINSERT 103 W\\nINSERT 104 B\\nINSERT 106 X\\nINSERT 109 M\\nINSERT 110 N\\nINSERT 111 C\\nINSERT 112 N\\nINSERT 113 E\\nINSERT 114 X\\nINSERT 115 O\\nINSERT 116 S\\nINSERT 117 K\\nINSERT 118 S\\nINSERT 119 U\\nINSERT 120 J\\nINSERT 121 L\\nINSERT 122 I\\nINSERT 123 S\\nINSERT 124 G\\nINSERT 125 C\\nINSERT 126 L\\nINSERT 127 L\\nINSERT 128 L\\nINSERT 129 X\\nINSERT 130 O\\nINSERT 131 K\\nINSERT 132 R\\nINSERT 133 S\\nINSERT 134 B\\nINSERT 135 N\\nINSERT 136 O\\nINSERT 137 Z\\nINSERT 138 T\\nINSERT 139 H\\nINSERT 140 A\\nINSERT 141 J\\nINSERT 142 N\\nINSERT 143 N\\nINSERT 144 L\\nINSERT 145 I\\nINSERT 146 L\\nINSERT 150 M\\nINSERT 151 S\\nINSERT 152 Y\\nINSERT 153 K\\nINSERT 154 O\\nINSERT 155 F\\nINSERT 156 P\\nINSERT 157 T\\nINSERT 158 X\\nINSERT 159 R\\nINSERT 160 N\\nINSERT 161 E\\nINSERT 162 F\\nINSERT 163 B\\nINSERT 164 S\\nINSERT 165 O\\nINSERT 166 U\\nINSERT 167 H\\nINSERT 168 F\\nINSERT 169 O\\nINSERT 170 L\\nINSERT 171 T\\nINSERT 172 I\\nINSERT 173 Q\\nINSERT 174 A\\nINSERT 175 I\\nINSERT 176 N\\nINSERT 177 R\\nINSERT 178 P\\nINSERT 179 X\\nINSERT 180 W\\nINSERT 181 R\\nINSERT 182 Q\\n'}, {'type': 'stdin_stdout', 'input': 'TJHGWKKCDOHRNAXZROCFIYFF\\nQRWXPRNIAQITLOFHUOSBFENRXTPFOKYSMFFYLILNNJAHTZONBSRKOXLLLCGSILJUSKSOXENCNMIWXCBWDOHHRXBTBTCHQRWZCLUOWETFCBRPDFAPMFOUWXMVLBKVKIDEGUWMAHXMUOZPPMQLWRJUAMZOSRHMEXDUMQIZLGACETAUOEVEHEUWBZ\\n', 'output': '166\\nINSERT 1 Q\\nINSERT 2 R\\nINSERT 3 W\\nINSERT 4 X\\nINSERT 5 P\\nINSERT 6 R\\nINSERT 7 N\\nINSERT 8 I\\nINSERT 9 A\\nINSERT 10 Q\\nINSERT 11 I\\nINSERT 13 L\\nINSERT 14 O\\nINSERT 15 F\\nINSERT 16 H\\nINSERT 17 U\\nINSERT 18 O\\nINSERT 19 S\\nINSERT 20 B\\nINSERT 21 F\\nINSERT 22 E\\nINSERT 23 N\\nINSERT 24 R\\nINSERT 25 X\\nINSERT 26 T\\nINSERT 27 P\\nINSERT 28 F\\nINSERT 29 O\\nINSERT 30 K\\nINSERT 31 Y\\nINSERT 32 S\\nINSERT 33 M\\nINSERT 34 F\\nINSERT 35 F\\nINSERT 36 Y\\nINSERT 37 L\\nINSERT 38 I\\nINSERT 39 L\\nINSERT 40 N\\nINSERT 41 N\\nINSERT 43 A\\nREPLACE 45 T\\nREPLACE 46 Z\\nINSERT 47 O\\nINSERT 48 N\\nINSERT 49 B\\nINSERT 50 S\\nINSERT 51 R\\nINSERT 53 O\\nINSERT 54 X\\nINSERT 55 L\\nINSERT 56 L\\nINSERT 57 L\\nINSERT 58 C\\nINSERT 59 G\\nINSERT 60 S\\nINSERT 61 I\\nINSERT 62 L\\nINSERT 63 J\\nINSERT 64 U\\nINSERT 65 S\\nINSERT 67 S\\nINSERT 68 O\\nINSERT 69 X\\nINSERT 70 E\\nINSERT 71 N\\nINSERT 73 N\\nINSERT 74 M\\nINSERT 75 I\\nINSERT 76 W\\nINSERT 77 X\\nINSERT 78 C\\nINSERT 79 B\\nINSERT 80 W\\nINSERT 84 H\\nREPLACE 86 X\\nINSERT 87 B\\nINSERT 88 T\\nINSERT 89 B\\nINSERT 90 T\\nINSERT 91 C\\nINSERT 92 H\\nINSERT 93 Q\\nINSERT 94 R\\nINSERT 95 W\\nINSERT 96 Z\\nINSERT 97 C\\nINSERT 98 L\\nINSERT 99 U\\nINSERT 100 O\\nINSERT 101 W\\nINSERT 102 E\\nINSERT 103 T\\nINSERT 104 F\\nINSERT 105 C\\nINSERT 106 B\\nINSERT 107 R\\nINSERT 108 P\\nINSERT 109 D\\nINSERT 110 F\\nINSERT 112 P\\nINSERT 113 M\\nINSERT 114 F\\nINSERT 115 O\\nINSERT 116 U\\nINSERT 117 W\\nINSERT 119 M\\nINSERT 120 V\\nINSERT 121 L\\nINSERT 122 B\\nINSERT 123 K\\nINSERT 124 V\\nINSERT 125 K\\nINSERT 126 I\\nINSERT 127 D\\nINSERT 128 E\\nINSERT 129 G\\nINSERT 130 U\\nINSERT 131 W\\nINSERT 132 M\\nINSERT 133 A\\nINSERT 134 H\\nINSERT 135 X\\nINSERT 136 M\\nINSERT 137 U\\nINSERT 138 O\\nINSERT 140 P\\nINSERT 141 P\\nINSERT 142 M\\nINSERT 143 Q\\nINSERT 144 L\\nINSERT 145 W\\nINSERT 147 J\\nINSERT 148 U\\nINSERT 149 A\\nINSERT 150 M\\nINSERT 151 Z\\nREPLACE 153 S\\nREPLACE 154 R\\nINSERT 155 H\\nINSERT 156 M\\nINSERT 157 E\\nINSERT 158 X\\nINSERT 159 D\\nINSERT 160 U\\nINSERT 161 M\\nINSERT 162 Q\\nREPLACE 164 Z\\nREPLACE 165 L\\nREPLACE 166 G\\nINSERT 167 A\\nINSERT 168 C\\nINSERT 169 E\\nINSERT 170 T\\nINSERT 171 A\\nINSERT 172 U\\nINSERT 173 O\\nINSERT 174 E\\nINSERT 175 V\\nINSERT 176 E\\nINSERT 177 H\\nINSERT 178 E\\nINSERT 179 U\\nINSERT 180 W\\nINSERT 181 B\\nINSERT 182 Z\\n'}, {'type': 'stdin_stdout', 'input': 'GXPLMUNZIRBHFJOOJHOMQNIKHVQSGFYSJLSWJQBUWYWHLQHLZYLPZWBOMPOLOLUGSBMHHLYGEIOUWDKPFIAAIRKYRLXTIFAZOPOLLPSNZHCIZDRTJPCYSCDTXBTMFSGEPRNOHJHNXZFYJPAMSHNOVZZYWCVEXLLOVHGAJBANAXVNTWCYTCUMQPEUUESQZTSDANIMUVJGDJCDLIAZKIAYAUQKPXRYKFRBVQJDRSUQZQZTIHWZDXQND\\nSIDAQUNXFHEGIDWMNKMPPDGSWREPOXPJVTKXDSNTEEVXQWLVIGXDGMVBEPBKWDWWCAVPMTJBTDIRVMVSEGBSCUJTY\\n', 'output': '209\\nREPLACE 1 S\\nREPLACE 2 I\\nREPLACE 3 D\\nREPLACE 4 A\\nREPLACE 5 Q\\nREPLACE 8 X\\nREPLACE 9 F\\nDELETE 10\\nDELETE 10\\nREPLACE 11 E\\nREPLACE 12 G\\nREPLACE 13 I\\nREPLACE 14 D\\nREPLACE 15 W\\nDELETE 16\\nDELETE 16\\nDELETE 17\\nDELETE 18\\nREPLACE 19 M\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nDELETE 21\\nDELETE 21\\nDELETE 21\\nDELETE 21\\nDELETE 21\\nREPLACE 22 D\\nDELETE 23\\nDELETE 23\\nDELETE 23\\nDELETE 23\\nREPLACE 25 W\\nREPLACE 26 R\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nREPLACE 28 P\\nREPLACE 30 X\\nDELETE 31\\nDELETE 31\\nDELETE 31\\nREPLACE 32 J\\nREPLACE 33 V\\nREPLACE 34 T\\nDELETE 35\\nDELETE 35\\nDELETE 35\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nREPLACE 37 D\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nREPLACE 41 E\\nREPLACE 42 E\\nREPLACE 43 V\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nREPLACE 45 Q\\nREPLACE 46 W\\nREPLACE 47 L\\nREPLACE 48 V\\nREPLACE 49 I\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nREPLACE 52 D\\nREPLACE 53 G\\nDELETE 54\\nDELETE 54\\nDELETE 54\\nDELETE 54\\nDELETE 55\\nDELETE 55\\nDELETE 55\\nDELETE 55\\nREPLACE 56 B\\nDELETE 57\\nDELETE 57\\nDELETE 57\\nDELETE 57\\nDELETE 57\\nREPLACE 58 P\\nDELETE 59\\nDELETE 59\\nDELETE 59\\nDELETE 59\\nDELETE 59\\nDELETE 59\\nDELETE 59\\nDELETE 59\\nREPLACE 60 K\\nREPLACE 61 W\\nREPLACE 62 D\\nREPLACE 63 W\\nDELETE 64\\nDELETE 64\\nDELETE 64\\nREPLACE 66 A\\nREPLACE 67 V\\nREPLACE 68 P\\nDELETE 69\\nREPLACE 70 T\\nREPLACE 71 J\\nREPLACE 72 B\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 74\\nREPLACE 75 I\\nREPLACE 76 R\\nREPLACE 77 V\\nREPLACE 79 V\\nREPLACE 80 S\\nREPLACE 81 E\\nREPLACE 83 B\\nREPLACE 84 S\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nREPLACE 89 Y\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\n'}, {'type': 'stdin_stdout', 'input': 'B\\nB\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'BPYEOOTCVXAZPTHUEAIUZTRZPHBWOEHGVHSDBYNXLHGOPBPCLPWQWVRYJGILKOOLASFSFYFGIMPVFGRRINJOXENOIMETWXUWCKXYBPBPPYRTMOZSBMBVJENPUSAEUPMQDGAQXUDIFUPOHYXPUWZLJP\\nYRWPQARABPMMBLUZJHDVOUODHRNLMOOVGVJIZDDLXEWCPUFYYPKCDDYGLOLTNHAVURLLEKNOYC\\n', 'output': '123\\nDELETE 1\\nDELETE 1\\nREPLACE 2 R\\nREPLACE 3 W\\nREPLACE 4 P\\nREPLACE 5 Q\\nREPLACE 6 A\\nREPLACE 7 R\\nDELETE 8\\nREPLACE 9 B\\nREPLACE 11 M\\nREPLACE 12 M\\nREPLACE 13 B\\nREPLACE 14 L\\nDELETE 15\\nDELETE 15\\nREPLACE 17 J\\nDELETE 18\\nDELETE 18\\nDELETE 18\\nREPLACE 19 D\\nREPLACE 20 V\\nREPLACE 22 U\\nREPLACE 23 O\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nREPLACE 27 N\\nDELETE 28\\nDELETE 28\\nDELETE 28\\nREPLACE 29 M\\nREPLACE 32 V\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 34\\nDELETE 34\\nDELETE 34\\nDELETE 35\\nDELETE 35\\nDELETE 35\\nDELETE 35\\nDELETE 35\\nDELETE 35\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nREPLACE 37 Z\\nREPLACE 38 D\\nREPLACE 39 D\\nREPLACE 40 L\\nREPLACE 42 E\\nREPLACE 45 P\\nREPLACE 46 U\\nINSERT 47 F\\nREPLACE 49 Y\\nREPLACE 51 K\\nREPLACE 52 C\\nREPLACE 53 D\\nREPLACE 54 D\\nREPLACE 55 Y\\nREPLACE 56 G\\nREPLACE 57 L\\nREPLACE 59 L\\nREPLACE 60 T\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nREPLACE 62 H\\nDELETE 63\\nDELETE 63\\nREPLACE 64 V\\nREPLACE 66 R\\nREPLACE 67 L\\nREPLACE 68 L\\nREPLACE 69 E\\nREPLACE 70 K\\nREPLACE 71 N\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 73\\nREPLACE 74 C\\nDELETE 75\\nDELETE 75\\nDELETE 75\\nDELETE 75\\nDELETE 75\\nDELETE 75\\nDELETE 75\\n'}, {'type': 'stdin_stdout', 'input': 'DETPECCA\\nWRONGANSXER\\n', 'output': '11\\nREPLACE 1 W\\nREPLACE 2 R\\nREPLACE 3 O\\nREPLACE 4 N\\nREPLACE 5 G\\nREPLACE 6 A\\nREPLACE 7 N\\nREPLACE 8 S\\nINSERT 9 X\\nINSERT 10 E\\nINSERT 11 R\\n'}, {'type': 'stdin_stdout', 'input': 'AAA\\nABABA\\n', 'output': '2\\nINSERT 2 B\\nINSERT 4 B\\n'}, {'type': 'stdin_stdout', 'input': 'W\\nBMBND\\n', 'output': '5\\nREPLACE 1 B\\nINSERT 2 M\\nINSERT 3 B\\nINSERT 4 N\\nINSERT 5 D\\n'}, {'type': 'stdin_stdout', 'input': 'OGIIQRUDOUJCZQEDAUKRWEGVHRAHSIPPMKELKAMRKVASOFWDUFIONMQJKYGDXAUCGLVHAASYCYUKUCJVLZIJWOIAFTGXABUUDNGSLWFCSMEOXVBUZOKSVPARIBJJWY\\nYWJJBIRAPVSKOZUBVXOEMSCFWLSGNDUUBAOGTFAIOWJIZLVJCUKUYCYSAAHVLGCUAXDGYKJQMNOIFUDWFOSAVKRMAKLEKMPISHARHVGEWRKUADEQZCJUXDVRQIIGO\\n', 'output': '111\\nREPLACE 1 Y\\nREPLACE 2 W\\nREPLACE 3 J\\nREPLACE 4 J\\nREPLACE 5 B\\nINSERT 6 I\\nREPLACE 8 A\\nREPLACE 9 P\\nREPLACE 10 V\\nREPLACE 11 S\\nREPLACE 12 K\\nREPLACE 13 O\\nREPLACE 15 U\\nREPLACE 16 B\\nREPLACE 17 V\\nREPLACE 18 X\\nREPLACE 19 O\\nDELETE 20\\nDELETE 20\\nDELETE 20\\nREPLACE 21 M\\nREPLACE 22 S\\nREPLACE 23 C\\nREPLACE 24 F\\nREPLACE 25 W\\nREPLACE 26 L\\nREPLACE 28 G\\nREPLACE 29 N\\nREPLACE 30 D\\nREPLACE 31 U\\nREPLACE 32 U\\nREPLACE 33 B\\nDELETE 34\\nDELETE 34\\nREPLACE 35 O\\nREPLACE 36 G\\nREPLACE 37 T\\nREPLACE 38 F\\nREPLACE 40 I\\nDELETE 42\\nREPLACE 43 J\\nREPLACE 44 I\\nREPLACE 45 Z\\nREPLACE 46 L\\nREPLACE 47 V\\nREPLACE 48 J\\nREPLACE 49 C\\nREPLACE 50 U\\nREPLACE 51 K\\nREPLACE 52 U\\nREPLACE 54 C\\nREPLACE 55 Y\\nREPLACE 56 S\\nREPLACE 58 A\\nREPLACE 59 H\\nREPLACE 60 V\\nREPLACE 62 G\\nREPLACE 63 C\\nREPLACE 64 U\\nREPLACE 66 X\\nREPLACE 67 D\\nREPLACE 68 G\\nREPLACE 70 K\\nREPLACE 71 J\\nREPLACE 72 Q\\nREPLACE 73 M\\nREPLACE 74 N\\nREPLACE 75 O\\nREPLACE 76 I\\nREPLACE 77 F\\nREPLACE 78 U\\nREPLACE 79 D\\nINSERT 81 F\\nREPLACE 83 S\\nREPLACE 85 V\\nREPLACE 86 K\\nREPLACE 87 R\\nREPLACE 88 M\\nREPLACE 90 K\\nREPLACE 91 L\\nREPLACE 92 E\\nREPLACE 93 K\\nREPLACE 94 M\\nREPLACE 95 P\\nINSERT 96 I\\nREPLACE 98 H\\nREPLACE 99 A\\nREPLACE 100 R\\nREPLACE 101 H\\nREPLACE 102 V\\nREPLACE 103 G\\nREPLACE 105 W\\nREPLACE 106 R\\nREPLACE 107 K\\nREPLACE 108 U\\nREPLACE 109 A\\nINSERT 110 D\\nINSERT 111 E\\nINSERT 112 Q\\nREPLACE 114 C\\nREPLACE 115 J\\nREPLACE 116 U\\nREPLACE 117 X\\nREPLACE 118 D\\nREPLACE 119 V\\nREPLACE 121 Q\\nREPLACE 122 I\\nREPLACE 123 I\\nREPLACE 124 G\\nREPLACE 125 O\\nDELETE 126\\n'}, {'type': 'stdin_stdout', 'input': 'SZDAVSVGK\\nLU\\n', 'output': '9\\nREPLACE 1 L\\nREPLACE 2 U\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\n'}, {'type': 'stdin_stdout', 'input': 'TJHGFKKCDOHRNAYZROCWIYFF\\nZYWUEHEVEOUATECAGLZIQMUDXEMHRSOZMAUJRWLQNPPZOUMXHAMWUGEDIKVKBLVMXWUOFMPAFDPRBCFTEWOULCZWRQHCTBTBXRHHODWBCXWIMNCNEXOSKSUJLISGCLLLXOKRSBNOZTHAJNNLILYFFMSBKOFPTXRNEFBSOUHFOLTIQAINRPXWRQ\\n', 'output': '165\\nINSERT 1 Z\\nINSERT 2 Y\\nINSERT 3 W\\nINSERT 4 U\\nINSERT 5 E\\nINSERT 6 H\\nINSERT 7 E\\nINSERT 8 V\\nINSERT 9 E\\nINSERT 10 O\\nINSERT 11 U\\nINSERT 12 A\\nINSERT 14 E\\nINSERT 15 C\\nINSERT 16 A\\nINSERT 17 G\\nINSERT 18 L\\nINSERT 19 Z\\nINSERT 20 I\\nINSERT 21 Q\\nINSERT 22 M\\nINSERT 23 U\\nINSERT 24 D\\nINSERT 25 X\\nINSERT 26 E\\nINSERT 27 M\\nINSERT 28 H\\nINSERT 29 R\\nINSERT 30 S\\nINSERT 31 O\\nINSERT 32 Z\\nINSERT 33 M\\nINSERT 34 A\\nINSERT 35 U\\nINSERT 37 R\\nINSERT 38 W\\nINSERT 39 L\\nINSERT 40 Q\\nINSERT 41 N\\nINSERT 42 P\\nINSERT 43 P\\nINSERT 44 Z\\nINSERT 45 O\\nINSERT 46 U\\nINSERT 47 M\\nINSERT 48 X\\nINSERT 50 A\\nINSERT 51 M\\nINSERT 52 W\\nINSERT 53 U\\nREPLACE 55 E\\nINSERT 56 D\\nINSERT 57 I\\nINSERT 59 V\\nREPLACE 61 B\\nREPLACE 62 L\\nINSERT 63 V\\nINSERT 64 M\\nINSERT 65 X\\nINSERT 66 W\\nINSERT 67 U\\nREPLACE 69 F\\nREPLACE 70 M\\nREPLACE 71 P\\nREPLACE 73 F\\nINSERT 74 D\\nINSERT 75 P\\nINSERT 76 R\\nINSERT 77 B\\nINSERT 78 C\\nINSERT 79 F\\nINSERT 80 T\\nINSERT 81 E\\nINSERT 82 W\\nINSERT 83 O\\nINSERT 84 U\\nINSERT 85 L\\nINSERT 86 C\\nINSERT 88 W\\nINSERT 90 Q\\nINSERT 91 H\\nINSERT 92 C\\nINSERT 93 T\\nINSERT 94 B\\nINSERT 95 T\\nINSERT 96 B\\nINSERT 97 X\\nINSERT 98 R\\nINSERT 99 H\\nINSERT 100 H\\nINSERT 102 D\\nINSERT 103 W\\nINSERT 104 B\\nINSERT 106 X\\nINSERT 109 M\\nINSERT 110 N\\nINSERT 111 C\\nINSERT 112 N\\nINSERT 113 E\\nINSERT 114 X\\nINSERT 115 O\\nINSERT 116 S\\nINSERT 117 K\\nINSERT 118 S\\nINSERT 119 U\\nINSERT 120 J\\nINSERT 121 L\\nINSERT 122 I\\nINSERT 123 S\\nINSERT 124 G\\nINSERT 125 C\\nINSERT 126 L\\nINSERT 127 L\\nINSERT 128 L\\nINSERT 129 X\\nINSERT 130 O\\nINSERT 131 K\\nINSERT 132 R\\nINSERT 133 S\\nINSERT 134 B\\nINSERT 135 N\\nINSERT 136 O\\nINSERT 137 Z\\nINSERT 138 T\\nINSERT 139 H\\nINSERT 140 A\\nINSERT 141 J\\nINSERT 142 N\\nINSERT 143 N\\nINSERT 144 L\\nINSERT 145 I\\nINSERT 146 L\\nINSERT 150 M\\nINSERT 151 S\\nINSERT 152 B\\nINSERT 153 K\\nINSERT 154 O\\nINSERT 155 F\\nINSERT 156 P\\nINSERT 157 T\\nINSERT 158 X\\nINSERT 159 R\\nINSERT 160 N\\nINSERT 161 E\\nINSERT 162 F\\nINSERT 163 B\\nINSERT 164 S\\nINSERT 165 O\\nINSERT 166 U\\nINSERT 167 H\\nINSERT 168 F\\nINSERT 169 O\\nINSERT 170 L\\nINSERT 171 T\\nINSERT 172 I\\nINSERT 173 Q\\nINSERT 174 A\\nINSERT 175 I\\nINSERT 176 N\\nINSERT 177 R\\nINSERT 178 P\\nINSERT 179 X\\nINSERT 180 W\\nINSERT 181 R\\nINSERT 182 Q\\n'}, {'type': 'stdin_stdout', 'input': 'BPYEOOTCVXAEPTHUEAIUZUOZPHBWOEHGVHSDBYNXLHGOPBPCLPWQWVRYJGILKOOLASFSFYFGIMPVFGRRINJRXZNOIMETWXUWCKXYBPBPPYRTMOZSBMBVJENPUSAEUPMQDGAQXUDIFUPOHYXPUWZLJP\\nYRWPQARABPMMBLUZJHDVOUODHRNLMOOVGVJIZDDLXEWCPUFYYPKCDDYGYOLSNHAVURLLEKNOLC\\n', 'output': '122\\nDELETE 1\\nDELETE 1\\nREPLACE 2 R\\nREPLACE 3 W\\nREPLACE 4 P\\nREPLACE 5 Q\\nREPLACE 6 A\\nREPLACE 7 R\\nDELETE 8\\nREPLACE 9 B\\nREPLACE 11 M\\nREPLACE 12 M\\nREPLACE 13 B\\nREPLACE 14 L\\nDELETE 15\\nDELETE 15\\nREPLACE 17 J\\nDELETE 18\\nDELETE 18\\nDELETE 18\\nREPLACE 19 D\\nREPLACE 20 V\\nREPLACE 22 U\\nREPLACE 23 O\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nREPLACE 27 N\\nDELETE 28\\nDELETE 28\\nDELETE 28\\nREPLACE 29 M\\nREPLACE 32 V\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 34\\nDELETE 34\\nDELETE 34\\nREPLACE 35 J\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nREPLACE 38 D\\nREPLACE 39 D\\nREPLACE 40 L\\nREPLACE 41 X\\nREPLACE 43 W\\nREPLACE 44 C\\nREPLACE 45 P\\nREPLACE 47 F\\nREPLACE 48 Y\\nDELETE 49\\nDELETE 49\\nREPLACE 50 P\\nREPLACE 51 K\\nREPLACE 52 C\\nREPLACE 53 D\\nREPLACE 54 D\\nREPLACE 56 G\\nREPLACE 57 Y\\nDELETE 58\\nREPLACE 59 L\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nREPLACE 62 H\\nDELETE 63\\nDELETE 63\\nREPLACE 64 V\\nREPLACE 66 R\\nREPLACE 67 L\\nREPLACE 68 L\\nREPLACE 69 E\\nREPLACE 70 K\\nREPLACE 71 N\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nREPLACE 74 C\\nDELETE 75\\n'}, {'type': 'stdin_stdout', 'input': 'TJHGWKKCDOHRNAXZRNCFIYFF\\nQRWXPRNIAQITLOFHUOSBFENRXTPFOKYSMFFYLILNNJAHTZONBSRKOXLLLCGSILJUSKSOXENCNMIWXCBWDOHHRXBTBTCHQRWZCLUOWETFCBRPDFAPMFOUWXMVLBKVKIDEGUWMAHXMUOZPPMQLWRJUAMZOSRHMEXDUMQIZLGACETAUOEVEHEUWBZ\\n', 'output': '167\\nINSERT 1 Q\\nINSERT 2 R\\nINSERT 3 W\\nINSERT 4 X\\nINSERT 5 P\\nINSERT 6 R\\nINSERT 7 N\\nINSERT 8 I\\nINSERT 9 A\\nINSERT 10 Q\\nINSERT 11 I\\nINSERT 13 L\\nINSERT 14 O\\nINSERT 15 F\\nINSERT 16 H\\nINSERT 17 U\\nINSERT 18 O\\nINSERT 19 S\\nINSERT 20 B\\nINSERT 21 F\\nINSERT 22 E\\nINSERT 23 N\\nINSERT 24 R\\nINSERT 25 X\\nINSERT 26 T\\nINSERT 27 P\\nINSERT 28 F\\nINSERT 29 O\\nINSERT 30 K\\nINSERT 31 Y\\nINSERT 32 S\\nINSERT 33 M\\nINSERT 34 F\\nINSERT 35 F\\nINSERT 36 Y\\nINSERT 37 L\\nINSERT 38 I\\nINSERT 39 L\\nINSERT 40 N\\nINSERT 41 N\\nINSERT 43 A\\nREPLACE 45 T\\nREPLACE 46 Z\\nINSERT 47 O\\nINSERT 48 N\\nINSERT 49 B\\nINSERT 50 S\\nINSERT 51 R\\nINSERT 53 O\\nINSERT 54 X\\nINSERT 55 L\\nINSERT 56 L\\nINSERT 57 L\\nINSERT 58 C\\nINSERT 59 G\\nINSERT 60 S\\nINSERT 61 I\\nINSERT 62 L\\nINSERT 63 J\\nINSERT 64 U\\nINSERT 65 S\\nINSERT 67 S\\nINSERT 68 O\\nINSERT 69 X\\nINSERT 70 E\\nINSERT 71 N\\nINSERT 73 N\\nINSERT 74 M\\nINSERT 75 I\\nINSERT 76 W\\nINSERT 77 X\\nINSERT 78 C\\nINSERT 79 B\\nINSERT 80 W\\nINSERT 84 H\\nREPLACE 86 X\\nREPLACE 87 B\\nREPLACE 88 T\\nREPLACE 89 B\\nINSERT 90 T\\nINSERT 91 C\\nINSERT 92 H\\nINSERT 93 Q\\nREPLACE 95 W\\nINSERT 96 Z\\nINSERT 98 L\\nINSERT 99 U\\nINSERT 100 O\\nINSERT 101 W\\nINSERT 102 E\\nINSERT 103 T\\nREPLACE 105 C\\nREPLACE 106 B\\nINSERT 107 R\\nINSERT 108 P\\nINSERT 109 D\\nINSERT 111 A\\nINSERT 112 P\\nINSERT 113 M\\nINSERT 115 O\\nINSERT 116 U\\nINSERT 117 W\\nINSERT 118 X\\nINSERT 119 M\\nINSERT 120 V\\nINSERT 121 L\\nINSERT 122 B\\nINSERT 123 K\\nINSERT 124 V\\nINSERT 125 K\\nINSERT 126 I\\nINSERT 127 D\\nINSERT 128 E\\nINSERT 129 G\\nINSERT 130 U\\nINSERT 131 W\\nINSERT 132 M\\nINSERT 133 A\\nINSERT 134 H\\nINSERT 135 X\\nINSERT 136 M\\nINSERT 137 U\\nINSERT 138 O\\nINSERT 139 Z\\nINSERT 140 P\\nINSERT 141 P\\nINSERT 142 M\\nINSERT 143 Q\\nINSERT 144 L\\nINSERT 145 W\\nINSERT 146 R\\nINSERT 147 J\\nINSERT 148 U\\nINSERT 149 A\\nINSERT 150 M\\nINSERT 151 Z\\nINSERT 152 O\\nINSERT 153 S\\nINSERT 154 R\\nINSERT 155 H\\nINSERT 156 M\\nINSERT 157 E\\nINSERT 158 X\\nINSERT 159 D\\nINSERT 160 U\\nINSERT 161 M\\nINSERT 162 Q\\nINSERT 163 I\\nINSERT 164 Z\\nINSERT 165 L\\nINSERT 166 G\\nINSERT 167 A\\nINSERT 168 C\\nINSERT 169 E\\nINSERT 170 T\\nINSERT 171 A\\nINSERT 172 U\\nINSERT 173 O\\nINSERT 174 E\\nINSERT 175 V\\nINSERT 176 E\\nINSERT 177 H\\nINSERT 178 E\\nINSERT 179 U\\nINSERT 180 W\\nINSERT 181 B\\nINSERT 182 Z\\n'}, {'type': 'stdin_stdout', 'input': 'A\\nB\\n', 'output': '1\\nREPLACE 1 B\\n'}, {'type': 'stdin_stdout', 'input': 'PJLZWUPXYHOPUFIDUXQAGDQMPUEASUPNEJVBMBSZOMTRYPPBPBYXKCWUXWTEMIONEXOJNIRRGFVPMIGFYFSFSALOOKLIGJYRVWQWPLCPBPOGHLXNYBDSHVGHEOWBHPZRTZUIAEUHTPZAXVCTOOEYPB\\nYRWPQARABPMMBLUZJHDVOUODHRNLMOOVGVJIZDDLXEWCPUFYYPKCDDYGLOLTNHAVURLLEKNOYC\\n', 'output': '123\\nREPLACE 1 Y\\nREPLACE 2 R\\nDELETE 3\\nDELETE 3\\nDELETE 4\\nDELETE 5\\nDELETE 5\\nDELETE 5\\nDELETE 5\\nDELETE 5\\nDELETE 5\\nDELETE 5\\nDELETE 5\\nDELETE 5\\nDELETE 5\\nDELETE 5\\nREPLACE 7 R\\nREPLACE 8 A\\nREPLACE 9 B\\nDELETE 10\\nREPLACE 11 M\\nREPLACE 12 M\\nREPLACE 13 B\\nREPLACE 14 L\\nREPLACE 16 Z\\nREPLACE 17 J\\nREPLACE 18 H\\nREPLACE 19 D\\nREPLACE 21 O\\nREPLACE 22 U\\nDELETE 23\\nDELETE 23\\nDELETE 23\\nREPLACE 24 D\\nREPLACE 25 H\\nREPLACE 27 N\\nREPLACE 28 L\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 29\\nDELETE 30\\nDELETE 31\\nDELETE 31\\nDELETE 31\\nREPLACE 32 V\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 34\\nREPLACE 35 J\\nDELETE 36\\nREPLACE 37 Z\\nREPLACE 38 D\\nREPLACE 39 D\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nREPLACE 41 X\\nREPLACE 42 E\\nREPLACE 43 W\\nREPLACE 44 C\\nREPLACE 45 P\\nREPLACE 46 U\\nREPLACE 47 F\\nREPLACE 49 Y\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nREPLACE 51 K\\nREPLACE 53 D\\nREPLACE 54 D\\nREPLACE 55 Y\\nDELETE 56\\nDELETE 57\\nDELETE 58\\nDELETE 58\\nDELETE 58\\nDELETE 58\\nDELETE 58\\nDELETE 58\\nDELETE 58\\nDELETE 58\\nDELETE 58\\nDELETE 58\\nDELETE 58\\nREPLACE 59 L\\nDELETE 60\\nDELETE 60\\nDELETE 60\\nDELETE 60\\nDELETE 60\\nREPLACE 61 N\\nREPLACE 62 H\\nDELETE 63\\nREPLACE 64 V\\nREPLACE 66 R\\nREPLACE 67 L\\nREPLACE 68 L\\nREPLACE 69 E\\nREPLACE 70 K\\nREPLACE 71 N\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 73\\nDELETE 73\\nREPLACE 74 C\\nDELETE 75\\n'}, {'type': 'stdin_stdout', 'input': '[\\nY\\n', 'output': '1\\nREPLACE 1 Y\\n'}, {'type': 'stdin_stdout', 'input': 'A@A\\nABABA\\n', 'output': '3\\nREPLACE 2 B\\nINSERT 4 B\\nINSERT 5 A\\n'}, {'type': 'stdin_stdout', 'input': 'KOYXNKFPY\\nGUD\\n', 'output': '9\\nREPLACE 1 G\\nREPLACE 2 U\\nREPLACE 3 D\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\n'}, {'type': 'stdin_stdout', 'input': 'OGIIQRUDOUJCZQEDAUKRWEGVHRAHSIPPMKELKAMRKVASOFWDUFIONMQJKYGDXAUCGLVHAASYCYUKUCJVLZIJWOIAFTGXABUUDNGSLWFCSMEOXVBUZOKSVPARIBJJWY\\nOGIIQRVDXUJCZQEDAUKRWEGVHRAHSIPMKELKAMRKVASOFWDUFIONMQJKYGDXAUCGLVHAASYCYUKUCJVLZIJWOIAFTGOABUUDNGSLWFCSMEOXVBUZOKSVPARIBJJWY\\n', 'output': '4\\nREPLACE 7 V\\nREPLACE 9 X\\nDELETE 32\\nREPLACE 91 O\\n'}, {'type': 'stdin_stdout', 'input': 'SZDAVSUGK\\nLU\\n', 'output': '8\\nREPLACE 1 L\\nDELETE 2\\nDELETE 2\\nDELETE 2\\nDELETE 2\\nDELETE 2\\nDELETE 3\\nDELETE 3\\n'}, {'type': 'stdin_stdout', 'input': 'FFYIWCORZYANRHODCKKFGHJT\\nZYWUEHEVEOUATECAGLZIQMUDXEMHRSOZMAUJRWLQNPPZOUMXHAMWUGEDIKVKBLVMXWUOFMPAFDPRBCFTEWOULCZWRQHCTBTBXRHHODWBCXWIMNCNEXOSKSUJLISGCLLLXOKRSBNOZTHAJNNLILYFFMSBKOFPTXRNEFBSOUHFOLTIQAINRPXWRQ\\n', 'output': '167\\nREPLACE 1 Z\\nREPLACE 2 Y\\nREPLACE 3 W\\nREPLACE 4 U\\nREPLACE 5 E\\nREPLACE 6 H\\nINSERT 7 E\\nINSERT 8 V\\nINSERT 9 E\\nINSERT 11 U\\nINSERT 12 A\\nINSERT 13 T\\nINSERT 14 E\\nINSERT 15 C\\nINSERT 16 A\\nINSERT 17 G\\nINSERT 18 L\\nINSERT 19 Z\\nINSERT 20 I\\nINSERT 21 Q\\nINSERT 22 M\\nINSERT 23 U\\nINSERT 24 D\\nINSERT 25 X\\nINSERT 26 E\\nINSERT 27 M\\nINSERT 28 H\\nINSERT 30 S\\nINSERT 31 O\\nREPLACE 33 M\\nINSERT 35 U\\nINSERT 36 J\\nINSERT 37 R\\nINSERT 38 W\\nINSERT 39 L\\nINSERT 40 Q\\nINSERT 42 P\\nINSERT 43 P\\nINSERT 44 Z\\nINSERT 45 O\\nINSERT 46 U\\nINSERT 47 M\\nINSERT 48 X\\nINSERT 49 H\\nINSERT 50 A\\nINSERT 51 M\\nINSERT 52 W\\nINSERT 53 U\\nINSERT 54 G\\nINSERT 55 E\\nINSERT 56 D\\nINSERT 57 I\\nINSERT 58 K\\nINSERT 59 V\\nINSERT 60 K\\nINSERT 61 B\\nINSERT 62 L\\nINSERT 63 V\\nINSERT 64 M\\nINSERT 65 X\\nINSERT 66 W\\nINSERT 67 U\\nINSERT 68 O\\nINSERT 69 F\\nINSERT 70 M\\nINSERT 71 P\\nINSERT 72 A\\nINSERT 73 F\\nINSERT 74 D\\nINSERT 75 P\\nINSERT 77 B\\nINSERT 78 C\\nINSERT 79 F\\nINSERT 80 T\\nINSERT 81 E\\nINSERT 82 W\\nINSERT 83 O\\nINSERT 84 U\\nINSERT 85 L\\nINSERT 86 C\\nINSERT 87 Z\\nINSERT 88 W\\nINSERT 89 R\\nINSERT 90 Q\\nINSERT 92 C\\nINSERT 93 T\\nINSERT 94 B\\nINSERT 95 T\\nINSERT 96 B\\nINSERT 97 X\\nINSERT 98 R\\nINSERT 99 H\\nINSERT 100 H\\nINSERT 103 W\\nINSERT 104 B\\nREPLACE 106 X\\nINSERT 107 W\\nINSERT 108 I\\nINSERT 109 M\\nINSERT 110 N\\nINSERT 111 C\\nINSERT 112 N\\nINSERT 113 E\\nINSERT 114 X\\nINSERT 115 O\\nINSERT 116 S\\nREPLACE 118 S\\nINSERT 119 U\\nINSERT 120 J\\nINSERT 121 L\\nINSERT 122 I\\nINSERT 123 S\\nINSERT 125 C\\nINSERT 126 L\\nINSERT 127 L\\nINSERT 128 L\\nINSERT 129 X\\nINSERT 130 O\\nINSERT 131 K\\nINSERT 132 R\\nINSERT 133 S\\nINSERT 134 B\\nINSERT 135 N\\nINSERT 136 O\\nINSERT 137 Z\\nINSERT 138 T\\nINSERT 140 A\\nINSERT 142 N\\nINSERT 143 N\\nINSERT 144 L\\nINSERT 145 I\\nINSERT 146 L\\nINSERT 147 Y\\nINSERT 148 F\\nINSERT 149 F\\nINSERT 150 M\\nINSERT 151 S\\nINSERT 152 B\\nINSERT 153 K\\nINSERT 154 O\\nINSERT 155 F\\nINSERT 156 P\\nINSERT 158 X\\nINSERT 159 R\\nINSERT 160 N\\nINSERT 161 E\\nINSERT 162 F\\nINSERT 163 B\\nINSERT 164 S\\nINSERT 165 O\\nINSERT 166 U\\nINSERT 167 H\\nINSERT 168 F\\nINSERT 169 O\\nINSERT 170 L\\nINSERT 171 T\\nINSERT 172 I\\nINSERT 173 Q\\nINSERT 174 A\\nINSERT 175 I\\nINSERT 176 N\\nINSERT 177 R\\nINSERT 178 P\\nINSERT 179 X\\nINSERT 180 W\\nINSERT 181 R\\nINSERT 182 Q\\n'}, {'type': 'stdin_stdout', 'input': 'BPYEOOTCVXAEPTHUEAIUZUOZPHBWOEHGVHSDBYNXLHGOPBPCLPWQWVRYJGILKOOLASFSFYFGIMPVFGRRINJRXZNOIMETWXUWCKXYBPBPPYRTMOZSBMBVJENPUSAEUPMQDGAQXUDIFUPOHYXPUWZLJP\\nYRWPQARABPMMBLUZIHDVOUODHRNLMOOVGVJIZDDLXEWCPUFYYPKCDDYGYOLSNHAVURLLEKNOLC\\n', 'output': '122\\nDELETE 1\\nDELETE 1\\nREPLACE 2 R\\nREPLACE 3 W\\nREPLACE 4 P\\nREPLACE 5 Q\\nREPLACE 6 A\\nREPLACE 7 R\\nDELETE 8\\nREPLACE 9 B\\nREPLACE 11 M\\nREPLACE 12 M\\nREPLACE 13 B\\nREPLACE 14 L\\nDELETE 15\\nDELETE 15\\nREPLACE 17 I\\nDELETE 18\\nDELETE 18\\nDELETE 18\\nREPLACE 19 D\\nREPLACE 20 V\\nREPLACE 22 U\\nREPLACE 23 O\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nREPLACE 27 N\\nDELETE 28\\nDELETE 28\\nDELETE 28\\nREPLACE 29 M\\nREPLACE 32 V\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 34\\nDELETE 34\\nDELETE 34\\nREPLACE 35 J\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nREPLACE 38 D\\nREPLACE 39 D\\nREPLACE 40 L\\nREPLACE 41 X\\nREPLACE 43 W\\nREPLACE 44 C\\nREPLACE 45 P\\nREPLACE 47 F\\nREPLACE 48 Y\\nDELETE 49\\nDELETE 49\\nREPLACE 50 P\\nREPLACE 51 K\\nREPLACE 52 C\\nREPLACE 53 D\\nREPLACE 54 D\\nREPLACE 56 G\\nREPLACE 57 Y\\nDELETE 58\\nREPLACE 59 L\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nREPLACE 62 H\\nDELETE 63\\nDELETE 63\\nREPLACE 64 V\\nREPLACE 66 R\\nREPLACE 67 L\\nREPLACE 68 L\\nREPLACE 69 E\\nREPLACE 70 K\\nREPLACE 71 N\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nREPLACE 74 C\\nDELETE 75\\n'}, {'type': 'stdin_stdout', 'input': 'TJHGWKKCDOHRNAXZRNCFIYFF\\nQRWXPRNIAQITLOFHUOSBFENRXTPFOKYSMFFYLILNNJAHTZONBSRKOXLLLCGSILJUSKSOXENCNMIWXCBWDOHHRXBTBTCHQRWZBLUOWETFCBRPDFAPMFOUWXMVLBKVKIDEGUWMAHXMUOZPPMQLWRJUAMZOSRHMEXDUMQIZLGACETAUOEVEHEUWBZ\\n', 'output': '167\\nINSERT 1 Q\\nINSERT 2 R\\nINSERT 3 W\\nINSERT 4 X\\nINSERT 5 P\\nINSERT 6 R\\nINSERT 7 N\\nINSERT 8 I\\nINSERT 9 A\\nINSERT 10 Q\\nINSERT 11 I\\nINSERT 13 L\\nINSERT 14 O\\nINSERT 15 F\\nINSERT 16 H\\nINSERT 17 U\\nINSERT 18 O\\nINSERT 19 S\\nINSERT 20 B\\nINSERT 21 F\\nINSERT 22 E\\nINSERT 23 N\\nINSERT 24 R\\nINSERT 25 X\\nINSERT 26 T\\nINSERT 27 P\\nINSERT 28 F\\nINSERT 29 O\\nINSERT 30 K\\nINSERT 31 Y\\nINSERT 32 S\\nINSERT 33 M\\nINSERT 34 F\\nINSERT 35 F\\nINSERT 36 Y\\nINSERT 37 L\\nINSERT 38 I\\nINSERT 39 L\\nINSERT 40 N\\nINSERT 41 N\\nINSERT 43 A\\nREPLACE 45 T\\nREPLACE 46 Z\\nINSERT 47 O\\nINSERT 48 N\\nINSERT 49 B\\nINSERT 50 S\\nINSERT 51 R\\nINSERT 53 O\\nINSERT 54 X\\nINSERT 55 L\\nINSERT 56 L\\nINSERT 57 L\\nINSERT 58 C\\nINSERT 59 G\\nINSERT 60 S\\nINSERT 61 I\\nINSERT 62 L\\nINSERT 63 J\\nINSERT 64 U\\nINSERT 65 S\\nINSERT 67 S\\nINSERT 68 O\\nINSERT 69 X\\nINSERT 70 E\\nINSERT 71 N\\nINSERT 73 N\\nINSERT 74 M\\nINSERT 75 I\\nINSERT 76 W\\nINSERT 77 X\\nINSERT 78 C\\nINSERT 79 B\\nINSERT 80 W\\nINSERT 84 H\\nREPLACE 86 X\\nINSERT 87 B\\nINSERT 88 T\\nINSERT 89 B\\nINSERT 90 T\\nINSERT 91 C\\nINSERT 92 H\\nINSERT 93 Q\\nINSERT 94 R\\nINSERT 95 W\\nINSERT 96 Z\\nINSERT 97 B\\nINSERT 98 L\\nINSERT 99 U\\nINSERT 100 O\\nINSERT 101 W\\nINSERT 102 E\\nINSERT 103 T\\nINSERT 104 F\\nINSERT 105 C\\nINSERT 106 B\\nINSERT 107 R\\nINSERT 108 P\\nINSERT 109 D\\nINSERT 110 F\\nINSERT 112 P\\nINSERT 113 M\\nINSERT 114 F\\nINSERT 115 O\\nINSERT 116 U\\nINSERT 117 W\\nINSERT 119 M\\nINSERT 120 V\\nINSERT 121 L\\nINSERT 122 B\\nINSERT 123 K\\nINSERT 124 V\\nINSERT 125 K\\nINSERT 126 I\\nINSERT 127 D\\nINSERT 128 E\\nINSERT 129 G\\nINSERT 130 U\\nINSERT 131 W\\nINSERT 132 M\\nINSERT 133 A\\nINSERT 134 H\\nINSERT 135 X\\nINSERT 136 M\\nINSERT 137 U\\nINSERT 138 O\\nINSERT 140 P\\nINSERT 141 P\\nINSERT 142 M\\nINSERT 143 Q\\nINSERT 144 L\\nINSERT 145 W\\nREPLACE 147 J\\nREPLACE 148 U\\nREPLACE 149 A\\nINSERT 150 M\\nINSERT 151 Z\\nINSERT 152 O\\nINSERT 153 S\\nINSERT 154 R\\nINSERT 155 H\\nINSERT 156 M\\nINSERT 157 E\\nINSERT 158 X\\nINSERT 159 D\\nINSERT 160 U\\nINSERT 161 M\\nINSERT 162 Q\\nREPLACE 164 Z\\nREPLACE 165 L\\nREPLACE 166 G\\nINSERT 167 A\\nINSERT 168 C\\nINSERT 169 E\\nINSERT 170 T\\nINSERT 171 A\\nINSERT 172 U\\nINSERT 173 O\\nINSERT 174 E\\nINSERT 175 V\\nINSERT 176 E\\nINSERT 177 H\\nINSERT 178 E\\nINSERT 179 U\\nINSERT 180 W\\nINSERT 181 B\\nINSERT 182 Z\\n'}, {'type': 'stdin_stdout', 'input': 'GXPLMUNZIRBHFJOOJHOMQNIKHVQSGFYSKLSWJQBUWYWHLQHLZYLPZWBOMPOLOLUGSBMHHLYGEIOUWDKPFIAAIRKYRLXTIFAZOPOLLPSNZHCIZDRTJPCYSCDTXBTMFSGEPRNOHJHNXZFYJPAMSHNOVZZYWCVEXLLOVHGAJBANAXVNTWCYTCUMQPEUUESQZTSDANIMUVJGDJCDLIAZKIAYAUQKPXRYKFRBVQJDRSUQZQZTIHWZDXQND\\nYTJUCSBGESVMVRIDTBJTMPVACWWDWKBPEBVMGDXGIVLVQXVEETNSDXKTVJPXOPERWSGDPPMKNMWDIGEHFXNUQADIS\\n', 'output': '210\\nREPLACE 1 Y\\nREPLACE 2 T\\nREPLACE 3 J\\nDELETE 4\\nDELETE 4\\nREPLACE 5 C\\nREPLACE 6 S\\nDELETE 7\\nDELETE 7\\nREPLACE 8 G\\nREPLACE 9 E\\nREPLACE 10 S\\nREPLACE 11 V\\nDELETE 12\\nDELETE 12\\nDELETE 12\\nDELETE 12\\nREPLACE 13 V\\nREPLACE 14 R\\nREPLACE 16 D\\nREPLACE 17 T\\nREPLACE 18 B\\nREPLACE 19 J\\nREPLACE 20 T\\nREPLACE 21 M\\nREPLACE 22 P\\nREPLACE 23 V\\nREPLACE 24 A\\nREPLACE 25 C\\nDELETE 26\\nDELETE 26\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nREPLACE 28 D\\nREPLACE 30 K\\nREPLACE 31 B\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nREPLACE 33 E\\nDELETE 34\\nREPLACE 35 V\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 38\\nDELETE 39\\nDELETE 39\\nDELETE 39\\nDELETE 39\\nDELETE 39\\nDELETE 39\\nDELETE 39\\nDELETE 39\\nDELETE 39\\nDELETE 39\\nDELETE 39\\nDELETE 39\\nREPLACE 40 G\\nREPLACE 42 V\\nDELETE 43\\nDELETE 43\\nDELETE 43\\nDELETE 43\\nDELETE 43\\nREPLACE 44 V\\nREPLACE 45 Q\\nREPLACE 46 X\\nREPLACE 47 V\\nREPLACE 48 E\\nREPLACE 49 E\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nREPLACE 51 N\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 53\\nDELETE 54\\nREPLACE 55 K\\nREPLACE 57 V\\nREPLACE 58 J\\nDELETE 59\\nDELETE 59\\nDELETE 59\\nREPLACE 60 X\\nDELETE 61\\nREPLACE 62 P\\nREPLACE 63 E\\nREPLACE 64 R\\nREPLACE 65 W\\nREPLACE 66 S\\nREPLACE 67 G\\nREPLACE 68 D\\nREPLACE 69 P\\nDELETE 70\\nDELETE 71\\nREPLACE 72 K\\nDELETE 73\\nREPLACE 74 M\\nREPLACE 75 W\\nREPLACE 76 D\\nREPLACE 77 I\\nREPLACE 78 G\\nDELETE 79\\nDELETE 79\\nDELETE 79\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nREPLACE 81 F\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 83\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 85\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\n'}, {'type': 'stdin_stdout', 'input': 'PJLZWUPXYHOPUFIDUXQAGDQMPUEASUPNEJVBMBSZOMTRYPPBPBYXKCWUXWTEMIONEXOJNIRRGFVPMIGFYFSFSALOOKLIGJYRVWQWPLCPBPOGHLXNYBDSHVGHEOWBHPZRTZUIAEUHTPZAXVCTOOEYPB\\nCYONKELLRUVAHNTLOLGYDDCKPYYFUPCWEXLDDZIJVGVOOMLNRHDOUOVDHJZULBMMPBARAQPWRY\\n', 'output': '123\\nREPLACE 1 C\\nDELETE 2\\nDELETE 2\\nDELETE 2\\nDELETE 2\\nDELETE 2\\nDELETE 2\\nDELETE 2\\nDELETE 3\\nREPLACE 4 N\\nREPLACE 5 K\\nREPLACE 6 E\\nREPLACE 7 L\\nREPLACE 8 L\\nREPLACE 9 R\\nDELETE 10\\nDELETE 10\\nDELETE 10\\nDELETE 10\\nDELETE 10\\nDELETE 10\\nDELETE 10\\nDELETE 10\\nREPLACE 11 V\\nREPLACE 13 H\\nDELETE 14\\nDELETE 14\\nREPLACE 15 T\\nREPLACE 16 L\\nREPLACE 17 O\\nREPLACE 18 L\\nREPLACE 19 G\\nREPLACE 20 Y\\nREPLACE 21 D\\nREPLACE 22 D\\nREPLACE 23 C\\nREPLACE 24 K\\nREPLACE 25 P\\nREPLACE 26 Y\\nREPLACE 28 F\\nREPLACE 29 U\\nDELETE 30\\nDELETE 31\\nDELETE 31\\nDELETE 31\\nDELETE 31\\nREPLACE 33 E\\nREPLACE 35 L\\nREPLACE 36 D\\nREPLACE 37 D\\nREPLACE 38 Z\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nREPLACE 41 V\\nDELETE 42\\nDELETE 42\\nDELETE 42\\nDELETE 43\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nDELETE 44\\nREPLACE 46 M\\nREPLACE 48 N\\nDELETE 49\\nDELETE 49\\nDELETE 49\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nREPLACE 52 O\\nREPLACE 53 U\\nDELETE 54\\nDELETE 54\\nDELETE 54\\nDELETE 54\\nREPLACE 55 V\\nREPLACE 56 D\\nREPLACE 58 J\\nDELETE 60\\nDELETE 60\\nDELETE 60\\nREPLACE 61 L\\nREPLACE 62 B\\nREPLACE 63 M\\nREPLACE 64 M\\nDELETE 65\\nDELETE 65\\nREPLACE 66 B\\nREPLACE 68 R\\nREPLACE 69 A\\nREPLACE 70 Q\\nREPLACE 71 P\\nREPLACE 72 W\\nREPLACE 73 R\\nDELETE 74\\nDELETE 75\\nDELETE 75\\n'}, {'type': 'stdin_stdout', 'input': '[\\nX\\n', 'output': '1\\nREPLACE 1 X\\n'}, {'type': 'stdin_stdout', 'input': 'A@B\\nABABA\\n', 'output': '3\\nREPLACE 2 B\\nINSERT 3 A\\nINSERT 5 A\\n'}, {'type': 'stdin_stdout', 'input': 'W\\nBNBND\\n', 'output': '5\\nREPLACE 1 B\\nINSERT 2 N\\nINSERT 3 B\\nINSERT 4 N\\nINSERT 5 D\\n'}, {'type': 'stdin_stdout', 'input': 'KOYXNKYPF\\nGDU\\n', 'output': '9\\nREPLACE 1 G\\nREPLACE 2 D\\nREPLACE 3 U\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\n'}, {'type': 'stdin_stdout', 'input': 'SZDAVSVGK\\nMU\\n', 'output': '9\\nREPLACE 1 M\\nREPLACE 2 U\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\nDELETE 3\\n'}, {'type': 'stdin_stdout', 'input': 'BPYEOOTCVXAEPTHUEAIUZUOZPHBWOEHGVHSDBYNXLHGOPBPCLPWQWVRYJGILKOOLASFSFYFGIMPVFGRRINJRXZNOIMETWXUWCKXYBPBPPYRTMOZSBMBVJENPUSAEUPMQDGAQXUDIFUPOHYXPUWZLJP\\nYRWPQARABPMMBLUZJHDVOUODHRNLMOOVGVJIZDDLXEWCPUFYYPKCDDYGYOLTNHAVURLLEKNOLC\\n', 'output': '123\\nDELETE 1\\nDELETE 1\\nREPLACE 2 R\\nREPLACE 3 W\\nREPLACE 4 P\\nREPLACE 5 Q\\nREPLACE 6 A\\nREPLACE 7 R\\nDELETE 8\\nREPLACE 9 B\\nREPLACE 11 M\\nREPLACE 12 M\\nREPLACE 13 B\\nREPLACE 14 L\\nDELETE 15\\nDELETE 15\\nREPLACE 17 J\\nDELETE 18\\nDELETE 18\\nDELETE 18\\nREPLACE 19 D\\nREPLACE 20 V\\nREPLACE 22 U\\nREPLACE 23 O\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 24\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 25\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nDELETE 26\\nREPLACE 27 N\\nDELETE 28\\nDELETE 28\\nDELETE 28\\nREPLACE 29 M\\nREPLACE 32 V\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 33\\nDELETE 34\\nDELETE 34\\nDELETE 34\\nREPLACE 35 J\\nDELETE 36\\nDELETE 36\\nDELETE 36\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nREPLACE 38 D\\nREPLACE 39 D\\nREPLACE 40 L\\nREPLACE 41 X\\nREPLACE 43 W\\nREPLACE 44 C\\nREPLACE 45 P\\nREPLACE 47 F\\nREPLACE 48 Y\\nDELETE 49\\nDELETE 49\\nREPLACE 50 P\\nREPLACE 51 K\\nREPLACE 52 C\\nREPLACE 53 D\\nREPLACE 54 D\\nREPLACE 56 G\\nREPLACE 57 Y\\nDELETE 58\\nREPLACE 59 L\\nREPLACE 60 T\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nDELETE 61\\nREPLACE 62 H\\nDELETE 63\\nDELETE 63\\nREPLACE 64 V\\nREPLACE 66 R\\nREPLACE 67 L\\nREPLACE 68 L\\nREPLACE 69 E\\nREPLACE 70 K\\nREPLACE 71 N\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 72\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nDELETE 73\\nREPLACE 74 C\\nDELETE 75\\n'}, {'type': 'stdin_stdout', 'input': '[\\nZ\\n', 'output': '1\\nREPLACE 1 Z\\n'}, {'type': 'stdin_stdout', 'input': 'KOYXNKFPY\\nGDU\\n', 'output': '9\\nREPLACE 1 G\\nREPLACE 2 D\\nREPLACE 3 U\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\nDELETE 4\\n'}, {'type': 'stdin_stdout', 'input': 'CU\\nWPL\\n', 'output': '3\\nREPLACE 1 W\\nREPLACE 2 P\\nINSERT 3 L\\n'}, {'type': 'stdin_stdout', 'input': 'GXPLMUNZIRBHFJOOJHOMQNIKHVQSGFYSKLSWJQBUWYWHLQHLZYLPZWBOMPOLOLUGSBMHHLYGEIOUWDKPFIAAIRKYRLXTIFAZOPOLLPSNZHCIZDRTJPCYSCDTXBTMFSGEPRNOHJHNXZFYJPAMSHNOVZZYWCVEXLLOVHGAJBANAXVNTWCYTCUMQPEUUESQZTSDANIMUVJGDJCDLIAZKIAYAUQKPXRYKFRBVQJDRSUQZQZTIHWZDXQND\\nYTJUCSBGESVMVRIDTBJTMPVACWWDWKBPEBVMGDXGIVLWQXVEETNSDXKTVJPXOPERWSGDPPMKNMWDIGEHFXNUQADIS\\n', 'output': '210\\nREPLACE 1 Y\\nREPLACE 2 T\\nREPLACE 3 J\\nDELETE 4\\nDELETE 4\\nREPLACE 5 C\\nREPLACE 6 S\\nDELETE 7\\nDELETE 7\\nREPLACE 8 G\\nREPLACE 9 E\\nREPLACE 10 S\\nREPLACE 11 V\\nDELETE 12\\nDELETE 12\\nDELETE 12\\nDELETE 12\\nREPLACE 13 V\\nREPLACE 14 R\\nREPLACE 16 D\\nREPLACE 17 T\\nREPLACE 18 B\\nREPLACE 19 J\\nREPLACE 20 T\\nREPLACE 21 M\\nREPLACE 22 P\\nREPLACE 23 V\\nREPLACE 24 A\\nREPLACE 25 C\\nDELETE 26\\nDELETE 26\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nDELETE 27\\nREPLACE 28 D\\nREPLACE 30 K\\nREPLACE 31 B\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nDELETE 32\\nREPLACE 33 E\\nDELETE 34\\nREPLACE 35 V\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nDELETE 37\\nREPLACE 38 D\\nREPLACE 39 X\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 40\\nDELETE 41\\nREPLACE 42 V\\nREPLACE 43 L\\nREPLACE 45 Q\\nREPLACE 46 X\\nREPLACE 47 V\\nREPLACE 48 E\\nREPLACE 49 E\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 50\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 51\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 52\\nDELETE 53\\nDELETE 54\\nREPLACE 55 K\\nREPLACE 57 V\\nREPLACE 58 J\\nDELETE 59\\nDELETE 59\\nDELETE 59\\nREPLACE 60 X\\nDELETE 61\\nREPLACE 62 P\\nREPLACE 63 E\\nREPLACE 64 R\\nREPLACE 65 W\\nREPLACE 66 S\\nREPLACE 67 G\\nREPLACE 68 D\\nREPLACE 69 P\\nDELETE 70\\nDELETE 71\\nREPLACE 72 K\\nDELETE 73\\nREPLACE 74 M\\nREPLACE 75 W\\nREPLACE 76 D\\nREPLACE 77 I\\nREPLACE 78 G\\nDELETE 79\\nDELETE 79\\nDELETE 79\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nDELETE 80\\nREPLACE 81 F\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 82\\nDELETE 83\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 84\\nDELETE 85\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 86\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 87\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 88\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 89\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\nDELETE 90\\n'}, {'type': 'stdin_stdout', 'input': 'DETOECCA\\nWRONGANSXER\\n', 'output': '11\\nREPLACE 1 W\\nREPLACE 2 R\\nREPLACE 3 O\\nREPLACE 4 N\\nREPLACE 5 G\\nREPLACE 6 A\\nREPLACE 7 N\\nREPLACE 8 S\\nINSERT 9 X\\nINSERT 10 E\\nINSERT 11 R\\n'}, {'type': 'stdin_stdout', 'input': 'X\\nBMBND\\n', 'output': '5\\nREPLACE 1 B\\nINSERT 2 M\\nINSERT 3 B\\nINSERT 4 N\\nINSERT 5 D\\n'}, {'type': 'stdin_stdout', 'input': 'CU\\nPWL\\n', 'output': '3\\nREPLACE 1 P\\nREPLACE 2 W\\nINSERT 3 L\\n'}, {'type': 'stdin_stdout', 'input': 'A\\nA\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'TEDOECCA\\nWRONGANSXER\\n', 'output': '11\\nREPLACE 1 W\\nREPLACE 2 R\\nREPLACE 3 O\\nREPLACE 4 N\\nREPLACE 5 G\\nREPLACE 6 A\\nREPLACE 7 N\\nREPLACE 8 S\\nINSERT 9 X\\nINSERT 10 E\\nINSERT 11 R\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77701","program":"```python\nimport sys\nfrom array import array # noqa: F401\n\n\ndef input():\n return sys.stdin.buffer.readline().decode('utf-8')\n\n\ns, t = input().rstrip(), input().rstrip()\nn, m = len(s), len(t)\n\ndp = [[10**9] * (m + 2) for _ in range(n + 2)]\ndp[n][m] = 0\nprev = [[(-1, -1)] * (m + 2) for _ in range(n + 2)]\n\nfor i in range(n, -1, -1):\n for j in range(m, -1, -1):\n if i < n and j < m and dp[i][j] > dp[i + 1][j + 1] + (0 if s[i] == t[j] else 1):\n dp[i][j] = dp[i + 1][j + 1] + (0 if s[i] == t[j] else 1)\n prev[i][j] = (i + 1, j + 1)\n if i < n and dp[i][j] > dp[i + 1][j] + 1:\n dp[i][j] = dp[i + 1][j] + 1\n prev[i][j] = (i + 1, j)\n if j < m and dp[i][j] > dp[i][j + 1] + 1:\n dp[i][j] = dp[i][j + 1] + 1\n prev[i][j] = (i, j + 1)\n\ni, j = 0, 0\nans = []\nwhile i < n or j < m:\n ti, tj = prev[i][j]\n if i + 1 == ti and j + 1 == tj:\n if s[i] != t[j]:\n ans.append(f'REPLACE {j+1} {t[j]}')\n elif i + 1 == ti:\n ans.append(f'DELETE {j+1}')\n elif j + 1 == tj:\n ans.append(f'INSERT {j+1} {t[j]}')\n i, j = ti, tj\n\n\nsys.stdout.buffer.write((str(len(ans)) + '\\n' + '\\n'.join(ans)).encode('utf-8'))\n\n```","inputs":"ACCEPTED\nWRONGANSWER\n","output":"10\nREPLACE 1 W\nREPLACE 2 R\nREPLACE 3 O\nREPLACE 4 N\nREPLACE 5 G\nREPLACE 6 A\nINSERT 7 N\nINSERT 8 S\nINSERT 9 W\nREPLACE 11 R\n","actual_output":"10\nREPLACE 1 W\nREPLACE 2 R\nREPLACE 3 O\nREPLACE 4 N\nREPLACE 5 G\nREPLACE 6 A\nINSERT 7 N\nINSERT 8 S\nINSERT 9 W\nREPLACE 11 R","execution_success":true,"sample_index":12401},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"591_B. Rebranding","prompt":"Solve the following coding problem using the programming language python:\n\nThe name of one small but proud corporation consists of n lowercase English letters. The Corporation has decided to try rebranding \u2014 an active marketing strategy, that includes a set of measures to change either the brand (both for the company and the goods it produces) or its components: the name, the logo, the slogan. They decided to start with the name.\n\nFor this purpose the corporation has consecutively hired m designers. Once a company hires the i-th designer, he immediately contributes to the creation of a new corporation name as follows: he takes the newest version of the name and replaces all the letters xi by yi, and all the letters yi by xi. This results in the new version. It is possible that some of these letters do no occur in the string. It may also happen that xi coincides with yi. The version of the name received after the work of the last designer becomes the new name of the corporation.\n\nManager Arkady has recently got a job in this company, but is already soaked in the spirit of teamwork and is very worried about the success of the rebranding. Naturally, he can't wait to find out what is the new name the Corporation will receive.\n\nSatisfy Arkady's curiosity and tell him the final version of the name.\n\nInput\n\nThe first line of the input contains two integers n and m (1 \u2264 n, m \u2264 200 000) \u2014 the length of the initial name and the number of designers hired, respectively.\n\nThe second line consists of n lowercase English letters and represents the original name of the corporation.\n\nNext m lines contain the descriptions of the designers' actions: the i-th of them contains two space-separated lowercase English letters xi and yi.\n\nOutput\n\nPrint the new name of the corporation.\n\nExamples\n\nInput\n\n6 1\npolice\np m\n\n\nOutput\n\nmolice\n\n\nInput\n\n11 6\nabacabadaba\na b\nb c\na d\ne g\nf a\nb b\n\n\nOutput\n\ncdcbcdcfcdc\n\nNote\n\nIn the second sample the name of the corporation consecutively changes as follows:\n\n\n\n\n\n\n\n\n\n\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport string\nN, M = map(int, input().split())\nS = input()\ndic = string.ascii_lowercase\nfor _ in range(M):\n x, y = input().split()\n dic = dic.translate(str.maketrans(x+y, y+x))\nprint(S.translate(str.maketrans(string.ascii_lowercase, dic)))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '11 6\\nabacabadaba\\na b\\nb c\\na d\\ne g\\nf a\\nb b\\n', 'output': 'cdcbcdcfcdc\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\npolice\\np m\\n', 'output': 'molice\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\ne l\\ne l\\ne l\\ne e\\nl l\\nl e\\nl l\\ne e\\n', 'output': 'lellelleel\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\na\\na b\\n', 'output': 'b\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\nf\\nz h\\n', 'output': 'f\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\ne l\\ne l\\ne l\\ne e\\nl l\\nl e\\nl l\\ne f\\n', 'output': 'lfllfllffl\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\nabacabadaba\\na b\\nb c\\na d\\ne g\\ne a\\nb b\\n', 'output': 'cdcbcdcecdc\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\necilop\\np m\\n', 'output': 'ecilom\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\ne l\\ne l\\ne l\\ne f\\nl l\\nl e\\nl l\\ne f\\n', 'output': 'efeefeeffe\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\nabacabadaba\\na b\\nb c\\na d\\ne g\\nd a\\nb b\\n', 'output': 'cacbcacdcac\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\ne l\\ne l\\ne l\\ne f\\nl l\\nl e\\nl l\\nd f\\n', 'output': 'deddeddeed\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\ne l\\ne l\\ne l\\nf f\\nl l\\nl e\\nl l\\nd f\\n', 'output': 'lellelleel\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\ne l\\ne l\\ne l\\nf f\\nl l\\nl e\\nl l\\nd f\\n', 'output': 'emeemeemme\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\ne l\\ne l\\ne l\\ne l\\nf f\\nl l\\nm e\\nl l\\nd f\\n', 'output': 'leleelllel\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\ne l\\ne l\\ne l\\ne l\\nf f\\nk l\\nm e\\nl l\\nd f\\n', 'output': 'kekeekkkek\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\ne m\\ne l\\ne l\\ne l\\nf f\\nk l\\nm e\\nl l\\nd f\\n', 'output': 'mkmkkmmmkm\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne l\\ne m\\ne l\\ne l\\ne l\\nf f\\nk l\\nm e\\nl l\\nd f\\n', 'output': 'ememmeeeme\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne l\\ne m\\ne l\\nf l\\ne l\\nf f\\nk l\\nm e\\nl l\\nd f\\n', 'output': 'ekekkeeeke\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne l\\ne m\\ne l\\nf l\\ne l\\nf f\\nk l\\nm e\\nl l\\ne f\\n', 'output': 'fkfkkfffkf\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellleelel\\ne l\\ne m\\ne l\\nf l\\ne l\\nf f\\nk l\\nm e\\nl l\\ne f\\n', 'output': 'fkfffkkfkf\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\nabacabadaba\\na b\\na c\\na d\\ne g\\nf a\\nb b\\n', 'output': 'bcbdbcbfbcb\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\npolice\\np n\\n', 'output': 'nolice\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\ne l\\ne l\\ne l\\ne e\\nl l\\nl e\\nl l\\ne f\\n', 'output': 'fmffmffmmf\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\necikop\\np m\\n', 'output': 'ecikom\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlelkelleel\\ne l\\ne l\\ne l\\ne l\\ne l\\ne f\\nl l\\nl e\\nl l\\ne f\\n', 'output': 'efekfeeffe\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\ne l\\ne m\\ne l\\ne f\\nl l\\nl e\\nl l\\nd f\\n', 'output': 'mdmmdmmddm\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\ne l\\ne k\\ne l\\nf f\\nl l\\nl e\\nl l\\nd f\\n', 'output': 'klkklkkllk\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\ne k\\ne l\\ne l\\nf f\\nl l\\nm e\\nl l\\nd f\\n', 'output': 'kekkekkeek\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\ne n\\ne l\\ne l\\ne l\\nf f\\nk l\\nm e\\nl l\\nd f\\n', 'output': 'memeemmmem\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\nf l\\ne m\\ne l\\ne l\\ne l\\nf f\\nk l\\nm e\\nl l\\nd f\\n', 'output': 'dedeeddded\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne l\\ne m\\ne l\\nf l\\ne l\\nf f\\nk k\\nm e\\nl l\\nd f\\n', 'output': 'elelleeele\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\nf l\\ne m\\ne l\\nf l\\ne l\\nf f\\nk l\\nm e\\nl l\\ne f\\n', 'output': 'mfmffmmmfm\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellleeldl\\ne l\\ne m\\ne l\\nf l\\ne l\\nf f\\nk l\\nm e\\nl l\\ne f\\n', 'output': 'fkfffkkfdf\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\nabacabadaba\\na b\\na c\\na d\\ne g\\nf a\\na b\\n', 'output': 'acadacafaca\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\ne l\\nd l\\ne l\\ne e\\nl l\\nl e\\nl l\\ne f\\n', 'output': 'dmddmddmmd\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlelkelleel\\ne l\\ne l\\ne l\\ne l\\ne l\\ne f\\nl l\\nl e\\nl l\\nf f\\n', 'output': 'fefkeffeef\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\ne l\\ne k\\ne l\\nf f\\nl l\\nl e\\nl k\\nd f\\n', 'output': 'lkllkllkkl\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\nd l\\ne l\\ne l\\nf f\\nl l\\nm e\\nl l\\nc f\\n', 'output': 'memmemmeem\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne l\\nd m\\ne l\\nf l\\ne l\\nf f\\nk k\\nm e\\nl l\\nd f\\n', 'output': 'dldlldddld\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellleeldl\\ne l\\ne m\\ne l\\nf l\\ne l\\nf f\\nk l\\nm e\\nl l\\nd f\\n', 'output': 'ekeeekkefe\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\nd l\\ne l\\ne l\\ne k\\ne l\\nf f\\nl l\\nl e\\nl k\\nd f\\n', 'output': 'flfflffllf\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\nd l\\ne l\\ne l\\ne f\\nl l\\nm e\\nl l\\nc f\\n', 'output': 'ceccecceec\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\nf n\\ne l\\ne l\\ne l\\nf f\\nk l\\nm d\\nl l\\nd f\\n', 'output': 'efeffeeefe\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne l\\nd m\\ne l\\nf l\\ne l\\nf f\\nl k\\nm e\\nl l\\nd f\\n', 'output': 'dkdkkdddkd\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\nf l\\ne m\\nd l\\nf l\\ne l\\nf f\\nk l\\nm e\\nl l\\ne g\\n', 'output': 'mgmggmmmgm\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellleeldl\\ne l\\ne m\\ne l\\nf l\\ne m\\nf f\\nk l\\nm e\\nl l\\nd f\\n', 'output': 'memmmeemfm\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\nabacabadaba\\na b\\na c\\na d\\ne g\\ng a\\na a\\n', 'output': 'bcbdbcbgbcb\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\ne l\\ne m\\ne l\\ne f\\nm l\\nl e\\nj l\\nd f\\n', 'output': 'edeedeedde\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellellfel\\nd l\\ne l\\ne l\\ne k\\ne l\\nf f\\nl l\\nl e\\nl k\\nd f\\n', 'output': 'flfflffdlf\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\nf n\\ne l\\ne l\\nf l\\nf f\\nk l\\nm d\\nl l\\nd f\\n', 'output': 'dfdffdddfd\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellleeldl\\ne l\\ne m\\ne l\\nf l\\ne m\\nf f\\nk l\\nm e\\nm l\\nd f\\n', 'output': 'lellleelfl\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\nabacabadaba\\nb b\\na c\\na d\\ne g\\ng a\\na a\\n', 'output': 'cbcdcbcgcbc\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\ne l\\nd l\\nf l\\nf e\\nl l\\nm e\\nl l\\ne f\\n', 'output': 'dfddfddffd\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\nd l\\ne m\\ne l\\ne f\\nm l\\nl e\\nj l\\nd f\\n', 'output': 'feffeffeef\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellellfel\\nd l\\ne l\\ne l\\ne k\\ne l\\nf f\\nl l\\nl e\\nk k\\nd f\\n', 'output': 'fkffkffdkf\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\ne l\\ne l\\ne l\\ne l\\ne g\\nk l\\nm d\\nk l\\nc f\\n', 'output': 'ldlddllldl\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nldleelllel\\ne l\\ne m\\ne l\\nf l\\ne m\\nf f\\nk l\\nm e\\nm l\\nd f\\n', 'output': 'lfleelllel\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne k\\nd l\\ne m\\ne l\\ne f\\nm l\\nl e\\nj l\\nd f\\n', 'output': 'kfkkfkkffk\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\ne j\\nf l\\ne l\\nf f\\nl l\\nm e\\nl l\\nc f\\n', 'output': 'jejjejjeej\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\ne l\\nd l\\ne l\\ne l\\ne g\\nk l\\nm d\\nk l\\nc f\\n', 'output': 'gdgddgggdg\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\nf l\\ne k\\nd l\\ne m\\ne l\\ne f\\nm l\\nl e\\nj l\\nd f\\n', 'output': 'jkjjkjjkkj\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleellellel\\ne m\\ne l\\ne j\\nf l\\ne l\\nf f\\nl l\\nm e\\nl l\\nc f\\n', 'output': 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l\\nl e\\nl l\\ne f\\n', 'output': 'dmddmddmmd\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlelkelleel\\ne l\\ne l\\ne l\\ne l\\ne l\\ne f\\nl l\\nl e\\nl m\\ne f\\n', 'output': 'efekfeeffe\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne l\\ne l\\ne l\\ne m\\ne l\\ne f\\nl l\\nl e\\nj l\\nd f\\n', 'output': 'mdmmdmmddm\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\nd k\\nf l\\ne l\\nf f\\nl l\\nm e\\nl l\\nd f\\n', 'output': 'lellelleel\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\ne l\\ne l\\ne l\\ne l\\ne g\\nk l\\nm e\\nl l\\nc f\\n', 'output': 'kekeekkkek\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\ne l\\nd l\\nf l\\nf e\\nl l\\nl e\\nl l\\ne f\\n', 'output': 'dmddmddmmd\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\ne k\\nf l\\ne l\\nf f\\nl l\\nm e\\nl l\\nd f\\n', 'output': 'kekkekkeek\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\ne l\\ne l\\ne l\\ne l\\ne g\\nk l\\nm e\\nk l\\nc f\\n', 'output': 'leleelllel\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne l\\nd m\\ne l\\nf l\\ne l\\nf f\\nl k\\nm e\\nl l\\ne f\\n', 'output': 'ekekkeeeke\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne l\\ne k\\nf l\\ne l\\nf f\\nl l\\nm e\\nl l\\nc f\\n', 'output': 'kekkekkeek\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\nf o\\ne l\\ne l\\nf l\\nf f\\nk l\\nm d\\nl l\\nd f\\n', 'output': 'dfdffdddfd\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\nf l\\nd m\\ne l\\nf l\\ne l\\nf f\\nl k\\nm e\\nl l\\ne f\\n', 'output': 'memeemmmem\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne k\\ne l\\nd l\\nf l\\nf e\\nl l\\nm e\\nl l\\ne f\\n', 'output': 'efeefeeffe\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellellfel\\nd l\\ne l\\ne l\\ne l\\ne l\\nf f\\nl l\\nl e\\nk k\\nd f\\n', 'output': 'flfflffdlf\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nleleelllel\\ne m\\nf o\\nd l\\ne l\\nf l\\nf f\\nk l\\nm d\\nl l\\nd f\\n', 'output': 'mfmffmmmfm\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nldleelllel\\ne l\\ne m\\ne l\\nf l\\ne m\\nf f\\nj l\\nm e\\nm l\\nd f\\n', 'output': 'lfleelllel\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne k\\ne l\\nd l\\nf l\\nf e\\nl l\\nn e\\nl l\\ne f\\n', 'output': 'emeemeemme\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellellfel\\nd l\\ne l\\ne l\\ne l\\ne l\\nf f\\nl l\\nl e\\nl k\\nd f\\n', 'output': 'fkffkffdkf\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nldleelllel\\ne l\\ne m\\ne l\\nf k\\ne m\\nf f\\nj l\\nm e\\nm l\\nd f\\n', 'output': 'lfleelllel\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nlellelleel\\ne m\\ne k\\ne l\\nd l\\nf l\\nf e\\nl l\\nn e\\nl k\\ne f\\n', 'output': 'emeemeemme\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77705","program":"```python\nimport string\nN, M = map(int, input().split())\nS = input()\ndic = string.ascii_lowercase\nfor _ in range(M):\n x, y = input().split()\n dic = dic.translate(str.maketrans(x+y, y+x))\nprint(S.translate(str.maketrans(string.ascii_lowercase, dic)))\n\n```","inputs":"11 6\nabacabadaba\na b\nb c\na d\ne g\nf a\nb b\n","output":"cdcbcdcfcdc\n","actual_output":"cdcbcdcfcdc\n","execution_success":true,"sample_index":12402},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"708_B. Recover the String","prompt":"Solve the following coding problem using the programming language python:\n\nFor each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}. \n\nIn these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.\n\nInput\n\nThe only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.\n\nOutput\n\nIf there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print \"Impossible\". The length of your answer must not exceed 1 000 000.\n\nExamples\n\nInput\n\n1 2 3 4\n\n\nOutput\n\nImpossible\n\n\nInput\n\n1 2 2 1\n\n\nOutput\n\n0110\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\n\ndef BS(x):\n l = 1\n r = 1000000\n while (r-l) > 1:\n m = (l+r)//2\n if m*(m-1)//2 > x:\n r = m\n else:\n l = m\n if l*(l-1)//2 != x:\n print(\"Impossible\")\n sys.exit()\n return l\n\na00,a01,a10,a11=map(int,input().split())\n\nif (a00 + a01 + a10 + a11) == 0:\n print(\"0\")\n sys.exit()\n\n\nc0 = BS(a00)\nc1 = BS(a11)\n\nif a00==0 or a11==0:\n if (a01 + a10) == 0:\n if c0 == 1:\n c0 = 0\n if c1 == 1:\n c1 = 0\n print(\"0\" * c0, end = \"\")\n print(\"1\" * c1)\n sys.exit()\n\nif (c0*c1) != (a01+a10):\n print(\"Impossible\")\n sys.exit()\n\ns = list(\"0\" * (c0+c1))\nfor i in range(c0+c1):\n if c0==0 or a01 < c1:\n s[i] = \"1\"\n a10 -+ c1\n c1 -= 1\n else:\n a01 -= c1\n c0 -= 1\n\nprint(\"\".join(s))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 2 2 1\\n', 'output': '0110'}, {'type': 'stdin_stdout', 'input': '1 2 3 4\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '1000000000 0 0 0\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '499517028 0 999381744 499833153\\n', 'output': '1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111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'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '49995000 584 9417 1\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '49995000 491217159 0 799980000\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '1 0 4 6\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '49995000 1406 8939 0\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '499422210 -1 998876025 499422210\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '647982000 324000000 120007597 364486500\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '499390606 944049019 0 499390606\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '1476904786 999729500 249063045 499359003\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '496 41513 39598 84511\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '450015000 147860287 152299718 46147928\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '487577 2571870 1758432 61721604\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '1 36 7 2\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '45 1 400000 799980000\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '799980000 400000 0 30\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '38226 6041195 7508527 999961560\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '499959631 14240 26685 2\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '1 0 3 0\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '1339886642 1000000000 264000000 499264200\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '762822270 999936000 234477180 197468498\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '0 1 0 1\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '8186 53524 2876 158766\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '0 43292 1429 1880077329\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '199990000 300000000 300000000 878934585\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '499422210 998876025 0 294636077\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '698849204 6502095 8718005 17279400\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '312487500 18661016 375000000 312487500\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '865592028 1496900866 316220800 499264200\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '406991591 0 0 0\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '123456789 987654321 123456789 0\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '799980000 1 400000 45\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '396021103 202805432 197214568 200010000\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '449985000 1566236474 0 449985000\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '525971082 300000000 300000000 199990000\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '2 0 0 6\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '658807465 0 998686404 499327401\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '89253 254334 472943 2741312\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '499959631 847639146 499266399 499959631\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '0 0 -1 999961560\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '10 7 28 11\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '654069038 449414656 450735344 450135010\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '93096 1461585 3613069 9687152\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '0 0 1 4\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '499517028 999065664 0 678682769\\n', 'output': 'Impossible\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77725","program":"```python\nimport sys\n\ndef BS(x):\n l = 1\n r = 1000000\n while (r-l) > 1:\n m = (l+r)//2\n if m*(m-1)//2 > x:\n r = m\n else:\n l = m\n if l*(l-1)//2 != x:\n print(\"Impossible\")\n sys.exit()\n return l\n\na00,a01,a10,a11=map(int,input().split())\n\nif (a00 + a01 + a10 + a11) == 0:\n print(\"0\")\n sys.exit()\n\n\nc0 = BS(a00)\nc1 = BS(a11)\n\nif a00==0 or a11==0:\n if (a01 + a10) == 0:\n if c0 == 1:\n c0 = 0\n if c1 == 1:\n c1 = 0\n print(\"0\" * c0, end = \"\")\n print(\"1\" * c1)\n sys.exit()\n\nif (c0*c1) != (a01+a10):\n print(\"Impossible\")\n sys.exit()\n\ns = list(\"0\" * (c0+c1))\nfor i in range(c0+c1):\n if c0==0 or a01 < c1:\n s[i] = \"1\"\n a10 -+ c1\n c1 -= 1\n else:\n a01 -= c1\n c0 -= 1\n\nprint(\"\".join(s))\n```","inputs":"1 2 2 1\n","output":"0110","actual_output":"0110\n","execution_success":true,"sample_index":12403},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"774_C. Maximum Number","prompt":"Solve the following coding problem using the programming language python:\n\nStepan has the newest electronic device with a display. Different digits can be shown on it. Each digit is shown on a seven-section indicator like it is shown on the picture below.\n\n\n\nSo, for example, to show the digit 3 on the display, 5 sections must be highlighted; and for the digit 6, 6 sections must be highlighted. \n\nThe battery of the newest device allows to highlight at most n sections on the display. \n\nStepan wants to know the maximum possible integer number which can be shown on the display of his newest device. Your task is to determine this number. Note that this number must not contain leading zeros. Assume that the size of the display is enough to show any integer.\n\nInput\n\nThe first line contains the integer n (2 \u2264 n \u2264 100 000) \u2014 the maximum number of sections which can be highlighted on the display.\n\nOutput\n\nPrint the maximum integer which can be shown on the display of Stepan's newest device.\n\nExamples\n\nInput\n\n2\n\n\nOutput\n\n1\n\n\nInput\n\n3\n\n\nOutput\n\n7\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = input()\nn = int(n)\nans = \"\"\nif(n % 2 == 1):\n ans += \"7\"\n n -= 3\nwhile(n > 0):\n ans += \"1\"\n n -= 2\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '8343\\n', 'output': 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{'type': 'stdin_stdout', 'input': '29\\n', 'output': '71111111111111\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77737","program":"```python\nn = input()\nn = int(n)\nans = \"\"\nif(n % 2 == 1):\n ans += \"7\"\n n -= 3\nwhile(n > 0):\n ans += \"1\"\n n -= 2\nprint(ans)\n```","inputs":"3\n","output":"7\n","actual_output":"7\n","execution_success":true,"sample_index":12404},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"799_C. Fountains","prompt":"Solve the following coding problem using the programming language python:\n\nArkady plays Gardenscapes a lot. Arkady wants to build two new fountains. There are n available fountains, for each fountain its beauty and cost are known. There are two types of money in the game: coins and diamonds, so each fountain cost can be either in coins or diamonds. No money changes between the types are allowed.\n\nHelp Arkady to find two fountains with maximum total beauty so that he can buy both at the same time.\n\nInput\n\nThe first line contains three integers n, c and d (2 \u2264 n \u2264 100 000, 0 \u2264 c, d \u2264 100 000) \u2014 the number of fountains, the number of coins and diamonds Arkady has.\n\nThe next n lines describe fountains. Each of these lines contain two integers bi and pi (1 \u2264 bi, pi \u2264 100 000) \u2014 the beauty and the cost of the i-th fountain, and then a letter \"C\" or \"D\", describing in which type of money is the cost of fountain i: in coins or in diamonds, respectively.\n\nOutput\n\nPrint the maximum total beauty of exactly two fountains Arkady can build. If he can't build two fountains, print 0.\n\nExamples\n\nInput\n\n3 7 6\n10 8 C\n4 3 C\n5 6 D\n\n\nOutput\n\n9\n\n\nInput\n\n2 4 5\n2 5 C\n2 1 D\n\n\nOutput\n\n0\n\n\nInput\n\n3 10 10\n5 5 C\n5 5 C\n10 11 D\n\n\nOutput\n\n10\n\nNote\n\nIn the first example Arkady should build the second fountain with beauty 4, which costs 3 coins. The first fountain he can't build because he don't have enough coins. Also Arkady should build the third fountain with beauty 5 which costs 6 diamonds. Thus the total beauty of built fountains is 9.\n\nIn the second example there are two fountains, but Arkady can't build both of them, because he needs 5 coins for the first fountain, and Arkady has only 4 coins. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport operator\n\nfc = []\nfd = []\n\nn, c, d = map(int, input().split())\n\nfor _ in range(n):\n b, p, m = input().split()\n b, p = int(b), int(p)\n if m == 'C':\n if p <= c:\n fc.append((b, p))\n else:\n if p <= d:\n fd.append((b, p))\n\nfc.sort(key=operator.itemgetter(0), reverse=True)\nfd.sort(key=operator.itemgetter(0), reverse=True)\n\nmx = fc[0][0] + fd[0][0] if fc and fd else 0\n\nfor l, m in ((fc, c), (fd, d)):\n for i in range(len(l) - 1):\n b1, p1 = l[i]\n if b1 * 2 <= mx:\n break\n for j in range(i + 1, len(l)):\n b2, p2 = l[j]\n if b1 + b2 <= mx:\n break\n if p1 + p2 <= m:\n mx = b1 + b2\n break\n\nprint(mx)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 10 10\\n5 5 C\\n5 5 C\\n10 11 D\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '2 4 5\\n2 5 C\\n2 1 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 7 6\\n10 8 C\\n4 3 C\\n5 6 D\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '6 68 40\\n6 16 D\\n11 16 D\\n1 18 D\\n2 20 D\\n7 23 D\\n16 30 D\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '6 68 40\\n1 18 D\\n6 16 D\\n11 16 D\\n7 23 D\\n16 30 D\\n2 20 D\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '2 100000 100000\\n100000 100000 C\\n100000 100000 D\\n', 'output': '200000\\n'}, {'type': 'stdin_stdout', 'input': '4 15 9\\n5 10 C\\n5 10 D\\n6 10 D\\n7 5 C\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '6 4 9\\n6 6 D\\n1 4 D\\n6 7 C\\n7 6 D\\n5 7 D\\n2 5 D\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 1 1\\n1 1 C\\n1 1 D\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n12 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n2 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 13 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n14 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 C\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n18 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '6 4 40\\n1 18 D\\n6 16 D\\n11 16 D\\n7 23 D\\n16 30 D\\n2 20 D\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '4 15 9\\n5 10 C\\n5 10 D\\n6 10 D\\n7 5 D\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '6 4 9\\n6 6 D\\n1 4 D\\n6 7 C\\n7 7 D\\n5 7 D\\n2 5 D\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 1 0\\n1 1 C\\n1 1 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n12 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n2 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 13 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n14 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 C\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '3 10 10\\n5 5 C\\n5 5 C\\n10 10 D\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '3 7 6\\n10 8 D\\n4 3 C\\n5 6 D\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 15 9\\n6 10 C\\n5 10 D\\n6 10 D\\n7 5 D\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '3 10 10\\n9 5 C\\n5 5 C\\n10 10 D\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '6 4 9\\n12 6 D\\n1 4 D\\n6 7 C\\n7 7 D\\n5 7 D\\n3 5 D\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '6 68 40\\n1 18 D\\n6 16 D\\n11 16 D\\n7 23 C\\n16 30 D\\n2 20 D\\n', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '4 15 9\\n4 10 C\\n5 10 D\\n6 10 D\\n7 5 C\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '2 2 1\\n1 1 C\\n1 1 D\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 7 6\\n10 8 C\\n3 3 C\\n5 6 D\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3 7 12\\n10 8 D\\n4 3 C\\n5 6 D\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '6 4 40\\n1 18 D\\n6 16 D\\n11 18 D\\n7 23 D\\n25 30 D\\n2 20 D\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n12 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n2 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 13 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n14 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 D\\n30 24 C\\n33 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '58\\n'}, {'type': 'stdin_stdout', 'input': '2 4 5\\n2 1 C\\n3 1 D\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '2 4 5\\n2 5 C\\n3 1 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6 4 40\\n1 18 D\\n6 16 D\\n11 16 D\\n7 23 D\\n25 30 D\\n2 20 D\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '6 4 9\\n12 6 D\\n1 4 D\\n6 7 C\\n7 7 D\\n5 7 D\\n2 5 D\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 1 0\\n1 1 D\\n1 1 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n12 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n2 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 13 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n14 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 D\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '2 4 5\\n2 10 C\\n3 1 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 7 6\\n10 9 D\\n4 3 C\\n5 6 D\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '6 4 40\\n1 18 D\\n6 16 D\\n11 16 D\\n7 23 D\\n25 30 D\\n0 20 D\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '4 15 9\\n6 10 C\\n5 10 D\\n6 19 D\\n7 5 D\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '2 1 0\\n0 1 D\\n1 1 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n12 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n2 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 13 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n20 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 D\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '3 10 10\\n9 5 C\\n7 5 C\\n10 10 D\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '2 4 5\\n0 10 C\\n3 1 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 7 7\\n10 9 D\\n4 3 C\\n5 6 D\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '6 4 9\\n12 6 D\\n1 5 D\\n6 7 C\\n7 7 D\\n5 7 D\\n3 5 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n16 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n2 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 13 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n20 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 D\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '2 4 5\\n0 10 C\\n3 1 C\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6 4 9\\n12 6 D\\n1 1 D\\n6 7 C\\n7 7 D\\n5 7 D\\n3 5 D\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n16 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n2 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 6 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n20 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 D\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '2 4 5\\n0 10 C\\n3 2 C\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n16 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n4 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 6 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n20 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 D\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '2 4 5\\n0 10 C\\n5 2 C\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 23 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n16 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n4 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 6 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n20 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 D\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 23 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n16 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n4 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 6 D\\n13 15 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n20 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 D\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 23 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n16 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n4 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 6 D\\n13 15 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n3 21 C\\n2 20 C\\n20 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 D\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '6 68 40\\n3 16 D\\n11 16 D\\n1 18 D\\n2 20 D\\n7 23 D\\n16 30 D\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '6 4 9\\n6 6 D\\n1 4 D\\n0 7 C\\n7 6 D\\n5 7 D\\n2 5 D\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n12 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n2 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 13 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n14 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 C\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n1 12 D\\n11 11 C\\n18 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '3 10 10\\n5 7 C\\n5 5 C\\n10 11 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 4 5\\n2 5 D\\n2 1 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6 4 9\\n6 6 D\\n1 4 D\\n6 7 C\\n7 7 D\\n5 7 D\\n2 1 D\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '2 1 0\\n1 1 C\\n0 1 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 23 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n12 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n2 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 13 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n4 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n14 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 C\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '3 10 10\\n8 5 C\\n5 5 C\\n10 10 D\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '4 15 9\\n6 10 C\\n5 10 D\\n7 10 D\\n7 5 D\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '6 4 9\\n12 6 D\\n1 4 D\\n5 7 C\\n7 7 D\\n5 7 D\\n2 5 D\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 1 0\\n1 1 D\\n2 1 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 7 6\\n16 9 D\\n4 3 C\\n5 6 D\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '6 4 16\\n1 18 D\\n6 16 D\\n11 16 D\\n7 23 D\\n25 30 D\\n0 20 D\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 15 9\\n6 10 C\\n2 10 D\\n6 19 D\\n7 5 D\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '6 4 9\\n12 6 D\\n1 4 D\\n6 7 C\\n7 7 D\\n5 3 D\\n3 5 D\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '52 38 22\\n9 25 D\\n28 29 C\\n29 25 D\\n4 28 D\\n23 29 D\\n24 25 D\\n17 12 C\\n11 19 C\\n13 14 C\\n12 15 D\\n7 25 C\\n2 25 C\\n6 17 C\\n2 20 C\\n15 23 D\\n8 21 C\\n13 15 D\\n29 15 C\\n25 20 D\\n22 20 C\\n2 13 D\\n13 22 D\\n27 20 C\\n1 21 D\\n22 17 C\\n14 21 D\\n2 25 D\\n5 23 C\\n9 21 C\\n2 20 C\\n20 18 C\\n29 24 C\\n14 29 D\\n9 27 C\\n23 21 D\\n18 26 D\\n7 23 C\\n13 25 C\\n21 26 D\\n30 24 C\\n21 24 C\\n28 22 C\\n8 29 C\\n3 12 C\\n21 22 D\\n22 26 C\\n13 17 D\\n12 12 D\\n11 11 C\\n29 24 D\\n7 13 D\\n3 11 C\\n', 'output': '57\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77741","program":"```python\nimport operator\n\nfc = []\nfd = []\n\nn, c, d = map(int, input().split())\n\nfor _ in range(n):\n b, p, m = input().split()\n b, p = int(b), int(p)\n if m == 'C':\n if p <= c:\n fc.append((b, p))\n else:\n if p <= d:\n fd.append((b, p))\n\nfc.sort(key=operator.itemgetter(0), reverse=True)\nfd.sort(key=operator.itemgetter(0), reverse=True)\n\nmx = fc[0][0] + fd[0][0] if fc and fd else 0\n\nfor l, m in ((fc, c), (fd, d)):\n for i in range(len(l) - 1):\n b1, p1 = l[i]\n if b1 * 2 <= mx:\n break\n for j in range(i + 1, len(l)):\n b2, p2 = l[j]\n if b1 + b2 <= mx:\n break\n if p1 + p2 <= m:\n mx = b1 + b2\n break\n\nprint(mx)\n\n```","inputs":"3 10 10\n5 5 C\n5 5 C\n10 11 D\n","output":"10\n","actual_output":"10\n","execution_success":true,"sample_index":12405},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"845_A. Chess Tourney","prompt":"Solve the following coding problem using the programming language python:\n\nBerland annual chess tournament is coming!\n\nOrganizers have gathered 2\u00b7n chess players who should be divided into two teams with n people each. The first team is sponsored by BerOil and the second team is sponsored by BerMobile. Obviously, organizers should guarantee the win for the team of BerOil.\n\nThus, organizers should divide all 2\u00b7n players into two teams with n people each in such a way that the first team always wins.\n\nEvery chess player has its rating ri. It is known that chess player with the greater rating always wins the player with the lower rating. If their ratings are equal then any of the players can win.\n\nAfter teams assignment there will come a drawing to form n pairs of opponents: in each pair there is a player from the first team and a player from the second team. Every chess player should be in exactly one pair. Every pair plays once. The drawing is totally random.\n\nIs it possible to divide all 2\u00b7n players into two teams with n people each so that the player from the first team in every pair wins regardless of the results of the drawing?\n\nInput\n\nThe first line contains one integer n (1 \u2264 n \u2264 100).\n\nThe second line contains 2\u00b7n integers a1, a2, ... a2n (1 \u2264 ai \u2264 1000).\n\nOutput\n\nIf it's possible to divide all 2\u00b7n players into two teams with n people each so that the player from the first team in every pair wins regardless of the results of the drawing, then print \"YES\". Otherwise print \"NO\".\n\nExamples\n\nInput\n\n2\n1 3 2 4\n\n\nOutput\n\nYES\n\n\nInput\n\n1\n3 3\n\n\nOutput\n\nNO\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\n\na = sorted(map(int, input().split()))\n\nprint('YES' if a[n] > a[n-1] else 'NO')\n\n\n\n# Made By Mostafa_Khaled\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n1 3 2 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 3 3 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 5 6 8 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 3 2 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 8 10 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3\\n100 99 1 1 1 1\\n', 'output': 'NO\\n'}, {'type': 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'stdin_stdout', 'input': '10\\n1000 1000 1000 1000 1000 1000 0000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 2 1 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1 2 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 4 4 5 8 3 1 5\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1 4 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10 7 4 5 319 19\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 1 1 2 3 5 6 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 4 3 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2 2 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 19 6 8 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 3 3 7\\n', 'output': 'NO\\n'}, {'type': 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 2 2 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3 1 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 4 2 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 7 0 5 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 3 1 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 0 3 5 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 3 4 4 6\\n', 'output': 'YES\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77749","program":"```python\nn = int(input())\n\na = sorted(map(int, input().split()))\n\nprint('YES' if a[n] > a[n-1] else 'NO')\n\n\n\n# Made By Mostafa_Khaled\n```","inputs":"2\n1 3 2 4\n","output":"YES\n","actual_output":"YES\n","execution_success":true,"sample_index":12406},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"961_E. Tufurama","prompt":"Solve the following coding problem using the programming language python:\n\nOne day Polycarp decided to rewatch his absolute favourite episode of well-known TV series \"Tufurama\". He was pretty surprised when he got results only for season 7 episode 3 with his search query of \"Watch Tufurama season 3 episode 7 online full hd free\". This got Polycarp confused \u2014 what if he decides to rewatch the entire series someday and won't be able to find the right episodes to watch? Polycarp now wants to count the number of times he will be forced to search for an episode using some different method.\n\nTV series have n seasons (numbered 1 through n), the i-th season has ai episodes (numbered 1 through ai). Polycarp thinks that if for some pair of integers x and y (x < y) exist both season x episode y and season y episode x then one of these search queries will include the wrong results. Help Polycarp to calculate the number of such pairs!\n\nInput\n\nThe first line contains one integer n (1 \u2264 n \u2264 2\u00b7105) \u2014 the number of seasons.\n\nThe second line contains n integers separated by space a1, a2, ..., an (1 \u2264 ai \u2264 109) \u2014 number of episodes in each season.\n\nOutput\n\nPrint one integer \u2014 the number of pairs x and y (x < y) such that there exist both season x episode y and season y episode x.\n\nExamples\n\nInput\n\n5\n1 2 3 4 5\n\n\nOutput\n\n0\n\n\nInput\n\n3\n8 12 7\n\n\nOutput\n\n3\n\n\nInput\n\n3\n3 2 1\n\n\nOutput\n\n2\n\nNote\n\nPossible pairs in the second example:\n\n 1. x = 1, y = 2 (season 1 episode 2 season 2 episode 1); \n 2. x = 2, y = 3 (season 2 episode 3 season 3 episode 2); \n 3. x = 1, y = 3 (season 1 episode 3 season 3 episode 1). \n\n\n\nIn the third example:\n\n 1. x = 1, y = 2 (season 1 episode 2 season 2 episode 1); \n 2. x = 1, y = 3 (season 1 episode 3 season 3 episode 1). \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom sys import stdin\nfrom sys import setrecursionlimit as SRL; SRL(10**7)\nrd = stdin.readline\nrrd = lambda: map(int, rd().strip().split())\n\nn = int(input())\na = list(rrd())\n\nbit = [0]*(n+100)\n\ndef ins(x):\n while x<=n:\n bit[x] += 1\n x += x&(-x)\n\ndef get(l):\n tot = 0\n while l:\n tot += bit[l]\n l -= l&(-l)\n return tot\n\nta = []\npans = 0\nfor i in range(len(a)):\n if a[i] > i:\n pans += 1\n ta.append([i+1, a[i]])\n\nta.sort(key=lambda x: x[1])\n\nans = 0\nnow = 0\nfor x in ta:\n while now < min(n,x[1]):\n if a[now] <= n:\n ins(a[now])\n now += 1\n ans += now - get(x[0]-1)\n\nprint((ans-pans)//2)\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 2 3 4 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 2 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 12 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\\n', 'output': '45\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 3 4 5 6\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '8\\n7 2 6 6 5 1 4 9\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 3 4 5 9\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '8\\n7 2 6 6 9 1 4 9\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n16 12 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n7 2 6 6 7 1 4 9\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '8\\n13 2 7 6 7 1 4 9\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 6 4 5 6\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '8\\n7 2 1 6 9 1 4 9\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '8\\n8 4 6 6 7 1 4 9\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 9 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n7 2 7 6 7 1 4 9\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 15 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 24 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 46 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n15 46 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n15 46 13\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n15 77 13\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n15 77 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n24 77 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n41 77 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n26 77 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n23 77 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n23 28 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n23 28 42\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n19 28 42\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n19 28 13\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n14 2 6 6 5 1 4 9\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n15 12 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 4 5 9\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 12 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '8\\n8 2 6 6 7 1 4 9\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 1 7\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '8\\n7 2 7 4 7 1 4 9\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3\\n15 15 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n10 2 7 6 7 1 4 9\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 35 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n15 46 5\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n27 46 13\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n15 34 13\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n15 77 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n24 27 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n72 77 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n31 77 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n23 47 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10 28 22\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n23 50 42\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n9 28 42\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n19 2 13\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 4 5 6\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n14 2 6 6 2 1 4 9\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3\\n15 19 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 4 5 9\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n8 2 1 6 9 1 4 9\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 12 7\\n', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77769","program":"```python\nfrom sys import stdin\nfrom sys import setrecursionlimit as SRL; SRL(10**7)\nrd = stdin.readline\nrrd = lambda: map(int, rd().strip().split())\n\nn = int(input())\na = list(rrd())\n\nbit = [0]*(n+100)\n\ndef ins(x):\n while x<=n:\n bit[x] += 1\n x += x&(-x)\n\ndef get(l):\n tot = 0\n while l:\n tot += bit[l]\n l -= l&(-l)\n return tot\n\nta = []\npans = 0\nfor i in range(len(a)):\n if a[i] > i:\n pans += 1\n ta.append([i+1, a[i]])\n\nta.sort(key=lambda x: x[1])\n\nans = 0\nnow = 0\nfor x in ta:\n while now < min(n,x[1]):\n if a[now] <= n:\n ins(a[now])\n now += 1\n ans += now - get(x[0]-1)\n\nprint((ans-pans)//2)\n\n\n\n```","inputs":"5\n1 2 3 4 5\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12407},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"989_D. A Shade of Moonlight","prompt":"Solve the following coding problem using the programming language python:\n\nGathering darkness shrouds the woods and the world. The moon sheds its light on the boat and the river.\n\n\"To curtain off the moonlight should be hardly possible; the shades present its mellow beauty and restful nature.\" Intonates Mino.\n\n\"See? The clouds are coming.\" Kanno gazes into the distance.\n\n\"That can't be better,\" Mino turns to Kanno. \n\nThe sky can be seen as a one-dimensional axis. The moon is at the origin whose coordinate is 0.\n\nThere are n clouds floating in the sky. Each cloud has the same length l. The i-th initially covers the range of (x_i, x_i + l) (endpoints excluded). Initially, it moves at a velocity of v_i, which equals either 1 or -1.\n\nFurthermore, no pair of clouds intersect initially, that is, for all 1 \u2264 i < j \u2264 n, \\lvert x_i - x_j \\rvert \u2265 l.\n\nWith a wind velocity of w, the velocity of the i-th cloud becomes v_i + w. That is, its coordinate increases by v_i + w during each unit of time. Note that the wind can be strong and clouds can change their direction.\n\nYou are to help Mino count the number of pairs (i, j) (i < j), such that with a proper choice of wind velocity w not exceeding w_max in absolute value (possibly negative and/or fractional), the i-th and j-th clouds both cover the moon at the same future moment. This w doesn't need to be the same across different pairs.\n\nInput\n\nThe first line contains three space-separated integers n, l, and w_max (1 \u2264 n \u2264 10^5, 1 \u2264 l, w_max \u2264 10^8) \u2014 the number of clouds, the length of each cloud and the maximum wind speed, respectively.\n\nThe i-th of the following n lines contains two space-separated integers x_i and v_i (-10^8 \u2264 x_i \u2264 10^8, v_i \u2208 \\{-1, 1\\}) \u2014 the initial position and the velocity of the i-th cloud, respectively.\n\nThe input guarantees that for all 1 \u2264 i < j \u2264 n, \\lvert x_i - x_j \\rvert \u2265 l.\n\nOutput\n\nOutput one integer \u2014 the number of unordered pairs of clouds such that it's possible that clouds from each pair cover the moon at the same future moment with a proper choice of wind velocity w.\n\nExamples\n\nInput\n\n5 1 2\n-2 1\n2 1\n3 -1\n5 -1\n7 -1\n\n\nOutput\n\n4\n\n\nInput\n\n4 10 1\n-20 1\n-10 -1\n0 1\n10 -1\n\n\nOutput\n\n1\n\nNote\n\nIn the first example, the initial positions and velocities of clouds are illustrated below.\n\n\n\nThe pairs are: \n\n * (1, 3), covering the moon at time 2.5 with w = -0.4; \n * (1, 4), covering the moon at time 3.5 with w = -0.6; \n * (1, 5), covering the moon at time 4.5 with w = -0.7; \n * (2, 5), covering the moon at time 2.5 with w = -2. \n\n\n\nBelow is the positions of clouds at time 2.5 with w = -0.4. At this moment, the 1-st and 3-rd clouds both cover the moon.\n\n\n\nIn the second example, the only pair is (1, 4), covering the moon at time 15 with w = 0.\n\nNote that all the times and wind velocities given above are just examples among infinitely many choices.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# Codeforces Round #487 (Div. 2)import collections\nfrom functools import cmp_to_key\n#key=cmp_to_key(lambda x,y: 1 if x not in y else -1 )\n\nimport sys\ndef getIntList():\n return list(map(int, input().split())) \nimport bisect\n \n \n \nN,L,WM = getIntList()\n\nz = {}\nz[-1] = {1:[], -1:[]}\nz[0] = {1:[], -1:[]}\nz[1] = {1:[], -1:[]}\nfor i in range(N):\n x0,v = getIntList()\n t = (x0,v)\n if x0+L <=0:\n z[-1][v].append(t)\n elif x0>=0:\n z[1][v].append(t)\n else:\n z[0][v].append(t)\nres = 0\n\nres += len(z[-1][1] ) * len(z[ 1][-1] )\nres += len(z[0][1] ) * len(z[ 1][-1] )\nres += len(z[-1][1] ) * len(z[ 0][-1] )\n\nif WM==1:\n print(res)\n sys.exit()\n\nz[1][-1].sort()\nz[-1][1].sort()\n#print(z[-1][1])\ntn = len(z[1][-1])\nfor t in z[1][1]:\n g = (-WM-1) * t[0] / (-WM+1) - L\n g = max(g, t[0]+ 0.5)\n p = bisect.bisect_right(z[1][-1], (g,2) )\n res += tn-p \n \ntn = len(z[-1][1])\nfor t in z[-1][-1]:\n g = (WM+1) * (t[0] + L)/ (WM-1)\n g = min(g, t[0] - 0.1)\n \n p = bisect.bisect_left(z[-1][1], (g,-2) )\n res += p \n\nprint(res)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 1 2\\n-2 1\\n2 1\\n3 -1\\n5 -1\\n7 -1\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '4 10 1\\n-20 1\\n-10 -1\\n0 1\\n10 -1\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '3 4 5\\n9 1\\n-4 1\\n-8 -1\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '2 5 1\\n-9 -1\\n-2 1\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 1 1\\n-6 1\\n15 1\\n-7 1\\n-13 -1\\n12 -1\\n', 'output': '2'}, 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list(map(int, input().split())) \nimport bisect\n \n \n \nN,L,WM = getIntList()\n\nz = {}\nz[-1] = {1:[], -1:[]}\nz[0] = {1:[], -1:[]}\nz[1] = {1:[], -1:[]}\nfor i in range(N):\n x0,v = getIntList()\n t = (x0,v)\n if x0+L <=0:\n z[-1][v].append(t)\n elif x0>=0:\n z[1][v].append(t)\n else:\n z[0][v].append(t)\nres = 0\n\nres += len(z[-1][1] ) * len(z[ 1][-1] )\nres += len(z[0][1] ) * len(z[ 1][-1] )\nres += len(z[-1][1] ) * len(z[ 0][-1] )\n\nif WM==1:\n print(res)\n sys.exit()\n\nz[1][-1].sort()\nz[-1][1].sort()\n#print(z[-1][1])\ntn = len(z[1][-1])\nfor t in z[1][1]:\n g = (-WM-1) * t[0] / (-WM+1) - L\n g = max(g, t[0]+ 0.5)\n p = bisect.bisect_right(z[1][-1], (g,2) )\n res += tn-p \n \ntn = len(z[-1][1])\nfor t in z[-1][-1]:\n g = (WM+1) * (t[0] + L)/ (WM-1)\n g = min(g, t[0] - 0.1)\n \n p = bisect.bisect_left(z[-1][1], (g,-2) )\n res += p \n\nprint(res)\n\n```","inputs":"5 1 2\n-2 1\n2 1\n3 -1\n5 -1\n7 -1\n","output":"4","actual_output":"4\n","execution_success":true,"sample_index":12408},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02602 M-SOLUTIONS Programming Contest 2020 - Marks","prompt":"Solve the following coding problem using the programming language python:\n\nM-kun is a student in Aoki High School, where a year is divided into N terms.\nThere is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows:\n\n* For the first through (K-1)-th terms: not given.\n* For each of the K-th through N-th terms: the multiplication of the scores in the last K exams, including the exam in the graded term.\n\n\n\nM-kun scored A_i in the exam at the end of the i-th term.\nFor each i such that K+1 \\leq i \\leq N, determine whether his grade for the i-th term is strictly greater than the grade for the (i-1)-th term.\n\nConstraints\n\n* 2 \\leq N \\leq 200000\n* 1 \\leq K \\leq N-1\n* 1 \\leq A_i \\leq 10^{9}\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN K\nA_1 A_2 A_3 \\ldots A_N\n\n\nOutput\n\nPrint the answer in N-K lines.\nThe i-th line should contain `Yes` if the grade for the (K+i)-th term is greater than the grade for the (K+i-1)-th term, and `No` otherwise.\n\nExamples\n\nInput\n\n5 3\n96 98 95 100 20\n\n\nOutput\n\nYes\nNo\n\n\nInput\n\n3 2\n1001 869120 1001\n\n\nOutput\n\nNo\n\n\nInput\n\n15 7\n3 1 4 1 5 9 2 6 5 3 5 8 9 7 9\n\n\nOutput\n\nYes\nYes\nNo\nYes\nYes\nNo\nYes\nYes\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN, K = map(int, input().split())\nA = list(map(int, input().split()))\nfor i in range(N-K):\n print('Yes' if A[i+K]>A[i] else 'No')\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 2\\n1001 869120 1001', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 4 1 5 9 2 6 5 3 5 8 9 7 9', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes'}, {'type': 'stdin_stdout', 'input': '5 3\\n96 98 95 100 20', 'output': 'Yes\\nNo'}, {'type': 'stdin_stdout', 'input': '3 1\\n1001 869120 1001', 'output': 'Yes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 4 1 5 9 2 6 5 3 5 7 9 7 9', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 4 1 5 9 2 6 5 5 5 7 9 7 9', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 8 1 5 9 1 8 1 5 9 7 9 7 16', 'output': 'Yes\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 9 1 5 5 0 8 1 5 9 8 9 7 15', 'output': 'Yes\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1011 869120 1001', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n96 98 95 000 20', 'output': 'No\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n96 98 162 100 39', 'output': 'No\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 8 1 5 8 1 6 5 5 9 7 9 7 9', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 11\\n3 1 8 1 5 9 1 6 5 5 9 7 9 7 16', 'output': 'Yes\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n0011 869120 1001', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 4 1 5 9 2 6 5 3 5 7 9 1 9', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n0 1 8 1 5 9 1 11 5 5 5 7 9 7 9', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 9 2 5 5 0 8 1 5 2 8 9 2 15', 'output': 'Yes\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 4 1 5 9 1 0 8 3 5 8 9 7 16', 'output': 'No\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 11\\n3 1 0 0 6 9 1 6 5 5 9 7 9 7 16', 'output': 'Yes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n3 1 8 1 5 9 1 8 1 5 9 13 9 3 28', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 8 1 5 9 4 6 5 5 10 0 7 4 9', 'output': 'Yes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n6 1 8 1 6 9 1 2 1 5 9 13 9 3 28', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n2 1 9 1 5 9 1 8 1 0 9 7 17 0 15', 'output': 'Yes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 2 8 1 3 9 2 11 1 5 9 10 11 7 3', 'output': 'Yes\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 0 17 1 5 9 1 8 5 11 9 5 0 3 18', 'output': 'Yes\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 2 6 1 5 1 4 6 5 5 10 0 7 4 7', 'output': 'Yes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 4\\n3 0 17 1 5 9 1 8 5 11 9 5 0 3 18', 'output': 'Yes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 2 8 1 3 17 2 11 1 6 9 10 11 7 3', 'output': 'Yes\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 4\\n3 0 17 1 5 9 2 8 9 11 9 5 0 3 18', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 2 4 1 5 2 4 5 5 5 10 0 7 4 7', 'output': 'Yes\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 4\\n3 0 17 1 3 9 2 8 9 11 9 5 0 3 18', 'output': 'No\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 6\\n3 0 17 1 3 9 2 8 9 11 9 5 0 3 18', 'output': 'No\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n4 1 9 2 0 5 0 8 1 5 4 0 17 2 54', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 11\\n1 1 9 0 0 5 0 16 1 5 6 -1 25 2 54', 'output': 'No\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 4 1 5 9 2 12 5 5 5 7 9 7 9', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 10\\n3 1 9 1 5 9 0 8 1 5 9 8 9 7 15', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 10\\n0 1 8 1 5 9 1 6 5 5 5 7 9 7 9', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 5\\n3 1 9 1 5 5 0 8 1 5 2 8 9 7 15', 'output': 'Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n1101 681697 1001', 'output': 'No\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 10\\n3 1 4 1 5 9 2 6 5 3 5 7 9 1 9', 'output': 'Yes\\nYes\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 6\\n3 1 8 1 5 9 1 8 5 5 9 7 9 3 18', 'output': 'No\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n1 1 12 1 5 9 0 8 1 5 1 8 9 7 15', 'output': 'Yes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n2 1 1 1 5 9 0 8 1 5 9 7 9 4 15', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 2 2 5 5 0 8 1 5 2 8 9 2 15', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 4 1 5 9 1 0 8 3 0 8 9 7 16', 'output': 'No\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n0 1 8 1 10 9 1 10 5 5 5 7 4 7 9', 'output': 'Yes\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 9 2 5 5 0 8 1 5 2 8 17 0 28', 'output': 'Yes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n2 1 4 1 6 9 2 10 5 3 5 7 9 2 9', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 13\\n3 2 8 1 3 9 1 11 1 5 9 10 11 7 16', 'output': 'Yes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n6 1 8 1 0 9 1 2 1 5 9 13 9 3 28', 'output': 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'stdin_stdout', 'input': '15 7\\n6 1 11 1 5 9 4 6 5 5 10 0 7 4 7', 'output': 'No\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 9\\n2 2 8 1 3 9 2 11 1 5 9 10 11 7 16', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n6 1 8 1 0 9 1 2 1 1 9 13 9 3 28', 'output': 'Yes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 2 8 2 5 9 4 6 2 5 10 0 7 4 7', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 5\\n3 0 17 1 3 9 2 10 9 11 9 5 0 3 18', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n0 1 8 1 7 9 2 11 8 8 1 7 3 7 39', 'output': 'Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n1 1 9 2 0 5 0 16 1 5 5 0 0 2 54', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 3\\n1 1 11 0 0 5 0 16 1 5 3 0 17 2 54', 'output': 'No\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 4 1 5 9 1 6 10 5 1 7 9 7 9', 'output': 'Yes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n1 1 8 1 5 8 1 6 5 5 9 8 9 7 1', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n3 1 9 1 5 5 0 8 1 5 4 8 9 7 15', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 6\\n3 1 8 1 5 12 1 6 5 5 9 1 0 7 9', 'output': 'No\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n4 1 4 0 6 9 2 6 5 3 5 7 9 1 9', 'output': 'No\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n3 1 9 2 6 9 1 0 1 5 9 13 9 3 28', 'output': 'Yes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 5\\n3 2 8 2 5 9 4 6 2 5 10 0 7 4 7', 'output': 'Yes\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n6 1 9 1 6 9 0 2 1 9 9 13 9 3 38', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 6 6 1 5 1 4 6 5 5 10 0 7 0 7', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 0 9 2 0 5 -1 0 1 5 4 8 17 3 55', 'output': 'No\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n0 0 0 2 0 5 0 8 2 5 4 8 17 2 54', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 3\\n3 0 4 1 5 2 4 5 4 6 10 0 7 4 7', 'output': 'No\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 2 4 1 5 2 4 2 4 10 10 0 7 4 11', 'output': 'No\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n0 1 8 0 2 9 3 3 8 8 4 7 3 7 54', 'output': 'Yes\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 1\\n3 0 8 1 6 9 1 6 5 5 9 7 2 7 16', 'output': 'No\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 4 1 9 9 0 6 5 3 4 7 11 3 9', 'output': 'Yes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 4 1 5 9 1 6 10 5 1 5 9 7 9', 'output': 'Yes\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n9 1 9 1 5 17 0 9 1 5 9 7 9 7 1', 'output': 'No\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n6 1 9 2 5 9 0 8 1 5 9 7 9 0 2', 'output': 'Yes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 1\\n3 2 8 1 7 9 4 6 5 5 5 7 4 4 9', 'output': 'No\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n2 1 1 2 5 9 0 2 1 5 17 7 9 4 15', 'output': 'No\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 5\\n3 1 4 1 2 9 1 -1 8 3 0 8 9 7 16', 'output': 'Yes\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 10\\n5 1 8 1 5 9 4 6 5 5 3 14 4 4 9', 'output': 'No\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n3 1 9 2 5 5 0 0 1 5 4 8 11 0 28', 'output': 'No\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 3\\n2 1 4 1 6 9 2 10 5 3 9 7 6 2 9', 'output': 'No\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n6 1 8 2 12 9 1 8 1 6 9 15 9 3 28', 'output': 'Yes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 8\\n1 1 12 0 0 10 0 8 2 7 9 8 9 7 15', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n-2 1 8 1 4 9 1 10 8 16 5 0 4 7 24', 'output': 'Yes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 5\\n3 0 17 1 1 9 2 10 9 11 9 1 0 3 18', 'output': 'Yes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 7\\n4 1 9 2 0 5 1 3 1 5 6 1 17 2 54', 'output': 'No\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 6\\n3 0 9 1 5 18 1 8 1 0 9 10 9 7 15', 'output': 'No\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 10\\n6 2 4 1 5 0 2 6 5 3 5 7 9 1 9', 'output': 'No\\nYes\\nYes\\nNo\\nYes\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_77817","program":"```python\nN, K = map(int, input().split())\nA = list(map(int, input().split()))\nfor i in range(N-K):\n print('Yes' if A[i+K]>A[i] else 'No')\n```","inputs":"3 2\n1001 869120 1001","output":"No","actual_output":"No\n","execution_success":true,"sample_index":12409},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02733 AtCoder Beginner Contest 159 - Dividing Chocolate","prompt":"Solve the following coding problem using the programming language python:\n\nWe have a chocolate bar partitioned into H horizontal rows and W vertical columns of squares.\n\nThe square (i, j) at the i-th row from the top and the j-th column from the left is dark if S_{i,j} is `0`, and white if S_{i,j} is `1`.\n\nWe will cut the bar some number of times to divide it into some number of blocks. In each cut, we cut the whole bar by a line running along some boundaries of squares from end to end of the bar.\n\nHow many times do we need to cut the bar so that every block after the cuts has K or less white squares?\n\nConstraints\n\n* 1 \\leq H \\leq 10\n* 1 \\leq W \\leq 1000\n* 1 \\leq K \\leq H \\times W\n* S_{i,j} is `0` or `1`.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nH W K\nS_{1,1}S_{1,2}...S_{1,W}\n:\nS_{H,1}S_{H,2}...S_{H,W}\n\n\nOutput\n\nPrint the number of minimum times the bar needs to be cut so that every block after the cuts has K or less white squares.\n\nExamples\n\nInput\n\n3 5 4\n11100\n10001\n00111\n\n\nOutput\n\n2\n\n\nInput\n\n3 5 8\n11100\n10001\n00111\n\n\nOutput\n\n0\n\n\nInput\n\n4 10 4\n1110010010\n1000101110\n0011101001\n1101000111\n\n\nOutput\n\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nH, W, K = map(int, input().split())\nS = [list(input()) for _ in range(H)]\n\nres = float('inf')\nfor i in range(2**(H-1)):\n c = bin(i).count('1')\n cnt = c\n sum_l = [0] * (c+1)\n j = 0\n flag = True\n while j < W:\n tmp = sum_l.copy()\n pos = 0\n for k in range(H):\n if S[k][j] == '1':\n tmp[pos] += 1\n if (i >> k) & 1:\n pos += 1\n if max(tmp) <= K:\n sum_l = tmp.copy()\n j += 1\n flag = False\n else:\n if flag:\n cnt = float('inf')\n break\n cnt += 1\n flag = True\n sum_l = [0] * (c+1)\n\n res = min(res, cnt)\n\nprint(res)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 10 4\\n1110010010\\n1000101110\\n0011101001\\n1101000111', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3 5 8\\n11100\\n10001\\n00111', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 5 4\\n11100\\n10001\\n00111', 'output': '2'}, {'type': 'stdin_stdout', 'input': '4 10 4\\n1110010010\\n1000101110\\n0011101001\\n1101000011', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 5 8\\n11100\\n10101\\n00111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 10 3\\n1110010010\\n1000101110\\n0011101101\\n1101000011', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3 5 8\\n11100\\n00101\\n00111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 10 3\\n1110010010\\n1000101110\\n0011101111\\n1101000011', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1110010010\\n1100101011\\n0011100111\\n1101000111', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 10 2\\n1010110011\\n1001101011\\n0011101111\\n1001000111', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3 5 4\\n11100\\n10001\\n00110', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 10 4\\n1110010010\\n1000101110\\n0011101101\\n1101000011', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 5 8\\n11100\\n10111\\n00111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 0 8\\n11100\\n00101\\n00111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 10 3\\n1110110010\\n1000101110\\n0011101111\\n1101000011', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5 0 8\\n11100\\n00101\\n00111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 10 3\\n1110110010\\n1000101010\\n0011101111\\n1101000011', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '8 0 8\\n11100\\n00101\\n00111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 10 3\\n1110110010\\n1000101010\\n0011101111\\n1101000111', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '8 0 8\\n11100\\n00101\\n01111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 10 3\\n1110110010\\n1000101011\\n0011101111\\n1101000111', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '8 0 8\\n11100\\n10101\\n01111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110110010\\n1000101011\\n0011101111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 0 8\\n11100\\n10101\\n01111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110110010\\n1000101011\\n0010101111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 0 8\\n11100\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110110010\\n1000101011\\n0010100111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 0 5\\n11100\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110110010\\n1100101011\\n0010100111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 0 5\\n11100\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110010010\\n1100101011\\n0010100111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '0 0 5\\n11100\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110010010\\n1100101011\\n0011100111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '0 0 5\\n11101\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 0 5\\n11101\\n10101\\n11011', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1110010010\\n1100101011\\n0011100011\\n1101000111', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '0 0 5\\n11101\\n00101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1110010010\\n1100101011\\n1011100011\\n1101000111', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '0 0 5\\n11101\\n00001\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1110010010\\n1110101011\\n1011100011\\n1101000111', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '0 1 5\\n11101\\n00001\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1110010010\\n1110101011\\n1011110011\\n1101000111', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '0 1 0\\n11101\\n00001\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1110010010\\n1110101011\\n1011110011\\n1101000011', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 0 4\\n1110010010\\n1000101110\\n0011101001\\n1101000111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 5 6\\n11100\\n10001\\n00111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 10 4\\n1110010010\\n1001101110\\n0011101001\\n1101000011', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 10 4\\n1110010010\\n1000100110\\n0011101101\\n1101000011', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 5 8\\n11100\\n10111\\n00011', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 3 3\\n1110010010\\n1000101110\\n0011101101\\n1101000011', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 5 8\\n11100\\n00101\\n00110', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 10 3\\n1110010010\\n1000101110\\n0011101111\\n1101000011', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3 0 8\\n11101\\n00101\\n00111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 10 3\\n1110110010\\n1000001110\\n0011101111\\n1101000011', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5 0 8\\n11100\\n00101\\n00101', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6 0 8\\n11100\\n00101\\n00111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 10 3\\n1110110010\\n1000101011\\n0011101111\\n1101000111', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '8 0 8\\n11000\\n10101\\n01111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 10 3\\n1110110011\\n1000101011\\n0011101111\\n1101000111', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '0 0 8\\n11100\\n10101\\n01111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110110110\\n1000101011\\n0011101111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 0 8\\n11100\\n10101\\n01101', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110110010\\n1000101011\\n1010101111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 1 8\\n11100\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 1\\n1110110010\\n1000101011\\n0010100111\\n1101000111', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 0 5\\n11101\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 4 3\\n1110110010\\n1100101011\\n0010100111\\n1101000111', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 0 5\\n11000\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110010010\\n1000101011\\n0010100111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '0 -1 5\\n11100\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110010010\\n1100101010\\n0011100111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '0 0 5\\n01101\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1110010010\\n1000101011\\n0011100111\\n1101000111', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '0 0 5\\n11101\\n10100\\n11011', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 1\\n1110010010\\n1100101011\\n0011100011\\n1101000111', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '0 0 5\\n11101\\n00101\\n01111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1110010010\\n1100101011\\n1111100011\\n1101000111', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 0 5\\n11101\\n00001\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 1 5\\n11001\\n00001\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 1\\n1110010010\\n1110101011\\n1011110011\\n1101000111', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110010010\\n1110101011\\n1011110011\\n1101000011', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 0 4\\n1110010010\\n1000101110\\n0011101001\\n1101000111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 5 6\\n11100\\n10011\\n00111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 10 4\\n1110010010\\n1001101100\\n0011101001\\n1101000011', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 10 4\\n1110010010\\n1000100110\\n0011101100\\n1101000011', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 5 8\\n11000\\n10111\\n00011', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 6 3\\n1110010010\\n1000101110\\n0011101101\\n1101000011', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 5 8\\n11100\\n00100\\n00110', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 10 2\\n1110010010\\n1000101110\\n0011101111\\n1101000011', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3 0 8\\n11101\\n01101\\n00111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6 0 8\\n01100\\n00101\\n00111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 10 3\\n1110110010\\n1000100011\\n0011101111\\n1101000111', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 0 8\\n11000\\n10101\\n01111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 10 3\\n1110110011\\n1000101011\\n0011101111\\n1001000111', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '0 0 2\\n11100\\n10101\\n01111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 4\\n1110110110\\n1000101011\\n0011101111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 0 8\\n11000\\n10101\\n01101', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1010110010\\n1000101011\\n1010101111\\n1101000111', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 1 8\\n01100\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 0 5\\n11101\\n10101\\n10111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 4 3\\n1110110010\\n1100100011\\n0010100111\\n1101000111', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 0 1\\n11000\\n10101\\n11111', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1110011010\\n1000101011\\n0010100111\\n1101000111', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_77821","program":"```python\nH, W, K = map(int, input().split())\nS = [list(input()) for _ in range(H)]\n\nres = float('inf')\nfor i in range(2**(H-1)):\n c = bin(i).count('1')\n cnt = c\n sum_l = [0] * (c+1)\n j = 0\n flag = True\n while j < W:\n tmp = sum_l.copy()\n pos = 0\n for k in range(H):\n if S[k][j] == '1':\n tmp[pos] += 1\n if (i >> k) & 1:\n pos += 1\n if max(tmp) <= K:\n sum_l = tmp.copy()\n j += 1\n flag = False\n else:\n if flag:\n cnt = float('inf')\n break\n cnt += 1\n flag = True\n sum_l = [0] * (c+1)\n\n res = min(res, cnt)\n\nprint(res)\n```","inputs":"4 10 4\n1110010010\n1000101110\n0011101001\n1101000111","output":"3","actual_output":"3\n","execution_success":true,"sample_index":12410},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02867 NIKKEI Programming Contest 2019-2 - Swaps","prompt":"Solve the following coding problem using the programming language python:\n\nGiven are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \\leq B_i holds:\n\n* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.\n\nConstraints\n\n* 2 \\leq N \\leq 10^5\n* 1 \\leq A_i,B_i \\leq 10^9\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nA_1 A_2 ... A_N\nB_1 B_2 ... B_N\n\n\nOutput\n\nIf the objective is achievable, print `Yes`; if it is not, print `No`.\n\nExamples\n\nInput\n\n3\n1 3 2\n1 2 3\n\n\nOutput\n\nYes\n\n\nInput\n\n3\n1 2 3\n2 2 2\n\n\nOutput\n\nNo\n\n\nInput\n\n6\n3 1 2 6 3 4\n2 2 8 3 4 3\n\n\nOutput\n\nYes\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom heapq import heappush, heappop\nfrom collections import deque\nimport re\nimport math\nimport functools\n\ndef sRaw():\n return input().rstrip(\"\\r\")\n\ndef iRaw():\n return int(input())\n\n\ndef ssRaw():\n return input().split()\n\n\ndef isRaw():\n return list(map(int, ssRaw()))\n\nINF = 1 << 29\n\n\ndef make1d_arr(n, val=INF):\n return [val for i in range(n)]\n\n\ndef make2d_arr(h, w, val=INF):\n return [[val for i in range(w)]for i in range(h)]\n\n\ndef gcd(a, b):\n if(b == 0):\n return a\n return gcd(b, a % b)\n\n\ndef BFord(n,es):\n v_cost = [INF]*n\n v_cost[0] = 0\n for v in range(n*2):\n for e in es:\n frm = e[0]\n to = e[1]\n if v_cost[to] > v_cost[frm]+e[2]:\n v_cost[to] = v_cost[frm]+e[2]\n if v >= n:\n v_cost[to] = -INF\n if v == n-1:\n prev = v_cost[:]\n v_cost = [-INF if prev[idx]!=v_cost[idx] else v_cost[idx] for idx in range(n)]\n return v_cost\n \ndef ZAlgo(s):\n l = len(s)\n A = [0]*l\n i =1\n j =0\n A[0]=l\n while iBAs[sIdx][0]:\n return \"No\"\n sAidx[idx]=sIdx\n cycleSize = 0\n curIdx = 0\n visited = [0]*len(AIs)\n while visited[curIdx]==0:\n visited[curIdx]=1\n cycleSize +=1\n curIdx = sAidx[curIdx]\n if cycleSize < N:\n return \"Yes\"\n\n for idx in range(N-1):\n if AIs[idx+1][0]<=BAs[idx][0]:\n return \"Yes\"\n return \"No\"\n\nif __name__ == \"__main__\":\n print(main())\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 2 3\\n2 2 2', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '6\\n3 1 2 6 3 4\\n2 2 8 3 4 3', 'output': 'Yes'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 2\\n1 2 3', 'output': 'Yes'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 3\\n2 2 2', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 2\\n2 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n3 1 2 6 3 4\\n2 2 8 2 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 6\\n2 2 2', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 2 6 3 4\\n2 2 8 3 4 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 2\\n3 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 6\\n2 2 4', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 4 6 3 4\\n2 2 8 3 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 2\\n3 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 6\\n3 2 4', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 4 6 3 4\\n2 2 8 6 4 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 2\\n5 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n3 2 4', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 4 7 3 4\\n2 2 8 6 4 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 2\\n5 4 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n2 2 4', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 2 7 3 4\\n2 2 8 6 4 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 6 2\\n5 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 0\\n2 2 4', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 2 7 3 4\\n2 2 8 6 4 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 6 2\\n5 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 3 0\\n2 2 4', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 2 3 3 4\\n2 2 8 6 4 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 6 3\\n5 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n2 2 4', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 2 3 3 6\\n2 2 8 6 4 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 6 3\\n1 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n2 4 4', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 1 2 3 3 6\\n2 2 8 6 4 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 6 5\\n1 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n2 8 4', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 1 2 3 3 6\\n2 2 8 6 1 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 6 5\\n0 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n2 8 6', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 1 2 3 3 6\\n1 2 8 6 1 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 6 5\\n-1 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n2 8 7', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 0 2 3 3 6\\n1 2 8 6 1 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 11 5\\n-1 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n2 8 14', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 0 1 3 3 6\\n1 2 8 6 1 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 3 5\\n-1 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0 8 14', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 0 1 3 3 6\\n1 2 8 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 6 9\\n-1 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 1\\n0 8 14', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 0 1 3 3 6\\n1 2 8 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 11 9\\n-1 4 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 1\\n0 8 14', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 0 1 2 3 6\\n1 2 8 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 11 9\\n-1 4 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 1\\n0 14 14', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 0 1 2 3 6\\n1 2 8 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 11 17\\n-1 4 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 1\\n0 14 14', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 0 1 2 3 6\\n1 2 14 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 11 17\\n-2 4 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 1\\n-1 14 14', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 0 1 2 3 6\\n0 2 14 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 11 17\\n-2 5 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -2 1\\n-1 14 14', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 0 1 2 3 12\\n0 2 14 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 11 17\\n-2 10 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -2 2\\n-1 14 14', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 0 1 2 3 12\\n0 2 14 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5 11 17\\n-2 10 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -3 2\\n-1 14 14', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 0 1 2 3 12\\n0 4 14 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 11 17\\n-2 10 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -3 2\\n-1 14 8', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 0 1 2 3 12\\n1 4 14 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 11 14\\n-2 10 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -3 2\\n-1 14 8', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 0 1 2 3 12\\n1 4 4 6 2 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 11 14\\n-2 10 4', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -3 2\\n-1 18 8', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 0 1 2 4 12\\n1 4 4 6 2 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 11 14\\n-2 10 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -3 2\\n-1 18 8', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 1 2 4 12\\n1 4 4 6 2 3', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 11 14\\n-1 10 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -3 0\\n-1 18 8', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 1 2 4 5\\n1 4 4 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 11 14\\n-1 11 6', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -3 -1\\n-1 18 8', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 1 2 4 5\\n1 1 4 6 2 3', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 11 14\\n-1 11 4', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -3 -1\\n-1 18 5', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 1 2 4 5\\n1 1 4 6 2 5', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 19 14\\n-1 11 4', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -3 -1\\n0 18 5', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 1 2 4 5\\n1 1 0 6 2 5', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 19 14\\n-1 11 4', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -3 -1\\n0 18 5', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 1 2 4 5\\n1 1 0 6 2 1', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 19 14\\n-2 11 4', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -3 -1\\n-1 18 5', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 1 4 4 5\\n1 1 0 6 2 1', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 19 14\\n-2 2 4', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 -3 -1\\n-1 18 5', 'output': 'Yes\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_77825","program":"```python\nfrom heapq import heappush, heappop\nfrom collections import deque\nimport re\nimport math\nimport functools\n\ndef sRaw():\n return input().rstrip(\"\\r\")\n\ndef iRaw():\n return int(input())\n\n\ndef ssRaw():\n return input().split()\n\n\ndef isRaw():\n return list(map(int, ssRaw()))\n\nINF = 1 << 29\n\n\ndef make1d_arr(n, val=INF):\n return [val for i in range(n)]\n\n\ndef make2d_arr(h, w, val=INF):\n return [[val for i in range(w)]for i in range(h)]\n\n\ndef gcd(a, b):\n if(b == 0):\n return a\n return gcd(b, a % b)\n\n\ndef BFord(n,es):\n v_cost = [INF]*n\n v_cost[0] = 0\n for v in range(n*2):\n for e in es:\n frm = e[0]\n to = e[1]\n if v_cost[to] > v_cost[frm]+e[2]:\n v_cost[to] = v_cost[frm]+e[2]\n if v >= n:\n v_cost[to] = -INF\n if v == n-1:\n prev = v_cost[:]\n v_cost = [-INF if prev[idx]!=v_cost[idx] else v_cost[idx] for idx in range(n)]\n return v_cost\n \ndef ZAlgo(s):\n l = len(s)\n A = [0]*l\n i =1\n j =0\n A[0]=l\n while iBAs[sIdx][0]:\n return \"No\"\n sAidx[idx]=sIdx\n cycleSize = 0\n curIdx = 0\n visited = [0]*len(AIs)\n while visited[curIdx]==0:\n visited[curIdx]=1\n cycleSize +=1\n curIdx = sAidx[curIdx]\n if cycleSize < N:\n return \"Yes\"\n\n for idx in range(N-1):\n if AIs[idx+1][0]<=BAs[idx][0]:\n return \"Yes\"\n return \"No\"\n\nif __name__ == \"__main__\":\n print(main())\n\n```","inputs":"3\n1 2 3\n2 2 2","output":"No","actual_output":"No\n","execution_success":true,"sample_index":12411},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03142 NIKKEI Programming Contest 2019 - Restore the Tree","prompt":"Solve the following coding problem using the programming language python:\n\nThere is a rooted tree (see Notes) with N vertices numbered 1 to N. Each of the vertices, except the root, has a directed edge coming from its parent. Note that the root may not be Vertex 1.\n\nTakahashi has added M new directed edges to this graph. Each of these M edges, u \\rightarrow v, extends from some vertex u to its descendant v.\n\nYou are given the directed graph with N vertices and N-1+M edges after Takahashi added edges. More specifically, you are given N-1+M pairs of integers, (A_1, B_1), ..., (A_{N-1+M}, B_{N-1+M}), which represent that the i-th edge extends from Vertex A_i to Vertex B_i.\n\nRestore the original rooted tree.\n\nConstraints\n\n* 3 \\leq N\n* 1 \\leq M\n* N + M \\leq 10^5\n* 1 \\leq A_i, B_i \\leq N\n* A_i \\neq B_i\n* If i \\neq j, (A_i, B_i) \\neq (A_j, B_j).\n* The graph in input can be obtained by adding M edges satisfying the condition in the problem statement to a rooted tree with N vertices.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN M\nA_1 B_1\n:\nA_{N-1+M} B_{N-1+M}\n\n\nOutput\n\nPrint N lines. In the i-th line, print `0` if Vertex i is the root of the original tree, and otherwise print the integer representing the parent of Vertex i in the original tree.\n\nNote that it can be shown that the original tree is uniquely determined.\n\nExamples\n\nInput\n\n3 1\n1 2\n1 3\n2 3\n\n\nOutput\n\n0\n1\n2\n\n\nInput\n\n6 3\n2 1\n2 3\n4 1\n4 2\n6 1\n2 6\n4 6\n6 5\n\n\nOutput\n\n6\n4\n2\n0\n6\n2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, m = map(int, input().split())\ninc = [0]*n\nout = [[] for _ in range(n)]\nparent = [[] for _ in range(n)]\nfor _ in range(n-1+m):\n a, b = map(int, input().split())\n a -= 1\n b -= 1\n out[a].append(b)\n parent[b].append(a)\n inc[b] += 1\n\nS = {i for i, c in enumerate(inc) if c == 0}\nL = []\n \nwhile S:\n k = S.pop()\n L.append(k)\n for m in out[k]:\n inc[m] -= 1\n if inc[m] == 0:\n S.add(m)\n\nA = [(float(\"inf\"), -1) for _ in range(n)]\nD = {j:i for i, j in enumerate(L)}\nA[L[0]] = (0, -1)\nfor i in range(1, n):\n now = L[i]\n d, t = A[now]\n for j in parent[now]:\n if d > i - D[j]:\n d = i - D[j]\n t = j\n A[now] = (d, t)\nfor i, j in A:\n print(j+1)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 3\\n2 1\\n2 3\\n4 1\\n4 2\\n6 1\\n2 6\\n4 6\\n6 5', 'output': '6\\n4\\n2\\n0\\n6\\n2'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 2\\n1 3\\n2 3', 'output': '0\\n1\\n2'}, {'type': 'stdin_stdout', 'input': '6 3\\n2 1\\n2 3\\n4 1\\n4 2\\n6 1\\n2 6\\n3 6\\n6 5', 'output': '6\\n4\\n2\\n0\\n6\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n2 1\\n2 3\\n4 1\\n4 2\\n6 1\\n2 6\\n3 6\\n4 5', 'output': '6\\n4\\n2\\n0\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n3 1\\n4 3\\n4 1\\n4 2\\n6 1\\n4 6\\n3 6\\n4 5', 'output': '6\\n4\\n4\\n0\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n2 1\\n2 3\\n4 1\\n4 2\\n6 1\\n2 6\\n3 6\\n1 5', 'output': '6\\n4\\n2\\n0\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n2 1\\n2 3\\n4 1\\n4 2\\n6 1\\n2 6\\n3 6\\n3 5', 'output': '6\\n4\\n2\\n0\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n3 1\\n4 3\\n4 1\\n4 2\\n6 2\\n4 6\\n3 6\\n4 5', 'output': '3\\n6\\n4\\n0\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n3 1\\n4 3\\n4 1\\n4 2\\n6 2\\n4 6\\n1 6\\n4 5', 'output': '3\\n6\\n4\\n0\\n4\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n3 1\\n4 3\\n4 1\\n4 2\\n1 2\\n4 6\\n3 6\\n4 5', 'output': '3\\n1\\n4\\n0\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n3 1\\n4 3\\n4 1\\n4 2\\n1 2\\n4 6\\n1 6\\n4 5', 'output': '3\\n1\\n4\\n0\\n4\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n3 1\\n4 3\\n4 1\\n4 2\\n1 2\\n4 5\\n1 6\\n1 5', 'output': '3\\n1\\n4\\n0\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n4 1\\n2 3\\n4 1\\n4 2\\n6 1\\n2 6\\n4 6\\n6 5', 'output': '6\\n4\\n2\\n0\\n6\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n3 1\\n4 3\\n4 1\\n4 2\\n1 2\\n4 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6\\n3 1\\n4 5', 'output': '3\\n1\\n4\\n0\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n3 1\\n4 3\\n6 2\\n4 2\\n1 2\\n4 5\\n1 6\\n4 2', 'output': '3\\n6\\n4\\n0\\n4\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n3 1\\n2 3\\n4 2\\n4 2\\n6 1\\n4 6\\n3 6\\n4 5', 'output': '6\\n4\\n2\\n0\\n4\\n3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_77833","program":"```python\nn, m = map(int, input().split())\ninc = [0]*n\nout = [[] for _ in range(n)]\nparent = [[] for _ in range(n)]\nfor _ in range(n-1+m):\n a, b = map(int, input().split())\n a -= 1\n b -= 1\n out[a].append(b)\n parent[b].append(a)\n inc[b] += 1\n\nS = {i for i, c in enumerate(inc) if c == 0}\nL = []\n \nwhile S:\n k = S.pop()\n L.append(k)\n for m in out[k]:\n inc[m] -= 1\n if inc[m] == 0:\n S.add(m)\n\nA = [(float(\"inf\"), -1) for _ in range(n)]\nD = {j:i for i, j in enumerate(L)}\nA[L[0]] = (0, -1)\nfor i in range(1, n):\n now = L[i]\n d, t = A[now]\n for j in parent[now]:\n if d > i - D[j]:\n d = i - D[j]\n t = j\n A[now] = (d, t)\nfor i, j in A:\n print(j+1)\n```","inputs":"6 3\n2 1\n2 3\n4 1\n4 2\n6 1\n2 6\n4 6\n6 5","output":"6\n4\n2\n0\n6\n2","actual_output":"6\n4\n2\n0\n6\n2\n","execution_success":true,"sample_index":12413},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03286 AtCoder Beginner Contest 105 - Base -2 Number","prompt":"Solve the following coding problem using the programming language python:\n\nGiven an integer N, find the base -2 representation of N.\n\nHere, S is the base -2 representation of N when the following are all satisfied:\n\n* S is a string consisting of `0` and `1`.\n* Unless S = `0`, the initial character of S is `1`.\n* Let S = S_k S_{k-1} ... S_0, then S_0 \\times (-2)^0 + S_1 \\times (-2)^1 + ... + S_k \\times (-2)^k = N.\n\n\n\nIt can be proved that, for any integer M, the base -2 representation of M is uniquely determined.\n\nConstraints\n\n* Every value in input is integer.\n* -10^9 \\leq N \\leq 10^9\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\n\n\nOutput\n\nPrint the base -2 representation of N.\n\nExamples\n\nInput\n\n-9\n\n\nOutput\n\n1011\n\n\nInput\n\n123456789\n\n\nOutput\n\n11000101011001101110100010101\n\n\nInput\n\n0\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\ns = \"\"\nwhile n!=0:\n s = str(n%2)+s\n n = -(n//2)\n #print(s, n)\nprint(0 if s==\"\" else s)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '123456789', 'output': 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'input': '-88', 'output': '11111000\\n'}, {'type': 'stdin_stdout', 'input': '34009', 'output': '11000010100101001\\n'}, {'type': 'stdin_stdout', 'input': '30', 'output': '1100010\\n'}, {'type': 'stdin_stdout', 'input': '-44', 'output': '11010100\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_77837","program":"```python\nn = int(input())\ns = \"\"\nwhile n!=0:\n s = str(n%2)+s\n n = -(n//2)\n #print(s, n)\nprint(0 if s==\"\" else s)\n```","inputs":"0","output":"0","actual_output":"0\n","execution_success":true,"sample_index":12414},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03442 AtCoder Petrozavodsk Contest 001 - XOR Tree","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a tree with N vertices. The vertices are numbered 0 through N-1, and the edges are numbered 1 through N-1. Edge i connects Vertex x_i and y_i, and has a value a_i. You can perform the following operation any number of times:\n\n* Choose a simple path and a non-negative integer x, then for each edge e that belongs to the path, change a_e by executing a_e \u2190 a_e \u2295 x (\u2295 denotes XOR).\n\n\n\nYour objective is to have a_e = 0 for all edges e. Find the minimum number of operations required to achieve it.\n\nConstraints\n\n* 2 \u2264 N \u2264 10^5\n* 0 \u2264 x_i,y_i \u2264 N-1\n* 0 \u2264 a_i \u2264 15\n* The given graph is a tree.\n* All input values are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nx_1 y_1 a_1\nx_2 y_2 a_2\n:\nx_{N-1} y_{N-1} a_{N-1}\n\n\nOutput\n\nFind the minimum number of operations required to achieve the objective.\n\nExamples\n\nInput\n\n5\n0 1 1\n0 2 3\n0 3 6\n3 4 4\n\n\nOutput\n\n3\n\n\nInput\n\n2\n1 0 0\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import Counter\nfrom functools import reduce\nfrom itertools import combinations\nfrom operator import xor\n\nn = int(input())\nnodes = [0] * n\nfor _ in range(n - 1):\n x, y, a = map(int, input().split())\n nodes[x] ^= a\n nodes[y] ^= a\n\nc = Counter(nodes)\nans = 0\nremains = set()\nfor i, v in c.items():\n if i == 0:\n continue\n ans += v // 2\n if v % 2:\n remains.add(i)\n\nfor r in (3, 4, 5):\n while True:\n for ns in combinations(remains, r):\n if reduce(xor, ns) == 0:\n remains.difference_update(ns)\n ans += r - 1\n break\n else:\n break\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 2 3\\n0 3 6\\n3 4 4', 'output': '3'}, {'type': 'stdin_stdout', 'input': '2\\n1 0 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 2 3\\n0 3 6\\n3 4 1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '2\\n1 1 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 3 3\\n0 3 5\\n4 4 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '2\\n0 1 2', 'output': '1'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 2 3\\n0 3 6\\n4 4 1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '2\\n1 1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': 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'2'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 2 3\\n0 3 6\\n4 4 0', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 2\\n0 3 3\\n-1 3 0\\n4 4 0', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 0\\n0 0 3\\n0 0 13\\n4 4 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 0\\n0 0 3\\n0 0 23\\n4 4 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 0\\n0 2 3\\n0 3 6\\n3 4 4', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 2 1\\n0 3 6\\n3 4 1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 2 3\\n0 3 11\\n4 4 1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 1\\n0 2 3\\n0 3 5\\n4 4 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '2\\n0 0 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 3 3\\n0 4 5\\n4 4 1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 0 4\\n0 3 7\\n4 4 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n0 0 1\\n0 0 0\\n0 3 7\\n4 4 2', 'output': '1'}, {'type': 'stdin_stdout', 'input': '5\\n0 2 1\\n0 0 0\\n0 3 7\\n4 3 2', 'output': '3'}, {'type': 'stdin_stdout', 'input': '2\\n0 0 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 2 3\\n1 3 8\\n3 4 1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 0\\n1 2 3\\n0 3 6\\n4 4 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '2\\n-1 2 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n0 2 2\\n0 2 3\\n0 3 5\\n4 4 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 2\\n0 3 3\\n0 3 5\\n4 4 2', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 0 3\\n0 3 13\\n4 4 2', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n0 1 0\\n0 3 5\\n4 4 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n1 0 1\\n0 0 0\\n0 3 7\\n4 4 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n1 0 0\\n0 3 10\\n4 3 2', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n1 2 3\\n0 3 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'5\\n0 1 1\\n1 0 0\\n0 3 7\\n4 3 2', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1\\n2 2 3\\n0 3 8\\n3 2 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n0 2 1\\n3 2 3\\n0 3 6\\n4 4 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n0 3 2\\n0 2 5\\n0 3 5\\n4 4 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 0\\n0 0 3\\n0 1 13\\n4 4 1', 'output': '1'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 1\\n0 3 3\\n0 1 8\\n3 2 1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 0\\n2 2 3\\n0 3 12\\n4 4 0', 'output': '1'}, {'type': 'stdin_stdout', 'input': '5\\n0 3 0\\n0 2 1\\n0 3 5\\n4 4 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '2\\n0 -2 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 3\\n0 1 3\\n0 3 0\\n4 4 0', 'output': '0'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_77841","program":"```python\nfrom collections import Counter\nfrom functools import reduce\nfrom itertools import combinations\nfrom operator import xor\n\nn = int(input())\nnodes = [0] * n\nfor _ in range(n - 1):\n x, y, a = map(int, input().split())\n nodes[x] ^= a\n nodes[y] ^= a\n\nc = Counter(nodes)\nans = 0\nremains = set()\nfor i, v in c.items():\n if i == 0:\n continue\n ans += v // 2\n if v % 2:\n remains.add(i)\n\nfor r in (3, 4, 5):\n while True:\n for ns in combinations(remains, r):\n if reduce(xor, ns) == 0:\n remains.difference_update(ns)\n ans += r - 1\n break\n else:\n break\nprint(ans)\n\n```","inputs":"5\n0 1 1\n0 2 3\n0 3 6\n3 4 4","output":"3","actual_output":"3\n","execution_success":true,"sample_index":12415},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03600 AtCoder Beginner Contest 074 - Restoring Road Network","prompt":"Solve the following coding problem using the programming language python:\n\nIn Takahashi Kingdom, which once existed, there are N cities, and some pairs of cities are connected bidirectionally by roads. The following are known about the road network:\n\n* People traveled between cities only through roads. It was possible to reach any city from any other city, via intermediate cities if necessary.\n* Different roads may have had different lengths, but all the lengths were positive integers.\n\n\n\nSnuke the archeologist found a table with N rows and N columns, A, in the ruin of Takahashi Kingdom. He thought that it represented the shortest distances between the cities along the roads in the kingdom.\n\nDetermine whether there exists a road network such that for each u and v, the integer A_{u, v} at the u-th row and v-th column of A is equal to the length of the shortest path from City u to City v. If such a network exist, find the shortest possible total length of the roads.\n\nConstraints\n\n* 1 \\leq N \\leq 300\n* If i \u2260 j, 1 \\leq A_{i, j} = A_{j, i} \\leq 10^9.\n* A_{i, i} = 0\n\nInputs\n\nInput is given from Standard Input in the following format:\n\n\nN\nA_{1, 1} A_{1, 2} ... A_{1, N}\nA_{2, 1} A_{2, 2} ... A_{2, N}\n...\nA_{N, 1} A_{N, 2} ... A_{N, N}\n\n\nOutputs\n\nIf there exists no network that satisfies the condition, print `-1`. If it exists, print the shortest possible total length of the roads.\n\nExamples\n\nInput\n\n3\n0 1 3\n1 0 2\n3 2 0\n\n\nOutput\n\n3\n\n\nInput\n\n3\n0 1 3\n1 0 1\n3 1 0\n\n\nOutput\n\n-1\n\n\nInput\n\n5\n0 21 18 11 28\n21 0 13 10 26\n18 13 0 23 13\n11 10 23 0 17\n28 26 13 17 0\n\n\nOutput\n\n82\n\n\nInput\n\n3\n0 1000000000 1000000000\n1000000000 0 1000000000\n1000000000 1000000000 0\n\n\nOutput\n\n3000000000\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport copy\n\nN = int(input())\nA = []\nfor i in range(N):\n A.append(list(map(int, input().split())))\n\nB = copy.deepcopy(A)\nfor i in range(N):\n for j in range(N):\n if i == j:\n continue\n for k in range(N):\n if j == k:\n continue\n if k == i:\n continue\n if A[i][j] > A[i][k] + A[k][j]:\n print(-1)\n exit()\n if A[i][j] == A[i][k] + A[k][j]:\n B[i][j] = 0\n\nans = 0\nfor i in range(N):\n for j in range(i, N):\n ans += B[i][j]\n\nprint(ans)\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n0 1000000000 1000000000\\n1000000000 0 1000000000\\n1000000000 1000000000 0', 'output': '3000000000'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 3\\n1 0 2\\n3 2 0', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 3\\n1 0 1\\n3 1 0', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '5\\n0 21 18 11 28\\n21 0 13 10 26\\n18 13 0 23 13\\n11 10 23 0 17\\n28 26 13 17 0', 'output': '82'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 3\\n1 0 1\\n3 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 1 3\\n1 0 1\\n3 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 1 3\\n1 0 1\\n5 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 3\\n1 0 1\\n5 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 0 1\\n3 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 5\\n1 0 1\\n3 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 3\\n1 0 1\\n5 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 -1 1\\n3 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 3\\n1 0 1\\n5 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 -1 1\\n3 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 4\\n1 0 1\\n5 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 -1 1\\n4 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 4\\n1 0 1\\n5 1 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 -1 1\\n4 0 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 4\\n1 0 2\\n5 1 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 -1 1\\n4 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 4\\n1 0 2\\n5 1 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 -1 0\\n4 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n1 0 2\\n5 1 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 -1 0\\n0 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n1 0 2\\n6 1 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 -2 0\\n0 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n1 -1 2\\n6 1 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n1 -1 2\\n6 0 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 4\\n1 0 1\\n3 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 1 3\\n1 0 1\\n3 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 1 5\\n1 0 1\\n3 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 3\\n1 0 1\\n9 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 3\\n1 -1 1\\n3 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 3\\n1 0 1\\n5 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 7\\n1 0 1\\n5 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 0 1\\n4 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 4\\n0 0 1\\n5 1 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 3\\n1 -1 1\\n4 0 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 4\\n1 0 2\\n5 1 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 2\\n1 -1 1\\n4 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 4\\n1 0 2\\n5 1 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 -1 0\\n4 0 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n1 0 2\\n5 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 3\\n1 -1 0\\n0 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 3\\n1 -2 0\\n0 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n1 0 2\\n6 0 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 5\\n1 0 1\\n3 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 1 5\\n1 0 1\\n3 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 3\\n1 1 1\\n9 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 3\\n1 -1 1\\n4 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 3\\n1 1 1\\n5 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 7\\n1 0 2\\n5 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 3\\n1 0 1\\n4 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 3\\n1 0 1\\n4 0 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 4\\n0 0 2\\n5 1 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 2\\n1 -1 1\\n4 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 4\\n1 0 0\\n5 1 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n1 -1 0\\n4 1 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 3\\n2 -1 0\\n0 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 -1 3\\n1 -2 0\\n0 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n1 0 3\\n6 0 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 5\\n1 -1 1\\n4 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 3\\n0 1 1\\n5 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 7\\n1 0 4\\n5 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 3\\n1 0 1\\n4 -1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 4\\n0 1 2\\n5 1 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 4\\n0 0 0\\n5 1 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 3\\n1 -1 0\\n4 1 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 3\\n2 -1 -1\\n0 0 2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n2 0 3\\n6 0 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 5\\n1 -1 1\\n4 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 3\\n0 1 1\\n5 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 7\\n2 0 4\\n5 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 3\\n1 0 1\\n0 -1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 3\\n0 0 0\\n5 1 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 3\\n0 -1 0\\n4 1 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 3\\n2 -1 -1\\n0 0 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n2 0 3\\n6 0 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 5\\n1 -1 2\\n4 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 3\\n0 1 1\\n5 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 7\\n2 0 4\\n5 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 6\\n1 0 1\\n0 -1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 3\\n0 0 0\\n3 1 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n0 -1 0\\n4 1 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 3\\n2 -1 -1\\n0 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n2 1 3\\n6 0 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 5\\n1 -1 2\\n4 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 5\\n0 1 1\\n5 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 7\\n2 0 4\\n5 0 -1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 6\\n1 0 0\\n0 -1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 3\\n0 0 0\\n3 2 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n-1 -1 0\\n4 1 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 1\\n2 -1 -1\\n0 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n2 1 4\\n6 0 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 7\\n1 -1 2\\n4 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 5\\n0 1 1\\n5 1 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 7\\n2 0 4\\n5 0 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 -1 6\\n1 0 0\\n0 -1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 3\\n0 0 1\\n3 2 -2', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n-1 -1 -1\\n4 1 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 1\\n2 -1 0\\n0 0 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 7\\n1 -1 4\\n4 1 0', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 7\\n0 1 1\\n5 1 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 1\\n2 0 4\\n5 0 -2', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_77845","program":"```python\nimport copy\n\nN = int(input())\nA = []\nfor i in range(N):\n A.append(list(map(int, input().split())))\n\nB = copy.deepcopy(A)\nfor i in range(N):\n for j in range(N):\n if i == j:\n continue\n for k in range(N):\n if j == k:\n continue\n if k == i:\n continue\n if A[i][j] > A[i][k] + A[k][j]:\n print(-1)\n exit()\n if A[i][j] == A[i][k] + A[k][j]:\n B[i][j] = 0\n\nans = 0\nfor i in range(N):\n for j in range(i, N):\n ans += B[i][j]\n\nprint(ans)\n\n\n```","inputs":"3\n0 1000000000 1000000000\n1000000000 0 1000000000\n1000000000 1000000000 0","output":"3000000000","actual_output":"3000000000\n","execution_success":true,"sample_index":12416},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03761 AtCoder Beginner Contest 058 - Dubious Document","prompt":"Solve the following coding problem using the programming language python:\n\nSnuke loves \"paper cutting\": he cuts out characters from a newspaper headline and rearranges them to form another string.\n\nHe will receive a headline which contains one of the strings S_1,...,S_n tomorrow. He is excited and already thinking of what string he will create. Since he does not know the string on the headline yet, he is interested in strings that can be created regardless of which string the headline contains.\n\nFind the longest string that can be created regardless of which string among S_1,...,S_n the headline contains. If there are multiple such strings, find the lexicographically smallest one among them.\n\nConstraints\n\n* 1 \\leq n \\leq 50\n* 1 \\leq |S_i| \\leq 50 for every i = 1, ..., n.\n* S_i consists of lowercase English letters (`a` - `z`) for every i = 1, ..., n.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nn\nS_1\n...\nS_n\n\n\nOutput\n\nPrint the lexicographically smallest string among the longest strings that satisfy the condition. If the answer is an empty string, print an empty line.\n\nExamples\n\nInput\n\n3\ncbaa\ndaacc\nacacac\n\n\nOutput\n\naac\n\n\nInput\n\n3\na\naa\nb\n\n\nOutput\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\n\nl = []\nfor i in range(n):\n l.append(input())\n\nl_sorted = sorted(list(set(l[0])))\nans =''\n\nfor ch in l_sorted:\n cnt = min(l[i].count(ch) for i in range(n))\n ans += ch * cnt\n\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\ncbaa\\ndaacc\\nacacac', 'output': 'aac'}, {'type': 'stdin_stdout', 'input': '3\\na\\naa\\nb', 'output': ''}, {'type': 'stdin_stdout', 'input': '3\\ncaaa\\ndaacc\\nacacac', 'output': 'aac\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncaaa\\nd`acc\\nacacac', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\naaca\\nbdb`c\\nacacac', 'output': 'c\\n'}, {'type': 'stdin_stdout', 'input': '3\\na\\naa\\na', 'output': 'a\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncaca\\ncca`d\\nacacac', 'output': 'acc\\n'}, {'type': 'stdin_stdout', 'input': '3\\nacba\\nda`cb\\nacacbc', 'output': 'abc\\n'}, {'type': 'stdin_stdout', 'input': '3\\n_a_b\\nc_bcb\\nabcada', 'output': 'b\\n'}, {'type': 'stdin_stdout', 'input': '3\\naad_\\nbdb_c\\nababcd', 'output': 'd\\n'}, {'type': 'stdin_stdout', 'input': '3\\nba`c\\nbcb`c\\nabdbcb', 'output': 'bc\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbcac\\ncc`be\\nacacbc', 'output': 'bcc\\n'}, {'type': 'stdin_stdout', 'input': '3\\n`cc`\\ncb`cb\\ncacaca', 'output': 'cc\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncacb\\nccabe\\n`cacbc', 'output': 'abcc\\n'}, {'type': 'stdin_stdout', 'input': '3\\naad`\\ncaacc\\nacadac', 'output': 'aa\\n'}, {'type': 'stdin_stdout', 'input': '3\\n_ab_\\nbda_c\\naacadb', 'output': 'ab\\n'}, {'type': 'stdin_stdout', 'input': '3\\nb\\\\`b\\n`cbbc\\nbabacd', 'output': 'bb\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncaaa\\nd`acc\\ncacaca', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncaaa\\ncca`d\\ncacaca', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncaaa\\n`cacd\\ncacaca', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\naaac\\ncca`d\\ncacaca', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\naaac\\ncca`d\\nacacac', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncaaa\\ncca`d\\nacacac', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\naaac\\ncda`c\\nacacac', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\naaac\\nc`adc\\nacacac', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\naaac\\nbda`c\\nacacac', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\naaca\\nbda`c\\nacacac', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '3\\naaca\\nbcb`c\\nacacac', 'output': 'c\\n'}, {'type': 'stdin_stdout', 'input': '3\\naaca\\nc`bcb\\nacacac', 'output': 'c\\n'}, {'type': 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'3\\ncaba\\nda`cc\\nacacac', 'output': 'ac\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_77849","program":"```python\nn = int(input())\n\nl = []\nfor i in range(n):\n l.append(input())\n\nl_sorted = sorted(list(set(l[0])))\nans =''\n\nfor ch in l_sorted:\n cnt = min(l[i].count(ch) for i in range(n))\n ans += ch * cnt\n\nprint(ans)\n```","inputs":"3\ncbaa\ndaacc\nacacac","output":"aac","actual_output":"aac\n","execution_success":true,"sample_index":12417},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03931 square869120Contest #3 - Solving XOR-Puzzles","prompt":"Solve the following coding problem using the programming language python:\n\nSample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)\n\nSnuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.\nHe made a sequence $b$, but actually, he is not remembered it.\nHowever, he is remembered a few things about sequence $b$.\n\n\n* All elements in $b$ are distinct.\n* All elements in $b$ is in $a$.\n* $b_1 \\oplus b_2 \\oplus \\cdots \\oplus b_r = k$. ($r$ is length of sequence $b$) [$\\oplus$ means XOR]\n\n\nFor example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.\nHe wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.\nSince the answer can be large, print the answer modulo $1,000,000,007$.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\n> $n \\ k$ $a_1 \\ a_2 \\ \\cdots \\ a_n$\n\nOutput\n\n* Print the number of ways to make sequence $b$.\n* Print the answer modulo $1,000,000,007$.\n\n\n\nConstraints\n\n* $1 \\le n \\le 100$\n* $1 \\le a_i, k \\le 255$\n* $i \\neq j \\Rightarrow a_i \\neq a_j$\n\n\n\nSubtasks\n\nSubtask 1 [ $50$ points ]\n\n\n* $1 \\le n \\le 4$\n\nSubtask 2 [ $170$ points ]\n\n\n* $1 \\le n \\le 20$\n\nSubtask 3 [ $180$ points ]\n\n\n* There are no additional constraints.\n\nOutput\n\n* Print the number of ways to make sequence $b$.\n* Print the answer modulo $1,000,000,007$.\n\n\n\nConstraints\n\n* $1 \\le n \\le 100$\n* $1 \\le a_i, k \\le 255$\n* $i \\neq j \\Rightarrow a_i \\neq a_j$\n\n\n\nSubtasks\n\nSubtask 1 [ $50$ points ]\n\n\n* $1 \\le n \\le 4$\n\nSubtask 2 [ $170$ points ]\n\n\n* $1 \\le n \\le 20$\n\nSubtask 3 [ $180$ points ]\n\n\n* There are no additional constraints.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\n> $n \\ k$ $a_1 \\ a_2 \\ \\cdots \\ a_n$\n\nExamples\n\nInput\n\n3 1\n1 2 3\n\n\nOutput\n\n3\n\n\nInput\n\n3 10\n8 7 5\n\n\nOutput\n\n6\n\n\nInput\n\n25 127\n5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125\n\n\nOutput\n\n235924722\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, k = map(int, input().split())\n*A, = map(int, input().split())\n\nMOD = 10**9 + 7\n\nC = {a for a in A}\nn = len(C)\nm = [[0]*256 for i in range(n+1)]\nm[0][0] = 1\nfor c in C:\n for i in range(n-1, -1, -1):\n s = m[i]; t = m[i+1]\n for j in range(256):\n t[c^j] += s[j]\n\nans = 0\nr = 1\nfor i in range(1, n+1):\n r = (r * i) % MOD\n ans += r * m[i][k]\n ans %= MOD\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '25 127\\n5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125', 'output': '235924722'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 2 3', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3 10\\n8 7 5', 'output': '6'}, {'type': 'stdin_stdout', 'input': '25 127\\n5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 000 105 110 115 120 125', 'output': '304424949\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 3 3', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '3 10\\n7 7 5', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n7 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 000 105 110 115 120 125', 'output': '307516362\\n'}, {'type': 'stdin_stdout', 'input': '3 7\\n7 7 5', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n7 10 4 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 000 105 110 115 120 125', 'output': 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65 70 70 80 85 90 95 100 6 110 115 185 125', 'output': '167909388\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n5 10 15 20 39 30 35 40 45 50 108 37 81 70 75 80 82 175 58 000 99 110 115 120 125', 'output': '712861496\\n'}, {'type': 'stdin_stdout', 'input': '25 50\\n7 9 15 7 7 33 35 40 45 50 56 60 65 105 92 87 85 90 95 000 105 110 115 120 125', 'output': '615460230\\n'}, {'type': 'stdin_stdout', 'input': '25 250\\n13 10 11 20 25 30 35 40 45 50 55 60 65 36 71 80 85 90 95 100 176 110 19 120 125', 'output': '199899805\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n7 10 1 20 34 30 35 40 45 52 19 60 80 70 75 80 85 90 95 000 176 110 115 120 33', 'output': '844080051\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n5 9 6 20 25 30 35 40 45 50 0 60 65 25 75 80 35 17 95 000 176 100 115 2 216', 'output': '374785576\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n3 10 2 40 25 30 51 18 45 50 55 60 65 80 70 80 85 90 95 100 6 110 115 185 125', 'output': '292088428\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n5 10 15 20 39 30 35 69 45 50 108 37 81 70 75 80 82 175 58 000 99 110 115 120 125', 'output': '504775448\\n'}, {'type': 'stdin_stdout', 'input': '25 50\\n7 9 15 7 7 33 35 40 45 50 56 60 65 105 92 87 85 90 0 000 105 110 115 120 125', 'output': '521766048\\n'}, {'type': 'stdin_stdout', 'input': '25 250\\n13 10 11 20 25 30 35 40 45 50 55 60 65 36 71 80 85 112 95 100 176 110 19 120 125', 'output': '898026517\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n8 10 1 20 34 30 35 40 45 52 19 60 80 70 75 80 85 90 95 000 176 110 115 120 33', 'output': '940416942\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n5 10 15 20 39 30 35 69 45 50 108 37 81 70 75 80 82 175 58 000 99 110 115 128 125', 'output': '172303811\\n'}, {'type': 'stdin_stdout', 'input': '25 50\\n7 9 15 7 7 33 35 40 45 50 56 60 65 105 92 87 85 90 0 000 105 110 115 191 125', 'output': '144120738\\n'}, {'type': 'stdin_stdout', 'input': '25 250\\n13 10 11 20 25 30 35 40 45 50 55 60 65 36 71 80 85 112 95 100 136 110 19 120 125', 'output': '259349163\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n8 8 1 20 34 30 35 40 45 52 19 60 80 70 75 80 85 90 95 000 176 110 115 120 33', 'output': '996082653\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n3 10 2 40 25 30 7 18 45 50 55 60 65 80 70 80 85 90 95 100 6 110 128 185 125', 'output': '538422789\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n5 10 15 20 39 30 8 69 45 50 108 37 81 70 75 80 82 175 58 000 99 110 115 128 125', 'output': '426652181\\n'}, {'type': 'stdin_stdout', 'input': '25 50\\n7 9 15 7 7 33 35 60 45 50 56 60 65 105 92 87 85 90 0 000 105 110 115 191 125', 'output': '629569757\\n'}, {'type': 'stdin_stdout', 'input': '25 250\\n13 10 11 20 25 30 35 40 45 50 55 60 65 36 71 36 85 112 95 100 136 110 19 120 125', 'output': '546520233\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n8 8 1 20 63 30 35 40 45 52 19 60 80 70 75 80 85 90 95 000 176 110 115 120 33', 'output': '159793780\\n'}, {'type': 'stdin_stdout', 'input': '25 127\\n4 10 2 40 25 30 7 18 45 50 55 60 65 80 70 80 85 90 95 100 6 110 128 185 125', 'output': '872561522\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_77853","program":"```python\nn, k = map(int, input().split())\n*A, = map(int, input().split())\n\nMOD = 10**9 + 7\n\nC = {a for a in A}\nn = len(C)\nm = [[0]*256 for i in range(n+1)]\nm[0][0] = 1\nfor c in C:\n for i in range(n-1, -1, -1):\n s = m[i]; t = m[i+1]\n for j in range(256):\n t[c^j] += s[j]\n\nans = 0\nr = 1\nfor i in range(1, n+1):\n r = (r * i) % MOD\n ans += r * m[i][k]\n ans %= MOD\nprint(ans)\n```","inputs":"25 127\n5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125","output":"235924722","actual_output":"235924722\n","execution_success":true,"sample_index":12418},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00024 Physical Experiments","prompt":"Solve the following coding problem using the programming language python:\n\nIgnoring the air resistance, velocity of a freely falling object $v$ after $t$ seconds and its drop $y$ in $t$ seconds are represented by the following formulas:\n\n$ v = 9.8 t $\n$ y = 4.9 t^2 $\n\n\nA person is trying to drop down a glass ball and check whether it will crack. Your task is to write a program to help this experiment.\n\nYou are given the minimum velocity to crack the ball. Your program should print the lowest possible floor of a building to crack the ball. The height of the $N$ floor of the building is defined by $5 \\times N - 5$.\n\n\n\nInput\n\nThe input consists of multiple datasets. Each dataset, a line, consists of the minimum velocity v (0 < v < 200) to crack the ball. The value is given by a decimal fraction, with at most 4 digits after the decimal point. The input ends with EOF. The number of datasets is less than or equal to 50.\n\nOutput\n\nFor each dataset, print the lowest possible floor where the ball cracks.\n\nExample\n\nInput\n\n25.4\n25.4\n\n\nOutput\n\n8\n8\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\nwhile 1:\n try:\n print(math.ceil(float(input())**2/98)+1)\n except:break\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '25.4\\n25.4', 'output': '8\\n8'}, {'type': 'stdin_stdout', 'input': '26.000450676027395\\n25.4', 'output': '8\\n8\\n'}, {'type': 'stdin_stdout', 'input': '26.601491934975797\\n25.4', 'output': '9\\n8\\n'}, {'type': 'stdin_stdout', 'input': '26.840499084692592\\n26.667646669726267', 'output': '9\\n9\\n'}, {'type': 'stdin_stdout', 'input': '28.332769442919567\\n26.667646669726267', 'output': '10\\n9\\n'}, {'type': 'stdin_stdout', 'input': 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'71.54243522757665\\n74.91117783695132', 'output': '54\\n59\\n'}, {'type': 'stdin_stdout', 'input': '71.54243522757665\\n75.52007039121814', 'output': '54\\n60\\n'}, {'type': 'stdin_stdout', 'input': '72.41718141310186\\n75.52007039121814', 'output': '55\\n60\\n'}, {'type': 'stdin_stdout', 'input': '73.36946681971843\\n75.52007039121814', 'output': '56\\n60\\n'}, {'type': 'stdin_stdout', 'input': '73.9111092448129\\n75.52007039121814', 'output': '57\\n60\\n'}, {'type': 'stdin_stdout', 'input': '74.12849798877802\\n75.85991934452677', 'output': '58\\n60\\n'}, {'type': 'stdin_stdout', 'input': '74.93378052146508\\n75.85991934452677', 'output': '59\\n60\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_77857","program":"```python\nimport math\nwhile 1:\n try:\n print(math.ceil(float(input())**2/98)+1)\n except:break\n\n```","inputs":"25.4\n25.4","output":"8\n8","actual_output":"8\n8\n","execution_success":true,"sample_index":12419},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00155 Spider Jin","prompt":"Solve the following coding problem using the programming language python:\n\nThe hero of justice, the Spider, can pull a rope out of his arm and jump from building to building. However, due to the short rope, you can only move to buildings that are less than 50 distances from you. To move to a building farther away, you have to jump to another building.\n\n\n\n\n\n\nCreate a program that inputs the information of n and n buildings, the start position and destination of the spider's movement, and outputs the shortest route of the movement. If you cannot move to the target building no matter how you go through the building, output NA. Each building is treated as a point, and there can be no more than one way to go through the building that travels the shortest distance.\n\n\n\nInput\n\nA sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:\n\n\nn\nb1 x1 y1\nb2 x2 y2\n::\nbn xn yn\nm\ns1 g1\ns2 g2\n::\nsm gm\n\n\nThe number of buildings n (1 \u2264 n \u2264 100) on the first line, the building number bi (1 \u2264 bi \u2264 n) of the i-th building on the following n lines, and the integers xi, yi representing the x and y coordinates of that building. (-1000 \u2264 xi, yi \u2264 1000) is given, separated by spaces.\n\nThe number of movement information m (1 \u2264 m \u2264 100) is given to the following line, and the i-th movement information is given to the following m line. As each move information, the number si of the building to start the move and the number gi of the destination building are given, separated by blanks.\n\nThe number of datasets does not exceed 10.\n\nOutput\n\nOutputs in the following format for each input dataset.\n\nThe route or NA for the i-th movement information is output to the i-th line on the i-th line. Each route is output in the following format.\n\n\nsi bri1 bri2 ... gi\n\n\nbrij represents the number of the building that goes through the jth in the ith movement information.\n\nExample\n\nInput\n\n4\n1 0 0\n2 30 0\n3 60 40\n4 0 60\n2\n1 3\n1 4\n22\n1 0 0\n2 150 40\n3 30 20\n4 180 150\n5 40 80\n6 130 130\n7 72 28\n8 172 118\n9 50 50\n10 160 82\n11 90 105\n12 144 131\n13 130 64\n14 80 140\n15 38 117\n16 190 90\n17 60 100\n18 100 70\n19 130 100\n20 71 69\n21 200 110\n22 120 150\n1\n1 22\n0\n\n\nOutput\n\n1 2 3\nNA\n1 3 9 20 11 6 22\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport heapq\n\ndef dijkstra(G, s, g, n):\n cost = [10**9] * n\n cost[s] = 0\n pre = [-1] * n\n q = []\n heapq.heappush(q, (0, s))\n while q:\n d, to = heapq.heappop(q)\n if to == g:\n break\n if cost[to] < d:\n continue\n for n, dist in G[to]:\n nd = d + dist\n if cost[n] > nd:\n cost[n] = nd\n heapq.heappush(q, (nd, n))\n pre[n] = to\n\n if pre[g] == -1:\n return []\n ans = [g]\n cur = g\n while True:\n ans.append(pre[cur])\n cur = pre[cur]\n if cur == s or cur == -1:\n break\n\n return ans[::-1]\n\nwhile True:\n n = int(input())\n if n == 0:\n break\n bldgs = [-1] * n\n G = [[] for _ in range(n)]\n for _ in range(n):\n b, x, y = map(int, input().strip().split(\" \"))\n bldgs[b-1] = (x, y)\n\n for i in range(n):\n x_i, y_i = bldgs[i]\n for j in range(i+1, n):\n x_j, y_j = bldgs[j]\n d = ((x_i-x_j)**2 + (y_i-y_j)**2) ** 0.5\n if d <= 50:\n G[i].append((j, d))\n G[j].append((i, d))\n m = int(input())\n for _ in range(m):\n s, g = map(int, input().strip().split(\" \"))\n ans = dijkstra(G, s-1, g-1, n)\n if ans == []:\n print(\"NA\")\n else:\n print(\" \".join([str(i+1) for i in ans]))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 20 11 6 22'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 20 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 2\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 36 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\n1 2\\n1 3 9 20 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 36 117\\n16 190 90\\n17 49 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 5 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 5 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 71 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 5\\n20 144 131\\n13 130 32\\n14 80 140\\n15 36 117\\n16 190 90\\n17 49 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 5 150\\n1\\n1 22\\n0', 'output': 'NA\\nNA\\n1 3 9 5 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 2\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 140 150\\n1\\n1 22\\n0', 'output': '1 2\\nNA\\n1 3 9 20 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -2 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 36 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 19\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 5 17 14 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 202\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 109 100\\n18 110 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 20 17 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 58 40\\n4 0 60\\n2\\n1 3\\n1 2\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 197 6\\n14 80 140\\n15 36 117\\n16 190 90\\n17 60 100\\n18 100 138\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\n1 2\\n1 3 9 20 11 18 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 2\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 202\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 109 100\\n18 110 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 7 20 17 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 2\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 202\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 109 100\\n18 110 70\\n19 130 100\\n20 31 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 7 9 5 15 14 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 50 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n2 180 150\\n5 32 80\\n6 40 130\\n7 72 28\\n8 172 118\\n9 50 50\\n4 160 82\\n11 90 105\\n12 260 131\\n13 127 64\\n14 145 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 010\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 20 18 19 14 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 36 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 12\\n0', 'output': '1 2 3\\nNA\\n1 3 9 20 11 6 12\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 54\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 36 117\\n16 190 90\\n17 49 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 5 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 5 17 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 2\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n20 144 131\\n13 130 64\\n14 80 140\\n15 36 117\\n16 190 90\\n17 49 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 5 150\\n1\\n1 22\\n0', 'output': '1 2 3\\n1 2\\n1 3 9 5 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 2\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 33\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\n1 2\\n1 3 5 20 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n2 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n4 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 145 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 21 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 5 17 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 4 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n2 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n4 160 82\\n11 90 105\\n12 144 131\\n13 127 64\\n14 145 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': 'NA\\nNA\\n1 3 9 20 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 2\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 202\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 109 100\\n18 110 70\\n19 130 100\\n20 69 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 7 20 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 27 0\\n3 58 40\\n4 0 60\\n2\\n1 3\\n1 2\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 203\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 197 6\\n14 80 140\\n15 36 117\\n16 190 90\\n17 60 100\\n18 100 138\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': 'NA\\n1 2\\n1 3 9 20 11 18 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 2\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 17 118\\n9 50 50\\n10 160 82\\n11 90 105\\n20 144 131\\n13 130 64\\n14 80 140\\n15 36 117\\n16 190 90\\n17 49 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 5 150\\n1\\n1 22\\n0', 'output': '1 2 3\\n1 2\\n1 3 9 5 8 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 71 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 0\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 6\\n20 144 131\\n13 130 32\\n14 80 140\\n15 36 117\\n16 190 90\\n17 49 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 5 150\\n1\\n1 22\\n0', 'output': 'NA\\nNA\\n1 3 9 20 17 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 27 0\\n3 58 40\\n4 0 60\\n2\\n1 3\\n1 2\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 203\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 189\\n12 144 131\\n13 197 6\\n14 80 140\\n15 36 117\\n16 190 90\\n17 60 100\\n18 100 138\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': 'NA\\n1 2\\n1 3 9 5 17 14 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 25\\n8 172 202\\n9 82 50\\n10 160 82\\n11 90 105\\n12 267 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 128 153\\n17 60 100\\n4 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 7 9 4 19 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 1 0\\n2 150 40\\n3 30 2\\n4 180 150\\n5 40 80\\n6 130 130\\n7 42 28\\n8 172 202\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 109 100\\n18 110 70\\n19 130 100\\n20 69 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 7 20 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 91 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 41 118\\n9 50 50\\n10 160 82\\n11 90 5\\n20 144 131\\n13 130 32\\n14 80 140\\n15 36 117\\n16 353 90\\n17 49 101\\n18 100 70\\n19 208 100\\n20 24 69\\n21 82 110\\n22 5 150\\n1\\n1 22\\n0', 'output': 'NA\\nNA\\n1 3 20 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 8 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 1\\n2 150 40\\n3 30 20\\n4 180 150\\n5 56 80\\n6 130 130\\n7 72 28\\n8 172 202\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n17 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 3\\n1 3 4\\n1 3 9 5 17 14 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 2\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 33\\n6 130 260\\n7 9 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 164\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\n1 2\\n1 3 5 20 18 19 12 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n2 180 242\\n5 32 80\\n6 130 130\\n7 72 43\\n8 172 118\\n9 50 50\\n4 160 82\\n11 90 105\\n12 144 131\\n13 127 64\\n14 200 140\\n15 38 117\\n4 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 124 69\\n21 200 010\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 7 18 19 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 8 40\\n4 0 82\\n2\\n1 3\\n1 4\\n22\\n1 0 1\\n2 150 40\\n3 30 20\\n4 180 150\\n5 75 80\\n6 130 130\\n7 72 28\\n8 172 202\\n9 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190 90\\n17 49 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 5 150\\n1\\n1 22\\n0', 'output': 'NA\\nNA\\n1 3 2 5 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 90 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 202\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 109 100\\n18 110 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': 'NA\\nNA\\n1 3 9 20 17 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -2 0\\n2 30 0\\n3 33 40\\n4 1 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 218 131\\n13 130 64\\n14 80 140\\n15 36 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\n1 2 3 4\\n1 3 9 20 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 74 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 82\\n14 80 93\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 128 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 5 14 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 2\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 33\\n6 130 260\\n7 9 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 62\\n12 144 131\\n13 130 64\\n14 80 164\\n15 38 117\\n16 190 90\\n17 60 000\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\n1 2\\n1 3 9 11 18 19 12 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 91 4\\n4 0 58\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 78 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 41 118\\n9 50 50\\n10 160 82\\n11 90 5\\n20 144 131\\n13 130 32\\n14 80 140\\n15 36 83\\n16 353 90\\n17 49 101\\n18 100 70\\n19 208 100\\n20 24 69\\n21 82 110\\n22 5 150\\n1\\n1 22\\n0', 'output': 'NA\\nNA\\n1 3 20 15 8 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 27 0\\n3 8 40\\n4 0 82\\n2\\n1 3\\n1 4\\n22\\n1 0 1\\n2 150 40\\n3 30 20\\n4 180 150\\n5 75 80\\n6 130 130\\n7 72 28\\n8 172 202\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n17 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n11 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 57 150\\n1\\n1 22\\n0', 'output': '1 3\\n1 3 4\\n1 3 9 20 11 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 27 0\\n3 8 40\\n4 0 82\\n2\\n1 3\\n1 4\\n22\\n1 0 1\\n2 150 40\\n3 30 20\\n4 180 150\\n5 75 80\\n6 130 130\\n7 72 28\\n8 172 202\\n9 50 50\\n8 16 82\\n11 90 105\\n12 144 131\\n17 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 79 150\\n1\\n1 22\\n0', 'output': '1 3\\n1 3 4\\n1 3 9 5 11 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 2\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 33\\n6 130 130\\n7 72 28\\n8 119 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 77\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\n1 2\\n1 3 5 20 11 8 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -2 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 202\\n9 50 50\\n10 160 82\\n11 58 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n13 190 90\\n17 60 100\\n18 110 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 5 11 14 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 91 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 259 118\\n9 50 50\\n10 160 82\\n11 90 5\\n20 209 131\\n13 130 32\\n14 80 140\\n10 36 117\\n16 190 90\\n17 49 101\\n18 100 70\\n19 208 100\\n20 71 69\\n21 200 110\\n22 5 150\\n1\\n1 22\\n0', 'output': 'NA\\nNA\\n1 3 9 5 10 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 91 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 32\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 41 118\\n9 50 50\\n10 160 82\\n11 90 5\\n20 144 131\\n13 130 32\\n14 80 140\\n15 36 117\\n16 190 90\\n4 49 101\\n18 100 70\\n19 208 100\\n20 71 69\\n21 82 110\\n22 5 150\\n1\\n1 22\\n0', 'output': 'NA\\nNA\\n1 3 5 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n2 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 17 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 5\\n20 144 131\\n13 130 10\\n14 80 140\\n15 36 117\\n16 190 90\\n17 49 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 9 150\\n1\\n1 22\\n0', 'output': '2 3\\nNA\\n1 3 9 5 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n2 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n8 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 5\\n20 144 131\\n13 130 10\\n14 80 140\\n15 36 117\\n16 39 90\\n17 49 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 9 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 2 9 16 15 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n10 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 36 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 20 11 6 22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0\\n2 30 0\\n3 60 40\\n4 0 60\\n2\\n1 3\\n1 4\\n22\\n1 0 0\\n2 150 40\\n3 30 20\\n4 180 150\\n5 40 80\\n6 130 130\\n7 72 28\\n8 172 118\\n9 50 50\\n4 160 82\\n11 90 105\\n12 144 131\\n13 130 64\\n14 80 140\\n15 38 117\\n16 190 90\\n17 60 100\\n18 100 70\\n19 130 100\\n20 71 69\\n21 200 110\\n22 120 150\\n1\\n1 22\\n0', 'output': '1 2 3\\nNA\\n1 3 9 20 11 6 22\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_77861","program":"```python\nimport heapq\n\ndef dijkstra(G, s, g, n):\n cost = [10**9] * n\n cost[s] = 0\n pre = [-1] * n\n q = []\n heapq.heappush(q, (0, s))\n while q:\n d, to = heapq.heappop(q)\n if to == g:\n break\n if cost[to] < d:\n continue\n for n, dist in G[to]:\n nd = d + dist\n if cost[n] > nd:\n cost[n] = nd\n heapq.heappush(q, (nd, n))\n pre[n] = to\n\n if pre[g] == -1:\n return []\n ans = [g]\n cur = g\n while True:\n ans.append(pre[cur])\n cur = pre[cur]\n if cur == s or cur == -1:\n break\n\n return ans[::-1]\n\nwhile True:\n n = int(input())\n if n == 0:\n break\n bldgs = [-1] * n\n G = [[] for _ in range(n)]\n for _ in range(n):\n b, x, y = map(int, input().strip().split(\" \"))\n bldgs[b-1] = (x, y)\n\n for i in range(n):\n x_i, y_i = bldgs[i]\n for j in range(i+1, n):\n x_j, y_j = bldgs[j]\n d = ((x_i-x_j)**2 + (y_i-y_j)**2) ** 0.5\n if d <= 50:\n G[i].append((j, d))\n G[j].append((i, d))\n m = int(input())\n for _ in range(m):\n s, g = map(int, input().strip().split(\" \"))\n ans = dijkstra(G, s-1, g-1, n)\n if ans == []:\n print(\"NA\")\n else:\n print(\" \".join([str(i+1) for i in ans]))\n\n```","inputs":"4\n1 0 0\n2 30 0\n3 60 40\n4 0 60\n2\n1 3\n1 4\n22\n1 0 0\n2 150 40\n3 30 20\n4 180 150\n5 40 80\n6 130 130\n7 72 28\n8 172 118\n9 50 50\n10 160 82\n11 90 105\n12 144 131\n13 130 64\n14 80 140\n15 38 117\n16 190 90\n17 60 100\n18 100 70\n19 130 100\n20 71 69\n21 200 110\n22 120 150\n1\n1 22\n0","output":"1 2 3\nNA\n1 3 9 20 11 6 22","actual_output":"1 2 3\nNA\n1 3 9 20 11 6 22\n","execution_success":true,"sample_index":12420},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00312 Frog Going Straight","prompt":"Solve the following coding problem using the programming language python:\n\nA frog is about to return to the burrow. The burrow is D centimeters ahead of the frog, and the frog goes straight toward the burrow. There are only two actions that a frog can do:\n\n* Large jump (go forward L centimeters)\n* Small jump (go 1 cm forward)\n\n\n\nThe frog aims to just land in the burrow without jumping over it.\n\nCreate a program that asks how many times a frog needs to jump to return to its burrow.\n\n\n\nInput\n\nThe input is given in the following format.\n\n\nDL\n\n\nThe input is one line, given the distance D (1 \u2264 D \u2264 10000) to the burrow and the distance L (2 \u2264 L \u2264 10000) for the frog to travel on a large jump.\n\nOutput\n\nPrint on one line how many times the frog needs to jump.\n\nExamples\n\nInput\n\n10 5\n\n\nOutput\n\n2\n\n\nInput\n\n7 4\n\n\nOutput\n\n4\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nD,L = map(int,input().split())\nprint(D//L + D%L)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10 5', 'output': '2'}, {'type': 'stdin_stdout', 'input': '7 4', 'output': '4'}, {'type': 'stdin_stdout', 'input': '10 8', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '7 7', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 7', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '14 7', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '19 7', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '0 4', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '22 13', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '11 7', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '20 7', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '21 13', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '34 12', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '6 7', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '21 23', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '14 1', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '11 1', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '45 3', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '68 25', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '73 4', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '146 4', 'output': '38\\n'}, {'type': 'stdin_stdout', 'input': '212 4', 'output': '53\\n'}, {'type': 'stdin_stdout', 'input': '115 65', 'output': '51\\n'}, {'type': 'stdin_stdout', 'input': '357 4', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '357 1', 'output': '357\\n'}, {'type': 'stdin_stdout', 'input': '115 172', 'output': '115\\n'}, {'type': 'stdin_stdout', 'input': '384 1', 'output': '384\\n'}, {'type': 'stdin_stdout', 'input': '115 79', 'output': '37\\n'}, {'type': 'stdin_stdout', 'input': '148 1', 'output': '148\\n'}, {'type': 'stdin_stdout', 'input': '115 66', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '115 4', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '115 5', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '115 10', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '99 10', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '99 3', 'output': '33\\n'}, {'type': 'stdin_stdout', 'input': '154 3', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '154 6', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '73 11', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '-1 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '25 38', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '17 1', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '68 76', 'output': '68\\n'}, {'type': 'stdin_stdout', 'input': '212 7', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '290 4', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '2 -1', 'output': '-2\\n'}, {'type': 'stdin_stdout', 'input': '3 -1', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '208 133', 'output': '76\\n'}, {'type': 'stdin_stdout', 'input': '9 -1', 'output': '-9\\n'}, {'type': 'stdin_stdout', 'input': '13 -1', 'output': '-13\\n'}, {'type': 'stdin_stdout', 'input': '168 3', 'output': '56\\n'}, {'type': 'stdin_stdout', 'input': '128 3', 'output': '44\\n'}, {'type': 'stdin_stdout', 'input': '154 1', 'output': '154\\n'}, {'type': 'stdin_stdout', 'input': '26 1', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '34 1', 'output': '34\\n'}, {'type': 'stdin_stdout', 'input': '4 -1', 'output': '-4\\n'}, {'type': 'stdin_stdout', 'input': '212 1', 'output': '212\\n'}, {'type': 'stdin_stdout', 'input': '134 57', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '519 4', 'output': '132\\n'}, {'type': 'stdin_stdout', 'input': '135 191', 'output': '135\\n'}, {'type': 'stdin_stdout', 'input': '134 1', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '194 102', 'output': '93\\n'}, {'type': 'stdin_stdout', 'input': '208 155', 'output': '54\\n'}, {'type': 'stdin_stdout', 'input': '15 -1', 'output': '-15\\n'}, {'type': 'stdin_stdout', 'input': '60 2', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '168 6', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '131 3', 'output': '45\\n'}, {'type': 'stdin_stdout', 'input': '168 1', 'output': '168\\n'}, {'type': 'stdin_stdout', 'input': '5 -1', 'output': '-5\\n'}, {'type': 'stdin_stdout', 'input': '24 1', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '6 -1', 'output': '-6\\n'}, {'type': 'stdin_stdout', 'input': '12 -1', 'output': '-12\\n'}, {'type': 'stdin_stdout', 'input': '111 57', 'output': '55\\n'}, {'type': 'stdin_stdout', 'input': '519 6', 'output': '89\\n'}, {'type': 'stdin_stdout', 'input': '81 191', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '133 1', 'output': '133\\n'}, {'type': 'stdin_stdout', 'input': '202 55', 'output': '40\\n'}, {'type': 'stdin_stdout', 'input': '8 -1', 'output': '-8\\n'}, {'type': 'stdin_stdout', 'input': '131 1', 'output': '131\\n'}, {'type': 'stdin_stdout', 'input': '168 2', 'output': '84\\n'}, {'type': 'stdin_stdout', 'input': '16 -1', 'output': '-16\\n'}, {'type': 'stdin_stdout', 'input': '7 -1', 'output': '-7\\n'}, {'type': 'stdin_stdout', 'input': '519 8', 'output': '71\\n'}, {'type': 'stdin_stdout', 'input': '201 1', 'output': '201\\n'}, {'type': 'stdin_stdout', 'input': '170 176', 'output': '170\\n'}, {'type': 'stdin_stdout', 'input': '302 1', 'output': '302\\n'}, {'type': 'stdin_stdout', 'input': '241 1', 'output': '241\\n'}, {'type': 'stdin_stdout', 'input': '140 1', 'output': '140\\n'}, {'type': 'stdin_stdout', 'input': '21 -1', 'output': '-21\\n'}, {'type': 'stdin_stdout', 'input': '686 8', 'output': '91\\n'}, {'type': 'stdin_stdout', 'input': '183 1', 'output': '183\\n'}, {'type': 'stdin_stdout', 'input': '194 50', 'output': '47\\n'}, {'type': 'stdin_stdout', 'input': '17 -1', 'output': '-17\\n'}, {'type': 'stdin_stdout', 'input': '303 1', 'output': '303\\n'}, {'type': 'stdin_stdout', 'input': '140 2', 'output': '70\\n'}, {'type': 'stdin_stdout', 'input': '205 35', 'output': '35\\n'}, {'type': 'stdin_stdout', 'input': '34 -1', 'output': '-34\\n'}, {'type': 'stdin_stdout', 'input': '27 1', 'output': '27\\n'}, {'type': 'stdin_stdout', 'input': '1155 8', 'output': '147\\n'}, {'type': 'stdin_stdout', 'input': '65 128', 'output': '65\\n'}, {'type': 'stdin_stdout', 'input': '351 1', 'output': '351\\n'}, {'type': 'stdin_stdout', 'input': '202 111', 'output': '92\\n'}, {'type': 'stdin_stdout', 'input': '19 -1', 'output': '-19\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_77865","program":"```python\nD,L = map(int,input().split())\nprint(D//L + D%L)\n```","inputs":"10 5","output":"2","actual_output":"2\n","execution_success":true,"sample_index":12421},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00811 Calling Extraterrestrial Intelligence Again","prompt":"Solve the following coding problem using the programming language python:\n\nA message from humans to extraterrestrial intelligence was sent through the Arecibo radio telescope in Puerto Rico on the afternoon of Saturday November l6, l974. The message consisted of l679 bits and was meant to be translated to a rectangular picture with 23 \u00d7 73 pixels. Since both 23 and 73 are prime numbers, 23 \u00d7 73 is the unique possible size of the translated rectangular picture each edge of which is longer than l pixel. Of course, there was no guarantee that the receivers would try to translate the message to a rectangular picture. Even if they would, they might put the pixels into the rectangle incorrectly. The senders of the Arecibo message were optimistic.\n\nWe are planning a similar project. Your task in the project is to find the most suitable width and height of the translated rectangular picture. The term ``most suitable'' is defined as follows. An integer m greater than 4 is given. A positive fraction a/b less than or equal to 1 is also given. The area of the picture should not be greater than m. Both of the width and the height of the translated picture should be prime numbers. The ratio of the width to the height should not be less than a/b nor greater than 1. You should maximize the area of the picture under these constraints.\n\nIn other words, you will receive an integer m and a fraction a/b . It holds that m > 4 and 0 < a/b \u2264 1 . You should find the pair of prime numbers p, q such that pq \u2264 m and a/b \u2264 p/q \u2264 1 , and furthermore, the product pq takes the maximum value among such pairs of two prime numbers. You should report p and q as the \"most suitable\" width and height of the translated picture.\n\n\n\nInput\n\nThe input is a sequence of at most 2000 triplets of positive integers, delimited by a space character in between. Each line contains a single triplet. The sequence is followed by a triplet of zeros, 0 0 0, which indicates the end of the input and should not be treated as data to be processed.\n\nThe integers of each input triplet are the integer m, the numerator a, and the denominator b described above, in this order. You may assume 4 < m < 100000 and 1 \u2264 a \u2264 b \u2264 1000.\n\nOutput\n\nThe output is a sequence of pairs of positive integers. The i-th output pair corresponds to the i-th input triplet. The integers of each output pair are the width p and the height q described above, in this order.\n\nEach output line contains a single pair. A space character is put between the integers as a delimiter. No other characters should appear in the output.\n\nExample\n\nInput\n\n5 1 2\n99999 999 999\n1680 5 16\n1970 1 1\n2002 4 11\n0 0 0\n\n\nOutput\n\n2 2\n313 313\n23 73\n43 43\n37 53\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nanswer = []\n\n\ndef prime(n):\n prime_flag = [0 for i in range(n + 1)]\n prime_list = []\n for i in range(2, n + 1):\n if prime_flag[i] == 0:\n prime_list.append(i)\n\n temp = 1\n while temp * i <= n:\n prime_flag[temp * i] = 1\n temp += 1\n return prime_list\n\n\nprime_list = prime(100000)\n\nwhile True:\n\n m, a, b = map(int, input().split())\n if m == a == b == 0:\n break\n rate = a / b\n ans = [0, 0]\n for i in prime_list:\n if i > m:\n break\n for j in prime_list:\n if i * j <= m:\n if i / j >= rate and i / j <= 1:\n if ans[0] * ans[1] < i * j:\n ans = [i, j]\n else:\n break\n\n answer.append(ans)\n\nfor i in answer:\n print(*i)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n1680 5 16\\n1970 1 1\\n2002 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n23 73\\n43 43\\n37 53'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n1680 5 16\\n1970 1 2\\n2002 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n23 73\\n37 53\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n2566 5 16\\n1970 1 1\\n2002 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n43 59\\n43 43\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n1680 5 16\\n973 1 2\\n2002 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n23 73\\n31 31\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n1680 5 16\\n1970 1 1\\n2886 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n23 73\\n43 43\\n43 67\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n90868 999 999\\n1680 5 16\\n1970 1 2\\n2002 4 11\\n0 0 0', 'output': '2 2\\n293 293\\n23 73\\n37 53\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n107 5 16\\n973 1 2\\n2002 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n7 13\\n31 31\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 4\\n99999 999 999\\n1680 5 16\\n973 1 2\\n3406 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n23 73\\n31 31\\n41 83\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n107 5 16\\n1284 1 2\\n2002 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n7 13\\n31 41\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n10985 999 999\\n2566 8 16\\n1970 1 1\\n2002 3 11\\n0 0 0', 'output': '2 2\\n103 103\\n43 59\\n43 43\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n1680 5 16\\n973 1 2\\n2365 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n23 73\\n31 31\\n29 79\\n'}, {'type': 'stdin_stdout', 'input': '7 1 4\\n99999 999 999\\n1680 5 16\\n973 1 2\\n2002 4 11\\n0 0 0', 'output': '2 3\\n313 313\\n23 73\\n31 31\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 1591\\n107 5 16\\n973 1 2\\n2002 4 11\\n0 0 0', 'output': '2 2\\n257 389\\n7 13\\n31 31\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n2566 8 16\\n1970 1 1\\n115 3 11\\n0 0 0', 'output': '2 2\\n313 313\\n43 59\\n43 43\\n7 13\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 1591\\n107 3 16\\n973 1 2\\n2002 4 11\\n0 0 0', 'output': '2 2\\n257 389\\n5 19\\n31 31\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 4\\n99999 999 999\\n103 5 21\\n973 1 2\\n3406 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n5 19\\n31 31\\n41 83\\n'}, {'type': 'stdin_stdout', 'input': '7 1 5\\n99999 999 999\\n1680 5 16\\n973 1 2\\n771 4 11\\n0 0 0', 'output': '2 3\\n313 313\\n23 73\\n31 31\\n17 43\\n'}, {'type': 'stdin_stdout', 'input': '5 1 4\\n99999 999 999\\n103 5 21\\n1506 1 2\\n3406 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n5 19\\n31 47\\n41 83\\n'}, {'type': 'stdin_stdout', 'input': '7 1 5\\n99999 999 999\\n1680 8 16\\n973 1 2\\n771 4 11\\n0 0 0', 'output': '2 3\\n313 313\\n31 53\\n31 31\\n17 43\\n'}, {'type': 'stdin_stdout', 'input': '5 1 4\\n99999 999 999\\n27 5 21\\n1506 1 2\\n3406 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n5 5\\n31 47\\n41 83\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n1680 10 16\\n1970 1 2\\n2002 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n37 43\\n37 53\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n2566 5 16\\n132 1 1\\n2002 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n43 59\\n11 11\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n10985 999 999\\n1188 8 16\\n1970 1 1\\n2002 3 11\\n0 0 0', 'output': '2 2\\n103 103\\n31 37\\n43 43\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 2 4\\n99999 999 999\\n1680 5 15\\n973 1 2\\n3406 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n31 53\\n31 31\\n41 83\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n1680 5 16\\n685 1 2\\n2365 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n23 73\\n23 29\\n29 79\\n'}, {'type': 'stdin_stdout', 'input': '7 1 4\\n40562 999 999\\n1680 5 16\\n973 1 2\\n2002 4 11\\n0 0 0', 'output': '2 3\\n199 199\\n23 73\\n31 31\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 1\\n10985 999 1486\\n2566 8 29\\n1970 1 1\\n2002 3 11\\n0 0 0', 'output': '2 2\\n97 113\\n43 59\\n43 43\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '12 1 5\\n99999 999 999\\n1680 8 16\\n973 1 2\\n771 4 11\\n0 0 0', 'output': '2 5\\n313 313\\n31 53\\n31 31\\n17 43\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n1680 9 16\\n973 1 4\\n2002 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n31 53\\n31 31\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n10985 999 1848\\n1188 8 16\\n1970 1 1\\n2002 3 11\\n0 0 0', 'output': '2 2\\n79 139\\n31 37\\n43 43\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '7 1 4\\n40562 999 999\\n1680 5 16\\n973 1 2\\n3108 4 11\\n0 0 0', 'output': '2 3\\n199 199\\n23 73\\n31 31\\n37 83\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 380 1591\\n107 5 16\\n973 1 2\\n1575 4 11\\n0 0 0', 'output': '2 2\\n257 389\\n7 13\\n31 31\\n29 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 1\\n10985 999 1486\\n2566 8 29\\n1970 1 1\\n1000 3 11\\n0 0 0', 'output': '2 2\\n97 113\\n43 59\\n43 43\\n23 43\\n'}, {'type': 'stdin_stdout', 'input': '7 1 2\\n99999 999 999\\n1680 5 16\\n973 1 2\\n2002 8 11\\n0 0 0', 'output': '2 3\\n313 313\\n23 73\\n31 31\\n41 47\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n29563 999 1591\\n107 3 16\\n973 1 2\\n2002 4 21\\n0 0 0', 'output': '2 2\\n163 181\\n5 19\\n31 31\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 1 7\\n99999 999 999\\n103 5 21\\n973 1 2\\n3406 4 4\\n0 0 0', 'output': '2 2\\n313 313\\n5 19\\n31 31\\n53 53\\n'}, {'type': 'stdin_stdout', 'input': '12 1 5\\n99999 999 999\\n1680 8 10\\n973 1 2\\n771 4 11\\n0 0 0', 'output': '2 5\\n313 313\\n37 43\\n31 31\\n17 43\\n'}, {'type': 'stdin_stdout', 'input': '5 1 4\\n99999 999 1594\\n27 5 11\\n1506 1 2\\n3406 4 11\\n0 0 0', 'output': '2 2\\n257 389\\n5 5\\n31 47\\n41 83\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n99999 999 999\\n1680 9 16\\n973 1 4\\n2002 4 5\\n0 0 0', 'output': '2 2\\n313 313\\n31 53\\n31 31\\n41 47\\n'}, {'type': 'stdin_stdout', 'input': '5 1 9\\n99999 999 999\\n1495 5 16\\n973 1 2\\n2002 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n31 47\\n31 31\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '5 2 2\\n99999 999 999\\n1680 5 16\\n685 1 2\\n1589 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n23 73\\n23 29\\n29 53\\n'}, {'type': 'stdin_stdout', 'input': '14 1 4\\n40562 999 999\\n1680 5 16\\n973 1 2\\n3108 4 11\\n0 0 0', 'output': '2 7\\n199 199\\n23 73\\n31 31\\n37 83\\n'}, {'type': 'stdin_stdout', 'input': '5 1 1\\n10985 999 1486\\n2566 8 29\\n1970 1 1\\n1010 3 11\\n0 0 0', 'output': '2 2\\n97 113\\n43 59\\n43 43\\n19 53\\n'}, {'type': 'stdin_stdout', 'input': '7 1 2\\n99999 999 999\\n1680 8 16\\n973 1 2\\n2002 8 11\\n0 0 0', 'output': '2 3\\n313 313\\n31 53\\n31 31\\n41 47\\n'}, {'type': 'stdin_stdout', 'input': '6 1 7\\n99999 999 999\\n103 5 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2\\n97 113\\n43 59\\n53 53\\n23 43\\n'}, {'type': 'stdin_stdout', 'input': '5 1 3\\n35438 999 999\\n1495 5 16\\n973 1 2\\n2002 4 11\\n0 0 0', 'output': '2 2\\n181 181\\n31 47\\n31 31\\n37 53\\n'}, {'type': 'stdin_stdout', 'input': '6 1 4\\n99999 601 1594\\n27 5 11\\n1506 2 3\\n3406 4 11\\n0 0 0', 'output': '2 3\\n257 389\\n5 5\\n37 37\\n41 83\\n'}, {'type': 'stdin_stdout', 'input': '10 1 9\\n99999 131 1768\\n1495 5 16\\n973 1 2\\n2107 4 11\\n0 0 0', 'output': '2 5\\n257 389\\n31 47\\n31 31\\n31 67\\n'}, {'type': 'stdin_stdout', 'input': '8 2 4\\n99999 999 999\\n1680 2 10\\n685 1 2\\n2976 4 11\\n0 0 0', 'output': '2 3\\n313 313\\n23 73\\n23 29\\n37 79\\n'}, {'type': 'stdin_stdout', 'input': '5 1 3\\n99999 999 999\\n1680 5 16\\n81 1 1\\n3259 4 11\\n0 0 0', 'output': '2 2\\n313 313\\n23 73\\n7 7\\n41 79\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_77877","program":"```python\nanswer = []\n\n\ndef prime(n):\n prime_flag = [0 for i in range(n + 1)]\n prime_list = []\n for i in range(2, n + 1):\n if prime_flag[i] == 0:\n prime_list.append(i)\n\n temp = 1\n while temp * i <= n:\n prime_flag[temp * i] = 1\n temp += 1\n return prime_list\n\n\nprime_list = prime(100000)\n\nwhile True:\n\n m, a, b = map(int, input().split())\n if m == a == b == 0:\n break\n rate = a / b\n ans = [0, 0]\n for i in prime_list:\n if i > m:\n break\n for j in prime_list:\n if i * j <= m:\n if i / j >= rate and i / j <= 1:\n if ans[0] * ans[1] < i * j:\n ans = [i, j]\n else:\n break\n\n answer.append(ans)\n\nfor i in answer:\n print(*i)\n\n```","inputs":"5 1 2\n99999 999 999\n1680 5 16\n1970 1 1\n2002 4 11\n0 0 0","output":"2 2\n313 313\n23 73\n43 43\n37 53","actual_output":"2 2\n313 313\n23 73\n43 43\n37 53\n","execution_success":true,"sample_index":12422},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01075 One-Time Path","prompt":"Solve the following coding problem using the programming language python:\n\nProblem\n\nThere are N islands and M bridges. Numbers from 1 to N are assigned to each of the N islands. Numbers from 1 to M are also assigned to each of the M bridges.\n\nGaccho is currently on the first island (at time 0). Gaccho can move from the ai-th island to the bi-th island in one direction by using the i-th bridge.\n\nHowever, at time 0, all the bridges were full of tide and sank into the sea. The i-th bridge will be able to cross the tide at time ci. And soon after the time ci, the tide rises again and the i-th bridge sinks again. When it sinks again, I don't know when the tide will pull and cross. So, Gaccho decided to think that such a bridge would never be crossed.\n\nGaccho wants to see the scenery of the 1st to N-1st islands for as long as possible, but since he is staying at the Nth island, he finally arrives at the Nth island. There must be. Also, because he keeps his parents waiting on the boat, Gacho must leave by boat and go home as soon as he arrives at the Nth island.\n\nThe time it takes for Gaccho to cross the bridge and travel around the island is very short, so you can assume it is 0. Find the maximum amount of time Gaccho can be on any of the 1st to N-1 islands. However, if you can't move to the Nth island no matter how you move, output -1 instead.\n\nConstraints\n\n* 2 \u2264 N \u2264 105\n* 1 \u2264 M \u2264 2 \u00d7 105\n* 1 \u2264 ai = INF: print(-1)\nelse:\n\tlast.sort(key=lambda x:(-x[1]))\n\tfor a, c in last:\n\t\tif dist[a] <= c: print(c); break\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 2\\n1 2 20\\n2 3 10', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 27\\n1 3 37\\n2 3 47\\n3 1 57', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 10\\n2 3 20', 'output': '20'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 10\\n2 3 10', 'output': '10'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 13\\n2 3 17\\n2 3 15', 'output': '17'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 20\\n3 3 10', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 10\\n2 3 37', 'output': '37\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 13\\n2 3 17\\n2 3 21', 'output': '21\\n'}, 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'stdin_stdout', 'input': '13 2\\n1 1 22\\n7 3 15', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 0\\n-1 4 2\\n3 3 13', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1 2 27\\n1 3 37\\n2 3 47\\n3 1 57', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 10\\n2 2 20', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 10\\n2 3 9', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 11\\n1 3 10\\n2 3 47\\n3 1 57', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 2 10\\n2 3 27', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n1 2 10\\n2 3 10', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 1 13\\n2 0 17\\n2 3 15', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 27\\n1 3 10\\n3 3 74\\n3 1 57', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '14 2\\n1 2 10\\n2 3 15', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '7 2\\n2 2 19\\n2 3 15', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n1 2 27\\n1 3 20\\n3 3 47\\n3 1 36', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 27\\n1 3 29\\n2 3 41\\n3 1 57', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 3\\n2 3 37', 'output': '37\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1 2 9\\n3 3 10', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 27\\n2 3 10\\n2 3 47\\n2 1 57', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 1 51\\n1 3 10\\n3 3 47\\n3 1 57', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '7 2\\n1 2 10\\n3 4 15', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '7 2\\n1 4 19\\n2 2 15', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 52\\n1 3 20\\n3 3 47\\n4 1 42', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 27\\n1 3 1\\n2 3 7\\n3 1 57', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 9\\n3 3 32', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 46\\n2 3 10\\n3 3 47\\n3 1 57', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\n1 2 8\\n3 3 19', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 1 27\\n1 3 10\\n3 3 47\\n3 1 136', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 27\\n1 3 0\\n4 3 47\\n3 1 57', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '9 2\\n1 2 14\\n3 3 15', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_77885","program":"```python\n# AOJ 590: One-Time Path\n# Python3 2018.7.13 bal4u\n\nINF = 0x7fffffff\nimport heapq\ndef dijkstra(V, to, start):\n\tdist = [INF]*V\n\tQ = []\n\tdist[start] = 0\n\theapq.heappush(Q, (0, start))\n\twhile Q:\n\t\tt, s = heapq.heappop(Q)\n\t\tif dist[s] < t: continue\n\t\tfor e, cost in to[s]:\n\t\t\tif t <= cost and cost < dist[e]:\n\t\t\t\tdist[e] = cost\n\t\t\t\theapq.heappush(Q, (cost, e))\n\treturn dist\n\nn, m = map(int, input().split())\nn1 = n - 1\nlast = []\nto = [[] for i in range(n)]\nfor i in range(m):\n\ta, b, c = map(int, input().split())\n\ta -= 1; b -= 1\n\tto[a].append((b, c))\n\tif b == n-1: last.append((a, c))\n\ndist = dijkstra(n, to, 0)\nif dist[n-1] >= INF: print(-1)\nelse:\n\tlast.sort(key=lambda x:(-x[1]))\n\tfor a, c in last:\n\t\tif dist[a] <= c: print(c); break\n\n\n```","inputs":"3 2\n1 2 20\n2 3 10","output":"-1","actual_output":"-1\n","execution_success":true,"sample_index":12423},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01827 Black Company","prompt":"Solve the following coding problem using the programming language python:\n\nExample\n\nInput\n\n3\n1 3 3\n2\n1 2\n1 3\n\n\nOutput\n\n5\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import deque\nimport sys\ndef main():\n readline = sys.stdin.readline\n write = sys.stdout.write\n def root(x):\n if x == p[x]:\n return x\n p[x] = y = root(p[x])\n return y\n def unite(x, y):\n px = root(x)\n py = root(y)\n if px < py:\n p[py] = px\n else:\n p[px] = py\n\n N = int(readline())\n *C, = map(int, readline().split())\n M = int(readline())\n *p, = range(N)\n G = [[] for i in range(N)]\n G0 = [[] for i in range(N)]\n for i in range(M):\n a, b = map(int, readline().split()); a -= 1; b -= 1\n G[a].append(b)\n G[b].append(a)\n ca = C[a]; cb = C[b]\n if ca < cb:\n G0[a].append(b)\n elif cb < ca:\n G0[b].append(a)\n for v in range(N):\n ws = G[v]\n if not ws:\n continue\n ws.sort(key = C.__getitem__)\n c = C[v]\n prv = ws[0]; pw = C[prv]\n if C[prv] == c:\n unite(v, prv)\n for w in ws[1:]:\n cw = C[w]\n if pw == cw:\n unite(prv, w)\n else:\n G0[prv].append(w)\n if cw == c:\n unite(v, w)\n prv = w; pw = cw\n\n G1 = [[] for i in range(N)]\n deg = [0]*N\n for v in range(N):\n pv = root(v)\n for w in G0[v]:\n pw = root(w)\n if pv != pw:\n G1[pv].append(pw)\n deg[pw] += 1\n\n que = deque()\n D = [0]*N\n for i in range(N):\n if root(i) != i:\n continue\n if deg[i] == 0:\n que.append(i)\n D[i] = 1\n while que:\n v = que.popleft()\n d = D[v]\n for w in G1[v]:\n deg[w] -= 1\n if deg[w] == 0:\n que.append(w)\n D[w] = max(D[w], d+1)\n for i in range(N):\n if root(i) == i:\n continue\n D[i] = D[root(i)]\n write(\"%d\\n\" % sum(D))\nmain()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 3 3\\n2\\n1 2\\n1 3', 'output': '5'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n2\\n1 2\\n1 3', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 0\\n2\\n1 2\\n1 3', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 3\\n2\\n1 2\\n2 3', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 3\\n2\\n1 2\\n3 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n2\\n1 2\\n2 3', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 3 1\\n2\\n1 2\\n2 3', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 3\\n2\\n1 2\\n2 3', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n2\\n1 2\\n3 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n2\\n1 2\\n1 3', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n0\\n1 2\\n1 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n1 2\\n1 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n0\\n1 2\\n1 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n0\\n1 2\\n1 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n0\\n1 2\\n0 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n0\\n2 2\\n0 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n1 2\\n0 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n1 2\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n2 2\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n2 1\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n3 1\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n0 1\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 3\\n2\\n1 3\\n1 3', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n2\\n2 2\\n1 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n2\\n1 2\\n1 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 3\\n2\\n1 2\\n2 3', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n0\\n1 2\\n3 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n1 2\\n1 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n0\\n1 1\\n1 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n1\\n1 2\\n1 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n-1\\n1 2\\n0 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 0\\n0\\n2 2\\n0 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n0 2\\n0 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n0\\n1 2\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n2 2\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 1\\n0\\n2 1\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n3 0\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n0 1\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 6\\n2\\n1 2\\n2 3', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n1 2\\n3 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 1\\n0\\n1 2\\n1 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n0\\n0 2\\n1 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n1\\n1 2\\n1 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n-1\\n1 2\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 0\\n0\\n3 2\\n0 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n0\\n1 2\\n-1 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n1 2\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 1\\n0\\n2 1\\n-1 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n3 0\\n0 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n0 1\\n-1 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 1 6\\n2\\n1 2\\n2 3', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n0 2\\n1 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 3 0\\n1\\n1 2\\n1 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 0\\n0\\n4 2\\n0 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n0\\n1 2\\n-1 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n0 2\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 1\\n0\\n2 1\\n-1 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n3 0\\n1 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n0 0\\n-1 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 1 6\\n2\\n1 2\\n2 3', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n0 2\\n2 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 0\\n1\\n1 2\\n1 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 0\\n0\\n4 2\\n0 4', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1\\n1 2\\n-1 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n0 4\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 1\\n0\\n2 1\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n6 0\\n1 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n0 0\\n-2 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 6\\n2\\n1 2\\n2 3', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n1 2\\n2 3', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 0\\n0\\n4 2\\n-1 4', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1\\n1 2\\n-2 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n1 4\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 1\\n0\\n1 1\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n0\\n6 0\\n1 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n0 1\\n-2 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n1 2\\n2 6', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 1\\n0\\n4 2\\n-1 4', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1\\n1 2\\n-2 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n1 5\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 1\\n0\\n1 1\\n1 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n0\\n6 0\\n1 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n0\\n0 2\\n-2 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1\\n1 2\\n-2 0', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 1\\n0\\n1 1\\n2 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n0\\n6 0\\n1 0', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n0 2\\n-2 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1\\n1 3\\n-2 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 1\\n0\\n1 1\\n4 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 0\\n0\\n6 0\\n1 0', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n0\\n0 2\\n0 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1\\n1 3\\n-2 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n0\\n1 1\\n4 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 0\\n0\\n6 1\\n1 0', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1\\n1 3\\n-2 4', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n1\\n1 1\\n4 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 0\\n0\\n6 1\\n1 0', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1\\n2 3\\n-2 4', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 3 0\\n1\\n1 1\\n4 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 0\\n0\\n9 1\\n1 0', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1\\n2 3\\n-2 0', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 5, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_77905","program":"```python\nfrom collections import deque\nimport sys\ndef main():\n readline = sys.stdin.readline\n write = sys.stdout.write\n def root(x):\n if x == p[x]:\n return x\n p[x] = y = root(p[x])\n return y\n def unite(x, y):\n px = root(x)\n py = root(y)\n if px < py:\n p[py] = px\n else:\n p[px] = py\n\n N = int(readline())\n *C, = map(int, readline().split())\n M = int(readline())\n *p, = range(N)\n G = [[] for i in range(N)]\n G0 = [[] for i in range(N)]\n for i in range(M):\n a, b = map(int, readline().split()); a -= 1; b -= 1\n G[a].append(b)\n G[b].append(a)\n ca = C[a]; cb = C[b]\n if ca < cb:\n G0[a].append(b)\n elif cb < ca:\n G0[b].append(a)\n for v in range(N):\n ws = G[v]\n if not ws:\n continue\n ws.sort(key = C.__getitem__)\n c = C[v]\n prv = ws[0]; pw = C[prv]\n if C[prv] == c:\n unite(v, prv)\n for w in ws[1:]:\n cw = C[w]\n if pw == cw:\n unite(prv, w)\n else:\n G0[prv].append(w)\n if cw == c:\n unite(v, w)\n prv = w; pw = cw\n\n G1 = [[] for i in range(N)]\n deg = [0]*N\n for v in range(N):\n pv = root(v)\n for w in G0[v]:\n pw = root(w)\n if pv != pw:\n G1[pv].append(pw)\n deg[pw] += 1\n\n que = deque()\n D = [0]*N\n for i in range(N):\n if root(i) != i:\n continue\n if deg[i] == 0:\n que.append(i)\n D[i] = 1\n while que:\n v = que.popleft()\n d = D[v]\n for w in G1[v]:\n deg[w] -= 1\n if deg[w] == 0:\n que.append(w)\n D[w] = max(D[w], d+1)\n for i in range(N):\n if root(i) == i:\n continue\n D[i] = D[root(i)]\n write(\"%d\\n\" % sum(D))\nmain()\n\n```","inputs":"3\n1 3 3\n2\n1 2\n1 3","output":"5","actual_output":"5\n","execution_success":true,"sample_index":12424},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02249 Pattern Search","prompt":"Solve the following coding problem using the programming language python:\n\nFind places where a R \u00d7 C pattern is found within a H \u00d7 W region. Print top-left coordinates (i, j) of sub-regions where the pattern found. The top-left and bottom-right coordinates of the region is (0, 0) and (H-1, W-1) respectively.\n\nConstraints\n\n* 1 \u2264 H, W \u2264 1000\n* 1 \u2264 R, C \u2264 1000\n* The input consists of alphabetical characters and digits\n\nInput\n\nIn the first line, two integers H and W are given. In the following H lines, i-th lines of the region are given.\n\nIn the next line, two integers R and C are given. In the following R lines, i-th lines of the pattern are given.\n\nExample\n\nInput\n\n4 5\n00010\n00101\n00010\n00100\n3 2\n10\n01\n10\n\n\nOutput\n\n0 3\n1 2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom typing import List\n\n\ndef calc_hash(tab: List[List[int]], row_num: int, col_num: int) -> None:\n global hash_table, R, C, baes1, base2, mask\n tmp_table = [[0] * col_num for _ in range(row_num)]\n diff_row, diff_col = row_num - R, col_num - C\n\n bit_mask = 1\n for _ in range(C):\n bit_mask = (bit_mask * base1) & mask\n for r in range(row_num):\n hash_v = 0\n for c in range(C):\n hash_v = hash_v * base1 + tab[r][c]\n for dc in range(diff_col):\n tmp_table[r][dc] = hash_v\n hash_v = (hash_v * base1 - bit_mask * tab[r][dc] + tab[r][dc + C]) & mask\n tmp_table[r][diff_col] = hash_v\n\n bit_mask = 1\n for _ in range(R):\n bit_mask = (bit_mask * base2) & mask\n for c in range(diff_col + 1):\n hash_v = 0\n for r in range(R):\n hash_v = hash_v * base2 + tmp_table[r][c]\n for dr in range(diff_row):\n hash_table[dr][c] = hash_v\n hash_v = (hash_v * base2 - bit_mask * tmp_table[dr][c]\n + tmp_table[dr + R][c]) & mask\n hash_table[diff_row][c] = hash_v\n\n\nif __name__ == \"__main__\":\n base1 = 1009 # The first prime number over 1000.\n base2 = 1013 # The second prime number over 1000.\n mask = (1 << 32) - 1 # Mask.\n\n H, W = map(lambda x: int(x), input().split())\n region = [[0] * W for _ in range(H)]\n for row in range(H):\n region[row] = [ord(s) for s in input()]\n\n R, C = map(lambda x: int(x), input().split())\n pattern = [[0] * C for _ in range(R)]\n for row in range(R):\n pattern[row] = [ord(s) for s in input()]\n\n if H >= R and W >= C:\n hash_table = [[0] * W for _ in range(H)]\n calc_hash(pattern, R, C) # Calc the target hash and save it into hash_table[0][0]\n key = hash_table[0][0] & mask\n calc_hash(region, H, W)\n for r in range(H - R + 1):\n for c in range(W - C + 1):\n if key == hash_table[r][c] & mask:\n print(f\"{r} {c}\")\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 5\\n00010\\n00101\\n00010\\n00100\\n3 2\\n10\\n01\\n10', 'output': '0 3\\n1 2'}, {'type': 'stdin_stdout', 'input': '4 5\\n00010\\n00101\\n00010\\n00100\\n2 2\\n10\\n01\\n10', 'output': '0 3\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00000\\n00101\\n00010\\n00100\\n2 2\\n10\\n01\\n10', 'output': '1 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00010\\n00001\\n00010\\n00000\\n2 2\\n10\\n01\\n11', 'output': '0 3\\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n00000\\n00100\\n01010\\n00100\\n2 2\\n10\\n01\\n24', 'output': '1 2\\n2 1\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00000\\n00100\\n00010\\n00100\\n1 2\\n10\\n01\\n10', 'output': '1 2\\n2 3\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00000\\n00100\\n00010\\n00000\\n1 2\\n10\\n0\\n10', 'output': '1 2\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00000\\n00000\\n00010\\n00100\\n1 2\\n10\\n0\\n10', 'output': '2 3\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n01000\\n00100\\n00010\\n00000\\n1 2\\n10\\n0\\n10', 'output': '0 1\\n1 2\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00000\\n00000\\n00000\\n00100\\n1 2\\n10\\n0\\n10', 'output': '3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00100\\n00100\\n01110\\n00100\\n1 2\\n10\\n0\\n16', 'output': '0 2\\n1 2\\n2 3\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n01000\\n00100\\n00010\\n00000\\n1 2\\n10\\n0\\n10', 'output': '0 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00001\\n00000\\n00110\\n00000\\n1 2\\n10\\n0\\n10', 'output': '2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n01000\\n00100\\n10010\\n00000\\n1 2\\n10\\n0\\n10', 'output': '0 1\\n1 2\\n2 0\\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n00000\\n00100\\n01010\\n00100\\n2 1\\n10\\n01\\n24', 'output': '1 2\\n2 1\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n00000\\n10100\\n00010\\n00100\\n2 1\\n10\\n01\\n14', 'output': '1 0\\n1 2\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n11010\\n00101\\n00011\\n00000\\n2 2\\n10\\n01\\n11', 'output': '0 1\\n0 3\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00000\\n00100\\n01110\\n10100\\n1 2\\n10\\n0\\n10', 'output': '1 2\\n2 3\\n3 0\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00001\\n00110\\n00110\\n00100\\n1 2\\n10\\n0\\n10', 'output': '1 3\\n2 3\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n01000\\n00100\\n00010\\n00100\\n1 2\\n10\\n0\\n10', 'output': '0 1\\n1 2\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n10000\\n00000\\n00000\\n00100\\n1 1\\n10\\n0\\n16', 'output': '0 0\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00010\\n00001\\n01011\\n00000\\n1 2\\n10\\n01\\n11', 'output': '0 3\\n2 1\\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n00000\\n11100\\n00010\\n00100\\n2 1\\n10\\n01\\n14', 'output': '1 0\\n1 1\\n1 2\\n2 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2\\n10\\n01\\n11', 'output': '0 1\\n0 3\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n11010\\n01001\\n01011\\n10000\\n2 1\\n10\\n01\\n11', 'output': '0 0\\n0 3\\n2 1\\n2 3\\n2 4\\n'}, {'type': 'stdin_stdout', 'input': '4 10\\n10000\\n10000\\n00010\\n00100\\n1 2\\n10\\n0\\n10', 'output': '0 0\\n1 0\\n2 3\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n11010\\n10001\\n10011\\n01100\\n2 2\\n10\\n01\\n11', 'output': '0 3\\n2 0\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00010\\n00101\\n01011\\n00001\\n1 2\\n10\\n01\\n11', 'output': '0 3\\n1 2\\n2 1\\n'}, {'type': 'stdin_stdout', 'input': '4 10\\n00010\\n00001\\n00010\\n01000\\n1 2\\n10\\n01\\n8', 'output': '0 3\\n2 3\\n3 1\\n'}, {'type': 'stdin_stdout', 'input': '4 10\\n10000\\n00110\\n00010\\n00000\\n1 2\\n10\\n0\\n18', 'output': '0 0\\n1 3\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 7\\n11000\\n00100\\n00010\\n00000\\n1 2\\n11\\n0\\n10', 'output': '0 0\\n'}, {'type': 'stdin_stdout', 'input': '4 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9\\n10000\\n01100\\n01010\\n01100\\n2 2\\n10\\n01\\n3', 'output': '0 0\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00001\\n00110\\n10110\\n00100\\n1 2\\n10\\n0\\n10', 'output': '1 3\\n2 0\\n2 3\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n01100\\n00100\\n00010\\n10000\\n1 2\\n10\\n0\\n10', 'output': '0 2\\n1 2\\n3 0\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n10001\\n00100\\n00110\\n00010\\n1 1\\n10\\n0\\n6', 'output': '0 0\\n0 4\\n1 2\\n2 2\\n2 3\\n3 3\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00010\\n00001\\n01011\\n00101\\n1 2\\n10\\n01\\n16', 'output': '0 3\\n2 1\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n11010\\n10101\\n10011\\n01100\\n2 2\\n10\\n01\\n8', 'output': '0 1\\n0 3\\n1 2\\n2 0\\n'}, {'type': 'stdin_stdout', 'input': '4 17\\n10010\\n10100\\n00110\\n10111\\n1 1\\n10\\n01\\n10', 'output': '0 0\\n0 3\\n1 0\\n1 2\\n2 2\\n2 3\\n3 0\\n3 2\\n3 3\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 17\\n10010\\n10100\\n01010\\n11101\\n1 1\\n10\\n1\\n10', 'output': '0 0\\n0 3\\n1 0\\n1 2\\n2 1\\n2 3\\n3 0\\n3 1\\n3 2\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 17\\n10010\\n00100\\n01000\\n10101\\n2 1\\n10\\n01\\n10', 'output': '0 0\\n0 3\\n1 2\\n2 1\\n'}, {'type': 'stdin_stdout', 'input': '4 20\\n10011\\n10100\\n01001\\n10101\\n1 1\\n10\\n0\\n10', 'output': '0 0\\n0 3\\n0 4\\n1 0\\n1 2\\n2 1\\n2 4\\n3 0\\n3 2\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 20\\n10010\\n10001\\n01000\\n10101\\n1 1\\n10\\n0\\n3', 'output': '0 0\\n0 3\\n1 0\\n1 4\\n2 1\\n3 0\\n3 2\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 20\\n10010\\n00100\\n01000\\n10101\\n1 2\\n10\\n0\\n3', 'output': '0 0\\n0 3\\n1 2\\n2 1\\n3 0\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 16\\n10000\\n10100\\n01010\\n10111\\n1 2\\n10\\n0\\n3', 'output': '0 0\\n1 0\\n1 2\\n2 1\\n2 3\\n3 0\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00000\\n00100\\n01110\\n01000\\n1 2\\n10\\n0\\n4', 'output': '1 2\\n2 3\\n3 1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n00000\\n00000\\n00000\\n00100\\n1 1\\n0\\n0\\n16', 'output': '0 0\\n0 1\\n0 2\\n0 3\\n1 0\\n1 1\\n1 2\\n1 3\\n2 0\\n2 1\\n2 2\\n2 3\\n3 0\\n3 1\\n3 3\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00100\\n01100\\n01110\\n00100\\n1 2\\n11\\n0\\n5', 'output': '1 1\\n2 1\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n00000\\n00111\\n00010\\n10100\\n2 1\\n10\\n01\\n10', 'output': '1 2\\n1 4\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00010\\n01001\\n00110\\n10000\\n2 1\\n10\\n01\\n11', 'output': '0 3\\n1 1\\n1 4\\n2 2\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n10000\\n00100\\n00110\\n00010\\n1 1\\n10\\n0\\n6', 'output': '0 0\\n1 2\\n2 2\\n2 3\\n3 3\\n'}, {'type': 'stdin_stdout', 'input': '4 7\\n10000\\n00000\\n00000\\n01101\\n1 1\\n10\\n0\\n7', 'output': '0 0\\n3 1\\n3 2\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n11010\\n01011\\n11011\\n10000\\n2 1\\n14\\n01\\n11', 'output': '0 0\\n2 1\\n2 3\\n2 4\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n11010\\n10101\\n10011\\n01100\\n1 2\\n10\\n01\\n8', 'output': '0 1\\n0 3\\n1 0\\n1 2\\n2 0\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00010\\n10101\\n01011\\n00001\\n1 2\\n10\\n2\\n11', 'output': '0 3\\n1 0\\n1 2\\n2 1\\n'}, {'type': 'stdin_stdout', 'input': '4 17\\n10011\\n10100\\n00110\\n10111\\n1 1\\n10\\n01\\n10', 'output': '0 0\\n0 3\\n0 4\\n1 0\\n1 2\\n2 2\\n2 3\\n3 0\\n3 2\\n3 3\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 20\\n10010\\n10100\\n01000\\n00101\\n1 1\\n10\\n1\\n13', 'output': '0 0\\n0 3\\n1 0\\n1 2\\n2 1\\n3 2\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 20\\n10001\\n10100\\n01001\\n10101\\n1 1\\n10\\n0\\n10', 'output': '0 0\\n0 4\\n1 0\\n1 2\\n2 1\\n2 4\\n3 0\\n3 2\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 20\\n10010\\n10000\\n01000\\n10101\\n1 1\\n10\\n0\\n3', 'output': '0 0\\n0 3\\n1 0\\n2 1\\n3 0\\n3 2\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 20\\n10010\\n00100\\n01000\\n10111\\n1 2\\n10\\n0\\n3', 'output': '0 0\\n0 3\\n1 2\\n2 1\\n3 0\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n00000\\n10000\\n00000\\n00100\\n1 1\\n0\\n0\\n16', 'output': '0 0\\n0 1\\n0 2\\n0 3\\n1 1\\n1 2\\n1 3\\n2 0\\n2 1\\n2 2\\n2 3\\n3 0\\n3 1\\n3 3\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n10000\\n00100\\n00110\\n00010\\n2 1\\n10\\n0\\n6', 'output': '0 0\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n00011\\n10101\\n01011\\n00001\\n1 2\\n10\\n2\\n11', 'output': '1 0\\n1 2\\n2 1\\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n10000\\n00110\\n00110\\n00100\\n1 2\\n10\\n0\\n4', 'output': '0 0\\n1 3\\n2 3\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '4 7\\n11100\\n00100\\n00000\\n00000\\n1 2\\n11\\n1\\n17', 'output': '0 0\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '4 20\\n10010\\n10100\\n00000\\n00101\\n1 1\\n10\\n1\\n13', 'output': '0 0\\n0 3\\n1 0\\n1 2\\n3 2\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 20\\n11010\\n10000\\n01000\\n10101\\n1 1\\n10\\n0\\n3', 'output': '0 0\\n0 1\\n0 3\\n1 0\\n2 1\\n3 0\\n3 2\\n3 4\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_77917","program":"```python\nfrom typing import List\n\n\ndef calc_hash(tab: List[List[int]], row_num: int, col_num: int) -> None:\n global hash_table, R, C, baes1, base2, mask\n tmp_table = [[0] * col_num for _ in range(row_num)]\n diff_row, diff_col = row_num - R, col_num - C\n\n bit_mask = 1\n for _ in range(C):\n bit_mask = (bit_mask * base1) & mask\n for r in range(row_num):\n hash_v = 0\n for c in range(C):\n hash_v = hash_v * base1 + tab[r][c]\n for dc in range(diff_col):\n tmp_table[r][dc] = hash_v\n hash_v = (hash_v * base1 - bit_mask * tab[r][dc] + tab[r][dc + C]) & mask\n tmp_table[r][diff_col] = hash_v\n\n bit_mask = 1\n for _ in range(R):\n bit_mask = (bit_mask * base2) & mask\n for c in range(diff_col + 1):\n hash_v = 0\n for r in range(R):\n hash_v = hash_v * base2 + tmp_table[r][c]\n for dr in range(diff_row):\n hash_table[dr][c] = hash_v\n hash_v = (hash_v * base2 - bit_mask * tmp_table[dr][c]\n + tmp_table[dr + R][c]) & mask\n hash_table[diff_row][c] = hash_v\n\n\nif __name__ == \"__main__\":\n base1 = 1009 # The first prime number over 1000.\n base2 = 1013 # The second prime number over 1000.\n mask = (1 << 32) - 1 # Mask.\n\n H, W = map(lambda x: int(x), input().split())\n region = [[0] * W for _ in range(H)]\n for row in range(H):\n region[row] = [ord(s) for s in input()]\n\n R, C = map(lambda x: int(x), input().split())\n pattern = [[0] * C for _ in range(R)]\n for row in range(R):\n pattern[row] = [ord(s) for s in input()]\n\n if H >= R and W >= C:\n hash_table = [[0] * W for _ in range(H)]\n calc_hash(pattern, R, C) # Calc the target hash and save it into hash_table[0][0]\n key = hash_table[0][0] & mask\n calc_hash(region, H, W)\n for r in range(H - R + 1):\n for c in range(W - C + 1):\n if key == hash_table[r][c] & mask:\n print(f\"{r} {c}\")\n\n\n```","inputs":"4 5\n00010\n00101\n00010\n00100\n3 2\n10\n01\n10","output":"0 3\n1 2","actual_output":"0 3\n1 2\n","execution_success":true,"sample_index":12425},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02397 Swapping Two Numbers","prompt":"Solve the following coding problem using the programming language python:\n\nWrite a program which reads two integers x and y, and prints them in ascending order.\n\nConstraints\n\n* 0 \u2264 x, y \u2264 10000\n* the number of datasets \u2264 3000\n\nInput\n\nThe input consists of multiple datasets. Each dataset consists of two integers x and y separated by a single space.\n\nThe input ends with two 0 (when both x and y are zero). Your program should not process for these terminal symbols.\n\nOutput\n\nFor each dataset, print x and y in ascending order in a line. Put a single space between x and y.\n\nExample\n\nInput\n\n3 2\n2 2\n5 3\n0 0\n\n\nOutput\n\n2 3\n2 2\n3 5\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nwhile True:\n ans = list(map(int, input().split()))\n if ans[0] ==0 and ans[1] ==0:\n break\n print(*sorted(ans))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 2\\n2 2\\n5 3\\n0 0', 'output': '2 3\\n2 2\\n3 5'}, {'type': 'stdin_stdout', 'input': '3 1\\n2 2\\n5 3\\n0 0', 'output': '1 3\\n2 2\\n3 5\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n2 2\\n9 3\\n0 0', 'output': '1 3\\n2 2\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n0 2\\n9 3\\n0 0', 'output': '1 3\\n0 2\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 2\\n9 3\\n0 0', 'output': '0 3\\n0 2\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 2\\n15 3\\n0 0', 'output': '0 3\\n0 2\\n3 15\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n-1 2\\n15 3\\n0 0', 'output': '0 3\\n-1 2\\n3 15\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n-1 2\\n0 3\\n0 0', 'output': '0 3\\n-1 2\\n0 3\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 2\\n5 6\\n0 0', 'output': '2 3\\n2 2\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n2 3\\n9 3\\n0 0', 'output': '1 3\\n2 3\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 2\\n9 5\\n0 0', 'output': '0 3\\n0 2\\n5 9\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n0 2\\n15 3\\n0 0', 'output': '0 4\\n0 2\\n3 15\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n-1 2\\n0 1\\n0 0', 'output': '0 3\\n-1 2\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 3\\n5 6\\n0 0', 'output': '2 3\\n2 3\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n2 3\\n9 3\\n0 0', 'output': '1 2\\n2 3\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 2\\n5 5\\n0 0', 'output': '0 3\\n0 2\\n5 5\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n0 2\\n15 0\\n0 0', 'output': '0 4\\n0 2\\n0 15\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n-1 2\\n0 1\\n0 0', 'output': '1 3\\n-1 2\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 6\\n5 6\\n0 0', 'output': '2 3\\n2 6\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n2 3\\n14 3\\n0 0', 'output': '1 2\\n2 3\\n3 14\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 2\\n5 2\\n0 0', 'output': '0 3\\n0 2\\n2 5\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n-1 3\\n0 1\\n0 0', 'output': '1 3\\n-1 3\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 5\\n5 6\\n0 0', 'output': '2 3\\n2 5\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n2 3\\n2 3\\n0 0', 'output': '1 2\\n2 3\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n2 5\\n5 6\\n0 0', 'output': '3 3\\n2 5\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n2 3\\n4 3\\n0 0', 'output': '1 2\\n2 3\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n2 5\\n5 6\\n0 0', 'output': '3 4\\n2 5\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n2 5\\n0 6\\n0 0', 'output': '3 4\\n2 5\\n0 6\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n2 2\\n9 3\\n0 0', 'output': '0 1\\n2 2\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n0 2\\n9 0\\n0 0', 'output': '1 3\\n0 2\\n0 9\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n0 2\\n15 3\\n0 0', 'output': '0 5\\n0 2\\n3 15\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 2\\n27 3\\n0 0', 'output': '0 3\\n0 2\\n3 27\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n-1 2\\n0 6\\n0 0', 'output': '0 3\\n-1 2\\n0 6\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 4\\n5 6\\n0 0', 'output': '2 3\\n2 4\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n2 3\\n9 3\\n0 0', 'output': '1 1\\n2 3\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n0 2\\n9 5\\n0 0', 'output': '1 3\\n0 2\\n5 9\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n0 2\\n3 3\\n0 0', 'output': '0 4\\n0 2\\n3 3\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 2\\n0 1\\n0 0', 'output': '0 3\\n0 2\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 3\\n9 3\\n0 0', 'output': '1 3\\n1 3\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n-1 2\\n5 5\\n0 0', 'output': '0 3\\n-1 2\\n5 5\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n-1 2\\n0 1\\n0 0', 'output': '2 3\\n-1 2\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n2 6\\n5 6\\n0 0', 'output': '3 4\\n2 6\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n-1 1\\n0 1\\n0 0', 'output': '1 3\\n-1 1\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n0 5\\n5 6\\n0 0', 'output': '2 3\\n0 5\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n2 1\\n2 3\\n0 0', 'output': '1 2\\n1 2\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n2 5\\n5 6\\n0 0', 'output': '3 5\\n2 5\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n4 3\\n4 3\\n0 0', 'output': '1 2\\n3 4\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 5\\n5 6\\n0 0', 'output': '3 4\\n1 5\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n3 5\\n0 6\\n0 0', 'output': '3 4\\n3 5\\n0 6\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n2 1\\n9 3\\n0 0', 'output': '0 1\\n1 2\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 -1\\n0 2\\n27 3\\n0 0', 'output': '-1 3\\n0 2\\n3 27\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n-1 2\\n0 6\\n0 0', 'output': '0 5\\n-1 2\\n0 6\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n2 3\\n5 6\\n0 0', 'output': '3 3\\n2 3\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1 3\\n9 3\\n0 0', 'output': '1 1\\n1 3\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 2\\n9 5\\n0 0', 'output': '1 3\\n1 2\\n5 9\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n0 0\\n3 3\\n0 0', 'output': '0 4\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 2\\n-1 1\\n0 0', 'output': '0 3\\n0 2\\n-1 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 3\\n9 3\\n0 0', 'output': '2 3\\n2 3\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n-1 1\\n5 5\\n0 0', 'output': '0 3\\n-1 1\\n5 5\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n-1 4\\n0 1\\n0 0', 'output': '2 3\\n-1 4\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n3 6\\n5 6\\n0 0', 'output': '3 4\\n3 6\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n0 1\\n0 1\\n0 0', 'output': '1 3\\n0 1\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n0 5\\n5 6\\n0 0', 'output': '3 3\\n0 5\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n1 1\\n2 3\\n0 0', 'output': '1 2\\n1 1\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n3 5\\n-1 6\\n0 0', 'output': '3 4\\n3 5\\n-1 6\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n2 1\\n11 3\\n0 0', 'output': '0 1\\n1 2\\n3 11\\n'}, {'type': 'stdin_stdout', 'input': '4 -1\\n0 2\\n27 3\\n0 0', 'output': '-1 4\\n0 2\\n3 27\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1 3\\n9 6\\n0 0', 'output': '1 1\\n1 3\\n6 9\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n0 0\\n3 3\\n0 0', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n0 2\\n0 1\\n0 0', 'output': '0 1\\n0 2\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n2 3\\n9 3\\n0 0', 'output': '0 3\\n2 3\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n-1 4\\n0 1\\n0 0', 'output': '0 3\\n-1 4\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n0 1\\n0 0\\n0 0', 'output': '1 3\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n1 0\\n2 3\\n0 0', 'output': '1 2\\n0 1\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n3 5\\n-2 6\\n0 0', 'output': '3 4\\n3 5\\n-2 6\\n'}, {'type': 'stdin_stdout', 'input': '4 -1\\n0 2\\n18 3\\n0 0', 'output': '-1 4\\n0 2\\n3 18\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n2 3\\n5 6\\n0 0', 'output': '2 2\\n2 3\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n0 0\\n3 3\\n0 0', 'output': '2 4\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n0 2\\n0 0\\n0 0', 'output': '0 1\\n0 2\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n2 1\\n9 3\\n0 0', 'output': '0 3\\n1 2\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 4\\n0 1\\n0 0', 'output': '0 3\\n0 4\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '4 -1\\n0 2\\n18 5\\n0 0', 'output': '-1 4\\n0 2\\n5 18\\n'}, {'type': 'stdin_stdout', 'input': '0 2\\n2 3\\n5 6\\n0 0', 'output': '0 2\\n2 3\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n2 1\\n9 3\\n0 0', 'output': '0 5\\n1 2\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '4 -1\\n1 2\\n18 5\\n0 0', 'output': '-1 4\\n1 2\\n5 18\\n'}, {'type': 'stdin_stdout', 'input': '0 2\\n2 6\\n5 6\\n0 0', 'output': '0 2\\n2 6\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n0 3\\n0 0\\n1 0', 'output': '0 1\\n0 3\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n2 1\\n18 3\\n0 0', 'output': '0 5\\n1 2\\n3 18\\n'}, {'type': 'stdin_stdout', 'input': '0 2\\n3 6\\n5 6\\n0 0', 'output': '0 2\\n3 6\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1 0\\n0 6\\n0 0', 'output': '2 4\\n0 1\\n0 6\\n'}, {'type': 'stdin_stdout', 'input': '0 3\\n3 6\\n5 6\\n0 0', 'output': '0 3\\n3 6\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '8 2\\n1 0\\n0 6\\n0 0', 'output': '2 8\\n0 1\\n0 6\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n0 3\\n0 0\\n2 0', 'output': '0 2\\n0 3\\n'}, {'type': 'stdin_stdout', 'input': '0 3\\n3 6\\n5 1\\n0 0', 'output': '0 3\\n3 6\\n1 5\\n'}, {'type': 'stdin_stdout', 'input': '7 2\\n1 0\\n0 6\\n0 0', 'output': '2 7\\n0 1\\n0 6\\n'}, {'type': 'stdin_stdout', 'input': '-1 3\\n3 6\\n5 1\\n0 0', 'output': '-1 3\\n3 6\\n1 5\\n'}, {'type': 'stdin_stdout', 'input': '7 2\\n1 0\\n1 6\\n0 0', 'output': '2 7\\n0 1\\n1 6\\n'}, {'type': 'stdin_stdout', 'input': '-1 2\\n3 6\\n5 1\\n0 0', 'output': '-1 2\\n3 6\\n1 5\\n'}, {'type': 'stdin_stdout', 'input': '7 2\\n1 1\\n1 6\\n0 0', 'output': '2 7\\n1 1\\n1 6\\n'}, {'type': 'stdin_stdout', 'input': '7 0\\n1 1\\n1 6\\n0 0', 'output': '0 7\\n1 1\\n1 6\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n-1 3\\n0 0\\n2 4', 'output': '0 1\\n-1 3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_77921","program":"```python\nwhile True:\n ans = list(map(int, input().split()))\n if ans[0] ==0 and ans[1] ==0:\n break\n print(*sorted(ans))\n\n```","inputs":"3 2\n2 2\n5 3\n0 0","output":"2 3\n2 2\n3 5","actual_output":"2 3\n2 2\n3 5\n","execution_success":true,"sample_index":12426},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1038_C. Gambling","prompt":"Solve the following coding problem using the programming language python:\n\nTwo players A and B have a list of n integers each. They both want to maximize the subtraction between their score and their opponent's score. \n\nIn one turn, a player can either add to his score any element from his list (assuming his list is not empty), the element is removed from the list afterward. Or remove an element from his opponent's list (assuming his opponent's list is not empty).\n\nNote, that in case there are equal elements in the list only one of them will be affected in the operations above. For example, if there are elements \\{1, 2, 2, 3\\} in a list and you decided to choose 2 for the next turn, only a single instance of 2 will be deleted (and added to the score, if necessary). \n\nThe player A starts the game and the game stops when both lists are empty. Find the difference between A's score and B's score at the end of the game, if both of the players are playing optimally.\n\nOptimal play between two players means that both players choose the best possible strategy to achieve the best possible outcome for themselves. In this problem, it means that each player, each time makes a move, which maximizes the final difference between his score and his opponent's score, knowing that the opponent is doing the same.\n\nInput\n\nThe first line of input contains an integer n (1 \u2264 n \u2264 100 000) \u2014 the sizes of the list.\n\nThe second line contains n integers a_i (1 \u2264 a_i \u2264 10^6), describing the list of the player A, who starts the game.\n\nThe third line contains n integers b_i (1 \u2264 b_i \u2264 10^6), describing the list of the player B.\n\nOutput\n\nOutput the difference between A's score and B's score (A-B) if both of them are playing optimally.\n\nExamples\n\nInput\n\n2\n1 4\n5 1\n\n\nOutput\n\n0\n\nInput\n\n3\n100 100 100\n100 100 100\n\n\nOutput\n\n0\n\nInput\n\n2\n2 1\n5 6\n\n\nOutput\n\n-3\n\nNote\n\nIn the first example, the game could have gone as follows: \n\n * A removes 5 from B's list. \n * B removes 4 from A's list. \n * A takes his 1. \n * B takes his 1. \n\n\n\nHence, A's score is 1, B's score is 1 and difference is 0.\n\nThere is also another optimal way of playing:\n\n * A removes 5 from B's list. \n * B removes 4 from A's list. \n * A removes 1 from B's list. \n * B removes 1 from A's list. \n\n\n\nThe difference in the scores is still 0.\n\nIn the second example, irrespective of the moves the players make, they will end up with the same number of numbers added to their score, so the difference will be 0.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN = int(input())\narr1 = list(map(int, input().split()))\narr2 = list(map(int, input().split()))\narr1.sort()\narr2.sort()\nmax1 = N-1\nmax2 = N-1\nA = 0\nB = 0\nturn = 0\nwhile(max1>=0 or max2>=0):\n if turn == 0:\n if arr1[max1]>=arr2[max2]:\n if max1>=0:\n A+=arr1[max1]\n max1-=1\n else:\n max2-=1\n else:\n if max2>=0: \n max2-=1\n else:\n A+=arr1[max1]\n max1-=1 \n else: \n if arr1[max1]<=arr2[max2]:\n if max2>=0:\n B+=arr2[max2]\n max2-=1\n else:\n max1-=1\n else:\n if max1>=0: \n max1-=1\n else:\n B+=arr2[max2]\n max2-=1 \n if turn == 0:\n turn = 1\n else:\n turn = 0\nprint(A-B)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n100 100 100\\n100 100 100\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 4\\n5 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1\\n5 6\\n', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n30518 196518 274071 359971 550121 204862 843967 173607 619138 690754\\n219513 171337 183499 549873 542337 661387 397647 495917 413076 918417\\n', 'output': '-47488\\n'}, {'type': 'stdin_stdout', 'input': '25\\n887969 76030 478041 100616 413694 211522 84038 225090 516869 914975 161226 96124 320457 162052 70329 776374 642303 711844 115276 37430 499330 577781 735069 364358 345168\\n829299 135662 972337 61003 836638 951395 543689 412218 135799 710787 140644 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0\nprint(A-B)\n\n```","inputs":"3\n100 100 100\n100 100 100\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12427},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1082_E. Increasing Frequency","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given array a of length n. You can choose one segment [l, r] (1 \u2264 l \u2264 r \u2264 n) and integer value k (positive, negative or even zero) and change a_l, a_{l + 1}, ..., a_r by k each (i.e. a_i := a_i + k for each l \u2264 i \u2264 r).\n\nWhat is the maximum possible number of elements with value c that can be obtained after one such operation?\n\nInput\n\nThe first line contains two integers n and c (1 \u2264 n \u2264 5 \u22c5 10^5, 1 \u2264 c \u2264 5 \u22c5 10^5) \u2014 the length of array and the value c to obtain.\n\nThe second line contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 5 \u22c5 10^5) \u2014 array a.\n\nOutput\n\nPrint one integer \u2014 the maximum possible number of elements with value c which can be obtained after performing operation described above.\n\nExamples\n\nInput\n\n\n6 9\n9 9 9 9 9 9\n\n\nOutput\n\n\n6\n\n\nInput\n\n\n3 2\n6 2 6\n\n\nOutput\n\n\n2\n\nNote\n\nIn the first example we can choose any segment and k = 0. The array will stay same.\n\nIn the second example we can choose segment [1, 3] and k = -4. The array will become [2, -2, 2].\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput=sys.stdin.readline\nn,c=map(int,input().split())\nar=list(map(int,input().split()))\nbr=[]\ncount=0\nfor i in range(n):\n if(ar[i]==c):\n count+=1\n br.append(count)\ndic={}\nfor i in range(n):\n if(ar[i]!=c):\n if(ar[i] in dic):\n dic[ar[i]].append(i)\n else:\n dic[ar[i]]=[i]\n\n\nans=0\nfor i in dic:\n le=len(dic[i])\n if(le==1):\n ans=max(ans,1)\n else:\n ans=max(ans,1)\n su=0\n flag=False\n for j in range(1,le):\n r=dic[i][j]\n l=dic[i][j-1]\n if(flag):\n su+=1-(br[r]-br[l])\n else:\n flag=True\n su+=2-(br[r]-br[l])\n ans=max(ans,su)\n if(su<=0):\n flag=False\n su=0\n\nprint(br[-1]+ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 2\\n6 2 6\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6 9\\n9 9 9 9 9 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4 1 3 8 2 3 6 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '13 3\\n1 4 3 5 2 3 4 1 1 1 5 3 3\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '11 14\\n1 0 3 4 3 3 2 4 1 0 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '18 2\\n3 3 3 2 3 2 0 2 2 2 6 0 1 3 3 3 5 1\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '18 5\\n1 4 9 2 7 3 8 9 8 5 8 1 1 9 6 4 9 6\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 8 2 2 6 2\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '13 5\\n1 4 3 5 2 3 4 1 1 1 5 3 4\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '18 5\\n1 4 9 2 7 3 8 9 8 5 8 1 1 9 6 6 9 6\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '18 2\\n5 0 1 2 6 4 3 4 1 5 4 1 3 8 2 2 6 2\\n', 'output': '7\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77961","program":"```python\nimport sys\ninput=sys.stdin.readline\nn,c=map(int,input().split())\nar=list(map(int,input().split()))\nbr=[]\ncount=0\nfor i in range(n):\n if(ar[i]==c):\n count+=1\n br.append(count)\ndic={}\nfor i in range(n):\n if(ar[i]!=c):\n if(ar[i] in dic):\n dic[ar[i]].append(i)\n else:\n dic[ar[i]]=[i]\n\n\nans=0\nfor i in dic:\n le=len(dic[i])\n if(le==1):\n ans=max(ans,1)\n else:\n ans=max(ans,1)\n su=0\n flag=False\n for j in range(1,le):\n r=dic[i][j]\n l=dic[i][j-1]\n if(flag):\n su+=1-(br[r]-br[l])\n else:\n flag=True\n su+=2-(br[r]-br[l])\n ans=max(ans,su)\n if(su<=0):\n flag=False\n su=0\n\nprint(br[-1]+ans)\n```","inputs":"3 2\n6 2 6\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12428},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1150_A. Stock Arbitraging","prompt":"Solve the following coding problem using the programming language python:\n\nWelcome to Codeforces Stock Exchange! We're pretty limited now as we currently allow trading on one stock, Codeforces Ltd. We hope you'll still be able to make profit from the market!\n\nIn the morning, there are n opportunities to buy shares. The i-th of them allows to buy as many shares as you want, each at the price of s_i bourles.\n\nIn the evening, there are m opportunities to sell shares. The i-th of them allows to sell as many shares as you want, each at the price of b_i bourles. You can't sell more shares than you have.\n\nIt's morning now and you possess r bourles and no shares.\n\nWhat is the maximum number of bourles you can hold after the evening?\n\nInput\n\nThe first line of the input contains three integers n, m, r (1 \u2264 n \u2264 30, 1 \u2264 m \u2264 30, 1 \u2264 r \u2264 1000) \u2014 the number of ways to buy the shares on the market, the number of ways to sell the shares on the market, and the number of bourles you hold now.\n\nThe next line contains n integers s_1, s_2, ..., s_n (1 \u2264 s_i \u2264 1000); s_i indicates the opportunity to buy shares at the price of s_i bourles.\n\nThe following line contains m integers b_1, b_2, ..., b_m (1 \u2264 b_i \u2264 1000); b_i indicates the opportunity to sell shares at the price of b_i bourles.\n\nOutput\n\nOutput a single integer \u2014 the maximum number of bourles you can hold after the evening.\n\nExamples\n\nInput\n\n\n3 4 11\n4 2 5\n4 4 5 4\n\n\nOutput\n\n\n26\n\n\nInput\n\n\n2 2 50\n5 7\n4 2\n\n\nOutput\n\n\n50\n\nNote\n\nIn the first example test, you have 11 bourles in the morning. It's optimal to buy 5 shares of a stock at the price of 2 bourles in the morning, and then to sell all of them at the price of 5 bourles in the evening. It's easy to verify that you'll have 26 bourles after the evening.\n\nIn the second example test, it's optimal not to take any action.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na=list(map(int,input().split()))\nb=list(map(int,input().split()))\nc=list(map(int,input().split()))\nm=a[2]//(min(b))\np=m*max(c)+a[2]%min(b)\nif(p>=a[2]):\n\tprint(p)\nelse:\n\tprint(a[2])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 4 11\\n4 2 5\\n4 4 5 4\\n', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '2 2 50\\n5 7\\n4 2\\n', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '1 5 10\\n1\\n2 2 2 2 5\\n', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '1 2 4\\n3\\n4 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1 3 4\\n1\\n1 5 2\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '1 3 100\\n5\\n1 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256000000}","problem_id":"vfc_77973","program":"```python\na=list(map(int,input().split()))\nb=list(map(int,input().split()))\nc=list(map(int,input().split()))\nm=a[2]//(min(b))\np=m*max(c)+a[2]%min(b)\nif(p>=a[2]):\n\tprint(p)\nelse:\n\tprint(a[2])\n```","inputs":"3 4 11\n4 2 5\n4 4 5 4\n","output":"26\n","actual_output":"26\n","execution_success":true,"sample_index":12429},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1172_B. Nauuo and Circle","prompt":"Solve the following coding problem using the programming language python:\n\nNauuo is a girl who loves drawing circles.\n\nOne day she has drawn a circle and wanted to draw a tree on it.\n\nThe tree is a connected undirected graph consisting of n nodes and n-1 edges. The nodes are numbered from 1 to n.\n\nNauuo wants to draw a tree on the circle, the nodes of the tree should be in n distinct points on the circle, and the edges should be straight without crossing each other.\n\n\"Without crossing each other\" means that every two edges have no common point or the only common point is an endpoint of both edges.\n\nNauuo wants to draw the tree using a permutation of n elements. A permutation of n elements is a sequence of integers p_1,p_2,\u2026,p_n in which every integer from 1 to n appears exactly once.\n\nAfter a permutation is chosen Nauuo draws the i-th node in the p_i-th point on the circle, then draws the edges connecting the nodes.\n\nThe tree is given, Nauuo wants to know how many permutations are there so that the tree drawn satisfies the rule (the edges are straight without crossing each other). She only wants to know the answer modulo 998244353, can you help her?\n\nIt is obvious that whether a permutation is valid or not does not depend on which n points on the circle are chosen.\n\nInput\n\nThe first line contains a single integer n (2\u2264 n\u2264 2\u22c5 10^5) \u2014 the number of nodes in the tree.\n\nEach of the next n-1 lines contains two integers u and v (1\u2264 u,v\u2264 n), denoting there is an edge between u and v.\n\nIt is guaranteed that the given edges form a tree.\n\nOutput\n\nThe output contains a single integer \u2014 the number of permutations suitable to draw the given tree on a circle satisfying the rule, modulo 998244353.\n\nExamples\n\nInput\n\n\n4\n1 2\n1 3\n2 4\n\n\nOutput\n\n\n16\n\nInput\n\n\n4\n1 2\n1 3\n1 4\n\n\nOutput\n\n\n24\n\nNote\n\nExample 1\n\nAll valid permutations and their spanning trees are as follows.\n\n\n\nHere is an example of invalid permutation: the edges (1,3) and (2,4) are crossed.\n\n\n\nExample 2\n\nEvery permutation leads to a valid tree, so the answer is 4! = 24.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom math import *\nfrom collections import *\nimport sys\nsys.setrecursionlimit(10**9)\n\nmod = 998244353\nn = int(input())\na = [0 for i in range(n+1)]\nans = n\nfor i in range(n-1):\n\tu,v = map(int,input().split())\n\ta[u] += 1\n\ta[v] += 1\n\tans *= a[u]\n\tans %= mod\n\tans *= a[v]\n\tans %= mod\nprint(ans%mod)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1 2\\n1 3\\n1 4\\n', 'output': '24'}, {'type': 'stdin_stdout', 'input': '4\\n1 2\\n1 3\\n2 4\\n', 'output': '16'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n2 3\\n2 8\\n4 7\\n2 4\\n', 'output': '2304'}, {'type': 'stdin_stdout', 'input': '9\\n5 6\\n1 3\\n2 3\\n7 6\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '7776'}, {'type': 'stdin_stdout', 'input': '6\\n2 1\\n3 2\\n4 1\\n5 4\\n1 6\\n', 'output': '144'}, {'type': 'stdin_stdout', 'input': '10\\n5 4\\n5 2\\n3 7\\n9 3\\n3 2\\n3 1\\n3 8\\n9 10\\n1 6\\n', 'output': '19200'}, {'type': 'stdin_stdout', 'input': '6\\n4 6\\n1 5\\n5 4\\n5 3\\n2 4\\n', 'output': '216'}, {'type': 'stdin_stdout', 'input': '2\\n2 1\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '7\\n2 7\\n2 6\\n4 7\\n7 3\\n7 5\\n1 7\\n', 'output': '1680'}, {'type': 'stdin_stdout', 'input': '5\\n3 5\\n4 3\\n2 4\\n1 2\\n', 'output': '40'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n3 2\\n', 'output': '6'}, {'type': 'stdin_stdout', 'input': '9\\n5 6\\n1 5\\n2 3\\n7 6\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 4\\n5 2\\n3 7\\n9 6\\n3 2\\n3 1\\n3 8\\n9 10\\n1 6\\n', 'output': '7680\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n3 7\\n9 6\\n3 2\\n3 1\\n3 8\\n9 10\\n1 6\\n', 'output': '11520\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n2 3\\n3 8\\n4 7\\n2 4\\n', 'output': '1728\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4 6\\n1 5\\n3 4\\n5 3\\n2 4\\n', 'output': '144\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 5\\n4 3\\n2 4\\n1 2\\n', 'output': '60\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n2 3\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n3 7\\n9 6\\n3 2\\n3 1\\n4 8\\n9 10\\n1 6\\n', 'output': '5760\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n2 3\\n3 8\\n4 7\\n3 4\\n', 'output': '2304\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n1 3\\n2 8\\n4 7\\n2 4\\n', 'output': '1152\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2 7\\n2 6\\n4 7\\n7 3\\n1 5\\n1 7\\n', 'output': '672\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 3\\n1 3\\n2 3\\n7 6\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '10368\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 4\\n5 2\\n3 7\\n9 3\\n3 2\\n3 1\\n3 8\\n9 10\\n1 6\\n', 'output': '19200\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 8\\n1 3\\n2 3\\n7 6\\n4 1\\n5 6\\n8 1\\n1 9\\n', 'output': '3456\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n1 3\\n2 8\\n1 7\\n1 4\\n', 'output': '1536\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 4\\n1 3\\n2 3\\n7 6\\n4 2\\n3 6\\n8 1\\n1 9\\n', 'output': '2592\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 3\\n1 3\\n2 3\\n7 2\\n4 2\\n3 6\\n8 1\\n1 9\\n', 'output': '7776\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 1\\n3 4\\n4 1\\n5 4\\n1 6\\n', 'output': '216\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 8\\n5 2\\n3 7\\n9 6\\n3 2\\n4 1\\n4 8\\n9 10\\n1 6\\n', 'output': '3840\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 1\\n1 3\\n2 3\\n7 6\\n4 1\\n5 6\\n8 1\\n1 9\\n', 'output': '8640\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 2\\n1 3\\n2 3\\n7 6\\n4 1\\n3 6\\n8 2\\n1 9\\n', 'output': '3888\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n3 7\\n9 6\\n3 2\\n3 1\\n3 8\\n9 10\\n2 6\\n', 'output': '23040\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 3\\n1 3\\n2 4\\n7 1\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '12960\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 6\\n1 6\\n5 4\\n5 3\\n2 4\\n', 'output': '96\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 6\\n1 3\\n2 3\\n7 6\\n4 1\\n4 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n2 4\\n3 8\\n4 7\\n3 4\\n', 'output': '2304\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 8\\n1 3\\n2 3\\n7 6\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 3\\n1 3\\n2 3\\n7 6\\n4 1\\n4 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n3 7\\n9 6\\n3 2\\n4 1\\n4 8\\n9 10\\n1 6\\n', 'output': '5760\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n2 3\\n3 8\\n2 7\\n3 4\\n', 'output': '2304\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n1 3\\n2 8\\n4 7\\n1 4\\n', 'output': '1152\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 3\\n1 3\\n2 4\\n7 6\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 3\\n1 3\\n2 3\\n7 6\\n4 2\\n3 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3\\n2 1\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n3 7\\n9 7\\n3 2\\n4 1\\n4 8\\n9 10\\n1 6\\n', 'output': '5760\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 3\\n1 3\\n2 3\\n7 2\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '10368\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 2\\n1 3\\n2 3\\n7 6\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 6\\n1 5\\n5 4\\n5 3\\n2 4\\n', 'output': '144\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 6\\n1 5\\n2 3\\n7 2\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '3456\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 4\\n5 2\\n3 7\\n9 6\\n3 2\\n3 1\\n1 8\\n9 10\\n1 6\\n', 'output': '5760\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4 6\\n1 5\\n3 4\\n5 3\\n2 3\\n', 'output': '144\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 5\\n4 3\\n2 4\\n1 2\\n', 'output': '60\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n3 7\\n9 6\\n1 2\\n3 1\\n4 8\\n9 10\\n1 6\\n', 'output': '5760\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 8\\n1 3\\n2 3\\n7 2\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n1 3\\n1 8\\n1 7\\n1 4\\n', 'output': '3840\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 1\\n3 4\\n3 1\\n5 4\\n1 6\\n', 'output': '144\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4 6\\n1 6\\n3 4\\n5 3\\n2 3\\n', 'output': '144\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n3 7\\n9 3\\n1 2\\n3 1\\n4 8\\n9 10\\n1 6\\n', 'output': '8640\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n1 3\\n1 8\\n1 7\\n1 5\\n', 'output': '3840\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 6\\n1 5\\n2 3\\n7 3\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 4\\n5 2\\n3 7\\n9 7\\n3 2\\n3 1\\n3 8\\n9 10\\n1 6\\n', 'output': '7680\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4 6\\n1 5\\n3 4\\n5 6\\n2 4\\n', 'output': '144\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n3 7\\n9 6\\n3 2\\n5 1\\n4 8\\n9 10\\n1 6\\n', 'output': '3840\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n6 7\\n9 6\\n3 2\\n4 1\\n4 8\\n9 10\\n1 6\\n', 'output': '8640\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 4\\n5 2\\n3 7\\n9 5\\n3 2\\n3 1\\n3 8\\n9 10\\n1 6\\n', 'output': '7680\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 3\\n1 3\\n2 3\\n7 2\\n4 1\\n4 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n2 7\\n9 6\\n1 2\\n3 1\\n4 8\\n9 10\\n1 6\\n', 'output': '11520\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 8\\n5 1\\n3 7\\n9 6\\n3 2\\n4 1\\n4 8\\n9 10\\n1 6\\n', 'output': '3840\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 4\\n5 2\\n3 7\\n9 3\\n1 2\\n3 1\\n4 8\\n9 10\\n1 6\\n', 'output': '11520\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n1 3\\n2 8\\n1 7\\n1 5\\n', 'output': '1536\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 6\\n1 5\\n2 5\\n7 3\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 3\\n1 3\\n2 3\\n7 4\\n4 1\\n4 6\\n8 1\\n1 9\\n', 'output': '7776\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 3\\n2 7\\n9 6\\n1 2\\n3 1\\n4 8\\n9 10\\n1 6\\n', 'output': '5760\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n1 3\\n2 8\\n1 7\\n2 5\\n', 'output': '1152\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 6\\n1 6\\n2 5\\n7 3\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 3\\n2 7\\n9 6\\n1 2\\n3 1\\n3 8\\n9 10\\n1 6\\n', 'output': '8640\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n2 3\\n2 8\\n1 7\\n2 5\\n', 'output': '1536\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 6\\n1 6\\n2 4\\n7 3\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '5184\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5 7\\n1 6\\n2 4\\n7 3\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '3456\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n2 6\\n2 8\\n4 7\\n2 4\\n', 'output': '2304\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 1\\n3 2\\n4 2\\n5 4\\n1 6\\n', 'output': '144\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 5\\n4 3\\n2 4\\n1 4\\n', 'output': '60\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 6\\n1 5\\n2 3\\n7 6\\n4 1\\n3 6\\n8 1\\n1 9\\n', 'output': '12960\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 4\\n5 2\\n3 7\\n9 6\\n3 2\\n3 1\\n3 8\\n9 10\\n1 6\\n', 'output': '7680\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n3 7\\n9 6\\n3 4\\n3 1\\n3 8\\n9 10\\n1 6\\n', 'output': '7680\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4\\n5 2\\n3 7\\n9 4\\n3 2\\n3 1\\n4 8\\n9 10\\n1 6\\n', 'output': '8640\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5\\n1 2\\n6 3\\n2 4\\n5 8\\n4 7\\n3 4\\n', 'output': '1536\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77977","program":"```python\nfrom math import *\nfrom collections import *\nimport sys\nsys.setrecursionlimit(10**9)\n\nmod = 998244353\nn = int(input())\na = [0 for i in range(n+1)]\nans = n\nfor i in range(n-1):\n\tu,v = map(int,input().split())\n\ta[u] += 1\n\ta[v] += 1\n\tans *= a[u]\n\tans %= mod\n\tans *= a[v]\n\tans %= mod\nprint(ans%mod)\n```","inputs":"4\n1 2\n1 3\n1 4\n","output":"24","actual_output":"24\n","execution_success":true,"sample_index":12430},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"118_C. Fancy Number","prompt":"Solve the following coding problem using the programming language python:\n\nA car number in Berland consists of exactly n digits. A number is called beautiful if it has at least k equal digits. Vasya wants to change the digits in his car's number so that the number became beautiful. To replace one of n digits Vasya has to pay the sum of money, equal to the absolute difference between the old digit and the new one.\n\nHelp Vasya: find the minimum sum of money he should pay to make the number of his car beautiful. You should also find the resulting beautiful number. If there are several such numbers, then print the lexicographically minimum one.\n\nInput\n\nThe first line contains two space-separated integers n and k (2 \u2264 n \u2264 104, 2 \u2264 k \u2264 n) which represent how many digits the number has and how many equal digits a beautiful number should have. The second line consists of n digits. It describes the old number of Vasya's car. It is guaranteed that the number contains no spaces and only contains digits.\n\nOutput\n\nOn the first line print the minimum sum of money Vasya needs to change the number. On the second line print the car's new number. If there are several solutions, print the lexicographically minimum one.\n\nExamples\n\nInput\n\n6 5\n898196\n\n\nOutput\n\n4\n888188\n\n\nInput\n\n3 2\n533\n\n\nOutput\n\n0\n533\n\n\nInput\n\n10 6\n0001112223\n\n\nOutput\n\n3\n0000002223\n\nNote\n\nIn the first sample replacing the second digit with an \"8\" costs |9 - 8| = 1. Replacing the fifth digit with an \"8\" costs the same. Replacing the sixth digit costs |6 - 8| = 2. As a result, Vasya will pay 1 + 1 + 2 = 4 for a beautiful number \"888188\".\n\nThe lexicographical comparison of strings is performed by the < operator in modern programming languages. The string x is lexicographically smaller than the string y, if there exists such i (1 \u2264 i \u2264 n), that xi < yi, and for any j (1 \u2264 j < i) xj = yj. The strings compared in this problem will always have the length n.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#------------------------template--------------------------#\nimport os\nimport sys\nfrom math import *\nfrom collections import *\nfrom fractions import *\nfrom bisect import *\nfrom heapq import*\nfrom io import BytesIO, IOBase\ndef vsInput():\n sys.stdin = open('input.txt', 'r')\n sys.stdout = open('output.txt', 'w')\nBUFSIZE = 8192\nclass FastIO(IOBase):\n newlines = 0\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\nALPHA='abcdefghijklmnopqrstuvwxyz'\nM=10**9+7\nEPS=1e-6\ndef value():return tuple(map(int,input().split()))\ndef array():return [int(i) for i in input().split()]\ndef Int():return int(input())\ndef Str():return input()\ndef arrayS():return [i for i in input().split()]\n\n\n#-------------------------code---------------------------#\n# vsInput()\n\n\ndef fun(a):\n \n if(a[1]==0): return a\n else: return (a[0],a[1],-a[2])\n\n return a\ndef operate(x):\n\n ans=list(s)\n c=[]\n\n for i in range(n):\n c.append((abs(x-int(s[i])),int(x>int(s[i])),i))\n\n c.sort(key=fun)\n cost=0\n\n # print(c)\n\n for i in range(k):\n cost+=c[i][0]\n ans[c[i][-1]]=str(x)\n\n return (cost,''.join(ans))\n\n\n\n\nn,k=value()\ns=input()\n\nminCost=inf\nans=s\n\n# operate(3)\n\nfor i in range(10):\n cost,t=operate(i)\n if(costint(s[i])),i))\n\n c.sort(key=fun)\n cost=0\n\n # print(c)\n\n for i in range(k):\n cost+=c[i][0]\n ans[c[i][-1]]=str(x)\n\n return (cost,''.join(ans))\n\n\n\n\nn,k=value()\ns=input()\n\nminCost=inf\nans=s\n\n# operate(3)\n\nfor i in range(10):\n cost,t=operate(i)\n if(cost Here is a graphic for the first example.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 100), the number of lights.\n\nThe next line contains a string s of n characters. The i-th character is \"1\", if the i-th lamp is initially on. Otherwise, i-th character is \"0\".\n\nThe i-th of the following n lines contains two integers a_i and b_i (1 \u2264 a_i, b_i \u2264 5) \u2014 the parameters of the i-th light.\n\nOutput\n\nPrint a single integer \u2014 the maximum number of lights that will ever be on at the same time.\n\nExamples\n\nInput\n\n\n3\n101\n3 3\n3 2\n3 1\n\n\nOutput\n\n\n2\n\n\nInput\n\n\n4\n1111\n3 4\n5 2\n3 1\n3 2\n\n\nOutput\n\n\n4\n\n\nInput\n\n\n6\n011100\n5 3\n5 5\n2 4\n3 5\n4 2\n1 5\n\n\nOutput\n\n\n6\n\nNote\n\nFor first example, the lamps' states are shown in the picture above. The largest number of simultaneously on lamps is 2 (e.g. at the moment 2).\n\nIn the second example, all lights are initially on. So the answer is 4.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\n\nn=int(input())\ns=input().strip()\n\nAB=[tuple(map(int,input().split())) for i in range(n)]\n\nANS=[[0]*n for i in range(3000)]\n\nfor i in range(n):\n k=int(s[i])\n a,b=AB[i]\n\n t=0\n while t<3000:\n if t>=b and (t-b)%a==0:\n k=1-k\n \n ANS[t][i]=k\n t+=1\n\n\n \nA=0\nfor t in range(3000):\n A=max(A,sum(ANS[t]))\n\nprint(A)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1111\\n3 4\\n5 2\\n3 1\\n3 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n101\\n3 3\\n3 2\\n3 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n011100\\n5 3\\n5 5\\n2 4\\n3 5\\n4 2\\n1 5\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '25\\n0101001100110001000000000\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '25\\n0111101111011110111101111\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '25\\n1011100111001110011100111\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n1 5\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20\\n00101101001100000010\\n1 1\\n5 3\\n3 3\\n4 5\\n1 4\\n5 2\\n4 2\\n4 4\\n5 1\\n1 1\\n5 3\\n2 4\\n2 4\\n1 2\\n2 3\\n1 4\\n1 5\\n1 3\\n3 4\\n4 3\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '25\\n1010111001100010000100001\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '25\\n0101110011000110001100011\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '25\\n1010100110001110011100111\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '25\\n1010111001111001111011111\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '25\\n0101001100011100111101111\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '25\\n1111111111111111111111111\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '70\\n0010011111011101101111000111101011010101000011000000010100010101010001\\n3 1\\n1 5\\n3 1\\n4 1\\n3 3\\n2 4\\n2 1\\n5 1\\n2 4\\n5 2\\n5 2\\n4 1\\n2 5\\n2 2\\n4 2\\n5 1\\n1 2\\n2 4\\n3 1\\n1 1\\n5 3\\n5 2\\n3 5\\n4 4\\n2 1\\n3 2\\n1 3\\n5 1\\n3 4\\n2 3\\n1 5\\n4 1\\n2 2\\n5 1\\n3 3\\n4 2\\n1 4\\n5 2\\n1 2\\n4 1\\n1 4\\n5 3\\n3 3\\n2 5\\n3 5\\n3 4\\n3 3\\n1 5\\n1 1\\n2 4\\n5 4\\n1 4\\n3 3\\n2 5\\n2 4\\n1 3\\n5 2\\n4 4\\n1 2\\n1 1\\n4 4\\n5 4\\n1 2\\n5 1\\n3 1\\n5 4\\n4 5\\n3 1\\n2 4\\n3 2\\n', 'output': '46\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0000111\\n3 3\\n4 3\\n5 3\\n1 5\\n3 4\\n4 4\\n5 4\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '2\\n10\\n1 3\\n1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '50\\n10011111101111011010001011111110110011101111100111\\n2 1\\n4 3\\n3 4\\n1 4\\n3 2\\n5 3\\n5 5\\n3 5\\n5 5\\n4 4\\n1 1\\n1 2\\n1 4\\n1 5\\n1 1\\n4 1\\n2 4\\n3 1\\n1 1\\n1 3\\n1 5\\n2 3\\n3 1\\n5 5\\n5 4\\n4 4\\n1 4\\n2 1\\n2 2\\n2 5\\n1 5\\n2 1\\n5 4\\n1 2\\n4 5\\n5 5\\n5 1\\n1 4\\n4 2\\n4 4\\n2 5\\n1 2\\n3 4\\n5 4\\n4 3\\n3 3\\n3 3\\n3 2\\n5 3\\n5 1\\n', 'output': '37\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n4 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '25\\n0101010011000110001100011\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '25\\n0111101111011110111101111\\n1 1\\n2 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n1 3\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '20\\n00101101001100000010\\n1 1\\n5 3\\n3 3\\n4 5\\n1 4\\n5 2\\n4 2\\n4 4\\n5 1\\n1 1\\n5 3\\n2 8\\n2 4\\n1 2\\n2 3\\n1 4\\n1 5\\n1 3\\n3 4\\n4 3\\n', 'output': '15'}, {'type': 'stdin_stdout', 'input': '25\\n1010111001100010000101001\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '24'}, {'type': 'stdin_stdout', 'input': '70\\n0010011111011101101111000111101011010101000011000000010100010101010001\\n3 1\\n1 5\\n3 1\\n4 1\\n3 3\\n2 4\\n2 1\\n5 1\\n2 4\\n5 2\\n5 2\\n4 1\\n2 5\\n2 2\\n4 2\\n5 1\\n1 2\\n2 4\\n3 1\\n1 1\\n5 3\\n5 2\\n3 5\\n4 4\\n2 1\\n3 2\\n1 3\\n5 1\\n3 4\\n2 3\\n1 5\\n4 1\\n2 2\\n5 1\\n3 3\\n4 2\\n1 4\\n5 2\\n1 2\\n4 1\\n1 4\\n5 3\\n3 3\\n2 5\\n3 5\\n3 4\\n3 3\\n1 5\\n1 1\\n2 4\\n5 4\\n1 4\\n3 6\\n2 5\\n2 4\\n1 3\\n5 2\\n4 4\\n1 2\\n1 1\\n4 4\\n5 4\\n1 2\\n5 1\\n3 1\\n5 4\\n4 5\\n3 1\\n2 4\\n3 2\\n', 'output': '45'}, {'type': 'stdin_stdout', 'input': '7\\n0000111\\n3 3\\n4 3\\n5 3\\n1 5\\n3 4\\n2 4\\n5 4\\n', 'output': '7'}, {'type': 'stdin_stdout', 'input': '2\\n10\\n1 5\\n1 1\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '50\\n10011111101111011010001011111110110011101111100111\\n2 1\\n4 3\\n3 4\\n1 4\\n3 2\\n5 3\\n5 5\\n3 5\\n5 1\\n4 4\\n1 1\\n1 2\\n1 4\\n1 5\\n1 1\\n4 1\\n2 4\\n3 1\\n1 1\\n1 3\\n1 5\\n2 3\\n3 1\\n5 5\\n5 4\\n4 4\\n1 4\\n2 1\\n2 2\\n2 5\\n1 5\\n2 1\\n5 4\\n1 2\\n4 5\\n5 5\\n5 1\\n1 4\\n4 2\\n4 4\\n2 5\\n1 2\\n3 4\\n5 4\\n4 3\\n3 3\\n3 3\\n3 2\\n5 3\\n5 1\\n', 'output': '38'}, {'type': 'stdin_stdout', 'input': '4\\n1111\\n5 4\\n5 2\\n3 1\\n3 2\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '3\\n101\\n4 3\\n3 2\\n3 1\\n', 'output': '3'}, {'type': 'stdin_stdout', 'input': '6\\n011100\\n5 3\\n6 5\\n2 4\\n3 5\\n4 2\\n1 5\\n', 'output': '6'}, {'type': 'stdin_stdout', 'input': '25\\n1010111001100010000101001\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n6 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '23'}, {'type': 'stdin_stdout', 'input': '6\\n011110\\n4 3\\n6 5\\n2 4\\n3 5\\n4 2\\n1 5\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '25\\n0101110011000110001100011\\n1 1\\n1 1\\n1 3\\n1 4\\n1 6\\n2 2\\n2 2\\n2 3\\n2 3\\n2 5\\n3 1\\n3 2\\n6 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n7 4\\n5 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '22'}, {'type': 'stdin_stdout', 'input': '25\\n1011100111001110011100111\\n1 1\\n2 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25'}, {'type': 'stdin_stdout', 'input': '25\\n0101110011000110001100011\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n7 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25'}, {'type': 'stdin_stdout', 'input': '25\\n1010100110001110011100111\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n1 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '24'}, {'type': 'stdin_stdout', 'input': '25\\n1111111111111111111111111\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 2\\n3 4\\n3 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n4 3\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '25\\n0101010011000110001100011\\n1 1\\n1 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n4 5\\n4 1\\n4 2\\n4 3\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n', 'output': '25'}, {'type': 'stdin_stdout', 'input': '25\\n0111101111011110111101111\\n1 1\\n2 2\\n1 3\\n1 4\\n1 5\\n2 1\\n2 2\\n2 3\\n2 4\\n2 5\\n3 1\\n3 2\\n3 3\\n3 4\\n3 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'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77985","program":"```python\nimport sys\ninput = sys.stdin.readline\n\nn=int(input())\ns=input().strip()\n\nAB=[tuple(map(int,input().split())) for i in range(n)]\n\nANS=[[0]*n for i in range(3000)]\n\nfor i in range(n):\n k=int(s[i])\n a,b=AB[i]\n\n t=0\n while t<3000:\n if t>=b and (t-b)%a==0:\n k=1-k\n \n ANS[t][i]=k\n t+=1\n\n\n \nA=0\nfor t in range(3000):\n A=max(A,sum(ANS[t]))\n\nprint(A)\n\n```","inputs":"4\n1111\n3 4\n5 2\n3 1\n3 2\n","output":"4\n","actual_output":"4\n","execution_success":true,"sample_index":12432},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1228_A. Distinct Digits","prompt":"Solve the following coding problem using the programming language python:\n\nYou have two integers l and r. Find an integer x which satisfies the conditions below:\n\n * l \u2264 x \u2264 r. \n * All digits of x are different. \n\n\n\nIf there are multiple answers, print any of them.\n\nInput\n\nThe first line contains two integers l and r (1 \u2264 l \u2264 r \u2264 10^{5}).\n\nOutput\n\nIf an answer exists, print any of them. Otherwise, print -1.\n\nExamples\n\nInput\n\n\n121 130\n\n\nOutput\n\n\n123\n\n\nInput\n\n\n98766 100000\n\n\nOutput\n\n\n-1\n\nNote\n\nIn the first example, 123 is one of the possible answers. However, 121 can't be the answer, because there are multiple 1s on different digits.\n\nIn the second example, there is no valid answer.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nl, r =map(int, input().split())\nfor i in range(l,r+1):\n n = 0\n a = str(i)\n for j in a:\n if a.count(j) == 1:\n n = n+1\n else:\n pass\n if n == len(a):\n break\nif n == len(a):\n print(a)\nelse:\n print('-1')\n\n \n \n \n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '98766 100000\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '121 130\\n', 'output': '123\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '25139 86116\\n', 'output': '25139\\n'}, {'type': 'stdin_stdout', 'input': '23452 23456\\n', 'output': '23456\\n'}, {'type': 'stdin_stdout', 'input': '8563 90197\\n', 'output': '8563\\n'}, {'type': 'stdin_stdout', 'input': '25610 80988\\n', 'output': '25610\\n'}, {'type': 'stdin_stdout', 'input': '111 121\\n', 'output': '120\\n'}, {'type': 'stdin_stdout', 'input': '999 1002\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '76330 80769\\n', 'output': '76340\\n'}, {'type': 'stdin_stdout', 'input': '112 112\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '47142 47149\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '99 101\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '9878 9999\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '22 22\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '99 1000\\n', 'output': '102\\n'}, {'type': 'stdin_stdout', 'input': '1 100000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '7 10\\n', 'output': '7\\n'}, {'type': 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{'type': 'stdin_stdout', 'input': '78 1001\\n', 'output': '78\\n'}, {'type': 'stdin_stdout', 'input': '2 100010\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '33426 60048\\n', 'output': '34012\\n'}, {'type': 'stdin_stdout', 'input': '3049 90197\\n', 'output': '3049\\n'}, {'type': 'stdin_stdout', 'input': '3 191\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '152 160\\n', 'output': '152\\n'}, {'type': 'stdin_stdout', 'input': '72073 145777\\n', 'output': '72081\\n'}, {'type': 'stdin_stdout', 'input': '4228 90197\\n', 'output': '4230\\n'}, {'type': 'stdin_stdout', 'input': '11097 145777\\n', 'output': '12034\\n'}, {'type': 'stdin_stdout', 'input': '4191 90197\\n', 'output': '4192\\n'}, {'type': 'stdin_stdout', 'input': '49951 59374\\n', 'output': '50123\\n'}, {'type': 'stdin_stdout', 'input': '6 39\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1767 59374\\n', 'output': '1768\\n'}, {'type': 'stdin_stdout', 'input': '562 59374\\n', 'output': '562\\n'}, {'type': 'stdin_stdout', 'input': '700 59374\\n', 'output': '701\\n'}, {'type': 'stdin_stdout', 'input': '910 59374\\n', 'output': '910\\n'}, {'type': 'stdin_stdout', 'input': '1339 59374\\n', 'output': '1340\\n'}, {'type': 'stdin_stdout', 'input': '806 17526\\n', 'output': '806\\n'}, {'type': 'stdin_stdout', 'input': '4 001111\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '8 7092\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '10 001101\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '99 111\\n', 'output': '102\\n'}, {'type': 'stdin_stdout', 'input': '99 1001\\n', 'output': '102\\n'}, {'type': 'stdin_stdout', 'input': '23452 60048\\n', 'output': '23456\\n'}, {'type': 'stdin_stdout', 'input': '25610 35660\\n', 'output': '25610\\n'}, {'type': 'stdin_stdout', 'input': '9 191\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '0 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '98766 110010\\n', 'output': '102345\\n'}, {'type': 'stdin_stdout', 'input': '121 160\\n', 'output': '123\\n'}, {'type': 'stdin_stdout', 'input': '38912 145777\\n', 'output': '38912\\n'}, {'type': 'stdin_stdout', 'input': '25610 64209\\n', 'output': '25610\\n'}, {'type': 'stdin_stdout', 'input': '18449 59273\\n', 'output': '18450\\n'}, {'type': 'stdin_stdout', 'input': '1 110010\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '33426 44116\\n', 'output': '34012\\n'}, {'type': 'stdin_stdout', 'input': '25610 59374\\n', 'output': '25610\\n'}, {'type': 'stdin_stdout', 'input': '3 39\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '0 110010\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '33426 67348\\n', 'output': '34012\\n'}, {'type': 'stdin_stdout', 'input': '1 111010\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '11097 157931\\n', 'output': '12034\\n'}, {'type': 'stdin_stdout', 'input': '33426 71451\\n', 'output': '34012\\n'}, {'type': 'stdin_stdout', 'input': '4191 65352\\n', 'output': '4192\\n'}, {'type': 'stdin_stdout', 'input': '6 25\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1 111110\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '11097 53980\\n', 'output': '12034\\n'}, {'type': 'stdin_stdout', 'input': '4191 7122\\n', 'output': '4192\\n'}, {'type': 'stdin_stdout', 'input': '0 25\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 110110\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '11097 75141\\n', 'output': '12034\\n'}, {'type': 'stdin_stdout', 'input': '0 41\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 011110\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '11097 28810\\n', 'output': '12034\\n'}, {'type': 'stdin_stdout', 'input': '0 10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 001110\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '11097 51224\\n', 'output': '12034\\n'}, {'type': 'stdin_stdout', 'input': '1 001010\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '11097 12307\\n', 'output': '12034\\n'}, {'type': 'stdin_stdout', 'input': '1339 58757\\n', 'output': '1340\\n'}, {'type': 'stdin_stdout', 'input': '2 001110\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1339 17526\\n', 'output': '1340\\n'}, {'type': 'stdin_stdout', 'input': '2 001111\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '806 7092\\n', 'output': '806\\n'}, {'type': 'stdin_stdout', 'input': '4 000111\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4 000101\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1 7092\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '8 000101\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1 5535\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '8 001101\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1 5424\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77989","program":"```python\nl, r =map(int, input().split())\nfor i in range(l,r+1):\n n = 0\n a = str(i)\n for j in a:\n if a.count(j) == 1:\n n = n+1\n else:\n pass\n if n == len(a):\n break\nif n == len(a):\n print(a)\nelse:\n print('-1')\n\n \n \n \n\n```","inputs":"98766 100000\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12433},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1270_A. Card Game","prompt":"Solve the following coding problem using the programming language python:\n\nTwo players decided to play one interesting card game.\n\nThere is a deck of n cards, with values from 1 to n. The values of cards are pairwise different (this means that no two different cards have equal values). At the beginning of the game, the deck is completely distributed between players such that each player has at least one card. \n\nThe game goes as follows: on each turn, each player chooses one of their cards (whichever they want) and puts on the table, so that the other player doesn't see which card they chose. After that, both cards are revealed, and the player, value of whose card was larger, takes both cards in his hand. Note that as all cards have different values, one of the cards will be strictly larger than the other one. Every card may be played any amount of times. The player loses if he doesn't have any cards.\n\nFor example, suppose that n = 5, the first player has cards with values 2 and 3, and the second player has cards with values 1, 4, 5. Then one possible flow of the game is:\n\n * The first player chooses the card 3. The second player chooses the card 1. As 3>1, the first player gets both cards. Now the first player has cards 1, 2, 3, the second player has cards 4, 5.\n\n * The first player chooses the card 3. The second player chooses the card 4. As 3<4, the second player gets both cards. Now the first player has cards 1, 2. The second player has cards 3, 4, 5.\n\n * The first player chooses the card 1. The second player chooses the card 3. As 1<3, the second player gets both cards. Now the first player has only the card 2. The second player has cards 1, 3, 4, 5.\n\n * The first player chooses the card 2. The second player chooses the card 4. As 2<4, the second player gets both cards. Now the first player is out of cards and loses. Therefore, the second player wins.\n\n\n\n\nWho will win if both players are playing optimally? It can be shown that one of the players has a winning strategy.\n\nInput\n\nEach test contains multiple test cases. The first line contains the number of test cases t (1 \u2264 t \u2264 100). The description of the test cases follows.\n\nThe first line of each test case contains three integers n, k_1, k_2 (2 \u2264 n \u2264 100, 1 \u2264 k_1 \u2264 n - 1, 1 \u2264 k_2 \u2264 n - 1, k_1 + k_2 = n) \u2014 the number of cards, number of cards owned by the first player and second player correspondingly.\n\nThe second line of each test case contains k_1 integers a_1, ..., a_{k_1} (1 \u2264 a_i \u2264 n) \u2014 the values of cards of the first player.\n\nThe third line of each test case contains k_2 integers b_1, ..., b_{k_2} (1 \u2264 b_i \u2264 n) \u2014 the values of cards of the second player.\n\nIt is guaranteed that the values of all cards are different.\n\nOutput\n\nFor each test case, output \"YES\" in a separate line, if the first player wins. Otherwise, output \"NO\" in a separate line. You can print each letter in any case (upper or lower).\n\nExample\n\nInput\n\n\n2\n2 1 1\n2\n1\n5 2 3\n2 3\n1 4 5\n\n\nOutput\n\n\nYES\nNO\n\nNote\n\nIn the first test case of the example, there is only one possible move for every player: the first player will put 2, the second player will put 1. 2>1, so the first player will get both cards and will win.\n\nIn the second test case of the example, it can be shown that it is the second player who has a winning strategy. One possible flow of the game is illustrated in the statement.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nT = int(input())\nfor _ in range(T) :\n in_li = list(map(int,input().split()))\n n = in_li[0]\n k1 = in_li[1]\n k2 = in_li[2]\n one = list(map(int,input().split()))\n two = list(map(int,input().split()))\n max1 = max(one)\n max2 = max(two)\n count1 = 0\n count2 = 0\n for num in one :\n if num > max2 :\n count1 += 1\n for num in two :\n if num > max1 :\n count2 += 1\n if count1 > count2 :\n print(\"YES\")\n else :\n print(\"NO\")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n1 4 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n1 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n1 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n4 3\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n0 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n2 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n0 6 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 3\\n2 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-1\\n5 2 3\\n2 3\\n2 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 4\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n3 4\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n1 3 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 3\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n4 6\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n4 3\\n0 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 4\\n4 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n0 3\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n-1 6 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-1\\n5 2 3\\n2 3\\n3 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-1\\n5 2 3\\n2 3\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 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'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 4\\n2 12 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n1 3\\n2 11 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n1 3\\n1 11 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n1 11 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 2\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 3\\n1 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-1\\n5 2 3\\n3 3\\n2 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 4\\n1 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 3\\n4 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 1\\n4 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-2\\n5 2 3\\n2 3\\n3 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-1\\n5 2 3\\n2 3\\n0 3 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n1 3\\n1 20 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 1\\n4 12 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-1\\n5 2 3\\n2 4\\n0 3 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n4 3\\n1 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n0 3\\n0 6 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 4\\n3 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n0 3 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n4 3\\n0 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n1 3\\n2 11 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 2\\n2 0 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n2 12 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n7 2 3\\n1 3\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 4\\n3 12 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-1\\n5 2 3\\n1 3\\n2 11 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n1 2\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 4\\n1 13 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n0 3\\n4 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 2\\n4 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n4 3\\n0 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n0 3\\n1 6 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n6 3\\n0 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n1 3\\n2 12 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 4\\n2 0 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n4 3\\n2 12 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n7 2 3\\n1 0\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n1 2\\n4 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 4\\n0 13 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n0 3\\n2 6 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 3\\n0 13 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n3 3\\n0 13 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 0\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 0\\n2 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 3\\n0 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n1 4\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n0 3\\n1 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-1\\n5 2 3\\n2 3\\n3 4 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-1\\n5 2 3\\n2 3\\n4 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 2\\n0 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 1\\n4 2 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 0\\n2 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n-1\\n5 2 3\\n3 3\\n2 1 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n5 2 3\\n2 4\\n1 3 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n0\\n5 2 3\\n2 3\\n6 7 5\\n', 'output': 'YES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1\\n2\\n1\\n7 2 3\\n2 1\\n4 7 5\\n', 'output': 'YES\\nNO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_77997","program":"```python\nT = int(input())\nfor _ in range(T) :\n in_li = list(map(int,input().split()))\n n = in_li[0]\n k1 = in_li[1]\n k2 = in_li[2]\n one = list(map(int,input().split()))\n two = list(map(int,input().split()))\n max1 = max(one)\n max2 = max(two)\n count1 = 0\n count2 = 0\n for num in one :\n if num > max2 :\n count1 += 1\n for num in two :\n if num > max1 :\n count2 += 1\n if count1 > count2 :\n print(\"YES\")\n else :\n print(\"NO\")\n\n```","inputs":"2\n2 1 1\n2\n1\n5 2 3\n2 3\n1 4 5\n","output":"YES\nNO\n","actual_output":"YES\nNO\n","execution_success":true,"sample_index":12434},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1312_F. Attack on Red Kingdom","prompt":"Solve the following coding problem using the programming language python:\n\nThe Red Kingdom is attacked by the White King and the Black King!\n\nThe Kingdom is guarded by n castles, the i-th castle is defended by a_i soldiers. To conquer the Red Kingdom, the Kings have to eliminate all the defenders. \n\nEach day the White King launches an attack on one of the castles. Then, at night, the forces of the Black King attack a castle (possibly the same one). Then the White King attacks a castle, then the Black King, and so on. The first attack is performed by the White King.\n\nEach attack must target a castle with at least one alive defender in it. There are three types of attacks:\n\n * a mixed attack decreases the number of defenders in the targeted castle by x (or sets it to 0 if there are already less than x defenders); \n * an infantry attack decreases the number of defenders in the targeted castle by y (or sets it to 0 if there are already less than y defenders); \n * a cavalry attack decreases the number of defenders in the targeted castle by z (or sets it to 0 if there are already less than z defenders). \n\n\n\nThe mixed attack can be launched at any valid target (at any castle with at least one soldier). However, the infantry attack cannot be launched if the previous attack on the targeted castle had the same type, no matter when and by whom it was launched. The same applies to the cavalry attack. A castle that was not attacked at all can be targeted by any type of attack.\n\nThe King who launches the last attack will be glorified as the conqueror of the Red Kingdom, so both Kings want to launch the last attack (and they are wise enough to find a strategy that allows them to do it no matter what are the actions of their opponent, if such strategy exists). The White King is leading his first attack, and you are responsible for planning it. Can you calculate the number of possible options for the first attack that allow the White King to launch the last attack? Each option for the first attack is represented by the targeted castle and the type of attack, and two options are different if the targeted castles or the types of attack are different.\n\nInput\n\nThe first line contains one integer t (1 \u2264 t \u2264 1000) \u2014 the number of test cases.\n\nThen, the test cases follow. Each test case is represented by two lines. \n\nThe first line contains four integers n, x, y and z (1 \u2264 n \u2264 3 \u22c5 10^5, 1 \u2264 x, y, z \u2264 5). \n\nThe second line contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 10^{18}).\n\nIt is guaranteed that the sum of values of n over all test cases in the input does not exceed 3 \u22c5 10^5.\n\nOutput\n\nFor each test case, print the answer to it: the number of possible options for the first attack of the White King (or 0, if the Black King can launch the last attack no matter how the White King acts).\n\nExamples\n\nInput\n\n\n3\n2 1 3 4\n7 6\n1 1 2 3\n1\n1 1 2 2\n3\n\n\nOutput\n\n\n2\n3\n0\n\n\nInput\n\n\n10\n6 5 4 5\n2 3 2 3 1 3\n1 5 2 3\n10\n4 4 2 3\n8 10 8 5\n2 2 1 4\n8 5\n3 5 3 5\n9 2 10\n4 5 5 5\n2 10 4 2\n2 3 1 4\n1 10\n3 1 5 3\n9 8 7\n2 5 4 5\n8 8\n3 5 1 4\n5 5 10\n\n\nOutput\n\n\n0\n2\n1\n2\n5\n12\n5\n0\n0\n2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nT = int(input())\n\n\ndef findPeriod(DP):\n for offset in range(0, len(DP)):\n for period in range(1, 500):\n is_period = True\n for j in range(offset, len(DP) - period):\n if (DP[j][0] == DP[j + period][0] and DP[j][1] == DP[j + period][1] and DP[j][2] == DP[j + period][2]):\n is_period = True\n else:\n is_period = False\n break\n if is_period and period < len(DP) - offset + 1:\n return period, offset\n return 0, 0\n\n\nWHERE = ''\nimport random\n\ntry:\n for _ in range(T):\n memo = {}\n n, x, y, z = list(map(int, input().split()))\n PILES = list(map(int, input().split()))\n # PILES = [random.randint(0, 1500) for _ in range(500)]\n\n DP = [[0 for _ in range(3)] for _ in range(1000)]\n # Compute DP\n for i in range(1,1000):\n for j in range(3):\n children = []\n for ind, attack in enumerate([x, y, z]):\n if ind != j or ind == 0:\n children.append((max(0, i - attack), ind))\n\n if len(children) == 0:\n DP[i][j] = 0\n else:\n s = set()\n for child in children:\n s.add(DP[child[0]][child[1]])\n\n grundy = 0\n while grundy in s:\n grundy += 1\n DP[i][j] = grundy\n WHERE = 'a'\n # Compute Period\n period, offset = findPeriod(DP)\n #print(\"Period \" + str(period))\n # print(offset)\n grundy = 0\n convert = lambda pile: (pile - offset) % period + offset if pile - offset >= 0 else pile\n # PILES_MOD = [str(convert(pile)) for pile in PILES]\n #print(len([x for x in PILES if x == 16]))\n #L = [str(x) for x in PILES if x != 16]\n\n #print(len([x for x in L if x == '15']))\n #L = [str(x) for x in L if x != '15']\n\n #print(len([x for x in L if x == '14']))\n #L = [str(x) for x in L if x != '14']\n\n #print(len([x for x in L if x == '13']))\n #L = [str(x) for x in L if x != '13']\n\n #print(\" \".join(L))\n # print(PILES)\n # print(PILES_MOD)\n # print(\" \".join(PILES_MOD))\n for pile in PILES:\n grundy ^= DP[convert(pile)][0]\n if grundy == 0:\n print(0)\n else:\n count = 0\n WHERE = 'b'\n for pile in PILES:\n\n grundy ^= DP[convert(pile)][0]\n # You must apply the modulo %period after having changed your state\n # Otherwise too easy to get error with the max function\n # Example : currentState = 10 ,attack = 5 period=10\n # If you apply modulo before you get currentState = 0\n # If you apply modulo after you get currentState = 5\n if (grundy ^ DP[convert(max(0, (pile - x)))][0] == 0): count += 1\n if (grundy ^ DP[convert(max(0, (pile - y)))][1] == 0): count += 1\n if (grundy ^ DP[convert(max(0, (pile - z)))][2] == 0): count += 1\n\n grundy ^= DP[convert(pile)][0]\n\n print(count)\nexcept Exception as e:\n print(e)\n print(WHERE)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10\\n6 5 4 5\\n2 3 2 3 1 3\\n1 5 2 3\\n10\\n4 4 2 3\\n8 10 8 5\\n2 2 1 4\\n8 5\\n3 5 3 5\\n9 2 10\\n4 5 5 5\\n2 10 4 2\\n2 3 1 4\\n1 10\\n3 1 5 3\\n9 8 7\\n2 5 4 5\\n8 8\\n3 5 1 4\\n5 5 10\\n', 'output': '0\\n2\\n1\\n2\\n5\\n12\\n5\\n0\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 3 4\\n7 6\\n1 1 2 3\\n1\\n1 1 2 2\\n3\\n', 'output': '2\\n3\\n0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 2 3 5\\n4 5\\n2 1 1 1\\n1 2\\n7 1 2 2\\n3 5 3 1 4 5 5\\n1 3 3 1\\n2\\n4 5 5 3\\n1 3 4 3\\n2 3 4 3\\n4 2\\n2 1 2 5\\n3 1\\n3 2 3 5\\n2 1 3\\n2 4 5 1\\n4 4\\n5 2 4 5\\n5 5 5 2 1\\n', 'output': '1\\n6\\n8\\n2\\n1\\n2\\n1\\n2\\n0\\n3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n6 5 4 5\\n2 3 2 3 1 3\\n1 5 4 3\\n10\\n4 4 2 3\\n8 10 8 5\\n2 2 1 4\\n8 5\\n3 5 3 5\\n9 2 10\\n4 5 5 5\\n2 10 4 2\\n2 3 1 4\\n1 10\\n3 1 5 3\\n9 8 7\\n2 5 4 5\\n8 8\\n3 5 1 4\\n5 5 10\\n', 'output': '0\\n2\\n1\\n2\\n5\\n12\\n5\\n0\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 3 4\\n7 6\\n1 1 2 3\\n1\\n1 1 1 2\\n3\\n', 'output': '2\\n3\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 3 4\\n7 6\\n1 1 2 3\\n1\\n1 1 1 2\\n2\\n', 'output': '2\\n3\\n1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n6 5 4 5\\n2 3 2 3 1 3\\n1 5 4 3\\n10\\n4 4 2 3\\n0 10 8 5\\n2 2 1 4\\n8 5\\n3 5 3 5\\n9 2 10\\n4 5 5 5\\n2 10 2 2\\n2 3 1 4\\n1 10\\n3 1 5 3\\n9 8 7\\n2 5 4 5\\n8 8\\n3 5 1 4\\n5 5 10\\n', 'output': '0\\n2\\n3\\n2\\n5\\n12\\n5\\n0\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n6 3 4 5\\n2 3 2 3 1 3\\n1 5 4 3\\n10\\n4 4 2 3\\n0 10 14 5\\n2 2 1 4\\n8 3\\n3 5 3 5\\n9 2 10\\n4 5 5 5\\n2 10 2 2\\n2 3 1 4\\n1 10\\n3 1 5 3\\n9 8 7\\n2 5 4 5\\n8 8\\n3 5 1 4\\n5 5 10\\n', 'output': '0\\n2\\n3\\n0\\n5\\n12\\n5\\n0\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n6 3 4 5\\n2 3 2 3 1 3\\n1 5 4 3\\n10\\n4 4 2 3\\n0 10 14 5\\n2 2 1 4\\n8 3\\n3 5 3 5\\n9 2 10\\n4 5 5 5\\n2 15 2 2\\n2 3 1 4\\n1 10\\n3 1 5 3\\n9 8 7\\n2 5 4 5\\n8 8\\n3 5 1 4\\n5 5 10\\n', 'output': '0\\n2\\n3\\n0\\n5\\n0\\n5\\n0\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n6 3 4 5\\n2 3 2 3 1 3\\n1 5 4 3\\n10\\n4 4 2 3\\n0 10 14 5\\n2 2 1 4\\n8 3\\n3 5 3 5\\n9 2 10\\n4 5 5 5\\n2 15 2 2\\n2 3 1 3\\n1 10\\n3 1 5 3\\n9 8 7\\n2 5 4 5\\n8 8\\n3 5 1 4\\n5 2 10\\n', 'output': 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10\\n4 5 5 5\\n2 10 2 2\\n2 3 1 4\\n1 10\\n3 1 5 3\\n11 8 7\\n2 5 4 5\\n8 8\\n3 5 1 4\\n5 2 10\\n', 'output': '0\\n2\\n3\\n2\\n5\\n12\\n5\\n0\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 2 3 5\\n4 5\\n2 1 1 2\\n1 2\\n7 1 2 2\\n3 5 3 1 4 5 5\\n1 3 3 1\\n2\\n4 5 5 3\\n1 3 4 3\\n2 3 4 3\\n4 2\\n2 1 2 5\\n3 1\\n3 2 3 5\\n2 1 3\\n2 1 5 1\\n4 4\\n5 1 4 5\\n5 5 5 2 1\\n', 'output': '1\\n2\\n8\\n2\\n1\\n2\\n1\\n2\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 1 4\\n7 6\\n1 1 1 3\\n2\\n1 1 1 2\\n3\\n', 'output': '2\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n6 3 4 5\\n2 3 2 3 1 3\\n1 5 4 2\\n10\\n4 4 2 3\\n0 10 8 5\\n2 2 1 4\\n8 5\\n3 5 3 5\\n3 2 2\\n4 5 5 5\\n2 10 2 2\\n2 3 1 4\\n1 10\\n3 1 5 3\\n9 8 7\\n2 5 4 5\\n8 8\\n3 5 1 4\\n5 5 10\\n', 'output': '0\\n2\\n3\\n2\\n9\\n12\\n5\\n0\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n6 3 4 5\\n2 3 2 3 1 3\\n1 5 4 3\\n10\\n4 4 2 3\\n0 10 8 5\\n2 2 1 2\\n8 5\\n3 5 3 3\\n3 2 2\\n4 5 5 5\\n2 10 2 2\\n2 3 1 4\\n1 10\\n3 1 5 3\\n9 8 7\\n2 5 4 5\\n16 8\\n3 5 1 4\\n5 5 10\\n', 'output': '0\\n2\\n3\\n0\\n9\\n12\\n5\\n0\\n0\\n2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 12, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_78005","program":"```python\nT = int(input())\n\n\ndef findPeriod(DP):\n for offset in range(0, len(DP)):\n for period in range(1, 500):\n is_period = True\n for j in range(offset, len(DP) - period):\n if (DP[j][0] == DP[j + period][0] and DP[j][1] == DP[j + period][1] and DP[j][2] == DP[j + period][2]):\n is_period = True\n else:\n is_period = False\n break\n if is_period and period < len(DP) - offset + 1:\n return period, offset\n return 0, 0\n\n\nWHERE = ''\nimport random\n\ntry:\n for _ in range(T):\n memo = {}\n n, x, y, z = list(map(int, input().split()))\n PILES = list(map(int, input().split()))\n # PILES = [random.randint(0, 1500) for _ in range(500)]\n\n DP = [[0 for _ in range(3)] for _ in range(1000)]\n # Compute DP\n for i in range(1,1000):\n for j in range(3):\n children = []\n for ind, attack in enumerate([x, y, z]):\n if ind != j or ind == 0:\n children.append((max(0, i - attack), ind))\n\n if len(children) == 0:\n DP[i][j] = 0\n else:\n s = set()\n for child in children:\n s.add(DP[child[0]][child[1]])\n\n grundy = 0\n while grundy in s:\n grundy += 1\n DP[i][j] = grundy\n WHERE = 'a'\n # Compute Period\n period, offset = findPeriod(DP)\n #print(\"Period \" + str(period))\n # print(offset)\n grundy = 0\n convert = lambda pile: (pile - offset) % period + offset if pile - offset >= 0 else pile\n # PILES_MOD = [str(convert(pile)) for pile in PILES]\n #print(len([x for x in PILES if x == 16]))\n #L = [str(x) for x in PILES if x != 16]\n\n #print(len([x for x in L if x == '15']))\n #L = [str(x) for x in L if x != '15']\n\n #print(len([x for x in L if x == '14']))\n #L = [str(x) for x in L if x != '14']\n\n #print(len([x for x in L if x == '13']))\n #L = [str(x) for x in L if x != '13']\n\n #print(\" \".join(L))\n # print(PILES)\n # print(PILES_MOD)\n # print(\" \".join(PILES_MOD))\n for pile in PILES:\n grundy ^= DP[convert(pile)][0]\n if grundy == 0:\n print(0)\n else:\n count = 0\n WHERE = 'b'\n for pile in PILES:\n\n grundy ^= DP[convert(pile)][0]\n # You must apply the modulo %period after having changed your state\n # Otherwise too easy to get error with the max function\n # Example : currentState = 10 ,attack = 5 period=10\n # If you apply modulo before you get currentState = 0\n # If you apply modulo after you get currentState = 5\n if (grundy ^ DP[convert(max(0, (pile - x)))][0] == 0): count += 1\n if (grundy ^ DP[convert(max(0, (pile - y)))][1] == 0): count += 1\n if (grundy ^ DP[convert(max(0, (pile - z)))][2] == 0): count += 1\n\n grundy ^= DP[convert(pile)][0]\n\n print(count)\nexcept Exception as e:\n print(e)\n print(WHERE)\n```","inputs":"10\n6 5 4 5\n2 3 2 3 1 3\n1 5 2 3\n10\n4 4 2 3\n8 10 8 5\n2 2 1 4\n8 5\n3 5 3 5\n9 2 10\n4 5 5 5\n2 10 4 2\n2 3 1 4\n1 10\n3 1 5 3\n9 8 7\n2 5 4 5\n8 8\n3 5 1 4\n5 5 10\n","output":"0\n2\n1\n2\n5\n12\n5\n0\n0\n2\n","actual_output":"0\n2\n1\n2\n5\n12\n5\n0\n0\n2\n","execution_success":true,"sample_index":12435},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1335_C. Two Teams Composing","prompt":"Solve the following coding problem using the programming language python:\n\nYou have n students under your control and you have to compose exactly two teams consisting of some subset of your students. Each student had his own skill, the i-th student skill is denoted by an integer a_i (different students can have the same skills).\n\nSo, about the teams. Firstly, these two teams should have the same size. Two more constraints:\n\n * The first team should consist of students with distinct skills (i.e. all skills in the first team are unique). \n * The second team should consist of students with the same skills (i.e. all skills in the second team are equal). \n\n\n\nNote that it is permissible that some student of the first team has the same skill as a student of the second team.\n\nConsider some examples (skills are given):\n\n * [1, 2, 3], [4, 4] is not a good pair of teams because sizes should be the same; \n * [1, 1, 2], [3, 3, 3] is not a good pair of teams because the first team should not contain students with the same skills; \n * [1, 2, 3], [3, 4, 4] is not a good pair of teams because the second team should contain students with the same skills; \n * [1, 2, 3], [3, 3, 3] is a good pair of teams; \n * [5], [6] is a good pair of teams. \n\n\n\nYour task is to find the maximum possible size x for which it is possible to compose a valid pair of teams, where each team size is x (skills in the first team needed to be unique, skills in the second team should be the same between them). A student cannot be part of more than one team.\n\nYou have to answer t independent test cases.\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 10^4) \u2014 the number of test cases. Then t test cases follow.\n\nThe first line of the test case contains one integer n (1 \u2264 n \u2264 2 \u22c5 10^5) \u2014 the number of students. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 n), where a_i is the skill of the i-th student. Different students can have the same skills.\n\nIt is guaranteed that the sum of n over all test cases does not exceed 2 \u22c5 10^5 (\u2211 n \u2264 2 \u22c5 10^5).\n\nOutput\n\nFor each test case, print the answer \u2014 the maximum possible size x for which it is possible to compose a valid pair of teams, where each team size is x.\n\nExample\n\nInput\n\n\n4\n7\n4 2 4 1 4 3 4\n5\n2 1 5 4 3\n1\n1\n4\n1 1 1 3\n\n\nOutput\n\n\n3\n1\n0\n2\n\nNote\n\nIn the first test case of the example, it is possible to construct two teams of size 3: the first team is [1, 2, 4] and the second team is [4, 4, 4]. Note, that there are some other ways to construct two valid teams of size 3.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nt = int(input())\nfor _ in range(t):\n n = int(input()) \n a = list(map(int, input().split()))\n d = {}\n maxd = 0\n for x in a:\n d[x] = d.get(x, 0) + 1\n if d[x] > maxd:\n maxd = d[x]\n \n print(max(min(len(d)-1, maxd), min(len(d), maxd-1)))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 1 1 3\\n', 'output': '3\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n', 'output': '0\\n0\\n0\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9\\n1 2 2 3 3 9 9 9 9\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 5 1 3\\n1\\n1\\n4\\n1 1 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 2 1 3\\n1\\n1\\n4\\n1 1 1 1\\n', 'output': '3\\n2\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 2 3 7\\n5\\n4 1 2 1 3\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '2\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9\\n1 2 2 3 3 9 9 0 9\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 1 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 2\\n', 'output': '3\\n1\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 6 1 1 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 2\\n', 'output': '2\\n1\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 6 1 1 3 6\\n5\\n2 1 5 3 3\\n1\\n1\\n4\\n1 2 1 2\\n', 'output': '2\\n2\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 7 3 7\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n2 1 1 3\\n', 'output': '2\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 2 1 3\\n1\\n1\\n4\\n1 1 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 5 1 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n4 1 2 1 3\\n1\\n1\\n4\\n1 1 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n4 1 2 1 3\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 7\\n5\\n4 1 2 1 3\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 1 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 2 3 7\\n5\\n4 1 2 1 3\\n1\\n1\\n4\\n1 2 2 3\\n', 'output': '2\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n2 1 1 3\\n', 'output': '3\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 5 3 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 5 1 3\\n1\\n1\\n4\\n1 2 1 4\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 0 4 1 4 3 4\\n5\\n4 1 2 1 3\\n1\\n1\\n4\\n1 1 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 2 3 7\\n5\\n4 2 2 1 3\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '2\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 0 2 3 7\\n5\\n4 2 2 1 3\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '2\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 6 1 1 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 2\\n', 'output': '3\\n1\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9\\n1 2 2 3 3 9 6 9 9\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n3 2 4 1 4 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 1 1 3\\n', 'output': '3\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 4 4\\n5\\n2 1 2 1 3\\n1\\n1\\n4\\n1 1 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 2 1 3\\n1\\n1\\n3\\n1 1 1 1\\n', 'output': '3\\n2\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 2 5 1 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 2 1 3\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 7\\n5\\n4 1 2 1 4\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 4 1 1 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 7 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n2 1 1 3\\n', 'output': '3\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 1 3 4\\n5\\n2 1 5 4 5\\n1\\n1\\n4\\n1 2 1 2\\n', 'output': '3\\n2\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 0 2 3 7\\n5\\n4 2 3 1 3\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '2\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 6 1 1 3 6\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 2\\n', 'output': '2\\n1\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9\\n1 2 2 3 3 9 6 9 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 4 1 1 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 2 3\\n', 'output': '3\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 1 3 4\\n5\\n2 1 5 4 5\\n1\\n1\\n4\\n1 2 1 4\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 6 1 1 3 6\\n5\\n2 1 5 3 3\\n1\\n1\\n4\\n1 2 1 4\\n', 'output': '2\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9\\n1 2 2 3 3 9 9 8 9\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 5 3 4\\n5\\n2 1 2 1 3\\n1\\n1\\n4\\n1 1 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 6\\n5\\n2 1 5 1 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 1 3 7\\n5\\n4 1 2 1 3\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '2\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 5 4\\n5\\n2 1 5 3 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 3 4\\n5\\n2 1 4 1 3\\n1\\n1\\n4\\n1 2 1 4\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 0 4 1 4 3 4\\n5\\n4 1 2 1 3\\n1\\n1\\n4\\n1 1 1 1\\n', 'output': '3\\n2\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 1 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n3\\n1 2 1 2\\n', 'output': '3\\n1\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 6 2 1 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 2\\n', 'output': '3\\n1\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9\\n2 2 2 3 3 9 6 9 9\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n7 2 4 1 4 3 4\\n5\\n2 2 5 1 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 4 1 1 3 2\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 1 3 4\\n5\\n1 1 5 4 5\\n1\\n1\\n4\\n1 2 1 2\\n', 'output': '3\\n2\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n3 2 4 0 2 3 7\\n5\\n4 2 3 1 3\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '2\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 6 2 1 3 6\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 2\\n', 'output': '2\\n1\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 4 1 1 3 4\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 2 4\\n', 'output': '3\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 6 3 6\\n5\\n2 1 5 1 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '2\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 4 5 4\\n5\\n2 1 5 5 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9\\n0 2 2 3 3 9 6 9 9\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n3 2 4 1 4 3 4\\n5\\n2 2 5 1 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '3\\n2\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 4 4 1 1 3 1\\n5\\n2 1 5 4 3\\n1\\n1\\n4\\n1 2 1 3\\n', 'output': '2\\n1\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n4 2 4 1 1 3 4\\n5\\n1 1 3 4 5\\n1\\n1\\n4\\n1 2 1 2\\n', 'output': '3\\n2\\n0\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n7\\n3 2 4 0 2 3 7\\n5\\n4 2 1 1 3\\n1\\n1\\n4\\n1 1 2 3\\n', 'output': '2\\n2\\n0\\n2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78009","program":"```python\nt = int(input())\nfor _ in range(t):\n n = int(input()) \n a = list(map(int, input().split()))\n d = {}\n maxd = 0\n for x in a:\n d[x] = d.get(x, 0) + 1\n if d[x] > maxd:\n maxd = d[x]\n \n print(max(min(len(d)-1, maxd), min(len(d), maxd-1)))\n\n```","inputs":"4\n7\n4 2 4 1 4 3 4\n5\n2 1 5 4 3\n1\n1\n4\n1 1 1 3\n","output":"3\n1\n0\n2\n","actual_output":"3\n1\n0\n2\n","execution_success":true,"sample_index":12436},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1355_E. Restorer Distance","prompt":"Solve the following coding problem using the programming language python:\n\nYou have to restore the wall. The wall consists of N pillars of bricks, the height of the i-th pillar is initially equal to h_{i}, the height is measured in number of bricks. After the restoration all the N pillars should have equal heights.\n\nYou are allowed the following operations:\n\n * put a brick on top of one pillar, the cost of this operation is A;\n * remove a brick from the top of one non-empty pillar, the cost of this operation is R;\n * move a brick from the top of one non-empty pillar to the top of another pillar, the cost of this operation is M.\n\n\n\nYou cannot create additional pillars or ignore some of pre-existing pillars even if their height becomes 0.\n\nWhat is the minimal total cost of restoration, in other words, what is the minimal total cost to make all the pillars of equal height?\n\nInput\n\nThe first line of input contains four integers N, A, R, M (1 \u2264 N \u2264 10^{5}, 0 \u2264 A, R, M \u2264 10^{4}) \u2014 the number of pillars and the costs of operations.\n\nThe second line contains N integers h_{i} (0 \u2264 h_{i} \u2264 10^{9}) \u2014 initial heights of pillars.\n\nOutput\n\nPrint one integer \u2014 the minimal cost of restoration.\n\nExamples\n\nInput\n\n\n3 1 100 100\n1 3 8\n\n\nOutput\n\n\n12\n\n\nInput\n\n\n3 100 1 100\n1 3 8\n\n\nOutput\n\n\n9\n\n\nInput\n\n\n3 100 100 1\n1 3 8\n\n\nOutput\n\n\n4\n\n\nInput\n\n\n5 1 2 4\n5 5 3 6 5\n\n\nOutput\n\n\n4\n\n\nInput\n\n\n5 1 2 2\n5 5 3 6 5\n\n\nOutput\n\n\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#!/usr/bin/env python3\nimport io\nimport os\nfrom bisect import bisect\ninput = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline\ndef get_str():\n return input().decode().strip()\ndef rint():\n return map(int, input().split())\ndef oint():\n return int(input())\n\ndef find_lu_value(th):\n hi = bisect(h, th) - 1\n lv = th * (hi + 1) - ps[hi]\n uv = (ps[n - 1] - ps[hi]) - (n - 1 - hi) * th\n return lv, uv\n\ndef calc_cost(th):\n cost = 0\n l, u = find_lu_value(th)\n if l > u:\n cost += u * m + (l - u) * a\n else:\n cost += l * m + (u - l) * r\n return cost\n\ndef calc_prefixsum(h):\n ps = [h[0]]\n for i in range(1, n):\n ps.append(h[i] + ps[-1])\n return ps\n\nn, a, r, m = rint()\nh = list(rint())\n\nm = min(m, a + r)\nh.sort()\nps = calc_prefixsum(h)\nans = 10**99\n\nlv = h[0]\nrv = h[-1]\n\n\nans = min(ans, calc_cost(lv), calc_cost(rv), calc_cost(lv+1))\nwhile rv-lv >= 2:\n mv = (rv-lv)//2 + lv\n mc = calc_cost(mv)\n rc = calc_cost(mv+1)\n ans = min(ans, rc, mc)\n if mc < rc:\n rv = mv\n elif mc > rc:\n lv = mv\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 1 100 100\\n1 3 8\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2 4\\n5 5 3 6 5\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3 100 100 1\\n1 3 8\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2 2\\n5 5 3 6 5\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 100 1 100\\n1 3 8\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '10 4078 1859 607\\n160396657 831922387 330524879 901162754 847008736 781626686 496115244 470330335 824475169 620982654\\n', 'output': '639731251326\\n'}, {'type': 'stdin_stdout', 'input': '1 0 0 0\\n0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '100 52 92 72\\n67 100 56 15 0 92 26 74 44 61 6 44 45 19 22 19 9 85 67 78 24 61 81 99 62 84 5 71 11 65 5 97 9 72 11 81 81 64 65 91 52 21 20 53 68 91 4 75 84 88 72 27 48 23 9 65 14 6 54 55 6 1 89 78 40 45 98 45 27 51 94 72 67 81 20 19 38 64 14 40 57 21 82 99 37 92 21 22 30 14 65 93 60 8 63 60 27 30 32 11\\n', 'output': '95816\\n'}, {'type': 'stdin_stdout', 'input': '2 0 0 0\\n1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10 7 8 3\\n3 10 4 9 2 7 6 10 4 8\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '10 7122 8827 3205\\n452685204 144160553 743427456 403576146 888744473 313727757 22025193 886601085 576370788 787974081\\n', 'output': '4081476227653\\n'}, {'type': 'stdin_stdout', 'input': '1 0 0 0\\n1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10 8521 9022 6018\\n195431204 251205289 385530059 954288541 703713298 183134963 983855337 409855471 11842043 921687235\\n', 'output': '9408102096630\\n'}, {'type': 'stdin_stdout', 'input': '10 1299 4362 8516\\n177913931 857265729 858027469 743427538 70328308 334897178 739985290 903278439 602456716 623851298\\n', 'output': '3721721948256\\n'}, {'type': 'stdin_stdout', 'input': '1 100 100 100\\n1000000000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 1 1 2\\n1000000000 1000000000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10 7901 3681 1769\\n286577406 276548631 281628869 796553324 632065579 736405456 932758091 211399795 789823590 924555879\\n', 'output': '2284083174243\\n'}, {'type': 'stdin_stdout', 'input': '10 4078 1859 607\\n160396657 831922387 330524879 379432862 847008736 781626686 496115244 470330335 824475169 620982654\\n', 'output': '628006955067\\n'}, {'type': 'stdin_stdout', 'input': '100 52 92 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input().decode().strip()\ndef rint():\n return map(int, input().split())\ndef oint():\n return int(input())\n\ndef find_lu_value(th):\n hi = bisect(h, th) - 1\n lv = th * (hi + 1) - ps[hi]\n uv = (ps[n - 1] - ps[hi]) - (n - 1 - hi) * th\n return lv, uv\n\ndef calc_cost(th):\n cost = 0\n l, u = find_lu_value(th)\n if l > u:\n cost += u * m + (l - u) * a\n else:\n cost += l * m + (u - l) * r\n return cost\n\ndef calc_prefixsum(h):\n ps = [h[0]]\n for i in range(1, n):\n ps.append(h[i] + ps[-1])\n return ps\n\nn, a, r, m = rint()\nh = list(rint())\n\nm = min(m, a + r)\nh.sort()\nps = calc_prefixsum(h)\nans = 10**99\n\nlv = h[0]\nrv = h[-1]\n\n\nans = min(ans, calc_cost(lv), calc_cost(rv), calc_cost(lv+1))\nwhile rv-lv >= 2:\n mv = (rv-lv)//2 + lv\n mc = calc_cost(mv)\n rc = calc_cost(mv+1)\n ans = min(ans, rc, mc)\n if mc < rc:\n rv = mv\n elif mc > rc:\n lv = mv\nprint(ans)\n\n```","inputs":"3 1 100 100\n1 3 8\n","output":"12\n","actual_output":"12\n","execution_success":true,"sample_index":12437},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1422_C. Bargain","prompt":"Solve the following coding problem using the programming language python:\n\nSometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price n, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names 1213121, Vova can remove the substring 1312, and the result is 121.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be 0.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo 10^9 + 7.\n\nInput\n\nThe first and only line contains a single integer n (1 \u2264 n < 10^{10^5}).\n\nOutput\n\nIn the only line print the required sum modulo 10^9 + 7.\n\nExamples\n\nInput\n\n\n107\n\n\nOutput\n\n\n42\n\n\nInput\n\n\n100500100500\n\n\nOutput\n\n\n428101984\n\nNote\n\nConsider the first example.\n\nVova can choose to remove 1, 0, 7, 10, 07, or 107. The results are 07, 17, 10, 7, 1, 0. Their sum is 42.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ns = [int(c) for c in input()][::-1]\nn = len(s)\n\nmod = 1000000007\ndef inv(x):\n return pow(x, mod - 2, mod)\nteninv = inv(10)\n\nP = [0]\np = 1\nfor x in s:\n P.append((P[-1] + x*p) % mod)\n p = p*10 % mod\n\nQ = [0]\nfor i in range(n+1):\n Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \n\ns = 0\nfor l in range(n):\n first = P[l] - P[0]\n s += (n - l)*first % mod\n s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\n d = Q[n+1] - Q[l+1]\n\n s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\nprint(s%mod)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '107\\n', 'output': '42\\n'}, {'type': 'stdin_stdout', 'input': '100500100500\\n', 'output': '428101984\\n'}, {'type': 'stdin_stdout', 'input': '1403665305\\n', 'output': '765601706\\n'}, {'type': 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range(n+1):\n Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \n\ns = 0\nfor l in range(n):\n first = P[l] - P[0]\n s += (n - l)*first % mod\n s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\n d = Q[n+1] - Q[l+1]\n\n s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\nprint(s%mod)\n\n```","inputs":"107\n","output":"42\n","actual_output":"42\n","execution_success":true,"sample_index":12439},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1440_B. Sum of Medians","prompt":"Solve the following coding problem using the programming language python:\n\nA median of an array of integers of length n is the number standing on the \u2308 {n/2} \u2309 (rounding up) position in the non-decreasing ordering of its elements. Positions are numbered starting with 1. For example, a median of the array [2, 6, 4, 1, 3, 5] is equal to 3. There exist some other definitions of the median, but in this problem, we will use the described one.\n\nGiven two integers n and k and non-decreasing array of nk integers. Divide all numbers into k arrays of size n, such that each number belongs to exactly one array.\n\nYou want the sum of medians of all k arrays to be the maximum possible. Find this maximum possible sum.\n\nInput\n\nThe first line contains a single integer t (1 \u2264 t \u2264 100) \u2014 the number of test cases. The next 2t lines contain descriptions of test cases.\n\nThe first line of the description of each test case contains two integers n, k (1 \u2264 n, k \u2264 1000).\n\nThe second line of the description of each test case contains nk integers a_1, a_2, \u2026, a_{nk} (0 \u2264 a_i \u2264 10^9) \u2014 given array. It is guaranteed that the array is non-decreasing: a_1 \u2264 a_2 \u2264 \u2026 \u2264 a_{nk}.\n\nIt is guaranteed that the sum of nk for all test cases does not exceed 2 \u22c5 10^5.\n\nOutput\n\nFor each test case print a single integer \u2014 the maximum possible sum of medians of all k arrays.\n\nExample\n\nInput\n\n\n6\n2 4\n0 24 34 58 62 64 69 78\n2 2\n27 61 81 91\n4 3\n2 4 16 18 21 27 36 53 82 91 92 95\n3 4\n3 11 12 22 33 35 38 67 69 71 94 99\n2 1\n11 41\n3 3\n1 1 1 1 1 1 1 1 1\n\n\nOutput\n\n\n165\n108\n145\n234\n11\n3\n\nNote\n\nThe examples of possible divisions into arrays for all test cases of the first test:\n\nTest case 1: [0, 24], [34, 58], [62, 64], [69, 78]. The medians are 0, 34, 62, 69. Their sum is 165.\n\nTest case 2: [27, 61], [81, 91]. The medians are 27, 81. Their sum is 108.\n\nTest case 3: [2, 91, 92, 95], [4, 36, 53, 82], [16, 18, 21, 27]. The medians are 91, 36, 18. Their sum is 145.\n\nTest case 4: [3, 33, 35], [11, 94, 99], [12, 38, 67], [22, 69, 71]. The medians are 33, 94, 38, 69. Their sum is 234.\n\nTest case 5: [11, 41]. The median is 11. The sum of the only median is 11.\n\nTest case 6: [1, 1, 1], [1, 1, 1], [1, 1, 1]. The medians are 1, 1, 1. Their sum is 3.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfor _ in range(int(input())):\n n, k = map(int, input().split())\n a = list(map(int, input().split()))\n total = 0\n a.reverse()\n t=n-(n+1)//2+1\n for i in range(1, k+1):\n total += a[t*i-1]\n print(total)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 24 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n2 4 16 18 21 27 36 53 82 91 92 95\\n3 4\\n3 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n11 41\\n3 3\\n1 1 1 1 1 1 1 1 1\\n', 'output': '165\\n108\\n145\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 24 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n2 4 16 18 21 27 36 53 82 91 92 95\\n3 4\\n3 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n11 41\\n3 3\\n1 1 1 1 1 1 1 1 0\\n', 'output': '165\\n108\\n145\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n2 4 16 18 22 27 36 53 82 89 92 95\\n3 4\\n3 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n11 41\\n3 3\\n1 1 1 1 1 1 1 1 1\\n', 'output': '165\\n108\\n143\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n44 61 81 91\\n4 3\\n2 4 16 18 22 27 36 53 82 89 92 95\\n3 4\\n3 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n11 41\\n3 3\\n1 1 1 1 1 1 1 1 1\\n', 'output': '165\\n125\\n143\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n2 4 16 18 22 27 36 53 82 89 92 95\\n3 4\\n0 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n7 41\\n3 3\\n1 1 1 1 1 1 1 1 1\\n', 'output': '165\\n108\\n143\\n234\\n7\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n40 61 81 91\\n4 3\\n0 4 16 18 21 27 36 75 82 89 92 95\\n3 4\\n0 11 3 22 33 35 38 67 69 71 94 99\\n2 1\\n11 41\\n3 3\\n1 1 1 1 -1 1 1 1 1\\n', 'output': '165\\n121\\n143\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n2 4 16 18 22 27 36 53 82 89 92 95\\n3 4\\n0 11 12 22 33 35 61 67 69 71 94 99\\n2 1\\n11 41\\n3 3\\n1 1 1 1 1 1 1 1 1\\n', 'output': '165\\n108\\n143\\n257\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n1 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 4 16 18 22 27 36 53 82 89 92 95\\n3 4\\n0 4 12 22 33 35 38 67 69 71 94 99\\n2 1\\n11 41\\n3 3\\n1 1 1 1 1 1 1 1 1\\n', 'output': '166\\n108\\n143\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 24 37 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 4 16 18 21 27 36 53 82 91 92 95\\n3 4\\n1 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n11 41\\n3 3\\n1 2 1 1 1 1 1 1 -1\\n', 'output': '168\\n108\\n145\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 4 16 18 21 27 36 75 82 89 92 95\\n3 4\\n-1 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n9 41\\n3 3\\n1 1 1 1 0 1 1 1 1\\n', 'output': '165\\n108\\n143\\n234\\n9\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n1 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 4 16 18 22 27 36 53 82 89 92 95\\n3 4\\n0 4 12 22 33 35 38 67 69 71 94 99\\n2 1\\n14 41\\n3 3\\n1 1 1 1 1 1 1 1 1\\n', 'output': '166\\n108\\n143\\n234\\n14\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 4 16 18 21 27 45 75 82 89 92 95\\n3 4\\n-1 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n9 41\\n3 3\\n1 1 1 1 0 1 1 1 1\\n', 'output': '165\\n108\\n152\\n234\\n9\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 4 16 18 21 27 36 53 82 89 92 95\\n3 4\\n0 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n18 41\\n3 3\\n1 1 1 1 0 1 1 1 1\\n', 'output': '165\\n108\\n143\\n234\\n18\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 24 25 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 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94 99\\n2 1\\n11 41\\n3 3\\n1 1 1 1 0 1 1 1 1\\n', 'output': '165\\n108\\n143\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 4 16 18 21 27 36 53 82 89 92 95\\n3 4\\n0 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n11 41\\n3 3\\n1 1 1 1 0 1 1 1 1\\n', 'output': '165\\n108\\n143\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 10 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n2 4 16 18 21 27 36 53 82 91 92 95\\n3 4\\n3 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n11 41\\n3 3\\n1 1 1 1 1 1 1 1 0\\n', 'output': '165\\n108\\n145\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n2 4 16 18 22 27 36 53 82 89 92 95\\n3 4\\n0 11 12 22 33 35 38 67 69 71 94 109\\n2 1\\n11 41\\n3 3\\n1 1 1 1 1 1 1 1 1\\n', 'output': '165\\n108\\n143\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 4 16 18 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76 94 99\\n2 1\\n11 62\\n3 3\\n1 1 1 1 1 1 1 1 0\\n', 'output': '165\\n108\\n145\\n234\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n2 4 16 18 22 27 36 53 82 89 92 95\\n3 4\\n0 11 12 22 33 35 61 67 69 71 94 99\\n2 1\\n11 66\\n3 3\\n1 0 1 1 1 1 1 1 1\\n', 'output': '165\\n108\\n143\\n257\\n11\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 0 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 4 16 18 21 27 45 75 82 89 92 95\\n3 4\\n-1 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n9 41\\n3 3\\n1 1 1 1 0 1 1 1 1\\n', 'output': '165\\n108\\n152\\n234\\n9\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4\\n0 4 34 58 62 64 69 78\\n2 2\\n27 61 81 91\\n4 3\\n0 4 16 18 21 27 36 53 82 89 92 95\\n3 4\\n0 11 12 22 33 35 38 67 69 71 94 99\\n2 1\\n18 41\\n3 3\\n1 2 1 1 0 1 1 1 1\\n', 'output': '165\\n108\\n143\\n234\\n18\\n3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78029","program":"```python\nfor _ in range(int(input())):\n n, k = map(int, input().split())\n a = list(map(int, input().split()))\n total = 0\n a.reverse()\n t=n-(n+1)//2+1\n for i in range(1, k+1):\n total += a[t*i-1]\n print(total)\n\n```","inputs":"6\n2 4\n0 24 34 58 62 64 69 78\n2 2\n27 61 81 91\n4 3\n2 4 16 18 21 27 36 53 82 91 92 95\n3 4\n3 11 12 22 33 35 38 67 69 71 94 99\n2 1\n11 41\n3 3\n1 1 1 1 1 1 1 1 1\n","output":"165\n108\n145\n234\n11\n3\n","actual_output":"165\n108\n145\n234\n11\n3\n","execution_success":true,"sample_index":12440},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1467_C. Three Bags","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given three bags. Each bag contains a non-empty multiset of numbers. You can perform a number of operations on these bags. In one operation, you can choose any two non-empty bags, and choose one number from each of the bags. Let's say that you choose number a from the first bag and number b from the second bag. Then, you remove b from the second bag and replace a with a-b in the first bag. Note that if there are multiple occurrences of these numbers, then you shall only remove/replace exactly one occurrence.\n\nYou have to perform these operations in such a way that you have exactly one number remaining in exactly one of the bags (the other two bags being empty). It can be shown that you can always apply these operations to receive such a configuration in the end. Among all these configurations, find the one which has the maximum number left in the end.\n\nInput\n\nThe first line of the input contains three space-separated integers n_1, n_2 and n_3 (1 \u2264 n_1, n_2, n_3 \u2264 3\u22c510^5, 1 \u2264 n_1+n_2+n_3 \u2264 3\u22c510^5) \u2014 the number of numbers in the three bags.\n\nThe i-th of the next three lines contain n_i space-separated integers a_{{i,1}}, a_{{i,2}}, ..., a_{{i,{{n_i}}}} (1 \u2264 a_{{i,j}} \u2264 10^9) \u2014 the numbers in the i-th bag.\n\nOutput\n\nPrint a single integer \u2014 the maximum number which you can achieve in the end.\n\nExamples\n\nInput\n\n\n2 4 1\n1 2\n6 3 4 5\n5\n\n\nOutput\n\n\n20\n\nInput\n\n\n3 2 2\n7 5 4\n2 9\n7 1\n\n\nOutput\n\n\n29\n\nNote\n\nIn the first example input, let us perform the following operations:\n\n[1, 2], [6, 3, 4, 5], [5]\n\n[-5, 2], [3, 4, 5], [5] (Applying an operation to (1, 6))\n\n[-10, 2], [3, 4], [5] (Applying an operation to (-5, 5))\n\n[2], [3, 4], [15] (Applying an operation to (5, -10))\n\n[-1], [4], [15] (Applying an operation to (2, 3))\n\n[-5], [], [15] (Applying an operation to (-1, 4))\n\n[], [], [20] (Applying an operation to (15, -5))\n\nYou can verify that you cannot achieve a bigger number. Hence, the answer is 20.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn1,n2,n3=map(int,input().split())\nval=[]\n\ndef func(a,b,c,d,e,f):\n dd=d-a[0]\n v1=b[0]-dd\n ff=f-c[-1]\n v2=a[0]-ff-(e-b[0])\n if v1<0:\n return (c[-1]-v1)-v2\n else:\n v2-=v1\n return (c[-1]-v2)\n\n\none=(list(map(int,input().split())))\ntwo=(list(map(int,input().split())))\nthree=(list(map(int,input().split())))\none.sort();two.sort();three.sort()\nos=sum(one)\nts=sum(two)\nths=sum(three)\nli=[]\nli.append(func(one,two,three,os,ts,ths))\nli.append(func(one,three,two,os,ths,ts))\nli.append(func(two,three,one,ts,ths,os))\nli.append(func(two,one,three,ts,os,ths))\nli.append(func(three,one,two,ths,os,ts))\nli.append(func(three,two,one,ths,ts,os))\nprint(max(li))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 2 2\\n7 5 4\\n2 9\\n7 1\\n', 'output': '\\n29'}, {'type': 'stdin_stdout', 'input': '2 4 1\\n1 2\\n6 3 4 5\\n5\\n', 'output': '\\n20'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n2 3 4\\n4 5 6\\n5\\n', 'output': '19'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1000 1000 1000\\n1000 1000 1000\\n1 1 1\\n', 'output': '5997'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n2 3 4\\n4 7 6\\n5\\n', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1000 1000 1000\\n1000 1000 1000\\n1 1 0\\n', 'output': '5998\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 5 4\\n2 9\\n7 1\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '2 4 1\\n1 4\\n6 3 4 5\\n5\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n3 3 4\\n4 7 6\\n5\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1000 1000 1000\\n1000 1000 1000\\n1 1 -1\\n', 'output': '5999\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 5 5\\n2 9\\n7 1\\n', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 5 10\\n2 9\\n7 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1\\n5 3 1\\n3 7 13\\n5\\n', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 1 0\\n2 16\\n13 1\\n', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n1 6 9\\n9 10 6\\n5\\n', 'output': '36\\n'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n0 2 4\\n1 7 10\\n2\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n1 6 0\\n3 10 7\\n5\\n', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n2 6 1\\n18 5 6\\n5\\n', 'output': '33\\n'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n1 10 1\\n3 10 4\\n4\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n1 8 5\\n3 10 4\\n7\\n', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n4 5 4\\n2 14\\n7 0\\n', 'output': '32\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78033","program":"```python\nn1,n2,n3=map(int,input().split())\nval=[]\n\ndef func(a,b,c,d,e,f):\n dd=d-a[0]\n v1=b[0]-dd\n ff=f-c[-1]\n v2=a[0]-ff-(e-b[0])\n if v1<0:\n return (c[-1]-v1)-v2\n else:\n v2-=v1\n return (c[-1]-v2)\n\n\none=(list(map(int,input().split())))\ntwo=(list(map(int,input().split())))\nthree=(list(map(int,input().split())))\none.sort();two.sort();three.sort()\nos=sum(one)\nts=sum(two)\nths=sum(three)\nli=[]\nli.append(func(one,two,three,os,ts,ths))\nli.append(func(one,three,two,os,ths,ts))\nli.append(func(two,three,one,ts,ths,os))\nli.append(func(two,one,three,ts,os,ths))\nli.append(func(three,one,two,ths,os,ts))\nli.append(func(three,two,one,ths,ts,os))\nprint(max(li))\n\n```","inputs":"3 2 2\n7 5 4\n2 9\n7 1\n","output":"\n29","actual_output":"29\n","execution_success":true,"sample_index":12441},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1514_C. Product 1 Modulo N","prompt":"Solve the following coding problem using the programming language python:\n\nNow you get Baby Ehab's first words: \"Given an integer n, find the longest subsequence of [1,2, \u2026, n-1] whose product is 1 modulo n.\" Please solve the problem.\n\nA sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly all) elements. The product of an empty subsequence is equal to 1.\n\nInput\n\nThe only line contains the integer n (2 \u2264 n \u2264 10^5).\n\nOutput\n\nThe first line should contain a single integer, the length of the longest subsequence.\n\nThe second line should contain the elements of the subsequence, in increasing order.\n\nIf there are multiple solutions, you can print any.\n\nExamples\n\nInput\n\n\n5\n\n\nOutput\n\n\n3\n1 2 3 \n\nInput\n\n\n8\n\n\nOutput\n\n\n4\n1 3 5 7 \n\nNote\n\nIn the first example, the product of the elements is 6 which is congruent to 1 modulo 5. The only longer subsequence is [1,2,3,4]. Its product is 24 which is congruent to 4 modulo 5. Hence, the answer is [1,2,3].\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\nn=int(input())\nans=[]\nprod=1\ncount=0\nfor i in range(1,n-1):\n if math.gcd(n,i)==1:\n ans.append(str(i))\n prod=(prod*i)%n\n count+=1\nif n==2:\n print(1)\n print(1)\nelse:\n if prod % n == 1:\n print(count)\n print(\" \".join(ans))\n else:\n print(count+1)\n print(\" \".join(ans),n-1)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n', 'output': '\\n3\\n1 2 3 '}, {'type': 'stdin_stdout', 'input': '8\\n', 'output': '\\n4\\n1 3 5 7 '}, {'type': 'stdin_stdout', 'input': '65536\\n', 'output': '32768\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131 133 135 137 139 141 143 145 147 149 151 153 155 157 159 161 163 165 167 169 171 173 175 177 179 181 183 185 187 189 191 193 195 197 199 201 203 205 207 209 211 213 215 217 219 221 223 225 227 229 231 233 235 237 239 241 243 245 247 249 251 253 255 257 259 261 263 265 267 269 271 273 275 277 279...'}, {'type': 'stdin_stdout', 'input': '6\\n', 'output': '1\\n1 '}, {'type': 'stdin_stdout', 'input': '30030\\n', 'output': '5760\\n1 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 289 293 307 311 313 317 323 331 337 347 349 353 359 361 367 373 379 383 389 391 397 401 409 419 421 431 433 437 439 443 449 457 461 463 467 479 487 491 493 499 503 509 521 523 527 529 541 547 551 557 563 569 571 577 587 589 593 599 601 607 613 617 619 629 631 641 643 647 653 659 661 667 673 677 683 69...'}, {'type': 'stdin_stdout', 'input': '3\\n', 'output': '1\\n1 '}, {'type': 'stdin_stdout', 'input': '59582\\n', 'output': '28829\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 95 97 99 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131 133 135 137 139 141 143 145 147 149 151 153 157 159 161 163 165 167 169 171 173 175 177 179 181 183 185 187 189 191 193 195 197 199 201 203 205 207 209 211 213 215 219 221 223 225 227 229 231 233 235 237 239 241 243 245 247 249 251 253 255 257 259 261 263 265 267 269 271 273 275 277 281 283 285 287 2...'}, {'type': 'stdin_stdout', 'input': '12972\\n', 'output': '4048\\n1 5 7 11 13 17 19 25 29 31 35 37 41 43 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103 107 109 113 119 121 125 127 131 133 137 139 143 145 149 151 155 157 163 167 169 173 175 179 181 185 187 191 193 197 199 203 205 209 211 215 217 221 223 227 229 233 239 241 245 247 251 257 259 263 265 269 271 275 277 281 283 287 289 293 295 301 305 307 311 313 317 319 323 325 331 335 337 341 343 347 349 353 355 359 361 365 367 371 373 377 379 383 385 389 395 397 401 403 407 409 413 415 419 421 425 427 431...'}, {'type': 'stdin_stdout', 'input': '7\\n', 'output': '5\\n1 2 3 4 5 '}, {'type': 'stdin_stdout', 'input': '2\\n', 'output': '1\\n1 '}, {'type': 'stdin_stdout', 'input': '26721\\n', 'output': '17808\\n1 2 4 5 7 8 10 11 13 14 16 17 19 20 22 23 25 26 28 29 31 32 34 35 37 38 40 41 43 44 46 47 49 50 52 53 55 56 58 59 61 62 64 65 67 68 70 71 73 74 76 77 79 80 82 83 85 86 88 89 91 92 94 95 97 98 100 101 103 104 106 107 109 110 112 113 115 116 118 119 121 122 124 125 127 128 130 131 133 134 136 137 139 140 142 143 145 146 148 149 151 152 154 155 157 158 160 161 163 164 166 167 169 170 172 173 175 176 178 179 181 182 184 185 187 188 190 191 193 194 196 197 199 200 202 203 205 206 208 209 211 212 214 215 ...'}, {'type': 'stdin_stdout', 'input': '8951\\n', 'output': '8949\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 1...'}, {'type': 'stdin_stdout', 'input': '9\\n', 'output': '5\\n1 2 4 5 7 '}, {'type': 'stdin_stdout', 'input': '4\\n', 'output': '1\\n1 '}, {'type': 'stdin_stdout', 'input': '51964\\n', 'output': '23600\\n1 3 5 7 9 13 15 17 19 21 23 25 27 29 31 35 37 39 41 43 45 47 49 51 53 57 59 61 63 65 67 69 71 73 75 79 81 83 85 87 89 91 93 95 97 101 103 105 107 109 111 113 115 117 119 123 125 127 129 131 133 135 137 139 141 145 147 149 151 153 155 157 159 161 163 167 169 171 173 175 177 179 181 183 185 189 191 193 195 197 199 201 203 205 207 211 213 215 217 219 221 223 225 227 229 233 235 237 239 241 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1984 1986 1987 1988 1989 1991 1992 1993 1994 1997 1998 1999 2001 2002 2003 2004 2006 2007 2008 2009 2011 2012 2013 2014 2016 2017 2018 2019 2021 2022 2023 2024 2026 2027 2028 2029 2031 2032 2033 2034 2036 2037 2038 2039 2041 2042 2043 2044 2046 2047 2048 2049 2051 2052 2053 2054 2056 2057 2058 2059 2061 2062 2063 2064 2066 2067 2068 2069 2071 2072 2073 2074 2076 2077 2078 2079 2081 2082 2083 2084 2086 2087 2088 2089 2091 2092 2093 2094 2096 2097 2098 2099 2101 2102 2103 2104 2106 2107 2108 2109 2111 2112 2113 2114 2116 2117 2118 2119 2121 2122 2123 2124 2126 2127 2128 2129 2131 2132 2133 2134 2136 2137 2138 2139 2141 2142 2143 2144 2146 2147 2148 2149 2151 2152 2153 2154 2156 2157 2158 2159 2161 2162 2163 2164 2166 2167 2168 2169 2171 2172 2173 2174 2176 2177 2178 2179 2181 2182 2183 2184 2186 2187 2188 2189 2191 2192 2193 2194 2196 2197 2198 2199 2201 2202 2203 2204 2206 2207 2208 2209 2211 2212 2213 2214 2216 2217 2218 2219 2221 2222 2223 2224 2226 2227 2228 2229 2231 2232 2233 2234 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3667 3669 3671 3673 3675 3677 3679 3681 3683 3685 3687 3689 3691 3693 3695 3697 3699 3701 3703 3705 3707 3709 3711 3713 3715 3717 3719 3721 3723 3725 3727 3729 3731 3733 3735 3737 3739 3741 3743 3745 3747 3749 3751 3753 3755 3757 3759 3761 3763 3765 3767 3769 3771 3773 3775 3777 3779 3781 3783 3785 3787 3789 3791 3793 3795 3797 3799 3801 3803 3805 3807 3809 3811 3813 3815 3817 3819 3821 3823 3825 3827 3829 3831 3833 3835 3837 3839 3841 3843 3845 3847 3849 3851 3853 3855 3857 3859 3861 3863 3865 3867 3869 3871 3873 3875 3877 3879 3881 3883 3885 3887 3889 3891 3893 3895 3897 3899 3901 3903 3905 3907 3909 3911 3913 3915 3917 3919 3921 3923 3925 3927 3929 3931 3933 3935 3937 3939 3941 3943 3945 3947 3949 3951 3953 3955 3957 3959 3961 3963 3965 3967 3969 3971 3973 3975 3977 3979 3981 3983 3985 3987 3989 3991 3993 3995 3997 3999 4001 4003 4005 4007 4009 4011 4013 4015 4017 4019 4021 4023 4025 4027 4029 4031 4033 4035 4037 4039 4041 4043 4045 4047 4049 4051 4053 4055 4057 4059 4061 4063 4065 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1103 1105 1109 1111 1115 1117 1121 1123 1129 1133 1135 1139 1145 1147 1151 1153 1157 1159 1163 1165 1171 1175 1177 1181 1187 1189 1193 1195 1199 1201 1205 1207 1213 1217 1219 1223 1229 1231 1235 1237 1241 1243 1247 1249 1255 1259 1261 1265 1271 1273 1277 1279 1283 1285 1289 1291 1297 1301 1303 1307 1313 1315 1319 1321 1325 1327 1331 1333 1339 1343 1345 1349 1355 1357 1361 1363 1367 1369 1373 1375 1381 1385 1387 1391 1397 1399 1403 1405 1409 1411 1415 1417 1423 1427 1429 1433 1439 1441 1445 1447 1451 1453 1457 1459 1465 1469 1471 1475 1481 1483 1487 1489 1493 1495 1499 1501 1507 1511 1513 1517 1523 1525 1529 1531 1535 1537 1541 1543 1549 1553 1555 1559 1565 1567 1571 1573 1577 1579 1583 1585 1591 1595 1597 1601 1607 1609 1613 1615 1619 1621 1625 1627 1633 1637 1639 1643 1649 1651 1655 1657 1661 1663 1667 1669 1675 1679 1681 1685 1691 1693 1697 1699 1703 1705 1709 1711 1717 1721 1723 1727 1733 1735 1739 1741 1745 1747 1751 1753 1759 1763 1765 1769 1775 1777 1781 1783 1787 1789 1793 1795 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19983 19987 19989 19991 19993 19995 19997 20001 20003 20005\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78041","program":"```python\nimport math\nn=int(input())\nans=[]\nprod=1\ncount=0\nfor i in range(1,n-1):\n if math.gcd(n,i)==1:\n ans.append(str(i))\n prod=(prod*i)%n\n count+=1\nif n==2:\n print(1)\n print(1)\nelse:\n if prod % n == 1:\n print(count)\n print(\" \".join(ans))\n else:\n print(count+1)\n print(\" \".join(ans),n-1)\n```","inputs":"5\n","output":"\n3\n1 2 3 ","actual_output":"3\n1 2 3\n","execution_success":true,"sample_index":12442},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1541_C. Great Graphs","prompt":"Solve the following coding problem using the programming language python:\n\nFarmer John has a farm that consists of n pastures connected by one-directional roads. Each road has a weight, representing the time it takes to go from the start to the end of the road. The roads could have negative weight, where the cows go so fast that they go back in time! However, Farmer John guarantees that it is impossible for the cows to get stuck in a time loop, where they can infinitely go back in time by traveling across a sequence of roads. Also, each pair of pastures is connected by at most one road in each direction.\n\nUnfortunately, Farmer John lost the map of the farm. All he remembers is an array d, where d_i is the smallest amount of time it took the cows to reach the i-th pasture from pasture 1 using a sequence of roads. The cost of his farm is the sum of the weights of each of the roads, and Farmer John needs to know the minimal cost of a farm that is consistent with his memory.\n\nInput\n\nThe first line contains one integer t (1 \u2264 t \u2264 10^4) \u2014 the number of test cases. Then t cases follow.\n\nThe first line of each test case contains a single integer n (1 \u2264 n \u2264 10^5) \u2014 the number of pastures.\n\nThe second line of each test case contains n space separated integers d_1, d_2, \u2026, d_n (0 \u2264 d_i \u2264 10^9) \u2014 the array d. It is guaranteed that d_1 = 0.\n\nIt is guaranteed that the sum of n over all test cases does not exceed 10^5.\n\nOutput\n\nFor each test case, output the minimum possible cost of a farm that is consistent with Farmer John's memory.\n\nExample\n\nInput\n\n\n3\n3\n0 2 3\n2\n0 1000000000\n1\n0\n\n\nOutput\n\n\n-3\n0\n0\n\nNote\n\nIn the first test case, you can add roads \n\n * from pasture 1 to pasture 2 with a time of 2, \n * from pasture 2 to pasture 3 with a time of 1, \n * from pasture 3 to pasture 1 with a time of -3, \n * from pasture 3 to pasture 2 with a time of -1, \n * from pasture 2 to pasture 1 with a time of -2. \n\nThe total cost is 2 + 1 + -3 + -1 + -2 = -3.\n\nIn the second test case, you can add a road from pasture 1 to pasture 2 with cost 1000000000 and a road from pasture 2 to pasture 1 with cost -1000000000. The total cost is 1000000000 + -1000000000 = 0.\n\nIn the third test case, you can't add any roads. The total cost is 0.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfor _ in range(int(input())):\n n=int(input())\n d=list(map(int,input().split()))\n d=sorted(d)\n if(n==1):\n print(d[n-1])\n continue\n l=[0]\n for i in range(n-2,-1,-1):\n l.append(d[i]-d[n-1])\n c=n-1\n S=sum(l)\n ans=S\n for i in range(n-2,0,-1):\n dis=(d[i]-d[i+1])*c\n S-=dis\n ans+=S;c-=1\n for i in range(1,n):\n ans+=d[i]-d[i-1]\n print(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n3\\n0 2 3\\n2\\n0 1000000000\\n1\\n0\\n', 'output': '-3\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 2 3\\n2\\n0 1000000000\\n', 'output': '0\\n-3\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 0 3\\n2\\n0 1000000000\\n', 'output': '0\\n-3\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n0 2 3\\n2\\n0 1000010000\\n1\\n0\\n', 'output': '-3\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 2 6\\n2\\n0 1000000000\\n', 'output': '0\\n-6\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n0 1 0\\n2\\n0 1000010000\\n1\\n0\\n', 'output': '-1\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n0 4 3\\n2\\n0 1001000000\\n1\\n0\\n', 'output': '-4\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 2 7\\n2\\n0 1000000000\\n', 'output': '0\\n-7\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 2 1\\n2\\n0 1000000000\\n', 'output': '0\\n-2\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 2 4\\n2\\n0 1001000000\\n', 'output': '0\\n-4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n0 8 3\\n2\\n0 0001000000\\n1\\n0\\n', 'output': '-8\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 2 5\\n2\\n0 1000010000\\n', 'output': '0\\n-5\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n0 2 6\\n2\\n0 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'input': '3\\n1\\n0\\n3\\n0 2 1\\n2\\n0 1000100000\\n', 'output': '0\\n-2\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 2 2\\n2\\n0 1000010000\\n', 'output': '0\\n-2\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n0 5 3\\n2\\n0 0001000000\\n1\\n0\\n', 'output': '-5\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 1 3\\n2\\n0 1001000001\\n', 'output': '0\\n-3\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 1 6\\n2\\n0 1100110000\\n', 'output': '0\\n-6\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n0 8 0\\n2\\n0 0001010000\\n1\\n0\\n', 'output': '-8\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n1 0 5\\n2\\n0 1100010010\\n', 'output': '0\\n-5\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n0\\n3\\n0 3 3\\n2\\n0 1000000100\\n', 'output': '0\\n-3\\n0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78045","program":"```python\nfor _ in range(int(input())):\n n=int(input())\n d=list(map(int,input().split()))\n d=sorted(d)\n if(n==1):\n print(d[n-1])\n continue\n l=[0]\n for i in range(n-2,-1,-1):\n l.append(d[i]-d[n-1])\n c=n-1\n S=sum(l)\n ans=S\n for i in range(n-2,0,-1):\n dis=(d[i]-d[i+1])*c\n S-=dis\n ans+=S;c-=1\n for i in range(1,n):\n ans+=d[i]-d[i-1]\n print(ans)\n```","inputs":"3\n3\n0 2 3\n2\n0 1000000000\n1\n0\n","output":"-3\n0\n0\n","actual_output":"-3\n0\n0\n","execution_success":true,"sample_index":12443},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"169_B. Replacing Digits","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given an integer a that consists of n digits. You are also given a sequence of digits s of length m. The digit in position j (1 \u2264 j \u2264 m) of sequence s means that you can choose an arbitrary position i (1 \u2264 i \u2264 n) in a and replace the digit in the chosen position i with sj. Each element in the sequence s can participate in no more than one replacing operation.\n\nYour task is to perform such sequence of replacements, that the given number a gets maximum value. You are allowed to use not all elements from s.\n\nInput\n\nThe first line contains positive integer a. Its length n is positive and doesn't exceed 105. The second line contains sequence of digits s. Its length m is positive and doesn't exceed 105. The digits in the sequence s are written consecutively without any separators.\n\nThe given number a doesn't contain leading zeroes. \n\nOutput\n\nPrint the maximum value that can be obtained from a after a series of replacements. You are allowed to use not all elements from s. The printed number shouldn't contain any leading zeroes.\n\nExamples\n\nInput\n\n1024\n010\n\n\nOutput\n\n1124\n\n\nInput\n\n987\n1234567\n\n\nOutput\n\n987\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = str(input())\ns = str(input())\nref = 10 * [0]\nfor j in range(len(s)):\n index = ord(s[j]) - 48\n ref[index] += 1\nfor j in range(len(n)):\n output = n[j]\n num = ord(n[j]) - 48\n for k in range(9, num, -1):\n if ref[k] > 0:\n output = str(k)\n ref[k] -= 1\n break\n print(end = output)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '987\\n1234567\\n', 'output': '987\\n'}, {'type': 'stdin_stdout', 'input': '1024\\n010\\n', 'output': '1124\\n'}, {'type': 'stdin_stdout', 'input': '111\\n2222222299999999\\n', 'output': '999\\n'}, {'type': 'stdin_stdout', 'input': '786796787566545376\\n00101\\n', 'output': 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'input': '1\\n219\\n', 'output': '9'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78049","program":"```python\nn = str(input())\ns = str(input())\nref = 10 * [0]\nfor j in range(len(s)):\n index = ord(s[j]) - 48\n ref[index] += 1\nfor j in range(len(n)):\n output = n[j]\n num = ord(n[j]) - 48\n for k in range(9, num, -1):\n if ref[k] > 0:\n output = str(k)\n ref[k] -= 1\n break\n print(end = output)\n\n```","inputs":"987\n1234567\n","output":"987\n","actual_output":"987","execution_success":true,"sample_index":12444},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"212_E. IT Restaurants","prompt":"Solve the following coding problem using the programming language python:\n\n\u0421ity N. has a huge problem with roads, food and IT-infrastructure. In total the city has n junctions, some pairs of them are connected by bidirectional roads. The road network consists of n - 1 roads, you can get from any junction to any other one by these roads. Yes, you're right \u2014 the road network forms an undirected tree.\n\nRecently, the Mayor came up with a way that eliminates the problems with the food and the IT-infrastructure at the same time! He decided to put at the city junctions restaurants of two well-known cafe networks for IT professionals: \"iMac D0naldz\" and \"Burger Bing\". Since the network owners are not friends, it is strictly prohibited to place two restaurants of different networks on neighboring junctions. There are other requirements. Here's the full list:\n\n * each junction must have at most one restaurant; \n * each restaurant belongs either to \"iMac D0naldz\", or to \"Burger Bing\"; \n * each network should build at least one restaurant; \n * there is no pair of junctions that are connected by a road and contains restaurants of different networks. \n\n\n\nThe Mayor is going to take a large tax from each restaurant, so he is interested in making the total number of the restaurants as large as possible.\n\nHelp the Mayor to analyze the situation. Find all such pairs of (a, b) that a restaurants can belong to \"iMac D0naldz\", b restaurants can belong to \"Burger Bing\", and the sum of a + b is as large as possible.\n\nInput\n\nThe first input line contains integer n (3 \u2264 n \u2264 5000) \u2014 the number of junctions in the city. Next n - 1 lines list all roads one per line. Each road is given as a pair of integers xi, yi (1 \u2264 xi, yi \u2264 n) \u2014 the indexes of connected junctions. Consider the junctions indexed from 1 to n.\n\nIt is guaranteed that the given road network is represented by an undirected tree with n vertexes.\n\nOutput\n\nPrint on the first line integer z \u2014 the number of sought pairs. Then print all sought pairs (a, b) in the order of increasing of the first component a.\n\nExamples\n\nInput\n\n5\n1 2\n2 3\n3 4\n4 5\n\n\nOutput\n\n3\n1 3\n2 2\n3 1\n\n\nInput\n\n10\n1 2\n2 3\n3 4\n5 6\n6 7\n7 4\n8 9\n9 10\n10 4\n\n\nOutput\n\n6\n1 8\n2 7\n3 6\n6 3\n7 2\n8 1\n\nNote\n\nThe figure below shows the answers to the first test case. The junctions with \"iMac D0naldz\" restaurants are marked red and \"Burger Bing\" restaurants are marked blue.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom sys import stdin\nn=int(stdin.readline())\ng=[[] for i in range(n)]\nfor _ in range(n-1):\n x,y=map(int,stdin.readline().split())\n x-=1\n y-=1\n g[x].append(y)\n g[y].append(x)\nsubtree_size=[0]*n\nstack=[[-1,0,0]]\nans=[]\nwhile stack:\n par,ver,state=stack.pop()\n if state==0:\n stack.append([par,ver,1])\n for to in g[ver]:\n if to!=par:\n stack.append([ver,to,0])\n else:\n if len(g[ver])==1:\n subtree_size[ver]=1\n else:\n cnt=0\n tmp=[]\n for to in g[ver]:\n if to!=par:\n cnt+=subtree_size[to]\n tmp.append(subtree_size[to])\n tmp.append(n-cnt-1)\n local=[0]*(n+1)\n local[0]=1\n for x in tmp:\n for i in range(n-x,-1,-1):\n if local[i]==1:\n local[i+x]=1\n if x+i!=0 and n-1-(x+i)!=0:\n ans.append(x+i)\n subtree_size[ver]=cnt+1\nans=sorted(list(set(ans)))\nprint(len(ans))\nfor x in ans:\n print(x,n-1-x)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10\\n1 2\\n2 3\\n3 4\\n5 6\\n6 7\\n7 4\\n8 9\\n9 10\\n10 4\\n', 'output': '6\\n1 8\\n2 7\\n3 6\\n6 3\\n7 2\\n8 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2\\n2 3\\n3 4\\n4 5\\n', 'output': '3\\n1 3\\n2 2\\n3 1\\n'}, {'type': 'stdin_stdout', 'input': '11\\n6 11\\n2 9\\n11 3\\n7 10\\n4 6\\n8 3\\n2 5\\n7 9\\n11 2\\n3 1\\n', 'output': '9\\n1 9\\n2 8\\n3 7\\n4 6\\n5 5\\n6 4\\n7 3\\n8 2\\n9 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 5\\n9 7\\n1 6\\n2 5\\n7 4\\n6 10\\n8 3\\n4 3\\n6 7\\n', 'output': '8\\n1 8\\n2 7\\n3 6\\n4 5\\n5 4\\n6 3\\n7 2\\n8 1\\n'}, {'type': 'stdin_stdout', 'input': '18\\n7 12\\n14 8\\n11 4\\n6 3\\n2 3\\n15 10\\n8 16\\n6 16\\n15 18\\n18 16\\n5 9\\n11 17\\n13 9\\n10 7\\n8 9\\n7 1\\n4 3\\n', 'output': '12\\n1 16\\n2 15\\n3 14\\n4 13\\n5 12\\n6 11\\n11 6\\n12 5\\n13 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4\\n6 3\\n2 3\\n15 10\\n8 16\\n6 16\\n15 18\\n18 16\\n5 9\\n8 17\\n13 9\\n10 7\\n8 9\\n7 1\\n4 6\\n', 'output': '12\\n1 16\\n2 15\\n3 14\\n4 13\\n5 12\\n6 11\\n11 6\\n12 5\\n13 4\\n14 3\\n15 2\\n16 1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 1, 'nanos': 500000000}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78057","program":"```python\nfrom sys import stdin\nn=int(stdin.readline())\ng=[[] for i in range(n)]\nfor _ in range(n-1):\n x,y=map(int,stdin.readline().split())\n x-=1\n y-=1\n g[x].append(y)\n g[y].append(x)\nsubtree_size=[0]*n\nstack=[[-1,0,0]]\nans=[]\nwhile stack:\n par,ver,state=stack.pop()\n if state==0:\n stack.append([par,ver,1])\n for to in g[ver]:\n if to!=par:\n stack.append([ver,to,0])\n else:\n if len(g[ver])==1:\n subtree_size[ver]=1\n else:\n cnt=0\n tmp=[]\n for to in g[ver]:\n if to!=par:\n cnt+=subtree_size[to]\n tmp.append(subtree_size[to])\n tmp.append(n-cnt-1)\n local=[0]*(n+1)\n local[0]=1\n for x in tmp:\n for i in range(n-x,-1,-1):\n if local[i]==1:\n local[i+x]=1\n if x+i!=0 and n-1-(x+i)!=0:\n ans.append(x+i)\n subtree_size[ver]=cnt+1\nans=sorted(list(set(ans)))\nprint(len(ans))\nfor x in ans:\n print(x,n-1-x)\n```","inputs":"10\n1 2\n2 3\n3 4\n5 6\n6 7\n7 4\n8 9\n9 10\n10 4\n","output":"6\n1 8\n2 7\n3 6\n6 3\n7 2\n8 1\n","actual_output":"6\n1 8\n2 7\n3 6\n6 3\n7 2\n8 1\n","execution_success":true,"sample_index":12445},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"261_C. Maxim and Matrix","prompt":"Solve the following coding problem using the programming language python:\n\nMaxim loves to fill in a matrix in a special manner. Here is a pseudocode of filling in a matrix of size (m + 1) \u00d7 (m + 1):\n\n\n\nMaxim asks you to count, how many numbers m (1 \u2264 m \u2264 n) are there, such that the sum of values in the cells in the row number m + 1 of the resulting matrix equals t.\n\nExpression (x xor y) means applying the operation of bitwise excluding \"OR\" to numbers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by character \"^\", in Pascal \u2014 by \"xor\".\n\nInput\n\nA single line contains two integers n and t (1 \u2264 n, t \u2264 1012, t \u2264 n + 1).\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\nOutput\n\nIn a single line print a single integer \u2014 the answer to the problem. \n\nExamples\n\nInput\n\n1 1\n\n\nOutput\n\n1\n\n\nInput\n\n3 2\n\n\nOutput\n\n1\n\n\nInput\n\n3 3\n\n\nOutput\n\n0\n\n\nInput\n\n1000000000000 1048576\n\n\nOutput\n\n118606527258\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, t = map(int, input().split())\ns = bin(n + 2)[2:]\nl = len(s)\n\nif t & (t - 1):\n ans = 0\nelse:\n t = t.bit_length()\n f = [[0] * (l + 1) for i in range(l + 1)]\n for i in range(l + 1):\n f[i][0] = f[i][i] = 1\n for j in range(1, i):\n f[i][j] = f[i - 1][j - 1] + f[i - 1][j]\n\n ans = c = 0\n for i in range(l):\n if s[i] == '1':\n if t - c <= l - i - 1:\n ans += f[l - i - 1][t - c]\n c += 1\n if t == 1: ans -= 1\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 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Building Permutation","prompt":"Solve the following coding problem using the programming language python:\n\nPermutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as pi. We'll call number n the size or the length of permutation p1, p2, ..., pn.\n\nYou have a sequence of integers a1, a2, ..., an. In one move, you are allowed to decrease or increase any number by one. Count the minimum number of moves, needed to build a permutation from this sequence.\n\nInput\n\nThe first line contains integer n (1 \u2264 n \u2264 3\u00b7105) \u2014 the size of the sought permutation. The second line contains n integers a1, a2, ..., an ( - 109 \u2264 ai \u2264 109).\n\nOutput\n\nPrint a single number \u2014 the minimum number of moves.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\nExamples\n\nInput\n\n2\n3 0\n\n\nOutput\n\n2\n\n\nInput\n\n3\n-1 -1 2\n\n\nOutput\n\n6\n\nNote\n\nIn the first sample you should decrease the first number by one and then increase the second number by one. The resulting permutation is (2, 1).\n\nIn the second sample you need 6 moves to build permutation (1, 3, 2).\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\nnums = sorted(list(map(int, input().split())))\nscore = 0\nfor i in range(n):\n score+=abs(nums[i]-i-1)\nprint(score)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n-1 -1 2\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n-3 5 -3 3 3\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 6 -2 4 1 1 1 9 6 2\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '100\\n-77 57 -95 -23 53 -28 82 -83 38 -73 85 28 25 6 -43 4 -10 -30 -9 -92 14 34 -93 61 36 -100 90 -68 28 16 100 -3 97 30 36 -55 62 -62 53 74 -50 -23 67 11 22 -30 -19 83 7 84 43 90 -65 -75 -15 97 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'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 -3 -1 1 1 1 2 14 2\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 10 -3 -1 1 1 1 3 14 2\\n', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 112\\n', 'output': '111\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 7\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 112\\n', 'output': '110\\n'}, {'type': 'stdin_stdout', 'input': '9\\n0 -1 1 31 4 15 1 16 2\\n', 'output': '52\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78069","program":"```python\nn = int(input())\nnums = sorted(list(map(int, input().split())))\nscore = 0\nfor i in range(n):\n score+=abs(nums[i]-i-1)\nprint(score)\n\n```","inputs":"3\n-1 -1 2\n","output":"6\n","actual_output":"6\n","execution_success":true,"sample_index":12447},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"30_C. Shooting Gallery","prompt":"Solve the following coding problem using the programming language python:\n\nOne warm and sunny day king Copa decided to visit the shooting gallery, located at the Central Park, and try to win the main prize \u2014 big pink plush panda. The king is not good at shooting, so he invited you to help him.\n\nThe shooting gallery is an infinite vertical plane with Cartesian coordinate system on it. The targets are points on this plane. Each target is described by it's coordinates xi, and yi, by the time of it's appearance ti and by the number pi, which gives the probability that Copa hits this target if he aims at it.\n\nA target appears and disappears instantly, so Copa can hit the target only if at the moment ti his gun sight aimed at (xi, yi). Speed of movement of the gun sight on the plane is equal to 1. Copa knows all the information about the targets beforehand (remember, he is a king!). He wants to play in the optimal way, which maximizes the expected value of the amount of hit targets. He can aim at any target at the moment 0.\n\nInput\n\nThe first line contains integer n (1 \u2264 n \u2264 1000) \u2014 amount of targets in the shooting gallery. Then n lines follow, each describing one target. Each description consists of four numbers xi, yi, ti, pi (where xi, yi, ti \u2014 integers, - 1000 \u2264 xi, yi \u2264 1000, 0 \u2264 ti \u2264 109, real number pi is given with no more than 6 digits after the decimal point, 0 \u2264 pi \u2264 1). No two targets may be at the same point.\n\nOutput\n\nOutput the maximum expected value of the amount of targets that was shot by the king. Your answer will be accepted if it differs from the correct answer by not more than 10 - 6.\n\nExamples\n\nInput\n\n1\n0 0 0 0.5\n\n\nOutput\n\n0.5000000000\n\n\nInput\n\n2\n0 0 0 0.6\n5 0 5 0.7\n\n\nOutput\n\n1.3000000000\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n##########################################################\nfrom collections import Counter\ndef nCk(n, k):\n res = 1\n for i in range(1, k + 1):\n res = res * (n - i + 1) // i\n return res\nimport math\ninf=10**20\nn=int(input())\nc=[]\ndp=[0]*(n+1)\nfor i in range(n):\n x,y, t,p = map(float, input().split())\n c.append([int(x),int(y),int(t),p])\n\nc.sort(key=lambda x:x[2])\n\nfor i in range(n):\n dp[i]=c[i][3]\n for j in range(i):\n if (c[i][0]-c[j][0])**2+(c[i][1]-c[j][1])**2 <= (c[i][2]-c[j][2])**2:\n dp[i]=max(dp[i],dp[j]+c[i][-1])\nprint(max(dp))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n0 0 0 0.5\\n', 'output': '0.5'}, {'type': 'stdin_stdout', 'input': '2\\n0 0 0 0.6\\n5 0 5 0.7\\n', 'output': '1.3'}, {'type': 'stdin_stdout', 'input': '10\\n-4 7 39 0.921693\\n3 -1 50 0.111185\\n-2 -8 27 0.976475\\n-9 -2 25 0.541029\\n6 -4 21 0.526054\\n-7 2 19 0.488637\\n-6 -5 50 0.819011\\n-7 3 39 0.987596\\n-3 -8 16 0.685997\\n4 10 1 0.246686\\n', 'output': '3.082959'}, {'type': 'stdin_stdout', 'input': '1\\n-5 2 3 0.886986\\n', 'output': '0.886986'}, {'type': 'stdin_stdout', 'input': '5\\n2 5 1 0.955925\\n9 -9 14 0.299977\\n0 1 97 0.114582\\n-4 -2 66 0.561033\\n0 -10 75 0.135937\\n', 'output': '1.767477'}, {'type': 'stdin_stdout', 'input': '4\\n10 -7 14 0.926305\\n-7 -8 12 0.121809\\n-7 7 14 0.413446\\n3 -8 6 0.859061\\n', 'output': '1.785366'}, {'type': 'stdin_stdout', 'input': '5\\n-2 -2 34 0.127276\\n5 -5 4 0.459998\\n10 3 15 0.293766\\n1 -3 7 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'output': '1.276103124742118\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 5 1 0.9678010160260926\\n11 -9 14 0.299977\\n0 1 68 0.5244127011989688\\n-4 0 36 0.561033\\n0 -20 75 0.5438733136672839\\n', 'output': '2.0727073296933765\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78073","program":"```python\n##########################################################\nfrom collections import Counter\ndef nCk(n, k):\n res = 1\n for i in range(1, k + 1):\n res = res * (n - i + 1) // i\n return res\nimport math\ninf=10**20\nn=int(input())\nc=[]\ndp=[0]*(n+1)\nfor i in range(n):\n x,y, t,p = map(float, input().split())\n c.append([int(x),int(y),int(t),p])\n\nc.sort(key=lambda x:x[2])\n\nfor i in range(n):\n dp[i]=c[i][3]\n for j in range(i):\n if (c[i][0]-c[j][0])**2+(c[i][1]-c[j][1])**2 <= (c[i][2]-c[j][2])**2:\n dp[i]=max(dp[i],dp[j]+c[i][-1])\nprint(max(dp))\n```","inputs":"1\n0 0 0 0.5\n","output":"0.5","actual_output":"0.5\n","execution_success":true,"sample_index":12448},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"333_A. Secrets","prompt":"Solve the following coding problem using the programming language python:\n\nGerald has been selling state secrets at leisure. All the secrets cost the same: n marks. The state which secrets Gerald is selling, has no paper money, only coins. But there are coins of all positive integer denominations that are powers of three: 1 mark, 3 marks, 9 marks, 27 marks and so on. There are no coins of other denominations. Of course, Gerald likes it when he gets money without the change. And all buyers respect him and try to give the desired sum without change, if possible. But this does not always happen.\n\nOne day an unlucky buyer came. He did not have the desired sum without change. Then he took out all his coins and tried to give Gerald a larger than necessary sum with as few coins as possible. What is the maximum number of coins he could get?\n\nThe formal explanation of the previous paragraph: we consider all the possible combinations of coins for which the buyer can not give Gerald the sum of n marks without change. For each such combination calculate the minimum number of coins that can bring the buyer at least n marks. Among all combinations choose the maximum of the minimum number of coins. This is the number we want.\n\nInput\n\nThe single line contains a single integer n (1 \u2264 n \u2264 1017).\n\nPlease, do not use the %lld specifier to read or write 64 bit integers in \u0421++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\nOutput\n\nIn a single line print an integer: the maximum number of coins the unlucky buyer could have paid with.\n\nExamples\n\nInput\n\n1\n\n\nOutput\n\n1\n\n\nInput\n\n4\n\n\nOutput\n\n2\n\nNote\n\nIn the first test case, if a buyer has exactly one coin of at least 3 marks, then, to give Gerald one mark, he will have to give this coin. In this sample, the customer can not have a coin of one mark, as in this case, he will be able to give the money to Gerald without any change.\n\nIn the second test case, if the buyer had exactly three coins of 3 marks, then, to give Gerald 4 marks, he will have to give two of these coins. The buyer cannot give three coins as he wants to minimize the number of coins that he gives.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\nn = int(input())\na=1\nwhile n%a==0:\n a*=3\nprint(n//a +1) \n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n', 'output': ' 2'}, {'type': 'stdin_stdout', 'input': '1\\n', 'output': ' 1'}, {'type': 'stdin_stdout', 'input': '100000000000000000\\n', 'output': '33333333333333334\\n'}, {'type': 'stdin_stdout', 'input': '29442431889534807\\n', 'output': '48\\n'}, {'type': 'stdin_stdout', 'input': '34391854792828422\\n', 'output': '582429080812\\n'}, {'type': 'stdin_stdout', 'input': '99999999999999999\\n', 'output': '3703703703703704\\n'}, {'type': 'stdin_stdout', 'input': '3\\n', 'output': ' 1'}, {'type': 'stdin_stdout', 'input': '58061299250691018\\n', 'output': '32\\n'}, 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256000000}","problem_id":"vfc_78077","program":"```python\nimport math\nn = int(input())\na=1\nwhile n%a==0:\n a*=3\nprint(n//a +1) \n\n```","inputs":"4\n","output":" 2","actual_output":"2\n","execution_success":true,"sample_index":12449},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"356_A. Knight Tournament","prompt":"Solve the following coding problem using the programming language python:\n\nHooray! Berl II, the king of Berland is making a knight tournament. The king has already sent the message to all knights in the kingdom and they in turn agreed to participate in this grand event.\n\nAs for you, you're just a simple peasant. There's no surprise that you slept in this morning and were late for the tournament (it was a weekend, after all). Now you are really curious about the results of the tournament. This time the tournament in Berland went as follows:\n\n * There are n knights participating in the tournament. Each knight was assigned his unique number \u2014 an integer from 1 to n. \n * The tournament consisted of m fights, in the i-th fight the knights that were still in the game with numbers at least li and at most ri have fought for the right to continue taking part in the tournament. \n * After the i-th fight among all participants of the fight only one knight won \u2014 the knight number xi, he continued participating in the tournament. Other knights left the tournament. \n * The winner of the last (the m-th) fight (the knight number xm) became the winner of the tournament. \n\n\n\nYou fished out all the information about the fights from your friends. Now for each knight you want to know the name of the knight he was conquered by. We think that the knight number b was conquered by the knight number a, if there was a fight with both of these knights present and the winner was the knight number a.\n\nWrite the code that calculates for each knight, the name of the knight that beat him.\n\nInput\n\nThe first line contains two integers n, m (2 \u2264 n \u2264 3\u00b7105; 1 \u2264 m \u2264 3\u00b7105) \u2014 the number of knights and the number of fights. Each of the following m lines contains three integers li, ri, xi (1 \u2264 li < ri \u2264 n; li \u2264 xi \u2264 ri) \u2014 the description of the i-th fight.\n\nIt is guaranteed that the input is correct and matches the problem statement. It is guaranteed that at least two knights took part in each battle.\n\nOutput\n\nPrint n integers. If the i-th knight lost, then the i-th number should equal the number of the knight that beat the knight number i. If the i-th knight is the winner, then the i-th number must equal 0.\n\nExamples\n\nInput\n\n4 3\n1 2 1\n1 3 3\n1 4 4\n\n\nOutput\n\n3 1 4 0 \n\nInput\n\n8 4\n3 5 4\n3 7 6\n2 8 8\n1 8 1\n\n\nOutput\n\n0 8 4 6 4 8 6 1 \n\nNote\n\nConsider the first test case. Knights 1 and 2 fought the first fight and knight 1 won. Knights 1 and 3 fought the second fight and knight 3 won. The last fight was between knights 3 and 4, knight 4 won.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#!/usr/bin/env python\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n\n\nBUFSIZE = 8192\n\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\n\n\ndef input(): return sys.stdin.readline().rstrip(\"\\r\\n\")\n\n\nclass SegmentTree:\n def __init__(self, n):\n self.tree = [0] * (2 * n)\n self.n = n\n\n # get interval[l,r)\n def query(self, l, r, val):\n l += self.n\n r += self.n\n while l < r:\n if l % 2 == 1:\n self.tree[l] = val\n l += 1\n\n if r % 2 == 1:\n r -= 1\n self.tree[r] = val\n\n l //= 2\n r //= 2\n\n def search(self, idx):\n idx += self.n\n res = [0, 0]\n while idx > 1:\n if self.tree[idx] and self.tree[idx][1] >= res[1]:\n res = self.tree[idx].copy()\n idx //= 2\n\n return res\n\n# submission 72248479\n\n\ndef solve1(n, fights):\n ans = [0] * (n + 1)\n tree = SegmentTree(n)\n c = 0\n for l, r, x in (fights[::-1]):\n tree.query(l - 1, x - 1, [x, c])\n tree.query(x, r, [x, c])\n c += 1\n\n for i in range(n):\n if fights[-1][2] != i + 1:\n ans[i + 1] = tree.search(i)[0]\n\n return ans[1:]\n\n\n# submission 42135285\ndef solve2(n, fights):\n ans = [0] * (n + 2)\n\n # if knight v is alive, then next[v]\u2009=\u2009v\n # if knight v is out of tournament, next[v] points\n # to some knight u (next[v]\u2009=\u2009u), such that there\n # are no alive knights between v and u;\n nxt = list(range(1, n + 3))\n\n for l, r, x in fights:\n while l < x: # knights in the interval with idx below the winner\n if ans[l]: # it is already beaten\n k = nxt[l] # store who did beat him\n nxt[l] = x # the next alive from l is current winner\n l = k # next iteration start from k since l+1..k-1 are beaten\n else: # he's alive\n nxt[l] = x # next alive from l is the current winner\n ans[l] = x\n l += 1\n\n l += 1 # l = x + 1\n\n # find out after the interval who is the next alive\n # last elm of ans handles the case when the current knight is the last\n # knight and is out of tournament\n r += 1\n while ans[r]:\n r = nxt[r]\n\n while l < r: # knights from x + 1 to the end\n if ans[l]: # it is already beaten\n k = nxt[l] # store who did beat him\n nxt[l] = r # the next alive from l is r\n l = k # next iteration start from k since l+1..k-1 are beaten\n else: # he is alive\n nxt[l] = r # next alive is r\n ans[l] = x # he's beaten by x\n l += 1\n\n return ans[1:-1]\n\n\ndef read():\n return list(map(int, input().split()))\n\n\ndef main():\n n, m = read()\n fights = [read() for _ in range(m)]\n ans = solve1(n, fights)\n print(*ans)\n\n\nif __name__ == \"__main__\":\n main()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 3\\n1 2 1\\n1 3 3\\n1 4 4\\n', 'output': '3 1 4 0 \\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n3 5 4\\n3 7 6\\n2 8 8\\n1 8 1\\n', 'output': '0 8 4 6 4 8 6 1 \\n'}, {'type': 'stdin_stdout', 'input': '10 7\\n7 8 7\\n7 9 9\\n5 9 5\\n5 10 10\\n1 2 2\\n3 4 4\\n2 10 4\\n', 'output': '2 4 4 0 10 5 9 7 5 4 \\n'}, {'type': 'stdin_stdout', 'input': '11 5\\n8 10 9\\n6 10 7\\n6 11 11\\n3 5 5\\n1 11 1\\n', 'output': '0 1 5 5 1 7 11 9 7 9 1 \\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 3 2\\n', 'output': '2 0 2 \\n'}, {'type': 'stdin_stdout', 'input': '11 7\\n7 8 8\\n5 6 5\\n1 3 3\\n7 9 9\\n5 10 10\\n10 11 11\\n1 11 4\\n', 'output': '3 3 4 0 10 5 8 9 10 11 4 \\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n1 2 2\\n', 'output': '2 0 \\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 2\\n1 3 3\\n1 4 4\\n', 'output': '2 3 4 0 \\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 2\\n7 8 7\\n3 4 4\\n6 9 6\\n5 10 10\\n2 11 11\\n', 'output': '2 11 4 11 10 10 6 7 6 11 0 \\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 2\\n1 3 2\\n', 'output': '2 0 2 \\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n6 7 6\\n5 7 5\\n3 7 4\\n2 8 2\\n2 10 10\\n1 10 10\\n', 'output': '10 10 4 2 4 5 6 2 10 0 \\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 3 3\\n1 3 3\\n', 'output': '3 3 0 \\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n1 2 1\\n8 10 8\\n3 6 4\\n4 7 7\\n1 8 7\\n', 'output': '7 1 4 7 4 4 0 7 8 8 \\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 3 3\\n', 'output': '3 3 0 \\n'}, {'type': 'stdin_stdout', 'input': '10 7\\n8 9 9\\n3 4 3\\n2 3 2\\n1 5 2\\n6 7 6\\n6 10 10\\n1 10 10\\n', 'output': '2 10 2 3 2 10 6 9 10 0 \\n'}, {'type': 'stdin_stdout', 'input': '11 8\\n3 5 5\\n8 9 9\\n4 6 6\\n8 10 10\\n5 7 7\\n2 7 2\\n10 11 11\\n1 11 1\\n', 'output': '0 1 5 5 6 7 2 9 10 11 1 \\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n1 2 1\\n', 'output': '0 1 \\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 3 1\\n', 'output': '0 1 1 \\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 1\\n1 3 3\\n', 'output': '3 1 0 \\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 1\\n8 9 9\\n3 5 5\\n3 6 6\\n9 10 10\\n1 11 10\\n', 'output': '10 1 5 5 6 10 10 9 10 0 10 \\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n9 10 10\\n6 7 7\\n2 4 2\\n2 5 5\\n1 7 5\\n4 10 8\\n', 'output': '5 5 2 2 8 7 5 0 10 8 \\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 2\\n1 3 3\\n1 3 4\\n', 'output': '2 3 4 0\\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n1 2 1\\n8 10 8\\n3 5 4\\n4 7 7\\n1 8 7\\n', 'output': '7 1 4 7 4 7 0 7 8 8\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 1\\n8 9 9\\n3 5 5\\n3 6 6\\n4 10 10\\n1 11 10\\n', 'output': '10 1 5 5 6 10 10 9 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '10 7\\n7 8 7\\n7 9 9\\n5 9 5\\n5 10 10\\n1 2 2\\n1 4 4\\n2 10 4\\n', 'output': '2 4 4 0 10 5 9 7 5 4\\n'}, {'type': 'stdin_stdout', 'input': '11 5\\n8 10 9\\n6 10 7\\n6 11 11\\n4 5 5\\n1 11 1\\n', 'output': '0 1 1 5 1 7 11 9 7 9 1\\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n6 6 6\\n5 7 5\\n3 7 4\\n2 8 2\\n2 10 10\\n1 10 10\\n', 'output': '10 10 4 2 4 5 5 2 10 0\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 2\\n8 9 9\\n3 5 5\\n3 6 6\\n9 10 10\\n1 11 10\\n', 'output': '2 10 5 5 6 10 10 9 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 2\\n1 3 3\\n', 'output': '2 3 0\\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n3 5 4\\n2 7 6\\n2 8 8\\n1 8 1\\n', 'output': '0 6 4 6 4 8 6 1\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 1\\n9 9 9\\n3 5 5\\n3 6 6\\n4 10 10\\n1 11 10\\n', 'output': '10 1 5 5 6 10 10 10 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n6 7 6\\n5 7 5\\n3 7 2\\n2 8 2\\n2 10 10\\n1 10 10\\n', 'output': '10 10 2 2 2 5 6 2 10 0\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 2\\n9 9 9\\n3 5 5\\n3 6 6\\n4 10 10\\n1 11 10\\n', 'output': '2 10 5 5 6 10 10 10 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 2\\n1 3 3\\n1 4 3\\n', 'output': '2 3 0 3\\n'}, {'type': 'stdin_stdout', 'input': '10 7\\n8 9 9\\n3 4 3\\n2 5 2\\n1 5 2\\n6 7 6\\n6 10 10\\n1 10 10\\n', 'output': '2 10 2 3 2 10 6 9 10 0\\n'}, {'type': 'stdin_stdout', 'input': '10 7\\n7 8 7\\n7 9 9\\n5 9 5\\n5 10 10\\n2 2 2\\n1 4 4\\n2 10 4\\n', 'output': '4 4 4 0 10 5 9 7 5 4\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n2 2 2\\n1 3 3\\n1 4 4\\n', 'output': '3 3 4 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2 2\\n2 3 2\\n', 'output': '2 0 2\\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n6 8 6\\n5 7 5\\n3 7 4\\n2 8 2\\n2 10 10\\n1 10 10\\n', 'output': '10 10 4 2 4 5 6 6 10 0\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 1\\n9 9 9\\n3 5 5\\n1 6 6\\n4 10 10\\n1 11 10\\n', 'output': '6 1 5 5 6 10 10 10 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n6 7 6\\n5 9 5\\n3 7 2\\n2 8 2\\n2 10 10\\n1 10 10\\n', 'output': '10 10 2 2 2 5 6 5 5 0\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 2\\n9 9 9\\n3 5 5\\n6 6 6\\n4 10 10\\n1 11 10\\n', 'output': '2 10 5 5 10 10 10 10 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 1\\n1 3 3\\n1 4 3\\n', 'output': '3 1 0 3\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 1 1\\n8 9 9\\n3 5 5\\n3 6 6\\n9 10 10\\n1 11 10\\n', 'output': '10 10 5 5 6 10 10 9 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n3 5 4\\n3 7 7\\n2 8 8\\n1 8 1\\n', 'output': '0 8 4 7 4 7 8 1\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 1 1\\n9 9 9\\n3 5 5\\n1 6 6\\n4 10 10\\n1 11 10\\n', 'output': '6 6 5 5 6 10 10 10 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 2\\n7 8 7\\n3 4 4\\n6 9 6\\n2 10 10\\n2 11 11\\n', 'output': '2 10 4 10 10 10 6 7 6 11 0\\n'}, {'type': 'stdin_stdout', 'input': '11 8\\n3 5 5\\n8 9 9\\n4 6 6\\n8 10 10\\n4 7 7\\n2 7 2\\n10 11 11\\n1 11 1\\n', 'output': '0 1 5 5 6 7 2 9 10 11 1\\n'}, {'type': 'stdin_stdout', 'input': '10 7\\n6 8 7\\n7 9 9\\n5 9 5\\n5 10 10\\n1 2 2\\n1 4 4\\n2 10 4\\n', 'output': '2 4 4 0 10 7 9 7 5 4\\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n2 5 4\\n2 7 6\\n2 8 8\\n1 8 1\\n', 'output': '0 4 4 6 4 8 6 1\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 1 1\\n8 9 9\\n3 5 5\\n3 7 6\\n9 10 10\\n1 11 10\\n', 'output': '10 10 5 5 6 10 6 9 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n3 5 4\\n6 7 7\\n2 8 8\\n1 8 1\\n', 'output': '0 8 4 8 4 7 8 1\\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n1 2 1\\n8 10 8\\n4 6 4\\n4 7 7\\n1 8 7\\n', 'output': '7 1 7 7 4 4 0 7 8 8\\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n3 5 3\\n3 7 6\\n2 8 8\\n1 8 1\\n', 'output': '0 8 6 3 3 8 6 1\\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n1 2 1\\n8 10 8\\n3 5 5\\n4 7 7\\n1 8 7\\n', 'output': '7 1 5 5 7 7 0 7 8 8\\n'}, {'type': 'stdin_stdout', 'input': '11 5\\n8 10 9\\n6 10 7\\n6 11 11\\n4 5 4\\n1 11 1\\n', 'output': '0 1 1 1 4 7 11 9 7 9 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 2 2\\n1 3 3\\n', 'output': '3 3 0\\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n6 6 6\\n5 7 5\\n3 5 4\\n2 5 2\\n2 10 10\\n1 10 10\\n', 'output': '10 10 4 2 4 5 5 10 10 0\\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n6 7 5\\n5 7 5\\n3 7 4\\n2 8 2\\n2 10 10\\n1 10 10\\n', 'output': '10 10 4 2 4 5 5 2 10 0\\n'}, {'type': 'stdin_stdout', 'input': '10 7\\n8 9 9\\n3 4 3\\n3 5 2\\n1 5 2\\n6 7 6\\n6 10 10\\n1 10 10\\n', 'output': '2 10 2 3 2 10 6 9 10 0\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 1\\n9 9 9\\n3 5 5\\n3 6 6\\n2 10 10\\n1 11 10\\n', 'output': '10 1 5 5 6 10 10 10 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 2\\n2 3 3\\n1 3 4\\n', 'output': '2 3 4 0\\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n6 6 6\\n5 7 5\\n3 5 4\\n2 8 2\\n2 10 10\\n1 10 10\\n', 'output': '10 10 4 2 4 5 5 2 10 0\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 2\\n2 3 3\\n2 3 4\\n', 'output': '2 3 4 0\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 2\\n1 3 3\\n2 3 4\\n', 'output': '2 3 4 0\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 2\\n2 3 3\\n1 4 4\\n', 'output': '2 3 4 0\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 2\\n2 3 3\\n1 4 3\\n', 'output': '2 3 0 3\\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n6 8 6\\n5 7 5\\n3 7 4\\n2 8 2\\n4 10 10\\n1 10 10\\n', 'output': '10 10 4 2 4 5 6 6 10 0\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 1 1\\n8 9 9\\n3 5 5\\n3 6 6\\n4 10 10\\n1 11 10\\n', 'output': '10 10 5 5 6 10 10 9 10 0 10\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n2 2 2\\n1 3 3\\n2 4 4\\n', 'output': '3 3 4 0\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n1 2 2\\n9 9 9\\n3 5 5\\n6 6 6\\n2 10 10\\n1 11 10\\n', 'output': '2 10 5 5 10 10 10 10 10 0 10\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78081","program":"```python\n#!/usr/bin/env python\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n\n\nBUFSIZE = 8192\n\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\n\n\ndef input(): return sys.stdin.readline().rstrip(\"\\r\\n\")\n\n\nclass SegmentTree:\n def __init__(self, n):\n self.tree = [0] * (2 * n)\n self.n = n\n\n # get interval[l,r)\n def query(self, l, r, val):\n l += self.n\n r += self.n\n while l < r:\n if l % 2 == 1:\n self.tree[l] = val\n l += 1\n\n if r % 2 == 1:\n r -= 1\n self.tree[r] = val\n\n l //= 2\n r //= 2\n\n def search(self, idx):\n idx += self.n\n res = [0, 0]\n while idx > 1:\n if self.tree[idx] and self.tree[idx][1] >= res[1]:\n res = self.tree[idx].copy()\n idx //= 2\n\n return res\n\n# submission 72248479\n\n\ndef solve1(n, fights):\n ans = [0] * (n + 1)\n tree = SegmentTree(n)\n c = 0\n for l, r, x in (fights[::-1]):\n tree.query(l - 1, x - 1, [x, c])\n tree.query(x, r, [x, c])\n c += 1\n\n for i in range(n):\n if fights[-1][2] != i + 1:\n ans[i + 1] = tree.search(i)[0]\n\n return ans[1:]\n\n\n# submission 42135285\ndef solve2(n, fights):\n ans = [0] * (n + 2)\n\n # if knight v is alive, then next[v]\u2009=\u2009v\n # if knight v is out of tournament, next[v] points\n # to some knight u (next[v]\u2009=\u2009u), such that there\n # are no alive knights between v and u;\n nxt = list(range(1, n + 3))\n\n for l, r, x in fights:\n while l < x: # knights in the interval with idx below the winner\n if ans[l]: # it is already beaten\n k = nxt[l] # store who did beat him\n nxt[l] = x # the next alive from l is current winner\n l = k # next iteration start from k since l+1..k-1 are beaten\n else: # he's alive\n nxt[l] = x # next alive from l is the current winner\n ans[l] = x\n l += 1\n\n l += 1 # l = x + 1\n\n # find out after the interval who is the next alive\n # last elm of ans handles the case when the current knight is the last\n # knight and is out of tournament\n r += 1\n while ans[r]:\n r = nxt[r]\n\n while l < r: # knights from x + 1 to the end\n if ans[l]: # it is already beaten\n k = nxt[l] # store who did beat him\n nxt[l] = r # the next alive from l is r\n l = k # next iteration start from k since l+1..k-1 are beaten\n else: # he is alive\n nxt[l] = r # next alive is r\n ans[l] = x # he's beaten by x\n l += 1\n\n return ans[1:-1]\n\n\ndef read():\n return list(map(int, input().split()))\n\n\ndef main():\n n, m = read()\n fights = [read() for _ in range(m)]\n ans = solve1(n, fights)\n print(*ans)\n\n\nif __name__ == \"__main__\":\n main()\n\n```","inputs":"4 3\n1 2 1\n1 3 3\n1 4 4\n","output":"3 1 4 0 \n","actual_output":"3 1 4 0\n","execution_success":true,"sample_index":12450},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"3_C. Tic-tac-toe","prompt":"Solve the following coding problem using the programming language python:\n\nCertainly, everyone is familiar with tic-tac-toe game. The rules are very simple indeed. Two players take turns marking the cells in a 3 \u00d7 3 grid (one player always draws crosses, the other \u2014 noughts). The player who succeeds first in placing three of his marks in a horizontal, vertical or diagonal line wins, and the game is finished. The player who draws crosses goes first. If the grid is filled, but neither Xs, nor 0s form the required line, a draw is announced.\n\nYou are given a 3 \u00d7 3 grid, each grid cell is empty, or occupied by a cross or a nought. You have to find the player (first or second), whose turn is next, or print one of the verdicts below: \n\n * illegal \u2014 if the given board layout can't appear during a valid game; \n * the first player won \u2014 if in the given board layout the first player has just won; \n * the second player won \u2014 if in the given board layout the second player has just won; \n * draw \u2014 if the given board layout has just let to a draw. \n\nInput\n\nThe input consists of three lines, each of the lines contains characters \".\", \"X\" or \"0\" (a period, a capital letter X, or a digit zero).\n\nOutput\n\nPrint one of the six verdicts: first, second, illegal, the first player won, the second player won or draw.\n\nExamples\n\nInput\n\nX0X\n.0.\n.X.\n\n\nOutput\n\nsecond\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfirst_row = input()\nsecond_row = input()\nthird_row = input()\nc = 0\no = 0\nfor i in range(0,3):\n if first_row[i] == 'X':\n c = c + 1\n elif first_row[i] == '0':\n o = o + 1\nfor i in range(0,3):\n if second_row[i] == 'X':\n c = c + 1\n elif second_row[i] == '0':\n o = o + 1\nfor i in range(0,3):\n if third_row[i] == 'X':\n c = c + 1\n elif third_row[i] == '0':\n o = o + 1\n\nr = 0\nif first_row[0] == \"X\" and second_row[1] == \"X\" and third_row[2] == \"X\":\n r = 1+r\nif first_row[0] == \"X\" and second_row[0] == \"X\" and third_row[0] ==\"X\":\n r = 1+r\nif first_row[0] == \"X\" and first_row[1] == \"X\" and first_row[2]== \"X\":\n r = 1+r\nif first_row[1] == \"X\" and second_row[1] == \"X\" and third_row[1] == \"X\":\n r = 1+r\nif first_row[2] == \"X\" and second_row[2] == \"X\" and third_row[2] == \"X\":\n r = 1+r\nif first_row[2] == \"X\" and second_row[1] == \"X\" and third_row[0] == \"X\":\n r = 1+r\nif second_row[0] == \"X\" and second_row[1] == \"X\" and second_row[2] == \"X\":\n r = r + 1\nif third_row[0] == \"X\" and third_row[1] == \"X\" and third_row[2] == \"X\":\n r = r + 1\n \nq = 0\nif first_row[0] == \"0\" and second_row[1] == \"0\" and third_row[2] == \"0\":\n q = 1+q\nif first_row[0] == \"0\" and second_row[0] == \"0\" and third_row[0] ==\"0\":\n q = 1+q\nif first_row[0] == \"0\" and first_row[1] == \"0\" and first_row[2] == \"0\":\n q = q + 1\nif first_row[1] == \"0\" and second_row[1] == \"0\" and third_row[1]== \"0\":\n q = 1 + q\n\nif first_row[2] == \"0\" and second_row[2] == \"0\" and third_row[2] == \"0\":\n q = 1 + q\nif first_row[2] == \"0\" and second_row[1] == \"0\" and third_row[0] == \"0\":\n q = 1 + q\nif second_row[0] == \"0\" and second_row[1] == \"0\" and second_row[2] == \"0\":\n q = q + 1\nif third_row[0] == \"0\" and third_row[1] == \"0\" and third_row[2] == \"0\":\n q = q + 1 \n \nif first_row[0] == \"X\" and first_row[2] == \"X\" and third_row[0] == \"X\" and third_row[2] == \"X\" and first_row[1] == \"0\" and second_row[0] == \"0\" and second_row[2] == \"0\" and third_row[1] == \"0\" and second_row[1] == \"X\":\n print(\"the first player won\")\nelif first_row[0] == \"X\" and first_row[1] == \"X\" and third_row[2] == \"X\" and second_row[2] == \"X\" and second_row[1] == \"0\" and third_row[1] == \"0\" and third_row[0] == \"0\" and second_row[0] == \"0\" and first_row[2] == \"X\":\n print(\"the first player won\")\nelif first_row[2] == \"0\" and first_row[1] == \"0\" and first_row[0] == \"X\" and second_row[2] == \"0\" and second_row[1] == \"0\" and third_row[1] == \"X\" and third_row[2] == \"X\" and second_row[0] == \"X\" and third_row[0] == \"X\":\n print(\"the first player won\")\nelif first_row[2] == \"0\" and first_row[1] == \"X\" and first_row[0] == \"0\" and second_row[2] == \"X\" and second_row[0] == \"X\" and third_row[1] == \"X\" and third_row[2] == \"0\" and third_row[0] == \"0\" and second_row[1] == \"X\":\n print(\"the first player won\")\nelif first_row[2] == \"0\" and first_row[1] == \"0\" and first_row[0] == \"X\" and second_row[2] == \"X\" and second_row[1] == \"X\" and third_row[1] == \"0\" and third_row[2] == \"0\" and third_row[0] == \"X\" and second_row[0] == \"X\":\n print(\"the first player won\")\nelif first_row[2] == \"X\" and first_row[1] == \"0\" and first_row[0] == \"0\" and second_row[0] == \"X\" and second_row[1] == \"X\" and third_row[1] == \"0\" and third_row[2] == \"X\" and third_row[0] == \"0\" and second_row[2] == \"X\":\n print(\"the first player won\")\nelif first_row[0] == \"X\" and first_row[1] == \"X\" and first_row[2] == \"X\" and second_row[2] == \"0\" and second_row[0] == \"X\" and second_row[2] == \"0\" and third_row[0] == \"X\" and third_row[1] == \"0\" and third_row[2] == \"0\": \n print(\"the first player won\")\nelif c-o > 1 or (o-c) >= 1 or (r==1 and q == 1):\n print(\"illegal\")\nelif q >= 1 and r == 0:\n if c == o:\n print(\"the second player won\")\n else:\n print(\"illegal\")\nelif r >= 1 and q == 0:\n if c-1 == o:\n print(\"the first player won\")\n else:\n print(\"illegal\")\nelif c - o == 1 and o+c != 9:\n print(\"second\")\nelif c-o == 0:\n print(\"first\")\nelse:\n print(\"draw\")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'X0X\\n.0.\\n.X.\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': '0X0\\nX0X\\n0X.\\n', 'output': 'the second player won\\n'}, {'type': 'stdin_stdout', 'input': '..0\\nXX.\\n00X\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': '.0.\\nX.X\\n0..\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': '00.\\n00.\\nX.X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'XXX\\n.00\\nX0.\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '0X.\\n.X.\\n0X0\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '.00\\nX.X\\n0..\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X0X\\n...\\n.X.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 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'illegal\\n'}, {'type': 'stdin_stdout', 'input': '0..\\n000\\n...\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'XXX\\n0.0\\n0..\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '0..\\n000\\nX0X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X0X\\nXXX\\nX.X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\n..0\\nX.X\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': 'XX0\\nX..\\nX00\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': 'X0X\\n0X0\\n..X\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': 'XXX\\nX..\\n.00\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\n.XX\\n00.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '.XX\\n000\\nXX0\\n', 'output': 'the second player won\\n'}, {'type': 'stdin_stdout', 'input': 'X0.\\nX.X\\nX00\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '.0X\\n.00\\n00.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '0.X\\n0X0\\n.00\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X.X\\nX.0\\n0.0\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': '00.\\n00.\\n.X.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X.0\\nX0.\\n0X.\\n', 'output': 'the second player won\\n'}, {'type': 'stdin_stdout', 'input': '.XX\\n.0.\\nX0X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\n0.0\\nXX0\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X.X\\n0X.\\n.0X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'XX0\\n0..\\n000\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'XXX\\nX.0\\n0.0\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': 'X.X\\nX..\\n00.\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': 'X0X\\n0X0\\nX0X\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\nXX.\\n0.X\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '000\\n000\\n000\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X0X\\n0X0\\nX..\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '0X0\\nXX0\\n.X.\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '0XX\\n.X0\\n0.0\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '0.0\\nX.X\\nXX.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X.0\\n00.\\nXXX\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '0XX\\nX0X\\n00X\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '..0\\n.00\\n.0X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'XXX\\n0..\\n.0.\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '.XX\\nXXX\\n0..\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '.0.\\nX0X\\nX00\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'XX.\\nX0X\\nX..\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '.0.\\nXX.\\n00X\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': 'XXX\\n.00\\n.0X\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '.00\\nX.X\\n..0\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '..0\\nX0X\\n..X\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': 'X.0\\nXX0\\n..0\\n', 'output': 'the second player won\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\n0.X\\n00X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X0X\\n.0X\\n0..\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': 'X..\\n.X0\\n.0X\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '.0X\\n.X.\\nX0.\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '0XX\\nXXX\\n0X0\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X0.\\n.X0\\n..X\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '0X.\\nX.0\\nX..\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\n0XX\\n00X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '..0\\n0.0\\n0.X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'XXX\\n00X\\nX00\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '00X\\nX0X\\n0X.\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': '.X0\\n...\\n0.X\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': '..X\\n00X\\n0X.\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': 'X..\\n00X\\nX.0\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\nX00\\n.0X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '..0\\nXX0\\n...\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': '.X0\\n00.\\n.X.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'XX0\\n.X.\\nXX0\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '0X.\\n..X\\n.X.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\nX0.\\nX.0\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X..\\n0X0\\nX..\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': 'X.0\\nXX.\\n000\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\n0XX\\n0X.\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': 'XX0\\nX00\\nX0X\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '.X.\\n.X0\\n0.X\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': '0.0\\nXX0\\n..0\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\n.0X\\nX..\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\n0XX\\n.0X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X0.\\n..0\\nX0.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X0.\\n.X.\\nX.0\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': 'XX0\\n0X0\\n.X0\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'XXX\\n..0\\n000\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '0.X\\n0XX\\n.X0\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': '.0.\\n00X\\nX0X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '0X0\\nX..\\n0.X\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': '0.X\\nX00\\n0XX\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': 'X.X\\n.XX\\n0.X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '0XX\\nX.X\\n00.\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': 'X..\\n.0.\\n0..\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '00X\\nXXX\\n0..\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '00X\\n0..\\n.0.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '0XX\\n0X0\\n.X0\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X.X\\n0.0\\n..X\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': '..0\\n000\\nX0X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X00\\n0..\\nX.X\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': 'X0.\\n.00\\n00.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X.0\\n0X0\\n.00\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '0.X\\nX0.\\n0X.\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': 'X0X\\n0X0\\n0XX\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '0X0\\n0XX\\n.X.\\n', 'output': 'the first player won\\n'}, {'type': 'stdin_stdout', 'input': '0XX\\nX0X\\nX00\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '..0\\n.00\\n0.X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '.XX\\nXXX\\n.0.\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'XX.\\nX0X\\n..X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X0X\\n.0.\\nX..\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': '0..\\nX0X\\n..X\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': '0X0\\n0.X\\n00X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': 'X0X\\nX0.\\n0..\\n', 'output': 'first\\n'}, {'type': 'stdin_stdout', 'input': '.X0\\n.X.\\nX0.\\n', 'output': 'second\\n'}, {'type': 'stdin_stdout', 'input': '0XX\\nXXX\\n00X\\n', 'output': 'illegal\\n'}, {'type': 'stdin_stdout', 'input': '.X0\\n...\\n.0X\\n', 'output': 'first\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 64000000}","problem_id":"vfc_78089","program":"```python\nfirst_row = input()\nsecond_row = input()\nthird_row = input()\nc = 0\no = 0\nfor i in range(0,3):\n if first_row[i] == 'X':\n c = c + 1\n elif first_row[i] == '0':\n o = o + 1\nfor i in range(0,3):\n if second_row[i] == 'X':\n c = c + 1\n elif second_row[i] == '0':\n o = o + 1\nfor i in range(0,3):\n if third_row[i] == 'X':\n c = c + 1\n elif third_row[i] == '0':\n o = o + 1\n\nr = 0\nif first_row[0] == \"X\" and second_row[1] == \"X\" and third_row[2] == \"X\":\n r = 1+r\nif first_row[0] == \"X\" and second_row[0] == \"X\" and third_row[0] ==\"X\":\n r = 1+r\nif first_row[0] == \"X\" and first_row[1] == \"X\" and first_row[2]== \"X\":\n r = 1+r\nif first_row[1] == \"X\" and second_row[1] == \"X\" and third_row[1] == \"X\":\n r = 1+r\nif first_row[2] == \"X\" and second_row[2] == \"X\" and third_row[2] == \"X\":\n r = 1+r\nif first_row[2] == \"X\" and second_row[1] == \"X\" and third_row[0] == \"X\":\n r = 1+r\nif second_row[0] == \"X\" and second_row[1] == \"X\" and second_row[2] == \"X\":\n r = r + 1\nif third_row[0] == \"X\" and third_row[1] == \"X\" and third_row[2] == \"X\":\n r = r + 1\n \nq = 0\nif first_row[0] == \"0\" and second_row[1] == \"0\" and third_row[2] == \"0\":\n q = 1+q\nif first_row[0] == \"0\" and second_row[0] == \"0\" and third_row[0] ==\"0\":\n q = 1+q\nif first_row[0] == \"0\" and first_row[1] == \"0\" and first_row[2] == \"0\":\n q = q + 1\nif first_row[1] == \"0\" and second_row[1] == \"0\" and third_row[1]== \"0\":\n q = 1 + q\n\nif first_row[2] == \"0\" and second_row[2] == \"0\" and third_row[2] == \"0\":\n q = 1 + q\nif first_row[2] == \"0\" and second_row[1] == \"0\" and third_row[0] == \"0\":\n q = 1 + q\nif second_row[0] == \"0\" and second_row[1] == \"0\" and second_row[2] == \"0\":\n q = q + 1\nif third_row[0] == \"0\" and third_row[1] == \"0\" and third_row[2] == \"0\":\n q = q + 1 \n \nif first_row[0] == \"X\" and first_row[2] == \"X\" and third_row[0] == \"X\" and third_row[2] == \"X\" and first_row[1] == \"0\" and second_row[0] == \"0\" and second_row[2] == \"0\" and third_row[1] == \"0\" and second_row[1] == \"X\":\n print(\"the first player won\")\nelif first_row[0] == \"X\" and first_row[1] == \"X\" and third_row[2] == \"X\" and second_row[2] == \"X\" and second_row[1] == \"0\" and third_row[1] == \"0\" and third_row[0] == \"0\" and second_row[0] == \"0\" and first_row[2] == \"X\":\n print(\"the first player won\")\nelif first_row[2] == \"0\" and first_row[1] == \"0\" and first_row[0] == \"X\" and second_row[2] == \"0\" and second_row[1] == \"0\" and third_row[1] == \"X\" and third_row[2] == \"X\" and second_row[0] == \"X\" and third_row[0] == \"X\":\n print(\"the first player won\")\nelif first_row[2] == \"0\" and first_row[1] == \"X\" and first_row[0] == \"0\" and second_row[2] == \"X\" and second_row[0] == \"X\" and third_row[1] == \"X\" and third_row[2] == \"0\" and third_row[0] == \"0\" and second_row[1] == \"X\":\n print(\"the first player won\")\nelif first_row[2] == \"0\" and first_row[1] == \"0\" and first_row[0] == \"X\" and second_row[2] == \"X\" and second_row[1] == \"X\" and third_row[1] == \"0\" and third_row[2] == \"0\" and third_row[0] == \"X\" and second_row[0] == \"X\":\n print(\"the first player won\")\nelif first_row[2] == \"X\" and first_row[1] == \"0\" and first_row[0] == \"0\" and second_row[0] == \"X\" and second_row[1] == \"X\" and third_row[1] == \"0\" and third_row[2] == \"X\" and third_row[0] == \"0\" and second_row[2] == \"X\":\n print(\"the first player won\")\nelif first_row[0] == \"X\" and first_row[1] == \"X\" and first_row[2] == \"X\" and second_row[2] == \"0\" and second_row[0] == \"X\" and second_row[2] == \"0\" and third_row[0] == \"X\" and third_row[1] == \"0\" and third_row[2] == \"0\": \n print(\"the first player won\")\nelif c-o > 1 or (o-c) >= 1 or (r==1 and q == 1):\n print(\"illegal\")\nelif q >= 1 and r == 0:\n if c == o:\n print(\"the second player won\")\n else:\n print(\"illegal\")\nelif r >= 1 and q == 0:\n if c-1 == o:\n print(\"the first player won\")\n else:\n print(\"illegal\")\nelif c - o == 1 and o+c != 9:\n print(\"second\")\nelif c-o == 0:\n print(\"first\")\nelse:\n print(\"draw\")\n\n```","inputs":"X0X\n.0.\n.X.\n","output":"second\n","actual_output":"second\n","execution_success":true,"sample_index":12451},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"44_H. Phone Number","prompt":"Solve the following coding problem using the programming language python:\n\nAlas, finding one's true love is not easy. Masha has been unsuccessful in that yet. Her friend Dasha told Masha about a way to determine the phone number of one's Prince Charming through arithmancy. \n\nThe phone number is divined like that. First one needs to write down one's own phone numbers. For example, let's suppose that Masha's phone number is 12345. After that one should write her favorite digit from 0 to 9 under the first digit of her number. That will be the first digit of the needed number. For example, Masha's favorite digit is 9. The second digit is determined as a half sum of the second digit of Masha's number and the already written down first digit from her beloved one's number. In this case the arithmetic average equals to (2 + 9) / 2 = 5.5. Masha can round the number up or down, depending on her wishes. For example, she chooses the digit 5. Having written down the resulting digit under the second digit of her number, Masha moves to finding the third digit in the same way, i.e. finding the half sum the the third digit of her number and the second digit of the new number. The result is (5 + 3) / 2 = 4. In this case the answer is unique. Thus, every i-th digit is determined as an arithmetic average of the i-th digit of Masha's number and the i - 1-th digit of her true love's number. If needed, the digit can be rounded up or down. For example, Masha can get: \n\n12345 95444 Unfortunately, when Masha tried dialing the number, she got disappointed: as it turned out, the number was unavailable or outside the coverage area. But Masha won't give up. Perhaps, she rounded to a wrong digit or chose the first digit badly. That's why she keeps finding more and more new numbers and calling them. Count the number of numbers Masha calls. Masha calls all the possible numbers that can be found by the described means of arithmancy, except for, perhaps, her own one.\n\nInput\n\nThe first line contains nonempty sequence consisting of digits from 0 to 9 \u2014 Masha's phone number. The sequence length does not exceed 50.\n\nOutput\n\nOutput the single number \u2014 the number of phone numbers Masha will dial.\n\nExamples\n\nInput\n\n12345\n\n\nOutput\n\n48\n\n\nInput\n\n09\n\n\nOutput\n\n15\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# import sys\n# input=sys.stdin.readline\n\na=input()\ndp=[]\nfor i in range(len(a)):\n dp.append([0]*10)\nfor i in range(10):\n dp[0][i]=1\n \nfor i in range(len(a)-1):\n for j in range(10):\n if dp[i][j]!=0:\n c=(int(a[i+1])+j)//2\n d=(int(a[i+1])+j+1)//2\n if c!=d:\n dp[i+1][c]+=dp[i][j]\n dp[i+1][d]+=dp[i][j]\n else:\n dp[i+1][c]+=dp[i][j]\ns=0\nfor i in range(10):\n s+=dp[-1][i]\nt=0\nc=int(a[0])\nf=[a[0]]\nfor i in range(1,len(a)):\n d=(c+int(a[i]))//2\n e=(c+int(a[i])+1)//2\n if int(a[i])==d:\n f.append(a[i])\n c=d\n elif int(a[i])==e:\n f.append(a[i])\n c=e\n else:\n break\nif \"\".join(f)==a:\n t=1\nprint(s-t)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '09\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '12345\\n', 'output': '48\\n'}, {'type': 'stdin_stdout', 'input': '3\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '36460576924876475371008334246121610\\n', 'output': '31319157\\n'}, {'type': 'stdin_stdout', 'input': '44444444444444444444444444444444444444444444444444\\n', 'output': '631\\n'}, {'type': 'stdin_stdout', 'input': '433488906230138\\n', 'output': '1399\\n'}, {'type': 'stdin_stdout', 'input': '67676566654565654332111011212211111223433222110012\\n', 'output': '5882859948\\n'}, {'type': 'stdin_stdout', 'input': '429622625617508557672595893160462042433748844995\\n', 'output': '284175107\\n'}, {'type': 'stdin_stdout', 'input': '0180990956\\n', 'output': '473\\n'}, {'type': 'stdin_stdout', 'input': '95066916647678224147260013920\\n', 'output': '446529\\n'}, {'type': 'stdin_stdout', 'input': 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'145866\\n'}, {'type': 'stdin_stdout', 'input': '52056884218028089650567882557609167736461846591193\\n', 'output': '1358962463\\n'}, {'type': 'stdin_stdout', 'input': '9876543210\\n', 'output': '157\\n'}, {'type': 'stdin_stdout', 'input': '00046142930690780976\\n', 'output': '35257\\n'}, {'type': 'stdin_stdout', 'input': '78767765544454334445445555455676565433343455432332\\n', 'output': '11031574582\\n'}, {'type': 'stdin_stdout', 'input': '96591550315931484452350406227169651758570705180260\\n', 'output': '6869183484\\n'}, {'type': 'stdin_stdout', 'input': '737\\n', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '55\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '2\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '71907438528033742120066305779792425\\n', 'output': '3447351\\n'}, {'type': 'stdin_stdout', 'input': '77479764203641549807447423003028416997653240472521\\n', 'output': '7755246781\\n'}, {'type': 'stdin_stdout', 'input': '467075073492974\\n', 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{'type': 'stdin_stdout', 'input': '380579308788179977140647493\\n', 'output': '188509\\n'}, {'type': 'stdin_stdout', 'input': '0\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '625\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '4\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1503\\n', 'output': '34\\n'}, {'type': 'stdin_stdout', 'input': '3097\\n', 'output': '34\\n'}], 'language': 'python'}","metadata":"{'difficulty': 14, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78097","program":"```python\n# import sys\n# input=sys.stdin.readline\n\na=input()\ndp=[]\nfor i in range(len(a)):\n dp.append([0]*10)\nfor i in range(10):\n dp[0][i]=1\n \nfor i in range(len(a)-1):\n for j in range(10):\n if dp[i][j]!=0:\n c=(int(a[i+1])+j)//2\n d=(int(a[i+1])+j+1)//2\n if c!=d:\n dp[i+1][c]+=dp[i][j]\n dp[i+1][d]+=dp[i][j]\n else:\n dp[i+1][c]+=dp[i][j]\ns=0\nfor i in range(10):\n s+=dp[-1][i]\nt=0\nc=int(a[0])\nf=[a[0]]\nfor i in range(1,len(a)):\n d=(c+int(a[i]))//2\n e=(c+int(a[i])+1)//2\n if int(a[i])==d:\n f.append(a[i])\n c=d\n elif int(a[i])==e:\n f.append(a[i])\n c=e\n else:\n break\nif \"\".join(f)==a:\n t=1\nprint(s-t)\n```","inputs":"09\n","output":"15\n","actual_output":"15\n","execution_success":true,"sample_index":12452},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"471_D. MUH and Cube Walls","prompt":"Solve the following coding problem using the programming language python:\n\nPolar bears Menshykov and Uslada from the zoo of St. Petersburg and elephant Horace from the zoo of Kiev got hold of lots of wooden cubes somewhere. They started making cube towers by placing the cubes one on top of the other. They defined multiple towers standing in a line as a wall. A wall can consist of towers of different heights.\n\nHorace was the first to finish making his wall. He called his wall an elephant. The wall consists of w towers. The bears also finished making their wall but they didn't give it a name. Their wall consists of n towers. Horace looked at the bears' tower and wondered: in how many parts of the wall can he \"see an elephant\"? He can \"see an elephant\" on a segment of w contiguous towers if the heights of the towers on the segment match as a sequence the heights of the towers in Horace's wall. In order to see as many elephants as possible, Horace can raise and lower his wall. He even can lower the wall below the ground level (see the pictures to the samples for clarification).\n\nYour task is to count the number of segments where Horace can \"see an elephant\".\n\nInput\n\nThe first line contains two integers n and w (1 \u2264 n, w \u2264 2\u00b7105) \u2014 the number of towers in the bears' and the elephant's walls correspondingly. The second line contains n integers ai (1 \u2264 ai \u2264 109) \u2014 the heights of the towers in the bears' wall. The third line contains w integers bi (1 \u2264 bi \u2264 109) \u2014 the heights of the towers in the elephant's wall.\n\nOutput\n\nPrint the number of segments in the bears' wall where Horace can \"see an elephant\".\n\nExamples\n\nInput\n\n13 5\n2 4 5 5 4 3 2 2 2 3 3 2 1\n3 4 4 3 2\n\n\nOutput\n\n2\n\nNote\n\nThe picture to the left shows Horace's wall from the sample, the picture to the right shows the bears' wall. The segments where Horace can \"see an elephant\" are in gray.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# Author : nitish420 --------------------------------------------------------------------\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n\n\ndef main():\n\tn,w=map(int,input().split())\n\tif n 0:\n pos += 1\nsigns = []\nfor i in qs:\n if i == '+':\n pos+=1\n signs.append(1)\n else:\n if i == '-':\n neg +=1\n signs.append(0)\nif pos == 0 and neg == 0 and v == 0:\n print(\"Possible\\n= 0\");\nelse:\n if (pos == 0 and neg == 0) or (pos*v - neg < v) or (pos - neg*v > v):\n print(\"Impossible\")\n else:\n print(\"Possible\")\n t = pos - neg\n print(1+max(0,min(v-1,v-t)),end=\" \")\n t += max(0,min(v-1,v-t))\n for i in signs:\n if i == 0:\n print(\"-\",end=\" \")\n print(1+max(0,(min(v-1,t-v))),end=\" \")\n t -= max(0,(min(v-1,t-v)))\n if i == 1:\n print(\"+\",end=\" \")\n print(1+max(0,(min(v-1,v-t))),end =\" \")\n t += max(0,(min(v-1,v-t)))\n\n print(\"= \" + str(v))\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '? + ? - ? + ? + ? = 42\\n', 'output': 'Possible\\n40 + 1 - 1 + 1 + 1 = 42\\n'}, {'type': 'stdin_stdout', 'input': '? = 1000000\\n', 'output': 'Possible\\n1000000 = 1000000\\n'}, {'type': 'stdin_stdout', 'input': '? - ? = 1\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '? - ? + ? + ? - ? + ? - ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? - ? + ? + ? - ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? - ? + ? + ? - ? + ? - ? + ? + ? + ? + ? + ? + ? - ? + ? - ? + ? - ? + ? + ? + ? + ? + ? + ? - ? + ? - ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? - ? - ? - ? + ? - ? + ? + ? + ? + ? - ? - ? + ? + ? - ? - ? + ? = 1000000\\n', 'output': 'Possible\\n999963 - 1 + 1 + 1 - 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 + 1 + 1 - 1 + 1 + 1 - 1 + 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 + 1 - 1 + 1 + 1 - 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 + 1 - 1 + 1 + 1 + 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 - 1 - 1 + 1 - 1 + 1 + 1 + 1 + 1 - 1 - 1 + 1 + 1 - 1 - 1 + 1 = 1000000\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? - ? = 2\\n', 'output': 'Possible\\n1 + 1 + 1 + 1 - 2 = 2\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? - ? + ? - ? - ? - ? - ? - ? + ? - ? + ? + ? - ? + ? - ? + ? + ? - ? + ? - ? + ? + ? + ? - ? - ? - ? + ? - ? - ? + ? - ? - ? + ? - ? + ? + ? - ? + ? - ? - ? + ? + ? - ? - ? - ? + ? - ? - ? - ? + ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? + ? - ? - ? + ? - ? - ? - ? - ? + ? + ? - ? + ? + ? - ? + ? - ? + ? - ? + ? - ? - ? - ? - ? - ? + ? - ? = 837454\\n', 'output': 'Possible\\n837454 + 28 + 1 - 1 + 1 - 1 - 1 - 1 - 1 - 1 + 1 - 1 + 1 + 1 - 1 + 1 - 1 + 1 + 1 - 1 + 1 - 1 + 1 + 1 + 1 - 1 - 1 - 1 + 1 - 1 - 1 + 1 - 1 - 1 + 1 - 1 + 1 + 1 - 1 + 1 - 1 - 1 + 1 + 1 - 1 - 1 - 1 + 1 - 1 - 1 - 1 + 1 - 1 - 1 - 1 + 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 1 - 1 + 1 - 1 - 1 + 1 - 1 - 1 - 1 - 1 + 1 + 1 - 1 + 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 - 1 - 1 - 1 - 1 + 1 - 1 = 837454\\n'}, {'type': 'stdin_stdout', 'input': '? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? = 93\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '? + ? - ? + ? + ? = 2\\n', 'output': 'Possible\\n1 + 1 - 2 + 1 + 1 = 2\\n'}, {'type': 'stdin_stdout', 'input': '? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? = 31\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? = 32\\n', 'output': 'Possible\\n32 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 32 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 32 - 1 - 1 - 1 - 1 + 32 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 = 32\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? = 5\\n', 'output': 'Possible\\n1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 5 = 5\\n'}, {'type': 'stdin_stdout', 'input': '? - ? + ? + ? + ? + ? - ? - ? - ? - ? + ? - ? - ? - ? + ? - ? + ? + ? + ? - ? + ? + ? + ? - ? + ? + ? - ? + ? - ? + ? - ? - ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? + ? - ? + ? + ? - ? - ? - ? - ? + ? - ? - ? + ? + ? - ? + ? + ? - ? - ? - ? + ? + ? - ? - ? + ? - ? - ? + ? - ? + ? - ? - ? - ? - ? + ? - ? + ? - ? + ? + ? + ? - ? + ? + ? - ? - ? + ? = 123456\\n', 'output': 'Possible\\n123456 - 1 + 2 + 1 + 1 + 1 - 1 - 1 - 1 - 1 + 1 - 1 - 1 - 1 + 1 - 1 + 1 + 1 + 1 - 1 + 1 + 1 + 1 - 1 + 1 + 1 - 1 + 1 - 1 + 1 - 1 - 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 + 1 + 1 + 1 + 1 - 1 - 1 - 1 + 1 - 1 - 1 - 1 - 1 - 1 - 1 + 1 - 1 + 1 + 1 - 1 - 1 - 1 - 1 + 1 - 1 - 1 + 1 + 1 - 1 + 1 + 1 - 1 - 1 - 1 + 1 + 1 - 1 - 1 + 1 - 1 - 1 + 1 - 1 + 1 - 1 - 1 - 1 - 1 + 1 - 1 + 1 - 1 + 1 + 1 + 1 - 1 + 1 + 1 - 1 - 1 + 1 = 123456\\n'}, {'type': 'stdin_stdout', 'input': '? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? = 999999\\n', 'output': 'Possible\\n999999 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 98 - 1 - 1 = 999999\\n'}, {'type': 'stdin_stdout', 'input': '? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? = 37\\n', 'output': 'Possible\\n37 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 37 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 37 - 1 - 1 - 1 + 20 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 = 37\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? - ? + ? - ? + ? + ? + ? + ? + ? + ? + ? - ? - ? + ? + ? + ? + ? + ? - ? - ? + ? + ? - ? + ? - ? - ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? - ? - ? + ? + ? + ? + ? - ? + ? + ? + ? - ? + ? - ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? = 3\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '? - ? + ? - ? + ? + ? - ? + ? - ? + ? + ? - ? + ? - ? - ? + ? - ? - ? + ? - ? + ? - ? - ? - ? - ? - ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? - ? - ? + ? - ? + ? + ? - ? + ? - ? + ? - ? - ? + ? - ? - ? + ? - ? - ? - ? + ? - ? - ? + ? - ? + ? + ? - ? - ? + ? - ? - ? + ? + ? - ? + ? - ? + ? + ? + ? + ? + ? - ? - ? + ? - ? - ? - ? + ? = 254253\\n', 'output': 'Possible\\n254253 - 1 + 2 - 1 + 1 + 1 - 1 + 1 - 1 + 1 + 1 - 1 + 1 - 1 - 1 + 1 - 1 - 1 + 1 - 1 + 1 - 1 - 1 - 1 - 1 - 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 - 1 + 1 - 1 + 1 + 1 - 1 + 1 - 1 + 1 - 1 - 1 + 1 - 1 - 1 + 1 - 1 - 1 - 1 + 1 - 1 - 1 + 1 - 1 + 1 + 1 - 1 - 1 + 1 - 1 - 1 + 1 + 1 - 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 - 1 - 1 + 1 - 1 - 1 - 1 + 1 = 254253\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? + ? - ? = 3\\n', 'output': 'Possible\\n1 + 1 + 1 + 1 + 1 - 2 = 3\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? + ? + ? + ? + ? - ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? - ? - ? + ? + ? - ? - ? + ? + ? + ? - ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? - ? + ? + ? + ? - ? + ? + ? - ? - ? + ? - ? + ? + ? + ? = 4\\n', 'output': 'Possible\\n1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 4 - 4 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 4 + 1 + 1 - 4 - 4 + 1 + 1 - 4 - 4 + 1 + 1 + 1 - 4 - 4 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 4 + 1 + 1 + 1 - 4 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 4 + 1 + 1 + 1 + 1 + 1 + 1 - 4 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 4 - 4 + 1 + 1 + 1 - 4 + 1 + 1 - 4 - 4 + 1 - 4 + 1 + 1 + 1 = 4\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? - ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? = 15\\n', 'output': 'Possible\\n1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 15 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 15 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 15 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 15 + 1 + 1 - 14 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 15\\n'}, {'type': 'stdin_stdout', 'input': '? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? + ? + ? - ? - ? - ? + ? - ? + ? - ? - ? - ? - ? - ? + ? - ? + ? - ? - ? - ? - ? - ? - ? + ? - ? + ? - ? + ? - ? - ? + ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? + ? - ? - ? - ? + ? - ? + ? - ? - ? = 4\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? + ? - ? - ? = 2\\n', 'output': 'Possible\\n1 + 1 + 1 + 1 + 1 - 2 - 1 = 2\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? = 33\\n', 'output': 'Possible\\n1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 33 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 33\\n'}, {'type': 'stdin_stdout', 'input': '? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? = 19\\n', 'output': 'Possible\\n19 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 19 - 1 - 1 - 1 - 1 - 1 - 1 + 19 - 1 - 1 - 1 - 1 - 1 - 1 + 19 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 19 - 1 - 1 - 1 - 1 + 11 - 1 - 1 - 1 - 1 - 1 + 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 = 19\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? = 100\\n', 'output': 'Possible\\n1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 100\\n'}, {'type': 'stdin_stdout', 'input': '? + ? - ? - ? - ? + ? + ? - ? + ? + ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? + ? - ? - ? - ? + ? - ? - ? - ? + ? - ? - ? - ? - ? - ? + ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? + ? - ? - ? - ? + ? - ? - ? + ? - ? + ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? = 5\\n', 'output': 'Possible\\n5 + 5 - 1 - 1 - 1 + 5 + 5 - 1 + 5 + 5 - 1 - 1 - 1 - 1 - 1 - 1 + 5 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 5 - 1 - 1 - 1 - 1 + 5 - 1 - 1 - 1 + 5 - 1 - 1 - 1 + 5 - 1 - 1 - 1 - 1 - 1 + 5 - 1 - 1 - 1 + 5 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 + 5 - 1 - 1 - 1 + 5 - 1 - 1 - 1 + 5 - 1 - 1 + 2 - 1 + 1 - 1 - 1 - 1 - 1 + 1 - 1 - 1 - 1 - 1 - 1 - 1 + 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 = 5\\n'}, {'type': 'stdin_stdout', 'input': '? + ? - ? + ? + ? - ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? - ? + ? + ? - ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? + ? + ? + ? - ? + ? - ? + ? - ? + ? + ? + ? + ? + ? + ? - ? + ? - ? - ? - ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? - ? + ? - ? + ? + ? + ? + ? + ? + ? - ? + ? + ? - ? - ? + ? + ? = 4\\n', 'output': 'Possible\\n1 + 1 - 4 + 1 + 1 - 4 + 1 + 1 + 1 - 4 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 4 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 4 + 1 + 1 - 4 + 1 + 1 - 4 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 4 + 1 + 1 + 1 + 1 - 4 + 1 - 4 + 1 - 4 + 1 + 1 + 1 + 1 + 1 + 1 - 4 + 1 - 4 - 4 - 4 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 4 + 1 - 4 + 1 + 1 + 1 + 1 + 1 + 1 - 4 + 1 + 1 - 3 - 1 + 1 + 1 = 4\\n'}, {'type': 'stdin_stdout', 'input': '? + ? - ? = 1\\n', 'output': 'Possible\\n1 + 1 - 1 = 1\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? = 9\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '? + ? - ? + ? + ? = 42\\n', 'output': 'Possible\\n40 + 1 - 1 + 1 + 1 = 42\\n'}, {'type': 'stdin_stdout', 'input': '? - ? + ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? = 57\\n', 'output': 'Possible\\n57 - 1 + 18 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 = 57\\n'}, {'type': 'stdin_stdout', 'input': '? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? = 43386\\n', 'output': 'Impossible\\n'}, {'type': 'stdin_stdout', 'input': '? - ? + ? - ? + ? + ? + ? + ? = 2\\n', 'output': 'Possible\\n1 - 2 + 1 - 2 + 1 + 1 + 1 + 1 = 2\\n'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? - ? = 4\\n', 'output': 'Possible\\n2 + 1 + 1 + 1 - 1 = 4'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? - ? = 0\\n', 'output': 'Impossible'}, {'type': 'stdin_stdout', 'input': '? = 1000010\\n', 'output': 'Possible\\n1000010 = 1000010'}, {'type': 'stdin_stdout', 'input': '? = 1010010\\n', 'output': 'Possible\\n1010010 = 1010010'}, {'type': 'stdin_stdout', 'input': '? = 1100000\\n', 'output': 'Possible\\n1100000 = 1100000'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? - ? = 8\\n', 'output': 'Possible\\n6 + 1 + 1 + 1 - 1 = 8'}, {'type': 'stdin_stdout', 'input': '? = 1000011\\n', 'output': 'Possible\\n1000011 = 1000011'}, {'type': 'stdin_stdout', 'input': '? = 1010011\\n', 'output': 'Possible\\n1010011 = 1010011'}, {'type': 'stdin_stdout', 'input': '? = 1010001\\n', 'output': 'Possible\\n1010001 = 1010001'}, {'type': 'stdin_stdout', 'input': '? = 0010001\\n', 'output': 'Possible\\n10001 = 10001'}, {'type': 'stdin_stdout', 'input': '? = 1000100\\n', 'output': 'Possible\\n1000100 = 1000100'}, {'type': 'stdin_stdout', 'input': '? = 0000100\\n', 'output': 'Possible\\n100 = 100'}, {'type': 'stdin_stdout', 'input': '? = 1000001\\n', 'output': 'Possible\\n1000001 = 1000001'}, {'type': 'stdin_stdout', 'input': '? = 0110001\\n', 'output': 'Possible\\n110001 = 110001'}, {'type': 'stdin_stdout', 'input': '? = 1100100\\n', 'output': 'Possible\\n1100100 = 1100100'}, {'type': 'stdin_stdout', 'input': '? = 1001100\\n', 'output': 'Possible\\n1001100 = 1001100'}, {'type': 'stdin_stdout', 'input': '? = 0100001\\n', 'output': 'Possible\\n100001 = 100001'}, {'type': 'stdin_stdout', 'input': '? + ? - ? + ? + ? = 4\\n', 'output': 'Possible\\n2 + 1 - 1 + 1 + 1 = 4'}, {'type': 'stdin_stdout', 'input': '? = 0010010\\n', 'output': 'Possible\\n10010 = 10010'}, {'type': 'stdin_stdout', 'input': '? = 1010000\\n', 'output': 'Possible\\n1010000 = 1010000'}, {'type': 'stdin_stdout', 'input': '? = 1000101\\n', 'output': 'Possible\\n1000101 = 1000101'}, {'type': 'stdin_stdout', 'input': '? = 1100101\\n', 'output': 'Possible\\n1100101 = 1100101'}, {'type': 'stdin_stdout', 'input': '? = 1001101\\n', 'output': 'Possible\\n1001101 = 1001101'}, {'type': 'stdin_stdout', 'input': '? = 1110000\\n', 'output': 'Possible\\n1110000 = 1110000'}, {'type': 'stdin_stdout', 'input': '? = 0100101\\n', 'output': 'Possible\\n100101 = 100101'}, {'type': 'stdin_stdout', 'input': '? = 1001001\\n', 'output': 'Possible\\n1001001 = 1001001'}, {'type': 'stdin_stdout', 'input': '? = 1101101\\n', 'output': 'Possible\\n1101101 = 1101101'}, {'type': 'stdin_stdout', 'input': '? = 1000110\\n', 'output': 'Possible\\n1000110 = 1000110'}, {'type': 'stdin_stdout', 'input': '? = 0100000\\n', 'output': 'Possible\\n100000 = 100000'}, {'type': 'stdin_stdout', 'input': '? = 1010111\\n', 'output': 'Possible\\n1010111 = 1010111'}, {'type': 'stdin_stdout', 'input': '? = 1110100\\n', 'output': 'Possible\\n1110100 = 1110100'}, {'type': 'stdin_stdout', 'input': '? = 0001100\\n', 'output': 'Possible\\n1100 = 1100'}, {'type': 'stdin_stdout', 'input': '? = 0011010\\n', 'output': 'Possible\\n11010 = 11010'}, {'type': 'stdin_stdout', 'input': '? = 1100001\\n', 'output': 'Possible\\n1100001 = 1100001'}, {'type': 'stdin_stdout', 'input': '? = 0000001\\n', 'output': 'Possible\\n1 = 1'}, {'type': 'stdin_stdout', 'input': '? = 1011111\\n', 'output': 'Possible\\n1011111 = 1011111'}, {'type': 'stdin_stdout', 'input': '? = 1110101\\n', 'output': 'Possible\\n1110101 = 1110101'}, {'type': 'stdin_stdout', 'input': '? = 0001010\\n', 'output': 'Possible\\n1010 = 1010'}, {'type': 'stdin_stdout', 'input': '? = 1011101\\n', 'output': 'Possible\\n1011101 = 1011101'}, {'type': 'stdin_stdout', 'input': '? = 1111101\\n', 'output': 'Possible\\n1111101 = 1111101'}, {'type': 'stdin_stdout', 'input': '? = 0000010\\n', 'output': 'Possible\\n10 = 10'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? + ? - ? - ? = 4\\n', 'output': 'Possible\\n2 + 1 + 1 + 1 + 1 - 1 - 1 = 4'}, {'type': 'stdin_stdout', 'input': '? + ? - ? = 2\\n', 'output': 'Possible\\n2 + 1 - 1 = 2'}, {'type': 'stdin_stdout', 'input': '? = 1010100\\n', 'output': 'Possible\\n1010100 = 1010100'}, {'type': 'stdin_stdout', 'input': '? = 1011001\\n', 'output': 'Possible\\n1011001 = 1011001'}, {'type': 'stdin_stdout', 'input': '? = 0010100\\n', 'output': 'Possible\\n10100 = 10100'}, {'type': 'stdin_stdout', 'input': '? = 1101100\\n', 'output': 'Possible\\n1101100 = 1101100'}, {'type': 'stdin_stdout', 'input': '? = 0010000\\n', 'output': 'Possible\\n10000 = 10000'}, {'type': 'stdin_stdout', 'input': '? = 1010101\\n', 'output': 'Possible\\n1010101 = 1010101'}, {'type': 'stdin_stdout', 'input': '? = 1101001\\n', 'output': 'Possible\\n1101001 = 1101001'}, {'type': 'stdin_stdout', 'input': '? = 0001101\\n', 'output': 'Possible\\n1101 = 1101'}, {'type': 'stdin_stdout', 'input': '? = 0111101\\n', 'output': 'Possible\\n111101 = 111101'}, {'type': 'stdin_stdout', 'input': '? = 1011011\\n', 'output': 'Possible\\n1011011 = 1011011'}, {'type': 'stdin_stdout', 'input': '? = 0010110\\n', 'output': 'Possible\\n10110 = 10110'}, {'type': 'stdin_stdout', 'input': '? = 1101011\\n', 'output': 'Possible\\n1101011 = 1101011'}, {'type': 'stdin_stdout', 'input': '? = 0110101\\n', 'output': 'Possible\\n110101 = 110101'}, {'type': 'stdin_stdout', 'input': '? = 0011011\\n', 'output': 'Possible\\n11011 = 11011'}, {'type': 'stdin_stdout', 'input': '? - ? = 2\\n', 'output': 'Impossible'}, {'type': 'stdin_stdout', 'input': '? + ? + ? + ? - ? = 1\\n', 'output': 'Impossible'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78133","program":"```python\ns = input().split(\"=\")\nv = int(s[1])\nqs = s[0].split()\npos =0\nneg =0\nif len(qs) > 0:\n pos += 1\nsigns = []\nfor i in qs:\n if i == '+':\n pos+=1\n signs.append(1)\n else:\n if i == '-':\n neg +=1\n signs.append(0)\nif pos == 0 and neg == 0 and v == 0:\n print(\"Possible\\n= 0\");\nelse:\n if (pos == 0 and neg == 0) or (pos*v - neg < v) or (pos - neg*v > v):\n print(\"Impossible\")\n else:\n print(\"Possible\")\n t = pos - neg\n print(1+max(0,min(v-1,v-t)),end=\" \")\n t += max(0,min(v-1,v-t))\n for i in signs:\n if i == 0:\n print(\"-\",end=\" \")\n print(1+max(0,(min(v-1,t-v))),end=\" \")\n t -= max(0,(min(v-1,t-v)))\n if i == 1:\n print(\"+\",end=\" \")\n print(1+max(0,(min(v-1,v-t))),end =\" \")\n t += max(0,(min(v-1,v-t)))\n\n print(\"= \" + str(v))\n\n\n```","inputs":"? + ? - ? + ? + ? = 42\n","output":"Possible\n40 + 1 - 1 + 1 + 1 = 42\n","actual_output":"Possible\n40 + 1 - 1 + 1 + 1 = 42\n","execution_success":true,"sample_index":12458},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"688_E. The Values You Can Make","prompt":"Solve the following coding problem using the programming language python:\n\nPari wants to buy an expensive chocolate from Arya. She has n coins, the value of the i-th coin is ci. The price of the chocolate is k, so Pari will take a subset of her coins with sum equal to k and give it to Arya.\n\nLooking at her coins, a question came to her mind: after giving the coins to Arya, what values does Arya can make with them? She is jealous and she doesn't want Arya to make a lot of values. So she wants to know all the values x, such that Arya will be able to make x using some subset of coins with the sum k.\n\nFormally, Pari wants to know the values x such that there exists a subset of coins with the sum k such that some subset of this subset has the sum x, i.e. there is exists some way to pay for the chocolate, such that Arya will be able to make the sum x using these coins.\n\nInput\n\nThe first line contains two integers n and k (1 \u2264 n, k \u2264 500) \u2014 the number of coins and the price of the chocolate, respectively.\n\nNext line will contain n integers c1, c2, ..., cn (1 \u2264 ci \u2264 500) \u2014 the values of Pari's coins.\n\nIt's guaranteed that one can make value k using these coins.\n\nOutput\n\nFirst line of the output must contain a single integer q\u2014 the number of suitable values x. Then print q integers in ascending order \u2014 the values that Arya can make for some subset of coins of Pari that pays for the chocolate.\n\nExamples\n\nInput\n\n6 18\n5 6 1 10 12 2\n\n\nOutput\n\n16\n0 1 2 3 5 6 7 8 10 11 12 13 15 16 17 18 \n\n\nInput\n\n3 50\n25 25 50\n\n\nOutput\n\n3\n0 25 50 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom sys import stdin,stdout\nn,m=map(int,input().split())\ns=[0]+list(map(int,stdin.readline().strip().split()))\ndp=[[[False for i in range(m+1)] for j in range(m+1)] for k in range(2)]\ndp[0][0][0]=True\ncur=0\nfor i in range(1,n+1):\n cur+=1\n cur%=2\n last=(cur+1)%2\n for j in range(m+1):\n for k in range(j+1):\n if j-s[i]>-1 and k-s[i]>-1:\n dp[cur][j][k]=dp[last][j][k] or dp[last][j-s[i]][k] or dp[last][j-s[i]][k-s[i]]\n elif j-s[i]>-1 :\n dp[cur][j][k]=dp[last][j][k] or dp[last][j-s[i]][k]\n elif k-s[i]>-1:\n dp[cur][j][k]=dp[last][j][k] or dp[last][j-s[i]][k-s[i]]\n else:\n dp[cur][j][k]=dp[last][j][k]\n \nn1=0\nans=\"\"\nfor i in range(k+1):\n if dp[cur][k][i]:\n ans+=str(i)+\" \"\n n1+=1\nstdout.write(str(n1)+chr(10))\nstdout.write(ans)\n \n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 18\\n5 6 1 10 12 2\\n', 'output': '16\\n0 1 2 3 5 6 7 8 10 11 12 13 15 16 17 18 '}, {'type': 'stdin_stdout', 'input': '3 50\\n25 25 50\\n', 'output': '3\\n0 25 50 '}, {'type': 'stdin_stdout', 'input': '5 34\\n28 32 91 6 70\\n', 'output': '4\\n0 6 28 34 '}, {'type': 'stdin_stdout', 'input': '8 15\\n13 3 5 5 6 14 5 5\\n', 'output': '4\\n0 5 10 15 '}, {'type': 'stdin_stdout', 'input': '10 67\\n58 39 56 7 51 47 20 26 24 54\\n', 'output': '4\\n0 20 47 67 '}, {'type': 'stdin_stdout', 'input': '9 436\\n1 2 4 8 16 32 64 128 256\\n', 'output': '32\\n0 4 16 20 32 36 48 52 128 132 144 148 160 164 176 180 256 260 272 276 288 292 304 308 384 388 400 404 416 420 432 436 '}, {'type': 'stdin_stdout', 'input': '9 442\\n1 2 4 8 16 32 64 128 256\\n', 'output': '64\\n0 2 8 10 16 18 24 26 32 34 40 42 48 50 56 58 128 130 136 138 144 146 152 154 160 162 168 170 176 178 184 186 256 258 264 266 272 274 280 282 288 290 296 298 304 306 312 314 384 386 392 394 400 402 408 410 416 418 424 426 432 434 440 442 '}, {'type': 'stdin_stdout', 'input': '10 58\\n20 25 11 37 4 48 20 54 2 26\\n', 'output': '18\\n0 2 4 11 13 20 22 25 27 31 33 36 38 45 47 54 56 58 '}, {'type': 'stdin_stdout', 'input': '10 58\\n57 2 18 35 3 35 38 7 38 3\\n', 'output': '16\\n0 2 3 5 18 20 21 23 35 37 38 40 53 55 56 58 '}, {'type': 'stdin_stdout', 'input': '10 34\\n1 28 14 4 11 24 4 11 7 28\\n', 'output': '24\\n0 1 4 5 7 8 9 11 12 14 15 16 18 19 20 22 23 25 26 27 29 30 33 34 '}, {'type': 'stdin_stdout', 'input': '10 10\\n7 4 6 2 9 6 8 8 10 10\\n', 'output': '6\\n0 2 4 6 8 10 '}, {'type': 'stdin_stdout', 'input': '10 58\\n30 51 7 29 25 2 44 28 49 45\\n', 'output': '10\\n0 2 7 9 28 30 49 51 56 58 '}, {'type': 'stdin_stdout', 'input': '15 185\\n69 61 185 127 169 42 140 93 12 115 36 46 19 80 123\\n', 'output': '34\\n0 12 19 31 36 42 46 55 58 61 69 73 78 80 82 88 92 93 97 103 105 107 112 116 124 127 130 139 143 149 154 166 173 185 '}, {'type': 'stdin_stdout', 'input': '15 388\\n33 232 106 369 266 135 22 169 367 37 14 181 232 25 154\\n', 'output': '59\\n0 14 22 25 33 37 39 47 51 58 59 62 70 72 84 135 149 157 160 168 169 172 174 181 182 183 186 191 193 194 195 197 202 205 206 207 214 216 219 220 228 231 239 253 304 316 318 326 329 330 337 341 349 351 355 363 366 374 388 '}, {'type': 'stdin_stdout', 'input': '1 79\\n79\\n', 'output': '2\\n0 79 '}, {'type': 'stdin_stdout', 'input': '10 38\\n16 21 7 12 20 37 34 7 6 20\\n', 'output': '8\\n0 6 12 18 20 26 32 38 '}, {'type': 'stdin_stdout', 'input': '5 1\\n1 500 205 6 355\\n', 'output': '2\\n0 1 '}, {'type': 'stdin_stdout', 'input': '10 86\\n64 5 30 53 65 24 32 36 23 23\\n', 'output': '8\\n0 24 30 32 54 56 62 86 '}, {'type': 'stdin_stdout', 'input': '15 109\\n92 60 14 9 22 99 17 22 82 28 105 98 109 20 32\\n', 'output': '28\\n0 17 20 22 28 32 37 39 42 44 45 48 49 50 59 60 61 64 65 67 70 72 77 81 87 89 92 109 '}, {'type': 'stdin_stdout', 'input': '9 474\\n1 2 4 8 16 32 64 128 256\\n', 'output': '64\\n0 2 8 10 16 18 24 26 64 66 72 74 80 82 88 90 128 130 136 138 144 146 152 154 192 194 200 202 208 210 216 218 256 258 264 266 272 274 280 282 320 322 328 330 336 338 344 346 384 386 392 394 400 402 408 410 448 450 456 458 464 466 472 474 '}, {'type': 'stdin_stdout', 'input': '10 1\\n1 1 1 1 1 1 1 1 1 1\\n', 'output': '2\\n0 1 '}, {'type': 'stdin_stdout', 'input': '14 24\\n18 16 15 24 18 19 19 8 8 2 4 9 18 9\\n', 'output': '14\\n0 2 4 6 8 9 11 13 15 16 18 20 22 24 '}, {'type': 'stdin_stdout', 'input': '14 176\\n66 109 148 141 65 52 147 65 171 11 157 60 151 19\\n', 'output': '4\\n0 19 157 176 '}, {'type': 'stdin_stdout', 'input': '14 54\\n54 39 2 16 17 18 41 22 25 30 54 4 27 2\\n', 'output': '23\\n0 2 4 6 8 16 18 20 22 24 25 27 29 30 32 34 36 38 46 48 50 52 54 '}, {'type': 'stdin_stdout', 'input': '5 182\\n134 18 48 91 25\\n', 'output': '15\\n0 18 25 43 48 66 73 91 109 116 134 139 157 164 182 '}, {'type': 'stdin_stdout', 'input': '8 39\\n38 17 25 33 7 29 15 22\\n', 'output': '8\\n0 7 15 17 22 24 32 39 '}, {'type': 'stdin_stdout', 'input': '15 182\\n63 17 134 113 18 48 112 175 91 25 176 55 78 177 175\\n', 'output': '15\\n0 18 25 43 48 66 73 91 109 116 134 139 157 164 182 '}, {'type': 'stdin_stdout', 'input': '8 42\\n7 24 22 25 31 12 17 26\\n', 'output': '4\\n0 17 25 42 '}, {'type': 'stdin_stdout', 'input': '10 195\\n157 4 183 125 63 121 113 3 145 103\\n', 'output': '16\\n0 3 4 7 63 66 67 70 125 128 129 132 188 191 192 195 '}, {'type': 'stdin_stdout', 'input': '8 91\\n74 25 66 50 62 30 50 50\\n', 'output': '4\\n0 25 66 91 '}, {'type': 'stdin_stdout', 'input': '10 147\\n15 76 48 111 39 111 145 16 34 68\\n', 'output': '16\\n0 15 16 31 48 63 64 68 79 83 84 99 116 131 132 147 '}, {'type': 'stdin_stdout', 'input': '10 9\\n5 2 5 2 5 1 4 1 3 1\\n', 'output': '10\\n0 1 2 3 4 5 6 7 8 9 '}, {'type': 'stdin_stdout', 'input': '10 10\\n5 10 10 10 2 3 4 7 3 5\\n', 'output': '9\\n0 2 3 4 5 6 7 8 10 '}, {'type': 'stdin_stdout', 'input': '5 6\\n2 71 7 27 6\\n', 'output': '2\\n0 6 '}, {'type': 'stdin_stdout', 'input': '1 114\\n114\\n', 'output': '2\\n0 114 '}, {'type': 'stdin_stdout', 'input': '9 457\\n1 2 4 8 16 32 64 128 256\\n', 'output': '32\\n0 1 8 9 64 65 72 73 128 129 136 137 192 193 200 201 256 257 264 265 320 321 328 329 384 385 392 393 448 449 456 457 '}, {'type': 'stdin_stdout', 'input': '8 15\\n13 3 5 3 6 14 5 5\\n', 'output': '4\\n0 5 10 15\\n'}, {'type': 'stdin_stdout', 'input': '10 67\\n58 39 56 6 51 47 20 26 24 54\\n', 'output': '4\\n0 20 47 67\\n'}, {'type': 'stdin_stdout', 'input': '10 58\\n20 25 11 37 4 28 20 54 2 26\\n', 'output': '22\\n0 2 4 11 13 20 22 25 26 27 28 30 31 32 33 36 38 45 47 54 56 58\\n'}, {'type': 'stdin_stdout', 'input': '10 110\\n57 2 18 35 3 35 38 7 38 3\\n', 'output': '54\\n0 2 3 5 6 7 8 9 10 12 13 15 18 35 37 38 40 41 43 44 45 46 47 48 50 51 53 57 59 60 62 63 64 65 66 67 69 70 72 73 75 92 95 97 98 100 101 102 103 104 105 107 108 110\\n'}, {'type': 'stdin_stdout', 'input': '10 34\\n1 28 14 4 11 24 4 11 7 46\\n', 'output': '24\\n0 1 4 5 7 8 9 11 12 14 15 16 18 19 20 22 23 25 26 27 29 30 33 34\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n7 4 6 2 9 6 8 8 18 10\\n', 'output': '6\\n0 2 4 6 8 10\\n'}, {'type': 'stdin_stdout', 'input': '10 58\\n22 51 7 29 25 2 44 28 49 45\\n', 'output': '11\\n0 2 7 9 22 29 36 49 51 56 58\\n'}, {'type': 'stdin_stdout', 'input': '15 185\\n69 61 185 127 169 42 140 93 12 215 36 46 19 80 123\\n', 'output': '34\\n0 12 19 31 36 42 46 55 58 61 69 73 78 80 82 88 92 93 97 103 105 107 112 116 124 127 130 139 143 149 154 166 173 185\\n'}, {'type': 'stdin_stdout', 'input': '15 388\\n33 232 106 369 266 135 22 169 367 37 14 181 232 25 257\\n', 'output': '89\\n0 14 22 25 33 36 37 39 47 51 55 58 59 61 62 69 70 72 73 76 80 84 92 94 95 98 106 109 117 131 135 149 157 160 168 169 172 174 181 182 183 186 191 193 194 195 197 202 205 206 207 214 216 219 220 228 231 239 253 257 271 279 282 290 293 294 296 304 308 312 315 316 318 319 326 327 329 330 333 337 341 349 351 352 355 363 366 374 388\\n'}, {'type': 'stdin_stdout', 'input': '10 38\\n16 21 7 12 20 37 34 7 3 20\\n', 'output': '19\\n0 3 7 10 12 14 15 16 17 19 21 22 23 24 26 28 31 35 38\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 422 205 6 355\\n', 'output': '2\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '10 86\\n64 5 30 53 41 24 32 36 23 23\\n', 'output': '8\\n0 24 30 32 54 56 62 86\\n'}, {'type': 'stdin_stdout', 'input': '15 109\\n154 60 14 9 22 99 17 22 82 28 105 98 109 20 32\\n', 'output': '28\\n0 17 20 22 28 32 37 39 42 44 45 48 49 50 59 60 61 64 65 67 70 72 77 81 87 89 92 109\\n'}, {'type': 'stdin_stdout', 'input': '9 474\\n2 2 4 8 16 32 64 128 256\\n', 'output': '64\\n0 2 8 10 16 18 24 26 64 66 72 74 80 82 88 90 128 130 136 138 144 146 152 154 192 194 200 202 208 210 216 218 256 258 264 266 272 274 280 282 320 322 328 330 336 338 344 346 384 386 392 394 400 402 408 410 448 450 456 458 464 466 472 474\\n'}, {'type': 'stdin_stdout', 'input': '14 24\\n18 16 15 24 18 19 19 8 8 2 4 9 18 15\\n', 'output': '12\\n0 2 4 6 8 9 15 16 18 20 22 24\\n'}, {'type': 'stdin_stdout', 'input': '14 176\\n66 109 148 141 65 52 147 75 171 11 157 60 151 19\\n', 'output': '4\\n0 19 157 176\\n'}, {'type': 'stdin_stdout', 'input': '14 54\\n8 39 2 16 17 18 41 22 25 30 54 4 27 2\\n', 'output': '37\\n0 2 4 6 8 10 12 14 16 17 18 19 20 21 22 24 25 26 27 28 29 30 32 33 34 35 36 37 38 40 42 44 46 48 50 52 54\\n'}, {'type': 'stdin_stdout', 'input': '5 182\\n134 18 48 17 25\\n', 'output': '4\\n0 48 134 182\\n'}, {'type': 'stdin_stdout', 'input': '8 39\\n38 17 25 33 7 37 15 22\\n', 'output': '8\\n0 7 15 17 22 24 32 39\\n'}, {'type': 'stdin_stdout', 'input': '15 182\\n63 17 134 183 18 48 112 175 91 25 176 55 78 177 175\\n', 'output': '15\\n0 18 25 43 48 66 73 91 109 116 134 139 157 164 182\\n'}, {'type': 'stdin_stdout', 'input': '8 42\\n7 24 22 25 43 12 17 26\\n', 'output': '4\\n0 17 25 42\\n'}, {'type': 'stdin_stdout', 'input': '10 195\\n157 4 183 129 63 121 113 3 145 103\\n', 'output': '8\\n0 3 63 66 129 132 192 195\\n'}, {'type': 'stdin_stdout', 'input': '10 147\\n15 76 48 101 39 111 145 16 34 68\\n', 'output': '16\\n0 15 16 31 48 63 64 68 79 83 84 99 116 131 132 147\\n'}, {'type': 'stdin_stdout', 'input': '10 13\\n5 2 5 2 5 1 4 1 3 1\\n', 'output': '14\\n0 1 2 3 4 5 6 7 8 9 10 11 12 13\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n5 10 10 16 2 3 4 7 3 5\\n', 'output': '9\\n0 2 3 4 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n0 71 7 27 6\\n', 'output': '2\\n0 6\\n'}, {'type': 'stdin_stdout', 'input': '9 457\\n1 2 4 8 11 32 64 128 256\\n', 'output': '32\\n0 1 8 9 64 65 72 73 128 129 136 137 192 193 200 201 256 257 264 265 320 321 328 329 384 385 392 393 448 449 456 457\\n'}, {'type': 'stdin_stdout', 'input': '6 18\\n5 3 1 10 12 2\\n', 'output': '18\\n0 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18\\n'}, {'type': 'stdin_stdout', 'input': '3 50\\n24 25 50\\n', 'output': '2\\n0 50\\n'}, {'type': 'stdin_stdout', 'input': '10 58\\n20 25 6 37 4 28 20 54 2 26\\n', 'output': '24\\n0 2 4 6 8 10 12 20 22 24 26 28 30 32 34 36 38 46 48 50 52 54 56 58\\n'}, {'type': 'stdin_stdout', 'input': '10 110\\n57 2 18 35 3 35 5 7 38 3\\n', 'output': '58\\n0 2 3 5 6 7 8 9 10 11 12 13 15 18 35 37 38 40 41 42 43 44 45 46 47 48 50 51 53 57 59 60 62 63 64 65 66 67 68 69 70 72 73 75 92 95 97 98 99 100 101 102 103 104 105 107 108 110\\n'}, {'type': 'stdin_stdout', 'input': '10 58\\n22 51 7 45 25 2 44 28 49 45\\n', 'output': '8\\n0 2 7 9 49 51 56 58\\n'}, {'type': 'stdin_stdout', 'input': '15 185\\n69 61 185 127 169 42 140 93 12 215 36 46 19 45 123\\n', 'output': '36\\n0 12 19 31 36 42 45 46 55 58 61 69 73 78 80 82 88 92 93 97 103 105 107 112 116 124 127 130 139 140 143 149 154 166 173 185\\n'}, {'type': 'stdin_stdout', 'input': '10 86\\n64 1 30 53 41 24 32 36 23 23\\n', 'output': '16\\n0 1 23 24 30 31 32 33 53 54 55 56 62 63 85 86\\n'}, {'type': 'stdin_stdout', 'input': '8 39\\n38 17 25 33 11 37 15 22\\n', 'output': '4\\n0 17 22 39\\n'}, {'type': 'stdin_stdout', 'input': '15 244\\n63 17 134 183 18 48 112 175 91 25 176 55 78 177 175\\n', 'output': '52\\n0 17 18 25 35 42 48 55 63 65 72 73 78 80 81 88 90 91 98 103 105 108 109 111 116 118 126 128 133 135 136 139 141 146 153 154 156 163 164 166 171 172 179 181 189 196 202 209 219 226 227 244\\n'}, {'type': 'stdin_stdout', 'input': '10 147\\n15 76 48 101 39 111 145 32 34 68\\n', 'output': '8\\n0 32 39 71 76 108 115 147\\n'}, {'type': 'stdin_stdout', 'input': '6 32\\n5 3 1 10 12 2\\n', 'output': '22\\n0 2 3 5 7 8 10 12 13 14 15 17 18 19 20 22 24 25 27 29 30 32\\n'}, {'type': 'stdin_stdout', 'input': '8 15\\n13 1 5 3 6 18 5 5\\n', 'output': '14\\n0 1 3 4 5 6 7 8 9 10 11 12 14 15\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n1 1 1 1 2 1 1 1 1 1\\n', 'output': '2\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '8 15\\n13 3 5 3 6 18 5 5\\n', 'output': '4\\n0 5 10 15\\n'}, {'type': 'stdin_stdout', 'input': '10 67\\n58 39 56 12 51 47 20 26 24 54\\n', 'output': '4\\n0 20 47 67\\n'}, {'type': 'stdin_stdout', 'input': '10 34\\n1 14 14 4 11 24 4 11 7 46\\n', 'output': '24\\n0 1 4 5 7 8 9 11 12 14 15 16 18 19 20 22 23 25 26 27 29 30 33 34\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n7 4 6 2 16 6 8 8 18 10\\n', 'output': '6\\n0 2 4 6 8 10\\n'}, {'type': 'stdin_stdout', 'input': '10 38\\n16 21 7 12 20 33 34 7 3 20\\n', 'output': '19\\n0 3 7 10 12 14 15 16 17 19 21 22 23 24 26 28 31 35 38\\n'}, {'type': 'stdin_stdout', 'input': '9 474\\n3 2 4 8 16 32 64 128 256\\n', 'output': '64\\n0 2 8 10 16 18 24 26 64 66 72 74 80 82 88 90 128 130 136 138 144 146 152 154 192 194 200 202 208 210 216 218 256 258 264 266 272 274 280 282 320 322 328 330 336 338 344 346 384 386 392 394 400 402 408 410 448 450 456 458 464 466 472 474\\n'}, {'type': 'stdin_stdout', 'input': '14 54\\n8 39 2 16 17 22 41 22 25 30 54 4 27 2\\n', 'output': '37\\n0 2 4 6 8 10 12 14 16 17 18 19 20 21 22 24 25 26 27 28 29 30 32 33 34 35 36 37 38 40 42 44 46 48 50 52 54\\n'}, {'type': 'stdin_stdout', 'input': '8 42\\n7 24 22 25 75 12 17 26\\n', 'output': '4\\n0 17 25 42\\n'}, {'type': 'stdin_stdout', 'input': '10 13\\n5 2 5 2 5 1 4 1 5 1\\n', 'output': '14\\n0 1 2 3 4 5 6 7 8 9 10 11 12 13\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n5 10 10 16 2 3 2 7 3 5\\n', 'output': '9\\n0 2 3 4 5 6 7 8 10\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n0 8 7 27 6\\n', 'output': '2\\n0 6\\n'}, {'type': 'stdin_stdout', 'input': '3 50\\n36 25 50\\n', 'output': '2\\n0 50\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78137","program":"```python\nfrom sys import stdin,stdout\nn,m=map(int,input().split())\ns=[0]+list(map(int,stdin.readline().strip().split()))\ndp=[[[False for i in range(m+1)] for j in range(m+1)] for k in range(2)]\ndp[0][0][0]=True\ncur=0\nfor i in range(1,n+1):\n cur+=1\n cur%=2\n last=(cur+1)%2\n for j in range(m+1):\n for k in range(j+1):\n if j-s[i]>-1 and k-s[i]>-1:\n dp[cur][j][k]=dp[last][j][k] or dp[last][j-s[i]][k] or dp[last][j-s[i]][k-s[i]]\n elif j-s[i]>-1 :\n dp[cur][j][k]=dp[last][j][k] or dp[last][j-s[i]][k]\n elif k-s[i]>-1:\n dp[cur][j][k]=dp[last][j][k] or dp[last][j-s[i]][k-s[i]]\n else:\n dp[cur][j][k]=dp[last][j][k]\n \nn1=0\nans=\"\"\nfor i in range(k+1):\n if dp[cur][k][i]:\n ans+=str(i)+\" \"\n n1+=1\nstdout.write(str(n1)+chr(10))\nstdout.write(ans)\n \n\n```","inputs":"6 18\n5 6 1 10 12 2\n","output":"16\n0 1 2 3 5 6 7 8 10 11 12 13 15 16 17 18 ","actual_output":"16\n0 1 2 3 5 6 7 8 10 11 12 13 15 16 17 18 ","execution_success":true,"sample_index":12459},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"710_D. Two Arithmetic Progressions","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given two arithmetic progressions: a1k + b1 and a2l + b2. Find the number of integers x such that L \u2264 x \u2264 R and x = a1k' + b1 = a2l' + b2, for some integers k', l' \u2265 0.\n\nInput\n\nThe only line contains six integers a1, b1, a2, b2, L, R (0 < a1, a2 \u2264 2\u00b7109, - 2\u00b7109 \u2264 b1, b2, L, R \u2264 2\u00b7109, L \u2264 R).\n\nOutput\n\nPrint the desired number of integers x.\n\nExamples\n\nInput\n\n2 0 3 3 5 21\n\n\nOutput\n\n3\n\n\nInput\n\n2 4 3 0 6 17\n\n\nOutput\n\n2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nimport bisect\nfrom bisect import bisect_left as lb\ninput_=lambda: sys.stdin.readline().strip(\"\\r\\n\")\nfrom math import log\nfrom math import gcd\nfrom math import atan2,acos\nfrom random import randint\nsa=lambda :input_()\nsb=lambda:int(input_())\nsc=lambda:input_().split()\nsd=lambda:list(map(int,input_().split()))\nsflo=lambda:list(map(float,input_().split()))\nse=lambda:float(input_())\nsf=lambda:list(input_())\nflsh=lambda: sys.stdout.flush()\n#sys.setrecursionlimit(10**6)\nmod=10**9+7\nmod1=998244353\ngp=[]\ncost=[]\ndp=[]\nmx=[]\nans1=[]\nans2=[]\nspecial=[]\nspecnode=[]\na=0\nkthpar=[]\ndef dfs(root,par):\n if par!=-1:\n dp[root]=dp[par]+1\n for i in range(1,20):\n if kthpar[root][i-1]!=-1:\n kthpar[root][i]=kthpar[kthpar[root][i-1]][i-1]\n for child in gp[root]:\n if child==par:continue\n kthpar[child][0]=root\n dfs(child,root)\nans=0\ndef hnbhai(tc):\n a1,b1,a2,b2,l,r=sd()\n if b1b1:\n if b1>b2:\n b2-=((b2-b1)//a2)*a2\n else:\n b1-=((b1-b2)//a1)*a1\n if mx>b1:\n print(1+(r-b1)//lcm)\n return\n print(0)\nfor _ in range(1):\n hnbhai(_+1)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 0 3 3 5 21\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 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:input_()\nsb=lambda:int(input_())\nsc=lambda:input_().split()\nsd=lambda:list(map(int,input_().split()))\nsflo=lambda:list(map(float,input_().split()))\nse=lambda:float(input_())\nsf=lambda:list(input_())\nflsh=lambda: sys.stdout.flush()\n#sys.setrecursionlimit(10**6)\nmod=10**9+7\nmod1=998244353\ngp=[]\ncost=[]\ndp=[]\nmx=[]\nans1=[]\nans2=[]\nspecial=[]\nspecnode=[]\na=0\nkthpar=[]\ndef dfs(root,par):\n if par!=-1:\n dp[root]=dp[par]+1\n for i in range(1,20):\n if kthpar[root][i-1]!=-1:\n kthpar[root][i]=kthpar[kthpar[root][i-1]][i-1]\n for child in gp[root]:\n if child==par:continue\n kthpar[child][0]=root\n dfs(child,root)\nans=0\ndef hnbhai(tc):\n a1,b1,a2,b2,l,r=sd()\n if b1b1:\n if b1>b2:\n b2-=((b2-b1)//a2)*a2\n else:\n b1-=((b1-b2)//a1)*a1\n if mx>b1:\n print(1+(r-b1)//lcm)\n return\n print(0)\nfor _ in range(1):\n hnbhai(_+1)\n\n```","inputs":"2 0 3 3 5 21\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12460},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"847_E. Packmen","prompt":"Solve the following coding problem using the programming language python:\n\nA game field is a strip of 1 \u00d7 n square cells. In some cells there are Packmen, in some cells \u2014 asterisks, other cells are empty.\n\nPackman can move to neighboring cell in 1 time unit. If there is an asterisk in the target cell then Packman eats it. Packman doesn't spend any time to eat an asterisk.\n\nIn the initial moment of time all Packmen begin to move. Each Packman can change direction of its move unlimited number of times, but it is not allowed to go beyond the boundaries of the game field. Packmen do not interfere with the movement of other packmen; in one cell there can be any number of packmen moving in any directions.\n\nYour task is to determine minimum possible time after which Packmen can eat all the asterisks.\n\nInput\n\nThe first line contains a single integer n (2 \u2264 n \u2264 105) \u2014 the length of the game field.\n\nThe second line contains the description of the game field consisting of n symbols. If there is symbol '.' in position i \u2014 the cell i is empty. If there is symbol '*' in position i \u2014 in the cell i contains an asterisk. If there is symbol 'P' in position i \u2014 Packman is in the cell i.\n\nIt is guaranteed that on the game field there is at least one Packman and at least one asterisk.\n\nOutput\n\nPrint minimum possible time after which Packmen can eat all asterisks.\n\nExamples\n\nInput\n\n7\n*..P*P*\n\n\nOutput\n\n3\n\n\nInput\n\n10\n.**PP.*P.*\n\n\nOutput\n\n2\n\nNote\n\nIn the first example Packman in position 4 will move to the left and will eat asterisk in position 1. He will spend 3 time units on it. During the same 3 time units Packman in position 6 will eat both of neighboring with it asterisks. For example, it can move to the left and eat asterisk in position 5 (in 1 time unit) and then move from the position 5 to the right and eat asterisk in the position 7 (in 2 time units). So in 3 time units Packmen will eat all asterisks on the game field.\n\nIn the second example Packman in the position 4 will move to the left and after 2 time units will eat asterisks in positions 3 and 2. Packmen in positions 5 and 8 will move to the right and in 2 time units will eat asterisks in positions 7 and 10, respectively. So 2 time units is enough for Packmen to eat all asterisks on the game field.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport bisect\n\nn = int(input())\ns = input()\npackmans = []\nstars = []\nfor i in range(n):\n if s[i] == '*':\n stars.append(i)\n elif s[i] == 'P':\n packmans.append(i)\n\nif len(stars) == 0:\n print(0)\n exit()\n\n\ndef check(t):\n first_to_eat = 0\n for i in range(len(packmans)):\n x = stars[first_to_eat]\n if packmans[i] > x:\n if packmans[i] - x > t:\n return False\n d1 = t - 2 * (packmans[i] - x)\n d2 = (t - (packmans[i] - x)) // 2\n first_to_eat = bisect.bisect_right(stars, packmans[i] + max(d1, d2))\n if first_to_eat < len(stars) and stars[first_to_eat] == packmans[i] + max(d1, d2):\n first_to_eat += 1\n\n else:\n j = bisect.bisect_right(stars, packmans[i] + t)\n if first_to_eat < len(stars) and stars[first_to_eat] == packmans[i] + t:\n first_to_eat += 1\n first_to_eat = max(j, first_to_eat)\n if first_to_eat >= len(stars):\n return True\n return first_to_eat >= len(stars)\n\n\nl = 0\nr = 2 * n + 1\n\nwhile r - l > 1:\n m = (l + r) // 2\n if check(m):\n r = m\n else:\n l = m\nprint(r)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10\\n.**PP.*P.*\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n*..P*P*\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '55\\n*.....*.*..**..*...***..**.**.*.*.P..*.*.**...**.*..*.*\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '100\\nPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP*PPPPPPPPPPPPP\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '40\\nP*....*.*....*...*..*.......*...**..***.\\n', 'output': '38\\n'}, {'type': 'stdin_stdout', 'input': '12\\nP**.*P*P*P**\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 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'55\\n.*..........*....**....P.P.*.P.*....P*.*P.....*.P......\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '55\\n*.*..****...**.*.*..P.*...**.**...**...*..**..*.**....*\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '40\\n...**P*P*...P.*PP***.*.*P..**.*.PP**.*.*\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '70\\n.....P*..P.**.*P*......*.P..**.P...P...PP..*....P...P*.....P*P**..*.P*\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '20\\n*PP**P*.P***P**PPPP.\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '55\\n*.*..*.**...**.*.*..P.*.*.**.**..***...*..**..*.*.....*\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '100\\n.....................P............P....P....*.............*........*.P.................P.......**...\\n', 'output': '11\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78165","program":"```python\nimport bisect\n\nn = int(input())\ns = input()\npackmans = []\nstars = []\nfor i in range(n):\n if s[i] == '*':\n stars.append(i)\n elif s[i] == 'P':\n packmans.append(i)\n\nif len(stars) == 0:\n print(0)\n exit()\n\n\ndef check(t):\n first_to_eat = 0\n for i in range(len(packmans)):\n x = stars[first_to_eat]\n if packmans[i] > x:\n if packmans[i] - x > t:\n return False\n d1 = t - 2 * (packmans[i] - x)\n d2 = (t - (packmans[i] - x)) // 2\n first_to_eat = bisect.bisect_right(stars, packmans[i] + max(d1, d2))\n if first_to_eat < len(stars) and stars[first_to_eat] == packmans[i] + max(d1, d2):\n first_to_eat += 1\n\n else:\n j = bisect.bisect_right(stars, packmans[i] + t)\n if first_to_eat < len(stars) and stars[first_to_eat] == packmans[i] + t:\n first_to_eat += 1\n first_to_eat = max(j, first_to_eat)\n if first_to_eat >= len(stars):\n return True\n return first_to_eat >= len(stars)\n\n\nl = 0\nr = 2 * n + 1\n\nwhile r - l > 1:\n m = (l + r) // 2\n if check(m):\n r = m\n else:\n l = m\nprint(r)\n\n```","inputs":"10\n.**PP.*P.*\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12462},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"939_A. Love Triangle","prompt":"Solve the following coding problem using the programming language python:\n\nAs you could know there are no male planes nor female planes. However, each plane on Earth likes some other plane. There are n planes on Earth, numbered from 1 to n, and the plane with number i likes the plane with number fi, where 1 \u2264 fi \u2264 n and fi \u2260 i.\n\nWe call a love triangle a situation in which plane A likes plane B, plane B likes plane C and plane C likes plane A. Find out if there is any love triangle on Earth.\n\nInput\n\nThe first line contains a single integer n (2 \u2264 n \u2264 5000) \u2014 the number of planes.\n\nThe second line contains n integers f1, f2, ..., fn (1 \u2264 fi \u2264 n, fi \u2260 i), meaning that the i-th plane likes the fi-th.\n\nOutput\n\nOutput \u00abYES\u00bb if there is a love triangle consisting of planes on Earth. Otherwise, output \u00abNO\u00bb.\n\nYou can output any letter in lower case or in upper case.\n\nExamples\n\nInput\n\n5\n2 4 5 1 3\n\n\nOutput\n\nYES\n\n\nInput\n\n5\n5 5 5 5 1\n\n\nOutput\n\nNO\n\nNote\n\nIn first example plane 2 likes plane 4, plane 4 likes plane 1, plane 1 likes plane 2 and that is a love triangle.\n\nIn second example there are no love triangles.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\na=list(map(int,input().split()))\nfor i in range(n):\n if a[a[a[i]-1]-1]==i+1:\n print('YES')\n exit(0)\nprint('NO')\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n2 4 5 1 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 5 5 5 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '100\\n50 40 60 87 39 58 44 84 46 68 16 57 77 87 92 95 42 31 74 15 36 84 30 3 47 15 87 90 76 66 6 63 74 19 40 49 6 84 41 9 77 34 7 12 11 73 58 24 81 14 81 29 65 100 1 85 64 32 38 4 54 67 32 81 80 7 100 71 29 80 4 52 47 7 78 56 52 75 81 37 16 41 27 28 58 60 62 47 29 40 37 14 59 91 12 54 25 58 12 43\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '2\\n2 1\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '100\\n25 6 46 37 87 99 70 31 46 12 94 40 87 56 28 8 94 39 13 12 67 13 71 39 83 48 40 14 62 41 16 71 20 41 83 41 68 98 23 82 62 83 62 35 49 22 31 21 66 98 54 39 34 52 11 28 47 89 25 44 68 36 91 46 82 86 88 48 27 93 7 9 53 36 16 100 84 84 44 25 58 66 16 46 72 21 91 78 4 17 44 17 47 67 93 89 75 44 56 50\\n', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': '10\\n4 10 9 5 3 1 5 10 6 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 1 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 4 5 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 5 4 9 10 9 9 5 3 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 4 5 5 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '100\\n50 40 60 87 39 58 44 84 46 68 16 57 77 87 92 95 42 31 74 15 36 84 30 3 47 3 87 90 76 66 6 63 74 19 40 49 6 84 41 9 77 34 7 12 11 73 58 24 81 14 81 29 65 100 1 85 64 32 38 4 54 67 32 81 80 7 100 71 29 80 4 52 47 7 78 56 52 75 81 37 16 41 27 28 58 60 62 47 29 40 37 14 59 91 12 54 25 58 12 43\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '100\\n25 6 46 37 87 99 70 31 46 12 94 40 87 56 28 8 94 39 13 12 67 13 71 39 83 48 40 14 62 41 16 71 20 41 83 41 68 98 23 82 62 83 62 35 49 22 31 21 66 98 54 39 34 52 11 28 47 89 25 44 68 36 91 46 82 86 88 48 27 93 7 9 53 36 16 100 84 84 44 25 58 66 16 46 72 21 91 78 4 17 3 17 47 67 93 89 75 44 56 50\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 6 9 5 3 1 5 10 6 4\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 1 4 5 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 4 5 5 4\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '100\\n50 40 60 87 39 58 44 84 46 68 16 57 77 87 92 95 42 31 74 15 36 84 30 3 47 3 87 90 76 66 6 63 74 19 40 49 6 84 41 9 77 34 7 12 11 73 58 24 81 14 81 29 65 100 1 85 64 32 38 4 54 67 32 81 80 7 100 71 29 80 4 52 47 7 78 56 52 75 81 37 16 41 27 28 21 60 62 47 29 40 37 14 59 91 12 54 25 58 12 43\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '100\\n25 6 46 37 87 99 70 31 46 12 94 40 87 56 28 8 94 39 25 12 67 13 71 39 83 48 40 14 62 41 16 71 20 41 83 41 68 98 23 82 62 83 62 35 49 22 31 21 66 98 54 39 34 52 11 28 47 89 25 44 68 36 91 46 82 86 88 48 27 93 7 9 53 36 16 100 84 84 44 25 58 66 16 46 72 21 91 78 4 17 3 17 47 67 93 89 75 44 56 50\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 3 5 5 4\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '100\\n50 40 60 87 39 58 44 84 46 68 16 57 77 87 92 95 42 31 74 15 36 84 30 3 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34 52 11 28 47 89 14 44 68 36 91 46 82 86 88 48 27 93 7 9 53 36 16 100 84 84 44 25 58 66 16 46 72 21 91 78 4 17 3 17 47 67 93 89 75 44 56 50\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '100\\n50 40 60 87 39 58 44 84 46 68 16 57 77 87 92 95 42 31 74 15 50 84 30 3 47 3 87 90 76 66 6 63 74 19 40 49 6 84 41 9 77 34 7 12 11 73 58 24 81 14 81 29 65 100 1 85 64 32 38 4 54 67 32 81 80 7 100 71 29 80 4 52 47 7 78 56 52 75 81 37 16 41 27 28 21 60 62 47 29 40 37 14 59 91 23 54 25 58 12 43\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '100\\n50 40 60 87 39 58 44 84 46 68 16 57 77 87 92 95 42 31 74 15 36 84 30 3 45 3 87 90 76 66 6 63 74 19 40 49 6 84 41 9 77 34 7 12 11 73 58 24 81 14 81 29 65 100 1 85 64 32 38 4 54 67 32 81 80 7 100 71 29 80 4 52 47 7 78 56 52 75 81 37 16 41 27 28 21 60 62 47 29 40 37 14 59 91 23 54 25 68 12 43\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '100\\n25 6 46 37 87 99 70 31 46 12 94 40 87 56 28 8 94 39 25 12 67 13 71 39 83 48 40 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'input': '100\\n50 40 6 87 39 58 44 84 46 68 16 57 77 87 92 95 42 31 74 15 50 84 30 3 47 3 87 90 76 66 6 63 74 19 40 49 6 84 41 9 77 34 7 12 2 73 58 24 81 14 81 29 65 100 1 85 64 32 38 4 78 67 32 81 80 7 100 71 29 80 6 96 47 7 78 62 52 75 12 37 16 41 27 28 21 60 47 47 21 40 37 14 59 91 23 54 33 58 12 43\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '100\\n50 40 60 87 39 58 44 84 46 68 16 57 77 87 92 95 42 31 74 15 36 84 30 3 47 15 87 90 76 66 6 63 74 19 40 49 6 84 41 9 77 34 7 12 11 73 58 24 81 14 81 29 65 100 1 85 64 32 38 4 54 67 32 81 80 7 100 71 29 80 4 52 47 7 78 56 52 75 81 37 16 41 27 28 58 60 62 47 29 40 37 8 59 91 12 54 25 96 12 43\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '100\\n25 6 46 37 87 99 70 31 46 12 94 40 87 56 28 8 94 39 13 12 67 13 71 39 83 48 40 14 62 41 16 71 20 41 83 41 68 98 23 82 62 83 62 35 49 22 31 21 66 98 54 39 34 52 11 28 33 89 25 44 68 36 91 46 82 86 88 48 27 93 7 9 65 36 16 100 84 84 44 25 58 66 16 46 72 21 91 78 4 17 44 17 47 67 93 89 75 44 56 50\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10\\n3 5 4 9 10 8 9 5 3 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '100\\n25 6 46 37 87 99 70 31 46 12 94 40 87 56 28 8 94 39 13 12 67 13 71 39 83 48 40 14 62 41 16 71 20 41 83 41 68 98 23 82 62 83 62 35 49 22 28 21 66 98 54 39 34 52 11 28 47 89 25 44 68 36 91 46 82 86 88 48 27 93 7 9 53 36 16 100 84 84 44 25 58 66 16 46 72 21 91 78 4 17 3 24 47 67 93 89 75 44 56 50\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '100\\n50 40 60 87 39 58 44 84 46 68 16 57 77 87 92 95 42 31 74 15 36 84 30 3 47 3 87 90 76 66 6 63 74 19 40 49 6 84 41 9 77 34 7 12 11 73 58 24 81 14 81 29 65 100 1 85 64 32 38 4 54 67 32 81 80 7 100 71 29 80 4 52 47 7 78 56 52 75 81 37 16 41 27 28 21 60 53 47 29 40 37 14 59 91 12 54 25 58 12 84\\n', 'output': 'No\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78181","program":"```python\nn=int(input())\na=list(map(int,input().split()))\nfor i in range(n):\n if a[a[a[i]-1]-1]==i+1:\n print('YES')\n exit(0)\nprint('NO')\n\n```","inputs":"5\n2 4 5 1 3\n","output":"YES\n","actual_output":"YES\n","execution_success":true,"sample_index":12463},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"964_C. Alternating Sum","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given two integers a and b. Moreover, you are given a sequence s_0, s_1, ..., s_{n}. All values in s are integers 1 or -1. It's known that sequence is k-periodic and k divides n+1. In other words, for each k \u2264 i \u2264 n it's satisfied that s_{i} = s_{i - k}.\n\nFind out the non-negative remainder of division of \u2211 _{i=0}^{n} s_{i} a^{n - i} b^{i} by 10^{9} + 9.\n\nNote that the modulo is unusual!\n\nInput\n\nThe first line contains four integers n, a, b and k (1 \u2264 n \u2264 10^{9}, 1 \u2264 a, b \u2264 10^{9}, 1 \u2264 k \u2264 10^{5}).\n\nThe second line contains a sequence of length k consisting of characters '+' and '-'. \n\nIf the i-th character (0-indexed) is '+', then s_{i} = 1, otherwise s_{i} = -1.\n\nNote that only the first k members of the sequence are given, the rest can be obtained using the periodicity property.\n\nOutput\n\nOutput a single integer \u2014 value of given expression modulo 10^{9} + 9.\n\nExamples\n\nInput\n\n2 2 3 3\n+-+\n\n\nOutput\n\n7\n\n\nInput\n\n4 1 5 1\n-\n\n\nOutput\n\n999999228\n\nNote\n\nIn the first example:\n\n(\u2211 _{i=0}^{n} s_{i} a^{n - i} b^{i}) = 2^{2} 3^{0} - 2^{1} 3^{1} + 2^{0} 3^{2} = 7\n\nIn the second example:\n\n(\u2211 _{i=0}^{n} s_{i} a^{n - i} b^{i}) = -1^{4} 5^{0} - 1^{3} 5^{1} - 1^{2} 5^{2} - 1^{1} 5^{3} - 1^{0} 5^{4} = -781 \u2261 999999228 \\pmod{10^{9} + 9}.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, a, b, k = map(int, input().split() )\ns = input()\n\nmod = (int)( 1e9 + 9 )\n\nans = 0\nt = (int)( (n + 1) / k )\n\ndef modInverse(a):\n return pow(a, mod - 2, mod) \n\ni = 0\nfor ind in range( len(s) ):\n \n first = ( pow(a, n - i, mod ) * pow( b, i, mod ) ) % mod\n num = ( pow( b, k, mod ) * modInverse( pow(a, k, mod) ) ) % mod\n \n if ( b >= a ) :\n den = ( num - 1 + mod ) % mod\n num = ( pow( num, t, mod ) - 1 + mod ) % mod\n else:\n den = ( 1 - num + mod ) % mod\n num = ( 1 - pow( num, t, mod ) + mod ) % mod\n \n if num == 0:\n temp = ( t * first ) % mod\n else:\n temp = ( num * modInverse(den) ) % mod\n temp = ( temp * first ) % mod\n \n if s[ind] == '+':\n ans = ( ans + temp )%mod\n elif s[ind] == '-':\n ans = ( ans - temp + mod ) % mod\n \n i += 1\n if ( i > n ):\n i = 0\n\nprint (ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 2 3 3\\n+-+\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '4 1 5 1\\n-\\n', 'output': '999999228\\n'}, {'type': 'stdin_stdout', 'input': '743329 973758 92942 82\\n++----+-++++----+--+++---+--++++-+-+---+++++--+--+++++++--++-+++----+--+++++-+--+-\\n', 'output': '299311566\\n'}, {'type': 'stdin_stdout', 'input': '403493428 317461491 556701240 1\\n-\\n', 'output': '936516261\\n'}, {'type': 'stdin_stdout', 'input': '938449224 59852396 219719125 1\\n-\\n', 'output': '648647459\\n'}, {'type': 'stdin_stdout', 'input': '5 1 1 6\\n++---+\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '234179195 430477711 115381398 12\\n++++-+-+-+++\\n', 'output': '549793323\\n'}, {'type': 'stdin_stdout', 'input': '397521 174985 279760 1\\n+\\n', 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(int)( 1e9 + 9 )\n\nans = 0\nt = (int)( (n + 1) / k )\n\ndef modInverse(a):\n return pow(a, mod - 2, mod) \n\ni = 0\nfor ind in range( len(s) ):\n \n first = ( pow(a, n - i, mod ) * pow( b, i, mod ) ) % mod\n num = ( pow( b, k, mod ) * modInverse( pow(a, k, mod) ) ) % mod\n \n if ( b >= a ) :\n den = ( num - 1 + mod ) % mod\n num = ( pow( num, t, mod ) - 1 + mod ) % mod\n else:\n den = ( 1 - num + mod ) % mod\n num = ( 1 - pow( num, t, mod ) + mod ) % mod\n \n if num == 0:\n temp = ( t * first ) % mod\n else:\n temp = ( num * modInverse(den) ) % mod\n temp = ( temp * first ) % mod\n \n if s[ind] == '+':\n ans = ( ans + temp )%mod\n elif s[ind] == '-':\n ans = ( ans - temp + mod ) % mod\n \n i += 1\n if ( i > n ):\n i = 0\n\nprint (ans)\n```","inputs":"2 2 3 3\n+-+\n","output":"7\n","actual_output":"7\n","execution_success":true,"sample_index":12464},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"991_D. Bishwock","prompt":"Solve the following coding problem using the programming language python:\n\nBishwock is a chess figure that consists of three squares resembling an \"L-bar\". This figure can be rotated by 90, 180 and 270 degrees so it can have four possible states:\n \n \n \n XX XX .X X. \n X. .X XX XX \n \n\nBishwocks don't attack any squares and can even occupy on the adjacent squares as long as they don't occupy the same square. \n\nVasya has a board with 2\u00d7 n squares onto which he wants to put some bishwocks. To his dismay, several squares on this board are already occupied by pawns and Vasya can't put bishwocks there. However, pawns also don't attack bishwocks and they can occupy adjacent squares peacefully.\n\nKnowing the positions of pawns on the board, help Vasya to determine the maximum amount of bishwocks he can put onto the board so that they wouldn't occupy the same squares and wouldn't occupy squares with pawns.\n\nInput\n\nThe input contains two nonempty strings that describe Vasya's board. Those strings contain only symbols \"0\" (zero) that denote the empty squares and symbols \"X\" (uppercase English letter) that denote the squares occupied by pawns. Strings are nonempty and are of the same length that does not exceed 100.\n\nOutput\n\nOutput a single integer \u2014 the maximum amount of bishwocks that can be placed onto the given board.\n\nExamples\n\nInput\n\n00\n00\n\n\nOutput\n\n1\n\nInput\n\n00X00X0XXX0\n0XXX0X00X00\n\n\nOutput\n\n4\n\nInput\n\n0X0X0\n0X0X0\n\n\nOutput\n\n0\n\nInput\n\n0XXX0\n00000\n\n\nOutput\n\n2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef main():\n a, b = [i for i in input()], [i for i in input()]\n l = len(a)\n c = 0\n for i in range(l - 1):\n if a[i] == '0':\n if b[i] == '0':\n if a[i + 1] == '0':\n c += 1\n a[i], b[i], a[i + 1] = 1, 1, 1\n elif b[i + 1] == '0':\n c += 1\n a[i], b[i], b[i + 1] = 1, 1, 1\n elif a[i + 1] == '0' and b[i + 1] == '0':\n c += 1\n a[i], a[i + 1], b[i + 1] = 1, 1, 1\n elif b[i] == '0' and b[i + 1] == '0' and a[i + 1] == '0':\n c += 1\n b[i], a[i + 1], b[i + 1] = 1, 1, 1\n print(c)\n return 0\nmain()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '0XXX0\\n00000\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '0X0X0\\n0X0X0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '00\\n00\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '00X00X0XXX0\\n0XXX0X00X00\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'X\\n0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '00000000\\nXXXXXXXX\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'XX\\nXX\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '00\\nX0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '000\\n00X\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'X0000X\\n00000X\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 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For each d=1,2,\\ldots,D, calculate the satisfaction at the end of day d.\n\n\n\nInput\n\nInput is given from Standard Input in the form of the input of Problem A followed by the output of Problem A.\n\n\nD\nc_1 c_2 \\cdots c_{26}\ns_{1,1} s_{1,2} \\cdots s_{1,26}\n\\vdots\ns_{D,1} s_{D,2} \\cdots s_{D,26}\nt_1\nt_2\n\\vdots\nt_D\n\n\n* The constraints and generation methods for the input part are the same as those for Problem A.\n* For each d, t_d is an integer satisfying 1\\leq t_d \\leq 26, and your program is expected to work correctly for any value that meets the constraints.\n\n\n\nOutput\n\nLet v_d be the satisfaction at the end of day d. Print D integers v_d to Standard Output in the following format:\n\n\nv_1\nv_2\n\\vdots\nv_D\n\nOutput\n\nLet v_d be the satisfaction at the end of day d. Print D integers v_d to Standard Output in the following format:\n\n\nv_1\nv_2\n\\vdots\nv_D\n\nExample\n\nInput\n\n5\n86 90 69 51 2 96 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 82\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\n6674 17707 13855 16407 12232 2886 11908 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 19745 16880 17773 18359 3921 14172 16730 11157 5439 256\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\n19855 17918 7990 10572 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\n1\n17\n13\n14\n13\n\n\nOutput\n\n18398\n35037\n51140\n65837\n79325\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nD=int(input())\nc=list(map(int, input().split()))\ns=[list(map(int, input().split())) for i in range(D)]\nt=[int(input()) for i in range(D)]\n\nd=[0]*(26)\nv=[0]*(D+1)\n\n\nfor i in range(D):\n v[i]=s[i][t[i]-1]\n d[t[i]-1]=-1\n sb=0 \n for j in range(26):\n d[j]+=1 \n sb+=d[j]*c[j]\n \n v[i]+=v[i-1]-sb\n print(v[i])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 96 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 11908 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 19745 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\\n19855 17918 7990 10572 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18398\\n35037\\n51140\\n65837\\n79325'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 96 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 19745 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\\n19855 17918 7990 10572 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18398\\n35037\\n51140\\n65837\\n79325\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 19745 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\\n19855 17918 7990 17084 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18429\\n35130\\n51326\\n66147\\n79790\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 5 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\\n19855 17918 7990 17084 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18428\\n35127\\n51320\\n66137\\n79775\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 33 47 88 34 45 46 89 34 31 38 97 84 41 80 14 5 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\\n19855 17918 7990 17084 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18466\\n35241\\n51548\\n66517\\n80345\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 33 47 88 34 45 46 89 34 31 38 97 84 41 80 14 5 50 83 7 82\\n19771 12979 18912 4763 10544 12928 13403 3047 23673 9740 8100 92 4424 14730 962 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 7416 17272 15364 19277 18094 2341 3705 2150 6159 18683 15410 11128 4570\\n6786 4239 19925 1799 714 9563 5780 5658 19857 11401 6997 6498 19933 3848 367 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 19\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 22483 3514 3959 5202 19850 4111 9790 4267 679 18500 10278 17975 5255 13532 197 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 4985 5042 4028 19922 12132 16259 27485 2976 547 21470 19830 16285 4806 4471 9457 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11678\\n28457\\n44768\\n59741\\n73573\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 33 47 88 34 45 46 89 34 31 38 97 84 41 80 14 5 50 83 7 71\\n19771 12979 18912 4763 10544 12928 13403 3047 42286 9740 8100 92 4424 14730 962 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 8629 1537 10440 10711 4917 7416 17272 15364 19277 18094 2341 3705 3037 6159 18683 15410 11128 4570\\n6786 4239 19925 1799 714 9563 5780 5658 19857 11401 6997 6498 19933 3848 367 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 19\\n8633 15862 15303 10749 18499 6000 10317 5901 9395 22483 3514 3959 5202 19850 4111 2264 4267 679 18500 10278 17975 5255 13532 197 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 4985 5042 4028 19922 12132 16259 48289 2976 547 21470 19830 16285 4806 4471 9457 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11689\\n28490\\n44834\\n59851\\n73738\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 33 47 88 34 45 46 89 34 31 38 97 154 41 80 14 5 50 83 7 71\\n19771 12979 18912 4763 10544 17930 13403 3047 42286 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2543 17935 1705 8629 1537 10440 10711 4917 7416 17272 15364 19277 18094 2341 3705 2115 6159 18683 15410 11128 4570\\n6786 4239 19925 1799 714 9563 5780 5658 19857 11401 6997 6498 19933 3848 367 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 19\\n14987 15862 15303 10749 18499 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 18500 10278 26645 5255 13532 197 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 4985 7825 4028 19922 12132 16259 48289 2976 547 21470 19830 27259 4806 4471 9457 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11619\\n28280\\n44414\\n59151\\n72688\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 33 47 117 34 45 46 89 34 31 38 97 154 41 80 14 5 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2543 17935 1705 8629 1537 10440 10711 4917 9460 17272 15364 19277 18094 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 714 9563 5780 5658 19857 11401 6997 6498 19933 3848 367 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 19\\n14987 15862 15303 10749 18499 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 18500 10278 33775 5255 13532 197 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 4985 7825 4028 19922 12132 16259 48289 2976 547 21470 19830 27259 4806 4753 9457 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11590\\n28193\\n44240\\n58861\\n72253\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 33 47 117 34 45 46 89 42 31 38 97 154 41 80 14 5 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2543 17935 1705 8629 459 10440 10711 4917 9460 17272 15364 19277 18094 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 714 9563 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 19\\n14987 15862 15303 10749 18499 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 18500 10278 33775 5255 13532 197 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 4985 7825 4028 19922 12132 16259 48289 2976 547 21470 19830 27259 4806 4753 9457 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11582\\n28169\\n44192\\n58813\\n72197\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 58 2 65 33 47 117 34 45 46 89 42 31 38 97 154 41 80 14 5 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2543 17935 1705 8629 459 10440 10711 4917 9460 17272 15364 19277 18094 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 714 9563 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 19\\n14987 15862 15303 10749 18499 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 18500 10278 33775 5255 13532 197 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 4985 7825 4028 19922 12132 16259 48289 2976 547 21470 19830 27259 4806 4753 9457 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11575\\n28148\\n44150\\n58743\\n72092\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 58 2 65 33 47 117 34 45 46 89 42 31 38 97 154 76 80 14 5 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 10899 16396 20655 11424\\n6674 17707 13855 28350 8405 2543 17935 1705 14983 459 10440 10711 4917 9460 17272 15364 19277 35685 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 9563 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 16730 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 33775 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 19922 12132 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11540\\n28043\\n43940\\n58393\\n71567\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 58 2 65 58 47 117 34 45 46 89 42 31 38 97 154 76 80 14 5 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 10899 16396 20655 11424\\n6674 17707 13855 28350 8405 2543 17935 1705 14983 459 10440 10711 4917 9460 17272 15364 19277 35685 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 33775 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 19922 12132 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11515\\n27968\\n43790\\n58143\\n71192\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 58 2 65 58 47 117 34 45 46 89 42 31 38 97 154 76 80 24 5 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 10899 16396 20655 11424\\n6674 17707 13855 28350 8405 2543 17935 1705 14983 459 10440 10711 4917 9460 6200 15364 19277 35685 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 33775 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 19922 12132 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11505\\n27938\\n43730\\n58043\\n71042\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 58 2 65 58 88 117 34 45 46 89 42 31 38 97 154 76 80 24 5 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 9648 16396 20655 11424\\n6674 17707 13855 28350 906 2543 17935 1705 14983 459 10440 10711 4917 9460 6200 15364 19277 35685 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 8395 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 19922 18174 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 3908\\n2\\n17\\n13\\n14\\n13', 'output': '11464\\n27815\\n43484\\n57633\\n70427\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 58 2 65 58 88 117 34 45 46 89 42 31 38 97 154 76 80 24 3 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 9648 16396 20655 11424\\n6674 17707 13855 28350 906 2543 17935 1705 14983 459 10440 10711 4917 9460 6200 15364 19277 35685 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 8395 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 19922 18174 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 3908\\n2\\n17\\n13\\n14\\n13', 'output': '11466\\n27821\\n43496\\n57653\\n70457\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 58 2 65 58 88 117 34 45 46 89 42 31 38 97 154 76 80 24 3 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 653 15905 6534 4650 11469 3628 8433 2994 9648 16396 20655 11424\\n6674 17707 13855 28350 906 2543 17935 1705 14983 459 10440 10711 4917 9460 6200 15364 19277 35685 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 8395 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 19922 18174 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 3908\\n2\\n17\\n13\\n14\\n10', 'output': '11466\\n27821\\n43496\\n57653\\n51532\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 58 69 58 2 65 58 88 117 34 45 46 89 42 31 38 97 154 76 80 24 3 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 653 15905 6534 4650 11469 3628 8433 2994 9648 16396 20655 11424\\n6674 17707 13855 28350 906 2543 17935 1705 14983 459 10440 10711 4917 9460 6200 15364 19277 35685 2341 611 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 8395 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 19922 18174 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 3908\\n2\\n17\\n13\\n14\\n10', 'output': '11466\\n27853\\n43592\\n57845\\n51852\\n'}, {'type': 'stdin_stdout', 'input': '5\\n131 58 69 58 2 65 58 88 117 34 45 46 89 42 31 38 97 154 76 80 24 3 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 653 15905 6534 4650 11469 3628 8433 2994 9648 16396 20655 11424\\n6674 17707 13855 28350 906 2543 17935 1705 14983 459 10440 10711 4917 9460 6200 15364 19277 35685 2341 611 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 8395 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 19922 18174 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 3908\\n2\\n17\\n13\\n14\\n10', 'output': '11421\\n27718\\n43322\\n57395\\n51177\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 96 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 121\\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 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83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 28350 8405 2543 17935 1705 8629 459 10440 10711 4917 9460 17272 15364 19277 35685 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 9563 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 16730 11157 5439 23\\n14987 15862 15303 10749 34354 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 33775 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 19922 12132 16259 48289 2976 547 21470 19830 3991 4806 4753 9881 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11585\\n28156\\n44166\\n58777\\n72154\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 58 2 65 33 47 117 34 45 46 89 42 31 38 97 154 41 80 14 5 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 28350 8405 2543 17935 1705 8629 459 10440 10711 4917 9460 17272 15364 19277 35685 2341 3705 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 9563 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 16730 11157 5439 23\\n14987 15862 15303 10749 35131 6000 10317 5901 9395 4386 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 33775 5255 13532 163 1298 7452\\n19855 1027 7367 42459 4333 438 5956 9104 14926 1005 7825 4028 7741 12132 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11575\\n28148\\n44150\\n58743\\n59911\\n'}, {'type': 'stdin_stdout', 'input': '5\\n125 90 69 58 2 65 33 47 117 34 45 46 89 42 31 38 97 154 76 80 14 5 50 83 7 71\\n33342 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 366 15905 6534 4650 11469 3628 8433 2994 10899 16396 20655 11424\\n6674 17707 13855 28350 8405 2543 17935 1705 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4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3393 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 5306 3959 5202 19850 4111 2264 4267 679 13613 10278 8395 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 9840 18174 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 3908\\n2\\n17\\n13\\n14\\n13', 'output': '11466\\n27821\\n43496\\n57653\\n60375\\n'}, {'type': 'stdin_stdout', 'input': '5\\n131 58 69 58 2 65 58 88 117 34 45 46 89 42 31 38 97 154 76 80 24 3 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 653 15905 6534 4650 11469 3628 8433 2994 9648 16396 20655 11424\\n6674 17707 13855 28350 906 2543 17935 1705 14983 459 10440 10711 4917 9460 6200 15364 19277 35685 2341 611 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 4462 9395 22483 5306 3959 9258 19850 4111 2264 4267 679 13613 10278 8395 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 32030 18174 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 3908\\n2\\n17\\n13\\n26\\n10', 'output': '11421\\n27718\\n43322\\n45113\\n39011\\n'}, {'type': 'stdin_stdout', 'input': '5\\n131 58 69 58 2 65 58 88 117 34 45 46 89 42 31 38 97 154 76 80 24 3 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 653 15905 6534 4650 11469 3628 8433 2994 9648 16396 20655 11424\\n6674 17707 13855 28350 906 2543 17935 1705 14983 459 10440 10711 4917 9460 6200 15364 19277 35685 2341 611 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 9328 3959 5202 19850 4111 2937 4267 679 13613 10278 9435 5255 13532 163 1298 7452\\n14767 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 32030 18174 16259 48289 2976 547 21470 19830 27259 4806 4753 3281 4957 3908\\n4\\n17\\n13\\n14\\n10', 'output': '3205\\n19502\\n35106\\n49179\\n42961\\n'}, {'type': 'stdin_stdout', 'input': '5\\n131 58 69 58 2 65 58 88 117 61 45 46 89 42 31 38 97 154 76 80 24 3 50 83 7 71\\n19771 12979 184 4763 10544 17930 13403 3047 67400 9740 8100 92 4424 14730 653 15905 6534 4650 11469 3628 8433 2994 9648 16396 20655 11424\\n6674 17707 13855 26160 906 2543 17935 1705 14983 459 10440 10711 4917 9460 6200 15364 16559 35685 2341 611 2115 6159 18683 15410 16089 4570\\n6786 4239 19925 1799 1133 13088 5780 5658 19857 11401 6997 6498 19933 3848 267 2146 5566 16880 17773 3869 3921 17400 15426 11157 5439 23\\n14987 15862 15303 10749 33407 6000 10317 5901 9395 22483 9328 3959 5202 19850 4111 2937 4267 679 6683 10278 9435 5255 13532 163 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 1005 7825 4028 32030 18174 16259 48289 2976 547 21470 19830 27259 4806 4753 9881 4957 3908\\n2\\n17\\n13\\n14\\n10', 'output': '11394\\n24919\\n40442\\n54407\\n48189\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 96 71 47 88 34 45 46 89 65 31 38 97 84 41 80 11 4 50 83 7 121\\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 27014 18355 11424\\n6674 17707 13855 16407 12232 2886 11908 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 19745 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\\n19855 17918 7990 10572 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18331\\n34836\\n50738\\n65291\\n78568\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 96 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 14366 16396 18355 11424\\n6674 17707 13855 16407 12232 2541 17935 1705 5000 1537 10440 10711 4917 7391 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 19745 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 28242 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\\n19855 17918 7990 10572 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18398\\n35037\\n51140\\n74229\\n87717\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 70 69 51 2 65 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 17998 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 10861 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\\n19855 17918 7990 17084 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 18472 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18449\\n35190\\n51446\\n66347\\n80090\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 56 47 88 34 45 46 89 34 31 38 97 84 41 156 14 5 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 2150 6159 18683 15410 9092 4570\\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 5615 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 11518 197 8471 7452\\n19855 17918 7990 17084 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18367\\n34944\\n50954\\n65527\\n78860\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 88 51 2 17 33 47 88 34 45 46 89 34 31 38 97 84 41 80 14 5 23 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 14986 9740 8100 92 4424 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 7416 17272 15364 19277 18094 3929 3705 2150 6159 18683 15410 11128 4570\\n7001 4239 19925 1799 375 9563 5780 5658 19857 11401 6997 6498 19933 3848 2426 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 13532 197 8471 7452\\n19855 17918 7990 9283 4333 438 5956 9104 14926 4985 12319 4028 19922 12132 16259 17476 2976 547 21470 19830 16285 4806 4471 9457 2864 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18522\\n35409\\n51884\\n67077\\n81185\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 63 33 47 88 34 45 46 89 34 31 38 97 84 41 80 14 5 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 14986 9740 8100 92 4424 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 18904 12920 2886 17935 1705 5000 1537 10440 10711 4917 7416 17272 15364 19277 18094 3929 3705 2150 6159 18683 15410 11128 4570\\n7001 4239 19925 1799 375 9563 5780 5658 19857 11401 6997 6498 19933 3848 2426 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 842 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10278 17975 16615 13532 197 8471 7452\\n19855 17918 7367 17084 4333 438 5956 9104 14926 4985 12319 4028 19922 12132 16259 17476 2976 547 21470 19830 16285 4806 4471 9457 4957 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18468\\n35247\\n51560\\n66537\\n80375\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 56 2 65 33 47 88 34 45 46 89 34 31 38 97 84 41 80 14 5 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 14986 9740 8100 92 4424 14730 962 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 7416 17272 15364 19277 18094 2341 3705 2150 6159 18683 15410 11128 4570\\n7001 4239 19925 1799 375 9563 5780 5658 19857 11401 6997 6498 19933 3848 2426 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10278 17975 16615 13532 197 1298 7452\\n19855 17918 7367 17084 4333 438 4180 9104 14926 4985 12319 4028 19922 12132 16259 17476 2976 547 25730 34951 16285 4806 4471 9457 4957 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18461\\n35226\\n51518\\n66467\\n80270\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 33 47 88 34 45 46 89 34 31 38 97 84 41 80 14 5 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 14986 9740 8100 92 4424 14730 962 15905 6534 4650 11469 1554 8433 2994 10899 16396 18355 11424\\n6674 25179 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 747 7416 17272 15364 19277 18094 2341 3705 2150 6159 18683 15410 11128 4570\\n6786 4239 19925 1799 375 9563 5780 5658 19857 11401 6997 6498 19933 3848 2426 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10278 17975 16615 13532 197 1298 7452\\n19855 17918 7367 25087 4333 438 5956 9104 14926 4985 12319 4028 19922 12132 16259 17476 2976 547 21470 19830 16285 4806 4471 9457 4957 2192\\n1\\n12\\n13\\n14\\n13', 'output': '18466\\n26573\\n42778\\n57645\\n71371\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 33 47 88 34 45 40 89 34 31 38 97 84 41 80 14 5 50 83 7 82\\n19771 12979 18912 10432 10544 12928 13403 3047 14986 9740 8100 92 4424 14730 962 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 7416 17272 15364 19277 18094 2341 3705 2150 6159 18683 15410 11128 4570\\n6786 4239 19925 1799 375 9563 5780 5658 19857 11401 6997 6498 19933 3848 2426 2146 5566 16880 21870 18359 3921 14172 16730 11479 5439 256\\n8633 15862 15303 10749 18499 11739 10317 5901 9395 22483 3514 3959 5202 19850 19469 9790 5653 784 18500 10278 17975 5255 13532 197 1298 7452\\n19855 1366 7367 25087 4333 438 5956 9104 14926 4985 12319 4028 19922 12132 16259 17476 2976 547 21470 19830 16285 4806 4471 9457 4957 2192\\n1\\n17\\n13\\n14\\n13', 'output': '18472\\n35259\\n51584\\n66577\\n80435\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 0 65 33 47 88 34 76 46 89 34 31 38 97 84 41 80 14 5 50 83 7 82\\n19771 12979 18912 4763 10544 12928 13403 3047 14986 9740 8100 92 4424 14730 962 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 17935 1705 5000 1537 10440 10711 4917 7416 17272 15364 19277 18094 2341 3705 2150 6159 18683 15410 11128 4570\\n6786 4239 19925 1799 375 9563 5780 5658 19857 11401 6997 6498 19933 3848 367 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 256\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 22483 3514 3959 5202 19850 19469 9790 5653 679 18500 10278 17975 5255 13532 197 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 4985 12319 4028 19922 12132 16259 17476 2976 547 21470 19830 16285 4806 4471 9457 4957 2945\\n1\\n17\\n13\\n14\\n12', 'output': '18437\\n35154\\n51374\\n66227\\n64068\\n'}, {'type': 'stdin_stdout', 'input': '5\\n86 90 69 51 2 65 33 47 88 34 45 46 89 34 2 38 97 84 41 80 14 5 50 83 7 82\\n19771 12979 18912 4763 10544 12928 13403 3047 42286 9740 8100 92 4424 14730 962 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\\n6674 17707 13855 16407 12232 2886 48364 1705 5000 1537 10440 10711 4917 7416 17272 15364 19277 18094 2341 3705 2150 6159 18683 15410 11128 4570\\n6786 4239 19925 1799 714 9563 5780 5658 19857 11401 6997 6498 19933 3848 367 2146 5566 16880 17773 18359 3921 14172 16730 11157 5439 19\\n8633 15862 15303 10749 18499 7792 10317 5901 9395 22483 3514 3959 5202 19850 4111 9790 4267 679 18500 10278 17975 5255 13532 197 1298 7452\\n19855 1027 7367 25087 4333 438 5956 9104 14926 4985 5042 4028 19922 12132 16259 27485 2976 566 21470 19830 16285 4806 4471 9457 4957 2192\\n2\\n17\\n13\\n14\\n13', 'output': '11707\\n28544\\n44942\\n60031\\n74008\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78233","program":"```python\nD=int(input())\nc=list(map(int, input().split()))\ns=[list(map(int, input().split())) for i in range(D)]\nt=[int(input()) for i in range(D)]\n\nd=[0]*(26)\nv=[0]*(D+1)\n\n\nfor i in range(D):\n v[i]=s[i][t[i]-1]\n d[t[i]-1]=-1\n sb=0 \n for j in range(26):\n d[j]+=1 \n sb+=d[j]*c[j]\n \n v[i]+=v[i-1]-sb\n print(v[i])\n```","inputs":"5\n86 90 69 51 2 96 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 82\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\n6674 17707 13855 16407 12232 2886 11908 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 19745 16880 17773 18359 3921 14172 16730 11157 5439 256\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\n19855 17918 7990 10572 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\n1\n17\n13\n14\n13","output":"18398\n35037\n51140\n65837\n79325","actual_output":"18398\n35037\n51140\n65837\n79325\n","execution_success":true,"sample_index":12466},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02750 Social Infrastructure Information Systems Division Hitachi Programming Contest 2020 - Manga Market","prompt":"Solve the following coding problem using the programming language python:\n\nThere are N stores called Store 1, Store 2, \\cdots, Store N. Takahashi, who is at his house at time 0, is planning to visit some of these stores.\n\nIt takes Takahashi one unit of time to travel from his house to one of the stores, or between any two stores.\n\nIf Takahashi reaches Store i at time t, he can do shopping there after standing in a queue for a_i \\times t + b_i units of time. (We assume that it takes no time other than waiting.)\n\nAll the stores close at time T + 0.5. If Takahashi is standing in a queue for some store then, he cannot do shopping there.\n\nTakahashi does not do shopping more than once in the same store.\n\nFind the maximum number of times he can do shopping before time T + 0.5.\n\nConstraints\n\n* All values in input are integers.\n* 1 \\leq N \\leq 2 \\times 10^5\n* 0 \\leq a_i \\leq 10^9\n* 0 \\leq b_i \\leq 10^9\n* 0 \\leq T \\leq 10^9\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN T\na_1 b_1\na_2 b_2\n\\vdots\na_N b_N\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n3 7\n2 0\n3 2\n0 3\n\n\nOutput\n\n2\n\n\nInput\n\n1 3\n0 3\n\n\nOutput\n\n0\n\n\nInput\n\n5 21600\n2 14\n3 22\n1 3\n1 10\n1 9\n\n\nOutput\n\n5\n\n\nInput\n\n7 57\n0 25\n3 10\n2 4\n5 15\n3 22\n2 14\n1 15\n\n\nOutput\n\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nreadline = sys.stdin.buffer.readline\n\nINF = 10**18+3\nN, T = map(int, readline().split())\n\nAB = [tuple(map(int, readline().split())) for _ in range(N)]\nABzero = [b for a, b in AB if a == 0]\nABnonzero = [(a, b) for a, b in AB if a]\nABnonzero.sort(key = lambda x: (x[1]+1)/x[0])\n\n\ndp = [0]\nfor a, b in ABnonzero:\n dp2 = dp + [INF]\n for j in range(1, len(dp2)):\n dp2[j] = min(dp2[j], (dp[j-1]+1)*(a+1)+b)\n dp = [d for d in dp2 if d <= T]\n\nABzero.sort()\ndpzero = [0] + [b+1 for b in ABzero]\nfor i in range(1, len(dpzero)):\n dpzero[i] += dpzero[i-1]\n\nDP = [INF]*(N+1)\nfor i in range(len(dp)):\n for j in range(len(dpzero)):\n DP[i+j] = min(DP[i+j], dp[i] + dpzero[j])\n\nDP = [d for d in DP if d <= T]\nprint(max(0, len(DP)-1))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 3\\n0 3', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 21600\\n2 14\\n3 22\\n1 3\\n1 10\\n1 9', 'output': '5'}, {'type': 'stdin_stdout', 'input': '3 7\\n2 0\\n3 2\\n0 3', 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{'type': 'stdin_stdout', 'input': '5 21600\\n2 14\\n4 22\\n1 3\\n0 10\\n1 2', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '7 57\\n0 25\\n5 10\\n3 4\\n5 20\\n3 22\\n2 14\\n1 9', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 21600\\n2 14\\n0 22\\n1 1\\n0 10\\n1 2', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '0 0\\n1 -1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7 57\\n0 25\\n3 10\\n2 4\\n5 1\\n3 22\\n2 23\\n1 9', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n0 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 21600\\n0 14\\n3 22\\n1 0\\n0 10\\n1 2', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '7 85\\n0 25\\n3 10\\n2 4\\n5 20\\n3 22\\n4 23\\n1 9', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1 -1\\n1 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7 85\\n0 25\\n3 10\\n2 4\\n5 20\\n3 22\\n1 23\\n1 18', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '0 -1\\n1 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7 99\\n0 25\\n3 10\\n2 4\\n5 1\\n3 22\\n2 23\\n1 18', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n0 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7 99\\n0 25\\n3 10\\n2 4\\n2 23\\n3 22\\n2 23\\n1 18', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n0 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7 99\\n0 25\\n3 10\\n2 4\\n2 20\\n3 22\\n3 23\\n1 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n1 2', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7 149\\n0 25\\n3 10\\n2 4\\n2 32\\n3 22\\n2 23\\n1 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n8 2', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7 149\\n0 25\\n3 10\\n2 4\\n2 8\\n3 23\\n2 23\\n1 2', 'output': '4\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78237","program":"```python\nimport sys\nreadline = sys.stdin.buffer.readline\n\nINF = 10**18+3\nN, T = map(int, readline().split())\n\nAB = [tuple(map(int, readline().split())) for _ in range(N)]\nABzero = [b for a, b in AB if a == 0]\nABnonzero = [(a, b) for a, b in AB if a]\nABnonzero.sort(key = lambda x: (x[1]+1)/x[0])\n\n\ndp = [0]\nfor a, b in ABnonzero:\n dp2 = dp + [INF]\n for j in range(1, len(dp2)):\n dp2[j] = min(dp2[j], (dp[j-1]+1)*(a+1)+b)\n dp = [d for d in dp2 if d <= T]\n\nABzero.sort()\ndpzero = [0] + [b+1 for b in ABzero]\nfor i in range(1, len(dpzero)):\n dpzero[i] += dpzero[i-1]\n\nDP = [INF]*(N+1)\nfor i in range(len(dp)):\n for j in range(len(dpzero)):\n DP[i+j] = min(DP[i+j], dp[i] + dpzero[j])\n\nDP = [d for d in DP if d <= T]\nprint(max(0, len(DP)-1))\n\n```","inputs":"1 3\n0 3","output":"0","actual_output":"0\n","execution_success":true,"sample_index":12467},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02885 AtCoder Beginner Contest 143 - Curtain","prompt":"Solve the following coding problem using the programming language python:\n\nThe window of Takahashi's room has a width of A. There are two curtains hung over the window, each of which has a horizontal length of B. (Vertically, the curtains are long enough to cover the whole window.)\n\nWe will close the window so as to minimize the total horizontal length of the uncovered part of the window. Find the total horizontal length of the uncovered parts of the window then.\n\nConstraints\n\n* 1 \\leq A \\leq 100\n* 1 \\leq B \\leq 100\n* A and B are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nA B\n\n\nOutput\n\nPrint the total horizontal length of the uncovered parts of the window.\n\nExamples\n\nInput\n\n12 4\n\n\nOutput\n\n4\n\n\nInput\n\n20 15\n\n\nOutput\n\n0\n\n\nInput\n\n20 30\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na,b=map(int,input().split())\nprint(a-2*b if a-2*b>=0 else 0)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '20 30', 'output': '0'}, {'type': 'stdin_stdout', 'input': '12 4', 'output': '4'}, {'type': 'stdin_stdout', 'input': '20 15', 'output': '0'}, {'type': 'stdin_stdout', 'input': '27 30', 'output': '0\\n'}, {'type': 'stdin_stdout', 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-23', 'output': '53\\n'}, {'type': 'stdin_stdout', 'input': '7 -43', 'output': '93\\n'}, {'type': 'stdin_stdout', 'input': '7 -79', 'output': '165\\n'}, {'type': 'stdin_stdout', 'input': '1 -79', 'output': '159\\n'}, {'type': 'stdin_stdout', 'input': '2 -79', 'output': '160\\n'}, {'type': 'stdin_stdout', 'input': '2 -147', 'output': '296\\n'}, {'type': 'stdin_stdout', 'input': '2 -166', 'output': '334\\n'}, {'type': 'stdin_stdout', 'input': '3 -166', 'output': '335\\n'}, {'type': 'stdin_stdout', 'input': '3 -290', 'output': '583\\n'}, {'type': 'stdin_stdout', 'input': '3 -487', 'output': '977\\n'}, {'type': 'stdin_stdout', 'input': '4 -487', 'output': '978\\n'}, {'type': 'stdin_stdout', 'input': '2 -487', 'output': '976\\n'}, {'type': 'stdin_stdout', 'input': '22 -2', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '2 -777', 'output': '1556\\n'}, {'type': 'stdin_stdout', 'input': '2 -839', 'output': '1680\\n'}, {'type': 'stdin_stdout', 'input': '35 -5', 'output': '45\\n'}, {'type': 'stdin_stdout', 'input': '1 -839', 'output': '1679\\n'}, {'type': 'stdin_stdout', 'input': '2 -370', 'output': '742\\n'}, {'type': 'stdin_stdout', 'input': '2 -415', 'output': '832\\n'}, {'type': 'stdin_stdout', 'input': '1 -415', 'output': '831\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78241","program":"```python\na,b=map(int,input().split())\nprint(a-2*b if a-2*b>=0 else 0)\n```","inputs":"20 30","output":"0","actual_output":"0\n","execution_success":true,"sample_index":12468},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03020 AtCoder Grand Contest 034 - Manhattan Max Matching","prompt":"Solve the following coding problem using the programming language python:\n\nSnuke is playing with red and blue balls, placing them on a two-dimensional plane.\n\nFirst, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i). Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i). The total number of red balls placed and the total number of blue balls placed are equal, that is, \\sum_{i=1}^{N} RC_i = \\sum_{i=1}^{N} BC_i. Let this value be S.\n\nSnuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair. Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.\n\nSnuke wants to maximize the sum of the scores of the pairs. Help him by finding the maximum possible sum of the scores of the pairs.\n\nConstraints\n\n* 1 \\leq N \\leq 1000\n* 0 \\leq RX_i,RY_i,BX_i,BY_i \\leq 10^9\n* 1 \\leq RC_i,BC_i \\leq 10\n* \\sum_{i=1}^{N} RC_i = \\sum_{i=1}^{N} BC_i\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nRX_1 RY_1 RC_1\nRX_2 RY_2 RC_2\n\\vdots\nRX_N RY_N RC_N\nBX_1 BY_1 BC_1\nBX_2 BY_2 BC_2\n\\vdots\nBX_N BY_N BC_N\n\n\nOutput\n\nPrint the maximum possible sum of the scores of the pairs.\n\nExamples\n\nInput\n\n2\n0 0 1\n3 2 1\n2 2 1\n5 0 1\n\n\nOutput\n\n8\n\n\nInput\n\n3\n0 0 1\n2 2 1\n0 0 2\n1 1 1\n1 1 1\n3 3 2\n\n\nOutput\n\n16\n\n\nInput\n\n10\n582463373 690528069 8\n621230322 318051944 4\n356524296 974059503 6\n372751381 111542460 9\n392867214 581476334 6\n606955458 513028121 5\n882201596 791660614 9\n250465517 91918758 3\n618624774 406956634 6\n426294747 736401096 5\n974896051 888765942 5\n726682138 336960821 3\n715144179 82444709 6\n599055841 501257806 6\n390484433 962747856 4\n912334580 219343832 8\n570458984 648862300 6\n638017635 572157978 10\n435958984 585073520 7\n445612658 234265014 6\n\n\nOutput\n\n45152033546\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nfrom collections import deque\n\n\ndef min_cost_flow(links, links_from, s, t, flow, n2):\n remain = flow\n result = 0\n INF = 10 ** 12\n predecessors = [0] * n2 # link_id\n\n while remain:\n # print(remain)\n distances = [INF] * n2\n updated = [False] * n2\n distances[s] = 0\n updated[s] = True\n q = deque([s])\n while q:\n v = q.popleft()\n vc = distances[v]\n updated[v] = False\n\n for li in links_from[v]:\n _, u, cap, cost = links[li]\n if cap == 0:\n continue\n new_cost = vc + cost\n if new_cost >= distances[u]:\n continue\n distances[u] = new_cost\n predecessors[u] = li\n if not updated[u]:\n updated[u] = True\n q.append(u)\n\n min_cap = remain\n v = t\n while v != s:\n li = predecessors[v]\n l = links[li]\n min_cap = min(min_cap, l[2])\n v = l[0]\n v = t\n while v != s:\n li = predecessors[v]\n l = links[li]\n l[2] -= min_cap\n links[li ^ 1][2] += min_cap\n v = l[0]\n remain -= min_cap\n result -= min_cap * distances[t]\n return result\n\n\nn = int(input())\nlines = sys.stdin.readlines()\nn2 = 2 * n + 6\ns, t = 0, 2 * n + 1\nk1, k2, k3, k4 = range(n2 - 4, n2)\nballs = 0\nlinks_from = [[] for _ in range(n2)]\nlinks = [] # [[src, tgt, capacity, unit_cost], ]\n\n\ndef add_link(s, t, cap, cost):\n i = len(links)\n links.append([s, t, cap, cost])\n links.append([t, s, 0, -cost])\n links_from[s].append(i)\n links_from[t].append(i + 1)\n\n\nfor i in range(n):\n ri = i + 1\n rx, ry, rc = map(int, lines[i].split())\n balls += rc\n add_link(s, ri, rc, 0)\n add_link(ri, k1, rc, rx + ry)\n add_link(ri, k2, rc, -rx + ry)\n add_link(ri, k3, rc, rx - ry)\n add_link(ri, k4, rc, -rx - ry)\n\nfor i in range(n, 2 * n):\n bi = i + 1\n bx, by, bc = map(int, lines[i].split())\n add_link(bi, t, bc, 0)\n add_link(k1, bi, bc, -bx - by)\n add_link(k2, bi, bc, bx - by)\n add_link(k3, bi, bc, -bx + by)\n add_link(k4, bi, bc, bx + by)\n\nprint(min_cost_flow(links, links_from, s, t, balls, n2))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n0 0 1\\n2 2 1\\n0 0 2\\n1 1 1\\n1 1 1\\n3 3 2', 'output': '16'}, {'type': 'stdin_stdout', 'input': '10\\n582463373 690528069 8\\n621230322 318051944 4\\n356524296 974059503 6\\n372751381 111542460 9\\n392867214 581476334 6\\n606955458 513028121 5\\n882201596 791660614 9\\n250465517 91918758 3\\n618624774 406956634 6\\n426294747 736401096 5\\n974896051 888765942 5\\n726682138 336960821 3\\n715144179 82444709 6\\n599055841 501257806 6\\n390484433 962747856 4\\n912334580 219343832 8\\n570458984 648862300 6\\n638017635 572157978 10\\n435958984 585073520 7\\n445612658 234265014 6', 'output': '45152033546'}, {'type': 'stdin_stdout', 'input': '2\\n0 0 1\\n3 2 1\\n2 2 1\\n5 0 1', 'output': '8'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 1\\n2 2 1\\n0 0 2\\n0 1 1\\n1 1 1\\n3 3 2', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '10\\n582463373 690528069 8\\n621230322 318051944 4\\n356524296 974059503 6\\n372751381 111542460 9\\n392867214 581476334 6\\n606955458 513028121 5\\n882201596 791660614 9\\n250465517 91918758 3\\n618624774 406956634 6\\n426294747 736401096 5\\n974896051 888765942 5\\n726682138 336960821 3\\n715144179 82444709 6\\n599055841 501257806 6\\n390484433 962747856 4\\n912334580 219343832 8\\n570458984 648862300 6\\n638017635 197597280 10\\n435958984 585073520 7\\n445612658 234265014 6', 'output': '48027008910\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 0 1\\n3 2 1\\n2 2 1\\n4 0 1', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n582463373 690528069 8\\n621230322 318051944 4\\n356524296 974059503 6\\n372751381 111542460 9\\n392867214 581476334 6\\n606955458 513028121 5\\n882201596 791660614 9\\n250465517 91918758 3\\n618624774 406956634 6\\n426294747 736401096 5\\n974896051 888765942 3\\n726682138 336960821 3\\n715144179 82444709 6\\n599055841 501257806 6\\n390484433 962747856 4\\n912334580 219343832 8\\n570458984 648862300 6\\n638017635 197597280 10\\n435958984 585073520 7\\n445612658 234265014 6', 'output': '46393666186\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 0 1\\n3 2 1\\n2 2 1\\n4 1 1', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 2\\n2 2 1\\n0 0 2\\n0 1 1\\n1 1 0\\n3 3 2', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '10\\n582463373 690528069 8\\n621230322 318051944 4\\n356524296 974059503 6\\n372751381 111542460 9\\n392867214 581476334 6\\n606955458 513028121 5\\n882201596 791660614 9\\n250465517 91918758 3\\n618624774 406956634 6\\n426294747 736401096 5\\n974896051 888765942 3\\n726682138 336960821 3\\n715144179 82444709 6\\n599055841 501257806 6\\n390484433 962747856 4\\n1704140162 219343832 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'input': '2\\n0 0 1\\n0 -1 1\\n2 2 1\\n4 1 1', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 2\\n2 2 1\\n0 0 2\\n0 1 1\\n1 0 0\\n3 3 4', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '10\\n582463373 690528069 8\\n621230322 318051944 4\\n356524296 974059503 6\\n372751381 111542460 9\\n392867214 581476334 6\\n606955458 513028121 5\\n882201596 791660614 9\\n250465517 178877476 3\\n618624774 406956634 6\\n426294747 736401096 5\\n974896051 888765942 3\\n726682138 336960821 3\\n715144179 82444709 5\\n761609744 501257806 6\\n390484433 962747856 4\\n1704140162 351122650 8\\n570458984 648862300 6\\n638017635 197597280 10\\n435958984 585073520 7\\n445612658 234265014 6', 'output': '51665236983\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 2\\n1 2 1\\n0 0 2\\n0 1 1\\n1 0 0\\n3 3 4', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '10\\n582463373 690528069 8\\n621230322 318051944 4\\n356524296 974059503 6\\n372751381 111542460 9\\n392867214 581476334 6\\n606955458 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513028121 5\\n882201596 791660614 9\\n250465517 110090143 3\\n618624774 406956634 9\\n426294747 736401096 0\\n974896051 888765942 3\\n424730474 653092928 3\\n868882655 111746962 4\\n761609744 501257806 6\\n390484433 912588475 4\\n1704140162 351122650 8\\n570458984 648862300 6\\n638017635 197597280 10\\n435958984 585073520 6\\n860421464 234265014 5', 'output': '48415956563\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 5, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78245","program":"```python\nimport sys\nfrom collections import deque\n\n\ndef min_cost_flow(links, links_from, s, t, flow, n2):\n remain = flow\n result = 0\n INF = 10 ** 12\n predecessors = [0] * n2 # link_id\n\n while remain:\n # print(remain)\n distances = [INF] * n2\n updated = [False] * n2\n distances[s] = 0\n updated[s] = True\n q = deque([s])\n while q:\n v = q.popleft()\n vc = distances[v]\n updated[v] = False\n\n for li in links_from[v]:\n _, u, cap, cost = links[li]\n if cap == 0:\n continue\n new_cost = vc + cost\n if new_cost >= distances[u]:\n continue\n distances[u] = new_cost\n predecessors[u] = li\n if not updated[u]:\n updated[u] = True\n q.append(u)\n\n min_cap = remain\n v = t\n while v != s:\n li = predecessors[v]\n l = links[li]\n min_cap = min(min_cap, l[2])\n v = l[0]\n v = t\n while v != s:\n li = predecessors[v]\n l = links[li]\n l[2] -= min_cap\n links[li ^ 1][2] += min_cap\n v = l[0]\n remain -= min_cap\n result -= min_cap * distances[t]\n return result\n\n\nn = int(input())\nlines = sys.stdin.readlines()\nn2 = 2 * n + 6\ns, t = 0, 2 * n + 1\nk1, k2, k3, k4 = range(n2 - 4, n2)\nballs = 0\nlinks_from = [[] for _ in range(n2)]\nlinks = [] # [[src, tgt, capacity, unit_cost], ]\n\n\ndef add_link(s, t, cap, cost):\n i = len(links)\n links.append([s, t, cap, cost])\n links.append([t, s, 0, -cost])\n links_from[s].append(i)\n links_from[t].append(i + 1)\n\n\nfor i in range(n):\n ri = i + 1\n rx, ry, rc = map(int, lines[i].split())\n balls += rc\n add_link(s, ri, rc, 0)\n add_link(ri, k1, rc, rx + ry)\n add_link(ri, k2, rc, -rx + ry)\n add_link(ri, k3, rc, rx - ry)\n add_link(ri, k4, rc, -rx - ry)\n\nfor i in range(n, 2 * n):\n bi = i + 1\n bx, by, bc = map(int, lines[i].split())\n add_link(bi, t, bc, 0)\n add_link(k1, bi, bc, -bx - by)\n add_link(k2, bi, bc, bx - by)\n add_link(k3, bi, bc, -bx + by)\n add_link(k4, bi, bc, bx + by)\n\nprint(min_cost_flow(links, links_from, s, t, balls, n2))\n\n```","inputs":"3\n0 0 1\n2 2 1\n0 0 2\n1 1 1\n1 1 1\n3 3 2","output":"16","actual_output":"16\n","execution_success":true,"sample_index":12469},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03160 Educational DP Contest - Frog 1","prompt":"Solve the following coding problem using the programming language python:\n\nThere are N stones, numbered 1, 2, \\ldots, N. For each i (1 \\leq i \\leq N), the height of Stone i is h_i.\n\nThere is a frog who is initially on Stone 1. He will repeat the following action some number of times to reach Stone N:\n\n* If the frog is currently on Stone i, jump to Stone i + 1 or Stone i + 2. Here, a cost of |h_i - h_j| is incurred, where j is the stone to land on.\n\n\n\nFind the minimum possible total cost incurred before the frog reaches Stone N.\n\nConstraints\n\n* All values in input are integers.\n* 2 \\leq N \\leq 10^5\n* 1 \\leq h_i \\leq 10^4\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nh_1 h_2 \\ldots h_N\n\n\nOutput\n\nPrint the minimum possible total cost incurred.\n\nExamples\n\nInput\n\n4\n10 30 40 20\n\n\nOutput\n\n30\n\n\nInput\n\n2\n10 10\n\n\nOutput\n\n0\n\n\nInput\n\n6\n30 10 60 10 60 50\n\n\nOutput\n\n40\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN = int(input())\nH = [0]+list(map(int, input().split()))\nC = [10**10] + [0]*N\nfor i in range(2,N+1):\n C[i] = min(C[i-1]+abs(H[i-1]-H[i]), C[i-2]+abs(H[i-2]-H[i]))\nprint(C[-1])\n```","verification_info":"{'test_cases': [{'type': 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{'type': 'stdin_stdout', 'input': '2\\n9 5', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '6\\n30 12 21 33 60 18', 'output': '36\\n'}, {'type': 'stdin_stdout', 'input': '2\\n11 5', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n30 0 26 33 60 18', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '4\\n10 11 1 12', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n30 0 26 33 122 14', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '2\\n14 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 0 26 33 122 14', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '4\\n12 11 1 24', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '2\\n14 3', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '4\\n17 11 1 24', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '2\\n18 2', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '2\\n31 2', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n44 1', 'output': '43\\n'}, {'type': 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'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 -1 -2 43', 'output': '45\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 -4 2 22', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-51 0', 'output': '51\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-48 -1', 'output': '47\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-48 -2', 'output': '46\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-48 1', 'output': '49\\n'}, {'type': 'stdin_stdout', 'input': '6\\n30 10 99 10 60 50', 'output': '60\\n'}, {'type': 'stdin_stdout', 'input': '2\\n50 10', 'output': '40\\n'}, {'type': 'stdin_stdout', 'input': '4\\n9 77 54 37', 'output': '62\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 77 54 37', 'output': '69\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 77 54 23', 'output': '83\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 77 54 13', 'output': '93\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 77 98 13', 'output': '139\\n'}, {'type': 'stdin_stdout', 'input': '6\\n30 10 35 18 154 1', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 77 45 13', 'output': '75\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 91 52 13', 'output': '89\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 91 71 13', 'output': '127\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 91 105 13', 'output': '167\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 91 105 15', 'output': '165\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 91 105 14', 'output': '166\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 91 105 14', 'output': '164\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 91 105 28', 'output': '150\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 146 105 28', 'output': '178\\n'}, {'type': 'stdin_stdout', 'input': '4\\n8 146 105 28', 'output': '174\\n'}, {'type': 'stdin_stdout', 'input': '4\\n8 146 162 28', 'output': '256\\n'}, {'type': 'stdin_stdout', 'input': '4\\n8 289 2 28', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '4\\n30 283 0 7', 'output': '37\\n'}, {'type': 'stdin_stdout', 'input': '4\\n39 283 1 7', 'output': '44\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 55', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-3 55', 'output': '58\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 -1 -68', 'output': '68\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 -1 -101', 'output': '101\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0 -101', 'output': '102\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 -1 2 -156', 'output': '157\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 -1 2 -156', 'output': '156\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 -1 2 -258', 'output': '258\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 -1 2 -52', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 1 2 -52', 'output': '55\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-2 1 2 -52', 'output': '56\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-2 0 2 -92', 'output': '94\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 2 -92', 'output': '92\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 2 -66', 'output': '67\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 2 -77', 'output': '78\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 1 2 -111', 'output': '113\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 169', 'output': '170\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 169', 'output': '171\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 255', 'output': '257\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78249","program":"```python\nN = int(input())\nH = [0]+list(map(int, input().split()))\nC = [10**10] + [0]*N\nfor i in range(2,N+1):\n C[i] = min(C[i-1]+abs(H[i-1]-H[i]), C[i-2]+abs(H[i-2]-H[i]))\nprint(C[-1])\n```","inputs":"6\n30 10 60 10 60 50","output":"40","actual_output":"40\n","execution_success":true,"sample_index":12470},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03303 SoundHound Inc. Programming Contest 2018 -Masters Tournament- - Acrostic","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a string S consisting of lowercase English letters. We will write down this string, starting a new line after every w letters. Print the string obtained by concatenating the letters at the beginnings of these lines from top to bottom.\n\nConstraints\n\n* 1 \\leq w \\leq |S| \\leq 1000\n* S consists of lowercase English letters.\n* w is an integer.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nS\nw\n\n\nOutput\n\nPrint the desired string in one line.\n\nExamples\n\nInput\n\nabcdefgh\n3\n\n\nOutput\n\nadg\n\n\nInput\n\nlllll\n1\n\n\nOutput\n\nlllll\n\n\nInput\n\nsouuundhound\n2\n\n\nOutput\n\nsuudon\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nS = list(input())\nw = int(input())\nans = S[::w]\nfor a in ans:\n print(a, end=\"\")\nprint()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'lllll\\n1', 'output': 'lllll'}, {'type': 'stdin_stdout', 'input': 'abcdefgh\\n3', 'output': 'adg'}, {'type': 'stdin_stdout', 'input': 'souuundhound\\n2', 'output': 'suudon'}, {'type': 'stdin_stdout', 'input': 'lllll\\n2', 'output': 'lll\\n'}, {'type': 'stdin_stdout', 'input': 'abcdefgh\\n4', 'output': 'ae\\n'}, {'type': 'stdin_stdout', 'input': 'dnuohdnuuuos\\n2', 'output': 'duhnuo\\n'}, {'type': 'stdin_stdout', 'input': 'llmll\\n2', 'output': 'lml\\n'}, {'type': 'stdin_stdout', 'input': 'dnuoodnuuuhs\\n2', 'output': 'duonuh\\n'}, {'type': 'stdin_stdout', 'input': 'llmll\\n4', 'output': 'll\\n'}, {'type': 'stdin_stdout', 'input': 'accdefgh\\n5', 'output': 'af\\n'}, {'type': 'stdin_stdout', 'input': 'dnuoodnuuuhs\\n4', 'output': 'dou\\n'}, {'type': 'stdin_stdout', 'input': 'llmll\\n6', 'output': 'l\\n'}, {'type': 'stdin_stdout', 'input': 'hgfedcca\\n5', 'output': 'hc\\n'}, {'type': 'stdin_stdout', 'input': 'dnuoodnuuuhs\\n7', 'output': 'du\\n'}, {'type': 'stdin_stdout', 'input': 'dnuoodnuuuhs\\n1', 'output': 'dnuoodnuuuhs\\n'}, {'type': 'stdin_stdout', 'input': 'llmll\\n1', 'output': 'llmll\\n'}, {'type': 'stdin_stdout', 'input': 'accdeggh\\n5', 'output': 'ag\\n'}, {'type': 'stdin_stdout', 'input': 'shuuundoound\\n1', 'output': 'shuuundoound\\n'}, {'type': 'stdin_stdout', 'input': 'shuuundoound\\n2', 'output': 'suudon\\n'}, {'type': 'stdin_stdout', 'input': 'mlmll\\n2', 'output': 'mml\\n'}, {'type': 'stdin_stdout', 'input': 'hhgedcca\\n9', 'output': 'h\\n'}, {'type': 'stdin_stdout', 'input': 'dnuondouuuhs\\n2', 'output': 'dunouh\\n'}, {'type': 'stdin_stdout', 'input': 'mlmll\\n4', 'output': 'ml\\n'}, {'type': 'stdin_stdout', 'input': 'hhgedcca\\n7', 'output': 'ha\\n'}, {'type': 'stdin_stdout', 'input': 'dnuondouuuhs\\n1', 'output': 'dnuondouuuhs\\n'}, {'type': 'stdin_stdout', 'input': 'llmlm\\n4', 'output': 'lm\\n'}, {'type': 'stdin_stdout', 'input': 'dnuondouuuis\\n2', 'output': 'dunoui\\n'}, {'type': 'stdin_stdout', 'input': 'siuuuodnound\\n1', 'output': 'siuuuodnound\\n'}, {'type': 'stdin_stdout', 'input': 'dnuondouuuis\\n1', 'output': 'dnuondouuuis\\n'}, {'type': 'stdin_stdout', 'input': 'siuuuodnound\\n3', 'output': 'sudu\\n'}, {'type': 'stdin_stdout', 'input': 'lmmlk\\n2', 'output': 'lmk\\n'}, {'type': 'stdin_stdout', 'input': 'dnuondouuuhs\\n3', 'output': 'doou\\n'}, {'type': 'stdin_stdout', 'input': 'souuundhound\\n4', 'output': 'suo\\n'}, {'type': 'stdin_stdout', 'input': 'llmlm\\n1', 'output': 'llmlm\\n'}, {'type': 'stdin_stdout', 'input': 'mlmll\\n1', 'output': 'mlmll\\n'}, {'type': 'stdin_stdout', 'input': 'dnuoocnuuuhs\\n1', 'output': 'dnuoocnuuuhs\\n'}, {'type': 'stdin_stdout', 'input': 'lmmll\\n1', 'output': 'lmmll\\n'}, {'type': 'stdin_stdout', 'input': 'llmlm\\n2', 'output': 'lmm\\n'}, {'type': 'stdin_stdout', 'input': 'dnvondouuuhs\\n1', 'output': 'dnvondouuuhs\\n'}, {'type': 'stdin_stdout', 'input': 'siuuuodnoumd\\n2', 'output': 'suudom\\n'}, {'type': 'stdin_stdout', 'input': 'siuuuodnovnd\\n1', 'output': 'siuuuodnovnd\\n'}, {'type': 'stdin_stdout', 'input': 'dnuoncouuuis\\n1', 'output': 'dnuoncouuuis\\n'}, {'type': 'stdin_stdout', 'input': 'mlmlk\\n5', 'output': 'm\\n'}, {'type': 'stdin_stdout', 'input': 'siuuuodnound\\n6', 'output': 'sd\\n'}, {'type': 'stdin_stdout', 'input': 'dnuondnuuuhs\\n3', 'output': 'donu\\n'}, {'type': 'stdin_stdout', 'input': 'abcdefgg\\n1', 'output': 'abcdefgg\\n'}, {'type': 'stdin_stdout', 'input': 'accdefgh\\n2', 'output': 'aceg\\n'}, {'type': 'stdin_stdout', 'input': 'llmln\\n1', 'output': 'llmln\\n'}, {'type': 'stdin_stdout', 'input': 'mllll\\n1', 'output': 'mllll\\n'}, {'type': 'stdin_stdout', 'input': 'gggedcca\\n10', 'output': 'g\\n'}, {'type': 'stdin_stdout', 'input': 'lnmll\\n1', 'output': 'lnmll\\n'}, {'type': 'stdin_stdout', 'input': 'accdeghh\\n6', 'output': 'ah\\n'}, {'type': 'stdin_stdout', 'input': 'dnvnndouuuhs\\n1', 'output': 'dnvnndouuuhs\\n'}, {'type': 'stdin_stdout', 'input': 'llmln\\n4', 'output': 'ln\\n'}, {'type': 'stdin_stdout', 'input': 'accdeghh\\n13', 'output': 'a\\n'}, {'type': 'stdin_stdout', 'input': 'nlmll\\n4', 'output': 'nl\\n'}, {'type': 'stdin_stdout', 'input': 'siuuvodnound\\n2', 'output': 'suvdon\\n'}, {'type': 'stdin_stdout', 'input': 'mlmkl\\n3', 'output': 'mk\\n'}, {'type': 'stdin_stdout', 'input': 'higeecca\\n3', 'output': 'hec\\n'}, {'type': 'stdin_stdout', 'input': 'dnvondouuuis\\n1', 'output': 'dnvondouuuis\\n'}, {'type': 'stdin_stdout', 'input': 'siuuuocnound\\n1', 'output': 'siuuuocnound\\n'}, {'type': 'stdin_stdout', 'input': 'mlmlk\\n1', 'output': 'mlmlk\\n'}, {'type': 'stdin_stdout', 'input': 'dnuondnuuuhs\\n6', 'output': 'dn\\n'}, {'type': 'stdin_stdout', 'input': 'souuuodhound\\n8', 'output': 'so\\n'}, {'type': 'stdin_stdout', 'input': 'llmkm\\n3', 'output': 'lk\\n'}, {'type': 'stdin_stdout', 'input': 'hgfedcca\\n2', 'output': 'hfdc\\n'}, {'type': 'stdin_stdout', 'input': 'shuuunuoodnd\\n3', 'output': 'suud\\n'}, {'type': 'stdin_stdout', 'input': 'lllln\\n1', 'output': 'lllln\\n'}, {'type': 'stdin_stdout', 'input': 'eghdfcca\\n5', 'output': 'ec\\n'}, {'type': 'stdin_stdout', 'input': 'shuuuodootnd\\n1', 'output': 'shuuuodootnd\\n'}, {'type': 'stdin_stdout', 'input': 'achdegch\\n6', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': 'shuuuodnnvnd\\n1', 'output': 'shuuuodnnvnd\\n'}, {'type': 'stdin_stdout', 'input': 'llmln\\n2', 'output': 'lmn\\n'}, {'type': 'stdin_stdout', 'input': 'nlmll\\n7', 'output': 'n\\n'}, {'type': 'stdin_stdout', 'input': 'dnvondpuuuis\\n1', 'output': 'dnvondpuuuis\\n'}, {'type': 'stdin_stdout', 'input': 'siuuuocnoune\\n1', 'output': 'siuuuocnoune\\n'}, {'type': 'stdin_stdout', 'input': 'mkmll\\n1', 'output': 'mkmll\\n'}, {'type': 'stdin_stdout', 'input': 'siuuuodnound\\n22', 'output': 's\\n'}, {'type': 'stdin_stdout', 'input': 'souuuodhound\\n7', 'output': 'sh\\n'}, {'type': 'stdin_stdout', 'input': 'llmjm\\n3', 'output': 'lj\\n'}, {'type': 'stdin_stdout', 'input': 'hgfeecca\\n2', 'output': 'hfec\\n'}, {'type': 'stdin_stdout', 'input': 'kllln\\n1', 'output': 'kllln\\n'}, {'type': 'stdin_stdout', 'input': 'eghdfcca\\n7', 'output': 'ea\\n'}, {'type': 'stdin_stdout', 'input': 'hhgdddda\\n5', 'output': 'hd\\n'}, {'type': 'stdin_stdout', 'input': 'dntoodouuuhs\\n1', 'output': 'dntoodouuuhs\\n'}, {'type': 'stdin_stdout', 'input': 'achdegch\\n3', 'output': 'adc\\n'}, {'type': 'stdin_stdout', 'input': 'shuuuodonvnd\\n1', 'output': 'shuuuodonvnd\\n'}, {'type': 'stdin_stdout', 'input': 'dnvondpuuujs\\n1', 'output': 'dnvondpuuujs\\n'}, {'type': 'stdin_stdout', 'input': 'siuuupcnoune\\n1', 'output': 'siuuupcnoune\\n'}, {'type': 'stdin_stdout', 'input': 'mklll\\n1', 'output': 'mklll\\n'}, {'type': 'stdin_stdout', 'input': 'dnuondouuuis\\n22', 'output': 'd\\n'}, {'type': 'stdin_stdout', 'input': 'unuondnduuhs\\n6', 'output': 'un\\n'}, {'type': 'stdin_stdout', 'input': 'klmjm\\n3', 'output': 'kj\\n'}, {'type': 'stdin_stdout', 'input': 'jllln\\n1', 'output': 'jllln\\n'}, {'type': 'stdin_stdout', 'input': 'eghdfcca\\n8', 'output': 'e\\n'}, {'type': 'stdin_stdout', 'input': 'llnlm\\n2', 'output': 'lnm\\n'}, {'type': 'stdin_stdout', 'input': 'nlmll\\n2', 'output': 'nml\\n'}, {'type': 'stdin_stdout', 'input': 'shutuodonvnd\\n1', 'output': 'shutuodonvnd\\n'}, {'type': 'stdin_stdout', 'input': 'dnvpndpuuujs\\n1', 'output': 'dnvpndpuuujs\\n'}, {'type': 'stdin_stdout', 'input': 'siuuuqcnoune\\n1', 'output': 'siuuuqcnoune\\n'}, {'type': 'stdin_stdout', 'input': 'lllkm\\n1', 'output': 'lllkm\\n'}, {'type': 'stdin_stdout', 'input': 'llljn\\n1', 'output': 'llljn\\n'}, {'type': 'stdin_stdout', 'input': 'gggeadbc\\n1', 'output': 'gggeadbc\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78253","program":"```python\nS = list(input())\nw = int(input())\nans = S[::w]\nfor a in ans:\n print(a, end=\"\")\nprint()\n\n```","inputs":"lllll\n1","output":"lllll","actual_output":"lllll\n","execution_success":true,"sample_index":12471},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03463 AtCoder Grand Contest 020 - Move and Win","prompt":"Solve the following coding problem using the programming language python:\n\nA game is played on a strip consisting of N cells consecutively numbered from 1 to N.\n\nAlice has her token on cell A. Borys has his token on a different cell B.\n\nPlayers take turns, Alice moves first. The moving player must shift his or her token from its current cell X to the neighboring cell on the left, cell X-1, or on the right, cell X+1. Note that it's disallowed to move the token outside the strip or to the cell with the other player's token. In one turn, the token of the moving player must be shifted exactly once.\n\nThe player who can't make a move loses, and the other player wins.\n\nBoth players want to win. Who wins if they play optimally?\n\nConstraints\n\n* 2 \\leq N \\leq 100\n* 1 \\leq A < B \\leq N\n* All input values are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN A B\n\n\nOutput\n\nPrint `Alice` if Alice wins, `Borys` if Borys wins, and `Draw` if nobody wins.\n\nExamples\n\nInput\n\n5 2 4\n\n\nOutput\n\nAlice\n\n\nInput\n\n2 1 2\n\n\nOutput\n\nBorys\n\n\nInput\n\n58 23 42\n\n\nOutput\n\nBorys\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, a, b = map(int, input().split())\nprint('Alice' if (a - b - 1) % 2 == 1 else 'Borys')\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '58 23 42', 'output': 'Borys'}, {'type': 'stdin_stdout', 'input': '2 1 2', 'output': 'Borys'}, {'type': 'stdin_stdout', 'input': '5 2 4', 'output': 'Alice'}, {'type': 'stdin_stdout', 'input': '9 23 42', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '8 2 4', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '3 1 2', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '9 23 18', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '8 2 3', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '9 23 23', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 2 2', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '7 2 3', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '9 44 23', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '7 2 5', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '9 44 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 0 1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '7 1 5', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '9 38 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 1 1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '7 1 4', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '1 38 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 1 0', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '8 1 4', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '1 38 1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '8 1 7', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '1 31 0', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '8 0 7', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '2 31 0', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '1 0 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '8 0 3', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '2 31 -1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 0 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '8 1 3', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 53 -1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 0 -1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '3 1 3', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 64 -1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '0 -1 -1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 1 3', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 64 -1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '-1 -1 -1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '-1 1 3', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 64 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 -2 -1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '-1 1 4', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '1 64 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 1 -1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '-1 1 7', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '1 103 0', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '1 1 -1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '-1 1 13', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '1 103 1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 1 -1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '-1 1 2', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '2 103 1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '4 1 -1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 1 2', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '2 79 1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '4 1 0', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '0 1 4', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '2 79 2', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '7 1 0', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '0 1 6', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '2 56 2', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '7 0 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 0 6', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 56 4', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '11 0 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '-1 0 6', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 12 4', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '11 -1 0', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '-1 0 8', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 21 4', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '21 -1 0', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '-1 0 10', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 21 0', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '21 -2 0', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '0 0 10', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 35 0', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '21 -2 1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '1 0 -1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '2 35 1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '16 -2 1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '1 -1 -1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 30 1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '16 -3 1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 -1 -1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '2 11 1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '16 -3 2', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '2 -1 -2', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '0 11 1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '5 -3 2', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '0 -1 -2', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '-1 11 1', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '7 -3 2', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '0 -1 -3', 'output': 'Alice\\n'}, {'type': 'stdin_stdout', 'input': '-1 22 1', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '13 -3 2', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '0 0 -3', 'output': 'Borys\\n'}, {'type': 'stdin_stdout', 'input': '-1 22 2', 'output': 'Alice\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 536870912}","problem_id":"vfc_78257","program":"```python\nn, a, b = map(int, input().split())\nprint('Alice' if (a - b - 1) % 2 == 1 else 'Borys')\n```","inputs":"58 23 42","output":"Borys","actual_output":"Borys\n","execution_success":true,"sample_index":12472},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03781 AtCoder Regular Contest 070 - Go Home","prompt":"Solve the following coding problem using the programming language python:\n\nThere is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0. During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right. That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i. The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible. Find the earliest possible time to reach coordinate X.\n\nConstraints\n\n* X is an integer.\n* 1\u2264X\u226410^9\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nX\n\n\nOutput\n\nPrint the earliest possible time for the kangaroo to reach coordinate X.\n\nExamples\n\nInput\n\n6\n\n\nOutput\n\n3\n\n\nInput\n\n2\n\n\nOutput\n\n2\n\n\nInput\n\n11\n\n\nOutput\n\n5\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\nX = int(input())\nlow_N = (-1 + (1 + 8 * X)**0.5) / 2\nhigh_N = (1 + (1 + 8 * X)**0.5) / 2\nif low_N % 1 == 0:\n print(int(low_N))\nelse:\n print(math.floor(high_N))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6', 'output': '3'}, {'type': 'stdin_stdout', 'input': '11', 'output': '5'}, {'type': 'stdin_stdout', 'input': '2', 'output': '2'}, {'type': 'stdin_stdout', 'input': '12', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '4', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '19', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '24', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '40', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '50', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '29', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '69', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '105', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '173', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '200', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '227', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '349', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '60', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '108', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '135', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '89', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '607', 'output': '35\\n'}, {'type': 'stdin_stdout', 'input': '312', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '979', 'output': '44\\n'}, {'type': 'stdin_stdout', 'input': '235', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '291', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '366', 'output': '27\\n'}, {'type': 'stdin_stdout', 'input': '1410', 'output': '53\\n'}, {'type': 'stdin_stdout', 'input': '398', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '138', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '414', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '533', 'output': '33\\n'}, {'type': 'stdin_stdout', 'input': '269', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '1000', 'output': '45\\n'}, {'type': 'stdin_stdout', 'input': '485', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '1717', 'output': '59\\n'}, {'type': 'stdin_stdout', 'input': '168', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '580', 'output': '34\\n'}, {'type': 'stdin_stdout', 'input': '2620', 'output': '72\\n'}, {'type': 'stdin_stdout', 'input': '2047', 'output': '64\\n'}, {'type': 'stdin_stdout', 'input': '2296', 'output': '68\\n'}, {'type': 'stdin_stdout', 'input': '1882', 'output': '61\\n'}, {'type': 'stdin_stdout', 'input': '1970', 'output': '63\\n'}, {'type': 'stdin_stdout', 'input': '2407', 'output': '69\\n'}, {'type': 'stdin_stdout', 'input': '926', 'output': '43\\n'}, {'type': 'stdin_stdout', 'input': '2431', 'output': '70\\n'}, {'type': 'stdin_stdout', 'input': '1572', 'output': '56\\n'}, {'type': 'stdin_stdout', 'input': '1896', 'output': '62\\n'}, {'type': 'stdin_stdout', 'input': '2085', 'output': '65\\n'}, {'type': 'stdin_stdout', 'input': '3071', 'output': '78\\n'}, {'type': 'stdin_stdout', 'input': '710', 'output': '38\\n'}, {'type': 'stdin_stdout', 'input': '1449', 'output': '54\\n'}, {'type': 'stdin_stdout', 'input': '1699', 'output': '58\\n'}, {'type': 'stdin_stdout', 'input': '2543', 'output': '71\\n'}, {'type': 'stdin_stdout', 'input': '2248', 'output': '67\\n'}, {'type': 'stdin_stdout', 'input': '3493', 'output': '84\\n'}, {'type': 'stdin_stdout', 'input': '2647', 'output': '73\\n'}, {'type': 'stdin_stdout', 'input': '4325', 'output': '93\\n'}, {'type': 'stdin_stdout', 'input': '5033', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '8030', 'output': '127\\n'}, {'type': 'stdin_stdout', 'input': '4035', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '12814', 'output': '160\\n'}, {'type': 'stdin_stdout', 'input': '6020', 'output': '110\\n'}, {'type': 'stdin_stdout', 'input': '19710', 'output': '199\\n'}, {'type': 'stdin_stdout', 'input': '4225', 'output': '92\\n'}, {'type': 'stdin_stdout', 'input': '36877', 'output': '272\\n'}, {'type': 'stdin_stdout', 'input': '7566', 'output': '123\\n'}, {'type': 'stdin_stdout', 'input': '49568', 'output': '315\\n'}, {'type': 'stdin_stdout', 'input': '44971', 'output': '300\\n'}, {'type': 'stdin_stdout', 'input': '34941', 'output': '264\\n'}, {'type': 'stdin_stdout', 'input': '27935', 'output': '236\\n'}, {'type': 'stdin_stdout', 'input': '43035', 'output': '293\\n'}, {'type': 'stdin_stdout', 'input': '7263', 'output': '121\\n'}, {'type': 'stdin_stdout', 'input': '12423', 'output': '158\\n'}, {'type': 'stdin_stdout', 'input': '10040', 'output': '142\\n'}, {'type': 'stdin_stdout', 'input': '18074', 'output': '190\\n'}, {'type': 'stdin_stdout', 'input': '698', 'output': '37\\n'}, {'type': 'stdin_stdout', 'input': '16383', 'output': '181\\n'}, {'type': 'stdin_stdout', 'input': '14154', 'output': '168\\n'}, {'type': 'stdin_stdout', 'input': '5452', 'output': '104\\n'}, {'type': 'stdin_stdout', 'input': '446', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '7441', 'output': '122\\n'}, {'type': 'stdin_stdout', 'input': '14699', 'output': '171\\n'}, {'type': 'stdin_stdout', 'input': '756', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '26152', 'output': '229\\n'}, {'type': 'stdin_stdout', 'input': '1053', 'output': '46\\n'}, {'type': 'stdin_stdout', 'input': '1338', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '1224', 'output': '49\\n'}, {'type': 'stdin_stdout', 'input': '2850', 'output': '75\\n'}, {'type': 'stdin_stdout', 'input': '5334', 'output': '103\\n'}, {'type': 'stdin_stdout', 'input': '1313', 'output': '51\\n'}, {'type': 'stdin_stdout', 'input': '8707', 'output': '132\\n'}, {'type': 'stdin_stdout', 'input': '825', 'output': '41\\n'}, {'type': 'stdin_stdout', 'input': '631', 'output': '36\\n'}, {'type': 'stdin_stdout', 'input': '4584', 'output': '96\\n'}, {'type': 'stdin_stdout', 'input': '9009', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '9766', 'output': '140\\n'}, {'type': 'stdin_stdout', 'input': '19255', 'output': '196\\n'}, {'type': 'stdin_stdout', 'input': '14963', 'output': '173\\n'}, {'type': 'stdin_stdout', 'input': '17808', 'output': '189\\n'}, {'type': 'stdin_stdout', 'input': '3133', 'output': '79\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_78265","program":"```python\nimport math\nX = int(input())\nlow_N = (-1 + (1 + 8 * X)**0.5) / 2\nhigh_N = (1 + (1 + 8 * X)**0.5) / 2\nif low_N % 1 == 0:\n print(int(low_N))\nelse:\n print(math.floor(high_N))\n```","inputs":"6","output":"3","actual_output":"3\n","execution_success":true,"sample_index":12473},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03951 AtCoder Grand Contest 006 - Prefix and Suffix","prompt":"Solve the following coding problem using the programming language python:\n\nSnuke is interested in strings that satisfy the following conditions:\n\n* The length of the string is at least N.\n* The first N characters equal to the string s.\n* The last N characters equal to the string t.\n\n\n\nFind the length of the shortest string that satisfies the conditions.\n\nConstraints\n\n* 1\u2264N\u2264100\n* The lengths of s and t are both N.\n* s and t consist of lowercase English letters.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN\ns\nt\n\n\nOutput\n\nPrint the length of the shortest string that satisfies the conditions.\n\nExamples\n\nInput\n\n3\nabc\ncde\n\n\nOutput\n\n5\n\n\nInput\n\n1\na\nz\n\n\nOutput\n\n2\n\n\nInput\n\n4\nexpr\nexpr\n\n\nOutput\n\n4\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN = int(input())\ns = input()\nt = input()\nx = s+t\nfor i in range(N):\n if (s[i:N] == t[0:N-i]):\n x = s + t[N-i:N]\n break\nprint(len(x))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\nabc\\ncde', 'output': '5'}, {'type': 'stdin_stdout', 'input': '1\\na\\nz', 'output': '2'}, {'type': 'stdin_stdout', 'input': '4\\nexpr\\nexpr', 'output': '4'}, {'type': 'stdin_stdout', 'input': '3\\nabc\\ncce', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\na\\n{', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\nexpr\\nexpq', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncba\\ncec', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '4\\nexpr\\nrxep', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '3\\nabc\\ncec', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n`\\nz', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\nexpr\\nepxq', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1\\n`\\n{', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\nexpr\\npexq', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbca\\ncec', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n`\\n|', 'output': '2\\n'}, {'type': 'stdin_stdout', 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'1\\n]\\n\\x7f', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\nrsgx\\nxoer', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n``d\\nefb', 'output': '6\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_78269","program":"```python\nN = int(input())\ns = input()\nt = input()\nx = s+t\nfor i in range(N):\n if (s[i:N] == t[0:N-i]):\n x = s + t[N-i:N]\n break\nprint(len(x))\n```","inputs":"3\nabc\ncde","output":"5","actual_output":"5\n","execution_success":true,"sample_index":12474},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00173 Haunted House","prompt":"Solve the following coding problem using the programming language python:\n\nAizu Gakuen High School holds a school festival every year. The most popular of these is the haunted house. The most popular reason is that 9 classes do haunted houses instead of 1 or 2 classes. Each one has its own unique haunted house. Therefore, many visitors come from the neighborhood these days.\n\nTherefore, the school festival executive committee decided to unify the admission fee for the haunted house in the school as shown in the table below, and based on this, total the total number of visitors and income for each class.\n\nAdmission fee list (admission fee per visitor)\n\n\nMorning Afternoon\n200 yen 300 yen\n\n\nEnter the number of visitors in the morning and afternoon for each class, and create a program that creates a list of the total number of visitors and income for each class.\n\n\n\nInput\n\nThe input is given in the following format:\n\n\nname1 a1 b1\nname2 a2 b2\n::\nname9 a9 b9\n\n\nThe input consists of 9 lines, the class name of the i-th class on the i-line namei (a half-width character string of 1 to 15 characters including numbers and alphabets), the number of visitors in the morning ai (0 \u2264 ai \u2264 400) , Afternoon attendance bi (0 \u2264 bi \u2264 400) is given.\n\nOutput\n\nOn the i-line, output the class name of the i-class, the total number of visitors, and the fee income on one line separated by blanks.\n\nExample\n\nInput\n\n1a 132 243\n1c 324 183\n1f 93 199\n2b 372 163\n2c 229 293\n2e 391 206\n3a 118 168\n3b 263 293\n3d 281 102\n\n\nOutput\n\n1a 375 99300\n1c 507 119700\n1f 292 78300\n2b 535 123300\n2c 522 133700\n2e 597 140000\n3a 286 74000\n3b 556 140500\n3d 383 86800\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nwhile True:\n try:a,b,c=input().split()\n except:break\n b,c=map(int,[b,c])\n print(a,b+c,b*200+c*300)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1a 132 243\\n1c 324 183\\n1f 93 199\\n2b 372 163\\n2c 229 293\\n2e 391 206\\n3a 118 168\\n3b 263 293\\n3d 281 102', 'output': '1a 375 99300\\n1c 507 119700\\n1f 292 78300\\n2b 535 123300\\n2c 522 133700\\n2e 597 140000\\n3a 286 74000\\n3b 556 140500\\n3d 383 86800'}, {'type': 'stdin_stdout', 'input': '1a 132 243\\n1c 324 183\\n1f 93 199\\n2b 372 163\\n2c 229 346\\n2e 391 206\\n3a 118 168\\n3b 263 293\\n3d 281 102', 'output': '1a 375 99300\\n1c 507 119700\\n1f 292 78300\\n2b 535 123300\\n2c 575 149600\\n2e 597 140000\\n3a 286 74000\\n3b 556 140500\\n3d 383 86800\\n'}, {'type': 'stdin_stdout', 'input': '1a 132 243\\n1c 324 183\\n1f 93 199\\n3b 372 163\\n2c 229 346\\n2e 391 206\\n3a 118 168\\n3b 263 293\\n3d 281 102', 'output': '1a 375 99300\\n1c 507 119700\\n1f 292 78300\\n3b 535 123300\\n2c 575 149600\\n2e 597 140000\\n3a 286 74000\\n3b 556 140500\\n3d 383 86800\\n'}, {'type': 'stdin_stdout', 'input': '1a 132 243\\n1c 324 183\\n1f 93 199\\n3b 372 163\\n2c 229 346\\n2e 12 206\\n3a 118 168\\n3b 263 293\\n3d 281 102', 'output': '1a 375 99300\\n1c 507 119700\\n1f 292 78300\\n3b 535 123300\\n2c 575 149600\\n2e 218 64200\\n3a 286 74000\\n3b 556 140500\\n3d 383 86800\\n'}, {'type': 'stdin_stdout', 'input': '1a 132 243\\n1c 324 183\\n1f 93 199\\n3b 372 163\\n2c 229 346\\n2e 12 206\\n3a 118 168\\n3b 263 103\\n3d 281 102', 'output': '1a 375 99300\\n1c 507 119700\\n1f 292 78300\\n3b 535 123300\\n2c 575 149600\\n2e 218 64200\\n3a 286 74000\\n3b 366 83500\\n3d 383 86800\\n'}, {'type': 'stdin_stdout', 'input': '1a 132 243\\n1c 324 122\\n1f 93 199\\n3b 372 163\\n2c 229 346\\n2e 12 206\\n3a 118 168\\n3b 263 103\\n3d 281 102', 'output': '1a 375 99300\\n1c 446 101400\\n1f 292 78300\\n3b 535 123300\\n2c 575 149600\\n2e 218 64200\\n3a 286 74000\\n3b 366 83500\\n3d 383 86800\\n'}, {'type': 'stdin_stdout', 'input': '1a 132 243\\n1c 324 122\\n1e 93 199\\n3b 372 163\\n2c 229 346\\n2e 12 206\\n3a 118 168\\n3b 263 103\\n3d 281 102', 'output': '1a 375 99300\\n1c 446 101400\\n1e 292 78300\\n3b 535 123300\\n2c 575 149600\\n2e 218 64200\\n3a 286 74000\\n3b 366 83500\\n3d 383 86800\\n'}, {'type': 'stdin_stdout', 'input': '1a 132 243\\n1c 324 122\\n1e 93 199\\n3b 372 163\\n2c 229 346\\n2e 12 206\\n3a 228 168\\n3b 263 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329 66900\\n'}, {'type': 'stdin_stdout', 'input': '0^ 3 746\\n0d 179 4\\n1e 8 1320\\n_4 20 147\\nd3 494 257\\nf2 13 50\\n3a 88 113\\n1c 78 14\\n2d 318 11', 'output': '0^ 749 224400\\n0d 183 37000\\n1e 1328 397600\\n_4 167 48100\\nd3 751 175900\\nf2 63 17600\\n3a 201 51500\\n1c 92 19800\\n2d 329 66900\\n'}, {'type': 'stdin_stdout', 'input': '0^ 3 746\\n0d 179 4\\n1e 8 1320\\n_4 20 77\\nd3 494 257\\nf2 13 50\\n3a 88 113\\n1c 78 14\\n2d 318 11', 'output': '0^ 749 224400\\n0d 183 37000\\n1e 1328 397600\\n_4 97 27100\\nd3 751 175900\\nf2 63 17600\\n3a 201 51500\\n1c 92 19800\\n2d 329 66900\\n'}, {'type': 'stdin_stdout', 'input': '0^ 3 746\\n0d 179 4\\n1e 8 1320\\n_4 20 77\\nd3 494 160\\nf2 13 50\\n3a 88 113\\n1c 78 14\\n2d 318 11', 'output': '0^ 749 224400\\n0d 183 37000\\n1e 1328 397600\\n_4 97 27100\\nd3 654 146800\\nf2 63 17600\\n3a 201 51500\\n1c 92 19800\\n2d 329 66900\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_78277","program":"```python\nwhile True:\n try:a,b,c=input().split()\n except:break\n b,c=map(int,[b,c])\n print(a,b+c,b*200+c*300)\n\n```","inputs":"1a 132 243\n1c 324 183\n1f 93 199\n2b 372 163\n2c 229 293\n2e 391 206\n3a 118 168\n3b 263 293\n3d 281 102","output":"1a 375 99300\n1c 507 119700\n1f 292 78300\n2b 535 123300\n2c 522 133700\n2e 597 140000\n3a 286 74000\n3b 556 140500\n3d 383 86800","actual_output":"1a 375 99300\n1c 507 119700\n1f 292 78300\n2b 535 123300\n2c 522 133700\n2e 597 140000\n3a 286 74000\n3b 556 140500\n3d 383 86800\n","execution_success":true,"sample_index":12476},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00502 Hot days","prompt":"Solve the following coding problem using the programming language python:\n\nproblem\n\nDuring this time of winter in Japan, hot days continue in Australia in the Southern Hemisphere. IOI, who lives in Australia, decided to plan what clothes to wear based on the weather forecast for a certain D day. The maximum temperature on day i (1 \u2264 i \u2264 D) is predicted to be Ti degrees.\n\nIOI has N kinds of clothes, which are numbered from 1 to N. Clothes j (1 \u2264 j \u2264 N) are suitable for wearing on days when the maximum temperature is above Aj and below Bj. In addition, each clothes has an integer called \"flashiness\", and the flashiness of clothes j is Cj.\n\nFor each of the D days, IOI chooses to wear one of the clothes suitable for wearing when the maximum temperature follows the weather forecast. You may choose the same clothes as many times as you like, or you may choose clothes that are never chosen in D days.\n\nIOI, who wanted to avoid wearing similar clothes in succession, decided to maximize the total absolute value of the difference in the flashiness of the clothes worn on consecutive days. That is, assuming that the clothes xi are selected on the i-day, we want to maximize the values \u200b\u200b| Cx1 --Cx2 | + | Cx2 --Cx3 | +\u2026 + | CxD-1 --CxD |. Create a program to find this maximum value.\n\ninput\n\nThe input consists of 1 + D + N lines.\n\nOn the first line, two integers D and N (2 \u2264 D \u2264 200, 1 \u2264 N \u2264 200) are written with a blank as a delimiter. D is the number of days to plan clothes and N is the number of clothes types IOI has.\n\nOne integer Ti (0 \u2264 Ti \u2264 60) is written in the i-th line (1 \u2264 i \u2264 D) of the following D lines. This means that the maximum temperature on day i is forecast to be Ti degrees.\n\nIn the jth line (1 \u2264 j \u2264 N) of the following N lines, three integers Aj, Bj, Cj (0 \u2264 Aj \u2264 Bj \u2264 60, 0 \u2264 Cj \u2264 100) are written. These indicate that clothing j is suitable for wearing on days when the maximum temperature is above Aj and below Bj, and the flashiness is Cj.\n\nIt is guaranteed that there will be at least one piece of clothing suitable for wearing when the maximum temperature follows the weather forecast for every D day.\n\noutput\n\nOutput the total absolute value of the difference in the flashiness of clothes worn on consecutive days, that is, the maximum value of the values \u200b\u200b| Cx1 --Cx2 | + | Cx2 --Cx3 | +\u2026 + | CxD-1 --CxD | in one line. ..\n\nInput / output example\n\nInput example 1\n\n\n3 4\n31\n27\n35\n20 25 30\n23 29 90\n21 35 60\n28 33 40\n\n\nOutput example 1\n\n\n80\n\n\nIn the input / output example 1, the candidates for clothes on the first day are clothes 3 and 4, the candidates for clothes on the second day are clothes 2 and clothes 3, and the candidates for clothes on the third day are only clothes 3. is there. Choose clothes 4 on the first day, clothes 2 on the second day, and clothes 3 on the third day. That is, x1 = 4, x2 = 2, x3 = 3. At this time, the absolute value of the difference in the flashiness of the clothes on the first day and the second day is | 40 --90 | = 50, and the absolute value of the difference in the flashiness of the clothes on the second and third days is | 90-60 | = 30. The total is 80, which is the maximum value.\n\nInput example 2\n\n\n5 2\n26\n28\n32\n29\n34\n30 35 0\n25 30 100\n\n\nOutput example 2\n\n\n300\n\n\nIn Example 2 of input / output, clothes 2 on the first day, clothes 2 on the second day, clothes 1 on the third day, clothes 2 on the fourth day, and clothes 1 on the fifth day. You have to choose. At this time, the required value is | 100 --100 | + | 100 --0 | + | 0 --100 | + | 100 --0 | = 300.\n\nThe question text and the data used for the automatic referee are the question text and the test data for scoring, which are created and published by the Japan Committee for Information Olympics.\n\n\n\n\n\nExample\n\nInput\n\n3 4\n31\n27\n35\n20 25 30\n23 29 90\n21 35 60\n28 33 40\n\n\nOutput\n\n80\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef solve():\n from sys import stdin\n f_i = stdin\n \n D, N = map(int, f_i.readline().split())\n T = tuple(int(f_i.readline()) for i in range(D))\n \n clothes = [tuple(map(int, f_i.readline().split())) for i in range(N)]\n clothes.sort(key=lambda x: x[2])\n \n candidate = []\n for t in T:\n ct = tuple(filter(lambda x: x[0] <= t <= x[1], clothes))\n c_min = ct[0][2]\n c_max = ct[-1][2]\n if c_min == c_max:\n candidate.append((c_min,))\n else:\n candidate.append((c_min, c_max))\n \n dp = [0] * len(candidate[0])\n for c1, c2 in zip(candidate, candidate[1:]):\n dp = [max(rec + abs(ci - cj) for rec, ci in zip(dp, c1)) for cj in c2]\n \n print(max(dp))\n \nsolve()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 4\\n31\\n27\\n35\\n20 25 30\\n23 29 90\\n21 35 60\\n28 33 40', 'output': '80'}, {'type': 'stdin_stdout', 'input': '3 4\\n34\\n27\\n35\\n20 25 30\\n23 29 90\\n21 35 60\\n28 33 40', 'output': '60\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n31\\n27\\n35\\n20 25 30\\n35 29 90\\n21 35 60\\n28 33 40', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n34\\n40\\n35\\n20 25 30\\n23 29 90\\n21 69 60\\n28 33 40', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n31\\n27\\n35\\n20 25 30\\n23 29 90\\n21 35 60\\n28 48 40', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n31\\n27\\n35\\n20 25 30\\n35 29 90\\n21 35 69\\n28 33 40', 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4\\n31\\n27\\n35\\n20 25 30\\n40 29 90\\n21 35 60\\n28 32 40', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n34\\n40\\n35\\n20 25 30\\n24 29 1\\n21 69 60\\n28 33 40', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n34\\n40\\n35\\n38 25 30\\n24 29 11\\n21 69 60\\n28 25 40', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n34\\n27\\n35\\n10 25 30\\n23 29 90\\n21 35 60\\n28 24 40', 'output': '60\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_78285","program":"```python\ndef solve():\n from sys import stdin\n f_i = stdin\n \n D, N = map(int, f_i.readline().split())\n T = tuple(int(f_i.readline()) for i in range(D))\n \n clothes = [tuple(map(int, f_i.readline().split())) for i in range(N)]\n clothes.sort(key=lambda x: x[2])\n \n candidate = []\n for t in T:\n ct = tuple(filter(lambda x: x[0] <= t <= x[1], clothes))\n c_min = ct[0][2]\n c_max = ct[-1][2]\n if c_min == c_max:\n candidate.append((c_min,))\n else:\n candidate.append((c_min, c_max))\n \n dp = [0] * len(candidate[0])\n for c1, c2 in zip(candidate, candidate[1:]):\n dp = [max(rec + abs(ci - cj) for rec, ci in zip(dp, c1)) for cj in c2]\n \n print(max(dp))\n \nsolve()\n\n```","inputs":"3 4\n31\n27\n35\n20 25 30\n23 29 90\n21 35 60\n28 33 40","output":"80","actual_output":"80\n","execution_success":true,"sample_index":12477},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00686 Where's Your Robot?","prompt":"Solve the following coding problem using the programming language python:\n\nYou have full control over a robot that walks around in a rectangular field paved with square tiles like a chessboard. There are m columns of tiles from west to east, and n rows of tiles from south to north (1 <= m, n <= 100). Each tile is given a pair of coordinates, such as (i, j), where 1 <= i <= m and 1 <= j <= n.\n\nYour robot is initially on the center of the tile at (1, 1), that is, one at the southwest corner of the field, facing straight north. It can move either forward or backward, or can change its facing direction by ninety degrees at a time, according to a command you give to it, which is one of the following.\n\n* `FORWARD` k\nGo forward by k tiles to its facing direction (1 <= k < 100).\n* `BACKWARD` k\nGo backward by k tiles, without changing its facing direction (1 <= k < 100).\n* `RIGHT`\nTurn to the right by ninety degrees.\n* `LEFT`\nTurn to the left by ninety degrees.\n* `STOP`\nStop.\n\n\nWhile executing either a \"`FORWARD`\" or a \"`BACKWARD`\" command, the robot may bump against the wall surrounding the field. If that happens, the robot gives up the command execution there and stands at the center of the tile right in front of the wall, without changing its direction.\n\nAfter finishing or giving up execution of a given command, your robot will stand by for your next command.\n\n\n\nInput\n\nThe input consists of one or more command sequences. Each input line has at most fifty characters.\n\nThe first line of a command sequence contains two integer numbers telling the size of the field, the first number being the number of columns and the second being the number of rows. There might be white spaces (blanks and/or tabs) before, in between, or after the two numbers. Two zeros as field size indicates the end of input.\n\nEach of the following lines of a command sequence contains a command to the robot. When a command has an argument, one or more white spaces are put between them. White spaces may also appear before and after the command and/or its argument.\n\nA command sequence is terminated by a line containing a \"`STOP`\" command. The next command sequence, if any, starts from the next line.\n\nOutput\n\nThe output should be one line for each command sequence in the input. It should contain two numbers i and j of the coordinate pair (i, j), in this order, of the tile on which your robot stops. Two numbers should be separated by one white spaces.\n\nExample\n\nInput\n\n6 5\nFORWARD 3\nRIGHT\nFORWARD 5\nLEFT\nBACKWARD 2\nSTOP\n3 1\nFORWARD 2\nSTOP\n0 0\n\n\nOutput\n\n6 2\n1 1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nwhile True:\n col, row = map(int, input().split())\n if col == 0:\n break\n else:\n robot = [1, 1]\n direction = \"up\"\n while True:\n str = input()\n if str == \"STOP\":\n print(robot[0], robot[1])\n break\n elif str == \"LEFT\":\n if direction == \"up\":\n direction = \"left\"\n elif direction == \"left\":\n direction = \"down\"\n elif direction == \"down\":\n direction = \"right\"\n else: # right\n direction = \"up\"\n elif str == \"RIGHT\":\n if direction == \"up\":\n direction = \"right\"\n elif direction == \"left\":\n direction = \"up\"\n elif direction == \"down\":\n direction = \"left\"\n else: # right\n direction = \"down\"\n else:\n di, step = str.split()\n step = int(step)\n if direction == \"up\":\n if di == \"FORWARD\":\n robot[1] = min(robot[1] + step, row)\n else:\n robot[1] = max(robot[1] - step, 1)\n elif direction == \"left\":\n if di == \"FORWARD\":\n robot[0] = max(robot[0] - step, 1)\n else:\n robot[0] = min(robot[0] + step, col)\n elif direction == \"down\":\n if di == \"FORWARD\":\n robot[1] = max(robot[1] - step, 1)\n else:\n robot[1] = min(robot[1] + step, row)\n else: # right\n if di == \"FORWARD\":\n robot[0] = min(robot[0] + step, col)\n else:\n robot[0] = max(robot[0] - step, 1)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 2\\n1 1'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n5 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 2\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n4 1\\nDRAWROF 2\\nSTOP\\n0 0', 'output': '1 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 7\\nLEFT\\nBACKWARD 0\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 4\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n4 1\\nDRAWROF 2\\nSTOP\\n0 0', 'output': '2 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '2 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 3\\nLEFT\\nBACKWARD 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'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 7\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 10\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 2\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n2 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 1\\nFORWARD 3\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 1\\nFOSWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n2 1\\nDRAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n4 1\\nERAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n3 1\\nFORWARD 5\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 2\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\nFORDARW 3\\nRIGHT\\nFORWARD 8\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 9\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '2 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORDASW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 1\\nFORWARD 3\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 6\\nSTOP\\n3 1\\nFOSWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n4 1\\nERAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '10 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n3 1\\nFORWARD 5\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\nFORDARW 3\\nRIGHT\\nFORWARD 8\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 1\\nSTOP\\n4 1\\nERAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '16 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n3 1\\nFORWARD 5\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 4\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 1\\nSTOP\\n4 1\\nERAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '16 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n3 1\\nFORVARD 5\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '14 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n3 1\\nFORVARD 5\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '9 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n5 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 4\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n5 1\\nFORWARD 3\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n5 1\\nFOSW@RD 2\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 10\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 1\\nSTOP\\n3 2\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\nFPRWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n2 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 1\\nFOSWARD 1\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORDARW 2\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n2 1\\nDRAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\nFORDARW 3\\nRIGHT\\nFORWARD 8\\nLEFT\\nBACKWARD 5\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '9 2\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 1\\nSTOP\\n4 1\\nERAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '16 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n4 1\\nFORWARD 5\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 1\\nSTOP\\n4 1\\nERAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '14 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 4\\nSTOP\\n3 1\\nFORVARD 5\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 10\\nFORDARX 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 1\\nSTOP\\n3 2\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\nFPRWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n2 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '2 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '14 8\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 4\\nSTOP\\n3 1\\nFORVARD 5\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '14 8\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 4\\nSTOP\\n3 1\\nFORVASD 5\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '14 8\\nFORWRAD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 4\\nSTOP\\n3 1\\nFORVASD 5\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '14 8\\nFORWRAD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 4\\nSTOP\\n3 1\\nFOQVASD 5\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n3 1\\nFORWARD 0\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n5 1\\nFORWARD 1\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '11 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n2 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORDARW 3\\nRIGHT\\nFORWARD 1\\nLEFT\\nBACKWARD 3\\nSTOP\\n4 1\\nDRAWROF 2\\nSTOP\\n0 0', 'output': '2 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n6 1\\nDRAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n4 1\\nDRAWROF 2\\nSTOP\\n0 0', 'output': '2 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n5 1\\nDRAWSOF 2\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 7\\nLEFT\\nBACKWARD 6\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 2\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBCAKWARD 3\\nSTOP\\n3 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 10\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n3 2\\nFORWARD 4\\nSTOP\\n0 0', 'output': '6 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORDARW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n1 1\\nDRAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n1 1\\nFORWARD 5\\nSTOP\\n0 0', 'output': '6 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 9\\nFORWARD 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 2\\nSTOP\\n4 1\\nFORWARD 2\\nSTOP\\n0 0', 'output': '2 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORDASW 3\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 3\\nSTOP\\n4 1\\nFORWARD 3\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 5\\nSTOP\\n3 1\\nFOSWARD 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 1\\nSTOP\\n4 1\\nERAWROF 3\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\nFORDARW 1\\nRIGHT\\nFORWARD 5\\nLEFT\\nBACKWARD 1\\nSTOP\\n4 1\\nERAWROF 2\\nSTOP\\n0 0', 'output': '6 1\\n1 1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_78289","program":"```python\nwhile True:\n col, row = map(int, input().split())\n if col == 0:\n break\n else:\n robot = [1, 1]\n direction = \"up\"\n while True:\n str = input()\n if str == \"STOP\":\n print(robot[0], robot[1])\n break\n elif str == \"LEFT\":\n if direction == \"up\":\n direction = \"left\"\n elif direction == \"left\":\n direction = \"down\"\n elif direction == \"down\":\n direction = \"right\"\n else: # right\n direction = \"up\"\n elif str == \"RIGHT\":\n if direction == \"up\":\n direction = \"right\"\n elif direction == \"left\":\n direction = \"up\"\n elif direction == \"down\":\n direction = \"left\"\n else: # right\n direction = \"down\"\n else:\n di, step = str.split()\n step = int(step)\n if direction == \"up\":\n if di == \"FORWARD\":\n robot[1] = min(robot[1] + step, row)\n else:\n robot[1] = max(robot[1] - step, 1)\n elif direction == \"left\":\n if di == \"FORWARD\":\n robot[0] = max(robot[0] - step, 1)\n else:\n robot[0] = min(robot[0] + step, col)\n elif direction == \"down\":\n if di == \"FORWARD\":\n robot[1] = max(robot[1] - step, 1)\n else:\n robot[1] = min(robot[1] + step, row)\n else: # right\n if di == \"FORWARD\":\n robot[0] = min(robot[0] + step, col)\n else:\n robot[0] = max(robot[0] - step, 1)\n\n```","inputs":"6 5\nFORWARD 3\nRIGHT\nFORWARD 5\nLEFT\nBACKWARD 2\nSTOP\n3 1\nFORWARD 2\nSTOP\n0 0","output":"6 2\n1 1","actual_output":"6 2\n1 1\n","execution_success":true,"sample_index":12478},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00828 Make a Sequence","prompt":"Solve the following coding problem using the programming language python:\n\nYour company\u2019s next product will be a new game, which is a three-dimensional variant of the classic game \u201cTic-Tac-Toe\u201d. Two players place balls in a three-dimensional space (board), and try to make a sequence of a certain length.\n\nPeople believe that it is fun to play the game, but they still cannot fix the values of some parameters of the game. For example, what size of the board makes the game most exciting? Parameters currently under discussion are the board size (we call it n in the following) and the length of the sequence (m). In order to determine these parameter values, you are requested to write a computer simulator of the game.\n\nYou can see several snapshots of the game in Figures 1-3. These figures correspond to the three datasets given in the Sample Input.\n\n\n\nFigure 1: A game with n = m = 3\n\nHere are the precise rules of the game.\n\n1. Two players, Black and White, play alternately. Black plays first.\n2. There are n \u00d7 n vertical pegs. Each peg can accommodate up to n balls. A peg can be specified by its x- and y-coordinates (1 \u2264 x, y \u2264 n). A ball on a peg can be specified by its z-coordinate (1 \u2264 z \u2264 n). At the beginning of a game, there are no balls on any of the pegs.\n\n\n\nFigure 2: A game with n = m = 3 (White made a 3-sequence before Black)\n\n3. On his turn, a player chooses one of n \u00d7 n pegs, and puts a ball of his color onto the peg. The ball follows the law of gravity. That is, the ball stays just above the top-most ball on the same peg or on the floor (if there are no balls on the peg). Speaking differently, a player can choose x- and y-coordinates of the ball, but he cannot choose its z-coordinate.\n4. The objective of the game is to make an m-sequence. If a player makes an m-sequence or longer of his color, he wins. An m-sequence is a row of m consecutive balls of the same color. For example, black balls in positions (5, 1, 2), (5, 2, 2) and (5, 3, 2) form a 3-sequence. A sequence can be horizontal, vertical, or diagonal. Precisely speaking, there are 13 possible directions to make a sequence, categorized as follows.\n\n\n\nFigure 3: A game with n = 4, m = 3 (Black made two 4-sequences)\n\n(a) One-dimensional axes. For example, (3, 1, 2), (4, 1, 2) and (5, 1, 2) is a 3-sequence. There are three directions in this category.\n(b) Two-dimensional diagonals. For example, (2, 3, 1), (3, 3, 2) and (4, 3, 3) is a 3-sequence. There are six directions in this category.\n(c) Three-dimensional diagonals. For example, (5, 1, 3), (4, 2, 4) and (3, 3, 5) is a 3- sequence. There are four directions in this category.\n\nNote that we do not distinguish between opposite directions.\n\n\n\n\nAs the evaluation process of the game, people have been playing the game several times changing the parameter values. You are given the records of these games. It is your job to write a computer program which determines the winner of each recorded game.\n\nSince it is difficult for a human to find three-dimensional sequences, players often do not notice the end of the game, and continue to play uselessly. In these cases, moves after the end of the game, i.e. after the winner is determined, should be ignored. For example, after a player won making an m-sequence, players may make additional m-sequences. In this case, all m-sequences but the first should be ignored, and the winner of the game is unchanged.\n\nA game does not necessarily end with the victory of one of the players. If there are no pegs left to put a ball on, the game ends with a draw. Moreover, people may quit a game before making any m-sequence. In such cases also, the game ends with a draw.\n\n\n\nInput\n\nThe input consists of multiple datasets each corresponding to the record of a game. A dataset starts with a line containing three positive integers n, m, and p separated by a space. The relations 3 \u2264 m \u2264 n \u2264 7 and 1 \u2264 p \u2264 n3 hold between them. n and m are the parameter values of the game as described above. p is the number of moves in the game.\n\nThe rest of the dataset is p lines each containing two positive integers x and y. Each of these lines describes a move, i.e. the player on turn puts his ball on the peg specified. You can assume that 1 \u2264 x \u2264 n and 1 \u2264 y \u2264 n. You can also assume that at most n balls are put on a peg throughout a game.\n\nThe end of the input is indicated by a line with three zeros separated by a space.\n\nOutput\n\nFor each dataset, a line describing the winner and the number of moves until the game ends should be output. The winner is either \u201cBlack\u201d or \u201cWhite\u201d. A single space should be inserted between the winner and the number of moves. No other extra characters are allowed in the output.\n\nIn case of a draw, the output line should be \u201cDraw\u201d.\n\nExample\n\nInput\n\n3 3 3\n1 1\n1 1\n1 1\n3 3 7\n2 2\n1 3\n1 1\n2 3\n2 1\n3 3\n3 1\n4 3 15\n1 1\n2 2\n1 1\n3 3\n3 3\n1 1\n3 3\n3 3\n4 4\n1 1\n4 4\n4 4\n4 4\n4 1\n2 2\n0 0 0\n\n\nOutput\n\nDraw\nWhite 6\nBlack 15\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nsys.setrecursionlimit(1000000000)\ninput=lambda : sys.stdin.readline().rstrip()\n\ndx=[1,1,0,-1,1,1,0,-1,-1,-1,0,1,0]\ndy=[0,1,1,1,0,1,1,1,0,-1,-1,-1,0]\ndz=[0,0,0,0,1,1,1,1,1,1,1,1,1]\n\nwhile True:\n n,m,q=map(int,input().split())\n if n==m==q==0:\n break\n field=[[[-1 for i in range(n)]for i in range(n)]for i in range(n)]\n d=True\n turn=1\n for t in range(q):\n x,y=map(int,input().split())\n if d==False:\n continue\n x,y=x-1,y-1\n z=n\n while z>0:\n if field[x][y][z-1]==-1:\n z-=1\n else:\n break\n field[x][y][z]=turn\n for i in range(13):\n tx,ty,tz=x,y,z\n count=0\n while 0<=tx=m:\n print('Black' if turn else 'White',t+1)\n d=False\n break\n turn=(turn+1)%2\n if d:\n print('Draw')\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 2\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n2 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nBlack 15'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 2\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 2\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n2 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nBlack 15\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n2 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nBlack 15\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n2 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nDraw\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 1\\n1 1\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n1 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nWhite 14\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 1\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n2 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 2\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nDraw\\nBlack 15\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 0\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 1\\n1 2\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 1\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nBlack 13\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 0\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n1 3\\n1 1\\n3 1\\n3 3\\n4 4\\n1 1\\n4 4\\n1 4\\n4 4\\n3 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nBlack 13\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 0\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n2 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n1 3\\n1 1\\n3 1\\n3 3\\n4 4\\n1 1\\n4 4\\n1 4\\n4 4\\n3 1\\n2 2\\n0 0 0', 'output': 'Draw\\nBlack 5\\nBlack 13\\n'}, {'type': 'stdin_stdout', 'input': '3 1 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 1\\n2 1\\n2 3\\n2 0\\n3 3\\n3 1\\n4 3 15\\n1 1\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Black 1\\nDraw\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n2 2\\n1 1\\n3 3\\n1 3\\n1 1\\n2 3\\n3 3\\n4 4\\n2 1\\n4 4\\n4 4\\n4 0\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nWhite 12\\n'}, {'type': 'stdin_stdout', 'input': '5 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 0\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 1\\n1 2\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 2\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nDraw\\nBlack 13\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n0 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 2\\n2 3\\n3 1\\n4 6 15\\n2 1\\n0 1\\n1 1\\n1 -1\\n3 0\\n1 1\\n3 3\\n3 3\\n4 3\\n1 1\\n4 4\\n2 4\\n4 4\\n4 0\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 5\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 1\\n1 1\\n1 3\\n3 3\\n1 1\\n3 1\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nBlack 7\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n1 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 3\\n1 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nWhite 14\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n2 1\\n1 1\\n1 1\\n3 2 7\\n3 2\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n2 2\\n1 1\\n3 3\\n3 3\\n1 0\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 0\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 4\\nBlack 15\\n'}, {'type': 'stdin_stdout', 'input': '3 1 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 0\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 4 15\\n1 2\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n2 3\\n4 0\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Black 1\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n2 1\\n4 3 15\\n2 1\\n0 1\\n1 1\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n1 1\\n6 2\\n0 0 0', 'output': 'Draw\\nDraw\\nWhite 14\\n'}, {'type': 'stdin_stdout', 'input': '1 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n1 0\\n4 3 15\\n2 1\\n0 1\\n1 1\\n3 3\\n3 3\\n1 1\\n3 1\\n0 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nDraw\\nBlack 7\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n2 1\\n1 1\\n1 1\\n3 3 7\\n3 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n6 1\\n4 3 15\\n1 1\\n2 2\\n1 1\\n3 3\\n3 3\\n1 0\\n3 3\\n3 3\\n4 0\\n1 1\\n4 4\\n4 4\\n4 0\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nBlack 5\\nBlack 15\\n'}, {'type': 'stdin_stdout', 'input': '3 1 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n1 3\\n1 1\\n3 3\\n3 3\\n4 4\\n2 1\\n4 1\\n4 4\\n4 3\\n4 1\\n2 2\\n0 0 0', 'output': 'Black 1\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n3 3\\n2 1\\n3 2\\n3 1\\n4 3 15\\n2 2\\n0 1\\n1 1\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 2\\n4 4\\n4 3\\n4 4\\n1 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nBlack 5\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 2\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n1 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n1 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n3 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 1\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 1\\n1 1\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 6 15\\n2 1\\n0 1\\n1 1\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 6 15\\n2 1\\n0 1\\n1 1\\n1 0\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 6 15\\n2 1\\n0 1\\n1 1\\n1 0\\n3 3\\n1 1\\n3 3\\n4 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 2\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n2 3\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 2\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 0\\n4 3 15\\n1 1\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 2\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n2 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 0\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nBlack 15\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 4\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n1 3\\n1 1\\n3 3\\n3 3\\n4 4\\n2 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n1 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 0\\n4 4\\n4 4\\n4 4\\n3 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n2 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nDraw\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '4 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 1\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 1\\n1 2\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 6 15\\n2 1\\n0 1\\n1 2\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n0 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 6 15\\n2 1\\n0 1\\n1 1\\n1 0\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n3 3\\n2 1\\n3 3\\n3 1\\n4 6 15\\n2 1\\n0 1\\n1 1\\n1 0\\n3 3\\n1 1\\n3 3\\n4 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n2 1\\n1 1\\n1 1\\n3 3 7\\n3 2\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n2 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 0\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nBlack 15\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n0 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 4\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 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6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 0\\n3 3\\n1 3\\n1 1\\n3 1\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n3 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nBlack 15\\n'}, {'type': 'stdin_stdout', 'input': '1 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n1 1\\n4 3 15\\n2 1\\n0 1\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n0 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nDraw\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 0\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 3\\n1 1\\n3 3\\n1 3\\n1 1\\n3 1\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n3 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nBlack 15\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 0\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n1 1\\n3 3\\n3 1\\n4 5 15\\n1 0\\n0 2\\n1 1\\n3 3\\n1 3\\n1 1\\n3 1\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n3 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '6 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n0 2\\n1 1\\n3 3\\n3 2\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n3 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n0 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n2 1\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 0\\n0 2\\n1 1\\n3 3\\n1 3\\n1 0\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 3\\n3 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 1\\n1 1\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n0 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n1 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 6 15\\n2 1\\n0 1\\n1 2\\n1 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n2 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nBlack 7\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n0 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 6 15\\n2 1\\n0 1\\n1 1\\n1 -1\\n3 3\\n1 1\\n3 3\\n4 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nDraw\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 2\\n2 3\\n1 1\\n1 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n2 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 0\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nWhite 6\\nBlack 15\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 1\\n2 1\\n2 3\\n2 1\\n3 3\\n3 1\\n4 3 15\\n1 1\\n1 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n2 2\\n0 0 0', 'output': 'Draw\\nDraw\\nDraw\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 2\\n1 1\\n1 1\\n3 3 7\\n3 3\\n1 3\\n2 1\\n2 3\\n2 0\\n3 3\\n3 1\\n4 3 15\\n2 1\\n0 2\\n1 1\\n3 3\\n3 3\\n1 1\\n3 3\\n3 3\\n4 4\\n1 1\\n4 4\\n4 4\\n4 4\\n4 1\\n4 2\\n0 0 0', 'output': 'Draw\\nDraw\\nDraw\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_78293","program":"```python\nimport sys\nsys.setrecursionlimit(1000000000)\ninput=lambda : sys.stdin.readline().rstrip()\n\ndx=[1,1,0,-1,1,1,0,-1,-1,-1,0,1,0]\ndy=[0,1,1,1,0,1,1,1,0,-1,-1,-1,0]\ndz=[0,0,0,0,1,1,1,1,1,1,1,1,1]\n\nwhile True:\n n,m,q=map(int,input().split())\n if n==m==q==0:\n break\n field=[[[-1 for i in range(n)]for i in range(n)]for i in range(n)]\n d=True\n turn=1\n for t in range(q):\n x,y=map(int,input().split())\n if d==False:\n continue\n x,y=x-1,y-1\n z=n\n while z>0:\n if field[x][y][z-1]==-1:\n z-=1\n else:\n break\n field[x][y][z]=turn\n for i in range(13):\n tx,ty,tz=x,y,z\n count=0\n while 0<=tx=m:\n print('Black' if turn else 'White',t+1)\n d=False\n break\n turn=(turn+1)%2\n if d:\n print('Draw')\n\n\n\n```","inputs":"3 3 3\n1 1\n1 1\n1 1\n3 3 7\n2 2\n1 3\n1 1\n2 3\n2 1\n3 3\n3 1\n4 3 15\n1 1\n2 2\n1 1\n3 3\n3 3\n1 1\n3 3\n3 3\n4 4\n1 1\n4 4\n4 4\n4 4\n4 1\n2 2\n0 0 0","output":"Draw\nWhite 6\nBlack 15","actual_output":"Draw\nWhite 6\nBlack 15\n","execution_success":true,"sample_index":12479},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00959 Medical Checkup","prompt":"Solve the following coding problem using the programming language python:\n\nProblem C Medical Checkup\n\nStudents of the university have to go for a medical checkup, consisting of lots of checkup items, numbered 1, 2, 3, and so on.\n\nStudents are now forming a long queue, waiting for the checkup to start. Students are also numbered 1, 2, 3, and so on, from the top of the queue. They have to undergo checkup items in the order of the item numbers, not skipping any of them nor changing the order. The order of students should not be changed either.\n\nMultiple checkup items can be carried out in parallel, but each item can be carried out for only one student at a time. Students have to wait in queues of their next checkup items until all the others before them finish.\n\nEach of the students is associated with an integer value called health condition. For a student with the health condition $h$, it takes $h$ minutes to finish each of the checkup items. You may assume that no interval is needed between two students on the same checkup item or two checkup items for a single student.\n\nYour task is to find the items students are being checked up or waiting for at a specified time $t$.\n\nInput\n\nThe input consists of a single test case in the following format.\n\n\n$n$ $t$\n$h_1$\n...\n$h_n$\n\n\n$n$ and $t$ are integers. $n$ is the number of the students ($1 \\leq n \\leq 10^5$). $t$ specifies the time of our concern ($0 \\leq t \\leq 10^9$). For each $i$, the integer $h_i$ is the health condition of student $i$ ($1 \\leq h_ \\leq 10^9$).\n\nOutput\n\nOutput $n$ lines each containing a single integer. The $i$-th line should contain the checkup item number of the item which the student $i$ is being checked up or is waiting for, at ($t+0.5$) minutes after the checkup starts. You may assume that all the students are yet to finish some of the checkup items at that moment.\n\nSample Input 1\n\n\n3 20\n5\n7\n3\n\n\nSample Output 1\n\n\n5\n3\n2\n\n\nSample Input 2\n\n\n5 1000000000\n5553\n2186\n3472\n2605\n1790\n\n\nSample Output 2\n\n\n180083\n180083\n180082\n180082\n180082\n\n\n\n\n\n\nExample\n\nInput\n\n3 20\n5\n7\n3\n\n\nOutput\n\n5\n3\n2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, t = map(int, input().split())\ns = x = y = 0\nfor i in range(n):\n h = int(input())\n s, x, y = s+x, h, max(h, y)\n print(max((t-x-s)//y+2,1))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 20\\n5\\n7\\n3', 'output': '5\\n3\\n2'}, {'type': 'stdin_stdout', 'input': '3 20\\n5\\n11\\n3', 'output': '5\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3 20\\n5\\n11\\n6', 'output': '5\\n2\\n1\\n'}, {'type': 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'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_78297","program":"```python\nn, t = map(int, input().split())\ns = x = y = 0\nfor i in range(n):\n h = int(input())\n s, x, y = s+x, h, max(h, y)\n print(max((t-x-s)//y+2,1))\n```","inputs":"3 20\n5\n7\n3","output":"5\n3\n2","actual_output":"5\n3\n2\n","execution_success":true,"sample_index":12480},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01228 Rhythm Machine","prompt":"Solve the following coding problem using the programming language python:\n\nAdvanced Computer Music (ACM) sold a rhythm machine that plays music according to a pre-programmed rhythm. At one point, ACM was trying to develop and sell a new rhythm machine. While ACM's old product could only play one sound at a time, the new product was able to play up to eight sounds at the same time, which was the main feature. Since songs that previously had to be played using multiple old products can now be played with one new product, ACM has rhythms for multiple old products in order to promote the transition to new products. I decided to create a program that converts the pattern into a rhythm pattern for one new product.\n\nACM's rhythm machine expresses which sound is played at the same time as a two-digit hexadecimal number. ACM's rhythm machine is capable of producing eight different sounds, each of which is assigned a number from 0 to 7. At a certain timing, si = 1 when the sound i (0 \u2264 i <8) is sounded, and si = 0 when it is not sounded. At this time, the chord that sounds each note at the same time is represented by the value \u03a3 \\ (s_i \u00d7 2 ^ i \\), and the \u201cchord expression\u201d that represents this value in 2-digit hexadecimal notation is included in the rhythm pattern. (Use uppercase letters for hexadecimal letters). For example, a chord that sounds 0, 6, and 7 sounds at the same time is expressed as \"` C1` \"because S = 20 + 26 + 27 = C1 (16), and a\" chord \"that sounds nothing is expressed. It is expressed as \"` 00` \".\n\nThe rhythm pattern is given as one or more of the above chord expressions. A certain rhythm pattern character string shows a performance pattern within one bar. The timing of each chord is expressed by the relative position t (0 \u2264 t <1) in the bar. A rhythm pattern string consisting of k chord expressions divides the measure into k equal parts and plays each chord in order at the timing of t = 0 / k, 1 / k, ..., (k\u22121) / k. It represents such a rhythm pattern. For example, the rhythm pattern \"` 01000003` \"means that sound 0 is played at the timing of t = 0/4 and sounds 0 and 1 are played at the timing of t = 3/4. Also, the rhythm pattern \"` 00` \"indicates that no sound is produced in the bar (note that the rhythm pattern requires one or more chord expressions).\n\nSince the old product can only play one sound at a time, \"` 00` \",\" `01`\", \"` 02` \",\" `04`\", \"` 08 \"in the rhythm pattern string for the old product Only one of the chord expressions of `\", \"` 10` \",\" `20`\", \"` 40` \", and\" `80`\" appears. Write a program that receives N rhythm patterns for old products (1 \u2264 N \u2264 8) and outputs rhythm patterns for new products that play those rhythm patterns at the same time.\n\nIt can be assumed that the same sound is not played at exactly the same timing in the given N rhythm patterns.\n\n\n\nInput\n\nThe number of datasets is given in the first row. From the next line onward, each dataset is described in turn. You can assume that the number of datasets does not exceed 120.\n\nEach dataset is given in the following format.\n\n\nN\nR1\nR2\n...\nRN\n\n\nRi (1 \u2264 i \u2264 N) is a rhythm pattern for older products.\n\nEach rhythm pattern has a maximum of 2048 characters (1024 chord expression). Note that the given rhythm pattern is not always the shortest expression.\n\nOutput\n\nFor each dataset, generate the shortest rhythm pattern that plays all the given N rhythm patterns at the same time, and output it in one line. If such a rhythm pattern exceeds 2048 characters, output the string \"` Too complex.` \"instead of the rhythm pattern.\n\nExample\n\nInput\n\n5\n2\n01000100\n00020202\n2\n0102\n00000810\n1\n0200020008000200\n5\n0001\n000001\n0000000001\n00000000000001\n0000000000000000000001\n1\n000000\n\n\nOutput\n\n01020302\n01000A10\n02020802\nToo complex.\n00\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef shorten(s):\n f = 1\n while f:\n l = len(s) // 2\n while f:\n f = 0\n if l % 2 == 0:\n for i in range(l):\n if s[2 * i:2 * i + 2] != \"00\" and i % 2:break\n else:\n f = 1\n t = \"\"\n for i in range(0, l, 2):t += s[2 * i:2 * i + 2]\n s = t\n l = len(s) // 2\n for k in range(3, l + 1, 2):\n f = 1\n while f:\n f = 0\n if l % k == 0:\n for i in range(l):\n if s[2 * i:2 * i + 2] != \"00\" and i % k:break\n else:\n f = 1\n t = \"\"\n for i in range(0, l, k):t += s[2 * i:2 * i + 2]\n s = t\n l = len(s) // 2\n return s\n\ndef lcm(a, b):\n p, q = max(a, b), min(a, b)\n while 1:\n if p % q:p, q = q, p % q\n else: return a * b // q\n\nfor _ in range(int(input())):\n n = int(input())\n r = [shorten(input()) for _ in range(n)]\n ls = [len(i) // 2 for i in r]\n l = ls[0]\n for i in range(1, n):l = lcm(l, ls[i])\n if l > 1024:print(\"Too complex.\");continue\n a = [0] * l\n for i in range(n):\n d = l // ls[i]\n for j in range(ls[i]):a[d * j] += int(r[i][2 * j: 2 * j + 2], 16)\n s = \"\"\n for i in a:s += format(i,\"02X\")\n print(s)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n2\\n01000100\\n00020202\\n2\\n0102\\n00000810\\n1\\n0200020008000200\\n5\\n0001\\n000001\\n0000000001\\n00000000000001\\n0000000000000000000001\\n1\\n000000', 'output': '01020302\\n01000A10\\n02020802\\nToo complex.\\n00'}, {'type': 'stdin_stdout', 'input': 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'5\\n2\\n01000000\\n00020202\\n2\\n0102\\n00000810\\n1\\n37056427527175\\n5\\n0001\\n010001\\n0000000001\\n00000000000001\\n0000000000000000000001\\n1\\n000000', 'output': '01020202\\n01000A10\\n37056427527175\\nToo complex.\\n00\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2\\n01000101\\n00020202\\n2\\n0102\\n00000810\\n1\\n0200020008000200\\n1\\n0111\\n000001\\n0000000001\\n00000000000001\\n0000000000000000000001\\n1\\n000000', 'output': '01020303\\n01000A10\\n02020802\\n0111\\n0000000001\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2\\n01000100\\n00020202\\n2\\n10\\n00000810\\n1\\n0200020008000200\\n1\\n0001\\n000001\\n0000000000\\n00000000000001\\n0000000000000000000001\\n1\\n001100', 'output': '01020302\\n10000810\\n02020802\\n0001\\n00\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2\\n01100100\\n00020202\\n2\\n0102\\n00000810\\n1\\n0200020008000200\\n1\\n0011\\n000001\\n1000000001\\n00100000000001\\n0000000000000000000001\\n1\\n000000', 'output': '01120302\\n01000A10\\n02020802\\n0011\\n1000000001\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 5, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_78305","program":"```python\ndef shorten(s):\n f = 1\n while f:\n l = len(s) // 2\n while f:\n f = 0\n if l % 2 == 0:\n for i in range(l):\n if s[2 * i:2 * i + 2] != \"00\" and i % 2:break\n else:\n f = 1\n t = \"\"\n for i in range(0, l, 2):t += s[2 * i:2 * i + 2]\n s = t\n l = len(s) // 2\n for k in range(3, l + 1, 2):\n f = 1\n while f:\n f = 0\n if l % k == 0:\n for i in range(l):\n if s[2 * i:2 * i + 2] != \"00\" and i % k:break\n else:\n f = 1\n t = \"\"\n for i in range(0, l, k):t += s[2 * i:2 * i + 2]\n s = t\n l = len(s) // 2\n return s\n\ndef lcm(a, b):\n p, q = max(a, b), min(a, b)\n while 1:\n if p % q:p, q = q, p % q\n else: return a * b // q\n\nfor _ in range(int(input())):\n n = int(input())\n r = [shorten(input()) for _ in range(n)]\n ls = [len(i) // 2 for i in r]\n l = ls[0]\n for i in range(1, n):l = lcm(l, ls[i])\n if l > 1024:print(\"Too complex.\");continue\n a = [0] * l\n for i in range(n):\n d = l // ls[i]\n for j in range(ls[i]):a[d * j] += int(r[i][2 * j: 2 * j + 2], 16)\n s = \"\"\n for i in a:s += format(i,\"02X\")\n print(s)\n\n```","inputs":"5\n2\n01000100\n00020202\n2\n0102\n00000810\n1\n0200020008000200\n5\n0001\n000001\n0000000001\n00000000000001\n0000000000000000000001\n1\n000000","output":"01020302\n01000A10\n02020802\nToo complex.\n00","actual_output":"01020302\n01000A10\n02020802\nToo complex.\n00\n","execution_success":true,"sample_index":12481},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01844 Land Inheritance","prompt":"Solve the following coding problem using the programming language python:\n\nF --Land inheritance\n\nProblem Statement\n\nOne $ N $ brother was discussing the inheritance of his parents. The vast heritage left by their parents included vast lands. The land has a rectangular shape extending $ H $ km from north to south and $ W $ km from east to west. This land is managed in units of 1 km square, 1 km square within the range of $ i $ to $ i + 1 $ km from the north end of the land and $ j $ to $ j + 1 $ km from the west end. The partition is called partition $ (i, j) $. ($ i $, $ j $ is an integer that satisfies $ 0 \\ leq i \n\n\nSample Input 2\n\n\n3 3 2\n0 1 0\n1 1 1\n0 1 0\n\nOutput for the Sample Input 2\n\n\n1\n\nSample Input 3\n\n\n2 5 3\n8 3 0 5 6\n2 5 2 5 2\n\nOutput for the Sample Input 3\n\n\n11\n\nSample Input 4\n\n\n3 3 4\n3 3 4\n3 3 4\n3 3 4\n\nOutput for the Sample Input 4\n\n\n7\n\nSample Input 5\n\n\n4 4 4\n2 2 2 2\n2 1 2 1\n2 2 2 2\n2 1 2 1\n\nOutput for the Sample Input 5\n\n\n7\n\n\n\n\n\nExample\n\nInput\n\n3 3 2\n1 2 2\n3 1 0\n0 4 3\n\n\nOutput\n\n7\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\ndef rotate(H, W, R0):\n R1 = [[0]*H for i in range(W)]\n for i in range(H):\n for j in range(W):\n R1[W-1-j][i] = R0[i][j]\n return R1\ndef make(H, W, R0):\n R1 = [[0]*(W+1) for i in range(H+1)]\n for i in range(H):\n c = 0\n for j in range(W):\n c += R0[i][j]\n R1[i+1][j+1] = c + R1[i][j+1]\n return R1\n\ndef solve():\n H, W, N = map(int, readline().split())\n S = [list(map(int, readline().split())) for i in range(H)]\n su = sum(map(sum, S))\n ans = 0\n if N == 2:\n T = make(H, W, S)\n for i in range(H+1):\n e = T[i][W]\n ans = max(ans, min(e, su-e))\n for i in range(W+1):\n e = T[H][i]\n ans = max(ans, min(e, su-e))\n elif N == 3:\n for t in range(4):\n T = make(H, W, S)\n for i in range(H+1):\n e0 = T[i][W]\n for j in range(W+1):\n e1 = T[H][j] - T[i][j]\n ans = max(ans, min(e0, e1, su - e0 - e1))\n if t < 2:\n for i in range(W+1):\n e0 = T[H][i]\n for j in range(i, W+1):\n e1 = T[H][j]\n ans = max(ans, min(e0, e1-e0, su-e1))\n S = rotate(H, W, S)\n H, W = W, H\n else:\n for t in range(4):\n T = make(H, W, S)\n for i in range(H+1):\n for j in range(W+1):\n e0 = T[i][j]\n if e0 < ans:\n continue\n k1 = 0\n while k1 < H and T[k1][W] - T[k1][j] < e0:\n k1 += 1\n k2 = 0\n while k2 < W and T[H][k2] - T[i][k2] < e0:\n k2 += 1\n if i < k1 and j < k2:\n continue\n if k1 <= i and k2 <= j:\n v1 = su - T[H][k2] - T[i][W] + T[i][k2]\n v2 = su - T[k1][W] - T[H][j] + T[k1][j]\n if max(v1, v2) >= e0:\n ans = max(e0, ans)\n else:\n v1 = su - T[H][k2] - T[k1][W] + T[k1][k2]\n if v1 >= e0:\n ans = max(e0, ans)\n for i in range(W, -1, -1):\n e0 = T[H][i]\n if e0 <= ans:\n break\n for j in range(i, W+1):\n e = T[H][j]\n e1 = e - e0; e2 = su - e\n if e1 <= ans or e2 <= ans:\n continue\n for k in range(j, W+1):\n f = T[H][k]\n if su-f <= ans:\n break\n ans = max(ans, min(e0, e1, f-e, su-f))\n for k in range(H+1):\n f = T[k][j] - T[k][i]\n if e1-f <= ans:\n break\n ans = max(ans, min(e0, f, e1-f, e2))\n for k in range(H+1):\n f = T[k][W] - T[k][j]\n if e2-f <= ans:\n break\n ans = max(ans, min(e0, e1, f, e2-f))\n for j in range(H+1):\n e1 = T[j][W] - T[j][i]\n e2 = su - e1 - e0\n if e1 <= ans or e2 <= ans:\n continue\n for k in range(i, W+1):\n f = T[j][k] - T[j][i]\n if e1-f <= ans:\n break\n ans = max(ans, min(e0, f, e1-f, e2))\n for k in range(i, W+1):\n f = T[H][k] - e0 - T[j][k] + T[j][i]\n if e2-f <= ans:\n break\n ans = max(ans, min(e0, e1, f, e2-f))\n for j in range(H, -1, -1):\n e1 = T[j][W] - T[j][i]\n if su - e0 - e1 <= ans:\n continue\n if e1 <= ans:\n break\n for k in range(j, H+1):\n e2 = T[k][W] - T[k][i]\n if su-e2-e0 <= ans:\n break\n ans = max(ans, min(e0, e1, e2-e1, su-e2-e0))\n S = rotate(H, W, S)\n H, W = W, H\n write(\"%d\\n\" % ans)\nsolve()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 3 2\\n1 2 2\\n3 1 0\\n0 4 3', 'output': '7'}, {'type': 'stdin_stdout', 'input': '3 3 2\\n1 2 2\\n3 1 0\\n1 4 3', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3 3 2\\n1 2 2\\n1 1 0\\n1 4 3', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '3 3 2\\n1 2 2\\n1 1 0\\n1 2 3', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1 3 2\\n2 2 2\\n1 1 0\\n1 2 3', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 3 0\\n1 3 2\\n1 2 -1\\n1 2 3', 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1\\n1 2 3', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '0 3 2\\n2 2 2\\n1 1 0\\n1 2 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 3 2\\n2 3 1\\n1 1 0\\n1 2 3', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 3 4\\n2 3 2\\n1 2 0\\n1 2 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 3 2\\n2 4 2\\n1 2 -1\\n1 2 3', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 3 2\\n1 3 2\\n1 2 0\\n1 2 3', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 3 0\\n1 3 2\\n1 2 -1\\n1 2 4', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 3 0\\n2 3 2\\n1 2 -1\\n1 2 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n2 3 2\\n1 2 -2\\n1 2 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n1 3 2\\n2 1 -2\\n2 2 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0\\n0 3 2\\n1 1 -2\\n2 2 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n0 3 2\\n0 1 -4\\n3 2 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n0 1 2\\n1 1 -5\\n3 2 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1\\n0 1 2\\n1 2 -4\\n3 2 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n0 1 2\\n1 2 -4\\n0 2 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-1 1 2\\n1 2 -4\\n1 2 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n0 1 2\\n1 4 -4\\n1 4 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-1 1 2\\n1 2 -4\\n0 4 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-2 1 1\\n1 2 -4\\n1 4 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-1 1 1\\n1 0 -3\\n1 4 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-1 1 1\\n1 -1 -4\\n1 4 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-2 1 1\\n1 0 -4\\n1 2 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-1 1 1\\n1 -1 -4\\n1 2 -1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-2 1 2\\n1 0 -4\\n1 2 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-1 1 2\\n1 -2 -4\\n1 2 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-1 1 0\\n1 -1 -4\\n1 2 -1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n0 1 0\\n1 -1 -4\\n1 0 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1\\n-1 1 -1\\n1 -1 -4\\n1 0 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1\\n0 1 1\\n1 -1 -4\\n1 0 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1\\n-1 4 1\\n1 -1 -4\\n1 0 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1\\n-1 2 1\\n1 0 -2\\n1 0 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 0\\n-1 2 1\\n1 -1 -2\\n1 -1 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 2\\n-1 2 1\\n2 -1 -2\\n2 -1 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1\\n-1 2 1\\n1 -1 -1\\n2 -1 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 2\\n-1 0 1\\n1 -1 -1\\n2 -1 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 2\\n-1 0 0\\n2 -1 -1\\n2 -1 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 3 2\\n1 2 2\\n4 1 0\\n1 4 3', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3 3 2\\n0 3 2\\n1 1 0\\n1 4 3', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1 3 2\\n1 2 2\\n1 1 1\\n1 2 3', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 536870912}","problem_id":"vfc_78321","program":"```python\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\ndef rotate(H, W, R0):\n R1 = [[0]*H for i in range(W)]\n for i in range(H):\n for j in range(W):\n R1[W-1-j][i] = R0[i][j]\n return R1\ndef make(H, W, R0):\n R1 = [[0]*(W+1) for i in range(H+1)]\n for i in range(H):\n c = 0\n for j in range(W):\n c += R0[i][j]\n R1[i+1][j+1] = c + R1[i][j+1]\n return R1\n\ndef solve():\n H, W, N = map(int, readline().split())\n S = [list(map(int, readline().split())) for i in range(H)]\n su = sum(map(sum, S))\n ans = 0\n if N == 2:\n T = make(H, W, S)\n for i in range(H+1):\n e = T[i][W]\n ans = max(ans, min(e, su-e))\n for i in range(W+1):\n e = T[H][i]\n ans = max(ans, min(e, su-e))\n elif N == 3:\n for t in range(4):\n T = make(H, W, S)\n for i in range(H+1):\n e0 = T[i][W]\n for j in range(W+1):\n e1 = T[H][j] - T[i][j]\n ans = max(ans, min(e0, e1, su - e0 - e1))\n if t < 2:\n for i in range(W+1):\n e0 = T[H][i]\n for j in range(i, W+1):\n e1 = T[H][j]\n ans = max(ans, min(e0, e1-e0, su-e1))\n S = rotate(H, W, S)\n H, W = W, H\n else:\n for t in range(4):\n T = make(H, W, S)\n for i in range(H+1):\n for j in range(W+1):\n e0 = T[i][j]\n if e0 < ans:\n continue\n k1 = 0\n while k1 < H and T[k1][W] - T[k1][j] < e0:\n k1 += 1\n k2 = 0\n while k2 < W and T[H][k2] - T[i][k2] < e0:\n k2 += 1\n if i < k1 and j < k2:\n continue\n if k1 <= i and k2 <= j:\n v1 = su - T[H][k2] - T[i][W] + T[i][k2]\n v2 = su - T[k1][W] - T[H][j] + T[k1][j]\n if max(v1, v2) >= e0:\n ans = max(e0, ans)\n else:\n v1 = su - T[H][k2] - T[k1][W] + T[k1][k2]\n if v1 >= e0:\n ans = max(e0, ans)\n for i in range(W, -1, -1):\n e0 = T[H][i]\n if e0 <= ans:\n break\n for j in range(i, W+1):\n e = T[H][j]\n e1 = e - e0; e2 = su - e\n if e1 <= ans or e2 <= ans:\n continue\n for k in range(j, W+1):\n f = T[H][k]\n if su-f <= ans:\n break\n ans = max(ans, min(e0, e1, f-e, su-f))\n for k in range(H+1):\n f = T[k][j] - T[k][i]\n if e1-f <= ans:\n break\n ans = max(ans, min(e0, f, e1-f, e2))\n for k in range(H+1):\n f = T[k][W] - T[k][j]\n if e2-f <= ans:\n break\n ans = max(ans, min(e0, e1, f, e2-f))\n for j in range(H+1):\n e1 = T[j][W] - T[j][i]\n e2 = su - e1 - e0\n if e1 <= ans or e2 <= ans:\n continue\n for k in range(i, W+1):\n f = T[j][k] - T[j][i]\n if e1-f <= ans:\n break\n ans = max(ans, min(e0, f, e1-f, e2))\n for k in range(i, W+1):\n f = T[H][k] - e0 - T[j][k] + T[j][i]\n if e2-f <= ans:\n break\n ans = max(ans, min(e0, e1, f, e2-f))\n for j in range(H, -1, -1):\n e1 = T[j][W] - T[j][i]\n if su - e0 - e1 <= ans:\n continue\n if e1 <= ans:\n break\n for k in range(j, H+1):\n e2 = T[k][W] - T[k][i]\n if su-e2-e0 <= ans:\n break\n ans = max(ans, min(e0, e1, e2-e1, su-e2-e0))\n S = rotate(H, W, S)\n H, W = W, H\n write(\"%d\\n\" % ans)\nsolve()\n\n```","inputs":"3 3 2\n1 2 2\n3 1 0\n0 4 3","output":"7","actual_output":"7\n","execution_success":true,"sample_index":12482},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02126 Ball","prompt":"Solve the following coding problem using the programming language python:\n\nProblem\n\nThere are $ N $ balls, each with its own color and value.\nThere are $ C $ types of ball colors from $ 1 $ to $ C $, and each color has an upper limit on the number of balls that can be selected.\nMaximize the total value you get when choosing at most $ M $ balls in total.\n\nConstraints\n\nThe input satisfies the following conditions.\n\n* $ 1 \\ leq M \\ leq N \\ leq 10 ^ 5 $\n* $ 1 \\ leq C \\ leq 10 ^ 5 $\n* $ 0 \\ leq l_i \\ leq N $\n* $ 1 \\ leq c_i \\ leq C $\n* $ 1 \\ leq w_i \\ leq 1000 $\n\nInput\n\nThe input is given in the following format.\n\n\n$ N $ $ M $ $ C $\n$ l_1 $ $ l_2 $ ... $ l_C $\n$ c_1 $ $ w_1 $\n$ c_2 $ $ w_2 $\n...\n$ c_N $ $ w_N $\n\n\nAll inputs are given as integers.\n$ N $, $ M $, $ C $ are given on the first line, separated by blanks.\nOn the second line, the upper limit of the number of balls that can be selected for the color $ i $ ($ 1 \\ leq i \\ leq C $) is given, separated by blanks.\nThe color $ c_i $ of the ball $ i $ and the value $ w_i $ ($ 1 \\ leq i \\ leq N $) are given in the third and subsequent lines of $ N $, separated by blanks.\n\nOutput\n\nOutput the maximum value you can get on one line.\n\nExamples\n\nInput\n\n3 3 2\n1 1\n1 1\n1 100\n2 10\n\n\nOutput\n\n110\n\n\nInput\n\n3 3 3\n1 0 1\n1 1\n2 100\n3 1\n\n\nOutput\n\n2\n\n\nInput\n\n22 7 26\n11 14 15 3 11 7 16 17 1 4 2 19 4 14 16 16 3 13 17 12 7 11 2 20 12 22\n6 10\n1 3\n13 1\n16 5\n4 1\n20 7\n18 4\n26 6\n9 1\n12 2\n21 1\n21 7\n18 1\n14 5\n24 5\n6 1\n3 1\n2 5\n21 2\n7 6\n10 9\n15 7\n\n\nOutput\n\n52\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# -*- coding: utf-8 -*-\ndef inpl(): return list(map(int, input().split()))\nN, M, C = inpl()\nL = {i+1:v for i, v in enumerate(inpl())}\n\nballs = []\nfor _ in range(N):\n c, w = inpl()\n balls.append([w, c])\n\nballs = sorted(balls, reverse=True)\n\ni = 0\ncount = 0\nans = 0\nfor i in range(N):\n w, c = balls[i]\n if count == M:\n break\n if L[c] == 0:\n continue\n else:\n count += 1\n ans += w\n L[c] -= 1\n\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '22 7 26\\n11 14 15 3 11 7 16 17 1 4 2 19 4 14 16 16 3 13 17 12 7 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 5\\n4 1\\n20 7\\n18 4\\n26 6\\n9 1\\n12 2\\n21 1\\n21 7\\n18 1\\n14 5\\n24 5\\n6 1\\n3 1\\n2 5\\n21 2\\n7 6\\n10 9\\n15 7', 'output': '52'}, {'type': 'stdin_stdout', 'input': '3 3 2\\n1 1\\n1 1\\n1 100\\n2 10', 'output': '110'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 0 1\\n1 1\\n2 100\\n3 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '22 7 26\\n11 14 15 3 11 7 16 17 1 4 2 19 4 14 16 16 3 13 17 12 7 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 5\\n4 1\\n20 7\\n18 4\\n26 6\\n9 1\\n12 2\\n21 1\\n21 7\\n18 1\\n14 5\\n24 5\\n6 1\\n1 1\\n2 5\\n21 2\\n7 6\\n10 9\\n15 7', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 0 1\\n1 1\\n2 100\\n1 1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '22 7 26\\n11 14 15 3 11 7 16 17 1 4 2 19 4 14 16 16 3 13 17 12 7 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 5\\n4 1\\n20 7\\n18 4\\n26 7\\n9 1\\n12 2\\n21 1\\n21 7\\n18 1\\n14 5\\n24 5\\n6 1\\n1 1\\n2 5\\n21 2\\n7 6\\n10 9\\n15 7', 'output': '53\\n'}, {'type': 'stdin_stdout', 'input': '3 3 2\\n1 1\\n1 1\\n1 100\\n2 16', 'output': '116\\n'}, {'type': 'stdin_stdout', 'input': '3 5 3\\n1 0 1\\n1 1\\n2 100\\n3 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '22 7 26\\n11 14 15 3 11 7 16 17 1 4 2 17 4 14 16 16 3 13 17 12 7 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 5\\n4 1\\n20 7\\n18 4\\n26 7\\n9 1\\n12 2\\n21 1\\n21 7\\n18 1\\n14 5\\n24 5\\n6 1\\n1 1\\n2 5\\n21 2\\n7 6\\n10 14\\n15 7', 'output': '58\\n'}, {'type': 'stdin_stdout', 'input': '22 7 26\\n11 14 15 3 11 7 16 7 1 4 2 19 4 14 16 16 5 13 33 12 11 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 5\\n4 1\\n20 7\\n18 4\\n26 7\\n9 1\\n12 2\\n5 1\\n21 7\\n18 1\\n14 5\\n24 8\\n6 1\\n1 1\\n2 5\\n23 2\\n7 5\\n10 9\\n15 7', 'output': '55\\n'}, {'type': 'stdin_stdout', 'input': '3 4 2\\n1 1\\n1 1\\n1 100\\n2 30', 'output': '130\\n'}, {'type': 'stdin_stdout', 'input': '22 12 26\\n11 14 15 3 11 7 16 7 1 4 2 19 4 14 16 16 3 13 17 12 11 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 5\\n6 1\\n20 7\\n18 4\\n26 7\\n9 1\\n12 2\\n5 1\\n21 7\\n18 1\\n14 5\\n24 1\\n6 1\\n1 1\\n2 5\\n21 2\\n7 5\\n10 9\\n15 7', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '3 4 2\\n1 0\\n1 1\\n1 100\\n2 30', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '22 10 26\\n11 14 15 3 11 7 16 7 1 4 2 19 4 14 16 16 3 13 17 12 11 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 5\\n6 1\\n20 7\\n18 4\\n26 7\\n9 1\\n24 2\\n5 1\\n21 7\\n18 1\\n14 5\\n24 1\\n6 1\\n1 1\\n2 5\\n21 2\\n7 5\\n10 9\\n15 7', 'output': '67\\n'}, {'type': 'stdin_stdout', 'input': '22 10 26\\n11 14 15 3 11 7 16 7 1 4 2 19 4 14 16 16 3 13 17 12 11 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 0\\n6 1\\n20 7\\n18 4\\n26 7\\n9 1\\n24 2\\n5 1\\n21 7\\n18 1\\n14 5\\n24 1\\n6 1\\n1 1\\n2 5\\n21 2\\n7 5\\n10 9\\n15 7', 'output': '66\\n'}, {'type': 'stdin_stdout', 'input': '22 10 26\\n11 14 15 3 11 7 16 7 1 4 2 19 4 14 16 16 3 13 17 12 11 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 0\\n6 1\\n20 7\\n18 4\\n26 1\\n9 1\\n24 2\\n5 1\\n21 7\\n18 1\\n14 5\\n24 1\\n6 1\\n1 1\\n2 5\\n21 2\\n7 5\\n10 9\\n15 7', 'output': '62\\n'}, {'type': 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7\\n9 2\\n12 2\\n5 1\\n21 2\\n4 1\\n5 5\\n24 8\\n6 1\\n1 1\\n2 5\\n3 2\\n7 5\\n10 17\\n15 7', 'output': '71\\n'}, {'type': 'stdin_stdout', 'input': '22 11 26\\n11 4 15 3 11 7 11 1 1 4 2 19 4 14 16 16 5 13 6 20 11 18 2 20 12 22\\n6 19\\n1 2\\n22 1\\n9 5\\n4 1\\n20 7\\n18 6\\n26 7\\n9 2\\n12 2\\n5 1\\n21 2\\n4 1\\n5 5\\n24 8\\n6 1\\n1 1\\n2 5\\n3 2\\n7 5\\n10 17\\n15 7', 'output': '91\\n'}, {'type': 'stdin_stdout', 'input': '22 11 26\\n11 4 15 3 11 7 11 1 1 4 2 19 4 14 16 16 5 13 6 20 11 18 2 20 8 22\\n6 19\\n0 2\\n22 1\\n9 5\\n4 0\\n20 7\\n18 6\\n26 14\\n9 2\\n12 2\\n5 1\\n21 2\\n4 1\\n5 5\\n24 8\\n9 1\\n1 1\\n2 5\\n3 2\\n7 5\\n10 17\\n15 7', 'output': '98\\n'}, {'type': 'stdin_stdout', 'input': '22 11 26\\n11 4 15 3 11 7 11 1 1 4 2 19 4 14 16 16 5 13 6 20 11 18 2 20 8 22\\n6 19\\n0 2\\n22 1\\n9 5\\n4 0\\n20 7\\n18 6\\n26 14\\n9 2\\n12 2\\n5 1\\n21 2\\n4 1\\n5 5\\n24 8\\n9 1\\n1 1\\n2 5\\n3 2\\n7 8\\n10 17\\n15 7', 'output': '101\\n'}, {'type': 'stdin_stdout', 'input': '22 11 26\\n11 4 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8\\n9 1\\n1 1\\n2 0\\n3 2\\n7 8\\n10 28\\n15 7', 'output': '105\\n'}, {'type': 'stdin_stdout', 'input': '22 11 26\\n11 4 15 3 11 7 11 1 1 4 2 21 1 14 16 16 5 13 6 20 11 18 2 20 8 22\\n6 19\\n0 2\\n16 1\\n9 5\\n4 0\\n20 7\\n18 1\\n26 14\\n9 2\\n14 2\\n5 1\\n21 2\\n4 1\\n5 5\\n24 8\\n9 1\\n1 1\\n2 0\\n3 2\\n7 5\\n10 28\\n15 7', 'output': '102\\n'}, {'type': 'stdin_stdout', 'input': '22 8 26\\n11 4 15 3 11 7 11 1 1 4 2 21 1 14 16 16 5 13 6 20 11 18 2 20 8 22\\n6 19\\n0 2\\n16 1\\n9 5\\n4 0\\n20 7\\n18 1\\n26 14\\n9 2\\n14 2\\n5 1\\n21 2\\n4 1\\n5 5\\n24 8\\n9 1\\n1 1\\n2 0\\n3 2\\n7 5\\n10 28\\n15 7', 'output': '93\\n'}, {'type': 'stdin_stdout', 'input': '11 7 26\\n11 14 15 4 9 5 16 4 1 3 2 19 4 14 16 27 3 21 17 21 11 11 2 17 12 18\\n6 20\\n2 1\\n17 2\\n5 5\\n4 1\\n20 7\\n18 5\\n25 7\\n16 1\\n8 2\\n3 0\\n7 7\\n18 1\\n9 5\\n45 5\\n6 1\\n0 0\\n2 5\\n23 2\\n10 7\\n10 17\\n2 7', 'output': '48\\n'}, {'type': 'stdin_stdout', 'input': '22 8 26\\n11 4 15 3 11 7 11 1 1 4 2 21 1 14 16 16 5 13 6 20 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7', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '22 7 26\\n11 14 15 3 11 7 2 7 1 4 2 19 4 14 16 16 3 13 17 12 7 11 2 20 12 4\\n6 10\\n1 5\\n13 1\\n16 5\\n4 1\\n20 7\\n18 4\\n3 7\\n9 2\\n12 2\\n21 1\\n21 7\\n18 1\\n14 5\\n24 5\\n6 1\\n1 1\\n2 5\\n21 2\\n7 6\\n10 9\\n15 7', 'output': '53\\n'}, {'type': 'stdin_stdout', 'input': '22 7 26\\n11 25 28 3 11 7 16 7 1 4 2 19 4 14 16 16 3 13 17 12 11 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 5\\n2 1\\n20 7\\n18 4\\n26 7\\n9 1\\n12 2\\n21 1\\n21 7\\n18 1\\n14 5\\n24 5\\n6 1\\n1 1\\n2 5\\n21 2\\n7 8\\n10 9\\n15 7', 'output': '55\\n'}, {'type': 'stdin_stdout', 'input': '22 7 26\\n11 4 15 3 11 7 16 7 1 4 2 19 4 14 16 16 5 13 33 20 11 18 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 5\\n4 1\\n20 7\\n18 4\\n26 7\\n9 1\\n12 2\\n5 1\\n21 7\\n18 1\\n14 5\\n24 8\\n6 1\\n1 1\\n2 5\\n23 2\\n7 5\\n10 9\\n15 7', 'output': '55\\n'}, {'type': 'stdin_stdout', 'input': '22 7 26\\n11 14 15 3 11 7 16 7 1 4 2 19 4 14 16 16 5 21 17 12 11 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n5 5\\n4 1\\n20 7\\n18 5\\n26 7\\n9 1\\n12 2\\n5 1\\n7 7\\n18 1\\n14 5\\n24 5\\n6 1\\n2 1\\n2 5\\n23 2\\n7 5\\n10 9\\n15 7', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '22 7 26\\n11 14 15 3 10 7 16 17 1 5 2 19 4 14 16 2 3 9 17 12 7 11 2 20 12 22\\n6 10\\n1 3\\n13 1\\n16 5\\n4 1\\n20 7\\n18 4\\n26 6\\n9 1\\n12 4\\n21 1\\n21 7\\n18 1\\n14 5\\n24 5\\n6 1\\n1 1\\n2 5\\n21 0\\n7 6\\n10 9\\n15 7', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '22 7 26\\n11 14 15 3 11 7 2 7 1 4 2 19 4 14 16 16 3 13 17 12 7 11 2 20 12 4\\n6 10\\n1 5\\n13 1\\n16 5\\n4 1\\n20 7\\n18 4\\n3 7\\n9 2\\n12 2\\n21 1\\n21 7\\n18 1\\n19 5\\n24 5\\n6 1\\n1 1\\n2 5\\n21 2\\n7 6\\n10 9\\n15 7', 'output': '53\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_78329","program":"```python\n# -*- coding: utf-8 -*-\ndef inpl(): return list(map(int, input().split()))\nN, M, C = inpl()\nL = {i+1:v for i, v in enumerate(inpl())}\n\nballs = []\nfor _ in range(N):\n c, w = inpl()\n balls.append([w, c])\n\nballs = sorted(balls, reverse=True)\n\ni = 0\ncount = 0\nans = 0\nfor i in range(N):\n w, c = balls[i]\n if count == M:\n break\n if L[c] == 0:\n continue\n else:\n count += 1\n ans += w\n L[c] -= 1\n\nprint(ans)\n\n```","inputs":"22 7 26\n11 14 15 3 11 7 16 17 1 4 2 19 4 14 16 16 3 13 17 12 7 11 2 20 12 22\n6 10\n1 3\n13 1\n16 5\n4 1\n20 7\n18 4\n26 6\n9 1\n12 2\n21 1\n21 7\n18 1\n14 5\n24 5\n6 1\n3 1\n2 5\n21 2\n7 6\n10 9\n15 7","output":"52","actual_output":"52\n","execution_success":true,"sample_index":12483},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02266 Areas on the Cross-Section Diagram","prompt":"Solve the following coding problem using the programming language python:\n\nAreas on the Cross-Section Diagram\n\nYour task is to simulate a flood damage.\n\nFor a given cross-section diagram, reports areas of flooded sections.\n\n\n\n\n\nAssume that rain is falling endlessly in the region and the water overflowing from the region is falling in the sea at the both sides. For example, for the above cross-section diagram, the rain will create floods which have areas of 4, 2, 1, 19 and 9 respectively.\n\noutput\n\nReport the areas of floods in the following format:\n\n$A$\n$k$ $L_1$ $L_2$ ... $L_k$\n\nIn the first line, print the total area $A$ of created floods.\n\nIn the second line, print the number of floods $k$ and areas $L_i (i = 1, 2, ..., k)$ for each flood from the left side of the cross-section diagram. Print a space character before $L_i$.\n\nConstraints\n\n* $1 \\leq$ length of the string $\\leq 20,000$\n\nInput\n\nA string, which represents slopes and flatlands by '/', '\\' and '_' respectively, is given in a line. For example, the region of the above example is given by a string \"\\\\\\///\\\\_/\\/\\\\\\\\\\\\\\/_/\\\\\\///__\\\\\\\\\\\\_\\\\\\/_\\/_/\\\".\n\nExamples\n\nInput\n\n\\\\//\n\n\nOutput\n\n4\n1 4\n\n\nInput\n\n\\\\///\\_/\\/\\\\\\\\/_/\\\\///__\\\\\\_\\\\/_\\/_/\\\n\n\nOutput\n\n35\n5 4 2 1 19 9\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef cross_section_diagram():\n\tdown = []\n\tedge = []\n\tpool = []\n\n\tfor i, c in enumerate(input()):\n\t\tif c == '\\\\':\n\t\t\tdown.append(i)\n\t\telif c == '/' and down:\n\t\t\tleft = down.pop()\n\t\t\tarea = i - left\n\n\t\t\twhile edge:\n\t\t\t\tif edge[-1] < left:\n\t\t\t\t\tbreak\n\t\t\t\tedge.pop()\n\t\t\t\tarea += pool.pop()\n\n\t\t\tedge.append(left)\n\t\t\tpool.append(area)\n\n\tprint(sum(pool))\n\tprint(len(pool), *pool)\n\nif __name__ == '__main__':\n\tcross_section_diagram()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '\\\\\\\\///\\\\_/\\\\/\\\\\\\\\\\\\\\\/_/\\\\\\\\///__\\\\\\\\\\\\_\\\\\\\\/_\\\\/_/\\\\', 'output': '35\\n5 4 2 1 19 9'}, {'type': 'stdin_stdout', 'input': '\\\\\\\\//', 'output': '4\\n1 4'}, {'type': 'stdin_stdout', 'input': '\\\\/_/\\\\_/\\\\\\\\_\\\\\\\\\\\\__///\\\\\\\\/_/\\\\\\\\\\\\\\\\/\\\\/_\\\\///\\\\\\\\', 'output': '44\\n5 1 2 15 5 21\\n'}, {'type': 'stdin_stdout', 'input': ']\\\\//', 'output': '1\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\/_/\\\\_/\\\\\\\\_/\\\\\\\\__///\\\\\\\\/_/\\\\\\\\\\\\\\\\/\\\\/_\\\\/\\\\/\\\\\\\\', 'output': '32\\n8 1 2 20 5 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\/_/\\\\_/\\\\\\\\_/\\\\\\\\__///\\\\\\\\/_/\\\\[\\\\\\\\0\\\\/_\\\\/\\\\/\\\\\\\\', 'output': '31\\n7 1 2 20 5 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '-/\\\\]', 'output': '0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '\\\\/_/\\\\_/\\\\\\\\_/\\\\\\\\__///\\\\\\\\/_0\\\\[\\\\\\\\0\\\\/_\\\\/\\\\/\\\\\\\\', 'output': '27\\n7 1 2 20 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\/_/\\\\_/\\\\\\\\_/\\\\\\\\__///\\\\\\\\/_0/[\\\\\\\\0\\\\/_\\\\/\\\\\\\\\\\\\\\\', 'output': '31\\n6 1 2 20 6 1 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\/_/\\\\_/\\\\\\\\_0\\\\\\\\__///\\\\\\\\/_0/[\\\\\\\\0\\\\/_\\\\/\\\\\\\\\\\\\\\\', 'output': '28\\n6 1 2 17 6 1 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\/__\\\\_/\\\\\\\\/0\\\\\\\\__///\\\\\\\\/_0/[\\\\\\\\0\\\\/_\\\\/\\\\\\\\\\\\\\\\', 'output': '30\\n6 1 2 19 6 1 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\\\\\\\\\\\\\/\\\\_/\\\\0\\\\\\\\[/0`/\\\\\\\\///__\\\\\\\\0/\\\\\\\\/_\\\\__/\\\\', 'output': '34\\n6 1 2 25 2 1 3\\n'}, {'type': 'stdin_stdout', 'input': ']\\\\-/', 'output': '2\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '\\\\0__\\\\_/\\\\\\\\/0\\\\\\\\__///\\\\\\\\/`0/[\\\\\\\\0\\\\/_\\\\/\\\\\\\\\\\\\\\\', 'output': '29\\n5 2 19 6 1 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\0__\\\\_/[\\\\/0\\\\\\\\__///\\\\\\\\/`0/[\\\\\\\\0\\\\/_\\\\/\\\\\\\\\\\\\\\\', 'output': '36\\n4 28 6 1 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\0__\\\\_/\\\\\\\\\\\\0\\\\\\\\__///\\\\\\\\/`0/Z\\\\\\\\0\\\\/_//\\\\\\\\\\\\\\\\', 'output': '37\\n4 2 16 6 13\\n'}, {'type': 'stdin_stdout', 'input': '\\\\0__\\\\_/\\\\\\\\\\\\0\\\\\\\\__///\\\\\\\\/`\\\\/Z0\\\\0\\\\/_//\\\\\\\\\\\\\\\\', 'output': '40\\n3 2 16 22\\n'}, {'type': 'stdin_stdout', 'input': '\\\\0__\\\\_/\\\\\\\\\\\\0\\\\\\\\__///\\\\\\\\/`\\\\/Z0\\\\0\\\\/_./\\\\\\\\\\\\\\\\', 'output': '27\\n5 2 16 1 1 7\\n'}, {'type': 'stdin_stdout', 'input': '\\\\\\\\\\\\\\\\/._/\\\\0\\\\0Z/\\\\`/\\\\\\\\///__\\\\\\\\0\\\\\\\\\\\\/_\\\\__0\\\\', 'output': '29\\n3 6 22 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\\\\\\\\\\\\\.._/\\\\0\\\\0Z/\\\\`/\\\\\\\\///__\\\\\\\\0\\\\\\\\\\\\/_\\\\__0\\\\', 'output': '27\\n3 4 22 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\\\\\\\\\\\\\.._0\\\\0\\\\0Z/\\\\`/\\\\\\\\///__\\\\\\\\0\\\\\\\\\\\\/_\\\\_`0\\\\', 'output': '23\\n2 22 1\\n'}, {'type': 'stdin_stdout', 'input': '0\\\\\\\\\\\\.._0\\\\0\\\\0\\\\/\\\\`/\\\\\\\\///__\\\\Z\\\\\\\\\\\\\\\\/_\\\\_`0\\\\', 'output': '19\\n2 18 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\0`_\\\\_/\\\\\\\\\\\\\\\\Z\\\\__///\\\\\\\\/`\\\\/\\\\0\\\\0\\\\0_..\\\\\\\\\\\\0', 'output': '21\\n4 2 17 1 1\\n'}, {'type': 'stdin_stdout', 'input': '0\\\\\\\\\\\\.._0\\\\0\\\\0\\\\/\\\\`/\\\\\\\\///_\\\\\\\\Z\\\\\\\\\\\\_/_\\\\_`0\\\\', 'output': '20\\n2 18 2\\n'}, {'type': 'stdin_stdout', 'input': '0\\\\\\\\\\\\.._0\\\\0]0\\\\/\\\\`/\\\\\\\\///_\\\\\\\\Z\\\\\\\\\\\\_/_\\\\_`0\\\\', 'output': '22\\n2 20 2\\n'}, {'type': 'stdin_stdout', 'input': '0\\\\\\\\\\\\..\\\\0\\\\0]0_/\\\\`/\\\\\\\\///_\\\\\\\\Z\\\\\\\\\\\\_/_`_\\\\0\\\\', 'output': '28\\n2 26 2\\n'}, {'type': 'stdin_stdout', 'input': '0\\\\\\\\\\\\..\\\\0\\\\0]0_/\\\\`/\\\\\\\\/_//\\\\\\\\Z\\\\\\\\\\\\_/_`_\\\\0\\\\', 'output': '30\\n2 28 2\\n'}, {'type': 'stdin_stdout', 'input': '0\\\\\\\\\\\\..\\\\0\\\\/]0_/\\\\`/\\\\\\\\/_//\\\\\\\\Z\\\\\\\\\\\\_/_`_\\\\0\\\\', 'output': '36\\n2 34 2\\n'}, {'type': 'stdin_stdout', 'input': 'Z0\\\\_`_/0\\\\\\\\\\\\\\\\\\\\\\\\//_/\\\\\\\\/`\\\\/__]/\\\\0\\\\..\\\\\\\\]0', 'output': '25\\n3 4 10 11\\n'}, {'type': 'stdin_stdout', 'input': 'Z0\\\\_`_/0\\\\\\\\\\\\\\\\\\\\\\\\//_/\\\\\\\\/`[/__]/\\\\0\\\\..\\\\\\\\]0', 'output': '37\\n2 4 33\\n'}, {'type': 'stdin_stdout', 'input': '0]\\\\\\\\..\\\\0\\\\/]__/[`/\\\\\\\\/_//\\\\\\\\\\\\\\\\\\\\\\\\0/_`_\\\\0Z', 'output': '48\\n2 46 2\\n'}, {'type': 'stdin_stdout', 'input': 'Z0\\\\_`_/0\\\\\\\\\\\\\\\\\\\\\\\\//_/\\\\\\\\/`[/__].\\\\0\\\\..\\\\\\\\]0', 'output': '20\\n3 4 10 6\\n'}, {'type': 'stdin_stdout', 'input': '0]\\\\\\\\..\\\\0\\\\.]\\\\_/[`/\\\\\\\\/_//\\\\\\\\\\\\_\\\\\\\\0/_`_\\\\0Z', 'output': '33\\n2 31 2\\n'}, {'type': 'stdin_stdout', 'input': '0]\\\\\\\\..\\\\0\\\\.]\\\\_/\\\\`/\\\\\\\\/_//\\\\\\\\\\\\_\\\\\\\\0/_`_\\\\0Z', 'output': '25\\n2 23 2\\n'}, {'type': 'stdin_stdout', 'input': '0]\\\\\\\\..\\\\0_.]\\\\\\\\/\\\\`/\\\\\\\\/_//\\\\\\\\\\\\_\\\\\\\\0/_`_\\\\0Z', 'output': '21\\n2 19 2\\n'}, {'type': 'stdin_stdout', 'input': 'Z0\\\\_`_/0\\\\\\\\_\\\\\\\\\\\\//_/\\\\\\\\/`\\\\/\\\\\\\\]._0\\\\..\\\\\\\\]0', 'output': '16\\n4 4 10 1 1\\n'}, {'type': 'stdin_stdout', 'input': 'Z0\\\\_`_/0\\\\\\\\_\\\\\\\\\\\\//_/\\\\\\\\/`\\\\/\\\\\\\\]._0\\\\..\\\\\\\\]/', 'output': '18\\n5 4 10 1 1 2\\n'}, {'type': 'stdin_stdout', 'input': 'Z0\\\\_`_/0\\\\\\\\_\\\\\\\\\\\\/0_/\\\\\\\\/`\\\\/\\\\\\\\]._0\\\\..\\\\\\\\]/', 'output': '14\\n5 4 6 1 1 2\\n'}, {'type': 'stdin_stdout', 'input': 'Z0\\\\_`_.0\\\\\\\\_\\\\\\\\\\\\/0_/\\\\\\\\/`\\\\/\\\\\\\\]._0\\\\..\\\\\\\\]/', 'output': '10\\n4 6 1 1 2\\n'}, {'type': 'stdin_stdout', 'input': '/]\\\\\\\\..\\\\0_.]\\\\\\\\/\\\\`/\\\\\\\\/_0/\\\\\\\\\\\\__\\\\0._`\\\\\\\\0Z', 'output': '9\\n3 1 2 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'input': 'Z\\\\\\\\]/_-0\\\\__`\\\\[\\\\0a/[\\\\/\\\\[00\\\\].]1/.-a\\\\]]', 'output': '11\\n4 2 3 1 5\\n'}, {'type': 'stdin_stdout', 'input': 'Z\\\\\\\\]/_-0\\\\__`\\\\[\\\\0a/[\\\\/\\\\[]0\\\\0.]1//-a\\\\]\\\\', 'output': '21\\n4 2 3 1 15\\n'}, {'type': 'stdin_stdout', 'input': '\\\\]\\\\a-//1].0\\\\0][\\\\/\\\\[/a0\\\\[\\\\`_`\\\\0-_/]\\\\\\\\Z', 'output': '16\\n4 9 1 2 4\\n'}, {'type': 'stdin_stdout', 'input': '\\\\]\\\\a-//1].0\\\\/][\\\\/\\\\[/a0\\\\[\\\\`_`\\\\0-_/]\\\\\\\\Z', 'output': '17\\n5 9 1 1 2 4\\n'}, {'type': 'stdin_stdout', 'input': '\\\\]\\\\a-/01].0\\\\/][\\\\/\\\\[/a0\\\\[\\\\`_`\\\\0-_/]\\\\\\\\Z', 'output': '11\\n5 3 1 1 2 4\\n'}, {'type': 'stdin_stdout', 'input': 'Z\\\\\\\\]/_-0\\\\`_`\\\\[\\\\0a/[\\\\/\\\\[]/\\\\0.]10/-a\\\\]\\\\', 'output': '15\\n5 2 3 1 3 6\\n'}, {'type': 'stdin_stdout', 'input': 'Z\\\\\\\\]/_-0[`_`\\\\\\\\\\\\0a/[\\\\0\\\\[]/\\\\0.]10/.a\\\\]\\\\', 'output': '14\\n4 2 3 3 6\\n'}, {'type': 'stdin_stdout', 'input': 'Z\\\\\\\\\\\\/_-0[`_`\\\\\\\\\\\\0a/[\\\\0\\\\[]/\\\\0.]10/.a\\\\]\\\\', 'output': '13\\n4 1 3 3 6\\n'}, {'type': 'stdin_stdout', 'input': 'Z\\\\\\\\\\\\/_-0[`_`\\\\\\\\\\\\0a/[\\\\0\\\\[]/\\\\0/]10/.a\\\\]\\\\', 'output': '21\\n3 1 3 17\\n'}, {'type': 'stdin_stdout', 'input': '\\\\]\\\\`./01]/0\\\\/][\\\\0\\\\[/a0\\\\\\\\\\\\a_`[0-_/\\\\\\\\\\\\Z', 'output': '23\\n4 12 1 2 8\\n'}, {'type': 'stdin_stdout', 'input': 'Z\\\\\\\\\\\\/_-0[`_a\\\\\\\\\\\\0a/[\\\\0[[]/\\\\0/]10/.`\\\\]\\\\', 'output': '29\\n2 1 28\\n'}, {'type': 'stdin_stdout', 'input': '\\\\]\\\\`.//1]/0\\\\/][[0\\\\[/a0\\\\\\\\\\\\a_`[0-_/\\\\\\\\\\\\Z', 'output': '20\\n4 9 1 2 8\\n'}, {'type': 'stdin_stdout', 'input': '\\\\]\\\\`.//1]/0\\\\/][[0\\\\[/a0\\\\\\\\\\\\a_`[\\\\-_/\\\\\\\\0Z', 'output': '15\\n4 9 1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '\\\\]\\\\`.//1]/0\\\\/][[0\\\\[/a0\\\\/\\\\a_`[\\\\-_\\\\]\\\\0Z', 'output': '13\\n4 9 1 2 1\\n'}, {'type': 'stdin_stdout', 'input': '[^\\\\`.//1]/0\\\\/]\\\\[0\\\\[/a0\\\\/\\\\a_`[\\\\-_\\\\][0Z', 'output': '7\\n4 3 1 2 1\\n'}, {'type': 'stdin_stdout', 'input': 'Z^\\\\`///1]/0\\\\/]\\\\[0\\\\[/a1\\\\/\\\\a_\\\\[\\\\-_`]]0Z', 'output': '6\\n4 2 1 2 1\\n'}, {'type': 'stdin_stdout', 'input': 'Z0]]`_-\\\\[\\\\_a\\\\/\\\\1a/[\\\\0[\\\\]/\\\\0/]1///`\\\\^Z', 'output': '66\\n1 66\\n'}, {'type': 'stdin_stdout', 'input': 'Z^\\\\`///1]/0\\\\/]\\\\[0[[/a1\\\\/\\\\a_\\\\[\\\\-_`]]0Z', 'output': '9\\n4 2 1 5 1\\n'}, {'type': 'stdin_stdout', 'input': 'Z0]]`_-\\\\[\\\\_a]/\\\\1a/[[0[\\\\]/\\\\0/]1///`\\\\^Z', 'output': '34\\n1 34\\n'}, {'type': 'stdin_stdout', 'input': 'Z0]]`_-\\\\[[_a]/\\\\1a/[[0Z\\\\]/\\\\0/]1///`\\\\^Y', 'output': '13\\n4 6 3 2 2\\n'}, {'type': 'stdin_stdout', 'input': 'Y^\\\\`///1]/0\\\\/]]Z0[[/a1\\\\/]a_[[\\\\-_`]]0Z', 'output': '4\\n3 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\^\\\\`///1]/0Y/]0Z0[[/a1\\\\/]a_[\\\\\\\\-_`]]Z]', 'output': '8\\n2 7 1\\n'}, {'type': 'stdin_stdout', 'input': '\\\\^\\\\`.//1]/0Y/]0Z0[[/a1\\\\/]a_[\\\\\\\\-_`]]Z]', 'output': '10\\n2 9 1\\n'}, {'type': 'stdin_stdout', 'input': ']Z]]`_-\\\\\\\\[_a]/\\\\1a/[[0Z0]/Y1/]1//.`\\\\^\\\\', 'output': '25\\n1 25\\n'}, {'type': 'stdin_stdout', 'input': '\\\\Z]]`_-\\\\\\\\[_a]/\\\\1a/[[0Z0]/Y1/]1//.`\\\\^]', 'output': '52\\n1 52\\n'}, {'type': 'stdin_stdout', 'input': '\\\\Z\\\\]`_-\\\\\\\\[_a]/\\\\1a/[[0Z0]/Y1/]1//.`\\\\^]', 'output': '80\\n1 80\\n'}, {'type': 'stdin_stdout', 'input': '\\\\Z\\\\]`_-\\\\\\\\[_a]/[1a/[\\\\0Z0]/Y0/]1//.`\\\\^]', 'output': '75\\n1 75\\n'}, {'type': 'stdin_stdout', 'input': ']^\\\\`///1]/0Y/]0Z0\\\\[/a1[/]a_[\\\\\\\\-_`]\\\\Z\\\\', 'output': '4\\n2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '[Z0]`_-\\\\\\\\[/a]_[1a/[]0Z0]/Y\\\\/]1///`\\\\^]', 'output': '13\\n2 12 1\\n'}, {'type': 'stdin_stdout', 'input': ']^\\\\`///10/\\\\]/]0ZY\\\\[/a1[_]b/[\\\\\\\\-_`^0Z[', 'output': '6\\n3 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '[Z0^`_-\\\\][/b]_[1a/[\\\\YZ0]/]\\\\/01///`\\\\^]', 'output': '9\\n3 3 5 1\\n'}, {'type': 'stdin_stdout', 'input': '[Z0^`1-\\\\^[.b]_[`a/[\\\\YZ0]/]\\\\/01///`[^]', 'output': '16\\n3 10 5 1\\n'}, {'type': 'stdin_stdout', 'input': '[Z0^`1-\\\\^[.b]_[`a/[^YZ0]/]\\\\/0_///1[\\\\]', 'output': '11\\n2 10 1\\n'}, {'type': 'stdin_stdout', 'input': ']\\\\[1///_0/\\\\]/]0ZY^[/a`[_]b.[^\\\\-1`^0Z[', 'output': '5\\n2 3 2\\n'}, {'type': 'stdin_stdout', 'input': ']\\\\[1///\\\\0]_]/]0ZY^[/a`[[/b.Z^\\\\-1`^0Z_', 'output': '8\\n2 3 5\\n'}, {'type': 'stdin_stdout', 'input': ']\\\\Z1//0]0]_]/Y/Z]][/a`[[/b.Z^\\\\-2`^0[_', 'output': '3\\n1 3\\n'}, {'type': 'stdin_stdout', 'input': '_[1^`2-\\\\^Z.b/[[`a/[]]Z0Y/]_]0]0//1Z\\\\]', 'output': '5\\n1 5\\n'}, {'type': 'stdin_stdout', 'input': '^\\\\Z0_/0]/]`]0X0Z]^[/b./[/b`Z^\\\\-2`^1Z[', 'output': '4\\n1 4\\n'}, {'type': 'stdin_stdout', 'input': '^\\\\Z0_20]/]`]0X0Z]^[/b./[/b`Z^\\\\./`^1Z[', 'output': '9\\n2 7 2\\n'}, {'type': 'stdin_stdout', 'input': '[Z1^`/.\\\\^Y`b0Y/.b/[]^Z0Z0]`^/]020_[\\\\^', 'output': '7\\n1 7\\n'}, {'type': 'stdin_stdout', 'input': '[Z1^`/.\\\\^Y`b0Y/.b/[\\\\_Z0Z0]`^/]020^[\\\\^', 'output': '16\\n2 7 9\\n'}, {'type': 'stdin_stdout', 'input': '[Z1^`/.\\\\^Y`b0Y/.b/[\\\\_Z0Z/]`^/]020^[\\\\^', 'output': '12\\n2 7 5\\n'}, {'type': 'stdin_stdout', 'input': '^\\\\[^030]/^`]/Z0Z_\\\\[/b./X1b`Y^\\\\./`^1Z[', 'output': '11\\n3 7 2 2\\n'}, {'type': 'stdin_stdout', 'input': '^\\\\[^030]/^`]/Z0Z_\\\\[0b./X1b`Y^\\\\./`^1Z[', 'output': '14\\n3 7 5 2\\n'}, {'type': 'stdin_stdout', 'input': '^\\\\[^030]/^`]/Z0Z_\\\\[0b./X1b`Y^\\\\//`^1Z[', 'output': '13\\n3 7 5 1\\n'}, {'type': 'stdin_stdout', 'input': '^\\\\[^020]/^`0/Z0Z_\\\\[]b..X1b`Y^\\\\//`^1Z[', 'output': '22\\n2 7 15\\n'}, {'type': 'stdin_stdout', 'input': '[Z1^`//\\\\]Y`c1^..b][\\\\__0Y/0`^/]020Z[\\\\X', 'output': '26\\n1 26\\n'}, {'type': 'stdin_stdout', 'input': '[[1^`//\\\\`Y`c1^..b][]_00Y/0]^_^020Z[\\\\X', 'output': '17\\n1 17\\n'}, {'type': 'stdin_stdout', 'input': '[[1^`//\\\\`Y`c1^./b][]_00Y/0]^_^020Z[\\\\X', 'output': '8\\n1 8\\n'}, {'type': 'stdin_stdout', 'input': 'X\\\\[Z020__^]0/Y00_][]b/.^1c`Y`\\\\//`^1[[', 'output': '12\\n2 11 1\\n'}, {'type': 'stdin_stdout', 'input': 'X\\\\[Z0/0__^]0/YY0_][]b/.^1c`2`\\\\0/`^0[[', 'output': '6\\n2 4 2\\n'}, {'type': 'stdin_stdout', 'input': 'X\\\\[Z0/0__^]0/YY0_][2b^.^1c`]`\\\\0.`/0[[', 'output': '8\\n2 4 4\\n'}, {'type': 'stdin_stdout', 'input': '[[0/a.0\\\\`]`c1^.^b2[\\\\_0YY/0]^__0/0Z[\\\\X', 'output': '29\\n1 29\\n'}, {'type': 'stdin_stdout', 'input': 'X][Z0/0__^.0/YX0_\\\\[2b^\\\\^1c`]`\\\\/.a/0[[', 'output': '12\\n1 12\\n'}, {'type': 'stdin_stdout', 'input': '[[0/a./\\\\`]`c1_\\\\^b2[\\\\_0XY/0.^__0/0Z[]X', 'output': '22\\n1 22\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_78333","program":"```python\ndef cross_section_diagram():\n\tdown = []\n\tedge = []\n\tpool = []\n\n\tfor i, c in enumerate(input()):\n\t\tif c == '\\\\':\n\t\t\tdown.append(i)\n\t\telif c == '/' and down:\n\t\t\tleft = down.pop()\n\t\t\tarea = i - left\n\n\t\t\twhile edge:\n\t\t\t\tif edge[-1] < left:\n\t\t\t\t\tbreak\n\t\t\t\tedge.pop()\n\t\t\t\tarea += pool.pop()\n\n\t\t\tedge.append(left)\n\t\t\tpool.append(area)\n\n\tprint(sum(pool))\n\tprint(len(pool), *pool)\n\nif __name__ == '__main__':\n\tcross_section_diagram()\n```","inputs":"\\\\///\\_/\\/\\\\\\\\/_/\\\\///__\\\\\\_\\\\/_\\/_/\\","output":"35\n5 4 2 1 19 9","actual_output":"35\n5 4 2 1 19 9\n","execution_success":true,"sample_index":12484},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02414 Matrix Multiplication","prompt":"Solve the following coding problem using the programming language python:\n\nWrite a program which reads a $n \\times m$ matrix $A$ and a $m \\times l$ matrix $B$, and prints their product, a $n \\times l$ matrix $C$. An element of matrix $C$ is obtained by the following formula:\n\n\\\\[ c_{ij} = \\sum_{k=1}^m a_{ik}b_{kj} \\\\]\n\nwhere $a_{ij}$, $b_{ij}$ and $c_{ij}$ are elements of $A$, $B$ and $C$ respectively.\n\nNote\n\n\u89e3\u8aac\n\nConstraints\n\n* $1 \\leq n, m, l \\leq 100$\n* $0 \\leq a_{ij}, b_{ij} \\leq 10000$\n\nInput\n\nIn the first line, three integers $n$, $m$ and $l$ are given separated by space characters\n\nIn the following lines, the $n \\times m$ matrix $A$ and the $m \\times l$ matrix $B$ are given.\n\nOutput\n\nPrint elements of the $n \\times l$ matrix $C$ ($c_{ij}$). Print a single space character between adjacent elements.\n\nExample\n\nInput\n\n3 2 3\n1 2\n0 3\n4 5\n1 2 1\n0 3 2\n\n\nOutput\n\n1 8 5\n0 9 6\n4 23 14\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,m,l = map(int,input().split())\nA = [list(map(int,input().split())) for i in range(n)]\nB = [list(map(int,input().split())) for j in range(m)]\n\nC = [[0 for k in range(l)]for i in range(n)]\n\nfor i in range(n) :\n for k in range(l) :\n for j in range(m) :\n C[i][k] = C[i][k] + A[i][j] * B[j][k]\nfor i in range(n):\n print(*C[i])\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n0 3\\n4 5\\n1 2 1\\n0 3 2', 'output': '1 8 5\\n0 9 6\\n4 23 14'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n0 3\\n4 5\\n1 2 1\\n1 3 2', 'output': '3 8 5\\n3 9 6\\n9 23 14\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n1 3\\n4 5\\n1 2 1\\n1 3 2', 'output': '3 8 5\\n4 11 7\\n9 23 14\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n2 3\\n4 5\\n1 2 1\\n1 3 2', 'output': '3 8 5\\n5 13 8\\n9 23 14\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n2 3\\n4 5\\n1 2 2\\n1 3 2', 'output': '3 8 6\\n5 13 10\\n9 23 18\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n3 3\\n4 5\\n1 2 2\\n1 3 2', 'output': '3 8 6\\n6 15 12\\n9 23 18\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n3 3\\n4 5\\n1 2 2\\n1 3 2', 'output': '2 5 4\\n6 15 12\\n9 23 18\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n3 3\\n4 9\\n1 2 2\\n1 3 2', 'output': '2 5 4\\n6 15 12\\n13 35 26\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n3 2\\n4 9\\n1 2 2\\n1 3 2', 'output': '2 5 4\\n5 12 10\\n13 35 26\\n'}, {'type': 'stdin_stdout', 'input': '3 0 3\\n1 1\\n3 2\\n4 9\\n1 2 2\\n1 3 2', 'output': '0 0 0\\n0 0 0\\n0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 0 5\\n1 1\\n3 2\\n4 9\\n1 2 2\\n1 3 2', 'output': '0 0 0 0 0\\n0 0 0 0 0\\n0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 0 5\\n1 1\\n2 2\\n4 9\\n1 2 2\\n1 5 2', 'output': '0 0 0 0 0\\n0 0 0 0 0\\n0 0 0 0 0\\n0 0 0 0 0\\n0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '4 0 5\\n2 1\\n2 2\\n4 15\\n0 0 3\\n2 3 2', 'output': '0 0 0 0 0\\n0 0 0 0 0\\n0 0 0 0 0\\n0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 0 5\\n2 1\\n2 4\\n4 15\\n-2 0 3\\n1 3 2', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '2 0 5\\n2 1\\n0 5\\n4 27\\n-6 -1 3\\n1 3 4', 'output': '0 0 0 0 0\\n0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n0 3\\n4 5\\n0 2 1\\n0 3 2', 'output': '0 8 5\\n0 9 6\\n0 23 14\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n0 3\\n0 5\\n1 2 1\\n1 3 2', 'output': '3 8 5\\n3 9 6\\n5 15 10\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n4 5\\n1 2 1\\n1 3 2', 'output': '2 5 3\\n5 13 8\\n9 23 14\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n2 3\\n4 5\\n0 2 2\\n1 3 2', 'output': '2 8 6\\n3 13 10\\n5 23 18\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n2 2\\n3 3\\n4 5\\n1 2 2\\n1 3 2', 'output': '4 10 8\\n6 15 12\\n9 23 18\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 1\\n3 3\\n4 5\\n1 2 2\\n1 3 2', 'output': '1 3 2\\n6 15 12\\n9 23 18\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n3 3\\n5 9\\n1 2 2\\n1 3 2', 'output': '2 5 4\\n6 15 12\\n14 37 28\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n2 1\\n3 2\\n4 9\\n1 2 2\\n1 3 2', 'output': '3 7 6\\n5 12 10\\n13 35 26\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n0 3\\n4 5\\n-1 2 1\\n0 3 2', 'output': '-1 8 5\\n0 9 6\\n-4 23 14\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n0 3\\n0 2\\n1 2 1\\n1 3 2', 'output': '3 8 5\\n3 9 6\\n2 6 4\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n4 1\\n1 2 1\\n1 3 2', 'output': '2 5 3\\n5 13 8\\n5 11 6\\n'}, {'type': 'stdin_stdout', 'input': '3 2 1\\n1 2\\n2 3\\n4 5\\n0 2 2\\n1 3 2', 'output': '2\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n2 2\\n3 3\\n4 10\\n1 2 2\\n1 3 2', 'output': '4 10 8\\n6 15 12\\n14 38 28\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 1\\n3 3\\n4 5\\n1 2 2\\n1 3 4', 'output': '1 3 4\\n6 15 18\\n9 23 28\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n3 3\\n5 9\\n1 2 2\\n1 6 2', 'output': '2 8 4\\n6 24 12\\n14 64 28\\n'}, {'type': 'stdin_stdout', 'input': '3 0 6\\n1 1\\n2 2\\n4 15\\n0 2 0\\n1 5 4', 'output': '0 0 0 0 0 0\\n0 0 0 0 0 0\\n0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 0 1\\n2 1\\n2 4\\n4 15\\n-3 -1 6\\n1 3 2', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n0 3\\n4 5\\n-1 0 1\\n0 3 2', 'output': '-1 6 5\\n0 9 6\\n-4 15 14\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 2\\n0 3\\n0 2\\n1 2 1\\n1 3 2', 'output': '2 6 4\\n3 9 6\\n2 6 4\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n4 1\\n2 2 1\\n1 3 2', 'output': '3 5 3\\n7 13 8\\n9 11 6\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n2 2\\n3 3\\n4 10\\n1 2 2\\n1 4 2', 'output': '4 12 8\\n6 18 12\\n14 48 28\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 1\\n3 3\\n4 5\\n2 2 2\\n1 3 4', 'output': '1 3 4\\n9 15 18\\n13 23 28\\n'}, {'type': 'stdin_stdout', 'input': '3 0 7\\n4 1\\n2 2\\n4 12\\n0 0 3\\n2 3 2', 'output': '0 0 0 0 0 0 0\\n0 0 0 0 0 0 0\\n0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n0 3\\n4 5\\n-1 0 1\\n0 3 4', 'output': '-1 6 9\\n0 9 12\\n-4 15 24\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 2\\n0 3\\n0 2\\n1 2 1\\n2 3 2', 'output': '4 6 4\\n6 9 6\\n4 6 4\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n1 1\\n2 2 1\\n1 3 2', 'output': '3 5 3\\n7 13 8\\n3 5 3\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n2 2\\n6 3\\n4 10\\n1 2 2\\n1 4 2', 'output': '4 12 8\\n9 24 18\\n14 48 28\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 1\\n3 4\\n4 5\\n2 2 2\\n1 3 4', 'output': '1 3 4\\n10 18 22\\n13 23 28\\n'}, {'type': 'stdin_stdout', 'input': '2 0 8\\n1 1\\n2 4\\n4 15\\n-1 0 2\\n1 5 2', 'output': '0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '4 0 10\\n2 0\\n1 2\\n0 15\\n-1 0 3\\n2 3 2', 'output': '0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 0 9\\n2 1\\n-1 4\\n4 15\\n-12 -1 3\\n0 3 2', 'output': '0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 -2 2\\n2 1\\n0 5\\n4 27\\n-6 -1 3\\n1 3 4', 'output': '0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n0 3\\n4 5\\n-1 0 1\\n0 1 4', 'output': '-1 2 9\\n0 3 12\\n-4 5 24\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n1 1\\n2 3 1\\n1 3 2', 'output': '3 6 3\\n7 15 8\\n3 6 3\\n'}, {'type': 'stdin_stdout', 'input': '3 2 1\\n1 2\\n2 3\\n4 3\\n0 2 2\\n1 5 4', 'output': '2\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 1\\n3 4\\n5 5\\n2 2 2\\n1 3 4', 'output': '1 3 4\\n10 18 22\\n15 25 30\\n'}, {'type': 'stdin_stdout', 'input': '2 0 13\\n1 1\\n2 4\\n4 15\\n-1 0 2\\n1 5 2', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 0 4\\n2 1\\n0 2\\n0 12\\n-6 -1 6\\n1 3 2', 'output': '0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n0 3\\n4 5\\n-1 0 1\\n0 2 4', 'output': '-1 4 9\\n0 6 12\\n-4 10 24\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n1 1\\n4 3 1\\n1 3 2', 'output': '5 6 3\\n11 15 8\\n5 6 3\\n'}, {'type': 'stdin_stdout', 'input': '4 0 13\\n1 1\\n2 4\\n4 15\\n-1 0 2\\n1 5 2', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 0 2\\n0 1\\n2 2\\n3 15\\n0 -1 2\\n0 5 2', 'output': '0 0\\n0 0\\n0 0\\n'}, {'type': 'stdin_stdout', 'input': '4 0 1\\n2 1\\n2 8\\n4 15\\n-3 1 4\\n2 3 2', 'output': '0\\n0\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '1 0 3\\n1 1\\n4 4\\n8 15\\n-2 0 3\\n1 1 0', 'output': '0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 4\\n0 3\\n4 5\\n-1 0 1\\n0 2 4', 'output': '-1 8 17\\n0 6 12\\n-4 10 24\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 1\\n0 3\\n0 2\\n1 4 0\\n2 3 2', 'output': '2 3 2\\n6 9 6\\n4 6 4\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n1 0\\n2 3 1\\n1 3 2', 'output': '3 6 3\\n7 15 8\\n2 3 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 2\\n2 3\\n4 3\\n0 0 2\\n1 5 4', 'output': '2 10\\n3 15\\n3 15\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 4\\n0 3\\n4 5\\n-1 0 1\\n0 2 0', 'output': '-1 8 1\\n0 6 0\\n-4 10 4\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 0\\n0 3\\n0 2\\n1 4 0\\n2 3 2', 'output': '0 0 0\\n6 9 6\\n4 6 4\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n2 0\\n2 3 1\\n1 3 2', 'output': '3 6 3\\n7 15 8\\n4 6 2\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 2\\n2 3\\n4 3\\n0 0 2\\n1 3 4', 'output': '2 6\\n3 9\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '3 1 3\\n0 2\\n6 3\\n4 10\\n2 2 2\\n1 4 2', 'output': '0 0 0\\n12 12 12\\n8 8 8\\n'}, {'type': 'stdin_stdout', 'input': '5 -1 2\\n1 1\\n1 1\\n4 15\\n1 0 0\\n1 5 4', 'output': '0 0\\n0 0\\n0 0\\n0 0\\n0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n-1 0\\n0 3\\n0 2\\n1 4 0\\n2 3 2', 'output': '-1 -4 0\\n6 9 6\\n4 6 4\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n2 0\\n2 2 1\\n1 3 2', 'output': '3 5 3\\n7 13 8\\n4 4 2\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 2\\n2 6\\n4 3\\n0 0 2\\n1 3 4', 'output': '2 6\\n6 18\\n3 9\\n'}, {'type': 'stdin_stdout', 'input': '2 -1 2\\n0 0\\n0 5\\n2 27\\n0 -1 3\\n1 2 1', 'output': '0 0\\n0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 0\\n0 3\\n0 2\\n1 4 0\\n2 2 2', 'output': '0 0 0\\n6 6 6\\n4 4 4\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n2 0\\n2 2 0\\n1 3 2', 'output': '3 5 2\\n7 13 6\\n4 4 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 2\\n2 6\\n4 3\\n0 0 2\\n1 5 4', 'output': '2 10\\n6 30\\n3 15\\n'}, {'type': 'stdin_stdout', 'input': '1 0 10\\n2 1\\n0 3\\n8 6\\n-3 -1 3\\n1 5 6', 'output': '0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 0\\n0 2\\n0 2\\n1 4 0\\n2 2 2', 'output': '0 0 0\\n4 4 4\\n4 4 4\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 1\\n2 3\\n2 0\\n2 4 0\\n1 3 2', 'output': '3 7 2\\n7 17 6\\n4 8 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 2\\n2 6\\n4 4\\n0 0 2\\n1 5 4', 'output': '2 10\\n6 30\\n4 20\\n'}, {'type': 'stdin_stdout', 'input': '1 0 7\\n2 1\\n0 2\\n0 9\\n-3 -1 6\\n1 3 2', 'output': '0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n0 1\\n0 2\\n0 2\\n1 4 0\\n2 2 2', 'output': '2 2 2\\n4 4 4\\n4 4 4\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n2 3\\n2 0\\n2 4 0\\n1 3 2', 'output': '4 10 4\\n7 17 6\\n4 8 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 2\\n2 11\\n4 4\\n0 0 2\\n1 5 4', 'output': '2 10\\n11 55\\n4 20\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n2 3\\n2 0\\n2 4 -1\\n1 3 2', 'output': '4 10 3\\n7 17 4\\n4 8 -2\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2\\n1 2\\n2 11\\n4 8\\n0 0 2\\n1 5 4', 'output': '2 10\\n11 55\\n8 40\\n'}, {'type': 'stdin_stdout', 'input': '2 -1 3\\n-1 1\\n0 3\\n4 1\\n1 1 2\\n3 5 1', 'output': '0 0 0\\n0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 0 6\\n1 1\\n-1 2\\n4 1\\n1 0 -1\\n1 12 5', 'output': '0 0 0 0 0 0\\n0 0 0 0 0 0\\n0 0 0 0 0 0\\n0 0 0 0 0 0\\n0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '4 -1 8\\n3 1\\n0 3\\n4 15\\n-3 -1 3\\n2 2 0', 'output': '0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n1 3\\n2 0\\n2 4 -1\\n1 3 2', 'output': '4 10 3\\n5 13 5\\n4 8 -2\\n'}, {'type': 'stdin_stdout', 'input': '4 0 6\\n1 1\\n-1 2\\n4 1\\n1 0 -1\\n1 12 5', 'output': '0 0 0 0 0 0\\n0 0 0 0 0 0\\n0 0 0 0 0 0\\n0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '4 1 1\\n2 0\\n0 3\\n4 2\\n-1 1 2\\n2 3 2', 'output': '4\\n0\\n8\\n-2\\n'}, {'type': 'stdin_stdout', 'input': '1 0 8\\n0 0\\n-2 8\\n7 6\\n-13 -1 5\\n1 3 2', 'output': '0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n1 3\\n2 -1\\n2 4 -1\\n1 3 2', 'output': '4 10 3\\n5 13 5\\n3 5 -4\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2\\n1 2\\n2 11\\n4 8\\n0 0 1\\n1 5 4', 'output': '10 27\\n'}, {'type': 'stdin_stdout', 'input': '4 0 12\\n1 1\\n-1 2\\n4 1\\n1 0 -1\\n1 12 5', 'output': '0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n1 3\\n2 -1\\n4 4 -1\\n1 3 2', 'output': '6 10 3\\n7 13 5\\n7 5 -4\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2\\n1 2\\n4 11\\n4 8\\n0 0 1\\n1 5 4', 'output': '12 27\\n'}, {'type': 'stdin_stdout', 'input': '3 2 3\\n1 2\\n1 3\\n2 -1\\n4 4 -2\\n1 3 2', 'output': '6 10 2\\n7 13 4\\n7 5 -6\\n'}, {'type': 'stdin_stdout', 'input': '1 -1 13\\n2 2\\n0 3\\n0 9\\n-3 0 6\\n2 3 2', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 1\\n1 2\\n1 3\\n2 -1\\n4 4 -2\\n1 3 2', 'output': '6\\n7\\n7\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_78337","program":"```python\nn,m,l = map(int,input().split())\nA = [list(map(int,input().split())) for i in range(n)]\nB = [list(map(int,input().split())) for j in range(m)]\n\nC = [[0 for k in range(l)]for i in range(n)]\n\nfor i in range(n) :\n for k in range(l) :\n for j in range(m) :\n C[i][k] = C[i][k] + A[i][j] * B[j][k]\nfor i in range(n):\n print(*C[i])\n\n```","inputs":"3 2 3\n1 2\n0 3\n4 5\n1 2 1\n0 3 2","output":"1 8 5\n0 9 6\n4 23 14","actual_output":"1 8 5\n0 9 6\n4 23 14\n","execution_success":true,"sample_index":12485},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1042_D. Petya and Array","prompt":"Solve the following coding problem using the programming language python:\n\nPetya has an array a consisting of n integers. He has learned partial sums recently, and now he can calculate the sum of elements on any segment of the array really fast. The segment is a non-empty sequence of elements standing one next to another in the array.\n\nNow he wonders what is the number of segments in his array with the sum less than t. Help Petya to calculate this number.\n\nMore formally, you are required to calculate the number of pairs l, r (l \u2264 r) such that a_l + a_{l+1} + ... + a_{r-1} + a_r < t.\n\nInput\n\nThe first line contains two integers n and t (1 \u2264 n \u2264 200 000, |t| \u2264 2\u22c510^{14}).\n\nThe second line contains a sequence of integers a_1, a_2, ..., a_n (|a_{i}| \u2264 10^{9}) \u2014 the description of Petya's array. Note that there might be negative, zero and positive elements.\n\nOutput\n\nPrint the number of segments in Petya's array with the sum of elements less than t.\n\nExamples\n\nInput\n\n5 4\n5 -1 3 4 -1\n\n\nOutput\n\n5\n\n\nInput\n\n3 0\n-1 2 -3\n\n\nOutput\n\n4\n\n\nInput\n\n4 -1\n-2 1 -2 3\n\n\nOutput\n\n3\n\nNote\n\nIn the first example the following segments have sum less than 4:\n\n * [2, 2], sum of elements is -1 \n * [2, 3], sum of elements is 2 \n * [3, 3], sum of elements is 3 \n * [4, 5], sum of elements is 3 \n * [5, 5], sum of elements is -1 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nmaxn = 2*10**5 + 5\nbit = [0]*(maxn)\n\ndef add(idx):\n idx += 1\n while idx < maxn:\n bit[idx] += 1\n idx += idx & -idx\n\ndef sm(idx):\n idx += 1\n tot = 0\n while idx > 0:\n tot += bit[idx]\n idx -= idx & -idx\n\n return tot\n\n\nn,t = map(int,input().split())\na = list(map(int,input().split()))\n\npsum = [0]*(n+1)\nfor i in range(n):\n psum[i+1] = psum[i] + a[i]\npsum.sort(reverse=True)\nupsum = [-10**18]\nfor i in range(n+1):\n if i == 0 or psum[i] != psum[i-1]:\n upsum.append(psum[i])\nupsum.sort(reverse = True)\n\ndef lower_bound(i):\n l = 0; r = len(upsum) - 1\n while l != r:\n m = (l+r)//2\n if upsum[m] <= i:\n r = m\n else:\n l = m + 1\n\n return l\n\nans = 0\ncurr = 0\nadd(lower_bound(0))\nfor i in a:\n curr += i\n ans += sm(lower_bound(curr-t)-1)\n add(lower_bound(curr))\n\n\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 4\\n5 -1 3 4 -1\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '3 0\\n-1 2 -3\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '4 -1\\n-2 1 -2 3\\n', 'output': '3'}, {'type': 'stdin_stdout', 'input': '1 -999999999\\n-999999999\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '10 -196228170\\n-181402541 328251238 624722764 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{'type': 'stdin_stdout', 'input': '5 4\\n5 -1 8 4 -1\\n', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78369","program":"```python\nmaxn = 2*10**5 + 5\nbit = [0]*(maxn)\n\ndef add(idx):\n idx += 1\n while idx < maxn:\n bit[idx] += 1\n idx += idx & -idx\n\ndef sm(idx):\n idx += 1\n tot = 0\n while idx > 0:\n tot += bit[idx]\n idx -= idx & -idx\n\n return tot\n\n\nn,t = map(int,input().split())\na = list(map(int,input().split()))\n\npsum = [0]*(n+1)\nfor i in range(n):\n psum[i+1] = psum[i] + a[i]\npsum.sort(reverse=True)\nupsum = [-10**18]\nfor i in range(n+1):\n if i == 0 or psum[i] != psum[i-1]:\n upsum.append(psum[i])\nupsum.sort(reverse = True)\n\ndef lower_bound(i):\n l = 0; r = len(upsum) - 1\n while l != r:\n m = (l+r)//2\n if upsum[m] <= i:\n r = m\n else:\n l = m + 1\n\n return l\n\nans = 0\ncurr = 0\nadd(lower_bound(0))\nfor i in a:\n curr += i\n ans += sm(lower_bound(curr-t)-1)\n add(lower_bound(curr))\n\n\nprint(ans)\n```","inputs":"5 4\n5 -1 3 4 -1\n","output":"5","actual_output":"5\n","execution_success":true,"sample_index":12486},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1065_C. Make It Equal","prompt":"Solve the following coding problem using the programming language python:\n\nThere is a toy building consisting of n towers. Each tower consists of several cubes standing on each other. The i-th tower consists of h_i cubes, so it has height h_i.\n\nLet's define operation slice on some height H as following: for each tower i, if its height is greater than H, then remove some top cubes to make tower's height equal to H. Cost of one \"slice\" equals to the total number of removed cubes from all towers.\n\nLet's name slice as good one if its cost is lower or equal to k (k \u2265 n).\n\n\n\nCalculate the minimum number of good slices you have to do to make all towers have the same height. Of course, it is always possible to make it so.\n\nInput\n\nThe first line contains two integers n and k (1 \u2264 n \u2264 2 \u22c5 10^5, n \u2264 k \u2264 10^9) \u2014 the number of towers and the restriction on slices, respectively.\n\nThe second line contains n space separated integers h_1, h_2, ..., h_n (1 \u2264 h_i \u2264 2 \u22c5 10^5) \u2014 the initial heights of towers.\n\nOutput\n\nPrint one integer \u2014 the minimum number of good slices you have to do to make all towers have the same heigth.\n\nExamples\n\nInput\n\n5 5\n3 1 2 2 4\n\n\nOutput\n\n2\n\n\nInput\n\n4 5\n2 3 4 5\n\n\nOutput\n\n2\n\nNote\n\nIn the first example it's optimal to make 2 slices. The first slice is on height 2 (its cost is 3), and the second one is on height 1 (its cost is 4).\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#########################################################################################################\\\n#########################################################################################################\n###################################The_Apurv_Rathore#####################################################\n#########################################################################################################\n#########################################################################################################\nimport sys,os,io\nfrom sys import stdin\nfrom math import log, gcd, ceil\nfrom collections import defaultdict, deque, Counter\nfrom heapq import heappush, heappop\nfrom bisect import bisect_left , bisect_right\nimport math \n\n\nalphabets = list('abcdefghijklmnopqrstuvwxyz')\n\ndef ncr(n, r, p): \n num = den = 1\n for i in range(r):\n num = (num * (n - i)) % p\n den = (den * (i + 1)) % p\n return (num * pow(den,\n p - 2, p)) % p\ndef primeFactors(n): \n l = []\n while n % 2 == 0: \n l.append(2)\n n = n / 2\n for i in range(3,int(math.sqrt(n))+1,2): \n while n % i== 0: \n l.append(int(i))\n n = n / i \n if n > 2: \n l.append(n)\n return list(set(l))\ndef power(x, y, p) : \n\tres = 1\n\tx = x % p \n\tif (x == 0) : \n\t\treturn 0\n\twhile (y > 0) : \n\t\tif ((y & 1) == 1) : \n\t\t\tres = (res * x) % p \n\t\ty = y >> 1\t # y = y/2 \n\t\tx = (x * x) % p \t\t\n\treturn res \ndef SieveOfEratosthenes(n):\n prime = [True for i in range(n+1)]\n p = 2\n while (p * p <= n):\n if (prime[p] == True):\n for i in range(p * p, n+1, p):\n prime[i] = False\n p += 1\n return prime\ndef countdig(n):\n c = 0\n while (n > 0):\n n //= 10\n c += 1\n return c\ndef si():\n return input()\ndef prefix_sum(arr):\n r = [0] * (len(arr)+1)\n for i, el in enumerate(arr):\n r[i+1] = r[i] + el\n return r\ndef divideCeil(n,x):\n if (n%x==0):\n return n//x\n return n//x+1\ndef ii():\n return int(input())\ndef li():\n return list(map(int,input().split()))\ndef ws(s): sys.stdout.write(s + '\\n')\ndef wi(n): sys.stdout.write(str(n) + '\\n')\ndef wia(a): sys.stdout.write(''.join([str(x) for x in a]) + '\\n')\n\n\n#__________________________TEMPLATE__________________OVER_______________________________________________________\n\n\nif(os.path.exists('input.txt')):\n sys.stdin = open(\"input.txt\",\"r\") ; sys.stdout = open(\"output.txt\",\"w\") \n# else:\n# input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline\nt = 1\n# t = int(input())\nfor _ in range(t):\n n,k = li()\n h = li()\n n = len(h)\n m = min(h)\n for i in range(n):\n h[i]-=m\n mx = max(h)\n arr = [0]*(mx+1)\n h.sort()\n h.reverse()\n for i in range(n):\n arr[h[i]]+=1\n c = 0\n # for i in range(mx,-1,-1):\n # arr[i]+=c\n # c+=arr[i]\n ans = 0\n cur = 0\n c = 0\n for i in range(mx,0,-1):\n c=arr[i]+c\n cur+=c\n if (cur>k):\n ans+=1\n cur = c\n if (cur>0):\n ans+=1\n print(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 5\\n2 3 4 5\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n3 1 2 2 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 10\\n2 2 2 2 3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 1 1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 1 1 1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 5\\n5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n4 4 4 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 100\\n5 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n2 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n3 3\\n', 'output': '0\\n'}, 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'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n8\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 1 2 1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 3\\n1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 25584\\n13182 14972\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 10\\n1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n4 4 4 8\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 2 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n2 3 3 3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n1 2 1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n3 3 3 3 1 3 3 3 3 3\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n2 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n2 2 2 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 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{'type': 'stdin_stdout', 'input': '4 4\\n2 3 4 5\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n4 4 7 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 1 1 1 2 1 1 1 1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 25584\\n12596 14972\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 8\\n1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n4 4 4 7\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n2 3 2 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n2 3 6 3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n1 2 2 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n2 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n2 4 2 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 18\\n10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n3 4 4 7\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n2 8 9 8 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n2 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n5 5 5 7 5\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n5 5 10 6 11\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 10\\n2 4 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 39609\\n200000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n411\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 1000000000\\n2 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n2 3 4 6\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n1 4 7 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 1 1 2 1 1 1 1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 25584\\n12596 15791\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 8\\n2 3 2 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n2 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n2 4 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 12\\n10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 4 4 7\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n5 5 9 7 5\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 17\\n2 4 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 20838\\n200000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n286\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 1000000000\\n2 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n2 2 4 6\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n1 4 9 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 1 1 3 1 1 1 1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n7\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n4 4 1 8\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4 8\\n2 5 2 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n2 4 1 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 9\\n10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 10\\n2 9 9 8 8\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n5 5 9 7 5\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n5 5 10 9 20\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3 17\\n4 4 2\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78373","program":"```python\n#########################################################################################################\\\n#########################################################################################################\n###################################The_Apurv_Rathore#####################################################\n#########################################################################################################\n#########################################################################################################\nimport sys,os,io\nfrom sys import stdin\nfrom math import log, gcd, ceil\nfrom collections import defaultdict, deque, Counter\nfrom heapq import heappush, heappop\nfrom bisect import bisect_left , bisect_right\nimport math \n\n\nalphabets = list('abcdefghijklmnopqrstuvwxyz')\n\ndef ncr(n, r, p): \n num = den = 1\n for i in range(r):\n num = (num * (n - i)) % p\n den = (den * (i + 1)) % p\n return (num * pow(den,\n p - 2, p)) % p\ndef primeFactors(n): \n l = []\n while n % 2 == 0: \n l.append(2)\n n = n / 2\n for i in range(3,int(math.sqrt(n))+1,2): \n while n % i== 0: \n l.append(int(i))\n n = n / i \n if n > 2: \n l.append(n)\n return list(set(l))\ndef power(x, y, p) : \n\tres = 1\n\tx = x % p \n\tif (x == 0) : \n\t\treturn 0\n\twhile (y > 0) : \n\t\tif ((y & 1) == 1) : \n\t\t\tres = (res * x) % p \n\t\ty = y >> 1\t # y = y/2 \n\t\tx = (x * x) % p \t\t\n\treturn res \ndef SieveOfEratosthenes(n):\n prime = [True for i in range(n+1)]\n p = 2\n while (p * p <= n):\n if (prime[p] == True):\n for i in range(p * p, n+1, p):\n prime[i] = False\n p += 1\n return prime\ndef countdig(n):\n c = 0\n while (n > 0):\n n //= 10\n c += 1\n return c\ndef si():\n return input()\ndef prefix_sum(arr):\n r = [0] * (len(arr)+1)\n for i, el in enumerate(arr):\n r[i+1] = r[i] + el\n return r\ndef divideCeil(n,x):\n if (n%x==0):\n return n//x\n return n//x+1\ndef ii():\n return int(input())\ndef li():\n return list(map(int,input().split()))\ndef ws(s): sys.stdout.write(s + '\\n')\ndef wi(n): sys.stdout.write(str(n) + '\\n')\ndef wia(a): sys.stdout.write(''.join([str(x) for x in a]) + '\\n')\n\n\n#__________________________TEMPLATE__________________OVER_______________________________________________________\n\n\nif(os.path.exists('input.txt')):\n sys.stdin = open(\"input.txt\",\"r\") ; sys.stdout = open(\"output.txt\",\"w\") \n# else:\n# input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline\nt = 1\n# t = int(input())\nfor _ in range(t):\n n,k = li()\n h = li()\n n = len(h)\n m = min(h)\n for i in range(n):\n h[i]-=m\n mx = max(h)\n arr = [0]*(mx+1)\n h.sort()\n h.reverse()\n for i in range(n):\n arr[h[i]]+=1\n c = 0\n # for i in range(mx,-1,-1):\n # arr[i]+=c\n # c+=arr[i]\n ans = 0\n cur = 0\n c = 0\n for i in range(mx,0,-1):\n c=arr[i]+c\n cur+=c\n if (cur>k):\n ans+=1\n cur = c\n if (cur>0):\n ans+=1\n print(ans)\n```","inputs":"4 5\n2 3 4 5\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12487},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1088_A. Ehab and another construction problem","prompt":"Solve the following coding problem using the programming language python:\n\nGiven an integer x, find 2 integers a and b such that: \n\n * 1 \u2264 a,b \u2264 x \n * b divides a (a is divisible by b). \n * a \u22c5 b>x. \n * a/b=3 and n%2==1:\n\tprint(n-1,2)\nelif n>=2 and n%2==0:\n\tprint(n,2)\nelse:\n\tprint(-1)\t\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n', 'output': '4 4\\n'}, {'type': 'stdin_stdout', 'input': '82\\n', 'output': '10 10\\n'}, {'type': 'stdin_stdout', 'input': '49\\n', 'output': '8 8\\n'}, {'type': 'stdin_stdout', 'input': '35\\n', 'output': '6 6\\n'}, {'type': 'stdin_stdout', 'input': '79\\n', 'output': '9 9\\n'}, {'type': 'stdin_stdout', 'input': '92\\n', 'output': '10 10\\n'}, {'type': 'stdin_stdout', 'input': '57\\n', 'output': '8 8\\n'}, {'type': 'stdin_stdout', 'input': '100\\n', 'output': '11 11\\n'}, {'type': 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'48\\n', 'output': '7 7\\n'}, {'type': 'stdin_stdout', 'input': '55\\n', 'output': '8 8\\n'}, {'type': 'stdin_stdout', 'input': '96\\n', 'output': '10 10\\n'}, {'type': 'stdin_stdout', 'input': '52\\n', 'output': '8 8\\n'}, {'type': 'stdin_stdout', 'input': '71\\n', 'output': '9 9\\n'}, {'type': 'stdin_stdout', 'input': '53\\n', 'output': '8 8\\n'}, {'type': 'stdin_stdout', 'input': '47\\n', 'output': '7 7\\n'}, {'type': 'stdin_stdout', 'input': '12\\n', 'output': '4 4\\n'}, {'type': 'stdin_stdout', 'input': '84\\n', 'output': '10 10\\n'}, {'type': 'stdin_stdout', 'input': '83\\n', 'output': '10 10\\n'}, {'type': 'stdin_stdout', 'input': '31\\n', 'output': '6 6\\n'}, {'type': 'stdin_stdout', 'input': '30\\n', 'output': '6 6\\n'}, {'type': 'stdin_stdout', 'input': '89\\n', 'output': '10 10\\n'}, {'type': 'stdin_stdout', 'input': '32\\n', 'output': '6 6\\n'}, {'type': 'stdin_stdout', 'input': '001\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '010\\n', 'output': '4 4\\n'}, {'type': 'stdin_stdout', 'input': '011\\n', 'output': '4 4\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78377","program":"```python\n\nn=int(input())\nif n>=3 and n%2==1:\n\tprint(n-1,2)\nelif n>=2 and n%2==0:\n\tprint(n,2)\nelse:\n\tprint(-1)\t\n```","inputs":"1\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12488},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1107_A. Digits Sequence Dividing","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a sequence s consisting of n digits from 1 to 9.\n\nYou have to divide it into at least two segments (segment \u2014 is a consecutive sequence of elements) (in other words, you have to place separators between some digits of the sequence) in such a way that each element belongs to exactly one segment and if the resulting division will be represented as an integer numbers sequence then each next element of this sequence will be strictly greater than the previous one.\n\nMore formally: if the resulting division of the sequence is t_1, t_2, ..., t_k, where k is the number of element in a division, then for each i from 1 to k-1 the condition t_{i} < t_{i + 1} (using numerical comparing, it means that the integer representations of strings are compared) should be satisfied.\n\nFor example, if s=654 then you can divide it into parts [6, 54] and it will be suitable division. But if you will divide it into parts [65, 4] then it will be bad division because 65 > 4. If s=123 then you can divide it into parts [1, 23], [1, 2, 3] but not into parts [12, 3].\n\nYour task is to find any suitable division for each of the q independent queries.\n\nInput\n\nThe first line of the input contains one integer q (1 \u2264 q \u2264 300) \u2014 the number of queries.\n\nThe first line of the i-th query contains one integer number n_i (2 \u2264 n_i \u2264 300) \u2014 the number of digits in the i-th query.\n\nThe second line of the i-th query contains one string s_i of length n_i consisting only of digits from 1 to 9.\n\nOutput\n\nIf the sequence of digits in the i-th query cannot be divided into at least two parts in a way described in the problem statement, print the single line \"NO\" for this query.\n\nOtherwise in the first line of the answer to this query print \"YES\", on the second line print k_i \u2014 the number of parts in your division of the i-th query sequence and in the third line print k_i strings t_{i, 1}, t_{i, 2}, ..., t_{i, k_i} \u2014 your division. Parts should be printed in order of the initial string digits. It means that if you write the parts one after another without changing their order then you'll get the string s_i.\n\nSee examples for better understanding.\n\nExample\n\nInput\n\n\n4\n6\n654321\n4\n1337\n2\n33\n4\n2122\n\n\nOutput\n\n\nYES\n3\n6 54 321\nYES\n3\n1 3 37\nNO\nYES\n2\n21 22\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfor _ in range(int(input())):\n n = int(input())\n z = input()\n if n==2 and z[0]>=z[1]:\n print(\"NO\")\n else:\n print(\"YES\")\n print(2)\n print(z[0],z[1::])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n6\\n654321\\n4\\n1337\\n2\\n33\\n4\\n2122\\n', 'output': 'YES\\n2\\n6 54321\\nYES\\n2\\n1 337\\nNO\\nYES\\n2\\n2 122\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n45\\n2\\n67\\n', 'output': 'YES\\n2\\n4 5\\nYES\\n2\\n6 7\\n'}, {'type': 'stdin_stdout', 'input': '21\\n3\\n123\\n3\\n123\\n3\\n123\\n3\\n123\\n3\\n123\\n3\\n213\\n3\\n123\\n3\\n123\\n3\\n123\\n3\\n321\\n3\\n123\\n3\\n321\\n3\\n132\\n3\\n322\\n3\\n321\\n3\\n341\\n3\\n123\\n3\\n421\\n3\\n421\\n3\\n421\\n3\\n421\\n', 'output': 'YES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n2 13\\nYES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n3 21\\nYES\\n2\\n1 23\\nYES\\n2\\n3 21\\nYES\\n2\\n1 32\\nYES\\n2\\n3 22\\nYES\\n2\\n3 21\\nYES\\n2\\n3 41\\nYES\\n2\\n1 23\\nYES\\n2\\n4 21\\nYES\\n2\\n4 21\\nYES\\n2\\n4 21\\nYES\\n2\\n4 21\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n9999\\n', 'output': 'YES\\n2\\n9 999\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n5234\\n', 'output': 'YES\\n2\\n5 234\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n654321\\n4\\n1337\\n2\\n33\\n4\\n2122\\n', 'output': 'YES\\n2\\n6 54321\\nYES\\n2\\n1 337\\nNO\\nYES\\n2\\n2 122\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n333\\n', 'output': 'YES\\n2\\n3 33\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n3333\\n', 'output': 'YES\\n2\\n3 333\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n45\\n2\\n45\\n', 'output': 'YES\\n2\\n4 5\\nYES\\n2\\n4 5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n5149\\n', 'output': 'YES\\n2\\n5 149\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n45\\n2\\n26\\n', 'output': 'YES\\n2\\n4 5\\nYES\\n2\\n2 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n8788\\n', 'output': 'YES\\n2\\n8 788\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n14\\n2\\n26\\n', 'output': 'YES\\n2\\n1 4\\nYES\\n2\\n2 6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n14\\n2\\n36\\n', 'output': 'YES\\n2\\n1 4\\nYES\\n2\\n3 6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n10\\n2\\n36\\n', 'output': 'NO\\nYES\\n2\\n3 6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n45\\n2\\n88\\n', 'output': 'YES\\n2\\n4 5\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1167\\n', 'output': 'YES\\n2\\n1 167\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n654321\\n4\\n1562\\n2\\n33\\n4\\n2122\\n', 'output': 'YES\\n2\\n6 54321\\nYES\\n2\\n1 562\\nNO\\nYES\\n2\\n2 122\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n79\\n2\\n45\\n', 'output': 'YES\\n2\\n7 9\\nYES\\n2\\n4 5\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n13\\n2\\n26\\n', 'output': 'YES\\n2\\n1 3\\nYES\\n2\\n2 6\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n654321\\n4\\n1562\\n2\\n19\\n4\\n2122\\n', 'output': 'YES\\n2\\n6 54321\\nYES\\n2\\n1 562\\nYES\\n2\\n1 9\\nYES\\n2\\n2 122\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n79\\n2\\n68\\n', 'output': 'YES\\n2\\n7 9\\nYES\\n2\\n6 8\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n654321\\n4\\n1562\\n2\\n25\\n4\\n2122\\n', 'output': 'YES\\n2\\n6 54321\\nYES\\n2\\n1 562\\nYES\\n2\\n2 5\\nYES\\n2\\n2 122\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n654321\\n4\\n1562\\n2\\n25\\n4\\n3053\\n', 'output': 'YES\\n2\\n6 54321\\nYES\\n2\\n1 562\\nYES\\n2\\n2 5\\nYES\\n2\\n3 053\\n'}, {'type': 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'output': 'YES\\n2\\n5 92906\\nYES\\n2\\n1 559\\nYES\\n2\\n2 5\\nYES\\n2\\n3 304\\n'}, {'type': 'stdin_stdout', 'input': '21\\n3\\n123\\n3\\n123\\n3\\n123\\n3\\n123\\n3\\n123\\n3\\n213\\n3\\n123\\n3\\n123\\n3\\n123\\n3\\n321\\n3\\n123\\n3\\n321\\n3\\n132\\n3\\n322\\n3\\n321\\n3\\n341\\n3\\n123\\n3\\n607\\n3\\n421\\n3\\n421\\n3\\n421\\n', 'output': 'YES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n2 13\\nYES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n1 23\\nYES\\n2\\n3 21\\nYES\\n2\\n1 23\\nYES\\n2\\n3 21\\nYES\\n2\\n1 32\\nYES\\n2\\n3 22\\nYES\\n2\\n3 21\\nYES\\n2\\n3 41\\nYES\\n2\\n1 23\\nYES\\n2\\n6 07\\nYES\\n2\\n4 21\\nYES\\n2\\n4 21\\nYES\\n2\\n4 21\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n5367\\n', 'output': 'YES\\n2\\n5 367\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n242\\n', 'output': 'YES\\n2\\n2 42\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n3041\\n', 'output': 'YES\\n2\\n3 041\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n45\\n2\\n18\\n', 'output': 'YES\\n2\\n4 5\\nYES\\n2\\n1 8\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n17\\n2\\n36\\n', 'output': 'YES\\n2\\n1 7\\nYES\\n2\\n3 6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n13\\n2\\n36\\n', 'output': 'YES\\n2\\n1 3\\nYES\\n2\\n3 6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n12\\n2\\n88\\n', 'output': 'YES\\n2\\n1 2\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n654321\\n4\\n2827\\n2\\n33\\n4\\n2122\\n', 'output': 'YES\\n2\\n6 54321\\nYES\\n2\\n2 827\\nNO\\nYES\\n2\\n2 122\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n11\\n2\\n24\\n', 'output': 'NO\\nYES\\n2\\n2 4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n47\\n2\\n68\\n', 'output': 'YES\\n2\\n4 7\\nYES\\n2\\n6 8\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n281738\\n4\\n1562\\n2\\n25\\n4\\n2122\\n', 'output': 'YES\\n2\\n2 81738\\nYES\\n2\\n1 562\\nYES\\n2\\n2 5\\nYES\\n2\\n2 122\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n11\\n2\\n36\\n', 'output': 'NO\\nYES\\n2\\n3 6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n45\\n2\\n30\\n', 'output': 'YES\\n2\\n4 5\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n45\\n2\\n75\\n', 'output': 'YES\\n2\\n4 5\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n51\\n2\\n88\\n', 'output': 'NO\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n31\\n2\\n40\\n', 'output': 'NO\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n71\\n2\\n88\\n', 'output': 'NO\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n654321\\n4\\n1562\\n2\\n11\\n4\\n2122\\n', 'output': 'YES\\n2\\n6 54321\\nYES\\n2\\n1 562\\nNO\\nYES\\n2\\n2 122\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78381","program":"```python\nfor _ in range(int(input())):\n n = int(input())\n z = input()\n if n==2 and z[0]>=z[1]:\n print(\"NO\")\n else:\n print(\"YES\")\n print(2)\n print(z[0],z[1::])\n```","inputs":"4\n6\n654321\n4\n1337\n2\n33\n4\n2122\n","output":"YES\n2\n6 54321\nYES\n2\n1 337\nNO\nYES\n2\n2 122\n","actual_output":"YES\n2\n6 54321\nYES\n2\n1 337\nNO\nYES\n2\n2 122\n","execution_success":true,"sample_index":12489},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1136_A. Nastya Is Reading a Book","prompt":"Solve the following coding problem using the programming language python:\n\nAfter lessons Nastya decided to read a book. The book contains n chapters, going one after another, so that one page of the book belongs to exactly one chapter and each chapter contains at least one page.\n\nYesterday evening Nastya did not manage to finish reading the book, so she marked the page with number k as the first page which was not read (i.e. she read all pages from the 1-st to the (k-1)-th).\n\nThe next day Nastya's friend Igor came and asked her, how many chapters remain to be read by Nastya? Nastya is too busy now, so she asks you to compute the number of chapters she has not completely read yet (i.e. the number of chapters she has not started to read or has finished reading somewhere in the middle).\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 100) \u2014 the number of chapters in the book.\n\nThere are n lines then. The i-th of these lines contains two integers l_i, r_i separated by space (l_1 = 1, l_i \u2264 r_i) \u2014 numbers of the first and the last pages of the i-th chapter. It's guaranteed that l_{i+1} = r_i + 1 for all 1 \u2264 i \u2264 n-1, and also that every chapter contains at most 100 pages.\n\nThe (n+2)-th line contains a single integer k (1 \u2264 k \u2264 r_n) \u2014 the index of the marked page. \n\nOutput\n\nPrint a single integer \u2014 the number of chapters which has not been completely read so far.\n\nExamples\n\nInput\n\n\n3\n1 3\n4 7\n8 11\n2\n\n\nOutput\n\n\n3\n\n\nInput\n\n\n3\n1 4\n5 9\n10 12\n9\n\n\nOutput\n\n\n2\n\n\nInput\n\n\n1\n1 7\n4\n\n\nOutput\n\n\n1\n\nNote\n\nIn the first example the book contains 11 pages and 3 chapters \u2014 [1;3], [4;7] and [8;11]. Nastya marked the 2-nd page, so she finished in the middle of the 1-st chapter. So, all chapters has not been read so far, so the answer is 3.\n\nThe book in the second example contains 12 pages and 3 chapters too, but Nastya finished reading in the middle of the 2-nd chapter, so that the answer is 2.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\np=[]\nfor x in range(n):\n a,b=list(map(int,input().split()))\n sam=list(range(a,b+1))\n p.append(sam)\nkam=int(input())\nfor x in p:\n if kam in x:\n print(n-p.index(x))\n break\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 4\\n5 9\\n10 12\\n9\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 7\\n4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3\\n4 7\\n8 11\\n2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 5\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1 1\\n2 2\\n3 3\\n4 4\\n5 5\\n6 6\\n7 7\\n8 8\\n9 9\\n10 10\\n11 11\\n12 12\\n13 13\\n14 14\\n15 15\\n16 16\\n17 17\\n18 18\\n19 19\\n13\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3\\n4 7\\n8 11\\n1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2\\n3 4\\n3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 2\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '66\\n1 1\\n2 2\\n3 3\\n4 4\\n5 5\\n6 6\\n7 7\\n8 8\\n9 9\\n10 10\\n11 11\\n12 12\\n13 13\\n14 14\\n15 15\\n16 16\\n17 17\\n18 18\\n19 19\\n20 20\\n21 21\\n22 22\\n23 23\\n24 24\\n25 25\\n26 26\\n27 27\\n28 28\\n29 29\\n30 30\\n31 31\\n32 32\\n33 33\\n34 34\\n35 35\\n36 36\\n37 37\\n38 38\\n39 39\\n40 40\\n41 41\\n42 42\\n43 43\\n44 44\\n45 45\\n46 46\\n47 47\\n48 48\\n49 49\\n50 50\\n51 51\\n52 52\\n53 53\\n54 54\\n55 55\\n56 56\\n57 57\\n58 58\\n59 59\\n60 60\\n61 61\\n62 62\\n63 63\\n64 64\\n65 65\\n66 66\\n1\\n', 'output': '66\\n'}, {'type': 'stdin_stdout', 'input': '11\\n1 8\\n9 15\\n16 18\\n19 23\\n24 25\\n26 27\\n28 29\\n30 36\\n37 39\\n40 44\\n45 54\\n49\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1\\n2 2\\n3 3\\n1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1\\n2 3\\n4 5\\n1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1\\n2 3\\n4 4\\n5 5\\n2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n3 4\\n5 6\\n3\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '68\\n1 1\\n2 2\\n3 3\\n4 4\\n5 5\\n6 6\\n7 7\\n8 8\\n9 9\\n10 10\\n11 11\\n12 12\\n13 13\\n14 14\\n15 15\\n16 16\\n17 17\\n18 18\\n19 19\\n20 20\\n21 21\\n22 22\\n23 23\\n24 24\\n25 25\\n26 26\\n27 27\\n28 28\\n29 29\\n30 30\\n31 31\\n32 32\\n33 33\\n34 34\\n35 35\\n36 36\\n37 37\\n38 38\\n39 39\\n40 40\\n41 41\\n42 42\\n43 43\\n44 44\\n45 45\\n46 46\\n47 47\\n48 48\\n49 49\\n50 50\\n51 51\\n52 52\\n53 53\\n54 54\\n55 55\\n56 56\\n57 57\\n58 58\\n59 59\\n60 60\\n61 61\\n62 62\\n63 63\\n64 64\\n65 65\\n66 66\\n67 67\\n68 68\\n53\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 3\\n4 7\\n4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '45\\n1 48\\n49 118\\n119 122\\n123 198\\n199 283\\n284 352\\n353 447\\n448 528\\n529 539\\n540 549\\n550 557\\n558 627\\n628 700\\n701 741\\n742 835\\n836 883\\n884 887\\n888 900\\n901 943\\n944 1032\\n1033 1131\\n1132 1158\\n1159 1222\\n1223 1281\\n1282 1315\\n1316 1397\\n1398 1469\\n1470 1520\\n1521 1558\\n1559 1631\\n1632 1688\\n1689 1699\\n1700 1766\\n1767 1775\\n1776 1778\\n1779 1878\\n1879 1904\\n1905 1984\\n1985 1987\\n1988 1999\\n2000 2059\\n2060 2126\\n2127 2168\\n2169 2189\\n2190 2206\\n1109\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '13\\n1 13\\n14 15\\n16 17\\n18 19\\n20 21\\n22 23\\n24 25\\n26 27\\n28 29\\n30 31\\n32 33\\n34 35\\n36 37\\n13\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 3\\n4 10\\n4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '71\\n1 1\\n2 2\\n3 3\\n4 4\\n5 5\\n6 6\\n7 7\\n8 8\\n9 9\\n10 10\\n11 11\\n12 12\\n13 13\\n14 14\\n15 15\\n16 16\\n17 17\\n18 18\\n19 19\\n20 20\\n21 21\\n22 22\\n23 23\\n24 24\\n25 25\\n26 26\\n27 27\\n28 28\\n29 29\\n30 30\\n31 31\\n32 32\\n33 33\\n34 34\\n35 35\\n36 36\\n37 37\\n38 38\\n39 39\\n40 40\\n41 41\\n42 42\\n43 43\\n44 44\\n45 45\\n46 46\\n47 47\\n48 48\\n49 49\\n50 50\\n51 51\\n52 52\\n53 53\\n54 54\\n55 55\\n56 56\\n57 57\\n58 58\\n59 59\\n60 60\\n61 61\\n62 62\\n63 63\\n64 64\\n65 65\\n66 66\\n67 67\\n68 68\\n69 69\\n70 70\\n71 71\\n69\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 6\\n7 12\\n13 19\\n20 28\\n29 37\\n38 39\\n21\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '12\\n1 1\\n2 2\\n3 3\\n4 4\\n5 5\\n6 6\\n7 7\\n8 8\\n9 9\\n10 10\\n11 11\\n12 12\\n9\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '49\\n1 17\\n18 115\\n116 211\\n212 269\\n270 345\\n346 404\\n405 441\\n442 467\\n468 526\\n527 583\\n584 664\\n665 757\\n758 794\\n795 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{'type': 'stdin_stdout', 'input': '3\\n1 3\\n4 5\\n6 6\\n1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1\\n2 2\\n2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3\\n4 7\\n8 11\\n4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 2\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1 1\\n2 3\\n3 3\\n4 4\\n5 5\\n6 6\\n7 7\\n8 8\\n9 9\\n10 10\\n11 11\\n12 12\\n13 13\\n14 14\\n15 15\\n16 16\\n17 17\\n18 18\\n19 19\\n13\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '66\\n1 1\\n2 2\\n3 3\\n4 4\\n5 5\\n6 6\\n7 7\\n8 8\\n9 9\\n10 10\\n11 11\\n12 12\\n13 13\\n14 14\\n15 15\\n16 16\\n17 17\\n18 18\\n19 19\\n20 20\\n21 21\\n22 22\\n23 23\\n24 24\\n25 25\\n26 26\\n27 27\\n28 28\\n29 29\\n30 30\\n31 31\\n32 32\\n33 33\\n34 34\\n35 35\\n36 36\\n37 37\\n38 38\\n39 39\\n40 40\\n41 41\\n42 42\\n43 43\\n44 44\\n45 45\\n46 46\\n47 47\\n48 48\\n49 49\\n50 50\\n51 51\\n52 52\\n53 53\\n54 54\\n55 55\\n56 56\\n57 57\\n58 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'stdin_stdout', 'input': '3\\n1 8\\n7 16\\n15 33\\n4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '27\\n1 0\\n2 2\\n3 3\\n4 4\\n5 5\\n11 6\\n9 7\\n12 8\\n9 9\\n10 10\\n11 11\\n12 12\\n13 13\\n2 14\\n15 15\\n16 16\\n17 17\\n18 18\\n19 19\\n20 20\\n21 21\\n22 22\\n23 23\\n24 24\\n25 25\\n26 26\\n27 27\\n25\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '9\\n0 81\\n82 177\\n178 254\\n236 338\\n218 410\\n30 412\\n413 474\\n475 534\\n535 555\\n426\\n', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78385","program":"```python\nn=int(input())\np=[]\nfor x in range(n):\n a,b=list(map(int,input().split()))\n sam=list(range(a,b+1))\n p.append(sam)\nkam=int(input())\nfor x in p:\n if kam in x:\n print(n-p.index(x))\n break\n\n\n```","inputs":"3\n1 4\n5 9\n10 12\n9\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12490},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1154_E. Two Teams","prompt":"Solve the following coding problem using the programming language python:\n\nThere are n students standing in a row. Two coaches are forming two teams \u2014 the first coach chooses the first team and the second coach chooses the second team.\n\nThe i-th student has integer programming skill a_i. All programming skills are distinct and between 1 and n, inclusive.\n\nFirstly, the first coach will choose the student with maximum programming skill among all students not taken into any team, and k closest students to the left of him and k closest students to the right of him (if there are less than k students to the left or to the right, all of them will be chosen). All students that are chosen leave the row and join the first team. Secondly, the second coach will make the same move (but all students chosen by him join the second team). Then again the first coach will make such move, and so on. This repeats until the row becomes empty (i. e. the process ends when each student becomes to some team).\n\nYour problem is to determine which students will be taken into the first team and which students will be taken into the second team.\n\nInput\n\nThe first line of the input contains two integers n and k (1 \u2264 k \u2264 n \u2264 2 \u22c5 10^5) \u2014 the number of students and the value determining the range of chosen students during each move, respectively.\n\nThe second line of the input contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 n), where a_i is the programming skill of the i-th student. It is guaranteed that all programming skills are distinct.\n\nOutput\n\nPrint a string of n characters; i-th character should be 1 if i-th student joins the first team, or 2 otherwise.\n\nExamples\n\nInput\n\n\n5 2\n2 4 5 3 1\n\n\nOutput\n\n\n11111\n\n\nInput\n\n\n5 1\n2 1 3 5 4\n\n\nOutput\n\n\n22111\n\n\nInput\n\n\n7 1\n7 2 1 3 5 4 6\n\n\nOutput\n\n\n1121122\n\n\nInput\n\n\n5 1\n2 4 5 3 1\n\n\nOutput\n\n\n21112\n\nNote\n\nIn the first example the first coach chooses the student on a position 3, and the row becomes empty (all students join the first team).\n\nIn the second example the first coach chooses the student on position 4, and the row becomes [2, 1] (students with programming skills [3, 4, 5] join the first team). Then the second coach chooses the student on position 1, and the row becomes empty (and students with programming skills [1, 2] join the second team).\n\nIn the third example the first coach chooses the student on position 1, and the row becomes [1, 3, 5, 4, 6] (students with programming skills [2, 7] join the first team). Then the second coach chooses the student on position 5, and the row becomes [1, 3, 5] (students with programming skills [4, 6] join the second team). Then the first coach chooses the student on position 3, and the row becomes [1] (students with programming skills [3, 5] join the first team). And then the second coach chooses the remaining student (and the student with programming skill 1 joins the second team).\n\nIn the fourth example the first coach chooses the student on position 3, and the row becomes [2, 1] (students with programming skills [3, 4, 5] join the first team). Then the second coach chooses the student on position 1, and the row becomes empty (and students with programming skills [1, 2] join the second team).\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\n\ndef main():\n n, k = map(int, input().split())\n A = list(map(int, input().split()))\n\n B = []\n for i, a in enumerate(A):\n B.append((a, i+1))\n B.sort()\n #print(B)\n\n bit = [0]*(n+1)\n\n def bit_query(i, bit):\n res = 0\n while i > 0:\n res += bit[i]\n i -= i & (-i)\n return res\n\n def bit_update(i, x, bit, n):\n while i <= n:\n bit[i] += x\n i += i & (-i)\n\n def lower_bound(x, bit, n):\n s = 0\n pos = 0\n depth = n.bit_length()\n v = 1 << depth\n for i in range(depth, -1, -1):\n k = pos + v\n if k <= n and s + bit[k] < x:\n s += bit[k]\n pos += v\n v >>= 1\n return pos+1\n\n for i in range(1, n+1):\n bit_update(i, 1, bit, n)\n\n ans = [0]*n\n who = 0\n while bit_query(n, bit):\n while B:\n a, i = B.pop()\n if bit_query(i, bit)-bit_query(i-1, bit) == 0:\n continue\n else:\n break\n temp = []\n pos = bit_query(i, bit)\n temp.append(i)\n for d in range(1, k+1):\n j = pos-d\n if j == 0:\n break\n else:\n p = lower_bound(j, bit, n)\n temp.append(p)\n for d in range(1, k+1):\n j = pos+d\n if j > bit_query(n, bit):\n break\n else:\n p = lower_bound(j, bit, n)\n temp.append(p)\n #print(temp)\n for p in temp:\n bit_update(p, -1, bit, n)\n ans[p-1] = str(1+who)\n who = 1-who\n print(''.join(ans))\n\nif __name__ == '__main__':\n main()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 1\\n2 4 5 3 1\\n', 'output': '21112\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n7 2 1 3 5 4 6\\n', 'output': '1121122\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n2 1 3 5 4\\n', 'output': '22111\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n2 4 5 3 1\\n', 'output': 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62\\n', 'output': '1121111111111111112222222222222211112222222222222221111111111112222222222222221111111111111111111111\\n'}, {'type': 'stdin_stdout', 'input': '100 7\\n20 27 16 53 17 24 18 43 44 46 6 97 93 52 51 29 8 50 31 94 81 61 4 25 35 12 36 99 57 86 79 11 5 23 28 92 59 82 48 26 78 67 38 62 63 73 15 45 88 87 95 56 9 39 1 96 66 19 76 40 42 69 41 34 30 89 7 83 37 14 84 54 13 80 65 71 47 32 70 100 85 64 60 21 75 2 91 90 3 77 49 33 68 98 74 22 58 10 55 72\\n', 'output': '2222222222222222222222222222222222222222222111111111111111111111111111111111111111111111111111111111\\n'}, {'type': 'stdin_stdout', 'input': '100 3\\n100 6 41 33 5 32 39 58 95 48 27 17 90 73 10 81 56 87 79 91 43 42 47 75 57 98 22 49 67 28 94 86 89 60 65 96 11 46 13 23 85 61 9 99 63 52 15 66 40 31 12 72 93 20 77 44 88 55 16 54 38 7 26 19 97 36 14 92 3 4 1 24 2 8 50 76 82 34 51 53 64 45 70 37 18 62 25 21 69 35 74 30 71 84 59 80 83 29 78 68\\n', 'output': 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22\\n81 45 55 5 13 10 42 44 18 4 6 72 89 78 3 100 73 91 47 33 99 93 98 2 11 92 49 69 8 21 43 41 46 36 40 7 87 14 76 62 29 58 38 56 19 24 35 61 53 1 77 79 80 67 15 28 94 51 64 96 57 95 63 30 54 71 22 68 59 97 27 32 85 52 88 90 65 60 17 12 20 86 26 39 37 48 16 83 66 34 70 9 74 75 84 82 50 25 23 31\\n', 'output': '1111111111111111111111111111111111111111111111122222222222222222222222222222222222222222222211111111\\n'}, {'type': 'stdin_stdout', 'input': '100 4\\n19 55 91 50 31 23 60 84 38 1 22 51 27 76 28 98 11 44 61 63 15 93 52 3 66 16 53 36 18 62 35 85 78 37 73 64 87 74 46 26 82 69 49 33 83 89 56 67 71 25 39 94 96 17 21 6 47 68 34 42 57 81 13 10 54 2 48 80 20 77 4 5 59 30 90 95 45 75 8 88 24 41 40 14 97 32 7 9 65 70 100 99 72 58 92 29 79 12 86 43\\n', 'output': '1111111222222222222222222221111111111111122222222222222222211112221222211111111111111111111111111122\\n'}, {'type': 'stdin_stdout', 'input': '100 1\\n19 55 91 50 31 23 60 84 38 1 22 51 27 76 28 98 11 44 61 63 15 93 52 3 66 16 53 36 18 62 35 85 78 37 73 64 87 74 46 26 82 69 49 33 83 89 56 67 71 25 39 94 96 17 21 6 47 68 34 42 57 81 13 10 54 2 48 80 20 77 4 5 59 30 90 95 45 75 8 88 24 41 40 14 97 32 7 9 65 70 100 99 72 58 92 29 79 12 86 43\\n', 'output': '2222222221112222221122211111221112211121112111111112221222222222211111111111112221111122211121112222\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n2 1 3 5 4\\n', 'output': '21112\\n'}, {'type': 'stdin_stdout', 'input': '7 2\\n7 2 1 3 5 4 6\\n', 'output': '1111222\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 3\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n2 1 3 5 4\\n', 'output': '11111\\n'}, {'type': 'stdin_stdout', 'input': '1 6\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 5\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 7\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 8\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 9\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n2 4 5 3 1\\n', 'output': '11111\\n'}, {'type': 'stdin_stdout', 'input': '1 4\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 12\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 17\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 22\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 8\\n2 4 5 3 1\\n', 'output': '11111\\n'}, {'type': 'stdin_stdout', 'input': '1 13\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n2 1 4 5 3\\n', 'output': '11111\\n'}, {'type': 'stdin_stdout', 'input': '1 10\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n2 1 3 5 4\\n', 'output': '11111\\n'}, {'type': 'stdin_stdout', 'input': '1 11\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 15\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n2 4 5 3 1\\n', 'output': '11111\\n'}, {'type': 'stdin_stdout', 'input': '1 21\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 19\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 28\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 31\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 29\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5 4\\n', 'output': '11111\\n'}, {'type': 'stdin_stdout', 'input': '1 14\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 16\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 35\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 18\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 11\\n2 4 5 3 1\\n', 'output': '11111\\n'}, {'type': 'stdin_stdout', 'input': '1 30\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 27\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 54\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 33\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n1 2 3 5 4\\n', 'output': '11111\\n'}, {'type': 'stdin_stdout', 'input': '1 71\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 82\\n1\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78389","program":"```python\nimport sys\ninput = sys.stdin.readline\n\ndef main():\n n, k = map(int, input().split())\n A = list(map(int, input().split()))\n\n B = []\n for i, a in enumerate(A):\n B.append((a, i+1))\n B.sort()\n #print(B)\n\n bit = [0]*(n+1)\n\n def bit_query(i, bit):\n res = 0\n while i > 0:\n res += bit[i]\n i -= i & (-i)\n return res\n\n def bit_update(i, x, bit, n):\n while i <= n:\n bit[i] += x\n i += i & (-i)\n\n def lower_bound(x, bit, n):\n s = 0\n pos = 0\n depth = n.bit_length()\n v = 1 << depth\n for i in range(depth, -1, -1):\n k = pos + v\n if k <= n and s + bit[k] < x:\n s += bit[k]\n pos += v\n v >>= 1\n return pos+1\n\n for i in range(1, n+1):\n bit_update(i, 1, bit, n)\n\n ans = [0]*n\n who = 0\n while bit_query(n, bit):\n while B:\n a, i = B.pop()\n if bit_query(i, bit)-bit_query(i-1, bit) == 0:\n continue\n else:\n break\n temp = []\n pos = bit_query(i, bit)\n temp.append(i)\n for d in range(1, k+1):\n j = pos-d\n if j == 0:\n break\n else:\n p = lower_bound(j, bit, n)\n temp.append(p)\n for d in range(1, k+1):\n j = pos+d\n if j > bit_query(n, bit):\n break\n else:\n p = lower_bound(j, bit, n)\n temp.append(p)\n #print(temp)\n for p in temp:\n bit_update(p, -1, bit, n)\n ans[p-1] = str(1+who)\n who = 1-who\n print(''.join(ans))\n\nif __name__ == '__main__':\n main()\n\n```","inputs":"5 1\n2 4 5 3 1\n","output":"21112\n","actual_output":"21112\n","execution_success":true,"sample_index":12491},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1176_C. Lose it!","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given an array a consisting of n integers. Each a_i is one of the six following numbers: 4, 8, 15, 16, 23, 42.\n\nYour task is to remove the minimum number of elements to make this array good.\n\nAn array of length k is called good if k is divisible by 6 and it is possible to split it into k/6 subsequences 4, 8, 15, 16, 23, 42.\n\nExamples of good arrays:\n\n * [4, 8, 15, 16, 23, 42] (the whole array is a required sequence); \n * [4, 8, 4, 15, 16, 8, 23, 15, 16, 42, 23, 42] (the first sequence is formed from first, second, fourth, fifth, seventh and tenth elements and the second one is formed from remaining elements); \n * [] (the empty array is good). \n\n\n\nExamples of bad arrays: \n\n * [4, 8, 15, 16, 42, 23] (the order of elements should be exactly 4, 8, 15, 16, 23, 42); \n * [4, 8, 15, 16, 23, 42, 4] (the length of the array is not divisible by 6); \n * [4, 8, 15, 16, 23, 42, 4, 8, 15, 16, 23, 23] (the first sequence can be formed from first six elements but the remaining array cannot form the required sequence). \n\nInput\n\nThe first line of the input contains one integer n (1 \u2264 n \u2264 5 \u22c5 10^5) \u2014 the number of elements in a.\n\nThe second line of the input contains n integers a_1, a_2, ..., a_n (each a_i is one of the following numbers: 4, 8, 15, 16, 23, 42), where a_i is the i-th element of a.\n\nOutput\n\nPrint one integer \u2014 the minimum number of elements you have to remove to obtain a good array.\n\nExamples\n\nInput\n\n\n5\n4 8 15 16 23\n\n\nOutput\n\n\n5\n\n\nInput\n\n\n12\n4 8 4 15 16 8 23 15 16 42 23 42\n\n\nOutput\n\n\n0\n\n\nInput\n\n\n15\n4 8 4 8 15 16 8 16 23 15 16 4 42 23 42\n\n\nOutput\n\n\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n_=int(input())\na=list(map(int,input().split()))\nb=[4,8,15,16,23,42]\nc=[0]*6\n\nfor i in range(len(a)):\n x = b.index(a[i])\n if x == 0:\n c[0] +=1\n elif c[x-1]!=0:\n c[x-1]-=1\n c[x]+=1\n \nprint(len(a)-6*c[5])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n4 8 15 16 23\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '15\\n4 8 4 8 15 16 8 16 23 15 16 4 42 23 42\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '12\\n4 8 4 15 16 8 23 15 16 42 23 42\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '123\\n4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4\\n', 'output': '123\\n'}, {'type': 'stdin_stdout', 'input': '100\\n4 42 23 23 8 42 16 23 42 16 42 8 4 23 4 4 23 42 16 42 23 23 23 42 4 42 8 8 16 23 15 23 16 4 42 15 15 23 16 15 16 4 4 15 23 42 42 15 8 23 8 23 4 15 16 15 42 8 23 16 15 42 23 8 4 16 15 16 23 16 16 4 23 16 8 23 16 15 23 4 4 8 15 4 4 15 8 23 23 4 4 8 8 4 42 15 4 4 42 16\\n', 'output': '64\\n'}, {'type': 'stdin_stdout', 'input': '1\\n42\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100\\n4 42 23 23 8 42 16 23 42 16 42 8 4 23 4 4 23 42 16 42 23 23 23 42 4 42 8 8 16 23 15 23 16 4 42 15 15 23 16 15 16 4 4 15 23 42 42 15 8 23 8 23 4 15 16 16 42 8 23 16 15 42 23 8 4 16 15 16 23 16 16 4 23 16 8 23 16 15 23 4 4 8 15 4 4 15 8 23 23 4 4 8 8 4 42 15 4 4 42 16\\n', 'output': '64\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 8 15 16 15\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '123\\n4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4\\n', 'output': '123\\n'}, {'type': 'stdin_stdout', 'input': '100\\n4 42 23 23 8 42 16 23 42 16 42 8 4 23 4 4 23 42 16 42 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'64\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78393","program":"```python\n_=int(input())\na=list(map(int,input().split()))\nb=[4,8,15,16,23,42]\nc=[0]*6\n\nfor i in range(len(a)):\n x = b.index(a[i])\n if x == 0:\n c[0] +=1\n elif c[x-1]!=0:\n c[x-1]-=1\n c[x]+=1\n \nprint(len(a)-6*c[5])\n```","inputs":"5\n4 8 15 16 23\n","output":"5\n","actual_output":"5\n","execution_success":true,"sample_index":12492},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1195_B. Sport Mafia","prompt":"Solve the following coding problem using the programming language python:\n\nEach evening after the dinner the SIS's students gather together to play the game of Sport Mafia. \n\nFor the tournament, Alya puts candies into the box, which will serve as a prize for a winner. To do that, she performs n actions. The first action performed is to put a single candy into the box. For each of the remaining moves she can choose from two options:\n\n * the first option, in case the box contains at least one candy, is to take exactly one candy out and eat it. This way the number of candies in the box decreased by 1; \n * the second option is to put candies in the box. In this case, Alya will put 1 more candy, than she put in the previous time. \n\n\n\nThus, if the box is empty, then it can only use the second option.\n\nFor example, one possible sequence of Alya's actions look as follows:\n\n * put one candy into the box; \n * put two candies into the box; \n * eat one candy from the box; \n * eat one candy from the box; \n * put three candies into the box; \n * eat one candy from the box; \n * put four candies into the box; \n * eat one candy from the box; \n * put five candies into the box; \n\n\n\nThis way she will perform 9 actions, the number of candies at the end will be 11, while Alya will eat 4 candies in total.\n\nYou know the total number of actions n and the number of candies at the end k. You need to find the total number of sweets Alya ate. That is the number of moves of the first option. It's guaranteed, that for the given n and k the answer always exists.\n\nPlease note, that during an action of the first option, Alya takes out and eats exactly one candy.\n\nInput\n\nThe first line contains two integers n and k (1 \u2264 n \u2264 10^9; 0 \u2264 k \u2264 10^9) \u2014 the total number of moves and the number of candies in the box at the end. \n\nIt's guaranteed, that for the given n and k the answer exists.\n\nOutput\n\nPrint a single integer \u2014 the number of candies, which Alya ate. Please note, that in this problem there aren't multiple possible answers \u2014 the answer is unique for any input data. \n\nExamples\n\nInput\n\n\n1 1\n\n\nOutput\n\n\n0\n\nInput\n\n\n9 11\n\n\nOutput\n\n\n4\n\nInput\n\n\n5 0\n\n\nOutput\n\n\n3\n\nInput\n\n\n3 2\n\n\nOutput\n\n\n1\n\nNote\n\nIn the first example, Alya has made one move only. According to the statement, the first move is always putting one candy in the box. Hence Alya ate 0 candies.\n\nIn the second example the possible sequence of Alya's actions looks as follows: \n\n * put 1 candy, \n * put 2 candies, \n * eat a candy, \n * eat a candy, \n * put 3 candies, \n * eat a candy, \n * put 4 candies, \n * eat a candy, \n * put 5 candies. \n\n\n\nThis way, she will make exactly n=9 actions and in the end the box will contain 1+2-1-1+3-1+4-1+5=11 candies. The answer is 4, since she ate 4 candies in total.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,x=map(int,input().split())\nformula=0\ni=0\nif(n==1):\n print(0)\nelse:\n formula=1000000\n while(abs(n-(i+formula))!=x):\n i=i+1\n formula=(i*(i+1))//2\n print(abs(n-i))\n \n\n \n \n \n \n \n \n \n\n \n\n\n\n \n \n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '9 11\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '107 3295\\n', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '999997 811911683\\n', 'output': '959677\\n'}, {'type': 'stdin_stdout', 'input': '999993 417284432\\n', 'output': '971071\\n'}, {'type': 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'stdin_stdout', 'input': '1003 189032\\n', 'output': '388\\n'}, {'type': 'stdin_stdout', 'input': '9 0\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1007 84070\\n', 'output': '596\\n'}, {'type': 'stdin_stdout', 'input': '999999992 437042862\\n', 'output': '999946383\\n'}, {'type': 'stdin_stdout', 'input': '51002 1000000000\\n', 'output': '6281\\n'}, {'type': 'stdin_stdout', 'input': '100004 114244998\\n', 'output': '84883\\n'}, {'type': 'stdin_stdout', 'input': '1000000000 315152540\\n', 'output': '999948715\\n'}, {'type': 'stdin_stdout', 'input': '18 26\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '7 13\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '8 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '18 2\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '104 3381\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '13 1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '20 7\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '20 0\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '28 7\\n', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '11 3\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5 9\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '102 2243\\n', 'output': '35\\n'}, {'type': 'stdin_stdout', 'input': '14 0\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '14 13\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '9 18\\n', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78397","program":"```python\nn,x=map(int,input().split())\nformula=0\ni=0\nif(n==1):\n print(0)\nelse:\n formula=1000000\n while(abs(n-(i+formula))!=x):\n i=i+1\n formula=(i*(i+1))//2\n print(abs(n-i))\n \n\n \n \n \n \n \n \n \n\n \n\n\n\n \n \n\n\n```","inputs":"1 1\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12493},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1234_D. Distinct Characters Queries","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a string s consisting of lowercase Latin letters and q queries for this string.\n\nRecall that the substring s[l; r] of the string s is the string s_l s_{l + 1} ... s_r. For example, the substrings of \"codeforces\" are \"code\", \"force\", \"f\", \"for\", but not \"coder\" and \"top\".\n\nThere are two types of queries: \n\n * 1~ pos~ c (1 \u2264 pos \u2264 |s|, c is lowercase Latin letter): replace s_{pos} with c (set s_{pos} := c); \n * 2~ l~ r (1 \u2264 l \u2264 r \u2264 |s|): calculate the number of distinct characters in the substring s[l; r]. \n\nInput\n\nThe first line of the input contains one string s consisting of no more than 10^5 lowercase Latin letters.\n\nThe second line of the input contains one integer q (1 \u2264 q \u2264 10^5) \u2014 the number of queries.\n\nThe next q lines contain queries, one per line. Each query is given in the format described in the problem statement. It is guaranteed that there is at least one query of the second type.\n\nOutput\n\nFor each query of the second type print the answer for it \u2014 the number of distinct characters in the required substring in this query.\n\nExamples\n\nInput\n\n\nabacaba\n5\n2 1 4\n1 4 b\n1 5 b\n2 4 6\n2 1 7\n\n\nOutput\n\n\n3\n1\n2\n\n\nInput\n\n\ndfcbbcfeeedbaea\n15\n1 6 e\n1 4 b\n2 6 14\n1 7 b\n1 12 c\n2 6 8\n2 1 6\n1 7 c\n1 2 f\n1 10 a\n2 7 9\n1 10 a\n1 14 b\n1 1 f\n2 1 11\n\n\nOutput\n\n\n5\n2\n5\n2\n6\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\n\n\ndef upd(bit, idx, inc):\n while idx < len(bit):\n bit[idx] += inc\n idx += idx & -idx\n\n\ndef query(bit, idx):\n ret = 0\n while idx > 0:\n ret += bit[idx]\n idx -= idx & -idx\n return ret\n\n\nif __name__ == '__main__':\n input = sys.stdin.readline\n inp = list(input().strip())\n dic = {}\n for i in range(26):\n cur = chr(ord('a') + i)\n arr = [0 for i in range(len(inp) + 1)]\n dic[cur] = arr\n for i in range(len(inp)):\n upd(dic[inp[i]], i + 1, 1)\n\n q = int(input().strip())\n for _ in range(q):\n a, b, c = input().strip().split()\n if a == '1':\n idx = int(b)\n cur_ch = inp[idx - 1]\n upd(dic[cur_ch], idx, -1)\n upd(dic[c], idx, 1)\n inp[idx - 1] = c\n else:\n l = int(b)\n r = int(c)\n ans = 0\n for x in dic:\n ll = query(dic[x], l)\n rr = query(dic[x], r)\n if ll == rr and ll != 0:\n if inp[l - 1] == x:\n ans += 1\n else:\n if rr - ll > 0:\n ans += 1\n print(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '5\\n2\\n5\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'abacaba\\n5\\n2 1 4\\n1 4 b\\n1 5 b\\n2 4 6\\n2 1 7\\n', 'output': '3\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': 'aaab\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'abacaba\\n5\\n2 1 4\\n1 4 b\\n1 5 b\\n2 4 6\\n2 2 7\\n', 'output': '3\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': 'abab\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 a\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '5\\n2\\n5\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 7 b\\n2 6 14\\n1 7 a\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '4\\n2\\n5\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 5 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '6\\n3\\n5\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'aaacaba\\n5\\n2 1 4\\n1 4 b\\n1 5 b\\n2 4 6\\n2 2 7\\n', 'output': '2\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeeabdea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 a\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '5\\n2\\n5\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': 'bbaa\\n1\\n2 2 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 9 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 e\\n2 1 11\\n', 'output': '5\\n2\\n5\\n3\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 2\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '5\\n2\\n2\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 2 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 e\\n2 1 11\\n', 'output': '5\\n2\\n4\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'abacaba\\n5\\n2 1 4\\n1 4 b\\n1 1 b\\n2 4 6\\n2 1 7\\n', 'output': '3\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 5 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 4 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '6\\n3\\n5\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 f\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 e\\n2 1 11\\n', 'output': '5\\n3\\n4\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 3 c\\n2 6 8\\n2 1 6\\n1 9 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 2 b\\n1 1 e\\n2 1 11\\n', 'output': '5\\n2\\n5\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 5 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 4 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 5\\n', 'output': '6\\n3\\n5\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 3 c\\n2 6 8\\n2 1 6\\n1 9 c\\n1 2 f\\n1 10 a\\n2 7 7\\n1 5 a\\n1 2 b\\n1 1 e\\n2 1 11\\n', 'output': '5\\n2\\n5\\n1\\n5\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 8 f\\n1 4 b\\n2 6 14\\n1 7 c\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 e\\n2 1 11\\n', 'output': '6\\n2\\n4\\n3\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 5 e\\n1 4 b\\n2 10 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '4\\n3\\n5\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 4 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 9 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 e\\n2 1 11\\n', 'output': '6\\n3\\n4\\n3\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 3 c\\n2 6 8\\n2 1 6\\n1 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9 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 e\\n2 1 1\\n', 'output': '4\\n2\\n4\\n3\\n1\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 1 e\\n1 4 b\\n2 10 15\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 11\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '4\\n3\\n4\\n4\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 8 f\\n1 4 b\\n2 6 14\\n1 7 d\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 4 f\\n1 10 a\\n2 7 14\\n1 2 a\\n1 14 b\\n1 1 e\\n2 1 11\\n', 'output': '6\\n3\\n4\\n5\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'decbbcfeeedbafa\\n15\\n1 1 e\\n1 4 b\\n2 10 15\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 11\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '5\\n3\\n3\\n4\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 g\\n2 1 11\\n', 'output': '5\\n2\\n5\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': 'abbb\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'abaa\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'baba\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'bbba\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'aaac\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '5\\n2\\n5\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'bbab\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'bbaa\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'aaba\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'baaa\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 e\\n2 1 11\\n', 'output': '5\\n2\\n5\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeeabdea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 a\\n1 12 c\\n2 6 7\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '5\\n2\\n5\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': 'aaac\\n1\\n2 2 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'aaba\\n1\\n2 2 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 b\\n1 3 c\\n2 6 8\\n2 1 6\\n1 9 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 e\\n2 1 11\\n', 'output': '5\\n2\\n5\\n3\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'abba\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'abacaba\\n5\\n2 2 4\\n1 4 b\\n1 1 b\\n2 4 6\\n2 1 7\\n', 'output': '3\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 f\\n1 4 b\\n2 6 14\\n1 7 c\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 e\\n2 1 11\\n', 'output': '5\\n3\\n4\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 c\\n2 6 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '5\\n2\\n5\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'abacaba\\n5\\n2 1 4\\n1 4 b\\n1 5 a\\n2 4 6\\n2 1 7\\n', 'output': '3\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': 'caaa\\n1\\n2 4 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeedbaea\\n15\\n1 6 e\\n1 4 b\\n2 7 14\\n1 7 b\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 f\\n1 10 a\\n2 7 9\\n1 5 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '5\\n2\\n5\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'dfcbbcfeeeabdea\\n15\\n1 6 e\\n1 4 b\\n2 6 14\\n1 7 a\\n1 12 c\\n2 6 8\\n2 1 6\\n1 7 c\\n1 2 g\\n1 10 a\\n2 7 9\\n1 10 a\\n1 14 b\\n1 1 f\\n2 1 11\\n', 'output': '5\\n2\\n5\\n2\\n6\\n'}, 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'6\\n3\\n4\\n3\\n6\\n'}, {'type': 'stdin_stdout', 'input': 'abacaba\\n5\\n2 1 4\\n1 4 b\\n1 4 b\\n2 4 6\\n2 1 7\\n', 'output': '3\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': 'abacaba\\n5\\n2 1 4\\n1 4 b\\n1 5 c\\n2 4 6\\n2 2 7\\n', 'output': '3\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'bbab\\n1\\n2 3 4\\n', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78405","program":"```python\nimport sys\n\n\ndef upd(bit, idx, inc):\n while idx < len(bit):\n bit[idx] += inc\n idx += idx & -idx\n\n\ndef query(bit, idx):\n ret = 0\n while idx > 0:\n ret += bit[idx]\n idx -= idx & -idx\n return ret\n\n\nif __name__ == '__main__':\n input = sys.stdin.readline\n inp = list(input().strip())\n dic = {}\n for i in range(26):\n cur = chr(ord('a') + i)\n arr = [0 for i in range(len(inp) + 1)]\n dic[cur] = arr\n for i in range(len(inp)):\n upd(dic[inp[i]], i + 1, 1)\n\n q = int(input().strip())\n for _ in range(q):\n a, b, c = input().strip().split()\n if a == '1':\n idx = int(b)\n cur_ch = inp[idx - 1]\n upd(dic[cur_ch], idx, -1)\n upd(dic[c], idx, 1)\n inp[idx - 1] = c\n else:\n l = int(b)\n r = int(c)\n ans = 0\n for x in dic:\n ll = query(dic[x], l)\n rr = query(dic[x], r)\n if ll == rr and ll != 0:\n if inp[l - 1] == x:\n ans += 1\n else:\n if rr - ll > 0:\n ans += 1\n print(ans)\n\n```","inputs":"dfcbbcfeeedbaea\n15\n1 6 e\n1 4 b\n2 6 14\n1 7 b\n1 12 c\n2 6 8\n2 1 6\n1 7 c\n1 2 f\n1 10 a\n2 7 9\n1 10 a\n1 14 b\n1 1 f\n2 1 11\n","output":"5\n2\n5\n2\n6\n","actual_output":"5\n2\n5\n2\n6\n","execution_success":true,"sample_index":12494},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1253_C. Sweets Eating","prompt":"Solve the following coding problem using the programming language python:\n\nTsumugi brought n delicious sweets to the Light Music Club. They are numbered from 1 to n, where the i-th sweet has a sugar concentration described by an integer a_i.\n\nYui loves sweets, but she can eat at most m sweets each day for health reasons.\n\nDays are 1-indexed (numbered 1, 2, 3, \u2026). Eating the sweet i at the d-th day will cause a sugar penalty of (d \u22c5 a_i), as sweets become more sugary with time. A sweet can be eaten at most once.\n\nThe total sugar penalty will be the sum of the individual penalties of each sweet eaten.\n\nSuppose that Yui chooses exactly k sweets, and eats them in any order she wants. What is the minimum total sugar penalty she can get?\n\nSince Yui is an undecided girl, she wants you to answer this question for every value of k between 1 and n.\n\nInput\n\nThe first line contains two integers n and m (1 \u2264 m \u2264 n \u2264 200\\ 000).\n\nThe second line contains n integers a_1, a_2, \u2026, a_n (1 \u2264 a_i \u2264 200\\ 000).\n\nOutput\n\nYou have to output n integers x_1, x_2, \u2026, x_n on a single line, separed by spaces, where x_k is the minimum total sugar penalty Yui can get if she eats exactly k sweets.\n\nExamples\n\nInput\n\n\n9 2\n6 19 3 4 4 2 6 7 8\n\n\nOutput\n\n\n2 5 11 18 30 43 62 83 121\n\n\nInput\n\n\n1 1\n7\n\n\nOutput\n\n\n7\n\nNote\n\nLet's analyze the answer for k = 5 in the first example. Here is one of the possible ways to eat 5 sweets that minimize total sugar penalty:\n\n * Day 1: sweets 1 and 4 \n * Day 2: sweets 5 and 3 \n * Day 3 : sweet 6 \n\n\n\nTotal penalty is 1 \u22c5 a_1 + 1 \u22c5 a_4 + 2 \u22c5 a_5 + 2 \u22c5 a_3 + 3 \u22c5 a_6 = 6 + 4 + 8 + 6 + 6 = 30. We can prove that it's the minimum total sugar penalty Yui can achieve if she eats 5 sweets, hence x_5 = 30.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,m = list(map(int,input().split()))\na = list(map(int,input().split()))\na.sort()\nf = [0] * 1000000\nsum = [0] * 1000000\nfor i in range(n):\n sum[i] = sum[i - 1] + a[i]\nfor i in range(n):\n f[i] = f[i - m] + sum[i]\n print(f[i], end = \" \")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 1\\n7\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '9 2\\n6 19 3 4 4 2 6 7 8\\n', 'output': '2 5 11 18 30 43 62 83 121\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n98816 43061 167639 85627 15007\\n', 'output': '15007 58068 143695 242511 410150\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n135072 38422\\n', 'output': '38422 211916\\n'}, {'type': 'stdin_stdout', 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14423 84443 105083 21782 130813 42829 98759 60103 198520 125068 59611 45609 124003 106143 54167 179002 103755 152802 146640 38512 111216 6660 131534 32533 67324 27272 49166 129157 41630\\n', 'output': '6660 15652 30075 51857 73675 100947 133480 171992 213622 256451 302060 351226 405393 471664 540759 622506 721809 826828 938543 1069835 1212102 1358815 1507787 1664612 1837781 2017016 2212444 2412352 2624969 2855806 3107465 3371982 3668097 3979163 4300861 4628835 4984180 \\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n3751 6003 92340 28129\\n', 'output': '3751 9754 41634 139977 \\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n15392 61512 45205 23445 51894\\n', 'output': '15392 54229 138271 274207 471655 \\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n100149 57949 44886 8167\\n', 'output': '8167 53053 111002 219318 \\n'}, {'type': 'stdin_stdout', 'input': '9 2\\n9 19 5 3 4 2 6 7 8\\n', 'output': '2 5 11 19 31 46 66 90 129 \\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n6052 42201\\n', 'output': '6052 54305 \\n'}, {'type': 'stdin_stdout', 'input': '37 23\\n164823 8992 21818 77521 130870 83201 174985 168799 9565 84443 105083 21782 130813 42829 98759 60103 198520 125068 59611 81797 35216 106143 54167 179002 103755 152802 146640 38512 91309 6660 131534 32533 67324 27272 49166 129157 41630\\n', 'output': '6660 15652 25217 46999 68817 96089 128622 163838 202350 243980 286809 335975 390142 449753 509856 577180 654701 736498 819699 904142 995451 1094210 1197965 1309708 1424843 1559476 1710415 1863046 2021188 2185255 2367111 2558425 2764878 2976506 3200657 3433826 3691957 \\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n16725 4342 41840 28129\\n', 'output': '4342 21067 53538 112103 \\n'}, {'type': 'stdin_stdout', 'input': '9 2\\n14 19 0 4 4 2 12 7 8\\n', 'output': '0 2 6 12 23 37 60 88 130 \\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n16725 601 126389 28129\\n', 'output': '601 17326 45455 172445 \\n'}, {'type': 'stdin_stdout', 'input': '9 2\\n13 19 0 4 8 3 6 7 8\\n', 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'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78409","program":"```python\nn,m = list(map(int,input().split()))\na = list(map(int,input().split()))\na.sort()\nf = [0] * 1000000\nsum = [0] * 1000000\nfor i in range(n):\n sum[i] = sum[i - 1] + a[i]\nfor i in range(n):\n f[i] = f[i - m] + sum[i]\n print(f[i], end = \" \")\n\n```","inputs":"1 1\n7\n","output":"7\n","actual_output":"7 ","execution_success":true,"sample_index":12495},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1277_B. Make Them Odd","prompt":"Solve the following coding problem using the programming language python:\n\nThere are n positive integers a_1, a_2, ..., a_n. For the one move you can choose any even value c and divide by two all elements that equal c.\n\nFor example, if a=[6,8,12,6,3,12] and you choose c=6, and a is transformed into a=[3,8,12,3,3,12] after the move.\n\nYou need to find the minimal number of moves for transforming a to an array of only odd integers (each element shouldn't be divisible by 2).\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 10^4) \u2014 the number of test cases in the input. Then t test cases follow.\n\nThe first line of a test case contains n (1 \u2264 n \u2264 2\u22c510^5) \u2014 the number of integers in the sequence a. The second line contains positive integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 10^9).\n\nThe sum of n for all test cases in the input doesn't exceed 2\u22c510^5.\n\nOutput\n\nFor t test cases print the answers in the order of test cases in the input. The answer for the test case is the minimal number of moves needed to make all numbers in the test case odd (i.e. not divisible by 2).\n\nExample\n\nInput\n\n\n4\n6\n40 6 40 3 20 1\n1\n1024\n4\n2 4 8 16\n3\n3 1 7\n\n\nOutput\n\n\n4\n10\n4\n0\n\nNote\n\nIn the first test case of the example, the optimal sequence of moves can be as follows:\n\n * before making moves a=[40, 6, 40, 3, 20, 1]; \n * choose c=6; \n * now a=[40, 3, 40, 3, 20, 1]; \n * choose c=40; \n * now a=[20, 3, 20, 3, 20, 1]; \n * choose c=20; \n * now a=[10, 3, 10, 3, 10, 1]; \n * choose c=10; \n * now a=[5, 3, 5, 3, 5, 1] \u2014 all numbers are odd. \n\n\n\nThus, all numbers became odd after 4 moves. In 3 or fewer moves, you cannot make them all odd.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfor _ in range(int(input())):\n n=int(input())\n a=[int(y) for y in input().split()]\n a=sorted(a)\n a=a[::-1]\n d={}\n count=0\n for i in range(n):\n d[a[i]]=0\n for i in range(n):\n if(d[a[i]] == 0):\n s=a[i]\n while(a[i]%2==0):\n a[i]/=2\n \n count+=1\n t=a[i]\n if t in d and d[t]==0:\n d[t]=1\n d[s]=1\n print(count) \n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n6\\n40 6 40 3 20 1\\n1\\n1024\\n4\\n2 4 8 16\\n3\\n3 1 7\\n', 'output': '4\\n10\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n40 6 40 3 20 1\\n1\\n2020\\n4\\n2 4 8 16\\n3\\n3 1 7\\n', 'output': '4\\n2\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n22 6 40 3 20 1\\n1\\n2020\\n4\\n2 4 8 16\\n3\\n3 1 7\\n', 'output': '5\\n2\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n37 6 40 3 20 1\\n1\\n1024\\n4\\n2 4 8 16\\n3\\n3 1 7\\n', 'output': '4\\n10\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n22 6 40 3 20 1\\n1\\n2038\\n4\\n2 4 8 30\\n1\\n3 1 7\\n', 'output': '5\\n1\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n22 6 18 5 20 1\\n1\\n311\\n4\\n2 4 8 16\\n3\\n3 1 7\\n', 'output': '5\\n0\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n40 6 40 2 20 1\\n1\\n1024\\n4\\n2 4 8 16\\n3\\n3 1 7\\n', 'output': '5\\n10\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n22 6 32 3 20 1\\n1\\n2020\\n4\\n2 4 8 30\\n3\\n3 1 7\\n', 'output': '9\\n2\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n37 6 40 3 20 1\\n1\\n1024\\n4\\n2 6 8 16\\n3\\n3 1 7\\n', 'output': '4\\n10\\n5\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n40 6 40 3 40 1\\n1\\n2020\\n4\\n2 4 8 16\\n3\\n6 1 7\\n', 'output': '4\\n2\\n4\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n22 6 40 3 34 1\\n1\\n2038\\n4\\n2 4 8 30\\n1\\n3 1 7\\n', 'output': '6\\n1\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n40 8 40 3 20 1\\n1\\n2020\\n4\\n2 4 1 16\\n3\\n3 1 7\\n', 'output': '6\\n2\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n37 6 40 3 20 1\\n1\\n1024\\n4\\n2 6 10 16\\n3\\n3 1 7\\n', 'output': '4\\n10\\n6\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n22 6 40 3 34 2\\n1\\n2038\\n4\\n2 4 8 30\\n1\\n3 1 7\\n', 'output': '7\\n1\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n40 6 40 5 40 1\\n1\\n2020\\n4\\n2 4 8 32\\n3\\n6 1 7\\n', 'output': '4\\n2\\n5\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n40 6 40 5 40 1\\n1\\n2020\\n4\\n2 4 8 32\\n3\\n6 2 7\\n', 'output': '4\\n2\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n22 6 32 3 19 2\\n1\\n2020\\n4\\n1 4 8 30\\n2\\n3 1 7\\n', 'output': '7\\n2\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n22 6 18 3 20 1\\n1\\n2020\\n4\\n2 4 8 16\\n3\\n2 1 7\\n', 'output': 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20 1\\n1\\n2020\\n4\\n3 4 8 30\\n3\\n3 1 7\\n', 'output': '8\\n2\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n4 6 40 3 34 2\\n1\\n2038\\n4\\n2 4 8 30\\n2\\n3 1 7\\n', 'output': '7\\n1\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n40 6 40 3 20 2\\n1\\n1024\\n4\\n2 4 8 16\\n3\\n3 2 7\\n', 'output': '5\\n10\\n4\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n22 6 32 3 21 2\\n1\\n2020\\n4\\n1 4 10 30\\n2\\n3 1 7\\n', 'output': '7\\n2\\n4\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n40 6 40 3 20 1\\n1\\n2020\\n4\\n3 4 8 16\\n3\\n2 1 11\\n', 'output': '4\\n2\\n4\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6\\n37 6 40 3 11 1\\n1\\n1619\\n4\\n2 4 8 16\\n3\\n3 1 7\\n', 'output': '4\\n0\\n4\\n0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78413","program":"```python\nfor _ in range(int(input())):\n n=int(input())\n a=[int(y) for y in input().split()]\n a=sorted(a)\n a=a[::-1]\n d={}\n count=0\n for i in range(n):\n d[a[i]]=0\n for i in range(n):\n if(d[a[i]] == 0):\n s=a[i]\n while(a[i]%2==0):\n a[i]/=2\n \n count+=1\n t=a[i]\n if t in d and d[t]==0:\n d[t]=1\n d[s]=1\n print(count) \n \n```","inputs":"4\n6\n40 6 40 3 20 1\n1\n1024\n4\n2 4 8 16\n3\n3 1 7\n","output":"4\n10\n4\n0\n","actual_output":"4\n10\n4\n0\n","execution_success":true,"sample_index":12496},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1320_C. World of Darkraft: Battle for Azathoth","prompt":"Solve the following coding problem using the programming language python:\n\nRoma is playing a new expansion for his favorite game World of Darkraft. He made a new character and is going for his first grind.\n\nRoma has a choice to buy exactly one of n different weapons and exactly one of m different armor sets. Weapon i has attack modifier a_i and is worth ca_i coins, and armor set j has defense modifier b_j and is worth cb_j coins.\n\nAfter choosing his equipment Roma can proceed to defeat some monsters. There are p monsters he can try to defeat. Monster k has defense x_k, attack y_k and possesses z_k coins. Roma can defeat a monster if his weapon's attack modifier is larger than the monster's defense, and his armor set's defense modifier is larger than the monster's attack. That is, a monster k can be defeated with a weapon i and an armor set j if a_i > x_k and b_j > y_k. After defeating the monster, Roma takes all the coins from them. During the grind, Roma can defeat as many monsters as he likes. Monsters do not respawn, thus each monster can be defeated at most one.\n\nThanks to Roma's excessive donations, we can assume that he has an infinite amount of in-game currency and can afford any of the weapons and armor sets. Still, he wants to maximize the profit of the grind. The profit is defined as the total coins obtained from all defeated monsters minus the cost of his equipment. Note that Roma must purchase a weapon and an armor set even if he can not cover their cost with obtained coins.\n\nHelp Roma find the maximum profit of the grind.\n\nInput\n\nThe first line contains three integers n, m, and p (1 \u2264 n, m, p \u2264 2 \u22c5 10^5) \u2014 the number of available weapons, armor sets and monsters respectively.\n\nThe following n lines describe available weapons. The i-th of these lines contains two integers a_i and ca_i (1 \u2264 a_i \u2264 10^6, 1 \u2264 ca_i \u2264 10^9) \u2014 the attack modifier and the cost of the weapon i.\n\nThe following m lines describe available armor sets. The j-th of these lines contains two integers b_j and cb_j (1 \u2264 b_j \u2264 10^6, 1 \u2264 cb_j \u2264 10^9) \u2014 the defense modifier and the cost of the armor set j.\n\nThe following p lines describe monsters. The k-th of these lines contains three integers x_k, y_k, z_k (1 \u2264 x_k, y_k \u2264 10^6, 1 \u2264 z_k \u2264 10^3) \u2014 defense, attack and the number of coins of the monster k.\n\nOutput\n\nPrint a single integer \u2014 the maximum profit of the grind.\n\nExample\n\nInput\n\n\n2 3 3\n2 3\n4 7\n2 4\n3 2\n5 11\n1 2 4\n2 1 6\n3 4 6\n\n\nOutput\n\n\n1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# quick input by @c1729 and @pajenegod\nimport io,os\ninput = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline\n\nfrom bisect import bisect_right\nfrom operator import itemgetter\n\nclass SegmTree:\n '''\n - increment on interval\n - get max on interval\n '''\n def __init__(self, size):\n N = 1\n h = 0\n while N < size:\n N <<= 1\n h += 1\n self.N = N\n self.h = h\n self.t = [0] * (2 * N)\n self.d = [0] * N\n \n def apply(self, p, value):\n self.t[p] += value\n if p < self.N:\n self.d[p] += value\n \n def build(self, p):\n t = self.t\n d = self.d\n while p > 1:\n p >>= 1\n t[p] = max(t[p<<1], t[p<<1|1]) + d[p]\n \n def rebuild(self):\n t = self.t\n for p in reversed(range(1, self.N)):\n t[p] = max(t[p<<1], t[p<<1|1])\n \n def push(self, p):\n d = self.d\n for s in range(self.h, 0, -1):\n i = p >> s\n if d[i] != 0:\n self.apply(i<<1, d[i])\n self.apply(i<<1|1, d[i])\n d[i] = 0\n \n def inc(self, l, r, value):\n if l >= r:\n return\n \n l += self.N\n r += self.N\n l0, r0 = l, r\n while l < r:\n if l & 1:\n self.apply(l, value)\n l += 1\n if r & 1:\n r -= 1\n self.apply(r, value)\n l >>= 1\n r >>= 1\n self.build(l0)\n self.build(r0 - 1)\n \n def query(self, l, r):\n if l >= r:\n return -float('inf')\n \n t = self.t\n l += self.N\n r += self.N\n self.push(l)\n self.push(r - 1)\n res = -float('inf')\n while l < r:\n if l & 1:\n res = max(res, t[l])\n l += 1\n if r & 1:\n r -= 1\n res = max(t[r], res)\n l >>= 1\n r >>= 1\n return res\n\n\nn, m, p = map(int, input().split())\nweapon = []\nfor _ in range(n):\n a, ca = map(int, input().split())\n # a, ca = n - _, n - _\n weapon.append((a, ca))\n\ndefense = []\nfor _ in range(m):\n b, cb = map(int, input().split())\n # b, cb = m - _, m - _\n defense.append((b, cb))\n\nmonster = []\nfor _ in range(p):\n x, y, z = map(int, input().split())\n # x, y, z = p - _, p - _, p - _\n monster.append((x, y, z))\n\nweapon.sort(key=itemgetter(0))\ndefense.sort(key=itemgetter(0))\nmonster.sort(key=itemgetter(0))\n\n# store score of each defense item\nst = SegmTree(m)\nN, t = st.N, st.t\nfor i, (b, cb) in enumerate(defense):\n t[i + N] = -cb\nst.rebuild()\n\ni = 0\nmaxScore = -float('inf')\nfor a, ca in weapon:\n st.inc(0, m, -ca)\n while i < p and monster[i][0] < a:\n x, y, z = monster[i]\n goodDef = bisect_right(defense, (y + 1, 0))\n st.inc(goodDef, m, z)\n i += 1\n currScore = st.query(0, m)\n maxScore = max(maxScore, currScore)\n st.inc(0, m, ca)\nprint(maxScore)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 3 3\\n2 3\\n4 7\\n2 4\\n3 2\\n5 11\\n1 2 4\\n2 1 6\\n3 4 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 4 5\\n5 10\\n6 2\\n10 3\\n9 5\\n7 7\\n4 3\\n9 2\\n3 6\\n7 1 6\\n8 3 2\\n2 6 9\\n3 8 2\\n1 2 9\\n', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n6 1010\\n9 1153\\n9 1159\\n9 1150\\n7 1058\\n9 1159\\n7 3 172\\n10 3 167\\n6 6 160\\n', 'output': '-1879\\n'}, {'type': 'stdin_stdout', 'input': '1 2 1\\n2 2\\n2 1\\n2 2\\n1 1 1\\n', 'output': '-2\\n'}, {'type': 'stdin_stdout', 'input': '10 10 10\\n51 87\\n68 743\\n82 1284\\n73 936\\n55 242\\n89 1554\\n58 357\\n66 666\\n62 512\\n51 87\\n92 1670\\n56 280\\n56 280\\n91 1631\\n77 1091\\n89 1554\\n61 473\\n98 1901\\n77 1091\\n77 1091\\n86 15 386\\n43 58 386\\n68 33 386\\n39 62 386\\n95 6 386\\n74 27 386\\n94 7 386\\n17 84 386\\n97 4 386\\n45 56 386\\n', 'output': '212\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n1 100\\n1 100\\n2 2 1\\n', 'output': '-200\\n'}, {'type': 'stdin_stdout', 'input': '4 4 5\\n5 10\\n6 2\\n10 3\\n9 5\\n7 7\\n4 3\\n9 2\\n2 6\\n7 1 6\\n8 3 2\\n2 6 9\\n3 8 2\\n1 2 9\\n', 'output': '23'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n6 1010\\n9 1153\\n17 1159\\n9 1150\\n7 1058\\n9 1159\\n7 3 172\\n10 3 167\\n6 6 160\\n', 'output': '-1718'}, {'type': 'stdin_stdout', 'input': '1 2 1\\n2 2\\n2 1\\n2 3\\n1 1 1\\n', 'output': '-2'}, {'type': 'stdin_stdout', 'input': '10 10 10\\n51 87\\n68 743\\n1 1284\\n73 936\\n55 242\\n89 1554\\n58 357\\n66 666\\n62 512\\n51 87\\n92 1670\\n56 280\\n56 280\\n91 1631\\n77 1091\\n89 1554\\n61 473\\n98 1901\\n77 1091\\n77 1091\\n86 15 386\\n43 58 386\\n68 33 386\\n39 62 386\\n95 6 386\\n74 27 386\\n94 7 386\\n17 84 386\\n97 4 386\\n45 56 386\\n', 'output': '212'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n1 100\\n1 100\\n2 4 1\\n', 'output': '-200'}, {'type': 'stdin_stdout', 'input': '2 3 3\\n2 3\\n4 7\\n2 6\\n3 2\\n5 11\\n1 2 4\\n2 1 6\\n3 4 6\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '4 4 5\\n5 10\\n6 2\\n10 3\\n9 5\\n7 7\\n4 0\\n9 3\\n2 6\\n7 1 6\\n8 3 2\\n2 6 9\\n3 8 2\\n1 2 9\\n', 'output': '22'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1010\\n9 1153\\n17 625\\n9 1729\\n7 1058\\n9 1159\\n7 3 172\\n10 3 167\\n6 6 160\\n', 'output': '-1184'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1010\\n9 1153\\n17 625\\n9 1729\\n7 1058\\n9 1159\\n7 3 172\\n10 3 158\\n6 6 160\\n', 'output': '-1193'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1010\\n9 1153\\n17 625\\n9 1729\\n7 1058\\n9 1159\\n7 3 172\\n10 3 56\\n6 6 160\\n', 'output': '-1295'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n6 1010\\n9 1012\\n9 1159\\n9 1150\\n7 1058\\n9 1159\\n7 3 172\\n10 3 167\\n6 6 160\\n', 'output': '-1738'}, {'type': 'stdin_stdout', 'input': '10 10 10\\n51 87\\n68 743\\n82 1284\\n73 936\\n55 242\\n89 1554\\n58 357\\n93 666\\n62 512\\n51 87\\n92 1670\\n56 280\\n56 280\\n91 1631\\n77 1091\\n89 1554\\n61 473\\n98 1901\\n77 1091\\n77 1091\\n86 15 386\\n43 58 386\\n68 33 386\\n39 62 386\\n95 6 386\\n74 27 386\\n94 7 386\\n17 84 386\\n97 4 386\\n45 56 386\\n', 'output': '791'}, {'type': 'stdin_stdout', 'input': '2 3 3\\n2 3\\n4 7\\n2 4\\n3 1\\n5 11\\n1 2 4\\n2 1 6\\n3 4 6\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '1 2 1\\n2 2\\n1 1\\n2 3\\n1 1 1\\n', 'output': '-3'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1010\\n9 1153\\n17 625\\n9 1729\\n7 1058\\n9 1159\\n7 3 131\\n10 3 56\\n6 6 160\\n', 'output': '-1336'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1010\\n9 1153\\n17 625\\n9 1729\\n7 1058\\n9 1159\\n3 3 172\\n17 3 56\\n6 6 160\\n', 'output': '-1351'}, {'type': 'stdin_stdout', 'input': '4 4 5\\n5 10\\n6 2\\n10 3\\n9 5\\n7 7\\n4 0\\n9 2\\n2 6\\n7 1 6\\n8 3 2\\n2 6 9\\n3 8 2\\n1 2 9\\n', 'output': '23'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1010\\n9 1153\\n17 1159\\n9 1150\\n7 1058\\n9 1159\\n7 3 172\\n10 3 167\\n6 6 160\\n', 'output': '-1718'}, {'type': 'stdin_stdout', 'input': '1 2 1\\n2 2\\n2 1\\n1 3\\n1 1 1\\n', 'output': '-2'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1010\\n9 1153\\n17 1159\\n9 1729\\n7 1058\\n9 1159\\n7 3 172\\n10 3 167\\n6 6 160\\n', 'output': '-1718'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1010\\n9 1153\\n17 625\\n9 1729\\n7 1058\\n9 1159\\n3 3 172\\n10 3 56\\n6 6 160\\n', 'output': '-1295'}, {'type': 'stdin_stdout', 'input': '4 4 5\\n5 10\\n6 2\\n10 3\\n9 5\\n7 7\\n4 3\\n9 2\\n3 6\\n7 2 6\\n8 3 2\\n2 6 9\\n3 8 2\\n1 2 9\\n', 'output': '23'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n1 100\\n1 100\\n2 0 1\\n', 'output': '-200'}, {'type': 'stdin_stdout', 'input': '4 4 5\\n5 10\\n8 2\\n10 3\\n9 5\\n7 7\\n4 3\\n9 2\\n2 6\\n7 1 6\\n8 3 2\\n2 6 9\\n3 8 2\\n1 2 9\\n', 'output': '23'}, {'type': 'stdin_stdout', 'input': '10 10 10\\n51 87\\n68 743\\n1 1284\\n73 936\\n55 242\\n89 1554\\n58 357\\n66 666\\n62 512\\n51 87\\n92 1670\\n56 280\\n56 280\\n91 2700\\n77 1091\\n89 1554\\n61 473\\n98 1901\\n77 1091\\n77 1091\\n86 15 386\\n43 58 386\\n68 33 386\\n39 62 386\\n95 6 386\\n74 27 386\\n94 7 386\\n17 84 386\\n97 4 386\\n45 56 386\\n', 'output': '212'}, {'type': 'stdin_stdout', 'input': '2 3 3\\n2 2\\n4 7\\n2 6\\n3 2\\n5 11\\n1 2 4\\n2 1 6\\n3 4 6\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '4 4 5\\n5 10\\n6 2\\n10 3\\n9 5\\n7 7\\n4 1\\n9 2\\n2 6\\n7 1 6\\n8 3 2\\n2 6 9\\n3 8 2\\n1 2 9\\n', 'output': '23'}, {'type': 'stdin_stdout', 'input': '1 2 1\\n2 2\\n2 1\\n1 2\\n1 1 1\\n', 'output': '-2'}, {'type': 'stdin_stdout', 'input': '4 4 5\\n5 10\\n6 2\\n10 3\\n9 5\\n7 7\\n4 0\\n9 3\\n1 6\\n7 1 6\\n8 3 2\\n2 6 9\\n3 8 2\\n1 2 9\\n', 'output': '22'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1010\\n9 1153\\n17 625\\n9 1729\\n7 1058\\n9 1159\\n7 3 172\\n10 5 167\\n6 6 160\\n', 'output': '-1184'}, {'type': 'stdin_stdout', 'input': '3 3 3\\n1 1010\\n9 1153\\n14 625\\n9 1729\\n7 1058\\n9 1159\\n7 3 172\\n10 3 158\\n6 6 160\\n', 'output': '-1193'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_78421","program":"```python\n# quick input by @c1729 and @pajenegod\nimport io,os\ninput = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline\n\nfrom bisect import bisect_right\nfrom operator import itemgetter\n\nclass SegmTree:\n '''\n - increment on interval\n - get max on interval\n '''\n def __init__(self, size):\n N = 1\n h = 0\n while N < size:\n N <<= 1\n h += 1\n self.N = N\n self.h = h\n self.t = [0] * (2 * N)\n self.d = [0] * N\n \n def apply(self, p, value):\n self.t[p] += value\n if p < self.N:\n self.d[p] += value\n \n def build(self, p):\n t = self.t\n d = self.d\n while p > 1:\n p >>= 1\n t[p] = max(t[p<<1], t[p<<1|1]) + d[p]\n \n def rebuild(self):\n t = self.t\n for p in reversed(range(1, self.N)):\n t[p] = max(t[p<<1], t[p<<1|1])\n \n def push(self, p):\n d = self.d\n for s in range(self.h, 0, -1):\n i = p >> s\n if d[i] != 0:\n self.apply(i<<1, d[i])\n self.apply(i<<1|1, d[i])\n d[i] = 0\n \n def inc(self, l, r, value):\n if l >= r:\n return\n \n l += self.N\n r += self.N\n l0, r0 = l, r\n while l < r:\n if l & 1:\n self.apply(l, value)\n l += 1\n if r & 1:\n r -= 1\n self.apply(r, value)\n l >>= 1\n r >>= 1\n self.build(l0)\n self.build(r0 - 1)\n \n def query(self, l, r):\n if l >= r:\n return -float('inf')\n \n t = self.t\n l += self.N\n r += self.N\n self.push(l)\n self.push(r - 1)\n res = -float('inf')\n while l < r:\n if l & 1:\n res = max(res, t[l])\n l += 1\n if r & 1:\n r -= 1\n res = max(t[r], res)\n l >>= 1\n r >>= 1\n return res\n\n\nn, m, p = map(int, input().split())\nweapon = []\nfor _ in range(n):\n a, ca = map(int, input().split())\n # a, ca = n - _, n - _\n weapon.append((a, ca))\n\ndefense = []\nfor _ in range(m):\n b, cb = map(int, input().split())\n # b, cb = m - _, m - _\n defense.append((b, cb))\n\nmonster = []\nfor _ in range(p):\n x, y, z = map(int, input().split())\n # x, y, z = p - _, p - _, p - _\n monster.append((x, y, z))\n\nweapon.sort(key=itemgetter(0))\ndefense.sort(key=itemgetter(0))\nmonster.sort(key=itemgetter(0))\n\n# store score of each defense item\nst = SegmTree(m)\nN, t = st.N, st.t\nfor i, (b, cb) in enumerate(defense):\n t[i + N] = -cb\nst.rebuild()\n\ni = 0\nmaxScore = -float('inf')\nfor a, ca in weapon:\n st.inc(0, m, -ca)\n while i < p and monster[i][0] < a:\n x, y, z = monster[i]\n goodDef = bisect_right(defense, (y + 1, 0))\n st.inc(goodDef, m, z)\n i += 1\n currScore = st.query(0, m)\n maxScore = max(maxScore, currScore)\n st.inc(0, m, ca)\nprint(maxScore)\n\n```","inputs":"2 3 3\n2 3\n4 7\n2 4\n3 2\n5 11\n1 2 4\n2 1 6\n3 4 6\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12497},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"133_A. HQ9+","prompt":"Solve the following coding problem using the programming language python:\n\nHQ9+ is a joke programming language which has only four one-character instructions:\n\n * \"H\" prints \"Hello, World!\",\n * \"Q\" prints the source code of the program itself,\n * \"9\" prints the lyrics of \"99 Bottles of Beer\" song, \n * \"+\" increments the value stored in the internal accumulator.\n\n\n\nInstructions \"H\" and \"Q\" are case-sensitive and must be uppercase. The characters of the program which are not instructions are ignored.\n\nYou are given a program written in HQ9+. You have to figure out whether executing this program will produce any output.\n\nInput\n\nThe input will consist of a single line p which will give a program in HQ9+. String p will contain between 1 and 100 characters, inclusive. ASCII-code of each character of p will be between 33 (exclamation mark) and 126 (tilde), inclusive.\n\nOutput\n\nOutput \"YES\", if executing the program will produce any output, and \"NO\" otherwise.\n\nExamples\n\nInput\n\nHi!\n\n\nOutput\n\nYES\n\n\nInput\n\nCodeforces\n\n\nOutput\n\nNO\n\nNote\n\nIn the first case the program contains only one instruction \u2014 \"H\", which prints \"Hello, World!\".\n\nIn the second case none of the program characters are language instructions.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ns=input()\nflag=0\nfor i in range(len(s)):\n\tif(s[i]=='H' or s[i]=='Q' or s[i]=='9'):\n\t\tprint('YES')\n\t\tflag=1\n\t\tbreak\nif flag==0:\n\tprint('NO')\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'Codeforces\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'Hi!\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '!3YPv@2JQ44@)R2O_4`GO\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'Q;R+aay]cL?Zh*uG\"YcmO*@Dts*Gjp}D~M7Z96+<4?9I3aH~0qNdO(RmyRy=ci,s8qD_kwj;QHFzD|5,5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'U_ilyOGMT+QiW/M8/D(1=6a7)_FA,h4`8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'UbkW=UVb>;z6)p@Phr;^Dn.|5O{_i||:Rv|KJ_ay~V(S&Jp\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '!0WKT:$O\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '!:!{~=9*\\\\P;Z6F?HC5GadFz)>k*=u|+\"Cm]ICTmB!`L{&oS/z6b~#Snbp/^\\\\Q>XWU-vY+/dP.7S=-#&whS@,\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'EL|xIP5_+Caon1hPpQ0[8+r@LX4;b?gMy>;/WH)pf@Ur*TiXu*e}b-*%acUA~A?>MDz#!\\\\Uh\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'mzbmweyydiadtlcouegmdbyfwurpwbpuvhifnuapwyndmhtqvkgkbhtytszotwflegsjzzszfwtzfpnscguemwrczqxycivdqnkH\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'Q\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '[:[SN-{r>[l+OggH3v3g{EPC*@YBATT@\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '~\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '+8\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'p-UXsbd&f\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '+++++++++++++++++++++++++++++++++++++++++++++++++++++++++\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'Kba/Q,SL~FMd)3hOWU\\'Jum{9\"$Ld4:GW}D]%tr@G{hpG:PV5-c\\'VIZ~m/6|3I?_4*1luKnOp`%p|0H{[|Y1A~4-ZdX,Rw2[\\\\\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'H+\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'HHHHHHH\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'HQ9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'Hello!\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'VK_Cup_2012!\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'e{}2vQ+/r@p0}cLKNe4MCk\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': \"2Y}\\\\A)>row{~c[g>:'.|ZC8%UTQ/jcdhK%6O)QRC.kd@%y}LJYk=V{G5pQK/yKJ%{G3C\\n\", 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'Uh3>ER](J\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '`WfODc\\\\?#ax~1xu@[ao+o_rN|L7%v,p,nDv>3+6cy.]q3)+A6b!q*Hc+#.t4f~vhUa~$^q\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'tt6l=RHOfStm.;Qd$-}zDes*E,.F7qn5-b%HC\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'O.&=qt(`z(\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'Progopedia\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'juq)k(FT.^G=G\\\\zcqnO\"uJIE1_]KFH9S=1c\"mJ;F9F)%>&.WOdp09+k`Yc6}\"6xw,Aos:M\\\\_^^:xBb[CcsHm?J\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': \"'F!_]tB(x&RFgG2~\\\\(\\n\", 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'Qv)X8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '@F%K2=%RyL/\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '+++H\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'dEHsbM\\'gS[\\\\brZ_dpjXw8f?L[4E\"s4Zc9*(,j:>p$}m7HD[_9nOWQ\\\\uvq2mHWR\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '+Q\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '+/`sAd&eB29E=Nu87${.u6GY@$^a$,}s^!p!F}B-z8<\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '~@Gb(S&N$mBuBUMAky-z^{5VwLNTzYg|ZUZncL@ahS?K*As<$iNUARM3r43J\\'jJB)$ujfPAq\"G]\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '\")1cL>{o\\\\dcYJzu?CefyN^bGRviOH&P7rJS3PT4:0V3F)%\\\\}L=AJouYsj_>j2|7^1NWu*%NbOP>ngv-ls<;b-4Sd3Na0R\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '[u3\"$+!:/.e1#Yly\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'P(^pix\"=oiEZu8?@d@J(I`Xp5TN^T3\\\\Z7P5\"ZrvZ{2Fwz3g-8`U!)(1$a6Jg!yr\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 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'YES\\n'}, {'type': 'stdin_stdout', 'input': '6G_\"Fq#SO4lF}*c`Q;mII9E{4.QodbqN]C\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '}do5RU<(w;oU7[acMIJn*n^bWm!cm3#E7Efr>{g-8bl\"DN4~_=f?[T;~Fq#&)aXq%l%9?aVEi7-{=,[QkHHGBZj2c\"=fhRlWd5;5K|GgU?7h]!;wl@\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': \"Iy^.,Aw*,5+f;l@Q;jLK'G5H-r1Pfmx?ei~`CjMmUe{K:lS9cu4ay8rqRh-W?Gqv!e-j*U)!Mzn{E8B6%~aSZ~iQ_QwlC9_cX(o8\\n\", 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '+SE_PgaP6fZ!\\\\6%A}_=y\"3Kf%^>vON,$bwG`U1+C\\\\18^:S},;kw!&4r|z`\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '+H\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '\"3YPv@2JQ44@)R2O_4`GO\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'UbkW=UVb>;z6)p@Phr;^Dn.|_O{5i||:Rv|KJ_ay~V(S&Jp\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5,5|DzFHQ;jwk_Dq8s,ic=yRymR(OdNq0~Ha3I9?4<+69Z7M~D}pjG*stD@*OmcY\"Gu*hZ?Lc]yaa+R;Q\\n', 'output': 'YES\\n'}, {'type': 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'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '+SE_PgbP6fZ!\\\\6%A}_=y!3Kf%^>vON Solid lines denote a matched color for the same index. Dashed lines denote a matched color at a different index. x is the number of solid lines, and y is the total number of lines. \n\nYou are given Bob's guess and two values x and y. Can you find one possibility of Alice's code so that the values of x and y are correct?\n\nInput\n\nThe first line contains a single integer t (1\u2264 t\u2264 1000) \u2014 the number of test cases. Next 2t lines contain descriptions of test cases.\n\nThe first line of each test case contains three integers n,x,y (1\u2264 n\u2264 10^5, 0\u2264 x\u2264 y\u2264 n) \u2014 the length of the codes, and two values Alice responds with.\n\nThe second line of each test case contains n integers b_1,\u2026,b_n (1\u2264 b_i\u2264 n+1) \u2014 Bob's guess, where b_i is the i-th color of the guess.\n\nIt is guaranteed that the sum of n across all test cases does not exceed 10^5.\n\nOutput\n\nFor each test case, on the first line, output \"YES\" if there is a solution, or \"NO\" if there is no possible secret code consistent with the described situation. You can print each character in any case (upper or lower).\n\nIf the answer is \"YES\", on the next line output n integers a_1,\u2026,a_n (1\u2264 a_i\u2264 n+1) \u2014 Alice's secret code, where a_i is the i-th color of the code.\n\nIf there are multiple solutions, output any.\n\nExample\n\nInput\n\n\n7\n5 2 4\n3 1 1 2 5\n5 3 4\n1 1 2 1 2\n4 0 4\n5 5 3 3\n4 1 4\n2 3 2 3\n6 1 2\n3 2 1 1 1 1\n6 2 4\n3 3 2 1 1 1\n6 2 6\n1 1 3 2 1 1\n\n\nOutput\n\n\nYES\n3 1 6 1 2\nYES\n3 1 1 1 2\nYES\n3 3 5 5\nNO\nYES\n4 4 4 4 3 1\nYES\n3 1 3 1 7 7\nYES\n2 3 1 1 1 1\n\nNote\n\nThe first test case is described in the statement.\n\nIn the second test case, x=3 because the colors are equal at indices 2,4,5. And y=4 because they share the colors 1,1,1,2.\n\nIn the third test case, x=0 because there is no index where the colors are the same. But y=4 because they share the colors 3,3,5,5.\n\nIn the fourth test case, it can be proved that no solution exists.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom sys import stdin, stdout\nfrom collections import defaultdict\nfrom heapq import heapify, heappop, heappush\ndef solve():\n n, s, y = map(int, stdin.readline().split())\n a = stdin.readline().split()\n d = defaultdict(list)\n for i, x in enumerate(a):\n d[x].append(i)\n for i in range(1, n + 2):\n e = str(i)\n if e not in d:\n break\n q = [(-len(d[x]), x) for x in d.keys()]\n heapify(q)\n ans = [0] * n\n for i in range(s):\n l, x = heappop(q)\n ans[d[x].pop()] = x\n l += 1\n if l:\n heappush(q, (l, x))\n p = []\n while q:\n l, x = heappop(q)\n p.extend(d[x])\n if p:\n h = (n - s) // 2\n y = n - y\n q = p[h:] + p[:h]\n for x, z in zip(p, q):\n if a[x] == a[z]:\n if y:\n ans[x] = e\n y -= 1\n else:\n stdout.write(\"NO\\n\")\n return\n else:\n ans[x] = a[z]\n for i in range(n - s):\n if y and ans[p[i]] != e:\n ans[p[i]] = e\n y -= 1\n stdout.write(\"YES\\n\")\n stdout.write(' '.join(ans))\n stdout.write(\"\\n\")\n\nT = int(stdin.readline())\nfor t in range(T):\n solve()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 1 1 2 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n5 1 1 4 2\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 1 1 2 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n5 1 1 4 2\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 0 0\\n1\\n1 0 0\\n2\\n1 0 1\\n1\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n2\\n', 'output': 'YES\\n2 \\nYES\\n1 \\nNO\\nNO\\nYES\\n1 \\nYES\\n2 \\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 1 1 2 5\\n5 3 0\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n5 1 1 4 2\\nYES\\n3 1 3 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n1\\n1 0 0\\n2\\n1 0 1\\n1\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n2\\n', 'output': 'YES\\n2\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 1 1 2 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 0 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n5 1 1 4 2\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 1 4 4 4 4\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 0 4\\n3 1 1 2 5\\n5 3 0\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n1 4 3 5 1\\nYES\\n3 1 3 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n1\\n1 0 0\\n2\\n1 0 1\\n1\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n0\\n', 'output': 'YES\\n2\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 8\\n3 1 1 2 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 0 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n4 1 1 4 4\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 1 4 4 4 4\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 0 4\\n3 1 1 2 5\\n5 3 0\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 0 1\\n', 'output': 'YES\\n1 4 3 5 1\\nYES\\n3 1 3 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nYES\\n3 1 1 0 2 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n0\\n1 0 0\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n0\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n0\\n1 0 0\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 0 0\\n1\\n1 1 2\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n2\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 2 1 2 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n5 4 1 2 2\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 1 1 2 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 2\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n5 1 1 4 2\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 4 4 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 1 1 4 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 0 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n2 1 1 5 3\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 1 4 4 4 4\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 0 4\\n3 1 1 2 5\\n5 4 0\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n1 4 3 5 1\\nYES\\n1 1 3 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 8\\n3 1 1 2 5\\n5 3 4\\n1 1 2 1 2\\n4 0 7\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 0 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n4 1 1 4 4\\nYES\\n3 1 1 1 2\\nYES\\n1 1 1 1\\nNO\\nYES\\n1 1 4 4 4 4\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 0 4\\n3 1 1 2 5\\n5 3 0\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 0 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 0 1\\n', 'output': 'YES\\n1 4 3 5 1\\nYES\\n3 1 3 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 1 4 4 4 4\\nYES\\n4 4 3 3 1 1\\nYES\\n3 1 1 0 2 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 1\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n-1\\n', 'output': 'YES\\n1\\nNO\\nNO\\nNO\\nYES\\n1\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 1\\n0\\n1 0 0\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 0 0\\n1\\n1 1 2\\n-1\\n', 'output': 'NO\\nYES\\n1\\nNO\\nNO\\nYES\\n2\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 0 1\\n4\\n1 0 1\\n2\\n1 0 0\\n1\\n1 0 0\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n2\\nYES\\n1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 2 1 2 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 1 1 1\\n', 'output': 'YES\\n5 4 1 2 2\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 1 1 2 5\\n5 3 4\\n1 1 4 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 2\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n5 1 1 4 2\\nYES\\n1 1 2 1 3\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 4 4 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n1\\n1 0 0\\n4\\n1 0 1\\n1\\n1 0 1\\n2\\n1 1 1\\n2\\n1 1 1\\n2\\n', 'output': 'YES\\n2\\nYES\\n1\\nNO\\nNO\\nYES\\n2\\nYES\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 1 1 4 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n2 1 1 5 3\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 0 4\\n3 1 1 0 5\\n5 4 0\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n1 2 3 5 1\\nYES\\n1 1 3 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n1\\n1 0 1\\n2\\n1 0 1\\n1\\n1 0 1\\n1\\n1 1 1\\n1\\n1 1 1\\n0\\n', 'output': 'YES\\n2\\nNO\\nNO\\nNO\\nYES\\n1\\nYES\\n0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 8\\n3 1 1 2 5\\n5 3 4\\n1 1 2 1 2\\n4 0 7\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 0 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 4 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n4 1 1 4 4\\nYES\\n3 1 1 1 2\\nYES\\n1 1 1 1\\nNO\\nYES\\n1 1 4 4 4 4\\nYES\\n4 4 3 3 1 1\\nYES\\n1 1 2 3 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n0\\n1 0 -1\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 1\\n2\\n1 1 1\\n0\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n2\\nYES\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 1\\n0\\n1 0 1\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n-1\\n', 'output': 'NO\\nNO\\nNO\\nNO\\nYES\\n1\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 1 1 2 1\\n5 3 4\\n1 1 4 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 1 1 1 1\\n6 2 2\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n1 4 1 3 1\\nYES\\n1 1 2 1 3\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 4 4 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n1\\n1 0 0\\n4\\n1 0 1\\n1\\n1 0 1\\n2\\n1 1 1\\n2\\n1 0 1\\n2\\n', 'output': 'YES\\n2\\nYES\\n1\\nNO\\nNO\\nYES\\n2\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 1 1 4 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n4 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 1 1\\n', 'output': 'YES\\n2 1 1 5 3\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 3 3 3 3 1\\nYES\\n4 4 3 3 1 1\\nYES\\n2 3 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n1\\n1 0 0\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n0\\n', 'output': 'YES\\n2\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 2\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 0\\n1\\n1 1 2\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 0 1\\n4\\n1 0 1\\n2\\n1 0 0\\n1\\n1 1 2\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n2\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 0 1\\n4\\n1 0 1\\n2\\n1 0 0\\n1\\n1 1 0\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n2\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n1\\n1 0 0\\n4\\n1 0 1\\n1\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n2\\n', 'output': 'YES\\n2\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n1\\n1 0 0\\n2\\n1 0 1\\n1\\n1 0 1\\n1\\n1 1 1\\n1\\n1 1 1\\n0\\n', 'output': 'YES\\n2\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -1 0\\n0\\n1 0 -1\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 1\\n0\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 0 1\\n2\\n1 0 1\\n2\\n1 1 1\\n1\\n1 1 2\\n0\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 -1 1\\n4\\n1 0 1\\n2\\n1 0 0\\n1\\n1 1 2\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n2\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 0 4\\n3 1 1 2 5\\n5 3 0\\n1 1 2 1 2\\n4 -1 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 0 2\\n3 2 1 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 2 0 1\\n', 'output': 'YES\\n1 4 3 5 1\\nYES\\n3 1 3 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 1 4 4 4 4\\nYES\\n4 4 3 3 1 1\\nYES\\n3 1 1 0 2 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 -1 1\\n4\\n1 0 1\\n2\\n1 0 0\\n0\\n1 1 2\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n1\\nYES\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 -2 0\\n0\\n1 0 0\\n2\\n1 -1 1\\n4\\n1 0 1\\n2\\n1 0 0\\n1\\n1 0 0\\n-1\\n', 'output': 'YES\\n1\\nYES\\n1\\nNO\\nNO\\nYES\\n2\\nYES\\n1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4\\n3 2 1 2 5\\n5 3 4\\n1 1 2 1 2\\n4 0 4\\n5 5 3 3\\n4 1 4\\n2 3 2 3\\n6 1 2\\n3 2 0 1 1 1\\n6 2 4\\n3 3 2 1 1 1\\n6 2 6\\n1 1 3 1 1 1\\n', 'output': 'YES\\n5 4 1 2 2\\nYES\\n3 1 1 1 2\\nYES\\n3 3 5 5\\nNO\\nYES\\n1 4 4 4 4 1\\nYES\\n4 4 3 3 1 1\\nNO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78433","program":"```python\nfrom sys import stdin, stdout\nfrom collections import defaultdict\nfrom heapq import heapify, heappop, heappush\ndef solve():\n n, s, y = map(int, stdin.readline().split())\n a = stdin.readline().split()\n d = defaultdict(list)\n for i, x in enumerate(a):\n d[x].append(i)\n for i in range(1, n + 2):\n e = str(i)\n if e not in d:\n break\n q = [(-len(d[x]), x) for x in d.keys()]\n heapify(q)\n ans = [0] * n\n for i in range(s):\n l, x = heappop(q)\n ans[d[x].pop()] = x\n l += 1\n if l:\n heappush(q, (l, x))\n p = []\n while q:\n l, x = heappop(q)\n p.extend(d[x])\n if p:\n h = (n - s) // 2\n y = n - y\n q = p[h:] + p[:h]\n for x, z in zip(p, q):\n if a[x] == a[z]:\n if y:\n ans[x] = e\n y -= 1\n else:\n stdout.write(\"NO\\n\")\n return\n else:\n ans[x] = a[z]\n for i in range(n - s):\n if y and ans[p[i]] != e:\n ans[p[i]] = e\n y -= 1\n stdout.write(\"YES\\n\")\n stdout.write(' '.join(ans))\n stdout.write(\"\\n\")\n\nT = int(stdin.readline())\nfor t in range(T):\n solve()\n```","inputs":"7\n5 2 4\n3 1 1 2 5\n5 3 4\n1 1 2 1 2\n4 0 4\n5 5 3 3\n4 1 4\n2 3 2 3\n6 1 2\n3 2 1 1 1 1\n6 2 4\n3 3 2 1 1 1\n6 2 6\n1 1 3 2 1 1\n","output":"YES\n5 1 1 4 2\nYES\n3 1 1 1 2\nYES\n3 3 5 5\nNO\nYES\n1 4 4 4 4 1\nYES\n4 4 3 3 1 1\nYES\n2 3 1 1 1 1\n","actual_output":"YES\n5 1 1 4 2\nYES\n3 1 1 1 2\nYES\n3 3 5 5\nNO\nYES\n1 4 4 4 4 1\nYES\n4 4 3 3 1 1\nYES\n2 3 1 1 1 1\n","execution_success":true,"sample_index":12500},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1401_D. Maximum Distributed Tree","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a tree that consists of n nodes. You should label each of its n-1 edges with an integer in such way that satisfies the following conditions: \n\n * each integer must be greater than 0; \n * the product of all n-1 numbers should be equal to k; \n * the number of 1-s among all n-1 integers must be minimum possible. \n\n\n\nLet's define f(u,v) as the sum of the numbers on the simple path from node u to node v. Also, let \u2211_{i=1}^{n-1} \u2211_{j=i+1}^n f(i,j) be a distribution index of the tree.\n\nFind the maximum possible distribution index you can get. Since answer can be too large, print it modulo 10^9 + 7.\n\nIn this problem, since the number k can be large, the result of the prime factorization of k is given instead.\n\nInput\n\nThe first line contains one integer t (1 \u2264 t \u2264 100) \u2014 the number of test cases.\n\nThe first line of each test case contains a single integer n (2 \u2264 n \u2264 10^5) \u2014 the number of nodes in the tree.\n\nEach of the next n-1 lines describes an edge: the i-th line contains two integers u_i and v_i (1 \u2264 u_i, v_i \u2264 n; u_i \u2260 v_i) \u2014 indices of vertices connected by the i-th edge.\n\nNext line contains a single integer m (1 \u2264 m \u2264 6 \u22c5 10^4) \u2014 the number of prime factors of k.\n\nNext line contains m prime numbers p_1, p_2, \u2026, p_m (2 \u2264 p_i < 6 \u22c5 10^4) such that k = p_1 \u22c5 p_2 \u22c5 \u2026 \u22c5 p_m.\n\nIt is guaranteed that the sum of n over all test cases doesn't exceed 10^5, the sum of m over all test cases doesn't exceed 6 \u22c5 10^4, and the given edges for each test cases form a tree.\n\nOutput\n\nPrint the maximum distribution index you can get. Since answer can be too large, print it modulo 10^9+7.\n\nExample\n\nInput\n\n\n3\n4\n1 2\n2 3\n3 4\n2\n2 2\n4\n3 4\n1 3\n3 2\n2\n3 2\n7\n6 1\n2 3\n4 6\n7 3\n5 1\n3 6\n4\n7 5 13 3\n\n\nOutput\n\n\n17\n18\n286\n\nNote\n\nIn the first test case, one of the optimal ways is on the following image:\n\n\n\nIn this case, f(1,2)=1, f(1,3)=3, f(1,4)=5, f(2,3)=2, f(2,4)=4, f(3,4)=2, so the sum of these 6 numbers is 17.\n\nIn the second test case, one of the optimal ways is on the following image:\n\n\n\nIn this case, f(1,2)=3, f(1,3)=1, f(1,4)=4, f(2,3)=2, f(2,4)=5, f(3,4)=3, so the sum of these 6 numbers is 18.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput=sys.stdin.readline\nfor _ in range(int(input())):\n n=int(input())\n dic={}\n dico={}\n for i in range(1,n+1):\n dic[i]=[]\n dico[i]=[]\n for i in range(n-1):\n x,y=map(int,input().split())\n dic[x].append(y)\n dic[y].append(x)\n dico[x].append(y)\n dico[y].append(x)\n dis={}\n dis[1]=0\n level=1\n se={1}\n ne={1}\n while(ne):\n tem=set({})\n for i in ne:\n xx=dic[i]\n for j in xx:\n if(not(j in se)):\n se.add(j)\n dis[j]=level\n tem.add(j)\n ne=tem.copy()\n level+=1\n for i in dic:\n dic[i].sort(key=lambda x:dis[x])\n people={}\n st=1\n se={1}\n people[1]=1\n while(dic[st]):\n ne=dic[st].pop()\n if(not(ne in se)):\n people[ne]=1\n se.add(ne)\n else:\n people[ne]+=people[st]\n st=ne\n size=[]\n se={1}\n ne={1}\n while(ne):\n tem=set({})\n for i in ne:\n xx=dico[i]\n for j in xx:\n if(not(j in se)):\n se.add(j)\n size.append(people[j]*(n-people[j]))\n tem.add(j)\n ne=tem.copy()\n size.sort(reverse=True)\n m=int(input())\n prime=list(map(int,input().split()))\n prime.sort(reverse=True)\n rem=1000000007\n ans=0\n if(m<=n-1):\n for i in range(m):\n ans=(ans+(prime[i]*size[i])%rem)%rem\n for i in range(m,n-1):\n ans=(ans%rem+size[i]%rem)%rem\n else:\n ext=m-(n-1)\n for i in range(ext):\n prime[i+1]=(prime[i+1]*prime[i])%rem\n for i in range(n-1):\n ans=(ans+(prime[i+ext]*size[i])%rem)%rem\n print(ans)\n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n4\\n1 2\\n2 3\\n3 4\\n2\\n2 2\\n4\\n3 4\\n1 3\\n3 2\\n2\\n3 2\\n7\\n6 1\\n2 3\\n4 6\\n7 3\\n5 1\\n3 6\\n4\\n7 5 13 3\\n', 'output': '17\\n18\\n286\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n3 1\\n2 1\\n4\\n22861 20707 59627 9293\\n3\\n3 1\\n1 2\\n6\\n15767 40973 20807 24419 46439 33757\\n3\\n3 2\\n1 2\\n6\\n16493 54493 10799 37529 59743 30529\\n3\\n3 1\\n2 1\\n1\\n42961\\n', 'output': '783349080\\n330291712\\n563526719\\n85924\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n2 2 2 2 2 3 3 7 109 109 167\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n2 2 2 2 2 3 3 7 109 109 123\\n', 'output': '946107806\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n2 2 2 2 3 3 3 7 109 109 123\\n', 'output': '419161696\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n4 2 2 2 3 3 3 7 109 109 123\\n', 'output': '838323380\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n3 1\\n2 1\\n4\\n22861 20707 59627 9293\\n3\\n3 1\\n1 2\\n6\\n15767 40973 20807 24419 46439 62816\\n3\\n3 2\\n1 2\\n6\\n16493 54493 10799 37529 59743 30529\\n3\\n3 1\\n2 1\\n1\\n42961\\n', 'output': '783349080\\n372565328\\n563526719\\n85924\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n4 2 2 2 3 3 3 7 10 109 123\\n', 'output': '810855372\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n4 2 2 2 3 3 6 7 10 109 123\\n', 'output': '621710725\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n4 2 3 2 3 3 6 7 10 109 123\\n', 'output': '432566078\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n3 1\\n2 1\\n4\\n22861 20707 59627 9293\\n3\\n3 1\\n1 2\\n6\\n15767 40973 20807 24419 46439 33757\\n3\\n3 2\\n1 2\\n6\\n16493 34019 10799 37529 59743 30529\\n3\\n3 1\\n2 1\\n1\\n42961\\n', 'output': '783349080\\n330291712\\n783294328\\n85924\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 2\\n2 3\\n3 4\\n2\\n2 2\\n4\\n3 4\\n1 3\\n3 2\\n2\\n3 2\\n7\\n6 1\\n2 3\\n4 2\\n7 3\\n5 1\\n3 6\\n4\\n7 5 13 3\\n', 'output': '17\\n18\\n306\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n2 2 2 2 3 3 3 2 109 109 123\\n', 'output': '262617637\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n3 1\\n2 1\\n4\\n22861 20707 59627 9293\\n3\\n3 1\\n1 2\\n6\\n15767 40973 20807 24419 46439 62816\\n3\\n3 2\\n1 2\\n6\\n31575 54493 10799 37529 59743 30529\\n3\\n3 1\\n2 1\\n1\\n42961\\n', 'output': '783349080\\n372565328\\n603348715\\n85924\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n4 2 2 2 3 3 3 7 10 109 54\\n', 'output': '355985292\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n4 2 3 2 3 3 6 7 4 109 123\\n', 'output': '973026444\\n'}, {'type': 'stdin_stdout', 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6\\n4\\n7 1 13 3\\n', 'output': '21\\n18\\n274\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n1 3\\n3 4\\n11\\n2 2 2 2 3 3 3 7 41 115 123\\n', 'output': '753753685\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 4\\n2 3\\n3 4\\n11\\n4 2 3 2 3 1 4 7 10 109 123\\n', 'output': '81140482\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n3 1\\n2 1\\n4\\n22861 20707 67190 9293\\n3\\n3 1\\n1 2\\n6\\n15767 40973 20807 24419 46439 33757\\n3\\n3 2\\n1 2\\n6\\n16493 16795 10799 37529 59743 30529\\n3\\n3 1\\n2 1\\n1\\n19680\\n', 'output': '170427555\\n330291712\\n695928755\\n39362\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 4\\n2 3\\n3 4\\n11\\n7 2 3 4 3 6 4 7 10 109 123\\n', 'output': '567983326\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 4\\n2 3\\n3 4\\n11\\n4 2 5 4 3 8 4 7 10 129 118\\n', 'output': '911129545\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 4\\n2 3\\n3 4\\n11\\n5 2 3 1 3 8 4 7 7 129 118\\n', 'output': '296257261\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 4\\n2 3\\n3 4\\n11\\n4 2 3 2 3 3 6 7 10 109 123\\n', 'output': '432566078\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n1 3\\n3 4\\n11\\n2 2 2 2 3 3 3 7 109 109 123\\n', 'output': '419161696\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 4\\n2 3\\n3 4\\n11\\n4 2 3 2 3 3 4 7 10 109 123\\n', 'output': '621710725\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n4 2 2 2 3 6 6 7 10 109 123\\n', 'output': '243421431\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n1 3\\n3 4\\n11\\n2 2 2 2 3 3 3 7 40 109 123\\n', 'output': '621710725\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n3 1\\n2 1\\n4\\n22861 20707 67190 9293\\n3\\n3 1\\n1 2\\n6\\n15767 40973 20807 24419 46439 33757\\n3\\n3 2\\n1 2\\n6\\n16493 16795 10799 37529 59743 30529\\n3\\n3 2\\n2 1\\n1\\n42961\\n', 'output': '170427555\\n330291712\\n695928755\\n85924\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n8 2 3 4 3 8 4 7 10 129 118\\n', 'output': '93355444\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n1 4\\n11\\n4 2 2 2 3 3 3 7 11 109 123\\n', 'output': '891940908\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n1 2\\n2 3\\n3 4\\n11\\n8 2 2 2 3 3 6 7 10 109 123\\n', 'output': '243421431\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 2\\n2 3\\n3 4\\n2\\n2 2\\n4\\n3 4\\n1 3\\n3 2\\n2\\n3 2\\n7\\n7 1\\n2 3\\n4 2\\n7 3\\n5 1\\n3 6\\n4\\n7 5 13 3\\n', 'output': '17\\n18\\n306\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78437","program":"```python\nimport sys\ninput=sys.stdin.readline\nfor _ in range(int(input())):\n n=int(input())\n dic={}\n dico={}\n for i in range(1,n+1):\n dic[i]=[]\n dico[i]=[]\n for i in range(n-1):\n x,y=map(int,input().split())\n dic[x].append(y)\n dic[y].append(x)\n dico[x].append(y)\n dico[y].append(x)\n dis={}\n dis[1]=0\n level=1\n se={1}\n ne={1}\n while(ne):\n tem=set({})\n for i in ne:\n xx=dic[i]\n for j in xx:\n if(not(j in se)):\n se.add(j)\n dis[j]=level\n tem.add(j)\n ne=tem.copy()\n level+=1\n for i in dic:\n dic[i].sort(key=lambda x:dis[x])\n people={}\n st=1\n se={1}\n people[1]=1\n while(dic[st]):\n ne=dic[st].pop()\n if(not(ne in se)):\n people[ne]=1\n se.add(ne)\n else:\n people[ne]+=people[st]\n st=ne\n size=[]\n se={1}\n ne={1}\n while(ne):\n tem=set({})\n for i in ne:\n xx=dico[i]\n for j in xx:\n if(not(j in se)):\n se.add(j)\n size.append(people[j]*(n-people[j]))\n tem.add(j)\n ne=tem.copy()\n size.sort(reverse=True)\n m=int(input())\n prime=list(map(int,input().split()))\n prime.sort(reverse=True)\n rem=1000000007\n ans=0\n if(m<=n-1):\n for i in range(m):\n ans=(ans+(prime[i]*size[i])%rem)%rem\n for i in range(m,n-1):\n ans=(ans%rem+size[i]%rem)%rem\n else:\n ext=m-(n-1)\n for i in range(ext):\n prime[i+1]=(prime[i+1]*prime[i])%rem\n for i in range(n-1):\n ans=(ans+(prime[i+ext]*size[i])%rem)%rem\n print(ans)\n \n```","inputs":"3\n4\n1 2\n2 3\n3 4\n2\n2 2\n4\n3 4\n1 3\n3 2\n2\n3 2\n7\n6 1\n2 3\n4 6\n7 3\n5 1\n3 6\n4\n7 5 13 3\n","output":"17\n18\n286\n","actual_output":"17\n18\n286\n","execution_success":true,"sample_index":12501},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1446_B. Catching Cheaters","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4\u22c5 LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. \n\nYou believe that only some part of the essays could have been copied, therefore you're interested in their substrings.\n\nCalculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. \n\nIf X is a string, |X| denotes its length.\n\nA string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.\n\nA string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. \n\nPay attention to the difference between the substring and subsequence, as they both appear in the problem statement. \n\nYou may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem).\n\nInput\n\nThe first line contains two positive integers n and m (1 \u2264 n, m \u2264 5000) \u2014 lengths of the two strings A and B. \n\nThe second line contains a string consisting of n lowercase Latin letters \u2014 string A.\n\nThe third line contains a string consisting of m lowercase Latin letters \u2014 string B. \n\nOutput\n\nOutput maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. \n\nExamples\n\nInput\n\n\n4 5\nabba\nbabab\n\n\nOutput\n\n\n5\n\nInput\n\n\n8 10\nbbbbabab\nbbbabaaaaa\n\n\nOutput\n\n\n12\n\nInput\n\n\n7 7\nuiibwws\nqhtkxcn\n\n\nOutput\n\n\n0\n\nNote\n\nFor the first case:\n\nabb from the first string and abab from the second string have LCS equal to abb.\n\nThe result is S(abb, abab) = (4 \u22c5 |abb|) - |abb| - |abab| = 4 \u22c5 3 - 3 - 4 = 5.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, m = map(int, input().split())\na = input()\nb = input()\nres = 0\ndp = [[0 for _ in range(m + 1)] for _ in range(n + 1)]\nfor i in range(1, n + 1):\n for j in range(1, m + 1):\n if a[i - 1] == b[j - 1]:\n dp[i][j] = max(dp[i][j], dp[i - 1][j - 1] + 2)\n dp[i][j] = max(dp[i][j], max(dp[i - 1][j], dp[i][j - 1]) - 1)\n res = max(res, dp[i][j])\nprint(res)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7 7\\nuiibwws\\nqhtkxcn\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '4 5\\nabba\\nbabab\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '8 10\\nbbbbabab\\nbbbabaaaaa\\n', 'output': '12'}, {'type': 'stdin_stdout', 'input': '11 18\\naaaagaaxaxa\\naiaiiaaaaiaaiaaaaa\\n', 'output': '11'}, {'type': 'stdin_stdout', 'input': '12 17\\nqqqqqqgqqgqq\\nqqqgqqqggqqqlqqqq\\n', 'output': '18'}, {'type': 'stdin_stdout', 'input': '6 9\\nvvvkvv\\nvgkkvvvgg\\n', 'output': '6'}, {'type': 'stdin_stdout', 'input': '153 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{'type': 'stdin_stdout', 'input': '7 19\\ndeecvee\\neeeeeveeceeeeeeeeee\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '9 16\\nffgfegggf\\nfffffffffffcffff\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '8 19\\nxophohoo\\nxhohxxxxooxoohjoooo\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '6 19\\npppror\\nrprpppppprpppppfprp\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '18 14\\nkuyyhajngylhmfhmkg\\nyugyglfkujguyu\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '9 19\\nyqyvovyqy\\nvvyvvyyvyyyyyyqjuvy\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '11 12\\nmmddmmarcnx\\nfypoegaspcyr\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '148 170\\nkksctttkkcejexktkseetekteekiksjzktecekitkkkeeiksststskitkettketktekiikksszkstctcikckkietziitksctecxsiznicktxttvkkktstikjjtkekiticksktiketkttkkktketi\\nkketkjetszteskskzekkkkekesskkkkktkxjistkkttsktskttkekekisskvkttcskckstkicickktkkctttskitxtetkseecktetkktcseekettkietkjstskettkkttettckktktkskteekictkkkketkczjisktiekktskk\\n', 'output': '55\\n'}, {'type': 'stdin_stdout', 'input': '17 15\\ntxreviyatymxyh`nx\\nmjyhpxxyvwhxtjv\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '14 13\\ndkkkljkkkkkkkk\\ndkkkkkdkhddkk\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '18 14\\nkuyyhajngxlhmfhmkg\\nyugyglfkujhuyu\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '12 18\\nlollmoolollo\\naoallaolllalalllol\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n`\\nd\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '9 16\\nfggfffggg\\nffffcfffffffffff\\n', 'output': '6\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78445","program":"```python\nn, m = map(int, input().split())\na = input()\nb = input()\nres = 0\ndp = [[0 for _ in range(m + 1)] for _ in range(n + 1)]\nfor i in range(1, n + 1):\n for j in range(1, m + 1):\n if a[i - 1] == b[j - 1]:\n dp[i][j] = max(dp[i][j], dp[i - 1][j - 1] + 2)\n dp[i][j] = max(dp[i][j], max(dp[i - 1][j], dp[i][j - 1]) - 1)\n res = max(res, dp[i][j])\nprint(res)\n```","inputs":"7 7\nuiibwws\nqhtkxcn\n","output":"0","actual_output":"0\n","execution_success":true,"sample_index":12502},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1470_B. Strange Definition","prompt":"Solve the following coding problem using the programming language python:\n\nLet us call two integers x and y adjacent if (lcm(x, y))/(gcd(x, y)) is a perfect square. For example, 3 and 12 are adjacent, but 6 and 9 are not.\n\nHere gcd(x, y) denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers x and y, and lcm(x, y) denotes the [least common multiple (LCM)](https://en.wikipedia.org/wiki/Least_common_multiple) of integers x and y.\n\nYou are given an array a of length n. Each second the following happens: each element a_i of the array is replaced by the product of all elements of the array (including itself), that are adjacent to the current value. \n\nLet d_i be the number of adjacent elements to a_i (including a_i itself). The beauty of the array is defined as max_{1 \u2264 i \u2264 n} d_i. \n\nYou are given q queries: each query is described by an integer w, and you have to output the beauty of the array after w seconds.\n\nInput\n\nThe first input line contains a single integer t (1 \u2264 t \u2264 10^5) \u2014 the number of test cases.\n\nThe first line of each test case contains a single integer n (1 \u2264 n \u2264 3 \u22c5 10^5) \u2014 the length of the array.\n\nThe following line contains n integers a_1, \u2026, a_n (1 \u2264 a_i \u2264 10^6) \u2014 array elements. \n\nThe next line contain a single integer q (1 \u2264 q \u2264 3 \u22c5 10^5) \u2014 the number of queries.\n\nThe following q lines contain a single integer w each (0 \u2264 w \u2264 10^{18}) \u2014 the queries themselves.\n\nIt is guaranteed that the sum of values n over all test cases does not exceed 3 \u22c5 10^5, and the sum of values q over all test cases does not exceed 3 \u22c5 10^5\n\nOutput\n\nFor each query output a single integer \u2014 the beauty of the array at the corresponding moment.\n\nExample\n\nInput\n\n\n2\n4\n6 8 4 2\n1\n0\n6\n12 3 20 5 80 1\n1\n1\n\n\nOutput\n\n\n2\n3\n\nNote\n\nIn the first test case, the initial array contains elements [6, 8, 4, 2]. Element a_4=2 in this array is adjacent to a_4=2 (since (lcm(2, 2))/(gcd(2, 2))=2/2=1=1^2) and a_2=8 (since (lcm(8,2))/(gcd(8, 2))=8/2=4=2^2). Hence, d_4=2, and this is the maximal possible value d_i in this array.\n\nIn the second test case, the initial array contains elements [12, 3, 20, 5, 80, 1]. The elements adjacent to 12 are \\{12, 3\\}, the elements adjacent to 3 are \\{12, 3\\}, the elements adjacent to 20 are \\{20, 5, 80\\}, the elements adjacent to 5 are \\{20, 5, 80\\}, the elements adjacent to 80 are \\{20, 5, 80\\}, the elements adjacent to 1 are \\{1\\}. After one second, the array is transformed into [36, 36, 8000, 8000, 8000, 1].\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom sys import stdin\ndct = {i:i for i in range(1000001)}\nfor i in range(2, 1001):\n\tfor j in range(1, (10 ** 6) // (i ** 2) + 1):\n\t\tdct[(i ** 2) * j] = j\nt = int(stdin.readline())\nfor _ in range(t):\n\tn = int(stdin.readline())\n\telements = map(int, stdin.readline().split())\n\tq = int(stdin.readline())\n\tdct2 = {}\n\tfor i in elements:\n\t\tif dct[i] not in dct2:\n\t\t\tdct2[dct[i]] = 1\n\t\telse:\n\t\t\tdct2[dct[i]] += 1\n\tchan = 0\n\tmaxx = 0\n\tfor so, gia in dct2.items():\n\t\tif so == 1:\n\t\t\tmaxx = max(gia, maxx)\n\t\t\tchan += gia\n\t\telse:\n\t\t\tmaxx = max(gia, maxx)\n\t\t\tif gia % 2 == 0:\n\t\t\t\tchan += gia\n\tmaxx2 = max(chan, maxx)\n\tfor times in range(q):\n\t\tquer = stdin.readline()\n\t\tif quer == \"0\\n\":\n\t\t\tprint(maxx)\n\t\telse:\n\t\t\tprint(maxx2)\n\t\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n4\\n6 8 4 2\\n1\\n0\\n6\\n12 3 20 5 80 1\\n1\\n1\\n', 'output': '\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n1 1 3 3 1\\n1\\n4294967296\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 7 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n0\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '31\\n31\\n17\\n31\\n31\\n31\\n31\\n31\\n17\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n17\\n31\\n17\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n2 2 3 3\\n5\\n0\\n1\\n4294967295\\n4294967296\\n4294967297\\n', 'output': '2\\n4\\n4\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2 8 16\\n2\\n4294967296\\n0\\n', 'output': '3\\n2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n1 1 3 3 1\\n1\\n7016655690\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n0\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n4 8 16\\n2\\n4294967296\\n0\\n', 'output': '2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n17\\n35\\n35\\n35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 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'21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n15\\n21\\n15\\n21\\n21\\n21\\n21\\n15\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n1 1 3 3 2\\n1\\n552244307\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 2 1 8 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 6 3 7 1\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n15\\n23\\n15\\n23\\n23\\n23\\n23\\n15\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 3 1 7 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10 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 6 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 2\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n4\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n15\\n19\\n15\\n19\\n19\\n19\\n19\\n15\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 12 10 4 2 10 18 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 2 7 8 1 7 9 3 17 7 2\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n13\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n14\\n24\\n14\\n24\\n24\\n24\\n24\\n14\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n'}, {'type': 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'26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n14\\n26\\n14\\n26\\n26\\n26\\n26\\n14\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 12 10 4 2 10 18 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 2 7 8 1 7 9 2 17 7 2\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n13\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n14\\n38\\n14\\n38\\n38\\n38\\n38\\n14\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 22 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n0\\n9\\n2\\n0\\n5\\n7\\n7\\n3\\n18\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n2\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '35\\n35\\n17\\n35\\n35\\n17\\n35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 4 1 1 4 1 7 8 1 8 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n2\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n1\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '25\\n25\\n17\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n17\\n25\\n17\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n17\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 10 10 4 2 10 10 6 3 1 4 1 3 7 2 9 10 6 2 4 1 9 1 1 2 1 7 8 1 7 9 3 10 7 2\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n4\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n14\\n22\\n14\\n22\\n22\\n22\\n22\\n14\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 5 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 4 1 1 4 1 7 8 1 8 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n2\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n1\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '26\\n26\\n16\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n16\\n26\\n16\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n16\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 10 2 1 16 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 6 3 7 1\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n16\\n38\\n38\\n38\\n16\\n38\\n16\\n38\\n38\\n38\\n38\\n16\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 2 1 7 8 1 7 9 3 10 7 1\\n40\\n2\\n7\\n0\\n3\\n1\\n18\\n9\\n2\\n1\\n6\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n1\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '28\\n28\\n16\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n16\\n28\\n16\\n28\\n28\\n28\\n28\\n16\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n16\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n'}, {'type': 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'32\\n32\\n16\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n16\\n32\\n16\\n32\\n32\\n32\\n32\\n16\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n16\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 1 5 6 2 10 12 10 4 2 17 18 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 2 7 8 1 7 9 2 17 7 2\\n40\\n1\\n10\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n13\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n9\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n2\\n2\\n8\\n4\\n1\\n', 'output': '33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n15\\n33\\n15\\n33\\n33\\n33\\n33\\n15\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 5 5 6 2 10 14 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 4 2 4 1 9 1 1 3 1 7 8 1 2 9 3 22 7 2\\n40\\n1\\n7\\n1\\n4\\n1\\n9\\n9\\n2\\n1\\n5\\n6\\n7\\n4\\n10\\n8\\n6\\n0\\n7\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n2\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n15\\n27\\n15\\n27\\n27\\n27\\n27\\n15\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 1 5 6 2 10 12 10 4 2 17 18 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 2 7 8 1 7 9 2 17 7 2\\n40\\n1\\n10\\n1\\n9\\n0\\n9\\n9\\n2\\n1\\n5\\n13\\n7\\n3\\n10\\n4\\n5\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n9\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n2\\n2\\n8\\n4\\n1\\n', 'output': '33\\n33\\n33\\n33\\n15\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n15\\n33\\n15\\n33\\n33\\n33\\n33\\n15\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 3 5 2 10 10 6 1 1 8 1 3 7 2 9 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2\\n40\\n1\\n7\\n1\\n4\\n1\\n9\\n9\\n2\\n1\\n5\\n6\\n7\\n4\\n10\\n8\\n6\\n0\\n7\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n0\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n2\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n15\\n27\\n15\\n27\\n27\\n27\\n27\\n15\\n27\\n15\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 10 2 1 16 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 6 6 7 1\\n18\\n0\\n7\\n1\\n7\\n1\\n9\\n8\\n2\\n1\\n5\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n-1\\n8\\n5\\n5\\n3\\n0\\n6\\n6\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n1\\n5\\n8\\n4\\n0\\n', 'output': '16\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n16\\n32\\n32\\n32\\n16\\n32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 1 5 6 2 10 12 10 4 2 17 18 6 3 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 2 7 8 1 7 9 2 17 7 2\\n40\\n1\\n10\\n1\\n9\\n0\\n12\\n9\\n2\\n1\\n5\\n13\\n7\\n3\\n10\\n4\\n5\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n9\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n2\\n2\\n8\\n4\\n1\\n', 'output': '27\\n27\\n27\\n27\\n15\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n15\\n27\\n15\\n27\\n27\\n27\\n27\\n15\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 10 2 1 16 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 6 6 7 1\\n3\\n0\\n7\\n1\\n7\\n1\\n9\\n8\\n2\\n1\\n5\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n-1\\n8\\n5\\n5\\n3\\n0\\n6\\n6\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n1\\n5\\n8\\n4\\n0\\n', 'output': '16\\n32\\n32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 5 5 6 2 10 14 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 4 2 4 1 9 1 1 3 1 7 8 1 2 9 3 28 7 2\\n40\\n1\\n7\\n1\\n4\\n1\\n9\\n9\\n2\\n1\\n5\\n6\\n7\\n4\\n10\\n8\\n6\\n0\\n7\\n0\\n8\\n1\\n5\\n3\\n0\\n6\\n0\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n2\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n15\\n31\\n15\\n31\\n31\\n31\\n31\\n15\\n31\\n15\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 10 2 1 16 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 6 6 7 1\\n3\\n0\\n7\\n1\\n7\\n1\\n9\\n8\\n2\\n1\\n5\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n-1\\n8\\n5\\n5\\n3\\n0\\n6\\n6\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n1\\n5\\n8\\n4\\n0\\n', 'output': '17\\n35\\n35\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 1 5 6 2 10 12 10 4 2 17 18 6 3 1 4 1 1 7 2 9 10 3 2 4 1 9 1 1 4 2 7 8 1 7 9 2 17 7 2\\n40\\n1\\n10\\n1\\n9\\n0\\n12\\n9\\n2\\n1\\n5\\n13\\n7\\n3\\n10\\n4\\n5\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n9\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n2\\n7\\n2\\n2\\n8\\n4\\n1\\n', 'output': '24\\n24\\n24\\n24\\n16\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n16\\n24\\n16\\n24\\n24\\n24\\n24\\n16\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 10 2 1 16 1 3 7 2 9 10 4 2 4 1 13 1 1 4 1 7 8 1 7 9 6 6 7 1\\n3\\n0\\n7\\n1\\n7\\n1\\n9\\n8\\n2\\n1\\n5\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n-1\\n8\\n5\\n5\\n3\\n0\\n6\\n6\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n1\\n5\\n8\\n4\\n0\\n', 'output': '16\\n34\\n34\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 5 5 6 2 10 14 10 4 2 10 10 6 2 2 4 1 3 7 2 9 10 4 2 4 1 9 1 1 3 1 7 8 1 2 9 3 28 7 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'38\\n38\\n16\\n38\\n38\\n38\\n38\\n38\\n16\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n16\\n38\\n16\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 6 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n17\\n27\\n17\\n27\\n27\\n27\\n27\\n17\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 15 4 2 10 10 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 3 17 7 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'21\\n21\\n21\\n21\\n15\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n15\\n21\\n15\\n21\\n21\\n21\\n21\\n15\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n2 3 5 6 2 10 14 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 2 7 8 1 7 9 3 17 7 2\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n13\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n13\\n23\\n13\\n23\\n23\\n23\\n23\\n13\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n1 1 5 3 2\\n1\\n552244307\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 22 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 5 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n0\\n5\\n7\\n7\\n3\\n18\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '39\\n39\\n17\\n39\\n39\\n39\\n39\\n39\\n17\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n17\\n39\\n17\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n0\\n3\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n0\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n17\\n35\\n35\\n35\\n35\\n17\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 2 1 8 1 3 7 2 9 10 3 1 4 1 9 1 1 4 1 7 8 1 7 9 6 3 7 1\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n16\\n30\\n16\\n30\\n30\\n30\\n30\\n16\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 3 1 7 1\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n8\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n0\\n1\\n', 'output': '33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n17\\n33\\n17\\n33\\n33\\n33\\n33\\n17\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n17\\n33\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 15 22 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n0\\n5\\n7\\n7\\n3\\n18\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '29\\n29\\n17\\n29\\n29\\n29\\n29\\n29\\n17\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n17\\n29\\n17\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n17\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 18 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 4 1 1 4 1 7 8 1 8 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n2\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '33\\n33\\n17\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n17\\n33\\n17\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 3 2 10 10 6 2 1 4 1 3 8 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 3 1 7 1\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n8\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n16\\n18\\n16\\n18\\n18\\n18\\n18\\n16\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 3 17 7 2\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n0\\n5\\n7\\n7\\n4\\n10\\n4\\n6\\n0\\n7\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n2\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n15\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n15\\n25\\n15\\n25\\n25\\n25\\n25\\n15\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 4 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n2\\n7\\n0\\n3\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n1\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '34\\n34\\n18\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n18\\n34\\n18\\n34\\n34\\n34\\n34\\n18\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n18\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 3 2 10 5 6 2 1 4 1 3 7 2 9 10 3 2 4 1 3 1 1 4 1 7 8 1 7 9 3 1 7 1\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n8\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n15\\n39\\n15\\n39\\n39\\n39\\n39\\n15\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 4 1 1 4 1 7 8 1 8 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n2\\n5\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n1\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '25\\n25\\n17\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n17\\n25\\n25\\n25\\n17\\n25\\n17\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n17\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 10 10 4 2 10 10 6 3 1 3 1 3 7 2 9 10 6 2 4 1 9 1 1 2 1 7 8 1 7 9 3 10 7 2\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n4\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n13\\n17\\n13\\n17\\n17\\n17\\n17\\n13\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 5 2 10 2 6 1 1 8 1 3 7 2 9 10 4 2 4 1 4 1 1 4 1 7 8 1 8 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n2\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n1\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '28\\n28\\n16\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n16\\n28\\n16\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n16\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 5 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n2\\n7\\n0\\n3\\n1\\n18\\n9\\n2\\n1\\n6\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n1\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '31\\n31\\n17\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n17\\n31\\n17\\n31\\n31\\n31\\n31\\n17\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n17\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 5 5 6 2 10 14 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 3 1 7 8 1 7 9 2 17 7 2\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n6\\n7\\n4\\n10\\n4\\n6\\n0\\n7\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n2\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n14\\n30\\n14\\n30\\n30\\n30\\n30\\n14\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n'}, {'type': 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2 10 12 10 4 3 17 18 6 3 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 2 7 8 1 7 9 2 17 7 2\\n40\\n1\\n10\\n1\\n9\\n0\\n12\\n9\\n2\\n1\\n5\\n13\\n7\\n3\\n10\\n4\\n5\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n9\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n2\\n2\\n8\\n4\\n1\\n', 'output': '31\\n31\\n31\\n31\\n15\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n15\\n31\\n15\\n31\\n31\\n31\\n31\\n15\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 12 10 4 2 10 10 10 2 1 16 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 6 6 7 1\\n3\\n0\\n7\\n1\\n7\\n1\\n9\\n8\\n2\\n1\\n5\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n-1\\n8\\n5\\n5\\n3\\n0\\n6\\n6\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n1\\n5\\n8\\n4\\n0\\n', 'output': '16\\n36\\n36\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 4 5 6 2 10 14 10 4 2 10 10 10 2 1 16 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 6 6 7 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'37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n13\\n37\\n13\\n37\\n37\\n37\\n37\\n13\\n37\\n13\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n2 2 4 4\\n5\\n0\\n1\\n4294967295\\n4294967296\\n4294967297\\n', 'output': '2\\n4\\n4\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 2 1 4 1 3 7 2 17 10 3 2 4 1 9 1 1 4 2 7 8 1 7 9 3 17 7 2\\n40\\n1\\n7\\n1\\n5\\n0\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '33\\n33\\n33\\n33\\n13\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n13\\n33\\n13\\n33\\n33\\n33\\n33\\n13\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 2 1 8 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 4 8 1 7 9 3 3 7 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'1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 8 1\\n2\\n5593576686\\n0\\n', 'output': '2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 8 2\\n2\\n5366841113\\n0\\n', 'output': '3\\n2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n8\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n16\\n38\\n16\\n38\\n38\\n38\\n38\\n16\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 10 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 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'stdin_stdout', 'input': '1\\n3\\n3 8 20\\n2\\n4294967296\\n0\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 4 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n0\\n5\\n1\\n9\\n9\\n2\\n2\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n3\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n1\\n7\\n0\\n3\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': 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'25\\n25\\n17\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n17\\n25\\n17\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 6 1 1 8 1 3 7 2 9 10 4 2 4 1 9 1 1 4 1 7 8 1 7 9 3 10 7 1\\n40\\n2\\n7\\n0\\n3\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n1\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n0\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n17\\n35\\n35\\n35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 10 2 1 16 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 6 3 7 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'35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n17\\n35\\n35\\n35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n17\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 10 2 1 16 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 6 3 7 1\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n2\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n16\\n38\\n16\\n38\\n38\\n38\\n38\\n16\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 3 2 10 5 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 3 1 7 1\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n7\\n7\\n3\\n10\\n4\\n6\\n0\\n9\\n0\\n8\\n5\\n5\\n4\\n0\\n6\\n5\\n1\\n8\\n8\\n8\\n3\\n1\\n1\\n4\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n16\\n34\\n16\\n34\\n34\\n34\\n34\\n16\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 5 5 6 2 10 14 10 4 2 10 10 6 2 1 4 1 3 7 2 9 10 3 2 4 1 9 1 1 4 1 7 8 1 7 9 3 17 7 2\\n40\\n1\\n7\\n1\\n5\\n1\\n9\\n9\\n2\\n1\\n5\\n6\\n7\\n4\\n10\\n4\\n6\\n0\\n7\\n0\\n8\\n5\\n5\\n3\\n0\\n6\\n5\\n1\\n10\\n8\\n8\\n3\\n1\\n1\\n2\\n7\\n1\\n5\\n8\\n4\\n1\\n', 'output': '23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n15\\n23\\n15\\n23\\n23\\n23\\n23\\n15\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 12 10 4 2 10 18 6 2 1 4 1 3 7 2 9 10 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2\\n40\\n1\\n7\\n1\\n4\\n1\\n9\\n9\\n2\\n1\\n5\\n6\\n7\\n4\\n10\\n8\\n2\\n0\\n7\\n0\\n8\\n1\\n5\\n3\\n0\\n6\\n0\\n1\\n10\\n8\\n6\\n3\\n1\\n1\\n2\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n14\\n36\\n14\\n36\\n36\\n36\\n36\\n14\\n36\\n14\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 10 2 1 16 1 3 7 2 9 10 5 2 4 1 13 1 1 4 1 10 8 1 7 9 6 6 7 1\\n3\\n0\\n7\\n1\\n7\\n1\\n9\\n8\\n2\\n1\\n5\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n-1\\n8\\n5\\n5\\n3\\n0\\n6\\n6\\n0\\n10\\n8\\n8\\n3\\n0\\n2\\n4\\n7\\n1\\n5\\n8\\n4\\n0\\n', 'output': '15\\n25\\n25\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 5 5 6 2 4 14 10 4 2 10 10 6 2 2 4 1 3 7 2 9 10 4 2 4 2 9 1 1 3 1 7 8 1 2 9 3 28 7 2\\n40\\n1\\n7\\n1\\n4\\n1\\n9\\n9\\n4\\n1\\n5\\n6\\n7\\n4\\n10\\n8\\n2\\n0\\n7\\n0\\n8\\n1\\n5\\n3\\n0\\n6\\n0\\n1\\n10\\n8\\n6\\n3\\n1\\n1\\n2\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n14\\n36\\n14\\n36\\n36\\n36\\n36\\n14\\n36\\n14\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 16 2 1 16 1 3 7 2 9 10 5 2 4 1 13 1 1 4 1 10 8 1 7 9 6 6 7 1\\n3\\n0\\n7\\n1\\n7\\n1\\n9\\n8\\n2\\n1\\n5\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n-1\\n8\\n5\\n5\\n3\\n0\\n6\\n6\\n0\\n10\\n8\\n8\\n3\\n0\\n2\\n4\\n7\\n1\\n5\\n8\\n4\\n0\\n', 'output': '16\\n32\\n32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 5 5 6 2 4 14 10 4 2 10 10 6 2 2 4 1 3 7 2 9 10 4 2 4 2 9 1 1 3 1 7 8 1 2 9 3 28 7 2\\n40\\n1\\n7\\n1\\n4\\n1\\n9\\n9\\n4\\n1\\n5\\n10\\n7\\n4\\n10\\n8\\n2\\n0\\n7\\n0\\n8\\n1\\n5\\n3\\n0\\n6\\n0\\n1\\n10\\n8\\n6\\n3\\n1\\n1\\n2\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n14\\n36\\n14\\n36\\n36\\n36\\n36\\n14\\n36\\n14\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 16 2 1 16 1 3 7 2 9 10 5 2 4 1 13 1 1 4 1 10 8 1 7 9 6 6 7 1\\n3\\n0\\n7\\n1\\n7\\n1\\n9\\n8\\n2\\n1\\n5\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n-1\\n8\\n5\\n5\\n3\\n0\\n6\\n6\\n0\\n10\\n8\\n8\\n3\\n0\\n2\\n4\\n7\\n0\\n5\\n8\\n4\\n0\\n', 'output': '16\\n32\\n32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 5 5 6 2 4 14 10 4 2 10 10 6 2 2 4 1 3 7 2 9 10 4 2 4 2 9 1 1 3 1 7 8 1 2 9 3 28 7 2\\n40\\n1\\n7\\n1\\n4\\n1\\n9\\n9\\n4\\n2\\n5\\n10\\n7\\n4\\n10\\n8\\n2\\n0\\n7\\n0\\n8\\n1\\n5\\n3\\n0\\n6\\n0\\n1\\n10\\n8\\n6\\n3\\n1\\n1\\n2\\n7\\n2\\n5\\n8\\n4\\n1\\n', 'output': '36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n14\\n36\\n14\\n36\\n36\\n36\\n36\\n14\\n36\\n14\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n'}, {'type': 'stdin_stdout', 'input': '1\\n40\\n1 3 5 6 2 10 14 10 4 2 10 10 16 2 1 16 1 3 7 2 9 10 5 2 4 1 13 1 1 4 1 10 8 1 7 9 6 6 7 1\\n3\\n0\\n7\\n1\\n7\\n1\\n9\\n8\\n2\\n1\\n7\\n7\\n7\\n0\\n10\\n4\\n6\\n0\\n9\\n-1\\n8\\n5\\n5\\n3\\n0\\n6\\n6\\n0\\n10\\n8\\n8\\n3\\n0\\n2\\n4\\n7\\n0\\n5\\n8\\n4\\n0\\n', 'output': '16\\n32\\n32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n1 1 3 3 1\\n1\\n2326244245\\n', 'output': '5\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78449","program":"```python\nfrom sys import stdin\ndct = {i:i for i in range(1000001)}\nfor i in range(2, 1001):\n\tfor j in range(1, (10 ** 6) // (i ** 2) + 1):\n\t\tdct[(i ** 2) * j] = j\nt = int(stdin.readline())\nfor _ in range(t):\n\tn = int(stdin.readline())\n\telements = map(int, stdin.readline().split())\n\tq = int(stdin.readline())\n\tdct2 = {}\n\tfor i in elements:\n\t\tif dct[i] not in dct2:\n\t\t\tdct2[dct[i]] = 1\n\t\telse:\n\t\t\tdct2[dct[i]] += 1\n\tchan = 0\n\tmaxx = 0\n\tfor so, gia in dct2.items():\n\t\tif so == 1:\n\t\t\tmaxx = max(gia, maxx)\n\t\t\tchan += gia\n\t\telse:\n\t\t\tmaxx = max(gia, maxx)\n\t\t\tif gia % 2 == 0:\n\t\t\t\tchan += gia\n\tmaxx2 = max(chan, maxx)\n\tfor times in range(q):\n\t\tquer = stdin.readline()\n\t\tif quer == \"0\\n\":\n\t\t\tprint(maxx)\n\t\telse:\n\t\t\tprint(maxx2)\n\t\n```","inputs":"2\n4\n6 8 4 2\n1\n0\n6\n12 3 20 5 80 1\n1\n1\n","output":"\n2\n3\n","actual_output":"2\n3\n","execution_success":true,"sample_index":12503},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"194_C. Cutting Figure","prompt":"Solve the following coding problem using the programming language python:\n\nYou've gotten an n \u00d7 m sheet of squared paper. Some of its squares are painted. Let's mark the set of all painted squares as A. Set A is connected. Your task is to find the minimum number of squares that we can delete from set A to make it not connected.\n\nA set of painted squares is called connected, if for every two squares a and b from this set there is a sequence of squares from the set, beginning in a and ending in b, such that in this sequence any square, except for the last one, shares a common side with the square that follows next in the sequence. An empty set and a set consisting of exactly one square are connected by definition.\n\nInput\n\nThe first input line contains two space-separated integers n and m (1 \u2264 n, m \u2264 50) \u2014 the sizes of the sheet of paper. \n\nEach of the next n lines contains m characters \u2014 the description of the sheet of paper: the j-th character of the i-th line equals either \"#\", if the corresponding square is painted (belongs to set A), or equals \".\" if the corresponding square is not painted (does not belong to set A). It is guaranteed that the set of all painted squares A is connected and isn't empty.\n\nOutput\n\nOn the first line print the minimum number of squares that need to be deleted to make set A not connected. If it is impossible, print -1. \n\nExamples\n\nInput\n\n5 4\n####\n#..#\n#..#\n#..#\n####\n\n\nOutput\n\n2\n\n\nInput\n\n5 5\n#####\n#...#\n#####\n#...#\n#####\n\n\nOutput\n\n2\n\nNote\n\nIn the first sample you can delete any two squares that do not share a side. After that the set of painted squares is not connected anymore.\n\nThe note to the second sample is shown on the figure below. To the left there is a picture of the initial set of squares. To the right there is a set with deleted squares. The deleted squares are marked with crosses. \n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, m = map(int, input().split())\np, s = [], {}\nx = 0\nfor i in range(n):\n for j, q in enumerate(input()):\n if q != '#': continue\n s[(i, j)] = x\n p.append([])\n if (i, j - 1) in s:\n p[x] += [x - 1]\n p[x - 1] += [x]\n if (i - 1, j) in s:\n y = s[(i - 1, j)]\n p[x] += [y]\n p[y] += [x]\n x += 1\n\nk = len(p)\nif k < 3:\n print(-1)\n exit()\n\nfor j in range(k):\n d = [1] * k\n d[j] = 0\n s = [p[j][0]]\n while s:\n j = s.pop()\n if not d[j]: continue\n d[j] = 0\n for i in p[j]:\n if d[i]: s.append(i)\n\n if 1 in d:\n print(1)\n break\n\nelse:\n print(2)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 5\\n#####\\n#...#\\n#####\\n#...#\\n#####\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n####\\n#..#\\n#..#\\n#..#\\n####\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n###\\n#.#\\n###\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n.#\\n.#\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n.#\\n##\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 5\\n#####\\n##.##\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n##\\n#.\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n###\\n###\\n.#.\\n###\\n###\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n##\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 7\\n.#####.\\n.#...#.\\n###.###\\n#.#.#.#\\n###.###\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n#####\\n#####\\n#....\\n#####\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 5\\n##.##\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n##\\n..\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n..........\\n.#####....\\n.#........\\n.#.###....\\n.#.###....\\n.#.###....\\n.#..##....\\n.#####....\\n..........\\n..........\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n##\\n##\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n##.##\\n#####\\n##.##\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n#########\\n#.......#\\n#.#####.#\\n#.#.#.#.#\\n#.#.#.#.#\\n#.#.#.#.#\\n#.#####.#\\n#...#...#\\n#########\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20 20\\n.....######.........\\n.....#....#.........\\n.....#....#.........\\n.....#....#.........\\n.....############...\\n.........##.....#...\\n..........#.....#...\\n..........#.....#...\\n..........###...#...\\n............#...#...\\n............#...#...\\n............#...#...\\n............#...#...\\n............#####...\\n....................\\n....................\\n....................\\n....................\\n....................\\n....................\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n.....\\n.....\\n..#..\\n..#..\\n.....\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\n##\\n##\\n#.\\n##\\n##\\n##\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 50\\n##................................................\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n...\\n.#.\\n...\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n####\\n####\\n####\\n####\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n#\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n..........\\n..........\\n..........\\n..........\\n...###....\\n...#.#....\\n...#####..\\n.....#.#..\\n.....###..\\n..........\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n.#.\\n.#.\\n...\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n###..\\n###..\\n#..##\\n#####\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '7 7\\n##.###.\\n#######\\n#..#..#\\n####.##\\n.....#.\\n######.\\n.##....\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 50\\n....##############################################\\n....#.......#...#..#....#..............#.........#\\n....##############################################\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n#\\n#\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n..........\\n..........\\n..........\\n..........\\n###.......\\n#.#.......\\n####......\\n####......\\n####......\\n###.......\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '50 1\\n#\\n#\\n#\\n#\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n#####\\n#####\\n##.##\\n##.##\\n##.##\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n.#.\\n###\\n.#.\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 10\\n.########.\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n###\\n##.\\n###\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 50\\n................................................##\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n#.\\n##\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n##\\n.#\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n###.#\\n#####\\n##.##\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n###..\\n..###\\n#..##\\n#####\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n#####\\n#####\\n#....\\n#####\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n###..\\n###..\\n#..##\\n#####\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 5\\n#.###\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n..........\\n.#####....\\n.#........\\n.#.###....\\n.#.###....\\n##.##.....\\n.#..##....\\n.#####....\\n..........\\n..........\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '7 7\\n##.###.\\n#######\\n#..#..#\\n####.##\\n.....#.\\n######.\\n....##.\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n...\\n.#.\\n...\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n.#.\\n###\\n#..\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n###..\\n###/.\\n#..##\\n#####\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n...\\n.#-\\n...\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n###..\\n###/.\\n#..#\"\\n#####\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n###..\\n###/.\\n#..#\"\\n####$\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n..........\\n..........\\n..........\\n..........\\n....###...\\n...#.#....\\n...#####..\\n.....#.#..\\n.....###..\\n..........\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n###..\\n###..\\n##..#\\n#####\\n#####\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 5\\n.########.\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78469","program":"```python\nn, m = map(int, input().split())\np, s = [], {}\nx = 0\nfor i in range(n):\n for j, q in enumerate(input()):\n if q != '#': continue\n s[(i, j)] = x\n p.append([])\n if (i, j - 1) in s:\n p[x] += [x - 1]\n p[x - 1] += [x]\n if (i - 1, j) in s:\n y = s[(i - 1, j)]\n p[x] += [y]\n p[y] += [x]\n x += 1\n\nk = len(p)\nif k < 3:\n print(-1)\n exit()\n\nfor j in range(k):\n d = [1] * k\n d[j] = 0\n s = [p[j][0]]\n while s:\n j = s.pop()\n if not d[j]: continue\n d[j] = 0\n for i in p[j]:\n if d[i]: s.append(i)\n\n if 1 in d:\n print(1)\n break\n\nelse:\n print(2)\n```","inputs":"5 5\n#####\n#...#\n#####\n#...#\n#####\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12506},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"218_C. Ice Skating","prompt":"Solve the following coding problem using the programming language python:\n\nBajtek is learning to skate on ice. He's a beginner, so his only mode of transportation is pushing off from a snow drift to the north, east, south or west and sliding until he lands in another snow drift. He has noticed that in this way it's impossible to get from some snow drifts to some other by any sequence of moves. He now wants to heap up some additional snow drifts, so that he can get from any snow drift to any other one. He asked you to find the minimal number of snow drifts that need to be created.\n\nWe assume that Bajtek can only heap up snow drifts at integer coordinates.\n\nInput\n\nThe first line of input contains a single integer n (1 \u2264 n \u2264 100) \u2014 the number of snow drifts. Each of the following n lines contains two integers xi and yi (1 \u2264 xi, yi \u2264 1000) \u2014 the coordinates of the i-th snow drift.\n\nNote that the north direction coin\u0441ides with the direction of Oy axis, so the east direction coin\u0441ides with the direction of the Ox axis. All snow drift's locations are distinct.\n\nOutput\n\nOutput the minimal number of snow drifts that need to be created in order for Bajtek to be able to reach any snow drift from any other one.\n\nExamples\n\nInput\n\n2\n2 1\n1 2\n\n\nOutput\n\n1\n\n\nInput\n\n2\n2 1\n4 1\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#start the code from here\nn=int(input())\nglobal parent\nparent=[i for i in range(n)]\n# n is total number of nodes \n# finding parent of a node\ndef find(w):\n\tglobal parent\n\tif parent[w]==w:\n\t\t\treturn w\n\telse:\n\t\treturn find(parent[w])\n\n\ndef union(a,b):\n\tglobal parent\n\tw=find(a)\n\ty=find(b)\n\tif w==y:\n\t\treturn \n\tparent[y]=w\n\n\n#start the code from here\nl=[]\nans=0\nfor i in range(n):\n\ta,b=map(int,input().split())\n\tfor u in range(len(l)):\n\t\tif l[u][0]==a or l[u][1]==b:\n\t\t\tunion(u,i)\n\t\telse:\n\t\t\tans+=1\n\tl.append([a,b])\npset=set()\nfor i in range(len(l)):\n\tpset.add(find(i))\nprint(len(pset)-1)\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n2 1\\n1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1\\n4 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n429 506\\n346 307\\n99 171\\n853 916\\n322 263\\n115 157\\n906 924\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1\\n1 2\\n2 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1\\n1 2\\n2 2\\n3 1\\n3 2\\n3 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '23\\n952 907\\n345 356\\n812 807\\n344 328\\n242 268\\n254 280\\n1000 990\\n80 78\\n424 396\\n595 608\\n755 813\\n383 380\\n55 56\\n598 633\\n203 211\\n508 476\\n600 593\\n206 192\\n855 882\\n517 462\\n967 994\\n642 657\\n493 488\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '24\\n171 35\\n261 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2\\n397 381\\n668 52\\n957 945\\n', 'output': '4\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78473","program":"```python\n#start the code from here\nn=int(input())\nglobal parent\nparent=[i for i in range(n)]\n# n is total number of nodes \n# finding parent of a node\ndef find(w):\n\tglobal parent\n\tif parent[w]==w:\n\t\t\treturn w\n\telse:\n\t\treturn find(parent[w])\n\n\ndef union(a,b):\n\tglobal parent\n\tw=find(a)\n\ty=find(b)\n\tif w==y:\n\t\treturn \n\tparent[y]=w\n\n\n#start the code from here\nl=[]\nans=0\nfor i in range(n):\n\ta,b=map(int,input().split())\n\tfor u in range(len(l)):\n\t\tif l[u][0]==a or l[u][1]==b:\n\t\t\tunion(u,i)\n\t\telse:\n\t\t\tans+=1\n\tl.append([a,b])\npset=set()\nfor i in range(len(l)):\n\tpset.add(find(i))\nprint(len(pset)-1)\n\n\n\n```","inputs":"2\n2 1\n1 2\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12507},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"267_A. Subtractions","prompt":"Solve the following coding problem using the programming language python:\n\nYou've got two numbers. As long as they are both larger than zero, they go through the same operation: subtract the lesser number from the larger one. If they equal substract one number from the another. For example, one operation transforms pair (4,17) to pair (4,13), it transforms (5,5) to (0,5).\n\nYou've got some number of pairs (ai, bi). How many operations will be performed for each of them?\n\nInput\n\nThe first line contains the number of pairs n (1 \u2264 n \u2264 1000). Then follow n lines, each line contains a pair of positive integers ai, bi (1 \u2264 ai, bi \u2264 109).\n\nOutput\n\nPrint the sought number of operations for each pair on a single line.\n\nExamples\n\nInput\n\n2\n4 17\n7 987654321\n\n\nOutput\n\n8\n141093479\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfor i in range(int(input())):\n a,b=map(int,input().split())\n sm=0\n while a and b:\n sm+=a//b\n t=b\n b=a%b\n a=t\n print(sm)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n4 17\\n7 987654321\\n', 'output': '8\\n141093479\\n'}, {'type': 'stdin_stdout', 'input': '20\\n1000000000 999999999\\n1000000000 999999999\\n1000000000 999999999\\n1000000000 999999999\\n1000000000 999999999\\n1000000000 999999999\\n1000000000 999999999\\n1000000000 999999999\\n1000000000 999999999\\n1000000000 999999999\\n1000000000 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Special Task","prompt":"Solve the following coding problem using the programming language python:\n\nSpecial Agent Smart Beaver works in a secret research department of ABBYY. He's been working there for a long time and is satisfied with his job, as it allows him to eat out in the best restaurants and order the most expensive and exotic wood types there. \n\nThe content special agent has got an important task: to get the latest research by British scientists on the English Language. These developments are encoded and stored in a large safe. The Beaver's teeth are strong enough, so the authorities assured that upon arriving at the place the beaver won't have any problems with opening the safe.\n\nAnd he finishes his aspen sprig and leaves for this important task. Of course, the Beaver arrived at the location without any problems, but alas. He can't open the safe with his strong and big teeth. At this point, the Smart Beaver get a call from the headquarters and learns that opening the safe with the teeth is not necessary, as a reliable source has sent the following information: the safe code consists of digits and has no leading zeroes. There also is a special hint, which can be used to open the safe. The hint is string s with the following structure:\n\n * if si = \"?\", then the digit that goes i-th in the safe code can be anything (between 0 to 9, inclusively); \n * if si is a digit (between 0 to 9, inclusively), then it means that there is digit si on position i in code; \n * if the string contains letters from \"A\" to \"J\", then all positions with the same letters must contain the same digits and the positions with distinct letters must contain distinct digits. \n * The length of the safe code coincides with the length of the hint. \n\n\n\nFor example, hint \"?JGJ9\" has such matching safe code variants: \"51919\", \"55959\", \"12329\", \"93539\" and so on, and has wrong variants such as: \"56669\", \"00111\", \"03539\" and \"13666\".\n\nAfter receiving such information, the authorities change the plan and ask the special agents to work quietly and gently and not to try to open the safe by mechanical means, and try to find the password using the given hint.\n\nAt a special agent school the Smart Beaver was the fastest in his platoon finding codes for such safes, but now he is not in that shape: the years take their toll ... Help him to determine the number of possible variants of the code to the safe, matching the given hint. After receiving this information, and knowing his own speed of entering codes, the Smart Beaver will be able to determine whether he will have time for tonight's show \"Beavers are on the trail\" on his favorite TV channel, or he should work for a sleepless night...\n\nInput\n\nThe first line contains string s \u2014 the hint to the safe code. String s consists of the following characters: ?, 0-9, A-J. It is guaranteed that the first character of string s doesn't equal to character 0.\n\nThe input limits for scoring 30 points are (subproblem A1): \n\n * 1 \u2264 |s| \u2264 5. \n\n\n\nThe input limits for scoring 100 points are (subproblems A1+A2): \n\n * 1 \u2264 |s| \u2264 105. \n\n\n\nHere |s| means the length of string s.\n\nOutput\n\nPrint the number of codes that match the given hint.\n\nExamples\n\nInput\n\nAJ\n\n\nOutput\n\n81\n\n\nInput\n\n1?AA\n\n\nOutput\n\n100\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nhint = input()\nseen = []\n\nif 'A' <= hint[0] <= 'J':\n num = 9\n seen = [hint[0]]\nelif '0' <= hint[0] <= '9':\n num = 1\nelif hint[0] == '?':\n num = 9\n\nfor l in hint[1:]:\n if 'A' <= l <= 'J':\n if not l in seen:\n num *= 10 - len(seen)\n seen += [l]\n elif l == '?':\n num *= 10\n\nprint(num)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1?AA\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': 'AJ\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '?C\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '?H2?H\\n', 'output': '900\\n'}, {'type': 'stdin_stdout', 'input': '9???\\n', 'output': '1000\\n'}, {'type': 'stdin_stdout', 'input': '??JG?\\n', 'output': '81000\\n'}, {'type': 'stdin_stdout', 'input': 'HH???\\n', 'output': '9000\\n'}, {'type': 'stdin_stdout', 'input': 'B??C?\\n', 'output': '81000\\n'}, {'type': 'stdin_stdout', 'input': 'IG5IJ\\n', 'output': '648\\n'}, {'type': 'stdin_stdout', 'input': '5???\\n', 'output': '1000\\n'}, {'type': 'stdin_stdout', 'input': '?J?5?\\n', 'output': '9000\\n'}, {'type': 'stdin_stdout', 'input': '3??\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '??C?C\\n', 'output': '9000\\n'}, {'type': 'stdin_stdout', 'input': '7\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'IJ?GH\\n', 'output': '45360\\n'}, {'type': 'stdin_stdout', 'input': 'CB?\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'BB?C?\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': 'H1I??\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': '???2\\n', 'output': '900\\n'}, {'type': 'stdin_stdout', 'input': 'CB\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '?BCB?\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': 'GJH2?\\n', 'output': '6480\\n'}, {'type': 'stdin_stdout', 'input': 'CC\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': 'BC??\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': 'JG50?\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'B?\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '?\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': 'I?GI?\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': 'BBB?\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '???\\n', 'output': '900\\n'}, {'type': 'stdin_stdout', 'input': 'A\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': 'C?\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '7I9G4\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '????\\n', 'output': '9000\\n'}, {'type': 'stdin_stdout', 'input': '1023456789??????????????????????????????????????ABCDIFGHIJ\\n', 'output': '362880000000000000000000000000000000000000000\\n'}, {'type': 'stdin_stdout', 'input': '5??\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '?BB\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'BC?\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': '?3?2\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'CDEFG\\n', 'output': '27216\\n'}, {'type': 'stdin_stdout', 'input': '??8\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'H?2H?\\n', 'output': '900\\n'}, {'type': 'stdin_stdout', 'input': '???HH\\n', 'output': '9000\\n'}, {'type': 'stdin_stdout', 'input': 'C??B?\\n', 'output': '81000\\n'}, {'type': 'stdin_stdout', 'input': 'JI5GI\\n', 'output': '648\\n'}, {'type': 'stdin_stdout', 'input': '??3\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'HG?JI\\n', 'output': '45360\\n'}, {'type': 'stdin_stdout', 'input': 'DB?\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'HI1??\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': '2???\\n', 'output': '1000\\n'}, {'type': 'stdin_stdout', 'input': 'BC\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': 'I?GH?\\n', 'output': '64800\\n'}, {'type': 'stdin_stdout', 'input': 'B\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': 'GFEDC\\n', 'output': '27216\\n'}, {'type': 'stdin_stdout', 'input': '8??\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': 'IJ?GI\\n', 'output': '6480\\n'}, {'type': 'stdin_stdout', 'input': '4J???\\n', 'output': '10000\\n'}, {'type': 'stdin_stdout', 'input': '???9\\n', 'output': '900\\n'}, {'type': 'stdin_stdout', 'input': '?J?4?\\n', 'output': '9000\\n'}, {'type': 'stdin_stdout', 'input': '?BDB?\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': 'HJH2?\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'DC\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': 'CC??\\n', 'output': '900\\n'}, {'type': 'stdin_stdout', 'input': '?05GJ\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': '?B\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'CBB?\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'D?\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '4G9I7\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '??5\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'BB?\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '?32?\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'AA?1\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'BJ\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '???GH\\n', 'output': '81000\\n'}, {'type': 'stdin_stdout', 'input': 'JJ5GI\\n', 'output': '648\\n'}, {'type': 'stdin_stdout', 'input': '?4?J?\\n', 'output': '9000\\n'}, {'type': 'stdin_stdout', 'input': '4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '?BD\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': '??1IH\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': '1???\\n', 'output': '1000\\n'}, {'type': 'stdin_stdout', 'input': 'BB\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '?B?BD\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': 'IJH2?\\n', 'output': '6480\\n'}, {'type': 'stdin_stdout', 'input': 'CD\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '?05JG\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'I?HH?\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': '?BBC\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'C\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '479IG\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '6??\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': 'B?C\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': '?23?\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'HFEDC\\n', 'output': '27216\\n'}, {'type': 'stdin_stdout', 'input': 'BI\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': 'IG5JJ\\n', 'output': '648\\n'}, {'type': 'stdin_stdout', 'input': 'J4???\\n', 'output': '9000\\n'}, {'type': 'stdin_stdout', 'input': '12\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'IG?JI\\n', 'output': '6480\\n'}, {'type': 'stdin_stdout', 'input': 'BD\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '?A?BD\\n', 'output': '64800\\n'}, {'type': 'stdin_stdout', 'input': 'IJI2?\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'DB\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '?15JG\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'H?IH?\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': '?BBD\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'D\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '478IG\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'C?B\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': '??32\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'HFEDB\\n', 'output': '27216\\n'}, {'type': 'stdin_stdout', 'input': 'CJ\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': 'IG5JI\\n', 'output': '648\\n'}, {'type': 'stdin_stdout', 'input': '21\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'JI?GI\\n', 'output': '6480\\n'}, {'type': 'stdin_stdout', 'input': 'EB\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': 'DB?B?\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': 'IJI1?\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'DA\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '?05JF\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': '?HI?H\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': '?DBB\\n', 'output': '810\\n'}, {'type': 'stdin_stdout', 'input': 'E\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '478HG\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '??42\\n', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': 'BDEFH\\n', 'output': '27216\\n'}, {'type': 'stdin_stdout', 'input': 'IB\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': 'JG5II\\n', 'output': '648\\n'}, {'type': 'stdin_stdout', 'input': 'JI?GJ\\n', 'output': '6480\\n'}, {'type': 'stdin_stdout', 'input': 'BE\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '?B?CD\\n', 'output': '64800\\n'}, {'type': 'stdin_stdout', 'input': 'IJH1?\\n', 'output': '6480\\n'}, {'type': 'stdin_stdout', 'input': 'AD\\n', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '50?JF\\n', 'output': '900\\n'}, {'type': 'stdin_stdout', 'input': '?II?H\\n', 'output': '8100\\n'}, {'type': 'stdin_stdout', 'input': 'BBD?\\n', 'output': '810\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78489","program":"```python\nhint = input()\nseen = []\n\nif 'A' <= hint[0] <= 'J':\n num = 9\n seen = [hint[0]]\nelif '0' <= hint[0] <= '9':\n num = 1\nelif hint[0] == '?':\n num = 9\n\nfor l in hint[1:]:\n if 'A' <= l <= 'J':\n if not l in seen:\n num *= 10 - len(seen)\n seen += [l]\n elif l == '?':\n num *= 10\n\nprint(num)\n\n```","inputs":"1?AA\n","output":"100\n","actual_output":"100\n","execution_success":true,"sample_index":12511},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"384_C. Milking cows","prompt":"Solve the following coding problem using the programming language python:\n\nIahub helps his grandfather at the farm. Today he must milk the cows. There are n cows sitting in a row, numbered from 1 to n from left to right. Each cow is either facing to the left or facing to the right. When Iahub milks a cow, all the cows that see the current cow get scared and lose one unit of the quantity of milk that they can give. A cow facing left sees all the cows with lower indices than her index, and a cow facing right sees all the cows with higher indices than her index. A cow that got scared once can get scared again (and lose one more unit of milk). A cow that has been milked once cannot get scared and lose any more milk. You can assume that a cow never loses all the milk she can give (a cow gives an infinitely amount of milk).\n\nIahub can decide the order in which he milks the cows. But he must milk each cow exactly once. Iahub wants to lose as little milk as possible. Print the minimum amount of milk that is lost.\n\nInput\n\nThe first line contains an integer n (1 \u2264 n \u2264 200000). The second line contains n integers a1, a2, ..., an, where ai is 0 if the cow number i is facing left, and 1 if it is facing right.\n\nOutput\n\nPrint a single integer, the minimum amount of lost milk.\n\nPlease, do not write the %lld specifier to read or write 64-bit integers in \u0421++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\nExamples\n\nInput\n\n4\n0 0 1 0\n\n\nOutput\n\n1\n\nInput\n\n5\n1 0 1 0 1\n\n\nOutput\n\n3\n\nNote\n\nIn the first sample Iahub milks the cows in the following order: cow 3, cow 4, cow 2, cow 1. When he milks cow 3, cow 4 loses 1 unit of milk. After that, no more milk is lost.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\nlis = list(map(int,input().split()))\nans=b=0\nfor i in range(n-1,-1,-1):\n if lis[i]==1:\n ans+=b\n else:\n b+=1\nprint(ans) \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 0 1 0 1\\n', 'output': '3'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 1 0\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '2\\n0 1\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '2\\n1 0\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1 1\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '2\\n0 0\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '50\\n1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0\\n', 'output': '416'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '2\\n1 1\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '100\\n1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0\\n', 'output': '1446'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '50\\n1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0\\n', 'output': '406\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 0 1 0 0\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 0 0 0 0\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-6\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-8\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-7\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-9\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-11\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-13\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-14\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-12\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-16\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-25\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-18\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n15\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-15\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-20\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-24\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n17\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-19\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-29\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-17\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-23\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-22\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-31\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n13\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n16\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-26\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-21\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-36\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n18\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-37\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-41\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-44\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-27\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-38\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-53\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n24\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n31\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n11\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n12\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-52\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n28\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-28\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-66\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-39\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-48\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-45\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-54\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n37\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n21\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n25\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-32\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-65\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n33\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-30\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78501","program":"```python\nn = int(input())\nlis = list(map(int,input().split()))\nans=b=0\nfor i in range(n-1,-1,-1):\n if lis[i]==1:\n ans+=b\n else:\n b+=1\nprint(ans) \n```","inputs":"5\n1 0 1 0 1\n","output":"3","actual_output":"3\n","execution_success":true,"sample_index":12512},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"405_B. Domino Effect","prompt":"Solve the following coding problem using the programming language python:\n\nLittle Chris knows there's no fun in playing dominoes, he thinks it's too random and doesn't require skill. Instead, he decided to play with the dominoes and make a \"domino show\".\n\nChris arranges n dominoes in a line, placing each piece vertically upright. In the beginning, he simultaneously pushes some of the dominoes either to the left or to the right. However, somewhere between every two dominoes pushed in the same direction there is at least one domino pushed in the opposite direction.\n\nAfter each second, each domino that is falling to the left pushes the adjacent domino on the left. Similarly, the dominoes falling to the right push their adjacent dominoes standing on the right. When a vertical domino has dominoes falling on it from both sides, it stays still due to the balance of the forces. The figure shows one possible example of the process.\n\n\n\nGiven the initial directions Chris has pushed the dominoes, find the number of the dominoes left standing vertically at the end of the process!\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 3000), the number of the dominoes in the line. The next line contains a character string s of length n. The i-th character of the string si is equal to \n\n * \"L\", if the i-th domino has been pushed to the left; \n * \"R\", if the i-th domino has been pushed to the right; \n * \".\", if the i-th domino has not been pushed. \n\n\n\nIt is guaranteed that if si = sj = \"L\" and i < j, then there exists such k that i < k < j and sk = \"R\"; if si = sj = \"R\" and i < j, then there exists such k that i < k < j and sk = \"L\".\n\nOutput\n\nOutput a single integer, the number of the dominoes that remain vertical at the end of the process.\n\nExamples\n\nInput\n\n14\n.L.R...LR..L..\n\n\nOutput\n\n4\n\n\nInput\n\n5\nR....\n\n\nOutput\n\n0\n\n\nInput\n\n1\n.\n\n\nOutput\n\n1\n\nNote\n\nThe first example case is shown on the figure. The four pieces that remain standing vertically are highlighted with orange.\n\nIn the second example case, all pieces fall down since the first piece topples all the other pieces.\n\nIn the last example case, a single piece has not been pushed in either direction.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\ns = input()+'R'\nr = 0\nflag = 'L'\na = 0\nfor _ in range(n+1):\n if s[_] == '.':\n a+=1\n elif s[_] == 'L':\n if flag =='L':\n a = 0\n else:\n if a%2==1:\n r+=1\n a = 0\n flag = 'L'\n else:\n if flag =='L':\n r += a\n a = 0\n flag = 'R'\n else:\n a = 0\n #print(r,a,flag)\nprint(r)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '14\\n.L.R...LR..L..\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '5\\nR....\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '1\\n.\\n', 'output': '1'}, 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'input': '4\\nR..L\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n..LR\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4\\nRL..\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '9\\nR...L....\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '8\\n.R.L....\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n.....R\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '10\\n.R........\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n.R..L\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\nL.R.......\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5\\nLR...\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n....R...L.\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '4\\nLR..\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\nL....R....\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '9\\n....L...R\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n........R.\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '10\\nR.......L.\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n.L.......R\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '11\\nL.....R..LR\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '10\\n.......L.R\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '14\\nL....RL...R.L.\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '9\\n.....L..R\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '8\\n.....L..\\n', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78505","program":"```python\nn = int(input())\ns = input()+'R'\nr = 0\nflag = 'L'\na = 0\nfor _ in range(n+1):\n if s[_] == '.':\n a+=1\n elif s[_] == 'L':\n if flag =='L':\n a = 0\n else:\n if a%2==1:\n r+=1\n a = 0\n flag = 'L'\n else:\n if flag =='L':\n r += a\n a = 0\n flag = 'R'\n else:\n a = 0\n #print(r,a,flag)\nprint(r)\n\n```","inputs":"14\n.L.R...LR..L..\n","output":"4","actual_output":"4\n","execution_success":true,"sample_index":12513},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"432_C. Prime Swaps","prompt":"Solve the following coding problem using the programming language python:\n\nYou have an array a[1], a[2], ..., a[n], containing distinct integers from 1 to n. Your task is to sort this array in increasing order with the following operation (you may need to apply it multiple times):\n\n * choose two indexes, i and j (1 \u2264 i < j \u2264 n; (j - i + 1) is a prime number); \n * swap the elements on positions i and j; in other words, you are allowed to apply the following sequence of assignments: tmp = a[i], a[i] = a[j], a[j] = tmp (tmp is a temporary variable). \n\n\n\nYou do not need to minimize the number of used operations. However, you need to make sure that there are at most 5n operations.\n\nInput\n\nThe first line contains integer n (1 \u2264 n \u2264 105). The next line contains n distinct integers a[1], a[2], ..., a[n] (1 \u2264 a[i] \u2264 n).\n\nOutput\n\nIn the first line, print integer k (0 \u2264 k \u2264 5n) \u2014 the number of used operations. Next, print the operations. Each operation must be printed as \"i j\" (1 \u2264 i < j \u2264 n; (j - i + 1) is a prime).\n\nIf there are multiple answers, you can print any of them.\n\nExamples\n\nInput\n\n3\n3 2 1\n\n\nOutput\n\n1\n1 3\n\n\nInput\n\n2\n1 2\n\n\nOutput\n\n0\n\n\nInput\n\n4\n4 2 3 1\n\n\nOutput\n\n3\n2 4\n1 2\n2 4\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef sieve(n): \n p = 2\n while (p * p <= n): \n if (prime[p] == True): \n for i in range(p * p, n+1, p): \n prime[i] = False\n p += 1\nn = int(input())\nprime = [True for i in range(n+2)] \nprime[0]=0\nprime[1]=0\nsieve(n+1)\naa=[0]*(n+1)\nfor i in range(n+1):\n if prime[i]:\n aa[i]=i\n else:\n aa[i]=aa[i-1] \nlis = [0]+list(map(int,input().split()))\nind=[0]*(n+1)\nct=0\nfor i in range(1,n+1):\n ind[lis[i]]=i\nans=[]\nfor i in range(1,n+1):\n j=ind[i]\n while j>i:\n t=i\n step=aa[j-t+1]-1 \n ct+=1\n ind[lis[j-step]]=j;ind[lis[j]]=j-step\n ans.append([j-step,j])\n lis[j-step],lis[j]=lis[j],lis[j-step]\n j-=step\nprint(ct)\nfor i in ans:\n print(*i) \n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n3 2 1\\n', 'output': '1\\n1 3\\n\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 2 3 1\\n', 'output': '3\\n2 4\\n1 2\\n2 4\\n\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 2\\n', 'output': '1\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3 4 1 2\\n', 'output': '2\\n1 3\\n2 4\\n\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 1 2\\n', 'output': '2\\n1 2\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 9 8 7 6 5 4 3 2 1\\n', 'output': '15\\n4 10\\n2 4\\n1 2\\n3 9\\n2 3\\n4 8\\n3 4\\n5 7\\n4 5\\n5 6\\n6 7\\n8 10\\n7 8\\n8 9\\n9 10\\n\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 3 5 7 8 6 4 2\\n', 'output': '6\\n2 8\\n4 8\\n3 4\\n5 7\\n4 5\\n7 8\\n\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1\\n', 'output': '1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '100\\n100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1\\n', 'output': '198\\n4 100\\n2 4\\n1 2\\n3 99\\n2 3\\n10 98\\n4 10\\n3 4\\n9 97\\n5 9\\n4 5\\n8 96\\n6 8\\n5 6\\n7 95\\n6 7\\n12 94\\n8 12\\n7 8\\n11 93\\n9 11\\n8 9\\n10 92\\n9 10\\n13 91\\n11 13\\n10 11\\n12 90\\n11 12\\n17 89\\n13 17\\n12 13\\n16 88\\n14 16\\n13 14\\n15 87\\n14 15\\n16 86\\n15 16\\n19 85\\n17 19\\n16 17\\n18 84\\n17 18\\n23 83\\n19 23\\n18 19\\n22 82\\n20 22\\n19 20\\n21 81\\n20 21\\n22 80\\n21 22\\n27 79\\n23 27\\n22 23\\n26 78\\n24 26\\n23 24\\n25 77\\n24 25\\n30 76\\n26 30\\n25 26\\n29 75\\n27 29\\n26 27\\n28 74\\n27 28\\n31 73\\n29 31\\n28 29\\n30 72\\n29 30\\n31 71\\n30 31\\n34 70\\n32 34\\n31 32\\n33 69\\n32 33\\n38 68\\n34 38\\n33 34\\n37 67\\n35 37\\n34 35\\n36 66\\n35 36\\n37 65\\n36 37\\n42 64\\n38 42\\n37 38\\n41 63\\n39 41\\n38 39\\n40 62\\n39 40\\n43 61\\n41 43\\n40 41\\n42 60\\n41 42\\n43 59\\n42 43\\n46 58\\n44 46\\n43 44\\n45 57\\n44 45\\n46 56\\n45 46\\n49 55\\n47 49\\n46 47\\n48 54\\n47 48\\n49 53\\n48 49\\n50 52\\n49 50\\n50 51\\n51 52\\n53 55\\n52 53\\n53 54\\n54 55\\n56 58\\n55 56\\n56 57\\n57 58\\n59 61\\n58 59\\n60 64\\n59 60\\n61 63\\n60 61\\n61 62\\n62 63\\n64 68\\n63 64\\n65 67\\n64 65\\n65 66\\n66 67\\n68 70\\n67 68\\n68 69\\n69 70\\n71 73\\n70 71\\n72 76\\n71 72\\n73 75\\n72 73\\n73 74\\n75 79\\n74 75\\n76 78\\n75 76\\n76 77\\n77 78\\n79 83\\n78 79\\n80 82\\n79 80\\n80 81\\n81 82\\n83 85\\n82 83\\n83 84\\n85 89\\n84 85\\n86 88\\n85 86\\n86 87\\n87 88\\n89 91\\n88 89\\n90 94\\n89 90\\n91 93\\n90 91\\n92 98\\n91 92\\n93 97\\n92 93\\n94 96\\n93 94\\n94 95\\n95 96\\n96 97\\n98 100\\n97 98\\n98 99\\n99 100\\n\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 3\\n', 'output': '1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 4 2 3 5\\n', 'output': '2\\n2 3\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 4 3 5\\n', 'output': '2\\n1 2\\n3 4\\n\\n'}, {'type': 'stdin_stdout', 'input': '6\\n5 3 6 1 4 2\\n', 'output': '6\\n2 4\\n1 2\\n2 6\\n3 4\\n4 5\\n5 6\\n\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 3 2 1\\n', 'output': '4\\n2 4\\n1 2\\n2 3\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 1 4 2 5\\n', 'output': '3\\n1 2\\n2 4\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 1\\n', 'output': '2\\n1 3\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 6 5 7 8 3 4 2\\n', 'output': '7\\n2 8\\n4 6\\n3 4\\n5 7\\n4 5\\n6 8\\n7 8\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 4 1 3\\n', 'output': '3\\n1 3\\n2 3\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '6\\n5 3 4 1 6 2\\n', 'output': '5\\n2 4\\n1 2\\n2 6\\n3 4\\n5 6\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78509","program":"```python\ndef sieve(n): \n p = 2\n while (p * p <= n): \n if (prime[p] == True): \n for i in range(p * p, n+1, p): \n prime[i] = False\n p += 1\nn = int(input())\nprime = [True for i in range(n+2)] \nprime[0]=0\nprime[1]=0\nsieve(n+1)\naa=[0]*(n+1)\nfor i in range(n+1):\n if prime[i]:\n aa[i]=i\n else:\n aa[i]=aa[i-1] \nlis = [0]+list(map(int,input().split()))\nind=[0]*(n+1)\nct=0\nfor i in range(1,n+1):\n ind[lis[i]]=i\nans=[]\nfor i in range(1,n+1):\n j=ind[i]\n while j>i:\n t=i\n step=aa[j-t+1]-1 \n ct+=1\n ind[lis[j-step]]=j;ind[lis[j]]=j-step\n ans.append([j-step,j])\n lis[j-step],lis[j]=lis[j],lis[j-step]\n j-=step\nprint(ct)\nfor i in ans:\n print(*i) \n \n```","inputs":"3\n3 2 1\n","output":"1\n1 3\n\n","actual_output":"1\n1 3\n","execution_success":true,"sample_index":12514},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"454_E. Little Pony and Summer Sun Celebration","prompt":"Solve the following coding problem using the programming language python:\n\nTwilight Sparkle learnt that the evil Nightmare Moon would return during the upcoming Summer Sun Celebration after one thousand years of imprisonment on the moon. She tried to warn her mentor Princess Celestia, but the princess ignored her and sent her to Ponyville to check on the preparations for the celebration.\n\n\n\nTwilight Sparkle wanted to track the path of Nightmare Moon. Unfortunately, she didn't know the exact path. What she knew is the parity of the number of times that each place Nightmare Moon visited. Can you help Twilight Sparkle to restore any path that is consistent with this information?\n\nPonyville can be represented as an undirected graph (vertices are places, edges are roads between places) without self-loops and multi-edges. The path can start and end at any place (also it can be empty). Each place can be visited multiple times. The path must not visit more than 4n places.\n\nInput\n\nThe first line contains two integers n and m (2 \u2264 n \u2264 105; 0 \u2264 m \u2264 105) \u2014 the number of places and the number of roads in Ponyville. Each of the following m lines contains two integers ui, vi (1 \u2264 ui, vi \u2264 n; ui \u2260 vi), these integers describe a road between places ui and vi.\n\nThe next line contains n integers: x1, x2, ..., xn (0 \u2264 xi \u2264 1) \u2014 the parity of the number of times that each place must be visited. If xi = 0, then the i-th place must be visited even number of times, else it must be visited odd number of times.\n\nOutput\n\nOutput the number of visited places k in the first line (0 \u2264 k \u2264 4n). Then output k integers \u2014 the numbers of places in the order of path. If xi = 0, then the i-th place must appear in the path even number of times, else i-th place must appear in the path odd number of times. Note, that given road system has no self-loops, therefore any two neighbouring places in the path must be distinct.\n\nIf there is no required path, output -1. If there multiple possible paths, you can output any of them.\n\nExamples\n\nInput\n\n3 2\n1 2\n2 3\n1 1 1\n\n\nOutput\n\n3\n1 2 3\n\n\nInput\n\n5 7\n1 2\n1 3\n1 4\n1 5\n3 4\n3 5\n4 5\n0 1 0 1 0\n\n\nOutput\n\n10\n2 1 3 4 5 4 5 4 3 1 \n\nInput\n\n2 0\n0 0\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n\"\"\"\nCodeforces Contest 259 Div 1 Problem C\n\nAuthor : chaotic_iak\nLanguage: Python 3.3.4\n\"\"\"\n\ndef main():\n\n # Read N and M from problem statement.\n n,m = read()\n\n # Set up an adjacency list for each vertex.\n edges = [[] for _ in range(n+1)]\n for i in range(m):\n a,b = read()\n edges[a].append(b)\n edges[b].append(a)\n\n # Read the parity array. Pad with 0 at the front to make it 1-based like in problem.\n parity = [0] + read()\n\n # Find odd vertex with minimum index.\n mn = 0\n while mn < n+1 and not parity[mn]: mn += 1\n\n # If none, then no need to output anything.\n if mn == n+1:\n print(0)\n return\n\n # Create the visited array, stack for DFS, and list to store the resulting path.\n visited = [0] * (n+1)\n dfs_stack = [mn]\n dfs_path = []\n\n # Call one step of DFS as long as the stack is not empty. (See below.)\n while dfs_stack: dfs(dfs_stack, dfs_path, visited, edges, parity)\n\n # If the root is odd, remove the last element of the path.\n if parity[mn]:\n dfs_path.pop()\n parity[mn] = 0\n\n # If there's still an odd vertex, then we have two separate components with\n # odd vertices; we failed.\n if sum(parity):\n print(-1)\n\n # Otherwise, print the resulting path.\n else:\n print(len(dfs_path))\n print(\" \".join(map(str, dfs_path)))\n\ndef dfs(dfs_stack, dfs_path, visited, edges, parity):\n\n # Take top element of the stack. This is positive if it's a downward edge (away\n # from root) and negative if it's an upward edge (to root), and its absolute\n # value is the index of the destination vertex.\n v = dfs_stack.pop()\n\n # If a downward edge:\n if v > 0:\n\n # If target vertex has been visited, no need to visit it again. Pop the\n # top item of the stack (which is a return edge for this vertex, but unused).\n if visited[v]:\n dfs_stack.pop()\n return\n\n # Set current vertex as visited and append it to path. Toggle the parity.\n visited[v] = 1\n dfs_path.append(v)\n parity[v] = 1 - parity[v]\n\n # Add a pair of downward/upward edges for each neighbor of this vertex.\n for i in edges[v]:\n dfs_stack.append(-v)\n dfs_stack.append(i)\n\n # If an upward edge:\n else:\n\n # Set v as absolute value. Take the child just visited, u, which is stored as\n # the last element of final path. Append the current vertex v to final path\n # and toggle the parity of v.\n v = -v\n u = dfs_path[-1]\n dfs_path.append(v)\n parity[v] = 1 - parity[v]\n\n # If u is odd, visit u and return back to v one more time. This toggles the\n # parity of u but not v.\n if parity[u]:\n dfs_path.append(u)\n dfs_path.append(v)\n parity[u] = 1 - parity[u]\n parity[v] = 1 - parity[v]\n\n # If u is even, we don't need to do anything.\n else:\n pass\n\n################################### NON-SOLUTION STUFF BELOW\n\ndef read(mode=2):\n # 0: String\n # 1: List of strings\n # 2: List of integers\n inputs = input().strip()\n if mode == 0: return inputs\n if mode == 1: return inputs.split()\n if mode == 2: return list(map(int, inputs.split()))\n\ndef read_str(): return read(0)\ndef read_int(): return read(2)[0]\n\ndef write(s=\"\\n\"):\n if isinstance(s, list): s = \" \".join(map(str, s))\n s = str(s)\n print(s, end=\"\")\n\nmain()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 0\\n0 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 7\\n1 2\\n1 3\\n1 4\\n1 5\\n3 4\\n3 5\\n4 5\\n0 1 0 1 0\\n', 'output': '10\\n2 1 3 4 5 4 5 4 3 1 '}, {'type': 'stdin_stdout', 'input': '3 2\\n1 2\\n2 3\\n1 1 1\\n', 'output': '7\\n1 2 3 2 1 2 1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n1 3\\n3 4\\n3 5\\n6 1\\n7 6\\n8 7\\n9 7\\n10 1\\n2 4\\n0 1 0 1 1 0 0 1 1 0\\n', 'output': '29\\n2 1 3 4 3 5 3 1 3 1 6 7 8 7 9 7 6 7 6 1 6 1 10 1 10 1 2 1 2\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1 2\\n3 4\\n0 0 0 1\\n', 'output': '5\\n4 3 4 3 4\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n2 3\\n0 1 1\\n', 'output': '2\\n2 3 '}, {'type': 'stdin_stdout', 'input': '2 0\\n1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n1 0\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n3 1\\n4 2\\n2 5\\n6 2\\n7 4\\n4 8\\n2 9\\n10 4\\n5 10\\n0 0 1 0 1 1 1 1 0 0\\n', 'output': '25\\n3 1 2 4 7 4 8 4 10 5 10 4 2 6 2 9 2 9 2 1 2 1 3 1 3\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n0 1\\n', 'output': '1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n2 3\\n3 4\\n2 5\\n3 6\\n7 4\\n8 7\\n9 1\\n7 10\\n5 3\\n1 0 0 1 1 0 0 1 1 1\\n', 'output': '26\\n1 2 3 4 7 8 7 10 7 4 7 4 3 6 3 6 3 5 3 2 3 2 1 2 1 9 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n3 1\\n4 3\\n1 5\\n6 5\\n7 4\\n8 7\\n9 5\\n10 4\\n6 10\\n1 0 0 1 1 0 0 1 0 0\\n', 'output': '22\\n1 2 1 2 1 3 4 7 8 7 4 10 6 5 9 5 9 5 6 10 4 3 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2 1\\n2 3\\n4 2\\n4 5\\n3 6\\n5 7\\n8 4\\n4 9\\n5 10\\n4 7\\n0 0 1 0 1 1 1 0 1 0\\n', 'output': '27\\n3 2 1 2 1 2 4 5 7 5 10 5 10 5 4 5 4 8 4 8 4 9 4 2 3 6 3\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1 3\\n2 4\\n0 1 0 1\\n', 'output': '2\\n2 4 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2 1\\n3 1\\n4 1\\n3 5\\n6 2\\n5 7\\n1 8\\n5 9\\n10 5\\n7 2\\n1 0 0 0 1 1 1 0 0 1\\n', 'output': '31\\n1 2 6 2 7 5 3 5 3 5 9 5 9 5 10 5 7 5 7 2 1 2 1 4 1 4 1 8 1 8 1\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n3 4\\n0 0 1 1\\n', 'output': '2\\n3 4 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n2 3\\n4 1\\n2 5\\n3 6\\n7 6\\n8 1\\n9 4\\n1 10\\n7 1\\n0 1 1 0 1 1 1 1 1 1\\n', 'output': '22\\n2 1 4 9 4 1 8 1 10 1 7 6 3 6 7 6 7 1 2 1 2 5 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n1 3\\n3 4\\n3 5\\n6 1\\n7 6\\n8 7\\n9 7\\n10 2\\n2 4\\n0 1 0 1 1 0 0 1 1 0\\n', 'output': '29\\n2 1 3 4 3 5 3 1 3 1 6 7 8 7 9 7 6 7 6 1 6 1 2 1 2 10 2 10 2 '}, {'type': 'stdin_stdout', 'input': '3 1\\n2 1\\n0 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n1 0\\n', 'output': '1\\n1 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n3 1\\n5 3\\n1 5\\n6 5\\n7 4\\n8 7\\n9 5\\n10 4\\n6 10\\n1 0 0 1 1 0 0 1 0 0\\n', 'output': '28\\n1 2 1 2 1 3 5 6 10 4 7 8 7 4 10 4 10 6 10 6 5 6 5 9 5 9 5 3 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2 1\\n2 3\\n4 2\\n4 2\\n3 6\\n5 7\\n8 4\\n4 9\\n5 10\\n4 7\\n0 0 1 0 1 1 1 0 1 0\\n', 'output': '27\\n3 2 1 2 1 2 4 8 4 8 4 9 4 7 5 10 5 10 5 7 4 7 4 2 3 6 3 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2 1\\n3 1\\n4 1\\n3 5\\n6 4\\n5 7\\n1 8\\n5 9\\n10 5\\n7 2\\n1 0 0 0 1 1 1 0 0 1\\n', 'output': '27\\n1 2 7 5 3 5 3 5 9 5 9 5 10 5 7 5 7 2 1 4 6 4 1 8 1 8 1 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n2 3\\n4 1\\n1 5\\n3 6\\n7 6\\n8 1\\n9 4\\n1 10\\n7 1\\n0 1 1 0 1 1 1 1 1 1\\n', 'output': '20\\n2 1 4 9 4 1 5 1 8 1 10 1 7 6 3 6 7 6 7 1 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2 1\\n2 3\\n4 2\\n4 2\\n3 6\\n5 7\\n8 4\\n4 9\\n5 10\\n2 7\\n0 0 1 0 1 1 1 0 1 0\\n', 'output': '27\\n3 2 1 2 1 2 4 8 4 8 4 9 4 2 7 5 10 5 10 5 7 2 7 2 3 6 3 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2 1\\n3 1\\n4 1\\n3 5\\n6 4\\n5 7\\n1 8\\n5 10\\n10 5\\n7 2\\n1 0 0 0 1 1 1 0 0 1\\n', 'output': '23\\n1 2 7 5 3 5 3 5 10 5 7 5 7 2 1 4 6 4 1 8 1 8 1 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n2 3\\n4 1\\n1 5\\n3 6\\n7 6\\n8 1\\n9 4\\n1 10\\n7 1\\n0 1 1 0 1 1 1 1 0 1\\n', 'output': '27\\n2 1 4 9 4 9 4 1 4 1 5 1 8 1 10 1 7 6 3 6 7 6 7 1 2 1 2 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2 1\\n3 1\\n7 1\\n3 5\\n6 4\\n5 4\\n1 8\\n5 10\\n10 5\\n7 2\\n1 0 0 0 1 1 1 0 0 1\\n', 'output': '19\\n1 2 7 2 1 3 5 4 6 4 5 10 5 3 1 8 1 8 1 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2 2\\n1 3\\n3 4\\n3 5\\n6 1\\n7 6\\n8 7\\n9 7\\n10 1\\n2 4\\n0 1 0 1 1 0 0 1 1 0\\n', 'output': '29\\n2 4 3 1 6 7 8 7 9 7 6 7 6 1 6 1 10 1 10 1 3 1 3 5 3 4 2 4 2 '}, {'type': 'stdin_stdout', 'input': '1 0\\n0 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n3 1\\n4 3\\n1 5\\n6 5\\n7 4\\n8 7\\n9 5\\n10 4\\n6 10\\n1 0 0 1 1 0 0 1 0 1\\n', 'output': '29\\n1 2 1 2 1 3 4 7 8 7 4 10 6 5 9 5 9 5 6 10 4 10 4 3 4 3 1 3 1 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2 1\\n3 1\\n4 1\\n3 5\\n6 2\\n5 7\\n1 8\\n5 9\\n10 5\\n4 2\\n1 0 0 0 1 1 1 0 0 1\\n', 'output': '25\\n1 2 6 2 4 2 4 2 1 3 5 7 5 9 5 9 5 10 5 3 1 8 1 8 1 '}, {'type': 'stdin_stdout', 'input': '5 7\\n1 2\\n1 2\\n1 4\\n1 5\\n3 4\\n3 5\\n4 5\\n0 1 0 1 0\\n', 'output': '12\\n2 1 4 3 5 3 5 3 4 3 4 1 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n1 1\\n3 4\\n3 5\\n6 1\\n7 6\\n8 7\\n9 7\\n10 2\\n2 4\\n0 1 0 1 1 0 0 1 1 0\\n', 'output': '29\\n2 1 6 7 8 7 9 7 6 7 6 1 6 1 2 1 2 10 2 10 2 4 3 5 3 4 2 4 2 '}, {'type': 'stdin_stdout', 'input': '10 10\\n4 1\\n3 1\\n4 1\\n3 5\\n6 4\\n5 7\\n1 8\\n5 9\\n10 5\\n7 2\\n1 0 0 0 1 1 1 0 0 1\\n', 'output': '25\\n1 4 6 4 1 3 5 7 2 7 2 7 5 9 5 9 5 10 5 3 1 8 1 8 1 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 3\\n2 3\\n4 1\\n1 5\\n3 6\\n7 6\\n8 1\\n9 4\\n1 10\\n7 1\\n0 1 1 0 1 1 1 1 1 1\\n', 'output': '22\\n2 3 1 4 9 4 1 5 1 8 1 10 1 7 6 7 1 7 1 3 1 3 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2 2\\n2 3\\n4 2\\n4 2\\n3 6\\n5 7\\n8 4\\n4 9\\n5 10\\n2 7\\n0 0 1 0 1 1 1 0 1 0\\n', 'output': '23\\n3 2 4 8 4 8 4 9 4 2 7 5 10 5 10 5 7 2 7 2 3 6 3 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n2 3\\n4 1\\n1 5\\n3 6\\n7 4\\n8 1\\n9 4\\n1 10\\n7 1\\n0 1 1 0 1 1 1 1 0 1\\n', 'output': '25\\n2 1 4 7 4 9 4 9 4 1 5 1 8 1 10 1 2 1 2 3 6 3 2 3 2 '}, {'type': 'stdin_stdout', 'input': '2 -1\\n0 1\\n', 'output': '1\\n2 '}, {'type': 'stdin_stdout', 'input': '4 1\\n3 3\\n0 0 1 0\\n', 'output': '1\\n3 '}, {'type': 'stdin_stdout', 'input': '10 10\\n4 1\\n3 1\\n4 1\\n3 5\\n6 4\\n5 7\\n1 8\\n5 9\\n10 5\\n7 2\\n1 1 0 0 1 1 1 0 0 1\\n', 'output': '28\\n1 4 6 4 1 3 5 7 2 7 5 7 5 9 5 9 5 10 5 3 5 3 1 3 1 8 1 8 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 3\\n2 3\\n4 1\\n1 5\\n3 6\\n7 6\\n8 1\\n9 4\\n1 10\\n7 1\\n0 1 1 0 0 1 1 1 1 1\\n', 'output': '25\\n2 3 1 4 9 4 1 5 1 5 1 8 1 10 1 7 6 7 1 7 1 3 2 3 2 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n2 3\\n4 1\\n1 5\\n3 6\\n7 4\\n8 1\\n9 4\\n1 10\\n7 1\\n0 1 1 0 1 1 1 1 0 0\\n', 'output': '24\\n2 1 4 7 4 9 4 9 4 1 5 1 8 1 10 1 10 1 2 3 6 3 2 3 '}, {'type': 'stdin_stdout', 'input': '3 0\\n1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n2 3\\n3 4\\n2 5\\n3 6\\n7 4\\n2 7\\n9 1\\n7 10\\n5 3\\n1 0 0 1 1 0 0 1 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n2 1\\n1 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 -1\\n1 0\\n', 'output': '1\\n1 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n1 3\\n3 4\\n2 5\\n3 6\\n7 4\\n2 7\\n9 1\\n7 10\\n5 3\\n1 0 0 1 1 0 0 1 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n2 1\\n1 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n1 3\\n3 4\\n2 5\\n3 6\\n7 4\\n2 7\\n9 1\\n7 10\\n5 3\\n1 0 0 1 1 0 1 1 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n2 1\\n3 1\\n7 1\\n3 5\\n6 4\\n5 7\\n1 8\\n5 10\\n10 5\\n7 2\\n1 0 0 0 1 1 1 0 0 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n4 1\\n1 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n4 1\\n1 1 2\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n3 3\\n0 0 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 -1\\n0 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n2 2\\n1 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n1 3\\n3 4\\n2 5\\n3 6\\n7 4\\n2 7\\n9 1\\n7 10\\n5 3\\n1 0 0 1 0 0 0 1 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n2 1\\n3 2\\n7 1\\n3 5\\n6 4\\n5 7\\n1 8\\n5 10\\n10 5\\n7 2\\n1 0 0 0 1 1 1 0 0 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n1 1\\n3 4\\n3 5\\n6 1\\n7 6\\n5 7\\n9 7\\n10 2\\n2 4\\n0 1 0 1 1 0 0 1 1 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2\\n1 3\\n3 4\\n1 5\\n3 6\\n7 4\\n2 7\\n9 1\\n7 10\\n5 3\\n1 0 0 1 0 0 0 1 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n2 2\\n2 3\\n4 2\\n4 2\\n3 6\\n5 7\\n8 4\\n4 9\\n5 10\\n2 7\\n1 0 1 0 1 1 1 0 1 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 -1\\n1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n4 1\\n3 1\\n4 1\\n3 5\\n6 4\\n5 10\\n1 8\\n5 9\\n10 5\\n7 2\\n1 1 0 0 1 1 1 0 0 1\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78513","program":"```python\n\"\"\"\nCodeforces Contest 259 Div 1 Problem C\n\nAuthor : chaotic_iak\nLanguage: Python 3.3.4\n\"\"\"\n\ndef main():\n\n # Read N and M from problem statement.\n n,m = read()\n\n # Set up an adjacency list for each vertex.\n edges = [[] for _ in range(n+1)]\n for i in range(m):\n a,b = read()\n edges[a].append(b)\n edges[b].append(a)\n\n # Read the parity array. Pad with 0 at the front to make it 1-based like in problem.\n parity = [0] + read()\n\n # Find odd vertex with minimum index.\n mn = 0\n while mn < n+1 and not parity[mn]: mn += 1\n\n # If none, then no need to output anything.\n if mn == n+1:\n print(0)\n return\n\n # Create the visited array, stack for DFS, and list to store the resulting path.\n visited = [0] * (n+1)\n dfs_stack = [mn]\n dfs_path = []\n\n # Call one step of DFS as long as the stack is not empty. (See below.)\n while dfs_stack: dfs(dfs_stack, dfs_path, visited, edges, parity)\n\n # If the root is odd, remove the last element of the path.\n if parity[mn]:\n dfs_path.pop()\n parity[mn] = 0\n\n # If there's still an odd vertex, then we have two separate components with\n # odd vertices; we failed.\n if sum(parity):\n print(-1)\n\n # Otherwise, print the resulting path.\n else:\n print(len(dfs_path))\n print(\" \".join(map(str, dfs_path)))\n\ndef dfs(dfs_stack, dfs_path, visited, edges, parity):\n\n # Take top element of the stack. This is positive if it's a downward edge (away\n # from root) and negative if it's an upward edge (to root), and its absolute\n # value is the index of the destination vertex.\n v = dfs_stack.pop()\n\n # If a downward edge:\n if v > 0:\n\n # If target vertex has been visited, no need to visit it again. Pop the\n # top item of the stack (which is a return edge for this vertex, but unused).\n if visited[v]:\n dfs_stack.pop()\n return\n\n # Set current vertex as visited and append it to path. Toggle the parity.\n visited[v] = 1\n dfs_path.append(v)\n parity[v] = 1 - parity[v]\n\n # Add a pair of downward/upward edges for each neighbor of this vertex.\n for i in edges[v]:\n dfs_stack.append(-v)\n dfs_stack.append(i)\n\n # If an upward edge:\n else:\n\n # Set v as absolute value. Take the child just visited, u, which is stored as\n # the last element of final path. Append the current vertex v to final path\n # and toggle the parity of v.\n v = -v\n u = dfs_path[-1]\n dfs_path.append(v)\n parity[v] = 1 - parity[v]\n\n # If u is odd, visit u and return back to v one more time. This toggles the\n # parity of u but not v.\n if parity[u]:\n dfs_path.append(u)\n dfs_path.append(v)\n parity[u] = 1 - parity[u]\n parity[v] = 1 - parity[v]\n\n # If u is even, we don't need to do anything.\n else:\n pass\n\n################################### NON-SOLUTION STUFF BELOW\n\ndef read(mode=2):\n # 0: String\n # 1: List of strings\n # 2: List of integers\n inputs = input().strip()\n if mode == 0: return inputs\n if mode == 1: return inputs.split()\n if mode == 2: return list(map(int, inputs.split()))\n\ndef read_str(): return read(0)\ndef read_int(): return read(2)[0]\n\ndef write(s=\"\\n\"):\n if isinstance(s, list): s = \" \".join(map(str, s))\n s = str(s)\n print(s, end=\"\")\n\nmain()\n```","inputs":"2 0\n0 0\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12515},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"477_C. Dreamoon and Strings","prompt":"Solve the following coding problem using the programming language python:\n\nDreamoon has a string s and a pattern string p. He first removes exactly x characters from s obtaining string s' as a result. Then he calculates that is defined as the maximal number of non-overlapping substrings equal to p that can be found in s'. He wants to make this number as big as possible.\n\nMore formally, let's define as maximum value of over all s' that can be obtained by removing exactly x characters from s. Dreamoon wants to know for all x from 0 to |s| where |s| denotes the length of string s.\n\nInput\n\nThe first line of the input contains the string s (1 \u2264 |s| \u2264 2 000).\n\nThe second line of the input contains the string p (1 \u2264 |p| \u2264 500).\n\nBoth strings will only consist of lower case English letters.\n\nOutput\n\nPrint |s| + 1 space-separated integers in a single line representing the for all x from 0 to |s|.\n\nExamples\n\nInput\n\naaaaa\naa\n\n\nOutput\n\n2 2 1 1 0 0\n\n\nInput\n\naxbaxxb\nab\n\n\nOutput\n\n0 1 1 2 1 1 0 0\n\nNote\n\nFor the first sample, the corresponding optimal values of s' after removal 0 through |s| = 5 characters from s are {\"aaaaa\", \"aaaa\", \"aaa\", \"aa\", \"a\", \"\"}. \n\nFor the second sample, possible corresponding optimal values of s' are {\"axbaxxb\", \"abaxxb\", \"axbab\", \"abab\", \"aba\", \"ab\", \"a\", \"\"}.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ns, p = input(), input()\nn, m = len(s) + 1, len(p)\nd = [[0] * n for t in range(n)]\nfor x in range(1, n):\n i, j = x, m\n while i and j:\n j -= s[i - 1] == p[j - 1]\n i -= 1\n if not j:\n for y in range(i + 1): d[x][y + x - i - m] = d[i][y] + 1\n for y in range(x): d[x][y] = max(d[x][y], d[x - 1][y])\nprint(*d[-1])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'aaaaa\\naa\\n', 'output': '2 2 1 1 0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'axbaxxb\\nab\\n', 'output': '0 1 1 2 1 1 0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'abxxxaxbxaxxxba\\naba\\n', 'output': '0 0 1 1 1 1 2 2 2 2 1 1 1 0 0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'ababababababababa\\naba\\n', 'output': '4 4 4 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'aaaaaaaaaaa\\nb\\n', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'a\\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\n', 'output': '0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'a\\naa\\n', 'output': '0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'aabb\\nab\\n', 'output': '1 1 1 0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'a\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\n', 'output': '0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'axxbaxxbaxxb\\nab\\n', 'output': '0 0 1 1 2 2 3 2 2 1 1 0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'a\\nb\\n', 'output': '0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'a\\na\\n', 'output': '1 0 \\n'}, {'type': 'stdin_stdout', 'input': 'axaxxbaxabxbaxxbxb\\nab\\n', 'output': '1 1 2 2 3 3 3 3 3 3 3 3 3 2 2 1 1 0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'a\\nab\\n', 'output': '0 0 \\n'}, {'type': 'stdin_stdout', 'input': 'aaaaaaaaaaaaaaa\\na\\n', 'output': '15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0\\n'}, {'type': 'stdin_stdout', 'input': 'ababcc\\nabc\\n', 'output': '1 1 1 1 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': 'abxxxaxbxaxxxba\\nabb\\n', 'output': '0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'ababababaaabababa\\naba\\n', 'output': '4 4 4 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'aa`aaaaaaaa\\nb\\n', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 '}, {'type': 'stdin_stdout', 'input': '`\\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'aabb\\nba\\n', 'output': '0 0 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'bxxbaxxbaxxb\\nab\\n', 'output': '0 0 1 1 2 2 2 2 2 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': 'axaxxbaxabxbaxxbyb\\nab\\n', 'output': '1 1 2 2 3 3 3 3 3 3 3 3 3 2 2 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': 'aaaaaaaaaaaaaab\\na\\n', 'output': '14 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 '}, {'type': 'stdin_stdout', 'input': 'bbabcc\\nabc\\n', 'output': '1 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'aaaa`\\naa\\n', 'output': '2 2 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': 'axbaxxb\\nbb\\n', 'output': '0 0 0 1 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': 'abxxxaxbxaxxxba\\nbbb\\n', 'output': '0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'ababababaaabababa\\nbaa\\n', 'output': '1 2 3 3 3 3 3 3 3 2 2 2 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'bxxbaxxbaxxb\\naa\\n', 'output': '0 0 0 1 1 1 1 1 1 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': 'axaxxbaxabxbaxxbxb\\nba\\n', 'output': '2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': 'aaaaabaaaaaaaab\\na\\n', 'output': '13 13 13 12 11 10 9 8 7 6 5 4 3 2 1 0 '}, {'type': 'stdin_stdout', 'input': 'bbbacc\\nabc\\n', 'output': '0 0 0 0 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'ababababaaabababa\\naab\\n', 'output': '1 2 3 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'aaaaaa`aaaa\\na\\n', 'output': '10 10 9 8 7 6 5 4 3 2 1 0 '}, {'type': 'stdin_stdout', 'input': 'bxxbaaxbxxxb\\naa\\n', 'output': '1 1 1 1 1 1 1 1 1 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': '`\\n`\\n', 'output': '1 0 '}, {'type': 'stdin_stdout', 'input': 'bxxabxa\\nab\\n', 'output': '1 1 1 1 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': 'ababababaaabababa\\nbab\\n', 'output': '3 3 3 3 3 3 3 3 3 2 2 2 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'a`aaaa`aaaa\\na\\n', 'output': '9 9 9 8 7 6 5 4 3 2 1 0 '}, {'type': 'stdin_stdout', 'input': 'xbxaxaxbxaxxxba\\nabb\\n', 'output': '0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'ababababaaabababa\\nabb\\n', 'output': '0 1 2 3 3 3 3 3 3 2 2 2 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'b\\naa\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'b\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': '`\\nb\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': '`\\na\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': '`\\nab\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'aaaaaa`aaaa\\nb\\n', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 '}, {'type': 'stdin_stdout', 'input': 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'b\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': '_\\na\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': '^\\na\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': '`\\nba\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'bxxabxa\\nbb\\n', 'output': '0 0 0 1 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': 'abxxxaxbxaxaxbx\\nbbb\\n', 'output': '0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'a\\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'a\\na`\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'a\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': '_\\nb\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'bxbxxabxbaxabxxaxa\\nba\\n', 'output': '1 1 2 2 3 3 3 3 3 3 3 3 3 2 2 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': 'a\\n`b\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'baaaaaaaabaaaaa\\na\\n', 'output': '13 13 13 12 11 10 9 8 7 6 5 4 3 2 1 0 '}, {'type': 'stdin_stdout', 'input': 'bbbacb\\nabc\\n', 'output': '0 0 0 0 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'abxxxaxbxaxaxbx\\nabb\\n', 'output': '0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 '}, {'type': 'stdin_stdout', 'input': 'b\\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'a\\n`a\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'a\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'axxbabxbxxxb\\naa\\n', 'output': '0 0 0 1 1 1 1 1 1 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': '_\\nc\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'axaxxbaxaxxbaxbbxb\\nba\\n', 'output': '2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 0 0 '}, {'type': 'stdin_stdout', 'input': 'b\\n`b\\n', 'output': '0 0 '}, {'type': 'stdin_stdout', 'input': 'bbcacb\\nabc\\n', 'output': '0 0 0 0 0 0 0 '}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78517","program":"```python\ns, p = input(), input()\nn, m = len(s) + 1, len(p)\nd = [[0] * n for t in range(n)]\nfor x in range(1, n):\n i, j = x, m\n while i and j:\n j -= s[i - 1] == p[j - 1]\n i -= 1\n if not j:\n for y in range(i + 1): d[x][y + x - i - m] = d[i][y] + 1\n for y in range(x): d[x][y] = max(d[x][y], d[x - 1][y])\nprint(*d[-1])\n```","inputs":"aaaaa\naa\n","output":"2 2 1 1 0 0 \n","actual_output":"2 2 1 1 0 0\n","execution_success":true,"sample_index":12516},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"4_D. Mysterious Present","prompt":"Solve the following coding problem using the programming language python:\n\nPeter decided to wish happy birthday to his friend from Australia and send him a card. To make his present more mysterious, he decided to make a chain. Chain here is such a sequence of envelopes A = {a1, a2, ..., an}, where the width and the height of the i-th envelope is strictly higher than the width and the height of the (i - 1)-th envelope respectively. Chain size is the number of envelopes in the chain. \n\nPeter wants to make the chain of the maximum size from the envelopes he has, the chain should be such, that he'll be able to put a card into it. The card fits into the chain if its width and height is lower than the width and the height of the smallest envelope in the chain respectively. It's forbidden to turn the card and the envelopes. \n\nPeter has very many envelopes and very little time, this hard task is entrusted to you.\n\nInput\n\nThe first line contains integers n, w, h (1 \u2264 n \u2264 5000, 1 \u2264 w, h \u2264 106) \u2014 amount of envelopes Peter has, the card width and height respectively. Then there follow n lines, each of them contains two integer numbers wi and hi \u2014 width and height of the i-th envelope (1 \u2264 wi, hi \u2264 106).\n\nOutput\n\nIn the first line print the maximum chain size. In the second line print the numbers of the envelopes (separated by space), forming the required chain, starting with the number of the smallest envelope. Remember, please, that the card should fit into the smallest envelope. If the chain of maximum size is not unique, print any of the answers.\n\nIf the card does not fit into any of the envelopes, print number 0 in the single line.\n\nExamples\n\nInput\n\n2 1 1\n2 2\n2 2\n\n\nOutput\n\n1\n1 \n\n\nInput\n\n3 3 3\n5 4\n12 11\n9 8\n\n\nOutput\n\n3\n1 3 2 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ninputi = [int(i) for i in input().split(\" \")]\namt = inputi[0]\ncardW = inputi[1]\ncardH = inputi[2]\nenvelopes = []\ncur_amt = 1\nfor i in range(amt):\n inputi = [int(i) for i in input().split(\" \")]\n if inputi[0] > cardW and inputi[1] > cardH:\n envelopes.append((inputi[0],inputi[1],inputi[0]*inputi[1], cur_amt))\n cur_amt +=1\n\nenvelopes = sorted(envelopes, key = lambda x: x[2])\n\namounts = [1 for a in envelopes]\nback_pointers = [-1 for a in envelopes]\n\nfor c in range(len(envelopes)):\n cur_tuple = envelopes[c]\n for prev in range(c):\n compare_tuple = envelopes[prev]\n if cur_tuple[0] > compare_tuple [0] and cur_tuple[1] > compare_tuple [1] and amounts[prev] + 1 > amounts[c]:\n amounts[c] = amounts[prev] + 1\n back_pointers[c] = prev\n\nmax_amt = None\nmax_idx = None\nfor c in range(len(envelopes)):\n cur_tuple = envelopes[c]\n if max_amt == None or amounts[c] > max_amt:\n max_idx = c\n max_amt = amounts[c]\n#print(max_idx)\n#print(back_pointers)\nif max_amt == None:\n print(0)\nelse:\n print(max_amt)\n tmp_back_ptr = back_pointers[max_idx]\n back_ptr_list = []\n back_ptr_list.append(envelopes[max_idx][3])\n\n while tmp_back_ptr != -1:\n back_ptr_list.append(envelopes[tmp_back_ptr][3])\n tmp_back_ptr = back_pointers[tmp_back_ptr]\n\n #print(back_ptr_list)\n for a in range(len(back_ptr_list)):\n print(back_ptr_list[len(back_ptr_list)-a-1], end = \" \")\n\n#print(envelopes)\n#print(amounts)\n#print(back_pointers)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 3 3\\n5 4\\n12 11\\n9 8\\n', 'output': '3\\n1 3 2\\n'}, {'type': 'stdin_stdout', 'input': '2 1 1\\n2 2\\n2 2\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5 13 13\\n4 4\\n10 10\\n7 7\\n1 1\\n13 13\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 12 140\\n172 60\\n71 95\\n125 149\\n53 82\\n', 'output': '1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '5 1000 998\\n5002 5005\\n5003 5004\\n5003 5002\\n5002 5001\\n5002 5002\\n', 'output': '2\\n4 3\\n'}, {'type': 'stdin_stdout', 'input': '3 5 5\\n6 2\\n7 8\\n10 2\\n', 'output': '1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3 500 789\\n56 32\\n64 42\\n74 55\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 10 10\\n15 15\\n16 16\\n', 'output': '2\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '5 10 10\\n22 23\\n17 19\\n13 17\\n8 12\\n2 6\\n', 'output': '3\\n3 2 1\\n'}, {'type': 'stdin_stdout', 'input': '4 100 100\\n332 350\\n232 250\\n32 50\\n132 150\\n', 'output': '3\\n4 2 1\\n'}, {'type': 'stdin_stdout', 'input': '30 900 15\\n1396 562\\n1265 475\\n3329 2605\\n1016 340\\n2369 1595\\n2085 1245\\n2677 1934\\n1953 1154\\n3002 2199\\n1688 855\\n1147 407\\n2762 2064\\n2202 1359\\n700 30\\n3265 2488\\n1884 1034\\n2571 1836\\n3067 2269\\n882 212\\n3505 2793\\n1602 785\\n2292 1460\\n2442 1712\\n2889 2127\\n3187 2361\\n1770 932\\n3624 2891\\n783 104\\n3410 2704\\n1521 696\\n', 'output': '27\\n4 11 2 1 30 21 10 26 16 8 6 13 22 5 23 17 7 12 24 9 18 25 15 3 29 20 27\\n'}, {'type': 'stdin_stdout', 'input': '14 12 800\\n166 847\\n205 889\\n223 907\\n93 785\\n110 803\\n136 829\\n189 871\\n149 839\\n40 740\\n48 750\\n180 857\\n76 777\\n125 820\\n63 766\\n', 'output': '9\\n5 13 6 8 1 11 7 2 3\\n'}, {'type': 'stdin_stdout', 'input': '6 1 1\\n900000 900000\\n902400 902400\\n901200 901200\\n903600 903600\\n906000 906000\\n904800 904800\\n', 'output': '6\\n1 3 2 4 6 5\\n'}, {'type': 'stdin_stdout', 'input': '15 600 875\\n1200 451\\n1664 852\\n1763 1355\\n1374 1724\\n1374 1587\\n1003 1513\\n1636 1002\\n431 367\\n1632 690\\n1257 778\\n410 1632\\n1045 1279\\n1762 1763\\n841 576\\n1165 705\\n', 'output': '3\\n12 5 13 '}, {'type': 'stdin_stdout', 'input': '5 13 13\\n4 4\\n10 10\\n6 7\\n1 1\\n13 13\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 12 140\\n172 60\\n39 95\\n125 149\\n53 82\\n', 'output': '1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '5 1000 998\\n5002 5005\\n5003 5004\\n5003 5002\\n5002 4253\\n5002 5002\\n', 'output': '2\\n4 3\\n'}, {'type': 'stdin_stdout', 'input': '2 10 10\\n15 15\\n16 0\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5 4 10\\n22 23\\n17 19\\n13 17\\n8 12\\n2 6\\n', 'output': '4\\n4 3 2 1\\n'}, {'type': 'stdin_stdout', 'input': '4 100 100\\n604 350\\n232 250\\n32 50\\n132 150\\n', 'output': '3\\n4 2 1\\n'}, {'type': 'stdin_stdout', 'input': '30 900 15\\n1396 562\\n1265 475\\n3329 2605\\n1016 340\\n2369 1595\\n2085 1245\\n2677 1934\\n1953 1154\\n3002 2199\\n1688 855\\n1147 407\\n2762 2064\\n2202 1359\\n700 30\\n3265 2488\\n1884 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{'type': 'stdin_stdout', 'input': '2 1 1\\n3 2\\n2 2\\n', 'output': '1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '5 1000 998\\n5002 5005\\n5003 5004\\n5003 3928\\n5002 4253\\n5002 5002\\n', 'output': '2\\n4 2\\n'}, {'type': 'stdin_stdout', 'input': '30 900 15\\n1396 562\\n1265 475\\n3329 2605\\n1016 340\\n2369 1595\\n567 1245\\n2677 1934\\n1953 1154\\n3002 2199\\n1688 855\\n1147 407\\n2762 2064\\n2202 1359\\n700 30\\n3265 2488\\n1884 1034\\n2571 1836\\n3067 2269\\n882 212\\n3505 2793\\n1602 785\\n2292 1460\\n2442 1712\\n2889 2127\\n3187 2361\\n1770 932\\n3624 2891\\n783 104\\n3410 2704\\n2103 696\\n', 'output': '25\\n4 11 2 1 21 10 26 16 8 13 22 5 23 17 7 12 24 9 18 25 15 3 29 20 27\\n'}, {'type': 'stdin_stdout', 'input': '14 12 800\\n166 847\\n380 889\\n223 907\\n93 785\\n110 803\\n136 829\\n189 518\\n149 839\\n40 740\\n48 750\\n180 857\\n76 777\\n125 820\\n63 766\\n', 'output': '7\\n5 13 6 8 1 11 3\\n'}, {'type': 'stdin_stdout', 'input': '6 1 1\\n1315762 900000\\n902400 902400\\n901200 901200\\n903600 903600\\n906000 906000\\n1732491 904800\\n', 'output': '4\\n3 2 4 5\\n'}, {'type': 'stdin_stdout', 'input': '15 600 875\\n1200 451\\n1664 852\\n1763 1355\\n1734 1724\\n1374 1587\\n1003 1513\\n1636 219\\n431 367\\n1632 690\\n1257 778\\n410 1632\\n1045 1279\\n1762 1763\\n841 576\\n1165 705\\n', 'output': '4\\n6 5 4 13\\n'}, {'type': 'stdin_stdout', 'input': '5 0 10\\n22 23\\n30 19\\n13 17\\n8 12\\n2 6\\n', 'output': '3\\n4 3 1\\n'}, {'type': 'stdin_stdout', 'input': '14 12 800\\n166 847\\n380 889\\n223 907\\n93 785\\n110 803\\n136 829\\n189 518\\n273 839\\n40 740\\n48 750\\n180 857\\n76 777\\n125 820\\n63 766\\n', 'output': '6\\n5 13 6 1 11 3\\n'}, {'type': 'stdin_stdout', 'input': '5 1000 998\\n5002 5005\\n7613 5004\\n5003 2065\\n5076 4253\\n5002 5002\\n', 'output': '3\\n3 4 2\\n'}, {'type': 'stdin_stdout', 'input': '30 900 15\\n1396 562\\n1265 475\\n3329 2605\\n1016 340\\n2369 1595\\n567 1245\\n2677 1934\\n1953 1154\\n3002 2199\\n1688 855\\n1147 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2199\\n1688 855\\n1147 82\\n2762 2064\\n2202 1359\\n700 30\\n3265 2488\\n1884 1034\\n2571 1836\\n3067 2269\\n882 212\\n3505 2793\\n1602 785\\n2292 1460\\n2442 1712\\n2889 2127\\n3187 2361\\n1770 932\\n3624 2891\\n783 104\\n3410 1460\\n70 1212\\n', 'output': '23\\n4 2 1 21 10 26 16 8 13 22 5 23 17 7 12 24 9 18 25 15 3 20 27\\n'}, {'type': 'stdin_stdout', 'input': '15 600 875\\n1200 451\\n537 852\\n1763 1355\\n3222 1724\\n1374 1587\\n1003 315\\n1636 219\\n431 367\\n1632 690\\n1257 778\\n25 1632\\n1045 1279\\n1762 1763\\n1563 576\\n1165 705\\n', 'output': '3\\n12 5 13\\n'}, {'type': 'stdin_stdout', 'input': '30 900 15\\n1396 617\\n1265 475\\n3329 2605\\n1016 340\\n2369 1595\\n949 1245\\n2677 1934\\n1953 1154\\n3002 2199\\n1688 855\\n1147 82\\n2762 2064\\n2202 1359\\n700 30\\n3265 2488\\n1884 1034\\n2571 1836\\n3067 2269\\n882 212\\n3505 2793\\n1602 785\\n2292 1460\\n2442 1712\\n2889 2127\\n3187 2361\\n1770 6\\n3624 3334\\n783 104\\n3410 1460\\n70 1212\\n', 'output': '22\\n4 2 1 21 10 16 8 13 22 5 23 17 7 12 24 9 18 25 15 3 20 27\\n'}, {'type': 'stdin_stdout', 'input': '5 1000 1177\\n5002 5005\\n20810 5004\\n5003 2977\\n5076 1293\\n2278 5002\\n', 'output': '2\\n5 1\\n'}, {'type': 'stdin_stdout', 'input': '30 900 15\\n1396 617\\n1265 475\\n3329 2605\\n790 340\\n2369 1595\\n949 1245\\n2677 1934\\n1953 1154\\n3002 2199\\n1688 855\\n1147 82\\n2762 2064\\n2202 1359\\n700 30\\n3265 2488\\n1884 1034\\n2571 1836\\n3067 2269\\n882 212\\n3505 2793\\n1602 785\\n2292 1460\\n2442 1712\\n2889 2127\\n3187 2361\\n1770 6\\n3624 3334\\n783 104\\n3410 1460\\n70 1212\\n', 'output': '22\\n11 2 1 21 10 16 8 13 22 5 23 17 7 12 24 9 18 25 15 3 20 27\\n'}, {'type': 'stdin_stdout', 'input': '30 900 15\\n1396 617\\n1265 475\\n3329 4281\\n790 340\\n2369 1595\\n949 1245\\n2677 1934\\n1953 1154\\n3002 2199\\n1688 855\\n1147 82\\n2762 2064\\n2202 1359\\n700 30\\n3265 2488\\n1884 1034\\n2571 1836\\n3067 2269\\n882 212\\n3505 2793\\n1602 785\\n2292 1460\\n2442 1712\\n2889 2127\\n3187 2361\\n1770 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'output': '25\\n4 11 2 1 21 10 26 16 8 13 22 5 23 17 7 12 24 9 18 25 15 3 29 20 27\\n'}, {'type': 'stdin_stdout', 'input': '14 12 800\\n166 847\\n380 889\\n223 907\\n93 785\\n110 803\\n136 829\\n189 518\\n273 704\\n40 740\\n48 750\\n180 857\\n76 777\\n125 820\\n63 766\\n', 'output': '6\\n5 13 6 1 11 3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 64000000}","problem_id":"vfc_78521","program":"```python\ninputi = [int(i) for i in input().split(\" \")]\namt = inputi[0]\ncardW = inputi[1]\ncardH = inputi[2]\nenvelopes = []\ncur_amt = 1\nfor i in range(amt):\n inputi = [int(i) for i in input().split(\" \")]\n if inputi[0] > cardW and inputi[1] > cardH:\n envelopes.append((inputi[0],inputi[1],inputi[0]*inputi[1], cur_amt))\n cur_amt +=1\n\nenvelopes = sorted(envelopes, key = lambda x: x[2])\n\namounts = [1 for a in envelopes]\nback_pointers = [-1 for a in envelopes]\n\nfor c in range(len(envelopes)):\n cur_tuple = envelopes[c]\n for prev in range(c):\n compare_tuple = envelopes[prev]\n if cur_tuple[0] > compare_tuple [0] and cur_tuple[1] > compare_tuple [1] and amounts[prev] + 1 > amounts[c]:\n amounts[c] = amounts[prev] + 1\n back_pointers[c] = prev\n\nmax_amt = None\nmax_idx = None\nfor c in range(len(envelopes)):\n cur_tuple = envelopes[c]\n if max_amt == None or amounts[c] > max_amt:\n max_idx = c\n max_amt = amounts[c]\n#print(max_idx)\n#print(back_pointers)\nif max_amt == None:\n print(0)\nelse:\n print(max_amt)\n tmp_back_ptr = back_pointers[max_idx]\n back_ptr_list = []\n back_ptr_list.append(envelopes[max_idx][3])\n\n while tmp_back_ptr != -1:\n back_ptr_list.append(envelopes[tmp_back_ptr][3])\n tmp_back_ptr = back_pointers[tmp_back_ptr]\n\n #print(back_ptr_list)\n for a in range(len(back_ptr_list)):\n print(back_ptr_list[len(back_ptr_list)-a-1], end = \" \")\n\n#print(envelopes)\n#print(amounts)\n#print(back_pointers)\n```","inputs":"3 3 3\n5 4\n12 11\n9 8\n","output":"3\n1 3 2\n","actual_output":"3\n1 3 2 ","execution_success":true,"sample_index":12517},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"525_C. Ilya and Sticks","prompt":"Solve the following coding problem using the programming language python:\n\nIn the evening, after the contest Ilya was bored, and he really felt like maximizing. He remembered that he had a set of n sticks and an instrument. Each stick is characterized by its length li.\n\nIlya decided to make a rectangle from the sticks. And due to his whim, he decided to make rectangles in such a way that maximizes their total area. Each stick is used in making at most one rectangle, it is possible that some of sticks remain unused. Bending sticks is not allowed.\n\nSticks with lengths a1, a2, a3 and a4 can make a rectangle if the following properties are observed:\n\n * a1 \u2264 a2 \u2264 a3 \u2264 a4\n * a1 = a2\n * a3 = a4\n\n\n\nA rectangle can be made of sticks with lengths of, for example, 3 3 3 3 or 2 2 4 4. A rectangle cannot be made of, for example, sticks 5 5 5 7.\n\nIlya also has an instrument which can reduce the length of the sticks. The sticks are made of a special material, so the length of each stick can be reduced by at most one. For example, a stick with length 5 can either stay at this length or be transformed into a stick of length 4.\n\nYou have to answer the question \u2014 what maximum total area of the rectangles can Ilya get with a file if makes rectangles from the available sticks?\n\nInput\n\nThe first line of the input contains a positive integer n (1 \u2264 n \u2264 105) \u2014 the number of the available sticks.\n\nThe second line of the input contains n positive integers li (2 \u2264 li \u2264 106) \u2014 the lengths of the sticks.\n\nOutput\n\nThe first line of the output must contain a single non-negative integer \u2014 the maximum total area of the rectangles that Ilya can make from the available sticks.\n\nExamples\n\nInput\n\n4\n2 4 4 2\n\n\nOutput\n\n8\n\n\nInput\n\n4\n2 2 3 5\n\n\nOutput\n\n0\n\n\nInput\n\n4\n100003 100004 100005 100006\n\n\nOutput\n\n10000800015\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\n\nrects = [int(s) for s in input().split()]\nrects.sort()\n\nsumsquare = 0\nstash = []\n\ni = len(rects) - 1\n\nwhile i > 0:\n\tif rects[i] - rects[i-1] == 1 or rects[i] == rects[i-1]:\n\t\tif len(stash) == 2:\n\t\t\tsumsquare += stash[0]*stash[1]\n\t\t\tstash.clear()\n\n\t\tstash.append(rects[i-1])\n\t\trects.pop()\n\t\trects.pop()\n\n\t\ti -= 2\n\telse:\n\t\ti -= 1\n\nif len(stash) == 2:\n\tsumsquare += stash[0]*stash[1]\n\tstash.clear()\n\nprint(sumsquare)\n\n\n\t\t\t\n\n\n\n\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n2 4 4 2\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 2 3 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n100003 100004 100005 100006\\n', 'output': '10000800015\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2 2 2 2 2 2 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '21\\n580 3221 3987 2012 35 629 1554 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'input': '4\\n2 8 9 6\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78525","program":"```python\nn = int(input())\n\nrects = [int(s) for s in input().split()]\nrects.sort()\n\nsumsquare = 0\nstash = []\n\ni = len(rects) - 1\n\nwhile i > 0:\n\tif rects[i] - rects[i-1] == 1 or rects[i] == rects[i-1]:\n\t\tif len(stash) == 2:\n\t\t\tsumsquare += stash[0]*stash[1]\n\t\t\tstash.clear()\n\n\t\tstash.append(rects[i-1])\n\t\trects.pop()\n\t\trects.pop()\n\n\t\ti -= 2\n\telse:\n\t\ti -= 1\n\nif len(stash) == 2:\n\tsumsquare += stash[0]*stash[1]\n\tstash.clear()\n\nprint(sumsquare)\n\n\n\t\t\t\n\n\n\n\n\n\n\n```","inputs":"4\n2 4 4 2\n","output":"8\n","actual_output":"8\n","execution_success":true,"sample_index":12518},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"550_D. Regular Bridge","prompt":"Solve the following coding problem using the programming language python:\n\nAn undirected graph is called k-regular, if the degrees of all its vertices are equal k. An edge of a connected graph is called a bridge, if after removing it the graph is being split into two connected components.\n\nBuild a connected undirected k-regular graph containing at least one bridge, or else state that such graph doesn't exist.\n\nInput\n\nThe single line of the input contains integer k (1 \u2264 k \u2264 100) \u2014 the required degree of the vertices of the regular graph.\n\nOutput\n\nPrint \"NO\" (without quotes), if such graph doesn't exist. \n\nOtherwise, print \"YES\" in the first line and the description of any suitable graph in the next lines.\n\nThe description of the made graph must start with numbers n and m \u2014 the number of vertices and edges respectively. \n\nEach of the next m lines must contain two integers, a and b (1 \u2264 a, b \u2264 n, a \u2260 b), that mean that there is an edge connecting the vertices a and b. A graph shouldn't contain multiple edges and edges that lead from a vertex to itself. A graph must be connected, the degrees of all vertices of the graph must be equal k. At least one edge of the graph must be a bridge. You can print the edges of the graph in any order. You can print the ends of each edge in any order.\n\nThe constructed graph must contain at most 106 vertices and 106 edges (it is guaranteed that if at least one graph that meets the requirements exists, then there also exists the graph with at most 106 vertices and at most 106 edges). \n\nExamples\n\nInput\n\n1\n\n\nOutput\n\nYES\n2 1\n1 2\n\nNote\n\nIn the sample from the statement there is a suitable graph consisting of two vertices, connected by a single edge.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef nextEdge():\n global v\n for i in range(1, v + 1):\n for j in range(i + 1, v + 1):\n yield (i, j)\n\nk = int(input())\n\nif k % 2 == 0:\n print(\"NO\")\nelif k == 1:\n print(\"YES\", \"2 1\", \"1 2\", sep = \"\\n\")\nelse:\n n = 2 * k + 4\n m = k * (k + 2)\n print(\"YES\")\n print(n, m, sep = \" \")\n a = [i for i in range(1, k)] + [i for i in range(k + 4, 2 * k + 3)]\n b = [k + 2] * (k - 1) + [k + 3] * (k - 1)\n a += [k + 2]\n b += [k + 3]\n\n v = k + 1\n curr = (1, 2)\n count = k - 1\n for i in nextEdge():\n if (count == 0) or (i != curr and count > 0):\n a.append(i[0])\n b.append(i[1])\n a.append(i[0] + k + 3)\n b.append(i[1] + k + 3)\n else:\n curr = (curr[1] + 1, curr[1] + 2)\n count -= 2\n \n for i in range(m):\n print(a[i], b[i], sep = \" \")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n', 'output': 'YES\\n2 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '30\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '68\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '22\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '66\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '26\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '98\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '82\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 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19\\n10 20\\n10 21\\n11 12\\n11 13\\n11 14\\n11 15\\n11 16\\n11 17\\n11 18\\n11 19\\n11 20\\n11 21\\n12 13\\n14 15\\n16 17\\n18 19\\n20 21\\n22 23\\n22 24\\n22 25\\n22 26\\n22 27\\n22 28\\n22 29\\n22 30\\n22 31\\n22 32\\n23 33\\n23 34\\n23 35\\n23 36\\n23 37\\n23 38\\n23 39\\n23 40\\n23 41\\n23 42\\n24 33\\n24 34\\n24 35\\n24 36\\n24 37\\n24 38\\n24 39\\n24 40\\n24 41\\n24 42\\n25 33\\n25 34\\n25 35\\n25 36\\n25 37\\n25 38\\n25 39\\n25 40\\n25 41\\n25 42\\n26 33\\n26 34\\n26 35\\n26 36\\n26 37\\n26 38\\n26 39\\n26 40\\n26 41\\n26 42\\n27 33\\n27 34\\n27 35\\n27 36\\n27 37\\n27 38\\n27 39\\n27 40\\n27 41\\n27 42\\n28 33\\n28 34\\n28 35\\n28 36\\n28 37\\n28 38\\n28 39\\n28 40\\n28 41\\n28 42\\n29 33\\n29 34\\n29 35\\n29 36\\n29 37\\n29 38\\n29 39\\n29 40\\n29 41\\n29 42\\n30 33\\n30 34\\n30 35\\n30 36\\n30 37\\n30 38\\n30 39\\n30 40\\n30 41\\n30 42\\n31 33\\n31 34\\n31 35\\n31 36\\n31 37\\n31 38\\n31 39\\n31 40\\n31 41\\n31 42\\n32 33\\n32 34\\n32 35\\n32 36\\n32 37\\n32 38\\n32 39\\n32 40\\n32 41\\n32 42\\n33 34\\n35 36\\n37 38\\n39 40\\n41 42\\n1 22\\n'}, {'type': 'stdin_stdout', 'input': '7\\n', 'output': 'YES\\n26 91\\n1 2\\n1 3\\n1 4\\n1 5\\n1 6\\n1 7\\n2 8\\n2 9\\n2 10\\n2 11\\n2 12\\n2 13\\n3 8\\n3 9\\n3 10\\n3 11\\n3 12\\n3 13\\n4 8\\n4 9\\n4 10\\n4 11\\n4 12\\n4 13\\n5 8\\n5 9\\n5 10\\n5 11\\n5 12\\n5 13\\n6 8\\n6 9\\n6 10\\n6 11\\n6 12\\n6 13\\n7 8\\n7 9\\n7 10\\n7 11\\n7 12\\n7 13\\n8 9\\n10 11\\n12 13\\n14 15\\n14 16\\n14 17\\n14 18\\n14 19\\n14 20\\n15 21\\n15 22\\n15 23\\n15 24\\n15 25\\n15 26\\n16 21\\n16 22\\n16 23\\n16 24\\n16 25\\n16 26\\n17 21\\n17 22\\n17 23\\n17 24\\n17 25\\n17 26\\n18 21\\n18 22\\n18 23\\n18 24\\n18 25\\n18 26\\n19 21\\n19 22\\n19 23\\n19 24\\n19 25\\n19 26\\n20 21\\n20 22\\n20 23\\n20 24\\n20 25\\n20 26\\n21 22\\n23 24\\n25 26\\n1 14\\n'}, {'type': 'stdin_stdout', 'input': '9\\n', 'output': 'YES\\n34 153\\n1 2\\n1 3\\n1 4\\n1 5\\n1 6\\n1 7\\n1 8\\n1 9\\n2 10\\n2 11\\n2 12\\n2 13\\n2 14\\n2 15\\n2 16\\n2 17\\n3 10\\n3 11\\n3 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30\\n31 32\\n33 34\\n1 18\\n'}, {'type': 'stdin_stdout', 'input': '43\\n', 'output': 'YES\\n90 1935\\n1 3\\n46 48\\n1 4\\n46 49\\n1 5\\n46 50\\n1 6\\n46 51\\n1 7\\n46 52\\n1 8\\n46 53\\n1 9\\n46 54\\n1 10\\n46 55\\n1 11\\n46 56\\n1 12\\n46 57\\n1 13\\n46 58\\n1 14\\n46 59\\n1 15\\n46 60\\n1 16\\n46 61\\n1 17\\n46 62\\n1 18\\n46 63\\n1 19\\n46 64\\n1 20\\n46 65\\n1 21\\n46 66\\n1 22\\n46 67\\n1 23\\n46 68\\n1 24\\n46 69\\n1 25\\n46 70\\n1 26\\n46 71\\n1 27\\n46 72\\n1 28\\n46 73\\n1 29\\n46 74\\n1 30\\n46 75\\n1 31\\n46 76\\n1 32\\n46 77\\n1 33\\n46 78\\n1 34\\n46 79\\n1 35\\n46 80\\n1 36\\n46 81\\n1 37\\n46 82\\n1 38\\n46 83\\n1 39\\n46 84\\n1 40\\n46 85\\n1 41\\n46 86\\n1 42\\n46 87\\n1 43\\n46 88\\n1 44\\n46 89\\n2 3\\n47 48\\n2 4\\n47 49\\n2 5\\n47 50\\n2 6\\n47 51\\n2 7\\n47 52\\n2 8\\n47 53\\n2 9\\n47 54\\n2 10\\n47 55\\n2 11\\n47 56\\n2 12\\n47 57\\n2 13\\n47 58\\n2 14\\n47 59\\n2 15\\n47 60\\n2 16\\n47 61\\n2 17\\n47 62\\n2 18\\n47 63\\n2 19\\n47 64\\n2 20\\n47 65\\n2 21\\n47 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67\\n22 33\\n57 68\\n22 34\\n57 69\\n22 35\\n57 70\\n23 25\\n58 60\\n23 26\\n58 61\\n23 27\\n58 62\\n23 28\\n58 63\\n23 29\\n58 64\\n23 30\\n58 65\\n23 31\\n58 66\\n23 32\\n58 67\\n23 33\\n58 68\\n23 34\\n58 69\\n23 35\\n58 70\\n24 25\\n59 60\\n24 26\\n59 61\\n24 27\\n59 62\\n24 28\\n59 63\\n24 29\\n59 64\\n24 30\\n59 65\\n24 31\\n59 66\\n24 32\\n59 67\\n24 33\\n59 68\\n24 34\\n59 69\\n24 35\\n59 70\\n25 27\\n60 62\\n25 28\\n60 63\\n25 29\\n60 64\\n25 30\\n60 65\\n25 31\\n60 66\\n25 32\\n60 67\\n25 33\\n60 68\\n25 34\\n60 69\\n25 35\\n60 70\\n26 27\\n61 62\\n26 28\\n61 63\\n26 29\\n61 64\\n26 30\\n61 65\\n26 31\\n61 66\\n26 32\\n61 67\\n26 33\\n61 68\\n26 34\\n61 69\\n26 35\\n61 70\\n27 29\\n62 64\\n27 30\\n62 65\\n27 31\\n62 66\\n27 32\\n62 67\\n27 33\\n62 68\\n27 34\\n62 69\\n27 35\\n62 70\\n28 29\\n63 64\\n28 30\\n63 65\\n28 31\\n63 66\\n28 32\\n63 67\\n28 33\\n63 68\\n28 34\\n63 69\\n28 35\\n63 70\\n29 31\\n64 66\\n29 32\\n64 67\\n29 33\\n64 68\\n29 34\\n64 69\\n29 35\\n64 70\\n30 31\\n65 66\\n30 32\\n65 67\\n30 33\\n65 68\\n30 34\\n65 69\\n30 35\\n65 70\\n31 33\\n66 68\\n31 34\\n66 69\\n31 35\\n66 70\\n32 33\\n67 68\\n32 34\\n67 69\\n32 35\\n67 70\\n33 35\\n68 70\\n34 35\\n69 70\\n1 36\\n'}, {'type': 'stdin_stdout', 'input': '23\\n', 'output': 'YES\\n50 575\\n1 3\\n26 28\\n1 4\\n26 29\\n1 5\\n26 30\\n1 6\\n26 31\\n1 7\\n26 32\\n1 8\\n26 33\\n1 9\\n26 34\\n1 10\\n26 35\\n1 11\\n26 36\\n1 12\\n26 37\\n1 13\\n26 38\\n1 14\\n26 39\\n1 15\\n26 40\\n1 16\\n26 41\\n1 17\\n26 42\\n1 18\\n26 43\\n1 19\\n26 44\\n1 20\\n26 45\\n1 21\\n26 46\\n1 22\\n26 47\\n1 23\\n26 48\\n1 24\\n26 49\\n2 3\\n27 28\\n2 4\\n27 29\\n2 5\\n27 30\\n2 6\\n27 31\\n2 7\\n27 32\\n2 8\\n27 33\\n2 9\\n27 34\\n2 10\\n27 35\\n2 11\\n27 36\\n2 12\\n27 37\\n2 13\\n27 38\\n2 14\\n27 39\\n2 15\\n27 40\\n2 16\\n27 41\\n2 17\\n27 42\\n2 18\\n27 43\\n2 19\\n27 44\\n2 20\\n27 45\\n2 21\\n27 46\\n2 22\\n27 47\\n2 23\\n27 48\\n2 24\\n27 49\\n2 25\\n27 50\\n3 5\\n28 30\\n3 6\\n28 31\\n3 7\\n28 32\\n3 8\\n28 33\\n3 9\\n28 34\\n3 10\\n28 35\\n3 11\\n28 36\\n3 12\\n28 37\\n3 13\\n28 38\\n3 14\\n28 39\\n3 15\\n28 40\\n3 16\\n28 41\\n3 17\\n28 42\\n3 18\\n28 43\\n3 19\\n28 44\\n3 20\\n28 45\\n3 21\\n28 46\\n3 22\\n28 47\\n3 23\\n28 48\\n3 24\\n28 49\\n3 25\\n28 50\\n4 5\\n29 30\\n4 6\\n29 31\\n4 7\\n29 32\\n4 8\\n29 33\\n4 9\\n29 34\\n4 10\\n29 35\\n4 11\\n29 36\\n4 12\\n29 37\\n4 13\\n29 38\\n4 14\\n29 39\\n4 15\\n29 40\\n4 16\\n29 41\\n4 17\\n29 42\\n4 18\\n29 43\\n4 19\\n29 44\\n4 20\\n29 45\\n4 21\\n29 46\\n4 22\\n29 47\\n4 23\\n29 48\\n4 24\\n29 49\\n4 25\\n29 50\\n5 7\\n30 32\\n5 8\\n30 33\\n5 9\\n30 34\\n5 10\\n30 35\\n5 11\\n30 36\\n5 12\\n30 37\\n5 13\\n30 38\\n5 14\\n30 39\\n5 15\\n30 40\\n5 16\\n30 41\\n5 17\\n30 42\\n5 18\\n30 43\\n5 19\\n30 44\\n5 20\\n30 45\\n5 21\\n30 46\\n5 22\\n30 47\\n5 23\\n30 48\\n5 24\\n30 49\\n5 25\\n30 50\\n6 7\\n31 32\\n6 8\\n31 33\\n6 9\\n31 34\\n6 10\\n31 35\\n6 11\\n31 36\\n6 12\\n31 37\\n6 13\\n31 38\\n6 14\\n31 39\\n6 15\\n31 40\\n6 16\\n31 41\\n6 17\\n31 42\\n6 18\\n31 43\\n6 19\\n31 44\\n6 20\\n31 45\\n6 21\\n31 46\\n6 22\\n31 47\\n6 23\\n31 48\\n6 24\\n31 49\\n6 25\\n31 50\\n7 9\\n32 34\\n7 10\\n32 35\\n7 11\\n32 36\\n7 12\\n32 37\\n7 13\\n32 38\\n7 14\\n32 39\\n7 15\\n32 40\\n7 16\\n32 41\\n7 17\\n32 42\\n7 18\\n32 43\\n7 19\\n32 44\\n7 20\\n32 45\\n7 21\\n32 46\\n7 22\\n32 47\\n7 23\\n32 48\\n7 24\\n32 49\\n7 25\\n32 50\\n8 9\\n33 34\\n8 10\\n33 35\\n8 11\\n33 36\\n8 12\\n33 37\\n8 13\\n33 38\\n8 14\\n33 39\\n8 15\\n33 40\\n8 16\\n33 41\\n8 17\\n33 42\\n8 18\\n33 43\\n8 19\\n33 44\\n8 20\\n33 45\\n8 21\\n33 46\\n8 22\\n33 47\\n8 23\\n33 48\\n8 24\\n33 49\\n8 25\\n33 50\\n9 11\\n34 36\\n9 12\\n34 37\\n9 13\\n34 38\\n9 14\\n34 39\\n9 15\\n34 40\\n9 16\\n34 41\\n9 17\\n34 42\\n9 18\\n34 43\\n9 19\\n34 44\\n9 20\\n34 45\\n9 21\\n34 46\\n9 22\\n34 47\\n9 23\\n34 48\\n9 24\\n34 49\\n9 25\\n34 50\\n10 11\\n35 36\\n10 12\\n35 37\\n10 13\\n35 38\\n10 14\\n35 39\\n10 15\\n35 40\\n10 16\\n35 41\\n10 17\\n35 42\\n10 18\\n35 43\\n10 19\\n35 44\\n10 20\\n35 45\\n10 21\\n35 46\\n10 22\\n35 47\\n10 23\\n35 48\\n10 24\\n35 49\\n10 25\\n35 50\\n11 13\\n36 38\\n11 14\\n36 39\\n11 15\\n36 40\\n11 16\\n36 41\\n11 17\\n36 42\\n11 18\\n36 43\\n11 19\\n36 44\\n11 20\\n36 45\\n11 21\\n36 46\\n11 22\\n36 47\\n11 23\\n36 48\\n11 24\\n36 49\\n11 25\\n36 50\\n12 13\\n37 38\\n12 14\\n37 39\\n12 15\\n37 40\\n12 16\\n37 41\\n12 17\\n37 42\\n12 18\\n37 43\\n12 19\\n37 44\\n12 20\\n37 45\\n12 21\\n37 46\\n12 22\\n37 47\\n12 23\\n37 48\\n12 24\\n37 49\\n12 25\\n37 50\\n13 15\\n38 40\\n13 16\\n38 41\\n13 17\\n38 42\\n13 18\\n38 43\\n13 19\\n38 44\\n13 20\\n38 45\\n13 21\\n38 46\\n13 22\\n38 47\\n13 23\\n38 48\\n13 24\\n38 49\\n13 25\\n38 50\\n14 15\\n39 40\\n14 16\\n39 41\\n14 17\\n39 42\\n14 18\\n39 43\\n14 19\\n39 44\\n14 20\\n39 45\\n14 21\\n39 46\\n14 22\\n39 47\\n14 23\\n39 48\\n14 24\\n39 49\\n14 25\\n39 50\\n15 17\\n40 42\\n15 18\\n40 43\\n15 19\\n40 44\\n15 20\\n40 45\\n15 21\\n40 46\\n15 22\\n40 47\\n15 23\\n40 48\\n15 24\\n40 49\\n15 25\\n40 50\\n16 17\\n41 42\\n16 18\\n41 43\\n16 19\\n41 44\\n16 20\\n41 45\\n16 21\\n41 46\\n16 22\\n41 47\\n16 23\\n41 48\\n16 24\\n41 49\\n16 25\\n41 50\\n17 19\\n42 44\\n17 20\\n42 45\\n17 21\\n42 46\\n17 22\\n42 47\\n17 23\\n42 48\\n17 24\\n42 49\\n17 25\\n42 50\\n18 19\\n43 44\\n18 20\\n43 45\\n18 21\\n43 46\\n18 22\\n43 47\\n18 23\\n43 48\\n18 24\\n43 49\\n18 25\\n43 50\\n19 21\\n44 46\\n19 22\\n44 47\\n19 23\\n44 48\\n19 24\\n44 49\\n19 25\\n44 50\\n20 21\\n45 46\\n20 22\\n45 47\\n20 23\\n45 48\\n20 24\\n45 49\\n20 25\\n45 50\\n21 23\\n46 48\\n21 24\\n46 49\\n21 25\\n46 50\\n22 23\\n47 48\\n22 24\\n47 49\\n22 25\\n47 50\\n23 25\\n48 50\\n24 25\\n49 50\\n1 26\\n'}, {'type': 'stdin_stdout', 'input': '27\\n', 'output': 'YES\\n58 783\\n1 3\\n30 32\\n1 4\\n30 33\\n1 5\\n30 34\\n1 6\\n30 35\\n1 7\\n30 36\\n1 8\\n30 37\\n1 9\\n30 38\\n1 10\\n30 39\\n1 11\\n30 40\\n1 12\\n30 41\\n1 13\\n30 42\\n1 14\\n30 43\\n1 15\\n30 44\\n1 16\\n30 45\\n1 17\\n30 46\\n1 18\\n30 47\\n1 19\\n30 48\\n1 20\\n30 49\\n1 21\\n30 50\\n1 22\\n30 51\\n1 23\\n30 52\\n1 24\\n30 53\\n1 25\\n30 54\\n1 26\\n30 55\\n1 27\\n30 56\\n1 28\\n30 57\\n2 3\\n31 32\\n2 4\\n31 33\\n2 5\\n31 34\\n2 6\\n31 35\\n2 7\\n31 36\\n2 8\\n31 37\\n2 9\\n31 38\\n2 10\\n31 39\\n2 11\\n31 40\\n2 12\\n31 41\\n2 13\\n31 42\\n2 14\\n31 43\\n2 15\\n31 44\\n2 16\\n31 45\\n2 17\\n31 46\\n2 18\\n31 47\\n2 19\\n31 48\\n2 20\\n31 49\\n2 21\\n31 50\\n2 22\\n31 51\\n2 23\\n31 52\\n2 24\\n31 53\\n2 25\\n31 54\\n2 26\\n31 55\\n2 27\\n31 56\\n2 28\\n31 57\\n2 29\\n31 58\\n3 5\\n32 34\\n3 6\\n32 35\\n3 7\\n32 36\\n3 8\\n32 37\\n3 9\\n32 38\\n3 10\\n32 39\\n3 11\\n32 40\\n3 12\\n32 41\\n3 13\\n32 42\\n3 14\\n32 43\\n3 15\\n32 44\\n3 16\\n32 45\\n3 17\\n32 46\\n3 18\\n32 47\\n3 19\\n32 48\\n3 20\\n32 49\\n3 21\\n32 50\\n3 22\\n32 51\\n3 23\\n32 52\\n3 24\\n32 53\\n3 25\\n32 54\\n3 26\\n32 55\\n3 27\\n32 56\\n3 28\\n32 57\\n3 29\\n32 58\\n4 5\\n33 34\\n4 6\\n33 35\\n4 7\\n33 36\\n4 8\\n33 37\\n4 9\\n33 38\\n4 10\\n33 39\\n4 11\\n33 40\\n4 12\\n33 41\\n4 13\\n33 42\\n4 14\\n33 43\\n4 15\\n33 44\\n4 16\\n33 45\\n4 17\\n33 46\\n4 18\\n33 47\\n4 19\\n33 48\\n4 20\\n33 49\\n4 21\\n33 50\\n4 22\\n33 51\\n4 23\\n33 52\\n4 24\\n33 53\\n4 25\\n33 54\\n4 26\\n33 55\\n4 27\\n33 56\\n4 28\\n33 57\\n4 29\\n33 58\\n5 7\\n34 36\\n5 8\\n34 37\\n5 9\\n34 38\\n5 10\\n34 39\\n5 11\\n34 40\\n5 12\\n34 41\\n5 13\\n34 42\\n5 14\\n34 43\\n5 15\\n34 44\\n5 16\\n34 45\\n5 17\\n34 46\\n5 18\\n34 47\\n5 19\\n34 48\\n5 20\\n34 49\\n5 21\\n34 50\\n5 22\\n34 51\\n5 23\\n34 52\\n5 24\\n34 53\\n5 25\\n34 54\\n5 26\\n34 55\\n5 27\\n34 56\\n5 28\\n34 57\\n5 29\\n34 58\\n6 7\\n35 36\\n6 8\\n35 37\\n6 9\\n35 38\\n6 10\\n35 39\\n6 11\\n35 40\\n6 12\\n35 41\\n6 13\\n35 42\\n6 14\\n35 43\\n6 15\\n35 44\\n6 16\\n35 45\\n6 17\\n35 46\\n6 18\\n35 47\\n6 19\\n35 48\\n6 20\\n35 49\\n6 21\\n35 50\\n6 22\\n35 51\\n6 23\\n35 52\\n6 24\\n35 53\\n6 25\\n35 54\\n6 26\\n35 55\\n6 27\\n35 56\\n6 28\\n35 57\\n6 29\\n35 58\\n7 9\\n36 38\\n7 10\\n36 39\\n7 11\\n36 40\\n7 12\\n36 41\\n7 13\\n36 42\\n7 14\\n36 43\\n7 15\\n36 44\\n7 16\\n36 45\\n7 17\\n36 46\\n7 18\\n36 47\\n7 19\\n36 48\\n7 20\\n36 49\\n7 21\\n36 50\\n7 22\\n36 51\\n7 23\\n36 52\\n7 24\\n36 53\\n7 25\\n36 54\\n7 26\\n36 55\\n7 27\\n36 56\\n7 28\\n36 57\\n7 29\\n36 58\\n8 9\\n37 38\\n8 10\\n37 39\\n8 11\\n37 40\\n8 12\\n37 41\\n8 13\\n37 42\\n8 14\\n37 43\\n8 15\\n37 44\\n8 16\\n37 45\\n8 17\\n37 46\\n8 18\\n37 47\\n8 19\\n37 48\\n8 20\\n37 49\\n8 21\\n37 50\\n8 22\\n37 51\\n8 23\\n37 52\\n8 24\\n37 53\\n8 25\\n37 54\\n8 26\\n37 55\\n8 27\\n37 56\\n8 28\\n37 57\\n8 29\\n37 58\\n9 11\\n38 40\\n9 12\\n38 41\\n9 13\\n38 42\\n9 14\\n38 43\\n9 15\\n38 44\\n9 16\\n38 45\\n9 17\\n38 46\\n9 18\\n38 47\\n9 19\\n38 48\\n9 20\\n38 49\\n9 21\\n38 50\\n9 22\\n38 51\\n9 23\\n38 52\\n9 24\\n38 53\\n9 25\\n38 54\\n9 26\\n38 55\\n9 27\\n38 56\\n9 28\\n38 57\\n9 29\\n38 58\\n10 11\\n39 40\\n10 12\\n39 41\\n10 13\\n39 42\\n10 14\\n39 43\\n10 15\\n39 44\\n10 16\\n39 45\\n10 17\\n39 46\\n10 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45\\n14 17\\n43 46\\n14 18\\n43 47\\n14 19\\n43 48\\n14 20\\n43 49\\n14 21\\n43 50\\n14 22\\n43 51\\n14 23\\n43 52\\n14 24\\n43 53\\n14 25\\n43 54\\n14 26\\n43 55\\n14 27\\n43 56\\n14 28\\n43 57\\n14 29\\n43 58\\n15 17\\n44 46\\n15 18\\n44 47\\n15 19\\n44 48\\n15 20\\n44 49\\n15 21\\n44 50\\n15 22\\n44 51\\n15 23\\n44 52\\n15 24\\n44 53\\n15 25\\n44 54\\n15 26\\n44 55\\n15 27\\n44 56\\n15 28\\n44 57\\n15 29\\n44 58\\n16 17\\n45 46\\n16 18\\n45 47\\n16 19\\n45 48\\n16 20\\n45 49\\n16 21\\n45 50\\n16 22\\n45 51\\n16 23\\n45 52\\n16 24\\n45 53\\n16 25\\n45 54\\n16 26\\n45 55\\n16 27\\n45 56\\n16 28\\n45 57\\n16 29\\n45 58\\n17 19\\n46 48\\n17 20\\n46 49\\n17 21\\n46 50\\n17 22\\n46 51\\n17 23\\n46 52\\n17 24\\n46 53\\n17 25\\n46 54\\n17 26\\n46 55\\n17 27\\n46 56\\n17 28\\n46 57\\n17 29\\n46 58\\n18 19\\n47 48\\n18 20\\n47 49\\n18 21\\n47 50\\n18 22\\n47 51\\n18 23\\n47 52\\n18 24\\n47 53\\n18 25\\n47 54\\n18 26\\n47 55\\n18 27\\n47 56\\n18 28\\n47 57\\n18 29\\n47 58\\n19 21\\n48 50\\n19 22\\n48 51\\n19 23\\n48 52\\n19 24\\n48 53\\n19 25\\n48 54\\n19 26\\n48 55\\n19 27\\n48 56\\n19 28\\n48 57\\n19 29\\n48 58\\n20 21\\n49 50\\n20 22\\n49 51\\n20 23\\n49 52\\n20 24\\n49 53\\n20 25\\n49 54\\n20 26\\n49 55\\n20 27\\n49 56\\n20 28\\n49 57\\n20 29\\n49 58\\n21 23\\n50 52\\n21 24\\n50 53\\n21 25\\n50 54\\n21 26\\n50 55\\n21 27\\n50 56\\n21 28\\n50 57\\n21 29\\n50 58\\n22 23\\n51 52\\n22 24\\n51 53\\n22 25\\n51 54\\n22 26\\n51 55\\n22 27\\n51 56\\n22 28\\n51 57\\n22 29\\n51 58\\n23 25\\n52 54\\n23 26\\n52 55\\n23 27\\n52 56\\n23 28\\n52 57\\n23 29\\n52 58\\n24 25\\n53 54\\n24 26\\n53 55\\n24 27\\n53 56\\n24 28\\n53 57\\n24 29\\n53 58\\n25 27\\n54 56\\n25 28\\n54 57\\n25 29\\n54 58\\n26 27\\n55 56\\n26 28\\n55 57\\n26 29\\n55 58\\n27 29\\n56 58\\n28 29\\n57 58\\n1 30\\n'}, {'type': 'stdin_stdout', 'input': '31\\n', 'output': 'YES\\n66 1023\\n1 3\\n34 36\\n1 4\\n34 37\\n1 5\\n34 38\\n1 6\\n34 39\\n1 7\\n34 40\\n1 8\\n34 41\\n1 9\\n34 42\\n1 10\\n34 43\\n1 11\\n34 44\\n1 12\\n34 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52\\n11 20\\n44 53\\n11 21\\n44 54\\n11 22\\n44 55\\n11 23\\n44 56\\n11 24\\n44 57\\n11 25\\n44 58\\n11 26\\n44 59\\n11 27\\n44 60\\n11 28\\n44 61\\n11 29\\n44 62\\n11 30\\n44 63\\n11 31\\n44 64\\n11 32\\n44 65\\n11 33\\n44 66\\n12 13\\n45 46\\n12 14\\n45 47\\n12 15\\n45 48\\n12 16\\n45 49\\n12 17\\n45 50\\n12 18\\n45 51\\n12 19\\n45 52\\n12 20\\n45 53\\n12 21\\n45 54\\n12 22\\n45 55\\n12 23\\n45 56\\n12 24\\n45 57\\n12 25\\n45 58\\n12 26\\n45 59\\n12 27\\n45 60\\n12 28\\n45 61\\n12 29\\n45 62\\n12 30\\n45 63\\n12 31\\n45 64\\n12 32\\n45 65\\n12 33\\n45 66\\n13 15\\n46 48\\n13 16\\n46 49\\n13 17\\n46 50\\n13 18\\n46 51\\n13 19\\n46 52\\n13 20\\n46 53\\n13 21\\n46 54\\n13 22\\n46 55\\n13 23\\n46 56\\n13 24\\n46 57\\n13 25\\n46 58\\n13 26\\n46 59\\n13 27\\n46 60\\n13 28\\n46 61\\n13 29\\n46 62\\n13 30\\n46 63\\n13 31\\n46 64\\n13 32\\n46 65\\n13 33\\n46 66\\n14 15\\n47 48\\n14 16\\n47 49\\n14 17\\n47 50\\n14 18\\n47 51\\n14 19\\n47 52\\n14 20\\n47 53\\n14 21\\n47 54\\n14 22\\n47 55\\n14 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54\\n18 22\\n51 55\\n18 23\\n51 56\\n18 24\\n51 57\\n18 25\\n51 58\\n18 26\\n51 59\\n18 27\\n51 60\\n18 28\\n51 61\\n18 29\\n51 62\\n18 30\\n51 63\\n18 31\\n51 64\\n18 32\\n51 65\\n18 33\\n51 66\\n19 21\\n52 54\\n19 22\\n52 55\\n19 23\\n52 56\\n19 24\\n52 57\\n19 25\\n52 58\\n19 26\\n52 59\\n19 27\\n52 60\\n19 28\\n52 61\\n19 29\\n52 62\\n19 30\\n52 63\\n19 31\\n52 64\\n19 32\\n52 65\\n19 33\\n52 66\\n20 21\\n53 54\\n20 22\\n53 55\\n20 23\\n53 56\\n20 24\\n53 57\\n20 25\\n53 58\\n20 26\\n53 59\\n20 27\\n53 60\\n20 28\\n53 61\\n20 29\\n53 62\\n20 30\\n53 63\\n20 31\\n53 64\\n20 32\\n53 65\\n20 33\\n53 66\\n21 23\\n54 56\\n21 24\\n54 57\\n21 25\\n54 58\\n21 26\\n54 59\\n21 27\\n54 60\\n21 28\\n54 61\\n21 29\\n54 62\\n21 30\\n54 63\\n21 31\\n54 64\\n21 32\\n54 65\\n21 33\\n54 66\\n22 23\\n55 56\\n22 24\\n55 57\\n22 25\\n55 58\\n22 26\\n55 59\\n22 27\\n55 60\\n22 28\\n55 61\\n22 29\\n55 62\\n22 30\\n55 63\\n22 31\\n55 64\\n22 32\\n55 65\\n22 33\\n55 66\\n23 25\\n56 58\\n23 26\\n56 59\\n23 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20\\n35 51\\n4 21\\n35 52\\n4 22\\n35 53\\n4 23\\n35 54\\n4 24\\n35 55\\n4 25\\n35 56\\n4 26\\n35 57\\n4 27\\n35 58\\n4 28\\n35 59\\n4 29\\n35 60\\n4 30\\n35 61\\n4 31\\n35 62\\n5 7\\n36 38\\n5 8\\n36 39\\n5 9\\n36 40\\n5 10\\n36 41\\n5 11\\n36 42\\n5 12\\n36 43\\n5 13\\n36 44\\n5 14\\n36 45\\n5 15\\n36 46\\n5 16\\n36 47\\n5 17\\n36 48\\n5 18\\n36 49\\n5 19\\n36 50\\n5 20\\n36 51\\n5 21\\n36 52\\n5 22\\n36 53\\n5 23\\n36 54\\n5 24\\n36 55\\n5 25\\n36 56\\n5 26\\n36 57\\n5 27\\n36 58\\n5 28\\n36 59\\n5 29\\n36 60\\n5 30\\n36 61\\n5 31\\n36 62\\n6 7\\n37 38\\n6 8\\n37 39\\n6 9\\n37 40\\n6 10\\n37 41\\n6 11\\n37 42\\n6 12\\n37 43\\n6 13\\n37 44\\n6 14\\n37 45\\n6 15\\n37 46\\n6 16\\n37 47\\n6 17\\n37 48\\n6 18\\n37 49\\n6 19\\n37 50\\n6 20\\n37 51\\n6 21\\n37 52\\n6 22\\n37 53\\n6 23\\n37 54\\n6 24\\n37 55\\n6 25\\n37 56\\n6 26\\n37 57\\n6 27\\n37 58\\n6 28\\n37 59\\n6 29\\n37 60\\n6 30\\n37 61\\n6 31\\n37 62\\n7 9\\n38 40\\n7 10\\n38 41\\n7 11\\n38 42\\n7 12\\n38 43\\n7 13\\n38 44\\n7 14\\n38 45\\n7 15\\n38 46\\n7 16\\n38 47\\n7 17\\n38 48\\n7 18\\n38 49\\n7 19\\n38 50\\n7 20\\n38 51\\n7 21\\n38 52\\n7 22\\n38 53\\n7 23\\n38 54\\n7 24\\n38 55\\n7 25\\n38 56\\n7 26\\n38 57\\n7 27\\n38 58\\n7 28\\n38 59\\n7 29\\n38 60\\n7 30\\n38 61\\n7 31\\n38 62\\n8 9\\n39 40\\n8 10\\n39 41\\n8 11\\n39 42\\n8 12\\n39 43\\n8 13\\n39 44\\n8 14\\n39 45\\n8 15\\n39 46\\n8 16\\n39 47\\n8 17\\n39 48\\n8 18\\n39 49\\n8 19\\n39 50\\n8 20\\n39 51\\n8 21\\n39 52\\n8 22\\n39 53\\n8 23\\n39 54\\n8 24\\n39 55\\n8 25\\n39 56\\n8 26\\n39 57\\n8 27\\n39 58\\n8 28\\n39 59\\n8 29\\n39 60\\n8 30\\n39 61\\n8 31\\n39 62\\n9 11\\n40 42\\n9 12\\n40 43\\n9 13\\n40 44\\n9 14\\n40 45\\n9 15\\n40 46\\n9 16\\n40 47\\n9 17\\n40 48\\n9 18\\n40 49\\n9 19\\n40 50\\n9 20\\n40 51\\n9 21\\n40 52\\n9 22\\n40 53\\n9 23\\n40 54\\n9 24\\n40 55\\n9 25\\n40 56\\n9 26\\n40 57\\n9 27\\n40 58\\n9 28\\n40 59\\n9 29\\n40 60\\n9 30\\n40 61\\n9 31\\n40 62\\n10 11\\n41 42\\n10 12\\n41 43\\n10 13\\n41 44\\n10 14\\n41 45\\n10 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53\\n13 23\\n44 54\\n13 24\\n44 55\\n13 25\\n44 56\\n13 26\\n44 57\\n13 27\\n44 58\\n13 28\\n44 59\\n13 29\\n44 60\\n13 30\\n44 61\\n13 31\\n44 62\\n14 15\\n45 46\\n14 16\\n45 47\\n14 17\\n45 48\\n14 18\\n45 49\\n14 19\\n45 50\\n14 20\\n45 51\\n14 21\\n45 52\\n14 22\\n45 53\\n14 23\\n45 54\\n14 24\\n45 55\\n14 25\\n45 56\\n14 26\\n45 57\\n14 27\\n45 58\\n14 28\\n45 59\\n14 29\\n45 60\\n14 30\\n45 61\\n14 31\\n45 62\\n15 17\\n46 48\\n15 18\\n46 49\\n15 19\\n46 50\\n15 20\\n46 51\\n15 21\\n46 52\\n15 22\\n46 53\\n15 23\\n46 54\\n15 24\\n46 55\\n15 25\\n46 56\\n15 26\\n46 57\\n15 27\\n46 58\\n15 28\\n46 59\\n15 29\\n46 60\\n15 30\\n46 61\\n15 31\\n46 62\\n16 17\\n47 48\\n16 18\\n47 49\\n16 19\\n47 50\\n16 20\\n47 51\\n16 21\\n47 52\\n16 22\\n47 53\\n16 23\\n47 54\\n16 24\\n47 55\\n16 25\\n47 56\\n16 26\\n47 57\\n16 27\\n47 58\\n16 28\\n47 59\\n16 29\\n47 60\\n16 30\\n47 61\\n16 31\\n47 62\\n17 19\\n48 50\\n17 20\\n48 51\\n17 21\\n48 52\\n17 22\\n48 53\\n17 23\\n48 54\\n17 24\\n48 55\\n17 25\\n48 56\\n17 26\\n48 57\\n17 27\\n48 58\\n17 28\\n48 59\\n17 29\\n48 60\\n17 30\\n48 61\\n17 31\\n48 62\\n18 19\\n49 50\\n18 20\\n49 51\\n18 21\\n49 52\\n18 22\\n49 53\\n18 23\\n49 54\\n18 24\\n49 55\\n18 25\\n49 56\\n18 26\\n49 57\\n18 27\\n49 58\\n18 28\\n49 59\\n18 29\\n49 60\\n18 30\\n49 61\\n18 31\\n49 62\\n19 21\\n50 52\\n19 22\\n50 53\\n19 23\\n50 54\\n19 24\\n50 55\\n19 25\\n50 56\\n19 26\\n50 57\\n19 27\\n50 58\\n19 28\\n50 59\\n19 29\\n50 60\\n19 30\\n50 61\\n19 31\\n50 62\\n20 21\\n51 52\\n20 22\\n51 53\\n20 23\\n51 54\\n20 24\\n51 55\\n20 25\\n51 56\\n20 26\\n51 57\\n20 27\\n51 58\\n20 28\\n51 59\\n20 29\\n51 60\\n20 30\\n51 61\\n20 31\\n51 62\\n21 23\\n52 54\\n21 24\\n52 55\\n21 25\\n52 56\\n21 26\\n52 57\\n21 27\\n52 58\\n21 28\\n52 59\\n21 29\\n52 60\\n21 30\\n52 61\\n21 31\\n52 62\\n22 23\\n53 54\\n22 24\\n53 55\\n22 25\\n53 56\\n22 26\\n53 57\\n22 27\\n53 58\\n22 28\\n53 59\\n22 29\\n53 60\\n22 30\\n53 61\\n22 31\\n53 62\\n23 25\\n54 56\\n23 26\\n54 57\\n23 27\\n54 58\\n23 28\\n54 59\\n23 29\\n54 60\\n23 30\\n54 61\\n23 31\\n54 62\\n24 25\\n55 56\\n24 26\\n55 57\\n24 27\\n55 58\\n24 28\\n55 59\\n24 29\\n55 60\\n24 30\\n55 61\\n24 31\\n55 62\\n25 27\\n56 58\\n25 28\\n56 59\\n25 29\\n56 60\\n25 30\\n56 61\\n25 31\\n56 62\\n26 27\\n57 58\\n26 28\\n57 59\\n26 29\\n57 60\\n26 30\\n57 61\\n26 31\\n57 62\\n27 29\\n58 60\\n27 30\\n58 61\\n27 31\\n58 62\\n28 29\\n59 60\\n28 30\\n59 61\\n28 31\\n59 62\\n29 31\\n60 62\\n30 31\\n61 62\\n1 32\\n'}, {'type': 'stdin_stdout', 'input': '17\\n', 'output': 'YES\\n38 323\\n1 3\\n20 22\\n1 4\\n20 23\\n1 5\\n20 24\\n1 6\\n20 25\\n1 7\\n20 26\\n1 8\\n20 27\\n1 9\\n20 28\\n1 10\\n20 29\\n1 11\\n20 30\\n1 12\\n20 31\\n1 13\\n20 32\\n1 14\\n20 33\\n1 15\\n20 34\\n1 16\\n20 35\\n1 17\\n20 36\\n1 18\\n20 37\\n2 3\\n21 22\\n2 4\\n21 23\\n2 5\\n21 24\\n2 6\\n21 25\\n2 7\\n21 26\\n2 8\\n21 27\\n2 9\\n21 28\\n2 10\\n21 29\\n2 11\\n21 30\\n2 12\\n21 31\\n2 13\\n21 32\\n2 14\\n21 33\\n2 15\\n21 34\\n2 16\\n21 35\\n2 17\\n21 36\\n2 18\\n21 37\\n2 19\\n21 38\\n3 5\\n22 24\\n3 6\\n22 25\\n3 7\\n22 26\\n3 8\\n22 27\\n3 9\\n22 28\\n3 10\\n22 29\\n3 11\\n22 30\\n3 12\\n22 31\\n3 13\\n22 32\\n3 14\\n22 33\\n3 15\\n22 34\\n3 16\\n22 35\\n3 17\\n22 36\\n3 18\\n22 37\\n3 19\\n22 38\\n4 5\\n23 24\\n4 6\\n23 25\\n4 7\\n23 26\\n4 8\\n23 27\\n4 9\\n23 28\\n4 10\\n23 29\\n4 11\\n23 30\\n4 12\\n23 31\\n4 13\\n23 32\\n4 14\\n23 33\\n4 15\\n23 34\\n4 16\\n23 35\\n4 17\\n23 36\\n4 18\\n23 37\\n4 19\\n23 38\\n5 7\\n24 26\\n5 8\\n24 27\\n5 9\\n24 28\\n5 10\\n24 29\\n5 11\\n24 30\\n5 12\\n24 31\\n5 13\\n24 32\\n5 14\\n24 33\\n5 15\\n24 34\\n5 16\\n24 35\\n5 17\\n24 36\\n5 18\\n24 37\\n5 19\\n24 38\\n6 7\\n25 26\\n6 8\\n25 27\\n6 9\\n25 28\\n6 10\\n25 29\\n6 11\\n25 30\\n6 12\\n25 31\\n6 13\\n25 32\\n6 14\\n25 33\\n6 15\\n25 34\\n6 16\\n25 35\\n6 17\\n25 36\\n6 18\\n25 37\\n6 19\\n25 38\\n7 9\\n26 28\\n7 10\\n26 29\\n7 11\\n26 30\\n7 12\\n26 31\\n7 13\\n26 32\\n7 14\\n26 33\\n7 15\\n26 34\\n7 16\\n26 35\\n7 17\\n26 36\\n7 18\\n26 37\\n7 19\\n26 38\\n8 9\\n27 28\\n8 10\\n27 29\\n8 11\\n27 30\\n8 12\\n27 31\\n8 13\\n27 32\\n8 14\\n27 33\\n8 15\\n27 34\\n8 16\\n27 35\\n8 17\\n27 36\\n8 18\\n27 37\\n8 19\\n27 38\\n9 11\\n28 30\\n9 12\\n28 31\\n9 13\\n28 32\\n9 14\\n28 33\\n9 15\\n28 34\\n9 16\\n28 35\\n9 17\\n28 36\\n9 18\\n28 37\\n9 19\\n28 38\\n10 11\\n29 30\\n10 12\\n29 31\\n10 13\\n29 32\\n10 14\\n29 33\\n10 15\\n29 34\\n10 16\\n29 35\\n10 17\\n29 36\\n10 18\\n29 37\\n10 19\\n29 38\\n11 13\\n30 32\\n11 14\\n30 33\\n11 15\\n30 34\\n11 16\\n30 35\\n11 17\\n30 36\\n11 18\\n30 37\\n11 19\\n30 38\\n12 13\\n31 32\\n12 14\\n31 33\\n12 15\\n31 34\\n12 16\\n31 35\\n12 17\\n31 36\\n12 18\\n31 37\\n12 19\\n31 38\\n13 15\\n32 34\\n13 16\\n32 35\\n13 17\\n32 36\\n13 18\\n32 37\\n13 19\\n32 38\\n14 15\\n33 34\\n14 16\\n33 35\\n14 17\\n33 36\\n14 18\\n33 37\\n14 19\\n33 38\\n15 17\\n34 36\\n15 18\\n34 37\\n15 19\\n34 38\\n16 17\\n35 36\\n16 18\\n35 37\\n16 19\\n35 38\\n17 19\\n36 38\\n18 19\\n37 38\\n1 20\\n'}, {'type': 'stdin_stdout', 'input': '25\\n', 'output': 'YES\\n54 675\\n1 3\\n28 30\\n1 4\\n28 31\\n1 5\\n28 32\\n1 6\\n28 33\\n1 7\\n28 34\\n1 8\\n28 35\\n1 9\\n28 36\\n1 10\\n28 37\\n1 11\\n28 38\\n1 12\\n28 39\\n1 13\\n28 40\\n1 14\\n28 41\\n1 15\\n28 42\\n1 16\\n28 43\\n1 17\\n28 44\\n1 18\\n28 45\\n1 19\\n28 46\\n1 20\\n28 47\\n1 21\\n28 48\\n1 22\\n28 49\\n1 23\\n28 50\\n1 24\\n28 51\\n1 25\\n28 52\\n1 26\\n28 53\\n2 3\\n29 30\\n2 4\\n29 31\\n2 5\\n29 32\\n2 6\\n29 33\\n2 7\\n29 34\\n2 8\\n29 35\\n2 9\\n29 36\\n2 10\\n29 37\\n2 11\\n29 38\\n2 12\\n29 39\\n2 13\\n29 40\\n2 14\\n29 41\\n2 15\\n29 42\\n2 16\\n29 43\\n2 17\\n29 44\\n2 18\\n29 45\\n2 19\\n29 46\\n2 20\\n29 47\\n2 21\\n29 48\\n2 22\\n29 49\\n2 23\\n29 50\\n2 24\\n29 51\\n2 25\\n29 52\\n2 26\\n29 53\\n2 27\\n29 54\\n3 5\\n30 32\\n3 6\\n30 33\\n3 7\\n30 34\\n3 8\\n30 35\\n3 9\\n30 36\\n3 10\\n30 37\\n3 11\\n30 38\\n3 12\\n30 39\\n3 13\\n30 40\\n3 14\\n30 41\\n3 15\\n30 42\\n3 16\\n30 43\\n3 17\\n30 44\\n3 18\\n30 45\\n3 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336\\n337 338\\n339 340\\n341 342\\n343 344\\n345 346\\n347 348\\n349 350\\n351 352\\n353 354\\n355 356\\n357 358\\n359 360\\n361 362\\n363 364\\n365 366\\n367 368\\n369 370\\n371 372\\n373 374\\n375 376\\n377 378\\n379 380\\n381 382\\n383 384\\n385 386\\n387 388\\n389 390\\n391 392\\n393 394\\n395 396\\n397 398\\n399 400\\n401 402\\n403 404\\n405 406\\n407 408\\n409 410\\n411 412\\n413 414\\n415 416\\n417 418\\n'}, {'type': 'stdin_stdout', 'input': '-2\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-4\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '136\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-6\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '110\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-8\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-16\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-12\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-14\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 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'NO'}, {'type': 'stdin_stdout', 'input': '-32\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-42\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-26\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-36\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-38\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '-80\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '104\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '120\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '108\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '150\\n', 'output': 'NO'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78529","program":"```python\ndef nextEdge():\n global v\n for i in range(1, v + 1):\n for j in range(i + 1, v + 1):\n yield (i, j)\n\nk = int(input())\n\nif k % 2 == 0:\n print(\"NO\")\nelif k == 1:\n print(\"YES\", \"2 1\", \"1 2\", sep = \"\\n\")\nelse:\n n = 2 * k + 4\n m = k * (k + 2)\n print(\"YES\")\n print(n, m, sep = \" \")\n a = [i for i in range(1, k)] + [i for i in range(k + 4, 2 * k + 3)]\n b = [k + 2] * (k - 1) + [k + 3] * (k - 1)\n a += [k + 2]\n b += [k + 3]\n\n v = k + 1\n curr = (1, 2)\n count = k - 1\n for i in nextEdge():\n if (count == 0) or (i != curr and count > 0):\n a.append(i[0])\n b.append(i[1])\n a.append(i[0] + k + 3)\n b.append(i[1] + k + 3)\n else:\n curr = (curr[1] + 1, curr[1] + 2)\n count -= 2\n \n for i in range(m):\n print(a[i], b[i], sep = \" \")\n\n```","inputs":"1\n","output":"YES\n2 1\n1 2\n","actual_output":"YES\n2 1\n1 2\n","execution_success":true,"sample_index":12519},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"59_C. Title","prompt":"Solve the following coding problem using the programming language python:\n\nVasya has recently finished writing a book. Now he faces the problem of giving it the title. Vasya wants the title to be vague and mysterious for his book to be noticeable among others. That's why the title should be represented by a single word containing at least once each of the first k Latin letters and not containing any other ones. Also, the title should be a palindrome, that is it should be read similarly from the left to the right and from the right to the left.\n\nVasya has already composed the approximate variant of the title. You are given the title template s consisting of lowercase Latin letters and question marks. Your task is to replace all the question marks by lowercase Latin letters so that the resulting word satisfies the requirements, described above. Each question mark should be replaced by exactly one letter, it is not allowed to delete characters or add new ones to the template. If there are several suitable titles, choose the first in the alphabetical order, for Vasya's book to appear as early as possible in all the catalogues.\n\nInput\n\nThe first line contains an integer k (1 \u2264 k \u2264 26) which is the number of allowed alphabet letters. The second line contains s which is the given template. In s only the first k lowercase letters of Latin alphabet and question marks can be present, the length of s is from 1 to 100 characters inclusively.\n\nOutput\n\nIf there is no solution, print IMPOSSIBLE. Otherwise, a single line should contain the required title, satisfying the given template. The title should be a palindrome and it can only contain the first k letters of the Latin alphabet. At that, each of those k letters must be present at least once. If there are several suitable titles, print the lexicographically minimal one. \n\nThe lexicographical comparison is performed by the standard < operator in modern programming languages. The line a is lexicographically smaller than the line b, if exists such an i (1 \u2264 i \u2264 |s|), that ai < bi, and for any j (1 \u2264 j < i) aj = bj. |s| stands for the length of the given template.\n\nExamples\n\nInput\n\n3\na?c\n\n\nOutput\n\nIMPOSSIBLE\n\n\nInput\n\n2\na??a\n\n\nOutput\n\nabba\n\n\nInput\n\n2\n?b?a\n\n\nOutput\n\nabba\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nfrom array import array # noqa: F401\n\n\ndef input():\n return sys.stdin.buffer.readline().decode('utf-8')\n\n\nk = int(input())\na = list(input().rstrip())\nn = len(a)\nunused = [1] * k\n\n\ndef ng():\n print('IMPOSSIBLE')\n exit()\n\n\ntry:\n for i in range(n):\n if a[i] == '?' and a[n - i - 1] != '?':\n a[i] = a[n - i - 1]\n if a[i] != '?':\n unused[ord(a[i]) - 97] = 0\nexcept IndexError:\n ng()\n\nfor i in range(n):\n if a[i] != a[n - i - 1]:\n ng()\n\nfor i in range(n // 2, n):\n if a[i] == '?':\n for cc in range(k - 1, -1, -1):\n if unused[cc]:\n a[i] = a[n - i - 1] = chr(cc + 97)\n unused[cc] = 0\n break\n else:\n a[i] = a[n - i - 1] = 'a'\n\nif any(unused):\n ng()\nprint(*a, sep='')\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\na?c\\n', 'output': 'IMPOSSIBLE\\n'}, {'type': 'stdin_stdout', 'input': '2\\na??a\\n', 'output': 'abba\\n'}, {'type': 'stdin_stdout', 'input': '2\\n?b?a\\n', 'output': 'abba\\n'}, {'type': 'stdin_stdout', 'input': '26\\nabcdefghijklmnopqrstuvwxyzfgvnsltvvohywvqhuhtydghtthgdythuhqvwyhovvtlsnvgfzyxwvutsrqponmlkjihgfedcba\\n', 'output': 'abcdefghijklmnopqrstuvwxyzfgvnsltvvohywvqhuhtydghtthgdythuhqvwyhovvtlsnvgfzyxwvutsrqponmlkjihgfedcba\\n'}, {'type': 'stdin_stdout', 'input': '26\\n?b????g????l?????rs???????s?f?ceiww??ok????u??qwm???q?fu??wkkoh??wie??f???yx?vuts?q??nm?????g??dc??\\n', 'output': 'abcdaagaaaalmnaaqrstuvaxyasafaceiwwahokkwajufpqwmzmwqpfujawkkohawwiecafasayxavutsrqaanmlaaaagaadcba\\n'}, {'type': 'stdin_stdout', 'input': '2\\nababaaaababaaaababbaaabaabaaaabbbabaababababaaaaaaaaaaaababababaababbbaaaabaabaaabbabaaa?babaaaababa\\n', 'output': 'ababaaaababaaaababbaaabaabaaaabbbabaababababaaaaaaaaaaaababababaababbbaaaabaabaaabbabaaaababaaaababa\\n'}, {'type': 'stdin_stdout', 'input': '5\\na?e?c?\\n', 'output': 'IMPOSSIBLE\\n'}, {'type': 'stdin_stdout', 'input': '5\\nabcdeeecdabbaaaeeedebedacccdebacbaeceaaeddabbaaeaccaeaabbaddeaaeceabcabedcccadebedeeeaaabbadceeedcba\\n', 'output': 'abcdeeecdabbaaaeeedebedacccdebacbaeceaaeddabbaaeaccaeaabbaddeaaeceabcabedcccadebedeeeaaabbadceeedcba\\n'}, {'type': 'stdin_stdout', 'input': '26\\n?b??ef??i?klmn?pqrst?vwxyzmkvg?g?t?ajr?x?oe?nq???pcc?????obx???aztx?g???m?yx?vu??rq????l?ji?gf?d?ba\\n', 'output': 'abadefgaijklmnapqrstuvwxyzmkvgggxtzajraxboeanqhccpcchqnaeobxarjaztxgggvkmzyxwvutsrqpanmlkjiagfedaba\\n'}, {'type': 'stdin_stdout', 'input': '9\\nabcdefghiiabddfhbfeaeifeibcdbbgbidbbgdhbccgdbedghdhgdebdgccbhdgbbdibgbb?cbiefieaefbhfddbaiihgfedcba\\n', 'output': 'abcdefghiiabddfhbfeaeifeibcdbbgbidbbgdhbccgdbedghdhgdebdgccbhdgbbdibgbbdcbiefieaefbhfddbaiihgfedcba\\n'}, {'type': 'stdin_stdout', 'input': '3\\n?bc?b??ac??c?bcb?c?b?cbb????ca????c??a?c?abb?ba?aba??b?bb????a?acbb?a??ab?cbb??a?ccb??bc???ab???cba\\n', 'output': 'IMPOSSIBLE\\n'}, {'type': 'stdin_stdout', 'input': '18\\nebcdefghijknmnodqroohmcicajbcikaiibrghrcccroprabiagegbjhcickhopmqponmakjnhgfedcbg\\n', 'output': 'IMPOSSIBLE\\n'}, {'type': 'stdin_stdout', 'input': '17\\nhdhjqblhfcf?phjoeiieojhp?fc?hlbqjhdh\\n', 'output': 'IMPOSSIBLE\\n'}, {'type': 'stdin_stdout', 'input': '26\\nab?defg??j??mnopqrs?uv?x???u?vpd??s?s??s?t?v?vp?is?iqp??v??ush?s??aadp?t?r?y?wv???rqp??mlk?ihgfe?c?a\\n', 'output': 'abcdefghijklmnopqrsauvwxyarutvpdaasasahsutavzvpqissiqpvzvatushasasaadpvturayxwvuasrqponmlkjihgfedcba\\n'}, {'type': 'stdin_stdout', 'input': '23\\nnkcip???????cn??cco?i??n\\n', 'output': 'IMPOSSIBLE\\n'}, {'type': 'stdin_stdout', 'input': '26\\n?b?d?f?h?jk??nopqrst???xyz?u?wobc??cyr?mdmtq?r?kzbzko?oq?m?myr??yocbowwu??yx???t????o???k?i?gfedc??\\n', 'output': 'abcdefghijkaanopqrstaalxyzvuwwobcoycyrymdmtqorokzbzkoroqtmdmyrycyocbowwuvzyxlaatsrqponaakjihgfedcba\\n'}, {'type': 'stdin_stdout', 'input': '13\\na?c??fghij?lmdla?ilg?d??gda?d??djc??g?afedkd?bgj?d?cj?b?dkd???igkkcj???d?????fdh?lij???mlkj?h?f??c??\\n', 'output': 'aacaafghijklmdlajilghdfagdaadaadjckkgiafedkdabgjcddcjgbadkdefaigkkcjdaadaadgafdhglijaldmlkjihgfaacaa\\n'}, {'type': 'stdin_stdout', 'input': '19\\na???efghi?k?mn?pqrshar?ib?jl?c?poh??lih?j?nr?jd????mdj??n??????s?ho????l?pb???ahsr?ponmlkji??fe?c?a\\n', 'output': 'aacaefghijklmnopqrsharaibpjlacapohaslihajanrajdmaaamdjarnajahilsahopacaljpbiarahsrqponmlkjihgfeacaa\\n'}, {'type': 'stdin_stdout', 'input': '9\\nf??e?f\\n', 'output': 'IMPOSSIBLE\\n'}, {'type': 'stdin_stdout', 'input': 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'3\\n?bcbacaca??a?c?abb??bb?abbaa?c?a?ac????bacb?b?a???c?ab??b?aba?c?c?babcca?bba?bbc??baccaa?ba????bc??\\n', 'output': 'abcbacacabaaaccabbacbbaabbaaccbabacacaabacbabbaacacaabbabcabaacacababccaabbaabbcabbaccaaabacacabcba\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78537","program":"```python\nimport sys\nfrom array import array # noqa: F401\n\n\ndef input():\n return sys.stdin.buffer.readline().decode('utf-8')\n\n\nk = int(input())\na = list(input().rstrip())\nn = len(a)\nunused = [1] * k\n\n\ndef ng():\n print('IMPOSSIBLE')\n exit()\n\n\ntry:\n for i in range(n):\n if a[i] == '?' and a[n - i - 1] != '?':\n a[i] = a[n - i - 1]\n if a[i] != '?':\n unused[ord(a[i]) - 97] = 0\nexcept IndexError:\n ng()\n\nfor i in range(n):\n if a[i] != a[n - i - 1]:\n ng()\n\nfor i in range(n // 2, n):\n if a[i] == '?':\n for cc in range(k - 1, -1, -1):\n if unused[cc]:\n a[i] = a[n - i - 1] = chr(cc + 97)\n unused[cc] = 0\n break\n else:\n a[i] = a[n - i - 1] = 'a'\n\nif any(unused):\n ng()\nprint(*a, sep='')\n\n```","inputs":"3\na?c\n","output":"IMPOSSIBLE\n","actual_output":"IMPOSSIBLE\n","execution_success":true,"sample_index":12520},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"621_A. Wet Shark and Odd and Even","prompt":"Solve the following coding problem using the programming language python:\n\nToday, Wet Shark is given n integers. Using any of these integers no more than once, Wet Shark wants to get maximum possible even (divisible by 2) sum. Please, calculate this value for Wet Shark. \n\nNote, that if Wet Shark uses no integers from the n integers, the sum is an even integer 0.\n\nInput\n\nThe first line of the input contains one integer, n (1 \u2264 n \u2264 100 000). The next line contains n space separated integers given to Wet Shark. Each of these integers is in range from 1 to 109, inclusive. \n\nOutput\n\nPrint the maximum possible even sum that can be obtained if we use some of the given integers. \n\nExamples\n\nInput\n\n3\n1 2 3\n\n\nOutput\n\n6\n\nInput\n\n5\n999999999 999999999 999999999 999999999 999999999\n\n\nOutput\n\n3999999996\n\nNote\n\nIn the first sample, we can simply take all three integers for a total sum of 6.\n\nIn the second sample Wet Shark should take any four out of five integers 999 999 999.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\nl=list(map(int,input().split()))\ns=sum(l)\nls=set(l)\nlss=list(ls)\nlss.sort()\nc=0\nfor i in range(len(lss)):\n if lss[i]%2!=0:\n c=lss[i]\n break\nif s%2==0:\n print(s)\nelse:\n \n print(s-c)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n999999999 999999999 999999999 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256000000}","problem_id":"vfc_78541","program":"```python\nn=int(input())\nl=list(map(int,input().split()))\ns=sum(l)\nls=set(l)\nlss=list(ls)\nlss.sort()\nc=0\nfor i in range(len(lss)):\n if lss[i]%2!=0:\n c=lss[i]\n break\nif s%2==0:\n print(s)\nelse:\n \n print(s-c)\n```","inputs":"5\n999999999 999999999 999999999 999999999 999999999\n","output":"3999999996","actual_output":"3999999996\n","execution_success":true,"sample_index":12521},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"691_A. Fashion in Berland","prompt":"Solve the following coding problem using the programming language python:\n\nAccording to rules of the Berland fashion, a jacket should be fastened by all the buttons except only one, but not necessarily it should be the last one. Also if the jacket has only one button, it should be fastened, so the jacket will not swinging open.\n\nYou are given a jacket with n buttons. Determine if it is fastened in a right way.\n\nInput\n\nThe first line contains integer n (1 \u2264 n \u2264 1000) \u2014 the number of buttons on the jacket.\n\nThe second line contains n integers ai (0 \u2264 ai \u2264 1). The number ai = 0 if the i-th button is not fastened. Otherwise ai = 1.\n\nOutput\n\nIn the only line print the word \"YES\" if the jacket is fastened in a right way. Otherwise print the word \"NO\".\n\nExamples\n\nInput\n\n3\n1 0 1\n\n\nOutput\n\nYES\n\n\nInput\n\n3\n1 0 0\n\n\nOutput\n\nNO\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\na = list(map(int,input().split()))\nc = a.count(0)\nif (c>1 or c<1) and n>1 :\n print('NO')\nelif n==1 and c==1:\n print('NO')\nelse:\n print('YES')\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 0 0 0 0 0 0 0 0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '231\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 1 0 0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 0 1 1 1 0 0 1 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 0 0 0 0 0 2 0 0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '231\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 0 1 1 2 1 1 1 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '124\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n', 'output': 'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78553","program":"```python\nn = int(input())\na = list(map(int,input().split()))\nc = a.count(0)\nif (c>1 or c<1) and n>1 :\n print('NO')\nelif n==1 and c==1:\n print('NO')\nelse:\n print('YES')\n\n```","inputs":"3\n1 0 0\n","output":"NO\n","actual_output":"NO\n","execution_success":true,"sample_index":12523},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"716_A. Crazy Computer","prompt":"Solve the following coding problem using the programming language python:\n\nZS the Coder is coding on a crazy computer. If you don't type in a word for a c consecutive seconds, everything you typed disappear! \n\nMore formally, if you typed a word at second a and then the next word at second b, then if b - a \u2264 c, just the new word is appended to other words on the screen. If b - a > c, then everything on the screen disappears and after that the word you have typed appears on the screen.\n\nFor example, if c = 5 and you typed words at seconds 1, 3, 8, 14, 19, 20 then at the second 8 there will be 3 words on the screen. After that, everything disappears at the second 13 because nothing was typed. At the seconds 14 and 19 another two words are typed, and finally, at the second 20, one more word is typed, and a total of 3 words remain on the screen.\n\nYou're given the times when ZS the Coder typed the words. Determine how many words remain on the screen after he finished typing everything.\n\nInput\n\nThe first line contains two integers n and c (1 \u2264 n \u2264 100 000, 1 \u2264 c \u2264 109) \u2014 the number of words ZS the Coder typed and the crazy computer delay respectively.\n\nThe next line contains n integers t1, t2, ..., tn (1 \u2264 t1 < t2 < ... < tn \u2264 109), where ti denotes the second when ZS the Coder typed the i-th word.\n\nOutput\n\nPrint a single positive integer, the number of words that remain on the screen after all n words was typed, in other words, at the second tn.\n\nExamples\n\nInput\n\n6 5\n1 3 8 14 19 20\n\n\nOutput\n\n3\n\nInput\n\n6 1\n1 3 5 7 9 10\n\n\nOutput\n\n2\n\nNote\n\nThe first sample is already explained in the problem statement.\n\nFor the second sample, after typing the first word at the second 1, it disappears because the next word is typed at the second 3 and 3 - 1 > 1. Similarly, only 1 word will remain at the second 9. Then, a word is typed at the second 10, so there will be two words on the screen, as the old word won't disappear because 10 - 9 \u2264 1.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n\"\"\"\n second a and then the next word at second b, then if b\u2009-\u2009a\u2009\u2264\u2009c,\n just the new word is appended to other words on the screen.\n\n If b\u2009-\u2009a\u2009>\u2009c, then everything on the screen disappears and after that the word\n you have typed appears on the screen.\n\"\"\"\n\nnum1 = input()\nnum2 = input()\na = []\nb = []\n\n\ndef get_the_data(count, num, arr):\n for i in range(0, len(num)):\n if num[i] == ' ':\n arr.append(int(num[count:i]))\n count = i+1\n elif i == len(num)-1:\n arr.append(int(num[count:len(num)]))\n return arr\n\n\narr1 = get_the_data(0, num1, a)\narr2 = get_the_data(0, num2, b)\n\ntime = arr1[1]\nchar = 0\nfor i in range(len(arr2)):\n if i == 0:\n # first word can be clicked anytime\n char += 1\n else:\n if arr2[i] - arr2[i-1] <= time:\n char += 1\n else:\n char = 1\n\nprint(char)\n\n\n\n\n\n\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 1\\n1 3 5 7 9 10\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 8 14 19 20\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 1000000000\\n1 1000000000\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n1 100\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 7 12 13 14\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n1 10 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1000000000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n1 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 2 10\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 10\\n1 2 3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n2 100\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 10\\n2 2 3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n1 4 5 7 9 10\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 7 12 16 20\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 8\\n1 7 12 16 20\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 7 12 13 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n0 10 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 2 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 8 2 19 20\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 7 12 13 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 7 12 26 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 14 12 26 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 14 12 26 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 4 12 26 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 4 12 32 34\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n-1 4 12 32 34\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n-1 1 12 32 34\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n-1 1 22 32 34\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n-1 1 22 32 34\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n-2 1 22 32 34\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n-2 1 22 32 52\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n-2 1 22 32 92\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n1 100\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n1 7 12 13 14\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 10 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n1000000000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n1 3 5 7 6 10\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 5 8 14 19 20\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n2 110\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 10 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n1 3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 10\\n2 2 6\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 7 12 13 35\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 9\\n1 14 12 26 34\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 14 12 9 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 5 12 26 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 4 12 32 38\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n-1 1 12 23 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 10\\n-1 1 22 32 34\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n-1 0 22 32 34\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n-2 1 36 32 52\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n-2 1 22 32 92\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 16 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n1000000000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n1 3 4 7 6 10\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 5 8 6 19 20\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n2 110\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 7\\n1 7 12 13 35\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 9\\n1 14 12 26 32\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 0 12 9 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 1 12 26 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 4 12 32 75\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 1 12 23 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 12\\n-1 1 22 32 34\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 8\\n-1 0 22 32 34\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n-2 1 36 32 43\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n-4 1 22 32 92\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1000000010\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n1 3 4 7 6 14\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n1 5 8 6 19 20\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n2 111\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 8\\n1 12 12 16 20\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 7\\n1 7 3 13 35\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 9\\n0 14 12 26 32\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 0 12 11 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n0 1 12 26 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 4 12 32 65\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 1 12 23 51\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n-1 1 22 32 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 9\\n-1 0 22 32 34\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n0 1 36 32 43\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 0\\n1 3 4 7 6 14\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n0 5 8 6 19 20\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n3 111\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 8\\n1 13 12 16 20\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 7\\n1 4 3 13 35\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 9\\n0 14 12 26 43\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n0 0 12 11 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n0 1 12 26 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 2 12 32 65\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n0 1 12 23 51\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n-1 0 22 32 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n0 1 36 32 43\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 9\\n0 5 8 6 19 20\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 8\\n1 4 3 13 35\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 9\\n0 14 12 26 31\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 2 12 32 54\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n0 1 16 23 51\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n0 0 22 32 34\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n0 0 36 32 43\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 9\\n0 5 8 6 19 18\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 9\\n0 14 12 26 45\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 1 12 32 54\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78557","program":"```python\n\"\"\"\n second a and then the next word at second b, then if b\u2009-\u2009a\u2009\u2264\u2009c,\n just the new word is appended to other words on the screen.\n\n If b\u2009-\u2009a\u2009>\u2009c, then everything on the screen disappears and after that the word\n you have typed appears on the screen.\n\"\"\"\n\nnum1 = input()\nnum2 = input()\na = []\nb = []\n\n\ndef get_the_data(count, num, arr):\n for i in range(0, len(num)):\n if num[i] == ' ':\n arr.append(int(num[count:i]))\n count = i+1\n elif i == len(num)-1:\n arr.append(int(num[count:len(num)]))\n return arr\n\n\narr1 = get_the_data(0, num1, a)\narr2 = get_the_data(0, num2, b)\n\ntime = arr1[1]\nchar = 0\nfor i in range(len(arr2)):\n if i == 0:\n # first word can be clicked anytime\n char += 1\n else:\n if arr2[i] - arr2[i-1] <= time:\n char += 1\n else:\n char = 1\n\nprint(char)\n\n\n\n\n\n\n\n\n\n```","inputs":"6 1\n1 3 5 7 9 10\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12524},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"736_C. Ostap and Tree","prompt":"Solve the following coding problem using the programming language python:\n\nOstap already settled down in Rio de Janiero suburb and started to grow a tree in his garden. Recall that a tree is a connected undirected acyclic graph. \n\nOstap's tree now has n vertices. He wants to paint some vertices of the tree black such that from any vertex u there is at least one black vertex v at distance no more than k. Distance between two vertices of the tree is the minimum possible number of edges of the path between them.\n\nAs this number of ways to paint the tree can be large, Ostap wants you to compute it modulo 109 + 7. Two ways to paint the tree are considered different if there exists a vertex that is painted black in one way and is not painted in the other one.\n\nInput\n\nThe first line of the input contains two integers n and k (1 \u2264 n \u2264 100, 0 \u2264 k \u2264 min(20, n - 1)) \u2014 the number of vertices in Ostap's tree and the maximum allowed distance to the nearest black vertex. Don't miss the unusual constraint for k.\n\nEach of the next n - 1 lines contain two integers ui and vi (1 \u2264 ui, vi \u2264 n) \u2014 indices of vertices, connected by the i-th edge. It's guaranteed that given graph is a tree.\n\nOutput\n\nPrint one integer \u2014 the remainder of division of the number of ways to paint the tree by 1 000 000 007 (109 + 7).\n\nExamples\n\nInput\n\n2 0\n1 2\n\n\nOutput\n\n1\n\n\nInput\n\n2 1\n1 2\n\n\nOutput\n\n3\n\n\nInput\n\n4 1\n1 2\n2 3\n3 4\n\n\nOutput\n\n9\n\n\nInput\n\n7 2\n1 2\n2 3\n1 4\n4 5\n1 6\n6 7\n\n\nOutput\n\n91\n\nNote\n\nIn the first sample, Ostap has to paint both vertices black.\n\nIn the second sample, it is enough to paint only one of two vertices, thus the answer is 3: Ostap can paint only vertex 1, only vertex 2, vertices 1 and 2 both.\n\nIn the third sample, the valid ways to paint vertices are: {1, 3}, {1, 4}, {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef main():\n n, k = map(int, input().split())\n cnt = [[[0] * 21 for _ in (0, 1)] for _ in range(n + 1)]\n edges, mod = [[] for _ in range(n + 1)], 1000000007\n for _ in range(n - 1):\n u, v = map(int, input().split())\n edges[u].append(v)\n edges[v].append(u)\n\n def dfs(u, f):\n cnt[u][0][0] = cnt[u][1][k] = 1\n for v in edges[u]:\n if v != f:\n dfs(v, u)\n tmp0, tmp1 = [0] * 21, [0] * 21\n for i in range(k + 1):\n for j in range(k + 1):\n if i != k:\n tmp0[j if i < j else i + 1] += cnt[u][0][j] * cnt[v][0][i]\n if i < j:\n tmp1[j] += cnt[u][1][j] * cnt[v][0][i]\n elif i != k:\n tmp0[i + 1] += cnt[u][1][j] * cnt[v][0][i]\n if i > j:\n tmp1[i - 1] += cnt[u][0][j] * cnt[v][1][i]\n else:\n tmp0[j] += cnt[u][0][j] * cnt[v][1][i]\n tmp1[max(i - 1, j)] += cnt[u][1][j] * cnt[v][1][i]\n for i in range(21):\n tmp0[i] %= mod\n tmp1[i] %= mod\n cnt[u][0] = tmp0\n cnt[u][1] = tmp1\n\n dfs(1, 1)\n print(sum(cnt[1][1][j] for j in range(k + 1)) % mod)\n\n\nif __name__ == '__main__':\n main()\n\n```","verification_info":"{'test_cases': [{'type': 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'output': '279'}, {'type': 'stdin_stdout', 'input': '63 5\\n2 31\\n5 41\\n15 20\\n38 12\\n54 7\\n31 54\\n24 47\\n13 19\\n54 39\\n57 50\\n25 18\\n59 11\\n47 30\\n60 49\\n13 24\\n7 11\\n16 4\\n28 59\\n43 36\\n3 33\\n10 32\\n40 48\\n63 35\\n49 56\\n29 20\\n44 18\\n7 24\\n49 18\\n36 11\\n9 13\\n58 23\\n34 47\\n3 51\\n5 61\\n1 16\\n26 6\\n37 57\\n26 8\\n48 52\\n25 43\\n26 28\\n22 39\\n14 31\\n44 21\\n5 17\\n33 23\\n48 41\\n42 44\\n12 51\\n59 50\\n12 62\\n25 41\\n53 23\\n16 28\\n51 32\\n63 27\\n55 57\\n33 20\\n45 39\\n32 46\\n50 63\\n3 43\\n', 'output': '560665636'}, {'type': 'stdin_stdout', 'input': '10 3\\n2 5\\n4 8\\n4 5\\n6 8\\n4 1\\n5 10\\n7 9\\n4 7\\n3 9\\n', 'output': '945'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 2\\n4 3\\n5 3\\n2 3\\n', 'output': '15'}, {'type': 'stdin_stdout', 'input': '10 4\\n4 6\\n3 5\\n7 3\\n4 9\\n10 2\\n1 9\\n4 8\\n10 3\\n8 7\\n', 'output': '993'}, {'type': 'stdin_stdout', 'input': '10 0\\n9 10\\n5 1\\n10 5\\n8 6\\n8 2\\n7 8\\n8 1\\n8 3\\n4 3\\n', 'output': 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63\\n3 43\\n', 'output': '210184602\\n'}, {'type': 'stdin_stdout', 'input': '10 2\\n2 5\\n3 8\\n4 5\\n6 4\\n4 1\\n10 10\\n7 9\\n4 7\\n3 10\\n', 'output': '99\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n6 4\\n4 1\\n7 5\\n8 7\\n2 9\\n3 6\\n8 6\\n10 3\\n6 9\\n', 'output': '295\\n'}, {'type': 'stdin_stdout', 'input': '10 4\\n4 6\\n3 5\\n7 10\\n4 9\\n8 2\\n1 9\\n2 8\\n10 3\\n8 7\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n6 4\\n4 1\\n7 5\\n8 7\\n2 9\\n3 6\\n8 6\\n10 3\\n9 9\\n', 'output': '97\\n'}, {'type': 'stdin_stdout', 'input': '10 2\\n7 10\\n2 1\\n2 5\\n10 6\\n3 1\\n10 4\\n3 4\\n9 3\\n8 4\\n', 'output': '765\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n7 10\\n2 1\\n6 5\\n10 6\\n3 1\\n10 4\\n3 4\\n9 2\\n8 4\\n', 'output': '279\\n'}, {'type': 'stdin_stdout', 'input': '63 5\\n2 31\\n5 41\\n15 20\\n38 12\\n54 7\\n31 54\\n24 47\\n13 19\\n54 39\\n57 50\\n25 18\\n59 11\\n47 30\\n60 49\\n13 24\\n7 11\\n16 4\\n28 59\\n43 36\\n3 33\\n10 32\\n40 48\\n63 35\\n49 56\\n29 20\\n44 18\\n7 24\\n49 18\\n36 11\\n9 13\\n58 28\\n34 47\\n3 51\\n5 61\\n1 16\\n26 6\\n37 57\\n26 8\\n48 52\\n25 43\\n26 28\\n22 39\\n14 31\\n44 21\\n5 17\\n33 23\\n48 41\\n42 44\\n12 51\\n59 50\\n12 62\\n25 41\\n53 25\\n16 28\\n51 32\\n63 27\\n55 57\\n33 20\\n45 39\\n32 46\\n50 63\\n3 43\\n', 'output': '87019812\\n'}, {'type': 'stdin_stdout', 'input': '10 4\\n4 6\\n3 5\\n9 3\\n4 9\\n8 2\\n1 9\\n4 8\\n10 3\\n8 7\\n', 'output': '1017\\n'}, {'type': 'stdin_stdout', 'input': '10 4\\n2 5\\n4 8\\n4 5\\n6 8\\n6 1\\n5 10\\n7 9\\n4 7\\n3 6\\n', 'output': '1013\\n'}, {'type': 'stdin_stdout', 'input': '10 2\\n1 7\\n10 9\\n1 5\\n3 10\\n2 4\\n5 8\\n6 1\\n2 1\\n6 10\\n', 'output': '743\\n'}, {'type': 'stdin_stdout', 'input': '10 0\\n9 10\\n5 1\\n10 5\\n8 6\\n8 2\\n7 8\\n8 1\\n8 3\\n4 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 4\\n9 6\\n10 8\\n9 2\\n9 10\\n3 7\\n7 9\\n10 4\\n1 7\\n6 5\\n', 'output': '1023\\n'}, {'type': 'stdin_stdout', 'input': '10 0\\n9 10\\n5 1\\n10 5\\n8 6\\n8 2\\n7 8\\n8 2\\n8 3\\n4 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 2\\n1 7\\n10 9\\n1 5\\n3 10\\n2 4\\n5 8\\n6 1\\n2 7\\n6 10\\n', 'output': '735\\n'}, {'type': 'stdin_stdout', 'input': '10 2\\n2 5\\n3 8\\n4 5\\n6 3\\n4 1\\n10 10\\n7 9\\n4 7\\n3 6\\n', 'output': '49\\n'}, {'type': 'stdin_stdout', 'input': '10 0\\n2 6\\n4 3\\n8 5\\n3 7\\n10 4\\n1 2\\n2 8\\n10 1\\n7 9\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n6 8\\n1 9\\n1 5\\n6 10\\n3 9\\n9 4\\n10 9\\n2 1\\n7 4\\n', 'output': '255\\n'}, {'type': 'stdin_stdout', 'input': '10 0\\n9 10\\n5 1\\n10 5\\n8 6\\n2 2\\n7 8\\n8 2\\n8 3\\n4 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 2\\n2 5\\n3 8\\n4 5\\n6 8\\n4 1\\n10 10\\n7 9\\n4 7\\n3 10\\n', 'output': '49\\n'}, {'type': 'stdin_stdout', 'input': '10 4\\n4 6\\n3 5\\n7 10\\n4 9\\n8 2\\n1 9\\n4 8\\n10 3\\n8 7\\n', 'output': '985\\n'}, {'type': 'stdin_stdout', 'input': '10 4\\n9 6\\n4 8\\n9 2\\n9 10\\n3 7\\n7 9\\n10 4\\n1 7\\n6 5\\n', 'output': '1015\\n'}, {'type': 'stdin_stdout', 'input': '10 0\\n5 6\\n4 3\\n8 5\\n3 7\\n10 4\\n1 2\\n2 8\\n10 2\\n7 9\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 0\\n9 10\\n5 1\\n10 6\\n8 6\\n8 2\\n7 8\\n8 1\\n8 3\\n4 3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 2\\n1 4\\n10 9\\n1 5\\n3 5\\n2 4\\n5 8\\n6 1\\n2 7\\n6 10\\n', 'output': '735\\n'}, {'type': 'stdin_stdout', 'input': '10 0\\n9 10\\n5 1\\n10 5\\n8 6\\n8 2\\n7 8\\n8 2\\n8 3\\n8 6\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78561","program":"```python\ndef main():\n n, k = map(int, input().split())\n cnt = [[[0] * 21 for _ in (0, 1)] for _ in range(n + 1)]\n edges, mod = [[] for _ in range(n + 1)], 1000000007\n for _ in range(n - 1):\n u, v = map(int, input().split())\n edges[u].append(v)\n edges[v].append(u)\n\n def dfs(u, f):\n cnt[u][0][0] = cnt[u][1][k] = 1\n for v in edges[u]:\n if v != f:\n dfs(v, u)\n tmp0, tmp1 = [0] * 21, [0] * 21\n for i in range(k + 1):\n for j in range(k + 1):\n if i != k:\n tmp0[j if i < j else i + 1] += cnt[u][0][j] * cnt[v][0][i]\n if i < j:\n tmp1[j] += cnt[u][1][j] * cnt[v][0][i]\n elif i != k:\n tmp0[i + 1] += cnt[u][1][j] * cnt[v][0][i]\n if i > j:\n tmp1[i - 1] += cnt[u][0][j] * cnt[v][1][i]\n else:\n tmp0[j] += cnt[u][0][j] * cnt[v][1][i]\n tmp1[max(i - 1, j)] += cnt[u][1][j] * cnt[v][1][i]\n for i in range(21):\n tmp0[i] %= mod\n tmp1[i] %= mod\n cnt[u][0] = tmp0\n cnt[u][1] = tmp1\n\n dfs(1, 1)\n print(sum(cnt[1][1][j] for j in range(k + 1)) % mod)\n\n\nif __name__ == '__main__':\n main()\n\n```","inputs":"2 1\n1 2\n","output":"3","actual_output":"3\n","execution_success":true,"sample_index":12525},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"760_C. Pavel and barbecue","prompt":"Solve the following coding problem using the programming language python:\n\nPavel cooks barbecue. There are n skewers, they lay on a brazier in a row, each on one of n positions. Pavel wants each skewer to be cooked some time in every of n positions in two directions: in the one it was directed originally and in the reversed direction.\n\nPavel has a plan: a permutation p and a sequence b1, b2, ..., bn, consisting of zeros and ones. Each second Pavel move skewer on position i to position pi, and if bi equals 1 then he reverses it. So he hope that every skewer will visit every position in both directions.\n\nUnfortunately, not every pair of permutation p and sequence b suits Pavel. What is the minimum total number of elements in the given permutation p and the given sequence b he needs to change so that every skewer will visit each of 2n placements? Note that after changing the permutation should remain a permutation as well.\n\nThere is no problem for Pavel, if some skewer visits some of the placements several times before he ends to cook. In other words, a permutation p and a sequence b suit him if there is an integer k (k \u2265 2n), so that after k seconds each skewer visits each of the 2n placements.\n\nIt can be shown that some suitable pair of permutation p and sequence b exists for any n.\n\nInput\n\nThe first line contain the integer n (1 \u2264 n \u2264 2\u00b7105) \u2014 the number of skewers.\n\nThe second line contains a sequence of integers p1, p2, ..., pn (1 \u2264 pi \u2264 n) \u2014 the permutation, according to which Pavel wants to move the skewers.\n\nThe third line contains a sequence b1, b2, ..., bn consisting of zeros and ones, according to which Pavel wants to reverse the skewers.\n\nOutput\n\nPrint single integer \u2014 the minimum total number of elements in the given permutation p and the given sequence b he needs to change so that every skewer will visit each of 2n placements.\n\nExamples\n\nInput\n\n4\n4 3 2 1\n0 1 1 1\n\n\nOutput\n\n2\n\n\nInput\n\n3\n2 3 1\n0 0 0\n\n\nOutput\n\n1\n\nNote\n\nIn the first example Pavel can change the permutation to 4, 3, 1, 2.\n\nIn the second example Pavel can change any element of b to 1.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\np = list(map(int, input().split()))\nb = list(map(int, input().split()))\ns = sum(b[i] for i in range(n))\nif s % 2 == 0:\n ans = 1\nelse:\n ans = 0\nvisited = [0] * n\nptr = 0\nstart = 1\nvisited[0] = 1\nq = 1\nc = 1\nwhile q < n:\n start = p[start - 1]\n if visited[start - 1] == 1:\n c += 1\n while ptr < n and visited[ptr] == 1:\n ptr += 1\n start = ptr + 1\n else:\n visited[start - 1] = 1\n q += 1\nif c == 1:\n print(ans)\nelse:\n print(ans + c)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n4 3 2 1\\n0 1 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 1\\n0 0 0\\n', 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27 72 7 32 93 46 83 30 26 37 39 31 95 59 47 24 67 16 4 15 1 98 19 81 84 61 90 41 17 20 63 60\\n1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 10 5 1 6 8 9 2 3 7\\n0 0 0 0 1 0 0 1 0 0\\n', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78565","program":"```python\nn = int(input())\np = list(map(int, input().split()))\nb = list(map(int, input().split()))\ns = sum(b[i] for i in range(n))\nif s % 2 == 0:\n ans = 1\nelse:\n ans = 0\nvisited = [0] * n\nptr = 0\nstart = 1\nvisited[0] = 1\nq = 1\nc = 1\nwhile q < n:\n start = p[start - 1]\n if visited[start - 1] == 1:\n c += 1\n while ptr < n and visited[ptr] == 1:\n ptr += 1\n start = ptr + 1\n else:\n visited[start - 1] = 1\n q += 1\nif c == 1:\n print(ans)\nelse:\n print(ans + c)\n```","inputs":"4\n4 3 2 1\n0 1 1 1\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12526},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"875_A. Classroom Watch","prompt":"Solve the following coding problem using the programming language python:\n\nEighth-grader Vova is on duty today in the class. After classes, he went into the office to wash the board, and found on it the number n. He asked what is this number and the teacher of mathematics Inna Petrovna answered Vova that n is the answer to the arithmetic task for first-graders. In the textbook, a certain positive integer x was given. The task was to add x to the sum of the digits of the number x written in decimal numeral system.\n\nSince the number n on the board was small, Vova quickly guessed which x could be in the textbook. Now he wants to get a program which will search for arbitrary values of the number n for all suitable values of x or determine that such x does not exist. Write such a program for Vova.\n\nInput\n\nThe first line contains integer n (1 \u2264 n \u2264 109).\n\nOutput\n\nIn the first line print one integer k \u2014 number of different values of x satisfying the condition. \n\nIn next k lines print these values in ascending order.\n\nExamples\n\nInput\n\n21\n\n\nOutput\n\n1\n15\n\n\nInput\n\n20\n\n\nOutput\n\n0\n\nNote\n\nIn the first test case x = 15 there is only one variant: 15 + 1 + 5 = 21.\n\nIn the second test case there are no such x.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n\nn = int(input())\n\nres = []\n\ndef sum_digits(x):\n return sum([int(i) for i in x])\n\nfor i in range(max(0, n - 80), n):\n # print(sum_digits(str(i)))\n if i + sum_digits(str(i)) == n:\n res.append(i)\n\nprint(len(res))\n\nif len(res) != 0:\n for r in sorted(res):\n print(r)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '21\\n', 'output': '1\\n15 '}, {'type': 'stdin_stdout', 'input': '20\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '75\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1000000000\\n', 'output': '1\\n999999932 '}, {'type': 'stdin_stdout', 'input': '100\\n', 'output': '1\\n86 '}, {'type': 'stdin_stdout', 'input': '999999979\\n', 'output': '2\\n999999899 999999908 '}, {'type': 'stdin_stdout', 'input': '39\\n', 'output': '1\\n33 '}, {'type': 'stdin_stdout', 'input': '3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '101\\n', 'output': '2\\n91 100 '}, {'type': 'stdin_stdout', 'input': '10\\n', 'output': '1\\n5 '}, {'type': 'stdin_stdout', 'input': '100000001\\n', 'output': '2\\n99999937 100000000'}, {'type': 'stdin_stdout', 'input': '9\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '66\\n', 'output': '1\\n60 '}, {'type': 'stdin_stdout', 'input': '11\\n', 'output': '1\\n10 '}, {'type': 'stdin_stdout', 'input': '999999994\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2014\\n', 'output': '2\\n1988 2006 '}, {'type': 'stdin_stdout', 'input': '2\\n', 'output': '1\\n1 '}, {'type': 'stdin_stdout', 'input': '37\\n', 'output': '1\\n32\\n'}, {'type': 'stdin_stdout', 'input': '110\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '71\\n', 'output': '1\\n58\\n'}, {'type': 'stdin_stdout', 'input': '6\\n', 'output': '1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '100000000\\n', 'output': '1\\n99999941\\n'}, {'type': 'stdin_stdout', 'input': '76\\n', 'output': '1\\n65\\n'}, {'type': 'stdin_stdout', 'input': '8\\n', 'output': '1\\n4\\n'}, {'type': 'stdin_stdout', 'input': '546191688\\n', 'output': '1\\n546191646\\n'}, {'type': 'stdin_stdout', 'input': '12\\n', 'output': '1\\n6\\n'}, {'type': 'stdin_stdout', 'input': '3169\\n', 'output': '1\\n3155\\n'}, {'type': 'stdin_stdout', 'input': '4\\n', 'output': '1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '23\\n', 'output': '1\\n16\\n'}, {'type': 'stdin_stdout', 'input': '15\\n', 'output': '1\\n12\\n'}, {'type': 'stdin_stdout', 'input': '111\\n', 'output': '2\\n96\\n 105\\n'}, {'type': 'stdin_stdout', 'input': '68\\n', 'output': '1\\n61\\n'}, {'type': 'stdin_stdout', 'input': '101000000\\n', 'output': '1\\n100999954\\n'}, {'type': 'stdin_stdout', 'input': '16\\n', 'output': '1\\n8\\n'}, {'type': 'stdin_stdout', 'input': '19\\n', 'output': '1\\n14\\n'}, {'type': 'stdin_stdout', 'input': '2303\\n', 'output': '1\\n2290\\n'}, {'type': 'stdin_stdout', 'input': '35\\n', 'output': '1\\n31\\n'}, {'type': 'stdin_stdout', 'input': '101000010\\n', 'output': '2\\n100999959\\n 101000004\\n'}, {'type': 'stdin_stdout', 'input': '139\\n', 'output': '1\\n128\\n'}, {'type': 'stdin_stdout', 'input': '13\\n', 'output': '1\\n11\\n'}, {'type': 'stdin_stdout', 'input': '145\\n', 'output': '1\\n140\\n'}, {'type': 'stdin_stdout', 'input': '18\\n', 'output': '1\\n9\\n'}, {'type': 'stdin_stdout', 'input': '14\\n', 'output': '1\\n7\\n'}, {'type': 'stdin_stdout', 'input': '001000010\\n', 'output': '1\\n999964\\n'}, {'type': 'stdin_stdout', 'input': '218\\n', 'output': '2\\n199\\n 208\\n'}, {'type': 'stdin_stdout', 'input': '22\\n', 'output': '1\\n20\\n'}, {'type': 'stdin_stdout', 'input': '17\\n', 'output': '1\\n13\\n'}, {'type': 'stdin_stdout', 'input': '001100010\\n', 'output': '2\\n1099968\\n 1100004\\n'}, {'type': 'stdin_stdout', 'input': '329\\n', 'output': '1\\n322\\n'}, {'type': 'stdin_stdout', 'input': '24\\n', 'output': '1\\n21\\n'}, {'type': 'stdin_stdout', 'input': '101100010\\n', 'output': '1\\n101099972\\n'}, {'type': 'stdin_stdout', 'input': '47\\n', 'output': '1\\n37\\n'}, {'type': 'stdin_stdout', 'input': '101110010\\n', 'output': '2\\n101109976\\n 101110003\\n'}, {'type': 'stdin_stdout', 'input': '391\\n', 'output': '1\\n380\\n'}, {'type': 'stdin_stdout', 'input': '27\\n', 'output': '1\\n18\\n'}, {'type': 'stdin_stdout', 'input': '101010010\\n', 'output': '1\\n101009981\\n'}, {'type': 'stdin_stdout', 'input': '287\\n', 'output': '1\\n274\\n'}, {'type': 'stdin_stdout', 'input': '33\\n', 'output': '1\\n30\\n'}, {'type': 'stdin_stdout', 'input': '100010010\\n', 'output': '2\\n100009977\\n 100010004\\n'}, {'type': 'stdin_stdout', 'input': '32\\n', 'output': '1\\n25\\n'}, {'type': 'stdin_stdout', 'input': '43\\n', 'output': '1\\n35\\n'}, {'type': 'stdin_stdout', 'input': '100010011\\n', 'output': '1\\n100009982\\n'}, {'type': 'stdin_stdout', 'input': '62\\n', 'output': '1\\n49\\n'}, {'type': 'stdin_stdout', 'input': '59\\n', 'output': '1\\n52\\n'}, {'type': 'stdin_stdout', 'input': '110010011\\n', 'output': '2\\n110009977\\n 110010004\\n'}, {'type': 'stdin_stdout', 'input': '50\\n', 'output': '1\\n43\\n'}, {'type': 'stdin_stdout', 'input': '72\\n', 'output': '1\\n63\\n'}, {'type': 'stdin_stdout', 'input': '110010001\\n', 'output': '1\\n110009972\\n'}, {'type': 'stdin_stdout', 'input': '60\\n', 'output': '1\\n48\\n'}, {'type': 'stdin_stdout', 'input': '91\\n', 'output': '1\\n77\\n'}, {'type': 'stdin_stdout', 'input': '110010101\\n', 'output': '1\\n110010085\\n'}, {'type': 'stdin_stdout', 'input': '98\\n', 'output': '1\\n85\\n'}, {'type': 'stdin_stdout', 'input': '156\\n', 'output': '1\\n150\\n'}, {'type': 'stdin_stdout', 'input': '111010001\\n', 'output': '1\\n111009967\\n'}, {'type': 'stdin_stdout', 'input': '111011001\\n', 'output': '1\\n111010980\\n'}, {'type': 'stdin_stdout', 'input': '152\\n', 'output': '1\\n139\\n'}, {'type': 'stdin_stdout', 'input': '111011101\\n', 'output': '1\\n111011084\\n'}, {'type': 'stdin_stdout', 'input': '280\\n', 'output': '1\\n266\\n'}, {'type': 'stdin_stdout', 'input': '110001101\\n', 'output': '1\\n110001085\\n'}, {'type': 'stdin_stdout', 'input': '010001101\\n', 'output': '1\\n10001090\\n'}, {'type': 'stdin_stdout', 'input': '000001101\\n', 'output': '1\\n1086\\n'}, {'type': 'stdin_stdout', 'input': '000101101\\n', 'output': '1\\n101090\\n'}, {'type': 'stdin_stdout', 'input': '000101111\\n', 'output': '2\\n101095\\n 101104\\n'}, {'type': 'stdin_stdout', 'input': '100101101\\n', 'output': '1\\n100101085\\n'}, {'type': 'stdin_stdout', 'input': '100101001\\n', 'output': '1\\n100100981\\n'}, {'type': 'stdin_stdout', 'input': '100101011\\n', 'output': '2\\n100100986\\n 100101004\\n'}, {'type': 'stdin_stdout', 'input': '000101011\\n', 'output': '1\\n100991\\n'}, {'type': 'stdin_stdout', 'input': '100111011\\n', 'output': '1\\n100110990\\n'}, {'type': 'stdin_stdout', 'input': '100111010\\n', 'output': '2\\n100110985\\n 100111003\\n'}, {'type': 'stdin_stdout', 'input': '100101010\\n', 'output': '1\\n100100990\\n'}, {'type': 'stdin_stdout', 'input': '000111010\\n', 'output': '1\\n110990\\n'}, {'type': 'stdin_stdout', 'input': '000111000\\n', 'output': '1\\n110976\\n'}, {'type': 'stdin_stdout', 'input': '101101010\\n', 'output': '2\\n101100985\\n 101101003\\n'}, {'type': 'stdin_stdout', 'input': '101101011\\n', 'output': '1\\n101100990\\n'}, {'type': 'stdin_stdout', 'input': '101101111\\n', 'output': '2\\n101101094\\n 101101103\\n'}, {'type': 'stdin_stdout', 'input': '001101110\\n', 'output': '2\\n1101094\\n 1101103\\n'}, {'type': 'stdin_stdout', 'input': '001100111\\n', 'output': '2\\n1100095\\n 1100104\\n'}, {'type': 'stdin_stdout', 'input': '001100011\\n', 'output': '1\\n1099973\\n'}, {'type': 'stdin_stdout', 'input': '001101011\\n', 'output': '2\\n1100986\\n 1101004\\n'}, {'type': 'stdin_stdout', 'input': '001101001\\n', 'output': '1\\n1100981\\n'}, {'type': 'stdin_stdout', 'input': '001101101\\n', 'output': '1\\n1101085\\n'}, {'type': 'stdin_stdout', 'input': '000111101\\n', 'output': '1\\n111085\\n'}, {'type': 'stdin_stdout', 'input': '100111100\\n', 'output': '1\\n100111084\\n'}, {'type': 'stdin_stdout', 'input': '000110000\\n', 'output': '1\\n109972\\n'}, {'type': 'stdin_stdout', 'input': '000110001\\n', 'output': '1\\n109968\\n'}, {'type': 'stdin_stdout', 'input': '000010001\\n', 'output': '2\\n9973\\n 10000\\n'}, {'type': 'stdin_stdout', 'input': '7\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '5\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '132\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '97\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '389\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '277\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '176\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '111001101\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '100101111\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '101111010\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '001101111\\n', 'output': '0\\n\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_78585","program":"```python\n\nn = int(input())\n\nres = []\n\ndef sum_digits(x):\n return sum([int(i) for i in x])\n\nfor i in range(max(0, n - 80), n):\n # print(sum_digits(str(i)))\n if i + sum_digits(str(i)) == n:\n res.append(i)\n\nprint(len(res))\n\nif len(res) != 0:\n for r in sorted(res):\n print(r)\n```","inputs":"21\n","output":"1\n15 ","actual_output":"1\n15\n","execution_success":true,"sample_index":12527},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"899_F. Letters Removing","prompt":"Solve the following coding problem using the programming language python:\n\nPetya has a string of length n consisting of small and large English letters and digits.\n\nHe performs m operations. Each operation is described with two integers l and r and a character c: Petya removes from the string all characters c on positions between l and r, inclusive. It's obvious that the length of the string remains the same or decreases after each operation.\n\nFind how the string will look like after Petya performs all m operations.\n\nInput\n\nThe first string contains two integers n and m (1 \u2264 n, m \u2264 2\u00b7105) \u2014 the length of the string and the number of operations.\n\nThe second line contains the string of length n, consisting of small and large English letters and digits. Positions in the string are enumerated from 1.\n\nEach of the next m lines contains two integers l and r (1 \u2264 l \u2264 r), followed by a character c, which is a small or large English letter or a digit. This line describes one operation. It is guaranteed that r doesn't exceed the length of the string s before current operation.\n\nOutput\n\nPrint the string Petya will obtain after performing all m operations. If the strings becomes empty after all operations, print an empty line.\n\nExamples\n\nInput\n\n4 2\nabac\n1 3 a\n2 2 c\n\n\nOutput\n\nb\n\n\nInput\n\n3 2\nA0z\n1 3 0\n1 1 z\n\n\nOutput\n\nAz\n\n\nInput\n\n10 4\nagtFrgF4aF\n2 5 g\n4 9 F\n1 5 4\n1 7 a\n\n\nOutput\n\ntFrg4\n\n\nInput\n\n9 5\naAAaBBccD\n1 4 a\n5 6 c\n2 3 B\n4 4 D\n2 3 A\n\n\nOutput\n\nAB\n\nNote\n\nIn the first example during the first operation both letters 'a' are removed, so the string becomes \"bc\". During the second operation the letter 'c' (on the second position) is removed, and the string becomes \"b\".\n\nIn the second example during the first operation Petya removes '0' from the second position. After that the string becomes \"Az\". During the second operations the string doesn't change.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#!/usr/bin/env python\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n\nclass FenwickTree:\n def __init__(self, x):\n \"\"\"transform list into BIT\"\"\"\n self.bit = x\n for i in range(len(x)):\n j = i | (i + 1)\n if j < len(x):\n x[j] += x[i]\n\n def update(self, idx, x):\n \"\"\"updates bit[idx] += x\"\"\"\n while idx < len(self.bit):\n self.bit[idx] += x\n idx |= idx + 1\n\n def query(self, end):\n \"\"\"calc sum(bit[:end])\"\"\"\n x = 0\n while end:\n x += self.bit[end - 1]\n end &= end - 1\n return x\n\n def findkth(self, k):\n \"\"\"Find largest idx such that sum(bit[:idx]) <= k\"\"\"\n idx = -1\n for d in reversed(range(len(self.bit).bit_length())):\n right_idx = idx + (1 << d)\n if right_idx < len(self.bit) and k >= self.bit[right_idx]:\n idx = right_idx\n k -= self.bit[idx]\n return idx + 1\n\ndef lb(a,x):\n l,r=-1,len(a)\n while(r-l>1):\n m=(l+r)//2\n if(a[m]= self.bit[right_idx]:\n idx = right_idx\n k -= self.bit[idx]\n return idx + 1\n\ndef lb(a,x):\n l,r=-1,len(a)\n while(r-l>1):\n m=(l+r)//2\n if(a[m] condition li - 1 \u2264 li holds.\n\nThe sum of n over all test cases doesn't exceed 1000.\n\nNote that in hacks you have to set t = 1.\n\nOutput\n\nFor each test case print n integers. i-th of them must be equal to the second when i-th student gets his tea, or 0 if he leaves without tea.\n\nExample\n\nInput\n\n2\n2\n1 3\n1 4\n3\n1 5\n1 1\n2 3\n\n\nOutput\n\n1 2 \n1 0 2 \n\nNote\n\nThe example contains 2 tests:\n\n 1. During 1-st second, students 1 and 2 come to the queue, and student 1 gets his tea. Student 2 gets his tea during 2-nd second. \n 2. During 1-st second, students 1 and 2 come to the queue, student 1 gets his tea, and student 2 leaves without tea. During 2-nd second, student 3 comes and gets his tea. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nif __name__ == '__main__':\n cin = input\n t = int(cin())\n\n while t > 0:\n n = int(cin())\n a, cnt = [0] * n, 0\n for i in range(n):\n l, r = map(int, cin().split())\n if r >= cnt + max(l - cnt, 1):\n cnt += max(l - cnt, 1)\n a[i] += cnt\n print(*a)\n t -= 1\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n2\\n1 3\\n1 4\\n3\\n1 5\\n1 1\\n2 3\\n', 'output': '1 2\\n1 0 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n1 1\\n1 2\\n1 5\\n1 1\\n1 1\\n', 'output': '1 2 3 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n11\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n', 'output': '1 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1\\n1 1\\n1\\n1 2\\n1\\n1 1000\\n1\\n1 2000\\n1\\n2 2\\n1\\n2 3\\n1\\n2 1000\\n1\\n2 2000\\n1\\n1999 1999\\n1\\n1999 2000\\n1\\n2000 2000\\n2\\n1 1\\n1 1\\n2\\n1 1\\n1 2\\n2\\n1 2\\n1 1\\n2\\n1 2000\\n1 1\\n2\\n1 1\\n1 2000\\n2\\n1 2000\\n2 2\\n2\\n2 2000\\n2 2\\n2\\n2 2\\n2 2000\\n', 'output': '1\\n1\\n1\\n1\\n2\\n2\\n2\\n2\\n1999\\n1999\\n2000\\n1 0\\n1 2\\n1 0\\n1 0\\n1 2\\n1 2\\n2 0\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n1 1\\n1 2\\n1 5\\n1 2\\n1 1\\n', 'output': '1 2 3 0 0\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1\\n1 1\\n1\\n1 2\\n1\\n1 1000\\n1\\n1 2000\\n1\\n2 2\\n1\\n2 3\\n1\\n2 1000\\n1\\n2 2118\\n1\\n1999 1999\\n1\\n1999 2000\\n1\\n2000 2000\\n2\\n1 1\\n1 1\\n2\\n1 1\\n1 2\\n2\\n1 2\\n1 1\\n2\\n1 2000\\n1 1\\n2\\n1 1\\n1 2000\\n2\\n1 2000\\n2 2\\n2\\n2 2000\\n2 2\\n2\\n2 2\\n2 2000\\n', 'output': '1\\n1\\n1\\n1\\n2\\n2\\n2\\n2\\n1999\\n1999\\n2000\\n1 0\\n1 2\\n1 0\\n1 0\\n1 2\\n1 2\\n2 0\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n1 3\\n1 4\\n3\\n1 10\\n1 1\\n2 3\\n', 'output': '1 2\\n1 0 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1\\n1 4\\n1 5\\n1 2\\n1 1\\n', 'output': '1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n1 1\\n1 4\\n1 5\\n1 2\\n1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n1 3\\n1 4\\n3\\n1 10\\n1 1\\n3 3\\n', 'output': '1 2\\n1 0 3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n1 6\\n1 2\\n3\\n1 5\\n1 2\\n1 3\\n', 'output': '1 2\\n1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n1 2\\n1 4\\n1 6\\n2 3\\n2 2\\n', 'output': '1 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n2 2\\n1 4\\n1 8\\n2 2\\n0 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n1 1\\n1 4\\n1 5\\n1 2\\n1 1\\n', 'output': '1 2 3 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1\\n1 4\\n1 4\\n1 2\\n1 1\\n', 'output': '1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1\\n1 4\\n1 6\\n1 2\\n1 1\\n', 'output': '1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1\\n1 4\\n1 6\\n2 2\\n1 1\\n', 'output': '1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1\\n1 4\\n1 6\\n2 2\\n1 2\\n', 'output': '1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n1 1\\n1 2\\n1 7\\n1 1\\n1 1\\n', 'output': '1 2 3 0 0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n1 6\\n1 4\\n3\\n1 5\\n1 1\\n2 3\\n', 'output': '1 2\\n1 0 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1\\n1 4\\n1 4\\n2 2\\n1 2\\n', 'output': '1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n1 6\\n1 2\\n3\\n1 5\\n1 1\\n2 3\\n', 'output': '1 2\\n1 0 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1\\n1 4\\n1 8\\n2 2\\n1 2\\n', 'output': '1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n1 1\\n1 2\\n3\\n1 5\\n1 1\\n2 3\\n', 'output': '1 2\\n1 0 2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n1 3\\n2 4\\n3\\n1 10\\n1 1\\n2 3\\n', 'output': '1 2\\n1 0 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1\\n1 4\\n1 5\\n1 2\\n0 1\\n', 'output': '1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n1 1\\n1 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2\\n', 'output': '1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n1 4\\n1 4\\n1 2\\n0 1\\n0 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n1 1\\n1 4\\n1 2\\n0 1\\n0 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n1 1\\n1 4\\n1 4\\n0 1\\n0 1\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78593","program":"```python\nif __name__ == '__main__':\n cin = input\n t = int(cin())\n\n while t > 0:\n n = int(cin())\n a, cnt = [0] * n, 0\n for i in range(n):\n l, r = map(int, cin().split())\n if r >= cnt + max(l - cnt, 1):\n cnt += max(l - cnt, 1)\n a[i] += cnt\n print(*a)\n t -= 1\n```","inputs":"2\n2\n1 3\n1 4\n3\n1 5\n1 1\n2 3\n","output":"1 2\n1 0 2\n","actual_output":"1 2\n1 0 2\n","execution_success":true,"sample_index":12529},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"976_E. Well played!","prompt":"Solve the following coding problem using the programming language python:\n\nRecently Max has got himself into popular CCG \"BrainStone\". As \"BrainStone\" is a pretty intellectual game, Max has to solve numerous hard problems during the gameplay. Here is one of them:\n\nMax owns n creatures, i-th of them can be described with two numbers \u2014 its health hpi and its damage dmgi. Max also has two types of spells in stock:\n\n 1. Doubles health of the creature (hpi := hpi\u00b72); \n 2. Assigns value of health of the creature to its damage (dmgi := hpi). \n\n\n\nSpell of first type can be used no more than a times in total, of the second type \u2014 no more than b times in total. Spell can be used on a certain creature multiple times. Spells can be used in arbitrary order. It isn't necessary to use all the spells.\n\nMax is really busy preparing for his final exams, so he asks you to determine what is the maximal total damage of all creatures he can achieve if he uses spells in most optimal way.\n\nInput\n\nThe first line contains three integers n, a, b (1 \u2264 n \u2264 2\u00b7105, 0 \u2264 a \u2264 20, 0 \u2264 b \u2264 2\u00b7105) \u2014 the number of creatures, spells of the first type and spells of the second type, respectively.\n\nThe i-th of the next n lines contain two number hpi and dmgi (1 \u2264 hpi, dmgi \u2264 109) \u2014 description of the i-th creature.\n\nOutput\n\nPrint single integer \u2014 maximum total damage creatures can deal.\n\nExamples\n\nInput\n\n2 1 1\n10 15\n6 1\n\n\nOutput\n\n27\n\n\nInput\n\n3 0 3\n10 8\n7 11\n5 2\n\n\nOutput\n\n26\n\nNote\n\nIn the first example Max should use the spell of the first type on the second creature, then the spell of the second type on the same creature. Then total damage will be equal to 15 + 6\u00b72 = 27.\n\nIn the second example Max should use the spell of the second type on the first creature, then the spell of the second type on the third creature. Total damage will be equal to 10 + 11 + 5 = 26.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nread=lambda:map(int,sys.stdin.buffer.readline().split())\nn,a,b=read()\nv=[tuple(read()) for _ in range(n)]\nans=0\nif b>0:\n\tc=[v[x][0]-v[x][1] for x in range(n)]\n\tw,r=list(range(n)),[0]*n\n\tw.sort(key=lambda x:c[x],reverse=True)\n\tfor i in range(n): r[w[i]]=i\n\tf=True;s=0;m=min(n,b)\n\tfor i in range(m):\n\t\tk=c[w[i]]\n\t\tif k<=0: f=False;m=i;break\n\t\ts+=k\n\tans=s\n\tif a>0:\n\t\tfor i in range(n):\n\t\t\tk=v[i][0]*(1<ans: ans=tmp\nprint(sum([v[i][1] for i in range(n)])+ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 1 1\\n10 15\\n6 1\\n', 'output': '27\\n'}, {'type': 'stdin_stdout', 'input': '3 0 3\\n10 8\\n7 11\\n5 2\\n', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '1 0 0\\n2 1\\n', 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{'type': 'stdin_stdout', 'input': '12 20 4\\n852 935\\n20 820\\n969 197\\n219 918\\n547 842\\n615 163\\n704 377\\n326 482\\n183 833\\n884 994\\n886 471\\n909 450\\n', 'output': '1016078755\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78601","program":"```python\nimport sys\nread=lambda:map(int,sys.stdin.buffer.readline().split())\nn,a,b=read()\nv=[tuple(read()) for _ in range(n)]\nans=0\nif b>0:\n\tc=[v[x][0]-v[x][1] for x in range(n)]\n\tw,r=list(range(n)),[0]*n\n\tw.sort(key=lambda x:c[x],reverse=True)\n\tfor i in range(n): r[w[i]]=i\n\tf=True;s=0;m=min(n,b)\n\tfor i in range(m):\n\t\tk=c[w[i]]\n\t\tif k<=0: f=False;m=i;break\n\t\ts+=k\n\tans=s\n\tif a>0:\n\t\tfor i in range(n):\n\t\t\tk=v[i][0]*(1<ans: ans=tmp\nprint(sum([v[i][1] for i in range(n)])+ans)\n```","inputs":"2 1 1\n10 15\n6 1\n","output":"27\n","actual_output":"27\n","execution_success":true,"sample_index":12530},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"996_C. Tesla","prompt":"Solve the following coding problem using the programming language python:\n\nAllen dreams of one day owning a enormous fleet of electric cars, the car of the future! He knows that this will give him a big status boost. As Allen is planning out all of the different types of cars he will own and how he will arrange them, he realizes that he has a problem. \n\nAllen's future parking lot can be represented as a rectangle with 4 rows and n (n \u2264 50) columns of rectangular spaces, each of which can contain at most one car at any time. He imagines having k (k \u2264 2n) cars in the grid, and all the cars are initially in the second and third rows. Each of the cars also has a different designated parking space in the first or fourth row. Allen has to put the cars into corresponding parking places.\n\n Illustration to the first example.\n\nHowever, since Allen would never entrust his cars to anyone else, only one car can be moved at a time. He can drive a car from a space in any of the four cardinal directions to a neighboring empty space. Furthermore, Allen can only move one of his cars into a space on the first or fourth rows if it is the car's designated parking space. \n\nAllen knows he will be a very busy man, and will only have time to move cars at most 20000 times before he realizes that moving cars is not worth his time. Help Allen determine if he should bother parking his cars or leave it to someone less important.\n\nInput\n\nThe first line of the input contains two space-separated integers n and k (1 \u2264 n \u2264 50, 1 \u2264 k \u2264 2n), representing the number of columns and the number of cars, respectively.\n\nThe next four lines will contain n integers each between 0 and k inclusive, representing the initial state of the parking lot. The rows are numbered 1 to 4 from top to bottom and the columns are numbered 1 to n from left to right.\n\nIn the first and last line, an integer 1 \u2264 x \u2264 k represents a parking spot assigned to car x (you can only move this car to this place), while the integer 0 represents a empty space (you can't move any car to this place).\n\nIn the second and third line, an integer 1 \u2264 x \u2264 k represents initial position of car x, while the integer 0 represents an empty space (you can move any car to this place).\n\nEach x between 1 and k appears exactly once in the second and third line, and exactly once in the first and fourth line.\n\nOutput\n\nIf there is a sequence of moves that brings all of the cars to their parking spaces, with at most 20000 car moves, then print m, the number of moves, on the first line. On the following m lines, print the moves (one move per line) in the format i r c, which corresponds to Allen moving car i to the neighboring space at row r and column c.\n\nIf it is not possible for Allen to move all the cars to the correct spaces with at most 20000 car moves, print a single line with the integer -1.\n\nExamples\n\nInput\n\n4 5\n1 2 0 4\n1 2 0 4\n5 0 0 3\n0 5 0 3\n\n\nOutput\n\n6\n1 1 1\n2 1 2\n4 1 4\n3 4 4\n5 3 2\n5 4 2\n\n\nInput\n\n1 2\n1\n2\n1\n2\n\n\nOutput\n\n-1\n\n\nInput\n\n1 2\n1\n1\n2\n2\n\n\nOutput\n\n2\n1 1 1\n2 4 1\n\nNote\n\nIn the first sample test case, all cars are in front of their spots except car 5, which is in front of the parking spot adjacent. The example shows the shortest possible sequence of moves, but any sequence of length at most 20000 will be accepted.\n\nIn the second sample test case, there is only one column, and the cars are in the wrong order, so no cars can move and the task is impossible.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, k = list(map(int, input().split()))\ntable = []\nfor row in range(4):\n table.append(list(map(int, input().split())))\n\nmoves = []\n\ndef make_move(start,finish):\n moves.append((table[start[0]][start[1]], finish[0]+1, finish[1]+1))\n table[finish[0]][finish[1]] = table[start[0]][start[1]]\n table[start[0]][start[1]] = 0\n\n\ndef move_all_to_places():\n for pos in range(n):\n if (table[1][pos] == table[0][pos]) and table[1][pos]:\n make_move((1,pos), (0,pos))\n if (table[2][pos] == table[3][pos]) and table[2][pos]:\n make_move((2,pos), (3,pos))\n\nmove_all_to_places()\n\n\n\nfound = False\nfor pos in range(n):\n if table[1][pos] == 0:\n found = True\n break\n if table[2][pos] == 0:\n found = True\n break\n\nif not found:\n print(-1)\n exit()\n\nfor cnt in range(20000):\n if (table[1][0] != 0) and (table[2][0] == 0) :\n make_move((1,0), (2,0)) # moved down\n if n == 1:\n continue\n for pos in range(1,n):\n if (table[1][pos-1] == 0) and (table[1][pos] != 0):\n make_move((1,pos), (1, pos-1))\n move_all_to_places()\n\n if (table[1][n-1] == 0) and (table[2][n-1] != 0) :\n make_move((2,n-1), (1,n-1)) # moved up\n for pos in range(n-2,-1, -1):\n if (table[2][pos+1] == 0) and (table[2][pos] != 0):\n make_move((2,pos), (2, pos+1))\n move_all_to_places()\n\nif len(moves) > 20000:\n print(-1)\n exit()\n\nprint(len(moves))\nfor m in moves:\n print(*m)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 2\\n1\\n1\\n2\\n2\\n', 'output': '2\\n1 1 1\\n2 4 1\\n'}, {'type': 'stdin_stdout', 'input': '4 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7\\n6 3 5\\n14 3 2\\n13 3 1\\n19 2 1\\n2 2 2\\n3 2 14\\n5 2 36\\n16 2 38\\n7 3 40\\n15 3 32\\n1 3 20\\n12 3 15\\n20 3 8\\n6 3 6\\n14 3 3\\n13 3 2\\n3 2 13\\n5 2 35\\n16 2 37\\n7 2 40\\n15 3 33\\n1 3 21\\n12 3 16\\n20 3 9\\n6 3 7\\n14 3 4\\n13 3 3\\n19 3 1\\n2 2 1\\n3 2 12\\n5 2 34\\n16 2 36\\n7 2 39\\n15 3 34\\n1 3 22\\n12 3 17\\n20 3 10\\n6 3 8\\n14 3 5\\n13 3 4\\n19 3 2\\n2 3 1\\n3 2 11\\n5 2 33\\n16 2 35\\n7 2 38\\n15 3 35\\n1 3 23\\n12 3 18\\n20 3 11\\n6 3 9\\n14 3 6\\n13 3 5\\n19 3 3\\n2 3 2\\n5 1 33\\n3 2 10\\n16 2 34\\n7 2 37\\n15 3 36\\n1 3 24\\n12 3 19\\n20 3 12\\n6 3 10\\n14 3 7\\n13 3 6\\n19 3 4\\n2 3 3\\n3 1 10\\n16 2 33\\n7 2 36\\n15 3 37\\n1 3 25\\n12 3 20\\n20 3 13\\n6 3 11\\n14 3 8\\n13 3 7\\n19 3 5\\n2 3 4\\n16 2 32\\n7 2 35\\n15 3 38\\n1 3 26\\n12 3 21\\n20 3 14\\n6 3 12\\n14 3 9\\n13 3 8\\n19 3 6\\n2 3 5\\n16 2 31\\n7 2 34\\n15 3 39\\n1 3 27\\n12 3 22\\n20 3 15\\n6 3 13\\n14 3 10\\n13 3 9\\n19 3 7\\n2 3 6\\n6 4 13\\n16 2 30\\n7 2 33\\n15 3 40\\n1 3 28\\n12 3 23\\n20 3 16\\n14 3 11\\n13 3 10\\n19 3 8\\n2 3 7\\n16 2 29\\n7 2 32\\n15 2 40\\n1 3 29\\n12 3 24\\n20 3 17\\n14 3 12\\n13 3 11\\n19 3 9\\n2 3 8\\n16 2 28\\n7 2 31\\n15 2 39\\n1 3 30\\n12 3 25\\n20 3 18\\n14 3 13\\n13 3 12\\n19 3 10\\n2 3 9\\n16 2 27\\n7 2 30\\n15 2 38\\n1 3 31\\n12 3 26\\n20 3 19\\n14 3 14\\n13 3 13\\n19 3 11\\n2 3 10\\n16 2 26\\n7 2 29\\n15 2 37\\n1 3 32\\n12 3 27\\n20 3 20\\n14 3 15\\n13 3 14\\n19 3 12\\n2 3 11\\n16 2 25\\n7 2 28\\n15 2 36\\n1 3 33\\n12 3 28\\n20 3 21\\n14 3 16\\n13 3 15\\n19 3 13\\n2 3 12\\n16 2 24\\n7 2 27\\n15 2 35\\n1 3 34\\n12 3 29\\n20 3 22\\n14 3 17\\n13 3 16\\n19 3 14\\n2 3 13\\n16 2 23\\n7 2 26\\n15 2 34\\n1 3 35\\n12 3 30\\n20 3 23\\n14 3 18\\n13 3 17\\n19 3 15\\n2 3 14\\n16 2 22\\n7 2 25\\n15 2 33\\n1 3 36\\n12 3 31\\n20 3 24\\n14 3 19\\n13 3 18\\n19 3 16\\n2 3 15\\n16 2 21\\n7 2 24\\n15 2 32\\n1 3 37\\n12 3 32\\n20 3 25\\n14 3 20\\n13 3 19\\n19 3 17\\n2 3 16\\n16 2 20\\n7 2 23\\n15 2 31\\n1 3 38\\n12 3 33\\n20 3 26\\n14 3 21\\n13 3 20\\n19 3 18\\n2 3 17\\n16 2 19\\n7 2 22\\n15 2 30\\n1 3 39\\n12 3 34\\n20 3 27\\n14 3 22\\n13 3 21\\n19 3 19\\n2 3 18\\n12 4 34\\n16 2 18\\n7 2 21\\n15 2 29\\n1 3 40\\n20 3 28\\n14 3 23\\n13 3 22\\n19 3 20\\n2 3 19\\n16 2 17\\n7 2 20\\n15 2 28\\n1 2 40\\n20 3 29\\n14 3 24\\n13 3 23\\n19 3 21\\n2 3 20\\n16 2 16\\n7 2 19\\n15 2 27\\n1 2 39\\n20 3 30\\n14 3 25\\n13 3 24\\n19 3 22\\n2 3 21\\n16 2 15\\n7 2 18\\n15 2 26\\n1 2 38\\n20 3 31\\n14 3 26\\n13 3 25\\n19 3 23\\n2 3 22\\n13 4 25\\n16 2 14\\n7 2 17\\n15 2 25\\n1 2 37\\n20 3 32\\n14 3 27\\n19 3 24\\n2 3 23\\n16 2 13\\n7 2 16\\n15 2 24\\n1 2 36\\n20 3 33\\n14 3 28\\n19 3 25\\n2 3 24\\n16 2 12\\n7 2 15\\n15 2 23\\n1 2 35\\n20 3 34\\n14 3 29\\n19 3 26\\n2 3 25\\n16 2 11\\n7 2 14\\n15 2 22\\n1 2 34\\n20 3 35\\n14 3 30\\n19 3 27\\n2 3 26\\n16 2 10\\n7 2 13\\n15 2 21\\n1 2 33\\n20 3 36\\n14 3 31\\n19 3 28\\n2 3 27\\n20 4 36\\n16 2 9\\n7 2 12\\n15 2 20\\n1 2 32\\n14 3 32\\n19 3 29\\n2 3 28\\n19 4 29\\n16 2 8\\n7 2 11\\n15 2 19\\n1 2 31\\n14 3 33\\n2 3 29\\n16 2 7\\n7 2 10\\n15 2 18\\n1 2 30\\n14 3 34\\n2 3 30\\n16 2 6\\n7 2 9\\n15 2 17\\n1 2 29\\n14 3 35\\n2 3 31\\n7 1 9\\n16 2 5\\n15 2 16\\n1 2 28\\n14 3 36\\n2 3 32\\n16 2 4\\n15 2 15\\n1 2 27\\n14 3 37\\n2 3 33\\n16 2 3\\n15 2 14\\n1 2 26\\n14 3 38\\n2 3 34\\n16 2 2\\n15 2 13\\n1 2 25\\n14 3 39\\n2 3 35\\n16 2 1\\n15 2 12\\n1 2 24\\n14 3 40\\n2 3 36\\n15 2 11\\n1 2 23\\n14 2 40\\n2 3 37\\n16 3 1\\n15 2 10\\n1 2 22\\n14 2 39\\n2 3 38\\n16 3 2\\n16 4 2\\n15 2 9\\n1 2 21\\n14 2 38\\n2 3 39\\n15 2 8\\n1 2 20\\n14 2 37\\n2 3 40\\n1 1 20\\n15 2 7\\n14 2 36\\n2 2 40\\n14 1 36\\n15 2 6\\n2 2 39\\n15 2 5\\n2 2 38\\n15 2 4\\n2 2 37\\n2 1 37\\n15 2 3\\n15 2 2\\n15 2 1\\n15 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10 20\\n18 9 4 5 12 20 16 1 18 20\\n11 13 16 6 18 5 20 17 4 1\\n12 5 15 28 8 10 2 19 1 7\\n6 9 13 2 7 19 10 3 8 17\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '15 30\\n20 24 17 13 26 4 5 6 27 14 18 22 25 2 15\\n4 12 6 25 4 5 28 11 15 21 9 26 7 17 13\\n19 20 24 16 2 23 1 29 22 30 1 27 10 14 18\\n9 54 3 7 12 28 10 16 23 19 15 1 30 11 2\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '7 14\\n2 2 1 14 9 8 5\\n1 6 7 1 6 3 3\\n8 13 9 8 5 4 11\\n10 6 4 3 12 7 14\\n', 'output': '-1'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78605","program":"```python\nn, k = list(map(int, input().split()))\ntable = []\nfor row in range(4):\n table.append(list(map(int, input().split())))\n\nmoves = []\n\ndef make_move(start,finish):\n moves.append((table[start[0]][start[1]], finish[0]+1, finish[1]+1))\n table[finish[0]][finish[1]] = table[start[0]][start[1]]\n table[start[0]][start[1]] = 0\n\n\ndef move_all_to_places():\n for pos in range(n):\n if (table[1][pos] == table[0][pos]) and table[1][pos]:\n make_move((1,pos), (0,pos))\n if (table[2][pos] == table[3][pos]) and table[2][pos]:\n make_move((2,pos), (3,pos))\n\nmove_all_to_places()\n\n\n\nfound = False\nfor pos in range(n):\n if table[1][pos] == 0:\n found = True\n break\n if table[2][pos] == 0:\n found = True\n break\n\nif not found:\n print(-1)\n exit()\n\nfor cnt in range(20000):\n if (table[1][0] != 0) and (table[2][0] == 0) :\n make_move((1,0), (2,0)) # moved down\n if n == 1:\n continue\n for pos in range(1,n):\n if (table[1][pos-1] == 0) and (table[1][pos] != 0):\n make_move((1,pos), (1, pos-1))\n move_all_to_places()\n\n if (table[1][n-1] == 0) and (table[2][n-1] != 0) :\n make_move((2,n-1), (1,n-1)) # moved up\n for pos in range(n-2,-1, -1):\n if (table[2][pos+1] == 0) and (table[2][pos] != 0):\n make_move((2,pos), (2, pos+1))\n move_all_to_places()\n\nif len(moves) > 20000:\n print(-1)\n exit()\n\nprint(len(moves))\nfor m in moves:\n print(*m)\n\n```","inputs":"1 2\n1\n1\n2\n2\n","output":"2\n1 1 1\n2 4 1\n","actual_output":"2\n1 1 1\n2 4 1\n","execution_success":true,"sample_index":12531},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02649 Tokio Marine & Nichido Fire Insurance Programming Contest 2020 - O(rand)","prompt":"Solve the following coding problem using the programming language python:\n\nGiven are N pairwise distinct non-negative integers A_1,A_2,\\ldots,A_N. Find the number of ways to choose a set of between 1 and K numbers (inclusive) from the given numbers so that the following two conditions are satisfied:\n\n* The bitwise AND of the chosen numbers is S.\n* The bitwise OR of the chosen numbers is T.\n\nConstraints\n\n* 1 \\leq N \\leq 50\n* 1 \\leq K \\leq N\n* 0 \\leq A_i < 2^{18}\n* 0 \\leq S < 2^{18}\n* 0 \\leq T < 2^{18}\n* A_i \\neq A_j (1 \\leq i < j \\leq N)\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN K S T\nA_1 A_2 ... A_N\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n3 3 0 3\n1 2 3\n\n\nOutput\n\n2\n\n\nInput\n\n5 3 1 7\n3 4 9 1 5\n\n\nOutput\n\n2\n\n\nInput\n\n5 4 0 15\n3 4 9 1 5\n\n\nOutput\n\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef popcount(x):\n x = x - ((x >> 1) & 0x55555555)\n x = (x & 0x33333333) + ((x >> 2) & 0x33333333)\n x = (x + (x >> 4)) & 0x0f0f0f0f\n x = x + (x >> 8)\n x = x + (x >> 16)\n return x & 0x0000007f\n\ncmb=[[0 for i in range(51)] for j in range(51)]\ncmb[0][0]=1\nfor i in range(51):\n for j in range(51):\n if i!=50:\n cmb[i+1][j]+=cmb[i][j]\n if j!=50 and i!=50:\n cmb[i+1][j+1]+=cmb[i][j]\n\n\nfor i in range(1,51):\n for j in range(2,51):\n cmb[i][j]+=cmb[i][j-1]\n\nimport random\nN,K,T,S=map(int,input().split())\na=list(map(int,input().split()))\n\nmust0=[i for i in range(18) if S>>i &1==0]\nmust1=[i for i in range(18) if T>>i &1==1]\n\nA=[]\nfor val in a:\n check=True\n for j in must0:\n check=check&(val>>j &1==0)\n for j in must1:\n check=check&(val>>j &1==1)\n if check:\n A.append(val)\n\nif not A:\n print(0)\n exit()\n\nbit=[]\nfor i in range(18):\n if i not in must0 and i not in must1:\n bit.append(i)\n\nfor i in range(len(A)):\n temp=0\n for j in range(len(bit)):\n temp+=(A[i]>>bit[j] &1==1)*2**j\n A[i]=temp\n\nans=0\nn=len(bit)\ndata=[0]*(2**n)\npc=[popcount(i) for i in range(2**n)]\nfor i in range(2**n):\n for a in A:\n data[a&i]+=1\n for a in A:\n if data[a&i]:\n ans+=cmb[data[a&i]][min(K,data[a&i])]*(-1)**pc[i]\n data[a&i]=0\n\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 3 0 3\\n1 2 3', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5 3 1 7\\n3 4 9 1 5', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5 4 0 15\\n3 4 9 1 5', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3 3 0 3\\n0 2 3', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5 4 0 15\\n3 6 9 1 5', 'output': '7'}, {'type': 'stdin_stdout', 'input': '3 3 0 6\\n0 2 3', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 4 1 15\\n3 11 1 0 5', 'output': '4'}, {'type': 'stdin_stdout', 'input': '5 3 1 7\\n3 4 9 0 5', 'output': '1'}, {'type': 'stdin_stdout', 'input': '5 4 0 15\\n3 4 9 1 1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5 4 0 15\\n3 6 1 1 8', 'output': '6'}, {'type': 'stdin_stdout', 'input': '5 5 1 7\\n3 4 9 1 5', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5 5 1 7\\n3 4 11 1 5', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5 4 1 15\\n3 6 9 1 5', 'output': '2'}, {'type': 'stdin_stdout', 'input': '3 3 -1 6\\n0 2 3', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 2 7\\n3 4 11 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 4 1 15\\n3 6 1 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 3 -1 7\\n0 2 3', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 2 7\\n1 4 11 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 4 1 15\\n3 11 1 1 5', 'output': '7'}, {'type': 'stdin_stdout', 'input': '3 3 -1 7\\n0 2 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 2 7\\n1 4 22 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 3 -1 5\\n0 2 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 2 7\\n1 4 37 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 4 1 15\\n3 11 1 0 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 3 -1 5\\n0 0 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 2 9\\n1 4 37 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 3 -1 5\\n0 0 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 2 9\\n2 4 37 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 3 -2 5\\n0 0 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 3 9\\n2 4 37 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 3 -2 5\\n0 0 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 1 3 9\\n2 4 37 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 4 -2 5\\n0 0 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 1 3 9\\n2 4 37 1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 4 -2 5\\n0 -1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 1 6 9\\n2 4 37 1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 4 0 5\\n0 -1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '7 1 6 9\\n2 4 37 1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '12 4 0 5\\n0 -1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '7 1 6 9\\n2 4 37 1 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '12 4 0 2\\n0 -1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '7 1 6 9\\n2 4 32 1 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '9 4 0 2\\n0 -1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '7 1 6 9\\n1 4 32 1 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '14 4 0 2\\n0 -1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '7 1 6 9\\n1 4 32 0 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '14 4 0 2\\n0 0 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '14 4 0 2\\n1 0 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '14 4 0 2\\n1 0 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '14 4 1 2\\n1 0 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '14 8 1 2\\n1 0 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '14 8 1 2\\n1 -1 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '15 8 1 2\\n1 -1 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '15 8 1 2\\n1 -1 -1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '15 5 1 2\\n1 -1 -1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '15 5 0 2\\n1 -1 -1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '15 5 0 4\\n1 -1 -1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '15 10 0 4\\n1 -1 -1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '15 10 0 4\\n1 -1 -2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '15 10 1 4\\n1 -1 -2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '15 10 2 4\\n1 -1 -2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '15 10 1 4\\n1 -2 -2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '10 10 1 4\\n1 -2 -2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 10 1 4\\n1 -2 -2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 10 2 4\\n1 -2 -2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 10 2 4\\n1 -2 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 10 3 4\\n1 -2 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 10 3 2\\n1 -2 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 10 3 2\\n0 -2 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 10 3 2\\n0 -2 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 10 3 2\\n0 -2 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 10 3 4\\n0 -2 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 10 3 4\\n1 -2 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 10 1 4\\n1 -2 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 10 0 4\\n1 -2 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 10 0 2\\n1 -2 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 10 0 2\\n1 0 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 10 0 2\\n1 0 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 4 0 3\\n1 2 3', 'output': '2'}, {'type': 'stdin_stdout', 'input': '3 6 0 3\\n0 2 3', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5 5 1 0\\n3 4 9 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 4 0 15\\n3 6 9 1 7', 'output': '7'}, {'type': 'stdin_stdout', 'input': '0 3 0 6\\n0 2 3', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 1 11\\n3 4 11 1 5', 'output': '2'}, {'type': 'stdin_stdout', 'input': '8 4 1 15\\n3 6 9 1 5', 'output': '2'}, {'type': 'stdin_stdout', 'input': '3 3 -1 6\\n0 0 3', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 2 7\\n3 4 13 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 4 1 15\\n3 6 1 1 8', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 3 -1 4\\n0 2 3', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 2 7\\n1 4 18 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 4 0 15\\n3 11 1 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 3 -1 7\\n0 2 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '9 5 2 7\\n1 4 22 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 4 1 15\\n1 11 1 0 5', 'output': '4'}, {'type': 'stdin_stdout', 'input': '3 3 -1 5\\n0 0 3', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 2 7\\n1 4 37 0 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 4 1 15\\n3 5 1 0 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 3 -2 5\\n0 0 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 5 2 9\\n1 4 37 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 1 -1 5\\n0 0 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 8 2 9\\n2 4 37 1 5', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 3 -2 5\\n1 0 2', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5 5 3 9\\n2 4 59 1 5', 'output': '0'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78649","program":"```python\ndef popcount(x):\n x = x - ((x >> 1) & 0x55555555)\n x = (x & 0x33333333) + ((x >> 2) & 0x33333333)\n x = (x + (x >> 4)) & 0x0f0f0f0f\n x = x + (x >> 8)\n x = x + (x >> 16)\n return x & 0x0000007f\n\ncmb=[[0 for i in range(51)] for j in range(51)]\ncmb[0][0]=1\nfor i in range(51):\n for j in range(51):\n if i!=50:\n cmb[i+1][j]+=cmb[i][j]\n if j!=50 and i!=50:\n cmb[i+1][j+1]+=cmb[i][j]\n\n\nfor i in range(1,51):\n for j in range(2,51):\n cmb[i][j]+=cmb[i][j-1]\n\nimport random\nN,K,T,S=map(int,input().split())\na=list(map(int,input().split()))\n\nmust0=[i for i in range(18) if S>>i &1==0]\nmust1=[i for i in range(18) if T>>i &1==1]\n\nA=[]\nfor val in a:\n check=True\n for j in must0:\n check=check&(val>>j &1==0)\n for j in must1:\n check=check&(val>>j &1==1)\n if check:\n A.append(val)\n\nif not A:\n print(0)\n exit()\n\nbit=[]\nfor i in range(18):\n if i not in must0 and i not in must1:\n bit.append(i)\n\nfor i in range(len(A)):\n temp=0\n for j in range(len(bit)):\n temp+=(A[i]>>bit[j] &1==1)*2**j\n A[i]=temp\n\nans=0\nn=len(bit)\ndata=[0]*(2**n)\npc=[popcount(i) for i in range(2**n)]\nfor i in range(2**n):\n for a in A:\n data[a&i]+=1\n for a in A:\n if data[a&i]:\n ans+=cmb[data[a&i]][min(K,data[a&i])]*(-1)**pc[i]\n data[a&i]=0\n\nprint(ans)\n```","inputs":"3 3 0 3\n1 2 3","output":"2","actual_output":"2\n","execution_success":true,"sample_index":12532},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02778 AtCoder Beginner Contest 154 - I miss you...","prompt":"Solve the following coding problem using the programming language python:\n\nGiven is a string S. Replace every character in S with `x` and print the result.\n\nConstraints\n\n* S is a string consisting of lowercase English letters.\n* The length of S is between 1 and 100 (inclusive).\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nS\n\n\nOutput\n\nReplace every character in S with `x` and print the result.\n\nExamples\n\nInput\n\nsardine\n\n\nOutput\n\nxxxxxxx\n\n\nInput\n\nxxxx\n\n\nOutput\n\nxxxx\n\n\nInput\n\ngone\n\n\nOutput\n\nxxxx\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ns = input()\n\nprint('x' * (len(s)))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'sardine', 'output': 'xxxxxxx'}, {'type': 'stdin_stdout', 'input': 'xxxx', 'output': 'xxxx'}, {'type': 'stdin_stdout', 'input': 'gone', 'output': 'xxxx'}, {'type': 'stdin_stdout', 'input': 'sardnie', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'xxwx', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'gpne', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'sardnif', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'wxwx', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'gpnd', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'findras', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'wwxx', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'gpnc', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'findrbs', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'xxww', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'fpnc', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'frndibs', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'wwyx', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'cnpf', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'frndics', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'wwzx', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'dnpf', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'fqndics', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'wvzx', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'dnpg', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'fqneics', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'xzvw', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'dmpg', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'fqndids', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'xzuw', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'dmqg', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'fqncids', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'yzuw', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'qmdg', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'sdicnqf', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'xztw', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'gdmq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'sdhcnqf', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'xwtz', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'dgmq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'sdhcoqf', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'xwt{', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'dfmq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'sdhcorf', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'xwt|', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'qmfd', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'frochds', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'xw|t', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'rmfd', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'crofhds', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 't|wx', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'rmed', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'crohfds', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 't|vx', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'rled', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'chorfds', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'u|vx', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'rlec', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'dhorfds', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'u|vw', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'qlec', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'dgorfds', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'u|uw', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'qlfc', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'dgorfdr', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'uu|w', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'celq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'rdfrogd', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': '|uuw', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'cflq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'rdfroge', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': '|wuu', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'cleq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'egorfdr', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': '}uuw', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'bleq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'egorfer', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'wuu}', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'qelb', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'egoqfer', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'uuw}', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'qemb', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'refqoge', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': '}wuu', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'qflb', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'refpoge', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'uuw|', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'blfq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'refpogf', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': '{wuu', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'flbq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'fgopfer', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': '{wtu', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'flcq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'ggopfer', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': '{wsu', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'qlcf', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'gropfeg', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'zwsu', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'fclq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'fropfeg', 'output': 'xxxxxxx\\n'}, {'type': 'stdin_stdout', 'input': 'zwsv', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'fckq', 'output': 'xxxx\\n'}, {'type': 'stdin_stdout', 'input': 'orfpfeg', 'output': 'xxxxxxx\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78653","program":"```python\ns = input()\n\nprint('x' * (len(s)))\n```","inputs":"sardine","output":"xxxxxxx","actual_output":"xxxxxxx\n","execution_success":true,"sample_index":12533},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02913 AtCoder Beginner Contest 141 - Who Says a Pun?","prompt":"Solve the following coding problem using the programming language python:\n\nGiven is a string S of length N.\n\nFind the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping.\n\nMore formally, find the maximum positive integer len such that there exist integers l_1 and l_2 ( 1 \\leq l_1, l_2 \\leq N - len + 1 ) that satisfy the following:\n\n* l_1 + len \\leq l_2\n\n* S[l_1+i] = S[l_2+i] (i = 0, 1, ..., len - 1)\n\n\n\n\nIf there is no such integer len, print 0.\n\nConstraints\n\n* 2 \\leq N \\leq 5 \\times 10^3\n* |S| = N\n* S consists of lowercase English letters.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nS\n\n\nOutput\n\nPrint the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping. If there is no such non-empty string, print 0 instead.\n\nExamples\n\nInput\n\n5\nababa\n\n\nOutput\n\n2\n\n\nInput\n\n2\nxy\n\n\nOutput\n\n0\n\n\nInput\n\n13\nstrangeorange\n\n\nOutput\n\n5\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\ns = input()\n\nl1 = l2 = length = 0\n\nwhile l2 + length < n:\n if s[l1 : l2] in s[l2:]:\n length = l2 - l1\n l2 += 1\n else:\n l1 += 1\n l2 = l1 + length + 1\n\nprint(length)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '13\\nstrangeorange', 'output': '5'}, {'type': 'stdin_stdout', 'input': '2\\nxy', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\nababa', 'output': '2'}, {'type': 'stdin_stdout', 'input': '13\\nstrangeoranfe', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\nwy', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n`baba', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5\\nabac`', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nefnaroegnarts', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\nvy', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\nabab`', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '13\\nefnarotgnares', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\nyx', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '13\\nserangtoranfe', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\nxz', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n`caba', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nseraogtoranfe', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\nzx', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n`cabb', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nseraoguoranfe', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\nx{', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\nac`bb', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nseraoguoqanfe', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\nzy', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\nbb`ca', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nsenaoguoqarfe', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\nyz', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\nbc`ba', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nsenaogunqarfe', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\nzz', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5\\nab`cb', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nsenaogunparfe', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\ny{', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\nabacb', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nsenaofunparfe', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n{x', 'output': '0\\n'}, {'type': 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'0\\n'}, {'type': 'stdin_stdout', 'input': '13\\nfqqapovdoaoff', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\ny\\x81', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n``\\\\_b', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nfqqapovdfaoof', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\x81y', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\nb_\\\\``', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nfqqopavdfaoof', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\x80y', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\nb`\\\\``', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\nfqqopavcfaoof', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78657","program":"```python\nn = int(input())\ns = input()\n\nl1 = l2 = length = 0\n\nwhile l2 + length < n:\n if s[l1 : l2] in s[l2:]:\n length = l2 - l1\n l2 += 1\n else:\n l1 += 1\n l2 = l1 + length + 1\n\nprint(length)\n```","inputs":"13\nstrangeorange","output":"5","actual_output":"5\n","execution_success":true,"sample_index":12534},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03049 diverta 2019 Programming Contest - AB Substrings","prompt":"Solve the following coding problem using the programming language python:\n\nSnuke has N strings. The i-th string is s_i.\n\nLet us concatenate these strings into one string after arranging them in some order. Find the maximum possible number of occurrences of `AB` in the resulting string.\n\nConstraints\n\n* 1 \\leq N \\leq 10^{4}\n* 2 \\leq |s_i| \\leq 10\n* s_i consists of uppercase English letters.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\ns_1\n\\vdots\ns_N\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n3\nABCA\nXBAZ\nBAD\n\n\nOutput\n\n2\n\n\nInput\n\n9\nBEWPVCRWH\nZZNQYIJX\nBAVREA\nPA\nHJMYITEOX\nBCJHMRMNK\nBP\nQVFABZ\nPRGKSPUNA\n\n\nOutput\n\n4\n\n\nInput\n\n7\nRABYBBE\nJOZ\nBMHQUVA\nBPA\nISU\nMCMABAOBHZ\nSZMEHMA\n\n\nOutput\n\n4\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport re\nn = int(input())\na = 0\nb = 0\nab = 0\ncnt = 0\nfor i in range(n):\n s = input()\n\n tmp = re.findall(r'AB',s)\n ab += len(tmp)\n\n if s[0] == \"B\":\n b += 1\n if s[-1] == \"A\":\n a += 1\n if s[0] == \"B\" and s[-1] == \"A\":\n cnt += 1 \nif a == b and a == cnt and a > 0:\n print(a-1+ab)\nelse:\n print(min(a,b)+ab)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '9\\nBEWPVCRWH\\nZZNQYIJX\\nBAVREA\\nPA\\nHJMYITEOX\\nBCJHMRMNK\\nBP\\nQVFABZ\\nPRGKSPUNA', 'output': '4'}, {'type': 'stdin_stdout', 'input': '7\\nRABYBBE\\nJOZ\\nBMHQUVA\\nBPA\\nISU\\nMCMABAOBHZ\\nSZMEHMA', 'output': '4'}, {'type': 'stdin_stdout', 'input': '3\\nABCA\\nXBAZ\\nBAD', 'output': '2'}, {'type': 'stdin_stdout', 'input': '9\\nBEWPVCRWH\\nZQNZYIJX\\nBAVREA\\nPA\\nHJMYITEOX\\nBCJHMRMNK\\nBP\\nQVFABZ\\nPRGKSPUNA', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '7\\nEBBYBAR\\nJOZ\\nBMHQUVA\\nBPA\\nISU\\nMCMABAOBHZ\\nSZMEHMA', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\nABCA\\nXBAZ\\nBAE', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\nACBA\\nZABX\\nAEB', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n@DBA\\nZAAX\\nAEB', 'output': '0\\n'}, {'type': 'stdin_stdout', 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'9\\nBEWPVCRWH\\nZQOZYIJX\\nAVRAEB\\n@R\\nTDMJIHYOX\\nINMLRHKCA\\nAO\\nZCAVGQ\\nPRGKSPUNA', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78661","program":"```python\nimport re\nn = int(input())\na = 0\nb = 0\nab = 0\ncnt = 0\nfor i in range(n):\n s = input()\n\n tmp = re.findall(r'AB',s)\n ab += len(tmp)\n\n if s[0] == \"B\":\n b += 1\n if s[-1] == \"A\":\n a += 1\n if s[0] == \"B\" and s[-1] == \"A\":\n cnt += 1 \nif a == b and a == cnt and a > 0:\n print(a-1+ab)\nelse:\n print(min(a,b)+ab)\n```","inputs":"9\nBEWPVCRWH\nZZNQYIJX\nBAVREA\nPA\nHJMYITEOX\nBCJHMRMNK\nBP\nQVFABZ\nPRGKSPUNA","output":"4","actual_output":"4\n","execution_success":true,"sample_index":12535},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03337 AtCoder Beginner Contest 098 - Add Sub Mul","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given two integers A and B. Find the largest value among A+B, A-B and A \\times B.\n\nConstraints\n\n* -1000 \\leq A,B \\leq 1000\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nA B\n\n\nOutput\n\nPrint the largest value among A+B, A-B and A \\times B.\n\nExamples\n\nInput\n\n3 1\n\n\nOutput\n\n4\n\n\nInput\n\n4 -2\n\n\nOutput\n\n6\n\n\nInput\n\n0 0\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nA, B = map(int, input().split())\nM = max(A+B,A-B,A*B)\nprint(M)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '0 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 1', 'output': '4'}, {'type': 'stdin_stdout', 'input': '4 -2', 'output': '6'}, {'type': 'stdin_stdout', 'input': '0 -1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 1', 'output': '7\\n'}, {'type': 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{'type': 'stdin_stdout', 'input': '-115 1', 'output': '-114\\n'}, {'type': 'stdin_stdout', 'input': '5 15', 'output': '75\\n'}, {'type': 'stdin_stdout', 'input': '-42 1', 'output': '-41\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_78669","program":"```python\nA, B = map(int, input().split())\nM = max(A+B,A-B,A*B)\nprint(M)\n```","inputs":"0 0","output":"0","actual_output":"0\n","execution_success":true,"sample_index":12536},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03499 AtCoder Regular Contest 086 - Smuggling Marbles","prompt":"Solve the following coding problem using the programming language python:\n\nSnuke has a rooted tree with N+1 vertices. The vertices are numbered 0 through N, and Vertex 0 is the root of the tree. The parent of Vertex i (1 \\leq i \\leq N) is Vertex p_i.\n\nBesides this tree, Snuke also has an box which is initially empty and many marbles, and playing with them. The play begins with placing one marble on some of the vertices, then proceeds as follows:\n\n1. If there is a marble on Vertex 0, move the marble into the box.\n2. Move each marble from the vertex to its parent (all at once).\n3. For each vertex occupied by two or more marbles, remove all the marbles from the vertex.\n4. If there exists a vertex with some marbles, go to Step 1. Otherwise, end the play.\n\n\n\nThere are 2^{N+1} ways to place marbles on some of the vertices. For each of them, find the number of marbles that will be in the box at the end of the play, and compute the sum of all those numbers modulo 1,000,000,007.\n\nConstraints\n\n* 1 \\leq N < 2 \\times 10^{5}\n* 0 \\leq p_i < i\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\np_1 p_2 ... p_{N}\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n2\n0 0\n\n\nOutput\n\n8\n\n\nInput\n\n5\n0 1 1 0 4\n\n\nOutput\n\n96\n\n\nInput\n\n31\n0 1 0 2 4 0 4 1 6 4 3 9 7 3 7 2 15 6 12 10 12 16 5 3 20 1 25 20 23 24 23\n\n\nOutput\n\n730395550\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, = map(int, input().split())\np = [-1] + [*map(int, input().split())]\n\nMOD = 10**9+7\ndp = [[] for _ in range(n+1)]\ndep = [0]*(n+1)\nnxt = [0]*(n+1)\n\nfor v in range(n,0,-1):\n _,nxt[p[v]],dep[p[v]] = sorted([nxt[p[v]],dep[p[v]],dep[v]+1])\n\ntot = [0]*(dep[0]+1)\nfor i in range(n+1): tot[dep[i]] += 1\n\ndef merge(p,v):\n if len(dp[p]) < len(dp[v]):\n dp[p],dp[v]=dp[v],dp[p]\n for i in range(-len(dp[v]),0):\n a,b,c = dp[p][i]\n d,e,f = dp[v][i]\n dp[p][i][:] = [a*d%MOD,(b*d+a*e)%MOD,c*f%MOD]\n\nfor v in range(n,-1,-1):\n dp[v].append([1,1,2])\n for i in range(-nxt[v]-1,0):\n dp[v][i][0] = dp[v][i][2] - dp[v][i][1]\n if v: merge(p[v],v)\n\nans = 0\nfor d in dp[0]:\n ans += pow(d[2],MOD-2,MOD)*d[1]%MOD\nprint(ans*pow(2,n+1,MOD)%MOD)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n0 0', 'output': '8'}, {'type': 'stdin_stdout', 'input': '31\\n0 1 0 2 4 0 4 1 6 4 3 9 7 3 7 2 15 6 12 10 12 16 5 3 20 1 25 20 23 24 23', 'output': '730395550'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 1 0 4', 'output': '96'}, {'type': 'stdin_stdout', 'input': '2\\n0 1', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '31\\n0 1 0 2 4 0 4 1 6 4 3 9 7 3 7 3 15 6 12 10 12 16 5 3 20 1 25 20 23 24 23', 'output': 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'input': '31\\n0 0 0 2 4 0 4 1 3 4 3 9 7 3 7 2 6 0 1 10 3 16 5 3 20 1 2 20 23 24 15', 'output': '875488705\\n'}, {'type': 'stdin_stdout', 'input': '31\\n0 1 1 2 4 0 4 0 6 1 3 9 8 3 7 3 13 6 12 18 12 7 5 6 4 1 12 8 23 22 23', 'output': '623099301\\n'}, {'type': 'stdin_stdout', 'input': '31\\n0 0 1 2 4 0 1 0 6 4 3 8 8 3 8 3 15 4 12 10 12 7 5 3 20 1 25 20 26 24 23', 'output': '801015724\\n'}, {'type': 'stdin_stdout', 'input': '31\\n0 0 0 2 4 0 4 0 6 4 3 9 7 3 7 2 6 0 1 10 3 21 5 3 20 1 25 20 23 24 15', 'output': '5853619\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 536870912}","problem_id":"vfc_78673","program":"```python\nn, = map(int, input().split())\np = [-1] + [*map(int, input().split())]\n\nMOD = 10**9+7\ndp = [[] for _ in range(n+1)]\ndep = [0]*(n+1)\nnxt = [0]*(n+1)\n\nfor v in range(n,0,-1):\n _,nxt[p[v]],dep[p[v]] = sorted([nxt[p[v]],dep[p[v]],dep[v]+1])\n\ntot = [0]*(dep[0]+1)\nfor i in range(n+1): tot[dep[i]] += 1\n\ndef merge(p,v):\n if len(dp[p]) < len(dp[v]):\n dp[p],dp[v]=dp[v],dp[p]\n for i in range(-len(dp[v]),0):\n a,b,c = dp[p][i]\n d,e,f = dp[v][i]\n dp[p][i][:] = [a*d%MOD,(b*d+a*e)%MOD,c*f%MOD]\n\nfor v in range(n,-1,-1):\n dp[v].append([1,1,2])\n for i in range(-nxt[v]-1,0):\n dp[v][i][0] = dp[v][i][2] - dp[v][i][1]\n if v: merge(p[v],v)\n\nans = 0\nfor d in dp[0]:\n ans += pow(d[2],MOD-2,MOD)*d[1]%MOD\nprint(ans*pow(2,n+1,MOD)%MOD)\n```","inputs":"2\n0 0","output":"8","actual_output":"8\n","execution_success":true,"sample_index":12537},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03658 AtCoder Beginner Contest 067 - Snake Toy","prompt":"Solve the following coding problem using the programming language python:\n\nSnuke has N sticks. The length of the i-th stick is l_i.\n\nSnuke is making a snake toy by joining K of the sticks together.\n\nThe length of the toy is represented by the sum of the individual sticks that compose it. Find the maximum possible length of the toy.\n\nConstraints\n\n* 1 \\leq K \\leq N \\leq 50\n* 1 \\leq l_i \\leq 50\n* l_i is an integer.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN K\nl_1 l_2 l_3 ... l_{N}\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n5 3\n1 2 3 4 5\n\n\nOutput\n\n12\n\n\nInput\n\n15 14\n50 26 27 21 41 7 42 35 7 5 5 36 39 1 45\n\n\nOutput\n\n386\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN,K=map(int,input().split(' '))\nprint(sum(sorted(list(map(int,input().split(' '))))[::-1][:K]))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '15 14\\n50 26 27 21 41 7 42 35 7 5 5 36 39 1 45', 'output': '386'}, {'type': 'stdin_stdout', 'input': '5 3\\n1 2 3 4 5', 'output': '12'}, {'type': 'stdin_stdout', 'input': '15 14\\n49 26 27 21 41 7 42 35 7 5 5 36 39 1 45', 'output': 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53 0 21 8 18 2 49 7 5 8 7 46 0 0', 'output': '230\\n'}, {'type': 'stdin_stdout', 'input': '15 15\\n6 7 0 21 25 18 2 49 7 5 8 7 46 0 0', 'output': '201\\n'}, {'type': 'stdin_stdout', 'input': '15 15\\n6 51 0 21 25 18 0 49 7 5 6 7 46 0 0', 'output': '241\\n'}, {'type': 'stdin_stdout', 'input': '15 15\\n6 37 0 21 25 18 0 12 7 5 8 7 46 0 0', 'output': '192\\n'}, {'type': 'stdin_stdout', 'input': '15 15\\n6 51 0 37 25 18 0 12 7 5 8 7 43 0 0', 'output': '219\\n'}, {'type': 'stdin_stdout', 'input': '15 15\\n6 51 0 37 25 18 0 12 7 5 8 3 26 0 0', 'output': '198\\n'}, {'type': 'stdin_stdout', 'input': '2 15\\n6 51 0 37 25 18 0 11 7 5 14 7 26 0 0', 'output': '207\\n'}, {'type': 'stdin_stdout', 'input': '2 15\\n6 90 0 37 27 18 0 12 7 5 14 7 26 2 0', 'output': '251\\n'}, {'type': 'stdin_stdout', 'input': '2 15\\n6 108 1 37 25 18 0 12 7 5 8 7 26 2 0', 'output': '262\\n'}, {'type': 'stdin_stdout', 'input': '2 15\\n3 108 0 37 25 18 0 12 3 5 16 0 26 2 0', 'output': '255\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_78677","program":"```python\nN,K=map(int,input().split(' '))\nprint(sum(sorted(list(map(int,input().split(' '))))[::-1][:K]))\n```","inputs":"15 14\n50 26 27 21 41 7 42 35 7 5 5 36 39 1 45","output":"386","actual_output":"386\n","execution_success":true,"sample_index":12538},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03814 AtCoder Beginner Contest 053 - A to Z String","prompt":"Solve the following coding problem using the programming language python:\n\nSnuke has decided to construct a string that starts with `A` and ends with `Z`, by taking out a substring of a string s (that is, a consecutive part of s).\n\nFind the greatest length of the string Snuke can construct. Here, the test set guarantees that there always exists a substring of s that starts with `A` and ends with `Z`.\n\nConstraints\n\n* 1 \u2266 |s| \u2266 200{,}000\n* s consists of uppercase English letters.\n* There exists a substring of s that starts with `A` and ends with `Z`.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\ns\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\nQWERTYASDFZXCV\n\n\nOutput\n\n5\n\n\nInput\n\nZABCZ\n\n\nOutput\n\n4\n\n\nInput\n\nHASFJGHOGAKZZFEGA\n\n\nOutput\n\n12\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN = input()\na = N.find(\"A\")\nz = N.rfind(\"Z\")\nprint(z - a + 1)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'HASFJGHOGAKZZFEGA', 'output': '12'}, {'type': 'stdin_stdout', 'input': 'ZABCZ', 'output': '4'}, {'type': 'stdin_stdout', 'input': 'QWERTYASDFZXCV', 'output': '5'}, {'type': 'stdin_stdout', 'input': 'HASFJGHOGAK[ZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'ZAACZ', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'AGEFZKKAGOHH[FSAH', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'IBAG[IHNGFKKZSFGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'ZCAAZ', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'QWERTAFSDXZXCV', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': 'ZCAZB', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'AIEFZGKAFOFGJZSAH', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': 'I@SCIGHEA[KFGOKZA', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': 'ICAF[IHNGFKZKSFGB', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': 'QWARTEFSDXZXCV', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': 'AGEFZJG@GNHHZFSAK', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': 'HASFEHFNGAJK[FGZA', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': 'HASGZIIZGAKKOFEGA', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': 'HASF[GHOGAKJZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASF[HHOGAKJZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASF[HHOGAKKZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'AGEFZKKAGOHI[FSAH', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'HASF[IHOGAKKZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASG[IHOGAKKZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASG[IHOGAKKZFEGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IASG[IHOGAKKZFEGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IASG[IHOGFKKZAEGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IASG[IHOGFKKZAFGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IAAG[IHOGFKKZSFGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IAAG[IHNGFKKZSFGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'ICAG[IHNGFKKZSFGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'ICAF[IHNGFKKZSFGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'SCAG[IHNGFKKZIFGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'SCAG[IHNGFKKZIEGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'SCAG[IHNGFKJZIEGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'SCAG[IHNGGKJZIEGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'HASHJGFOGAKZZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'QWERTXASDFZXCV', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'HASFJGGOGAK[ZFEHA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASH[GFOGAKJZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASF[HHNGAKJZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASF[HHOGAKKZFDGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASF[GHOIAKKZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HARF[IHOGAKKZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASG[IHOGAKJZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASG[OHIGAKKZFEGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IASG[IHOGFKGZAEKB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IASG[IHOGFKFZAKGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IAAG[IHOGFKJZSFGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IAAG[IHNHFKKZSFGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IBAH[IHNGFKKZSFGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'ICAF[IFNGFKKZSHGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'TCAG[IHNGFKKZIFGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'SCAG[IHNGFKJZHEGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'SCAG[IHNGGKJZJEGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'HASHJGFOGAKZZFEHA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'QWERTFASDXZXCV', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'HASFJGGOGAK[ZFEIA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'ZCABZ', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'HASF[HHNG@KJZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'AGDFZKKAGOHH[FSAH', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'HASE[GHOIAKKZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HARF[IHPGAKKZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASG\\\\IHOGAKJZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HBSG[OHIGAKKZFEGB', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'IASG[IHPGFKGZAEKB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IFSG[IHOGAKFZAKGB', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'IAAG[IHOHFKKZSFGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IBAH[GHNGFKKZSFIB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'TCAG[IHNGFGKZIFKB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'SEAG[IHNGFKJZHCGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'TCAG[IHNGGKJZJEGB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'HASHJGFOGAKZZFEIA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASGJGGOGAK[ZFEIA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'GASF[HHNG@KJZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'AGDFZKK@GOHH[FSAH', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'HASD[GHOIAKKZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IARF[IHPGAKKZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASF\\\\IHOGAKJZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'BKEAZGKFGPHI[GSAI', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'BGKAZFKAGOHI[GSFI', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'IAAG[HHOGFKKZSFGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'IBAH[GHNGFKKZSFIA', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'TCAG[IHNGFHKZIFKB', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'HASGJGFOGAKZZFEIA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'RWERTAFSDXZXCV', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': 'HBSGJGGOGAK[ZFEIA', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'BZACZ', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'AGEFZJK@GNHH[FSAG', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'AGDFZKK?GOHH[FSAH', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'AGEFZKKAIOHG[DSAH', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'IARF[IHPGAKKZFEGB', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'HASF\\\\IHOGBKJZFEGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'BJEAZGKFGPHI[GSAI', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'BGKAZFJAGOHI[GSFI', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'IBAH[GHOGFKKZSFIA', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'TCAG[IHNGFHKZIFKA', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'HASZJGFOGAKGZFEIA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'AIEFZ[KAGOGGJGSBH', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'AGEFZJG@GNHH[FSAK', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'HASF[HHOG?KKZFDGA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'AGKFZKEAIOHG[DSAH', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'HASF\\\\IHOGBKJZFEFA', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': 'BJEAZGKFGPHH[GSAI', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_78681","program":"```python\nN = input()\na = N.find(\"A\")\nz = N.rfind(\"Z\")\nprint(z - a + 1)\n```","inputs":"HASFJGHOGAKZZFEGA","output":"12","actual_output":"12\n","execution_success":true,"sample_index":12539},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00071 Bombs Chain","prompt":"Solve the following coding problem using the programming language python:\n\nThere is a plane like Figure 1 with 8 vertical and 8 horizontal squares. There are several bombs on that plane. Figure 2 shows an example (\u25cf = bomb).\n\n| \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n--- | --- | --- | --- | --- | --- | --- | ---\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n| \u25a1 | \u25a1 | \u25a1 | \u25cf | \u25a1 | \u25a1 | \u25cf | \u25a1\n--- | --- | --- | --- | --- | --- | --- | ---\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25cf | \u25a1 | \u25a1\n\u25cf | \u25a1 | \u25a1 | \u25a1 | \u25cf | \u25a1 | \u25a1 | \u25cf\n\u25a1 | \u25a1 | \u25cf | \u25a1 | \u25a1 | \u25a1 | \u25cf | \u25a1\n\u25a1 | \u25cf | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25cf | \u25a1 | \u25a1 | \u25a1\n\u25cf | \u25a1 | \u25cf | \u25a1 | \u25a1 | \u25a1 | \u25cf | \u25a1\n\u25a1 | \u25cf | \u25a1 | \u25cf | \u25a1 | \u25a1 | \u25cf | \u25a1\nFigure 1 | Figure 2\n\n\n\nWhen a bomb explodes, the blast affects the three squares above, below, left, and right of the bomb, and the bombs placed in those squares also explode in a chain reaction. For example, if the bomb shown in Fig. 3 explodes, the square shown in Fig. 4 will be affected by the blast.\n\n| \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n--- | --- | --- | --- | --- | --- | --- | ---\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25cf | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n| \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n--- | --- | --- | --- | --- | --- | --- | ---\n\u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a0 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a0 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a0 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a0| \u25a0| \u25a0| \u25cf| \u25a0| \u25a0| \u25a0| \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a0 | \u25a1 | \u25a1 | \u25a1 | \u25a1\n\u25a1 | \u25a1 | \u25a1 | \u25a0 | \u25a1 | \u25a1 | \u25a1 | \u25a1\nFigure 3 | Figure 4\n\n\n\nCreate a program that reads the state where the bomb is placed and the position of the bomb that explodes first, and outputs the state of the final plane.\n\n\n\nInput\n\nThe input is given in the following format:\n\n\nn\n(Blank line)\nData set 1\n(Blank line)\nData set 2\n..\n..\nData set n\n\n\nThe first line gives the number of datasets n (n \u2264 20). Then n datasets are given. One blank line is given immediately before each dataset. Each dataset is given in the following format:\n\n\ng1,1g2,1 ... g8,1\ng1,2g2,2 ... g8,2\n::\ng1,8g2,8 ... g8,8\nX\nY\n\n\nThe first eight lines are given eight strings representing the plane. Each string is a sequence of 8 characters, with 1 representing the square with the bomb and 0 representing the square without the bomb. The next two lines give the X and Y coordinates of the first bomb to explode. The coordinates of the upper left, lower left, upper right, and lower right are (1, 1), (1, 8), (8, 1), and (8, 8), respectively. For example, when the bomb shown in Figure 4 explodes for the first time, the coordinates given are (4, 6).\n\nOutput\n\nPlease output as follows for each data set.\n\nLet 1 be the square with the bomb left without exploding, and 0 be the square without the bomb. Make one line of the plane one line consisting of eight numbers, and output the final plane state with a character string of eight lines. The beginning of each dataset must be output from Data x: as in the sample output. Where x is the dataset number.\n\nExample\n\nInput\n\n2\n\n00010010\n00000100\n10001001\n00100010\n01000000\n00001000\n10100010\n01010010\n2\n5\n\n00010010\n00000100\n10001001\n00100010\n01000000\n00001000\n10100010\n01010010\n2\n5\n\n\nOutput\n\nData 1:\n00000000\n00000100\n10001001\n00100000\n00000000\n00001000\n10100000\n00000000\nData 2:\n00000000\n00000100\n10001001\n00100000\n00000000\n00001000\n10100000\n00000000\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef e(x,y):\n A[y][x]='0'\n for d in range(-3,4):\n 0<=x+d<8and'1'==A[y][x+d]and e(x+d,y)\n 0<=y+d<8and'1'==A[y+d][x]and e(x,y+d)\nfor i in range(int(input())):\n print(f'Data {i+1}:');input()\n A=[list(input())for _ in[0]*8]\n e(int(input())-1,int(input())-1)\n for r in A:print(*r,sep='')\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00000000\\n00000100\\n10001001\\n00100000\\n00000000\\n00001000\\n10100000\\n00000000\\nData 2:\\n00000000\\n00000100\\n10001001\\n00100000\\n00000000\\n00001000\\n10100000\\n00000000'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00000000\\n00000100\\n10001001\\n00100000\\n00000000\\n00001000\\n10100000\\n00000000\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n01000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00000000\\n00000100\\n00001001\\n00100000\\n00000000\\n00001000\\n10100000\\n00000000\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n01010110\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000100\\n10001001\\n00100000\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': 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'2\\n\\n00010010\\n00000100\\n00001001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n01010110\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000100\\n10001001\\n00100000\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100000\\n00010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001101\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n00001101\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n11000010\\n00001100\\n10100000\\n00010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n11000010\\n00001100\\n10100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': 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'2\\n\\n00010010\\n00000000\\n00001001\\n00100010\\n00000000\\n00001000\\n10100000\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000000\\n00001001\\n00100010\\n00000000\\n00001000\\n10100000\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00011000\\n10100010\\n01010010\\n2\\n5\\n\\n01010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100000\\n01010110\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00011000\\n10100010\\n01010010\\nData 2:\\n01010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01100010\\n00001000\\n10100000\\n01010110\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000100\\n10001001\\n00000000\\n00000000\\n00001000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n01010010\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000100\\n10001001\\n00100000\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': 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'2\\n\\n00010010\\n00000100\\n00001001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01100010\\n00001000\\n10100000\\n01010110\\n2\\n2', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01100010\\n00001000\\n10100000\\n01010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n00000010\\n00001000\\n10100000\\n01010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000100\\n10001001\\n00100000\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10101000\\n01010010\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000100\\n10001001\\n00100000\\n00000000\\n00001000\\n10101000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100011\\n01000000\\n10001000\\n10100000\\n00010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100011\\n01000000\\n10001000\\n10100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00011101\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000110\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n00011101\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000110\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001011\\n00100010\\n11000010\\n00001100\\n10100000\\n00010100\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n00001001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001011\\n00100010\\n11000010\\n00001100\\n10100000\\n00010100\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n10001001\\n00100010\\n01010000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n01000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n00010010\\n2\\n5', 'output': 'Data 1:\\n00000000\\n00000000\\n10001001\\n00100000\\n00000000\\n00001000\\n10100000\\n00000000\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100010\\n00010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n10010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\n2\\n4\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01010000\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n10010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00100100\\n00001001\\n00100010\\n01000000\\n00001000\\n10100010\\n01010010\\n2\\n7\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00011000\\n10100000\\n01010010\\n2\\n4', 'output': 'Data 1:\\n00010010\\n00100100\\n00001001\\n00100010\\n01000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00011000\\n10100000\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001001\\n00100010\\n00000000\\n00001000\\n10100001\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000000\\n00001001\\n00100010\\n00000000\\n00001000\\n10100001\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n01000100\\n00001001\\n00100000\\n00000000\\n00011000\\n10100010\\n01010010\\n2\\n5\\n\\n01010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100000\\n01010110\\n2\\n5', 'output': 'Data 1:\\n00010010\\n01000100\\n00001001\\n00100000\\n00000000\\n00011000\\n10100010\\n01010010\\nData 2:\\n01010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001000\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01100010\\n00001000\\n10100000\\n01010110\\n2\\n2', 'output': 'Data 1:\\n00010010\\n00000100\\n00001000\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01100010\\n00001000\\n10100000\\n01010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001000\\n00100010\\n00000010\\n00001000\\n10100000\\n01010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000100\\n10001000\\n00100000\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10101000\\n11010010\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000100\\n10000000\\n00000000\\n00000000\\n00000000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00011101\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n10010010\\n00000110\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n00011101\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n10010010\\n00000110\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00101001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001011\\n00100010\\n11000010\\n00001100\\n10100000\\n00010100\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n00101001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001011\\n00100010\\n11000010\\n00001100\\n10100000\\n00010100\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\n2\\n4\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01010000\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00100100\\n00001001\\n00100010\\n01000000\\n00001000\\n10100010\\n01110010\\n2\\n7\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00011000\\n10100000\\n01010010\\n2\\n4', 'output': 'Data 1:\\n00010010\\n00100100\\n00001001\\n00100010\\n01000000\\n00001000\\n10100010\\n01110010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00011000\\n10100000\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001001\\n00100010\\n00000000\\n00001000\\n10100001\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000001\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000000\\n00001001\\n00100010\\n00000000\\n00001000\\n10100001\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000001\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n01000000\\n00001001\\n00100000\\n00000000\\n00011000\\n10100010\\n01010010\\n2\\n5\\n\\n01010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100000\\n01010110\\n2\\n5', 'output': 'Data 1:\\n00010010\\n01000000\\n00001001\\n00100000\\n00000000\\n00011000\\n10100010\\n01010010\\nData 2:\\n01010010\\n00000100\\n10001001\\n00100010\\n00000000\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001000\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00001100\\n10001001\\n00100010\\n01100010\\n00001000\\n10100000\\n01010110\\n2\\n2', 'output': 'Data 1:\\n00010010\\n00000100\\n00001000\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00001100\\n10001001\\n00100010\\n01100010\\n00001000\\n10100000\\n01010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00000100\\n10001000\\n00100010\\n00000010\\n00001000\\n10100000\\n01011110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000100\\n10000000\\n00100000\\n00000000\\n00000000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100010\\n00010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10101000\\n11010010\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100010\\n00010010\\nData 2:\\n00000000\\n00000100\\n10000000\\n00000000\\n00000000\\n00000000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00011101\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n10010010\\n00000111\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n00011101\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n10010010\\n00000111\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n10101001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001011\\n00100010\\n11000010\\n00001100\\n10100000\\n00010100\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n10101001\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001011\\n00100010\\n11000010\\n00001100\\n10100000\\n00010100\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\n2\\n4\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01010000\\n00001000\\n10100000\\n01010010\\n2\\n7', 'output': 'Data 1:\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01010000\\n00001000\\n10100000\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00100100\\n00001001\\n00100010\\n01010000\\n00001000\\n10100010\\n01110010\\n2\\n7\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00011000\\n10100000\\n01010010\\n2\\n4', 'output': 'Data 1:\\n00010010\\n00100100\\n00001001\\n00100010\\n01010000\\n00001000\\n10100010\\n01110010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00011000\\n10100000\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001001\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000001\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000000\\n00001001\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000001\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n01000000\\n00001001\\n00100000\\n00000000\\n00011000\\n10100010\\n01010010\\n2\\n5\\n\\n01010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100100\\n01010110\\n2\\n5', 'output': 'Data 1:\\n00010010\\n01000000\\n00001001\\n00100000\\n00000000\\n00011000\\n10100010\\n01010010\\nData 2:\\n01010010\\n00000100\\n10001001\\n00000010\\n00000000\\n00001000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001000\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00001100\\n10001001\\n00100010\\n01100010\\n00001000\\n00100000\\n01010110\\n2\\n2', 'output': 'Data 1:\\n00010010\\n00000100\\n00001000\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00001100\\n10001001\\n00100010\\n01100010\\n00001000\\n00100000\\n01010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100010\\n00010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10101000\\n11010010\\n2\\n1', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100010\\n00010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10101000\\n11010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000001\\n00011101\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n10010010\\n00000111\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000001\\n00011101\\n00100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n10010010\\n00000111\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n10101001\\n00100010\\n00000000\\n00001000\\n00100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001011\\n00100010\\n11000010\\n00001100\\n10100000\\n00010100\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n10101001\\n00100010\\n00000000\\n00001000\\n00100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001011\\n00100010\\n11000010\\n00001100\\n10100000\\n00010100\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00100100\\n00001001\\n00100010\\n01010000\\n00001000\\n10100010\\n01110010\\n2\\n8\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00011000\\n10100000\\n01010010\\n2\\n4', 'output': 'Data 1:\\n00000000\\n00000000\\n00001001\\n00000000\\n00000000\\n00001000\\n00000000\\n00000000\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00011000\\n10100000\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001011\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000001\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000000\\n00001011\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n00000001\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n01000000\\n00001001\\n00100000\\n00000000\\n00011000\\n10100010\\n01010010\\n2\\n5\\n\\n01010010\\n00000110\\n10001001\\n00100010\\n01000000\\n00001000\\n10100100\\n01010110\\n2\\n5', 'output': 'Data 1:\\n00010010\\n01000000\\n00001001\\n00100000\\n00000000\\n00011000\\n10100010\\n01010010\\nData 2:\\n01010010\\n00000110\\n10001001\\n00000010\\n00000000\\n00001000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001000\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00001100\\n10001011\\n00100010\\n01100010\\n00001000\\n00100000\\n01010110\\n2\\n2', 'output': 'Data 1:\\n00010010\\n00000100\\n00001000\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00001100\\n10001011\\n00100010\\n01100010\\n00001000\\n00100000\\n01010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100000\\n00010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10101000\\n11010010\\n2\\n1', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100000\\n00010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01000010\\n00001000\\n10101000\\n11010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n10101001\\n00100010\\n00000000\\n00001000\\n00100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n10101001\\n00100010\\n00000000\\n00001000\\n00100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\n2\\n4\\n\\n00010010\\n00000100\\n10001001\\n10100010\\n01010000\\n00001000\\n10100000\\n01010010\\n2\\n4', 'output': 'Data 1:\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n10100010\\n01010000\\n00001000\\n10100000\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00100100\\n00011001\\n00100010\\n01010000\\n00001000\\n10100010\\n01110010\\n2\\n8\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00011000\\n10100000\\n01010010\\n2\\n4', 'output': 'Data 1:\\n00000000\\n00000000\\n00000000\\n00000000\\n00000000\\n00000000\\n00000000\\n00000000\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01000000\\n00011000\\n10100000\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001011\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100110\\n01000001\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000000\\n00001011\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100110\\n00000001\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n01010000\\n00001001\\n00100000\\n00000000\\n00011000\\n10100010\\n01010010\\n2\\n5\\n\\n01010010\\n00000110\\n10001001\\n00100010\\n01000000\\n00001000\\n10100100\\n01010110\\n2\\n5', 'output': 'Data 1:\\n00010010\\n01010000\\n00001001\\n00100000\\n00000000\\n00011000\\n10100010\\n01010010\\nData 2:\\n01010010\\n00000110\\n10001001\\n00000010\\n00000000\\n00001000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001000\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n2\\n5\\n\\n00010010\\n00001100\\n10001011\\n00100010\\n01100010\\n00001000\\n00100000\\n01010110\\n2\\n2', 'output': 'Data 1:\\n00010010\\n00000000\\n00001000\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00010010\\n00001100\\n10001011\\n00100010\\n01100010\\n00001000\\n00100000\\n01010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n1\\n5\\n\\n00010010\\n01000100\\n10001000\\n00100010\\n00000010\\n01001000\\n10100000\\n01011110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00000000\\n01000100\\n10000000\\n00100000\\n00000000\\n00000000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000001\\n00011101\\n00110010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n10010010\\n00000111\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n2\\n6', 'output': 'Data 1:\\n00010010\\n00000001\\n00011101\\n00110010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n10010010\\n00000111\\n10001001\\n00100010\\n01000010\\n00001000\\n10100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n10101001\\n00100010\\n10000000\\n00001000\\n00100010\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n10101001\\n00100010\\n10000000\\n00001000\\n00100010\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\n2\\n4\\n\\n00010010\\n00100100\\n10001001\\n10100010\\n01010000\\n00001000\\n10100000\\n01010010\\n2\\n4', 'output': 'Data 1:\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\nData 2:\\n00010010\\n00100100\\n10001001\\n10100010\\n01010000\\n00001000\\n10100000\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001001\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100110\\n01000001\\n00001000\\n10100000\\n01010010\\n2\\n5', 'output': 'Data 1:\\n00010010\\n00000000\\n00001001\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100110\\n00000001\\n00001000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n1\\n5\\n\\n00010010\\n01100100\\n10001000\\n00100010\\n00000010\\n01001000\\n10100000\\n01011110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00000000\\n01100100\\n10000000\\n00100000\\n00000000\\n00000000\\n10100000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100000\\n00010010\\n1\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100010\\n01001010\\n00001000\\n10101000\\n11010010\\n2\\n1', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100000\\n00010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100010\\n01001010\\n00001000\\n10101000\\n11010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000001\\n00011101\\n00110010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n10010010\\n00000111\\n10001001\\n00100010\\n01000010\\n00001000\\n00100000\\n00010110\\n2\\n6', 'output': 'Data 1:\\n00010010\\n00000001\\n00011101\\n00110010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n10010010\\n00000111\\n10001001\\n00100010\\n01000010\\n00001000\\n00100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n10101001\\n00100010\\n10000000\\n00001000\\n00100011\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n10101001\\n00100010\\n10000000\\n00001000\\n00100011\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\n2\\n4\\n\\n00010010\\n00100100\\n10001001\\n10100010\\n01010000\\n00001000\\n10100000\\n01010010\\n3\\n4', 'output': 'Data 1:\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\nData 2:\\n00010010\\n00000000\\n00001001\\n00000010\\n01010000\\n00001000\\n00000000\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001001\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100110\\n01000001\\n00001000\\n10100000\\n01010010\\n2\\n6', 'output': 'Data 1:\\n00010010\\n00000000\\n00001001\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100110\\n01000001\\n00001000\\n10100000\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n01010000\\n00001001\\n00100001\\n00000000\\n00011000\\n10100010\\n01010010\\n2\\n5\\n\\n01010010\\n00000110\\n10001001\\n00100010\\n01000000\\n00001000\\n10100100\\n01010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n01010000\\n00001001\\n00100001\\n00000000\\n00011000\\n10100010\\n01010010\\nData 2:\\n01010010\\n00000110\\n10001001\\n00000010\\n00000000\\n00001000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\n1\\n5\\n\\n00010010\\n01100100\\n10001000\\n00100010\\n00000010\\n01001000\\n10110000\\n01011110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00101001\\n10100010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000000\\n10000000\\n00000000\\n00000000\\n00000000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100000\\n00010010\\n1\\n5\\n\\n00010010\\n00000100\\n10011001\\n00100010\\n01001010\\n00001000\\n10101000\\n11010010\\n2\\n1', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100000\\n00010010\\nData 2:\\n00010010\\n00000100\\n10011001\\n00100010\\n01001010\\n00001000\\n10101000\\n11010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000001\\n00011101\\n00110010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n10010010\\n00000111\\n10001001\\n00100000\\n01000010\\n00001000\\n00100000\\n00010110\\n2\\n6', 'output': 'Data 1:\\n00010010\\n00000001\\n00011101\\n00110010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n10010010\\n00000111\\n10001001\\n00100000\\n01000010\\n00001000\\n00100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n10101001\\n00100010\\n10000000\\n00001000\\n00100011\\n01010010\\n4\\n5\\n\\n10010010\\n00000100\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n10101001\\n00100010\\n10000000\\n00001000\\n00100011\\n01010010\\nData 2:\\n10010010\\n00000100\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\n2\\n4\\n\\n00010010\\n00100100\\n10001001\\n10100010\\n01010000\\n00001000\\n10100010\\n01010010\\n3\\n4', 'output': 'Data 1:\\n10010110\\n00000100\\n10001001\\n00100010\\n01000000\\n00001000\\n10100010\\n11010010\\nData 2:\\n00010010\\n00000000\\n00001001\\n00000010\\n01010000\\n00001000\\n00000010\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001001\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100110\\n01000001\\n00001000\\n10100000\\n01011010\\n2\\n6', 'output': 'Data 1:\\n00010010\\n00000000\\n00001001\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100110\\n01000001\\n00001000\\n10100000\\n01011010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n01010000\\n00001001\\n00100001\\n00000000\\n00011000\\n10100010\\n01010010\\n2\\n5\\n\\n01010010\\n00000110\\n10001101\\n00100010\\n01000000\\n00001000\\n10100100\\n01010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n01010000\\n00001001\\n00100001\\n00000000\\n00011000\\n10100010\\n01010010\\nData 2:\\n01010010\\n00000110\\n10001101\\n00000010\\n00000000\\n00001000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00101001\\n10100010\\n00001000\\n00001000\\n10100010\\n01010010\\n1\\n5\\n\\n00010010\\n01100100\\n10001000\\n00100010\\n00000010\\n01001000\\n10110000\\n01011110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000100\\n00101001\\n10100010\\n00001000\\n00001000\\n10100010\\n01010010\\nData 2:\\n00000000\\n00000000\\n10000000\\n00000000\\n00000000\\n00000000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100000\\n00010010\\n1\\n5\\n\\n00010010\\n00000100\\n10011001\\n00100010\\n01001010\\n00001001\\n10101000\\n11010010\\n2\\n1', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100000\\n00010010\\nData 2:\\n00010010\\n00000100\\n10011001\\n00100010\\n01001010\\n00001001\\n10101000\\n11010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010011\\n00000001\\n00011101\\n00110010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n10010010\\n00000111\\n10001001\\n00100000\\n01000010\\n00001000\\n00100000\\n00010110\\n2\\n6', 'output': 'Data 1:\\n00010011\\n00000001\\n00011101\\n00110010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n10010010\\n00000111\\n10001001\\n00100000\\n01000010\\n00001000\\n00100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n10101001\\n00100010\\n10000100\\n00001000\\n00100011\\n01010010\\n4\\n5\\n\\n10010010\\n00000100\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n10101001\\n00100010\\n10000100\\n00001000\\n00100011\\n01010010\\nData 2:\\n10010010\\n00000100\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n10010110\\n00000100\\n10001001\\n00100010\\n01000001\\n00001000\\n10100010\\n11010010\\n2\\n4\\n\\n00010010\\n00100100\\n10001001\\n10100010\\n01010000\\n00001000\\n10100010\\n01010010\\n3\\n4', 'output': 'Data 1:\\n10010110\\n00000100\\n10001001\\n00100010\\n01000001\\n00001000\\n10100010\\n11010010\\nData 2:\\n00010010\\n00000000\\n00001001\\n00000010\\n01010000\\n00001000\\n00000010\\n01010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n00001001\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\n4\\n5\\n\\n00010010\\n00000100\\n10001001\\n00100110\\n01000001\\n00001000\\n10101000\\n01011010\\n2\\n6', 'output': 'Data 1:\\n00010010\\n00000000\\n00001001\\n01100010\\n00000000\\n00001000\\n10100001\\n01010010\\nData 2:\\n00010010\\n00000100\\n10001001\\n00100110\\n01000001\\n00001000\\n10101000\\n01011010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n01010000\\n00001011\\n00100001\\n00000000\\n00011000\\n10100010\\n01010010\\n2\\n5\\n\\n01010010\\n00000110\\n10001101\\n00100010\\n01000000\\n00001000\\n10100100\\n01010110\\n2\\n8', 'output': 'Data 1:\\n00010010\\n01010000\\n00001011\\n00100001\\n00000000\\n00011000\\n10100010\\n01010010\\nData 2:\\n01010010\\n00000110\\n10001101\\n00000010\\n00000000\\n00001000\\n00000000\\n00000000\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100000\\n10010010\\n1\\n5\\n\\n00010010\\n00000100\\n10011001\\n00100010\\n01001010\\n00001001\\n10101000\\n11010010\\n2\\n1', 'output': 'Data 1:\\n00010010\\n00000100\\n00001001\\n00100010\\n00000000\\n00001010\\n10100000\\n10010010\\nData 2:\\n00010010\\n00000100\\n10011001\\n00100010\\n01001010\\n00001001\\n10101000\\n11010010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010011\\n00000001\\n00011101\\n00110010\\n00000000\\n00001000\\n10100010\\n01010010\\n4\\n5\\n\\n10010010\\n00000111\\n10001001\\n00101000\\n01000010\\n00001000\\n00100000\\n00010110\\n2\\n6', 'output': 'Data 1:\\n00010011\\n00000001\\n00011101\\n00110010\\n00000000\\n00001000\\n10100010\\n01010010\\nData 2:\\n10010010\\n00000111\\n10001001\\n00101000\\n01000010\\n00001000\\n00100000\\n00010110\\n'}, {'type': 'stdin_stdout', 'input': '2\\n\\n00010010\\n00000000\\n10101001\\n00100010\\n10000100\\n00001000\\n00100011\\n01010010\\n4\\n5\\n\\n10010010\\n00000110\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n2\\n8', 'output': 'Data 1:\\n00010010\\n00000000\\n10101001\\n00100010\\n10000100\\n00001000\\n00100011\\n01010010\\nData 2:\\n10010010\\n00000110\\n10001011\\n00100010\\n11000000\\n00001100\\n10100000\\n00010100\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_78689","program":"```python\ndef e(x,y):\n A[y][x]='0'\n for d in range(-3,4):\n 0<=x+d<8and'1'==A[y][x+d]and e(x+d,y)\n 0<=y+d<8and'1'==A[y+d][x]and e(x,y+d)\nfor i in range(int(input())):\n print(f'Data {i+1}:');input()\n A=[list(input())for _ in[0]*8]\n e(int(input())-1,int(input())-1)\n for r in A:print(*r,sep='')\n\n```","inputs":"2\n\n00010010\n00000100\n10001001\n00100010\n01000000\n00001000\n10100010\n01010010\n2\n5\n\n00010010\n00000100\n10001001\n00100010\n01000000\n00001000\n10100010\n01010010\n2\n5","output":"Data 1:\n00000000\n00000100\n10001001\n00100000\n00000000\n00001000\n10100000\n00000000\nData 2:\n00000000\n00000100\n10001001\n00100000\n00000000\n00001000\n10100000\n00000000","actual_output":"Data 1:\n00000000\n00000100\n10001001\n00100000\n00000000\n00001000\n10100000\n00000000\nData 2:\n00000000\n00000100\n10001001\n00100000\n00000000\n00001000\n10100000\n00000000\n","execution_success":true,"sample_index":12540},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00203 A New Plan of Aizu Ski Resort","prompt":"Solve the following coding problem using the programming language python:\n\nYukiya, the owner of Aizuyama Ski Resort, has prepared a course for advanced skiers with obstacles and jumping hills. There are various ways to slide on the course, and users who can slide in all patterns during the season will be given a gift.\n\nLet's create a program for the oil tree shop that outputs the number of patterns of how to slide based on the floor plan of the course.\n\n\n\n\n\nThe course is represented by a grid of X x Y squares as shown above. It is assumed that the origin is at the upper left, the x coordinate increases as it goes to the right, and the y coordinate increases as it goes down.\n\nEach gliding pattern starts at the highest point (y = 1, but without obstacles) and progresses towards the goal (y = Y). A runner in a grid square (x, y) can move to either (x \u2212 1, y + 1), (x, y + 1), or (x + 1, y + 1). I will. There are obstacles and jumping platforms in the squares, and you cannot enter the squares with obstacles, and when you enter the squares with jumping platforms, you will move to (x, y + 2). However, there is no jumping platform in the highest cell (the cell with y = 1), and when entering a cell with a jumping platform, you can only enter from the cell with the same x coordinate. Starting from the top of the course (y = 1) and crossing the bottom without deviating from the course (y \u2265 Y), it is considered as one way of sliding and ends.\n\nCreate a program that takes the course information as input and outputs the total number of slips.\n\n\n\nInput\n\nA sequence of multiple datasets is given as input. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format:\n\n\nX Y\nc11 c21 ... cX1\nc12 c22 ... cX2\n::\nc1Y c2Y ... cXY\n\n\nThe first line gives the course size X, Y (1 \u2264 X, Y \u2264 15). Course information is given in the Y line that follows. cij (one of 0, 1, or 2) is an integer that represents the information of the squares of x = i, y = j, where 0 is a movable square, 1 is a square with an obstacle, and 2 is a square with a jumping platform. Represents.\n\nThe number of datasets does not exceed 50.\n\nOutput\n\nFor each input dataset, the number of patterns of how to slide the course is output on one line.\n\nExample\n\nInput\n\n5 5\n0 0 0 0 1\n2 1 0 2 0\n1 0 0 1 1\n0 2 1 2 0\n0 1 0 0 0\n5 5\n0 0 1 0 0\n2 1 0 2 0\n1 0 0 1 1\n0 2 1 2 0\n0 1 0 0 0\n15 15\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0\n\n\nOutput\n\n8\n6\n52694573\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# -*- coding: utf-8 -*-\n\"\"\"\nhttp://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0203\n\n\"\"\"\nimport sys\nfrom sys import stdin\nfrom collections import deque, defaultdict\ninput = stdin.readline\n\n\ndef solve(field):\n BLANK, OBSTACLE, JUMP = 0, 1, 2\n ans = 0 # ??????????????\u00b0???????????\u00b0\n\n dy = [1, 1, 1] # ?????????????????????????????????????\u00a7???????\n dx = [0, -1, 1]\n x_limit = len(field[0])\n y_limit = len(field)\n\n path = defaultdict(int) # ??????????????????????????\u00b0???????????\u00b0????????????'x???_y???'???????????????\n Q = deque()\n for x, m in enumerate(field[0]):\n if m == BLANK: # ?????????????????\u00b0?????\u00b4?????????????????????????????????\n t = '{}_{}'.format(x, 0)\n Q.append((x, 0))\n path[t] = 1\n\n while Q:\n cx, cy = Q.popleft() # ?????\u00a8??\u00b0?????\u00a7?\u00a8?\n t = '{}_{}'.format(cx, cy)\n num = path.pop(t)\n\n if field[cy][cx] == OBSTACLE:\n continue\n elif field[cy][cx] == JUMP: # ?????\u00a3????????\u00a7?????\u00b0?????????????????\u00a3????????\u00b0\n if cy+2 > y_limit-1:\n ans += num\n else:\n t = '{}_{}'.format(cx, cy+2)\n if not path[t]:\n Q.append((cx, cy+2))\n path[t] += num\n continue\n elif cy == y_limit -1:\n ans += num\n continue\n\n for i in range(3): # ?????????3???len(dy)?????????\n nx = cx + dx[i] # ?????\u00b0????????\u00a7?\u00a8?\n ny = cy + dy[i]\n\n if 0<= nx < x_limit:\n if field[ny][nx] == JUMP and dx[i] == 0: # ?????\u00a3????????\u00b0????????\u00a3??????????????\\????????\u00b4???\n if ny+2 > y_limit - 1:\n ans += num\n else:\n t = '{}_{}'.format(nx, ny+2)\n if not path[t]:\n Q.append((nx, ny+2))\n path[t] += num\n elif field[ny][nx] == BLANK:\n if (ny >= y_limit - 1):\n ans += num\n else:\n t = '{}_{}'.format(nx, ny)\n if not path[t]:\n Q.append((nx, ny))\n path[t] += num\n return ans\n\n\ndef main(args):\n while True:\n X, Y = map(int, input().strip().split())\n if X == 0 and Y == 0:\n break\n field = []\n for _ in range(Y):\n temp = [int(x) for x in input().strip().split()]\n field.append(temp)\n result = solve(field)\n print(result)\n\n\nif __name__ == '__main__':\n main(sys.argv[1:])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 5\\n0 0 0 0 1\\n2 1 0 2 0\\n1 0 0 1 1\\n0 2 1 2 0\\n0 1 0 0 0\\n5 5\\n0 0 1 0 0\\n2 1 0 2 0\\n1 0 0 1 1\\n0 2 1 2 0\\n0 1 0 0 0\\n15 15\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n0 0', 'output': '8\\n6\\n52694573'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 0 0 0 1\\n2 1 0 2 0\\n1 0 0 1 1\\n0 2 1 2 0\\n0 1 0 0 0\\n5 5\\n0 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?????????????????????????????????????\u00a7???????\n dx = [0, -1, 1]\n x_limit = len(field[0])\n y_limit = len(field)\n\n path = defaultdict(int) # ??????????????????????????\u00b0???????????\u00b0????????????'x???_y???'???????????????\n Q = deque()\n for x, m in enumerate(field[0]):\n if m == BLANK: # ?????????????????\u00b0?????\u00b4?????????????????????????????????\n t = '{}_{}'.format(x, 0)\n Q.append((x, 0))\n path[t] = 1\n\n while Q:\n cx, cy = Q.popleft() # ?????\u00a8??\u00b0?????\u00a7?\u00a8?\n t = '{}_{}'.format(cx, cy)\n num = path.pop(t)\n\n if field[cy][cx] == OBSTACLE:\n continue\n elif field[cy][cx] == JUMP: # ?????\u00a3????????\u00a7?????\u00b0?????????????????\u00a3????????\u00b0\n if cy+2 > y_limit-1:\n ans += num\n else:\n t = '{}_{}'.format(cx, cy+2)\n if not path[t]:\n Q.append((cx, cy+2))\n path[t] += num\n continue\n elif cy == y_limit -1:\n ans += num\n continue\n\n for i in range(3): # ?????????3???len(dy)?????????\n nx = cx + dx[i] # ?????\u00b0????????\u00a7?\u00a8?\n ny = cy + dy[i]\n\n if 0<= nx < x_limit:\n if field[ny][nx] == JUMP and dx[i] == 0: # ?????\u00a3????????\u00b0????????\u00a3??????????????\\????????\u00b4???\n if ny+2 > y_limit - 1:\n ans += num\n else:\n t = '{}_{}'.format(nx, ny+2)\n if not path[t]:\n Q.append((nx, ny+2))\n path[t] += num\n elif field[ny][nx] == BLANK:\n if (ny >= y_limit - 1):\n ans += num\n else:\n t = '{}_{}'.format(nx, ny)\n if not path[t]:\n Q.append((nx, ny))\n path[t] += num\n return ans\n\n\ndef main(args):\n while True:\n X, Y = map(int, input().strip().split())\n if X == 0 and Y == 0:\n break\n field = []\n for _ in range(Y):\n temp = [int(x) for x in input().strip().split()]\n field.append(temp)\n result = solve(field)\n print(result)\n\n\nif __name__ == '__main__':\n main(sys.argv[1:])\n```","inputs":"5 5\n0 0 0 0 1\n2 1 0 2 0\n1 0 0 1 1\n0 2 1 2 0\n0 1 0 0 0\n5 5\n0 0 1 0 0\n2 1 0 2 0\n1 0 0 1 1\n0 2 1 2 0\n0 1 0 0 0\n15 15\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0","output":"8\n6\n52694573","actual_output":"8\n6\n52694573\n","execution_success":true,"sample_index":12541},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00359 Dungeon","prompt":"Solve the following coding problem using the programming language python:\n\nBob is playing a popular game called \"Dungeon\". The game is played on a rectangular board consisting of W \u00d7 H squares. Each square is identified with its column and row number, thus the square located in the x-th column and the y-th row is represented as (x, y). The left-most square in the top row is (0, 0) and the right-most square in the bottom row is (W-1, H-1).\n\nBob moves a character \"BomBom\" to clear the game. BomBom is initially located at (0, 0). The game is won if Bob successfully destroys all the enemy characters on the board by manipulating BomBom cleverly. The enemy characters are fixed on specific squares, and Bob can manipulate BomBom using the following two operations any number of times.\n\n* One-square movement in the up, down, left, or right direction within the board\n* Using a bomb, eliminate all the enemy characters that are located in the same column and row as that of BomBom\n\n\n\nBomBom consumes a Cost when it moves from one square to another. BomBom can use a bomb any number of times without consuming a Cost. Use of a bomb has no effect on BomBom\u2019s behavior and it can move even to a square where an enemy character is located.\n\nGiven the board size and enemy information, make a program to evaluate the minimum Cost BomBom consumes before it destroys all enemy characters.\n\n\n\nInput\n\nThe input is given in the following format.\n\n\nW H N\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\n\n\nThe first line provides the number of squares in the horizontal direction W (1 \u2264 W \u2264 105), in the vertical direction H (1 \u2264 H \u2264 105), and the number of enemy characters N (1 \u2264 N \u2264 105). Each of the subsequent N lines provides location information of the i-th enemy, column x_i (0 \u2264 x_i \u2264 W-1) and row y_i (0 \u2264 y_i \u2264 H-1). The number of enemy characters in a specific square can be either one or zero.\n\nOutput\n\nOutput the minimum Cost in a line.\n\nExamples\n\nInput\n\n5 4 4\n0 3\n1 1\n2 2\n2 3\n\n\nOutput\n\n2\n\n\nInput\n\n6 6 5\n2 1\n5 2\n3 3\n1 4\n1 5\n\n\nOutput\n\n4\n\n\nInput\n\n8 8 4\n6 0\n7 0\n0 6\n0 7\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nw, h, n = map(int, input().split())\nxys = sorted([list(map(int, input().split())) for _ in range(n)])\ny_max = [0]\nfor _, y in reversed(xys):\n y_max.append(max(y_max[-1], y))\nxs = [0] + [x for x, _ in xys]\nprint(min([xs[i] + y_max[n - i] for i in range(n + 1)]))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 4 4\\n0 3\\n1 1\\n2 2\\n2 3', 'output': '2'}, {'type': 'stdin_stdout', 'input': '6 6 5\\n2 1\\n5 2\\n3 3\\n1 4\\n1 5', 'output': '4'}, {'type': 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268435456}","problem_id":"vfc_78697","program":"```python\nw, h, n = map(int, input().split())\nxys = sorted([list(map(int, input().split())) for _ in range(n)])\ny_max = [0]\nfor _, y in reversed(xys):\n y_max.append(max(y_max[-1], y))\nxs = [0] + [x for x, _ in xys]\nprint(min([xs[i] + y_max[n - i] for i in range(n + 1)]))\n\n```","inputs":"5 4 4\n0 3\n1 1\n2 2\n2 3","output":"2","actual_output":"2\n","execution_success":true,"sample_index":12542},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00570 Stove","prompt":"Solve the following coding problem using the programming language python:\n\nJOI has a stove in your room. JOI himself is resistant to the cold, so he doesn't need to put on the stove when he is alone in the room, but he needs to put on the stove when there are visitors.\n\nOn this day, there are N guests under JOI. The ith (1 \\ leq i \\ leq N) visitor arrives at time T_i and leaves at time T_i + 1. There can never be more than one visitor at the same time.\n\nJOI can turn the stove on and off at any time. However, each time you turn on the stove, you will consume one match. JOI has only K matches, so he can only stove up to K times. The stove is gone at the beginning of the day.\n\nWhen the stove is on, fuel is consumed by that amount, so I want to set the time when the stove is on and off and minimize the total time when the stove is on.\n\n\n\n\n\nExample\n\nInput\n\n3 2\n1\n3\n6\n\n\nOutput\n\n4\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, k = map(int, input().split())\nli = [int(input()) for i in range(n)]\ndiff = []\nfor j in range(n-1):\n diff.append(li[j+1]-li[j]-1)\ndiff.sort(reverse=True)\nprint(n+sum(diff[k-1:]))\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 2\\n1\\n3\\n6', 'output': '4'}, {'type': 'stdin_stdout', 'input': '3 2\\n1\\n3\\n11', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n0\\n3\\n11', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1\\n3\\n14', 'output': '3\\n'}, {'type': 'stdin_stdout', 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2\\n2\\n5\\n9', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n0\\n3\\n10', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2\\n6\\n24', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n4\\n1\\n10', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n-1\\n12\\n20', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n0\\n0\\n23', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2\\n4\\n3', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1\\n1\\n14', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n2\\n5\\n9', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n-1\\n3\\n10', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2\\n6\\n1', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n4\\n1\\n10', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n-2\\n12\\n20', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n-1\\n0\\n23', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n2\\n4\\n3', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1\\n1\\n14', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_78701","program":"```python\nn, k = map(int, input().split())\nli = [int(input()) for i in range(n)]\ndiff = []\nfor j in range(n-1):\n diff.append(li[j+1]-li[j]-1)\ndiff.sort(reverse=True)\nprint(n+sum(diff[k-1:]))\n\n\n```","inputs":"3 2\n1\n3\n6","output":"4","actual_output":"4\n","execution_success":true,"sample_index":12543},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00717 Polygonal Line Search","prompt":"Solve the following coding problem using the programming language python:\n\nMultiple polygonal lines are given on the xy-plane. Given a list of polygonal lines and a template, you must find out polygonal lines which have the same shape as the template.\n\nA polygonal line consists of several line segments parallel to x-axis or y-axis. It is defined by a list of xy-coordinates of vertices from the start-point to the end-point in order, and always turns 90 degrees at each vertex. A single polygonal line does not pass the same point twice. Two polygonal lines have the same shape when they fully overlap each other only with rotation and translation within xy-plane (i.e. without magnification or a flip). The vertices given in reverse order from the start-point to the end-point is the same as that given in order.\n\nFigure 1 shows examples of polygonal lines. In this figure, polygonal lines A and B have the same shape.\n\nWrite a program that answers polygonal lines which have the same shape as the template.\n\n\n---\nFigure 1: Polygonal lines\n\n\n\nInput\n\nThe input consists of multiple datasets. The end of the input is indicated by a line which contains a zero.\n\nA dataset is given as follows.\n\n> n\n> Polygonal line0\n> Polygonal line1\n> Polygonal line2\n> ...\n> Polygonal linen\n\nn is the number of polygonal lines for the object of search on xy-plane. n is an integer, and 1 <= n <= 50. Polygonal line0 indicates the template.\n\nA polygonal line is given as follows.\n\n> m\n> x1 y1\n> x2 y2\n> ...\n> xm ym\n>\n\nm is the number of the vertices of a polygonal line (3 <= m <= 10). xi and yi, separated by a space, are the x- and y-coordinates of a vertex, respectively (-10000 < xi < 10000, -10000 \n\nTally Counters\n\nA number of tally counters are placed in a row. Pushing the button on a counter will increment the displayed value by one, or, when the value is already the maximum, it goes down to one. All the counters are of the same model with the same maximum value.\n\n Fig. D-1 Tally Counters\n\nStarting from the values initially displayed on each of the counters, you want to change all the displayed values to target values specified for each. As you don't want the hassle, however, of pushing buttons of many counters one be one, you devised a special tool. Using the tool, you can push buttons of one or more adjacent counters, one push for each, in a single operation. You can choose an arbitrary number of counters at any position in each operation, as far as they are consecutively lined up.\n\nHow many operations are required at least to change the displayed values on counters to the target values?\n\nInput\n\nThe input consists of multiple datasets, each in the following format.\n\n> n m\n> a1 a2 ... an\n> b1 b2 ... bn\n>\n\nEach dataset consists of 3 lines. The first line contains n (1 \u2264 n \u2264 1000) and m (1 \u2264 m \u2264 10000), the number of counters and the maximum value displayed on counters, respectively. The second line contains the initial values on counters, ai (1 \u2264 ai \u2264 m), separated by spaces. The third line contains the target values on counters, bi (1 \u2264 bi \u2264 m), separated by spaces.\n\nThe end of the input is indicated by a line containing two zeros. The number of datasets does not exceed 100.\n\nOutput\n\nFor each dataset, print in a line the minimum number of operations required to make all of the counters display the target values.\n\nSample Input\n\n\n4 5\n2 3 1 4\n2 5 5 2\n3 100\n1 10 100\n1 10 100\n5 10000\n4971 7482 1238 8523 1823\n3287 9013 9812 297 1809\n0 0\n\n\nOutput for the Sample Input\n\n\n4\n0\n14731\n\n\n\n\n\n\nExample\n\nInput\n\n4 5\n2 3 1 4\n2 5 5 2\n3 100\n1 10 100\n1 10 100\n5 10000\n4971 7482 1238 8523 1823\n3287 9013 9812 297 1809\n0 0\n\n\nOutput\n\n4\n0\n14731\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\ndef solve(C, N, M, range = range, min = min):\n K = N // 4 + 1\n S = [0]*K\n T = [0]*K\n U = [0]*(K+1)\n for i in range(N-1):\n U[0] = 10**18\n for j in range(K):\n U[j+1] = min(U[j], S[j])\n k = K-1\n ci = C[i]; cj = C[i+1]\n r = 10**18\n for j in range(K-1, -1, -1):\n while ci + k*M > cj + j*M:\n r = min(r, ci + k*M + S[k])\n k -= 1\n T[j] = min(r - j*M - cj, U[k+1])\n S, T = T, S\n ci = C[-1]\n for i in range(K):\n S[i] += ci + i*M\n write(\"%d\\n\" % min(S))\nwhile 1:\n N, M = map(int, readline().split())\n if N == 0:\n break\n *A, = map(int, readline().split())\n *B, = map(int, readline().split())\n C = [(b - a) % M for a, b in zip(A, B)]\n solve(C, N, M)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 10 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9812 297 1809\\n0 0', 'output': '4\\n0\\n14731'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 10 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 1809\\n0 0', 'output': '4\\n0\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 14 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 1809\\n0 0', 'output': '4\\n4\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 10 100\\n5 10000\\n4971 7482 1238 105 1823\\n3287 9013 9812 297 1809\\n0 0', 'output': '4\\n0\\n13149\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n0 10 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 1809\\n0 0', 'output': '4\\n99\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 2 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 14 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 1809\\n0 0', 'output': '3\\n4\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n3 3 1 4\\n2 3 5 2\\n3 100\\n1 10 100\\n1 14 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 360\\n0 0', 'output': '5\\n4\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 10 100\\n5 10000\\n4971 7482 1238 105 1209\\n519 9013 9812 297 1809\\n0 0', 'output': '4\\n0\\n11939\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n3 3 1 4\\n2 3 5 2\\n3 100\\n1 10 100\\n1 14 110\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 360\\n0 0', 'output': '5\\n10\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n3 3 1 4\\n2 3 5 2\\n3 100\\n1 10 100\\n1 14 110\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9783 9928 297 360\\n0 0', 'output': '5\\n10\\n15385\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n0 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 1 100\\n5 10000\\n4971 7482 1238 105 1209\\n519 9013 9812 297 1809\\n0 0', 'output': '4\\n91\\n11939\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 7 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9812 297 1809\\n0 0', 'output': '4\\n97\\n14731\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n2 10 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 1809\\n0 0', 'output': '4\\n1\\n14615\\n'}, {'type': 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7482 1238 8523 1823\\n3287 9013 9928 393 360\\n0 0', 'output': '4\\n1\\n14711\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n0 3 1 5\\n2 5 5 2\\n3 100\\n1 10 110\\n0 10 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 1809\\n0 0', 'output': '4\\n100\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n3 3 0 4\\n2 3 5 2\\n3 100\\n1 10 100\\n1 14 100\\n5 10001\\n4971 7482 1238 8523 1823\\n49 9013 9928 297 360\\n0 0', 'output': '5\\n4\\n14618\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 2 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 10 100\\n5 10000\\n4971 3428 1238 105 1823\\n519 9013 2581 297 1809\\n0 0', 'output': '3\\n0\\n11343\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 3 4 2\\n3 101\\n1 10 100\\n1 14 100\\n5 10000\\n4971 7482 1238 3626 1823\\n3287 9013 9928 393 360\\n0 0', 'output': '3\\n4\\n13301\\n'}, {'type': 'stdin_stdout', 'input': '1 5\\n2 3 2 4\\n2 5 4 2\\n3 100\\n1 10 100\\n1 10 100\\n5 10000\\n992 7482 1238 105 1823\\n415 9013 9812 297 1809\\n0 0', 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5\\n0 5 0 2\\n3 100\\n1 10 100\\n0 12 100\\n5 10000\\n4971 9366 1238 4581 1823\\n3287 9013 9928 297 1809\\n0 0', 'output': '4\\n99\\n13917\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 6 1 4\\n2 4 5 2\\n3 100\\n1 10 100\\n2 10 000\\n5 10000\\n2846 13457 1238 8523 1676\\n3287 9013 9928 158 1809\\n0 0', 'output': '4\\n1\\n8690\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n0 10 101\\n1 14 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3802 7343 9928 297 1809\\n0 0', 'output': '4\\n99\\n12945\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 10 010\\n5 10000\\n4971 7482 1238 105 1823\\n958 9013 9812 297 1760\\n0 0', 'output': '4\\n10\\n13149\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 5 1 4\\n4 5 5 2\\n3 100\\n0 10 100\\n1 10 100\\n5 10000\\n4971 7482 1238 205 1209\\n519 9013 9812 297 1809\\n0 0', 'output': '5\\n1\\n12039\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n3 3 1 4\\n2 3 5 2\\n3 100\\n1 10 100\\n0 14 101\\n5 10000\\n4971 7482 1238 8523 1823\\n5923 9013 9928 297 360\\n0 0', 'output': '5\\n99\\n11774\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n0 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 1 100\\n5 10010\\n4971 7482 1238 105 1209\\n129 1496 9812 297 421\\n0 0', 'output': '4\\n91\\n11346\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 14 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 360\\n0 0', 'output': '4\\n4\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 3 5 2\\n3 100\\n1 10 100\\n1 14 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 360\\n0 0', 'output': '4\\n4\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 10 100\\n5 10000\\n4971 7482 1238 105 1823\\n519 9013 9812 297 1809\\n0 0', 'output': '4\\n0\\n13149\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 2 4\\n4 5 5 2\\n3 100\\n1 10 100\\n1 14 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 1809\\n0 0', 'output': '3\\n4\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n0 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 10 100\\n5 10000\\n4971 7482 1238 105 1209\\n519 9013 9812 297 1809\\n0 0', 'output': '4\\n0\\n11939\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n0 3 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 1 100\\n5 10000\\n4971 7482 1238 105 1209\\n261 9013 9812 297 1809\\n0 0', 'output': '4\\n91\\n11939\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 5 2\\n3 101\\n1 10 100\\n1 14 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 360\\n0 0', 'output': '4\\n4\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 5\\n2 5 5 2\\n3 100\\n1 10 100\\n0 10 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 1809\\n0 0', 'output': '4\\n99\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n3 3 0 4\\n2 3 5 2\\n3 100\\n1 10 100\\n1 14 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 360\\n0 0', 'output': '5\\n4\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n0 2 1 4\\n2 5 5 2\\n3 100\\n1 10 100\\n1 1 100\\n5 10000\\n4971 7482 1238 105 1209\\n519 9013 9812 297 1809\\n0 0', 'output': '4\\n91\\n11939\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 1 4\\n2 5 4 2\\n3 100\\n1 10 100\\n1 10 100\\n5 10000\\n4971 7482 1238 105 1823\\n415 9013 9812 297 1809\\n0 0', 'output': '3\\n0\\n13149\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n0 3 1 5\\n2 5 5 2\\n3 100\\n1 10 100\\n0 10 100\\n5 10000\\n4971 7482 1238 8523 1823\\n3287 9013 9928 297 1809\\n0 0', 'output': '4\\n99\\n14615\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n3 3 0 4\\n2 3 5 2\\n3 100\\n1 10 100\\n1 14 100\\n5 10000\\n4971 7482 1238 8523 1823\\n49 9013 9928 297 360\\n0 0', 'output': '5\\n4\\n14615\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_78717","program":"```python\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\ndef solve(C, N, M, range = range, min = min):\n K = N // 4 + 1\n S = [0]*K\n T = [0]*K\n U = [0]*(K+1)\n for i in range(N-1):\n U[0] = 10**18\n for j in range(K):\n U[j+1] = min(U[j], S[j])\n k = K-1\n ci = C[i]; cj = C[i+1]\n r = 10**18\n for j in range(K-1, -1, -1):\n while ci + k*M > cj + j*M:\n r = min(r, ci + k*M + S[k])\n k -= 1\n T[j] = min(r - j*M - cj, U[k+1])\n S, T = T, S\n ci = C[-1]\n for i in range(K):\n S[i] += ci + i*M\n write(\"%d\\n\" % min(S))\nwhile 1:\n N, M = map(int, readline().split())\n if N == 0:\n break\n *A, = map(int, readline().split())\n *B, = map(int, readline().split())\n C = [(b - a) % M for a, b in zip(A, B)]\n solve(C, N, M)\n\n```","inputs":"4 5\n2 3 1 4\n2 5 5 2\n3 100\n1 10 100\n1 10 100\n5 10000\n4971 7482 1238 8523 1823\n3287 9013 9812 297 1809\n0 0","output":"4\n0\n14731","actual_output":"4\n0\n14731\n","execution_success":true,"sample_index":12545},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01419 On or Off","prompt":"Solve the following coding problem using the programming language python:\n\nSaving electricity is very important!\n\nYou are in the office represented as R \\times C grid that consists of walls and rooms. It is guaranteed that, for any pair of rooms in the office, there exists exactly one route between the two rooms. It takes 1 unit of time for you to move to the next room (that is, the grid adjacent to the current room). Rooms are so dark that you need to switch on a light when you enter a room. When you leave the room, you can either leave the light on, or of course you can switch off the light. Each room keeps consuming electric power while the light is on.\n\nToday you have a lot of tasks across the office. Tasks are given as a list of coordinates, and they need to be done in the specified order. To save electricity, you want to finish all the tasks with the minimal amount of electric power.\n\nThe problem is not so easy though, because you will consume electricity not only when light is on, but also when you switch on/off the light. Luckily, you know the cost of power consumption per unit time and also the cost to switch on/off the light for all the rooms in the office. Besides, you are so smart that you don't need any time to do the tasks themselves. So please figure out the optimal strategy to minimize the amount of electric power consumed.\n\nAfter you finished all the tasks, please DO NOT leave the light on at any room. It's obviously wasting!\n\n\n\nInput\n\nThe first line of the input contains three positive integers R (0 \\lt R \\leq 50), C (0 \\lt C \\leq 50) and M (2 \\leq M \\leq 1000). The following R lines, which contain C characters each, describe the layout of the office. '.' describes a room and '#' describes a wall.\n\nThis is followed by three matrices with R rows, C columns each. Every elements of the matrices are positive integers. The (r, c) element in the first matrix describes the power consumption per unit of time for the room at the coordinate (r, c). The (r, c) element in the second matrix and the third matrix describe the cost to turn on the light and the cost to turn off the light, respectively, in the room at the coordinate (r, c).\n\nEach of the last M lines contains two positive integers, which describe the coodinates of the room for you to do the task.\n\nNote that you cannot do the i-th task if any of the j-th task (0 \\leq j \\leq i) is left undone.\n\nOutput\n\nPrint one integer that describes the minimal amount of electric power consumed when you finished all the tasks.\n\nExamples\n\nInput\n\n1 3 2\n...\n1 1 1\n1 2 1\n1 1 1\n0 0\n0 2\n\n\nOutput\n\n7\n\n\nInput\n\n3 3 5\n...\n.##\n..#\n1 1 1\n1 0 0\n1 1 0\n3 3 3\n3 0 0\n3 3 0\n5 4 5\n4 0 0\n5 4 0\n1 0\n2 1\n0 2\n2 0\n0 0\n\n\nOutput\n\n77\n\n\nInput\n\n5 5 10\n.###\n....\n.#\n..#.#\n....\n0 12 0 0 0\n0 4 3 2 10\n0 0 0 99 0\n11 13 0 2 0\n0 1 1 2 1\n0 4 0 0 0\n0 13 8 2 4\n0 0 0 16 0\n1 1 0 2 0\n0 2 3 1 99\n0 2 0 0 0\n0 12 2 12 2\n0 0 0 3 0\n4 14 0 16 0\n0 2 14 2 90\n0 1\n3 0\n4 4\n1 4\n1 1\n4 4\n1 1\n4 3\n3 0\n1 4\n\n\nOutput\n\n777\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools\n\nsys.setrecursionlimit(10**7)\ninf = 10**20\neps = 1.0 / 10**13\nmod = 10**9+7\ndd = [(-1,0),(0,1),(1,0),(0,-1)]\nddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\n\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\ndef LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]\ndef LF(): return [float(x) for x in sys.stdin.readline().split()]\ndef LS(): return sys.stdin.readline().split()\ndef I(): return int(sys.stdin.readline())\ndef F(): return float(sys.stdin.readline())\ndef S(): return input()\ndef pf(s): return print(s, flush=True)\n\ndef main():\n rr = []\n\n def f():\n r,c,m = LI()\n a = [[1] * (c+2)] + [[1] + [None if c == '.' else 1 for c in S()] + [1] for _ in range(r)] + [[1] * (c+2)]\n cost = [[1] * (c+2)] + [[1] + LI() + [1] for _ in range(r)] + [[1] * (c+2)]\n on = [[1] * (c+2)] + [[1] + LI() + [1] for _ in range(r)] + [[1] * (c+2)]\n off = [[1] * (c+2)] + [[1] + LI() + [1] for _ in range(r)] + [[1] * (c+2)]\n ms = [tuple(map(lambda x: x+1, LI())) for _ in range(m)]\n e = collections.defaultdict(list)\n for i in range(1,r+1):\n for j in range(1,c+1):\n if a[i][j]:\n continue\n for di,dj in dd:\n if a[i+di][j+dj]:\n continue\n e[(i,j)].append(((i+di,j+dj), 1))\n\n def search(s):\n d = collections.defaultdict(lambda: inf)\n d[s] = 0\n q = []\n heapq.heappush(q, (0, s))\n v = collections.defaultdict(bool)\n while len(q):\n k, u = heapq.heappop(q)\n if v[u]:\n continue\n v[u] = True\n\n for uv, ud in e[u]:\n if v[uv]:\n continue\n vd = k + ud\n if d[uv] > vd:\n d[uv] = vd\n heapq.heappush(q, (vd, uv))\n\n return d\n\n ad = {}\n for k in ms:\n if k in ad:\n continue\n ad[k] = search(k)\n ti = 0\n td = collections.defaultdict(list)\n c = ms[0]\n td[c].append(0)\n for t in ms[1:]:\n while c != t:\n cc = ad[t][c]\n for di,dj in dd:\n ni = c[0] + di\n nj = c[1] + dj\n n = (ni, nj)\n if ad[t][n] == cc - 1:\n ti += 1\n td[n].append(ti)\n c = n\n break\n\n r = 0\n for k,v in sorted(td.items()):\n i = k[0]\n j = k[1]\n cs = cost[i][j]\n onf = on[i][j] + off[i][j]\n tr = onf\n for vi in range(len(v)-1):\n sa = v[vi+1] - v[vi]\n tr += min(cs * sa, onf)\n r += tr\n\n return r\n\n while True:\n rr.append(f())\n break\n\n return '\\n'.join(map(str,rr))\n\n\nprint(main())\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 3 5\\n...\\n.##\\n..#\\n1 1 1\\n1 0 0\\n1 1 0\\n3 3 3\\n3 0 0\\n3 3 0\\n5 4 5\\n4 0 0\\n5 4 0\\n1 0\\n2 1\\n0 2\\n2 0\\n0 0', 'output': '77'}, {'type': 'stdin_stdout', 'input': '1 3 2\\n...\\n1 1 1\\n1 2 1\\n1 1 1\\n0 0\\n0 2', 'output': '7'}, {'type': 'stdin_stdout', 'input': '5 5 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'input': '2 5 16\\n.###\\n....\\n.#\\n..#.#\\n....\\n0 12 0 0 0\\n0 4 3 0 13\\n0 0 0 99 0\\n11 13 0 0 0\\n0 1 0 1 0\\n0 2 0 0 0\\n0 13 0 2 4\\n0 0 1 16 0\\n1 2 0 1 0\\n0 2 3 1 99\\n0 0 0 1 0\\n0 13 2 9 2\\n0 0 0 3 0\\n0 14 1 16 0\\n0 2 14 8 45\\n0 1\\n6 0\\n2 4\\n1 4\\n2 1\\n4 0\\n1 0\\n4 3\\n3 1\\n1 6', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 -1 0\\n,..\\n1 0 11\\n1 8 -2\\n0 1 1\\n0 1\\n1 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 5 16\\n.###\\n....\\n.#\\n..#.#\\n....\\n0 12 0 0 0\\n0 4 3 0 13\\n0 0 0 99 0\\n11 13 0 0 0\\n0 1 0 1 0\\n0 2 0 0 0\\n0 13 0 2 4\\n0 0 1 16 0\\n1 2 0 1 0\\n0 2 3 1 99\\n0 0 1 1 0\\n0 13 2 9 2\\n0 0 0 3 0\\n0 14 1 16 0\\n0 2 14 8 45\\n0 1\\n6 0\\n2 4\\n1 4\\n2 1\\n4 0\\n1 0\\n4 3\\n3 1\\n1 6', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 5, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_78725","program":"```python\nimport math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools\n\nsys.setrecursionlimit(10**7)\ninf = 10**20\neps = 1.0 / 10**13\nmod = 10**9+7\ndd = [(-1,0),(0,1),(1,0),(0,-1)]\nddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\n\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\ndef LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]\ndef LF(): return [float(x) for x in sys.stdin.readline().split()]\ndef LS(): return sys.stdin.readline().split()\ndef I(): return int(sys.stdin.readline())\ndef F(): return float(sys.stdin.readline())\ndef S(): return input()\ndef pf(s): return print(s, flush=True)\n\ndef main():\n rr = []\n\n def f():\n r,c,m = LI()\n a = [[1] * (c+2)] + [[1] + [None if c == '.' else 1 for c in S()] + [1] for _ in range(r)] + [[1] * (c+2)]\n cost = [[1] * (c+2)] + [[1] + LI() + [1] for _ in range(r)] + [[1] * (c+2)]\n on = [[1] * (c+2)] + [[1] + LI() + [1] for _ in range(r)] + [[1] * (c+2)]\n off = [[1] * (c+2)] + [[1] + LI() + [1] for _ in range(r)] + [[1] * (c+2)]\n ms = [tuple(map(lambda x: x+1, LI())) for _ in range(m)]\n e = collections.defaultdict(list)\n for i in range(1,r+1):\n for j in range(1,c+1):\n if a[i][j]:\n continue\n for di,dj in dd:\n if a[i+di][j+dj]:\n continue\n e[(i,j)].append(((i+di,j+dj), 1))\n\n def search(s):\n d = collections.defaultdict(lambda: inf)\n d[s] = 0\n q = []\n heapq.heappush(q, (0, s))\n v = collections.defaultdict(bool)\n while len(q):\n k, u = heapq.heappop(q)\n if v[u]:\n continue\n v[u] = True\n\n for uv, ud in e[u]:\n if v[uv]:\n continue\n vd = k + ud\n if d[uv] > vd:\n d[uv] = vd\n heapq.heappush(q, (vd, uv))\n\n return d\n\n ad = {}\n for k in ms:\n if k in ad:\n continue\n ad[k] = search(k)\n ti = 0\n td = collections.defaultdict(list)\n c = ms[0]\n td[c].append(0)\n for t in ms[1:]:\n while c != t:\n cc = ad[t][c]\n for di,dj in dd:\n ni = c[0] + di\n nj = c[1] + dj\n n = (ni, nj)\n if ad[t][n] == cc - 1:\n ti += 1\n td[n].append(ti)\n c = n\n break\n\n r = 0\n for k,v in sorted(td.items()):\n i = k[0]\n j = k[1]\n cs = cost[i][j]\n onf = on[i][j] + off[i][j]\n tr = onf\n for vi in range(len(v)-1):\n sa = v[vi+1] - v[vi]\n tr += min(cs * sa, onf)\n r += tr\n\n return r\n\n while True:\n rr.append(f())\n break\n\n return '\\n'.join(map(str,rr))\n\n\nprint(main())\n\n\n```","inputs":"3 3 5\n...\n.##\n..#\n1 1 1\n1 0 0\n1 1 0\n3 3 3\n3 0 0\n3 3 0\n5 4 5\n4 0 0\n5 4 0\n1 0\n2 1\n0 2\n2 0\n0 0","output":"77","actual_output":"77\n","execution_success":true,"sample_index":12546},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01735 Optimal alpha beta pruning","prompt":"Solve the following coding problem using the programming language python:\n\nFox Ciel is developing an artificial intelligence (AI) for a game. This game is described as a game tree T with n vertices. Each node in the game has an evaluation value which shows how good a situation is. This value is the same as maximum value of child nodes\u2019 values multiplied by -1. Values on leaf nodes are evaluated with Ciel\u2019s special function -- which is a bit heavy. So, she will use alpha-beta pruning for getting root node\u2019s evaluation value to decrease the number of leaf nodes to be calculated.\n\nBy the way, changing evaluation order of child nodes affects the number of calculation on the leaf nodes. Therefore, Ciel wants to know the minimum and maximum number of times to calculate in leaf nodes when she could evaluate child node in arbitrary order. She asked you to calculate minimum evaluation number of times and maximum evaluation number of times in leaf nodes.\n\nCiel uses following algotithm:\n\n\nfunction negamax(node, \u03b1, \u03b2)\nif node is a terminal node\nreturn value of leaf node\nelse\nforeach child of node\nval := -negamax(child, -\u03b2, -\u03b1)\nif val >= \u03b2\nreturn val\nif val > \u03b1\n\u03b1 := val\nreturn \u03b1\n\n\n[NOTE] negamax algorithm\n\nInput\n\nInput follows following format:\n\n\nn\np_1 p_2 ... p_n\nk_1 t_{11} t_{12} ... t_{1k}\n:\n:\nk_n t_{n1} t_{n2} ... t_{nk}\n\n\nThe first line contains an integer n, which means the number of vertices in game tree T.\nThe second line contains n integers p_i, which means the evaluation value of vertex i.\nThen, next n lines which contain the information of game tree T.\nk_i is the number of child nodes of vertex i, and t_{ij} is the indices of the child node of vertex i.\nInput follows following constraints:\n\n* 2 \\leq n \\leq 100\n* -10,000 \\leq p_i \\leq 10,000\n* 0 \\leq k_i \\leq 5\n* 2 \\leq t_{ij} \\leq n\n* Index of root node is 1.\n* Evaluation value except leaf node is always 0. This does not mean the evaluation values of non-leaf nodes are 0. You have to calculate them if necessary.\n* Leaf node sometimes have evaluation value of 0.\n* Game tree T is tree structure.\n\n\n\nOutput\n\nPrint the minimum evaluation number of times and the maximum evaluation number of times in leaf node.\nPlease separated by whitespace between minimum and maximum.\n\n\nminimum maximum\n\nSample Input 1\n\n\n3\n0 1 1\n2 2 3\n0\n0\n\n\nOutput for the Sample Input 1\n\n\n2 2\n\n\nSample Input 2\n\n\n8\n0 0 100 100 0 -100 -100 -100\n2 2 5\n2 3 4\n0\n0\n3 6 7 8\n0\n0\n0\n\n\nOutput for the Sample Input 2\n\n\n3 5\n\n\nSample Input 3\n\n\n8\n0 0 100 100 0 100 100 100\n2 2 5\n2 3 4\n0\n0\n3 6 7 8\n0\n0\n0\n\n\nOutput for the Sample Input 3\n\n\n3 4\n\n\nSample Input 4\n\n\n19\n0 100 0 100 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10\n2 2 3\n0\n2 4 5\n0\n3 6 7 8\n3 9 10 11\n3 12 13 14\n3 15 16 17\n2 18 19\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n\n\nOutput for the Sample Input 4\n\n\n7 12\n\n\n\n\n\n\nExample\n\nInput\n\n3\n0 1 1\n2 2 3\n0\n0\n\n\nOutput\n\n2 2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import deque\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\ndef solve():\n N = int(readline())\n *P, = map(int, readline().split())\n G = []\n prt = [0]*N\n for i in range(N):\n k, *t = map(int, readline().split())\n G.append([e-1 for e in t])\n for e in t:\n prt[e-1] = i\n *D, = map(len, G)\n A = [0]*N\n deg = D[:]\n que = deque()\n for v in range(N):\n if deg[v] == 0:\n A[v] = P[v]\n que.append(v)\n while que:\n v = que.popleft()\n p = prt[v]\n deg[p] -= 1\n if deg[p] == 0:\n A[p] = max(-A[w] for w in G[p])\n que.append(p)\n\n for v in range(N):\n if D[v] == 0:\n A[v] = P[v]\n else:\n A[v] = max(-A[w] for w in G[v])\n\n memo = {}\n def dfs(v, state, c, a, b):\n key = (v, state, a, b)\n if key in memo:\n return memo[key]\n if c == D[v]:\n if c == 0:\n return 1, 1\n return 0, 0\n c0 = N+1; c1 = 0\n Gv = G[v]\n for k in range(D[v]):\n if state & (1 << k):\n continue\n w = Gv[k]\n s0, s1 = dfs(w, 0, 0, -b, -a)\n val = -A[w]\n if val >= b:\n c0 = min(c0, s0); c1 = max(c1, s1)\n continue\n t0, t1 = dfs(v, state | (1 << k), c+1, max(a, val), b)\n c0 = min(c0, s0+t0)\n c1 = max(c1, s1+t1)\n memo[key] = c0, c1\n return c0, c1\n INF = 10**9\n r0, r1 = dfs(0, 0, 0, -INF, INF)\n write(\"%d %d\\n\" % (r0, r1))\nsolve()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n0 1 1\\n2 2 3\\n0\\n0', 'output': '2 2'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 1\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 2\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 2 2\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 2 0\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 2\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 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'stdin_stdout', 'input': '3\\n-1 2 -1\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 3 1\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 4 0\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 2\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 2 0\\n2 2 2\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 4 2\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 2\\n2 3 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 3\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 1 1\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 3 0\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 3\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 4 -1\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 4 2\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 4 3\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 2 2\\n2 3 2\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 3\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 0 -1\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-4 4 -1\\n2 3 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 2 0\\n2 2 2\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 6 2\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 4 -2\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-3 4 3\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 2 1\\n2 3 2\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-3 0 -1\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-4 1 -1\\n2 3 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 -1\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 12 2\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-6 4 3\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 -1\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 2 2\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 1 2\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-3 1 2\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-3 1 2\\n2 3 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 1\\n2 3 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 2 0\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 2 4\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 2\\n2 3 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 2 -2\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-3 4 0\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 4\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 1 0\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 0 0\\n2 2 3\\n0\\n1', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 6 3\\n2 2 3\\n0\\n0', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 2\\n2 3 2\\n0\\n0', 'output': '2 2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_78733","program":"```python\nfrom collections import deque\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\ndef solve():\n N = int(readline())\n *P, = map(int, readline().split())\n G = []\n prt = [0]*N\n for i in range(N):\n k, *t = map(int, readline().split())\n G.append([e-1 for e in t])\n for e in t:\n prt[e-1] = i\n *D, = map(len, G)\n A = [0]*N\n deg = D[:]\n que = deque()\n for v in range(N):\n if deg[v] == 0:\n A[v] = P[v]\n que.append(v)\n while que:\n v = que.popleft()\n p = prt[v]\n deg[p] -= 1\n if deg[p] == 0:\n A[p] = max(-A[w] for w in G[p])\n que.append(p)\n\n for v in range(N):\n if D[v] == 0:\n A[v] = P[v]\n else:\n A[v] = max(-A[w] for w in G[v])\n\n memo = {}\n def dfs(v, state, c, a, b):\n key = (v, state, a, b)\n if key in memo:\n return memo[key]\n if c == D[v]:\n if c == 0:\n return 1, 1\n return 0, 0\n c0 = N+1; c1 = 0\n Gv = G[v]\n for k in range(D[v]):\n if state & (1 << k):\n continue\n w = Gv[k]\n s0, s1 = dfs(w, 0, 0, -b, -a)\n val = -A[w]\n if val >= b:\n c0 = min(c0, s0); c1 = max(c1, s1)\n continue\n t0, t1 = dfs(v, state | (1 << k), c+1, max(a, val), b)\n c0 = min(c0, s0+t0)\n c1 = max(c1, s1+t1)\n memo[key] = c0, c1\n return c0, c1\n INF = 10**9\n r0, r1 = dfs(0, 0, 0, -INF, INF)\n write(\"%d %d\\n\" % (r0, r1))\nsolve()\n\n```","inputs":"3\n0 1 1\n2 2 3\n0\n0","output":"2 2","actual_output":"2 2\n","execution_success":true,"sample_index":12547},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02442 Lexicographical Comparison","prompt":"Solve the following coding problem using the programming language python:\n\nCompare given two sequence $A = \\\\{a_0, a_1, ..., a_{n-1}\\\\}$ and $B = \\\\{b_0, b_1, ..., b_{m-1}$ lexicographically.\n\nConstraints\n\n* $1 \\leq n, m \\leq 1,000$\n* $0 \\leq a_i, b_i \\leq 1,000$\n\nInput\n\nThe input is given in the following format.\n\n\n$n$\n$a_0 \\; a_1, ..., \\; a_{n-1}$\n$m$\n$b_0 \\; b_1, ..., \\; b_{m-1}$\n\n\nThe number of elements in $A$ and its elements $a_i$ are given in the first and second lines respectively. The number of elements in $B$ and its elements $b_i$ are given in the third and fourth lines respectively. All input are given in integers.\n\nOutput\n\nPrint 1 $B$ is greater than $A$, otherwise 0.\n\nExamples\n\nInput\n\n3\n1 2 3\n2\n2 4\n\n\nOutput\n\n1\n\n\nInput\n\n4\n5 4 7 0\n5\n1 2 3 4 5\n\n\nOutput\n\n0\n\n\nInput\n\n3\n1 1 2\n4\n1 1 2 2\n\n\nOutput\n\n1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ninput()\na = list(map(int, input().split(' ')))\ninput()\nb = list(map(int, input().split(' ')))\nprint(1 if a b_i) \u2014 the initial size of the i-th song and the size of the i-th song after compression.\n\nOutput\n\nIf it is impossible to compress a subset of the songs in such a way that all songs fit on the flash drive, print \"-1\". Otherwise print the minimum number of the songs to compress.\n\nExamples\n\nInput\n\n4 21\n10 8\n7 4\n3 1\n5 4\n\n\nOutput\n\n2\n\n\nInput\n\n4 16\n10 8\n7 4\n3 1\n5 4\n\n\nOutput\n\n-1\n\nNote\n\nIn the first example Ivan can compress the first and the third songs so after these moves the sum of sizes will be equal to 8 + 7 + 1 + 5 = 21 \u2264 21. Also Ivan can compress the first and the second songs, then the sum of sizes will be equal 8 + 4 + 3 + 5 = 20 \u2264 21. Note that compressing any single song is not sufficient to copy all the songs on the flash drive (for example, after compressing the second song the sum of sizes will be equal to 10 + 4 + 3 + 5 = 22 > 21).\n\nIn the second example even if Ivan compresses all the songs the sum of sizes will be equal 8 + 4 + 1 + 4 = 17 > 16.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,m = input().split()\nn=int(n)\nm=int(m)\n\nsongs=list()\n\nfor i in range(n):\n songs.append([int(c) for c in input().split()])\n\n\ndef sumList(lista,inx):\n sum=0\n for i in range(len(lista)):\n sum+=lista[i][inx]\n return sum\n\nsongs=sorted(songs,key=lambda x: x[1]-x[0])\n\n\nsuma = sumList(songs,0)\n\n\nfor i in range(n):\n if(suma<=m):\n print(i)\n exit()\n suma-= songs[i][0]-songs[i][1]\n\nif(suma<=m):\n print(n)\nelse:\n print(-1)\n\n```","verification_info":"{'test_cases': 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'1 1992779579\\n1000010000 999999999\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 110\\n2 1\\n3 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n4 2\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 1992779579\\n1000100000 257873703\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 783437387\\n1000100010 999999999\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 190054531\\n1100100010 999999999\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 7\\n2 1\\n2 0\\n2 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 1000000000\\n0000010000 999999999\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n2 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 10\\n2 0\\n4 1\\n2 1\\n2 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 100\\n2 3\\n3 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 3\\n2 2\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78781","program":"```python\nn,m = input().split()\nn=int(n)\nm=int(m)\n\nsongs=list()\n\nfor i in range(n):\n songs.append([int(c) for c in input().split()])\n\n\ndef sumList(lista,inx):\n sum=0\n for i in range(len(lista)):\n sum+=lista[i][inx]\n return sum\n\nsongs=sorted(songs,key=lambda x: x[1]-x[0])\n\n\nsuma = sumList(songs,0)\n\n\nfor i in range(n):\n if(suma<=m):\n print(i)\n exit()\n suma-= songs[i][0]-songs[i][1]\n\nif(suma<=m):\n print(n)\nelse:\n print(-1)\n\n```","inputs":"4 16\n10 8\n7 4\n3 1\n5 4\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12550},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1039_A. Timetable","prompt":"Solve the following coding problem using the programming language python:\n\nThere are two bus stops denoted A and B, and there n buses that go from A to B every day. The shortest path from A to B takes t units of time but some buses might take longer paths. Moreover, buses are allowed to overtake each other during the route.\n\nAt each station one can find a sorted list of moments of time when a bus is at this station. We denote this list as a_1 < a_2 < \u2026 < a_n for stop A and as b_1 < b_2 < \u2026 < b_n for stop B. The buses always depart from A and arrive to B according to the timetable, but the order in which the buses arrive may differ. Let's call an order of arrivals valid if each bus arrives at least t units of time later than departs.\n\nIt is known that for an order to be valid the latest possible arrival for the bus that departs at a_i is b_{x_i}, i.e. x_i-th in the timetable. In other words, for each i there exists such a valid order of arrivals that the bus departed i-th arrives x_i-th (and all other buses can arrive arbitrary), but there is no valid order of arrivals in which the i-th departed bus arrives (x_i + 1)-th.\n\nFormally, let's call a permutation p_1, p_2, \u2026, p_n valid, if b_{p_i} \u2265 a_i + t for all i. Then x_i is the maximum value of p_i among all valid permutations.\n\nYou are given the sequences a_1, a_2, \u2026, a_n and x_1, x_2, \u2026, x_n, but not the arrival timetable. Find out any suitable timetable for stop B b_1, b_2, \u2026, b_n or determine that there is no such timetable.\n\nInput\n\nThe first line of the input contains two integers n and t (1 \u2264 n \u2264 200 000, 1 \u2264 t \u2264 10^{18}) \u2014 the number of buses in timetable for and the minimum possible travel time from stop A to stop B.\n\nThe second line contains n integers a_1, a_2, \u2026, a_n (1 \u2264 a_1 < a_2 < \u2026 < a_n \u2264 10^{18}), defining the moments of time when the buses leave stop A.\n\nThe third line contains n integers x_1, x_2, \u2026, x_n (1 \u2264 x_i \u2264 n), the i-th of them stands for the maximum possible timetable position, at which the i-th bus leaving stop A can arrive at stop B. \n\nOutput\n\nIf a solution exists, print \"Yes\" (without quotes) in the first line of the output.\n\nIn the second line print n integers b_1, b_2, \u2026, b_n (1 \u2264 b_1 < b_2 < \u2026 < b_n \u2264 3 \u22c5 10^{18}). We can show that if there exists any solution, there exists a solution that satisfies such constraints on b_i. If there are multiple valid answers you can print any of them.\n\nIf there is no valid timetable, print \"No\" (without quotes) in the only line of the output.\n\nExamples\n\nInput\n\n3 10\n4 6 8\n2 2 3\n\n\nOutput\n\nYes\n16 17 21 \n\n\nInput\n\n2 1\n1 2\n2 1\n\n\nOutput\n\nNo\n\nNote\n\nConsider the first example and the timetable b_1, b_2, \u2026, b_n from the output.\n\nTo get x_1 = 2 the buses can arrive in the order (2, 1, 3). To get x_2 = 2 and x_3 = 3 the buses can arrive in the order (1, 2, 3). x_1 is not 3, because the permutations (3, 1, 2) and (3, 2, 1) (all in which the 1-st bus arrives 3-rd) are not valid (sube buses arrive too early), x_2 is not 3 because of similar reasons.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef read():\n return list(map(int, input().split(' ')))\ndef fail():\n print('No')\n exit(0)\n\nn, t = read()\naa = read()\nxx = read()\n\nres = [0] * n\nprevX = 0\nprevV = -10\n\nfor i in range(n):\n x = xx[i] - 1\n if x < prevX or x < i:\n fail()\n\n prevX = x\n res[i] = prevV = max(aa[i + 1] + t if x > i else aa[i] + t , prevV + 1)\n\nfor i in range(n):\n x = xx[i] - 1\n if x + 1 < n and res[x] >= aa[x + 1] + t:\n fail()\n\nprint('Yes')\nprint(*res)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 1\\n1 2\\n2 1\\n', 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0\\n2 1 2\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n7 2 1\\n2 2 2\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '2 0000000000\\n133259944 1000000000\\n2 1\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n0 5\\n1 1\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3 32\\n7 6 15\\n2 3 2\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n3 10\\n2 1\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n4 6 1\\n2 2 1\\n', 'output': 'No\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_78785","program":"```python\ndef read():\n return list(map(int, input().split(' ')))\ndef fail():\n print('No')\n exit(0)\n\nn, t = read()\naa = read()\nxx = read()\n\nres = [0] * n\nprevX = 0\nprevV = -10\n\nfor i in range(n):\n x = xx[i] - 1\n if x < prevX or x < i:\n fail()\n\n prevX = x\n res[i] = prevV = max(aa[i + 1] + t if x > i else aa[i] + t , prevV + 1)\n\nfor i in range(n):\n x = xx[i] - 1\n if x + 1 < n and res[x] >= aa[x + 1] + t:\n fail()\n\nprint('Yes')\nprint(*res)\n\n```","inputs":"2 1\n1 2\n2 1\n","output":"No\n","actual_output":"No\n","execution_success":true,"sample_index":12551},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1061_C. Multiplicity","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given an integer array a_1, a_2, \u2026, a_n.\n\nThe array b is called to be a subsequence of a if it is possible to remove some elements from a to get b.\n\nArray b_1, b_2, \u2026, b_k is called to be good if it is not empty and for every i (1 \u2264 i \u2264 k) b_i is divisible by i.\n\nFind the number of good subsequences in a modulo 10^9 + 7. \n\nTwo subsequences are considered different if index sets of numbers included in them are different. That is, the values \u200bof the elements \u200bdo not matter in the comparison of subsequences. In particular, the array a has exactly 2^n - 1 different subsequences (excluding an empty subsequence).\n\nInput\n\nThe first line contains an integer n (1 \u2264 n \u2264 100 000) \u2014 the length of the array a.\n\nThe next line contains integers a_1, a_2, \u2026, a_n (1 \u2264 a_i \u2264 10^6).\n\nOutput\n\nPrint exactly one integer \u2014 the number of good subsequences taken modulo 10^9 + 7.\n\nExamples\n\nInput\n\n2\n1 2\n\n\nOutput\n\n3\n\nInput\n\n5\n2 2 1 22 14\n\n\nOutput\n\n13\n\nNote\n\nIn the first example, all three non-empty possible subsequences are good: \\{1\\}, \\{1, 2\\}, \\{2\\}\n\nIn the second example, the possible good subsequences are: \\{2\\}, \\{2, 2\\}, \\{2, 22\\}, \\{2, 14\\}, \\{2\\}, \\{2, 22\\}, \\{2, 14\\}, \\{1\\}, \\{1, 22\\}, \\{1, 14\\}, \\{22\\}, \\{22, 14\\}, \\{14\\}.\n\nNote, that some subsequences are listed more than once, since they occur in the original array multiple times.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\n\ndef nextDiv(a):\n ret = []\n i = 1;\n while (i*i <= a):\n if (a%i == 0):\n ret.append(i)\n j = a//i\n if (i != j):\n ret.append(j)\n i += 1\n return reversed(ret)\n\nMOD = int(1e9+7)\n\ndef solve(n, lis):\n dp = [0] * (max(lis)+1)\n dp[0] = 1\n\n for i in lis:\n for j in nextDiv(i):\n dp[j] += dp[j-1]\n dp[j] %= MOD\n\n return (sum(dp)-1) % MOD\n\n###########################\n###########################\n\nfrom sys import stdin\ndef intRead():\n while True:\n ln = stdin.readline().strip()\n if not ln:\n return\n for i in map(int, ln.split()):\n yield i\n\nif __name__ == \"__main__\":\n ipt = intRead()\n n = next(ipt)\n lis = [next(ipt) for _ in range(n)]\n print(solve(n, lis))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n1 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 1 22 14\\n', 'output': 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'1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78789","program":"```python\nimport math\n\ndef nextDiv(a):\n ret = []\n i = 1;\n while (i*i <= a):\n if (a%i == 0):\n ret.append(i)\n j = a//i\n if (i != j):\n ret.append(j)\n i += 1\n return reversed(ret)\n\nMOD = int(1e9+7)\n\ndef solve(n, lis):\n dp = [0] * (max(lis)+1)\n dp[0] = 1\n\n for i in lis:\n for j in nextDiv(i):\n dp[j] += dp[j-1]\n dp[j] %= MOD\n\n return (sum(dp)-1) % MOD\n\n###########################\n###########################\n\nfrom sys import stdin\ndef intRead():\n while True:\n ln = stdin.readline().strip()\n if not ln:\n return\n for i in map(int, ln.split()):\n yield i\n\nif __name__ == \"__main__\":\n ipt = intRead()\n n = next(ipt)\n lis = [next(ipt) for _ in range(n)]\n print(solve(n, lis))\n\n```","inputs":"2\n1 2\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12552},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1083_B. The Fair Nut and Strings","prompt":"Solve the following coding problem using the programming language python:\n\nRecently, the Fair Nut has written k strings of length n, consisting of letters \"a\" and \"b\". He calculated c \u2014 the number of strings that are prefixes of at least one of the written strings. Every string was counted only one time.\n\nThen, he lost his sheet with strings. He remembers that all written strings were lexicographically not smaller than string s and not bigger than string t. He is interested: what is the maximum value of c that he could get.\n\nA string a is lexicographically smaller than a string b if and only if one of the following holds:\n\n * a is a prefix of b, but a \u2260 b;\n * in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.\n\nInput\n\nThe first line contains two integers n and k (1 \u2264 n \u2264 5 \u22c5 10^5, 1 \u2264 k \u2264 10^9).\n\nThe second line contains a string s (|s| = n) \u2014 the string consisting of letters \"a\" and \"b.\n\nThe third line contains a string t (|t| = n) \u2014 the string consisting of letters \"a\" and \"b.\n\nIt is guaranteed that string s is lexicographically not bigger than t.\n\nOutput\n\nPrint one number \u2014 maximal value of c.\n\nExamples\n\nInput\n\n\n2 4\naa\nbb\n\n\nOutput\n\n\n6\n\n\nInput\n\n\n3 3\naba\nbba\n\n\nOutput\n\n\n8\n\n\nInput\n\n\n4 5\nabbb\nbaaa\n\n\nOutput\n\n\n8\n\nNote\n\nIn the first example, Nut could write strings \"aa\", \"ab\", \"ba\", \"bb\". These 4 strings are prefixes of at least one of the written strings, as well as \"a\" and \"b\". Totally, 6 strings.\n\nIn the second example, Nut could write strings \"aba\", \"baa\", \"bba\".\n\nIn the third example, there are only two different strings that Nut could write. If both of them are written, c=8.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nd = {'a': 0, 'b': 1}\ndef process(s, t, k):\n n = len(s)\n answer = 0\n D = 0\n final_i = n\n for i in range(n):\n d1 = d[s[i]]\n d2 = d[t[i]]\n D = 2*(D)+d2-d1\n if D+1 < k:\n answer+=(D+1)\n else:\n final_i = i\n break \n answer+=k*(n-final_i)\n return answer\n\nn, k = [int(x) for x in input().split()]\ns = input()\nt = input()\nprint(process(s, t, k))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 4\\naa\\nbb\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\nabbb\\nbaaa\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\naba\\nbba\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '100 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= 0\n final_i = n\n for i in range(n):\n d1 = d[s[i]]\n d2 = d[t[i]]\n D = 2*(D)+d2-d1\n if D+1 < k:\n answer+=(D+1)\n else:\n final_i = i\n break \n answer+=k*(n-final_i)\n return answer\n\nn, k = [int(x) for x in input().split()]\ns = input()\nt = input()\nprint(process(s, t, k))\n```","inputs":"2 4\naa\nbb\n","output":"6\n","actual_output":"6\n","execution_success":true,"sample_index":12553},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1102_D. Balanced Ternary String","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a string s consisting of exactly n characters, and each character is either '0', '1' or '2'. Such strings are called ternary strings.\n\nYour task is to replace minimum number of characters in this string with other characters to obtain a balanced ternary string (balanced ternary string is a ternary string such that the number of characters '0' in this string is equal to the number of characters '1', and the number of characters '1' (and '0' obviously) is equal to the number of characters '2').\n\nAmong all possible balanced ternary strings you have to obtain the lexicographically (alphabetically) smallest.\n\nNote that you can neither remove characters from the string nor add characters to the string. Also note that you can replace the given characters only with characters '0', '1' and '2'.\n\nIt is guaranteed that the answer exists.\n\nInput\n\nThe first line of the input contains one integer n (3 \u2264 n \u2264 3 \u22c5 10^5, n is divisible by 3) \u2014 the number of characters in s.\n\nThe second line contains the string s consisting of exactly n characters '0', '1' and '2'.\n\nOutput\n\nPrint one string \u2014 the lexicographically (alphabetically) smallest balanced ternary string which can be obtained from the given one with minimum number of replacements.\n\nBecause n is divisible by 3 it is obvious that the answer exists. And it is obvious that there is only one possible answer.\n\nExamples\n\nInput\n\n\n3\n121\n\n\nOutput\n\n\n021\n\n\nInput\n\n\n6\n000000\n\n\nOutput\n\n\n001122\n\n\nInput\n\n\n6\n211200\n\n\nOutput\n\n\n211200\n\n\nInput\n\n\n6\n120110\n\n\nOutput\n\n\n120120\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom bisect import bisect_left as bl, bisect_right as br, insort\nimport sys\nimport heapq\n# from math import *\nfrom collections import defaultdict as dd, deque\ndef data(): return sys.stdin.readline().strip()\ndef mdata(): return map(int, data().split())\n# sys.setrecursionlimit(1000000)\nmod = 998244353\n\nn=int(data())\ns=data()\ns1=list(s)\nd={'0':0,'1':0,'2':0}\nfor i in range(n):\n d[s[i]]+=1\nt=n//3\nif d['0']t:\n for j in sorted(d.keys()):\n if d[j]t:\n for j in sorted(d.keys(),reverse=True):\n if d[j]s1[i]:\n d[j]+=1\n d[s1[i]] -= 1\n s1[i]=j\n break\nprint(''.join(s1))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6\\n000000\\n', 'output': '001122\\n'}, {'type': 'stdin_stdout', 'input': '3\\n121\\n', 'output': '021\\n'}, {'type': 'stdin_stdout', 'input': '6\\n120110\\n', 'output': '120120\\n'}, {'type': 'stdin_stdout', 'input': '6\\n211200\\n', 'output': '211200\\n'}, {'type': 'stdin_stdout', 'input': '12\\n000022220000\\n', 'output': '000022221111\\n'}, {'type': 'stdin_stdout', 'input': '3\\n122\\n', 'output': '102\\n'}, {'type': 'stdin_stdout', 'input': '12\\n111111111111\\n', 'output': '000011112222\\n'}, {'type': 'stdin_stdout', 'input': '12\\n012012222000\\n', 'output': '011012222001\\n'}, {'type': 'stdin_stdout', 'input': '6\\n002202\\n', 'output': '001212\\n'}, {'type': 'stdin_stdout', 'input': '3\\n022\\n', 'output': '012\\n'}, {'type': 'stdin_stdout', 'input': '3\\n020\\n', 'output': '021\\n'}, {'type': 'stdin_stdout', 'input': '3\\n211\\n', 'output': '201\\n'}, {'type': 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'stdin_stdout', 'input': '12\\n100011101110\\n', 'output': '100011102222\\n'}, {'type': 'stdin_stdout', 'input': '6\\n100010\\n', 'output': '100212\\n'}, {'type': 'stdin_stdout', 'input': '12\\n100011100110\\n', 'output': '100011102222\\n'}, {'type': 'stdin_stdout', 'input': '6\\n101010\\n', 'output': '101022\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78797","program":"```python\nfrom bisect import bisect_left as bl, bisect_right as br, insort\nimport sys\nimport heapq\n# from math import *\nfrom collections import defaultdict as dd, deque\ndef data(): return sys.stdin.readline().strip()\ndef mdata(): return map(int, data().split())\n# sys.setrecursionlimit(1000000)\nmod = 998244353\n\nn=int(data())\ns=data()\ns1=list(s)\nd={'0':0,'1':0,'2':0}\nfor i in range(n):\n d[s[i]]+=1\nt=n//3\nif d['0']t:\n for j in sorted(d.keys()):\n if d[j]t:\n for j in sorted(d.keys(),reverse=True):\n if d[j]s1[i]:\n d[j]+=1\n d[s1[i]] -= 1\n s1[i]=j\n break\nprint(''.join(s1))\n```","inputs":"6\n000000\n","output":"001122\n","actual_output":"001122\n","execution_success":true,"sample_index":12554},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1130_D1. Toy Train (Simplified)","prompt":"Solve the following coding problem using the programming language python:\n\nThis is a simplified version of the task Toy Train. These two versions differ only in the constraints. Hacks for this version are disabled.\n\nAlice received a set of Toy Train\u2122 from Bob. It consists of one train and a connected railway network of n stations, enumerated from 1 through n. The train occupies one station at a time and travels around the network of stations in a circular manner. More precisely, the immediate station that the train will visit after station i is station i+1 if 1 \u2264 i < n or station 1 if i = n. It takes the train 1 second to travel to its next station as described.\n\nBob gave Alice a fun task before he left: to deliver m candies that are initially at some stations to their independent destinations using the train. The candies are enumerated from 1 through m. Candy i (1 \u2264 i \u2264 m), now at station a_i, should be delivered to station b_i (a_i \u2260 b_i).\n\n The blue numbers on the candies correspond to b_i values. The image corresponds to the 1-st example.\n\nThe train has infinite capacity, and it is possible to load off any number of candies at a station. However, only at most one candy can be loaded from a station onto the train before it leaves the station. You can choose any candy at this station. The time it takes to move the candies is negligible.\n\nNow, Alice wonders how much time is needed for the train to deliver all candies. Your task is to find, for each station, the minimum time the train would need to deliver all the candies were it to start from there.\n\nInput\n\nThe first line contains two space-separated integers n and m (2 \u2264 n \u2264 100; 1 \u2264 m \u2264 200) \u2014 the number of stations and the number of candies, respectively.\n\nThe i-th of the following m lines contains two space-separated integers a_i and b_i (1 \u2264 a_i, b_i \u2264 n; a_i \u2260 b_i) \u2014 the station that initially contains candy i and the destination station of the candy, respectively.\n\nOutput\n\nIn the first and only line, print n space-separated integers, the i-th of which is the minimum time, in seconds, the train would need to deliver all the candies were it to start from station i.\n\nExamples\n\nInput\n\n\n5 7\n2 4\n5 1\n2 3\n3 4\n4 1\n5 3\n3 5\n\n\nOutput\n\n\n10 9 10 10 9 \n\n\nInput\n\n\n2 3\n1 2\n1 2\n1 2\n\n\nOutput\n\n\n5 6 \n\nNote\n\nConsider the second sample.\n\nIf the train started at station 1, the optimal strategy is as follows.\n\n 1. Load the first candy onto the train. \n 2. Proceed to station 2. This step takes 1 second. \n 3. Deliver the first candy. \n 4. Proceed to station 1. This step takes 1 second. \n 5. Load the second candy onto the train. \n 6. Proceed to station 2. This step takes 1 second. \n 7. Deliver the second candy. \n 8. Proceed to station 1. This step takes 1 second. \n 9. Load the third candy onto the train. \n 10. Proceed to station 2. This step takes 1 second. \n 11. Deliver the third candy. \n\n\n\nHence, the train needs 5 seconds to complete the tasks.\n\nIf the train were to start at station 2, however, it would need to move to station 1 before it could load the first candy, which would take one additional second. Thus, the answer in this scenario is 5+1 = 6 seconds.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import defaultdict as dd\nn,m=[int(i) for i in input().split(' ')]\na=[]\nb=[]\n\ndef fnx(i,j):\n if i2:\n return \"cslnb\"\n if dic[x]==2:\n count.add(x)\n y=x-1\n if y in dic:\n return \"cslnb\"\n if len(count)>1:\n return \"cslnb\"\n \n if 0 in count:\n return \"cslnb\"\n \n temp=0\n for i in range(N):\n temp+=A[i]-i\n if temp%2==1:\n return \"sjfnb\"\n return \"cslnb\"\ninput()\nA=list(map(int,input().strip().split(' ')))\nprint(find(A))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n2 2\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 0\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 1\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 2 1 0\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 3\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n22534187 22534186 22534186\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '9\\n8004 5687 1235 8004 5687 1235 999 789555 1222235\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '14\\n6 66 89 84 89 66 123456 98745 3685 21457 15987 36528 14578 98633\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 2 2 5\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 0 0 999 555\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 2 10000\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 5\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 3 4 4\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 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{'type': 'stdin_stdout', 'input': '3\\n21062719 8398348 21062719\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n78701038 78701035 28019751\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 0 0 5 9\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 5 5\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n44450762 44450762 72146840\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '4\\n11 14 12 14\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 0 1 5 6\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 4 4\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8579732 11134051 8579732\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 3\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 6\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 2\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 5 7 6\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 3\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '14\\n6 66 89 84 89 66 123456 177370 3685 21457 15987 36528 14578 98658\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 4 6\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 2 4\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 1 2 1\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 4 4\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 5 5 5 8\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 1 14 9 9\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 1 2\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n96067438 167610868 96067435\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2766251 4178848 4178848\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 12 7 8\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 5 3 5\\n', 'output': 'sjfnb\\n'}, {'type': 'stdin_stdout', 'input': '9\\n8004 6956 1235 8004 5687 1235 999 789555 1222230\\n', 'output': 'cslnb\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 0 4 4 7\\n', 'output': 'sjfnb\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78813","program":"```python\ndef find(A):\n from collections import defaultdict\n A=sorted(A)\n N=len(A)\n dic=defaultdict(int)\n for i in range(N):\n dic[A[i]]+=1\n \n checked=[]\n count=set([])\n for x in A:\n if dic[x]>2:\n return \"cslnb\"\n if dic[x]==2:\n count.add(x)\n y=x-1\n if y in dic:\n return \"cslnb\"\n if len(count)>1:\n return \"cslnb\"\n \n if 0 in count:\n return \"cslnb\"\n \n temp=0\n for i in range(N):\n temp+=A[i]-i\n if temp%2==1:\n return \"sjfnb\"\n return \"cslnb\"\ninput()\nA=list(map(int,input().strip().split(' ')))\nprint(find(A))\n```","inputs":"2\n2 2\n","output":"sjfnb\n","actual_output":"sjfnb\n","execution_success":true,"sample_index":12556},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1228_E. Another Filling the Grid","prompt":"Solve the following coding problem using the programming language python:\n\nYou have n \u00d7 n square grid and an integer k. Put an integer in each cell while satisfying the conditions below.\n\n * All numbers in the grid should be between 1 and k inclusive. \n * Minimum number of the i-th row is 1 (1 \u2264 i \u2264 n). \n * Minimum number of the j-th column is 1 (1 \u2264 j \u2264 n). \n\n\n\nFind the number of ways to put integers in the grid. Since the answer can be very large, find the answer modulo (10^{9} + 7).\n\n These are the examples of valid and invalid grid when n=k=2. \n\nInput\n\nThe only line contains two integers n and k (1 \u2264 n \u2264 250, 1 \u2264 k \u2264 10^{9}).\n\nOutput\n\nPrint the answer modulo (10^{9} + 7).\n\nExamples\n\nInput\n\n\n2 2\n\n\nOutput\n\n\n7\n\n\nInput\n\n\n123 456789\n\n\nOutput\n\n\n689974806\n\nNote\n\nIn the first example, following 7 cases are possible.\n\n\n\nIn the second example, make sure you print the answer modulo (10^{9} + 7).\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef Solve(n,k):\n mod = 10**9+7\n max_n = 10**4\n#precalcular los factoriales\n fac = [1] + [0] * max_n\n fac_i = [1] + [0] * max_n\n for i in range(1,n+1):\n fac[i] = fac[i-1] * (i) % mod\n fac_i[i] = fac_i[i- 1] * pow(i,mod-2,mod) % mod\n\n#calculo de las combinaciones con factorial inverso\n def mod_nCr(n,r):\n if n==0 and r==0:\n return 1\n if n 0:\n print(\"No\")\n else:\n print(\"Yes\")\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 5\\n2 3\\n1 4\\n2 4\\n2 3\\n1 4\\n', 'output': 'Yes\\nNo\\nNo\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '76183 37\\n1 68009\\n2 68008\\n2 68008\\n2 51883\\n1 51882\\n2 51883\\n2 51881\\n2 51881\\n2 51881\\n2 51881\\n2 68008\\n2 68008\\n2 68008\\n2 68008\\n2 51881\\n2 40751\\n2 51881\\n2 51881\\n2 51881\\n2 2204\\n1 40750\\n2 40751\\n2 62512\\n2 68008\\n2 68008\\n2 40749\\n2 33598\\n2 40749\\n1 33597\\n2 33598\\n2 33596\\n2 54671\\n1 65682\\n2 33596\\n1 62511\\n2 62512\\n2 62510\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 4\\n', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '327 22\\n2 68\\n1 67\\n1 214\\n2 68\\n2 213\\n2 213\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 213\\n2 213\\n1 15\\n2 14\\n2 14\\n2 213\\n2 213\\n2 66\\n2 66\\n2 14\\n', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 42\\n1 4\\n1 2\\n2 2\\n2 8\\n1 10\\n1 7\\n2 8\\n2 3\\n1 9\\n1 2\\n2 4\\n2 8\\n2 4\\n1 7\\n2 3\\n1 9\\n1 6\\n2 7\\n2 7\\n1 10\\n1 2\\n1 10\\n2 7\\n1 5\\n2 2\\n1 4\\n1 10\\n1 2\\n2 6\\n2 9\\n1 7\\n1 2\\n1 7\\n2 3\\n1 10\\n2 7\\n2 5\\n2 5\\n1 10\\n1 8\\n2 9\\n1 6\\n', 'output': 'Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '100000 46\\n1 82674\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 87908\\n2 58694\\n1 58693\\n2 58694\\n2 82673\\n2 82673\\n1 87907\\n2 87908\\n2 82673\\n2 82673\\n1 64610\\n2 64609\\n2 64609\\n2 58692\\n2 58692\\n2 64609\\n2 64609\\n2 64609\\n2 64609\\n2 87906\\n2 87906\\n2 64609\\n2 22164\\n2 2840\\n2 43302\\n2 64609\\n2 58692\\n2 58692\\n2 87906\\n2 87906\\n1 22163\\n2 76010\\n2 22164\\n2 64609\\n2 64609\\n1 43301\\n2 43302\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n2 1\\n1 2\\n', 'output': 'Yes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n2 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '100000 6\\n2 72326\\n1 72325\\n2 72326\\n2 72324\\n2 72324\\n2 91418\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '3 68\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 3\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n1 2\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '73034 53\\n2 21523\\n1 21522\\n2 21523\\n2 21521\\n2 37146\\n2 21521\\n2 21521\\n2 21521\\n1 37145\\n2 37146\\n1 54737\\n2 66924\\n2 21521\\n2 28767\\n2 21521\\n2 21521\\n2 21521\\n1 28766\\n2 28767\\n2 54736\\n2 54736\\n2 31558\\n2 37144\\n2 41201\\n1 60566\\n2 15970\\n2 37144\\n2 25868\\n1 277\\n2 1743\\n1 25867\\n2 25868\\n1 40857\\n1 38088\\n2 21521\\n2 21521\\n1 15969\\n2 39373\\n1 51066\\n2 15970\\n1 24859\\n2 28765\\n2 28765\\n2 60565\\n2 60565\\n2 21521\\n2 21521\\n2 38087\\n2 38087\\n2 21521\\n2 21521\\n2 45056\\n2 21521\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '3 27\\n2 2\\n2 2\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n1 2\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n1 3\\n2 2\\n2 2\\n2 1\\n', 'output': 'Yes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n2 1\\n1 2\\n1 2\\n1 2\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '327 22\\n2 68\\n1 67\\n1 214\\n2 68\\n2 213\\n2 213\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 213\\n2 213\\n1 17\\n2 14\\n2 14\\n2 213\\n2 213\\n2 66\\n2 66\\n2 14\\n', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '10 42\\n1 4\\n1 2\\n2 2\\n2 8\\n1 10\\n1 7\\n2 8\\n2 3\\n1 9\\n1 2\\n2 4\\n2 8\\n2 4\\n1 7\\n2 3\\n1 9\\n1 6\\n2 7\\n2 7\\n1 10\\n1 2\\n1 10\\n2 7\\n1 5\\n2 2\\n1 4\\n1 10\\n1 2\\n2 4\\n2 9\\n1 7\\n1 2\\n1 7\\n2 3\\n1 10\\n2 7\\n2 5\\n2 5\\n1 10\\n1 8\\n2 9\\n1 6\\n', 'output': 'Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n2 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 68\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 3\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n1 2\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 42\\n1 4\\n1 2\\n2 2\\n2 8\\n1 10\\n1 7\\n2 8\\n2 3\\n1 9\\n1 2\\n2 4\\n2 8\\n2 4\\n1 2\\n2 3\\n1 9\\n1 6\\n2 7\\n2 7\\n1 10\\n1 2\\n1 10\\n2 7\\n1 5\\n2 2\\n1 4\\n1 10\\n1 2\\n2 4\\n2 9\\n1 7\\n1 2\\n1 7\\n2 3\\n1 10\\n2 7\\n2 5\\n2 5\\n1 10\\n1 8\\n2 9\\n1 6\\n', 'output': 'Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '100000 46\\n1 82674\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 61968\\n2 82673\\n2 82673\\n2 87908\\n2 58694\\n1 58693\\n2 58694\\n2 82673\\n2 82673\\n1 87907\\n2 87908\\n2 82673\\n2 82673\\n1 64610\\n2 64609\\n2 64609\\n2 58692\\n2 58692\\n2 64609\\n2 64609\\n2 64609\\n2 64609\\n2 87906\\n2 87906\\n2 64609\\n2 22164\\n2 2840\\n2 43302\\n2 64609\\n2 58692\\n2 58692\\n2 87906\\n2 87906\\n1 22163\\n2 76010\\n2 22164\\n2 64609\\n2 64609\\n1 43301\\n2 43302\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n2 8\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '3 27\\n2 2\\n2 2\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n1 2\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 2\\n2 1\\n2 1\\n1 3\\n2 2\\n2 2\\n2 1\\n', 'output': 'Yes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n1 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 42\\n1 6\\n1 2\\n2 2\\n2 8\\n1 10\\n1 7\\n2 8\\n2 3\\n1 9\\n1 2\\n2 4\\n2 8\\n2 4\\n1 2\\n2 3\\n1 9\\n1 6\\n2 7\\n2 7\\n1 10\\n1 2\\n1 10\\n2 7\\n1 5\\n2 2\\n1 4\\n1 10\\n1 2\\n2 4\\n2 9\\n1 7\\n1 2\\n1 7\\n2 3\\n1 10\\n2 7\\n2 5\\n2 5\\n1 10\\n1 8\\n2 9\\n1 6\\n', 'output': 'Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 3\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n1 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '3 27\\n2 2\\n2 2\\n1 2\\n2 1\\n2 1\\n2 1\\n2 2\\n2 1\\n1 2\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 2\\n2 1\\n2 1\\n1 3\\n2 2\\n2 2\\n2 1\\n', 'output': 'Yes\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n1 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n1 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n2 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 3\\n2 2\\n2 2\\n2 2\\n1 4\\n1 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n1 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n2 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '1260 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 68\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '1260 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 2\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 68\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '76183 37\\n1 68009\\n2 68008\\n2 68008\\n2 51883\\n1 51882\\n2 51883\\n2 51881\\n1 51881\\n2 51881\\n2 51881\\n2 68008\\n2 68008\\n2 68008\\n2 68008\\n2 51881\\n2 40751\\n2 51881\\n2 51881\\n2 51881\\n2 2204\\n1 40750\\n2 40751\\n2 62512\\n2 68008\\n2 68008\\n2 40749\\n2 33598\\n2 40749\\n1 33597\\n2 33598\\n2 33596\\n2 54671\\n1 65682\\n2 33596\\n1 62511\\n2 62512\\n2 62510\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 4\\n', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '327 22\\n2 68\\n1 67\\n1 214\\n2 63\\n2 213\\n2 213\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 213\\n2 213\\n1 15\\n2 14\\n2 14\\n2 213\\n2 213\\n2 66\\n2 66\\n2 14\\n', 'output': 'Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '100000 46\\n1 82674\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 87908\\n2 58694\\n1 58693\\n2 58694\\n2 82673\\n2 82673\\n1 87907\\n2 87908\\n2 82673\\n2 82673\\n1 64610\\n2 64609\\n2 64609\\n2 58692\\n2 58692\\n2 64609\\n2 64609\\n2 64609\\n2 64609\\n2 87906\\n2 87906\\n2 64609\\n2 22164\\n2 2840\\n2 43302\\n2 64609\\n2 58692\\n2 58692\\n2 87906\\n2 87906\\n1 22163\\n2 76010\\n2 22164\\n2 64609\\n2 64609\\n1 37649\\n2 43302\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n2 5\\n1 4\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n2 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '3 27\\n2 2\\n2 2\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n1 2\\n1 2\\n2 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n1 3\\n2 2\\n2 2\\n2 1\\n', 'output': 'Yes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 82\\n1 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n2 1\\n1 2\\n1 2\\n1 2\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '327 22\\n1 68\\n1 67\\n1 214\\n2 68\\n2 213\\n2 213\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 213\\n2 213\\n1 17\\n2 14\\n2 14\\n2 213\\n2 213\\n2 66\\n2 66\\n2 14\\n', 'output': 'Yes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '100000 46\\n1 82674\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 61968\\n2 82673\\n2 82673\\n2 30744\\n2 58694\\n1 58693\\n2 58694\\n2 82673\\n2 82673\\n1 87907\\n2 87908\\n2 82673\\n2 82673\\n1 64610\\n2 64609\\n2 64609\\n2 58692\\n2 58692\\n2 64609\\n2 64609\\n2 64609\\n2 64609\\n2 87906\\n2 87906\\n2 64609\\n2 22164\\n2 2840\\n2 43302\\n2 64609\\n2 58692\\n2 58692\\n2 87906\\n2 87906\\n1 22163\\n2 76010\\n2 22164\\n2 64609\\n2 64609\\n1 43301\\n2 43302\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n1 74\\n2 74\\n2 74\\n1 323\\n2 87\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 309\\n2 702\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 3\\n2 2\\n2 2\\n2 2\\n1 4\\n1 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 5\\n1 5\\n2 6\\n2 9\\n1 2\\n1 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n2 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '1260 14\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '1260 26\\n1 75\\n2 74\\n2 74\\n2 56\\n2 87\\n2 2\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 68\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '100000 46\\n1 82674\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 87908\\n2 58694\\n1 58693\\n2 58694\\n2 82673\\n2 82673\\n1 87907\\n2 87908\\n2 82673\\n2 82673\\n1 64610\\n2 64609\\n2 64609\\n2 58692\\n2 58692\\n2 94017\\n2 64609\\n2 64609\\n2 64609\\n2 87906\\n2 87906\\n2 64609\\n2 22164\\n2 2840\\n2 43302\\n2 64609\\n2 58692\\n2 58692\\n2 87906\\n2 87906\\n1 22163\\n2 76010\\n2 22164\\n2 64609\\n2 64609\\n1 37649\\n2 43302\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n2 5\\n1 4\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 9\\n2 6\\n2 4\\n2 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 82\\n1 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 526\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n2 1\\n1 2\\n1 2\\n2 2\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 3\\n2 2\\n2 2\\n2 2\\n1 4\\n1 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 4\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 5\\n1 5\\n2 6\\n2 9\\n1 2\\n1 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n2 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '1260 14\\n1 75\\n2 74\\n2 74\\n2 114\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '1260 26\\n1 75\\n2 74\\n1 74\\n2 56\\n2 87\\n2 2\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 68\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 82\\n1 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 14\\n2 322\\n2 322\\n2 322\\n2 791\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 526\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 7\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n2 2\\n2 4\\n2 4\\n2 3\\n1 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n1 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n1 6\\n2 6\\n2 6\\n2 5\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 82\\n1 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 142\\n2 74\\n2 14\\n2 322\\n2 322\\n2 322\\n2 791\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 526\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '76183 37\\n1 68009\\n2 68008\\n2 68008\\n2 51883\\n1 51882\\n2 51883\\n2 51881\\n2 51881\\n2 51881\\n2 51881\\n2 68008\\n2 68008\\n2 68008\\n2 68008\\n2 51881\\n2 40751\\n2 51881\\n2 51881\\n2 51881\\n2 3317\\n1 40750\\n2 40751\\n2 62512\\n2 68008\\n2 68008\\n2 40749\\n2 33598\\n2 40749\\n1 33597\\n2 33598\\n2 33596\\n2 54671\\n1 65682\\n2 33596\\n1 62511\\n2 62512\\n2 62510\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '327 22\\n2 68\\n1 67\\n1 214\\n2 68\\n2 213\\n2 213\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 185\\n2 213\\n1 15\\n2 14\\n2 14\\n2 213\\n2 213\\n2 66\\n2 66\\n2 14\\n', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '100000 46\\n1 82674\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 87908\\n2 58694\\n1 58693\\n2 58694\\n2 82673\\n2 82673\\n1 87907\\n2 87908\\n2 82673\\n2 82673\\n1 64610\\n2 64609\\n2 64609\\n2 58692\\n2 58692\\n2 64609\\n2 64609\\n2 64609\\n2 64609\\n2 87906\\n2 87906\\n2 64609\\n2 22164\\n2 2840\\n2 43302\\n2 64609\\n2 58692\\n2 58692\\n2 87906\\n2 87906\\n1 6213\\n2 76010\\n2 22164\\n2 64609\\n2 64609\\n1 43301\\n2 43302\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 310\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n2 3\\n2 4\\n2 4\\n2 3\\n1 4\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '327 22\\n2 68\\n1 67\\n1 214\\n2 68\\n2 213\\n2 213\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 213\\n2 213\\n1 14\\n2 14\\n2 14\\n2 213\\n2 213\\n2 66\\n2 66\\n2 14\\n', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 68\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 4\\n2 2\\n2 2\\n1 3\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n1 2\\n1 2\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n2 1\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 39\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n1 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n1 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n1 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 42\\n1 4\\n1 2\\n2 2\\n2 8\\n1 10\\n1 7\\n2 8\\n2 3\\n1 9\\n1 2\\n2 4\\n2 8\\n2 4\\n1 2\\n2 3\\n1 9\\n1 6\\n2 7\\n2 7\\n1 10\\n1 2\\n1 10\\n2 7\\n1 5\\n2 2\\n1 4\\n1 10\\n1 2\\n2 4\\n2 9\\n1 7\\n1 2\\n1 7\\n2 3\\n1 10\\n2 7\\n1 5\\n2 5\\n1 10\\n1 8\\n2 9\\n1 6\\n', 'output': 'Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n1 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 5\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '327 22\\n2 68\\n1 67\\n1 214\\n2 68\\n2 213\\n2 213\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 213\\n2 213\\n1 17\\n2 14\\n2 2\\n2 213\\n2 213\\n2 66\\n2 66\\n2 14\\n', 'output': 'Yes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n1 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n2 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 7\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n1 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 5\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '100000 46\\n1 82674\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 82673\\n2 61968\\n2 82673\\n2 82673\\n2 87908\\n2 58694\\n1 58693\\n2 58694\\n2 82673\\n2 82673\\n1 87907\\n2 87908\\n2 82673\\n2 82673\\n1 64610\\n2 64609\\n2 64609\\n2 58692\\n2 58692\\n2 6012\\n2 64609\\n2 64609\\n2 64609\\n2 87906\\n2 87906\\n2 64609\\n2 22164\\n2 2840\\n2 43302\\n2 64609\\n2 58692\\n2 58692\\n2 87906\\n2 87906\\n1 22163\\n2 76010\\n2 22164\\n2 64609\\n2 64609\\n1 43301\\n2 43302\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 74\\n1 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 309\\n2 702\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 42\\n1 6\\n1 2\\n2 2\\n2 8\\n1 10\\n1 7\\n2 8\\n2 3\\n1 9\\n1 2\\n2 4\\n2 8\\n2 4\\n1 2\\n2 3\\n1 9\\n1 6\\n2 7\\n2 7\\n1 10\\n1 2\\n1 10\\n2 7\\n1 5\\n2 2\\n1 4\\n1 10\\n1 2\\n2 4\\n2 9\\n1 7\\n1 2\\n1 7\\n2 3\\n1 5\\n2 7\\n2 5\\n2 5\\n1 10\\n1 8\\n2 9\\n1 6\\n', 'output': 'Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '1260 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '1260 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 298\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 42\\n1 4\\n1 2\\n2 2\\n2 8\\n1 10\\n1 7\\n2 8\\n2 3\\n1 9\\n1 2\\n2 4\\n2 8\\n2 4\\n2 2\\n2 3\\n1 9\\n1 6\\n2 7\\n2 7\\n1 10\\n1 2\\n1 10\\n2 7\\n1 5\\n2 2\\n1 4\\n1 10\\n1 2\\n2 4\\n2 9\\n1 7\\n1 2\\n1 7\\n2 3\\n1 10\\n2 7\\n1 5\\n2 5\\n1 10\\n1 8\\n2 9\\n1 6\\n', 'output': 'Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 85\\n1 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '327 22\\n2 42\\n1 67\\n1 214\\n2 68\\n2 213\\n2 213\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 213\\n2 213\\n1 17\\n2 14\\n2 2\\n2 213\\n2 213\\n2 66\\n2 66\\n2 14\\n', 'output': 'Yes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 7\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n1 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n1 6\\n2 6\\n2 6\\n2 5\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 548\\n2 322\\n2 322\\n1 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '327 22\\n1 68\\n1 67\\n1 214\\n2 68\\n2 213\\n2 213\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 66\\n2 213\\n2 213\\n1 17\\n2 8\\n2 14\\n2 213\\n2 213\\n2 66\\n2 66\\n2 14\\n', 'output': 'Yes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 298\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 7\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n1 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n1 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n1 6\\n2 6\\n2 6\\n2 5\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 548\\n2 322\\n2 322\\n1 649\\n1 703\\n1 251\\n2 457\\n2 342\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 74\\n2 82\\n1 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 791\\n1 703\\n1 251\\n2 457\\n2 322\\n2 702\\n2 382\\n2 526\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 7\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n2 2\\n2 4\\n2 4\\n2 3\\n1 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n1 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n1 6\\n2 6\\n2 6\\n2 5\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '1260 14\\n1 75\\n2 74\\n2 74\\n2 114\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 359\\n2 74\\n2 74\\n2 74\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '1260 26\\n1 75\\n2 74\\n1 74\\n2 56\\n2 87\\n2 2\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 68\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 637\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '1260 14\\n1 75\\n2 74\\n2 74\\n2 114\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 359\\n2 74\\n2 74\\n2 74\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 382\\n3 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '1260 26\\n1 75\\n2 74\\n1 74\\n2 56\\n2 87\\n2 2\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 68\\n2 74\\n2 548\\n2 322\\n2 322\\n2 649\\n1 703\\n1 82\\n2 457\\n2 322\\n2 702\\n1 252\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 6\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 7\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n2 2\\n2 4\\n2 4\\n2 3\\n1 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n1 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n1 6\\n2 6\\n2 6\\n2 5\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n2 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 2\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n2 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '855 26\\n1 75\\n2 74\\n2 74\\n2 74\\n2 87\\n2 74\\n2 74\\n2 74\\n2 74\\n1 323\\n2 74\\n2 74\\n2 74\\n2 74\\n2 322\\n2 322\\n2 322\\n2 649\\n1 703\\n1 251\\n2 457\\n2 322\\n2 469\\n2 382\\n2 702\\n2 500\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 42\\n1 4\\n1 2\\n2 2\\n2 8\\n1 10\\n1 7\\n2 8\\n2 3\\n1 9\\n1 2\\n2 4\\n2 8\\n2 4\\n1 2\\n2 3\\n1 9\\n1 6\\n2 7\\n2 7\\n1 10\\n1 2\\n1 10\\n2 7\\n1 5\\n2 2\\n1 4\\n1 10\\n1 2\\n2 4\\n2 9\\n1 8\\n1 2\\n1 7\\n2 3\\n1 10\\n2 7\\n2 5\\n2 5\\n1 10\\n1 8\\n2 9\\n1 6\\n', 'output': 'Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 83\\n1 3\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n1 4\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 6\\n2 3\\n1 4\\n1 5\\n1 7\\n2 2\\n2 2\\n1 5\\n2 2\\n1 3\\n2 1\\n2 6\\n1 5\\n2 6\\n2 9\\n1 2\\n2 5\\n1 2\\n2 5\\n2 4\\n2 4\\n1 3\\n1 2\\n1 4\\n2 6\\n2 6\\n2 4\\n2 4\\n1 2\\n1 2\\n2 4\\n2 4\\n2 3\\n2 3\\n1 2\\n2 9\\n1 2\\n1 2\\n1 2\\n2 6\\n2 6\\n2 4\\n1 4\\n2 3\\n2 5\\n2 5\\n2 3\\n2 3\\n2 3\\n2 6\\n2 6\\n2 3\\n2 3\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 6\\n2 3\\n2 3\\n1 2\\n1 2\\n2 6\\n2 1\\n2 6\\n2 6\\n2 6\\n2 7\\n', 'output': 'Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 500000000}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78833","program":"```python\n#!/usr/bin/env python3\nimport sys\ninput = sys.stdin.readline\n \nn, q = [int(item) for item in input().split()]\nblock = [[0] * (n + 6) for _ in range(2)]\nwall = 0\nfor _ in range(q):\n x, y = [int(item) - 1 for item in input().split()]\n y += 3\n invx = (x + 1) % 2\n if block[x][y]:\n block[x][y] = 0\n wall -= block[invx][y-1] + block[invx][y] + block[invx][y+1]\n else:\n block[x][y] = 1\n wall += block[invx][y-1] + block[invx][y] + block[invx][y+1]\n if wall > 0:\n print(\"No\")\n else:\n print(\"Yes\")\n```","inputs":"5 5\n2 3\n1 4\n2 4\n2 3\n1 4\n","output":"Yes\nNo\nNo\nNo\nYes\n","actual_output":"Yes\nNo\nNo\nNo\nYes\n","execution_success":true,"sample_index":12559},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1313_C1. Skyscrapers (easy version)","prompt":"Solve the following coding problem using the programming language python:\n\nThis is an easier version of the problem. In this version n \u2264 1000\n\nThe outskirts of the capital are being actively built up in Berland. The company \"Kernel Panic\" manages the construction of a residential complex of skyscrapers in New Berlskva. All skyscrapers are built along the highway. It is known that the company has already bought n plots along the highway and is preparing to build n skyscrapers, one skyscraper per plot.\n\nArchitects must consider several requirements when planning a skyscraper. Firstly, since the land on each plot has different properties, each skyscraper has a limit on the largest number of floors it can have. Secondly, according to the design code of the city, it is unacceptable for a skyscraper to simultaneously have higher skyscrapers both to the left and to the right of it.\n\nFormally, let's number the plots from 1 to n. Then if the skyscraper on the i-th plot has a_i floors, it must hold that a_i is at most m_i (1 \u2264 a_i \u2264 m_i). Also there mustn't be integers j and k such that j < i < k and a_j > a_i < a_k. Plots j and k are not required to be adjacent to i.\n\nThe company wants the total number of floors in the built skyscrapers to be as large as possible. Help it to choose the number of floors for each skyscraper in an optimal way, i.e. in such a way that all requirements are fulfilled, and among all such construction plans choose any plan with the maximum possible total number of floors.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 1000) \u2014 the number of plots.\n\nThe second line contains the integers m_1, m_2, \u2026, m_n (1 \u2264 m_i \u2264 10^9) \u2014 the limit on the number of floors for every possible number of floors for a skyscraper on each plot.\n\nOutput\n\nPrint n integers a_i \u2014 the number of floors in the plan for each skyscraper, such that all requirements are met, and the total number of floors in all skyscrapers is the maximum possible.\n\nIf there are multiple answers possible, print any of them.\n\nExamples\n\nInput\n\n5\n1 2 3 2 1\n\n\nOutput\n\n1 2 3 2 1 \n\n\nInput\n\n3\n10 6 8\n\n\nOutput\n\n10 6 6 \n\nNote\n\nIn the first example, you can build all skyscrapers with the highest possible height.\n\nIn the second test example, you cannot give the maximum height to all skyscrapers as this violates the design code restriction. The answer [10, 6, 6] is optimal. Note that the answer of [6, 6, 8] also satisfies all restrictions, but is not optimal.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport os, sys\nfrom io import BytesIO, IOBase\nfrom types import GeneratorType\nfrom bisect import *\nfrom collections import defaultdict, deque, Counter\nimport math, string\nfrom heapq import *\nfrom operator import add\nfrom itertools import accumulate\n\nBUFSIZE = 8192\nsys.setrecursionlimit(10 ** 5)\n\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n import os\n\n self.os = os\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n\n def read(self):\n while True:\n b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n self.os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\n\n\ninf = float(\"inf\")\nen = lambda x: list(enumerate(x))\nceil_ = lambda a, b: (a + b - 1) // b\n\n\nii = lambda: int(input())\nr = lambda: map(int, input().split())\nrr = lambda: list(r())\n\n\n# --------------------------\n\n\nn = ii()\narr = rr()\nans = 0\n\n\ndef go(a, x):\n arr = a[:]\n i = x - 1\n while i > -1:\n arr[i] = min(arr[i], arr[i + 1])\n i -= 1\n\n i = x + 1\n while i < len(a):\n arr[i] = min(arr[i - 1], arr[i])\n i += 1\n\n return arr if 0 not in arr else inf\n\n\nval = inf\nfor i in range(n):\n x = go(arr, i)\n if x == inf:\n continue\n\n if sum(x) > ans:\n # print('i' , i)\n ans = sum(x)\n val = x\n\nprint(*val)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n10 6 8\\n', 'output': '10 6 6\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 3 2 1\\n', 'output': '1 2 3 2 1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4 1 2 3 2 1\\n', 'output': '1 1 2 3 2 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n6 2 2 6 5 7 7\\n', 'output': '2 2 2 5 5 7 7\\n'}, {'type': 'stdin_stdout', 'input': '6\\n3 2 1 7 3 7\\n', 'output': '1 1 1 7 3 3\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 4 2 2\\n', 'output': '1 1 4 2 2\\n'}, {'type': 'stdin_stdout', 'input': '100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n', 'output': '3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 22 53 99 59 52 52 31 31 31 31 23 23 9 9 9 7 7 7 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1 2 1 3 1\\n', 'output': '1 1 1 1 1 3 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1 2 1 2 1\\n', 'output': '1 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 4 3 5 4\\n', 'output': '1 3 3 3 5 4\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2 4 1 2 3 1 2\\n', 'output': '2 4 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 2 4 2 4 1 1\\n', 'output': '5 2 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2 1 2 1 2 2 1\\n', 'output': '1 1 1 1 2 2 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4 1 2 3 2 2\\n', 'output': '1 1 2 3 2 2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 2 2 2\\n', 'output': '1 1 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 22 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n', 'output': '8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 10 10 10 12 12 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 87 87 69 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1 1 1 3 1\\n', 'output': '1 1 1 1 1 3 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 4 3 5 2\\n', 'output': '1 3 3 3 5 2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2 4 1 2 1 1 2\\n', 'output': '2 4 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 4 4 2 4 1 1\\n', 'output': '5 4 4 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2 1 2 1 4 2 1\\n', 'output': '1 1 1 1 4 2 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10 3 8\\n', 'output': '10 3 3\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 3 1 1\\n', 'output': '1 2 3 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4 1 1 3 2 2\\n', 'output': '1 1 1 3 2 2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 2 4 2\\n', 'output': '1 1 2 4 2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n4 4 1 2 1 1 2\\n', 'output': '4 4 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 3 8\\n', 'output': '3 3 8\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 6 2 1\\n', 'output': '1 2 6 2 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 2 6 2\\n', 'output': '1 1 2 6 2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n4 4 2 2 1 1 2\\n', 'output': '4 4 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 4 1 2 5 1 1\\n', 'output': '5 4 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 3 16\\n', 'output': '3 3 16\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 6 2 2\\n', 'output': '1 2 6 2 2\\n'}, {'type': 'stdin_stdout', 'input': '100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 2 100 25 92 47 21 78 20 63 22 49 41 36 41 79 16 87 87 69 3 76 80 45 100 49 70 59 72 8 38 71 45 97 71 14 87 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n', 'output': '2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 22 53 99 59 52 52 31 31 31 31 23 23 9 9 9 7 7 7 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 4 2 2 1 1 2\\n', 'output': '1 4 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 4 2 2 5 1 1\\n', 'output': '5 4 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 6 16\\n', 'output': '4 6 16\\n'}, {'type': 'stdin_stdout', 'input': '100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 2 100 25 92 47 21 78 20 63 22 49 41 36 41 79 16 87 87 69 3 76 80 45 100 49 70 59 72 8 38 71 45 97 71 14 87 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 3 82 47 7 40 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n', 'output': '2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 22 53 99 59 52 52 31 31 31 31 23 23 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 6 16\\n', 'output': '6 6 16\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 4 2 2 7 1 1\\n', 'output': '7 4 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 9 16\\n', 'output': '8 9 16\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 3 2 2 7 1 1\\n', 'output': '7 3 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 3 1 2 7 1 1\\n', 'output': '7 3 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 5 16\\n', 'output': '5 5 16\\n'}, {'type': 'stdin_stdout', 'input': '100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 100 77 66 15 15 2 100 25 92 47 21 123 20 63 22 49 41 36 41 79 16 87 87 69 3 76 80 45 100 49 70 59 72 8 38 71 45 97 71 14 87 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 3 82 47 7 40 12 9 1 55 37 85 46 22 84 52 98 41 34 77 63 17 62 91\\n', 'output': '2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 22 53 99 59 52 52 31 31 31 31 23 23 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10 8 16\\n', 'output': '8 8 16\\n'}, {'type': 'stdin_stdout', 'input': '100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 100 77 66 15 15 2 100 25 92 47 21 123 20 63 22 49 41 36 55 79 16 87 87 9 3 76 80 45 100 49 70 59 72 1 38 71 45 97 71 14 87 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 3 82 47 7 40 12 9 1 55 37 85 46 22 84 52 98 41 34 77 63 17 62 91\\n', 'output': '1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 22 53 99 59 52 52 31 31 31 31 23 23 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n13 7 16\\n', 'output': '7 7 16\\n'}, {'type': 'stdin_stdout', 'input': '3\\n13 7 10\\n', 'output': '13 7 7\\n'}, {'type': 'stdin_stdout', 'input': '100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 100 77 66 15 15 2 100 25 92 47 21 123 20 63 22 49 41 36 55 79 16 87 87 9 3 76 80 45 100 49 70 59 72 1 38 71 45 97 71 14 87 54 81 4 59 46 39 29 92 3 49 22 53 99 66 52 74 31 92 43 42 23 44 3 82 47 7 40 12 12 1 55 37 85 46 22 84 52 98 41 34 77 63 17 62 91\\n', 'output': '1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 22 53 99 66 52 52 31 31 31 31 23 23 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n24 7 10\\n', 'output': '24 7 7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n20 7 10\\n', 'output': '20 7 7\\n'}, {'type': 'stdin_stdout', 'input': '100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 100 77 66 15 15 2 100 25 92 47 21 123 20 63 22 49 41 36 55 79 16 87 87 9 3 76 80 45 100 49 70 59 72 1 38 71 45 97 71 14 87 54 81 4 59 46 39 29 92 3 49 22 53 99 66 76 74 31 92 43 42 23 44 3 82 47 7 40 12 12 1 2 37 85 46 22 68 52 98 41 34 77 63 17 62 91\\n', 'output': '1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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37 8 78 143 64 15 8 86 89 8 100 77 103 15 15 2 100 27 92 47 39 123 10 63 22 49 41 48 55 79 16 87 87 9 3 76 80 45 100 49 102 59 72 1 38 41 45 97 12 14 87 54 81 4 59 46 39 29 92 3 49 22 53 99 66 76 74 31 92 43 42 14 44 3 82 23 7 40 12 12 2 2 37 85 13 1 68 52 98 41 34 33 63 17 52 120\\n', 'output': '1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 22 53 99 66 66 66 31 31 31 31 14 14 3 3 3 3 3 3 3 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '100\\n82 20 133 13 37 8 78 143 64 15 8 86 89 8 100 77 103 15 15 2 100 27 92 47 39 123 10 63 22 49 41 48 55 79 16 87 87 9 3 76 80 45 100 49 102 59 72 1 38 41 45 97 12 14 87 54 81 4 59 46 39 29 92 3 49 22 53 99 66 76 73 31 92 43 42 14 44 3 82 23 7 40 12 12 2 2 37 85 13 1 68 52 98 41 34 33 63 17 52 120\\n', 'output': '1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 22 53 99 66 66 66 31 31 31 31 14 14 3 3 3 3 3 3 3 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_78837","program":"```python\nimport os, sys\nfrom io import BytesIO, IOBase\nfrom types import GeneratorType\nfrom bisect import *\nfrom collections import defaultdict, deque, Counter\nimport math, string\nfrom heapq import *\nfrom operator import add\nfrom itertools import accumulate\n\nBUFSIZE = 8192\nsys.setrecursionlimit(10 ** 5)\n\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n import os\n\n self.os = os\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n\n def read(self):\n while True:\n b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n self.os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\n\n\ninf = float(\"inf\")\nen = lambda x: list(enumerate(x))\nceil_ = lambda a, b: (a + b - 1) // b\n\n\nii = lambda: int(input())\nr = lambda: map(int, input().split())\nrr = lambda: list(r())\n\n\n# --------------------------\n\n\nn = ii()\narr = rr()\nans = 0\n\n\ndef go(a, x):\n arr = a[:]\n i = x - 1\n while i > -1:\n arr[i] = min(arr[i], arr[i + 1])\n i -= 1\n\n i = x + 1\n while i < len(a):\n arr[i] = min(arr[i - 1], arr[i])\n i += 1\n\n return arr if 0 not in arr else inf\n\n\nval = inf\nfor i in range(n):\n x = go(arr, i)\n if x == inf:\n continue\n\n if sum(x) > ans:\n # print('i' , i)\n ans = sum(x)\n val = x\n\nprint(*val)\n\n```","inputs":"3\n10 6 8\n","output":"10 6 6\n","actual_output":"10 6 6\n","execution_success":true,"sample_index":12560},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1335_F. Robots on a Grid","prompt":"Solve the following coding problem using the programming language python:\n\nThere is a rectangular grid of size n \u00d7 m. Each cell of the grid is colored black ('0') or white ('1'). The color of the cell (i, j) is c_{i, j}. You are also given a map of directions: for each cell, there is a direction s_{i, j} which is one of the four characters 'U', 'R', 'D' and 'L'.\n\n * If s_{i, j} is 'U' then there is a transition from the cell (i, j) to the cell (i - 1, j); \n * if s_{i, j} is 'R' then there is a transition from the cell (i, j) to the cell (i, j + 1); \n * if s_{i, j} is 'D' then there is a transition from the cell (i, j) to the cell (i + 1, j); \n * if s_{i, j} is 'L' then there is a transition from the cell (i, j) to the cell (i, j - 1). \n\n\n\nIt is guaranteed that the top row doesn't contain characters 'U', the bottom row doesn't contain characters 'D', the leftmost column doesn't contain characters 'L' and the rightmost column doesn't contain characters 'R'.\n\nYou want to place some robots in this field (at most one robot in a cell). The following conditions should be satisfied.\n\n * Firstly, each robot should move every time (i.e. it cannot skip the move). During one move each robot goes to the adjacent cell depending on the current direction. \n * Secondly, you have to place robots in such a way that there is no move before which two different robots occupy the same cell (it also means that you cannot place two robots in the same cell). I.e. if the grid is \"RL\" (one row, two columns, colors does not matter there) then you can place two robots in cells (1, 1) and (1, 2), but if the grid is \"RLL\" then you cannot place robots in cells (1, 1) and (1, 3) because during the first second both robots will occupy the cell (1, 2). \n\n\n\nThe robots make an infinite number of moves.\n\nYour task is to place the maximum number of robots to satisfy all the conditions described above and among all such ways, you have to choose one where the number of black cells occupied by robots before all movements is the maximum possible. Note that you can place robots only before all movements.\n\nYou have to answer t independent test cases.\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 5 \u22c5 10^4) \u2014 the number of test cases. Then t test cases follow.\n\nThe first line of the test case contains two integers n and m (1 < nm \u2264 10^6) \u2014 the number of rows and the number of columns correspondingly.\n\nThe next n lines contain m characters each, where the j-th character of the i-th line is c_{i, j} (c_{i, j} is either '0' if the cell (i, j) is black or '1' if the cell (i, j) is white).\n\nThe next n lines also contain m characters each, where the j-th character of the i-th line is s_{i, j} (s_{i, j} is 'U', 'R', 'D' or 'L' and describes the direction of the cell (i, j)).\n\nIt is guaranteed that the sum of the sizes of fields does not exceed 10^6 (\u2211 nm \u2264 10^6).\n\nOutput\n\nFor each test case, print two integers \u2014 the maximum number of robots you can place to satisfy all the conditions described in the problem statement and the maximum number of black cells occupied by robots before all movements if the number of robots placed is maximized. Note that you can place robots only before all movements.\n\nExample\n\nInput\n\n\n3\n1 2\n01\nRL\n3 3\n001\n101\n110\nRLL\nDLD\nULL\n3 3\n000\n000\n000\nRRD\nRLD\nULL\n\n\nOutput\n\n\n2 1\n4 3\n2 2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\n\nint1 = lambda x: int(x) - 1\np2D = lambda x: print(*x, sep=\"\\n\")\ndef II(): return int(sys.stdin.readline())\ndef MI(): return map(int, sys.stdin.readline().split())\ndef LI(): return list(map(int, sys.stdin.readline().split()))\ndef LLI(rows_number): return [LI() for _ in range(rows_number)]\ndef SI(): return sys.stdin.readline()[:-1]\n\ndef main():\n for _ in range(II()):\n h,w=MI()\n cc=[list(map(int,list(SI()))) for _ in range(h)]\n ss=[SI() for _ in range(h)]\n aa=[[0]*w for _ in range(h)]\n mm=[[0]*w for _ in range(h)]\n cyc=[0]\n ci=1\n dir=\"UDLR\"\n dij=[(-1,0),(1,0),(0,-1),(0,1)]\n for si in range(h):\n for sj in range(w):\n if aa[si][sj]!=0:continue\n i,j=si,sj\n d=-1\n stack=[]\n while aa[i][j]==0:\n aa[i][j]=d\n stack.append((i,j))\n d-=1\n di,dj=dij[dir.index(ss[i][j])]\n i,j=i+di,j+dj\n if aa[i][j]>0:\n a=aa[i][j]\n dist=cyc[a]\n m=(mm[i][j]+1)%dist\n for i,j in stack[::-1]:\n aa[i][j]=a\n mm[i][j]=m\n m=(m+1)%dist\n else:\n dist=aa[i][j]-d\n cyc.append(dist)\n m=0\n for i, j in stack[::-1]:\n aa[i][j] = ci\n mm[i][j]=m\n m=(m+1)%dist\n ci+=1\n #print(cyc)\n #p2D(aa)\n one=[set() for _ in range(ci)]\n for i in range(h):\n for j in range(w):\n if cc[i][j]==0:\n one[aa[i][j]].add(mm[i][j])\n #print(one)\n ans1=sum(cyc)\n ans2=sum(min(ck,len(ok)) for ck,ok in zip(cyc,one))\n print(ans1,ans2)\n\nmain()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n000\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n000\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n011\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n010\\n000\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 2\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n001\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n110\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n100\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n010\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n010\\n000\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n010\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n000\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n100\\n000\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n001\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n011\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n010\\n100\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 2\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n001\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n011\\n101\\n100\\nRLL\\nDLD\\nULL\\n3 3\\n010\\n100\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n110\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n001\\n110\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n000\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n110\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n001\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n011\\n101\\n100\\nRLL\\nDLD\\nULL\\n3 3\\n010\\n100\\n001\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n000\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n101\\n111\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n001\\n110\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n000\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n100\\n110\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n001\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n000\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n111\\n101\\n100\\nRLL\\nDLD\\nULL\\n3 3\\n010\\n100\\n001\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 2\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n100\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n100\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n100\\n110\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n101\\n100\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n100\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n100\\n100\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n100\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n000\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n110\\n010\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n001\\n111\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n001\\n110\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n100\\n100\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n110\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n001\\n111\\nRLL\\nDLD\\nULL\\n3 3\\n100\\n001\\n110\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n001\\n101\\nRLL\\nDLD\\nULL\\n3 3\\n100\\n001\\n110\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n001\\n001\\nRLL\\nDLD\\nULL\\n3 3\\n100\\n001\\n110\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n001\\n001\\nRLL\\nDLD\\nULL\\n3 3\\n110\\n001\\n110\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n100\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n100\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n100\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n100\\n010\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n011\\n101\\n010\\nRLL\\nDLD\\nULL\\n3 3\\n010\\n000\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 2\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n111\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n001\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n111\\n101\\n100\\nRLL\\nDLD\\nULL\\n3 3\\n010\\n100\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 2\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n101\\n000\\n110\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n110\\n010\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n110\\n100\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n110\\n100\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n011\\n101\\nRLL\\nDLD\\nULL\\n3 3\\n100\\n001\\n110\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n000\\n001\\n011\\nRLL\\nDLD\\nULL\\n3 3\\n100\\n001\\n110\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 4\\n2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n01\\nRL\\n3 3\\n001\\n101\\n010\\nRLL\\nDLD\\nULL\\n3 3\\n000\\n100\\n000\\nRRD\\nRLD\\nULL\\n', 'output': '2 1\\n4 3\\n2 2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 12, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78841","program":"```python\nimport sys\n\nint1 = lambda x: int(x) - 1\np2D = lambda x: print(*x, sep=\"\\n\")\ndef II(): return int(sys.stdin.readline())\ndef MI(): return map(int, sys.stdin.readline().split())\ndef LI(): return list(map(int, sys.stdin.readline().split()))\ndef LLI(rows_number): return [LI() for _ in range(rows_number)]\ndef SI(): return sys.stdin.readline()[:-1]\n\ndef main():\n for _ in range(II()):\n h,w=MI()\n cc=[list(map(int,list(SI()))) for _ in range(h)]\n ss=[SI() for _ in range(h)]\n aa=[[0]*w for _ in range(h)]\n mm=[[0]*w for _ in range(h)]\n cyc=[0]\n ci=1\n dir=\"UDLR\"\n dij=[(-1,0),(1,0),(0,-1),(0,1)]\n for si in range(h):\n for sj in range(w):\n if aa[si][sj]!=0:continue\n i,j=si,sj\n d=-1\n stack=[]\n while aa[i][j]==0:\n aa[i][j]=d\n stack.append((i,j))\n d-=1\n di,dj=dij[dir.index(ss[i][j])]\n i,j=i+di,j+dj\n if aa[i][j]>0:\n a=aa[i][j]\n dist=cyc[a]\n m=(mm[i][j]+1)%dist\n for i,j in stack[::-1]:\n aa[i][j]=a\n mm[i][j]=m\n m=(m+1)%dist\n else:\n dist=aa[i][j]-d\n cyc.append(dist)\n m=0\n for i, j in stack[::-1]:\n aa[i][j] = ci\n mm[i][j]=m\n m=(m+1)%dist\n ci+=1\n #print(cyc)\n #p2D(aa)\n one=[set() for _ in range(ci)]\n for i in range(h):\n for j in range(w):\n if cc[i][j]==0:\n one[aa[i][j]].add(mm[i][j])\n #print(one)\n ans1=sum(cyc)\n ans2=sum(min(ck,len(ok)) for ck,ok in zip(cyc,one))\n print(ans1,ans2)\n\nmain()\n```","inputs":"3\n1 2\n01\nRL\n3 3\n001\n101\n110\nRLL\nDLD\nULL\n3 3\n000\n000\n000\nRRD\nRLD\nULL\n","output":"2 1\n4 3\n2 2\n","actual_output":"2 1\n4 3\n2 2\n","execution_success":true,"sample_index":12561},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1358_C. Celex Update","prompt":"Solve the following coding problem using the programming language python:\n\nDuring the quarantine, Sicromoft has more free time to create the new functions in \"Celex-2021\". The developers made a new function GAZ-GIZ, which infinitely fills an infinite table to the right and down from the upper left corner as follows:\n\n The cell with coordinates (x, y) is at the intersection of x-th row and y-th column. Upper left cell (1,1) contains an integer 1.\n\nThe developers of the SUM function don't sleep either. Because of the boredom, they teamed up with the developers of the RAND function, so they added the ability to calculate the sum on an arbitrary path from one cell to another, moving down or right. Formally, from the cell (x,y) in one step you can move to the cell (x+1, y) or (x, y+1). \n\nAfter another Dinwows update, Levian started to study \"Celex-2021\" (because he wants to be an accountant!). After filling in the table with the GAZ-GIZ function, he asked you to calculate the quantity of possible different amounts on the path from a given cell (x_1, y_1) to another given cell (x_2, y_2), if you can only move one cell down or right.\n\nFormally, consider all the paths from the cell (x_1, y_1) to cell (x_2, y_2) such that each next cell in the path is located either to the down or to the right of the previous one. Calculate the number of different sums of elements for all such paths.\n\nInput\n\nThe first line contains one integer t (1 \u2264 t \u2264 57179) \u2014 the number of test cases.\n\nEach of the following t lines contains four natural numbers x_1, y_1, x_2, y_2 (1 \u2264 x_1 \u2264 x_2 \u2264 10^9, 1 \u2264 y_1 \u2264 y_2 \u2264 10^9) \u2014 coordinates of the start and the end cells. \n\nOutput\n\nFor each test case, in a separate line, print the number of possible different sums on the way from the start cell to the end cell.\n\nExample\n\nInput\n\n\n4\n1 1 2 2\n1 2 2 4\n179 1 179 100000\n5 7 5 7\n\n\nOutput\n\n\n2\n3\n1\n1\n\nNote\n\nIn the first test case there are two possible sums: 1+2+5=8 and 1+3+5=9. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nt = int(input())\nfor _ in range(t):\n x1, y1, x2, y2 = map(int, input().split())\n print((x2-x1)*(y2-y1)+1)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1 1 2 2\\n1 2 2 4\\n179 1 179 100000\\n5 7 5 7\\n', 'output': '2\\n3\\n1\\n1'}, {'type': 'stdin_stdout', 'input': '1\\n1 1 3 6\\n', 'output': '11'}, {'type': 'stdin_stdout', 'input': '1\\n118730819 699217111 995255402 978426672\\n', 'output': '244734044025138064'}, {'type': 'stdin_stdout', 'input': '2\\n57 179 1329 2007\\n179 444 239 1568\\n', 'output': '2325217\\n67441'}, {'type': 'stdin_stdout', 'input': '1\\n0 1 3 6\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '1\\n118730819 699217111 1229905591 978426672\\n', 'output': '310250620284395093\\n'}, {'type': 'stdin_stdout', 'input': '2\\n57 179 1329 2007\\n179 444 239 2807\\n', 'output': '2325217\\n141781\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 2\\n1 2 2 4\\n179 0 179 100000\\n5 7 5 7\\n', 'output': '2\\n3\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 1 6 6\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '2\\n57 179 1329 2007\\n179 132 239 2807\\n', 'output': '2325217\\n160501\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 2\\n1 2 1 4\\n179 0 179 100000\\n5 7 5 7\\n', 'output': '2\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 1 5 6\\n', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '2\\n57 179 284 2007\\n179 132 239 2807\\n', 'output': '414957\\n160501\\n'}, {'type': 'stdin_stdout', 'input': '2\\n57 179 437 2007\\n179 132 239 2807\\n', 'output': '694641\\n160501\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 1 6 3\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 0 3 6\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '1\\n118730819 699217111 995255402 1762535216\\n', 'output': '932024458581475216\\n'}, {'type': 'stdin_stdout', 'input': '2\\n71 179 1329 2007\\n179 444 239 1568\\n', 'output': '2299625\\n67441\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 2 2\\n1 2 2 4\\n179 1 179 100000\\n5 7 5 7\\n', 'output': '1\\n3\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 0 3 6\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '1\\n118730819 699217111 1571293294 978426672\\n', 'output': '405569330969823476\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 1 6 6\\n', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '2\\n19 179 1329 2007\\n179 132 239 2807\\n', 'output': '2394681\\n160501\\n'}, {'type': 'stdin_stdout', 'input': '2\\n57 179 284 2007\\n179 55 239 2807\\n', 'output': '414957\\n165121\\n'}, {'type': 'stdin_stdout', 'input': '2\\n57 179 437 2007\\n218 132 239 2807\\n', 'output': '694641\\n56176\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 1 6 3\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 0 3 6\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n56903005 699217111 995255402 1762535216\\n', 'output': '997767092600247686\\n'}, {'type': 'stdin_stdout', 'input': '2\\n71 179 1329 2007\\n179 41 239 1568\\n', 'output': '2299625\\n91621\\n'}, {'type': 'stdin_stdout', 'input': '1\\n159574671 699217111 1571293294 978426672\\n', 'output': '394165336983354504\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 1 2 2\\n1 2 1 4\\n179 0 179 100000\\n5 7 5 7\\n', 'output': '1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n19 179 1329 2007\\n179 132 437 2807\\n', 'output': '2394681\\n690151\\n'}, {'type': 'stdin_stdout', 'input': '2\\n57 193 284 2007\\n179 55 239 2807\\n', 'output': '411779\\n165121\\n'}, {'type': 'stdin_stdout', 'input': '2\\n57 179 437 2007\\n228 132 239 2807\\n', 'output': '694641\\n29426\\n'}, {'type': 'stdin_stdout', 'input': '1\\n56903005 699217111 995255402 1937828237\\n', 'output': '1162253719032969023\\n'}, {'type': 'stdin_stdout', 'input': '2\\n51 179 1329 2007\\n179 41 239 1568\\n', 'output': '2336185\\n91621\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 2 4\\n1 2 2 4\\n179 1 179 100000\\n3 7 5 7\\n', 'output': '3\\n3\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 1 1 6\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n307120728 699217111 1571293294 978426672\\n', 'output': '352969067181103527\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 1 2 2\\n1 2 1 4\\n179 0 208 100000\\n5 7 5 7\\n', 'output': '1\\n1\\n2900001\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 0 6 4\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '2\\n19 134 1329 2007\\n179 132 437 2807\\n', 'output': '2453631\\n690151\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 2 7 6\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '2\\n29 193 284 2007\\n179 55 239 2807\\n', 'output': '462571\\n165121\\n'}, {'type': 'stdin_stdout', 'input': '2\\n95 179 437 2007\\n228 132 239 2807\\n', 'output': '625177\\n29426\\n'}, {'type': 'stdin_stdout', 'input': '1\\n19655809 699217111 995255402 1937828237\\n', 'output': '1208388510410871719\\n'}, {'type': 'stdin_stdout', 'input': '2\\n51 179 1329 2007\\n179 23 239 1568\\n', 'output': '2336185\\n92701\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 2 4\\n2 2 2 4\\n179 1 179 100000\\n3 7 5 7\\n', 'output': '3\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 1 1 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 0 10 4\\n', 'output': '33\\n'}, {'type': 'stdin_stdout', 'input': '2\\n19 134 1329 2007\\n179 132 437 3062\\n', 'output': '2453631\\n755941\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 2 7 8\\n', 'output': '37\\n'}, {'type': 'stdin_stdout', 'input': '2\\n29 193 284 2007\\n179 71 239 2807\\n', 'output': '462571\\n164161\\n'}, {'type': 'stdin_stdout', 'input': '2\\n95 179 437 2007\\n228 132 424 2807\\n', 'output': '625177\\n524301\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8901423 699217111 995255402 1937828237\\n', 'output': '1221709012563770355\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 0 10 6\\n', 'output': '49\\n'}, {'type': 'stdin_stdout', 'input': '2\\n19 134 1019 2007\\n179 132 437 3062\\n', 'output': '1873001\\n755941\\n'}, {'type': 'stdin_stdout', 'input': '2\\n29 94 284 2007\\n179 71 239 2807\\n', 'output': '487816\\n164161\\n'}, {'type': 'stdin_stdout', 'input': '2\\n95 179 437 2007\\n228 132 424 1863\\n', 'output': '625177\\n339277\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5926574 699217111 995255402 1937828237\\n', 'output': '1225393693633340329\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 4\\n2 2 2 4\\n179 1 179 110000\\n3 7 5 7\\n', 'output': '4\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 0 20 6\\n', 'output': '109\\n'}, {'type': 'stdin_stdout', 'input': '2\\n19 134 1019 2007\\n166 132 437 3062\\n', 'output': '1873001\\n794031\\n'}, {'type': 'stdin_stdout', 'input': '2\\n29 94 482 2007\\n179 71 239 2807\\n', 'output': '866590\\n164161\\n'}, {'type': 'stdin_stdout', 'input': '2\\n95 203 437 2007\\n228 132 424 1863\\n', 'output': '616969\\n339277\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5926574 1328195020 995255402 1937828237\\n', 'output': '603127716084479677\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 1 20 6\\n', 'output': '91\\n'}, {'type': 'stdin_stdout', 'input': '2\\n19 134 1019 2007\\n166 132 844 3062\\n', 'output': '1873001\\n1986541\\n'}, {'type': 'stdin_stdout', 'input': '2\\n29 94 137 2007\\n179 71 239 2807\\n', 'output': '206605\\n164161\\n'}, {'type': 'stdin_stdout', 'input': '2\\n95 203 437 2007\\n70 132 424 1863\\n', 'output': '616969\\n612775\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 1 16 6\\n', 'output': '71\\n'}, {'type': 'stdin_stdout', 'input': '2\\n19 134 1019 2007\\n166 132 1468 3062\\n', 'output': '1873001\\n3814861\\n'}, {'type': 'stdin_stdout', 'input': '2\\n29 94 137 2007\\n179 71 239 2226\\n', 'output': '206605\\n129301\\n'}, {'type': 'stdin_stdout', 'input': '2\\n95 283 437 2007\\n70 132 424 1863\\n', 'output': '589609\\n612775\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 1 16 10\\n', 'output': '127\\n'}, {'type': 'stdin_stdout', 'input': '2\\n29 94 137 2007\\n179 71 395 2226\\n', 'output': '206605\\n465481\\n'}, {'type': 'stdin_stdout', 'input': '2\\n95 283 437 2007\\n70 183 424 1863\\n', 'output': '589609\\n594721\\n'}, {'type': 'stdin_stdout', 'input': '2\\n29 94 137 2007\\n179 71 395 1772\\n', 'output': '206605\\n367417\\n'}, {'type': 'stdin_stdout', 'input': '2\\n95 283 437 2007\\n39 183 424 1863\\n', 'output': '589609\\n646801\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 2\\n1 2 1 4\\n179 0 179 100000\\n5 3 5 7\\n', 'output': '2\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 1 6 6\\n', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 2\\n1 2 1 6\\n179 0 179 100000\\n5 3 5 7\\n', 'output': '2\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 1 2 2\\n1 2 2 4\\n179 0 179 100000\\n5 7 5 7\\n', 'output': '1\\n3\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 2\\n1 2 1 4\\n179 0 179 110000\\n5 7 5 7\\n', 'output': '2\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 1 5 6\\n', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 0 6 6\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 2\\n1 2 1 6\\n179 0 179 100000\\n5 5 5 7\\n', 'output': '2\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 2 2\\n1 2 2 4\\n179 1 179 100000\\n3 7 5 7\\n', 'output': '1\\n3\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 0 1 6\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 1 6 4\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 2 6 6\\n', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 2\\n1 0 1 6\\n179 0 179 100000\\n5 5 5 7\\n', 'output': '2\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 2\\n1 0 1 8\\n179 0 179 100000\\n5 5 5 7\\n', 'output': '2\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 1 2 2\\n1 2 1 4\\n179 0 208 100000\\n5 7 9 7\\n', 'output': '1\\n1\\n2900001\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 2 4\\n2 2 2 4\\n179 1 179 110000\\n3 7 5 7\\n', 'output': '3\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 1 1 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 2 7 8\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 2 2 8\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 0 2 8\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 1 16 10\\n', 'output': '109\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78845","program":"```python\nt = int(input())\nfor _ in range(t):\n x1, y1, x2, y2 = map(int, input().split())\n print((x2-x1)*(y2-y1)+1)\n\n```","inputs":"4\n1 1 2 2\n1 2 2 4\n179 1 179 100000\n5 7 5 7\n","output":"2\n3\n1\n1","actual_output":"2\n3\n1\n1\n","execution_success":true,"sample_index":12562},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1399_D. Binary String To Subsequences","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a binary string s consisting of n zeros and ones.\n\nYour task is to divide the given string into the minimum number of subsequences in such a way that each character of the string belongs to exactly one subsequence and each subsequence looks like \"010101 ...\" or \"101010 ...\" (i.e. the subsequence should not contain two adjacent zeros or ones).\n\nRecall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements. For example, subsequences of \"1011101\" are \"0\", \"1\", \"11111\", \"0111\", \"101\", \"1001\", but not \"000\", \"101010\" and \"11100\".\n\nYou have to answer t independent test cases.\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 2 \u22c5 10^4) \u2014 the number of test cases. Then t test cases follow.\n\nThe first line of the test case contains one integer n (1 \u2264 n \u2264 2 \u22c5 10^5) \u2014 the length of s. The second line of the test case contains n characters '0' and '1' \u2014 the string s.\n\nIt is guaranteed that the sum of n does not exceed 2 \u22c5 10^5 (\u2211 n \u2264 2 \u22c5 10^5).\n\nOutput\n\nFor each test case, print the answer: in the first line print one integer k (1 \u2264 k \u2264 n) \u2014 the minimum number of subsequences you can divide the string s to. In the second line print n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 k), where a_i is the number of subsequence the i-th character of s belongs to.\n\nIf there are several answers, you can print any.\n\nExample\n\nInput\n\n\n4\n4\n0011\n6\n111111\n5\n10101\n8\n01010000\n\n\nOutput\n\n\n2\n1 2 2 1 \n6\n1 2 3 4 5 6 \n1\n1 1 1 1 1 \n4\n1 1 1 1 1 2 3 4 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nt=int(input())\nfor _ in range(t):\n n=int(input())\n s=str(input())\n arr=[]\n for i in range(n):\n arr.append(int(s[i]))\n ones=[]\n zeros=[]\n vals=[]\n k=0\n for i in range(n):\n p=arr[i]\n if(p==0):\n if(ones==[]):\n zeros.append(k+1)\n vals.append(k+1)\n k+=1\n else:\n zeros.append(ones[-1])\n vals.append(ones[-1])\n ones.pop()\n else:\n if(zeros==[]):\n ones.append(k+1)\n vals.append(k+1)\n k+=1\n else:\n ones.append(zeros[-1])\n vals.append(ones[-1])\n zeros.pop()\n print(max(vals))\n for i in vals:\n print(i,end=\" \")\n print()\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n4\\n0011\\n6\\n111111\\n5\\n10101\\n8\\n01010000\\n', 'output': '2\\n1 2 2 1 \\n6\\n1 2 3 4 5 6 \\n1\\n1 1 1 1 1 \\n4\\n1 1 1 1 1 2 3 4 \\n'}, {'type': 'stdin_stdout', 'input': '4\\n4\\n0011\\n6\\n111111\\n5\\n10101\\n8\\n01000000\\n', 'output': '2\\n1 2 2 1\\n6\\n1 2 3 4 5 6\\n1\\n1 1 1 1 1\\n6\\n1 1 1 2 3 4 5 6\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4\\n1011\\n6\\n111111\\n5\\n10101\\n8\\n01000000\\n', 'output': '2\\n1 1 1 2\\n6\\n1 2 3 4 5 6\\n1\\n1 1 1 1 1\\n6\\n1 1 1 2 3 4 5 6\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4\\n1011\\n6\\n111111\\n5\\n10101\\n8\\n01010000\\n', 'output': '2\\n1 1 1 2\\n6\\n1 2 3 4 5 6\\n1\\n1 1 1 1 1\\n4\\n1 1 1 1 1 2 3 4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4\\n0001\\n6\\n111111\\n5\\n10101\\n8\\n01000000\\n', 'output': '3\\n1 2 3 3\\n6\\n1 2 3 4 5 6\\n1\\n1 1 1 1 1\\n6\\n1 1 1 2 3 4 5 6\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4\\n0000\\n6\\n111111\\n5\\n10101\\n8\\n01000000\\n', 'output': '4\\n1 2 3 4\\n6\\n1 2 3 4 5 6\\n1\\n1 1 1 1 1\\n6\\n1 1 1 2 3 4 5 6\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4\\n0010\\n6\\n111111\\n5\\n10101\\n8\\n01000000\\n', 'output': '2\\n1 2 2 2\\n6\\n1 2 3 4 5 6\\n1\\n1 1 1 1 1\\n6\\n1 1 1 2 3 4 5 6\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4\\n1000\\n6\\n111111\\n5\\n10101\\n8\\n01000000\\n', 'output': '3\\n1 1 2 3\\n6\\n1 2 3 4 5 6\\n1\\n1 1 1 1 1\\n6\\n1 1 1 2 3 4 5 6\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4\\n1011\\n6\\n111111\\n5\\n10101\\n8\\n01000100\\n', 'output': '2\\n1 1 1 2\\n6\\n1 2 3 4 5 6\\n1\\n1 1 1 1 1\\n4\\n1 1 1 2 3 3 3 4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4\\n0010\\n6\\n111111\\n5\\n10101\\n8\\n01001000\\n', 'output': '2\\n1 2 2 2\\n6\\n1 2 3 4 5 6\\n1\\n1 1 1 1 1\\n4\\n1 1 1 2 2 2 3 4\\n'}, {'type': 'stdin_stdout', 'input': 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{'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78853","program":"```python\nt=int(input())\nfor _ in range(t):\n n=int(input())\n s=str(input())\n arr=[]\n for i in range(n):\n arr.append(int(s[i]))\n ones=[]\n zeros=[]\n vals=[]\n k=0\n for i in range(n):\n p=arr[i]\n if(p==0):\n if(ones==[]):\n zeros.append(k+1)\n vals.append(k+1)\n k+=1\n else:\n zeros.append(ones[-1])\n vals.append(ones[-1])\n ones.pop()\n else:\n if(zeros==[]):\n ones.append(k+1)\n vals.append(k+1)\n k+=1\n else:\n ones.append(zeros[-1])\n vals.append(ones[-1])\n zeros.pop()\n print(max(vals))\n for i in vals:\n print(i,end=\" \")\n print()\n\n\n```","inputs":"4\n4\n0011\n6\n111111\n5\n10101\n8\n01010000\n","output":"2\n1 2 2 1 \n6\n1 2 3 4 5 6 \n1\n1 1 1 1 1 \n4\n1 1 1 1 1 2 3 4 \n","actual_output":"2\n1 2 2 1 \n6\n1 2 3 4 5 6 \n1\n1 1 1 1 1 \n4\n1 1 1 1 1 2 3 4 \n","execution_success":true,"sample_index":12563},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1492_A. Three swimmers","prompt":"Solve the following coding problem using the programming language python:\n\nThree swimmers decided to organize a party in the swimming pool! At noon, they started to swim from the left side of the pool.\n\nIt takes the first swimmer exactly a minutes to swim across the entire pool and come back, exactly b minutes for the second swimmer and c minutes for the third. Hence, the first swimmer will be on the left side of the pool after 0, a, 2a, 3a, ... minutes after the start time, the second one will be at 0, b, 2b, 3b, ... minutes, and the third one will be on the left side of the pool after 0, c, 2c, 3c, ... minutes.\n\nYou came to the left side of the pool exactly p minutes after they started swimming. Determine how long you have to wait before one of the swimmers arrives at the left side of the pool.\n\nInput\n\nThe first line of the input contains a single integer t (1 \u2264 t \u2264 1000) \u2014 the number of test cases. Next t lines contains test case descriptions, one per line.\n\nEach line contains four integers p, a, b and c (1 \u2264 p, a, b, c \u2264 10^{18}), time in minutes after the start, when you came to the pool and times in minutes it take the swimmers to cross the entire pool and come back.\n\nOutput\n\nFor each test case, output one integer \u2014 how long you have to wait (in minutes) before one of the swimmers arrives at the left side of the pool.\n\nExample\n\nInput\n\n\n4\n9 5 4 8\n2 6 10 9\n10 2 5 10\n10 9 9 9\n\n\nOutput\n\n\n1\n4\n0\n8\n\nNote\n\nIn the first test case, the first swimmer is on the left side in 0, 5, 10, 15, \u2026 minutes after the start time, the second swimmer is on the left side in 0, 4, 8, 12, \u2026 minutes after the start time, and the third swimmer is on the left side in 0, 8, 16, 24, \u2026 minutes after the start time. You arrived at the pool in 9 minutes after the start time and in a minute you will meet the first swimmer on the left side.\n\nIn the second test case, the first swimmer is on the left side in 0, 6, 12, 18, \u2026 minutes after the start time, the second swimmer is on the left side in 0, 10, 20, 30, \u2026 minutes after the start time, and the third swimmer is on the left side in 0, 9, 18, 27, \u2026 minutes after the start time. You arrived at the pool 2 minutes after the start time and after 4 minutes meet the first swimmer on the left side.\n\nIn the third test case, you came to the pool 10 minutes after the start time. At the same time, all three swimmers are on the left side. A rare stroke of luck!\n\nIn the fourth test case, all swimmers are located on the left side in 0, 9, 18, 27, \u2026 minutes after the start time. You arrived at the pool 10 minutes after the start time and after 8 minutes meet all three swimmers on the left side.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nt=int(input())\nfor i in range(t):\n p,a,b,c=map(int,input().split())\n if(p%a==0 or p%b==0 or p%c==0):\n print(0)\n else:\n a1=a-p%a\n b1=b-p%b\n c1=c-p%c\n print(min(a1,b1,c1))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n9 5 4 8\\n2 6 10 9\\n10 2 5 10\\n10 9 9 9\\n', 'output': '\\n1\\n4\\n0\\n8\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2 3 4\\n1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000\\n', 'output': '1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 1 1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n100 10 10 10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8 2 2 2\\n', 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2\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_78869","program":"```python\nt=int(input())\nfor i in range(t):\n p,a,b,c=map(int,input().split())\n if(p%a==0 or p%b==0 or p%c==0):\n print(0)\n else:\n a1=a-p%a\n b1=b-p%b\n c1=c-p%c\n print(min(a1,b1,c1))\n```","inputs":"4\n9 5 4 8\n2 6 10 9\n10 2 5 10\n10 9 9 9\n","output":"\n1\n4\n0\n8\n","actual_output":"1\n4\n0\n8\n","execution_success":true,"sample_index":12564},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1515_B. Phoenix and Puzzle","prompt":"Solve the following coding problem using the programming language python:\n\nPhoenix is playing with a new puzzle, which consists of n identical puzzle pieces. Each puzzle piece is a right isosceles triangle as shown below.\n\n A puzzle piece\n\nThe goal of the puzzle is to create a square using the n pieces. He is allowed to rotate and move the pieces around, but none of them can overlap and all n pieces must be used (of course, the square shouldn't contain any holes as well). Can he do it?\n\nInput\n\nThe input consists of multiple test cases. The first line contains an integer t (1 \u2264 t \u2264 10^4) \u2014 the number of test cases.\n\nThe first line of each test case contains an integer n (1 \u2264 n \u2264 10^9) \u2014 the number of puzzle pieces.\n\nOutput\n\nFor each test case, if Phoenix can create a square with the n puzzle pieces, print YES. Otherwise, print NO.\n\nExample\n\nInput\n\n\n3\n2\n4\n6\n\n\nOutput\n\n\nYES\nYES\nNO\n\nNote\n\nFor n=2, Phoenix can create a square like this:\n\n\n\nFor n=4, Phoenix can create a square like this:\n\n\n\nFor n=6, it is impossible for Phoenix to create a square.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\n\ndef issqr(x):\n root = int(math.sqrt(x))\n return root*root == x\n\n\nfor i in range(int(input())):\n n = int(input())\n print(\"YES\" if (n % 4 == 0 and issqr(n//4)) or (n % 2 == 0 and issqr(n//2)) else \"NO\")\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n2\\n4\\n6\\n', 'output': '\\nYES\\nYES\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n200040002\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1458\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 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'3\\n161593\\n795679\\n9732885\\n', 'output': 'NO\\nNO\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9064\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n21\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\n190294334\\n', 'output': 'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78873","program":"```python\nimport math\n\ndef issqr(x):\n root = int(math.sqrt(x))\n return root*root == x\n\n\nfor i in range(int(input())):\n n = int(input())\n print(\"YES\" if (n % 4 == 0 and issqr(n//4)) or (n % 2 == 0 and issqr(n//2)) else \"NO\")\n\n\n```","inputs":"3\n2\n4\n6\n","output":"\nYES\nYES\nNO\n","actual_output":"YES\nYES\nNO\n","execution_success":true,"sample_index":12565},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"16_A. Flag","prompt":"Solve the following coding problem using the programming language python:\n\nAccording to a new ISO standard, a flag of every country should have a chequered field n \u00d7 m, each square should be of one of 10 colours, and the flag should be \u00abstriped\u00bb: each horizontal row of the flag should contain squares of the same colour, and the colours of adjacent horizontal rows should be different. Berland's government asked you to find out whether their flag meets the new ISO standard.\n\nInput\n\nThe first line of the input contains numbers n and m (1 \u2264 n, m \u2264 100), n \u2014 the amount of rows, m \u2014 the amount of columns on the flag of Berland. Then there follows the description of the flag: each of the following n lines contain m characters. Each character is a digit between 0 and 9, and stands for the colour of the corresponding square.\n\nOutput\n\nOutput YES, if the flag meets the new ISO standard, and NO otherwise.\n\nExamples\n\nInput\n\n3 3\n000\n111\n222\n\n\nOutput\n\nYES\n\n\nInput\n\n3 3\n000\n000\n111\n\n\nOutput\n\nNO\n\n\nInput\n\n3 3\n000\n111\n002\n\n\nOutput\n\nNO\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#--------------------#\n#INCLUDE \n#INCLUDE \n#Mitchell Broom - Ascension\n#--------------------#\n_=list(map(int,input().split()))\n__=True\n____=\"WTF\"\nfor _i_ in range(_[0]):\n ___=input()\n if((___.count(___[0])!=_[1]) or (___[0]==____)):__=False\n ____=___[0]\n \nprint(\"YES\" if(__) else \"NO\")\n\n'''UseFull Code\na=list(map(int,input().split()))\nprint(\"Yes\" if() else \"No\")\ndef func(a):\n return a\n'''\n\n\n\n\n```","verification_info":"{'test_cases': 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'NO\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n2222222222\\n5555555555\\n0000000000\\n1818298371\\n1111111111\\n3333333393\\n3333333333\\n5555555555\\n0000001000\\n8888888888\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '100 1\\n3\\n6\\n4\\n3\\n0\\n2\\n8\\n7\\n3\\n2\\n1\\n7\\n1\\n3\\n2\\n3\\n6\\n9\\n0\\n8\\n5\\n9\\n7\\n9\\n2\\n1\\n4\\n5\\n1\\n5\\n2\\n5\\n1\\n4\\n6\\n4\\n9\\n1\\n0\\n2\\n1\\n4\\n7\\n1\\n4\\n8\\n0\\n9\\n2\\n1\\n5\\n2\\n8\\n6\\n9\\n5\\n8\\n6\\n4\\n5\\n9\\n2\\n7\\n4\\n1\\n5\\n8\\n0\\n9\\n5\\n4\\n6\\n5\\n0\\n6\\n3\\n6\\n9\\n7\\n2\\n0\\n9\\n7\\n3\\n2\\n4\\n9\\n4\\n7\\n1\\n2\\n3\\n1\\n7\\n9\\n1\\n9\\n0\\n4\\n0\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '100 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{'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 64000000}","problem_id":"vfc_78881","program":"```python\n#--------------------#\n#INCLUDE \n#INCLUDE \n#Mitchell Broom - Ascension\n#--------------------#\n_=list(map(int,input().split()))\n__=True\n____=\"WTF\"\nfor _i_ in range(_[0]):\n ___=input()\n if((___.count(___[0])!=_[1]) or (___[0]==____)):__=False\n ____=___[0]\n \nprint(\"YES\" if(__) else \"NO\")\n\n'''UseFull Code\na=list(map(int,input().split()))\nprint(\"Yes\" if() else \"No\")\ndef func(a):\n return a\n'''\n\n\n\n\n```","inputs":"3 3\n000\n111\n222\n","output":"YES\n","actual_output":"YES\n","execution_success":true,"sample_index":12567},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"18_D. Seller Bob","prompt":"Solve the following coding problem using the programming language python:\n\nLast year Bob earned by selling memory sticks. During each of n days of his work one of the two following events took place: \n\n * A customer came to Bob and asked to sell him a 2x MB memory stick. If Bob had such a stick, he sold it and got 2x berllars. \n * Bob won some programming competition and got a 2x MB memory stick as a prize. Bob could choose whether to present this memory stick to one of his friends, or keep it. \n\n\n\nBob never kept more than one memory stick, as he feared to mix up their capacities, and deceive a customer unintentionally. It is also known that for each memory stick capacity there was at most one customer, who wanted to buy that memory stick. Now, knowing all the customers' demands and all the prizes won at programming competitions during the last n days, Bob wants to know, how much money he could have earned, if he had acted optimally.\n\nInput\n\nThe first input line contains number n (1 \u2264 n \u2264 5000) \u2014 amount of Bob's working days. The following n lines contain the description of the days. Line sell x stands for a day when a customer came to Bob to buy a 2x MB memory stick (0 \u2264 x \u2264 2000). It's guaranteed that for each x there is not more than one line sell x. Line win x stands for a day when Bob won a 2x MB memory stick (0 \u2264 x \u2264 2000).\n\nOutput\n\nOutput the maximum possible earnings for Bob in berllars, that he would have had if he had known all the events beforehand. Don't forget, please, that Bob can't keep more than one memory stick at a time.\n\nExamples\n\nInput\n\n7\nwin 10\nwin 5\nwin 3\nsell 5\nsell 3\nwin 10\nsell 10\n\n\nOutput\n\n1056\n\n\nInput\n\n3\nwin 5\nsell 6\nsell 4\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN = int(input())\nL = [-1]*2010\nDP = [0]*5010 \nfor i in range(N):\n type, cost = input().split()\n cost = int(cost)\n if type == 'win':\n L[cost] = i\n elif L[cost] >= 0:\n DP[i+1] = DP[L[cost]]+(2**cost)\n DP[i+1] = max(DP[i], DP[i+1])\n\nprint(DP[N])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7\\nwin 10\\nwin 5\\nwin 3\\nsell 5\\nsell 3\\nwin 10\\nsell 10\\n', 'output': '1056'}, {'type': 'stdin_stdout', 'input': '3\\nwin 5\\nsell 6\\nsell 4\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '10\\nsell 1898\\nsell 173\\nsell 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'37459511778596727480858760720167552241582636504705413766024169777495064333423937410125519624693990051069809575647477719465460756326341562228323606665869931977125977431028709943048934214062888966581139223580790503937962827597404798307897711090567429316074325427043388117806141094834711707585035634104732053207572824560382256822381896137634917837418011451418600670420262233038302769514657987275395603183231932590514967758448684812835077179931120264124255904131622324626826482075849954994562117191444873727266355570044116588593617660577322335922552832\\n'}, {'type': 'stdin_stdout', 'input': '3\\nwin 5\\nsell 5\\nsell 4\\n', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '50\\nwin 879\\nwin 1153\\nwin 698\\nwin 157\\nwin 827\\nwin 679\\nsell 1229\\nwin 454\\nsell 879\\nsell 1222\\nwin 924\\nwin 1299\\nsell 1366\\nwin 879\\nsell 754\\nwin 1153\\nwin 679\\nwin 1185\\nsell 1469\\nsell 454\\nsell 679\\nsell 1153\\nwin 1469\\nwin 827\\nwin 1469\\nwin 1024\\nwin 1222\\nsell 157\\nsell 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'50\\nwin 1591\\nwin 312\\nwin 1591\\nwin 1277\\nwin 1732\\nwin 1277\\nwio 312\\nwin 1591\\nwin 210\\nwin 1591\\nwin 210\\nsell 1732\\nwin 312\\nwin 1732\\nwin 27\\nwin 806\\nwin 312\\nwin 335\\nwin 1732\\nwin 1732\\nwin 1591\\nwin 1732\\nwin 312\\nwin 1732\\nsell 1277\\nwin 1732\\nwin 122\\nwin 1277\\nwin 1277\\nwin 312\\nwin 1732\\nsell 312\\nsell 1591\\nwin 312\\nsell 210\\nwin 1732\\nwin 312\\nwin 210\\nwin 1591\\nwin 1591\\nwin 1732\\nwin 210\\nwin 1591\\nwin 312\\nwin 1277\\nwin 1591\\nwin 210\\nwin 1277\\nwin 1732\\nwin 312\\n', 'output': '242076421085601533121480182229588271844683586517707293607002496132411388729940774296845920178420062834624757301763441746010546631764156379581707477186085071202076812331089925164562628051526427012787429215360336068956545137295317100874974947680765612791480196235312998044554168362117288724043949686944398076090584492158866870105340458144509288773298578659308033230246800934736490650674288806394915879489475670424368581394758154921413642738814892708785895233344029541505059055047991576663770535319340081784952493339253407744\\n'}, {'type': 'stdin_stdout', 'input': '50\\nwin 1591\\nwin 312\\nwin 1591\\nwin 1277\\nwin 1732\\nwin 1277\\nwio 312\\nwin 1591\\nwin 210\\nwin 1591\\nwin 210\\nsell 1732\\nwin 312\\nwin 1732\\nwin 27\\nwin 806\\nwin 312\\nwin 335\\nwin 1732\\nwin 1732\\nwin 1591\\nwin 1732\\nwin 312\\nwin 1732\\nsell 1277\\nwin 1732\\nwin 122\\nwin 1277\\nwin 1277\\nwin 312\\nwin 1732\\nsekl 312\\nsell 1591\\nwin 312\\nsell 210\\nwin 1732\\nwin 312\\nwin 210\\nwin 1591\\nwin 1591\\nwin 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'242076421085601533121480182229588271844683586517707293607002496132411388729940774296845920178420062834624757301763441746010546631764156379581707477186085071202076812331089925164562628051526427012787429215360336068956545137295317100874974947680765612791480196235312998044554168362117288724043949686944398076090584492158866870105340458144509288773298578659308033230246800934736490650674288806394915879489475670424368581394758154921413642738814892708785895233344029541505059055047991576663770535319340081784952493339253407744\\n'}, {'type': 'stdin_stdout', 'input': '50\\nwin 879\\nwin 1153\\nwin 1469\\nwin 157\\nwin 827\\nwin 679\\nsell 1229\\nwin 454\\nsell 879\\nsell 1222\\nwin 924\\nwin 1299\\nsell 1366\\nwin 879\\nsell 754\\nwin 1153\\nwin 679\\nwin 1185\\nsell 1469\\nsell 454\\nsell 679\\nsell 1153\\nwin 1469\\nwin 827\\nwin 1469\\nwin 1024\\nwin 1222\\nsell 157\\nsell 1185\\nsell 827\\nwin 1469\\nsell 1569\\nwin 754\\nsell 1024\\nwin 924\\nwin 924\\nsell 1876\\nsell 479\\nsell 435\\nwin 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'16332912310228701097717316802721870128775022868221080314403305773060286348016616983179506327297989866534783694332203603069900790667846028602603898749788769867206327097934433881603593880774778104853105937620753202513845830781396468839434689035327911539335925798473899153215505268301939672678983012311225261177070282290958328569587449928340374890197297462448526671963786572758011646874155763250281850311510811863346015732742889066278088442118144\\n'}, {'type': 'stdin_stdout', 'input': '10\\nsell 1898\\nsell 173\\nsell 1635\\nsell 19\\nsell 1145\\nsell 434\\nsell 1236\\nsell 14\\nwin 29\\nsell 1165\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '50\\nwin 879\\nwin 1153\\nwin 1469\\nwin 157\\nwin 827\\nwin 679\\nsell 1229\\nwin 454\\nsell 879\\nsell 1222\\nwin 924\\nwin 1299\\nsell 1366\\nwin 879\\nsell 754\\nwin 1153\\nwin 679\\nwin 1185\\nsell 1469\\nsell 454\\nsell 679\\nsell 1153\\nwin 1469\\nwin 827\\nwin 1469\\nwin 1024\\nwin 1222\\nsell 157\\nslle 1185\\nsell 827\\nwin 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1591\\nwin 1732\\nwin 210\\nwin 1591\\nwin 312\\nwin 1277\\nwin 1591\\nwin 339\\nwin 1277\\nwin 1732\\nwin 312\\n', 'output': '242076421085601533121480182229588271844683586517707293607002496132411388729940774296845920178420062834624757301763441746010546631764156379581707477186085071202076812331089925164562628051526427012787429215360336068956545137295317100874974947680765612791480196235312998044554168362117288724043949686944398076090584492158866870105340458144509288773298578659308033230246800934736490650674288806394915879489475670424368581394758154921413642738814892708785895233344029541505059055047991576663770535319340081784952493339253407744\\n'}, {'type': 'stdin_stdout', 'input': '2\\nwin 2000\\nsell 350\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\nsell 944\\nsell 173\\nsell 1635\\nsell 29\\nsell 1145\\nsell 276\\nsell 1236\\nsell 14\\nwin 29\\nsell 1165\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '50\\nwin 1591\\nwin 312\\nwin 1591\\nwin 1277\\nwin 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'242076421085601533121480182229588271844683586517707293607002496132411388729940774296845920178420062834624757301763441746010546631764156379581707477186085071202076812331089925164562628051526427012787429215360336068956545137295317100874974947680765612791480196235312998044554168362117288724043949686944398076090584492158866870105340458144509288773298578659308033230246800934736490650674288806394915879489475670424368581394758154921413642738814892708785895233344029541505059055047991576663770535319340081784952493339253407744\\n'}, {'type': 'stdin_stdout', 'input': '50\\nsell 1549\\nwin 1168\\nsell 1120\\nwin 741\\nsell 633\\nwin 274\\nsell 1936\\nwin 1168\\nsell 614\\nwin 33\\nsell 1778\\nwin 127\\nsell 1168\\nwin 64\\nwin 256\\nsell 1474\\nwin 518\\nwin 1685\\nsell 1796\\nsell 741\\nsell 485\\nwin 747\\nsell 588\\nsell 1048\\nwin 1580\\nwin 60\\nsell 1685\\nsell 1580\\nsell 1535\\nwin 485\\nsell 31\\nsell 747\\nsell 1473\\nsell 518\\nwin 633\\nsell 1313\\nwin 1580\\nsell 1560\\nsell 127\\nsell 274\\nwin 123\\nwin 31\\nsell 2\\nsell 33\\nwin 1778\\nsell 1834\\nsell 60\\nsell 1751\\nsell 1287\\nwin 1549\\n', 'output': '1720056425011773151265118871077591733216276990085092619030835675616738576936900493041118761959770055340668032173576279597675976622004777210845027112875371906527379337573212312341811682481516081119925150514042583039122963732518350292624889782510925425243478590699982487521431988980734651291693696303059520879874887472437061826782122289965998009474317347011699360401227487786089319043200666474560882786695043543699741809763479940250459103751744852630592882730442346682844060264911915000945522663154937378111488\\n'}, {'type': 'stdin_stdout', 'input': '50\\nwin 1591\\nwin 312\\nwin 1591\\nwin 1277\\nwin 1732\\nwin 1277\\nwio 312\\nwin 1591\\nwin 210\\nwin 1591\\nwin 210\\nsell 1732\\nwin 312\\nwin 1732\\nwin 27\\nwin 806\\nwin 312\\nwin 335\\nwin 1732\\nwin 1732\\nwin 1591\\nwin 1732\\nwin 312\\nwin 1732\\nsell 620\\nwin 1732\\nwin 122\\nwin 1277\\nwin 1277\\nwin 312\\nwin 1732\\nsell 45\\nsell 1591\\nwin 312\\nsell 210\\nwin 1732\\nwin 312\\nwin 210\\nwin 1591\\nwin 1591\\nwin 1732\\nwin 210\\nwin 1591\\nwin 312\\nwin 1277\\nwin 1591\\nwin 210\\nwin 1277\\nwin 1732\\nwin 312\\n', 'output': '242076421085601533121480182229588271844683586517707293607002496132411388729940774296845920178420062834624757301763441746010546631764156379581707477186085071202076812331089925164562628051526427012787429215360336068956545137295317100874974947680765612791480196235312998044554168362117288724043949686944398076090584492158866870105340458144509288773298578659308033230246800934736490650674288806394915879489475670424368581394758154921413642738814892708785895233344029541505059055047991576663770535319340081784952493339253407744\\n'}, {'type': 'stdin_stdout', 'input': '50\\nwin 1591\\nwin 312\\nwin 1591\\nwin 1277\\nwin 1732\\nwin 1277\\nwio 312\\nwin 1591\\nwin 210\\nwin 1591\\nniw 210\\nsell 1732\\nwin 312\\nwin 1732\\nwin 27\\nwin 806\\nwin 312\\nwin 335\\nwin 1732\\nwin 1732\\nwin 1591\\nwin 1732\\nniw 312\\nwin 1732\\nsell 1277\\nwin 1732\\nwin 122\\nwin 1277\\nwin 1277\\nwin 312\\nwin 1732\\nsekl 312\\nsell 1591\\nwin 312\\nsell 210\\nwin 1732\\nwin 312\\nwin 210\\nwin 1591\\nwin 1591\\nwin 1732\\nwin 210\\nwin 1591\\nwin 312\\nwin 1277\\nwin 1591\\nwin 210\\nwin 1277\\nwin 1732\\nwin 312\\n', 'output': '242076421085601533121480182229588271844683586517707293607002496132411388729940774296845920178420062834624757301763441746010546631764156379581707477186085071202076812331089925164562628051526427012787429215360336068956545137295317100874974947680765612791480196235312998044554168362117288724043949686944398076090584492158866870105340458144509288773298578659308033230246800934736490650674288806394915879489475670424368581394758154921413642738814892708785895233344029541505059055047991576663770535319340081784952493339253407744\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 128000000}","problem_id":"vfc_78885","program":"```python\nN = int(input())\nL = [-1]*2010\nDP = [0]*5010 \nfor i in range(N):\n type, cost = input().split()\n cost = int(cost)\n if type == 'win':\n L[cost] = i\n elif L[cost] >= 0:\n DP[i+1] = DP[L[cost]]+(2**cost)\n DP[i+1] = max(DP[i], DP[i+1])\n\nprint(DP[N])\n```","inputs":"7\nwin 10\nwin 5\nwin 3\nsell 5\nsell 3\nwin 10\nsell 10\n","output":"1056","actual_output":"1056\n","execution_success":true,"sample_index":12568},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"237_D. T-decomposition","prompt":"Solve the following coding problem using the programming language python:\n\nYou've got a undirected tree s, consisting of n nodes. Your task is to build an optimal T-decomposition for it. Let's define a T-decomposition as follows.\n\nLet's denote the set of all nodes s as v. Let's consider an undirected tree t, whose nodes are some non-empty subsets of v, we'll call them xi . The tree t is a T-decomposition of s, if the following conditions holds:\n\n 1. the union of all xi equals v; \n 2. for any edge (a, b) of tree s exists the tree node t, containing both a and b; \n 3. if the nodes of the tree t xi and xj contain the node a of the tree s, then all nodes of the tree t, lying on the path from xi to xj also contain node a. So this condition is equivalent to the following: all nodes of the tree t, that contain node a of the tree s, form a connected subtree of tree t. \n\n\n\nThere are obviously many distinct trees t, that are T-decompositions of the tree s. For example, a T-decomposition is a tree that consists of a single node, equal to set v.\n\nLet's define the cardinality of node xi as the number of nodes in tree s, containing in the node. Let's choose the node with the maximum cardinality in t. Let's assume that its cardinality equals w. Then the weight of T-decomposition t is value w. The optimal T-decomposition is the one with the minimum weight.\n\nYour task is to find the optimal T-decomposition of the given tree s that has the minimum number of nodes.\n\nInput\n\nThe first line contains a single integer n (2 \u2264 n \u2264 105), that denotes the number of nodes in tree s.\n\nEach of the following n - 1 lines contains two space-separated integers ai, bi (1 \u2264 ai, bi \u2264 n; ai \u2260 bi), denoting that the nodes of tree s with indices ai and bi are connected by an edge.\n\nConsider the nodes of tree s indexed from 1 to n. It is guaranteed that s is a tree.\n\nOutput\n\nIn the first line print a single integer m that denotes the number of nodes in the required T-decomposition.\n\nThen print m lines, containing descriptions of the T-decomposition nodes. In the i-th (1 \u2264 i \u2264 m) of them print the description of node xi of the T-decomposition. The description of each node xi should start from an integer ki, that represents the number of nodes of the initial tree s, that are contained in the node xi. Then you should print ki distinct space-separated integers \u2014 the numbers of nodes from s, contained in xi, in arbitrary order.\n\nThen print m - 1 lines, each consisting two integers pi, qi (1 \u2264 pi, qi \u2264 m; pi \u2260 qi). The pair of integers pi, qi means there is an edge between nodes xpi and xqi of T-decomposition.\n\nThe printed T-decomposition should be the optimal T-decomposition for the given tree s and have the minimum possible number of nodes among all optimal T-decompositions. If there are multiple optimal T-decompositions with the minimum number of nodes, print any of them.\n\nExamples\n\nInput\n\n2\n1 2\n\n\nOutput\n\n1\n2 1 2\n\n\nInput\n\n3\n1 2\n2 3\n\n\nOutput\n\n2\n2 1 2\n2 2 3\n1 2\n\n\nInput\n\n4\n2 1\n3 1\n4 1\n\n\nOutput\n\n3\n2 2 1\n2 3 1\n2 4 1\n1 2\n2 3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\nN = 10**5 + 5\ng = [[] for _ in range(N)]\np = [0]*N\ndef bfs(cur):\n\tq = [cur]\n\ti = 0\n\twhile i < len(q):\n\t\tcur = q[i]\n\t\ti += 1\n\t\tfor nxt in g[cur]:\n\t\t\tif(nxt != p[cur]):\n\t\t\t\tp[nxt] = cur\n\t\t\t\tq.append(nxt)\nn = int(input())\nfor i in range(n-1):\n\ta, b = map(int, input().split())\n\tg[a].append(b)\n\tg[b].append(a)\nbfs(1)\nprint(n-1)\nfor i in range(2, n+1):\n\tprint(2, i, p[i])\nfor i in range(len(g[1])-1):\n\tprint(g[1][i]-1, g[1][i+1]-1)\nfor i in range(2, n+1):\n\tfor c in g[i]:\n\t\tif c != p[i]:\n\t\t\tprint(i-1, c-1)\n\t\t\n \t \t\t \t \t \t \t\t \t \t\t \t\t\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n2 1\\n3 1\\n4 1\\n', 'output': '3\\n2 2 1\\n2 3 1\\n2 4 1\\n1 2\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2\\n', 'output': '1\\n2 1 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2\\n2 3\\n', 'output': '2\\n2 1 2\\n2 2 3\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '23\\n10 19\\n11 2\\n15 18\\n8 14\\n15 7\\n23 6\\n21 5\\n14 1\\n10 13\\n8 23\\n19 16\\n12 3\\n8 10\\n8 21\\n14 11\\n6 22\\n7 8\\n4 15\\n9 12\\n15 9\\n1 20\\n11 17\\n', 'output': '22\\n2 10 19\\n2 11 2\\n2 15 18\\n2 8 14\\n2 15 7\\n2 23 6\\n2 21 5\\n2 14 1\\n2 10 13\\n2 8 23\\n2 19 16\\n2 12 3\\n2 8 10\\n2 8 21\\n2 14 11\\n2 6 22\\n2 7 8\\n2 4 15\\n2 9 12\\n2 15 9\\n2 1 20\\n2 11 17\\n8 21\\n6 16\\n5 17\\n4 10\\n10 13\\n13 14\\n14 17\\n19 20\\n1 9\\n9 13\\n2 15\\n15 22\\n12 19\\n4 8\\n8 15\\n3 5\\n5 18\\n18 20\\n1 11\\n7 14\\n6 10\\n'}, {'type': 'stdin_stdout', 'input': '23\\n10 19\\n11 2\\n15 18\\n8 14\\n15 7\\n23 6\\n21 5\\n14 1\\n10 13\\n8 23\\n19 16\\n12 3\\n8 10\\n8 21\\n14 11\\n6 22\\n7 8\\n4 15\\n9 12\\n15 9\\n1 20\\n11 17\\n', 'output': '22\\n2 10 19\\n2 11 2\\n2 15 18\\n2 8 14\\n2 15 7\\n2 23 6\\n2 21 5\\n2 14 1\\n2 10 13\\n2 8 23\\n2 19 16\\n2 12 3\\n2 8 10\\n2 8 21\\n2 14 11\\n2 6 22\\n2 7 8\\n2 4 15\\n2 9 12\\n2 15 9\\n2 1 20\\n2 11 17\\n8 21\\n6 16\\n5 17\\n4 10\\n10 13\\n13 14\\n14 17\\n19 20\\n1 9\\n9 13\\n2 15\\n15 22\\n12 19\\n4 8\\n8 15\\n3 5\\n5 18\\n18 20\\n1 11\\n7 14\\n6 10\\n'}, {'type': 'stdin_stdout', 'input': '22\\n10 11\\n8 10\\n8 15\\n3 17\\n8 20\\n15 5\\n10 1\\n10 13\\n11 9\\n19 3\\n9 14\\n5 7\\n19 2\\n8 18\\n11 4\\n15 22\\n15 19\\n15 6\\n8 12\\n17 21\\n13 16\\n', 'output': '21\\n2 10 11\\n2 8 10\\n2 8 15\\n2 3 17\\n2 8 20\\n2 15 5\\n2 10 1\\n2 10 13\\n2 11 9\\n2 19 3\\n2 9 14\\n2 5 7\\n2 19 2\\n2 8 18\\n2 11 4\\n2 15 22\\n2 15 19\\n2 15 6\\n2 8 12\\n2 17 21\\n2 13 16\\n4 10\\n6 12\\n2 3\\n3 5\\n5 14\\n14 19\\n9 11\\n1 2\\n2 7\\n7 8\\n1 9\\n9 15\\n8 21\\n3 6\\n6 16\\n16 17\\n17 18\\n4 20\\n10 13\\n13 17\\n'}, {'type': 'stdin_stdout', 'input': '20\\n19 2\\n19 18\\n20 9\\n20 10\\n18 4\\n17 5\\n17 13\\n11 17\\n20 3\\n11 1\\n18 7\\n11 20\\n20 16\\n5 15\\n19 6\\n11 14\\n20 8\\n17 12\\n11 19\\n', 'output': '19\\n2 19 2\\n2 19 18\\n2 20 9\\n2 20 10\\n2 18 4\\n2 17 5\\n2 17 13\\n2 11 17\\n2 20 3\\n2 11 1\\n2 18 7\\n2 11 20\\n2 20 16\\n2 5 15\\n2 19 6\\n2 11 14\\n2 20 8\\n2 17 12\\n2 11 19\\n6 14\\n8 10\\n10 12\\n12 16\\n16 19\\n6 7\\n7 8\\n8 18\\n2 5\\n5 11\\n1 2\\n2 15\\n15 19\\n3 4\\n4 9\\n9 12\\n12 13\\n13 17\\n'}, {'type': 'stdin_stdout', 'input': '24\\n12 22\\n4 12\\n11 9\\n14 19\\n20 3\\n16 24\\n3 14\\n14 23\\n15 8\\n8 20\\n1 11\\n1 7\\n11 13\\n2 15\\n3 10\\n16 5\\n14 21\\n6 2\\n11 16\\n24 17\\n8 1\\n3 4\\n7 18\\n', 'output': '23\\n2 12 22\\n2 4 12\\n2 11 9\\n2 14 19\\n2 20 3\\n2 16 24\\n2 3 14\\n2 14 23\\n2 15 8\\n2 8 20\\n2 1 11\\n2 1 7\\n2 11 13\\n2 2 15\\n2 3 10\\n2 16 5\\n2 14 21\\n2 6 2\\n2 11 16\\n2 24 17\\n2 8 1\\n2 3 4\\n2 7 18\\n11 12\\n12 21\\n14 18\\n5 7\\n7 15\\n15 22\\n2 22\\n12 23\\n9 10\\n10 21\\n3 11\\n11 13\\n13 19\\n1 2\\n4 7\\n7 8\\n8 17\\n9 14\\n6 16\\n16 19\\n5 10\\n6 20\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 5\\n4 3\\n4 2\\n4 6\\n3 1\\n', 'output': '5\\n2 2 5\\n2 4 3\\n2 4 2\\n2 4 6\\n2 3 1\\n1 3\\n2 5\\n2 3\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '24\\n12 22\\n4 12\\n11 9\\n14 19\\n20 3\\n16 24\\n3 14\\n14 23\\n15 8\\n8 20\\n1 11\\n1 7\\n11 13\\n2 15\\n3 10\\n16 5\\n14 21\\n6 2\\n11 16\\n24 17\\n8 1\\n3 4\\n7 18\\n', 'output': '23\\n2 12 22\\n2 4 12\\n2 11 9\\n2 14 19\\n2 20 3\\n2 16 24\\n2 3 14\\n2 14 23\\n2 15 8\\n2 8 20\\n2 1 11\\n2 1 7\\n2 11 13\\n2 2 15\\n2 3 10\\n2 16 5\\n2 14 21\\n2 6 2\\n2 11 16\\n2 24 17\\n2 8 1\\n2 3 4\\n2 7 18\\n11 12\\n12 21\\n14 18\\n5 7\\n7 15\\n15 22\\n2 22\\n12 23\\n9 10\\n10 21\\n3 11\\n11 13\\n13 19\\n1 2\\n4 7\\n7 8\\n8 17\\n9 14\\n6 16\\n16 19\\n5 10\\n6 20\\n'}, {'type': 'stdin_stdout', 'input': '20\\n19 2\\n19 18\\n20 9\\n20 10\\n18 4\\n17 5\\n17 13\\n11 17\\n20 3\\n11 1\\n18 7\\n11 20\\n20 16\\n5 15\\n19 6\\n11 14\\n20 8\\n17 12\\n11 19\\n', 'output': '19\\n2 19 2\\n2 19 18\\n2 20 9\\n2 20 10\\n2 18 4\\n2 17 5\\n2 17 13\\n2 11 17\\n2 20 3\\n2 11 1\\n2 18 7\\n2 11 20\\n2 20 16\\n2 5 15\\n2 19 6\\n2 11 14\\n2 20 8\\n2 17 12\\n2 11 19\\n6 14\\n8 10\\n10 12\\n12 16\\n16 19\\n6 7\\n7 8\\n8 18\\n2 5\\n5 11\\n1 2\\n2 15\\n15 19\\n3 4\\n4 9\\n9 12\\n12 13\\n13 17\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 4\\n3 1\\n3 2\\n', 'output': '3\\n2 1 4\\n2 3 1\\n2 3 2\\n1 2\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n3 6\\n4 2\\n3 4\\n3 1\\n6 5\\n', 'output': '5\\n2 3 6\\n2 4 2\\n2 3 4\\n2 3 1\\n2 6 5\\n1 3\\n3 4\\n2 3\\n1 5\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2\\n1 3\\n4 5\\n4 1\\n', 'output': '4\\n2 1 2\\n2 1 3\\n2 4 5\\n2 4 1\\n1 2\\n2 4\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '21\\n2 8\\n9 15\\n7 5\\n14 6\\n19 7\\n9 1\\n2 10\\n16 14\\n16 17\\n19 2\\n2 12\\n19 11\\n16 18\\n2 13\\n19 9\\n19 16\\n1 20\\n14 21\\n1 3\\n2 4\\n', 'output': '20\\n2 2 8\\n2 9 15\\n2 7 5\\n2 14 6\\n2 19 7\\n2 9 1\\n2 2 10\\n2 16 14\\n2 16 17\\n2 19 2\\n2 2 12\\n2 19 11\\n2 16 18\\n2 2 13\\n2 19 9\\n2 19 16\\n2 1 20\\n2 14 21\\n2 1 3\\n2 2 4\\n6 17\\n17 19\\n1 7\\n7 10\\n10 11\\n11 14\\n14 20\\n3 5\\n2 6\\n6 15\\n4 8\\n8 18\\n8 9\\n9 13\\n13 16\\n5 10\\n10 12\\n12 15\\n15 16\\n'}, {'type': 'stdin_stdout', 'input': '25\\n13 1\\n4 17\\n15 25\\n3 21\\n1 6\\n1 9\\n12 15\\n13 4\\n24 19\\n22 24\\n8 20\\n4 11\\n11 14\\n17 16\\n15 7\\n23 3\\n22 13\\n3 5\\n6 10\\n16 18\\n24 23\\n10 2\\n9 8\\n7 22\\n', 'output': '24\\n2 13 1\\n2 4 17\\n2 15 25\\n2 3 21\\n2 1 6\\n2 1 9\\n2 12 15\\n2 13 4\\n2 24 19\\n2 22 24\\n2 8 20\\n2 4 11\\n2 11 14\\n2 17 16\\n2 15 7\\n2 23 3\\n2 22 13\\n2 3 5\\n2 6 10\\n2 16 18\\n2 24 23\\n2 10 2\\n2 9 8\\n2 7 22\\n1 5\\n5 6\\n4 16\\n16 18\\n2 8\\n8 12\\n5 19\\n15 24\\n11 23\\n6 23\\n19 22\\n12 13\\n1 8\\n8 17\\n3 7\\n7 15\\n14 20\\n2 14\\n10 17\\n17 24\\n16 21\\n9 10\\n10 21\\n'}, {'type': 'stdin_stdout', 'input': '6\\n3 2\\n6 5\\n1 3\\n1 4\\n6 1\\n', 'output': '5\\n2 3 2\\n2 6 5\\n2 1 3\\n2 1 4\\n2 6 1\\n3 4\\n4 5\\n1 3\\n2 5\\n'}, {'type': 'stdin_stdout', 'input': '22\\n10 11\\n8 10\\n8 15\\n3 17\\n8 20\\n15 5\\n10 1\\n10 13\\n11 9\\n19 3\\n9 14\\n5 7\\n19 2\\n8 18\\n11 4\\n15 22\\n15 19\\n15 6\\n8 12\\n17 21\\n13 16\\n', 'output': '21\\n2 10 11\\n2 8 10\\n2 8 15\\n2 3 17\\n2 8 20\\n2 15 5\\n2 10 1\\n2 10 13\\n2 11 9\\n2 19 3\\n2 9 14\\n2 5 7\\n2 19 2\\n2 8 18\\n2 11 4\\n2 15 22\\n2 15 19\\n2 15 6\\n2 8 12\\n2 17 21\\n2 13 16\\n4 10\\n6 12\\n2 3\\n3 5\\n5 14\\n14 19\\n9 11\\n1 2\\n2 7\\n7 8\\n1 9\\n9 15\\n8 21\\n3 6\\n6 16\\n16 17\\n17 18\\n4 20\\n10 13\\n13 17\\n'}, {'type': 'stdin_stdout', 'input': '21\\n2 8\\n9 15\\n7 5\\n14 6\\n19 7\\n9 1\\n2 10\\n16 14\\n16 17\\n19 2\\n2 12\\n19 11\\n16 18\\n2 13\\n19 9\\n19 16\\n1 20\\n14 21\\n1 3\\n2 4\\n', 'output': '20\\n2 2 8\\n2 9 15\\n2 7 5\\n2 14 6\\n2 19 7\\n2 9 1\\n2 2 10\\n2 16 14\\n2 16 17\\n2 19 2\\n2 2 12\\n2 19 11\\n2 16 18\\n2 2 13\\n2 19 9\\n2 19 16\\n2 1 20\\n2 14 21\\n2 1 3\\n2 2 4\\n6 17\\n17 19\\n1 7\\n7 10\\n10 11\\n11 14\\n14 20\\n3 5\\n2 6\\n6 15\\n4 8\\n8 18\\n8 9\\n9 13\\n13 16\\n5 10\\n10 12\\n12 15\\n15 16\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5\\n5 3\\n2 4\\n4 1\\n', 'output': '4\\n2 1 5\\n2 5 3\\n2 2 4\\n2 4 1\\n1 4\\n3 4\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5\\n5 2\\n1 4\\n1 3\\n', 'output': '4\\n2 1 5\\n2 5 2\\n2 1 4\\n2 1 3\\n1 3\\n3 4\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '25\\n13 1\\n4 17\\n15 25\\n3 21\\n1 6\\n1 9\\n12 15\\n13 4\\n24 19\\n22 24\\n8 20\\n4 11\\n11 14\\n17 16\\n15 7\\n23 3\\n22 13\\n3 5\\n6 10\\n16 18\\n24 23\\n10 2\\n9 8\\n7 22\\n', 'output': '24\\n2 13 1\\n2 4 17\\n2 15 25\\n2 3 21\\n2 1 6\\n2 1 9\\n2 12 15\\n2 13 4\\n2 24 19\\n2 22 24\\n2 8 20\\n2 4 11\\n2 11 14\\n2 17 16\\n2 15 7\\n2 23 3\\n2 22 13\\n2 3 5\\n2 6 10\\n2 16 18\\n2 24 23\\n2 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10\\n2 16 5\\n2 14 21\\n2 6 2\\n2 11 16\\n2 24 17\\n2 8 1\\n2 3 4\\n2 7 18\\n11 12\\n12 21\\n14 18\\n5 7\\n7 15\\n15 22\\n2 22\\n10 12\\n12 23\\n9 10\\n10 21\\n3 11\\n3 13\\n13 19\\n1 2\\n4 7\\n7 8\\n8 17\\n9 14\\n6 16\\n16 19\\n6 20\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78893","program":"```python\nimport sys\ninput = sys.stdin.readline\nN = 10**5 + 5\ng = [[] for _ in range(N)]\np = [0]*N\ndef bfs(cur):\n\tq = [cur]\n\ti = 0\n\twhile i < len(q):\n\t\tcur = q[i]\n\t\ti += 1\n\t\tfor nxt in g[cur]:\n\t\t\tif(nxt != p[cur]):\n\t\t\t\tp[nxt] = cur\n\t\t\t\tq.append(nxt)\nn = int(input())\nfor i in range(n-1):\n\ta, b = map(int, input().split())\n\tg[a].append(b)\n\tg[b].append(a)\nbfs(1)\nprint(n-1)\nfor i in range(2, n+1):\n\tprint(2, i, p[i])\nfor i in range(len(g[1])-1):\n\tprint(g[1][i]-1, g[1][i+1]-1)\nfor i in range(2, n+1):\n\tfor c in g[i]:\n\t\tif c != p[i]:\n\t\t\tprint(i-1, c-1)\n\t\t\n \t \t\t \t \t \t \t\t \t \t\t \t\t\n```","inputs":"4\n2 1\n3 1\n4 1\n","output":"3\n2 2 1\n2 3 1\n2 4 1\n1 2\n2 3\n","actual_output":"3\n2 2 1\n2 3 1\n2 4 1\n1 2\n2 3\n","execution_success":true,"sample_index":12569},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"262_B. Roma and Changing Signs","prompt":"Solve the following coding problem using the programming language python:\n\nRoma works in a company that sells TVs. Now he has to prepare a report for the last year.\n\nRoma has got a list of the company's incomes. The list is a sequence that consists of n integers. The total income of the company is the sum of all integers in sequence. Roma decided to perform exactly k changes of signs of several numbers in the sequence. He can also change the sign of a number one, two or more times.\n\nThe operation of changing a number's sign is the operation of multiplying this number by -1.\n\nHelp Roma perform the changes so as to make the total income of the company (the sum of numbers in the resulting sequence) maximum. Note that Roma should perform exactly k changes.\n\nInput\n\nThe first line contains two integers n and k (1 \u2264 n, k \u2264 105), showing, how many numbers are in the sequence and how many swaps are to be made.\n\nThe second line contains a non-decreasing sequence, consisting of n integers ai (|ai| \u2264 104).\n\nThe numbers in the lines are separated by single spaces. Please note that the given sequence is sorted in non-decreasing order.\n\nOutput\n\nIn the single line print the answer to the problem \u2014 the maximum total income that we can obtain after exactly k changes.\n\nExamples\n\nInput\n\n3 2\n-1 -1 1\n\n\nOutput\n\n3\n\n\nInput\n\n3 1\n-1 -1 1\n\n\nOutput\n\n1\n\nNote\n\nIn the first sample we can get sequence [1, 1, 1], thus the total income equals 3.\n\nIn the second test, the optimal strategy is to get sequence [-1, 1, 1], thus the total income equals 1.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nrd = lambda: list(map(int, input().split()))\n\nk = kk = rd()[1]\n\na = rd()\n\nk -= sum(x<0 for x in a)\n\na[:kk] = list(map(abs, a[:kk]))\n\nprint(sum(a)-(2*min(a) if k>0 and k&1 else 0))\n\n\n\n# Made By Mostafa_Khaled\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 2\\n-1 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'4\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n-3 0 2\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n-3 1 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n-2 1 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n-2 0 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n-3 0 2\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n-3 0 4\\n', 'output': '7\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78897","program":"```python\nrd = lambda: list(map(int, input().split()))\n\nk = kk = rd()[1]\n\na = rd()\n\nk -= sum(x<0 for x in a)\n\na[:kk] = list(map(abs, a[:kk]))\n\nprint(sum(a)-(2*min(a) if k>0 and k&1 else 0))\n\n\n\n# Made By Mostafa_Khaled\n```","inputs":"3 2\n-1 -1 1\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12570},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"400_C. Inna and Huge Candy Matrix","prompt":"Solve the following coding problem using the programming language python:\n\nInna and Dima decided to surprise Sereja. They brought a really huge candy matrix, it's big even for Sereja! Let's number the rows of the giant matrix from 1 to n from top to bottom and the columns \u2014 from 1 to m, from left to right. We'll represent the cell on the intersection of the i-th row and j-th column as (i, j). Just as is expected, some cells of the giant candy matrix contain candies. Overall the matrix has p candies: the k-th candy is at cell (xk, yk).\n\nThe time moved closer to dinner and Inna was already going to eat p of her favourite sweets from the matrix, when suddenly Sereja (for the reason he didn't share with anyone) rotated the matrix x times clockwise by 90 degrees. Then he performed the horizontal rotate of the matrix y times. And then he rotated the matrix z times counterclockwise by 90 degrees. The figure below shows how the rotates of the matrix looks like.\n\n\n\nInna got really upset, but Duma suddenly understood two things: the candies didn't get damaged and he remembered which cells contained Inna's favourite sweets before Sereja's strange actions. Help guys to find the new coordinates in the candy matrix after the transformation Sereja made!\n\nInput\n\nThe first line of the input contains fix integers n, m, x, y, z, p (1 \u2264 n, m \u2264 109; 0 \u2264 x, y, z \u2264 109; 1 \u2264 p \u2264 105).\n\nEach of the following p lines contains two integers xk, yk (1 \u2264 xk \u2264 n; 1 \u2264 yk \u2264 m) \u2014 the initial coordinates of the k-th candy. Two candies can lie on the same cell.\n\nOutput\n\nFor each of the p candies, print on a single line its space-separated new coordinates.\n\nExamples\n\nInput\n\n3 3 3 1 1 9\n1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2\n3 3\n\n\nOutput\n\n1 3\n1 2\n1 1\n2 3\n2 2\n2 1\n3 3\n3 2\n3 1\n\nNote\n\nJust for clarity. Horizontal rotating is like a mirroring of the matrix. For matrix:\n \n \n \n QWER REWQ \n ASDF -> FDSA \n ZXCV VCXZ \n \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,m,x,y,z,p=map(int,input().split())\nx=x%4\ny=y%2\nz=z%4\nn0,m0=n,m\nfor i in range(p):\n n,m=n0,m0\n x1,y1=map(int,input().split())\n for j in range(x):\n x1,y1=y1,n-x1+1\n n,m=m,n\n if y==1:\n y1=m-y1+1\n# print(x1,y1) \n for i in range(z): \n x1,y1=m-y1+1,x1\n n,m=m,n\n print(x1,y1) \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 3 3 1 1 9\\n1 1\\n1 2\\n1 3\\n2 1\\n2 2\\n2 3\\n3 1\\n3 2\\n3 3\\n', 'output': '1 3\\n1 2\\n1 1\\n2 3\\n2 2\\n2 1\\n3 3\\n3 2\\n3 1\\n'}, {'type': 'stdin_stdout', 'input': '85 26 48272945 423830401 423026164 3\\n35 1\\n50 17\\n55 2\\n', 'output': '1 35\\n17 50\\n2 55\\n'}, {'type': 'stdin_stdout', 'input': '67 61 443905131 226973811 158369983 1\\n52 51\\n', 'output': '16 51\\n'}, 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n,m=m,n\n if y==1:\n y1=m-y1+1\n# print(x1,y1) \n for i in range(z): \n x1,y1=m-y1+1,x1\n n,m=m,n\n print(x1,y1) \n```","inputs":"3 3 3 1 1 9\n1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2\n3 3\n","output":"1 3\n1 2\n1 1\n2 3\n2 2\n2 1\n3 3\n3 2\n3 1\n","actual_output":"1 3\n1 2\n1 1\n2 3\n2 2\n2 1\n3 3\n3 2\n3 1\n","execution_success":true,"sample_index":12571},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"450_B. Jzzhu and Sequences","prompt":"Solve the following coding problem using the programming language python:\n\nJzzhu has invented a kind of sequences, they meet the following property:\n\n\n\nYou are given x and y, please calculate fn modulo 1000000007 (109 + 7).\n\nInput\n\nThe first line contains two integers x and y (|x|, |y| \u2264 109). The second line contains a single integer n (1 \u2264 n \u2264 2\u00b7109).\n\nOutput\n\nOutput a single integer representing fn modulo 1000000007 (109 + 7).\n\nExamples\n\nInput\n\n2 3\n3\n\n\nOutput\n\n1\n\n\nInput\n\n0 -1\n2\n\n\nOutput\n\n1000000006\n\nNote\n\nIn the first sample, f2 = f1 + f3, 3 = 2 + f3, f3 = 1.\n\nIn the second sample, f2 = - 1; - 1 modulo (109 + 7) equals (109 + 6).\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,m=map(int,input().split())\nk=int(input())\nl=m-n\ns=[n,m,l]\nz=(k-1)//3\nif(z%2==0):\n print((s[k%3-1])%1000000007)\nelse:\n print((-1*s[k%3-1])%1000000007)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '0 -1\\n2\\n', 'output': '1000000006\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n6\\n', 'output': '1000000006\\n'}, 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print((-1*s[k%3-1])%1000000007)\n\n```","inputs":"0 -1\n2\n","output":"1000000006\n","actual_output":"1000000006\n","execution_success":true,"sample_index":12572},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"472_C. Design Tutorial: Make It Nondeterministic","prompt":"Solve the following coding problem using the programming language python:\n\nA way to make a new task is to make it nondeterministic or probabilistic. For example, the hard task of Topcoder SRM 595, Constellation, is the probabilistic version of a convex hull.\n\nLet's try to make a new task. Firstly we will use the following task. There are n people, sort them by their name. It is just an ordinary sorting problem, but we can make it more interesting by adding nondeterministic element. There are n people, each person will use either his/her first name or last name as a handle. Can the lexicographical order of the handles be exactly equal to the given permutation p?\n\nMore formally, if we denote the handle of the i-th person as hi, then the following condition must hold: .\n\nInput\n\nThe first line contains an integer n (1 \u2264 n \u2264 105) \u2014 the number of people.\n\nThe next n lines each contains two strings. The i-th line contains strings fi and si (1 \u2264 |fi|, |si| \u2264 50) \u2014 the first name and last name of the i-th person. Each string consists only of lowercase English letters. All of the given 2n strings will be distinct.\n\nThe next line contains n distinct integers: p1, p2, ..., pn (1 \u2264 pi \u2264 n).\n\nOutput\n\nIf it is possible, output \"YES\", otherwise output \"NO\".\n\nExamples\n\nInput\n\n3\ngennady korotkevich\npetr mitrichev\ngaoyuan chen\n1 2 3\n\n\nOutput\n\nNO\n\n\nInput\n\n3\ngennady korotkevich\npetr mitrichev\ngaoyuan chen\n3 1 2\n\n\nOutput\n\nYES\n\n\nInput\n\n2\ngalileo galilei\nnicolaus copernicus\n2 1\n\n\nOutput\n\nYES\n\n\nInput\n\n10\nrean schwarzer\nfei claussell\nalisa reinford\neliot craig\nlaura arseid\njusis albarea\nmachias regnitz\nsara valestin\nemma millstein\ngaius worzel\n1 2 3 4 5 6 7 8 9 10\n\n\nOutput\n\nNO\n\n\nInput\n\n10\nrean schwarzer\nfei claussell\nalisa reinford\neliot craig\nlaura arseid\njusis albarea\nmachias regnitz\nsara valestin\nemma millstein\ngaius worzel\n2 4 9 6 5 7 1 3 8 10\n\n\nOutput\n\nYES\n\nNote\n\nIn example 1 and 2, we have 3 people: tourist, Petr and me (cgy4ever). You can see that whatever handle is chosen, I must be the first, then tourist and Petr must be the last.\n\nIn example 3, if Copernicus uses \"copernicus\" as his handle, everything will be alright.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# itne me hi thakk gaye?\nn = int(input())\narr = []\nfor i in range(n):\n arr.append(sorted(input().split()))\nto_get = [i-1 for i in list(map(int, input().split()))]\n# print(arr)\n# print(to_get)\nok = True\nchecked = \"\"\nfor i in to_get:\n if(arr[i][0] > checked):\n curr = arr[i][0]\n else:\n curr = arr[i][1]\n # print(curr, checked)\n if (curr < checked):\n ok = False\n break\n checked = curr\nif ok:\n print(\"YES\")\nelse:\n print(\"NO\")\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\ngennady korotkevich\\npetr mitrichev\\ngaoyuan chen\\n3 1 2\\n', 'output': 'YES\\n'}, 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mitrichev\\ngaoyuan nhce\\n3 1 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3\\nydannef hcivektorok\\noetr mitrichev\\ngaoyuan nhec\\n3 1 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3\\na a\\nzzz zzzz\\nz {z\\n1 2 3\\n', 'output': 'YES\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78933","program":"```python\n# itne me hi thakk gaye?\nn = int(input())\narr = []\nfor i in range(n):\n arr.append(sorted(input().split()))\nto_get = [i-1 for i in list(map(int, input().split()))]\n# print(arr)\n# print(to_get)\nok = True\nchecked = \"\"\nfor i in to_get:\n if(arr[i][0] > checked):\n curr = arr[i][0]\n else:\n curr = arr[i][1]\n # print(curr, checked)\n if (curr < checked):\n ok = False\n break\n checked = curr\nif ok:\n print(\"YES\")\nelse:\n print(\"NO\")\n```","inputs":"3\ngennady korotkevich\npetr mitrichev\ngaoyuan chen\n3 1 2\n","output":"YES\n","actual_output":"YES\n","execution_success":true,"sample_index":12573},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"496_D. Tennis Game","prompt":"Solve the following coding problem using the programming language python:\n\nPetya and Gena love playing table tennis. A single match is played according to the following rules: a match consists of multiple sets, each set consists of multiple serves. Each serve is won by one of the players, this player scores one point. As soon as one of the players scores t points, he wins the set; then the next set starts and scores of both players are being set to 0. As soon as one of the players wins the total of s sets, he wins the match and the match is over. Here s and t are some positive integer numbers.\n\nTo spice it up, Petya and Gena choose new numbers s and t before every match. Besides, for the sake of history they keep a record of each match: that is, for each serve they write down the winner. Serve winners are recorded in the chronological order. In a record the set is over as soon as one of the players scores t points and the match is over as soon as one of the players wins s sets.\n\nPetya and Gena have found a record of an old match. Unfortunately, the sequence of serves in the record isn't divided into sets and numbers s and t for the given match are also lost. The players now wonder what values of s and t might be. Can you determine all the possible options?\n\nInput\n\nThe first line contains a single integer n \u2014 the length of the sequence of games (1 \u2264 n \u2264 105).\n\nThe second line contains n space-separated integers ai. If ai = 1, then the i-th serve was won by Petya, if ai = 2, then the i-th serve was won by Gena.\n\nIt is not guaranteed that at least one option for numbers s and t corresponds to the given record.\n\nOutput\n\nIn the first line print a single number k \u2014 the number of options for numbers s and t.\n\nIn each of the following k lines print two integers si and ti \u2014 the option for numbers s and t. Print the options in the order of increasing si, and for equal si \u2014 in the order of increasing ti.\n\nExamples\n\nInput\n\n5\n1 2 1 2 1\n\n\nOutput\n\n2\n1 3\n3 1\n\n\nInput\n\n4\n1 1 1 1\n\n\nOutput\n\n3\n1 4\n2 2\n4 1\n\n\nInput\n\n4\n1 2 1 2\n\n\nOutput\n\n0\n\n\nInput\n\n8\n2 1 2 1 1 1 1 1\n\n\nOutput\n\n3\n1 6\n2 3\n6 1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#!/usr/bin/env python3\n\nimport itertools\n\nn = int(input())\na = [int(x) for x in input().split()]\n\nwinner = a[-1]\nlooser = 3 - winner\nserve_win_cnt, serve_loose_cnt, win_pos, loose_pos, result = [0], [0], [-1], [-1], []\nwin_cnt = a.count(winner)\n\nfor i in range(n):\n if a[i] == winner:\n win_pos.append(i)\n else:\n loose_pos.append(i)\n serve_win_cnt.append(serve_win_cnt[-1] + (a[i] == winner))\n serve_loose_cnt.append(serve_loose_cnt[-1] + (a[i] == looser))\n\nwin_pos += [n * 10] * n\nloose_pos += [n * 10] * n\nserve_win_cnt += [0] * n\nserve_loose_cnt += [0] * n\n\nfor t in itertools.chain(range(1, 1 + win_cnt // 2), [win_cnt]):\n s = l = i = 0\n sw = sl = 0\n while i < n:\n xw = win_pos[serve_win_cnt[i] + t]\n xl = loose_pos[serve_loose_cnt[i] + t]\n if xw < xl:\n s += 1\n else:\n l += 1\n i = min(xw, xl) + 1\n if s > l and i <= n and serve_win_cnt[i] == win_cnt:\n result.append((s, t))\n\nprint(len(result))\nfor (x, y) in sorted(result):\n print(x, y)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '8\\n2 1 2 1 1 1 1 1\\n', 'output': '3\\n1 6\\n2 3\\n6 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1 1\\n', 'output': '3\\n1 4\\n2 2\\n4 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 1 2 1\\n', 'output': '2\\n1 3\\n3 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 1 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 2 2 1 1 2 2 1 1\\n', 'output': '4\\n1 6\\n2 3\\n3 2\\n6 1\\n'}, {'type': 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a[-1]\nlooser = 3 - winner\nserve_win_cnt, serve_loose_cnt, win_pos, loose_pos, result = [0], [0], [-1], [-1], []\nwin_cnt = a.count(winner)\n\nfor i in range(n):\n if a[i] == winner:\n win_pos.append(i)\n else:\n loose_pos.append(i)\n serve_win_cnt.append(serve_win_cnt[-1] + (a[i] == winner))\n serve_loose_cnt.append(serve_loose_cnt[-1] + (a[i] == looser))\n\nwin_pos += [n * 10] * n\nloose_pos += [n * 10] * n\nserve_win_cnt += [0] * n\nserve_loose_cnt += [0] * n\n\nfor t in itertools.chain(range(1, 1 + win_cnt // 2), [win_cnt]):\n s = l = i = 0\n sw = sl = 0\n while i < n:\n xw = win_pos[serve_win_cnt[i] + t]\n xl = loose_pos[serve_loose_cnt[i] + t]\n if xw < xl:\n s += 1\n else:\n l += 1\n i = min(xw, xl) + 1\n if s > l and i <= n and serve_win_cnt[i] == win_cnt:\n result.append((s, t))\n\nprint(len(result))\nfor (x, y) in sorted(result):\n print(x, y)\n\n```","inputs":"8\n2 1 2 1 1 1 1 1\n","output":"3\n1 6\n2 3\n6 1\n","actual_output":"3\n1 6\n2 3\n6 1\n","execution_success":true,"sample_index":12574},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"520_A. Pangram","prompt":"Solve the following coding problem using the programming language python:\n\nA word or a sentence in some language is called a pangram if all the characters of the alphabet of this language appear in it at least once. Pangrams are often used to demonstrate fonts in printing or test the output devices.\n\nYou are given a string consisting of lowercase and uppercase Latin letters. Check whether this string is a pangram. We say that the string contains a letter of the Latin alphabet if this letter occurs in the string in uppercase or lowercase.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 100) \u2014 the number of characters in the string.\n\nThe second line contains the string. The string consists only of uppercase and lowercase Latin letters.\n\nOutput\n\nOutput \"YES\", if the string is a pangram and \"NO\" otherwise.\n\nExamples\n\nInput\n\n12\ntoosmallword\n\n\nOutput\n\nNO\n\n\nInput\n\n35\nTheQuickBrownFoxJumpsOverTheLazyDog\n\n\nOutput\n\nYES\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport string\n\ngauge = set(string.ascii_lowercase)\n\nn = int(input())\nline = set(input().lower())\n\nif line == gauge:\n print(\"YES\")\nelse:\n print(\"NO\")\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '12\\ntoosmallword\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '35\\nTheQuickBrownFoxJumpsOverTheLazyDog\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '26\\nxKwzRMpunYaqsdfaBgJcVElTHo\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 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Warrior and Archer","prompt":"Solve the following coding problem using the programming language python:\n\nIn the official contest this problem has a different statement, for which jury's solution was working incorrectly, and for this reason it was excluded from the contest. This mistake have been fixed and the current given problem statement and model solution corresponds to what jury wanted it to be during the contest.\n\nVova and Lesha are friends. They often meet at Vova's place and compete against each other in a computer game named The Ancient Papyri: Swordsink. Vova always chooses a warrior as his fighter and Leshac chooses an archer. After that they should choose initial positions for their characters and start the fight. A warrior is good at melee combat, so Vova will try to make the distance between fighters as small as possible. An archer prefers to keep the enemy at a distance, so Lesha will try to make the initial distance as large as possible.\n\nThere are n (n is always even) possible starting positions for characters marked along the Ox axis. The positions are given by their distinct coordinates x1, x2, ..., xn, two characters cannot end up at the same position.\n\nVova and Lesha take turns banning available positions, Vova moves first. During each turn one of the guys bans exactly one of the remaining positions. Banned positions cannot be used by both Vova and Lesha. They continue to make moves until there are only two possible positions remaining (thus, the total number of moves will be n - 2). After that Vova's character takes the position with the lesser coordinate and Lesha's character takes the position with the bigger coordinate and the guys start fighting.\n\nVova and Lesha are already tired by the game of choosing positions, as they need to play it before every fight, so they asked you (the developer of the The Ancient Papyri: Swordsink) to write a module that would automatically determine the distance at which the warrior and the archer will start fighting if both Vova and Lesha play optimally.\n\nInput\n\nThe first line on the input contains a single integer n (2 \u2264 n \u2264 200 000, n is even) \u2014 the number of positions available initially. The second line contains n distinct integers x1, x2, ..., xn (0 \u2264 xi \u2264 109), giving the coordinates of the corresponding positions.\n\nOutput\n\nPrint the distance between the warrior and the archer at the beginning of the fight, provided that both Vova and Lesha play optimally.\n\nExamples\n\nInput\n\n6\n0 1 3 7 15 31\n\n\nOutput\n\n7\n\n\nInput\n\n2\n73 37\n\n\nOutput\n\n36\n\nNote\n\nIn the first sample one of the optimum behavior of the players looks like that:\n\n 1. Vova bans the position at coordinate 15; \n 2. Lesha bans the position at coordinate 3; \n 3. Vova bans the position at coordinate 31; \n 4. Lesha bans the position at coordinate 1. \n\n\n\nAfter these actions only positions 0 and 7 will remain, and the distance between them is equal to 7.\n\nIn the second sample there are only two possible positions, so there will be no bans.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#!/usr/bin/env python3\n\nn = int(input())\nn_2 = n // 2\nx = sorted([int(tok) for tok in input().split()])\nres = min((x[j] - x[j-n_2] for j in range(n_2, n)))\nprint(res)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n73 37\\n', 'output': '36'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 3 7 15 31\\n', 'output': '7'}, {'type': 'stdin_stdout', 'input': '8\\n729541013 135019377 88372488 319157478 682081360 558614617 258129110 790518782\\n', 'output': '470242129'}, {'type': 'stdin_stdout', 'input': '18\\n515925896 832652240 279975694 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Voting for Photos","prompt":"Solve the following coding problem using the programming language python:\n\nAfter celebrating the midcourse the students of one of the faculties of the Berland State University decided to conduct a vote for the best photo. They published the photos in the social network and agreed on the rules to choose a winner: the photo which gets most likes wins. If multiple photoes get most likes, the winner is the photo that gets this number first.\n\nHelp guys determine the winner photo by the records of likes.\n\nInput\n\nThe first line of the input contains a single integer n (1 \u2264 n \u2264 1000) \u2014 the total likes to the published photoes. \n\nThe second line contains n positive integers a1, a2, ..., an (1 \u2264 ai \u2264 1 000 000), where ai is the identifier of the photo which got the i-th like.\n\nOutput\n\nPrint the identifier of the photo which won the elections.\n\nExamples\n\nInput\n\n5\n1 3 2 2 1\n\n\nOutput\n\n2\n\n\nInput\n\n9\n100 200 300 200 100 300 300 100 200\n\n\nOutput\n\n300\n\nNote\n\nIn the first test sample the photo with id 1 got two likes (first and fifth), photo with id 2 got two likes (third and fourth), and photo with id 3 got one like (second). \n\nThus, the winner is the photo with identifier 2, as it got:\n\n * more likes than the photo with id 3; \n * as many likes as the photo with id 1, but the photo with the identifier 2 got its second like earlier. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import Counter\nn=int(input())\na=[int(i) for i in input().split(' ')]\nc=Counter()\nmx=-1\nmxid=-1\nfor i in range(n):\n c[a[i]]+=1\n if c[a[i]]>mx:\n mx=c[a[i]]\n mxid=a[i]\nprint(mxid)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '9\\n100 200 300 200 100 300 300 100 200\\n', 'output': '300'}, {'type': 'stdin_stdout', 'input': '5\\n1 3 2 2 1\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n1 3 4 2 2\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '2\\n1000000 1000000\\n', 'output': '1000000'}, {'type': 'stdin_stdout', 'input': '12\\n2 3 1 2 3 3 3 2 1 1 2 1\\n', 'output': '3'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 2 3 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640039 640039 587006 974886 474463 474463 474463 640039 708667 474463 693628 352609 512959 517819 640039 474463 345011 517819\\n', 'output': '474463\\n'}, {'type': 'stdin_stdout', 'input': '15\\n137419 91032 531977 438949 137419 160606 438949 137419 438949 24407 531977 531977 138011 438949 855793\\n', 'output': '438949\\n'}, {'type': 'stdin_stdout', 'input': '9\\n100 200 206 200 001 215 230 101 167\\n', 'output': '200\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2 2 3 4 1 8 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '15\\n010 200 300 500 300 400 600 408 100 155 400 300 98 213 110\\n', 'output': '300\\n'}, {'type': 'stdin_stdout', 'input': '20\\n474463 517819 640039 640039 587006 974886 474463 474463 51436 640039 708667 474463 693628 352609 512959 517819 640039 474463 345011 517819\\n', 'output': '474463\\n'}, {'type': 'stdin_stdout', 'input': '15\\n137419 91032 531977 438949 137419 160606 438949 137419 438949 24407 892917 531977 138011 438949 855793\\n', 'output': '438949\\n'}, {'type': 'stdin_stdout', 'input': '7\\n3 2 3 4 1 8 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '15\\n010 200 300 500 300 400 600 408 100 155 400 280 98 213 110\\n', 'output': '300\\n'}, {'type': 'stdin_stdout', 'input': '20\\n474463 517819 640039 640039 829744 974886 474463 474463 51436 640039 708667 474463 693628 352609 512959 517819 640039 474463 345011 517819\\n', 'output': '474463\\n'}, {'type': 'stdin_stdout', 'input': '15\\n30702 91032 531977 438949 137419 160606 438949 137419 438949 24407 892917 531977 138011 438949 855793\\n', 'output': '438949\\n'}, {'type': 'stdin_stdout', 'input': '7\\n3 2 3 3 1 8 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '15\\n010 200 300 500 300 400 464 408 100 155 400 280 98 213 110\\n', 'output': '300\\n'}, {'type': 'stdin_stdout', 'input': '20\\n474463 517819 640039 640039 829744 974886 474463 474463 54686 640039 708667 474463 693628 352609 512959 517819 640039 474463 345011 517819\\n', 'output': '474463\\n'}, {'type': 'stdin_stdout', 'input': '7\\n3 2 3 3 1 13 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '15\\n010 200 300 500 300 400 464 408 100 155 255 280 98 213 110\\n', 'output': '300\\n'}, {'type': 'stdin_stdout', 'input': '7\\n3 4 3 3 1 13 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '15\\n010 200 300 500 300 400 464 408 110 155 255 280 98 213 110\\n', 'output': '300\\n'}, {'type': 'stdin_stdout', 'input': '7\\n3 7 3 3 1 13 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '15\\n010 200 300 500 300 400 464 408 110 155 255 280 66 213 110\\n', 'output': '300\\n'}, {'type': 'stdin_stdout', 'input': '7\\n3 6 3 3 1 13 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '15\\n010 200 300 500 300 400 464 408 110 155 163 280 66 213 110\\n', 'output': '300\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78961","program":"```python\nfrom collections import Counter\nn=int(input())\na=[int(i) for i in input().split(' ')]\nc=Counter()\nmx=-1\nmxid=-1\nfor i in range(n):\n c[a[i]]+=1\n if c[a[i]]>mx:\n mx=c[a[i]]\n mxid=a[i]\nprint(mxid)\n```","inputs":"9\n100 200 300 200 100 300 300 100 200\n","output":"300","actual_output":"300\n","execution_success":true,"sample_index":12577},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"665_A. Buses Between Cities","prompt":"Solve the following coding problem using the programming language python:\n\nBuses run between the cities A and B, the first one is at 05:00 AM and the last one departs not later than at 11:59 PM. A bus from the city A departs every a minutes and arrives to the city B in a ta minutes, and a bus from the city B departs every b minutes and arrives to the city A in a tb minutes.\n\nThe driver Simion wants to make his job diverse, so he counts the buses going towards him. Simion doesn't count the buses he meet at the start and finish.\n\nYou know the time when Simion departed from the city A to the city B. Calculate the number of buses Simion will meet to be sure in his counting.\n\nInput\n\nThe first line contains two integers a, ta (1 \u2264 a, ta \u2264 120) \u2014 the frequency of the buses from the city A to the city B and the travel time. Both values are given in minutes.\n\nThe second line contains two integers b, tb (1 \u2264 b, tb \u2264 120) \u2014 the frequency of the buses from the city B to the city A and the travel time. Both values are given in minutes.\n\nThe last line contains the departure time of Simion from the city A in the format hh:mm. It is guaranteed that there are a bus from the city A at that time. Note that the hours and the minutes are given with exactly two digits.\n\nOutput\n\nPrint the only integer z \u2014 the number of buses Simion will meet on the way. Note that you should not count the encounters in cities A and B.\n\nExamples\n\nInput\n\n10 30\n10 35\n05:20\n\n\nOutput\n\n5\n\n\nInput\n\n60 120\n24 100\n13:00\n\n\nOutput\n\n9\n\nNote\n\nIn the first example Simion departs form the city A at 05:20 AM and arrives to the city B at 05:50 AM. He will meet the first 5 buses from the city B that departed in the period [05:00 AM - 05:40 AM]. Also Simion will meet a bus in the city B at 05:50 AM, but he will not count it.\n\nAlso note that the first encounter will be between 05:26 AM and 05:27 AM (if we suggest that the buses are go with the sustained speed).\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef solve(a, t1, t2):\n l1 = t1 - (t1 - 300) % a + a\n if (l1 < 300):\n l1 = 300\n l2 = t2 - (t2 - 300) % a\n if (l2 > 1439):\n l2 = 1439\n if (l2 < l1):\n return 0\n return (l2-l1) // a + 1 - (l2 == t2)\n \ndef trans(h, m):\n return 60 * h + m\n \ndata1 = [int(x) for x in input().split()]\ndata2 = [int(x) for x in input().split()]\ndata3 = input()\nh0 = int(data3[0:2])\nm0 = int(data3[-2:])\nt0 = trans(h0, m0)\nsol = solve(data2[0], t0 - data2[1], t0 + data1[1])\nprint(sol)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10 30\\n10 35\\n05:20\\n', 'output': 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35\\n56 112\\n22:30\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '111 10\\n37 101\\n10:03\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '11 13\\n20 4\\n10:30\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '107 66\\n79 78\\n10:40\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 70\\n109 90\\n07:00\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '37 6\\n92 18\\n19:22\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 30\\n2 12\\n11:52\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '16 26\\n48 16\\n07:04\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '30 13\\n56 112\\n22:30\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '11 13\\n25 4\\n10:30\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '107 66\\n114 78\\n10:40\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 70\\n109 90\\n07:00\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '37 6\\n92 1\\n19:22\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '16 26\\n79 16\\n07:04\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '57 13\\n56 112\\n22:30\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '11 13\\n25 6\\n10:30\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '107 66\\n114 46\\n10:40\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 70\\n109 145\\n07:00\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '44 6\\n92 1\\n19:22\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78965","program":"```python\ndef solve(a, t1, t2):\n l1 = t1 - (t1 - 300) % a + a\n if (l1 < 300):\n l1 = 300\n l2 = t2 - (t2 - 300) % a\n if (l2 > 1439):\n l2 = 1439\n if (l2 < l1):\n return 0\n return (l2-l1) // a + 1 - (l2 == t2)\n \ndef trans(h, m):\n return 60 * h + m\n \ndata1 = [int(x) for x in input().split()]\ndata2 = [int(x) for x in input().split()]\ndata3 = input()\nh0 = int(data3[0:2])\nm0 = int(data3[-2:])\nt0 = trans(h0, m0)\nsol = solve(data2[0], t0 - data2[1], t0 + data1[1])\nprint(sol)\n```","inputs":"10 30\n10 35\n05:20\n","output":"5\n","actual_output":"5\n","execution_success":true,"sample_index":12578},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"689_D. Friends and Subsequences","prompt":"Solve the following coding problem using the programming language python:\n\nMike and !Mike are old childhood rivals, they are opposite in everything they do, except programming. Today they have a problem they cannot solve on their own, but together (with you) \u2014 who knows? \n\nEvery one of them has an integer sequences a and b of length n. Being given a query of the form of pair of integers (l, r), Mike can instantly tell the value of while !Mike can instantly tell the value of .\n\nNow suppose a robot (you!) asks them all possible different queries of pairs of integers (l, r) (1 \u2264 l \u2264 r \u2264 n) (so he will make exactly n(n + 1) / 2 queries) and counts how many times their answers coincide, thus for how many pairs is satisfied.\n\nHow many occasions will the robot count?\n\nInput\n\nThe first line contains only integer n (1 \u2264 n \u2264 200 000).\n\nThe second line contains n integer numbers a1, a2, ..., an ( - 109 \u2264 ai \u2264 109) \u2014 the sequence a.\n\nThe third line contains n integer numbers b1, b2, ..., bn ( - 109 \u2264 bi \u2264 109) \u2014 the sequence b.\n\nOutput\n\nPrint the only integer number \u2014 the number of occasions the robot will count, thus for how many pairs is satisfied.\n\nExamples\n\nInput\n\n6\n1 2 3 2 1 4\n6 7 1 2 3 2\n\n\nOutput\n\n2\n\n\nInput\n\n3\n3 3 3\n1 1 1\n\n\nOutput\n\n0\n\nNote\n\nThe occasions in the first sample case are:\n\n1.l = 4,r = 4 since max{2} = min{2}.\n\n2.l = 4,r = 5 since max{2, 1} = min{2, 3}.\n\nThere are no occasions in the second sample case since Mike will answer 3 to any query pair, but !Mike will always answer 1.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom bisect import bisect\n\nHISENTINEL = 10**9 + 1\nLOSENTINEL = -HISENTINEL\n\ndef main():\n length = int(input())\n a = [int(fld) for fld in input().strip().split()]\n b = [int(fld) for fld in input().strip().split()]\n print(countmaxminsubseq(a, b))\n \ndef countmaxminsubseq(a, b):\n leq, lgt = getleftbounds(a, b, 0)\n req, rgt = getleftbounds(reversed(a), reversed(b), 1)\n req = reverseindex(req)\n rgt = reverseindex(rgt)\n count = 0\n for i, (leq1, lgt1, req1, rgt1) in enumerate(zip(leq, lgt, req, rgt)):\n count += (leq1 - lgt1)*(rgt1 - i) + (i - leq1)*(rgt1 - req1)\n return count\n \ndef getleftbounds(a, b, bias):\n astack = [(HISENTINEL, -1)]\n bstack = [(LOSENTINEL, -1)]\n leqarr, lgtarr = [], []\n for i, (aelt, belt) in enumerate(zip(a, b)):\n while astack[-1][0] < aelt + bias:\n astack.pop()\n lgt = astack[-1][1]\n while bstack[-1][0] > belt:\n bstack.pop()\n if belt < aelt:\n leq = lgt = i\n elif belt == aelt:\n leq = i\n istack = bisect(bstack, (aelt, -2)) - 1\n lgt = max(lgt, bstack[istack][1])\n else:\n istack = bisect(bstack, (aelt, i)) - 1\n val, pos = bstack[istack]\n if val < aelt:\n lgt = leq = max(lgt, pos)\n else:\n leq = pos\n istack = bisect(bstack, (aelt, -2)) - 1\n val, pos = bstack[istack]\n lgt = max(lgt, pos)\n leq = max(leq, lgt)\n \n leqarr.append(leq)\n lgtarr.append(lgt)\n astack.append((aelt, i))\n bstack.append((belt, i))\n return leqarr, lgtarr\n \ndef reverseindex(rind):\n pivot = len(rind) - 1\n return [pivot - i for i in reversed(rind)]\n \n \nmain() \n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n3 3 3\\n1 1 1\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 3 2 1 4\\n6 7 1 2 3 2\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '17\\n714413739 -959271262 714413739 -745891378 926207665 -404845105 -404845105 -959271262 -189641729 -670860364 714413739 -189641729 192457837 -745891378 -670860364 536388097 -959271262\\n-417715348 -959271262 -959271262 714413739 -189641729 571055593 571055593 571055593 -417715348 -417715348 192457837 -745891378 536388097 571055593 -189641729 571055593 -670860364\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '1\\n509658558\\n509658558\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 1\\n2 2 2\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '1\\n509658558\\n-544591380\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '17\\n714413739 -959271262 714413739 -745891378 926207665 -404845105 -404845105 -959271262 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'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 -1\\n-1 2 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 1 1\\n1 1 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 2 4 1 0\\n6 3 0 2 6 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '17\\n714413739 -959271262 43767541 -745891378 563275725 -404845105 -404845105 -959271262 -189641729 -670860364 714413739 -189641729 192457837 -745891378 -670860364 536388097 -1159907595\\n-417715348 -959271262 -499828716 714413739 -189641729 559486188 571055593 571055593 -786317052 -729547240 192457837 -745891378 536388097 571055593 -189641729 571055593 -670860364\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 -1\\n-1 3 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 1 1\\n1 0 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 1 4 1 0\\n6 3 0 2 6 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '17\\n714413739 -959271262 43767541 -745891378 563275725 -404845105 -404845105 -959271262 -189641729 -670860364 714413739 -189641729 378872092 -745891378 -670860364 536388097 -1159907595\\n-417715348 -959271262 -499828716 714413739 -189641729 559486188 571055593 571055593 -786317052 -729547240 192457837 -745891378 536388097 571055593 -189641729 571055593 -670860364\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 -1\\n-1 6 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11 1 1\\n1 1 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '17\\n714413739 -959271262 43767541 -745891378 563275725 -404845105 -404845105 -959271262 -189641729 -670860364 714413739 -189641729 378872092 -745891378 -670860364 536388097 -1159907595\\n-417715348 -959271262 -499828716 714413739 -137746773 559486188 571055593 571055593 -786317052 -729547240 192457837 -745891378 536388097 571055593 -189641729 571055593 -670860364\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 -1\\n-1 6 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n19 1 1\\n1 1 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 1 2 1 0\\n3 3 0 2 6 0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '17\\n714413739 -959271262 43767541 -745891378 563275725 -404845105 -404845105 -959271262 -189641729 -670860364 714413739 -300423556 378872092 -745891378 -670860364 536388097 -1159907595\\n-417715348 -959271262 -499828716 714413739 -137746773 559486188 571055593 571055593 -786317052 -729547240 192457837 -745891378 536388097 571055593 -189641729 571055593 -670860364\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 -1\\n-1 6 -1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n19 1 1\\n1 0 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 1 2 1 0\\n3 5 0 2 6 0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '17\\n714413739 -959271262 43767541 -745891378 563275725 -404845105 -404845105 -959271262 -189641729 -670860364 714413739 -300423556 378872092 -745891378 -670860364 536388097 -1159907595\\n-417715348 -959271262 -499828716 714413739 -137746773 559486188 571055593 571055593 -786317052 -729547240 192457837 -846356631 536388097 571055593 -189641729 571055593 -670860364\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 -1\\n0 6 -1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n19 1 2\\n1 0 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 2 2 1 0\\n3 5 0 2 6 0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 -1\\n0 6 -1\\n', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_78969","program":"```python\nfrom bisect import bisect\n\nHISENTINEL = 10**9 + 1\nLOSENTINEL = -HISENTINEL\n\ndef main():\n length = int(input())\n a = [int(fld) for fld in input().strip().split()]\n b = [int(fld) for fld in input().strip().split()]\n print(countmaxminsubseq(a, b))\n \ndef countmaxminsubseq(a, b):\n leq, lgt = getleftbounds(a, b, 0)\n req, rgt = getleftbounds(reversed(a), reversed(b), 1)\n req = reverseindex(req)\n rgt = reverseindex(rgt)\n count = 0\n for i, (leq1, lgt1, req1, rgt1) in enumerate(zip(leq, lgt, req, rgt)):\n count += (leq1 - lgt1)*(rgt1 - i) + (i - leq1)*(rgt1 - req1)\n return count\n \ndef getleftbounds(a, b, bias):\n astack = [(HISENTINEL, -1)]\n bstack = [(LOSENTINEL, -1)]\n leqarr, lgtarr = [], []\n for i, (aelt, belt) in enumerate(zip(a, b)):\n while astack[-1][0] < aelt + bias:\n astack.pop()\n lgt = astack[-1][1]\n while bstack[-1][0] > belt:\n bstack.pop()\n if belt < aelt:\n leq = lgt = i\n elif belt == aelt:\n leq = i\n istack = bisect(bstack, (aelt, -2)) - 1\n lgt = max(lgt, bstack[istack][1])\n else:\n istack = bisect(bstack, (aelt, i)) - 1\n val, pos = bstack[istack]\n if val < aelt:\n lgt = leq = max(lgt, pos)\n else:\n leq = pos\n istack = bisect(bstack, (aelt, -2)) - 1\n val, pos = bstack[istack]\n lgt = max(lgt, pos)\n leq = max(leq, lgt)\n \n leqarr.append(leq)\n lgtarr.append(lgt)\n astack.append((aelt, i))\n bstack.append((belt, i))\n return leqarr, lgtarr\n \ndef reverseindex(rind):\n pivot = len(rind) - 1\n return [pivot - i for i in reversed(rind)]\n \n \nmain() \n\n\n```","inputs":"3\n3 3 3\n1 1 1\n","output":"0","actual_output":"0\n","execution_success":true,"sample_index":12579},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"711_B. Chris and Magic Square","prompt":"Solve the following coding problem using the programming language python:\n\nZS the Coder and Chris the Baboon arrived at the entrance of Udayland. There is a n \u00d7 n magic grid on the entrance which is filled with integers. Chris noticed that exactly one of the cells in the grid is empty, and to enter Udayland, they need to fill a positive integer into the empty cell.\n\nChris tried filling in random numbers but it didn't work. ZS the Coder realizes that they need to fill in a positive integer such that the numbers in the grid form a magic square. This means that he has to fill in a positive integer so that the sum of the numbers in each row of the grid (), each column of the grid (), and the two long diagonals of the grid (the main diagonal \u2014 and the secondary diagonal \u2014 ) are equal. \n\nChris doesn't know what number to fill in. Can you help Chris find the correct positive integer to fill in or determine that it is impossible?\n\nInput\n\nThe first line of the input contains a single integer n (1 \u2264 n \u2264 500) \u2014 the number of rows and columns of the magic grid.\n\nn lines follow, each of them contains n integers. The j-th number in the i-th of them denotes ai, j (1 \u2264 ai, j \u2264 109 or ai, j = 0), the number in the i-th row and j-th column of the magic grid. If the corresponding cell is empty, ai, j will be equal to 0. Otherwise, ai, j is positive.\n\nIt is guaranteed that there is exactly one pair of integers i, j (1 \u2264 i, j \u2264 n) such that ai, j = 0.\n\nOutput\n\nOutput a single integer, the positive integer x (1 \u2264 x \u2264 1018) that should be filled in the empty cell so that the whole grid becomes a magic square. If such positive integer x does not exist, output - 1 instead.\n\nIf there are multiple solutions, you may print any of them.\n\nExamples\n\nInput\n\n3\n4 0 2\n3 5 7\n8 1 6\n\n\nOutput\n\n9\n\n\nInput\n\n4\n1 1 1 1\n1 1 0 1\n1 1 1 1\n1 1 1 1\n\n\nOutput\n\n1\n\n\nInput\n\n4\n1 1 1 1\n1 1 0 1\n1 1 2 1\n1 1 1 1\n\n\nOutput\n\n-1\n\nNote\n\nIn the first sample case, we can fill in 9 into the empty cell to make the resulting grid a magic square. Indeed, \n\nThe sum of numbers in each row is:\n\n4 + 9 + 2 = 3 + 5 + 7 = 8 + 1 + 6 = 15.\n\nThe sum of numbers in each column is:\n\n4 + 3 + 8 = 9 + 5 + 1 = 2 + 7 + 6 = 15.\n\nThe sum of numbers in the two diagonals is:\n\n4 + 5 + 6 = 2 + 5 + 8 = 15.\n\nIn the third sample case, it is impossible to fill a number in the empty square such that the resulting grid is a magic square.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nlines = int(input())\nif lines == 1:\n print(1)\n exit(0)\ngrid = []\nnumber_with_zero = set()\nimpossible = False\nno_zero = -1\n\nfor x in range(lines):\n num = list(map(int, input().split()))\n grid.append(num)\n\nfor line in grid:\n have_zero = False\n s = 0\n for n in line:\n if n ==0:\n have_zero = True\n else:\n s += n\n if have_zero:\n number_with_zero.add(s)\n elif no_zero == -1:\n no_zero = s\n elif no_zero != s:\n impossible = True\n\n# print(impossible, 1)\nfor x in range(lines):\n have_zero = False\n s = 0\n for y in range(lines):\n n = grid[y][x]\n if n ==0:\n have_zero = True\n else:\n s += n\n if have_zero:\n number_with_zero.add(s)\n elif no_zero == -1:\n no_zero = s\n elif no_zero != s:\n impossible = True\n# print(impossible, 2)\n\ns = 0\nhave_zero = False\nfor x in range(lines):\n n = grid[x][x]\n if n ==0:\n have_zero = True\n else:\n s += n\n\n# print(s, no_zero)\nif have_zero:\n number_with_zero.add(s)\nelif no_zero == -1:\n no_zero = s\nelif no_zero != s:\n impossible = True\n# print(impossible, 3)\n\ns = 0\nhave_zero = False\nfor x in range(lines):\n n = grid[x][lines -1 - x]\n if n ==0:\n have_zero = True\n else:\n s += n\n\nif have_zero:\n # print(\"COME\")\n number_with_zero.add(s)\nelif no_zero == -1:\n no_zero = s\nelif no_zero != s:\n impossible = True\n# print(impossible, 4)\n\nif impossible:\n print(-1)\nelse:\n if len(number_with_zero) == 1:\n num = list(number_with_zero)[0]\n # print(num)\n if (no_zero - num <= 0):\n print(-1)\n else:\n print(no_zero - num)\n else:\n print(-1)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1 1 1 1\\n1 1 0 1\\n1 1 1 1\\n1 1 1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 0 2\\n3 5 7\\n8 1 6\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1 1\\n1 1 0 1\\n1 1 2 1\\n1 1 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '11\\n5 5 5 5 5 5 5 5 5 5 5\\n5 5 5 5 5 5 5 5 5 5 5\\n5 5 5 5 5 5 5 5 5 5 5\\n5 5 5 5 5 5 5 5 5 5 5\\n5 5 5 5 5 5 5 5 5 5 5\\n5 5 5 5 5 5 5 5 5 5 5\\n5 5 5 5 5 5 5 5 5 5 5\\n5 5 5 5 5 5 5 5 5 5 5\\n5 5 5 5 13 1 1 5 5 5 5\\n5 5 5 5 5 9 1 5 5 5 5\\n5 5 5 5 0 5 13 5 5 5 5\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 22 1\\n4 10 16\\n19 0 13\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 6 0\\n3 3 5\\n5 2 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 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'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78973","program":"```python\nlines = int(input())\nif lines == 1:\n print(1)\n exit(0)\ngrid = []\nnumber_with_zero = set()\nimpossible = False\nno_zero = -1\n\nfor x in range(lines):\n num = list(map(int, input().split()))\n grid.append(num)\n\nfor line in grid:\n have_zero = False\n s = 0\n for n in line:\n if n ==0:\n have_zero = True\n else:\n s += n\n if have_zero:\n number_with_zero.add(s)\n elif no_zero == -1:\n no_zero = s\n elif no_zero != s:\n impossible = True\n\n# print(impossible, 1)\nfor x in range(lines):\n have_zero = False\n s = 0\n for y in range(lines):\n n = grid[y][x]\n if n ==0:\n have_zero = True\n else:\n s += n\n if have_zero:\n number_with_zero.add(s)\n elif no_zero == -1:\n no_zero = s\n elif no_zero != s:\n impossible = True\n# print(impossible, 2)\n\ns = 0\nhave_zero = False\nfor x in range(lines):\n n = grid[x][x]\n if n ==0:\n have_zero = True\n else:\n s += n\n\n# print(s, no_zero)\nif have_zero:\n number_with_zero.add(s)\nelif no_zero == -1:\n no_zero = s\nelif no_zero != s:\n impossible = True\n# print(impossible, 3)\n\ns = 0\nhave_zero = False\nfor x in range(lines):\n n = grid[x][lines -1 - x]\n if n ==0:\n have_zero = True\n else:\n s += n\n\nif have_zero:\n # print(\"COME\")\n number_with_zero.add(s)\nelif no_zero == -1:\n no_zero = s\nelif no_zero != s:\n impossible = True\n# print(impossible, 4)\n\nif impossible:\n print(-1)\nelse:\n if len(number_with_zero) == 1:\n num = list(number_with_zero)[0]\n # print(num)\n if (no_zero - num <= 0):\n print(-1)\n else:\n print(no_zero - num)\n else:\n print(-1)\n\n```","inputs":"4\n1 1 1 1\n1 1 0 1\n1 1 1 1\n1 1 1 1\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12580},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"732_B. Cormen \u2014 The Best Friend Of a Man","prompt":"Solve the following coding problem using the programming language python:\n\nRecently a dog was bought for Polycarp. The dog's name is Cormen. Now Polycarp has a lot of troubles. For example, Cormen likes going for a walk. \n\nEmpirically Polycarp learned that the dog needs at least k walks for any two consecutive days in order to feel good. For example, if k = 5 and yesterday Polycarp went for a walk with Cormen 2 times, today he has to go for a walk at least 3 times. \n\nPolycarp analysed all his affairs over the next n days and made a sequence of n integers a1, a2, ..., an, where ai is the number of times Polycarp will walk with the dog on the i-th day while doing all his affairs (for example, he has to go to a shop, throw out the trash, etc.).\n\nHelp Polycarp determine the minimum number of walks he needs to do additionaly in the next n days so that Cormen will feel good during all the n days. You can assume that on the day before the first day and on the day after the n-th day Polycarp will go for a walk with Cormen exactly k times. \n\nWrite a program that will find the minumum number of additional walks and the appropriate schedule \u2014 the sequence of integers b1, b2, ..., bn (bi \u2265 ai), where bi means the total number of walks with the dog on the i-th day.\n\nInput\n\nThe first line contains two integers n and k (1 \u2264 n, k \u2264 500) \u2014 the number of days and the minimum number of walks with Cormen for any two consecutive days. \n\nThe second line contains integers a1, a2, ..., an (0 \u2264 ai \u2264 500) \u2014 the number of walks with Cormen on the i-th day which Polycarp has already planned. \n\nOutput\n\nIn the first line print the smallest number of additional walks that Polycarp should do during the next n days so that Cormen will feel good during all days. \n\nIn the second line print n integers b1, b2, ..., bn, where bi \u2014 the total number of walks on the i-th day according to the found solutions (ai \u2264 bi for all i from 1 to n). If there are multiple solutions, print any of them. \n\nExamples\n\nInput\n\n3 5\n2 0 1\n\n\nOutput\n\n4\n2 3 2\n\n\nInput\n\n3 1\n0 0 0\n\n\nOutput\n\n1\n0 1 0\n\n\nInput\n\n4 6\n2 4 3 5\n\n\nOutput\n\n0\n2 4 3 5\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\nn,k=map(int,input().split())\nl2=[]\na=list(map(int,input().split()))\nfor i in a:\n l2.append(i)\ni=1\nl=[a[0]]\nwhile i<=n-1:\n if a[i]+a[i-1] -1:\n if array[b + 1] >= array[b]:\n b = b - 1\n else:\n if len(array[b]) > len(array[b + 1]):\n array[b] = array[b][:len(array[b + 1])]\n array[b] = cut_to_lexicographic(array[b], array[b+1])\nprint(\"\\n\".join(array))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n#book\\n#bigtown\\n#big\\n', 'output': '#b\\n#big\\n#big\\n'}, {'type': 'stdin_stdout', 'input': '3\\n#book\\n#cool\\n#cold\\n', 'output': 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array[b + 1] >= array[b]:\n b = b - 1\n else:\n if len(array[b]) > len(array[b + 1]):\n array[b] = array[b][:len(array[b + 1])]\n array[b] = cut_to_lexicographic(array[b], array[b+1])\nprint(\"\\n\".join(array))\n```","inputs":"3\n#book\n#bigtown\n#big\n","output":"#b\n#big\n#big\n","actual_output":"#b\n#big\n#big\n","execution_success":true,"sample_index":12582},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"802_B. Heidi and Library (medium)","prompt":"Solve the following coding problem using the programming language python:\n\nWhereas humans nowadays read fewer and fewer books on paper, book readership among marmots has surged. Heidi has expanded the library and is now serving longer request sequences.\n\nInput\n\nSame as the easy version, but the limits have changed: 1 \u2264 n, k \u2264 400 000.\n\nOutput\n\nSame as the easy version.\n\nExamples\n\nInput\n\n4 100\n1 2 2 1\n\n\nOutput\n\n2\n\n\nInput\n\n4 1\n1 2 2 1\n\n\nOutput\n\n3\n\n\nInput\n\n4 2\n1 2 3 1\n\n\nOutput\n\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\nfrom collections import deque, defaultdict\nfrom heapq import heappush, heappop\nn, k = map(int, input().split())\nA = list(map(int, input().split()))\ndic = defaultdict(deque)\nfor i, a in enumerate(A):\n dic[a].append(i)\nhp = []\n# for d in dic:\n# heappush(hp, (-dic[d][0], d))\nS = set()\nans = 0\nfor i, a in enumerate(A):\n dic[a].popleft()\n\n if a not in S:\n if len(S) < k:\n S.add(a)\n ans += 1\n else:\n idx = heappop(hp)[1]\n S.discard(idx)\n S.add(a)\n ans += 1\n\n if dic[a]: heappush(hp, (-dic[a][0], a))\n else: heappush(hp, (float(\"-inf\"), a))\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 100\\n1 2 2 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1 2 3 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 2 2 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n1 2 3 1 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1 2 3 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n1 2 3 5 1 10 10 1 1 3 5\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n1 3 3 1 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n1 4 3 5 1 10 10 1 1 3 5\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 110\\n1 2 2 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n1 3 5 1 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n1 2 3 5 1 10 8 1 1 3 5\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 1 1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n2 2 3 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 2 2 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n2 4 3 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 2 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n1 3 5 2 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n2 4 3 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 4 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n1 2 2 1 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 100\\n1 2 4 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1 2 2 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n1 3 3 2 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 110\\n1 3 2 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n2 2 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 010\\n1 3 2 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n3 2 1 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 010\\n1 3 2 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n3 2 1 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 010\\n1 3 2 4\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n3 1 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 010\\n1 1 2 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 110\\n1 1 2 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 1 1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 110\\n2 1 2 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n1 3 3 2 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n1 2 3 10 1 10 10 1 1 3 5\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1 1 3 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 110\\n2 2 2 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n2 2 3 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n2 1 3 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 1 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n1 2 3 5 1 10 8 1 1 3 8\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '4 100\\n1 2 4 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n1 5 3 2 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n2 2 1 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n3 2 2 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n3 4 1 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n3 1 2 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 010\\n2 1 2 4\\n', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 10, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_78989","program":"```python\nimport sys\ninput = sys.stdin.readline\nfrom collections import deque, defaultdict\nfrom heapq import heappush, heappop\nn, k = map(int, input().split())\nA = list(map(int, input().split()))\ndic = defaultdict(deque)\nfor i, a in enumerate(A):\n dic[a].append(i)\nhp = []\n# for d in dic:\n# heappush(hp, (-dic[d][0], d))\nS = set()\nans = 0\nfor i, a in enumerate(A):\n dic[a].popleft()\n\n if a not in S:\n if len(S) < k:\n S.add(a)\n ans += 1\n else:\n idx = heappop(hp)[1]\n S.discard(idx)\n S.add(a)\n ans += 1\n\n if dic[a]: heappush(hp, (-dic[a][0], a))\n else: heappush(hp, (float(\"-inf\"), a))\nprint(ans)\n```","inputs":"4 100\n1 2 2 1\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12583},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"895_C. Square Subsets","prompt":"Solve the following coding problem using the programming language python:\n\nPetya was late for the lesson too. The teacher gave him an additional task. For some array a Petya should find the number of different ways to select non-empty subset of elements from it in such a way that their product is equal to a square of some integer.\n\nTwo ways are considered different if sets of indexes of elements chosen by these ways are different.\n\nSince the answer can be very large, you should find the answer modulo 109 + 7.\n\nInput\n\nFirst line contains one integer n (1 \u2264 n \u2264 105) \u2014 the number of elements in the array.\n\nSecond line contains n integers ai (1 \u2264 ai \u2264 70) \u2014 the elements of the array.\n\nOutput\n\nPrint one integer \u2014 the number of different ways to choose some elements so that their product is a square of a certain integer modulo 109 + 7.\n\nExamples\n\nInput\n\n4\n1 1 1 1\n\n\nOutput\n\n15\n\n\nInput\n\n4\n2 2 2 2\n\n\nOutput\n\n7\n\n\nInput\n\n5\n1 2 4 5 8\n\n\nOutput\n\n7\n\nNote\n\nIn first sample product of elements chosen by any way is 1 and 1 = 12. So the answer is 24 - 1 = 15.\n\nIn second sample there are six different ways to choose elements so that their product is 4, and only one way so that their product is 16. So the answer is 6 + 1 = 7.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import *\n\nl = int(input())\nc = Counter(map(int, input().split()))\nt = defaultdict(int)\np = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67]\n\nfor k, s in c.items():\n d = 0\n for i, q in enumerate(p):\n while k % q == 0:\n k //= q\n d ^= 1 << i\n t[d] += s\n\nu = defaultdict(int)\nu[0] = 1\n\nfor x in t:\n if x: l -= 1\n if 0 < x < 2048:\n v = u.copy()\n for y in u: v[x ^ y] += u[y]\n u = v\n\ne = 1000000007\nprint((u[0] * pow(2, l, e) - 1) % e)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1 1 1 1\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 2 2 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 4 5 8\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 66 19 60 34 27 15 27 42 51\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 2 2 2\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '7\\n53 59 56 9 13 1 28\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n38 58 51 41 61 12 17 47 18 24\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n4 9 16 25 36 49 64\\n', 'output': '127\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 3 4 5 6\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '17\\n44 57 54 57 54 65 40 57 59 16 39 51 32 51 20 9 8\\n', 'output': '511\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 28 46 57 39 26 45\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n27 44 40 3 33 38 56 37 43 36\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n51 4 25 46 15 21 32 9 43 8\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 3 5 7 11\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '18\\n22 41 40 8 36 48 23 5 58 12 26 44 53 49 3 56 58 57\\n', 'output': '127\\n'}, {'type': 'stdin_stdout', 'input': '15\\n66 34 43 45 61 14 12 67 38 25 55 9 30 41 16\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '1\\n64\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n70 70\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n15 45\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n67 52 58 62 38 26 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 3 5 7 11 13 17 19 23 29\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '13\\n64 65 40 26 36 46 53 31 63 11 2 46 59\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '20\\n20 34 51 40 70 64 14 30 24 20 6 1 70 28 38 43 9 60 31 69\\n', 'output': '2047\\n'}, {'type': 'stdin_stdout', 'input': '5\\n19 51 55 29 13\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n19 60 48 64 56 27\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 66 19 60 34 27 15 27 42 36\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '7\\n53 59 56 9 13 1 53\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n38 58 51 41 61 3 17 47 18 24\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n4 3 16 25 36 49 64\\n', 'output': '63\\n'}, {'type': 'stdin_stdout', 'input': '17\\n44 58 54 57 54 65 40 57 59 16 39 51 32 51 20 9 8\\n', 'output': '255\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2 28 46 57 39 26 45\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 5 7 11\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '17\\n44 58 54 57 54 65 40 57 32 16 39 51 32 51 20 9 8\\n', 'output': '511\\n'}, {'type': 'stdin_stdout', 'input': '15\\n66 34 43 45 61 14 12 67 38 45 55 9 30 28 16\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 4 2 2 2\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '15\\n66 34 43 45 61 14 12 67 38 45 55 9 30 41 16\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '1\\n33\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n15 12\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n67 12 58 62 38 26 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 3 5 11 11 13 17 19 23 29\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\n64 65 40 26 60 46 53 31 63 11 2 46 59\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n19 51 55 45 13\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n19 60 48 29 56 27\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 1\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 2 4 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 66 19 56 34 27 15 27 42 36\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 4 3 2 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n38 58 51 41 46 3 17 47 18 24\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n4 2 16 25 36 49 64\\n', 'output': '63\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2 28 46 57 39 26 55\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n42\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n15 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 3 5 11 5 13 17 19 23 29\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\n64 65 40 26 60 46 53 20 63 11 2 46 59\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n19 60 48 34 56 27\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 2 4 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 66 3 56 34 27 15 27 42 36\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 4 3 2 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n38 2 51 41 46 3 17 47 18 24\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '7\\n8 2 16 25 36 49 64\\n', 'output': '63\\n'}, {'type': 'stdin_stdout', 'input': '17\\n44 58 54 57 54 65 40 57 32 16 39 51 32 69 20 9 8\\n', 'output': '255\\n'}, {'type': 'stdin_stdout', 'input': '1\\n69\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n15 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 3 5 11 5 13 17 32 23 29\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '13\\n64 65 40 26 60 46 53 20 63 11 2 61 59\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '6\\n19 60 48 34 42 27\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 2 8 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 66 3 56 34 27 15 31 42 36\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 4 3 4 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n56 2 51 41 46 3 17 47 18 24\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '7\\n6 2 16 25 36 49 64\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '17\\n44 58 54 57 54 65 40 57 32 13 39 51 32 69 20 9 8\\n', 'output': '255\\n'}, {'type': 'stdin_stdout', 'input': '2\\n15 10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 3 5 11 5 13 17 43 23 29\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n19 60 48 34 42 39\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 2 8 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 66 3 56 34 27 15 12 42 36\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 4 3 4 1\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '10\\n56 2 51 41 19 3 17 47 18 24\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '7\\n6 2 16 25 36 49 21\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '17\\n44 58 54 57 54 65 40 57 32 13 39 51 32 69 26 9 8\\n', 'output': '255\\n'}, {'type': 'stdin_stdout', 'input': '2\\n15 13\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 3 5 11 5 13 17 43 23 11\\n', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 4, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79005","program":"```python\nfrom collections import *\n\nl = int(input())\nc = Counter(map(int, input().split()))\nt = defaultdict(int)\np = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67]\n\nfor k, s in c.items():\n d = 0\n for i, q in enumerate(p):\n while k % q == 0:\n k //= q\n d ^= 1 << i\n t[d] += s\n\nu = defaultdict(int)\nu[0] = 1\n\nfor x in t:\n if x: l -= 1\n if 0 < x < 2048:\n v = u.copy()\n for y in u: v[x ^ y] += u[y]\n u = v\n\ne = 1000000007\nprint((u[0] * pow(2, l, e) - 1) % e)\n```","inputs":"4\n1 1 1 1\n","output":"15\n","actual_output":"15\n","execution_success":true,"sample_index":12584},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"965_B. Battleship","prompt":"Solve the following coding problem using the programming language python:\n\nArkady is playing Battleship. The rules of this game aren't really important.\n\nThere is a field of n \u00d7 n cells. There should be exactly one k-decker on the field, i. e. a ship that is k cells long oriented either horizontally or vertically. However, Arkady doesn't know where it is located. For each cell Arkady knows if it is definitely empty or can contain a part of the ship.\n\nConsider all possible locations of the ship. Find such a cell that belongs to the maximum possible number of different locations of the ship.\n\nInput\n\nThe first line contains two integers n and k (1 \u2264 k \u2264 n \u2264 100) \u2014 the size of the field and the size of the ship.\n\nThe next n lines contain the field. Each line contains n characters, each of which is either '#' (denotes a definitely empty cell) or '.' (denotes a cell that can belong to the ship).\n\nOutput\n\nOutput two integers \u2014 the row and the column of a cell that belongs to the maximum possible number of different locations of the ship.\n\nIf there are multiple answers, output any of them. In particular, if no ship can be placed on the field, you can output any cell.\n\nExamples\n\nInput\n\n4 3\n#..#\n#.#.\n....\n.###\n\n\nOutput\n\n3 2\n\n\nInput\n\n10 4\n#....##...\n.#...#....\n..#..#..#.\n...#.#....\n.#..##.#..\n.....#...#\n...#.##...\n.#...#.#..\n.....#..#.\n...#.#...#\n\n\nOutput\n\n6 1\n\n\nInput\n\n19 6\n##..............###\n#......#####.....##\n.....#########.....\n....###########....\n...#############...\n..###############..\n.#################.\n.#################.\n.#################.\n.#################.\n#####....##....####\n####............###\n####............###\n#####...####...####\n.#####..####..#####\n...###........###..\n....###########....\n.........##........\n#.................#\n\n\nOutput\n\n1 8\n\nNote\n\nThe picture below shows the three possible locations of the ship that contain the cell (3, 2) in the first sample.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, k = [int(x) for x in input().split()]\np = [0]*n\nfor x in range(n):\n p[x] = [x for x in input()]\nres = [[0]*n for x in range(n)]\nfor y in range(n):\n for x in range(n):\n if x + k <= n:\n a = True\n for b in range(k):\n if p[y][x + b] == \"#\":\n a = False\n if a:\n for b in range(k):\n res[y][x+b] += 1\n if y + k <= n:\n a = True\n for b in range(k):\n if p[y + b][x] == \"#\":\n a = False\n if a:\n for b in range(k):\n res[y + b][x] += 1\nans = [0, 0]\nm = 0\nfor y in range(n):\n for x in range(n):\n if res[y][x] > m:\n m = res[y][x]\n ans = [y, x]\nprint(ans[0] + 1, ans[1] + 1)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10 4\\n#....##...\\n.#...#....\\n..#..#..#.\\n...#.#....\\n.#..##.#..\\n.....#...#\\n...#.##...\\n.#...#.#..\\n.....#..#.\\n...#.#...#\\n', 'output': '6 1'}, {'type': 'stdin_stdout', 'input': '19 6\\n##..............###\\n#......#####.....##\\n.....#########.....\\n....###########....\\n...#############...\\n..###############..\\n.#################.\\n.#################.\\n.#################.\\n.#################.\\n#####....##....####\\n####............###\\n####............###\\n#####...####...####\\n.#####..####..#####\\n...###........###..\\n....###########....\\n.........##........\\n#.................#\\n', 'output': '1 8'}, {'type': 'stdin_stdout', 'input': '4 3\\n#..#\\n#.#.\\n....\\n.###\\n', 'output': '3 2'}, {'type': 'stdin_stdout', 'input': '3 2\\n###\\n###\\n###\\n', 'output': '1 1'}, {'type': 'stdin_stdout', 'input': '5 2\\n..##.\\n####.\\n#####\\n.####\\n..#..\\n', 'output': '5 1'}, {'type': 'stdin_stdout', 'input': '2 2\\n#.\\n.#\\n', 'output': '1 1'}, {'type': 'stdin_stdout', 'input': '4 3\\n####\\n####\\n####\\n####\\n', 'output': '1 1'}, {'type': 'stdin_stdout', 'input': '1 1\\n#\\n', 'output': '1 1'}, {'type': 'stdin_stdout', 'input': '5 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'input': '5 4\\n..##.\\n\"###-\\n#####\\n#\"##/\\n.#...\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '2 21\\n$.\\n-#\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n..##-\\n\"###-\\n#####\\n#\"##/\\n.#...\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '2 27\\n$.\\n-#\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n..##-\\n\"###-\\n#####\\n#\"##/\\n...#.\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '2 27\\n.$\\n-#\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n..##-\\n\"###-\\n#####\\n/\"###\\n...#.\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '2 27\\n-$\\n-#\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n.-##-\\n\"###-\\n#####\\n/\"###\\n...#.\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '2 27\\n$-\\n-#\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n.-##-\\n\"###-\\n#####\\n0\"###\\n...#.\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '2 27\\n$-\\n-$\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n.-##-\\n-###\"\\n#####\\n0\"###\\n...#.\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '2 37\\n$-\\n-$\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n.-##.\\n-###\"\\n#####\\n0\"###\\n...#.\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n.-##.\\n-###\"\\n#####\\n0###\"\\n...#.\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n.-##.\\n-$##\"\\n#####\\n0###\"\\n...#.\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n###\\n#$#\\n###\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n####\\n####\\n####\\n###\"\\n', 'output': '1 1\\n\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n#\\n', 'output': '1 1\\n\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 500000000}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79017","program":"```python\nn, k = [int(x) for x in input().split()]\np = [0]*n\nfor x in range(n):\n p[x] = [x for x in input()]\nres = [[0]*n for x in range(n)]\nfor y in range(n):\n for x in range(n):\n if x + k <= n:\n a = True\n for b in range(k):\n if p[y][x + b] == \"#\":\n a = False\n if a:\n for b in range(k):\n res[y][x+b] += 1\n if y + k <= n:\n a = True\n for b in range(k):\n if p[y + b][x] == \"#\":\n a = False\n if a:\n for b in range(k):\n res[y + b][x] += 1\nans = [0, 0]\nm = 0\nfor y in range(n):\n for x in range(n):\n if res[y][x] > m:\n m = res[y][x]\n ans = [y, x]\nprint(ans[0] + 1, ans[1] + 1)\n\n```","inputs":"10 4\n#....##...\n.#...#....\n..#..#..#.\n...#.#....\n.#..##.#..\n.....#...#\n...#.##...\n.#...#.#..\n.....#..#.\n...#.#...#\n","output":"6 1","actual_output":"6 1\n","execution_success":true,"sample_index":12586},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"992_B. Nastya Studies Informatics","prompt":"Solve the following coding problem using the programming language python:\n\nToday on Informatics class Nastya learned about GCD and LCM (see links below). Nastya is very intelligent, so she solved all the tasks momentarily and now suggests you to solve one of them as well.\n\nWe define a pair of integers (a, b) good, if GCD(a, b) = x and LCM(a, b) = y, where GCD(a, b) denotes the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) of a and b, and LCM(a, b) denotes the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of a and b.\n\nYou are given two integers x and y. You are to find the number of good pairs of integers (a, b) such that l \u2264 a, b \u2264 r. Note that pairs (a, b) and (b, a) are considered different if a \u2260 b.\n\nInput\n\nThe only line contains four integers l, r, x, y (1 \u2264 l \u2264 r \u2264 109, 1 \u2264 x \u2264 y \u2264 109).\n\nOutput\n\nIn the only line print the only integer \u2014 the answer for the problem.\n\nExamples\n\nInput\n\n1 2 1 2\n\n\nOutput\n\n2\n\n\nInput\n\n1 12 1 12\n\n\nOutput\n\n4\n\n\nInput\n\n50 100 3 30\n\n\nOutput\n\n0\n\nNote\n\nIn the first example there are two suitable good pairs of integers (a, b): (1, 2) and (2, 1).\n\nIn the second example there are four suitable good pairs of integers (a, b): (1, 12), (12, 1), (3, 4) and (4, 3).\n\nIn the third example there are good pairs of integers, for example, (3, 30), but none of them fits the condition l \u2264 a, b \u2264 r.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import defaultdict\n\nl, r, x, y = map(int, input().split())\n\nif x == y == 1:\n if l == 1:\n print(1)\n exit()\n\n print(0)\n exit()\n\nif y % x != 0:\n print(0)\n exit()\n\nc = x * y\n\nc_ = y // x\ni = 2\ndel_ = defaultdict(int)\nwhile c_ > 1:\n while c_ % i == 0:\n c_ //= i\n del_[i] += 1\n\n i += 1\n\nmas = tuple(k ** v for k, v in del_.items())\nln = len(mas)\n\nans = 0\nfor i in range(2 ** ln):\n b = bin(i)[2:].zfill(ln)\n\n a = x\n for j in range(ln):\n if b[j] == '1':\n a *= mas[j]\n\n b = c // a\n\n if l <= a <= r and l <= b <= r:\n ans += 1\n\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 2 1 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '50 100 3 30\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 12 1 12\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1321815 935845020 1321815 935845020\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '321399 1651014 603 879990462\\n', 'output': '4\\n'}, 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bin(i)[2:].zfill(ln)\n\n a = x\n for j in range(ln):\n if b[j] == '1':\n a *= mas[j]\n\n b = c // a\n\n if l <= a <= r and l <= b <= r:\n ans += 1\n\nprint(ans)\n\n```","inputs":"1 2 1 2\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12587},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02623 AtCoder Beginner Contest 172 - Tsundoku","prompt":"Solve the following coding problem using the programming language python:\n\nWe have two desks: A and B. Desk A has a vertical stack of N books on it, and Desk B similarly has M books on it.\n\nIt takes us A_i minutes to read the i-th book from the top on Desk A (1 \\leq i \\leq N), and B_i minutes to read the i-th book from the top on Desk B (1 \\leq i \\leq M).\n\nConsider the following action:\n\n* Choose a desk with a book remaining, read the topmost book on that desk, and remove it from the desk.\n\n\n\nHow many books can we read at most by repeating this action so that it takes us at most K minutes in total? We ignore the time it takes to do anything other than reading.\n\nConstraints\n\n* 1 \\leq N, M \\leq 200000\n* 1 \\leq K \\leq 10^9\n* 1 \\leq A_i, B_i \\leq 10^9\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN M K\nA_1 A_2 \\ldots A_N\nB_1 B_2 \\ldots B_M\n\n\nOutput\n\nPrint an integer representing the maximum number of books that can be read.\n\nExamples\n\nInput\n\n3 4 240\n60 90 120\n80 150 80 150\n\n\nOutput\n\n3\n\n\nInput\n\n3 4 730\n60 90 120\n80 150 80 150\n\n\nOutput\n\n7\n\n\nInput\n\n5 4 1\n1000000000 1000000000 1000000000 1000000000 1000000000\n1000000000 1000000000 1000000000 1000000000\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom bisect import*\nfrom itertools import*\nn,m,k,*x=map(int,open(0).read().split());c=accumulate;b=[*c(x[n:])];print(max(i+bisect(b,k-v)for i,v in enumerate(c([0]+x[:n]))if v<=k))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 4 1\\n1000000000 1000000000 1000000000 1000000000 1000000000\\n1000000000 1000000000 1000000000 1000000000', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3 4 240\\n60 90 120\\n80 150 80 150', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3 4 730\\n60 90 120\\n80 150 80 150', 'output': '7'}, {'type': 'stdin_stdout', 'input': '5 4 1\\n1000000000 1000000000 1000000000 1000000000 1000000000\\n1000000000 1000000000 1000000010 1000000000', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 4 194\\n60 90 120\\n80 150 80 150', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 4 730\\n60 9 120\\n80 150 80 150', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '3 4 194\\n60 90 120\\n80 34 80 150', 'output': '3\\n'}, {'type': 'stdin_stdout', 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14', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 3 001\\n32 16 147\\n83 94 18 14', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 3 010\\n57 16 109\\n83 94 18 14', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 3 000\\n15 30 109\\n83 48 18 14', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '-1 3 000\\n15 16 87\\n83 94 18 59', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '-1 3 000\\n26 18 87\\n83 94 10 14', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n1000000000 1000000001 1000000000 1000000000 1000000000\\n1000000000 1001000000 1000000000 1000000000', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 4 1088\\n60 127 60\\n80 150 80 185', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '3 4 120\\n60 142 51\\n80 34 80 150', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 4 402\\n16 9 120\\n80 150 80 150', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3 3 101\\n60 16 153\\n34 150 80 291', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79065","program":"```python\nfrom bisect import*\nfrom itertools import*\nn,m,k,*x=map(int,open(0).read().split());c=accumulate;b=[*c(x[n:])];print(max(i+bisect(b,k-v)for i,v in enumerate(c([0]+x[:n]))if v<=k))\n```","inputs":"5 4 1\n1000000000 1000000000 1000000000 1000000000 1000000000\n1000000000 1000000000 1000000000 1000000000","output":"0","actual_output":"0\n","execution_success":true,"sample_index":12588},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02754 AtCoder Beginner Contest 158 - Count Balls","prompt":"Solve the following coding problem using the programming language python:\n\nTakahashi has many red balls and blue balls. Now, he will place them in a row.\n\nInitially, there is no ball placed.\n\nTakahashi, who is very patient, will do the following operation 10^{100} times:\n\n* Place A blue balls at the end of the row of balls already placed. Then, place B red balls at the end of the row.\n\n\n\nHow many blue balls will be there among the first N balls in the row of balls made this way?\n\nConstraints\n\n* 1 \\leq N \\leq 10^{18}\n* A, B \\geq 0\n* 0 < A + B \\leq 10^{18}\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN A B\n\n\nOutput\n\nPrint the number of blue balls that will be there among the first N balls in the row of balls.\n\nExamples\n\nInput\n\n8 3 4\n\n\nOutput\n\n4\n\n\nInput\n\n8 0 4\n\n\nOutput\n\n0\n\n\nInput\n\n6 2 4\n\n\nOutput\n\n2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,a,b = map(int,input().split())\nprint((n//(a+b)) * a + min((n%(a+b),a)))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '8 0 4', 'output': '0'}, {'type': 'stdin_stdout', 'input': '8 3 4', 'output': '4'}, 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0 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 0 2', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 0 4', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 1 4', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 1 7', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 1 5', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 5', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 8', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '0 2 7', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79069","program":"```python\nn,a,b = map(int,input().split())\nprint((n//(a+b)) * a + min((n%(a+b),a)))\n```","inputs":"8 0 4","output":"0","actual_output":"0\n","execution_success":true,"sample_index":12589},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02889 AtCoder Beginner Contest 143 - Travel by Car","prompt":"Solve the following coding problem using the programming language python:\n\nThere are N towns numbered 1 to N and M roads. The i-th road connects Town A_i and Town B_i bidirectionally and has a length of C_i.\n\nTakahashi will travel between these towns by car, passing through these roads. The fuel tank of his car can contain at most L liters of fuel, and one liter of fuel is consumed for each unit distance traveled. When visiting a town while traveling, he can full the tank (or choose not to do so). Travel that results in the tank becoming empty halfway on the road cannot be done.\n\nProcess the following Q queries:\n\n* The tank is now full. Find the minimum number of times he needs to full his tank while traveling from Town s_i to Town t_i. If Town t_i is unreachable, print -1.\n\nConstraints\n\n* All values in input are integers.\n* 2 \\leq N \\leq 300\n* 0 \\leq M \\leq \\frac{N(N-1)}{2}\n* 1 \\leq L \\leq 10^9\n* 1 \\leq A_i, B_i \\leq N\n* A_i \\neq B_i\n* \\left(A_i, B_i\\right) \\neq \\left(A_j, B_j\\right) (if i \\neq j)\n* \\left(A_i, B_i\\right) \\neq \\left(B_j, A_j\\right) (if i \\neq j)\n* 1 \\leq C_i \\leq 10^9\n* 1 \\leq Q \\leq N\\left(N-1\\right)\n* 1 \\leq s_i, t_i \\leq N\n* s_i \\neq t_i\n* \\left(s_i, t_i\\right) \\neq \\left(s_j, t_j\\right) (if i \\neq j)\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN M L\nA_1 B_1 C_1\n:\nA_M B_M C_M\nQ\ns_1 t_1\n:\ns_Q t_Q\n\n\nOutput\n\nPrint Q lines.\n\nThe i-th line should contain the minimum number of times the tank needs to be fulled while traveling from Town s_i to Town t_i. If Town t_i is unreachable, the line should contain -1 instead.\n\nExamples\n\nInput\n\n3 2 5\n1 2 3\n2 3 3\n2\n3 2\n1 3\n\n\nOutput\n\n0\n1\n\n\nInput\n\n4 0 1\n1\n2 1\n\n\nOutput\n\n-1\n\n\nInput\n\n5 4 4\n1 2 2\n2 3 2\n3 4 3\n4 5 2\n20\n2 1\n3 1\n4 1\n5 1\n1 2\n3 2\n4 2\n5 2\n1 3\n2 3\n4 3\n5 3\n1 4\n2 4\n3 4\n5 4\n1 5\n2 5\n3 5\n4 5\n\n\nOutput\n\n0\n0\n1\n2\n0\n0\n1\n2\n0\n0\n0\n1\n1\n1\n0\n0\n2\n2\n1\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\nN, M, L = map(int, input().split())\nd = [[10 ** 16 * (i != j) for j in range(N + 1)] for i in range(N + 1)]\nfor _ in range(M):\n x, y, c = map(int, input().split())\n d[x][y] = c\n d[y][x] = c\nfor k in range(N + 1):\n for i in range(N + 1):\n for j in range(N + 1): d[i][j] = min(d[i][j], d[i][k] + d[k][j])\n\ndd = [[(d[i][j] <= L) + (d[i][j] > L) * 10 ** 16 for j in range(N + 1)] for i in range(N + 1)]\nfor k in range(N + 1):\n for i in range(N + 1):\n for j in range(N + 1): dd[i][j] = min(dd[i][j], dd[i][k] + dd[k][j])\n\nfor _ in range(int(input())):\n s, t = map(int, input().split())\n if dd[s][t] != 10 ** 16: print(dd[s][t] - 1)\n else: print(-1)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 0 1\\n1\\n2 1', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5', 'output': '0\\n0\\n1\\n2\\n0\\n0\\n1\\n2\\n0\\n0\\n0\\n1\\n1\\n1\\n0\\n0\\n2\\n2\\n1\\n0'}, {'type': 'stdin_stdout', 'input': '3 2 5\\n1 2 3\\n2 3 3\\n2\\n3 2\\n1 3', 'output': '0\\n1'}, {'type': 'stdin_stdout', 'input': '4 0 0\\n1\\n2 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5', 'output': '0\\n0\\n1\\n2\\n0\\n0\\n1\\n2\\n0\\n1\\n0\\n1\\n1\\n1\\n0\\n0\\n2\\n2\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5', 'output': '0\\n0\\n0\\n2\\n0\\n0\\n1\\n2\\n0\\n0\\n0\\n1\\n1\\n1\\n0\\n0\\n2\\n2\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 5\\n1 2 3\\n2 2 3\\n2\\n3 2\\n1 3', 'output': '-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5', 'output': '0\\n1\\n2\\n3\\n0\\n0\\n1\\n2\\n1\\n1\\n0\\n1\\n2\\n1\\n0\\n0\\n3\\n2\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '5 4 4\\n1 2 2\\n2 3 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 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'-1\\n-1\\n-1\\n-1\\n-1\\n0\\n0\\n1\\n-1\\n1\\n0\\n1\\n-1\\n0\\n0\\n0\\n-1\\n1\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '5 4 4\\n1 2 2\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n5 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5', 'output': '0\\n0\\n1\\n2\\n0\\n2\\n1\\n2\\n0\\n0\\n0\\n1\\n1\\n1\\n0\\n0\\n2\\n2\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3 2 5\\n2 2 3\\n2 3 3\\n2\\n3 2\\n1 3', 'output': '0\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '5 4 4\\n1 2 2\\n3 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5', 'output': '0\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n0\\n1\\n-1\\n-1\\n0\\n0\\n-1\\n-1\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '5 4 2\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5', 'output': '-1\\n-1\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '5 4 4\\n2 2 2\\n2 3 0\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n1 5\\n3 5\\n4 5', 'output': '-1\\n-1\\n-1\\n-1\\n-1\\n0\\n0\\n1\\n-1\\n0\\n0\\n1\\n-1\\n0\\n0\\n0\\n-1\\n-1\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '5 4 4\\n1 2 2\\n3 5 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n3 1\\n5 1\\n1 2\\n3 2\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n5 3\\n1 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5', 'output': '0\\n-1\\n-1\\n-1\\n0\\n-1\\n-1\\n-1\\n-1\\n-1\\n0\\n0\\n-1\\n-1\\n0\\n0\\n-1\\n-1\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '5 4 4\\n1 2 4\\n2 3 2\\n3 4 3\\n4 5 2\\n20\\n2 1\\n3 1\\n4 1\\n5 1\\n1 4\\n3 2\\n4 2\\n5 2\\n1 3\\n2 4\\n4 3\\n5 3\\n1 4\\n2 3\\n5 4\\n5 4\\n1 5\\n2 5\\n3 5\\n4 5', 'output': 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0\\n4 2\\n5 2\\n1 3\\n2 3\\n4 3\\n4 3\\n0 4\\n2 4\\n3 4\\n5 4\\n1 5\\n2 5\\n3 5\\n6 5', 'output': '0\\n0\\n1\\n2\\n0\\n-1\\n1\\n2\\n0\\n0\\n0\\n0\\n-1\\n1\\n0\\n0\\n2\\n2\\n1\\n-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79073","program":"```python\nimport sys\ninput = sys.stdin.readline\nN, M, L = map(int, input().split())\nd = [[10 ** 16 * (i != j) for j in range(N + 1)] for i in range(N + 1)]\nfor _ in range(M):\n x, y, c = map(int, input().split())\n d[x][y] = c\n d[y][x] = c\nfor k in range(N + 1):\n for i in range(N + 1):\n for j in range(N + 1): d[i][j] = min(d[i][j], d[i][k] + d[k][j])\n\ndd = [[(d[i][j] <= L) + (d[i][j] > L) * 10 ** 16 for j in range(N + 1)] for i in range(N + 1)]\nfor k in range(N + 1):\n for i in range(N + 1):\n for j in range(N + 1): dd[i][j] = min(dd[i][j], dd[i][k] + dd[k][j])\n\nfor _ in range(int(input())):\n s, t = map(int, input().split())\n if dd[s][t] != 10 ** 16: print(dd[s][t] - 1)\n else: print(-1)\n```","inputs":"4 0 1\n1\n2 1","output":"-1","actual_output":"-1\n","execution_success":true,"sample_index":12590},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03024 M-SOLUTIONS Programming Contest - Sumo","prompt":"Solve the following coding problem using the programming language python:\n\nTakahashi is competing in a sumo tournament. The tournament lasts for 15 days, during which he performs in one match per day. If he wins 8 or more matches, he can also participate in the next tournament.\n\nThe matches for the first k days have finished. You are given the results of Takahashi's matches as a string S consisting of `o` and `x`. If the i-th character in S is `o`, it means that Takahashi won the match on the i-th day; if that character is `x`, it means that Takahashi lost the match on the i-th day.\n\nPrint `YES` if there is a possibility that Takahashi can participate in the next tournament, and print `NO` if there is no such possibility.\n\nConstraints\n\n* 1 \\leq k \\leq 15\n* S is a string of length k consisting of `o` and `x`.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nS\n\n\nOutput\n\nPrint `YES` if there is a possibility that Takahashi can participate in the next tournament, and print `NO` otherwise.\n\nExamples\n\nInput\n\noxoxoxoxoxoxox\n\n\nOutput\n\nYES\n\n\nInput\n\nxxxxxxxx\n\n\nOutput\n\nNO\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ns = input()\nprint('YES' if s.count('x') <= 7 else \"NO\")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'oxoxoxoxoxoxox', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'xxxxxxxx', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'xoxoxoxoxoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxowoxoxoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxowoooxoxxx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xxxoxooowoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxoxooxwoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxoyoxoxoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xxxoxoooooxwxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxowooxwoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxoxoxoyoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxoxoxoxoyoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xxxoxooovoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxowooxwoxowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxoyoxoyoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoyoxoxoxoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxovoooxoxxx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxowooywoxowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxxowooywoxowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owoxowyoowoxxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owoyowyoowoxxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxxowooywoyowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxoxoxowoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxoxoxoyoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxowxooxoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoyoxoxoyoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxwxoooooxoxxx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxovooxwoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoyoxoooxxxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxxwooowoxowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxoyoxoyoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owoxowyoowoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxxowooowoxowy', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owoyowyoowowxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxowoxoxoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxowowxooxoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoyoxoooyxxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xxxovooowoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oooyoxoxoxxxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owoxowooowxxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxowoozwoxowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'wxxowoooooxowy', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owoyowyoowowyo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxxwoxoxoooxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oyowowxooxoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoooxoooyxxyxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxxovxoowoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oooyoyoxoxxxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxxwooowowowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owoxowzoowoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxxowowoooxowy', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oywowooywoyowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoyxwoxoxoooxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxxxoxoyoyooo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxxxooowowowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owoxowzooxoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'ywoxooowowoxxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oooyooyxoxxxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxxxoooxowowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owzxowoooxoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oooyooywoxxxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owowoxoooxxxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxoxooowoxzwo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oooyooyooxxxwx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owowoxooowxxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxzxooowoxowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'ooxyooyooxoxwx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxxwoooxowowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxzooxowoxowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'ooxyooxooxoywx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxzooxowooxwo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xwyoxooxooyxoo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owxoowoxoozxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'ooxyooyooxoywx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xwyoxooyooyxoo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xwooxooyoyyxoo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xwooxoozoyyxoo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'ooxyyozooxoowx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxoxoxoxowox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxovoxoxoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxoxoooxoxxx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxxoxooxwoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoooyoxxxoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxxxoooooxowxx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oooxoxoxxyoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'ooxoxoxxxoyoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxovoooxowxx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xwxowooxwoxooo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxowoyoxoyoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoyoxoxxooxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owoxovoooxoxxx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxxowooyvoxowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'owoxowyoowoxyo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxxowoozwoyowo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxoyoxoxoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oooxowxooxxxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoyoxoxoyoxxoo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxoowooxoxxx', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'oxoxowxoovoxox', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'yoxowoxoxoxoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoxoxooxwowoxo', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'xoyoyoooyxxoxo', 'output': 'YES\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79077","program":"```python\ns = input()\nprint('YES' if s.count('x') <= 7 else \"NO\")\n\n```","inputs":"oxoxoxoxoxoxox","output":"YES","actual_output":"YES\n","execution_success":true,"sample_index":12591},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03165 Educational DP Contest - LCS","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given strings s and t. Find one longest string that is a subsequence of both s and t.\n\nConstraints\n\n* s and t are strings consisting of lowercase English letters.\n* 1 \\leq |s|, |t| \\leq 3000\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\ns\nt\n\n\nOutput\n\nPrint one longest string that is a subsequence of both s and t. If there are multiple such strings, any of them will be accepted.\n\nExamples\n\nInput\n\naxyb\nabyxb\n\n\nOutput\n\naxb\n\n\nInput\n\naa\nxayaz\n\n\nOutput\n\naa\n\n\nInput\n\na\nz\n\n\nOutput\n\n\n\n\nInput\n\nabracadabra\navadakedavra\n\n\nOutput\n\naaadara\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ns1=input()\ns2=input()\ndp=[0]*(len(s1)+1)\ndp[0]=[0]*(len(s2)+1)\nfor i in range(1,len(s1)+1):\n\tdp[i]=[0]*(len(s2)+1)\n\tfor j in range(1,len(s2)+1):\n\t\tif s1[i-1]==s2[j-1]:\n\t\t\tdp[i][j]=dp[i-1][j-1]+1\n\t\telse:\n\t\t\tdp[i][j]=max(dp[i-1][j],dp[i][j-1])\n# for i in range(len(s1)+1):\n# \tprint(dp[i])\ns=\"\"\ni,j=len(s1),len(s2)\nwhile(i>0 and j>0):\n\tif s1[i-1]==s2[j-1]:\n\t\ts+=s1[i-1]\n\t\ti-=1\n\t\tj-=1\n\telif dp[i][j-1]>dp[i-1][j]:\n\t\tj-=1\n\telse:\n\t\ti-=1\nprint(s[::-1])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'abracadabra\\navadakedavra', 'output': 'aaadara'}, {'type': 'stdin_stdout', 'input': 'a\\nz', 'output': ''}, {'type': 'stdin_stdout', 'input': 'axyb\\nabyxb', 'output': 'axb'}, {'type': 'stdin_stdout', 'input': 'aa\\nxayaz', 'output': 'aa'}, {'type': 'stdin_stdout', 'input': 'abracadabra\\navaeakedavra', 'output': 'aaadara\\n'}, {'type': 'stdin_stdout', 'input': '`xyb\\nabyxb', 'output': 'yb\\n'}, {'type': 'stdin_stdout', 'input': 'aa\\nxaybz', 'output': 'a\\n'}, {'type': 'stdin_stdout', 'input': 'byx`\\nabyxb', 'output': 'byx\\n'}, {'type': 'stdin_stdout', 'input': '`yxb\\nabyxb', 'output': 'yxb\\n'}, {'type': 'stdin_stdout', 'input': '`yxb\\nzbaxb', 'output': 'xb\\n'}, {'type': 'stdin_stdout', 'input': 'bxy`\\nzbaxb', 'output': 'bx\\n'}, {'type': 'stdin_stdout', 'input': 'xy_c\\nzbaxb', 'output': 'x\\n'}, {'type': 'stdin_stdout', 'input': 'abracbdaara\\navadakedavra', 'output': 'aadaara\\n'}, {'type': 'stdin_stdout', 'input': 'axya\\nabyxb', 'output': 'ay\\n'}, {'type': 'stdin_stdout', 'input': 'aa\\nxayay', 'output': 'aa\\n'}, {'type': 'stdin_stdout', 'input': 'abrac`dabra\\navaeakedavra', 'output': 'aadara\\n'}, {'type': 'stdin_stdout', 'input': 'byx`\\nabywb', 'output': 'by\\n'}, {'type': 'stdin_stdout', 'input': 'ba\\nbayyz', 'output': 'ba\\n'}, {'type': 'stdin_stdout', 'input': '`ywb\\nzbaxb', 'output': 'b\\n'}, {'type': 'stdin_stdout', 'input': 'abracbdaara\\narvadekadava', 'output': 'aradaaa\\n'}, {'type': 'stdin_stdout', 'input': 'axya\\nabxxb', 'output': 'ax\\n'}, {'type': 'stdin_stdout', 'input': '`yxa\\nabyxb', 'output': 'yx\\n'}, {'type': 'stdin_stdout', 'input': 'ab\\nyabyy', 'output': 'ab\\n'}, {'type': 'stdin_stdout', 'input': '`ywb\\nzb`xb', 'output': '`b\\n'}, {'type': 'stdin_stdout', 'input': 'bxya\\nbxabz', 'output': 'bxa\\n'}, {'type': 'stdin_stdout', 'input': 'axya\\nbxxba', 'output': 'xa\\n'}, {'type': 'stdin_stdout', 'input': 'd_yx\\nzbaby', 'output': 'y\\n'}, {'type': 'stdin_stdout', 'input': '_xyb\\n`cbxy', 'output': 'xy\\n'}, {'type': 'stdin_stdout', 'input': 'bxya\\nbyaaz', 'output': 'bya\\n'}, {'type': 'stdin_stdout', 'input': 'ayz_\\nbbaxz', 'output': 'az\\n'}, {'type': 'stdin_stdout', 'input': 'abqacbdaara\\nauadakedavsa', 'output': 'aadaaa\\n'}, {'type': 'stdin_stdout', 'input': 'arbad`carba\\navferakdavaa', 'output': 'aradaa\\n'}, {'type': 'stdin_stdout', 'input': 'byz_\\nbbaxz', 'output': 'bz\\n'}, {'type': 'stdin_stdout', 'input': 'axya\\naxaxb', 'output': 'axa\\n'}, {'type': 'stdin_stdout', 'input': 'axya\\nbybaz', 'output': 'ya\\n'}, {'type': 'stdin_stdout', 'input': 'arbad`carba\\navferbkdava`', 'output': 'arbdaa\\n'}, {'type': 'stdin_stdout', 'input': 'arbad`carba\\n`vferbkdavaa', 'output': 'rbdaa\\n'}, {'type': 'stdin_stdout', 'input': 'byz_\\nzx`cb', 'output': 'z\\n'}, {'type': 'stdin_stdout', 'input': 'rrbad`caaba\\n`vferbkdavaa', 'output': 'rbdaaa\\n'}, {'type': 'stdin_stdout', 'input': 'bw`y\\nwabay', 'output': 'wy\\n'}, {'type': 'stdin_stdout', 'input': 'rrbad`caaba\\n`vfekbrdavaa', 'output': 'bdaaa\\n'}, {'type': 'stdin_stdout', 'input': 'yw`b\\nwabay', 'output': 'wb\\n'}, {'type': 'stdin_stdout', 'input': '_xzb\\nzx`cb', 'output': 'zb\\n'}, {'type': 'stdin_stdout', 'input': 'yw`c\\nwabay', 'output': 'w\\n'}, {'type': 'stdin_stdout', 'input': '`xxa\\nxabxa', 'output': 'xxa\\n'}, {'type': 'stdin_stdout', 'input': 'abaac`dabrr\\n`vfejbrdavaa', 'output': 'baaa\\n'}, {'type': 'stdin_stdout', 'input': '_xzc\\nyx`cb', 'output': 'xc\\n'}, {'type': 'stdin_stdout', 'input': '`xxc\\nxabxa', 'output': 'xx\\n'}, {'type': 'stdin_stdout', 'input': 'yd`w\\nxab`y', 'output': '`\\n'}, {'type': 'stdin_stdout', 'input': 'yc`z\\nycxba', 'output': 'yc\\n'}, {'type': 'stdin_stdout', 'input': '`xcx\\nbycax', 'output': 'cx\\n'}, {'type': 'stdin_stdout', 'input': 'b_zx\\n_cbyz', 'output': '_z\\n'}, {'type': 'stdin_stdout', 'input': 'yc`y\\nacxby', 'output': 'cy\\n'}, {'type': 'stdin_stdout', 'input': 'abaabacrbaq\\naavaerbjegv`', 'output': 'aaarb\\n'}, {'type': 'stdin_stdout', 'input': 'yc`z\\nacxby', 'output': 'c\\n'}, {'type': 'stdin_stdout', 'input': 'qabrcabaaba\\naavafrbjegv`', 'output': 'aaab\\n'}, {'type': 'stdin_stdout', 'input': 'c_zx\\n`cybz', 'output': 'cz\\n'}, {'type': 'stdin_stdout', 'input': 'ycxa\\nbcyax', 'output': 'ca\\n'}, {'type': 'stdin_stdout', 'input': '_zxc\\nzbyc`', 'output': 'zc\\n'}, {'type': 'stdin_stdout', 'input': 'y{f^\\na{ycb', 'output': '{\\n'}, {'type': 'stdin_stdout', 'input': 'abaabacbbrq\\naavafrbjfgv`', 'output': 'aaar\\n'}, {'type': 'stdin_stdout', 'input': '^f{y\\na{ycb', 'output': '{y\\n'}, {'type': 'stdin_stdout', 'input': 'abaabacbbrq\\n`avafrbjfgv`', 'output': 'aar\\n'}, {'type': 'stdin_stdout', 'input': 'cw_{\\nbcwya', 'output': 'cw\\n'}, {'type': 'stdin_stdout', 'input': 'ybay\\ncbxay', 'output': 'bay\\n'}, {'type': 'stdin_stdout', 'input': 'xxca\\nx`yca', 'output': 'xca\\n'}, {'type': 'stdin_stdout', 'input': 'qrbccabaaba\\n`avafrbjfgv`', 'output': 'aab\\n'}, {'type': 'stdin_stdout', 'input': 'yaby\\nyaxbc', 'output': 'yab\\n'}, {'type': 'stdin_stdout', 'input': 'xz_c\\nc_zzc', 'output': '_c\\n'}, {'type': 'stdin_stdout', 'input': 'ybyb\\nyaxbb', 'output': 'ybb\\n'}, {'type': 'stdin_stdout', 'input': 'xzc_\\nc_zzc', 'output': 'c_\\n'}, {'type': 'stdin_stdout', 'input': 'byby\\nbbxay', 'output': 'bby\\n'}, {'type': 'stdin_stdout', 'input': '_zcx\\nc_zzc', 'output': '_zc\\n'}, {'type': 'stdin_stdout', 'input': 'abaqbbdcbra\\n`avbfrhjfav`', 'output': 'abra\\n'}, {'type': 'stdin_stdout', 'input': '_ydw\\nc_zzc', 'output': '_\\n'}, {'type': 'stdin_stdout', 'input': 'zyc`\\nxczb`', 'output': 'c`\\n'}, {'type': 'stdin_stdout', 'input': 'zyc`\\nxbzb`', 'output': 'z`\\n'}, {'type': 'stdin_stdout', 'input': '^y{e\\nycda{', 'output': 'y{\\n'}, {'type': 'stdin_stdout', 'input': '`cxz\\nxbzba', 'output': 'xz\\n'}, {'type': 'stdin_stdout', 'input': 'abracadabra\\navadrkedavaa', 'output': 'aadra\\n'}, {'type': 'stdin_stdout', 'input': 'axzb\\nabyxb', 'output': 'axb\\n'}, {'type': 'stdin_stdout', 'input': 'abracadabsa\\navaeakedavra', 'output': 'aaadaa\\n'}, {'type': 'stdin_stdout', 'input': 'abrac`dabra\\navaeaaedavrk', 'output': 'aadar\\n'}, {'type': 'stdin_stdout', 'input': 'abbacrdaara\\narvadekadava', 'output': 'ardaaa\\n'}, {'type': 'stdin_stdout', 'input': 'axya\\nabxyb', 'output': 'axy\\n'}, {'type': 'stdin_stdout', 'input': 'arbad`carba\\navaeakedavqa', 'output': 'aadaa\\n'}, {'type': 'stdin_stdout', 'input': '_xyb\\naxycb', 'output': 'xyb\\n'}, {'type': 'stdin_stdout', 'input': 'bwy`\\nzb`xb', 'output': 'b`\\n'}, {'type': 'stdin_stdout', 'input': 'bxy`\\nbx`bz', 'output': 'bx`\\n'}, {'type': 'stdin_stdout', 'input': 'araadbcarba\\narvadekadaua', 'output': 'araadaa\\n'}, {'type': 'stdin_stdout', 'input': 'xyab\\nbxaxb', 'output': 'xab\\n'}, {'type': 'stdin_stdout', 'input': 'arbac`carba\\navfeaakdavra', 'output': 'aaara\\n'}, {'type': 'stdin_stdout', 'input': 'bxz_\\nbbaxz', 'output': 'bxz\\n'}, {'type': 'stdin_stdout', 'input': 'asbad`carba\\navferbkdava`', 'output': 'abdaa\\n'}, {'type': 'stdin_stdout', 'input': 'bayx\\nxbabx', 'output': 'bax\\n'}, {'type': 'stdin_stdout', 'input': 'rrbac`caaba\\n`vferbkdavaa', 'output': 'rbaaa\\n'}, {'type': 'stdin_stdout', 'input': 'yyac\\nxbacx', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': 'bxy`\\naxc`{', 'output': 'x`\\n'}, {'type': 'stdin_stdout', 'input': 'aaaac`drbar\\n`vfejbrdavaa', 'output': '`br\\n'}, {'type': 'stdin_stdout', 'input': '_xyc\\ny_bbx', 'output': '_x\\n'}, {'type': 'stdin_stdout', 'input': 'yd`w\\nxaby`', 'output': 'y`\\n'}, {'type': 'stdin_stdout', 'input': 'araacadrbab\\n`vgejbreavaa', 'output': 'raaa\\n'}, {'type': 'stdin_stdout', 'input': '_bzx\\n_cybz', 'output': '_bz\\n'}, {'type': 'stdin_stdout', 'input': '_wc{\\naywcb', 'output': 'wc\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79081","program":"```python\ns1=input()\ns2=input()\ndp=[0]*(len(s1)+1)\ndp[0]=[0]*(len(s2)+1)\nfor i in range(1,len(s1)+1):\n\tdp[i]=[0]*(len(s2)+1)\n\tfor j in range(1,len(s2)+1):\n\t\tif s1[i-1]==s2[j-1]:\n\t\t\tdp[i][j]=dp[i-1][j-1]+1\n\t\telse:\n\t\t\tdp[i][j]=max(dp[i-1][j],dp[i][j-1])\n# for i in range(len(s1)+1):\n# \tprint(dp[i])\ns=\"\"\ni,j=len(s1),len(s2)\nwhile(i>0 and j>0):\n\tif s1[i-1]==s2[j-1]:\n\t\ts+=s1[i-1]\n\t\ti-=1\n\t\tj-=1\n\telif dp[i][j-1]>dp[i-1][j]:\n\t\tj-=1\n\telse:\n\t\ti-=1\nprint(s[::-1])\n```","inputs":"abracadabra\navadakedavra","output":"aaadara","actual_output":"aaadara\n","execution_success":true,"sample_index":12592},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03307 AtCoder Beginner Contest 102 - Multiple of 2 and N","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a positive integer N. Find the minimum positive integer divisible by both 2 and N.\n\nConstraints\n\n* 1 \\leq N \\leq 10^9\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\n\n\nOutput\n\nPrint the minimum positive integer divisible by both 2 and N.\n\nExamples\n\nInput\n\n3\n\n\nOutput\n\n6\n\n\nInput\n\n10\n\n\nOutput\n\n10\n\n\nInput\n\n999999999\n\n\nOutput\n\n1999999998\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\nif n % 2 == 0:\n print(n)\nelse:\n print(2*n)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '999999999', 'output': '1999999998'}, {'type': 'stdin_stdout', 'input': '3', 'output': '6'}, {'type': 'stdin_stdout', 'input': '10', 'output': '10'}, {'type': 'stdin_stdout', 'input': '1604548808', 'output': '1604548808\\n'}, {'type': 'stdin_stdout', 'input': '5', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '17', 'output': '34\\n'}, {'type': 'stdin_stdout', 'input': '1558666763', 'output': '3117333526\\n'}, {'type': 'stdin_stdout', 'input': '8', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '20', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '1031129102', 'output': '1031129102\\n'}, {'type': 'stdin_stdout', 'input': '12', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '30', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '1937535494', 'output': '1937535494\\n'}, {'type': 'stdin_stdout', 'input': '1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '31', 'output': '62\\n'}, {'type': 'stdin_stdout', 'input': '2049048611', 'output': '4098097222\\n'}, {'type': 'stdin_stdout', 'input': '0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '21', 'output': '42\\n'}, {'type': 'stdin_stdout', 'input': '1295498732', 'output': '1295498732\\n'}, {'type': 'stdin_stdout', 'input': '9', 'output': 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'stdin_stdout', 'input': '5095773', 'output': '10191546\\n'}, {'type': 'stdin_stdout', 'input': '97', 'output': '194\\n'}, {'type': 'stdin_stdout', 'input': '94', 'output': '94\\n'}, {'type': 'stdin_stdout', 'input': '1629294', 'output': '1629294\\n'}, {'type': 'stdin_stdout', 'input': '187', 'output': '374\\n'}, {'type': 'stdin_stdout', 'input': '78', 'output': '78\\n'}, {'type': 'stdin_stdout', 'input': '613474', 'output': '613474\\n'}, {'type': 'stdin_stdout', 'input': '157', 'output': '314\\n'}, {'type': 'stdin_stdout', 'input': '136', 'output': '136\\n'}, {'type': 'stdin_stdout', 'input': '679012', 'output': '679012\\n'}, {'type': 'stdin_stdout', 'input': '219', 'output': '438\\n'}, {'type': 'stdin_stdout', 'input': '36', 'output': '36\\n'}, {'type': 'stdin_stdout', 'input': '1018479', 'output': '2036958\\n'}, {'type': 'stdin_stdout', 'input': '-21', 'output': '-42\\n'}, {'type': 'stdin_stdout', 'input': '56', 'output': '56\\n'}, {'type': 'stdin_stdout', 'input': '1753816', 'output': '1753816\\n'}, {'type': 'stdin_stdout', 'input': '-18', 'output': '-18\\n'}, {'type': 'stdin_stdout', 'input': '168366', 'output': '168366\\n'}, {'type': 'stdin_stdout', 'input': '-22', 'output': '-22\\n'}, {'type': 'stdin_stdout', 'input': '41', 'output': '82\\n'}, {'type': 'stdin_stdout', 'input': '119314', 'output': '119314\\n'}, {'type': 'stdin_stdout', 'input': '68', 'output': '68\\n'}, {'type': 'stdin_stdout', 'input': '40', 'output': '40\\n'}, {'type': 'stdin_stdout', 'input': '199002', 'output': '199002\\n'}, {'type': 'stdin_stdout', 'input': '64', 'output': '64\\n'}, {'type': 'stdin_stdout', 'input': '155477', 'output': '310954\\n'}, {'type': 'stdin_stdout', 'input': '55', 'output': '110\\n'}, {'type': 'stdin_stdout', 'input': '-24', 'output': '-24\\n'}, {'type': 'stdin_stdout', 'input': '215616', 'output': '215616\\n'}, {'type': 'stdin_stdout', 'input': '50', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '-15', 'output': '-30\\n'}, {'type': 'stdin_stdout', 'input': '63978', 'output': '63978\\n'}, {'type': 'stdin_stdout', 'input': '-29', 'output': '-58\\n'}, {'type': 'stdin_stdout', 'input': '101054', 'output': '101054\\n'}, {'type': 'stdin_stdout', 'input': '43', 'output': '86\\n'}, {'type': 'stdin_stdout', 'input': '-20', 'output': '-20\\n'}, {'type': 'stdin_stdout', 'input': '4713', 'output': '9426\\n'}, {'type': 'stdin_stdout', 'input': '33', 'output': '66\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79085","program":"```python\nn = int(input())\nif n % 2 == 0:\n print(n)\nelse:\n print(2*n)\n```","inputs":"999999999","output":"1999999998","actual_output":"1999999998\n","execution_success":true,"sample_index":12593},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03629 AtCoder Regular Contest 081 - Don't Be a Subsequence","prompt":"Solve the following coding problem using the programming language python:\n\nA subsequence of a string S is a string that can be obtained by deleting zero or more characters from S without changing the order of the remaining characters. For example, `arc`, `artistic` and (an empty string) are all subsequences of `artistic`; `abc` and `ci` are not.\n\nYou are given a string A consisting of lowercase English letters. Find the shortest string among the strings consisting of lowercase English letters that are not subsequences of A. If there are more than one such string, find the lexicographically smallest one among them.\n\nConstraints\n\n* 1 \\leq |A| \\leq 2 \\times 10^5\n* A consists of lowercase English letters.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nA\n\n\nOutput\n\nPrint the lexicographically smallest string among the shortest strings consisting of lowercase English letters that are not subsequences of A.\n\nExamples\n\nInput\n\natcoderregularcontest\n\n\nOutput\n\nb\n\n\nInput\n\nabcdefghijklmnopqrstuvwxyz\n\n\nOutput\n\naa\n\n\nInput\n\nfrqnvhydscshfcgdemurlfrutcpzhopfotpifgepnqjxupnskapziurswqazdwnwbgdhyktfyhqqxpoidfhjdakoxraiedxskywuepzfniuyskxiyjpjlxuqnfgmnjcvtlpnclfkpervxmdbvrbrdn\n\n\nOutput\n\naca\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\n\nA = input().rstrip()\ndp = [chr(c) for c in range(ord('a'), ord('z')+1)]\nfor c in A[::-1]:\n s = min(dp, key=lambda x: len(x))\n dp[ord(c) - ord('a')] = c + s\nprint(min(dp, key=lambda x: len(x)))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'frqnvhydscshfcgdemurlfrutcpzhopfotpifgepnqjxupnskapziurswqazdwnwbgdhyktfyhqqxpoidfhjdakoxraiedxskywuepzfniuyskxiyjpjlxuqnfgmnjcvtlpnclfkpervxmdbvrbrdn', 'output': 'aca'}, {'type': 'stdin_stdout', 'input': 'abcdefghijklmnopqrstuvwxyz', 'output': 'aa'}, {'type': 'stdin_stdout', 'input': 'atcoderregularcontest', 'output': 'b'}, {'type': 'stdin_stdout', 'input': 'frqnvhydscshfcgdemurlfrutcpzhopfotpifgepnqjxupnskapziurswqazdwnwbgdhzktfyhqqxpoidfhjdakoxraiedxskywuepzfniuyskxiyjpjlxuqnfgmnjcvtlpnclfkpervxmdbvrbrdn', 'output': 'aca\\n'}, {'type': 'stdin_stdout', 'input': 'atcoddrregularcontest', 'output': 'b\\n'}, {'type': 'stdin_stdout', 'input': 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{'type': 'stdin_stdout', 'input': 'qsadmbdbqok^r`qtmore_', 'output': 'c\\n'}, {'type': 'stdin_stdout', 'input': 'abcdefghijklmnopqrstzvwxyu', 'output': 'aa\\n'}, {'type': 'stdin_stdout', 'input': 'frqnvhydscshfcgdemurlfrutcpzhopfotpifgepnqjxupnskapziurswqazdwnwagdhzktfyhqqxpoidfhjdakoxraiedxskywuepzfniuyskxiyjpjlxuqnfgmnjcvtlpnclfkpervxmdbvrbrdn', 'output': 'ba\\n'}, {'type': 'stdin_stdout', 'input': 'frqnvhydscshfcgdemurlfrutcpzhopfotpifgepnqjxupnskapziurswqazdwnwbgdhzktfyhqqxpoidfhjdakoxraiedxskywuepzfnhuyskxiyjpjlxuqnfgmnjcvtlpnclfkpervxmdbvrbrdn', 'output': 'aca\\n'}, {'type': 'stdin_stdout', 'input': 'atooddrregularccntest', 'output': 'b\\n'}, {'type': 'stdin_stdout', 'input': 'frqnvhydscshfcgdemurlfrutcpzhopfotpifgepnqjxupnskapziurswqazdwnwbgdhzktfyhqqxpoidfhjjakoxraiedxskywuepzfnhuyskxiyjpdlxuqnfgmnjcvtlpnclfkpervxmdbvrbrdn', 'output': 'aca\\n'}, {'type': 'stdin_stdout', 'input': 'atooddrregumarccntest', 'output': 'b\\n'}, {'type': 'stdin_stdout', 'input': 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'frqnvhydsdshftgdemvrlfrutcpzhopfotsifgebnqkxupnskaqzidrswqazdwnpogthzltfyhqqxpyiefhjjajoxraivdxpkywuepzfhnuoskxhyjpdmxuqnegmnjcvclvnclflperexmdavrbrdn', 'output': 'jt\\n'}, {'type': 'stdin_stdout', 'input': 'ssetabfbpdtrmrmcecrsn', 'output': 'g\\n'}, {'type': 'stdin_stdout', 'input': 'ndrbrvadmxereplflcnvlcvcjnmgenquxmdpjyhxksounhfzpeuwykpxdviarxojajjhfeiypxqqhyftlzhtgopnwdzaqwsrdizqaksnpuxkqnbegfistofpohzpcturflrvmedgtfhsdsdyhvnqrf', 'output': 'tj\\n'}, {'type': 'stdin_stdout', 'input': 'nsrcecmrmrtdpbfbatess', 'output': 'g\\n'}, {'type': 'stdin_stdout', 'input': 'ndrbrvadmxereplfmcnvlcvcjnmgenquxmdpjyhxksounhfzpeuwykpxdviarxojajjhfeiypxqqhyftlzhtgopnwdzaqwsrdizqaksnpuxkqnbegfistofpohzpcturflrvmedgtfhsdsdyhvnqrf', 'output': 'tj\\n'}, {'type': 'stdin_stdout', 'input': 'nstcecmrmrtdpbfbaress', 'output': 'g\\n'}, {'type': 'stdin_stdout', 'input': 'sserabfbpdtrmrmcectsn', 'output': 'g\\n'}, {'type': 'stdin_stdout', 'input': 'frqnvhydsdshftgdedvrlfrutcpzhopfotsifgebnqkxupnskaqzidrswqazdwnpogthzltfyhqqxpyiefhjjajoxraivdxpkywuepzfhnuoskxhyjpdmxuqnegmnjcvclvncmflperexmmavrbrdn', 'output': 'jt\\n'}, {'type': 'stdin_stdout', 'input': 'nstcecmrmrtdpbfcaress', 'output': 'g\\n'}, {'type': 'stdin_stdout', 'input': 'frqnvhydsdshftgdedvrlfrutcpzhopfotsifhebnqkxupnskaqzidrswqazdwnpogthzltfyhqqxpyiefhjjajoxraivdxpkywuepzfhnuoskxhyjpdmxuqnegmnjcvclvncmflperexmmavrbrdn', 'output': 'jt\\n'}, {'type': 'stdin_stdout', 'input': 'sseracfbpdtrmrmcectsn', 'output': 'g\\n'}, {'type': 'stdin_stdout', 'input': 'faqnvhydsdshftgdedvrlfrutcpzhopfotsifhebnqkxupnskrqzidrswqazdwnpogthzltfyhqqxpyiefhjjajoxraivdxpkywuepzfhnuoskxhyjpdmxuqnegmnjcvclvncmflperexmmavrbrdn', 'output': 'jt\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79093","program":"```python\nimport sys\ninput = sys.stdin.readline\n\nA = input().rstrip()\ndp = [chr(c) for c in range(ord('a'), ord('z')+1)]\nfor c in A[::-1]:\n s = min(dp, key=lambda x: len(x))\n dp[ord(c) - ord('a')] = c + s\nprint(min(dp, key=lambda x: len(x)))\n```","inputs":"frqnvhydscshfcgdemurlfrutcpzhopfotpifgepnqjxupnskapziurswqazdwnwbgdhyktfyhqqxpoidfhjdakoxraiedxskywuepzfniuyskxiyjpjlxuqnfgmnjcvtlpnclfkpervxmdbvrbrdn","output":"aca","actual_output":"aca\n","execution_success":true,"sample_index":12594},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03787 AtCoder Grand Contest 011 - Squared Graph","prompt":"Solve the following coding problem using the programming language python:\n\nTakahashi has received an undirected graph with N vertices, numbered 1, 2, ..., N. The edges in this graph are represented by (u_i, v_i). There are no self-loops and multiple edges in this graph.\n\nBased on this graph, Takahashi is now constructing a new graph with N^2 vertices, where each vertex is labeled with a pair of integers (a, b) (1 \\leq a \\leq N, 1 \\leq b \\leq N). The edges in this new graph are generated by the following rule:\n\n* Span an edge between vertices (a, b) and (a', b') if and only if both of the following two edges exist in the original graph: an edge between vertices a and a', and an edge between vertices b and b'.\n\n\n\nHow many connected components are there in this new graph?\n\nConstraints\n\n* 2 \\leq N \\leq 100,000\n* 0 \\leq M \\leq 200,000\n* 1 \\leq u_i < v_i \\leq N\n* There exists no pair of distinct integers i and j such that u_i = u_j and v_i = v_j.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN M\nu_1 v_1\nu_2 v_2\n:\nu_M v_M\n\n\nOutput\n\nPrint the number of the connected components in the graph constructed by Takahashi.\n\nExamples\n\nInput\n\n3 1\n1 2\n\n\nOutput\n\n7\n\n\nInput\n\n7 5\n1 2\n3 4\n3 5\n4 5\n2 6\n\n\nOutput\n\n18\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\n\nn, m = map(int, input().split())\nG = [[] for _ in range(n)]\nfor _ in range(m):\n u, v = map(int, input().split())\n u -= 1\n v -= 1\n G[u].append(v)\n G[v].append(u)\nseen = [-1]*n\np, q, r = 0, 0, 0\ndef dfs(v):\n global p, q\n stack = [(v, 0)]\n seen[v] = 0\n f = False\n while stack:\n v, c = stack.pop()\n for nv in G[v]:\n if seen[nv] == -1:\n seen[nv] = c^1\n stack.append((nv, c^1))\n else:\n if seen[nv]^c == 0:\n f = True\n if f:\n p += 1\n else:\n q += 1\nfor v in range(n):\n if seen[v] != -1:\n continue\n if not G[v]:\n r += 1\n else:\n dfs(v)\nans = r*(2*n-r) + (p+q)*(p+q) + q*q\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7 5\\n1 2\\n3 4\\n3 5\\n4 5\\n2 6', 'output': '18'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 2', 'output': '7'}, {'type': 'stdin_stdout', 'input': '7 5\\n1 2\\n3 4\\n3 5\\n4 1\\n2 6', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '7 5\\n1 2\\n3 7\\n3 5\\n4 1\\n2 6', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '7 5\\n1 2\\n3 7\\n3 5\\n4 1\\n2 2', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '7 5\\n1 2\\n3 7\\n6 5\\n4 1\\n2 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '12 5\\n1 2\\n3 4\\n3 5\\n4 1\\n2 6', 'output': '110\\n'}, {'type': 'stdin_stdout', 'input': '7 5\\n1 2\\n3 7\\n3 7\\n4 1\\n2 3', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '12 5\\n1 2\\n3 4\\n3 5\\n4 1\\n2 2', 'output': '120\\n'}, {'type': 'stdin_stdout', 'input': '7 5\\n1 2\\n2 6\\n6 5\\n4 1\\n2 2', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '7 5\\n2 2\\n2 6\\n6 5\\n4 1\\n2 2', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n1 2\\n3 4\\n2 5\\n4 1\\n2 2', 'output': '76\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 2\\n3 4\\n2 5\\n4 1\\n2 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '7 5\\n1 2\\n2 7\\n6 5\\n4 1\\n1 2', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n1 2\\n6 7\\n3 5\\n4 1\\n2 2', 'output': '64\\n'}, {'type': 'stdin_stdout', 'input': '21 5\\n1 2\\n3 4\\n3 5\\n4 1\\n4 6', 'output': '407\\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n1 2\\n2 7\\n6 5\\n4 1\\n1 2', 'output': '72\\n'}, {'type': 'stdin_stdout', 'input': '12 5\\n1 2\\n3 1\\n3 5\\n3 1\\n2 2', 'output': '129\\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n1 2\\n3 7\\n6 5\\n4 1\\n1 2', 'output': '69\\n'}, {'type': 'stdin_stdout', 'input': '21 5\\n1 2\\n3 4\\n3 5\\n4 1\\n6 10', 'output': '400\\n'}, {'type': 'stdin_stdout', 'input': '21 5\\n1 2\\n3 3\\n3 5\\n4 1\\n6 10', 'output': '405\\n'}, {'type': 'stdin_stdout', 'input': '12 5\\n1 2\\n3 4\\n3 5\\n4 1\\n2 1', 'output': '121\\n'}, {'type': 'stdin_stdout', 'input': '7 5\\n1 2\\n3 7\\n3 7\\n4 1\\n1 4', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 2\\n3 4\\n2 5\\n4 1\\n3 2', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '21 5\\n1 2\\n3 4\\n3 3\\n4 1\\n4 6', 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'stdin_stdout', 'input': '78 5\\n2 3\\n3 1\\n3 6\\n6 1\\n2 2', 'output': '6069\\n'}, {'type': 'stdin_stdout', 'input': '19 5\\n1 3\\n2 8\\n4 7\\n2 5\\n3 6', 'output': '315\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79097","program":"```python\nimport sys\ninput = sys.stdin.readline\n\nn, m = map(int, input().split())\nG = [[] for _ in range(n)]\nfor _ in range(m):\n u, v = map(int, input().split())\n u -= 1\n v -= 1\n G[u].append(v)\n G[v].append(u)\nseen = [-1]*n\np, q, r = 0, 0, 0\ndef dfs(v):\n global p, q\n stack = [(v, 0)]\n seen[v] = 0\n f = False\n while stack:\n v, c = stack.pop()\n for nv in G[v]:\n if seen[nv] == -1:\n seen[nv] = c^1\n stack.append((nv, c^1))\n else:\n if seen[nv]^c == 0:\n f = True\n if f:\n p += 1\n else:\n q += 1\nfor v in range(n):\n if seen[v] != -1:\n continue\n if not G[v]:\n r += 1\n else:\n dfs(v)\nans = r*(2*n-r) + (p+q)*(p+q) + q*q\nprint(ans)\n```","inputs":"7 5\n1 2\n3 4\n3 5\n4 5\n2 6","output":"18","actual_output":"18\n","execution_success":true,"sample_index":12595},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03955 AtCoder Grand Contest 006 - Rotate 3x3","prompt":"Solve the following coding problem using the programming language python:\n\nWe have a grid with 3 rows and N columns. The cell at the i-th row and j-th column is denoted (i, j). Initially, each cell (i, j) contains the integer i+3j-3.\n\n\n\nA grid with N=5 columns\n\nSnuke can perform the following operation any number of times:\n\n* Choose a 3\u00d73 subrectangle of the grid. The placement of integers within the subrectangle is now rotated by 180\u00b0.\n\n\n\n\n\nAn example sequence of operations (each chosen subrectangle is colored blue)\n\nSnuke's objective is to manipulate the grid so that each cell (i, j) contains the integer a_{i,j}. Determine whether it is achievable.\n\nConstraints\n\n* 5\u2264N\u226410^5\n* 1\u2264a_{i,j}\u22643N\n* All a_{i,j} are distinct.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN\na_{1,1} a_{1,2} ... a_{1,N}\na_{2,1} a_{2,2} ... a_{2,N}\na_{3,1} a_{3,2} ... a_{3,N}\n\n\nOutput\n\nIf Snuke's objective is achievable, print `Yes`. Otherwise, print `No`.\n\nExamples\n\nInput\n\n5\n9 6 15 12 1\n8 5 14 11 2\n7 4 13 10 3\n\n\nOutput\n\nYes\n\n\nInput\n\n5\n1 2 3 4 5\n6 7 8 9 10\n11 12 13 14 15\n\n\nOutput\n\nNo\n\n\nInput\n\n5\n1 4 7 10 13\n2 5 8 11 14\n3 6 9 12 15\n\n\nOutput\n\nYes\n\n\nInput\n\n6\n15 10 3 4 9 16\n14 11 2 5 8 17\n13 12 1 6 7 18\n\n\nOutput\n\nYes\n\n\nInput\n\n7\n21 12 1 16 13 6 7\n20 11 2 17 14 5 8\n19 10 3 18 15 4 9\n\n\nOutput\n\nNo\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef merge_and_count_rec(A, W, l, r):\n if l+1 >= r:\n return 0\n m = (l+r)//2\n cnt = merge_and_count_rec(A, W, l, m)\n cnt += merge_and_count_rec(A, W, m, r)\n i,j,k = l,m,l\n while i= r:\n return 0\n m = (l+r)//2\n cnt = merge_and_count_rec(A, W, l, m)\n cnt += merge_and_count_rec(A, W, m, r)\n i,j,k = l,m,l\n while i 1$, it always holds that\n$z^n > $ max { $x^n + y^n | x > 0, y > 0, x^n + y^n \\leq z^n$ }.\n\n\nYour mission is to write a program that verifies this in the case $n$ = 3 for a given $z$. Your program should read in integer numbers greater than 1, and, corresponding to each input $z$, it should output the following:\n$z^3 - $ max { $x^3 + y^3 | x > 0, y > 0, x^3 + y^3 \\leq z^3$ }.\n\n\n\nInput\n\nThe input is a sequence of lines each containing one positive integer number followed by a line containing a zero. You may assume that all of the input integers are greater than 1 and less than 1111.\n\nOutput\n\nThe output should consist of lines each containing a single integer number. Each output integer should be\n$z^3 - $ max { $x^3 + y^3 | x > 0, y > 0, x^3 + y^3 \\leq z^3$ }.\n\n\nfor the corresponding input integer z. No other characters should appear in any output line.\n\nExample\n\nInput\n\n6\n4\n2\n0\n\n\nOutput\n\n27\n10\n6\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na=1/3\nwhile 1:\n z=int(input())\n if z==0:break\n m,zz=0,z*z*z\n for x in range(1,int(z/pow(2,a))+1):\n xx=x*x*x\n y=int(pow(zz-xx,a))\n yy=y*y*y\n m=max(m,yy+xx)\n print(zz-m)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6\\n4\\n2\\n0', 'output': '27\\n10\\n6'}, {'type': 'stdin_stdout', 'input': '6\\n6\\n2\\n0', 'output': '27\\n27\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n6\\n0\\n0', 'output': '27\\n27\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4\\n4\\n0', 'output': '27\\n10\\n10\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4\\n0\\n-1', 'output': '27\\n10\\n'}, {'type': 'stdin_stdout', 'input': '6\\n5\\n2\\n0', 'output': '27\\n34\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0\\n0\\n1', 'output': '27\\n'}, {'type': 'stdin_stdout', 'input': '6\\n3\\n2\\n0', 'output': '27\\n11\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n5\\n0\\n1', 'output': '27\\n34\\n'}, {'type': 'stdin_stdout', 'input': '6\\n7\\n4\\n0', 'output': '27\\n2\\n10\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2\\n2\\n0', 'output': '27\\n6\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2\\n4\\n0', 'output': '27\\n6\\n10\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n0\\n0', 'output': '27\\n44\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2\\n0\\n2', 'output': '27\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n13\\n0\\n0', 'output': '27\\n126\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n2\\n0', 'output': '27\\n44\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2\\n7\\n0', 'output': '27\\n6\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n12\\n0\\n0', 'output': '27\\n54\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n4\\n0', 'output': 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'stdin_stdout', 'input': '6\\n16\\n2\\n0', 'output': '27\\n21\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n6\\n0', 'output': '27\\n44\\n27\\n'}, {'type': 'stdin_stdout', 'input': '6\\n40\\n0\\n-1', 'output': '27\\n307\\n'}, {'type': 'stdin_stdout', 'input': '6\\n3\\n8\\n0', 'output': '27\\n11\\n44\\n'}, {'type': 'stdin_stdout', 'input': '6\\n50\\n0\\n4', 'output': '27\\n259\\n'}, {'type': 'stdin_stdout', 'input': '6\\n7\\n7\\n0', 'output': '27\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n8\\n0', 'output': '27\\n44\\n44\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4\\n11\\n0', 'output': '27\\n10\\n90\\n'}, {'type': 'stdin_stdout', 'input': '6\\n3\\n3\\n0', 'output': '27\\n11\\n11\\n'}, {'type': 'stdin_stdout', 'input': '6\\n17\\n2\\n0', 'output': '27\\n88\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n6\\n15\\n0', 'output': '27\\n27\\n119\\n'}, {'type': 'stdin_stdout', 'input': '6\\n14\\n3\\n0', 'output': '27\\n16\\n11\\n'}, {'type': 'stdin_stdout', 'input': '6\\n9\\n3\\n0', 'output': '27\\n1\\n11\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4\\n16\\n0', 'output': '27\\n10\\n21\\n'}, {'type': 'stdin_stdout', 'input': '6\\n9\\n9\\n0', 'output': '27\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n18\\n3\\n0', 'output': '27\\n8\\n11\\n'}, {'type': 'stdin_stdout', 'input': '6\\n9\\n6\\n0', 'output': '27\\n1\\n27\\n'}, {'type': 'stdin_stdout', 'input': '6\\n10\\n3\\n0', 'output': '27\\n55\\n11\\n'}, {'type': 'stdin_stdout', 'input': '6\\n11\\n8\\n0', 'output': '27\\n90\\n44\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4\\n36\\n0', 'output': '27\\n10\\n64\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79121","program":"```python\na=1/3\nwhile 1:\n z=int(input())\n if z==0:break\n m,zz=0,z*z*z\n for x in range(1,int(z/pow(2,a))+1):\n xx=x*x*x\n y=int(pow(zz-xx,a))\n yy=y*y*y\n m=max(m,yy+xx)\n print(zz-m)\n```","inputs":"6\n4\n2\n0","output":"27\n10\n6","actual_output":"27\n10\n6\n","execution_success":true,"sample_index":12601},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00832 Dice Puzzle","prompt":"Solve the following coding problem using the programming language python:\n\nLet\u2019s try a dice puzzle. The rules of this puzzle are as follows.\n\n1. Dice with six faces as shown in Figure 1 are used in the puzzle.\n\n\n\nFigure 1: Faces of a die\n\n2. With twenty seven such dice, a 3 \u00d7 3 \u00d7 3 cube is built as shown in Figure 2.\n\n\n\nFigure 2: 3 \u00d7 3 \u00d7 3 cube\n\n3. When building up a cube made of dice, the sum of the numbers marked on the faces of adjacent dice that are placed against each other must be seven (See Figure 3). For example, if one face of the pair is marked \u201c2\u201d, then the other face must be \u201c5\u201d.\n\n\n\nFigure 3: A pair of faces placed against each other\n\n4. The top and the front views of the cube are partially given, i.e. the numbers on faces of some of the dice on the top and on the front are given.\n\n\n\nFigure 4: Top and front views of the cube\n\n5. The goal of the puzzle is to find all the plausible dice arrangements that are consistent with the given top and front view information.\n\n\n\nYour job is to write a program that solves this puzzle.\n\n\n\nInput\n\nThe input consists of multiple datasets in the following format.\n\n\nN\nDataset1\nDataset2\n...\nDatasetN\n\n\nN is the number of the datasets.\n\nThe format of each dataset is as follows.\n\n\nT11 T12 T13\nT21 T22 T23\nT31 T32 T33\nF11 F12 F13\nF21 F22 F23\nF31 F32 F33\n\n\nTij and Fij (1 \u2264 i \u2264 3, 1 \u2264 j \u2264 3) are the faces of dice appearing on the top and front views, as shown in Figure 2, or a zero. A zero means that the face at the corresponding position is unknown.\n\nOutput\n\nFor each plausible arrangement of dice, compute the sum of the numbers marked on the nine faces appearing on the right side of the cube, that is, with the notation given in Figure 2, \u22113i=1\u22113j=1Rij.\n\nFor each dataset, you should output the right view sums for all the plausible arrangements, in ascending order and without duplicates. Numbers should be separated by a single space.\n\nWhen there are no plausible arrangements for a dataset, output a zero.\n\nFor example, suppose that the top and the front views are given as follows.\n\n\n\nFigure 5: Example\n\nThere are four plausible right views as shown in Figure 6. The right view sums are 33, 36, 32, and 33, respectively. After rearranging them into ascending order and eliminating duplicates, the answer should be \u201c32 33 36\u201d.\n\n\n\nFigure 6: Plausible right views\n\nThe output should be one line for each dataset. The output may have spaces at ends of lines.\n\nExample\n\nInput\n\n4\n1 1 1\n1 1 1\n1 1 1\n2 2 2\n2 2 2\n2 2 2\n4 3 3\n5 2 2\n4 3 3\n6 1 1\n6 1 1\n6 1 0\n1 0 0\n0 2 0\n0 0 0\n5 1 2\n5 1 2\n0 0 0\n2 0 0\n0 3 0\n0 0 0\n0 0 0\n0 0 0\n3 0 1\n\n\nOutput\n\n27\n24\n32 33 36\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\n\nD = [\n (1, 5, 2, 3, 0, 4), # 'U'\n (3, 1, 0, 5, 4, 2), # 'R'\n (4, 0, 2, 3, 5, 1), # 'D'\n (2, 1, 5, 0, 4, 3), # 'L'\n]\np_dice = (0, 0, 0, 1, 1, 2, 2, 3)*3\n\ndef enumerate_dice(L0):\n L = L0[:]\n for k in p_dice:\n yield L\n L[:] = (L[e] for e in D[k])\n\nL = [1, 2, 3, 4, 5, 6]\nLS = []\nfor l in enumerate_dice(L):\n LS.append(l[:])\n\ndef solve():\n T = [list(map(int, readline().split())) for i in range(3)]\n F = [list(map(int, readline().split())) for i in range(3)]\n\n T0 = [[-1]*3 for i in range(3)]\n F0 = [[-1]*3 for i in range(3)]\n R0 = [[-1]*3 for i in range(3)]\n res = set()\n def dfs(i, s):\n if i == 27:\n res.add(s)\n return\n x = i % 3; y = (i // 3) % 3; z = (i // 9) % 3\n t0 = T0[y][x]\n f0 = F0[z][x]\n r0 = R0[z][y]\n for l in LS:\n if t0 == -1:\n e = T[y][x]\n if e != 0 and e != l[0]:\n continue\n T0[y][x] = l[0]\n else:\n if l[0] != t0:\n continue\n if f0 == -1:\n e = F[z][x]\n if e != 0 and e != l[1]:\n continue\n F0[z][x] = l[1]\n else:\n if l[1] != f0:\n continue\n if r0 == -1:\n R0[z][y] = l[2]\n s0 = s + l[2]\n else:\n if l[2] != r0:\n continue\n s0 = s\n dfs(i+1, s0)\n if t0 == -1:\n T0[y][x] = -1\n if f0 == -1:\n F0[z][x] = -1\n if r0 == -1:\n R0[z][y] = -1\n dfs(0, 0)\n if res:\n ans = sorted(res)\n write(\" \".join(map(str, ans)))\n write(\"\\n\")\n else:\n write(\"0\\n\")\n\nN = int(readline())\nfor i in range(N):\n solve()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 1 1\\n1 1 1\\n2 2 2\\n2 2 2\\n2 2 2\\n4 3 3\\n5 2 2\\n4 3 3\\n6 1 1\\n6 1 1\\n6 1 0\\n1 0 0\\n0 2 0\\n0 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n0 0 0\\n3 0 1', 'output': '27\\n24\\n32 33 36\\n0'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 1 1\\n1 1 1\\n2 2 2\\n2 2 2\\n2 2 2\\n4 3 3\\n5 2 2\\n4 3 3\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n0 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n0 0 0\\n3 0 1', 'output': '27\\n0\\n32 33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 2 1\\n1 1 1\\n2 2 2\\n2 2 2\\n2 2 2\\n4 3 3\\n5 2 2\\n4 3 3\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n0 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 0 1', 'output': '0\\n0\\n32 33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 2 1\\n1 1 1\\n2 2 2\\n2 2 2\\n2 2 2\\n4 6 3\\n5 2 2\\n4 3 3\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n1 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 1', 'output': '0\\n0\\n33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n0 2 1\\n1 1 0\\n2 2 2\\n0 2 2\\n6 2 2\\n4 6 3\\n5 2 2\\n4 3 0\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n1 -1 0\\n5 1 2\\n5 1 2\\n0 0 0\\n3 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 0', 'output': '0\\n0\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 1 1\\n1 1 1\\n2 2 2\\n2 2 2\\n2 2 2\\n4 3 3\\n5 2 2\\n4 3 3\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n0 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 0 1', 'output': '27\\n0\\n32 33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 2 1\\n1 1 1\\n2 2 2\\n2 2 2\\n2 2 2\\n4 3 3\\n5 2 2\\n4 3 3\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n0 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 1', 'output': '0\\n0\\n32 33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 2 1\\n1 1 1\\n2 2 2\\n2 2 2\\n2 2 2\\n4 6 3\\n5 2 2\\n4 3 3\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n0 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 1', 'output': '0\\n0\\n32 33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 2 1\\n1 1 1\\n2 2 2\\n2 2 2\\n2 2 2\\n4 6 3\\n5 2 2\\n4 3 3\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n1 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 0', 'output': '0\\n0\\n33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 2 1\\n1 1 1\\n2 2 2\\n2 2 2\\n2 2 2\\n4 6 3\\n5 2 2\\n4 3 0\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n1 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 0', 'output': '0\\n0\\n33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 2 1\\n1 1 0\\n2 2 2\\n2 2 2\\n2 2 2\\n4 6 3\\n5 2 2\\n4 3 0\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n1 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 0', 'output': '0\\n0\\n33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 2 1\\n1 1 0\\n2 2 2\\n2 2 2\\n4 2 2\\n4 6 3\\n5 2 2\\n4 3 0\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n1 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 0', 'output': '0\\n0\\n33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n1 2 1\\n1 1 0\\n2 2 2\\n0 2 2\\n4 2 2\\n4 6 3\\n5 2 2\\n4 3 0\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n1 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 0', 'output': '0\\n0\\n33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n0 2 1\\n1 1 0\\n2 2 2\\n0 2 2\\n4 2 2\\n4 6 3\\n5 2 2\\n4 3 0\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n1 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 0', 'output': '0\\n0\\n33 36\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1\\n0 2 1\\n1 1 0\\n2 2 2\\n0 2 2\\n6 2 2\\n4 6 3\\n5 2 2\\n4 3 0\\n6 1 1\\n6 1 1\\n6 1 -1\\n1 0 0\\n0 2 0\\n1 0 0\\n5 1 2\\n5 1 2\\n0 0 0\\n2 0 0\\n0 3 0\\n0 0 0\\n0 0 0\\n-1 0 0\\n3 1 0', 'output': '0\\n0\\n33 36\\n0\\n'}, {'type': 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in p_dice:\n yield L\n L[:] = (L[e] for e in D[k])\n\nL = [1, 2, 3, 4, 5, 6]\nLS = []\nfor l in enumerate_dice(L):\n LS.append(l[:])\n\ndef solve():\n T = [list(map(int, readline().split())) for i in range(3)]\n F = [list(map(int, readline().split())) for i in range(3)]\n\n T0 = [[-1]*3 for i in range(3)]\n F0 = [[-1]*3 for i in range(3)]\n R0 = [[-1]*3 for i in range(3)]\n res = set()\n def dfs(i, s):\n if i == 27:\n res.add(s)\n return\n x = i % 3; y = (i // 3) % 3; z = (i // 9) % 3\n t0 = T0[y][x]\n f0 = F0[z][x]\n r0 = R0[z][y]\n for l in LS:\n if t0 == -1:\n e = T[y][x]\n if e != 0 and e != l[0]:\n continue\n T0[y][x] = l[0]\n else:\n if l[0] != t0:\n continue\n if f0 == -1:\n e = F[z][x]\n if e != 0 and e != l[1]:\n continue\n F0[z][x] = l[1]\n else:\n if l[1] != f0:\n continue\n if r0 == -1:\n R0[z][y] = l[2]\n s0 = s + l[2]\n else:\n if l[2] != r0:\n continue\n s0 = s\n dfs(i+1, s0)\n if t0 == -1:\n T0[y][x] = -1\n if f0 == -1:\n F0[z][x] = -1\n if r0 == -1:\n R0[z][y] = -1\n dfs(0, 0)\n if res:\n ans = sorted(res)\n write(\" \".join(map(str, ans)))\n write(\"\\n\")\n else:\n write(\"0\\n\")\n\nN = int(readline())\nfor i in range(N):\n solve()\n\n```","inputs":"4\n1 1 1\n1 1 1\n1 1 1\n2 2 2\n2 2 2\n2 2 2\n4 3 3\n5 2 2\n4 3 3\n6 1 1\n6 1 1\n6 1 0\n1 0 0\n0 2 0\n0 0 0\n5 1 2\n5 1 2\n0 0 0\n2 0 0\n0 3 0\n0 0 0\n0 0 0\n0 0 0\n3 0 1","output":"27\n24\n32 33 36\n0","actual_output":"27\n24\n32 33 36\n0\n","execution_success":true,"sample_index":12602},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00963 Rendezvous on a Tetrahedron","prompt":"Solve the following coding problem using the programming language python:\n\nProblem G Rendezvous on a Tetrahedron\n\nOne day, you found two worms $P$ and $Q$ crawling on the surface of a regular tetrahedron with four vertices $A$, $B$, $C$ and $D$. Both worms started from the vertex $A$, went straight ahead, and stopped crawling after a while.\n\nWhen a worm reached one of the edges of the tetrahedron, it moved on to the adjacent face and kept going without changing the angle to the crossed edge (Figure G.1).\n\nWrite a program which tells whether or not $P$ and $Q$ were on the same face of the tetrahedron when they stopped crawling.\n\nYou may assume that each of the worms is a point without length, area, or volume.\n\n\n\nFigure G.1. Crossing an edge\n\nIncidentally, lengths of the two trails the worms left on the tetrahedron were exact integral multiples of the unit length. Here, the unit length is the edge length of the tetrahedron. Each trail is more than 0:001 unit distant from any vertices, except for its start point and its neighborhood. This means that worms have crossed at least one edge. Both worms stopped at positions more than 0:001 unit distant from any of the edges.\n\nThe initial crawling direction of a worm is specified by two items: the edge $XY$ which is the first edge the worm encountered after its start, and the angle $d$ between the edge $AX$ and the direction of the worm, in degrees.\n\n\n\nFigure G.2. Trails of the worms corresponding to Sample Input 1\n\nFigure G.2 shows the case of Sample Input 1. In this case, $P$ went over the edge $CD$ and stopped on the face opposite to the vertex $A$, while $Q$ went over the edge $DB$ and also stopped on the same face.\n\nInput\n\nThe input consists of a single test case, formatted as follows.\n\n\n$X_PY_P$ $d_P$ $l_P$\n$X_QY_Q$ $d_Q$ $l_Q$\n\n\n$X_WY_W$ ($W = P,Q$) is the first edge the worm $W$ crossed after its start. $X_WY_W$ is one of BC, CD or DB.\n\nAn integer $d_W$ ($1 \\leq d_W \\leq 59$) is the angle in degrees between edge $AX_W$ and the initial direction of the worm $W$ on the face $\\triangle AX_WY_W$.\n\nAn integer $l_W$ ($1 \\leq l_W \\leq 20$) is the length of the trail of worm $W$ left on the surface, in unit lengths.\n\nOutput\n\nOutput YES when and only when the two worms stopped on the same face of the tetrahedron. Otherwise, output NO.\n\nSample Input 1\n\n\nCD 30 1\nDB 30 1\n\n\nSample Output 1\n\n\nYES\n\n\nSample Input 2\n\n\nBC 1 1\nDB 59 1\n\n\nSample Output 2\n\n\nYES\n\n\nSample Input 3\n\n\nBC 29 20\nBC 32 20\n\n\nSample Output 3\n\n\nNO\n\n\n\n\n\n\nExample\n\nInput\n\nCD 30 1\nDB 30 1\n\n\nOutput\n\nYES\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom math import cos, sin, pi, sqrt\nB = [\"BC\", \"CD\", \"DB\"]\nXY0, d0, l0, XY1, d1, l1 = open(0).read().split()\nd0, l0, d1, l1 = map(int, [d0, l0, d1, l1])\n\ndef calc(XY, d, l):\n angle = B.index(XY) * 60 + d\n x = l * cos(pi*angle/180)\n y = l * sin(pi*angle/180)\n x = x + y/sqrt(3)\n y = y * 2/sqrt(3)\n x = x%2; y = y%2\n A = [[\"AC\", \"BD\"], [\"DB\", \"CA\"]][int(x)][int(y)]\n return A[x%1>y%1]\nprint(\"YES\"*(calc(XY0, d0, l0)==calc(XY1, d1, l1))or\"NO\")\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'CD 30 1\\nDB 30 1', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 30 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 0\\nDB 55 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 55 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 19 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 55 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 0\\nDB 56 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 14 1\\nDB 55 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 20 1\\nDB 55 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 30 1\\nDB 30 2', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 0\\nDB 54 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 19 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 56 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 14 1\\nDB 61 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 20 1\\nDB 103 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 29 1\\nDB 30 2', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 0\\nDB 23 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 33 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 14 1\\nDB 78 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 20 1\\nDB 204 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 29 1\\nDB 25 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 19 1\\nDB 33 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 14 1\\nDB 39 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 30 1\\nDB 204 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 28 1\\nDB 33 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 15 1\\nDB 39 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 30 1\\nDB 30 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 44 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 0\\nDB 47 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 1\\nDB 19 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 42 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 8 1\\nDB 55 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 23 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 29 1\\nDB 30 3', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 29 1\\nDB 25 3', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 1\\nDB 33 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 6 0\\nDB 47 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 2\\nDB 19 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 42 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 0 1\\nDB 23 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 29 1\\nDB 54 3', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 29 2\\nDB 25 3', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 1\\nDB 39 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 2\\nDB 11 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 28 1\\nDB 54 3', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 1\\nDB 39 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 0\\nDB 11 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 28 1\\nDB 54 6', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 1\\nDB 8 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 30 1\\nDB 42 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 0\\nDB 19 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 60 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 1\\nDB 55 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 4 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 5 1\\nDB 56 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 28 1\\nDB 103 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 29 1\\nDB 52 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 33 2', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 14 1\\nDB 73 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 32 1\\nDB 204 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 18 1\\nDB 25 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 19 1\\nDB 33 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 30 1\\nDB 85 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 28 0\\nDB 33 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 15 1\\nDB 39 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 88 0\\nDB 47 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 3 1\\nDB 55 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 1\\nDB 9 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 0 2\\nDB 19 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 29 1\\nDB 54 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 29 4\\nDB 25 3', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 2 1\\nDB 39 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 2 2\\nDB 11 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 0\\nDB 19 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 1\\nDB 8 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 1\\nDB 16 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 32 1\\nDB 103 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 40 1\\nDB 33 2', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 10 1\\nDB 73 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 19 1\\nDB 50 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 7 1\\nDB 85 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 4 1\\nDB 55 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 2 1\\nDB 9 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 40 4\\nDB 25 3', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 1 0\\nDB 4 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 40 2\\nDB 33 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 10 1\\nDB 30 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 2 1\\nDB 55 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 2 1\\nDB 9 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 15 2\\nDB 33 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 2 1\\nDB 14 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 14 2\\nDB 33 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 14 2\\nDB 33 3', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 14 1\\nDB 30 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 30 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 43 1\\nDB 55 1', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'CD 0 0\\nDB 55 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 107 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 20 1\\nDB 93 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 30 1\\nDB 30 3', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'CD 51 1\\nDB 54 1', 'output': 'YES\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79129","program":"```python\nfrom math import cos, sin, pi, sqrt\nB = [\"BC\", \"CD\", \"DB\"]\nXY0, d0, l0, XY1, d1, l1 = open(0).read().split()\nd0, l0, d1, l1 = map(int, [d0, l0, d1, l1])\n\ndef calc(XY, d, l):\n angle = B.index(XY) * 60 + d\n x = l * cos(pi*angle/180)\n y = l * sin(pi*angle/180)\n x = x + y/sqrt(3)\n y = y * 2/sqrt(3)\n x = x%2; y = y%2\n A = [[\"AC\", \"BD\"], [\"DB\", \"CA\"]][int(x)][int(y)]\n return A[x%1>y%1]\nprint(\"YES\"*(calc(XY0, d0, l0)==calc(XY1, d1, l1))or\"NO\")\n```","inputs":"CD 30 1\nDB 30 1","output":"YES","actual_output":"YES\n","execution_success":true,"sample_index":12603},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01096 Daruma Otoshi","prompt":"Solve the following coding problem using the programming language python:\n\nDaruma Otoshi\n\nYou are playing a variant of a game called \"Daruma Otoshi (Dharma Block Striking)\".\n\nAt the start of a game, several wooden blocks of the same size but with varying weights are stacked on top of each other, forming a tower. Another block symbolizing Dharma is placed atop. You have a wooden hammer with its head thicker than the height of a block, but not twice that.\n\nYou can choose any two adjacent blocks, except Dharma on the top, differing at most 1 in their weight, and push both of them out of the stack with a single blow of your hammer. The blocks above the removed ones then fall straight down, without collapsing the tower. You cannot hit a block pair with weight difference of 2 or more, for that makes too hard to push out blocks while keeping the balance of the tower. There is no chance in hitting three blocks out at a time, for that would require superhuman accuracy.\n\nThe goal of the game is to remove as many blocks as you can. Your task is to decide the number of blocks that can be removed by repeating the blows in an optimal order.\n\n\n\nFigure D1. Striking out two blocks at a time\n\nIn the above figure, with a stack of four blocks weighing 1, 2, 3, and 1, in this order from the bottom, you can hit middle two blocks, weighing 2 and 3, out from the stack. The blocks above will then fall down, and two blocks weighing 1 and the Dharma block will remain. You can then push out the remaining pair of weight-1 blocks after that.\n\nInput\n\nThe input consists of multiple datasets. The number of datasets is at most 50. Each dataset is in the following format.\n\nn\nw1 w2 \u2026 wn\n\n\nn is the number of blocks, except Dharma on the top. n is a positive integer not exceeding 300. wi gives the weight of the i-th block counted from the bottom. wi is an integer between 1 and 1000, inclusive.\n\nThe end of the input is indicated by a line containing a zero.\n\nOutput\n\nFor each dataset, output in a line the maximum number of blocks you can remove.\n\nSample Input\n\n\n4\n1 2 3 4\n4\n1 2 3 1\n5\n5 1 2 3 6\n14\n8 7 1 4 3 5 4 1 6 8 10 4 6 5\n5\n1 3 5 1 3\n0\n\n\nOutput for the Sample Input\n\n\n4\n4\n2\n12\n0\n\n\n\n\n\n\nExample\n\nInput\n\n4\n1 2 3 4\n4\n1 2 3 1\n5\n5 1 2 3 6\n14\n8 7 1 4 3 5 4 1 6 8 10 4 6 5\n5\n1 3 5 1 3\n0\n\n\nOutput\n\n4\n4\n2\n12\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\nwhile n!=0:\n w=list(map(int,input().split()))\n check=[[False]*n for i in range(n)]\n for i in range(n-1):\n if abs(w[i+1]-w[i])<=1:\n check[i][i+1]=True\n for i in range(3,n,2):\n for j in range(n-i):\n for k in range(j+1,j+i):\n if check[j][j+i]==False and check[j][k] and check[k+1][j+i]:\n check[j][j+i]=True\n break\n if check[j][j+i]==False and abs(w[j]-w[j+i])<=1 and check[j+1][j+i-1]:\n check[j][j+i]=True\n dp=[0]*(n+1)\n for k in range(n):\n for m in range(k):\n if check[m][k]:\n dp[k]=max(dp[k],dp[m-1]+k-m+1)\n dp[k]=max(dp[k],dp[k-1])\n print(dp[n-1])\n n=int(input())\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1 2 3 4\\n4\\n1 2 3 1\\n5\\n5 1 2 3 6\\n14\\n8 7 1 4 3 5 4 1 6 8 10 4 6 5\\n5\\n1 3 5 1 3\\n0', 'output': '4\\n4\\n2\\n12\\n0'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 4\\n4\\n1 2 3 1\\n5\\n5 1 2 3 6\\n14\\n8 7 1 4 3 5 4 1 6 8 10 4 6 5\\n5\\n1 3 5 2 3\\n0', 'output': '4\\n4\\n2\\n12\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 2\\n4\\n1 2 3 1\\n5\\n2 1 2 3 6\\n14\\n8 7 1 4 3 5 4 2 6 8 10 4 6 5\\n5\\n1 3 5 2 3\\n0', 'output': '4\\n4\\n4\\n12\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 3 2\\n4\\n1 2 3 1\\n5\\n2 1 2 3 6\\n14\\n8 7 1 4 3 5 4 2 6 8 10 4 1 5\\n5\\n1 3 5 2 3\\n0', 'output': '4\\n4\\n4\\n10\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 3 2\\n4\\n1 2 3 1\\n5\\n2 1 2 3 6\\n14\\n8 7 1 4 3 5 8 2 6 8 10 4 1 5\\n5\\n1 3 5 2 3\\n0', 'output': '4\\n4\\n4\\n4\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 4\\n4\\n1 2 3 1\\n5\\n5 0 2 3 6\\n14\\n8 7 1 4 3 5 4 1 6 8 10 4 6 5\\n5\\n1 3 5 1 3\\n0', 'output': '4\\n4\\n2\\n12\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 2\\n4\\n1 2 3 1\\n5\\n5 1 2 3 6\\n14\\n8 7 1 4 3 5 0 1 6 8 10 4 6 5\\n5\\n1 3 5 2 3\\n0', 'output': '4\\n4\\n2\\n10\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 3 2\\n4\\n1 2 3 1\\n5\\n2 1 2 3 6\\n14\\n8 7 1 4 3 5 8 2 6 8 10 1 1 5\\n5\\n1 3 5 2 3\\n0', 'output': '4\\n4\\n4\\n6\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 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'2\\n4\\n4\\n8\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 2\\n4\\n0 1 3 1\\n5\\n6 1 0 3 6\\n14\\n8 7 1 4 6 5 1 2 11 8 10 8 6 5\\n5\\n1 3 3 2 5\\n0', 'output': '4\\n2\\n2\\n8\\n4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 3 2\\n4\\n1 3 3 1\\n5\\n2 1 1 1 6\\n14\\n8 7 0 4 3 5 2 2 11 8 2 4 8 4\\n5\\n1 3 5 0 3\\n0', 'output': '4\\n4\\n4\\n6\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 3 2\\n4\\n1 3 3 1\\n5\\n2 2 1 1 6\\n14\\n8 7 0 4 3 5 2 2 11 8 2 4 8 4\\n5\\n1 3 5 0 3\\n0', 'output': '4\\n4\\n4\\n6\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 2\\n4\\n0 1 3 1\\n5\\n6 1 0 3 6\\n14\\n10 7 1 6 6 5 1 2 11 8 10 8 6 5\\n5\\n1 3 3 2 5\\n0', 'output': '4\\n2\\n2\\n6\\n4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 3 2\\n4\\n1 3 4 1\\n5\\n2 2 1 1 6\\n14\\n8 7 0 4 3 5 2 0 11 8 2 4 8 4\\n5\\n1 3 5 0 3\\n0', 'output': '4\\n4\\n4\\n4\\n0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79133","program":"```python\nn=int(input())\nwhile n!=0:\n w=list(map(int,input().split()))\n check=[[False]*n for i in range(n)]\n for i in range(n-1):\n if abs(w[i+1]-w[i])<=1:\n check[i][i+1]=True\n for i in range(3,n,2):\n for j in range(n-i):\n for k in range(j+1,j+i):\n if check[j][j+i]==False and check[j][k] and check[k+1][j+i]:\n check[j][j+i]=True\n break\n if check[j][j+i]==False and abs(w[j]-w[j+i])<=1 and check[j+1][j+i-1]:\n check[j][j+i]=True\n dp=[0]*(n+1)\n for k in range(n):\n for m in range(k):\n if check[m][k]:\n dp[k]=max(dp[k],dp[m-1]+k-m+1)\n dp[k]=max(dp[k],dp[k-1])\n print(dp[n-1])\n n=int(input())\n\n```","inputs":"4\n1 2 3 4\n4\n1 2 3 1\n5\n5 1 2 3 6\n14\n8 7 1 4 3 5 4 1 6 8 10 4 6 5\n5\n1 3 5 1 3\n0","output":"4\n4\n2\n12\n0","actual_output":"4\n4\n2\n12\n0\n","execution_success":true,"sample_index":12604},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01366 Road Construction","prompt":"Solve the following coding problem using the programming language python:\n\nKing Mercer is the king of ACM kingdom. There are one capital and some cities in his kingdom. Amazingly, there are no roads in the kingdom now. Recently, he planned to construct roads between the capital and the cities, but it turned out that the construction cost of his plan is much higher than expected.\n\nIn order to reduce the cost, he has decided to create a new construction plan by removing some roads from the original plan. However, he believes that a new plan should satisfy the following conditions:\n\n* For every pair of cities, there is a route (a set of roads) connecting them.\n* The minimum distance between the capital and each city does not change from his original plan.\n\n\n\nMany plans may meet the conditions above, but King Mercer wants to know the plan with minimum cost. Your task is to write a program which reads his original plan and calculates the cost of a new plan with the minimum cost.\n\n\n\nInput\n\nThe input consists of several datasets. Each dataset is formatted as follows.\n\nN M\nu1 v1 d1 c1\n.\n.\n.\nuM vM dM cM\n\n\nThe first line of each dataset begins with two integers, N and M (1 \u2264 N \u2264 10000, 0 \u2264 M \u2264 20000). N and M indicate the number of cities and the number of roads in the original plan, respectively.\n\nThe following M lines describe the road information in the original plan. The i-th line contains four integers, ui, vi, di and ci (1 \u2264 ui, vi \u2264 N , ui \u2260 vi , 1 \u2264 di \u2264 1000, 1 \u2264 ci \u2264 1000). ui , vi, di and ci indicate that there is a road which connects ui-th city and vi-th city, whose length is di and whose cost needed for construction is ci.\n\nEach road is bidirectional. No two roads connect the same pair of cities. The 1-st city is the capital in the kingdom.\n\nThe end of the input is indicated by a line containing two zeros separated by a space. You should not process the line as a dataset.\n\nOutput\n\nFor each dataset, print the minimum cost of a plan which satisfies the conditions in a line.\n\nExample\n\nInput\n\n3 3\n1 2 1 2\n2 3 2 1\n3 1 3 2\n5 5\n1 2 2 2\n2 3 1 1\n1 4 1 1\n4 5 1 1\n5 3 1 1\n5 10\n1 2 32 10\n1 3 43 43\n1 4 12 52\n1 5 84 23\n2 3 58 42\n2 4 86 99\n2 5 57 83\n3 4 11 32\n3 5 75 21\n4 5 23 43\n5 10\n1 2 1 53\n1 3 1 65\n1 4 1 24\n1 5 1 76\n2 3 1 19\n2 4 1 46\n2 5 1 25\n3 4 1 13\n3 5 1 65\n4 5 1 34\n0 0\n\n\nOutput\n\n3\n5\n137\n218\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom heapq import heappush, heappop\n\n\ndef dijkstra(edges, size, source):\n distance = [float('inf')] * size\n distance[source] = 0\n visited = [False] * size\n pq = []\n heappush(pq, (0, source))\n while pq:\n dist_u, u = heappop(pq)\n visited[u] = True\n for v, weight, _ in edges[u]:\n if not visited[v]:\n new_dist = dist_u + weight\n if distance[v] > new_dist:\n distance[v] = new_dist\n heappush(pq, (new_dist, v))\n return distance\n\n\nwhile True:\n N, M = map(int, input().split())\n if N == M == 0:\n break\n edges = [[] for i in range(N)]\n\n for i in range(M):\n u, v, d, c = map(int, input().split())\n u -= 1\n v -= 1\n edges[u].append((v, d, c))\n edges[v].append((u, d, c))\n\n dist = dijkstra(edges, N, 0)\n ans = 0\n for u in range(1, N):\n cost = 1000\n for v, d, c in edges[u]:\n if dist[u] == dist[v] + d:\n cost = min(cost, c)\n ans += cost\n print(ans)\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 1 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n137\\n218'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n137\\n218\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n162\\n218\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n162\\n207\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 1 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 1 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '4\\n5\\n137\\n218\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n162\\n190\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n6\\n162\\n207\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '5\\n5\\n162\\n207\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 16\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n6\\n168\\n207\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 3 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n162\\n173\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 4\\n2 3 3 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '6\\n5\\n162\\n207\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 4\\n2 3 3 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 83\\n3 4 11 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 5 2 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '6\\n5\\n162\\n218\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 4 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 3 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n194\\n173\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n1 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 120\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n137\\n262\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 28 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 3\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n162\\n168\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 1 84 23\\n2 3 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5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 3 0 76\\n2 3 2 33\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n162\\n179\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 16 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 52\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n6\\n173\\n207\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 4 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 3 0 82\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n194\\n179\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 4 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 52\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 1 65\\n1 2 1 24\\n1 3 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n204\\n178\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 28 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 40\\n1 5 0 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 3\\n3 4 1 13\\n3 2 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n162\\n178\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 1\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n1 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 120\\n2 3 2 19\\n3 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 0 24\\n0 0', 'output': '3\\n5\\n137\\n166\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 52\\n3 4 11 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 84\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0', 'output': '3\\n6\\n162\\n238\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 4 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 85\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0', 'output': '3\\n5\\n162\\n239\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n1 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 85\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 25\\n3 4 1 13\\n3 5 1 65\\n4 1 1 36\\n0 0', 'output': '3\\n6\\n162\\n262\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n1 4 86 99\\n2 5 57 52\\n3 4 9 32\\n3 5 75 21\\n2 5 17 43\\n5 10\\n1 2 1 61\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 2 44\\n3 4 1 13\\n3 5 1 65\\n4 5 1 36\\n0 0', 'output': '3\\n6\\n162\\n215\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 8\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '9\\n8\\n162\\n194\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 4\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n2 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0', 'output': '5\\n8\\n195\\n142\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 0\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 16 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0', 'output': '1\\n8\\n162\\n142\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 1 1 4\\n2 3 2 2\\n3 1 3 0\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 3 2 1\\n5 10\\n1 2 16 10\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 163\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 5 0 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 11\\n2 4 0 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0', 'output': '2\\n8\\n162\\n142\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 4\\n2 3 2 2\\n3 1 3 0\\n5 5\\n1 3 2 4\\n2 4 1 2\\n1 4 1 1\\n4 5 1 1\\n5 4 2 1\\n5 10\\n1 2 16 13\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 142\\n2 3 57 133\\n3 4 19 32\\n3 5 75 41\\n4 5 17 43\\n5 10\\n2 2 1 53\\n1 3 0 88\\n2 4 1 24\\n1 5 1 76\\n2 3 2 11\\n2 4 0 46\\n2 5 1 30\\n3 4 1 13\\n3 5 2 65\\n4 5 1 34\\n0 0', 'output': '4\\n8\\n165\\n223\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 2 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 52\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 23 43\\n5 10\\n1 2 2 53\\n1 3 1 65\\n1 4 1 24\\n1 5 1 76\\n2 3 1 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n6\\n137\\n184\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n2 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 1 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 10\\n1 3 43 43\\n1 4 12 42\\n1 5 84 23\\n2 2 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n6\\n127\\n207\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 1 2\\n1 3 2 1\\n3 1 3 2\\n5 5\\n1 3 2 2\\n2 3 1 1\\n1 4 0 2\\n4 5 1 1\\n5 3 1 1\\n5 10\\n1 2 32 16\\n1 3 43 43\\n1 4 12 77\\n1 5 84 23\\n2 3 58 42\\n2 4 86 99\\n2 5 57 83\\n3 4 11 32\\n3 5 75 21\\n4 5 17 43\\n5 10\\n1 2 1 53\\n1 3 1 65\\n2 4 1 24\\n1 5 1 76\\n2 3 2 19\\n2 4 1 46\\n2 5 1 25\\n3 4 1 13\\n3 5 1 65\\n4 5 1 34\\n0 0', 'output': '3\\n5\\n168\\n207\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79141","program":"```python\nfrom heapq import heappush, heappop\n\n\ndef dijkstra(edges, size, source):\n distance = [float('inf')] * size\n distance[source] = 0\n visited = [False] * size\n pq = []\n heappush(pq, (0, source))\n while pq:\n dist_u, u = heappop(pq)\n visited[u] = True\n for v, weight, _ in edges[u]:\n if not visited[v]:\n new_dist = dist_u + weight\n if distance[v] > new_dist:\n distance[v] = new_dist\n heappush(pq, (new_dist, v))\n return distance\n\n\nwhile True:\n N, M = map(int, input().split())\n if N == M == 0:\n break\n edges = [[] for i in range(N)]\n\n for i in range(M):\n u, v, d, c = map(int, input().split())\n u -= 1\n v -= 1\n edges[u].append((v, d, c))\n edges[v].append((u, d, c))\n\n dist = dijkstra(edges, N, 0)\n ans = 0\n for u in range(1, N):\n cost = 1000\n for v, d, c in edges[u]:\n if dist[u] == dist[v] + d:\n cost = min(cost, c)\n ans += cost\n print(ans)\n\n\n```","inputs":"3 3\n1 2 1 2\n2 3 2 1\n3 1 3 2\n5 5\n1 2 2 2\n2 3 1 1\n1 4 1 1\n4 5 1 1\n5 3 1 1\n5 10\n1 2 32 10\n1 3 43 43\n1 4 12 52\n1 5 84 23\n2 3 58 42\n2 4 86 99\n2 5 57 83\n3 4 11 32\n3 5 75 21\n4 5 23 43\n5 10\n1 2 1 53\n1 3 1 65\n1 4 1 24\n1 5 1 76\n2 3 1 19\n2 4 1 46\n2 5 1 25\n3 4 1 13\n3 5 1 65\n4 5 1 34\n0 0","output":"3\n5\n137\n218","actual_output":"3\n5\n137\n218\n","execution_success":true,"sample_index":12605},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01848 Early Morning Work at Summer Camp","prompt":"Solve the following coding problem using the programming language python:\n\nEarly morning in summer camp\n\nThe morning of JAG summer training camp is early. To be exact, it is not so fast, but many participants feel that it is fast.\n\nAt the facility that is the venue for the training camp every year, participants must collect and clean the sheets when they move out. If even one room is delayed, no participant should oversleep, as it will affect the use of the facility from next year onwards.\n\nThat said, all human beings sometimes oversleep. However, if the person who wakes up makes a wake-up call to someone who knows the contact information, one should be able to try not to oversleep.\n\nYou, who have been entrusted with the operation of the JAG summer training camp, decided to investigate how likely it is that everyone will be able to wake up properly as a preparation for taking steps to absolutely prevent oversleeping. As a preparation, we first obtained the probability of each participant oversleeping and a list of people who each knew their contact information. Here, since the rooms are private rooms, whether or not each of them oversleeps is independent of whether or not the other participants oversleep. From this information, calculate the probability that everyone will wake up properly, assuming that the person who wakes up always makes a wake-up call to all known contacts, and that the person who receives the wake-up call always wakes up.\n\nInput\n\nThe input consists of multiple datasets. Each dataset is represented in the following format.\n\n> N\n> p1 m1 a (1,1) ... a (1, m1)\n> ...\n> pN mN a (N, 1) ... a (N, mN)\n\nN is the number of participants, a positive integer not exceeding 100. pi is the probability that the i-th participant will oversleep, and is a real number between 0 and 1 within two decimal places. mi is the number of contacts known to the i-th participant, an integer greater than or equal to 0 and less than or equal to N. a (i, j) indicates that the jth contact known to the ith participant belongs to the a (i, j) th participant. a (i, j) is a positive integer that does not exceed N.\n\nThe end of the input is indicated by a single zero line.\n\nOutput\n\nFor each dataset, output the probability that everyone can wake up on one line. The output must not contain more than 0.00001 error.\n\nSample Input\n\n\n2\n0.60 1 2\n0.60 0\n2\n0.60 1 2\n0.60 1 1\nFive\n0.10 1 2\n0.20 1 3\n0.30 1 4\n0.40 1 5\n0.50 1 1\nFive\n0.10 0\n0.20 1 1\n0.30 1 1\n0.40 1 1\n0.50 1 1\nFive\n0.10 4 2 3 4 5\n0.20 0\n0.30 0\n0.40 0\n0.50 0\nFour\n0.10 1 2\n0.20 0\n0.30 1 4\n0.40 1 3\nFive\n0.10 0\n0.20 0\n0.30 0\n0.40 0\n0.50 0\n0\n\nOutput for Sample Input\n\n\n0.400000000\n0.640000000\n0.998800000\n0.168000000\n0.900000000\n0.792000000\n0.151200000\n\n\n\n\n\nExample\n\nInput\n\n2\n0.60 1 2\n0.60 0\n2\n0.60 1 2\n0.60 1 1\n5\n0.10 1 2\n0.20 1 3\n0.30 1 4\n0.40 1 5\n0.50 1 1\n5\n0.10 0\n0.20 1 1\n0.30 1 1\n0.40 1 1\n0.50 1 1\n5\n0.10 4 2 3 4 5\n0.20 0\n0.30 0\n0.40 0\n0.50 0\n4\n0.10 1 2\n0.20 0\n0.30 1 4\n0.40 1 3\n5\n0.10 0\n0.20 0\n0.30 0\n0.40 0\n0.50 0\n0\n\n\nOutput\n\n0.400000000\n0.640000000\n0.998800000\n0.168000000\n0.900000000\n0.792000000\n0.151200000\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n\ndef dfs(s):\n for t in G[s]:\n if not used[t]:\n used[t] = 1\n dfs(t)\n res.append(s)\ndef rdfs(s, l):\n for t in RG[s]:\n if label[t] is None:\n label[t] = l\n rdfs(t, l)\n\nwhile 1:\n n = int(input())\n if n == 0:\n break\n G = [[] for i in range(n)]\n RG = [[] for i in range(n)]\n P = []\n for i in range(n):\n p, m, *A = input().split()\n P.append(float(p))\n for t in map(int, A):\n G[i].append(t-1)\n RG[t-1].append(i)\n used = [0]*n\n res = []\n for i in range(n):\n if not used[i]:\n used[i] = 1\n dfs(i)\n label = [None]*n; k = 0\n for i in reversed(res):\n if label[i] is None:\n label[i] = k\n rdfs(i, k)\n k += 1\n GP = [1.]*k; GF = [0]*k\n for s in range(n):\n l = label[s]\n GP[l] *= P[s]\n for t in G[s]:\n if label[s] != label[t]:\n GF[label[t]] += 1\n ans = 1.\n for i in range(k):\n if GF[i] == 0:\n ans *= 1.-GP[i]\n print(\"%.9f\" % (ans))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n0.60 1 2\\n0.60 0\\n2\\n0.60 1 2\\n0.60 1 1\\n5\\n0.10 1 2\\n0.20 1 3\\n0.30 1 4\\n0.40 1 5\\n0.50 1 1\\n5\\n0.10 0\\n0.20 1 1\\n0.30 1 1\\n0.40 1 1\\n0.50 1 1\\n5\\n0.10 4 2 3 4 5\\n0.20 0\\n0.30 0\\n0.40 0\\n0.50 0\\n4\\n0.10 1 2\\n0.20 0\\n0.30 1 4\\n0.40 1 3\\n5\\n0.10 0\\n0.20 0\\n0.30 0\\n0.40 0\\n0.50 0\\n0', 'output': '0.400000000\\n0.640000000\\n0.998800000\\n0.168000000\\n0.900000000\\n0.792000000\\n0.151200000'}, {'type': 'stdin_stdout', 'input': '2\\n0.60 1 2\\n0.60 0\\n2\\n0.60 1 2\\n0.60 1 1\\n5\\n0.10 1 2\\n0.20 1 3\\n0.30 1 4\\n0.40 1 5\\n0.50 1 1\\n5\\n0.10 0\\n0.20 1 1\\n0.8904968944594156 1 1\\n0.40 1 1\\n0.50 1 1\\n5\\n0.10 4 2 3 4 5\\n0.20 0\\n0.30 0\\n0.40 0\\n0.50 0\\n4\\n0.10 1 2\\n0.20 0\\n0.30 1 4\\n0.40 1 3\\n5\\n0.10 0\\n0.20 0\\n0.30 0\\n0.40 0\\n0.50 0\\n0', 'output': 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0\\n0.50 0\\n0', 'output': '-0.00986018590032959998\\n0.63999999999999999999\\n0.99833364304410397900\\n0.19184098297948903201\\n0.89999999999999999998\\n0.79199999999999999995\\n-0.04056542603710909200\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 536870912}","problem_id":"vfc_79153","program":"```python\n\ndef dfs(s):\n for t in G[s]:\n if not used[t]:\n used[t] = 1\n dfs(t)\n res.append(s)\ndef rdfs(s, l):\n for t in RG[s]:\n if label[t] is None:\n label[t] = l\n rdfs(t, l)\n\nwhile 1:\n n = int(input())\n if n == 0:\n break\n G = [[] for i in range(n)]\n RG = [[] for i in range(n)]\n P = []\n for i in range(n):\n p, m, *A = input().split()\n P.append(float(p))\n for t in map(int, A):\n G[i].append(t-1)\n RG[t-1].append(i)\n used = [0]*n\n res = []\n for i in range(n):\n if not used[i]:\n used[i] = 1\n dfs(i)\n label = [None]*n; k = 0\n for i in reversed(res):\n if label[i] is None:\n label[i] = k\n rdfs(i, k)\n k += 1\n GP = [1.]*k; GF = [0]*k\n for s in range(n):\n l = label[s]\n GP[l] *= P[s]\n for t in G[s]:\n if label[s] != label[t]:\n GF[label[t]] += 1\n ans = 1.\n for i in range(k):\n if GF[i] == 0:\n ans *= 1.-GP[i]\n print(\"%.9f\" % (ans))\n```","inputs":"2\n0.60 1 2\n0.60 0\n2\n0.60 1 2\n0.60 1 1\n5\n0.10 1 2\n0.20 1 3\n0.30 1 4\n0.40 1 5\n0.50 1 1\n5\n0.10 0\n0.20 1 1\n0.30 1 1\n0.40 1 1\n0.50 1 1\n5\n0.10 4 2 3 4 5\n0.20 0\n0.30 0\n0.40 0\n0.50 0\n4\n0.10 1 2\n0.20 0\n0.30 1 4\n0.40 1 3\n5\n0.10 0\n0.20 0\n0.30 0\n0.40 0\n0.50 0\n0","output":"0.400000000\n0.640000000\n0.998800000\n0.168000000\n0.900000000\n0.792000000\n0.151200000","actual_output":"0.400000000\n0.640000000\n0.998800000\n0.168000000\n0.900000000\n0.792000000\n0.151200000\n","execution_success":true,"sample_index":12607},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01984 Tanka Number","prompt":"Solve the following coding problem using the programming language python:\n\nNumber of tanka\n\nWishing to die in the spring under the flowers\n\nThis is one of the famous tanka poems that Saigyo Hoshi wrote. Tanka is a type of waka poem that has been popular in Japan for a long time, and most of it consists of five phrases and thirty-one sounds of 5, 7, 5, 7, and 7.\n\nBy the way, the number 57577 consists of two types, 5 and 7. Such a positive integer whose decimal notation consists of exactly two types of numbers is called a tanka number. For example, 10, 12, 57577, 25252 are tanka numbers, but 5, 11, 123, 20180701 are not tanka songs.\n\nA positive integer N is given. Find the Nth smallest tanka number.\n\nInput\n\nThe input consists of up to 100 datasets. Each dataset is represented in the following format.\n\n> N\n\nThe integer N satisfies 1 \u2264 N \u2264 1018.\n\nThe end of the input is represented by a single zero line.\n\nOutput\n\nFor each dataset, output the Nth smallest tanka number on one line.\n\nSample Input\n\n\n1\n2\n3\n390\n1124\n1546\n314159265358979323\n0\n\n\nOutput for the Sample Input\n\n\nTen\n12\n13\n2020\n25252\n57577\n7744444777744474777777774774744777747477444774744744\n\n\n\n\n\n\nExample\n\nInput\n\n1\n2\n3\n390\n1124\n1546\n314159265358979323\n0\n\n\nOutput\n\n10\n12\n13\n2020\n25252\n57577\n7744444777744474777777774774744777747477444774744744\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef solve(N):\n k = 0\n rng = 0\n for i in range(54):\n if cl[i] < N <= cl[i+1]:\n k = i + 2\n rng2 = cl[i]\n rng = cl[i+1] - cl[i]\n # print(k)\n posrng = (N-rng2)%(rng//9)\n perrng = (N-rng2)//(rng//9)+1\n if posrng == 0:\n posrng = rng//9\n perrng -= 1\n ans = [perrng]\n for i in range(k-1):\n if i == k-2:\n tmp = [0 if j == perrng else 1 for j in range(10)]\n else:\n tmp = [(cl[k-i-2]-cl[k-i-3])//9 if j == perrng else 2**(k-i-2) for j in range(10)]\n if posrng <= tmp[0]:\n ans.append(0)\n # posrng = posrng\n for j in range(1, 10):\n tmp[j] += tmp[j-1]\n if tmp[j-1] < posrng <=tmp[j]:\n ans.append(j)\n posrng -= tmp[j-1]\n if max(ans) != min(ans):\n break\n for i in range(k-len(ans), 0, -1):\n if posrng <= 2**(i-1):\n ans.append(min(ans))\n else:\n ans.append(max(ans))\n posrng -= 2**(i-1)\n print(''.join(map(str, ans)))\n\ncl = [sum([9*2**j for j in range(i)])*9 for i in range(55)]\nfor i in range(1, 55):\n cl[i] += cl[i-1]\nwhile True:\n N = int(input())\n if N == 0:\n break\n solve(N)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n2\\n3\\n390\\n1124\\n1546\\n314159265358979323\\n0', 'output': 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'10\\n12\\n13\\n2020\\n474\\n57577\\n7744444777744474777777774774744777747477444774744744\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79157","program":"```python\ndef solve(N):\n k = 0\n rng = 0\n for i in range(54):\n if cl[i] < N <= cl[i+1]:\n k = i + 2\n rng2 = cl[i]\n rng = cl[i+1] - cl[i]\n # print(k)\n posrng = (N-rng2)%(rng//9)\n perrng = (N-rng2)//(rng//9)+1\n if posrng == 0:\n posrng = rng//9\n perrng -= 1\n ans = [perrng]\n for i in range(k-1):\n if i == k-2:\n tmp = [0 if j == perrng else 1 for j in range(10)]\n else:\n tmp = [(cl[k-i-2]-cl[k-i-3])//9 if j == perrng else 2**(k-i-2) for j in range(10)]\n if posrng <= tmp[0]:\n ans.append(0)\n # posrng = posrng\n for j in range(1, 10):\n tmp[j] += tmp[j-1]\n if tmp[j-1] < posrng <=tmp[j]:\n ans.append(j)\n posrng -= tmp[j-1]\n if max(ans) != min(ans):\n break\n for i in range(k-len(ans), 0, -1):\n if posrng <= 2**(i-1):\n ans.append(min(ans))\n else:\n ans.append(max(ans))\n posrng -= 2**(i-1)\n print(''.join(map(str, ans)))\n\ncl = [sum([9*2**j for j in range(i)])*9 for i in range(55)]\nfor i in range(1, 55):\n cl[i] += cl[i-1]\nwhile True:\n N = int(input())\n if N == 0:\n break\n solve(N)\n\n```","inputs":"1\n2\n3\n390\n1124\n1546\n314159265358979323\n0","output":"10\n12\n13\n2020\n25252\n57577\n7744444777744474777777774774744777747477444774744744","actual_output":"10\n12\n13\n2020\n25252\n57577\n7744444777744474777777774774744777747477444774744744\n","execution_success":true,"sample_index":12608},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02130 Combine Two Elements","prompt":"Solve the following coding problem using the programming language python:\n\nProblem\n\nGiven $ N $ a pair of non-negative integers $ (a_i, b_i) $ and non-negative integers $ A $, $ B $.\nI want to do as many of the following operations as possible.\n\n\n* $ | a_i --b_i | \\ leq A $ or $ B \\ leq | a_i --b_i | \\ leq Take out and delete the element $ i $ that satisfies 2A $\n* $ | (a_i + a_j)-(b_i + b_j) | \\ leq A $ or $ B \\ leq | (a_i + a_j)-(b_i + b_j) | Extract and delete the pair of j $ ($ i \\ neq j $)\n\nFind the maximum number of operations.\n\nConstraints\n\nThe input satisfies the following conditions.\n\n* $ 1 \\ leq N \\ leq 800 $\n* $ 0 \\ leq A, B \\ leq 10 ^ 5 $\n* $ 0 \\ leq a_i, b_i \\ leq 10 ^ 5 $\n* $ A \\ leq B $ and $ B \\ leq 2A $\n\nInput\n\nThe input is given in the following format.\n\n\n$ N $ $ A $ $ B $\n$ a_1 $ $ b_1 $\n$ a_2 $ $ b_2 $\n...\n$ a_N $ $ b_N $\n\n\nAll inputs are given as integers.\n$ N $, $ A $, $ B $ are given on the first line, separated by blanks.\nThe $ i $ th pair $ a_i $ and $ b_i $ ($ 1 \\ leq i \\ leq N $) are given in the second and subsequent $ N $ lines, separated by blanks.\n\nOutput\n\nOutput the maximum number of operations on one line.\n\nExamples\n\nInput\n\n5 3 5\n7 2\n13 1\n1 1\n2 9\n2 4\n\n\nOutput\n\n4\n\n\nInput\n\n10 7 12\n34 70\n36 0\n12 50\n76 46\n33 45\n61 21\n0 1\n24 3\n98 41\n23 84\n\n\nOutput\n\n5\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN, A, B = map(int, input().split())\nP = []\nQ = []\nans = 0\nfor i in range(N):\n a, b = map(int, input().split())\n v = abs(a-b)\n if v <= A or B <= v <= 2*A:\n ans += 1\n continue\n if a > b:\n P.append(a-b)\n else:\n Q.append(a-b)\n\nimport collections\nclass Dinic:\n def __init__(self, n):\n self.n = n\n self.g = [[] for i in range(n)]\n def add_edge(self, fr, to, cap):\n self.g[fr].append([to, cap, len(self.g[to])])\n self.g[to].append([fr, 0, len(self.g[fr])-1])\n def add_multi_edge(self, v1, v2, cap1, cap2):\n self.g[v1].append([v2, cap1, len(self.g[v2])])\n self.g[v2].append([v1, cap2, len(self.g[v1])-1])\n def bfs(self, s):\n level = [-1]*self.n\n deq = collections.deque()\n level[s] = 0\n deq.append(s)\n while deq:\n v = deq.popleft()\n for e in self.g[v]:\n if e[1]>0 and level[e[0]]<0:\n level[e[0]] = level[v] + 1\n deq.append(e[0])\n self.level = level\n def dfs(self, v, t, f):\n if v==t: return f\n es = self.g[v]\n level = self.level\n for i in range(self.it[v], len(self.g[v])):\n e = es[i]\n if e[1]>0 and level[v]0:\n e[1] -= d\n self.g[e[0]][e[2]][1] += d\n self.it[v] = i\n return d\n self.it[v] = len(self.g[v])\n return 0\n def max_flow(self, s, t):\n flow = 0\n while True:\n self.bfs(s)\n if self.level[t]<0: break\n self.it = [0]*self.n\n while True:\n f = self.dfs(s, t, 10**9+7)\n if f>0:\n flow += f\n else:\n break\n return flow\n\ndinic = Dinic(2+len(P)+len(Q))\nLP = len(P)\nfor i in range(len(P)):\n dinic.add_edge(0, 2+i, 1)\nfor j in range(len(Q)):\n dinic.add_edge(2+LP+j, 1, 1)\nfor i, p in enumerate(P):\n for j, q in enumerate(Q):\n v = abs(p+q)\n if v <= A or B <= v <= 2*A:\n dinic.add_edge(2+i, 2+LP+j, 1)\nans += dinic.max_flow(0, 1)\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10 7 12\\n34 70\\n36 0\\n12 50\\n76 46\\n33 45\\n61 21\\n0 1\\n24 3\\n98 41\\n23 84', 'output': '5'}, {'type': 'stdin_stdout', 'input': '5 3 5\\n7 2\\n13 1\\n1 1\\n2 9\\n2 4', 'output': '4'}, {'type': 'stdin_stdout', 'input': '10 7 12\\n34 70\\n36 0\\n12 50\\n76 46\\n33 45\\n61 21\\n0 0\\n24 3\\n98 41\\n23 84', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5 3 4\\n7 2\\n13 1\\n1 1\\n2 9\\n2 4', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10 7 12\\n34 70\\n36 0\\n12 50\\n19 46\\n33 45\\n61 21\\n0 0\\n24 3\\n98 41\\n23 84', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '2 3 4\\n7 3\\n13 1\\n1 1\\n2 9\\n2 4', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 3 5\\n7 3\\n13 1\\n1 1\\n2 9\\n2 4', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10 1 12\\n34 70\\n36 0\\n12 50\\n19 46\\n33 45\\n61 21\\n0 0\\n24 3\\n98 73\\n23 84', 'output': '2\\n'}, {'type': 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31\\n-1 -1\\n22 5\\n92 58\\n23 10', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 536870912}","problem_id":"vfc_79161","program":"```python\nN, A, B = map(int, input().split())\nP = []\nQ = []\nans = 0\nfor i in range(N):\n a, b = map(int, input().split())\n v = abs(a-b)\n if v <= A or B <= v <= 2*A:\n ans += 1\n continue\n if a > b:\n P.append(a-b)\n else:\n Q.append(a-b)\n\nimport collections\nclass Dinic:\n def __init__(self, n):\n self.n = n\n self.g = [[] for i in range(n)]\n def add_edge(self, fr, to, cap):\n self.g[fr].append([to, cap, len(self.g[to])])\n self.g[to].append([fr, 0, len(self.g[fr])-1])\n def add_multi_edge(self, v1, v2, cap1, cap2):\n self.g[v1].append([v2, cap1, len(self.g[v2])])\n self.g[v2].append([v1, cap2, len(self.g[v1])-1])\n def bfs(self, s):\n level = [-1]*self.n\n deq = collections.deque()\n level[s] = 0\n deq.append(s)\n while deq:\n v = deq.popleft()\n for e in self.g[v]:\n if e[1]>0 and level[e[0]]<0:\n level[e[0]] = level[v] + 1\n deq.append(e[0])\n self.level = level\n def dfs(self, v, t, f):\n if v==t: return f\n es = self.g[v]\n level = self.level\n for i in range(self.it[v], len(self.g[v])):\n e = es[i]\n if e[1]>0 and level[v]0:\n e[1] -= d\n self.g[e[0]][e[2]][1] += d\n self.it[v] = i\n return d\n self.it[v] = len(self.g[v])\n return 0\n def max_flow(self, s, t):\n flow = 0\n while True:\n self.bfs(s)\n if self.level[t]<0: break\n self.it = [0]*self.n\n while True:\n f = self.dfs(s, t, 10**9+7)\n if f>0:\n flow += f\n else:\n break\n return flow\n\ndinic = Dinic(2+len(P)+len(Q))\nLP = len(P)\nfor i in range(len(P)):\n dinic.add_edge(0, 2+i, 1)\nfor j in range(len(Q)):\n dinic.add_edge(2+LP+j, 1, 1)\nfor i, p in enumerate(P):\n for j, q in enumerate(Q):\n v = abs(p+q)\n if v <= A or B <= v <= 2*A:\n dinic.add_edge(2+i, 2+LP+j, 1)\nans += dinic.max_flow(0, 1)\nprint(ans)\n\n```","inputs":"10 7 12\n34 70\n36 0\n12 50\n76 46\n33 45\n61 21\n0 1\n24 3\n98 41\n23 84","output":"5","actual_output":"5\n","execution_success":true,"sample_index":12609},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02271 Exhaustive Search","prompt":"Solve the following coding problem using the programming language python:\n\nWrite a program which reads a sequence A of n elements and an integer M, and outputs \"yes\" if you can make M by adding elements in A, otherwise \"no\". You can use an element only once.\n\nYou are given the sequence A and q questions where each question contains Mi.\n\nNotes\n\nYou can solve this problem by a Burte Force approach. Suppose solve(p, t) is a function which checkes whether you can make t by selecting elements after p-th element (inclusive). Then you can recursively call the following functions:\n\nsolve(0, M)\nsolve(1, M-{sum created from elements before 1st element})\nsolve(2, M-{sum created from elements before 2nd element})\n...\n\nThe recursive function has two choices: you selected p-th element and not. So, you can check solve(p+1, t-A[p]) and solve(p+1, t) in solve(p, t) to check the all combinations.\n\nFor example, the following figure shows that 8 can be made by A[0] + A[2].\n\n\n\nConstraints\n\n* n \u2264 20\n* q \u2264 200\n* 1 \u2264 elements in A \u2264 2000\n* 1 \u2264 Mi \u2264 2000\n\nInput\n\nIn the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers (Mi) are given.\n\nOutput\n\nFor each question Mi, print yes or no.\n\nExample\n\nInput\n\n5\n1 5 7 10 21\n8\n2 4 17 8 22 21 100 35\n\n\nOutput\n\nno\nno\nyes\nyes\nyes\nyes\nno\nno\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\nA=list(map(int,input().split()))\nq=int(input())\nM=list(map(int,input().split()))\n\npattern=[]\n\nfor i in range(2**n):\n s=0\n for j in range(n):\n if i >> j & 1:\n s+=A[j]\n pattern.append(s)\nP=set(pattern)\n\nfor m in M:\n print('yes' if m in P else 'no')\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 5 7 10 21\\n8\\n2 4 17 8 22 21 100 35', 'output': 'no\\nno\\nyes\\nyes\\nyes\\nyes\\nno\\nno'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 7 10 21\\n8\\n2 4 17 10 22 21 100 35', 'output': 'no\\nno\\nyes\\nyes\\nyes\\nyes\\nno\\nno\\n'}, 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'yes\\nyes\\nno\\nno\\nno\\nno\\nyes\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 3 9 -1 22\\n8\\n0 2 18 5 17 21 011 0', 'output': 'yes\\nyes\\nno\\nno\\nno\\nyes\\nyes\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 3 14 5 10\\n8\\n0 0 17 7 62 1 111 13', 'output': 'yes\\nyes\\nyes\\nno\\nno\\nno\\nno\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 3 9 -1 13\\n8\\n0 2 18 5 2 21 011 0', 'output': 'yes\\nyes\\nno\\nno\\nyes\\nyes\\nyes\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 14 5 10\\n8\\n0 -1 17 7 62 1 111 13', 'output': 'yes\\nno\\nno\\nno\\nno\\nno\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 3 15 -1 13\\n8\\n0 2 18 5 2 21 011 0', 'output': 'yes\\nyes\\nyes\\nno\\nyes\\nno\\nno\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n-1 3 15 -1 13\\n8\\n0 2 18 5 2 21 011 0', 'output': 'yes\\nyes\\nyes\\nno\\nyes\\nno\\nyes\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 14 5 13\\n8\\n-1 -1 17 7 40 1 111 13', 'output': 'no\\nno\\nno\\nno\\nno\\nno\\nno\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 7 10 21\\n8\\n2 4 17 10 22 14 100 42', 'output': 'no\\nno\\nyes\\nyes\\nyes\\nno\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 11 3 21\\n8\\n2 4 17 10 22 21 100 42', 'output': 'no\\nyes\\nyes\\nno\\nyes\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 7 6 21\\n8\\n0 4 17 11 22 21 110 42', 'output': 'yes\\nno\\nno\\nyes\\nyes\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 13 3 21\\n8\\n0 4 17 11 22 21 010 42', 'output': 'yes\\nyes\\nyes\\nno\\nyes\\nyes\\nno\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 8 13 -1 21\\n8\\n1 2 17 11 8 14 011 41', 'output': 'no\\nno\\nno\\nno\\nyes\\nno\\nno\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 9 3 36\\n8\\n2 4 17 10 22 21 100 42', 'output': 'no\\nyes\\nyes\\nyes\\nno\\nno\\nno\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 8 3 21\\n8\\n0 4 17 10 22 21 101 42', 'output': 'yes\\nyes\\nyes\\nno\\nyes\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 7 3 39\\n8\\n0 4 17 11 22 21 010 74', 'output': 'yes\\nyes\\nno\\nyes\\nno\\nno\\nyes\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 7 3 21\\n8\\n0 4 17 11 26 21 010 47', 'output': 'yes\\nno\\nno\\nno\\nyes\\nyes\\nyes\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n-1 5 10 -1 21\\n8\\n1 7 17 11 8 14 010 41', 'output': 'no\\nno\\nno\\nno\\nyes\\nyes\\nyes\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 7 4 3 21\\n8\\n0 4 17 11 22 21 100 42', 'output': 'yes\\nyes\\nno\\nyes\\nno\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 5 7 3 21\\n8\\n1 4 17 11 22 21 010 74', 'output': 'no\\nno\\nyes\\nno\\nno\\nyes\\nyes\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 11 3 21\\n8\\n2 5 17 11 22 14 010 42', 'output': 'no\\nyes\\nno\\nyes\\nno\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 10 -1 21\\n8\\n0 2 17 11 9 14 011 15', 'output': 'yes\\nno\\nno\\nno\\nyes\\nyes\\nno\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 7 10 3\\n8\\n2 4 17 10 42 18 110 42', 'output': 'no\\nyes\\nyes\\nyes\\nno\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 10 3 21\\n8\\n1 7 7 13 31 16 011 41', 'output': 'no\\nno\\nno\\nyes\\nyes\\nno\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 7 3 17\\n8\\n-1 4 17 10 26 21 101 72', 'output': 'no\\nyes\\nyes\\nyes\\nyes\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 3 7 3 21\\n8\\n0 4 15 9 38 21 110 57', 'output': 'yes\\nyes\\nno\\nno\\nno\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 7 3 21\\n8\\n0 4 33 5 22 21 001 47', 'output': 'yes\\nno\\nyes\\nyes\\nno\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 4 10 23\\n8\\n2 4 17 10 42 18 110 42', 'output': 'no\\nyes\\nno\\nyes\\nyes\\nno\\nno\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 7 7 2 36\\n8\\n2 5 16 10 22 21 100 60', 'output': 'yes\\nno\\nyes\\nyes\\nno\\nno\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 9 3 21\\n8\\n0 4 15 9 38 21 010 57', 'output': 'yes\\nyes\\nyes\\nyes\\nyes\\nyes\\nyes\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 6 10 0 21\\n8\\n2 6 9 11 22 14 111 41', 'output': 'no\\nyes\\nno\\nyes\\nyes\\nno\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 10 -1 21\\n8\\n0 2 19 11 9 18 011 76', 'output': 'yes\\nno\\nno\\nyes\\nyes\\nno\\nyes\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 8 10 0 21\\n8\\n-1 4 18 2 39 21 011 42', 'output': 'no\\nno\\nyes\\nno\\nyes\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 5 14 -1 21\\n8\\n0 2 19 11 9 14 011 76', 'output': 'yes\\nyes\\nyes\\nno\\nno\\nyes\\nno\\nno\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 5 12 5 23\\n8\\n2 4 17 18 42 18 110 42', 'output': 'yes\\nno\\nyes\\nno\\nyes\\nno\\nno\\nyes\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 5 12 5 23\\n8\\n2 4 17 8 42 18 110 12', 'output': 'no\\nno\\nyes\\nno\\nno\\nyes\\nno\\nyes\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 5, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79165","program":"```python\nn=int(input())\nA=list(map(int,input().split()))\nq=int(input())\nM=list(map(int,input().split()))\n\npattern=[]\n\nfor i in range(2**n):\n s=0\n for j in range(n):\n if i >> j & 1:\n s+=A[j]\n pattern.append(s)\nP=set(pattern)\n\nfor m in M:\n print('yes' if m in P else 'no')\n\n```","inputs":"5\n1 5 7 10 21\n8\n2 4 17 8 22 21 100 35","output":"no\nno\nyes\nyes\nyes\nyes\nno\nno","actual_output":"no\nno\nyes\nyes\nyes\nyes\nno\nno\n","execution_success":true,"sample_index":12610},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02418 Ring","prompt":"Solve the following coding problem using the programming language python:\n\nWrite a program which finds a pattern $p$ in a ring shaped text $s$.\n\n\n\n\nConstraints\n\n* $1 \\leq $ length of $p \\leq $ length of $s \\leq 100$\n* $s$ and $p$ consists of lower-case letters\n\nInput\n\nIn the first line, the text $s$ is given.\nIn the second line, the pattern $p$ is given.\n\nOutput\n\nIf $p$ is in $s$, print Yes in a line, otherwise No.\n\nExamples\n\nInput\n\nvanceknowledgetoad\nadvance\n\n\nOutput\n\nYes\n\n\nInput\n\nvanceknowledgetoad\nadvanced\n\n\nOutput\n\nNo\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ns = input()\np = input()\nprint(\"Yes\" if p in (s + s) else \"No\")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'vanceknowledgetoad\\nadvance', 'output': 'Yes'}, {'type': 'stdin_stdout', 'input': 'vanceknowledgetoad\\nadvanced', 'output': 'No'}, {'type': 'stdin_stdout', 'input': 'vanceknowledgetoad\\nedvanca', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanceknowledgetoad\\nbdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanceknowledgetoad\\nedvamca', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanceknowledgetoad\\ncdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'daotegdelwonkecnav\\nedvamca', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanceknowmedgetoad\\ncdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'daotegdelwonkecnav\\nadvamce', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vbnceknowmedgetoad\\ncdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'daovegdelwonkecnat\\nadvamce', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vbnceknowledgetoad\\ncdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'daovegdelwonkecnat\\nacvamde', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vbncekoowledgetoad\\ncdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovegddlwonkecnat\\nacvamde', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vbncekonwledgetoad\\ncdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgddewonkecnat\\nacvamde', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vbnbekonwledgetoad\\ncdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedewonkecnat\\nacvamde', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vbnbekonwlddgetoad\\ncdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedewonkecnat\\nedmavca', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vbnbelonwlddgetoad\\ncdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'tanceknowedeglvoae\\nedmavca', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelonwlddgetoad\\ncdvanced', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'tanceknowedeglvoae\\nedaavcm', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelonwlddgetoad\\ncdvancee', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedewonkecnat\\nddmavca', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelonwlddgdtoad\\ncdvancee', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedewonkecnat\\nddnavca', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbeloowlddgdtnad\\ncdvancee', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedexonkecnat\\nddnavca', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbeloowlddgdtnad\\ncdvanbee', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedexonkecnat\\ndenavca', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbeloowldegdtnad\\ncdvanbee', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedexonkecnat\\ndencvaa', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbeloowldegdtnad\\ncdwanbee', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'tanceknoxedeglvoae\\ndencvaa', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbeloowldegdtnad\\ncdwenbea', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedexonkecnat\\naavcned', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbeloowmdegdtnad\\ncdwenbea', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedexonkecnat\\n`avcned', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelpowmdegdtnad\\ncdwenbea', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedexonkecnat\\n`avcndd', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelpowmdegetnad\\ncdwenbea', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedexonkecnat\\n`avcdnd', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelpowmdegetnad\\ncdewnbea', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedexonkecnat\\ndndcva`', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelpowmeegetnad\\ncdewnbea', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaevlgedoxonkecnat\\ndndcva`', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelpowmeegetnad\\nddewnbea', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaevlgedoxonkecnat\\ndnccva`', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelpowmeegetnad\\nddewnbda', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaevlgedoxonkectan\\ndnccva`', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelpowmeegdtnae\\nddewnbda', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaevlgedoxonkectan\\ndn`cvac', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelpowmeegdtnae\\ndeewnbda', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaevlgedoconkextan\\ndn`cvac', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbelpowmeegdtnae\\nadbnweed', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedeconkextan\\ndn`cvac', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vanbetpowmeegdlnae\\nadbnweed', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eaovlgedeconkextan\\ndnvc`ac', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vatbenpowmeegdlnae\\nadbnweed', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'faovlgedeconkextan\\ndnvc`ac', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vatbenpowmefgdlnae\\nadbnweed', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'faovlgedeconkextan\\ndnvcaac', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vadbenpowmefgtlnae\\nadbnweed', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'faovlgedeconkextan\\ndcvcaan', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vadbenpowmefgtlnae\\nadboweed', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'faovlgedeconkextan\\ndcvcaam', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vadbenpowmefgtlnae\\ndeewobda', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'faovlgedeconkextan\\ndcvcabm', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vadbenpowmefgtlnae\\nddewobda', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'faovlgedeconkextan\\ndcbcavm', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vadbenpowmefgtlnae\\ncdewobda', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favolgedeconkextan\\ndcbcavm', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vadbenpowmefgtlnae\\nadbowedc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favolgedeconkextan\\nmvacbcd', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eanltgfemwopnebdav\\nadbowedc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favolgedeconkdxtan\\nmvacbcd', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eanetgfemwopnlbdav\\nadbowedc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favolgedeconkdxtan\\nmvacbbd', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'vadblnpowmefgtenae\\nadbowedc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favolgedeconkdxtan\\nmvbcbbd', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'v`dblnpowmefgtenae\\nadbowedc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favolgedeconkdxtan\\nmvbcbbe', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'v`dblnpowmefgtenae\\nadbovedc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favolgedeconkdxtan\\nnvbcbbe', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eanetgfemwopnlbd`v\\nadbovedc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favolgececonkdxtan\\nnvbcbbe', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eanetgfemwopnkbd`v\\nadbovedc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favolgececonkdxtan\\nnvbcbbd', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eanetgfemwopnkbd`v\\nadbcvedo', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favolgececonkdxtan\\nnvbcbbc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'eanetgfemwopnkbd`v\\nacbdvedo', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favomgececonkdxtan\\nnvbcbbc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'v`dbknpowmefgtenae\\nacbdvedo', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favomgececonkdxtan\\novbcbbc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'v`dbknpowmefgtenae\\nadbdvedo', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favomfececonkdxtan\\novbcbbc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'v`dblnpowmefgtenae\\nadbdvedo', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'favomfececonkdxtan\\nobvcbbc', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'w`dblnpovmefgtenae\\nadbdvedo', 'output': 'No\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79169","program":"```python\ns = input()\np = input()\nprint(\"Yes\" if p in (s + s) else \"No\")\n\n```","inputs":"vanceknowledgetoad\nadvance","output":"Yes","actual_output":"Yes\n","execution_success":true,"sample_index":12611},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1057_B. DDoS","prompt":"Solve the following coding problem using the programming language python:\n\nWe get more and more news about DDoS-attacks of popular websites.\n\nArseny is an admin and he thinks that a website is under a DDoS-attack if the total number of requests for a some period of time exceeds 100 \u22c5 t, where t \u2014 the number of seconds in this time segment. \n\nArseny knows statistics on the number of requests per second since the server is booted. He knows the sequence r_1, r_2, ..., r_n, where r_i \u2014 the number of requests in the i-th second after boot. \n\nDetermine the length of the longest continuous period of time, which Arseny considers to be a DDoS-attack. A seeking time period should not go beyond the boundaries of the segment [1, n].\n\nInput\n\nThe first line contains n (1 \u2264 n \u2264 5000) \u2014 number of seconds since server has been booted. The second line contains sequence of integers r_1, r_2, ..., r_n (0 \u2264 r_i \u2264 5000), r_i \u2014 number of requests in the i-th second.\n\nOutput\n\nPrint the only integer number \u2014 the length of the longest time period which is considered to be a DDoS-attack by Arseny. If it doesn't exist print 0.\n\nExamples\n\nInput\n\n5\n100 200 1 1 1\n\n\nOutput\n\n3\n\n\nInput\n\n5\n1 2 3 4 5\n\n\nOutput\n\n0\n\n\nInput\n\n2\n101 99\n\n\nOutput\n\n1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom itertools import accumulate as ac\nfrom collections import Counter as cc\nfrom bisect import bisect_left as bsl\nfrom bisect import bisect as bs\nfrom math import factorial as f\nfrom collections import *\nfrom itertools import *\nfrom string import *\nfrom bisect import *\nfrom queue import *\nfrom heapq import *\nfrom math import *\nfrom sys import *\nfrom re import *\ndef fast(): return stdin.readline().strip()\ndef zzz(): return [int(i) for i in fast().split()]\n\n\nz, zz = input, lambda: list(map(int, z().split()))\nszz, graph, mod, szzz = lambda: sorted(\n zz()), {}, 10**9+7, lambda: sorted(zzz())\n\n\ndef lcd(xnum1, xnum2): return (xnum1*xnum2//gcd(xnum1, xnum2))\ndef output(answer): stdout.write(str(answer))\n\n\n###########################---Test-Case---#################################\n\"\"\"\n\n If you Know me , Then you probably don't know me !\n\n\n\"\"\"\n###########################---START-CODING---##############################\n\nn=int(input())\nl=zzz()\nm=0\nfor i in range(n):\n s=0\n for j in range(i,n):\n s=s+l[j]\n if(s>(j-i+1)*100):\n m=max(m,j-i+1)\nprint(m)\n\n\n\n\n\n\n\n\n \n\n \t\t\t\t \t\t\t \t\t \t \t \t \t\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n100 200 1 1 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 3 4 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n101 99\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4657\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4660\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4669\\n', 'output': '1\\n'}, {'type': 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'stdin_stdout', 'input': '1\\n107\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n64 200\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2918\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100\\n214 96 67 98 4 61 1 82 1 31 98 49 32 60 7 33 80 95 78 33 20 13 52 82 25 240 85 42 239 74 19 17 22 83 14 99 169 223 52 90 32 62 19 50 86 86 31 74 25 3 85 36 71 188 77 4 42 256 34 67 81 91 11 94 58 77 21 26 80 25 65 78 37 40 62 97 29 48 77 45 18 19 151 80 123 43 94 63 279 50 182 27 83 53 91 48 230 91 141 162\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3924\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n7810\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n155 9 196 23 79 35 25 194 63 57\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6489\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n561\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n000 200 1 1 2\\n', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79205","program":"```python\nfrom itertools import accumulate as ac\nfrom collections import Counter as cc\nfrom bisect import bisect_left as bsl\nfrom bisect import bisect as bs\nfrom math import factorial as f\nfrom collections import *\nfrom itertools import *\nfrom string import *\nfrom bisect import *\nfrom queue import *\nfrom heapq import *\nfrom math import *\nfrom sys import *\nfrom re import *\ndef fast(): return stdin.readline().strip()\ndef zzz(): return [int(i) for i in fast().split()]\n\n\nz, zz = input, lambda: list(map(int, z().split()))\nszz, graph, mod, szzz = lambda: sorted(\n zz()), {}, 10**9+7, lambda: sorted(zzz())\n\n\ndef lcd(xnum1, xnum2): return (xnum1*xnum2//gcd(xnum1, xnum2))\ndef output(answer): stdout.write(str(answer))\n\n\n###########################---Test-Case---#################################\n\"\"\"\n\n If you Know me , Then you probably don't know me !\n\n\n\"\"\"\n###########################---START-CODING---##############################\n\nn=int(input())\nl=zzz()\nm=0\nfor i in range(n):\n s=0\n for j in range(i,n):\n s=s+l[j]\n if(s>(j-i+1)*100):\n m=max(m,j-i+1)\nprint(m)\n\n\n\n\n\n\n\n\n \n\n \t\t\t\t \t\t\t \t\t \t \t \t \t\n```","inputs":"5\n100 200 1 1 1\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12612},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1080_A. Petya and Origami","prompt":"Solve the following coding problem using the programming language python:\n\nPetya is having a party soon, and he has decided to invite his n friends.\n\nHe wants to make invitations in the form of origami. For each invitation, he needs two red sheets, five green sheets, and eight blue sheets. The store sells an infinite number of notebooks of each color, but each notebook consists of only one color with k sheets. That is, each notebook contains k sheets of either red, green, or blue.\n\nFind the minimum number of notebooks that Petya needs to buy to invite all n of his friends.\n\nInput\n\nThe first line contains two integers n and k (1\u2264 n, k\u2264 10^8) \u2014 the number of Petya's friends and the number of sheets in each notebook respectively.\n\nOutput\n\nPrint one number \u2014 the minimum number of notebooks that Petya needs to buy.\n\nExamples\n\nInput\n\n\n3 5\n\n\nOutput\n\n\n10\n\n\nInput\n\n\n15 6\n\n\nOutput\n\n\n38\n\nNote\n\nIn the first example, we need 2 red notebooks, 3 green notebooks, and 5 blue notebooks.\n\nIn the second example, we need 5 red notebooks, 13 green notebooks, and 20 blue notebooks.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndata=[int(i) for i in input().split()]\nn=data.pop(0)\nk=data.pop(0)\nred=n*2\ngreen=n*5\nblue=n*8\nanswer=0\nif red%k==0:\n answer+=red//k\nelse:\n answer+=red//k+1\nif blue%k==0:\n answer+=blue//k\nelse:\n answer+=blue//k+1\nif green%k==0:\n answer+=green//k\nelse:\n answer+=green//k+1\nprint(int(answer))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 5\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '15 6\\n', 'output': '38\\n'}, {'type': 'stdin_stdout', 'input': '30931310 20\\n', 'output': '23198483\\n'}, {'type': 'stdin_stdout', 'input': '51400703 5644\\n', 'output': '136609\\n'}, {'type': 'stdin_stdout', 'input': '96865066 63740710\\n', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '75431019 54776881\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '64345128 22\\n', 'output': '43871680\\n'}, {'type': 'stdin_stdout', 'input': '98979868 1\\n', 'output': '1484698020\\n'}, {'type': 'stdin_stdout', 'input': '53904449 44920372\\n', 'output': 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'19390509 2\\n', 'output': '145428818\\n'}, {'type': 'stdin_stdout', 'input': '17018712 4084\\n', 'output': '62509\\n'}, {'type': 'stdin_stdout', 'input': '123420612 3373\\n', 'output': '548863\\n'}, {'type': 'stdin_stdout', 'input': '92314891 126308874\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '63521620 96212643\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '19478739 22329904\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '25414526 39163052\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n', 'output': '60\\n'}, {'type': 'stdin_stdout', 'input': '1 5\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '37473715 53176588\\n', 'output': '12\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79209","program":"```python\ndata=[int(i) for i in input().split()]\nn=data.pop(0)\nk=data.pop(0)\nred=n*2\ngreen=n*5\nblue=n*8\nanswer=0\nif red%k==0:\n answer+=red//k\nelse:\n answer+=red//k+1\nif blue%k==0:\n answer+=blue//k\nelse:\n answer+=blue//k+1\nif green%k==0:\n answer+=green//k\nelse:\n answer+=green//k+1\nprint(int(answer))\n```","inputs":"3 5\n","output":"10\n","actual_output":"10\n","execution_success":true,"sample_index":12613},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1148_A. Another One Bites The Dust","prompt":"Solve the following coding problem using the programming language python:\n\nLet's call a string good if and only if it consists of only two types of letters \u2014 'a' and 'b' and every two consecutive letters are distinct. For example \"baba\" and \"aba\" are good strings and \"abb\" is a bad string.\n\nYou have a strings \"a\", b strings \"b\" and c strings \"ab\". You want to choose some subset of these strings and concatenate them in any arbitrarily order.\n\nWhat is the length of the longest good string you can obtain this way?\n\nInput\n\nThe first line contains three positive integers a, b, c (1 \u2264 a, b, c \u2264 10^9) \u2014 the number of strings \"a\", \"b\" and \"ab\" respectively.\n\nOutput\n\nPrint a single number \u2014 the maximum possible length of the good string you can obtain.\n\nExamples\n\nInput\n\n\n1 1 1\n\n\nOutput\n\n\n4\n\n\nInput\n\n\n2 1 2\n\n\nOutput\n\n\n7\n\n\nInput\n\n\n3 5 2\n\n\nOutput\n\n\n11\n\n\nInput\n\n\n2 2 1\n\n\nOutput\n\n\n6\n\n\nInput\n\n\n1000000000 1000000000 1000000000\n\n\nOutput\n\n\n4000000000\n\nNote\n\nIn the first example the optimal string is \"baba\".\n\nIn the second example the optimal string is \"abababa\".\n\nIn the third example the optimal string is \"bababababab\".\n\nIn the fourth example the optimal string is \"ababab\".\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na,b,c=map(int,input().split())\ndif=abs(a-b)\nif dif <=1:\n print(a+b+c*2)\nelse:\n print(min(a,b)*2+1+c*2)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 2 1\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2 1 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1000000000 1000000000 1000000000\\n', 'output': '4000000000\\n'}, {'type': 'stdin_stdout', 'input': '3 5 2\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '1 1 2\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '11 9 6\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '10 2 5\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '6 1 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '2 100 1\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': 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'input': '0 8 4\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '101 001 99\\n', 'output': '201\\n'}, {'type': 'stdin_stdout', 'input': '2 3 1\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1 3 10\\n', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '0 6 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 6 7\\n', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '3 1 0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '-1 5 10\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '4 0 1\\n', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79221","program":"```python\na,b,c=map(int,input().split())\ndif=abs(a-b)\nif dif <=1:\n print(a+b+c*2)\nelse:\n print(min(a,b)*2+1+c*2)\n```","inputs":"2 2 1\n","output":"6\n","actual_output":"6\n","execution_success":true,"sample_index":12615},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1169_C. Increasing by Modulo","prompt":"Solve the following coding problem using the programming language python:\n\nToad Zitz has an array of integers, each integer is between 0 and m-1 inclusive. The integers are a_1, a_2, \u2026, a_n.\n\nIn one operation Zitz can choose an integer k and k indices i_1, i_2, \u2026, i_k such that 1 \u2264 i_1 < i_2 < \u2026 < i_k \u2264 n. He should then change a_{i_j} to ((a_{i_j}+1) mod m) for each chosen integer i_j. The integer m is fixed for all operations and indices.\n\nHere x mod y denotes the remainder of the division of x by y.\n\nZitz wants to make his array non-decreasing with the minimum number of such operations. Find this minimum number of operations.\n\nInput\n\nThe first line contains two integers n and m (1 \u2264 n, m \u2264 300 000) \u2014 the number of integers in the array and the parameter m.\n\nThe next line contains n space-separated integers a_1, a_2, \u2026, a_n (0 \u2264 a_i < m) \u2014 the given array.\n\nOutput\n\nOutput one integer: the minimum number of described operations Zitz needs to make his array non-decreasing. If no operations required, print 0.\n\nIt is easy to see that with enough operations Zitz can always make his array non-decreasing.\n\nExamples\n\nInput\n\n\n5 3\n0 0 0 1 2\n\n\nOutput\n\n\n0\n\n\nInput\n\n\n5 7\n0 6 1 3 2\n\n\nOutput\n\n\n1\n\nNote\n\nIn the first example, the array is already non-decreasing, so the answer is 0.\n\nIn the second example, you can choose k=2, i_1 = 2, i_2 = 5, the array becomes [0,0,1,3,3]. It is non-decreasing, so the answer is 1.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, m = map(int, input().split())\na = list(map(int, input().split()))\n\nl, r = 0, m-1\n\nwhile r > l:\n mid = (l + r) >> 1\n p = 0\n f = False\n for i in a:\n if i <= p <= i+mid or i <= p+m <= i+mid:\n continue\n if i < p:\n f = True\n break\n p = max(p, i)\n if f:\n l = mid+1\n else:\n r = mid\nprint(r)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 3\\n0 0 0 1 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 7\\n0 6 1 3 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n0 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '100 10\\n8 4 4 9 0 7 9 5 1 1 2 3 7 1 8 4 8 8 6 0 8 7 8 3 7 0 6 4 8 4 2 7 0 0 3 8 4 4 2 0 0 4 7 2 4 7 9 1 3 3 6 2 9 6 0 6 3 5 6 5 5 3 0 0 8 7 1 4 2 4 1 3 9 7 9 0 6 6 7 4 2 3 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4 4 9 0 7 9 5 1 1 2 3 7 1 8 4 8 8 6 0 8 7 8 3 7 0 6 4 8 4 1 7 0 0 3 8 4 4 2 0 0 4 7 2 4 7 9 1 3 3 6 2 9 6 0 6 3 5 6 5 5 3 0 0 8 7 1 4 2 4 1 3 9 7 9 0 6 6 7 4 2 3 7 1 7 3 5 1 4 3 7 5 7 5 0 5 1 9 0 9\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n5 0 5 9 4 6 3 5 0 0\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 3 4 5 6 4 8 9 0\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '10 300000\\n111862 91787 271781 182224 260248 142019 30716 102643 109238 19206\\n', 'output': '208213\\n'}, {'type': 'stdin_stdout', 'input': '100 2\\n1 1 0 1 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 7\\n1 6 1 3 2\\n', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 500000000}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79225","program":"```python\nn, m = map(int, input().split())\na = list(map(int, input().split()))\n\nl, r = 0, m-1\n\nwhile r > l:\n mid = (l + r) >> 1\n p = 0\n f = False\n for i in a:\n if i <= p <= i+mid or i <= p+m <= i+mid:\n continue\n if i < p:\n f = True\n break\n p = max(p, i)\n if f:\n l = mid+1\n else:\n r = mid\nprint(r)\n\n```","inputs":"5 3\n0 0 0 1 2\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12616},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1187_E. Tree Painting","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a tree (an undirected connected acyclic graph) consisting of n vertices. You are playing a game on this tree.\n\nInitially all vertices are white. On the first turn of the game you choose one vertex and paint it black. Then on each turn you choose a white vertex adjacent (connected by an edge) to any black vertex and paint it black.\n\nEach time when you choose a vertex (even during the first turn), you gain the number of points equal to the size of the connected component consisting only of white vertices that contains the chosen vertex. The game ends when all vertices are painted black.\n\nLet's see the following example:\n\n\n\nVertices 1 and 4 are painted black already. If you choose the vertex 2, you will gain 4 points for the connected component consisting of vertices 2, 3, 5 and 6. If you choose the vertex 9, you will gain 3 points for the connected component consisting of vertices 7, 8 and 9.\n\nYour task is to maximize the number of points you gain.\n\nInput\n\nThe first line contains an integer n \u2014 the number of vertices in the tree (2 \u2264 n \u2264 2 \u22c5 10^5).\n\nEach of the next n - 1 lines describes an edge of the tree. Edge i is denoted by two integers u_i and v_i, the indices of vertices it connects (1 \u2264 u_i, v_i \u2264 n, u_i \u2260 v_i).\n\nIt is guaranteed that the given edges form a tree.\n\nOutput\n\nPrint one integer \u2014 the maximum number of points you gain if you will play optimally.\n\nExamples\n\nInput\n\n\n9\n1 2\n2 3\n2 5\n2 6\n1 4\n4 9\n9 7\n9 8\n\n\nOutput\n\n\n36\n\n\nInput\n\n\n5\n1 2\n1 3\n2 4\n2 5\n\n\nOutput\n\n\n14\n\nNote\n\nThe first example tree is shown in the problem statement.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\n\ninput = sys.stdin.readline\n\nn = int(input())\nG = [[] for _ in range(n)]\n\nfor _ in range(n-1):\n a,b = map(int,input().split())\n G[a-1].append(b-1)\n G[b-1].append(a-1)\n\nF = [0]*n\nstk = [0]\nvisited = [0]*n\n\nwhile stk:\n x = stk[-1]\n if not visited[x]:\n visited[x] = 1\n for y in G[x]:\n if not visited[y]:\n stk.append(y)\n else:\n x = stk.pop()\n F[x] = 1\n for y in G[x]: \n F[x] += F[y]\n\nDP = [0]*n\nstk = [0]\nvisited = [0]*n\n\nwhile stk:\n x = stk[-1]\n if not visited[x]:\n visited[x] = 1\n for y in G[x]:\n if not visited[y]:\n stk.append(y)\n else:\n x = stk.pop()\n DP[x] = F[x]\n for y in G[x]:\n DP[x] += DP[y]\n\nans = [0]*n\nans[0] = DP[0]\nstk = [0]\nZ = DP[0]\n\nwhile stk:\n x = stk.pop()\n for y in G[x]:\n if not ans[y]:\n ay = ans[x] + n - 2 * F[y]\n ans[y] = ay \n Z = max(Z,ay)\n stk.append(y)\n\nprint(Z)\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 2\\n1 3\\n2 4\\n2 5\\n', 'output': '14'}, {'type': 'stdin_stdout', 'input': '9\\n1 2\\n2 3\\n2 5\\n2 6\\n1 4\\n4 9\\n9 7\\n9 8\\n', 'output': '36'}, {'type': 'stdin_stdout', 'input': '2\\n1 2\\n', 'output': '3'}, {'type': 'stdin_stdout', 'input': '6\\n5 3\\n5 6\\n5 1\\n5 4\\n5 2\\n', 'output': '15'}, {'type': 'stdin_stdout', 'input': '7\\n7 5\\n7 3\\n7 6\\n7 4\\n7 1\\n7 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10\\n10 8\\n5 2\\n1 6\\n6 2\\n8 9\\n9 2\\n2 3\\n9 7\\n', 'output': '45\\n'}, {'type': 'stdin_stdout', 'input': '6\\n5 3\\n5 6\\n5 1\\n3 4\\n5 2\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 8\\n8 4\\n4 9\\n9 6\\n6 1\\n6 2\\n2 7\\n6 3\\n6 10\\n', 'output': '46\\n'}, {'type': 'stdin_stdout', 'input': '9\\n3 2\\n3 1\\n3 8\\n3 5\\n1 6\\n3 9\\n3 4\\n3 7\\n', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '6\\n6 5\\n5 2\\n2 3\\n5 4\\n4 1\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 4\\n2 6\\n3 6\\n6 7\\n7 4\\n1 5\\n', 'output': '27\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 10\\n10 8\\n5 4\\n1 6\\n6 2\\n8 9\\n9 2\\n2 3\\n9 7\\n', 'output': '49\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 1\\n8 4\\n4 9\\n9 6\\n8 1\\n6 2\\n2 7\\n6 3\\n6 10\\n', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 10\\n10 6\\n6 4\\n4 5\\n5 3\\n8 2\\n2 1\\n1 3\\n3 9\\n', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n4 3\\n2 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'10\\n8 2\\n8 10\\n10 3\\n2 4\\n5 6\\n8 1\\n2 7\\n10 9\\n4 5\\n', 'output': '46\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2\\n2 3\\n2 5\\n3 6\\n1 4\\n4 9\\n9 7\\n9 8\\n', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '6\\n5 4\\n5 6\\n5 1\\n3 4\\n5 2\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 1\\n8 4\\n4 9\\n9 6\\n6 1\\n6 2\\n2 7\\n6 3\\n6 10\\n', 'output': '42\\n'}, {'type': 'stdin_stdout', 'input': '6\\n5 4\\n5 6\\n5 1\\n3 5\\n5 2\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 3\\n1 4\\n1 2\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '9\\n3 2\\n3 1\\n3 8\\n3 5\\n4 6\\n3 9\\n3 4\\n3 7\\n', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '8\\n6 2\\n6 1\\n6 8\\n6 5\\n3 7\\n6 3\\n6 4\\n', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '10\\n8 2\\n8 10\\n10 3\\n2 4\\n3 6\\n8 1\\n2 7\\n10 9\\n1 5\\n', 'output': '42\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2\\n1 3\\n1 4\\n2 5\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 8\\n8 4\\n4 1\\n9 6\\n6 1\\n6 2\\n6 7\\n6 3\\n6 10\\n', 'output': '45\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2\\n2 4\\n3 6\\n6 7\\n7 4\\n1 5\\n', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 2\\n1 3\\n3 6\\n6 2\\n2 7\\n7 5\\n1 8\\n', 'output': '34\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2\\n1 3\\n1 4\\n4 5\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '6\\n5 3\\n5 6\\n5 1\\n2 4\\n5 2\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 3\\n2 4\\n1 2\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 8\\n8 4\\n4 9\\n9 6\\n6 1\\n5 2\\n2 7\\n6 3\\n6 10\\n', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 1\\n7 6\\n5 2\\n5 8\\n5 3\\n5 4\\n5 10\\n5 9\\n5 7\\n', 'output': '35\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2\\n2 3\\n1 5\\n3 6\\n1 4\\n4 9\\n9 7\\n9 8\\n', 'output': '40\\n'}, {'type': 'stdin_stdout', 'input': '10\\n5 1\\n8 4\\n4 9\\n9 6\\n6 1\\n8 2\\n2 7\\n6 3\\n6 10\\n', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 2\\n1 3\\n3 6\\n6 2\\n4 7\\n7 5\\n1 8\\n', 'output': '36\\n'}, {'type': 'stdin_stdout', 'input': '6\\n5 3\\n5 6\\n5 1\\n5 4\\n4 2\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 10\\n10 6\\n6 4\\n4 5\\n5 8\\n8 2\\n2 1\\n1 3\\n6 9\\n', 'output': '53\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79229","program":"```python\nimport sys\n\ninput = sys.stdin.readline\n\nn = int(input())\nG = [[] for _ in range(n)]\n\nfor _ in range(n-1):\n a,b = map(int,input().split())\n G[a-1].append(b-1)\n G[b-1].append(a-1)\n\nF = [0]*n\nstk = [0]\nvisited = [0]*n\n\nwhile stk:\n x = stk[-1]\n if not visited[x]:\n visited[x] = 1\n for y in G[x]:\n if not visited[y]:\n stk.append(y)\n else:\n x = stk.pop()\n F[x] = 1\n for y in G[x]: \n F[x] += F[y]\n\nDP = [0]*n\nstk = [0]\nvisited = [0]*n\n\nwhile stk:\n x = stk[-1]\n if not visited[x]:\n visited[x] = 1\n for y in G[x]:\n if not visited[y]:\n stk.append(y)\n else:\n x = stk.pop()\n DP[x] = F[x]\n for y in G[x]:\n DP[x] += DP[y]\n\nans = [0]*n\nans[0] = DP[0]\nstk = [0]\nZ = DP[0]\n\nwhile stk:\n x = stk.pop()\n for y in G[x]:\n if not ans[y]:\n ay = ans[x] + n - 2 * F[y]\n ans[y] = ay \n Z = max(Z,ay)\n stk.append(y)\n\nprint(Z)\n\n\n```","inputs":"5\n1 2\n1 3\n2 4\n2 5\n","output":"14","actual_output":"14\n","execution_success":true,"sample_index":12617},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1206_D. Shortest Cycle","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given n integer numbers a_1, a_2, ..., a_n. Consider graph on n nodes, in which nodes i, j (i\u2260 j) are connected if and only if, a_i AND a_j\u2260 0, where AND denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).\n\nFind the length of the shortest cycle in this graph or determine that it doesn't have cycles at all.\n\nInput\n\nThe first line contains one integer n (1 \u2264 n \u2264 10^5) \u2014 number of numbers.\n\nThe second line contains n integer numbers a_1, a_2, ..., a_n (0 \u2264 a_i \u2264 10^{18}).\n\nOutput\n\nIf the graph doesn't have any cycles, output -1. Else output the length of the shortest cycle.\n\nExamples\n\nInput\n\n\n4\n3 6 28 9\n\n\nOutput\n\n\n4\n\nInput\n\n\n5\n5 12 9 16 48\n\n\nOutput\n\n\n3\n\nInput\n\n\n4\n1 2 4 8\n\n\nOutput\n\n\n-1\n\nNote\n\nIn the first example, the shortest cycle is (9, 3, 6, 28).\n\nIn the second example, the shortest cycle is (5, 12, 9).\n\nThe graph has no cycles in the third example.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys, os, re, datetime, copy\nfrom collections import *\nfrom bisect import *\ndef mat(v, *dims):\n\tdef dim(i): return [copy.copy(v) for _ in range(dims[-1])] if i == len(dims)-1 else [dim(i+1) for _ in range(dims[i])]\n\treturn dim(0)\n__cin__ = None\ndef cin():\n\tglobal __cin__\n\tif __cin__ is None: __cin__ = iter(input().split(\" \"))\n\ttry: return next(__cin__)\n\texcept StopIteration:\n\t\t__cin__ = iter(input().split(\" \"))\n\t\treturn next(__cin__)\ndef iarr(n): return [int(cin()) for _ in range(n)]\ndef farr(n): return [float(cin()) for _ in range(n)]\ndef sarr(n): return [cin() for _ in range(n)]\ndef carr(n): return input()\ndef imat(n, m): return [iarr(m) for _ in range(n)]\ndef fmat(n, m): return [farr(m) for _ in range(n)]\ndef smat(n, m): return [sarr(m) for _ in range(n)]\ndef cmat(n, m): return [input() for _ in range(n)]\n\ndef bfs(i):\n\tdist = mat(INF, n)\n\tq = deque()\n\tq.append(i)\n\tdist[i] = 0\n\t\n\twhile len(q) > 0:\n\t\tu = q.popleft()\n\t\tfor v in adj[u]:\n\t\t\tif dist[v] == INF:\n\t\t\t\tq.append(v)\n\t\t\t\tdist[v] = dist[u]+1\n\t\t\telif dist[v]+1 != dist[u]:\n\t\t\t\treturn dist[v]+dist[u]+1\n\treturn INF\n\nN = 64\nn = int(cin())\ntmp = iarr(n)\nt = mat(0, N)\ng = mat([], N)\nadj = mat(set(), n)\nINF = 100000\nans = INF\n\na = list(filter(lambda x: x > 0, tmp))\nn = len(a)\n\t\nfor j in range(N):\n\tfor i in range(n):\n\t\tv = a[i]\n\t\tt[j] += (v>>j)&1\n\t\tif t[j] >= 3:\n\t\t\tprint(\"3\")\n\t\t\texit(0)\n\t\tif ((v>>j)&1) == 1:\n\t\t\tg[j].append(i)\n\t\nfor i in range(N):\n\tif len(g[i]) == 2:\n\t\tadj[g[i][0]].add(g[i][1])\n\t\tadj[g[i][1]].add(g[i][0])\n \nfor i in range(n):\n\tans = min(ans, bfs(i))\n\nprint(-1 if ans == INF else ans)\n\nmmap = {0: \"Hola\", 1: \"Mundo\"}\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n3 6 28 9\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 4 8\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 12 9 16 48\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '20\\n17592722915328 137438953728 0 549755822096 2251800350556160 70368744185856 0 2251804108652544 0 1099511628288 17592186045440 8864812498944 79164837199872 0 68719477760 1236950581248 549755814400 0 17179869456 21474836480\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5\\n292733975779082240 18014398509482240 306244774661193728 4504699138998272 1099511628032\\n', 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*\nfrom bisect import *\ndef mat(v, *dims):\n\tdef dim(i): return [copy.copy(v) for _ in range(dims[-1])] if i == len(dims)-1 else [dim(i+1) for _ in range(dims[i])]\n\treturn dim(0)\n__cin__ = None\ndef cin():\n\tglobal __cin__\n\tif __cin__ is None: __cin__ = iter(input().split(\" \"))\n\ttry: return next(__cin__)\n\texcept StopIteration:\n\t\t__cin__ = iter(input().split(\" \"))\n\t\treturn next(__cin__)\ndef iarr(n): return [int(cin()) for _ in range(n)]\ndef farr(n): return [float(cin()) for _ in range(n)]\ndef sarr(n): return [cin() for _ in range(n)]\ndef carr(n): return input()\ndef imat(n, m): return [iarr(m) for _ in range(n)]\ndef fmat(n, m): return [farr(m) for _ in range(n)]\ndef smat(n, m): return [sarr(m) for _ in range(n)]\ndef cmat(n, m): return [input() for _ in range(n)]\n\ndef bfs(i):\n\tdist = mat(INF, n)\n\tq = deque()\n\tq.append(i)\n\tdist[i] = 0\n\t\n\twhile len(q) > 0:\n\t\tu = q.popleft()\n\t\tfor v in adj[u]:\n\t\t\tif dist[v] == INF:\n\t\t\t\tq.append(v)\n\t\t\t\tdist[v] = dist[u]+1\n\t\t\telif dist[v]+1 != dist[u]:\n\t\t\t\treturn dist[v]+dist[u]+1\n\treturn INF\n\nN = 64\nn = int(cin())\ntmp = iarr(n)\nt = mat(0, N)\ng = mat([], N)\nadj = mat(set(), n)\nINF = 100000\nans = INF\n\na = list(filter(lambda x: x > 0, tmp))\nn = len(a)\n\t\nfor j in range(N):\n\tfor i in range(n):\n\t\tv = a[i]\n\t\tt[j] += (v>>j)&1\n\t\tif t[j] >= 3:\n\t\t\tprint(\"3\")\n\t\t\texit(0)\n\t\tif ((v>>j)&1) == 1:\n\t\t\tg[j].append(i)\n\t\nfor i in range(N):\n\tif len(g[i]) == 2:\n\t\tadj[g[i][0]].add(g[i][1])\n\t\tadj[g[i][1]].add(g[i][0])\n \nfor i in range(n):\n\tans = min(ans, bfs(i))\n\nprint(-1 if ans == INF else ans)\n\nmmap = {0: \"Hola\", 1: \"Mundo\"}\n```","inputs":"4\n3 6 28 9\n","output":"4\n","actual_output":"4\n","execution_success":true,"sample_index":12618},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1249_C1. Good Numbers (easy version)","prompt":"Solve the following coding problem using the programming language python:\n\nThe only difference between easy and hard versions is the maximum value of n.\n\nYou are given a positive integer number n. You really love good numbers so you want to find the smallest good number greater than or equal to n.\n\nThe positive integer is called good if it can be represented as a sum of distinct powers of 3 (i.e. no duplicates of powers of 3 are allowed).\n\nFor example:\n\n * 30 is a good number: 30 = 3^3 + 3^1, \n * 1 is a good number: 1 = 3^0, \n * 12 is a good number: 12 = 3^2 + 3^1, \n * but 2 is not a good number: you can't represent it as a sum of distinct powers of 3 (2 = 3^0 + 3^0), \n * 19 is not a good number: you can't represent it as a sum of distinct powers of 3 (for example, the representations 19 = 3^2 + 3^2 + 3^0 = 3^2 + 3^1 + 3^1 + 3^1 + 3^0 are invalid), \n * 20 is also not a good number: you can't represent it as a sum of distinct powers of 3 (for example, the representation 20 = 3^2 + 3^2 + 3^0 + 3^0 is invalid). \n\n\n\nNote, that there exist other representations of 19 and 20 as sums of powers of 3 but none of them consists of distinct powers of 3.\n\nFor the given positive integer n find such smallest m (n \u2264 m) that m is a good number.\n\nYou have to answer q independent queries.\n\nInput\n\nThe first line of the input contains one integer q (1 \u2264 q \u2264 500) \u2014 the number of queries. Then q queries follow.\n\nThe only line of the query contains one integer n (1 \u2264 n \u2264 10^4).\n\nOutput\n\nFor each query, print such smallest integer m (where n \u2264 m) that m is a good number.\n\nExample\n\nInput\n\n\n7\n1\n2\n6\n13\n14\n3620\n10000\n\n\nOutput\n\n\n1\n3\n9\n13\n27\n6561\n19683\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef ternary (n):\n if n == 0:\n return '0'\n nums = []\n while n:\n n, r = divmod(n, 3)\n nums.append(str(r))\n return ''.join(reversed(nums))\nfor xyz in range(0,int(input())):\n n=int(input())\n s=ternary(n)\n f=0\n for i in range(0,len(s)):\n if s[i]=='2':\n f=1\n break\n if f==1:\n f=0\n #print(s)\n for i in range(i,-1,-1):\n if s[i]=='0':\n f=1\n #print(\"hey\")\n #print(i)\n break\n if f==1:\n st=s[0:i]\n #print(st)\n st+='1'\n st+='0'*(len(s)-i-1)\n else:\n st='1'\n st+='0'*len(s)\n t=0\n p=len(st)\n for i in range(0,p):\n if st[i]=='1':\n t+=3**(p-i-1)\n print(t)\n else:\n print(n)\n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7\\n1\\n2\\n6\\n13\\n14\\n3620\\n10000\\n', 'output': '1\\n3\\n9\\n13\\n27\\n6561\\n19683\\n'}, {'type': 'stdin_stdout', 'input': '1\\n450283905890997363\\n', 'output': '450283905890997363\\n'}, {'type': 'stdin_stdout', 'input': '100\\n1\\n8\\n4\\n6\\n5\\n4\\n4\\n6\\n8\\n3\\n9\\n5\\n7\\n8\\n8\\n5\\n9\\n6\\n9\\n4\\n5\\n6\\n4\\n4\\n7\\n1\\n2\\n2\\n5\\n6\\n1\\n5\\n10\\n9\\n10\\n9\\n3\\n1\\n2\\n3\\n2\\n6\\n9\\n2\\n9\\n5\\n7\\n7\\n2\\n6\\n9\\n5\\n1\\n7\\n8\\n3\\n7\\n9\\n3\\n1\\n7\\n1\\n2\\n4\\n7\\n2\\n7\\n1\\n1\\n10\\n8\\n5\\n7\\n7\\n10\\n8\\n1\\n7\\n5\\n10\\n7\\n6\\n6\\n6\\n7\\n4\\n9\\n3\\n4\\n9\\n10\\n5\\n1\\n2\\n6\\n9\\n3\\n8\\n10\\n9\\n', 'output': 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'8\\n1\\n2\\n7\\n13\\n14\\n3620\\n10000\\n1000000000000000000\\n', 'output': '1\\n3\\n9\\n13\\n27\\n6561\\n19683\\n1350851717672992089\\n'}, {'type': 'stdin_stdout', 'input': '100\\n1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n14\\n10\\n11\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n61\\n62\\n63\\n64\\n65\\n66\\n67\\n68\\n69\\n70\\n71\\n72\\n73\\n74\\n75\\n76\\n77\\n78\\n79\\n80\\n81\\n82\\n83\\n84\\n85\\n86\\n87\\n88\\n89\\n90\\n91\\n92\\n93\\n94\\n95\\n96\\n97\\n98\\n99\\n100\\n', 'output': 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'1\\n116503335\\n', 'output': '129140163\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79241","program":"```python\ndef ternary (n):\n if n == 0:\n return '0'\n nums = []\n while n:\n n, r = divmod(n, 3)\n nums.append(str(r))\n return ''.join(reversed(nums))\nfor xyz in range(0,int(input())):\n n=int(input())\n s=ternary(n)\n f=0\n for i in range(0,len(s)):\n if s[i]=='2':\n f=1\n break\n if f==1:\n f=0\n #print(s)\n for i in range(i,-1,-1):\n if s[i]=='0':\n f=1\n #print(\"hey\")\n #print(i)\n break\n if f==1:\n st=s[0:i]\n #print(st)\n st+='1'\n st+='0'*(len(s)-i-1)\n else:\n st='1'\n st+='0'*len(s)\n t=0\n p=len(st)\n for i in range(0,p):\n if st[i]=='1':\n t+=3**(p-i-1)\n print(t)\n else:\n print(n)\n \n```","inputs":"7\n1\n2\n6\n13\n14\n3620\n10000\n","output":"1\n3\n9\n13\n27\n6561\n19683\n","actual_output":"1\n3\n9\n13\n27\n6561\n19683\n","execution_success":true,"sample_index":12619},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1267_J. Just Arrange the Icons","prompt":"Solve the following coding problem using the programming language python:\n\nBerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like \"game\", \"business\", or \"education\"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i. \n\nYou can choose m \u2014 the number of screens and s \u2014 the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements:\n\n * On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category); \n * Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1). \n\n\n\nYour task is to find the minimal possible number of screens m.\n\nInput\n\nThe first line contains an integer t (1 \u2264 t \u2264 10 000) \u2014 the number of test cases in the input. Then t test cases follow.\n\nThe first line of each test case contains an integer n (1 \u2264 n \u2264 2\u22c510^6) \u2014 the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 \u2264 c_i \u2264 n), where c_i is the category of the i-th application.\n\nIt is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2\u22c510^6.\n\nOutput\n\nPrint t integers \u2014 the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m \u2014 the minimum number of screens on which all n icons can be placed satisfying the given requirements.\n\nExample\n\nInput\n\n\n3\n11\n1 5 1 5 1 5 1 1 1 1 5\n6\n1 2 2 2 2 1\n5\n4 3 3 1 2\n\n\nOutput\n\n\n3\n3\n4\n\nNote\n\nIn the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nt = int(input())\nfor i in range(t):\n n = int(input())\n c =[int(x) for x in input().split()]\n dt = [0]*n\n for j in c:\n dt[j-1]+=1\n # print('dt: ', dt)\n dt = sorted(dt)\n # print ('dt: ',dt)\n for i in range(len(dt)):\n if dt[i]!=0:\n dt=dt[i:]\n break\n\n # print ('dt:',dt)\n\n # dt = [int(x) for x in input().split()]\n\n for k in range(1, dt[0]+1):\n apps = dt[0]//k\n\n\n tr = True\n sums=0\n for i in dt:\n mn = i // (apps + 1)\n sums += mn\n r = i % (apps + 1)\n if (r>0) and (r+mn >= apps):\n sums+=1\n elif r>0:\n tr = False\n break\n if tr:\n print (sums)\n break\n\n tr = True\n sums = 0\n for i in dt:\n mn = i // apps\n sums += mn\n r = i % apps\n if (r>0) and (r +mn >= apps-1):\n sums += 1\n elif r > 0:\n tr = False\n break\n if tr:\n print(sums)\n break\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 5 1 5 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '3\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 5 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 2 1 1 1 1 5\\n6\\n1 2 2 2 4 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 2 2 1 1 1 1 5\\n6\\n1 2 2 2 4 2\\n5\\n4 3 3 1 2\\n', 'output': '6\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 2 2 2 1 1 1 1 5\\n6\\n1 2 2 2 4 2\\n5\\n4 3 3 1 2\\n', 'output': '4\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n2 5 1 5 1 5 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '6\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 2 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n1 3 3 1 2\\n', 'output': '7\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 2 2 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n1 3 3 1 2\\n', 'output': '6\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 2 2 1 1 1 1 5\\n6\\n1 2 2 2 4 2\\n5\\n4 3 3 2 2\\n', 'output': '6\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 6 1 3 1 2 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n1 3 3 1 2\\n', 'output': '8\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n2 5 1 5 1 5 2 1 1 1 5\\n6\\n2 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '5\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 2 3 1 2 2 1 1 1 5\\n6\\n1 4 2 2 2 1\\n5\\n1 3 3 1 2\\n', 'output': '7\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n2 5 1 5 1 5 2 2 1 1 5\\n6\\n2 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '3\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 2 3 1 2 2 1 1 1 8\\n6\\n1 4 2 2 2 1\\n5\\n1 3 3 1 2\\n', 'output': '8\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 2 1 1 1 1 5\\n6\\n1 4 3 2 2 1\\n5\\n4 5 3 1 2\\n', 'output': '7\\n4\\n5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 2 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 5 1 1 1 1 8\\n6\\n1 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 2 1 1 1 1 5\\n6\\n1 2 2 2 4 2\\n5\\n4 3 3 1 2\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 2 1 5 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 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'7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n2 5 1 10 1 5 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 7 2 5 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 2 2 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n1 3 1 1 2\\n', 'output': '6\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n4 5 1 10 1 5 1 1 1 1 5\\n6\\n2 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 2 7 1 3 1 1 1 1 5\\n6\\n1 2 2 2 4 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 2 3 1 2 2 1 2 1 5\\n6\\n1 2 2 3 2 1\\n5\\n1 3 3 1 2\\n', 'output': '6\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n2 5 1 4 1 6 1 1 1 1 5\\n6\\n2 2 2 2 2 1\\n5\\n4 3 3 1 3\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n2 5 1 4 1 5 1 2 1 1 5\\n6\\n2 2 2 2 2 1\\n5\\n4 2 3 1 3\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n4 5 1 4 1 5 1 2 2 1 5\\n6\\n2 2 2 2 2 1\\n5\\n4 3 3 1 3\\n', 'output': '5\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 2 1 1 1 1 5\\n6\\n1 4 3 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 7 2 5 1 1 2 1 5\\n6\\n1 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 6 1 3 1 2 1 1 1 1 9\\n6\\n1 2 2 2 2 1\\n5\\n1 3 3 1 2\\n', 'output': '8\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n4 5 1 10 1 5 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n2 5 1 4 1 6 1 1 1 1 5\\n6\\n2 2 2 2 3 1\\n5\\n4 3 3 1 3\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 7 2 5 1 1 2 1 5\\n6\\n1 2 2 2 3 1\\n5\\n4 3 3 1 2\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 6 1 5 1 2 1 1 1 1 9\\n6\\n1 2 2 2 2 1\\n5\\n1 3 3 1 2\\n', 'output': '8\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n4 5 1 10 1 5 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n2 3 3 1 2\\n', 'output': '7\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 2 3 1 2 2 1 1 1 8\\n6\\n1 2 2 2 2 1\\n5\\n1 3 3 1 2\\n', 'output': '8\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n2 5 1 4 1 9 1 1 1 1 5\\n6\\n2 2 2 2 3 1\\n5\\n4 3 3 1 3\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 2 1 1 1 1 5\\n6\\n1 4 3 2 2 1\\n5\\n4 5 3 1 1\\n', 'output': '7\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n4 5 1 10 1 9 1 1 1 1 5\\n6\\n1 2 2 2 2 1\\n5\\n2 3 3 1 2\\n', 'output': '7\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 2 3 1 2 2 1 1 1 8\\n6\\n1 2 2 3 2 1\\n5\\n1 3 3 1 2\\n', 'output': '8\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n11\\n1 5 1 3 1 2 1 1 1 2 5\\n6\\n1 4 3 2 2 1\\n5\\n4 5 3 1 1\\n', 'output': '6\\n4\\n4\\n'}], 'language': 'python'}","metadata":"{'difficulty': 16, 'time_limit': {'seconds': 5, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_79245","program":"```python\nt = int(input())\nfor i in range(t):\n n = int(input())\n c =[int(x) for x in input().split()]\n dt = [0]*n\n for j in c:\n dt[j-1]+=1\n # print('dt: ', dt)\n dt = sorted(dt)\n # print ('dt: ',dt)\n for i in range(len(dt)):\n if dt[i]!=0:\n dt=dt[i:]\n break\n\n # print ('dt:',dt)\n\n # dt = [int(x) for x in input().split()]\n\n for k in range(1, dt[0]+1):\n apps = dt[0]//k\n\n\n tr = True\n sums=0\n for i in dt:\n mn = i // (apps + 1)\n sums += mn\n r = i % (apps + 1)\n if (r>0) and (r+mn >= apps):\n sums+=1\n elif r>0:\n tr = False\n break\n if tr:\n print (sums)\n break\n\n tr = True\n sums = 0\n for i in dt:\n mn = i // apps\n sums += mn\n r = i % apps\n if (r>0) and (r +mn >= apps-1):\n sums += 1\n elif r > 0:\n tr = False\n break\n if tr:\n print(sums)\n break\n\n```","inputs":"3\n11\n1 5 1 5 1 5 1 1 1 1 5\n6\n1 2 2 2 2 1\n5\n4 3 3 1 2\n","output":"3\n3\n4\n","actual_output":"3\n3\n4\n","execution_success":true,"sample_index":12620},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"128_D. Numbers","prompt":"Solve the following coding problem using the programming language python:\n\nOne day Anna got the following task at school: to arrange several numbers in a circle so that any two neighboring numbers differs exactly by 1. Anna was given several numbers and arranged them in a circle to fulfill the task. Then she wanted to check if she had arranged the numbers correctly, but at this point her younger sister Maria came and shuffled all numbers. Anna got sick with anger but what's done is done and the results of her work had been destroyed. But please tell Anna: could she have hypothetically completed the task using all those given numbers?\n\nInput\n\nThe first line contains an integer n \u2014 how many numbers Anna had (3 \u2264 n \u2264 105). The next line contains those numbers, separated by a space. All numbers are integers and belong to the range from 1 to 109.\n\nOutput\n\nPrint the single line \"YES\" (without the quotes), if Anna could have completed the task correctly using all those numbers (using all of them is necessary). If Anna couldn't have fulfilled the task, no matter how hard she would try, print \"NO\" (without the quotes).\n\nExamples\n\nInput\n\n4\n1 2 3 2\n\n\nOutput\n\nYES\n\n\nInput\n\n6\n1 1 2 2 2 3\n\n\nOutput\n\nYES\n\n\nInput\n\n6\n2 4 1 1 2 2\n\n\nOutput\n\nNO\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\ng={}\nfor i in list(map(int,input().split())):g[i]=g.get(i,0)+2\nmx=max(g)\nfor i in sorted(g)[:-1]:\n\tif i+1 not in g:exit(print('NO'))\n\tg[i+1]-=g[i]\n\tif g[i+1]<0:exit(print('NO'))\nprint('YES'if g[mx]==0 and list(g.values()).count(0)==1else'NO')\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6\\n1 1 2 2 2 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4 1 1 2 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 11 10 11 10 11 10 11 10 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '20\\n2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 5 6 5 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 2 2 2 2 3 3 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4\\n294368194 294368194 294368194 294368195\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 1000000000\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n650111756 650111755 650111754 650111755 650111756\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 2 3 2 3 2 3 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 3 4 5 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n473416369 473416371 473416370 473416371 473416370\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n913596052 913596055 913596054 913596053 913596055 913596054 913596053 913596054 913596052 913596053\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6 7 6 7 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '50\\n363510947 363510954 363510943 363510964 363510969 363510950 363510951 363510960 363510967 363510952 363510956 363510948 363510944 363510946 363510965 363510946 363510963 363510962 363510947 363510955 363510954 363510948 363510961 363510964 363510963 363510945 363510965 363510953 363510952 363510968 363510955 363510966 363510968 363510950 363510967 363510949 363510958 363510957 363510956 363510959 363510953 363510951 363510966 363510949 363510944 363510962 363510945 363510958 363510961 363510957\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n5 4 3 2 1 2 3 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 2 2 2 3 3 3 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4\\n999999998 1000000000 999999999 999999999\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '16\\n1 2 2 2 3 3 3 4 4 5 5 5 6 6 6 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '16\\n20101451 20101452 20101452 20101452 20101453 20101452 20101451 20101451 20101452 20101451 20101452 20101451 20101454 20101454 20101451 20101451\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 1 2 2 5 5 6 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n3 5 8 4 7 6 4 7\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '13\\n981311157 104863150 76378528 37347249 494793049 33951775 3632297 791848390 926461729 94158141 54601123 332909757 722201692\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n637256245 637256246 637256248 637256247 637256247\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 11 10 11 7 11 10 11 10 11\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 2 1 2 3 2 3 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '20\\n2 3 7 5 6 7 8 9 8 7 6 5 4 3 2 1 5 6 5 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 2 2 3 2 3 3 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\n294368194 548664130 294368194 294368195\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 1000000000\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n650111756 242204643 650111754 650111755 650111756\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 3 4 0 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n473416369 907033324 473416370 473416371 473416370\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n913596052 913596055 1773388658 913596053 913596055 913596054 913596053 913596054 913596052 913596053\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6 11 6 7 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '50\\n363510947 363510954 363510943 363510964 363510969 363510950 363510951 363510960 363510967 363510952 363510956 363510948 363510944 363510946 363510965 363510946 363510963 479113745 363510947 363510955 363510954 363510948 363510961 363510964 363510963 363510945 363510965 363510953 363510952 363510968 363510955 363510966 363510968 363510950 363510967 363510949 363510958 363510957 363510956 363510959 363510953 363510951 363510966 363510949 363510944 363510962 363510945 363510958 363510961 363510957\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n5 4 3 2 1 2 3 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 2 2 2 4 3 3 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\n713526911 1000000000 999999999 999999999\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '16\\n0 2 2 2 3 3 3 4 4 5 5 5 6 6 6 7\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '16\\n20101451 20101452 20101452 20101452 20101453 20101452 20101451 20101451 20101452 20101451 20101452 20101451 10730496 20101454 20101451 20101451\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 1 2 2 5 6 6 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n3 5 12 4 7 6 4 7\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '13\\n981311157 104863150 76378528 37347249 494793049 33951775 3632297 791848390 926461729 94158141 54601123 337622303 722201692\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1045577431 637256246 637256248 637256247 637256247\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 3 2 2 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 2 3 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4 1 1 2 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 11 10 10 7 11 10 11 10 11\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '20\\n2 3 7 5 6 11 8 9 8 7 6 5 4 3 2 1 5 6 5 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 2 2 3 2 3 6 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\n294368194 548664130 294368194 291482892\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 1000000000\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n650111756 101598586 650111754 650111755 650111756\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 2 1 2 3 2 5 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 2 3 4 0 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n473416369 907033324 152783635 473416371 473416370\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n913596052 913596055 1773388658 913596053 913596055 913596054 913596053 913596054 913596052 1540645845\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6 11 6 6 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '50\\n363510947 363510954 363510943 363510964 363510969 363510950 363510951 363510960 363510967 363510952 363510956 363510948 363510944 363510946 363510965 363510946 363510963 479113745 363510947 363510955 363510954 363510948 363510961 363510964 363510963 363510945 363510965 363510953 363510952 363510968 363510955 363510966 344053784 363510950 363510967 363510949 363510958 363510957 363510956 363510959 363510953 363510951 363510966 363510949 363510944 363510962 363510945 363510958 363510961 363510957\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n9 4 3 2 1 2 3 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 2 2 2 4 4 3 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\n713526911 1000000000 999999999 776244905\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '16\\n0 2 2 2 3 3 3 4 4 5 5 10 6 6 6 7\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '16\\n20101451 20101452 20101452 20101452 20101453 20101452 20101451 20101451 20101452 20101451 20101452 20101451 10730496 20101454 35035099 20101451\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2 1 2 2 5 6 6 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n6 5 12 4 7 6 4 7\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1045577431 637256246 188094898 637256247 637256247\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 3 2 2 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 2 4 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 4 1 2 2 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 8 10 10 7 11 10 11 10 11\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '20\\n2 3 7 5 6 11 8 9 8 7 6 5 4 3 2 1 8 6 5 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 4 2 3 2 3 6 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\n294368194 548664130 73485973 291482892\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 1000000100\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n650111756 28480204 650111754 650111755 650111756\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1 2 1 2 3 2 5 0\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 2 3 4 1 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n473416369 950646540 152783635 473416371 473416370\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6 11 5 6 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '50\\n363510947 363510954 363510943 363510964 363510969 363510950 363510951 363510960 363510967 363510952 363510956 363510948 363510944 363510946 363510965 363510946 363510963 479113745 363510947 363510955 363510954 363510948 363510961 363510964 363510963 363510945 363510965 363510953 363510952 363510968 363510955 363510966 344053784 363510950 363510967 363510949 363510958 363510957 363510956 363510959 363510953 363510951 363510966 363510949 363510944 363510962 431463492 363510958 363510961 363510957\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n9 4 1 2 1 2 3 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8\\n0 2 2 2 4 4 3 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\n713526911 1000000000 999999999 1009272130\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '16\\n0 2 2 2 3 3 3 4 4 5 5 7 6 6 6 7\\n', 'output': 'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79249","program":"```python\nn=int(input())\ng={}\nfor i in list(map(int,input().split())):g[i]=g.get(i,0)+2\nmx=max(g)\nfor i in sorted(g)[:-1]:\n\tif i+1 not in g:exit(print('NO'))\n\tg[i+1]-=g[i]\n\tif g[i+1]<0:exit(print('NO'))\nprint('YES'if g[mx]==0 and list(g.values()).count(0)==1else'NO')\n```","inputs":"6\n1 1 2 2 2 3\n","output":"YES\n","actual_output":"YES\n","execution_success":true,"sample_index":12621},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1332_E. Height All the Same","prompt":"Solve the following coding problem using the programming language python:\n\nAlice has got addicted to a game called Sirtet recently.\n\nIn Sirtet, player is given an n \u00d7 m grid. Initially a_{i,j} cubes are stacked up in the cell (i,j). Two cells are called adjacent if they share a side. Player can perform the following operations: \n\n * stack up one cube in two adjacent cells; \n * stack up two cubes in one cell. \n\n\n\nCubes mentioned above are identical in height.\n\nHere is an illustration of the game. States on the right are obtained by performing one of the above operations on the state on the left, and grey cubes are added due to the operation.\n\n\n\nPlayer's goal is to make the height of all cells the same (i.e. so that each cell has the same number of cubes in it) using above operations. \n\nAlice, however, has found out that on some starting grids she may never reach the goal no matter what strategy she uses. Thus, she is wondering the number of initial grids such that \n\n * L \u2264 a_{i,j} \u2264 R for all 1 \u2264 i \u2264 n, 1 \u2264 j \u2264 m; \n * player can reach the goal using above operations. \n\n\n\nPlease help Alice with it. Notice that the answer might be large, please output the desired value modulo 998,244,353.\n\nInput\n\nThe only line contains four integers n, m, L and R (1\u2264 n,m,L,R \u2264 10^9, L \u2264 R, n \u22c5 m \u2265 2).\n\nOutput\n\nOutput one integer, representing the desired answer modulo 998,244,353.\n\nExamples\n\nInput\n\n\n2 2 1 1\n\n\nOutput\n\n\n1\n\n\nInput\n\n\n1 2 1 2\n\n\nOutput\n\n\n2\n\nNote\n\nIn the first sample, the only initial grid that satisfies the requirements is a_{1,1}=a_{2,1}=a_{1,2}=a_{2,2}=1. Thus the answer should be 1.\n\nIn the second sample, initial grids that satisfy the requirements are a_{1,1}=a_{1,2}=1 and a_{1,1}=a_{1,2}=2. Thus the answer should be 2.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport io\nimport os\n\nfrom collections import Counter, defaultdict, deque\n\nDEBUG = False\n\n\ndef modInverse(a, p):\n # Fermat's little theorem, a**(p-1) = 1 mod p\n return pow(a, p - 2, p)\n\n\ndef solve(N, M, L, R):\n MOD = 998244353\n\n num = R - L + 1\n numCells = N * M\n\n # Answer doesn't have to lie with L and R so can always add 2 so that only parity matters\n # Once it's a 0 and 1 matrix, adding to two adjacent is equivalent to a swap, so order doesn't matter\n # If the number of odd cells is even or number of even cells is even, flip their parity so the matrix is all odd or all even\n if numCells % 2 == 1:\n # Anything works since one of the parity must be even count\n return pow(num, numCells, MOD)\n\n # If num cells is even, can't have odd even cells and odd odd cells. Can only have even even cell and even odd cells\n # Want to choose `2 * i` odd cells within numCells\n # Once parity is fixed the number of choices is numOdds^(2 * i) * numEvens^(numCells - 2 * i)\n\n # Plug into wolfram alpha:\n # numCells = 2 * K\n # \\sum_{i=0}^{K} binomial(2 * K, 2 * i) * X^(2 * i) * Y^(2 * K - 2 * i)\n K = numCells // 2\n X = num // 2 # number of values within range [L, R] that are odd\n Y = num // 2 # ditto for even\n if num % 2 != 0:\n if L % 2 == 0:\n X += 1\n else:\n Y += 1\n\n assert numCells % 2 == 0\n\n ans = (\n (pow(X + Y, numCells, MOD) + pow(X - Y, numCells, MOD)) * modInverse(2, MOD)\n ) % MOD\n if DEBUG:\n\n def nCr(n, r):\n def fact(i):\n if i == 0:\n return 1\n return i * fact(i - 1)\n\n return fact(n) // (fact(n - r) * fact(r))\n\n brute = 0\n for i in range(numCells // 2 + 1):\n brute += nCr(numCells, 2 * i) * pow(X, 2 * i) * pow(Y, numCells - 2 * i)\n print(brute % MOD, ans)\n assert brute % MOD == ans\n\n return ans\n\n\nif DEBUG:\n for n in range(1, 5):\n for m in range(1, 5):\n for l in range(1, 5):\n for r in range(l, 5):\n if n * m < 2:\n continue\n solve(n, m, l, r)\n\n\nif __name__ == \"__main__\":\n input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline\n\n N, M, L, R = [int(x) for x in input().split()]\n ans = solve(N, M, L, R)\n print(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 2 1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 2 1 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2 2 3 4\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '290186487 840456810 858082702 987072033\\n', 'output': '366829057\\n'}, {'type': 'stdin_stdout', 'input': '646353335 282521795 600933409 772270276\\n', 'output': '13680108\\n'}, {'type': 'stdin_stdout', 'input': '763237207 414005655 302120151 421405724\\n', 'output': '193545831\\n'}, {'type': 'stdin_stdout', 'input': '692 210 44175861 843331069\\n', 'output': '714028205\\n'}, {'type': 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'memory_limit_bytes': 512000000}","problem_id":"vfc_79257","program":"```python\nimport io\nimport os\n\nfrom collections import Counter, defaultdict, deque\n\nDEBUG = False\n\n\ndef modInverse(a, p):\n # Fermat's little theorem, a**(p-1) = 1 mod p\n return pow(a, p - 2, p)\n\n\ndef solve(N, M, L, R):\n MOD = 998244353\n\n num = R - L + 1\n numCells = N * M\n\n # Answer doesn't have to lie with L and R so can always add 2 so that only parity matters\n # Once it's a 0 and 1 matrix, adding to two adjacent is equivalent to a swap, so order doesn't matter\n # If the number of odd cells is even or number of even cells is even, flip their parity so the matrix is all odd or all even\n if numCells % 2 == 1:\n # Anything works since one of the parity must be even count\n return pow(num, numCells, MOD)\n\n # If num cells is even, can't have odd even cells and odd odd cells. Can only have even even cell and even odd cells\n # Want to choose `2 * i` odd cells within numCells\n # Once parity is fixed the number of choices is numOdds^(2 * i) * numEvens^(numCells - 2 * i)\n\n # Plug into wolfram alpha:\n # numCells = 2 * K\n # \\sum_{i=0}^{K} binomial(2 * K, 2 * i) * X^(2 * i) * Y^(2 * K - 2 * i)\n K = numCells // 2\n X = num // 2 # number of values within range [L, R] that are odd\n Y = num // 2 # ditto for even\n if num % 2 != 0:\n if L % 2 == 0:\n X += 1\n else:\n Y += 1\n\n assert numCells % 2 == 0\n\n ans = (\n (pow(X + Y, numCells, MOD) + pow(X - Y, numCells, MOD)) * modInverse(2, MOD)\n ) % MOD\n if DEBUG:\n\n def nCr(n, r):\n def fact(i):\n if i == 0:\n return 1\n return i * fact(i - 1)\n\n return fact(n) // (fact(n - r) * fact(r))\n\n brute = 0\n for i in range(numCells // 2 + 1):\n brute += nCr(numCells, 2 * i) * pow(X, 2 * i) * pow(Y, numCells - 2 * i)\n print(brute % MOD, ans)\n assert brute % MOD == ans\n\n return ans\n\n\nif DEBUG:\n for n in range(1, 5):\n for m in range(1, 5):\n for l in range(1, 5):\n for r in range(l, 5):\n if n * m < 2:\n continue\n solve(n, m, l, r)\n\n\nif __name__ == \"__main__\":\n input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline\n\n N, M, L, R = [int(x) for x in input().split()]\n ans = solve(N, M, L, R)\n print(ans)\n\n```","inputs":"2 2 1 1\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12622},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1353_A. Most Unstable Array","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given two integers n and m. You have to construct the array a of length n consisting of non-negative integers (i.e. integers greater than or equal to zero) such that the sum of elements of this array is exactly m and the value \u2211_{i=1}^{n-1} |a_i - a_{i+1}| is the maximum possible. Recall that |x| is the absolute value of x.\n\nIn other words, you have to maximize the sum of absolute differences between adjacent (consecutive) elements. For example, if the array a=[1, 3, 2, 5, 5, 0] then the value above for this array is |1-3| + |3-2| + |2-5| + |5-5| + |5-0| = 2 + 1 + 3 + 0 + 5 = 11. Note that this example doesn't show the optimal answer but it shows how the required value for some array is calculated.\n\nYou have to answer t independent test cases.\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 10^4) \u2014 the number of test cases. Then t test cases follow.\n\nThe only line of the test case contains two integers n and m (1 \u2264 n, m \u2264 10^9) \u2014 the length of the array and its sum correspondingly.\n\nOutput\n\nFor each test case, print the answer \u2014 the maximum possible value of \u2211_{i=1}^{n-1} |a_i - a_{i+1}| for the array a consisting of n non-negative integers with the sum m.\n\nExample\n\nInput\n\n\n5\n1 100\n2 2\n5 5\n2 1000000000\n1000000000 1000000000\n\n\nOutput\n\n\n0\n2\n10\n1000000000\n2000000000\n\nNote\n\nIn the first test case of the example, the only possible array is [100] and the answer is obviously 0.\n\nIn the second test case of the example, one of the possible arrays is [2, 0] and the answer is |2-0| = 2.\n\nIn the third test case of the example, one of the possible arrays is [0, 2, 0, 3, 0] and the answer is |0-2| + |2-0| + |0-3| + |3-0| = 10.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nt = int(input())\nfor i in range(t):\n n, m = map(int, input().split())\n if n >= 3:\n print(2 * m)\n if n == 2:\n print(m)\n if n == 1:\n print(0)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 100\\n2 2\\n5 5\\n2 1000000000\\n1000000000 1000000000\\n', 'output': '0\\n2\\n10\\n1000000000\\n2000000000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9041 222\\n', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '1\\n343800 343800\\n', 'output': '687600\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9021 100\\n', 'output': '200\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9210 10000\\n', 'output': '20000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n103 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9021 10000\\n', 'output': '20000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n60 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n12345 12345\\n1 1\\n', 'output': '24690\\n0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9021 5\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n153 153\\n', 'output': '306\\n'}, {'type': 'stdin_stdout', 'input': '1\\n153 6\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n54 33\\n', 'output': '66\\n'}, {'type': 'stdin_stdout', 'input': '1\\n153 10\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '1\\n153 16\\n', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1001 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n53 100\\n', 'output': '200\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9022 222\\n', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '1\\n153 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n103 5\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n165 165\\n', 'output': '330\\n'}, {'type': 'stdin_stdout', 'input': '1\\n154 1002\\n', 'output': '2004\\n'}, {'type': 'stdin_stdout', 'input': '1\\n70 70\\n', 'output': '140\\n'}, {'type': 'stdin_stdout', 'input': '2\\n12345 12345\\n12345 12345\\n', 'output': '24690\\n24690\\n'}, {'type': 'stdin_stdout', 'input': '1\\n165 1000\\n', 'output': '2000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9021 222\\n', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '1\\n53 5\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n13616 222\\n', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '1\\n52916 343800\\n', 'output': '687600\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10012 100\\n', 'output': '200\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6955 10000\\n', 'output': '20000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n203 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9021 00000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n12345 6355\\n1 1\\n', 'output': '12710\\n0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9021 7\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '1\\n214 153\\n', 'output': '306\\n'}, {'type': 'stdin_stdout', 'input': '1\\n272 6\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n153 9\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '1\\n241 16\\n', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1001 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9022 234\\n', 'output': '468\\n'}, {'type': 'stdin_stdout', 'input': '1\\n104 5\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n165 98\\n', 'output': '196\\n'}, {'type': 'stdin_stdout', 'input': '1\\n162 1002\\n', 'output': '2004\\n'}, {'type': 'stdin_stdout', 'input': '1\\n70 86\\n', 'output': '172\\n'}, {'type': 'stdin_stdout', 'input': '2\\n12345 12345\\n12345 10662\\n', 'output': '24690\\n21324\\n'}, {'type': 'stdin_stdout', 'input': '1\\n165 1100\\n', 'output': '2200\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 100\\n2 0\\n5 5\\n2 1000000000\\n1000000000 1000000000\\n', 'output': '0\\n0\\n10\\n1000000000\\n2000000000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n13616 8\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '1\\n52916 42716\\n', 'output': '85432\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10012 110\\n', 'output': '220\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6955 11000\\n', 'output': '22000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9021 00010\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '2\\n12345 2376\\n1 1\\n', 'output': '4752\\n0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 33\\n', 'output': '33\\n'}, {'type': 'stdin_stdout', 'input': '1\\n241 29\\n', 'output': '58\\n'}, {'type': 'stdin_stdout', 'input': '1\\n165 172\\n', 'output': '344\\n'}, {'type': 'stdin_stdout', 'input': '1\\n162 1590\\n', 'output': '3180\\n'}, {'type': 'stdin_stdout', 'input': '2\\n12345 12345\\n12345 16965\\n', 'output': '24690\\n33930\\n'}, {'type': 'stdin_stdout', 'input': '1\\n13616 11\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '1\\n52916 78612\\n', 'output': '157224\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9021 10010\\n', 'output': '20020\\n'}, {'type': 'stdin_stdout', 'input': '1\\n152 151\\n', 'output': '302\\n'}, {'type': 'stdin_stdout', 'input': '1\\n418 12\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '1\\n256 14\\n', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '1\\n744 233\\n', 'output': '466\\n'}, {'type': 'stdin_stdout', 'input': '1\\n17 150\\n', 'output': '300\\n'}, {'type': 'stdin_stdout', 'input': '2\\n12345 12345\\n12345 10402\\n', 'output': '24690\\n20804\\n'}, {'type': 'stdin_stdout', 'input': '1\\n101 3\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 100\\n2 -1\\n5 5\\n2 1000000000\\n1000100000 1000000000\\n', 'output': '0\\n-1\\n10\\n1000000000\\n2000000000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n52916 132417\\n', 'output': '264834\\n'}, {'type': 'stdin_stdout', 'input': '1\\n890 111\\n', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3751 1500\\n1 1\\n', 'output': '3000\\n0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2654 15\\n', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '1\\n152 58\\n', 'output': '116\\n'}, {'type': 'stdin_stdout', 'input': '1\\n256 23\\n', 'output': '46\\n'}, {'type': 'stdin_stdout', 'input': '1\\n135 48\\n', 'output': '96\\n'}, {'type': 'stdin_stdout', 'input': '1\\n106 101\\n', 'output': '202\\n'}, {'type': 'stdin_stdout', 'input': '1\\n60 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 33\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n66 100\\n', 'output': '200\\n'}, {'type': 'stdin_stdout', 'input': '1\\n231 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2340 222\\n', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '1\\n100 5\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n242 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n91 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2654 7\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '1\\n152 153\\n', 'output': '306\\n'}, {'type': 'stdin_stdout', 'input': '1\\n418 6\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n256 9\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1011 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n66 110\\n', 'output': '220\\n'}, {'type': 'stdin_stdout', 'input': '1\\n744 234\\n', 'output': '468\\n'}, {'type': 'stdin_stdout', 'input': '1\\n231 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n201 5\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n17 86\\n', 'output': '172\\n'}, {'type': 'stdin_stdout', 'input': '1\\n123 1100\\n', 'output': '2200\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2340 6\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n101 5\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 100\\n2 0\\n5 5\\n2 1000000000\\n1000100000 1000000000\\n', 'output': '0\\n0\\n10\\n1000000000\\n2000000000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n890 110\\n', 'output': '220\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2453 11000\\n', 'output': '22000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n95 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n91 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3751 2376\\n1 1\\n', 'output': '4752\\n0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2654 9\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '1\\n135 29\\n', 'output': '58\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0001 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n106 100\\n', 'output': '200\\n'}, {'type': 'stdin_stdout', 'input': '1\\n201 8\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '1\\n291 172\\n', 'output': '344\\n'}, {'type': 'stdin_stdout', 'input': '1\\n320 1590\\n', 'output': '3180\\n'}, {'type': 'stdin_stdout', 'input': '1\\n123 0100\\n', 'output': '200\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2340 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n19657 11\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2001 11000\\n', 'output': '22000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4621 00010\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '1\\n91 3\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n719 12\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1163 233\\n', 'output': '466\\n'}, {'type': 'stdin_stdout', 'input': '1\\n201 12\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '1\\n181 172\\n', 'output': '344\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79261","program":"```python\nt = int(input())\nfor i in range(t):\n n, m = map(int, input().split())\n if n >= 3:\n print(2 * m)\n if n == 2:\n print(m)\n if n == 1:\n print(0)\n\n```","inputs":"5\n1 100\n2 2\n5 5\n2 1000000000\n1000000000 1000000000\n","output":"0\n2\n10\n1000000000\n2000000000\n","actual_output":"0\n2\n10\n1000000000\n2000000000\n","execution_success":true,"sample_index":12623},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"141_A. Amusing Joke","prompt":"Solve the following coding problem using the programming language python:\n\nSo, the New Year holidays are over. Santa Claus and his colleagues can take a rest and have guests at last. When two \"New Year and Christmas Men\" meet, thear assistants cut out of cardboard the letters from the guest's name and the host's name in honor of this event. Then the hung the letters above the main entrance. One night, when everyone went to bed, someone took all the letters of our characters' names. Then he may have shuffled the letters and put them in one pile in front of the door.\n\nThe next morning it was impossible to find the culprit who had made the disorder. But everybody wondered whether it is possible to restore the names of the host and his guests from the letters lying at the door? That is, we need to verify that there are no extra letters, and that nobody will need to cut more letters.\n\nHelp the \"New Year and Christmas Men\" and their friends to cope with this problem. You are given both inscriptions that hung over the front door the previous night, and a pile of letters that were found at the front door next morning.\n\nInput\n\nThe input file consists of three lines: the first line contains the guest's name, the second line contains the name of the residence host and the third line contains letters in a pile that were found at the door in the morning. All lines are not empty and contain only uppercase Latin letters. The length of each line does not exceed 100.\n\nOutput\n\nPrint \"YES\" without the quotes, if the letters in the pile could be permuted to make the names of the \"New Year and Christmas Men\". Otherwise, print \"NO\" without the quotes.\n\nExamples\n\nInput\n\nSANTACLAUS\nDEDMOROZ\nSANTAMOROZDEDCLAUS\n\n\nOutput\n\nYES\n\n\nInput\n\nPAPAINOEL\nJOULUPUKKI\nJOULNAPAOILELUPUKKI\n\n\nOutput\n\nNO\n\n\nInput\n\nBABBONATALE\nFATHERCHRISTMAS\nBABCHRISTMASBONATALLEFATHER\n\n\nOutput\n\nNO\n\nNote\n\nIn the first sample the letters written in the last line can be used to write the names and there won't be any extra letters left.\n\nIn the second sample letter \"P\" is missing from the pile and there's an extra letter \"L\".\n\nIn the third sample there's an extra letter \"L\".\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na = input()\nb = input()\n\nn = list(a) + list(b)\nn = sorted(n)\n\np = sorted(list(input()))\n\nif n == p:\n print(\"YES\")\nelse:\n print(\"NO\")\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'BABBONATALE\\nFATHERCHRISTMAS\\nBABCHRISTMASBONATALLEFATHER\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'SANTACLAUS\\nDEDMOROZ\\nSANTAMOROZDEDCLAUS\\n', 'output': 'YES'}, {'type': 'stdin_stdout', 'input': 'PAPAINOEL\\nJOULUPUKKI\\nJOULNAPAOILELUPUKKI\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'IDQRX\\nWETHO\\nODPDGBHVUVSSISROHQJTUKPUCLXABIZQQPPBPKOSEWGEHRSRRNBAVLYEMZISMWWGKHVTXKUGUXEFBSWOIWUHRJGMWBMHQLDZHBWA\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'PMUKBTRKFIAYVGBKHZHUSJYSSEPEOEWPOSPJLWLOCTUYZODLTUAFCMVKGQKRRUSOMPAYOTBTFPXYAZXLOADDEJBDLYOTXJCJYTHA\\nTWRRAJLCQJTKOKWCGUH\\nEWDPNXVCXWCDQCOYKKSOYTFSZTOOPKPRDKFJDETKSRAJRVCPDOBWUGPYRJPUWJYWCBLKOOTUPBESTOFXZHTYLLMCAXDYAEBUTAHM\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'EUHTSCENIPXLTSBMLFHD\\nIZAVSZPDLXOAGESUSE\\nLXAELAZ\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'KKK\\nKKK\\nZZZZZ\\n', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': 'B\\nA\\nAB\\n', 'output': 'YES'}, 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Specific Tastes of Andre ","prompt":"Solve the following coding problem using the programming language python:\n\nAndre has very specific tastes. Recently he started falling in love with arrays.\n\nAndre calls an nonempty array b good, if sum of its elements is divisible by the length of this array. For example, array [2, 3, 1] is good, as sum of its elements \u2014 6 \u2014 is divisible by 3, but array [1, 1, 2, 3] isn't good, as 7 isn't divisible by 4. \n\nAndre calls an array a of length n perfect if the following conditions hold: \n\n * Every nonempty subarray of this array is good. \n * For every i (1 \u2264 i \u2264 n), 1 \u2264 a_i \u2264 100. \n\n\n\nGiven a positive integer n, output any perfect array of length n. We can show that for the given constraints such an array always exists.\n\nAn array c is a subarray of an array d if c can be obtained from d by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.\n\nInput\n\nEach test contains multiple test cases. The first line contains the number of test cases t (1 \u2264 t \u2264 100). Description of the test cases follows.\n\nThe first and only line of every test case contains a single integer n (1 \u2264 n \u2264 100).\n\nOutput\n\nFor every test, output any perfect array of length n on a separate line. \n\nExample\n\nInput\n\n\n3\n1\n2\n4\n\n\nOutput\n\n\n24\n19 33\n7 37 79 49\n\nNote\n\nArray [19, 33] is perfect as all 3 its subarrays: [19], [33], [19, 33], have sums divisible by their lengths, and therefore are good.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nt=int(input())\nfor i in range(t):\n n= int(input())\n l=[1]*n\n print(*l)\n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1\\n2\\n4\\n', 'output': '1\\n1 1\\n1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n2\\n4\\n', 'output': '1\\n1 1\\n1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '100\\n1\\n0\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\n10\\n11\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n61\\n62\\n63\\n64\\n65\\n66\\n67\\n68\\n69\\n70\\n71\\n72\\n73\\n74\\n75\\n76\\n77\\n78\\n79\\n80\\n81\\n82\\n83\\n84\\n85\\n86\\n87\\n88\\n89\\n90\\n91\\n92\\n93\\n94\\n95\\n96\\n97\\n98\\n99\\n100\\n', 'output': '1 \\n\\n1 1 1 \\n1 1 1 1 \\n1 1 1 1 1 \\n1 1 1 1 1 1 \\n1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 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1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79277","program":"```python\nt=int(input())\nfor i in range(t):\n n= int(input())\n l=[1]*n\n print(*l)\n \n```","inputs":"3\n1\n2\n4\n","output":"1\n1 1\n1 1 1 1\n","actual_output":"1\n1 1\n1 1 1 1\n","execution_success":true,"sample_index":12625},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1462_F. The Treasure of The Segments","prompt":"Solve the following coding problem using the programming language python:\n\nPolycarp found n segments on the street. A segment with the index i is described by two integers l_i and r_i \u2014 coordinates of the beginning and end of the segment, respectively. Polycarp realized that he didn't need all the segments, so he wanted to delete some of them.\n\nPolycarp believes that a set of k segments is good if there is a segment [l_i, r_i] (1 \u2264 i \u2264 k) from the set, such that it intersects every segment from the set (the intersection must be a point or segment). For example, a set of 3 segments [[1, 4], [2, 3], [3, 6]] is good, since the segment [2, 3] intersects each segment from the set. Set of 4 segments [[1, 2], [2, 3], [3, 5], [4, 5]] is not good.\n\nPolycarp wonders, what is the minimum number of segments he has to delete so that the remaining segments form a good set?\n\nInput\n\nThe first line contains a single integer t (1 \u2264 t \u2264 2 \u22c5 10^5) \u2014 number of test cases. Then t test cases follow.\n\nThe first line of each test case contains a single integer n (1 \u2264 n \u2264 2 \u22c5 10^5) \u2014 the number of segments. This is followed by n lines describing the segments.\n\nEach segment is described by two integers l and r (1 \u2264 l \u2264 r \u2264 10^9) \u2014 coordinates of the beginning and end of the segment, respectively.\n\nIt is guaranteed that the sum of n for all test cases does not exceed 2 \u22c5 10^5.\n\nOutput\n\nFor each test case, output a single integer \u2014 the minimum number of segments that need to be deleted in order for the set of remaining segments to become good.\n\nExample\n\nInput\n\n\n4\n3\n1 4\n2 3\n3 6\n4\n1 2\n2 3\n3 5\n4 5\n5\n1 2\n3 8\n4 5\n6 7\n9 10\n5\n1 5\n2 4\n3 5\n3 8\n4 8\n\n\nOutput\n\n\n0\n1\n2\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n# region fastio\nBUFSIZE = 8192\nclass FastIO(IOBase):\n newlines = 0\n \n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n \n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n \n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n \n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n \n \nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n \n \nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline()\n \n# --------------------------------------------------------------------\n\ndef RL(): return map(int, sys.stdin.readline().split())\ndef RLL(): return list(map(int, sys.stdin.readline().split()))\ndef N(): return int(input())\ndef print_list(l):\n print(' '.join(map(str,l)))\n \n# sys.setrecursionlimit(100000)\n# import random\n# from functools import reduce\n# from functools import lru_cache\n# from heapq import *\n# from collections import deque as dq\n# import math\nimport bisect as bs\n# from collections import Counter\n# from collections import defaultdict as dc \n\nfor _ in range(N()):\n n = N()\n s = [tuple(RL()) for _ in range(n)]\n s0, s1 = sorted(p[0] for p in s), sorted(p[1] for p in s)\n print(n - max(bs.bisect_right(s0, p[1]) - bs.bisect_left(s1, p[0]) for p in s))\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 3\\n3 6\\n4\\n1 2\\n2 3\\n3 5\\n4 5\\n5\\n1 2\\n3 8\\n4 5\\n6 7\\n9 10\\n5\\n1 5\\n2 4\\n3 5\\n3 8\\n4 8\\n', 'output': '\\n0\\n1\\n2\\n0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1\\n1 2\\n1\\n1 2\\n1\\n1 2\\n1\\n1 2\\n1\\n1 2\\n1\\n1 2\\n1\\n1 2\\n', 'output': '0\\n0\\n0\\n0\\n0\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1\\n1 2\\n1\\n1 2\\n1\\n1 2\\n1\\n1 2\\n1\\n1 2\\n1\\n1 2\\n1\\n1 1\\n', 'output': '0\\n0\\n0\\n0\\n0\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 3\\n3 6\\n4\\n1 2\\n2 3\\n3 5\\n4 5\\n5\\n0 2\\n3 8\\n4 5\\n6 7\\n9 10\\n5\\n1 5\\n2 4\\n3 5\\n3 8\\n4 8\\n', 'output': '0\\n1\\n2\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 3\\n3 6\\n4\\n1 2\\n2 3\\n3 5\\n4 5\\n5\\n0 2\\n2 8\\n4 5\\n6 7\\n9 10\\n5\\n1 5\\n2 4\\n3 5\\n3 8\\n4 8\\n', 'output': '0\\n1\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 3\\n3 6\\n4\\n1 2\\n2 3\\n3 5\\n2 5\\n5\\n1 2\\n3 8\\n4 5\\n6 7\\n9 10\\n5\\n1 5\\n2 4\\n3 5\\n1 8\\n4 8\\n', 'output': '0\\n0\\n2\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n1 3\\n3 6\\n4\\n1 2\\n2 3\\n5 5\\n4 5\\n5\\n0 2\\n2 8\\n4 5\\n6 7\\n9 10\\n5\\n1 5\\n2 4\\n3 5\\n2 8\\n4 8\\n', 'output': '0\\n2\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 3\\n3 6\\n4\\n1 2\\n2 1\\n3 5\\n4 5\\n5\\n1 2\\n3 8\\n4 5\\n6 7\\n9 10\\n5\\n1 5\\n2 4\\n3 5\\n3 8\\n4 8\\n', 'output': '0\\n2\\n2\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 3\\n3 6\\n4\\n1 2\\n2 3\\n3 5\\n2 5\\n5\\n0 0\\n1 13\\n4 1\\n6 7\\n9 10\\n5\\n1 5\\n2 4\\n3 5\\n2 8\\n4 8\\n', 'output': '0\\n0\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n4 3\\n3 6\\n4\\n1 2\\n2 3\\n3 5\\n4 5\\n5\\n0 2\\n2 8\\n4 5\\n6 7\\n3 10\\n5\\n1 5\\n2 4\\n3 5\\n3 8\\n4 8\\n', 'output': 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2\\n1\\n1 2\\n1\\n1 2\\n1\\n2 3\\n1\\n1 3\\n1\\n1 7\\n1\\n1 4\\n', 'output': '0\\n0\\n0\\n0\\n0\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n1 3\\n3 6\\n4\\n1 2\\n2 3\\n5 5\\n4 5\\n5\\n0 0\\n2 8\\n4 5\\n7 7\\n9 10\\n5\\n1 9\\n2 8\\n3 5\\n2 2\\n4 16\\n', 'output': '0\\n2\\n2\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 1\\n3 6\\n4\\n1 3\\n2 3\\n3 5\\n2 5\\n5\\n0 0\\n1 13\\n4 1\\n6 3\\n9 10\\n5\\n1 5\\n2 4\\n3 5\\n2 8\\n4 8\\n', 'output': '0\\n0\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 6\\n3 6\\n4\\n1 2\\n4 3\\n3 5\\n4 5\\n5\\n1 2\\n3 7\\n4 8\\n6 7\\n9 10\\n5\\n1 5\\n2 3\\n3 5\\n1 8\\n3 12\\n', 'output': '0\\n1\\n2\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 1\\n3 6\\n4\\n0 1\\n2 3\\n3 5\\n2 5\\n5\\n0 2\\n3 7\\n4 5\\n6 7\\n3 10\\n5\\n1 5\\n2 11\\n3 5\\n1 8\\n3 8\\n', 'output': '0\\n1\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 3\\n3 6\\n4\\n1 3\\n2 1\\n3 5\\n4 5\\n5\\n1 2\\n3 8\\n4 5\\n6 7\\n9 10\\n5\\n1 5\\n3 4\\n1 9\\n3 8\\n4 8\\n', 'output': '0\\n1\\n2\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 3\\n3 10\\n4\\n1 2\\n2 3\\n3 5\\n4 5\\n5\\n0 2\\n4 8\\n1 10\\n6 7\\n5 10\\n5\\n1 4\\n2 4\\n3 5\\n2 8\\n4 8\\n', 'output': '0\\n1\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n2 6\\n3 6\\n4\\n1 2\\n4 3\\n3 5\\n2 5\\n5\\n1 2\\n3 7\\n4 8\\n6 14\\n9 10\\n5\\n1 6\\n2 3\\n1 5\\n1 8\\n3 8\\n', 'output': '0\\n0\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n2 4\\n2 3\\n3 6\\n4\\n0 2\\n2 3\\n3 5\\n2 5\\n5\\n0 0\\n1 26\\n4 1\\n6 3\\n9 10\\n5\\n1 5\\n2 4\\n5 5\\n2 8\\n4 8\\n', 'output': '0\\n0\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n3 6\\n3 6\\n4\\n1 2\\n4 3\\n3 5\\n2 5\\n5\\n1 2\\n3 7\\n4 8\\n2 7\\n9 10\\n5\\n1 6\\n2 3\\n3 5\\n1 8\\n4 8\\n', 'output': '0\\n0\\n1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3\\n1 4\\n3 6\\n3 6\\n4\\n1 2\\n4 3\\n3 5\\n2 5\\n5\\n1 2\\n3 7\\n4 8\\n6 7\\n6 10\\n5\\n1 6\\n5 3\\n3 5\\n1 8\\n3 8\\n', 'output': '0\\n0\\n1\\n0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 12, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79281","program":"```python\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n# region fastio\nBUFSIZE = 8192\nclass FastIO(IOBase):\n newlines = 0\n \n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n \n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n \n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n \n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n \n \nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n \n \nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline()\n \n# --------------------------------------------------------------------\n\ndef RL(): return map(int, sys.stdin.readline().split())\ndef RLL(): return list(map(int, sys.stdin.readline().split()))\ndef N(): return int(input())\ndef print_list(l):\n print(' '.join(map(str,l)))\n \n# sys.setrecursionlimit(100000)\n# import random\n# from functools import reduce\n# from functools import lru_cache\n# from heapq import *\n# from collections import deque as dq\n# import math\nimport bisect as bs\n# from collections import Counter\n# from collections import defaultdict as dc \n\nfor _ in range(N()):\n n = N()\n s = [tuple(RL()) for _ in range(n)]\n s0, s1 = sorted(p[0] for p in s), sorted(p[1] for p in s)\n print(n - max(bs.bisect_right(s0, p[1]) - bs.bisect_left(s1, p[0]) for p in s))\n\n\n\n```","inputs":"4\n3\n1 4\n2 3\n3 6\n4\n1 2\n2 3\n3 5\n4 5\n5\n1 2\n3 8\n4 5\n6 7\n9 10\n5\n1 5\n2 4\n3 5\n3 8\n4 8\n","output":"\n0\n1\n2\n0\n","actual_output":"0\n1\n2\n0\n","execution_success":true,"sample_index":12626},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1539_B. Love Song","prompt":"Solve the following coding problem using the programming language python:\n\nPetya once wrote a sad love song and shared it to Vasya. The song is a string consisting of lowercase English letters. Vasya made up q questions about this song. Each question is about a subsegment of the song starting from the l-th letter to the r-th letter. Vasya considers a substring made up from characters on this segment and repeats each letter in the subsegment k times, where k is the index of the corresponding letter in the alphabet. For example, if the question is about the substring \"abbcb\", then Vasya repeats letter 'a' once, each of the letters 'b' twice, letter 'c\" three times, so that the resulting string is \"abbbbcccbb\", its length is 10. Vasya is interested about the length of the resulting string.\n\nHelp Petya find the length of each string obtained by Vasya.\n\nInput\n\nThe first line contains two integers n and q (1\u2264 n\u2264 100 000, 1\u2264 q \u2264 100 000) \u2014 the length of the song and the number of questions. \n\nThe second line contains one string s \u2014 the song, consisting of n lowercase letters of English letters.\n\nVasya's questions are contained in the next q lines. Each line contains two integers l and r (1 \u2264 l \u2264 r \u2264 n) \u2014 the bounds of the question.\n\nOutput\n\nPrint q lines: for each question print the length of the string obtained by Vasya.\n\nExamples\n\nInput\n\n\n7 3\nabacaba\n1 3\n2 5\n1 7\n\n\nOutput\n\n\n4\n7\n11\n\n\nInput\n\n\n7 4\nabbabaa\n1 3\n5 7\n6 6\n2 4\n\n\nOutput\n\n\n5\n4\n1\n5\n\n\nInput\n\n\n13 7\nsonoshikumiwo\n1 5\n2 10\n7 7\n1 13\n4 8\n2 5\n3 9\n\n\nOutput\n\n\n82\n125\n9\n191\n62\n63\n97\n\nNote\n\nIn the first example Vasya is interested in three questions. In the first question Vasya considers the substring \"aba\", that transforms to \"abba\", so the answer is equal to 4. In the second question Vasya considers \"baca\", that transforms to \"bbaccca\", so the answer is 7. In the third question Vasya considers the string \"abacaba\",that transforms to \"abbacccabba\" of length 11.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\n\ninput = sys.stdin.readline\n\nn, q = map(int, input().split())\ns, psa = [ord(char) - 96 for char in input().strip()], [0]\nfor i in range(n):\n psa.append(s[i] + psa[i])\n\nfor _ in range(q):\n l, r = map(int, input().split())\n print(psa[r] - psa[l - 1])\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7 3\\nabacaba\\n1 3\\n2 5\\n1 7\\n', 'output': '4\\n7\\n11\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonoshikumiwo\\n1 5\\n2 10\\n7 7\\n1 13\\n4 8\\n2 5\\n3 9\\n', 'output': '82\\n125\\n9\\n191\\n62\\n63\\n97\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\nabbabaa\\n1 3\\n5 7\\n6 6\\n2 4\\n', 'output': '5\\n4\\n1\\n5\\n'}, {'type': 'stdin_stdout', 'input': '2 8\\nab\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n', 'output': '3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\nabacaba\\n2 3\\n2 5\\n1 7\\n', 'output': '3\\n7\\n11\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonokhisumiwo\\n1 5\\n2 10\\n7 7\\n1 13\\n4 8\\n2 5\\n3 9\\n', 'output': '74\\n125\\n9\\n191\\n62\\n55\\n97\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\nabacaba\\n2 6\\n2 5\\n1 7\\n', 'output': '9\\n7\\n11\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonokhisumiwo\\n1 7\\n2 10\\n7 7\\n1 13\\n4 8\\n2 5\\n3 9\\n', 'output': '91\\n125\\n9\\n191\\n62\\n55\\n97\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\nabacaba\\n2 6\\n2 6\\n1 7\\n', 'output': '9\\n9\\n11\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonokhisumiwo\\n1 2\\n2 10\\n7 7\\n1 13\\n4 8\\n2 5\\n3 9\\n', 'output': '34\\n125\\n9\\n191\\n62\\n55\\n97\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonoshikumiwo\\n1 5\\n2 10\\n7 7\\n1 13\\n4 8\\n2 5\\n1 9\\n', 'output': '82\\n125\\n9\\n191\\n62\\n63\\n131\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\nabbabaa\\n1 3\\n5 7\\n6 6\\n3 4\\n', 'output': '5\\n4\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\nabacaba\\n2 3\\n4 5\\n1 7\\n', 'output': '3\\n4\\n11\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\nabacaba\\n2 6\\n2 5\\n1 7\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonokhisumiwo\\n1 7\\n2 10\\n7 7\\n2 13\\n4 8\\n2 5\\n3 9\\n', 'output': '91\\n125\\n9\\n172\\n62\\n55\\n97\\n'}, {'type': 'stdin_stdout', 'input': '7 2\\nabacaba\\n2 6\\n2 6\\n1 7\\n', 'output': '9\\n9\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonokhisumiwo\\n1 2\\n2 10\\n7 7\\n1 13\\n4 9\\n2 5\\n3 9\\n', 'output': '34\\n125\\n9\\n191\\n83\\n55\\n97\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonoshikumiwo\\n1 5\\n2 10\\n7 7\\n1 13\\n4 8\\n2 5\\n2 9\\n', 'output': '82\\n125\\n9\\n191\\n62\\n63\\n112\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\nabbabaa\\n1 3\\n5 7\\n4 6\\n3 4\\n', 'output': '5\\n4\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\nabacaba\\n2 3\\n4 5\\n2 7\\n', 'output': '3\\n4\\n10\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonoshikumiwo\\n2 5\\n2 10\\n7 7\\n1 13\\n4 8\\n2 5\\n2 9\\n', 'output': '63\\n125\\n9\\n191\\n62\\n63\\n112\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\nabacaba\\n2 3\\n4 5\\n2 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\nabacaba\\n1 3\\n1 5\\n1 7\\n', 'output': '4\\n8\\n11\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonoshikumiwo\\n1 5\\n2 10\\n7 7\\n1 13\\n3 8\\n2 5\\n3 9\\n', 'output': '82\\n125\\n9\\n191\\n76\\n63\\n97\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonokhisumiwo\\n1 5\\n2 10\\n7 7\\n1 13\\n4 8\\n4 5\\n3 9\\n', 'output': '74\\n125\\n9\\n191\\n62\\n26\\n97\\n'}, {'type': 'stdin_stdout', 'input': '13 4\\nsonokhisumiwo\\n1 7\\n2 10\\n7 7\\n1 13\\n4 8\\n2 5\\n3 9\\n', 'output': '91\\n125\\n9\\n191\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonokhisumiwo\\n1 2\\n4 10\\n7 7\\n1 13\\n4 8\\n2 5\\n3 9\\n', 'output': '34\\n96\\n9\\n191\\n62\\n55\\n97\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\nabacaba\\n2 3\\n4 5\\n1 1\\n', 'output': '3\\n4\\n1\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonokhisumiwo\\n1 7\\n2 10\\n7 7\\n2 13\\n2 8\\n2 5\\n3 9\\n', 'output': '91\\n125\\n9\\n172\\n91\\n55\\n97\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\nabbabaa\\n1 3\\n5 7\\n4 6\\n3 6\\n', 'output': '5\\n4\\n4\\n6\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\nabacaba\\n2 3\\n5 5\\n2 7\\n', 'output': '3\\n1\\n10\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonoshikumiwo\\n2 5\\n2 10\\n7 7\\n1 13\\n4 8\\n2 5\\n2 12\\n', 'output': '63\\n125\\n9\\n191\\n62\\n63\\n157\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonoshikumiwo\\n1 5\\n2 10\\n7 7\\n1 13\\n3 12\\n2 5\\n3 9\\n', 'output': '82\\n125\\n9\\n191\\n142\\n63\\n97\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonokhisumiwo\\n1 5\\n2 10\\n7 7\\n1 13\\n1 8\\n4 5\\n3 9\\n', 'output': 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'output': '7\\n10\\n'}, {'type': 'stdin_stdout', 'input': '13 1\\nsonoshikumiwo\\n3 5\\n2 11\\n7 7\\n1 13\\n12 8\\n1 5\\n2 12\\n', 'output': '48\\n'}, {'type': 'stdin_stdout', 'input': '13 4\\nknnoshisumiwo\\n1 5\\n1 10\\n4 7\\n1 13\\n2 8\\n5 5\\n3 6\\n', 'output': '73\\n143\\n51\\n190\\n'}, {'type': 'stdin_stdout', 'input': '13 7\\nsonoshikumiwo\\n1 5\\n3 10\\n7 7\\n1 13\\n4 8\\n2 5\\n3 9\\n', 'output': '82\\n110\\n9\\n191\\n62\\n63\\n97\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\nabbabaa\\n1 3\\n3 7\\n6 6\\n3 4\\n', 'output': '5\\n7\\n1\\n3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79293","program":"```python\nimport sys\n\ninput = sys.stdin.readline\n\nn, q = map(int, input().split())\ns, psa = [ord(char) - 96 for char in input().strip()], [0]\nfor i in range(n):\n psa.append(s[i] + psa[i])\n\nfor _ in range(q):\n l, r = map(int, input().split())\n print(psa[r] - psa[l - 1])\n\n```","inputs":"7 3\nabacaba\n1 3\n2 5\n1 7\n","output":"4\n7\n11\n","actual_output":"4\n7\n11\n","execution_success":true,"sample_index":12628},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"233_A. Perfect Permutation","prompt":"Solve the following coding problem using the programming language python:\n\nA permutation is a sequence of integers p1, p2, ..., pn, consisting of n distinct positive integers, each of them doesn't exceed n. Let's denote the i-th element of permutation p as pi. We'll call number n the size of permutation p1, p2, ..., pn.\n\nNickolas adores permutations. He likes some permutations more than the others. He calls such permutations perfect. A perfect permutation is such permutation p that for any i (1 \u2264 i \u2264 n) (n is the permutation size) the following equations hold ppi = i and pi \u2260 i. Nickolas asks you to print any perfect permutation of size n for the given n.\n\nInput\n\nA single line contains a single integer n (1 \u2264 n \u2264 100) \u2014 the permutation size.\n\nOutput\n\nIf a perfect permutation of size n doesn't exist, print a single integer -1. Otherwise print n distinct integers from 1 to n, p1, p2, ..., pn \u2014 permutation p, that is perfect. Separate printed numbers by whitespaces.\n\nExamples\n\nInput\n\n1\n\n\nOutput\n\n-1\n\n\nInput\n\n2\n\n\nOutput\n\n2 1 \n\n\nInput\n\n4\n\n\nOutput\n\n2 1 4 3 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\nif n%2==1:\n print(-1)\nelse:\n arr1=[2*int(x) for x in range(1,int((n+2)/2))]\n arr2=[x-1 for x in arr1]\n for i in range(n//2):\n print(arr1[i],end=\" \")\n print(arr2[i],end=\" \")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n', 'output': '2 1 4 3 '}, {'type': 'stdin_stdout', 'input': '1\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '2\\n', 'output': '2 1 '}, {'type': 'stdin_stdout', 'input': '98\\n', 'output': '2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 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Rectangle Puzzle II","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a rectangle grid. That grid's size is n \u00d7 m. Let's denote the coordinate system on the grid. So, each point on the grid will have coordinates \u2014 a pair of integers (x, y) (0 \u2264 x \u2264 n, 0 \u2264 y \u2264 m).\n\nYour task is to find a maximum sub-rectangle on the grid (x1, y1, x2, y2) so that it contains the given point (x, y), and its length-width ratio is exactly (a, b). In other words the following conditions must hold: 0 \u2264 x1 \u2264 x \u2264 x2 \u2264 n, 0 \u2264 y1 \u2264 y \u2264 y2 \u2264 m, .\n\nThe sides of this sub-rectangle should be parallel to the axes. And values x1, y1, x2, y2 should be integers.\n\n\n\nIf there are multiple solutions, find the rectangle which is closest to (x, y). Here \"closest\" means the Euclid distance between (x, y) and the center of the rectangle is as small as possible. If there are still multiple solutions, find the lexicographically minimum one. Here \"lexicographically minimum\" means that we should consider the sub-rectangle as sequence of integers (x1, y1, x2, y2), so we can choose the lexicographically minimum one.\n\nInput\n\nThe first line contains six integers n, m, x, y, a, b (1 \u2264 n, m \u2264 109, 0 \u2264 x \u2264 n, 0 \u2264 y \u2264 m, 1 \u2264 a \u2264 n, 1 \u2264 b \u2264 m).\n\nOutput\n\nPrint four integers x1, y1, x2, y2, which represent the founded sub-rectangle whose left-bottom point is (x1, y1) and right-up point is (x2, y2).\n\nExamples\n\nInput\n\n9 9 5 5 2 1\n\n\nOutput\n\n1 3 9 7\n\n\nInput\n\n100 100 52 50 46 56\n\n\nOutput\n\n17 8 86 92\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#!/usr/bin/python3\n\ndef gcd(a, b):\n while a:\n a, b = b % a, a\n return b\n\nn, m, x, y, a, b = tuple(map(int, input().strip().split()))\ng = gcd(a, b)\na //= g\nb //= g\nk = min(n // a, m // b)\nw = k * a\nh = k * b\nans = [x - w + w // 2, y - h + h // 2, x + w // 2, y + h // 2]\nif ans[0] < 0:\n ans[2] -= ans[0]\n ans[0] = 0;\nif ans[1] < 0:\n ans[3] -= ans[1]\n ans[1] = 0\nif ans[2] > n:\n ans[0] -= ans[2] - n\n ans[2] = n\nif ans[3] > m:\n ans[1] -= ans[3] - m\n ans[3] = m\nprint('%d %d %d %d' % tuple(ans))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '100 100 52 50 46 56\\n', 'output': '17 8 86 92\\n'}, {'type': 'stdin_stdout', 'input': '9 9 5 5 2 1\\n', 'output': '1 3 9 7\\n'}, {'type': 'stdin_stdout', 'input': '1000000000 1000000000 500000000 500000000 500000000 500000001\\n', 'output': '250000000 249999999 750000000 750000000\\n'}, {'type': 'stdin_stdout', 'input': '47001271 53942737 7275347 1652337 33989593 48660013\\n', 'output': '0 0 33989593 48660013\\n'}, {'type': 'stdin_stdout', 'input': '5664399 63519726 1914884 13554302 2435218 44439020\\n', 'output': '697275 0 3132493 44439020\\n'}, {'type': 'stdin_stdout', 'input': 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'stdin_stdout', 'input': '100 100 21 63 2 41\\n', 'output': '19 18 23 100\\n'}, {'type': 'stdin_stdout', 'input': '4309493 76088457 2523467 46484812 199386 53662610\\n', 'output': '2423774 19653507 2623160 73316117\\n'}, {'type': 'stdin_stdout', 'input': '1000000000 1000001000 286536427 579261823 230782719 1150170645\\n', 'output': '209608854 195871608 363464000 962652038\\n'}, {'type': 'stdin_stdout', 'input': '41635044 16614992 15367724 11150551 30440245 12131698\\n', 'output': '147601 4483294 30587846 16614992\\n'}, {'type': 'stdin_stdout', 'input': '100 100 14 53 6 35\\n', 'output': '8 18 20 88\\n'}, {'type': 'stdin_stdout', 'input': '87453374 60940601 66348783 197017 78082907 33553425\\n', 'output': '9370467 0 87453374 33553425\\n'}, {'type': 'stdin_stdout', 'input': '33417574 19362112 17938303 4013355 4543381 2596692\\n', 'output': '1613907 0 33417574 18176844\\n'}, {'type': 'stdin_stdout', 'input': '47001271 53942737 4507392 1652337 33989593 48660013\\n', 'output': '0 0 33989593 48660013\\n'}, {'type': 'stdin_stdout', 'input': '1000010000 1000000000 448240235 35540513 992352294 907572080\\n', 'output': '0 0 992352294 907572080\\n'}, {'type': 'stdin_stdout', 'input': '36830763 28058366 30827357 2425729 11047103 20670351\\n', 'output': '25303805 0 36350908 20670351\\n'}, {'type': 'stdin_stdout', 'input': '85759276 125975096 9472017 1957176 10225118 547026\\n', 'output': '0 0 81800944 4376208\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79321","program":"```python\n#!/usr/bin/python3\n\ndef gcd(a, b):\n while a:\n a, b = b % a, a\n return b\n\nn, m, x, y, a, b = tuple(map(int, input().strip().split()))\ng = gcd(a, b)\na //= g\nb //= g\nk = min(n // a, m // b)\nw = k * a\nh = k * b\nans = [x - w + w // 2, y - h + h // 2, x + w // 2, y + h // 2]\nif ans[0] < 0:\n ans[2] -= ans[0]\n ans[0] = 0;\nif ans[1] < 0:\n ans[3] -= ans[1]\n ans[1] = 0\nif ans[2] > n:\n ans[0] -= ans[2] - n\n ans[2] = n\nif ans[3] > m:\n ans[1] -= ans[3] - m\n ans[3] = m\nprint('%d %d %d %d' % tuple(ans))\n```","inputs":"100 100 52 50 46 56\n","output":"17 8 86 92\n","actual_output":"17 8 86 92\n","execution_success":true,"sample_index":12630},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"352_C. Jeff and Rounding","prompt":"Solve the following coding problem using the programming language python:\n\nJeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly \"adjust\" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:\n\n * choose indexes i and j (i \u2260 j) that haven't been chosen yet; \n * round element ai to the nearest integer that isn't more than ai (assign to ai: \u230a ai \u230b); \n * round element aj to the nearest integer that isn't less than aj (assign to aj: \u2308 aj \u2309). \n\n\n\nNevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.\n\nInput\n\nThe first line contains integer n (1 \u2264 n \u2264 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 \u2264 ai \u2264 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.\n\nOutput\n\nIn a single line print a single real number \u2014 the required difference with exactly three digits after the decimal point.\n\nExamples\n\nInput\n\n3\n0.000 0.500 0.750 1.000 2.000 3.000\n\n\nOutput\n\n0.250\n\n\nInput\n\n3\n4469.000 6526.000 4864.000 9356.383 7490.000 995.896\n\n\nOutput\n\n0.279\n\nNote\n\nIn the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\nAs = list(map(float, input().split()))\n\nB = list(x - int(x) for x in As if x - int(x) > 0.000)\nl = len(B)\nif l == 0:\n\tprint('{:.3f}'.format(0))\n\texit(0)\n\nS = sum(x for x in B)\n\n\nll = l if l % 2 == 0 else l + 1\nans = 1e10\nfor i in range(max(0, l - n), (n if l > n else l) + 1):\n\tans = min(ans, abs(i - S))\n\nprint('{:.3f}'.format(ans))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n0.000 0.500 0.750 1.000 2.000 3.000\\n', 'output': '0.250\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4469.000 6526.000 4864.000 9356.383 7490.000 995.896\\n', 'output': '0.279\\n'}, {'type': 'stdin_stdout', 'input': '10\\n8003.867 4368.000 2243.298 3340.000 5384.489 1036.000 3506.115 4463.317 1477.000 2420.314 9391.186 1696.000 5857.833 244.314 8220.000 5879.647 5424.482 2631.000 7111.130 9157.536\\n', 'output': '0.472\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1.100 1.200\\n', 'output': '0.700\\n'}, {'type': 'stdin_stdout', 'input': '2\\n950.000 8019.170 3179.479 9482.963\\n', 'output': '0.388\\n'}, {'type': 'stdin_stdout', 'input': '3\\n673.674 9263.142 6780.000 9801.000 4640.000 8244.000\\n', 'output': '0.184\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6470.000 8295.000 8486.000 9855.000 223.000 579.549\\n', 'output': '0.451\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0.001 0.001 0.001 0.001\\n', 'output': '1.996\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0.061 0.330\\n', 'output': '0.609\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6418.669 157.986\\n', 'output': '0.655\\n'}, {'type': 'stdin_stdout', 'input': '7\\n223.999 322.000 677.000 3852.477 2568.390 2410.000 3202.511 2122.870 1566.000 8841.000 8176.424 74.586 3834.000 6847.427\\n', 'output': '0.316\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5528.000 205.000 5245.000 8832.000 385.000 7126.000 3988.538 9542.484 3044.000 5288.351 9342.000 9979.000 7096.000 5159.000 9400.000 4996.000 1698.000 5403.000\\n', 'output': '0.373\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2341.538 9232.119 6646.930 9316.834 5684.000 9078.705 7773.000 3823.674 6357.022 9866.925 310.271 6554.778 8341.098 8407.987\\n', 'output': '0.119\\n'}, {'type': 'stdin_stdout', 'input': '7\\n223.000 322.652 677.700 3852.000 2568.390 2410.713 3202.511 2122.870 1566.689 8841.790 8176.424 74.586 3834.000 6847.000\\n', 'output': '0.325\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0.999 0.999 0.999 0.999 0.999 0.999 0.000 0.000\\n', 'output': '1.994\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4469.437 6526.605 4864.154 9356.383 7490.717 995.896\\n', 'output': '0.192\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0.900 0.900\\n', 'output': '0.800\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001\\n', 'output': '4.990\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2341.000 9232.000 6646.000 9316.000 5684.000 9078.000 7773.978 3823.000 6357.000 9866.000 310.000 6554.000 8341.000 8407.987\\n', 'output': '0.035\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4103.000 6413.459 1796.000 3486.799 9011.590 5564.000 9044.473 5922.000 3350.039 3746.000\\n', 'output': '0.360\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0.200 0.200 0.200 0.200\\n', 'output': '1.200\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5528.000 205.031 5245.169 8832.592 385.656 7126.360 3988.000 9542.000 3044.042 5288.351 9342.000 9979.021 7096.000 5159.200 9400.000 4996.735 1698.000 5403.939\\n', 'output': '0.096\\n'}, {'type': 'stdin_stdout', 'input': '3\\n673.000 9263.000 6780.254 9801.548 4640.663 8244.038\\n', 'output': '0.497\\n'}, {'type': 'stdin_stdout', 'input': '10\\n8003.000 4368.194 2243.000 3340.287 5384.000 1036.456 3506.000 4463.000 1477.787 2420.000 9391.000 1696.913 5857.000 244.000 8220.322 5879.000 5424.000 2631.197 7111.000 9157.000\\n', 'output': '0.156\\n'}, {'type': 'stdin_stdout', 'input': '7\\n2341.538 9232.119 6646.930 9316.834 5684.640 9078.705 7773.000 3823.674 6357.022 9866.925 310.271 6554.778 8341.098 8407.000\\n', 'output': '0.466\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6470.649 8295.000 8486.000 9855.000 223.000 579.549\\n', 'output': '0.198\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6418.000 157.986\\n', 'output': '0.014\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900\\n', 'output': '8.000\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6470.649 8295.806 8486.730 9855.351 223.102 579.000\\n', 'output': '0.362\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0.999 0.999 0.999 0.999\\n', 'output': '1.996\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4469.000 6526.000 4864.000 9356.000 7490.000 995.000\\n', 'output': '0.000\\n'}, {'type': 'stdin_stdout', 'input': '7\\n223.999 322.000 677.000 3852.477 2568.000 2410.000 3202.000 2122.000 1566.000 8841.000 8176.000 74.000 3834.286 6847.427\\n', 'output': '0.189\\n'}, {'type': 'stdin_stdout', 'input': '10\\n8003.867 4368.000 2243.000 3340.287 5384.000 1036.456 3506.000 4463.000 1477.000 2420.314 9391.000 1696.000 5857.833 244.000 8220.000 5879.000 5424.482 2631.197 7111.000 9157.536\\n', 'output': '0.028\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0.001 0.001\\n', 'output': '0.998\\n'}, {'type': 'stdin_stdout', 'input': '9\\n5528.947 205.031 5245.169 8832.592 385.656 7126.360 3988.000 9542.000 3044.042 5288.000 9342.837 9979.021 7096.022 5159.200 9400.485 4996.735 1698.000 5403.939\\n', 'output': '0.036\\n'}, {'type': 'stdin_stdout', 'input': '2\\n950.335 8019.000 3179.000 9482.000\\n', 'output': '0.335\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4103.449 6413.000 1796.581 3486.000 9011.000 5564.010 9044.000 5922.539 3350.000 3746.191\\n', 'output': '0.230\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0.900 0.900 0.900 0.900 0.900 0.000\\n', 'output': '1.500\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0.100 0.100 0.100 0.100\\n', 'output': '1.600\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6418.000 157.000\\n', 'output': '0.000\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4103.000 6413.459 1796.000 3486.000 9011.000 5564.000 9044.000 5922.539 3350.039 3746.000\\n', 'output': '0.037\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79329","program":"```python\nn = int(input())\nAs = list(map(float, input().split()))\n\nB = list(x - int(x) for x in As if x - int(x) > 0.000)\nl = len(B)\nif l == 0:\n\tprint('{:.3f}'.format(0))\n\texit(0)\n\nS = sum(x for x in B)\n\n\nll = l if l % 2 == 0 else l + 1\nans = 1e10\nfor i in range(max(0, l - n), (n if l > n else l) + 1):\n\tans = min(ans, abs(i - S))\n\nprint('{:.3f}'.format(ans))\n\n```","inputs":"3\n0.000 0.500 0.750 1.000 2.000 3.000\n","output":"0.250\n","actual_output":"0.250\n","execution_success":true,"sample_index":12631},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"399_A. Pages","prompt":"Solve the following coding problem using the programming language python:\n\nUser ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:\n\n<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>\n\nWhen someone clicks the button \"<<\" he is redirected to page 1, and when someone clicks the button \">>\" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.\n\nThere are some conditions in the navigation:\n\n * If page 1 is in the navigation, the button \"<<\" must not be printed. \n * If page n is in the navigation, the button \">>\" must not be printed. \n * If the page number is smaller than 1 or greater than n, it must not be printed. \n\n\n\nYou can see some examples of the navigations. Make a program that prints the navigation.\n\nInput\n\nThe first and the only line contains three integers n, p, k (3 \u2264 n \u2264 100; 1 \u2264 p \u2264 n; 1 \u2264 k \u2264 n)\n\nOutput\n\nPrint the proper navigation. Follow the format of the output from the test samples.\n\nExamples\n\nInput\n\n17 5 2\n\n\nOutput\n\n<< 3 4 (5) 6 7 >> \n\nInput\n\n6 5 2\n\n\nOutput\n\n<< 3 4 (5) 6 \n\nInput\n\n6 1 2\n\n\nOutput\n\n(1) 2 3 >> \n\nInput\n\n6 2 2\n\n\nOutput\n\n1 (2) 3 4 >>\n\nInput\n\n9 6 3\n\n\nOutput\n\n<< 3 4 5 (6) 7 8 9\n\nInput\n\n10 6 3\n\n\nOutput\n\n<< 3 4 5 (6) 7 8 9 >>\n\nInput\n\n8 5 4\n\n\nOutput\n\n1 2 3 4 (5) 6 7 8 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, p, k = map(int, input().split())\nx = 0\nclose_symbol = True\npages = \"\"\nif((p-k) > 1):\n pages += \"<< \"\n\nif(k<=p):\n for x in range (k):\n if(p-k+x == 0):\n continue #means that p == k and need to ommit first navigation number\n pages += str(p-k+x) + \" \"\n\nelse:\n for x in range(1,p):\n pages += str(x) + \" \"\n if x == 0:\n x = k-p # we want to start in 2 for second part\n else:\n x = k-1#x = x+p\n\npages += \"(\" + str(p) + \") \"\n\nwhile(x >=0):\n if(p+k-x <= n):\n pages += str(p+k-x) + \" \"\n if(p+k-x >= n):\n close_symbol = False #no >> required\n x -= 1;\n\nif(close_symbol):\n pages += \">>\"\nprint(pages)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 5 2\\n', 'output': '<< 3 4 (5) 6 \\n'}, {'type': 'stdin_stdout', 'input': '6 1 2\\n', 'output': '(1) 2 3 >>\\n'}, {'type': 'stdin_stdout', 'input': '8 5 4\\n', 'output': '1 2 3 4 (5) 6 7 8 \\n'}, {'type': 'stdin_stdout', 'input': '6 2 2\\n', 'output': '1 (2) 3 4 >>\\n'}, {'type': 'stdin_stdout', 'input': '9 6 3\\n', 'output': '<< 3 4 5 (6) 7 8 9 \\n'}, {'type': 'stdin_stdout', 'input': '17 5 2\\n', 'output': '<< 3 4 (5) 6 7 >>\\n'}, {'type': 'stdin_stdout', 'input': '10 6 3\\n', 'output': '<< 3 4 5 (6) 7 8 9 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 35 12\\n', 'output': '<< 23 24 25 26 27 28 29 30 31 32 33 34 (35) 36 37 38 39 40 41 42 43 44 45 46 47 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 46 48\\n', 'output': '1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 (46) 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 >>\\n'}, {'type': 'stdin_stdout', 'input': '7 5 1\\n', 'output': '<< 4 (5) 6 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 46 38\\n', 'output': '<< 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 (46) 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 >>\\n'}, {'type': 'stdin_stdout', 'input': '6 1 2\\n', 'output': '(1) 2 3 >>\\n'}, {'type': 'stdin_stdout', 'input': '17 5 2\\n', 'output': '<< 3 4 (5) 6 7 >>\\n'}, {'type': 'stdin_stdout', 'input': '6 2 2\\n', 'output': '1 (2) 3 4 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 10 20\\n', 'output': '1 2 3 4 5 6 7 8 9 (10) 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 100 17\\n', 'output': '<< 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 (100) \\n'}, {'type': 'stdin_stdout', 'input': '3 1 3\\n', 'output': '(1) 2 3 \\n'}, {'type': 'stdin_stdout', 'input': '100 99 15\\n', 'output': '<< 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 (99) 100 \\n'}, {'type': 'stdin_stdout', 'input': '100 99 5\\n', 'output': '<< 94 95 96 97 98 (99) 100 \\n'}, {'type': 'stdin_stdout', 'input': '9 6 3\\n', 'output': '<< 3 4 5 (6) 7 8 9 \\n'}, {'type': 'stdin_stdout', 'input': '10 6 3\\n', 'output': '<< 3 4 5 (6) 7 8 9 >>\\n'}, {'type': 'stdin_stdout', 'input': '17 5 3\\n', 'output': '<< 2 3 4 (5) 6 7 8 >>\\n'}, {'type': 'stdin_stdout', 'input': '3 1 1\\n', 'output': '(1) 2 >>\\n'}, {'type': 'stdin_stdout', 'input': '5 2 1\\n', 'output': '1 (2) 3 >>\\n'}, {'type': 'stdin_stdout', 'input': '6 5 2\\n', 'output': '<< 3 4 (5) 6 \\n'}, {'type': 'stdin_stdout', 'input': '5 3 1\\n', 'output': '<< 2 (3) 4 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 25 11\\n', 'output': '<< 14 15 16 17 18 19 20 21 22 23 24 (25) 26 27 28 29 30 31 32 33 34 35 36 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 10 100\\n', 'output': '1 2 3 4 5 6 7 8 9 (10) 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 \\n'}, {'type': 'stdin_stdout', 'input': '5 5 5\\n', 'output': '1 2 3 4 (5) \\n'}, {'type': 'stdin_stdout', 'input': '3 2 1\\n', 'output': '1 (2) 3 \\n'}, {'type': 'stdin_stdout', 'input': '5 3 5\\n', 'output': '1 2 (3) 4 5 \\n'}, {'type': 'stdin_stdout', 'input': '100 35 28\\n', 'output': '<< 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 (35) 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 44 12\\n', 'output': '<< 32 33 34 35 36 37 38 39 40 41 42 43 (44) 45 46 47 48 49 50 51 52 53 54 55 56 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 45 48\\n', 'output': '1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 (45) 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 >>\\n'}, {'type': 'stdin_stdout', 'input': '10 5 1\\n', 'output': '<< 4 (5) 6 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 46 18\\n', 'output': '<< 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 (46) 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 >>\\n'}, {'type': 'stdin_stdout', 'input': '6 1 3\\n', 'output': '(1) 2 3 4 >>\\n'}, {'type': 'stdin_stdout', 'input': '17 10 3\\n', 'output': '<< 7 8 9 (10) 11 12 13 >>\\n'}, {'type': 'stdin_stdout', 'input': '6 2 1\\n', 'output': '1 (2) 3 >>\\n'}, {'type': 'stdin_stdout', 'input': '4 1 3\\n', 'output': '(1) 2 3 4\\n'}, {'type': 'stdin_stdout', 'input': '9 5 3\\n', 'output': '<< 2 3 4 (5) 6 7 8 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 24 11\\n', 'output': '<< 13 14 15 16 17 18 19 20 21 22 23 (24) 25 26 27 28 29 30 31 32 33 34 35 >>\\n'}, {'type': 'stdin_stdout', 'input': '6 3 1\\n', 'output': '<< 2 (3) 4 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 35 41\\n', 'output': '1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 (35) 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 >>\\n'}, {'type': 'stdin_stdout', 'input': '6 5 3\\n', 'output': '<< 2 3 4 (5) 6\\n'}, {'type': 'stdin_stdout', 'input': '6 1 1\\n', 'output': '(1) 2 >>\\n'}, {'type': 'stdin_stdout', 'input': '8 5 8\\n', 'output': '1 2 3 4 (5) 6 7 8\\n'}, {'type': 'stdin_stdout', 'input': '6 3 2\\n', 'output': '1 2 (3) 4 5 >>\\n'}, {'type': 'stdin_stdout', 'input': '9 8 3\\n', 'output': '<< 5 6 7 (8) 9\\n'}, {'type': 'stdin_stdout', 'input': '17 7 2\\n', 'output': '<< 5 6 (7) 8 9 >>\\n'}, {'type': 'stdin_stdout', 'input': '16 6 3\\n', 'output': '<< 3 4 5 (6) 7 8 9 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 47 12\\n', 'output': '<< 35 36 37 38 39 40 41 42 43 44 45 46 (47) 48 49 50 51 52 53 54 55 56 57 58 59 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 45 21\\n', 'output': '<< 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 (45) 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 >>\\n'}, {'type': 'stdin_stdout', 'input': '10 7 1\\n', 'output': '<< 6 (7) 8 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 14 18\\n', 'output': '1 2 3 4 5 6 7 8 9 10 11 12 13 (14) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 >>\\n'}, {'type': 'stdin_stdout', 'input': '17 8 3\\n', 'output': '<< 5 6 7 (8) 9 10 11 >>\\n'}, {'type': 'stdin_stdout', 'input': '18 5 5\\n', 'output': '1 2 3 4 (5) 6 7 8 9 10 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 24 3\\n', 'output': '<< 21 22 23 (24) 25 26 27 >>\\n'}, {'type': 'stdin_stdout', 'input': '6 4 1\\n', 'output': '<< 3 (4) 5 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 26 41\\n', 'output': '1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 (26) 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 >>\\n'}, {'type': 'stdin_stdout', 'input': '6 1 4\\n', 'output': '(1) 2 3 4 5 >>\\n'}, {'type': 'stdin_stdout', 'input': '9 3 3\\n', 'output': '1 2 (3) 4 5 6 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 72 12\\n', 'output': '<< 60 61 62 63 64 65 66 67 68 69 70 71 (72) 73 74 75 76 77 78 79\\n'}, {'type': 'stdin_stdout', 'input': '100 17 18\\n', 'output': '1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (17) 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 >>\\n'}, {'type': 'stdin_stdout', 'input': '4 1 2\\n', 'output': '(1) 2 3 >>\\n'}, {'type': 'stdin_stdout', 'input': '17 8 4\\n', 'output': '<< 4 5 6 7 (8) 9 10 11 12 >>\\n'}, {'type': 'stdin_stdout', 'input': '15 5 6\\n', 'output': '1 2 3 4 (5) 6 7 8 9 10 11 >>\\n'}, {'type': 'stdin_stdout', 'input': '9 3 4\\n', 'output': '1 2 (3) 4 5 6 7 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 72 9\\n', 'output': '<< 63 64 65 66 67 68 69 70 71 (72) 73 74 75 76 77 78 79\\n'}, {'type': 'stdin_stdout', 'input': '100 17 36\\n', 'output': '1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (17) 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 >>\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n', 'output': '1 (2) 3 4\\n'}, {'type': 'stdin_stdout', 'input': '12 9 5\\n', 'output': '<< 4 5 6 7 8 (9) 10 11 12\\n'}, {'type': 'stdin_stdout', 'input': '3 3 2\\n', 'output': '1 2 (3)\\n'}, {'type': 'stdin_stdout', 'input': '9 6 4\\n', 'output': '<< 2 3 4 5 (6) 7 8 9\\n'}, {'type': 'stdin_stdout', 'input': '79 29 9\\n', 'output': '<< 20 21 22 23 24 25 26 27 28 (29) 30 31 32 33 34 35 36 37 38 >>\\n'}, {'type': 'stdin_stdout', 'input': '100 3 36\\n', 'output': '1 2 (3) 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 >>\\n'}, {'type': 'stdin_stdout', 'input': '18 8 8\\n', 'output': '1 2 3 4 5 6 7 (8) 9 10 11 12 13 14 15 16 >>\\n'}, {'type': 'stdin_stdout', 'input': '12 10 5\\n', 'output': '<< 5 6 7 8 9 (10) 11 12\\n'}, {'type': 'stdin_stdout', 'input': '9 6 8\\n', 'output': '1 2 3 4 5 (6) 7 8 9\\n'}, {'type': 'stdin_stdout', 'input': '79 29 8\\n', 'output': '<< 21 22 23 24 25 26 27 28 (29) 30 31 32 33 34 35 36 37 >>\\n'}, {'type': 'stdin_stdout', 'input': '4 4 4\\n', 'output': '1 2 3 (4)\\n'}, {'type': 'stdin_stdout', 'input': '18 4 8\\n', 'output': '1 2 3 (4) 5 6 7 8 9 10 11 12 >>\\n'}, {'type': 'stdin_stdout', 'input': '26 9 5\\n', 'output': '<< 4 5 6 7 8 (9) 10 11 12 13 14 >>\\n'}, {'type': 'stdin_stdout', 'input': '9 6 1\\n', 'output': '<< 5 (6) 7 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 6 8\\n', 'output': '1 2 3 4 5 (6) 7 8 9 10 11 12 13 14 >>\\n'}, {'type': 'stdin_stdout', 'input': '46 9 9\\n', 'output': '1 2 3 4 5 6 7 8 (9) 10 11 12 13 14 15 16 17 18 >>\\n'}, {'type': 'stdin_stdout', 'input': '46 9 17\\n', 'output': '1 2 3 4 5 6 7 8 (9) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 >>\\n'}, {'type': 'stdin_stdout', 'input': '17 14 1\\n', 'output': '<< 13 (14) 15 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 15 8\\n', 'output': '<< 7 8 9 10 11 12 13 14 (15) 16 17 18 19 20 21 22 23 >>\\n'}, {'type': 'stdin_stdout', 'input': '46 1 17\\n', 'output': '(1) 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 >>\\n'}, {'type': 'stdin_stdout', 'input': '17 9 1\\n', 'output': '<< 8 (9) 10 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 14 8\\n', 'output': '<< 6 7 8 9 10 11 12 13 (14) 15 16 17 18 19 20 21 22 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 14 7\\n', 'output': '<< 7 8 9 10 11 12 13 (14) 15 16 17 18 19 20 21 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 12 7\\n', 'output': '<< 5 6 7 8 9 10 11 (12) 13 14 15 16 17 18 19 >>\\n'}, {'type': 'stdin_stdout', 'input': '18 5 3\\n', 'output': '<< 2 3 4 (5) 6 7 8 >>\\n'}, {'type': 'stdin_stdout', 'input': '4 1 4\\n', 'output': '(1) 2 3 4\\n'}, {'type': 'stdin_stdout', 'input': '8 2 1\\n', 'output': '1 (2) 3 >>\\n'}, {'type': 'stdin_stdout', 'input': '4 1 1\\n', 'output': '(1) 2 >>\\n'}, {'type': 'stdin_stdout', 'input': '15 5 3\\n', 'output': '<< 2 3 4 (5) 6 7 8 >>\\n'}, {'type': 'stdin_stdout', 'input': '12 3 2\\n', 'output': '1 2 (3) 4 5 >>\\n'}, {'type': 'stdin_stdout', 'input': '26 7 2\\n', 'output': '<< 5 6 (7) 8 9 >>\\n'}, {'type': 'stdin_stdout', 'input': '16 5 3\\n', 'output': '<< 2 3 4 (5) 6 7 8 >>\\n'}, {'type': 'stdin_stdout', 'input': '17 7 1\\n', 'output': '<< 6 (7) 8 >>\\n'}, {'type': 'stdin_stdout', 'input': '5 1 1\\n', 'output': '(1) 2 >>\\n'}, {'type': 'stdin_stdout', 'input': '12 5 5\\n', 'output': '1 2 3 4 (5) 6 7 8 9 10 >>\\n'}, {'type': 'stdin_stdout', 'input': '23 3 2\\n', 'output': '1 2 (3) 4 5 >>\\n'}, {'type': 'stdin_stdout', 'input': '16 5 1\\n', 'output': '<< 4 (5) 6 >>\\n'}, {'type': 'stdin_stdout', 'input': '18 8 4\\n', 'output': '<< 4 5 6 7 (8) 9 10 11 12 >>\\n'}, {'type': 'stdin_stdout', 'input': '10 1 1\\n', 'output': '(1) 2 >>\\n'}, {'type': 'stdin_stdout', 'input': '15 5 5\\n', 'output': '1 2 3 4 (5) 6 7 8 9 10 >>\\n'}, {'type': 'stdin_stdout', 'input': '4 2 4\\n', 'output': '1 (2) 3 4\\n'}, {'type': 'stdin_stdout', 'input': '26 5 5\\n', 'output': '1 2 3 4 (5) 6 7 8 9 10 >>\\n'}, {'type': 'stdin_stdout', 'input': '9 6 7\\n', 'output': '1 2 3 4 5 (6) 7 8 9\\n'}, {'type': 'stdin_stdout', 'input': '79 4 8\\n', 'output': '1 2 3 (4) 5 6 7 8 9 10 11 12 >>\\n'}, {'type': 'stdin_stdout', 'input': '46 9 5\\n', 'output': '<< 4 5 6 7 8 (9) 10 11 12 13 14 >>\\n'}, {'type': 'stdin_stdout', 'input': '9 7 1\\n', 'output': '<< 6 (7) 8 >>\\n'}, {'type': 'stdin_stdout', 'input': '79 8 8\\n', 'output': '1 2 3 4 5 6 7 (8) 9 10 11 12 13 14 15 16 >>\\n'}, {'type': 'stdin_stdout', 'input': '11 9 1\\n', 'output': '<< 8 (9) 10 >>\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79337","program":"```python\nn, p, k = map(int, input().split())\nx = 0\nclose_symbol = True\npages = \"\"\nif((p-k) > 1):\n pages += \"<< \"\n\nif(k<=p):\n for x in range (k):\n if(p-k+x == 0):\n continue #means that p == k and need to ommit first navigation number\n pages += str(p-k+x) + \" \"\n\nelse:\n for x in range(1,p):\n pages += str(x) + \" \"\n if x == 0:\n x = k-p # we want to start in 2 for second part\n else:\n x = k-1#x = x+p\n\npages += \"(\" + str(p) + \") \"\n\nwhile(x >=0):\n if(p+k-x <= n):\n pages += str(p+k-x) + \" \"\n if(p+k-x >= n):\n close_symbol = False #no >> required\n x -= 1;\n\nif(close_symbol):\n pages += \">>\"\nprint(pages)\n\n```","inputs":"6 5 2\n","output":"<< 3 4 (5) 6 \n","actual_output":"<< 3 4 (5) 6 \n","execution_success":true,"sample_index":12632},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"421_B. Start Up","prompt":"Solve the following coding problem using the programming language python:\n\nRecently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?\n\nThe market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.\n\nThere are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.\n\nInput\n\nThe first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font: \n\n\n\nOutput\n\nPrint 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).\n\nExamples\n\nInput\n\nAHA\n\n\nOutput\n\nYES\n\n\nInput\n\nZ\n\n\nOutput\n\nNO\n\n\nInput\n\nXO\n\n\nOutput\n\nNO\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef main():\n s = input()\n print((\"NO\", \"YES\")[s == s[::-1] and all(c in \"AHIMOTUVWXY\" for c in s)])\n\n\nif __name__ == '__main__':\n main()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'XO\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'Z\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'AHA\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'WYYW\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'Q\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'R\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'A\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'Y\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'OVWIHIWVYXMVAAAATOXWOIUUHYXHIHHVUIOOXWHOXTUUMUUVHVWWYUTIAUAITAOMHXWMTTOIVMIVOTHOVOIOHYHAOXWAUVWAVIVM\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'C\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'QDPINBMCRFWXPDBFGOZVVOCEMJRUCTOADEWEGTVBVBFWWRPGYEEYGPRWWFBVBVTGEWEDAOTCURJMECOVVZOGFBDPXWFRCMBNIPDQ\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'ZZ\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'JL\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'S\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'V\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'MITIM\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'E\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'ABA\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'I\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'HNCMEEMCNH\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'H\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'YYHUIUGYI\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'OMMMAAMMMO\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'AABAA\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'K\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'AAAAAABAAAAAA\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'AAAKTAAA\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'W\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': 'AAJAA\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'AEEA\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'D\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'VO\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'F\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'AZA\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': 'SSS\\n', 'output': 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'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79341","program":"```python\ndef main():\n s = input()\n print((\"NO\", \"YES\")[s == s[::-1] and all(c in \"AHIMOTUVWXY\" for c in s)])\n\n\nif __name__ == '__main__':\n main()\n\n```","inputs":"XO\n","output":"NO\n","actual_output":"NO\n","execution_success":true,"sample_index":12633},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"46_A. Ball Game","prompt":"Solve the following coding problem using the programming language python:\n\nA kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count. \n\nThe game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.\n\nThe problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.\n\nInput\n\nThe first line contains integer n (2 \u2264 n \u2264 100) which indicates the number of kids in the circle.\n\nOutput\n\nIn the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.\n\nExamples\n\nInput\n\n10\n\n\nOutput\n\n2 4 7 1 6 2 9 7 6\n\n\nInput\n\n3\n\n\nOutput\n\n2 1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#----Kuzlyaev-Nikita-Codeforces-----\n#------------03.04.2020-------------\n\nalph=\"abcdefghijklmnopqrstuvwxyz\"\n\n#-----------------------------------\n\nn=int(input())\nnow_child=1\nfor i in range(1,n):\n now_child+=i\n if now_child>n:\n now_child=now_child%n\n print(now_child,end=\" \")\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10\\n', 'output': '2 4 7 1 6 2 9 7 6 '}, {'type': 'stdin_stdout', 'input': '3\\n', 'output': '2 1 '}, {'type': 'stdin_stdout', 'input': '6\\n', 'output': '2 4 1 5 4 '}, {'type': 'stdin_stdout', 'input': '9\\n', 'output': '2 4 7 2 7 4 2 1 '}, {'type': 'stdin_stdout', 'input': '25\\n', 'output': '2 4 7 11 16 22 4 12 21 6 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","execution_success":true,"sample_index":12634},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"516_A. Drazil and Factorial","prompt":"Solve the following coding problem using the programming language python:\n\nDrazil is playing a math game with Varda.\n\nLet's define for positive integer x as a product of factorials of its digits. For example, .\n\nFirst, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:\n\n1. x doesn't contain neither digit 0 nor digit 1.\n\n2. = .\n\nHelp friends find such number.\n\nInput\n\nThe first line contains an integer n (1 \u2264 n \u2264 15) \u2014 the number of digits in a.\n\nThe second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.\n\nOutput\n\nOutput a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.\n\nExamples\n\nInput\n\n4\n1234\n\n\nOutput\n\n33222\n\n\nInput\n\n3\n555\n\n\nOutput\n\n555\n\nNote\n\nIn the first case, \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n\ndef add(x, i):\n if i == 1:\n pass\n if i == 2:\n x.append(2)\n if i == 3:\n x.append(3)\n if i == 4:\n x.append(2)\n x.append(2)\n x.append(3)\n if i == 5:\n x.append(5)\n if i == 6:\n x.append(5)\n x.append(3)\n if i == 7:\n x.append(7)\n if i == 8:\n x.append(7)\n x.append(2)\n x.append(2)\n x.append(2)\n if i == 9:\n x.append(7)\n x.append(2)\n x.append(3)\n x.append(3)\n\n\ndef work(a):\n x = []\n for i in a:\n add(x, int(i))\n x.sort(reverse=True)\n print(''.join([str(c) for c in x]))\n\n\n\ninput()\nwork(input())\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1234\\n', 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i):\n if i == 1:\n pass\n if i == 2:\n x.append(2)\n if i == 3:\n x.append(3)\n if i == 4:\n x.append(2)\n x.append(2)\n x.append(3)\n if i == 5:\n x.append(5)\n if i == 6:\n x.append(5)\n x.append(3)\n if i == 7:\n x.append(7)\n if i == 8:\n x.append(7)\n x.append(2)\n x.append(2)\n x.append(2)\n if i == 9:\n x.append(7)\n x.append(2)\n x.append(3)\n x.append(3)\n\n\ndef work(a):\n x = []\n for i in a:\n add(x, int(i))\n x.sort(reverse=True)\n print(''.join([str(c) for c in x]))\n\n\n\ninput()\nwork(input())\n\n```","inputs":"4\n1234\n","output":"33222\n","actual_output":"33222\n","execution_success":true,"sample_index":12636},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"543_A. Writing Code","prompt":"Solve the following coding problem using the programming language python:\n\nProgrammers working on a large project have just received a task to write exactly m lines of code. There are n programmers working on a project, the i-th of them makes exactly ai bugs in every line of code that he writes. \n\nLet's call a sequence of non-negative integers v1, v2, ..., vn a plan, if v1 + v2 + ... + vn = m. The programmers follow the plan like that: in the beginning the first programmer writes the first v1 lines of the given task, then the second programmer writes v2 more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan good, if all the written lines of the task contain at most b bugs in total.\n\nYour task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer mod.\n\nInput\n\nThe first line contains four integers n, m, b, mod (1 \u2264 n, m \u2264 500, 0 \u2264 b \u2264 500; 1 \u2264 mod \u2264 109 + 7) \u2014 the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively and the modulo you should use when printing the answer.\n\nThe next line contains n space-separated integers a1, a2, ..., an (0 \u2264 ai \u2264 500) \u2014 the number of bugs per line for each programmer.\n\nOutput\n\nPrint a single integer \u2014 the answer to the problem modulo mod.\n\nExamples\n\nInput\n\n3 3 3 100\n1 1 1\n\n\nOutput\n\n10\n\n\nInput\n\n3 6 5 1000000007\n1 2 3\n\n\nOutput\n\n0\n\n\nInput\n\n3 5 6 11\n1 2 1\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nimport copy\ninput=sys.stdin.readline\nn,m,b,mod=map(int,input().split())\na=list(map(int,input().split()))\ndp=[[0]*(m+1) for i in range(b+1)]\ndp[0][0]=1\nfor i in range(n):\n for j in range(a[i],b+1):\n for k in range(1,m+1):\n dp[j][k]=(dp[j][k]+dp[j-a[i]][k-1])%mod\nans=0\nfor i in range(b+1):\n ans+=dp[i][m]\n ans%=mod\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 6 5 1000000007\\n1 2 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 3 3 100\\n1 1 1\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '3 5 6 11\\n1 2 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '100 100 100 960694994\\n1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1\\n', 'output': '527886216\\n'}, {'type': 'stdin_stdout', 'input': 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Corporation Mail","prompt":"Solve the following coding problem using the programming language python:\n\nThe Beroil corporation structure is hierarchical, that is it can be represented as a tree. Let's examine the presentation of this structure as follows:\n\n * employee ::= name. | name:employee1,employee2, ... ,employeek.\n * name ::= name of an employee \n\n\n\nThat is, the description of each employee consists of his name, a colon (:), the descriptions of all his subordinates separated by commas, and, finally, a dot. If an employee has no subordinates, then the colon is not present in his description.\n\nFor example, line MIKE:MAX.,ARTEM:MIKE..,DMITRY:DMITRY.,DMITRY... is the correct way of recording the structure of a corporation where the director MIKE has subordinates MAX, ARTEM and DMITRY. ARTEM has a subordinate whose name is MIKE, just as the name of his boss and two subordinates of DMITRY are called DMITRY, just like himself.\n\nIn the Beroil corporation every employee can only correspond with his subordinates, at that the subordinates are not necessarily direct. Let's call an uncomfortable situation the situation when a person whose name is s writes a letter to another person whose name is also s. In the example given above are two such pairs: a pair involving MIKE, and two pairs for DMITRY (a pair for each of his subordinates).\n\nYour task is by the given structure of the corporation to find the number of uncomfortable pairs in it.\n\n\n\nInput\n\nThe first and single line contains the corporation structure which is a string of length from 1 to 1000 characters. It is guaranteed that the description is correct. Every name is a string consisting of capital Latin letters from 1 to 10 symbols in length.\n\nOutput\n\nPrint a single number \u2014 the number of uncomfortable situations in the company.\n\nExamples\n\nInput\n\nMIKE:MAX.,ARTEM:MIKE..,DMITRY:DMITRY.,DMITRY...\n\n\nOutput\n\n3\n\n\nInput\n\nA:A..\n\n\nOutput\n\n1\n\n\nInput\n\nA:C:C:C:C.....\n\n\nOutput\n\n6\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#!/usr/bin/env python3 \n\ntree = input().strip()\n\ndef get_answer(tree, start_index = 0, prev = []):\n colon_index = tree.find(':', start_index)\n period_index = tree.find('.', start_index)\n name_end_index = colon_index if ((colon_index != -1) and (colon_index < period_index)) else period_index\n name = tree[start_index:name_end_index]\n answer = prev.count(name)\n if ((colon_index == -1) or (period_index < colon_index)):\n return (answer, 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get_answer(tree, start_index = 0, prev = []):\n colon_index = tree.find(':', start_index)\n period_index = tree.find('.', start_index)\n name_end_index = colon_index if ((colon_index != -1) and (colon_index < period_index)) else period_index\n name = tree[start_index:name_end_index]\n answer = prev.count(name)\n if ((colon_index == -1) or (period_index < colon_index)):\n return (answer, period_index+1)\n else:\n # Recurse\n prev_names = prev + [name]\n next_start = colon_index\n while tree[next_start] != '.':\n (sub_answer, next_start) = get_answer(tree, next_start+1, prev_names)\n answer += sub_answer\n return (answer, next_start+1)\n\nprint(get_answer(tree)[0])\n```","inputs":"MIKE:MAX.,ARTEM:MIKE..,DMITRY:DMITRY.,DMITRY...\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12638},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"591_A. Wizards' Duel","prompt":"Solve the following coding problem using the programming language python:\n\nHarry Potter and He-Who-Must-Not-Be-Named engaged in a fight to the death once again. This time they are located at opposite ends of the corridor of length l. Two opponents simultaneously charge a deadly spell in the enemy. We know that the impulse of Harry's magic spell flies at a speed of p meters per second, and the impulse of You-Know-Who's magic spell flies at a speed of q meters per second.\n\nThe impulses are moving through the corridor toward each other, and at the time of the collision they turn round and fly back to those who cast them without changing their original speeds. Then, as soon as the impulse gets back to it's caster, the wizard reflects it and sends again towards the enemy, without changing the original speed of the impulse.\n\nSince Harry has perfectly mastered the basics of magic, he knows that after the second collision both impulses will disappear, and a powerful explosion will occur exactly in the place of their collision. However, the young wizard isn't good at math, so he asks you to calculate the distance from his position to the place of the second meeting of the spell impulses, provided that the opponents do not change positions during the whole fight.\n\nInput\n\nThe first line of the input contains a single integer l (1 \u2264 l \u2264 1 000) \u2014 the length of the corridor where the fight takes place.\n\nThe second line contains integer p, the third line contains integer q (1 \u2264 p, q \u2264 500) \u2014 the speeds of magical impulses for Harry Potter and He-Who-Must-Not-Be-Named, respectively.\n\nOutput\n\nPrint a single real number \u2014 the distance from the end of the corridor, where Harry is located, to the place of the second meeting of the spell impulses. Your answer will be considered correct if its absolute or relative error will not exceed 10 - 4. \n\nNamely: let's assume that your answer equals a, and the answer of the jury is b. The checker program will consider your answer correct if .\n\nExamples\n\nInput\n\n100\n50\n50\n\n\nOutput\n\n50\n\n\nInput\n\n199\n60\n40\n\n\nOutput\n\n119.4\n\nNote\n\nIn the first sample the speeds of the impulses are equal, so both of their meetings occur exactly in the middle of the corridor.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nl=int(input())\np=int(input())\nq=int(input())\nv=p+q\nt=l/v\nd=p*t\nprint(d)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '199\\n60\\n40\\n', 'output': '119.4'}, {'type': 'stdin_stdout', 'input': '100\\n50\\n50\\n', 'output': '50'}, {'type': 'stdin_stdout', 'input': '978\\n467\\n371\\n', 'output': '545.0190930787589\\n'}, {'type': 'stdin_stdout', 'input': '101\\n11\\n22\\n', 'output': '33.666666666666664\\n'}, {'type': 'stdin_stdout', 'input': '349\\n478\\n378\\n', 'output': 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'input': '978\\n884\\n81\\n', 'output': '895.9088082901554\\n'}, {'type': 'stdin_stdout', 'input': '349\\n116\\n260\\n', 'output': '107.67021276595744\\n'}, {'type': 'stdin_stdout', 'input': '600\\n356\\n23\\n', 'output': '563.5883905013192\\n'}, {'type': 'stdin_stdout', 'input': '425\\n244\\n68\\n', 'output': '332.37179487179486\\n'}, {'type': 'stdin_stdout', 'input': '961\\n116\\n18\\n', 'output': '831.9104477611941\\n'}, {'type': 'stdin_stdout', 'input': '961\\n593\\n50\\n', 'output': '886.2721617418351\\n'}, {'type': 'stdin_stdout', 'input': '133\\n15\\n82\\n', 'output': '20.567010309278352\\n'}, {'type': 'stdin_stdout', 'input': '690\\n499\\n79\\n', 'output': '595.6920415224914\\n'}, {'type': 'stdin_stdout', 'input': '539\\n105\\n61\\n', 'output': '340.933734939759\\n'}, {'type': 'stdin_stdout', 'input': '496\\n622\\n901\\n', 'output': '202.56861457649376\\n'}, {'type': 'stdin_stdout', 'input': '1\\n104\\n205\\n', 'output': '0.3365695792880259\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79369","program":"```python\nl=int(input())\np=int(input())\nq=int(input())\nv=p+q\nt=l/v\nd=p*t\nprint(d)\n```","inputs":"199\n60\n40\n","output":"119.4","actual_output":"119.4\n","execution_success":true,"sample_index":12639},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"612_E. Square Root of Permutation","prompt":"Solve the following coding problem using the programming language python:\n\nA permutation of length n is an array containing each integer from 1 to n exactly once. For example, q = [4, 5, 1, 2, 3] is a permutation. For the permutation q the square of permutation is the permutation p that p[i] = q[q[i]] for each i = 1... n. For example, the square of q = [4, 5, 1, 2, 3] is p = q2 = [2, 3, 4, 5, 1].\n\nThis problem is about the inverse operation: given the permutation p you task is to find such permutation q that q2 = p. If there are several such q find any of them.\n\nInput\n\nThe first line contains integer n (1 \u2264 n \u2264 106) \u2014 the number of elements in permutation p.\n\nThe second line contains n distinct integers p1, p2, ..., pn (1 \u2264 pi \u2264 n) \u2014 the elements of permutation p.\n\nOutput\n\nIf there is no permutation q such that q2 = p print the number \"-1\".\n\nIf the answer exists print it. The only line should contain n different integers qi (1 \u2264 qi \u2264 n) \u2014 the elements of the permutation q. If there are several solutions print any of them.\n\nExamples\n\nInput\n\n4\n2 1 4 3\n\n\nOutput\n\n3 4 2 1\n\n\nInput\n\n4\n2 1 3 4\n\n\nOutput\n\n-1\n\n\nInput\n\n5\n2 3 4 5 1\n\n\nOutput\n\n4 5 1 2 3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\n#import random\nfrom bisect import bisect_right as rb\nfrom collections import deque\n#sys.setrecursionlimit(10**8)\nfrom queue import PriorityQueue\nfrom math import *\ninput_ = lambda: sys.stdin.readline().strip(\"\\r\\n\")\nii = lambda : int(input_())\nil = lambda : list(map(int, input_().split()))\nilf = lambda : list(map(float, input_().split()))\nip = lambda : input_()\nfi = lambda : float(input_())\nap = lambda ab,bc,cd : ab[bc].append(cd)\nli = lambda : list(input_())\npr = lambda x : print(x)\nprinT = lambda x : print(x)\nf = lambda : sys.stdout.flush()\nmod = 10**9 + 7\n\nn = ii()\na = [0] + il()\n\ndef dfs (i) :\n vis[i] = 1\n g.append(i)\n if (vis[a[i]] == 0) :\n dfs(a[i])\n\ng = []\nd = {}\nvis = [0 for i in range (n+2)]\n\nans = [0 for i in range (n+1)]\n\nfor i in range (1,n+1) :\n if (vis[i] == 0) :\n i1 = i\n while True :\n vis[i1] = 1\n g.append(i1)\n\n if (vis[a[i1]] == 0) :\n i1 = a[i1]\n else :\n break\n\n l = len(g)\n\n if (l%2) :\n x = (l+1)//2\n\n for j in range (l) :\n ans[g[j]] = g[(x+j)%l]\n\n elif (d.get(l)) :\n v = d[l]\n\n for j in range (l) :\n ans[g[j]] = v[(j+1)%l]\n ans[v[j]] = g[j]\n\n del d[l]\n\n else :\n d[l] = g\n\n g = []\n\nfor i in d :\n print(-1)\n exit(0)\n\nprint(*ans[1:])\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n2 1 3 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 1 4 3\\n', 'output': '3 4 2 1 '}, {'type': 'stdin_stdout', 'input': '5\\n2 3 4 5 1\\n', 'output': '4 5 1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n3 5 1 2 10 8 7 6 4 9\\n', 'output': '6 9 8 10 4 3 7 1 5 2 '}, {'type': 'stdin_stdout', 'input': '100\\n11 9 35 34 51 74 16 67 26 21 14 80 84 79 7 61 28 3 53 43 42 5 56 36 69 30 22 88 1 27 65 91 46 31 59 50 17 96 25 18 64 55 78 2 63 24 95 48 93 13 38 76 89 94 15 90 45 81 52 87 83 73 44 49 23 82 85 75 86 33 47 19 58 97 37 20 40 10 92 4 6 68 77 54 71 12 62 60 100 39 41 99 72 29 57 8 70 32 66 98\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100\\n94 22 24 99 58 97 20 29 67 30 38 64 77 50 15 44 92 88 39 42 25 70 2 76 84 6 37 49 17 71 31 19 26 79 10 35 65 63 32 95 5 8 52 27 83 18 53 93 13 81 48 68 54 82 34 60 87 23 16 86 55 40 61 45 28 7 74 41 14 91 3 72 33 11 98 89 90 69 78 36 80 59 56 21 43 1 75 46 47 12 96 73 57 51 4 85 9 100 66 62\\n', 'output': '78 52 95 76 96 49 53 59 77 100 64 11 9 48 15 17 44 46 32 54 84 68 43 4 21 28 73 6 16 62 31 39 65 86 98 75 33 45 19 3 91 82 2 92 63 88 7 50 97 93 14 22 20 42 60 55 80 85 29 34 56 71 83 38 26 47 90 70 51 41 40 72 37 12 35 99 67 94 1 87 57 8 61 25 23 79 36 18 66 74 5 27 81 69 24 58 13 10 89 30\\n'}, {'type': 'stdin_stdout', 'input': '10\\n8 2 10 3 4 6 1 7 9 5\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 4 3\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 4 2 3\\n', 'output': '1 3 4 2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3 1 2 4\\n', 'output': '2 3 1 4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n8 3 10 2 4 6 1 7 9 5\\n', 'output': '7 5 4 10 3 6 8 1 9 2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n3 5 2 1 10 8 7 6 4 9\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 3 4 5 2\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 3 2 5 1\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79373","program":"```python\nimport sys\n#import random\nfrom bisect import bisect_right as rb\nfrom collections import deque\n#sys.setrecursionlimit(10**8)\nfrom queue import PriorityQueue\nfrom math import *\ninput_ = lambda: sys.stdin.readline().strip(\"\\r\\n\")\nii = lambda : int(input_())\nil = lambda : list(map(int, input_().split()))\nilf = lambda : list(map(float, input_().split()))\nip = lambda : input_()\nfi = lambda : float(input_())\nap = lambda ab,bc,cd : ab[bc].append(cd)\nli = lambda : list(input_())\npr = lambda x : print(x)\nprinT = lambda x : print(x)\nf = lambda : sys.stdout.flush()\nmod = 10**9 + 7\n\nn = ii()\na = [0] + il()\n\ndef dfs (i) :\n vis[i] = 1\n g.append(i)\n if (vis[a[i]] == 0) :\n dfs(a[i])\n\ng = []\nd = {}\nvis = [0 for i in range (n+2)]\n\nans = [0 for i in range (n+1)]\n\nfor i in range (1,n+1) :\n if (vis[i] == 0) :\n i1 = i\n while True :\n vis[i1] = 1\n g.append(i1)\n\n if (vis[a[i1]] == 0) :\n i1 = a[i1]\n else :\n break\n\n l = len(g)\n\n if (l%2) :\n x = (l+1)//2\n\n for j in range (l) :\n ans[g[j]] = g[(x+j)%l]\n\n elif (d.get(l)) :\n v = d[l]\n\n for j in range (l) :\n ans[g[j]] = v[(j+1)%l]\n ans[v[j]] = g[j]\n\n del d[l]\n\n else :\n d[l] = g\n\n g = []\n\nfor i in d :\n print(-1)\n exit(0)\n\nprint(*ans[1:])\n\n\n\n```","inputs":"4\n2 1 3 4\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12640},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"685_B. Kay and Snowflake","prompt":"Solve the following coding problem using the programming language python:\n\nAfter the piece of a devilish mirror hit the Kay's eye, he is no longer interested in the beauty of the roses. Now he likes to watch snowflakes.\n\nOnce upon a time, he found a huge snowflake that has a form of the tree (connected acyclic graph) consisting of n nodes. The root of tree has index 1. Kay is very interested in the structure of this tree.\n\nAfter doing some research he formed q queries he is interested in. The i-th query asks to find a centroid of the subtree of the node vi. Your goal is to answer all queries.\n\nSubtree of a node is a part of tree consisting of this node and all it's descendants (direct or not). In other words, subtree of node v is formed by nodes u, such that node v is present on the path from u to root.\n\nCentroid of a tree (or a subtree) is a node, such that if we erase it from the tree, the maximum size of the connected component will be at least two times smaller than the size of the initial tree (or a subtree).\n\nInput\n\nThe first line of the input contains two integers n and q (2 \u2264 n \u2264 300 000, 1 \u2264 q \u2264 300 000) \u2014 the size of the initial tree and the number of queries respectively.\n\nThe second line contains n - 1 integer p2, p3, ..., pn (1 \u2264 pi \u2264 n) \u2014 the indices of the parents of the nodes from 2 to n. Node 1 is a root of the tree. It's guaranteed that pi define a correct tree.\n\nEach of the following q lines contain a single integer vi (1 \u2264 vi \u2264 n) \u2014 the index of the node, that define the subtree, for which we want to find a centroid.\n\nOutput\n\nFor each query print the index of a centroid of the corresponding subtree. If there are many suitable nodes, print any of them. It's guaranteed, that each subtree has at least one centroid.\n\nExample\n\nInput\n\n7 4\n1 1 3 3 5 3\n1\n2\n3\n5\n\n\nOutput\n\n3\n2\n3\n6\n\nNote\n\n\n\nThe first query asks for a centroid of the whole tree \u2014 this is node 3. If we delete node 3 the tree will split in four components, two of size 1 and two of size 2.\n\nThe subtree of the second node consists of this node only, so the answer is 2.\n\nNode 3 is centroid of its own subtree.\n\nThe centroids of the subtree of the node 5 are nodes 5 and 6 \u2014 both answers are considered correct.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport operator\nimport bisect\n\nn, q = [int(s) for s in input().split()]\n\nps = [int(s) for s in input().split()]\n\nchilds = [[] for _ in range(n)]\n\nfor (c,pa) in enumerate(ps):\n childs[pa-1].append(c+1)\ntoposort = []\nthis_level = [0]\nnext_level = []\nwhile len(this_level) > 0:\n for this_n in this_level:\n toposort.append(this_n)\n for c in childs[this_n]:\n next_level.append(c)\n this_level = next_level\n next_level = []\n\nsz = [0]*n\npotentials = [0]*n\npotential_sz = [0]*n\npotential_lo = [0]*n\ncentr = [0]*n\n\nfor node in reversed(toposort):\n if len(childs[node]) == 0:\n centr[node] = node\n sz[node] = 1\n else:\n s = 1\n lg_c = -1\n lg_c_sz = 0\n for c in childs[node]:\n s += sz[c]\n if sz[c] > lg_c_sz:\n lg_c_sz = sz[c]\n lg_c = c\n sz[node] = s\n if lg_c_sz <= sz[node]//2:\n centr[node] = node\n potentials[node] = [node]\n potential_sz[node] = [sz[node]]\n continue\n\n potentials[node] = potentials[lg_c]\n potential_sz[node] = potential_sz[lg_c]\n\n i = bisect.bisect_right(potential_sz[node], sz[node]//2, lo=potential_lo[lg_c])\n centr[node] = potentials[node][i]\n\n potentials[node].append(node)\n potential_lo[node] = i\n potential_sz[node].append(sz[node])\n\nvs = [int(input()) - 1 for i in range(q)]\nprint('\\n'.join([str(centr[v]+1) for v in vs]))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n1\\n2\\n3\\n5\\n', 'output': '3\\n2\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n1\\n1\\n2\\n', 'output': '1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n2\\n2\\n3\\n5\\n', 'output': '2\\n2\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n2\\n4\\n3\\n5\\n', 'output': '2\\n4\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n2\\n3\\n3\\n5\\n', 'output': '2\\n3\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n2\\n4\\n3\\n3\\n', 'output': '2\\n4\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 6\\n2\\n4\\n3\\n5\\n', 'output': '2\\n4\\n5\\n6\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n2\\n5\\n3\\n3\\n', 'output': '2\\n5\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n1\\n2\\n3\\n2\\n', 'output': '3\\n2\\n3\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n4\\n4\\n3\\n5\\n', 'output': '4\\n4\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 1 3 3 5 3\\n2\\n4\\n3\\n3\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n3\\n5\\n3\\n3\\n', 'output': '3\\n5\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n7\\n4\\n3\\n5\\n', 'output': '7\\n4\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n3\\n5\\n2\\n3\\n', 'output': '3\\n5\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n5\\n5\\n2\\n3\\n', 'output': '5\\n5\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 2 5 3\\n5\\n5\\n2\\n3\\n', 'output': '5\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n1\\n1\\n1\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n1\\n2\\n3\\n7\\n', 'output': '3\\n2\\n3\\n7\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n4\\n2\\n3\\n5\\n', 'output': '4\\n2\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n1\\n4\\n3\\n2\\n', 'output': '3\\n4\\n3\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n4\\n7\\n3\\n5\\n', 'output': '4\\n7\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n4\\n5\\n2\\n3\\n', 'output': '4\\n5\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n1\\n4\\n3\\n7\\n', 'output': '3\\n4\\n3\\n7\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n4\\n2\\n2\\n5\\n', 'output': '4\\n2\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 4 5 3\\n2\\n4\\n3\\n3\\n', 'output': '2\\n5\\n4\\n4\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 2 3 3 5 3\\n1\\n2\\n3\\n2\\n', 'output': '3\\n3\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n4\\n5\\n3\\n5\\n', 'output': '4\\n5\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 4 5 3\\n7\\n4\\n3\\n5\\n', 'output': '7\\n5\\n4\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 5\\n3\\n5\\n2\\n3\\n', 'output': '5\\n5\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n4\\n2\\n3\\n4\\n', 'output': '4\\n2\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 2 3 3 5 3\\n1\\n4\\n3\\n2\\n', 'output': '3\\n4\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 1 3 3 5 3\\n4\\n7\\n3\\n5\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n4\\n2\\n2\\n3\\n', 'output': '4\\n2\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n2\\n4\\n3\\n7\\n', 'output': '2\\n4\\n3\\n7\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n7\\n2\\n2\\n5\\n', 'output': '7\\n2\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n2\\n3\\n5\\n5\\n', 'output': '2\\n3\\n5\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n2\\n7\\n3\\n3\\n', 'output': '2\\n7\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n4\\n4\\n2\\n5\\n', 'output': '4\\n4\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 6 3 5 3\\n5\\n5\\n2\\n3\\n', 'output': '6\\n6\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n1\\n3\\n3\\n7\\n', 'output': '3\\n3\\n3\\n7\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 2 3 3 5 3\\n4\\n2\\n3\\n5\\n', 'output': '4\\n3\\n3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 4 5 3\\n1\\n4\\n3\\n2\\n', 'output': '3\\n5\\n4\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 5\\n4\\n5\\n3\\n5\\n', 'output': '4\\n5\\n5\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 2 3 3 5 3\\n2\\n5\\n3\\n3\\n', 'output': '3\\n5\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 1 6 3 5 3\\n4\\n7\\n3\\n5\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n3\\n5\\n3\\n1\\n', 'output': '3\\n5\\n3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 1 3 3 5 3\\n4\\n1\\n3\\n5\\n', 'output': '4\\n3\\n3\\n5\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79385","program":"```python\nimport operator\nimport bisect\n\nn, q = [int(s) for s in input().split()]\n\nps = [int(s) for s in input().split()]\n\nchilds = [[] for _ in range(n)]\n\nfor (c,pa) in enumerate(ps):\n childs[pa-1].append(c+1)\ntoposort = []\nthis_level = [0]\nnext_level = []\nwhile len(this_level) > 0:\n for this_n in this_level:\n toposort.append(this_n)\n for c in childs[this_n]:\n next_level.append(c)\n this_level = next_level\n next_level = []\n\nsz = [0]*n\npotentials = [0]*n\npotential_sz = [0]*n\npotential_lo = [0]*n\ncentr = [0]*n\n\nfor node in reversed(toposort):\n if len(childs[node]) == 0:\n centr[node] = node\n sz[node] = 1\n else:\n s = 1\n lg_c = -1\n lg_c_sz = 0\n for c in childs[node]:\n s += sz[c]\n if sz[c] > lg_c_sz:\n lg_c_sz = sz[c]\n lg_c = c\n sz[node] = s\n if lg_c_sz <= sz[node]//2:\n centr[node] = node\n potentials[node] = [node]\n potential_sz[node] = [sz[node]]\n continue\n\n potentials[node] = potentials[lg_c]\n potential_sz[node] = potential_sz[lg_c]\n\n i = bisect.bisect_right(potential_sz[node], sz[node]//2, lo=potential_lo[lg_c])\n centr[node] = potentials[node][i]\n\n potentials[node].append(node)\n potential_lo[node] = i\n potential_sz[node].append(sz[node])\n\nvs = [int(input()) - 1 for i in range(q)]\nprint('\\n'.join([str(centr[v]+1) for v in vs]))\n\n```","inputs":"7 4\n1 1 3 3 5 3\n1\n2\n3\n5\n","output":"3\n2\n3\n5\n","actual_output":"3\n2\n3\n5\n","execution_success":true,"sample_index":12641},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"708_A. Letters Cyclic Shift","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a non-empty string s consisting of lowercase English letters. You have to pick exactly one non-empty substring of s and shift all its letters 'z' 'y' 'x' 'b' 'a' 'z'. In other words, each character is replaced with the previous character of English alphabet and 'a' is replaced with 'z'.\n\nWhat is the lexicographically minimum string that can be obtained from s by performing this shift exactly once?\n\nInput\n\nThe only line of the input contains the string s (1 \u2264 |s| \u2264 100 000) consisting of lowercase English letters.\n\nOutput\n\nPrint the lexicographically minimum string that can be obtained from s by shifting letters of exactly one non-empty substring.\n\nExamples\n\nInput\n\ncodeforces\n\n\nOutput\n\nbncdenqbdr\n\n\nInput\n\nabacaba\n\n\nOutput\n\naaacaba\n\nNote\n\nString s is lexicographically smaller than some other string t of the same length if there exists some 1 \u2264 i \u2264 |s|, such that s1 = t1, s2 = t2, ..., si - 1 = ti - 1, and si < ti.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nn=input()\ni=0\nn=n+'a'\nm=\"\"\nwhile n[i]=='a' and len(n)>i+1:\n i+=1\n m=m+'a'\nif i+1==len(n):\n w=m[0:len(m)-1]+'z'\n print(w)\n sys.exit()\nwhile n[i]!='a' and len(n)>i:\n m=m+chr(ord(n[i])-1)\n i+=1\nm=m+n[i:len(n)-1]\n\nprint(m)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'codeforces\\n', 'output': 'bncdenqbdr'}, {'type': 'stdin_stdout', 'input': 'abacaba\\n', 'output': 'aaacaba'}, {'type': 'stdin_stdout', 'input': 'cabaccaacccabaacdbdcbcdbccbccbabbdadbdcdcdbdbcdcdbdadcbcda\\n', 'output': 'babaccaacccabaacdbdcbcdbccbccbabbdadbdcdcdbdbcdcdbdadcbcda'}, {'type': 'stdin_stdout', 'input': 'aaaaaaaaaa\\n', 'output': 'aaaaaaaaaz'}, {'type': 'stdin_stdout', 'input': 'babbbabaababbaa\\n', 'output': 'aabbbabaababbaa'}, {'type': 'stdin_stdout', 'input': 'abbabaaaaa\\n', 'output': 'aaaabaaaaa'}, {'type': 'stdin_stdout', 'input': 'a\\n', 'output': 'z'}, {'type': 'stdin_stdout', 'input': 'aabaaaaaaaaaaaa\\n', 'output': 'aaaaaaaaaaaaaaa'}, {'type': 'stdin_stdout', 'input': 'aaa\\n', 'output': 'aaz'}, {'type': 'stdin_stdout', 'input': 'eeeedddccbceaabdaecaebaeaecccbdeeeaadcecdbeacecdcdcceabaadbcbbadcdaeddbcccaaeebccecaeeeaebcaaccbdaccbdcadadaaeacbbdcbaeeaecedeeeedadec\\n', 'output': 'ddddcccbbabdaabdaecaebaeaecccbdeeeaadcecdbeacecdcdcceabaadbcbbadcdaeddbcccaaeebccecaeeeaebcaaccbdaccbdcadadaaeacbbdcbaeeaecedeeeedadec'}, {'type': 'stdin_stdout', 'input': 'aaaaaaaaaaaaaaaaaaaa\\n', 'output': 'aaaaaaaaaaaaaaaaaaaz'}, {'type': 'stdin_stdout', 'input': 'abbbbbbbabbbbbbbbbbbbbbbbbbbbbbbabbabbbbbabbbbbbbbbbbabbbbbbbbabbabbbbbbbbbbbbbbabbabbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbabbbbbbbbbaababbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbabbbbbaabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbaabbbbbbbbbbbbababbabbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbabbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbabbbbbbbabbbbbbb\\n', 'output': 'aaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbabbabbbbbabbbbbbbbbbbabbbbbbbbabbabbbbbbbbbbbbbbabbabbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbabbbbbbbbbaababbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbabbbbbaabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbaabbbbbbbbbbbbababbabbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbabbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbabbbbbbbabbbbbbb'}, {'type': 'stdin_stdout', 'input': 'aa\\n', 'output': 'az'}, {'type': 'stdin_stdout', 'input': 'bcbacaabcababaccccaaaabacbbcbbaa\\n', 'output': 'abaacaabcababaccccaaaabacbbcbbaa'}, {'type': 'stdin_stdout', 'input': 'abaabaaaaaabbaaaaaaabaaaaaaaaabaaaabaaaaaaabaaaaaaaaaabaaaaaaaaaaaaaaabaaaabbaaaaabaaaaaaaabaaaaaaaa\\n', 'output': 'aaaabaaaaaabbaaaaaaabaaaaaaaaabaaaabaaaaaaabaaaaaaaaaabaaaaaaaaaaaaaaabaaaabbaaaaabaaaaaaaabaaaaaaaa'}, {'type': 'stdin_stdout', 'input': 'aaaaa\\n', 'output': 'aaaaz'}, {'type': 'stdin_stdout', 'input': 'bbbbbbbbbbbb\\n', 'output': 'aaaaaaaaaaaa'}, {'type': 'stdin_stdout', 'input': 'fddfbabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddefbafdcafdfcbdffeeaffcaebbbedabddeaecdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdceebcebbfeaccfafdccdcecedeedadcadbfefccfdedfaaefabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n', 'output': 'ecceaabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddefbafdcafdfcbdffeeaffcaebbbedabddeaecdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdceebcebbfeaccfafdccdcecedeedadcadbfefccfdedfaaefabbaeebdebeecaadbebcfeafbfeeefcfaecadfe'}, {'type': 'stdin_stdout', 'input': 'cabaccaacccabaacdbdcbcdbccbccbabbdadbdbdcdbdbcdcdbdadcccda\\n', 'output': 'babaccaacccabaacdbdcbcdbccbccbabbdadbdbdcdbdbcdcdbdadcccda\\n'}, {'type': 'stdin_stdout', 'input': 'babbbabaababbba\\n', 'output': 'aabbbabaababbba\\n'}, {'type': 'stdin_stdout', 'input': 'abaabaaaaa\\n', 'output': 'aaaabaaaaa\\n'}, {'type': 'stdin_stdout', 'input': 'aabaaaaaaaaaaab\\n', 'output': 'aaaaaaaaaaaaaab\\n'}, {'type': 'stdin_stdout', 'input': 'eeeedddccbdeaabdaecaebaeaecccbdeeeaadcecdbeacecdcdcceabaadbcbbadcdaeddbcccaaeebccecaeeeaebcaaccbdaccbdcadadaaeacbbdcbaeeaecedeeeedadec\\n', 'output': 'ddddcccbbacdaabdaecaebaeaecccbdeeeaadcecdbeacecdcdcceabaadbcbbadcdaeddbcccaaeebccecaeeeaebcaaccbdaccbdcadadaaeacbbdcbaeeaecedeeeedadec\\n'}, {'type': 'stdin_stdout', 'input': 'abbbbbbbabbbbbbbbbbbbbbbbbbbbbbbabbabbbbbabbbbbbbbbbbabbbbbbbbabbabbbbbbbbbbbbbbabbabbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbabbbbbbbbbaababbbbbbbbabbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbabbbbbaabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbaabbbbbbbbbbbbababbabbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbabbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbabbbbbbbabbbbbbb\\n', 'output': 'aaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbabbabbbbbabbbbbbbbbbbabbbbbbbbabbabbbbbbbbbbbbbbabbabbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbabbbbbbbbbaababbbbbbbbabbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbabbbbbaabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbaabbbbbbbbbbbbababbabbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbabbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbabbbbbbbabbbbbbb\\n'}, {'type': 'stdin_stdout', 'input': 'bcbacaabcababaccccbaaabacbbcbbaa\\n', 'output': 'abaacaabcababaccccbaaabacbbcbbaa\\n'}, {'type': 'stdin_stdout', 'input': 'bbcbbbbbbbbb\\n', 'output': 'aabaaaaaaaaa\\n'}, {'type': 'stdin_stdout', 'input': 'fddfbabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddefbacdcafdfcbdffeeaffcaebbbedabddeaecdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdceebcebbfeaccfafdfcdcecedeedadcadbfefccfdedfaaefabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n', 'output': 'ecceaabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddefbacdcafdfcbdffeeaffcaebbbedabddeaecdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdceebcebbfeaccfafdfcdcecedeedadcadbfefccfdedfaaefabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n'}, {'type': 'stdin_stdout', 'input': 'dodeforces\\n', 'output': 'cncdenqbdr\\n'}, {'type': 'stdin_stdout', 'input': 'baacaba\\n', 'output': 'aaacaba\\n'}, {'type': 'stdin_stdout', 'input': 'cabaccaacccabaacbbdcbcdbccbccdabbdadbdbdcdbdbcdcdbdadcccda\\n', 'output': 'babaccaacccabaacbbdcbcdbccbccdabbdadbdbdcdbdbcdcdbdadcccda\\n'}, {'type': 'stdin_stdout', 'input': 'aaaaababba\\n', 'output': 'aaaaaaabba\\n'}, {'type': 'stdin_stdout', 'input': 'aabaaaaaabaaaab\\n', 'output': 'aaaaaaaaabaaaab\\n'}, {'type': 'stdin_stdout', 'input': 'abbbbbbbabbbbbbbbbbbbbbbbbbbbbbbabbabbbbbabbbbbbbbbbbabbbbbbbbabbabbbbbbbbbbbbbbabbabbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbabbbbbbbbbaababbbbbbbbabbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbbbbbbaabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbaabbbbbbbbbbbbababbabbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbabbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbababbbbbabbbbbbb\\n', 'output': 'aaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbabbabbbbbabbbbbbbbbbbabbbbbbbbabbabbbbbbbbbbbbbbabbabbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbabbbbbbbbbaababbbbbbbbabbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbbbbbbaabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbaabbbbbbbbbbbbababbabbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbabbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbababbbbbabbbbbbb\\n'}, {'type': 'stdin_stdout', 'input': 'aabbcbbcabaaabccccababacbaacabcb\\n', 'output': 'aaaabaababaaabccccababacbaacabcb\\n'}, {'type': 'stdin_stdout', 'input': 'bbccbbbbbbbb\\n', 'output': 'aabbaaaaaaaa\\n'}, {'type': 'stdin_stdout', 'input': 'fddfbabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddefbacdcafdfcbdffeeaffcaebbbedabddeaecdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdceebcebbfeaccfafdfcdcecedeedadcadbfefccfdeefaaefabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n', 'output': 'ecceaabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddefbacdcafdfcbdffeeaffcaebbbedabddeaecdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdceebcebbfeaccfafdfcdcecedeedadcadbfefccfdeefaaefabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n'}, {'type': 'stdin_stdout', 'input': 'secrofedod\\n', 'output': 'rdbqnedcnc\\n'}, {'type': 'stdin_stdout', 'input': 'baadaba\\n', 'output': 'aaadaba\\n'}, {'type': 'stdin_stdout', 'input': 'adcccdadbdcdcbdbdcdbdbdadbbadccbccbdcbcdbbcaabacccaaccabac\\n', 'output': 'acbbbcadbdcdcbdbdcdbdbdadbbadccbccbdcbcdbbcaabacccaaccabac\\n'}, {'type': 'stdin_stdout', 'input': 'aabaababba\\n', 'output': 'aaaaababba\\n'}, {'type': 'stdin_stdout', 'input': 'baaaabaaaaaabaa\\n', 'output': 'aaaaabaaaaaabaa\\n'}, {'type': 'stdin_stdout', 'input': 'abbbbbbbabbbbbabbbbbbbbbbbbbbbbbabbabbbbbabbbbbbbbbbbabbbbbbbbabbabbbbbbbbbbbbbbabbabbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbabbbbbbbbbaababbbbbbbbabbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbbbbbbaabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbaabbbbbbbbbbbbababbabbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbabbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbababbbbbabbbbbbb\\n', 'output': 'aaaaaaaaabbbbbabbbbbbbbbbbbbbbbbabbabbbbbabbbbbbbbbbbabbbbbbbbabbabbbbbbbbbbbbbbabbabbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbabbbbbbbbbaababbbbbbbbabbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbbbbbbaabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbaabbbbbbbbbbbbababbabbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbabbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbababbbbbabbbbbbb\\n'}, {'type': 'stdin_stdout', 'input': 'bcbacaabcacabaccccbaaabacbbcbbaa\\n', 'output': 'abaacaabcacabaccccbaaabacbbcbbaa\\n'}, {'type': 'stdin_stdout', 'input': 'bbbbbbbbccbb\\n', 'output': 'aaaaaaaabbaa\\n'}, {'type': 'stdin_stdout', 'input': 'fddfbabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddefbacdcafdfcbdffeeaffcaebbbedabddeafcdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdceebcebbfeaccfafdfcdcecedeedadcadbfefccfdeefaaefabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n', 'output': 'ecceaabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddefbacdcafdfcbdffeeaffcaebbbedabddeafcdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdceebcebbfeaccfafdfcdcecedeedadcadbfefccfdeefaaefabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n'}, {'type': 'stdin_stdout', 'input': 'secrpfedod\\n', 'output': 'rdbqoedcnc\\n'}, {'type': 'stdin_stdout', 'input': 'abadaab\\n', 'output': 'aaadaab\\n'}, {'type': 'stdin_stdout', 'input': 'adcccdadcdcdcbdbdcdbdbdadbbadccbccbdcbcdbbcaabacccaaccabac\\n', 'output': 'acbbbcadcdcdcbdbdcdbdbdadbbadccbccbdcbcdbbcaabacccaaccabac\\n'}, {'type': 'stdin_stdout', 'input': 'abbabaabaa\\n', 'output': 'aaaabaabaa\\n'}, {'type': 'stdin_stdout', 'input': 'abbbbbbbabbbbbabbbbbbbbbbbbbbbbbabbabbbbbabbbbbbbbbbbabbbbbbbbabbabbbbbbbbbbbbbbabbabbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbabbbbbbbbbaababbbbbbbbabbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbbbbbbaabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbcbbbbbbbbbbbbaabbbbbbbbbbbbababbabbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbabbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbababbbbbabbbbbbb\\n', 'output': 'aaaaaaaaabbbbbabbbbbbbbbbbbbbbbbabbabbbbbabbbbbbbbbbbabbbbbbbbabbabbbbbbbbbbbbbbabbabbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbabbbbbbbbbaababbbbbbbbabbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbabbbbbbbbbaabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbcbbbbbbbbbbbbaabbbbbbbbbbbbababbabbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbabbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbababbbbbabbbbbbb\\n'}, {'type': 'stdin_stdout', 'input': 'bcbacaabcacabaccccbaaabacbbccbaa\\n', 'output': 'abaacaabcacabaccccbaaabacbbccbaa\\n'}, {'type': 'stdin_stdout', 'input': 'bbbbbbbbbccb\\n', 'output': 'aaaaaaaaabba\\n'}, {'type': 'stdin_stdout', 'input': 'fddfbabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddefbacdcafdfcbdffeeaffcaebbbedacddeafcdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdbeebcebbfeaccfafdfcdcecedeedadcadbfefccfdeefaaefabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n', 'output': 'ecceaabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddefbacdcafdfcbdffeeaffcaebbbedacddeafcdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdbeebcebbfeaccfafdfcdcecedeedadcadbfefccfdeefaaefabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n'}, {'type': 'stdin_stdout', 'input': 'sedrpfedod\\n', 'output': 'rdcqoedcnc\\n'}, {'type': 'stdin_stdout', 'input': 'abadaac\\n', 'output': 'aaadaac\\n'}, {'type': 'stdin_stdout', 'input': 'adcccdadcdcdcbdbdcdbdbdadbbadccbccbdcbcdbccaabacccaaccabac\\n', 'output': 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'aaabaaabaacaabbcccababacbaacbcdb\\n'}, {'type': 'stdin_stdout', 'input': 'bbdabbcbbcbb\\n', 'output': 'aacabbcbbcbb\\n'}, {'type': 'stdin_stdout', 'input': 'fddfbabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddeccacccagdfbbdffeeaffcaebbbedafddeafcdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdbeebcebbfeaccfafdfcdcecedeedadcadbfefccfdeefaadfabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n', 'output': 'ecceaabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddeccacccagdfbbdffeeaffcaebbbedafddeafcdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffeeaefebdbeebcebbfeaccfafdfcdcecedeedadcadbfefccfdeefaadfabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n'}, {'type': 'stdin_stdout', 'input': 'qedrofecod\\n', 'output': 'pdcqnedbnc\\n'}, {'type': 'stdin_stdout', 'input': 'caeaccaacccabaaccbccbcdbccbccdabbdadbdbdcdbdbddcdcbadccdda\\n', 'output': 'baeaccaacccabaaccbccbcdbccbccdabbdadbdbdcdbdbddcdcbadccdda\\n'}, {'type': 'stdin_stdout', 'input': 'bbbbbbbabbbbbababbbbbbbbbbbbbbbbbbabbbabbbbbbbbbbbabbbbbbbcbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbbabbababbbbbbbbbbbbaababbbbbbbbbbcbbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbaabbbbbbbbbabbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbabbbbbbbbabaabbbbbbbbbabbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabaabbbabbabbbbbbbbbbbbbbabbabbbbbbbbabbbbbbbbbbbabbbbbabbabbbbbbbbbbbbbbbbbabbbbbabbbbabba\\n', 'output': 'aaaaaaaabbbbbababbbbbbbbbbbbbbbbbbabbbabbbbbbbbbbbabbbbbbbcbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbbabbababbbbbbbbbbbbaababbbbbbbbbbcbbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbaabbbbbbbbbabbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbabbbbbbbbabaabbbbbbbbbabbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabaabbbabbabbbbbbbbbbbbbbabbabbbbbbbbabbbbbbbbbbbabbbbbabbabbbbbbbbbbbbbbbbbabbbbbabbbbabba\\n'}, {'type': 'stdin_stdout', 'input': 'aabcbbbcaacaabbcccababacbaacbddb\\n', 'output': 'aaabaaabaacaabbcccababacbaacbddb\\n'}, {'type': 'stdin_stdout', 'input': 'bbdabacbbcbb\\n', 'output': 'aacabacbbcbb\\n'}, {'type': 'stdin_stdout', 'input': 'fddfbabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddeccacccagdfbbdffeeaffcaebbbedafddeafcdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffedaefebdbeebcebbfeaccfafdfcdcecedeedadcadbfefccfdeefaadfabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n', 'output': 'ecceaabadaadaddfbfecadfaefaefefabcccdbbeeabcbbddeccacccagdfbbdffeeaffcaebbbedafddeafcdddffcbeaafffcddccccfffdbcddcfccefafdbeaacbdeeebdeaaacdfdecadfeafaeaefbfdfffedaefebdbeebcebbfeaccfafdfcdcecedeedadcadbfefccfdeefaadfabbaeebdebeecaadbebcfeafbfeeefcfaecadfe\\n'}, {'type': 'stdin_stdout', 'input': 'qfdrofecod\\n', 'output': 'pecqnedbnc\\n'}, {'type': 'stdin_stdout', 'input': 'caeaccaacccabaaccbccbcdbccbccdabbdadbdbdcdbdbddcdcbadccdca\\n', 'output': 'baeaccaacccabaaccbccbcdbccbccdabbdadbdbdcdbdbddcdcbadccdca\\n'}, {'type': 'stdin_stdout', 'input': 'bbbbbbbabbbbbababbbbbbbbbbbbbbbbbbabbbabbbcbbbbbbbabbbbbbbcbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbbabbababbbbbbbbbbbbaababbbbbbbbbbcbbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbaabbbbbbbbbabbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbabbbbbbbbabaabbbbbbbbbabbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabaabbbabbabbbbbbbbbbbbbbabbabbbbbbbbabbbbbbbbbbbabbbbbabbabbbbbbbbbbbbbbbbbabbbbbabbbbabba\\n', 'output': 'aaaaaaaabbbbbababbbbbbbbbbbbbbbbbbabbbabbbcbbbbbbbabbbbbbbcbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbbabbababbbbbbbbbbbbaababbbbbbbbbbcbbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbaabbbbbbbbbabbbbbbbbbbbbbbbbabbabbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbabbbbabbbbbbbbabaabbbbbbbbbabbbbbbbbbbbbbbbabbbbabbbbbbbbbbbbbbbbaababbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabaabbbabbabbbbbbbbbbbbbbabbabbbbbbbbabbbbbbbbbbbabbbbbabbabbbbbbbbbbbbbbbbbabbbbbabbbbabba\\n'}, {'type': 'stdin_stdout', 'input': 'aabcbbbbaacaacbcccababacbaacbddb\\n', 'output': 'aaabaaaaaacaacbcccababacbaacbddb\\n'}, {'type': 'stdin_stdout', 'input': 'bcdababbbcbb\\n', 'output': 'abcababbbcbb\\n'}, {'type': 'stdin_stdout', 'input': 'efdaceafcfeeefbfaefcbebdaaceebedbeeabbafdaafeedfccfefbdacdadeedececdcfdfafccaefbbecbeebdbefeadefffdfbfeaeafaefdacedfdcaaaedbeeedbcaaebdfafeccfcddcbdfffccccddcfffaaebcffdddcfaeddfadebbbeacffaeeffdbbfdgacccacceddbbcbaeebbdcccbafefeafeafdacefbfddadaadababfddf\\n', 'output': 'decaceafcfeeefbfaefcbebdaaceebedbeeabbafdaafeedfccfefbdacdadeedececdcfdfafccaefbbecbeebdbefeadefffdfbfeaeafaefdacedfdcaaaedbeeedbcaaebdfafeccfcddcbdfffccccddcfffaaebcffdddcfaeddfadebbbeacffaeeffdbbfdgacccacceddbbcbaeebbdcccbafefeafeafdacefbfddadaadababfddf\\n'}, {'type': 'stdin_stdout', 'input': 'qfdrofeocd\\n', 'output': 'pecqnednbc\\n'}, {'type': 'stdin_stdout', 'input': 'bbbabaabaa\\n', 'output': 'aaaabaabaa\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79389","program":"```python\nimport sys\nn=input()\ni=0\nn=n+'a'\nm=\"\"\nwhile n[i]=='a' and len(n)>i+1:\n i+=1\n m=m+'a'\nif i+1==len(n):\n w=m[0:len(m)-1]+'z'\n print(w)\n sys.exit()\nwhile n[i]!='a' and len(n)>i:\n m=m+chr(ord(n[i])-1)\n i+=1\nm=m+n[i:len(n)-1]\n\nprint(m)\n\n```","inputs":"codeforces\n","output":"bncdenqbdr","actual_output":"bncdenqbdr\n","execution_success":true,"sample_index":12642},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"750_D. New Year and Fireworks","prompt":"Solve the following coding problem using the programming language python:\n\nOne tradition of welcoming the New Year is launching fireworks into the sky. Usually a launched firework flies vertically upward for some period of time, then explodes, splitting into several parts flying in different directions. Sometimes those parts also explode after some period of time, splitting into even more parts, and so on.\n\nLimak, who lives in an infinite grid, has a single firework. The behaviour of the firework is described with a recursion depth n and a duration for each level of recursion t1, t2, ..., tn. Once Limak launches the firework in some cell, the firework starts moving upward. After covering t1 cells (including the starting cell), it explodes and splits into two parts, each moving in the direction changed by 45 degrees (see the pictures below for clarification). So, one part moves in the top-left direction, while the other one moves in the top-right direction. Each part explodes again after covering t2 cells, splitting into two parts moving in directions again changed by 45 degrees. The process continues till the n-th level of recursion, when all 2n - 1 existing parts explode and disappear without creating new parts. After a few levels of recursion, it's possible that some parts will be at the same place and at the same time \u2014 it is allowed and such parts do not crash.\n\nBefore launching the firework, Limak must make sure that nobody stands in cells which will be visited at least once by the firework. Can you count the number of those cells?\n\nInput\n\nThe first line of the input contains a single integer n (1 \u2264 n \u2264 30) \u2014 the total depth of the recursion.\n\nThe second line contains n integers t1, t2, ..., tn (1 \u2264 ti \u2264 5). On the i-th level each of 2i - 1 parts will cover ti cells before exploding.\n\nOutput\n\nPrint one integer, denoting the number of cells which will be visited at least once by any part of the firework.\n\nExamples\n\nInput\n\n4\n4 2 2 3\n\n\nOutput\n\n39\n\n\nInput\n\n6\n1 1 1 1 1 3\n\n\nOutput\n\n85\n\n\nInput\n\n1\n3\n\n\nOutput\n\n3\n\nNote\n\nFor the first sample, the drawings below show the situation after each level of recursion. Limak launched the firework from the bottom-most red cell. It covered t1 = 4 cells (marked red), exploded and divided into two parts (their further movement is marked green). All explosions are marked with an 'X' character. On the last drawing, there are 4 red, 4 green, 8 orange and 23 pink cells. So, the total number of visited cells is 4 + 4 + 8 + 23 = 39.\n\n\n\nFor the second sample, the drawings below show the situation after levels 4, 5 and 6. The middle drawing shows directions of all parts that will move in the next level.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\n\nplane = set()\ncrackers = {((0, -1), (0, 1))}\n\nn = int(input())\na = [int(x) for x in input().split()]\n\ncrack_dict = {\n (1, 0): ((1, -1), (1, 1)),\n (1, 1): ((1, 0), (0, 1)),\n (0, 1): ((1, 1), (-1, 1)),\n (-1, 1): ((0, 1), (-1, 0)),\n (-1, 0): ((-1, 1), (-1, -1)),\n (-1, -1): ((-1, 0), (0, -1)),\n (0, -1): ((-1, -1), (1, -1)),\n (1, -1): ((0, -1), (1, 0)),\n}\n\ndef move(cracker):\n point, direc = cracker\n point2 = (point[0] + direc[0], point[1] + direc[1])\n return (point2, direc)\n\ndef crack(cracker):\n point, direc = cracker\n direc1, direc2 = crack_dict[direc]\n return ((point, direc1), (point, direc2))\n \nfor x in a:\n for i in range(x):\n crackers = set((move(cracker) for cracker in crackers))\n plane.update((cracker[0] for cracker in crackers))\n # print(plane, file=sys.stderr)\n new_crackers = set()\n for cracker in crackers:\n new_crackers.update(crack(cracker))\n crackers = new_crackers\n\nprint(len(plane))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6\\n1 1 1 1 1 3\\n', 'output': '85\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 2 2 3\\n', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '30\\n4 1 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5\\n', 'output': '60096\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 2 4 1\\n', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '30\\n1 3 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5\\n', 'output': '61237\\n'}, {'type': 'stdin_stdout', 'input': '30\\n2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5\\n', 'output': '43348\\n'}, {'type': 'stdin_stdout', 'input': '20\\n4 5 3 4 5 4 2 4 2 1 5 3 3 1 4 1 2 4 4 3\\n', 'output': '10495\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '30\\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\\n', 'output': '10479\\n'}, {'type': 'stdin_stdout', 'input': '11\\n5 5 5 5 5 5 5 5 5 4 4\\n', 'output': '3544\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 5 5 5 5\\n', 'output': '147\\n'}, {'type': 'stdin_stdout', 'input': '30\\n1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5\\n', 'output': '43348\\n'}, {'type': 'stdin_stdout', 'input': '7\\n5 3 3 5 5 4 4\\n', 'output': '480\\n'}, {'type': 'stdin_stdout', 'input': '30\\n5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n', 'output': '2744\\n'}, {'type': 'stdin_stdout', 'input': '8\\n3 3 3 3 3 3 3 1\\n', 'output': '384\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 5 3 1\\n', 'output': '65\\n'}, {'type': 'stdin_stdout', 'input': '30\\n5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5\\n', 'output': '43348\\n'}, {'type': 'stdin_stdout', 'input': '29\\n3 1 3 3 1 2 2 3 5 3 2 2 3 2 5 2 3 1 5 4 3 4 1 3 3 3 4 4 4\\n', 'output': '21903\\n'}, {'type': 'stdin_stdout', 'input': '30\\n4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4\\n', 'output': '30781\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 3 1 4 2 2 2 5 2 3\\n', 'output': '1145\\n'}, {'type': 'stdin_stdout', 'input': '28\\n1 3 4 4 4 3 1 4 5 1 3 5 3 2 5 1 4 4 5 3 4 2 5 4 2 5 3 2\\n', 'output': '26461\\n'}, {'type': 'stdin_stdout', 'input': '8\\n3 3 3 3 5 5 5 5\\n', 'output': '905\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 3 4 2 1 2 3 4 2 1\\n', 'output': '928\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5 3 3\\n', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '30\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n', 'output': '2744\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '30\\n5 5 1 1 4 4 3 1 5 3 5 5 1 2 2 3 4 5 2 1 4 3 1 1 4 5 4 4 2 2\\n', 'output': '24339\\n'}, {'type': 'stdin_stdout', 'input': '15\\n4 4 4 3 2 1 5 3 5 3 4 1 2 4 4\\n', 'output': '5661\\n'}, {'type': 'stdin_stdout', 'input': '2\\n5 5\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '30\\n1 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n', 'output': '23706\\n'}, {'type': 'stdin_stdout', 'input': '30\\n2 5 4 3 2 3 4 2 4 4 1 2 1 2 4 4 1 3 3 2 1 5 4 2 2 2 1 5 2 4\\n', 'output': '21249\\n'}, {'type': 'stdin_stdout', 'input': '19\\n5 1 2 1 1 2 1 2 1 2 1 2 1 2 5 5 5 5 5\\n', 'output': '6535\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 3 4 5\\n', 'output': '122\\n'}, {'type': 'stdin_stdout', 'input': '30\\n1 4 5 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5\\n', 'output': '59453\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 4 3 2 1\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 1\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '30\\n4 1 3 5 5 5 5 5 5 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5\\n', 'output': '60616'}, {'type': 'stdin_stdout', 'input': '30\\n2 5 5 5 5 5 5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5\\n', 'output': '60991'}, {'type': 'stdin_stdout', 'input': '20\\n4 5 3 4 5 4 2 4 2 1 5 3 3 1 4 1 2 4 4 4\\n', 'output': '10726'}, {'type': 'stdin_stdout', 'input': '30\\n2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\\n', 'output': '10361'}, {'type': 'stdin_stdout', 'input': '30\\n1 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5\\n', 'output': '62027'}, {'type': 'stdin_stdout', 'input': '7\\n5 3 3 5 1 4 4\\n', 'output': '396'}, {'type': 'stdin_stdout', 'input': '30\\n5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1\\n', 'output': '2970'}, {'type': 'stdin_stdout', 'input': '8\\n3 4 3 3 3 3 3 1\\n', 'output': '399'}, {'type': 'stdin_stdout', 'input': '30\\n5 5 5 5 5 5 5 5 5 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5\\n', 'output': '60014'}, {'type': 'stdin_stdout', 'input': '30\\n4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4\\n', 'output': '39965'}, {'type': 'stdin_stdout', 'input': '30\\n1 3 4 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n', 'output': '23363'}, {'type': 'stdin_stdout', 'input': '19\\n5 1 2 1 1 2 1 2 1 2 1 2 1 2 5 5 5 5 3\\n', 'output': '6019'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 3 4 5\\n', 'output': '123'}, {'type': 'stdin_stdout', 'input': '5\\n5 4 3 3 1\\n', 'output': '64'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 1 2 1 3\\n', 'output': '100'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '4\\n4 4 2 3\\n', 'output': '44'}, {'type': 'stdin_stdout', 'input': '20\\n4 5 3 4 5 4 2 4 2 1 5 3 3 1 4 1 4 4 4 4\\n', 'output': '11402'}, {'type': 'stdin_stdout', 'input': '30\\n2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2\\n', 'output': '10033'}, {'type': 'stdin_stdout', 'input': '30\\n5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1\\n', 'output': '3150'}, {'type': 'stdin_stdout', 'input': '8\\n3 4 3 5 3 3 3 1\\n', 'output': '431'}, {'type': 'stdin_stdout', 'input': '30\\n5 5 5 5 5 5 5 5 5 1 5 5 5 5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5\\n', 'output': '59004'}, {'type': 'stdin_stdout', 'input': '30\\n1 3 4 3 3 3 3 3 1 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\\n', 'output': '23083'}, {'type': 'stdin_stdout', 'input': '19\\n5 1 2 1 1 2 2 2 1 2 1 2 1 2 5 5 5 5 3\\n', 'output': '6275'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 4 4 5\\n', 'output': '127'}, {'type': 'stdin_stdout', 'input': '5\\n5 4 3 3 2\\n', 'output': '78'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 1 4 1 3\\n', 'output': '121'}, {'type': 'stdin_stdout', 'input': '4\\n4 4 3 3\\n', 'output': '48'}, {'type': 'stdin_stdout', 'input': '30\\n2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 1 2 2 2\\n', 'output': '10897'}, {'type': 'stdin_stdout', 'input': '8\\n3 4 3 5 3 3 2 1\\n', 'output': '385'}, {'type': 'stdin_stdout', 'input': '19\\n5 1 2 1 1 2 2 2 1 2 1 2 1 2 5 5 5 5 1\\n', 'output': '5767'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 2 4 1 3\\n', 'output': '133'}, {'type': 'stdin_stdout', 'input': '4\\n4 4 3 4\\n', 'output': '55'}, {'type': 'stdin_stdout', 'input': '30\\n2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 4 2 2 2 2 1 2 2 2\\n', 'output': '10679'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 2 4 1 3\\n', 'output': '139'}, {'type': 'stdin_stdout', 'input': '30\\n2 2 2 2 3 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 4 2 2 2 2 1 2 2 2\\n', 'output': '11019'}, {'type': 'stdin_stdout', 'input': '30\\n2 2 2 2 3 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 4 2 2 2 2 1 2 2 2\\n', 'output': '11363'}, {'type': 'stdin_stdout', 'input': '30\\n2 2 2 2 3 2 2 2 2 2 2 1 2 4 2 2 2 2 2 2 2 4 2 2 2 2 1 2 2 2\\n', 'output': '12283'}, {'type': 'stdin_stdout', 'input': '30\\n2 2 2 2 3 2 2 2 2 2 2 1 2 4 2 1 2 2 2 2 2 4 2 2 2 2 1 2 2 2\\n', 'output': '11819'}, {'type': 'stdin_stdout', 'input': '30\\n2 2 2 2 3 2 2 2 2 2 1 1 2 4 2 1 2 2 2 2 2 4 2 2 2 2 1 2 2 2\\n', 'output': '11467'}, {'type': 'stdin_stdout', 'input': '30\\n2 3 2 2 3 2 2 2 2 2 1 1 2 4 2 1 2 2 2 2 2 4 2 2 2 2 1 2 2 2\\n', 'output': '11687'}, {'type': 'stdin_stdout', 'input': '4\\n4 4 4 1\\n', 'output': '36'}, {'type': 'stdin_stdout', 'input': '30\\n1 3 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 5\\n', 'output': '58940'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 500000000}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79397","program":"```python\nimport sys\n\nplane = set()\ncrackers = {((0, -1), (0, 1))}\n\nn = int(input())\na = [int(x) for x in input().split()]\n\ncrack_dict = {\n (1, 0): ((1, -1), (1, 1)),\n (1, 1): ((1, 0), (0, 1)),\n (0, 1): ((1, 1), (-1, 1)),\n (-1, 1): ((0, 1), (-1, 0)),\n (-1, 0): ((-1, 1), (-1, -1)),\n (-1, -1): ((-1, 0), (0, -1)),\n (0, -1): ((-1, -1), (1, -1)),\n (1, -1): ((0, -1), (1, 0)),\n}\n\ndef move(cracker):\n point, direc = cracker\n point2 = (point[0] + direc[0], point[1] + direc[1])\n return (point2, direc)\n\ndef crack(cracker):\n point, direc = cracker\n direc1, direc2 = crack_dict[direc]\n return ((point, direc1), (point, direc2))\n \nfor x in a:\n for i in range(x):\n crackers = set((move(cracker) for cracker in crackers))\n plane.update((cracker[0] for cracker in crackers))\n # print(plane, file=sys.stderr)\n new_crackers = set()\n for cracker in crackers:\n new_crackers.update(crack(cracker))\n crackers = new_crackers\n\nprint(len(plane))\n\n```","inputs":"6\n1 1 1 1 1 3\n","output":"85\n","actual_output":"85\n","execution_success":true,"sample_index":12643},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"774_B. Significant Cups","prompt":"Solve the following coding problem using the programming language python:\n\nStepan is a very experienced olympiad participant. He has n cups for Physics olympiads and m cups for Informatics olympiads. Each cup is characterized by two parameters \u2014 its significance ci and width wi.\n\nStepan decided to expose some of his cups on a shelf with width d in such a way, that:\n\n * there is at least one Physics cup and at least one Informatics cup on the shelf, \n * the total width of the exposed cups does not exceed d, \n * from each subjects (Physics and Informatics) some of the most significant cups are exposed (i. e. if a cup for some subject with significance x is exposed, then all the cups for this subject with significance greater than x must be exposed too). \n\n\n\nYour task is to determine the maximum possible total significance, which Stepan can get when he exposes cups on the shelf with width d, considering all the rules described above. The total significance is the sum of significances of all the exposed cups.\n\nInput\n\nThe first line contains three integers n, m and d (1 \u2264 n, m \u2264 100 000, 1 \u2264 d \u2264 109) \u2014 the number of cups for Physics olympiads, the number of cups for Informatics olympiads and the width of the shelf.\n\nEach of the following n lines contains two integers ci and wi (1 \u2264 ci, wi \u2264 109) \u2014 significance and width of the i-th cup for Physics olympiads.\n\nEach of the following m lines contains two integers cj and wj (1 \u2264 cj, wj \u2264 109) \u2014 significance and width of the j-th cup for Informatics olympiads.\n\nOutput\n\nPrint the maximum possible total significance, which Stepan can get exposing cups on the shelf with width d, considering all the rules described in the statement.\n\nIf there is no way to expose cups on the shelf, then print 0.\n\nExamples\n\nInput\n\n3 1 8\n4 2\n5 5\n4 2\n3 2\n\n\nOutput\n\n8\n\n\nInput\n\n4 3 12\n3 4\n2 4\n3 5\n3 4\n3 5\n5 2\n3 4\n\n\nOutput\n\n11\n\n\nInput\n\n2 2 2\n5 3\n6 3\n4 2\n8 1\n\n\nOutput\n\n0\n\nNote\n\nIn the first example Stepan has only one Informatics cup which must be exposed on the shelf. Its significance equals 3 and width equals 2, so after Stepan exposes it, the width of free space on the shelf becomes equal to 6. Also, Stepan must expose the second Physics cup (which has width 5), because it is the most significant cup for Physics (its significance equals 5). After that Stepan can not expose more cups on the shelf, because there is no enough free space. Thus, the maximum total significance of exposed cups equals to 8.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, m, d = map(int, input().split())\nph = [[int(j) for j in input().split()] for i in range(n)]\ninf = [[int(j) for j in input().split()] for i in range(m)]\nfor i in range(n):\n ph[i][1] = -ph[i][1]\nfor i in range(m):\n inf[i][1] = -inf[i][1]\nph.sort(reverse=True)\ninf.sort(reverse=True)\nsw, sc = 0, 0\nfor p in inf:\n sc += p[0]\n d += p[1]\nans = 0\nz = m - 1\nfor p in ph:\n sc += p[0]\n d += p[1]\n #print(sc, d)\n while z > 0 and d < 0:\n sc -= inf[z][0]\n d -= inf[z][1]\n z -= 1\n #print(sc, d)\n if d >= 0:\n ans = max(ans, sc)\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 1 8\\n4 2\\n5 5\\n4 2\\n3 2\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '2 2 2\\n5 3\\n6 3\\n4 2\\n8 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 3 12\\n3 4\\n2 4\\n3 5\\n3 4\\n3 5\\n5 2\\n3 4\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1000000000\\n4 500000000\\n6 500000000\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n1 1\\n1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1000000000\\n1 1000000000\\n1 1000000000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10 10 229\\n15 17\\n5 4\\n4 15\\n4 17\\n15 11\\n7 6\\n5 19\\n14 8\\n4 1\\n10 12\\n20 13\\n20 14\\n16 13\\n7 15\\n2 16\\n11 11\\n19 20\\n6 7\\n4 11\\n14 16\\n', 'output': '198\\n'}, {'type': 'stdin_stdout', 'input': '4 2 8\\n1000000000 2\\n1000000000 2\\n1000000000 2\\n1000000000 2\\n1000000000 2\\n1000000000 2\\n', 'output': '4000000000\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n42 41\\n47 7\\n35 6\\n22 40\\n15 2\\n47 28\\n46 47\\n3 45\\n12 19\\n44 41\\n46 2\\n49 23\\n9 8\\n7 41\\n5 3\\n16 42\\n12 50\\n17 22\\n25 9\\n45 12\\n41 44\\n34 47\\n33 35\\n32 47\\n49 6\\n27 18\\n43 36\\n23 6\\n39 22\\n38 45\\n', 'output': '900\\n'}, {'type': 'stdin_stdout', 'input': '10 20 498\\n40 12\\n23 25\\n20 9\\n8 1\\n23 8\\n31 24\\n33 2\\n22 33\\n4 13\\n25 20\\n40 5\\n27 5\\n17 6\\n8 5\\n4 19\\n33 23\\n30 19\\n27 12\\n13 22\\n16 32\\n28 36\\n20 18\\n36 38\\n9 24\\n21 35\\n20 9\\n33 29\\n29 33\\n18 25\\n11 8\\n', 'output': '644\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1000000000\\n4 500000000\\n2 500000000\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10 10 229\\n15 17\\n5 4\\n4 15\\n4 17\\n15 11\\n7 6\\n5 19\\n14 8\\n4 1\\n10 12\\n20 13\\n20 14\\n16 8\\n7 15\\n2 16\\n11 11\\n19 20\\n6 7\\n4 11\\n14 16\\n', 'output': '200\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n42 41\\n47 7\\n35 6\\n22 40\\n15 2\\n47 28\\n46 47\\n3 45\\n12 19\\n44 41\\n46 2\\n49 23\\n9 8\\n7 41\\n5 3\\n16 42\\n12 50\\n17 22\\n25 9\\n45 12\\n56 44\\n34 47\\n33 35\\n32 47\\n49 6\\n27 18\\n43 36\\n23 6\\n39 22\\n38 45\\n', 'output': '915\\n'}, {'type': 'stdin_stdout', 'input': '10 20 498\\n40 12\\n23 25\\n20 9\\n8 0\\n23 8\\n31 24\\n33 2\\n22 33\\n4 13\\n25 20\\n40 5\\n27 5\\n17 6\\n8 5\\n4 19\\n33 23\\n30 19\\n27 12\\n13 22\\n16 32\\n28 36\\n20 18\\n36 38\\n9 24\\n21 35\\n20 9\\n33 29\\n29 33\\n18 25\\n11 8\\n', 'output': '644\\n'}, {'type': 'stdin_stdout', 'input': '3 1 8\\n0 2\\n5 5\\n4 2\\n3 2\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '2 2 2\\n5 3\\n6 3\\n4 2\\n8 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 3 12\\n3 4\\n0 4\\n3 5\\n3 4\\n3 5\\n5 2\\n3 4\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1000000000\\n0 500000000\\n2 500000000\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n66 41\\n47 7\\n35 6\\n22 40\\n15 2\\n47 28\\n46 47\\n3 45\\n12 19\\n44 41\\n46 2\\n49 23\\n9 8\\n7 41\\n5 3\\n16 42\\n12 50\\n17 22\\n25 9\\n45 12\\n56 44\\n34 47\\n33 35\\n32 47\\n49 6\\n27 18\\n43 36\\n23 6\\n39 22\\n38 45\\n', 'output': '939\\n'}, 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{'type': 'stdin_stdout', 'input': '10 20 498\\n40 12\\n23 25\\n20 9\\n8 0\\n23 8\\n31 24\\n33 2\\n22 33\\n4 13\\n25 20\\n40 10\\n27 5\\n17 6\\n8 5\\n4 19\\n33 23\\n30 19\\n27 12\\n13 22\\n16 32\\n18 36\\n20 18\\n36 38\\n9 24\\n21 35\\n20 9\\n33 29\\n29 33\\n27 25\\n11 8\\n', 'output': '643\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n66 41\\n47 7\\n35 6\\n22 40\\n15 2\\n47 28\\n46 47\\n3 45\\n19 19\\n44 41\\n46 2\\n49 23\\n9 8\\n7 41\\n5 3\\n16 42\\n12 50\\n17 22\\n25 9\\n45 12\\n56 44\\n34 47\\n33 35\\n32 47\\n119 6\\n27 18\\n43 36\\n23 6\\n39 22\\n38 45\\n', 'output': '1016\\n'}, {'type': 'stdin_stdout', 'input': '10 20 498\\n40 12\\n23 25\\n20 9\\n8 0\\n23 8\\n31 24\\n33 2\\n22 33\\n4 13\\n25 20\\n40 10\\n27 5\\n17 6\\n8 5\\n4 19\\n33 23\\n30 19\\n27 12\\n13 22\\n16 32\\n18 36\\n20 18\\n36 38\\n9 24\\n21 35\\n20 9\\n33 29\\n29 33\\n27 25\\n17 8\\n', 'output': '649\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n66 41\\n47 7\\n35 6\\n22 40\\n15 2\\n47 28\\n46 47\\n3 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36\\n20 18\\n36 38\\n9 24\\n29 35\\n20 9\\n45 29\\n29 33\\n27 25\\n17 8\\n', 'output': '669\\n'}, {'type': 'stdin_stdout', 'input': '10 20 498\\n40 12\\n23 25\\n20 9\\n8 0\\n23 8\\n31 24\\n33 2\\n22 33\\n4 13\\n25 31\\n40 10\\n27 5\\n17 6\\n8 5\\n4 19\\n33 23\\n30 19\\n27 12\\n13 22\\n16 32\\n18 36\\n20 18\\n36 38\\n9 24\\n29 35\\n20 9\\n45 29\\n29 33\\n27 25\\n17 8\\n', 'output': '660\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n66 41\\n47 7\\n35 6\\n22 40\\n15 2\\n47 28\\n46 47\\n3 45\\n11 19\\n44 41\\n46 2\\n49 23\\n9 8\\n7 42\\n5 3\\n16 42\\n12 50\\n17 22\\n25 9\\n45 12\\n74 44\\n34 47\\n20 35\\n32 47\\n119 6\\n27 18\\n43 36\\n23 6\\n39 22\\n38 45\\n', 'output': '1013\\n'}, {'type': 'stdin_stdout', 'input': '10 20 498\\n40 12\\n23 25\\n20 9\\n8 0\\n23 8\\n31 24\\n33 2\\n22 33\\n4 13\\n25 31\\n40 10\\n27 5\\n17 6\\n8 5\\n4 19\\n33 23\\n30 19\\n27 12\\n13 22\\n16 32\\n18 36\\n20 18\\n24 38\\n9 24\\n29 35\\n20 9\\n45 29\\n18 33\\n27 25\\n17 8\\n', 'output': '637\\n'}, {'type': 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13\\n60 41\\n46 2\\n49 23\\n9 4\\n7 65\\n5 3\\n16 42\\n12 20\\n20 22\\n25 9\\n7 12\\n74 44\\n34 47\\n20 42\\n32 47\\n119 6\\n27 18\\n43 45\\n23 6\\n39 22\\n38 45\\n', 'output': '992\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n66 41\\n47 7\\n35 6\\n36 40\\n15 2\\n47 28\\n44 47\\n1 45\\n11 13\\n60 41\\n46 2\\n49 23\\n9 4\\n7 65\\n5 3\\n16 42\\n12 20\\n20 22\\n25 9\\n7 12\\n74 44\\n34 47\\n20 42\\n32 47\\n119 6\\n27 18\\n43 45\\n23 6\\n39 22\\n38 45\\n', 'output': '1006\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n66 41\\n47 7\\n35 6\\n36 40\\n15 2\\n47 28\\n44 47\\n1 45\\n11 13\\n60 41\\n46 2\\n49 23\\n8 4\\n7 65\\n5 3\\n16 42\\n12 20\\n20 22\\n25 9\\n7 12\\n74 44\\n34 47\\n20 42\\n32 47\\n119 6\\n27 18\\n43 45\\n23 6\\n39 22\\n38 45\\n', 'output': '1005\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n17 41\\n47 7\\n35 6\\n36 40\\n15 2\\n47 28\\n44 47\\n1 45\\n11 13\\n60 41\\n46 2\\n49 23\\n8 4\\n7 65\\n5 3\\n16 42\\n12 20\\n20 22\\n25 9\\n7 12\\n74 44\\n34 47\\n20 42\\n32 47\\n119 6\\n27 18\\n43 45\\n23 6\\n39 22\\n38 45\\n', 'output': '956\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n17 41\\n47 7\\n35 1\\n36 40\\n15 2\\n47 28\\n44 47\\n1 45\\n11 13\\n60 41\\n46 2\\n49 23\\n8 4\\n7 65\\n5 3\\n16 42\\n12 20\\n20 22\\n25 9\\n7 20\\n74 44\\n34 47\\n24 42\\n32 47\\n119 6\\n27 18\\n43 45\\n23 6\\n39 22\\n38 45\\n', 'output': '960\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n17 41\\n47 7\\n35 1\\n36 40\\n15 2\\n47 28\\n44 47\\n1 45\\n11 13\\n22 41\\n46 2\\n49 23\\n8 4\\n7 65\\n5 3\\n16 42\\n12 20\\n20 22\\n25 9\\n7 20\\n74 44\\n34 47\\n24 42\\n32 47\\n119 6\\n27 18\\n43 45\\n23 6\\n39 22\\n38 45\\n', 'output': '922\\n'}, {'type': 'stdin_stdout', 'input': '20 10 761\\n17 41\\n47 7\\n35 1\\n36 40\\n15 2\\n47 28\\n44 47\\n1 45\\n11 13\\n22 41\\n46 2\\n49 23\\n8 4\\n7 65\\n5 3\\n16 42\\n12 20\\n20 22\\n25 9\\n7 20\\n74 44\\n34 47\\n24 42\\n32 47\\n119 6\\n27 18\\n43 45\\n30 6\\n39 22\\n38 45\\n', 'output': '929\\n'}, {'type': 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sc += p[0]\n d += p[1]\n #print(sc, d)\n while z > 0 and d < 0:\n sc -= inf[z][0]\n d -= inf[z][1]\n z -= 1\n #print(sc, d)\n if d >= 0:\n ans = max(ans, sc)\nprint(ans)\n```","inputs":"3 1 8\n4 2\n5 5\n4 2\n3 2\n","output":"8\n","actual_output":"8\n","execution_success":true,"sample_index":12644},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"799_B. T-shirt buying","prompt":"Solve the following coding problem using the programming language python:\n\nA new pack of n t-shirts came to a shop. Each of the t-shirts is characterized by three integers pi, ai and bi, where pi is the price of the i-th t-shirt, ai is front color of the i-th t-shirt and bi is back color of the i-th t-shirt. All values pi are distinct, and values ai and bi are integers from 1 to 3.\n\nm buyers will come to the shop. Each of them wants to buy exactly one t-shirt. For the j-th buyer we know his favorite color cj.\n\nA buyer agrees to buy a t-shirt, if at least one side (front or back) is painted in his favorite color. Among all t-shirts that have colors acceptable to this buyer he will choose the cheapest one. If there are no such t-shirts, the buyer won't buy anything. Assume that the buyers come one by one, and each buyer is served only after the previous one is served.\n\nYou are to compute the prices each buyer will pay for t-shirts.\n\nInput\n\nThe first line contains single integer n (1 \u2264 n \u2264 200 000) \u2014 the number of t-shirts.\n\nThe following line contains sequence of integers p1, p2, ..., pn (1 \u2264 pi \u2264 1 000 000 000), where pi equals to the price of the i-th t-shirt.\n\nThe following line contains sequence of integers a1, a2, ..., an (1 \u2264 ai \u2264 3), where ai equals to the front color of the i-th t-shirt.\n\nThe following line contains sequence of integers b1, b2, ..., bn (1 \u2264 bi \u2264 3), where bi equals to the back color of the i-th t-shirt.\n\nThe next line contains single integer m (1 \u2264 m \u2264 200 000) \u2014 the number of buyers. \n\nThe following line contains sequence c1, c2, ..., cm (1 \u2264 cj \u2264 3), where cj equals to the favorite color of the j-th buyer. The buyers will come to the shop in the order they are given in the input. Each buyer is served only after the previous one is served.\n\nOutput\n\nPrint to the first line m integers \u2014 the j-th integer should be equal to the price of the t-shirt which the j-th buyer will buy. If the j-th buyer won't buy anything, print -1.\n\nExamples\n\nInput\n\n5\n300 200 400 500 911\n1 2 1 2 3\n2 1 3 2 1\n6\n2 3 1 2 1 1\n\n\nOutput\n\n200 400 300 500 911 -1 \n\n\nInput\n\n2\n1000000000 1\n1 1\n1 2\n2\n2 1\n\n\nOutput\n\n1 1000000000 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\np = map(int,input().split())\na = map(int,input().split())\nb = map(int,input().split())\nm = int(input())\npos = map(int,input().split())\n\nfut = zip(p,a,b)\nfut=list(fut)\ndef sravni(elem):\n return elem[0]\nfut.sort(key=sravni)\n\nvz = []\nfor i in range(n):\n vz.append(False)\n\nlastc = [0,0,0]\nresult = \"\"\nfor poset in pos:\n ctoim=-1\n for i in range(lastc[poset-1],n):\n if vz[i] == False:\n if fut[i][1] == poset or fut[i][2] ==poset:\n vz[i] = True\n ctoim = fut[i][0]\n lastc[poset - 1] = i+1\n break\n if ctoim == -1:\n lastc[poset-1] = n+1\n result+=str(ctoim)+\" \"\nprint(result)\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n300 200 400 500 911\\n1 2 1 2 3\\n2 1 3 2 1\\n6\\n2 3 1 2 1 1\\n', 'output': '200 400 300 500 911 -1 \\n'}, {'type': 'stdin_stdout', 'input': '2\\n1000000000 1\\n1 1\\n1 2\\n2\\n2 1\\n', 'output': '1 1000000000 \\n'}, {'type': 'stdin_stdout', 'input': '10\\n251034796 163562337 995167403 531046374 341924810 828969071 971837553 183763940 857690534 687685084\\n3 2 1 3 2 3 1 3 2 1\\n2 3 3 1 2 3 2 3 3 2\\n10\\n1 3 2 3 2 3 3 1 2 3\\n', 'output': '531046374 163562337 251034796 183763940 341924810 828969071 857690534 687685084 971837553 995167403 \\n'}, {'type': 'stdin_stdout', 'input': '1\\n529469903\\n1\\n3\\n1\\n3\\n', 'output': '529469903 \\n'}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 2 2 3 1 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 368277336 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 \\n'}, {'type': 'stdin_stdout', 'input': '10\\n251034796 163562337 995167403 531046374 341924810 828969071 971837553 235656340 857690534 687685084\\n3 2 1 3 2 3 1 3 2 1\\n2 3 3 1 2 3 2 3 3 2\\n10\\n1 3 2 3 2 3 3 1 2 3\\n', 'output': '531046374 163562337 251034796 235656340 341924810 828969071 857690534 687685084 971837553 995167403 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 1 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 368277336 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '5\\n300 200 400 500 911\\n1 2 1 2 3\\n2 2 3 2 1\\n6\\n2 3 1 2 1 1\\n', 'output': '200 400 300 500 911 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 440654676 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 2 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 440654676 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '10\\n251034796 297387269 995167403 531046374 341924810 828969071 971837553 183763940 857690534 687685084\\n3 2 1 3 2 3 1 3 2 1\\n2 3 3 1 2 3 2 3 3 2\\n10\\n1 3 2 3 2 3 3 1 2 3\\n', 'output': '531046374 183763940 251034796 297387269 341924810 828969071 857690534 687685084 971837553 995167403 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 1 2 3 1 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 368277336 414468312 440421387 531635095 584924603 495316522 670032002 586382273 666547477 838268432 -1 726095027 786936631 940941705 -1 959075599 -1 -1 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 2 2 3 2 1 1 2 1 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 240727854 368277336 276840253 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 23763176 106106409 584924603 666547477 670032002 726095027 276840253 440654676 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 2 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '23763176 213813062 106106409 276840253 240727854 440654676 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 23763176 106106409 584924603 666547477 670032002 726095027 276840253 440654676 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 2 2 3 2 1 1 1 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '23763176 213813062 106106409 276840253 240727854 440654676 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 959075599 -1 670032002 726095027 786936631 -1 940941705 -1 -1 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '10\\n251034796 163562337 995167403 531046374 588930023 828969071 971837553 183763940 857690534 687685084\\n3 2 1 3 2 3 1 3 2 1\\n2 3 3 1 2 3 2 3 3 2\\n10\\n1 3 2 3 2 3 3 1 2 3\\n', 'output': '531046374 163562337 251034796 183763940 588930023 828969071 857690534 687685084 971837553 995167403 '}, {'type': 'stdin_stdout', 'input': '1\\n529469903\\n1\\n1\\n1\\n3\\n', 'output': '-1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 2 2 3 1 3 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 495316522 368277336 440421387 414468312 531635095 586382273 584924603 666547477 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '5\\n300 200 359 500 911\\n1 2 1 2 3\\n2 2 3 2 1\\n6\\n2 3 1 2 1 1\\n', 'output': '200 359 300 500 911 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 440654676 940941705 531635095 213813062 440421387 959075599 360017086 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 2 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 360017086 440654676 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n595014774 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 1 2 3 1 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 368277336 440421387 495316522 531635095 584924603 586382273 670032002 595014774 666547477 838268432 -1 726095027 786936631 940941705 -1 959075599 -1 -1 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '10\\n251034796 163562337 990140914 531046374 341924810 828969071 971837553 235656340 857690534 687685084\\n3 2 1 3 2 3 1 3 2 1\\n2 3 3 1 2 1 2 3 3 2\\n10\\n1 3 2 3 2 3 3 1 2 3\\n', 'output': '531046374 163562337 251034796 235656340 341924810 828969071 857690534 687685084 971837553 990140914 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 692068873 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 2 2 3 1 3 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 495316522 414468312 440421387 531635095 584924603 586382273 666547477 692068873 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '5\\n300 200 359 500 1650\\n1 2 1 2 3\\n2 2 3 2 1\\n6\\n2 3 1 2 1 1\\n', 'output': '200 359 300 500 1650 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 107191858 584924603 666547477 670032002 726095027 276840253 440654676 940941705 531635095 213813062 440421387 959075599 360017086 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 2 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 107191858 276840253 360017086 440654676 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n595014774 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 358739832 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 1 2 3 1 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 368277336 358739832 495316522 531635095 584924603 586382273 670032002 595014774 666547477 838268432 -1 726095027 786936631 940941705 -1 959075599 -1 -1 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 23763176 106106409 584924603 666547477 670032002 726095027 276840253 440654676 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 1 2 3 2 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 3 1 2 3 2 2 1 2 1 2 2\\n', 'output': '23763176 213813062 106106409 276840253 240727854 440654676 414468312 440421387 531635095 584924603 495316522 670032002 586382273 666547477 838268432 -1 726095027 786936631 940941705 -1 959075599 -1 -1 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 692068873 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 332988424 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 2 2 3 1 3 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 495316522 332988424 440421387 414468312 531635095 586382273 584924603 666547477 838268432 -1 -1 670032002 692068873 726095027 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '5\\n300 200 359 500 1650\\n2 2 1 2 3\\n2 2 3 2 1\\n6\\n2 3 1 2 1 1\\n', 'output': '200 359 1650 300 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n595014774 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 358739832 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 1 2 3 1 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 2 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 368277336 358739832 495316522 531635095 584924603 670032002 726095027 586382273 666547477 838268432 -1 806443734 595014774 786936631 -1 940941705 -1 959075599 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 692068873 940941705 531635095 213813062 695142765 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2 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 1 2 2 1 2 1 2 2\\n', 'output': '20329584 54422884 106106409 213813062 76996922 240727854 368277336 276840253 440421387 531635095 586382273 584924603 666547477 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 23763176 106106409 584924603 666547477 670032002 726095027 276840253 440654676 940941705 531635095 213813062 440421387 959075599 361509332 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 1 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 1 2 3 3 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 2 3 1 3 1 3 1 2 2 3 3 1 3 1 2 3 2 2 1 2 1 2 2\\n', 'output': '23763176 213813062 106106409 276840253 361509332 440654676 414468312 440421387 531635095 584924603 495316522 670032002 586382273 666547477 726095027 838268432 806443734 940941705 786936631 -1 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786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 2 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 3 1 2 3 2 2 1 2 1 2 2\\n', 'output': '23763176 213813062 106106409 276840253 240727854 440654676 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 692068873 940941705 531635095 213813062 695142765 959075599 240727854 495316522 838268432 332988424 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 1 3 2 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 495316522 332988424 586382273 414468312 531635095 695142765 584924603 666547477 838268432 -1 -1 670032002 692068873 726095027 -1 959075599 -1 -1 -1 806443734 940941705 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 2 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 1 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 368277336 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '10\\n251034796 163562337 995167403 531046374 341924810 828969071 971837553 235656340 857690534 687685084\\n3 2 1 3 2 3 1 3 2 1\\n2 3 3 1 3 1 2 3 3 2\\n10\\n1 3 2 3 2 3 3 1 2 3\\n', 'output': '531046374 163562337 251034796 235656340 341924810 828969071 857690534 687685084 971837553 995167403 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 2 2 3 2 2 3 2 1 1 2 1 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 1 3 3 1 3 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 240727854 368277336 276840253 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 23763176 106106409 584924603 666547477 670032002 726095027 276840253 440654676 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 2 2 3 2 2 3 2 1 1 1 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '23763176 213813062 106106409 276840253 240727854 440654676 414468312 440421387 531635095 584924603 495316522 666547477 586382273 838268432 959075599 -1 670032002 726095027 786936631 -1 940941705 -1 -1 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 2 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 2 2 3 1 3 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 495316522 368277336 440421387 414468312 531635095 586382273 584924603 666547477 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n595014774 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 358739832 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 1 2 3 1 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 2 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 3 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 368277336 358739832 495316522 531635095 584924603 670032002 726095027 586382273 666547477 838268432 -1 806443734 595014774 786936631 -1 940941705 -1 959075599 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n595014774 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 358739832 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 1 2 3 1 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 2 2 3 1 1 1 2 3 3 1 3 1 3 1 2 3 3 3 1 2 1 2 3 2 2 1 2 1 3 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 368277336 358739832 495316522 531635095 584924603 670032002 726095027 586382273 666547477 838268432 -1 806443734 595014774 786936631 -1 940941705 -1 959075599 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 692068873 940941705 531635095 213813062 695142765 959075599 240727854 89740580 838268432 332988424 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 2 2 2 2 2 3 1 3 2 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 3 3 1 3 1 3 1 2 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 89740580 106106409 213813062 240727854 531635095 332988424 276840253 414468312 584924603 586382273 666547477 692068873 695142765 838268432 -1 670032002 726095027 959075599 -1 -1 -1 -1 -1 806443734 940941705 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 1 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 2 2 3 1 2 3 1 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 2 1 2 3 1 1 1 2 3 3 1 3 1 3 1 3 2 3 3 1 2 1 2 3 2 2 1 2 1 2 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 368277336 414468312 440421387 531635095 495316522 586382273 584924603 666547477 838268432 -1 -1 670032002 726095027 786936631 -1 940941705 -1 959075599 -1 -1 806443734 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '2\\n1000000100 1\\n1 1\\n1 3\\n2\\n2 1\\n', 'output': '-1 1 '}, {'type': 'stdin_stdout', 'input': '20\\n414468312 23763176 106106409 584924603 666547477 670032002 726095027 276840253 440654676 940941705 531635095 213813062 440421387 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 1 1 3 2 3 2 3 3 2 2 1 3 1 2\\n3 1 2 2 1 2 3 3 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 2 3 1 3 3 1 2 3 1 1 1 2 2 3 1 3 1 3 1 2 2 3 3 1 3 1 2 3 2 2 1 2 1 2 2\\n', 'output': '23763176 213813062 106106409 276840253 240727854 440654676 414468312 440421387 531635095 584924603 495316522 670032002 586382273 666547477 726095027 838268432 806443734 940941705 786936631 -1 959075599 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}, {'type': 'stdin_stdout', 'input': '20\\n595014774 20329584 106106409 584924603 666547477 670032002 726095027 276840253 368277336 940941705 531635095 213813062 358739832 959075599 240727854 495316522 838268432 786936631 586382273 806443734\\n3 1 2 3 3 2 2 2 3 2 3 2 3 3 3 2 1 3 1 2\\n3 1 2 2 1 2 3 1 2 3 2 1 1 2 3 1 2 3 3 2\\n40\\n1 1 2 1 3 1 3 1 3 3 2 2 3 1 1 1 2 3 3 1 3 1 3 1 2 3 3 3 1 2 1 2 3 2 2 1 2 1 3 2\\n', 'output': '20329584 213813062 106106409 276840253 240727854 358739832 368277336 495316522 531635095 584924603 670032002 726095027 586382273 666547477 838268432 -1 806443734 595014774 786936631 -1 940941705 -1 959075599 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 '}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79405","program":"```python\nn = int(input())\np = map(int,input().split())\na = map(int,input().split())\nb = map(int,input().split())\nm = int(input())\npos = map(int,input().split())\n\nfut = zip(p,a,b)\nfut=list(fut)\ndef sravni(elem):\n return elem[0]\nfut.sort(key=sravni)\n\nvz = []\nfor i in range(n):\n vz.append(False)\n\nlastc = [0,0,0]\nresult = \"\"\nfor poset in pos:\n ctoim=-1\n for i in range(lastc[poset-1],n):\n if vz[i] == False:\n if fut[i][1] == poset or fut[i][2] ==poset:\n vz[i] = True\n ctoim = fut[i][0]\n lastc[poset - 1] = i+1\n break\n if ctoim == -1:\n lastc[poset-1] = n+1\n result+=str(ctoim)+\" \"\nprint(result)\n\n\n```","inputs":"5\n300 200 400 500 911\n1 2 1 2 3\n2 1 3 2 1\n6\n2 3 1 2 1 1\n","output":"200 400 300 500 911 -1 \n","actual_output":"200 400 300 500 911 -1 \n","execution_success":true,"sample_index":12645},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"819_B. Mister B and PR Shifts","prompt":"Solve the following coding problem using the programming language python:\n\nSome time ago Mister B detected a strange signal from the space, which he started to study.\n\nAfter some transformation the signal turned out to be a permutation p of length n or its cyclic shift. For the further investigation Mister B need some basis, that's why he decided to choose cyclic shift of this permutation which has the minimum possible deviation.\n\nLet's define the deviation of a permutation p as .\n\nFind a cyclic shift of permutation p with minimum possible deviation. If there are multiple solutions, print any of them.\n\nLet's denote id k (0 \u2264 k < n) of a cyclic shift of permutation p as the number of right shifts needed to reach this shift, for example:\n\n * k = 0: shift p1, p2, ... pn, \n * k = 1: shift pn, p1, ... pn - 1, \n * ..., \n * k = n - 1: shift p2, p3, ... pn, p1. \n\nInput\n\nFirst line contains single integer n (2 \u2264 n \u2264 106) \u2014 the length of the permutation.\n\nThe second line contains n space-separated integers p1, p2, ..., pn (1 \u2264 pi \u2264 n) \u2014 the elements of the permutation. It is guaranteed that all elements are distinct.\n\nOutput\n\nPrint two integers: the minimum deviation of cyclic shifts of permutation p and the id of such shift. If there are multiple solutions, print any of them.\n\nExamples\n\nInput\n\n3\n1 2 3\n\n\nOutput\n\n0 0\n\n\nInput\n\n3\n2 3 1\n\n\nOutput\n\n0 1\n\n\nInput\n\n3\n3 2 1\n\n\nOutput\n\n2 1\n\nNote\n\nIn the first sample test the given permutation p is the identity permutation, that's why its deviation equals to 0, the shift id equals to 0 as well.\n\nIn the second sample test the deviation of p equals to 4, the deviation of the 1-st cyclic shift (1, 2, 3) equals to 0, the deviation of the 2-nd cyclic shift (3, 1, 2) equals to 4, the optimal is the 1-st cyclic shift.\n\nIn the third sample test the deviation of p equals to 4, the deviation of the 1-st cyclic shift (1, 3, 2) equals to 2, the deviation of the 2-nd cyclic shift (2, 1, 3) also equals to 2, so the optimal are both 1-st and 2-nd cyclic shifts.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef main():\n\tn = int(input())\n\tdata = input().split()\n\n\t#print(str(n) + \" \" + str(data))\n\n\tdata = list(map(lambda x: int(x), data))\n\tres = 0\n\tires = 0\n\tneg = 0\n\twhen = [0] * n\n\n\tfor i in range(n):\n\t\tdata[i] = i + 1 - data[i]\n\t\tres += abs(data[i])\n\t\tif data[i] <= 0:\n\t\t\tneg += 1\n\t\ta = -data[i]\n\t\tif a < 0:\n\t\t\ta = a + n\n\t\twhen[a] += 1\n\t#print(when)\n\t\n\tares = res\t\n\t#print(str(res) + \" \" + str(ires) + \" \" + str(neg))\n\tfor i in range(n):\n\t\tneg -= when[i]\n\t\tares -= neg\n\t\tares += (n - neg)\n\t\tx = data[n - i - 1] + i + 1\n\t\tares -= x\n\t\tares += n - x\n\t\t#print(str(res) + \" \" + str(ires) + \" \" + str(ares) + \" \" + str(i) + \" \" + str(neg))\n\t\tneg += 1\n\t\tif ares < res:\n\t\t\tres = ares\n\t\t\tires = i + 1\n\n\tprint(str(res) + \" \" + str(ires))\n\t\nmain()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 2 3\\n', 'output': '0 0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 2 1\\n', 'output': '2 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 1\\n', 'output': '0 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 5 10 3 6 4 9 1 8 7\\n', 'output': '28 0\\n'}, {'type': 'stdin_stdout', 'input': '108\\n1 102 33 99 6 83 4 20 61 100 76 71 44 9 24 87 57 2 81 82 90 85 12 30 66 53 47 36 43 29 31 64 96 84 77 23 93 78 58 68 42 55 13 70 62 19 92 14 10 65 63 75 91 48 11 105 37 50 32 94 18 26 52 89 104 106 86 97 80 95 17 72 40 22 79 103 25 101 35 51 15 98 67 5 34 69 54 27 45 88 56 16 46 60 74 108 21 41 73 39 107 59 3 8 28 49 7 38\\n', 'output': '3428 30\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 2 1 3\\n', 'output': '2 3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n10 1 9 2 8 3 7 4 6 5\\n', 'output': '24 7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 7 10 1 6 3 4 8 9 5\\n', 'output': '20 7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 4 6 5 7 9 10 8\\n', 'output': '6 0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 2 3 1\\n', 'output': '4 1\\n'}, 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'stdin_stdout', 'input': '4\\n3 2 4 2\\n', 'output': '3 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3 2 2 4\\n', 'output': '3 0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 4 1\\n', 'output': '2 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 7 10 10 5 2 3 8 9 4\\n', 'output': '22 6\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 3 3 4\\n', 'output': '1 0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 4 10 8 9 2 3 6 7 9\\n', 'output': '24 5\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 3 1 3\\n', 'output': '3 2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 5 4 6 5 7 9 10 8\\n', 'output': '8 0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 4 10 6 9 1 5 7 8 6\\n', 'output': '25 5\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 4 4 2\\n', 'output': '3 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 4 2 4\\n', 'output': '3 0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 3\\n', 'output': '1 0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79409","program":"```python\ndef main():\n\tn = int(input())\n\tdata = input().split()\n\n\t#print(str(n) + \" \" + str(data))\n\n\tdata = list(map(lambda x: int(x), data))\n\tres = 0\n\tires = 0\n\tneg = 0\n\twhen = [0] * n\n\n\tfor i in range(n):\n\t\tdata[i] = i + 1 - data[i]\n\t\tres += abs(data[i])\n\t\tif data[i] <= 0:\n\t\t\tneg += 1\n\t\ta = -data[i]\n\t\tif a < 0:\n\t\t\ta = a + n\n\t\twhen[a] += 1\n\t#print(when)\n\t\n\tares = res\t\n\t#print(str(res) + \" \" + str(ires) + \" \" + str(neg))\n\tfor i in range(n):\n\t\tneg -= when[i]\n\t\tares -= neg\n\t\tares += (n - neg)\n\t\tx = data[n - i - 1] + i + 1\n\t\tares -= x\n\t\tares += n - x\n\t\t#print(str(res) + \" \" + str(ires) + \" \" + str(ares) + \" \" + str(i) + \" \" + str(neg))\n\t\tneg += 1\n\t\tif ares < res:\n\t\t\tres = ares\n\t\t\tires = i + 1\n\n\tprint(str(res) + \" \" + str(ires))\n\t\nmain()\n\n```","inputs":"3\n1 2 3\n","output":"0 0\n","actual_output":"0 0\n","execution_success":true,"sample_index":12646},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"865_B. Ordering Pizza","prompt":"Solve the following coding problem using the programming language python:\n\nIt's another Start[c]up finals, and that means there is pizza to order for the onsite contestants. There are only 2 types of pizza (obviously not, but let's just pretend for the sake of the problem), and all pizzas contain exactly S slices.\n\nIt is known that the i-th contestant will eat si slices of pizza, and gain ai happiness for each slice of type 1 pizza they eat, and bi happiness for each slice of type 2 pizza they eat. We can order any number of type 1 and type 2 pizzas, but we want to buy the minimum possible number of pizzas for all of the contestants to be able to eat their required number of slices. Given that restriction, what is the maximum possible total happiness that can be achieved?\n\nInput\n\nThe first line of input will contain integers N and S (1 \u2264 N \u2264 105, 1 \u2264 S \u2264 105), the number of contestants and the number of slices per pizza, respectively. N lines follow.\n\nThe i-th such line contains integers si, ai, and bi (1 \u2264 si \u2264 105, 1 \u2264 ai \u2264 105, 1 \u2264 bi \u2264 105), the number of slices the i-th contestant will eat, the happiness they will gain from each type 1 slice they eat, and the happiness they will gain from each type 2 slice they eat, respectively.\n\nOutput\n\nPrint the maximum total happiness that can be achieved.\n\nExamples\n\nInput\n\n3 12\n3 5 7\n4 6 7\n5 9 5\n\n\nOutput\n\n84\n\n\nInput\n\n6 10\n7 4 7\n5 8 8\n12 5 8\n6 11 6\n3 3 7\n5 9 6\n\n\nOutput\n\n314\n\nNote\n\nIn the first example, you only need to buy one pizza. If you buy a type 1 pizza, the total happiness will be 3\u00b75 + 4\u00b76 + 5\u00b79 = 84, and if you buy a type 2 pizza, the total happiness will be 3\u00b77 + 4\u00b77 + 5\u00b75 = 74.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef solve(ls):\n\n ls.sort(key=lambda q: q[1] - q[0])\n\n m = sum(si for a, b, si in ls)\n\n k = s * (m // s)\n\n n = m - k\n\n x = y = z = 0\n\n for a, b, si in ls:\n\n if k >= si:\n\n k -= si\n\n z += si * a\n\n elif k:\n\n z += k * a\n\n x = (si - k) * a\n\n y = (si - k) * b\n\n k = 0\n\n else:\n\n x += si * a\n\n y += si * b\n\n return x, y, z, n\n\n\n\nn,s = map(int,input().split())\n\nfirst=[]\n\nsecond=[]\n\nfor i in range(n):\n\n\tsi, ai, bi = map(int,input().split())\n\n\tif ai>bi:\n\n\t\tfirst.append((ai,bi,si))\n\n\telse:\n\n\t\tsecond.append((bi,ai,si))\n\nx1,y1,z1,n1 = solve(first)\n\nx2,y2,z2,n2 = solve(second)\n\nd = x1+x2 if n1+n2>s else max(x1+y2,x2+y1)\n\nprint(z1+z2+d)\n\n\n\n\n\n# Made By Mostafa_Khaled\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 12\\n3 5 7\\n4 6 7\\n5 9 5\\n', 'output': '84\\n'}, {'type': 'stdin_stdout', 'input': '6 10\\n7 4 7\\n5 8 8\\n12 5 8\\n6 11 6\\n3 3 7\\n5 9 6\\n', 'output': '314\\n'}, {'type': 'stdin_stdout', 'input': '1 100\\n97065 97644 98402\\n', 'output': '9551390130\\n'}, {'type': 'stdin_stdout', 'input': '1 100000\\n1 82372 5587\\n', 'output': '82372\\n'}, {'type': 'stdin_stdout', 'input': '2 10\\n9 1 2\\n9 2 1\\n', 'output': '36\\n'}, {'type': 'stdin_stdout', 'input': '3 10\\n10 3 4\\n5 1 100\\n5 100 1\\n', 'output': '1035\\n'}, {'type': 'stdin_stdout', 'input': '2 100000\\n50000 1 100000\\n50000 100000 1\\n', 'output': '5000050000\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n6 4 5\\n6 5 5\\n8 7 5\\n', 'output': '116\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n2 1 10\\n1 2 1\\n1 3 1\\n', 'output': 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'input': '3 8\\n2 10 4\\n6 3 5\\n6 5 6\\n', 'output': '82\\n'}, {'type': 'stdin_stdout', 'input': '2 10\\n5 10 9\\n11 5 10\\n', 'output': '155\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n7 4 7\\n1 16 8\\n12 5 8\\n6 11 6\\n3 0 7\\n5 9 6\\n', 'output': '293\\n'}, {'type': 'stdin_stdout', 'input': '6 10\\n7 4 7\\n5 16 8\\n12 5 8\\n6 11 6\\n3 3 7\\n5 9 6\\n', 'output': '351\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n5 10 10\\n5 12 5\\n', 'output': '110\\n'}, {'type': 'stdin_stdout', 'input': '10 8\\n7 1 4\\n4 8 9\\n3 7 10\\n5 5 9\\n1 5 6\\n1 8 5\\n5 7 4\\n5 4 6\\n10 5 7\\n9 7 3\\n', 'output': '351\\n'}, {'type': 'stdin_stdout', 'input': '3 8\\n2 5 4\\n6 5 9\\n6 5 6\\n', 'output': '98\\n'}, {'type': 'stdin_stdout', 'input': '2 13\\n7 2 1\\n7 0 2\\n', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '3 12\\n3 5 0\\n4 6 3\\n5 9 5\\n', 'output': '84\\n'}, {'type': 'stdin_stdout', 'input': '6 10\\n7 4 7\\n5 16 8\\n12 5 8\\n6 11 6\\n3 0 7\\n5 9 6\\n', 'output': '351\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n2 1 10\\n1 0 2\\n1 3 1\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n5 10 4\\n5 12 5\\n', 'output': '110\\n'}, {'type': 'stdin_stdout', 'input': '10 15\\n7 1 4\\n4 8 9\\n3 7 10\\n5 5 9\\n1 5 6\\n1 8 5\\n5 7 4\\n5 4 6\\n10 5 7\\n9 7 3\\n', 'output': '351\\n'}, {'type': 'stdin_stdout', 'input': '2 13\\n7 1 1\\n7 0 2\\n', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '2 5\\n5 10 9\\n9 5 10\\n', 'output': '140\\n'}, {'type': 'stdin_stdout', 'input': '25 6\\n1 10 5\\n1 8 4\\n1 5 2\\n4 8 9\\n3 2 8\\n1 9 5\\n2 10 10\\n1 9 6\\n3 5 4\\n2 7 8\\n2 3 0\\n2 6 8\\n3 7 8\\n4 3 7\\n1 8 1\\n3 6 4\\n3 2 8\\n2 2 1\\n4 8 8\\n4 13 4\\n3 10 2\\n3 6 6\\n2 2 5\\n1 6 2\\n4 1 5\\n', 'output': '448\\n'}, {'type': 'stdin_stdout', 'input': '3 8\\n2 10 4\\n6 5 5\\n6 5 6\\n', 'output': '86\\n'}, {'type': 'stdin_stdout', 'input': '2 10\\n5 10 9\\n9 5 10\\n', 'output': '140\\n'}, {'type': 'stdin_stdout', 'input': '3 12\\n3 5 1\\n4 6 3\\n5 4 5\\n', 'output': '59\\n'}, {'type': 'stdin_stdout', 'input': '2 7\\n2 1 10\\n2 0 2\\n1 3 1\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n5 10 4\\n3 16 5\\n', 'output': '98\\n'}, {'type': 'stdin_stdout', 'input': '2 13\\n0 0 1\\n7 0 2\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3 12\\n3 5 0\\n7 6 3\\n5 4 5\\n', 'output': '82\\n'}, {'type': 'stdin_stdout', 'input': '2 7\\n2 1 10\\n2 0 2\\n1 4 1\\n', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '25 6\\n1 10 5\\n1 8 4\\n1 5 2\\n4 8 9\\n4 2 8\\n1 9 5\\n2 10 10\\n1 9 6\\n3 5 3\\n2 7 8\\n2 3 0\\n2 6 8\\n3 7 8\\n4 3 7\\n1 8 1\\n3 6 4\\n3 2 8\\n2 2 1\\n4 8 8\\n4 13 4\\n3 10 2\\n3 6 6\\n2 2 5\\n1 6 2\\n4 1 5\\n', 'output': '456\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79417","program":"```python\ndef solve(ls):\n\n ls.sort(key=lambda q: q[1] - q[0])\n\n m = sum(si for a, b, si in ls)\n\n k = s * (m // s)\n\n n = m - k\n\n x = y = z = 0\n\n for a, b, si in ls:\n\n if k >= si:\n\n k -= si\n\n z += si * a\n\n elif k:\n\n z += k * a\n\n x = (si - k) * a\n\n y = (si - k) * b\n\n k = 0\n\n else:\n\n x += si * a\n\n y += si * b\n\n return x, y, z, n\n\n\n\nn,s = map(int,input().split())\n\nfirst=[]\n\nsecond=[]\n\nfor i in range(n):\n\n\tsi, ai, bi = map(int,input().split())\n\n\tif ai>bi:\n\n\t\tfirst.append((ai,bi,si))\n\n\telse:\n\n\t\tsecond.append((bi,ai,si))\n\nx1,y1,z1,n1 = solve(first)\n\nx2,y2,z2,n2 = solve(second)\n\nd = x1+x2 if n1+n2>s else max(x1+y2,x2+y1)\n\nprint(z1+z2+d)\n\n\n\n\n\n# Made By Mostafa_Khaled\n```","inputs":"3 12\n3 5 7\n4 6 7\n5 9 5\n","output":"84\n","actual_output":"84\n","execution_success":true,"sample_index":12647},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"913_E. Logical Expression","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a boolean function of three variables which is defined by its truth table. You need to find an expression of minimum length that equals to this function. The expression may consist of: \n\n * Operation AND ('&', ASCII code 38) \n * Operation OR ('|', ASCII code 124) \n * Operation NOT ('!', ASCII code 33) \n * Variables x, y and z (ASCII codes 120-122) \n * Parentheses ('(', ASCII code 40, and ')', ASCII code 41) \n\n\n\nIf more than one expression of minimum length exists, you should find the lexicographically smallest one.\n\nOperations have standard priority. NOT has the highest priority, then AND goes, and OR has the lowest priority. The expression should satisfy the following grammar:\n\nE ::= E '|' T | T\n\nT ::= T '&' F | F\n\nF ::= '!' F | '(' E ')' | 'x' | 'y' | 'z'\n\nInput\n\nThe first line contains one integer n \u2014 the number of functions in the input (1 \u2264 n \u2264 10 000).\n\nThe following n lines contain descriptions of functions, the i-th of them contains a string of length 8 that consists of digits 0 and 1 \u2014 the truth table of the i-th function. The digit on position j (0 \u2264 j < 8) equals to the value of the function in case of , and .\n\nOutput\n\nYou should output n lines, the i-th line should contain the expression of minimum length which equals to the i-th function. If there is more than one such expression, output the lexicographically smallest of them. Expressions should satisfy the given grammar and shouldn't contain white spaces.\n\nExample\n\nInput\n\n4\n00110011\n00000111\n11110000\n00011111\n\n\nOutput\n\ny\n(y|z)&x\n!x\nx|y&z\n\nNote\n\nThe truth table for the second function:\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nanswers = [\n'!x&x',\n'x&y&z',\n'!z&x&y',\n'x&y',\n'!y&x&z',\n'x&z',\n'!y&x&z|!z&x&y',\n'(y|z)&x',\n'!y&!z&x',\n'!y&!z&x|x&y&z',\n'!z&x',\n'!z&x|x&y',\n'!y&x',\n'!y&x|x&z',\n'!(y&z)&x',\n'x',\n'!x&y&z',\n'y&z',\n'!x&y&z|!z&x&y',\n'(x|z)&y',\n'!x&y&z|!y&x&z',\n'(x|y)&z',\n'!x&y&z|!y&x&z|!z&x&y',\n'(x|y)&z|x&y',\n'!x&y&z|!y&!z&x',\n'!y&!z&x|y&z',\n'!x&y&z|!z&x',\n'!z&x|y&z',\n'!x&y&z|!y&x',\n'!y&x|y&z',\n'!(y&z)&x|!x&y&z',\n'x|y&z',\n'!x&!z&y',\n'!x&!z&y|x&y&z',\n'!z&y',\n'!z&y|x&y',\n'!x&!z&y|!y&x&z',\n'!x&!z&y|x&z',\n'!y&x&z|!z&y',\n'!z&y|x&z',\n'!(!x&!y|x&y|z)',\n'!(!x&!y|x&y|z)|x&y&z',\n'!z&(x|y)',\n'!z&(x|y)|x&y',\n'!x&!z&y|!y&x',\n'!x&!z&y|!y&x|x&z',\n'!y&x|!z&y',\n'!z&y|x',\n'!x&y',\n'!x&y|y&z',\n'!(x&z)&y',\n'y',\n'!x&y|!y&x&z',\n'!x&y|x&z',\n'!(x&z)&y|!y&x&z',\n'x&z|y',\n'!x&y|!y&!z&x',\n'!x&y|!y&!z&x|y&z',\n'!x&y|!z&x',\n'!z&x|y',\n'!x&y|!y&x',\n'!x&y|!y&x|x&z',\n'!(x&z)&y|!y&x',\n'x|y',\n'!x&!y&z',\n'!x&!y&z|x&y&z',\n'!x&!y&z|!z&x&y',\n'!x&!y&z|x&y',\n'!y&z',\n'!y&z|x&z',\n'!y&z|!z&x&y',\n'!y&z|x&y',\n'!(!x&!z|x&z|y)',\n'!(!x&!z|x&z|y)|x&y&z',\n'!x&!y&z|!z&x',\n'!x&!y&z|!z&x|x&y',\n'!y&(x|z)',\n'!y&(x|z)|x&z',\n'!y&z|!z&x',\n'!y&z|x',\n'!x&z',\n'!x&z|y&z',\n'!x&z|!z&x&y',\n'!x&z|x&y',\n'!(x&y)&z',\n'z',\n'!(x&y)&z|!z&x&y',\n'x&y|z',\n'!x&z|!y&!z&x',\n'!x&z|!y&!z&x|y&z',\n'!x&z|!z&x',\n'!x&z|!z&x|x&y',\n'!x&z|!y&x',\n'!y&x|z',\n'!(x&y)&z|!z&x',\n'x|z',\n'!(!y&!z|x|y&z)',\n'!(!y&!z|x|y&z)|x&y&z',\n'!x&!y&z|!z&y',\n'!x&!y&z|!z&y|x&y',\n'!x&!z&y|!y&z',\n'!x&!z&y|!y&z|x&z',\n'!y&z|!z&y',\n'!y&z|!z&y|x&y',\n'!(!x&!y|x&y|z)|!x&!y&z',\n'!(!x&!y|x&y|z)|!x&!y&z|x&y&z',\n'!x&!y&z|!z&(x|y)',\n'!x&!y&z|!z&(x|y)|x&y',\n'!x&!z&y|!y&(x|z)',\n'!x&!z&y|!y&(x|z)|x&z',\n'!y&(x|z)|!z&y',\n'!y&z|!z&y|x',\n'!x&(y|z)',\n'!x&(y|z)|y&z',\n'!x&z|!z&y',\n'!x&z|y',\n'!x&y|!y&z',\n'!x&y|z',\n'!(x&y)&z|!z&y',\n'y|z',\n'!x&(y|z)|!y&!z&x',\n'!x&(y|z)|!y&!z&x|y&z',\n'!x&(y|z)|!z&x',\n'!x&z|!z&x|y',\n'!x&(y|z)|!y&x',\n'!x&y|!y&x|z',\n'!x&y|!y&z|!z&x',\n'x|y|z',\n'!(x|y|z)',\n'!(x|y|z)|x&y&z',\n'!(!x&y|!y&x|z)',\n'!(x|y|z)|x&y',\n'!(!x&z|!z&x|y)',\n'!(x|y|z)|x&z',\n'!(!x&y|!y&x|z)|!y&x&z',\n'!(x|y|z)|(y|z)&x',\n'!y&!z',\n'!y&!z|x&y&z',\n'!(!x&y|z)',\n'!y&!z|x&y',\n'!(!x&z|y)',\n'!y&!z|x&z',\n'!(!x&y|z)|!y&x',\n'!y&!z|x',\n'!(!y&z|!z&y|x)',\n'!(x|y|z)|y&z',\n'!(!x&y|!y&x|z)|!x&y&z',\n'!(x|y|z)|(x|z)&y',\n'!(!x&z|!z&x|y)|!x&y&z',\n'!(x|y|z)|(x|y)&z',\n'!(!x&y|!y&x|z)|!x&y&z|!y&x&z',\n'!(x|y|z)|(x|y)&z|x&y',\n'!x&y&z|!y&!z',\n'!y&!z|y&z',\n'!(!x&y|z)|!x&y&z',\n'!(!x&y|z)|y&z',\n'!(!x&z|y)|!x&y&z',\n'!(!x&z|y)|y&z',\n'!(!x&y|z)|!x&y&z|!y&x',\n'!y&!z|x|y&z',\n'!x&!z',\n'!x&!z|x&y&z',\n'!(!y&x|z)',\n'!x&!z|x&y',\n'!x&!z|!y&x&z',\n'!x&!z|x&z',\n'!(!y&x|z)|!y&x&z',\n'!(!y&x|z)|x&z',\n'!(x&y|z)',\n'!(x&y|z)|x&y&z',\n'!z',\n'!z|x&y',\n'!x&!z|!y&x',\n'!(x&y|z)|x&z',\n'!y&x|!z',\n'!z|x',\n'!(!y&z|x)',\n'!x&!z|y&z',\n'!(!y&x|z)|!x&y',\n'!x&!z|y',\n'!(!y&z|x)|!y&x&z',\n'!(!y&z|x)|x&z',\n'!(!y&x|z)|!x&y|!y&x&z',\n'!x&!z|x&z|y',\n'!x&y|!y&!z',\n'!(x&y|z)|y&z',\n'!x&y|!z',\n'!z|y',\n'!(!x&!y&z|x&y)',\n'!x&!z|!y&x|y&z',\n'!x&y|!y&x|!z',\n'!z|x|y',\n'!x&!y',\n'!x&!y|x&y&z',\n'!x&!y|!z&x&y',\n'!x&!y|x&y',\n'!(!z&x|y)',\n'!x&!y|x&z',\n'!(!z&x|y)|!z&x&y',\n'!(!z&x|y)|x&y',\n'!(x&z|y)',\n'!(x&z|y)|x&y&z',\n'!x&!y|!z&x',\n'!(x&z|y)|x&y',\n'!y',\n'!y|x&z',\n'!y|!z&x',\n'!y|x',\n'!(!z&y|x)',\n'!x&!y|y&z',\n'!(!z&y|x)|!z&x&y',\n'!(!z&y|x)|x&y',\n'!(!z&x|y)|!x&z',\n'!x&!y|z',\n'!(!z&x|y)|!x&z|!z&x&y',\n'!x&!y|x&y|z',\n'!x&z|!y&!z',\n'!(x&z|y)|y&z',\n'!(!x&!z&y|x&z)',\n'!x&!y|!z&x|y&z',\n'!x&z|!y',\n'!y|z',\n'!x&z|!y|!z&x',\n'!y|x|z',\n'!(x|y&z)',\n'!(x|y&z)|x&y&z',\n'!x&!y|!z&y',\n'!(x|y&z)|x&y',\n'!x&!z|!y&z',\n'!(x|y&z)|x&z',\n'!(!y&!z&x|y&z)',\n'!x&!y|!z&y|x&z',\n'!((x|y)&z|x&y)',\n'!((x|y)&z|x&y)|x&y&z',\n'!x&!y|!z',\n'!x&!y|!z|x&y',\n'!x&!z|!y',\n'!x&!z|!y|x&z',\n'!y|!z',\n'!y|!z|x',\n'!x',\n'!x|y&z',\n'!x|!z&y',\n'!x|y',\n'!x|!y&z',\n'!x|z',\n'!x|!y&z|!z&y',\n'!x|y|z',\n'!x|!y&!z',\n'!x|!y&!z|y&z',\n'!x|!z',\n'!x|!z|y',\n'!x|!y',\n'!x|!y|z',\n'!(x&y&z)',\n'!x|x']\n\nN = int(input())\nfor i in range(N):\n q = int(input(), 2)\n print(answers[q])\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n00110011\\n00000111\\n11110000\\n00011111\\n', 'output': 'y\\n(y|z)&x\\n!x\\nx|y&z\\n'}, {'type': 'stdin_stdout', 'input': '4\\n11000010\\n11000010\\n11001110\\n10001001\\n', 'output': '!x&!y|!z&x&y\\n!x&!y|!z&x&y\\n!y|!z&x\\n!y&!z|x&y&z\\n'}, {'type': 'stdin_stdout', 'input': '1\\n11001110\\n', 'output': '!y|!z&x\\n'}, {'type': 'stdin_stdout', 'input': '2\\n11001110\\n01001001\\n', 'output': '!y|!z&x\\n!(!x&!z|x&z|y)|x&y&z\\n'}, {'type': 'stdin_stdout', 'input': '5\\n01111000\\n00110110\\n00011100\\n01110111\\n01010011\\n', 'output': '!x&(y|z)|!y&!z&x\\n!(x&z)&y|!y&x&z\\n!x&y&z|!y&x\\ny|z\\n!x&z|x&y\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10001001\\n10111011\\n10111101\\n', 'output': '!y&!z|x&y&z\\n!z|y\\n!x&!z|!y&x|y&z\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110011\\n00000111\\n11110000\\n00011111\\n', 'output': 'y\\n(y|z)&x\\n!x\\nx|y&z\\n'}, {'type': 'stdin_stdout', 'input': '4\\n11000010\\n11000000\\n11001110\\n10001001\\n', 'output': '!x&!y|!z&x&y\\n!x&!y\\n!y|!z&x\\n!y&!z|x&y&z\\n'}, {'type': 'stdin_stdout', 'input': '1\\n01001110\\n', 'output': '!y&z|!z&x\\n'}, {'type': 'stdin_stdout', 'input': '2\\n11001110\\n01001000\\n', 'output': '!y|!z&x\\n!(!x&!z|x&z|y)\\n'}, {'type': 'stdin_stdout', 'input': '5\\n01111000\\n00110110\\n00011100\\n01110111\\n01010010\\n', 'output': '!x&(y|z)|!y&!z&x\\n!(x&z)&y|!y&x&z\\n!x&y&z|!y&x\\ny|z\\n!x&z|!z&x&y\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10001011\\n10111011\\n10111101\\n', 'output': '!y&!z|x&y\\n!z|y\\n!x&!z|!y&x|y&z\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110011\\n00000111\\n11110000\\n00011110\\n', 'output': 'y\\n(y|z)&x\\n!x\\n!(y&z)&x|!x&y&z\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110011\\n10000111\\n11110000\\n00011111\\n', 'output': 'y\\n!(x|y|z)|(y|z)&x\\n!x\\nx|y&z\\n'}, {'type': 'stdin_stdout', 'input': '4\\n11000010\\n01000000\\n11001110\\n10001001\\n', 'output': '!x&!y|!z&x&y\\n!x&!y&z\\n!y|!z&x\\n!y&!z|x&y&z\\n'}, {'type': 'stdin_stdout', 'input': '1\\n11000110\\n', 'output': '!(!z&x|y)|!z&x&y\\n'}, {'type': 'stdin_stdout', 'input': '2\\n01001110\\n01001000\\n', 'output': '!y&z|!z&x\\n!(!x&!z|x&z|y)\\n'}, {'type': 'stdin_stdout', 'input': '5\\n01111000\\n00110110\\n00011000\\n01110111\\n01010010\\n', 'output': '!x&(y|z)|!y&!z&x\\n!(x&z)&y|!y&x&z\\n!x&y&z|!y&!z&x\\ny|z\\n!x&z|!z&x&y\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10001011\\n10011011\\n10111101\\n', 'output': '!y&!z|x&y\\n!(!x&y|z)|y&z\\n!x&!z|!y&x|y&z\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110011\\n00000111\\n11100000\\n00011110\\n', 'output': 'y\\n(y|z)&x\\n!(x|y&z)\\n!(y&z)&x|!x&y&z\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110011\\n10001111\\n11110000\\n00011111\\n', 'output': 'y\\n!y&!z|x\\n!x\\nx|y&z\\n'}, {'type': 'stdin_stdout', 'input': '4\\n10000010\\n01000000\\n11001110\\n10001001\\n', 'output': '!(!x&y|!y&x|z)\\n!x&!y&z\\n!y|!z&x\\n!y&!z|x&y&z\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10000110\\n', 'output': '!(!x&y|!y&x|z)|!y&x&z\\n'}, {'type': 'stdin_stdout', 'input': '2\\n01001110\\n01101000\\n', 'output': '!y&z|!z&x\\n!(!x&!y|x&y|z)|!x&!y&z\\n'}, {'type': 'stdin_stdout', 'input': '5\\n01111000\\n00110010\\n00011000\\n01110111\\n01010010\\n', 'output': '!x&(y|z)|!y&!z&x\\n!(x&z)&y\\n!x&y&z|!y&!z&x\\ny|z\\n!x&z|!z&x&y\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10001011\\n10011011\\n10111111\\n', 'output': '!y&!z|x&y\\n!(!x&y|z)|y&z\\n!z|x|y\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110011\\n00000111\\n11100000\\n00011010\\n', 'output': 'y\\n(y|z)&x\\n!(x|y&z)\\n!x&y&z|!z&x\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110011\\n10001111\\n11110000\\n00011011\\n', 'output': 'y\\n!y&!z|x\\n!x\\n!z&x|y&z\\n'}, {'type': 'stdin_stdout', 'input': '4\\n10000010\\n01000000\\n11001111\\n10001001\\n', 'output': '!(!x&y|!y&x|z)\\n!x&!y&z\\n!y|x\\n!y&!z|x&y&z\\n'}, {'type': 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'stdin_stdout', 'input': '2\\n11101110\\n01101000\\n', 'output': '!y|!z\\n!(!x&!y|x&y|z)|!x&!y&z\\n'}, {'type': 'stdin_stdout', 'input': '5\\n01111000\\n00100010\\n00011000\\n01110111\\n01000010\\n', 'output': '!x&(y|z)|!y&!z&x\\n!z&y\\n!x&y&z|!y&!z&x\\ny|z\\n!x&!y&z|!z&x&y\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10001011\\n10111011\\n10110111\\n', 'output': '!y&!z|x&y\\n!z|y\\n!x&!z|x&z|y\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110011\\n00000111\\n11100010\\n00001010\\n', 'output': 'y\\n(y|z)&x\\n!x&!y|!z&y\\n!z&x\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110001\\n10001111\\n11110000\\n00010011\\n', 'output': '!x&y|y&z\\n!y&!z|x\\n!x\\n(x|z)&y\\n'}, {'type': 'stdin_stdout', 'input': '4\\n10000010\\n11000000\\n11001111\\n10101001\\n', 'output': '!(!x&y|!y&x|z)\\n!x&!y\\n!y|x\\n!(x&y|z)|x&y&z\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10001101\\n', 'output': '!y&!z|x&z\\n'}, {'type': 'stdin_stdout', 'input': '2\\n10101110\\n01101000\\n', 'output': '!y&x|!z\\n!(!x&!y|x&y|z)|!x&!y&z\\n'}, {'type': 'stdin_stdout', 'input': '5\\n00111000\\n00100010\\n00011000\\n01110111\\n01000010\\n', 'output': '!x&y|!y&!z&x\\n!z&y\\n!x&y&z|!y&!z&x\\ny|z\\n!x&!y&z|!z&x&y\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10001011\\n10011011\\n10110111\\n', 'output': '!y&!z|x&y\\n!(!x&y|z)|y&z\\n!x&!z|x&z|y\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110011\\n00000111\\n11100010\\n10001010\\n', 'output': 'y\\n(y|z)&x\\n!x&!y|!z&y\\n!(!x&y|z)\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110001\\n10001111\\n11110010\\n00010011\\n', 'output': '!x&y|y&z\\n!y&!z|x\\n!x|!z&y\\n(x|z)&y\\n'}, {'type': 'stdin_stdout', 'input': '4\\n10000010\\n11000000\\n11001111\\n00101001\\n', 'output': '!(!x&y|!y&x|z)\\n!x&!y\\n!y|x\\n!(!x&!y|x&y|z)|x&y&z\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10101101\\n', 'output': '!(x&y|z)|x&z\\n'}, {'type': 'stdin_stdout', 'input': '2\\n10101111\\n01101000\\n', 'output': '!z|x\\n!(!x&!y|x&y|z)|!x&!y&z\\n'}, {'type': 'stdin_stdout', 'input': '5\\n00111000\\n00100010\\n00011000\\n01110111\\n00000010\\n', 'output': '!x&y|!y&!z&x\\n!z&y\\n!x&y&z|!y&!z&x\\ny|z\\n!z&x&y\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10001011\\n10011011\\n10010111\\n', 'output': '!y&!z|x&y\\n!(!x&y|z)|y&z\\n!(x|y|z)|(x|y)&z|x&y\\n'}, {'type': 'stdin_stdout', 'input': '4\\n00110011\\n00010111\\n11100010\\n10001010\\n', 'output': 'y\\n(x|y)&z|x&y\\n!x&!y|!z&y\\n!(!x&y|z)\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79425","program":"```python\nanswers = [\n'!x&x',\n'x&y&z',\n'!z&x&y',\n'x&y',\n'!y&x&z',\n'x&z',\n'!y&x&z|!z&x&y',\n'(y|z)&x',\n'!y&!z&x',\n'!y&!z&x|x&y&z',\n'!z&x',\n'!z&x|x&y',\n'!y&x',\n'!y&x|x&z',\n'!(y&z)&x',\n'x',\n'!x&y&z',\n'y&z',\n'!x&y&z|!z&x&y',\n'(x|z)&y',\n'!x&y&z|!y&x&z',\n'(x|y)&z',\n'!x&y&z|!y&x&z|!z&x&y',\n'(x|y)&z|x&y',\n'!x&y&z|!y&!z&x',\n'!y&!z&x|y&z',\n'!x&y&z|!z&x',\n'!z&x|y&z',\n'!x&y&z|!y&x',\n'!y&x|y&z',\n'!(y&z)&x|!x&y&z',\n'x|y&z',\n'!x&!z&y',\n'!x&!z&y|x&y&z',\n'!z&y',\n'!z&y|x&y',\n'!x&!z&y|!y&x&z',\n'!x&!z&y|x&z',\n'!y&x&z|!z&y',\n'!z&y|x&z',\n'!(!x&!y|x&y|z)',\n'!(!x&!y|x&y|z)|x&y&z',\n'!z&(x|y)',\n'!z&(x|y)|x&y',\n'!x&!z&y|!y&x',\n'!x&!z&y|!y&x|x&z',\n'!y&x|!z&y',\n'!z&y|x',\n'!x&y',\n'!x&y|y&z',\n'!(x&z)&y',\n'y',\n'!x&y|!y&x&z',\n'!x&y|x&z',\n'!(x&z)&y|!y&x&z',\n'x&z|y',\n'!x&y|!y&!z&x',\n'!x&y|!y&!z&x|y&z',\n'!x&y|!z&x',\n'!z&x|y',\n'!x&y|!y&x',\n'!x&y|!y&x|x&z',\n'!(x&z)&y|!y&x',\n'x|y',\n'!x&!y&z',\n'!x&!y&z|x&y&z',\n'!x&!y&z|!z&x&y',\n'!x&!y&z|x&y',\n'!y&z',\n'!y&z|x&z',\n'!y&z|!z&x&y',\n'!y&z|x&y',\n'!(!x&!z|x&z|y)',\n'!(!x&!z|x&z|y)|x&y&z',\n'!x&!y&z|!z&x',\n'!x&!y&z|!z&x|x&y',\n'!y&(x|z)',\n'!y&(x|z)|x&z',\n'!y&z|!z&x',\n'!y&z|x',\n'!x&z',\n'!x&z|y&z',\n'!x&z|!z&x&y',\n'!x&z|x&y',\n'!(x&y)&z',\n'z',\n'!(x&y)&z|!z&x&y',\n'x&y|z',\n'!x&z|!y&!z&x',\n'!x&z|!y&!z&x|y&z',\n'!x&z|!z&x',\n'!x&z|!z&x|x&y',\n'!x&z|!y&x',\n'!y&x|z',\n'!(x&y)&z|!z&x',\n'x|z',\n'!(!y&!z|x|y&z)',\n'!(!y&!z|x|y&z)|x&y&z',\n'!x&!y&z|!z&y',\n'!x&!y&z|!z&y|x&y',\n'!x&!z&y|!y&z',\n'!x&!z&y|!y&z|x&z',\n'!y&z|!z&y',\n'!y&z|!z&y|x&y',\n'!(!x&!y|x&y|z)|!x&!y&z',\n'!(!x&!y|x&y|z)|!x&!y&z|x&y&z',\n'!x&!y&z|!z&(x|y)',\n'!x&!y&z|!z&(x|y)|x&y',\n'!x&!z&y|!y&(x|z)',\n'!x&!z&y|!y&(x|z)|x&z',\n'!y&(x|z)|!z&y',\n'!y&z|!z&y|x',\n'!x&(y|z)',\n'!x&(y|z)|y&z',\n'!x&z|!z&y',\n'!x&z|y',\n'!x&y|!y&z',\n'!x&y|z',\n'!(x&y)&z|!z&y',\n'y|z',\n'!x&(y|z)|!y&!z&x',\n'!x&(y|z)|!y&!z&x|y&z',\n'!x&(y|z)|!z&x',\n'!x&z|!z&x|y',\n'!x&(y|z)|!y&x',\n'!x&y|!y&x|z',\n'!x&y|!y&z|!z&x',\n'x|y|z',\n'!(x|y|z)',\n'!(x|y|z)|x&y&z',\n'!(!x&y|!y&x|z)',\n'!(x|y|z)|x&y',\n'!(!x&z|!z&x|y)',\n'!(x|y|z)|x&z',\n'!(!x&y|!y&x|z)|!y&x&z',\n'!(x|y|z)|(y|z)&x',\n'!y&!z',\n'!y&!z|x&y&z',\n'!(!x&y|z)',\n'!y&!z|x&y',\n'!(!x&z|y)',\n'!y&!z|x&z',\n'!(!x&y|z)|!y&x',\n'!y&!z|x',\n'!(!y&z|!z&y|x)',\n'!(x|y|z)|y&z',\n'!(!x&y|!y&x|z)|!x&y&z',\n'!(x|y|z)|(x|z)&y',\n'!(!x&z|!z&x|y)|!x&y&z',\n'!(x|y|z)|(x|y)&z',\n'!(!x&y|!y&x|z)|!x&y&z|!y&x&z',\n'!(x|y|z)|(x|y)&z|x&y',\n'!x&y&z|!y&!z',\n'!y&!z|y&z',\n'!(!x&y|z)|!x&y&z',\n'!(!x&y|z)|y&z',\n'!(!x&z|y)|!x&y&z',\n'!(!x&z|y)|y&z',\n'!(!x&y|z)|!x&y&z|!y&x',\n'!y&!z|x|y&z',\n'!x&!z',\n'!x&!z|x&y&z',\n'!(!y&x|z)',\n'!x&!z|x&y',\n'!x&!z|!y&x&z',\n'!x&!z|x&z',\n'!(!y&x|z)|!y&x&z',\n'!(!y&x|z)|x&z',\n'!(x&y|z)',\n'!(x&y|z)|x&y&z',\n'!z',\n'!z|x&y',\n'!x&!z|!y&x',\n'!(x&y|z)|x&z',\n'!y&x|!z',\n'!z|x',\n'!(!y&z|x)',\n'!x&!z|y&z',\n'!(!y&x|z)|!x&y',\n'!x&!z|y',\n'!(!y&z|x)|!y&x&z',\n'!(!y&z|x)|x&z',\n'!(!y&x|z)|!x&y|!y&x&z',\n'!x&!z|x&z|y',\n'!x&y|!y&!z',\n'!(x&y|z)|y&z',\n'!x&y|!z',\n'!z|y',\n'!(!x&!y&z|x&y)',\n'!x&!z|!y&x|y&z',\n'!x&y|!y&x|!z',\n'!z|x|y',\n'!x&!y',\n'!x&!y|x&y&z',\n'!x&!y|!z&x&y',\n'!x&!y|x&y',\n'!(!z&x|y)',\n'!x&!y|x&z',\n'!(!z&x|y)|!z&x&y',\n'!(!z&x|y)|x&y',\n'!(x&z|y)',\n'!(x&z|y)|x&y&z',\n'!x&!y|!z&x',\n'!(x&z|y)|x&y',\n'!y',\n'!y|x&z',\n'!y|!z&x',\n'!y|x',\n'!(!z&y|x)',\n'!x&!y|y&z',\n'!(!z&y|x)|!z&x&y',\n'!(!z&y|x)|x&y',\n'!(!z&x|y)|!x&z',\n'!x&!y|z',\n'!(!z&x|y)|!x&z|!z&x&y',\n'!x&!y|x&y|z',\n'!x&z|!y&!z',\n'!(x&z|y)|y&z',\n'!(!x&!z&y|x&z)',\n'!x&!y|!z&x|y&z',\n'!x&z|!y',\n'!y|z',\n'!x&z|!y|!z&x',\n'!y|x|z',\n'!(x|y&z)',\n'!(x|y&z)|x&y&z',\n'!x&!y|!z&y',\n'!(x|y&z)|x&y',\n'!x&!z|!y&z',\n'!(x|y&z)|x&z',\n'!(!y&!z&x|y&z)',\n'!x&!y|!z&y|x&z',\n'!((x|y)&z|x&y)',\n'!((x|y)&z|x&y)|x&y&z',\n'!x&!y|!z',\n'!x&!y|!z|x&y',\n'!x&!z|!y',\n'!x&!z|!y|x&z',\n'!y|!z',\n'!y|!z|x',\n'!x',\n'!x|y&z',\n'!x|!z&y',\n'!x|y',\n'!x|!y&z',\n'!x|z',\n'!x|!y&z|!z&y',\n'!x|y|z',\n'!x|!y&!z',\n'!x|!y&!z|y&z',\n'!x|!z',\n'!x|!z|y',\n'!x|!y',\n'!x|!y|z',\n'!(x&y&z)',\n'!x|x']\n\nN = int(input())\nfor i in range(N):\n q = int(input(), 2)\n print(answers[q])\n\n```","inputs":"4\n00110011\n00000111\n11110000\n00011111\n","output":"y\n(y|z)&x\n!x\nx|y&z\n","actual_output":"y\n(y|z)&x\n!x\nx|y&z\n","execution_success":true,"sample_index":12649},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"935_E. Fafa and Ancient Mathematics","prompt":"Solve the following coding problem using the programming language python:\n\nAncient Egyptians are known to have understood difficult concepts in mathematics. The ancient Egyptian mathematician Ahmes liked to write a kind of arithmetic expressions on papyrus paper which he called as Ahmes arithmetic expression.\n\nAn Ahmes arithmetic expression can be defined as: \n\n * \"d\" is an Ahmes arithmetic expression, where d is a one-digit positive integer; \n * \"(E1 op E2)\" is an Ahmes arithmetic expression, where E1 and E2 are valid Ahmes arithmetic expressions (without spaces) and op is either plus ( + ) or minus ( - ). \n\nFor example 5, (1-1) and ((1+(2-3))-5) are valid Ahmes arithmetic expressions.\n\nOn his trip to Egypt, Fafa found a piece of papyrus paper having one of these Ahmes arithmetic expressions written on it. Being very ancient, the papyrus piece was very worn out. As a result, all the operators were erased, keeping only the numbers and the brackets. Since Fafa loves mathematics, he decided to challenge himself with the following task:\n\nGiven the number of plus and minus operators in the original expression, find out the maximum possible value for the expression on the papyrus paper after putting the plus and minus operators in the place of the original erased operators.\n\nInput\n\nThe first line contains a string E (1 \u2264 |E| \u2264 104) \u2014 a valid Ahmes arithmetic expression. All operators are erased and replaced with '?'.\n\nThe second line contains two space-separated integers P and M (0 \u2264 min(P, M) \u2264 100) \u2014 the number of plus and minus operators, respectively. \n\nIt is guaranteed that P + M = the number of erased operators.\n\nOutput\n\nPrint one line containing the answer to the problem.\n\nExamples\n\nInput\n\n(1?1)\n1 0\n\n\nOutput\n\n2\n\n\nInput\n\n(2?(1?2))\n1 1\n\n\nOutput\n\n1\n\n\nInput\n\n((1?(5?7))?((6?2)?7))\n3 2\n\n\nOutput\n\n18\n\n\nInput\n\n((1?(5?7))?((6?2)?7))\n2 3\n\n\nOutput\n\n16\n\nNote\n\n * The first sample will be (1 + 1) = 2. \n * The second sample will be (2 + (1 - 2)) = 1. \n * The third sample will be ((1 - (5 - 7)) + ((6 + 2) + 7)) = 18. \n * The fourth sample will be ((1 + (5 + 7)) - ((6 - 2) - 7)) = 16. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom math import inf\n\nclass Node:\n def __init__(self, parent = None, leftExp = None, rightExp = None, signQ = 0):\n self.parent, self.leftExp, self.rightExp, self.signQ = parent, leftExp, rightExp, signQ\n def __str__(self):\n return \"Node\"\n\nmemo = {}\n\ndef Memoize(node, p, maxValue, minValue):\n if not node in memo:\n memo.update({node : {p : [maxValue, minValue]} })\n else:\n memo[node].update({p : [maxValue, minValue]})\n\ndef ExpMaxValue(root: Node, p):\n\n m = root.signQ - p\n \"\"\"if root.signQ == 1:\n if p == 1:\n return [root.leftExp.value + root.rightExp.value, root.leftExp.value + root.rightExp.value]\n else:\n return [root.leftExp.value - root.rightExp.value, root.leftExp.value - root.rightExp.value]\"\"\"\n\n if root.signQ == 0:\n return [root.value, root.value]\n \n if root in memo:\n if p in memo[root]:\n return memo[root][p]\n\n if m == 0:\n value = ExpMaxValue(root.leftExp, root.leftExp.signQ)[0] + ExpMaxValue(root.rightExp, root.rightExp.signQ)[0]\n Memoize(root, p, value, value)\n return [value, value]\n if p == 0:\n value = ExpMaxValue(root.leftExp, 0)[0] - ExpMaxValue(root.rightExp, 0)[0]\n Memoize(root, p, value, value)\n return [value, value]\n \n maxValue = -inf\n minValue = inf\n if m >= p:\n for pQMid in range(2):\n pQLeftMin = min(p - pQMid, root.leftExp.signQ)\n for pQLeft in range(pQLeftMin + 1):\n if root.leftExp.signQ - pQLeft + (1 - pQMid) > m:\n continue\n \n resLeft = ExpMaxValue(root.leftExp, pQLeft)\n resRight = ExpMaxValue(root.rightExp, p - pQMid - pQLeft)\n \n if pQMid == 1:\n maxValue = max(resLeft[0] + resRight[0], maxValue)\n minValue = min(resLeft[1] + resRight[1], minValue)\n else:\n maxValue = max(resLeft[0] - resRight[1], maxValue)\n minValue = min(resLeft[1] - resRight[0], minValue)\n else:\n for mQMid in range(2):\n mQLeftMin = min(m - mQMid, root.leftExp.signQ)\n for mQLeft in range(mQLeftMin + 1):\n pQLeft = root.leftExp.signQ - mQLeft\n if pQLeft + (1 - mQMid) > p:\n continue\n \n resLeft = ExpMaxValue(root.leftExp, pQLeft)\n resRight = ExpMaxValue(root.rightExp, p - (1 - mQMid) - pQLeft)\n \n if mQMid == 0:\n maxValue = max(resLeft[0] + resRight[0], maxValue)\n minValue = min(resLeft[1] + resRight[1], minValue)\n else:\n maxValue = max(resLeft[0] - resRight[1], maxValue)\n minValue = min(resLeft[1] - resRight[0], minValue)\n\n Memoize(root, p, int(maxValue), int(minValue))\n\n return [int(maxValue), int(minValue)]\n \n \n\ndef PrintNodes(root: Node):\n if root.signQ != 0:\n leftExp = root.leftExp if root.leftExp.signQ != 0 else root.leftExp.value\n rightExp = root.rightExp if root.rightExp.signQ != 0 else root.rightExp.value\n check = root.signQ == root.leftExp.signQ + root.rightExp.signQ + 1\n print(root.signQ, root.parent, leftExp, rightExp, check)\n PrintNodes(root.leftExp)\n PrintNodes(root.rightExp)\n\n \n\ndef main():\n exp = str(input())\n if len(exp) == 1:\n print(exp)\n return\n \n #root = Node(None, None, None)\n #root.parent = root\n cNode = Node()\n isRight = False\n \n for i in range(1, len(exp) - 1):\n if exp[i] == '(':\n if not isRight:\n cNode.leftExp = Node(cNode)\n cNode = cNode.leftExp\n else:\n cNode.rightExp = Node(cNode)\n cNode = cNode.rightExp\n isRight = False\n elif exp[i] == '?':\n isRight = True\n cNode.signQ += 1\n elif exp[i] == ')':\n if cNode.parent != None:\n cNode.parent.signQ += cNode.signQ\n cNode = cNode.parent\n isRight = False\n else:\n if not isRight:\n cNode.leftExp = Node(cNode)\n cNode.leftExp.value = int(exp[i])\n else:\n cNode.rightExp = Node(cNode)\n cNode.rightExp.value = int(exp[i])\n\n \n #PrintNodes(cNode)\n\n ss = str(input()).split()\n p, m = int(ss[0]), int(ss[1])\n\n print(ExpMaxValue(cNode, p)[0])\n \n\n\n \n\nmain()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '((1?(5?7))?((6?2)?7))\\n3 2\\n', 'output': '18'}, {'type': 'stdin_stdout', 'input': '(1?1)\\n1 0\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '((1?(5?7))?((6?2)?7))\\n2 3\\n', 'output': '16'}, {'type': 'stdin_stdout', 'input': '(2?(1?2))\\n1 1\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '(((6?((2?(9?(3?(2?((3?((1?(1?(6?(9?(((6?((3?(((((6?(1?(1?((((2?(1?(1?((6?(6?(4?(8?((9?(((7?((5?(9?(3?((((7?((9?(4?(8?(((((9?(1?(((8?(6?(6?((5?(((5?(7?((((1?((1?(4?((7?(8?(((3?((((4?((((((1?((3?((5?1)?9))?3))?9)?7)?7)?2)?8))?9)?1)?6))?9)?2)))?6)))?7))?4)?1)?1)))?6)?1))?9))))?8)?7)))?9)?3)?7)?7))))?1))?9)?6)?1))))?2))?2)?6))?6)))))?4))))?2)?3)?8))))?9)?1)?3)?1))?3))?9)?4)))))?2))?7)))))?4))?1)?7)\\n50 49\\n', 'output': '422'}, {'type': 'stdin_stdout', 'input': '8\\n0 0\\n', 'output': '8'}, {'type': 'stdin_stdout', 'input': '(((4?7)?(9?((6?(3?2))?((6?3)?7))))?((5?((7?(7?(8?3)))?(4?2)))?2))\\n16 0\\n', 'output': '85'}, {'type': 'stdin_stdout', 'input': '((4?3)?(((2?(4?((4?((2?(3?(7?3)))?(((((3?(6?2))?3)?(((((6?6)?(1?5))?((8?8)?1))?(5?((7?((6?((((3?8)?8)?(8?5))?7))?8))?((8?(2?8))?3))))?6))?(8?(7?5)))?8)))?((((7?(4?3))?4)?5)?((1?(((2?2)?((((4?((7?6)?(1?4)))?(8?(1?(((1?3)?(((2?2)?(3?(8?(9?((2?(4?6))?(7?8))))))?(9?(7?9))))?(7?3)))))?((2?((2?((8?6)?1))?(3?1)))?(7?1)))?5))?((((6?(9?(((5?4)?7)?((5?8)?8))))?5)?7)?(2?2))))?4)))))?2)?(7?(4?((6?6)?6)))))\\n50 49\\n', 'output': '423'}, {'type': 'stdin_stdout', 'input': '((((4?6)?9)?((5?(7?1))?(6?(4?(((((((7?3)?7)?(((((8?(6?7))?((1?2)?(5?8)))?8)?7)?4))?6)?7)?1)?((7?(2?((1?(((8?(((((2?7)?(((((3?6)?3)?(((((9?5)?7)?(1?(5?5)))?(8?((3?(1?2))?((8?5)?(7?((9?((9?8)?7))?1))))))?1))?1)?(9?2)))?((7?5)?((9?(4?(9?6)))?(8?(((5?7)?2)?(6?(3?8)))))))?(((4?(2?2))?(7?9))?((7?((((4?(3?(7?3)))?8)?3)?(5?(((9?2)?(9?((((2?(7?3))?(3?(1?(9?(6?(9?8))))))?2)?2)))?2))))?((9?((2?(2?3))?((9?((7?4)?1))?5)))?((((9?6)?3)?(4?1))?7)))))?5))?4)?4))?7)))?5))))))?1)\\n2 114\\n', 'output': '86'}, {'type': 'stdin_stdout', 'input': '((((3?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?1)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(9?5))?(8?(3?((5?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((7?(2?1))?6)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))\\n100 12\\n', 'output': '550'}, {'type': 'stdin_stdout', 'input': '(9?((1?(3?(5?((9?7)?(((((4?5)?2)?1)?(7?6))?(3?(9?7)))))))?(1?4)))\\n0 16\\n', 'output': '11'}, {'type': 'stdin_stdout', 'input': 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'((1?(2?7))?((6?5)?7))\\n2 3\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '(4?(((3?2)?((((((4?(4?((2?3)?((7?((3?3)?(6?(((2?(3?6))?6)?(((1?5)?8)?(((8?1)?(5?7))?6))))))?(3?8)))))?((8?8)?5))?(7?(8?((((8?((((2?(8?(((3?6)?8)?7)))?5)?(8?(7?((4?(3?4))?(5?((1?(2?((2?(4?7))?(((6?1)?(4?(8?1)))?(1?(3?(((2?(2?(3?(8?9))))?(((((2?4)?6)?7)?(8?9))?7))?(((9?(7?3))?2)?((((((2?8)?6)?(1?3))?1)?7)?1)))))))))?(5?(6?(9?(5?4))))))))))?7))?5)?(8?(8?((5?7)?2))))?2))))?4)?(1?((7?4)?6)))?6))?6))\\n50 49\\n', 'output': '438\\n'}, {'type': 'stdin_stdout', 'input': '(2?(1?2))\\n0 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '(2?(2?2))\\n0 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '(2?2)\\n1 0\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '(((6?((2?(9?(3?(2?((3?((1?(1?(6?(9?(((6?((3?(((((6?(1?(1?((((2?(1?(1?((6?(6?(4?(8?((9?(((7?((5?(9?(3?((((7?((9?(4?(8?(((((9?(1?(((8?(6?(6?((5?(((5?(7?((((1?((1?(4?((7?(8?(((3?((((5?((((((1?((3?((5?1)?9))?3))?9)?7)?7)?2)?8))?9)?1)?6))?9)?2)))?6)))?7))?4)?1)?1)))?6)?1))?9))))?8)?7)))?9)?3)?7)?7))))?1))?9)?6)?1))))?2))?2)?6))?6)))))?4))))?2)?3)?8))))?9)?1)?3)?1))?3))?9)?4)))))?2))?7)))))?4))?1)?7)\\n50 49\\n', 'output': '423\\n'}, {'type': 'stdin_stdout', 'input': '((1?(5?7))?((6?2)?6))\\n3 2\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '(2?(1?2))\\n2 0\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '((1?(7?5))?((6?2)?7))\\n3 2\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '((1?(5?7))?((6?2)?8))\\n3 2\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': 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'input': '((((2?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?1)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(9?5))?(8?(3?((5?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((7?(2?1))?5)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))\\n100 12\\n', 'output': '548\\n'}, {'type': 'stdin_stdout', 'input': '(((6?((2?(9?(3?(2?((3?((1?(1?(6?(9?(((6?((3?(((((6?(1?(1?((((2?(1?(1?((6?(6?(4?(8?((9?(((7?((5?(9?(3?((((7?((9?(4?(8?(((((9?(1?(((8?(6?(6?((5?(((5?(7?((((1?((1?(4?((7?(8?(((3?((((3?((((((1?((3?((5?1)?9))?3))?9)?7)?7)?2)?8))?9)?1)?6))?9)?2)))?6)))?7))?4)?1)?1)))?6)?1))?9))))?8)?7)))?9)?3)?7)?7))))?1))?9)?6)?1))))?2))?2)?6))?6)))))?4))))?2)?3)?8))))?9)?1)?3)?1))?3))?9)?4)))))?1))?7)))))?4))?1)?7)\\n50 49\\n', 'output': '420\\n'}, {'type': 'stdin_stdout', 'input': '((1?(2?7))?((6?5)?6))\\n2 3\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '((7?(5?1))?((6?2)?7))\\n3 2\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '(2?4)\\n1 0\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '((((4?6)?9)?((5?(7?1))?(6?(4?(((((((7?3)?7)?(((((8?(6?7))?((1?2)?(5?8)))?8)?7)?4))?6)?7)?1)?((7?(2?((1?(((8?(((((2?7)?(((((3?6)?3)?(((((9?4)?7)?(1?(5?5)))?(8?((3?(1?2))?((8?5)?(7?((9?((9?8)?7))?1))))))?1))?1)?(9?2)))?((7?5)?((9?(4?(9?6)))?(8?(((5?7)?2)?(6?(3?8)))))))?(((4?(2?2))?(7?9))?((7?((((4?(3?(7?3)))?8)?3)?(5?(((9?2)?(9?((((2?(7?3))?(3?(1?(9?(6?(9?8))))))?2)?2)))?2))))?((9?((2?(2?3))?((9?((7?4)?1))?5)))?((((9?6)?3)?(4?1))?7)))))?5))?4)?4))?7)))?5))))))?1)\\n2 114\\n', 'output': '85\\n'}, {'type': 'stdin_stdout', 'input': '(1?(3?2))\\n0 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '((((4?6)?9)?((5?(7?1))?(6?(4?(((((((7?3)?7)?(((((8?(6?7))?((1?2)?(5?8)))?8)?7)?4))?6)?7)?1)?((7?(2?((1?(((8?(((((2?7)?(((((3?6)?3)?(((((9?4)?7)?(1?(5?5)))?(8?((3?(1?2))?((8?5)?(7?((9?((9?8)?7))?1))))))?1))?1)?(9?2)))?((7?5)?((9?(4?(9?6)))?(8?(((5?7)?2)?(6?(3?8)))))))?(((4?(2?2))?(7?9))?((7?((((4?(3?(7?3)))?8)?3)?(5?(((9?2)?(9?((((2?(7?3))?(3?(1?(9?(6?(9?8))))))?2)?2)))?2))))?((9?((2?(2?3))?((9?((7?4)?1))?5)))?((((9?6)?4)?(4?1))?7)))))?5))?4)?4))?7)))?5))))))?1)\\n2 114\\n', 'output': '86\\n'}, {'type': 'stdin_stdout', 'input': '((((3?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?1)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(9?5))?(8?(3?((5?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((6?(2?1))?6)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))\\n100 12\\n', 'output': '549\\n'}, {'type': 'stdin_stdout', 'input': '(1?2)\\n1 0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '((((2?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?9)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(1?5))?(8?(3?((5?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((7?(2?1))?6)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))\\n100 12\\n', 'output': '549\\n'}, {'type': 'stdin_stdout', 'input': '(2?1)\\n1 0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '(1?(1?2))\\n0 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '(2?(3?2))\\n0 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '(2?3)\\n1 0\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '(2?(1?3))\\n0 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '(3?2)\\n1 0\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '((((2?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?1)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(9?5))?(8?(3?((6?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((7?(2?1))?5)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))\\n100 12\\n', 'output': '549\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79429","program":"```python\nfrom math import inf\n\nclass Node:\n def __init__(self, parent = None, leftExp = None, rightExp = None, signQ = 0):\n self.parent, self.leftExp, self.rightExp, self.signQ = parent, leftExp, rightExp, signQ\n def __str__(self):\n return \"Node\"\n\nmemo = {}\n\ndef Memoize(node, p, maxValue, minValue):\n if not node in memo:\n memo.update({node : {p : [maxValue, minValue]} })\n else:\n memo[node].update({p : [maxValue, minValue]})\n\ndef ExpMaxValue(root: Node, p):\n\n m = root.signQ - p\n \"\"\"if root.signQ == 1:\n if p == 1:\n return [root.leftExp.value + root.rightExp.value, root.leftExp.value + root.rightExp.value]\n else:\n return [root.leftExp.value - root.rightExp.value, root.leftExp.value - root.rightExp.value]\"\"\"\n\n if root.signQ == 0:\n return [root.value, root.value]\n \n if root in memo:\n if p in memo[root]:\n return memo[root][p]\n\n if m == 0:\n value = ExpMaxValue(root.leftExp, root.leftExp.signQ)[0] + ExpMaxValue(root.rightExp, root.rightExp.signQ)[0]\n Memoize(root, p, value, value)\n return [value, value]\n if p == 0:\n value = ExpMaxValue(root.leftExp, 0)[0] - ExpMaxValue(root.rightExp, 0)[0]\n Memoize(root, p, value, value)\n return [value, value]\n \n maxValue = -inf\n minValue = inf\n if m >= p:\n for pQMid in range(2):\n pQLeftMin = min(p - pQMid, root.leftExp.signQ)\n for pQLeft in range(pQLeftMin + 1):\n if root.leftExp.signQ - pQLeft + (1 - pQMid) > m:\n continue\n \n resLeft = ExpMaxValue(root.leftExp, pQLeft)\n resRight = ExpMaxValue(root.rightExp, p - pQMid - pQLeft)\n \n if pQMid == 1:\n maxValue = max(resLeft[0] + resRight[0], maxValue)\n minValue = min(resLeft[1] + resRight[1], minValue)\n else:\n maxValue = max(resLeft[0] - resRight[1], maxValue)\n minValue = min(resLeft[1] - resRight[0], minValue)\n else:\n for mQMid in range(2):\n mQLeftMin = min(m - mQMid, root.leftExp.signQ)\n for mQLeft in range(mQLeftMin + 1):\n pQLeft = root.leftExp.signQ - mQLeft\n if pQLeft + (1 - mQMid) > p:\n continue\n \n resLeft = ExpMaxValue(root.leftExp, pQLeft)\n resRight = ExpMaxValue(root.rightExp, p - (1 - mQMid) - pQLeft)\n \n if mQMid == 0:\n maxValue = max(resLeft[0] + resRight[0], maxValue)\n minValue = min(resLeft[1] + resRight[1], minValue)\n else:\n maxValue = max(resLeft[0] - resRight[1], maxValue)\n minValue = min(resLeft[1] - resRight[0], minValue)\n\n Memoize(root, p, int(maxValue), int(minValue))\n\n return [int(maxValue), int(minValue)]\n \n \n\ndef PrintNodes(root: Node):\n if root.signQ != 0:\n leftExp = root.leftExp if root.leftExp.signQ != 0 else root.leftExp.value\n rightExp = root.rightExp if root.rightExp.signQ != 0 else root.rightExp.value\n check = root.signQ == root.leftExp.signQ + root.rightExp.signQ + 1\n print(root.signQ, root.parent, leftExp, rightExp, check)\n PrintNodes(root.leftExp)\n PrintNodes(root.rightExp)\n\n \n\ndef main():\n exp = str(input())\n if len(exp) == 1:\n print(exp)\n return\n \n #root = Node(None, None, None)\n #root.parent = root\n cNode = Node()\n isRight = False\n \n for i in range(1, len(exp) - 1):\n if exp[i] == '(':\n if not isRight:\n cNode.leftExp = Node(cNode)\n cNode = cNode.leftExp\n else:\n cNode.rightExp = Node(cNode)\n cNode = cNode.rightExp\n isRight = False\n elif exp[i] == '?':\n isRight = True\n cNode.signQ += 1\n elif exp[i] == ')':\n if cNode.parent != None:\n cNode.parent.signQ += cNode.signQ\n cNode = cNode.parent\n isRight = False\n else:\n if not isRight:\n cNode.leftExp = Node(cNode)\n cNode.leftExp.value = int(exp[i])\n else:\n cNode.rightExp = Node(cNode)\n cNode.rightExp.value = int(exp[i])\n\n \n #PrintNodes(cNode)\n\n ss = str(input()).split()\n p, m = int(ss[0]), int(ss[1])\n\n print(ExpMaxValue(cNode, p)[0])\n \n\n\n \n\nmain()\n```","inputs":"((1?(5?7))?((6?2)?7))\n3 2\n","output":"18","actual_output":"18\n","execution_success":true,"sample_index":12650},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"961_D. Pair Of Lines","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given n points on Cartesian plane. Every point is a lattice point (i. e. both of its coordinates are integers), and all points are distinct.\n\nYou may draw two straight lines (not necessarily distinct). Is it possible to do this in such a way that every point lies on at least one of these lines?\n\nInput\n\nThe first line contains one integer n (1 \u2264 n \u2264 105) \u2014 the number of points you are given.\n\nThen n lines follow, each line containing two integers xi and yi (|xi|, |yi| \u2264 109)\u2014 coordinates of i-th point. All n points are distinct.\n\nOutput\n\nIf it is possible to draw two straight lines in such a way that each of given points belongs to at least one of these lines, print YES. Otherwise, print NO.\n\nExamples\n\nInput\n\n5\n0 0\n0 1\n1 1\n1 -1\n2 2\n\n\nOutput\n\nYES\n\n\nInput\n\n5\n0 0\n1 0\n2 1\n1 1\n2 3\n\n\nOutput\n\nNO\n\nNote\n\nIn the first example it is possible to draw two lines, the one containing the points 1, 3 and 5, and another one containing two remaining points.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\n\nlst = []\nfor x in range(n):\n (a, b) = map(int, input().split())\n lst.append((a, b))\n\ndef scal(x1, y1, x2, y2, x3, y3):\n if (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1) == 0:\n return True\n return False\n\ndef check():\n for x in range(n - 2):\n if len(s2) >= 3:\n if not scal(lst[s2[-3]][0], lst[s2[-3]][1], lst[s2[-2]][0], lst[s2[-2]][1], lst[s2[-1]][0], lst[s2[-1]][1]):\n return False\n if scal(lst[0][0], lst[0][1], lst[1][0], lst[1][1], lst[x + 2][0], lst[x + 2][1]):\n s1.append(x + 2)\n else:\n s2.append(x + 2)\n if len(s2) >= 3:\n if not scal(lst[s2[-3]][0], lst[s2[-3]][1], lst[s2[-2]][0], lst[s2[-2]][1], lst[s2[-1]][0], lst[s2[-1]][1]):\n return False\n return True\n\nflag = True\n\nif n >= 5:\n s1 = []\n s2 = []\n if not check():\n lst[1], lst[s2[0]] = lst[s2[0]], lst[1]\n x = s2[0]\n s1 = []\n s2 = []\n if not check():\n lst[0], lst[s2[0]] = lst[s2[0]], lst[0]\n s1 = []\n s2 = []\n if not check():\n flag = False\n\nif flag:\n print(\"YES\")\nelse:\n print(\"NO\")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n0 0\\n0 1\\n1 1\\n1 -1\\n2 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 0\\n1 0\\n2 1\\n1 1\\n2 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 0\\n2 0\\n1 1\\n0 2\\n5 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 0\\n-1 0\\n-1 1\\n1 0\\n1 -1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '8\\n0 0\\n1 0\\n2 0\\n3 0\\n0 1\\n1 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56008\\n0 87048\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 -1\\n-4 1\\n0 -9\\n5 -9\\n1 -10\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 0\\n-1 1\\n0 -1\\n1 1\\n1 0\\n2 -1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1\\n0 0\\n-1 0\\n-1 1\\n2 0\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n-1 2\\n-1 1\\n2 1\\n-5 2\\n1 1\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n10000000 76667672\\n3 112\\n2 400000100\\n2 104\\n1000000 701789036\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 1\\n-1 -1\\n0 0\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5\\n9 2\\n10 5\\n10 -2\\n-2 -10\\n-4 -9\\n', 'output': 'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79433","program":"```python\nn = int(input())\n\nlst = []\nfor x in range(n):\n (a, b) = map(int, input().split())\n lst.append((a, b))\n\ndef scal(x1, y1, x2, y2, x3, y3):\n if (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1) == 0:\n return True\n return False\n\ndef check():\n for x in range(n - 2):\n if len(s2) >= 3:\n if not scal(lst[s2[-3]][0], lst[s2[-3]][1], lst[s2[-2]][0], lst[s2[-2]][1], lst[s2[-1]][0], lst[s2[-1]][1]):\n return False\n if scal(lst[0][0], lst[0][1], lst[1][0], lst[1][1], lst[x + 2][0], lst[x + 2][1]):\n s1.append(x + 2)\n else:\n s2.append(x + 2)\n if len(s2) >= 3:\n if not scal(lst[s2[-3]][0], lst[s2[-3]][1], lst[s2[-2]][0], lst[s2[-2]][1], lst[s2[-1]][0], lst[s2[-1]][1]):\n return False\n return True\n\nflag = True\n\nif n >= 5:\n s1 = []\n s2 = []\n if not check():\n lst[1], lst[s2[0]] = lst[s2[0]], lst[1]\n x = s2[0]\n s1 = []\n s2 = []\n if not check():\n lst[0], lst[s2[0]] = lst[s2[0]], lst[0]\n s1 = []\n s2 = []\n if not check():\n flag = False\n\nif flag:\n print(\"YES\")\nelse:\n print(\"NO\")\n\n```","inputs":"5\n0 0\n0 1\n1 1\n1 -1\n2 2\n","output":"YES\n","actual_output":"YES\n","execution_success":true,"sample_index":12651},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02601 M-SOLUTIONS Programming Contest 2020 - Magic 2","prompt":"Solve the following coding problem using the programming language python:\n\nM-kun has the following three cards:\n\n* A red card with the integer A.\n* A green card with the integer B.\n* A blue card with the integer C.\n\n\n\nHe is a genius magician who can do the following operation at most K times:\n\n* Choose one of the three cards and multiply the written integer by 2.\n\n\n\nHis magic is successful if both of the following conditions are satisfied after the operations:\n\n* The integer on the green card is strictly greater than the integer on the red card.\n* The integer on the blue card is strictly greater than the integer on the green card.\n\n\n\nDetermine whether the magic can be successful.\n\nConstraints\n\n* 1 \\leq A, B, C \\leq 7\n* 1 \\leq K \\leq 7\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nA B C\nK\n\n\nOutput\n\nIf the magic can be successful, print `Yes`; otherwise, print `No`.\n\nExamples\n\nInput\n\n7 2 5\n3\n\n\nOutput\n\nYes\n\n\nInput\n\n7 4 2\n3\n\n\nOutput\n\nNo\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na,b,c,k=map(int,open(0).read().split())\nfor i in' '*k:\n if a>=b:b*=2\n elif b>=c:c*=2\nprint('NYoe s'[a=b:b*=2\n elif b>=c:c*=2\nprint('NYoe s'[a kenjiro:\n print('hiroshi')\n elif kenjiro > hiroshi:\n print('kenjiro')\n else:\n print('even')\n\nif __name__ == '__main__':\n main()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 1\\n3 1\\n1 2 5 5', 'output': 'hiroshi'}, {'type': 'stdin_stdout', 'input': '0 20\\n10 0\\n1 1 10 0', 'output': 'even'}, {'type': 'stdin_stdout', 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'stdin_stdout', 'input': '2 0\\n1 2\\n0 1 6 1', 'output': 'kenjiro\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n13 1\\n-1 0 24 -4', 'output': 'kenjiro\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n1 2\\n0 1 6 1', 'output': 'kenjiro\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n7 1\\n-1 0 24 -4', 'output': 'hiroshi\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 2\\n0 1 6 1', 'output': 'kenjiro\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n7 1\\n0 0 24 -4', 'output': 'even\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 2\\n1 1 6 1', 'output': 'hiroshi\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n7 1\\n0 0 24 -4', 'output': 'even\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 2\\n1 1 6 2', 'output': 'hiroshi\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n7 1\\n0 0 24 -2', 'output': 'even\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n2 2\\n1 1 6 2', 'output': 'hiroshi\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n7 1\\n0 0 20 -2', 'output': 'even\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n2 0\\n1 1 6 2', 'output': 'hiroshi\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n7 1\\n0 0 0 -2', 'output': 'even\\n'}, {'type': 'stdin_stdout', 'input': '8 1\\n2 0\\n1 1 6 2', 'output': 'hiroshi\\n'}, {'type': 'stdin_stdout', 'input': '0 1\\n7 2\\n0 0 0 -2', 'output': 'even\\n'}, {'type': 'stdin_stdout', 'input': '8 1\\n2 0\\n1 1 9 2', 'output': 'hiroshi\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79529","program":"```python\ndef main():\n h1, h2 = map(int, input().split())\n k1, k2 = map(int, input().split())\n a, b, c, d = map(int, input().split())\n\n hiroshi = h1 * a + int(h1 / 10) * c + h2 * b + int(h2 / 20) *d\n kenjiro = k1 * a + int(k1 / 10) * c + k2 * b + int(k2 / 20) *d\n\n if hiroshi > kenjiro:\n print('hiroshi')\n elif kenjiro > hiroshi:\n print('kenjiro')\n else:\n print('even')\n\nif __name__ == '__main__':\n main()\n```","inputs":"5 1\n3 1\n1 2 5 5","output":"hiroshi","actual_output":"hiroshi\n","execution_success":true,"sample_index":12665},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00475 Exposition","prompt":"Solve the following coding problem using the programming language python:\n\nproblem\n\nJOI City will hold a large-scale exposition.\n\nThere are two themes for this exposition, and each of the N exhibition facilities in JOI City will exhibit on one of the two themes.\n\nThe location of the facility is represented by plane coordinates (x, y). To move from the facility at position (x, y) to the facility at (x \u2032, y \u2032), | x \u2212 x \u2032 | + It takes only | y \u2212 y \u2032 | (for the integer a, | a | represents the absolute value of a). To create a sense of unity within the same theme, and to be interested in only one theme. In order not to make people feel inconvenience, I would like to assign the theme so that the travel time between two facilities exhibiting on the same theme is as short as possible. Unless the same theme is assigned to all exhibition facilities. , How can you divide the theme.\n\nLet M be the maximum travel time between two facilities exhibiting on the same theme. Create a program to find the minimum value of M given the locations of N exhibition facilities.\n\noutput\n\nThe output consists of only one line. Output the maximum value M of the maximum travel time between two facilities exhibiting on the same theme.\n\nInput / output example\n\nInput example 1\n\n\nFive\n0 0\nTen\n-1 -2\n0 1\n-1 1\n\nOutput example 1\n\n\n3\n\nIn this case, for example, one theme for the facility at coordinates (0, 0), (1, 0), (0, 1), and another theme for the facility at (\u22121, \u22122), (\u22121, 1). When one theme is assigned, the travel time between two facilities exhibiting on the same theme is all 3 or less. Since the travel time cannot be all 2 or less, 3 is output.\n\nThe above question sentences and the data used for the automatic referee are the question sentences created and published by the Japan Committee for Information Olympics and the test data for scoring.\n\n\n\ninput\n\nThe first line of input contains the number of facilities N (3 \u2264 N \u2264 100000 = 105). The first line of input i + 1 (1 \u2264 i \u2264 N) represents the coordinates of each facility. The two integers xi, yi (| xi | \u2264 100000 = 105, | yi | \u2264 100000 = 105) are separated by blanks. This is where the coordinates of the i-th facility are (xi, yi). It means that there can be no more than one facility at the same coordinates.\n\nOf the scoring data, 40% of the points are N \u2264 2000.\n\nExample\n\nInput\n\n5\n0 0\n1 0\n-1 -2\n0 1\n-1 1\n\n\nOutput\n\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# AOJ 0552: Exposition\n# Python3 2018.7.1 bal4u\n\nimport sys\nfrom sys import stdin\ninput = stdin.readline\n\nx, y = [], []\nn = int(input())\nfor i in range(n):\n\ta, b = map(int, input().split())\n\tx.append(a+b)\n\ty.append(a-b)\nxmin, xmax = min(x), max(x)\nymin, ymax = min(y), max(y)\nans1 = ans2 = 0\nfor i in range(n):\n\td1 = max(x[i]-xmin, y[i]-ymin)\n\td2 = max(xmax-x[i], ymax-y[i])\n\tans1 = max(ans1, min(d1, d2))\n\n\td1 = max(x[i]-xmin, ymax-y[i])\n\td2 = max(xmax-x[i], y[i]-ymin)\n\tans2 = max(ans2, min(d1, d2))\nprint(min(ans1, ans2))\n\n```","verification_info":"{'test_cases': [{'type': 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= max(x[i]-xmin, y[i]-ymin)\n\td2 = max(xmax-x[i], ymax-y[i])\n\tans1 = max(ans1, min(d1, d2))\n\n\td1 = max(x[i]-xmin, ymax-y[i])\n\td2 = max(xmax-x[i], y[i]-ymin)\n\tans2 = max(ans2, min(d1, d2))\nprint(min(ans1, ans2))\n\n```","inputs":"5\n0 0\n1 0\n-1 -2\n0 1\n-1 1","output":"3","actual_output":"3\n","execution_success":true,"sample_index":12666},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00810 Super Star","prompt":"Solve the following coding problem using the programming language python:\n\nDuring a voyage of the starship Hakodate-maru (see Problem A), researchers found strange synchronized movements of stars. Having heard these observations, Dr. Extreme proposed a theory of \"super stars\". Do not take this term as a description of actors or singers. It is a revolutionary theory in astronomy.\n\nAccording to this theory, stars we are observing are not independent objects, but only small portions of larger objects called super stars. A super star is filled with invisible (or transparent) material, and only a number of points inside or on its surface shine. These points are observed as stars by us.\n\nIn order to verify this theory, Dr. Extreme wants to build motion equations of super stars and to compare the solutions of these equations with observed movements of stars. As the first step, he assumes that a super star is sphere-shaped, and has the smallest possible radius such that the sphere contains all given stars in or on it. This assumption makes it possible to estimate the volume of a super star, and thus its mass (the density of the invisible material is known).\n\nYou are asked to help Dr. Extreme by writing a program which, given the locations of a number of stars, finds the smallest sphere containing all of them in or on it. In this computation, you should ignore the sizes of stars. In other words, a star should be regarded as a point. You may assume the universe is a Euclidean space.\n\n\n\nInput\n\nThe input consists of multiple data sets. Each data set is given in the following format.\n\n\nn\nx1 y1 z1\nx2 y2 z2\n...\nxn yn zn\n\n\nThe first line of a data set contains an integer n, which is the number of points. It satisfies the condition 4 \u2264 n \u2264 30.\n\nThe locations of n points are given by three-dimensional orthogonal coordinates: (xi, yi, zi) (i = 1,..., n). Three coordinates of a point appear in a line, separated by a space character.\n\nEach value is given by a decimal fraction, and is between 0.0 and 100.0 (both ends inclusive). Points are at least 0.01 distant from each other.\n\nThe end of the input is indicated by a line containing a zero.\n\nOutput\n\nFor each data set, the radius ofthe smallest sphere containing all given points should be printed, each in a separate line. The printed values should have 5 digits after the decimal point. They may not have an error greater than 0.00001.\n\nExample\n\nInput\n\n4\n10.00000 10.00000 10.00000\n20.00000 10.00000 10.00000\n20.00000 20.00000 10.00000\n10.00000 20.00000 10.00000\n4\n10.00000 10.00000 10.00000\n10.00000 50.00000 50.00000\n50.00000 10.00000 50.00000\n50.00000 50.00000 10.00000\n0\n\n\nOutput\n\n7.07107\n34.64102\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef distance(star, position):\n return sum([(a - b)**2 for a, b in zip(star, position)])**(1 / 2)\n\n\ndef difference(star, position):\n return [(a - b) for a, b in zip(star, position)]\n\n\nwhile True:\n n = int(input())\n if n == 0:\n break\n stars = [list(map(float, input().split())) for i in range(n)]\n position = [sum([s[i] for s in stars]) / len(stars) for i in range(3)]\n move_rate = 1\n for i in range(3000):\n if i % 100 == 0:\n move_rate /= 2\n index = 0\n dis_max = 0\n for j, star in enumerate(stars):\n dis = distance(star, position)\n if dis_max < dis:\n dis_max = dis\n index = j\n diff = difference(stars[index], position)\n position = [(position[i] + diff[i] * move_rate) for i in range(3)]\n\n print(format(dis_max, \".5f\"))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n10.00000 10.00000 10.00000\\n20.00000 10.00000 10.00000\\n20.00000 20.00000 10.00000\\n10.00000 20.00000 10.00000\\n4\\n10.00000 10.00000 10.00000\\n10.00000 50.00000 50.00000\\n50.00000 10.00000 50.00000\\n50.00000 50.00000 10.00000\\n0', 'output': '7.07107\\n34.64102'}, {'type': 'stdin_stdout', 'input': '4\\n10.00000 10.00000 10.00000\\n20.00000 10.00000 10.00000\\n20.00000 20.00000 10.00000\\n10.00000 20.00000 10.00000\\n4\\n10.00000 10.063097698119668 10.00000\\n10.00000 50.00000 50.00000\\n50.00000 10.00000 50.00000\\n50.00000 50.00000 10.00000\\n0', 'output': '7.071068\\n34.631926\\n'}, {'type': 'stdin_stdout', 'input': '4\\n10.00000 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50.80394306057471\\n50.76544467856901 10.00000 50.00000\\n50.00000 50.00000 10.00000\\n0', 'output': '7.335041\\n34.679962\\n'}, {'type': 'stdin_stdout', 'input': '4\\n10.00000 10.00000 10.00000\\n20.00000 10.00000 10.00000\\n20.00000 20.733652859881403 10.550652353511412\\n10.329100593991518 20.00000 10.00000\\n4\\n11.03531062521475 10.879748232123 10.00000\\n10.00000 50.00000 50.70404839090845\\n51.179610990935714 10.00000 50.00299745166928\\n50.00000 50.00000 10.00000\\n0', 'output': '7.340207\\n34.653628\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79541","program":"```python\ndef distance(star, position):\n return sum([(a - b)**2 for a, b in zip(star, position)])**(1 / 2)\n\n\ndef difference(star, position):\n return [(a - b) for a, b in zip(star, position)]\n\n\nwhile True:\n n = int(input())\n if n == 0:\n break\n stars = [list(map(float, input().split())) for i in range(n)]\n position = [sum([s[i] for s in stars]) / len(stars) for i in range(3)]\n move_rate = 1\n for i in range(3000):\n if i % 100 == 0:\n move_rate /= 2\n index = 0\n dis_max = 0\n for j, star in enumerate(stars):\n dis = distance(star, position)\n if dis_max < dis:\n dis_max = dis\n index = j\n diff = difference(stars[index], position)\n position = [(position[i] + diff[i] * move_rate) for i in range(3)]\n\n print(format(dis_max, \".5f\"))\n\n```","inputs":"4\n10.00000 10.00000 10.00000\n20.00000 10.00000 10.00000\n20.00000 20.00000 10.00000\n10.00000 20.00000 10.00000\n4\n10.00000 10.00000 10.00000\n10.00000 50.00000 50.00000\n50.00000 10.00000 50.00000\n50.00000 50.00000 10.00000\n0","output":"7.07107\n34.64102","actual_output":"7.07107\n34.64102\n","execution_success":true,"sample_index":12667},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00941 Do Geese See God?","prompt":"Solve the following coding problem using the programming language python:\n\nExample\n\nInput\n\ncrc\n1\n\n\nOutput\n\ncrc\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom heapq import heappush, heappop\n\ndef solve():\n S = input()\n K = int(input())\n L = len(S)\n INF = 10**9\n cost = [[INF]*(L+1) for i in range(L+1)]\n cost[0][L] = 0\n ss = []\n que = [(0, 0, L)]\n while que:\n d, a, b = heappop(que)\n if cost[a][b] < d:\n continue\n ss.append((a, b))\n if a+1 == b:\n if d+1 < cost[a+1][b]:\n cost[a+1][b] = d + 1\n continue\n if S[a] == S[b-1]:\n if d+2 < cost[a+1][b-1]:\n cost[a+1][b-1] = d + 2\n if a+1 < b-1:\n heappush(que, (d+2, a+1, b-1))\n else:\n if d+2 < cost[a+1][b]:\n cost[a+1][b] = d + 2\n if a+1 < b:\n heappush(que, (d+2, a+1, b))\n if d+2 < cost[a][b-1]:\n cost[a][b-1] = d + 2\n if a < b-1:\n heappush(que, (d+2, a, b-1))\n ln = min(cost[i][i] for i in range(L+1))\n ss.reverse()\n dp = [[0]*(L+1) for i in range(L+1)]\n for i in range(L+1):\n if cost[i][i] == ln:\n dp[i][i] = 1\n for a, b in ss:\n d = cost[a][b]\n r = 0\n if a+1 == b:\n if d+1 == cost[a+1][b]:\n r = dp[a+1][b]\n else:\n if S[a] == S[b-1]:\n if d+2 == cost[a+1][b-1]:\n r = dp[a+1][b-1]\n else:\n if d+2 == cost[a+1][b]:\n r += dp[a+1][b]\n if d+2 == cost[a][b-1]:\n r += dp[a][b-1]\n dp[a][b] = r\n if dp[a][b] < K:\n print(\"NONE\")\n return True\n SL = []; SR = []\n a = 0; b = L\n while a < b:\n if a+1 == b:\n assert cost[a][b]+1 == cost[a+1][b]\n SL.append(S[a])\n a += 1\n continue\n if S[a] == S[b-1]:\n assert cost[a][b]+2 == cost[a+1][b-1]\n SL.append(S[a])\n SR.append(S[b-1])\n a += 1; b -= 1\n elif S[a] < S[b-1]:\n c = (cost[a][b]+2 == cost[a+1][b])\n if c and K <= dp[a+1][b]:\n SL.append(S[a])\n SR.append(S[a])\n a += 1\n else:\n if c:\n K -= dp[a+1][b]\n SL.append(S[b-1])\n SR.append(S[b-1])\n b -= 1\n else:\n c = (cost[a][b]+2 == cost[a][b-1])\n if c and K <= dp[a][b-1]:\n SL.append(S[b-1])\n SR.append(S[b-1])\n b -= 1\n else:\n if c:\n K -= dp[a][b-1]\n SL.append(S[a])\n SR.append(S[a])\n a += 1\n SR.reverse()\n SL.extend(SR)\n print(\"\".join(SL))\nsolve()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'crc\\n1', 'output': 'crc'}, {'type': 'stdin_stdout', 'input': 'crb\\n1', 'output': 'bcrcb\\n'}, {'type': 'stdin_stdout', 'input': 'bqc\\n1', 'output': 'bcqcb\\n'}, {'type': 'stdin_stdout', 'input': 'bcq\\n2', 'output': 'bqcqb\\n'}, {'type': 'stdin_stdout', 'input': 'ccq\\n2', 'output': 'NONE\\n'}, {'type': 'stdin_stdout', 'input': 'cdq\\n2', 'output': 'cqdqc\\n'}, {'type': 'stdin_stdout', 'input': 'dcq\\n2', 'output': 'dqcqd\\n'}, {'type': 'stdin_stdout', 'input': 'dcq\\n4', 'output': 'qdcdq\\n'}, {'type': 'stdin_stdout', 'input': 'qcd\\n3', 'output': 'qcdcq\\n'}, {'type': 'stdin_stdout', 'input': 'qce\\n3', 'output': 'qcecq\\n'}, {'type': 'stdin_stdout', 'input': 'qce\\n4', 'output': 'qeceq\\n'}, {'type': 'stdin_stdout', 'input': 'pde\\n1', 'output': 'edpde\\n'}, {'type': 'stdin_stdout', 'input': 'pdf\\n1', 'output': 'fdpdf\\n'}, {'type': 'stdin_stdout', 'input': 'ode\\n0', 'output': 'edode\\n'}, {'type': 'stdin_stdout', 'input': 'ecp\\n0', 'output': 'ecpce\\n'}, {'type': 'stdin_stdout', 'input': 'dcp\\n0', 'output': 'dcpcd\\n'}, {'type': 'stdin_stdout', 'input': 'ecp\\n2', 'output': 'epcpe\\n'}, {'type': 'stdin_stdout', 'input': 'pce\\n3', 'output': 'pcecp\\n'}, {'type': 'stdin_stdout', 'input': 'eep\\n0', 'output': 'peep\\n'}, {'type': 'stdin_stdout', 'input': 'fep\\n0', 'output': 'fepef\\n'}, {'type': 'stdin_stdout', 'input': 'feq\\n0', 'output': 'feqef\\n'}, {'type': 'stdin_stdout', 'input': 'ffq\\n0', 'output': 'qffq\\n'}, {'type': 'stdin_stdout', 'input': 'ffp\\n0', 'output': 'pffp\\n'}, {'type': 'stdin_stdout', 'input': 'gfp\\n0', 'output': 'gfpfg\\n'}, {'type': 'stdin_stdout', 'input': 'hfp\\n0', 'output': 'hfpfh\\n'}, {'type': 'stdin_stdout', 'input': 'ifp\\n0', 'output': 'ifpfi\\n'}, {'type': 'stdin_stdout', 'input': 'ipf\\n0', 'output': 'fipif\\n'}, {'type': 'stdin_stdout', 'input': 'epi\\n-2', 'output': 'eipie\\n'}, {'type': 'stdin_stdout', 'input': 'eoi\\n-2', 'output': 'eioie\\n'}, {'type': 'stdin_stdout', 'input': 'eoj\\n-2', 'output': 'ejoje\\n'}, {'type': 'stdin_stdout', 'input': 'enj\\n-2', 'output': 'ejnje\\n'}, {'type': 'stdin_stdout', 'input': 'fnj\\n-2', 'output': 'fjnjf\\n'}, {'type': 'stdin_stdout', 'input': 'crc\\n0', 'output': 'crc\\n'}, {'type': 'stdin_stdout', 'input': 'crb\\n2', 'output': 'brcrb\\n'}, {'type': 'stdin_stdout', 'input': 'brd\\n1', 'output': 'bdrdb\\n'}, {'type': 'stdin_stdout', 'input': 'bdq\\n1', 'output': 'bdqdb\\n'}, {'type': 'stdin_stdout', 'input': 'bdq\\n2', 'output': 'bqdqb\\n'}, {'type': 'stdin_stdout', 'input': 'ccq\\n0', 'output': 'qccq\\n'}, {'type': 'stdin_stdout', 'input': 'cdq\\n0', 'output': 'cdqdc\\n'}, {'type': 'stdin_stdout', 'input': 'qce\\n2', 'output': 'eqcqe\\n'}, {'type': 'stdin_stdout', 'input': 'rce\\n4', 'output': 'recer\\n'}, {'type': 'stdin_stdout', 'input': 'pde\\n2', 'output': 'epdpe\\n'}, {'type': 'stdin_stdout', 'input': 'pdf\\n2', 'output': 'fpdpf\\n'}, {'type': 'stdin_stdout', 'input': 'fpd\\n0', 'output': 'dfpfd\\n'}, {'type': 'stdin_stdout', 'input': 'fdo\\n0', 'output': 'fdodf\\n'}, {'type': 'stdin_stdout', 'input': 'dpe\\n2', 'output': 'dpepd\\n'}, {'type': 'stdin_stdout', 'input': 'epd\\n0', 'output': 'deped\\n'}, {'type': 'stdin_stdout', 'input': 'dcq\\n0', 'output': 'dcqcd\\n'}, {'type': 'stdin_stdout', 'input': 'fcp\\n1', 'output': 'fcpcf\\n'}, {'type': 'stdin_stdout', 'input': 'pec\\n0', 'output': 'cepec\\n'}, {'type': 'stdin_stdout', 'input': 'pce\\n4', 'output': 'pecep\\n'}, {'type': 'stdin_stdout', 'input': 'eeq\\n1', 'output': 'qeeq\\n'}, {'type': 'stdin_stdout', 'input': 'eeo\\n1', 'output': 'oeeo\\n'}, {'type': 'stdin_stdout', 'input': 'ifq\\n0', 'output': 'ifqfi\\n'}, {'type': 'stdin_stdout', 'input': 'fpj\\n-1', 'output': 'fjpjf\\n'}, {'type': 'stdin_stdout', 'input': 'eph\\n-2', 'output': 'ehphe\\n'}, {'type': 'stdin_stdout', 'input': 'fni\\n-2', 'output': 'finif\\n'}, {'type': 'stdin_stdout', 'input': 'rcc\\n0', 'output': 'rccr\\n'}, {'type': 'stdin_stdout', 'input': 'crd\\n1', 'output': 'cdrdc\\n'}, {'type': 'stdin_stdout', 'input': 'bdp\\n1', 'output': 'bdpdb\\n'}, {'type': 'stdin_stdout', 'input': 'cdr\\n2', 'output': 'crdrc\\n'}, {'type': 'stdin_stdout', 'input': 'rcd\\n4', 'output': 'rdcdr\\n'}, {'type': 'stdin_stdout', 'input': 'pcd\\n2', 'output': 'dpcpd\\n'}, {'type': 'stdin_stdout', 'input': 'pdf\\n4', 'output': 'pfdfp\\n'}, {'type': 'stdin_stdout', 'input': 'fco\\n0', 'output': 'fcocf\\n'}, {'type': 'stdin_stdout', 'input': 'oed\\n1', 'output': 'deoed\\n'}, {'type': 'stdin_stdout', 'input': 'qdf\\n1', 'output': 'fdqdf\\n'}, {'type': 'stdin_stdout', 'input': 'ddp\\n1', 'output': 'pddp\\n'}, {'type': 'stdin_stdout', 'input': 'cfp\\n1', 'output': 'cfpfc\\n'}, {'type': 'stdin_stdout', 'input': 'feo\\n1', 'output': 'feoef\\n'}, {'type': 'stdin_stdout', 'input': 'qfe\\n0', 'output': 'efqfe\\n'}, {'type': 'stdin_stdout', 'input': 'gep\\n0', 'output': 'gepeg\\n'}, {'type': 'stdin_stdout', 'input': 'fph\\n-2', 'output': 'fhphf\\n'}, {'type': 'stdin_stdout', 'input': 'eqh\\n-2', 'output': 'ehqhe\\n'}, {'type': 'stdin_stdout', 'input': 'ekn\\n-2', 'output': 'eknke\\n'}, {'type': 'stdin_stdout', 'input': 'fnh\\n-2', 'output': 'fhnhf\\n'}, {'type': 'stdin_stdout', 'input': 'jfn\\n0', 'output': 'jfnfj\\n'}, {'type': 'stdin_stdout', 'input': 'bqb\\n1', 'output': 'bqb\\n'}, {'type': 'stdin_stdout', 'input': 'cdr\\n3', 'output': 'rcdcr\\n'}, {'type': 'stdin_stdout', 'input': 'qce\\n0', 'output': 'ecqce\\n'}, {'type': 'stdin_stdout', 'input': 'pbf\\n0', 'output': 'fbpbf\\n'}, {'type': 'stdin_stdout', 'input': 'gpd\\n-1', 'output': 'dgpgd\\n'}, {'type': 'stdin_stdout', 'input': 'eco\\n0', 'output': 'ecoce\\n'}, {'type': 'stdin_stdout', 'input': 'dfp\\n2', 'output': 'dpfpd\\n'}, {'type': 'stdin_stdout', 'input': 'dco\\n0', 'output': 'dcocd\\n'}, {'type': 'stdin_stdout', 'input': 'feo\\n2', 'output': 'foeof\\n'}, {'type': 'stdin_stdout', 'input': 'qeg\\n0', 'output': 'geqeg\\n'}, {'type': 'stdin_stdout', 'input': 'gfp\\n2', 'output': 'gpfpg\\n'}, {'type': 'stdin_stdout', 'input': 'hfq\\n1', 'output': 'hfqfh\\n'}, {'type': 'stdin_stdout', 'input': 'doi\\n0', 'output': 'dioid\\n'}, {'type': 'stdin_stdout', 'input': 'jfo\\n0', 'output': 'jfofj\\n'}, {'type': 'stdin_stdout', 'input': 'sdc\\n1', 'output': 'cdsdc\\n'}, {'type': 'stdin_stdout', 'input': 'qbb\\n1', 'output': 'qbbq\\n'}, {'type': 'stdin_stdout', 'input': 'aqc\\n-1', 'output': 'acqca\\n'}, {'type': 'stdin_stdout', 'input': 'ccs\\n0', 'output': 'sccs\\n'}, {'type': 'stdin_stdout', 'input': 'eqc\\n0', 'output': 'ceqec\\n'}, {'type': 'stdin_stdout', 'input': 'dcr\\n1', 'output': 'dcrcd\\n'}, {'type': 'stdin_stdout', 'input': 'qcf\\n0', 'output': 'fcqcf\\n'}, {'type': 'stdin_stdout', 'input': 'qbd\\n1', 'output': 'dbqbd\\n'}, {'type': 'stdin_stdout', 'input': 'qfc\\n0', 'output': 'cfqfc\\n'}, {'type': 'stdin_stdout', 'input': 'fcp\\n3', 'output': 'pcfcp\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79545","program":"```python\nfrom heapq import heappush, heappop\n\ndef solve():\n S = input()\n K = int(input())\n L = len(S)\n INF = 10**9\n cost = [[INF]*(L+1) for i in range(L+1)]\n cost[0][L] = 0\n ss = []\n que = [(0, 0, L)]\n while que:\n d, a, b = heappop(que)\n if cost[a][b] < d:\n continue\n ss.append((a, b))\n if a+1 == b:\n if d+1 < cost[a+1][b]:\n cost[a+1][b] = d + 1\n continue\n if S[a] == S[b-1]:\n if d+2 < cost[a+1][b-1]:\n cost[a+1][b-1] = d + 2\n if a+1 < b-1:\n heappush(que, (d+2, a+1, b-1))\n else:\n if d+2 < cost[a+1][b]:\n cost[a+1][b] = d + 2\n if a+1 < b:\n heappush(que, (d+2, a+1, b))\n if d+2 < cost[a][b-1]:\n cost[a][b-1] = d + 2\n if a < b-1:\n heappush(que, (d+2, a, b-1))\n ln = min(cost[i][i] for i in range(L+1))\n ss.reverse()\n dp = [[0]*(L+1) for i in range(L+1)]\n for i in range(L+1):\n if cost[i][i] == ln:\n dp[i][i] = 1\n for a, b in ss:\n d = cost[a][b]\n r = 0\n if a+1 == b:\n if d+1 == cost[a+1][b]:\n r = dp[a+1][b]\n else:\n if S[a] == S[b-1]:\n if d+2 == cost[a+1][b-1]:\n r = dp[a+1][b-1]\n else:\n if d+2 == cost[a+1][b]:\n r += dp[a+1][b]\n if d+2 == cost[a][b-1]:\n r += dp[a][b-1]\n dp[a][b] = r\n if dp[a][b] < K:\n print(\"NONE\")\n return True\n SL = []; SR = []\n a = 0; b = L\n while a < b:\n if a+1 == b:\n assert cost[a][b]+1 == cost[a+1][b]\n SL.append(S[a])\n a += 1\n continue\n if S[a] == S[b-1]:\n assert cost[a][b]+2 == cost[a+1][b-1]\n SL.append(S[a])\n SR.append(S[b-1])\n a += 1; b -= 1\n elif S[a] < S[b-1]:\n c = (cost[a][b]+2 == cost[a+1][b])\n if c and K <= dp[a+1][b]:\n SL.append(S[a])\n SR.append(S[a])\n a += 1\n else:\n if c:\n K -= dp[a+1][b]\n SL.append(S[b-1])\n SR.append(S[b-1])\n b -= 1\n else:\n c = (cost[a][b]+2 == cost[a][b-1])\n if c and K <= dp[a][b-1]:\n SL.append(S[b-1])\n SR.append(S[b-1])\n b -= 1\n else:\n if c:\n K -= dp[a][b-1]\n SL.append(S[a])\n SR.append(S[a])\n a += 1\n SR.reverse()\n SL.extend(SR)\n print(\"\".join(SL))\nsolve()\n\n```","inputs":"crc\n1","output":"crc","actual_output":"crc\n","execution_success":true,"sample_index":12668},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01074 Unhappy Class","prompt":"Solve the following coding problem using the programming language python:\n\nProblem\n\nYamano Mifune Gakuen's 1st grade G group is a class where female students carrying misfortune gather. They face various challenges every day with the goal of being happy.\n\nIn their class, they can take practical happiness courses as part of the test of happiness.\nFrom Monday to Friday, there are classes from 1st to Nth, and there are M courses that can be taken.\n\nSubject i starts from the ai period of the day of the week di (di = 0, 1, 2, 3, 4 corresponds to Monday, Tuesday, Wednesday, Thursday, and Friday, respectively), and is performed in consecutive ki frames. The degree of happiness obtained when taking the course is ti.\n\nEach student is free to choose up to L subjects so that they do not overlap each other. How do you choose the subject to get the highest level of happiness? Please find the maximum value of happiness that can be obtained from the information of the given subject.\n\nConstraints\n\n* 2 \u2264 N \u2264 8\n* 0 \u2264 M \u2264 300\n* 0 \u2264 L \u2264 min (N \u00d7 5, M)\n* 0 \u2264 di \u2264 4\n* 1 \u2264 ai \u2264 N\n* 1 \u2264 ki\n* ai + ki --1 \u2264 N\n* 1 \u2264 ti \u2264 100\n\nInput\n\nThe input is given in the following format.\n\n\nN M L\nd1 a1 k1 t1\nd2 a2 k2 t2\n...\ndM aM kM tM\n\n\nThe first line is given three integers N, M, L separated by blanks.\nThe four integers di, ai, ki, and ti are given on the 2nd to M + 1th lines, separated by blanks.\n\nOutput\n\nOutput the maximum value of the sum of happiness on one line.\n\nExamples\n\nInput\n\n3 7 3\n0 1 1 1\n0 1 1 2\n1 1 3 4\n1 1 1 1\n1 2 1 2\n2 1 1 3\n2 2 2 1\n\n\nOutput\n\n9\n\n\nInput\n\n5 10 5\n0 1 1 2\n0 2 1 2\n0 1 2 3\n1 2 1 2\n1 4 2 3\n2 1 1 1\n2 1 1 2\n3 3 2 3\n4 1 1 2\n4 2 1 2\n\n\nOutput\n\n13\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom itertools import product\n\nn, m, l = map(int, input().split())\nsubjects = [[] for _ in range(5)]\nfor _ in range(m):\n d, a, k, t = map(int, input().split())\n subjects[d].append((a, a + k - 1, t))\n\nfor i in range(5):\n subjects[i].sort(key=lambda x:x[1])\n \n#\u5404\u66dc\u65e5\u306e\u79d1\u76ee\u6570\u3054\u3068\u306e\u6700\u5927\u5e78\u798f\ndef calcDp(i):\n #dp[y][x] ... y\u79d1\u76eex\u30b3\u30de\u307e\u3067\u306e\u6700\u5927\u5e78\u798f\n dp = [[0] * (n + 1) for _ in range(n + 1)]\n sub = subjects[i]\n for init, end, value in sub:\n for y in range(n):\n new_score = dp[y][init - 1] + value\n for x in range(end, n + 1):\n dp[y + 1][x] = max(dp[y + 1][x], new_score)\n ret = []\n for i in range(n + 1):\n ret.append(max(dp[i]))\n return ret\n\nlst = [calcDp(i) for i in range(5)]\n\nans = 0\nfor t in product(range(n + 1), repeat=5):\n if sum(t) > l:continue\n score = 0\n for i, v in enumerate(t):\n score += lst[i][v]\n ans = max(score, ans)\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n2 1 1 3\\n2 2 2 1', 'output': '9'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '13'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 4\\n4 1 1 2\\n4 2 0 2', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n1 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n2 1 1 3\\n2 2 2 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 1 1 2\\n4 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 4\\n0 2 1 2\\n0 2 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 2', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n0 1 1 1\\n1 1 3 0\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 2 1\\n1 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n3 1 1 2\\n2 2 2 1', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n0 1 1 1\\n2 2 1 2\\n3 3 2 1\\n4 2 1 0\\n4 2 1 0', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 1\\n0 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 2 1 0\\n4 2 1 2', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '5 10 0\\n0 1 1 1\\n0 2 1 2\\n0 1 3 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 4\\n4 1 1 2\\n4 2 0 2', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 10 7\\n0 1 1 4\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 1\\n3 3 2 2\\n4 1 1 2\\n2 2 1 2', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '5 10 7\\n0 1 1 4\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 1\\n3 3 2 2\\n4 1 1 2\\n2 2 1 1', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '5 10 7\\n1 1 1 4\\n1 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 2 1 1\\n4 1 1 1\\n3 3 2 3\\n4 1 1 2\\n0 2 1 1', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 2 1\\n1 2 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n1 1 1 2\\n1 2 2 1', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '4 7 1\\n0 1 1 1\\n0 1 1 2\\n2 1 1 4\\n1 1 1 1\\n1 3 0 2\\n3 1 1 3\\n2 2 1 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 2 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n0 1 1 1\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n1 1 1 2\\n1 1 3 4\\n2 1 1 1\\n1 2 1 2\\n2 1 1 3\\n2 2 2 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 1 1 0\\n4 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n1 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n0 1 1 0\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 2 1 0\\n4 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n1 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 4\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n1 1 1 0\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 0 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 2 1 0\\n4 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 2 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n2 1 1 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 2 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 1 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n2 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 2 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 3 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 4\\n4 1 1 2\\n4 2 0 2', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n1 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n2 1 1 3\\n2 2 1 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 1 1 2\\n2 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 2 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n1 2 1 2\\n0 1 2 3\\n1 2 0 2\\n0 4 2 3\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n0 1 1 0\\n1 1 3 4\\n1 1 1 1\\n2 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n0 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 2 1 0\\n4 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n2 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 4\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n1 1 1 0\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 1 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 2 1\\n1 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 1 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 1 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 2 3\\n3 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 1\\n0 2 1 2\\n0 1 3 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 4\\n4 1 1 2\\n4 2 0 2', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 1\\n3 3 2 1\\n4 1 1 2\\n2 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 4\\n0 2 1 2\\n0 2 3 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 2', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n0 2 1 1\\n1 1 3 0\\n1 1 1 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1', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '4 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 1 4\\n1 1 1 1\\n1 3 0 2\\n3 1 1 3\\n2 2 1 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 0\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 1 0\\n3 1 2 3\\n3 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 1\\n0 2 1 2\\n0 1 3 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 4\\n4 1 1 2\\n4 0 0 2', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '5 10 7\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 1\\n3 3 2 2\\n4 1 1 2\\n2 2 1 2', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 2 2 1\\n1 1 3 0\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 2 1\\n1 2 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n1 1 1 2\\n2 2 2 1', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 0\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 1 0\\n3 1 2 6\\n3 2 2 1', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 10 7\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 1\\n3 3 2 2\\n4 1 1 2\\n2 2 1 1', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 2 1\\n1 2 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n1 1 1 2\\n2 2 2 2', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5 10 7\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 2 1 1\\n3 3 2 2\\n4 1 1 2\\n2 2 1 1', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '5 10 7\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 3 1 2\\n1 4 2 3\\n2 1 1 1\\n2 2 1 1\\n3 3 2 2\\n4 1 1 2\\n2 2 1 1', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '5 10 7\\n0 2 1 2\\n0 2 1 2\\n0 1 2 3\\n1 3 1 2\\n1 4 2 3\\n2 1 1 1\\n2 2 1 1\\n3 3 2 2\\n4 1 1 2\\n2 2 1 1', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n2 1 1 3\\n0 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 0\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 3 2\\n1 1 1 1\\n1 2 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 2 1 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 0\\n2 1 1 2\\n3 3 2 4\\n4 1 1 2\\n4 2 0 2', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n1 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 2 2\\n2 1 1 3\\n2 2 2 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 1 1 2\\n0 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 3 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 2 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 0\\n4 2 0 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '5 7 3\\n0 1 0 1\\n0 1 1 1\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n1 1 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 2\\n4 2 1 0\\n4 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 2 2\\n1 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 4\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n1 1 1 0\\n1 1 3 4\\n1 1 2 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 0 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 2 1 0\\n3 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 2 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n2 1 2 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 2 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n3 1 1 3\\n4 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 1 1\\n0 1 1 0\\n1 1 1 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n2 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 0', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 2 2\\n3 1 2 3\\n2 2 2 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n0 1 1 2\\n3 3 2 1\\n4 1 1 2\\n2 2 1 2', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 2 1\\n2 0 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '5 10 5\\n0 1 1 4\\n0 2 1 0\\n0 2 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 2', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '3 7 3\\n0 1 0 1\\n0 1 1 1\\n1 1 3 1\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1', 'output': '6\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79549","program":"```python\nfrom itertools import product\n\nn, m, l = map(int, input().split())\nsubjects = [[] for _ in range(5)]\nfor _ in range(m):\n d, a, k, t = map(int, input().split())\n subjects[d].append((a, a + k - 1, t))\n\nfor i in range(5):\n subjects[i].sort(key=lambda x:x[1])\n \n#\u5404\u66dc\u65e5\u306e\u79d1\u76ee\u6570\u3054\u3068\u306e\u6700\u5927\u5e78\u798f\ndef calcDp(i):\n #dp[y][x] ... y\u79d1\u76eex\u30b3\u30de\u307e\u3067\u306e\u6700\u5927\u5e78\u798f\n dp = [[0] * (n + 1) for _ in range(n + 1)]\n sub = subjects[i]\n for init, end, value in sub:\n for y in range(n):\n new_score = dp[y][init - 1] + value\n for x in range(end, n + 1):\n dp[y + 1][x] = max(dp[y + 1][x], new_score)\n ret = []\n for i in range(n + 1):\n ret.append(max(dp[i]))\n return ret\n\nlst = [calcDp(i) for i in range(5)]\n\nans = 0\nfor t in product(range(n + 1), repeat=5):\n if sum(t) > l:continue\n score = 0\n for i, v in enumerate(t):\n score += lst[i][v]\n ans = max(score, ans)\nprint(ans)\n\n```","inputs":"3 7 3\n0 1 1 1\n0 1 1 2\n1 1 3 4\n1 1 1 1\n1 2 1 2\n2 1 1 3\n2 2 2 1","output":"9","actual_output":"9\n","execution_success":true,"sample_index":12669},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02248 String Search","prompt":"Solve the following coding problem using the programming language python:\n\nFind places where a string P is found within a text T. Print all indices of T where P found. The indices of T start with 0.\n\nConstraints\n\n* 1 \u2264 length of T \u2264 1000000\n* 1 \u2264 length of P \u2264 10000\n* The input consists of alphabetical characters and digits\n\nInput\n\nIn the first line, a text T is given. In the second line, a string P is given.\n\nOutput\n\nPrint an index of T where P found in a line. Print the indices in ascending order.\n\nExamples\n\nInput\n\naabaaa\naa\n\n\nOutput\n\n0\n3\n4\n\n\nInput\n\nxyzz\nyz\n\n\nOutput\n\n1\n\n\nInput\n\nabc\nxyz\n\n\nOutput\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ns=input();t=input()\n[print(x) for x in range(len(s)-len(t)+1) if s[x:x+len(t)]==t]\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'xyzz\\nyz', 'output': '1'}, {'type': 'stdin_stdout', 'input': 'aabaaa\\naa', 'output': '0\\n3\\n4'}, {'type': 'stdin_stdout', 'input': 'aaabaa\\naa', 'output': '0\\n1\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'aabbaa\\naa', 'output': '0\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'aabaab\\naa', 'output': '0\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'aababb\\naa', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'aaabaa\\nab', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'aabba`\\na`', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'cbabaa\\nba', 'output': '1\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'cbaaaa\\nba', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'dbaaba\\nba', 'output': '1\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'dbaaba\\nab', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'babaaa\\naa', 'output': '3\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'aaaaab\\naa', 'output': '0\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'baaaab\\naa', 'output': '1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'eababa\\nba', 'output': '2\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'yzyz\\nyz', 'output': '0\\n2\\n'}, {'type': 'stdin_stdout', 'input': 'aaaabb\\naa', 'output': '0\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '`aaabb\\naa', 'output': '1\\n2\\n'}, {'type': 'stdin_stdout', 'input': 'aaa`ba\\naa', 'output': '0\\n1\\n'}, {'type': 'stdin_stdout', 'input': 'bbaaa`\\naa', 'output': '2\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'baaaaa\\naa', 'output': '1\\n2\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'b`aaaa\\naa', 'output': '2\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '``a```\\n``', 'output': '0\\n3\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'a`a`a`\\na`', 'output': '0\\n2\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'aababc\\naa', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'cbabaa\\naa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'dbaaaa\\nba', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'dbaaba\\naa', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'xzyz\\nyz', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'bbabaa\\naa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'ccabaa\\naa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'aaabaa\\nba', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'abbba`\\na`', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'cba`aa\\nba', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'ebaaba\\nba', 'output': '1\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'abaabd\\naa', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'bbabaa\\nba', 'output': '1\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'a`abaa\\nab', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'cba`aa\\naa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'eaaaba\\nba', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'baaaab\\nba', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'bcabaa\\nba', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'bcabaa\\nab', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'eab`ba\\nba', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'aabacb\\nab', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'eab`ba\\nab', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'cabaab\\nab', 'output': '1\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'ab`bae\\nab', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'cbbaab\\nab', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'a`abaa\\naa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'aabbaa\\nba', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'aababa\\naa', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'aabaaa\\nab', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'cbabaa\\nab', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'aababc\\nba', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'dbabba\\nbb', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'abaabd\\nab', 'output': '0\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'ababaa\\naa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'aa`aab\\naa', 'output': '0\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'bbbaaa\\naa', 'output': '3\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'ccaba`\\na`', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'cbaa`a\\nba', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'ebaaba\\nab', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'bbaabd\\naa', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'bbbbaa\\nba', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'aaba`a\\nab', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'abaaae\\nba', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'bcabaa\\naa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'eababa\\nab', 'output': '1\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'ab`bae\\nba', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'aabacb\\nba', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'caaabb\\nab', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'aaba`a\\naa', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'aabbaa\\nab', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'aababa\\nab', 'output': '1\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'dbabba\\nab', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'zyzy\\nyz', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'ababaa\\nba', 'output': '1\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'baa`aa\\naa', 'output': '1\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'bbbaaa\\nba', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'cbab`a\\nba', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'abaabe\\nab', 'output': '0\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'dbaabb\\naa', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'aaba`a\\nba', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'aababc\\nab', 'output': '1\\n3\\n'}, {'type': 'stdin_stdout', 'input': 'daaabb\\nab', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'aaba`a\\na`', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'aabbaa\\nbb', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'aabbba\\nab', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'dbabba\\nba', 'output': '1\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'ababaa\\nab', 'output': '0\\n2\\n'}, {'type': 'stdin_stdout', 'input': 'a`abaa\\nba', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'a`ba`a\\na`', 'output': '0\\n3\\n'}, {'type': 'stdin_stdout', 'input': '`abbaa\\nbb', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'abacaa\\nab', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'aaa`aa\\naa', 'output': '0\\n1\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'a`ba`a\\n`a', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'abbaaa\\nba', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '`aa`aa\\naa', 'output': '1\\n4\\n'}, {'type': 'stdin_stdout', 'input': 'abbaab\\nba', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '`aa``a\\naa', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79581","program":"```python\ns=input();t=input()\n[print(x) for x in range(len(s)-len(t)+1) if s[x:x+len(t)]==t]\n```","inputs":"xyzz\nyz","output":"1","actual_output":"1\n","execution_success":true,"sample_index":12670},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02396 Print Test Cases","prompt":"Solve the following coding problem using the programming language python:\n\nIn the online judge system, a judge file may include multiple datasets to check whether the submitted program outputs a correct answer for each test case. This task is to practice solving a problem with multiple datasets.\n\nWrite a program which reads an integer x and print it as is. Note that multiple datasets are given for this problem.\n\nConstraints\n\n* 1 \u2264 x \u2264 10000\n* The number of datasets \u2264 10000\n\nInput\n\nThe input consists of multiple datasets. Each dataset consists of an integer x in a line.\n\nThe input ends with an integer 0. You program should not process (print) for this terminal symbol.\n\nOutput\n\nFor each dataset, print x in the following format:\n\n\nCase i: x\n\n\nwhere i is the case number which starts with 1. Put a single space between \"Case\" and i. Also, put a single space between ':' and x.\n\nExample\n\nInput\n\n3\n5\n11\n7\n8\n19\n0\n\n\nOutput\n\nCase 1: 3\nCase 2: 5\nCase 3: 11\nCase 4: 7\nCase 5: 8\nCase 6: 19\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ni = 0\n\nwhile True:\n n = int(input())\n i += 1\n if n == 0:\n break\n print(\"Case {}: {}\".format(i, n))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n7\\n8\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 7\\nCase 5: 8\\nCase 6: 19'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n3\\n8\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 3\\nCase 5: 8\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n7\\n8\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 7\\nCase 5: 8\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n4\\n8\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 4\\nCase 5: 8\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n7\\n14\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 7\\nCase 5: 14\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n4\\n2\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 4\\nCase 5: 2\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n7\\n26\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 7\\nCase 5: 26\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n9\\n4\\n2\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 9\\nCase 4: 4\\nCase 5: 2\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n11\\n7\\n26\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 2\\nCase 3: 11\\nCase 4: 7\\nCase 5: 26\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n11\\n7\\n26\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 11\\nCase 4: 7\\nCase 5: 26\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n11\\n7\\n2\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 11\\nCase 4: 7\\nCase 5: 2\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n11\\n7\\n2\\n58\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 11\\nCase 4: 7\\nCase 5: 2\\nCase 6: 58\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n11\\n7\\n2\\n58\\n0', 'output': 'Case 1: 3\\nCase 2: 8\\nCase 3: 11\\nCase 4: 7\\nCase 5: 2\\nCase 6: 58\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n11\\n14\\n2\\n58\\n0', 'output': 'Case 1: 3\\nCase 2: 8\\nCase 3: 11\\nCase 4: 14\\nCase 5: 2\\nCase 6: 58\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n11\\n14\\n2\\n58\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 11\\nCase 4: 14\\nCase 5: 2\\nCase 6: 58\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n2\\n14\\n2\\n58\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 2\\nCase 4: 14\\nCase 5: 2\\nCase 6: 58\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n2\\n14\\n2\\n25\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 2\\nCase 4: 14\\nCase 5: 2\\nCase 6: 25\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n2\\n14\\n2\\n28\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 2\\nCase 4: 14\\nCase 5: 2\\nCase 6: 28\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n2\\n14\\n2\\n28\\n0', 'output': 'Case 1: 3\\nCase 2: 3\\nCase 3: 2\\nCase 4: 14\\nCase 5: 2\\nCase 6: 28\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n2\\n14\\n2\\n30\\n0', 'output': 'Case 1: 3\\nCase 2: 3\\nCase 3: 2\\nCase 4: 14\\nCase 5: 2\\nCase 6: 30\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6\\n2\\n14\\n2\\n30\\n0', 'output': 'Case 1: 3\\nCase 2: 6\\nCase 3: 2\\nCase 4: 14\\nCase 5: 2\\nCase 6: 30\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6\\n11\\n7\\n8\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 6\\nCase 3: 11\\nCase 4: 7\\nCase 5: 8\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n5\\n3\\n8\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 5\\nCase 4: 3\\nCase 5: 8\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n4\\n1\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 4\\nCase 5: 1\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n9\\n14\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 9\\nCase 5: 14\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n3\\n4\\n2\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 3\\nCase 4: 4\\nCase 5: 2\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n14\\n26\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 14\\nCase 5: 26\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n9\\n6\\n2\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 9\\nCase 4: 6\\nCase 5: 2\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n11\\n8\\n26\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 2\\nCase 3: 11\\nCase 4: 8\\nCase 5: 26\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n16\\n7\\n26\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 16\\nCase 4: 7\\nCase 5: 26\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n11\\n9\\n2\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 11\\nCase 4: 9\\nCase 5: 2\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n11\\n7\\n2\\n44\\n0', 'output': 'Case 1: 3\\nCase 2: 8\\nCase 3: 11\\nCase 4: 7\\nCase 5: 2\\nCase 6: 44\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n11\\n14\\n0\\n58\\n0', 'output': 'Case 1: 3\\nCase 2: 8\\nCase 3: 11\\nCase 4: 14\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n15\\n14\\n2\\n58\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 15\\nCase 4: 14\\nCase 5: 2\\nCase 6: 58\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n2\\n10\\n2\\n58\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 2\\nCase 4: 10\\nCase 5: 2\\nCase 6: 58\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n2\\n14\\n2\\n35\\n0', 'output': 'Case 1: 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'input': '3\\n5\\n11\\n9\\n19\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 9\\nCase 5: 19\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n3\\n1\\n2\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 3\\nCase 4: 1\\nCase 5: 2\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n20\\n14\\n26\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 20\\nCase 4: 14\\nCase 5: 26\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n9\\n6\\n2\\n2\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 9\\nCase 4: 6\\nCase 5: 2\\nCase 6: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n19\\n8\\n26\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 2\\nCase 3: 19\\nCase 4: 8\\nCase 5: 26\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n11\\n2\\n2\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 11\\nCase 4: 2\\nCase 5: 2\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6\\n11\\n7\\n2\\n44\\n0', 'output': 'Case 1: 3\\nCase 2: 6\\nCase 3: 11\\nCase 4: 7\\nCase 5: 2\\nCase 6: 44\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n2\\n14\\n0\\n58\\n0', 'output': 'Case 1: 3\\nCase 2: 8\\nCase 3: 2\\nCase 4: 14\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n0\\n10\\n2\\n58\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n2\\n12\\n0\\n28\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 2\\nCase 4: 12\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n2\\n18\\n2\\n24\\n0', 'output': 'Case 1: 3\\nCase 2: 3\\nCase 3: 2\\nCase 4: 18\\nCase 5: 2\\nCase 6: 24\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6\\n2\\n11\\n3\\n30\\n0', 'output': 'Case 1: 3\\nCase 2: 6\\nCase 3: 2\\nCase 4: 11\\nCase 5: 3\\nCase 6: 30\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n15\\n4\\n1\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 3\\nCase 3: 15\\nCase 4: 4\\nCase 5: 1\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n9\\n19\\n0\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 9\\nCase 5: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n1\\n1\\n2\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 1\\nCase 4: 1\\nCase 5: 2\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n20\\n9\\n26\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 20\\nCase 4: 9\\nCase 5: 26\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n9\\n6\\n3\\n2\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 9\\nCase 4: 6\\nCase 5: 3\\nCase 6: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n19\\n8\\n13\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 2\\nCase 3: 19\\nCase 4: 8\\nCase 5: 13\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n11\\n2\\n0\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 11\\nCase 4: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6\\n11\\n7\\n2\\n6\\n0', 'output': 'Case 1: 3\\nCase 2: 6\\nCase 3: 11\\nCase 4: 7\\nCase 5: 2\\nCase 6: 6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n2\\n14\\n-1\\n35\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 2\\nCase 4: 14\\nCase 5: -1\\nCase 6: 35\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n4\\n12\\n0\\n28\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 4\\nCase 4: 12\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n2\\n18\\n2\\n17\\n0', 'output': 'Case 1: 3\\nCase 2: 3\\nCase 3: 2\\nCase 4: 18\\nCase 5: 2\\nCase 6: 17\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n11\\n9\\n24\\n0\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 11\\nCase 4: 9\\nCase 5: 24\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n1\\n2\\n2\\n19\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 1\\nCase 4: 2\\nCase 5: 2\\nCase 6: 19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n20\\n9\\n23\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 20\\nCase 4: 9\\nCase 5: 23\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n9\\n5\\n3\\n2\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 9\\nCase 4: 5\\nCase 5: 3\\nCase 6: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n19\\n10\\n13\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 2\\nCase 3: 19\\nCase 4: 10\\nCase 5: 13\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n9\\n11\\n7\\n2\\n6\\n0', 'output': 'Case 1: 3\\nCase 2: 9\\nCase 3: 11\\nCase 4: 7\\nCase 5: 2\\nCase 6: 6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n2\\n26\\n0\\n58\\n-1', 'output': 'Case 1: 3\\nCase 2: 8\\nCase 3: 2\\nCase 4: 26\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n2\\n22\\n-1\\n35\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 2\\nCase 4: 22\\nCase 5: -1\\nCase 6: 35\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n4\\n16\\n0\\n28\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 4\\nCase 4: 16\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0\\n2\\n18\\n2\\n17\\n0', 'output': 'Case 1: 3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n11\\n9\\n24\\n0\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 11\\nCase 4: 9\\nCase 5: 24\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n1\\n2\\n2\\n33\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 1\\nCase 4: 2\\nCase 5: 2\\nCase 6: 33\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n20\\n9\\n23\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 1\\nCase 3: 20\\nCase 4: 9\\nCase 5: 23\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n9\\n1\\n3\\n2\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 9\\nCase 4: 1\\nCase 5: 3\\nCase 6: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n19\\n9\\n13\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 2\\nCase 3: 19\\nCase 4: 9\\nCase 5: 13\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n15\\n2\\n0\\n4\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 15\\nCase 4: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n9\\n11\\n7\\n3\\n6\\n0', 'output': 'Case 1: 3\\nCase 2: 9\\nCase 3: 11\\nCase 4: 7\\nCase 5: 3\\nCase 6: 6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n1\\n10\\n0\\n58\\n1', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 1\\nCase 4: 10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n2\\n33\\n-1\\n35\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 2\\nCase 4: 33\\nCase 5: -1\\nCase 6: 35\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6\\n11\\n9\\n24\\n0\\n0', 'output': 'Case 1: 3\\nCase 2: 6\\nCase 3: 11\\nCase 4: 9\\nCase 5: 24\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7\\n1\\n2\\n2\\n33\\n0', 'output': 'Case 1: 3\\nCase 2: 7\\nCase 3: 1\\nCase 4: 2\\nCase 5: 2\\nCase 6: 33\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n9\\n1\\n4\\n2\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 9\\nCase 4: 1\\nCase 5: 4\\nCase 6: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n19\\n1\\n13\\n34\\n0', 'output': 'Case 1: 3\\nCase 2: 2\\nCase 3: 19\\nCase 4: 1\\nCase 5: 13\\nCase 6: 34\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n15\\n2\\n0\\n4\\n0', 'output': 'Case 1: 3\\nCase 2: 8\\nCase 3: 15\\nCase 4: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n3\\n33\\n-1\\n35\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 3\\nCase 4: 33\\nCase 5: -1\\nCase 6: 35\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n4\\n16\\n1\\n6\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 4\\nCase 4: 16\\nCase 5: 1\\nCase 6: 6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6\\n11\\n9\\n24\\n-1\\n0', 'output': 'Case 1: 3\\nCase 2: 6\\nCase 3: 11\\nCase 4: 9\\nCase 5: 24\\nCase 6: -1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1\\n2\\n2\\n33\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 1\\nCase 4: 2\\nCase 5: 2\\nCase 6: 33\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n9\\n2\\n4\\n2\\n0', 'output': 'Case 1: 3\\nCase 2: 5\\nCase 3: 9\\nCase 4: 2\\nCase 5: 4\\nCase 6: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n-1\\n10\\n0\\n66\\n1', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: -1\\nCase 4: 10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n22\\n4\\n16\\n1\\n6\\n0', 'output': 'Case 1: 3\\nCase 2: 22\\nCase 3: 4\\nCase 4: 16\\nCase 5: 1\\nCase 6: 6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6\\n10\\n9\\n24\\n-1\\n0', 'output': 'Case 1: 3\\nCase 2: 6\\nCase 3: 10\\nCase 4: 9\\nCase 5: 24\\nCase 6: -1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1\\n2\\n0\\n33\\n0', 'output': 'Case 1: 3\\nCase 2: 4\\nCase 3: 1\\nCase 4: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n15\\n2\\n0\\n7\\n0', 'output': 'Case 1: 3\\nCase 2: 1\\nCase 3: 15\\nCase 4: 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n14\\n1\\n33\\n-1\\n35\\n0', 'output': 'Case 1: 3\\nCase 2: 14\\nCase 3: 1\\nCase 4: 33\\nCase 5: -1\\nCase 6: 35\\n'}, {'type': 'stdin_stdout', 'input': '3\\n22\\n4\\n16\\n1\\n7\\n0', 'output': 'Case 1: 3\\nCase 2: 22\\nCase 3: 4\\nCase 4: 16\\nCase 5: 1\\nCase 6: 7\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79585","program":"```python\ni = 0\n\nwhile True:\n n = int(input())\n i += 1\n if n == 0:\n break\n print(\"Case {}: {}\".format(i, n))\n```","inputs":"3\n5\n11\n7\n8\n19\n0","output":"Case 1: 3\nCase 2: 5\nCase 3: 11\nCase 4: 7\nCase 5: 8\nCase 6: 19","actual_output":"Case 1: 3\nCase 2: 5\nCase 3: 11\nCase 4: 7\nCase 5: 8\nCase 6: 19\n","execution_success":true,"sample_index":12671},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1015_B. Obtaining the String","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given two strings s and t. Both strings have length n and consist of lowercase Latin letters. The characters in the strings are numbered from 1 to n.\n\nYou can successively perform the following move any number of times (possibly, zero):\n\n * swap any two adjacent (neighboring) characters of s (i.e. for any i = \\{1, 2, ..., n - 1\\} you can swap s_i and s_{i + 1}). \n\n\n\nYou can't apply a move to the string t. The moves are applied to the string s one after another.\n\nYour task is to obtain the string t from the string s. Find any way to do it with at most 10^4 such moves.\n\nYou do not have to minimize the number of moves, just find any sequence of moves of length 10^4 or less to transform s into t.\n\nInput\n\nThe first line of the input contains one integer n (1 \u2264 n \u2264 50) \u2014 the length of strings s and t.\n\nThe second line of the input contains the string s consisting of n lowercase Latin letters.\n\nThe third line of the input contains the string t consisting of n lowercase Latin letters.\n\nOutput\n\nIf it is impossible to obtain the string t using moves, print \"-1\".\n\nOtherwise in the first line print one integer k \u2014 the number of moves to transform s to t. Note that k must be an integer number between 0 and 10^4 inclusive.\n\nIn the second line print k integers c_j (1 \u2264 c_j < n), where c_j means that on the j-th move you swap characters s_{c_j} and s_{c_j + 1}.\n\nIf you do not need to apply any moves, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.\n\nExamples\n\nInput\n\n6\nabcdef\nabdfec\n\n\nOutput\n\n4\n3 5 4 5 \n\n\nInput\n\n4\nabcd\naccd\n\n\nOutput\n\n-1\n\nNote\n\nIn the first example the string s changes as follows: \"abcdef\" \u2192 \"abdcef\" \u2192 \"abdcfe\" \u2192 \"abdfce\" \u2192 \"abdfec\".\n\nIn the second example there is no way to transform the string s into the string t through any allowed moves.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\ns = input()\nt = input()\nif s == t:\n print(0)\nelif sorted(s) != sorted(t):\n print(-1)\nelse:\n res = list()\n ls = list(s)\n lt = list(t)\n for i in range(n):\n if ls[i] != lt[i]:\n pos = ls.index(lt[i], i+1)\n j = pos-1\n while j >= i:\n ls[j], ls[j+1] = ls[j+1], ls[j]\n res.append(j+1)\n j -= 1\n print(len(res))\n print(*res)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\nabcd\\naccd\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '6\\nabcdef\\nabdfec\\n', 'output': '4\\n3 5 4 5 '}, {'type': 'stdin_stdout', 'input': '50\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4\\naaab\\naabb\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '50\\nbababababababababababababababababababababababababa\\nababababababababababababababababababababababababab\\n', 'output': '25\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 '}, {'type': 'stdin_stdout', 'input': '50\\nvpdgzvgvgbichiiqdhytvcooetcgeecyueoylqzbtzzgaqhalt\\nvpdgzvgvgbichiiqdhytvcooetcgeecuyeoylqzbtzzgaqhalt\\n', 'output': '1\\n32 '}, {'type': 'stdin_stdout', 'input': '2\\nab\\nba\\n', 'output': '1\\n1 '}, {'type': 'stdin_stdout', 'input': '48\\naaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbcccccccccccccccc\\nccccccccccccccccbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaa\\n', 'output': '768\\n32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32\\n'}, {'type': 'stdin_stdout', 'input': '50\\nnyqahbyyoxltryqdmvenemaqnbakglgqolxnaifnqtoclnnqia\\nnyqahbyyoxltryqdmvenemaqnbakglgqolxnaifnqtoclnnqia\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\naa\\nba\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '1\\no\\nk\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '50\\naclojlojlojlojlojlojlojlojlojlojlojlojlojlojlojloj\\nlojlojlojlojlojlojlojlojlojlojlojlojlojlojlojlojac\\n', 'output': '96\\n2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 20 19 21 20 22 21 23 22 24 23 25 24 26 25 27 26 28 27 29 28 30 29 31 30 32 31 33 32 34 33 35 34 36 35 37 36 38 37 39 38 40 39 41 40 42 41 43 42 44 43 45 44 46 45 47 46 48 47 49 48\\n'}, {'type': 'stdin_stdout', 'input': '3\\nxaa\\nxxa\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '50\\nnyqahbyyoxltryqdmvenemaqnbakglgqolxnaifnqtoclnnqia\\nnyqahbyyoxlnryqdmvenemaqnbakglgqolxnaifnqtocltnqia\\n', 'output': '62\\n19 18 17 16 15 14 13 12 13 14 15 16 17 18 19 24 23 22 21 20 21 22 23 24 35 34 33 32 31 30 29 28 27 26 25 26 27 28 29 30 31 32 33 34 35 39 38 37 36 37 38 39 45 44 43 42 41 40 41 43 44 45\\n'}, {'type': 'stdin_stdout', 'input': '50\\npqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpq\\nqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqp\\n', 'output': '25\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 '}, {'type': 'stdin_stdout', 'input': '50\\nkekekekekekekekekekekekekekekekekekekekekekekekeke\\nekekekekekekekekekekekekekekekekekekekekekekekekek\\n', 'output': '25\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 '}, {'type': 'stdin_stdout', 'input': '50\\nokokokokokokokokokokokokokokokokokokokokokokokokok\\nkokokokokokokokokokokokokokokokokokokokokokokokoko\\n', 'output': '25\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 '}, {'type': 'stdin_stdout', 'input': '2\\nab\\nbb\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '50\\nacuojuojuojuojuojuojuojuojuojuojuojuojuojuojuojuoj\\nuojuojuojuojuojuojuojuojuojuojuojuojuojuojuojuojac\\n', 'output': '96\\n2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 20 19 21 20 22 21 23 22 24 23 25 24 26 25 27 26 28 27 29 28 30 29 31 30 32 31 33 32 34 33 35 34 36 35 37 36 38 37 39 38 40 39 41 40 42 41 43 42 44 43 45 44 46 45 47 46 48 47 49 48\\n'}, {'type': 'stdin_stdout', 'input': '50\\nxjjesjesjesjesjesjesjesjesjesjesjesjesjesjesjesjes\\njesjesjesjesjesjesjesjesjesjesjesjesjesjesjesjesxj\\n', 'output': '80\\n1 3 2 4 3 4 6 5 7 6 7 9 8 10 9 10 12 11 13 12 13 15 14 16 15 16 18 17 19 18 19 21 20 22 21 22 24 23 25 24 25 27 26 28 27 28 30 29 31 30 31 33 32 34 33 34 36 35 37 36 37 39 38 40 39 40 42 41 43 42 43 45 44 46 45 46 48 47 49 48\\n'}, {'type': 'stdin_stdout', 'input': '1\\nk\\nk\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '50\\nsorrywawawawawawawawawawawawawawawawawawawawawawax\\nsorryawawawawawawawawawawawawawawawawawawawawawawx\\n', 'output': '22\\n6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 '}, {'type': 'stdin_stdout', 'input': '50\\nababababababababababababababababababababababababab\\nbbabababababababababababababababababababababababaa\\n', 'output': '49\\n1 3 2 5 4 7 6 9 8 11 10 13 12 15 14 17 16 19 18 21 20 23 22 25 24 27 26 29 28 31 30 33 32 35 34 37 36 39 38 41 40 43 42 45 44 47 46 49 48\\n'}, {'type': 'stdin_stdout', 'input': '50\\nxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxd\\ndxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdx\\n', 'output': '25\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 '}, {'type': 'stdin_stdout', 'input': '50\\nnyqahbyyoxltryqdmvenemaqnbakglgqolxnaifnqtoclnnqia\\nloicknqalegaqlnqaeantxqqloyyqagnnrodxmbyinhbmnyftv\\n', 'output': '520\\n10 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 7 8 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 22 21 20 19 18 17 16 15 14 13 12 11 10 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 21 20 19 18 17 16 15 14 13 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 26 25 24 23 22 21 20 19 18 17 16 15 29 28 27 26 25 24 23 22 21 20 19 18 17 16 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 29 28 27 26 25 24 23 22 21 20 19 18 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 32 31 30 29 28 27 26 25 24 23 22 21 20 26 25 24 23 22 21 26 25 24 23 22 35 34 33 32 31 30 29 28 27 26 25 24 23 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 38 37 36 35 34 33 32 31 30 29 28 27 26 29 28 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 40 39 38 37 36 35 34 33 32 31 42 41 40 39 38 37 36 35 34 33 32 44 43 42 41 40 39 38 37 36 35 34 33 36 35 34 46 45 44 43 42 41 40 39 38 37 36 35 39 38 37 36 44 43 42 41 40 39 38 37 41 40 39 38 39 40 49 48 47 46 45 44 43 42 41 48 47 46 45 44 43 42 46 45 44 46 45 49 48 47 46 48 49\\n'}, {'type': 'stdin_stdout', 'input': '6\\nababbb\\nabbbab\\n', 'output': '2\\n3 4 '}, {'type': 'stdin_stdout', 'input': '50\\nvjrvahvokiudpiocpvoqsqhukavyrckhcbctrbprqxizcofrfr\\nvjrvahvokuidpoicpvoqsqhukavyrckhcbctrbprqxizcofrfr\\n', 'output': '2\\n10 14 '}, {'type': 'stdin_stdout', 'input': '50\\naaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbccccccccccccccccc\\ncbacbacbacbacbacbacbacbacbacbacbacbacbacbacbacbacb\\n', 'output': '425\\n33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 21 20 19 18 17 16 15 14 13 12 11 10 9 8 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 23 22 21 20 19 18 17 16 15 14 13 12 11 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 25 24 23 22 21 20 19 18 17 16 15 14 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 27 26 25 24 23 22 21 20 19 18 17 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 29 28 27 26 25 24 23 22 21 20 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 31 30 29 28 27 26 25 24 23 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 33 32 31 30 29 28 27 26 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 35 34 33 32 31 30 29 43 42 41 40 39 38 37 36 35 34 33 32 31 37 36 35 34 33 32 44 43 42 41 40 39 38 37 36 35 34 39 38 37 36 35 45 44 43 42 41 40 39 38 37 41 40 39 38 46 45 44 43 42 41 40 43 42 41 47 46 45 44 43 45 44 48 47 46 47 49\\n'}, {'type': 'stdin_stdout', 'input': '50\\nababababababababababababababababababababababababab\\nababababababababababababababababababababababababab\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '50\\nyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyx\\nxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxy\\n', 'output': '25\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 '}, {'type': 'stdin_stdout', 'input': '50\\nxxvvttrrppnnlljjhhffddbbaacceeggiikkmmooqqssuuwwyy\\nyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaa\\n', 'output': '624\\n48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 48 47 46 45 44 43 42 41 40 39 38 37 49 48 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17 16 15 14 13 12 11 10 9 8 7 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 33 32 31 30 29 28 27 26 25 24 23 22 21 20 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 35 34 33 32 31 30 29 28 27 26 25 24 23 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 37 36 35 34 33 32 31 30 29 28 27 26 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 39 38 37 36 35 34 33 32 31 30 29 40 39 38 37 36 35 34 33 32 31 41 40 39 38 37 36 35 34 33 42 41 40 39 38 37 36 35 43 42 41 40 39 38 37 44 43 42 41 40 39 45 44 43 42 41 46 45 44 43 47 46 45 48 47 49\\n'}, {'type': 'stdin_stdout', 'input': '3\\naab\\nabb\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '50\\naddddddddddddddddddddddddddddddddddddddddddddddddd\\ndadddddddddddddddddddddddddddddddddddddddddddddddd\\n', 'output': '1\\n1 '}, {'type': 'stdin_stdout', 'input': '50\\nabcdefghijklmnopqrstuvwxyabcdefghijklmnopqrstuvwxy\\nyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaa\\n', 'output': '900\\n24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 34 33 32 31 30 29 28 27 26 25 24 23 22 21 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 35 34 33 32 31 30 29 28 27 26 25 24 23 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 36 35 34 33 32 31 30 29 28 27 26 25 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 37 36 35 34 33 32 31 30 29 28 27 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 38 37 36 35 34 33 32 31 30 29 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 39 38 37 36 35 34 33 32 31 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 40 39 38 37 36 35 34 33 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 41 40 39 38 37 36 35 49 48 47 46 45 44 43 42 41 40 39 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print(*res)\n\n```","inputs":"4\nabcd\naccd\n","output":"-1","actual_output":"-1\n","execution_success":true,"sample_index":12672},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1038_F. Wrap Around","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a binary string s.\n\nFind the number of distinct cyclical binary strings of length n which contain s as a substring.\n\nThe cyclical string t contains s as a substring if there is some cyclical shift of string t, such that s is a substring of this cyclical shift of t.\n\nFor example, the cyclical string \"000111\" contains substrings \"001\", \"01110\" and \"10\", but doesn't contain \"0110\" and \"10110\".\n\nTwo cyclical strings are called different if they differ from each other as strings. For example, two different strings, which differ from each other by a cyclical shift, are still considered different cyclical strings.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 40) \u2014 the length of the target string t.\n\nThe next line contains the string s (1 \u2264 |s| \u2264 n) \u2014 the string which must be a substring of cyclical string t. String s contains only characters '0' and '1'.\n\nOutput\n\nPrint the only integer \u2014 the number of distinct cyclical binary strings t, which contain s as a substring.\n\nExamples\n\nInput\n\n2\n0\n\n\nOutput\n\n3\n\nInput\n\n4\n1010\n\n\nOutput\n\n2\n\nInput\n\n20\n10101010101010\n\n\nOutput\n\n962\n\nNote\n\nIn the first example, there are three cyclical strings, which contain \"0\" \u2014 \"00\", \"01\" and \"10\".\n\nIn the second example, there are only two such strings \u2014 \"1010\", \"0101\".\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\ns=[c=='1' for c in input()]\nm=len(s)\nz=[[0,0]]\nfor c in s:\n ind = z[-1][c]\n z[-1][c] = len(z)\n z.append(z[ind][:])\nassert(len(z) == m+1)\nz[m][0] = z[m][1] = m # make it sticky\n\n# how many things match directly\ndp = [0 for _ in range(m+1)]\ndp[0] = 1\nfor i in range(n):\n ndp = [0 for _ in range(m+1)]\n for i in range(m+1):\n ndp[z[i][0]] += dp[i]\n ndp[z[i][1]] += dp[i]\n dp = ndp\nres = dp[m]\n\nfor k in range(1, m):\n s0 = 0\n for c in s[-k:]:\n s0 = z[s0][c]\n dp = [0 for _ in range(m+1)]\n dp[s0] = 1\n for i in range(n - k):\n ndp = [0 for _ in range(m+1)]\n for i in range(m+1):\n ndp[z[i][0]] += dp[i]\n ndp[z[i][1]] += dp[i]\n dp = ndp\n for s1 in range(m): # skip m\n v = dp[s1]\n for c in s[-k:]:\n if s1 == m: v = 0\n s1 = z[s1][c]\n if s1 == m: res += v\nprint(res)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1010\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '20\\n10101010101010\\n', 'output': '962\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1\\n', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '40\\n0010\\n', 'output': '1029761794578\\n'}, {'type': 'stdin_stdout', 'input': '39\\n00111\\n', 'output': '419341377312\\n'}, {'type': 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'python'}","metadata":"{'difficulty': 12, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79617","program":"```python\nn=int(input())\ns=[c=='1' for c in input()]\nm=len(s)\nz=[[0,0]]\nfor c in s:\n ind = z[-1][c]\n z[-1][c] = len(z)\n z.append(z[ind][:])\nassert(len(z) == m+1)\nz[m][0] = z[m][1] = m # make it sticky\n\n# how many things match directly\ndp = [0 for _ in range(m+1)]\ndp[0] = 1\nfor i in range(n):\n ndp = [0 for _ in range(m+1)]\n for i in range(m+1):\n ndp[z[i][0]] += dp[i]\n ndp[z[i][1]] += dp[i]\n dp = ndp\nres = dp[m]\n\nfor k in range(1, m):\n s0 = 0\n for c in s[-k:]:\n s0 = z[s0][c]\n dp = [0 for _ in range(m+1)]\n dp[s0] = 1\n for i in range(n - k):\n ndp = [0 for _ in range(m+1)]\n for i in range(m+1):\n ndp[z[i][0]] += dp[i]\n ndp[z[i][1]] += dp[i]\n dp = ndp\n for s1 in range(m): # skip m\n v = dp[s1]\n for c in s[-k:]:\n if s1 == m: v = 0\n s1 = z[s1][c]\n if s1 == m: res += v\nprint(res)\n```","inputs":"4\n1010\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12673},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1061_B. Views Matter","prompt":"Solve the following coding problem using the programming language python:\n\nYou came to the exhibition and one exhibit has drawn your attention. It consists of n stacks of blocks, where the i-th stack consists of a_i blocks resting on the surface.\n\nThe height of the exhibit is equal to m. Consequently, the number of blocks in each stack is less than or equal to m.\n\nThere is a camera on the ceiling that sees the top view of the blocks and a camera on the right wall that sees the side view of the blocks.\n\n\n\nFind the maximum number of blocks you can remove such that the views for both the cameras would not change.\n\nNote, that while originally all blocks are stacked on the floor, it is not required for them to stay connected to the floor after some blocks are removed. There is no gravity in the whole exhibition, so no block would fall down, even if the block underneath is removed. It is not allowed to move blocks by hand either.\n\nInput\n\nThe first line contains two integers n and m (1 \u2264 n \u2264 100 000, 1 \u2264 m \u2264 10^9) \u2014 the number of stacks and the height of the exhibit.\n\nThe second line contains n integers a_1, a_2, \u2026, a_n (1 \u2264 a_i \u2264 m) \u2014 the number of blocks in each stack from left to right.\n\nOutput\n\nPrint exactly one integer \u2014 the maximum number of blocks that can be removed.\n\nExamples\n\nInput\n\n5 6\n3 3 3 3 3\n\n\nOutput\n\n10\n\nInput\n\n3 5\n1 2 4\n\n\nOutput\n\n3\n\nInput\n\n5 5\n2 3 1 4 4\n\n\nOutput\n\n9\n\nInput\n\n1 1000\n548\n\n\nOutput\n\n0\n\nInput\n\n3 3\n3 1 1\n\n\nOutput\n\n1\n\nNote\n\nThe following pictures illustrate the first example and its possible solution.\n\nBlue cells indicate removed blocks. There are 10 blue cells, so the answer is 10.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,m=map(int,input().split(' '))\na=list(map(int,input().split(' ')))\na.sort()\ncount=0\nprev=0\nfor i in range(n):\n count+=1\n if a[i]>prev:\n prev+=1\ncount+=a[n-1]-prev\nprint(sum(a)-count)\n \n \n \n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 5\\n1 2 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n3 3 3 3 3\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n2 3 1 4 4\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n3 1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 1000\\n548\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '9 12\\n3 3 3 3 3 5 8 8 11\\n', 'output': '34\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n4 2 2 2 2\\n', 'output': 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'stdin_stdout', 'input': '1 1010\\n477\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79621","program":"```python\nn,m=map(int,input().split(' '))\na=list(map(int,input().split(' ')))\na.sort()\ncount=0\nprev=0\nfor i in range(n):\n count+=1\n if a[i]>prev:\n prev+=1\ncount+=a[n-1]-prev\nprint(sum(a)-count)\n \n \n \n\n```","inputs":"3 5\n1 2 4\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12674},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1083_A. The Fair Nut and the Best Path","prompt":"Solve the following coding problem using the programming language python:\n\nThe Fair Nut is going to travel to the Tree Country, in which there are n cities. Most of the land of this country is covered by forest. Furthermore, the local road system forms a tree (connected graph without cycles). Nut wants to rent a car in the city u and go by a simple path to city v. He hasn't determined the path, so it's time to do it. Note that chosen path can consist of only one vertex.\n\nA filling station is located in every city. Because of strange law, Nut can buy only w_i liters of gasoline in the i-th city. We can assume, that he has infinite money. Each road has a length, and as soon as Nut drives through this road, the amount of gasoline decreases by length. Of course, Nut can't choose a path, which consists of roads, where he runs out of gasoline. He can buy gasoline in every visited city, even in the first and the last.\n\nHe also wants to find the maximum amount of gasoline that he can have at the end of the path. Help him: count it.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 3 \u22c5 10^5) \u2014 the number of cities.\n\nThe second line contains n integers w_1, w_2, \u2026, w_n (0 \u2264 w_{i} \u2264 10^9) \u2014 the maximum amounts of liters of gasoline that Nut can buy in cities.\n\nEach of the next n - 1 lines describes road and contains three integers u, v, c (1 \u2264 u, v \u2264 n, 1 \u2264 c \u2264 10^9, u \u2260 v), where u and v \u2014 cities that are connected by this road and c \u2014 its length.\n\nIt is guaranteed that graph of road connectivity is a tree.\n\nOutput\n\nPrint one number \u2014 the maximum amount of gasoline that he can have at the end of the path.\n\nExamples\n\nInput\n\n3\n1 3 3\n1 2 2\n1 3 2\n\n\nOutput\n\n3\n\n\nInput\n\n5\n6 3 2 5 0\n1 2 10\n2 3 3\n2 4 1\n1 5 1\n\n\nOutput\n\n7\n\nNote\n\nThe optimal way in the first example is 2 \u2192 1 \u2192 3. \n\n\n\nThe optimal way in the second example is 2 \u2192 4. \n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\n\nn = int(input())\na = list(map(int, input().split()))\nadj = [[] for i in range(n)]\nfor i in range(n-1):\n u, v, w = map(int, input().split())\n u -= 1\n v -= 1\n adj[u].append((v, w))\n adj[v].append((u, w))\nbest = [0] * n\nans = 0\n\ndef dfs(u):\n stack = list()\n visit = [False] * n\n stack.append((u, -1))\n while stack:\n u, par = stack[-1]\n if not visit[u]:\n visit[u] = True\n for v, w in adj[u]:\n if v != par:\n stack.append((v, u))\n else:\n cand = []\n for v, w in adj[u]:\n if v != par:\n cand.append(best[v] + a[v] - w)\n cand.sort(reverse=True)\n cur = a[u]\n for i in range(2):\n if i < len(cand) and cand[i] > 0:\n cur += cand[i]\n global ans\n ans = max(ans, cur)\n best[u] = cand[0] if len(cand) > 0 and cand[0] > 0 else 0\n stack.pop()\n\ndfs(0)\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 3 3\\n1 2 2\\n1 3 2\\n', 'output': ' 3\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6 3 2 5 0\\n1 2 10\\n2 3 3\\n2 4 1\\n1 5 1\\n', 'output': ' 7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n81 34 31 38 69 62 54 18 72 29\\n4 8 12\\n2 9 25\\n4 5 17\\n5 7 35\\n10 1 13\\n9 3 53\\n7 6 22\\n1 6 82\\n3 10 42\\n', 'output': ' 187\\n'}, {'type': 'stdin_stdout', 'input': '10\\n11 43 11 96 18 53 25 89 31 41\\n2 4 41\\n7 1 88\\n3 2 19\\n10 3 38\\n8 4 97\\n7 5 21\\n7 2 71\\n3 6 69\\n9 5 19\\n', 'output': ' 98\\n'}, {'type': 'stdin_stdout', 'input': '10\\n96 72 39 45 93 64 13 7 3 28\\n9 1 18\\n1 7 15\\n1 10 52\\n4 1 93\\n1 6 94\\n1 5 23\\n1 2 20\\n8 1 13\\n3 1 34\\n', 'output': ' 218\\n'}, {'type': 'stdin_stdout', 'input': '10\\n67 9 7 2 33 5 1 7 43 55\\n2 4 38\\n2 5 77\\n9 8 91\\n9 5 8\\n10 5 4\\n2 6 49\\n9 1 5\\n7 5 100\\n3 10 13\\n', 'output': ' 181\\n'}, {'type': 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9\\n6 5 78\\n8 4 38\\n3 10 74\\n4 6 24\\n7 2 21\\n9 2 54\\n2 6 90\\n4 1 39\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '4\\n10408 154571 2215 494619\\n1 4 1032269\\n4 3 65934\\n4 2 98094\\n', 'output': '551096\\n'}, {'type': 'stdin_stdout', 'input': '10\\n28 8 0 1 5 0 9 1 2 81\\n10 1 9\\n6 5 78\\n8 4 38\\n3 10 142\\n4 6 41\\n7 2 21\\n9 2 54\\n2 6 40\\n4 1 39\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '4\\n10408 154571 53650 494619\\n1 4 1032269\\n4 3 79823\\n4 2 98094\\n', 'output': '551096\\n'}, {'type': 'stdin_stdout', 'input': '10\\n28 8 0 1 9 0 9 1 2 81\\n10 1 9\\n6 5 78\\n8 4 38\\n3 10 142\\n4 6 41\\n7 2 21\\n9 3 54\\n2 4 90\\n4 1 39\\n', 'output': '100\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79625","program":"```python\nimport sys\ninput = sys.stdin.readline\n\nn = int(input())\na = list(map(int, input().split()))\nadj = [[] for i in range(n)]\nfor i in range(n-1):\n u, v, w = map(int, input().split())\n u -= 1\n v -= 1\n adj[u].append((v, w))\n adj[v].append((u, w))\nbest = [0] * n\nans = 0\n\ndef dfs(u):\n stack = list()\n visit = [False] * n\n stack.append((u, -1))\n while stack:\n u, par = stack[-1]\n if not visit[u]:\n visit[u] = True\n for v, w in adj[u]:\n if v != par:\n stack.append((v, u))\n else:\n cand = []\n for v, w in adj[u]:\n if v != par:\n cand.append(best[v] + a[v] - w)\n cand.sort(reverse=True)\n cur = a[u]\n for i in range(2):\n if i < len(cand) and cand[i] > 0:\n cur += cand[i]\n global ans\n ans = max(ans, cur)\n best[u] = cand[0] if len(cand) > 0 and cand[0] > 0 else 0\n stack.pop()\n\ndfs(0)\nprint(ans)\n```","inputs":"3\n1 3 3\n1 2 2\n1 3 2\n","output":" 3\n","actual_output":"3\n","execution_success":true,"sample_index":12675},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1102_C. Doors Breaking and Repairing","prompt":"Solve the following coding problem using the programming language python:\n\nYou are policeman and you are playing a game with Slavik. The game is turn-based and each turn consists of two phases. During the first phase you make your move and during the second phase Slavik makes his move.\n\nThere are n doors, the i-th door initially has durability equal to a_i.\n\nDuring your move you can try to break one of the doors. If you choose door i and its current durability is b_i then you reduce its durability to max(0, b_i - x) (the value x is given).\n\nDuring Slavik's move he tries to repair one of the doors. If he chooses door i and its current durability is b_i then he increases its durability to b_i + y (the value y is given). Slavik cannot repair doors with current durability equal to 0.\n\nThe game lasts 10^{100} turns. If some player cannot make his move then he has to skip it.\n\nYour goal is to maximize the number of doors with durability equal to 0 at the end of the game. You can assume that Slavik wants to minimize the number of such doors. What is the number of such doors in the end if you both play optimally?\n\nInput\n\nThe first line of the input contains three integers n, x and y (1 \u2264 n \u2264 100, 1 \u2264 x, y \u2264 10^5) \u2014 the number of doors, value x and value y, respectively.\n\nThe second line of the input contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 10^5), where a_i is the initial durability of the i-th door.\n\nOutput\n\nPrint one integer \u2014 the number of doors with durability equal to 0 at the end of the game, if you and Slavik both play optimally.\n\nExamples\n\nInput\n\n\n6 3 2\n2 3 1 3 4 2\n\n\nOutput\n\n\n6\n\n\nInput\n\n\n5 3 3\n1 2 4 2 3\n\n\nOutput\n\n\n2\n\n\nInput\n\n\n5 5 6\n1 2 6 10 3\n\n\nOutput\n\n\n2\n\nNote\n\nClarifications about the optimal strategy will be ignored.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, x, y = map(int, input().split())\na = list(map(int,input().split()))\n\nif x > y:\n print( n )\nelse:\n m = 0\n for i in a:\n if i <= x:\n m += 1\n print( m - m // 2 )\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 5 6\\n1 2 6 10 3\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6 3 2\\n2 3 1 3 4 2\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5 3 3\\n1 2 4 2 3\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 2 3\\n3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '69 2 3\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n', 'output': '35\\n'}, {'type': 'stdin_stdout', 'input': '100 1 2\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n', 'output': '50\\n'}, {'type': 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1 58367 1 4764 1 69648 27938 30022 81474 40472 3180 58977 12594 25682 40434 22585 35248 1 2 10355 1 64044 1 2 92565\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '100 2 1\\n2 1 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1 1 2 1 1 1 1 1 2 1 1 2 2 2 2 1 1 2 1 1 1 1 2 2 1 1 2 1 1 1 1 1 2 1 1 2 1 1 1 1 1 2 1 1 4 2 3 1 2 1 2 1 2 1 2 0 1 2 1 1 1 2 2 2 2 2 1 1 1 2 1 2 1 1 2 2 1 2 2 1 1 2 2 2\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '5 1 6\\n1 2 18 24 3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100 2 1\\n2 1 2 2 2 2 1 1 2 1 2 2 2 2 2 2 1 1 2 1 1 1 1 1 2 1 1 2 2 0 2 1 1 2 1 1 1 1 2 2 1 1 2 1 1 1 1 1 2 1 1 2 1 1 1 1 1 2 1 1 4 2 3 1 2 1 2 1 2 1 2 0 1 2 1 1 1 2 2 2 2 2 1 1 1 2 1 2 1 1 2 2 1 2 2 1 1 0 2 2\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n1 2 18 11 3\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79629","program":"```python\nn, x, y = map(int, input().split())\na = list(map(int,input().split()))\n\nif x > y:\n print( n )\nelse:\n m = 0\n for i in a:\n if i <= x:\n m += 1\n print( m - m // 2 )\n\n```","inputs":"5 5 6\n1 2 6 10 3\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12676},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1130_C. Connect","prompt":"Solve the following coding problem using the programming language python:\n\nAlice lives on a flat planet that can be modeled as a square grid of size n \u00d7 n, with rows and columns enumerated from 1 to n. We represent the cell at the intersection of row r and column c with ordered pair (r, c). Each cell in the grid is either land or water.\n\n An example planet with n = 5. It also appears in the first sample test.\n\nAlice resides in land cell (r_1, c_1). She wishes to travel to land cell (r_2, c_2). At any moment, she may move to one of the cells adjacent to where she is\u2014in one of the four directions (i.e., up, down, left, or right).\n\nUnfortunately, Alice cannot swim, and there is no viable transportation means other than by foot (i.e., she can walk only on land). As a result, Alice's trip may be impossible.\n\nTo help Alice, you plan to create at most one tunnel between some two land cells. The tunnel will allow Alice to freely travel between the two endpoints. Indeed, creating a tunnel is a lot of effort: the cost of creating a tunnel between cells (r_s, c_s) and (r_t, c_t) is (r_s-r_t)^2 + (c_s-c_t)^2.\n\nFor now, your task is to find the minimum possible cost of creating at most one tunnel so that Alice could travel from (r_1, c_1) to (r_2, c_2). If no tunnel needs to be created, the cost is 0.\n\nInput\n\nThe first line contains one integer n (1 \u2264 n \u2264 50) \u2014 the width of the square grid.\n\nThe second line contains two space-separated integers r_1 and c_1 (1 \u2264 r_1, c_1 \u2264 n) \u2014 denoting the cell where Alice resides.\n\nThe third line contains two space-separated integers r_2 and c_2 (1 \u2264 r_2, c_2 \u2264 n) \u2014 denoting the cell to which Alice wishes to travel.\n\nEach of the following n lines contains a string of n characters. The j-th character of the i-th such line (1 \u2264 i, j \u2264 n) is 0 if (i, j) is land or 1 if (i, j) is water.\n\nIt is guaranteed that (r_1, c_1) and (r_2, c_2) are land.\n\nOutput\n\nPrint an integer that is the minimum possible cost of creating at most one tunnel so that Alice could travel from (r_1, c_1) to (r_2, c_2).\n\nExamples\n\nInput\n\n\n5\n1 1\n5 5\n00001\n11111\n00111\n00110\n00110\n\n\nOutput\n\n\n10\n\n\nInput\n\n\n3\n1 3\n3 1\n010\n101\n010\n\n\nOutput\n\n\n8\n\nNote\n\nIn the first sample, a tunnel between cells (1, 4) and (4, 5) should be created. The cost of doing so is (1-4)^2 + (4-5)^2 = 10, which is optimal. This way, Alice could walk from (1, 1) to (1, 4), use the tunnel from (1, 4) to (4, 5), and lastly walk from (4, 5) to (5, 5).\n\nIn the second sample, clearly a tunnel between cells (1, 3) and (3, 1) needs to be created. The cost of doing so is (1-3)^2 + (3-1)^2 = 8.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#complexity - O(n^2)\nimport math\nimport sys\n\nsys.setrecursionlimit(2600)\n\nclass UnionFind():\n def __init__(self, num_elements):\n self.parent = list(range(num_elements))\n self.rank = [1] * num_elements\n\n def union(self, a, b):\n par_a = self.find(a)\n par_b = self.find(b)\n \n if par_a == par_b:\n return\n \n if self.rank[par_a] > self.rank[par_b]:\n self.parent[par_b] = par_a \n self.rank[par_a] = self.rank[par_a] + self.rank[par_b]\n else:\n self.parent[par_a] = par_b \n self.rank[par_b] = self.rank[par_a] + self.rank[par_b]\n \n def find(self, a):\n if self.parent[a] == a:\n return a\n par_a = self.find(self.parent[a])\n curr_parent = self.parent[a]\n if par_a != curr_parent:\n self.rank[curr_parent] -= self.rank[a]\n self.parent[a] = par_a\n\n return par_a\n\nn = int(input())\nr1, c1 = map(lambda x:int(x)-1, input().split())\nr2, c2 = map(lambda x:int(x)-1, input().split())\n\narr = []\nfor i in range(n):\n arr.append(input())\n\ndef dfs():\n seen = set()\n directions = [(-1, 0), (0, -1), (0, 1), (1, 0)]\n uf = UnionFind(n*n)\n\n def find_index(i, j):\n return i*n+j\n \n def _dfs(i, j):\n if (i, j) in seen:\n return\n seen.add((i, j)) \n if arr[i][j] == '1':\n return\n for direction in directions:\n ni, nj = i+direction[0], j+direction[1]\n if ni >= 0 and ni < n and nj >= 0 and nj < n and (ni, nj) not in seen and arr[ni][nj] == '0':\n uf.union(i*n+j, ni*n+nj)\n _dfs(ni, nj)\n\n for i in range(n):\n for j in range(n):\n _dfs(i, j)\n\n if uf.find(r1*n+c1) == uf.find(r2*n+c2):\n return 0 \n parent1 = uf.find(r1*n+c1)\n parent2 = uf.find(r2*n+c2)\n min_distance = math.inf\n set_a = set()\n set_b = set()\n\n for i in range(n):\n for j in range(n):\n parent = uf.find(find_index(i, j))\n if parent == parent1:\n set_a.add((i, j))\n elif parent == parent2:\n set_b.add((i, j))\n \n for el1 in set_a:\n for el2 in set_b:\n dist = pow(el1[0]-el2[0], 2) + pow(el1[1]-el2[1], 2)\n min_distance = min(min_distance, dist)\n \n return min_distance\n\n\nprint(dfs())\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 1\\n5 5\\n00001\\n11111\\n00111\\n00110\\n00110\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3\\n3 1\\n010\\n101\\n010\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 5\\n1 1\\n01111\\n11111\\n11110\\n11010\\n11000\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '10\\n9 9\\n2 2\\n1111111111\\n1000111111\\n1000111111\\n1111111111\\n1111000001\\n1111011111\\n1111010001\\n1111010101\\n1111000101\\n1111111111\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 3\\n5 3\\n00000\\n11110\\n00000\\n01111\\n00000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n4 5\\n1 2\\n0001000\\n0111110\\n0110110\\n1100011\\n0110110\\n0111110\\n0001000\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 2\\n9 9\\n1111111111\\n1000111111\\n1000111111\\n1111111111\\n1111000001\\n1111011111\\n1111010001\\n1111010101\\n1111000101\\n1111111111\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 1\\n1 1\\n0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 5\\n1 1\\n01111\\n11111\\n11110\\n11010\\n10000\\n', 'output': '13'}, {'type': 'stdin_stdout', 'input': '10\\n9 9\\n2 2\\n1111111111\\n1000111111\\n1000111111\\n1111111111\\n1111000011\\n1111011111\\n1111010001\\n1111010101\\n1111000101\\n1111111111\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '5\\n1 3\\n5 3\\n10000\\n11110\\n00000\\n01111\\n00000\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '10\\n2 2\\n9 9\\n1111111111\\n1000111111\\n1000111111\\n1111011111\\n1111000001\\n1111011111\\n1111010001\\n1111010101\\n1111000001\\n1111111111\\n', 'output': '2'}, 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9\\n1111111110\\n1000111101\\n1000111111\\n1111111111\\n1111000001\\n1111011111\\n1111010001\\n1111010101\\n1111000101\\n1111111111\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '5\\n1 1\\n5 5\\n00101\\n11110\\n00111\\n00110\\n00110\\n', 'output': '18'}, {'type': 'stdin_stdout', 'input': '7\\n4 5\\n1 2\\n0001000\\n0001110\\n0110100\\n1000011\\n0110110\\n0111110\\n0001000\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n1 1\\n5 1\\n00001\\n10101\\n00111\\n00110\\n00111\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n1 1\\n5 2\\n00001\\n11101\\n10111\\n00010\\n00110\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '5\\n1 3\\n5 3\\n00000\\n11010\\n00000\\n00011\\n00000\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n1 1\\n5 3\\n00101\\n11111\\n00111\\n00110\\n00010\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '5\\n4 5\\n1 1\\n00101\\n11011\\n11110\\n11010\\n11010\\n', 'output': '13'}, {'type': 'stdin_stdout', 'input': '7\\n4 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2\\n1111111111\\n1000111101\\n1000111111\\n1111111111\\n1111000001\\n1111011111\\n1101010001\\n1111010101\\n1111000101\\n0111111111\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '5\\n1 1\\n5 3\\n00000\\n11010\\n01000\\n01111\\n00000\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '7\\n4 3\\n1 2\\n0001000\\n0011110\\n0110110\\n1000001\\n0110110\\n0111110\\n0001000\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n1 1\\n5 1\\n00000\\n01101\\n00111\\n00110\\n00110\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '10\\n2 2\\n9 9\\n1111111110\\n1000011101\\n1000111111\\n1111111111\\n1111000001\\n1111011111\\n1111010001\\n1111010101\\n1111000101\\n1111111111\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '10\\n9 9\\n2 2\\n1111111111\\n1000111111\\n1000111111\\n1111111111\\n1111100001\\n1111011111\\n1101110001\\n1101010101\\n1111000101\\n1111111111\\n', 'output': '25'}, {'type': 'stdin_stdout', 'input': '7\\n4 5\\n1 2\\n0001000\\n0001100\\n0110100\\n1000011\\n0110110\\n0111110\\n0001000\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n1 1\\n5 1\\n00001\\n10101\\n00111\\n10110\\n00111\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n1 3\\n5 3\\n00000\\n11010\\n00000\\n00011\\n00010\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n4 5\\n1 1\\n00101\\n11011\\n11110\\n11000\\n11010\\n', 'output': '10'}, {'type': 'stdin_stdout', 'input': '5\\n1 1\\n5 1\\n00001\\n11001\\n00011\\n00110\\n00110\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '5\\n1 2\\n5 3\\n00010\\n11110\\n00001\\n00011\\n00000\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '5\\n1 1\\n5 1\\n00001\\n10001\\n00100\\n00100\\n00110\\n', 'output': '0'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79633","program":"```python\n#complexity - O(n^2)\nimport math\nimport sys\n\nsys.setrecursionlimit(2600)\n\nclass UnionFind():\n def __init__(self, num_elements):\n self.parent = list(range(num_elements))\n self.rank = [1] * num_elements\n\n def union(self, a, b):\n par_a = self.find(a)\n par_b = self.find(b)\n \n if par_a == par_b:\n return\n \n if self.rank[par_a] > self.rank[par_b]:\n self.parent[par_b] = par_a \n self.rank[par_a] = self.rank[par_a] + self.rank[par_b]\n else:\n self.parent[par_a] = par_b \n self.rank[par_b] = self.rank[par_a] + self.rank[par_b]\n \n def find(self, a):\n if self.parent[a] == a:\n return a\n par_a = self.find(self.parent[a])\n curr_parent = self.parent[a]\n if par_a != curr_parent:\n self.rank[curr_parent] -= self.rank[a]\n self.parent[a] = par_a\n\n return par_a\n\nn = int(input())\nr1, c1 = map(lambda x:int(x)-1, input().split())\nr2, c2 = map(lambda x:int(x)-1, input().split())\n\narr = []\nfor i in range(n):\n arr.append(input())\n\ndef dfs():\n seen = set()\n directions = [(-1, 0), (0, -1), (0, 1), (1, 0)]\n uf = UnionFind(n*n)\n\n def find_index(i, j):\n return i*n+j\n \n def _dfs(i, j):\n if (i, j) in seen:\n return\n seen.add((i, j)) \n if arr[i][j] == '1':\n return\n for direction in directions:\n ni, nj = i+direction[0], j+direction[1]\n if ni >= 0 and ni < n and nj >= 0 and nj < n and (ni, nj) not in seen and arr[ni][nj] == '0':\n uf.union(i*n+j, ni*n+nj)\n _dfs(ni, nj)\n\n for i in range(n):\n for j in range(n):\n _dfs(i, j)\n\n if uf.find(r1*n+c1) == uf.find(r2*n+c2):\n return 0 \n parent1 = uf.find(r1*n+c1)\n parent2 = uf.find(r2*n+c2)\n min_distance = math.inf\n set_a = set()\n set_b = set()\n\n for i in range(n):\n for j in range(n):\n parent = uf.find(find_index(i, j))\n if parent == parent1:\n set_a.add((i, j))\n elif parent == parent2:\n set_b.add((i, j))\n \n for el1 in set_a:\n for el2 in set_b:\n dist = pow(el1[0]-el2[0], 2) + pow(el1[1]-el2[1], 2)\n min_distance = min(min_distance, dist)\n \n return min_distance\n\n\nprint(dfs())\n\n```","inputs":"5\n1 1\n5 5\n00001\n11111\n00111\n00110\n00110\n","output":"10\n","actual_output":"10\n","execution_success":true,"sample_index":12677},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1190_A. Tokitsukaze and Discard Items","prompt":"Solve the following coding problem using the programming language python:\n\nRecently, Tokitsukaze found an interesting game. Tokitsukaze had n items at the beginning of this game. However, she thought there were too many items, so now she wants to discard m (1 \u2264 m \u2264 n) special items of them.\n\nThese n items are marked with indices from 1 to n. In the beginning, the item with index i is placed on the i-th position. Items are divided into several pages orderly, such that each page contains exactly k positions and the last positions on the last page may be left empty.\n\nTokitsukaze would do the following operation: focus on the first special page that contains at least one special item, and at one time, Tokitsukaze would discard all special items on this page. After an item is discarded or moved, its old position would be empty, and then the item below it, if exists, would move up to this empty position. The movement may bring many items forward and even into previous pages, so Tokitsukaze would keep waiting until all the items stop moving, and then do the operation (i.e. check the special page and discard the special items) repeatedly until there is no item need to be discarded.\n\n Consider the first example from the statement: n=10, m=4, k=5, p=[3, 5, 7, 10]. The are two pages. Initially, the first page is special (since it is the first page containing a special item). So Tokitsukaze discards the special items with indices 3 and 5. After, the first page remains to be special. It contains [1, 2, 4, 6, 7], Tokitsukaze discards the special item with index 7. After, the second page is special (since it is the first page containing a special item). It contains [9, 10], Tokitsukaze discards the special item with index 10.\n\nTokitsukaze wants to know the number of operations she would do in total.\n\nInput\n\nThe first line contains three integers n, m and k (1 \u2264 n \u2264 10^{18}, 1 \u2264 m \u2264 10^5, 1 \u2264 m, k \u2264 n) \u2014 the number of items, the number of special items to be discarded and the number of positions in each page.\n\nThe second line contains m distinct integers p_1, p_2, \u2026, p_m (1 \u2264 p_1 < p_2 < \u2026 < p_m \u2264 n) \u2014 the indices of special items which should be discarded.\n\nOutput\n\nPrint a single integer \u2014 the number of operations that Tokitsukaze would do in total.\n\nExamples\n\nInput\n\n\n10 4 5\n3 5 7 10\n\n\nOutput\n\n\n3\n\n\nInput\n\n\n13 4 5\n7 8 9 10\n\n\nOutput\n\n\n1\n\nNote\n\nFor the first example:\n\n * In the first operation, Tokitsukaze would focus on the first page [1, 2, 3, 4, 5] and discard items with indices 3 and 5; \n * In the second operation, Tokitsukaze would focus on the first page [1, 2, 4, 6, 7] and discard item with index 7; \n * In the third operation, Tokitsukaze would focus on the second page [9, 10] and discard item with index 10. \n\n\n\nFor the second example, Tokitsukaze would focus on the second page [6, 7, 8, 9, 10] and discard all special items at once.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n##n,m,k=list(map(int,input().split()))\n##p=list(map(int,input().split()))\n##p.sort()\n##import math\n##ok=k\n##ip=0\n##s=1\n##cnt=0\n##a=False\n##for i in p:\n## \n## if ipu:\n print('{} {}'.format(u,v))\n sys.stdout.flush()\n \ninf=float('inf')\nMOD=10**9+7\n# MOD=998244353\n\nfrom math import gcd,floor,ceil\n# from math import floor,ceil # for Python2\n \nfor _abc in range(1):\n main()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 2 4\\n3 6\\n4 1 5 2 10 4\\n8 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '12\\n29\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 1 100\\n1 3 1\\n2 100 100\\n1 3 1\\n', 'output': '302\\n'}, {'type': 'stdin_stdout', 'input': '40\\n2 2\\n5 2\\n1 5\\n1 1\\n3\\n1 2\\n1 1\\n1 2\\n1 1\\n1 2\\n2 3\\n2 1\\n1\\n1\\n1 1\\n1\\n2 1\\n1\\n1\\n1 2\\n2 3\\n2 2\\n1 3\\n3 3\\n1 1\\n1\\n2 1\\n3\\n4\\n1 1\\n2\\n2 2\\n1 1\\n1 1\\n2 2\\n1 1\\n1 1\\n1 1\\n1\\n2 1\\n1\\n1\\n2 1\\n5\\n3\\n1 1\\n2\\n1 2\\n2 2\\n2 1\\n1\\n1\\n2 2\\n3 2\\n2 4\\n1 1\\n5\\n1 2\\n2 1\\n1 2\\n1 1\\n1 2\\n1 1\\n1 2\\n1 1\\n1 1\\n3\\n2 2\\n1 2\\n2 2\\n1 2\\n4 3\\n1 1\\n3\\n2 1\\n2\\n2\\n1 2\\n3 2\\n2 1\\n3\\n1\\n2 1\\n1\\n1\\n2 1\\n1\\n2\\n2 2\\n2 1\\n2 1\\n1 1\\n2\\n1 2\\n3 5\\n1 1\\n2\\n', 'output': '10\\n3\\n1\\n1\\n3\\n2\\n1\\n2\\n3\\n6\\n1\\n7\\n2\\n2\\n2\\n1\\n2\\n8\\n2\\n2\\n2\\n7\\n5\\n2\\n1\\n1\\n1\\n3\\n4\\n4\\n3\\n4\\n3\\n4\\n2\\n3\\n4\\n2\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3\\n2 5 7\\n4 2 4\\n3 6\\n4 1 5 2 10 4\\n8 6 6 4 9 10\\n5 4 9 5 8 7\\n3 3\\n9 9 9\\n1 1 1\\n1 1 1\\n', 'output': '12\\n29\\n27\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 2\\n1 1\\n2 1\\n1 2\\n2 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 1 100\\n2 3 1\\n2 100 100\\n1 3 1\\n', 'output': '302\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 2\\n1 2\\n2 1\\n1 2\\n2 2\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 3 4\\n3 6\\n4 1 5 2 10 4\\n8 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '12\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 6 4\\n3 6\\n4 1 5 2 10 4\\n8 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '13\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 6 4\\n3 6\\n4 1 4 2 10 4\\n4 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '15\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 6 4\\n3 6\\n4 1 4 2 5 4\\n4 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '15\\n28\\n'}, {'type': 'stdin_stdout', 'input': '40\\n2 2\\n5 2\\n1 5\\n1 1\\n3\\n1 2\\n1 1\\n1 2\\n1 1\\n1 2\\n2 3\\n2 1\\n1\\n1\\n1 1\\n1\\n2 1\\n1\\n1\\n1 2\\n2 3\\n2 2\\n1 3\\n3 3\\n1 1\\n1\\n2 1\\n3\\n4\\n1 1\\n2\\n2 2\\n1 1\\n1 1\\n2 2\\n1 1\\n1 1\\n1 1\\n1\\n2 1\\n1\\n1\\n2 1\\n5\\n3\\n1 1\\n2\\n1 2\\n2 2\\n2 1\\n1\\n1\\n2 2\\n3 2\\n2 4\\n1 1\\n5\\n1 2\\n2 1\\n1 2\\n1 1\\n1 2\\n1 2\\n1 2\\n1 1\\n1 1\\n3\\n2 2\\n1 2\\n2 2\\n1 2\\n4 3\\n1 1\\n3\\n2 1\\n2\\n2\\n1 2\\n3 2\\n2 1\\n3\\n1\\n2 1\\n1\\n1\\n2 1\\n1\\n2\\n2 2\\n2 1\\n2 1\\n1 1\\n2\\n1 2\\n3 5\\n1 1\\n2\\n', 'output': '10\\n3\\n1\\n1\\n3\\n2\\n1\\n2\\n3\\n6\\n1\\n7\\n2\\n2\\n2\\n1\\n2\\n8\\n2\\n2\\n2\\n7\\n5\\n2\\n1\\n2\\n1\\n3\\n4\\n4\\n3\\n4\\n3\\n4\\n2\\n3\\n4\\n2\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3\\n2 5 7\\n4 2 4\\n3 6\\n4 1 5 2 10 4\\n8 6 11 4 9 10\\n5 4 9 5 8 7\\n3 3\\n9 9 9\\n1 1 1\\n1 1 1\\n', 'output': '12\\n31\\n27\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 2\\n1 1\\n2 1\\n1 2\\n2 1\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 2\\n1 2\\n2 1\\n1 3\\n2 2\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 1 100\\n1 3 2\\n2 110 100\\n1 3 1\\n', 'output': '312\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 2\\n1 2\\n2 1\\n1 5\\n2 2\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3\\n2 5 7\\n4 2 4\\n3 6\\n4 1 5 2 10 4\\n8 6 1 4 9 10\\n5 4 9 10 8 7\\n3 3\\n9 9 9\\n1 1 1\\n1 1 1\\n', 'output': '12\\n30\\n27\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 2\\n1 2\\n3 1\\n1 5\\n2 2\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 10 7\\n4 2 4\\n3 6\\n4 1 4 2 10 8\\n4 6 6 5 9 10\\n5 4 9 4 8 7\\n', 'output': '17\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 1\\n4 2 4\\n3 6\\n4 1 5 2 10 4\\n8 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '9\\n29\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 1 100\\n4 3 1\\n2 100 100\\n1 3 1\\n', 'output': '304\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 6 4\\n3 6\\n4 1 5 2 10 4\\n14 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '13\\n34\\n'}, {'type': 'stdin_stdout', 'input': '40\\n2 2\\n5 2\\n1 5\\n1 1\\n3\\n1 2\\n1 1\\n1 2\\n1 1\\n1 2\\n2 3\\n2 1\\n1\\n1\\n1 1\\n1\\n2 1\\n1\\n1\\n1 2\\n2 3\\n2 2\\n1 3\\n3 3\\n1 1\\n1\\n2 1\\n3\\n4\\n1 1\\n2\\n2 2\\n1 1\\n1 1\\n2 2\\n1 1\\n1 1\\n1 1\\n1\\n2 1\\n1\\n1\\n2 1\\n5\\n3\\n1 1\\n2\\n1 2\\n2 2\\n2 1\\n1\\n1\\n2 2\\n3 2\\n2 4\\n1 1\\n5\\n1 2\\n2 1\\n1 2\\n1 1\\n1 2\\n1 2\\n1 2\\n1 1\\n1 1\\n3\\n2 2\\n1 2\\n2 2\\n1 2\\n4 3\\n1 1\\n3\\n2 1\\n2\\n2\\n1 2\\n3 2\\n2 1\\n3\\n1\\n2 1\\n1\\n1\\n2 1\\n1\\n2\\n2 2\\n2 1\\n2 1\\n1 1\\n1\\n1 2\\n3 5\\n1 1\\n2\\n', 'output': '10\\n3\\n1\\n1\\n3\\n2\\n1\\n2\\n3\\n6\\n1\\n7\\n2\\n2\\n2\\n1\\n2\\n8\\n2\\n2\\n2\\n7\\n5\\n2\\n1\\n2\\n1\\n3\\n4\\n4\\n3\\n4\\n3\\n4\\n2\\n3\\n4\\n1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3 2\\n1 1\\n2 1\\n1 2\\n2 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 6 4\\n3 6\\n4 1 4 2 10 4\\n4 12 6 4 9 10\\n5 8 9 5 8 7\\n', 'output': '13\\n32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 1 101\\n2 1 1\\n2 110 100\\n1 3 1\\n', 'output': '313\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 3 4\\n3 6\\n4 2 5 2 10 4\\n8 1 6 4 9 13\\n5 4 9 5 8 7\\n', 'output': '12\\n32\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3\\n2 5 7\\n4 2 4\\n3 6\\n4 1 5 2 10 4\\n8 6 1 4 9 10\\n5 4 9 20 8 7\\n3 3\\n9 9 9\\n1 1 1\\n1 1 1\\n', 'output': '12\\n40\\n27\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 2\\n1 2\\n3 1\\n1 5\\n3 2\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 6 4\\n3 6\\n4 1 5 2 10 4\\n7 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '13\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 6 4\\n3 6\\n4 1 4 2 10 4\\n7 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '13\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 6 4\\n3 6\\n4 1 4 2 10 4\\n4 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '13\\n29\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 1 100\\n1 3 2\\n2 100 100\\n1 3 1\\n', 'output': '302\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 2 4\\n3 6\\n4 1 3 2 10 4\\n8 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '12\\n29\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 1 100\\n2 1 1\\n2 100 100\\n1 3 1\\n', 'output': '302\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 3 4\\n3 6\\n4 2 5 2 10 4\\n8 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '12\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 6 4\\n3 6\\n4 1 4 2 10 4\\n4 6 6 4 9 10\\n5 8 9 5 8 7\\n', 'output': '13\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 6 4\\n3 6\\n4 1 4 2 10 8\\n4 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '15\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 6 4\\n3 6\\n4 1 5 2 5 4\\n4 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '15\\n28\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3\\n2 5 7\\n4 2 4\\n3 6\\n4 1 5 2 10 4\\n8 6 11 4 9 10\\n5 4 9 10 8 7\\n3 3\\n9 9 9\\n1 1 1\\n1 1 1\\n', 'output': '12\\n31\\n27\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 1 100\\n2 1 1\\n2 110 100\\n1 3 1\\n', 'output': '312\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 3 4\\n3 6\\n4 2 5 2 10 4\\n8 1 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '12\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 4 4\\n3 6\\n4 1 4 2 10 4\\n4 6 6 4 9 10\\n5 8 9 5 8 7\\n', 'output': '12\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 6 4\\n3 6\\n4 1 4 2 10 8\\n4 6 6 7 9 10\\n5 4 9 5 8 7\\n', 'output': '15\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 4 4\\n3 6\\n4 1 8 2 10 4\\n4 6 6 4 9 10\\n5 8 9 5 8 7\\n', 'output': '12\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 2 4\\n3 6\\n4 1 4 2 10 8\\n4 6 6 7 9 10\\n5 4 9 5 8 7\\n', 'output': '15\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 2 4\\n3 6\\n4 1 4 2 10 8\\n4 6 6 5 9 10\\n5 4 9 5 8 7\\n', 'output': '15\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 2 4\\n3 6\\n4 1 4 2 10 8\\n4 6 6 5 9 10\\n5 4 9 4 8 7\\n', 'output': '15\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 10 7\\n4 1 4\\n3 6\\n4 1 4 2 10 8\\n4 6 6 5 9 10\\n5 4 9 4 8 7\\n', 'output': '17\\n29\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 2 100\\n1 3 1\\n2 100 100\\n1 3 1\\n', 'output': '302\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 2\\n1 1\\n2 1\\n1 1\\n2 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 2\\n1 2\\n3 1\\n1 2\\n2 2\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 3 6\\n3 6\\n4 1 5 2 10 4\\n8 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '13\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 6 4\\n3 6\\n4 1 5 2 10 6\\n8 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '13\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 6 4\\n3 6\\n4 2 4 2 5 4\\n4 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '15\\n28\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 1 100\\n1 3 2\\n2 100 110\\n1 3 1\\n', 'output': '312\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3\\n2 5 7\\n4 2 4\\n3 6\\n4 1 5 2 10 4\\n8 6 11 4 9 10\\n5 4 9 5 8 7\\n3 3\\n9 9 9\\n1 1 2\\n1 1 1\\n', 'output': '12\\n31\\n27\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 5 7\\n4 2 4\\n3 6\\n4 1 3 2 10 4\\n8 8 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '12\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 5 4\\n3 6\\n4 1 4 2 10 8\\n4 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '15\\n29\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 6 4\\n3 6\\n4 1 5 2 10 4\\n4 6 6 4 9 10\\n5 4 9 5 8 7\\n', 'output': '15\\n29\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 3\\n1 1 100\\n1 5 2\\n2 110 100\\n1 3 1\\n', 'output': '312\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 3\\n2 5 7\\n4 2 4\\n3 6\\n4 1 5 2 10 4\\n8 6 11 4 9 10\\n5 4 9 10 8 7\\n3 3\\n9 9 9\\n1 1 1\\n2 1 1\\n', 'output': '12\\n31\\n27\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3\\n2 8 7\\n4 6 4\\n3 6\\n4 1 4 2 10 8\\n4 6 6 7 9 10\\n5 4 4 5 8 7\\n', 'output': '15\\n29\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79649","program":"```python\n\ndef naiveSolve():\n \n \n \n return\n\n\n\ndef main():\n \n t=int(input())\n allans=[]\n for _ in range(t):\n n,m=readIntArr()\n grid=[]\n for __ in range(n):\n grid.append(readIntArr())\n columns=[]\n for col in range(m):\n temp=[grid[i][col] for i in range(n)]\n columns.append(temp)\n \n valCol=[] # (value, column)\n for i in range(n):\n for j in range(m):\n valCol.append((grid[i][j],j))\n valCol.sort(reverse=True)\n \n # try all possible shifts for top n columns\n topCols=set()\n for val,col in valCol:\n topCols.add(col)\n if len(topCols)==n:\n break\n \n # try all configurations\n m2=len(topCols)\n grid2=[[-1 for __ in range(m2)] for ___ in range(n)]\n topColsList=list(topCols)\n for j in range(m2):\n col=topColsList[j]\n for i in range(n):\n grid2[i][j]=grid[i][col]\n ans=-inf\n for mask in range(n**m2):\n grid3=[[-1 for __ in range(m2)] for ___ in range(n)]\n for col in range(m2):\n shift=mask%n\n for row in range(n):\n grid3[row][col]=grid2[(shift+row)%n][col]\n mask//=n\n tempAns=0\n for row in range(n):\n maxx=-inf\n for col in range(m2):\n maxx=max(maxx,grid3[row][col])\n tempAns+=maxx\n ans=max(ans,tempAns)\n allans.append(ans)\n \n multiLineArrayPrint(allans)\n \n return\n\n\n\nimport sys\ninput=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)\n# input=lambda: sys.stdin.readline().rstrip(\"\\r\\n\") #FOR READING STRING/TEXT INPUTS.\n\ndef oneLineArrayPrint(arr):\n print(' '.join([str(x) for x in arr]))\ndef multiLineArrayPrint(arr):\n print('\\n'.join([str(x) for x in arr]))\ndef multiLineArrayOfArraysPrint(arr):\n print('\\n'.join([' '.join([str(x) for x in y]) for y in arr]))\n \ndef readIntArr():\n return [int(x) for x in input().split()]\n# def readFloatArr():\n# return [float(x) for x in input().split()]\n \ndef makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m])\n dv=defaultValFactory;da=dimensionArr\n if len(da)==1:return [dv() for _ in range(da[0])]\n else:return [makeArr(dv,da[1:]) for _ in range(da[0])]\n \ndef queryInteractive(r):\n print('? {}'.format(r))\n sys.stdout.flush()\n return readIntArr()\n \ndef answerInteractive(adj,n):\n print('!')\n for u in range(1,n+1):\n for v in adj[u]:\n if v>u:\n print('{} {}'.format(u,v))\n sys.stdout.flush()\n \ninf=float('inf')\nMOD=10**9+7\n# MOD=998244353\n\nfrom math import gcd,floor,ceil\n# from math import floor,ceil # for Python2\n \nfor _abc in range(1):\n main()\n```","inputs":"2\n2 3\n2 5 7\n4 2 4\n3 6\n4 1 5 2 10 4\n8 6 6 4 9 10\n5 4 9 5 8 7\n","output":"12\n29\n","actual_output":"12\n29\n","execution_success":true,"sample_index":12679},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1228_D. Complete Tripartite","prompt":"Solve the following coding problem using the programming language python:\n\nYou have a simple undirected graph consisting of n vertices and m edges. The graph doesn't contain self-loops, there is at most one edge between a pair of vertices. The given graph can be disconnected.\n\nLet's make a definition.\n\nLet v_1 and v_2 be two some nonempty subsets of vertices that do not intersect. Let f(v_{1}, v_{2}) be true if and only if all the conditions are satisfied:\n\n 1. There are no edges with both endpoints in vertex set v_1. \n 2. There are no edges with both endpoints in vertex set v_2. \n 3. For every two vertices x and y such that x is in v_1 and y is in v_2, there is an edge between x and y. \n\n\n\nCreate three vertex sets (v_{1}, v_{2}, v_{3}) which satisfy the conditions below;\n\n 1. All vertex sets should not be empty. \n 2. Each vertex should be assigned to only one vertex set. \n 3. f(v_{1}, v_{2}), f(v_{2}, v_{3}), f(v_{3}, v_{1}) are all true. \n\n\n\nIs it possible to create such three vertex sets? If it's possible, print matching vertex set for each vertex.\n\nInput\n\nThe first line contains two integers n and m (3 \u2264 n \u2264 10^{5}, 0 \u2264 m \u2264 min(3 \u22c5 10^{5}, (n(n-1))/(2))) \u2014 the number of vertices and edges in the graph.\n\nThe i-th of the next m lines contains two integers a_{i} and b_{i} (1 \u2264 a_{i} < b_{i} \u2264 n) \u2014 it means there is an edge between a_{i} and b_{i}. The graph doesn't contain self-loops, there is at most one edge between a pair of vertices. The given graph can be disconnected.\n\nOutput\n\nIf the answer exists, print n integers. i-th integer means the vertex set number (from 1 to 3) of i-th vertex. Otherwise, print -1.\n\nIf there are multiple answers, print any.\n\nExamples\n\nInput\n\n\n6 11\n1 2\n1 3\n1 4\n1 5\n1 6\n2 4\n2 5\n2 6\n3 4\n3 5\n3 6\n\n\nOutput\n\n\n1 2 2 3 3 3 \n\nInput\n\n\n4 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4\n\n\nOutput\n\n\n-1\n\nNote\n\nIn the first example, if v_{1} = \\{ 1 \\}, v_{2} = \\{ 2, 3 \\}, and v_{3} = \\{ 4, 5, 6 \\} then vertex sets will satisfy all conditions. But you can assign vertices to vertex sets in a different way; Other answers like \"2 3 3 1 1 1\" will be accepted as well.\n\n\n\nIn the second example, it's impossible to make such vertex sets.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import defaultdict,deque\nimport sys,heapq,bisect,math,itertools,string,queue,copy,time\nsys.setrecursionlimit(10**8)\nINF = float('inf')\nmod = 10**9+7\neps = 10**-7\ndef inp(): return int(sys.stdin.readline())\ndef inpl(): return list(map(int, sys.stdin.readline().split()))\ndef inpl_str(): return list(sys.stdin.readline().split())\n\nN,M = inpl()\n\nif M == 0:\n print(-1)\n exit()\n\ncnts = [0]*N\nlines = defaultdict(set)\nfor _ in range(M):\n a,b = inpl()\n a-=1 ; b-=1\n cnts[a] += 1\n cnts[b] += 1\n lines[a].add(b)\n lines[b].add(a)\n\nsetc = set(cnts)\nL = len(setc)\nans = [-1]*N\nif L == 1:\n ans[a] = 1\n ans[b] = 2\n for i in range(N):\n if ans[i] != 0:\n if i not in lines[a]:\n ans[i] = 1\n elif i not in lines[b]:\n ans[i] = 2\n else:\n ans[i] = 3\nelif L == 2:\n c1,c2 = list(setc)\n if c1*2 + c2 == N*2:\n i1 = cnts.index(c1)\n i2 = cnts.index(c2)\n for i,c in enumerate(cnts):\n if c == c2:\n ans[i] = 2\n else:\n if i not in lines[i1]:\n ans[i] = 1\n else:\n ans[i] = 3\n elif c1 + c2*2 == N*2:\n i1 = cnts.index(c1)\n i2 = cnts.index(c2)\n for i,c in enumerate(cnts):\n if c == c1:\n ans[i] = 1\n else:\n if i not in lines[i2]:\n ans[i] = 2\n else:\n ans[i] = 3\n else:\n print(-1)\n exit()\nelif L == 3:\n c1,c2,c3 = list(setc)\n for i,c in enumerate(cnts):\n if c == c1:\n ans[i] = 1\n elif c == c2:\n ans[i] = 2\n elif c == c3:\n ans[i] = 3\nelse:\n print(-1)\n exit()\n\n\nif len(set(ans)) != 3:\n print(-1)\n exit()\n\nfor s in range(N):\n for t in lines[s]:\n if ans[s] == ans[t]:\n print(-1)\n exit()\n\nprint(' '.join(map(str,ans)))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 6\\n1 2\\n1 3\\n1 4\\n2 3\\n2 4\\n3 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 11\\n1 2\\n1 3\\n1 4\\n1 5\\n1 6\\n2 4\\n2 5\\n2 6\\n3 4\\n3 5\\n3 6\\n', 'output': '1 2 2 3 3 3\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 4\\n2 4\\n3 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 3\\n1 4\\n2 3\\n2 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '21 35\\n1 4\\n2 4\\n1 5\\n2 5\\n1 6\\n2 6\\n1 7\\n2 7\\n1 8\\n2 8\\n1 9\\n2 9\\n1 10\\n2 10\\n1 11\\n2 11\\n1 12\\n2 12\\n1 13\\n2 13\\n1 14\\n2 14\\n1 15\\n2 15\\n1 16\\n2 16\\n1 17\\n2 17\\n1 18\\n2 18\\n1 19\\n2 19\\n1 20\\n2 20\\n3 21\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '12 17\\n1 4\\n2 4\\n1 5\\n2 5\\n1 6\\n2 6\\n1 7\\n2 7\\n1 8\\n2 8\\n1 9\\n2 9\\n1 10\\n2 10\\n1 11\\n2 11\\n3 12\\n', 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4\\n4 5\\n3 2\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '21 35\\n1 4\\n2 4\\n1 5\\n2 5\\n1 6\\n2 6\\n1 7\\n2 7\\n1 8\\n2 8\\n1 4\\n2 9\\n1 10\\n2 5\\n1 11\\n2 11\\n1 12\\n2 12\\n1 13\\n2 13\\n1 14\\n1 14\\n2 12\\n2 15\\n1 1\\n2 16\\n1 17\\n2 17\\n1 18\\n2 18\\n1 19\\n2 19\\n1 20\\n2 20\\n3 21\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '9 0\\n1 1\\n4 6\\n1 3\\n3 4\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79653","program":"```python\nfrom collections import defaultdict,deque\nimport sys,heapq,bisect,math,itertools,string,queue,copy,time\nsys.setrecursionlimit(10**8)\nINF = float('inf')\nmod = 10**9+7\neps = 10**-7\ndef inp(): return int(sys.stdin.readline())\ndef inpl(): return list(map(int, sys.stdin.readline().split()))\ndef inpl_str(): return list(sys.stdin.readline().split())\n\nN,M = inpl()\n\nif M == 0:\n print(-1)\n exit()\n\ncnts = [0]*N\nlines = defaultdict(set)\nfor _ in range(M):\n a,b = inpl()\n a-=1 ; b-=1\n cnts[a] += 1\n cnts[b] += 1\n lines[a].add(b)\n lines[b].add(a)\n\nsetc = set(cnts)\nL = len(setc)\nans = [-1]*N\nif L == 1:\n ans[a] = 1\n ans[b] = 2\n for i in range(N):\n if ans[i] != 0:\n if i not in lines[a]:\n ans[i] = 1\n elif i not in lines[b]:\n ans[i] = 2\n else:\n ans[i] = 3\nelif L == 2:\n c1,c2 = list(setc)\n if c1*2 + c2 == N*2:\n i1 = cnts.index(c1)\n i2 = cnts.index(c2)\n for i,c in enumerate(cnts):\n if c == c2:\n ans[i] = 2\n else:\n if i not in lines[i1]:\n ans[i] = 1\n else:\n ans[i] = 3\n elif c1 + c2*2 == N*2:\n i1 = cnts.index(c1)\n i2 = cnts.index(c2)\n for i,c in enumerate(cnts):\n if c == c1:\n ans[i] = 1\n else:\n if i not in lines[i2]:\n ans[i] = 2\n else:\n ans[i] = 3\n else:\n print(-1)\n exit()\nelif L == 3:\n c1,c2,c3 = list(setc)\n for i,c in enumerate(cnts):\n if c == c1:\n ans[i] = 1\n elif c == c2:\n ans[i] = 2\n elif c == c3:\n ans[i] = 3\nelse:\n print(-1)\n exit()\n\n\nif len(set(ans)) != 3:\n print(-1)\n exit()\n\nfor s in range(N):\n for t in lines[s]:\n if ans[s] == ans[t]:\n print(-1)\n exit()\n\nprint(' '.join(map(str,ans)))\n\n```","inputs":"4 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12680},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1293_B. JOE is on TV!","prompt":"Solve the following coding problem using the programming language python:\n\n[3R2 - Standby for Action](https://www.youtube.com/watch?v=P2ZVC9aoiKo)\n\nOur dear Cafe's owner, JOE Miller, will soon take part in a new game TV-show \"1 vs. n\"!\n\nThe game goes in rounds, where in each round the host asks JOE and his opponents a common question. All participants failing to answer are eliminated. The show ends when only JOE remains (we assume that JOE never answers a question wrong!).\n\nFor each question JOE answers, if there are s (s > 0) opponents remaining and t (0 \u2264 t \u2264 s) of them make a mistake on it, JOE receives \\displaystylet/s dollars, and consequently there will be s - t opponents left for the next question.\n\nJOE wonders what is the maximum possible reward he can receive in the best possible scenario. Yet he has little time before show starts, so can you help him answering it instead?\n\nInput\n\nThe first and single line contains a single integer n (1 \u2264 n \u2264 10^5), denoting the number of JOE's opponents in the show.\n\nOutput\n\nPrint a number denoting the maximum prize (in dollars) JOE could have.\n\nYour answer will be considered correct if it's absolute or relative error won't exceed 10^{-4}. In other words, if your answer is a and the jury answer is b, then it must hold that (|a - b|)/(max(1, b)) \u2264 10^{-4}.\n\nExamples\n\nInput\n\n\n1\n\n\nOutput\n\n\n1.000000000000\n\n\nInput\n\n\n2\n\n\nOutput\n\n\n1.500000000000\n\nNote\n\nIn the second example, the best scenario would be: one contestant fails at the first question, the other fails at the next one. The total reward will be \\displaystyle 1/2 + 1/1 = 1.5 dollars.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\nc = 0\nwhile n>0:\n c += 1/n\n n -= 1\nprint(c)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n', 'output': '1.0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n', 'output': '1.5\\n'}, {'type': 'stdin_stdout', 'input': '8212\\n', 'output': '9.590628328312143\\n'}, {'type': 'stdin_stdout', 'input': '99998\\n', 'output': '12.090126129763334\\n'}, {'type': 'stdin_stdout', 'input': '12\\n', 'output': '3.103210678210678\\n'}, {'type': 'stdin_stdout', 'input': '43\\n', 'output': '4.349998620601827\\n'}, {'type': 'stdin_stdout', 'input': '19\\n', 'output': '3.547739657143682\\n'}, {'type': 'stdin_stdout', 'input': '99999\\n', 'output': '12.090136129863335\\n'}, {'type': 'stdin_stdout', 'input': '5\\n', 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'output': '7.05341859978337\\n'}, {'type': 'stdin_stdout', 'input': '000101\\n', 'output': '5.1972785077386305\\n'}, {'type': 'stdin_stdout', 'input': '68\\n', 'output': '4.804058289729168\\n'}, {'type': 'stdin_stdout', 'input': '111\\n', 'output': '5.291243607252987\\n'}, {'type': 'stdin_stdout', 'input': '64\\n', 'output': '4.743890903705768\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79665","program":"```python\nn = int(input())\nc = 0\nwhile n>0:\n c += 1/n\n n -= 1\nprint(c)\n```","inputs":"1\n","output":"1.0\n","actual_output":"1.0\n","execution_success":true,"sample_index":12682},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1313_B. Different Rules","prompt":"Solve the following coding problem using the programming language python:\n\nNikolay has only recently started in competitive programming, but already qualified to the finals of one prestigious olympiad. There going to be n participants, one of whom is Nikolay. Like any good olympiad, it consists of two rounds. Tired of the traditional rules, in which the participant who solved the largest number of problems wins, the organizers came up with different rules.\n\nSuppose in the first round participant A took x-th place and in the second round \u2014 y-th place. Then the total score of the participant A is sum x + y. The overall place of the participant A is the number of participants (including A) having their total score less than or equal to the total score of A. Note, that some participants may end up having a common overall place. It is also important to note, that in both the first and the second round there were no two participants tying at a common place. In other words, for every i from 1 to n exactly one participant took i-th place in first round and exactly one participant took i-th place in second round.\n\nRight after the end of the Olympiad, Nikolay was informed that he got x-th place in first round and y-th place in the second round. Nikolay doesn't know the results of other participants, yet he wonders what is the minimum and maximum place he can take, if we consider the most favorable and unfavorable outcome for him. Please help Nikolay to find the answer to this question.\n\nInput\n\nThe first line contains an integer t (1 \u2264 t \u2264 100) \u2014 the number of test cases to solve.\n\nEach of the following t lines contains integers n, x, y (1 \u2264 n \u2264 10^9, 1 \u2264 x, y \u2264 n) \u2014 the number of participants in the olympiad, the place that Nikolay took in the first round and the place that Nikolay took in the second round.\n\nOutput\n\nPrint two integers \u2014 the minimum and maximum possible overall place Nikolay could take.\n\nExamples\n\nInput\n\n1\n5 1 3\n\n\nOutput\n\n1 3\n\n\nInput\n\n1\n6 3 4\n\n\nOutput\n\n2 6\n\nNote\n\nExplanation for the first example:\n\nSuppose there were 5 participants A-E. Let's denote Nikolay as A. The the most favorable results for Nikolay could look as follows:\n\n\n\nHowever, the results of the Olympiad could also look like this:\n\n\n\nIn the first case Nikolay would have taken first place, and in the second \u2014 third place.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n\"\"\"\n1\n6 3 4\n\"\"\"\nn = int(input())\nfor _ in range(n):\n nums = list(map(int,input().split()))\n if nums[0] == 1:\n print(1,1)\n continue\n if nums[1]+nums[2] <= nums[0]:\n ans = 1\n else:\n ans = min(nums[0], nums[1]+nums[2]-nums[0]+1)\n res = nums[0] if nums[1]+nums[2] > nums[0] else nums[1]+nums[2]-1\n print(ans,res)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n6 3 4\\n', 'output': '2 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '25\\n5 1 1\\n5 2 3\\n5 5 5\\n5 5 1\\n5 4 4\\n10 1 2\\n10 3 7\\n10 10 10\\n10 3 1\\n10 7 6\\n1000000 21232 1234\\n999999 999999 999999\\n1000000 300001 701321\\n1000000 290001 679121\\n500000 98765 123456\\n100 1 1\\n1000000000 1 1000000000\\n1000000000 1 500000000\\n100000000 1 12345678\\n1000000000 1 499999999\\n1000000000 1 1\\n1000000000 727147900 673366700\\n1000000000 525064181 561222627\\n1000000000 198446857 735445702\\n1000000000 1000000000 1000000000\\n', 'output': '1 1\\n1 4\\n5 5\\n2 5\\n4 5\\n1 2\\n1 9\\n10 10\\n1 3\\n4 10\\n1 22465\\n999999 999999\\n1323 1000000\\n1 969121\\n1 222220\\n1 1\\n2 1000000000\\n1 500000000\\n1 12345678\\n1 499999999\\n1 1\\n400514601 1000000000\\n86286809 1000000000\\n1 933892558\\n1000000000 1000000000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 3 3\\n', 'output': '1 5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3 1 3\\n', 'output': '2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 2 3\\n', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 2 2\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '25\\n5 1 1\\n5 2 3\\n5 5 5\\n5 5 1\\n5 4 4\\n10 1 2\\n10 3 7\\n10 10 10\\n10 3 1\\n10 7 6\\n1000000 21232 1234\\n999999 999999 999999\\n1000000 300001 966605\\n1000000 290001 679121\\n500000 98765 123456\\n100 1 1\\n1000000000 1 1000000000\\n1000000000 1 500000000\\n100000000 1 12345678\\n1000000000 1 499999999\\n1000000000 1 1\\n1000000000 727147900 673366700\\n1000000000 525064181 561222627\\n1000000000 198446857 735445702\\n1000000000 1000000000 1000000000\\n', 'output': '1 1\\n1 4\\n5 5\\n2 5\\n4 5\\n1 2\\n1 9\\n10 10\\n1 3\\n4 10\\n1 22465\\n999999 999999\\n266607 1000000\\n1 969121\\n1 222220\\n1 1\\n2 1000000000\\n1 500000000\\n1 12345678\\n1 499999999\\n1 1\\n400514601 1000000000\\n86286809 1000000000\\n1 933892558\\n1000000000 1000000000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 5 3\\n', 'output': '3 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3 2 3\\n', 'output': '3 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 2 3\\n', 'output': '2 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 2 5\\n', 'output': '2 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 1 9\\n', 'output': '1 9\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 2 9\\n', 'output': '2 10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 4 9\\n', 'output': '4 10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 7 9\\n', 'output': '7 10\\n'}, {'type': 'stdin_stdout', 'input': '25\\n5 1 1\\n5 2 3\\n5 5 5\\n5 5 1\\n5 4 4\\n10 1 2\\n10 3 7\\n10 10 10\\n10 3 1\\n10 7 6\\n1000000 21232 1234\\n999999 999999 999999\\n1000000 300001 966605\\n1000000 290001 679121\\n500000 111099 123456\\n100 1 1\\n1000000000 1 1000000000\\n1000000000 1 500000000\\n100000000 1 12345678\\n1000000000 1 499999999\\n1000000000 1 1\\n1000000000 727147900 673366700\\n1000000000 525064181 561222627\\n1000000000 198446857 735445702\\n1000000000 1000000000 1000000000\\n', 'output': '1 1\\n1 4\\n5 5\\n2 5\\n4 5\\n1 2\\n1 9\\n10 10\\n1 3\\n4 10\\n1 22465\\n999999 999999\\n266607 1000000\\n1 969121\\n1 234554\\n1 1\\n2 1000000000\\n1 500000000\\n1 12345678\\n1 499999999\\n1 1\\n400514601 1000000000\\n86286809 1000000000\\n1 933892558\\n1000000000 1000000000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n12 5 3\\n', 'output': '1 7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9 2 5\\n', 'output': '1 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n11 4 9\\n', 'output': '3 11\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 1 1\\n', 'output': '1 1\\n'}, {'type': 'stdin_stdout', 'input': '25\\n5 1 1\\n5 2 3\\n5 5 5\\n6 5 1\\n5 4 4\\n10 1 2\\n10 3 7\\n10 10 10\\n10 3 1\\n10 7 6\\n1000000 21232 1234\\n999999 999999 999999\\n1000000 300001 966605\\n1000000 290001 679121\\n500000 111099 123456\\n100 1 1\\n1000000000 1 1000000000\\n1000000000 1 500000000\\n100000000 1 12345678\\n1000000000 1 499999999\\n1000000000 1 1\\n1000000000 727147900 673366700\\n1000000000 525064181 561222627\\n1000000000 198446857 735445702\\n1000000000 1000000000 1000000000\\n', 'output': '1 1\\n1 4\\n5 5\\n1 5\\n4 5\\n1 2\\n1 9\\n10 10\\n1 3\\n4 10\\n1 22465\\n999999 999999\\n266607 1000000\\n1 969121\\n1 234554\\n1 1\\n2 1000000000\\n1 500000000\\n1 12345678\\n1 499999999\\n1 1\\n400514601 1000000000\\n86286809 1000000000\\n1 933892558\\n1000000000 1000000000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n12 10 3\\n', 'output': '2 12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 1 2\\n', 'output': '1 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n7 1 7\\n', 'output': '2 7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 1 2\\n', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26 2 7\\n', 'output': '1 8\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26 2 13\\n', 'output': '1 14\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26 2 9\\n', 'output': '1 10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26 4 9\\n', 'output': '1 12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n29 8 9\\n', 'output': '1 16\\n'}, {'type': 'stdin_stdout', 'input': '25\\n5 1 1\\n5 2 3\\n5 5 5\\n5 5 1\\n5 4 4\\n10 1 2\\n10 3 7\\n10 10 10\\n10 3 1\\n10 7 6\\n1000000 21232 1234\\n999999 999999 999999\\n1000000 300001 701321\\n1000000 290001 679121\\n500000 98765 123456\\n100 1 1\\n1000000000 1 1000000000\\n1000000000 1 500000000\\n100000000 1 12345678\\n1000000000 1 499999999\\n1000000000 1 1\\n1000000000 727147900 673366700\\n1000000000 525064181 561222627\\n1000000000 61298188 735445702\\n1000000000 1000000000 1000000000\\n', 'output': '1 1\\n1 4\\n5 5\\n2 5\\n4 5\\n1 2\\n1 9\\n10 10\\n1 3\\n4 10\\n1 22465\\n999999 999999\\n1323 1000000\\n1 969121\\n1 222220\\n1 1\\n2 1000000000\\n1 500000000\\n1 12345678\\n1 499999999\\n1 1\\n400514601 1000000000\\n86286809 1000000000\\n1 796743889\\n1000000000 1000000000\\n'}, {'type': 'stdin_stdout', 'input': '25\\n5 1 1\\n5 3 3\\n5 5 5\\n5 5 1\\n5 4 4\\n10 1 2\\n10 3 7\\n10 10 10\\n10 3 1\\n10 7 6\\n1000000 21232 1234\\n999999 999999 999999\\n1000000 300001 966605\\n1000000 290001 679121\\n500000 98765 123456\\n100 1 1\\n1000000000 1 1000000000\\n1000000000 1 500000000\\n100000000 1 12345678\\n1000000000 1 499999999\\n1000000000 1 1\\n1000000000 727147900 673366700\\n1000000000 525064181 561222627\\n1000000000 198446857 735445702\\n1000000000 1000000000 1000000000\\n', 'output': '1 1\\n2 5\\n5 5\\n2 5\\n4 5\\n1 2\\n1 9\\n10 10\\n1 3\\n4 10\\n1 22465\\n999999 999999\\n266607 1000000\\n1 969121\\n1 222220\\n1 1\\n2 1000000000\\n1 500000000\\n1 12345678\\n1 499999999\\n1 1\\n400514601 1000000000\\n86286809 1000000000\\n1 933892558\\n1000000000 1000000000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 4 3\\n', 'output': '4 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 8 9\\n', 'output': '8 10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 3 9\\n', 'output': '3 10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n11 3 9\\n', 'output': '2 11\\n'}, {'type': 'stdin_stdout', 'input': '25\\n5 1 1\\n5 2 3\\n5 5 5\\n6 5 1\\n5 4 4\\n10 1 2\\n10 3 7\\n10 10 10\\n10 3 1\\n10 7 6\\n1000000 21232 1234\\n999999 999999 999999\\n1000000 300001 966605\\n1000000 290001 679121\\n500000 111099 123456\\n100 1 1\\n1000000000 1 1000000000\\n1000000000 1 500000000\\n100000000 1 12345678\\n1000000000 1 499999999\\n1000000000 1 1\\n1000000000 727147900 673366700\\n1000000000 526839036 561222627\\n1000000000 198446857 735445702\\n1000000000 1000000000 1000000000\\n', 'output': '1 1\\n1 4\\n5 5\\n1 5\\n4 5\\n1 2\\n1 9\\n10 10\\n1 3\\n4 10\\n1 22465\\n999999 999999\\n266607 1000000\\n1 969121\\n1 234554\\n1 1\\n2 1000000000\\n1 500000000\\n1 12345678\\n1 499999999\\n1 1\\n400514601 1000000000\\n88061664 1000000000\\n1 933892558\\n1000000000 1000000000\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26 2 17\\n', 'output': '1 18\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26 4 14\\n', 'output': '1 17\\n'}, {'type': 'stdin_stdout', 'input': '1\\n29 4 8\\n', 'output': '1 11\\n'}, {'type': 'stdin_stdout', 'input': '1\\n41 8 16\\n', 'output': '1 23\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5 2 2\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 1 4\\n', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 2 4\\n', 'output': '1 5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 1 4\\n', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 1 5\\n', 'output': '1 5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 3 1\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n7 3 1\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 1 4\\n', 'output': '2 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8 2 3\\n', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 1 7\\n', 'output': '1 7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n7 3 2\\n', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8 1 7\\n', 'output': '1 7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n13 2 5\\n', 'output': '1 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n7 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n17 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n11 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n17 1 5\\n', 'output': '1 5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 2 2\\n', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n21 1 5\\n', 'output': '1 5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n39 1 5\\n', 'output': '1 5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26 1 5\\n', 'output': '1 5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26 2 5\\n', 'output': '1 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n24 4 9\\n', 'output': '1 12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n29 4 9\\n', 'output': '1 12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n41 8 9\\n', 'output': '1 16\\n'}, {'type': 'stdin_stdout', 'input': '1\\n12 1 4\\n', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 2 3\\n', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 1 6\\n', 'output': '2 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5 1 2\\n', 'output': '1 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n12 2 5\\n', 'output': '1 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 1 1\\n', 'output': '1 1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n16 4 9\\n', 'output': '1 12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6 3 2\\n', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9 1 4\\n', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n12 5 2\\n', 'output': '1 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8 2 6\\n', 'output': '1 7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 2 7\\n', 'output': '1 8\\n'}, {'type': 'stdin_stdout', 'input': '1\\n11 2 5\\n', 'output': '1 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2 1 1\\n', 'output': '1 1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9 3 2\\n', 'output': '1 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n15 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8 1 2\\n', 'output': '1 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n13 4 5\\n', 'output': '1 8\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9 1 2\\n', 'output': '1 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n9 1 7\\n', 'output': '1 7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3 2 2\\n', 'output': '2 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n18 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n17 1 1\\n', 'output': '1 1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n21 2 5\\n', 'output': '1 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n39 1 3\\n', 'output': '1 3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n51 1 5\\n', 'output': '1 5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26 2 6\\n', 'output': '1 7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26 1 7\\n', 'output': '1 7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n45 4 9\\n', 'output': '1 12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n18 8 9\\n', 'output': '1 16\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79669","program":"```python\n\"\"\"\n1\n6 3 4\n\"\"\"\nn = int(input())\nfor _ in range(n):\n nums = list(map(int,input().split()))\n if nums[0] == 1:\n print(1,1)\n continue\n if nums[1]+nums[2] <= nums[0]:\n ans = 1\n else:\n ans = min(nums[0], nums[1]+nums[2]-nums[0]+1)\n res = nums[0] if nums[1]+nums[2] > nums[0] else nums[1]+nums[2]-1\n print(ans,res)\n```","inputs":"1\n6 3 4\n","output":"2 6\n","actual_output":"2 6\n","execution_success":true,"sample_index":12683},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1335_E2. Three Blocks Palindrome (hard version)","prompt":"Solve the following coding problem using the programming language python:\n\nThe only difference between easy and hard versions is constraints.\n\nYou are given a sequence a consisting of n positive integers.\n\nLet's define a three blocks palindrome as the sequence, consisting of at most two distinct elements (let these elements are a and b, a can be equal b) and is as follows: [\\underbrace{a, a, ..., a}_{x}, \\underbrace{b, b, ..., b}_{y}, \\underbrace{a, a, ..., a}_{x}]. There x, y are integers greater than or equal to 0. For example, sequences [], [2], [1, 1], [1, 2, 1], [1, 2, 2, 1] and [1, 1, 2, 1, 1] are three block palindromes but [1, 2, 3, 2, 1], [1, 2, 1, 2, 1] and [1, 2] are not.\n\nYour task is to choose the maximum by length subsequence of a that is a three blocks palindrome.\n\nYou have to answer t independent test cases.\n\nRecall that the sequence t is a a subsequence of the sequence s if t can be derived from s by removing zero or more elements without changing the order of the remaining elements. For example, if s=[1, 2, 1, 3, 1, 2, 1], then possible subsequences are: [1, 1, 1, 1], [3] and [1, 2, 1, 3, 1, 2, 1], but not [3, 2, 3] and [1, 1, 1, 1, 2].\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 10^4) \u2014 the number of test cases. Then t test cases follow.\n\nThe first line of the test case contains one integer n (1 \u2264 n \u2264 2 \u22c5 10^5) \u2014 the length of a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 200), where a_i is the i-th element of a. Note that the maximum value of a_i can be up to 200.\n\nIt is guaranteed that the sum of n over all test cases does not exceed 2 \u22c5 10^5 (\u2211 n \u2264 2 \u22c5 10^5).\n\nOutput\n\nFor each test case, print the answer \u2014 the maximum possible length of some subsequence of a that is a three blocks palindrome.\n\nExample\n\nInput\n\n\n6\n8\n1 1 2 2 3 2 1 1\n3\n1 3 3\n4\n1 10 10 1\n1\n26\n2\n2 1\n3\n1 1 1\n\n\nOutput\n\n\n7\n2\n4\n1\n1\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef max_tbp(xs, a, b, O, C):\n m = 1\n occs = O[a]\n b_cnts = C[b]\n \n for i in range(len(occs)//2):\n st = occs[i]\n en = occs[len(occs)-1-i]\n \n cnt = b_cnts[en-1] - b_cnts[st]\n m = max(m, (i+1)*2 + cnt)\n return m\n \nt = int(input())\nfor _ in range(t):\n n = int(input())\n A = list(map(int, input().split()))\n \n m = 0\n sA = set(A)\n \n occs = {}\n cnts = {}\n for a in sA:\n a_occs = []\n a_cnts = []\n cur = 0\n for i, x in enumerate(A):\n if x == a:\n cur += 1\n a_occs.append(i)\n a_cnts.append(cur)\n occs[a] = a_occs\n cnts[a] = a_cnts\n \n for a in sA:\n for b in sA:\n m = max(m, max_tbp(A, a, b, occs, cnts))\n \n print(m)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '7\\n2\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 2\\n3\\n1 1 1\\n', 'output': '7\\n2\\n4\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 2\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '7\\n1\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 1 2 1 2\\n3\\n1 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 2\\n3\\n1 1 1\\n', 'output': '6\\n2\\n4\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 2\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n2 1 1\\n', 'output': '7\\n1\\n4\\n1\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 1\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n2 1 1\\n', 'output': '7\\n3\\n4\\n1\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 3 1 1\\n3\\n1 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 1 2 1 1\\n3\\n1 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 3\\n3\\n1 1 1\\n', 'output': '7\\n2\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 1 1 2 1 2\\n3\\n1 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 2\\n3\\n1 1 1\\n', 'output': '5\\n2\\n4\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 1\\n4\\n1 10 3 1\\n1\\n26\\n2\\n2 1\\n3\\n2 1 1\\n', 'output': '7\\n3\\n3\\n1\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 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1\\n1\\n26\\n2\\n2 2\\n3\\n1 1 1\\n', 'output': '6\\n2\\n3\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 4 2 3 2 1 1\\n3\\n1 3 2\\n4\\n1 10 11 1\\n1\\n26\\n2\\n2 1\\n3\\n2 1 1\\n', 'output': '6\\n1\\n3\\n1\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 4 2 2 2 1 1\\n3\\n1 3 6\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 5\\n3\\n1 1 1\\n', 'output': '7\\n1\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 4 4 1 2 2 1\\n3\\n1 3 6\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 5\\n3\\n1 1 1\\n', 'output': '6\\n1\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 4 2 1 2 2 1\\n3\\n1 3 6\\n4\\n1 10 10 1\\n1\\n10\\n2\\n2 4\\n3\\n2 1 1\\n', 'output': '5\\n1\\n4\\n1\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n2 1 2 2 3 2 1 1\\n3\\n2 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 2\\n3\\n1 1 1\\n', 'output': '5\\n2\\n4\\n1\\n2\\n3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79673","program":"```python\ndef max_tbp(xs, a, b, O, C):\n m = 1\n occs = O[a]\n b_cnts = C[b]\n \n for i in range(len(occs)//2):\n st = occs[i]\n en = occs[len(occs)-1-i]\n \n cnt = b_cnts[en-1] - b_cnts[st]\n m = max(m, (i+1)*2 + cnt)\n return m\n \nt = int(input())\nfor _ in range(t):\n n = int(input())\n A = list(map(int, input().split()))\n \n m = 0\n sA = set(A)\n \n occs = {}\n cnts = {}\n for a in sA:\n a_occs = []\n a_cnts = []\n cur = 0\n for i, x in enumerate(A):\n if x == a:\n cur += 1\n a_occs.append(i)\n a_cnts.append(cur)\n occs[a] = a_occs\n cnts[a] = a_cnts\n \n for a in sA:\n for b in sA:\n m = max(m, max_tbp(A, a, b, occs, cnts))\n \n print(m)\n\n```","inputs":"6\n8\n1 1 2 2 3 2 1 1\n3\n1 3 3\n4\n1 10 10 1\n1\n26\n2\n2 1\n3\n1 1 1\n","output":"7\n2\n4\n1\n1\n3\n","actual_output":"7\n2\n4\n1\n1\n3\n","execution_success":true,"sample_index":12684},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1358_B. Maria Breaks the Self-isolation","prompt":"Solve the following coding problem using the programming language python:\n\nMaria is the most active old lady in her house. She was tired of sitting at home. She decided to organize a ceremony against the coronavirus.\n\nShe has n friends who are also grannies (Maria is not included in this number). The i-th granny is ready to attend the ceremony, provided that at the time of her appearance in the courtyard there will be at least a_i other grannies there. Note that grannies can come into the courtyard at the same time. Formally, the granny i agrees to come if the number of other grannies who came earlier or at the same time with her is greater than or equal to a_i.\n\nGrannies gather in the courtyard like that.\n\n * Initially, only Maria is in the courtyard (that is, the initial number of grannies in the courtyard is 1). All the remaining n grannies are still sitting at home.\n * On each step Maria selects a subset of grannies, none of whom have yet to enter the courtyard. She promises each of them that at the time of her appearance there will be at least a_i other grannies (including Maria) in the courtyard. Maria can call several grannies at once. In this case, the selected grannies will go out into the courtyard at the same moment of time.\n * She cannot deceive grannies, that is, the situation when the i-th granny in the moment of appearing in the courtyard, finds that now there are strictly less than a_i other grannies (except herself, but including Maria), is prohibited. Please note that if several grannies appeared in the yard at the same time, then each of them sees others at the time of appearance. \n\n\n\nYour task is to find what maximum number of grannies (including herself) Maria can collect in the courtyard for the ceremony. After all, the more people in one place during quarantine, the more effective the ceremony!\n\nConsider an example: if n=6 and a=[1,5,4,5,1,9], then:\n\n * at the first step Maria can call grannies with numbers 1 and 5, each of them will see two grannies at the moment of going out into the yard (note that a_1=1 \u2264 2 and a_5=1 \u2264 2); \n * at the second step, Maria can call grannies with numbers 2, 3 and 4, each of them will see five grannies at the moment of going out into the yard (note that a_2=5 \u2264 5, a_3=4 \u2264 5 and a_4=5 \u2264 5); \n * the 6-th granny cannot be called into the yard \u2014 therefore, the answer is 6 (Maria herself and another 5 grannies). \n\nInput\n\nThe first line contains a single integer t (1 \u2264 t \u2264 10^4) \u2014 the number of test cases in the input. Then test cases follow.\n\nThe first line of a test case contains a single integer n (1 \u2264 n \u2264 10^5) \u2014 the number of grannies (Maria is not included in this number).\n\nThe second line contains n integers a_1, a_2, \u2026, a_n (1 \u2264 a_i \u2264 2\u22c510^5).\n\nIt is guaranteed that the sum of the values n over all test cases of the input does not exceed 10^5.\n\nOutput\n\nFor each test case, print a single integer k (1 \u2264 k \u2264 n + 1) \u2014 the maximum possible number of grannies in the courtyard.\n\nExample\n\nInput\n\n\n4\n5\n1 1 2 2 1\n6\n2 3 4 5 6 7\n6\n1 5 4 5 1 9\n5\n1 2 3 5 6\n\n\nOutput\n\n\n6\n1\n6\n4\n\nNote\n\nIn the first test case in the example, on the first step Maria can call all the grannies. Then each of them will see five grannies when they come out. Therefore, Maria and five other grannies will be in the yard.\n\nIn the second test case in the example, no one can be in the yard, so Maria will remain there alone.\n\nThe third test case in the example is described in the details above.\n\nIn the fourth test case in the example, on the first step Maria can call grannies with numbers 1, 2 and 3. If on the second step Maria calls 4 or 5 (one of them), then when a granny appears in the yard, she will see only four grannies (but it is forbidden). It means that Maria can't call the 4-th granny or the 5-th granny separately (one of them). If she calls both: 4 and 5, then when they appear, they will see 4+1=5 grannies. Despite the fact that it is enough for the 4-th granny, the 5-th granny is not satisfied. So, Maria cannot call both the 4-th granny and the 5-th granny at the same time. That is, Maria and three grannies from the first step will be in the yard in total.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n\n\n\nt = int(input())\nfor i in range(t):\n n = int(input())\n nums = list(map(int, input().split()))\n ans = False\n nums.sort()\n for j in range(n-1, -1,-1):\n if nums[j] <= j+1:\n print(j+2)\n ans = True\n break\n if not ans:\n print(1)\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n5\\n1 1 2 2 1\\n6\\n2 3 4 5 6 7\\n6\\n1 5 4 5 1 9\\n5\\n1 2 3 5 6\\n', 'output': '6\\n1\\n6\\n4\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1\\n1\\n1\\n2\\n1\\n3\\n1\\n4\\n1\\n5\\n1\\n6\\n1\\n7\\n1\\n8\\n', 'output': '2\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n179 57\\n2\\n444 1329\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1\\n1\\n1\\n2\\n1\\n3\\n1\\n8\\n1\\n5\\n1\\n6\\n1\\n7\\n1\\n8\\n', 'output': '2\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2\\n179 32\\n2\\n444 1329\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n5\\n1 1 2 2 1\\n6\\n2 3 4 5 6 7\\n6\\n2 5 4 5 1 9\\n5\\n1 2 3 5 6\\n', 'output': '6\\n1\\n6\\n4\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1\\n1\\n1\\n0\\n1\\n3\\n1\\n8\\n1\\n5\\n1\\n6\\n1\\n7\\n1\\n8\\n', 'output': '2\\n2\\n1\\n1\\n1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n5\\n1 1 2 2 1\\n6\\n2 3 4 5 6 3\\n6\\n2 5 4 5 1 9\\n5\\n1 2 1 5 6\\n', 'output': '6\\n7\\n6\\n4\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1\\n2\\n1\\n0\\n1\\n3\\n1\\n8\\n1\\n5\\n1\\n9\\n1\\n7\\n1\\n8\\n', 'output': '1\\n2\\n1\\n1\\n1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n5\\n1 1 2 2 1\\n6\\n2 3 0 5 3 3\\n6\\n1 5 4 5 1 9\\n5\\n1 2 0 4 6\\n', 'output': '6\\n7\\n6\\n5\\n'}, 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'stdin_stdout', 'input': '8\\n1\\n1\\n1\\n2\\n1\\n2\\n1\\n8\\n1\\n0\\n1\\n8\\n1\\n6\\n1\\n16\\n', 'output': '2\\n1\\n1\\n1\\n2\\n1\\n1\\n1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79677","program":"```python\n\n\n\nt = int(input())\nfor i in range(t):\n n = int(input())\n nums = list(map(int, input().split()))\n ans = False\n nums.sort()\n for j in range(n-1, -1,-1):\n if nums[j] <= j+1:\n print(j+2)\n ans = True\n break\n if not ans:\n print(1)\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n```","inputs":"4\n5\n1 1 2 2 1\n6\n2 3 4 5 6 7\n6\n1 5 4 5 1 9\n5\n1 2 3 5 6\n","output":"6\n1\n6\n4\n","actual_output":"6\n1\n6\n4\n","execution_success":true,"sample_index":12685},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1375_G. Tree Modification","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a tree with n vertices. You are allowed to modify the structure of the tree through the following multi-step operation:\n\n 1. Choose three vertices a, b, and c such that b is adjacent to both a and c. \n 2. For every vertex d other than b that is adjacent to a, remove the edge connecting d and a and add the edge connecting d and c. \n 3. Delete the edge connecting a and b and add the edge connecting a and c. \n\n\n\nAs an example, consider the following tree:\n\n\n\nThe following diagram illustrates the sequence of steps that happen when we apply an operation to vertices 2, 4, and 5:\n\n\n\nIt can be proven that after each operation, the resulting graph is still a tree.\n\nFind the minimum number of operations that must be performed to transform the tree into a star. A star is a tree with one vertex of degree n - 1, called its center, and n - 1 vertices of degree 1.\n\nInput\n\nThe first line contains an integer n (3 \u2264 n \u2264 2 \u22c5 10^5) \u2014 the number of vertices in the tree.\n\nThe i-th of the following n - 1 lines contains two integers u_i and v_i (1 \u2264 u_i, v_i \u2264 n, u_i \u2260 v_i) denoting that there exists an edge connecting vertices u_i and v_i. It is guaranteed that the given edges form a tree.\n\nOutput\n\nPrint a single integer \u2014 the minimum number of operations needed to transform the tree into a star.\n\nIt can be proven that under the given constraints, it is always possible to transform the tree into a star using at most 10^{18} operations.\n\nExamples\n\nInput\n\n\n6\n4 5\n2 6\n3 2\n1 2\n2 4\n\n\nOutput\n\n\n1\n\n\nInput\n\n\n4\n2 4\n4 1\n3 4\n\n\nOutput\n\n\n0\n\nNote\n\nThe first test case corresponds to the tree shown in the statement. As we have seen before, we can transform the tree into a star with center at vertex 5 by applying a single operation to vertices 2, 4, and 5.\n\nIn the second test case, the given tree is already a star with the center at vertex 4, so no operations have to be performed.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\nn=int(input())\ngraph=[[] for _ in range(n)]\nfor j in range(n-1):\n x,y=map(int,input().split())\n x-=1\n y-=1\n graph[x].append(y)\n graph[y].append(x)\n\ncolor=[-1]*n\ntem=[0]\nvisit=[0]*n\ncolor[0]=0\n\nwhile(tem!=[]):\n x=tem.pop()\n for i in graph[x]:\n if(color[i]==-1):\n visit[i]=1\n color[i]=1-color[x]\n tem.append(i)\nk=color.count(1) \n\nprint(min(k,n-k)-1) \n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6\\n4 5\\n2 6\\n3 2\\n1 2\\n2 4\\n', 'output': '1\\n'}, 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4\\n2 4\\n1 5\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '15\\n1 9\\n8 3\\n12 4\\n13 11\\n14 3\\n6 15\\n6 7\\n11 7\\n2 5\\n4 3\\n4 6\\n3 1\\n1 2\\n10 9\\n', 'output': '5\\n'}], 'language': 'python'}","metadata":"{'difficulty': 13, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79681","program":"```python\nimport sys\ninput = sys.stdin.readline\nn=int(input())\ngraph=[[] for _ in range(n)]\nfor j in range(n-1):\n x,y=map(int,input().split())\n x-=1\n y-=1\n graph[x].append(y)\n graph[y].append(x)\n\ncolor=[-1]*n\ntem=[0]\nvisit=[0]*n\ncolor[0]=0\n\nwhile(tem!=[]):\n x=tem.pop()\n for i in graph[x]:\n if(color[i]==-1):\n visit[i]=1\n color[i]=1-color[x]\n tem.append(i)\nk=color.count(1) \n\nprint(min(k,n-k)-1) \n\n```","inputs":"6\n4 5\n2 6\n3 2\n1 2\n2 4\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12686},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1399_C. Boats Competition","prompt":"Solve the following coding problem using the programming language python:\n\nThere are n people who want to participate in a boat competition. The weight of the i-th participant is w_i. Only teams consisting of two people can participate in this competition. As an organizer, you think that it's fair to allow only teams with the same total weight.\n\nSo, if there are k teams (a_1, b_1), (a_2, b_2), ..., (a_k, b_k), where a_i is the weight of the first participant of the i-th team and b_i is the weight of the second participant of the i-th team, then the condition a_1 + b_1 = a_2 + b_2 = ... = a_k + b_k = s, where s is the total weight of each team, should be satisfied.\n\nYour task is to choose such s that the number of teams people can create is the maximum possible. Note that each participant can be in no more than one team.\n\nYou have to answer t independent test cases.\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 1000) \u2014 the number of test cases. Then t test cases follow.\n\nThe first line of the test case contains one integer n (1 \u2264 n \u2264 50) \u2014 the number of participants. The second line of the test case contains n integers w_1, w_2, ..., w_n (1 \u2264 w_i \u2264 n), where w_i is the weight of the i-th participant.\n\nOutput\n\nFor each test case, print one integer k: the maximum number of teams people can compose with the total weight s, if you choose s optimally.\n\nExample\n\nInput\n\n\n5\n5\n1 2 3 4 5\n8\n6 6 6 6 6 6 8 8\n8\n1 2 2 1 2 1 1 2\n3\n1 3 3\n6\n1 1 3 4 2 2\n\n\nOutput\n\n\n2\n3\n4\n1\n2\n\nNote\n\nIn the first test case of the example, we can reach the optimal answer for s=6. Then the first boat is used by participants 1 and 5 and the second boat is used by participants 2 and 4 (indices are the same as weights).\n\nIn the second test case of the example, we can reach the optimal answer for s=12. Then first 6 participants can form 3 pairs.\n\nIn the third test case of the example, we can reach the optimal answer for s=3. The answer is 4 because we have 4 participants with weight 1 and 4 participants with weight 2.\n\nIn the fourth test case of the example, we can reach the optimal answer for s=4 or s=6.\n\nIn the fifth test case of the example, we can reach the optimal answer for s=3. Note that participant with weight 3 can't use the boat because there is no suitable pair for him in the list.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import Counter\ndef solve():\n n=int(input())\n A=list(map(int,input().split()))\n if n==1:\n return 0\n A.sort()\n mi=A[0]+A[1]\n ma=A[-1]+A[-2]\n a=Counter(A)\n t=0\n q=-1\n for i in range(mi,ma+1):\n t=0\n for j in a:\n if i-j in a:\n # print(j,i-j)\n if j == i-j:\n t+=a[j]\n else:\n t+=min(a[i-j],a[j])\n # print(t)\n q=max(q,t//2)\n return q\nt=int(input())\nfor l in range(t):\n # print(\"Case #{}: {}\".format(l+1,1))\n print(solve())\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n5\\n1 2 3 4 5\\n8\\n6 6 6 6 6 6 8 8\\n8\\n1 2 2 1 2 1 1 2\\n3\\n1 3 3\\n6\\n1 1 3 4 2 2\\n', 'output': '2\\n3\\n4\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': 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{'type': 'stdin_stdout', 'input': '4\\n14\\n2 6 8 9 5 8 13 14 12 5 6 14 5 2\\n36\\n15 22 27 7 23 36 10 17 5 21 18 22 3 4 32 24 8 19 36 22 17 11 24 10 33 3 30 2 2 17 22 16 18 2 2 20\\n2\\n2 2\\n12\\n4 9 10 6 1 9 5 8 12 9 9 12\\n', 'output': '4\\n10\\n1\\n4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n14\\n4 6 8 9 5 11 13 14 12 5 6 14 5 2\\n36\\n15 22 27 7 23 36 10 17 7 21 18 22 3 4 32 24 8 19 36 22 17 11 24 10 33 4 30 6 2 17 11 16 18 2 2 20\\n2\\n2 2\\n12\\n4 2 10 6 1 9 5 8 12 9 9 12\\n', 'output': '4\\n10\\n1\\n4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n14\\n2 6 3 9 5 8 13 14 12 5 6 14 5 2\\n36\\n15 22 27 14 23 36 10 17 33 21 18 22 3 2 32 24 8 19 36 22 17 11 24 10 33 4 20 6 2 17 11 16 18 1 2 20\\n2\\n2 2\\n12\\n4 9 10 6 1 9 5 8 12 9 9 12\\n', 'output': '4\\n11\\n1\\n4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n14\\n2 6 5 9 10 8 13 14 8 5 6 14 5 2\\n36\\n15 22 27 7 23 36 10 17 33 21 18 7 3 4 32 24 8 19 36 22 17 11 24 3 26 4 30 6 2 17 11 19 18 1 2 20\\n2\\n2 2\\n12\\n4 9 10 6 1 9 5 8 12 9 9 12\\n', 'output': '4\\n10\\n1\\n4\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79685","program":"```python\nfrom collections import Counter\ndef solve():\n n=int(input())\n A=list(map(int,input().split()))\n if n==1:\n return 0\n A.sort()\n mi=A[0]+A[1]\n ma=A[-1]+A[-2]\n a=Counter(A)\n t=0\n q=-1\n for i in range(mi,ma+1):\n t=0\n for j in a:\n if i-j in a:\n # print(j,i-j)\n if j == i-j:\n t+=a[j]\n else:\n t+=min(a[i-j],a[j])\n # print(t)\n q=max(q,t//2)\n return q\nt=int(input())\nfor l in range(t):\n # print(\"Case #{}: {}\".format(l+1,1))\n print(solve())\n\n```","inputs":"5\n5\n1 2 3 4 5\n8\n6 6 6 6 6 6 8 8\n8\n1 2 2 1 2 1 1 2\n3\n1 3 3\n6\n1 1 3 4 2 2\n","output":"2\n3\n4\n1\n2\n","actual_output":"2\n3\n4\n1\n2\n","execution_success":true,"sample_index":12687},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1468_A. LaIS","prompt":"Solve the following coding problem using the programming language python:\n\nLet's call a sequence b_1, b_2, b_3 ..., b_{k - 1}, b_k almost increasing if $$$min(b_1, b_2) \u2264 min(b_2, b_3) \u2264 ... \u2264 min(b_{k - 1}, b_k).$$$ In particular, any sequence with no more than two elements is almost increasing.\n\nYou are given a sequence of integers a_1, a_2, ..., a_n. Calculate the length of its longest almost increasing subsequence.\n\nYou'll be given t test cases. Solve each test case independently.\n\nReminder: a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.\n\nInput\n\nThe first line contains a single integer t (1 \u2264 t \u2264 1000) \u2014 the number of independent test cases.\n\nThe first line of each test case contains a single integer n (2 \u2264 n \u2264 5 \u22c5 10^5) \u2014 the length of the sequence a.\n\nThe second line of each test case contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 n) \u2014 the sequence itself.\n\nIt's guaranteed that the total sum of n over all test cases doesn't exceed 5 \u22c5 10^5.\n\nOutput\n\nFor each test case, print one integer \u2014 the length of the longest almost increasing subsequence.\n\nExample\n\nInput\n\n\n3\n8\n1 2 7 3 2 1 2 3\n2\n2 1\n7\n4 1 5 2 6 3 7\n\n\nOutput\n\n\n6\n2\n7\n\nNote\n\nIn the first test case, one of the optimal answers is subsequence 1, 2, 7, 2, 2, 3.\n\nIn the second and third test cases, the whole sequence a is already almost increasing.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport bisect as bs\nfor _ in range(int(input())):\n n = int(input())\n a = list(map(int, input().split()))\n if n <= 2:\n print(n)\n continue\n stack, m, p = [a[0]], [], [(1000000, 0)]\n for v in a[1:]:\n k = bs.bisect_right(m, v)\n if k == len(m):\n stack.append(v)\n m.append(min(stack[-1], stack[-2]))\n else:\n stack[k + 1] = m[k] = v \n while p[-1][0] <= v:\n vv, kk = p.pop()\n m[kk] = min(m[kk], vv) \n stack[kk + 1] = min(stack[kk + 1], v)\n if k + 1 < len(m):\n p.append((v, k + 1))\n print(len(stack))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 3 2 1 2 3\\n2\\n2 1\\n7\\n4 1 5 2 6 3 7\\n', 'output': '\\n6\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 3 2 1 2 5\\n2\\n2 1\\n7\\n4 1 5 2 6 3 7\\n', 'output': '6\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 6 2 1 1 3\\n2\\n2 1\\n7\\n4 1 5 2 6 3 7\\n', 'output': '5\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 1 2 1 1 3\\n2\\n2 1\\n7\\n4 1 5 2 6 3 7\\n', 'output': '7\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 6 2 1 4 4\\n2\\n2 1\\n7\\n7 3 3 2 6 3 7\\n', 'output': '6\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 1 2 1 1 3\\n2\\n2 1\\n7\\n4 1 5 2 6 1 7\\n', 'output': '7\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 1 3 1 1 2 7\\n2\\n2 1\\n7\\n4 1 5 2 4 3 7\\n', 'output': '8\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 5 6 2 1 1 5\\n2\\n2 1\\n7\\n1 1 6 2 1 6 7\\n', 'output': '5\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 6 2 1 4 4\\n2\\n2 1\\n7\\n7 6 3 2 6 3 7\\n', 'output': '6\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 1 7 3 2 1 2 3\\n2\\n2 1\\n7\\n4 2 1 6 6 5 1\\n', 'output': '6\\n2\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 6 2 2 4 4\\n2\\n2 1\\n7\\n7 6 3 4 6 3 7\\n', 'output': '7\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 1 7 3 1 1 2 6\\n2\\n2 1\\n7\\n6 2 1 6 6 5 1\\n', 'output': '7\\n2\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n2 4 7 3 2 1 1 3\\n2\\n1 1\\n7\\n7 1 6 2 6 5 7\\n', 'output': '4\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 4 5 6 2 1 1 3\\n2\\n2 2\\n7\\n1 1 5 4 6 3 3\\n', 'output': '5\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 1 7 1 2 1 2 3\\n2\\n2 1\\n7\\n4 2 1 6 2 5 1\\n', 'output': '8\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 6 2 1 2 3\\n2\\n2 1\\n7\\n4 1 5 2 6 3 7\\n', 'output': '6\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 3 2 1 2 7\\n2\\n2 1\\n7\\n4 1 5 2 6 3 7\\n', 'output': '6\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 7 3 2 1 2 7\\n2\\n2 1\\n7\\n4 1 5 2 4 3 7\\n', 'output': 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'output': '6\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 2 5 3 1 1 2 1\\n2\\n2 1\\n7\\n4 2 5 2 3 3 7\\n', 'output': '6\\n2\\n7\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8\\n1 1 5 6 2 1 1 1\\n2\\n2 1\\n7\\n1 1 5 2 3 6 7\\n', 'output': '6\\n2\\n7\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_79697","program":"```python\nimport bisect as bs\nfor _ in range(int(input())):\n n = int(input())\n a = list(map(int, input().split()))\n if n <= 2:\n print(n)\n continue\n stack, m, p = [a[0]], [], [(1000000, 0)]\n for v in a[1:]:\n k = bs.bisect_right(m, v)\n if k == len(m):\n stack.append(v)\n m.append(min(stack[-1], stack[-2]))\n else:\n stack[k + 1] = m[k] = v \n while p[-1][0] <= v:\n vv, kk = p.pop()\n m[kk] = min(m[kk], vv) \n stack[kk + 1] = min(stack[kk + 1], v)\n if k + 1 < len(m):\n p.append((v, k + 1))\n print(len(stack))\n```","inputs":"3\n8\n1 2 7 3 2 1 2 3\n2\n2 1\n7\n4 1 5 2 6 3 7\n","output":"\n6\n2\n7\n","actual_output":"6\n2\n7\n","execution_success":true,"sample_index":12689},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"18_C. Stripe","prompt":"Solve the following coding problem using the programming language python:\n\nOnce Bob took a paper stripe of n squares (the height of the stripe is 1 square). In each square he wrote an integer number, possibly negative. He became interested in how many ways exist to cut this stripe into two pieces so that the sum of numbers from one piece is equal to the sum of numbers from the other piece, and each piece contains positive integer amount of squares. Would you help Bob solve this problem?\n\nInput\n\nThe first input line contains integer n (1 \u2264 n \u2264 105) \u2014 amount of squares in the stripe. The second line contains n space-separated numbers \u2014 they are the numbers written in the squares of the stripe. These numbers are integer and do not exceed 10000 in absolute value.\n\nOutput\n\nOutput the amount of ways to cut the stripe into two non-empty pieces so that the sum of numbers from one piece is equal to the sum of numbers from the other piece. Don't forget that it's allowed to cut the stripe along the squares' borders only.\n\nExamples\n\nInput\n\n9\n1 5 -6 7 9 -16 0 -2 2\n\n\nOutput\n\n3\n\n\nInput\n\n3\n1 1 1\n\n\nOutput\n\n0\n\n\nInput\n\n2\n0 0\n\n\nOutput\n\n1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\nl=list(map(int,input().split()))\ns=[0]*n\nfor i in range(n):\n if i==0:\n s[i]=l[i]\n else:\n s[i]=l[i]+s[i-1]\nans=0\nfor i in range(1,n):\n if s[i-1]==s[-1]-s[i-1]:\n ans=ans+1\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n0 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 5 -6 7 9 -16 0 -2 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 3 -3 0 -3 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 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'stdin_stdout', 'input': '1\\n4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '15\\n-1 5 0 4 -1 4 -2 0 -4 -4 3 2 4 -1 -3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-13269\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 64000000}","problem_id":"vfc_79717","program":"```python\nn=int(input())\nl=list(map(int,input().split()))\ns=[0]*n\nfor i in range(n):\n if i==0:\n s[i]=l[i]\n else:\n s[i]=l[i]+s[i-1]\nans=0\nfor i in range(1,n):\n if s[i-1]==s[-1]-s[i-1]:\n ans=ans+1\nprint(ans)\n```","inputs":"2\n0 0\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12691},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"237_C. Primes on Interval","prompt":"Solve the following coding problem using the programming language python:\n\nYou've decided to carry out a survey in the theory of prime numbers. Let us remind you that a prime number is a positive integer that has exactly two distinct positive integer divisors.\n\nConsider positive integers a, a + 1, ..., b (a \u2264 b). You want to find the minimum integer l (1 \u2264 l \u2264 b - a + 1) such that for any integer x (a \u2264 x \u2264 b - l + 1) among l integers x, x + 1, ..., x + l - 1 there are at least k prime numbers. \n\nFind and print the required minimum l. If no value l meets the described limitations, print -1.\n\nInput\n\nA single line contains three space-separated integers a, b, k (1 \u2264 a, b, k \u2264 106; a \u2264 b).\n\nOutput\n\nIn a single line print a single integer \u2014 the required minimum l. If there's no solution, print -1.\n\nExamples\n\nInput\n\n2 4 2\n\n\nOutput\n\n3\n\n\nInput\n\n6 13 1\n\n\nOutput\n\n4\n\n\nInput\n\n1 4 3\n\n\nOutput\n\n-1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\np=[1]*(1000005)\np[0]=0\np[1]=0\nfor i in range(2,1001):\n if p[i]:\n for j in range(2*i,1000005,i):\n p[j]=0\nfor i in range(1,1000001):\n p[i]+=p[i-1]\na,b,k=map(int,input().split())\nif p[b]-p[a-1]1):\n print(-1)\nelse:\n ans=[0]*(n+1)\n i,j,a,b=1,n,1,n\n while(i=1):\n ans[i],ans[j]=a+1,b-1\n ans[i+1],ans[j-1]=b,a\n i+=2\n j-=2\n a+=2\n b-=2\n if(i==j):\n ans[i]=a\n for i in range(1,n+1):\n print(ans[i],end=' ')\n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n', 'output': '2 4 1 3 '}, {'type': 'stdin_stdout', 'input': '2\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '1\\n', 'output': '1 '}, {'type': 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197 19804 195 19806 193 19808 191 19810 189 19812 187 19814 185 19816 183 19818 181 19820 179 19822 177 19824 175 19826 173 19828 171 19830 169 19832 167 19834 165 19836 163 19838 161 19840 159 19842 157 19844 155 19846 153 19848 151 19850 149 19852 147 19854 145 19856 143 19858 141 19860 139 19862 137 19864 135 19866 133 19868 131 19870 129 19872 127 19874 125 19876 123 19878 121 19880 119 19882 117 19884 115 19886 113 19888 111 19890 109 19892 107 19894 105 19896 103 19898 101 19900 99 19902 97 19904 95 19906 93 19908 91 19910 89 19912 87 19914 85 19916 83 19918 81 19920 79 19922 77 19924 75 19926 73 19928 71 19930 69 19932 67 19934 65 19936 63 19938 61 19940 59 19942 57 19944 55 19946 53 19948 51 19950 49 19952 47 19954 45 19956 43 19958 41 19960 39 19962 37 19964 35 19966 33 19968 31 19970 29 19972 27 19974 25 19976 23 19978 21 19980 19 19982 17 19984 15 19986 13 19988 11 19990 9 19992 7 19994 5 19996 3 19998 1 20000 '}, {'type': 'stdin_stdout', 'input': '25\\n', 'output': '2 25 4 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19224 775 19226 773 19228 771 19230 769 19232 767 19234 765 19236 763 19238 761 19240 759 19242 757 19244 755 19246 753 19248 751 19250 749 19252 747 19254 745 19256 743 19258 741 19260 739 19262 737 19264 735 19266 733 19268 731 19270 729 19272 727 19274 725 19276 723 19278 721 19280 719 19282 717 19284 715 19286 713 19288 711 19290 709 19292 707 19294 705 19296 703 19298 701 19300 699 19302 697 19304 695 19306 693 19308 691 19310 689 19312 687 19314 685 19316 683 19318 681 19320 679 19322 677 19324 675 19326 673 19328 671 19330 669 19332 667 19334 665 19336 663 19338 661 19340 659 19342 657 19344 655 19346 653 19348 651 19350 649 19352 647 19354 645 19356 643 19358 641 19360 639 19362 637 19364 635 19366 633 19368 631 19370 629 19372 627 19374 625 19376 623 19378 621 19380 619 19382 617 19384 615 19386 613 19388 611 19390 609 19392 607 19394 605 19396 603 19398 601 19400 599 19402 597 19404 595 19406 593 19408 591 19410 589 19412 587 19414 585 19416 583 19418 581 19420 579 19422 577 19424 575 19426 573 19428 571 19430 569 19432 567 19434 565 19436 563 19438 561 19440 559 19442 557 19444 555 19446 553 19448 551 19450 549 19452 547 19454 545 19456 543 19458 541 19460 539 19462 537 19464 535 19466 533 19468 531 19470 529 19472 527 19474 525 19476 523 19478 521 19480 519 19482 517 19484 515 19486 513 19488 511 19490 509 19492 507 19494 505 19496 503 19498 501 19500 499 19502 497 19504 495 19506 493 19508 491 19510 489 19512 487 19514 485 19516 483 19518 481 19520 479 19522 477 19524 475 19526 473 19528 471 19530 469 19532 467 19534 465 19536 463 19538 461 19540 459 19542 457 19544 455 19546 453 19548 451 19550 449 19552 447 19554 445 19556 443 19558 441 19560 439 19562 437 19564 435 19566 433 19568 431 19570 429 19572 427 19574 425 19576 423 19578 421 19580 419 19582 417 19584 415 19586 413 19588 411 19590 409 19592 407 19594 405 19596 403 19598 401 19600 399 19602 397 19604 395 19606 393 19608 391 19610 389 19612 387 19614 385 19616 383 19618 381 19620 379 19622 377 19624 375 19626 373 19628 371 19630 369 19632 367 19634 365 19636 363 19638 361 19640 359 19642 357 19644 355 19646 353 19648 351 19650 349 19652 347 19654 345 19656 343 19658 341 19660 339 19662 337 19664 335 19666 333 19668 331 19670 329 19672 327 19674 325 19676 323 19678 321 19680 319 19682 317 19684 315 19686 313 19688 311 19690 309 19692 307 19694 305 19696 303 19698 301 19700 299 19702 297 19704 295 19706 293 19708 291 19710 289 19712 287 19714 285 19716 283 19718 281 19720 279 19722 277 19724 275 19726 273 19728 271 19730 269 19732 267 19734 265 19736 263 19738 261 19740 259 19742 257 19744 255 19746 253 19748 251 19750 249 19752 247 19754 245 19756 243 19758 241 19760 239 19762 237 19764 235 19766 233 19768 231 19770 229 19772 227 19774 225 19776 223 19778 221 19780 219 19782 217 19784 215 19786 213 19788 211 19790 209 19792 207 19794 205 19796 203 19798 201 19800 199 19802 197 19804 195 19806 193 19808 191 19810 189 19812 187 19814 185 19816 183 19818 181 19820 179 19822 177 19824 175 19826 173 19828 171 19830 169 19832 167 19834 165 19836 163 19838 161 19840 159 19842 157 19844 155 19846 153 19848 151 19850 149 19852 147 19854 145 19856 143 19858 141 19860 139 19862 137 19864 135 19866 133 19868 131 19870 129 19872 127 19874 125 19876 123 19878 121 19880 119 19882 117 19884 115 19886 113 19888 111 19890 109 19892 107 19894 105 19896 103 19898 101 19900 99 19902 97 19904 95 19906 93 19908 91 19910 89 19912 87 19914 85 19916 83 19918 81 19920 79 19922 77 19924 75 19926 73 19928 71 19930 69 19932 67 19934 65 19936 63 19938 61 19940 59 19942 57 19944 55 19946 53 19948 51 19950 49 19952 47 19954 45 19956 43 19958 41 19960 39 19962 37 19964 35 19966 33 19968 31 19970 29 19972 27 19974 25 19976 23 19978 21 19980 19 19982 17 19984 15 19986 13 19988 11 19990 9 19992 7 19994 5 19996 3 19998 1 20000 '}, {'type': 'stdin_stdout', 'input': '101\\n', 'output': '2 101 4 99 6 97 8 95 10 93 12 91 14 89 16 87 18 85 20 83 22 81 24 79 26 77 28 75 30 73 32 71 34 69 36 67 38 65 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186 321 188 319 190 317 192 315 194 313 196 311 198 309 200 307 202 305 204 303 206 301 208 299 210 297 212 295 214 293 216 291 218 289 220 287 222 285 224 283 226 281 228 279 230 277 232 275 234 273 236 271 238 269 240 267 242 265 244 263 246 261 248 259 250 257 252 255 253 251 254 249 256 247 258 245 260 243 262 241 264 239 266 237 268 235 270 233 272 231 274 229 276 227 278 225 280 223 282 221 284 219 286 217 288 215 290 213 292 211 294 209 296 207 298 205 300 203 302 201 304 199 306 197 308 195 310 193 312 191 314 189 316 187 318 185 320 183 322 181 324 179 326 177 328 175 330 173 332 171 334 169 336 167 338 165 340 163 342 161 344 159 346 157 348 155 350 153 352 151 354 149 356 147 358 145 360 143 362 141 364 139 366 137 368 135 370 133 372 131 374 129 376 127 378 125 380 123 382 121 384 119 386 117 388 115 390 113 392 111 394 109 396 107 398 105 400 103 402 101 404 99 406 97 408 95 410 93 412 91 414 89 416 87 418 85 420 83 422 81 424 79 426 77 428 75 430 73 432 71 434 69 436 67 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9832 172 9830 174 9828 176 9826 178 9824 180 9822 182 9820 184 9818 186 9816 188 9814 190 9812 192 9810 194 9808 196 9806 198 9804 200 9802 202 9800 204 9798 206 9796 208 9794 210 9792 212 9790 214 9788 216 9786 218 9784 220 9782 222 9780 224 9778 226 9776 228 9774 230 9772 232 9770 234 9768 236 9766 238 9764 240 9762 242 9760 244 9758 246 9756 248 9754 250 9752 252 9750 254 9748 256 9746 258 9744 260 9742 262 9740 264 9738 266 9736 268 9734 270 9732 272 9730 274 9728 276 9726 278 9724 280 9722 282 9720 284 9718 286 9716 288 9714 290 9712 292 9710 294 9708 296 9706 298 9704 300 9702 302 9700 304 9698 306 9696 308 9694 310 9692 312 9690 314 9688 316 9686 318 9684 320 9682 322 9680 324 9678 326 9676 328 9674 330 9672 332 9670 334 9668 336 9666 338 9664 340 9662 342 9660 344 9658 346 9656 348 9654 350 9652 352 9650 354 9648 356 9646 358 9644 360 9642 362 9640 364 9638 366 9636 368 9634 370 9632 372 9630 374 9628 376 9626 378 9624 380 9622 382 9620 384 9618 386 9616 388 9614 390 9612 392 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9388 616 9386 618 9384 620 9382 622 9380 624 9378 626 9376 628 9374 630 9372 632 9370 634 9368 636 9366 638 9364 640 9362 642 9360 644 9358 646 9356 648 9354 650 9352 652 9350 654 9348 656 9346 658 9344 660 9342 662 9340 664 9338 666 9336 668 9334 670 9332 672 9330 674 9328 676 9326 678 9324 680 9322 682 9320 684 9318 686 9316 688 9314 690 9312 692 9310 694 9308 696 9306 698 9304 700 9302 702 9300 704 9298 706 9296 708 9294 710 9292 712 9290 714 9288 716 9286 718 9284 720 9282 722 9280 724 9278 726 9276 728 9274 730 9272 732 9270 734 9268 736 9266 738 9264 740 9262 742 9260 744 9258 746 9256 748 9254 750 9252 752 9250 754 9248 756 9246 758 9244 760 9242 762 9240 764 9238 766 9236 768 9234 770 9232 772 9230 774 9228 776 9226 778 9224 780 9222 782 9220 784 9218 786 9216 788 9214 790 9212 792 9210 794 9208 796 9206 798 9204 800 9202 802 9200 804 9198 806 9196 808 9194 810 9192 812 9190 814 9188 816 9186 818 9184 820 9182 822 9180 824 9178 826 9176 828 9174 830 9172 832 9170 834 9168 836 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6880 4119 6882 4117 6884 4115 6886 4113 6888 4111 6890 4109 6892 4107 6894 4105 6896 4103 6898 4101 6900 4099 6902 4097 6904 4095 6906 4093 6908 4091 6910 4089 6912 4087 6914 4085 6916 4083 6918 4081 6920 4079 6922 4077 6924 4075 6926 4073 6928 4071 6930 4069 6932 4067 6934 4065 6936 4063 6938 4061 6940 4059 6942 4057 6944 4055 6946 4053 6948 4051 6950 4049 6952 4047 6954 4045 6956 4043 6958 4041 6960 4039 6962 4037 6964 4035 6966 4033 6968 4031 6970 4029 6972 4027 6974 4025 6976 4023 6978 4021 6980 4019 6982 4017 6984 4015 6986 4013 6988 4011 6990 4009 6992 4007 6994 4005 6996 4003 6998 4001 7000 3999 7002 3997 7004 3995 7006 3993 7008 3991 7010 3989 7012 3987 7014 3985 7016 3983 7018 3981 7020 3979 7022 3977 7024 3975 7026 3973 7028 3971 7030 3969 7032 3967 7034 3965 7036 3963 7038 3961 7040 3959 7042 3957 7044 3955 7046 3953 7048 3951 7050 3949 7052 3947 7054 3945 7056 3943 7058 3941 7060 3939 7062 3937 7064 3935 7066 3933 7068 3931 7070 3929 7072 3927 7074 3925 7076 3923 7078 3921 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7480 3519 7482 3517 7484 3515 7486 3513 7488 3511 7490 3509 7492 3507 7494 3505 7496 3503 7498 3501 7500 3499 7502 3497 7504 3495 7506 3493 7508 3491 7510 3489 7512 3487 7514 3485 7516 3483 7518 3481 7520 3479 7522 3477 7524 3475 7526 3473 7528 3471 7530 3469 7532 3467 7534 3465 7536 3463 7538 3461 7540 3459 7542 3457 7544 3455 7546 3453 7548 3451 7550 3449 7552 3447 7554 3445 7556 3443 7558 3441 7560 3439 7562 3437 7564 3435 7566 3433 7568 3431 7570 3429 7572 3427 7574 3425 7576 3423 7578 3421 7580 3419 7582 3417 7584 3415 7586 3413 7588 3411 7590 3409 7592 3407 7594 3405 7596 3403 7598 3401 7600 3399 7602 3397 7604 3395 7606 3393 7608 3391 7610 3389 7612 3387 7614 3385 7616 3383 7618 3381 7620 3379 7622 3377 7624 3375 7626 3373 7628 3371 7630 3369 7632 3367 7634 3365 7636 3363 7638 3361 7640 3359 7642 3357 7644 3355 7646 3353 7648 3351 7650 3349 7652 3347 7654 3345 7656 3343 7658 3341 7660 3339 7662 3337 7664 3335 7666 3333 7668 3331 7670 3329 7672 3327 7674 3325 7676 3323 7678 3321 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'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '17171\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '111\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '19\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '37010\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '011\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '879\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10010\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '487\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '11\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '8395\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10111\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '24206\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '18\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '010\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '14\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '23323\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '16594\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1571\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '00011\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '15\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '30\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '22\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '74\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10110\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '37438\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '001\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '51\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79733","program":"```python\nn=int(input())\nif(n%4>1):\n print(-1)\nelse:\n ans=[0]*(n+1)\n i,j,a,b=1,n,1,n\n while(i=1):\n ans[i],ans[j]=a+1,b-1\n ans[i+1],ans[j-1]=b,a\n i+=2\n j-=2\n a+=2\n b-=2\n if(i==j):\n ans[i]=a\n for i in range(1,n+1):\n print(ans[i],end=' ')\n \n```","inputs":"4\n","output":"2 4 1 3 ","actual_output":"2 4 1 3 ","execution_success":true,"sample_index":12694},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"37_C. Old Berland Language","prompt":"Solve the following coding problem using the programming language python:\n\nBerland scientists know that the Old Berland language had exactly n words. Those words had lengths of l1, l2, ..., ln letters. Every word consisted of two letters, 0 and 1. Ancient Berland people spoke quickly and didn\u2019t make pauses between the words, but at the same time they could always understand each other perfectly. It was possible because no word was a prefix of another one. The prefix of a string is considered to be one of its substrings that starts from the initial symbol.\n\nHelp the scientists determine whether all the words of the Old Berland language can be reconstructed and if they can, output the words themselves.\n\nInput\n\nThe first line contains one integer N (1 \u2264 N \u2264 1000) \u2014 the number of words in Old Berland language. The second line contains N space-separated integers \u2014 the lengths of these words. All the lengths are natural numbers not exceeding 1000.\n\nOutput\n\nIf there\u2019s no such set of words, in the single line output NO. Otherwise, in the first line output YES, and in the next N lines output the words themselves in the order their lengths were given in the input file. If the answer is not unique, output any.\n\nExamples\n\nInput\n\n3\n1 2 3\n\n\nOutput\n\nYES\n0\n10\n110\n\n\nInput\n\n3\n1 1 1\n\n\nOutput\n\nNO\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#!/usr/bin/python3\n\ncounts = [0]*1024\nfor x in range(len(counts)): counts[x] = []\nN = int(input())\nx = [int(t) for t in input().strip().split()]\nfor i,t in enumerate(x): counts[t].append(i)\n\n\ncurr = 0\nans = [0]*N\nfor i in range(1,1024):\n\twhile len(counts[i]) > 0:\n\t\tx = bin(curr)[2:]\n\t\tif len(x) > i:\n\t\t\tprint(\"NO\")\n\t\t\texit(0)\n\t\telse: x = \"0\"*(i-len(x)) + x\n\t\tans[counts[i].pop()] = x\n\t\tcurr += 1\n\tcurr = 2*curr\nprint(\"YES\")\nprint(\"\\n\".join(ans))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 2 3\\n', 'output': 'YES\\n0\\n10\\n110'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 1\\n', 'output': 'NO\\n\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 1000\\n', 'output': 'YES\\n0\\n10\\n1100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'}, {'type': 'stdin_stdout', 'input': '2\\n1 1\\n', 'output': 'YES\\n0\\n1'}, {'type': 'stdin_stdout', 'input': '30\\n6 7 7 6 7 7 7 7 7 7 7 7 7 7 7 5 7 7 7 7 2 1 5 3 7 3 2 7 5 1\\n', 'output': 'NO\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n'}, {'type': 'stdin_stdout', 'input': '20\\n4 4 3 4 4 4 4 4 4 4 4 3 3 2 1 4 4 3 3 3\\n', 'output': 'NO\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 2\\n', 'output': 'NO\\n\\n'}, {'type': 'stdin_stdout', 'input': '200\\n11 23 6 1 15 6 5 9 8 9 13 11 7 21 14 17 8 8 12 6 18 4 9 20 3 9 6 9 9 12 18 5 22 5 16 20 11 6 22 10 5 6 8 19 9 12 14 2 10 6 7 7 18 17 4 16 9 13 3 10 15 8 8 9 13 7 8 18 12 12 13 14 9 8 5 5 22 19 23 15 11 7 23 7 5 3 9 3 15 9 22 9 2 11 21 8 12 7 6 8 10 6 12 9 11 8 7 6 5 7 8 9 10 7 19 12 14 9 6 7 2 7 8 4 12 21 14 4 11 12 9 13 17 4 10 8 17 3 9 5 11 6 4 11 1 13 10 10 8 10 14 23 17 8 20 23 23 23 14 7 18 5 10 21 9 7 7 7 4 23 13 8 9 22 7 4 8 12 8 19 17 11 10 8 8 7 7 13 6 13 14 14 22 2 10 11 5 1 14 13\\n', 'output': 'NO\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n'}, {'type': 'stdin_stdout', 'input': '30\\n6 6 6 5 6 7 3 4 6 5 2 4 6 4 5 4 6 5 4 4 6 6 2 1 4 4 6 1 6 7\\n', 'output': 'NO\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n', 'output': 'YES\\n0'}, {'type': 'stdin_stdout', 'input': '85\\n9 10 4 5 10 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'10\\n4 4 4 4 4 4 4 4 4 4\\n', 'output': 'YES\\n0000\\n0001\\n0010\\n0011\\n0100\\n0101\\n0110\\n0111\\n1000\\n1001'}, {'type': 'stdin_stdout', 'input': '2\\n1000 1\\n', 'output': 'YES\\n1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\\n0'}, {'type': 'stdin_stdout', 'input': '30\\n7 8 6 4 2 8 8 7 7 10 4 6 4 7 4 4 7 6 7 9 7 3 5 5 10 4 5 8 5 8\\n', 'output': 'YES\\n1110110\\n11111010\\n111000\\n0110\\n00\\n11111011\\n11111100\\n1110111\\n1111000\\n1111111110\\n0111\\n111001\\n1000\\n1111001\\n1001\\n1010\\n1111010\\n111010\\n1111011\\n111111110\\n1111100\\n010\\n11000\\n11001\\n1111111111\\n1011\\n11010\\n11111101\\n11011\\n11111110'}, {'type': 'stdin_stdout', 'input': '65\\n9 7 8 6 6 10 3 9 10 4 8 3 2 8 9 1 6 3 2 7 9 7 8 10 10 4 5 6 8 8 7 10 10 8 6 6 4 8 8 7 6 9 10 7 8 7 3 3 10 8 9 10 1 9 6 9 2 7 9 10 8 10 3 7 3\\n', 'output': 'NO\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n'}, {'type': 'stdin_stdout', 'input': '50\\n4 7 9 7 7 5 5 5 8 9 9 7 9 7 7 6 5 6 4 9 6 5 6 6 5 7 7 6 6 6 5 8 2 7 8 7 6 5 7 9 8 7 5 6 6 8 6 6 7 7\\n', 'output': 'YES\\n0100\\n1101110\\n111111010\\n1101111\\n1110000\\n01100\\n01101\\n01110\\n11111000\\n111111011\\n111111100\\n1110001\\n111111101\\n1110010\\n1110011\\n101010\\n01111\\n101011\\n0101\\n111111110\\n101100\\n10000\\n101101\\n101110\\n10001\\n1110100\\n1110101\\n101111\\n110000\\n110001\\n10010\\n11111001\\n00\\n1110110\\n11111010\\n1110111\\n110010\\n10011\\n1111000\\n111111111\\n11111011\\n1111001\\n10100\\n110011\\n110100\\n11111100\\n110101\\n110110\\n1111010\\n1111011'}, {'type': 'stdin_stdout', 'input': '20\\n6 7 7 7 7 6 7 7 7 7 7 7 7 7 7 7 7 7 6 7\\n', 'output': 'YES\\n000000\\n0000110\\n0000111\\n0001000\\n0001001\\n000001\\n0001010\\n0001011\\n0001100\\n0001101\\n0001110\\n0001111\\n0010000\\n0010001\\n0010010\\n0010011\\n0010100\\n0010101\\n000010\\n0010110'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 1000\\n', 'output': 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{'type': 'stdin_stdout', 'input': '30\\n9 10 8 10 10 10 10 10 7 7 10 10 10 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 4 3\\n', 'output': 'YES\\n001101010\\n0011011000\\n00110100\\n0011011001\\n0011011010\\n0011011011\\n0011011100\\n0011011101\\n0011000\\n0011001\\n0011011110\\n0011011111\\n0011100000\\n0011100001\\n0011100010\\n0011100011\\n0011100100\\n0011100101\\n0011100110\\n0011100111\\n001101011\\n0011101000\\n0011101001\\n0011101010\\n0011101011\\n0011101100\\n0011101101\\n0011101110\\n0010\\n000'}, {'type': 'stdin_stdout', 'input': '100\\n8 12 6 10 6 11 5 11 11 7 5 6 7 9 11 9 4 11 7 8 12 7 7 7 10 9 6 6 5 7 6 7 10 7 8 7 7 8 9 8 5 10 7 7 6 6 7 8 12 11 5 7 12 10 7 7 10 7 11 11 5 7 6 10 8 6 8 11 8 7 5 7 7 5 6 8 7 7 10 6 5 9 5 5 11 8 7 6 7 8 8 7 7 7 6 6 6 5 8 7\\n', 'output': 'YES\\n11101100\\n111111111100\\n011100\\n1111110010\\n011101\\n11111110100\\n00010\\n11111110101\\n11111110110\\n1011000\\n00011\\n011110\\n1011001\\n111110100\\n11111110111\\n111110101\\n0000\\n11111111000\\n1011010\\n11101101\\n111111111101\\n1011011\\n1011100\\n1011101\\n1111110011\\n111110110\\n011111\\n100000\\n00100\\n1011110\\n100001\\n1011111\\n1111110100\\n1100000\\n11101110\\n1100001\\n1100010\\n11101111\\n111110111\\n11110000\\n00101\\n1111110101\\n1100011\\n1100100\\n100010\\n100011\\n1100101\\n11110001\\n111111111110\\n11111111001\\n00110\\n1100110\\n111111111111\\n1111110110\\n1100111\\n1101000\\n1111110111\\n1101001\\n11111111010\\n11111111011\\n00111\\n1101010\\n100100\\n1111111000\\n11110010\\n100101\\n11110011\\n11111111100\\n11110100\\n1101011\\n01000\\n1101100\\n1101101\\n01001\\n100110\\n11110101\\n1101110\\n1101111\\n1111111001\\n100111\\n01010\\n111111000\\n01011\\n01100\\n11111111101\\n11110110\\n1110000\\n101000\\n1110001\\n11110111\\n11111000\\n1110010\\n1110011\\n1110100\\n101001\\n101010\\n101011\\n01101\\n11111001\\n1110101'}, {'type': 'stdin_stdout', 'input': '10\\n4 4 4 4 4 4 4 4 2 2\\n', 'output': 'YES\\n1000\\n1001\\n1010\\n1011\\n1100\\n1101\\n1110\\n1111\\n00\\n01'}, {'type': 'stdin_stdout', 'input': '100\\n17 18 22 15 14 18 9 21 14 19 14 20 12 15 9 23 19 20 19 22 13 22 17 11 21 22 8 17 23 18 21 23 22 23 15 18 21 17 17 9 13 21 23 19 18 23 15 14 17 19 22 23 12 16 23 16 20 9 12 17 18 11 10 17 16 21 8 21 16 19 21 17 12 20 14 16 17 10 22 20 17 13 15 19 9 22 12 20 20 13 19 16 18 7 15 18 6 18 19 21\\n', 'output': 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{'type': 'stdin_stdout', 'input': '50\\n10 10 10 10 10 10 9 9 10 10 9 10 10 10 10 9 8 7 8 10 10 10 7 9 10 10 9 9 9 10 10 10 9 10 10 10 10 10 9 10 10 7 8 9 9 8 9 6 6 6\\n', 'output': 'YES\\n0001110010\\n0001110011\\n0001110100\\n0001110101\\n0001110110\\n0001110111\\n000101100\\n000101101\\n0001111000\\n0001111001\\n000101110\\n0001111010\\n0001111011\\n0001111100\\n0001111101\\n000101111\\n00010010\\n0000110\\n00010011\\n0001111110\\n0001111111\\n0010000000\\n0000111\\n000110000\\n0010000001\\n0010000010\\n000110001\\n000110010\\n000110011\\n0010000011\\n0010000100\\n0010000101\\n000110100\\n0010000110\\n0010000111\\n0010001000\\n0010001001\\n0010001010\\n000110101\\n0010001011\\n0010001100\\n0001000\\n00010100\\n000110110\\n000110111\\n00010101\\n000111000\\n000000\\n000001\\n000010'}, {'type': 'stdin_stdout', 'input': '50\\n10 10 10 10 10 10 9 9 10 10 9 10 10 10 10 9 8 7 8 10 10 10 7 9 10 10 9 9 9 10 10 10 9 10 10 10 10 10 9 10 10 7 8 9 9 8 9 6 6 6\\n', 'output': 'YES\\n0001110010\\n0001110011\\n0001110100\\n0001110101\\n0001110110\\n0001110111\\n000101100\\n000101101\\n0001111000\\n0001111001\\n000101110\\n0001111010\\n0001111011\\n0001111100\\n0001111101\\n000101111\\n00010010\\n0000110\\n00010011\\n0001111110\\n0001111111\\n0010000000\\n0000111\\n000110000\\n0010000001\\n0010000010\\n000110001\\n000110010\\n000110011\\n0010000011\\n0010000100\\n0010000101\\n000110100\\n0010000110\\n0010000111\\n0010001000\\n0010001001\\n0010001010\\n000110101\\n0010001011\\n0010001100\\n0001000\\n00010100\\n000110110\\n000110111\\n00010101\\n000111000\\n000000\\n000001\\n000010'}, {'type': 'stdin_stdout', 'input': '50\\n4 7 9 7 7 5 5 5 8 9 9 7 9 7 7 6 5 6 4 9 6 5 6 6 5 7 7 6 6 6 5 8 2 7 8 7 6 5 7 9 8 7 5 6 6 8 6 6 7 7\\n', 'output': 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'NO\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1000 1\\n', 'output': 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{'type': 'stdin_stdout', 'input': '20\\n5 4 5 5 5 6 5 6 4 5 6 4 5 4 2 4 6 4 4 5\\n', 'output': 'YES\\n10110\\n0100\\n10111\\n11000\\n11001\\n111100\\n11010\\n111101\\n0101\\n11011\\n111110\\n0110\\n11100\\n0111\\n00\\n1000\\n111111\\n1001\\n1010\\n11101'}, {'type': 'stdin_stdout', 'input': '85\\n7 9 8 9 5 6 9 8 10 10 9 10 10 10 10 7 7 4 8 7 7 7 9 10 10 9 10 9 10 10 10 8 8 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 7 10 4 2 9 3 3 6 2 6 5 6 4 1 7 3 7 7 5 8 4 5 4 1 10 2 9 3 1 4 2 9 9 3 5 6 8\\n', 'output': 'NO\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n'}, {'type': 'stdin_stdout', 'input': '100\\n8 12 6 10 6 11 5 11 11 7 5 6 7 9 11 9 4 11 7 8 12 7 7 7 10 9 6 6 5 7 6 7 10 7 8 7 7 8 9 8 5 10 7 7 6 6 7 8 12 11 5 7 12 10 7 7 10 7 11 11 5 7 6 10 8 6 8 11 8 7 5 7 7 5 6 8 7 7 10 6 5 9 5 5 11 8 7 6 7 8 8 7 7 7 6 6 6 5 8 7\\n', 'output': 'YES\\n11101100\\n111111111100\\n011100\\n1111110010\\n011101\\n11111110100\\n00010\\n11111110101\\n11111110110\\n1011000\\n00011\\n011110\\n1011001\\n111110100\\n11111110111\\n111110101\\n0000\\n11111111000\\n1011010\\n11101101\\n111111111101\\n1011011\\n1011100\\n1011101\\n1111110011\\n111110110\\n011111\\n100000\\n00100\\n1011110\\n100001\\n1011111\\n1111110100\\n1100000\\n11101110\\n1100001\\n1100010\\n11101111\\n111110111\\n11110000\\n00101\\n1111110101\\n1100011\\n1100100\\n100010\\n100011\\n1100101\\n11110001\\n111111111110\\n11111111001\\n00110\\n1100110\\n111111111111\\n1111110110\\n1100111\\n1101000\\n1111110111\\n1101001\\n11111111010\\n11111111011\\n00111\\n1101010\\n100100\\n1111111000\\n11110010\\n100101\\n11110011\\n11111111100\\n11110100\\n1101011\\n01000\\n1101100\\n1101101\\n01001\\n100110\\n11110101\\n1101110\\n1101111\\n1111111001\\n100111\\n01010\\n111111000\\n01011\\n01100\\n11111111101\\n11110110\\n1110000\\n101000\\n1110001\\n11110111\\n11111000\\n1110010\\n1110011\\n1110100\\n101001\\n101010\\n101011\\n01101\\n11111001\\n1110101'}, {'type': 'stdin_stdout', 'input': '200\\n11 23 6 1 15 6 5 9 8 9 13 11 7 21 14 17 8 8 12 6 18 4 9 20 3 9 6 9 9 12 18 5 22 5 16 20 11 6 22 10 5 6 8 19 9 12 14 2 10 6 7 7 18 17 4 16 9 13 3 10 15 8 8 9 13 7 8 18 12 12 13 14 9 8 5 5 22 19 23 15 11 7 23 7 5 3 9 3 15 9 22 9 2 11 21 8 12 7 6 8 10 6 12 9 11 8 7 6 5 7 8 9 10 7 19 12 14 9 6 7 2 7 8 4 12 21 14 4 11 12 9 13 17 4 10 8 17 3 9 5 11 6 4 11 1 13 10 10 8 10 14 23 17 8 20 23 23 23 14 7 18 5 10 21 9 7 7 12 4 23 13 8 9 22 7 4 8 12 8 19 17 11 10 8 8 7 7 13 6 13 14 14 22 2 10 11 5 1 14 13\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 4 3 4 4 4 4 4 4 4\\n', 'output': 'YES\\n0010\\n0011\\n000\\n0100\\n0101\\n0110\\n0111\\n1000\\n1001\\n1010\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1000 2\\n', 'output': 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{'type': 'stdin_stdout', 'input': '20\\n6 7 7 7 7 6 7 7 7 7 7 7 7 7 7 8 7 7 6 7\\n', 'output': 'YES\\n000000\\n0000110\\n0000111\\n0001000\\n0001001\\n000001\\n0001010\\n0001011\\n0001100\\n0001101\\n0001110\\n0001111\\n0010000\\n0010001\\n0010010\\n00101100\\n0010011\\n0010100\\n000010\\n0010101\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 4 1000\\n', 'output': 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{'type': 'stdin_stdout', 'input': '30\\n9 10 8 10 10 10 10 10 7 7 10 10 10 16 10 10 10 10 10 10 9 10 10 10 10 10 10 10 4 3\\n', 'output': 'YES\\n001101010\\n0011011000\\n00110100\\n0011011001\\n0011011010\\n0011011011\\n0011011100\\n0011011101\\n0011000\\n0011001\\n0011011110\\n0011011111\\n0011100000\\n0011101110000000\\n0011100001\\n0011100010\\n0011100011\\n0011100100\\n0011100101\\n0011100110\\n001101011\\n0011100111\\n0011101000\\n0011101001\\n0011101010\\n0011101011\\n0011101100\\n0011101101\\n0010\\n000\\n'}, {'type': 'stdin_stdout', 'input': '100\\n17 18 22 15 14 7 9 21 14 19 14 20 12 15 9 23 19 20 19 22 13 22 17 11 21 22 8 17 23 18 21 23 22 23 15 18 21 17 17 9 13 21 23 19 18 23 15 14 17 19 22 23 12 16 23 16 20 9 12 17 18 11 10 17 16 21 8 21 16 19 21 17 12 20 14 16 17 10 22 20 17 13 15 19 9 22 12 20 20 13 19 16 18 7 15 18 6 18 19 21\\n', 'output': 'YES\\n00001101110101100\\n000011011101101110\\n0000110111011111010110\\n000011011100010\\n00001101101100\\n0000010\\n000010100\\n000011011101111100010\\n00001101101101\\n0000110111011101100\\n00001101101110\\n00001101110111101010\\n000011010100\\n000011011100011\\n000010101\\n00001101110111110111100\\n0000110111011101101\\n00001101110111101011\\n0000110111011101110\\n0000110111011111010111\\n0000110110010\\n0000110111011111011000\\n00001101110101101\\n00001101000\\n000011011101111100011\\n0000110111011111011001\\n00001000\\n00001101110101110\\n00001101110111110111101\\n000011011101101111\\n000011011101111100100\\n00001101110111110111110\\n0000110111011111011010\\n00001101110111110111111\\n000011011100100\\n000011011101110000\\n000011011101111100101\\n00001101110101111\\n00001101110110000\\n000010110\\n0000110110011\\n000011011101111100110\\n00001101110111111000000\\n0000110111011101111\\n000011011101110001\\n00001101110111111000001\\n000011011100101\\n00001101101111\\n00001101110110001\\n0000110111011110000\\n0000110111011111011011\\n00001101110111111000010\\n000011010101\\n0000110111010000\\n00001101110111111000011\\n0000110111010001\\n00001101110111101100\\n000010111\\n000011010110\\n00001101110110010\\n000011011101110010\\n00001101001\\n0000110010\\n00001101110110011\\n0000110111010010\\n000011011101111100111\\n00001001\\n000011011101111101000\\n0000110111010011\\n0000110111011110001\\n000011011101111101001\\n00001101110110100\\n000011010111\\n00001101110111101101\\n00001101110000\\n0000110111010100\\n00001101110110101\\n0000110011\\n0000110111011111011100\\n00001101110111101110\\n00001101110110110\\n0000110110100\\n000011011100110\\n0000110111011110010\\n000011000\\n0000110111011111011101\\n000011011000\\n00001101110111101111\\n00001101110111110000\\n0000110110101\\n0000110111011110011\\n0000110111010101\\n000011011101110011\\n0000011\\n000011011100111\\n000011011101110100\\n000000\\n000011011101110101\\n0000110111011110100\\n000011011101111101010\\n'}, {'type': 'stdin_stdout', 'input': '50\\n10 10 10 10 10 10 9 9 10 10 9 10 9 10 10 9 8 7 8 10 10 10 7 9 10 10 9 9 9 10 10 10 9 10 10 10 10 10 9 10 10 7 8 9 9 8 9 6 6 6\\n', 'output': 'YES\\n0001110100\\n0001110101\\n0001110110\\n0001110111\\n0001111000\\n0001111001\\n000101100\\n000101101\\n0001111010\\n0001111011\\n000101110\\n0001111100\\n000101111\\n0001111101\\n0001111110\\n000110000\\n00010010\\n0000110\\n00010011\\n0001111111\\n0010000000\\n0010000001\\n0000111\\n000110001\\n0010000010\\n0010000011\\n000110010\\n000110011\\n000110100\\n0010000100\\n0010000101\\n0010000110\\n000110101\\n0010000111\\n0010001000\\n0010001001\\n0010001010\\n0010001011\\n000110110\\n0010001100\\n0010001101\\n0001000\\n00010100\\n000110111\\n000111000\\n00010101\\n000111001\\n000000\\n000001\\n000010\\n'}, {'type': 'stdin_stdout', 'input': '50\\n10 10 10 12 10 10 9 9 10 10 9 10 10 10 10 9 8 7 8 10 10 10 7 9 10 10 9 9 9 10 10 10 9 10 10 10 10 10 9 10 10 7 8 9 9 8 9 6 6 6\\n', 'output': 'YES\\n0001110010\\n0001110011\\n0001110100\\n001000110000\\n0001110101\\n0001110110\\n000101100\\n000101101\\n0001110111\\n0001111000\\n000101110\\n0001111001\\n0001111010\\n0001111011\\n0001111100\\n000101111\\n00010010\\n0000110\\n00010011\\n0001111101\\n0001111110\\n0001111111\\n0000111\\n000110000\\n0010000000\\n0010000001\\n000110001\\n000110010\\n000110011\\n0010000010\\n0010000011\\n0010000100\\n000110100\\n0010000101\\n0010000110\\n0010000111\\n0010001000\\n0010001001\\n000110101\\n0010001010\\n0010001011\\n0001000\\n00010100\\n000110110\\n000110111\\n00010101\\n000111000\\n000000\\n000001\\n000010\\n'}, {'type': 'stdin_stdout', 'input': '20\\n5 4 5 5 5 6 5 6 4 5 6 5 5 4 2 4 6 4 4 5\\n', 'output': 'YES\\n10100\\n0100\\n10101\\n10110\\n10111\\n111010\\n11000\\n111011\\n0101\\n11001\\n111100\\n11010\\n11011\\n0110\\n00\\n0111\\n111101\\n1000\\n1001\\n11100\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 3\\n', 'output': 'YES\\n00\\n01\\n100\\n'}, {'type': 'stdin_stdout', 'input': '20\\n6 7 7 7 7 6 7 7 7 7 7 7 7 7 7 8 4 7 6 7\\n', 'output': 'YES\\n000100\\n0001110\\n0001111\\n0010000\\n0010001\\n000101\\n0010010\\n0010011\\n0010100\\n0010101\\n0010110\\n0010111\\n0011000\\n0011001\\n0011010\\n00111010\\n0000\\n0011011\\n000110\\n0011100\\n'}, {'type': 'stdin_stdout', 'input': '30\\n9 10 8 10 10 10 10 10 7 7 10 10 10 16 12 10 10 10 10 10 9 10 10 10 10 10 10 10 4 3\\n', 'output': 'YES\\n001101010\\n0011011000\\n00110100\\n0011011001\\n0011011010\\n0011011011\\n0011011100\\n0011011101\\n0011000\\n0011001\\n0011011110\\n0011011111\\n0011100000\\n0011101101010000\\n001110110100\\n0011100001\\n0011100010\\n0011100011\\n0011100100\\n0011100101\\n001101011\\n0011100110\\n0011100111\\n0011101000\\n0011101001\\n0011101010\\n0011101011\\n0011101100\\n0010\\n000\\n'}, {'type': 'stdin_stdout', 'input': '100\\n17 18 10 15 14 7 9 21 14 19 14 20 12 15 9 23 19 20 19 22 13 22 17 11 21 22 8 17 23 18 21 23 22 23 15 18 21 17 17 9 13 21 23 19 18 23 15 14 17 19 22 23 12 16 23 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'YES\\n00001110000101100\\n000011100001101110\\n0000110010\\n000011100000010\\n00001101111100\\n0000010\\n000010100\\n000011100001111100010\\n00001101111101\\n0000111000011101100\\n00001101111110\\n00001110000111101010\\n000011011000\\n000011100000011\\n000010101\\n00001110000111110111010\\n0000111000011101101\\n00001110000111101011\\n0000111000011101110\\n0000111000011111010110\\n0000110111010\\n0000111000011111010111\\n00001110000101101\\n00001101010\\n000011100001111100011\\n0000111000011111011000\\n00001000\\n00001110000101110\\n00001110000111110111011\\n000011100001101111\\n000011100001111100100\\n00001110000111110111100\\n0000111000011111011001\\n00001110000111110111101\\n000011100000100\\n000011100001110000\\n000011100001111100101\\n00001110000101111\\n00001110000110000\\n000010110\\n0000110111011\\n000011100001111100110\\n00001110000111110111110\\n0000111000011101111\\n000011100001110001\\n00001110000111110111111\\n000011100000101\\n00001101111111\\n00001110000110001\\n0000111000011110000\\n0000111000011111011010\\n00001110000111111000000\\n000011011001\\n0000111000010000\\n00001110000111111000001\\n0000111000010001\\n00001110000111101100\\n000010111\\n000011011010\\n00001110000110010\\n000011100001110010\\n00001101011\\n0000110011\\n00001110000110011\\n0000111000010010\\n000011100001111100111\\n00001001\\n000011100001111101000\\n0000111000010011\\n0000111000011110001\\n000011100001111101001\\n00001110000110100\\n000011011011\\n00001110000111101101\\n00001110000000\\n0000111000010100\\n00001110000110101\\n0000110100\\n0000111000011111011011\\n00001110000111101110\\n00001110000110110\\n0000110111100\\n000011100000110\\n0000111000011110010\\n000011000\\n0000111000011111011100\\n000011011100\\n00001110000111101111\\n00001110000111110000\\n0000110111101\\n0000111000011110011\\n0000111000010101\\n000011100001110011\\n0000011\\n000011100000111\\n000011100001110100\\n000000\\n000011100001110101\\n0000111000011110100\\n000011100001111101010\\n'}, {'type': 'stdin_stdout', 'input': '50\\n10 10 10 10 10 10 9 9 10 10 9 10 9 10 10 9 8 7 4 10 10 10 7 9 10 10 9 9 9 10 10 10 9 10 10 10 10 10 9 10 10 7 8 9 9 8 9 6 6 6\\n', 'output': 'YES\\n0010110000\\n0010110001\\n0010110010\\n0010110011\\n0010110100\\n0010110101\\n001001010\\n001001011\\n0010110110\\n0010110111\\n001001100\\n0010111000\\n001001101\\n0010111001\\n0010111010\\n001001110\\n00100010\\n0001110\\n0000\\n0010111011\\n0010111100\\n0010111101\\n0001111\\n001001111\\n0010111110\\n0010111111\\n001010000\\n001010001\\n001010010\\n0011000000\\n0011000001\\n0011000010\\n001010011\\n0011000011\\n0011000100\\n0011000101\\n0011000110\\n0011000111\\n001010100\\n0011001000\\n0011001001\\n0010000\\n00100011\\n001010101\\n001010110\\n00100100\\n001010111\\n000100\\n000101\\n000110\\n'}, {'type': 'stdin_stdout', 'input': '50\\n10 10 10 12 10 10 9 9 10 10 9 10 10 10 10 9 8 7 8 10 10 10 7 9 10 10 9 9 9 10 10 10 9 10 10 10 10 10 9 19 10 7 8 9 9 8 9 6 6 6\\n', 'output': 'YES\\n0001110010\\n0001110011\\n0001110100\\n001000101100\\n0001110101\\n0001110110\\n000101100\\n000101101\\n0001110111\\n0001111000\\n000101110\\n0001111001\\n0001111010\\n0001111011\\n0001111100\\n000101111\\n00010010\\n0000110\\n00010011\\n0001111101\\n0001111110\\n0001111111\\n0000111\\n000110000\\n0010000000\\n0010000001\\n000110001\\n000110010\\n000110011\\n0010000010\\n0010000011\\n0010000100\\n000110100\\n0010000101\\n0010000110\\n0010000111\\n0010001000\\n0010001001\\n000110101\\n0010001011010000000\\n0010001010\\n0001000\\n00010100\\n000110110\\n000110111\\n00010101\\n000111000\\n000000\\n000001\\n000010\\n'}, {'type': 'stdin_stdout', 'input': '50\\n4 7 9 7 7 5 5 5 8 9 8 7 9 7 7 6 5 6 4 9 6 5 6 6 5 7 7 6 6 10 5 8 2 7 8 7 6 5 7 9 8 7 5 6 6 8 6 6 7 7\\n', 'output': 'YES\\n0100\\n1101100\\n111110100\\n1101101\\n1101110\\n01100\\n01101\\n01110\\n11110100\\n111110101\\n11110101\\n1101111\\n111110110\\n1110000\\n1110001\\n101010\\n01111\\n101011\\n0101\\n111110111\\n101100\\n10000\\n101101\\n101110\\n10001\\n1110010\\n1110011\\n101111\\n110000\\n1111110010\\n10010\\n11110110\\n00\\n1110100\\n11110111\\n1110101\\n110001\\n10011\\n1110110\\n111111000\\n11111000\\n1110111\\n10100\\n110010\\n110011\\n11111001\\n110100\\n110101\\n1111000\\n1111001\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 2 3\\n', 'output': 'YES\\n0110\\n00\\n010\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 2\\n', 'output': 'YES\\n10\\n0\\n11\\n'}, {'type': 'stdin_stdout', 'input': '20\\n6 7 7 7 7 6 7 7 7 7 7 7 11 7 7 8 4 7 6 7\\n', 'output': 'YES\\n000100\\n0001110\\n0001111\\n0010000\\n0010001\\n000101\\n0010010\\n0010011\\n0010100\\n0010101\\n0010110\\n0010111\\n00111001000\\n0011000\\n0011001\\n00111000\\n0000\\n0011010\\n000110\\n0011011\\n'}, {'type': 'stdin_stdout', 'input': '30\\n9 10 8 10 10 9 10 10 7 7 10 10 10 16 12 10 10 10 10 10 9 10 10 10 10 10 10 10 4 3\\n', 'output': 'YES\\n001101010\\n0011011010\\n00110100\\n0011011011\\n0011011100\\n001101011\\n0011011101\\n0011011110\\n0011000\\n0011001\\n0011011111\\n0011100000\\n0011100001\\n0011101110010000\\n001110111000\\n0011100010\\n0011100011\\n0011100100\\n0011100101\\n0011100110\\n001101100\\n0011100111\\n0011101000\\n0011101001\\n0011101010\\n0011101011\\n0011101100\\n0011101101\\n0010\\n000\\n'}, {'type': 'stdin_stdout', 'input': '100\\n17 18 10 15 14 7 9 21 14 19 14 20 12 15 9 23 19 20 19 22 13 22 17 11 21 22 8 17 7 18 21 23 22 23 15 18 21 17 17 9 13 21 23 19 18 23 15 14 17 19 22 23 12 16 23 16 20 9 12 17 18 11 10 17 16 21 8 21 16 19 21 17 12 20 14 16 17 10 22 20 17 13 15 19 9 22 12 20 20 13 19 16 18 7 15 18 6 18 19 21\\n', 'output': 'YES\\n00010000000101100\\n000100000001101110\\n0000111010\\n000100000000010\\n00001111111100\\n0000010\\n000011000\\n000100000001111100010\\n00001111111101\\n0001000000011101100\\n00001111111110\\n00010000000111101010\\n000011111000\\n000100000000011\\n000011001\\n00010000000111110111010\\n0001000000011101101\\n00010000000111101011\\n0001000000011101110\\n0001000000011111010110\\n0000111111010\\n0001000000011111010111\\n00010000000101101\\n00001111010\\n000100000001111100011\\n0001000000011111011000\\n00001010\\n00010000000101110\\n0000011\\n000100000001101111\\n000100000001111100100\\n00010000000111110111011\\n0001000000011111011001\\n00010000000111110111100\\n000100000000100\\n000100000001110000\\n000100000001111100101\\n00010000000101111\\n00010000000110000\\n000011010\\n0000111111011\\n000100000001111100110\\n00010000000111110111101\\n0001000000011101111\\n000100000001110001\\n00010000000111110111110\\n000100000000101\\n00001111111111\\n00010000000110001\\n0001000000011110000\\n0001000000011111011010\\n00010000000111110111111\\n000011111001\\n0001000000010000\\n00010000000111111000000\\n0001000000010001\\n00010000000111101100\\n000011011\\n000011111010\\n00010000000110010\\n000100000001110010\\n00001111011\\n0000111011\\n00010000000110011\\n0001000000010010\\n000100000001111100111\\n00001011\\n000100000001111101000\\n0001000000010011\\n0001000000011110001\\n000100000001111101001\\n00010000000110100\\n000011111011\\n00010000000111101101\\n00010000000000\\n0001000000010100\\n00010000000110101\\n0000111100\\n0001000000011111011011\\n00010000000111101110\\n00010000000110110\\n0000111111100\\n000100000000110\\n0001000000011110010\\n000011100\\n0001000000011111011100\\n000011111100\\n00010000000111101111\\n00010000000111110000\\n0000111111101\\n0001000000011110011\\n0001000000010101\\n000100000001110011\\n0000100\\n000100000000111\\n000100000001110100\\n000000\\n000100000001110101\\n0001000000011110100\\n000100000001111101010\\n'}, 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'YES\\n0001110010\\n0001110011\\n0001110100\\n001000101000\\n0001110101\\n0001110110\\n000101100\\n000101101\\n0001110111\\n0001111000\\n000101110\\n0001111001\\n0001111010\\n0001111011\\n0001111100\\n000101111\\n00010010\\n0000110\\n00010011\\n0001111101\\n0001111110\\n0001111111\\n0000111\\n000110000\\n0010000000\\n0010000001\\n000110001\\n000110010\\n000110011\\n0010000010\\n0010000011\\n0010000100\\n000110100\\n0010000101\\n0010000110\\n0010000111\\n0010001000\\n001000101001000000\\n000110101\\n0010001010010000010\\n0010001001\\n0001000\\n00010100\\n000110110\\n000110111\\n00010101\\n000111000\\n000000\\n000001\\n000010\\n'}, {'type': 'stdin_stdout', 'input': '50\\n4 7 9 7 7 5 5 5 8 9 8 6 9 7 7 6 5 6 4 9 6 5 6 6 5 7 7 6 6 10 5 8 2 7 8 7 6 5 7 9 8 7 5 6 6 8 6 6 7 7\\n', 'output': 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'30\\n9 10 8 10 10 9 10 10 7 7 10 10 10 16 12 10 10 10 15 10 9 10 10 10 10 10 10 10 4 3\\n', 'output': 'YES\\n001101010\\n0011011010\\n00110100\\n0011011011\\n0011011100\\n001101011\\n0011011101\\n0011011110\\n0011000\\n0011001\\n0011011111\\n0011100000\\n0011100001\\n0011101101010010\\n001110110100\\n0011100010\\n0011100011\\n0011100100\\n001110110101000\\n0011100101\\n001101100\\n0011100110\\n0011100111\\n0011101000\\n0011101001\\n0011101010\\n0011101011\\n0011101100\\n0010\\n000\\n'}, {'type': 'stdin_stdout', 'input': '100\\n17 18 10 15 14 7 9 21 14 19 14 20 12 15 9 23 19 20 19 22 13 22 17 11 21 22 8 17 7 18 21 23 22 23 15 18 21 17 26 9 13 21 23 19 18 23 15 14 17 19 22 23 12 16 23 16 20 9 12 17 18 11 10 17 16 21 8 21 16 19 21 17 12 20 14 16 17 10 22 20 17 13 15 19 9 22 12 20 20 13 19 16 18 7 15 18 6 18 19 21\\n', 'output': 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'65\\n9 7 8 6 6 10 3 9 10 4 8 3 2 8 9 1 6 3 2 7 9 7 4 16 10 4 5 6 8 8 4 10 10 8 6 6 4 8 8 7 7 9 10 7 8 7 3 3 10 8 9 10 1 9 6 9 2 7 9 10 8 10 3 7 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '50\\n4 7 9 7 7 5 5 5 8 9 9 7 9 7 7 6 5 6 4 9 6 5 6 6 5 7 7 6 6 6 5 8 2 7 8 7 6 5 7 14 8 7 5 5 6 12 6 6 7 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '100\\n8 12 6 10 6 22 5 11 11 7 5 6 7 9 11 9 4 11 7 8 12 7 7 7 10 9 6 6 5 7 6 7 10 7 8 7 7 8 9 8 5 10 7 7 6 6 7 8 12 11 5 7 12 10 7 7 10 7 11 11 5 7 6 10 8 6 8 11 8 7 5 7 7 5 6 8 7 7 10 6 5 9 5 5 1 8 5 6 7 8 8 7 7 7 6 11 6 5 8 7\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '50\\n4 7 9 2 7 5 5 5 8 9 8 6 9 7 7 6 5 6 4 9 6 5 6 6 5 7 7 6 6 10 5 8 2 7 8 7 6 5 7 9 8 7 5 6 6 8 6 6 7 7\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '20\\n2 3 4 4 2 4 4 2 4 7 3 4 4 6 1 1 3 3 4 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '85\\n7 9 8 9 5 6 9 8 10 10 9 10 10 10 3 7 7 4 8 7 7 7 9 10 10 9 10 9 10 10 10 8 8 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 7 10 4 2 9 3 3 6 2 6 5 6 7 1 7 3 7 12 5 8 3 5 4 1 10 2 9 3 1 4 2 9 9 3 5 6 8\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '100\\n8 12 6 10 8 11 5 11 11 7 5 6 7 9 11 9 4 11 7 8 12 7 7 7 10 9 4 6 5 7 6 7 10 7 8 7 7 8 9 8 5 10 7 7 6 6 7 8 12 11 5 7 12 10 7 7 10 7 11 11 5 7 6 10 8 6 8 11 8 7 5 7 7 5 6 2 7 7 10 1 5 9 5 5 11 8 7 6 7 8 8 7 7 7 6 6 6 5 8 7\\n', 'output': 'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79749","program":"```python\n#!/usr/bin/python3\n\ncounts = [0]*1024\nfor x in range(len(counts)): counts[x] = []\nN = int(input())\nx = [int(t) for t in input().strip().split()]\nfor i,t in enumerate(x): counts[t].append(i)\n\n\ncurr = 0\nans = [0]*N\nfor i in range(1,1024):\n\twhile len(counts[i]) > 0:\n\t\tx = bin(curr)[2:]\n\t\tif len(x) > i:\n\t\t\tprint(\"NO\")\n\t\t\texit(0)\n\t\telse: x = \"0\"*(i-len(x)) + x\n\t\tans[counts[i].pop()] = x\n\t\tcurr += 1\n\tcurr = 2*curr\nprint(\"YES\")\nprint(\"\\n\".join(ans))\n```","inputs":"3\n1 2 3\n","output":"YES\n0\n10\n110","actual_output":"YES\n0\n10\n110\n","execution_success":true,"sample_index":12696},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"400_B. Inna and New Matrix of Candies","prompt":"Solve the following coding problem using the programming language python:\n\nInna likes sweets and a game called the \"Candy Matrix\". Today, she came up with the new game \"Candy Matrix 2: Reload\".\n\nThe field for the new game is a rectangle table of size n \u00d7 m. Each line of the table contains one cell with a dwarf figurine, one cell with a candy, the other cells of the line are empty. The game lasts for several moves. During each move the player should choose all lines of the matrix where dwarf is not on the cell with candy and shout \"Let's go!\". After that, all the dwarves from the chosen lines start to simultaneously move to the right. During each second, each dwarf goes to the adjacent cell that is located to the right of its current cell. The movement continues until one of the following events occurs:\n\n * some dwarf in one of the chosen lines is located in the rightmost cell of his row; \n * some dwarf in the chosen lines is located in the cell with the candy. \n\n\n\nThe point of the game is to transport all the dwarves to the candy cells.\n\nInna is fabulous, as she came up with such an interesting game. But what about you? Your task is to play this game optimally well. Specifically, you should say by the given game field what minimum number of moves the player needs to reach the goal of the game.\n\nInput\n\nThe first line of the input contains two integers n and m (1 \u2264 n \u2264 1000; 2 \u2264 m \u2264 1000). \n\nNext n lines each contain m characters \u2014 the game field for the \"Candy Martix 2: Reload\". Character \"*\" represents an empty cell of the field, character \"G\" represents a dwarf and character \"S\" represents a candy. The matrix doesn't contain other characters. It is guaranteed that each line contains exactly one character \"G\" and one character \"S\".\n\nOutput\n\nIn a single line print a single integer \u2014 either the minimum number of moves needed to achieve the aim of the game, or -1, if the aim cannot be achieved on the given game field.\n\nExamples\n\nInput\n\n3 4\n*G*S\nG**S\n*G*S\n\n\nOutput\n\n2\n\n\nInput\n\n1 3\nS*G\n\n\nOutput\n\n-1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, m = (int(x) for x in input().split())\nst = set()\nfor i in range(n):\n\ts = input()\n\tg = s.index('G')\n\ts = s.index('S')\n\tif g > s:\n\t\tprint(-1)\n\t\texit(0)\n\tst.add(s - g)\nprint(len(st))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 4\\n*G*S\\nG**S\\n*G*S\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 3\\nS*G\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 10\\n***G****S*\\n*****GS***\\nG****S****\\nG*******S*\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 8\\nG*S*****\\n****G*S*\\nG*****S*\\n**G***S*\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 10\\nG***S*****\\nG****S****\\n***GS*****\\nG*S*******\\nG***S*****\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\nSG\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 4\\nSG**\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\nGS\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nG********S\\n*G*******S\\n**G******S\\n***G*****S\\n****G****S\\n*****G***S\\n******G**S\\n*******G*S\\n********GS\\nG********S\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 8\\nG*S*****\\n****G*S*\\nG*****S*\\n)*G***S*\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n*G*S\\nG**S\\nS*G*\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 4\\n**GS\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nG********S\\n*G*******S\\n**G******S\\n***G*****S\\n****G****S\\n***G*****S\\n******G**S\\n*******G*S\\n********GS\\nG********S\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '4 8\\nG*S*****\\n****G*S*\\nG*****S*\\n)***G*S*\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\nG********S\\n*G*******S\\n**G******S\\n***G*****S\\n****G****S\\n*****G***S\\n******G**S\\n***)***G*S\\n********GS\\nG********S\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n*G*S\\nG**S\\n*GS*\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 8\\nG*S*****\\n****G*S*\\nG*****S*\\n(*G***S*\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\nSG**\\nG**S\\n*GS*\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 8\\nG*S*****\\n****G*S*\\nG*****S*\\n*S***G*(\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\nSG*+\\nG**S\\n*GS*\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 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'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79753","program":"```python\nn, m = (int(x) for x in input().split())\nst = set()\nfor i in range(n):\n\ts = input()\n\tg = s.index('G')\n\ts = s.index('S')\n\tif g > s:\n\t\tprint(-1)\n\t\texit(0)\n\tst.add(s - g)\nprint(len(st))\n\n```","inputs":"3 4\n*G*S\nG**S\n*G*S\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12697},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"427_C. Checkposts","prompt":"Solve the following coding problem using the programming language python:\n\nYour city has n junctions. There are m one-way roads between the junctions. As a mayor of the city, you have to ensure the security of all the junctions.\n\nTo ensure the security, you have to build some police checkposts. Checkposts can only be built in a junction. A checkpost at junction i can protect junction j if either i = j or the police patrol car can go to j from i and then come back to i.\n\nBuilding checkposts costs some money. As some areas of the city are more expensive than others, building checkpost at some junctions might cost more money than other junctions.\n\nYou have to determine the minimum possible money needed to ensure the security of all the junctions. Also you have to find the number of ways to ensure the security in minimum price and in addition in minimum number of checkposts. Two ways are different if any of the junctions contains a checkpost in one of them and do not contain in the other.\n\nInput\n\nIn the first line, you will be given an integer n, number of junctions (1 \u2264 n \u2264 105). In the next line, n space-separated integers will be given. The ith integer is the cost of building checkpost at the ith junction (costs will be non-negative and will not exceed 109).\n\nThe next line will contain an integer m (0 \u2264 m \u2264 3\u00b7105). And each of the next m lines contains two integers ui and vi (1 \u2264 ui, vi \u2264 n; u \u2260 v). A pair ui, vi means, that there is a one-way road which goes from ui to vi. There will not be more than one road between two nodes in the same direction.\n\nOutput\n\nPrint two integers separated by spaces. The first one is the minimum possible money needed to ensure the security of all the junctions. And the second one is the number of ways you can ensure the security modulo 1000000007 (109 + 7).\n\nExamples\n\nInput\n\n3\n1 2 3\n3\n1 2\n2 3\n3 2\n\n\nOutput\n\n3 1\n\n\nInput\n\n5\n2 8 0 6 0\n6\n1 4\n1 3\n2 4\n3 4\n4 5\n5 1\n\n\nOutput\n\n8 2\n\n\nInput\n\n10\n1 3 2 2 1 3 1 4 10 10\n12\n1 2\n2 3\n3 1\n3 4\n4 5\n5 6\n5 7\n6 4\n7 3\n8 9\n9 10\n10 9\n\n\nOutput\n\n15 6\n\n\nInput\n\n2\n7 91\n2\n1 2\n2 1\n\n\nOutput\n\n7 1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nMOD = int(1e9) + 7\n\nn = int(input())\nw = [0] + list(map(int, input().split()))\nq = [[] for i in range(n+1)]\np = [[] for i in range(n+1)]\nm = int(input())\nedges = [list(map(int, input().split())) for _ in range(m)]\nfor u, v in edges:\n p[u].append(v)\n q[v].append(u)\n \ns, t = 0, 1\nr = set(i for i in range(1, n+1) if not p[i] or not q[i])\nwhile r:\n i = r.pop()\n s += w[i]\n for j in p[i]:\n q[j].remove(i)\n if not q[j]: \n r.add(j)\n for j in q[i]:\n p[j].remove(i)\n if not p[j]: \n r.add(j)\n \nr = set(i for i in range(1, n+1) if p[i] and q[i])\nwhile r:\n i = r.pop()\n h = p[i]\n d, k = w[i], 1\n while h:\n i = h.pop()\n if i not in r: \n continue\n r.remove(i)\n h += p[i]\n if w[i] == d: \n k += 1\n elif w[i] < d: \n d, k = w[i], 1\n s += d\n t = (t * k) % MOD\nprint(s, t)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n2 8 0 6 0\\n6\\n1 4\\n1 3\\n2 4\\n3 4\\n4 5\\n5 1\\n', 'output': '8 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 3\\n3\\n1 2\\n2 3\\n3 2\\n', 'output': '3 1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n7 91\\n2\\n1 2\\n2 1\\n', 'output': '7 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 3 2 2 1 3 1 4 10 10\\n12\\n1 2\\n2 3\\n3 1\\n3 4\\n4 5\\n5 6\\n5 7\\n6 4\\n7 3\\n8 9\\n9 10\\n10 9\\n', 'output': '15 6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n0\\n', 'output': '0 1\\n'}, {'type': 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178 119 65 134 166 45 174 39 9 85 94 15 166 64 43 177 123 186 7 64 124 118 81 11 47 000 0 20 34 138 79 336 90 111 50 149 116 170 41 80 192 11 182 92 157 72 136 152 36 48 34 42 2 164 134 117 75 186 17 28 125 86 19 244 12 166 169 116 44 19 99 55 179 85 187 150 19 45 42 244 79 100 143 128 2 132 20\\n0\\n', 'output': '9994 1\\n'}, {'type': 'stdin_stdout', 'input': '100\\n221 174 49 152 10 185 101 55 28 178 164 69 274 178 119 65 134 166 45 174 25 9 85 94 15 166 64 43 177 123 186 7 64 124 118 81 11 47 000 0 20 34 138 79 336 90 111 50 149 116 170 41 80 192 11 182 92 157 72 136 152 36 48 34 42 2 164 134 117 75 186 17 28 125 86 19 244 12 166 169 116 44 19 99 55 179 85 187 150 19 45 42 244 79 100 143 128 2 132 20\\n0\\n', 'output': '9980 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 1\\n3\\n2 2\\n2 3\\n3 2\\n', 'output': '2 1\\n'}, {'type': 'stdin_stdout', 'input': '100\\n174 174 49 152 10 185 101 157 28 177 105 94 155 178 119 123 197 197 45 174 39 53 85 94 72 166 71 43 177 123 186 13 64 82 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169 116 44 19 99 55 179 85 187 150 29 49 42 251 79 110 143 47 135 81 20\\n0\\n', 'output': '10224 1\\n'}, {'type': 'stdin_stdout', 'input': '100\\n221 174 49 152 10 185 101 55 28 178 164 69 274 178 119 65 134 166 45 174 39 9 85 94 15 166 64 43 177 123 186 7 64 82 118 81 11 47 000 0 20 34 138 79 336 90 111 50 149 116 170 41 80 192 11 182 92 157 72 136 152 36 48 34 42 2 164 134 117 75 186 17 28 125 86 19 244 12 166 169 116 44 19 99 55 179 85 187 150 14 45 42 244 79 100 143 128 2 132 20\\n0\\n', 'output': '9947 1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79757","program":"```python\nMOD = int(1e9) + 7\n\nn = int(input())\nw = [0] + list(map(int, input().split()))\nq = [[] for i in range(n+1)]\np = [[] for i in range(n+1)]\nm = int(input())\nedges = [list(map(int, input().split())) for _ in range(m)]\nfor u, v in edges:\n p[u].append(v)\n q[v].append(u)\n \ns, t = 0, 1\nr = set(i for i in range(1, n+1) if not p[i] or not q[i])\nwhile r:\n i = r.pop()\n s += w[i]\n for j in p[i]:\n q[j].remove(i)\n if not q[j]: \n r.add(j)\n for j in q[i]:\n p[j].remove(i)\n if not p[j]: \n r.add(j)\n \nr = set(i for i in range(1, n+1) if p[i] and q[i])\nwhile r:\n i = r.pop()\n h = p[i]\n d, k = w[i], 1\n while h:\n i = h.pop()\n if i not in r: \n continue\n r.remove(i)\n h += p[i]\n if w[i] == d: \n k += 1\n elif w[i] < d: \n d, k = w[i], 1\n s += d\n t = (t * k) % MOD\nprint(s, t)\n```","inputs":"5\n2 8 0 6 0\n6\n1 4\n1 3\n2 4\n3 4\n4 5\n5 1\n","output":"8 2\n","actual_output":"8 2\n","execution_success":true,"sample_index":12698},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"450_A. Jzzhu and Children","prompt":"Solve the following coding problem using the programming language python:\n\nThere are n children in Jzzhu's school. Jzzhu is going to give some candies to them. Let's number all the children from 1 to n. The i-th child wants to get at least ai candies.\n\nJzzhu asks children to line up. Initially, the i-th child stands at the i-th place of the line. Then Jzzhu start distribution of the candies. He follows the algorithm:\n\n 1. Give m candies to the first child of the line. \n 2. If this child still haven't got enough candies, then the child goes to the end of the line, else the child go home. \n 3. Repeat the first two steps while the line is not empty. \n\n\n\nConsider all the children in the order they go home. Jzzhu wants to know, which child will be the last in this order?\n\nInput\n\nThe first line contains two integers n, m (1 \u2264 n \u2264 100; 1 \u2264 m \u2264 100). The second line contains n integers a1, a2, ..., an (1 \u2264 ai \u2264 100).\n\nOutput\n\nOutput a single integer, representing the number of the last child.\n\nExamples\n\nInput\n\n5 2\n1 3 1 4 2\n\n\nOutput\n\n4\n\n\nInput\n\n6 4\n1 1 2 2 3 3\n\n\nOutput\n\n6\n\nNote\n\nLet's consider the first sample. \n\nFirstly child 1 gets 2 candies and go home. Then child 2 gets 2 candies and go to the end of the line. Currently the line looks like [3, 4, 5, 2] (indices of the children in order of the line). Then child 3 gets 2 candies and go home, and then child 4 gets 2 candies and goes to the end of the line. Currently the line looks like [5, 2, 4]. Then child 5 gets 2 candies and goes home. Then child 2 gets two candies and goes home, and finally child 4 gets 2 candies and goes home.\n\nChild 4 is the last one who goes home.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\nn,k=map(int,input().split())\nl=list(map(int,input().split()))\nfor i in range(n):\n l[i]=math.ceil(l[i]/k)\nf=max(l)\nfor i in range(n-1,-1,-1):\n if f==l[i]:\n print(i+1)\n break\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 2\\n1 3 1 4 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '6 4\\n1 1 2 2 3 3\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '100 7\\n6 73 7 54 92 33 66 65 80 47 2 53 28 59 61 16 54 89 37 48 77 40 49 59 27 52 17 22 78 80 81 80 8 93 50 7 87 57 29 16 89 55 20 7 51 54 30 98 44 96 27 70 1 1 32 61 22 92 84 98 31 89 91 90 28 56 49 25 86 49 55 16 19 1 18 8 88 47 16 18 73 86 2 96 16 91 74 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Design Tutorial: Learn from Life","prompt":"Solve the following coding problem using the programming language python:\n\nOne way to create a task is to learn from life. You can choose some experience in real life, formalize it and then you will get a new task.\n\nLet's think about a scene in real life: there are lots of people waiting in front of the elevator, each person wants to go to a certain floor. We can formalize it in the following way. We have n people standing on the first floor, the i-th person wants to go to the fi-th floor. Unfortunately, there is only one elevator and its capacity equal to k (that is at most k people can use it simultaneously). Initially the elevator is located on the first floor. The elevator needs |a - b| seconds to move from the a-th floor to the b-th floor (we don't count the time the people need to get on and off the elevator).\n\nWhat is the minimal number of seconds that is needed to transport all the people to the corresponding floors and then return the elevator to the first floor?\n\nInput\n\nThe first line contains two integers n and k (1 \u2264 n, k \u2264 2000) \u2014 the number of people and the maximal capacity of the elevator.\n\nThe next line contains n integers: f1, f2, ..., fn (2 \u2264 fi \u2264 2000), where fi denotes the target floor of the i-th person.\n\nOutput\n\nOutput a single integer \u2014 the minimal time needed to achieve the goal.\n\nExamples\n\nInput\n\n3 2\n2 3 4\n\n\nOutput\n\n8\n\n\nInput\n\n4 2\n50 100 50 100\n\n\nOutput\n\n296\n\n\nInput\n\n10 3\n2 2 2 2 2 2 2 2 2 2\n\n\nOutput\n\n8\n\nNote\n\nIn first sample, an optimal solution is: \n\n 1. The elevator takes up person #1 and person #2. \n 2. It goes to the 2nd floor. \n 3. Both people go out of the elevator. \n 4. The elevator goes back to the 1st floor. \n 5. Then the elevator takes up person #3. \n 6. And it goes to the 2nd floor. \n 7. It picks up person #2. \n 8. Then it goes to the 3rd floor. \n 9. Person #2 goes out. \n 10. Then it goes to the 4th floor, where person #3 goes out. \n 11. The elevator goes back to the 1st floor. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, k = map(int, input().split())\narr = list(map(int, input().split()))\narr.sort()\nans = 0\np = 1\ni = 0\nwhile n != 0:\n tp = arr[i]\n ans += 2 * (tp - p) * (round(n / k + 0.49999999999999))\n while n != 0 and arr[i] == tp:\n n -= 1\n i += 1\n p = tp\nprint(ans)\n\n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10 3\\n2 2 2 2 2 2 2 2 2 2\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n50 100 50 100\\n', 'output': '296\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 3 4\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '100 100\\n100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 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964 1317 1487 1322 1281 843 1051 1220 790 1121 1442 726 957 1465 974 1314 993 1286 1163 938 1000 1197 859 807 718 916 783 1450\\n', 'output': '3582\\n'}, {'type': 'stdin_stdout', 'input': '22 1481\\n622 1499 1615 54 399 1153 593 1830 628 292 278 1173 1501 1779 317 1110 1855 1631 435 775 186 1312\\n', 'output': '3708\\n'}, {'type': 'stdin_stdout', 'input': '70 1311\\n1146 769 1530 1132 307 1352 1295 1282 1086 914 852 1351 1432 847 1105 497 1343 1154 1435 1100 1320 869 812 1179 1239 1426 1403 1792 1489 1018 668 1215 1278 1203 1386 1113 812 896 1287 733 1328 1517 964 1317 1487 1322 1281 1234 1051 1220 790 1121 1442 917 957 1465 974 1314 192 1286 1163 938 675 1197 859 807 718 916 783 1450\\n', 'output': '3582\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79765","program":"```python\nn, k = map(int, input().split())\narr = list(map(int, input().split()))\narr.sort()\nans = 0\np = 1\ni = 0\nwhile n != 0:\n tp = arr[i]\n ans += 2 * (tp - p) * (round(n / k + 0.49999999999999))\n while n != 0 and arr[i] == tp:\n n -= 1\n i += 1\n p = tp\nprint(ans)\n\n \n```","inputs":"10 3\n2 2 2 2 2 2 2 2 2 2\n","output":"8\n","actual_output":"8\n","execution_success":true,"sample_index":12700},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"496_C. Removing Columns","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given an n \u00d7 m rectangular table consisting of lower case English letters. In one operation you can completely remove one column from the table. The remaining parts are combined forming a new table. For example, after removing the second column from the table\n \n \n \n abcd \n edfg \n hijk \n \n\nwe obtain the table:\n \n \n \n acd \n efg \n hjk \n \n\nA table is called good if its rows are ordered from top to bottom lexicographically, i.e. each row is lexicographically no larger than the following one. Determine the minimum number of operations of removing a column needed to make a given table good.\n\nInput\n\nThe first line contains two integers \u2014 n and m (1 \u2264 n, m \u2264 100).\n\nNext n lines contain m small English letters each \u2014 the characters of the table.\n\nOutput\n\nPrint a single number \u2014 the minimum number of columns that you need to remove in order to make the table good.\n\nExamples\n\nInput\n\n1 10\ncodeforces\n\n\nOutput\n\n0\n\n\nInput\n\n4 4\ncase\ncare\ntest\ncode\n\n\nOutput\n\n2\n\n\nInput\n\n5 4\ncode\nforc\nesco\ndefo\nrces\n\n\nOutput\n\n4\n\nNote\n\nIn the first sample the table is already good.\n\nIn the second sample you may remove the first and third column.\n\nIn the third sample you have to remove all the columns (note that the table where all rows are empty is considered good by definition).\n\nLet strings s and t have equal length. Then, s is lexicographically larger than t if they are not equal and the character following the largest common prefix of s and t (the prefix may be empty) in s is alphabetically larger than the corresponding character of t.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys,heapq,math\nfrom collections import defaultdict,deque\ninput=sys.stdin.readline\n\n\n\n\n \nr,c=map(int,input().split())\ngrid=[]\nfor i in range(r):\n grid.append(input().strip())\nequal=[0 for _ in range(c)]\nless=[0 for _ in range(c)]\nfor i in range(c):\n for row in range(1,r):\n if(grid[row-1][i]==grid[row][i]):\n equal[i]=1\n elif(grid[row-1][i]>grid[row][i]):\n equal[i]=0\n break\n less[i]=1\n for row in range(1,r):\n if(equal[i]==1):\n less[i]=0\n break\n elif(grid[row-1][i]>grid[row][i]):\n less[i]=0\n break\nans=0\nfor i in range(c):\n if(less[i]==1):\n ans=max(ans,c-i)\n break\n elif(equal[i]==1):\n cnt=1\n l=[]\n for row in range(1,r):\n if(grid[row-1][i]==grid[row][i]):\n start=row-1\n while(rowgrid[row][col]):\n f=1\n break\n if(f==1):\n break\n if(f==0):\n cnt+=1\n ptr=0\n nl=[]\n while(ptrgrid[row][i]):\n equal[i]=0\n break\n less[i]=1\n for row in range(1,r):\n if(equal[i]==1):\n less[i]=0\n break\n elif(grid[row-1][i]>grid[row][i]):\n less[i]=0\n break\nans=0\nfor i in range(c):\n if(less[i]==1):\n ans=max(ans,c-i)\n break\n elif(equal[i]==1):\n cnt=1\n l=[]\n for row in range(1,r):\n if(grid[row-1][i]==grid[row][i]):\n start=row-1\n while(rowgrid[row][col]):\n f=1\n break\n if(f==1):\n break\n if(f==0):\n cnt+=1\n ptr=0\n nl=[]\n while(ptr\n\nA group of bears is a non-empty contiguous segment of the line. The size of a group is the number of bears in that group. The strength of a group is the minimum height of the bear in that group.\n\nMike is a curious to know for each x such that 1 \u2264 x \u2264 n the maximum strength among all groups of size x.\n\nInput\n\nThe first line of input contains integer n (1 \u2264 n \u2264 2 \u00d7 105), the number of bears.\n\nThe second line contains n integers separated by space, a1, a2, ..., an (1 \u2264 ai \u2264 109), heights of bears.\n\nOutput\n\nPrint n integers in one line. For each x from 1 to n, print the maximum strength among all groups of size x.\n\nExamples\n\nInput\n\n10\n1 2 3 4 5 4 3 2 1 6\n\n\nOutput\n\n6 4 4 3 3 2 2 1 1 1 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\nimport random\n\nclass AVLTree():\n def __init__(self, x):\n self.left = None\n self.rght = None\n self.val = x\n self.height = 1\n \ndef getHeight0(root):\n if root==None: return 0\n return max(getHeight0(root.left), getHeight0(root.rght))+1\n\ndef getHeight(root):\n if root==None: return 0\n return root.height\n #return max(getHeight(root.left), getHeight(root.rght))+1\n\ndef insert(root, x):\n if root==None: return AVLTree(x)\n if x==root.val: return root\n if xroot.val:\n root.rght = insert(root.rght, x)\n hl = getHeight(root.left)\n hr = getHeight(root.rght)\n root.height = max(hl,hr)+1\n \n if hr-hl>1:\n assert hr-hl==2\n hrr=getHeight(root.rght.rght)\n hrl=getHeight(root.rght.left)\n if hrr==hrl+1:\n new_root = root.rght\n root.rght = new_root.left\n new_root.left = root\n root.height -= 2\n return new_root\n elif hrl==hrr+1:\n new_root = root.rght.left\n root.rght.left = new_root.rght\n new_root.rght = root.rght\n root.rght = new_root.left\n new_root.left = root\n root.height -= 2\n new_root.height += 1\n new_root.rght.height -= 1\n return new_root\n else:\n assert False\n elif hl-hr>1:\n assert hl-hr==2\n hlr=getHeight(root.left.rght)\n hll=getHeight(root.left.left)\n if hll==hlr+1:\n new_root = root.left\n root.left = new_root.rght\n new_root.rght = root\n root.height -= 2\n return new_root\n elif hlr==hll+1:\n new_root = root.left.rght\n root.left.rght = new_root.left\n new_root.left = root.left\n root.left = new_root.rght\n new_root.rght = root\n root.height -= 2\n new_root.height += 1\n new_root.left.height -= 1\n return new_root\n else:\n assert False\n return root\n\ndef findUpperBound(root, x):\n if root==None: return None\n if x>=root.val:\n return findUpperBound(root.rght, x)\n tmp_bound = findUpperBound(root.left, x)\n if tmp_bound==None: return root.val\n return tmp_bound\n \ndef findLowerBound(root, x):\n if root==None: return None\n if x<=root.val:\n return findLowerBound(root.left, x)\n tmp_bound = findLowerBound(root.rght, x)\n if tmp_bound==None: return root.val\n return tmp_bound\n \ndef inorder(root):\n if root==None: return []\n return inorder(root.left)+[root.val]+inorder(root.rght)\n\ndef checkHeight(root):\n if root==None: return True\n if not checkHeight(root.left): return False\n if not checkHeight(root.rght): return False\n return abs(getHeight0(root.left)-getHeight0(root.rght))<=1\n \ndef testAVL():\n l = [x for x in range(100)]\n for i in range(100):\n ni = random.randint(0,99)\n l[i],l[ni] = l[ni],l[i]\n\n tree = None\n for v in l:\n tree = insert(tree, v)\n assert inorder(tree)==[i for i in range(100)]\n assert checkHeight(tree)==True\n\n\nclass HeapObj():\n def __init__(self, v, n):\n self.val = v\n self.hpidx = n\n \ndef shiftup(n, r, hp):\n while r>=0:\n j = r*2+1\n if jhp[j].val: j+=1\n if hp[j].val <= hp[r].val: return\n hp[r],hp[j] = hp[j],hp[r]\n hp[r].hpidx = r\n hp[j].hpidx = j\n if r==0: break\n r = int((r-1)/2)\n\ndef shiftdown(n, r, hp):\n while r=n: return\n if j+1hp[j].val: j+=1\n if hp[j].val<=hp[r].val: return\n hp[r],hp[j] = hp[j],hp[r]\n hp[r].hpidx = r\n hp[j].hpidx = j\n r = j\n\ndef testHeap():\n hp = []\n for _ in range(100):\n obj = HeapObj(random.randint(0,9999), len(hp))\n hp.append(obj)\n shiftup(len(hp),len(hp)-1,hp)\n res = []\n while hp:\n res.append(hp[0].val)\n hp[0],hp[-1] = hp[-1],hp[0]\n hp[0].hpidx = 0\n hp.pop()\n shiftdown(len(hp), 0, hp)\n assert res==sorted(res, reverse=True)\n \ndef calc(n, a):\n ia = [x for x in enumerate(a)]\n ia.sort(key=lambda tp:tp[1])\n #print('ia={ia}'.format(ia=ia))\n tree = None\n tree = insert(tree, -1)\n tree = insert(tree, n)\n \n hpobj = HeapObj(n,0)\n hp = [hpobj]\n itv2hpobj = {(0,n-1):hpobj}\n ret = []\n nxt = n\n for idx,val in ia:\n #Get interval\n interval_end = findUpperBound(tree, idx)-1\n interval_bgn = findLowerBound(tree, idx)+1\n itv = (interval_bgn, interval_end)\n assert itv in itv2hpobj\n tree = insert(tree, idx)\n #Delete this interval from heap\n itv2hpobj[itv].val = 2*n\n hpidx = itv2hpobj[itv].hpidx\n shiftup(len(hp), hpidx, hp)\n hp[0],hp[-1] = hp[-1],hp[0]\n hp[0].hpidx = 0\n hp.pop()\n del itv2hpobj[itv]\n shiftdown(len(hp), 0, hp)\n \n #Add new interval(s) to heap\n if idx>interval_bgn:\n new_obj = HeapObj(idx-interval_bgn, len(hp))\n hp.append(new_obj)\n itv2hpobj[(interval_bgn,idx-1)] = new_obj\n shiftup(len(hp), len(hp)-1, hp)\n if idx0: NA = hp[0].val\n while nxt>NA:\n ret.append(val)\n nxt -= 1\n assert len(ret)==n\n ret.reverse()\n return ret\n\ndef calc_bf(n, a):\n ans = [None for _ in range(n)]\n for i in range(n):\n minij = None\n for j in range(i,n):\n l=j-i\n if minij == None or minij>a[j]:\n minij = a[j]\n if ans[l]==None or ans[l]root.val:\n root.rght = insert(root.rght, x)\n hl = getHeight(root.left)\n hr = getHeight(root.rght)\n root.height = max(hl,hr)+1\n \n if hr-hl>1:\n assert hr-hl==2\n hrr=getHeight(root.rght.rght)\n hrl=getHeight(root.rght.left)\n if hrr==hrl+1:\n new_root = root.rght\n root.rght = new_root.left\n new_root.left = root\n root.height -= 2\n return new_root\n elif hrl==hrr+1:\n new_root = root.rght.left\n root.rght.left = new_root.rght\n new_root.rght = root.rght\n root.rght = new_root.left\n new_root.left = root\n root.height -= 2\n new_root.height += 1\n new_root.rght.height -= 1\n return new_root\n else:\n assert False\n elif hl-hr>1:\n assert hl-hr==2\n hlr=getHeight(root.left.rght)\n hll=getHeight(root.left.left)\n if hll==hlr+1:\n new_root = root.left\n root.left = new_root.rght\n new_root.rght = root\n root.height -= 2\n return new_root\n elif hlr==hll+1:\n new_root = root.left.rght\n root.left.rght = new_root.left\n new_root.left = root.left\n root.left = new_root.rght\n new_root.rght = root\n root.height -= 2\n new_root.height += 1\n new_root.left.height -= 1\n return new_root\n else:\n assert False\n return root\n\ndef findUpperBound(root, x):\n if root==None: return None\n if x>=root.val:\n return findUpperBound(root.rght, x)\n tmp_bound = findUpperBound(root.left, x)\n if tmp_bound==None: return root.val\n return tmp_bound\n \ndef findLowerBound(root, x):\n if root==None: return None\n if x<=root.val:\n return findLowerBound(root.left, x)\n tmp_bound = findLowerBound(root.rght, x)\n if tmp_bound==None: return root.val\n return tmp_bound\n \ndef inorder(root):\n if root==None: return []\n return inorder(root.left)+[root.val]+inorder(root.rght)\n\ndef checkHeight(root):\n if root==None: return True\n if not checkHeight(root.left): return False\n if not checkHeight(root.rght): return False\n return abs(getHeight0(root.left)-getHeight0(root.rght))<=1\n \ndef testAVL():\n l = [x for x in range(100)]\n for i in range(100):\n ni = random.randint(0,99)\n l[i],l[ni] = l[ni],l[i]\n\n tree = None\n for v in l:\n tree = insert(tree, v)\n assert inorder(tree)==[i for i in range(100)]\n assert checkHeight(tree)==True\n\n\nclass HeapObj():\n def __init__(self, v, n):\n self.val = v\n self.hpidx = n\n \ndef shiftup(n, r, hp):\n while r>=0:\n j = r*2+1\n if jhp[j].val: j+=1\n if hp[j].val <= hp[r].val: return\n hp[r],hp[j] = hp[j],hp[r]\n hp[r].hpidx = r\n hp[j].hpidx = j\n if r==0: break\n r = int((r-1)/2)\n\ndef shiftdown(n, r, hp):\n while r=n: return\n if j+1hp[j].val: j+=1\n if hp[j].val<=hp[r].val: return\n hp[r],hp[j] = hp[j],hp[r]\n hp[r].hpidx = r\n hp[j].hpidx = j\n r = j\n\ndef testHeap():\n hp = []\n for _ in range(100):\n obj = HeapObj(random.randint(0,9999), len(hp))\n hp.append(obj)\n shiftup(len(hp),len(hp)-1,hp)\n res = []\n while hp:\n res.append(hp[0].val)\n hp[0],hp[-1] = hp[-1],hp[0]\n hp[0].hpidx = 0\n hp.pop()\n shiftdown(len(hp), 0, hp)\n assert res==sorted(res, reverse=True)\n \ndef calc(n, a):\n ia = [x for x in enumerate(a)]\n ia.sort(key=lambda tp:tp[1])\n #print('ia={ia}'.format(ia=ia))\n tree = None\n tree = insert(tree, -1)\n tree = insert(tree, n)\n \n hpobj = HeapObj(n,0)\n hp = [hpobj]\n itv2hpobj = {(0,n-1):hpobj}\n ret = []\n nxt = n\n for idx,val in ia:\n #Get interval\n interval_end = findUpperBound(tree, idx)-1\n interval_bgn = findLowerBound(tree, idx)+1\n itv = (interval_bgn, interval_end)\n assert itv in itv2hpobj\n tree = insert(tree, idx)\n #Delete this interval from heap\n itv2hpobj[itv].val = 2*n\n hpidx = itv2hpobj[itv].hpidx\n shiftup(len(hp), hpidx, hp)\n hp[0],hp[-1] = hp[-1],hp[0]\n hp[0].hpidx = 0\n hp.pop()\n del itv2hpobj[itv]\n shiftdown(len(hp), 0, hp)\n \n #Add new interval(s) to heap\n if idx>interval_bgn:\n new_obj = HeapObj(idx-interval_bgn, len(hp))\n hp.append(new_obj)\n itv2hpobj[(interval_bgn,idx-1)] = new_obj\n shiftup(len(hp), len(hp)-1, hp)\n if idx0: NA = hp[0].val\n while nxt>NA:\n ret.append(val)\n nxt -= 1\n assert len(ret)==n\n ret.reverse()\n return ret\n\ndef calc_bf(n, a):\n ans = [None for _ in range(n)]\n for i in range(n):\n minij = None\n for j in range(i,n):\n l=j-i\n if minij == None or minij>a[j]:\n minij = a[j]\n if ans[l]==None or ans[l] 1) is a secret integer known only to them. It is also known that each thief's bag can carry at most n chocolates (if they intend to take more, the deal is cancelled) and that there were exactly four thieves involved. \n\nSadly, only the thieves know the value of n, but rumours say that the numbers of ways they could have taken the chocolates (for a fixed n, but not fixed k) is m. Two ways are considered different if one of the thieves (they should be numbered in the order they take chocolates) took different number of chocolates in them.\n\nMike want to track the thieves down, so he wants to know what their bags are and value of n will help him in that. Please find the smallest possible value of n or tell him that the rumors are false and there is no such n.\n\nInput\n\nThe single line of input contains the integer m (1 \u2264 m \u2264 1015) \u2014 the number of ways the thieves might steal the chocolates, as rumours say.\n\nOutput\n\nPrint the only integer n \u2014 the maximum amount of chocolates that thieves' bags can carry. If there are more than one n satisfying the rumors, print the smallest one.\n\nIf there is no such n for a false-rumoured m, print - 1.\n\nExamples\n\nInput\n\n1\n\n\nOutput\n\n8\n\n\nInput\n\n8\n\n\nOutput\n\n54\n\n\nInput\n\n10\n\n\nOutput\n\n-1\n\nNote\n\nIn the first sample case the smallest n that leads to exactly one way of stealing chocolates is n = 8, whereas the amounts of stealed chocolates are (1, 2, 4, 8) (the number of chocolates stolen by each of the thieves).\n\nIn the second sample case the smallest n that leads to exactly 8 ways is n = 54 with the possibilities: (1, 2, 4, 8), (1, 3, 9, 27), (2, 4, 8, 16), (2, 6, 18, 54), (3, 6, 12, 24), (4, 8, 16, 32), (5, 10, 20, 40), (6, 12, 24, 48).\n\nThere is no n leading to exactly 10 ways of stealing chocolates in the third sample case.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef main():\n m = int(input())\n if m < 1000000:\n lo = m*4\n hi = m*8\n else:\n lo = int(4.949 * m)\n hi = int(4.9492 * m)\n while lo < hi - 1:\n mid = (lo + hi)//2\n nposs = countposs(mid)\n if nposs < m:\n lo = mid\n else:\n hi = mid\n if m == countposs(hi):\n print(hi)\n else:\n print(-1)\n\ndef countposs(maxtake):\n k = 2\n ans = 0\n while True:\n term = maxtake//(k*k*k)\n if term == 0:\n return ans\n ans += term\n k += 1\n\nmain()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '8\\n', 'output': '54\\n'}, {'type': 'stdin_stdout', 'input': '149344197\\n', 'output': '739123875\\n'}, {'type': 'stdin_stdout', 'input': '13\\n', 'output': '80\\n'}, {'type': 'stdin_stdout', 'input': '1000000000000000\\n', 'output': '4949100894494448\\n'}, {'type': 'stdin_stdout', 'input': '4\\n', 'output': '27\\n'}, {'type': 'stdin_stdout', 'input': '999999999999999\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '998749999999991\\n', 'output': '4942914518376840\\n'}, {'type': 'stdin_stdout', 'input': '49729446417673\\n', 'output': '246116048009288\\n'}, {'type': 'stdin_stdout', 'input': '57857854\\n', 'output': '286347520\\n'}, {'type': 'stdin_stdout', 'input': '550368702711851\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n', 'output': '48\\n'}, {'type': 'stdin_stdout', 'input': '151269640772354\\n', 'output': '748648714769352\\n'}, {'type': 'stdin_stdout', 'input': '6\\n', 'output': '40\\n'}, {'type': 'stdin_stdout', 'input': '99999\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '116003\\n', 'output': '574506\\n'}, {'type': 'stdin_stdout', 'input': '81258\\n', 'output': '402496\\n'}, {'type': 'stdin_stdout', 'input': '27\\n', 'output': '152\\n'}, {'type': 'stdin_stdout', 'input': '106559547884220\\n', 'output': '527373954052328\\n'}, {'type': 'stdin_stdout', 'input': '121463490731834\\n', 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'stdin_stdout', 'input': '113249897037670\\n', 'output': '560485167034608\\n'}, {'type': 'stdin_stdout', 'input': '48049569\\n', 'output': '237805160\\n'}, {'type': 'stdin_stdout', 'input': '15\\n', 'output': '88\\n'}, {'type': 'stdin_stdout', 'input': '199410\\n', 'output': '987363\\n'}, {'type': 'stdin_stdout', 'input': '74410\\n', 'output': '368616\\n'}, {'type': 'stdin_stdout', 'input': '16654\\n', 'output': '82624\\n'}, {'type': 'stdin_stdout', 'input': '580054265372580\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '69895\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '271103659949808\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '229520343251547\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '207274415092263\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79801","program":"```python\ndef main():\n m = int(input())\n if m < 1000000:\n lo = m*4\n hi = m*8\n else:\n lo = int(4.949 * m)\n hi = int(4.9492 * m)\n while lo < hi - 1:\n mid = (lo + hi)//2\n nposs = countposs(mid)\n if nposs < m:\n lo = mid\n else:\n hi = mid\n if m == countposs(hi):\n print(hi)\n else:\n print(-1)\n\ndef countposs(maxtake):\n k = 2\n ans = 0\n while True:\n term = maxtake//(k*k*k)\n if term == 0:\n return ans\n ans += term\n k += 1\n\nmain()\n```","inputs":"10\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12705},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"711_A. Bus to Udayland","prompt":"Solve the following coding problem using the programming language python:\n\nZS the Coder and Chris the Baboon are travelling to Udayland! To get there, they have to get on the special IOI bus. The IOI bus has n rows of seats. There are 4 seats in each row, and the seats are separated into pairs by a walkway. When ZS and Chris came, some places in the bus was already occupied.\n\nZS and Chris are good friends. They insist to get a pair of neighbouring empty seats. Two seats are considered neighbouring if they are in the same row and in the same pair. Given the configuration of the bus, can you help ZS and Chris determine where they should sit?\n\nInput\n\nThe first line of the input contains a single integer n (1 \u2264 n \u2264 1000) \u2014 the number of rows of seats in the bus.\n\nThen, n lines follow. Each line contains exactly 5 characters, the first two of them denote the first pair of seats in the row, the third character denotes the walkway (it always equals '|') and the last two of them denote the second pair of seats in the row. \n\nEach character, except the walkway, equals to 'O' or to 'X'. 'O' denotes an empty seat, 'X' denotes an occupied seat. See the sample cases for more details. \n\nOutput\n\nIf it is possible for Chris and ZS to sit at neighbouring empty seats, print \"YES\" (without quotes) in the first line. In the next n lines print the bus configuration, where the characters in the pair of seats for Chris and ZS is changed with characters '+'. Thus the configuration should differ from the input one by exactly two charaters (they should be equal to 'O' in the input and to '+' in the output).\n\nIf there is no pair of seats for Chris and ZS, print \"NO\" (without quotes) in a single line.\n\nIf there are multiple solutions, you may print any of them.\n\nExamples\n\nInput\n\n6\nOO|OX\nXO|XX\nOX|OO\nXX|OX\nOO|OO\nOO|XX\n\n\nOutput\n\nYES\n++|OX\nXO|XX\nOX|OO\nXX|OX\nOO|OO\nOO|XX\n\n\nInput\n\n4\nXO|OX\nXO|XX\nOX|OX\nXX|OX\n\n\nOutput\n\nNO\n\n\nInput\n\n5\nXX|XX\nXX|XX\nXO|OX\nXO|OO\nOX|XO\n\n\nOutput\n\nYES\nXX|XX\nXX|XX\nXO|OX\nXO|++\nOX|XO\n\nNote\n\nNote that the following is an incorrect configuration for the first sample case because the seats must be in the same pair.\n\nO+|+X\n\nXO|XX\n\nOX|OO\n\nXX|OX\n\nOO|OO\n\nOO|XX\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\nresult = []\nz = 0\nfor i in range(n):\n place = input()\n if place.count('OO') > 0:\n if z == 0:\n result.append(place.replace('OO', '++', 1))\n z += 1\n else:\n result.append(place)\n else:\n result.append(place)\nif z == 1:\n print('YES')\n for elem in result:\n print(elem, end=\"\\n\")\nelse:\n print('NO')\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\nXO|OX\\nXO|XX\\nOX|OX\\nXX|OX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\nXX|XX\\nXX|XX\\nXO|OX\\nXO|OO\\nOX|XO\\n', 'output': 'YES\\nXX|XX\\nXX|XX\\nXO|OX\\nXO|++\\nOX|XO\\n'}, {'type': 'stdin_stdout', 'input': '6\\nOO|OX\\nXO|XX\\nOX|OO\\nXX|OX\\nOO|OO\\nOO|XX\\n', 'output': 'YES\\n++|OX\\nXO|XX\\nOX|OO\\nXX|OX\\nOO|OO\\nOO|XX\\n'}, {'type': 'stdin_stdout', 'input': '4\\nXO|XX\\nXX|XO\\nOX|XX\\nXO|XO\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6\\nOO|XX\\nXO|XX\\nOX|OO\\nXX|OX\\nOO|XX\\nOX|XX\\n', 'output': 'YES\\n++|XX\\nXO|XX\\nOX|OO\\nXX|OX\\nOO|XX\\nOX|XX\\n'}, {'type': 'stdin_stdout', 'input': '10\\nOO|XX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXX|XX\\n', 'output': 'YES\\n++|XX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXX|XX\\n'}, {'type': 'stdin_stdout', 'input': '61\\nOX|XX\\nOX|XX\\nOX|XX\\nXO|XO\\nXX|XO\\nXX|XX\\nXX|XX\\nOX|XX\\nXO|XO\\nOX|XO\\nXO|OX\\nXX|XX\\nXX|XX\\nOX|OX\\nXX|OX\\nOX|XO\\nOX|XO\\nXO|OX\\nXO|XX\\nOX|XX\\nOX|XX\\nXO|OX\\nXO|XX\\nXO|XX\\nOX|XX\\nXX|XX\\nXX|XO\\nXO|XX\\nXX|XX\\nXO|OX\\nXX|XO\\nXO|XX\\nXO|XO\\nXO|OX\\nXX|OX\\nXO|OX\\nOX|XX\\nXX|OX\\nXX|XX\\nOX|XO\\nOX|XX\\nXO|OX\\nOX|XX\\nOX|XX\\nXO|XO\\nXO|XX\\nOX|XX\\nXO|XO\\nOX|XX\\nXX|XX\\nOX|XO\\nXO|XO\\nXO|XO\\nOX|OX\\nXX|OX\\nXX|OX\\nOX|XO\\nOX|XX\\nOX|OX\\nXO|XX\\nOX|XX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\nXX|XX\\nXX|XX\\nXO|OX\\nOO|OX\\nOX|XO\\n', 'output': 'YES\\nXX|XX\\nXX|XX\\nXO|OX\\n++|OX\\nOX|XO\\n'}, {'type': 'stdin_stdout', 'input': '1\\nXO|OX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\nOO|OO\\n', 'output': 'YES\\n++|OO\\n'}, {'type': 'stdin_stdout', 'input': '10\\nXX|XX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXX|OO\\n', 'output': 'YES\\nXX|XX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXX|++\\n'}, {'type': 'stdin_stdout', 'input': '1\\nOO|XX\\n', 'output': 'YES\\n++|XX\\n'}, {'type': 'stdin_stdout', 'input': '9\\nOX|XO\\nOX|XO\\nXO|OX\\nOX|OX\\nXO|OX\\nXX|OO\\nOX|OX\\nOX|XO\\nOX|OX\\n', 'output': 'YES\\nOX|XO\\nOX|XO\\nXO|OX\\nOX|OX\\nXO|OX\\nXX|++\\nOX|OX\\nOX|XO\\nOX|OX\\n'}, {'type': 'stdin_stdout', 'input': '4\\nXO|YX\\nXX|XO\\nOX|XX\\nXO|XO\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6\\nOO|XX\\nXX|OX\\nOX|OO\\nXX|OX\\nOO|XX\\nOX|XX\\n', 'output': 'YES\\n++|XX\\nXX|OX\\nOX|OO\\nXX|OX\\nOO|XX\\nOX|XX\\n'}, {'type': 'stdin_stdout', 'input': '10\\nXX|XX\\nXO|PX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXO|OX\\nXX|OO\\n', 'output': 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'61\\nOX|XX\\nOX|XY\\nOX|XX\\nXO|XO\\nXX|XO\\nXX|XX\\nXX|XX\\nOX|XX\\nXO|XO\\nOX|XO\\nXO|OX\\nXX|XX\\nXX|XX\\nOXO|X\\nXX|OX\\nOX|XO\\nOX|XO\\nXO|OX\\nXO|XX\\nOX|XX\\nOX|XX\\nXO|OX\\nXO|XX\\nXO|XX\\nOX|XX\\nXX|XX\\nXX|XO\\nXO|XX\\nXX|XX\\nXO|OX\\nXX|XO\\nXO|XX\\nXO|XO\\nXO|OX\\nXX|OX\\nXO|OX\\nXX|XO\\nXX|OX\\nXX|XX\\nOX|XO\\nOX|XX\\nXO|OX\\nOX|XX\\nOX|XX\\nXO|XO\\nXO|XX\\nOX|XX\\nXO|XO\\nOX|XX\\nXX|XX\\nOX|XO\\nXO|XO\\nXO|XO\\nOX|OX\\nXX|OX\\nXX|OX\\nOX|XO\\nOX|XX\\nOX|OX\\nXO|XX\\nOX|XX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\nXO|OX\\nXO|XX\\nXO|XO\\nXP|XX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\nXO|OX\\nPX|XX\\nXO|XO\\nXO|XX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\nXO|NX\\nOX|YX\\nOX|OX\\nXO|XX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1\\nXO|MX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\nXN|OX\\nXO|XX\\nOX|OX\\nXO|XX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\nXN|XX\\nXO|XW\\nOX|XX\\nXO|XO\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4\\nXO|OX\\nXO|XX\\nXO|XO\\nXX|PX\\n', 'output': 'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79805","program":"```python\nn = int(input())\nresult = []\nz = 0\nfor i in range(n):\n place = input()\n if place.count('OO') > 0:\n if z == 0:\n result.append(place.replace('OO', '++', 1))\n z += 1\n else:\n result.append(place)\n else:\n result.append(place)\nif z == 1:\n print('YES')\n for elem in result:\n print(elem, end=\"\\n\")\nelse:\n print('NO')\n\n```","inputs":"4\nXO|OX\nXO|XX\nOX|OX\nXX|OX\n","output":"NO\n","actual_output":"NO\n","execution_success":true,"sample_index":12706},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"732_A. Buy a Shovel","prompt":"Solve the following coding problem using the programming language python:\n\nPolycarp urgently needs a shovel! He comes to the shop and chooses an appropriate one. The shovel that Policarp chooses is sold for k burles. Assume that there is an unlimited number of such shovels in the shop.\n\nIn his pocket Polycarp has an unlimited number of \"10-burle coins\" and exactly one coin of r burles (1 \u2264 r \u2264 9).\n\nWhat is the minimum number of shovels Polycarp has to buy so that he can pay for the purchase without any change? It is obvious that he can pay for 10 shovels without any change (by paying the requied amount of 10-burle coins and not using the coin of r burles). But perhaps he can buy fewer shovels and pay without any change. Note that Polycarp should buy at least one shovel.\n\nInput\n\nThe single line of input contains two integers k and r (1 \u2264 k \u2264 1000, 1 \u2264 r \u2264 9) \u2014 the price of one shovel and the denomination of the coin in Polycarp's pocket that is different from \"10-burle coins\". \n\nRemember that he has an unlimited number of coins in the denomination of 10, that is, Polycarp has enough money to buy any number of shovels.\n\nOutput\n\nPrint the required minimum number of shovels Polycarp has to buy so that he can pay for them without any change. \n\nExamples\n\nInput\n\n117 3\n\n\nOutput\n\n9\n\n\nInput\n\n237 7\n\n\nOutput\n\n1\n\n\nInput\n\n15 2\n\n\nOutput\n\n2\n\nNote\n\nIn the first example Polycarp can buy 9 shovels and pay 9\u00b7117 = 1053 burles. Indeed, he can pay this sum by using 10-burle coins and one 3-burle coin. He can't buy fewer shovels without any change.\n\nIn the second example it is enough for Polycarp to buy one shovel.\n\nIn the third example Polycarp should buy two shovels and pay 2\u00b715 = 30 burles. It is obvious that he can pay this sum without any change. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nprice, change = map(int, input().split())\nans = 1\ntotal = price\nwhile not((total % 10 != 0 and change == total % 10) or (total % 10 == 0)):\n total += price\n ans += 1\n\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '237 7\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '15 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '117 3\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1000 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 8\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1000 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 5\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '998 9\\n', 'output': '5\\n'}, {'type': 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{'type': 'stdin_stdout', 'input': '50 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '11 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10 3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '94 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '19 1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '60 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13 3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '8 13\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '19 2\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '59 1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '13 4\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '12 13\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '20 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '59 2\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '13 6\\n', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79809","program":"```python\nprice, change = map(int, input().split())\nans = 1\ntotal = price\nwhile not((total % 10 != 0 and change == total % 10) or (total % 10 == 0)):\n total += price\n ans += 1\n\nprint(ans)\n\n```","inputs":"237 7\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12707},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"756_B. Travel Card","prompt":"Solve the following coding problem using the programming language python:\n\nA new innovative ticketing systems for public transport is introduced in Bytesburg. Now there is a single travel card for all transport. To make a trip a passenger scan his card and then he is charged according to the fare.\n\nThe fare is constructed in the following manner. There are three types of tickets: \n\n 1. a ticket for one trip costs 20 byteland rubles, \n 2. a ticket for 90 minutes costs 50 byteland rubles, \n 3. a ticket for one day (1440 minutes) costs 120 byteland rubles. \n\n\n\nNote that a ticket for x minutes activated at time t can be used for trips started in time range from t to t + x - 1, inclusive. Assume that all trips take exactly one minute.\n\nTo simplify the choice for the passenger, the system automatically chooses the optimal tickets. After each trip starts, the system analyses all the previous trips and the current trip and chooses a set of tickets for these trips with a minimum total cost. Let the minimum total cost of tickets to cover all trips from the first to the current is a, and the total sum charged before is b. Then the system charges the passenger the sum a - b.\n\nYou have to write a program that, for given trips made by a passenger, calculates the sum the passenger is charged after each trip.\n\nInput\n\nThe first line of input contains integer number n (1 \u2264 n \u2264 105) \u2014 the number of trips made by passenger.\n\nEach of the following n lines contains the time of trip ti (0 \u2264 ti \u2264 109), measured in minutes from the time of starting the system. All ti are different, given in ascending order, i. e. ti + 1 > ti holds for all 1 \u2264 i < n.\n\nOutput\n\nOutput n integers. For each trip, print the sum the passenger is charged after it.\n\nExamples\n\nInput\n\n3\n10\n20\n30\n\n\nOutput\n\n20\n20\n10\n\n\nInput\n\n10\n13\n45\n46\n60\n103\n115\n126\n150\n256\n516\n\n\nOutput\n\n20\n20\n10\n0\n20\n0\n0\n20\n20\n10\n\nNote\n\nIn the first example, the system works as follows: for the first and second trips it is cheaper to pay for two one-trip tickets, so each time 20 rubles is charged, after the third trip the system understands that it would be cheaper to buy a ticket for 90 minutes. This ticket costs 50 rubles, and the passenger had already paid 40 rubles, so it is necessary to charge 10 rubles only.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef lower_bound(arr, left, right, target):\n if arr[right]> 1\n if arr[mid] >= target:\n right = mid\n else:\n left = mid + 1\n return left\n\nT = int(input())\narr = [0] * T\ndp = [0] * (T + 1)\nfor i in range(T):\n arr[i] = int(input())\nfor i in range(T):\n dp[i + 1] = dp[i] + 20\n dp[i + 1] = min(dp[i + 1], dp[lower_bound(arr, 0, T-1, arr[i] - 89)] + 50)\n dp[i + 1] = min(dp[i + 1], dp[lower_bound(arr, 0, T-1, arr[i] - 1439)] + 120)\n print(dp[i + 1] - dp[i])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10\\n13\\n45\\n46\\n60\\n103\\n115\\n126\\n150\\n256\\n516\\n', 'output': '20\\n20\\n10\\n0\\n20\\n0\\n0\\n20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 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'input': '8\\n0\\n2\\n51\\n63\\n73\\n75\\n80\\n90\\n', 'output': '20\\n20\\n10\\n0\\n0\\n0\\n0\\n20\\n'}, {'type': 'stdin_stdout', 'input': '7\\n100\\n138\\n279\\n308\\n396\\n697\\n821\\n', 'output': '20\\n20\\n20\\n20\\n20\\n20\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10\\n20\\n29\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n20\\n30\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n4\\n30\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6\\n20\\n53\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3\\n8\\n30\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10\\n23\\n90\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n16\\n30\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n12\\n60\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '7\\n100\\n168\\n279\\n308\\n396\\n697\\n821\\n', 'output': '20\\n20\\n20\\n20\\n20\\n20\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10\\n28\\n29\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n20\\n37\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n14\\n30\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6\\n21\\n53\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n8\\n30\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n16\\n30\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n22\\n60\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n5\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '7\\n100\\n155\\n279\\n308\\n396\\n697\\n821\\n', 'output': '20\\n20\\n20\\n20\\n20\\n20\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n20\\n28\\n29\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1\\n14\\n30\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5\\n21\\n53\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n6\\n30\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n22\\n45\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '7\\n101\\n155\\n279\\n308\\n396\\n697\\n821\\n', 'output': '20\\n20\\n20\\n20\\n20\\n20\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7\\n21\\n53\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n6\\n7\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n3\\n45\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n17\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '7\\n101\\n155\\n279\\n303\\n396\\n697\\n821\\n', 'output': '20\\n20\\n20\\n20\\n20\\n20\\n0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n12\\n21\\n53\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0\\n6\\n7\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2\\n3\\n82\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n11\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0\\n6\\n11\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n12\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0\\n4\\n11\\n', 'output': '20\\n20\\n10\\n'}, {'type': 'stdin_stdout', 'input': '1\\n24\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8\\n', 'output': '20\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79813","program":"```python\ndef lower_bound(arr, left, right, target):\n if arr[right]> 1\n if arr[mid] >= target:\n right = mid\n else:\n left = mid + 1\n return left\n\nT = int(input())\narr = [0] * T\ndp = [0] * (T + 1)\nfor i in range(T):\n arr[i] = int(input())\nfor i in range(T):\n dp[i + 1] = dp[i] + 20\n dp[i + 1] = min(dp[i + 1], dp[lower_bound(arr, 0, T-1, arr[i] - 89)] + 50)\n dp[i + 1] = min(dp[i + 1], dp[lower_bound(arr, 0, T-1, arr[i] - 1439)] + 120)\n print(dp[i + 1] - dp[i])\n```","inputs":"10\n13\n45\n46\n60\n103\n115\n126\n150\n256\n516\n","output":"20\n20\n10\n0\n20\n0\n0\n20\n20\n10\n","actual_output":"20\n20\n10\n0\n20\n0\n0\n20\n20\n10\n","execution_success":true,"sample_index":12708},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"777_C. Alyona and Spreadsheet","prompt":"Solve the following coding problem using the programming language python:\n\nDuring the lesson small girl Alyona works with one famous spreadsheet computer program and learns how to edit tables.\n\nNow she has a table filled with integers. The table consists of n rows and m columns. By ai, j we will denote the integer located at the i-th row and the j-th column. We say that the table is sorted in non-decreasing order in the column j if ai, j \u2264 ai + 1, j for all i from 1 to n - 1.\n\nTeacher gave Alyona k tasks. For each of the tasks two integers l and r are given and Alyona has to answer the following question: if one keeps the rows from l to r inclusive and deletes all others, will the table be sorted in non-decreasing order in at least one column? Formally, does there exist such j that ai, j \u2264 ai + 1, j for all i from l to r - 1 inclusive.\n\nAlyona is too small to deal with this task and asks you to help!\n\nInput\n\nThe first line of the input contains two positive integers n and m (1 \u2264 n\u00b7m \u2264 100 000) \u2014 the number of rows and the number of columns in the table respectively. Note that your are given a constraint that bound the product of these two integers, i.e. the number of elements in the table.\n\nEach of the following n lines contains m integers. The j-th integers in the i of these lines stands for ai, j (1 \u2264 ai, j \u2264 109).\n\nThe next line of the input contains an integer k (1 \u2264 k \u2264 100 000) \u2014 the number of task that teacher gave to Alyona.\n\nThe i-th of the next k lines contains two integers li and ri (1 \u2264 li \u2264 ri \u2264 n).\n\nOutput\n\nPrint \"Yes\" to the i-th line of the output if the table consisting of rows from li to ri inclusive is sorted in non-decreasing order in at least one column. Otherwise, print \"No\".\n\nExample\n\nInput\n\n5 4\n1 2 3 5\n3 1 3 2\n4 5 2 3\n5 5 3 2\n4 4 3 4\n6\n1 1\n2 5\n4 5\n3 5\n1 3\n1 5\n\n\nOutput\n\nYes\nNo\nYes\nYes\nYes\nNo\n\nNote\n\nIn the sample, the whole table is not sorted in any column. However, rows 1\u20133 are sorted in column 1, while rows 4\u20135 are sorted in column 3.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys, os\nfrom io import BytesIO, IOBase\nfrom math import floor, gcd, fabs, factorial, fmod, sqrt, inf, log\nfrom collections import defaultdict as dd, deque\nfrom heapq import merge, heapify, heappop, heappush, nsmallest\nfrom bisect import bisect_left as bl, bisect_right as br, bisect\n\n# region fastio\nBUFSIZE = 8192\n \nclass FastIO(IOBase):\n newlines = 0\n \n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n \n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n \n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n \n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n \nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\nstdin, stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) \n\nmod = pow(10, 9) + 7\nmod2 = 998244353\n \ndef inp(): return stdin.readline().strip()\ndef iinp(): return int(inp())\ndef out(var, end=\"\\n\"): stdout.write(str(var)+\"\\n\")\ndef outa(*var, end=\"\\n\"): stdout.write(' '.join(map(str, var)) + end)\ndef lmp(): return list(mp())\ndef mp(): return map(int, inp().split())\ndef l1d(n, val=0): return [val for i in range(n)]\ndef l2d(n, m, val=0): return [l1d(m, val) for j in range(n)]\ndef ceil(a, b): return (a+b-1)//b\nS1 = 'abcdefghijklmnopqrstuvwxyz'\nS2 = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'\ndef isprime(x):\n if x<=1: return False\n if x in (2, 3): return True\n if x%2 == 0: return False\n for i in range(3, int(sqrt(x))+1, 2):\n if x%i == 0: return False\n return True\n \nn, m = mp()\nml = [lmp() for i in range(n)]\nmaxEnd = dd(int)\nfor j in range(m):\n c = 1\n for i in range(1, n):\n if ml[i][j] < ml[i-1][j]:\n for x in range(i-c, i):\n maxEnd[x] = max(i, maxEnd[x])\n c = 1\n else:\n c += 1\n for x in range(n-c, n):\n maxEnd[x] = max(n, maxEnd[x]) \n\nk = iinp()\nfor i in range(k):\n l, r = mp()\n l-=1\n print(\"Yes\" if maxEnd[l] >= r else \"No\")\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n5 5 3 2\\n4 4 3 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n523130301\\n127101624\\n15573616\\n703140639\\n628818570\\n957494759\\n161270109\\n386865653\\n67832626\\n53360557\\n17\\n4 5\\n4 7\\n8 8\\n9 9\\n3 9\\n8 10\\n8 9\\n7 9\\n4 5\\n2 9\\n4 6\\n2 4\\n2 6\\n4 6\\n7 9\\n2 4\\n8 10\\n', 'output': 'No\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n4 6\\n1 7\\n4 4\\n1 6\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n3 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1\\n1\\n1 1\\n', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '15 1\\n556231456\\n573340933\\n626155933\\n397229387\\n10255952\\n376567394\\n906742013\\n269437009\\n31298788\\n712285290\\n620239975\\n379221898\\n229140718\\n95080095\\n997123854\\n18\\n5 15\\n1 12\\n4 10\\n2 15\\n12 15\\n15 15\\n2 2\\n15 15\\n15 15\\n13 13\\n10 14\\n3 6\\n14 15\\n3 6\\n4 4\\n14 15\\n12 14\\n1 9\\n', 'output': 'No\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n870535974\\n127101624\\n15573616\\n703140639\\n628818570\\n957494759\\n161270109\\n386865653\\n67832626\\n53360557\\n17\\n4 5\\n4 7\\n8 8\\n9 9\\n3 9\\n8 10\\n8 9\\n7 9\\n4 5\\n2 9\\n4 6\\n2 4\\n2 6\\n4 6\\n7 9\\n2 4\\n8 10\\n', 'output': 'No\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n3 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 1\\n556231456\\n573340933\\n626155933\\n397229387\\n10255952\\n376567394\\n906742013\\n269437009\\n31298788\\n970882498\\n620239975\\n379221898\\n229140718\\n95080095\\n997123854\\n18\\n5 15\\n1 12\\n4 10\\n2 15\\n12 15\\n15 15\\n2 2\\n15 15\\n15 15\\n13 13\\n10 14\\n3 6\\n14 15\\n3 6\\n4 4\\n14 15\\n12 14\\n1 9\\n', 'output': 'No\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n5 5 3 2\\n4 4 4 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n4 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n2 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n4 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n2 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n10 11\\n1 2\\n9 11\\n2 6\\n4 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n4 5 4 2\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 2\\n5 5 3 2\\n4 4 3 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n3 7\\n11 11\\n2 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n2 2\\n9 11\\n2 6\\n3 7\\n11 11\\n2 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 6\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n1 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n4 7\\n11 11\\n6 6\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 9\\n3 0 3 2\\n0 5 2 3\\n5 10 4 2\\n4 4 4 4\\n6\\n1 1\\n4 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n2\\n1\\n1 1\\n', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n7 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n3 7\\n11 11\\n2 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 6\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n4 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 2\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n5 5 4 2\\n4 4 4 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n5 5 4 2\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n5 5 4 2\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n838773455\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n2 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n10 11\\n1 2\\n9 11\\n2 6\\n4 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n5 5 2 3\\n4 5 4 2\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n5 5 2 3\\n4 5 4 2\\n4 3 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n5 5 3 3\\n4 5 4 2\\n4 3 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n523130301\\n127101624\\n15573616\\n703140639\\n628818570\\n957494759\\n161270109\\n386865653\\n67832626\\n53360557\\n17\\n4 5\\n4 7\\n8 8\\n9 9\\n3 9\\n3 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'No\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 6\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n4 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 9\\n3 1 3 2\\n4 5 2 3\\n5 5 4 2\\n4 4 4 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n4 0 4 2\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 2 3 2\\n5 5 2 3\\n4 5 4 2\\n4 3 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n5 5 3 3\\n4 5 4 2\\n4 3 0 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n523130301\\n127101624\\n15573616\\n703140639\\n628818570\\n957494759\\n161270109\\n386865653\\n67832626\\n53360557\\n17\\n4 5\\n4 7\\n8 8\\n9 9\\n3 9\\n3 10\\n8 9\\n7 9\\n4 5\\n2 9\\n4 6\\n2 4\\n1 6\\n4 6\\n7 9\\n2 4\\n8 10\\n', 'output': 'No\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 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'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 9\\n3 0 3 2\\n4 5 2 3\\n5 5 4 2\\n4 4 4 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n4 0 4 0\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n5 5 3 3\\n4 5 4 2\\n4 3 -1 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 7\\n3 1 3 2\\n4 6 2 2\\n5 5 3 2\\n4 4 3 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 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1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 9\\n3 0 3 2\\n4 5 2 3\\n5 10 4 2\\n4 4 4 4\\n6\\n1 1\\n4 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n4 0 4 1\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 4\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 8 2 3\\n4 0 4 1\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 4\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 13\\n3 0 3 2\\n0 5 2 3\\n5 10 4 2\\n4 4 4 4\\n6\\n1 1\\n4 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 4\\n3 1 3 2\\n4 8 2 3\\n4 0 4 1\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 4\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 13\\n3 0 3 2\\n0 5 4 3\\n5 10 4 2\\n4 4 4 4\\n6\\n1 1\\n4 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 4\\n3 1 3 2\\n4 8 2 4\\n4 0 4 1\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 4\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 13\\n3 0 3 2\\n0 5 4 3\\n5 10 4 2\\n4 4 4 4\\n6\\n1 1\\n4 5\\n2 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 3 3 4\\n3 1 3 2\\n4 8 2 4\\n4 0 4 1\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 4\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 13\\n3 0 3 2\\n1 5 4 3\\n5 10 4 2\\n4 4 4 4\\n6\\n1 1\\n4 5\\n2 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 13\\n3 0 3 2\\n1 5 4 3\\n5 10 4 2\\n4 4 4 4\\n6\\n1 2\\n4 5\\n2 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 13\\n3 0 3 2\\n1 5 4 3\\n7 10 4 2\\n4 4 4 4\\n6\\n1 2\\n4 5\\n2 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n4 6\\n1 7\\n4 4\\n1 4\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n3 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '15 1\\n556231456\\n573340933\\n626155933\\n397229387\\n10255952\\n376567394\\n906742013\\n269437009\\n31298788\\n712285290\\n620239975\\n107732076\\n229140718\\n95080095\\n997123854\\n18\\n5 15\\n1 12\\n4 10\\n2 15\\n12 15\\n15 15\\n2 2\\n15 15\\n15 15\\n13 13\\n10 14\\n3 6\\n14 15\\n3 6\\n4 4\\n14 15\\n12 14\\n1 9\\n', 'output': 'No\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n94046223\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n4 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n3 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 0 3 2\\n4 5 2 3\\n5 5 3 2\\n4 4 4 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 1 2\\n4 5 2 3\\n5 5 4 2\\n4 4 4 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n2 7\\n10 11\\n1 9\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n5 11\\n1 2\\n9 11\\n2 6\\n4 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n697044413\\n894369800\\n812743722\\n23684788\\n466526046\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 3\\n2 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n10 11\\n1 2\\n9 11\\n2 6\\n4 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 2 3 2\\n4 5 2 3\\n5 5 4 2\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '11 1\\n501465490\\n366941771\\n415080944\\n385243536\\n445132523\\n838773455\\n894369800\\n812743722\\n23684788\\n910458117\\n953916313\\n45\\n2 4\\n8 9\\n7 7\\n4 9\\n2 9\\n2 11\\n4 4\\n5 7\\n1 2\\n5 10\\n5 6\\n1 7\\n4 4\\n1 6\\n2 7\\n10 11\\n1 8\\n6 11\\n8 8\\n8 10\\n1 1\\n5 10\\n9 10\\n6 9\\n6 11\\n1 1\\n9 9\\n10 11\\n1 2\\n9 11\\n2 6\\n4 7\\n11 11\\n6 7\\n11 11\\n7 8\\n5 8\\n11 11\\n5 6\\n4 5\\n2 6\\n5 10\\n9 9\\n1 1\\n1 1\\n', 'output': 'No\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n4 5 4 2\\n4 3 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n5 5 2 3\\n4 5 4 2\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n2 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n5 5 3 3\\n4 5 4 3\\n4 3 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n523130301\\n127101624\\n15573616\\n703140639\\n628818570\\n957494759\\n161270109\\n386865653\\n67832626\\n53360557\\n17\\n4 5\\n4 7\\n8 8\\n9 9\\n3 9\\n3 10\\n2 9\\n7 9\\n4 5\\n2 9\\n4 6\\n2 4\\n2 6\\n4 6\\n7 9\\n2 4\\n8 10\\n', 'output': 'No\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '15 1\\n556231456\\n1125310574\\n626155933\\n397229387\\n10255952\\n376567394\\n906742013\\n269437009\\n31298788\\n712285290\\n620239975\\n379221898\\n229140718\\n95080095\\n997123854\\n18\\n5 15\\n1 12\\n4 10\\n4 15\\n12 15\\n15 15\\n2 2\\n15 15\\n15 15\\n13 13\\n10 14\\n3 6\\n14 15\\n3 6\\n4 4\\n14 15\\n12 14\\n1 9\\n', 'output': 'No\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n2 2 3 5\\n3 1 3 2\\n4 5 2 2\\n5 5 3 2\\n4 4 3 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n870535974\\n127101624\\n4010521\\n703140639\\n628818570\\n957494759\\n161270109\\n386865653\\n67832626\\n49258033\\n17\\n4 5\\n4 7\\n8 8\\n9 9\\n3 9\\n8 10\\n8 9\\n7 9\\n4 5\\n2 9\\n4 6\\n2 4\\n2 6\\n4 6\\n7 9\\n2 4\\n8 10\\n', 'output': 'No\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 9\\n3 1 3 2\\n4 5 2 3\\n5 5 4 2\\n4 4 4 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n2 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 5 2 3\\n4 0 4 1\\n4 4 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n6 2 3 2\\n5 5 2 3\\n4 5 4 2\\n4 3 4 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n5 5 3 3\\n4 0 4 2\\n4 3 0 5\\n6\\n1 1\\n2 5\\n4 5\\n5 5\\n1 3\\n1 5\\n', 'output': 'Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n523130301\\n127101624\\n15573616\\n703140639\\n628818570\\n957494759\\n161270109\\n386865653\\n67832626\\n53360557\\n17\\n4 5\\n4 7\\n8 8\\n9 9\\n3 9\\n1 10\\n8 9\\n7 9\\n4 5\\n2 9\\n4 6\\n2 4\\n1 6\\n4 6\\n7 9\\n2 4\\n8 10\\n', 'output': 'No\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 5\\n3 1 3 2\\n4 6 2 2\\n5 5 3 2\\n4 4 3 4\\n6\\n1 1\\n2 5\\n4 5\\n3 5\\n1 3\\n2 5\\n', 'output': 'Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79817","program":"```python\nimport sys, os\nfrom io import BytesIO, IOBase\nfrom math import floor, gcd, fabs, factorial, fmod, sqrt, inf, log\nfrom collections import defaultdict as dd, deque\nfrom heapq import merge, heapify, heappop, heappush, nsmallest\nfrom bisect import bisect_left as bl, bisect_right as br, bisect\n\n# region fastio\nBUFSIZE = 8192\n \nclass FastIO(IOBase):\n newlines = 0\n \n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n \n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n \n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n \n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n \nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\nstdin, stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) \n\nmod = pow(10, 9) + 7\nmod2 = 998244353\n \ndef inp(): return stdin.readline().strip()\ndef iinp(): return int(inp())\ndef out(var, end=\"\\n\"): stdout.write(str(var)+\"\\n\")\ndef outa(*var, end=\"\\n\"): stdout.write(' '.join(map(str, var)) + end)\ndef lmp(): return list(mp())\ndef mp(): return map(int, inp().split())\ndef l1d(n, val=0): return [val for i in range(n)]\ndef l2d(n, m, val=0): return [l1d(m, val) for j in range(n)]\ndef ceil(a, b): return (a+b-1)//b\nS1 = 'abcdefghijklmnopqrstuvwxyz'\nS2 = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'\ndef isprime(x):\n if x<=1: return False\n if x in (2, 3): return True\n if x%2 == 0: return False\n for i in range(3, int(sqrt(x))+1, 2):\n if x%i == 0: return False\n return True\n \nn, m = mp()\nml = [lmp() for i in range(n)]\nmaxEnd = dd(int)\nfor j in range(m):\n c = 1\n for i in range(1, n):\n if ml[i][j] < ml[i-1][j]:\n for x in range(i-c, i):\n maxEnd[x] = max(i, maxEnd[x])\n c = 1\n else:\n c += 1\n for x in range(n-c, n):\n maxEnd[x] = max(n, maxEnd[x]) \n\nk = iinp()\nfor i in range(k):\n l, r = mp()\n l-=1\n print(\"Yes\" if maxEnd[l] >= r else \"No\")\n```","inputs":"5 4\n1 2 3 5\n3 1 3 2\n4 5 2 3\n5 5 3 2\n4 4 3 4\n6\n1 1\n2 5\n4 5\n3 5\n1 3\n1 5\n","output":"Yes\nNo\nYes\nYes\nYes\nNo\n","actual_output":"Yes\nNo\nYes\nYes\nYes\nNo\n","execution_success":true,"sample_index":12709},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"802_A. Heidi and Library (easy)","prompt":"Solve the following coding problem using the programming language python:\n\nYour search for Heidi is over \u2013 you finally found her at a library, dressed up as a human. In fact, she has spent so much time there that she now runs the place! Her job is to buy books and keep them at the library so that people can borrow and read them. There are n different books, numbered 1 through n.\n\nWe will look at the library's operation during n consecutive days. Heidi knows in advance that on the i-th day (1 \u2264 i \u2264 n) precisely one person will come to the library, request to borrow the book ai, read it in a few hours, and return the book later on the same day.\n\nHeidi desperately wants to please all her guests, so she will make sure to always have the book ai available in the library on the i-th day. During the night before the i-th day, she has the option of going to the bookstore (which operates at nights to avoid competition with the library) and buying any book for the price of 1 CHF. Of course, if she already has a book at the library, she does not need to buy it again. Initially, the library contains no books.\n\nThere is a problem, though. The capacity of the library is k \u2013 this means that at any time, there can be at most k books at the library. If buying a new book would cause Heidi to have more than k books, she must first get rid of some book that she already has, in order to make room for the new book. If she later needs a book that she got rid of, she will need to buy that book again.\n\nYou are given k and the sequence of requests for books a1, a2, ..., an. What is the minimum cost (in CHF) of buying new books to satisfy all the requests?\n\nInput\n\nThe first line of input will contain two integers n and k (1 \u2264 n, k \u2264 80). The second line will contain n integers a1, a2, ..., an (1 \u2264 ai \u2264 n) \u2013 the sequence of book requests.\n\nOutput\n\nOn a single line print the minimum cost of buying books at the store so as to satisfy all requests.\n\nExamples\n\nInput\n\n4 80\n1 2 2 1\n\n\nOutput\n\n2\n\n\nInput\n\n4 1\n1 2 2 1\n\n\nOutput\n\n3\n\n\nInput\n\n4 2\n1 2 3 1\n\n\nOutput\n\n3\n\nNote\n\nIn the first test case, Heidi is able to keep all books forever. Therefore, she only needs to buy the book 1 before the first day and the book 2 before the second day.\n\nIn the second test case, she can only keep one book at a time. Therefore she will need to buy new books on the first, second and fourth day.\n\nIn the third test case, before buying book 3 on the third day, she must decide which of the books 1 and 2 she should get rid of. Of course, she should keep the book 1, which will be requested on the fourth day.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,k=map(int,input().split())\na=list(map(int,input().split()))\nz=[0]*81\nkz,ans=0,0\nfor i in range(n):\n if z[a[i]]: continue\n ans+=1\n if k>kz:\n z[a[i]]=1; kz+=1\n else:\n h=-1\n for j in range(1,n+1):\n if z[j]:\n m=n+1\n for p in range(i,n):\n if j==a[p]:\n m=p\n break\n if m>h:\n h=m;\n t=j\n z[t]=0\n z[a[i]]=1\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 2\\n1 2 3 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 80\\n1 2 2 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 2 2 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '80 32\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14\\n', 'output': '34\\n'}, {'type': 'stdin_stdout', 'input': '80 8\\n8 72 32 27 27 20 69 28 77 25 8 4 75 11 41 71 57 17 45 65 79 8 61 15 24 80 39 36 34 13 76 37 16 71 64 77 11 58 30 26 61 23 18 30 68 65 12 47 69 65 3 55 71 3 32 4 20 39 47 25 75 49 34 60 48 56 77 70 59 59 75 6 5 23 55 30 62 66 4 4\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '80 16\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '80 4\\n10 19 20 18 16 7 13 18 15 5 7 13 16 8 14 8 3 15 19 19 7 13 17 9 18 16 4 14 10 18 1 3 5 3 20 18 9 4 17 19 13 20 16 12 15 5 5 18 17 16 4 5 20 10 18 4 7 19 10 15 8 15 17 3 10 16 19 2 6 6 3 12 10 7 15 3 17 15 6 8\\n', 'output': '49\\n'}, {'type': 'stdin_stdout', 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'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79821","program":"```python\nn,k=map(int,input().split())\na=list(map(int,input().split()))\nz=[0]*81\nkz,ans=0,0\nfor i in range(n):\n if z[a[i]]: continue\n ans+=1\n if k>kz:\n z[a[i]]=1; kz+=1\n else:\n h=-1\n for j in range(1,n+1):\n if z[j]:\n m=n+1\n for p in range(i,n):\n if j==a[p]:\n m=p\n break\n if m>h:\n h=m;\n t=j\n z[t]=0\n z[a[i]]=1\nprint(ans)\n\n```","inputs":"4 2\n1 2 3 1\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12710},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"822_C. Hacker, pack your bags!","prompt":"Solve the following coding problem using the programming language python:\n\nIt's well known that the best way to distract from something is to do one's favourite thing. Job is such a thing for Leha.\n\nSo the hacker began to work hard in order to get rid of boredom. It means that Leha began to hack computers all over the world. For such zeal boss gave the hacker a vacation of exactly x days. You know the majority of people prefer to go somewhere for a vacation, so Leha immediately went to the travel agency. There he found out that n vouchers left. i-th voucher is characterized by three integers li, ri, costi \u2014 day of departure from Vi\u010dkopolis, day of arriving back in Vi\u010dkopolis and cost of the voucher correspondingly. The duration of the i-th voucher is a value ri - li + 1.\n\nAt the same time Leha wants to split his own vocation into two parts. Besides he wants to spend as little money as possible. Formally Leha wants to choose exactly two vouchers i and j (i \u2260 j) so that they don't intersect, sum of their durations is exactly x and their total cost is as minimal as possible. Two vouchers i and j don't intersect if only at least one of the following conditions is fulfilled: ri < lj or rj < li.\n\nHelp Leha to choose the necessary vouchers!\n\nInput\n\nThe first line contains two integers n and x (2 \u2264 n, x \u2264 2\u00b7105) \u2014 the number of vouchers in the travel agency and the duration of Leha's vacation correspondingly.\n\nEach of the next n lines contains three integers li, ri and costi (1 \u2264 li \u2264 ri \u2264 2\u00b7105, 1 \u2264 costi \u2264 109) \u2014 description of the voucher.\n\nOutput\n\nPrint a single integer \u2014 a minimal amount of money that Leha will spend, or print - 1 if it's impossible to choose two disjoint vouchers with the total duration exactly x.\n\nExamples\n\nInput\n\n4 5\n1 3 4\n1 2 5\n5 6 1\n1 2 4\n\n\nOutput\n\n5\n\n\nInput\n\n3 2\n4 6 3\n2 4 1\n3 5 4\n\n\nOutput\n\n-1\n\nNote\n\nIn the first sample Leha should choose first and third vouchers. Hereupon the total duration will be equal to (3 - 1 + 1) + (6 - 5 + 1) = 5 and the total cost will be 4 + 1 = 5.\n\nIn the second sample the duration of each voucher is 3 therefore it's impossible to choose two vouchers with the total duration equal to 2.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom bisect import bisect_left\nf = lambda: map(int, input().split())\nn, x = f()\ns, t = {}, {}\nfor i in range(n):\n l, r, c = f()\n d = r - l\n if d not in s: s[d] = []\n s[d].append((l, c))\nfor d, p in s.items():\n p.sort(key=lambda q: q[0])\n q = t[d] = [[l, c] for l, c in p]\n for i in range(1, len(q))[::-1]:\n q[i - 1][1] = min(q[i - 1][1], q[i][1])\nm = 3e9\nfor d in s:\n p = t.get(x - 2 - d, [])\n if p:\n for l, c in s[d]:\n i = bisect_left(p, [l + d + 1, 0])\n if i < len(p): m = min(m, c + p[i][1])\nprint(-1 if m == 3e9 else m)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 5\\n1 3 4\\n1 2 5\\n5 6 1\\n1 2 4\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '3 2\\n4 6 3\\n2 4 1\\n3 5 4\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '2 2\\n1 1 1000000000\\n2 2 1000\\n', 'output': '1000001000'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 1 2\\n1 1 3\\n2 3 3\\n2 3 4\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '3 3\\n11 11 2\\n3 4 3\\n8 9 2\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 500000000\\n1 2 500000000\\n5 6 500000000\\n1 2 500000000\\n', 'output': '1000000000'}, {'type': 'stdin_stdout', 'input': '2 5\\n1 3 1000000000\\n4 5 1000000000\\n', 'output': '2000000000'}, {'type': 'stdin_stdout', 'input': '2 2\\n1 1 1000000000\\n2 2 7\\n', 'output': '1000000007'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 2 2\\n1 2 5\\n3 5 6\\n3 5 8\\n', 'output': '8'}, {'type': 'stdin_stdout', 'input': '15 7\\n16 18 6\\n11 15 2\\n5 17 3\\n4 5 1\\n3 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s[d].append((l, c))\nfor d, p in s.items():\n p.sort(key=lambda q: q[0])\n q = t[d] = [[l, c] for l, c in p]\n for i in range(1, len(q))[::-1]:\n q[i - 1][1] = min(q[i - 1][1], q[i][1])\nm = 3e9\nfor d in s:\n p = t.get(x - 2 - d, [])\n if p:\n for l, c in s[d]:\n i = bisect_left(p, [l + d + 1, 0])\n if i < len(p): m = min(m, c + p[i][1])\nprint(-1 if m == 3e9 else m)\n```","inputs":"4 5\n1 3 4\n1 2 5\n5 6 1\n1 2 4\n","output":"5","actual_output":"5\n","execution_success":true,"sample_index":12711},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"847_H. Load Testing","prompt":"Solve the following coding problem using the programming language python:\n\nPolycarp plans to conduct a load testing of its new project Fakebook. He already agreed with his friends that at certain points in time they will send requests to Fakebook. The load testing will last n minutes and in the i-th minute friends will send ai requests.\n\nPolycarp plans to test Fakebook under a special kind of load. In case the information about Fakebook gets into the mass media, Polycarp hopes for a monotone increase of the load, followed by a monotone decrease of the interest to the service. Polycarp wants to test this form of load.\n\nYour task is to determine how many requests Polycarp must add so that before some moment the load on the server strictly increases and after that moment strictly decreases. Both the increasing part and the decreasing part can be empty (i. e. absent). The decrease should immediately follow the increase. In particular, the load with two equal neigbouring values is unacceptable.\n\nFor example, if the load is described with one of the arrays [1, 2, 8, 4, 3], [1, 3, 5] or [10], then such load satisfies Polycarp (in each of the cases there is an increasing part, immediately followed with a decreasing part). If the load is described with one of the arrays [1, 2, 2, 1], [2, 1, 2] or [10, 10], then such load does not satisfy Polycarp.\n\nHelp Polycarp to make the minimum number of additional requests, so that the resulting load satisfies Polycarp. He can make any number of additional requests at any minute from 1 to n.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 100 000) \u2014 the duration of the load testing.\n\nThe second line contains n integers a1, a2, ..., an (1 \u2264 ai \u2264 109), where ai is the number of requests from friends in the i-th minute of the load testing.\n\nOutput\n\nPrint the minimum number of additional requests from Polycarp that would make the load strictly increasing in the beginning and then strictly decreasing afterwards.\n\nExamples\n\nInput\n\n5\n1 4 3 2 5\n\n\nOutput\n\n6\n\n\nInput\n\n5\n1 2 2 2 1\n\n\nOutput\n\n1\n\n\nInput\n\n7\n10 20 40 50 70 90 30\n\n\nOutput\n\n0\n\nNote\n\nIn the first example Polycarp must make two additional requests in the third minute and four additional requests in the fourth minute. So the resulting load will look like: [1, 4, 5, 6, 5]. In total, Polycarp will make 6 additional requests.\n\nIn the second example it is enough to make one additional request in the third minute, so the answer is 1.\n\nIn the third example the load already satisfies all conditions described in the statement, so the answer is 0.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\n\na = list(map(int, input().split()))\n\nlp,rp = [0 for i in range(n)],[0 for i in range(n)]\nlnr, rnr = [a[i] for i in range(n)],[a[i] for i in range(n)]\nmx = a[0]\nfor i in range(1,n):\n if a[i] > mx:\n mx = a[i]\n lp[i] = lp[i-1]\n else:\n mx += 1\n lp[i] = lp[i-1] + mx - a[i]\n lnr[i] = mx\n\nmx = a[-1]\nfor i in range(n-2,-1,-1):\n if a[i] > mx:\n mx = a[i]\n rp[i] = rp[i+1]\n else:\n mx += 1\n rp[i] = rp[i+1] + mx - a[i]\n rnr[i] = mx\n \nans = min(rp[0], lp[-1])\nfor i in range(1,n-1):\n ca = lp[i-1] + rp[i+1]\n if max(lnr[i-1], rnr[i+1]) + 1 > a[i]:\n ca += max(lnr[i-1], rnr[i+1]) + 1 - a[i]\n ans = min(ans, ca)\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 4 3 2 5\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 2 2 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n10 20 40 50 70 90 30\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 15\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4\\n36 54 55 9\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n984181411 215198610 969039668 60631313 85746445\\n', 'output': '778956192\\n'}, {'type': 'stdin_stdout', 'input': '10\\n12528139 986722043 1595702 997595062 997565216 997677838 999394520 999593240 772077 998195916\\n', 'output': '1982580029\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '100\\n9997 9615 4045 2846 7656 2941 2233 9214 837 2369 5832 578 6146 8773 164 7303 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lp[i-1] + mx - a[i]\n lnr[i] = mx\n\nmx = a[-1]\nfor i in range(n-2,-1,-1):\n if a[i] > mx:\n mx = a[i]\n rp[i] = rp[i+1]\n else:\n mx += 1\n rp[i] = rp[i+1] + mx - a[i]\n rnr[i] = mx\n \nans = min(rp[0], lp[-1])\nfor i in range(1,n-1):\n ca = lp[i-1] + rp[i+1]\n if max(lnr[i-1], rnr[i+1]) + 1 > a[i]:\n ca += max(lnr[i-1], rnr[i+1]) + 1 - a[i]\n ans = min(ans, ca)\nprint(ans)\n```","inputs":"5\n1 4 3 2 5\n","output":"6\n","actual_output":"6\n","execution_success":true,"sample_index":12712},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"869_C. The Intriguing Obsession","prompt":"Solve the following coding problem using the programming language python:\n\n\u2014 This is not playing but duty as allies of justice, Nii-chan!\n\n\u2014 Not allies but justice itself, Onii-chan!\n\nWith hands joined, go everywhere at a speed faster than our thoughts! This time, the Fire Sisters \u2014 Karen and Tsukihi \u2014 is heading for somewhere they've never reached \u2014 water-surrounded islands!\n\nThere are three clusters of islands, conveniently coloured red, blue and purple. The clusters consist of a, b and c distinct islands respectively.\n\nBridges have been built between some (possibly all or none) of the islands. A bridge bidirectionally connects two different islands and has length 1. For any two islands of the same colour, either they shouldn't be reached from each other through bridges, or the shortest distance between them is at least 3, apparently in order to prevent oddities from spreading quickly inside a cluster.\n\nThe Fire Sisters are ready for the unknown, but they'd also like to test your courage. And you're here to figure out the number of different ways to build all bridges under the constraints, and give the answer modulo 998 244 353. Two ways are considered different if a pair of islands exist, such that there's a bridge between them in one of them, but not in the other.\n\nInput\n\nThe first and only line of input contains three space-separated integers a, b and c (1 \u2264 a, b, c \u2264 5 000) \u2014 the number of islands in the red, blue and purple clusters, respectively.\n\nOutput\n\nOutput one line containing an integer \u2014 the number of different ways to build bridges, modulo 998 244 353.\n\nExamples\n\nInput\n\n1 1 1\n\n\nOutput\n\n8\n\n\nInput\n\n1 2 2\n\n\nOutput\n\n63\n\n\nInput\n\n1 3 5\n\n\nOutput\n\n3264\n\n\nInput\n\n6 2 9\n\n\nOutput\n\n813023575\n\nNote\n\nIn the first example, there are 3 bridges that can possibly be built, and no setup of bridges violates the restrictions. Thus the answer is 23 = 8.\n\nIn the second example, the upper two structures in the figure below are instances of valid ones, while the lower two are invalid due to the blue and purple clusters, respectively.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na,b,c = list(map(int, input().split(' ')))\n\n\nMOD = 998244353\n\ndef d(a, b):\n\ts = 1\n\tfor i in range(a, b+1):\n\t\ts*=i\n\t\ts%=MOD\n\treturn s\n\n\n\n\ndef cnk(n,k):\n\ts = 1\n\tfor i in range(n-k+1, n+1):\n\t\ts*=i\n\tfor i in range(1,k+1):\n\t\ts/=i\n\treturn s\n\n\ndef factorial(n):\n\ts = 1\n\tfor i in range(1, n+1):\n\t\ts*=i\t\n\treturn s\n\n\n\ndef pow(a, b):\n\tc = 1\n\n\twhile b>0:\n\t\tif b%2==0:\n\t\t\tb//=2\n\t\t\ta *=a\n\t\t\ta%=MOD\n\t\telse:\n\t\t\tb-=1\n\t\t\tc*=a\n\t\t\tc%=MOD\n\treturn c\n\n\ndef inv(i):\n\treturn pow(i, MOD-2)\n\"\"\"\ndef factinv(i):\n\n\treturn 1.0/factorial(i)\n\n\"\"\"\nfi = [1, 1]\ndef sp(n, m):\n\ts = 1\n\td1 = 1\n\td2 = 1\n\t#print(d1,d2,\"!\")\n\tfor i in range(1, n+1):\n\t\td1*=n-i+1\n\t\td2*=m-i+1\n\n\t\t#print(i, d1,d2)\n\t\td1%=MOD\n\t\td2%=MOD\n\t\ts+= d1*d2 *(fi[i]%MOD)\n\t\t#print(d1*d2 *(fi[i]%MOD))\n\t\ts%= MOD\n\n\treturn s\n\n\n\ns = 1\nfor i in range(2, max(a,max(b,c))+1):\n\ts *=i\n\ts %= MOD\n\tfi.append(inv(s))\n\n\nprint((sp(a,b)*sp(a,c)*sp(b,c))%MOD)\n#print(sp(1,2))\n#print(sp(2,2))\n#print()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 3 5\\n', 'output': '3264\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '6 2 9\\n', 'output': '813023575\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2\\n', 'output': '63\\n'}, {'type': 'stdin_stdout', 'input': '84 29 61\\n', 'output': '391253501\\n'}, {'type': 'stdin_stdout', 'input': '2048 4096 1024\\n', 'output': '445542375\\n'}, {'type': 'stdin_stdout', 'input': '1 2 3\\n', 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'input': '12 581 771\\n', 'output': '975133168\\n'}, {'type': 'stdin_stdout', 'input': '1925 1379 4\\n', 'output': '550165137\\n'}, {'type': 'stdin_stdout', 'input': '14 9 3\\n', 'output': '748368213\\n'}, {'type': 'stdin_stdout', 'input': '139 68 10\\n', 'output': '269203186\\n'}, {'type': 'stdin_stdout', 'input': '84 22 7\\n', 'output': '163134056\\n'}, {'type': 'stdin_stdout', 'input': '1576 3729 1024\\n', 'output': '286359650\\n'}, {'type': 'stdin_stdout', 'input': '1065 36 102\\n', 'output': '886898595\\n'}, {'type': 'stdin_stdout', 'input': '1 43 1\\n', 'output': '3872\\n'}, {'type': 'stdin_stdout', 'input': '21 46 4\\n', 'output': '349126068\\n'}, {'type': 'stdin_stdout', 'input': '3 3 1\\n', 'output': '544\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79833","program":"```python\na,b,c = list(map(int, input().split(' ')))\n\n\nMOD = 998244353\n\ndef d(a, b):\n\ts = 1\n\tfor i in range(a, b+1):\n\t\ts*=i\n\t\ts%=MOD\n\treturn s\n\n\n\n\ndef cnk(n,k):\n\ts = 1\n\tfor i in range(n-k+1, n+1):\n\t\ts*=i\n\tfor i in range(1,k+1):\n\t\ts/=i\n\treturn s\n\n\ndef factorial(n):\n\ts = 1\n\tfor i in range(1, n+1):\n\t\ts*=i\t\n\treturn s\n\n\n\ndef pow(a, b):\n\tc = 1\n\n\twhile b>0:\n\t\tif b%2==0:\n\t\t\tb//=2\n\t\t\ta *=a\n\t\t\ta%=MOD\n\t\telse:\n\t\t\tb-=1\n\t\t\tc*=a\n\t\t\tc%=MOD\n\treturn c\n\n\ndef inv(i):\n\treturn pow(i, MOD-2)\n\"\"\"\ndef factinv(i):\n\n\treturn 1.0/factorial(i)\n\n\"\"\"\nfi = [1, 1]\ndef sp(n, m):\n\ts = 1\n\td1 = 1\n\td2 = 1\n\t#print(d1,d2,\"!\")\n\tfor i in range(1, n+1):\n\t\td1*=n-i+1\n\t\td2*=m-i+1\n\n\t\t#print(i, d1,d2)\n\t\td1%=MOD\n\t\td2%=MOD\n\t\ts+= d1*d2 *(fi[i]%MOD)\n\t\t#print(d1*d2 *(fi[i]%MOD))\n\t\ts%= MOD\n\n\treturn s\n\n\n\ns = 1\nfor i in range(2, max(a,max(b,c))+1):\n\ts *=i\n\ts %= MOD\n\tfi.append(inv(s))\n\n\nprint((sp(a,b)*sp(a,c)*sp(b,c))%MOD)\n#print(sp(1,2))\n#print(sp(2,2))\n#print()\n```","inputs":"1 3 5\n","output":"3264\n","actual_output":"3264\n","execution_success":true,"sample_index":12713},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"895_B. XK Segments","prompt":"Solve the following coding problem using the programming language python:\n\nWhile Vasya finished eating his piece of pizza, the lesson has already started. For being late for the lesson, the teacher suggested Vasya to solve one interesting problem. Vasya has an array a and integer x. He should find the number of different ordered pairs of indexes (i, j) such that ai \u2264 aj and there are exactly k integers y such that ai \u2264 y \u2264 aj and y is divisible by x.\n\nIn this problem it is meant that pair (i, j) is equal to (j, i) only if i is equal to j. For example pair (1, 2) is not the same as (2, 1).\n\nInput\n\nThe first line contains 3 integers n, x, k (1 \u2264 n \u2264 105, 1 \u2264 x \u2264 109, 0 \u2264 k \u2264 109), where n is the size of the array a and x and k are numbers from the statement.\n\nThe second line contains n integers ai (1 \u2264 ai \u2264 109) \u2014 the elements of the array a.\n\nOutput\n\nPrint one integer \u2014 the answer to the problem.\n\nExamples\n\nInput\n\n4 2 1\n1 3 5 7\n\n\nOutput\n\n3\n\n\nInput\n\n4 2 0\n5 3 1 7\n\n\nOutput\n\n4\n\n\nInput\n\n5 3 1\n3 3 3 3 3\n\n\nOutput\n\n25\n\nNote\n\nIn first sample there are only three suitable pairs of indexes \u2014 (1, 2), (2, 3), (3, 4).\n\nIn second sample there are four suitable pairs of indexes(1, 1), (2, 2), (3, 3), (4, 4).\n\nIn third sample every pair (i, j) is suitable, so the answer is 5 * 5 = 25.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom bisect import bisect_left\nR=lambda:map(int,input().split())\nn,x,k=R()\na=sorted(R())\nz=zip(a,(((u-1)//x+k)*x for u in a))\nprint(sum(bisect_left(a,l+x)-bisect_left(a,max(u,l)) for u,l in z))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 2 1\\n1 3 5 7\\n', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5 3 1\\n3 3 3 3 3\\n', 'output': '25'}, {'type': 'stdin_stdout', 'input': '4 2 0\\n5 3 1 7\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '3 5 0\\n4 4 4\\n', 'output': '9'}, {'type': 'stdin_stdout', 'input': '5 3 4\\n24 13 1 24 24\\n', 'output': '4'}, {'type': 'stdin_stdout', 'input': '1 13 1\\n13\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n1\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '2 1 1000000000\\n1 1000000000\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '100 2 1\\n1 2 2 2 1 2 1 2 2 2 2 1 2 1 1 2 1 2 2 1 1 2 1 1 2 2 1 1 2 1 2 2 2 2 2 1 1 1 2 1 2 1 2 1 2 1 2 2 1 2 2 2 1 1 1 2 2 1 1 2 2 1 1 1 1 1 1 2 2 1 1 2 2 1 2 2 1 2 1 2 2 1 2 1 1 1 2 2 1 1 2 1 2 2 1 1 2 2 2 1\\n', 'output': '5200'}, {'type': 'stdin_stdout', 'input': '1 1000000000 1\\n1000000000\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '2 5 0\\n3 4\\n', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5 3 2\\n2 3 4 5 8\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5 1000000000 1\\n1000000000 1 1 1 1\\n', 'output': '5'}, {'type': 'stdin_stdout', 'input': '2 1000 1000000\\n1 1000000000\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '2 1000000000 1\\n1 1000000000\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '7 3 1\\n3 3 6 9 12 15 18\\n', 'output': '9'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1 3 5 7\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '1 600000000 1\\n500000000\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '4 65536 65536\\n1 2 3 4\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '10 2 1\\n2 2 2 2 2 2 2 1 2 1\\n', 'output': '80'}, {'type': 'stdin_stdout', 'input': '3 6 0\\n3 4 5\\n', 'output': '6'}, {'type': 'stdin_stdout', 'input': '5 1 0\\n10 12 14 20 30\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '6 2 10\\n1 1 1 20 20 20\\n', 'output': '9'}, {'type': 'stdin_stdout', 'input': '3 5 0\\n4 4 8\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1 13 1\\n24\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '7 3 1\\n3 6 6 9 12 15 18\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3 6 0\\n1 4 5\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5 3 1\\n6 3 3 3 3\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '4 2 0\\n5 3 1 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 3 2\\n2 3 6 5 5\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 3 0\\n5 3 1 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3 5 0\\n4 3 4\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5 1000000000 0\\n1000000000 1 1 1 1\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '7 3 1\\n3 3 6 9 9 15 18\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '5 1000000001 0\\n1000000000 1 1 1 1\\n', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '7 3 1\\n3 6 10 9 12 15 18\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '2 2 1000000000\\n1 1000000000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 1000000000 2\\n1000000000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 3 2\\n2 3 4 5 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 1000000001 1\\n1000000000 1 1 1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 1000 1000000\\n2 1000000000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 65536 65536\\n1 2 2 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1 3 5 7\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 26 1\\n24\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 65536 56203\\n1 2 2 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 6 0\\n2 4 5\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1 6 5 7\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 26 1\\n42\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 3 2\\n2 2 6 5 5\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1 6 5 13\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 3 0\\n5 3 1 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1 23 1\\n42\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 3 2\\n2 2 6 5 10\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4 2 3\\n1 6 5 6\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 3 0\\n9 3 1 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1 23 0\\n42\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n2 2 6 5 10\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 2 5\\n1 6 5 6\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 3 0\\n13 3 1 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n2 2 6 5 6\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 2 5\\n2 6 5 6\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 3 0\\n13 3 1 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n1 2 6 5 6\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 1 2\\n1 2 6 8 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 2 2\\n1 2 6 8 6\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 1 4\\n24 13 1 24 24\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 13 2\\n13\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 5 0\\n3 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 1000 1000000\\n1 1000000100\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 1000000000 1\\n1 1000000001\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1 2 5 7\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 757355189 1\\n500000000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 65536 122257\\n1 2 3 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 6 0\\n3 4 8\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '6 2 10\\n1 1 2 20 20 20\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 2 1\\n2 3 5 7\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 6 1\\n3 3 3 3 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 2 1\\n5 3 1 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 5 0\\n4 4 13\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1 13 1\\n48\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1\\n4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 1000000000 4\\n1000000000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 3 2\\n4 3 4 5 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 1 3\\n1 3 5 7\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 5 1\\n6 3 3 3 3\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1 1 2\\n3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 3 2\\n3 3 6 5 5\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 65536 43961\\n1 2 2 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 6 0\\n4 4 5\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1 26 1\\n69\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 3 2\\n1 2 6 5 5\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 23 1\\n34\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 3 1\\n2 2 6 5 10\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1 12 0\\n42\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79837","program":"```python\nfrom bisect import bisect_left\nR=lambda:map(int,input().split())\nn,x,k=R()\na=sorted(R())\nz=zip(a,(((u-1)//x+k)*x for u in a))\nprint(sum(bisect_left(a,l+x)-bisect_left(a,max(u,l)) for u,l in z))\n\n```","inputs":"4 2 1\n1 3 5 7\n","output":"3","actual_output":"3\n","execution_success":true,"sample_index":12714},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"939_D. Love Rescue","prompt":"Solve the following coding problem using the programming language python:\n\nValya and Tolya are an ideal pair, but they quarrel sometimes. Recently, Valya took offense at her boyfriend because he came to her in t-shirt with lettering that differs from lettering on her pullover. Now she doesn't want to see him and Tolya is seating at his room and crying at her photos all day long.\n\nThis story could be very sad but fairy godmother (Tolya's grandmother) decided to help them and restore their relationship. She secretly took Tolya's t-shirt and Valya's pullover and wants to make the letterings on them same. In order to do this, for one unit of mana she can buy a spell that can change some letters on the clothes. Your task is calculate the minimum amount of mana that Tolya's grandmother should spend to rescue love of Tolya and Valya.\n\nMore formally, letterings on Tolya's t-shirt and Valya's pullover are two strings with same length n consisting only of lowercase English letters. Using one unit of mana, grandmother can buy a spell of form (c1, c2) (where c1 and c2 are some lowercase English letters), which can arbitrary number of times transform a single letter c1 to c2 and vise-versa on both Tolya's t-shirt and Valya's pullover. You should find the minimum amount of mana that grandmother should spend to buy a set of spells that can make the letterings equal. In addition you should output the required set of spells. \n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 105) \u2014 the length of the letterings.\n\nThe second line contains a string with length n, consisting of lowercase English letters \u2014 the lettering on Valya's pullover.\n\nThe third line contains the lettering on Tolya's t-shirt in the same format.\n\nOutput\n\nIn the first line output a single integer \u2014 the minimum amount of mana t required for rescuing love of Valya and Tolya.\n\nIn the next t lines output pairs of space-separated lowercase English letters \u2014 spells that Tolya's grandmother should buy. Spells and letters in spells can be printed in any order.\n\nIf there are many optimal answers, output any.\n\nExamples\n\nInput\n\n3\nabb\ndad\n\n\nOutput\n\n2\na d\nb a\n\nInput\n\n8\ndrpepper\ncocacola\n\n\nOutput\n\n7\nl e\ne d\nd c\nc p\np o\no r\nr a\n\nNote\n\nIn first example it's enough to buy two spells: ('a','d') and ('b','a'). Then first letters will coincide when we will replace letter 'a' with 'd'. Second letters will coincide when we will replace 'b' with 'a'. Third letters will coincide when we will at first replace 'b' with 'a' and then 'a' with 'd'.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nlength=int(input())\ns1=input()\ns2=input()\nconnect=[{0},{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11},{12},{13},{14},{15},{16},{17},{18},{19},{20},{21},{22},{23},{24},{25}]\ntot=0\nspells=[]\nfor i in range(0, length):\n l1=ord(s1[i])-97\n l2=ord(s2[i])-97\n if not (l1 in connect[l2]):\n tot=tot+1\n spells.append(s1[i]+\" \"+s2[i])\n x=connect[l1].union(connect[l2])\n connect[l1]=x\n connect[l2]=x\n for i in connect[l1]:\n connect[i]=connect[i].union(connect[l1])\nprint(str(tot))\nfor i in spells:\n print(i)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\nabb\\ndad\\n', 'output': '2\\na d\\nb a\\n'}, {'type': 'stdin_stdout', 'input': '8\\ndrpepper\\ncocacola\\n', 'output': '7\\nd c\\nr o\\np c\\ne a\\np o\\ne l\\nr a\\n'}, {'type': 'stdin_stdout', 'input': '3\\nabb\\ndad\\n', 'output': '2\\na d\\nb a\\n'}, {'type': 'stdin_stdout', 'input': '10\\ndaefcecfae\\nccdaceefca\\n', 'output': '4\\nd c\\na c\\ne d\\nf a\\n'}, {'type': 'stdin_stdout', 'input': '100\\npfkskdknmbxxslokqdliigxyvntsmaziljamlflwllvbhqnzpyvvzirhhhglsskiuogfoytcxjmospipybckwmkjhnfjddweyqqi\\nakvzmboxlcfwccaoknrzrhvqcdqkqnywstmxinqbkftnbjmahrvexoipikkqfjjmasnxofhklxappvufpsyujdtrpjeejhznoeai\\n', 'output': '25\\np a\\nf k\\nk v\\ns z\\nk m\\nd b\\nk o\\nn x\\nm l\\nb c\\nx f\\nx w\\ns c\\nl c\\no a\\nq k\\nl r\\ni z\\ng h\\ny q\\nt q\\nj t\\nh b\\nv e\\nu a\\n'}, {'type': 'stdin_stdout', 'input': '100\\nbltlukvrharrgytdxnbjailgafwdmeowqvwwsadryzquqzvfhjnpkwvgpwvohvjwzafcxqmisgyyuidvvjqljqshflzywmcccksk\\njmgilzxkrvntkvqpsemrmyrasfqrofkwjwfznctwrmegghlhbbomjlojyapmrpkowqhsvwmrccfbnictnntjevynqilptaoharqv\\n', 'output': '25\\nb j\\nl m\\nt g\\nl i\\nu l\\nk z\\nv x\\nr k\\nh r\\na v\\nr n\\nr t\\ny v\\nt q\\nd p\\nx s\\nn e\\nb m\\nj r\\na m\\nw q\\nd r\\nm o\\ne f\\na c\\n'}, {'type': 'stdin_stdout', 'input': '3\\nwhw\\nuuh\\n', 'output': '2\\nw u\\nh u\\n'}, {'type': 'stdin_stdout', 'input': '10\\nfdfbffedbc\\ncfcdddfbed\\n', 'output': '4\\nf c\\nd f\\nb d\\ne f\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbaa\\nbba\\n', 'output': '1\\na b\\n'}, {'type': 'stdin_stdout', 'input': '15\\nxrezbaoiksvhuww\\ndcgcjrkafntbpbl\\n', 'output': '15\\nx d\\nr c\\ne g\\nz c\\nb j\\na r\\no k\\ni a\\nk f\\ns n\\nv t\\nh b\\nu p\\nw b\\nw l\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbab\\naab\\n', 'output': '1\\nb a\\n'}, {'type': 'stdin_stdout', 'input': '1\\nh\\np\\n', 'output': '1\\nh p\\n'}, {'type': 'stdin_stdout', 'input': '242\\nrrrrrrrrrrrrrmmmmmmmmmmmmmgggggggggggggwwwwwwwwwwwwwyyyyyyyyyyyyyhhhhhhhhhhhhhoooooooooooooqqqqqqqqqqqqqjjjjjjjjjjjjjvvvvvvvvvvvvvlllllllllllllnnnnnnnnnnnnnfffffffffffffeeeeeeeeaaaaaaaaiiiiiiiiuuuuuuuuzzzzzzzzbbbbbbbbxxxxxxxxttttttttsscckppdd\\nrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfeaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxtscsckpdpd\\n', 'output': '21\\nr m\\nr g\\nr w\\nr y\\nr h\\nr o\\nr q\\nr j\\nr v\\nr l\\nr n\\nr f\\ne a\\ne i\\ne u\\ne z\\ne b\\ne x\\ne t\\ns c\\np d\\n'}, {'type': 'stdin_stdout', 'input': '2\\nxc\\nda\\n', 'output': '2\\nx d\\nc a\\n'}, {'type': 'stdin_stdout', 'input': '1\\nw\\nl\\n', 'output': '1\\nw l\\n'}, {'type': 'stdin_stdout', 'input': '10\\neaefcecfae\\nccdaceefca\\n', 'output': '4\\ne c\\na c\\ne d\\nf a\\n'}, {'type': 'stdin_stdout', 'input': '100\\niqqyewddjfnhjkmwkcbypipsomjxctyofgouiksslghhhrizvvypznqhbvllwlflmajlizamstnvyxgiildqkolsxxbmnkdkskfp\\nakvzmboxlcfwccaoknrzrhvqcdqkqnywstmxinqbkftnbjmahrvexoipikkqfjjmasnxofhklxappvufpsyujdtrpjeejhznoeai\\n', 'output': '25\\ni a\\nq k\\nq v\\ny z\\ne m\\nw b\\nd o\\nd x\\nj l\\nf c\\nn f\\nh w\\nj c\\nk c\\nm a\\nw o\\nb r\\np r\\ni h\\np v\\ns q\\nt n\\ng t\\nu x\\nz a\\n'}, {'type': 'stdin_stdout', 'input': '100\\nbltlukvrharrgytdxnbjailgafwdmeowqvxwsadryzquqzvfhjnpkwvgpwvohvjwzafcxqmisgyyuidvvjqljqshflzywmcccksk\\njmgilzxkrvntkvqpsemrmyrasfqrofkwjwfznctwrmegghlhbbomjlojyapmrpkowqhsvwmrccfbnictnntjevynqilptaoharqv\\n', 'output': '25\\nb j\\nl m\\nt g\\nl i\\nu l\\nk z\\nv x\\nr k\\nh r\\na v\\nr n\\nr t\\ny v\\nt q\\nd p\\nx s\\nn e\\nb m\\nj r\\na m\\nw q\\nd r\\nm o\\ne f\\na c\\n'}, {'type': 'stdin_stdout', 'input': '3\\nwwh\\nuuh\\n', 'output': '1\\nw u\\n'}, {'type': 'stdin_stdout', 'input': '10\\nfdfbffedbc\\ncfcdddebed\\n', 'output': '4\\nf c\\nd f\\nb d\\nb e\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbaa\\naba\\n', 'output': '1\\nb a\\n'}, {'type': 'stdin_stdout', 'input': '15\\nxrezbaoiksvhuvw\\ndcgcjrkafntbpbl\\n', 'output': '15\\nx d\\nr c\\ne g\\nz c\\nb j\\na r\\no k\\ni a\\nk f\\ns n\\nv t\\nh b\\nu p\\nv b\\nw l\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbab\\naac\\n', 'output': '2\\nb a\\nb c\\n'}, {'type': 'stdin_stdout', 'input': '1\\ng\\np\\n', 'output': '1\\ng p\\n'}, {'type': 'stdin_stdout', 'input': '242\\nrrrrrrrrrrrrrmmmmmmmmmmmmmgggggggggggggwwwwwwwwwwwwwyyyyyyyyyyyyyhhhhhhhhhhhhhoooooooooooooqqqqqqqqqqqqqjjjjjjjjjjjjjvvvvvvvvvvvvvlllllllllllllnnnnnnnnnnnnnfffffffffffffeeeeeeeeaaaaaaaaiiiiiiiiuuuuuuuuzzyzzzzzbbbbbbbbxxxxxxxxttttttttsscckppdd\\nrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfeaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxtscsckpdpd\\n', 'output': '22\\nr m\\nr g\\nr w\\nr y\\nr h\\nr o\\nr q\\nr j\\nr v\\nr l\\nr n\\nr f\\ne a\\ne i\\ne u\\ne z\\ne b\\ne x\\ne t\\ny i\\ns c\\np d\\n'}, {'type': 'stdin_stdout', 'input': '2\\nxc\\nea\\n', 'output': '2\\nx e\\nc a\\n'}, {'type': 'stdin_stdout', 'input': '1\\nv\\nl\\n', 'output': '1\\nv l\\n'}, {'type': 'stdin_stdout', 'input': '8\\ndrpepper\\naocacolc\\n', 'output': '6\\nd a\\nr o\\np c\\ne a\\np o\\ne l\\n'}, {'type': 'stdin_stdout', 'input': '100\\niqqyewddjfnhjkmwkcbyqipsomjxctyofgouiksslghhhrizvvypznqhbvllwlflmajlizamstnvyxgiildqkolsxxbmnkdkskfp\\nakvzmboxlcfwccaoknrzrhvqcdqkqnywstmxinqbkftnbjmahrvexoipikkqfjjmasnxofhklxappvufpsyujdtrpjeejhznoeai\\n', 'output': '25\\ni a\\nq k\\nq v\\ny z\\ne m\\nw b\\nd o\\nd x\\nj l\\nf c\\nn f\\nh w\\nj c\\nk c\\nm a\\nw o\\nb r\\nq r\\ni h\\np v\\ns q\\nt n\\ng t\\nu x\\nz a\\n'}, {'type': 'stdin_stdout', 'input': '3\\nwwh\\nuug\\n', 'output': '2\\nw u\\nh g\\n'}, {'type': 'stdin_stdout', 'input': '10\\nfdfbffedbc\\ncfcdddebdd\\n', 'output': '3\\nf c\\nd f\\nb d\\n'}, {'type': 'stdin_stdout', 'input': '15\\nxrezbaoiksvhuvw\\ndcgcjrkbfntbpbl\\n', 'output': '15\\nx d\\nr c\\ne g\\nz c\\nb j\\na r\\no k\\ni b\\nk f\\ns n\\nv t\\nh b\\nu p\\nv b\\nw l\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbaa\\naac\\n', 'output': '2\\nb a\\na c\\n'}, {'type': 'stdin_stdout', 'input': '1\\nf\\np\\n', 'output': '1\\nf p\\n'}, {'type': 'stdin_stdout', 'input': '242\\nrrrrrrrrrrrrrmmmmmmmmmmmmmgggggggggggggwwwwwwwwwwwwwyyyyyyyyyyyyyhhhhhhhhhhhhhoooooooooooooqqqqqqqqqqqqqjjjjjjjjjjjjjvvvvvvvvvvvvvlllllllllllllnnnnnnnnnnnnnfffffffffffffeeeeeeeeaaaaaaaaiiiiiiiiuuuuuuuuzzyzzzzzbbbbbbbbxxxxxxxxttttttttsscckppdd\\nrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfeaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiudbxteaiuzbxteaiuzbxtscsckpdpz\\n', 'output': '23\\nr m\\nr g\\nr w\\nr y\\nr h\\nr o\\nr q\\nr j\\nr v\\nr l\\nr n\\nr f\\ne a\\ne i\\ne u\\ne z\\ne b\\ne x\\ne t\\ny i\\nb d\\ns c\\np d\\n'}, {'type': 'stdin_stdout', 'input': '2\\nwc\\nea\\n', 'output': '2\\nw e\\nc a\\n'}, {'type': 'stdin_stdout', 'input': '1\\nv\\nk\\n', 'output': '1\\nv k\\n'}, {'type': 'stdin_stdout', 'input': '8\\ndrpepper\\nclocacoa\\n', 'output': '7\\nd c\\nr l\\np o\\ne c\\np a\\np c\\nr a\\n'}, {'type': 'stdin_stdout', 'input': '10\\neaefcecfae\\naceeecadcc\\n', 'output': '4\\ne a\\na c\\nf e\\nf d\\n'}, {'type': 'stdin_stdout', 'input': '100\\npfkskdknmbxxslokqdliigxyvntsmaziljamlflwllvbhqnzpyvvzirhhhglsskiuogfoytcxjmospiqybckwmkjhnfjddweyqqi\\nakvzmboxlcfwccaoknrzrhvqcdqkqnywstmxinqbkftnbjmahrvexoipikkqfjjmasnxofhklxappvufpsyujdtrpjeejhznoeai\\n', 'output': '25\\np a\\nf k\\nk v\\ns z\\nk m\\nd b\\nk o\\nn x\\nm l\\nb c\\nx f\\nx w\\ns c\\nl c\\no a\\nq k\\nl r\\ni z\\ng h\\ny q\\nt q\\nj t\\nh b\\nv e\\nu a\\n'}, {'type': 'stdin_stdout', 'input': '3\\nvwh\\nuug\\n', 'output': '3\\nv u\\nw u\\nh g\\n'}, {'type': 'stdin_stdout', 'input': '10\\nfdfbffdebc\\ncfcdddebdd\\n', 'output': '4\\nf c\\nd f\\nb d\\nd e\\n'}, {'type': 'stdin_stdout', 'input': '15\\nxrezbaoikswhuvw\\ndcgcjrkbfntbpbl\\n', 'output': '15\\nx d\\nr c\\ne g\\nz c\\nb j\\na r\\no k\\ni b\\nk f\\ns n\\nw t\\nh b\\nu p\\nv b\\nw l\\n'}, {'type': 'stdin_stdout', 'input': '1\\nf\\no\\n', 'output': '1\\nf o\\n'}, {'type': 'stdin_stdout', 'input': '242\\nrrrrrrrrrrrrrmmmmmmmmmmmmmgggggggggggggwwwwwwwwwwwwwyyyyyyyyyyyyyhhhhhhhhhhhhhoooooooooooooqqqqqqqqqqqqqjjjjjjjjjjjjjvvvvvvvvvvvvvlllllllllllllnnnnnnnnnnnnnfffffffffffffeeeeeeeeaaaaaaaaiiiiiiiiuuuuuuuuzzyzzzzzbbbbbbbbxxxxxxxxttttttttsscckppdd\\nrmgwyhoqjvlnfrmgwxhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfeaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiudbxteaiuzbxteaiuzbxtscsckpdpz\\n', 'output': '23\\nr m\\nr g\\nr w\\nr y\\nr h\\nr o\\nr q\\nr j\\nr v\\nr l\\nr n\\nr f\\nm x\\ne a\\ne i\\ne u\\ne z\\ne b\\ne x\\ne t\\nb d\\ns c\\np d\\n'}, {'type': 'stdin_stdout', 'input': '2\\nwd\\nea\\n', 'output': '2\\nw e\\nd a\\n'}, {'type': 'stdin_stdout', 'input': '1\\nu\\nk\\n', 'output': '1\\nu k\\n'}, {'type': 'stdin_stdout', 'input': '8\\ndrpepper\\nccolacoa\\n', 'output': '7\\nd c\\nr c\\np o\\ne l\\np a\\np c\\ne o\\n'}, {'type': 'stdin_stdout', 'input': '100\\nbltlukvrharrgytdxnbjailgafwdmeowqvxwsadryzquqzvfhjnpkwvgpwvohvjwzafcxqmisgyyuidvvjqljqshflzywmcccksk\\njmgilzxkrwntkvqpsemrmyrasfqrofkvjwfznctwrmegghlhbbomjlojyapmcpkowqhsvwmrrcfbnictnntjfvynqilptaoharqv\\n', 'output': '25\\nb j\\nl m\\nt g\\nl i\\nu l\\nk z\\nv x\\nr k\\nh r\\na w\\nr n\\nr t\\ny v\\nt q\\nd p\\nx s\\nn e\\nb m\\nj r\\na m\\ni y\\nd r\\nm o\\ne f\\na c\\n'}, {'type': 'stdin_stdout', 'input': '3\\nhww\\nuug\\n', 'output': '3\\nh u\\nw u\\nw g\\n'}, {'type': 'stdin_stdout', 'input': '10\\nfdfbffdebc\\nfccdddebdd\\n', 'output': '4\\nd c\\nf c\\nb d\\nd e\\n'}, {'type': 'stdin_stdout', 'input': '15\\nxrezbaoikswhuvw\\nlbpbtnfbkrjcgcd\\n', 'output': '14\\nx l\\nr b\\ne p\\nz b\\nb t\\na n\\no f\\ni b\\ns r\\nw j\\nh c\\nu g\\nv c\\nw d\\n'}, {'type': 'stdin_stdout', 'input': '1\\ng\\no\\n', 'output': '1\\ng o\\n'}, {'type': 'stdin_stdout', 'input': '2\\nwd\\nfa\\n', 'output': '2\\nw f\\nd a\\n'}, {'type': 'stdin_stdout', 'input': '1\\nu\\nl\\n', 'output': '1\\nu l\\n'}, {'type': 'stdin_stdout', 'input': '8\\ndrpeppfr\\nccolacoa\\n', 'output': '7\\nd c\\nr c\\np o\\ne l\\np a\\np c\\nf o\\n'}, {'type': 'stdin_stdout', 'input': '3\\nhww\\nutg\\n', 'output': '3\\nh u\\nw t\\nw g\\n'}, {'type': 'stdin_stdout', 'input': '10\\ncbedffbfdf\\nfccdddebdd\\n', 'output': '4\\nc f\\nb c\\ne c\\nf d\\n'}, {'type': 'stdin_stdout', 'input': '15\\nvrezbaoikswhuxw\\nlbpbtnfbkrjcgcd\\n', 'output': '14\\nv l\\nr b\\ne p\\nz b\\nb t\\na n\\no f\\ni b\\ns r\\nw j\\nh c\\nu g\\nx c\\nw d\\n'}, {'type': 'stdin_stdout', 'input': '1\\ng\\nq\\n', 'output': '1\\ng q\\n'}, {'type': 'stdin_stdout', 'input': '242\\nrrrrrrrrrrrrrmmmmmmmmmmmmmgggggggggggggwwwwwwwwwwwwwyyyyyyyyyyyyyhhhhhhhhhhhhhoooooooooooooqqqqqqqqqqqqqjjjjjjjjjjjjjvvvvvvvvvvvvvlllllllllllllnnnnnnnnnnnnnfffffffffffffeeeeeeeeaaaaaaaaiiiiiiiiuuuuuuuuzzyzzzzzbbbbbbbbxxxxxxxxttttttttsscckppdd\\nzpdpkcscstxbzuiaetxbzuiaetxbduiaetxbzuiaetxbzuiaetxbzuiaetxbzuiaetxbzuiaefnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohjwgmrfnlvjqohywgmrfnlvyqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohxwgmrfnlvjqohywgmr\\n', 'output': '25\\nr z\\nr p\\nr d\\nr k\\nr c\\nr s\\nr t\\nr x\\nr b\\nm u\\nm i\\nm a\\nm e\\nm t\\ng x\\nw a\\ny z\\nh t\\nh f\\nh n\\nh l\\nh v\\nh j\\no q\\no h\\n'}, {'type': 'stdin_stdout', 'input': '2\\nxd\\nfa\\n', 'output': '2\\nx f\\nd a\\n'}, {'type': 'stdin_stdout', 'input': '1\\nt\\nl\\n', 'output': '1\\nt l\\n'}, {'type': 'stdin_stdout', 'input': '8\\ndrpeppfr\\nocclacoa\\n', 'output': '6\\nd o\\nr c\\np c\\ne l\\np a\\nf o\\n'}, {'type': 'stdin_stdout', 'input': '100\\nbltlukvrharrgytdxnbjailgafwdmeowqvxwsadryzquqzvfhjnpkwvgpwvohvjwzafcxqmisgyyuidvvjqljqshflzywmbccksk\\nvqrahoatpliqnyvfjtnntcinbfcrrmwvshqwokpcmpayjoljmobbhlhggemrwtcnzfwjvkforqfsarymrmespqvktnwrkxzligmj\\n', 'output': '25\\nb v\\nl q\\nt r\\nl a\\nu h\\nk o\\nv a\\nh p\\nr i\\nr q\\ng n\\nd f\\nx j\\nn t\\nj n\\ni c\\nw c\\nd r\\nm r\\ne m\\no w\\nq s\\nv h\\ny m\\nz p\\n'}, {'type': 'stdin_stdout', 'input': '3\\nhww\\ntug\\n', 'output': '3\\nh t\\nw u\\nw g\\n'}, {'type': 'stdin_stdout', 'input': '10\\ndbedffbfdf\\nfccdddebdd\\n', 'output': '4\\nd f\\nb c\\ne c\\nf b\\n'}, {'type': 'stdin_stdout', 'input': '15\\nvrezbaoikswhuxw\\nlbpctnfbkrjcgcd\\n', 'output': '14\\nv l\\nr b\\ne p\\nz c\\nb t\\na n\\no f\\ni b\\ns r\\nw j\\nh c\\nu g\\nx c\\nw d\\n'}, {'type': 'stdin_stdout', 'input': '1\\nh\\nq\\n', 'output': '1\\nh q\\n'}, {'type': 'stdin_stdout', 'input': '2\\ndx\\nfa\\n', 'output': '2\\nd f\\nx a\\n'}, {'type': 'stdin_stdout', 'input': '1\\ns\\nl\\n', 'output': '1\\ns l\\n'}, {'type': 'stdin_stdout', 'input': '8\\ndqpeppfr\\nocclacoa\\n', 'output': '7\\nd o\\nq c\\np c\\ne l\\np a\\nf o\\nr a\\n'}, {'type': 'stdin_stdout', 'input': '100\\niqqyewddjfnhjkmwkcbyqicsomjxptyofgouiksslghhhrizvvypznqhbvllwlflmajlizamstnvyxgiildqkolsxxbmnkdkskfp\\nakvzmboxlcfwccaoknrzrhvqcdqkqnywstmxinqbkftnbjmbhrvexoipikkqfjjmasnjofhklxappvufpsyujdtrpjeexhznoeai\\n', 'output': '25\\ni a\\nq k\\nq v\\ny z\\ne m\\nw b\\nd o\\nd x\\nj l\\nf c\\nn f\\nh w\\nj c\\nk c\\nm a\\nw o\\nb r\\nq r\\ni h\\ns q\\np q\\nt n\\ng t\\nu x\\nz b\\n'}, {'type': 'stdin_stdout', 'input': '100\\nbltlukvrharrgytdxnbjailgafwdmeowqvxwsadryzquqzvfhjnpkwvgpwvohvjwzafcxqmisgyyuidvvjqljqshflzywmbccksk\\nvqrahoatplhqnyvfjtnntcinbfcrrmwvshqwokpcmpayjoljmobbhlhggemrwtcnzfwjvkforqfsarymrmespqvktnwrkxzligmj\\n', 'output': '25\\nb v\\nl q\\nt r\\nl a\\nu h\\nk o\\nv a\\nh p\\nr h\\nr q\\ng n\\nd f\\nx j\\nn t\\nj n\\ni c\\nl i\\nw c\\nd r\\nm r\\ne m\\no w\\nq s\\ny m\\nz p\\n'}, {'type': 'stdin_stdout', 'input': '3\\nhww\\nsug\\n', 'output': '3\\nh s\\nw u\\nw g\\n'}, {'type': 'stdin_stdout', 'input': '15\\nvrezbboikswhuxw\\nlbpctnfbkrjcgcd\\n', 'output': '14\\nv l\\nr b\\ne p\\nz c\\nb t\\nb n\\no f\\ni b\\ns r\\nw j\\nh c\\nu g\\nx c\\nw d\\n'}, {'type': 'stdin_stdout', 'input': '1\\nh\\nr\\n', 'output': '1\\nh r\\n'}, {'type': 'stdin_stdout', 'input': '2\\nyd\\nfa\\n', 'output': '2\\ny f\\nd a\\n'}, {'type': 'stdin_stdout', 'input': '1\\nt\\nk\\n', 'output': '1\\nt k\\n'}, {'type': 'stdin_stdout', 'input': '8\\ndqpfppfr\\nocclacoa\\n', 'output': '7\\nd o\\nq c\\np c\\nf l\\np a\\nf o\\nr a\\n'}, {'type': 'stdin_stdout', 'input': '3\\nwwh\\nsug\\n', 'output': '3\\nw s\\nw u\\nh g\\n'}, {'type': 'stdin_stdout', 'input': '10\\nfefbffdebd\\nfccdddebdd\\n', 'output': '4\\ne c\\nf c\\nb d\\nf d\\n'}, {'type': 'stdin_stdout', 'input': '15\\nvrezbboikswhuxw\\ndcgcjrkbfntcpbl\\n', 'output': '15\\nv d\\nr c\\ne g\\nz c\\nb j\\nb r\\no k\\ni b\\nk f\\ns n\\nw t\\nh c\\nu p\\nx b\\nw l\\n'}, {'type': 'stdin_stdout', 'input': '1\\ni\\nr\\n', 'output': '1\\ni r\\n'}, {'type': 'stdin_stdout', 'input': '2\\nyd\\nga\\n', 'output': '2\\ny g\\nd a\\n'}, {'type': 'stdin_stdout', 'input': '1\\nt\\nm\\n', 'output': '1\\nt m\\n'}, {'type': 'stdin_stdout', 'input': '8\\ndqpfppfr\\nccolacoa\\n', 'output': '8\\nd c\\nq c\\np o\\nf l\\np a\\np c\\nf o\\nr a\\n'}, {'type': 'stdin_stdout', 'input': '3\\nwwh\\nsvg\\n', 'output': '3\\nw s\\nw v\\nh g\\n'}, {'type': 'stdin_stdout', 'input': '10\\ndbedffbfef\\nfccdddeddb\\n', 'output': '4\\nd f\\nb c\\ne c\\ne d\\n'}, {'type': 'stdin_stdout', 'input': '15\\nvrezbboikswhuxw\\ndcgljrkbfntcpbc\\n', 'output': '15\\nv d\\nr c\\ne g\\nz l\\nb j\\nb r\\no k\\ni b\\nk f\\ns n\\nw t\\nh c\\nu p\\nx b\\nw c\\n'}, {'type': 'stdin_stdout', 'input': '1\\nj\\nr\\n', 'output': '1\\nj r\\n'}, {'type': 'stdin_stdout', 'input': '2\\nyc\\nga\\n', 'output': '2\\ny g\\nc a\\n'}, {'type': 'stdin_stdout', 'input': '1\\ns\\nm\\n', 'output': '1\\ns m\\n'}, {'type': 'stdin_stdout', 'input': '8\\ndqpfppfr\\ndcolacoa\\n', 'output': '7\\nq c\\np o\\nf l\\np a\\np c\\nf o\\nr a\\n'}, {'type': 'stdin_stdout', 'input': '3\\nwwh\\nsvh\\n', 'output': '2\\nw s\\nw v\\n'}, {'type': 'stdin_stdout', 'input': '15\\nvkezbboirswhuxw\\ndcgljrkbfntcpbc\\n', 'output': '15\\nv d\\nk c\\ne g\\nz l\\nb j\\nb r\\no k\\ni b\\nr f\\ns n\\nw t\\nh c\\nu p\\nx b\\nw c\\n'}, {'type': 'stdin_stdout', 'input': '10\\neaefcecfae\\nccdaceeeca\\n', 'output': '4\\ne c\\na c\\ne d\\nf a\\n'}, {'type': 'stdin_stdout', 'input': '100\\nbltlukvrharrgytdxnbjailgafwdmeowqvxwsadryzquqzvfhjnpkwvgpwvohvjwzafcxqmisgyyuidvvjqljqshflzywmcccksk\\njmgilzxkrvntkvqpsemrmyrasfqrofkwjwfznctwrmegghlhbbomjlojyapmcpkowqhsvwmrrcfbnictnntjevynqilptaoharqv\\n', 'output': '25\\nb j\\nl m\\nt g\\nl i\\nu l\\nk z\\nv x\\nr k\\nh r\\na v\\nr n\\nr t\\ny v\\nt q\\nd p\\nx s\\nn e\\nb m\\nj r\\na m\\nw q\\nd r\\nm o\\ne f\\na c\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbba\\naba\\n', 'output': '1\\nb a\\n'}, {'type': 'stdin_stdout', 'input': '100\\nbltlukvrharrgytdxnbjailgafwdmeowqvxwsadryzquqzvfhjnpkwvgpwvohvjwzafcxqmisgyyuidvvjqljqshflzywmcccksk\\njmgilzxkrvntkvqpsemrmyrasfqrofkwjwfznctwrmegghlhbbomjlojyapmcpkowqhsvwmrrcfbnictnntjfvynqilptaoharqv\\n', 'output': '25\\nb j\\nl m\\nt g\\nl i\\nu l\\nk z\\nv x\\nr k\\nh r\\na v\\nr n\\nr t\\ny v\\nt q\\nd p\\nx s\\nn e\\nb m\\nj r\\na m\\nw q\\nd r\\nm o\\ne f\\na c\\n'}, {'type': 'stdin_stdout', 'input': '3\\nabb\\naba\\n', 'output': '1\\nb a\\n'}, {'type': 'stdin_stdout', 'input': '100\\npfkskdknmbxxslokqdliigxyvntsmaziljamlflwllvbhqnzpyvvzirhhhglsskiuogfoytpxjmosciqybckwmkjhnfjddweyqqi\\nakvzmboxlcfwccaoknrzrhvqcdqkqnywstmxinqbkftnbjmahrvexoipikkqfjjmasnxofhklxappvufpsyujdtrpjeejhznoeai\\n', 'output': '25\\np a\\nf k\\nk v\\ns z\\nk m\\nd b\\nk o\\nn x\\nm l\\nb c\\nx f\\nx w\\ns c\\nl c\\no a\\nq k\\nl r\\ni z\\ng h\\ny q\\nt q\\nj t\\nh b\\nv e\\nu a\\n'}, {'type': 'stdin_stdout', 'input': '242\\nrrrrrrrrrrrrrmmmmmmmmmmmmmgggggggggggggwwwwwwwwwwwwwyyyyyyyyyyyyyhhhhhhhhhhhhhoooooooooooooqqqqqqqqqqqqqjjjjjjjjjjjjjvvvvvvvvvvvvvlllllllllllllnnnnnnnnnnnnnfffffffffffffeeeeeeeeaaaaaaaaiiiiiiiiuuuuuuuuzzyzzzzzbbbbbbbbxxxxxxxxttttttttsscckppdd\\nrmgwyhoqjvlnfrmgwxhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqyvlnfrmgwyhoqjvlnfrmgwjhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfrmgwyhoqjvlnfeaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiuzbxteaiudbxteaiuzbxteaiuzbxtscsckpdpz\\n', 'output': '23\\nr m\\nr g\\nr w\\nr y\\nr h\\nr o\\nr q\\nr j\\nr v\\nr l\\nr n\\nr f\\nm x\\ne a\\ne i\\ne u\\ne z\\ne b\\ne x\\ne t\\nb d\\ns c\\np d\\n'}, {'type': 'stdin_stdout', 'input': '100\\npfkskdknmbxxslokqdliigxyvntsmaziljamlflwllvbhqnzpyvvzirhhhglsskiuogfoytpxjmosciqybckwmkjhnfjddweyqqi\\nakvzmboxlcfwccaoknrzrhvqcdqkqnywstmxinqbkftnbjmbhrvexoipikkqfjjmasnxofhklxappvufpsyujdtrpjeejhznoeai\\n', 'output': '25\\np a\\nf k\\nk v\\ns z\\nk m\\nd b\\nk o\\nn x\\nm l\\nb c\\nx f\\nx w\\ns c\\nl c\\no a\\nq k\\nl r\\ni z\\ng h\\ny q\\nt q\\nj t\\nh b\\nv e\\nu a\\n'}, {'type': 'stdin_stdout', 'input': '100\\nbltlukvrharrgytdxnbjailgafwdmeowqvxwsadryzquqzvfhjnpkwvgpwvohvjwzafcxqmisgyyuidvvjqljqshflzywmbccksk\\njmgilzxkrwntkvqpsemrmyrasfqrofkvjwfznctwrmegghlhbbomjlojyapmcpkowqhsvwmrrcfbnictnntjfvynqilptaoharqv\\n', 'output': '25\\nb j\\nl m\\nt g\\nl i\\nu l\\nk z\\nv x\\nr k\\nh r\\na w\\nr n\\nr t\\ny v\\nt q\\nd p\\nx s\\nn e\\nb m\\nj r\\na m\\ni y\\nd r\\nm o\\ne f\\na c\\n'}, {'type': 'stdin_stdout', 'input': '100\\npfkskdknmbxxslokqdliigxyvntsmaziljamlflwllvbhqnzpyvvzirhhhglsskiuogfoytpxjmosciqybckwmkjhnfjddweyqqi\\nakvzmboxlcfwccaoknrzrhvqcdqkqnywstmxinqbkftnbjmbhrvexoipikkqfjjmasnjofhklxappvufpsyujdtrpjeexhznoeai\\n', 'output': '25\\np a\\nf k\\nk v\\ns z\\nk m\\nd b\\nk o\\nn x\\nm l\\nb c\\nx f\\nx w\\ns c\\nl c\\no a\\nq k\\nl r\\ni z\\ng h\\ny q\\nt q\\nj t\\nh b\\nv e\\nu a\\n'}, {'type': 'stdin_stdout', 'input': '242\\nrrrrrrrrrrrrrmmmmmmmmmmmmmgggggggggggggwwwwwwwwwwwwwyyyyyyyyyyyyyhhhhhhhhhhhhhooooovoooooooqqqqqqqqqqqqqjjjjjjjjjjjjjvvvvvvvvvvovvlllllllllllllnnnnnnnnnnnnnfffffffffffffeeeeeeeeaaaaaaaaiiiiiiiiuuuuuuuuzzyzzzzzbbbbbbbbxxxxxxxxttttttttsscckppdd\\nzpdpkcscstxbzuiaetxbzuiaetxbduiaetxbzuiaetxbzuiaetxbzuiaetxbzuiaetxbzuiaefnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohjwgmrfnlvjqohywgmrfnlvyqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohxwgmrfnlvjqohywgmr\\n', 'output': '25\\nr z\\nr p\\nr d\\nr k\\nr c\\nr s\\nr t\\nr x\\nr b\\nm u\\nm i\\nm a\\nm e\\nm t\\ng x\\nw a\\ny z\\nh t\\nh f\\nh n\\nh l\\nh v\\nh j\\no q\\no h\\n'}, {'type': 'stdin_stdout', 'input': '10\\ndbedffbfef\\nfccdddebdd\\n', 'output': '4\\nd f\\nb c\\ne c\\nf b\\n'}, {'type': 'stdin_stdout', 'input': '242\\nrrrrrrrrrrrrrmmmmmmmmmmmmmgggggggggggggwwwwwswwwwwwwyyyyyyyyyyyyyhhhhhhhhhhhhhooooovoooooooqqqqqqqqqqqqqjjjjjjjjjjjjjvvvvvvvvvvovvlllllllllllllnnnnnnnnnnnnnfffffffffffffeeeeeeeeaaaaaaaaiiiiiiiiuuuuuuuuzzyzzzzzbbbbbbbbxxxxxxxxttttttttwscckppdd\\nzpdpkcscstxbzuiaetxbzuiaetxbduiaetxbzuiaetxbzuiaetxbzuiaetxbzuiaetxbzuiaefnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohjwgmrfnlvjqohywgmrfnlvyqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohxwgmrfnlvjqohywgmr\\n', 'output': '25\\nr z\\nr p\\nr d\\nr k\\nr c\\nr s\\nr t\\nr x\\nr b\\nm u\\nm i\\nm a\\nm e\\nm t\\ng x\\nw a\\ny z\\nh t\\nh f\\nh n\\nh l\\nh v\\nh j\\no q\\no h\\n'}, {'type': 'stdin_stdout', 'input': '100\\niqqyewddjfnhjkmwkcbyqicsomjxptyofgouiksslghhhrizvvypznqhbvllwlflmajlizamstnvyxgiildqkolsxxbmnkdkskfp\\nakvzmboxlcfwccaoknrzrhvqcdqkqnywstmxinqbkftnbjmbhrvexoipikkqfjjmasnjofhklxappvufqsyujdtrpjeexhznoeai\\n', 'output': '25\\ni a\\nq k\\nq v\\ny z\\ne m\\nw b\\nd o\\nd x\\nj l\\nf c\\nn f\\nh w\\nj c\\nk c\\nm a\\nw o\\nb r\\nq r\\ni h\\ns q\\np q\\nt n\\ng t\\nu x\\nz b\\n'}, {'type': 'stdin_stdout', 'input': '100\\nbltlukvrharrgytdxnbjailgafwdmeowqvxwsadryzquqzvfhjnpkwvgpwvohvjwzafcxqmisgyyuidvvjqljqshflzywmbccksk\\nvqrahoatplhqnyvfjtnntcinbfcrrmwvshqwokpcmpayjoljmobbhlgggemrwtcnzfwjvkforqfsarymrmespqvktnwrkxzligmj\\n', 'output': '25\\nb v\\nl q\\nt r\\nl a\\nu h\\nk o\\nv a\\nh p\\nr h\\nr q\\ng n\\nd f\\nx j\\nn t\\nj n\\ni c\\nl i\\nw c\\nd r\\nm r\\ne m\\no w\\nq s\\ny m\\nz p\\n'}, {'type': 'stdin_stdout', 'input': '242\\nrrrrrrrrrrrrrmmmmmmmmmmmmmgggggggggggggwwwwwswwwwwwwyyyyyyyyyyyyyhhhhhhhhhhhhhooooovoooooooqqqqqqqqqqqqqjjjjjjjjjjjjjvvvvvvvvvvovvlllllllllllllnnnnnnnnnnnnnfffffffffffffeeeeeeeeaaaaaaaaixiiiiiiuuuuuuuuzzyzzzzzbbbbbbbbxxxixxxxttttttttwscckppdd\\nzpdpkcscstxbzuiaetxbzuiaetxbduiaetxbzuiaetxbzuiaetxbzuiaetxbzuiaetxbzuiaefnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohjwgmrfnlvjqohywgmrfnlvyqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohxwgmrfnlvjqohywgmr\\n', 'output': '25\\nr z\\nr p\\nr d\\nr k\\nr c\\nr s\\nr t\\nr x\\nr b\\nm u\\nm i\\nm a\\nm e\\nm t\\ng x\\nw a\\ny z\\nh t\\nh f\\nh n\\nh l\\nh v\\nh j\\no q\\no h\\n'}, {'type': 'stdin_stdout', 'input': '100\\niqqyewddjfnhjkmwkcbyqicsomjxptyofgouikaslghhhrizvvypznqhbvllwlflmajlizsmstnvyxgiildqkolsxxbmnkdkskfp\\nakvzmboxlcfwccaoknrzrhvqcdqkqnywstmxinqbkftnbjmbhrvexoipikkqfjjmasnjofhklxappvufqsyujdtrpjeexhznoeai\\n', 'output': '25\\ni a\\nq k\\nq v\\ny z\\ne m\\nw b\\nd o\\nd x\\nj l\\nf c\\nn f\\nh w\\nj c\\nk c\\nm a\\nw o\\nb r\\nq r\\ni h\\ns q\\np q\\nt n\\ng t\\nu x\\nz b\\n'}, {'type': 'stdin_stdout', 'input': '100\\nbltlukvrharrgytdxnbjailgafwdmeowqvxwsadryzquqzvfhinpkwvgpwvohvjwzafcxqmisgyyuidvvjqljqshflzywmbccksk\\nvqrahoatplhqnyvfjtnntcinbfcrrmwvshqwokpcmpayjoljmobbhlgggemrwtcnzfwjvkforqfsarymrmespqvktnwrkxzligmj\\n', 'output': '25\\nb v\\nl q\\nt r\\nl a\\nu h\\nk o\\nv a\\nh p\\nr h\\nr q\\ng n\\nd f\\nx j\\nn t\\nj n\\ni c\\nl i\\nw c\\nd r\\nm r\\ne m\\no w\\nq s\\ny m\\nz p\\n'}, {'type': 'stdin_stdout', 'input': '242\\nrrrrrrrrrrrrrmmmmmmmmmmmmmgggggggggggggwwwwwswwwwwwwyyyyyyyyyyyyyhhhhhhhhhhhhhooooovoooooooqqqqqqqqqqqqqjjjjjjjjjjjjjvvvvvvvvvvovvlllllllllllllnnnnnnnnnnnnnfffffffffffffeeeeeeeeaaaaaaaaixiiiiiiuuuuuuuuzzyzzzzzbbbbbbbbxxxixxxxttttttttwscckppdd\\nzpdpkcscstxbzuiaetxbzuiaetxbduiaetxbzuiaetxbzuiaetxbzuiaetxbzuiaetxbzuiaefnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohywgmrfnlvjqohjwgmrfnlvjqohywgmrfnlvyqohywgmrfnlvjqohywgmrfnlvjqohywhmrfnlvjqohxwgmrfnlvjqohywgmr\\n', 'output': '25\\nr z\\nr p\\nr d\\nr k\\nr c\\nr s\\nr t\\nr x\\nr b\\nm u\\nm i\\nm a\\nm e\\nm t\\ng x\\nw a\\ny z\\nh t\\nh f\\nh n\\nh l\\nh v\\nh j\\no q\\no h\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79845","program":"```python\nlength=int(input())\ns1=input()\ns2=input()\nconnect=[{0},{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11},{12},{13},{14},{15},{16},{17},{18},{19},{20},{21},{22},{23},{24},{25}]\ntot=0\nspells=[]\nfor i in range(0, length):\n l1=ord(s1[i])-97\n l2=ord(s2[i])-97\n if not (l1 in connect[l2]):\n tot=tot+1\n spells.append(s1[i]+\" \"+s2[i])\n x=connect[l1].union(connect[l2])\n connect[l1]=x\n connect[l2]=x\n for i in connect[l1]:\n connect[i]=connect[i].union(connect[l1])\nprint(str(tot))\nfor i in spells:\n print(i)\n```","inputs":"3\nabb\ndad\n","output":"2\na d\nb a\n","actual_output":"2\na d\nb a\n","execution_success":true,"sample_index":12716},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"965_A. Paper Airplanes","prompt":"Solve the following coding problem using the programming language python:\n\nTo make a paper airplane, one has to use a rectangular piece of paper. From a sheet of standard size you can make s airplanes.\n\nA group of k people decided to make n airplanes each. They are going to buy several packs of paper, each of them containing p sheets, and then distribute the sheets between the people. Each person should have enough sheets to make n airplanes. How many packs should they buy?\n\nInput\n\nThe only line contains four integers k, n, s, p (1 \u2264 k, n, s, p \u2264 10^4) \u2014 the number of people, the number of airplanes each should make, the number of airplanes that can be made using one sheet and the number of sheets in one pack, respectively.\n\nOutput\n\nPrint a single integer \u2014 the minimum number of packs they should buy.\n\nExamples\n\nInput\n\n5 3 2 3\n\n\nOutput\n\n4\n\n\nInput\n\n5 3 100 1\n\n\nOutput\n\n5\n\nNote\n\nIn the first sample they have to buy 4 packs of paper: there will be 12 sheets in total, and giving 2 sheets to each person is enough to suit everyone's needs.\n\nIn the second sample they have to buy a pack for each person as they can't share sheets.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nk, n, s, p = map(int, input().split())\n\none = (n + s - 1) // s\nprint((one * k + p - 1) // p)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 3 2 3\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 3 100 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1 2 1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 1 10 10\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10000 10000 1 1\\n', 'output': '100000000\\n'}, {'type': 'stdin_stdout', 'input': '2 400 23 57\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10000 10000 3 2\\n', 'output': '16670000\\n'}, {'type': 'stdin_stdout', 'input': '300 2 37 51\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '9000 1 2432 1\\n', 'output': '9000\\n'}, {'type': 'stdin_stdout', 'input': '11 1 1 1\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '1 1 10000 10000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 1 2 2\\n', 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'stdin_stdout', 'input': '4 566 23 57\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '8 6 4 1\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '4 576 23 57\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 749 19 57\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 91 23 57\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 91 23 6\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '6 91 23 6\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '6 91 27 6\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1 2 1 3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 1 10 17\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 400 21 57\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 1 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '11 1 2 1\\n', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '1 2 4 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '34 1234 9124 23\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 4 100 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1 2 9 10\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 1 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4131 1 1302 1\\n', 'output': '4131\\n'}, {'type': 'stdin_stdout', 'input': '10 2 5 7\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '77 1234 9124 9\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3 3 100 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 439 32 57\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 4 1 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 1 1 7\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '77 1234 9124 21\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2 897 23 57\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '300 3 47 3\\n', 'output': '100\\n'}, {'type': 'stdin_stdout', 'input': '1 1 5 7\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '77 2300 1683 20\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '8 2 4 1\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '4 566 23 36\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '8 6 4 2\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '4 195 23 57\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 386 23 57\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4 749 26 57\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 73 23 57\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 26 23 6\\n', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79849","program":"```python\nk, n, s, p = map(int, input().split())\n\none = (n + s - 1) // s\nprint((one * k + p - 1) // p)\n\n```","inputs":"5 3 2 3\n","output":"4\n","actual_output":"4\n","execution_success":true,"sample_index":12717},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"992_A. Nastya and an Array","prompt":"Solve the following coding problem using the programming language python:\n\nNastya owns too many arrays now, so she wants to delete the least important of them. However, she discovered that this array is magic! Nastya now knows that the array has the following properties:\n\n * In one second we can add an arbitrary (possibly negative) integer to all elements of the array that are not equal to zero. \n * When all elements of the array become equal to zero, the array explodes. \n\n\n\nNastya is always busy, so she wants to explode the array as fast as possible. Compute the minimum time in which the array can be exploded.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 105) \u2014 the size of the array.\n\nThe second line contains n integers a1, a2, ..., an ( - 105 \u2264 ai \u2264 105) \u2014 the elements of the array.\n\nOutput\n\nPrint a single integer \u2014 the minimum number of seconds needed to make all elements of the array equal to zero.\n\nExamples\n\nInput\n\n5\n1 1 1 1 1\n\n\nOutput\n\n1\n\n\nInput\n\n3\n2 0 -1\n\n\nOutput\n\n2\n\n\nInput\n\n4\n5 -6 -5 1\n\n\nOutput\n\n4\n\nNote\n\nIn the first example you can add - 1 to all non-zero elements in one second and make them equal to zero.\n\nIn the second example you can add - 2 on the first second, then the array becomes equal to [0, 0, - 3]. On the second second you can add 3 to the third (the only non-zero) element.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\nl=list(map(int,input().split()))\nl=set(l)\nif 0 in l:\n\tprint(len(l)-1)\nelse:\n\tprint(len(l))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n5 -6 -5 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 1 1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 0 -1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 4 5 6 7 8 9 10\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 0 0 -1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 0 0 0 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 0 0 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 2\\n', 'output': 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'stdin_stdout', 'input': '8\\n10 12 -1 0 0 0 2 3\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 106114 -28230\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 0 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 0 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 -8 -5 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 0 1 1 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 -1 -2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n6 0 1 -1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 -1 0 -1 0\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 0 -2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -2 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6 0 4 0 0\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 3 0 2 0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 0 0 1 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 0 1 6 3\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 1 -1 -1 0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -1 -1\\n', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_79853","program":"```python\nn=int(input())\nl=list(map(int,input().split()))\nl=set(l)\nif 0 in l:\n\tprint(len(l)-1)\nelse:\n\tprint(len(l))\n```","inputs":"4\n5 -6 -5 1\n","output":"4\n","actual_output":"4\n","execution_success":true,"sample_index":12718},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02622 AtCoder Beginner Contest 172 - Minor Change","prompt":"Solve the following coding problem using the programming language python:\n\nGiven are strings S and T. Consider changing S to T by repeating the operation below. Find the minimum number of operations required to do so.\n\nOperation: Choose one character of S and replace it with a different character.\n\nConstraints\n\n* S and T have lengths between 1 and 2\\times 10^5 (inclusive).\n* S and T consists of lowercase English letters.\n* S and T have equal lengths.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nS\nT\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\ncupofcoffee\ncupofhottea\n\n\nOutput\n\n4\n\n\nInput\n\nabcde\nbcdea\n\n\nOutput\n\n5\n\n\nInput\n\napple\napple\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nS=input()\nT=input()\ncc=0\nfor i in range(len(S)):\n cc+=int(S[i]!=T[i])\n\nprint(cc)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'apple\\napple', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'abcde\\nbcdea', 'output': '5'}, {'type': 'stdin_stdout', 'input': 'cupofcoffee\\ncupofhottea', 'output': '4'}, {'type': 'stdin_stdout', 'input': 'apple\\nelppa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'abcdd\\nbcdea', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'eeffocfopuc\\ncupofhottea', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'elppa\\nelppa', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': 'elppa\\nelppb', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'elpap\\nelppb', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'ddc`a\\nbbcfa', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'ffgdmdfqpuc\\noeutaieppud', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': 'ffgdmdfqpuc\\noevt`ieuppd', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': 'hcfrahdjpmr\\nwvfxmhpcema', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': 'fhlrglsctdc\\nffljyboxtdl', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': 'ddcba\\nbcdea', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'efffocfopuc\\ncupofhottea', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'cdcba\\nbcdea', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'efffodfopuc\\ncupofhottea', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'cdcba\\nbcdfa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'efffndfopuc\\ncupofhottea', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'elpap\\nplepb', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'cdcba\\nbbdfa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'efffndfopuc\\ncupofhotuea', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'paple\\nplepb', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'abcdc\\nbbdfa', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'efffmdfopuc\\ncupofhotuea', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'paple\\nplfpb', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'cdcaa\\nbbdfa', 'output': '4\\n'}, {'type': 'stdin_stdout', 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'stdin_stdout', 'input': 'cupqgdmdggf\\ndopuei`tvep', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': 'pknad\\noahoj', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'd`bdd\\ngccdb', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'cupqgdmdggf\\npevt`ieupod', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'pknad\\njohao', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'd`bdd\\nbdccg', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'cumqgdpdggf\\ndopuei`tvep', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'dankp\\njohao', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'd`bdd\\nbgccd', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'ctmqgdpdggf\\ndopuei`tvep', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'dankp\\noahoj', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'd`bcd\\nbgccd', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': 'btmqgdpdggf\\ndopuei`tvep', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'dankp\\noahpj', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': 'b`dcd\\nbgccd', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': 'btmqgdpdggf\\ndopuei_tvep', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'pknad\\noahpj', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'b`ccd\\nbgccd', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': 'btmqgdpdggf\\ndopeui_tvep', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': 'pknad\\noajph', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': 'b`cbd\\nbgccd', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79897","program":"```python\nS=input()\nT=input()\ncc=0\nfor i in range(len(S)):\n cc+=int(S[i]!=T[i])\n\nprint(cc)\n```","inputs":"apple\napple","output":"0","actual_output":"0\n","execution_success":true,"sample_index":12719},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02753 AtCoder Beginner Contest 158 - Station and Bus","prompt":"Solve the following coding problem using the programming language python:\n\nIn AtCoder City, there are three stations numbered 1, 2, and 3.\n\nEach of these stations is operated by one of the two railway companies, A and B. A string S of length 3 represents which company operates each station. If S_i is `A`, Company A operates Station i; if S_i is `B`, Company B operates Station i.\n\nTo improve the transportation condition, for each pair of a station operated by Company A and one operated by Company B, there will be a bus service connecting them.\n\nDetermine if there is a pair of stations that will be connected by a bus service.\n\nConstraints\n\n* Each character of S is `A` or `B`.\n* |S| = 3\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nS\n\n\nOutput\n\nIf there is a pair of stations that will be connected by a bus service, print `Yes`; otherwise, print `No`.\n\nExamples\n\nInput\n\nABA\n\n\nOutput\n\nYes\n\n\nInput\n\nBBA\n\n\nOutput\n\nYes\n\n\nInput\n\nBBB\n\n\nOutput\n\nNo\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nS = input()\n\nprint(\"No\" if len(set(S)) == 1 else \"Yes\")\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'ABA', 'output': 'Yes'}, {'type': 'stdin_stdout', 'input': 'BBA', 'output': 'Yes'}, {'type': 'stdin_stdout', 'input': 'BBB', 'output': 'No'}, {'type': 'stdin_stdout', 'input': 'AAB', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': 'AAA', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'ABB', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': 'BAA', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': 'BAB', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': 'BAA', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': 'BAB', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': 'AAA', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': 'AAB', 'output': 'Yes\\n'}, {'type': 'stdin_stdout', 'input': 'ABB', 'output': 'Yes\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79901","program":"```python\nS = input()\n\nprint(\"No\" if len(set(S)) == 1 else \"Yes\")\n\n```","inputs":"ABA","output":"Yes","actual_output":"Yes\n","execution_success":true,"sample_index":12720},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02888 AtCoder Beginner Contest 143 - Triangles","prompt":"Solve the following coding problem using the programming language python:\n\nTakahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.\n\nHe is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:\n\n* a < b + c\n* b < c + a\n* c < a + b\n\n\n\nHow many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.\n\nConstraints\n\n* All values in input are integers.\n* 3 \\leq N \\leq 2 \\times 10^3\n* 1 \\leq L_i \\leq 10^3\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nL_1 L_2 ... L_N\n\n\nConstraints\n\nPrint the number of different triangles that can be formed.\n\nConstraints\n\nPrint the number of different triangles that can be formed.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nL_1 L_2 ... L_N\n\nExamples\n\nInput\n\n4\n3 4 2 1\n\n\nOutput\n\n1\n\n\nInput\n\n3\n1 1000 1\n\n\nOutput\n\n0\n\n\nInput\n\n7\n218 786 704 233 645 728 389\n\n\nOutput\n\n23\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport bisect\nN=int(input())\nL=sorted(list(map(int,input().split())))\n\nans=0\nfor i in range(N-2):\n for j in range(i+1,N-1):\n ans+=bisect.bisect_left(L,L[i]+L[j])-j-1\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n3 4 2 1', 'output': '1'}, {'type': 'stdin_stdout', 'input': '7\\n218 786 704 233 645 728 389', 'output': '23'}, {'type': 'stdin_stdout', 'input': '3\\n1 1000 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '4\\n5 4 2 1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '7\\n218 1140 704 233 645 728 389', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1000 2', 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40 1181 890 389', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '7\\n218 1140 205 40 636 890 389', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '7\\n218 1140 551 25 636 890 487', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '7\\n218 1140 551 49 660 890 487', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '7\\n116 1140 551 39 660 890 487', 'output': '11\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79905","program":"```python\nimport bisect\nN=int(input())\nL=sorted(list(map(int,input().split())))\n\nans=0\nfor i in range(N-2):\n for j in range(i+1,N-1):\n ans+=bisect.bisect_left(L,L[i]+L[j])-j-1\nprint(ans)\n\n```","inputs":"4\n3 4 2 1","output":"1","actual_output":"1\n","execution_success":true,"sample_index":12721},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03023 M-SOLUTIONS Programming Contest - Sum of Interior Angles","prompt":"Solve the following coding problem using the programming language python:\n\nGiven an integer N not less than 3, find the sum of the interior angles of a regular polygon with N sides.\n\nPrint the answer in degrees, but do not print units.\n\nConstraints\n\n* 3 \\leq N \\leq 100\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\n\n\nOutput\n\nPrint an integer representing the sum of the interior angles of a regular polygon with N sides.\n\nExamples\n\nInput\n\n3\n\n\nOutput\n\n180\n\n\nInput\n\n100\n\n\nOutput\n\n17640\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na = int(input())\nprint(int(a * 180 - 360))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3', 'output': '180'}, {'type': 'stdin_stdout', 'input': '100', 'output': '17640'}, {'type': 'stdin_stdout', 'input': '5', 'output': '540\\n'}, {'type': 'stdin_stdout', 'input': '000', 'output': '-360\\n'}, {'type': 'stdin_stdout', 'input': '9', 'output': '1260\\n'}, {'type': 'stdin_stdout', 'input': '001', 'output': '-180\\n'}, {'type': 'stdin_stdout', 'input': '7', 'output': '900\\n'}, {'type': 'stdin_stdout', 'input': '110', 'output': '19440\\n'}, {'type': 'stdin_stdout', 'input': '101', 'output': '17820\\n'}, {'type': 'stdin_stdout', 'input': '2', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '111', 'output': '19620\\n'}, {'type': 'stdin_stdout', 'input': '-1', 'output': '-540\\n'}, {'type': 'stdin_stdout', 'input': '4', 'output': '360\\n'}, {'type': 'stdin_stdout', 'input': '8', 'output': '1080\\n'}, {'type': 'stdin_stdout', 'input': '11', 'output': '1620\\n'}, {'type': 'stdin_stdout', 'input': '-2', 'output': '-720\\n'}, {'type': 'stdin_stdout', 'input': '-3', 'output': '-900\\n'}, {'type': 'stdin_stdout', 'input': '-6', 'output': '-1440\\n'}, {'type': 'stdin_stdout', 'input': '6', 'output': '720\\n'}, {'type': 'stdin_stdout', 'input': '10', 'output': '1440\\n'}, {'type': 'stdin_stdout', 'input': '-4', 'output': '-1080\\n'}, {'type': 'stdin_stdout', 'input': '-8', 'output': '-1800\\n'}, {'type': 'stdin_stdout', 'input': '-16', 'output': '-3240\\n'}, {'type': 'stdin_stdout', 'input': '-32', 'output': '-6120\\n'}, {'type': 'stdin_stdout', 'input': '-57', 'output': '-10620\\n'}, {'type': 'stdin_stdout', 'input': '-60', 'output': '-11160\\n'}, {'type': 'stdin_stdout', 'input': '-91', 'output': '-16740\\n'}, {'type': 'stdin_stdout', 'input': '-48', 'output': '-9000\\n'}, {'type': 'stdin_stdout', 'input': '-39', 'output': '-7380\\n'}, {'type': 'stdin_stdout', 'input': '-35', 'output': '-6660\\n'}, {'type': 'stdin_stdout', 'input': '-67', 'output': '-12420\\n'}, {'type': 'stdin_stdout', 'input': '-102', 'output': '-18720\\n'}, {'type': 'stdin_stdout', 'input': '-161', 'output': '-29340\\n'}, {'type': 'stdin_stdout', 'input': '-151', 'output': '-27540\\n'}, {'type': 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'5040\\n'}, {'type': 'stdin_stdout', 'input': '49', 'output': '8460\\n'}, {'type': 'stdin_stdout', 'input': '40', 'output': '6840\\n'}, {'type': 'stdin_stdout', 'input': '79', 'output': '13860\\n'}, {'type': 'stdin_stdout', 'input': '102', 'output': '18000\\n'}, {'type': 'stdin_stdout', 'input': '44', 'output': '7560\\n'}, {'type': 'stdin_stdout', 'input': '66', 'output': '11520\\n'}, {'type': 'stdin_stdout', 'input': '71', 'output': '12420\\n'}, {'type': 'stdin_stdout', 'input': '186', 'output': '33120\\n'}, {'type': 'stdin_stdout', 'input': '324', 'output': '57960\\n'}, {'type': 'stdin_stdout', 'input': '239', 'output': '42660\\n'}, {'type': 'stdin_stdout', 'input': '144', 'output': '25560\\n'}, {'type': 'stdin_stdout', 'input': '166', 'output': '29520\\n'}, {'type': 'stdin_stdout', 'input': '320', 'output': '57240\\n'}, {'type': 'stdin_stdout', 'input': '382', 'output': '68400\\n'}, {'type': 'stdin_stdout', 'input': '58', 'output': '10080\\n'}, {'type': 'stdin_stdout', 'input': '-11', 'output': '-2340\\n'}, {'type': 'stdin_stdout', 'input': '-7', 'output': '-1620\\n'}, {'type': 'stdin_stdout', 'input': '-12', 'output': '-2520\\n'}, {'type': 'stdin_stdout', 'input': '-24', 'output': '-4680\\n'}, {'type': 'stdin_stdout', 'input': '-34', 'output': '-6480\\n'}, {'type': 'stdin_stdout', 'input': '-14', 'output': '-2880\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79909","program":"```python\na = int(input())\nprint(int(a * 180 - 360))\n```","inputs":"3","output":"180","actual_output":"180\n","execution_success":true,"sample_index":12722},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03164 Educational DP Contest - Knapsack 2","prompt":"Solve the following coding problem using the programming language python:\n\nThere are N items, numbered 1, 2, \\ldots, N. For each i (1 \\leq i \\leq N), Item i has a weight of w_i and a value of v_i.\n\nTaro has decided to choose some of the N items and carry them home in a knapsack. The capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.\n\nFind the maximum possible sum of the values of items that Taro takes home.\n\nConstraints\n\n* All values in input are integers.\n* 1 \\leq N \\leq 100\n* 1 \\leq W \\leq 10^9\n* 1 \\leq w_i \\leq W\n* 1 \\leq v_i \\leq 10^3\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN W\nw_1 v_1\nw_2 v_2\n:\nw_N v_N\n\n\nOutput\n\nPrint the maximum possible sum of the values of items that Taro takes home.\n\nExamples\n\nInput\n\n3 8\n3 30\n4 50\n5 60\n\n\nOutput\n\n90\n\n\nInput\n\n1 1000000000\n1000000000 10\n\n\nOutput\n\n10\n\n\nInput\n\n6 15\n6 5\n5 6\n6 4\n6 6\n3 5\n7 2\n\n\nOutput\n\n17\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN,W = map(int,input().split())\ndp = [0]+[W+1]*(N*10**3)\nfor i in range(N):\n w,v = map(int,input().split())\n for j in range(N*10**3+1-v)[::-1]:\n dp[j+v] = min(dp[j+v],dp[j]+w)\nfor i in range(N*10**3+1)[::-1]:\n if dp[i]<=W:\n print(i)\n exit()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 1000000000\\n1000000000 10', 'output': '10'}, {'type': 'stdin_stdout', 'input': '6 15\\n6 5\\n5 6\\n6 4\\n6 6\\n3 5\\n7 2', 'output': '17'}, {'type': 'stdin_stdout', 'input': '3 8\\n3 30\\n4 50\\n5 60', 'output': '90'}, {'type': 'stdin_stdout', 'input': '1 1000000000\\n0000000000 10', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '6 15\\n6 5\\n5 6\\n3 4\\n6 6\\n3 5\\n7 2', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '3 8\\n3 30\\n4 35\\n5 60', 'output': '90\\n'}, {'type': 'stdin_stdout', 'input': '3 8\\n3 30\\n4 35\\n5 78', 'output': '108\\n'}, {'type': 'stdin_stdout', 'input': '6 15\\n6 5\\n0 6\\n3 4\\n6 6\\n3 5\\n7 3', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '3 8\\n3 30\\n0 35\\n5 78', 'output': '143\\n'}, 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10","output":"10","actual_output":"10\n","execution_success":true,"sample_index":12723},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03306 SoundHound Inc. Programming Contest 2018 -Masters Tournament- - + Graph","prompt":"Solve the following coding problem using the programming language python:\n\nKenkoooo found a simple connected graph. The vertices are numbered 1 through n. The i-th edge connects Vertex u_i and v_i, and has a fixed integer s_i.\n\nKenkoooo is trying to write a positive integer in each vertex so that the following condition is satisfied:\n\n* For every edge i, the sum of the positive integers written in Vertex u_i and v_i is equal to s_i.\n\n\n\nFind the number of such ways to write positive integers in the vertices.\n\nConstraints\n\n* 2 \\leq n \\leq 10^5\n* 1 \\leq m \\leq 10^5\n* 1 \\leq u_i < v_i \\leq n\n* 2 \\leq s_i \\leq 10^9\n* If i\\neq j, then u_i \\neq u_j or v_i \\neq v_j.\n* The graph is connected.\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nn m\nu_1 v_1 s_1\n:\nu_m v_m s_m\n\n\nOutput\n\nPrint the number of ways to write positive integers in the vertices so that the condition is satisfied.\n\nExamples\n\nInput\n\n3 3\n1 2 3\n2 3 5\n1 3 4\n\n\nOutput\n\n1\n\n\nInput\n\n4 3\n1 2 6\n2 3 7\n3 4 5\n\n\nOutput\n\n3\n\n\nInput\n\n8 7\n1 2 1000000000\n2 3 2\n3 4 1000000000\n4 5 2\n5 6 1000000000\n6 7 2\n7 8 1000000000\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nfrom sys import setrecursionlimit\nfrom collections import deque\nfrom heapq import heappop, heappush\n\nsetrecursionlimit(10**9)\n#input = sys.stdin.readline\n\ndef inpl(): return map(int, input().split())\nINF = 2**31\n\nN, M = inpl()\nD = [[] for _ in range(N+1)]\n\nfor _ in range(M):\n u, v, s = inpl()\n D[u].append((v, s))\n D[v].append((u, s))\n\nS = [2**31] * (N+1)\nC = [-1] * (N+1)\nS[1] = 0\nC[1] = 0\n\nL = [1] * (N+1)\nR = [2**31] * (N+1)\n\nQ = [1]\n\nstate = 1\nwhile Q:\n p = Q.pop()\n for q, s in D[p]:\n if C[q] == -1:\n C[q] = int(not C[p])\n S[q] = s - S[p]\n if C[q]:\n R[q] = min(R[q], S[q] - 1)\n else:\n L[q] = max(1, -S[q] + 1)\n Q.append(q)\n elif C[q] == C[p]:\n if C[p] == 0:\n a = s - S[p]\n b = S[q]\n else:\n a = S[q]\n b = s - S[p]\n\n if (a-b)%2:\n state = 0\n Q = []\n break\n t = (a-b)//2\n if t == L[q] == R[q]:\n continue\n R[q] = t\n L[q] = t\n Q.append(q)\n\n\n else:\n if S[q] != s - S[p]:\n state = 0\n Q = []\n break\n\nif state == 0:\n print(0)\nelif state == 1:\n print(max(0, min(R) - max(L) + 1))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 3\\n1 2 6\\n2 3 7\\n3 4 5', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 3\\n2 3 5\\n1 3 4', 'output': '1'}, {'type': 'stdin_stdout', 'input': '8 7\\n1 2 1000000000\\n2 3 2\\n3 4 1000000000\\n4 5 2\\n5 6 1000000000\\n6 7 2\\n7 8 1000000000', 'output': '0'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 6\\n2 3 7\\n3 4 7', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 3\\n2 3 0\\n1 3 4', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 6\\n2 3 7\\n3 4 3', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 4\\n2 3 7\\n3 4 7', 'output': 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1010010000\\n4 5 2\\n5 6 1000000000\\n6 7 2\\n2 8 1000000000', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_79917","program":"```python\nimport sys\nfrom sys import setrecursionlimit\nfrom collections import deque\nfrom heapq import heappop, heappush\n\nsetrecursionlimit(10**9)\n#input = sys.stdin.readline\n\ndef inpl(): return map(int, input().split())\nINF = 2**31\n\nN, M = inpl()\nD = [[] for _ in range(N+1)]\n\nfor _ in range(M):\n u, v, s = inpl()\n D[u].append((v, s))\n D[v].append((u, s))\n\nS = [2**31] * (N+1)\nC = [-1] * (N+1)\nS[1] = 0\nC[1] = 0\n\nL = [1] * (N+1)\nR = [2**31] * (N+1)\n\nQ = [1]\n\nstate = 1\nwhile Q:\n p = Q.pop()\n for q, s in D[p]:\n if C[q] == -1:\n C[q] = int(not C[p])\n S[q] = s - S[p]\n if C[q]:\n R[q] = min(R[q], S[q] - 1)\n else:\n L[q] = max(1, -S[q] + 1)\n Q.append(q)\n elif C[q] == C[p]:\n if C[p] == 0:\n a = s - S[p]\n b = S[q]\n else:\n a = S[q]\n b = s - S[p]\n\n if (a-b)%2:\n state = 0\n Q = []\n break\n t = (a-b)//2\n if t == L[q] == R[q]:\n continue\n R[q] = t\n L[q] = t\n Q.append(q)\n\n\n else:\n if S[q] != s - S[p]:\n state = 0\n Q = []\n break\n\nif state == 0:\n print(0)\nelif state == 1:\n print(max(0, min(R) - max(L) + 1))\n\n```","inputs":"4 3\n1 2 6\n2 3 7\n3 4 5","output":"3","actual_output":"3\n","execution_success":true,"sample_index":12724},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03466 AtCoder Grand Contest 020 - Min Max Repetition","prompt":"Solve the following coding problem using the programming language python:\n\nLet f(A, B), where A and B are positive integers, be the string satisfying the following conditions:\n\n* f(A, B) has length A + B;\n* f(A, B) contains exactly A letters `A` and exactly B letters `B`;\n* The length of the longest substring of f(A, B) consisting of equal letters (ex., `AAAAA` or `BBBB`) is as small as possible under the conditions above;\n* f(A, B) is the lexicographically smallest string satisfying the conditions above.\n\n\n\nFor example, f(2, 3) = `BABAB`, and f(6, 4) = `AABAABAABB`.\n\nAnswer Q queries: find the substring of f(A_i, B_i) from position C_i to position D_i (1-based).\n\nConstraints\n\n* 1 \\leq Q \\leq 10^3\n* 1 \\leq A_i, B_i \\leq 5 \\times 10^8\n* 1 \\leq C_i \\leq D_i \\leq A_i + B_i\n* D_i - C_i + 1 \\leq 100\n* All input values are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nQ\nA_1 B_1 C_1 D_1\nA_2 B_2 C_2 D_2\n:\nA_Q B_Q C_Q D_Q\n\n\nOutput\n\nFor each query i in order of input, print a line containing the substring of f(A_i, B_i) from position C_i to position D_i (1-based).\n\nExample\n\nInput\n\n5\n2 3 1 5\n6 4 1 10\n2 3 4 4\n6 4 3 7\n8 10 5 8\n\n\nOutput\n\nBABAB\nAABAABAABB\nA\nBAABA\nABAB\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nT=int(input())\nfor TT in range(T):\n\ta,b,c,d=map(int,input().split(' '))\n\tl,x,y=(a+b)//(min(a,b)+1),0,0\n\tif a*l<=b:\n\t\ty=a+b\n\telif b*l<=a:\n\t\tx=a+b\n\telse:\n\t\tx,y=(a*l-b)//(l-1),(b*l-a)//(l-1) #Like G2 tong long\n\tout=\"\"\n\tfor i in range(c,d+1):\n\t\tif i<=x:\n\t\t\tout+=\"AB\"[i%(l+1)==0]\n\t\telif a+b-i+1<=y:\n\t\t\tout+=\"BA\"[(a+b-i+1)%(l+1)==0]\n\t\telse:\n\t\t\tout+=\"AB\"[a-x+x//(l+1)-y//(l+1)==0]\n\tprint(out)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n2 3 1 5\\n6 4 1 10\\n2 3 4 4\\n6 4 3 7\\n8 10 5 8', 'output': 'BABAB\\nAABAABAABB\\nA\\nBAABA\\nABAB'}, {'type': 'stdin_stdout', 'input': '5\\n2 3 1 5\\n6 4 1 10\\n2 3 4 4\\n6 4 3 7\\n8 10 5 14', 'output': 'BABAB\\nAABAABAABB\\nA\\nBAABA\\nABABBABBAB\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 3 1 5\\n6 4 1 10\\n2 3 4 4\\n6 4 3 7\\n8 2 5 8', 'output': 'BABAB\\nAABAABAABB\\nA\\nBAABA\\nAAAB\\n'}, {'type': 'stdin_stdout', 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1 7\\n8 4 5 7', 'output': 'BBBAB\\nBB\\n\\nAABAABA\\nABA\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 6 2 5\\n9 4 1 2\\n2 3 6 4\\n5 4 3 7\\n12 1 3 10', 'output': 'BABB\\nAA\\n\\nABABA\\nAAAABAAA\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 6 2 7\\n9 7 1 1\\n1 2 6 4\\n6 4 3 7\\n12 2 9 8', 'output': 'BBABBB\\nA\\n\\nBAABA\\n\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 6 1 5\\n6 7 1 2\\n2 3 6 4\\n2 4 3 2\\n8 2 4 2', 'output': 'BBBBB\\nBA\\n\\n\\n\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 3 1 0\\n9 8 1 10\\n2 1 11 4\\n6 4 3 4\\n12 2 4 0', 'output': '\\nABABABABAB\\n\\nBA\\n\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 6 1 5\\n1 6 1 2\\n2 3 6 1\\n6 4 1 8\\n8 4 5 7', 'output': 'BBBAB\\nBB\\n\\nAABAABAA\\nABA\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 3 1 5\\n18 4 1 10\\n4 3 4 4\\n6 4 3 7\\n8 2 10 8', 'output': 'ABABA\\nAAAABAAAAB\\nB\\nBAABA\\n\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 3 1 4\\n11 6 1 7\\n2 3 4 4\\n7 3 3 7\\n12 2 5 8', 'output': 'BABA\\nAABAABA\\nA\\nBAABA\\nBAAA\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 1 5\\n6 4 4 0\\n2 8 10 4\\n6 2 1 1\\n15 1 5 8', 'output': 'BBBBB\\n\\n\\nA\\nAAAA\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 3 1 4\\n11 6 1 7\\n2 3 4 4\\n7 2 3 7\\n12 2 5 8', 'output': 'BABA\\nAABAABA\\nA\\nABAAA\\nBAAA\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 12 2 5\\n9 4 1 2\\n2 3 6 4\\n5 5 3 7\\n12 1 3 10', 'output': 'BBBA\\nAA\\n\\nABABA\\nAAAABAAA\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 1 5\\n6 4 4 0\\n2 8 10 4\\n6 2 1 1\\n15 1 5 10', 'output': 'BBBBB\\n\\n\\nA\\nAAAABA\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0 5 1 5\\n6 4 4 0\\n2 8 10 4\\n6 2 1 1\\n15 2 5 10', 'output': 'BBBBB\\n\\n\\nA\\nABAAAA\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 536870912}","problem_id":"vfc_79921","program":"```python\nT=int(input())\nfor TT in range(T):\n\ta,b,c,d=map(int,input().split(' '))\n\tl,x,y=(a+b)//(min(a,b)+1),0,0\n\tif a*l<=b:\n\t\ty=a+b\n\telif b*l<=a:\n\t\tx=a+b\n\telse:\n\t\tx,y=(a*l-b)//(l-1),(b*l-a)//(l-1) #Like G2 tong long\n\tout=\"\"\n\tfor i in range(c,d+1):\n\t\tif i<=x:\n\t\t\tout+=\"AB\"[i%(l+1)==0]\n\t\telif a+b-i+1<=y:\n\t\t\tout+=\"BA\"[(a+b-i+1)%(l+1)==0]\n\t\telse:\n\t\t\tout+=\"AB\"[a-x+x//(l+1)-y//(l+1)==0]\n\tprint(out)\n\n```","inputs":"5\n2 3 1 5\n6 4 1 10\n2 3 4 4\n6 4 3 7\n8 10 5 8","output":"BABAB\nAABAABAABB\nA\nBAABA\nABAB","actual_output":"BABAB\nAABAABAABB\nA\nBAABA\nABAB\n","execution_success":true,"sample_index":12725},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03626 AtCoder Beginner Contest 071 - Coloring Dominoes","prompt":"Solve the following coding problem using the programming language python:\n\nWe have a board with a 2 \\times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \\times 2 or 2 \\times 1 square.\n\nThen, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.\n\nFind the number of such ways to paint the dominoes, modulo 1000000007.\n\nThe arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:\n\n* Each domino is represented by a different English letter (lowercase or uppercase).\n* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.\n\nConstraints\n\n* 1 \\leq N \\leq 52\n* |S_1| = |S_2| = N\n* S_1 and S_2 consist of lowercase and uppercase English letters.\n* S_1 and S_2 represent a valid arrangement of dominoes.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nS_1\nS_2\n\n\nOutput\n\nPrint the number of such ways to paint the dominoes, modulo 1000000007.\n\nExamples\n\nInput\n\n3\naab\nccb\n\n\nOutput\n\n6\n\n\nInput\n\n1\nZ\nZ\n\n\nOutput\n\n3\n\n\nInput\n\n52\nRvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn\nRLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn\n\n\nOutput\n\n958681902\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN = int(input())\ngrids = [[s for s in input()],[s for s in input()]]\nMOD = 1000000007\n\nif grids[0][0] == grids[1][0]:\n prv_row_type = 1\n ans = 3\n posx = 1\nelse:\n prv_row_type = -1\n ans = 6\n posx = 2\n\nwhile posx < N:\n if grids[0][posx] == grids[1][posx]:\n if prv_row_type == 1: ans *= 2\n else: ans *= 1\n prv_row_type = 1\n posx += 1\n else:\n if prv_row_type == 1: ans *= 2\n else: ans *= 3\n prv_row_type = -1\n posx += 2\n\nprint(ans%MOD)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\nZ\\nZ', 'output': '3'}, 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'52\\nnHHppJGGCCjlAhrYebbicqKDSSakkEEffssZZFFQPPyyIWdttvvR\\nnzzTuJTuOOjlAhrYemmicqKDggaBBooMMVUXYUUQNNxxIWdxwLLR', 'output': '958681902\\n'}, {'type': 'stdin_stdout', 'input': '3\\naab\\nebb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbaa\\nbfb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\nb_b\\nb`b', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbaa\\nbdb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncaa\\ncca', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbab\\nbhb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\nb^b\\nb`b', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '52\\nRvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn\\nRLLwwdWImxNNQUUXXVVMMooBBaggDKqcixmeYrhAljOOTTJuuzzn', 'output': '958681902\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbbb\\nacb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '52\\nnHHppJGGCCjlAhrYebbicqKDSSakkEEffssZZFFQPPyyIWdttvvR\\nnzzuuJTTOOjlAhrYemmicqKDggaBBooMMVVXXUUQNNwxIWdwwLLR', 'output': '958681902\\n'}, {'type': 'stdin_stdout', 'input': '3\\naab\\naeb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\naab\\nbgb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\naac\\ncbc', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbaa\\nbc`', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\naaa\\ndea', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\na^b\\nacb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '52\\nnHHppJGGCCjlAhrYebbicqKDSSakkEEffssZZFFQPPyyIWdttvvR\\nnzzuuJTTOOjlAhrYemmicqKDggaBBooMMVUWYUUQLNxxIWdxwLNR', 'output': '958681902\\n'}, {'type': 'stdin_stdout', 'input': '3\\naab\\ncfb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n`^b\\n`bb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncaa\\ncda', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\ncaa\\ncba', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '52\\nRvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn\\nRLLwwdWIxxNUQNUXXVVMLooCBaggDKqcinmeYrhAljOOTTJuuzzn', 'output': '958681902\\n'}, {'type': 'stdin_stdout', 'input': '3\\naab\\nbhb', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\nbaa\\nbfc', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '52\\nRvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn\\nRKLwwdWImxNNQUUXXVVMMooBBaggDKqcixmeYrhAljOOTTJuuzzn', 'output': '958681902\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79925","program":"```python\nN = int(input())\ngrids = [[s for s in input()],[s for s in input()]]\nMOD = 1000000007\n\nif grids[0][0] == grids[1][0]:\n prv_row_type = 1\n ans = 3\n posx = 1\nelse:\n prv_row_type = -1\n ans = 6\n posx = 2\n\nwhile posx < N:\n if grids[0][posx] == grids[1][posx]:\n if prv_row_type == 1: ans *= 2\n else: ans *= 1\n prv_row_type = 1\n posx += 1\n else:\n if prv_row_type == 1: ans *= 2\n else: ans *= 3\n prv_row_type = -1\n posx += 2\n\nprint(ans%MOD)\n```","inputs":"1\nZ\nZ","output":"3","actual_output":"3\n","execution_success":true,"sample_index":12726},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03786 AtCoder Grand Contest 011 - Colorful Creatures","prompt":"Solve the following coding problem using the programming language python:\n\nSnuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.\n\nEvery creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \\leq 2 \\times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.\n\nSnuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.\n\nConstraints\n\n* 2 \\leq N \\leq 100000\n* 1 \\leq A_i \\leq 10^9\n* A_i is an integer.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN\nA_1 A_2 \u2026 A_N\n\n\nOutput\n\nPrint the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.\n\nExamples\n\nInput\n\n3\n3 1 4\n\n\nOutput\n\n2\n\n\nInput\n\n5\n1 1 1 1 1\n\n\nOutput\n\n5\n\n\nInput\n\n6\n40 1 30 2 7 20\n\n\nOutput\n\n4\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN = int(input())\nA = list(map(int, input().split()))\nA.sort()\nsumA = sum(A)-A[N-1]\nmemo = 0\n\nfor i in range(N-1,-1,-1):\n if sumA*2\n\nA pyramid with N=4 steps\n\nSnuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:\n\n* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.\n\n\n\n\n\nWriting integers into the blocks\n\nAfterwards, he erased all integers written into the blocks. Now, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, ..., a_{2N-1}).\n\nFind the integer written into the block of step 1.\n\nConstraints\n\n* 2\u2264N\u226410^5\n* (a_1, a_2, ..., a_{2N-1}) is a permutation of (1, 2, ..., 2N-1).\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN\na_1 a_2 ... a_{2N-1}\n\n\nOutput\n\nPrint the integer written into the block of step 1.\n\nExamples\n\nInput\n\n4\n1 6 3 7 4 5 2\n\n\nOutput\n\n4\n\n\nInput\n\n2\n1 2 3\n\n\nOutput\n\n2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# def makelist(n, m):\n# \treturn [[0 for i in range(m)] for j in range(n)]\n\nN = int(input())\na = [0] + list(map(int, input().split()))\n\ndef check(n):\n\tb = [False]*(len(a))\n\tfor i in range(1, len(a)):\n\t\tif a[i] >= n:\n\t\t\tb[i] = True\n\t\telse:\n\t\t\tb[i] = False\n\n\tr = int(1e9)\n\tl = int(1e9)\n\trb = b[N]\n\tlb = b[N]\n\tfor i in range(1, N):\n\t\tif lb == b[N-i]:\n\t\t\tl = i\n\t\t\tbreak\n\t\telse:\n\t\t\tlb = b[N-i]\n\t\t\n\tfor i in range(1, N):\n\t\tif rb == b[N+i]:\n\t\t\tr = i\n\t\t\tbreak\n\t\telse:\n\t\t\trb = b[N+i]\n\tif r == int(1e9) and l == int(1e9):\n\t\tif N % 2 == 1:\n\t\t\treturn b[N]\n\t\telse:\n\t\t\treturn not b[N]\n\telse:\n\t\tif r < l:\n\t\t\treturn rb\n\t\telse:\n\t\t\treturn lb\n\n# \u6761\u4ef6\u3092\u6e80\u305f\u3059\u6700\u5c0f\u306e\u5024\u3092\u8fd4\u3059\ndef binarySearch(small, big):\n\tmid = (big + small) // 2\n\tif big - small <= 1:\n\t\tif check(small): return small\n\t\telse: return big\n\telse:\n\t\tif not check(mid):\n\t\t\treturn binarySearch(small, mid)\n\t\telse:\n\t\t\treturn binarySearch(mid, big)\n\nprint(binarySearch(2, 2*N-2))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n1 2 3', 'output': '2'}, {'type': 'stdin_stdout', 'input': '4\\n1 6 3 7 4 5 2', 'output': '4'}, {'type': 'stdin_stdout', 'input': '2\\n0 2 3', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 6 3 7 4 5 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 1 7', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 3 1 4 9 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 5 5 0 8 2 0', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-2 3 3 7 7 5 0', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-2 3 3 7 6 1 0', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 2 3', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 6 3 4 4 5 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 2 5', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 4 3 4 4 5 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 2 7', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 3 4 4 5 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 3 4 4 9 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 1 7', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 1 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 0 1 4 9 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 1 4', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 0 1 2 9 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-4 1 4', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 2 0 1 2 9 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-4 1 8', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 2 0 1 2 18 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 3 0 1 2 18 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2 1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 6 0 7 4 5 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 2 6', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 6 3 7 4 1 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 1 3', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 6 3 4 4 5 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 2 10', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 4 2 4 4 5 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 2 9', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 3 4 4 4 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 1 11', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 10 3 4 4 9 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 2 7', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 3 1 2 9 2', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 8 0 1 4 9 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 1 3', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 0 2 2 9 2', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 2 0 1 2 9 0', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 2 0 1 2 18 4', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 1 0 1 2 18 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 3 1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 6 1 7 4 5 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 1 6', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 6 3 14 4 1 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-2 6 3 4 4 5 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 2 13', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 4 2 4 4 5 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2 9', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 5 3 4 4 4 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1 11', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 3 4 4 9 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-4 2 7', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 3 1 2 9 0', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 1 5', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 2 0 1 2 4 0', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 2 0 1 2 29 4', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 1 0 1 2 18 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1 1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 6 1 0 4 5 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1 6', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 6 3 14 4 1 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-2 8 3 4 4 5 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2 6', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 4 0 4 4 5 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2 14', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 5 5 4 4 4 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 3 4 1 9 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-5 2 7', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 6 1 2 9 0', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 1 1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 2 0 1 4 4 0', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 0 1 2 29 4', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-2 1 0 1 2 18 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 1 1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 6 1 -1 4 5 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1 9', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 6 3 14 4 1 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-2 8 3 4 4 5 0', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 3 6', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 4 -1 4 4 5 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2 28', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-1 5 5 4 4 4 0', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 3 4 1 0 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-5 2 12', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 5 6 0 2 9 0', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-3 1 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 2 -1 1 4 4 0', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 2 1 1 2 29 4', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 1 0 1 2 24 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 1 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 12 1 -1 4 5 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1 13', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 6 3 13 4 1 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n-2 2 3 4 4 5 0', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 3 6', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 4 -1 4 7 5 1', 'output': '4\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79933","program":"```python\n# def makelist(n, m):\n# \treturn [[0 for i in range(m)] for j in range(n)]\n\nN = int(input())\na = [0] + list(map(int, input().split()))\n\ndef check(n):\n\tb = [False]*(len(a))\n\tfor i in range(1, len(a)):\n\t\tif a[i] >= n:\n\t\t\tb[i] = True\n\t\telse:\n\t\t\tb[i] = False\n\n\tr = int(1e9)\n\tl = int(1e9)\n\trb = b[N]\n\tlb = b[N]\n\tfor i in range(1, N):\n\t\tif lb == b[N-i]:\n\t\t\tl = i\n\t\t\tbreak\n\t\telse:\n\t\t\tlb = b[N-i]\n\t\t\n\tfor i in range(1, N):\n\t\tif rb == b[N+i]:\n\t\t\tr = i\n\t\t\tbreak\n\t\telse:\n\t\t\trb = b[N+i]\n\tif r == int(1e9) and l == int(1e9):\n\t\tif N % 2 == 1:\n\t\t\treturn b[N]\n\t\telse:\n\t\t\treturn not b[N]\n\telse:\n\t\tif r < l:\n\t\t\treturn rb\n\t\telse:\n\t\t\treturn lb\n\n# \u6761\u4ef6\u3092\u6e80\u305f\u3059\u6700\u5c0f\u306e\u5024\u3092\u8fd4\u3059\ndef binarySearch(small, big):\n\tmid = (big + small) // 2\n\tif big - small <= 1:\n\t\tif check(small): return small\n\t\telse: return big\n\telse:\n\t\tif not check(mid):\n\t\t\treturn binarySearch(small, mid)\n\t\telse:\n\t\t\treturn binarySearch(mid, big)\n\nprint(binarySearch(2, 2*N-2))\n\n```","inputs":"2\n1 2 3","output":"2","actual_output":"2\n","execution_success":true,"sample_index":12728},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00044 Prime Number II","prompt":"Solve the following coding problem using the programming language python:\n\nA prime number is an integer that is greater than 1 and can only be divided by itself or 1. For example, 2 is a prime number because it is divisible only by 2 and 1, but 12 is not a prime number because it is divisible by 2, 3, 4, 6 in addition to 12 and 1.\n\nWhen you enter the integer n, write a program that outputs the largest prime number less than n and the smallest prime number greater than n.\n\n\n\nInput\n\nGiven multiple datasets. Each dataset is given n (3 \u2264 n \u2264 50,000) on one row.\n\nThe number of datasets does not exceed 50.\n\nOutput\n\nFor each dataset, output the largest prime number less than n and the smallest prime number greater than n on one line, separated by a space.\n\nExample\n\nInput\n\n19\n3517\n\n\nOutput\n\n17 23\n3511 3527\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom math import sqrt, ceil\n\nN = 53000\ntemp = [True]*(N+1)\ntemp[0] = temp[1] = False\nfor i in range(2, ceil(sqrt(N+1))):\n if temp[i]:\n temp[i+i::i] = [False]*(len(temp[i+i::i]))\n\nwhile True:\n try:\n n = int(input())\n print(n-1-temp[n-1:0:-1].index(True), n+1+temp[n+1:].index(True))\n except EOFError: break\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '19\\n3517', 'output': '17 23\\n3511 3527'}, {'type': 'stdin_stdout', 'input': '19\\n5214', 'output': '17 23\\n5209 5227\\n'}, {'type': 'stdin_stdout', 'input': '19\\n3257', 'output': '17 23\\n3253 3259\\n'}, {'type': 'stdin_stdout', 'input': '19\\n6476', 'output': '17 23\\n6473 6481\\n'}, {'type': 'stdin_stdout', 'input': '19\\n10887', 'output': '17 23\\n10883 10889\\n'}, {'type': 'stdin_stdout', 'input': '19\\n17073', 'output': '17 23\\n17053 17077\\n'}, {'type': 'stdin_stdout', 'input': '19\\n30085', 'output': '17 23\\n30071 30089\\n'}, {'type': 'stdin_stdout', 'input': '19\\n357', 'output': '17 23\\n353 359\\n'}, {'type': 'stdin_stdout', 'input': '19\\n443', 'output': '17 23\\n439 449\\n'}, {'type': 'stdin_stdout', 'input': '19\\n631', 'output': '17 23\\n619 641\\n'}, {'type': 'stdin_stdout', 'input': '19\\n862', 'output': '17 23\\n859 863\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1431', 'output': '17 23\\n1429 1433\\n'}, {'type': 'stdin_stdout', 'input': '19\\n2850', 'output': '17 23\\n2843 2851\\n'}, {'type': 'stdin_stdout', 'input': '19\\n995', 'output': '17 23\\n991 997\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1278', 'output': '17 23\\n1277 1279\\n'}, {'type': 'stdin_stdout', 'input': '19\\n507', 'output': '17 23\\n503 509\\n'}, {'type': 'stdin_stdout', 'input': '19\\n774', 'output': '17 23\\n773 787\\n'}, {'type': 'stdin_stdout', 'input': '19\\n502', 'output': '17 23\\n499 503\\n'}, {'type': 'stdin_stdout', 'input': '19\\n734', 'output': '17 23\\n733 739\\n'}, {'type': 'stdin_stdout', 'input': '19\\n755', 'output': '17 23\\n751 757\\n'}, {'type': 'stdin_stdout', 'input': '19\\n52', 'output': '17 23\\n47 53\\n'}, {'type': 'stdin_stdout', 'input': '19\\n74', 'output': '17 23\\n73 79\\n'}, {'type': 'stdin_stdout', 'input': '19\\n116', 'output': '17 23\\n113 127\\n'}, {'type': 'stdin_stdout', 'input': '19\\n38', 'output': '17 23\\n37 41\\n'}, {'type': 'stdin_stdout', 'input': '19\\n13', 'output': '17 23\\n11 17\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1437', 'output': '17 23\\n1433 1439\\n'}, {'type': 'stdin_stdout', 'input': '19\\n3994', 'output': '17 23\\n3989 4001\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1836', 'output': '17 23\\n1831 1847\\n'}, {'type': 'stdin_stdout', 'input': '19\\n7459', 'output': '17 23\\n7457 7477\\n'}, {'type': 'stdin_stdout', 'input': '19\\n21592', 'output': '17 23\\n21589 21599\\n'}, {'type': 'stdin_stdout', 'input': '19\\n16181', 'output': '17 23\\n16141 16183\\n'}, {'type': 'stdin_stdout', 'input': '19\\n38456', 'output': '17 23\\n38453 38459\\n'}, {'type': 'stdin_stdout', 'input': '19\\n540', 'output': '17 23\\n523 541\\n'}, {'type': 'stdin_stdout', 'input': '19\\n627', 'output': '17 23\\n619 631\\n'}, {'type': 'stdin_stdout', 'input': '19\\n795', 'output': '17 23\\n787 797\\n'}, {'type': 'stdin_stdout', 'input': '19\\n591', 'output': '17 23\\n587 593\\n'}, {'type': 'stdin_stdout', 'input': '19\\n937', 'output': '17 23\\n929 941\\n'}, {'type': 'stdin_stdout', 'input': '19\\n3625', 'output': '17 23\\n3623 3631\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1163', 'output': '17 23\\n1153 1171\\n'}, {'type': 'stdin_stdout', 'input': '19\\n863', 'output': '17 23\\n859 877\\n'}, {'type': 'stdin_stdout', 'input': '19\\n209', 'output': '17 23\\n199 211\\n'}, {'type': 'stdin_stdout', 'input': '19\\n853', 'output': '17 23\\n839 857\\n'}, {'type': 'stdin_stdout', 'input': '19\\n933', 'output': '17 23\\n929 937\\n'}, {'type': 'stdin_stdout', 'input': '19\\n869', 'output': '17 23\\n863 877\\n'}, {'type': 'stdin_stdout', 'input': '19\\n24', 'output': '17 23\\n23 29\\n'}, {'type': 'stdin_stdout', 'input': '19\\n30', 'output': '17 23\\n29 31\\n'}, {'type': 'stdin_stdout', 'input': '19\\n231', 'output': '17 23\\n229 233\\n'}, {'type': 'stdin_stdout', 'input': '19\\n217', 'output': '17 23\\n211 223\\n'}, {'type': 'stdin_stdout', 'input': '19\\n58', 'output': '17 23\\n53 59\\n'}, {'type': 'stdin_stdout', 'input': '19\\n92', 'output': '17 23\\n89 97\\n'}, {'type': 'stdin_stdout', 'input': '19\\n6777', 'output': '17 23\\n6763 6779\\n'}, {'type': 'stdin_stdout', 'input': '19\\n2232', 'output': '17 23\\n2221 2237\\n'}, {'type': 'stdin_stdout', 'input': '19\\n14650', 'output': '17 23\\n14639 14653\\n'}, {'type': 'stdin_stdout', 'input': '19\\n11037', 'output': '17 23\\n11027 11047\\n'}, {'type': 'stdin_stdout', 'input': '19\\n25278', 'output': '17 23\\n25261 25301\\n'}, {'type': 'stdin_stdout', 'input': '19\\n882', 'output': '17 23\\n881 883\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1040', 'output': '17 23\\n1039 1049\\n'}, {'type': 'stdin_stdout', 'input': '19\\n740', 'output': '17 23\\n739 743\\n'}, {'type': 'stdin_stdout', 'input': '19\\n973', 'output': '17 23\\n971 977\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1861', 'output': '17 23\\n1847 1867\\n'}, {'type': 'stdin_stdout', 'input': '19\\n260', 'output': '17 23\\n257 263\\n'}, {'type': 'stdin_stdout', 'input': '19\\n112', 'output': '17 23\\n109 113\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1455', 'output': '17 23\\n1453 1459\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1499', 'output': '17 23\\n1493 1511\\n'}, {'type': 'stdin_stdout', 'input': '19\\n9', 'output': '17 23\\n7 11\\n'}, {'type': 'stdin_stdout', 'input': '19\\n69', 'output': '17 23\\n67 71\\n'}, {'type': 'stdin_stdout', 'input': '19\\n432', 'output': '17 23\\n431 433\\n'}, {'type': 'stdin_stdout', 'input': '19\\n263', 'output': '17 23\\n257 269\\n'}, {'type': 'stdin_stdout', 'input': '19\\n36', 'output': '17 23\\n31 37\\n'}, {'type': 'stdin_stdout', 'input': '19\\n46', 'output': '17 23\\n43 47\\n'}, {'type': 'stdin_stdout', 'input': '19\\n9573', 'output': '17 23\\n9551 9587\\n'}, {'type': 'stdin_stdout', 'input': '19\\n3645', 'output': '17 23\\n3643 3659\\n'}, {'type': 'stdin_stdout', 'input': '19\\n28682', 'output': '17 23\\n28669 28687\\n'}, {'type': 'stdin_stdout', 'input': '19\\n3906', 'output': '17 23\\n3889 3907\\n'}, {'type': 'stdin_stdout', 'input': '19\\n23319', 'output': '17 23\\n23311 23321\\n'}, {'type': 'stdin_stdout', 'input': '19\\n613', 'output': '17 23\\n607 617\\n'}, {'type': 'stdin_stdout', 'input': '19\\n462', 'output': '17 23\\n461 463\\n'}, {'type': 'stdin_stdout', 'input': '19\\n226', 'output': '17 23\\n223 227\\n'}, {'type': 'stdin_stdout', 'input': '19\\n1017', 'output': '17 23\\n1013 1019\\n'}, {'type': 'stdin_stdout', 'input': '19\\n103', 'output': '17 23\\n101 107\\n'}, {'type': 'stdin_stdout', 'input': '19\\n2325', 'output': '17 23\\n2311 2333\\n'}, {'type': 'stdin_stdout', 'input': '19\\n332', 'output': '17 23\\n331 337\\n'}, {'type': 'stdin_stdout', 'input': '19\\n12', 'output': '17 23\\n11 13\\n'}, {'type': 'stdin_stdout', 'input': '19\\n130', 'output': '17 23\\n127 131\\n'}, {'type': 'stdin_stdout', 'input': '19\\n199', 'output': '17 23\\n197 211\\n'}, {'type': 'stdin_stdout', 'input': '19\\n294', 'output': '17 23\\n293 307\\n'}, {'type': 'stdin_stdout', 'input': '19\\n63', 'output': '17 23\\n61 67\\n'}, {'type': 'stdin_stdout', 'input': '19\\n21', 'output': '17 23\\n19 23\\n'}, {'type': 'stdin_stdout', 'input': '19\\n8247', 'output': '17 23\\n8243 8263\\n'}, {'type': 'stdin_stdout', 'input': '19\\n2184', 'output': '17 23\\n2179 2203\\n'}, {'type': 'stdin_stdout', 'input': '19\\n3490', 'output': '17 23\\n3469 3491\\n'}, {'type': 'stdin_stdout', 'input': '19\\n5780', 'output': '17 23\\n5779 5783\\n'}, {'type': 'stdin_stdout', 'input': '19\\n37649', 'output': '17 23\\n37643 37657\\n'}, {'type': 'stdin_stdout', 'input': '19\\n761', 'output': '17 23\\n757 769\\n'}, {'type': 'stdin_stdout', 'input': '19\\n81', 'output': '17 23\\n79 83\\n'}, {'type': 'stdin_stdout', 'input': '19\\n693', 'output': '17 23\\n691 701\\n'}, {'type': 'stdin_stdout', 'input': '19\\n759', 'output': '17 23\\n757 761\\n'}, {'type': 'stdin_stdout', 'input': '19\\n442', 'output': '17 23\\n439 443\\n'}, {'type': 'stdin_stdout', 'input': '19\\n191', 'output': '17 23\\n181 193\\n'}, {'type': 'stdin_stdout', 'input': '19\\n2085', 'output': '17 23\\n2083 2087\\n'}, {'type': 'stdin_stdout', 'input': '19\\n109', 'output': '17 23\\n107 113\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79937","program":"```python\nfrom math import sqrt, ceil\n\nN = 53000\ntemp = [True]*(N+1)\ntemp[0] = temp[1] = False\nfor i in range(2, ceil(sqrt(N+1))):\n if temp[i]:\n temp[i+i::i] = [False]*(len(temp[i+i::i]))\n\nwhile True:\n try:\n n = int(input())\n print(n-1-temp[n-1:0:-1].index(True), n+1+temp[n+1:].index(True))\n except EOFError: break\n\n```","inputs":"19\n3517","output":"17 23\n3511 3527","actual_output":"17 23\n3511 3527\n","execution_success":true,"sample_index":12729},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00176 What Color?","prompt":"Solve the following coding problem using the programming language python:\n\nTaro, who aims to become a web designer, is currently training. My senior at the office tells me that the background color of this page is # ffe085, which is a color number peculiar to web design, but I can't think of what kind of color it is.\n\nThis color number represents the intensity of each of the three primary colors of light, red, green, and blue. Specifically, it is a combination of three 2-digit hexadecimal numbers, and when the color number is \u201c#RGB\u201d, R is the intensity of red, G is the intensity of green, and is the intensity of blue. .. Each value is from 00 to ff.\n\nFor Taro who is not familiar with color numbers, please create a program that inputs the color number and outputs the name of the closest color from the color table. The table of colors used is as follows.\n\n| Color name | Red intensity | Green intensity | Blue intensity\n--- | --- | --- | --- | ---\n| black | 00 | 00 | 00\n| blue | 00 | 00 | ff\n| lime | 00 | ff | 00\naqua | 00 | ff | ff\n| red | ff | 00 | 00\n| fuchsia | ff | 00 | ff\n| yellow | ff | ff | 00\n| white | ff | ff | ff\n\n\n\n\nThe \"closest color\" is defined as follows. When the intensities of red, green, and blue at a given color number are R, G, and B, respectively, and the intensities of red, green, and blue of the kth color in the table are Rk, Gk, and Bk, respectively. The color with the smallest dk value calculated by the following formula is the closest color.\n\n\n\n\n\nIf there are multiple colors with the same dk value, the color at the top of the table will be the closest color.\n\n\n\nInput\n\nA sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. For each dataset, a string representing the color number is given on one line in #RGB format.\n\nThe number of datasets does not exceed 1000.\n\nOutput\n\nOutputs the name of the closest color for each dataset on one line.\n\nExamples\n\nInput\n\n#ffe085\n#787878\n#decade\n#ff55ff\n0\n\n\nOutput\n\nwhite\nblack\nwhite\nfuchsia\n\n\nInput\n\nffe085\n787878\ndecade\nff55ff\n0\n\n\nOutput\n\nwhite\nblack\nwhite\nfuchsia\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nCOLOR = {\n \"000000\": \"black\",\n \"0000ff\": \"blue\",\n \"00ff00\": \"lime\",\n \"00ffff\": \"aqua\",\n \"ff0000\": \"red\",\n \"ff00ff\": \"fuchsia\",\n \"ffff00\": \"yellow\",\n \"ffffff\": \"white\"\n}\n\nwhile True:\n\n input_data = input()\n\n if len(input_data) == 1:\n break\n\n color_code = \"\"\n\n for first, second in zip(input_data[1::2], input_data[2::2]):\n if int(first + second, 16) <= 127:\n color_code += \"00\"\n else:\n color_code += \"ff\"\n\n print(COLOR[color_code])\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '#ffe085\\n#787878\\n#decade\\n#ff55ff\\n0', 'output': 'white\\nblack\\nwhite\\nfuchsia'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n787878\\ndecade\\nff55ff\\n0', 'output': 'white\\nblack\\nwhite\\nfuchsia'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n787878\\ndfcade\\nff55ff\\n0', 'output': 'red\\nyellow\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '#ffe085\\n#787878\\n\"decade\\n#ff55ff\\n0', 'output': 'white\\nblack\\nwhite\\nfuchsia\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f5\\n976991\\ndebade\\nff55ff\\n0', 'output': 'red\\nlime\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f5\\n1006397\\ndebade\\nff55ff\\n0', 'output': 'red\\nblue\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '#ffe075\\n#787878\\n#decade\\n#ff55ff\\n0', 'output': 'yellow\\nblack\\nwhite\\nfuchsia\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n1502551\\ndfcaed\\nff55ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ff80e5\\n787878\\ndfcade\\nff5f5f\\n0', 'output': 'red\\nyellow\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f5\\n1830286\\nbedade\\nff55ff\\n0', 'output': 'red\\nfuchsia\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n935354\\ndfaced\\nf5f5ff\\n0', 'output': 'red\\nblack\\nyellow\\nblack\\n'}, {'type': 'stdin_stdout', 'input': '580eff\\n310329\\ndebade\\ngf55ff\\n0', 'output': 'yellow\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '5f0ef8\\n1830286\\ndedabe\\nff45fe\\n0', 'output': 'yellow\\nfuchsia\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ef04f8\\n391744\\nebcdea\\nfe45ff\\n0', 'output': 'red\\nred\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'eff408\\n159071\\naedcbe\\nfe4ff5\\n0', 'output': 'red\\nblack\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '804ffe\\n159071\\nafdcbe\\nfe4ef5\\n0', 'output': 'lime\\nblack\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f5\\n1006397\\nbedade\\nff5ff5\\n0', 'output': 'red\\nblue\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n454885\\ndfaced\\nf5f5ff\\n0', 'output': 'red\\nlime\\nyellow\\nblack\\n'}, {'type': 'stdin_stdout', 'input': 'ff81e5\\n787878\\ncfcadf\\nf6f5ff\\n0', 'output': 'red\\nyellow\\nyellow\\nblack\\n'}, {'type': 'stdin_stdout', 'input': 'ef04f8\\n391744\\nebcdea\\nfe4f5f\\n0', 'output': 'red\\nred\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '5e08ff\\n850039\\ndfcadf\\nff5f6f\\n0', 'output': 'yellow\\nblack\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'e0f4f8\\n199441\\nfadcbe\\nfe4ef5\\n0', 'output': 'black\\nred\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'ff0e85\\n787878\\ndfcead\\nff55ef\\n0', 'output': 'yellow\\nyellow\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '4e08ff\\n787878\\ndfcade\\nf5f5ff\\n0', 'output': 'yellow\\nyellow\\nyellow\\nblack\\n'}, {'type': 'stdin_stdout', 'input': '508eff\\n935354\\ndecafd\\nff55ff\\n0', 'output': 'lime\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'f5e08e\\n310329\\ndebade\\ngf55ff\\n0', 'output': 'black\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '580efe\\n442825\\ndebade\\ngf56ff\\n0', 'output': 'yellow\\nlime\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '5f08ff\\n1408162\\ndfcadf\\nff5f6f\\n0', 'output': 'yellow\\nlime\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f4\\n1298398\\necdeea\\nfe45ff\\n0', 'output': 'red\\naqua\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '4e08ff\\n787878\\ndfcade\\nff6f5f\\n0', 'output': 'yellow\\nyellow\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'e0f4f8\\n224219\\nfbdcae\\nee4ff5\\n0', 'output': 'black\\nblack\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'gf80e5\\n4921737\\nedfaec\\nf55fff\\n0', 'output': 'red\\nred\\nyellow\\nlime\\n'}, {'type': 'stdin_stdout', 'input': 'f5e08e\\n387761\\ncebdae\\ngf55ff\\n0', 'output': 'black\\nred\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '58f0ef\\n2992289\\ndaddfc\\n5f5fef\\n0', 'output': 'red\\nfuchsia\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'ff80e5\\n504999\\ndfcadf\\nff5f6f\\n0', 'output': 'red\\nlime\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '804ffe\\n299342\\nfadcbe\\nfe4ef5\\n0', 'output': 'lime\\nred\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '4f0ef8\\n184234\\necdeea\\nfe45ff\\n0', 'output': 'yellow\\nred\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n732786\\neecadf\\nf55fff\\n0', 'output': 'red\\nblack\\nyellow\\nlime\\n'}, {'type': 'stdin_stdout', 'input': '4e08ff\\n781713\\ndfcade\\nf5f6ff\\n0', 'output': 'yellow\\nred\\nyellow\\nblack\\n'}, {'type': 'stdin_stdout', 'input': '80e5ff\\n3306089\\ndebade\\nef55ff\\n0', 'output': 'black\\nblue\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'gf80e5\\n7529039\\nedfaec\\nf5fff5\\n0', 'output': 'red\\nlime\\nyellow\\nlime\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n382417\\ndfaced\\ne5f5ff\\n0', 'output': 'red\\nred\\nyellow\\nblack\\n'}, {'type': 'stdin_stdout', 'input': '580eff\\n1809084\\ndfaced\\nff55ff\\n0', 'output': 'yellow\\nwhite\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '580eff\\n1764590\\ndebbde\\nff55ff\\n0', 'output': 'yellow\\nblue\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'gf80e5\\n1549482\\nfdacfc\\nef5e5f\\n0', 'output': 'red\\naqua\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '5f0ef8\\n1225493\\ndebbde\\n5f5fff\\n0', 'output': 'yellow\\nblue\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '5f08ef\\n1408162\\ndfcadf\\nf65fff\\n0', 'output': 'yellow\\nlime\\nyellow\\nlime\\n'}, {'type': 'stdin_stdout', 'input': '804ffe\\n255990\\nbfdace\\nff45ff\\n0', 'output': 'lime\\nlime\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'gf81f5\\n1510681\\nedfadc\\ne5fff5\\n0', 'output': 'red\\nblue\\nyellow\\nlime\\n'}, {'type': 'stdin_stdout', 'input': '804ffe\\n246837\\nebcdaf\\nef4ef5\\n0', 'output': 'lime\\nlime\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'f740ef\\n808873\\nebcdea\\nfe44ff\\n0', 'output': 'black\\nlime\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '5f08ef\\n232747\\ndfcadf\\nf65fff\\n0', 'output': 'yellow\\nblack\\nyellow\\nlime\\n'}, {'type': 'stdin_stdout', 'input': 'ff80e5\\n1485485\\nffdadc\\nf6f5ff\\n0', 'output': 'red\\nblue\\nyellow\\nblack\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n787878\\ndfcaed\\nff55ff\\n0', 'output': 'red\\nyellow\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n787878\\ndebade\\nff55ff\\n0', 'output': 'red\\nyellow\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f5\\n787878\\ndebade\\nff55ff\\n0', 'output': 'red\\nyellow\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n787878\\ndecadf\\nff55ff\\n0', 'output': 'red\\nyellow\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ff80e5\\n787878\\ndfcade\\nff55ff\\n0', 'output': 'red\\nyellow\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n1041244\\ndebade\\nff55ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '8ff0f5\\n787878\\ndebade\\nff55ff\\n0', 'output': 'red\\nyellow\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '8fe05f\\n976991\\ndebade\\nff55ff\\n0', 'output': 'red\\nlime\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f5\\n1006397\\nbedade\\nff55ff\\n0', 'output': 'red\\nblue\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '#ffe075\\n#787878\\n#decace\\n#ff55ff\\n0', 'output': 'yellow\\nblack\\nwhite\\nfuchsia\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n1233823\\ndecadf\\nff55ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n1502551\\ndfaced\\nff55ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n310329\\ndebade\\nff55ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'gfe085\\n1233823\\ndecadf\\nff55ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ff80e5\\n787878\\ndfcade\\nff5f6f\\n0', 'output': 'red\\nyellow\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n935354\\ndfaced\\nff55ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ffe085\\n310329\\ndebade\\ngf55ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f5\\n1830286\\ndedabe\\nff55ff\\n0', 'output': 'red\\nfuchsia\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'gfe085\\n2115943\\ndecadf\\nff55ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ff80e5\\n787878\\ndfcadf\\nff5f6f\\n0', 'output': 'red\\nyellow\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f5\\n1830286\\ndedabe\\nff45ff\\n0', 'output': 'red\\nfuchsia\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'gfe085\\n2115943\\ndecadf\\nf5f5ff\\n0', 'output': 'red\\nblack\\nyellow\\nblack\\n'}, {'type': 'stdin_stdout', 'input': 'ff80e5\\n787878\\ncfcadf\\nff5f6f\\n0', 'output': 'red\\nyellow\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '580eff\\n310329\\ndebadd\\ngf55ff\\n0', 'output': 'yellow\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f5\\n1830286\\ndedabe\\nff54ff\\n0', 'output': 'red\\nfuchsia\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'gfe085\\n3294614\\ndecadf\\nf5f5ff\\n0', 'output': 'red\\nblack\\nyellow\\nblack\\n'}, {'type': 'stdin_stdout', 'input': 'ff81e5\\n787878\\ncfcadf\\nff5f6f\\n0', 'output': 'red\\nyellow\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '580eff\\n310329\\ncebadd\\ngf55ff\\n0', 'output': 'yellow\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '8fe0f5\\n1830286\\ndedabe\\nff45fe\\n0', 'output': 'red\\nfuchsia\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ff81e5\\n787878\\ncfcadf\\nff5e6f\\n0', 'output': 'red\\nyellow\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'ff81e5\\n787878\\nfdacfc\\nff5e6f\\n0', 'output': 'red\\nyellow\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '5f0ef8\\n1830286\\ndedabe\\nfe45ff\\n0', 'output': 'yellow\\nfuchsia\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ff81e5\\n787878\\nfdacfc\\nef5e6f\\n0', 'output': 'red\\nyellow\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '4f0ef8\\n1830286\\ndedabe\\nfe45ff\\n0', 'output': 'yellow\\nfuchsia\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '4f0ef8\\n2375126\\ndedabe\\nfe45ff\\n0', 'output': 'yellow\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '4f0ef8\\n2375126\\nebaded\\nfe45ff\\n0', 'output': 'yellow\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '4f0ef8\\n2375126\\nebddea\\nfe45ff\\n0', 'output': 'yellow\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': '4f0ef8\\n2375126\\nebcdea\\nfe45ff\\n0', 'output': 'yellow\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ef04f8\\n2375126\\nebcdea\\nfe45ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ef04f8\\n678627\\nebcdea\\nfe45ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ef04f8\\n473362\\nebcdea\\nfe45ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ef04f8\\n473362\\naedcbe\\nfe45ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'ef04f8\\n159071\\naedcbe\\nfe45ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'eff408\\n159071\\naedcbe\\nfe45ff\\n0', 'output': 'red\\nblack\\nyellow\\nred\\n'}, {'type': 'stdin_stdout', 'input': 'eff408\\n159071\\naedcbe\\nfe4ef5\\n0', 'output': 'red\\nblack\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'eff408\\n159071\\nafdcbe\\nfe4ef5\\n0', 'output': 'red\\nblack\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '804ffe\\n159071\\nfadcbe\\nfe4ef5\\n0', 'output': 'lime\\nblack\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': '804ffe\\n159071\\nebcdaf\\nfe4ef5\\n0', 'output': 'lime\\nblack\\nyellow\\nyellow\\n'}, {'type': 'stdin_stdout', 'input': 'eff408\\n159071\\nfadcbe\\nfe4ef5\\n0', 'output': 'red\\nblack\\nyellow\\nyellow\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79941","program":"```python\nCOLOR = {\n \"000000\": \"black\",\n \"0000ff\": \"blue\",\n \"00ff00\": \"lime\",\n \"00ffff\": \"aqua\",\n \"ff0000\": \"red\",\n \"ff00ff\": \"fuchsia\",\n \"ffff00\": \"yellow\",\n \"ffffff\": \"white\"\n}\n\nwhile True:\n\n input_data = input()\n\n if len(input_data) == 1:\n break\n\n color_code = \"\"\n\n for first, second in zip(input_data[1::2], input_data[2::2]):\n if int(first + second, 16) <= 127:\n color_code += \"00\"\n else:\n color_code += \"ff\"\n\n print(COLOR[color_code])\n\n\n```","inputs":"#ffe085\n#787878\n#decade\n#ff55ff\n0","output":"white\nblack\nwhite\nfuchsia","actual_output":"white\nblack\nwhite\nfuchsia\n","execution_success":true,"sample_index":12730},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00332 Japanese Calendar","prompt":"Solve the following coding problem using the programming language python:\n\nThe \"Western calendar\" is a concept imported from the West, but in Japan there is a concept called the Japanese calendar, which identifies the \"era name\" by adding a year as a method of expressing the year on the calendar. For example, this year is 2016 in the Christian era, but 2016 in the Japanese calendar. Both are commonly used expressions of years, but have you ever experienced a situation where you know the year of a year but do not know how many years it is in the Japanese calendar, or vice versa?\n\nCreate a program that outputs the year of the Japanese calendar when the year is given in the Christian era, and the year of the Western calendar when the year is given in the Japanese calendar. However, the correspondence between the Western calendar and the Japanese calendar is as follows for the sake of simplicity.\n\nWestern calendar | Japanese calendar\n--- | ---\nFrom 1868 to 1911 | From the first year of the Meiji era to the 44th year of the Meiji era\n1912 to 1925 | Taisho 1st year to Taisho 14th year\nFrom 1926 to 1988 | From the first year of Showa to 1988\n1989-2016 | 1989-2016\n\n\n\n\nInput\n\nThe input is given in the following format.\n\n\nE Y\n\n\nThe input consists of one line, where E (0 \u2264 E \u2264 4) is the type of calendar given, Y is the year in that calendar, and when E is 0, the year Y (1868 \u2264 Y \u2264 2016), 1 When is the Meiji Y (1 \u2264 Y \u2264 44) year of the Japanese calendar, when it is 2, the Taisho Y (1 \u2264 Y \u2264 14) year of the Japanese calendar, and when it is 3, the Showa Y (1 \u2264 Y \u2264 63) of the Japanese calendar ) Year, 4 represents the Heisei Y (1 \u2264 Y \u2264 28) year of the Japanese calendar.\n\nOutput\n\nIf it is the Western calendar, it is converted to the Japanese calendar, and if it is the Japanese calendar, it is converted to the Western calendar. However, the result of converting the Western calendar to the Japanese calendar is output with the letter \"M\" in the Meiji era, the letter \"T\" in the Taisho era, the letter \"S\" in the Showa era, and the letter \"H\" in the Heisei era.\n\nExamples\n\nInput\n\n0 2015\n\n\nOutput\n\nH27\n\n\nInput\n\n0 1912\n\n\nOutput\n\nT1\n\n\nInput\n\n2 1\n\n\nOutput\n\n1912\n\n\nInput\n\n4 28\n\n\nOutput\n\n2016\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ne, y = map(int,input().split())\n\nif e == 0:\n if y < 1912:\n a = y - 1867\n print(\"M\", a, sep = '')\n elif y < 1926:\n a = y - 1911\n print(\"T\", a, sep = '')\n elif y < 1989:\n a = y - 1925\n print(\"S\", a, sep = '')\n elif y < 2017:\n a = y - 1988\n print(\"H\", a, sep = '')\nelif e == 1:\n a = 1867 + y\n print(a)\nelif e == 2:\n a = 1911 + y\n print(a)\nelif e == 3:\n a = 1925 + y\n print(a)\nelif e == 4:\n a = 1988 + y\n print(a)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '0 2015', 'output': 'H27'}, {'type': 'stdin_stdout', 'input': '0 1912', 'output': 'T1'}, {'type': 'stdin_stdout', 'input': '4 28', 'output': '2016'}, {'type': 'stdin_stdout', 'input': '2 1', 'output': '1912'}, {'type': 'stdin_stdout', 'input': '4 2', 'output': '1990\\n'}, {'type': 'stdin_stdout', 'input': '3 1', 'output': '1926\\n'}, {'type': 'stdin_stdout', 'input': '1 28', 'output': '1895\\n'}, {'type': 'stdin_stdout', 'input': '2 0', 'output': '1911\\n'}, {'type': 'stdin_stdout', 'input': '3 2', 'output': '1927\\n'}, {'type': 'stdin_stdout', 'input': '4 1', 'output': '1989\\n'}, {'type': 'stdin_stdout', 'input': '1 42', 'output': '1909\\n'}, {'type': 'stdin_stdout', 'input': '1 0', 'output': '1867\\n'}, {'type': 'stdin_stdout', 'input': '3 0', 'output': '1925\\n'}, {'type': 'stdin_stdout', 'input': '4 0', 'output': '1988\\n'}, {'type': 'stdin_stdout', 'input': '1 81', 'output': '1948\\n'}, {'type': 'stdin_stdout', 'input': '2 -1', 'output': '1910\\n'}, {'type': 'stdin_stdout', 'input': '3 -1', 'output': '1924\\n'}, {'type': 'stdin_stdout', 'input': '4 -1', 'output': '1987\\n'}, {'type': 'stdin_stdout', 'input': '1 125', 'output': '1992\\n'}, {'type': 'stdin_stdout', 'input': '1 -1', 'output': '1866\\n'}, {'type': 'stdin_stdout', 'input': '4 -2', 'output': '1986\\n'}, {'type': 'stdin_stdout', 'input': '1 68', 'output': '1935\\n'}, {'type': 'stdin_stdout', 'input': '1 -2', 'output': '1865\\n'}, {'type': 'stdin_stdout', 'input': '4 -4', 'output': '1984\\n'}, {'type': 'stdin_stdout', 'input': '1 36', 'output': '1903\\n'}, {'type': 'stdin_stdout', 'input': '1 -3', 'output': '1864\\n'}, {'type': 'stdin_stdout', 'input': '2 36', 'output': '1947\\n'}, {'type': 'stdin_stdout', 'input': '1 -4', 'output': '1863\\n'}, {'type': 'stdin_stdout', 'input': '2 45', 'output': '1956\\n'}, {'type': 'stdin_stdout', 'input': '2 17', 'output': '1928\\n'}, {'type': 'stdin_stdout', 'input': '2 25', 'output': '1936\\n'}, {'type': 'stdin_stdout', 'input': '2 3', 'output': '1914\\n'}, {'type': 'stdin_stdout', 'input': '2 5', 'output': '1916\\n'}, {'type': 'stdin_stdout', 'input': '0 1914', 'output': 'T3\\n'}, {'type': 'stdin_stdout', 'input': '4 46', 'output': '2034\\n'}, {'type': 'stdin_stdout', 'input': '1 1', 'output': '1868\\n'}, {'type': 'stdin_stdout', 'input': '4 3', 'output': '1991\\n'}, {'type': 'stdin_stdout', 'input': '1 30', 'output': '1897\\n'}, {'type': 'stdin_stdout', 'input': '1 2', 'output': '1869\\n'}, {'type': 'stdin_stdout', 'input': '1 14', 'output': '1881\\n'}, {'type': 'stdin_stdout', 'input': '2 2', 'output': '1913\\n'}, {'type': 'stdin_stdout', 'input': '2 125', 'output': '2036\\n'}, {'type': 'stdin_stdout', 'input': '1 4', 'output': '1871\\n'}, {'type': 'stdin_stdout', 'input': '2 27', 'output': '1938\\n'}, {'type': 'stdin_stdout', 'input': '1 -6', 'output': '1861\\n'}, {'type': 'stdin_stdout', 'input': '4 25', 'output': '2013\\n'}, {'type': 'stdin_stdout', 'input': '1 3', 'output': '1870\\n'}, {'type': 'stdin_stdout', 'input': '2 6', 'output': '1917\\n'}, {'type': 'stdin_stdout', 'input': '1 1914', 'output': '3781\\n'}, {'type': 'stdin_stdout', 'input': '4 16', 'output': '2004\\n'}, {'type': 'stdin_stdout', 'input': '2 30', 'output': '1941\\n'}, {'type': 'stdin_stdout', 'input': '3 4', 'output': '1929\\n'}, {'type': 'stdin_stdout', 'input': '1 12', 'output': '1879\\n'}, {'type': 'stdin_stdout', 'input': '2 141', 'output': '2052\\n'}, {'type': 'stdin_stdout', 'input': '1 6', 'output': '1873\\n'}, {'type': 'stdin_stdout', 'input': '1 -12', 'output': '1855\\n'}, {'type': 'stdin_stdout', 'input': '4 29', 'output': '2017\\n'}, {'type': 'stdin_stdout', 'input': '1 5', 'output': '1872\\n'}, {'type': 'stdin_stdout', 'input': '2 12', 'output': '1923\\n'}, {'type': 'stdin_stdout', 'input': '4 21', 'output': '2009\\n'}, {'type': 'stdin_stdout', 'input': '2 51', 'output': '1962\\n'}, {'type': 'stdin_stdout', 'input': '2 222', 'output': '2133\\n'}, {'type': 'stdin_stdout', 'input': '4 6', 'output': '1994\\n'}, {'type': 'stdin_stdout', 'input': '2 10', 'output': '1921\\n'}, {'type': 'stdin_stdout', 'input': '1 -17', 'output': '1850\\n'}, {'type': 'stdin_stdout', 'input': '2 29', 'output': '1940\\n'}, {'type': 'stdin_stdout', 'input': '1 9', 'output': '1876\\n'}, {'type': 'stdin_stdout', 'input': '3 12', 'output': '1937\\n'}, {'type': 'stdin_stdout', 'input': '4 26', 'output': '2014\\n'}, {'type': 'stdin_stdout', 'input': '4 51', 'output': '2039\\n'}, {'type': 'stdin_stdout', 'input': '2 219', 'output': '2130\\n'}, {'type': 'stdin_stdout', 'input': '2 -17', 'output': '1894\\n'}, {'type': 'stdin_stdout', 'input': '2 9', 'output': '1920\\n'}, {'type': 'stdin_stdout', 'input': '1 18', 'output': '1885\\n'}, {'type': 'stdin_stdout', 'input': '4 24', 'output': '2012\\n'}, {'type': 'stdin_stdout', 'input': '1 25', 'output': '1892\\n'}, {'type': 'stdin_stdout', 'input': '0 1891', 'output': 'M24\\n'}, {'type': 'stdin_stdout', 'input': '2 28', 'output': '1939\\n'}, {'type': 'stdin_stdout', 'input': '2 4', 'output': '1915\\n'}, {'type': 'stdin_stdout', 'input': '3 -3', 'output': '1922\\n'}, {'type': 'stdin_stdout', 'input': '1 250', 'output': '2117\\n'}, {'type': 'stdin_stdout', 'input': '2 -4', 'output': '1907\\n'}, {'type': 'stdin_stdout', 'input': '2 -3', 'output': '1908\\n'}, {'type': 'stdin_stdout', 'input': '2 65', 'output': '1976\\n'}, {'type': 'stdin_stdout', 'input': '2 71', 'output': '1982\\n'}, {'type': 'stdin_stdout', 'input': '2 33', 'output': '1944\\n'}, {'type': 'stdin_stdout', 'input': '3 25', 'output': '1950\\n'}, {'type': 'stdin_stdout', 'input': '3 6', 'output': '1931\\n'}, {'type': 'stdin_stdout', 'input': '1 10', 'output': '1877\\n'}, {'type': 'stdin_stdout', 'input': '2 146', 'output': '2057\\n'}, {'type': 'stdin_stdout', 'input': '1 7', 'output': '1874\\n'}, {'type': 'stdin_stdout', 'input': '2 -6', 'output': '1905\\n'}, {'type': 'stdin_stdout', 'input': '1 8', 'output': '1875\\n'}, {'type': 'stdin_stdout', 'input': '2 1914', 'output': '3825\\n'}, {'type': 'stdin_stdout', 'input': '4 8', 'output': '1996\\n'}, {'type': 'stdin_stdout', 'input': '4 30', 'output': '2018\\n'}, {'type': 'stdin_stdout', 'input': '1 24', 'output': '1891\\n'}, {'type': 'stdin_stdout', 'input': '2 70', 'output': '1981\\n'}, {'type': 'stdin_stdout', 'input': '2 43', 'output': '1954\\n'}, {'type': 'stdin_stdout', 'input': '1 -11', 'output': '1856\\n'}, {'type': 'stdin_stdout', 'input': '4 37', 'output': '2025\\n'}, {'type': 'stdin_stdout', 'input': '2 23', 'output': '1934\\n'}, {'type': 'stdin_stdout', 'input': '2 264', 'output': '2175\\n'}, {'type': 'stdin_stdout', 'input': '4 55', 'output': '2043\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79945","program":"```python\ne, y = map(int,input().split())\n\nif e == 0:\n if y < 1912:\n a = y - 1867\n print(\"M\", a, sep = '')\n elif y < 1926:\n a = y - 1911\n print(\"T\", a, sep = '')\n elif y < 1989:\n a = y - 1925\n print(\"S\", a, sep = '')\n elif y < 2017:\n a = y - 1988\n print(\"H\", a, sep = '')\nelif e == 1:\n a = 1867 + y\n print(a)\nelif e == 2:\n a = 1911 + y\n print(a)\nelif e == 3:\n a = 1925 + y\n print(a)\nelif e == 4:\n a = 1988 + y\n print(a)\n\n```","inputs":"0 2015","output":"H27","actual_output":"H27\n","execution_success":true,"sample_index":12731},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00690 A Long Ride on a Railway","prompt":"Solve the following coding problem using the programming language python:\n\nTravelling by train is fun and exciting. But more than that indeed. Young challenging boys often tried to purchase the longest single tickets and to single ride the longest routes of various railway systems. Route planning was like solving puzzles. However, once assisted by computers, and supplied with machine readable databases, it is not any more than elaborating or hacking on the depth-first search algorithms.\n\nMap of a railway system is essentially displayed in the form of a graph. (See the Figures below.) The vertices (i.e. points) correspond to stations and the edges (i.e. lines) correspond to direct routes between stations. The station names (denoted by positive integers and shown in the upright letters in the Figures) and direct route distances (shown in the slanted letters) are also given.\n\n\n\nThe problem is to find the length of the longest path and to form the corresponding list of stations on the path for each system. The longest of such paths is one that starts from one station and, after travelling many direct routes as far as possible without passing any direct route more than once, arrives at a station which may be the starting station or different one and is longer than any other sequence of direct routes. Any station may be visited any number of times in travelling the path if you like.\n\n\n\nInput\n\nThe graph of a system is defined by a set of lines of integers of the form:\n\nns| nl\n---|---\ns1,1 | s1,2 | d1\ns2,1 | s2,2 | d2\n...\nsnl,1 | snl,2 | dnl\n\nHere 1 <= ns <= 10 is the number of stations (so, station names are 1, 2, ..., ns), and 1 <= nl <= 20 is the number of direct routes in this graph.\n\nsi,1 and si,2 (i = 1, 2, ..., nl) are station names at the both ends of the i-th direct route. di >= 1 (i = 1, 2, ..., nl) is the direct route distance between two different stations si,1 and si,2.\n\nIt is also known that there is at most one direct route between any pair of stations, and all direct routes can be travelled in either directions. Each station has at most four direct routes leaving from it.\n\nThe integers in an input line are separated by at least one white space (i.e. a space character (ASCII code 32) or a tab character (ASCII code 9)), and possibly preceded and followed by a number of white spaces.\n\nThe whole input of this problem consists of a few number of sets each of which represents one graph (i.e. system) and the input terminates with two integer `0`'s in the line of next ns and nl.\n\nOutput\n\nPaths may be travelled from either end; loops can be traced clockwise or anticlockwise. So, the station lists for the longest path for Figure A are multiple like (in lexicographic order):\n\n\n2 3 4 5\n5 4 3 2\n\n\nFor Figure B, the station lists for the longest path are also multiple like (again in lexicographic order):\n\n\n6 2 5 9 6 7\n6 9 5 2 6 7\n7 6 2 5 9 6\n7 6 9 5 2 6\n\n\nYet there may be the case where the longest paths are not unique. (That is, multiple independent paths happen to have the same longest distance.) To make the answer canonical, it is required to answer the lexicographically least station list of the path(s) for each set. Thus for Figure A,\n\n\n2 3 4 5\n\n\nand for Figure B,\n\n\n6 2 5 9 6 7\n\nmust be reported as the answer station list in a single line. The integers in a station list must be separated by at least one white space. The line of station list must be preceded by a separate line that gives the length of the corresponding path. Every output line may start with white spaces. (See output sample.)\n\nExamples\n\nInput\n\n6 5\n 1 3 10\n 2 3 12\n 3 4 2\n 4 5 13\n 4 6 11\n10 10\n 1 2 11\n 2 3 25\n 2 5 81\n 2 6 82\n 4 5 58\n 5 9 68\n 6 7 80\n 6 9 67\n 8 9 44\n 9 10 21\n 0 0\n\n\nOutput\n\n27\n2 3 4 5\n378\n6 2 5 9 6 7\n\n\nInput\n\n6 5\n1 3 10\n2 3 12\n3 4 2\n4 5 13\n4 6 11\n10 10\n1 2 11\n2 3 25\n2 5 81\n2 6 82\n4 5 58\n5 9 68\n6 7 80\n6 9 67\n8 9 44\n9 10 21\n0 0\n\n\nOutput\n\n27\n2 3 4 5\n378\n6 2 5 9 6 7\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# AOJ 1108: A Long Ride on a Railway\n# Python3 2018.7.14 bal4u\n\ndef combi(k, a, w):\n\tglobal len, ans\n\tfor b in range(1, n+1):\n\t\tif b == a: continue\n\t\tfor i in range(m):\n\t\t\tif not f[i] and ((tbl[i][0] == a and tbl[i][1] == b) or\n\t\t\t (tbl[i][0] == b and tbl[i][1] == a)):\n\t\t\t\tf[i] = 1\n\t\t\t\ttmp[k] = b\n\t\t\t\tcombi(k+1, b, w + tbl[i][2])\n\t\t\t\tf[i] = 0\n\tif w > len:\n\t\tlen = w\n\t\tans = tmp[:k]\t\n\nans, tmp = [0]*12, [0]*12\nwhile True:\n\tn, m = map(int, input().split())\n\tif n == 0: break\n\ttbl = [list(map(int, input().split())) for i in range(m)]\n\tf, ans = [0]*m, []\n\tlen = 0\n\tfor a in range(1, n+1):\n\t\tfor b in range(1, n+1):\n\t\t\tif a == b: continue\n\t\t\tfor i in range(m):\n\t\t\t\tif not f[i] and ((tbl[i][0] == a and tbl[i][1] == b) or\n\t\t\t\t (tbl[i][0] == b and tbl[i][1] == a)):\n\t\t\t\t\tf[i] = 1\n\t\t\t\t\ttmp[0], tmp[1] = a, b\n\t\t\t\t\tcombi(2, b, tbl[i][2])\n\t\t\t\t\tf[i] = 0\n\tprint(len)\n\tprint(*ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '27\\n2 3 4 5\\n378\\n6 2 5 9 6 7'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 12\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 44\\n9 10 21\\n0 0', 'output': '27\\n2 3 4 5\\n378\\n6 2 5 9 6 7'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 12\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n4 9 68\\n6 7 80\\n6 9 67\\n8 9 44\\n9 10 21\\n0 0', 'output': '27\\n2 3 4 5\\n436\\n6 2 5 4 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 2 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '38\\n5 2 3 4 6\\n378\\n6 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 12\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 44\\n9 4 21\\n0 0', 'output': '27\\n2 3 4 5\\n421\\n5 2 6 9 4 5 9 8\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 12\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 82\\n9 4 21\\n0 0', 'output': '27\\n2 3 4 5\\n459\\n5 2 6 9 4 5 9 8\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 0\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 82\\n9 4 21\\n0 0', 'output': '25\\n1 3 4 5\\n459\\n5 2 6 9 4 5 9 8\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 12\\n 3 4 2\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '25\\n1 3 4 5\\n378\\n6 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 12\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n3 6 82\\n4 5 58\\n4 9 68\\n6 7 80\\n6 9 67\\n8 9 44\\n9 10 21\\n0 0', 'output': '27\\n2 3 4 5\\n461\\n6 3 2 5 4 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 12\\n 3 4 2\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 128\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '25\\n1 3 4 5\\n438\\n6 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 2 5 13\\n 4 6 11\\n10 10\\n 1 3 11\\n 2 3 25\\n 2 5 81\\n 3 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '38\\n5 2 3 4 6\\n403\\n6 3 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 12\\n 3 4 2\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 128\\n 6 7 80\\n 1 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '25\\n1 3 4 5\\n474\\n3 2 1 9 5 2 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 3 11\\n 2 3 25\\n 2 5 81\\n 3 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '27\\n2 3 4 5\\n403\\n6 3 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 16\\n 3 4 3\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 128\\n 6 7 80\\n 1 9 67\\n 8 9 44\\n 6 10 10\\n 0 0', 'output': '26\\n1 3 4 5\\n474\\n3 2 1 9 5 2 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 45\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '27\\n2 3 4 5\\n341\\n6 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 12\\n3 4 1\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 44\\n9 10 21\\n0 0', 'output': '26\\n2 3 4 5\\n378\\n6 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 2 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 1 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '38\\n5 2 3 4 6\\n389\\n6 1 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 12\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n3 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 82\\n9 4 21\\n0 0', 'output': '27\\n2 3 4 5\\n406\\n1 2 3 5 2 6 9 8\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 3 5 13\\n 4 6 11\\n10 10\\n 1 3 11\\n 2 3 25\\n 2 5 81\\n 3 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '26\\n5 3 4 6\\n403\\n6 3 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 16\\n 3 4 2\\n 4 5 25\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 128\\n 6 7 80\\n 1 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '37\\n1 3 4 5\\n474\\n3 2 1 9 5 2 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 16\\n 3 4 4\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 128\\n 6 7 80\\n 1 9 67\\n 8 9 44\\n 6 10 10\\n 0 0', 'output': '27\\n1 3 4 5\\n474\\n3 2 1 9 5 2 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 12\\n 3 4 2\\n 6 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 28\\n 9 10 21\\n 0 0', 'output': '36\\n1 3 4 6 5\\n378\\n6 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 3 5 13\\n 4 6 11\\n10 10\\n 1 3 11\\n 2 3 25\\n 2 5 81\\n 3 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 9\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '26\\n5 3 4 6\\n380\\n7 6 3 2 5 9 8\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 4 5 20\\n 4 6 11\\n10 10\\n 1 2 21\\n 2 3 25\\n 2 5 81\\n 2 6 45\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '34\\n2 3 4 5\\n341\\n6 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 12\\n 3 4 2\\n 6 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 1 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 28\\n 9 10 21\\n 0 0', 'output': '36\\n1 3 4 6 5\\n389\\n6 2 1 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 12\\n 3 4 2\\n 4 5 20\\n 4 6 11\\n10 10\\n 1 2 21\\n 2 3 25\\n 2 5 81\\n 2 6 45\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '32\\n1 3 4 5\\n341\\n6 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 10\\n 3 4 2\\n 6 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 12\\n 1 5 81\\n 2 6 65\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 28\\n 9 10 21\\n 0 0', 'output': '36\\n1 3 4 6 5\\n372\\n6 2 1 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 12\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n2 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 44\\n9 10 21\\n0 0', 'output': '27\\n2 3 4 5\\n389\\n6 2 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 13\\n2 3 12\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n4 9 68\\n6 7 80\\n6 9 67\\n8 9 44\\n9 10 21\\n0 0', 'output': '28\\n1 3 4 5\\n436\\n6 2 5 4 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 12\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n9 9 44\\n9 4 21\\n0 0', 'output': '27\\n2 3 4 5\\n434\\n5 4 9 9 5 2 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 12\\n3 4 2\\n4 5 13\\n2 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 82\\n9 4 21\\n0 0', 'output': '38\\n5 4 3 2 6\\n459\\n5 2 6 9 4 5 9 8\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 0\\n3 4 2\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n5 9 68\\n1 7 80\\n6 9 67\\n8 9 82\\n9 4 21\\n0 0', 'output': '25\\n1 3 4 5\\n469\\n7 1 2 6 9 4 5 9 8\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 2 5 13\\n 3 6 11\\n10 10\\n 1 3 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '36\\n5 2 3 6\\n378\\n6 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 0\\n3 4 2\\n4 5 13\\n4 6 12\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 10 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 82\\n9 4 21\\n0 0', 'output': '25\\n1 3 4 5\\n389\\n7 6 9 4 5 2 10\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 12\\n 3 4 2\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 2 81\\n 2 6 82\\n 4 5 58\\n 5 9 128\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '25\\n1 3 4 5\\n441\\n3 2 2 6 9 5 4\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 2 5 13\\n 4 6 11\\n10 10\\n 1 3 11\\n 2 3 25\\n 2 5 81\\n 3 6 82\\n 4 10 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '38\\n5 2 3 4 6\\n446\\n4 10 9 5 2 3 6 9 8\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 3 12\\n 3 4 2\\n 4 5 13\\n 4 6 22\\n10 10\\n 1 3 11\\n 2 3 25\\n 2 5 81\\n 3 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '36\\n2 3 4 6\\n403\\n6 3 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 16\\n 3 4 2\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 8\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 128\\n 6 7 80\\n 1 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '25\\n1 3 4 5\\n471\\n3 2 1 9 5 2 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 16\\n 3 4 2\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 7 5 58\\n 5 9 128\\n 6 7 80\\n 1 9 67\\n 8 9 44\\n 9 10 10\\n 0 0', 'output': '25\\n1 3 4 5\\n532\\n3 2 1 9 5 2 6 7 5\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 2 2 16\\n 3 4 3\\n 4 5 13\\n 4 6 11\\n10 10\\n 1 2 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 128\\n 3 7 80\\n 1 9 67\\n 8 9 44\\n 6 10 10\\n 0 0', 'output': '26\\n1 3 4 5\\n484\\n7 3 2 1 9 5 2 6 10\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 10\\n2 3 8\\n3 4 1\\n4 5 13\\n4 6 11\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 6 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 44\\n9 10 21\\n0 0', 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9 68\\n1 7 80\\n6 9 67\\n8 9 82\\n9 4 21\\n0 0', 'output': '25\\n1 3 4 5\\n454\\n7 1 2 6 9 4 5 9 8\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n 1 3 10\\n 3 3 12\\n 3 4 2\\n 2 5 13\\n 3 6 11\\n10 10\\n 1 3 11\\n 2 3 25\\n 2 5 81\\n 2 6 82\\n 4 5 58\\n 5 9 68\\n 6 7 80\\n 6 9 67\\n 8 9 44\\n 9 10 21\\n 0 0', 'output': '33\\n1 3 3 6\\n378\\n6 2 5 9 6 7\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 17\\n2 3 0\\n3 4 2\\n4 5 13\\n4 6 12\\n10 10\\n1 2 11\\n2 3 25\\n2 5 81\\n2 10 82\\n4 5 58\\n5 9 68\\n6 7 80\\n6 9 67\\n8 9 82\\n9 4 21\\n0 0', 'output': '32\\n1 3 4 5\\n389\\n7 6 9 4 5 2 10\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79953","program":"```python\n# AOJ 1108: A Long Ride on a Railway\n# Python3 2018.7.14 bal4u\n\ndef combi(k, a, w):\n\tglobal len, ans\n\tfor b in range(1, n+1):\n\t\tif b == a: continue\n\t\tfor i in range(m):\n\t\t\tif not f[i] and ((tbl[i][0] == a and tbl[i][1] == b) or\n\t\t\t (tbl[i][0] == b and tbl[i][1] == a)):\n\t\t\t\tf[i] = 1\n\t\t\t\ttmp[k] = b\n\t\t\t\tcombi(k+1, b, w + tbl[i][2])\n\t\t\t\tf[i] = 0\n\tif w > len:\n\t\tlen = w\n\t\tans = tmp[:k]\t\n\nans, tmp = [0]*12, [0]*12\nwhile True:\n\tn, m = map(int, input().split())\n\tif n == 0: break\n\ttbl = [list(map(int, input().split())) for i in range(m)]\n\tf, ans = [0]*m, []\n\tlen = 0\n\tfor a in range(1, n+1):\n\t\tfor b in range(1, n+1):\n\t\t\tif a == b: continue\n\t\t\tfor i in range(m):\n\t\t\t\tif not f[i] and ((tbl[i][0] == a and tbl[i][1] == b) or\n\t\t\t\t (tbl[i][0] == b and tbl[i][1] == a)):\n\t\t\t\t\tf[i] = 1\n\t\t\t\t\ttmp[0], tmp[1] = a, b\n\t\t\t\t\tcombi(2, b, tbl[i][2])\n\t\t\t\t\tf[i] = 0\n\tprint(len)\n\tprint(*ans)\n\n```","inputs":"6 5\n 1 3 10\n 2 3 12\n 3 4 2\n 4 5 13\n 4 6 11\n10 10\n 1 2 11\n 2 3 25\n 2 5 81\n 2 6 82\n 4 5 58\n 5 9 68\n 6 7 80\n 6 9 67\n 8 9 44\n 9 10 21\n 0 0","output":"27\n2 3 4 5\n378\n6 2 5 9 6 7","actual_output":"27\n2 3 4 5\n378\n6 2 5 9 6 7\n","execution_success":true,"sample_index":12732},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00831 Confusing Login Names","prompt":"Solve the following coding problem using the programming language python:\n\nMeikyokan University is very famous for its research and education in the area of computer science. This university has a computer center that has advanced and secure computing facilities including supercomputers and many personal computers connected to the Internet.\n\nOne of the policies of the computer center is to let the students select their own login names. Unfortunately, students are apt to select similar login names, and troubles caused by mistakes in entering or specifying login names are relatively common. These troubles are a burden on the staff of the computer center.\n\nTo avoid such troubles, Dr. Choei Takano, the chief manager of the computer center, decided to stamp out similar and confusing login names. To this end, Takano has to develop a program that detects confusing login names.\n\nBased on the following four operations on strings, the distance between two login names is determined as the minimum number of operations that transforms one login name to the other.\n\n1. Deleting a character at an arbitrary position.\n2. Inserting a character into an arbitrary position.\n3. Replacing a character at an arbitrary position with another character.\n4. Swapping two adjacent characters at an arbitrary position.\n\n\n\nFor example, the distance between \u201comura\u201d and \u201cmurai\u201d is two, because the following sequence of operations transforms \u201comura\u201d to \u201cmurai\u201d.\n\n\ndelete \u2018o\u2019 insert \u2018i\u2019\nomura --> mura --> murai\n\n\nAnother example is that the distance between \u201cakasan\u201d and \u201ckaason\u201d is also two.\n\n\nswap \u2018a\u2019 and \u2018k\u2019 replace \u2018a\u2019 with \u2018o\u2019\nakasan --> kaasan --> kaason\n\n\nTakano decided that two login names with a small distance are confusing and thus must be avoided.\n\nYour job is to write a program that enumerates all the confusing pairs of login names.\n\nBeware that the rules may combine in subtle ways. For instance, the distance between \u201cant\u201d and \u201cneat\u201d is two.\n\n\nswap \u2018a\u2019 and \u2018n\u2019 insert \u2018e\u2019\nant --> nat --> neat\n\n\n\n\nInput\n\nThe input consists of multiple datasets. Each dataset is given in the following format.\n\n\nn\nd\nname1\nname2\n...\nnamen\n\n\nThe first integer n is the number of login names. Then comes a positive integer d. Two login names whose distance is less than or equal to d are deemed to be confusing. You may assume that 0 < n \u2264 200 and 0 < d \u2264 2. The i-th student\u2019s login name is given by namei, which is composed of only lowercase letters. Its length is less than 16. You can assume that there are no duplicates in namei (1 \u2264 i \u2264 n).\n\nThe end of the input is indicated by a line that solely contains a zero.\n\nOutput\n\nFor each dataset, your program should output all pairs of confusing login names, one pair per line, followed by the total number of confusing pairs in the dataset.\n\nIn each pair, the two login names are to be separated only by a comma character (,), and the login name that is alphabetically preceding the other should appear first. The entire output of confusing pairs for each dataset must be sorted as follows. For two pairs \u201cw1,w2\u201d and \u201cw3,w4\u201d, if w1 alphabetically precedes w3, or they are the same and w2 precedes w4, then \u201cw1,w2\u201d must appear before \u201cw3,w4\u201d.\n\nExample\n\nInput\n\n8\n2\nomura\ntoshio\nraku\ntanaka\nimura\nyoshoi\nhayashi\nmiura\n3\n1\ntasaka\nnakata\ntanaka\n1\n1\nfoo\n5\n2\npsqt\nabcdef\nabzdefa\npqrst\nabdxcef\n0\n\n\nOutput\n\nimura,miura\nimura,omura\nmiura,omura\ntoshio,yoshoi\n4\ntanaka,tasaka\n1\n0\nabcdef,abdxcef\nabcdef,abzdefa\npqrst,psqt\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import Counter\nfrom itertools import permutations\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\n\ndef solve():\n N = int(readline())\n if N == 0:\n return False\n def dist(a, b):\n LA = len(a); LB = len(b)\n dp = [[10**18]*(LB+1) for i in range(LA+1)]\n dp[0][0] = 0\n for i in range(LA):\n for j in range(LB):\n v = dp[i][j]\n if a[i] == b[j]:\n dp[i+1][j+1] = min(dp[i+1][j+1], v)\n else:\n dp[i+1][j+1] = min(dp[i+1][j+1], v+1)\n dp[i+1][j] = min(dp[i+1][j], v+1)\n dp[i][j+1] = min(dp[i][j+1], v+1)\n dp[i+1][LB] = min(dp[i+1][LB], dp[i][LB]+1)\n for j in range(LB):\n dp[LA][j+1] = min(dp[LA][j+1], dp[LA][j] + 1)\n return dp[LA][LB]\n def check(a, b):\n LA = len(a); LB = len(b)\n if abs(LA - LB) > D:\n return False\n d = dist(a, b)\n if d <= D:\n return True\n if d == 2 and LA == LB:\n ra = []; rb = []; rp = []\n for i in range(LA):\n if a[i] != b[i]:\n rp.append(i)\n ra.append(a[i])\n rb.append(b[i])\n if len(rp) == 2 and rp[1] - rp[0] == 1:\n ra.reverse()\n if ra == rb:\n return True\n if D == 2:\n if d == 4 and LA == LB:\n ra = []; rb = []; rp = []\n for i in range(LA):\n if a[i] != b[i]:\n rp.append(i)\n ra.append(a[i])\n rb.append(b[i])\n if len(rp) == 4 and rp[1] - rp[0] == 1 and rp[3] - rp[2] == 1:\n ra[0], ra[1] = ra[1], ra[0]\n ra[2], ra[3] = ra[3], ra[2]\n return ra == rb\n if d == 3 and abs(LA - LB) < D:\n a = list(a); b = list(b)\n if not LA < LB:\n LA, LB = LB, LA\n a, b = b, a\n for i in range(LA-1):\n a[i], a[i+1] = a[i+1], a[i]\n if dist(a, b) <= D-1:\n return True\n for j in range(LA-1):\n a[j], a[j+1] = a[j+1], a[j]\n if a == b:\n return True\n a[j], a[j+1] = a[j+1], a[j]\n a[i], a[i+1] = a[i+1], a[i]\n return False\n D = int(readline())\n S = [readline().strip() for i in range(N)]\n ans = []\n for i in range(N):\n for j in range(i+1, N):\n if check(S[i], S[j]):\n ans.append((S[i], S[j]) if S[i] < S[j] else (S[j], S[i]))\n ans.sort()\n for e in ans:\n write(\"%s,%s\\n\" % e)\n write(\"%d\\n\" % len(ans))\n return True\nwhile solve():\n ...\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\ntanaka\\nimura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': 'imura,miura\\nimura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\ntanaka\\ninura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': 'inura,miura\\ninura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\nt`naka\\nioura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': 'ioura,miura\\nioura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\nt`naka\\niotra\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': 'miura,omura\\ntoshio,yoshoi\\n2\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\noihsot\\nraku\\nt`naka\\niotra\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': 'miura,omura\\n1\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\ntanaka\\nimura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\ntsrqp\\nabdxcef\\n0', 'output': 'imura,miura\\nimura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\n2\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\nt`naka\\nioura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefb\\npqrst\\nabdxcef\\n0', 'output': 'ioura,miura\\nioura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefb\\npqrst,psqt\\n3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\ntanaka\\narumi\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\ntsrqp\\nabdxcef\\n0', 'output': 'miura,omura\\ntoshio,yoshoi\\n2\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\n2\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\ntanaak\\ninura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nfbdxcea\\n0', 'output': 'inura,miura\\ninura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\ntanaka,tasaka\\n1\\n0\\nabcdef,abzdefa\\npqrst,psqt\\n2\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\nt`naka\\nioura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\naanakt\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefb\\npqrst\\nabdxcef\\n0', 'output': 'ioura,miura\\nioura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\n0\\n0\\nabcdef,abdxcef\\nabcdef,abzdefb\\npqrst,psqt\\n3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\nakan`t\\niotra\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\naacdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': 'miura,omura\\ntoshio,yoshoi\\n2\\ntanaka,tasaka\\n1\\n0\\npqrst,psqt\\n1\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\ntanaka\\narumi\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntaraka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\ntsrqp\\nabdxcef\\n0', 'output': 'miura,omura\\ntoshio,yoshoi\\n2\\ntanaka,taraka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\n2\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\ntanaak\\ninura\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\ntsrqp\\nfbdxcea\\n0', 'output': 'inura,miura\\ninura,omura\\nmiura,omura\\ntoshio,yoshoi\\n4\\ntanaka,tasaka\\n1\\n0\\nabcdef,abzdefa\\n1\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\nt`naka\\nioura\\nyoshoi\\nhayashi\\nimura\\n3\\n1\\ntasaka\\nnakata\\naanakt\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefb\\npqrst\\nabdxcef\\n0', 'output': 'imura,ioura\\nimura,omura\\nioura,omura\\ntoshio,yoshoi\\n4\\n0\\n0\\nabcdef,abdxcef\\nabcdef,abzdefb\\npqrst,psqt\\n3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\nakan`t\\niotra\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\ntsqp\\naacdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': 'miura,omura\\ntoshio,yoshoi\\n2\\ntanaka,tasaka\\n1\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomusa\\noihsot\\nraku\\nt`naka\\nartoh\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': '0\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\ntanaka\\narumi\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntaraka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\ntsrqp\\nabfxced\\n0', 'output': 'miura,omura\\ntoshio,yoshoi\\n2\\ntanaka,taraka\\n1\\n0\\nabcdef,abzdefa\\n1\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\narumo\\ntoshio\\nraku\\nakan`t\\niotra\\nyoshoi\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntanaka\\n1\\n1\\nfoo\\n5\\n2\\ntsqp\\naacdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': 'toshio,yoshoi\\n1\\ntanaka,tasaka\\n1\\n0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\nomura\\ntoshio\\nraku\\nt`naka\\nioura\\nyoshoi\\nhayashi\\nimura\\n3\\n1\\ntasak`\\nnakata\\nabnakt\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabceef\\nabzdefb\\npqrst\\nabdxcef\\n0', 'output': 'imura,ioura\\nimura,omura\\nioura,omura\\ntoshio,yoshoi\\n4\\n0\\n0\\npqrst,psqt\\n1\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1\\nomusa\\noihsot\\nraku\\nt`naka\\nartoh\\niohsoy\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntbnaka\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': '0\\n0\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1\\nomusa\\noihsot\\nraku\\nt`naka\\nartoh\\niohsoy\\nhayashi\\nmiura\\n3\\n1\\ntasaka\\nnakata\\ntbnaka\\n1\\n1\\nfoo\\n5\\n2\\npsqs\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': '0\\n0\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\n2\\n'}, {'type': 'stdin_stdout', 'input': '8\\n2\\narumo\\ntoshio\\nraku\\nt`naka\\nioura\\nyoshoi\\nhayashi\\nimura\\n3\\n1\\ntasak`\\nnakata\\nabnakt\\n1\\n1\\nfoo\\n5\\n2\\npsqt\\nabceef\\nabzdefb\\npqrst\\nabdxcef\\n0', 'output': 'imura,ioura\\ntoshio,yoshoi\\n2\\n0\\n0\\npqrst,psqt\\n1\\n'}, {'type': 'stdin_stdout', 'input': '8\\n1\\nomusa\\noihsot\\nraku\\nt`naka\\nartoh\\niohsoy\\nhayashi\\nmiura\\n3\\n2\\ntasaka\\nnakata\\ntbnaka\\n1\\n1\\nfoo\\n5\\n2\\npsqs\\nabcdef\\nabzdefa\\npqrst\\nabdxcef\\n0', 'output': '0\\ntasaka,tbnaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\n2\\n'}, {'type': 'stdin_stdout', 'input': 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'0\\ntanaka,tasaka\\n1\\n0\\nabcdef,abdxcef\\nabcdef,abzdefa\\npqrst,psqt\\n3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79957","program":"```python\nfrom collections import Counter\nfrom itertools import permutations\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\n\ndef solve():\n N = int(readline())\n if N == 0:\n return False\n def dist(a, b):\n LA = len(a); LB = len(b)\n dp = [[10**18]*(LB+1) for i in range(LA+1)]\n dp[0][0] = 0\n for i in range(LA):\n for j in range(LB):\n v = dp[i][j]\n if a[i] == b[j]:\n dp[i+1][j+1] = min(dp[i+1][j+1], v)\n else:\n dp[i+1][j+1] = min(dp[i+1][j+1], v+1)\n dp[i+1][j] = min(dp[i+1][j], v+1)\n dp[i][j+1] = min(dp[i][j+1], v+1)\n dp[i+1][LB] = min(dp[i+1][LB], dp[i][LB]+1)\n for j in range(LB):\n dp[LA][j+1] = min(dp[LA][j+1], dp[LA][j] + 1)\n return dp[LA][LB]\n def check(a, b):\n LA = len(a); LB = len(b)\n if abs(LA - LB) > D:\n return False\n d = dist(a, b)\n if d <= D:\n return True\n if d == 2 and LA == LB:\n ra = []; rb = []; rp = []\n for i in range(LA):\n if a[i] != b[i]:\n rp.append(i)\n ra.append(a[i])\n rb.append(b[i])\n if len(rp) == 2 and rp[1] - rp[0] == 1:\n ra.reverse()\n if ra == rb:\n return True\n if D == 2:\n if d == 4 and LA == LB:\n ra = []; rb = []; rp = []\n for i in range(LA):\n if a[i] != b[i]:\n rp.append(i)\n ra.append(a[i])\n rb.append(b[i])\n if len(rp) == 4 and rp[1] - rp[0] == 1 and rp[3] - rp[2] == 1:\n ra[0], ra[1] = ra[1], ra[0]\n ra[2], ra[3] = ra[3], ra[2]\n return ra == rb\n if d == 3 and abs(LA - LB) < D:\n a = list(a); b = list(b)\n if not LA < LB:\n LA, LB = LB, LA\n a, b = b, a\n for i in range(LA-1):\n a[i], a[i+1] = a[i+1], a[i]\n if dist(a, b) <= D-1:\n return True\n for j in range(LA-1):\n a[j], a[j+1] = a[j+1], a[j]\n if a == b:\n return True\n a[j], a[j+1] = a[j+1], a[j]\n a[i], a[i+1] = a[i+1], a[i]\n return False\n D = int(readline())\n S = [readline().strip() for i in range(N)]\n ans = []\n for i in range(N):\n for j in range(i+1, N):\n if check(S[i], S[j]):\n ans.append((S[i], S[j]) if S[i] < S[j] else (S[j], S[i]))\n ans.sort()\n for e in ans:\n write(\"%s,%s\\n\" % e)\n write(\"%d\\n\" % len(ans))\n return True\nwhile solve():\n ...\n\n```","inputs":"8\n2\nomura\ntoshio\nraku\ntanaka\nimura\nyoshoi\nhayashi\nmiura\n3\n1\ntasaka\nnakata\ntanaka\n1\n1\nfoo\n5\n2\npsqt\nabcdef\nabzdefa\npqrst\nabdxcef\n0","output":"imura,miura\nimura,omura\nmiura,omura\ntoshio,yoshoi\n4\ntanaka,tasaka\n1\n0\nabcdef,abdxcef\nabcdef,abzdefa\npqrst,psqt\n3","actual_output":"imura,miura\nimura,omura\nmiura,omura\ntoshio,yoshoi\n4\ntanaka,tasaka\n1\n0\nabcdef,abdxcef\nabcdef,abzdefa\npqrst,psqt\n3\n","execution_success":true,"sample_index":12733},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00962 Pizza Delivery","prompt":"Solve the following coding problem using the programming language python:\n\nProblem F Pizza Delivery\n\nAlyssa is a college student, living in New Tsukuba City. All the streets in the city are one-way. A new social experiment starting tomorrow is on alternative traffic regulation reversing the one-way directions of street sections. Reversals will be on one single street section between two adjacent intersections for each day; the directions of all the other sections will not change, and the reversal will be canceled on the next day.\n\nAlyssa orders a piece of pizza everyday from the same pizzeria. The pizza is delivered along the shortest route from the intersection with the pizzeria to the intersection with Alyssa's house.\n\nAltering the traffic regulation may change the shortest route. Please tell Alyssa how the social experiment will affect the pizza delivery route.\n\nInput\n\nThe input consists of a single test case in the following format.\n\n\n$n$ $m$\n$a_1$ $b_1$ $c_1$\n...\n$a_m$ $b_m$ $c_m$\n\n\nThe first line contains two integers, $n$, the number of intersections, and $m$, the number of street sections in New Tsukuba City ($2 \\leq n \\leq 100 000, 1 \\leq m \\leq 100 000$). The intersections are numbered $1$ through $n$ and the street sections are numbered $1$ through $m$.\n\nThe following $m$ lines contain the information about the street sections, each with three integers $a_i$, $b_i$, and $c_i$ ($1 \\leq a_i n, 1 \\leq b_i \\leq n, a_i \\ne b_i, 1 \\leq c_i \\leq 100 000$). They mean that the street section numbered $i$ connects two intersections with the one-way direction from $a_i$ to $b_i$, which will be reversed on the $i$-th day. The street section has the length of $c_i$. Note that there may be more than one street section connecting the same pair of intersections.\n\nThe pizzeria is on the intersection 1 and Alyssa's house is on the intersection 2. It is guaranteed that at least one route exists from the pizzeria to Alyssa's before the social experiment starts.\n\nOutput\n\nThe output should contain $m$ lines. The $i$-th line should be\n\n* HAPPY if the shortest route on the $i$-th day will become shorter,\n* SOSO if the length of the shortest route on the $i$-th day will not change, and\n* SAD if the shortest route on the $i$-th day will be longer or if there will be no route from the pizzeria to Alyssa's house.\n\n\n\nAlyssa doesn't mind whether the delivery bike can go back to the pizzeria or not.\n\nSample Input 1\n\n\n4 5\n1 3 5\n3 4 6\n4 2 7\n2 1 18\n2 3 12\n\n\nSample Output 1\n\n\nSAD\nSAD\nSAD\nSOSO\nHAPPY\n\n\nSample Input 2\n\n\n7 5\n1 3 2\n1 6 3\n4 2 4\n6 2 5\n7 5 6\n\n\nSample Output 2\n\n\nSOSO\nSAD\nSOSO\nSAD\nSOSO\n\n\nSample Input 3\n\n\n10 14\n1 7 9\n1 8 3\n2 8 4\n2 6 11\n3 7 8\n3 4 4\n3 2 1\n3 2 7\n4 8 4\n5 6 11\n5 8 12\n6 10 6\n7 10 8\n8 3 6\n\n\nSample Output 3\n\n\nSOSO\nSAD\nHAPPY\nSOSO\nSOSO\nSOSO\nSAD\nSOSO\nSOSO\nSOSO\nSOSO\nSOSO\nSOSO\nSAD\n\n\n\n\n\n\nExample\n\nInput\n\n4 5\n1 3 5\n3 4 6\n4 2 7\n2 1 18\n2 3 12\n\n\nOutput\n\nSAD\nSAD\nSAD\nSOSO\nHAPPY\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom heapq import heappush, heappop\nfrom collections import deque\nimport sys\nsys.setrecursionlimit(10**6)\nn, m = map(int, input().split())\nE = []\nG = [[] for i in range(n)]\nRG = [[] for i in range(n)]\nfor i in range(m):\n a, b, c = map(int, input().split())\n E.append((a-1, b-1, c))\n G[a-1].append((b-1, c, i))\n RG[b-1].append((a-1, c, i))\ndef dijkstra(G, s):\n dist = [10**18]*n\n dist[s] = 0\n que = [(0, s)]\n while que:\n co, v = heappop(que)\n if dist[v] < co:\n continue\n for w, c, i in G[v]:\n if co + c < dist[w]:\n dist[w] = co + c\n heappush(que, (co + c, w))\n return dist\nD = dijkstra(G, 0)\nRD = dijkstra(RG, 1)\n\nG0 = [[] for i in range(n)]\nused = set([1])\ndeq = deque([1])\nP = set()\nwhile deq:\n v = deq.popleft()\n for w, c, i in RG[v]:\n if D[w] + c == D[v]:\n P.add(i)\n if w not in used:\n used.add(w)\n deq.append(w)\n G0[v].append((w, i))\n G0[w].append((v, i))\n\nPB = set()\nlabel = [None]*n\ngen = 1\ncost = [0]*n\ndef dfs(u, p, i):\n global gen\n res = 0\n p_cnt = 0\n for v, j in G0[u]:\n if v == p:\n p_cnt += 1\n continue\n if label[v] is not None:\n if label[v] < label[u]:\n cost[v] += 1\n res += 1\n else:\n label[v] = gen; gen += 1\n res += dfs(v, u, j)\n res -= cost[u]\n if res == 0 and p != -1 and p_cnt == 1:\n PB.add(i)\n return res\nlabel[0] = 0\ndfs(0, -1, None)\n\nans = []\nfor i in range(m):\n if i in P:\n if i in PB:\n ans.append(\"SAD\")\n else:\n ans.append(\"SOSO\")\n else:\n a, b, c = E[i]\n if D[b] + c + RD[a] < D[1]:\n ans.append(\"HAPPY\")\n else:\n ans.append(\"SOSO\")\nprint(*ans, sep='\\n')\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 4 6\\n4 2 7\\n2 1 18\\n2 3 12', 'output': 'SAD\\nSAD\\nSAD\\nSOSO\\nHAPPY'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 4 6\\n4 2 7\\n2 1 18\\n2 3 17', 'output': 'SAD\\nSAD\\nSAD\\nSOSO\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 4 6\\n4 2 7\\n2 1 6\\n2 3 17', 'output': 'SAD\\nSAD\\nSAD\\nHAPPY\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 2 6\\n4 2 7\\n2 1 18\\n2 3 12', 'output': 'SAD\\nSAD\\nSOSO\\nSOSO\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 4 6\\n4 2 13\\n2 1 6\\n2 3 17', 'output': 'SAD\\nSAD\\nSAD\\nHAPPY\\nHAPPY\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n3 2 6\\n4 2 7\\n2 1 18\\n2 3 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '8 5\\n1 3 5\\n3 4 6\\n4 2 7\\n2 1 18\\n2 3 12', 'output': 'SAD\\nSAD\\nSAD\\nSOSO\\nHAPPY\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 1 5\\n3 4 6\\n4 2 13\\n2 1 6\\n2 3 17', 'output': 'SOSO\\nSOSO\\nSOSO\\nHAPPY\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 2 5\\n4 4 3\\n4 2 7\\n0 1 25\\n2 6 12', 'output': 'SAD\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 4 6\\n2 2 7\\n2 1 1\\n2 3 17', 'output': 'SOSO\\nSOSO\\nSOSO\\nHAPPY\\nHAPPY\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 2 5\\n3 4 6\\n2 2 7\\n2 1 1\\n2 3 26', 'output': 'SAD\\nSOSO\\nSOSO\\nHAPPY\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 2 5\\n3 4 6\\n2 2 7\\n1 1 2\\n2 3 26', 'output': 'SAD\\nSOSO\\nSOSO\\nSOSO\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 4 5\\n3 4 6\\n3 2 7\\n1 1 2\\n2 3 26', 'output': 'SOSO\\nHAPPY\\nSOSO\\nSOSO\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\n1 3 6\\n3 2 6\\n1 1 1\\n-1 1 18\\n4 6 16', 'output': 'SAD\\nSAD\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\n2 3 6\\n3 2 6\\n1 1 1\\n-1 1 18\\n4 10 16', 'output': 'SOSO\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '6 2\\n1 2 6\\n3 1 1\\n1 1 1\\n0 1 28\\n6 6 3', 'output': 'SAD\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 7\\n3 2 6\\n1 3 7\\n2 1 34\\n2 3 12', 'output': 'SOSO\\nSAD\\nSOSO\\nSOSO\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 7\\n4 2 6\\n4 3 0\\n2 1 34\\n3 3 12', 'output': 'SOSO\\nSOSO\\nHAPPY\\nHAPPY\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 4 6\\n4 2 7\\n2 1 26\\n2 3 17', 'output': 'SAD\\nSAD\\nSAD\\nSOSO\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n3 2 6\\n4 2 7\\n2 1 18\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n3 2 6\\n4 2 7\\n0 1 18\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 2 6\\n4 2 7\\n0 1 18\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 3 6\\n4 2 7\\n0 1 18\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 4 6\\n4 2 7\\n0 1 18\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 4 6\\n4 2 7\\n0 1 25\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 4 3\\n4 2 7\\n0 1 25\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n4 4 3\\n4 2 7\\n0 1 25\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n4 4 3\\n4 2 7\\n0 1 27\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n4 4 3\\n4 2 14\\n0 1 27\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n3 4 3\\n4 2 14\\n0 1 27\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n3 7 3\\n4 2 14\\n0 1 27\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n3 7 3\\n4 3 14\\n0 1 27\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n3 7 3\\n4 3 14\\n0 1 10\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 3\\n4 3 14\\n0 1 10\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 3\\n4 4 14\\n0 1 10\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 4\\n4 4 14\\n0 1 10\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 4\\n8 4 14\\n0 1 10\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 4\\n8 4 14\\n0 2 10\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 4\\n8 4 14\\n0 2 10\\n2 1 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 10\\n3 7 4\\n8 4 14\\n0 2 10\\n2 1 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 10\\n3 7 4\\n8 4 14\\n1 2 10\\n2 1 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 4 9\\n4 2 7\\n2 1 18\\n2 3 17', 'output': 'SAD\\nSAD\\nSAD\\nHAPPY\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 4 6\\n4 2 7\\n2 1 1\\n2 3 17', 'output': 'SAD\\nSAD\\nSAD\\nHAPPY\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 2 6\\n4 3 7\\n2 1 18\\n2 3 12', 'output': 'SAD\\nSAD\\nSOSO\\nSOSO\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n3 2 6\\n4 2 11\\n2 1 18\\n2 3 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n3 2 4\\n4 2 7\\n2 1 18\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n3 2 6\\n4 1 7\\n0 1 18\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 2 6\\n4 2 7\\n0 1 18\\n2 6 21', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 4 6\\n4 2 7\\n0 1 18\\n3 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 4 6\\n4 2 7\\n1 1 25\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 4 0\\n4 2 7\\n0 1 25\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n4 4 3\\n4 2 14\\n0 1 27\\n2 6 18', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n2 3 5\\n3 4 3\\n4 2 14\\n0 1 27\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n3 7 3\\n4 2 14\\n0 1 27\\n1 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n3 7 3\\n8 3 14\\n0 1 27\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n3 7 3\\n4 3 14\\n0 1 10\\n2 6 13', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 3\\n4 4 14\\n0 1 17\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 1\\n3 7 4\\n4 4 14\\n0 1 10\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 6\\n8 4 14\\n0 1 10\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 4\\n8 4 14\\n0 2 10\\n2 2 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n4 7 4\\n8 4 14\\n0 2 10\\n2 1 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 10\\n3 13 4\\n8 4 14\\n0 2 10\\n2 1 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 10\\n0 7 4\\n8 4 14\\n1 2 10\\n2 1 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 4 9\\n4 2 7\\n2 1 0\\n2 3 17', 'output': 'SAD\\nSAD\\nSAD\\nHAPPY\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 7\\n3 2 6\\n4 3 7\\n2 1 18\\n2 3 12', 'output': 'SAD\\nSAD\\nSOSO\\nSOSO\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n0 2 6\\n4 2 11\\n2 1 18\\n2 3 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n3 2 4\\n4 2 7\\n2 0 18\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n3 2 6\\n4 1 7\\n0 1 18\\n2 6 16', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 2 6\\n5 2 7\\n0 1 18\\n2 6 21', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 4 6\\n4 2 7\\n1 1 18\\n3 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 8 0\\n4 2 7\\n0 1 25\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 2 5\\n4 4 3\\n4 2 7\\n0 1 49\\n2 6 12', 'output': 'SAD\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n4 4 3\\n4 2 14\\n0 1 27\\n2 6 33', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n2 3 5\\n3 4 3\\n4 2 14\\n0 1 27\\n2 12 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n3 7 3\\n4 2 14\\n0 1 0\\n1 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n3 7 3\\n8 3 14\\n0 1 27\\n2 10 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 1\\n3 7 3\\n4 3 14\\n0 1 10\\n2 6 13', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 3\\n4 6 14\\n0 1 17\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 1\\n3 7 0\\n4 4 14\\n0 1 10\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 6\\n8 4 14\\n0 1 10\\n4 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n4 7 4\\n8 4 14\\n0 3 10\\n2 1 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 10\\n3 13 4\\n8 4 14\\n0 2 10\\n2 1 8', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 10\\n0 7 4\\n8 4 14\\n2 2 10\\n2 1 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n2 3 5\\n3 4 9\\n4 2 7\\n2 1 0\\n2 3 17', 'output': 'SOSO\\nSOSO\\nSOSO\\nHAPPY\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 5\\n3 4 6\\n2 2 7\\n2 1 1\\n2 3 26', 'output': 'SOSO\\nSOSO\\nSOSO\\nHAPPY\\nHAPPY\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 3 7\\n3 2 6\\n4 3 7\\n2 1 34\\n2 3 12', 'output': 'SAD\\nSAD\\nSOSO\\nSOSO\\nSOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n0 2 6\\n4 2 11\\n4 1 18\\n2 3 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n3 2 4\\n1 2 7\\n2 0 18\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n3 2 6\\n1 1 7\\n0 1 18\\n2 6 16', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 2 6\\n5 2 7\\n0 2 18\\n2 6 21', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1 3 5\\n4 4 6\\n4 2 7\\n1 1 18\\n5 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n1 3 5\\n4 8 0\\n4 2 7\\n0 1 25\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 2 5\\n4 4 3\\n4 2 11\\n0 1 49\\n2 6 12', 'output': 'SAD\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n4 4 3\\n4 2 14\\n0 1 27\\n2 6 11', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n2 3 5\\n3 0 3\\n4 2 14\\n0 1 27\\n2 12 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 5\\n3 6 3\\n8 3 14\\n0 1 27\\n2 10 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '7 1\\n1 3 1\\n3 7 3\\n4 3 14\\n0 0 10\\n2 6 13', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 0 3\\n4 6 14\\n0 1 17\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 1\\n3 7 0\\n4 4 9\\n0 1 10\\n2 6 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n3 7 6\\n8 4 14\\n0 1 10\\n4 12 12', 'output': 'SOSO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n1 3 5\\n4 7 4\\n8 4 14\\n0 4 10\\n2 1 12', 'output': 'SOSO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79961","program":"```python\nfrom heapq import heappush, heappop\nfrom collections import deque\nimport sys\nsys.setrecursionlimit(10**6)\nn, m = map(int, input().split())\nE = []\nG = [[] for i in range(n)]\nRG = [[] for i in range(n)]\nfor i in range(m):\n a, b, c = map(int, input().split())\n E.append((a-1, b-1, c))\n G[a-1].append((b-1, c, i))\n RG[b-1].append((a-1, c, i))\ndef dijkstra(G, s):\n dist = [10**18]*n\n dist[s] = 0\n que = [(0, s)]\n while que:\n co, v = heappop(que)\n if dist[v] < co:\n continue\n for w, c, i in G[v]:\n if co + c < dist[w]:\n dist[w] = co + c\n heappush(que, (co + c, w))\n return dist\nD = dijkstra(G, 0)\nRD = dijkstra(RG, 1)\n\nG0 = [[] for i in range(n)]\nused = set([1])\ndeq = deque([1])\nP = set()\nwhile deq:\n v = deq.popleft()\n for w, c, i in RG[v]:\n if D[w] + c == D[v]:\n P.add(i)\n if w not in used:\n used.add(w)\n deq.append(w)\n G0[v].append((w, i))\n G0[w].append((v, i))\n\nPB = set()\nlabel = [None]*n\ngen = 1\ncost = [0]*n\ndef dfs(u, p, i):\n global gen\n res = 0\n p_cnt = 0\n for v, j in G0[u]:\n if v == p:\n p_cnt += 1\n continue\n if label[v] is not None:\n if label[v] < label[u]:\n cost[v] += 1\n res += 1\n else:\n label[v] = gen; gen += 1\n res += dfs(v, u, j)\n res -= cost[u]\n if res == 0 and p != -1 and p_cnt == 1:\n PB.add(i)\n return res\nlabel[0] = 0\ndfs(0, -1, None)\n\nans = []\nfor i in range(m):\n if i in P:\n if i in PB:\n ans.append(\"SAD\")\n else:\n ans.append(\"SOSO\")\n else:\n a, b, c = E[i]\n if D[b] + c + RD[a] < D[1]:\n ans.append(\"HAPPY\")\n else:\n ans.append(\"SOSO\")\nprint(*ans, sep='\\n')\n```","inputs":"4 5\n1 3 5\n3 4 6\n4 2 7\n2 1 18\n2 3 12","output":"SAD\nSAD\nSAD\nSOSO\nHAPPY","actual_output":"SAD\nSAD\nSAD\nSOSO\nHAPPY\n","execution_success":true,"sample_index":12734},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01095 Bamboo Blossoms","prompt":"Solve the following coding problem using the programming language python:\n\nBamboo Blossoms\n\nThe bamboos live for decades, and at the end of their lives, they flower to make their seeds. Dr. ACM, a biologist, was fascinated by the bamboos in blossom in his travel to Tsukuba. He liked the flower so much that he was tempted to make a garden where the bamboos bloom annually. Dr. ACM started research of improving breed of the bamboos, and finally, he established a method to develop bamboo breeds with controlled lifetimes. With this method, he can develop bamboo breeds that flower after arbitrarily specified years.\n\nLet us call bamboos that flower k years after sowing \"k-year-bamboos.\" k years after being sowed, k-year-bamboos make their seeds and then die, hence their next generation flowers after another k years. In this way, if he sows seeds of k-year-bamboos, he can see bamboo blossoms every k years. For example, assuming that he sows seeds of 15-year-bamboos, he can see bamboo blossoms every 15 years; 15 years, 30 years, 45 years, and so on, after sowing.\n\nDr. ACM asked you for designing his garden. His garden is partitioned into blocks, in each of which only a single breed of bamboo can grow. Dr. ACM requested you to decide which breeds of bamboos should he sow in the blocks in order to see bamboo blossoms in at least one block for as many years as possible.\n\nYou immediately suggested to sow seeds of one-year-bamboos in all blocks. Dr. ACM, however, said that it was difficult to develop a bamboo breed with short lifetime, and would like a plan using only those breeds with long lifetimes. He also said that, although he could wait for some years until he would see the first bloom, he would like to see it in every following year. Then, you suggested a plan to sow seeds of 10-year-bamboos, for example, in different blocks each year, that is, to sow in a block this year and in another block next year, and so on, for 10 years. Following this plan, he could see bamboo blossoms in one block every year except for the first 10 years. Dr. ACM objected again saying he had determined to sow in all blocks this year.\n\nAfter all, you made up your mind to make a sowing plan where the bamboos bloom in at least one block for as many consecutive years as possible after the first m years (including this year) under the following conditions:\n\n* the plan should use only those bamboo breeds whose lifetimes are m years or longer, and\n* Dr. ACM should sow the seeds in all the blocks only this year.\n\n\nInput\n\nThe input consists of at most 50 datasets, each in the following format.\n\nm n\n\n\nAn integer m (2 \u2264 m \u2264 100) represents the lifetime (in years) of the bamboos with the shortest lifetime that Dr. ACM can use for gardening. An integer n (1 \u2264 n \u2264 500,000) represents the number of blocks.\n\nThe end of the input is indicated by a line containing two zeros.\n\nOutput\n\nNo matter how good your plan is, a \"dull-year\" would eventually come, in which the bamboos do not flower in any block. For each dataset, output in a line an integer meaning how many years from now the first dull-year comes after the first m years.\n\nNote that the input of m = 2 and n = 500,000 (the last dataset of the Sample Input) gives the largest answer.\n\nSample Input\n\n\n3 1\n3 4\n10 20\n100 50\n2 500000\n0 0\n\n\nOutput for the Sample Input\n\n\n4\n11\n47\n150\n7368791\n\n\n\n\n\n\nExample\n\nInput\n\n3 1\n3 4\n10 20\n100 50\n2 500000\n0 0\n\n\nOutput\n\n4\n11\n47\n150\n7368791\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom bisect import bisect_left\n\ndef rwh_primes2(n):\n # https://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python/3035188#3035188\n \"\"\" Input n>=6, Returns a list of primes, 2 <= p < n \"\"\"\n correction = (n%6>1)\n n = {0:n,1:n-1,2:n+4,3:n+3,4:n+2,5:n+1}[n%6]\n sieve = [True] * (n//3)\n sieve[0] = False\n for i in range(int(n**0.5)//3+1):\n if sieve[i]:\n k=3*i+1|1\n sieve[ ((k*k)//3) ::2*k]=[False]*((n//6-(k*k)//6-1)//k+1)\n sieve[(k*k+4*k-2*k*(i&1))//3::2*k]=[False]*((n//6-(k*k+4*k-2*k*(i&1))//6-1)//k+1)\n return [2,3] + [3*i+1|1 for i in range(1,n//3-correction) if sieve[i]]\n\nif __name__ == \"__main__\":\n prime = rwh_primes2(7368791+10)\n while True:\n m,n = map(int,input().split())\n if m == 0 and n == 0:\n break\n small_prime = prime[:bisect_left(prime,m**2)]\n composite = []\n for i in range(1,m+1):\n for j in range(i,m+1):\n x = i*j\n if m <= x <= m**2 and x not in small_prime:\n for p in small_prime:\n if x%p == 0:\n if x < m*p:\n composite.append(x)\n break\n composite = sorted(list(set(composite)))\n pp = bisect_left(prime,m)\n cp = 0\n sz = len(composite)\n for i in range(n+1):\n if cp < sz:\n if composite[cp] < prime[pp]:\n ans = composite[cp]\n cp += 1\n else:\n ans = prime[pp]\n pp += 1\n else:\n ans = prime[pp+n-i]\n break\n print(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n10 20\\n100 50\\n2 500000\\n0 0', 'output': '4\\n11\\n47\\n150\\n7368791'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n10 20\\n100 50\\n2 500000\\n0 0', 'output': '5\\n11\\n47\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n13 20\\n100 50\\n2 500000\\n0 0', 'output': '5\\n11\\n43\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n22 20\\n100 50\\n2 500000\\n0 0', 'output': '5\\n11\\n42\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n10 20\\n100 50\\n3 500000\\n0 0', 'output': '4\\n11\\n47\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n13 20\\n100 50\\n4 500000\\n0 0', 'output': '5\\n11\\n43\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n10 20\\n100 52\\n2 500000\\n0 0', 'output': '5\\n11\\n47\\n152\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n3 4\\n10 20\\n100 50\\n3 500000\\n0 0', 'output': '7\\n11\\n47\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n3 4\\n10 20\\n100 50\\n3 202868\\n0 0', 'output': '7\\n11\\n47\\n150\\n2792771\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n3 4\\n13 22\\n100 50\\n4 500000\\n0 0', 'output': '5\\n11\\n49\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n10 20\\n101 50\\n2 500000\\n0 0', 'output': '4\\n11\\n47\\n151\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 7\\n13 20\\n100 50\\n2 500000\\n0 0', 'output': '5\\n19\\n43\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n13 20\\n100 50\\n4 500000\\n0 0', 'output': '4\\n11\\n43\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n3 1\\n13 20\\n100 50\\n4 500000\\n0 0', 'output': '5\\n4\\n43\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 4\\n10 20\\n110 52\\n2 500000\\n0 0', 'output': '5\\n11\\n47\\n162\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n3 4\\n13 22\\n100 5\\n4 500000\\n0 0', 'output': '5\\n11\\n49\\n105\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 7\\n13 20\\n101 50\\n2 500000\\n0 0', 'output': '5\\n19\\n43\\n151\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n3 4\\n13 20\\n100 50\\n4 500000\\n0 0', 'output': '6\\n11\\n43\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n3 1\\n13 20\\n100 50\\n4 500000\\n0 0', 'output': '11\\n4\\n43\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 4\\n10 15\\n110 52\\n2 500000\\n0 0', 'output': '5\\n11\\n31\\n162\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n3 4\\n13 20\\n100 50\\n8 500000\\n0 0', 'output': '6\\n11\\n43\\n150\\n7368709\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n3 1\\n19 20\\n100 50\\n4 500000\\n0 0', 'output': '11\\n4\\n41\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 6\\n10 15\\n110 52\\n2 500000\\n0 0', 'output': '5\\n17\\n31\\n162\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n3 1\\n19 20\\n100 50\\n2 500000\\n0 0', 'output': '11\\n4\\n41\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 6\\n10 15\\n110 52\\n2 371896\\n0 0', 'output': '5\\n17\\n31\\n162\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n3 1\\n19 20\\n100 50\\n2 500000\\n0 0', 'output': '3\\n4\\n41\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 6\\n10 15\\n110 93\\n2 371896\\n0 0', 'output': '5\\n17\\n31\\n203\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 6\\n10 6\\n110 93\\n2 371896\\n0 0', 'output': '5\\n17\\n16\\n203\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 6\\n10 6\\n110 181\\n2 371896\\n0 0', 'output': '5\\n17\\n16\\n379\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 6\\n10 10\\n110 181\\n2 371896\\n0 0', 'output': '5\\n17\\n21\\n379\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n5 4\\n10 20\\n100 50\\n2 500000\\n0 0', 'output': '4\\n9\\n47\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n10 20\\n100 58\\n2 500000\\n0 0', 'output': '5\\n11\\n47\\n158\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n13 20\\n100 50\\n2 485634\\n0 0', 'output': '5\\n11\\n43\\n150\\n7141699\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n3 1\\n10 20\\n100 50\\n3 202868\\n0 0', 'output': '7\\n4\\n47\\n150\\n2792771\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n3 4\\n16 22\\n100 50\\n4 500000\\n0 0', 'output': '5\\n11\\n45\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n3 4\\n10 20\\n100 52\\n3 500000\\n0 0', 'output': '7\\n11\\n47\\n152\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 7\\n13 20\\n100 50\\n2 278453\\n0 0', 'output': '5\\n19\\n43\\n150\\n3928013\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n10 17\\n100 50\\n3 500000\\n0 0', 'output': '5\\n11\\n37\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n13 20\\n100 50\\n2 500000\\n0 0', 'output': '4\\n11\\n43\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n4 1\\n13 20\\n100 50\\n4 500000\\n0 0', 'output': '5\\n5\\n43\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n6 7\\n13 20\\n101 50\\n2 500000\\n0 0', 'output': '5\\n15\\n43\\n151\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n3 1\\n13 20\\n100 49\\n4 500000\\n0 0', 'output': '11\\n4\\n43\\n149\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n3 4\\n13 20\\n100 82\\n8 500000\\n0 0', 'output': '6\\n11\\n43\\n182\\n7368709\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 6\\n10 15\\n110 69\\n2 371896\\n0 0', 'output': '5\\n17\\n31\\n179\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n3 1\\n19 20\\n100 50\\n6 500000\\n0 0', 'output': '3\\n4\\n41\\n150\\n7368737\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 3\\n10 6\\n110 93\\n2 371896\\n0 0', 'output': '5\\n7\\n16\\n203\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n2 6\\n10 6\\n110 181\\n2 371896\\n0 0', 'output': '7\\n17\\n16\\n379\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n10 20\\n100 14\\n2 500000\\n0 0', 'output': '5\\n11\\n47\\n114\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n13 20\\n100 50\\n4 485634\\n0 0', 'output': '5\\n11\\n43\\n150\\n7141691\\n'}, {'type': 'stdin_stdout', 'input': '12 1\\n3 1\\n10 20\\n100 50\\n3 202868\\n0 0', 'output': '13\\n4\\n47\\n150\\n2792771\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n3 6\\n10 20\\n100 52\\n3 500000\\n0 0', 'output': '7\\n17\\n47\\n152\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n7 20\\n101 50\\n2 500000\\n0 0', 'output': '4\\n11\\n61\\n151\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 7\\n13 20\\n110 50\\n2 278453\\n0 0', 'output': '5\\n19\\n43\\n160\\n3928013\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n10 2\\n100 50\\n3 500000\\n0 0', 'output': '5\\n11\\n12\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n4 20\\n100 50\\n2 500000\\n0 0', 'output': '4\\n11\\n71\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n3 1\\n13 20\\n100 47\\n4 500000\\n0 0', 'output': '11\\n4\\n43\\n147\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n3 4\\n13 30\\n100 82\\n8 500000\\n0 0', 'output': '6\\n11\\n77\\n182\\n7368709\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 6\\n10 15\\n110 37\\n2 371896\\n0 0', 'output': '5\\n17\\n31\\n147\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n3 1\\n19 20\\n100 50\\n6 500000\\n0 0', 'output': '5\\n4\\n41\\n150\\n7368737\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n13 20\\n100 50\\n4 485634\\n0 0', 'output': '4\\n11\\n43\\n150\\n7141691\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n3 1\\n16 22\\n100 50\\n5 500000\\n0 0', 'output': '5\\n4\\n45\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n7 28\\n101 50\\n2 500000\\n0 0', 'output': '4\\n11\\n101\\n151\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 7\\n13 20\\n111 50\\n2 278453\\n0 0', 'output': '5\\n19\\n43\\n161\\n3928013\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n4 20\\n100 83\\n2 500000\\n0 0', 'output': '4\\n11\\n71\\n183\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n3 1\\n13 20\\n100 47\\n4 346519\\n0 0', 'output': '11\\n4\\n43\\n147\\n4969351\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n3 4\\n13 30\\n110 82\\n8 500000\\n0 0', 'output': '6\\n11\\n77\\n192\\n7368709\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 6\\n10 15\\n110 37\\n2 407647\\n0 0', 'output': '5\\n17\\n31\\n147\\n5918399\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n3 1\\n19 20\\n100 50\\n6 297497\\n0 0', 'output': '5\\n4\\n41\\n150\\n4217893\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n2 3\\n10 6\\n110 93\\n2 371896\\n0 0', 'output': '3\\n7\\n16\\n203\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n13 20\\n110 50\\n4 485634\\n0 0', 'output': '4\\n11\\n43\\n160\\n7141691\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n3 1\\n16 22\\n100 50\\n8 500000\\n0 0', 'output': '5\\n4\\n45\\n150\\n7368709\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n7 28\\n101 21\\n2 500000\\n0 0', 'output': '4\\n11\\n101\\n122\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 7\\n13 20\\n111 50\\n2 278453\\n0 0', 'output': '4\\n19\\n43\\n161\\n3928013\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n4 20\\n100 83\\n2 500000\\n0 0', 'output': '5\\n11\\n71\\n183\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n3 1\\n13 35\\n100 47\\n4 346519\\n0 0', 'output': '11\\n4\\n101\\n147\\n4969351\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n2 6\\n10 15\\n110 37\\n2 407647\\n0 0', 'output': '7\\n17\\n31\\n147\\n5918399\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n2 3\\n10 6\\n100 93\\n2 371896\\n0 0', 'output': '3\\n7\\n16\\n193\\n5361757\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n13 20\\n110 50\\n7 485634\\n0 0', 'output': '4\\n11\\n43\\n160\\n7141657\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n3 1\\n16 22\\n100 50\\n8 500000\\n0 0', 'output': '3\\n4\\n45\\n150\\n7368709\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n7 28\\n101 39\\n2 500000\\n0 0', 'output': '4\\n11\\n101\\n140\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n8 20\\n100 83\\n2 500000\\n0 0', 'output': '5\\n11\\n49\\n183\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n2 6\\n10 15\\n110 19\\n2 407647\\n0 0', 'output': '7\\n17\\n31\\n129\\n5918399\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n4 4\\n13 20\\n110 50\\n7 485634\\n0 0', 'output': '4\\n9\\n43\\n160\\n7141657\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n3 1\\n16 22\\n100 50\\n8 124983\\n0 0', 'output': '3\\n4\\n45\\n150\\n1654853\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n8 20\\n101 83\\n2 500000\\n0 0', 'output': '5\\n11\\n49\\n184\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n2 6\\n10 15\\n110 38\\n2 407647\\n0 0', 'output': '7\\n17\\n31\\n148\\n5918399\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n4 4\\n13 20\\n111 50\\n7 485634\\n0 0', 'output': '4\\n9\\n43\\n161\\n7141657\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n3 1\\n16 27\\n100 50\\n8 124983\\n0 0', 'output': '3\\n4\\n59\\n150\\n1654853\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n2 6\\n10 15\\n111 38\\n2 407647\\n0 0', 'output': '7\\n17\\n31\\n149\\n5918399\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n2 4\\n13 20\\n111 50\\n7 485634\\n0 0', 'output': '4\\n11\\n43\\n161\\n7141657\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n3 1\\n16 27\\n100 50\\n8 7948\\n0 0', 'output': '3\\n4\\n59\\n150\\n81157\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n2 6\\n10 15\\n111 38\\n2 407647\\n0 0', 'output': '6\\n17\\n31\\n149\\n5918399\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n2 8\\n13 20\\n111 50\\n7 485634\\n0 0', 'output': '4\\n23\\n43\\n161\\n7141657\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n2 6\\n15 15\\n110 38\\n2 407647\\n0 0', 'output': '6\\n17\\n31\\n148\\n5918399\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n2 6\\n15 15\\n010 38\\n2 407647\\n0 0', 'output': '6\\n17\\n31\\n131\\n5918399\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n2 6\\n15 15\\n010 38\\n2 407647\\n0 0', 'output': '7\\n17\\n31\\n131\\n5918399\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n2 6\\n15 18\\n010 38\\n2 407647\\n0 0', 'output': '7\\n17\\n37\\n131\\n5918399\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 4\\n18 20\\n100 50\\n2 500000\\n0 0', 'output': '5\\n11\\n41\\n150\\n7368791\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n3 4\\n10 20\\n100 50\\n3 127819\\n0 0', 'output': '4\\n11\\n47\\n150\\n1695611\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n3 4\\n13 20\\n100 50\\n4 500000\\n0 0', 'output': '7\\n11\\n43\\n150\\n7368787\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n3 3\\n10 20\\n100 52\\n2 500000\\n0 0', 'output': '5\\n7\\n47\\n152\\n7368791\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79965","program":"```python\nfrom bisect import bisect_left\n\ndef rwh_primes2(n):\n # https://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python/3035188#3035188\n \"\"\" Input n>=6, Returns a list of primes, 2 <= p < n \"\"\"\n correction = (n%6>1)\n n = {0:n,1:n-1,2:n+4,3:n+3,4:n+2,5:n+1}[n%6]\n sieve = [True] * (n//3)\n sieve[0] = False\n for i in range(int(n**0.5)//3+1):\n if sieve[i]:\n k=3*i+1|1\n sieve[ ((k*k)//3) ::2*k]=[False]*((n//6-(k*k)//6-1)//k+1)\n sieve[(k*k+4*k-2*k*(i&1))//3::2*k]=[False]*((n//6-(k*k+4*k-2*k*(i&1))//6-1)//k+1)\n return [2,3] + [3*i+1|1 for i in range(1,n//3-correction) if sieve[i]]\n\nif __name__ == \"__main__\":\n prime = rwh_primes2(7368791+10)\n while True:\n m,n = map(int,input().split())\n if m == 0 and n == 0:\n break\n small_prime = prime[:bisect_left(prime,m**2)]\n composite = []\n for i in range(1,m+1):\n for j in range(i,m+1):\n x = i*j\n if m <= x <= m**2 and x not in small_prime:\n for p in small_prime:\n if x%p == 0:\n if x < m*p:\n composite.append(x)\n break\n composite = sorted(list(set(composite)))\n pp = bisect_left(prime,m)\n cp = 0\n sz = len(composite)\n for i in range(n+1):\n if cp < sz:\n if composite[cp] < prime[pp]:\n ans = composite[cp]\n cp += 1\n else:\n ans = prime[pp]\n pp += 1\n else:\n ans = prime[pp+n-i]\n break\n print(ans)\n\n```","inputs":"3 1\n3 4\n10 20\n100 50\n2 500000\n0 0","output":"4\n11\n47\n150\n7368791","actual_output":"4\n11\n47\n150\n7368791\n","execution_success":true,"sample_index":12735},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01847 Curtain","prompt":"Solve the following coding problem using the programming language python:\n\ncurtain\n\nSummer is coming soon. You decide to redecorate your room for the summer. It is expected that the sun will be very strong this summer, and it will be a difficult season for you who are not good at dazzling. So you thought about installing a curtain on the window of the room to adjust the brightness of the room.\n\nThe curtain to be attached is rectangular and is attached so that the sides are perpendicular to or parallel to the ground. Also, the windows in your room have a very special shape and are represented by N-sided polygons where each side is parallel or perpendicular to the ground. Therefore, it is difficult to determine the area of \u200b\u200ba window that is not covered by the curtain when the curtain is attached. In order to adjust the brightness of the room, it is important to know how much the window can cover when deciding where to install the curtain. So you decided to create a program to find the area of \u200b\u200ba window that is not covered by a curtain, given the location and shape of the window and curtain.\n\nAs an example, consider the following method of installing windows and curtains. In this case, the area of \u200b\u200bthe window not hidden by the curtain is 8. This example corresponds to the third case of sample input.\n\n\n\n\nInput\n\nThe input consists of multiple datasets. Each dataset is given in the following format.\n\n> N\n> x1 y1\n>::\n>::\n> xN yN\n> a1 b1\n> a2 b2\n> a3 b3\n> a4 b4\n\nThe first line is given the integer N, which represents the number of vertices the window has (4 \u2264 N \u2264 100). The following N lines are given the integer xi representing the x-coordinates of the different vertices of the window and the integer yi representing the y-coordinate (-20,000 \u2264 xi, yi \u2264 20,000, 1 \u2264 i \u2264 N). Here, the positive direction of the y-axis is the direction rotated 90 degrees counterclockwise from the positive direction of the x-axis. In addition, the next four lines are given the integer aj, which represents the x-coordinate of the different vertices of the curtain, and the integer bj, which represents the y-coordinate (-20,000 \u2264 aj, bj \u2264 20,000, 1 \u2264 j \u2264 4). The vertices of both windows and curtains are given in counterclockwise order. In addition, the figures representing windows and curtains are figures without self-intersection.\n\nThe end of the input is indicated by a single 0 line.\n\nOutput\n\nFor each dataset, output the area of \u200b\u200bthe window not covered by the curtain on one line. However, note that the area is always an integer value.\n\nSample Input\n\n\nFour\n0 0\n10 0\n10 10\n0 10\n0 0\n5 0\n5 10\n0 10\n6\n0 0\n10 0\n10 5\n5 5\n5 10\n0 10\n2 0\n8 0\n8 10\n2 10\n12\n1 1\n13\n-13\n-1 1\n-3 1\n-3 -1\n-1 -1\n-13\n13\n1 -1\n3 -1\n3 1\ntwenty two\n-twenty two\n-twenty two\ntwenty two\nFour\n20000 20000\n-20000 20000\n-20000 -20000\n20000 -20000\n1000 1000\n-1000 1000\n-1000 -1000\n1000 -1000\nFour\n1000 1000\n-1000 1000\n-1000 -1000\n1000 -1000\n20000 20000\n-20000 20000\n-20000 -20000\n20000 -20000\nFour\n0 0\n10 0\n10 10\n0 10\n20 0\n30 0\n30 10\n20 10\n0\n\nOutput for Sample Input\n\n\n50\n30\n8\n1596000000\n0\n100\n\n\n\n\n\nExample\n\nInput\n\n4\n0 0\n10 0\n10 10\n0 10\n0 0\n5 0\n5 10\n0 10\n6\n0 0\n10 0\n10 5\n5 5\n5 10\n0 10\n2 0\n8 0\n8 10\n2 10\n12\n1 1\n1 3\n-1 3\n-1 1\n-3 1\n-3 -1\n-1 -1\n-1 -3\n1 -3\n1 -1\n3 -1\n3 1\n2 2\n-2 2\n-2 -2\n2 -2\n4\n20000 20000\n-20000 20000\n-20000 -20000\n20000 -20000\n1000 1000\n-1000 1000\n-1000 -1000\n1000 -1000\n4\n1000 1000\n-1000 1000\n-1000 -1000\n1000 -1000\n20000 20000\n-20000 20000\n-20000 -20000\n20000 -20000\n4\n0 0\n10 0\n10 10\n0 10\n20 0\n30 0\n30 10\n20 10\n0\n\n\nOutput\n\n50\n30\n8\n1596000000\n0\n100\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import defaultdict\nINF = 10**9\nwhile 1:\n N = int(input())\n if N == 0:\n break\n P = [list(map(int, input().split())) for i in range(N)]\n S = defaultdict(list)\n X = set()\n x0 = y0 = INF; x1 = y1 = -INF\n for i in range(4):\n x, y = map(int, input().split())\n x0 = min(x0, x); x1 = max(x1, x)\n y0 = min(y0, y); y1 = max(y1, y)\n S[y0] = [INF]; S[y1] = [INF]\n X.add(x0); X.add(x1)\n for x, y in P:\n S[y].append(x)\n X.add(x)\n xs = sorted(X)\n MP = {x: i for i, x in enumerate(xs)}\n L = len(xs)\n\n su = 0\n for i in range(N):\n xa, ya = P[i-1]\n xb, yb = P[i]\n su += xa*yb - ya*xb\n su = abs(su) // 2\n res = 0\n *ps, = S.items()\n ps.sort()\n mode = 0\n prv = -1\n U = [0]*L\n for y, vs in ps:\n if mode:\n px = 0; c = 0\n d = y - prv\n for i in range(L):\n if U[i]:\n x = min(max(xs[i], x0), x1)\n if c == 1:\n res += d * (x - px)\n c ^= 1\n px = x\n for x in vs:\n if x == INF:\n mode ^= 1\n else:\n U[MP[x]] ^= 1\n prv = y\n print(su - res)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n0 0\\n10 0\\n10 10\\n0 10\\n0 0\\n5 0\\n5 10\\n0 10\\n6\\n0 0\\n10 0\\n10 5\\n5 5\\n5 10\\n0 10\\n2 0\\n8 0\\n8 10\\n2 10\\n12\\n1 1\\n1 3\\n-1 3\\n-1 1\\n-3 1\\n-3 -1\\n-1 -1\\n-1 -3\\n1 -3\\n1 -1\\n3 -1\\n3 1\\n2 2\\n-2 2\\n-2 -2\\n2 -2\\n4\\n20000 20000\\n-20000 20000\\n-20000 -20000\\n20000 -20000\\n1000 1000\\n-1000 1000\\n-1000 -1000\\n1000 -1000\\n4\\n1000 1000\\n-1000 1000\\n-1000 -1000\\n1000 -1000\\n20000 20000\\n-20000 20000\\n-20000 -20000\\n20000 -20000\\n4\\n0 0\\n10 0\\n10 10\\n0 10\\n20 0\\n30 0\\n30 10\\n20 10\\n0', 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{'type': 'stdin_stdout', 'input': '4\\n0 0\\n10 0\\n10 10\\n0 10\\n0 0\\n5 0\\n5 15\\n0 10\\n0\\n0 0\\n10 0\\n10 5\\n5 5\\n5 10\\n0 10\\n2 0\\n8 0\\n8 10\\n2 10\\n12\\n1 1\\n1 3\\n-1 6\\n-1 2\\n-3 1\\n-3 -1\\n-1 -1\\n-1 -3\\n1 -3\\n1 -1\\n3 -1\\n3 1\\n2 2\\n-2 2\\n-2 -2\\n4 -2\\n4\\n20000 20000\\n-20000 20000\\n-20000 -20000\\n20000 -20000\\n1000 1000\\n-1000 1000\\n-1000 -1000\\n1000 -1000\\n4\\n1000 0000\\n-1000 1000\\n-1000 -1000\\n1000 -1000\\n29582 33707\\n-20000 20000\\n-37652 -20000\\n20000 -20000\\n4\\n0 0\\n10 0\\n10 10\\n0 10\\n20 0\\n30 0\\n30 10\\n20 10\\n0', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0\\n10 0\\n10 10\\n0 10\\n0 0\\n5 0\\n5 15\\n0 10\\n0\\n0 0\\n10 0\\n10 5\\n5 5\\n5 10\\n0 10\\n2 0\\n8 0\\n8 10\\n2 10\\n12\\n1 2\\n1 3\\n-1 3\\n-1 1\\n-3 1\\n-3 -1\\n-1 -1\\n-1 -3\\n1 -3\\n1 0\\n3 -1\\n3 0\\n2 2\\n-2 2\\n-2 -2\\n4 -2\\n4\\n20000 20000\\n-20000 20000\\n-20000 -20000\\n20000 -20000\\n1000 1000\\n-1000 1000\\n-1000 -1000\\n1000 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1\\n-3 -1\\n-1 0\\n-1 -3\\n1 -3\\n1 -1\\n3 -1\\n3 1\\n2 2\\n-2 2\\n-2 -2\\n8 -2\\n4\\n20000 20000\\n-20000 20000\\n-20000 -20000\\n20000 -20000\\n1000 1000\\n-1000 1000\\n-1000 -1000\\n1000 -1000\\n4\\n1000 0000\\n-1000 1000\\n-1000 -1000\\n1000 -1000\\n20000 33707\\n-20000 20000\\n-37652 -20000\\n20000 -20000\\n4\\n0 0\\n10 0\\n10 10\\n0 10\\n20 0\\n17 0\\n30 2\\n20 10\\n0', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0\\n10 0\\n10 10\\n0 10\\n0 0\\n5 0\\n5 15\\n0 10\\n0\\n0 0\\n10 0\\n10 5\\n5 5\\n5 10\\n0 7\\n2 0\\n8 0\\n8 10\\n2 10\\n12\\n1 1\\n1 3\\n-1 3\\n-1 1\\n-3 1\\n-3 -1\\n-1 0\\n-1 -3\\n1 -3\\n2 -1\\n3 -1\\n3 1\\n2 2\\n-2 2\\n-2 -2\\n4 -2\\n4\\n20000 4028\\n-20000 20000\\n-20000 -20000\\n20000 -20000\\n1000 1000\\n-1000 1000\\n-1000 -1000\\n1000 -1000\\n4\\n1000 0000\\n-1000 1000\\n-1000 -1000\\n1000 -1000\\n20000 33707\\n-20000 20000\\n-37652 -20000\\n20000 -20000\\n4\\n0 0\\n19 0\\n10 10\\n0 10\\n20 0\\n2 0\\n30 10\\n20 10\\n0', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0\\n10 0\\n10 10\\n0 10\\n0 0\\n5 0\\n5 15\\n0 10\\n0\\n0 0\\n10 0\\n10 5\\n5 5\\n5 10\\n0 7\\n2 0\\n8 0\\n8 10\\n2 10\\n12\\n1 1\\n1 3\\n-1 3\\n-1 1\\n-3 1\\n-3 -1\\n-1 0\\n-2 -3\\n1 -3\\n1 -1\\n3 -1\\n3 1\\n2 2\\n-2 2\\n-2 -2\\n4 -2\\n4\\n20000 20000\\n-20000 20000\\n-20000 -20000\\n26379 -20000\\n1000 1000\\n-1000 1000\\n-1000 -174\\n1000 -1000\\n4\\n1000 0000\\n-1000 1000\\n-1000 -1000\\n1000 -1000\\n20000 33707\\n-5787 20000\\n-37652 -20000\\n20000 -20000\\n4\\n0 0\\n10 0\\n10 10\\n0 10\\n20 0\\n2 0\\n30 10\\n20 10\\n0', 'output': '50\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 536870912}","problem_id":"vfc_79985","program":"```python\nfrom collections import defaultdict\nINF = 10**9\nwhile 1:\n N = int(input())\n if N == 0:\n break\n P = [list(map(int, input().split())) for i in range(N)]\n S = defaultdict(list)\n X = set()\n x0 = y0 = INF; x1 = y1 = -INF\n for i in range(4):\n x, y = map(int, input().split())\n x0 = min(x0, x); x1 = max(x1, x)\n y0 = min(y0, y); y1 = max(y1, y)\n S[y0] = [INF]; S[y1] = [INF]\n X.add(x0); X.add(x1)\n for x, y in P:\n S[y].append(x)\n X.add(x)\n xs = sorted(X)\n MP = {x: i for i, x in enumerate(xs)}\n L = len(xs)\n\n su = 0\n for i in range(N):\n xa, ya = P[i-1]\n xb, yb = P[i]\n su += xa*yb - ya*xb\n su = abs(su) // 2\n res = 0\n *ps, = S.items()\n ps.sort()\n mode = 0\n prv = -1\n U = [0]*L\n for y, vs in ps:\n if mode:\n px = 0; c = 0\n d = y - prv\n for i in range(L):\n if U[i]:\n x = min(max(xs[i], x0), x1)\n if c == 1:\n res += d * (x - px)\n c ^= 1\n px = x\n for x in vs:\n if x == INF:\n mode ^= 1\n else:\n U[MP[x]] ^= 1\n prv = y\n print(su - res)\n\n```","inputs":"4\n0 0\n10 0\n10 10\n0 10\n0 0\n5 0\n5 10\n0 10\n6\n0 0\n10 0\n10 5\n5 5\n5 10\n0 10\n2 0\n8 0\n8 10\n2 10\n12\n1 1\n1 3\n-1 3\n-1 1\n-3 1\n-3 -1\n-1 -1\n-1 -3\n1 -3\n1 -1\n3 -1\n3 1\n2 2\n-2 2\n-2 -2\n2 -2\n4\n20000 20000\n-20000 20000\n-20000 -20000\n20000 -20000\n1000 1000\n-1000 1000\n-1000 -1000\n1000 -1000\n4\n1000 1000\n-1000 1000\n-1000 -1000\n1000 -1000\n20000 20000\n-20000 20000\n-20000 -20000\n20000 -20000\n4\n0 0\n10 0\n10 10\n0 10\n20 0\n30 0\n30 10\n20 10\n0","output":"50\n30\n8\n1596000000\n0\n100","actual_output":"50\n30\n8\n1596000000\n0\n100\n","execution_success":true,"sample_index":12736},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01983 Proof of Knowledge","prompt":"Solve the following coding problem using the programming language python:\n\nProof of knowledge\n\nThe entrance door of the apartment you live in has a password-type lock. This password consists of exactly four digits, ranging from 0 to 9, and you always use the password P given to you by the apartment manager to unlock this door.\n\nOne day, you wondered if all the residents of the apartment were using the same password P as you, and decided to ask a friend who lives in the same apartment. You and your friends can tell each other that they are using the same password by sharing their password with each other. However, this method is not preferable considering the possibility that passwords are individually assigned to each inhabitant. You should only know your password, not others.\n\nTo prevent this from happening, you and your friend decided to enter their password into the hash function and communicate the resulting hash value to each other. The hash function formula S used here is the lowercase alphabet'a','b','c','d' and the symbols'[',']','+','*','^' It consists of and is represented by defined by the following BNF.\n\n> :: = |'[' ']' :: ='+' |'*' |'^' :: =' a'|'b' |'c' |'d'\n\nHere,'a',' b',' c', and'd' represent the first, second, third, and fourth digits of the 4-digit password, respectively. '+','*','^' Are operators and have the following meanings.\n\n*'+': OR the following two in binary.\n*'*': Takes the logical product of the following two in binary.\n*'^': Take the exclusive OR when the following two are expressed in binary.\n\n\n\nHere, the truth tables of OR, AND, and Exclusive OR are as follows.\n\nA | B | [+ AB]\n--- | --- | ---\n0 | 0 | 0\n1 | 0 | 1\n0 | 1 | 1\n1 | 1 | 1\nA | B | [* AB]\n--- | --- | ---\n0 | 0 | 0\n1 | 0 | 0\n0 | 1 | 0\n1 | 1 | 1\nA | B | [^ AB]\n--- | --- | ---\n0 | 0 | 0\n1 | 0 | 1\n0 | 1 | 1\n1 | 1 | 0\n\nAs an example, if you enter the password 0404 in the hash function [+ c [+ a [^ bd]]], you will get 0 as the hash value. There are 0000, 0101, 0202, 0303, 0505, 0606, 0707, 0808, 0909 as passwords that can obtain the same hash value.\n\nOutput the result of entering your password P into the hash function S. Also, to prevent the use of a hash function that can uniquely identify the password from the hash value, output the number of passwords that have the same hash value as your password.\n\nInput\n\nThe input consists of up to 50 datasets. Each dataset is represented in the following format.\n\n> SP\n\nThe first line of each dataset is the hash function formula S. The second line of each dataset is the password P, which consists of four digits in the range 0-9. It can be assumed that the length of the hash function S is 80 or less.\n\nThe end of the input is represented by a line containing only one character,'.'.\n\nOutput\n\nFor each dataset, output the hash value obtained by entering P in S and the number of passwords that can obtain the same hash value as P, separated by blanks.\n\nSample Input\n\n\n[+ c [+ a [^ bd]]]]\n0404\n[* b [* [* cd] a]]\n7777\n[^ [^ ab] [^ cd]]\n1295\na\n9876\n[^ dd]\n9090\n..\n\n\nOutput for the Sample Input\n\n\n0 10\n7 1\n15 544\n9 1000\n0 10000\n\n\n\n\n\n\nExample\n\nInput\n\n[+c[+a[^bd]]]\n0404\n[*b[*[*cd]a]]\n7777\n[^[^ab][^cd]]\n1295\na\n9876\n[^dd]\n9090\n.\n\n\nOutput\n\n0 10\n7 1\n15 544\n9 1000\n0 10000\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools\n\nsys.setrecursionlimit(10**7)\ninf = 10**20\neps = 1.0 / 10**10\nmod = 10**9+7\ndd = [(-1,0),(0,1),(1,0),(0,-1)]\nddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\n\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\ndef LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]\ndef LF(): return [float(x) for x in sys.stdin.readline().split()]\ndef LS(): return sys.stdin.readline().split()\ndef I(): return int(sys.stdin.readline())\ndef F(): return float(sys.stdin.readline())\ndef S(): return input()\ndef pf(s): return print(s, flush=True)\n\n\ndef main():\n rr = []\n\n def f(s):\n t = [int(c) for c in S()]\n a = [t[ord(c) - ord('a')] if c in 'abcd' else c for c in s]\n\n def ff(a):\n if len(a) == 1:\n return a[0]\n l = len(a)\n for i in range(l-4):\n if a[i] == '[' and a[i+4] == ']':\n op = a[i+1]\n b = a[i+2]\n c = a[i+3]\n t = -1\n if op == '+':\n t = b | c\n elif op == '*':\n t = b & c\n elif op == '^':\n t = b ^ c\n return ff(a[:i] + [t] + a[i+5:])\n return -1\n\n r = ff(a)\n c = 0\n for k in range(10000):\n tt = [k//(10**i)%10 for i in range(4)]\n aa = [tt[ord(c) - ord('a')] if c in 'abcd' else c for c in s]\n kk = ff(aa)\n if kk == r:\n c += 1\n return '{} {}'.format(r,c)\n\n while 1:\n n = S()\n if n == '.':\n break\n rr.append(f(n))\n\n return '\\n'.join(map(str, rr))\n\n\nprint(main())\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n1295\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 10\\n7 1\\n15 544\\n9 1000\\n0 10000'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n2570\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 10\\n7 1\\n0 712\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n2570\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 450\\n7 1\\n0 712\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[^a[+bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n1295\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '4 220\\n7 1\\n15 544\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n2570\\na\\n1679\\n[^dd]\\n9090\\n.', 'output': '0 10\\n7 1\\n0 712\\n1 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n15341\\n[^[^ab][^cd]]\\n1295\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 10\\n0 8895\\n15 544\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n166\\n[^[^ab][^cd]]\\n2570\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 10\\n0 8895\\n0 712\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^ab][^cd]]\\n2570\\nb\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 10\\n0 8895\\n0 712\\n8 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n1295\\nb\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 10\\n7 1\\n15 544\\n8 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7777\\n[^[^ab][^cd]]\\n2570\\na\\n9876\\n[^dc]\\n9090\\n.', 'output': '0 10\\n7 1\\n0 712\\n9 1000\\n9 400\\n'}, {'type': 'stdin_stdout', 'input': '[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n7601\\n[^[^ab][^cd]]\\n2570\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 450\\n0 8895\\n0 712\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^ab][^cd]]\\n2303\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 10\\n0 8895\\n2 704\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': 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'[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n1479\\nb\\n9876\\n[^dd]\\n4997\\n.', 'output': '0 10\\n0 8895\\n11 544\\n8 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n343\\n[^[^ab][^cd]]\\n2570\\nb\\n3236\\n[^dd]\\n9090\\n.', 'output': '0 10\\n0 8895\\n0 712\\n2 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n2489\\nb\\n9876\\n[^dd]\\n4997\\n.', 'output': '0 10\\n0 8895\\n7 704\\n8 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n166\\n[^[^ab][^cd]]\\n2570\\na\\n7287\\n[^dd]\\n9090\\n.', 'output': '0 10\\n0 8895\\n0 712\\n7 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[*a[^cd]]]\\n0404\\n[*b[*[*cd]a]]\\n7601\\n[^[^ab][^cd]]\\n2570\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 510\\n0 8895\\n0 712\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': 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'[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^ab][^cd]]\\n1973\\na\\n2640\\n[^dd]\\n9090\\n.', 'output': '0 10\\n0 8895\\n12 544\\n2 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n30432\\n[^[^ab][^cd]]\\n1295\\na\\n5955\\n[^dd]\\n1131\\n.', 'output': '0 10\\n0 8895\\n15 544\\n5 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*bd]a]]\\n30432\\n[^[^ab][^cd]]\\n1295\\na\\n4682\\n[^cd]\\n1131\\n.', 'output': '0 10\\n0 7630\\n15 544\\n4 1000\\n2 800\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n2528\\nc\\n9876\\n[^dd]\\n4997\\n.', 'output': '0 10\\n0 8895\\n13 544\\n7 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[*a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n3131\\n[^[^ab][^cd]]\\n1991\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 450\\n1 593\\n0 712\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': 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'[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^ab][^cd]]\\n2570\\na\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 10\\n0 8895\\n0 712\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n15341\\n[^[^ab][^cd]]\\n1295\\na\\n9876\\n[^dd]\\n1131\\n.', 'output': '0 10\\n0 8895\\n15 544\\n9 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n183\\n[^[^cb][^ad]]\\n2570\\nb\\n9876\\n[^dd]\\n9090\\n.', 'output': '0 10\\n0 8895\\n0 712\\n8 1000\\n0 10000\\n'}, {'type': 'stdin_stdout', 'input': '[+c[+a[^bd]]]\\n0404\\n[*b[*[*cd]a]]\\n9100\\n[^[^ab][^cd]]\\n1295\\nb\\n9876\\n[^dd]\\n4997\\n.', 'output': '0 10\\n0 8895\\n15 544\\n8 1000\\n0 10000\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_79989","program":"```python\nimport math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools\n\nsys.setrecursionlimit(10**7)\ninf = 10**20\neps = 1.0 / 10**10\nmod = 10**9+7\ndd = [(-1,0),(0,1),(1,0),(0,-1)]\nddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\n\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\ndef LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]\ndef LF(): return [float(x) for x in sys.stdin.readline().split()]\ndef LS(): return sys.stdin.readline().split()\ndef I(): return int(sys.stdin.readline())\ndef F(): return float(sys.stdin.readline())\ndef S(): return input()\ndef pf(s): return print(s, flush=True)\n\n\ndef main():\n rr = []\n\n def f(s):\n t = [int(c) for c in S()]\n a = [t[ord(c) - ord('a')] if c in 'abcd' else c for c in s]\n\n def ff(a):\n if len(a) == 1:\n return a[0]\n l = len(a)\n for i in range(l-4):\n if a[i] == '[' and a[i+4] == ']':\n op = a[i+1]\n b = a[i+2]\n c = a[i+3]\n t = -1\n if op == '+':\n t = b | c\n elif op == '*':\n t = b & c\n elif op == '^':\n t = b ^ c\n return ff(a[:i] + [t] + a[i+5:])\n return -1\n\n r = ff(a)\n c = 0\n for k in range(10000):\n tt = [k//(10**i)%10 for i in range(4)]\n aa = [tt[ord(c) - ord('a')] if c in 'abcd' else c for c in s]\n kk = ff(aa)\n if kk == r:\n c += 1\n return '{} {}'.format(r,c)\n\n while 1:\n n = S()\n if n == '.':\n break\n rr.append(f(n))\n\n return '\\n'.join(map(str, rr))\n\n\nprint(main())\n\n\n```","inputs":"[+c[+a[^bd]]]\n0404\n[*b[*[*cd]a]]\n7777\n[^[^ab][^cd]]\n1295\na\n9876\n[^dd]\n9090\n.","output":"0 10\n7 1\n15 544\n9 1000\n0 10000","actual_output":"0 10\n7 1\n15 544\n9 1000\n0 10000\n","execution_success":true,"sample_index":12737},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02129 Ghost Legs","prompt":"Solve the following coding problem using the programming language python:\n\nProblem\n\nThere are $ N $ Amidakuji with 3 vertical lines.\nNo matter which line you start from, the Amidakuji that ends at the starting line is considered a good Amidakuji.\nYou can select one or more Amidakuji and connect them vertically in any order.\nOutput \"yes\" if you can make a good Amidakuji, otherwise output \"no\".\n\nThere are $ w_i $ horizontal lines in the $ i $ th Amidakuji.\n$ a_ {i, j} $ indicates whether the $ j $ th horizontal bar from the top of Amidakuji $ i $ extends from the central vertical line to the left or right.\nIf $ a_ {i, j} $ is 0, it means that it extends to the left, and if it is 1, it means that it extends to the right.\n\nConstraints\n\nThe input satisfies the following conditions.\n\n* $ 1 \\ le N \\ le 50 $\n* $ 0 \\ le w_i \\ le 100 $\n* $ a_ {i, j} $ is 0 or 1\n\nInput\n\nThe input is given in the following format.\n\n\n$ N $\n$ w_1 $ $ a_ {1,1} $ $ a_ {1,2} $ ... $ a_ {1, w_1} $\n$ w_2 $ $ a_ {2,1} $ $ a_ {2,2} $ ... $ a_ {2, w_2} $\n...\n$ w_N $ $ a_ {N, 1} $ $ a_ {N, 2} $ ... $ a_ {N, w_N} $\n\n\nAll inputs are given as integers.\n$ N $ is given on the first line.\n$ W_i $ and $ w_i $ $ a_ {i, j} $ are given on the following $ N $ line, separated by blanks.\n\nOutput\n\nIf you can make a good Amidakuji, it outputs \"yes\", otherwise it outputs \"no\".\n\nExamples\n\nInput\n\n3\n2 0 0\n1 1\n5 1 0 0 1 0\n\n\nOutput\n\nyes\n\n\nInput\n\n2\n1 1\n1 0\n\n\nOutput\n\nno\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef amida():\n line = list(map(int, input().split()))[1:]\n res = [0, 1, 2]\n for i in line:\n if i:\n res[1], res[2] = res[2], res[1]\n else:\n res[0], res[1] = res[1], res[0]\n return res\n\n\ndef func(x, line, flag):\n if line == [0, 1, 2] and flag:\n return True\n for i in range(27):\n if x[i] == 0:\n continue\n swaps = tolist(i)\n x[i] -= 1\n res = func(x, [line[swaps[0]], line[swaps[1]], line[swaps[2]]], True)\n x[i] += 1\n if res:\n return True\n return False\n\n\nn = int(input())\nif n >= 7:\n print(\"yes\")\n exit()\namidas = [amida() for _ in range(n)]\ntoint = lambda x: x[0] * 9 + x[1] * 3 + x[2]\ntolist = lambda x: [x // 9, x % 9 // 3, x % 3]\naa = [0 for _ in range(27)]\nfor i in amidas:\n aa[toint(i)] += 1\n\nflag = False\nfor i in range(27):\n if aa[i] == 0:\n continue\n line = [0, 1, 2]\n for j in range(aa[i]):\n swaps = tolist(i)\n line = [line[swaps[0]], line[swaps[1]], line[swaps[2]]]\n if line == [0, 1, 2]:\n flag = True\n break\nif flag:\n print(\"yes\")\n exit()\nif func(aa, [0, 1, 2], False):\n print(\"yes\")\n exit()\nprint(\"no\")\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n2 0 0\\n1 1\\n5 1 0 0 1 0', 'output': 'yes'}, {'type': 'stdin_stdout', 'input': '2\\n1 1\\n1 0', 'output': 'no'}, {'type': 'stdin_stdout', 'input': '3\\n2 0 0\\n1 1\\n10 1 0 0 1 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1\\n3 0', 'output': 'no\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1\\n2 0', 'output': 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'2\\n1 2\\n0 -1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 0\\n1 1\\n5 1 0 0 1 -1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1\\n3 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 0 0\\n1 2\\n10 1 0 0 0 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1\\n6 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 0\\n1 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 0 0\\n1 1\\n10 3 0 0 2 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2\\n2 -3', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 -1 0\\n0 1\\n1 0 0 0 2 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1\\n0 -4', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 0\\n0 -1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 2\\n0 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2\\n4 2', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 0 0\\n0 1\\n10 1 0 0 1 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2\\n0 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 -1\\n1 -1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 0 1\\n1 1\\n10 4 1 0 2 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 0\\n2 -4', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 -1 0\\n0 1\\n1 1 0 0 2 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1\\n-1 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0\\n1 1\\n10 4 1 0 2 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 -1 0\\n0 1\\n1 3 0 1 2 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1\\n4 1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2\\n-1 1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1 1\\n10 3 0 0 2 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 -1 0\\n0 1\\n1 2 0 2 2 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 0\\n4 1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1\\n1 1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0\\n1 1\\n8 3 1 0 2 -1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 -1 0\\n0 1\\n1 1 -1 1 2 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 0\\n5 0', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 0\\n1 2', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 -1 0\\n0 1\\n1 2 0 1 3 1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 -1 0\\n0 1\\n1 2 -1 0 3 1', 'output': 'yes\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 0 0\\n1 2\\n5 1 0 0 2 0', 'output': 'yes\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 536870912}","problem_id":"vfc_79993","program":"```python\ndef amida():\n line = list(map(int, input().split()))[1:]\n res = [0, 1, 2]\n for i in line:\n if i:\n res[1], res[2] = res[2], res[1]\n else:\n res[0], res[1] = res[1], res[0]\n return res\n\n\ndef func(x, line, flag):\n if line == [0, 1, 2] and flag:\n return True\n for i in range(27):\n if x[i] == 0:\n continue\n swaps = tolist(i)\n x[i] -= 1\n res = func(x, [line[swaps[0]], line[swaps[1]], line[swaps[2]]], True)\n x[i] += 1\n if res:\n return True\n return False\n\n\nn = int(input())\nif n >= 7:\n print(\"yes\")\n exit()\namidas = [amida() for _ in range(n)]\ntoint = lambda x: x[0] * 9 + x[1] * 3 + x[2]\ntolist = lambda x: [x // 9, x % 9 // 3, x % 3]\naa = [0 for _ in range(27)]\nfor i in amidas:\n aa[toint(i)] += 1\n\nflag = False\nfor i in range(27):\n if aa[i] == 0:\n continue\n line = [0, 1, 2]\n for j in range(aa[i]):\n swaps = tolist(i)\n line = [line[swaps[0]], line[swaps[1]], line[swaps[2]]]\n if line == [0, 1, 2]:\n flag = True\n break\nif flag:\n print(\"yes\")\n exit()\nif func(aa, [0, 1, 2], False):\n print(\"yes\")\n exit()\nprint(\"no\")\n\n\n```","inputs":"3\n2 0 0\n1 1\n5 1 0 0 1 0","output":"yes","actual_output":"yes\n","execution_success":true,"sample_index":12738},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02270 Allocation","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given $n$ packages of $w_i$ kg from a belt conveyor in order ($i = 0, 1, ... n-1$). You should load all packages onto $k$ trucks which have the common maximum load $P$. Each truck can load consecutive packages (more than or equals to zero) from the belt conveyor unless the total weights of the packages in the sequence does not exceed the maximum load $P$.\n\nWrite a program which reads $n$, $k$ and $w_i$, and reports the minimum value of the maximum load $P$ to load all packages from the belt conveyor.\n\nConstraints\n\n* $1 \\leq n \\leq 100,000$\n* $1 \\leq k \\leq 100,000$\n* $1 \\leq w_i \\leq 10,000$\n\nInput\n\nIn the first line, two integers $n$ and $k$ are given separated by a space character. In the following $n$ lines, $w_i$ are given respectively.\n\nOutput\n\nPrint the minimum value of $P$ in a line.\n\nExamples\n\nInput\n\n5 3\n8\n1\n7\n3\n9\n\n\nOutput\n\n10\n\n\nInput\n\n4 2\n1\n2\n2\n6\n\n\nOutput\n\n6\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom sys import stdin\n\ndef binSearch(k, p_min, p_max):\n global w\n while p_max-p_min > 1:\n mid = p_min + (p_max-p_min)//2\n if k >= countTrack(w, mid):\n p_max = mid\n else:\n p_min = mid\n\n return p_max\n\ndef countTrack(w, p):\n rest = []\n for wi in w:\n if len(rest) != 0 and rest[-1] >= wi:\n rest[-1] -= wi\n else:\n rest.append(p-wi)\n\n return len(rest)\n\nn, k = [int(x) for x in stdin.readline().rstrip().split()]\nw = [int(stdin.readline().rstrip()) for _ in range(n)]\nprint(binSearch(k, max(w)-1, 10000*100000+1))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 3\\n8\\n1\\n7\\n3\\n9', 'output': '10'}, {'type': 'stdin_stdout', 'input': '4 2\\n1\\n2\\n2\\n6', 'output': '6'}, {'type': 'stdin_stdout', 'input': '5 3\\n4\\n1\\n7\\n3\\n9', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1\\n1\\n2\\n6', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n4\\n1\\n7\\n3\\n5', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n4\\n1\\n7\\n3\\n5', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1\\n1\\n3\\n1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1\\n1\\n3\\n0', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1\\n4\\n3\\n0', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n2\\n8\\n5\\n4', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n2\\n8\\n7\\n4', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n8\\n2\\n9\\n7\\n5', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n6\\n1\\n8\\n3\\n5', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n6\\n2\\n8\\n5\\n4', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n6\\n2\\n8\\n3\\n5', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-1\\n4\\n18\\n5\\n4', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n1\\n0\\n2\\n6', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n6\\n0\\n8\\n5\\n4', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-1\\n2\\n17\\n1\\n4', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n3\\n4\\n14\\n7\\n0', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n-2\\n3\\n5\\n13\\n8', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '1 6\\n1\\n-1\\n9\\n23\\n8', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n6\\n2\\n8\\n6\\n4', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n6\\n1\\n8\\n3\\n1', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n20\\n1\\n6\\n3\\n0', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n5\\n2\\n8\\n2\\n5', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n6\\n3\\n29\\n0\\n3', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n11\\n12\\n5\\n2\\n6', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n7\\n2\\n9\\n1\\n5', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n10\\n4\\n9\\n7\\n5', 'output': '35\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n10\\n4\\n9\\n7\\n5', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n14\\n2\\n9\\n1\\n4', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n0\\n1\\n39\\n5\\n4', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n11\\n17\\n10\\n0\\n6', 'output': '27\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1\\n1\\n3\\n6', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n5\\n1\\n7\\n3\\n5', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n6\\n1\\n7\\n3\\n5', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1\\n2\\n3\\n0', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n6\\n1\\n8\\n3\\n5', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n6\\n1\\n8\\n3\\n4', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n1\\n8\\n3\\n4', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n2\\n8\\n3\\n4', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n2\\n8\\n6\\n4', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n2\\n9\\n7\\n4', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n8\\n2\\n9\\n7\\n4', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n7\\n2\\n9\\n7\\n5', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n7\\n2\\n9\\n7\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n0\\n2\\n9\\n7\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n0\\n2\\n9\\n5\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n0\\n2\\n9\\n5\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-1\\n2\\n9\\n5\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-1\\n3\\n9\\n5\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-1\\n3\\n9\\n5\\n4', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-2\\n3\\n9\\n5\\n4', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-2\\n3\\n4\\n5\\n4', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n8\\n2\\n7\\n3\\n9', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1\\n0\\n2\\n6', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n4\\n2\\n7\\n3\\n5', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1\\n1\\n0\\n6', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1\\n1\\n3\\n1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n5\\n2\\n7\\n3\\n5', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n6\\n1\\n7\\n3\\n4', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1\\n2\\n3\\n0', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n6\\n0\\n8\\n3\\n4', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n6\\n1\\n8\\n3\\n4', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n10\\n2\\n8\\n3\\n4', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n0\\n8\\n6\\n4', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n4\\n8\\n7\\n4', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n3\\n9\\n7\\n4', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n8\\n3\\n9\\n7\\n4', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n7\\n4\\n9\\n7\\n5', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n7\\n1\\n9\\n7\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n0\\n2\\n9\\n7\\n7', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n0\\n2\\n9\\n4\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n0\\n3\\n9\\n5\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-1\\n3\\n2\\n5\\n5', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-1\\n4\\n9\\n5\\n4', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-2\\n3\\n9\\n4\\n4', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-2\\n3\\n4\\n5\\n5', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n8\\n2\\n7\\n3\\n9', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1\\n0\\n2\\n6', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n4\\n4\\n7\\n3\\n5', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1\\n2\\n0\\n6', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n5\\n2\\n3\\n3\\n5', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1\\n1\\n3\\n0', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5 10\\n6\\n0\\n8\\n3\\n4', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n6\\n1\\n8\\n3\\n0', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n11\\n2\\n8\\n3\\n4', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n6\\n2\\n8\\n5\\n4', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n4\\n8\\n7\\n1', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n6\\n3\\n9\\n5\\n4', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n12\\n3\\n9\\n7\\n4', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n7\\n1\\n9\\n7\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n-1\\n2\\n9\\n7\\n7', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n0\\n2\\n9\\n4\\n1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n0\\n2\\n9\\n1\\n5', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-1\\n3\\n2\\n6\\n5', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n-2\\n3\\n11\\n4\\n4', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '4 7\\n-2\\n3\\n4\\n5\\n4', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1\\n2\\n0\\n6', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n1\\n2\\n3\\n3\\n5', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n1\\n1\\n3\\n1', 'output': '6\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_79997","program":"```python\nfrom sys import stdin\n\ndef binSearch(k, p_min, p_max):\n global w\n while p_max-p_min > 1:\n mid = p_min + (p_max-p_min)//2\n if k >= countTrack(w, mid):\n p_max = mid\n else:\n p_min = mid\n\n return p_max\n\ndef countTrack(w, p):\n rest = []\n for wi in w:\n if len(rest) != 0 and rest[-1] >= wi:\n rest[-1] -= wi\n else:\n rest.append(p-wi)\n\n return len(rest)\n\nn, k = [int(x) for x in stdin.readline().rstrip().split()]\nw = [int(stdin.readline().rstrip()) for _ in range(n)]\nprint(binSearch(k, max(w)-1, 10000*100000+1))\n\n```","inputs":"5 3\n8\n1\n7\n3\n9","output":"10","actual_output":"10\n","execution_success":true,"sample_index":12739},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02417 Counting Characters","prompt":"Solve the following coding problem using the programming language python:\n\nWrite a program which counts and reports the number of each alphabetical letter. Ignore the case of characters.\n\nConstraints\n\n* The number of characters in the sentence < 1200\n\nInput\n\nA sentence in English is given in several lines.\n\nOutput\n\nPrints the number of alphabetical letters in the following format:\n\n\na : The number of 'a'\nb : The number of 'b'\nc : The number of 'c'\n.\n.\nz : The number of 'z'\n\n\nExample\n\nInput\n\nThis is a pen.\n\n\nOutput\n\na : 1\nb : 0\nc : 0\nd : 0\ne : 1\nf : 0\ng : 0\nh : 1\ni : 2\nj : 0\nk : 0\nl : 0\nm : 0\nn : 1\no : 0\np : 1\nq : 0\nr : 0\ns : 2\nt : 1\nu : 0\nv : 0\nw : 0\nx : 0\ny : 0\nz : 0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nx=sys.stdin.read().lower()\nfor i in range(97,123):\n print(chr(i),':',x.count(chr(i)))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'This is a pen.', 'output': 'a : 1\\nb : 0\\nc : 0\\nd : 0\\ne : 1\\nf : 0\\ng : 0\\nh : 1\\ni : 2\\nj : 0\\nk : 0\\nl : 0\\nm : 0\\nn : 1\\no : 0\\np : 1\\nq : 0\\nr : 0\\ns : 2\\nt : 1\\nu : 0\\nv : 0\\nw : 0\\nx : 0\\ny : 0\\nz : 0'}, {'type': 'stdin_stdout', 'input': 'This is ` pen.', 'output': 'a : 0\\nb : 0\\nc : 0\\nd : 0\\ne : 1\\nf : 0\\ng : 0\\nh : 1\\ni : 2\\nj : 0\\nk : 0\\nl : 0\\nm : 0\\nn : 1\\no : 0\\np : 1\\nq : 0\\nr : 0\\ns : 2\\nt : 1\\nu : 0\\nv : 0\\nw : 0\\nx : 0\\ny : 0\\nz : 0\\n'}, {'type': 'stdin_stdout', 'input': 'This si a pen.', 'output': 'a : 1\\nb : 0\\nc : 0\\nd : 0\\ne : 1\\nf : 0\\ng : 0\\nh : 1\\ni : 2\\nj : 0\\nk : 0\\nl : 0\\nm : 0\\nn : 1\\no : 0\\np : 1\\nq : 0\\nr : 0\\ns : 2\\nt : 1\\nu : 0\\nv : 0\\nw : 0\\nx : 0\\ny : 0\\nz : 0\\n'}, {'type': 'stdin_stdout', 'input': 'hTit si a pen.', 'output': 'a : 1\\nb : 0\\nc : 0\\nd : 0\\ne : 1\\nf : 0\\ng : 0\\nh : 1\\ni : 2\\nj : 0\\nk : 0\\nl : 0\\nm : 0\\nn : 1\\no : 0\\np : 1\\nq : 0\\nr : 0\\ns : 1\\nt : 2\\nu : 0\\nv : 0\\nw : 0\\nx : 0\\ny : 0\\nz : 0\\n'}, 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print(chr(i),':',x.count(chr(i)))\n\n```","inputs":"This is a pen.","output":"a : 1\nb : 0\nc : 0\nd : 0\ne : 1\nf : 0\ng : 0\nh : 1\ni : 2\nj : 0\nk : 0\nl : 0\nm : 0\nn : 1\no : 0\np : 1\nq : 0\nr : 0\ns : 2\nt : 1\nu : 0\nv : 0\nw : 0\nx : 0\ny : 0\nz : 0","actual_output":"a : 1\nb : 0\nc : 0\nd : 0\ne : 1\nf : 0\ng : 0\nh : 1\ni : 2\nj : 0\nk : 0\nl : 0\nm : 0\nn : 1\no : 0\np : 1\nq : 0\nr : 0\ns : 2\nt : 1\nu : 0\nv : 0\nw : 0\nx : 0\ny : 0\nz : 0\n","execution_success":true,"sample_index":12740},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"102_A. Clothes","prompt":"Solve the following coding problem using the programming language python:\n\nA little boy Gerald entered a clothes shop and found out something very unpleasant: not all clothes turns out to match. For example, Gerald noticed that he looks rather ridiculous in a smoking suit and a baseball cap.\n\nOverall the shop sells n clothing items, and exactly m pairs of clothing items match. Each item has its price, represented by an integer number of rubles. Gerald wants to buy three clothing items so that they matched each other. Besides, he wants to spend as little money as possible. Find the least possible sum he can spend.\n\nInput\n\nThe first input file line contains integers n and m \u2014 the total number of clothing items in the shop and the total number of matching pairs of clothing items ().\n\nNext line contains n integers ai (1 \u2264 ai \u2264 106) \u2014 the prices of the clothing items in rubles.\n\nNext m lines each contain a pair of space-separated integers ui and vi (1 \u2264 ui, vi \u2264 n, ui \u2260 vi). Each such pair of numbers means that the ui-th and the vi-th clothing items match each other. It is guaranteed that in each pair ui and vi are distinct and all the unordered pairs (ui, vi) are different.\n\nOutput\n\nPrint the only number \u2014 the least possible sum in rubles that Gerald will have to pay in the shop. If the shop has no three clothing items that would match each other, print \"-1\" (without the quotes).\n\nExamples\n\nInput\n\n3 3\n1 2 3\n1 2\n2 3\n3 1\n\n\nOutput\n\n6\n\n\nInput\n\n3 2\n2 3 4\n2 3\n2 1\n\n\nOutput\n\n-1\n\n\nInput\n\n4 4\n1 1 1 1\n1 2\n2 3\n3 4\n4 1\n\n\nOutput\n\n-1\n\nNote\n\nIn the first test there only are three pieces of clothing and they all match each other. Thus, there is only one way \u2014 to buy the 3 pieces of clothing; in this case he spends 6 roubles.\n\nThe second test only has three pieces of clothing as well, yet Gerald can't buy them because the first piece of clothing does not match the third one. Thus, there are no three matching pieces of clothing. The answer is -1.\n\nIn the third example there are 4 pieces of clothing, but Gerald can't buy any 3 of them simultaneously. The answer is -1.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nI=lambda:map(int,input().split())\nn,m=I()\nN=list(I())\np=set()\nfor i in range(m):\n\tx,y=I();x-=1;y-=1\n\tp.add((x,y)if x1e8 else r)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 4\\n1 1 1 1\\n1 2\\n2 3\\n3 4\\n4 1\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 3\\n1 2\\n2 3\\n3 1\\n', 'output': '6'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 3 4\\n2 3\\n2 1\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '3 3\\n1000000 1000000 1000000\\n2 1\\n1 3\\n3 2\\n', 'output': '3000000'}, {'type': 'stdin_stdout', 'input': '4 3\\n10 10 5 1\\n2 1\\n3 1\\n3 4\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 8 6\\n1 3\\n1 4\\n3 4\\n', 'output': '15'}, {'type': 'stdin_stdout', 'input': '6 8\\n69 36 41 23 91 35\\n1 2\\n3 1\\n3 2\\n1 4\\n3 4\\n3 5\\n5 4\\n4 6\\n', 'output': '133'}, {'type': 'stdin_stdout', 'input': '6 7\\n85 2 34 6 83 61\\n1 2\\n2 3\\n4 2\\n4 3\\n1 5\\n4 5\\n6 3\\n', 'output': '42'}, {'type': 'stdin_stdout', 'input': '6 6\\n92 56 15 83 30 28\\n3 1\\n4 1\\n2 5\\n5 4\\n2 6\\n6 3\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '6 6\\n33 76 98 59 4 69\\n1 2\\n3 2\\n5 1\\n2 5\\n4 5\\n6 5\\n', 'output': '113'}, {'type': 'stdin_stdout', 'input': '4 4\\n9 3 3 1\\n1 2\\n3 1\\n3 2\\n4 3\\n', 'output': '15'}, {'type': 'stdin_stdout', 'input': '4 3\\n5 3 4 4\\n2 1\\n4 1\\n3 4\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '4 3\\n5 1 10 1\\n2 1\\n3 2\\n1 4\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '6 5\\n59 69 52 38 93 53\\n4 2\\n1 5\\n6 1\\n4 6\\n5 6\\n', 'output': '205'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 31 14 16\\n1 2\\n1 3\\n1 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 4\\n', 'output': '85'}, {'type': 'stdin_stdout', 'input': '4 5\\n4 10 3 9\\n1 2\\n3 1\\n3 2\\n2 4\\n4 3\\n', 'output': '17'}, {'type': 'stdin_stdout', 'input': '4 2\\n2 9 8 4\\n1 3\\n4 2\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '6 10\\n17 5 55 24 55 74\\n1 3\\n2 3\\n3 4\\n5 1\\n5 2\\n5 3\\n4 5\\n6 2\\n6 3\\n6 5\\n', 'output': '115'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 1 999999\\n1 2\\n2 3\\n3 1\\n', 'output': '1000001'}, {'type': 'stdin_stdout', 'input': '3 3\\n1000000 1000000 1000000\\n1 2\\n2 3\\n1 3\\n', 'output': '3000000'}, {'type': 'stdin_stdout', 'input': '6 6\\n39 15 73 82 37 40\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 6\\n', 'output': '94'}, {'type': 'stdin_stdout', 'input': '6 8\\n36 19 99 8 52 77\\n2 1\\n3 1\\n4 2\\n4 3\\n1 5\\n5 4\\n1 6\\n6 2\\n', 'output': '132'}, {'type': 'stdin_stdout', 'input': '3 0\\n1 1 1\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '4 3\\n5 5 9 6\\n3 2\\n1 4\\n3 4\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '3 3\\n100000 100000 100001\\n1 2\\n2 3\\n3 1\\n', 'output': '300001'}, {'type': 'stdin_stdout', 'input': '6 11\\n95 81 74 94 60 69\\n3 2\\n1 4\\n4 2\\n3 4\\n1 5\\n5 2\\n5 3\\n1 6\\n2 6\\n3 6\\n4 6\\n', 'output': '215'}, {'type': 'stdin_stdout', 'input': '3 3\\n999999 1 1\\n1 2\\n2 3\\n3 1\\n', 'output': '1000001'}, {'type': 'stdin_stdout', 'input': '4 0\\n9 8 2 10\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '4 3\\n6 8 10 1\\n2 3\\n1 4\\n3 4\\n', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '4 3\\n16 10 5 1\\n2 1\\n3 1\\n3 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n92 56 15 83 30 28\\n3 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 3\\n', 'output': '135\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n33 76 98 59 4 18\\n1 2\\n3 2\\n5 1\\n2 5\\n4 5\\n6 5\\n', 'output': '113\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n59 69 52 38 93 52\\n4 2\\n1 5\\n6 1\\n4 6\\n5 6\\n', 'output': '204\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 31 14 16\\n1 2\\n1 3\\n1 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 1\\n', 'output': '85\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n4 10 3 9\\n1 2\\n4 1\\n3 2\\n2 4\\n4 3\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '6 10\\n17 5 55 24 55 74\\n1 4\\n2 3\\n3 4\\n5 1\\n5 2\\n5 3\\n4 5\\n6 2\\n6 3\\n6 5\\n', 'output': '96\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n39 15 73 82 37 40\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 1\\n', 'output': '94\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n36 19 53 8 52 77\\n2 1\\n3 1\\n4 2\\n4 3\\n1 5\\n5 4\\n1 6\\n6 2\\n', 'output': '132\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n4 10 3 9\\n1 2\\n4 1\\n4 2\\n2 4\\n4 3\\n', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n38 15 73 82 37 40\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 1\\n', 'output': '93\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 31 14 16\\n1 2\\n1 2\\n1 4\\n2 5\\n3 5\\n6 2\\n6 3\\n6 1\\n', 'output': '124\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n43 15 73 82 37 40\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 1\\n', 'output': '98\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n43 26 73 82 37 40\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 1\\n', 'output': '109\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 56 18 16\\n1 2\\n1 2\\n1 4\\n2 5\\n6 5\\n6 2\\n6 3\\n6 1\\n', 'output': '78\\n'}, {'type': 'stdin_stdout', 'input': '6 7\\n85 2 34 6 83 61\\n1 2\\n2 3\\n4 2\\n4 3\\n1 3\\n4 5\\n6 3\\n', 'output': '42\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n0 1 999999\\n1 2\\n2 3\\n3 1\\n', 'output': '1000000\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n39 15 73 82 37 19\\n2 1\\n5 1\\n1 6\\n2 6\\n6 3\\n4 6\\n', 'output': '73\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n36 19 99 8 52 77\\n2 1\\n3 1\\n4 2\\n4 3\\n2 5\\n5 4\\n1 6\\n6 2\\n', 'output': '79\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 1 3\\n1 2\\n2 3\\n3 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n33 116 98 59 4 18\\n1 2\\n3 2\\n5 1\\n2 5\\n4 5\\n6 5\\n', 'output': '153\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n94 69 52 38 93 52\\n4 2\\n1 5\\n6 1\\n4 6\\n5 6\\n', 'output': '239\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n104 44 5 31 14 16\\n1 2\\n1 3\\n1 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 1\\n', 'output': '125\\n'}, {'type': 'stdin_stdout', 'input': '6 10\\n29 5 55 24 55 74\\n1 4\\n2 3\\n3 4\\n5 1\\n5 2\\n5 3\\n4 5\\n6 2\\n6 3\\n6 5\\n', 'output': '108\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n9 3 3 1\\n1 2\\n2 1\\n3 2\\n4 3\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n5 1 10 0\\n2 1\\n3 2\\n1 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 1 999999\\n1 2\\n2 3\\n2 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n9 12 2 10\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n6 8 10 1\\n2 1\\n1 4\\n3 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n92 56 15 83 30 28\\n2 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 3\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n33 76 98 59 4 18\\n1 2\\n3 2\\n5 1\\n3 5\\n4 5\\n6 5\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 1 10 0\\n2 1\\n3 2\\n1 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 31 14 16\\n1 2\\n1 2\\n1 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n9 23 2 10\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n6 8 10 1\\n2 1\\n2 4\\n3 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n92 56 15 83 30 28\\n4 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 3\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n9 0 2 10\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n5 8 10 1\\n2 1\\n2 4\\n3 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n92 56 15 83 30 21\\n4 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 3\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 31 18 16\\n1 2\\n1 2\\n1 4\\n2 5\\n3 5\\n6 2\\n6 3\\n6 1\\n', 'output': '124\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n9 0 2 7\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n92 44 15 83 30 21\\n4 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 3\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 36 18 16\\n1 2\\n1 2\\n1 4\\n2 5\\n3 5\\n6 2\\n6 3\\n6 1\\n', 'output': '124\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n9 0 2 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 56 18 16\\n1 2\\n1 2\\n1 4\\n2 5\\n3 5\\n6 2\\n6 3\\n6 1\\n', 'output': '124\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n9 0 3 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 56 18 16\\n1 2\\n1 2\\n1 4\\n1 5\\n6 5\\n6 2\\n6 3\\n6 1\\n', 'output': '98\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n3 1 10 1\\n2 1\\n3 2\\n1 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n59 69 52 38 93 53\\n4 2\\n1 5\\n6 1\\n4 6\\n5 2\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 31 14 16\\n1 4\\n1 3\\n1 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 4\\n', 'output': '85\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n0 9 8 4\\n1 3\\n4 2\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n0 1 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n5 9 9 6\\n3 2\\n1 4\\n3 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n9 8 2 17\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 3 3\\n2 3\\n2 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n28 10 5 1\\n2 1\\n3 1\\n3 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n92 56 15 83 30 28\\n3 1\\n4 1\\n2 5\\n5 4\\n1 6\\n6 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n5 0 10 0\\n2 1\\n3 2\\n1 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n2 8 10 1\\n2 1\\n1 4\\n3 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n64 44 5 31 14 16\\n1 2\\n1 2\\n2 4\\n2 5\\n3 5\\n6 1\\n6 3\\n6 1\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80033","program":"```python\nI=lambda:map(int,input().split())\nn,m=I()\nN=list(I())\np=set()\nfor i in range(m):\n\tx,y=I();x-=1;y-=1\n\tp.add((x,y)if x1e8 else r)\n```","inputs":"4 4\n1 1 1 1\n1 2\n2 3\n3 4\n4 1\n","output":"-1","actual_output":"-1\n","execution_success":true,"sample_index":12742},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1073_B. Vasya and Books","prompt":"Solve the following coding problem using the programming language python:\n\nVasya has got n books, numbered from 1 to n, arranged in a stack. The topmost book has number a_1, the next one \u2014 a_2, and so on. The book at the bottom of the stack has number a_n. All numbers are distinct.\n\nVasya wants to move all the books to his backpack in n steps. During i-th step he wants to move the book number b_i into his backpack. If the book with number b_i is in the stack, he takes this book and all the books above the book b_i, and puts them into the backpack; otherwise he does nothing and begins the next step. For example, if books are arranged in the order [1, 2, 3] (book 1 is the topmost), and Vasya moves the books in the order [2, 1, 3], then during the first step he will move two books (1 and 2), during the second step he will do nothing (since book 1 is already in the backpack), and during the third step \u2014 one book (the book number 3). Note that b_1, b_2, ..., b_n are distinct.\n\nHelp Vasya! Tell him the number of books he will put into his backpack during each step.\n\nInput\n\nThe first line contains one integer n~(1 \u2264 n \u2264 2 \u22c5 10^5) \u2014 the number of books in the stack.\n\nThe second line contains n integers a_1, a_2, ..., a_n~(1 \u2264 a_i \u2264 n) denoting the stack of books.\n\nThe third line contains n integers b_1, b_2, ..., b_n~(1 \u2264 b_i \u2264 n) denoting the steps Vasya is going to perform.\n\nAll numbers a_1 ... a_n are distinct, the same goes for b_1 ... b_n.\n\nOutput\n\nPrint n integers. The i-th of them should be equal to the number of books Vasya moves to his backpack during the i-th step.\n\nExamples\n\nInput\n\n3\n1 2 3\n2 1 3\n\n\nOutput\n\n2 0 1 \n\n\nInput\n\n5\n3 1 4 2 5\n4 5 1 3 2\n\n\nOutput\n\n3 2 0 0 0 \n\n\nInput\n\n6\n6 5 4 3 2 1\n6 5 3 4 2 1\n\n\nOutput\n\n1 1 2 0 1 1 \n\nNote\n\nThe first example is described in the statement.\n\nIn the second example, during the first step Vasya will move the books [3, 1, 4]. After that only books 2 and 5 remain in the stack (2 is above 5). During the second step Vasya will take the books 2 and 5. After that the stack becomes empty, so during next steps Vasya won't move any books.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#------------------------template--------------------------#\nimport os\nimport sys\nfrom math import *\nfrom collections import *\n# from fractions import *\n# from functools import *\nfrom heapq import *\nfrom bisect import *\nfrom io import BytesIO, IOBase\ndef vsInput():\n sys.stdin = open('input.txt', 'r')\n sys.stdout = open('output.txt', 'w')\nBUFSIZE = 8192\nclass FastIO(IOBase):\n newlines = 0\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\nALPHA='abcdefghijklmnopqrstuvwxyz'\nM = 998244353\nEPS = 1e-6\ndef Ceil(a,b): return a//b+int(a%b>0)\ndef value():return tuple(map(int,input().split()))\ndef array():return [int(i) for i in input().split()]\ndef Int():return int(input())\ndef Str():return input()\ndef arrayS():return [i for i in input().split()]\n\n\n#-------------------------code---------------------------#\n# vsInput()\n\nfor _ in range(1):\n\n n = Int()\n a = array()\n b = array()\n \n ans = []\n C = Counter(a)\n j = 0\n \n for i in b:\n # print(i)\n here = 0\n if(C[i]): \n while(j < n and a[j] != i):\n C[a[j]] -= 1\n here += 1\n j += 1\n C[a[j]] -= 1\n here += 1\n j += 1\n \n ans.append(here)\n \n print(*ans)\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n\n\n \n \n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 2 3\\n2 1 3\\n', 'output': '2 0 1 '}, {'type': 'stdin_stdout', 'input': '6\\n6 5 4 3 2 1\\n6 5 3 4 2 1\\n', 'output': '1 1 2 0 1 1 '}, {'type': 'stdin_stdout', 'input': '5\\n3 1 4 2 5\\n4 5 1 3 2\\n', 'output': '3 2 0 0 0 '}, {'type': 'stdin_stdout', 'input': '1\\n1\\n1\\n', 'output': '1 '}, {'type': 'stdin_stdout', 'input': '10\\n4 7 10 2 1 8 3 5 9 6\\n4 2 7 1 8 10 5 3 9 6\\n', 'output': '1 3 0 1 1 0 2 0 1 1 '}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 3 1 6 4 7 5\\n', 'output': '7 0 0 0 0 0 0 '}, {'type': 'stdin_stdout', 'input': '5\\n3 1 4 2 5\\n4 5 1 3 3\\n', 'output': '3 2 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 3 1 6 4 7 7\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 1 4 2 5\\n2 5 1 3 3\\n', 'output': '4 1 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 3\\n2 1 1\\n', 'output': '2 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 1 4 2 5\\n4 3 1 3 3\\n', 'output': '3 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 1 4 2 5\\n4 3 2 3 3\\n', 'output': '3 0 1 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n3 4 1 6 1 7 6\\n', 'output': '3 3 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 7 10 2 1 8 3 5 9 6\\n4 2 7 1 8 10 5 3 7 6\\n', 'output': '1 3 0 1 1 0 2 0 0 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 3\\n3 1 1\\n', 'output': '3 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 1 4 2 5\\n2 4 1 3 3\\n', 'output': '4 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n3 4 2 6 1 7 6\\n', 'output': '3 3 1 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 1 4 2 5\\n4 3 1 2 3\\n', 'output': '3 0 0 1 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n4 5 1 6 1 7 7\\n', 'output': '6 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 7 10 2 1 8 3 5 9 6\\n4 2 7 1 7 10 5 3 9 6\\n', 'output': '1 3 0 1 0 0 3 0 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 1 4 2 5\\n3 5 2 1 1\\n', 'output': '1 4 0 0 0\\n'}, 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'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 4 1 6 1 1 1\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 3 1 6 1 6 4\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n4 6 1 6 6 1 5\\n', 'output': '6 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 4 1 6 1 6 6\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 3 1 6 4 1 5\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 4 1 3 1 1 1\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n4 6 1 6 6 1 1\\n', 'output': '6 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 4 1 6 1 6 1\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 3 1 6 4 1 7\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 4 1 1 1 1 1\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 1 1 1 1 1 1\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 6 1 6 4 7 5\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 1 4 2 5\\n4 1 1 1 3\\n', 'output': '3 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 4 1 6 3 7 7\\n', 'output': '7 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 6 3 1 5 4 2\\n2 3 1 5 1 5 6\\n', 'output': '7 0 0 0 0 0 0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80041","program":"```python\n#------------------------template--------------------------#\nimport os\nimport sys\nfrom math import *\nfrom collections import *\n# from fractions import *\n# from functools import *\nfrom heapq import *\nfrom bisect import *\nfrom io import BytesIO, IOBase\ndef vsInput():\n sys.stdin = open('input.txt', 'r')\n sys.stdout = open('output.txt', 'w')\nBUFSIZE = 8192\nclass FastIO(IOBase):\n newlines = 0\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\nALPHA='abcdefghijklmnopqrstuvwxyz'\nM = 998244353\nEPS = 1e-6\ndef Ceil(a,b): return a//b+int(a%b>0)\ndef value():return tuple(map(int,input().split()))\ndef array():return [int(i) for i in input().split()]\ndef Int():return int(input())\ndef Str():return input()\ndef arrayS():return [i for i in input().split()]\n\n\n#-------------------------code---------------------------#\n# vsInput()\n\nfor _ in range(1):\n\n n = Int()\n a = array()\n b = array()\n \n ans = []\n C = Counter(a)\n j = 0\n \n for i in b:\n # print(i)\n here = 0\n if(C[i]): \n while(j < n and a[j] != i):\n C[a[j]] -= 1\n here += 1\n j += 1\n C[a[j]] -= 1\n here += 1\n j += 1\n \n ans.append(here)\n \n print(*ans)\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n\n\n \n \n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n\n\n\n```","inputs":"3\n1 2 3\n2 1 3\n","output":"2 0 1 ","actual_output":"2 0 1\n","execution_success":true,"sample_index":12744},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1095_B. Array Stabilization","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given an array a consisting of n integer numbers.\n\nLet instability of the array be the following value: max_{i = 1}^{n} a_i - min_{i = 1}^{n} a_i.\n\nYou have to remove exactly one element from this array to minimize instability of the resulting (n-1)-elements array. Your task is to calculate the minimum possible instability.\n\nInput\n\nThe first line of the input contains one integer n (2 \u2264 n \u2264 10^5) \u2014 the number of elements in the array a.\n\nThe second line of the input contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 10^5) \u2014 elements of the array a.\n\nOutput\n\nPrint one integer \u2014 the minimum possible instability of the array if you have to remove exactly one element from the array a.\n\nExamples\n\nInput\n\n\n4\n1 3 3 7\n\n\nOutput\n\n\n2\n\n\nInput\n\n\n2\n1 100000\n\n\nOutput\n\n\n0\n\nNote\n\nIn the first example you can remove 7 then instability of the remaining array will be 3 - 1 = 2.\n\nIn the second example you can remove either 1 or 100000 then instability of the remaining array will be 100000 - 100000 = 0 and 1 - 1 = 0 correspondingly.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ninput()\n\nsequence = [int(i) for i in input().split(' ')]\nsequence.sort()\na, b = sequence[-2] - sequence[0], sequence[-1] - sequence[1]\nprint(a) if a < b else print(b)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1 3 3 7\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 100000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '30\\n28 69 21 75 45 3 30 78 95 30 49 53 29 50 44 90 15 47 84 88 15 80 29 83 12 43 36 71 75 23\\n', 'output': '83\\n'}, {'type': 'stdin_stdout', 'input': '6\\n67 100 5 97 83 85\\n', 'output': '33\\n'}, {'type': 'stdin_stdout', 'input': '60\\n36 91 2 38 37 49 48 11 59 67 53 56 35 60 87 59 60 16 73 34 15 4 57 40 38 44 4 80 63 26 94 99 68 47 88 4 96 36 15 54 54 19 9 88 78 47 99 90 63 23 23 77 79 31 68 68 75 71 100 37\\n', 'output': '96\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '23\\n48 76 49 46 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7\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12745},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1114_C. Trailing Loves (or L'oeufs?)","prompt":"Solve the following coding problem using the programming language python:\n\nThe number \"zero\" is called \"love\" (or \"l'oeuf\" to be precise, literally means \"egg\" in French), for example when denoting the zero score in a game of tennis. \n\nAki is fond of numbers, especially those with trailing zeros. For example, the number 9200 has two trailing zeros. Aki thinks the more trailing zero digits a number has, the prettier it is.\n\nHowever, Aki believes, that the number of trailing zeros of a number is not static, but depends on the base (radix) it is represented in. Thus, he considers a few scenarios with some numbers and bases. And now, since the numbers he used become quite bizarre, he asks you to help him to calculate the beauty of these numbers.\n\nGiven two integers n and b (in decimal notation), your task is to calculate the number of trailing zero digits in the b-ary (in the base/radix of b) representation of n ! ([factorial](https://en.wikipedia.org/wiki/Factorial) of n). \n\nInput\n\nThe only line of the input contains two integers n and b (1 \u2264 n \u2264 10^{18}, 2 \u2264 b \u2264 10^{12}).\n\nOutput\n\nPrint an only integer \u2014 the number of trailing zero digits in the b-ary representation of n!\n\nExamples\n\nInput\n\n6 9\n\n\nOutput\n\n1\n\n\nInput\n\n38 11\n\n\nOutput\n\n3\n\n\nInput\n\n5 2\n\n\nOutput\n\n3\n\n\nInput\n\n5 10\n\n\nOutput\n\n1\n\nNote\n\nIn the first example, 6!_{(10)} = 720_{(10)} = 880_{(9)}.\n\nIn the third and fourth example, 5!_{(10)} = 120_{(10)} = 1111000_{(2)}.\n\nThe representation of the number x in the b-ary base is d_1, d_2, \u2026, d_k if x = d_1 b^{k - 1} + d_2 b^{k - 2} + \u2026 + d_k b^0, where d_i are integers and 0 \u2264 d_i \u2264 b - 1. For example, the number 720 from the first example is represented as 880_{(9)} since 720 = 8 \u22c5 9^2 + 8 \u22c5 9 + 0 \u22c5 1.\n\nYou can read more about bases [here](https://en.wikipedia.org/wiki/Radix).\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\nfrom collections import Counter\ndef checkprime(x):\n if x==1:\n return False\n i=2\n while i*i<=x:\n if x%i==0:\n return False\n i+=1\n return True\ndef pfactors(n):\n lt=[]\n while n % 2 == 0:\n lt.append(2)\n n = (n // 2)\n for i in range(3,int(math.sqrt(n))+1,2): \n while n % i== 0: \n lt.append(i)\n n = (n//i)\n if n > 2: \n lt.append(n)\n return lt\ndef sum(no,bs):\n d=(no//bs)\n #print (d,no%bs)\n s=0\n while d!=0:\n s+=d\n d=(d//bs)\n #print (d,no%bs)\n return s\n\ns=input(\"\")\nl=list(map(int,s.split()))\nn,b=l[0],l[1]\nif checkprime(b)==True:\n print (sum(n,b))\nelse:\n new1=pfactors(b)\n nd=Counter(new1)\n dd={}\n for i in nd.keys():\n dd[i]=sum(n,i)\n newbb=min(j//nd[i] for i,j in dd.items())\n print(newbb)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 9\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 10\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '38 11\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '36 110075314176\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '36 322687697779\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '912222 250880942892\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '72 250880942892\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '72 999999998141\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '912222 193773\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '57 10080\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': 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2: \n lt.append(n)\n return lt\ndef sum(no,bs):\n d=(no//bs)\n #print (d,no%bs)\n s=0\n while d!=0:\n s+=d\n d=(d//bs)\n #print (d,no%bs)\n return s\n\ns=input(\"\")\nl=list(map(int,s.split()))\nn,b=l[0],l[1]\nif checkprime(b)==True:\n print (sum(n,b))\nelse:\n new1=pfactors(b)\n nd=Counter(new1)\n dd={}\n for i in nd.keys():\n dd[i]=sum(n,i)\n newbb=min(j//nd[i] for i,j in dd.items())\n print(newbb)\n\n```","inputs":"6 9\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12746},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1183_E. Subsequences (easy version)","prompt":"Solve the following coding problem using the programming language python:\n\nThe only difference between the easy and the hard versions is constraints.\n\nA subsequence is a string that can be derived from another string by deleting some or no symbols without changing the order of the remaining symbols. Characters to be deleted are not required to go successively, there can be any gaps between them. For example, for the string \"abaca\" the following strings are subsequences: \"abaca\", \"aba\", \"aaa\", \"a\" and \"\" (empty string). But the following strings are not subsequences: \"aabaca\", \"cb\" and \"bcaa\".\n\nYou are given a string s consisting of n lowercase Latin letters.\n\nIn one move you can take any subsequence t of the given string and add it to the set S. The set S can't contain duplicates. This move costs n - |t|, where |t| is the length of the added subsequence (i.e. the price equals to the number of the deleted characters).\n\nYour task is to find out the minimum possible total cost to obtain a set S of size k or report that it is impossible to do so.\n\nInput\n\nThe first line of the input contains two integers n and k (1 \u2264 n, k \u2264 100) \u2014 the length of the string and the size of the set, correspondingly.\n\nThe second line of the input contains a string s consisting of n lowercase Latin letters.\n\nOutput\n\nPrint one integer \u2014 if it is impossible to obtain the set S of size k, print -1. Otherwise, print the minimum possible total cost to do it.\n\nExamples\n\nInput\n\n\n4 5\nasdf\n\n\nOutput\n\n\n4\n\n\nInput\n\n\n5 6\naaaaa\n\n\nOutput\n\n\n15\n\n\nInput\n\n\n5 7\naaaaa\n\n\nOutput\n\n\n-1\n\n\nInput\n\n\n10 100\najihiushda\n\n\nOutput\n\n\n233\n\nNote\n\nIn the first example we can generate S = { \"asdf\", \"asd\", \"adf\", \"asf\", \"sdf\" }. The cost of the first element in S is 0 and the cost of the others is 1. So the total cost of S is 4.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nR = lambda: map(int, input().split())\nn,k = R()\ns = input()\np = [s]\nans = 0\nd= set()\nwhile p:\n q = p.pop(0)\n if q not in d:\n k -= 1\n ans += (n-len(q))\n if k == 0:\n print(ans)\n quit()\n d.add(q)\n for i in range(len(q)):\n t = q[:i]+q[i+1:]\n if t not in p:p.append(t)\nprint(-1)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 5\\nasdf\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\naaaaa\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '5 7\\naaaaa\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10 100\\najihiushda\\n', 'output': '233\\n'}, {'type': 'stdin_stdout', 'input': '1 50\\ns\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '100 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'input': '4 9\\nasdg\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '3 7\\naaaaa\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 40\\nt\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '28 111\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '100 1\\nzqdvwjzmgfmgngaxzgvuuukxyfzecafuflxpkvemenkorwhmnsxuoxsatlymxjugwjmusfxcksnwhxrwruyqbouyflxhwqhflczz\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7 111\\nasafgsa\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '25 33\\ncffokplppsawfiwviiijnyxdm\\n', 'output': '43\\n'}, {'type': 'stdin_stdout', 'input': '6 69\\nfdjfid\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '25 35\\nqbntoutmcylbrtfzauvxlqvyn\\n', 'output': '43\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80061","program":"```python\nR = lambda: map(int, input().split())\nn,k = R()\ns = input()\np = [s]\nans = 0\nd= set()\nwhile p:\n q = p.pop(0)\n if q not in d:\n k -= 1\n ans += (n-len(q))\n if k == 0:\n print(ans)\n quit()\n d.add(q)\n for i in range(len(q)):\n t = q[:i]+q[i+1:]\n if t not in p:p.append(t)\nprint(-1)\n```","inputs":"4 5\nasdf\n","output":"4\n","actual_output":"4\n","execution_success":true,"sample_index":12747},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1200_F. Graph Traveler","prompt":"Solve the following coding problem using the programming language python:\n\nGildong is experimenting with an interesting machine Graph Traveler. In Graph Traveler, there is a directed graph consisting of n vertices numbered from 1 to n. The i-th vertex has m_i outgoing edges that are labeled as e_i[0], e_i[1], \u2026, e_i[m_i-1], each representing the destination vertex of the edge. The graph can have multiple edges and self-loops. The i-th vertex also has an integer k_i written on itself.\n\nA travel on this graph works as follows. \n\n 1. Gildong chooses a vertex to start from, and an integer to start with. Set the variable c to this integer. \n 2. After arriving at the vertex i, or when Gildong begins the travel at some vertex i, add k_i to c. \n 3. The next vertex is e_i[x] where x is an integer 0 \u2264 x \u2264 m_i-1 satisfying x \u2261 c \\pmod {m_i}. Go to the next vertex and go back to step 2. \n\n\n\nIt's obvious that a travel never ends, since the 2nd and the 3rd step will be repeated endlessly.\n\nFor example, assume that Gildong starts at vertex 1 with c = 5, and m_1 = 2, e_1[0] = 1, e_1[1] = 2, k_1 = -3. Right after he starts at vertex 1, c becomes 2. Since the only integer x (0 \u2264 x \u2264 1) where x \u2261 c \\pmod {m_i} is 0, Gildong goes to vertex e_1[0] = 1. After arriving at vertex 1 again, c becomes -1. The only integer x satisfying the conditions is 1, so he goes to vertex e_1[1] = 2, and so on.\n\nSince Gildong is quite inquisitive, he's going to ask you q queries. He wants to know how many distinct vertices will be visited infinitely many times, if he starts the travel from a certain vertex with a certain value of c. Note that you should not count the vertices that will be visited only finite times.\n\nInput\n\nThe first line of the input contains an integer n (1 \u2264 n \u2264 1000), the number of vertices in the graph.\n\nThe second line contains n integers. The i-th integer is k_i (-10^9 \u2264 k_i \u2264 10^9), the integer written on the i-th vertex.\n\nNext 2 \u22c5 n lines describe the edges of each vertex. The (2 \u22c5 i + 1)-st line contains an integer m_i (1 \u2264 m_i \u2264 10), the number of outgoing edges of the i-th vertex. The (2 \u22c5 i + 2)-nd line contains m_i integers e_i[0], e_i[1], \u2026, e_i[m_i-1], each having an integer value between 1 and n, inclusive.\n\nNext line contains an integer q (1 \u2264 q \u2264 10^5), the number of queries Gildong wants to ask.\n\nNext q lines contains two integers x and y (1 \u2264 x \u2264 n, -10^9 \u2264 y \u2264 10^9) each, which mean that the start vertex is x and the starting value of c is y.\n\nOutput\n\nFor each query, print the number of distinct vertices that will be visited infinitely many times, if Gildong starts at vertex x with starting integer y.\n\nExamples\n\nInput\n\n\n4\n0 0 0 0\n2\n2 3\n1\n2\n3\n2 4 1\n4\n3 1 2 1\n6\n1 0\n2 0\n3 -1\n4 -2\n1 1\n1 5\n\n\nOutput\n\n\n1\n1\n2\n1\n3\n2\n\n\nInput\n\n\n4\n4 -5 -3 -1\n2\n2 3\n1\n2\n3\n2 4 1\n4\n3 1 2 1\n6\n1 0\n2 0\n3 -1\n4 -2\n1 1\n1 5\n\n\nOutput\n\n\n1\n1\n1\n3\n1\n1\n\nNote\n\nThe first example can be shown like the following image:\n\n\n\nThree integers are marked on i-th vertex: i, k_i, and m_i respectively. The outgoing edges are labeled with an integer representing the edge number of i-th vertex.\n\nThe travel for each query works as follows. It is described as a sequence of phrases, each in the format \"vertex (c after k_i added)\".\n\n * 1(0) \u2192 2(0) \u2192 2(0) \u2192 \u2026 \n * 2(0) \u2192 2(0) \u2192 \u2026 \n * 3(-1) \u2192 1(-1) \u2192 3(-1) \u2192 \u2026 \n * 4(-2) \u2192 2(-2) \u2192 2(-2) \u2192 \u2026 \n * 1(1) \u2192 3(1) \u2192 4(1) \u2192 1(1) \u2192 \u2026 \n * 1(5) \u2192 3(5) \u2192 1(5) \u2192 \u2026 \n\n\n\nThe second example is same as the first example, except that the vertices have non-zero values. Therefore the answers to the queries also differ from the first example.\n\n\n\nThe queries for the second example works as follows:\n\n * 1(4) \u2192 2(-1) \u2192 2(-6) \u2192 \u2026 \n * 2(-5) \u2192 2(-10) \u2192 \u2026 \n * 3(-4) \u2192 1(0) \u2192 2(-5) \u2192 2(-10) \u2192 \u2026 \n * 4(-3) \u2192 1(1) \u2192 3(-2) \u2192 4(-3) \u2192 \u2026 \n * 1(5) \u2192 3(2) \u2192 1(6) \u2192 2(1) \u2192 2(-4) \u2192 \u2026 \n * 1(9) \u2192 3(6) \u2192 2(1) \u2192 2(-4) \u2192 \u2026 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport io, sys\ninput = lambda f=io.StringIO(sys.stdin.buffer.read().decode()).readline: f().rstrip()\nLCM = 2520\n\nn = int(input())\nk = list(map(int, input().split()))\nm, e = [0] * n, [None] * n\nfor i in range(n):\n m[i] = int(input())\n e[i] = list(map(int, input().split()))\n\nnxt = []\nfor i in range(n):\n for j in range(LCM):\n x = (j + k[i]) % LCM\n y = e[i][x % m[i]] - 1\n nxt.append(y * LCM + x)\n\nloop = [None] * (n * LCM)\nfor i in range(n * LCM):\n if loop[i]: continue\n loop[i] = set()\n cur, rec = nxt[i], [i]\n while True:\n if loop[cur] is not None:\n break\n loop[cur] = loop[i]\n rec.append(cur)\n cur = nxt[cur]\n if loop[cur]:\n for u in rec:\n loop[u] = loop[cur]\n else:\n while rec[-1] != cur:\n loop[i].add(rec.pop() // LCM)\n loop[i].add(cur // LCM)\n\nout = []\nfor _ in range(int(input())):\n x, y = map(int, input().split())\n out.append(len(loop[(x - 1) * LCM + y % LCM]))\nprint(*out, sep='\\n')\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n0 0 0 0\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n3 1 2 1\\n6\\n1 0\\n2 0\\n3 -1\\n4 -2\\n1 1\\n1 5\\n', 'output': '1\\n1\\n2\\n1\\n3\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 -5 -3 -1\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n3 1 2 1\\n6\\n1 0\\n2 0\\n3 -1\\n4 -2\\n1 1\\n1 5\\n', 'output': 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1\\n4\\n3 1 2 2\\n6\\n1 0\\n2 0\\n3 0\\n4 -2\\n1 2\\n3 3\\n', 'output': '1\\n1\\n1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-3\\n1\\n1\\n1\\n1 -1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 -9 -1 -1\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n3 1 2 1\\n6\\n1 -1\\n3 0\\n3 -1\\n4 -4\\n2 1\\n1 5\\n', 'output': '1\\n1\\n1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 0 0\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n3 1 2 2\\n6\\n1 0\\n2 2\\n3 -1\\n4 -2\\n1 2\\n3 3\\n', 'output': '1\\n1\\n2\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 0 0\\n2\\n2 3\\n1\\n1\\n3\\n2 4 1\\n4\\n3 1 2 2\\n6\\n1 0\\n2 1\\n3 -1\\n4 -2\\n2 2\\n3 3\\n', 'output': '2\\n3\\n2\\n2\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 0 0\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n2 1 2 2\\n6\\n1 0\\n2 0\\n3 -1\\n4 -2\\n1 2\\n2 3\\n', 'output': '1\\n1\\n2\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 -9 -1 -1\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n3 1 2 1\\n6\\n1 -1\\n3 -1\\n3 -1\\n4 -4\\n2 1\\n1 5\\n', 'output': '1\\n1\\n1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 -5 -3 -2\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n3 1 2 1\\n6\\n1 0\\n2 0\\n3 -1\\n4 -2\\n1 1\\n1 5\\n', 'output': '1\\n1\\n1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 0 0\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n3 1 2 2\\n6\\n1 0\\n2 0\\n3 -1\\n4 -2\\n1 2\\n1 5\\n', 'output': '1\\n1\\n2\\n1\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 -1 0 0\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n3 1 2 2\\n6\\n1 0\\n2 0\\n3 -1\\n4 -2\\n1 1\\n2 5\\n', 'output': '1\\n1\\n2\\n1\\n3\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 0 0\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n3 1 2 2\\n6\\n1 0\\n2 0\\n3 -2\\n4 -2\\n1 2\\n2 5\\n', 'output': '1\\n1\\n1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 0 0 0\\n2\\n2 3\\n1\\n2\\n3\\n2 3 1\\n4\\n3 1 2 2\\n6\\n1 0\\n2 0\\n3 -1\\n4 -2\\n1 2\\n2 3\\n', 'output': '1\\n1\\n2\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 -9 -1 -1\\n2\\n2 3\\n1\\n2\\n3\\n4 4 1\\n4\\n3 1 2 1\\n6\\n1 0\\n3 0\\n3 -1\\n4 -2\\n2 1\\n1 5\\n', 'output': '1\\n1\\n1\\n1\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 0 0 0\\n2\\n2 3\\n1\\n2\\n3\\n2 4 1\\n4\\n3 1 2 2\\n6\\n1 0\\n2 0\\n3 -1\\n4 -2\\n1 2\\n3 3\\n', 'output': '1\\n1\\n1\\n1\\n1\\n1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 12, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_80065","program":"```python\nimport io, sys\ninput = lambda f=io.StringIO(sys.stdin.buffer.read().decode()).readline: f().rstrip()\nLCM = 2520\n\nn = int(input())\nk = list(map(int, input().split()))\nm, e = [0] * n, [None] * n\nfor i in range(n):\n m[i] = int(input())\n e[i] = list(map(int, input().split()))\n\nnxt = []\nfor i in range(n):\n for j in range(LCM):\n x = (j + k[i]) % LCM\n y = e[i][x % m[i]] - 1\n nxt.append(y * LCM + x)\n\nloop = [None] * (n * LCM)\nfor i in range(n * LCM):\n if loop[i]: continue\n loop[i] = set()\n cur, rec = nxt[i], [i]\n while True:\n if loop[cur] is not None:\n break\n loop[cur] = loop[i]\n rec.append(cur)\n cur = nxt[cur]\n if loop[cur]:\n for u in rec:\n loop[u] = loop[cur]\n else:\n while rec[-1] != cur:\n loop[i].add(rec.pop() // LCM)\n loop[i].add(cur // LCM)\n\nout = []\nfor _ in range(int(input())):\n x, y = map(int, input().split())\n out.append(len(loop[(x - 1) * LCM + y % LCM]))\nprint(*out, sep='\\n')\n```","inputs":"4\n0 0 0 0\n2\n2 3\n1\n2\n3\n2 4 1\n4\n3 1 2 1\n6\n1 0\n2 0\n3 -1\n4 -2\n1 1\n1 5\n","output":"1\n1\n2\n1\n3\n2\n","actual_output":"1\n1\n2\n1\n3\n2\n","execution_success":true,"sample_index":12748},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1284_A. New Year and Naming","prompt":"Solve the following coding problem using the programming language python:\n\nHappy new year! The year 2020 is also known as Year Gyeongja (\uacbd\uc790\ub144, gyeongja-nyeon) in Korea. Where did the name come from? Let's briefly look at the Gapja system, which is traditionally used in Korea to name the years.\n\nThere are two sequences of n strings s_1, s_2, s_3, \u2026, s_{n} and m strings t_1, t_2, t_3, \u2026, t_{m}. These strings contain only lowercase letters. There might be duplicates among these strings.\n\nLet's call a concatenation of strings x and y as the string that is obtained by writing down strings x and y one right after another without changing the order. For example, the concatenation of the strings \"code\" and \"forces\" is the string \"codeforces\".\n\nThe year 1 has a name which is the concatenation of the two strings s_1 and t_1. When the year increases by one, we concatenate the next two strings in order from each of the respective sequences. If the string that is currently being used is at the end of its sequence, we go back to the first string in that sequence.\n\nFor example, if n = 3, m = 4, s = {\"a\", \"b\", \"c\"}, t = {\"d\", \"e\", \"f\", \"g\"}, the following table denotes the resulting year names. Note that the names of the years may repeat.\n\n\n\nYou are given two sequences of strings of size n and m and also q queries. For each query, you will be given the current year. Could you find the name corresponding to the given year, according to the Gapja system?\n\nInput\n\nThe first line contains two integers n, m (1 \u2264 n, m \u2264 20).\n\nThe next line contains n strings s_1, s_2, \u2026, s_{n}. Each string contains only lowercase letters, and they are separated by spaces. The length of each string is at least 1 and at most 10.\n\nThe next line contains m strings t_1, t_2, \u2026, t_{m}. Each string contains only lowercase letters, and they are separated by spaces. The length of each string is at least 1 and at most 10.\n\nAmong the given n + m strings may be duplicates (that is, they are not necessarily all different).\n\nThe next line contains a single integer q (1 \u2264 q \u2264 2 020).\n\nIn the next q lines, an integer y (1 \u2264 y \u2264 10^9) is given, denoting the year we want to know the name for.\n\nOutput\n\nPrint q lines. For each line, print the name of the year as per the rule described above.\n\nExample\n\nInput\n\n\n10 12\nsin im gye gap eul byeong jeong mu gi gyeong\nyu sul hae ja chuk in myo jin sa o mi sin\n14\n1\n2\n3\n4\n10\n11\n12\n13\n73\n2016\n2017\n2018\n2019\n2020\n\n\nOutput\n\n\nsinyu\nimsul\ngyehae\ngapja\ngyeongo\nsinmi\nimsin\ngyeyu\ngyeyu\nbyeongsin\njeongyu\nmusul\ngihae\ngyeongja\n\nNote\n\nThe first example denotes the actual names used in the Gapja system. These strings usually are either a number or the name of some animal.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom sys import stdin, stdout\n\n\ndef main():\n (n1, n2) = tuple([int(x) for x in stdin.readline().split()])\n\n arr1 = [x for x in stdin.readline().split()]\n arr2 = [x for x in stdin.readline().split()]\n\n q = int(stdin.readline())\n res = []\n\n for i in range(0, q):\n year = int(stdin.readline())\n part_1 = arr1[(year - 1) % n1]\n part_2 = arr2[(year - 1)% n2]\n res.append(part_1 + part_2)\n\n stdout.write(\"\\n\".join(str(x) for x in res))\n\n\nif __name__ == '__main__':\n main()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gi gyeong\\nyu sul hae ja chuk in myo jin sa o mi sin\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n2017\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nimsul\\ngyehae\\ngapja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\njeongyu\\nmusul\\ngihae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '2 6\\na a\\nb b c d e f\\n1\\n3\\n', 'output': 'ac\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\na b c d e\\nhola mundo\\n1\\n5\\n', 'output': 'ehola\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gi gyeong\\nyu sul hae ja chuk in myo jin sa o mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\na b c b\\na b c b\\n1\\n3\\n', 'output': 'cc\\n'}, {'type': 'stdin_stdout', 'input': '12 10\\nyu sul hae ja chuk in myo jin sa o mi sin\\nsin im gye gap eul byeong jeong mu gi gyeong\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n2017\\n2018\\n2019\\n2020\\n', 'output': 'yusin\\nsulim\\nhaegye\\njagap\\nogyeong\\nmisin\\nsinim\\nyugye\\nyugye\\nsinbyeong\\nyujeong\\nsulmu\\nhaegi\\njagyeong\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\na\\na\\n1\\n1\\n', 'output': 'aa\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\na b c d d\\nhola mundo\\n1\\n5\\n', 'output': 'dhola\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gi gyeong\\nyu sum hae ja chuk in myo jin sa o mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '12 10\\nyu sul hae ja chuk in myo jin sa o mi sin\\nsin im gye gap eul byeong jeong mu gi gyeong\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n21\\n73\\n2016\\n2017\\n2018\\n2019\\n2020\\n', 'output': 'yusin\\nsulim\\nhaegye\\njagap\\nogyeong\\nmisin\\nsinim\\nsasin\\nyugye\\nsinbyeong\\nyujeong\\nsulmu\\nhaegi\\njagyeong\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gi gyeong\\nyu sul hae ja chuk in myo jin sa o mi sin\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nimsul\\ngyehae\\ngapja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngihae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gi gyeong\\nyu sul hae ja chuk in myo jin sa o mi sin\\n14\\n1\\n1\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngihae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gj gyeong\\nyu sul hae ja chuk in myo jin sa o mi sin\\n14\\n1\\n1\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngjhae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gj gyeong\\nyu sul hae ja chuk in myo jin as o mi sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapja\\njeongchuk\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngjhae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gj gyeong\\nyu sul hae jb chuk in myo jin as o mi sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapjb\\njeongchuk\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gj gyeong\\nyu sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapjb\\njeongchuk\\nsinli\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul bynoeg jeong mu gj gyeong\\nyu sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapjb\\njeongchuk\\nsinli\\nimsin\\ngyeyu\\ngyeyu\\nbynoegsin\\nimjin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul bynoeg jeong mu gj gyeong\\nyu sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapjb\\njeongchuk\\nsinli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nmijin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu hi gyeong\\n{u smu hae ja chuk in oym jin ta p mi nis\\n1\\n2016\\n', 'output': 'byeongnis\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul bynoeg jeong mu gj gyeong\\nyu sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\nmisul\\njeongchuk\\nsinli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nmijin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul bynoeg jeong mu jg gyeong\\nyu sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\nmisul\\njeongchuk\\nsinli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nmijin\\nmusul\\njghae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeong mu jg gyeong\\nyu sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyehae\\nmisul\\njeongchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nmijin\\nmusul\\njghae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeong mu jg gyeong\\nyu sul eah jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeongchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nmijin\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeong mu jg gyeong\\nyu sul eah jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeongchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeonh mu jg gyeong\\nyu sul eah jb chuk in myo jjn `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeonhchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeonh mu jg gyeong\\nyu sul eah jb chuk in myo jjn `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n19\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeonhchuk\\njgmyo\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg ieonh mu jg gyeong\\nyu sul eah jb chuk in myo jjn `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n19\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\nieonhchuk\\njgmyo\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg ieonh mu jg gyeong\\nyu sul eah jb chuk in myo njj `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n19\\n12\\n13\\n73\\n2016\\n61\\n2223\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\nieonhchuk\\njgmyo\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\ngyeeah\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '2 6\\n` a\\nb b c d e f\\n1\\n3\\n', 'output': '`c\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\na b c d e\\nhola mundo\\n1\\n1\\n', 'output': 'ahola\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\na b c b\\na a c b\\n1\\n3\\n', 'output': 'cc\\n'}, {'type': 'stdin_stdout', 'input': '12 10\\nyu sul hae ja cuhk in myo jin sa o mi sin\\nsin im gye gap eul byeong jeong mu gi gyeong\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n2017\\n2018\\n2019\\n2020\\n', 'output': 'yusin\\nsulim\\nhaegye\\njagap\\nogyeong\\nmisin\\nsinim\\nyugye\\nyugye\\nsinbyeong\\nyujeong\\nsulmu\\nhaegi\\njagyeong\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye pag eul byeong jeong mu gi gyeong\\nyu sul hae ja chuk in myo jin sa o mi sin\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n2017\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nimsul\\ngyehae\\npagja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\njeongyu\\nmusul\\ngihae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\na b c d d\\nhola mundo\\n1\\n7\\n', 'output': 'bhola\\n'}, {'type': 'stdin_stdout', 'input': '12 10\\nyu sul hae ja chuk in myo jin sa o mi sin\\nsin im gye gap eul byeong jeong mu gi gyeong\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n21\\n73\\n3415\\n2017\\n2018\\n2019\\n2020\\n', 'output': 'yusin\\nsulim\\nhaegye\\njagap\\nogyeong\\nmisin\\nsinim\\nsasin\\nyugye\\nmyoeul\\nyujeong\\nsulmu\\nhaegi\\njagyeong\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu gi gyeong\\nyu sum hae ja chuk in myo jin ta o mi sin\\n1\\n1911\\n', 'output': 'nishae\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gj gyeong\\nyu sul hae ja chuk in myo jin sa o mi sin\\n14\\n1\\n1\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n32\\n634\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\ngapo\\ngjhae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gj gyeong\\nyu sul hae jb chuk in myo jin as o mi sin\\n14\\n1\\n1\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapjb\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gj gyeong\\nyu sul hae ja chuk in myo jin as o mi sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n1640\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapja\\njeongchuk\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\ngyeongjin\\nimjin\\nmusul\\ngjhae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul byeong jeong mu gj gyeong\\nyu sul hae jb chuk in myo jin as o mi sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapjb\\njeongchuk\\nsinmi\\nmisin\\ngyeyu\\ngyeyu\\nbyeongsin\\nmijin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul bynoeg jeong mu gj gyeong\\nyu sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n4\\n17\\n17\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapjb\\njeongchuk\\njeongchuk\\nimsin\\ngyeyu\\ngyeyu\\nbynoegsin\\nimjin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul bydong jeong mu hi gyeong\\n{u smu hae ja chuk in oym jin ta p mi sin\\n1\\n2016\\n', 'output': 'bydongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul bynoeg jeong mu gj gyeong\\nuy sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinuy\\nsinuy\\ngyehae\\ngapjb\\njeongchuk\\nsinli\\nmisin\\ngyeuy\\ngyeuy\\nbynoegsin\\nmijin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul bynoeg jeong mu gj gyeong\\nyu sul hae jb chvk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\nmisul\\njeongchvk\\nsinli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nmijin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul bynoeg jeong mv jg gyeong\\nyu sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\nmisul\\njeongchuk\\nsinli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nmijin\\nmvsul\\njghae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeong mu jg gyeong\\nyu sul eah jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n1618\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeongchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nmijin\\nmuo\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeong mu jg gyeong\\nyu sul eah jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n3\\n17\\n11\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\ngyeeah\\njeongchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoef jeong mu jg gyeong\\nyu sul eah jb chuk in myo jjn as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeongchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoefsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeong mu jg gyeong\\nyu sul eah jb chuk in myo jjn `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n1698\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeongchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\nmuin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeonh mu jg gyeong\\nyu sul eah jb chuk in myo jjn `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n131\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeonhchuk\\nshnli\\nmisin\\ngyeyu\\nshnli\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeonh mu jg gyeong\\nyu sul eah jb chuk in oym jjn `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n19\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeonhchuk\\njgoym\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg ieonh mu jg gyeong\\nyu sul eah jb chuk in myo njj `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n15\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\nieonhchuk\\neuleah\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg ieonh mu jg gyeong\\nyv sul eah jb chuk in myo njj `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n19\\n12\\n13\\n73\\n2016\\n61\\n2223\\n2019\\n2020\\n', 'output': 'shnyv\\nshnyv\\ngyeeah\\nmisul\\nieonhchuk\\njgmyo\\nmisin\\ngyeyv\\ngyeyv\\nbynoegsin\\nshnyv\\ngyeeah\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye pag eul byeong jeong mu gi gyeong\\nyu sul hae aj chuk in myo jin sa o mi sin\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n2017\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nimsul\\ngyehae\\npagaj\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\njeongyu\\nmusul\\ngihae\\ngyeongaj\\n'}, {'type': 'stdin_stdout', 'input': '12 10\\nyu sul hae ja chuk in myo jin sa o ni sin\\nsin im gye gap eul byeong jeong mu gi gyeong\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n21\\n73\\n3415\\n2017\\n2018\\n2019\\n2020\\n', 'output': 'yusin\\nsulim\\nhaegye\\njagap\\nogyeong\\nnisin\\nsinim\\nsasin\\nyugye\\nmyoeul\\nyujeong\\nsulmu\\nhaegi\\njagyeong\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gi gyeong\\nyu sul hae ja chuk ni myo jin sa o mi sin\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n13\\n134\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nimsul\\ngyehae\\ngapja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngapsul\\nbyeongsin\\nimjin\\nmusul\\ngihae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gi gyeong\\nyu sul hae ja uhck in myo jin sa o mi sin\\n14\\n1\\n1\\n3\\n4\\n10\\n18\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapja\\ngyeongo\\nmuin\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngihae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul byeong jeoog mu gj gyeong\\nyu sul hae jb chuk in myo jin as o mi sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapjb\\njeoogchuk\\nsinmi\\nmisin\\ngyeyu\\ngyeyu\\nbyeongsin\\nmijin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul bynoeg jeong mu gj gyeong\\nyu sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n4\\n17\\n17\\n12\\n13\\n73\\n1028\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapjb\\njeongchuk\\njeongchuk\\nimsin\\ngyeyu\\ngyeyu\\nmujin\\nimjin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis mi gye gap eul byeong jeong mu hi gynoeg\\n{u smu hae ja chuk in oym jin ta p mi mis\\n1\\n2016\\n', 'output': 'byeongmis\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul bynoeg jeong mv jg gyeong\\nyu sul hae jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\nimsul\\njeongchuk\\nsinli\\nimsin\\ngyeyu\\ngyeyu\\nbynoegsin\\nimjin\\nmvsul\\njghae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeomg mu jg gyeong\\nyu sul eah jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n1618\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeomgchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nmijin\\nmuo\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeong mu jg gyeong\\nuy sul eah jb chuk in myo jin as o li sin\\n14\\n1\\n1\\n3\\n3\\n17\\n11\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnuy\\nshnuy\\ngyeeah\\ngyeeah\\njeongchuk\\nshnli\\nmisin\\ngyeuy\\ngyeuy\\nbynoegsin\\nshnuy\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu gi gyeong\\nyu sum hae ja chuk in myo jin sa o mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu gi gyeong\\nyu sum hae ja chuk in myo jin ta o mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu gi gyeong\\nyu sum hae ja chuk in myo jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gj gyeong\\nyu sul hae ja chuk in myo jin as o mi sin\\n14\\n1\\n1\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngjhae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu hi gyeong\\nyu sum hae ja chuk in myo jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu hi gyeong\\nyu smu hae ja chuk in myo jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu hi gyeong\\nzu smu hae ja chuk in myo jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu hi gyeong\\nzu smu hae ja chuk in oym jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu hi gyeong\\n{u smu hae ja chuk in oym jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu hi gynoeg\\n{u smu hae ja chuk in oym jin ta p mi nis\\n1\\n2016\\n', 'output': 'byeongnis\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeong mu jg gyeong\\nyu sul eah jb chuk in myo jjn as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeongchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg jeong mu jg gyeong\\nyu sul eah jb chuk in myo jjn `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\njeongchuk\\nshnli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nshn mi gye gap eul bynoeg ieonh mu jg gyeong\\nyu sul eah jb chuk in myo njj `s o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n19\\n12\\n13\\n73\\n2016\\n61\\n2018\\n2019\\n2020\\n', 'output': 'shnyu\\nshnyu\\ngyeeah\\nmisul\\nieonhchuk\\njgmyo\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nshnyu\\nmusul\\njgeah\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gi gyeong\\nyu sul hae ja chuk ni myo jin sa o mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu ig gyeong\\nyu sum hae ja chuk in myo jin sa o mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gi gyeong\\nyu sul hae ja chuk ni myo jin sa o mi sin\\n14\\n1\\n2\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nimsul\\ngyehae\\ngapja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngihae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu gi gyeong\\nyu sum hae ka chuk in myo jin sa o mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gi gyeong\\nyu sul hae ja uhck in myo jin sa o mi sin\\n14\\n1\\n1\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\nmusul\\ngihae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu gi gyeong\\nyu sum hae ja chuk ni myo jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu hi gyeong\\nyu sum hae ja chuk ni myo jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu gi gyeong\\nzu smu hae ja chuk in oym jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu hi gyeong\\n{u smu hae ja chuk in oym jin ta p ni nis\\n1\\n2016\\n', 'output': 'byeongnis\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis mi gye gap eul byeong jeong mu hi gynoeg\\n{u smu hae ja chuk in oym jin ta p mi nis\\n1\\n2016\\n', 'output': 'byeongnis\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\nb b c d e\\nhola mundo\\n1\\n1\\n', 'output': 'bhola\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul byeong jeong mu gi gyeong\\nyu sul hae ja chuk ni myo jin sa o mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\na c c b\\na a c b\\n1\\n3\\n', 'output': 'cc\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\na b c d d\\nhola mtndo\\n1\\n7\\n', 'output': 'bhola\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu ig gyeong\\nyu sum hae ja chuk jn myo jin sa o mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnhs im gye gap eul byeong jeong mu gi gyeong\\nyu sum hae ka chuk in myo jin sa o mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong gnoej mu gi gyeong\\nyu sum hae ja chuk in myo jin ta o mi sin\\n1\\n1911\\n', 'output': 'nishae\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong nu gj gyeong\\nyu sul hae ja chuk in myo jin sa o mi sin\\n14\\n1\\n1\\n3\\n4\\n10\\n11\\n12\\n13\\n73\\n2016\\n32\\n634\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapja\\ngyeongo\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\nbyeongsin\\nimjin\\ngapo\\ngjhae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu gi gyeong\\nuy sum hae ja chuk ni myo jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin im gye gap eul byeong jeong mu gj gyeong\\nyu sul hae ja chuk jn myo jin as o mi sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n1640\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\ngapja\\njeongchuk\\nsinmi\\nimsin\\ngyeyu\\ngyeyu\\ngyeongjin\\nimjin\\nmusul\\ngjhae\\ngyeongja\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu ig gyeong\\nzu smu hae ja chuk in oym jin ta p mi sin\\n1\\n2016\\n', 'output': 'byeongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap lue bydong jeong mu hi gyeong\\n{u smu hae ja chuk in oym jin ta p mi sin\\n1\\n2016\\n', 'output': 'bydongsin\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul bynoeg jeong mu gj gyeong\\nuy sul hae jb chuk io myo jin as o li sin\\n14\\n1\\n1\\n3\\n4\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinuy\\nsinuy\\ngyehae\\ngapjb\\njeongchuk\\nsinli\\nmisin\\ngyeuy\\ngyeuy\\nbynoegsin\\nmijin\\nmusul\\ngjhae\\ngyeongjb\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nnis im gye gap eul byeong jeong mu gi gyeong\\n{u smu hae ja chuk in oym jin ta p ni nis\\n1\\n2016\\n', 'output': 'byeongnis\\n'}, {'type': 'stdin_stdout', 'input': '10 12\\nsin mi gye gap eul bynoeg jeong mu gj gyeong\\nyu sul hae jb chvk jn myo jin as o li sin\\n14\\n1\\n1\\n3\\n2\\n17\\n11\\n12\\n13\\n73\\n2016\\n32\\n2018\\n2019\\n2020\\n', 'output': 'sinyu\\nsinyu\\ngyehae\\nmisul\\njeongchvk\\nsinli\\nmisin\\ngyeyu\\ngyeyu\\nbynoegsin\\nmijin\\nmusul\\ngjhae\\ngyeongjb\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 1024000000}","problem_id":"vfc_80081","program":"```python\nfrom sys import stdin, stdout\n\n\ndef main():\n (n1, n2) = tuple([int(x) for x in stdin.readline().split()])\n\n arr1 = [x for x in stdin.readline().split()]\n arr2 = [x for x in stdin.readline().split()]\n\n q = int(stdin.readline())\n res = []\n\n for i in range(0, q):\n year = int(stdin.readline())\n part_1 = arr1[(year - 1) % n1]\n part_2 = arr2[(year - 1)% n2]\n res.append(part_1 + part_2)\n\n stdout.write(\"\\n\".join(str(x) for x in res))\n\n\nif __name__ == '__main__':\n main()\n\n```","inputs":"10 12\nsin im gye gap eul byeong jeong mu gi gyeong\nyu sul hae ja chuk in myo jin sa o mi sin\n14\n1\n2\n3\n4\n10\n11\n12\n13\n73\n2016\n2017\n2018\n2019\n2020\n","output":"sinyu\nimsul\ngyehae\ngapja\ngyeongo\nsinmi\nimsin\ngyeyu\ngyeyu\nbyeongsin\njeongyu\nmusul\ngihae\ngyeongja\n","actual_output":"sinyu\nimsul\ngyehae\ngapja\ngyeongo\nsinmi\nimsin\ngyeyu\ngyeyu\nbyeongsin\njeongyu\nmusul\ngihae\ngyeongja","execution_success":true,"sample_index":12749},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1327_D. Infinite Path","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a colored permutation p_1, p_2, ..., p_n. The i-th element of the permutation has color c_i.\n\nLet's define an infinite path as infinite sequence i, p[i], p[p[i]], p[p[p[i]]] ... where all elements have same color (c[i] = c[p[i]] = c[p[p[i]]] = ...).\n\nWe can also define a multiplication of permutations a and b as permutation c = a \u00d7 b where c[i] = b[a[i]]. Moreover, we can define a power k of permutation p as p^k=\\underbrace{p \u00d7 p \u00d7 ... \u00d7 p}_{k times}.\n\nFind the minimum k > 0 such that p^k has at least one infinite path (i.e. there is a position i in p^k such that the sequence starting from i is an infinite path).\n\nIt can be proved that the answer always exists.\n\nInput\n\nThe first line contains single integer T (1 \u2264 T \u2264 10^4) \u2014 the number of test cases.\n\nNext 3T lines contain test cases \u2014 one per three lines. The first line contains single integer n (1 \u2264 n \u2264 2 \u22c5 10^5) \u2014 the size of the permutation.\n\nThe second line contains n integers p_1, p_2, ..., p_n (1 \u2264 p_i \u2264 n, p_i \u2260 p_j for i \u2260 j) \u2014 the permutation p.\n\nThe third line contains n integers c_1, c_2, ..., c_n (1 \u2264 c_i \u2264 n) \u2014 the colors of elements of the permutation.\n\nIt is guaranteed that the total sum of n doesn't exceed 2 \u22c5 10^5.\n\nOutput\n\nPrint T integers \u2014 one per test case. For each test case print minimum k > 0 such that p^k has at least one infinite path.\n\nExample\n\nInput\n\n\n3\n4\n1 3 4 2\n1 2 2 3\n5\n2 3 4 5 1\n1 2 3 4 5\n8\n7 4 5 6 1 8 3 2\n5 3 6 4 7 5 8 4\n\n\nOutput\n\n\n1\n5\n2\n\nNote\n\nIn the first test case, p^1 = p = [1, 3, 4, 2] and the sequence starting from 1: 1, p[1] = 1, ... is an infinite path.\n\nIn the second test case, p^5 = [1, 2, 3, 4, 5] and it obviously contains several infinite paths.\n\nIn the third test case, p^2 = [3, 6, 1, 8, 7, 2, 5, 4] and the sequence starting from 4: 4, p^2[4]=8, p^2[8]=4, ... is an infinite path since c_4 = c_8 = 4.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef monocolor_subcycle(start, divisor):\n for i in range(start, len(cycle), divisor):\n v = cycle[i]\n if c[v] != c[cycle[start]]:\n return False\n return True\n\n\ndef any_monocolor_subcycle(divisor):\n for start in range(divisor):\n if monocolor_subcycle(start, divisor):\n return True\n return False\n\n\ndef min_in_cycle():\n length = len(cycle)\n local_ans = length\n divisor = 1\n while divisor * divisor <= length:\n if length % divisor == 0:\n if any_monocolor_subcycle(divisor):\n local_ans = min(local_ans, divisor)\n break\n if any_monocolor_subcycle(length // divisor):\n local_ans = min(local_ans, length // divisor)\n divisor += 1\n return local_ans\n\n\ndef find_cycle(v):\n global used, cycle\n used[v] = test\n cycle.append(v)\n while p[v] != cycle[0]:\n v = p[v]\n used[v] = test\n cycle.append(v)\n\n\ndef solution():\n global used, cycle\n ans = n\n for v in range(n):\n if used[v] != test:\n cycle = []\n find_cycle(v)\n ans = min(ans, min_in_cycle())\n answers.append(str(ans))\n\n\nt = int(input())\nused = [-1] * 2 * 10 ** 5\ncycle = []\nanswers = []\nfor test in range(t):\n n = int(input())\n p = [int(x) - 1 for x in input().split()]\n c = list(map(int, input().split()))\n solution()\n\nprint('\\n'.join(answers))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 3 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 3 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 8 7 5 8 4\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 0 4 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 3 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 5 7 5 8 4\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 0\\n5\\n2 3 4 5 1\\n1 2 3 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 8 7 5 8 4\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 10 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 5 7 5 8 4\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 5 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 5 7 5 8 4\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 5 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 6\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 10 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 6\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 10 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 9\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 10 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 4 4 7 5 8 9\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 5\\n8\\n7 4 5 6 1 8 3 2\\n0 3 6 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 0 4 4\\n8\\n7 4 5 6 1 8 3 2\\n1 3 6 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 3 3\\n5\\n2 3 4 5 1\\n1 2 5 4 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 5 11 5 8 4\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 0 5 5 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 6\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 10 1\\n8\\n7 4 5 6 1 8 3 2\\n5 3 4 4 7 5 8 9\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 3 3\\n5\\n2 3 4 5 1\\n0 2 5 4 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n0 2 3 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 8 7 5 8 4\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 4 7 5 2 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 0 4 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 4 6 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 3 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 5 7 5 8 4\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 1 3\\n5\\n2 3 4 5 1\\n1 2 10 4 5\\n8\\n7 4 5 6 1 8 3 2\\n5 3 6 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 8 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 2\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 5 7 5 8 4\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 8 5 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 6\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 4 3\\n5\\n2 3 4 5 1\\n1 2 5 10 4\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 6\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 5 10 3\\n8\\n7 4 5 6 1 8 3 2\\n5 3 2 4 7 5 8 9\\n', 'output': '1\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 2 2 3\\n5\\n2 3 4 5 1\\n1 2 5 4 9\\n8\\n7 4 5 6 1 8 3 2\\n0 3 6 4 7 5 8 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 2 0 4 4\\n8\\n7 4 5 6 1 8 3 2\\n1 3 6 4 7 5 11 4\\n', 'output': '1\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4\\n1 3 4 2\\n1 1 2 3\\n5\\n2 3 4 5 1\\n1 0 5 5 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'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80089","program":"```python\ndef monocolor_subcycle(start, divisor):\n for i in range(start, len(cycle), divisor):\n v = cycle[i]\n if c[v] != c[cycle[start]]:\n return False\n return True\n\n\ndef any_monocolor_subcycle(divisor):\n for start in range(divisor):\n if monocolor_subcycle(start, divisor):\n return True\n return False\n\n\ndef min_in_cycle():\n length = len(cycle)\n local_ans = length\n divisor = 1\n while divisor * divisor <= length:\n if length % divisor == 0:\n if any_monocolor_subcycle(divisor):\n local_ans = min(local_ans, divisor)\n break\n if any_monocolor_subcycle(length // divisor):\n local_ans = min(local_ans, length // divisor)\n divisor += 1\n return local_ans\n\n\ndef find_cycle(v):\n global used, cycle\n used[v] = test\n cycle.append(v)\n while p[v] != cycle[0]:\n v = p[v]\n used[v] = test\n cycle.append(v)\n\n\ndef solution():\n global used, cycle\n ans = n\n for v in range(n):\n if used[v] != test:\n cycle = []\n find_cycle(v)\n ans = min(ans, min_in_cycle())\n answers.append(str(ans))\n\n\nt = int(input())\nused = [-1] * 2 * 10 ** 5\ncycle = []\nanswers = []\nfor test in range(t):\n n = int(input())\n p = [int(x) - 1 for x in input().split()]\n c = list(map(int, input().split()))\n solution()\n\nprint('\\n'.join(answers))\n\n```","inputs":"3\n4\n1 3 4 2\n1 2 2 3\n5\n2 3 4 5 1\n1 2 3 4 5\n8\n7 4 5 6 1 8 3 2\n5 3 6 4 7 5 8 4\n","output":"1\n5\n2\n","actual_output":"1\n5\n2\n","execution_success":true,"sample_index":12751},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1368_D. AND, OR and square sum","prompt":"Solve the following coding problem using the programming language python:\n\nGottfried learned about binary number representation. He then came up with this task and presented it to you.\n\nYou are given a collection of n non-negative integers a_1, \u2026, a_n. You are allowed to perform the following operation: choose two distinct indices 1 \u2264 i, j \u2264 n. If before the operation a_i = x, a_j = y, then after the operation a_i = x~AND~y, a_j = x~OR~y, where AND and OR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).\n\nAfter all operations are done, compute \u2211_{i=1}^n a_i^2 \u2014 the sum of squares of all a_i. What is the largest sum of squares you can achieve?\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 2 \u22c5 10^5).\n\nThe second line contains n integers a_1, \u2026, a_n (0 \u2264 a_i < 2^{20}).\n\nOutput\n\nPrint a single integer \u2014 the largest possible sum of squares that can be achieved after several (possibly zero) operations.\n\nExamples\n\nInput\n\n\n1\n123\n\n\nOutput\n\n\n15129\n\n\nInput\n\n\n3\n1 3 5\n\n\nOutput\n\n\n51\n\n\nInput\n\n\n2\n349525 699050\n\n\nOutput\n\n\n1099509530625\n\nNote\n\nIn the first sample no operation can be made, thus the answer is 123^2.\n\nIn the second sample we can obtain the collection 1, 1, 7, and 1^2 + 1^2 + 7^2 = 51.\n\nIf x and y are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x~AND~y is set to 1 if and only if both corresponding bits of x and y are set to 1. Similarly, each bit of x~OR~y is set to 1 if and only if at least one of the corresponding bits of x and y are set to 1. For example, x = 3 and y = 5 are represented as 011_2 and 101_2 (highest bit first). Then, x~AND~y = 001_2 = 1, and x~OR~y = 111_2 = 7.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom sys import stdin\ninput = stdin.readline\nn = int(input())\na = [*map(lambda x: bin(int(x))[:1:-1], input().split())]\nc1 = len(max(a, key=len))\na = [x + '0' * (c1 - len(x)) for x in a]\nb = [sum(c[i] == '1' for c in a) for i in range(c1)]\nc2 = max(b)\nans = 0\nfor i in range(c2):\n\tnum = ''\n\tfor i in range(c1):\n\t\tif b[i] != 0:\n\t\t\tb[i] -= 1\n\t\t\tnum += '1'\n\t\telse:\n\t\t\tnum += '0'\n\tans += int(num[::-1], 2) ** 2\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n123\\n', 'output': '15129\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 5\\n', 'output': '51\\n'}, {'type': 'stdin_stdout', 'input': '2\\n349525 699050\\n', 'output': '1099509530625\\n'}, {'type': 'stdin_stdout', 'input': '10\\n35 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'stdin_stdout', 'input': '3\\n3 2 11\\n', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5 1 2\\n', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 6\\n', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 6\\n', 'output': '49\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n847 5 366 53 6\\n', 'output': '935795\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_80097","program":"```python\nfrom sys import stdin\ninput = stdin.readline\nn = int(input())\na = [*map(lambda x: bin(int(x))[:1:-1], input().split())]\nc1 = len(max(a, key=len))\na = [x + '0' * (c1 - len(x)) for x in a]\nb = [sum(c[i] == '1' for c in a) for i in range(c1)]\nc2 = max(b)\nans = 0\nfor i in range(c2):\n\tnum = ''\n\tfor i in range(c1):\n\t\tif b[i] != 0:\n\t\t\tb[i] -= 1\n\t\t\tnum += '1'\n\t\telse:\n\t\t\tnum += '0'\n\tans += int(num[::-1], 2) ** 2\nprint(ans)\n```","inputs":"1\n123\n","output":"15129\n","actual_output":"15129\n","execution_success":true,"sample_index":12752},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1389_F. Bicolored Segments","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given n segments [l_1, r_1], [l_2, r_2], ..., [l_n, r_n]. Each segment has one of two colors: the i-th segment's color is t_i.\n\nLet's call a pair of segments i and j bad if the following two conditions are met:\n\n * t_i \u2260 t_j; \n * the segments [l_i, r_i] and [l_j, r_j] intersect, embed or touch, i. e. there exists an integer x such that x \u2208 [l_i, r_i] and x \u2208 [l_j, r_j]. \n\n\n\nCalculate the maximum number of segments that can be selected from the given ones, so that there is no bad pair among the selected ones.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 2 \u22c5 10^5) \u2014 number of segments.\n\nThe next n lines contains three integers l_i, r_i, t_i (1 \u2264 l_i \u2264 r_i \u2264 10^9; t_i \u2208 \\{1, 2\\}) \u2014 description of the i-th segment.\n\nOutput\n\nPrint the maximum number of segments that can be selected, so that there is no bad pair among the selected segments.\n\nExamples\n\nInput\n\n\n3\n1 3 1\n4 6 2\n2 5 1\n\n\nOutput\n\n\n2\n\n\nInput\n\n\n5\n5 8 1\n1 3 2\n3 4 2\n6 6 1\n2 10 2\n\n\nOutput\n\n\n4\n\n\nInput\n\n\n7\n19 20 1\n13 15 2\n6 11 2\n4 10 1\n14 17 1\n13 13 2\n5 9 1\n\n\nOutput\n\n\n5\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom operator import add\n\nclass LazySegmentTree():\n def __init__(self,n,init,merge=max,merge_unit=-10**18,operate=add,operate_unit=0):\n self.merge=merge\n self.merge_unit=merge_unit\n self.operate=operate\n self.operate_unit=operate_unit\n\n self.n=(n-1).bit_length()\n self.data=[0 for i in range(1<<(self.n+1))]\n self.lazy=[0 for i in range(1<<(self.n+1))]\n for i in range(n):\n self.data[2**self.n+i]=init[i]\n for i in range(2**self.n-1,0,-1):\n self.data[i]=self.merge(self.data[2*i],self.data[2*i+1])\n\n def propagate_above(self,i):\n m=i.bit_length()-1\n for bit in range(m,0,-1):\n v=i>>bit\n add=self.lazy[v]\n self.lazy[v]=0\n self.data[2*v]=self.operate(self.data[2*v],add)\n self.data[2*v+1]=self.operate(self.data[2*v+1],add)\n self.lazy[2*v]=self.operate(self.lazy[2*v],add)\n self.lazy[2*v+1]=self.operate(self.lazy[2*v+1],add)\n\n\n def remerge_above(self,i):\n while i:\n i>>=1\n self.data[i]=self.operate(self.merge(self.data[2*i],self.data[2*i+1]),self.lazy[i])\n\n def update(self,l,r,x):\n l+=1<>=1\n r>>=1\n self.remerge_above(l0)\n self.remerge_above(r0)\n\n def query(self,l,r):\n l+=1<>=1\n r>>=1\n return res\n\nimport sys\n\ninput=sys.stdin.buffer.readline\n\nn=int(input())\na=[]\nb=[]\nval=set()\nfor i in range(n):\n l,r,t=map(int,input().split())\n if t==1:\n a.append((l,r))\n else:\n b.append((l,r))\n val.add(l)\n val.add(r)\n\nval=sorted(list(val))\ncomp={i:e for e,i in enumerate(val)}\nN=len(val)\n\nquerya=[[] for i in range(N)]\nqueryb=[[] for i in range(N)]\nfor i in range(len(a)):\n l,r=a[i]\n a[i]=(comp[l],comp[r])\n querya[comp[r]].append(comp[l])\nfor i in range(len(b)):\n l,r=b[i]\n b[i]=(comp[l],comp[r])\n queryb[comp[r]].append(comp[l])\n\ninit=[0]*N\nLSTA=LazySegmentTree(N,init)\nLSTB=LazySegmentTree(N,init)\n\ndp=[0]*N\nfor i in range(N):\n for l in querya[i]:\n LSTA.update(0,l+1,1)\n for l in queryb[i]:\n LSTB.update(0,l+1,1)\n temp1=LSTA.query(0,i+1)\n temp2=LSTB.query(0,i+1)\n dp[i]=max(temp1,temp2)\n if i!=N-1:\n LSTA.update(i+1,i+2,dp[i])\n LSTB.update(i+1,i+2,dp[i])\n\nprint(dp[N-1])\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7\\n19 20 1\\n13 15 2\\n6 11 2\\n4 10 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 8 1\\n1 3 2\\n3 4 2\\n6 6 1\\n2 10 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n4 6 2\\n2 5 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 20 1\\n11 17 2\\n3 15 2\\n3 9 2\\n3 14 1\\n16 18 2\\n6 9 2\\n13 17 2\\n10 17 2\\n7 13 1\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '12\\n1 2 2\\n6 7 2\\n2 4 1\\n3 7 2\\n5 5 2\\n1 5 1\\n2 2 1\\n4 7 2\\n3 6 1\\n4 6 2\\n2 5 1\\n4 6 1\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '13\\n3 7 2\\n7 7 2\\n5 12 2\\n1 8 1\\n10 12 1\\n3 7 1\\n10 12 1\\n11 13 2\\n2 3 2\\n11 12 1\\n1 12 2\\n11 13 1\\n9 11 1\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '11\\n7 12 2\\n5 11 1\\n1 13 1\\n12 12 2\\n6 10 2\\n9 11 1\\n8 11 1\\n2 6 1\\n2 10 1\\n5 6 2\\n1 4 2\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 20 1\\n11 17 2\\n3 15 2\\n3 9 1\\n3 14 1\\n16 18 2\\n6 9 2\\n13 17 2\\n10 17 2\\n7 13 1\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 33 1\\n13 15 2\\n6 11 2\\n4 10 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 8 1\\n1 3 2\\n3 8 2\\n6 6 1\\n2 10 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n4 6 2\\n2 5 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 33 1\\n13 15 2\\n6 11 2\\n4 10 1\\n14 17 1\\n13 13 2\\n5 14 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '13\\n3 7 2\\n7 7 2\\n5 12 2\\n1 8 1\\n10 12 1\\n3 7 2\\n10 12 1\\n11 13 2\\n2 3 2\\n11 12 1\\n1 12 2\\n11 13 1\\n9 11 1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '11\\n7 12 1\\n5 11 1\\n1 13 1\\n12 12 2\\n6 10 2\\n9 11 1\\n8 11 1\\n2 6 1\\n2 10 1\\n5 6 2\\n1 4 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '11\\n7 12 2\\n5 11 1\\n1 13 1\\n12 12 2\\n6 10 2\\n9 11 1\\n8 11 1\\n1 6 1\\n2 10 1\\n5 6 2\\n1 4 2\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 20 1\\n11 17 2\\n3 15 2\\n3 9 1\\n3 14 1\\n6 18 2\\n6 9 2\\n13 17 2\\n10 17 2\\n7 13 1\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n4 7 2\\n2 5 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 33 1\\n13 15 2\\n6 11 2\\n4 10 1\\n16 17 1\\n13 13 2\\n5 14 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n6 7 2\\n2 5 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 20 1\\n11 17 2\\n3 15 2\\n3 9 1\\n3 14 1\\n16 18 2\\n6 9 2\\n13 17 2\\n10 17 2\\n7 20 1\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 8 1\\n1 3 2\\n3 4 2\\n6 6 1\\n2 2 2\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n4 6 1\\n2 5 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 20 1\\n11 17 2\\n3 15 2\\n3 9 1\\n1 14 1\\n16 18 2\\n6 9 2\\n13 17 2\\n10 17 2\\n7 13 1\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 33 1\\n13 15 2\\n6 11 2\\n4 19 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 33 1\\n13 15 2\\n6 11 2\\n8 10 1\\n14 17 1\\n13 13 2\\n5 14 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 1\\n4 7 2\\n2 10 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 30 1\\n13 15 2\\n6 11 2\\n4 10 1\\n16 17 1\\n13 13 2\\n5 14 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 2\\n6 7 2\\n2 5 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '13\\n3 7 2\\n7 7 2\\n5 12 2\\n1 3 1\\n10 12 1\\n3 7 2\\n10 12 1\\n11 13 2\\n2 3 2\\n11 12 1\\n1 12 2\\n11 13 1\\n9 11 1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 33 1\\n13 15 2\\n6 11 2\\n4 36 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 2\\n4 7 2\\n2 10 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 57 1\\n13 15 2\\n6 11 2\\n4 10 1\\n16 17 1\\n13 13 2\\n5 14 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 2\\n6 7 2\\n2 5 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '13\\n3 7 2\\n7 7 2\\n5 12 2\\n1 3 1\\n10 12 1\\n3 7 2\\n10 12 1\\n11 13 2\\n2 3 2\\n12 12 1\\n1 12 2\\n11 13 1\\n9 11 1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 33 1\\n13 25 2\\n6 11 2\\n4 36 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 2\\n5 7 2\\n2 10 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 57 1\\n13 15 2\\n6 11 2\\n4 10 1\\n16 17 1\\n13 25 2\\n5 14 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 2\\n5 7 2\\n2 5 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '13\\n3 7 2\\n7 7 2\\n5 12 2\\n1 6 1\\n10 12 1\\n3 7 2\\n10 12 1\\n11 13 2\\n2 3 2\\n12 12 1\\n1 12 2\\n11 13 1\\n9 11 1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 33 1\\n13 32 2\\n6 11 2\\n4 36 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 2\\n2 7 2\\n2 10 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '13\\n3 7 2\\n7 7 2\\n5 12 2\\n1 6 1\\n10 12 1\\n3 7 2\\n10 11 1\\n11 13 2\\n2 3 2\\n12 12 1\\n1 12 2\\n11 13 1\\n9 11 1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 33 1\\n12 32 2\\n6 11 2\\n4 36 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 4 2\\n2 7 2\\n2 10 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 33 1\\n12 32 2\\n4 11 2\\n4 36 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 4 2\\n2 7 2\\n4 10 2\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 35 1\\n12 32 2\\n4 11 2\\n4 36 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 4 1\\n2 7 2\\n4 10 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 35 1\\n12 32 2\\n4 13 2\\n4 36 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 4 1\\n2 7 2\\n4 10 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n19 35 1\\n12 32 2\\n4 13 1\\n4 36 1\\n14 17 1\\n13 13 2\\n5 9 1\\n', 'output': '5\\n'}], 'language': 'python'}","metadata":"{'difficulty': 12, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80101","program":"```python\nfrom operator import add\n\nclass LazySegmentTree():\n def __init__(self,n,init,merge=max,merge_unit=-10**18,operate=add,operate_unit=0):\n self.merge=merge\n self.merge_unit=merge_unit\n self.operate=operate\n self.operate_unit=operate_unit\n\n self.n=(n-1).bit_length()\n self.data=[0 for i in range(1<<(self.n+1))]\n self.lazy=[0 for i in range(1<<(self.n+1))]\n for i in range(n):\n self.data[2**self.n+i]=init[i]\n for i in range(2**self.n-1,0,-1):\n self.data[i]=self.merge(self.data[2*i],self.data[2*i+1])\n\n def propagate_above(self,i):\n m=i.bit_length()-1\n for bit in range(m,0,-1):\n v=i>>bit\n add=self.lazy[v]\n self.lazy[v]=0\n self.data[2*v]=self.operate(self.data[2*v],add)\n self.data[2*v+1]=self.operate(self.data[2*v+1],add)\n self.lazy[2*v]=self.operate(self.lazy[2*v],add)\n self.lazy[2*v+1]=self.operate(self.lazy[2*v+1],add)\n\n\n def remerge_above(self,i):\n while i:\n i>>=1\n self.data[i]=self.operate(self.merge(self.data[2*i],self.data[2*i+1]),self.lazy[i])\n\n def update(self,l,r,x):\n l+=1<>=1\n r>>=1\n self.remerge_above(l0)\n self.remerge_above(r0)\n\n def query(self,l,r):\n l+=1<>=1\n r>>=1\n return res\n\nimport sys\n\ninput=sys.stdin.buffer.readline\n\nn=int(input())\na=[]\nb=[]\nval=set()\nfor i in range(n):\n l,r,t=map(int,input().split())\n if t==1:\n a.append((l,r))\n else:\n b.append((l,r))\n val.add(l)\n val.add(r)\n\nval=sorted(list(val))\ncomp={i:e for e,i in enumerate(val)}\nN=len(val)\n\nquerya=[[] for i in range(N)]\nqueryb=[[] for i in range(N)]\nfor i in range(len(a)):\n l,r=a[i]\n a[i]=(comp[l],comp[r])\n querya[comp[r]].append(comp[l])\nfor i in range(len(b)):\n l,r=b[i]\n b[i]=(comp[l],comp[r])\n queryb[comp[r]].append(comp[l])\n\ninit=[0]*N\nLSTA=LazySegmentTree(N,init)\nLSTB=LazySegmentTree(N,init)\n\ndp=[0]*N\nfor i in range(N):\n for l in querya[i]:\n LSTA.update(0,l+1,1)\n for l in queryb[i]:\n LSTB.update(0,l+1,1)\n temp1=LSTA.query(0,i+1)\n temp2=LSTB.query(0,i+1)\n dp[i]=max(temp1,temp2)\n if i!=N-1:\n LSTA.update(i+1,i+2,dp[i])\n LSTB.update(i+1,i+2,dp[i])\n\nprint(dp[N-1])\n\n```","inputs":"7\n19 20 1\n13 15 2\n6 11 2\n4 10 1\n14 17 1\n13 13 2\n5 9 1\n","output":"5\n","actual_output":"5\n","execution_success":true,"sample_index":12753},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1454_C. Sequence Transformation","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a sequence a, initially consisting of n integers.\n\nYou want to transform this sequence so that all elements in it are equal (i. e. it contains several occurrences of the same element).\n\nTo achieve this, you choose some integer x that occurs at least once in a, and then perform the following operation any number of times (possibly zero): choose some segment [l, r] of the sequence and remove it. But there is one exception: you are not allowed to choose a segment that contains x. More formally, you choose some contiguous subsequence [a_l, a_{l + 1}, ..., a_r] such that a_i \u2260 x if l \u2264 i \u2264 r, and remove it. After removal, the numbering of elements to the right of the removed segment changes: the element that was the (r+1)-th is now l-th, the element that was (r+2)-th is now (l+1)-th, and so on (i. e. the remaining sequence just collapses).\n\nNote that you can not change x after you chose it.\n\nFor example, suppose n = 6, a = [1, 3, 2, 4, 1, 2]. Then one of the ways to transform it in two operations is to choose x = 1, then:\n\n 1. choose l = 2, r = 4, so the resulting sequence is a = [1, 1, 2]; \n 2. choose l = 3, r = 3, so the resulting sequence is a = [1, 1]. \n\n\n\nNote that choosing x is not an operation. Also, note that you can not remove any occurrence of x.\n\nYour task is to find the minimum number of operations required to transform the sequence in a way described above.\n\nYou have to answer t independent test cases.\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 2 \u22c5 10^4) \u2014 the number of test cases. Then t test cases follow.\n\nThe first line of the test case contains one integer n (1 \u2264 n \u2264 2 \u22c5 10^5) \u2014 the number of elements in a. The second line of the test case contains n integers a_1, a_2, \u2026, a_n (1 \u2264 a_i \u2264 n), where a_i is the i-th element of a.\n\nIt is guaranteed that the sum of n does not exceed 2 \u22c5 10^5 (\u2211 n \u2264 2 \u22c5 10^5).\n\nOutput\n\nFor each test case, print the answer \u2014 the minimum number of operations required to transform the given sequence in a way described in the problem statement. It can be proven that it is always possible to perform a finite sequence of operations so the sequence is transformed in the required way.\n\nExample\n\nInput\n\n\n5\n3\n1 1 1\n5\n1 2 3 4 5\n5\n1 2 3 2 1\n7\n1 2 3 1 2 3 1\n11\n2 2 1 2 3 2 1 2 3 1 2\n\n\nOutput\n\n\n0\n1\n1\n2\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfor _ in range(int(input())):\n n = int(input())\n x = list(map(int, input().split()))\n o = {x[0]: [0]}\n for i in range(1, n):\n if x[i] in o:\n o[x[i]].append(i)\n else:\n o[x[i]] = [i]\n m = n\n if len(o) == 1:\n print(0)\n else:\n for k, l in o.items():\n ans = 0\n for i in range(1, len(l)):\n if l[i - 1] + 1 < l[i]:\n ans += 1\n \n if 0 not in l:\n ans += 1\n \n if n - 1 not in l:\n ans += 1\n \n m = min(m, ans)\n print(m)\n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n3\\n1 1 1\\n5\\n1 2 3 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'1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n13\\n12 12 3 12 12 12 12 12 3 7 2 12 13\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n13\\n12 12 12 12 9 5 12 12 3 7 1 12 13\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80113","program":"```python\nfor _ in range(int(input())):\n n = int(input())\n x = list(map(int, input().split()))\n o = {x[0]: [0]}\n for i in range(1, n):\n if x[i] in o:\n o[x[i]].append(i)\n else:\n o[x[i]] = [i]\n m = n\n if len(o) == 1:\n print(0)\n else:\n for k, l in o.items():\n ans = 0\n for i in range(1, len(l)):\n if l[i - 1] + 1 < l[i]:\n ans += 1\n \n if 0 not in l:\n ans += 1\n \n if n - 1 not in l:\n ans += 1\n \n m = min(m, ans)\n print(m)\n \n```","inputs":"5\n3\n1 1 1\n5\n1 2 3 4 5\n5\n1 2 3 2 1\n7\n1 2 3 1 2 3 1\n11\n2 2 1 2 3 2 1 2 3 1 2\n","output":"\n0\n1\n1\n2\n3\n","actual_output":"0\n1\n1\n2\n3\n","execution_success":true,"sample_index":12756},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1478_A. Nezzar and Colorful Balls","prompt":"Solve the following coding problem using the programming language python:\n\nNezzar has n balls, numbered with integers 1, 2, \u2026, n. Numbers a_1, a_2, \u2026, a_n are written on them, respectively. Numbers on those balls form a non-decreasing sequence, which means that a_i \u2264 a_{i+1} for all 1 \u2264 i < n.\n\nNezzar wants to color the balls using the minimum number of colors, such that the following holds.\n\n * For any color, numbers on balls will form a strictly increasing sequence if he keeps balls with this chosen color and discards all other balls. \n\n\n\nNote that a sequence with the length at most 1 is considered as a strictly increasing sequence.\n\nPlease help Nezzar determine the minimum number of colors.\n\nInput\n\nThe first line contains a single integer t (1 \u2264 t \u2264 100) \u2014 the number of testcases. \n\nThe first line of each test case contains a single integer n (1 \u2264 n \u2264 100).\n\nThe second line of each test case contains n integers a_1,a_2,\u2026,a_n (1 \u2264 a_i \u2264 n). It is guaranteed that a_1 \u2264 a_2 \u2264 \u2026 \u2264 a_n.\n\nOutput\n\nFor each test case, output the minimum number of colors Nezzar can use.\n\nExample\n\nInput\n\n\n5\n6\n1 1 1 2 3 4\n5\n1 1 2 2 3\n4\n2 2 2 2\n3\n1 2 3\n1\n1\n\n\nOutput\n\n\n3\n2\n4\n1\n1\n\nNote\n\nLet's match each color with some numbers. Then:\n\nIn the first test case, one optimal color assignment is [1,2,3,3,2,1].\n\nIn the second test case, one optimal color assignment is [1,2,1,2,1].\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfor _ in range(int(input())):\n\tn = int(input())\n\ta = list(map(int, input().split()))\n\tb = set(a)\n\tmaxBall = 0\n\tfor i in b:\n\t\tif a.count(i)>maxBall:\n\t\t\tmaxBall=a.count(i)\n\tprint(maxBall)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 4\\n5\\n1 1 2 2 3\\n4\\n2 2 2 2\\n3\\n1 2 3\\n1\\n1\\n', 'output': '\\n3\\n2\\n4\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 4\\n5\\n1 1 2 2 3\\n4\\n2 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '3\\n2\\n4\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 3\\n5\\n1 1 2 2 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '3\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 2 2 3 3\\n5\\n1 1 2 2 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 6\\n5\\n1 1 2 2 3\\n4\\n2 2 2 2\\n3\\n1 2 3\\n1\\n1\\n', 'output': '3\\n2\\n4\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 4\\n5\\n1 2 2 2 3\\n4\\n2 2 2 2\\n3\\n1 2 3\\n1\\n1\\n', 'output': '3\\n3\\n4\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 2 2 2 3 3\\n5\\n1 1 2 2 3\\n4\\n1 2 2 2\\n3\\n1 2 3\\n1\\n1\\n', 'output': '3\\n2\\n3\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 3\\n5\\n1 1 4 2 4\\n4\\n2 2 2 2\\n3\\n2 2 2\\n1\\n1\\n', 'output': '3\\n2\\n4\\n3\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 2 3\\n5\\n1 1 4 4 4\\n4\\n1 2 2 2\\n3\\n2 3 3\\n1\\n1\\n', 'output': '3\\n3\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 2 1 2 3 3\\n5\\n1 1 2 2 3\\n4\\n2 2 2 2\\n3\\n2 3 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'stdin_stdout', 'input': '5\\n6\\n1 1 2 3 3 6\\n5\\n1 1 5 2 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 4 3 3\\n5\\n1 1 4 3 5\\n4\\n1 2 2 3\\n3\\n2 2 3\\n1\\n1\\n', 'output': '3\\n2\\n2\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 2 3 3 5\\n5\\n1 1 5 2 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 4 3 3\\n5\\n1 1 4 3 5\\n4\\n1 2 2 3\\n3\\n2 3 3\\n1\\n1\\n', 'output': '3\\n2\\n2\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 4\\n5\\n1 1 2 2 3\\n4\\n2 2 2 2\\n3\\n2 2 2\\n1\\n1\\n', 'output': '3\\n2\\n4\\n3\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 3\\n5\\n1 2 2 2 3\\n4\\n2 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '3\\n3\\n4\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 6\\n5\\n1 1 2 2 3\\n4\\n2 2 2 4\\n3\\n2 2 3\\n1\\n1\\n', 'output': '3\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 4\\n5\\n1 2 2 2 3\\n4\\n2 2 2 4\\n3\\n1 2 3\\n1\\n1\\n', 'output': '3\\n3\\n3\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 3\\n5\\n1 1 2 2 3\\n4\\n2 2 2 4\\n3\\n2 2 3\\n1\\n1\\n', 'output': '3\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 2 1 2 3 3\\n5\\n1 1 2 2 5\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 2 2 2 4 3\\n5\\n1 1 2 2 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '3\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 6 3\\n5\\n1 1 2 4 3\\n4\\n2 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '3\\n2\\n4\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 5 3\\n5\\n1 1 4 2 5\\n4\\n1 1 2 2\\n3\\n2 3 3\\n1\\n1\\n', 'output': '3\\n2\\n2\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 3 3 3\\n5\\n1 1 4 2 4\\n4\\n2 2 2 2\\n3\\n2 3 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3\\n5\\n1 1 4 2 5\\n4\\n1 2 2 3\\n3\\n2 3 3\\n1\\n1\\n', 'output': '3\\n2\\n2\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 1 3 6\\n5\\n1 1 2 2 3\\n4\\n2 2 2 4\\n3\\n2 2 3\\n1\\n1\\n', 'output': '4\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 2 1 2 3 3\\n5\\n1 2 2 2 5\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n3\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 2 2 5 3\\n5\\n1 1 4 2 5\\n4\\n1 1 2 2\\n3\\n2 3 3\\n1\\n1\\n', 'output': '2\\n2\\n2\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 3 3 3\\n5\\n1 1 4 2 4\\n4\\n2 2 2 3\\n3\\n2 3 3\\n1\\n1\\n', 'output': '3\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 2 2 4 4\\n5\\n1 1 2 3 3\\n4\\n2 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n2\\n4\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 2 2 3 6 3\\n5\\n1 1 2 2 2\\n4\\n1 2 2 2\\n3\\n2 2 2\\n1\\n1\\n', 'output': '2\\n3\\n3\\n3\\n1\\n'}, {'type': 'stdin_stdout', 'input': 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'stdin_stdout', 'input': '5\\n6\\n1 2 2 2 3 3\\n5\\n1 1 4 2 3\\n4\\n1 2 2 2\\n3\\n1 2 3\\n1\\n1\\n', 'output': '3\\n2\\n3\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 2 2 4 5 3\\n5\\n1 1 2 2 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 3\\n5\\n1 1 4 2 4\\n4\\n2 2 2 2\\n3\\n1 2 3\\n1\\n1\\n', 'output': '3\\n2\\n4\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 4 3 3\\n5\\n1 1 3 2 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '3\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 3 3 3 3\\n5\\n1 1 2 2 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '4\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 2 2 3 3\\n5\\n1 1 3 3 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n3\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 2 3 6\\n5\\n1 2 2 2 5\\n4\\n2 2 2 2\\n3\\n1 2 3\\n1\\n1\\n', 'output': '3\\n3\\n4\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 1 1 5 3\\n5\\n1 1 3 2 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '4\\n2\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 2 3 6 3\\n5\\n1 1 1 2 3\\n4\\n1 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n3\\n3\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 2 2 3 6\\n5\\n1 1 2 2 3\\n4\\n1 2 2 2\\n3\\n1 2 3\\n1\\n1\\n', 'output': '2\\n2\\n3\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 2 2 3 6\\n5\\n1 1 3 2 3\\n4\\n2 2 2 2\\n3\\n1 2 3\\n1\\n1\\n', 'output': '2\\n2\\n4\\n1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 1 2 2 3 6\\n5\\n1 1 2 3 3\\n4\\n2 2 2 2\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n2\\n4\\n2\\n1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n6\\n1 2 1 2 3 3\\n5\\n1 1 2 4 3\\n4\\n1 1 2 3\\n3\\n2 2 3\\n1\\n1\\n', 'output': '2\\n2\\n2\\n2\\n1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_80117","program":"```python\nfor _ in range(int(input())):\n\tn = int(input())\n\ta = list(map(int, input().split()))\n\tb = set(a)\n\tmaxBall = 0\n\tfor i in b:\n\t\tif a.count(i)>maxBall:\n\t\t\tmaxBall=a.count(i)\n\tprint(maxBall)\n```","inputs":"5\n6\n1 1 1 2 3 4\n5\n1 1 2 2 3\n4\n2 2 2 2\n3\n1 2 3\n1\n1\n","output":"\n3\n2\n4\n1\n1\n","actual_output":"3\n2\n4\n1\n1\n","execution_success":true,"sample_index":12757},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1505_D. Xenolith? Hippodrome?","prompt":"Solve the following coding problem using the programming language python:\n\n\n\nInput\n\nThe input contains two integers N, M (1 \u2264 N \u2264 1024, 2 \u2264 M \u2264 16), separated by a single space.\n\nOutput\n\nOutput \"YES\" or \"NO\".\n\nExamples\n\nInput\n\n\n2 3\n\n\nOutput\n\n\nYES\n\n\nInput\n\n\n3 2\n\n\nOutput\n\n\nNO\n\n\nInput\n\n\n33 16\n\n\nOutput\n\n\nYES\n\n\nInput\n\n\n26 5\n\n\nOutput\n\n\nNO\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nimport math\nimport heapq\nimport bisect\nfrom collections import Counter\nfrom collections import defaultdict\nfrom io import BytesIO, IOBase\nimport string\n\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n import os\n self.os = os\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n self.BUFSIZE = 8192\n\n def read(self):\n while True:\n b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, self.BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, self.BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n self.os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\n\n\ndef get_int():\n return int(input())\n\n\ndef get_ints():\n return list(map(int, input().split(' ')))\n\n\ndef get_int_grid(n):\n return [get_ints() for _ in range(n)]\n\n\ndef get_str():\n return input().strip()\n\n\ndef get_strs():\n return get_str().split(' ')\n\n\ndef flat_list(arr):\n return [item for subarr in arr for item in subarr]\n\n\ndef yes_no(b):\n if b:\n return \"YES\"\n else:\n return \"NO\"\n\n\ndef binary_search(good, left, right, delta=1, right_true=False):\n \"\"\"\n Performs binary search\n ----------\n Parameters\n ----------\n :param good: Function used to perform the binary search\n :param left: Starting value of left limit\n :param right: Starting value of the right limit\n :param delta: Margin of error, defaults value of 1 for integer binary search\n :param right_true: Boolean, for whether the right limit is the true invariant\n :return: Returns the most extremal value interval [left, right] which is good function evaluates to True,\n alternatively returns False if no such value found\n \"\"\"\n\n limits = [left, right]\n while limits[1] - limits[0] > delta:\n if delta == 1:\n mid = sum(limits) // 2\n else:\n mid = sum(limits) / 2\n if good(mid):\n limits[int(right_true)] = mid\n else:\n limits[int(~right_true)] = mid\n if good(limits[int(right_true)]):\n return limits[int(right_true)]\n else:\n return False\n\n\ndef prefix_sums(a):\n p = [0]\n for x in a:\n p.append(p[-1] + x)\n return p\n\n\ndef solve_a():\n while True:\n try:\n x = input().strip()\n if x == 'Is it rated?':\n print('NO')\n sys.stdout.flush()\n except:\n break\n\n\ndef solve_b():\n n = get_int()\n while len(str(n)) > 1:\n n = sum([int(char) for char in str(n)])\n return n\n\n\ndef solve_c():\n alpha = {char: i for (i, char) in enumerate(string.ascii_lowercase)}\n s = get_str().lower()\n n = len(s)\n for i in range(2, n):\n if (alpha[s[i - 1]] + alpha[s[i - 2]] - alpha[s[i]]) % 26 != 0:\n return \"NO\"\n return \"YES\"\n\n\ndef solve_d():\n n, m = get_ints()\n S = set()\n while n:\n if n % m in S:\n return \"NO\"\n else:\n S.add(n % m)\n n //= m\n return \"YES\"\n\n\nprint(solve_d())\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 3\\n', 'output': '\\nYES\\n'}, {'type': 'stdin_stdout', 'input': '33 16\\n', 'output': '\\nYES\\n'}, {'type': 'stdin_stdout', 'input': '26 5\\n', 'output': '\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n', 'output': '\\nNO\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '33 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '33 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '14 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '16 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 16\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 15\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '26 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '30 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '26 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '12 16\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '7 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '11 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 20\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '15 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 16\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 26\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '15 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '29 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '26 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '7 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '26 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 26\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '20 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '18 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 20\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '8 26\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '48 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '7 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '13 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '20 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 14\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 28\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 26\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '48 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '20 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '20 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 28\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 27\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '29 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '17 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 28\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 16\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '14 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 14\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '17 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 10\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 28\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '14 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '33 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '14 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '7 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '33 25\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 12\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '46 6\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '16 5\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 5\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '19 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 22\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '7 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '15 12\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 13\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '26 10\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '7 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 31\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 10\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '14 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 35\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '15 18\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 8\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '28 4\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '16 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 10\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '8 7\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '22 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '18 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4 13\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 40\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4 26\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '23 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '13 14\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '35 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 19\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '8 28\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '20 14\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '20 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '10 44\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 15\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 10\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '7 28\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '25 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '33 15\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '7 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 12\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '26 25\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '9 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '40 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '19 2\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '18 5\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 10\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '17 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4 22\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4 11\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '26 19\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4 12\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '1 14\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '4 28\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '15 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11 66\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '8 18\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 8\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '13 16\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '22 7\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 10\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '8 20\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5 26\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5 9\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '23 4\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 14\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '66 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 25\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '17 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 22\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12 14\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '20 10\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 16\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 11\\n', 'output': 'YES\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80121","program":"```python\nimport sys\nimport math\nimport heapq\nimport bisect\nfrom collections import Counter\nfrom collections import defaultdict\nfrom io import BytesIO, IOBase\nimport string\n\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n import os\n self.os = os\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n self.BUFSIZE = 8192\n\n def read(self):\n while True:\n b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, self.BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, self.BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n self.os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\n\n\ndef get_int():\n return int(input())\n\n\ndef get_ints():\n return list(map(int, input().split(' ')))\n\n\ndef get_int_grid(n):\n return [get_ints() for _ in range(n)]\n\n\ndef get_str():\n return input().strip()\n\n\ndef get_strs():\n return get_str().split(' ')\n\n\ndef flat_list(arr):\n return [item for subarr in arr for item in subarr]\n\n\ndef yes_no(b):\n if b:\n return \"YES\"\n else:\n return \"NO\"\n\n\ndef binary_search(good, left, right, delta=1, right_true=False):\n \"\"\"\n Performs binary search\n ----------\n Parameters\n ----------\n :param good: Function used to perform the binary search\n :param left: Starting value of left limit\n :param right: Starting value of the right limit\n :param delta: Margin of error, defaults value of 1 for integer binary search\n :param right_true: Boolean, for whether the right limit is the true invariant\n :return: Returns the most extremal value interval [left, right] which is good function evaluates to True,\n alternatively returns False if no such value found\n \"\"\"\n\n limits = [left, right]\n while limits[1] - limits[0] > delta:\n if delta == 1:\n mid = sum(limits) // 2\n else:\n mid = sum(limits) / 2\n if good(mid):\n limits[int(right_true)] = mid\n else:\n limits[int(~right_true)] = mid\n if good(limits[int(right_true)]):\n return limits[int(right_true)]\n else:\n return False\n\n\ndef prefix_sums(a):\n p = [0]\n for x in a:\n p.append(p[-1] + x)\n return p\n\n\ndef solve_a():\n while True:\n try:\n x = input().strip()\n if x == 'Is it rated?':\n print('NO')\n sys.stdout.flush()\n except:\n break\n\n\ndef solve_b():\n n = get_int()\n while len(str(n)) > 1:\n n = sum([int(char) for char in str(n)])\n return n\n\n\ndef solve_c():\n alpha = {char: i for (i, char) in enumerate(string.ascii_lowercase)}\n s = get_str().lower()\n n = len(s)\n for i in range(2, n):\n if (alpha[s[i - 1]] + alpha[s[i - 2]] - alpha[s[i]]) % 26 != 0:\n return \"NO\"\n return \"YES\"\n\n\ndef solve_d():\n n, m = get_ints()\n S = set()\n while n:\n if n % m in S:\n return \"NO\"\n else:\n S.add(n % m)\n n //= m\n return \"YES\"\n\n\nprint(solve_d())\n```","inputs":"2 3\n","output":"\nYES\n","actual_output":"YES\n","execution_success":true,"sample_index":12758},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"15_C. Industrial Nim","prompt":"Solve the following coding problem using the programming language python:\n\nThere are n stone quarries in Petrograd.\n\nEach quarry owns mi dumpers (1 \u2264 i \u2264 n). It is known that the first dumper of the i-th quarry has xi stones in it, the second dumper has xi + 1 stones in it, the third has xi + 2, and the mi-th dumper (the last for the i-th quarry) has xi + mi - 1 stones in it.\n\nTwo oligarchs play a well-known game Nim. Players take turns removing stones from dumpers. On each turn, a player can select any dumper and remove any non-zero amount of stones from it. The player who cannot take a stone loses.\n\nYour task is to find out which oligarch will win, provided that both of them play optimally. The oligarchs asked you not to reveal their names. So, let's call the one who takes the first stone \u00abtolik\u00bb and the other one \u00abbolik\u00bb.\n\nInput\n\nThe first line of the input contains one integer number n (1 \u2264 n \u2264 105) \u2014 the amount of quarries. Then there follow n lines, each of them contains two space-separated integers xi and mi (1 \u2264 xi, mi \u2264 1016) \u2014 the amount of stones in the first dumper of the i-th quarry and the number of dumpers at the i-th quarry.\n\nOutput\n\nOutput \u00abtolik\u00bb if the oligarch who takes a stone first wins, and \u00abbolik\u00bb otherwise.\n\nExamples\n\nInput\n\n2\n2 1\n3 2\n\n\nOutput\n\ntolik\n\n\nInput\n\n4\n1 1\n1 1\n1 1\n1 1\n\n\nOutput\n\nbolik\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n__author__ = 'Darren'\n\n\n\n\n\ndef solve():\n\n n = int(input())\n\n xor = 0\n\n for _i in range(n):\n\n x, m = map(int, input().split())\n\n xor ^= xor_range(x - 1) ^ xor_range(x + m - 1)\n\n print([\"tolik\", \"bolik\"][xor == 0])\n\n\n\n\n\ndef xor_range(n):\n\n return [n, 1, n+1, 0][n % 4]\n\n\n\n\n\nif __name__ == '__main__':\n\n solve()\n\n\n\n\n\n# Made By Mostafa_Khaled\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n2 1\\n3 2\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1\\n1 1\\n1 1\\n1 1\\n', 'output': 'bolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 80\\n13 75\\n37 45\\n44 86\\n1 85\\n13 33\\n17 50\\n12 26\\n97 48\\n52 40\\n2 71\\n95 79\\n38 76\\n24 54\\n91 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n39 94\\n31 56\\n28 16\\n20 44\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 3\\n1 4\\n5 8\\n4 10\\n10 8\\n7 2\\n1 2\\n1 7\\n4 10\\n5 3\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 6\\n6 3\\n2 9\\n7 8\\n9 1\\n2 4\\n3 6\\n6 3\\n5 6\\n5 3\\n6 5\\n2 10\\n2 9\\n6 3\\n10 6\\n10 10\\n10 7\\n3 9\\n16 1\\n1 3\\n', 'output': 'bolik\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3737203222172202 1\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 80\\n13 75\\n37 45\\n44 86\\n1 85\\n13 33\\n17 50\\n12 26\\n97 48\\n52 40\\n2 71\\n95 79\\n38 50\\n24 54\\n91 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n39 94\\n31 56\\n28 16\\n20 44\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 6\\n6 3\\n2 9\\n7 8\\n9 1\\n2 4\\n3 6\\n6 3\\n5 6\\n5 3\\n6 6\\n2 10\\n2 9\\n6 3\\n10 6\\n10 10\\n10 7\\n3 9\\n16 1\\n1 3\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6893622727484635 1\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 0\\n3 2\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 80\\n13 75\\n37 45\\n44 86\\n1 85\\n13 33\\n17 50\\n12 26\\n97 48\\n52 40\\n2 71\\n95 79\\n38 50\\n24 2\\n91 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n39 94\\n31 56\\n28 16\\n20 44\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 6\\n6 3\\n2 9\\n7 8\\n9 1\\n2 4\\n3 6\\n6 3\\n5 4\\n5 3\\n6 6\\n2 10\\n2 9\\n6 3\\n10 6\\n10 10\\n10 7\\n3 9\\n16 1\\n1 3\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 0\\n5 2\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 80\\n13 75\\n37 45\\n44 86\\n1 85\\n13 33\\n17 50\\n12 26\\n97 53\\n52 40\\n2 71\\n95 79\\n38 50\\n24 2\\n91 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n39 94\\n31 56\\n28 16\\n20 44\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 6\\n6 3\\n2 9\\n7 8\\n9 1\\n2 4\\n3 6\\n6 3\\n5 4\\n5 3\\n6 6\\n2 10\\n2 9\\n3 3\\n10 6\\n10 10\\n10 7\\n3 9\\n16 1\\n1 3\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 0\\n1 2\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 80\\n13 75\\n37 45\\n44 86\\n1 85\\n13 33\\n17 50\\n12 26\\n97 53\\n52 40\\n2 52\\n95 79\\n38 50\\n24 2\\n91 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n39 94\\n31 56\\n28 16\\n20 44\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 6\\n6 3\\n2 9\\n7 8\\n17 1\\n2 4\\n3 6\\n6 3\\n5 4\\n5 3\\n6 6\\n2 10\\n2 9\\n3 3\\n10 6\\n10 10\\n10 7\\n3 9\\n16 1\\n1 3\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 0\\n2 2\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 80\\n13 75\\n37 45\\n44 86\\n1 85\\n13 33\\n17 50\\n12 26\\n97 53\\n52 40\\n2 52\\n48 79\\n38 50\\n24 2\\n91 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n39 94\\n31 56\\n28 16\\n20 44\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 6\\n6 3\\n2 9\\n7 8\\n17 1\\n2 4\\n3 6\\n6 3\\n5 4\\n5 3\\n6 6\\n2 10\\n2 9\\n3 3\\n10 5\\n10 10\\n10 7\\n3 9\\n16 1\\n1 3\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 0\\n4 2\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 80\\n13 75\\n37 45\\n44 86\\n1 85\\n13 33\\n17 50\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n38 50\\n24 2\\n91 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n39 94\\n31 56\\n28 16\\n20 44\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 6\\n6 3\\n2 9\\n7 8\\n17 1\\n2 4\\n3 6\\n6 3\\n5 4\\n5 3\\n6 6\\n2 10\\n2 9\\n3 3\\n10 9\\n10 10\\n10 7\\n3 9\\n16 1\\n1 3\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0\\n4 2\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 80\\n13 75\\n37 45\\n44 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n38 50\\n24 2\\n91 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n39 94\\n31 56\\n28 16\\n20 44\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 6\\n6 3\\n2 9\\n7 8\\n17 1\\n2 4\\n3 6\\n6 1\\n5 4\\n5 3\\n6 6\\n2 10\\n2 9\\n3 3\\n10 9\\n10 10\\n10 7\\n3 9\\n16 1\\n1 3\\n', 'output': 'tolik\\n'}, {'type': 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45\\n39 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n48 50\\n24 2\\n78 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n39 16\\n31 56\\n11 16\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 80\\n13 75\\n37 45\\n39 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n78 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n39 16\\n31 56\\n11 16\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 80\\n13 75\\n37 45\\n39 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n78 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n9 16\\n31 56\\n11 16\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 100\\n13 75\\n37 45\\n39 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n78 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n9 16\\n31 56\\n11 16\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 100\\n13 75\\n37 45\\n39 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n78 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n9 16\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n53 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 100\\n13 75\\n37 45\\n39 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n78 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n10 16\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 100\\n13 75\\n37 45\\n39 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n78 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n10 16\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 100\\n13 75\\n37 45\\n39 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n10 16\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 100\\n13 75\\n37 45\\n38 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 53\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n10 16\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 100\\n13 75\\n37 45\\n38 86\\n1 85\\n13 33\\n17 71\\n12 2\\n97 9\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n22 91\\n10 16\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n13 98\\n21 60\\n76 58\\n39 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52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n10 16\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n13 98\\n21 60\\n76 58\\n39 5\\n62 58\\n73 100\\n25 75\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 2\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n10 29\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n13 176\\n21 60\\n76 58\\n39 5\\n62 58\\n73 100\\n25 75\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 2\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n10 29\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n13 176\\n21 60\\n76 58\\n39 5\\n121 58\\n73 100\\n25 75\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 2\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n10 29\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n13 176\\n21 60\\n76 58\\n39 5\\n121 58\\n73 100\\n25 75\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 2\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n13 176\\n21 60\\n76 58\\n39 5\\n121 58\\n73 100\\n25 75\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n18 176\\n21 60\\n76 58\\n39 5\\n121 58\\n73 100\\n25 75\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n18 176\\n21 60\\n76 58\\n39 7\\n121 58\\n73 100\\n25 75\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 18\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n18 176\\n21 60\\n76 58\\n39 7\\n121 58\\n73 100\\n25 75\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 2\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 4\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n18 176\\n21 60\\n76 58\\n39 7\\n121 58\\n73 100\\n25 75\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 4\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 4\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n18 176\\n21 60\\n76 58\\n39 7\\n121 58\\n73 100\\n25 63\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 4\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 4\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n18 176\\n21 60\\n76 54\\n39 7\\n121 58\\n73 100\\n25 63\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 4\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 4\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n18 176\\n21 60\\n76 54\\n39 7\\n121 58\\n98 100\\n25 63\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 40\\n2 52\\n48 79\\n55 50\\n24 4\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 4\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n18 176\\n21 60\\n76 54\\n39 7\\n121 58\\n98 100\\n25 63\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 40\\n2 52\\n48 79\\n55 6\\n24 4\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 4\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 12\\n18 176\\n21 60\\n76 54\\n39 7\\n121 58\\n98 100\\n25 63\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 25\\n2 52\\n48 79\\n55 6\\n24 4\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 4\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 10\\n18 176\\n21 60\\n76 54\\n39 7\\n121 58\\n98 100\\n25 63\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 25\\n2 52\\n48 79\\n55 6\\n24 4\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 4\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 10\\n18 176\\n21 60\\n76 54\\n39 7\\n121 58\\n98 100\\n25 63\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 25\\n2 52\\n48 79\\n55 6\\n24 7\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 4\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 10\\n18 176\\n21 60\\n76 54\\n39 7\\n121 58\\n98 100\\n25 63\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n12 3\\n97 1\\n52 25\\n2 52\\n48 79\\n55 6\\n24 7\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 5\\n20 15\\n', 'output': 'tolik\\n'}, {'type': 'stdin_stdout', 'input': '30\\n42 10\\n18 176\\n21 60\\n76 54\\n39 7\\n121 58\\n98 100\\n25 63\\n37 45\\n38 86\\n2 85\\n13 33\\n17 71\\n3 3\\n97 1\\n52 25\\n2 52\\n48 79\\n55 6\\n24 7\\n129 39\\n97 92\\n94 80\\n50 61\\n33 56\\n6 91\\n15 29\\n31 56\\n11 5\\n20 15\\n', 'output': 'tolik\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 64000000}","problem_id":"vfc_80129","program":"```python\n__author__ = 'Darren'\n\n\n\n\n\ndef solve():\n\n n = int(input())\n\n xor = 0\n\n for _i in range(n):\n\n x, m = map(int, input().split())\n\n xor ^= xor_range(x - 1) ^ xor_range(x + m - 1)\n\n print([\"tolik\", \"bolik\"][xor == 0])\n\n\n\n\n\ndef xor_range(n):\n\n return [n, 1, n+1, 0][n % 4]\n\n\n\n\n\nif __name__ == '__main__':\n\n solve()\n\n\n\n\n\n# Made By Mostafa_Khaled\n```","inputs":"2\n2 1\n3 2\n","output":"tolik\n","actual_output":"tolik\n","execution_success":true,"sample_index":12760},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"202_A. LLPS","prompt":"Solve the following coding problem using the programming language python:\n\nThis problem's actual name, \"Lexicographically Largest Palindromic Subsequence\" is too long to fit into the page headline.\n\nYou are given string s consisting of lowercase English letters only. Find its lexicographically largest palindromic subsequence.\n\nWe'll call a non-empty string s[p1p2... pk] = sp1sp2... spk (1 \u2264 p1 < p2 < ... < pk \u2264 |s|) a subsequence of string s = s1s2... s|s|, where |s| is the length of string s. For example, strings \"abcb\", \"b\" and \"abacaba\" are subsequences of string \"abacaba\".\n\nString x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y| if either |x| > |y| and x1 = y1, x2 = y2, ..., x|y| = y|y|, or there exists such number r (r < |x|, r < |y|) that x1 = y1, x2 = y2, ..., xr = yr and xr + 1 > yr + 1. Characters in the strings are compared according to their ASCII codes. For example, string \"ranger\" is lexicographically larger than string \"racecar\" and string \"poster\" is lexicographically larger than string \"post\".\n\nString s = s1s2... s|s| is a palindrome if it matches string rev(s) = s|s|s|s| - 1... s1. In other words, a string is a palindrome if it reads the same way from left to right and from right to left. For example, palindromic strings are \"racecar\", \"refer\" and \"z\".\n\nInput\n\nThe only input line contains a non-empty string s consisting of lowercase English letters only. Its length does not exceed 10.\n\nOutput\n\nPrint the lexicographically largest palindromic subsequence of string s.\n\nExamples\n\nInput\n\nradar\n\n\nOutput\n\nrr\n\n\nInput\n\nbowwowwow\n\n\nOutput\n\nwwwww\n\n\nInput\n\ncodeforces\n\n\nOutput\n\ns\n\n\nInput\n\nmississipp\n\n\nOutput\n\nssss\n\nNote\n\nAmong all distinct subsequences of string \"radar\" the following ones are palindromes: \"a\", \"d\", \"r\", \"aa\", \"rr\", \"ada\", \"rar\", \"rdr\", \"raar\" and \"radar\". The lexicographically largest of them is \"rr\".\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# -*- coding: utf-8 -*-\n\"\"\"\nCreated on Thu Apr 2 19:56:34 2020\n\n@author: roastedcoder\n\nThis is for CodeForces\n\"\"\"\nmod = 1000000007\nssi = lambda : map(int,input().split())\n\n# RoastedCoder\n\ns = input()\nl = [0]*26\nfor i in range(len(s)):\n l[ord(s[i])-97] += 1\n \nfor i in range(25,-1,-1):\n if(l[i] >= 1):\n print(chr(i+97)*l[i])\n break\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'mississipp\\n', 'output': 'ssss\\n'}, {'type': 'stdin_stdout', 'input': 'bowwowwow\\n', 'output': 'wwwww\\n'}, {'type': 'stdin_stdout', 'input': 'codeforces\\n', 'output': 's\\n'}, {'type': 'stdin_stdout', 'input': 'radar\\n', 'output': 'rr\\n'}, {'type': 'stdin_stdout', 'input': 'sets\\n', 'output': 't\\n'}, {'type': 'stdin_stdout', 'input': 'hellhellhe\\n', 'output': 'llll\\n'}, {'type': 'stdin_stdout', 'input': 'aburvabur\\n', 'output': 'v\\n'}, {'type': 'stdin_stdout', 'input': 'b\\n', 'output': 'b\\n'}, {'type': 'stdin_stdout', 'input': 'zzzzzzwait\\n', 'output': 'zzzzzz\\n'}, {'type': 'stdin_stdout', 'input': 'zzzzzzzzzz\\n', 'output': 'zzzzzzzzzz\\n'}, {'type': 'stdin_stdout', 'input': 'a\\n', 'output': 'a\\n'}, {'type': 'stdin_stdout', 'input': 'testcase\\n', 'output': 'tt\\n'}, {'type': 'stdin_stdout', 'input': 'aa\\n', 'output': 'aa\\n'}, {'type': 'stdin_stdout', 'input': 'aabcdefghh\\n', 'output': 'hh\\n'}, {'type': 'stdin_stdout', 'input': 'zzzzzzzazz\\n', 'output': 'zzzzzzzzz\\n'}, {'type': 'stdin_stdout', 'input': 'referee\\n', 'output': 'rr\\n'}, {'type': 'stdin_stdout', 'input': 'seriously\\n', 'output': 'y\\n'}, {'type': 'stdin_stdout', 'input': 'test\\n', 'output': 'tt\\n'}, {'type': 'stdin_stdout', 'input': 'helloworld\\n', 'output': 'w\\n'}, {'type': 'stdin_stdout', 'input': 'z\\n', 'output': 'z\\n'}, {'type': 'stdin_stdout', 'input': 'buzz\\n', 'output': 'zz\\n'}, {'type': 'stdin_stdout', 'input': 'zz\\n', 'output': 'zz\\n'}, {'type': 'stdin_stdout', 'input': 'zzazazzzaz\\n', 'output': 'zzzzzzz\\n'}, {'type': 'stdin_stdout', 'input': 'aru\\n', 'output': 'u\\n'}, {'type': 'stdin_stdout', 'input': 'aaaaaaaaaa\\n', 'output': 'aaaaaaaaaa\\n'}, {'type': 'stdin_stdout', 'input': 'rrrrrqponm\\n', 'output': 'rrrrr\\n'}, {'type': 'stdin_stdout', 'input': 'uraura\\n', 'output': 'uu\\n'}, {'type': 'stdin_stdout', 'input': 'klmgameklm\\n', 'output': 'mmm\\n'}, {'type': 'stdin_stdout', 'input': 'aaaaaaaaab\\n', 'output': 'b\\n'}, {'type': 'stdin_stdout', 'input': 'tourist\\n', 'output': 'u\\n'}, {'type': 'stdin_stdout', 'input': 'hhgfedcbaa\\n', 'output': 'hh\\n'}, {'type': 'stdin_stdout', 'input': 'aababb\\n', 'output': 'bbb\\n'}, {'type': 'stdin_stdout', 'input': 'ura\\n', 'output': 'u\\n'}, {'type': 'stdin_stdout', 'input': 'abbbbbbbbb\\n', 'output': 'bbbbbbbbb\\n'}, {'type': 'stdin_stdout', 'input': 'dfkjafdkdd\\n', 'output': 'kk\\n'}, {'type': 'stdin_stdout', 'input': 'joking\\n', 'output': 'o\\n'}, {'type': 'stdin_stdout', 'input': 'edcbabcde\\n', 'output': 'ee\\n'}, {'type': 'stdin_stdout', 'input': 'y\\n', 'output': 'y\\n'}, {'type': 'stdin_stdout', 'input': 'abcdeabcd\\n', 'output': 'e\\n'}, {'type': 'stdin_stdout', 'input': 'testzzzzzz\\n', 'output': 'zzzzzz\\n'}, {'type': 'stdin_stdout', 'input': 'zanzibar\\n', 'output': 'zz\\n'}, {'type': 'stdin_stdout', 'input': 'bb\\n', 'output': 'bb\\n'}, {'type': 'stdin_stdout', 'input': 'romka\\n', 'output': 'r\\n'}, {'type': 'stdin_stdout', 'input': 'dcbaedcba\\n', 'output': 'e\\n'}, {'type': 'stdin_stdout', 'input': 'yy\\n', 'output': 'yy\\n'}, {'type': 'stdin_stdout', 'input': 'hellohello\\n', 'output': 'oo\\n'}, {'type': 'stdin_stdout', 'input': 'refer\\n', 'output': 'rr\\n'}, {'type': 'stdin_stdout', 'input': 'aruaru\\n', 'output': 'uu\\n'}, {'type': 'stdin_stdout', 'input': 'eurottat\\n', 'output': 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{'type': 'stdin_stdout', 'input': 'reefr\\n', 'output': 'rr\\n'}, {'type': 'stdin_stdout', 'input': 'yzzzyy\\n', 'output': 'zzz\\n'}, {'type': 'stdin_stdout', 'input': 'ahahahahah\\n', 'output': 'hhhhh\\n'}, {'type': 'stdin_stdout', 'input': 'nississipp\\n', 'output': 'ssss\\n'}, {'type': 'stdin_stdout', 'input': 'bowwowwwo\\n', 'output': 'wwwww\\n'}, {'type': 'stdin_stdout', 'input': 'codfeorces\\n', 'output': 's\\n'}, {'type': 'stdin_stdout', 'input': 'd\\n', 'output': 'd\\n'}, {'type': 'stdin_stdout', 'input': 'zzazzzzyzz\\n', 'output': 'zzzzzzzz\\n'}, {'type': 'stdin_stdout', 'input': 'zzzyzztset\\n', 'output': 'zzzzz\\n'}, {'type': 'stdin_stdout', 'input': 'hahahaiaha\\n', 'output': 'i\\n'}, {'type': 'stdin_stdout', 'input': 'zzazzzzzzz\\n', 'output': 'zzzzzzzzz\\n'}, {'type': 'stdin_stdout', 'input': 'sest\\n', 'output': 't\\n'}, {'type': 'stdin_stdout', 'input': 'aaaaabaaaa\\n', 'output': 'b\\n'}, {'type': 'stdin_stdout', 'input': 'tourhst\\n', 'output': 'u\\n'}, {'type': 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'output': 'hh\\n'}, {'type': 'stdin_stdout', 'input': 'reffqee\\n', 'output': 'r\\n'}, {'type': 'stdin_stdout', 'input': 'sersouilx\\n', 'output': 'x\\n'}, {'type': 'stdin_stdout', 'input': 'tses\\n', 'output': 't\\n'}, {'type': 'stdin_stdout', 'input': 'lelhoworkd\\n', 'output': 'w\\n'}, {'type': 'stdin_stdout', 'input': 'zyub\\n', 'output': 'z\\n'}, {'type': 'stdin_stdout', 'input': 'uar\\n', 'output': 'u\\n'}, {'type': 'stdin_stdout', 'input': 'aabaaaaaaa\\n', 'output': 'b\\n'}, {'type': 'stdin_stdout', 'input': 'mnopprrrrr\\n', 'output': 'rrrrr\\n'}, {'type': 'stdin_stdout', 'input': 'uqatra\\n', 'output': 'u\\n'}, {'type': 'stdin_stdout', 'input': 'tourhss\\n', 'output': 'u\\n'}, {'type': 'stdin_stdout', 'input': 'bbabba\\n', 'output': 'bbbb\\n'}, {'type': 'stdin_stdout', 'input': 'bbbbcbbbba\\n', 'output': 'c\\n'}, {'type': 'stdin_stdout', 'input': 'dfkjadkddf\\n', 'output': 'kk\\n'}, {'type': 'stdin_stdout', 'input': 'joghnk\\n', 'output': 'o\\n'}, {'type': 'stdin_stdout', 'input': 'edbbacdde\\n', 'output': 'ee\\n'}, {'type': 'stdin_stdout', 'input': 'dcbbedcba\\n', 'output': 'e\\n'}, {'type': 'stdin_stdout', 'input': 'zaayibnr\\n', 'output': 'z\\n'}, {'type': 'stdin_stdout', 'input': 'db\\n', 'output': 'd\\n'}, {'type': 'stdin_stdout', 'input': 'aklor\\n', 'output': 'r\\n'}, {'type': 'stdin_stdout', 'input': 'zy\\n', 'output': 'z\\n'}, {'type': 'stdin_stdout', 'input': 'ollehomleh\\n', 'output': 'oo\\n'}, {'type': 'stdin_stdout', 'input': 'reeer\\n', 'output': 'rr\\n'}, {'type': 'stdin_stdout', 'input': 'urubra\\n', 'output': 'uu\\n'}, {'type': 'stdin_stdout', 'input': 'sattorue\\n', 'output': 'u\\n'}, {'type': 'stdin_stdout', 'input': 'yyzzzy\\n', 'output': 'zzz\\n'}, {'type': 'stdin_stdout', 'input': 'ybz\\n', 'output': 'z\\n'}, {'type': 'stdin_stdout', 'input': 'ppississin\\n', 'output': 'ssss\\n'}, {'type': 'stdin_stdout', 'input': 'owwwowwob\\n', 'output': 'wwwww\\n'}, {'type': 'stdin_stdout', 'input': 'codfeorcfs\\n', 'output': 's\\n'}, {'type': 'stdin_stdout', 'input': 'sadaq\\n', 'output': 's\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80137","program":"```python\n# -*- coding: utf-8 -*-\n\"\"\"\nCreated on Thu Apr 2 19:56:34 2020\n\n@author: roastedcoder\n\nThis is for CodeForces\n\"\"\"\nmod = 1000000007\nssi = lambda : map(int,input().split())\n\n# RoastedCoder\n\ns = input()\nl = [0]*26\nfor i in range(len(s)):\n l[ord(s[i])-97] += 1\n \nfor i in range(25,-1,-1):\n if(l[i] >= 1):\n print(chr(i+97)*l[i])\n break\n```","inputs":"mississipp\n","output":"ssss\n","actual_output":"ssss\n","execution_success":true,"sample_index":12761},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"250_C. Movie Critics","prompt":"Solve the following coding problem using the programming language python:\n\nA film festival is coming up in the city N. The festival will last for exactly n days and each day will have a premiere of exactly one film. Each film has a genre \u2014 an integer from 1 to k.\n\nOn the i-th day the festival will show a movie of genre ai. We know that a movie of each of k genres occurs in the festival programme at least once. In other words, each integer from 1 to k occurs in the sequence a1, a2, ..., an at least once.\n\nValentine is a movie critic. He wants to watch some movies of the festival and then describe his impressions on his site.\n\nAs any creative person, Valentine is very susceptive. After he watched the movie of a certain genre, Valentine forms the mood he preserves until he watches the next movie. If the genre of the next movie is the same, it does not change Valentine's mood. If the genres are different, Valentine's mood changes according to the new genre and Valentine has a stress.\n\nValentine can't watch all n movies, so he decided to exclude from his to-watch list movies of one of the genres. In other words, Valentine is going to choose exactly one of the k genres and will skip all the movies of this genre. He is sure to visit other movies.\n\nValentine wants to choose such genre x (1 \u2264 x \u2264 k), that the total number of after-movie stresses (after all movies of genre x are excluded) were minimum.\n\nInput\n\nThe first line of the input contains two integers n and k (2 \u2264 k \u2264 n \u2264 105), where n is the number of movies and k is the number of genres.\n\nThe second line of the input contains a sequence of n positive integers a1, a2, ..., an (1 \u2264 ai \u2264 k), where ai is the genre of the i-th movie. It is guaranteed that each number from 1 to k occurs at least once in this sequence.\n\nOutput\n\nPrint a single number \u2014 the number of the genre (from 1 to k) of the excluded films. If there are multiple answers, print the genre with the minimum number.\n\nExamples\n\nInput\n\n10 3\n1 1 2 3 2 3 3 1 1 3\n\n\nOutput\n\n3\n\nInput\n\n7 3\n3 1 3 2 3 1 2\n\n\nOutput\n\n1\n\nNote\n\nIn the first sample if we exclude the movies of the 1st genre, the genres 2, 3, 2, 3, 3, 3 remain, that is 3 stresses; if we exclude the movies of the 2nd genre, the genres 1, 1, 3, 3, 3, 1, 1, 3 remain, that is 3 stresses; if we exclude the movies of the 3rd genre the genres 1, 1, 2, 2, 1, 1 remain, that is 2 stresses.\n\nIn the second sample whatever genre Valentine excludes, he will have exactly 3 stresses.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# ------------------- fast io --------------------\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n\nBUFSIZE = 8192\n\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\n\n# ------------------- fast io --------------------\nfrom math import gcd, ceil\n\ndef pre(s):\n n = len(s)\n pi = [0] * n\n for i in range(1, n):\n j = pi[i - 1]\n while j and s[i] != s[j]:\n j = pi[j - 1]\n if s[i] == s[j]:\n j += 1\n pi[i] = j\n return pi\n\n\ndef prod(a):\n ans = 1\n for each in a:\n ans = (ans * each)\n return ans\n\ndef lcm(a, b): return a * b // gcd(a, b)\n\n\ndef binary(x, length=16):\n y = bin(x)[2:]\n return y if len(y) >= length else \"0\" * (length - len(y)) + y\n\n\nfor _ in range(int(input()) if not True else 1):\n #n = int(input())\n n, k = map(int, input().split())\n #a, b = map(int, input().split())\n #c, d = map(int, input().split())\n a = list(map(int, input().split()))\n #b = list(map(int, input().split()))\n #s = input()\n b = [a[0]]\n for i in range(1, n):\n if a[i] == b[-1]:\n continue\n else:\n b += [a[i]]\n di = {}\n for i in range(len(b)):\n if b[i] not in di:\n di[b[i]] = []\n di[b[i]] += [i]\n total = len(b) - 1\n ans = [0]*(k+1)\n for i in range(1, k+1):\n ans[i] = total - len(di[i])\n for i in range(1, k+1):\n for j in range(len(di[i])):\n if di[i][j] and di[i][j]+1 != len(b) and b[di[i][j]-1] == b[di[i][j]+1]:\n ans[i] -= 1\n ans[0] = 9999999999999\n print(ans.index(min(ans)))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7 3\\n3 1 3 2 3 1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 3\\n1 1 2 3 2 3 3 1 1 3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n5 7 8 2 4 10 1 3 9 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100 12\\n9 12 3 3 1 3 12 12 7 9 6 5 8 12 10 7 8 3 4 8 5 9 9 10 9 7 4 5 10 7 4 1 11 6 5 9 1 2 9 9 1 10 6 8 9 10 7 9 10 3 6 4 9 12 11 10 4 4 2 12 11 8 4 9 12 6 4 7 5 1 5 2 7 4 10 2 5 6 4 2 5 8 6 9 6 4 8 6 2 11 4 12 3 1 1 11 1 6 1 10\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 6 1 12 13 9 5 3 7 3 5 2 2 10 1 3 8 9 4 4 4 2 10 12 11 1 5 7 13 4 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 8 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '129 37\\n15 22 28 15 30 16 11 20 4 26 14 37 29 17 15 15 14 18 1 9 16 22 13 32 5 18 25 11 6 33 33 22 17 9 1 5 27 27 37 4 6 1 3 18 11 33 6 17 2 24 23 1 1 37 35 21 21 17 18 6 31 17 29 18 10 10 30 31 8 3 25 20 34 11 12 12 24 13 5 27 20 31 28 3 36 2 4 13 14 9 33 25 4 26 36 6 2 7 15 9 20 33 24 33 28 12 23 1 28 12 29 3 35 33 26 15 3 19 1 23 23 32 2 27 11 7 36 34 36\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 2\\n1 2 2 1 1 2 1 1 2 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '74 10\\n10 5 4 7 1 9 3 5 10 7 1 4 8 8 4 1 3 9 3 3 10 6 10 4 2 8 9 7 3 2 5 3 6 7 10 4 4 7 8 2 3 10 5 10 5 10 7 9 9 6 1 10 8 9 7 8 9 10 3 6 10 9 9 5 10 6 4 3 5 3 6 8 9 3\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '100 10\\n6 2 8 1 7 1 2 9 2 6 10 4 2 8 7 5 2 9 5 2 3 2 8 3 7 2 4 3 1 8 8 5 7 10 2 1 8 4 1 4 9 4 2 1 9 3 7 2 4 8 4 3 10 3 9 5 7 7 1 2 10 7 7 8 9 7 1 7 4 8 9 4 1 10 2 4 2 10 9 6 10 5 1 4 2 1 3 1 6 9 10 1 8 9 1 9 1 1 7 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '113 3\\n1 3 2 2 1 3 1 2 2 2 3 1 1 3 1 3 3 1 2 2 1 3 2 3 3 1 3 1 1 3 3 1 2 3 3 1 3 3 2 3 3 1 1 1 1 2 3 2 2 3 3 2 3 1 3 2 1 3 2 1 1 2 2 2 2 2 1 1 3 3 2 1 1 3 2 2 1 3 1 1 1 3 3 2 1 2 2 3 3 1 3 1 2 2 1 2 2 3 3 2 3 1 3 1 1 2 3 2 3 2 3 1 3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '100 12\\n9 12 3 3 1 3 12 12 7 9 6 5 8 12 10 7 8 3 4 8 5 9 9 10 9 7 4 5 10 7 4 1 11 6 5 9 1 2 9 9 1 10 6 8 9 10 7 9 10 3 6 4 9 12 11 10 4 4 2 12 11 8 4 9 12 6 4 7 5 1 5 2 7 4 10 2 5 6 4 2 5 8 6 9 6 1 8 6 2 11 4 12 3 1 1 11 1 6 1 10\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 6 1 12 13 9 5 3 7 3 5 2 2 10 1 3 8 9 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 8 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '129 37\\n15 22 28 15 30 16 11 20 4 26 14 37 29 17 15 15 14 18 1 9 16 22 13 32 5 18 25 11 6 33 33 22 17 9 1 5 27 27 37 4 6 1 3 18 11 33 6 17 2 24 23 1 1 37 35 21 21 17 18 6 31 17 29 18 10 10 30 31 8 3 25 20 34 11 12 12 24 13 5 27 20 31 28 1 36 2 4 13 14 9 33 25 4 26 36 6 2 7 15 9 20 33 24 33 28 12 23 1 28 12 29 3 35 33 26 15 3 19 1 23 23 32 2 27 11 7 36 34 36\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '74 10\\n10 5 4 7 1 9 3 5 10 7 1 4 8 8 4 1 3 9 3 3 10 6 10 4 2 8 9 7 3 2 5 6 6 7 10 4 4 7 8 2 3 10 5 10 5 10 7 9 9 6 1 10 8 9 7 8 9 10 3 6 10 9 9 5 10 6 4 3 5 3 6 8 9 3\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '100 12\\n9 12 3 3 1 3 12 12 7 9 6 5 8 12 10 7 8 3 4 8 5 9 9 10 9 7 4 5 10 7 4 1 11 6 5 9 1 2 9 9 1 10 6 8 9 10 7 5 10 3 6 4 9 12 11 10 4 4 2 12 11 8 4 9 12 6 4 7 5 1 5 2 7 4 10 2 5 6 4 2 5 8 6 9 6 4 8 6 2 11 4 12 3 1 1 11 1 6 1 10\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10 3\\n1 2 2 3 2 3 3 1 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '129 37\\n15 22 28 15 30 16 11 20 4 26 14 37 29 17 15 15 3 18 1 9 16 22 13 32 5 18 25 11 6 33 33 22 17 9 1 5 27 27 37 4 6 1 3 18 11 33 6 17 2 24 23 1 1 37 35 21 21 17 18 6 31 17 29 18 10 17 30 31 8 3 25 20 34 11 12 12 24 13 5 27 20 31 28 1 36 2 4 13 14 9 33 25 4 26 36 6 2 7 15 9 20 33 24 5 28 12 23 1 28 12 29 3 35 33 26 15 3 19 1 23 23 32 2 27 11 7 36 17 36\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '100 12\\n9 12 3 3 1 3 12 12 7 9 6 5 8 12 10 7 8 3 4 8 5 9 9 10 9 7 4 5 10 7 4 1 11 6 5 9 1 2 9 9 1 10 6 8 9 10 7 9 10 3 6 4 9 6 11 10 4 4 2 12 11 8 4 9 12 6 4 7 5 1 5 2 7 4 10 2 5 6 4 2 5 8 6 9 6 4 8 6 2 11 4 12 3 1 1 11 1 6 1 10\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '100 10\\n6 2 8 1 7 1 2 9 2 6 10 4 2 8 7 5 2 9 5 2 3 2 8 3 7 2 4 3 1 8 8 5 7 10 2 1 8 4 1 4 9 4 2 1 9 3 7 2 4 8 4 3 10 3 9 5 7 7 1 2 10 7 7 8 9 7 1 7 4 8 9 4 1 10 2 4 2 10 9 6 10 5 1 4 2 1 3 1 6 9 10 1 9 9 1 9 1 1 7 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '113 3\\n1 3 2 2 1 3 1 2 2 2 3 1 1 3 1 3 3 1 2 2 1 3 2 3 3 1 3 1 1 3 3 1 2 3 3 1 3 3 2 3 3 1 1 1 1 2 3 2 2 3 3 2 3 1 3 2 1 3 2 1 1 2 2 2 2 2 1 2 3 3 2 1 1 3 2 2 1 3 1 1 1 3 3 2 1 2 2 3 3 1 3 1 2 2 1 2 2 3 3 2 3 1 3 1 1 2 3 2 3 2 3 1 3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 4 1 12 13 9 5 3 7 3 5 2 2 10 1 3 8 9 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 8 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 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5 3 7 3 5 2 2 10 1 2 8 9 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 8 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 6 1 12 13 9 5 3 7 3 5 2 2 10 1 2 8 9 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 10 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 6 1 12 13 9 5 3 7 4 5 2 2 10 1 2 8 9 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 10 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 6 1 12 13 9 5 3 7 4 5 2 2 10 1 2 8 9 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 10 13 4 4 3 7 12 2 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 6 1 12 13 9 5 3 7 4 5 2 2 10 1 2 8 3 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 10 13 4 4 3 7 12 2 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '74 10\\n10 5 4 7 1 9 3 5 10 7 1 4 8 8 4 1 3 8 3 3 10 6 10 4 2 8 9 7 3 2 5 3 6 7 10 4 4 7 8 2 3 10 5 10 5 10 7 9 9 6 1 10 8 9 7 8 9 10 3 6 10 9 9 5 10 6 4 3 5 3 6 8 9 3\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\n3 1 2 2 3 1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 3\\n1 2 2 3 2 3 3 1 1 3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '100 12\\n9 12 3 3 1 3 12 12 7 9 6 5 8 12 10 7 8 3 4 8 5 9 9 10 9 7 4 5 10 7 4 1 11 6 5 9 1 2 9 9 1 10 6 8 9 10 7 9 10 3 6 4 9 12 11 10 4 4 2 12 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36 6 2 7 15 9 20 33 24 33 28 12 23 1 28 12 29 3 35 33 26 15 3 19 1 23 23 32 2 27 11 7 36 17 36\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100 10\\n6 2 8 1 7 1 2 9 2 6 10 4 2 8 7 5 2 9 5 2 3 2 8 3 7 2 4 3 1 8 8 5 7 10 2 1 8 1 1 4 9 4 4 1 9 3 7 2 4 8 4 3 10 3 9 5 7 7 1 2 10 7 7 8 9 7 1 7 4 8 9 4 1 10 2 4 2 10 9 6 10 5 1 4 2 1 3 1 6 9 10 1 9 9 1 9 1 1 7 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 6 1 12 13 9 5 3 7 3 5 2 2 10 1 2 8 9 4 4 4 2 10 12 6 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 8 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 6 1 12 13 9 5 3 7 3 5 2 2 10 1 2 8 9 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 5 8 8 9 10 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '10\\n'}, {'type': 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1 8 4 1 4 9 4 2 1 9 3 7 2 4 8 4 3 10 3 9 5 7 7 1 2 10 7 7 8 9 7 1 7 6 8 9 4 1 10 2 4 2 10 9 6 10 5 1 4 2 1 3 1 6 9 10 1 9 9 1 9 1 1 7 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 4 1 12 13 9 5 3 7 3 5 2 2 10 1 3 8 9 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 8 13 4 4 3 1 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '129 37\\n15 22 28 15 30 16 11 20 4 26 14 37 29 17 15 15 14 18 1 9 16 22 13 32 5 18 25 11 6 33 33 22 17 9 1 5 27 27 37 4 6 1 3 18 17 33 6 17 2 24 23 1 1 37 35 21 21 17 18 6 31 17 29 18 10 10 30 31 8 3 25 20 34 11 12 12 24 13 5 27 20 31 28 1 36 2 4 13 14 9 33 25 4 26 36 6 2 7 15 9 20 33 24 33 28 12 23 1 28 12 29 3 35 33 26 15 3 19 1 23 23 32 2 27 11 7 36 17 36\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '74 10\\n10 5 4 7 1 9 1 5 10 7 1 4 8 8 4 1 3 9 3 3 10 6 10 4 2 8 9 6 3 2 5 6 6 7 10 4 4 7 8 2 3 10 5 10 5 10 7 9 9 6 1 10 8 9 7 8 9 10 3 6 10 9 9 5 10 6 4 3 5 3 6 8 9 3\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 4 1 12 13 9 5 3 7 3 5 2 2 10 1 2 8 9 4 4 4 2 4 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 8 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '129 37\\n15 22 28 15 30 16 11 20 4 26 14 37 29 17 15 15 14 18 1 9 16 22 13 32 5 18 25 11 6 33 33 22 17 9 1 5 27 27 37 4 6 1 3 18 11 33 9 17 2 16 23 1 1 37 35 21 21 17 18 6 31 17 29 18 10 10 30 31 8 3 25 20 34 11 12 12 24 13 5 27 20 31 28 1 36 2 4 13 14 9 33 25 4 26 36 6 2 7 15 9 20 33 24 33 28 12 23 1 28 12 29 3 35 33 26 15 3 19 1 23 23 32 2 27 11 7 36 17 36\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '74 10\\n10 5 4 7 1 8 3 5 10 7 1 4 8 8 4 1 3 9 3 3 10 6 10 4 2 8 9 6 3 2 5 6 6 7 10 4 4 7 8 2 3 10 5 10 5 10 7 9 9 6 1 10 8 9 7 7 9 10 3 6 10 9 9 5 10 6 4 3 5 3 6 8 9 3\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 6 1 12 13 9 5 3 7 3 5 2 2 10 1 2 8 9 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 2 1 7 2 2 4 10 2 10 6 11 13 1 4 3 8 8 9 8 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '100 13\\n1 1 9 10 6 1 12 13 9 5 3 7 3 5 2 2 10 1 2 8 9 4 4 4 2 10 12 11 1 5 7 13 6 12 5 9 3 13 5 10 7 1 1 7 2 2 4 10 3 10 6 11 13 1 4 3 8 8 9 10 13 4 4 3 7 12 5 5 8 13 1 9 8 12 12 10 4 7 7 12 1 4 3 4 9 6 4 13 10 12 10 9 8 13 13 5 6 9 7 13\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '100 12\\n9 12 3 3 1 3 12 12 7 9 6 5 8 12 10 7 8 3 4 8 5 9 9 10 9 7 4 5 10 7 4 1 11 6 5 9 1 2 9 9 1 10 6 8 9 10 7 5 10 3 6 4 1 12 11 10 4 4 2 12 11 8 4 9 12 6 4 7 5 1 5 2 7 4 10 2 5 6 4 2 5 8 6 9 6 4 8 6 2 11 4 12 3 1 1 11 1 6 1 10\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '74 10\\n10 5 4 7 1 9 3 5 10 7 1 4 8 8 4 1 3 8 3 3 10 6 10 4 2 8 9 7 3 2 5 3 6 7 10 4 4 7 8 2 3 7 5 10 5 10 7 9 9 6 1 10 8 9 7 8 9 10 3 6 10 9 9 5 10 6 4 3 5 3 6 8 9 3\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\n3 1 2 3 3 1 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10 3\\n1 2 2 3 2 3 1 1 1 3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '100 12\\n9 12 3 3 1 3 12 12 7 9 6 5 8 12 10 7 8 3 4 8 5 9 9 10 9 7 4 5 10 7 4 1 11 6 5 9 1 2 9 9 1 10 6 8 9 10 7 9 10 3 6 4 9 12 11 10 4 4 2 12 11 8 3 9 12 6 4 7 5 1 1 2 7 4 10 2 5 6 4 2 5 8 6 9 6 1 8 6 2 11 4 12 3 1 1 11 1 6 1 10\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '129 37\\n15 22 28 15 30 16 11 20 4 26 14 37 29 17 15 15 3 18 1 9 16 22 13 32 5 18 25 11 6 33 33 22 17 9 1 5 27 27 37 4 6 1 3 18 11 33 6 17 2 24 23 1 1 37 35 21 21 17 18 6 31 17 29 18 10 10 30 31 8 4 25 20 34 11 12 12 24 13 5 27 20 31 28 1 36 2 4 13 14 9 33 25 4 26 36 6 2 7 15 9 20 33 24 33 28 12 23 1 28 12 29 3 35 33 26 15 3 19 1 23 23 32 2 27 11 7 36 17 36\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80145","program":"```python\n# ------------------- fast io --------------------\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n\nBUFSIZE = 8192\n\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\n\n# ------------------- fast io --------------------\nfrom math import gcd, ceil\n\ndef pre(s):\n n = len(s)\n pi = [0] * n\n for i in range(1, n):\n j = pi[i - 1]\n while j and s[i] != s[j]:\n j = pi[j - 1]\n if s[i] == s[j]:\n j += 1\n pi[i] = j\n return pi\n\n\ndef prod(a):\n ans = 1\n for each in a:\n ans = (ans * each)\n return ans\n\ndef lcm(a, b): return a * b // gcd(a, b)\n\n\ndef binary(x, length=16):\n y = bin(x)[2:]\n return y if len(y) >= length else \"0\" * (length - len(y)) + y\n\n\nfor _ in range(int(input()) if not True else 1):\n #n = int(input())\n n, k = map(int, input().split())\n #a, b = map(int, input().split())\n #c, d = map(int, input().split())\n a = list(map(int, input().split()))\n #b = list(map(int, input().split()))\n #s = input()\n b = [a[0]]\n for i in range(1, n):\n if a[i] == b[-1]:\n continue\n else:\n b += [a[i]]\n di = {}\n for i in range(len(b)):\n if b[i] not in di:\n di[b[i]] = []\n di[b[i]] += [i]\n total = len(b) - 1\n ans = [0]*(k+1)\n for i in range(1, k+1):\n ans[i] = total - len(di[i])\n for i in range(1, k+1):\n for j in range(len(di[i])):\n if di[i][j] and di[i][j]+1 != len(b) and b[di[i][j]-1] == b[di[i][j]+1]:\n ans[i] -= 1\n ans[0] = 9999999999999\n print(ans.index(min(ans)))\n```","inputs":"7 3\n3 1 3 2 3 1 2\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12762},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"275_D. Zero Tree","prompt":"Solve the following coding problem using the programming language python:\n\nA tree is a graph with n vertices and exactly n - 1 edges; this graph should meet the following condition: there exists exactly one shortest (by number of edges) path between any pair of its vertices.\n\nA subtree of a tree T is a tree with both vertices and edges as subsets of vertices and edges of T.\n\nYou're given a tree with n vertices. Consider its vertices numbered with integers from 1 to n. Additionally an integer is written on every vertex of this tree. Initially the integer written on the i-th vertex is equal to vi. In one move you can apply the following operation:\n\n 1. Select the subtree of the given tree that includes the vertex with number 1. \n 2. Increase (or decrease) by one all the integers which are written on the vertices of that subtree. \n\n\n\nCalculate the minimum number of moves that is required to make all the integers written on the vertices of the given tree equal to zero.\n\nInput\n\nThe first line of the input contains n (1 \u2264 n \u2264 105). Each of the next n - 1 lines contains two integers ai and bi (1 \u2264 ai, bi \u2264 n; ai \u2260 bi) indicating there's an edge between vertices ai and bi. It's guaranteed that the input graph is a tree. \n\nThe last line of the input contains a list of n space-separated integers v1, v2, ..., vn (|vi| \u2264 109).\n\nOutput\n\nPrint the minimum number of operations needed to solve the task.\n\nPlease, do not write the %lld specifier to read or write 64-bit integers in \u0421++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\nExamples\n\nInput\n\n3\n1 2\n1 3\n1 -1 1\n\n\nOutput\n\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\n\ndef minp():\n\treturn sys.stdin.readline().strip()\n\nn = int(minp())\ne = [0]\np = [None]*(n+1)\nfor i in range(n):\n\te.append([])\nfor i in range(n-1):\n\ta, b = map(int,minp().split())\n\te[a].append(b)\n\te[b].append(a)\nv = list(map(int,minp().split()))\nplus = [0]*(n+1)\nminus = [0]*(n+1)\n\nwas = [False]*(n+1)\nwas[1] = True\ni = 0\nj = 1\nq = [0]*(n+100)\nq[0] = 1\np[1] = 0\nwhile i < j:\n\tx = q[i]\n\ti += 1\n\tfor y in e[x]:\n\t\tif not was[y]:\n\t\t\twas[y] = True\n\t\t\tp[y] = x\n\t\t\tq[j] = y\n\t\t\tj += 1\n\ni = j-1\nwhile i >= 0:\n\tx = q[i]\n\ti -= 1\n\ts = minus[x] - plus[x]\n\tz = v[x-1] + s\n\tpp = p[x]\n\t#print(x, p[x], plus[x], minus[x], '-', s[x], v[x-1]+s[x], v[0]+s[1])\n\t#print(-(plus[x]-minus[x]),s[x])\n\tminus[pp] = max(minus[x],minus[pp])\n\tplus[pp] = max(plus[x],plus[pp])\n\tif z > 0:\n\t\tplus[pp] = max(plus[pp],plus[x]+z)\n\telif z < 0:\n\t\tminus[pp] = max(minus[pp],minus[x]-z)\n#print(v[0])\n#print(plus[0], minus[0])\nprint(plus[0] + minus[0])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 2\\n1 3\\n1 -1 1\\n', 'output': '3'}, {'type': 'stdin_stdout', 'input': '5\\n2 3\\n4 5\\n2 5\\n1 3\\n0 2 1 4 3\\n', 'output': '8'}, {'type': 'stdin_stdout', 'input': '5\\n3 1\\n2 4\\n3 4\\n2 5\\n0 -3 -1 2 4\\n', 'output': '20'}, {'type': 'stdin_stdout', 'input': '12\\n1 6\\n10 1\\n4 1\\n7 1\\n1 2\\n5 1\\n1 8\\n1 11\\n3 1\\n12 1\\n9 1\\n580660007 861441526 -264928594 488291045 253254575 -974301934 709266786 926718320 87511873 514836444 -702876508 848928657\\n', 'output': '2529263875'}, {'type': 'stdin_stdout', 'input': '10\\n5 6\\n8 2\\n9 3\\n4 1\\n6 10\\n9 8\\n7 10\\n7 4\\n5 2\\n0 -6 -9 -1 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256000000}","problem_id":"vfc_80149","program":"```python\nimport sys\n\ndef minp():\n\treturn sys.stdin.readline().strip()\n\nn = int(minp())\ne = [0]\np = [None]*(n+1)\nfor i in range(n):\n\te.append([])\nfor i in range(n-1):\n\ta, b = map(int,minp().split())\n\te[a].append(b)\n\te[b].append(a)\nv = list(map(int,minp().split()))\nplus = [0]*(n+1)\nminus = [0]*(n+1)\n\nwas = [False]*(n+1)\nwas[1] = True\ni = 0\nj = 1\nq = [0]*(n+100)\nq[0] = 1\np[1] = 0\nwhile i < j:\n\tx = q[i]\n\ti += 1\n\tfor y in e[x]:\n\t\tif not was[y]:\n\t\t\twas[y] = True\n\t\t\tp[y] = x\n\t\t\tq[j] = y\n\t\t\tj += 1\n\ni = j-1\nwhile i >= 0:\n\tx = q[i]\n\ti -= 1\n\ts = minus[x] - plus[x]\n\tz = v[x-1] + s\n\tpp = p[x]\n\t#print(x, p[x], plus[x], minus[x], '-', s[x], v[x-1]+s[x], v[0]+s[1])\n\t#print(-(plus[x]-minus[x]),s[x])\n\tminus[pp] = max(minus[x],minus[pp])\n\tplus[pp] = max(plus[x],plus[pp])\n\tif z > 0:\n\t\tplus[pp] = max(plus[pp],plus[x]+z)\n\telif z < 0:\n\t\tminus[pp] = max(minus[pp],minus[x]-z)\n#print(v[0])\n#print(plus[0], minus[0])\nprint(plus[0] + minus[0])\n```","inputs":"3\n1 2\n1 3\n1 -1 1\n","output":"3","actual_output":"3\n","execution_success":true,"sample_index":12763},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"299_A. Ksusha and Array","prompt":"Solve the following coding problem using the programming language python:\n\nKsusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers.\n\nHer university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number!\n\nInput\n\nThe first line contains integer n (1 \u2264 n \u2264 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 \u2264 ai \u2264 109) \u2014 the array elements.\n\nOutput\n\nPrint a single integer \u2014 the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1.\n\nIf there are multiple answers, you are allowed to print any of them.\n\nExamples\n\nInput\n\n3\n2 2 4\n\n\nOutput\n\n2\n\n\nInput\n\n5\n2 1 3 1 6\n\n\nOutput\n\n1\n\n\nInput\n\n3\n2 3 5\n\n\nOutput\n\n-1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ninput()\nline = list(map(int, input().split()))\nline.sort()\nfor i in line:\n if i % line[0] != 0:\n print(-1)\n break\nelse:\n print(line[0])\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n2 3 5\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 3 1 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6 4\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 2 2 1000000000\\n', 'output': '2\\n'}, {'type': 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'2\\n1652727252 1100100001\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 20\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1652727252 0100100001\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1652727252 0100000001\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n257465809 0100000001\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80153","program":"```python\ninput()\nline = list(map(int, input().split()))\nline.sort()\nfor i in line:\n if i % line[0] != 0:\n print(-1)\n break\nelse:\n print(line[0])\n\n```","inputs":"3\n2 3 5\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12764},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"346_B. Lucky Common Subsequence","prompt":"Solve the following coding problem using the programming language python:\n\nIn mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence BDF is a subsequence of ABCDEF. A substring of a string is a continuous subsequence of the string. For example, BCD is a substring of ABCDEF.\n\nYou are given two strings s1, s2 and another string called virus. Your task is to find the longest common subsequence of s1 and s2, such that it doesn't contain virus as a substring.\n\nInput\n\nThe input contains three strings in three separate lines: s1, s2 and virus (1 \u2264 |s1|, |s2|, |virus| \u2264 100). Each string consists only of uppercase English letters.\n\nOutput\n\nOutput the longest common subsequence of s1 and s2 without virus as a substring. If there are multiple answers, any of them will be accepted. \n\nIf there is no valid common subsequence, output 0.\n\nExamples\n\nInput\n\nAJKEQSLOBSROFGZ\nOVGURWZLWVLUXTH\nOZ\n\n\nOutput\n\nORZ\n\n\nInput\n\nAA\nA\nA\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n#Not actually my code, solved mentally, only submitting to mark as solved so I don't do it again.\n\ndef gen(i, j):\n if a[i][j] == -1:\n a[i][j] = max(gen(i - 1, j - 1) + s2[i - 1] * (s2[i - 1] == s1[j - 1]), gen(i - 1, j), gen(i, j - 1), key = lambda x: [len(x), -x.count(viru)])\n return a[i][j]\n\n\ns1, s2, viru = [input() for x in range(3)]\na = [[''] * (len(s1) + 1)] + [[''] + [-1] * (len(s1)) for x in range(len(s2))]\nans = gen(len(s2), len(s1))\nwhile viru in ans:\n ans = min(ans.replace(viru, viru[:-1]), ans.replace(viru, viru[1:]), key = lambda x: x.count(viru))\nprint(ans + '0' * (ans == ''))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'AA\\nA\\nA\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'AJKEQSLOBSROFGZ\\nOVGURWZLWVLUXTH\\nOZ\\n', 'output': 'OGZ'}, {'type': 'stdin_stdout', 'input': 'ABABBB\\nABABBB\\nABB\\n', 'output': 'BBBB'}, {'type': 'stdin_stdout', 'input': 'ABABABAC\\nABABABAC\\nABABAC\\n', 'output': 'ABBABAC'}, {'type': 'stdin_stdout', 'input': 'DASSDASDASDDAASDASDADASDASASDAS\\nSDADASDASSDAASDASDASDADASSDDA\\nSD\\n', 'output': 'DADADADAADADADADASSA\\n'}, {'type': 'stdin_stdout', 'input': 'ABBB\\nABBB\\nABB\\n', 'output': 'BBB'}, {'type': 'stdin_stdout', 'input': 'GOZVMIRQIGYGVAGOREQTXFXPEZYOJOXPNDGAESICXHMKQDXQPRLMRVWHXFEJVCWZDLYMQLDURUXZPTLEHPTSKXGSNEQDKLVFFLDX\\nIMEVFCZXACKRRJVXDRKFWTLTRTLQQDHEBZLCOCNVPABQMIWJHRLKFUKWOVVWGGNWCJNRYOYOAJFQWCLHQIQRBZTVWKBFOXKEHHQP\\nSZ\\n', 'output': 'IEFZXACKRRVXFWLRTLHPKGNQLVFX'}, {'type': 'stdin_stdout', 'input': 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== s1[j - 1]), gen(i - 1, j), gen(i, j - 1), key = lambda x: [len(x), -x.count(viru)])\n return a[i][j]\n\n\ns1, s2, viru = [input() for x in range(3)]\na = [[''] * (len(s1) + 1)] + [[''] + [-1] * (len(s1)) for x in range(len(s2))]\nans = gen(len(s2), len(s1))\nwhile viru in ans:\n ans = min(ans.replace(viru, viru[:-1]), ans.replace(viru, viru[1:]), key = lambda x: x.count(viru))\nprint(ans + '0' * (ans == ''))\n```","inputs":"AA\nA\nA\n","output":"0","actual_output":"0\n","execution_success":true,"sample_index":12765},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"414_A. Mashmokh and Numbers","prompt":"Solve the following coding problem using the programming language python:\n\nIt's holiday. Mashmokh and his boss, Bimokh, are playing a game invented by Mashmokh. \n\nIn this game Mashmokh writes sequence of n distinct integers on the board. Then Bimokh makes several (possibly zero) moves. On the first move he removes the first and the second integer from from the board, on the second move he removes the first and the second integer of the remaining sequence from the board, and so on. Bimokh stops when the board contains less than two numbers. When Bimokh removes numbers x and y from the board, he gets gcd(x, y) points. At the beginning of the game Bimokh has zero points.\n\nMashmokh wants to win in the game. For this reason he wants his boss to get exactly k points in total. But the guy doesn't know how choose the initial sequence in the right way. \n\nPlease, help him. Find n distinct integers a1, a2, ..., an such that his boss will score exactly k points. Also Mashmokh can't memorize too huge numbers. Therefore each of these integers must be at most 109.\n\nInput\n\nThe first line of input contains two space-separated integers n, k (1 \u2264 n \u2264 105; 0 \u2264 k \u2264 108).\n\nOutput\n\nIf such sequence doesn't exist output -1 otherwise output n distinct space-separated integers a1, a2, ..., an (1 \u2264 ai \u2264 109).\n\nExamples\n\nInput\n\n5 2\n\n\nOutput\n\n1 2 3 4 5\n\n\nInput\n\n5 3\n\nOutput\n\n2 4 3 7 1\n\nInput\n\n7 2\n\n\nOutput\n\n-1\n\nNote\n\ngcd(x, y) is greatest common divisor of x and y.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom __future__ import division, print_function\n\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n\n\ndef main():\n n, k = [ int(x) for x in input().split() ]\n\n x = k - (n // 2 - 1)\n\n if x < 1 or (n < 2 and k > 0):\n print(-1)\n return\n\n sequence = [0] * n\n sequence[0] = x\n\n if n > 1:\n sequence[1] = 2*x\n\n if n >= 3:\n newValue = 1\n\n while newValue == x or newValue == 2*x \\\n or newValue + 1 == x or newValue + 1 == 2*x:\n newValue += 1\n\n sequence[2] = newValue\n\n for i in range(3, n):\n newValue = sequence[i-1] + 1\n\n if not(i & 1):\n while newValue == x or newValue == 2*x \\\n or newValue + 1 == x or newValue + 1 == 2*x:\n newValue += 1\n\n sequence[i] = newValue\n\n print(' '.join(map(lambda x: str(x), sequence)))\n\n\nBUFFSIZE = 8192\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\n\ndef print(*args, **kwargs):\n sep = kwargs.pop(\"sep\", \" \")\n file = kwargs.pop(\"file\", sys.stdout)\n\n atStart = True\n for x in args:\n if not atStart:\n file.write(sep)\n file.write(str(x))\n atStart = False\n file.write(kwargs.pop(\"end\", \"\\n\"))\n\n if kwargs.pop(\"flush\", False):\n file.flush()\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\n\nmain()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7 2\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n', 'output': '1 2 3 4 5'}, {'type': 'stdin_stdout', 'input': '5 3', 'output': '2 4 5 6 7'}, {'type': 'stdin_stdout', 'input': '4 1257\\n', 'output': '1256 2512 2513 2514 '}, {'type': 'stdin_stdout', 'input': '25095 2372924\\n', 'output': '2360378 4720756 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 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21399 21400 21401 21402 21403 21404 21405 21406 21407 21408 21409 21410 21411 21412 21413 21414 21415 21416 21417 21418 21419 21420 21421 21422 21423 21424 21425 21426 21427 21428 21429 21430 21431 21432 21433 21434 21435 21436 21437 21438 21439 21440 21441 21442 21443 21444 21445 21446 21447 21448 21449 21450 21451 21452 21453 21454 21455 21456 21457 21458 '}, {'type': 'stdin_stdout', 'input': '10 50000006\\n', 'output': '50000002 100000004 100000005 100000006 100000007 100000008 100000009 100000010 100000011 100000012 '}, {'type': 'stdin_stdout', 'input': '10 3000004\\n', 'output': '3000000 6000000 6000001 6000002 6000003 6000004 6000005 6000006 6000007 6000008 '}, {'type': 'stdin_stdout', 'input': '7695 94816808\\n', 'output': '94812962 189625924 189625925 189625926 189625927 189625928 189625929 189625930 189625931 189625932 189625933 189625934 189625935 189625936 189625937 189625938 189625939 189625940 189625941 189625942 189625943 189625944 189625945 189625946 189625947 189625948 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13301 13302 13303 13304 13305 13306 13307 13308 13309 13310 13311 13312 13313 13314 13315 13316 13317 13318 13319 \\n'}, {'type': 'stdin_stdout', 'input': '3 1\\n', 'output': '1 2 3 \\n'}, {'type': 'stdin_stdout', 'input': '5 99999997\\n', 'output': '99999996 199999992 1 2 3 \\n'}, {'type': 'stdin_stdout', 'input': '30997 73830196\\n', 'output': '73814699 147629398 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 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30874 30875 30876 30877 30878 30879 30880 30881 30882 30883 30884 30885 30886 30887 30888 30889 30890 30891 30892 30893 30894 30895 30896 30897 30898 30899 30900 30901 30902 30903 30904 30905 30906 30907 30908 30909 30910 30911 30912 30913 30914 30915 30916 30917 30918 30919 30920 30921 30922 30923 30924 30925 30926 30927 30928 30929 30930 30931 30932 30933 30934 30935 30936 30937 30938 30939 30940 30941 30942 30943 30944 30945 30946 30947 30948 30949 30950 30951 30952 30953 30954 30955 30956 30957 30958 30959 30960 30961 30962 30963 30964 30965 30966 30967 30968 30969 30970 30971 30972 30973 30974 30975 30976 30977 30978 30979 30980 30981 30982 30983 30984 30985 30986 30987 30988 30989 30990 30991 30992 30993 30994 30995 \\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '10000 16\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '101 1\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1 10000003\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '7 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '4 0\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '12 3\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80173","program":"```python\nfrom __future__ import division, print_function\n\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n\n\ndef main():\n n, k = [ int(x) for x in input().split() ]\n\n x = k - (n // 2 - 1)\n\n if x < 1 or (n < 2 and k > 0):\n print(-1)\n return\n\n sequence = [0] * n\n sequence[0] = x\n\n if n > 1:\n sequence[1] = 2*x\n\n if n >= 3:\n newValue = 1\n\n while newValue == x or newValue == 2*x \\\n or newValue + 1 == x or newValue + 1 == 2*x:\n newValue += 1\n\n sequence[2] = newValue\n\n for i in range(3, n):\n newValue = sequence[i-1] + 1\n\n if not(i & 1):\n while newValue == x or newValue == 2*x \\\n or newValue + 1 == x or newValue + 1 == 2*x:\n newValue += 1\n\n sequence[i] = newValue\n\n print(' '.join(map(lambda x: str(x), sequence)))\n\n\nBUFFSIZE = 8192\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\ninput = lambda: sys.stdin.readline().rstrip(\"\\r\\n\")\n\ndef print(*args, **kwargs):\n sep = kwargs.pop(\"sep\", \" \")\n file = kwargs.pop(\"file\", sys.stdout)\n\n atStart = True\n for x in args:\n if not atStart:\n file.write(sep)\n file.write(str(x))\n atStart = False\n file.write(kwargs.pop(\"end\", \"\\n\"))\n\n if kwargs.pop(\"flush\", False):\n file.flush()\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\n\nmain()\n\n```","inputs":"7 2\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12766},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"440_C. One-Based Arithmetic","prompt":"Solve the following coding problem using the programming language python:\n\nProf. Vasechkin wants to represent positive integer n as a sum of addends, where each addends is an integer number containing only 1s. For example, he can represent 121 as 121=111+11+\u20131. Help him to find the least number of digits 1 in such sum.\n\nInput\n\nThe first line of the input contains integer n (1 \u2264 n < 1015).\n\nOutput\n\nPrint expected minimal number of digits 1.\n\nExamples\n\nInput\n\n121\n\n\nOutput\n\n6\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\n\ndef find(n,i):\n\tans = 0\n\tk = n // ones[i]\n\tn = n % ones[i]\n\tans = ans + k * i\t\n\tif n == 0:\n\t\treturn ans\n\treturn ans + min(find(n, i-1), i + find(ones[i] - n, i-1))\n\nn = int(input())\nones = [0]\nfor i in range(1,17):\n\tone = 10 * ones[i-1] + 1\n\tones.append(one)\n\nprint(find(n,16))\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '121\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '5\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '768617061415848\\n', 'output': '390\\n'}, {'type': 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'input': '170806\\n', 'output': '66\\n'}, {'type': 'stdin_stdout', 'input': '15\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '623388\\n', 'output': '66\\n'}, {'type': 'stdin_stdout', 'input': '75\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '2486916438\\n', 'output': '137\\n'}, {'type': 'stdin_stdout', 'input': '1683620105259\\n', 'output': '252\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 0, 'nanos': 500000000}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80177","program":"```python\nimport math\n\ndef find(n,i):\n\tans = 0\n\tk = n // ones[i]\n\tn = n % ones[i]\n\tans = ans + k * i\t\n\tif n == 0:\n\t\treturn ans\n\treturn ans + min(find(n, i-1), i + find(ones[i] - n, i-1))\n\nn = int(input())\nones = [0]\nfor i in range(1,17):\n\tone = 10 * ones[i-1] + 1\n\tones.append(one)\n\nprint(find(n,16))\n\n\n```","inputs":"121\n","output":"6\n","actual_output":"6\n","execution_success":true,"sample_index":12767},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"486_D. Valid Sets","prompt":"Solve the following coding problem using the programming language python:\n\nAs you know, an undirected connected graph with n nodes and n - 1 edges is called a tree. You are given an integer d and a tree consisting of n nodes. Each node i has a value ai associated with it.\n\nWe call a set S of tree nodes valid if following conditions are satisfied:\n\n 1. S is non-empty.\n 2. S is connected. In other words, if nodes u and v are in S, then all nodes lying on the simple path between u and v should also be presented in S.\n 3. .\n\n\n\nYour task is to count the number of valid sets. Since the result can be very large, you must print its remainder modulo 1000000007 (109 + 7).\n\nInput\n\nThe first line contains two space-separated integers d (0 \u2264 d \u2264 2000) and n (1 \u2264 n \u2264 2000).\n\nThe second line contains n space-separated positive integers a1, a2, ..., an(1 \u2264 ai \u2264 2000).\n\nThen the next n - 1 line each contain pair of integers u and v (1 \u2264 u, v \u2264 n) denoting that there is an edge between u and v. It is guaranteed that these edges form a tree.\n\nOutput\n\nPrint the number of valid sets modulo 1000000007.\n\nExamples\n\nInput\n\n1 4\n2 1 3 2\n1 2\n1 3\n3 4\n\n\nOutput\n\n8\n\n\nInput\n\n0 3\n1 2 3\n1 2\n2 3\n\n\nOutput\n\n3\n\n\nInput\n\n4 8\n7 8 7 5 4 6 4 10\n1 6\n1 2\n5 8\n1 3\n3 5\n6 7\n3 4\n\n\nOutput\n\n41\n\nNote\n\nIn the first sample, there are exactly 8 valid sets: {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {3, 4} and {1, 3, 4}. Set {1, 2, 3, 4} is not valid, because the third condition isn't satisfied. Set {1, 4} satisfies the third condition, but conflicts with the second condition.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\n\n\ndef readInts(): return [int(x) for x in sys.stdin.readline().split()]\n\n\ndef readInt(): return int(sys.stdin.readline())\n\n\n# def print(x):\n # sys.stdout.write(str(x) + '\\n')\n\n\ndef solve():\n MOD = int(1e9 + 7)\n d, n = readInts()\n a = readInts()\n adj: list = [[] for _ in range(n)]\n for _ in range(n - 1):\n u, v = readInts()\n adj[u - 1].append(v - 1)\n adj[v - 1].append(u - 1)\n\n vis = [False for _ in range(n)]\n f = [0 for _ in range(n)]\n\n def dfs(cur, root):\n vis[cur] = True\n\n f[cur] = 1\n for neigh in adj[cur]:\n if vis[neigh]:\n continue\n if not (a[root] <= a[neigh] <= a[root] + d):\n continue\n if a[neigh] == a[root] and neigh < root:\n continue\n dfs(neigh, root)\n f[cur] *= f[neigh] + 1\n f[cur] %= MOD\n\n ans = 0\n for i in range(0, n):\n vis = [False for _ in range(n)]\n f = [0 for _ in range(n)]\n dfs(i, i)\n ans += f[i]\n ans %= MOD\n print(ans)\n\n\ndef main():\n t = 1\n # t = readInt()\n for _ in range(t):\n solve()\n\n\nmain()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 8\\n7 8 7 5 4 6 4 10\\n1 6\\n1 2\\n5 8\\n1 3\\n3 5\\n6 7\\n3 4\\n', 'output': '41'}, {'type': 'stdin_stdout', 'input': '0 3\\n1 2 3\\n1 2\\n2 3\\n', 'output': '3'}, {'type': 'stdin_stdout', 'input': '1 4\\n2 1 3 2\\n1 2\\n1 3\\n3 4\\n', 'output': '8'}, {'type': 'stdin_stdout', 'input': '18 29\\n18 2 24 10 8 10 19 12 16 2 2 23 15 17 29 13 10 14 21 8 2 13 23 29 20 3 18 16 22\\n11 23\\n10 19\\n14 22\\n14 17\\n25 26\\n7 25\\n7 11\\n6 13\\n1 3\\n12 28\\n1 2\\n8 18\\n6 8\\n9 12\\n2 9\\n4 14\\n1 20\\n6 15\\n4 10\\n5 6\\n21 27\\n2 16\\n7 21\\n1 5\\n19 29\\n6 7\\n9 24\\n1 4\\n', 'output': '13297'}, {'type': 'stdin_stdout', 'input': '0 22\\n1656 1462 1355 1133 1809 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12 35 10 37 29 39 35 10\\n4 6\\n7 12\\n9 15\\n2 5\\n4 8\\n4 17\\n6 21\\n22 23\\n21 22\\n6 10\\n1 9\\n1 14\\n1 4\\n11 13\\n1 24\\n1 2\\n6 18\\n7 16\\n6 25\\n8 11\\n17 19\\n10 20\\n2 3\\n4 7\\n', 'output': '125\\n'}, {'type': 'stdin_stdout', 'input': '0 20\\n78 1918 620 127 1022 1498 65 908 403 508 155 588 505 1277 104 1970 1408 285 1304 998\\n10 11\\n9 10\\n4 12\\n1 6\\n2 13\\n1 2\\n8 9\\n6 7\\n4 5\\n4 8\\n1 4\\n19 20\\n2 3\\n9 14\\n8 15\\n11 18\\n14 17\\n13 16\\n16 19\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '0 12\\n943 479 214 1646 151 565 846 1315 347 1766 1547 945\\n3 8\\n1 4\\n3 4\\n1 7\\n2 5\\n7 10\\n2 9\\n10 11\\n1 2\\n10 12\\n1 6\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '285 8\\n529 1024 747 126 492 1260 1837 251\\n2 4\\n2 7\\n4 8\\n1 3\\n1 5\\n1 2\\n5 6\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '13 5\\n83 118 129 146 190\\n3 4\\n1 3\\n1 2\\n4 5\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '0 21\\n688 744 568 726 814 204 732 87 590 367 813 339 148 682 913 361 617 471 120 123 717\\n2 4\\n2 12\\n14 15\\n3 5\\n1 8\\n1 6\\n3 20\\n8 21\\n2 3\\n2 14\\n6 10\\n13 18\\n1 2\\n4 19\\n6 16\\n10 13\\n4 11\\n6 7\\n1 17\\n7 9\\n', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '0 3\\n30 7 9\\n1 2\\n2 3\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '14 9\\n17 23 33 17 19 35 32 32 1\\n7 8\\n2 7\\n3 5\\n1 2\\n3 4\\n2 9\\n2 3\\n1 6\\n', 'output': '20\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80185","program":"```python\nimport sys\n\n\ndef readInts(): return [int(x) for x in sys.stdin.readline().split()]\n\n\ndef readInt(): return int(sys.stdin.readline())\n\n\n# def print(x):\n # sys.stdout.write(str(x) + '\\n')\n\n\ndef solve():\n MOD = int(1e9 + 7)\n d, n = readInts()\n a = readInts()\n adj: list = [[] for _ in range(n)]\n for _ in range(n - 1):\n u, v = readInts()\n adj[u - 1].append(v - 1)\n adj[v - 1].append(u - 1)\n\n vis = [False for _ in range(n)]\n f = [0 for _ in range(n)]\n\n def dfs(cur, root):\n vis[cur] = True\n\n f[cur] = 1\n for neigh in adj[cur]:\n if vis[neigh]:\n continue\n if not (a[root] <= a[neigh] <= a[root] + d):\n continue\n if a[neigh] == a[root] and neigh < root:\n continue\n dfs(neigh, root)\n f[cur] *= f[neigh] + 1\n f[cur] %= MOD\n\n ans = 0\n for i in range(0, n):\n vis = [False for _ in range(n)]\n f = [0 for _ in range(n)]\n dfs(i, i)\n ans += f[i]\n ans %= MOD\n print(ans)\n\n\ndef main():\n t = 1\n # t = readInt()\n for _ in range(t):\n solve()\n\n\nmain()\n\n```","inputs":"4 8\n7 8 7 5 4 6 4 10\n1 6\n1 2\n5 8\n1 3\n3 5\n6 7\n3 4\n","output":"41","actual_output":"41\n","execution_success":true,"sample_index":12768},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"50_C. Happy Farm 5","prompt":"Solve the following coding problem using the programming language python:\n\nThe Happy Farm 5 creators decided to invent the mechanism of cow grazing. The cows in the game are very slow and they move very slowly, it can even be considered that they stand still. However, carnivores should always be chased off them. \n\nFor that a young player Vasya decided to make the shepherd run round the cows along one and the same closed path. It is very important that the cows stayed strictly inside the area limited by the path, as otherwise some cows will sooner or later be eaten. To be absolutely sure in the cows' safety, Vasya wants the path completion time to be minimum.\n\nThe new game is launched for different devices, including mobile phones. That's why the developers decided to quit using the arithmetics with the floating decimal point and use only the arithmetics of integers. The cows and the shepherd in the game are represented as points on the plane with integer coordinates. The playing time is modeled by the turns. During every turn the shepherd can either stay where he stands or step in one of eight directions: horizontally, vertically, or diagonally. As the coordinates should always remain integer, then the length of a horizontal and vertical step is equal to 1, and the length of a diagonal step is equal to . The cows do not move. You have to minimize the number of moves the shepherd needs to run round the whole herd.\n\nInput\n\nThe first line contains an integer N which represents the number of cows in the herd (1 \u2264 N \u2264 105). Each of the next N lines contains two integers Xi and Yi which represent the coordinates of one cow of (|Xi|, |Yi| \u2264 106). Several cows can stand on one point.\n\nOutput\n\nPrint the single number \u2014 the minimum number of moves in the sought path.\n\nExamples\n\nInput\n\n4\n1 1\n5 1\n5 3\n1 3\n\n\nOutput\n\n16\n\nNote\n\nPicture for the example test: The coordinate grid is painted grey, the coordinates axes are painted black, the cows are painted red and the sought route is painted green.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\n\nn = int(input())\n\nl = []\nfor i in range(n):\n l.append(tuple(list(map(int, input().split(\" \")))))\nl = list(set(l))\nn = len(l)\n\npmin = 0\nfor i in range(1, n):\n if(l[i][1] < l[pmin][1] or (l[i][1] == l[pmin][1] and l[i][0] < l[pmin][0])):\n pmin = i\n\nl[pmin], l[0] = l[0], l[pmin]\n\ndef orientation(p0, p1, p2):\n x = (p1[1] - p0[1]) * (p2[0] - p1[0]) - (p1[0] - p0[0]) * (p2[1] - p1[1])\n if(x < 0):\n return -1\n if(x > 0):\n return 1\n return 0\n\nl = [(p[0] - l[0][0], p[1] - l[0][1]) for p in l[1:]]\nl.sort(key = lambda p: (-p[0]/p[1] if(p[1] != 0) else -10e14, p[0] ** 2 + p[1] ** 2))\nl = [(0, 0)] + l\n\nt = [l[0]]\ni = 1\nn = len(l)\nwhile(1):\n while(i < n - 1 and orientation(l[0], l[i], l[i + 1]) == 0):\n i += 1\n if(i >= n - 1):\n break\n t.append(l[i])\n i += 1\n \nt.append(l[-1])\n\nif(len(t) == 1):\n print(4)\nelif(len(t) == 2):\n print(max(abs(t[1][1] - t[0][1]), abs(t[1][0] - t[0][0])) * 2 + 4)\nelse:\n stack = [t[0], t[1], t[2]]\n for i in range(3, len(t)):\n while(orientation(stack[-2], stack[-1], t[i]) == 1):\n stack.pop()\n stack.append(t[i])\n \n n = len(stack)\n s = 4\n for i in range(n - 1):\n s += max(abs(stack[i + 1][1] - stack[i][1]), abs(stack[i + 1][0] - stack[i][0]))\n s += max(abs(stack[0][1] - stack[n - 1][1]), abs(stack[0][0] - stack[n - 1][0]))\n print(s)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1 1\\n5 1\\n5 3\\n1 3\\n', 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l[pmin][0])):\n pmin = i\n\nl[pmin], l[0] = l[0], l[pmin]\n\ndef orientation(p0, p1, p2):\n x = (p1[1] - p0[1]) * (p2[0] - p1[0]) - (p1[0] - p0[0]) * (p2[1] - p1[1])\n if(x < 0):\n return -1\n if(x > 0):\n return 1\n return 0\n\nl = [(p[0] - l[0][0], p[1] - l[0][1]) for p in l[1:]]\nl.sort(key = lambda p: (-p[0]/p[1] if(p[1] != 0) else -10e14, p[0] ** 2 + p[1] ** 2))\nl = [(0, 0)] + l\n\nt = [l[0]]\ni = 1\nn = len(l)\nwhile(1):\n while(i < n - 1 and orientation(l[0], l[i], l[i + 1]) == 0):\n i += 1\n if(i >= n - 1):\n break\n t.append(l[i])\n i += 1\n \nt.append(l[-1])\n\nif(len(t) == 1):\n print(4)\nelif(len(t) == 2):\n print(max(abs(t[1][1] - t[0][1]), abs(t[1][0] - t[0][0])) * 2 + 4)\nelse:\n stack = [t[0], t[1], t[2]]\n for i in range(3, len(t)):\n while(orientation(stack[-2], stack[-1], t[i]) == 1):\n stack.pop()\n stack.append(t[i])\n \n n = len(stack)\n s = 4\n for i in range(n - 1):\n s += max(abs(stack[i + 1][1] - stack[i][1]), abs(stack[i + 1][0] - stack[i][0]))\n s += max(abs(stack[0][1] - stack[n - 1][1]), abs(stack[0][0] - stack[n - 1][0]))\n print(s)\n```","inputs":"4\n1 1\n5 1\n5 3\n1 3\n","output":"16\n","actual_output":"16\n","execution_success":true,"sample_index":12769},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"534_E. Berland Local Positioning System","prompt":"Solve the following coding problem using the programming language python:\n\nIn Berland a bus travels along the main street of the capital. The street begins from the main square and looks like a very long segment. There are n bus stops located along the street, the i-th of them is located at the distance ai from the central square, all distances are distinct, the stops are numbered in the order of increasing distance from the square, that is, ai < ai + 1 for all i from 1 to n - 1. The bus starts its journey from the first stop, it passes stops 2, 3 and so on. It reaches the stop number n, turns around and goes in the opposite direction to stop 1, passing all the intermediate stops in the reverse order. After that, it again starts to move towards stop n. During the day, the bus runs non-stop on this route.\n\nThe bus is equipped with the Berland local positioning system. When the bus passes a stop, the system notes down its number.\n\nOne of the key features of the system is that it can respond to the queries about the distance covered by the bus for the parts of its path between some pair of stops. A special module of the system takes the input with the information about a set of stops on a segment of the path, a stop number occurs in the set as many times as the bus drove past it. This module returns the length of the traveled segment of the path (or -1 if it is impossible to determine the length uniquely). The operation of the module is complicated by the fact that stop numbers occur in the request not in the order they were visited but in the non-decreasing order.\n\nFor example, if the number of stops is 6, and the part of the bus path starts at the bus stop number 5, ends at the stop number 3 and passes the stops as follows: , then the request about this segment of the path will have form: 3, 4, 5, 5, 6. If the bus on the segment of the path from stop 5 to stop 3 has time to drive past the 1-th stop (i.e., if we consider a segment that ends with the second visit to stop 3 on the way from 5), then the request will have form: 1, 2, 2, 3, 3, 4, 5, 5, 6.\n\nYou will have to repeat the Berland programmers achievement and implement this function.\n\nInput\n\nThe first line contains integer n (2 \u2264 n \u2264 2\u00b7105) \u2014 the number of stops.\n\nThe second line contains n integers (1 \u2264 ai \u2264 109) \u2014 the distance from the i-th stop to the central square. The numbers in the second line go in the increasing order.\n\nThe third line contains integer m (1 \u2264 m \u2264 4\u00b7105) \u2014 the number of stops the bus visited on some segment of the path.\n\nThe fourth line contains m integers (1 \u2264 bi \u2264 n) \u2014 the sorted list of numbers of the stops visited by the bus on the segment of the path. The number of a stop occurs as many times as it was visited by a bus.\n\nIt is guaranteed that the query corresponds to some segment of the path.\n\nOutput\n\nIn the single line please print the distance covered by a bus. If it is impossible to determine it unambiguously, print - 1.\n\nExamples\n\nInput\n\n6\n2 3 5 7 11 13\n5\n3 4 5 5 6\n\n\nOutput\n\n10\n\n\nInput\n\n6\n2 3 5 7 11 13\n9\n1 2 2 3 3 4 5 5 6\n\n\nOutput\n\n16\n\n\nInput\n\n3\n10 200 300\n4\n1 2 2 3\n\n\nOutput\n\n-1\n\n\nInput\n\n3\n1 2 3\n4\n1 2 2 3\n\n\nOutput\n\n3\n\nNote\n\nThe first test from the statement demonstrates the first example shown in the statement of the problem.\n\nThe second test from the statement demonstrates the second example shown in the statement of the problem.\n\nIn the third sample there are two possible paths that have distinct lengths, consequently, the sought length of the segment isn't defined uniquely.\n\nIn the fourth sample, even though two distinct paths correspond to the query, they have the same lengths, so the sought length of the segment is defined uniquely.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nr = lambda: list(map(int, input().split()))\nri = lambda: int(input())\nn, a, m, b = ri(), r(), ri(), r()\nc = [0] * n\nfor e in b: c[e - 1] += 1\nc[0] *= 2; c[-1] *= 2\nd = 0\ndf= 0\nr = max(e // 2 for e in c)\nc = [e - r * 2 for e in c]\nif any(c):\n for i in range(n - 1):\n de = a[i+1] - a[i]\n d += min(c[i], c[i+1]) * de\n df += de \n print(d + r * 2 * df)\nelse:\n de = a[1] - a[0]\n for i in range(1, n - 1):\n if a[i + 1] - a[i] != de: print(-1); break\n else: print(r * de * 2 * (n - 1) - de)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n10 200 300\\n4\\n1 2 2 3\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 3\\n4\\n1 2 2 3\\n', 'output': ' 3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 3 5 7 11 13\\n5\\n3 4 5 5 6\\n', 'output': ' 10\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 3 5 7 11 13\\n9\\n1 2 2 3 3 4 5 5 6\\n', 'output': ' 16\\n'}, {'type': 'stdin_stdout', 'input': 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'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1001010000\\n1\\n2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 11\\n2\\n2 3\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 10\\n4\\n1 2 2 3\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1001000000\\n1\\n2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1011000000\\n1\\n2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1001000100\\n1\\n1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10 202 27\\n4\\n1 2 2 3\\n', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80193","program":"```python\nr = lambda: list(map(int, input().split()))\nri = lambda: int(input())\nn, a, m, b = ri(), r(), ri(), r()\nc = [0] * n\nfor e in b: c[e - 1] += 1\nc[0] *= 2; c[-1] *= 2\nd = 0\ndf= 0\nr = max(e // 2 for e in c)\nc = [e - r * 2 for e in c]\nif any(c):\n for i in range(n - 1):\n de = a[i+1] - a[i]\n d += min(c[i], c[i+1]) * de\n df += de \n print(d + r * 2 * df)\nelse:\n de = a[1] - a[0]\n for i in range(1, n - 1):\n if a[i + 1] - a[i] != de: print(-1); break\n else: print(r * de * 2 * (n - 1) - de)\n```","inputs":"3\n10 200 300\n4\n1 2 2 3\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12770},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"607_C. Marbles","prompt":"Solve the following coding problem using the programming language python:\n\nIn the spirit of the holidays, Saitama has given Genos two grid paths of length n (a weird gift even by Saitama's standards). A grid path is an ordered sequence of neighbouring squares in an infinite grid. Two squares are neighbouring if they share a side.\n\nOne example of a grid path is (0, 0) \u2192 (0, 1) \u2192 (0, 2) \u2192 (1, 2) \u2192 (1, 1) \u2192 (0, 1) \u2192 ( - 1, 1). Note that squares in this sequence might be repeated, i.e. path has self intersections.\n\nMovement within a grid path is restricted to adjacent squares within the sequence. That is, from the i-th square, one can only move to the (i - 1)-th or (i + 1)-th squares of this path. Note that there is only a single valid move from the first and last squares of a grid path. Also note, that even if there is some j-th square of the path that coincides with the i-th square, only moves to (i - 1)-th and (i + 1)-th squares are available. For example, from the second square in the above sequence, one can only move to either the first or third squares.\n\nTo ensure that movement is not ambiguous, the two grid paths will not have an alternating sequence of three squares. For example, a contiguous subsequence (0, 0) \u2192 (0, 1) \u2192 (0, 0) cannot occur in a valid grid path.\n\nOne marble is placed on the first square of each grid path. Genos wants to get both marbles to the last square of each grid path. However, there is a catch. Whenever he moves one marble, the other marble will copy its movement if possible. For instance, if one marble moves east, then the other marble will try and move east as well. By try, we mean if moving east is a valid move, then the marble will move east.\n\nMoving north increases the second coordinate by 1, while moving south decreases it by 1. Similarly, moving east increases first coordinate by 1, while moving west decreases it.\n\nGiven these two valid grid paths, Genos wants to know if it is possible to move both marbles to the ends of their respective paths. That is, if it is possible to move the marbles such that both marbles rest on the last square of their respective paths.\n\nInput\n\nThe first line of the input contains a single integer n (2 \u2264 n \u2264 1 000 000) \u2014 the length of the paths.\n\nThe second line of the input contains a string consisting of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') \u2014 the first grid path. The characters can be thought of as the sequence of moves needed to traverse the grid path. For example, the example path in the problem statement can be expressed by the string \"NNESWW\".\n\nThe third line of the input contains a string of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') \u2014 the second grid path.\n\nOutput\n\nPrint \"YES\" (without quotes) if it is possible for both marbles to be at the end position at the same time. Print \"NO\" (without quotes) otherwise. In both cases, the answer is case-insensitive.\n\nExamples\n\nInput\n\n7\nNNESWW\nSWSWSW\n\n\nOutput\n\nYES\n\n\nInput\n\n3\nNN\nSS\n\n\nOutput\n\nNO\n\nNote\n\nIn the first sample, the first grid path is the one described in the statement. Moreover, the following sequence of moves will get both marbles to the end: NNESWWSWSW.\n\nIn the second sample, no sequence of moves can get both marbles to the end.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom time import time\n\n\nopposite = {\n 'N': 'S',\n 'S': 'N',\n 'E': 'W',\n 'W': 'E'\n}\notr = str.maketrans(opposite)\n\nbits = {\n 'N': 0,\n 'S': 1,\n 'E': 2,\n 'W': 3,\n}\n\nQ = 4294967291\n\n\ndef combine(h, v, q):\n return (h<<2 | v) % q\n\n\ndef combinel(h, v, q, s):\n return (v*s + h) % q\n\n\ndef flip(s):\n return ''.join(reversed(s.translate(otr)))\n\n\ndef solvable(p1, p2):\n h1 = 0\n h2 = 0\n s = 1\n for i in reversed(range(len(p1))):\n n1 = bits[p1[i]]\n n2 = bits[opposite[p2[i]]]\n h1 = combine(h1, n1, Q)\n h2 = combinel(h2, n2, Q, s)\n if h1 == h2 and p1[i:] == flip(p2[i:]):\n return False\n s = (s<<2) % Q\n return True\n\n\nif __name__ == '__main__':\n n = int(input())\n p1 = input()\n p2 = input()\n print('YES' if solvable(p1, p2) else 'NO')\n\n\n\n\n# Made By Mostafa_Khaled\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7\\nNNESWW\\nSWSWSW\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3\\nNN\\nSS\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\nW\\nS\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12\\nWNNWSWWSSSE\\nNESWNNNWSSS\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11\\nWWNNNNWNWN\\nENWSWWSSEE\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '200\\nNESENEESEESWWWNWWSWSWNWNNWNNESWSWNNWNWNENESENNESSWSESWWSSSEEEESSENNNESSWWSSSSESWSWWNNEESSWWNNWSWSSWWNWNNEENNENWWNESSSENWNESWNESWNESEESSWNESSSSSESESSWNNENENESSWWNNWWSWWNESEENWWWWNWWNWWNENESESSWWSWWSES\\nNWNESESSENNNESWNWWSWWWNWSESSSWWNWWNNWSENWSWNENNNWWSWWSWNNNESWWWSSESSWWWSSENWSENWWNENESESWNENNESWNWNNENNWWWSENWSWSSSENNWWNEESENNESEESSEESWWWWWWNWNNNESESWSSEEEESWNENWSESEEENWNNWWNWNNNNWWSSWNEENENEEEEEE\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2\\nS\\nN\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5\\nWSSE\\nWNNE\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2\\nE\\nE\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3\\nES\\nNW\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '100\\nWNWWSWWSESWWWSSSSWSSEENWNWWWWNNENESWSESSENEENNWWWWWSSWSWSENESWNEENESWWNNEESESWSEEENWWNWNNWWNNWWWWSW\\nEESEESSENWNWWWNWWNWWNWWSWNNWNWNWSWNNEENWSWNNESWSWNWSESENWSWSWWWWNNEESSSWSSESWWSSWSSWSWNEEESWWSSSSEN\\n', 'output': 'NO\\n'}, {'type': 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{'type': 'stdin_stdout', 'input': '12\\nESSWWWSWNNS\\nNWSWNNNESSS\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12\\nESSSWWSWNNW\\nWNSENNNWSSS\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12\\nSNNESWWSSWW\\nNESWNNNWSSS\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11\\nNWNWNNNNWW\\nENWSWWSSEE\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '200\\nNESENEESEESWWWNWWSWSWNWNNSNNESWSWNNWNWNENESENNESSWSESWWSSSEEEESSENNNESSWWSSSSESWSWWNNEEWSWWNNWSWSSWWNWNNEENNENWWNESSSENWNESWNESWNESEESSWEESSSSSESESSWNNNNENESSWWNNWWSWWNESEENWWWWNWWNWWNENESESSWWSWWSES\\nNWNESESSENNNESWNWWSWWWNWSESSSWWNWWNNWSENWSWNENNNWWSWWSWNNNESWWWSSESSWWWSSENWSENWWNENESESWNENNESWNWNNENNWWWSENWSWSSSENNWWNEESENNESEESSEESWWWWWWNWNNNESESWSSEEEESWNENWSESEEENWNNWWNWNNNNWWSSWNEENENEEEEEE\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12\\nSNNWSWWWSSE\\nNWSWNNNESSS\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12\\nWNNWSWWSSSE\\nWNSENNNWSSS\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12\\nSNNESWWSSWW\\nNENWNNSWSSS\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '11\\nNWNWNNNNWW\\nEESSWWSWNE\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '200\\nNESENEESEESWWWNWWSWSWNWNNSNNESWSWNNWNWNENESENNESSWSESWWSSSEEEESSENNNESSWWSSSSESWSWWNNEEWSWWNNWSWSSWWNWNNEENNENWWNESSSENWNEEWNSSWNESEESSWEESSSSSESESSWNNNNENESSWWNNWWSWWNESEENWWWWNWWNWWNENESESSWWSWWSES\\nNWNESESSENNNESWNWWSWWWNWSESSSWWNWWNNWSENWSWNENNNWWSWWSWNNNESWWWSSESSWWWSSENWSENWWNENESESWNENNESWNWNNENNWWWSENWSWSSSENNWWNEESENNESEESSEESWWWWWWNWNNNESESWSSEEEESWNENWSESEEENWNNWWNWNNNNWWSSWNEENENEEEEEE\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '12\\nSNNESWWSSWW\\nSENWNNSWSNS\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '200\\nNESENEESEESWWWNWWSWSWNWNNSNNESWSWNNWNWNENESENNESSWSESWWSSSEEEESSENNNESSWWSSSSESWSWWNNEEWSWWNNWSWNSWWNWNNEESNENWWNESSSENWNEEWNSSWNESEESSWEESSSSSESESSWNNNNENESSWWNNWWSWWNESEENWWWWNWWNWWNENESESSWWSWWSES\\nNWNESESSENNNESWNWWSWWWNWSESSSWWNWWNNWSENWSWNENNNWWSWWSWNNNESWWWSSESSWWWSSENWSENWWNENESESWNENNESWNWNNENNWWWSENWSWSSSENNWWNEESENNESEESSEESWWWWWWNWNNNESESWSSEEEESWNENWSESEEENWNNWWNWNNNNWWSSWNEENENEEEEEE\\n', 'output': 'YES\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80205","program":"```python\nfrom time import time\n\n\nopposite = {\n 'N': 'S',\n 'S': 'N',\n 'E': 'W',\n 'W': 'E'\n}\notr = str.maketrans(opposite)\n\nbits = {\n 'N': 0,\n 'S': 1,\n 'E': 2,\n 'W': 3,\n}\n\nQ = 4294967291\n\n\ndef combine(h, v, q):\n return (h<<2 | v) % q\n\n\ndef combinel(h, v, q, s):\n return (v*s + h) % q\n\n\ndef flip(s):\n return ''.join(reversed(s.translate(otr)))\n\n\ndef solvable(p1, p2):\n h1 = 0\n h2 = 0\n s = 1\n for i in reversed(range(len(p1))):\n n1 = bits[p1[i]]\n n2 = bits[opposite[p2[i]]]\n h1 = combine(h1, n1, Q)\n h2 = combinel(h2, n2, Q, s)\n if h1 == h2 and p1[i:] == flip(p2[i:]):\n return False\n s = (s<<2) % Q\n return True\n\n\nif __name__ == '__main__':\n n = int(input())\n p1 = input()\n p2 = input()\n print('YES' if solvable(p1, p2) else 'NO')\n\n\n\n\n# Made By Mostafa_Khaled\n```","inputs":"7\nNNESWW\nSWSWSW\n","output":"YES\n","actual_output":"YES\n","execution_success":true,"sample_index":12771},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"629_B. Far Relative\u2019s Problem","prompt":"Solve the following coding problem using the programming language python:\n\nFamil Door wants to celebrate his birthday with his friends from Far Far Away. He has n friends and each of them can come to the party in a specific range of days of the year from ai to bi. Of course, Famil Door wants to have as many friends celebrating together with him as possible.\n\nFar cars are as weird as Far Far Away citizens, so they can only carry two people of opposite gender, that is exactly one male and one female. However, Far is so far from here that no other transportation may be used to get to the party.\n\nFamil Door should select some day of the year and invite some of his friends, such that they all are available at this moment and the number of male friends invited is equal to the number of female friends invited. Find the maximum number of friends that may present at the party.\n\nInput\n\nThe first line of the input contains a single integer n (1 \u2264 n \u2264 5000) \u2014 then number of Famil Door's friends.\n\nThen follow n lines, that describe the friends. Each line starts with a capital letter 'F' for female friends and with a capital letter 'M' for male friends. Then follow two integers ai and bi (1 \u2264 ai \u2264 bi \u2264 366), providing that the i-th friend can come to the party from day ai to day bi inclusive.\n\nOutput\n\nPrint the maximum number of people that may come to Famil Door's party.\n\nExamples\n\nInput\n\n4\nM 151 307\nF 343 352\nF 117 145\nM 24 128\n\n\nOutput\n\n2\n\n\nInput\n\n6\nM 128 130\nF 128 131\nF 131 140\nF 131 141\nM 131 200\nM 140 200\n\n\nOutput\n\n4\n\nNote\n\nIn the first sample, friends 3 and 4 can come on any day in range [117, 128].\n\nIn the second sample, friends with indices 3, 4, 5 and 6 can come on day 140.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = (int)(input())\nF1=[0]*n\nF2=[0]*n\nM1=[0]*n\nM2=[0]*n\nm=0\nf=0\nfor i in range(n):\n c = (input().split())\n if(c[0]=='M'):\n M1[m]=(int)(c[1])\n M2[m]=(int)(c[2])\n m=m+1\n if(c[0]=='F'):\n F1[f]=(int)(c[1])\n F2[f]=(int)(c[2])\n f=f+1\nF=[0]*3232\nM=[0]*3266\nfor i in range(f):\n for j in range(F1[i], F2[i]+1):\n F[j]=F[j]+1\nfor i in range(m):\n for j in range(M1[i], M2[i]+1):\n M[j]=M[j]+1\nmax=0\nfor j in range(367):\n if((F[j]>max)and(M[j]>max)):\n max=F[j]\n if(max>M[j]):\n max=M[j]\nprint(max*2)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\nM 151 307\\nF 343 352\\nF 117 145\\nM 24 128\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\nM 128 130\\nF 128 131\\nF 131 140\\nF 131 141\\nM 131 200\\nM 140 200\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\nF 1 1\\nM 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 117 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 107 264\\nF 34 318\\nM 44 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 135 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 300\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 8 111\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '1\\nF 1 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\nM 1 1\\nF 1 1\\nM 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 3 4\\nM 5 6\\nM 5 6\\nM 5 6\\nM 5 6\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 8\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\nF 68 307\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\nM 1 1\\nF 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 1 2\\nM 2 3\\nF 3 4\\nF 4 5\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\nF 1 2\\nM 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 117 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 107 264\\nF 34 318\\nM 44 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 197 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 300\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 8 111\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '1\\nF 1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 3 4\\nM 5 6\\nM 5 6\\nM 5 6\\nM 5 6\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '6\\nM 129 130\\nF 128 131\\nF 131 140\\nF 131 141\\nM 131 200\\nM 140 200\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\nM 1 1\\nF 1 1\\nM 1 0\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 1 2\\nM 2 3\\nF 4 4\\nF 4 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 151 307\\nF 343 352\\nF 117 145\\nM 24 131\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\nF 2 2\\nM 1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 3 2\\nM 5 6\\nM 5 6\\nM 5 6\\nM 5 6\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 117 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 107 264\\nF 34 318\\nM 44 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 135 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 126\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 8 111\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '1\\nF 1 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\nM 1 1\\nF 1 1\\nM 2 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 151 307\\nF 343 352\\nF 117 145\\nM 24 143\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 3 4\\nM 5 6\\nM 5 6\\nM 6 6\\nM 5 6\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 199 307\\nF 343 352\\nF 117 145\\nM 24 131\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 117 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 163 264\\nF 34 318\\nM 44 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 135 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 126\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 8 111\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '3\\nM 1 1\\nF 1 2\\nM 2 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 199 307\\nF 343 352\\nF 117 145\\nM 1 131\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 230 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 163 264\\nF 34 318\\nM 44 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 135 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 126\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 8 111\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '1\\nF 1 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 6 6\\nM 3 4\\nM 3 4\\nM 5 6\\nM 5 6\\nM 5 6\\nM 5 6\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 8\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '2\\nM 1 1\\nF 1 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 1 2\\nM 2 3\\nF 2 4\\nF 4 5\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 117 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 107 264\\nF 34 318\\nM 69 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 197 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 300\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 8 111\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '3\\nM 1 2\\nF 1 1\\nM 1 0\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 3 4\\nM 5 6\\nM 5 6\\nM 5 0\\nM 5 6\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 117 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 107 264\\nF 34 318\\nM 78 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 135 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 126\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 8 111\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '3\\nM 1 1\\nF 1 1\\nM 2 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 151 307\\nF 343 352\\nF 98 145\\nM 24 143\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 3 4\\nM 5 6\\nM 5 6\\nM 6 6\\nM 5 4\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 117 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 101 264\\nF 34 318\\nM 44 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 135 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 126\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 8 111\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '1\\nF 2 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\nM 1 1\\nF 2 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 1 2\\nM 2 6\\nF 2 4\\nF 4 5\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\nM 1 2\\nF 1 1\\nM 1 -1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 6 4\\nM 5 6\\nM 5 6\\nM 6 6\\nM 5 4\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 6 4\\nM 5 6\\nM 5 6\\nM 6 6\\nM 5 4\\nF 7 8\\nF 7 8\\nF 2 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '2\\nF 1 1\\nM 1 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 5 4\\nM 5 6\\nM 5 6\\nM 5 6\\nM 5 6\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 8\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '6\\nM 128 130\\nF 128 131\\nF 131 140\\nF 131 141\\nM 131 200\\nM 20 200\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 203 307\\nF 343 352\\nF 117 145\\nM 24 131\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\nM 1 1\\nF 1 2\\nM 2 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 230 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 163 264\\nF 34 318\\nM 44 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 135 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 126\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 4 111\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 8 6\\nM 3 4\\nM 3 4\\nM 5 6\\nM 5 6\\nM 5 6\\nM 5 6\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 8\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 6\\nF 5 6\\nM 3 4\\nM 3 4\\nM 5 6\\nM 5 6\\nM 5 0\\nM 5 6\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 117 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 107 264\\nF 34 318\\nM 78 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 135 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 126\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 8 011\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 151 307\\nF 343 352\\nF 33 145\\nM 24 143\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\nF 4 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\nM 1 1\\nF 2 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\nM 1 2\\nF 1 1\\nM 0 -1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 6 4\\nM 5 6\\nM 5 6\\nM 6 6\\nM 5 2\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 6 4\\nM 5 6\\nM 5 6\\nM 6 6\\nM 5 4\\nF 7 10\\nF 7 8\\nF 2 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '2\\nF 1 2\\nM 1 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\nM 128 130\\nF 154 131\\nF 131 140\\nF 131 141\\nM 131 200\\nM 20 200\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 203 307\\nF 343 352\\nF 117 145\\nM 46 131\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 230 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 163 264\\nF 34 318\\nM 44 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 135 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 126\\nF 47 303\\nF 201 311\\nF 287 288\\nM 135 352\\nM 227 351\\nF 4 111\\nF 39 229\\nM 163 315\\nF 269 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 6\\nF 5 6\\nM 3 4\\nM 3 4\\nM 5 6\\nM 5 6\\nM 5 0\\nM 5 6\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 6 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '40\\nM 55 363\\nF 117 252\\nM 157 282\\nF 322 345\\nM 330 363\\nF 154 231\\nF 216 352\\nF 357 365\\nM 279 292\\nF 353 359\\nF 82 183\\nM 78 297\\nM 231 314\\nM 107 264\\nF 34 318\\nM 78 244\\nF 42 339\\nM 253 307\\nM 128 192\\nF 119 328\\nM 135 249\\nF 303 358\\nF 348 352\\nF 8 364\\nF 126 303\\nM 226 346\\nF 110 126\\nF 47 303\\nF 201 311\\nF 287 288\\nM 270 352\\nM 227 351\\nF 8 011\\nF 39 229\\nM 163 315\\nF 186 335\\nF 147 351\\nF 96 143\\nM 97 99\\nM 177 295\\n', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 151 343\\nF 343 352\\nF 33 145\\nM 24 143\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\nM 1 2\\nF 2 3\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\nM 1 2\\nF 1 2\\nM 0 -1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 2 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 6 4\\nM 5 6\\nM 5 6\\nM 6 6\\nM 5 2\\nF 7 8\\nF 7 8\\nF 7 8\\nM 7 8\\nM 7 12\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '18\\nF 3 4\\nF 3 4\\nF 3 4\\nF 3 4\\nF 5 6\\nF 5 6\\nM 3 4\\nM 6 4\\nM 5 6\\nM 5 6\\nM 6 6\\nM 5 4\\nF 7 10\\nF 7 8\\nF 2 8\\nM 7 8\\nM 7 22\\nM 7 8\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '4\\nM 203 307\\nF 343 352\\nF 117 145\\nM 14 131\\n', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80209","program":"```python\nn = (int)(input())\nF1=[0]*n\nF2=[0]*n\nM1=[0]*n\nM2=[0]*n\nm=0\nf=0\nfor i in range(n):\n c = (input().split())\n if(c[0]=='M'):\n M1[m]=(int)(c[1])\n M2[m]=(int)(c[2])\n m=m+1\n if(c[0]=='F'):\n F1[f]=(int)(c[1])\n F2[f]=(int)(c[2])\n f=f+1\nF=[0]*3232\nM=[0]*3266\nfor i in range(f):\n for j in range(F1[i], F2[i]+1):\n F[j]=F[j]+1\nfor i in range(m):\n for j in range(M1[i], M2[i]+1):\n M[j]=M[j]+1\nmax=0\nfor j in range(367):\n if((F[j]>max)and(M[j]>max)):\n max=F[j]\n if(max>M[j]):\n max=M[j]\nprint(max*2)\n```","inputs":"4\nM 151 307\nF 343 352\nF 117 145\nM 24 128\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12772},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"653_C. Bear and Up-Down","prompt":"Solve the following coding problem using the programming language python:\n\nThe life goes up and down, just like nice sequences. Sequence t1, t2, ..., tn is called nice if the following two conditions are satisfied: \n\n * ti < ti + 1 for each odd i < n; \n * ti > ti + 1 for each even i < n. \n\n\n\nFor example, sequences (2, 8), (1, 5, 1) and (2, 5, 1, 100, 99, 120) are nice, while (1, 1), (1, 2, 3) and (2, 5, 3, 2) are not.\n\nBear Limak has a sequence of positive integers t1, t2, ..., tn. This sequence is not nice now and Limak wants to fix it by a single swap. He is going to choose two indices i < j and swap elements ti and tj in order to get a nice sequence. Count the number of ways to do so. Two ways are considered different if indices of elements chosen for a swap are different.\n\nInput\n\nThe first line of the input contains one integer n (2 \u2264 n \u2264 150 000) \u2014 the length of the sequence.\n\nThe second line contains n integers t1, t2, ..., tn (1 \u2264 ti \u2264 150 000) \u2014 the initial sequence. It's guaranteed that the given sequence is not nice.\n\nOutput\n\nPrint the number of ways to swap two elements exactly once in order to get a nice sequence.\n\nExamples\n\nInput\n\n5\n2 8 4 7 7\n\n\nOutput\n\n2\n\n\nInput\n\n4\n200 150 100 50\n\n\nOutput\n\n1\n\n\nInput\n\n10\n3 2 1 4 1 4 1 4 1 4\n\n\nOutput\n\n8\n\n\nInput\n\n9\n1 2 3 4 5 6 7 8 9\n\n\nOutput\n\n0\n\nNote\n\nIn the first sample, there are two ways to get a nice sequence with one swap: \n\n 1. Swap t2 = 8 with t4 = 7. \n 2. Swap t1 = 2 with t5 = 7. \n\n\n\nIn the second sample, there is only one way \u2014 Limak should swap t1 = 200 with t4 = 50.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef main():\n n, l = int(input()), list(map(int, input().split()))\n if not (n & 1):\n l.append(0)\n l.append(150001)\n a, b, fails, res = 0, 150001, [], 0\n for i, c in enumerate(l, -1):\n if i & 1:\n if a >= b or b <= c:\n if len(fails) > 5:\n print(0)\n return\n fails.append(i)\n else:\n if a <= b or b >= c:\n if len(fails) > 5:\n print(0)\n return\n fails.append(i)\n a, b = b, c\n check = compile(\"and\".join(\n \"(l[{:n}]{:s}l[{:n}]{:s}l[{:n}])\".format(i - 1, \"><\"[i & 1], i, \"<>\"[i & 1], i + 1) for i in fails),\n \"\", \"eval\")\n for i in fails:\n a = l[i]\n for j in range(n):\n l[i], l[j] = l[j], a\n if eval(check) and ((l[j - 1] < l[j] > l[j + 1]) if j & 1 else (l[j - 1] > l[j] < l[j + 1])):\n res += 1 if j in fails else 2\n l[j] = l[i]\n l[i] = a\n print(res // 2)\n\n\nif __name__ == '__main__':\n main()\n\n\n\n# Made By Mostafa_Khaled\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n2 8 4 7 7\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '4\\n200 150 100 50\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '10\\n3 2 1 4 1 4 1 4 1 4\\n', 'output': '8'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 3 4 5 6 7 8 9\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '30\\n18647 31594 58075 122543 49766 65303 48728 102863 22542 140297 5300 90685 50141 86948 27074 40214 17945 147095 97758 140835 121469 139920 63817 138623 85609 110002 70046 128002 122139 116109\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '50\\n11836 28308 72527 92281 139289 93797 134555 148444 40866 111317 21564 87813 65466 20541 99238 2287 74647 128071 18163 61672 39766 55589 138385 147443 138100 142683 60703 15444 52566 72976 147412 116006 115986 110545 79993 100440 9876 71470 75209 62443 64906 88987 72232 2246 63160 45041 729 148611 103397 78474\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 7 8 10 5 10 1 5 2 6\\n', 'output': '2'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 1 4 3\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '2\\n10 10\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '10\\n522 309 276 454 566 978 175 388 289 276\\n', 'output': '0'}, {'type': 'stdin_stdout', 'input': '2\\n5 1\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '39\\n18329 39326 21115 36341 3916 40060 23262 41923 17476 42107 17052 23198 10756 32540 14873 28454 23912 35765 9459 45834 85 46756 31859 40087 35420 47585 9781 46544 31859 49453 7394 17459 2816 34051 12519 4077 692 44098 23345\\n', 'output': '15'}, {'type': 'stdin_stdout', 'input': '20\\n8 9 1 10 7 9 5 8 5 7 5 6 1 3 2 7 3 2 6 9\\n', 'output': '3'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 1 2 2 2\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '12\\n10 15 10 15 10 8 10 15 10 20 30 20\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '25\\n25 20 58 95 47 68 38 39 24 83 36 68 28 67 25 40 62 99 11 88 74 75 38 90 42\\n', 'output': '1'}, {'type': 'stdin_stdout', 'input': '30\\n18647 31594 58075 122543 49766 65303 48728 102863 22542 140297 5300 90685 50141 86948 27074 40214 17945 147095 97758 140835 121469 139920 63817 138623 63026 110002 70046 128002 122139 116109\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '50\\n11836 28308 72527 92281 139289 93797 134555 148444 40866 111317 21564 87813 65466 20541 99238 2287 74647 128071 18163 61672 39766 55589 138385 147443 79352 142683 60703 15444 52566 72976 147412 116006 115986 110545 79993 100440 9876 71470 75209 62443 64906 88987 72232 2246 63160 45041 729 148611 103397 78474\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '39\\n18329 39326 21115 36341 3916 40060 21172 41923 17476 42107 17052 23198 10756 32540 14873 28454 23912 35765 9459 45834 85 46756 31859 40087 35420 47585 9781 46544 31859 49453 7394 17459 2816 34051 12519 4077 692 44098 23345\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 9 1 10 7 9 5 8 5 7 5 6 0 3 2 7 3 2 6 9\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 14 4 7 7\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n3 2 1 4 1 4 1 6 1 4\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 9 1 10 7 9 5 8 5 7 5 6 0 3 2 7 3 4 6 9\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 9 1 10 1 9 5 8 5 7 5 6 0 3 2 7 3 4 6 9\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 3 8 10 5 10 1 5 2 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n522 309 276 454 566 978 175 388 289 358\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n5 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 1 2 2 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '12\\n10 15 10 15 10 3 10 15 10 20 30 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '25\\n25 20 58 95 47 68 38 39 24 83 36 68 28 67 25 40 62 50 11 88 74 75 38 90 42\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n200 150 000 50\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 3 4 5 1 7 8 9\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '30\\n18647 31594 58075 122543 49766 65303 48728 102863 22542 140297 5300 90685 50141 86948 27074 40214 17945 147095 97758 140835 121469 221264 63817 138623 63026 110002 70046 128002 122139 116109\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '50\\n11836 28308 72527 92281 139289 93797 134555 148444 40866 111317 21564 87813 65466 20541 99238 1006 74647 128071 18163 61672 39766 55589 138385 147443 79352 142683 60703 15444 52566 72976 147412 116006 115986 110545 79993 100440 9876 71470 75209 62443 64906 88987 72232 2246 63160 45041 729 148611 103397 78474\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 3 8 10 8 10 1 5 2 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n522 309 276 454 566 978 175 388 289 118\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n5 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '39\\n18329 39326 21115 36341 3916 40060 21172 41923 17476 42107 17052 23198 10756 32540 14873 28454 23912 35765 9459 45834 85 81675 31859 40087 35420 47585 9781 46544 31859 49453 7394 17459 2816 34051 12519 4077 692 44098 23345\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 2 1 2 2 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '12\\n10 15 10 15 10 3 7 15 10 20 30 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '25\\n25 20 58 95 47 68 38 39 24 83 36 68 28 67 25 40 62 95 11 88 74 75 38 90 42\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 14 4 7 14\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n200 150 000 11\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n3 2 1 5 1 4 1 6 1 4\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 3 4 5 1 14 8 9\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '30\\n18647 31594 58075 122543 49766 65303 48728 102863 22542 140297 5300 90685 50141 86948 27074 40214 17945 147095 97758 140835 121469 221264 63817 138623 63026 110002 70046 208788 122139 116109\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '50\\n11836 28308 72527 92281 139289 93797 134555 148444 40866 111317 21564 87813 65466 20541 99238 1006 74647 128071 18163 61672 39209 55589 138385 147443 79352 142683 60703 15444 52566 72976 147412 116006 115986 110545 79993 100440 9876 71470 75209 62443 64906 88987 72232 2246 63160 45041 729 148611 103397 78474\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 4 8 10 8 10 1 5 2 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n522 309 276 521 566 978 175 388 289 118\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '39\\n18329 39326 21115 36341 3916 40060 31717 41923 17476 42107 17052 23198 10756 32540 14873 28454 23912 35765 9459 45834 85 81675 31859 40087 35420 47585 9781 46544 31859 49453 7394 17459 2816 34051 12519 4077 692 44098 23345\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 2 1 2 0 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '12\\n10 15 10 15 7 3 7 15 10 20 30 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '25\\n25 20 58 95 47 68 38 39 24 83 36 68 28 67 25 40 62 110 11 88 74 75 38 90 42\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 14 4 7 14\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n200 150 000 16\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n3 2 1 5 1 4 1 10 1 4\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 3 4 5 1 11 8 9\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '30\\n18647 31594 58075 122543 49766 65303 48728 102863 22542 140297 5300 90685 50141 14262 27074 40214 17945 147095 97758 140835 121469 221264 63817 138623 63026 110002 70046 208788 122139 116109\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '50\\n11836 38025 72527 92281 139289 93797 134555 148444 40866 111317 21564 87813 65466 20541 99238 1006 74647 128071 18163 61672 39209 55589 138385 147443 79352 142683 60703 15444 52566 72976 147412 116006 115986 110545 79993 100440 9876 71470 75209 62443 64906 88987 72232 2246 63160 45041 729 148611 103397 78474\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 4 8 10 8 10 2 5 2 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n522 309 276 521 566 978 175 699 289 118\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '39\\n18329 39326 21115 36341 3916 40060 31717 41923 17476 42107 17052 23198 10756 32540 14873 28454 23912 35765 9459 45834 85 90079 31859 40087 35420 47585 9781 46544 31859 49453 7394 17459 2816 34051 12519 4077 692 44098 23345\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '20\\n8 9 1 10 0 9 5 8 5 7 5 6 0 3 2 7 3 4 6 9\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 2 1 2 1 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '12\\n10 15 10 15 7 3 7 15 7 20 30 20\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '25\\n25 20 58 95 47 68 38 39 33 83 36 68 28 67 25 40 62 110 11 88 74 75 38 90 42\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n8 14 4 7 14\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n200 150 000 23\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n3 2 1 10 1 4 1 10 1 4\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 3 6 5 1 11 8 9\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '30\\n18647 31594 58075 122543 49766 65303 48728 102863 22542 140297 5300 90685 50141 14262 27074 40214 17945 147095 97758 290 121469 221264 63817 138623 63026 110002 70046 208788 122139 116109\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '50\\n11836 38025 72527 92281 139289 93797 134555 148444 40866 111317 21564 87813 65466 20541 99238 1006 74647 128071 18163 61672 39209 55589 138385 147443 79352 142683 60703 3395 52566 72976 147412 116006 115986 110545 79993 100440 9876 71470 75209 62443 64906 88987 72232 2246 63160 45041 729 148611 103397 78474\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n7 4 8 4 8 10 2 5 2 6\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n522 309 276 521 566 978 175 699 505 118\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80213","program":"```python\ndef main():\n n, l = int(input()), list(map(int, input().split()))\n if not (n & 1):\n l.append(0)\n l.append(150001)\n a, b, fails, res = 0, 150001, [], 0\n for i, c in enumerate(l, -1):\n if i & 1:\n if a >= b or b <= c:\n if len(fails) > 5:\n print(0)\n return\n fails.append(i)\n else:\n if a <= b or b >= c:\n if len(fails) > 5:\n print(0)\n return\n fails.append(i)\n a, b = b, c\n check = compile(\"and\".join(\n \"(l[{:n}]{:s}l[{:n}]{:s}l[{:n}])\".format(i - 1, \"><\"[i & 1], i, \"<>\"[i & 1], i + 1) for i in fails),\n \"\", \"eval\")\n for i in fails:\n a = l[i]\n for j in range(n):\n l[i], l[j] = l[j], a\n if eval(check) and ((l[j - 1] < l[j] > l[j + 1]) if j & 1 else (l[j - 1] > l[j] < l[j + 1])):\n res += 1 if j in fails else 2\n l[j] = l[i]\n l[i] = a\n print(res // 2)\n\n\nif __name__ == '__main__':\n main()\n\n\n\n# Made By Mostafa_Khaled\n```","inputs":"5\n2 8 4 7 7\n","output":"2","actual_output":"2\n","execution_success":true,"sample_index":12773},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"701_B. Cells Not Under Attack","prompt":"Solve the following coding problem using the programming language python:\n\nVasya has the square chessboard of size n \u00d7 n and m rooks. Initially the chessboard is empty. Vasya will consequently put the rooks on the board one after another.\n\nThe cell of the field is under rook's attack, if there is at least one rook located in the same row or in the same column with this cell. If there is a rook located in the cell, this cell is also under attack.\n\nYou are given the positions of the board where Vasya will put rooks. For each rook you have to determine the number of cells which are not under attack after Vasya puts it on the board.\n\nInput\n\nThe first line of the input contains two integers n and m (1 \u2264 n \u2264 100 000, 1 \u2264 m \u2264 min(100 000, n2)) \u2014 the size of the board and the number of rooks. \n\nEach of the next m lines contains integers xi and yi (1 \u2264 xi, yi \u2264 n) \u2014 the number of the row and the number of the column where Vasya will put the i-th rook. Vasya puts rooks on the board in the order they appear in the input. It is guaranteed that any cell will contain no more than one rook.\n\nOutput\n\nPrint m integer, the i-th of them should be equal to the number of cells that are not under attack after first i rooks are put.\n\nExamples\n\nInput\n\n3 3\n1 1\n3 1\n2 2\n\n\nOutput\n\n4 2 0 \n\n\nInput\n\n5 2\n1 5\n5 1\n\n\nOutput\n\n16 9 \n\n\nInput\n\n100000 1\n300 400\n\n\nOutput\n\n9999800001 \n\nNote\n\nOn the picture below show the state of the board after put each of the three rooks. The cells which painted with grey color is not under the attack.\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, m = map(int, input().strip().split())\n\nremains = n*n\ndeleted_rows = set()\ndeleted_cols = set()\nanswer = []\nfor _ in range(m):\n c, r = map(int, input().strip().split())\n col_deleted = c in deleted_cols\n row_deleted = r in deleted_rows\n if not (col_deleted and row_deleted):\n if col_deleted:\n remains -= (n - len(deleted_cols))\n elif row_deleted:\n remains -= (n - len(deleted_rows))\n else: # not x_in and not y_in\n remains -= (2*n - len(deleted_cols) - len(deleted_rows) - 1)\n\n deleted_cols.add(c)\n deleted_rows.add(r)\n\n answer.append(str(remains))\n\nprint(' '.join(answer))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 2\\n1 5\\n5 1\\n', 'output': '16 9\\n'}, {'type': 'stdin_stdout', 'input': '100000 1\\n300 400\\n', 'output': '9999800001\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 1\\n3 1\\n2 2\\n', 'output': '4 2 0\\n'}, {'type': 'stdin_stdout', 'input': '99999 1\\n54016 16192\\n', 'output': '9999600004\\n'}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n12100 98787\\n9390 76191\\n5628 47659\\n80075 25361\\n75330 1630\\n38758 99962\\n33848 40352\\n43732 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '330 17\\n259 262\\n146 20\\n235 69\\n84 74\\n131 267\\n153 101\\n32 232\\n214 212\\n239 157\\n121 156\\n10 45\\n266 78\\n52 258\\n109 279\\n193 276\\n239 142\\n321 89\\n', 'output': '108241 107584 106929 106276 105625 104976 104329 103684 103041 102400 101761 101124 100489 99856 99225 98910 98282\\n'}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n460 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n220 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 221840 220899 219960 219023 218088 217620 216688 215758 214830 213904 212980 212058 211138 210220\\n'}, {'type': 'stdin_stdout', 'input': '10 4\\n2 8\\n1 8\\n9 8\\n6 9\\n', 'output': '81 72 63 48\\n'}, {'type': 'stdin_stdout', 'input': '30 30\\n3 13\\n27 23\\n18 24\\n18 19\\n14 20\\n7 10\\n27 13\\n20 27\\n11 1\\n21 10\\n2 9\\n28 12\\n29 19\\n28 27\\n27 29\\n30 12\\n27 2\\n4 5\\n8 19\\n21 2\\n24 27\\n14 22\\n20 3\\n18 3\\n23 9\\n28 6\\n15 12\\n2 2\\n16 27\\n1 14\\n', 'output': '841 784 729 702 650 600 600 552 506 484 441 400 380 380 361 342 324 289 272 272 255 240 225 225 210 196 182 182 168 143\\n'}, {'type': 'stdin_stdout', 'input': '70 31\\n22 39\\n33 43\\n50 27\\n70 9\\n20 67\\n61 24\\n60 4\\n60 28\\n4 25\\n30 29\\n46 47\\n51 48\\n37 5\\n14 29\\n45 44\\n68 35\\n52 21\\n7 37\\n18 43\\n44 22\\n26 12\\n39 37\\n51 55\\n50 23\\n51 16\\n16 49\\n22 62\\n35 45\\n56 2\\n20 51\\n3 37\\n', 'output': '4761 4624 4489 4356 4225 4096 3969 3906 3782 3660 3540 3422 3306 3249 3136 3025 2916 2809 2756 2652 2550 2499 2450 2401 2352 2256 2208 2115 2024 1978 1935\\n'}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n12100 98787\\n9390 76191\\n5628 47659\\n80075 25361\\n75330 1630\\n38758 99962\\n33848 33049\\n43732 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324 '}, {'type': 'stdin_stdout', 'input': '330 17\\n259 262\\n146 20\\n235 69\\n84 68\\n131 267\\n153 101\\n32 232\\n214 212\\n239 157\\n121 156\\n10 45\\n266 78\\n52 258\\n109 279\\n193 276\\n239 142\\n321 89\\n', 'output': '108241 107584 106929 106276 105625 104976 104329 103684 103041 102400 101761 101124 100489 99856 99225 98910 98282 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n220 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 221840 220899 219960 219023 218088 217620 216688 215758 214830 213904 212980 212058 211138 210220 '}, {'type': 'stdin_stdout', 'input': '10 4\\n4 8\\n1 8\\n9 8\\n6 9\\n', 'output': '81 72 63 48 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n171 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 222312 221370 220430 219492 218556 218088 217155 216224 215295 214368 213443 212520 211599 210680 '}, {'type': 'stdin_stdout', 'input': '99999 1\\n69293 16192\\n', 'output': '9999600004 '}, {'type': 'stdin_stdout', 'input': '10 4\\n2 8\\n1 7\\n9 8\\n6 9\\n', 'output': '81 64 56 42 '}, {'type': 'stdin_stdout', 'input': '30 30\\n3 13\\n27 23\\n18 24\\n18 19\\n14 20\\n7 10\\n27 13\\n20 27\\n11 1\\n21 10\\n2 9\\n28 14\\n29 19\\n28 27\\n27 29\\n30 12\\n27 2\\n4 5\\n8 19\\n21 2\\n24 27\\n14 22\\n20 3\\n18 3\\n23 9\\n28 6\\n15 12\\n2 2\\n16 27\\n1 14\\n', 'output': '841 784 729 702 650 600 600 552 506 484 441 400 380 380 361 324 306 272 256 256 240 225 210 210 196 182 169 169 156 143 '}, {'type': 'stdin_stdout', 'input': '100001 1\\n300 400\\n', 'output': '10000000000 '}, {'type': 'stdin_stdout', 'input': '10 4\\n4 8\\n1 8\\n1 8\\n6 9\\n', 'output': '81 72 72 56 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 10\\n290 88\\n309 318\\n280 415\\n485 169\\n106 22\\n355 156\\n180 301\\n205 347\\n148 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n171 218\\n144 369\\n340 91\\n274 212\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 221841 220900 219961 219024 218089 217622 216690 215760 214832 213906 212982 212060 211140 210222 '}, {'type': 'stdin_stdout', 'input': '10 4\\n2 3\\n1 7\\n9 8\\n6 9\\n', 'output': '81 64 49 36 '}, {'type': 'stdin_stdout', 'input': '30 30\\n3 13\\n27 23\\n18 24\\n18 19\\n14 20\\n7 10\\n27 13\\n20 27\\n11 1\\n21 10\\n2 9\\n28 14\\n29 19\\n28 27\\n27 29\\n30 12\\n27 2\\n4 5\\n8 19\\n21 2\\n24 27\\n14 22\\n20 3\\n18 3\\n23 11\\n28 6\\n15 12\\n2 2\\n16 27\\n1 14\\n', 'output': '841 784 729 702 650 600 600 552 506 484 441 400 380 380 361 324 306 272 256 256 240 225 210 210 182 168 156 156 144 132 '}, {'type': 'stdin_stdout', 'input': '100000 1\\n419 400\\n', 'output': '9999800001 '}, {'type': 'stdin_stdout', 'input': '330 17\\n259 262\\n146 20\\n235 69\\n84 28\\n131 267\\n153 101\\n32 232\\n214 212\\n239 157\\n121 156\\n10 45\\n266 69\\n52 258\\n109 279\\n193 276\\n239 142\\n321 89\\n', 'output': '108241 107584 106929 106276 105625 104976 104329 103684 103041 102400 101761 101442 100806 100172 99540 99225 98596 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 10\\n290 88\\n309 203\\n280 415\\n485 169\\n106 22\\n355 156\\n180 301\\n205 347\\n148 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n171 218\\n144 369\\n340 91\\n274 212\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235225 234256 233289 232324 231361 230400 229441 228484 227529 226576 225625 224676 223729 222784 221841 221370 220430 219492 218556 217622 217156 216225 215296 214369 213444 212521 211600 210681 209764 '}, {'type': 'stdin_stdout', 'input': '591 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 10\\n290 88\\n309 318\\n280 415\\n485 169\\n106 22\\n355 156\\n180 301\\n205 347\\n148 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 75\\n171 218\\n144 369\\n340 91\\n184 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '348100 346921 345744 344569 343396 342225 341056 339889 338724 337561 336400 335241 334084 332929 332352 331200 330050 328902 327756 326612 325470 324330 323192 322056 320922 319790 318660 317532 316406 316406 315282 314160 313040 311922 311363 310248 309135 308024 306915 305808 304703 303600 302499 '}, {'type': 'stdin_stdout', 'input': '591 43\\n176 85\\n294 171\\n233 260\\n73 397\\n485 10\\n290 88\\n309 318\\n280 415\\n485 169\\n106 22\\n355 156\\n180 301\\n205 347\\n148 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 75\\n171 218\\n144 369\\n340 91\\n184 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '348100 346921 345744 344569 343396 342225 341056 339889 339306 338142 336980 335820 334662 333506 332929 331776 330625 329476 328329 327184 326041 324900 323761 322624 321489 320356 319225 318096 316969 316969 315844 314721 313600 312481 311922 310806 309692 308580 307470 306362 305256 304152 303050 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 10\\n290 88\\n309 318\\n280 415\\n485 169\\n106 22\\n355 156\\n180 301\\n263 347\\n148 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n171 103\\n144 369\\n340 91\\n184 360\\n171 360\\n41 251\\n346 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n28 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 236196 235225 234256 233289 232324 231361 230400 229441 228484 227529 226576 225625 224676 223729 222784 222784 221841 220900 219961 219024 218556 217622 216690 215760 214832 213906 212982 212060 211140 '}, {'type': 'stdin_stdout', 'input': '30 30\\n3 13\\n27 23\\n18 24\\n18 19\\n14 20\\n7 10\\n27 13\\n20 27\\n11 1\\n21 10\\n2 9\\n28 14\\n29 19\\n28 27\\n27 29\\n30 12\\n27 2\\n4 5\\n8 19\\n21 2\\n24 27\\n14 22\\n20 3\\n18 3\\n23 11\\n28 6\\n15 12\\n1 2\\n16 27\\n1 14\\n', 'output': '841 784 729 702 650 600 600 552 506 484 441 400 380 380 361 324 306 272 256 256 240 225 210 210 182 168 156 144 132 132 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 216\\n280 415\\n485 169\\n106 13\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n8 376\\n236 17\\n94 73\\n116 204\\n166 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n220 374\\n163 316\\n155 158\\n26 110\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235225 234256 233289 232324 231361 230400 229441 228484 227529 226576 225625 224676 223729 222784 221841 221370 220430 219492 218556 217622 217155 216224 215295 214368 213443 212520 211599 210680 209763 '}, {'type': 'stdin_stdout', 'input': '30 30\\n3 13\\n27 23\\n18 24\\n18 19\\n14 20\\n7 10\\n27 13\\n20 27\\n11 1\\n21 10\\n2 9\\n28 14\\n29 19\\n28 27\\n27 29\\n30 12\\n27 1\\n4 5\\n8 19\\n21 2\\n24 27\\n14 22\\n20 3\\n18 3\\n23 11\\n28 6\\n15 12\\n1 2\\n16 27\\n1 14\\n', 'output': '841 784 729 702 650 600 600 552 506 484 441 400 380 380 361 324 324 289 272 256 240 225 210 210 182 168 156 144 132 132 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 216\\n280 415\\n485 169\\n106 13\\n355 129\\n171 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n8 376\\n236 17\\n94 73\\n116 204\\n166 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n220 374\\n163 316\\n155 158\\n26 110\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235225 234256 233289 232324 231361 230400 229441 228484 227529 226576 225625 224676 223729 222784 221841 221841 220900 219961 219024 218089 217622 216690 215760 214832 213906 212982 212060 211140 210222 '}, {'type': 'stdin_stdout', 'input': '30 30\\n3 13\\n27 23\\n16 24\\n18 19\\n14 20\\n7 10\\n27 13\\n20 27\\n11 1\\n21 10\\n2 9\\n28 14\\n29 19\\n28 27\\n27 29\\n30 12\\n27 1\\n4 5\\n8 19\\n21 2\\n24 27\\n14 22\\n20 3\\n18 3\\n23 11\\n28 6\\n15 12\\n1 2\\n16 27\\n1 14\\n', 'output': '841 784 729 676 625 576 576 529 484 462 420 380 360 360 342 306 306 272 255 240 224 210 196 196 169 156 144 132 132 132 '}, {'type': 'stdin_stdout', 'input': '10 4\\n2 9\\n1 8\\n9 8\\n6 9\\n', 'output': '81 64 56 48 '}, {'type': 'stdin_stdout', 'input': '30 30\\n3 13\\n27 23\\n18 24\\n18 19\\n14 20\\n7 10\\n27 13\\n20 27\\n11 1\\n21 10\\n2 9\\n28 12\\n29 19\\n28 27\\n27 29\\n30 12\\n27 4\\n4 5\\n8 19\\n21 2\\n24 27\\n14 22\\n20 3\\n18 3\\n23 9\\n28 6\\n15 12\\n2 2\\n16 27\\n1 14\\n', 'output': '841 784 729 702 650 600 600 552 506 484 441 400 380 380 361 342 324 289 272 256 240 225 210 210 196 182 169 169 156 132 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n73 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n220 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226576 225625 224676 223729 222784 222312 221370 220430 219492 218556 218088 217155 216224 215295 214368 213443 212520 211599 210680 '}, {'type': 'stdin_stdout', 'input': '10 4\\n2 8\\n1 8\\n9 9\\n6 9\\n', 'output': '81 72 56 48 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n155 50\\n171 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 222312 221370 220430 219492 218556 218088 217155 216224 215295 214368 213443 212520 212060 211140 '}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n12100 98787\\n9390 76191\\n5628 47659\\n80075 25361\\n75330 1630\\n38758 99962\\n33848 33049\\n73621 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 221840 220899 219960 219023 218088 217620 216688 215758 214830 213904 212980 212058 211138 210220 '}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n12100 98787\\n9390 76191\\n5628 47659\\n80075 42685\\n75330 1630\\n38758 99962\\n33848 33049\\n73621 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324 '}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n6035 98787\\n9390 76191\\n5628 47659\\n80075 42685\\n75330 1630\\n38758 99962\\n33848 33049\\n73621 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 10\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n171 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 222312 221370 220430 219492 218556 218088 217155 216224 215295 214368 213443 212520 211599 210680 '}, {'type': 'stdin_stdout', 'input': '500 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248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 222312 221370 220430 219492 218556 218088 217155 216224 215295 214368 213443 212520 211599 210680 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 10\\n290 88\\n309 318\\n280 415\\n485 169\\n106 22\\n355 156\\n180 301\\n205 347\\n148 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n171 218\\n144 369\\n340 91\\n184 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 222312 221370 220430 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'input': '500 43\\n215 85\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n164 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 256\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 221840 220899 219960 219023 218088 217620 216688 215758 214830 213904 212980 212058 211138 210220 '}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n6035 98787\\n9390 76191\\n5628 47659\\n80075 42685\\n75330 456\\n38758 99962\\n27478 33049\\n38514 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 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'9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324 '}, {'type': 'stdin_stdout', 'input': '591 43\\n176 85\\n294 171\\n233 260\\n73 397\\n485 10\\n290 88\\n309 318\\n280 415\\n485 169\\n106 22\\n355 156\\n180 301\\n205 347\\n148 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 69\\n116 204\\n166 75\\n171 218\\n144 369\\n340 91\\n184 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '348100 346921 345744 344569 343396 342225 341056 339889 339306 338142 336980 335820 334662 333506 332929 331776 330625 329476 328329 327184 326041 324900 323761 322624 321489 320356 319225 318096 316969 316969 315844 314721 313600 312481 311922 310806 309692 308580 307470 306362 305256 304152 303050 '}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n8163 98787\\n9390 76191\\n5628 47659\\n80075 42685\\n75330 456\\n48412 99962\\n27478 33049\\n38514 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324 '}, {'type': 'stdin_stdout', 'input': '591 43\\n176 85\\n294 171\\n233 260\\n73 397\\n485 10\\n290 88\\n309 318\\n280 415\\n485 169\\n106 22\\n355 156\\n180 301\\n205 347\\n148 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 69\\n116 204\\n166 75\\n171 218\\n144 369\\n340 91\\n184 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n25 126\\n', 'output': '348100 346921 345744 344569 343396 342225 341056 339889 339306 338142 336980 335820 334662 333506 332929 331776 330625 329476 328329 327184 326041 324900 323761 322624 321489 320356 319225 318096 316969 316969 315844 314721 313600 312481 311922 310806 309692 308580 307470 306362 305256 304152 303050 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 216\\n280 415\\n485 169\\n106 13\\n355 129\\n171 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n8 376\\n236 17\\n94 73\\n116 204\\n166 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n220 374\\n23 316\\n155 158\\n26 110\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235225 234256 233289 232324 231361 230400 229441 228484 227529 226576 225625 224676 223729 222784 221841 221841 220900 219961 219024 218089 217622 216690 215760 214832 213906 212982 212060 211140 210222 '}, {'type': 'stdin_stdout', 'input': '30 30\\n3 13\\n27 23\\n16 24\\n18 19\\n14 20\\n7 10\\n27 13\\n20 27\\n11 1\\n21 10\\n2 9\\n28 14\\n29 19\\n28 27\\n27 29\\n30 12\\n27 1\\n4 5\\n8 19\\n21 2\\n24 27\\n14 22\\n20 3\\n18 3\\n23 11\\n28 6\\n15 12\\n1 2\\n24 27\\n1 14\\n', 'output': '841 784 729 676 625 576 576 529 484 462 420 380 360 360 342 306 306 272 255 240 224 210 196 196 169 156 144 132 132 132 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 96\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 216\\n280 415\\n485 169\\n106 13\\n355 129\\n171 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n8 376\\n236 17\\n94 73\\n116 204\\n166 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n220 374\\n23 316\\n155 158\\n26 110\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235225 234256 233289 232324 231361 230400 229441 228484 227529 226576 225625 224676 223729 222784 221841 221841 220900 219961 219024 218089 217622 216690 215760 214832 213906 212982 212060 211140 210222 '}, {'type': 'stdin_stdout', 'input': '99999 1\\n54016 12049\\n', 'output': '9999600004 '}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n12100 98787\\n9390 76191\\n5628 47659\\n80075 25361\\n75330 1630\\n38758 99962\\n33848 46686\\n43732 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324 '}, {'type': 'stdin_stdout', 'input': '330 17\\n259 262\\n146 20\\n235 69\\n84 74\\n131 267\\n153 101\\n32 232\\n214 212\\n239 157\\n121 156\\n10 45\\n266 78\\n52 258\\n109 279\\n193 276\\n239 142\\n321 86\\n', 'output': '108241 107584 106929 106276 105625 104976 104329 103684 103041 102400 101761 101124 100489 99856 99225 98910 98282 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n460 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n150 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n220 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 221840 220899 219960 219023 218088 217620 216688 215758 214830 213904 212980 212058 211138 210220 '}, {'type': 'stdin_stdout', 'input': '100000 1\\n300 493\\n', 'output': '9999800001 '}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n12100 98787\\n9390 76191\\n1023 47659\\n80075 25361\\n75330 1630\\n38758 99962\\n33848 33049\\n43732 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324 '}, {'type': 'stdin_stdout', 'input': '330 17\\n259 262\\n146 20\\n235 69\\n84 68\\n131 267\\n154 101\\n32 232\\n214 212\\n239 157\\n121 156\\n10 45\\n266 78\\n52 258\\n109 279\\n193 276\\n239 142\\n321 89\\n', 'output': '108241 107584 106929 106276 105625 104976 104329 103684 103041 102400 101761 101124 100489 99856 99225 98910 98282 '}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n12100 98787\\n9390 76191\\n3830 47659\\n80075 25361\\n75330 1630\\n38758 99962\\n33848 33049\\n73621 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 86\\n294 171\\n233 260\\n73 397\\n474 35\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n168 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 221840 220899 219960 219023 218088 217620 216688 215758 214830 213904 212980 212058 211138 210220 '}, {'type': 'stdin_stdout', 'input': '99991 9\\n80814 65974\\n12100 98787\\n9390 76191\\n5628 47659\\n80075 42685\\n75330 1630\\n27047 99962\\n33848 33049\\n73621 52281\\n', 'output': '9998000100 9997800121 9997600144 9997400169 9997200196 9997000225 9996800256 9996600289 9996400324 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 10\\n290 422\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n197 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n171 218\\n144 369\\n340 91\\n274 360\\n222 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 221840 220899 219960 219023 218088 217620 216688 215758 214830 213904 212980 212058 211138 210220 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 10\\n339 88\\n309 318\\n280 415\\n485 169\\n106 22\\n355 129\\n180 301\\n205 347\\n148 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n171 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 222312 221370 220430 219492 218556 218088 217155 216224 215295 214368 213443 212520 211599 210680 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 171\\n233 260\\n73 397\\n474 10\\n290 88\\n309 318\\n280 415\\n485 169\\n106 22\\n355 156\\n180 301\\n205 347\\n148 93\\n263 318\\n336 344\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n171 218\\n144 369\\n340 91\\n274 360\\n171 360\\n41 251\\n262 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 222312 221370 220430 219492 218556 218088 217155 216224 215295 214368 213443 212520 211599 210680 '}, {'type': 'stdin_stdout', 'input': '500 43\\n176 85\\n294 40\\n233 260\\n73 397\\n474 10\\n290 88\\n309 318\\n280 415\\n485 169\\n106 22\\n355 156\\n180 301\\n205 347\\n148 93\\n263 318\\n336 382\\n314 350\\n476 214\\n367 277\\n333 166\\n500 376\\n236 17\\n94 73\\n116 204\\n166 50\\n171 218\\n144 369\\n340 91\\n184 360\\n171 360\\n41 251\\n346 478\\n27 163\\n151 491\\n208 415\\n448 386\\n293 486\\n371 479\\n330 435\\n391 374\\n163 316\\n155 158\\n26 126\\n', 'output': '249001 248004 247009 246016 245025 244036 243049 242064 241081 240100 239121 238144 237169 236196 235710 234740 233772 232806 231842 230880 229920 228962 228006 227052 226100 225150 224202 223256 222312 222312 221370 220430 219492 218556 218088 217155 216224 215295 214368 213443 212520 211599 210680 '}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80221","program":"```python\nn, m = map(int, input().strip().split())\n\nremains = n*n\ndeleted_rows = set()\ndeleted_cols = set()\nanswer = []\nfor _ in range(m):\n c, r = map(int, input().strip().split())\n col_deleted = c in deleted_cols\n row_deleted = r in deleted_rows\n if not (col_deleted and row_deleted):\n if col_deleted:\n remains -= (n - len(deleted_cols))\n elif row_deleted:\n remains -= (n - len(deleted_rows))\n else: # not x_in and not y_in\n remains -= (2*n - len(deleted_cols) - len(deleted_rows) - 1)\n\n deleted_cols.add(c)\n deleted_rows.add(r)\n\n answer.append(str(remains))\n\nprint(' '.join(answer))\n\n```","inputs":"5 2\n1 5\n5 1\n","output":"16 9\n","actual_output":"16 9\n","execution_success":true,"sample_index":12775},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"723_C. Polycarp at the Radio","prompt":"Solve the following coding problem using the programming language python:\n\nPolycarp is a music editor at the radio station. He received a playlist for tomorrow, that can be represented as a sequence a1, a2, ..., an, where ai is a band, which performs the i-th song. Polycarp likes bands with the numbers from 1 to m, but he doesn't really like others. \n\nWe define as bj the number of songs the group j is going to perform tomorrow. Polycarp wants to change the playlist in such a way that the minimum among the numbers b1, b2, ..., bm will be as large as possible.\n\nFind this maximum possible value of the minimum among the bj (1 \u2264 j \u2264 m), and the minimum number of changes in the playlist Polycarp needs to make to achieve it. One change in the playlist is a replacement of the performer of the i-th song with any other group.\n\nInput\n\nThe first line of the input contains two integers n and m (1 \u2264 m \u2264 n \u2264 2000).\n\nThe second line contains n integers a1, a2, ..., an (1 \u2264 ai \u2264 109), where ai is the performer of the i-th song.\n\nOutput\n\nIn the first line print two integers: the maximum possible value of the minimum among the bj (1 \u2264 j \u2264 m), where bj is the number of songs in the changed playlist performed by the j-th band, and the minimum number of changes in the playlist Polycarp needs to make.\n\nIn the second line print the changed playlist.\n\nIf there are multiple answers, print any of them.\n\nExamples\n\nInput\n\n4 2\n1 2 3 2\n\n\nOutput\n\n2 1\n1 2 1 2 \n\n\nInput\n\n7 3\n1 3 2 2 2 2 1\n\n\nOutput\n\n2 1\n1 3 3 2 2 2 1 \n\n\nInput\n\n4 4\n1000000000 100 7 1000000000\n\n\nOutput\n\n1 4\n1 2 3 4 \n\nNote\n\nIn the first sample, after Polycarp's changes the first band performs two songs (b1 = 2), and the second band also performs two songs (b2 = 2). Thus, the minimum of these values equals to 2. It is impossible to achieve a higher minimum value by any changes in the playlist. \n\nIn the second sample, after Polycarp's changes the first band performs two songs (b1 = 2), the second band performs three songs (b2 = 3), and the third band also performs two songs (b3 = 2). Thus, the best minimum value is 2. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import Counter\n\nn, m = map(int, input().split())\nnums = list(map(int, input().split()))\n\ncnts = dict(Counter(nums))\nfor i in range(1, m+1):\n if i not in cnts:\n cnts[i] = 0\n\n\ndef minner():\n return min(cnts.items(), key=lambda x: x[1])\n\nn //= m\n\nres = 0\nfor i, num in enumerate(nums):\n if num > m or cnts[num] > n:\n for r in range(1, m+1):\n if cnts[r] < n:\n cnts[num] -= 1\n nums[i] = r\n cnts[r] += 1\n res += 1\n break\n\nprint(n, res)\nprint(' '.join(map(str, nums)))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 2\\n1 2 3 2\\n', 'output': '2 1\\n1 2 1 2 '}, {'type': 'stdin_stdout', 'input': '7 3\\n1 3 2 2 2 2 1\\n', 'output': '2 1\\n1 3 3 2 2 2 1 '}, {'type': 'stdin_stdout', 'input': '4 4\\n1000000000 100 7 1000000000\\n', 'output': '1 4\\n1 2 3 4 '}, {'type': 'stdin_stdout', 'input': '10 4\\n1 1 2 2 3 3 4 4 4 4\\n', 'output': '2 0\\n1 1 2 2 3 3 4 4 4 4 '}, {'type': 'stdin_stdout', 'input': '1 1\\n381183829\\n', 'output': '1 1\\n1 '}, {'type': 'stdin_stdout', 'input': '10 2\\n1 1 1 1 1 1 3 4 5 6\\n', 'output': '5 5\\n2 1 1 1 1 1 2 2 2 2 '}, {'type': 'stdin_stdout', 'input': '7 3\\n2 2 2 1 3 7 6\\n', 'output': '2 2\\n1 2 2 1 3 3 6 '}, {'type': 'stdin_stdout', 'input': '7 2\\n2 2 2 2 2 2 3\\n', 'output': '3 3\\n1 1 1 2 2 2 3 '}, {'type': 'stdin_stdout', 'input': '10 2\\n20515728 1 580955166 856585851 1 738372422 1 2 1 900189620\\n', 'output': '5 5\\n1 1 2 2 1 2 1 2 1 2 '}, {'type': 'stdin_stdout', 'input': '2 1\\n1 1000000000\\n', 'output': '2 1\\n1 1 '}, {'type': 'stdin_stdout', 'input': '4 2\\n1 1 1 1\\n', 'output': '2 2\\n2 2 1 1 '}, {'type': 'stdin_stdout', 'input': '6 3\\n3 3 3 100 1 2\\n', 'output': '2 2\\n1 3 3 2 1 2 '}, {'type': 'stdin_stdout', 'input': '9 2\\n4681851 569491424 579550098 1 554288395 496088833 49710380 904873068 189406728\\n', 'output': '4 7\\n1 1 1 1 2 2 2 2 189406728 '}, {'type': 'stdin_stdout', 'input': '2 1\\n234089514 461271539\\n', 'output': '2 2\\n1 1 '}, {'type': 'stdin_stdout', 'input': '13 4\\n1 1 1 1 2 2 2 2 3 3 4 4 4\\n', 'output': '3 1\\n3 1 1 1 2 2 2 2 3 3 4 4 4 '}, {'type': 'stdin_stdout', 'input': '80 79\\n17 59 54 75 68 69 69 67 62 77 65 78 54 69 59 73 68 57 65 54 66 46 68 68 67 65 75 39 62 63 45 78 72 62 78 34 74 68 78 68 79 60 64 56 68 76 66 44 43 69 74 75 44 66 71 78 41 75 71 77 59 56 78 52 61 64 64 53 79 34 79 79 65 45 79 67 65 78 68 74\\n', 'output': '1 46\\n17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 73 15 57 16 54 18 46 19 20 21 22 23 39 24 63 25 26 72 62 27 28 29 30 31 32 33 60 35 36 37 76 38 40 43 69 42 47 44 66 48 49 41 75 71 77 59 56 50 52 61 51 64 53 55 34 58 70 65 45 79 67 65 78 68 74 '}, {'type': 'stdin_stdout', 'input': '12 4\\n1 1 1 1 2 2 2 2 3 3 4 4\\n', 'output': '3 2\\n3 1 1 1 4 2 2 2 3 3 4 4 '}, {'type': 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'1 4\\n1 2 3 4\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n142622420\\n', 'output': '1 1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n5 1000000000\\n', 'output': '2 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1010000000 100 4 1000000010\\n', 'output': '1 3\\n1 2 4 3\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n3 2 2 1 3 2 5\\n', 'output': '1 1\\n4 2 2 1 3 2 5\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80225","program":"```python\nfrom collections import Counter\n\nn, m = map(int, input().split())\nnums = list(map(int, input().split()))\n\ncnts = dict(Counter(nums))\nfor i in range(1, m+1):\n if i not in cnts:\n cnts[i] = 0\n\n\ndef minner():\n return min(cnts.items(), key=lambda x: x[1])\n\nn //= m\n\nres = 0\nfor i, num in enumerate(nums):\n if num > m or cnts[num] > n:\n for r in range(1, m+1):\n if cnts[r] < n:\n cnts[num] -= 1\n nums[i] = r\n cnts[r] += 1\n res += 1\n break\n\nprint(n, res)\nprint(' '.join(map(str, nums)))\n\n```","inputs":"4 2\n1 2 3 2\n","output":"2 1\n1 2 1 2 ","actual_output":"2 1\n1 2 1 2\n","execution_success":true,"sample_index":12776},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"745_B. Hongcow Solves A Puzzle","prompt":"Solve the following coding problem using the programming language python:\n\nHongcow likes solving puzzles.\n\nOne day, Hongcow finds two identical puzzle pieces, with the instructions \"make a rectangle\" next to them. The pieces can be described by an n by m grid of characters, where the character 'X' denotes a part of the puzzle and '.' denotes an empty part of the grid. It is guaranteed that the puzzle pieces are one 4-connected piece. See the input format and samples for the exact details on how a jigsaw piece will be specified.\n\nThe puzzle pieces are very heavy, so Hongcow cannot rotate or flip the puzzle pieces. However, he is allowed to move them in any directions. The puzzle pieces also cannot overlap.\n\nYou are given as input the description of one of the pieces. Determine if it is possible to make a rectangle from two identical copies of the given input. The rectangle should be solid, i.e. there should be no empty holes inside it or on its border. Keep in mind that Hongcow is not allowed to flip or rotate pieces and they cannot overlap, i.e. no two 'X' from different pieces can share the same position.\n\nInput\n\nThe first line of input will contain two integers n and m (1 \u2264 n, m \u2264 500), the dimensions of the puzzle piece.\n\nThe next n lines will describe the jigsaw piece. Each line will have length m and will consist of characters '.' and 'X' only. 'X' corresponds to a part of the puzzle piece, '.' is an empty space.\n\nIt is guaranteed there is at least one 'X' character in the input and that the 'X' characters form a 4-connected region.\n\nOutput\n\nOutput \"YES\" if it is possible for Hongcow to make a rectangle. Output \"NO\" otherwise.\n\nExamples\n\nInput\n\n2 3\nXXX\nXXX\n\n\nOutput\n\nYES\n\n\nInput\n\n2 2\n.X\nXX\n\n\nOutput\n\nNO\n\n\nInput\n\n5 5\n.....\n..X..\n.....\n.....\n.....\n\n\nOutput\n\nYES\n\nNote\n\nFor the first sample, one example of a rectangle we can form is as follows \n \n \n \n 111222 \n 111222 \n \n\nFor the second sample, it is impossible to put two of those pieces without rotating or flipping to form a rectangle.\n\nIn the third sample, we can shift the first tile by one to the right, and then compose the following rectangle: \n \n \n \n ..... \n ..XX. \n ..... \n ..... \n ..... \n \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, m = map(int, input().split())\no1 = set()\nfor i in range(n):\n s = input()\n if s.count('X') != 0:\n o1.add((s.count('X'), s.find('X'), s.rfind('X')))\nif len(o1) == 1:\n print('YES')\nelse:\n print('NO')\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 2\\n.X\\nXX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n.....\\n..X..\\n.....\\n.....\\n.....\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\nXXX\\nXXX\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\nXXX..\\n.XXX.\\n..XXX\\nXXX..\\n.XXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\nXX..\\n.XX.\\n..XX\\n....\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n.XX\\nXX.\\nXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10 1\\n.\\n.\\n.\\n.\\nX\\n.\\n.\\n.\\n.\\n.\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\nXXXXXX..\\nXXXXXXXX\\n.X.X..X.\\n.XXXX..X\\nXX.XXXXX\\nX...X..X\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\nXXXX\\nXXXX\\nXX..\\nXX..\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\nXXX\\nX.X\\n..X\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8 5\\nXX.XX\\nX.XXX\\nX.XXX\\nXXX.X\\nXX.XX\\nXX..X\\nXXX.X\\nXXXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\nXXX.\\nXXX.\\nX.X.\\n..X.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n...\\n.X.\\nXXX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\nXXX\\nX.X\\nX..\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\nXXX...\\n.XXX..\\n..XXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n.XX\\nXX.\\n...\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n.XXX\\nXXX.\\n.XXX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n.X.XX\\n.XXX.\\n.XXX.\\n.XXX.\\n.XXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\nXXXX.\\n.XXXX\\nXXXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n.XX\\nXX.\\n.XX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n..XX\\n.XX.\\n', 'output': 'NO\\n'}, 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'input': '2 5\\nXY.XX\\nXXX.Y\\nXXX/X\\nXXX.X\\nXX.XX\\nXY.X.\\nXXX.X\\nXXXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 5\\nXY.XX\\nXXX.Y\\nXXX/X\\nXXX.X\\nXX.XX\\nXY.X.\\nXXX.X\\nXXXY.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\nXY..\\n.XX.\\n..XX\\n....\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n.XX\\nXX.\\nXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\nXXXX\\nXXXX\\nXX.-\\nXX..\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8 5\\nXX.XX\\nX.XXX\\nX.XXX\\nXXX.X\\nXXXX.\\nXX..X\\nXXX.X\\nXXXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\nXXX/\\nXXX.\\nX.X.\\n..X.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\nXXX...\\n.XXX.-\\n..XXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\nXX.\\nXX.\\n...\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n.XXX\\nXXX.\\nX.XX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n.X.XX\\n.XXX.\\n.XXX/\\n.XXX.\\n.XXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\nXXXX.\\n.XWXX\\nXXXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n.....\\n.XXX.\\n.X.XX\\n..../\\n.....\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n.XXX.\\n.XXX.\\n..XXX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\nXXX.\\nX.X.\\n.XXX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n.X.\\nXX.\\nX..\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n....\\nXXX.\\nX.XX\\nX.XX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 8\\n.XXXXXX.\\nXXX..XXX\\n.XXXXXX-\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 3\\nX..\\n...\\n', 'output': 'YES\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n.XX\\n.XX\\nXX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 6\\n...XXX\\n.XXX./\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n.....\\n..XXX\\nXXX./\\n..XXX\\n.....\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n....\\n.XX.\\n..XX\\n/...\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\nXX.-\\n.XX.\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\nXXX.\\nYX.X\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\nXX-\\nXX.\\n.XX\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\nXXXXXX..\\nXXXXXXXX\\n.X.X..X.\\nX..XX.XX\\nXX.XXXXX\\nX...X..X\\n', 'output': 'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80229","program":"```python\nn, m = map(int, input().split())\no1 = set()\nfor i in range(n):\n s = input()\n if s.count('X') != 0:\n o1.add((s.count('X'), s.find('X'), s.rfind('X')))\nif len(o1) == 1:\n print('YES')\nelse:\n print('NO')\n```","inputs":"2 2\n.X\nXX\n","output":"NO\n","actual_output":"NO\n","execution_success":true,"sample_index":12777},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"768_D. Jon and Orbs","prompt":"Solve the following coding problem using the programming language python:\n\nJon Snow is on the lookout for some orbs required to defeat the white walkers. There are k different types of orbs and he needs at least one of each. One orb spawns daily at the base of a Weirwood tree north of the wall. The probability of this orb being of any kind is equal. As the north of wall is full of dangers, he wants to know the minimum number of days he should wait before sending a ranger to collect the orbs such that the probability of him getting at least one of each kind of orb is at least , where \u03b5 < 10 - 7.\n\nTo better prepare himself, he wants to know the answer for q different values of pi. Since he is busy designing the battle strategy with Sam, he asks you for your help.\n\nInput\n\nFirst line consists of two space separated integers k, q (1 \u2264 k, q \u2264 1000) \u2014 number of different kinds of orbs and number of queries respectively.\n\nEach of the next q lines contain a single integer pi (1 \u2264 pi \u2264 1000) \u2014 i-th query.\n\nOutput\n\nOutput q lines. On i-th of them output single integer \u2014 answer for i-th query.\n\nExamples\n\nInput\n\n1 1\n1\n\n\nOutput\n\n1\n\n\nInput\n\n2 2\n1\n2\n\n\nOutput\n\n2\n2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nk, q = map(int, input().split())\nt = [0] * (k + 1)\nt[1] = 1\nc = [0]\nn = i = 1\nwhile i < 1001:\n if (2000 * t[k] > i - (10**-7)):\n c.append(n)\n i += 1\n else:\n t = [0] + [(j * t[j] + (k - j + 1) * t[j - 1]) / k for j in range(1, k + 1)]\n n += 1\nfor i in range(q): \n print(c[int(input())])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 1\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n1\\n2\\n', 'output': '2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n1\\n4\\n20\\n50\\n300\\n', 'output': '3\\n3\\n3\\n3\\n3\\n'}, 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'9\\n9\\n10\\n10\\n11\\n9\\n'}], 'language': 'python'}","metadata":"{'difficulty': 10, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80233","program":"```python\nk, q = map(int, input().split())\nt = [0] * (k + 1)\nt[1] = 1\nc = [0]\nn = i = 1\nwhile i < 1001:\n if (2000 * t[k] > i - (10**-7)):\n c.append(n)\n i += 1\n else:\n t = [0] + [(j * t[j] + (k - j + 1) * t[j - 1]) / k for j in range(1, k + 1)]\n n += 1\nfor i in range(q): \n print(c[int(input())])\n```","inputs":"1 1\n1\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12778},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"792_C. Divide by Three","prompt":"Solve the following coding problem using the programming language python:\n\nA positive integer number n is written on a blackboard. It consists of not more than 105 digits. You have to transform it into a beautiful number by erasing some of the digits, and you want to erase as few digits as possible.\n\nThe number is called beautiful if it consists of at least one digit, doesn't have leading zeroes and is a multiple of 3. For example, 0, 99, 10110 are beautiful numbers, and 00, 03, 122 are not.\n\nWrite a program which for the given n will find a beautiful number such that n can be transformed into this number by erasing as few digits as possible. You can erase an arbitraty set of digits. For example, they don't have to go one after another in the number n.\n\nIf it's impossible to obtain a beautiful number, print -1. If there are multiple answers, print any of them.\n\nInput\n\nThe first line of input contains n \u2014 a positive integer number without leading zeroes (1 \u2264 n < 10100000).\n\nOutput\n\nPrint one number \u2014 any beautiful number obtained by erasing as few as possible digits. If there is no answer, print - 1.\n\nExamples\n\nInput\n\n1033\n\n\nOutput\n\n33\n\n\nInput\n\n10\n\n\nOutput\n\n0\n\n\nInput\n\n11\n\n\nOutput\n\n-1\n\nNote\n\nIn the first example it is enough to erase only the first digit to obtain a multiple of 3. But if we erase the first digit, then we obtain a number with a leading zero. So the minimum number of digits to be erased is two.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na = input()\nif len(a) == 1:\n if int(a) % 3 == 0:\n print(a)\n else:\n print(-1)\n exit(0)\none = []\ntwo = []\nsum = 0\nzs, zf = 0, 0\nfor i in range(len(a)):\n q = int(a[i])\n sum += q\n if q == 0:\n if zs == 0:\n zs = i\n else:\n if zs != 0 and zf == 0:\n zf = i\n if q % 3 == 1:\n if len(one) <= 4:\n one.append(i)\n elif q % 3 == 2:\n if len(two) <= 4:\n two.append(i)\n\n\nif zf == 0 and zs != 0:\n zf = len(a) - 1\n\nsol = []\ns = \"\"\nif sum % 3 == 1:\n if len(one) > 0:\n s = a[:one[-1]] + a[one[-1] + 1:]\n sol.append(s)\n if len(a) > 1 and len(two) > 1:\n s = a[:two[-2]] + a[two[-2] + 1:two[-1]] + a[two[-1] + 1:]\n sol.append(s)\nif sum % 3 == 2:\n if len(two) > 0:\n s = a[:two[-1]] + a[two[-1] + 1:]\n sol.append(s)\n if len(a) > 1 and len(one) > 1:\n s = a[:one[-2]] + a[one[-2] + 1:one[-1]] + a[one[-1] + 1:]\n sol.append(s)\nif sum % 3 == 0:\n print(a)\nelse:\n mini = 0\n max = 0\n for i in range(len(sol)):\n if sol[i] == \"\":\n sol[i] = \"-1\"\n elif sol[i][0] == \"0\":\n sol[i] = sol[i][zf - zs:]\n if len(sol[i]) > 0:\n if sol[i][0] == \"0\":\n f = -1\n for j in range(len(sol[i])):\n if sol[i][j] != \"0\":\n f = j\n break\n if f != -1:\n sol[i] = sol[i][f:]\n else:\n sol[i] = \"0\"\n if len(sol[i]) == 0:\n sol[i] = \"0\"\n if len(sol[i]) > max:\n max = len(sol[i])\n mini = i\n\n print(sol[mini])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '11\\n', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1033\\n', 'output': '33\\n'}, {'type': 'stdin_stdout', 'input': '100020001\\n', 'output': '10002000\\n'}, {'type': 'stdin_stdout', 'input': '100000000000000000222\\n', 'output': '1000000000000000002\\n'}, {'type': 'stdin_stdout', 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'1000000000000000000000000010000000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '31\\n', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80237","program":"```python\na = input()\nif len(a) == 1:\n if int(a) % 3 == 0:\n print(a)\n else:\n print(-1)\n exit(0)\none = []\ntwo = []\nsum = 0\nzs, zf = 0, 0\nfor i in range(len(a)):\n q = int(a[i])\n sum += q\n if q == 0:\n if zs == 0:\n zs = i\n else:\n if zs != 0 and zf == 0:\n zf = i\n if q % 3 == 1:\n if len(one) <= 4:\n one.append(i)\n elif q % 3 == 2:\n if len(two) <= 4:\n two.append(i)\n\n\nif zf == 0 and zs != 0:\n zf = len(a) - 1\n\nsol = []\ns = \"\"\nif sum % 3 == 1:\n if len(one) > 0:\n s = a[:one[-1]] + a[one[-1] + 1:]\n sol.append(s)\n if len(a) > 1 and len(two) > 1:\n s = a[:two[-2]] + a[two[-2] + 1:two[-1]] + a[two[-1] + 1:]\n sol.append(s)\nif sum % 3 == 2:\n if len(two) > 0:\n s = a[:two[-1]] + a[two[-1] + 1:]\n sol.append(s)\n if len(a) > 1 and len(one) > 1:\n s = a[:one[-2]] + a[one[-2] + 1:one[-1]] + a[one[-1] + 1:]\n sol.append(s)\nif sum % 3 == 0:\n print(a)\nelse:\n mini = 0\n max = 0\n for i in range(len(sol)):\n if sol[i] == \"\":\n sol[i] = \"-1\"\n elif sol[i][0] == \"0\":\n sol[i] = sol[i][zf - zs:]\n if len(sol[i]) > 0:\n if sol[i][0] == \"0\":\n f = -1\n for j in range(len(sol[i])):\n if sol[i][j] != \"0\":\n f = j\n break\n if f != -1:\n sol[i] = sol[i][f:]\n else:\n sol[i] = \"0\"\n if len(sol[i]) == 0:\n sol[i] = \"0\"\n if len(sol[i]) > max:\n max = len(sol[i])\n mini = i\n\n print(sol[mini])\n```","inputs":"10\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12779},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"812_E. Sagheer and Apple Tree","prompt":"Solve the following coding problem using the programming language python:\n\nSagheer is playing a game with his best friend Soliman. He brought a tree with n nodes numbered from 1 to n and rooted at node 1. The i-th node has ai apples. This tree has a special property: the lengths of all paths from the root to any leaf have the same parity (i.e. all paths have even length or all paths have odd length).\n\nSagheer and Soliman will take turns to play. Soliman will make the first move. The player who can't make a move loses.\n\nIn each move, the current player will pick a single node, take a non-empty subset of apples from it and do one of the following two things:\n\n 1. eat the apples, if the node is a leaf. \n 2. move the apples to one of the children, if the node is non-leaf. \n\n\n\nBefore Soliman comes to start playing, Sagheer will make exactly one change to the tree. He will pick two different nodes u and v and swap the apples of u with the apples of v.\n\nCan you help Sagheer count the number of ways to make the swap (i.e. to choose u and v) after which he will win the game if both players play optimally? (u, v) and (v, u) are considered to be the same pair.\n\nInput\n\nThe first line will contain one integer n (2 \u2264 n \u2264 105) \u2014 the number of nodes in the apple tree.\n\nThe second line will contain n integers a1, a2, ..., an (1 \u2264 ai \u2264 107) \u2014 the number of apples on each node of the tree.\n\nThe third line will contain n - 1 integers p2, p3, ..., pn (1 \u2264 pi \u2264 n) \u2014 the parent of each node of the tree. Node i has parent pi (for 2 \u2264 i \u2264 n). Node 1 is the root of the tree.\n\nIt is guaranteed that the input describes a valid tree, and the lengths of all paths from the root to any leaf will have the same parity.\n\nOutput\n\nOn a single line, print the number of different pairs of nodes (u, v), u \u2260 v such that if they start playing after swapping the apples of both nodes, Sagheer will win the game. (u, v) and (v, u) are considered to be the same pair.\n\nExamples\n\nInput\n\n3\n2 2 3\n1 1\n\n\nOutput\n\n1\n\n\nInput\n\n3\n1 2 3\n1 1\n\n\nOutput\n\n0\n\n\nInput\n\n8\n7 2 2 5 4 3 1 1\n1 1 1 4 4 5 6\n\n\nOutput\n\n4\n\nNote\n\nIn the first sample, Sagheer can only win if he swapped node 1 with node 3. In this case, both leaves will have 2 apples. If Soliman makes a move in a leaf node, Sagheer can make the same move in the other leaf. If Soliman moved some apples from a root to a leaf, Sagheer will eat those moved apples. Eventually, Soliman will not find a move.\n\nIn the second sample, There is no swap that will make Sagheer win the game.\n\nNote that Sagheer must make the swap even if he can win with the initial tree.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn= int(input())\na = [int(_) for _ in input().split()]\nc = [int(_) for _ in input().split()]\ndepth = [0] * (n)\nfor i in range(1,n):\n depth[i] = depth[c[i-1]-1] + 1\nMAX = max(depth)\nt = 0\nstore = {}\ntodo = []\np = 0\n\nfor i in range(n):\n if (MAX-depth[i]) % 2 == 0: # odd, useful\n t ^= a[i]\n todo.append(a[i])\n else:\n store[a[i]] = store.get(a[i],0) + 1\n p += 1\n\nans = 0\nfor i in todo:\n ans += store.get(i^t,0)\n\nif t == 0:\n ans += (p*(p-1)//2) + (n-p)*(n-p-1)//2\n\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '8\\n7 2 2 5 4 3 1 1\\n1 1 1 4 4 5 6\\n', 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'0\\n'}, {'type': 'stdin_stdout', 'input': '7\\n15 16 49 1 2 2 18\\n1 1 2 2 3 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n191029 160180 159138 387479 61727 310778 534080 300097 442549 542174\\n1 2 3 4 4 1 7 1 9\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n13365 9661 17230\\n1 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n49 140 47 18 59 63\\n1 2 2 1 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 0 1\\n1 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n16 101 12 90 19\\n1 1 3 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n191029 160180 159138 387479 61727 357477 534080 300097 442549 542174\\n1 2 3 4 4 1 7 1 9\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n13365 10310 17230\\n1 1\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80241","program":"```python\nn= int(input())\na = [int(_) for _ in input().split()]\nc = [int(_) for _ in input().split()]\ndepth = [0] * (n)\nfor i in range(1,n):\n depth[i] = depth[c[i-1]-1] + 1\nMAX = max(depth)\nt = 0\nstore = {}\ntodo = []\np = 0\n\nfor i in range(n):\n if (MAX-depth[i]) % 2 == 0: # odd, useful\n t ^= a[i]\n todo.append(a[i])\n else:\n store[a[i]] = store.get(a[i],0) + 1\n p += 1\n\nans = 0\nfor i in todo:\n ans += store.get(i^t,0)\n\nif t == 0:\n ans += (p*(p-1)//2) + (n-p)*(n-p-1)//2\n\nprint(ans)\n```","inputs":"8\n7 2 2 5 4 3 1 1\n1 1 1 4 4 5 6\n","output":"4\n","actual_output":"4\n","execution_success":true,"sample_index":12780},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"859_B. Lazy Security Guard","prompt":"Solve the following coding problem using the programming language python:\n\nYour security guard friend recently got a new job at a new security company. The company requires him to patrol an area of the city encompassing exactly N city blocks, but they let him choose which blocks. That is, your friend must walk the perimeter of a region whose area is exactly N blocks. Your friend is quite lazy and would like your help to find the shortest possible route that meets the requirements. The city is laid out in a square grid pattern, and is large enough that for the sake of the problem it can be considered infinite.\n\nInput\n\nInput will consist of a single integer N (1 \u2264 N \u2264 106), the number of city blocks that must be enclosed by the route.\n\nOutput\n\nPrint the minimum perimeter that can be achieved.\n\nExamples\n\nInput\n\n4\n\n\nOutput\n\n8\n\n\nInput\n\n11\n\n\nOutput\n\n14\n\n\nInput\n\n22\n\n\nOutput\n\n20\n\nNote\n\nHere are some possible shapes for the examples:\n\n\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\nn=int(input())\nprint(math.ceil(math.sqrt(n)*2)*2)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '22\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '11\\n', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '4\\n', 'output': '8\\n'}, {'type': 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'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '49\\n', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '10563\\n', 'output': '412\\n'}, {'type': 'stdin_stdout', 'input': '211\\n', 'output': '60\\n'}, {'type': 'stdin_stdout', 'input': '11001\\n', 'output': '420\\n'}, {'type': 'stdin_stdout', 'input': '46\\n', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '54\\n', 'output': '30\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80249","program":"```python\nimport math\nn=int(input())\nprint(math.ceil(math.sqrt(n)*2)*2)\n```","inputs":"22\n","output":"20\n","actual_output":"20\n","execution_success":true,"sample_index":12781},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"884_A. Book Reading","prompt":"Solve the following coding problem using the programming language python:\n\nRecently Luba bought a very interesting book. She knows that it will take t seconds to read the book. Luba wants to finish reading as fast as she can.\n\nBut she has some work to do in each of n next days. The number of seconds that Luba has to spend working during i-th day is ai. If some free time remains, she can spend it on reading.\n\nHelp Luba to determine the minimum number of day when she finishes reading.\n\nIt is guaranteed that the answer doesn't exceed n.\n\nRemember that there are 86400 seconds in a day.\n\nInput\n\nThe first line contains two integers n and t (1 \u2264 n \u2264 100, 1 \u2264 t \u2264 106) \u2014 the number of days and the time required to read the book.\n\nThe second line contains n integers ai (0 \u2264 ai \u2264 86400) \u2014 the time Luba has to spend on her work during i-th day.\n\nOutput\n\nPrint the minimum day Luba can finish reading the book.\n\nIt is guaranteed that answer doesn't exceed n.\n\nExamples\n\nInput\n\n2 2\n86400 86398\n\n\nOutput\n\n2\n\n\nInput\n\n2 86400\n0 86400\n\n\nOutput\n\n1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,t=map(int,input().split())\na=input().split()\ni=0\nwhile t > 0:\n t-=(86400-int(a[i]))\n i += 1\nprint(i)\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 2\\n86400 86398\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2 86400\\n0 86400\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 1200\\n86400 86400 86000 86000 86000 86400\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '4 172799\\n1 1 86400 0\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n1 1 86400 1 86399 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100 1000000\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n86399\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 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-1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '100 1000000\\n0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 1 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 -1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 -1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '100 1000000\\n0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 1 0 0 1 -1 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 -1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 -1 0 0 0\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n0 1 15557 1 86399 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100 1000000\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '2 86400\\n0 72809\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2 86400\\n0 70855\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '100 1000000\\n0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0\\n', 'output': '12\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80253","program":"```python\nn,t=map(int,input().split())\na=input().split()\ni=0\nwhile t > 0:\n t-=(86400-int(a[i]))\n i += 1\nprint(i)\n\n\n```","inputs":"2 2\n86400 86398\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12782},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"908_C. New Year and Curling","prompt":"Solve the following coding problem using the programming language python:\n\nCarol is currently curling.\n\nShe has n disks each with radius r on the 2D plane. \n\nInitially she has all these disks above the line y = 10100.\n\nShe then will slide the disks towards the line y = 0 one by one in order from 1 to n. \n\nWhen she slides the i-th disk, she will place its center at the point (xi, 10100). She will then push it so the disk\u2019s y coordinate continuously decreases, and x coordinate stays constant. The disk stops once it touches the line y = 0 or it touches any previous disk. Note that once a disk stops moving, it will not move again, even if hit by another disk. \n\nCompute the y-coordinates of centers of all the disks after all disks have been pushed.\n\nInput\n\nThe first line will contain two integers n and r (1 \u2264 n, r \u2264 1 000), the number of disks, and the radius of the disks, respectively.\n\nThe next line will contain n integers x1, x2, ..., xn (1 \u2264 xi \u2264 1 000) \u2014 the x-coordinates of the disks.\n\nOutput\n\nPrint a single line with n numbers. The i-th number denotes the y-coordinate of the center of the i-th disk. The output will be accepted if it has absolute or relative error at most 10 - 6.\n\nNamely, let's assume that your answer for a particular value of a coordinate is a and the answer of the jury is b. The checker program will consider your answer correct if for all coordinates.\n\nExample\n\nInput\n\n6 2\n5 5 6 8 3 12\n\n\nOutput\n\n2 6.0 9.87298334621 13.3370849613 12.5187346573 13.3370849613\n\nNote\n\nThe final positions of the disks will look as follows:\n\n\n\nIn particular, note the position of the last disk. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, r = map(int, input().split())\na = input().split()\nans = []\nfor i in range(n):\n res = r\n for j in range(i):\n if (abs(int(a[j]) - int(a[i])) <= 2 * r):\n res = max(res, ans[j] + (4 * r * r - abs(int(a[j]) - int(a[i])) ** 2) ** 0.5)\n ans.append(res)\nfor i in range(n):\n print(ans[i], end = ' ')\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 2\\n5 5 6 8 3 12\\n', 'output': '2 6.0 9.872983346207416 13.33708496134517 12.518734657272006 13.33708496134517\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n5\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 10\\n1 100 1000\\n', 'output': '10 10 10\\n'}, {'type': 'stdin_stdout', 'input': '5 300\\n939 465 129 611 532\\n', 'output': '300 667.8641053432639 1164.9596695962555 1522.2774553276686 2117.0538839123933\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n416 387 336 116 81\\n', 'output': '1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n2 20\\n', 'output': '1 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n10 10 100\\n', 'output': '2 6.0 2\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3 10\\n1 000 1000\\n', 'output': '10 29.974984355438178 10\\n'}, {'type': 'stdin_stdout', 'input': '5 300\\n939 465 246 611 532\\n', 'output': '300 667.8641053432639 1226.468616603243 1702.6776043386699 2297.4540329233946\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n416 387 230 116 81\\n', 'output': '1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n0 20\\n', 'output': '1 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n10 10 000\\n', 'output': '2 6.0 2\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 300\\n939 465 246 611 989\\n', 'output': '300 667.8641053432639 1226.468616603243 1702.6776043386699 2168.634683907164\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n10 11 000\\n', 'output': '2 5.872983346207417 2\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n10 7 000\\n', 'output': '2 4.645751311064591 2\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n445 387 230 116 19\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n9 7 001\\n', 'output': '2 5.464101615137754 2\\n'}, {'type': 'stdin_stdout', 'input': '3 15\\n1 100 1000\\n', 'output': '15 15 15\\n'}, {'type': 'stdin_stdout', 'input': '5 300\\n594 465 129 611 532\\n', 'output': '300 885.9684291836891 1383.0639934366804 1740.3817791680935 2335.1582077528183\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n2 20\\n', 'output': '0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n10 10 100\\n', 'output': '4 12.0 4\\n'}, {'type': 'stdin_stdout', 'input': '6 0\\n5 5 6 8 3 12\\n', 'output': '0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 300\\n899 465 246 611 532\\n', 'output': '300 714.2994086406593 1272.9039199006384 1749.1129076360653 2343.88933622079\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n20 10 000\\n', 'output': '2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '3 4\\n10 7 000\\n', 'output': '4 11.416198487095663 15.28918183330308\\n'}, {'type': 'stdin_stdout', 'input': '5 300\\n594 221 129 611 532\\n', 'output': '300 769.9691479235632 1362.8738620218742 1720.1916477532873 2314.968076338012\\n'}, {'type': 'stdin_stdout', 'input': '1 3\\n0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3 0\\n10 11 100\\n', 'output': '0 0 0\\n'}, 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'stdin_stdout', 'input': '5 0\\n445 135 73 30 19\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n445 135 73 30 33\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n348 135 73 30 33\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n416 387 336 129 81\\n', 'output': '1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n416 387 230 116 81\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n0\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n445 224 230 116 81\\n', 'output': '1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n10 11 100\\n', 'output': '2 5.872983346207417 2\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n445 387 64 116 19\\n', 'output': '1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n445 472 230 116 19\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n12 7 001\\n', 'output': '2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n445 387 73 216 19\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n9 10 001\\n', 'output': '2 5.872983346207417 2\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n445 135 73 92 19\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n445 135 73 30 14\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n445 228 73 30 33\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 15\\n1 110 1000\\n', 'output': '15 15 15\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n416 387 662 129 81\\n', 'output': '1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n2 0\\n', 'output': '0 0\\n'}, {'type': 'stdin_stdout', 'input': '6 0\\n5 5 6 4 3 12\\n', 'output': '0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n416 387 230 222 81\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n20 16 000\\n', 'output': '2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n445 224 230 116 103\\n', 'output': '1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n445 387 4 116 19\\n', 'output': '1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n773 472 230 116 19\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n22 7 001\\n', 'output': '2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n445 387 73 216 32\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n773 135 73 30 14\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n445 228 30 30 33\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 0\\n2 1\\n', 'output': '0 0\\n'}, {'type': 'stdin_stdout', 'input': '6 0\\n5 5 6 4 3 17\\n', 'output': '0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 0\\n416 387 230 52 81\\n', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n20 16 010\\n', 'output': '2 2 2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80257","program":"```python\nn, r = map(int, input().split())\na = input().split()\nans = []\nfor i in range(n):\n res = r\n for j in range(i):\n if (abs(int(a[j]) - int(a[i])) <= 2 * r):\n res = max(res, ans[j] + (4 * r * r - abs(int(a[j]) - int(a[i])) ** 2) ** 0.5)\n ans.append(res)\nfor i in range(n):\n print(ans[i], end = ' ')\n```","inputs":"6 2\n5 5 6 8 3 12\n","output":"2 6.0 9.872983346207416 13.33708496134517 12.518734657272006 13.33708496134517\n","actual_output":"2 6.0 9.872983346207416 13.33708496134517 12.518734657272006 13.33708496134517 ","execution_success":true,"sample_index":12783},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"92_B. Binary Number","prompt":"Solve the following coding problem using the programming language python:\n\nLittle walrus Fangy loves math very much. That's why when he is bored he plays with a number performing some operations.\n\nFangy takes some positive integer x and wants to get a number one from it. While x is not equal to 1, Fangy repeats the following action: if x is odd, then he adds 1 to it, otherwise he divides x by 2. Fangy knows that for any positive integer number the process ends in finite time.\n\nHow many actions should Fangy perform to get a number one from number x?\n\nInput\n\nThe first line contains a positive integer x in a binary system. It is guaranteed that the first digit of x is different from a zero and the number of its digits does not exceed 106.\n\nOutput\n\nPrint the required number of actions.\n\nExamples\n\nInput\n\n1\n\n\nOutput\n\n0\n\n\nInput\n\n1001001\n\n\nOutput\n\n12\n\n\nInput\n\n101110\n\n\nOutput\n\n8\n\nNote\n\nLet's consider the third sample. Number 101110 is even, which means that we should divide it by 2. After the dividing Fangy gets an odd number 10111 and adds one to it. Number 11000 can be divided by 2 three times in a row and get number 11. All that's left is to increase the number by one (we get 100), and then divide it by 2 two times in a row. As a result, we get 1.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import *\n\n\ndef add(n):\n for i in range(len(n) - 1, -1, -1):\n if n[i] == '1':\n n[i] = '0'\n else:\n n[i] = '1'\n return n\n n.appendleft('1')\n return n\n\n\ndef main():\n n, ans = deque(input()), 0\n\n while (len(n) != 1):\n if n[-1] == '1':\n n = add(n)\n else:\n n.pop()\n ans += 1\n\n print(ans)\n\n\nif __name__ == '__main__':\n main()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '101110\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1001001\\n', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '11100000110100011110101001101111100000011001111000011110000000111110111\\n', 'output': '106\\n'}, {'type': 'stdin_stdout', 'input': '1000101100110000000001111010110000000010001001111110011011000011101011001001010010111\\n', 'output': '133\\n'}, {'type': 'stdin_stdout', 'input': '10000100000\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '1010101001001111000111110011111000010101011111101010\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '11000111111110110110100110110101111100010100110110010\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '11\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1100000010010100111011100011110101111\\n', 'output': '55\\n'}, {'type': 'stdin_stdout', 'input': '1000000000000000000000000000000000000000000000000000000000000000000000000\\n', 'output': '72\\n'}, {'type': 'stdin_stdout', 'input': '11110001101\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '11100000110100011010101001101111100000011001111000011110000000111110111\\n', 'output': '107\\n'}, {'type': 'stdin_stdout', 'input': '1000101100100000000001111010110000000010001001111110011011000011101011001001010010111\\n', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '10000100100\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '1010001001001111000111110011111000010101011111101010\\n', 'output': '75\\n'}, {'type': 'stdin_stdout', 'input': '1100000010010000111011100011110101111\\n', 'output': '56\\n'}, {'type': 'stdin_stdout', 'input': '1000000000000000000000000000010000000000000000000000000000000000000000000\\n', 'output': '102\\n'}, {'type': 'stdin_stdout', 'input': '11110001001\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '101010\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1001000\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '11101000110100011010101001101111100000011001111000011110000000111110111\\n', 'output': '106\\n'}, {'type': 'stdin_stdout', 'input': '1000101100100000000001111010100000000010001001111110011011000011101011001001010010111\\n', 'output': '135\\n'}, {'type': 'stdin_stdout', 'input': '10000000100\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '1010001001001111010111110011111000010101011111101010\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '10000111111100110110100110110101111100010100110110010\\n', 'output': '76\\n'}, {'type': 'stdin_stdout', 'input': '1100000010010000111011100011100101111\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '11110001011\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '111010\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1000101100100000000001111010100000000010001001111110011010000011101011001001010010111\\n', 'output': '136\\n'}, {'type': 'stdin_stdout', 'input': '111110\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1000000000000000000000010000010000000000000000010000000000000001000000000\\n', 'output': '133\\n'}, {'type': 'stdin_stdout', 'input': 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'1000101001001101010111110111011010011111011111111010\\n', 'output': '71\\n'}, {'type': 'stdin_stdout', 'input': '1000100000000000000000011000010000000000001100010000000001000001001001000\\n', 'output': '132\\n'}, {'type': 'stdin_stdout', 'input': '1000111001001101010111110111011010011111011111111010\\n', 'output': '70\\n'}, {'type': 'stdin_stdout', 'input': '10000111111110110110100110110101111100010100110110010\\n', 'output': '75\\n'}, {'type': 'stdin_stdout', 'input': '1000000000000000000000000000010000000000000000000000000000000001000000000\\n', 'output': '135\\n'}, {'type': 'stdin_stdout', 'input': '1011000\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '11101000110100011010101001101111100000011001111000011110000000111110011\\n', 'output': '107\\n'}, {'type': 'stdin_stdout', 'input': '10000001100\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '1000001001001111010111110011111000010101011111101010\\n', 'output': '75\\n'}, {'type': 'stdin_stdout', 'input': '10000111111100110110100110110101111100110100110110010\\n', 'output': '75\\n'}, {'type': 'stdin_stdout', 'input': '1101000010010000111011100011100101111\\n', 'output': '56\\n'}, {'type': 'stdin_stdout', 'input': '1000000000000000000000000000010000000000000000010000000000000001000000000\\n', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '1010000\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '11101100110100011010101001101111100000011001111000011110000000111110011\\n', 'output': '106\\n'}, {'type': 'stdin_stdout', 'input': '1000101100100000000001111010110000000010001001111110011010000011101011001001010010111\\n', 'output': '135\\n'}, {'type': 'stdin_stdout', 'input': '11000001100\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '1000001001001111010111110011111000010101011111111010\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '10000111011100110110100110110101111100110100110110010\\n', 'output': '76\\n'}, {'type': 'stdin_stdout', 'input': '1101000010010000111011100011100101011\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '110010\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1110000\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1000101100100000000001111010110000000010001001111110011010000111101011001001010010111\\n', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '11100001100\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '1000001001001111010111110011011000010101011111111010\\n', 'output': '75\\n'}, {'type': 'stdin_stdout', 'input': '1101000010010000111011100011100111011\\n', 'output': '56\\n'}, {'type': 'stdin_stdout', 'input': '1000000000000000000000010000010000000000000000010000000000000001001000000\\n', 'output': '135\\n'}, {'type': 'stdin_stdout', 'input': '110011\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1111000\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '11101100110110011010101001101111100000011001111000001110000000111110011\\n', 'output': '106\\n'}, {'type': 'stdin_stdout', 'input': '1000101100100000000001111010110000000010001001111110011010000101101011001001010010111\\n', 'output': '135\\n'}, {'type': 'stdin_stdout', 'input': '1000001001001111010111110011011000011101011111111010\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '10000111011100110110100110110101111100111100110110010\\n', 'output': '75\\n'}, {'type': 'stdin_stdout', 'input': '1101000010010000111011100011100011011\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '1000100000000000000000010000010000000000000000010000000000000001001000000\\n', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '111011\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1111001\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '11101100110110011010101001101111100001011001111000001110000000111110011\\n', 'output': '105\\n'}, {'type': 'stdin_stdout', 'input': '1000101100100000001001111010110000000010001001111110011010000101101011001001010010111\\n', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '10000111111100110110100110110101111100111100110110010\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '1000100000000000000000010000010000000000000000010000000000000001001001000\\n', 'output': '136\\n'}, {'type': 'stdin_stdout', 'input': '111111\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1000101000100000001001111010110000000010001001111110011010000101101011001001010010111\\n', 'output': '135\\n'}, {'type': 'stdin_stdout', 'input': '11110011101\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '10000111111100110110110110110101111100111100110110010\\n', 'output': '73\\n'}, {'type': 'stdin_stdout', 'input': '1111000010010000111011100011100011001\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '1000100000000000000000010000010000000000001000010000000000000001001001000\\n', 'output': '135\\n'}, {'type': 'stdin_stdout', 'input': '111101\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1000101000100000001001111010110000000010001001111110011010000101101011001001010011111\\n', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '11110001111\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '1000001001001101010111110011011010011111011111111010\\n', 'output': '73\\n'}, {'type': 'stdin_stdout', 'input': '11000111111100110110110110110101111100111100110110010\\n', 'output': '72\\n'}, {'type': 'stdin_stdout', 'input': '1111000010010000111011000011100011001\\n', 'output': '58\\n'}, {'type': 'stdin_stdout', 'input': '1000100000000000000000011000010000000000001000010000000000000001001001000\\n', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '110111\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '10101100110110011010101001101111100001011001111010001110000010111110011\\n', 'output': '104\\n'}, {'type': 'stdin_stdout', 'input': '1000101000100000001001111010110000010010001001111110011010000101101011001001010011111\\n', 'output': '133\\n'}, {'type': 'stdin_stdout', 'input': '11010001111\\n', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '1000001001001101010111110111011010011111011111111010\\n', 'output': '72\\n'}, {'type': 'stdin_stdout', 'input': '11000111111100110110110110110101111100110100110110010\\n', 'output': '73\\n'}, {'type': 'stdin_stdout', 'input': '1111000010010100111011000011100011001\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '1000100000000000000000011000010000000000001000010000000001000001001001000\\n', 'output': '133\\n'}, {'type': 'stdin_stdout', 'input': '10101100110110011010101101101111100001011001111010001110000010111110011\\n', 'output': '103\\n'}, {'type': 'stdin_stdout', 'input': '1000101000100000001001111000110000010010001001111110011010000101101011001001010011111\\n', 'output': '134\\n'}, {'type': 'stdin_stdout', 'input': '11000001111\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '11000111111100110110010110110101111100110100110110010\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '1011000010010100111011000011100011001\\n', 'output': '58\\n'}, {'type': 'stdin_stdout', 'input': '10101100110110011010101101101111100001011001111010011110000010111110011\\n', 'output': '102\\n'}, {'type': 'stdin_stdout', 'input': '1000101000100000011001111000110000010010001001111110011010000101101011001001010011111\\n', 'output': '133\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80261","program":"```python\nfrom collections import *\n\n\ndef add(n):\n for i in range(len(n) - 1, -1, -1):\n if n[i] == '1':\n n[i] = '0'\n else:\n n[i] = '1'\n return n\n n.appendleft('1')\n return n\n\n\ndef main():\n n, ans = deque(input()), 0\n\n while (len(n) != 1):\n if n[-1] == '1':\n n = add(n)\n else:\n n.pop()\n ans += 1\n\n print(ans)\n\n\nif __name__ == '__main__':\n main()\n\n```","inputs":"1\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12784},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"983_B. XOR-pyramid","prompt":"Solve the following coding problem using the programming language python:\n\nFor an array b of length m we define the function f as \n\n f(b) = \\begin{cases} b[1] & if m = 1 \\\\\\ f(b[1] \u2295 b[2],b[2] \u2295 b[3],...,b[m-1] \u2295 b[m]) & otherwise, \\end{cases} \n\nwhere \u2295 is [bitwise exclusive OR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).\n\nFor example, f(1,2,4,8)=f(1\u22952,2\u22954,4\u22958)=f(3,6,12)=f(3\u22956,6\u229512)=f(5,10)=f(5\u229510)=f(15)=15\n\nYou are given an array a and a few queries. Each query is represented as two integers l and r. The answer is the maximum value of f on all continuous subsegments of the array a_l, a_{l+1}, \u2026, a_r.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 5000) \u2014 the length of a.\n\nThe second line contains n integers a_1, a_2, ..., a_n (0 \u2264 a_i \u2264 2^{30}-1) \u2014 the elements of the array.\n\nThe third line contains a single integer q (1 \u2264 q \u2264 100 000) \u2014 the number of queries.\n\nEach of the next q lines contains a query represented as two integers l, r (1 \u2264 l \u2264 r \u2264 n).\n\nOutput\n\nPrint q lines \u2014 the answers for the queries.\n\nExamples\n\nInput\n\n3\n8 4 1\n2\n2 3\n1 2\n\n\nOutput\n\n5\n12\n\n\nInput\n\n6\n1 2 4 8 16 32\n4\n1 6\n2 5\n3 4\n1 2\n\n\nOutput\n\n60\n30\n12\n3\n\nNote\n\nIn first sample in both queries the maximum value of the function is reached on the subsegment that is equal to the whole segment.\n\nIn second sample, optimal segment for first query are [3,6], for second query \u2014 [2,5], for third \u2014 [3,4], for fourth \u2014 [1,2].\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\narr = list(map(int, input().split()))\n\naux = [[0] * n for i in range(n)]\n\nfor i in range(n):\n aux[0][i] = arr[i]\n\nfor i in range(1, n):\n for j in range(n-i):\n aux[i][j] = aux[i-1][j] ^ aux[i-1][j+1]\n \nfor i in range(1, n):\n for j in range(n-i):\n aux[i][j] = max(aux[i][j], aux[i-1][j], aux[i-1][j+1])\n \nq = int(input())\nfor i in range(q):\n buscaEsquerda, buscaDireita = map(int, input().split())\n buscaEsquerda, buscaDireita = buscaEsquerda-1, buscaDireita-1\n print(aux[buscaDireita-buscaEsquerda][buscaEsquerda])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6\\n1 2 4 8 16 32\\n4\\n1 6\\n2 5\\n3 4\\n1 2\\n', 'output': '60\\n30\\n12\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 4 1\\n2\\n2 3\\n1 2\\n', 'output': '5\\n12\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 16 32\\n4\\n1 6\\n2 5\\n3 4\\n1 2\\n', 'output': '56\\n28\\n12\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 4 1\\n2\\n2 3\\n1 2\\n', 'output': '5\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 2 4 12 16 32\\n4\\n2 6\\n2 5\\n3 4\\n1 2\\n', 'output': '56\\n28\\n12\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 2 4 12 16 32\\n4\\n2 3\\n2 5\\n3 4\\n1 2\\n', 'output': '6\\n28\\n12\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 4 1\\n2\\n2 3\\n2 2\\n', 'output': '5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 16 32\\n4\\n1 6\\n2 6\\n3 4\\n1 2\\n', 'output': '56\\n56\\n12\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 12 16 32\\n4\\n2 6\\n2 5\\n3 4\\n1 2\\n', 'output': '56\\n28\\n12\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 0 1\\n2\\n2 3\\n2 2\\n', 'output': '1\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 16 32\\n4\\n1 6\\n2 6\\n3 4\\n1 4\\n', 'output': '56\\n56\\n12\\n14\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 1 1\\n2\\n2 3\\n2 2\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 32 32\\n4\\n1 6\\n2 6\\n3 4\\n1 4\\n', 'output': '44\\n44\\n12\\n14\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 5 16 32\\n4\\n1 6\\n2 5\\n3 4\\n1 2\\n', 'output': '51\\n21\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 4 1\\n2\\n1 3\\n1 2\\n', 'output': '12\\n12\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 0 4 12 16 32\\n4\\n2 6\\n2 5\\n3 4\\n1 2\\n', 'output': '56\\n28\\n12\\n1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 4 1\\n2\\n1 3\\n2 2\\n', 'output': '12\\n4\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 4 4 12 16 32\\n4\\n1 6\\n2 6\\n3 4\\n1 2\\n', 'output': '56\\n56\\n12\\n5\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 12 16 32\\n4\\n2 5\\n2 5\\n3 4\\n1 2\\n', 'output': '28\\n28\\n12\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 0 1\\n2\\n2 2\\n2 2\\n', 'output': '0\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 12 16 32\\n4\\n2 6\\n2 5\\n3 6\\n2 2\\n', 'output': '56\\n28\\n56\\n4\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 32 32\\n4\\n1 6\\n2 6\\n3 3\\n1 4\\n', 'output': '44\\n44\\n4\\n14\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 4 2\\n2\\n2 3\\n1 1\\n', 'output': '6\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 0 4 12 16 32\\n4\\n1 6\\n2 6\\n3 4\\n1 2\\n', 'output': '56\\n56\\n12\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 6 4 12 16 32\\n4\\n2 6\\n2 5\\n4 4\\n1 2\\n', 'output': '56\\n30\\n12\\n7\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 7 16 32\\n4\\n2 6\\n2 5\\n3 6\\n2 2\\n', 'output': '51\\n23\\n51\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 1\\n2\\n2 3\\n2 3\\n', 'output': '3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 4 12 32 32\\n4\\n1 6\\n2 6\\n3 3\\n1 4\\n', 'output': '44\\n44\\n4\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 12 16 32\\n4\\n2 5\\n2 5\\n4 4\\n1 1\\n', 'output': '28\\n28\\n12\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 7 16 32\\n4\\n2 6\\n2 5\\n3 6\\n2 4\\n', 'output': '51\\n23\\n51\\n7\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 4 12 44 32\\n4\\n1 6\\n2 6\\n3 3\\n1 4\\n', 'output': '45\\n44\\n4\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 6 12 44 32\\n4\\n1 6\\n2 6\\n3 3\\n1 4\\n', 'output': '45\\n44\\n6\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 6 12 51 32\\n4\\n1 6\\n2 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n6\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 0 6 12 51 57\\n4\\n1 6\\n2 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n6\\n12\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 6 12 51 57\\n4\\n1 6\\n2 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n6\\n13\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 5 12 51 57\\n4\\n1 6\\n2 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n5\\n13\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 16 32\\n4\\n1 6\\n2 5\\n3 3\\n1 2\\n', 'output': '56\\n28\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 4 1\\n2\\n2 3\\n1 3\\n', 'output': '5\\n7\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 13 16 32\\n4\\n2 6\\n2 5\\n3 4\\n1 2\\n', 'output': '57\\n29\\n13\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 2 4 12 16 32\\n4\\n2 5\\n2 5\\n3 4\\n1 2\\n', 'output': '28\\n28\\n12\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 4 12 16 32\\n4\\n2 3\\n2 5\\n3 4\\n1 2\\n', 'output': '5\\n28\\n12\\n1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 1\\n2\\n2 3\\n2 2\\n', 'output': '3\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 24 16 32\\n4\\n2 6\\n2 5\\n3 4\\n1 2\\n', 'output': '56\\n28\\n28\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 0 1\\n2\\n1 3\\n2 2\\n', 'output': '9\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 16 31\\n4\\n1 6\\n2 6\\n3 4\\n1 4\\n', 'output': '31\\n31\\n12\\n14\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 12 16 58\\n4\\n2 6\\n2 5\\n3 4\\n2 2\\n', 'output': '62\\n28\\n12\\n4\\n'}, {'type': 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'45\\n45\\n4\\n12\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 6 4 12 16 32\\n4\\n2 5\\n2 5\\n4 4\\n1 1\\n', 'output': '30\\n30\\n12\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 4 7 44 32\\n4\\n1 6\\n2 6\\n3 3\\n1 4\\n', 'output': '45\\n44\\n4\\n7\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 4 4 12 16 32\\n4\\n4 5\\n2 5\\n4 4\\n1 1\\n', 'output': '28\\n28\\n12\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 6 20 44 32\\n4\\n1 6\\n2 6\\n3 3\\n1 4\\n', 'output': '61\\n61\\n6\\n23\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 5 12 44 32\\n4\\n1 6\\n2 6\\n3 3\\n2 4\\n', 'output': '45\\n44\\n5\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 6 12 51 68\\n4\\n1 6\\n2 6\\n3 3\\n2 4\\n', 'output': '125\\n125\\n6\\n13\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 5 12 51 57\\n4\\n1 6\\n2 6\\n3 3\\n2 5\\n', 'output': '63\\n63\\n5\\n63\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 1 4 12 16 32\\n4\\n1 6\\n2 5\\n3 3\\n1 2\\n', 'output': '56\\n28\\n4\\n1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5 4 1\\n2\\n2 3\\n1 3\\n', 'output': '5\\n5\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 2 4 13 16 32\\n4\\n2 6\\n2 5\\n3 4\\n1 2\\n', 'output': '57\\n29\\n13\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 16 32\\n4\\n1 6\\n1 3\\n3 4\\n1 2\\n', 'output': '56\\n6\\n12\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 24 16 32\\n4\\n2 6\\n2 3\\n3 4\\n1 2\\n', 'output': '56\\n4\\n28\\n4\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 16 31\\n4\\n1 5\\n2 6\\n3 4\\n1 4\\n', 'output': '28\\n31\\n12\\n14\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 12 16 58\\n4\\n2 6\\n2 4\\n3 4\\n2 2\\n', 'output': '62\\n12\\n12\\n4\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 53 32\\n4\\n1 6\\n4 6\\n3 4\\n1 4\\n', 'output': '63\\n57\\n12\\n14\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 4 4 4 4 32\\n4\\n1 6\\n2 6\\n3 4\\n1 2\\n', 'output': '36\\n36\\n4\\n5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 0 2\\n2\\n2 3\\n2 3\\n', 'output': '2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 16 32\\n4\\n2 6\\n2 5\\n3 4\\n1 2\\n', 'output': '56\\n28\\n12\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 4 12 16 32\\n4\\n2 6\\n2 5\\n3 4\\n1 2\\n', 'output': '56\\n28\\n12\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 12 16 32\\n4\\n2 6\\n2 5\\n3 4\\n2 2\\n', 'output': '56\\n28\\n12\\n4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 4 1\\n2\\n2 3\\n1 1\\n', 'output': '5\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 4 12 16 32\\n4\\n2 6\\n2 5\\n4 4\\n1 2\\n', 'output': '56\\n28\\n12\\n3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 1 1\\n2\\n2 3\\n2 3\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 12 16 32\\n4\\n2 5\\n2 5\\n4 4\\n1 2\\n', 'output': '28\\n28\\n12\\n4\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 4 4 12 16 32\\n4\\n4 5\\n2 5\\n4 4\\n1 1\\n', 'output': '28\\n28\\n12\\n0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 6 12 44 32\\n4\\n1 6\\n2 6\\n3 3\\n2 4\\n', 'output': '45\\n44\\n6\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 6 12 51 57\\n4\\n1 6\\n2 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n6\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 3 6 12 51 57\\n4\\n1 6\\n2 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n6\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 5 12 51 57\\n4\\n2 6\\n2 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n5\\n13\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 16 32\\n4\\n1 6\\n1 6\\n3 4\\n1 2\\n', 'output': '56\\n56\\n12\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 32 32\\n4\\n1 6\\n4 6\\n3 4\\n1 4\\n', 'output': '44\\n44\\n12\\n14\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 1 2\\n2\\n2 3\\n2 3\\n', 'output': '3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 32 32\\n4\\n1 6\\n4 6\\n3 3\\n1 4\\n', 'output': '44\\n44\\n4\\n14\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 2 4 7 16 32\\n4\\n2 6\\n2 5\\n3 6\\n2 4\\n', 'output': '51\\n23\\n51\\n7\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 6 12 51 32\\n4\\n1 6\\n1 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n6\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 6 12 51 57\\n4\\n2 6\\n2 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n6\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 0 6 12 51 57\\n4\\n1 6\\n4 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n6\\n12\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 5 12 51 57\\n4\\n2 6\\n4 6\\n3 3\\n2 4\\n', 'output': '63\\n63\\n5\\n13\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 2 4 12 16 63\\n4\\n2 5\\n2 5\\n3 4\\n1 2\\n', 'output': '28\\n28\\n12\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 4 12 16 43\\n4\\n2 3\\n2 5\\n3 4\\n1 2\\n', 'output': '5\\n28\\n12\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n0 1 4 12 16 32\\n4\\n2 6\\n2 5\\n3 4\\n1 2\\n', 'output': '56\\n28\\n12\\n1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 4 12 3 32\\n4\\n1 6\\n4 6\\n3 3\\n1 4\\n', 'output': '44\\n44\\n4\\n14\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 512000000}","problem_id":"vfc_80269","program":"```python\nn = int(input())\narr = list(map(int, input().split()))\n\naux = [[0] * n for i in range(n)]\n\nfor i in range(n):\n aux[0][i] = arr[i]\n\nfor i in range(1, n):\n for j in range(n-i):\n aux[i][j] = aux[i-1][j] ^ aux[i-1][j+1]\n \nfor i in range(1, n):\n for j in range(n-i):\n aux[i][j] = max(aux[i][j], aux[i-1][j], aux[i-1][j+1])\n \nq = int(input())\nfor i in range(q):\n buscaEsquerda, buscaDireita = map(int, input().split())\n buscaEsquerda, buscaDireita = buscaEsquerda-1, buscaDireita-1\n print(aux[buscaDireita-buscaEsquerda][buscaEsquerda])\n```","inputs":"6\n1 2 4 8 16 32\n4\n1 6\n2 5\n3 4\n1 2\n","output":"60\n30\n12\n3\n","actual_output":"60\n30\n12\n3\n","execution_success":true,"sample_index":12785},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02565 AtCoder Library Practice Contest - Two SAT","prompt":"Solve the following coding problem using the programming language python:\n\nConsider placing N flags on a line. Flags are numbered through 1 to N.\n\nFlag i can be placed on the coordinate X_i or Y_i. For any two different flags, the distance between them should be at least D.\n\nDecide whether it is possible to place all N flags. If it is possible, print such a configulation.\n\nConstraints\n\n* 1 \\leq N \\leq 1000\n* 0 \\leq D \\leq 10^9\n* 0 \\leq X_i < Y_i \\leq 10^9\n* All values in Input are integer.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN D\nX_1 Y_1\nX_2 Y_2\n\\vdots\nX_N Y_N\n\n\nOutput\n\nPrint `No` if it is impossible to place N flags.\n\nIf it is possible, print `Yes` first. After that, print N lines. i-th line of them should contain the coodinate of flag i.\n\nExamples\n\nInput\n\n3 2\n1 4\n2 5\n0 6\n\n\nOutput\n\nYes\n4\n2\n0\n\n\nInput\n\n3 3\n1 4\n2 5\n0 6\n\n\nOutput\n\nNo\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nclass Two_SAT:\n \"\"\"2-SAT\u3092\u5b9a\u7fa9\u3059\u308b.\n\n \"\"\"\n\n #\u5165\u529b\u5b9a\u7fa9\n def __init__(self,variable=[]):\n self.variable=set(variable)\n\n self.clause_number=0\n self.variable_number=len(variable)\n\n self.adjacent_out={(v,b):set() for v in variable for b in [True,False]} #\u51fa\u8fd1\u508d(v\u304c\u59cb\u70b9)\n self.adjacent_in={(v,b):set() for v in variable for b in [True,False]} #\u5165\u8fd1\u508d(v\u304c\u7d42\u70b9)\n #\u203b (X,False)\u304c not X\u306b\u5bfe\u5fdc\n\n #\u5909\u6570\u306e\u8ffd\u52a0\n def add_variable(self,*adder):\n \"\"\"\u5909\u6570\u3092\u52a0\u3048\u308b.\n\n adder(\u53ef\u5909\u9577):\u52a0\u3048\u308b\u5909\u6570\u306e\u540d\u524d\n \"\"\"\n for v in adder:\n if v not in self.variable:\n self.adjacent_in[(v,True)]=set()\n self.adjacent_in[(v,False)]=set()\n self.adjacent_out[(v,True)]=set()\n self.adjacent_out[(v,False)]=set()\n\n self.variable_number+=1\n self.variable.add(v)\n\n #\u7bc0\u306e\u8ffd\u52a0\n def add_clause(self,X,F,Y,G):\n \"\"\"(X=F) or (Y=G) \u3068\u3044\u3046\u7bc0\u3092\u52a0\u3048\u308b.\n\n X,Y:\u5909\u6570\u306e\u540d\u524d\n F,G:\u771f\u507d\u5024(True or False)\n \"\"\"\n\n assert isinstance(F,bool),\"F\u304c\u771f\u507d\u5024\u3067\u306f\u306a\u3044\"\n assert isinstance(G,bool),\"G\u304c\u771f\u507d\u5024\u3067\u306f\u306a\u3044\"\n\n for v in [X,Y]:\n if v not in self.variable:\n self.add_variable(v)\n\n if (Y,G) not in self.adjacent_out[(X,not F)]:\n self.clause_number+=1\n\n #(X,not F)\u2192(Y,G)\u3092\u8ffd\u52a0\n self.adjacent_out[(X,not F)].add((Y,G))\n self.adjacent_in[(Y,G)].add((X,not F))\n\n #(Y,not G) \u2192 (X,F)\u3092\u8ffd\u52a0\n self.adjacent_out[(Y,not G)].add((X,F))\n self.adjacent_in[(X,F)].add((Y,not G))\n\n #\u7bc0\u3092\u9664\u304f\n def remove_edge(self,X,F,Y,G):\n pass\n\n #\u5909\u6570\u3092\u9664\u304f\n def remove_vertex(self,*vertexes):\n pass\n\n #\u5909\u6570\u304c\u5b58\u5728\u3059\u308b\u304b\u5426\u304b\n def variable_exist(self,v):\n \"\"\"\u5909\u6570 X \u304c\u5b58\u5728\u3059\u308b\u304b?\n\n X,Y:\u5909\u6570\u306e\u540d\u524d\n \"\"\"\n return v in self.variable\n\n #\u30b0\u30e9\u30d5\u306b\u7bc0\u304c\u5b58\u5728\u3059\u308b\u304b\u5426\u304b\n def clause_exist(self,X,F,Y,G):\n \"\"\"(X=F) or (Y=G) \u3068\u3044\u3046\u7bc0\u304c\u5b58\u5728\u3059\u308b\u304b?\n\n X,Y:\u5909\u6570\u306e\u540d\u524d\n F,G:\u771f\u507d\u5024(True or False)\n \"\"\"\n if not(self.variable_exist(X) and self.variable_exist(Y)):\n return False\n return (Y,G) in self.adjacent_out[(X,not F)]\n\n #\u8fd1\u508d\n def neighbohood(self,v):\n pass\n\n #\u51fa\u6b21\u6570\n def out_degree(self,v):\n pass\n\n #\u5165\u6b21\u6570\n def in_degree(self,v):\n pass\n\n #\u6b21\u6570\n def degree(self,v):\n pass\n\n #\u5909\u6570\u306e\u6570\n def variable_count(self):\n return len(self.vertex)\n\n #\u7bc0\u306e\u6570\n def clause_count(self):\n return self.edge_number\n\n #\u5145\u8db3\u53ef\u80fd?\n def Is_Satisfy(self,Mode):\n \"\"\"\u6709\u5411\u30b0\u30e9\u30d5D\u3092\u5f37\u9023\u7d50\u6210\u5206\u306b\u5206\u89e3\n\n Mode:\n 0(Defalt)---\u5145\u8db3\u53ef\u80fd?\n 1 ---\u5145\u8db3\u53ef\u80fd\u306a\u3089\u3070,\u305d\u306e\u5909\u6570\u306e\u5272\u5f53\u3092\u5909\u3048\u308b.(\u4e0d\u53ef\u80fd\u306a\u3068\u304d\u306fNone)\n \"\"\"\n import sys\n from collections import deque\n\n T={(x,b):-1 for b in [True,False] for x in self.variable}\n Q=deque([])\n\n def f(v):\n T[v]=0\n for w in self.adjacent_out[v]:\n if T[w]==-1:\n f(w)\n\n Q.appendleft(v)\n T[v]=len(Q)\n\n x=self.variable.pop()\n self.variable.add(x)\n\n RT=sys.getrecursionlimit()\n sys.setrecursionlimit(3*10**5)\n\n for b in [True,False]:\n for v in self.variable:\n w=(v,b)\n if T[w]==-1:\n f(w)\n\n sys.setrecursionlimit(RT)\n\n T={(x,b):-1 for b in [True,False] for x in self.variable }\n C=[]\n p=0\n\n for v in Q:\n if T[v]==-1:\n T[v]=p\n P=[v]\n R=deque([v])\n\n while R:\n u=R.popleft()\n for w in self.adjacent_in[u]:\n if T[w]==-1:\n T[w]=p\n R.append(w)\n P.append(w)\n C.append(P)\n p+=1\n\n\n if Mode==0:\n for x in self.variable:\n if T[(x,True)]==T[(x,False)]:\n return False\n\n return True\n else:\n X={x:None for x in self.variable}\n for x in self.variable:\n if T[(x,True)]==T[(x,False)]:\n return None\n else:\n X[x]=(T[(x,False)] ret: ret = tmp\n if ret*L > 2*ls:\n return -1\n return ret\n\n\nimport sys\ninput = sys.stdin.buffer.readline\n\nS = input().rstrip()\nT = input().rstrip()\n\nls = len(S)\nlt = len(T)\nS = S*((2*lt+3*ls-1)//ls)\nans = RollingHash(S, T, ls)\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'aa\\naaaaaaa', 'output': '-1'}, {'type': 'stdin_stdout', 'input': 'aba\\nbaaab', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'abcabab\\nab', 'output': '3'}, {'type': 'stdin_stdout', 'input': 'aa\\nabaaaaa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'abcaabb\\nab', 'output': '1'}, {'type': 'stdin_stdout', 'input': 'aba\\naaaab', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa\\naaaaaba', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aba\\naa`ab', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'accaabb\\nab', 'output': '1'}, {'type': 'stdin_stdout', 'input': 'ab\\naaaaaba', 'output': '0'}, {'type': 'stdin_stdout', 'input': '`ba\\naa`ab', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'acdaabb\\nab', 'output': '1'}, {'type': 'stdin_stdout', 'input': 'ab\\nabaaaaa', 'output': '0'}, {'type': 'stdin_stdout', 'input': '`ab\\naa`ab', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'acda`bb\\nab', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'ab\\nabaaaba', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'ab`\\naa`ab', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'acda`bb\\naa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'ab\\nab`aaba', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'ab`\\naa`ac', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'bb`adca\\naa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'ba\\nab`aaba', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'ac`\\naa`ac', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'bb`adca\\na`', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'ba\\naa`aaba', 'output': '0'}, {'type': 'stdin_stdout', 'input': '`ca\\naa`ac', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'bb`adca\\n`a', 'output': '1'}, {'type': 'stdin_stdout', 'input': 'b`\\naa`aaba', 'output': '0'}, {'type': 'stdin_stdout', 'input': '`c`\\naa`ac', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'ab`bdca\\naa', 'output': '1'}, {'type': 'stdin_stdout', 'input': 'b_\\naa`aaba', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c``\\naa`ac', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa`bdca\\naa', 'output': '1'}, {'type': 'stdin_stdout', 'input': '_b\\naa`aaba', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c``\\na``ac', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa`bdcb\\naa', 'output': '1'}, {'type': 'stdin_stdout', 'input': '`b\\naa`aaba', 'output': '0'}, {'type': 'stdin_stdout', 'input': '``c\\na``ac', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa_bdcb\\naa', 'output': '1'}, {'type': 'stdin_stdout', 'input': '`b\\nba`aaaa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c``\\nca``a', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa_bdcb\\na`', 'output': '0'}, {'type': 'stdin_stdout', 'input': '`b\\nbaaa`aa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c`_\\nca``a', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa_bdcb\\n``', 'output': '0'}, {'type': 'stdin_stdout', 'input': '`b\\nbaaa`a`', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c__\\nca``a', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa_bdcb\\n`_', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'b`\\nbaaa`a`', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c__\\nc``aa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa_bdcb\\n__', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'b`\\nbaaaaa`', 'output': '0'}, {'type': 'stdin_stdout', 'input': '__c\\nc``aa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa_bdcb\\n^_', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'b`\\nbbaaaa`', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^_c\\nc``aa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa`bdcb\\n^_', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'b_\\nbbaaaa`', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^_c\\nc`_aa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa`bdca\\n^_', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c_\\nbbaaaa`', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^^c\\nc`_aa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa`bdca\\n_^', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c_\\n`aaaabb', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^^b\\nc`_aa', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'aa`bdca\\n__', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c^\\n`aaaabb', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^^b\\nc`_a`', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'a``bdca\\n__', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c]\\n`aaaabb', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'b^^\\nc`_a`', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'a``bdac\\n__', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'd]\\n`aaaabb', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^^b\\nb`_a`', 'output': '0'}, {'type': 'stdin_stdout', 'input': '```bdac\\n__', 'output': '0'}, {'type': 'stdin_stdout', 'input': ']d\\n`aaaabb', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^^b\\na`_a`', 'output': '0'}, {'type': 'stdin_stdout', 'input': '```bcac\\n__', 'output': '0'}, {'type': 'stdin_stdout', 'input': ']d\\n`baaaab', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'b^^\\na`_a`', 'output': '0'}, {'type': 'stdin_stdout', 'input': '```bcac\\n_`', 'output': '0'}, {'type': 'stdin_stdout', 'input': ']d\\nabaaaab', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'c^^\\na`_a`', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'cacb```\\n_`', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'd]\\nabaaaab', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^c^\\na`_a`', 'output': '0'}, {'type': 'stdin_stdout', 'input': '```bcad\\n_`', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'd]\\nabaaabb', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^c^\\n`a_`a', 'output': '0'}, {'type': 'stdin_stdout', 'input': '`b``cad\\n_`', 'output': '0'}, {'type': 'stdin_stdout', 'input': ']d\\nabaaabb', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^c^\\n`_a`a', 'output': '0'}, {'type': 'stdin_stdout', 'input': '`b``cad\\n`_', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^d\\nabaaabb', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^c^\\na`a_`', 'output': '0'}, {'type': 'stdin_stdout', 'input': '`b``cad\\n__', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^d\\naba`abb', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^c_\\na`a_`', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'dac``b`\\n__', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^d\\naca`abb', 'output': '0'}, {'type': 'stdin_stdout', 'input': '^c_\\na`b_`', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'dbc``b`\\n__', 'output': '0'}, {'type': 'stdin_stdout', 'input': 'd^\\naca`abb', 'output': '0'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_80325","program":"```python\n# AOJ ALDS1_14_B \"String Search\"\n# returns i s.t. S[i+j] = T[j] for 0 <= j < len(T)\n\ndef RollingHash(S, T, ls):\n if len(S) < len(T):\n return []\n # gcd(h, b) = 1\n h = 10**11+7\n b = 10**7+7\n L = len(T)\n\n bL = 1\n for i in range(L):\n bL = bL * b % h\n\n hashS = 0\n for i in range(L):\n hashS = (hashS * b + S[i]) % h\n\n hashT = 0\n for i in range(L):\n hashT = (hashT * b + T[i]) % h\n \n correctIndexes = [0]*len(S)\n ret = 0\n if hashS == hashT:\n correctIndexes[0] = 1\n for j in range(len(S)-L):\n hashS = (hashS * b - S[j]*bL + S[L+j]) % h\n if hashS == hashT:\n tmp = correctIndexes[j+1-L] + 1\n correctIndexes[j+1] = tmp\n if tmp > ret: ret = tmp\n if ret*L > 2*ls:\n return -1\n return ret\n\n\nimport sys\ninput = sys.stdin.buffer.readline\n\nS = input().rstrip()\nT = input().rstrip()\n\nls = len(S)\nlt = len(T)\nS = S*((2*lt+3*ls-1)//ls)\nans = RollingHash(S, T, ls)\nprint(ans)\n```","inputs":"aa\naaaaaaa","output":"-1","actual_output":"-1\n","execution_success":true,"sample_index":12789},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03097 AtCoder Grand Contest 031 - Differ by 1 Bit","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given integers N,\\ A and B. Determine if there exists a permutation (P_0,\\ P_1,\\ ...\\ P_{2^N-1}) of (0,\\ 1,\\ ...\\ 2^N-1) that satisfies all of the following conditions, and create one such permutation if it exists.\n\n* P_0=A\n* P_{2^N-1}=B\n* For all 0 \\leq i < 2^N-1, the binary representations of P_i and P_{i+1} differ by exactly one bit.\n\nConstraints\n\n* 1 \\leq N \\leq 17\n* 0 \\leq A \\leq 2^N-1\n* 0 \\leq B \\leq 2^N-1\n* A \\neq B\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN A B\n\n\nOutput\n\nIf there is no permutation that satisfies the conditions, print `NO`.\n\nIf there is such a permutation, print `YES` in the first line. Then, print (P_0,\\ P_1,\\ ...\\ P_{2^N-1}) in the second line, with spaces in between. If there are multiple solutions, any of them is accepted.\n\nExamples\n\nInput\n\n2 1 3\n\n\nOutput\n\nYES\n1 0 2 3\n\n\nInput\n\n3 2 1\n\n\nOutput\n\nNO\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN, A, B = map(int, input().split())\n\n\ndef f(n, a, b):\n if n == 1:\n return [a, b]\n\n mask = 1 << (n-1)\n if a & mask == b & mask:\n v1 = f(n-1, a, b)\n v2 = f(n-1, a ^ mask, v1[1] ^ mask)\n ret = v1[:1]\n ret.extend(v2)\n ret.extend(v1[1:])\n return ret\n else:\n v1 = f(n-1, a, a ^ 1)\n v2 = f(n-1, a ^ 1 ^ mask, b)\n v1.extend(v2)\n return v1\n\n\nif bin(A ^ B).count('1') % 2 == 0:\n print(\"NO\")\nelse:\n print(\"YES\")\n res = f(N, A, B)\n for p in res:\n print(p)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 2 1', 'output': 'NO'}, {'type': 'stdin_stdout', 'input': '2 1 3', 'output': 'YES\\n1 0 2 3'}, {'type': 'stdin_stdout', 'input': '2 1 0', 'output': 'YES\\n1 3 2 0\\n'}, {'type': 'stdin_stdout', 'input': '2 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 0 1', 'output': 'YES\\n0 1\\n'}, {'type': 'stdin_stdout', 'input': '2 2 0', 'output': 'YES\\n2 3 1 0\\n'}, {'type': 'stdin_stdout', 'input': '1 2 3', 'output': 'YES\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '1 3 2', 'output': 'YES\\n3 2\\n'}, {'type': 'stdin_stdout', 'input': '2 3 2', 'output': 'YES\\n3 1 0 2\\n'}, {'type': 'stdin_stdout', 'input': '2 0 2', 'output': 'YES\\n0 1 3 2\\n'}, {'type': 'stdin_stdout', 'input': '2 2 3', 'output': 'YES\\n2 0 1 3\\n'}, {'type': 'stdin_stdout', 'input': '2 3 1', 'output': 'YES\\n3 2 0 1\\n'}, {'type': 'stdin_stdout', 'input': '2 0 1', 'output': 'YES\\n0 2 3 1\\n'}, {'type': 'stdin_stdout', 'input': '1 1 0', 'output': 'YES\\n1 0\\n'}, {'type': 'stdin_stdout', 'input': '1 -2 -1', 'output': 'YES\\n-2 -1\\n'}, {'type': 'stdin_stdout', 'input': '1 -1 -2', 'output': 'YES\\n-1 -2\\n'}, {'type': 'stdin_stdout', 'input': '4 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '7 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-1 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-2 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '15 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-1 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 4 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 2 4', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-2 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '7 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '9 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 2 7', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '14 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '9 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '14 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '13 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '18 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 1 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10 1 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 1 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '11 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '11 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '13 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-1 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-4 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 1 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '15 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-2 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 4 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '14 1 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '13 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 3 3', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '7 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '13 1 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 1 4', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 1 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-4 0 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-1 4 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 3 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '13 4 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '1 3 3', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '7 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 6 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '13 0 3', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 3 3', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '8 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 1 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-1 6 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 0 3', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 3 0', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 1 4', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-1 1 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-1 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '18 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-2 1 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '15 4 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 8 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '0 2 4', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '-5 2 1', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '11 2 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '9 4 2', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '14 4 1', 'output': 'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_80329","program":"```python\nN, A, B = map(int, input().split())\n\n\ndef f(n, a, b):\n if n == 1:\n return [a, b]\n\n mask = 1 << (n-1)\n if a & mask == b & mask:\n v1 = f(n-1, a, b)\n v2 = f(n-1, a ^ mask, v1[1] ^ mask)\n ret = v1[:1]\n ret.extend(v2)\n ret.extend(v1[1:])\n return ret\n else:\n v1 = f(n-1, a, a ^ 1)\n v2 = f(n-1, a ^ 1 ^ mask, b)\n v1.extend(v2)\n return v1\n\n\nif bin(A ^ B).count('1') % 2 == 0:\n print(\"NO\")\nelse:\n print(\"YES\")\n res = f(N, A, B)\n for p in res:\n print(p)\n\n```","inputs":"3 2 1","output":"NO","actual_output":"NO\n","execution_success":true,"sample_index":12790},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03243 AtCoder Beginner Contest 111 - AtCoder Beginner Contest 111","prompt":"Solve the following coding problem using the programming language python:\n\nKurohashi has never participated in AtCoder Beginner Contest (ABC).\n\nThe next ABC to be held is ABC N (the N-th ABC ever held). Kurohashi wants to make his debut in some ABC x such that all the digits of x in base ten are the same.\n\nWhat is the earliest ABC where Kurohashi can make his debut?\n\nConstraints\n\n* 100 \\leq N \\leq 999\n* N is an integer.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\n\n\nOutput\n\nIf the earliest ABC where Kurohashi can make his debut is ABC n, print n.\n\nExamples\n\nInput\n\n111\n\n\nOutput\n\n111\n\n\nInput\n\n112\n\n\nOutput\n\n222\n\n\nInput\n\n750\n\n\nOutput\n\n777\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN=int(input());print(111*(-(-N//111)))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '750', 'output': '777'}, {'type': 'stdin_stdout', 'input': '112', 'output': '222'}, {'type': 'stdin_stdout', 'input': '111', 'output': '111'}, {'type': 'stdin_stdout', 'input': '426', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '101', 'output': '111\\n'}, {'type': 'stdin_stdout', 'input': '638', 'output': '666\\n'}, {'type': 'stdin_stdout', 'input': '268', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '457', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '000', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '985', 'output': '999\\n'}, {'type': 'stdin_stdout', 'input': '846', 'output': '888\\n'}, {'type': 'stdin_stdout', 'input': '198', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '706', 'output': '777\\n'}, {'type': 'stdin_stdout', 'input': '110', 'output': '111\\n'}, {'type': 'stdin_stdout', 'input': '001', 'output': '111\\n'}, {'type': 'stdin_stdout', 'input': '409', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '100', 'output': '111\\n'}, {'type': 'stdin_stdout', 'input': '662', 'output': '666\\n'}, {'type': 'stdin_stdout', 'input': '011', 'output': '111\\n'}, {'type': 'stdin_stdout', 'input': '010', 'output': '111\\n'}, {'type': 'stdin_stdout', 'input': '514', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '583', 'output': '666\\n'}, {'type': 'stdin_stdout', 'input': '223', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '625', 'output': '666\\n'}, {'type': 'stdin_stdout', 'input': '266', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '645', 'output': '666\\n'}, {'type': 'stdin_stdout', 'input': '195', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '398', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '155', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '517', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '375', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '281', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '341', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '261', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '477', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '284', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '382', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '471', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '528', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '201', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '209', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '406', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '646', 'output': '666\\n'}, {'type': 'stdin_stdout', 'input': '357', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '186', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '465', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '590', 'output': '666\\n'}, {'type': 'stdin_stdout', 'input': '363', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '134', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '812', 'output': '888\\n'}, {'type': 'stdin_stdout', 'input': '442', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '219', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '563', 'output': '666\\n'}, {'type': 'stdin_stdout', 'input': '450', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '291', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '297', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '259', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '481', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '669', 'output': '777\\n'}, {'type': 'stdin_stdout', 'input': '141', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '150', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '138', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '139', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '257', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '421', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '152', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '187', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '174', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '15', 'output': '111\\n'}, {'type': 'stdin_stdout', 'input': '335', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '290', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '359', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '425', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '486', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '124', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '113', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '116', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '747', 'output': '777\\n'}, {'type': 'stdin_stdout', 'input': '239', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '752', 'output': '777\\n'}, {'type': 'stdin_stdout', 'input': '303', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '437', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '467', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '299', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '447', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '698', 'output': '777\\n'}, {'type': 'stdin_stdout', 'input': '441', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '327', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '202', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '410', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '543', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '499', 'output': '555\\n'}, {'type': 'stdin_stdout', 'input': '431', 'output': '444\\n'}, {'type': 'stdin_stdout', 'input': '213', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '128', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '296', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '295', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '171', 'output': '222\\n'}, {'type': 'stdin_stdout', 'input': '10', 'output': '111\\n'}, {'type': 'stdin_stdout', 'input': '647', 'output': '666\\n'}, {'type': 'stdin_stdout', 'input': '288', 'output': '333\\n'}, {'type': 'stdin_stdout', 'input': '840', 'output': '888\\n'}, {'type': 'stdin_stdout', 'input': '568', 'output': '666\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_80333","program":"```python\nN=int(input());print(111*(-(-N//111)))\n```","inputs":"750","output":"777","actual_output":"777\n","execution_success":true,"sample_index":12791},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03561 AtCoder Regular Contest 084 - Finite Encyclopedia of Integer Sequences","prompt":"Solve the following coding problem using the programming language python:\n\nIn Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between 1 and N (inclusive) consisting of integers between 1 and K (inclusive) are listed.\n\nLet the total number of sequences listed in FEIS be X. Among those sequences, find the (X/2)-th (rounded up to the nearest integer) lexicographically smallest one.\n\nConstraints\n\n* 1 \\leq N,K \\leq 3 \u00d7 10^5\n* N and K are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nK N\n\n\nOutput\n\nPrint the (X/2)-th (rounded up to the nearest integer) lexicographically smallest sequence listed in FEIS, with spaces in between, where X is the total number of sequences listed in FEIS.\n\nExamples\n\nInput\n\n3 2\n\n\nOutput\n\n2 1\n\n\nInput\n\n2 4\n\n\nOutput\n\n1 2 2 2\n\n\nInput\n\n5 14\n\n\nOutput\n\n3 3 3 3 3 3 3 3 3 3 3 3 2 2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\n\nK,N = map(int,input().split())\n\nif K % 2 == 0:\n L = K // 2\n R = L + 1\n # \u5148\u982d\u306e\u6587\u5b57\u304c L \u306e\u3082\u306e\u306e\u6700\u5f8c\u3001R \u306e\u3082\u306e\u306e\u6700\u521d\u3001\u3067\u5883\u754c\n arr = [L] + [K] * (N-1)\nelse:\n \"\"\"\n [3,3,3,3,3] \u3060\u3068 \u624b\u524d\u306b3 33 333 3333 \u304c\u4f59\u5206\u30022\u6b69\u623b\u308b\u3002\n \"\"\"\n arr = [(K+1)//2] * N\n x = N//2# x\u6b69 \u623b\u308b\n for i in range(x):\n arr[-1] -= 1\n if arr[-1] == 0:\n arr.pop()\n continue\n L = len(arr)\n if L < N:\n arr += [K] * (N-L)\n\nanswer = ' '.join(map(str,arr))\nprint(answer)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 4', 'output': '1 2 2 2'}, {'type': 'stdin_stdout', 'input': '5 14', 'output': '3 3 3 3 3 3 3 3 3 3 3 3 2 2'}, {'type': 'stdin_stdout', 'input': '3 2', 'output': '2 1'}, {'type': 'stdin_stdout', 'input': '0 4', 'output': '0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '8 14', 'output': '4 8 8 8 8 8 8 8 8 8 8 8 8 8\\n'}, {'type': 'stdin_stdout', 'input': '0 14', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '1 14', 'output': '1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 14', 'output': '1 2 2 2 2 2 2 2 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '2 1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '0 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 5', 'output': '1 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '2 26', 'output': '1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '2 2', 'output': '1 2\\n'}, {'type': 'stdin_stdout', 'input': '0 5', 'output': '0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '9 14', 'output': '5 5 5 5 5 5 5 5 5 5 5 5 4 8\\n'}, {'type': 'stdin_stdout', 'input': '0 28', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '2 10', 'output': '1 2 2 2 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '0 2', 'output': '0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 5', 'output': '1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 11', 'output': '1 2 2 2 2 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '0 3', 'output': '0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '9 12', 'output': '5 5 5 5 5 5 5 5 5 5 4 9\\n'}, {'type': 'stdin_stdout', 'input': '1 28', 'output': '1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '1 10', 'output': '1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4 2', 'output': '2 4\\n'}, {'type': 'stdin_stdout', 'input': '1 4', 'output': '1 1\\n'}, {'type': 'stdin_stdout', 'input': '3 11', 'output': '2 2 2 2 2 2 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9 18', 'output': '5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 6\\n'}, {'type': 'stdin_stdout', 'input': '1 7', 'output': '1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '2 6', 'output': '1 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '3 5', 'output': '2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '9 6', 'output': '5 5 5 5 5 2\\n'}, {'type': 'stdin_stdout', 'input': '1 12', 'output': '1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '0 6', 'output': '0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 5', 'output': '3 3 3 3 1\\n'}, {'type': 'stdin_stdout', 'input': '9 3', 'output': '5 5 4\\n'}, {'type': 'stdin_stdout', 'input': '2 12', 'output': '1 2 2 2 2 2 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '2 3', 'output': '1 2 2\\n'}, {'type': 'stdin_stdout', 'input': '5 7', 'output': '3 3 3 3 3 3\\n'}, {'type': 'stdin_stdout', 'input': '9 2', 'output': '5 4\\n'}, {'type': 'stdin_stdout', 'input': '4 12', 'output': '2 4 4 4 4 4 4 4 4 4 4 4\\n'}, {'type': 'stdin_stdout', 'input': '4 3', 'output': '2 4 4\\n'}, {'type': 'stdin_stdout', 'input': '5 9', 'output': '3 3 3 3 3 3 3 2 5\\n'}, {'type': 'stdin_stdout', 'input': '5 3', 'output': '3 3 2\\n'}, {'type': 'stdin_stdout', 'input': '1 24', 'output': '1 1 1 1 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '7 9', 'output': '4 4 4 4 4 4 4 4\\n'}, {'type': 'stdin_stdout', 'input': '10 3', 'output': '5 10 10\\n'}, {'type': 'stdin_stdout', 'input': '0 24', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '5 2', 'output': '3 2\\n'}, {'type': 'stdin_stdout', 'input': '7 14', 'output': '4 4 4 4 4 4 4 4 4 4 4 4 3 5\\n'}, {'type': 'stdin_stdout', 'input': '10 2', 'output': '5 10\\n'}, {'type': 'stdin_stdout', 'input': '13 14', 'output': '7 7 7 7 7 7 7 7 7 7 7 7 7\\n'}, {'type': 'stdin_stdout', 'input': '13 27', 'output': '7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 8\\n'}, {'type': 'stdin_stdout', 'input': '7 1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '13 23', 'output': '7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 10\\n'}, {'type': 'stdin_stdout', 'input': '7 2', 'output': '4 3\\n'}, {'type': 'stdin_stdout', 'input': '13 17', 'output': '7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 13\\n'}, {'type': 'stdin_stdout', 'input': '13 15', 'output': '7 7 7 7 7 7 7 7 7 7 7 7 7 7\\n'}, {'type': 'stdin_stdout', 'input': '13 20', 'output': '7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 11\\n'}, {'type': 'stdin_stdout', 'input': '3 20', 'output': '2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 3 1\\n'}, {'type': 'stdin_stdout', 'input': '5 20', 'output': '3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 5\\n'}, {'type': 'stdin_stdout', 'input': '0 20', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '8 2', 'output': '4 8\\n'}, {'type': 'stdin_stdout', 'input': '14 14', 'output': '7 14 14 14 14 14 14 14 14 14 14 14 14 14\\n'}, {'type': 'stdin_stdout', 'input': '3 6', 'output': '2 2 2 2 1 3\\n'}, {'type': 'stdin_stdout', 'input': '0 9', 'output': '0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '-2 1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3 26', 'output': '2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2\\n'}, {'type': 'stdin_stdout', 'input': '6 3', 'output': '3 6 6\\n'}, {'type': 'stdin_stdout', 'input': '-2 5', 'output': '-1 -2 -2 -2 -2\\n'}, {'type': 'stdin_stdout', 'input': '9 8', 'output': '5 5 5 5 5 5 5 1\\n'}, {'type': 'stdin_stdout', 'input': '0 39', 'output': '0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '2 7', 'output': '1 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '-2 2', 'output': '-1 -2\\n'}, {'type': 'stdin_stdout', 'input': '2 9', 'output': '1 2 2 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '0 11', 'output': '0 0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '14 12', 'output': '7 14 14 14 14 14 14 14 14 14 14 14\\n'}, {'type': 'stdin_stdout', 'input': '1 16', 'output': '1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4 5', 'output': '2 4 4 4 4\\n'}, {'type': 'stdin_stdout', 'input': '0 10', 'output': '0 0 0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '-2 4', 'output': '-1 -2 -2 -2\\n'}, {'type': 'stdin_stdout', 'input': '4 11', 'output': '2 4 4 4 4 4 4 4 4 4 4\\n'}, {'type': 'stdin_stdout', 'input': '9 22', 'output': '5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4\\n'}, {'type': 'stdin_stdout', 'input': '4 9', 'output': '2 4 4 4 4 4 4 4 4\\n'}, {'type': 'stdin_stdout', 'input': '0 7', 'output': '0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '3 9', 'output': '2 2 2 2 2 2 2 1 2\\n'}, {'type': 'stdin_stdout', 'input': '3 7', 'output': '2 2 2 2 2 1 3\\n'}, {'type': 'stdin_stdout', 'input': '9 1', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '2 8', 'output': '1 2 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '0 8', 'output': '0 0 0 0 0 0 0 0\\n'}, {'type': 'stdin_stdout', 'input': '4 6', 'output': '2 4 4 4 4 4\\n'}, {'type': 'stdin_stdout', 'input': '2 23', 'output': '1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '13 1', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '5 10', 'output': '3 3 3 3 3 3 3 3 2 4\\n'}, {'type': 'stdin_stdout', 'input': '15 1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '4 4', 'output': '2 4 4 4\\n'}, {'type': 'stdin_stdout', 'input': '3 10', 'output': '2 2 2 2 2 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '18 3', 'output': '9 18 18\\n'}, {'type': 'stdin_stdout', 'input': '2 24', 'output': '1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '7 11', 'output': '4 4 4 4 4 4 4 4 4 3 7\\n'}, {'type': 'stdin_stdout', 'input': '2 27', 'output': '1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_80341","program":"```python\nimport sys\ninput = sys.stdin.readline\n\nK,N = map(int,input().split())\n\nif K % 2 == 0:\n L = K // 2\n R = L + 1\n # \u5148\u982d\u306e\u6587\u5b57\u304c L \u306e\u3082\u306e\u306e\u6700\u5f8c\u3001R \u306e\u3082\u306e\u306e\u6700\u521d\u3001\u3067\u5883\u754c\n arr = [L] + [K] * (N-1)\nelse:\n \"\"\"\n [3,3,3,3,3] \u3060\u3068 \u624b\u524d\u306b3 33 333 3333 \u304c\u4f59\u5206\u30022\u6b69\u623b\u308b\u3002\n \"\"\"\n arr = [(K+1)//2] * N\n x = N//2# x\u6b69 \u623b\u308b\n for i in range(x):\n arr[-1] -= 1\n if arr[-1] == 0:\n arr.pop()\n continue\n L = len(arr)\n if L < N:\n arr += [K] * (N-L)\n\nanswer = ' '.join(map(str,arr))\nprint(answer)\n```","inputs":"2 4","output":"1 2 2 2","actual_output":"1 2 2 2\n","execution_success":true,"sample_index":12792},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03714 AtCoder Beginner Contest 062 - 3N Numbers","prompt":"Solve the following coding problem using the programming language python:\n\nLet N be a positive integer.\n\nThere is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').\n\nFind the maximum possible score of a'.\n\nConstraints\n\n* 1 \u2264 N \u2264 10^5\n* a_i is an integer.\n* 1 \u2264 a_i \u2264 10^9\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\na_1 a_2 ... a_{3N}\n\n\nOutput\n\nPrint the maximum possible score of a'.\n\nExamples\n\nInput\n\n2\n3 1 4 1 5 9\n\n\nOutput\n\n1\n\n\nInput\n\n1\n1 2 3\n\n\nOutput\n\n-1\n\n\nInput\n\n3\n8 2 2 7 4 6 5 3 8\n\n\nOutput\n\n5\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef f(x):\n y=x[:n];heapify(y);z=sum(y);s=[z]\n for i in x[n:n*2]:z+=i-heappushpop(y,i);s+=[z]\n return s\nfrom heapq import*;n,*a=map(int,open(0).read().split());print(max(map(sum,zip(f([-i for i in a[n:][::-1]]),f(a)[::-1]))))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2\\n3 1 4 1 5 9', 'output': '1'}, {'type': 'stdin_stdout', 'input': '1\\n1 2 3', 'output': '-1'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 2 7 4 6 5 3 8', 'output': '5'}, {'type': 'stdin_stdout', 'input': '2\\n3 1 4 1 7 9', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 2 7 4 6 6 3 8', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 1 4 1 7 0', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 0 5', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 -1 5', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 1 2 7 4 6 6 0 8', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 0 5', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 2 4 2 11 0', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 2 7 4 6 4 0 15', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 2 7 4 6 4 -1 15', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 2 13 4 6 4 -1 15', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 2 13 4 6 4 0 11', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 2 13 8 6 4 0 11', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 2 2 13 8 6 4 0 11', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 0 1 2 7 0', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 2 2 13 8 6 4 1 11', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 4 2 13 8 0 4 1 11', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 4 2 13 8 0 1 1 11', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 4 2 13 8 1 1 1 11', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 4 2 13 8 1 1 2 11', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 9 -2', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 12 -2', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 2 2 18 8 1 1 2 11', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 2 2 18 8 1 2 2 11', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 1 2 18 11 1 2 2 11', 'output': '31\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 2 2 18 7 1 2 2 11', 'output': '27\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 2 18 7 1 2 2 11', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 2 18 7 2 2 2 11', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 2 32 0 2 2 2 11', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 4 2 32 0 2 2 2 11', 'output': '34\\n'}, {'type': 'stdin_stdout', 'input': '2\\n5 -1 2 1 2 -2', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 4 2 32 0 2 2 2 11', 'output': '35\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 8 2 6 0 2 2 3 11', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 8 1 2 1 4 -1 6 1', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 3 5', 'output': '-2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n13 2 2 13 4 6 4 0 11', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 1 2 18 11 1 2 0 11', 'output': '33\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 2 36 7 2 2 2 11', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 4 2 51 0 2 2 2 11', 'output': '54\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 4 2 36 8 1 2 2 11', 'output': '46\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 0 2 2 4 4', 'output': '-4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 2 2 18 11 2 2 2 9', 'output': '30\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 2 36 7 1 2 2 11', 'output': '40\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 4 2 32 0 0 2 2 11', 'output': '36\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2 4 1 12 9', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 4 2 26 14 1 1 1 13', 'output': '44\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 4 2 32 0 0 0 2 11', 'output': '38\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 4 2 51 1 2 3 2 11', 'output': '53\\n'}, {'type': 'stdin_stdout', 'input': '3\\n10 1 2 36 8 1 2 4 11', 'output': '47\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 3 36 7 1 2 3 2', 'output': '41\\n'}, {'type': 'stdin_stdout', 'input': '3\\n23 1 2 -2 1 12 -2 -1 3', 'output': '37\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 2 5', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 1 2 7 4 6 6 3 8', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 2 4 1 7 0', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 2 4 1 14 0', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 -1 5', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 1 2 7 4 6 6 0 15', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 2 4 1 11 0', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 2 7 4 6 6 0 15', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 0 8', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 2 4 2 11 -1', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 0 12', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 2 4 2 11 -1', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 0 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 2 4 2 11 0', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 1 0', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 2 2 13 4 6 4 -1 11', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 2 3 2 11 0', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0 1 -1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 2 3 2 7 0', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 1 -1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 0 3 2 7 0', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 1 0', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 2 -1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 -1 1 2 7 0', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 3 -1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 4 2 13 8 6 4 1 11', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '2\\n4 -1 1 2 1 0', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 3 0', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 -1 1 2 1 0', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 6 0', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0 1 2 1 0', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 6 -1', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0 1 2 1 1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 9 -1', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0 1 2 2 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 1 2 13 8 1 1 2 11', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0 1 2 2 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 2 2 13 8 1 1 2 11', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0 0 2 2 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 1 -2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0 2 2 2 2', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 0 -2', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n5 0 2 2 2 2', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1 0 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 1 2 18 8 1 2 2 11', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '2\\n5 0 2 2 2 4', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-2 0 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2\\n5 0 2 1 2 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-2 0 1', 'output': '-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_80345","program":"```python\ndef f(x):\n y=x[:n];heapify(y);z=sum(y);s=[z]\n for i in x[n:n*2]:z+=i-heappushpop(y,i);s+=[z]\n return s\nfrom heapq import*;n,*a=map(int,open(0).read().split());print(max(map(sum,zip(f([-i for i in a[n:][::-1]]),f(a)[::-1]))))\n```","inputs":"2\n3 1 4 1 5 9","output":"1","actual_output":"1\n","execution_success":true,"sample_index":12793},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p04037 AtCoder Grand Contest 002 - Candy Piles","prompt":"Solve the following coding problem using the programming language python:\n\nThere are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.\n\nSnuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:\n\n1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.\n2. From each pile with one or more candies remaining, eat one candy.\n\n\n\nThe player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.\n\nConstraints\n\n* 1\u2264N\u226410^5\n* 1\u2264a_i\u226410^9\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN\na_1 a_2 \u2026 a_N\n\n\nOutput\n\nIf Snuke will win, print `First`. If Ciel will win, print `Second`.\n\nExamples\n\nInput\n\n2\n1 3\n\n\nOutput\n\nFirst\n\n\nInput\n\n3\n1 2 1\n\n\nOutput\n\nFirst\n\n\nInput\n\n3\n1 2 3\n\n\nOutput\n\nSecond\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN=int(input())\nA=list(map(int,input().split()))\nA.append(0)\nA.sort()\nwinner=\"\"\nfor i in range(N+1):\n if A[N-i]>i:\n if (A[N-i]-i)%2==0:\n winner=\"First\"\n else:\n winner=\"Second\"\n elif A[N-i]==i:\n if (A[N-i+1]-A[N-i])%2==1:\n winner=\"First\"\n break\n else:\n count=0\n for j in range(N-i,-1,-1):\n if A[j]==i:\n count+=1\n else:\n break\n if count%2==1:\n winner=\"First\"\n else:\n winner=\"Second\"\n break\n else:\n break\n\nprint(winner)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 2 1', 'output': 'First'}, {'type': 'stdin_stdout', 'input': '2\\n1 3', 'output': 'First'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 3', 'output': 'Second'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 3', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 3', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 0 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 4', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 0 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 4', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n5 0 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 4', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 2', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 4 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 4', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 5', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 0', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 6', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 6', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 0 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 -1 4', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 2', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 5', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-1 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 6', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 1 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -2 4', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 9', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 0 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 2 1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -2 4', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 5', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 3 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 -2 4', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 3 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 5 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 5 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n13 5 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 2', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 6', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 4 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 3', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 0 1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 4', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 1 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -1 0', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 4', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 2', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 6', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 6', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 0 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 4 2', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 6', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 6', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 1 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 1 1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -2 2', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 12', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n-2 1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 6 1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 -2 4', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 3 2', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 5 1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 5 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 4 3', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 6 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-1 -1 1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 2', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n4 6 2', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 -1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 4 6', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n12 0 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 4 4', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 8 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 -1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 7', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 0 -1', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 1 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 6 2', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n-2 -4 4', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n7 1 2', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n8 5 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 1 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 3', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 2', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 -2 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 6 2', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n6 0 1', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 10 0', 'output': 'First\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 -2', 'output': 'Second\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 14', 'output': 'First\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_80353","program":"```python\nN=int(input())\nA=list(map(int,input().split()))\nA.append(0)\nA.sort()\nwinner=\"\"\nfor i in range(N+1):\n if A[N-i]>i:\n if (A[N-i]-i)%2==0:\n winner=\"First\"\n else:\n winner=\"Second\"\n elif A[N-i]==i:\n if (A[N-i+1]-A[N-i])%2==1:\n winner=\"First\"\n break\n else:\n count=0\n for j in range(N-i,-1,-1):\n if A[j]==i:\n count+=1\n else:\n break\n if count%2==1:\n winner=\"First\"\n else:\n winner=\"Second\"\n break\n else:\n break\n\nprint(winner)\n\n```","inputs":"3\n1 2 1","output":"First","actual_output":"First\n","execution_success":true,"sample_index":12794},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00251 Points for a Perfect Scorer","prompt":"Solve the following coding problem using the programming language python:\n\nWelcome to PC Koshien, players. This year marks the 10th anniversary of Computer Koshien, but the number of questions and the total score will vary from year to year. Scores are set for each question according to the difficulty level. When the number of questions is 10 and the score of each question is given, create a program that outputs the total of them.\n\n\n\ninput\n\nThe input is given in the following format.\n\n\ns1\ns2\n..\n..\ns10\n\n\nThe input consists of 10 lines, and the i line is given the integer si (0 \u2264 si \u2264 100) representing the score of problem i.\n\noutput\n\nOutput the total score on one line.\n\nExample\n\nInput\n\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n\n\nOutput\n\n55\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ns1=int(input())\ns2=int(input())\ns3=int(input())\ns4=int(input())\ns5=int(input())\ns6=int(input())\ns7=int(input())\ns8=int(input())\ns9=int(input())\ns10=int(input())\n\ntotal=0\ntotal+=s1\ntotal+=s2\ntotal+=s3\ntotal+=s4\ntotal+=s5\ntotal+=s6\ntotal+=s7\ntotal+=s8\ntotal+=s9\ntotal+=s10\n\nprint(total)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\n10', 'output': '55'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n4\\n4\\n5\\n6\\n7\\n8\\n9\\n10', 'output': '56\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n8\\n4\\n5\\n6\\n7\\n8\\n9\\n10', 'output': '60\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n8\\n4\\n3\\n6\\n7\\n8\\n9\\n10', 'output': '58\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n8\\n3\\n3\\n6\\n7\\n8\\n9\\n10', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n8\\n3\\n3\\n6\\n7\\n5\\n9\\n10', 'output': '54\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n8\\n4\\n3\\n6\\n7\\n5\\n9\\n10', 'output': '55\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n2\\n4\\n3\\n6\\n7\\n5\\n9\\n10', 'output': '49\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n2\\n4\\n3\\n6\\n7\\n5\\n12\\n10', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2\\n4\\n3\\n6\\n7\\n5\\n12\\n10', 'output': '53\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2\\n1\\n3\\n6\\n7\\n5\\n12\\n10', 'output': '50\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2\\n2\\n3\\n6\\n7\\n5\\n12\\n10', 'output': '51\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2\\n2\\n5\\n6\\n7\\n6\\n21\\n10', 'output': '63\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n2\\n2\\n5\\n6\\n7\\n6\\n38\\n10', 'output': '80\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n2\\n2\\n5\\n6\\n7\\n6\\n38\\n10', 'output': '83\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n0\\n2\\n5\\n6\\n7\\n6\\n38\\n10', 'output': '81\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n2\\n5\\n6\\n9\\n6\\n38\\n10', 'output': '82\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n2\\n5\\n6\\n9\\n6\\n38\\n2', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n3\\n5\\n6\\n9\\n6\\n38\\n2', 'output': '75\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n3\\n5\\n10\\n9\\n6\\n38\\n2', 'output': '79\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n3\\n5\\n3\\n9\\n6\\n38\\n2', 'output': '72\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n4\\n5\\n3\\n9\\n6\\n38\\n2', 'output': '73\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n4\\n5\\n4\\n9\\n6\\n63\\n2', 'output': '99\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n8\\n5\\n4\\n9\\n6\\n63\\n2', 'output': '103\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n7\\n5\\n4\\n9\\n6\\n63\\n2', 'output': '102\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n9\\n5\\n4\\n9\\n6\\n63\\n2', 'output': '104\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6\\n-1\\n6\\n5\\n4\\n9\\n6\\n63\\n2', 'output': '101\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8\\n-1\\n6\\n8\\n4\\n9\\n6\\n63\\n2', 'output': '106\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8\\n-1\\n6\\n8\\n4\\n9\\n6\\n26\\n2', 'output': '69\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8\\n-1\\n6\\n8\\n4\\n9\\n6\\n19\\n2', 'output': '62\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-1\\n6\\n0\\n6\\n6\\n2\\n19\\n2', 'output': '42\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-1\\n6\\n0\\n3\\n6\\n2\\n19\\n2', 'output': '39\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-1\\n6\\n0\\n3\\n6\\n2\\n3\\n2', 'output': '23\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-1\\n6\\n0\\n3\\n6\\n1\\n3\\n2', 'output': '22\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-1\\n6\\n0\\n3\\n7\\n1\\n4\\n2', 'output': '24\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-1\\n6\\n0\\n3\\n2\\n1\\n4\\n2', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-1\\n11\\n0\\n3\\n3\\n1\\n4\\n2', 'output': '25\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-1\\n5\\n0\\n3\\n3\\n1\\n4\\n1', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-1\\n5\\n0\\n3\\n3\\n0\\n4\\n1', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-1\\n5\\n0\\n3\\n1\\n1\\n4\\n1', 'output': '16\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n0\\n5\\n0\\n5\\n2\\n1\\n4\\n1', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n0\\n5\\n0\\n6\\n2\\n1\\n4\\n1', 'output': '21\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n-2\\n0\\n-1\\n3\\n4\\n0\\n7\\n-1', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-1\\n3\\n6\\n0\\n7\\n-1', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-1\\n3\\n6\\n0\\n6\\n-1', 'output': '12\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-1\\n3\\n6\\n-1\\n6\\n-1', 'output': '11\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-1\\n3\\n11\\n-2\\n6\\n-2', 'output': '14\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-1\\n3\\n0\\n-3\\n6\\n-2', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-1\\n3\\n0\\n0\\n6\\n-2', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-1\\n3\\n0\\n0\\n6\\n-1', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-1\\n6\\n0\\n0\\n6\\n-1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-2\\n6\\n0\\n0\\n6\\n-1', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-2\\n6\\n-1\\n0\\n6\\n-1', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-2\\n6\\n-1\\n0\\n3\\n-1', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-2\\n6\\n-1\\n-1\\n3\\n-1', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-3\\n6\\n0\\n-1\\n0\\n-1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-3\\n6\\n-1\\n-1\\n0\\n-1', 'output': '-1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n-2\\n-1\\n-3\\n8\\n-1\\n-1\\n0\\n-1', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n-2\\n-1\\n-1\\n6\\n-1\\n-4\\n0\\n-2', 'output': '-2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n-2\\n-1\\n-1\\n6\\n-3\\n-3\\n1\\n-3', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n-2\\n-2\\n-1\\n1\\n-3\\n-3\\n1\\n0', 'output': '-5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n-2\\n-2\\n-1\\n1\\n-3\\n-5\\n1\\n0', 'output': '-7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n-2\\n-2\\n-2\\n1\\n-3\\n-5\\n1\\n0', 'output': '-8\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n-3\\n-2\\n-2\\n1\\n-3\\n-5\\n1\\n0', 'output': '-9\\n'}, {'type': 'stdin_stdout', 'input': '1\\n3\\n-3\\n-1\\n-2\\n1\\n1\\n-5\\n1\\n0', 'output': '-4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n-1\\n-1\\n-2\\n1\\n1\\n-6\\n1\\n0', 'output': '-6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1\\n0\\n-4\\n0\\n1\\n1\\n-14\\n2\\n1', 'output': '-13\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1\\n0\\n-4\\n0\\n0\\n1\\n-14\\n2\\n1', 'output': '-14\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1\\n0\\n-4\\n0\\n0\\n1\\n-22\\n2\\n1', 'output': '-22\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1\\n0\\n-6\\n0\\n0\\n1\\n-22\\n2\\n1', 'output': '-24\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1\\n0\\n-6\\n0\\n0\\n1\\n-22\\n2\\n2', 'output': '-23\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1\\n0\\n-6\\n1\\n0\\n1\\n-44\\n2\\n2', 'output': '-44\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1\\n0\\n-6\\n2\\n0\\n1\\n-44\\n2\\n2', 'output': '-43\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1\\n0\\n-6\\n2\\n0\\n1\\n-57\\n2\\n2', 'output': '-56\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1\\n0\\n-6\\n1\\n0\\n1\\n-57\\n2\\n2', 'output': '-57\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1\\n0\\n-6\\n1\\n1\\n1\\n-56\\n2\\n2', 'output': '-55\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n0\\n-6\\n1\\n1\\n1\\n-56\\n2\\n2', 'output': '-54\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n0\\n-6\\n1\\n1\\n1\\n-73\\n1\\n2', 'output': '-72\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n1\\n-6\\n1\\n1\\n1\\n-73\\n1\\n2', 'output': '-71\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n1\\n-6\\n0\\n1\\n0\\n-73\\n1\\n2', 'output': '-73\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n1\\n-6\\n0\\n1\\n0\\n-73\\n0\\n2', 'output': '-74\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n1\\n-12\\n0\\n1\\n0\\n-73\\n0\\n2', 'output': '-80\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n1\\n-12\\n0\\n1\\n0\\n-73\\n0\\n2', 'output': '-79\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n2\\n-13\\n0\\n1\\n0\\n-10\\n0\\n1', 'output': '-17\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n0\\n-13\\n0\\n1\\n0\\n-17\\n0\\n1', 'output': '-26\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n0\\n-13\\n0\\n1\\n0\\n-17\\n1\\n1', 'output': '-25\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n0\\n-13\\n0\\n1\\n0\\n-17\\n-1\\n1', 'output': '-27\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n0\\n-19\\n0\\n1\\n0\\n-17\\n-1\\n1', 'output': '-32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n0\\n-19\\n0\\n1\\n0\\n-17\\n0\\n1', 'output': '-31\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n0\\n-38\\n0\\n1\\n0\\n-17\\n0\\n1', 'output': '-50\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n0\\n-38\\n-1\\n1\\n0\\n-17\\n0\\n1', 'output': '-51\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n0\\n-38\\n-1\\n1\\n-1\\n-17\\n0\\n1', 'output': '-52\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n0\\n-38\\n-1\\n1\\n-1\\n-32\\n0\\n1', 'output': '-67\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n0\\n-8\\n-1\\n1\\n-1\\n-32\\n0\\n1', 'output': '-37\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n0\\n-8\\n-1\\n2\\n-1\\n-32\\n0\\n1', 'output': '-36\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n-1\\n-9\\n-1\\n2\\n-1\\n-32\\n0\\n1', 'output': '-38\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n-1\\n-9\\n-1\\n2\\n-1\\n-32\\n-1\\n1', 'output': '-39\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n0\\n-9\\n0\\n4\\n-2\\n-32\\n-2\\n0', 'output': '-40\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n0\\n-9\\n1\\n4\\n-2\\n-59\\n-2\\n1', 'output': '-64\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n0\\n-9\\n1\\n4\\n-2\\n-59\\n-2\\n1', 'output': '-63\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0\\n0\\n-9\\n1\\n4\\n-2\\n-59\\n-2\\n1', 'output': '-65\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_80361","program":"```python\ns1=int(input())\ns2=int(input())\ns3=int(input())\ns4=int(input())\ns5=int(input())\ns6=int(input())\ns7=int(input())\ns8=int(input())\ns9=int(input())\ns10=int(input())\n\ntotal=0\ntotal+=s1\ntotal+=s2\ntotal+=s3\ntotal+=s4\ntotal+=s5\ntotal+=s6\ntotal+=s7\ntotal+=s8\ntotal+=s9\ntotal+=s10\n\nprint(total)\n\n```","inputs":"1\n2\n3\n4\n5\n6\n7\n8\n9\n10","output":"55","actual_output":"55\n","execution_success":true,"sample_index":12795},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00628 Yes","prompt":"Solve the following coding problem using the programming language python:\n\nDr .: Peter, do you know \"Yes, I have a number\"?\n\nPeter: I used to do it on TV the other day. You remember something by the number of characters in each word contained in a sentence. \"Yes, I have a number\", so it means \"the number 3.14\" and is a keyword for remembering pi.\n\nDr .: Peter, that's not the case. This should be interpreted as 3.1416. The circumference ratio is 3.14159 ... That's why.\n\nPeter: Then, did you forcibly omit that program just because Japan teaches that the circumference ratio is 3.14? ??\n\nDr .: ... Let's just say that the pi taught in elementary school has finally returned from 3 to 3.14.\n\nPeter: Do you really remember this in the first place?\n\nDr .: It may be difficult for Japanese people. It seems that English-speaking people use it, because it is difficult to make a ground ball in English.\n\nPeter: Even so, it seems to be a hassle to check.\n\nDr .: Then, I want you to make a program that converts sentences into a sequence of the number of characters in a word.\n\nPeter: I understand. Please tell me the detailed specifications.\n\nDr .: Let's enter one line of text. For simplicity, you can use sentences that contain only alphabets and blanks. For this sentence, output the length of the character string between the blank, the beginning of the sentence, and the end of the sentence in order. You can proceed if the number of characters in the string does not exceed 9.\nFor example, Yes in \"Yes I have\" has 3 characters because it is separated by the beginning and the first space, and I is separated by the first and second spaces and has 1 character.\n\nDr .: Then, don't forget the character string where the number of characters becomes 0 when there are consecutive blanks.\n\n\n\nInput\n\nMultiple datasets are given as input. For each dataset, a string containing alphabets and spaces is given on one line.\n\nWhen the character string is \"END OF INPUT\", it is the end of input. Do not output to this input.\n\nOutput\n\nFor each dataset, output a sequence of the number of characters for the string on one line.\n\nExample\n\nInput\n\nYes I have a number\nHow I wish I could calculate an unused color for space\nThank you\nEND OF INPUT\n\n\nOutput\n\n31416\n31415926535\n53\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\nsys.setrecursionlimit(10**6)\ndef main():\n s = input()\n if s == \"END OF INPUT\":\n return False\n if s[0] == \" \":\n s[0] = \".\"\n for _ in range(100):\n s = s.replace(\" \", \" . \")\n lst = s.split()\n ans = []\n for i in lst:\n if i == \".\":\n ans += [0]\n else:\n ans += [len(i)]\n print(\"\".join(map(str, ans)))\n return True\n\nwhile main():\n pass\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'Yes I have a number\\nHow I wish I could calculate an unused color for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53'}, {'type': 'stdin_stdout', 'input': 'Yes I have a number\\nHow I wish I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I have a rebmun\\nHow I wish I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I have a rebmun\\nHow J wish I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H have a rebmun\\nHow J wish I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H have a rebmun\\nHow J hisw I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H have a rebmun\\nHow J hisw J could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H have a rebmun\\nHow J hisw J could calculate an unused bolor rof space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H havd a rebmun\\nHow J hisw J could calculate an unused bolor rof space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nHow J hisw J could calculate an unused bolor rof space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nHow J hisw J could calculate an unused bolor rof space\\nTiank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nHow J hisw I could calculate an unused bolor rof space\\nTiank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I could calculate an unused bolor rof space\\nTiank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I could calculate an unused bolor rof space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I could calculate bn unused bolor rof space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I dluoc calculate bn unused bolor rof space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I dluoc calculate bn unused bolor for space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I oludc calculate bn unused bolor for space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I oludc calculate bn unused bolor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHnw J hisw I oludc calculate bn unused bolor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nwnH J hisw I oludc calculate bn unused bolor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nwnH J hisw I oludc cakculate bn unused bolor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nwnH J hisw I oludc cakculate bn unused bplor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet H davh a rebmun\\nwnH J hisw I oludc cakculate bn unused bplor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet H davh a rebmun\\nwnH J hisw I oludc cakculate bn unused bplor for ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I davh a rebmun\\nwnH J hisw I oludc cakculate bn unused bplor for ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I davh a rebmun\\nwnH J hisw I oludc cakculate bn unused bplor eor ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I hvad a rebmun\\nwnH J hisw I oludc cakculate bn unused bplor eor ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I hvad a rebmun\\nwnH J hisw I oludc cakcueatl bn unused bplor eor ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I hvad a rebmun\\nwnH J hisw I oludc ltaeuckac bn unused bplor eor ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I hvad a rebmun\\nwnH J hisw I oludc ltaeuckac bn unused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I hvad a rebmun\\nwnH J hjsw I oludc ltaeuckac bn unused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I hvad a rebmun\\nwnH J hjsw I oludc ltaeuckac bn unused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I hvad a rebmun\\nwnH J hjsw I oludc ltaeuckac bn tnused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I hvad a rebmun\\nwnH J hjsw I cdulo ltaeuckac bn tnused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I hvbd a rebmun\\nwnH J hjsw I cdulo ltaeuckac bn tnused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I have a number\\nIow I wish I could calculate an unused color for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I have a nrmbeu\\nHow I wish I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I hawe a rebmun\\nHow I wish I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'seY I have a rebmun\\nHow J wish I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet H have a rebmun\\nHow J wish I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H have a rebmun\\nHow I hisw J could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H have a rebmun\\nwoH J hisw J could calculate an unused bolor rof space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H havd a rebmun\\nHow J hisw J could calculate an unused bnlor rof space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nHow J hisw J could calculate an unused bolor sof space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nHow J hitw I could calculate an unused bolor rof space\\nTiank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I could calcutale an unused bolor rof space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebumn\\nHow J hisw I could calculate bn unused bolor rof space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I dluoc aalculcte bn unused bolor rof space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I dluoc calculate bn unusdd bolor for space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a qebmun\\nHow J hisw I oludc calculate bn unused bolor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHnw J hisw I oludc calculate bn unused bolor for space\\nTkani uox\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nwnH J hisw I oludc caclulate bn unused bolor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rnbmue\\nwnH J hisw I oludc cakculate bn unused bolor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHnw J hisw I oludc cakculate bn unused bplor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet H davh a rebmun\\nwnH J hisw I oludc cakculate bn unused bplor rof ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet H davh a rebmun\\nwnH K hisw I oludc cakculate bn unused bplor for ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I davh a rebmun\\nwnH J hisw I oludc cakculate bn unused bplor for ecaps\\nTkani xnu\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I davh a rebmun\\nwnH J hjsw I oludc cakculate bn unused bplor eor ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I hvad a rebmun\\nwnH J hisw I oludc cakculate bn unused bplor eor ecaps\\nTkaoi xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I hvad a rebmun\\nwnH J hisw H oludc cakcueatl bn unused bplor eor ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I hvad a rebmun\\nwnH J hisw I oludc ltaeuckac bn unused bplor for ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I huad a rebmun\\nwnH J hisw I oludc ltaeuckac bn unused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I hvad a rebmun\\nwnH J hjsw I oludc lt`euckac bn unused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I hvad a rebmvn\\nwnH J hjsw I oludc ltaeuckac bn unused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nwnH J hjsw I oludc ltaeuckac bn tnused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I hvbd a rebmun\\nwnH J hjsw I cdulo ltaeuckac nb tnused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I have a numbdr\\nIow I wish I could calculate an unused color for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I have a nrmbeu\\nHow I wish I dluoc calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'seY I have a rebmun\\nHow J wish H could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet H have a rebmun\\nHow J hsiw I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H have a rebmun\\nHow I hisw J could calculate an unused bolor for space\\nThank zou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H have a rebmun\\nwoH J hisw K could calculate an unused bolor rof space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H havd a rebmun\\nHow J hisw J could calculate an unused bnlor rof space\\nThank ynu\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nHow J hisw J could calculate an unused bolor sof space\\nknahT you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nHow J hitw I could calculate an unused bolor rof space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow K hisw I could calcutale an unused bolor rof space\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I dluoc aalculcte bn unused bolor rof space\\nThank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHow J hisw I dluoc calculate bn unusdd bolor for spacf\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yfs H davh a qebmun\\nHow J hisw I oludc calculate bn unused bolor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nwnH J hisw I oludc caclulate nb unused bolor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rnbmue\\nHnw J hisw I oludc cakculate bn unused bolor for space\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H davh a rebmun\\nHnw J hisw I oludc cakculate bn unused bplor for space\\ninakT xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet H davh a rebmun\\nwnH J hisw I oludc cakculate bn snuued bplor rof ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'teY H davh a rebmun\\nwnH K hisw I oludc cakculate bn unused bplor for ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I davh a rebmun\\nwnH J hisw I pludc cakculate bn unused bplor for ecaps\\nTkani xnu\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I davh a rebmun\\nwnH J hjsw I oludc cakculate bn unused bplor eor ecpas\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet J hvad a rebmun\\nwnH J hisw I oludc ltaeuckac bn unused bplor for ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I huad a rebmun\\nwnH J hisw I oludc ltaeuckac bn unused bplor fro ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yet I hvad b rebmun\\nwnH J hjsw I oludc lt`euckac bn unused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I hvad a rebmvn\\nwnH J hjsw I oludc ktaeuclac bn unused bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nwnH J hjsw I oludc ltaeuckac bn tntsed bplor ero ecaps\\nTkani xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I hawe a numbdr\\nIow I wish I could calculate an unused color for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes I have a nrmbeu\\nHow I wish I dluoc calculate an unused boloq for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'seY I have a rebmun\\nHow J iwsh H could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yte H have a rebmun\\nHow J hsiw I could calculate an unused bolor for space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H have a rebmun\\nHow I hisw J could calculate na unused bolor for space\\nThank zou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H have a rebmun\\nwoH J hisw K could calculate an unused bolor rnf space\\nThank you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nHow J hisw J could calculate an usuned bolor sof space\\nknahT you\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yes H hvad a rebmun\\nHow J hitw I could calculate an unused bolor rof sp`ce\\nTiank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}, {'type': 'stdin_stdout', 'input': 'Yfs H davh a rebmun\\nHow J hisw I dluoc aalculcte bn unused bolor rof space\\nThank xou\\nEND OF INPUT', 'output': '31416\\n31415926535\\n53\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_80369","program":"```python\nimport sys\nsys.setrecursionlimit(10**6)\ndef main():\n s = input()\n if s == \"END OF INPUT\":\n return False\n if s[0] == \" \":\n s[0] = \".\"\n for _ in range(100):\n s = s.replace(\" \", \" . \")\n lst = s.split()\n ans = []\n for i in lst:\n if i == \".\":\n ans += [0]\n else:\n ans += [len(i)]\n print(\"\".join(map(str, ans)))\n return True\n\nwhile main():\n pass\n\n```","inputs":"Yes I have a number\nHow I wish I could calculate an unused color for space\nThank you\nEND OF INPUT","output":"31416\n31415926535\n53","actual_output":"31416\n31415926535\n53\n","execution_success":true,"sample_index":12796},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p00903 Round Trip","prompt":"Solve the following coding problem using the programming language python:\n\nJim is planning to visit one of his best friends in a town in the mountain area. First, he leaves his hometown and goes to the destination town. This is called the go phase. Then, he comes back to his hometown. This is called the return phase. You are expected to write a program to find the minimum total cost of this trip, which is the sum of the costs of the go phase and the return phase.\n\nThere is a network of towns including these two towns. Every road in this network is one-way, i.e., can only be used towards the specified direction. Each road requires a certain cost to travel.\n\nIn addition to the cost of roads, it is necessary to pay a specified fee to go through each town on the way. However, since this is the visa fee for the town, it is not necessary to pay the fee on the second or later visit to the same town.\n\nThe altitude (height) of each town is given. On the go phase, the use of descending roads is inhibited. That is, when going from town a to b, the altitude of a should not be greater than that of b. On the return phase, the use of ascending roads is inhibited in a similar manner. If the altitudes of a and b are equal, the road from a to b can be used on both phases.\n\n\n\nInput\n\nThe input consists of multiple datasets, each in the following format.\n\nn m\nd2 e2\nd3 e3\n.\n.\n.\ndn-1 en-1\na1 b1 c1\na2 b2 c2\n.\n.\n.\nam bm cm\n\nEvery input item in a dataset is a non-negative integer. Input items in a line are separated by a space.\n\nn is the number of towns in the network. m is the number of (one-way) roads. You can assume the inequalities 2 \u2264 n \u2264 50 and 0 \u2264 m \u2264 n(n\u22121) hold. Towns are numbered from 1 to n, inclusive. The town 1 is Jim's hometown, and the town n is the destination town.\n\ndi is the visa fee of the town i, and ei is its altitude. You can assume 1 \u2264 di \u2264 1000 and 1\u2264ei \u2264 999 for 2\u2264i\u2264n\u22121. The towns 1 and n do not impose visa fee. The altitude of the town 1 is 0, and that of the town n is 1000. Multiple towns may have the same altitude, but you can assume that there are no more than 10 towns with the same altitude.\n\nThe j-th road is from the town aj to bj with the cost cj (1 \u2264 j \u2264 m). You can assume 1 \u2264 aj \u2264 n, 1 \u2264 bj \u2264 n, and 1 \u2264 cj \u2264 1000. You can directly go from aj to bj, but not from bj to aj unless a road from bj to aj is separately given. There are no two roads connecting the same pair of towns towards the same direction, that is, for any i and j such that i \u2260 j, ai \u2260 aj or bi \u2260 bj. There are no roads connecting a town to itself, that is, for any j, aj \u2260 bj.\n\nThe last dataset is followed by a line containing two zeros (separated by a space).\n\nOutput\n\nFor each dataset in the input, a line containing the minimum total cost, including the visa fees, of the trip should be output. If such a trip is not possible, output \"-1\".\n\nExample\n\nInput\n\n3 6\n3 1\n1 2 1\n2 3 1\n3 2 1\n2 1 1\n1 3 4\n3 1 4\n3 6\n5 1\n1 2 1\n2 3 1\n3 2 1\n2 1 1\n1 3 4\n3 1 4\n4 5\n3 1\n3 1\n1 2 5\n2 3 5\n3 4 5\n4 2 5\n3 1 5\n2 1\n2 1 1\n0 0\n\n\nOutput\n\n7\n8\n36\n-1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom heapq import heappush, heappop\nfrom collections import defaultdict\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\ndef solve():\n N, M = map(int, readline().split())\n if N == M == 0:\n return False\n D = [0]*N; E = [0]*N\n B = [0]*N\n H = defaultdict(int)\n H[0] = 1\n H[1000] += 1\n E[N-1] = 1000\n for i in range(1, N-1):\n D[i], e = map(int, readline().split())\n E[i] = e\n B[i] = H[e]\n H[e] += 1\n\n G = [[] for i in range(N)]\n RG = [[] for i in range(N)]\n for i in range(M):\n a, b, c = map(int, readline().split()); a -= 1; b -= 1\n if E[a] <= E[b]:\n G[a].append((b, c))\n if E[b] <= E[a]:\n RG[b].append((a, c))\n dist = {(0, 0, 1): 0}\n que = [(0, 0, 0, 1)]\n INF = 10**18\n while que:\n cost, v0, v1, state = heappop(que)\n if dist[v0, v1, state] < cost:\n continue\n d0 = E[v0]; d1 = E[v1]\n if d0 < d1:\n for w0, d in G[v0]:\n if E[w0] == d1:\n if w0 == v1:\n de = cost + d\n n_state = (1 << B[w0])\n else:\n de = cost + d + D[w0]\n n_state = (1 << B[w0]) | (1 << B[v1])\n n_key = (w0, v1, n_state)\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, w0, v1, n_state))\n else:\n n_key = (w0, v1, 0)\n de = cost + d + D[w0]\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, w0, v1, 0))\n elif d0 > d1:\n for w1, d in RG[v1]:\n if E[w1] == d0:\n if w1 == v0:\n de = cost + d\n n_state = (1 << B[w1])\n else:\n de = cost + d + D[w1]\n n_state = (1 << B[w1]) | (1 << B[v0])\n n_key = (v0, w1, n_state)\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, v0, w1, n_state))\n else:\n n_key = (v0, w1, 0)\n de = cost + d + D[w1]\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, v0, w1, 0))\n else:\n ds = d0\n for w0, d in G[v0]:\n if ds == E[w0]:\n b = (1 << B[w0])\n if state & b:\n de = cost + d\n n_state = state\n else:\n de = cost + d + D[w0]\n n_state = state | b\n n_key = (w0, v1, n_state)\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, w0, v1, n_state))\n else:\n n_key = (w0, v1, 0)\n de = cost + d + D[w0]\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, w0, v1, 0))\n for w1, d in RG[v1]:\n if ds == E[w1]:\n b = (1 << B[w1])\n if state & b:\n de = cost + d\n n_state = state\n else:\n de = cost + d + D[w1]\n n_state = state | b\n n_key = (v0, w1, n_state)\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, v0, w1, n_state))\n else:\n n_key = (v0, w1, 0)\n de = cost + d + D[w1]\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, v0, w1, 0))\n g_key = (N-1, N-1, 1)\n if g_key in dist:\n write(\"%d\\n\" % dist[g_key])\n else:\n write(\"-1\\n\")\n return True\nwhile solve():\n ...\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '7\\n8\\n36\\n-1'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '7\\n8\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 4 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n26\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 3\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '7\\n7\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '4\\n8\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n2 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '7\\n8\\n35\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 3\\n3 1 4\\n6 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '7\\n7\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 10\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '4\\n8\\n41\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 2\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 10\\n4 2 5\\n2 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '5\\n8\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 2\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '7\\n6\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 2 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 1\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n2 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '5\\n8\\n35\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 2\\n3 2 1\\n2 1 2\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 10\\n4 2 5\\n2 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '6\\n8\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 1 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 3\\n3 1 4\\n6 5\\n3 1\\n3 1\\n1 2 5\\n2 2 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '8\\n7\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 2 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n3 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 10\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '6\\n8\\n41\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 1\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n32\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n2 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '7\\n-1\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 3\\n3 1 4\\n4 5\\n3 0\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '7\\n7\\n-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 0\\n4 5\\n2 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '7\\n4\\n35\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 0\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n2 2 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '6\\n-1\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 0\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n2 2 4\\n3 1 4\\n4 5\\n3 1\\n3 0\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '6\\n-1\\n-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 1 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 0\\n2 1 1\\n1 3 3\\n3 1 4\\n4 5\\n3 0\\n6 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '8\\n7\\n-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n6 1\\n1 2 1\\n2 3 1\\n2 2 2\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 2\\n2 2 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 6\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n37\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 2\\n2 1\\n2 1 1\\n0 0', 'output': '7\\n8\\n33\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 10\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n41\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 2\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '7\\n8\\n-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 3\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '8\\n7\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n1 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 10\\n4 2 5\\n2 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '4\\n5\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 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'output': '8\\n10\\n26\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n1 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 0\\n2 1 1\\n1 3 3\\n3 1 4\\n4 5\\n3 0\\n6 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '5\\n7\\n-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n6 1\\n1 2 1\\n2 3 1\\n2 2 2\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 2\\n2 2 1\\n2 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n-1\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 10\\n2 3 5\\n3 4 4\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n40\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 3\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 2\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '8\\n7\\n33\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 0\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 7\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 10\\n4 2 5\\n2 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '3\\n9\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 2\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 0\\n3 2 0\\n2 1 1\\n1 3 3\\n3 1 8\\n6 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n5 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '7\\n9\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n6 1\\n1 2 1\\n2 3 1\\n2 2 2\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 2\\n2 2 1\\n1 3 4\\n3 1 4\\n4 5\\n6 1\\n3 1\\n1 2 6\\n2 3 5\\n3 4 3\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n38\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n2 2 1\\n2 1 1\\n1 3 4\\n3 1 1\\n4 5\\n3 1\\n3 1\\n1 2 10\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n5\\n41\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 1\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 2 5\\n4 3 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '8\\n5\\n-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '7\\n8\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 10\\n4 2 5\\n2 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '4\\n8\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '4\\n8\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 4 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n26\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 3\\n3 1 4\\n6 5\\n3 1\\n3 1\\n1 2 5\\n2 2 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '7\\n7\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n3 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 10\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '4\\n8\\n41\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 3 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 2 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 3 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 2 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n2 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 0\\n3 2 1\\n2 1 1\\n1 3 3\\n3 1 4\\n6 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 1 5\\n2 1\\n2 1 0\\n0 0', 'output': '7\\n7\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n0 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 10\\n4 2 5\\n2 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '4\\n8\\n36\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 2 5\\n2 3 5\\n3 4 9\\n4 2 5\\n3 2 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n-1\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n3 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n5 1\\n2 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 4 5\\n2 3 5\\n3 4 2\\n4 2 5\\n3 1 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n26\\n-1\\n'}, {'type': 'stdin_stdout', 'input': '3 6\\n5 1\\n1 2 1\\n2 3 1\\n3 3 1\\n2 1 1\\n1 3 4\\n3 1 4\\n3 6\\n8 1\\n1 2 1\\n2 3 1\\n3 2 1\\n2 1 1\\n1 3 4\\n3 1 4\\n4 5\\n3 1\\n3 1\\n1 3 5\\n2 3 5\\n3 4 5\\n4 2 5\\n3 2 5\\n2 1\\n2 1 1\\n0 0', 'output': '8\\n8\\n-1\\n-1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_80377","program":"```python\nfrom heapq import heappush, heappop\nfrom collections import defaultdict\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\ndef solve():\n N, M = map(int, readline().split())\n if N == M == 0:\n return False\n D = [0]*N; E = [0]*N\n B = [0]*N\n H = defaultdict(int)\n H[0] = 1\n H[1000] += 1\n E[N-1] = 1000\n for i in range(1, N-1):\n D[i], e = map(int, readline().split())\n E[i] = e\n B[i] = H[e]\n H[e] += 1\n\n G = [[] for i in range(N)]\n RG = [[] for i in range(N)]\n for i in range(M):\n a, b, c = map(int, readline().split()); a -= 1; b -= 1\n if E[a] <= E[b]:\n G[a].append((b, c))\n if E[b] <= E[a]:\n RG[b].append((a, c))\n dist = {(0, 0, 1): 0}\n que = [(0, 0, 0, 1)]\n INF = 10**18\n while que:\n cost, v0, v1, state = heappop(que)\n if dist[v0, v1, state] < cost:\n continue\n d0 = E[v0]; d1 = E[v1]\n if d0 < d1:\n for w0, d in G[v0]:\n if E[w0] == d1:\n if w0 == v1:\n de = cost + d\n n_state = (1 << B[w0])\n else:\n de = cost + d + D[w0]\n n_state = (1 << B[w0]) | (1 << B[v1])\n n_key = (w0, v1, n_state)\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, w0, v1, n_state))\n else:\n n_key = (w0, v1, 0)\n de = cost + d + D[w0]\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, w0, v1, 0))\n elif d0 > d1:\n for w1, d in RG[v1]:\n if E[w1] == d0:\n if w1 == v0:\n de = cost + d\n n_state = (1 << B[w1])\n else:\n de = cost + d + D[w1]\n n_state = (1 << B[w1]) | (1 << B[v0])\n n_key = (v0, w1, n_state)\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, v0, w1, n_state))\n else:\n n_key = (v0, w1, 0)\n de = cost + d + D[w1]\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, v0, w1, 0))\n else:\n ds = d0\n for w0, d in G[v0]:\n if ds == E[w0]:\n b = (1 << B[w0])\n if state & b:\n de = cost + d\n n_state = state\n else:\n de = cost + d + D[w0]\n n_state = state | b\n n_key = (w0, v1, n_state)\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, w0, v1, n_state))\n else:\n n_key = (w0, v1, 0)\n de = cost + d + D[w0]\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, w0, v1, 0))\n for w1, d in RG[v1]:\n if ds == E[w1]:\n b = (1 << B[w1])\n if state & b:\n de = cost + d\n n_state = state\n else:\n de = cost + d + D[w1]\n n_state = state | b\n n_key = (v0, w1, n_state)\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, v0, w1, n_state))\n else:\n n_key = (v0, w1, 0)\n de = cost + d + D[w1]\n if de < dist.get(n_key, INF):\n dist[n_key] = de\n heappush(que, (de, v0, w1, 0))\n g_key = (N-1, N-1, 1)\n if g_key in dist:\n write(\"%d\\n\" % dist[g_key])\n else:\n write(\"-1\\n\")\n return True\nwhile solve():\n ...\n\n```","inputs":"3 6\n3 1\n1 2 1\n2 3 1\n3 2 1\n2 1 1\n1 3 4\n3 1 4\n3 6\n5 1\n1 2 1\n2 3 1\n3 2 1\n2 1 1\n1 3 4\n3 1 4\n4 5\n3 1\n3 1\n1 2 5\n2 3 5\n3 4 5\n4 2 5\n3 1 5\n2 1\n2 1 1\n0 0","output":"7\n8\n36\n-1","actual_output":"7\n8\n36\n-1\n","execution_success":true,"sample_index":12797},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01036 Yu-kun Likes To Play Darts","prompt":"Solve the following coding problem using the programming language python:\n\nBackground\n\nThe kindergarten attached to the University of Aizu is a kindergarten where children who love programming gather. Yu, one of the kindergarten children, loves darts as much as programming. Yu-kun was addicted to darts recently, but he got tired of ordinary darts, so he decided to make his own darts board.\n\nSee darts for darts.\n\nProblem\n\nThe contents of the darts that Yu-kun thought about are as follows.\n\nThe infinitely wide darts board has several polygons with scores. The player has only one darts arrow. The player throws an arrow and stabs the arrow into one of the polygons to get the score written there. If you stab it in any other way, you will not get any points.\n\nYu-kun decided where to throw the arrow, but it doesn't always stick exactly. The darts board is a two-dimensional plane, and the position Yu-kun is aiming for is a point (cx, cy). The place where the arrow thrown by Yu-kun sticks is selected with a uniform probability from any point included in the circle with radius r centered on the point (cx, cy). The coordinates of the exposed points do not have to be integers.\n\nSince the information on the darts board, the position (cx, cy) that Yu-kun aims at, and the radius r are given, answer the expected value of the score that Yu-kun can get.\n\nConstraints\n\nThe input satisfies the following conditions.\n\n* All inputs are given as integers\n* 1 \u2264 n \u2264 50\n* 0 \u2264 cx, cy, x, y \u2264 1000\n* 1 \u2264 r \u2264 100\n* 3 \u2264 p \u2264 10\n* 1 \u2264 score \u2264 100\n* Polygon vertices are given in such an order that they visit adjacent vertices clockwise or counterclockwise.\n* The sides of a polygon do not have anything in common with the sides of another polygon\n* A polygon does not contain another polygon\n* If the arrow sticks on the side of the polygon, no score will be given.\n\nInput\n\n\nn cx cy r\nInformation on the 0th polygon\nInformation on the first polygon\n...\nInformation on the (n-1) th polygon\n\n\nn is the number of polygons on the darts board. Polygonal information is given in the following format.\n\n\np score\nx0 y0\nx1 y1\n...\nx (p-1) y (p-1)\n\n\np represents the number of vertices of the polygon, and score represents the score written on the polygon. Each line segment of the polygon is a line segment connecting the vertices of (xi, yi) and (xi + 1, yi + 1) (i = 0 else -1.0\n area += sign * r * r * t / 2 # \u6247\u5f62\u306e\u9762\u7a4d\n return area\n\ndef cross(v1, v2): # \u5916\u7a4d\n x1, y1 = v1\n x2, y2 = v2\n return x1 * y2 - x2 * y1\n\ndef dot(v1, v2): # \u5185\u7a4d\n x1, y1 = v1\n x2, y2 = v2\n return x1 * x2 + y1 * y2\n\ndef seg_intersection(circle, seg):\n # \u5186\u3068\u7dda\u5206\u306e\u4ea4\u70b9\uff08\u5186\u306e\u4e2d\u5fc3\u304c\u539f\u70b9\u3067\u306a\u3044\u5834\u5408\u306f\u672a\u691c\u8a3c\uff09\n x0, y0, r = circle\n p1, p2 = seg\n x1, y1 = p1\n x2, y2 = p2\n\n p1p2 = (x2 - x1) ** 2 + (y2 - y1) ** 2\n op1 = (x1 - x0) ** 2 + (y1 - y0) ** 2\n rr = r * r\n dp = dot((x1 - x0, y1 - y0), (x2 - x1, y2 - y1))\n\n d = dp * dp - p1p2 * (op1 - rr)\n ps = []\n\n if isclose(d, 0.0, abs_tol=1e-9):\n t = -dp / p1p2\n if ge(t, 0.0) and le(t, 1.0):\n ps.append((x1 + t * (x2 - x1), y1 + t * (y2 - y1)))\n elif d > 0.0:\n t1 = (-dp - sqrt(d)) / p1p2\n if ge(t1, 0.0) and le(t1, 1.0):\n ps.append((x1 + t1 * (x2 - x1), y1 + t1 * (y2 - y1)))\n t2 = (-dp + sqrt(d)) / p1p2\n if ge(t2, 0.0) and le(t2, 1.0):\n ps.append((x1 + t2 * (x2 - x1), y1 + t2 * (y2 - y1)))\n\n # assert all(isclose(r, hypot(x, y)) for x, y in ps)\n return ps\n\ndef le(f1, f2): # less equal\n return f1 < f2 or isclose(f1, f2, abs_tol=1e-9)\n\ndef ge(f1, f2): # greater equal\n return f1 > f2 or isclose(f1, f2, abs_tol=1e-9)\n\nN, cx, cy, r = map(int, input().split())\nans = 0\nfrom math import pi\ncircle_area = pi * r * r\nfor _ in range(N):\n p, score = map(int, input().split())\n ps = []\n for _ in range(p):\n x, y = map(int, input().split())\n ps.append((x, y))\n area = intersection((cx, cy, r), ps)\n ans += abs(area) * score / circle_area\n\nprint(f\"{ans:.10f}\")\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 2 2 1\\n4 1\\n0 0\\n5 0\\n5 5\\n0 5', 'output': '1.0000000000'}, {'type': 'stdin_stdout', 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'0.0649727831\\n'}, {'type': 'stdin_stdout', 'input': '4 3 4 2\\n3 2\\n0 1\\n3 3\\n1 5\\n4 2\\n0 0\\n5 0\\n4 2\\n3 2\\n3 3\\n8 3\\n6 0\\n6 5\\n4 1\\n3 2\\n4 4\\n5 6\\n2 6', 'output': '0.8251337458\\n'}, {'type': 'stdin_stdout', 'input': '1 0 2 1\\n4 2\\n0 0\\n5 -1\\n5 5\\n-1 5', 'output': '1.4862872886\\n'}, {'type': 'stdin_stdout', 'input': '4 3 3 2\\n3 1\\n1 1\\n3 3\\n1 5\\n4 2\\n2 0\\n3 0\\n4 0\\n0 4\\n3 3\\n4 3\\n6 1\\n6 5\\n4 4\\n3 4\\n4 4\\n5 6\\n2 6', 'output': '1.0395113763\\n'}, {'type': 'stdin_stdout', 'input': '1 2 1 1\\n4 1\\n0 0\\n1 0\\n3 3\\n0 3', 'output': '0.3257239824\\n'}, {'type': 'stdin_stdout', 'input': '4 3 3 1\\n3 1\\n2 1\\n3 3\\n1 5\\n4 2\\n2 0\\n5 0\\n4 2\\n3 2\\n3 3\\n4 3\\n6 1\\n6 4\\n4 1\\n3 1\\n4 4\\n5 6\\n2 6', 'output': '0.9182440873\\n'}, {'type': 'stdin_stdout', 'input': '4 3 4 2\\n3 1\\n0 1\\n3 3\\n1 5\\n4 2\\n2 0\\n5 0\\n4 2\\n3 2\\n3 3\\n4 3\\n4 0\\n6 5\\n4 1\\n3 4\\n4 4\\n4 10\\n2 6', 'output': '0.5986020107\\n'}, {'type': 'stdin_stdout', 'input': '1 3 0 2\\n4 1\\n-1 0\\n7 1\\n4 5\\n0 5', 'output': '0.3437091145\\n'}, {'type': 'stdin_stdout', 'input': '4 3 4 2\\n3 1\\n0 1\\n3 3\\n1 5\\n4 2\\n3 0\\n5 0\\n4 0\\n3 2\\n3 0\\n4 3\\n6 0\\n6 10\\n4 1\\n3 4\\n4 4\\n5 10\\n2 9', 'output': '0.4002936422\\n'}, {'type': 'stdin_stdout', 'input': '1 2 1 1\\n4 1\\n0 -1\\n1 0\\n2 1\\n-1 1', 'output': '0.1250000000\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2 1\\n4 1\\n-1 -1\\n2 -1\\n5 4\\n1 1', 'output': '0.3735300391\\n'}, {'type': 'stdin_stdout', 'input': '1 2 3 1\\n4 1\\n0 1\\n1 2\\n2 4\\n-1 0', 'output': '0.0827139379\\n'}, {'type': 'stdin_stdout', 'input': '4 3 2 2\\n3 2\\n2 1\\n3 3\\n1 5\\n4 2\\n2 0\\n5 0\\n4 2\\n3 2\\n3 3\\n4 3\\n6 0\\n8 5\\n4 1\\n1 2\\n4 5\\n5 10\\n2 6', 'output': '1.1664320138\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2 1\\n4 1\\n-1 0\\n3 -1\\n5 5\\n3 4', 'output': '0.9091549431\\n'}, {'type': 'stdin_stdout', 'input': '4 3 2 2\\n3 2\\n1 1\\n3 2\\n1 5\\n4 2\\n2 0\\n6 0\\n4 2\\n4 3\\n3 3\\n4 3\\n6 0\\n6 5\\n4 1\\n3 0\\n4 5\\n5 10\\n2 6', 'output': '1.4612645052\\n'}, {'type': 'stdin_stdout', 'input': '4 3 2 4\\n3 2\\n1 1\\n3 3\\n1 5\\n4 4\\n2 0\\n5 0\\n4 1\\n4 3\\n3 3\\n4 3\\n6 0\\n6 5\\n4 1\\n3 2\\n4 1\\n5 10\\n2 6', 'output': '0.8873523624\\n'}, {'type': 'stdin_stdout', 'input': '1 4 1 1\\n4 1\\n-1 0\\n0 0\\n12 5\\n0 9', 'output': '0.1346004373\\n'}, {'type': 'stdin_stdout', 'input': '1 2 2 1\\n4 2\\n-1 0\\n8 0\\n0 2\\n2 5', 'output': '0.4075443579\\n'}, {'type': 'stdin_stdout', 'input': '4 3 4 2\\n3 1\\n0 1\\n3 3\\n1 5\\n4 2\\n2 0\\n5 0\\n4 2\\n3 2\\n3 3\\n4 3\\n4 0\\n6 5\\n3 1\\n3 4\\n4 4\\n4 10\\n2 6', 'output': '0.4985259735\\n'}, {'type': 'stdin_stdout', 'input': '4 3 4 2\\n3 2\\n0 1\\n3 3\\n1 5\\n4 2\\n2 0\\n5 0\\n4 2\\n3 2\\n3 3\\n4 4\\n6 0\\n6 5\\n4 1\\n9 4\\n4 5\\n5 10\\n2 5', 'output': '0.7912187057\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_80381","program":"```python\n# \u53c2\u8003 http://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=3277276#1\nfrom math import acos, hypot, isclose, sqrt\n\ndef intersection(circle, polygon):\n # \u5186\u3068\u591a\u89d2\u5f62\u306e\u5171\u901a\u90e8\u5206\u306e\u9762\u7a4d\n # \u591a\u89d2\u5f62\u306e\u70b9\u304c\u53cd\u6642\u8a08\u56de\u308a\u3067\u4e0e\u3048\u3089\u308c\u308c\u3070\u6b63\u306e\u5024\u3001\u6642\u8a08\u56de\u308a\u306a\u3089\u8ca0\u306e\u5024\u3092\u8fd4\u3059\n x, y, r = circle\n polygon = [(xp-x, yp-y) for xp, yp in polygon]\n area = 0.0\n for p1, p2 in zip(polygon, polygon[1:] + [polygon[0]]):\n ps = seg_intersection((0, 0, r), (p1, p2))\n for pp1, pp2 in zip([p1] + ps, ps + [p2]):\n c = cross(pp1, pp2) # pp1 \u3068 pp2 \u306e\u4f4d\u7f6e\u95a2\u4fc2\u306b\u3088\u3063\u3066\u6b63\u8ca0\u304c\u5909\u308f\u308b\n if c == 0: # pp1, pp2, \u539f\u70b9\u304c\u540c\u4e00\u76f4\u7dda\u4e0a\u306b\u3042\u308b\u5834\u5408\n continue\n d1 = hypot(*pp1)\n d2 = hypot(*pp2)\n if le(d1, r) and le(d2, r):\n area += c / 2 # pp1, pp2, \u539f\u70b9\u3092\u7d50\u3093\u3060\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\n else:\n t = acos(dot(pp1, pp2) / (d1 * d2)) # pp1-\u539f\u70b9\u3068pp2-\u539f\u70b9\u306e\u6210\u3059\u89d2\n sign = 1.0 if c >= 0 else -1.0\n area += sign * r * r * t / 2 # \u6247\u5f62\u306e\u9762\u7a4d\n return area\n\ndef cross(v1, v2): # \u5916\u7a4d\n x1, y1 = v1\n x2, y2 = v2\n return x1 * y2 - x2 * y1\n\ndef dot(v1, v2): # \u5185\u7a4d\n x1, y1 = v1\n x2, y2 = v2\n return x1 * x2 + y1 * y2\n\ndef seg_intersection(circle, seg):\n # \u5186\u3068\u7dda\u5206\u306e\u4ea4\u70b9\uff08\u5186\u306e\u4e2d\u5fc3\u304c\u539f\u70b9\u3067\u306a\u3044\u5834\u5408\u306f\u672a\u691c\u8a3c\uff09\n x0, y0, r = circle\n p1, p2 = seg\n x1, y1 = p1\n x2, y2 = p2\n\n p1p2 = (x2 - x1) ** 2 + (y2 - y1) ** 2\n op1 = (x1 - x0) ** 2 + (y1 - y0) ** 2\n rr = r * r\n dp = dot((x1 - x0, y1 - y0), (x2 - x1, y2 - y1))\n\n d = dp * dp - p1p2 * (op1 - rr)\n ps = []\n\n if isclose(d, 0.0, abs_tol=1e-9):\n t = -dp / p1p2\n if ge(t, 0.0) and le(t, 1.0):\n ps.append((x1 + t * (x2 - x1), y1 + t * (y2 - y1)))\n elif d > 0.0:\n t1 = (-dp - sqrt(d)) / p1p2\n if ge(t1, 0.0) and le(t1, 1.0):\n ps.append((x1 + t1 * (x2 - x1), y1 + t1 * (y2 - y1)))\n t2 = (-dp + sqrt(d)) / p1p2\n if ge(t2, 0.0) and le(t2, 1.0):\n ps.append((x1 + t2 * (x2 - x1), y1 + t2 * (y2 - y1)))\n\n # assert all(isclose(r, hypot(x, y)) for x, y in ps)\n return ps\n\ndef le(f1, f2): # less equal\n return f1 < f2 or isclose(f1, f2, abs_tol=1e-9)\n\ndef ge(f1, f2): # greater equal\n return f1 > f2 or isclose(f1, f2, abs_tol=1e-9)\n\nN, cx, cy, r = map(int, input().split())\nans = 0\nfrom math import pi\ncircle_area = pi * r * r\nfor _ in range(N):\n p, score = map(int, input().split())\n ps = []\n for _ in range(p):\n x, y = map(int, input().split())\n ps.append((x, y))\n area = intersection((cx, cy, r), ps)\n ans += abs(area) * score / circle_area\n\nprint(f\"{ans:.10f}\")\n\n\n```","inputs":"1 2 2 1\n4 1\n0 0\n5 0\n5 5\n0 5","output":"1.0000000000","actual_output":"1.0000000000\n","execution_success":true,"sample_index":12798},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p01306 Unit Converter","prompt":"Solve the following coding problem using the programming language python:\n\nIn the International System of Units (SI), various physical quantities are expressed in the form of \"numerical value + prefix + unit\" using prefixes such as kilo, mega, and giga. For example, \"3.5 kilometers\", \"5.1 milligrams\", and so on.\n\nOn the other hand, these physical quantities can be expressed as \"3.5 * 10 ^ 3 meters\" and \"5.1 * 10 ^ -3 grams\" using exponential notation.\n\nMeasurement of physical quantities always includes errors. Therefore, there is a concept of significant figures to express how accurate the measured physical quantity is. In the notation considering significant figures, the last digit may contain an error, but the other digits are considered reliable. For example, if you write \"1.23\", the true value is 1.225 or more and less than 1.235, and the digits with one decimal place or more are reliable, but the second decimal place contains an error. The number of significant digits when a physical quantity is expressed in the form of \"reliable digit + 1 digit including error\" is called the number of significant digits. For example, \"1.23\" has 3 significant digits.\n\nIf there is a 0 before the most significant non-zero digit, that 0 is not included in the number of significant digits. For example, \"0.45\" has two significant digits. If there is a 0 after the least significant non-zero digit, whether or not that 0 is included in the number of significant digits depends on the position of the decimal point. If there is a 0 to the right of the decimal point, that 0 is included in the number of significant digits. For example, \"12.300\" has 5 significant digits. On the other hand, when there is no 0 to the right of the decimal point like \"12300\", it is not clear whether to include the 0 on the right side in the number of significant digits, but it will be included in this problem. That is, the number of significant digits of \"12300\" is five.\n\nNatsume was given a physics problem as a school task. I have to do calculations related to significant figures and units, but the trouble is that I still don't understand how to use significant figures and units. Therefore, I would like you to create a program that automatically calculates them and help Natsume.\n\nWhat you write is a program that, given a prefixed notation, converts it to exponential notation with the same number of significant digits. The following 20 prefixes are used.\n\n* yotta = 10 ^ 24\n* zetta = 10 ^ 21\n* exa = 10 ^ 18\n* peta = 10 ^ 15\n* tera = 10 ^ 12\n* giga = 10 ^ 9\n* mega = 10 ^ 6\n* kilo = 10 ^ 3\n* hecto = 10 ^ 2\n* deca = 10 ^ 1\n* deci = 10 ^ -1\n* centi = 10 ^ -2\n* milli = 10 ^ -3\n* micro = 10 ^ -6\n* nano = 10 ^ -9\n* pico = 10 ^ -12\n* femto = 10 ^ -15\n* ato = 10 ^ -18\n* zepto = 10 ^ -21\n* yocto = 10 ^ -24\n\nNotes on Submission\n\nMultiple datasets are given in the above format. The first line of input data gives the number of datasets. Create a program that outputs the output for each data set in order in the above format.\n\n\n\nInput\n\nThe input consists of only one line, which contains numbers, unit prefixes (if any), and units. Each is separated by a blank. In some cases, there is no unit prefix, in which case only numbers and units are included in the line. Units with the same name as the unit prefix do not appear. The most significant digit is never 0, except for the ones digit when a decimal is given. The number given is positive. The number given is 1000 digits or less including the decimal point, and the unit name is 50 characters or less.\n\nOutput\n\nOutput the quantity expressed in exponential notation in the form of a * 10 ^ b [unit]. However, 1 <= a <10. The difference between the singular and plural forms of the unit name is not considered. Output the unit name given to the input as it is.\n\nExample\n\nInput\n\n7\n12.3 kilo meters\n0.45 mega watts\n0.000000000000000000000001 yotta grams\n1000000000000000000000000 yocto seconds\n42 amperes\n0.42 joules\n1234.56789012345678901234567890 hecto pascals\n\n\nOutput\n\n1.23 * 10^4 meters\n4.5 * 10^5 watts\n1 * 10^0 grams\n1.000000000000000000000000 * 10^0 seconds\n4.2 * 10^1 amperes\n4.2 * 10^-1 joules\n1.23456789012345678901234567890 * 10^5 pascals\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nm = {\"yotta\":24, \"zetta\":21, \"exa\":18, \"peta\":15, \"tera\":12, \"giga\":9, \"mega\":6, \"kilo\":3, \"hecto\":2, \"deca\":1, \"deci\":-1, \"centi\":-2, \"milli\":-3, \"micro\":-6, \"nano\":-9, \"pico\":-12, \"femto\":-15, \"ato\":-18, \"zepto\":-21, \"yocto\":-24}\nfor _ in range(int(input())):\n v, *b = input().split()\n if len(b) == 2:\n k, b = b[0], b[1]\n a = m[k]\n else:b = b[0];a = 0\n s = 0\n for i in range(len(v)):\n if v[i] in \"123456789\":\n if i != 0:\n a -= i - 1\n if i != len(v) - 1:v = v[i] + \".\" + v[i + 1:]\n else:v = v[i]\n else:\n try:\n j = v[i:].index(\".\")\n a += j - 1\n v = v[0] + \".\" + v[1:j] + v[j + 1:]\n except:\n a += len(v) - 1\n v = v[0] + \".\" + v[1:]\n break\n print(\"{} * 10^{} {}\".format(v, a, b))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.000000000000000000000001 yotta grams\\n1000000000000000000000000 yocto seconds\\n42 amperes\\n0.42 joules\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n1 * 10^0 grams\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n4.2 * 10^-1 joules\\n1.23456789012345678901234567890 * 10^5 pascals'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.000000000000000000000001 yotta grams\\n1000000000000000000000000 yocto seconds\\n42 amperes\\n0.951642419825234 joules\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n1 * 10^0 grams\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n9.51642419825234 * 10^-1 joules\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.5868394692236264 yotta grams\\n1000000000000000000000000 yocto seconds\\n42 amperes\\n0.951642419825234 joules\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n5.868394692236264 * 10^23 grams\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n9.51642419825234 * 10^-1 joules\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.6843066209821149 yotta grams\\n1000000000000000000000000 yocto seconds\\n42 amperes\\n0.951642419825234 joules\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n6.843066209821149 * 10^23 grams\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n9.51642419825234 * 10^-1 joules\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.000000000000000000000001 yotta grams\\n1000000000000000010000000 yocto seconds\\n42 amperes\\n0.42 joules\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n1 * 10^0 grams\\n1.000000000000000010000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n4.2 * 10^-1 joules\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.000000000000000000000001 yotta grams\\n1000000000000000000000000 yocto seconds\\n42 amperes\\n0.951642419825234 joules\\n1234.56789012345678901234567890 hecto pascalr', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n1 * 10^0 grams\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n9.51642419825234 * 10^-1 joules\\n1.23456789012345678901234567890 * 10^5 pascalr\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.5868394692236264 yotta grams\\n1000000000000000000000000 yocto seconds\\n42 amperes\\n0.951642419825234 joules\\n1235.0324885234443 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n5.868394692236264 * 10^23 grams\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n9.51642419825234 * 10^-1 joules\\n1.2350324885234443 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.6843066209821149 yotta grams\\n1000000000000000000000000 yocto seconds\\n42 amperes\\n0.951642419825234 seluoj\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n6.843066209821149 * 10^23 grams\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n9.51642419825234 * 10^-1 seluoj\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.000000000000000000000001 yotta grams\\n1000000000000000010000000 yocto seconds\\n42 amperes\\n0.42 seluoj\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n1 * 10^0 grams\\n1.000000000000000010000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n4.2 * 10^-1 seluoj\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega wauts\\n0.5868394692236264 yotta grams\\n1000000000000000000000000 yocto seconds\\n42 amperes\\n0.951642419825234 joules\\n1235.0324885234443 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 wauts\\n5.868394692236264 * 10^23 grams\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n9.51642419825234 * 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seconds\\n6 amserep\\n0.42 seluoj\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n1 * 10^0 grams\\n1.000000000000000010000000 * 10^0 seconds\\n6 * 10^0 amserep\\n4.2 * 10^-1 seluoj\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.811915426426053 kilo meters\\n0.45 mega wauts\\n0.5868394692236264 yotta gmars\\n1000000000000000000000000 yocto secondr\\n42 serepma\\n0.951642419825234 joules\\n1235.0324885234443 hecto pascals', 'output': '1.2811915426426053 * 10^4 meters\\n4.5 * 10^5 wauts\\n5.868394692236264 * 10^23 gmars\\n1.000000000000000000000000 * 10^0 secondr\\n4.2 * 10^1 serepma\\n9.51642419825234 * 10^-1 joules\\n1.2350324885234443 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega wstta\\n0.5306518539261769 yotta grals\\n1000000000000000010000000 yocto seconds\\n1 amperes\\n0.42 seluoj\\n1234.924397029936 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 wstta\\n5.306518539261769 * 10^23 grals\\n1.000000000000000010000000 * 10^0 seconds\\n1 * 10^0 amperes\\n4.2 * 10^-1 seluoj\\n1.234924397029936 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.578975550100722 kilo meters\\n0.45 mega wauts\\n0.5868394692236264 yotta gmars\\n1000000000000000100000000 yocto seconds\\n4 serepma\\n0.951642419825234 jpvles\\n1235.0324885234443 hecto pascals', 'output': '1.2578975550100722 * 10^4 meters\\n4.5 * 10^5 wauts\\n5.868394692236264 * 10^23 gmars\\n1.000000000000000100000000 * 10^0 seconds\\n4 * 10^0 serepma\\n9.51642419825234 * 10^-1 jpvles\\n1.2350324885234443 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo metert\\n0.5125616408370866 mega watts\\n0.000000000000000000000001 yotta mrags\\n1000000000000000000000000 yocto seconds\\n42 amperes\\n0.951642419825234 joules\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 metert\\n5.125616408370866 * 10^5 watts\\n1 * 10^0 mrags\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n9.51642419825234 * 10^-1 joules\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega wbtts\\n0.000000000000000000000001 yotta grams\\n1000000000000000010000000 yocto seconds\\n49 amperes\\n0.42 soulej\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 wbtts\\n1 * 10^0 grams\\n1.000000000000000010000000 * 10^0 seconds\\n4.9 * 10^1 amperes\\n4.2 * 10^-1 soulej\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watst\\n0.000000000000000000000001 yotta grams\\n1000000000000000010000000 yocto seconds\\n6 amperfs\\n0.42 seluoj\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watst\\n1 * 10^0 grams\\n1.000000000000000010000000 * 10^0 seconds\\n6 * 10^0 amperfs\\n4.2 * 10^-1 seluoj\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n13.551170275871279 kilo meters\\n0.45 mega wauts\\n0.8734064229004153 yotta gmars\\n1000000000000000100000010 yocto seconds\\n42 serepma\\n0.951642419825234 jpvles\\n1235.0324885234443 hecto pascals', 'output': '1.3551170275871279 * 10^4 meters\\n4.5 * 10^5 wauts\\n8.734064229004153 * 10^23 gmars\\n1.000000000000000100000010 * 10^0 seconds\\n4.2 * 10^1 serepma\\n9.51642419825234 * 10^-1 jpvles\\n1.2350324885234443 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo metert\\n0.45 mega watts\\n0.000000000000000000000001 yotta mrags\\n1000000000000000000000000 yocto seconds\\n42 amperes\\n0.951642419825234 joulfs\\n1234.56789012345678901234567890 hecto slacsap', 'output': '1.23 * 10^4 metert\\n4.5 * 10^5 watts\\n1 * 10^0 mrags\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n9.51642419825234 * 10^-1 joulfs\\n1.23456789012345678901234567890 * 10^5 slacsap\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega wbtts\\n0.606796701735519 yotta grams\\n1000000000000000010000000 yocto seconds\\n3 amperes\\n0.42 soulej\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 wbtts\\n6.06796701735519 * 10^23 grams\\n1.000000000000000010000000 * 10^0 seconds\\n3 * 10^0 amperes\\n4.2 * 10^-1 soulej\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watst\\n0.000000000000000000000001 yotta gramr\\n1000000000000000010000000 yocto seconds\\n6 amperes\\n0.5409021934885971 seluoj\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watst\\n1 * 10^0 gramr\\n1.000000000000000010000000 * 10^0 seconds\\n6 * 10^0 amperes\\n5.409021934885971 * 10^-1 seluoj\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega wbtts\\n0.000000000000000000000001 yotta grams\\n1000000000100000010000000 yocto teconds\\n3 amperes\\n0.42 soulej\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 wbtts\\n1 * 10^0 grams\\n1.000000000100000010000000 * 10^0 teconds\\n3 * 10^0 amperes\\n4.2 * 10^-1 soulej\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega wbtts\\n0.000000000000000000000001 yotta grams\\n1000000000100000010000000 yocto seconds\\n3 apmeres\\n0.42 soumej\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 wbtts\\n1 * 10^0 grams\\n1.000000000100000010000000 * 10^0 seconds\\n3 * 10^0 apmeres\\n4.2 * 10^-1 soumej\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.729479136172973 kilo metfrt\\n0.45 mega sttaw\\n0.000000000000000000000001 yotta mrags\\n1000000000000000000000000 yocto seconds\\n42 ampdres\\n0.951642419825234 joulfs\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.2729479136172973 * 10^4 metfrt\\n4.5 * 10^5 sttaw\\n1 * 10^0 mrags\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 ampdres\\n9.51642419825234 * 10^-1 joulfs\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.729479136172973 kilo mfteru\\n0.45 mega sttaw\\n0.000000000000000000000001 yotta mrags\\n1000000000000000000000000 yocto seconds\\n36 amperes\\n0.951642419825234 joulfs\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.2729479136172973 * 10^4 mfteru\\n4.5 * 10^5 sttaw\\n1 * 10^0 mrags\\n1.000000000000000000000000 * 10^0 seconds\\n3.6 * 10^1 amperes\\n9.51642419825234 * 10^-1 joulfs\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.942815183124743 kilo metfru\\n0.45 mega sttaw\\n0.000000000000000000000001 yotta nrags\\n1000000000000000000000000 yocto seconds\\n36 amperes\\n0.951642419825234 joulfs\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.2942815183124743 * 10^4 metfru\\n4.5 * 10^5 sttaw\\n1 * 10^0 nrags\\n1.000000000000000000000000 * 10^0 seconds\\n3.6 * 10^1 amperes\\n9.51642419825234 * 10^-1 joulfs\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.000000000000000000000001 yotta grams\\n1000000000000000000100000 yocto seconds\\n42 amperes\\n0.951642419825234 joules\\n1234.7494951906465 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n1 * 10^0 grams\\n1.000000000000000000100000 * 10^0 seconds\\n4.2 * 10^1 amperes\\n9.51642419825234 * 10^-1 joules\\n1.2347494951906465 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.000000000000000000000001 yotta grams\\n1000000000000000010000000 yocto seconds\\n43 amperet\\n0.42 seluoj\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n1 * 10^0 grams\\n1.000000000000000010000000 * 10^0 seconds\\n4.3 * 10^1 amperet\\n4.2 * 10^-1 seluoj\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega wauts\\n0.5868394692236264 yotta glars\\n1000000000000000000000000 yocto sdnoces\\n42 amperes\\n0.951642419825234 joules\\n1235.0324885234443 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 wauts\\n5.868394692236264 * 10^23 glars\\n1.000000000000000000000000 * 10^0 sdnoces\\n4.2 * 10^1 amperes\\n9.51642419825234 * 10^-1 joules\\n1.2350324885234443 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega watts\\n0.6843066209821149 yotta grans\\n1000000100000000000000000 yocto seconds\\n42 amperet\\n0.951642419825234 seluoj\\n1235.1827627986022 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 watts\\n6.843066209821149 * 10^23 grans\\n1.000000100000000000000000 * 10^0 seconds\\n4.2 * 10^1 amperet\\n9.51642419825234 * 10^-1 seluoj\\n1.2351827627986022 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.3 kilo meters\\n0.45 mega wstta\\n0.000000000000000000000001 yotta grams\\n1001000000000000010000000 yocto secoods\\n1 amperes\\n0.42 seluoj\\n1234.56789012345678901234567890 hecto pascals', 'output': '1.23 * 10^4 meters\\n4.5 * 10^5 wstta\\n1 * 10^0 grams\\n1.001000000000000010000000 * 10^0 secoods\\n1 * 10^0 amperes\\n4.2 * 10^-1 seluoj\\n1.23456789012345678901234567890 * 10^5 pascals\\n'}, {'type': 'stdin_stdout', 'input': '7\\n12.578975550100722 kilo meters\\n0.45 mega stubw\\n0.5868394692236264 yotta gmars\\n1000000000000000000000000 yocto seconds\\n42 serepma\\n0.951642419825234 joules\\n1235.0324885234443 hecto pascals', 'output': '1.2578975550100722 * 10^4 meters\\n4.5 * 10^5 stubw\\n5.868394692236264 * 10^23 gmars\\n1.000000000000000000000000 * 10^0 seconds\\n4.2 * 10^1 serepma\\n9.51642419825234 * 10^-1 joules\\n1.2350324885234443 * 10^5 pascals\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 8, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_80389","program":"```python\nm = {\"yotta\":24, \"zetta\":21, \"exa\":18, \"peta\":15, \"tera\":12, \"giga\":9, \"mega\":6, \"kilo\":3, \"hecto\":2, \"deca\":1, \"deci\":-1, \"centi\":-2, \"milli\":-3, \"micro\":-6, \"nano\":-9, \"pico\":-12, \"femto\":-15, \"ato\":-18, \"zepto\":-21, \"yocto\":-24}\nfor _ in range(int(input())):\n v, *b = input().split()\n if len(b) == 2:\n k, b = b[0], b[1]\n a = m[k]\n else:b = b[0];a = 0\n s = 0\n for i in range(len(v)):\n if v[i] in \"123456789\":\n if i != 0:\n a -= i - 1\n if i != len(v) - 1:v = v[i] + \".\" + v[i + 1:]\n else:v = v[i]\n else:\n try:\n j = v[i:].index(\".\")\n a += j - 1\n v = v[0] + \".\" + v[1:j] + v[j + 1:]\n except:\n a += len(v) - 1\n v = v[0] + \".\" + v[1:]\n break\n print(\"{} * 10^{} {}\".format(v, a, b))\n\n```","inputs":"7\n12.3 kilo meters\n0.45 mega watts\n0.000000000000000000000001 yotta grams\n1000000000000000000000000 yocto seconds\n42 amperes\n0.42 joules\n1234.56789012345678901234567890 hecto pascals","output":"1.23 * 10^4 meters\n4.5 * 10^5 watts\n1 * 10^0 grams\n1.000000000000000000000000 * 10^0 seconds\n4.2 * 10^1 amperes\n4.2 * 10^-1 joules\n1.23456789012345678901234567890 * 10^5 pascals","actual_output":"1.23 * 10^4 meters\n4.5 * 10^5 watts\n1 * 10^0 grams\n1.000000000000000000000000 * 10^0 seconds\n4.2 * 10^1 amperes\n4.2 * 10^-1 joules\n1.23456789012345678901234567890 * 10^5 pascals\n","execution_success":true,"sample_index":12799},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02060 Four Tea","prompt":"Solve the following coding problem using the programming language python:\n\nA: four tea\n\nproblem\n\nTea is indispensable for programming contests. Tea has the effect of relieving constant tension [citation needed]\n\nThere are N players participating in the contest, so I would like to prepare tea for this number of people. There are four types of tea packages, A, B, C, and D, all of which are the same variety but have different contents. For a package X, the price of one package is p_X yen, and it is known that if you buy one, you can make t_X cups of tea.\n\nFind the minimum amount needed to make tea for N people. You may have a package that you don't buy at all, and you don't have to buy a package for just N people (if you can make more than N people).\n\nInput format\n\nThe input is given in the following format.\n\n\nN\np_A p_B p_C p_D\nt_A t_B t_C t_D\n\n\n* The first line gives the number of players participating in the contest.\n* In the second line, the prices of tea in packages A, B, C and D are given separated by blanks.\n* The third line gives the number of cups of tea that can be made from packages A, B, C, and D, separated by blanks.\n\n\n\nConstraint\n\n* 1 \\ leq N \\ leq 100\n* 1 \\ leq p_X \\ leq 100\n* 1 \\ leq t_X \\ leq 100\n* All inputs are given as integers.\n\n\n\nOutput format\n\nOutput the minimum amount required to make tea for N people in one line.\n\nInput example 1\n\n\nTen\n1 2 3 4\n1 2 4 8\n\n\nOutput example 1\n\n\n6\n\n* It's best to buy one package B and one D.\n\n\n\nInput example 2\n\n\nFive\n2 9 9 8\n1 4 5 100\n\n\nOutput example 2\n\n\n8\n\n* You will have 20 times more tea than you need, but buying one Package D is the cheapest way to get more than 5 cups of tea.\n\n\n\nInput example 3\n\n\ntwenty four\n2 3 4 7\n7 9 11 20\n\n\nOutput example 3\n\n\n8\n\n* It's best to buy two packages A and one C. It may not be possible to make just enough tea for the number of people as in this case.\n\n\n\n\n\nExample\n\nInput\n\n10\n1 2 3 4\n1 2 4 8\n\n\nOutput\n\n6\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn,pa,pb,pc,pd,ta,tb,tc,td=map(int,open(0).read().split())\nr=range(n+1)\nm=1e9\nfor i in r:\n for j in r:\n for k in r:\n l=0--(n-ta*i-tb*j-tc*k)//td\n m=min(m,pa*i+pb*j+pc*k+pd*l*(l>=0))\nprint(m)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10\\n1 2 3 4\\n1 2 4 8', 'output': '6'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 2\\n1 2 4 8', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 3 2\\n0 2 3 8', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 3 2\\n0 2 3 16', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 3 2\\n1 2 3 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 4\\n1 3 4 8', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 3 2\\n0 2 3 1', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 6 1\\n0 0 1 50', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 2 1 4\\n0 1 0 8', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 2\\n0 0 4 3', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 6 2\\n1 1 2 1', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 5 1\\n0 1 6 1', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 3 0 3\\n0 2 0 2', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 2\\n0 2 4 8', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 2\\n0 2 3 8', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 3 2\\n0 2 3 16', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 3 2\\n0 2 3 16', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 3 2\\n1 1 3 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 3 2\\n1 1 1 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 3 2\\n1 1 1 23', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 6 2\\n1 1 1 23', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 6 2\\n1 1 1 23', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 2\\n1 1 1 23', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 2\\n1 1 1 31', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 2\\n2 1 1 31', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 2\\n2 2 1 31', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 3\\n2 2 1 31', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 2\\n1 2 4 7', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 1\\n0 2 4 8', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 5 2\\n0 2 3 8', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 3 2\\n0 2 3 8', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 0 3 2\\n0 2 3 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 3 2\\n0 2 3 12', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 3 2\\n2 2 3 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 4 2\\n1 1 1 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 3 2\\n1 1 1 10', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 6 2\\n1 1 1 32', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 6 2\\n1 1 1 13', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 2\\n1 1 0 23', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 7 2\\n1 1 1 31', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 7 2\\n2 1 1 31', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 3\\n2 2 1 19', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 3\\n2 2 1 25', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 2\\n1 3 4 7', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 3 1\\n0 2 4 8', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 5 2\\n0 2 0 8', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 3 2\\n0 2 0 8', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 3 2\\n0 2 6 1', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 0 3 1\\n0 2 3 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 1 2\\n0 2 3 12', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 2 3 2\\n2 2 3 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 4 2\\n1 1 1 21', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 3 2\\n1 1 1 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 6 2\\n1 0 1 32', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 6 2\\n1 1 2 13', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 7 2\\n1 1 1 48', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 2\\n3 1 1 31', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 3\\n2 2 2 19', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 3\\n2 2 1 38', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 1 2\\n1 3 4 7', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 3 1\\n0 2 4 8', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 5 2\\n0 2 0 15', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 3 2\\n0 1 0 8', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 3 2\\n0 2 6 1', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 0 3 1\\n0 2 3 2', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 1 4\\n0 2 3 12', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 2 3 4\\n2 2 3 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 4 2\\n1 1 1 21', 'output': '2\\n'}, 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4\\n2 2 3 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 4 2\\n1 1 1 42', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 0 6 2\\n1 0 2 13', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 7 1\\n1 0 1 48', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 3\\n3 1 1 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 0 7 3\\n2 2 0 19', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 2 3\\n2 2 1 38', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 1 2\\n0 3 2 7', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 3 1\\n0 2 2 8', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 10 2\\n0 0 0 15', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 5 4\\n0 1 0 8', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 4 3 2\\n0 1 6 1', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 3 3 4\\n2 2 4 16', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 4 2\\n1 1 1 42', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 0 6 2\\n1 0 2 17', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 1 7 1\\n1 0 1 50', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 7 3\\n0 1 1 3', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 7 3\\n2 2 0 19', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 2 3\\n1 2 1 38', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 3 0\\n0 2 2 8', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 7 2\\n0 0 0 15', 'output': '2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_80409","program":"```python\nn,pa,pb,pc,pd,ta,tb,tc,td=map(int,open(0).read().split())\nr=range(n+1)\nm=1e9\nfor i in r:\n for j in r:\n for k in r:\n l=0--(n-ta*i-tb*j-tc*k)//td\n m=min(m,pa*i+pb*j+pc*k+pd*l*(l>=0))\nprint(m)\n\n```","inputs":"10\n1 2 3 4\n1 2 4 8","output":"6","actual_output":"6\n","execution_success":true,"sample_index":12801},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02202 Gag","prompt":"Solve the following coding problem using the programming language python:\n\nGag\n\nSegtree has $ N $ of \"gags\", each with a value of $ V_i $.\n\nSegtree decided to publish all the gags in any order.\n\nHere, the \"joy\" you get when you publish the $ i $ th gag to the $ j $ th is expressed as $ V_i --j $.\n\nFind the maximum sum of the \"joy\" you can get.\n\ninput\n\nInput is given from standard input in the following format.\n\n\n$ N $\n$ V_1 $ $ V_2 $ $ \\ ldots $ $ V_N $\n\n\noutput\n\nPlease output the maximum value of the sum of \"joy\". However, the value does not always fit in a 32-bit integer.\n\nInsert a line break at the end.\n\nConstraint\n\n* $ 1 \\ leq N \\ leq 10 ^ 5 $\n* $ 1 \\ leq V_i \\ leq 10 ^ 5 $\n* All inputs are integers.\n\n\n\nInput example 1\n\n\n1\n59549\n\n\nOutput example 1\n\n\n59548\n\n\nInput example 2\n\n\nFive\n2 1 8 5 7\n\n\nOutput example 2\n\n\n8\n\n\n\n\n\n\nExample\n\nInput\n\n1\n59549\n\n\nOutput\n\n59548\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\nv = list(map(int,input().split()))\ncount = 0\nans = 0\ns = -1\nwhile count != n:\n ans -= s\n s -= 1\n count += 1\nprint(sum(v)-ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n59549', 'output': '59548'}, {'type': 'stdin_stdout', 'input': '1\\n114525', 'output': '114524\\n'}, {'type': 'stdin_stdout', 'input': '1\\n105905', 'output': '105904\\n'}, {'type': 'stdin_stdout', 'input': '1\\n196252', 'output': '196251\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26794', 'output': '26793\\n'}, {'type': 'stdin_stdout', 'input': '1\\n22977', 'output': '22976\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6310', 'output': '6309\\n'}, {'type': 'stdin_stdout', 'input': '1\\n12378', 'output': '12377\\n'}, {'type': 'stdin_stdout', 'input': '1\\n20899', 'output': '20898\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6312', 'output': '6311\\n'}, {'type': 'stdin_stdout', 'input': '1\\n6759', 'output': '6758\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1599', 'output': '1598\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1545', 'output': '1544\\n'}, {'type': 'stdin_stdout', 'input': '1\\n545', 'output': '544\\n'}, {'type': 'stdin_stdout', 'input': '1\\n834', 'output': '833\\n'}, {'type': 'stdin_stdout', 'input': '1\\n736', 'output': '735\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1350', 'output': '1349\\n'}, {'type': 'stdin_stdout', 'input': 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'stdin_stdout', 'input': '1\\n867', 'output': '866\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1042', 'output': '1041\\n'}, {'type': 'stdin_stdout', 'input': '1\\n651', 'output': '650\\n'}, {'type': 'stdin_stdout', 'input': '1\\n231', 'output': '230\\n'}, {'type': 'stdin_stdout', 'input': '1\\n33', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '1\\n69', 'output': '68\\n'}, {'type': 'stdin_stdout', 'input': '1\\n44', 'output': '43\\n'}, {'type': 'stdin_stdout', 'input': '1\\n679', 'output': '678\\n'}, {'type': 'stdin_stdout', 'input': '1\\n392', 'output': '391\\n'}, {'type': 'stdin_stdout', 'input': '1\\n695', 'output': '694\\n'}, {'type': 'stdin_stdout', 'input': '1\\n53', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '1\\n289', 'output': '288\\n'}, {'type': 'stdin_stdout', 'input': '1\\n29', 'output': '28\\n'}, {'type': 'stdin_stdout', 'input': '1\\n27', 'output': '26\\n'}, {'type': 'stdin_stdout', 'input': '1\\n50', 'output': '49\\n'}, {'type': 'stdin_stdout', 'input': '1\\n116', 'output': '115\\n'}, {'type': 'stdin_stdout', 'input': '1\\n61', 'output': '60\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-1', 'output': '-2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n8', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '1\\n20', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-2', 'output': '-3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n-4', 'output': '-5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n26', 'output': '25\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_80413","program":"```python\nn = int(input())\nv = list(map(int,input().split()))\ncount = 0\nans = 0\ns = -1\nwhile count != n:\n ans -= s\n s -= 1\n count += 1\nprint(sum(v)-ans)\n\n```","inputs":"1\n59549","output":"59548","actual_output":"59548\n","execution_success":true,"sample_index":12802},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p02356 The Number of Windows","prompt":"Solve the following coding problem using the programming language python:\n\nFor a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and $Q$ integers $x_i$ as queries, for each query, print the number of combinations of two integers $(l, r)$ which satisfies the condition: $1 \\leq l \\leq r \\leq N$ and $a_l + a_{l+1} + ... + a_{r-1} + a_r \\leq x_i$.\n\nConstraints\n\n* $1 \\leq N \\leq 10^5$\n* $1 \\leq Q \\leq 500$\n* $1 \\leq a_i \\leq 10^9$\n* $1 \\leq x_i \\leq 10^{14}$\n\nInput\n\nThe input is given in the following format.\n\n$N$ $Q$\n$a_1$ $a_2$ ... $a_N$\n$x_1$ $x_2$ ... $x_Q$\n\nOutput\n\nFor each query, print the number of combinations in a line.\n\nExample\n\nInput\n\n6 5\n1 2 3 4 5 6\n6 9 12 21 15\n\n\nOutput\n\n9\n12\n15\n21\n18\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom bisect import bisect_right\n\ndef main():\n N, Q = map(int, input().split())\n a = [-1 for i in range(N)]\n sum = [0 for i in range(N + 1)]\n for i, val in enumerate(input().split()):\n a[i] = int(val)\n sum[i + 1] = sum[i] + a[i]\n X = list(map(int, input().split()))\n\n # print(\"DEBUG: sum={}\".format(sum))\n for x in X:\n ans = solve3(a, x, N, sum)\n print(ans)\n\n\ndef solve1(a, x, N, sum):\n l, r = 0, 0\n ret = 0\n while l < N:\n if r < N + 1:\n r = bisect_right(sum, sum[l] + x, r)\n if r > l:\n ret += (r - 1 - l)\n l += 1\n\n return ret\n\ndef solve2(a, x, N, sum):\n l, r, sum = 0, 0, 0\n ret = 0\n while l < N:\n while r < N and sum + a[r] <= x:\n sum += a[r]\n r += 1\n ret += (r - l)\n sum -= a[l]\n l += 1\n\n return ret\n\n\ndef solve3(a, x, N, sum):\n l, sum, ans = 0, 0, 0\n for r in range(N):\n sum += a[r]\n while sum > x:\n sum -= a[l]\n l += 1\n ans += r - l + 1\n return ans\n\n\nmain()\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 4 5 6\\n6 9 12 21 15', 'output': '9\\n12\\n15\\n21\\n18'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 4 7 6\\n6 9 12 21 15', 'output': '8\\n11\\n13\\n19\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 2 7 6\\n6 9 12 21 15', 'output': '9\\n13\\n14\\n21\\n18\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 2 7 6\\n6 12 12 21 15', 'output': '9\\n14\\n14\\n21\\n18\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 2 7 6\\n0 12 12 21 15', 'output': '0\\n14\\n14\\n21\\n18\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 5 5 6\\n6 9 12 21 15', 'output': '9\\n10\\n14\\n20\\n16\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 4 7 6\\n6 9 12 21 21', 'output': '8\\n11\\n13\\n19\\n19\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 2 7 6\\n6 1 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'10\\n13\\n20\\n21\\n18\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 2 7 1\\n5 12 12 21 15', 'output': '8\\n16\\n16\\n21\\n20\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n2 2 3 2 7 2\\n0 12 12 21 15', 'output': '0\\n16\\n16\\n21\\n18\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 0 3 5 5 6\\n6 9 12 21 15', 'output': '9\\n12\\n14\\n21\\n17\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 4 2 6\\n6 9 12 21 39', 'output': '10\\n14\\n18\\n21\\n21\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 4 0 2 7 11\\n6 1 3 21 15', 'output': '9\\n2\\n4\\n19\\n16\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 1 3 7 7 6\\n12 9 12 21 15', 'output': '12\\n9\\n12\\n18\\n14\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 8 7 6\\n6 9 22 31 21', 'output': '7\\n9\\n18\\n21\\n18\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 1 10 7 6\\n2 9 12 21 15', 'output': '3\\n8\\n10\\n17\\n13\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n2 2 3 10 7 11\\n6 9 12 21 21', 'output': '5\\n7\\n9\\n15\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 1 2 7 10\\n9 1 12 21 15', 'output': '12\\n2\\n14\\n19\\n16\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 6 3 7 12\\n6 9 12 21 28', 'output': '5\\n9\\n13\\n17\\n19\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 0 3 10 7 6\\n6 9 12 21 5', 'output': '7\\n8\\n9\\n17\\n6\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 3 0 7 10\\n6 2 12 16 15', 'output': '8\\n2\\n14\\n16\\n16\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 10 7 5\\n2 9 16 21 28', 'output': '2\\n8\\n13\\n15\\n21\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 3 3 2 13 10\\n6 2 11 21 21', 'output': '7\\n2\\n11\\n15\\n15\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 4 2 10 5\\n6 9 5 21 15', 'output': '8\\n11\\n6\\n19\\n14\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n2 2 3 0 7 6\\n6 9 16 31 28', 'output': '9\\n13\\n19\\n21\\n21\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 4 2 6 7\\n12 11 5 21 8', 'output': '14\\n13\\n5\\n20\\n12\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 1 3 0 1 6\\n6 9 16 21 29', 'output': '16\\n18\\n21\\n21\\n21\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 4 2 6 13\\n1 11 5 21 15', 'output': '1\\n12\\n5\\n18\\n16\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 4 3 0 12 1\\n10 1 22 25 16', 'output': '11\\n3\\n21\\n21\\n17\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 134217728}","problem_id":"vfc_80417","program":"```python\nfrom bisect import bisect_right\n\ndef main():\n N, Q = map(int, input().split())\n a = [-1 for i in range(N)]\n sum = [0 for i in range(N + 1)]\n for i, val in enumerate(input().split()):\n a[i] = int(val)\n sum[i + 1] = sum[i] + a[i]\n X = list(map(int, input().split()))\n\n # print(\"DEBUG: sum={}\".format(sum))\n for x in X:\n ans = solve3(a, x, N, sum)\n print(ans)\n\n\ndef solve1(a, x, N, sum):\n l, r = 0, 0\n ret = 0\n while l < N:\n if r < N + 1:\n r = bisect_right(sum, sum[l] + x, r)\n if r > l:\n ret += (r - 1 - l)\n l += 1\n\n return ret\n\ndef solve2(a, x, N, sum):\n l, r, sum = 0, 0, 0\n ret = 0\n while l < N:\n while r < N and sum + a[r] <= x:\n sum += a[r]\n r += 1\n ret += (r - l)\n sum -= a[l]\n l += 1\n\n return ret\n\n\ndef solve3(a, x, N, sum):\n l, sum, ans = 0, 0, 0\n for r in range(N):\n sum += a[r]\n while sum > x:\n sum -= a[l]\n l += 1\n ans += r - l + 1\n return ans\n\n\nmain()\n\n\n```","inputs":"6 5\n1 2 3 4 5 6\n6 9 12 21 15","output":"9\n12\n15\n21\n18","actual_output":"9\n12\n15\n21\n18\n","execution_success":true,"sample_index":12803},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1015_A. Points in Segments","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 \u2264 l_i \u2264 r_i \u2264 m) \u2014 coordinates of the left and of the right endpoints. \n\nConsider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l \u2264 x \u2264 r.\n\nInput\n\nThe first line of the input contains two integers n and m (1 \u2264 n, m \u2264 100) \u2014 the number of segments and the upper bound for coordinates.\n\nThe next n lines contain two integers each l_i and r_i (1 \u2264 l_i \u2264 r_i \u2264 m) \u2014 the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.\n\nOutput\n\nIn the first line print one integer k \u2014 the number of points that don't belong to any segment.\n\nIn the second line print exactly k integers in any order \u2014 the points that don't belong to any segment. All points you print should be distinct.\n\nIf there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.\n\nExamples\n\nInput\n\n3 5\n2 2\n1 2\n5 5\n\n\nOutput\n\n2\n3 4 \n\n\nInput\n\n1 7\n1 7\n\n\nOutput\n\n0\n\nNote\n\nIn the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.\n\nIn the second example all the points from 1 to 7 belong to the first segment.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, m = [int(x) for x in input().split()]\ns = set(range(1, m+1))\n\nfor _ in range(n):\n a, b = [int(x) for x in input().split()]\n s -= set(range(a, b+1))\n\nprint(len(s))\nprint(*s)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 7\\n1 7\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n2 2\\n1 2\\n5 5\\n', 'output': '2\\n3 4\\n'}, {'type': 'stdin_stdout', 'input': '100 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n2 2\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '1 7\\n5 5\\n', 'output': '6\\n1 2 3 4 6 7\\n'}, {'type': 'stdin_stdout', 'input': '1 100\\n54 54\\n', 'output': '99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\\n'}, {'type': 'stdin_stdout', 'input': '1 100\\n2 99\\n', 'output': '2\\n1 100\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 1\\n1 1\\n1 1\\n2 2\\n', 'output': '1\\n3\\n'}, {'type': 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'0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n2 5\\n9 11\\n1 7\\n5 6\\n1 3\\n2 7\\n11 11\\n9 9\\n6 7\\n5 9\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n2 5\\n9 11\\n1 7\\n5 6\\n3 3\\n2 7\\n1 11\\n9 10\\n4 7\\n5 9\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 16\\n2 8\\n9 11\\n1 6\\n5 6\\n1 3\\n2 7\\n11 11\\n9 9\\n8 7\\n5 9\\n', 'output': '5\\n12 13 14 15 16\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n2 5\\n9 11\\n1 7\\n5 6\\n2 3\\n2 7\\n1 11\\n9 10\\n1 8\\n5 9\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n5 5\\n4 5\\n5 5\\n', 'output': '3\\n1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '100 100\\n1 2\\n1 3\\n1 3\\n2 3\\n1 1\\n1 2\\n1 1\\n1 2\\n1 3\\n1 2\\n1 2\\n1 5\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 2\\n1 1\\n1 1\\n1 2\\n2 2\\n1 1\\n1 5\\n1 4\\n1 1\\n2 2\\n2 9\\n1 1\\n1 5\\n2 3\\n2 3\\n1 5\\n1 2\\n2 2\\n2 2\\n1 2\\n1 2\\n3 4\\n1 5\\n1 1\\n1 1\\n1 1\\n1 1\\n2 2\\n1 3\\n1 2\\n1 2\\n1 2\\n1 1\\n2 2\\n1 4\\n1 3\\n1 1\\n1 2\\n1 1\\n1 3\\n1 2\\n2 2\\n1 1\\n1 5\\n1 2\\n2 2\\n1 1\\n1 1\\n1 2\\n1 4\\n2 3\\n1 2\\n1 1\\n2 2\\n1 5\\n1 1\\n1 6\\n1 1\\n1 1\\n1 2\\n1 1\\n1 4\\n2 2\\n2 1\\n1 1\\n1 4\\n1 2\\n1 2\\n1 1\\n1 2\\n2 3\\n1 1\\n1 1\\n1 3\\n1 3\\n1 2\\n1 2\\n1 1\\n1 2\\n1 2\\n1 1\\n1 2\\n', 'output': '91\\n10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\\n'}, {'type': 'stdin_stdout', 'input': '100 100\\n1 2\\n1 3\\n1 3\\n2 3\\n1 1\\n1 2\\n1 1\\n1 2\\n1 3\\n1 2\\n1 2\\n1 5\\n1 1\\n1 1\\n1 1\\n2 1\\n1 1\\n1 2\\n1 2\\n1 1\\n1 1\\n1 2\\n2 2\\n1 1\\n1 5\\n1 4\\n1 1\\n2 2\\n2 9\\n1 1\\n1 5\\n2 3\\n2 3\\n1 5\\n1 2\\n2 2\\n2 2\\n1 2\\n1 2\\n6 4\\n1 5\\n1 1\\n1 1\\n1 1\\n1 1\\n2 2\\n1 3\\n1 2\\n1 2\\n1 2\\n1 1\\n2 2\\n1 4\\n1 3\\n1 1\\n1 2\\n1 1\\n1 3\\n1 2\\n2 2\\n1 1\\n1 5\\n1 2\\n2 2\\n1 1\\n1 1\\n1 2\\n1 4\\n2 3\\n1 2\\n1 1\\n2 2\\n1 5\\n1 1\\n1 6\\n1 1\\n1 1\\n1 2\\n1 1\\n1 4\\n2 2\\n1 1\\n1 1\\n1 2\\n1 2\\n1 2\\n1 1\\n1 2\\n2 3\\n1 1\\n1 1\\n1 3\\n1 3\\n1 2\\n1 2\\n1 1\\n1 2\\n1 2\\n1 1\\n1 2\\n', 'output': '91\\n10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n2 5\\n9 11\\n1 7\\n5 6\\n3 3\\n2 7\\n1 11\\n9 10\\n4 7\\n3 9\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 16\\n3 8\\n9 11\\n1 6\\n5 6\\n1 3\\n2 7\\n11 11\\n9 9\\n8 7\\n5 9\\n', 'output': '5\\n12 13 14 15 16\\n'}, {'type': 'stdin_stdout', 'input': '100 100\\n1 2\\n1 2\\n1 3\\n2 3\\n1 1\\n1 2\\n1 1\\n1 2\\n1 3\\n1 2\\n1 2\\n1 5\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 2\\n1 1\\n1 1\\n1 2\\n2 2\\n1 1\\n1 5\\n1 4\\n1 1\\n2 2\\n2 9\\n1 1\\n1 5\\n2 3\\n2 3\\n1 5\\n1 2\\n2 2\\n2 2\\n1 2\\n1 2\\n3 4\\n1 5\\n1 1\\n1 1\\n1 1\\n1 1\\n2 2\\n1 3\\n1 2\\n1 2\\n1 2\\n1 1\\n2 2\\n1 4\\n1 3\\n1 1\\n1 2\\n1 1\\n1 3\\n1 2\\n2 2\\n1 1\\n1 5\\n1 2\\n2 2\\n1 1\\n1 1\\n1 2\\n1 4\\n2 3\\n1 2\\n1 1\\n2 2\\n1 5\\n1 1\\n1 6\\n1 1\\n1 1\\n1 2\\n1 1\\n1 4\\n2 2\\n2 1\\n1 1\\n1 4\\n1 2\\n1 2\\n1 1\\n1 2\\n2 3\\n1 1\\n1 1\\n1 3\\n1 3\\n1 2\\n1 2\\n1 1\\n1 2\\n1 2\\n1 1\\n1 2\\n', 'output': '91\\n10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n2 5\\n9 11\\n1 7\\n5 6\\n3 3\\n2 7\\n1 11\\n9 10\\n4 5\\n3 9\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n2 5\\n9 11\\n1 7\\n5 6\\n3 3\\n2 7\\n1 11\\n9 10\\n4 5\\n5 9\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 20\\n3 8\\n9 11\\n1 6\\n5 6\\n1 3\\n2 7\\n11 11\\n9 9\\n2 7\\n5 9\\n', 'output': '9\\n12 13 14 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n2 5\\n9 11\\n1 7\\n5 6\\n3 3\\n3 7\\n1 11\\n9 10\\n4 5\\n5 9\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 20\\n3 3\\n9 11\\n1 6\\n5 6\\n1 3\\n2 7\\n11 11\\n9 9\\n2 7\\n5 9\\n', 'output': '9\\n12 13 14 15 16 17 18 19 20\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n2 5\\n9 11\\n1 7\\n5 6\\n3 3\\n3 7\\n2 11\\n9 10\\n4 5\\n5 9\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n2 5\\n9 11\\n1 7\\n5 6\\n3 3\\n3 7\\n2 3\\n9 10\\n4 5\\n5 9\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '10 11\\n2 5\\n2 11\\n1 7\\n5 6\\n1 3\\n2 7\\n11 11\\n9 10\\n4 7\\n5 9\\n', 'output': '0\\n\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n3 4\\n5 5\\n5 5\\n', 'output': '2\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '100 100\\n1 2\\n1 3\\n1 3\\n2 3\\n1 1\\n1 2\\n1 1\\n1 2\\n1 3\\n1 3\\n1 2\\n1 5\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 2\\n1 1\\n1 1\\n1 2\\n2 2\\n1 1\\n1 5\\n1 4\\n1 1\\n2 2\\n2 9\\n1 1\\n1 5\\n2 3\\n2 3\\n1 5\\n1 2\\n2 2\\n2 2\\n1 2\\n1 2\\n3 4\\n1 5\\n1 1\\n1 1\\n1 1\\n1 1\\n2 2\\n1 3\\n1 2\\n1 2\\n1 2\\n1 1\\n2 2\\n1 4\\n1 3\\n1 1\\n1 2\\n1 1\\n1 3\\n1 2\\n2 2\\n1 1\\n1 5\\n1 2\\n2 2\\n1 1\\n1 1\\n1 2\\n1 4\\n2 3\\n1 2\\n1 1\\n2 2\\n1 5\\n1 1\\n1 6\\n1 1\\n1 1\\n1 2\\n1 1\\n1 4\\n2 2\\n1 1\\n1 1\\n1 2\\n1 2\\n1 2\\n1 1\\n1 2\\n2 3\\n1 1\\n1 1\\n1 3\\n1 3\\n1 2\\n1 2\\n1 1\\n1 2\\n1 2\\n1 1\\n1 2\\n', 'output': '91\\n10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\n2 2\\n2 2\\n4 5\\n', 'output': '2\\n1 3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80445","program":"```python\nn, m = [int(x) for x in input().split()]\ns = set(range(1, m+1))\n\nfor _ in range(n):\n a, b = [int(x) for x in input().split()]\n s -= set(range(a, b+1))\n\nprint(len(s))\nprint(*s)\n\n```","inputs":"1 7\n1 7\n","output":"0\n\n","actual_output":"0\n\n","execution_success":true,"sample_index":12804},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1038_E. Maximum Matching","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given n blocks, each of them is of the form [color_1|value|color_2], where the block can also be flipped to get [color_2|value|color_1]. \n\nA sequence of blocks is called valid if the touching endpoints of neighboring blocks have the same color. For example, the sequence of three blocks A, B and C is valid if the left color of the B is the same as the right color of the A and the right color of the B is the same as the left color of C.\n\nThe value of the sequence is defined as the sum of the values of the blocks in this sequence.\n\nFind the maximum possible value of the valid sequence that can be constructed from the subset of the given blocks. The blocks from the subset can be reordered and flipped if necessary. Each block can be used at most once in the sequence.\n\nInput\n\nThe first line of input contains a single integer n (1 \u2264 n \u2264 100) \u2014 the number of given blocks.\n\nEach of the following n lines describes corresponding block and consists of color_{1,i}, value_i and color_{2,i} (1 \u2264 color_{1,i}, color_{2,i} \u2264 4, 1 \u2264 value_i \u2264 100 000).\n\nOutput\n\nPrint exactly one integer \u2014 the maximum total value of the subset of blocks, which makes a valid sequence.\n\nExamples\n\nInput\n\n6\n2 1 4\n1 2 4\n3 4 4\n2 8 3\n3 16 3\n1 32 2\n\n\nOutput\n\n63\n\nInput\n\n7\n1 100000 1\n1 100000 2\n1 100000 2\n4 50000 3\n3 50000 4\n4 50000 4\n3 50000 3\n\n\nOutput\n\n300000\n\nInput\n\n4\n1 1000 1\n2 500 2\n3 250 3\n4 125 4\n\n\nOutput\n\n1000\n\nNote\n\nIn the first example, it is possible to form a valid sequence from all blocks.\n\nOne of the valid sequences is the following:\n\n[4|2|1] [1|32|2] [2|8|3] [3|16|3] [3|4|4] [4|1|2]\n\nThe first block from the input ([2|1|4] \u2192 [4|1|2]) and second ([1|2|4] \u2192 [4|2|1]) are flipped.\n\nIn the second example, the optimal answers can be formed from the first three blocks as in the following (the second or the third block from the input is flipped):\n\n[2|100000|1] [1|100000|1] [1|100000|2]\n\nIn the third example, it is not possible to form a valid sequence of two or more blocks, so the answer is a sequence consisting only of the first block since it is the block with the largest value.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef min(a, b):\n if a < b:\n return a\n return b\ndef max(a,b):\n return abs(min(-a,-b))\nbeen = [0 for i in range(4)]\nans = 0\nminw = 10**18\ndegpar = [0 for i in range(4)]\nw = [0 for i in range(4)]\ngr = [list() for i in range(4)]\nrem = [[0 for i in range(4)] for j in range(4)]\ndef dfs(x, l):\n l.append(w[x])\n if been[x]:\n return\n been[x] = 1\n for i in gr[x]:\n if been[i] == 0 and rem[x][i] > 0:\n dfs(i, l)\nn = int(input())\nblocks = []\nfor i in range(n):\n a,v,b = map(int, input().split())\n a -= 1\n b -= 1\n if a != b:\n blocks.append([a,v,b])\n w[b] += v\n if a != b:\n minw = min(minw, v)\n degpar[a] += 1\n degpar[a] %= 2\n degpar[b] += 1\n degpar[b] %= 2\n gr[a].append(b)\n gr[b].append(a)\n rem[a][b] += 1\n rem[b][a] += 1\nok = True\nfor i in range(4):\n l = []\n if been[i] == 0:\n dfs(i, l)\n if i == 0 and all(been) and all(degpar):\n ok = False\n break\n ans = max(ans, sum(l))\nif ok:\n print(ans)\n exit()\nfor p in blocks:\n i = p[0]\n j = p[2]\n w[j] -= p[1]\n been = [0 for i in range(4)]\n rem[i][j] -= 1\n rem[j][i] -= 1\n #print(i)\n #print(j)\n #print(':')\n for x in range(4):\n l = []\n if been[x] == 0:\n dfs(x,l)\n ans = max(ans, sum(l))\n #print(sum(l))\n w[j] += p[1]\n rem[i][j] += 1\n rem[j][i] += 1\nprint(ans)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n1 1000 1\\n2 500 2\\n3 250 3\\n4 125 4\\n', 'output': '1000'}, {'type': 'stdin_stdout', 'input': '7\\n1 100000 1\\n1 100000 2\\n1 100000 2\\n4 50000 3\\n3 50000 4\\n4 50000 4\\n3 50000 3\\n', 'output': '300000'}, {'type': 'stdin_stdout', 'input': '6\\n2 1 4\\n1 2 4\\n3 4 4\\n2 8 3\\n3 16 3\\n1 32 2\\n', 'output': '63'}, {'type': 'stdin_stdout', 'input': '34\\n1 91618 4\\n4 15565 2\\n1 27127 3\\n3 71241 1\\n1 72886 4\\n3 67359 2\\n4 91828 2\\n2 79231 4\\n1 2518 4\\n2 91908 2\\n3 8751 4\\n1 78216 1\\n4 86652 4\\n1 42983 1\\n4 17501 4\\n4 49048 3\\n1 9781 1\\n3 7272 4\\n4 50885 1\\n4 3897 1\\n2 33253 4\\n1 66074 2\\n3 99395 2\\n3 41446 4\\n3 74336 2\\n3 80002 4\\n3 48871 2\\n3 93650 4\\n2 32944 4\\n3 30204 4\\n4 78805 4\\n1 40801 1\\n2 94708 2\\n3 19544 3\\n', 'output': '1800300'}, {'type': 'stdin_stdout', 'input': '9\\n3 7 1\\n3 91 2\\n2 7 3\\n1 100 4\\n1 96 2\\n3 10 1\\n1 50 1\\n3 2 3\\n2 96 3\\n', 'output': '459'}, {'type': 'stdin_stdout', 'input': '1\\n3 52 4\\n', 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'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80449","program":"```python\ndef min(a, b):\n if a < b:\n return a\n return b\ndef max(a,b):\n return abs(min(-a,-b))\nbeen = [0 for i in range(4)]\nans = 0\nminw = 10**18\ndegpar = [0 for i in range(4)]\nw = [0 for i in range(4)]\ngr = [list() for i in range(4)]\nrem = [[0 for i in range(4)] for j in range(4)]\ndef dfs(x, l):\n l.append(w[x])\n if been[x]:\n return\n been[x] = 1\n for i in gr[x]:\n if been[i] == 0 and rem[x][i] > 0:\n dfs(i, l)\nn = int(input())\nblocks = []\nfor i in range(n):\n a,v,b = map(int, input().split())\n a -= 1\n b -= 1\n if a != b:\n blocks.append([a,v,b])\n w[b] += v\n if a != b:\n minw = min(minw, v)\n degpar[a] += 1\n degpar[a] %= 2\n degpar[b] += 1\n degpar[b] %= 2\n gr[a].append(b)\n gr[b].append(a)\n rem[a][b] += 1\n rem[b][a] += 1\nok = True\nfor i in range(4):\n l = []\n if been[i] == 0:\n dfs(i, l)\n if i == 0 and all(been) and all(degpar):\n ok = False\n break\n ans = max(ans, sum(l))\nif ok:\n print(ans)\n exit()\nfor p in blocks:\n i = p[0]\n j = p[2]\n w[j] -= p[1]\n been = [0 for i in range(4)]\n rem[i][j] -= 1\n rem[j][i] -= 1\n #print(i)\n #print(j)\n #print(':')\n for x in range(4):\n l = []\n if been[x] == 0:\n dfs(x,l)\n ans = max(ans, sum(l))\n #print(sum(l))\n w[j] += p[1]\n rem[i][j] += 1\n rem[j][i] += 1\nprint(ans)\n\n```","inputs":"4\n1 1000 1\n2 500 2\n3 250 3\n4 125 4\n","output":"1000","actual_output":"1000\n","execution_success":true,"sample_index":12805},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1061_A. Coins","prompt":"Solve the following coding problem using the programming language python:\n\nYou have unlimited number of coins with values 1, 2, \u2026, n. You want to select some set of coins having the total value of S. \n\nIt is allowed to have multiple coins with the same value in the set. What is the minimum number of coins required to get sum S?\n\nInput\n\nThe only line of the input contains two integers n and S (1 \u2264 n \u2264 100 000, 1 \u2264 S \u2264 10^9)\n\nOutput\n\nPrint exactly one integer \u2014 the minimum number of coins required to obtain sum S.\n\nExamples\n\nInput\n\n5 11\n\n\nOutput\n\n3\n\nInput\n\n6 16\n\n\nOutput\n\n3\n\nNote\n\nIn the first example, some of the possible ways to get sum 11 with 3 coins are: \n\n * (3, 4, 4)\n * (2, 4, 5)\n * (1, 5, 5)\n * (3, 3, 5) \n\n\n\nIt is impossible to get sum 11 with less than 3 coins.\n\nIn the second example, some of the possible ways to get sum 16 with 3 coins are: \n\n * (5, 5, 6)\n * (4, 6, 6) \n\n\n\nIt is impossible to get sum 16 with less than 3 coins.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, s = map(int, input().split())\nprint((s + n - 1) // n)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 16\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 11\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '5 29\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '2 999999999\\n', 'output': '500000000\\n'}, {'type': 'stdin_stdout', 'input': '42482 352232377\\n', 'output': '8292\\n'}, {'type': 'stdin_stdout', 'input': '10 46\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '22951 747845288\\n', 'output': '32585\\n'}, {'type': 'stdin_stdout', 'input': '46602 894472145\\n', 'output': '19194\\n'}, {'type': 'stdin_stdout', 'input': '4821 917142246\\n', 'output': '190240\\n'}, {'type': 'stdin_stdout', 'input': '2 193379347\\n', 'output': '96689674\\n'}, {'type': 'stdin_stdout', 'input': '7156 806580442\\n', 'output': '112714\\n'}, {'type': 'stdin_stdout', 'input': '90952 904040054\\n', 'output': '9940\\n'}, {'type': 'stdin_stdout', 'input': '73439 384841883\\n', 'output': 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'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80453","program":"```python\nn, s = map(int, input().split())\nprint((s + n - 1) // n)\n\n```","inputs":"6 16\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12806},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1082_G. Petya and Graph","prompt":"Solve the following coding problem using the programming language python:\n\nPetya has a simple graph (that is, a graph without loops or multiple edges) consisting of n vertices and m edges.\n\nThe weight of the i-th vertex is a_i.\n\nThe weight of the i-th edge is w_i.\n\nA subgraph of a graph is some set of the graph vertices and some set of the graph edges. The set of edges must meet the condition: both ends of each edge from the set must belong to the chosen set of vertices. \n\nThe weight of a subgraph is the sum of the weights of its edges, minus the sum of the weights of its vertices. You need to find the maximum weight of subgraph of given graph. The given graph does not contain loops and multiple edges.\n\nInput\n\nThe first line contains two numbers n and m (1 \u2264 n \u2264 10^3, 0 \u2264 m \u2264 10^3) - the number of vertices and edges in the graph, respectively.\n\nThe next line contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 10^9) - the weights of the vertices of the graph.\n\nThe following m lines contain edges: the i-e edge is defined by a triple of integers v_i, u_i, w_i (1 \u2264 v_i, u_i \u2264 n, 1 \u2264 w_i \u2264 10^9, v_i \u2260 u_i). This triple means that between the vertices v_i and u_i there is an edge of weight w_i. It is guaranteed that the graph does not contain loops and multiple edges.\n\nOutput\n\nPrint one integer \u2014 the maximum weight of the subgraph of the given graph.\n\nExamples\n\nInput\n\n\n4 5\n1 5 2 2\n1 3 4\n1 4 4\n3 4 5\n3 2 2\n4 2 2\n\n\nOutput\n\n\n8\n\n\nInput\n\n\n3 3\n9 7 8\n1 2 1\n2 3 2\n1 3 3\n\n\nOutput\n\n\n0\n\nNote\n\nIn the first test example, the optimal subgraph consists of the vertices {1, 3, 4} and has weight 4 + 4 + 5 - (1 + 2 + 2) = 8. In the second test case, the optimal subgraph is empty.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nclass edge(object):\n\tdef __init__(self,ne,to,fl):\n\t\tself.ne=ne\n\t\tself.to=to\n\t\tself.fl=fl\n\ndef add(x,y,z):\n\tglobal tot\n\ttot+=1\n\te.append(edge(he[x],y,z))\n\the[x]=tot\n\ndef addedge(x,y,z):\n\tadd(x,y,z)\n\tadd(y,x,0)\n\ndef bfs():\n\tglobal deep\n\tdeep=[0 for i in range(T+1)]\n\tq=[]\n\tq.append(S)\n\tdeep[S]=1\n\twhile (len(q)>0):\n\t\tx=q[0]\n\t\tdel(q[0])\n\t\ti=he[x]\n\t\twhile (i):\n\t\t\ty=e[i].to\n\t\t\tif ((deep[y]==0)and(e[i].fl!=0)):\n\t\t\t\tdeep[y]=deep[x]+1\n\t\t\t\tq.append(y)\n\t\t\ti=e[i].ne\n\treturn deep[T]!=0\n\ndef dfs(x,flow):\n\tglobal deep\n\tif ((x==T)or(flow==0)):\n\t\treturn flow\n\tused=0\n\ti=he[x]\n\twhile (i):\n\t\ty=e[i].to\n\t\tif ((deep[y]==deep[x]+1)and(e[i].fl!=0)):\n\t\t\tnow=dfs(y,min(flow-used,e[i].fl))\n\t\t\tused+=now\n\t\t\te[i].fl-=now\n\t\t\te[i^1].fl+=now\n\t\t\tif (flow==used):\n\t\t\t\tbreak;\n\t\ti=e[i].ne\n\tif (used==0):\n\t\tdeep[x]=-1\n\treturn used\n\ndef dinic():\n\tres=0\n\twhile (bfs()):\n\t\tres+=dfs(S,INF)\n\treturn res\n\nn,m=map(int,input().split())\nans=0\nweight=[0]+list(map(int,input().split()))\n\ne=[0,0]\ntot=1\nS=n+m+1\nT=S+1\nhe=[0 for i in range(T+1)]\nINF=1000000007\n\nfor i in range(1,n+1):\n\taddedge(S,i,weight[i]);\nfor i in range(1,m+1):\n\tx,y,w=map(int,input().split())\n\taddedge(n+i,T,w)\n\taddedge(x,n+i,INF)\n\taddedge(y,n+i,INF)\n\tans+=w\nans-=dinic()\nprint(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3 3\\n9 7 8\\n1 2 1\\n2 3 2\\n1 3 3\\n', 'output': ' 0\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 5 2 2\\n1 3 4\\n1 4 4\\n3 4 5\\n3 2 2\\n4 2 2\\n', 'output': ' 8\\n'}, {'type': 'stdin_stdout', 'input': '20 10\\n487490574 766859182 860731945 956220596 584871933 815478522 698429627 781975977 485357256 396825095 566947997 680691964 834523631 323163346 665972495 5503804 738797202 410201497 91359028 708811641\\n16 15 598574211\\n8 7 332007499\\n11 1 942159718\\n3 1 24779817\\n20 4 192862192\\n16 6 965177283\\n20 5 267339195\\n19 2 634372580\\n20 14 285875387\\n20 8 689483375\\n', 'output': ' 144194957\\n'}, {'type': 'stdin_stdout', 'input': '1 0\\n1\\n', 'output': ' 0\\n'}, {'type': 'stdin_stdout', 'input': '13 15\\n531739709 635168245 234231026 281038754 623215180 692418771 741999464 557020273 415476010 65027535 509994318 572183511 764999869\\n12 10 77113307\\n6 4 493243408\\n9 7 884704622\\n12 1 332486025\\n5 3 96756243\\n10 5 455964540\\n7 4 81872575\\n13 6 526080427\\n8 4 429617508\\n7 5 992146684\\n12 9 214298703\\n11 8 232430976\\n13 3 674735569\\n8 5 255487152\\n4 1 577497633\\n', 'output': ' 612654294\\n'}, {'type': 'stdin_stdout', 'input': '20 10\\n487490574 766859182 860731945 1597893797 584871933 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'8\\n'}, {'type': 'stdin_stdout', 'input': '13 15\\n531739709 635168245 234231026 281038754 623215180 692418771 741999464 557020273 712743953 65027535 509994318 572183511 764999869\\n12 10 77113307\\n6 4 493243408\\n9 7 884704622\\n12 1 661648514\\n5 3 96756243\\n10 5 455964540\\n7 4 81872575\\n13 6 526080427\\n8 4 429617508\\n7 5 992146684\\n12 9 214298703\\n11 8 6082457\\n13 3 674735569\\n8 5 255487152\\n4 1 577497633\\n', 'output': '644548840\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 5 2 2\\n1 3 3\\n1 4 4\\n3 4 5\\n1 2 2\\n4 2 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '13 15\\n531739709 635168245 234231026 281038754 623215180 692418771 741999464 557020273 415476010 65027535 509994318 448254177 764999869\\n12 10 77113307\\n6 4 493243408\\n9 7 884704622\\n12 1 661648514\\n5 3 96756243\\n10 5 455964540\\n7 4 81872575\\n13 6 526080427\\n8 7 429617508\\n7 5 992146684\\n12 9 214298703\\n11 8 232430976\\n13 3 674735569\\n8 5 255487152\\n4 1 577497633\\n', 'output': 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6 429617508\\n7 5 992146684\\n12 9 214298703\\n11 8 4718901\\n13 3 674735569\\n8 5 255487152\\n4 1 577497633\\n', 'output': '941816783\\n'}, {'type': 'stdin_stdout', 'input': '20 10\\n817030036 766859182 860731945 956220596 584871933 815478522 698429627 781975977 485357256 396825095 566947997 680691964 834523631 323163346 665972495 5503804 738797202 410201497 91359028 708811641\\n16 15 598574211\\n8 7 332007499\\n11 1 942159718\\n3 1 24779817\\n20 4 192862192\\n16 6 965177283\\n20 5 267339195\\n19 2 634372580\\n20 8 285875387\\n20 8 689483375\\n', 'output': '144194957\\n'}], 'language': 'python'}","metadata":"{'difficulty': 13, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80457","program":"```python\nclass edge(object):\n\tdef __init__(self,ne,to,fl):\n\t\tself.ne=ne\n\t\tself.to=to\n\t\tself.fl=fl\n\ndef add(x,y,z):\n\tglobal tot\n\ttot+=1\n\te.append(edge(he[x],y,z))\n\the[x]=tot\n\ndef addedge(x,y,z):\n\tadd(x,y,z)\n\tadd(y,x,0)\n\ndef bfs():\n\tglobal deep\n\tdeep=[0 for i in range(T+1)]\n\tq=[]\n\tq.append(S)\n\tdeep[S]=1\n\twhile (len(q)>0):\n\t\tx=q[0]\n\t\tdel(q[0])\n\t\ti=he[x]\n\t\twhile (i):\n\t\t\ty=e[i].to\n\t\t\tif ((deep[y]==0)and(e[i].fl!=0)):\n\t\t\t\tdeep[y]=deep[x]+1\n\t\t\t\tq.append(y)\n\t\t\ti=e[i].ne\n\treturn deep[T]!=0\n\ndef dfs(x,flow):\n\tglobal deep\n\tif ((x==T)or(flow==0)):\n\t\treturn flow\n\tused=0\n\ti=he[x]\n\twhile (i):\n\t\ty=e[i].to\n\t\tif ((deep[y]==deep[x]+1)and(e[i].fl!=0)):\n\t\t\tnow=dfs(y,min(flow-used,e[i].fl))\n\t\t\tused+=now\n\t\t\te[i].fl-=now\n\t\t\te[i^1].fl+=now\n\t\t\tif (flow==used):\n\t\t\t\tbreak;\n\t\ti=e[i].ne\n\tif (used==0):\n\t\tdeep[x]=-1\n\treturn used\n\ndef dinic():\n\tres=0\n\twhile (bfs()):\n\t\tres+=dfs(S,INF)\n\treturn res\n\nn,m=map(int,input().split())\nans=0\nweight=[0]+list(map(int,input().split()))\n\ne=[0,0]\ntot=1\nS=n+m+1\nT=S+1\nhe=[0 for i in range(T+1)]\nINF=1000000007\n\nfor i in range(1,n+1):\n\taddedge(S,i,weight[i]);\nfor i in range(1,m+1):\n\tx,y,w=map(int,input().split())\n\taddedge(n+i,T,w)\n\taddedge(x,n+i,INF)\n\taddedge(y,n+i,INF)\n\tans+=w\nans-=dinic()\nprint(ans)\n```","inputs":"3 3\n9 7 8\n1 2 1\n2 3 2\n1 3 3\n","output":" 0\n","actual_output":"0\n","execution_success":true,"sample_index":12807},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1102_B. Array K-Coloring","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given an array a consisting of n integer numbers.\n\nYou have to color this array in k colors in such a way that: \n\n * Each element of the array should be colored in some color; \n * For each i from 1 to k there should be at least one element colored in the i-th color in the array; \n * For each i from 1 to k all elements colored in the i-th color should be distinct. \n\n\n\nObviously, such coloring might be impossible. In this case, print \"NO\". Otherwise print \"YES\" and any coloring (i.e. numbers c_1, c_2, ... c_n, where 1 \u2264 c_i \u2264 k and c_i is the color of the i-th element of the given array) satisfying the conditions above. If there are multiple answers, you can print any.\n\nInput\n\nThe first line of the input contains two integers n and k (1 \u2264 k \u2264 n \u2264 5000) \u2014 the length of the array a and the number of colors, respectively.\n\nThe second line of the input contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 5000) \u2014 elements of the array a.\n\nOutput\n\nIf there is no answer, print \"NO\". Otherwise print \"YES\" and any coloring (i.e. numbers c_1, c_2, ... c_n, where 1 \u2264 c_i \u2264 k and c_i is the color of the i-th element of the given array) satisfying the conditions described in the problem statement. If there are multiple answers, you can print any.\n\nExamples\n\nInput\n\n\n4 2\n1 2 2 3\n\n\nOutput\n\n\nYES\n1 1 2 2\n\n\nInput\n\n\n5 2\n3 2 1 2 3\n\n\nOutput\n\n\nYES\n2 1 1 2 1\n\n\nInput\n\n\n5 2\n2 1 1 2 1\n\n\nOutput\n\n\nNO\n\nNote\n\nIn the first example the answer 2~ 1~ 2~ 1 is also acceptable.\n\nIn the second example the answer 1~ 1~ 1~ 2~ 2 is also acceptable.\n\nThere exist other acceptable answers for both examples.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import defaultdict\nn,k=map(int,input().split())\narr=list(map(int,input().split()))\ntemp=[0]*5001\nfor i in arr:\n temp[i]+=1\nif(max(temp)>k):\n print('NO')\nelif(k>n):\n print('NO')\nelse:\n print('YES')\n d=defaultdict(list)\n c=0\n t=[0]*n\n for i in range(n):\n t[i]=arr[i]\n t.sort()\n for i in range(len(t)):\n d[t[i]].append(c+1)\n c=(c+1)%k\n p=[0]*5001\n for i in range(len(arr)):\n print(d[arr[i]][p[arr[i]]],end=' ')\n p[arr[i]]+=1\n\n\n\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 2\\n2 1 1 2 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n3 2 1 2 3\\n', 'output': 'YES\\n2 2 1 1 1 '}, {'type': 'stdin_stdout', 'input': '4 2\\n1 2 2 3\\n', 'output': 'YES\\n1 2 1 2 '}, {'type': 'stdin_stdout', 'input': '5 5\\n1 1 2 2 3\\n', 'output': 'YES\\n1 2 3 4 5 '}, {'type': 'stdin_stdout', 'input': '6 6\\n1 2 1 2 4 5\\n', 'output': 'YES\\n1 3 2 4 5 6 '}, {'type': 'stdin_stdout', 'input': '6 2\\n100 100 101 101 102 102\\n', 'output': 'YES\\n1 2 1 2 1 2 '}, {'type': 'stdin_stdout', 'input': '5 1\\n5 2 3 4 5\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n25 2 3 2 2\\n', 'output': 'YES\\n1 1 4 2 3 '}, {'type': 'stdin_stdout', 'input': '9 9\\n1 1 1 1 2 2 2 2 2\\n', 'output': 'YES\\n1 2 3 4 5 6 7 8 9 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 3 1 2 3 1 2 4 5\\n', 'output': 'YES\\n1 4 7 2 5 8 3 6 9 10 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 3 3 2 1 4 5 7 10\\n', 'output': 'YES\\n1 3 5 6 4 2 7 8 9 10 '}, {'type': 'stdin_stdout', 'input': '10 7\\n1 2 3 1 2 3 1 2 3 1\\n', 'output': 'YES\\n1 5 1 2 6 2 3 7 3 4 '}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 2 3\\n', 'output': 'YES\\n1 2 3 4 '}, {'type': 'stdin_stdout', 'input': '4 2\\n1 2 2 3\\n', 'output': 'YES\\n1 2 1 2 '}, {'type': 'stdin_stdout', 'input': '5 5\\n2 2 1 1 2\\n', 'output': 'YES\\n3 4 1 2 5 '}, {'type': 'stdin_stdout', 'input': '3 2\\n500 500 500\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 4 6 6 3\\n', 'output': 'YES\\n1 3 4 1 2 '}, {'type': 'stdin_stdout', 'input': '6 5\\n1 1 2 2 3 3\\n', 'output': 'YES\\n1 2 3 4 5 1 '}, {'type': 'stdin_stdout', 'input': '10 10\\n2017 2018 2019 2017 2018 2019 2020 2021 2022 2023\\n', 'output': 'YES\\n1 3 5 2 4 6 7 8 9 10 '}, {'type': 'stdin_stdout', 'input': '8 8\\n1 1 2 2 3 3 4 4\\n', 'output': 'YES\\n1 2 3 4 5 6 7 8 '}, {'type': 'stdin_stdout', 'input': '10 9\\n1 2 1 1 1 1 1 1 2 1\\n', 'output': 'YES\\n1 9 2 3 4 5 6 7 1 8 '}, {'type': 'stdin_stdout', 'input': '5 2\\n3 2 1 2 3\\n', 'output': 'YES\\n2 2 1 1 1 '}, {'type': 'stdin_stdout', 'input': '9 9\\n1 2 2 3 2 5 3 6 8\\n', 'output': 'YES\\n1 2 3 5 4 7 6 8 9 '}, {'type': 'stdin_stdout', 'input': '8 6\\n1 2 3 4 1 2 3 4\\n', 'output': 'YES\\n1 3 5 1 2 4 6 2 '}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 1 2\\n', 'output': 'YES\\n1 3 2 4 '}, {'type': 'stdin_stdout', 'input': '5 5\\n1 2 3 3 3\\n', 'output': 'YES\\n1 2 3 4 5 '}, {'type': 'stdin_stdout', 'input': '3 2\\n5000 5000 5000\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 1 2 2\\n', 'output': 'YES\\n1 2 3 4 '}, {'type': 'stdin_stdout', 'input': '7 6\\n1 2 3 4 2 3 4\\n', 'output': 'YES\\n1 2 4 6 3 5 1 '}, {'type': 'stdin_stdout', 'input': '6 6\\n2 1 1 2 1 3\\n', 'output': 'YES\\n4 1 2 5 3 6 '}, {'type': 'stdin_stdout', 'input': '3 3\\n5 5 5\\n', 'output': 'YES\\n1 2 3 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2 2 1 1 3 3\\n', 'output': 'YES\\n1 4 5 6 2 3 7 8 '}, {'type': 'stdin_stdout', 'input': '7 7\\n1 1 1 1 2 3 4\\n', 'output': 'YES\\n1 2 3 4 5 6 7 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 3 3 2 1 4 5 6 10\\n', 'output': 'YES\\n1 3 5 6 4 2 7 8 9 10 '}, {'type': 'stdin_stdout', 'input': '5 5\\n1 2 1 2 4\\n', 'output': 'YES\\n1 3 2 4 5 '}, {'type': 'stdin_stdout', 'input': '50 20\\n1 1 1 1 1 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50\\n', 'output': 'YES\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 '}, {'type': 'stdin_stdout', 'input': '6 6\\n1 2 3 3 3 3\\n', 'output': 'YES\\n1 2 3 4 5 6 '}, {'type': 'stdin_stdout', 'input': '3 1\\n2 2 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n2 1 2 3\\n', 'output': 'YES\\n2 1 3 4 '}, {'type': 'stdin_stdout', 'input': '1 1\\n5000\\n', 'output': 'YES\\n1 '}, {'type': 'stdin_stdout', 'input': '8 8\\n2 1 1 1 1 1 1 1\\n', 'output': 'YES\\n8 1 2 3 4 5 6 7 '}, {'type': 'stdin_stdout', 'input': '5 4\\n1 1 1 2 2\\n', 'output': 'YES\\n1 2 3 4 1 '}, {'type': 'stdin_stdout', 'input': '5 5\\n3 2 1 2 3\\n', 'output': 'YES\\n4 2 1 3 5 '}, {'type': 'stdin_stdout', 'input': '10 10\\n1 1 2 2 3 3 4 4 5 5\\n', 'output': 'YES\\n1 2 3 4 5 6 7 8 9 10 '}, {'type': 'stdin_stdout', 'input': '18 18\\n10 9 8 7 5 3 6 2 2 9 7 8 2 9 2 8 10 7\\n', 'output': 'YES\\n17 14 11 8 6 5 7 1 2 15 9 12 3 16 4 13 18 10 '}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 4 4 4\\n', 'output': 'YES\\n1 2 3 4 5 1 '}, {'type': 'stdin_stdout', 'input': '5 5\\n1 1 2 1 1\\n', 'output': 'YES\\n1 2 5 3 4 '}, {'type': 'stdin_stdout', 'input': '6 6\\n1 1 1 1 2 3\\n', 'output': 'YES\\n1 2 3 4 5 6 '}, {'type': 'stdin_stdout', 'input': '11 9\\n1 1 2 2 2 2 2 2 3 4 5\\n', 'output': 'YES\\n1 2 3 4 5 6 7 8 9 1 2 '}, {'type': 'stdin_stdout', 'input': '4 2\\n2000 2000 2000 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n2 2 1 1\\n', 'output': 'YES\\n3 1 1 2 '}, {'type': 'stdin_stdout', 'input': '4 4\\n3 3 3 5\\n', 'output': 'YES\\n1 2 3 4 '}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 1 2 4\\n', 'output': 'YES\\n1 3 2 4 1 '}, {'type': 'stdin_stdout', 'input': '6 6\\n1 1 2 1 2 2\\n', 'output': 'YES\\n1 2 4 3 5 6 '}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2 2 1\\n', 'output': 'YES\\n1 3 4 2 '}, {'type': 'stdin_stdout', 'input': '5 4\\n3 2 1 2 3\\n', 'output': 'YES\\n4 2 1 3 1 '}, {'type': 'stdin_stdout', 'input': '7 6\\n1 1 1 1 1 2 2\\n', 'output': 'YES\\n1 2 3 4 5 6 1 '}, {'type': 'stdin_stdout', 'input': '5 5\\n1 1 2 2 1\\n', 'output': 'YES\\n1 2 4 5 3 '}, {'type': 'stdin_stdout', 'input': '3 2\\n2019 2019 2019\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n6 7 8\\n', 'output': 'YES\\n1 2 3 '}, {'type': 'stdin_stdout', 'input': '9 8\\n1 2 2 3 3 3 4 5 4\\n', 'output': 'YES\\n1 2 3 4 5 6 7 1 8 '}, {'type': 'stdin_stdout', 'input': '6 4\\n1 1 2 2 3 3\\n', 'output': 'YES\\n1 2 3 4 1 2 '}, {'type': 'stdin_stdout', 'input': '5 5\\n1 1 1 3 3\\n', 'output': 'YES\\n1 2 3 4 5 '}, {'type': 'stdin_stdout', 'input': '6 3\\n2 1 3 4 5 1\\n', 'output': 'YES\\n3 1 1 2 3 2 '}, {'type': 'stdin_stdout', 'input': '1 1\\n2\\n', 'output': 'YES\\n1 '}, {'type': 'stdin_stdout', 'input': '7 5\\n2 3 2 1 1 1 3\\n', 'output': 'YES\\n4 1 5 1 2 3 2 '}, {'type': 'stdin_stdout', 'input': '9 9\\n9 8 1 3 4 5 3 8 9\\n', 'output': 'YES\\n8 6 1 2 4 5 3 7 9 '}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2 2\\n', 'output': 'YES\\n1 2 3 '}, {'type': 'stdin_stdout', 'input': '1 1\\n1\\n', 'output': 'YES\\n1 '}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 1 2 1 2\\n', 'output': 'YES\\n1 4 2 5 3 1 '}, {'type': 'stdin_stdout', 'input': '5 5\\n1 1 4 2 3\\n', 'output': 'YES\\n1 2 5 3 4\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n5 2 3 1 5\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 2 2\\n', 'output': 'YES\\n1 2 1 3 4\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n1 1 1 1 2 2 2 4 2\\n', 'output': 'YES\\n1 2 3 4 5 6 7 9 8\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 3 1 2 3 1 2 4 6\\n', 'output': 'YES\\n1 4 7 2 5 8 3 6 9 10\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 3 3 2 1 5 5 7 10\\n', 'output': 'YES\\n1 3 5 6 4 2 7 8 9 10\\n'}, {'type': 'stdin_stdout', 'input': '10 7\\n1 2 6 1 2 3 1 2 3 1\\n', 'output': 'YES\\n1 5 3 2 6 1 3 7 2 4\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 3 2 3\\n', 'output': 'YES\\n1 3 2 4\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 2 3\\n', 'output': 'YES\\n1 2 3 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n500 972 500\\n', 'output': 'YES\\n1 1 2\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n2 4 6 6 3\\n', 'output': 'YES\\n1 3 4 1 2\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 1 2 2 3 1\\n', 'output': 'YES\\n1 2 4 5 1 3\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n2017 2018 2019 2017 2018 2055 2020 2021 2022 2023\\n', 'output': 'YES\\n1 3 5 2 4 10 6 7 8 9\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n3 4 1 2 3\\n', 'output': 'YES\\n1 1 1 2 2\\n'}, {'type': 'stdin_stdout', 'input': '8 6\\n1 1 3 4 1 2 3 4\\n', 'output': 'YES\\n1 2 5 1 3 4 6 2\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n5000 494 5000\\n', 'output': 'YES\\n2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n2 1 2 2 1 3\\n', 'output': 'YES\\n3 1 4 5 2 6\\n'}, {'type': 'stdin_stdout', 'input': '12 12\\n8 8 8 8 8 8 4 4 1 4 2 2\\n', 'output': 'YES\\n7 8 9 10 11 12 4 5 1 6 2 3\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n1 1 1 2 3 4\\n', 'output': 'YES\\n1 2 3 4 5 6\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 2 2 3\\n', 'output': 'YES\\n1 2 3 4 1\\n'}, {'type': 'stdin_stdout', 'input': '8 8\\n1 1 1 1 1 2 4 3\\n', 'output': 'YES\\n1 2 3 4 5 6 8 7\\n'}, {'type': 'stdin_stdout', 'input': '8 8\\n1 2 8 2 3 2 3 3\\n', 'output': 'YES\\n1 2 8 3 5 4 6 7\\n'}, {'type': 'stdin_stdout', 'input': '8 6\\n1 1 2 2 3 4 5 4\\n', 'output': 'YES\\n1 2 3 4 5 6 2 1\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n237\\n', 'output': 'YES\\n1\\n'}, {'type': 'stdin_stdout', 'input': '8 5\\n9 3 9 6 10 4 8 2\\n', 'output': 'YES\\n1 2 2 4 3 3 5 1\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n5000 5000\\n', 'output': 'YES\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 2 3 4 3\\n', 'output': 'YES\\n1 2 3 5 4\\n'}, {'type': 'stdin_stdout', 'input': '10 5\\n1 2 3 5 1 2 3 4 1 2\\n', 'output': 'YES\\n1 4 2 5 2 5 3 4 3 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1014 2018 2018\\n', 'output': 'YES\\n1 2 1\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 3 1 2 3 4 5 10 42\\n', 'output': 'YES\\n1 3 5 2 4 6 7 8 9 10\\n'}, {'type': 'stdin_stdout', 'input': '8 8\\n1 2 2 1 1 1 1 1\\n', 'output': 'YES\\n1 7 8 2 3 4 5 6\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n7 3\\n', 'output': 'YES\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n2 1 3 1\\n', 'output': 'YES\\n3 1 4 2\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n4630 5000 5000 4999\\n', 'output': 'YES\\n1 3 4 2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n2 1 2 1 3\\n', 'output': 'YES\\n3 1 4 2 5\\n'}, {'type': 'stdin_stdout', 'input': '8 6\\n1 2 3 3 1 2 3 1\\n', 'output': 'YES\\n1 4 6 1 2 5 2 3\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\n1 2 3 2 5 5 1\\n', 'output': 'YES\\n1 3 2 1 3 1 2\\n'}, {'type': 'stdin_stdout', 'input': '7 7\\n2 1 1 1 2 3 4\\n', 'output': 'YES\\n4 1 2 3 5 6 7\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n2 2 1 2 4\\n', 'output': 'YES\\n2 3 1 4 5\\n'}, {'type': 'stdin_stdout', 'input': '50 20\\n1 1 1 1 1 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 53 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50\\n', 'output': 'YES\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9\\n'}, {'type': 'stdin_stdout', 'input': '5 3\\n3 2 1 4 3\\n', 'output': 'YES\\n3 2 1 2 1\\n'}, {'type': 'stdin_stdout', 'input': '18 18\\n10 9 8 7 5 3 6 2 2 9 7 8 2 9 2 8 3 7\\n', 'output': 'YES\\n18 15 12 9 7 5 8 1 2 16 10 13 3 17 4 14 6 11\\n'}, {'type': 'stdin_stdout', 'input': '6 5\\n1 2 3 4 5 4\\n', 'output': 'YES\\n1 2 3 4 1 5\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n2 2 2 1\\n', 'output': 'YES\\n2 3 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 1 1 4\\n', 'output': 'YES\\n1 4 2 3 1\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n3 2 2 2 3\\n', 'output': 'YES\\n4 1 2 3 1\\n'}, {'type': 'stdin_stdout', 'input': '6 4\\n1 1 2 3 3 3\\n', 'output': 'YES\\n1 2 3 4 1 2\\n'}, {'type': 'stdin_stdout', 'input': '6 3\\n2 1 3 3 5 1\\n', 'output': 'YES\\n3 1 1 2 3 2\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 3 2\\n', 'output': 'YES\\n1 3 2\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n1 2 3 2 1\\n', 'output': 'YES\\n1 3 1 4 2\\n'}, {'type': 'stdin_stdout', 'input': '9 9\\n1 1 1 1 2 2 2 1 2\\n', 'output': 'YES\\n1 2 3 4 6 7 8 5 9\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 3 1 2 3 2 2 4 6\\n', 'output': 'YES\\n1 3 7 2 4 8 5 6 9 10\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n1 2 3 3 2 2 5 5 7 10\\n', 'output': 'YES\\n1 2 5 6 3 4 7 8 9 10\\n'}, {'type': 'stdin_stdout', 'input': '4 2\\n1 3 2 3\\n', 'output': 'YES\\n1 1 2 2\\n'}, {'type': 'stdin_stdout', 'input': '10 10\\n2017 2018 2019 2017 2018 2055 2020 3169 2022 2023\\n', 'output': 'YES\\n1 3 5 2 4 9 6 10 7 8\\n'}, {'type': 'stdin_stdout', 'input': '8 6\\n1 1 3 4 1 2 3 3\\n', 'output': 'YES\\n1 2 5 2 3 4 6 1\\n'}, {'type': 'stdin_stdout', 'input': '12 12\\n8 8 8 8 8 8 8 4 1 4 2 2\\n', 'output': 'YES\\n6 7 8 9 10 11 12 4 1 5 2 3\\n'}, {'type': 'stdin_stdout', 'input': '8 6\\n9 3 9 6 10 4 8 2\\n', 'output': 'YES\\n6 2 1 4 2 3 5 1\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 2 3 1 3\\n', 'output': 'YES\\n1 3 4 2 5\\n'}, {'type': 'stdin_stdout', 'input': '8 8\\n2 2 2 1 1 1 1 1\\n', 'output': 'YES\\n6 7 8 1 2 3 4 5\\n'}, {'type': 'stdin_stdout', 'input': '8 4\\n1 2 3 3 1 2 3 1\\n', 'output': 'YES\\n1 4 2 3 2 1 4 3\\n'}, {'type': 'stdin_stdout', 'input': '7 3\\n1 2 3 3 5 5 1\\n', 'output': 'YES\\n1 3 1 2 3 1 2\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n1 1 1 2 2 3\\n', 'output': 'YES\\n1 2 3 4 5 6\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 1 3 1 2\\n', 'output': 'YES\\n1 2 5 3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n2 1 2 1\\n', 'output': 'YES\\n3 1 4 2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 1 3 1 1\\n', 'output': 'YES\\n1 2 5 3 4\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n2000 2000 2000 3\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2019 2019 393\\n', 'output': 'YES\\n2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5 2\\n0 1 1 2 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 1\\n5 1 3 1 5\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2 2 5\\n', 'output': 'YES\\n1 2 3 1\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n500 1174 500\\n', 'output': 'YES\\n1 1 2\\n'}, {'type': 'stdin_stdout', 'input': '5 4\\n2 6 6 6 3\\n', 'output': 'YES\\n1 3 4 1 2\\n'}, {'type': 'stdin_stdout', 'input': '6 1\\n1 1 2 2 3 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n5000 494 567\\n', 'output': 'YES\\n1 1 2\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n1072 2018 2018\\n', 'output': 'YES\\n1 2 1\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n1 3\\n', 'output': 'YES\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 6\\n1 1 2 2 2 3\\n', 'output': 'YES\\n1 2 3 4 5 6\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80461","program":"```python\nfrom collections import defaultdict\nn,k=map(int,input().split())\narr=list(map(int,input().split()))\ntemp=[0]*5001\nfor i in arr:\n temp[i]+=1\nif(max(temp)>k):\n print('NO')\nelif(k>n):\n print('NO')\nelse:\n print('YES')\n d=defaultdict(list)\n c=0\n t=[0]*n\n for i in range(n):\n t[i]=arr[i]\n t.sort()\n for i in range(len(t)):\n d[t[i]].append(c+1)\n c=(c+1)%k\n p=[0]*5001\n for i in range(len(arr)):\n print(d[arr[i]][p[arr[i]]],end=' ')\n p[arr[i]]+=1\n\n\n\n\n\n\n```","inputs":"5 2\n2 1 1 2 1\n","output":"NO\n","actual_output":"NO\n","execution_success":true,"sample_index":12808},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1130_B. Two Cakes","prompt":"Solve the following coding problem using the programming language python:\n\nSasha and Dima want to buy two n-tier cakes. Each cake should consist of n different tiers: from the size of 1 to the size of n. Tiers should go in order from the smallest to the biggest (from top to bottom).\n\nThey live on the same street, there are 2 \u22c5 n houses in a row from left to right. Each house has a pastry shop where you can buy a cake tier. Unfortunately, in each pastry shop you can buy only one tier of only one specific size: in the i-th house you can buy a tier of the size a_i (1 \u2264 a_i \u2264 n).\n\nSince the guys carry already purchased tiers, and it is impossible to insert a new tier in the middle of the cake, they agreed to buy tiers from the smallest to the biggest. That is, each of them buys tiers in order: 1, then 2, then 3 and so on up to n.\n\nInitially, Sasha and Dima are located near the first (leftmost) house. Output the minimum distance that they will have to walk in total to buy both cakes. The distance between any two neighboring houses is exactly 1.\n\nInput\n\nThe first line of the input contains an integer number n \u2014 the number of tiers in each cake (1 \u2264 n \u2264 10^5).\n\nThe second line contains 2 \u22c5 n integers a_1, a_2, ..., a_{2n} (1 \u2264 a_i \u2264 n), where a_i is equal to the size of the tier, which can be bought in the i-th house. Remember that in each house you can buy only one tier. It is guaranteed that every number from 1 to n occurs in a exactly two times.\n\nOutput\n\nPrint one number \u2014 the minimum distance that the guys have to walk in total to buy both cakes. Guys can be near same house at the same time. They begin near the first (leftmost) house. Each of the guys should buy n tiers in ascending order of their sizes.\n\nExamples\n\nInput\n\n\n3\n1 1 2 2 3 3\n\n\nOutput\n\n\n9\n\n\nInput\n\n\n2\n2 1 1 2\n\n\nOutput\n\n\n5\n\n\nInput\n\n\n4\n4 1 3 2 2 3 1 4\n\n\nOutput\n\n\n17\n\nNote\n\nIn the first example, the possible optimal sequence of actions is:\n\n * Sasha buys a tier of size 1 near the 1-st house (a_1=1); \n * Dima goes to the house 2; \n * Dima buys a tier of size 1 near the 2-nd house (a_2=1); \n * Sasha goes to the house 4; \n * Sasha buys a tier of size 2 near the 4-th house (a_4=2); \n * Sasha goes to the house 5; \n * Sasha buys a tier of size 3 near the 5-th house (a_5=3); \n * Dima goes to the house 3; \n * Dima buys a tier of size 2 near the 3-rd house (a_3=2); \n * Dima goes to the house 6; \n * Dima buys a tier of size 3 near the 6-th house (a_6=3). \n\n\n\nSo, Sasha goes the distance 3+1=4, and Dima goes the distance 1+1+3=5. In total, they cover a distance of 4+5=9. You can make sure that with any other sequence of actions they will walk no less distance.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nl2=[]\nn=int(input())\nl=list(map(int,input().split()))\nfor i in range(2*n):\n l2.append([l[i],i])\nl2.sort()\nsd,dd=l2[0][1],l2[1][1]\nfor i in range(2,2*n):\n if i%2:\n dd+=abs(l2[i][1]-l2[i-2][1])\n else:\n sd+=abs(l2[i][1]-l2[i-2][1])\nprint(sd+dd)\n \n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n4 1 3 2 2 3 1 4\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 2 2 3 3\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 1 2\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 3 2 1 2\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 4 3 1 1 3 2 4\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '6\\n6 4 5 2 6 4 3 3 1 2 1 5\\n', 'output': '52\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 2 1 2 3 5 4 3 1 4\\n', 'output': '37\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3 2 1 1 4 2 3 4\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '7\\n4 2 3 2 7 1 3 1 4 7 5 5 6 6\\n', 'output': '57\\n'}, {'type': 'stdin_stdout', 'input': '8\\n4 5 7 8 2 7 6 3 6 1 1 3 5 8 4 2\\n', 'output': '74\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 2 1 1 3 2\\n', 'output': '10\\n'}, {'type': 'stdin_stdout', 'input': '6\\n4 2 3 5 2 5 1 6 6 4 3 1\\n', 'output': '53\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3 1 2 5 1 5 3 2 4 4\\n', 'output': '32\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 3 6 1 4 9 2 8 3 4 8 7 5 7 2 5 9 6\\n', 'output': '89\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 2 1 1\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1 2 2\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '10\\n8 8 3 9 7 1 9 6 10 6 4 2 7 3 4 10 5 5 1 2\\n', 'output': '123\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 3 2 2 1\\n', 'output': '13\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 1 3 1 2 3 2 4\\n', 'output': '17\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 2 1 1 3 5 4 3 2 4\\n', 'output': '29\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3 1 2 1 4 2 3 4\\n', 'output': '15\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 3 3 1 2\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2 1 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 4 3 1 2 3 1 4\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '7\\n7 2 3 2 7 1 3 1 4 4 5 5 6 6\\n', 'output': '62\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 1 2 3 3\\n', 'output': '9\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 1 3 2 1 3 2 4\\n', 'output': '15\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80465","program":"```python\nl2=[]\nn=int(input())\nl=list(map(int,input().split()))\nfor i in range(2*n):\n l2.append([l[i],i])\nl2.sort()\nsd,dd=l2[0][1],l2[1][1]\nfor i in range(2,2*n):\n if i%2:\n dd+=abs(l2[i][1]-l2[i-2][1])\n else:\n sd+=abs(l2[i][1]-l2[i-2][1])\nprint(sd+dd)\n \n```","inputs":"4\n4 1 3 2 2 3 1 4\n","output":"17\n","actual_output":"17\n","execution_success":true,"sample_index":12809},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1150_C. Prefix Sum Primes","prompt":"Solve the following coding problem using the programming language python:\n\nWe're giving away nice huge bags containing number tiles! A bag we want to present to you contains n tiles. Each of them has a single number written on it \u2014 either 1 or 2.\n\nHowever, there is one condition you must fulfill in order to receive the prize. You will need to put all the tiles from the bag in a sequence, in any order you wish. We will then compute the sums of all prefixes in the sequence, and then count how many of these sums are prime numbers. If you want to keep the prize, you will need to maximize the number of primes you get.\n\nCan you win the prize? Hurry up, the bags are waiting!\n\nInput\n\nThe first line of the input contains a single integer n (1 \u2264 n \u2264 200 000) \u2014 the number of number tiles in the bag. The following line contains n space-separated integers a_1, a_2, ..., a_n (a_i \u2208 \\{1, 2\\}) \u2014 the values written on the tiles.\n\nOutput\n\nOutput a permutation b_1, b_2, ..., b_n of the input sequence (a_1, a_2, ..., a_n) maximizing the number of the prefix sums being prime numbers. If there are multiple optimal permutations, output any.\n\nExamples\n\nInput\n\n\n5\n1 2 1 2 1\n\n\nOutput\n\n\n1 1 1 2 2\n\n\nInput\n\n\n9\n1 1 2 1 1 1 2 1 1\n\n\nOutput\n\n\n1 1 1 2 1 1 1 2 1\n\nNote\n\nThe first solution produces the prefix sums 1, \\mathbf{\\color{blue}{2}}, \\mathbf{\\color{blue}{3}}, \\mathbf{\\color{blue}{5}}, \\mathbf{\\color{blue}{7}} (four primes constructed), while the prefix sums in the second solution are 1, \\mathbf{\\color{blue}{2}}, \\mathbf{\\color{blue}{3}}, \\mathbf{\\color{blue}{5}}, 6, \\mathbf{\\color{blue}{7}}, 8, 10, \\mathbf{\\color{blue}{11}} (five primes). Primes are marked bold and blue. In each of these cases, the number of produced primes is maximum possible.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\nl=list(map(int,input().split()))\nn1,n2=0,0\nfor i in l:\n if i==1:\n n1+=1\n else:\n n2+=1\n\n\nr=[]\nif n1==0 or n2==0:\n r=l\nelse:\n r.append(2)\n r.append(1)\n n1-=1\n n2-=1\n while n2!=0:\n r.append(2)\n n2-=1\n while n1!=0:\n r.append(1)\n n1-=1\n\nfor i in range(n):\n print(r[i],end=\" \")\nprint()\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 1 1 2 1 1\\n', 'output': '2 1 2 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 1 2 1\\n', 'output': '2 1 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 2 2 2\\n', 'output': '2 1 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 2\\n', 'output': '2 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 2\\n', 'output': '2 1 2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1\\n', 'output': '1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 1 2 1 1 1 2 2 2\\n', 'output': '2 1 2 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '41\\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2\\n', 'output': '2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 1 1 2 2 2 2 2 2\\n', 'output': '2 1 2 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2\\n', 'output': '2 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 2\\n', 'output': '2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 1 1\\n', 'output': '1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 1 2 2\\n', 'output': '2 1 2 2 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1 1\\n', 'output': '1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 2 2\\n', 'output': '2 1 2 2\\n'}, {'type': 'stdin_stdout', 'input': '214\\n1 2 2 1 1 1 2 2 2 2 1 1 1 2 2 2 2 2 2 1 2 1 1 2 2 1 1 2 2 2 2 1 2 2 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 2 2 1 2 1 2 1 1 2 2 1 1 2 1 2 2 2 2 2 2 2 1 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 2 2 2 2 1 2 2 2 1 1 2 2 2 2 2 2 1 2 2 2 2 1 1 1 2 2 2 1 2 1 2 1 1 2 1 1 1 2 2 2 1 2 2 2 2 2 2 2 1 2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 1 1 2 2 1 2 1 2 1\\n', 'output': '2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 2 2 2\\n', 'output': '2 2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 2 1\\n', 'output': '2 1 2 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 1 1 1\\n', 'output': '2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 1 1 1\\n', 'output': '2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 2 2 2\\n', 'output': '2 1 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 1\\n', 'output': '2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 2 2 1\\n', 'output': '2 1 2 2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 1 2 1\\n', 'output': '2 1 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 1 1 1 1 1\\n', 'output': '2 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 2 2 2\\n', 'output': '2 1 2 2 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 1 1 1 2 1\\n', 'output': '2 1 2 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 2 1 1 2 1\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 2 1 2 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 1 2 1 1 2 2 2 2\\n', 'output': '2 1 2 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 1 1 2 2 2 2 2 2\\n', 'output': '2 1 2 2 2 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 2\\n', 'output': '2 1 2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 1 1 2 1 2 2 2 2\\n', 'output': '2 1 2 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 1 1\\n', 'output': '2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 2\\n', 'output': '2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 2 1 1\\n', 'output': '2 1 2 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 2 2 1 1 2 1\\n', 'output': '2 1 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 1 1 1 1 2 2 2 2\\n', 'output': '2 1 2 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 2 2 1 1 2 2\\n', 'output': '2 1 2 2 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1\\n', 'output': '2 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 2 2 2\\n', 'output': '2 2 2 2\\n'}, {'type': 'stdin_stdout', 'input': '214\\n1 2 2 1 1 1 2 2 2 2 1 1 1 2 2 2 2 2 2 1 2 1 1 2 2 1 1 2 2 2 2 1 2 2 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 2 2 1 2 1 2 1 1 2 2 1 1 2 1 2 2 2 2 2 2 2 1 2 1 2 2 1 2 2 2 1 2 2 1 2 1 1 2 2 2 2 1 2 2 2 1 1 2 2 2 2 2 2 1 2 2 2 2 1 1 1 2 2 2 1 2 1 2 1 1 2 1 1 1 2 2 2 1 2 2 2 2 2 2 2 1 2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 1 1 2 2 1 2 1 2 1\\n', 'output': '2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 1 2\\n', 'output': '2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 1 1\\n', 'output': '2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 1 2 1 1 1\\n', 'output': '2 1 2 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 1 2 1 1 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 1 2 1 2 1 2 2 2\\n', 'output': '2 1 2 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 1\\n', 'output': '2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 1 1 2 1 2\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 2 2 1\\n', 'output': '2 1 2 2 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 1 2 1\\n', 'output': '2 1 2 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 2 1 2\\n', 'output': '2 1 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 1 1 1 1 2 1\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 2 2 1 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 1 1 2\\n', 'output': '2 1 2 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 1\\n', 'output': '2 1 2\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 2 1 2\\n', 'output': '2 1 2 2 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 2 1 1 1 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 2 2 2 1 1 1 2 1\\n', 'output': '2 1 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 1 1 1 2 1 1\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n1 1 2 2\\n', 'output': '2 1 2 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 1 1 1 1 2\\n', 'output': '2 1 2 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 1 2 1 1 1 1 2 1\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 1 2 1 2 1 2 2 1\\n', 'output': '2 1 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 1 2 1 2 2 1\\n', 'output': '2 1 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 1 1 2 2 1 2 1\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 1 2 2\\n', 'output': '2 1 2 2\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 2 2 2 2 1 1 2 1\\n', 'output': '2 1 2 2 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 1 1 1 1 1 2\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 1 2 1 1 2 1 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 1 1 2 1 2 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 1 1 2 1 1 2\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 1 1 1 1 2 2 1\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 1 1 1 2 1 1 2\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 1 2 1 1 2 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 1 1 2 1 1 1 2 2 2\\n', 'output': '2 1 2 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 1 1 2 2 2 2 2 1\\n', 'output': '2 1 2 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 1 2 2\\n', 'output': '2 1 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 2 1 2 1\\n', 'output': '2 1 2 2 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 1 1 1 1 1 1\\n', 'output': '2 1 2 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 1 2 1 2 1 1 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 2 1 1 2 1 2 2 2 2\\n', 'output': '2 1 2 2 2 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 1 1 2 1 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 2 2 2 2 1\\n', 'output': '2 1 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 2 1 1\\n', 'output': '2 1 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 1 1 1 1 1 1 2 1\\n', 'output': '2 1 2 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 1 1 2 1 2 2 2 2\\n', 'output': '2 1 2 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 2 2 1 2 1 2 2 1\\n', 'output': '2 1 2 2 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 2 1 2 2 1 1 2 1\\n', 'output': '2 1 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 1 1 2 2 1 2\\n', 'output': '2 1 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 1 2 1 1 2 2 2 1\\n', 'output': '2 1 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 1 1 2 1 2 2 1\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 2 1 1 1 1 2 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 1 1 1 2 1 1 2\\n', 'output': '2 1 2 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 2 2 1 1 1 2 2 1\\n', 'output': '2 1 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 1 1 2 2 2 1 2 1\\n', 'output': '2 1 2 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 1 2 2 1\\n', 'output': '2 1 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 2 1 1 1 1 1\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 2 1 1 2 1 2 2 1 2\\n', 'output': '2 1 2 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n2 1 2 1 2 2 2 2 1\\n', 'output': '2 1 2 2 2 2 2 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 2 2 1 1 1 2 1 2\\n', 'output': '2 1 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 1 1 2 2 2 1 2 1\\n', 'output': '2 1 2 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 2 2 1 2 2 2 1 2 1\\n', 'output': '2 1 2 2 2 2 2 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 2 2 1\\n', 'output': '2 1 2 2 1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 1 1 2 2 2 2 1 2\\n', 'output': '2 1 2 2 2 2 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 2 1 2 1 1\\n', 'output': '2 1 2 2 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 1 1 1 1 1 2 1\\n', 'output': '2 1 1 1 1 1 1 1 1\\n'}, {'type': 'stdin_stdout', 'input': '9\\n1 1 2 1 2 1 2 2 2\\n', 'output': '2 1 2 2 2 2 1 1 1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80469","program":"```python\nn=int(input())\nl=list(map(int,input().split()))\nn1,n2=0,0\nfor i in l:\n if i==1:\n n1+=1\n else:\n n2+=1\n\n\nr=[]\nif n1==0 or n2==0:\n r=l\nelse:\n r.append(2)\n r.append(1)\n n1-=1\n n2-=1\n while n2!=0:\n r.append(2)\n n2-=1\n while n1!=0:\n r.append(1)\n n1-=1\n\nfor i in range(n):\n print(r[i],end=\" \")\nprint()\n\n\n```","inputs":"9\n1 1 2 1 1 1 2 1 1\n","output":"2 1 2 1 1 1 1 1 1\n","actual_output":"2 1 2 1 1 1 1 1 1 \n","execution_success":true,"sample_index":12810},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1172_C2. Nauuo and Pictures (hard version)","prompt":"Solve the following coding problem using the programming language python:\n\nThe only difference between easy and hard versions is constraints.\n\nNauuo is a girl who loves random picture websites.\n\nOne day she made a random picture website by herself which includes n pictures.\n\nWhen Nauuo visits the website, she sees exactly one picture. The website does not display each picture with equal probability. The i-th picture has a non-negative weight w_i, and the probability of the i-th picture being displayed is \\frac{w_i}{\u2211_{j=1}^nw_j}. That is to say, the probability of a picture to be displayed is proportional to its weight.\n\nHowever, Nauuo discovered that some pictures she does not like were displayed too often. \n\nTo solve this problem, she came up with a great idea: when she saw a picture she likes, she would add 1 to its weight; otherwise, she would subtract 1 from its weight.\n\nNauuo will visit the website m times. She wants to know the expected weight of each picture after all the m visits modulo 998244353. Can you help her?\n\nThe expected weight of the i-th picture can be denoted by \\frac {q_i} {p_i} where \\gcd(p_i,q_i)=1, you need to print an integer r_i satisfying 0\u2264 r_i<998244353 and r_i\u22c5 p_i\u2261 q_i\\pmod{998244353}. It can be proved that such r_i exists and is unique.\n\nInput\n\nThe first line contains two integers n and m (1\u2264 n\u2264 2\u22c5 10^5, 1\u2264 m\u2264 3000) \u2014 the number of pictures and the number of visits to the website.\n\nThe second line contains n integers a_1,a_2,\u2026,a_n (a_i is either 0 or 1) \u2014 if a_i=0 , Nauuo does not like the i-th picture; otherwise Nauuo likes the i-th picture. It is guaranteed that there is at least one picture which Nauuo likes.\n\nThe third line contains n positive integers w_1,w_2,\u2026,w_n (w_i \u2265 1) \u2014 the initial weights of the pictures. It is guaranteed that the sum of all the initial weights does not exceed 998244352-m.\n\nOutput\n\nThe output contains n integers r_1,r_2,\u2026,r_n \u2014 the expected weights modulo 998244353.\n\nExamples\n\nInput\n\n\n2 1\n0 1\n2 1\n\n\nOutput\n\n\n332748119\n332748119\n\n\nInput\n\n\n1 2\n1\n1\n\n\nOutput\n\n\n3\n\n\nInput\n\n\n3 3\n0 1 1\n4 3 5\n\n\nOutput\n\n\n160955686\n185138929\n974061117\n\nNote\n\nIn the first example, if the only visit shows the first picture with a probability of \\frac 2 3, the final weights are (1,1); if the only visit shows the second picture with a probability of \\frac1 3, the final weights are (2,2).\n\nSo, both expected weights are \\frac2 3\u22c5 1+\\frac 1 3\u22c5 2=\\frac4 3 .\n\nBecause 332748119\u22c5 3\u2261 4\\pmod{998244353}, you need to print 332748119 instead of \\frac4 3 or 1.3333333333.\n\nIn the second example, there is only one picture which Nauuo likes, so every time Nauuo visits the website, w_1 will be increased by 1.\n\nSo, the expected weight is 1+2=3.\n\nNauuo is very naughty so she didn't give you any hint of the third example.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nP = 998244353\nN, M = map(int, input().split())\nA = [int(a) for a in input().split()]\nB = [int(a) for a in input().split()]\nli = sum([A[i]*B[i] for i in range(N)])\ndi = sum([(A[i]^1)*B[i] for i in range(N)])\nX = [1]\nSU = li+di\nPO = [0] * (5*M+10)\nfor i in range(-M-5, 2*M+5):\n PO[i] = pow((SU+i)%P, P-2, P)\n\ndef calc(L):\n su = sum(L)\n pl = 0\n pd = 0\n RE = []\n for i in range(len(L)):\n a = li + i\n b = di - (len(L) - 1 - i)\n pd = b * L[i] * PO[a+b-SU]\n RE.append((pl+pd)%P)\n pl = a * L[i] * PO[a+b-SU]\n RE.append(pl%P)\n return RE\n\nfor i in range(M):\n X = calc(X)\nne = 0\npo = 0\nfor i in range(M+1):\n po = (po + X[i] * (li + i)) % P\n ne = (ne + X[i] * (di - M + i)) % P\ninvli = pow(li, P-2, P)\ninvdi = pow(di, P-2, P)\nfor i in range(N):\n print(po * B[i] * invli % P if A[i] else ne * B[i] * invdi % P)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 1\\n0 1\\n2 1\\n', 'output': '332748119\\n332748119\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n0 1 1\\n4 3 5\\n', 'output': '160955686\\n185138929\\n974061117\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n1\\n1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 2 1 3 1 4 1 5 1 1 2 3 1 1 3 3 2 2 1 2\\n', 'output': '902255482\\n806266611\\n902255482\\n710277740\\n902255482\\n537377994\\n902255482\\n518299998\\n902255482\\n902255482\\n806266611\\n710277740\\n902255482\\n902255482\\n710277740\\n710277740\\n806266611\\n806266611\\n902255482\\n806266611\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n126679203 179924771 16639504 67055540 14134870 36407782 15024189 39367944 121531542 5400023 5834434 8539193 3686913 11287136 36370086 71808281 138206490 59846864 19052959 21446598\\n', 'output': '615913610\\n488825486\\n773371096\\n742795989\\n193664548\\n323188752\\n32686082\\n709701410\\n293733249\\n161181348\\n193396792\\n354491196\\n708550409\\n644392716\\n323187536\\n646345011\\n487479735\\n1930544\\n322628919\\n966734748\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0\\n34095514 37349809 60555988 40280455 19504485 77297461 41415742 66290058 20631093 185280391 7151718 64927972 15611855 4317891 24600598 24588269 60808977 9108470 13217752 191209824\\n', 'output': '313283482\\n21804622\\n682197550\\n361027027\\n756362680\\n151917509\\n716108102\\n131732975\\n237068086\\n731869119\\n190595295\\n847684643\\n847454143\\n501579235\\n129856516\\n246699402\\n205385635\\n639100445\\n614421017\\n227076269\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n1 1 3 2 1 3 2 1 1 2 1 1 2 2 4 2 1 5 2 3\\n', 'output': '249561090\\n249561090\\n748683270\\n499122180\\n249561090\\n748683270\\n499122180\\n249561090\\n249561090\\n499122180\\n249561090\\n249561090\\n499122180\\n499122180\\n7\\n499122180\\n249561090\\n249561097\\n499122180\\n748683270\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661 26210661\\n', 'output': '76898501\\n989279651\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n76898501\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0\\n1 1 3 2 3 1 2 2 3 2 2 2 2 2 2 3 3 1 1 2\\n', 'output': '550803098\\n550803098\\n654164941\\n103361843\\n654164941\\n550803098\\n103361843\\n103361843\\n654164941\\n103361843\\n103361843\\n103361843\\n103361843\\n103361843\\n276551708\\n654164941\\n654164941\\n138275854\\n550803098\\n103361843\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0\\n9380933 34450681 12329733 7732927 73910078 16165679 149467043 56914401 21809098 36934833 71019254 168559440 12033996 40465391 7156881 3312348 37150678 130625432 42709585 66115911\\n', 'output': '813231583\\n458087744\\n445793615\\n651101155\\n484645642\\n506668954\\n896602699\\n556862659\\n145127201\\n302005399\\n558418033\\n213871822\\n57299634\\n564466143\\n767349204\\n290138481\\n12657688\\n925337836\\n827843024\\n119362169\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1\\n144831196 28660251 62050800 52660762 23189000 12771861 73096012 25119113 119648684 16011144 51600638 74708999 6312006 26945863 68746869 58112898 5070 19157938 74351320 60263898\\n', 'output': '132556548\\n711988928\\n6999755\\n208709864\\n320161276\\n865416376\\n320896979\\n458941660\\n671806481\\n158009043\\n351362956\\n78248147\\n927871852\\n882014191\\n988190329\\n830735503\\n1958329\\n787106839\\n942059547\\n341315444\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n0 1 0 0 1\\n2 4 1 2 1\\n', 'output': '665717847\\n333191345\\n831981100\\n665717847\\n831981101\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803 5766803\\n', 'output': '504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n504888981\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0\\n3 4 1 2 1 1 1 2 5 2 1 2 3 1 1 2 3 2 1 2\\n', 'output': '441078046\\n920852179\\n479774133\\n959548266\\n479774133\\n479774133\\n479774133\\n959548266\\n402381959\\n263018694\\n479774133\\n959548266\\n441078046\\n479774133\\n479774133\\n959548266\\n441078046\\n959548266\\n479774133\\n959548266\\n'}, {'type': 'stdin_stdout', 'input': '20 20\\n0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0\\n109 1 24 122 136 42 25 112 110 15 26 48 35 10 86 13 41 6 24 15\\n', 'output': '217595927\\n149660176\\n322657182\\n290143118\\n388896876\\n296261274\\n86540143\\n507489163\\n979723241\\n248413934\\n896431517\\n195977977\\n246884395\\n633562669\\n891842900\\n947337935\\n146601098\\n897961056\\n597111165\\n451221827\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0\\n61 849 320 1007 624 441 1332 3939 1176 718 419 634 657 914 858 882 1019 1567 62 2521\\n', 'output': '514012356\\n393871659\\n166092575\\n569465276\\n74319433\\n306884170\\n254628439\\n656312237\\n485609669\\n216694535\\n825782618\\n110704962\\n294216114\\n131255421\\n733108087\\n613768340\\n14181299\\n610566194\\n624888021\\n887363731\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0\\n244 1901 938 1350 1010 763 318 2158 1645 534 1356 563 295 1449 2306 224 1302 195 639 810\\n', 'output': '300071414\\n595185476\\n40756239\\n113904636\\n440148868\\n947268885\\n456535325\\n542868956\\n183161324\\n427608407\\n61171180\\n375813928\\n43680359\\n55509680\\n30410255\\n360521133\\n535772284\\n722568686\\n663107799\\n390646234\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n0 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1\\n1 2 2 2 2 2 1 1 2 1 4 1 2 5 3 4 1 1 2 1\\n', 'output': '297511613\\n595023226\\n756311680\\n756311680\\n756311680\\n595023226\\n297511613\\n378155840\\n595023226\\n297511613\\n514379007\\n297511613\\n595023226\\n892534847\\n136223167\\n514379007\\n378155840\\n297511613\\n595023226\\n378155840\\n'}, {'type': 'stdin_stdout', 'input': '100 3000\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n10 8 1 9 7 5 12 9 15 7 16 5 17 5 17 21 11 3 4 4 30 17 3 84 12 30 2 8 2 2 22 24 15 11 15 13 7 17 1 12 8 4 3 6 5 15 1 3 4 2 27 3 11 11 3 3 3 5 14 2 5 13 6 2 6 5 6 19 3 16 4 12 11 2 2 3 25 14 6 11 22 4 10 32 9 19 14 2 2 3 4 3 2 5 18 14 2 7 3 8\\n', 'output': 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'415389157\\n280934094\\n7121772\\n694921751\\n281736164\\n371678270\\n878152076\\n105305203\\n325645818\\n290496673\\n396144757\\n837661602\\n675958772\\n344770976\\n886509402\\n743356540\\n908620256\\n571430767\\n114550299\\n417969788\\n'}, {'type': 'stdin_stdout', 'input': '20 30\\n1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1\\n1078 1317 1275 234 857 1531 785 265 679 767 678 16 918 1146 1137 71 813 245 6580 489\\n', 'output': '204038033\\n933599876\\n951578767\\n898076246\\n465015304\\n509245028\\n495836260\\n52935818\\n873959674\\n503541499\\n708013684\\n658647134\\n605016041\\n507677470\\n12407913\\n801477407\\n151102215\\n726993430\\n843536371\\n289796517\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 4, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80473","program":"```python\nP = 998244353\nN, M = map(int, input().split())\nA = [int(a) for a in input().split()]\nB = [int(a) for a in input().split()]\nli = sum([A[i]*B[i] for i in range(N)])\ndi = sum([(A[i]^1)*B[i] for i in range(N)])\nX = [1]\nSU = li+di\nPO = [0] * (5*M+10)\nfor i in range(-M-5, 2*M+5):\n PO[i] = pow((SU+i)%P, P-2, P)\n\ndef calc(L):\n su = sum(L)\n pl = 0\n pd = 0\n RE = []\n for i in range(len(L)):\n a = li + i\n b = di - (len(L) - 1 - i)\n pd = b * L[i] * PO[a+b-SU]\n RE.append((pl+pd)%P)\n pl = a * L[i] * PO[a+b-SU]\n RE.append(pl%P)\n return RE\n\nfor i in range(M):\n X = calc(X)\nne = 0\npo = 0\nfor i in range(M+1):\n po = (po + X[i] * (li + i)) % P\n ne = (ne + X[i] * (di - M + i)) % P\ninvli = pow(li, P-2, P)\ninvdi = pow(di, P-2, P)\nfor i in range(N):\n print(po * B[i] * invli % P if A[i] else ne * B[i] * invdi % P)\n\n```","inputs":"2 1\n0 1\n2 1\n","output":"332748119\n332748119\n","actual_output":"332748119\n332748119\n","execution_success":true,"sample_index":12811},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"118_E. Bertown roads","prompt":"Solve the following coding problem using the programming language python:\n\nBertown has n junctions and m bidirectional roads. We know that one can get from any junction to any other one by the existing roads. \n\nAs there were more and more cars in the city, traffic jams started to pose real problems. To deal with them the government decided to make the traffic one-directional on all the roads, thus easing down the traffic. Your task is to determine whether there is a way to make the traffic one-directional so that there still is the possibility to get from any junction to any other one. If the answer is positive, you should also find one of the possible ways to orient the roads.\n\nInput\n\nThe first line contains two space-separated integers n and m (2 \u2264 n \u2264 105, n - 1 \u2264 m \u2264 3\u00b7105) which represent the number of junctions and the roads in the town correspondingly. Then follow m lines, each containing two numbers which describe the roads in the city. Each road is determined by two integers ai and bi (1 \u2264 ai, bi \u2264 n, ai \u2260 bi) \u2014 the numbers of junctions it connects.\n\nIt is guaranteed that one can get from any junction to any other one along the existing bidirectional roads. Each road connects different junctions, there is no more than one road between each pair of junctions.\n\nOutput\n\nIf there's no solution, print the single number 0. Otherwise, print m lines each containing two integers pi and qi \u2014 each road's orientation. That is the traffic flow will move along a one-directional road from junction pi to junction qi. You can print the roads in any order. If there are several solutions to that problem, print any of them.\n\nExamples\n\nInput\n\n6 8\n1 2\n2 3\n1 3\n4 5\n4 6\n5 6\n2 4\n3 5\n\n\nOutput\n\n1 2\n2 3\n3 1\n4 5\n5 6\n6 4\n4 2\n3 5\n\n\nInput\n\n6 7\n1 2\n2 3\n1 3\n4 5\n4 6\n5 6\n2 4\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom sys import stdin,setrecursionlimit\nimport threading\ninput = lambda: stdin.readline().rstrip(\"\\r\\n\")\nfrom collections import deque as que\ninin = lambda: int(input())\ninar = lambda: list(map(int,input().split()))\nfrom types import GeneratorType\n\n\ndef bootstrap(f, stack=[]):\n def wrappedfunc(*args, **kwargs):\n if stack:\n return f(*args, **kwargs)\n else:\n to = f(*args, **kwargs)\n while True:\n if type(to) is GeneratorType:\n stack.append(to)\n to = next(to)\n else:\n stack.pop()\n if not stack:\n break\n to = stack[-1].send(to)\n return to\n\n return wrappedfunc\n\nfrom collections import defaultdict\nadj=defaultdict(list)\nvisited=[False]*(100001)\nintime=[0]*(100001)\nouttime=[0]*(100001)\nres=[]\nbridge=False\ntimer=0\n@bootstrap\ndef dfs(node,par):\n global adj, visited, intime, outtime, res, bridge,timer\n visited[node]=True\n intime[node]=timer\n outtime[node]=timer\n timer+=1\n for j in adj[node]:\n if j==par:\n continue\n if visited[j]:\n outtime[node]=min(outtime[node],intime[j])\n if intime[node]>intime[j]:\n res.append((node,j))\n else:\n yield dfs(j,node)\n if outtime[j]>intime[node]:\n bridge=True\n yield None\n \n res.append((node,j))\n outtime[node] = min(outtime[node], outtime[j])\n yield\ndef main():\n n,m=map(int,input().split())\n global adj,visited,intime,outtime,res,bridge,timer\n timer=0\n bridge=False\n for i in range(m):\n u,v=map(int,input().split())\n adj[u].append(v)\n adj[v].append(u)\n dfs(1,-1)\n if bridge:\n print(0)\n else:\n for i in range(len(res)):\n print(*res[i])\n\nmain()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6 7\\n1 2\\n2 3\\n1 3\\n4 5\\n4 6\\n5 6\\n2 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n1 2\\n2 3\\n1 3\\n4 5\\n4 6\\n5 6\\n2 4\\n3 5\\n', 'output': '3 1\\n6 5\\n4 6\\n4 2\\n5 4\\n3 5\\n2 3\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '18 75\\n17 1\\n13 18\\n15 11\\n6 3\\n18 16\\n9 18\\n6 15\\n6 14\\n10 7\\n17 16\\n12 6\\n15 13\\n5 1\\n4 13\\n8 1\\n11 5\\n16 9\\n3 2\\n4 16\\n4 18\\n12 9\\n8 11\\n5 18\\n5 3\\n7 11\\n2 11\\n14 16\\n16 15\\n13 6\\n10 8\\n6 7\\n7 4\\n12 16\\n1 14\\n8 4\\n11 17\\n3 7\\n3 8\\n14 4\\n7 17\\n13 9\\n9 7\\n17 13\\n4 6\\n6 5\\n5 16\\n18 3\\n4 3\\n8 18\\n6 16\\n7 18\\n9 3\\n17 5\\n2 5\\n16 7\\n15 7\\n12 4\\n5 4\\n1 16\\n1 7\\n11 3\\n5 10\\n13 5\\n4 10\\n9 5\\n8 13\\n10 18\\n3 15\\n16 10\\n5 12\\n2 7\\n18 12\\n10 3\\n8 15\\n10 1\\n', 'output': '5 1\\n5 18\\n6 15\\n14 16\\n14 1\\n4 13\\n4 16\\n4 18\\n8 1\\n8 11\\n8 4\\n8 3\\n8 18\\n8 13\\n8 15\\n10 8\\n10 5\\n10 4\\n10 18\\n10 16\\n10 3\\n10 1\\n7 10\\n7 11\\n7 6\\n7 3\\n7 17\\n9 18\\n9 16\\n12 6\\n12 16\\n12 4\\n12 5\\n12 18\\n9 12\\n9 13\\n9 3\\n9 5\\n7 9\\n7 18\\n7 16\\n7 15\\n7 1\\n2 3\\n2 11\\n2 5\\n7 2\\n4 7\\n4 6\\n4 3\\n4 5\\n14 4\\n6 14\\n6 13\\n6 5\\n6 16\\n3 6\\n3 18\\n3 11\\n3 15\\n5 3\\n5 16\\n5 17\\n5 13\\n11 5\\n11 17\\n15 11\\n15 16\\n13 15\\n13 17\\n18 13\\n16 18\\n16 1\\n17 16\\n1 17\\n'}, {'type': 'stdin_stdout', 'input': '12 32\\n5 4\\n10 11\\n4 2\\n9 4\\n9 11\\n10 6\\n6 12\\n12 4\\n10 4\\n7 12\\n1 12\\n3 6\\n9 6\\n5 9\\n3 12\\n8 3\\n11 2\\n5 1\\n1 3\\n11 12\\n11 1\\n2 5\\n8 1\\n11 4\\n10 2\\n7 8\\n5 6\\n8 5\\n5 12\\n12 2\\n11 6\\n11 7\\n', 'output': '5 9\\n5 1\\n2 4\\n2 11\\n2 10\\n2 12\\n5 2\\n5 6\\n3 6\\n3 12\\n3 1\\n8 3\\n8 1\\n7 12\\n7 11\\n8 7\\n5 8\\n5 12\\n4 5\\n4 12\\n4 10\\n4 11\\n9 4\\n9 6\\n11 9\\n11 12\\n11 1\\n11 6\\n10 11\\n6 10\\n12 6\\n1 12\\n'}, {'type': 'stdin_stdout', 'input': '14 28\\n8 9\\n8 4\\n3 11\\n12 6\\n14 2\\n9 6\\n8 3\\n12 10\\n2 8\\n3 14\\n5 7\\n5 8\\n7 4\\n3 7\\n11 14\\n13 11\\n8 13\\n11 9\\n5 13\\n5 2\\n5 14\\n3 12\\n7 13\\n6 11\\n6 4\\n12 5\\n6 10\\n1 13\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '9 29\\n1 3\\n9 3\\n3 6\\n4 5\\n4 6\\n3 8\\n7 6\\n4 2\\n8 5\\n2 9\\n5 3\\n3 2\\n4 7\\n1 6\\n1 2\\n8 6\\n9 8\\n1 9\\n3 4\\n9 7\\n2 8\\n5 9\\n1 4\\n2 5\\n7 5\\n4 8\\n7 8\\n2 6\\n8 1\\n', 'output': '8 3\\n6 3\\n6 4\\n7 4\\n7 9\\n7 5\\n7 8\\n6 7\\n6 1\\n6 2\\n8 6\\n8 9\\n8 2\\n8 4\\n8 1\\n5 8\\n5 3\\n5 9\\n5 2\\n4 5\\n4 3\\n4 1\\n2 4\\n2 3\\n2 1\\n9 2\\n9 1\\n3 9\\n1 3\\n'}, {'type': 'stdin_stdout', 'input': '7 19\\n3 4\\n3 1\\n7 3\\n1 5\\n7 4\\n2 5\\n5 4\\n1 6\\n4 1\\n2 6\\n2 3\\n6 7\\n5 3\\n7 5\\n7 2\\n7 1\\n5 6\\n6 4\\n3 6\\n', 'output': '7 3\\n6 1\\n5 1\\n5 4\\n5 3\\n5 7\\n5 6\\n2 5\\n2 3\\n2 7\\n6 2\\n6 4\\n6 3\\n7 6\\n7 1\\n4 7\\n4 1\\n3 4\\n1 3\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n1 2\\n2 3\\n3 4\\n4 1\\n2 4\\n', 'output': '1 2\\n2 3\\n3 4\\n4 1\\n4 2\\n'}, {'type': 'stdin_stdout', 'input': '6 8\\n1 2\\n2 3\\n1 3\\n4 5\\n4 6\\n5 6\\n2 4\\n3 5\\n', 'output': '3 1\\n6 5\\n4 6\\n4 2\\n5 4\\n3 5\\n2 3\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\n1 2\\n2 3\\n3 1\\n1 4\\n3 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 1\\n1 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6 7\\n1 2\\n2 3\\n3 1\\n1 4\\n3 5\\n5 6\\n6 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '15 54\\n4 9\\n14 9\\n3 1\\n5 8\\n2 7\\n1 6\\n10 12\\n10 9\\n15 3\\n10 13\\n7 10\\n5 1\\n12 8\\n13 15\\n4 5\\n4 8\\n14 12\\n7 4\\n15 7\\n7 6\\n5 6\\n3 11\\n10 3\\n13 3\\n15 10\\n2 8\\n15 2\\n4 2\\n2 6\\n14 2\\n6 4\\n8 10\\n1 12\\n10 14\\n10 4\\n3 14\\n9 7\\n8 9\\n7 12\\n5 9\\n14 13\\n13 8\\n4 3\\n6 12\\n11 15\\n7 14\\n14 5\\n5 7\\n8 15\\n15 6\\n6 11\\n14 15\\n3 12\\n8 11\\n', 'output': '5 1\\n14 12\\n7 10\\n7 4\\n7 15\\n6 1\\n6 5\\n6 2\\n6 4\\n6 12\\n6 15\\n11 3\\n11 15\\n11 8\\n6 11\\n7 6\\n7 9\\n7 12\\n7 14\\n7 5\\n2 7\\n2 8\\n2 15\\n2 4\\n14 2\\n14 10\\n14 3\\n14 13\\n14 5\\n14 15\\n9 14\\n9 10\\n9 8\\n9 5\\n4 9\\n4 8\\n4 10\\n4 3\\n5 4\\n8 5\\n8 10\\n8 13\\n8 15\\n12 8\\n12 1\\n12 3\\n10 12\\n10 3\\n10 15\\n13 10\\n13 3\\n15 13\\n3 15\\n1 3\\n'}, {'type': 'stdin_stdout', 'input': '3 2\\n2 1\\n2 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\n1 2\\n1 3\\n3 2\\n', 'output': '3 1\\n2 3\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '9 12\\n2 8\\n2 9\\n9 8\\n1 2\\n2 3\\n3 1\\n1 4\\n4 7\\n7 1\\n3 5\\n5 6\\n6 3\\n', 'output': '9 2\\n8 9\\n2 8\\n3 1\\n6 3\\n5 6\\n3 5\\n2 3\\n1 2\\n7 1\\n4 7\\n1 4\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2\\n2 3\\n3 4\\n4 2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 4\\n1 2\\n2 3\\n3 4\\n4 1\\n', 'output': '1 2\\n2 3\\n3 4\\n4 1\\n'}, {'type': 'stdin_stdout', 'input': '21 78\\n12 2\\n21 13\\n17 5\\n11 1\\n12 17\\n12 7\\n21 8\\n16 18\\n3 2\\n5 10\\n6 7\\n13 8\\n3 16\\n20 7\\n16 1\\n17 20\\n2 13\\n21 17\\n9 19\\n19 11\\n12 14\\n2 17\\n6 12\\n6 13\\n7 18\\n18 13\\n3 12\\n17 8\\n16 19\\n21 9\\n17 10\\n12 16\\n8 10\\n12 15\\n14 13\\n5 7\\n13 7\\n3 5\\n4 2\\n18 14\\n4 5\\n19 7\\n19 5\\n14 7\\n5 14\\n16 13\\n11 18\\n13 1\\n9 15\\n11 12\\n13 5\\n17 11\\n10 14\\n15 6\\n13 3\\n13 19\\n1 19\\n18 8\\n9 7\\n3 21\\n10 21\\n12 1\\n16 11\\n21 1\\n13 12\\n12 8\\n14 4\\n5 11\\n20 4\\n9 16\\n6 21\\n19 20\\n10 4\\n4 17\\n7 2\\n5 6\\n2 5\\n11 9\\n', 'output': '8 21\\n10 17\\n10 8\\n7 12\\n6 12\\n6 13\\n15 12\\n15 9\\n6 15\\n6 21\\n6 5\\n7 6\\n20 17\\n4 2\\n4 5\\n4 14\\n4 10\\n4 17\\n20 4\\n20 19\\n7 20\\n7 5\\n7 13\\n7 19\\n7 14\\n7 9\\n7 2\\n18 7\\n18 13\\n18 14\\n18 11\\n18 8\\n16 18\\n16 1\\n16 19\\n16 12\\n16 13\\n16 11\\n16 9\\n3 16\\n3 12\\n3 5\\n3 13\\n3 21\\n2 3\\n2 13\\n2 17\\n2 5\\n12 2\\n12 17\\n12 11\\n12 1\\n12 13\\n12 8\\n14 12\\n14 13\\n14 5\\n10 14\\n10 21\\n5 10\\n5 19\\n5 13\\n5 11\\n17 5\\n17 21\\n17 11\\n8 17\\n13 8\\n13 1\\n13 19\\n21 13\\n21 1\\n9 21\\n9 11\\n19 9\\n19 1\\n11 19\\n1 11\\n'}, {'type': 'stdin_stdout', 'input': '6 11\\n2 4\\n1 6\\n3 1\\n3 6\\n5 6\\n4 5\\n2 6\\n4 1\\n1 5\\n4 6\\n3 4\\n', 'output': '3 1\\n2 6\\n4 2\\n5 6\\n5 1\\n4 5\\n4 1\\n4 6\\n3 4\\n6 3\\n1 6\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n4 1\\n4 2\\n4 3\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 3\\n1 2\\n2 3\\n3 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 6\\n1 2\\n2 3\\n3 4\\n4 1\\n1 3\\n4 2\\n', 'output': '4 1\\n4 2\\n3 4\\n3 1\\n2 3\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '4 5\\n4 1\\n1 2\\n1 3\\n2 3\\n3 4\\n', 'output': '3 1\\n2 1\\n3 2\\n4 3\\n1 4\\n'}, {'type': 'stdin_stdout', 'input': '6 14\\n5 4\\n1 5\\n5 2\\n2 6\\n4 2\\n6 1\\n6 3\\n3 2\\n1 2\\n1 4\\n6 5\\n4 6\\n5 3\\n1 3\\n', 'output': '2 5\\n6 1\\n3 2\\n3 5\\n3 1\\n6 3\\n6 5\\n6 4\\n2 6\\n2 1\\n4 2\\n4 1\\n5 4\\n1 5\\n'}, {'type': 'stdin_stdout', 'input': '10 19\\n6 8\\n5 8\\n8 3\\n1 9\\n3 6\\n4 8\\n10 8\\n8 7\\n5 3\\n10 1\\n5 10\\n4 10\\n2 1\\n3 2\\n7 6\\n8 2\\n1 6\\n10 7\\n2 10\\n', 'output': '0\\n'}, {'type': 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'0\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 4\\n2 3\\n6 1\\n2 3\\n4 1\\n7 1\\n3 5\\n8 6\\n2 6\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 4\\n2 3\\n6 1\\n2 3\\n4 1\\n7 1\\n3 0\\n8 6\\n2 6\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n1 4\\n2 3\\n6 1\\n2 3\\n4 0\\n7 1\\n3 0\\n8 6\\n2 6\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 5, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80477","program":"```python\nfrom sys import stdin,setrecursionlimit\nimport threading\ninput = lambda: stdin.readline().rstrip(\"\\r\\n\")\nfrom collections import deque as que\ninin = lambda: int(input())\ninar = lambda: list(map(int,input().split()))\nfrom types import GeneratorType\n\n\ndef bootstrap(f, stack=[]):\n def wrappedfunc(*args, **kwargs):\n if stack:\n return f(*args, **kwargs)\n else:\n to = f(*args, **kwargs)\n while True:\n if type(to) is GeneratorType:\n stack.append(to)\n to = next(to)\n else:\n stack.pop()\n if not stack:\n break\n to = stack[-1].send(to)\n return to\n\n return wrappedfunc\n\nfrom collections import defaultdict\nadj=defaultdict(list)\nvisited=[False]*(100001)\nintime=[0]*(100001)\nouttime=[0]*(100001)\nres=[]\nbridge=False\ntimer=0\n@bootstrap\ndef dfs(node,par):\n global adj, visited, intime, outtime, res, bridge,timer\n visited[node]=True\n intime[node]=timer\n outtime[node]=timer\n timer+=1\n for j in adj[node]:\n if j==par:\n continue\n if visited[j]:\n outtime[node]=min(outtime[node],intime[j])\n if intime[node]>intime[j]:\n res.append((node,j))\n else:\n yield dfs(j,node)\n if outtime[j]>intime[node]:\n bridge=True\n yield None\n \n res.append((node,j))\n outtime[node] = min(outtime[node], outtime[j])\n yield\ndef main():\n n,m=map(int,input().split())\n global adj,visited,intime,outtime,res,bridge,timer\n timer=0\n bridge=False\n for i in range(m):\n u,v=map(int,input().split())\n adj[u].append(v)\n adj[v].append(u)\n dfs(1,-1)\n if bridge:\n print(0)\n else:\n for i in range(len(res)):\n print(*res[i])\n\nmain()\n```","inputs":"6 7\n1 2\n2 3\n1 3\n4 5\n4 6\n5 6\n2 4\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12812},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1209_D. Cow and Snacks","prompt":"Solve the following coding problem using the programming language python:\n\nThe legendary Farmer John is throwing a huge party, and animals from all over the world are hanging out at his house. His guests are hungry, so he instructs his cow Bessie to bring out the snacks! Moo!\n\nThere are n snacks flavors, numbered with integers 1, 2, \u2026, n. Bessie has n snacks, one snack of each flavor. Every guest has exactly two favorite flavors. The procedure for eating snacks will go as follows:\n\n * First, Bessie will line up the guests in some way. \n * Then in this order, guests will approach the snacks one by one. \n * Each guest in their turn will eat all remaining snacks of their favorite flavor. In case no favorite flavors are present when a guest goes up, they become very sad. \n\n\n\nHelp Bessie to minimize the number of sad guests by lining the guests in an optimal way.\n\nInput\n\nThe first line contains integers n and k (2 \u2264 n \u2264 10^5, 1 \u2264 k \u2264 10^5), the number of snacks and the number of guests. \n\nThe i-th of the following k lines contains two integers x_i and y_i (1 \u2264 x_i, y_i \u2264 n, x_i \u2260 y_i), favorite snack flavors of the i-th guest.\n\nOutput\n\nOutput one integer, the smallest possible number of sad guests.\n\nExamples\n\nInput\n\n\n5 4\n1 2\n4 3\n1 4\n3 4\n\n\nOutput\n\n\n1\n\n\nInput\n\n\n6 5\n2 3\n2 1\n3 4\n6 5\n4 5\n\n\nOutput\n\n\n0\n\nNote\n\nIn the first example, Bessie can order the guests like this: 3, 1, 2, 4. Guest 3 goes first and eats snacks 1 and 4. Then the guest 1 goes and eats the snack 2 only, because the snack 1 has already been eaten. Similarly, the guest 2 goes up and eats the snack 3 only. All the snacks are gone, so the guest 4 will be sad. \n\nIn the second example, one optimal ordering is 2, 1, 3, 5, 4. All the guests will be satisfied.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nfrom collections import defaultdict\nimport sys\nimport typing\n\n\nclass DSU:\n '''\n Implement (union by size) + (path halving)\n\n Reference:\n Zvi Galil and Giuseppe F. Italiano,\n Data structures and algorithms for disjoint set union problems\n '''\n\n def __init__(self, n: int = 0) -> None:\n self._n = n\n self.parent_or_size = [-1] * n\n\n def merge(self, a: int, b: int) -> int:\n assert 0 <= a < self._n\n assert 0 <= b < self._n\n\n x = self.leader(a)\n y = self.leader(b)\n\n if x == y:\n return x\n\n if -self.parent_or_size[x] < -self.parent_or_size[y]:\n x, y = y, x\n\n self.parent_or_size[x] += self.parent_or_size[y]\n self.parent_or_size[y] = x\n\n return x\n\n def same(self, a: int, b: int) -> bool:\n assert 0 <= a < self._n\n assert 0 <= b < self._n\n\n return self.leader(a) == self.leader(b)\n\n def leader(self, a: int) -> int:\n assert 0 <= a < self._n\n\n parent = self.parent_or_size[a]\n while parent >= 0:\n if self.parent_or_size[parent] < 0:\n return parent\n self.parent_or_size[a], a, parent = (\n self.parent_or_size[parent],\n self.parent_or_size[parent],\n self.parent_or_size[self.parent_or_size[parent]]\n )\n\n return a\n\n def size(self, a: int) -> int:\n assert 0 <= a < self._n\n\n return -self.parent_or_size[self.leader(a)]\n\n def groups(self) -> typing.List[typing.List[int]]:\n leader_buf = [self.leader(i) for i in range(self._n)]\n\n result: typing.List[typing.List[int]] = [[] for _ in range(self._n)]\n for i in range(self._n):\n result[leader_buf[i]].append(i)\n\n return list(filter(lambda r: r, result))\n\n\ndef input():\n return sys.stdin.readline().rstrip()\n\n\ndef slv():\n n, k = map(int, input().split())\n dsu = DSU(n)\n Edge = []\n for i in range(k):\n u, v = map(int, input().split())\n u -= 1\n v -= 1\n Edge.append((u, v))\n dsu.merge(u, v)\n ans = k - n + len(set([dsu.leader(i) for i in range(n)]))\n print(ans)\n return\n\n\ndef main():\n t = 1\n for i in range(t):\n slv()\n return\n\n\nif __name__ == \"__main__\":\n main()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 4\\n1 2\\n4 3\\n1 4\\n3 4\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6 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256000000}","problem_id":"vfc_80481","program":"```python\nfrom collections import defaultdict\nimport sys\nimport typing\n\n\nclass DSU:\n '''\n Implement (union by size) + (path halving)\n\n Reference:\n Zvi Galil and Giuseppe F. Italiano,\n Data structures and algorithms for disjoint set union problems\n '''\n\n def __init__(self, n: int = 0) -> None:\n self._n = n\n self.parent_or_size = [-1] * n\n\n def merge(self, a: int, b: int) -> int:\n assert 0 <= a < self._n\n assert 0 <= b < self._n\n\n x = self.leader(a)\n y = self.leader(b)\n\n if x == y:\n return x\n\n if -self.parent_or_size[x] < -self.parent_or_size[y]:\n x, y = y, x\n\n self.parent_or_size[x] += self.parent_or_size[y]\n self.parent_or_size[y] = x\n\n return x\n\n def same(self, a: int, b: int) -> bool:\n assert 0 <= a < self._n\n assert 0 <= b < self._n\n\n return self.leader(a) == self.leader(b)\n\n def leader(self, a: int) -> int:\n assert 0 <= a < self._n\n\n parent = self.parent_or_size[a]\n while parent >= 0:\n if self.parent_or_size[parent] < 0:\n return parent\n self.parent_or_size[a], a, parent = (\n self.parent_or_size[parent],\n self.parent_or_size[parent],\n self.parent_or_size[self.parent_or_size[parent]]\n )\n\n return a\n\n def size(self, a: int) -> int:\n assert 0 <= a < self._n\n\n return -self.parent_or_size[self.leader(a)]\n\n def groups(self) -> typing.List[typing.List[int]]:\n leader_buf = [self.leader(i) for i in range(self._n)]\n\n result: typing.List[typing.List[int]] = [[] for _ in range(self._n)]\n for i in range(self._n):\n result[leader_buf[i]].append(i)\n\n return list(filter(lambda r: r, result))\n\n\ndef input():\n return sys.stdin.readline().rstrip()\n\n\ndef slv():\n n, k = map(int, input().split())\n dsu = DSU(n)\n Edge = []\n for i in range(k):\n u, v = map(int, input().split())\n u -= 1\n v -= 1\n Edge.append((u, v))\n dsu.merge(u, v)\n ans = k - n + len(set([dsu.leader(i) for i in range(n)]))\n print(ans)\n return\n\n\ndef main():\n t = 1\n for i in range(t):\n slv()\n return\n\n\nif __name__ == \"__main__\":\n main()\n\n```","inputs":"5 4\n1 2\n4 3\n1 4\n3 4\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12813},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1228_C. Primes and Multiplication","prompt":"Solve the following coding problem using the programming language python:\n\nLet's introduce some definitions that will be needed later.\n\nLet prime(x) be the set of prime divisors of x. For example, prime(140) = \\{ 2, 5, 7 \\}, prime(169) = \\{ 13 \\}.\n\nLet g(x, p) be the maximum possible integer p^k where k is an integer such that x is divisible by p^k. For example:\n\n * g(45, 3) = 9 (45 is divisible by 3^2=9 but not divisible by 3^3=27), \n * g(63, 7) = 7 (63 is divisible by 7^1=7 but not divisible by 7^2=49). \n\n\n\nLet f(x, y) be the product of g(y, p) for all p in prime(x). For example:\n\n * f(30, 70) = g(70, 2) \u22c5 g(70, 3) \u22c5 g(70, 5) = 2^1 \u22c5 3^0 \u22c5 5^1 = 10, \n * f(525, 63) = g(63, 3) \u22c5 g(63, 5) \u22c5 g(63, 7) = 3^2 \u22c5 5^0 \u22c5 7^1 = 63. \n\n\n\nYou have integers x and n. Calculate f(x, 1) \u22c5 f(x, 2) \u22c5 \u2026 \u22c5 f(x, n) mod{(10^{9} + 7)}.\n\nInput\n\nThe only line contains integers x and n (2 \u2264 x \u2264 10^{9}, 1 \u2264 n \u2264 10^{18}) \u2014 the numbers used in formula.\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n\n10 2\n\n\nOutput\n\n\n2\n\n\nInput\n\n\n20190929 1605\n\n\nOutput\n\n\n363165664\n\n\nInput\n\n\n947 987654321987654321\n\n\nOutput\n\n\n593574252\n\nNote\n\nIn the first example, f(10, 1) = g(1, 2) \u22c5 g(1, 5) = 1, f(10, 2) = g(2, 2) \u22c5 g(2, 5) = 2.\n\nIn the second example, actual value of formula is approximately 1.597 \u22c5 10^{171}. Make sure you print the answer modulo (10^{9} + 7).\n\nIn the third example, be careful about overflow issue.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n\"\"\"\n\nimport math\n\nMOD=1000000007\n\ndef powr(n,N):\n temp=1\n while(N>0):\n if(N%2!=0):\n temp=(temp*n)%MOD\n n=(n*n)%MOD\n N=N//2\n return (temp%MOD)\n\nx,n=map(int,input().split())\n\nn1=x\nL=[]\nwhile(n1%2==0): \n L.append(2) \n n1=n1//2\n\nfor i in range(3,int(math.sqrt(n1))+1,2): \n\n while(n1%i==0): \n L.append(i) \n n1=n1//i \n \nif(n1>2): \n L.append(n1)\n\nL=list(set(L))\nmul=1\nfor i in range(0,len(L)):\n d=L[i]\n nn=n\n tot=0\n while(nn>0):\n tot=(tot+(nn//d))%MOD\n nn=(nn//d)%MOD\n\n mul=(mul*powr(d,tot))%MOD\n\nprint(mul)\n\"\"\"\n\"\"\"\n\nimport math\n\nMOD=1000000007\n\ndef powr(n,N):\n temp=1\n while(N>0):\n if(N%2!=0):\n temp=(temp*n)%MOD\n n=(n*n)%MOD\n N=N//2\n return (temp%MOD)\n\ndef MODI(a,b):\n ans=(powr(a,b)%MOD)\n return ans\n \n\nx,n=map(int,input().split())\n\nn1=x\nL=[]\nwhile(n1%2==0): \n L.append(2) \n n1=n1//2\n\nfor i in range(3,int(math.sqrt(n1))+1,2): \n\n while(n1%i==0): \n L.append(i) \n n1=n1//i \n \nif(n1>2): \n L.append(n1)\n\nL=list(set(L))\nmul=1\nfor i in range(0,len(L)):\n d=L[i]\n t=MODI(d,MOD-2)%MOD\n nn=n\n while(nn>0):\n rem=nn%d\n nn=(nn-rem)%MOD\n nn=(nn*t)%MOD\n mul=(mul*powr(d,nn))%MOD\n\n \n\nprint(mul)\n\n\"\"\"\n\nimport math\n\nMOD=1000000007\n\ndef powr(n,N):\n temp=1\n while(N>0):\n if(N%2!=0):\n temp=(temp*n)%MOD\n n=(n*n)%MOD\n N=N//2\n return (temp%MOD)\n\nx,n=map(int,input().split())\n\nn1=x\nL=[]\nwhile(n1%2==0): \n L.append(2) \n n1=n1//2\n\nfor i in range(3,int(math.sqrt(n1))+1,2): \n\n while(n1%i==0): \n L.append(i) \n n1=n1//i \n \nif(n1>2): \n L.append(n1)\n\nL=list(set(L))\nmul=1\nfor i in range(0,len(L)):\n d=L[i]\n nn=n\n while(nn>0):\n mul=(mul*powr(d,nn//d))%MOD\n nn=nn//d\n\nprint(mul)\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '20190929 1605\\n', 'output': '363165664\\n'}, {'type': 'stdin_stdout', 'input': '10 2\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '947 987654321987654321\\n', 'output': '593574252\\n'}, {'type': 'stdin_stdout', 'input': '183 183\\n', 'output': '387952563\\n'}, {'type': 'stdin_stdout', 'input': '848817679 656378982730193530\\n', 'output': '62821476\\n'}, {'type': 'stdin_stdout', 'input': '9 188\\n', 'output': '954137859\\n'}, {'type': 'stdin_stdout', 'input': '84649 916822936406978638\\n', 'output': '246601699\\n'}, {'type': 'stdin_stdout', 'input': '1000000000 1000000000000000000\\n', 'output': '997440007\\n'}, {'type': 'stdin_stdout', 'input': '2 576460752303423488\\n', 'output': '222384588\\n'}, {'type': 'stdin_stdout', 'input': '602555209 363072779893033681\\n', 'output': '506211588\\n'}, {'type': 'stdin_stdout', 'input': '5 298023223876953125\\n', 'output': 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'input': '15 2\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '232 183\\n', 'output': '515936653\\n'}, {'type': 'stdin_stdout', 'input': '985936988 334139255862703034\\n', 'output': '340153993\\n'}, {'type': 'stdin_stdout', 'input': '84649 943216986775713144\\n', 'output': '112241969\\n'}, {'type': 'stdin_stdout', 'input': '1000001001 1000000000010000000\\n', 'output': '141474221\\n'}, {'type': 'stdin_stdout', 'input': '2 563675444468456415\\n', 'output': '112751609\\n'}, {'type': 'stdin_stdout', 'input': '176599536 58573008766471010\\n', 'output': '390340884\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80485","program":"```python\n\"\"\"\n\nimport math\n\nMOD=1000000007\n\ndef powr(n,N):\n temp=1\n while(N>0):\n if(N%2!=0):\n temp=(temp*n)%MOD\n n=(n*n)%MOD\n N=N//2\n return (temp%MOD)\n\nx,n=map(int,input().split())\n\nn1=x\nL=[]\nwhile(n1%2==0): \n L.append(2) \n n1=n1//2\n\nfor i in range(3,int(math.sqrt(n1))+1,2): \n\n while(n1%i==0): \n L.append(i) \n n1=n1//i \n \nif(n1>2): \n L.append(n1)\n\nL=list(set(L))\nmul=1\nfor i in range(0,len(L)):\n d=L[i]\n nn=n\n tot=0\n while(nn>0):\n tot=(tot+(nn//d))%MOD\n nn=(nn//d)%MOD\n\n mul=(mul*powr(d,tot))%MOD\n\nprint(mul)\n\"\"\"\n\"\"\"\n\nimport math\n\nMOD=1000000007\n\ndef powr(n,N):\n temp=1\n while(N>0):\n if(N%2!=0):\n temp=(temp*n)%MOD\n n=(n*n)%MOD\n N=N//2\n return (temp%MOD)\n\ndef MODI(a,b):\n ans=(powr(a,b)%MOD)\n return ans\n \n\nx,n=map(int,input().split())\n\nn1=x\nL=[]\nwhile(n1%2==0): \n L.append(2) \n n1=n1//2\n\nfor i in range(3,int(math.sqrt(n1))+1,2): \n\n while(n1%i==0): \n L.append(i) \n n1=n1//i \n \nif(n1>2): \n L.append(n1)\n\nL=list(set(L))\nmul=1\nfor i in range(0,len(L)):\n d=L[i]\n t=MODI(d,MOD-2)%MOD\n nn=n\n while(nn>0):\n rem=nn%d\n nn=(nn-rem)%MOD\n nn=(nn*t)%MOD\n mul=(mul*powr(d,nn))%MOD\n\n \n\nprint(mul)\n\n\"\"\"\n\nimport math\n\nMOD=1000000007\n\ndef powr(n,N):\n temp=1\n while(N>0):\n if(N%2!=0):\n temp=(temp*n)%MOD\n n=(n*n)%MOD\n N=N//2\n return (temp%MOD)\n\nx,n=map(int,input().split())\n\nn1=x\nL=[]\nwhile(n1%2==0): \n L.append(2) \n n1=n1//2\n\nfor i in range(3,int(math.sqrt(n1))+1,2): \n\n while(n1%i==0): \n L.append(i) \n n1=n1//i \n \nif(n1>2): \n L.append(n1)\n\nL=list(set(L))\nmul=1\nfor i in range(0,len(L)):\n d=L[i]\n nn=n\n while(nn>0):\n mul=(mul*powr(d,nn//d))%MOD\n nn=nn//d\n\nprint(mul)\n\n\n```","inputs":"20190929 1605\n","output":"363165664\n","actual_output":"363165664\n","execution_success":true,"sample_index":12814},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1293_A. ConneR and the A.R.C. Markland-N","prompt":"Solve the following coding problem using the programming language python:\n\n[Sakuzyo - Imprinting](https://www.youtube.com/watch?v=55Ca6av1kAY)\n\nA.R.C. Markland-N is a tall building with n floors numbered from 1 to n. Between each two adjacent floors in the building, there is a staircase connecting them.\n\nIt's lunchtime for our sensei Colin \"ConneR\" Neumann Jr, and he's planning for a location to enjoy his meal.\n\nConneR's office is at floor s of the building. On each floor (including floor s, of course), there is a restaurant offering meals. However, due to renovations being in progress, k of the restaurants are currently closed, and as a result, ConneR can't enjoy his lunch there.\n\nCooneR wants to reach a restaurant as quickly as possible to save time. What is the minimum number of staircases he needs to walk to reach a closest currently open restaurant.\n\nPlease answer him quickly, and you might earn his praise and even enjoy the lunch with him in the elegant Neumanns' way!\n\nInput\n\nThe first line contains one integer t (1 \u2264 t \u2264 1000) \u2014 the number of test cases in the test. Then the descriptions of t test cases follow.\n\nThe first line of a test case contains three integers n, s and k (2 \u2264 n \u2264 10^9, 1 \u2264 s \u2264 n, 1 \u2264 k \u2264 min(n-1, 1000)) \u2014 respectively the number of floors of A.R.C. Markland-N, the floor where ConneR is in, and the number of closed restaurants.\n\nThe second line of a test case contains k distinct integers a_1, a_2, \u2026, a_k (1 \u2264 a_i \u2264 n) \u2014 the floor numbers of the currently closed restaurants.\n\nIt is guaranteed that the sum of k over all test cases does not exceed 1000.\n\nOutput\n\nFor each test case print a single integer \u2014 the minimum number of staircases required for ConneR to walk from the floor s to a floor with an open restaurant.\n\nExample\n\nInput\n\n\n5\n5 2 3\n1 2 3\n4 3 3\n4 1 2\n10 2 6\n1 2 3 4 5 7\n2 1 1\n2\n100 76 8\n76 75 36 67 41 74 10 77\n\n\nOutput\n\n\n2\n0\n4\n0\n2\n\nNote\n\nIn the first example test case, the nearest floor with an open restaurant would be the floor 4.\n\nIn the second example test case, the floor with ConneR's office still has an open restaurant, so Sensei won't have to go anywhere.\n\nIn the third example test case, the closest open restaurant is on the 6-th floor.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nt = int(input())\n\nfor _ in range(t):\n variables = [int(_) for _ in input().split()]\n n = variables[0]\n s = variables[1]\n k = variables[2]\n closed = set([int(i) for i in input().split()])\n minimum = n\n tmp = n\n for x in range(s, 0, -1):\n if x not in closed:\n tmp = abs(s-x)\n if tmp < minimum:\n minimum = tmp\n break\n for x in range(s, n+1):\n if x not in closed:\n tmp = abs(s-x)\n if tmp < minimum:\n minimum = tmp\n break\n\n print(minimum)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n5 2 3\\n1 2 3\\n4 3 3\\n4 1 2\\n10 2 6\\n1 2 3 4 5 7\\n2 1 1\\n2\\n100 76 8\\n76 75 36 67 41 74 10 77\\n', 'output': '2\\n0\\n4\\n0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 8 6\\n4 8 7 9 6 10\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n10 6 9\\n8 3 6 10 9 5 2 4 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256000000}","problem_id":"vfc_80497","program":"```python\nt = int(input())\n\nfor _ in range(t):\n variables = [int(_) for _ in input().split()]\n n = variables[0]\n s = variables[1]\n k = variables[2]\n closed = set([int(i) for i in input().split()])\n minimum = n\n tmp = n\n for x in range(s, 0, -1):\n if x not in closed:\n tmp = abs(s-x)\n if tmp < minimum:\n minimum = tmp\n break\n for x in range(s, n+1):\n if x not in closed:\n tmp = abs(s-x)\n if tmp < minimum:\n minimum = tmp\n break\n\n print(minimum)\n```","inputs":"5\n5 2 3\n1 2 3\n4 3 3\n4 1 2\n10 2 6\n1 2 3 4 5 7\n2 1 1\n2\n100 76 8\n76 75 36 67 41 74 10 77\n","output":"2\n0\n4\n0\n2\n","actual_output":"2\n0\n4\n0\n2\n","execution_success":true,"sample_index":12816},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1313_A. Fast Food Restaurant","prompt":"Solve the following coding problem using the programming language python:\n\nTired of boring office work, Denis decided to open a fast food restaurant.\n\nOn the first day he made a portions of dumplings, b portions of cranberry juice and c pancakes with condensed milk.\n\nThe peculiarity of Denis's restaurant is the procedure of ordering food. For each visitor Denis himself chooses a set of dishes that this visitor will receive. When doing so, Denis is guided by the following rules:\n\n * every visitor should receive at least one dish (dumplings, cranberry juice, pancakes with condensed milk are all considered to be dishes); \n * each visitor should receive no more than one portion of dumplings, no more than one portion of cranberry juice and no more than one pancake with condensed milk; \n * all visitors should receive different sets of dishes. \n\n\n\nWhat is the maximum number of visitors Denis can feed?\n\nInput\n\nThe first line contains an integer t (1 \u2264 t \u2264 500) \u2014 the number of test cases to solve.\n\nEach of the remaining t lines contains integers a, b and c (0 \u2264 a, b, c \u2264 10) \u2014 the number of portions of dumplings, the number of portions of cranberry juice and the number of condensed milk pancakes Denis made.\n\nOutput\n\nFor each test case print a single integer \u2014 the maximum number of visitors Denis can feed.\n\nExample\n\nInput\n\n7\n1 2 1\n0 0 0\n9 1 7\n2 2 3\n2 3 2\n3 2 2\n4 4 4\n\n\nOutput\n\n3\n0\n4\n5\n5\n5\n7\n\nNote\n\nIn the first test case of the example, Denis can feed the first visitor with dumplings, give the second a portion of cranberry juice, and give the third visitor a portion of cranberry juice and a pancake with a condensed milk.\n\nIn the second test case of the example, the restaurant Denis is not very promising: he can serve no customers.\n\nIn the third test case of the example, Denise can serve four visitors. The first guest will receive a full lunch of dumplings, a portion of cranberry juice and a pancake with condensed milk. The second visitor will get only dumplings. The third guest will receive a pancake with condensed milk, and the fourth guest will receive a pancake and a portion of dumplings. Please note that Denis hasn't used all of the prepared products, but is unable to serve more visitors.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n\n\ndef solution(a, b, c):\n if a == 0 and b == 0 and c == 0:\n print(0)\n return\n\n res = 0\n comb = ['001', '010', '100', '011', '101', '110', '111']\n comb2 = ['01', '10', '11']\n a, b, c = sorted([a, b, c])\n\n if a == 0 and b == 0:\n print(1)\n return\n\n if a == 0:\n for co in comb2:\n bb, cc = map(int, co)\n b -= bb\n c -= cc\n if b < 0 or c < 0:\n break\n res += 1\n else:\n for co in comb:\n aa, bb, cc = map(int, co)\n a -= aa\n b -= bb\n c -= cc\n if a < 0 or b < 0 or c < 0:\n break\n res += 1\n\n print(res)\n\n\ndef main():\n for _ in range(int(input())):\n a, b, c = [int(x) for x in input().split()]\n solution(a, b, c)\n\n\nBUFSIZE = 8192\n\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\n\n\ndef input():\n return sys.stdin.readline().rstrip(\"\\r\\n\")\n\n\nif __name__ == \"__main__\":\n main()\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 7\\n2 2 3\\n2 3 2\\n3 2 2\\n4 4 4\\n', 'output': '3\\n0\\n4\\n5\\n5\\n5\\n7\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 2 8\\n3 2 2\\n', 'output': '5\\n5\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 2 8\\n3 3 2\\n', 'output': '5\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 7\\n2 2 3\\n2 3 2\\n3 2 2\\n0 4 4\\n', 'output': '3\\n0\\n4\\n5\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 1\\n2 2 3\\n2 3 2\\n3 2 2\\n0 4 4\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 2 7\\n3 3 0\\n', 'output': '5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 1\\n2 2 2\\n2 3 2\\n3 2 2\\n0 4 4\\n', 'output': '3\\n0\\n3\\n4\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2 7\\n3 3 0\\n', 'output': '4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 2\\n3 2 2\\n0 4 1\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 3 7\\n5 0 0\\n', 'output': '4\\n1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 3 7\\n5 0 1\\n', 'output': '4\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 1 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 3\\n4 2 2\\n0 6 1\\n', 'output': '2\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 1 2\\n0 0 0\\n9 1 1\\n2 0 4\\n2 2 3\\n4 2 2\\n0 6 1\\n', 'output': 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3\\n4 2 1\\n0 4 1\\n', 'output': '3\\n0\\n3\\n5\\n5\\n4\\n2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2 8\\n2 2 2\\n', 'output': '3\\n4\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 2 1\\n0 0 0\\n9 1 7\\n2 2 3\\n2 3 2\\n3 2 2\\n7 4 4\\n', 'output': '2\\n0\\n4\\n5\\n5\\n5\\n7\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 8\\n3 4 2\\n', 'output': '4\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 7\\n2 0 3\\n2 3 2\\n3 2 2\\n0 4 7\\n', 'output': '3\\n0\\n4\\n3\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0 7\\n3 3 2\\n', 'output': '3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 0 7\\n4 3 0\\n', 'output': '2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 1 1\\n2 1 4\\n2 3 2\\n3 2 0\\n0 4 1\\n', 'output': '3\\n0\\n3\\n4\\n5\\n3\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 1 2\\n0 0 0\\n9 1 1\\n2 2 4\\n1 2 3\\n6 2 2\\n0 6 1\\n', 'output': '2\\n0\\n3\\n5\\n4\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 2 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0\\n9 1 7\\n2 2 3\\n2 3 2\\n3 1 2\\n7 4 0\\n', 'output': '2\\n0\\n4\\n5\\n5\\n4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1 7\\n3 3 1\\n', 'output': '2\\n4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 2 7\\n3 3 2\\n', 'output': '5\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 1 1\\n2 2 2\\n2 3 2\\n3 2 2\\n0 4 4\\n', 'output': '3\\n0\\n3\\n4\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2 7\\n5 3 0\\n', 'output': '4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 2\\n3 2 2\\n0 4 4\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 3 7\\n5 3 0\\n', 'output': '4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 2\\n4 2 2\\n0 4 1\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 3\\n4 2 2\\n0 4 1\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 3\\n4 2 2\\n0 6 1\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 1 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 2 3\\n4 2 2\\n0 6 1\\n', 'output': '2\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 1 2\\n0 0 0\\n9 1 1\\n2 2 4\\n2 2 3\\n4 2 2\\n0 6 1\\n', 'output': '2\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 2 8\\n3 4 2\\n', 'output': '5\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 7\\n2 2 3\\n2 3 2\\n3 2 2\\n0 4 7\\n', 'output': '3\\n0\\n4\\n5\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 2 7\\n3 3 2\\n', 'output': '5\\n5\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 2 2\\n3 3 0\\n', 'output': '4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n16 1 1\\n2 2 2\\n2 3 2\\n3 2 2\\n0 4 4\\n', 'output': '3\\n0\\n3\\n4\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 1 1\\n2 4 2\\n2 3 2\\n3 2 2\\n0 4 4\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 2 7\\n4 3 0\\n', 'output': '4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 2\\n4 2 2\\n0 4 1\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 3\\n5 2 2\\n0 6 1\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 1 1\\n0 0 0\\n6 1 1\\n2 2 4\\n2 3 3\\n4 2 2\\n0 6 1\\n', 'output': '2\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 1 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 3\\n4 2 3\\n0 6 1\\n', 'output': '2\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 1 2\\n0 0 0\\n9 1 1\\n2 2 4\\n2 2 3\\n6 2 2\\n0 6 1\\n', 'output': '2\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 2 2\\n0 0 0\\n9 1 1\\n3 0 4\\n2 2 3\\n4 2 2\\n0 6 1\\n', 'output': '3\\n0\\n3\\n3\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 1\\n2 2 3\\n3 3 2\\n3 2 2\\n1 4 4\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 4 1\\n0 0 0\\n16 1 1\\n2 2 2\\n2 3 2\\n3 2 2\\n0 4 4\\n', 'output': '3\\n0\\n3\\n4\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 7\\n3 3 0\\n', 'output': '4\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 2 1\\n2 4 2\\n2 3 2\\n3 2 2\\n0 4 4\\n', 'output': '3\\n0\\n4\\n5\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3 7\\n5 3 1\\n', 'output': '5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 0\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 2\\n4 2 2\\n0 4 1\\n', 'output': '2\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 3 7\\n5 1 1\\n', 'output': '3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 3\\n4 2 1\\n0 4 1\\n', 'output': '3\\n0\\n3\\n5\\n5\\n4\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 1\\n2 2 4\\n2 3 3\\n5 2 2\\n0 6 1\\n', 'output': '3\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 2 1\\n0 0 0\\n6 1 1\\n2 2 4\\n2 3 3\\n4 2 2\\n0 6 1\\n', 'output': '2\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 1 1\\n0 0 0\\n11 1 1\\n2 2 4\\n2 3 3\\n4 2 3\\n0 6 1\\n', 'output': '2\\n0\\n3\\n5\\n5\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2 8\\n2 2 3\\n', 'output': '3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 8\\n5 4 2\\n', 'output': '4\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 7\\n2 0 3\\n2 3 2\\n3 4 2\\n0 4 7\\n', 'output': '3\\n0\\n4\\n3\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0 7\\n3 6 2\\n', 'output': '3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 1 7\\n3 3 0\\n', 'output': '2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 1 1\\n0 0 0\\n9 2 1\\n2 4 2\\n2 3 2\\n5 2 2\\n0 4 4\\n', 'output': '3\\n0\\n4\\n5\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 1 7\\n4 3 0\\n', 'output': '3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 3 7\\n4 3 1\\n', 'output': '5\\n4\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 3 7\\n5 1 0\\n', 'output': '3\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n9 1 1\\n2 2 8\\n2 3 3\\n4 2 1\\n0 4 1\\n', 'output': '3\\n0\\n3\\n5\\n5\\n4\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 1 2\\n0 0 0\\n9 1 1\\n2 2 4\\n1 2 3\\n3 2 2\\n0 6 1\\n', 'output': '2\\n0\\n3\\n5\\n4\\n5\\n2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n0 2 2\\n0 0 0\\n9 2 1\\n3 0 4\\n2 2 3\\n4 2 2\\n0 6 2\\n', 'output': '3\\n0\\n4\\n3\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0 2 8\\n4 2 3\\n', 'output': '3\\n5\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2 1 8\\n5 2 2\\n', 'output': '4\\n5\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 2 1\\n0 0 0\\n6 1 7\\n2 0 3\\n2 3 2\\n3 4 2\\n0 4 7\\n', 'output': '3\\n0\\n4\\n3\\n5\\n5\\n3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n3 0 7\\n3 0 2\\n', 'output': '3\\n3\\n'}, {'type': 'stdin_stdout', 'input': '7\\n1 4 1\\n0 0 0\\n16 0 1\\n2 2 1\\n2 3 2\\n3 2 2\\n0 4 4\\n', 'output': '3\\n0\\n2\\n4\\n5\\n5\\n3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80501","program":"```python\nimport os\nimport sys\nfrom io import BytesIO, IOBase\n\n\ndef solution(a, b, c):\n if a == 0 and b == 0 and c == 0:\n print(0)\n return\n\n res = 0\n comb = ['001', '010', '100', '011', '101', '110', '111']\n comb2 = ['01', '10', '11']\n a, b, c = sorted([a, b, c])\n\n if a == 0 and b == 0:\n print(1)\n return\n\n if a == 0:\n for co in comb2:\n bb, cc = map(int, co)\n b -= bb\n c -= cc\n if b < 0 or c < 0:\n break\n res += 1\n else:\n for co in comb:\n aa, bb, cc = map(int, co)\n a -= aa\n b -= bb\n c -= cc\n if a < 0 or b < 0 or c < 0:\n break\n res += 1\n\n print(res)\n\n\ndef main():\n for _ in range(int(input())):\n a, b, c = [int(x) for x in input().split()]\n solution(a, b, c)\n\n\nBUFSIZE = 8192\n\n\nclass FastIO(IOBase):\n newlines = 0\n\n def __init__(self, file):\n self._fd = file.fileno()\n self.buffer = BytesIO()\n self.writable = \"x\" in file.mode or \"r\" not in file.mode\n self.write = self.buffer.write if self.writable else None\n\n def read(self):\n while True:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n if not b:\n break\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines = 0\n return self.buffer.read()\n\n def readline(self):\n while self.newlines == 0:\n b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))\n self.newlines = b.count(b\"\\n\") + (not b)\n ptr = self.buffer.tell()\n self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)\n self.newlines -= 1\n return self.buffer.readline()\n\n def flush(self):\n if self.writable:\n os.write(self._fd, self.buffer.getvalue())\n self.buffer.truncate(0), self.buffer.seek(0)\n\n\nclass IOWrapper(IOBase):\n def __init__(self, file):\n self.buffer = FastIO(file)\n self.flush = self.buffer.flush\n self.writable = self.buffer.writable\n self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))\n self.read = lambda: self.buffer.read().decode(\"ascii\")\n self.readline = lambda: self.buffer.readline().decode(\"ascii\")\n\n\nsys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)\n\n\ndef input():\n return sys.stdin.readline().rstrip(\"\\r\\n\")\n\n\nif __name__ == \"__main__\":\n main()\n\n```","inputs":"7\n1 2 1\n0 0 0\n9 1 7\n2 2 3\n2 3 2\n3 2 2\n4 4 4\n","output":"3\n0\n4\n5\n5\n5\n7\n","actual_output":"3\n0\n4\n5\n5\n5\n7\n","execution_success":true,"sample_index":12817},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1335_E1. Three Blocks Palindrome (easy version)","prompt":"Solve the following coding problem using the programming language python:\n\nThe only difference between easy and hard versions is constraints.\n\nYou are given a sequence a consisting of n positive integers.\n\nLet's define a three blocks palindrome as the sequence, consisting of at most two distinct elements (let these elements are a and b, a can be equal b) and is as follows: [\\underbrace{a, a, ..., a}_{x}, \\underbrace{b, b, ..., b}_{y}, \\underbrace{a, a, ..., a}_{x}]. There x, y are integers greater than or equal to 0. For example, sequences [], [2], [1, 1], [1, 2, 1], [1, 2, 2, 1] and [1, 1, 2, 1, 1] are three block palindromes but [1, 2, 3, 2, 1], [1, 2, 1, 2, 1] and [1, 2] are not.\n\nYour task is to choose the maximum by length subsequence of a that is a three blocks palindrome.\n\nYou have to answer t independent test cases.\n\nRecall that the sequence t is a a subsequence of the sequence s if t can be derived from s by removing zero or more elements without changing the order of the remaining elements. For example, if s=[1, 2, 1, 3, 1, 2, 1], then possible subsequences are: [1, 1, 1, 1], [3] and [1, 2, 1, 3, 1, 2, 1], but not [3, 2, 3] and [1, 1, 1, 1, 2].\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 2000) \u2014 the number of test cases. Then t test cases follow.\n\nThe first line of the test case contains one integer n (1 \u2264 n \u2264 2000) \u2014 the length of a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 26), where a_i is the i-th element of a. Note that the maximum value of a_i can be up to 26.\n\nIt is guaranteed that the sum of n over all test cases does not exceed 2000 (\u2211 n \u2264 2000).\n\nOutput\n\nFor each test case, print the answer \u2014 the maximum possible length of some subsequence of a that is a three blocks palindrome.\n\nExample\n\nInput\n\n\n6\n8\n1 1 2 2 3 2 1 1\n3\n1 3 3\n4\n1 10 10 1\n1\n26\n2\n2 1\n3\n1 1 1\n\n\nOutput\n\n\n7\n2\n4\n1\n1\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nT = int(input())\n\nQ = []\n\n# Read all inputs before computing (see last comment, the goal is to print once)\nfor t in range(T):\n N = int(input())\n A = [int(_) for _ in input().split()]\n Q.append((N, A))\n\nR = []\nfor N, A in Q:\n # Switch the 2 dimensions of the array to maybe prevent cache miss on loops l26 and l30\n prefC = [[0] * (26) for _ in range(N+1)]\n for c in range(26):\n for i in range(N):\n prefC[i+1][c] = prefC[i][c]\n if A[i] == c+1:\n prefC[i+1][c] += 1\n\n answer = 0\n for l in range(N):\n for r in range(l, N):\n cntin = 0\n # Write the explicit loop, don't use max on the list comprehension (x2 constant factor inside the N\u00b2 loop)\n for c in range(26):\n cntin = max(cntin, prefC[r+1][c] - prefC[l][c])\n cntout = 0\n # Write the explicit loop, don't use max on the list comprehension (x2 constant factor inside the N\u00b2 loop)\n for c in range(26):\n cntout = max(cntout, min(prefC[l][c], prefC[N][c] - prefC[r+1][c]))\n answer = max(answer, 2 * cntout + cntin)\n R.append(answer)\n\n# Do only one print instead of T prints (less stdout flushing I guess)\nprint('\\n'.join(map(str, R)))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '7\\n2\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 3 1 1\\n3\\n1 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 3\\n4\\n1 10 14 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '7\\n2\\n3\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 3 3\\n4\\n1 10 14 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n3\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 3 3\\n4\\n2 10 14 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n1\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 3 3\\n4\\n2 10 14 1\\n1\\n26\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n1\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 3 2 1 1\\n3\\n2 1 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n1\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n3 1\\n3\\n1 1 1\\n', 'output': '7\\n2\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 3 1 1\\n3\\n1 3 2\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 2 3\\n4\\n2 10 14 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n1\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 2 2 4 3 2 1 1\\n3\\n1 3 3\\n4\\n2 10 14 1\\n1\\n26\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '5\\n2\\n1\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 3 2 1 1\\n3\\n2 3 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '6\\n2\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 3 2 1 1\\n3\\n2 1 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '6\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 3 3\\n4\\n1 11 14 1\\n1\\n26\\n2\\n2 1\\n3\\n2 1 1\\n', 'output': '6\\n2\\n3\\n1\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 3 2 1 2\\n3\\n2 1 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '4\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 3 2 1 2\\n3\\n2 1 3\\n4\\n2 10 9 2\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '4\\n1\\n3\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 2 2 4 3 2 1 1\\n3\\n1 4 3\\n4\\n2 10 14 1\\n1\\n26\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '5\\n1\\n1\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 3 2 1 2\\n3\\n2 3 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '4\\n2\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 2 2 1 2\\n3\\n2 3 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '5\\n2\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n2 1 2 6 1 2 1 1\\n3\\n2 1 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '5\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 1 3 3 1 1\\n3\\n1 5 2\\n4\\n2 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n2\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 2 2 4 3 2 1 1\\n3\\n1 3 3\\n4\\n1 11 5 1\\n1\\n26\\n2\\n2 1\\n3\\n2 1 1\\n', 'output': '5\\n2\\n3\\n1\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 2 2 2 3 3 1 1\\n3\\n1 3 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '5\\n2\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 3\\n4\\n2 10 10 1\\n1\\n26\\n2\\n3 1\\n3\\n1 1 1\\n', 'output': '7\\n2\\n2\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 2 2 2 3 3 1 1\\n3\\n1 3 2\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '5\\n1\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 2 2 1 1\\n3\\n2 1 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '7\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 3 1 1\\n3\\n1 5 2\\n4\\n1 10 10 1\\n1\\n26\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n4\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n2 3 3\\n4\\n2 10 14 1\\n1\\n26\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n1\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n2 3 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n1\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 3 2 1 1\\n3\\n2 3 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n1\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 3 3\\n4\\n1 11 14 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n3\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 3 1 1\\n3\\n1 5 2\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 3 2 1 1\\n3\\n2 4 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '6\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 10 3 2 1 1\\n3\\n2 4 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '6\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 10 3 2 1 1\\n3\\n2 4 1\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '6\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 3 1 1\\n3\\n1 4 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 3 3\\n4\\n1 10 14 1\\n1\\n26\\n2\\n3 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n3\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 3 3\\n4\\n2 4 14 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n1\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n2 3 3\\n4\\n2 10 14 1\\n1\\n12\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n1\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 3\\n4\\n1 10 9 1\\n1\\n26\\n2\\n3 1\\n3\\n1 1 1\\n', 'output': '7\\n2\\n3\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 2 3\\n4\\n2 10 14 1\\n1\\n26\\n2\\n3 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n1\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n2 1 2 6 3 2 1 1\\n3\\n2 1 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '4\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 1 3 3 1 1\\n3\\n1 5 2\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 3 3\\n4\\n1 11 5 1\\n1\\n26\\n2\\n2 1\\n3\\n2 1 1\\n', 'output': '6\\n2\\n3\\n1\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 4 2 1 1\\n3\\n2 4 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '6\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 10 3 2 1 1\\n3\\n2 4 3\\n4\\n2 10 11 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '6\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 3 1 1\\n3\\n2 4 3\\n4\\n1 10 10 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n4\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n1 2 3\\n4\\n2 10 14 1\\n1\\n15\\n2\\n3 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n1\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 4 1 1 1\\n3\\n2 4 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '5\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 3 4 3 2 1 1\\n3\\n1 2 3\\n4\\n2 10 14 1\\n1\\n15\\n2\\n3 1\\n3\\n1 1 1\\n', 'output': '6\\n1\\n1\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n2 1 2 6 2 2 1 2\\n3\\n2 3 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '5\\n2\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 2 2 1 3 2 1 1\\n3\\n1 3 3\\n4\\n1 11 5 1\\n1\\n26\\n2\\n2 1\\n3\\n2 1 1\\n', 'output': '5\\n2\\n3\\n1\\n1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 4 1 1 2\\n3\\n2 4 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '5\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n2 1 2 9 2 2 1 2\\n3\\n2 3 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '5\\n2\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 4 1 1 2\\n3\\n2 4 3\\n4\\n2 18 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '5\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 4 1 1 3\\n3\\n2 4 3\\n4\\n2 18 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '5\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 2 3 2 1 1\\n3\\n1 3 3\\n4\\n1 3 14 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '7\\n2\\n3\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 2 2 1 1\\n3\\n1 3 3\\n4\\n1 10 14 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '7\\n2\\n3\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 2 1\\n3\\n1 3 3\\n4\\n2 10 14 1\\n1\\n26\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '5\\n2\\n1\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n2 3 3\\n4\\n3 10 14 1\\n1\\n26\\n2\\n1 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n1\\n1\\n2\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n2 3 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 2\\n3\\n1 1 1\\n', 'output': '6\\n2\\n1\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 4 3 2 1 1\\n3\\n2 3 3\\n4\\n1 11 14 1\\n1\\n26\\n2\\n2 1\\n3\\n1 1 1\\n', 'output': '6\\n2\\n3\\n1\\n1\\n3\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 3 2 1 1\\n3\\n2 3 4\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '6\\n1\\n1\\n1\\n2\\n2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n8\\n1 1 2 6 3 2 1 3\\n3\\n2 1 3\\n4\\n2 10 9 1\\n1\\n26\\n2\\n1 1\\n3\\n2 1 1\\n', 'output': '4\\n1\\n1\\n1\\n2\\n2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80505","program":"```python\nT = int(input())\n\nQ = []\n\n# Read all inputs before computing (see last comment, the goal is to print once)\nfor t in range(T):\n N = int(input())\n A = [int(_) for _ in input().split()]\n Q.append((N, A))\n\nR = []\nfor N, A in Q:\n # Switch the 2 dimensions of the array to maybe prevent cache miss on loops l26 and l30\n prefC = [[0] * (26) for _ in range(N+1)]\n for c in range(26):\n for i in range(N):\n prefC[i+1][c] = prefC[i][c]\n if A[i] == c+1:\n prefC[i+1][c] += 1\n\n answer = 0\n for l in range(N):\n for r in range(l, N):\n cntin = 0\n # Write the explicit loop, don't use max on the list comprehension (x2 constant factor inside the N\u00b2 loop)\n for c in range(26):\n cntin = max(cntin, prefC[r+1][c] - prefC[l][c])\n cntout = 0\n # Write the explicit loop, don't use max on the list comprehension (x2 constant factor inside the N\u00b2 loop)\n for c in range(26):\n cntout = max(cntout, min(prefC[l][c], prefC[N][c] - prefC[r+1][c]))\n answer = max(answer, 2 * cntout + cntin)\n R.append(answer)\n\n# Do only one print instead of T prints (less stdout flushing I guess)\nprint('\\n'.join(map(str, R)))\n\n```","inputs":"6\n8\n1 1 2 2 3 2 1 1\n3\n1 3 3\n4\n1 10 10 1\n1\n26\n2\n2 1\n3\n1 1 1\n","output":"7\n2\n4\n1\n1\n3\n","actual_output":"7\n2\n4\n1\n1\n3\n","execution_success":true,"sample_index":12818},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1358_A. Park Lighting","prompt":"Solve the following coding problem using the programming language python:\n\nDue to the coronavirus pandemic, city authorities obligated citizens to keep a social distance. The mayor of the city Semyon wants to light up Gluharniki park so that people could see each other even at night to keep the social distance.\n\nThe park is a rectangular table with n rows and m columns, where the cells of the table are squares, and the boundaries between the cells are streets. External borders are also streets. Every street has length 1. For example, park with n=m=2 has 12 streets.\n\nYou were assigned to develop a plan for lighting the park. You can put lanterns in the middle of the streets. The lamp lights two squares near it (or only one square if it stands on the border of the park).\n\n The park sizes are: n=4, m=5. The lighted squares are marked yellow. Please note that all streets have length 1. Lanterns are placed in the middle of the streets. In the picture not all the squares are lit.\n\nSemyon wants to spend the least possible amount of money on lighting but also wants people throughout the park to keep a social distance. So he asks you to find the minimum number of lanterns that are required to light all the squares.\n\nInput\n\nThe first line contains a single integer t (1 \u2264 t \u2264 10^4) \u2014 the number of test cases in the input. Then t test cases follow.\n\nEach test case is a line containing two integers n, m (1 \u2264 n, m \u2264 10^4) \u2014 park sizes.\n\nOutput\n\nPrint t answers to the test cases. Each answer must be a single integer \u2014 the minimum number of lanterns that are required to light all the squares.\n\nExample\n\nInput\n\n\n5\n1 1\n1 3\n2 2\n3 3\n5 3\n\n\nOutput\n\n\n1\n2\n2\n5\n8\n\nNote\n\nPossible optimal arrangement of the lanterns for the 2-nd test case of input data example: \n\nPossible optimal arrangement of the lanterns for the 3-rd test case of input data example: \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport math\nt=int(input())\nwhile(t>0):\n t-=1\n n,m=map(int,input().split())\n print(math.floor((n*m+1)/2))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 1\\n1 3\\n2 2\\n3 3\\n5 3\\n', 'output': '1\\n2\\n2\\n5\\n8\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1329 2007\\n179 57\\n', 'output': '1333652\\n5102\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1329 2007\\n118 57\\n', 'output': '1333652\\n3363\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 3\\n2 2\\n3 3\\n5 3\\n', 'output': '1\\n2\\n2\\n5\\n8\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1329 2465\\n118 57\\n', 'output': '1637993\\n3363\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 3\\n2 2\\n1 3\\n5 3\\n', 'output': '1\\n2\\n2\\n2\\n8\\n'}, {'type': 'stdin_stdout', 'input': '2\\n152 2465\\n118 57\\n', 'output': '187340\\n3363\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 1\\n1 3\\n2 2\\n1 3\\n5 3\\n', 'output': '2\\n2\\n2\\n2\\n8\\n'}, {'type': 'stdin_stdout', 'input': '2\\n152 3396\\n118 57\\n', 'output': '258096\\n3363\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 3396\\n118 57\\n', 'output': '448272\\n3363\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 3396\\n118 98\\n', 'output': '448272\\n5782\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 4075\\n118 98\\n', 'output': '537900\\n5782\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 5299\\n118 98\\n', 'output': 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'6159\\n594\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6 624\\n132 9\\n', 'output': '1872\\n594\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6 624\\n235 9\\n', 'output': '1872\\n1058\\n'}, {'type': 'stdin_stdout', 'input': '2\\n670 2007\\n179 57\\n', 'output': '672345\\n5102\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1439 2007\\n118 57\\n', 'output': '1444037\\n3363\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 3\\n2 2\\n1 3\\n5 4\\n', 'output': '1\\n2\\n2\\n2\\n10\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2556 2465\\n118 57\\n', 'output': '3150270\\n3363\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 3\\n2 1\\n1 3\\n5 3\\n', 'output': '1\\n2\\n1\\n2\\n8\\n'}, {'type': 'stdin_stdout', 'input': '2\\n152 2465\\n118 55\\n', 'output': '187340\\n3245\\n'}, {'type': 'stdin_stdout', 'input': '5\\n4 1\\n1 3\\n2 4\\n1 3\\n5 3\\n', 'output': '2\\n2\\n4\\n2\\n8\\n'}, {'type': 'stdin_stdout', 'input': '2\\n152 1431\\n118 57\\n', 'output': '108756\\n3363\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 3396\\n118 28\\n', 'output': '448272\\n1652\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 6140\\n118 98\\n', 'output': '810480\\n5782\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 439\\n118 98\\n', 'output': '57948\\n5782\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 7484\\n118 98\\n', 'output': '987888\\n5782\\n'}, {'type': 'stdin_stdout', 'input': '2\\n461 5299\\n118 177\\n', 'output': '1221420\\n10443\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 198\\n118 95\\n', 'output': '26136\\n5605\\n'}, {'type': 'stdin_stdout', 'input': '2\\n56 5299\\n118 4\\n', 'output': '148372\\n236\\n'}, {'type': 'stdin_stdout', 'input': '2\\n473 2053\\n118 4\\n', 'output': '485535\\n236\\n'}, {'type': 'stdin_stdout', 'input': '2\\n78 1627\\n118 4\\n', 'output': '63453\\n236\\n'}, {'type': 'stdin_stdout', 'input': '2\\n79 2053\\n118 4\\n', 'output': '81094\\n236\\n'}, {'type': 'stdin_stdout', 'input': '2\\n106 2053\\n52 7\\n', 'output': '108809\\n182\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6 2053\\n118 3\\n', 'output': '6159\\n177\\n'}, {'type': 'stdin_stdout', 'input': '2\\n10 2053\\n132 7\\n', 'output': '10265\\n462\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6 2053\\n132 12\\n', 'output': '6159\\n792\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6 624\\n56 9\\n', 'output': '1872\\n252\\n'}, {'type': 'stdin_stdout', 'input': '2\\n670 142\\n179 57\\n', 'output': '47570\\n5102\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1439 2007\\n69 57\\n', 'output': '1444037\\n1967\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 3\\n2 2\\n1 3\\n3 4\\n', 'output': '1\\n2\\n2\\n2\\n6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2556 2465\\n118 92\\n', 'output': '3150270\\n5428\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 3\\n2 1\\n1 3\\n5 2\\n', 'output': '1\\n2\\n1\\n2\\n5\\n'}, {'type': 'stdin_stdout', 'input': '2\\n232 2465\\n118 55\\n', 'output': '285940\\n3245\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 1\\n1 3\\n2 4\\n1 3\\n5 3\\n', 'output': '3\\n2\\n4\\n2\\n8\\n'}, {'type': 'stdin_stdout', 'input': '2\\n40 1431\\n118 57\\n', 'output': '28620\\n3363\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 3396\\n143 28\\n', 'output': '448272\\n2002\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 6140\\n118 42\\n', 'output': '810480\\n2478\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 439\\n14 98\\n', 'output': '57948\\n686\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 13162\\n118 98\\n', 'output': '1737384\\n5782\\n'}, {'type': 'stdin_stdout', 'input': '2\\n461 5299\\n176 177\\n', 'output': '1221420\\n15576\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 272\\n118 95\\n', 'output': '35904\\n5605\\n'}, {'type': 'stdin_stdout', 'input': '2\\n98 5299\\n118 4\\n', 'output': '259651\\n236\\n'}, {'type': 'stdin_stdout', 'input': '2\\n473 2053\\n118 3\\n', 'output': '485535\\n177\\n'}, {'type': 'stdin_stdout', 'input': '2\\n143 1627\\n118 4\\n', 'output': '116331\\n236\\n'}, {'type': 'stdin_stdout', 'input': '2\\n79 2053\\n112 4\\n', 'output': '81094\\n224\\n'}, {'type': 'stdin_stdout', 'input': '2\\n106 2036\\n52 7\\n', 'output': '107908\\n182\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6 2053\\n118 2\\n', 'output': '6159\\n118\\n'}, {'type': 'stdin_stdout', 'input': '2\\n9 2053\\n132 7\\n', 'output': '9239\\n462\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6 2053\\n22 12\\n', 'output': '6159\\n132\\n'}, {'type': 'stdin_stdout', 'input': '2\\n670 131\\n179 57\\n', 'output': '43885\\n5102\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1439 1530\\n69 57\\n', 'output': '1100835\\n1967\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 3\\n2 2\\n2 3\\n3 4\\n', 'output': '1\\n2\\n2\\n3\\n6\\n'}, {'type': 'stdin_stdout', 'input': '2\\n2556 2846\\n118 92\\n', 'output': '3637188\\n5428\\n'}, {'type': 'stdin_stdout', 'input': '2\\n276 2465\\n118 55\\n', 'output': '340170\\n3245\\n'}, {'type': 'stdin_stdout', 'input': '5\\n5 1\\n1 3\\n2 4\\n1 3\\n7 3\\n', 'output': '3\\n2\\n4\\n2\\n11\\n'}, {'type': 'stdin_stdout', 'input': '2\\n40 1431\\n118 114\\n', 'output': '28620\\n6726\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 3396\\n143 30\\n', 'output': '448272\\n2145\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 6140\\n194 42\\n', 'output': '810480\\n4074\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 439\\n15 98\\n', 'output': '57948\\n735\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 13162\\n66 98\\n', 'output': '1737384\\n3234\\n'}, {'type': 'stdin_stdout', 'input': '2\\n461 5299\\n176 213\\n', 'output': '1221420\\n18744\\n'}, {'type': 'stdin_stdout', 'input': '2\\n264 380\\n118 95\\n', 'output': '50160\\n5605\\n'}, {'type': 'stdin_stdout', 'input': '2\\n96 5299\\n118 4\\n', 'output': '254352\\n236\\n'}, {'type': 'stdin_stdout', 'input': '2\\n473 2053\\n118 1\\n', 'output': '485535\\n59\\n'}, {'type': 'stdin_stdout', 'input': '2\\n143 1627\\n70 4\\n', 'output': '116331\\n140\\n'}, {'type': 'stdin_stdout', 'input': '2\\n79 2053\\n133 4\\n', 'output': '81094\\n266\\n'}, {'type': 'stdin_stdout', 'input': '2\\n106 2036\\n52 14\\n', 'output': '107908\\n364\\n'}, {'type': 'stdin_stdout', 'input': '2\\n6 987\\n118 2\\n', 'output': '2961\\n118\\n'}, {'type': 'stdin_stdout', 'input': '2\\n9 1188\\n132 7\\n', 'output': '5346\\n462\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1\\n1 3\\n2 1\\n1 3\\n8 2\\n', 'output': '1\\n2\\n1\\n2\\n8\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80509","program":"```python\nimport math\nt=int(input())\nwhile(t>0):\n t-=1\n n,m=map(int,input().split())\n print(math.floor((n*m+1)/2))\n```","inputs":"5\n1 1\n1 3\n2 2\n3 3\n5 3\n","output":"1\n2\n2\n5\n8\n","actual_output":"1\n2\n2\n5\n8\n","execution_success":true,"sample_index":12819},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1399_B. Gifts Fixing","prompt":"Solve the following coding problem using the programming language python:\n\nYou have n gifts and you want to give all of them to children. Of course, you don't want to offend anyone, so all gifts should be equal between each other. The i-th gift consists of a_i candies and b_i oranges.\n\nDuring one move, you can choose some gift 1 \u2264 i \u2264 n and do one of the following operations:\n\n * eat exactly one candy from this gift (decrease a_i by one); \n * eat exactly one orange from this gift (decrease b_i by one); \n * eat exactly one candy and exactly one orange from this gift (decrease both a_i and b_i by one). \n\n\n\nOf course, you can not eat a candy or orange if it's not present in the gift (so neither a_i nor b_i can become less than zero).\n\nAs said above, all gifts should be equal. This means that after some sequence of moves the following two conditions should be satisfied: a_1 = a_2 = ... = a_n and b_1 = b_2 = ... = b_n (and a_i equals b_i is not necessary).\n\nYour task is to find the minimum number of moves required to equalize all the given gifts.\n\nYou have to answer t independent test cases.\n\nInput\n\nThe first line of the input contains one integer t (1 \u2264 t \u2264 1000) \u2014 the number of test cases. Then t test cases follow.\n\nThe first line of the test case contains one integer n (1 \u2264 n \u2264 50) \u2014 the number of gifts. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 10^9), where a_i is the number of candies in the i-th gift. The third line of the test case contains n integers b_1, b_2, ..., b_n (1 \u2264 b_i \u2264 10^9), where b_i is the number of oranges in the i-th gift.\n\nOutput\n\nFor each test case, print one integer: the minimum number of moves required to equalize all the given gifts.\n\nExample\n\nInput\n\n\n5\n3\n3 5 6\n3 2 3\n5\n1 2 3 4 5\n5 4 3 2 1\n3\n1 1 1\n2 2 2\n6\n1 1000000000 1000000000 1000000000 1000000000 1000000000\n1 1 1 1 1 1\n3\n10 12 8\n7 5 4\n\n\nOutput\n\n\n6\n16\n0\n4999999995\n7\n\nNote\n\nIn the first test case of the example, we can perform the following sequence of moves:\n\n * choose the first gift and eat one orange from it, so a = [3, 5, 6] and b = [2, 2, 3]; \n * choose the second gift and eat one candy from it, so a = [3, 4, 6] and b = [2, 2, 3]; \n * choose the second gift and eat one candy from it, so a = [3, 3, 6] and b = [2, 2, 3]; \n * choose the third gift and eat one candy and one orange from it, so a = [3, 3, 5] and b = [2, 2, 2]; \n * choose the third gift and eat one candy from it, so a = [3, 3, 4] and b = [2, 2, 2]; \n * choose the third gift and eat one candy from it, so a = [3, 3, 3] and b = [2, 2, 2]. \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# Gifts Fixing\n# https://codeforces.com/problemset/problem/1399/B\n\n\nt = int(input())\n\nfor _ in range(t):\n\t\n\tn = int(input())\n\ta = list(map(int, input().split()))\n\tb = list(map(int, input().split()))\n\t\n\tmin_a = min(a)\n\tmin_b = min(b)\n\n\tcount = 0\n\t\n\tfor i in range(n):\n\t\tdiff_a = a[i] - min_a\n\t\tdiff_b = b[i] - min_b\n\t\t\n\t\tcount += max(diff_a, diff_b)\n\t\n\tprint(count)\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n3 2 3\\n5\\n1 2 3 4 5\\n5 4 3 2 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1000000000 1000000000 1000000000 1000000000\\n1 1 1 1 1 1\\n3\\n10 12 8\\n7 5 4\\n', 'output': '6\\n16\\n0\\n4999999995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n3 2 3\\n5\\n1 2 3 4 5\\n5 4 3 2 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1000000000 1000000000 1000000000 1000000000\\n1 1 2 1 1 1\\n3\\n10 12 8\\n7 5 4\\n', 'output': '6\\n16\\n0\\n4999999995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n3 2 3\\n5\\n1 2 3 4 5\\n5 4 3 2 1\\n3\\n1 1 1\\n2 1 2\\n6\\n1 1000000000 1000000000 1000000000 1000000000 1000000000\\n1 1 1 1 1 1\\n3\\n10 12 8\\n7 5 4\\n', 'output': '6\\n16\\n2\\n4999999995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 12\\n3 2 3\\n5\\n1 2 3 4 5\\n5 4 3 2 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1000000000 1000000000 1000000000 1000000000\\n1 1 2 1 1 1\\n3\\n10 12 8\\n7 5 4\\n', 'output': '12\\n16\\n0\\n4999999995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n3 2 3\\n5\\n1 2 3 4 5\\n5 4 3 3 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1010000000 1000000000 1000000000 1000000000\\n1 1 2 1 1 1\\n3\\n10 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{'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n3 2 3\\n5\\n1 2 3 4 5\\n5 4 1 3 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1000000000 1000000000 1000000000 1000000000\\n1 1 2 1 1 1\\n3\\n10 12 8\\n7 5 4\\n', 'output': '6\\n16\\n0\\n4999999995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 12\\n3 2 3\\n5\\n1 2 3 4 5\\n5 4 1 2 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1000000000 1000000000 1000000000 1000000000\\n1 1 2 1 1 1\\n3\\n10 12 8\\n7 5 4\\n', 'output': '12\\n16\\n0\\n4999999995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 12\\n3 2 4\\n5\\n1 2 3 4 5\\n5 4 3 2 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1000000000 1000000000 1000000000 1000000000\\n1 2 2 1 1 1\\n3\\n10 12 8\\n7 5 4\\n', 'output': '12\\n16\\n0\\n4999999995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n3 2 3\\n5\\n1 2 3 4 5\\n5 4 3 1 1\\n3\\n1 1 1\\n2 2 2\\n6\\n2 1000000000 1010000000 1000000000 1001000000 1000000000\\n1 1 2 1 1 1\\n3\\n10 12 8\\n7 5 4\\n', 'output': '6\\n16\\n0\\n5010999990\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n3 2 3\\n5\\n1 2 3 4 5\\n5 4 3 3 1\\n3\\n1 1 1\\n2 2 2\\n6\\n2 1000000000 1010000000 1000000000 1001000000 1000000000\\n0 1 2 1 1 1\\n3\\n8 12 8\\n2 5 4\\n', 'output': '6\\n16\\n0\\n5010999990\\n6\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n3 1 3\\n5\\n1 2 3 4 5\\n5 4 3 2 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1000000000 1000000000 1000000000 1000000000\\n0 1 2 1 1 1\\n3\\n10 12 8\\n7 5 4\\n', 'output': '7\\n16\\n0\\n4999999995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n3 2 3\\n5\\n1 2 3 4 5\\n5 1 3 3 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1010000000 1000000000 1000000000 1000000000\\n1 1 2 1 1 1\\n3\\n10 12 8\\n7 4 4\\n', 'output': '6\\n14\\n0\\n5009999995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 12\\n3 2 4\\n5\\n1 2 3 4 5\\n5 4 3 2 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1000000000 1000000000 1000000000 1000000000\\n1 2 2 1 1 2\\n3\\n10 12 8\\n7 5 4\\n', 'output': '12\\n16\\n0\\n4999999995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 7\\n3 2 0\\n5\\n1 2 3 4 5\\n5 4 3 2 1\\n3\\n0 1 1\\n2 2 2\\n6\\n1 1000000000 1000000000 1000000000 1000000000 1000000000\\n1 1 2 1 1 2\\n3\\n10 23 8\\n7 5 4\\n', 'output': '9\\n16\\n2\\n4999999995\\n18\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n1 2 1\\n5\\n1 0 3 3 5\\n5 5 3 2 1\\n3\\n1 1 1\\n2 2 2\\n6\\n1 1000000000 1000000000 1000010000 1000000000 1000000000\\n1 1 1 1 1 1\\n3\\n10 12 8\\n7 5 4\\n', 'output': '5\\n19\\n0\\n5000009995\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 6\\n3 2 3\\n5\\n1 2 3 5 5\\n5 1 3 3 1\\n3\\n1 1 1\\n0 2 2\\n6\\n1 1000000000 1010000000 1000000000 1000000000 0000000000\\n1 1 3 1 1 1\\n3\\n10 12 8\\n7 4 4\\n', 'output': '6\\n15\\n4\\n4010000001\\n7\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 5 7\\n6 2 4\\n5\\n1 4 3 4 5\\n5 5 3 2 1\\n3\\n1 1 2\\n2 2 2\\n6\\n1 1000000001 1000000000 1000000000 1000000000 1000000000\\n1 1 2 1 1 1\\n3\\n10 23 11\\n7 5 4\\n', 'output': '10\\n17\\n1\\n4999999996\\n17\\n'}, {'type': 'stdin_stdout', 'input': '5\\n3\\n3 3 6\\n3 2 3\\n5\\n1 2 3 8 5\\n5 1 3 3 2\\n3\\n1 0 1\\n2 2 2\\n6\\n2 1000000000 1010000000 1000000000 1001000000 1000000000\\n1 1 2 1 1 1\\n3\\n5 12 8\\n2 5 4\\n', 'output': '4\\n18\\n2\\n5010999990\\n10\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80517","program":"```python\n# Gifts Fixing\n# https://codeforces.com/problemset/problem/1399/B\n\n\nt = int(input())\n\nfor _ in range(t):\n\t\n\tn = int(input())\n\ta = list(map(int, input().split()))\n\tb = list(map(int, input().split()))\n\t\n\tmin_a = min(a)\n\tmin_b = min(b)\n\n\tcount = 0\n\t\n\tfor i in range(n):\n\t\tdiff_a = a[i] - min_a\n\t\tdiff_b = b[i] - min_b\n\t\t\n\t\tcount += max(diff_a, diff_b)\n\t\n\tprint(count)\n\n\n\n```","inputs":"5\n3\n3 5 6\n3 2 3\n5\n1 2 3 4 5\n5 4 3 2 1\n3\n1 1 1\n2 2 2\n6\n1 1000000000 1000000000 1000000000 1000000000 1000000000\n1 1 1 1 1 1\n3\n10 12 8\n7 5 4\n","output":"6\n16\n0\n4999999995\n7\n","actual_output":"6\n16\n0\n4999999995\n7\n","execution_success":true,"sample_index":12820},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1422_E. Minlexes","prompt":"Solve the following coding problem using the programming language python:\n\nSome time ago Lesha found an entertaining string s consisting of lowercase English letters. Lesha immediately developed an unique algorithm for this string and shared it with you. The algorithm is as follows.\n\nLesha chooses an arbitrary (possibly zero) number of pairs on positions (i, i + 1) in such a way that the following conditions are satisfied: \n\n * for each pair (i, i + 1) the inequality 0 \u2264 i < |s| - 1 holds; \n * for each pair (i, i + 1) the equality s_i = s_{i + 1} holds; \n * there is no index that is contained in more than one pair. \n\nAfter that Lesha removes all characters on indexes contained in these pairs and the algorithm is over. \n\nLesha is interested in the lexicographically smallest strings he can obtain by applying the algorithm to the suffixes of the given string.\n\nInput\n\nThe only line contains the string s (1 \u2264 |s| \u2264 10^5) \u2014 the initial string consisting of lowercase English letters only.\n\nOutput\n\nIn |s| lines print the lengths of the answers and the answers themselves, starting with the answer for the longest suffix. The output can be large, so, when some answer is longer than 10 characters, instead print the first 5 characters, then \"...\", then the last 2 characters of the answer.\n\nExamples\n\nInput\n\n\nabcdd\n\n\nOutput\n\n\n3 abc\n2 bc\n1 c\n0 \n1 d\n\n\nInput\n\n\nabbcdddeaaffdfouurtytwoo\n\n\nOutput\n\n\n18 abbcd...tw\n17 bbcdd...tw\n16 bcddd...tw\n15 cddde...tw\n14 dddea...tw\n13 ddeaa...tw\n12 deaad...tw\n11 eaadf...tw\n10 aadfortytw\n9 adfortytw\n8 dfortytw\n9 fdfortytw\n8 dfortytw\n7 fortytw\n6 ortytw\n5 rtytw\n6 urtytw\n5 rtytw\n4 tytw\n3 ytw\n2 tw\n1 w\n0 \n1 o\n\nNote\n\nConsider the first example.\n\n * The longest suffix is the whole string \"abcdd\". Choosing one pair (4, 5), Lesha obtains \"abc\". \n * The next longest suffix is \"bcdd\". Choosing one pair (3, 4), we obtain \"bc\". \n * The next longest suffix is \"cdd\". Choosing one pair (2, 3), we obtain \"c\". \n * The next longest suffix is \"dd\". Choosing one pair (1, 2), we obtain \"\" (an empty string). \n * The last suffix is the string \"d\". No pair can be chosen, so the answer is \"d\". \n\n\n\nIn the second example, for the longest suffix \"abbcdddeaaffdfouurtytwoo\" choose three pairs (11, 12), (16, 17), (23, 24) and we obtain \"abbcdddeaadfortytw\"\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ns = input().strip()\nN = len(s)\nif len(s) == 1:\n print(1, s[0])\n sys.exit()\nX = [s[-1], s[-2]+s[-1] if s[-2]!=s[-1] else \"\"]\nY = [1, 2 if s[-2]!=s[-1] else 0]\nfor i in range(N-3, -1, -1):\n c = s[i]\n k1 = c+X[-1]\n ng = Y[-1]+1\n if ng > 10:\n k1 = k1[:5] + \"...\" + k1[-2:]\n if c == s[i+1] and k1 > X[-2]:\n k1 = X[-2]\n ng = Y[-2]\n X.append(k1)\n Y.append(ng)\nfor i in range(N-1, -1, -1):\n print(Y[i], X[i])\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': 'abcdd\\n', 'output': '3 abc\\n2 bc\\n1 c\\n0 \\n1 d\\n'}, {'type': 'stdin_stdout', 'input': 'abbcdddeaaffdfouurtytwoo\\n', 'output': '18 abbcd...tw\\n17 bbcdd...tw\\n16 bcddd...tw\\n15 cddde...tw\\n14 dddea...tw\\n13 ddeaa...tw\\n12 deaad...tw\\n11 eaadf...tw\\n10 aadfortytw\\n9 adfortytw\\n8 dfortytw\\n9 fdfortytw\\n8 dfortytw\\n7 fortytw\\n6 ortytw\\n5 rtytw\\n6 urtytw\\n5 rtytw\\n4 tytw\\n3 ytw\\n2 tw\\n1 w\\n0 \\n1 o\\n'}, {'type': 'stdin_stdout', 'input': 'nnnnnnnnnnnnnnnnaaag\\n', 'output': '4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n3 aag\\n2 ag\\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'arexjrujgilmbbao\\n', 'output': '14 arexj...ao\\n13 rexjr...ao\\n12 exjru...ao\\n11 xjruj...ao\\n10 jrujgilmao\\n9 rujgilmao\\n8 ujgilmao\\n7 jgilmao\\n6 gilmao\\n5 ilmao\\n4 lmao\\n3 mao\\n2 ao\\n3 bao\\n2 ao\\n1 o\\n'}, {'type': 'stdin_stdout', 'input': 'gggggggggggggglllll\\n', 'output': '15 ggggg...gl\\n14 ggggg...gl\\n13 ggggg...gl\\n12 ggggg...gl\\n11 ggggg...gl\\n10 gggggggggl\\n9 ggggggggl\\n8 gggggggl\\n7 ggggggl\\n6 gggggl\\n5 ggggl\\n4 gggl\\n3 ggl\\n2 gl\\n1 l\\n0 \\n1 l\\n0 \\n1 l\\n'}, {'type': 'stdin_stdout', 'input': 'bbccccbbbccccbbbccccbbbcccca\\n', 'output': '4 bbba\\n5 bbbba\\n4 bbba\\n5 cbbba\\n4 bbba\\n5 cbbba\\n4 bbba\\n3 bba\\n4 bbba\\n3 bba\\n4 cbba\\n3 bba\\n4 cbba\\n3 bba\\n2 ba\\n3 bba\\n2 ba\\n3 cba\\n2 ba\\n3 cba\\n2 ba\\n1 a\\n2 ba\\n1 a\\n2 ca\\n1 a\\n2 ca\\n1 a\\n'}, {'type': 'stdin_stdout', 'input': 'iiiiiitttttyyyyyyyyp\\n', 'output': '8 iiiiiitp\\n7 iiiiitp\\n6 iiiitp\\n5 iiitp\\n4 iitp\\n3 itp\\n2 tp\\n1 p\\n2 tp\\n1 p\\n2 tp\\n1 p\\n2 yp\\n1 p\\n2 yp\\n1 p\\n2 yp\\n1 p\\n2 yp\\n1 p\\n'}, {'type': 'stdin_stdout', 'input': 'yaryoznawafbayjwkfl\\n', 'output': '19 yaryo...fl\\n18 aryoz...fl\\n17 ryozn...fl\\n16 yozna...fl\\n15 oznaw...fl\\n14 znawa...fl\\n13 nawaf...fl\\n12 awafb...fl\\n11 wafba...fl\\n10 afbayjwkfl\\n9 fbayjwkfl\\n8 bayjwkfl\\n7 ayjwkfl\\n6 yjwkfl\\n5 jwkfl\\n4 wkfl\\n3 kfl\\n2 fl\\n1 l\\n'}, {'type': 'stdin_stdout', 'input': 'hhgxwyrjemygfgs\\n', 'output': '13 gxwyr...gs\\n14 hgxwy...gs\\n13 gxwyr...gs\\n12 xwyrj...gs\\n11 wyrje...gs\\n10 yrjemygfgs\\n9 rjemygfgs\\n8 jemygfgs\\n7 emygfgs\\n6 mygfgs\\n5 ygfgs\\n4 gfgs\\n3 fgs\\n2 gs\\n1 s\\n'}, {'type': 'stdin_stdout', 'input': 'rrrccccccyyyyyyyyyyf\\n', 'output': '8 rccccccf\\n7 ccccccf\\n8 rccccccf\\n7 ccccccf\\n6 cccccf\\n5 ccccf\\n4 cccf\\n3 ccf\\n2 cf\\n1 f\\n2 yf\\n1 f\\n2 yf\\n1 f\\n2 yf\\n1 f\\n2 yf\\n1 f\\n2 yf\\n1 f\\n'}, {'type': 'stdin_stdout', 'input': 'nnnnnnwwwwwwxll\\n', 'output': '13 nnnnn...wx\\n12 nnnnn...wx\\n11 nnnnw...wx\\n10 nnnwwwwwwx\\n9 nnwwwwwwx\\n8 nwwwwwwx\\n7 wwwwwwx\\n6 wwwwwx\\n5 wwwwx\\n4 wwwx\\n3 wwx\\n2 wx\\n1 x\\n0 \\n1 l\\n'}, {'type': 'stdin_stdout', 'input': 'xxxxxxxxxxxxxxtttttt\\n', 'output': '0 \\n1 x\\n0 \\n1 x\\n0 \\n1 x\\n0 \\n1 x\\n0 \\n1 x\\n0 \\n1 x\\n0 \\n1 x\\n0 \\n1 t\\n0 \\n1 t\\n0 \\n1 t\\n'}, {'type': 'stdin_stdout', 'input': 'tt\\n', 'output': '0 \\n1 t\\n'}, {'type': 'stdin_stdout', 'input': 'ttttpppppppppopppppo\\n', 'output': '4 popo\\n5 tpopo\\n4 popo\\n5 tpopo\\n4 popo\\n3 opo\\n4 popo\\n3 opo\\n4 popo\\n3 opo\\n4 popo\\n3 opo\\n4 popo\\n3 opo\\n2 po\\n1 o\\n2 po\\n1 o\\n2 po\\n1 o\\n'}, {'type': 'stdin_stdout', 'input': 'kkkkkccaaaaaqqqqqqqq\\n', 'output': '2 ka\\n1 a\\n2 ka\\n1 a\\n2 ka\\n1 a\\n2 ca\\n1 a\\n0 \\n1 a\\n0 \\n1 a\\n0 \\n1 q\\n0 \\n1 q\\n0 \\n1 q\\n0 \\n1 q\\n'}, {'type': 'stdin_stdout', 'input': 'g\\n', 'output': '1 g\\n'}, {'type': 'stdin_stdout', 'input': 'pcsblopqyxnngyztsn\\n', 'output': '16 pcsbl...sn\\n15 csblo...sn\\n14 sblop...sn\\n13 blopq...sn\\n12 lopqy...sn\\n11 opqyx...sn\\n10 pqyxgyztsn\\n9 qyxgyztsn\\n8 yxgyztsn\\n7 xgyztsn\\n6 gyztsn\\n7 ngyztsn\\n6 gyztsn\\n5 yztsn\\n4 ztsn\\n3 tsn\\n2 sn\\n1 n\\n'}, {'type': 'stdin_stdout', 'input': 'jvzzkkhhssppkxxegfcc\\n', 'output': '8 jvhhkegf\\n7 vhhkegf\\n6 hhkegf\\n7 zhhkegf\\n6 hhkegf\\n7 khhkegf\\n6 hhkegf\\n5 hkegf\\n4 kegf\\n5 skegf\\n4 kegf\\n5 pkegf\\n4 kegf\\n3 egf\\n4 xegf\\n3 egf\\n2 gf\\n1 f\\n0 \\n1 c\\n'}, {'type': 'stdin_stdout', 'input': 'ggggggggggggggggggoa\\n', 'output': '20 ggggg...oa\\n19 ggggg...oa\\n18 ggggg...oa\\n17 ggggg...oa\\n16 ggggg...oa\\n15 ggggg...oa\\n14 ggggg...oa\\n13 ggggg...oa\\n12 ggggg...oa\\n11 ggggg...oa\\n10 ggggggggoa\\n9 gggggggoa\\n8 ggggggoa\\n7 gggggoa\\n6 ggggoa\\n5 gggoa\\n4 ggoa\\n3 goa\\n2 oa\\n1 a\\n'}, {'type': 'stdin_stdout', 'input': 'iiiiiddddpx\\n', 'output': '7 iddddpx\\n6 ddddpx\\n7 iddddpx\\n6 ddddpx\\n7 iddddpx\\n6 ddddpx\\n5 dddpx\\n4 ddpx\\n3 dpx\\n2 px\\n1 x\\n'}, {'type': 'stdin_stdout', 'input': 'yzzyx\\n', 'output': '3 yyx\\n2 yx\\n3 zyx\\n2 yx\\n1 x\\n'}, {'type': 'stdin_stdout', 'input': 'fffffffffffffffppppr\\n', 'output': '20 fffff...pr\\n19 fffff...pr\\n18 fffff...pr\\n17 fffff...pr\\n16 fffff...pr\\n15 fffff...pr\\n14 fffff...pr\\n13 fffff...pr\\n12 fffff...pr\\n11 fffff...pr\\n10 fffffppppr\\n9 ffffppppr\\n8 fffppppr\\n7 ffppppr\\n6 fppppr\\n5 ppppr\\n4 pppr\\n3 ppr\\n2 pr\\n1 r\\n'}, {'type': 'stdin_stdout', 'input': 'vvwwkkppwrrpooiidrfb\\n', 'output': '10 kkppwpdrfb\\n11 vkkpp...fb\\n10 kkppwpdrfb\\n11 wkkpp...fb\\n10 kkppwpdrfb\\n9 kppwpdrfb\\n8 ppwpdrfb\\n7 pwpdrfb\\n6 wpdrfb\\n5 pdrfb\\n6 rpdrfb\\n5 pdrfb\\n4 drfb\\n5 odrfb\\n4 drfb\\n5 idrfb\\n4 drfb\\n3 rfb\\n2 fb\\n1 b\\n'}, {'type': 'stdin_stdout', 'input': 'eefffffffkkkkxxxx\\n', 'output': '3 eef\\n2 ef\\n1 f\\n0 \\n1 f\\n0 \\n1 f\\n0 \\n1 f\\n0 \\n1 k\\n0 \\n1 k\\n0 \\n1 x\\n0 \\n1 x\\n'}, {'type': 'stdin_stdout', 'input': 'eaaccuuznlcoaaxxmmgg\\n', 'output': '12 eaacc...co\\n11 aaccu...co\\n10 accuuznlco\\n9 ccuuznlco\\n8 cuuznlco\\n7 uuznlco\\n6 uznlco\\n5 znlco\\n4 nlco\\n3 lco\\n2 co\\n1 o\\n0 \\n1 a\\n0 \\n1 x\\n0 \\n1 m\\n0 \\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'jjjjjjjjkkdddddiirg\\n', 'output': '9 dddddiirg\\n10 jdddddiirg\\n9 dddddiirg\\n10 jdddddiirg\\n9 dddddiirg\\n10 jdddddiirg\\n9 dddddiirg\\n10 jdddddiirg\\n9 dddddiirg\\n10 kdddddiirg\\n9 dddddiirg\\n8 ddddiirg\\n7 dddiirg\\n6 ddiirg\\n5 diirg\\n4 iirg\\n3 irg\\n2 rg\\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'abba\\n', 'output': '2 aa\\n1 a\\n2 ba\\n1 a\\n'}, {'type': 'stdin_stdout', 'input': 'go\\n', 'output': '2 go\\n1 o\\n'}, {'type': 'stdin_stdout', 'input': 'bbbbbbkkyya\\n', 'output': '1 a\\n2 ba\\n1 a\\n2 ba\\n1 a\\n2 ba\\n1 a\\n2 ka\\n1 a\\n2 ya\\n1 a\\n'}, {'type': 'stdin_stdout', 'input': 'iiiiilleeeeeejjjjjjn\\n', 'output': '14 ieeee...jn\\n13 eeeee...jn\\n14 ieeee...jn\\n13 eeeee...jn\\n14 ieeee...jn\\n13 eeeee...jn\\n14 leeee...jn\\n13 eeeee...jn\\n12 eeeee...jn\\n11 eeeej...jn\\n10 eeejjjjjjn\\n9 eejjjjjjn\\n8 ejjjjjjn\\n7 jjjjjjn\\n6 jjjjjn\\n5 jjjjn\\n4 jjjn\\n3 jjn\\n2 jn\\n1 n\\n'}, {'type': 'stdin_stdout', 'input': 'iivvottssxllnaaaessn\\n', 'output': '14 iioss...en\\n13 iossx...en\\n12 ossxl...en\\n13 vossx...en\\n12 ossxl...en\\n11 ssxll...en\\n12 tssxl...en\\n11 ssxll...en\\n10 sxllnaaaen\\n9 xllnaaaen\\n8 llnaaaen\\n7 lnaaaen\\n6 naaaen\\n5 aaaen\\n4 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xzccc...rw\\n207 zcccc...rw\\n206 ccccc...rw\\n207 zcccc...rw\\n206 ccccc...rw\\n207 zcccc...rw\\n206 ccccc...rw\\n207 zcccc...rw\\n206 ccccc...rw\\n207 zcccc...rw\\n206 ccccc...rw\\n207 zcccc...rw\\n206 ccccc...rw\\n205 ccccc...rw\\n204 ccccj...rw\\n203 cccjb...rw\\n202 ccjbb...rw\\n201 cjbbb...rw\\n200 jbbbb...rw\\n199 bbbbb...rw\\n200 jbbbb...rw\\n199 bbbbb...rw\\n200 jbbbb...rw\\n199 bbbbb...rw\\n200 lbbbb...rw\\n199 bbbbb...rw\\n198 bbbbb...rw\\n197 bbbbb...rw\\n196 bbbbh...rw\\n195 bbbha...rw\\n194 bbhaa...rw\\n193 bhaaa...rw\\n192 haaas...rw\\n191 aaasf...rw\\n192 haaas...rw\\n191 aaasf...rw\\n192 haaas...rw\\n191 aaasf...rw\\n192 gaaas...rw\\n191 aaasf...rw\\n192 gaaas...rw\\n191 aaasf...rw\\n192 gaaas...rw\\n191 aaasf...rw\\n192 laaas...rw\\n191 aaasf...rw\\n192 laaas...rw\\n191 aaasf...rw\\n192 laaas...rw\\n191 aaasf...rw\\n190 aasff...rw\\n189 asfff...rw\\n188 sffff...rw\\n187 fffff...rw\\n188 sffff...rw\\n187 fffff...rw\\n188 sffff...rw\\n187 fffff...rw\\n188 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zcccc...rw\\n117 ccccc...rw\\n118 ycccc...rw\\n117 ccccc...rw\\n118 ycccc...rw\\n117 ccccc...rw\\n118 ycccc...rw\\n117 ccccc...rw\\n118 ycccc...rw\\n117 ccccc...rw\\n118 ycccc...rw\\n117 ccccc...rw\\n116 ccccl...rw\\n115 cccll...rw\\n114 ccllo...rw\\n113 cllog...rw\\n112 llogg...rw\\n113 ullog...rw\\n112 llogg...rw\\n113 ullog...rw\\n112 llogg...rw\\n113 ullog...rw\\n112 llogg...rw\\n113 ullog...rw\\n112 llogg...rw\\n113 nllog...rw\\n112 llogg...rw\\n113 nllog...rw\\n112 llogg...rw\\n113 nllog...rw\\n112 llogg...rw\\n113 nllog...rw\\n112 llogg...rw\\n113 vllog...rw\\n112 llogg...rw\\n113 vllog...rw\\n112 llogg...rw\\n113 vllog...rw\\n112 llogg...rw\\n113 vllog...rw\\n112 llogg...rw\\n113 vllog...rw\\n112 llogg...rw\\n113 sllog...rw\\n112 llogg...rw\\n111 loggg...rw\\n110 ogggg...rw\\n109 ggggg...rw\\n110 ogggg...rw\\n109 ggggg...rw\\n110 ogggg...rw\\n109 ggggg...rw\\n108 ggggg...rw\\n107 ggggg...rw\\n106 ggggg...rw\\n105 ggggl...rw\\n104 gggll...rw\\n103 gglll...rw\\n102 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stbbs...rw\\n29 tbbsq...rw\\n30 vtbbs...rw\\n29 tbbsq...rw\\n30 vtbbs...rw\\n29 tbbsq...rw\\n30 vtbbs...rw\\n29 tbbsq...rw\\n30 vtbbs...rw\\n29 tbbsq...rw\\n28 bbsqq...rw\\n29 tbbsq...rw\\n28 bbsqq...rw\\n29 tbbsq...rw\\n28 bbsqq...rw\\n29 tbbsq...rw\\n28 bbsqq...rw\\n29 mbbsq...rw\\n28 bbsqq...rw\\n29 mbbsq...rw\\n28 bbsqq...rw\\n29 wbbsq...rw\\n28 bbsqq...rw\\n29 wbbsq...rw\\n28 bbsqq...rw\\n29 wbbsq...rw\\n28 bbsqq...rw\\n27 bsqqq...rw\\n26 sqqqq...rw\\n25 qqqqq...rw\\n26 sqqqq...rw\\n25 qqqqq...rw\\n26 sqqqq...rw\\n25 qqqqq...rw\\n26 sqqqq...rw\\n25 qqqqq...rw\\n24 qqqqs...rw\\n23 qqqss...rw\\n22 qqssu...rw\\n21 qssug...rw\\n20 ssugg...rw\\n21 zssug...rw\\n20 ssugg...rw\\n21 zssug...rw\\n20 ssugg...rw\\n19 suggg...rw\\n18 ugggg...rw\\n17 ggggg...rw\\n18 jgggg...rw\\n17 ggggg...rw\\n16 ggggg...rw\\n15 ggggg...rw\\n14 ggggg...rw\\n13 ggggr...rw\\n12 gggrr...rw\\n11 ggrrr...rw\\n10 grrrrrrrrw\\n9 rrrrrrrrw\\n10 wrrrrrrrrw\\n9 rrrrrrrrw\\n10 wrrrrrrrrw\\n9 rrrrrrrrw\\n10 wrrrrrrrrw\\n9 rrrrrrrrw\\n10 wrrrrrrrrw\\n9 rrrrrrrrw\\n8 rrrrrrrw\\n7 rrrrrrw\\n6 rrrrrw\\n5 rrrrw\\n4 rrrw\\n3 rrw\\n2 rw\\n1 w\\n2 xw\\n1 w\\n2 xw\\n1 w\\n2 xw\\n1 w\\n0 \\n1 w\\n0 \\n1 a\\n0 \\n1 a\\n0 \\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'nnnnnnmnnnnnnnnnaaag\\n', 'output': '6 mnaaag\\n7 nmnaaag\\n6 mnaaag\\n7 nmnaaag\\n6 mnaaag\\n7 nmnaaag\\n6 mnaaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n3 aag\\n2 ag\\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'oabbmligjurjxera\\n', 'output': '16 oabbm...ra\\n15 abbml...ra\\n14 bbmli...ra\\n13 bmlig...ra\\n12 mligj...ra\\n11 ligju...ra\\n10 igjurjxera\\n9 gjurjxera\\n8 jurjxera\\n7 urjxera\\n6 rjxera\\n5 jxera\\n4 xera\\n3 era\\n2 ra\\n1 a\\n'}, {'type': 'stdin_stdout', 'input': 'lllllgggggggggggggg\\n', 'output': '1 l\\n0 \\n1 l\\n0 \\n1 l\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'accccbbbccccbbbccccbbbccccbb\\n', 'output': '4 abbb\\n3 bbb\\n4 cbbb\\n3 bbb\\n4 cbbb\\n3 bbb\\n2 bb\\n3 bbb\\n2 bb\\n3 cbb\\n2 bb\\n3 cbb\\n2 bb\\n1 b\\n2 bb\\n1 b\\n2 cb\\n1 b\\n2 cb\\n1 b\\n0 \\n1 b\\n0 \\n1 c\\n0 \\n1 c\\n0 \\n1 b\\n'}, {'type': 'stdin_stdout', 'input': 'iiyiiitttttyyyyyyyip\\n', 'output': '14 iiyii...ip\\n13 iyiii...ip\\n12 yiiit...ip\\n11 iiitt...ip\\n10 iitttttyip\\n9 itttttyip\\n8 tttttyip\\n7 ttttyip\\n6 tttyip\\n5 ttyip\\n4 tyip\\n3 yip\\n2 ip\\n3 yip\\n2 ip\\n3 yip\\n2 ip\\n3 yip\\n2 ip\\n1 p\\n'}, {'type': 'stdin_stdout', 'input': 'yarynznawafbayjwkfl\\n', 'output': '19 yaryn...fl\\n18 arynz...fl\\n17 rynzn...fl\\n16 ynzna...fl\\n15 nznaw...fl\\n14 znawa...fl\\n13 nawaf...fl\\n12 awafb...fl\\n11 wafba...fl\\n10 afbayjwkfl\\n9 fbayjwkfl\\n8 bayjwkfl\\n7 ayjwkfl\\n6 yjwkfl\\n5 jwkfl\\n4 wkfl\\n3 kfl\\n2 fl\\n1 l\\n'}, {'type': 'stdin_stdout', 'input': 'hsgxwyrjemygfgh\\n', 'output': '15 hsgxw...gh\\n14 sgxwy...gh\\n13 gxwyr...gh\\n12 xwyrj...gh\\n11 wyrje...gh\\n10 yrjemygfgh\\n9 rjemygfgh\\n8 jemygfgh\\n7 emygfgh\\n6 mygfgh\\n5 ygfgh\\n4 gfgh\\n3 fgh\\n2 gh\\n1 h\\n'}, {'type': 'stdin_stdout', 'input': 'fyyyyyyyyyyccccccrrr\\n', 'output': '8 fccccccr\\n7 ccccccr\\n8 yccccccr\\n7 ccccccr\\n8 yccccccr\\n7 ccccccr\\n8 yccccccr\\n7 ccccccr\\n8 yccccccr\\n7 ccccccr\\n8 yccccccr\\n7 ccccccr\\n6 cccccr\\n5 ccccr\\n4 cccr\\n3 ccr\\n2 cr\\n1 r\\n0 \\n1 r\\n'}, {'type': 'stdin_stdout', 'input': 'llxwwwwwwnnnnnn\\n', 'output': '3 llx\\n2 lx\\n1 x\\n0 \\n1 w\\n0 \\n1 w\\n0 \\n1 w\\n0 \\n1 n\\n0 \\n1 n\\n0 \\n1 n\\n'}, {'type': 'stdin_stdout', 'input': 'ttttttxxxxxxxxxxxxxx\\n', 'output': '0 \\n1 t\\n0 \\n1 t\\n0 \\n1 t\\n0 \\n1 x\\n0 \\n1 x\\n0 \\n1 x\\n0 \\n1 x\\n0 \\n1 x\\n0 \\n1 x\\n0 \\n1 x\\n'}, {'type': 'stdin_stdout', 'input': 'ut\\n', 'output': '2 ut\\n1 t\\n'}, {'type': 'stdin_stdout', 'input': 'ttttpopppppppopppppo\\n', 'output': '6 popopo\\n7 tpopopo\\n6 popopo\\n7 tpopopo\\n6 popopo\\n5 opopo\\n4 popo\\n3 opo\\n4 popo\\n3 opo\\n4 popo\\n3 opo\\n4 popo\\n3 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'aogggggggggggggggggg\\n', 'output': '2 ao\\n1 o\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'iiiiideddpx\\n', 'output': '7 ideddpx\\n6 deddpx\\n7 ideddpx\\n6 deddpx\\n7 ideddpx\\n6 deddpx\\n5 eddpx\\n4 ddpx\\n3 dpx\\n2 px\\n1 x\\n'}, {'type': 'stdin_stdout', 'input': 'yxzyz\\n', 'output': '5 yxzyz\\n4 xzyz\\n3 zyz\\n2 yz\\n1 z\\n'}, {'type': 'stdin_stdout', 'input': 'ffffffffffffgffppppr\\n', 'output': '20 fffff...pr\\n19 fffff...pr\\n18 fffff...pr\\n17 fffff...pr\\n16 fffff...pr\\n15 fffff...pr\\n14 fffff...pr\\n13 fffff...pr\\n12 ffffg...pr\\n11 fffgf...pr\\n10 ffgffppppr\\n9 fgffppppr\\n8 gffppppr\\n7 ffppppr\\n6 fppppr\\n5 ppppr\\n4 pppr\\n3 ppr\\n2 pr\\n1 r\\n'}, {'type': 'stdin_stdout', 'input': 'vvrwkkppwrwpooiidrfb\\n', 'output': '14 rwkkp...fb\\n15 vrwkk...fb\\n14 rwkkp...fb\\n13 wkkpp...fb\\n12 kkppw...fb\\n11 kppwr...fb\\n10 ppwrwpdrfb\\n9 pwrwpdrfb\\n8 wrwpdrfb\\n7 rwpdrfb\\n6 wpdrfb\\n5 pdrfb\\n4 drfb\\n5 odrfb\\n4 drfb\\n5 idrfb\\n4 drfb\\n3 rfb\\n2 fb\\n1 b\\n'}, {'type': 'stdin_stdout', 'input': 'eefffffffkkxkkxxx\\n', 'output': '15 eefff...kx\\n14 effff...kx\\n13 fffff...kx\\n12 fffff...kx\\n11 fffff...kx\\n10 ffffkkxkkx\\n9 fffkkxkkx\\n8 ffkkxkkx\\n7 fkkxkkx\\n6 kkxkkx\\n5 kxkkx\\n4 xkkx\\n3 kkx\\n2 kx\\n1 x\\n0 \\n1 x\\n'}, {'type': 'stdin_stdout', 'input': 'ggmmxxaaoclnzuuccaae\\n', 'output': '10 aaoclnzaae\\n11 gaaoc...ae\\n10 aaoclnzaae\\n11 maaoc...ae\\n10 aaoclnzaae\\n11 xaaoc...ae\\n10 aaoclnzaae\\n9 aoclnzaae\\n8 oclnzaae\\n7 clnzaae\\n6 lnzaae\\n5 nzaae\\n4 zaae\\n3 aae\\n4 uaae\\n3 aae\\n4 caae\\n3 aae\\n2 ae\\n1 e\\n'}, {'type': 'stdin_stdout', 'input': 'jjjjjjjjkkdddddihrg\\n', 'output': '9 dddddihrg\\n10 jdddddihrg\\n9 dddddihrg\\n10 jdddddihrg\\n9 dddddihrg\\n10 jdddddihrg\\n9 dddddihrg\\n10 jdddddihrg\\n9 dddddihrg\\n10 kdddddihrg\\n9 dddddihrg\\n8 ddddihrg\\n7 dddihrg\\n6 ddihrg\\n5 dihrg\\n4 ihrg\\n3 hrg\\n2 rg\\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'bbba\\n', 'output': '2 ba\\n1 a\\n2 ba\\n1 a\\n'}, {'type': 'stdin_stdout', 'input': 'og\\n', 'output': '2 og\\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'ayykkbbbbbb\\n', 'output': '1 a\\n0 \\n1 y\\n0 \\n1 k\\n0 \\n1 b\\n0 \\n1 b\\n0 \\n1 b\\n'}, {'type': 'stdin_stdout', 'input': 'njjjjjjeeeeeelliiiii\\n', 'output': '8 neeeeeei\\n7 eeeeeei\\n8 jeeeeeei\\n7 eeeeeei\\n8 jeeeeeei\\n7 eeeeeei\\n8 jeeeeeei\\n7 eeeeeei\\n6 eeeeei\\n5 eeeei\\n4 eeei\\n3 eei\\n2 ei\\n1 i\\n2 li\\n1 i\\n0 \\n1 i\\n0 \\n1 i\\n'}, {'type': 'stdin_stdout', 'input': 'iivuottssxllnaaaessn\\n', 'output': '16 iivuo...en\\n15 ivuos...en\\n14 vuoss...en\\n13 uossx...en\\n12 ossxl...en\\n11 ssxll...en\\n12 tssxl...en\\n11 ssxll...en\\n10 sxllnaaaen\\n9 xllnaaaen\\n8 llnaaaen\\n7 lnaaaen\\n6 naaaen\\n5 aaaen\\n4 aaen\\n3 aen\\n2 en\\n1 n\\n2 sn\\n1 n\\n'}, {'type': 'stdin_stdout', 'input': 'qqppennigzzyydooljjk\\n', 'output': '8 eigdljjk\\n9 qeigdljjk\\n8 eigdljjk\\n9 peigdljjk\\n8 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zxxxxxy\\n6 xxxxxy\\n7 zxxxxxy\\n6 xxxxxy\\n7 zxxxxxy\\n6 xxxxxy\\n5 xxxxy\\n4 xxxy\\n3 xxy\\n2 xy\\n1 y\\n'}, {'type': 'stdin_stdout', 'input': 'abddc\\n', 'output': '3 abc\\n2 bc\\n1 c\\n2 dc\\n1 c\\n'}, {'type': 'stdin_stdout', 'input': 'oowtytruuofdffaaedddcbba\\n', 'output': '16 oowty...ca\\n15 owtyt...ca\\n14 wtytr...ca\\n13 tytro...ca\\n12 ytrof...ca\\n11 trofd...ca\\n10 rofdaaedca\\n9 ofdaaedca\\n10 uofdaaedca\\n9 ofdaaedca\\n8 fdaaedca\\n7 daaedca\\n6 aaedca\\n7 faaedca\\n6 aaedca\\n5 aedca\\n4 edca\\n3 dca\\n2 ca\\n3 dca\\n2 ca\\n1 a\\n2 ba\\n1 a\\n'}, {'type': 'stdin_stdout', 'input': 'nnnnnmmnnnnnnnnnaaag\\n', 'output': '8 nmmnaaag\\n7 mmnaaag\\n8 nmmnaaag\\n7 mmnaaag\\n8 nmmnaaag\\n7 mmnaaag\\n6 mnaaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n5 naaag\\n4 aaag\\n3 aag\\n2 ag\\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'oabamligjurjxerb\\n', 'output': '16 oabam...rb\\n15 abaml...rb\\n14 bamli...rb\\n13 amlig...rb\\n12 mligj...rb\\n11 ligju...rb\\n10 igjurjxerb\\n9 gjurjxerb\\n8 jurjxerb\\n7 urjxerb\\n6 rjxerb\\n5 jxerb\\n4 xerb\\n3 erb\\n2 rb\\n1 b\\n'}, {'type': 'stdin_stdout', 'input': 'lllllggggghgggggggg\\n', 'output': '7 lgggggh\\n6 gggggh\\n7 lgggggh\\n6 gggggh\\n7 lgggggh\\n6 gggggh\\n5 ggggh\\n4 gggh\\n3 ggh\\n2 gh\\n1 h\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n0 \\n1 g\\n'}, {'type': 'stdin_stdout', 'input': 'accccbbbccccbbbccccbbbcccccb\\n', 'output': '12 abbbb...cb\\n11 bbbbb...cb\\n12 cbbbb...cb\\n11 bbbbb...cb\\n12 cbbbb...cb\\n11 bbbbb...cb\\n10 bbbbbbbbcb\\n9 bbbbbbbcb\\n8 bbbbbbcb\\n9 cbbbbbbcb\\n8 bbbbbbcb\\n9 cbbbbbbcb\\n8 bbbbbbcb\\n7 bbbbbcb\\n6 bbbbcb\\n5 bbbcb\\n6 cbbbcb\\n5 bbbcb\\n6 cbbbcb\\n5 bbbcb\\n4 bbcb\\n3 bcb\\n2 cb\\n1 b\\n2 cb\\n1 b\\n2 cb\\n1 b\\n'}, {'type': 'stdin_stdout', 'input': 'ihyiiitttttyyyyyyyip\\n', 'output': '14 ihyii...ip\\n13 hyiii...ip\\n12 yiiit...ip\\n11 iiitt...ip\\n10 iitttttyip\\n9 itttttyip\\n8 tttttyip\\n7 ttttyip\\n6 tttyip\\n5 ttyip\\n4 tyip\\n3 yip\\n2 ip\\n3 yip\\n2 ip\\n3 yip\\n2 ip\\n3 yip\\n2 ip\\n1 p\\n'}, {'type': 'stdin_stdout', 'input': 'yarynznbwafbayjwkfl\\n', 'output': '19 yaryn...fl\\n18 arynz...fl\\n17 rynzn...fl\\n16 ynznb...fl\\n15 nznbw...fl\\n14 znbwa...fl\\n13 nbwaf...fl\\n12 bwafb...fl\\n11 wafba...fl\\n10 afbayjwkfl\\n9 fbayjwkfl\\n8 bayjwkfl\\n7 ayjwkfl\\n6 yjwkfl\\n5 jwkfl\\n4 wkfl\\n3 kfl\\n2 fl\\n1 l\\n'}, {'type': 'stdin_stdout', 'input': 'hsgywyrjemxgfgh\\n', 'output': '15 hsgyw...gh\\n14 sgywy...gh\\n13 gywyr...gh\\n12 ywyrj...gh\\n11 wyrje...gh\\n10 yrjemxgfgh\\n9 rjemxgfgh\\n8 jemxgfgh\\n7 emxgfgh\\n6 mxgfgh\\n5 xgfgh\\n4 gfgh\\n3 fgh\\n2 gh\\n1 h\\n'}, {'type': 'stdin_stdout', 'input': 'fcyyyyyyyyycccyccrrr\\n', 'output': '10 fcycccyccr\\n9 cycccyccr\\n8 ycccyccr\\n7 cccyccr\\n8 ycccyccr\\n7 cccyccr\\n8 ycccyccr\\n7 cccyccr\\n8 ycccyccr\\n7 cccyccr\\n8 ycccyccr\\n7 cccyccr\\n6 ccyccr\\n5 cyccr\\n4 yccr\\n3 ccr\\n2 cr\\n1 r\\n0 \\n1 r\\n'}, {'type': 'stdin_stdout', 'input': 'nnnnnnwwwwwwxkl\\n', 'output': '15 nnnnn...kl\\n14 nnnnn...kl\\n13 nnnnw...kl\\n12 nnnww...kl\\n11 nnwww...kl\\n10 nwwwwwwxkl\\n9 wwwwwwxkl\\n8 wwwwwxkl\\n7 wwwwxkl\\n6 wwwxkl\\n5 wwxkl\\n4 wxkl\\n3 xkl\\n2 kl\\n1 l\\n'}, {'type': 'stdin_stdout', 'input': 'xxxxxxxxxxxxxxsttttt\\n', 'output': '2 st\\n3 xst\\n2 st\\n3 xst\\n2 st\\n3 xst\\n2 st\\n3 xst\\n2 st\\n3 xst\\n2 st\\n3 xst\\n2 st\\n3 xst\\n2 st\\n1 t\\n0 \\n1 t\\n0 \\n1 t\\n'}, {'type': 'stdin_stdout', 'input': 'uu\\n', 'output': '0 \\n1 u\\n'}, {'type': 'stdin_stdout', 'input': 'opppppopppppppoptttt\\n', 'output': '6 opopop\\n5 popop\\n4 opop\\n5 popop\\n4 opop\\n5 popop\\n4 opop\\n3 pop\\n2 op\\n3 pop\\n2 op\\n3 pop\\n2 op\\n3 pop\\n2 op\\n1 p\\n0 \\n1 t\\n0 \\n1 t\\n'}, {'type': 'stdin_stdout', 'input': 'kkkkkccbaaaaqqqqqqqq\\n', 'output': '2 kb\\n1 b\\n2 kb\\n1 b\\n2 kb\\n1 b\\n2 cb\\n1 b\\n0 \\n1 a\\n0 \\n1 a\\n0 \\n1 q\\n0 \\n1 q\\n0 \\n1 q\\n0 \\n1 q\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80521","program":"```python\nimport sys\ns = input().strip()\nN = len(s)\nif len(s) == 1:\n print(1, s[0])\n sys.exit()\nX = [s[-1], s[-2]+s[-1] if s[-2]!=s[-1] else \"\"]\nY = [1, 2 if s[-2]!=s[-1] else 0]\nfor i in range(N-3, -1, -1):\n c = s[i]\n k1 = c+X[-1]\n ng = Y[-1]+1\n if ng > 10:\n k1 = k1[:5] + \"...\" + k1[-2:]\n if c == s[i+1] and k1 > X[-2]:\n k1 = X[-2]\n ng = Y[-2]\n X.append(k1)\n Y.append(ng)\nfor i in range(N-1, -1, -1):\n print(Y[i], X[i])\n\n```","inputs":"abcdd\n","output":"3 abc\n2 bc\n1 c\n0 \n1 d\n","actual_output":"3 abc\n2 bc\n1 c\n0 \n1 d\n","execution_success":true,"sample_index":12821},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1467_E. Distinctive Roots in a Tree","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given a tree with n vertices. Each vertex i has a value a_i associated with it.\n\nLet us root the tree at some vertex v. The vertex v is called a distinctive root if the following holds: in all paths that start at v and end at some other node, all the values encountered are distinct. Two different paths may have values in common but a single path must have all distinct values.\n\nFind the number of distinctive roots in the tree.\n\nInput\n\nThe first line of the input contains a single integer n (1 \u2264 n \u2264 2\u22c510^5) \u2014 the number of vertices in the tree.\n\nThe next line contains n space-separated integers a_1, a_2, ..., a_n (1 \u2264 a_i \u2264 10^9).\n\nThe following n-1 lines each contain two space-separated integers u and v (1 \u2264 u, v \u2264 n), denoting an edge from u to v.\n\nIt is guaranteed that the edges form a tree.\n\nOutput\n\nPrint a single integer \u2014 the number of distinctive roots in the tree.\n\nExamples\n\nInput\n\n\n5\n2 5 1 1 4\n1 2\n1 3\n2 4\n2 5\n\n\nOutput\n\n\n3\n\nInput\n\n\n5\n2 1 1 1 4\n1 2\n1 3\n2 4\n2 5\n\n\nOutput\n\n\n0\n\nNote\n\nIn the first example, 1, 2 and 5 are distinctive roots.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport io, os\nfrom collections import Counter, defaultdict, deque\n\nclass LazySegmentTree:\n def __init__(self, data, default=0, func=max):\n _default = default\n self._func = func\n\n self._len = len(data)\n self._size = _size = 1 << (self._len - 1).bit_length()\n self._lazy = [0] * (2 * _size)\n\n self.data = [default] * (2 * _size)\n self.data[_size : _size + self._len] = data\n for i in reversed(range(_size)):\n self.data[i] = func(self.data[i + i], self.data[i + i + 1])\n\n def __len__(self):\n return self._len\n\n def _push(self, idx):\n q, self._lazy[idx] = self._lazy[idx], 0\n\n self._lazy[2 * idx] += q\n self._lazy[2 * idx + 1] += q\n self.data[2 * idx] += q\n self.data[2 * idx + 1] += q\n\n def _update(self, idx):\n for i in reversed(range(1, idx.bit_length())):\n self._push(idx >> i)\n\n def _build(self, idx):\n idx >>= 1\n while idx:\n self.data[idx] = (\n self._func(self.data[2 * idx], self.data[2 * idx + 1]) + self._lazy[idx]\n )\n idx >>= 1\n\n def add(self, start, stop, value):\n if start == stop:\n return\n start = start_copy = start + self._size\n stop = stop_copy = stop + self._size\n while start < stop:\n if start & 1:\n self._lazy[start] += value\n self.data[start] += value\n start += 1\n if stop & 1:\n stop -= 1\n self._lazy[stop] += value\n self.data[stop] += value\n start >>= 1\n stop >>= 1\n self._build(start_copy)\n self._build(stop_copy - 1)\n\n def query(self, start, stop, default=0):\n start += self._size\n stop += self._size\n self._update(start)\n self._update(stop - 1)\n\n res = default\n while start < stop:\n if start & 1:\n res = self._func(res, self.data[start])\n start += 1\n if stop & 1:\n stop -= 1\n res = self._func(res, self.data[stop])\n start >>= 1\n stop >>= 1\n return res\n\n def __repr__(self):\n return \"LazySegmentTree({0})\".format(self.data)\n\n\ndef solve(N, A, edges):\n\n graph = [[] for i in range(N)]\n for u, indices in edges:\n graph[u].append(indices)\n graph[indices].append(u)\n\n # Build euler tour\n eulerTour = []\n root = 0\n stack = [root]\n seen = [False] * len(graph)\n while stack:\n node = stack.pop()\n eulerTour.append(node)\n if not seen[node]:\n seen[node] = True\n for nbr in graph[node]:\n if not seen[nbr]:\n stack.append(node)\n stack.append(nbr)\n\n assert eulerTour[0] == eulerTour[-1]\n eulerTour.pop()\n tourByValues = defaultdict(list)\n for i, x in enumerate(eulerTour):\n tourByValues[A[x]].append(i)\n segTree = LazySegmentTree([0] * len(eulerTour), 0, lambda x, y: x + y)\n\n for k, indices in tourByValues.items():\n nodes = set(eulerTour[i] for i in indices)\n if len(nodes) >= 2:\n for i in indices:\n segTree.add(i, i + 1, 1)\n subtour = []\n for i, j in zip(indices, indices[1:]):\n x = eulerTour[i]\n y = eulerTour[j]\n if x == y:\n segTree.add(i, j + 1, 1)\n else:\n subtour.append(i)\n i = indices[-1]\n j = indices[0]\n x = eulerTour[i]\n y = eulerTour[j]\n if x == y:\n segTree.add(i, len(eulerTour), 1)\n segTree.add(0, j + 1, 1)\n else:\n subtour.append(i)\n\n if len(nodes) != len(subtour):\n # Subtour has non leaves, impossible\n return 0\n if False:\n print(\"label\", k, \"visits\", indices, \"nodes\", nodes)\n print(\n \"\\t\".join(\n str(eulerTour[i]) + \":\" + str(A[eulerTour[i]])\n for i in range(len(eulerTour))\n )\n )\n for i in range(len(eulerTour)):\n if segTree.query(i, i + 1) != 0:\n print(\"x\", end=\"\\t\")\n else:\n print(\"o\", end=\"\\t\")\n print()\n print()\n return N - len(set([eulerTour[i] for i in range(len(eulerTour)) if segTree.query(i, i + 1) != 0]))\n\ninput = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline\nN = int(input());A = [int(x) for x in input().split()];e = [[int(x) - 1 for x in input().split()] for i in range(N - 1)];print(solve(N, A, e))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n2 5 1 1 4\\n1 2\\n1 3\\n2 4\\n2 5\\n', 'output': '\\n3'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 1 1 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'input': '12\\n4 1 6 1 7 1 1 3 2 5 3 2\\n1 2\\n1 10\\n1 3\\n3 4\\n7 9\\n3 5\\n5 7\\n7 8\\n1 11\\n11 12\\n3 6\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n14 3 13 26 4 14 1 6 5 28\\n2 1\\n3 2\\n4 2\\n5 4\\n6 2\\n7 4\\n8 2\\n9 5\\n10 4\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '10\\n14 3 13 19 6 20 1 6 5 28\\n2 1\\n3 2\\n4 2\\n5 4\\n6 2\\n7 4\\n8 4\\n9 5\\n10 4\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 6 3 1 12 4\\n1 3\\n1 6\\n4 3\\n2 4\\n3 5\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '12\\n4 1 6 1 4 1 1 3 2 5 3 2\\n1 2\\n2 10\\n1 3\\n3 4\\n7 9\\n3 5\\n5 7\\n7 8\\n1 11\\n11 12\\n3 6\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 3 2 1 4 2\\n1 2\\n1 6\\n2 3\\n2 4\\n2 5\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n3 3 5 3 1 1\\n1 2\\n2 3\\n3 4\\n1 5\\n1 6\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 1 6 1\\n1 2\\n1 4\\n3 4\\n4 5\\n', 'output': '2\\n'}, {'type': 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'0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n2 1 1 1 0\\n1 2\\n1 3\\n2 4\\n1 5\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1 2 2 1 2 4\\n1 2\\n2 3\\n1 4\\n1 5\\n1 6\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '12\\n7 1 6 2 4 1 0 3 2 1 3 2\\n1 2\\n2 10\\n1 3\\n6 4\\n7 9\\n3 5\\n5 7\\n6 8\\n1 11\\n11 12\\n3 6\\n', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80529","program":"```python\nimport io, os\nfrom collections import Counter, defaultdict, deque\n\nclass LazySegmentTree:\n def __init__(self, data, default=0, func=max):\n _default = default\n self._func = func\n\n self._len = len(data)\n self._size = _size = 1 << (self._len - 1).bit_length()\n self._lazy = [0] * (2 * _size)\n\n self.data = [default] * (2 * _size)\n self.data[_size : _size + self._len] = data\n for i in reversed(range(_size)):\n self.data[i] = func(self.data[i + i], self.data[i + i + 1])\n\n def __len__(self):\n return self._len\n\n def _push(self, idx):\n q, self._lazy[idx] = self._lazy[idx], 0\n\n self._lazy[2 * idx] += q\n self._lazy[2 * idx + 1] += q\n self.data[2 * idx] += q\n self.data[2 * idx + 1] += q\n\n def _update(self, idx):\n for i in reversed(range(1, idx.bit_length())):\n self._push(idx >> i)\n\n def _build(self, idx):\n idx >>= 1\n while idx:\n self.data[idx] = (\n self._func(self.data[2 * idx], self.data[2 * idx + 1]) + self._lazy[idx]\n )\n idx >>= 1\n\n def add(self, start, stop, value):\n if start == stop:\n return\n start = start_copy = start + self._size\n stop = stop_copy = stop + self._size\n while start < stop:\n if start & 1:\n self._lazy[start] += value\n self.data[start] += value\n start += 1\n if stop & 1:\n stop -= 1\n self._lazy[stop] += value\n self.data[stop] += value\n start >>= 1\n stop >>= 1\n self._build(start_copy)\n self._build(stop_copy - 1)\n\n def query(self, start, stop, default=0):\n start += self._size\n stop += self._size\n self._update(start)\n self._update(stop - 1)\n\n res = default\n while start < stop:\n if start & 1:\n res = self._func(res, self.data[start])\n start += 1\n if stop & 1:\n stop -= 1\n res = self._func(res, self.data[stop])\n start >>= 1\n stop >>= 1\n return res\n\n def __repr__(self):\n return \"LazySegmentTree({0})\".format(self.data)\n\n\ndef solve(N, A, edges):\n\n graph = [[] for i in range(N)]\n for u, indices in edges:\n graph[u].append(indices)\n graph[indices].append(u)\n\n # Build euler tour\n eulerTour = []\n root = 0\n stack = [root]\n seen = [False] * len(graph)\n while stack:\n node = stack.pop()\n eulerTour.append(node)\n if not seen[node]:\n seen[node] = True\n for nbr in graph[node]:\n if not seen[nbr]:\n stack.append(node)\n stack.append(nbr)\n\n assert eulerTour[0] == eulerTour[-1]\n eulerTour.pop()\n tourByValues = defaultdict(list)\n for i, x in enumerate(eulerTour):\n tourByValues[A[x]].append(i)\n segTree = LazySegmentTree([0] * len(eulerTour), 0, lambda x, y: x + y)\n\n for k, indices in tourByValues.items():\n nodes = set(eulerTour[i] for i in indices)\n if len(nodes) >= 2:\n for i in indices:\n segTree.add(i, i + 1, 1)\n subtour = []\n for i, j in zip(indices, indices[1:]):\n x = eulerTour[i]\n y = eulerTour[j]\n if x == y:\n segTree.add(i, j + 1, 1)\n else:\n subtour.append(i)\n i = indices[-1]\n j = indices[0]\n x = eulerTour[i]\n y = eulerTour[j]\n if x == y:\n segTree.add(i, len(eulerTour), 1)\n segTree.add(0, j + 1, 1)\n else:\n subtour.append(i)\n\n if len(nodes) != len(subtour):\n # Subtour has non leaves, impossible\n return 0\n if False:\n print(\"label\", k, \"visits\", indices, \"nodes\", nodes)\n print(\n \"\\t\".join(\n str(eulerTour[i]) + \":\" + str(A[eulerTour[i]])\n for i in range(len(eulerTour))\n )\n )\n for i in range(len(eulerTour)):\n if segTree.query(i, i + 1) != 0:\n print(\"x\", end=\"\\t\")\n else:\n print(\"o\", end=\"\\t\")\n print()\n print()\n return N - len(set([eulerTour[i] for i in range(len(eulerTour)) if segTree.query(i, i + 1) != 0]))\n\ninput = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline\nN = int(input());A = [int(x) for x in input().split()];e = [[int(x) - 1 for x in input().split()] for i in range(N - 1)];print(solve(N, A, e))\n```","inputs":"5\n2 5 1 1 4\n1 2\n1 3\n2 4\n2 5\n","output":"\n3","actual_output":"3\n","execution_success":true,"sample_index":12823},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"1541_E1. Converging Array (Easy Version)","prompt":"Solve the following coding problem using the programming language python:\n\nThis is the easy version of the problem. The only difference is that in this version q = 1. You can make hacks only if both versions of the problem are solved.\n\nThere is a process that takes place on arrays a and b of length n and length n-1 respectively. \n\nThe process is an infinite sequence of operations. Each operation is as follows: \n\n * First, choose a random integer i (1 \u2264 i \u2264 n-1). \n * Then, simultaneously set a_i = min\\left(a_i, \\frac{a_i+a_{i+1}-b_i}{2}\\right) and a_{i+1} = max\\left(a_{i+1}, \\frac{a_i+a_{i+1}+b_i}{2}\\right) without any rounding (so values may become non-integer). \n\nSee notes for an example of an operation.\n\nIt can be proven that array a converges, i. e. for each i there exists a limit a_i converges to. Let function F(a, b) return the value a_1 converges to after a process on a and b.\n\nYou are given array b, but not array a. However, you are given a third array c. Array a is good if it contains only integers and satisfies 0 \u2264 a_i \u2264 c_i for 1 \u2264 i \u2264 n.\n\nYour task is to count the number of good arrays a where F(a, b) \u2265 x for q values of x. Since the number of arrays can be very large, print it modulo 10^9+7.\n\nInput\n\nThe first line contains a single integer n (2 \u2264 n \u2264 100).\n\nThe second line contains n integers c_1, c_2 \u2026, c_n (0 \u2264 c_i \u2264 100).\n\nThe third line contains n-1 integers b_1, b_2, \u2026, b_{n-1} (0 \u2264 b_i \u2264 100).\n\nThe fourth line contains a single integer q (q=1).\n\nThe fifth line contains q space separated integers x_1, x_2, \u2026, x_q (-10^5 \u2264 x_i \u2264 10^5).\n\nOutput\n\nOutput q integers, where the i-th integer is the answer to the i-th query, i. e. the number of good arrays a where F(a, b) \u2265 x_i modulo 10^9+7.\n\nExample\n\nInput\n\n\n3\n2 3 4\n2 1\n1\n-1\n\n\nOutput\n\n\n56\n\nNote\n\nThe following explanation assumes b = [2, 1] and c=[2, 3, 4] (as in the sample).\n\nExamples of arrays a that are not good: \n\n * a = [3, 2, 3] is not good because a_1 > c_1; \n * a = [0, -1, 3] is not good because a_2 < 0. \n\n\n\nOne possible good array a is [0, 2, 4]. We can show that no operation has any effect on this array, so F(a, b) = a_1 = 0.\n\nAnother possible good array a is [0, 1, 4]. In a single operation with i = 1, we set a_1 = min((0+1-2)/(2), 0) and a_2 = max((0+1+2)/(2), 1). So, after a single operation with i = 1, a becomes equal to [-1/2, 3/2, 4]. We can show that no operation has any effect on this array, so F(a, b) = -1/2.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = lambda: sys.stdin.readline().rstrip()\n\nN = int(input())\nC = [int(a) for a in input().split()]\nB = [int(a) for a in input().split()]\nQ = int(input())\nx = int(input())\nP = 10 ** 9 + 7\ndp = [[0] * 20100 for _ in range(N + 1)]\ndp[0][0] = 1\nans = 0\ns = x\nt = s\nfor i in range(N):\n for j in range(20050, t - 1, -1):\n if j < 0: break\n dp[i+1][j] = (dp[i+1][j+1] + dp[i][max(j-C[i], 0)] - dp[i][j+1]) % P\n for j in range(min(t - 1, 20050), -1, -1):\n dp[i+1][j] = dp[i+1][j+1]\n \n if i < N - 1:\n s += B[i]\n t += s\nprint(dp[-1][0] % P)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n2 3 4\\n2 1\\n1\\n-1\\n', 'output': '56'}, {'type': 'stdin_stdout', 'input': '10\\n77 16 42 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int(input())\nx = int(input())\nP = 10 ** 9 + 7\ndp = [[0] * 20100 for _ in range(N + 1)]\ndp[0][0] = 1\nans = 0\ns = x\nt = s\nfor i in range(N):\n for j in range(20050, t - 1, -1):\n if j < 0: break\n dp[i+1][j] = (dp[i+1][j+1] + dp[i][max(j-C[i], 0)] - dp[i][j+1]) % P\n for j in range(min(t - 1, 20050), -1, -1):\n dp[i+1][j] = dp[i+1][j+1]\n \n if i < N - 1:\n s += B[i]\n t += s\nprint(dp[-1][0] % P)\n```","inputs":"3\n2 3 4\n2 1\n1\n-1\n","output":"56","actual_output":"56\n","execution_success":true,"sample_index":12824},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"18_B. Platforms","prompt":"Solve the following coding problem using the programming language python:\n\nIn one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down.\n\nInput\n\nThe first input line contains 4 integer numbers n, d, m, l (1 \u2264 n, d, m, l \u2264 106, l < m) \u2014 respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l].\n\nOutput\n\nOutput the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down.\n\nExamples\n\nInput\n\n2 2 5 3\n\n\nOutput\n\n4\n\n\nInput\n\n5 4 11 8\n\n\nOutput\n\n20\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nclass Platforms:\n @classmethod\n def read_input(cls):\n nums = list(map(int, input('').split()))\n return nums[0], nums[1], nums[2], nums[3]\n\n @classmethod\n def run(cls):\n n, d, m, l = cls.read_input()\n end_plat = (n - 1) * m + l\n for cur_jump in range(d, (m + 1) * d, d):\n if (cur_jump % m) > l or cur_jump > end_plat:\n print(cur_jump)\n return\n print(end_plat - (end_plat % d) + d)\n\nif __name__ == \"__main__\":\n Platforms.run()\n\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5 4 11 8\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '2 2 5 3\\n', 'output': '4\\n'}, {'type': 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'output': '135514\\n'}, {'type': 'stdin_stdout', 'input': '112931 310109 38798 16487\\n', 'output': '310109\\n'}, {'type': 'stdin_stdout', 'input': '1 1100010 5 1\\n', 'output': '1100010\\n'}, {'type': 'stdin_stdout', 'input': '36732 192314 444368 279509\\n', 'output': '384628\\n'}, {'type': 'stdin_stdout', 'input': '112931 310109 38798 24841\\n', 'output': '310109\\n'}, {'type': 'stdin_stdout', 'input': '42990 45035 229034 229024\\n', 'output': '1288316245\\n'}, {'type': 'stdin_stdout', 'input': '615188 1062781 924417 65934\\n', 'output': '1062781\\n'}, {'type': 'stdin_stdout', 'input': '76517 635488 177979 87345\\n', 'output': '635488\\n'}, {'type': 'stdin_stdout', 'input': '388430 90581 43771 74\\n', 'output': '90581\\n'}, {'type': 'stdin_stdout', 'input': '83952 310109 38798 24841\\n', 'output': '310109\\n'}, {'type': 'stdin_stdout', 'input': '388430 90581 43771 79\\n', 'output': '90581\\n'}, {'type': 'stdin_stdout', 'input': '46793 5061087 699604 157872\\n', 'output': '5061087\\n'}, {'type': 'stdin_stdout', 'input': '388430 90581 43771 22\\n', 'output': '90581\\n'}, {'type': 'stdin_stdout', 'input': '596073 90581 43771 22\\n', 'output': '90581\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 64000000}","problem_id":"vfc_80549","program":"```python\nclass Platforms:\n @classmethod\n def read_input(cls):\n nums = list(map(int, input('').split()))\n return nums[0], nums[1], nums[2], nums[3]\n\n @classmethod\n def run(cls):\n n, d, m, l = cls.read_input()\n end_plat = (n - 1) * m + l\n for cur_jump in range(d, (m + 1) * d, d):\n if (cur_jump % m) > l or cur_jump > end_plat:\n print(cur_jump)\n return\n print(end_plat - (end_plat % d) + d)\n\nif __name__ == \"__main__\":\n Platforms.run()\n\n\n\n```","inputs":"5 4 11 8\n","output":"20\n","actual_output":"20\n","execution_success":true,"sample_index":12825},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"237_B. Young Table","prompt":"Solve the following coding problem using the programming language python:\n\nYou've got table a, consisting of n rows, numbered from 1 to n. The i-th line of table a contains ci cells, at that for all i (1 < i \u2264 n) holds ci \u2264 ci - 1. \n\nLet's denote s as the total number of cells of table a, that is, . We know that each cell of the table contains a single integer from 1 to s, at that all written integers are distinct. \n\nLet's assume that the cells of the i-th row of table a are numbered from 1 to ci, then let's denote the number written in the j-th cell of the i-th row as ai, j. Your task is to perform several swap operations to rearrange the numbers in the table so as to fulfill the following conditions:\n\n 1. for all i, j (1 < i \u2264 n; 1 \u2264 j \u2264 ci) holds ai, j > ai - 1, j; \n 2. for all i, j (1 \u2264 i \u2264 n; 1 < j \u2264 ci) holds ai, j > ai, j - 1. \n\n\n\nIn one swap operation you are allowed to choose two different cells of the table and swap the recorded there numbers, that is the number that was recorded in the first of the selected cells before the swap, is written in the second cell after it. Similarly, the number that was recorded in the second of the selected cells, is written in the first cell after the swap.\n\nRearrange the numbers in the required manner. Note that you are allowed to perform any number of operations, but not more than s. You do not have to minimize the number of operations.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 50) that shows the number of rows in the table. The second line contains n space-separated integers ci (1 \u2264 ci \u2264 50; ci \u2264 ci - 1) \u2014 the numbers of cells on the corresponding rows.\n\nNext n lines contain table \u0430. The i-th of them contains ci space-separated integers: the j-th integer in this line represents ai, j.\n\nIt is guaranteed that all the given numbers ai, j are positive and do not exceed s. It is guaranteed that all ai, j are distinct.\n\nOutput\n\nIn the first line print a single integer m (0 \u2264 m \u2264 s), representing the number of performed swaps.\n\nIn the next m lines print the description of these swap operations. In the i-th line print four space-separated integers xi, yi, pi, qi (1 \u2264 xi, pi \u2264 n; 1 \u2264 yi \u2264 cxi; 1 \u2264 qi \u2264 cpi). The printed numbers denote swapping the contents of cells axi, yi and api, qi. Note that a swap operation can change the contents of distinct table cells. Print the swaps in the order, in which they should be executed.\n\nExamples\n\nInput\n\n3\n3 2 1\n4 3 5\n6 1\n2\n\n\nOutput\n\n2\n1 1 2 2\n2 1 3 1\n\n\nInput\n\n1\n4\n4 3 2 1\n\n\nOutput\n\n2\n1 1 1 4\n1 2 1 3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\nI = lambda : map(int,input().split())\nli = list (I())\ndd = {}\narr = [ [0 for i in range(51)] for j in range(51) ] \nl2 = [ ]\nc=0\nfor i in range (1,n+1) :\n l1 = list(I())\n l2 = l2 + l1\n c = c + len(l1)\n for j in range(li[i-1]) :\n arr[i][j+1] = l1[j]\n dd[l1[j]] = [i , j+1]\n#print(dd)\n#print(l2)\nl3 = l2[:]\nl3.sort()\n#print(l3)\nans= 0 \nd1 = {}\nfor i,j in enumerate(l2) :\n d1[j]=i\n#print(d1)\nanswer = [ ]\n#print(dd)\n#print(l2)\nfor i in range(c) :\n if l2[i]!=l3[i] :\n t1 = l2[i]\n t2 = i+1\n #print(t1,t2)\n #temp = dd[t1]\n #temp1 = dd[t2]\n answer = answer + [dd[t1] + dd[t2]]\n l2[i] = i+1\n l2[d1[t2]] = t1\n d1[t1] = d1[t2]\n d1[i+1] = i\n temp2 = dd[t1]\n dd[t1] = dd[t2]\n dd[t2] = temp2\n ans+=1\n #print(l2)\nprint(ans)\nfor i in range(ans) :\n print(*answer[i])\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1\\n4\\n4 3 2 1\\n', 'output': '2\\n1 1 1 4\\n1 2 1 3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n3 2 1\\n4 3 5\\n6 1\\n2\\n', 'output': '5\\n1 1 2 2\\n1 2 3 1\\n1 3 3 1\\n2 1 2 2\\n2 2 3 1\\n'}, {'type': 'stdin_stdout', 'input': '2\\n35 7\\n6 8 35 9 28 25 10 41 33 39 19 24 5 12 30 40 18 2 4 11 32 13 31 21 14 27 3 34 37 16 17 29 1 42 36\\n20 23 38 15 26 7 22\\n', 'output': '39\\n1 1 1 33\\n1 2 1 18\\n1 3 1 27\\n1 4 1 19\\n1 5 1 13\\n1 6 1 33\\n1 7 2 6\\n1 8 1 18\\n1 9 1 19\\n1 10 2 6\\n1 11 1 20\\n1 12 1 14\\n1 13 1 22\\n1 14 1 25\\n1 15 2 4\\n1 16 1 30\\n1 17 1 31\\n1 18 1 31\\n1 19 1 20\\n1 20 2 1\\n1 21 1 24\\n1 22 2 7\\n1 23 2 2\\n1 24 1 25\\n1 25 1 33\\n1 26 2 5\\n1 27 2 5\\n1 28 2 7\\n1 29 1 32\\n1 30 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6 10\\n8 9 3\\n12\\n', 'output': '13\\n1 1 2 2\\n1 2 2 3\\n1 3 4 3\\n1 4 4 3\\n2 1 2 4\\n2 2 3 2\\n2 3 3 1\\n2 4 4 1\\n3 1 4 2\\n3 2 3 3\\n3 3 4 1\\n4 1 5 1\\n4 3 5 1\\n'}, {'type': 'stdin_stdout', 'input': '48\\n3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n90 26 28\\n70 20 1\\n11 10 9\\n69 84 30\\n73 63 61\\n17 58 41\\n54 57 51\\n88 4 32\\n85 33 34\\n40 80 77\\n93 7 3\\n38 75 53\\n79 74 81\\n91 76 87\\n22 2 59\\n86 82 60\\n24 52\\n92 72\\n49 6\\n8 65\\n50 25\\n46 16\\n42 48\\n78 37\\n39 71\\n31 5\\n19 43\\n64 67\\n36 45\\n18\\n89\\n55\\n15\\n56\\n13\\n27\\n47\\n23\\n14\\n68\\n62\\n83\\n66\\n29\\n35\\n44\\n21\\n12\\n', 'output': '88\\n1 1 2 3\\n1 2 15 2\\n1 3 11 3\\n2 1 8 2\\n2 2 26 2\\n2 3 19 2\\n3 1 11 2\\n3 2 20 1\\n4 1 20 1\\n4 2 11 2\\n4 3 48 1\\n5 1 35 1\\n5 2 39 1\\n5 3 33 1\\n6 1 22 2\\n6 2 22 2\\n6 3 30 1\\n7 1 27 1\\n7 2 26 2\\n7 3 47 1\\n8 1 15 1\\n8 2 38 1\\n8 3 17 1\\n9 1 21 2\\n9 2 15 2\\n9 3 36 1\\n10 1 11 3\\n10 2 44 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33 11 8 39 2 6 9 3\\n13 37 27 24 26 1 17\\n36 10 35 21 7 16\\n22 23 4 12\\n34 25 14\\n', 'output': '33\\n1 1 3 6\\n1 2 2 6\\n1 3 2 9\\n1 4 5 3\\n1 6 2 7\\n1 7 4 5\\n1 8 2 4\\n1 9 2 8\\n1 10 4 2\\n2 1 2 3\\n2 2 5 4\\n2 3 3 1\\n2 4 6 3\\n2 5 4 2\\n2 6 4 6\\n2 7 3 7\\n2 8 3 6\\n2 9 5 3\\n3 1 4 6\\n3 2 4 4\\n3 3 5 1\\n3 4 5 2\\n3 5 5 2\\n3 6 6 2\\n3 7 5 2\\n4 1 5 1\\n4 2 5 2\\n4 3 5 3\\n4 4 6 3\\n4 6 6 2\\n5 1 5 4\\n5 2 6 1\\n6 1 6 3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n40 40 24 5\\n56 14 59 76 92 34 43 96 33 44 72 37 81 27 42 5 7 95 22 4 60 18 61 103 74 84 93 55 3 62 70 82 77 51 86 102 29 67 91 9\\n71 53 21 64 17 45 46 101 97 30 109 100 57 16 80 87 28 12 94 23 39 98 32 52 54 10 19 41 90 11 66 65 99 89 40 36 58 20 78 108\\n35 88 73 75 104 63 79 31 1 26 2 50 24 83 15 49 106 48 105 47 8 68 107 38\\n69 85 13 25 6\\n', 'output': '106\\n1 1 3 9\\n1 2 3 11\\n1 3 1 29\\n1 4 1 20\\n1 5 1 16\\n1 6 4 5\\n1 7 1 17\\n1 8 3 21\\n1 9 1 40\\n1 10 2 26\\n1 11 2 30\\n1 12 2 18\\n1 13 4 3\\n1 14 3 11\\n1 15 3 15\\n1 16 2 14\\n1 17 2 5\\n1 18 1 22\\n1 19 2 27\\n1 20 2 38\\n1 21 2 3\\n1 22 2 27\\n1 23 2 20\\n1 24 3 13\\n1 25 4 4\\n1 26 3 10\\n1 27 3 11\\n1 28 2 17\\n1 29 1 37\\n1 30 2 10\\n1 31 3 8\\n1 32 2 23\\n1 33 1 40\\n1 34 4 5\\n1 35 3 1\\n1 36 2 36\\n1 37 2 18\\n1 38 3 24\\n1 39 2 21\\n1 40 2 35\\n2 1 2 28\\n2 2 3 15\\n2 3 2 5\\n2 4 2 26\\n2 5 2 6\\n2 6 2 7\\n2 7 3 20\\n2 8 3 18\\n2 9 3 16\\n2 10 3 12\\n2 11 4 5\\n2 12 2 24\\n2 13 3 15\\n2 14 2 25\\n2 15 2 17\\n2 16 3 9\\n2 17 3 15\\n2 18 2 37\\n2 19 2 37\\n2 20 3 20\\n2 21 3 20\\n2 22 3 12\\n2 23 3 6\\n2 24 2 26\\n2 25 2 32\\n2 26 2 31\\n2 27 3 24\\n2 28 3 22\\n2 29 4 1\\n2 30 3 8\\n2 31 3 22\\n2 32 3 8\\n2 33 3 3\\n2 34 4 4\\n2 35 3 4\\n2 36 2 38\\n2 37 3 4\\n2 38 2 39\\n2 39 3 7\\n2 40 3 15\\n3 1 4 3\\n3 2 3 6\\n3 3 3 14\\n3 4 3 10\\n3 5 4 2\\n3 6 4 3\\n3 7 3 9\\n3 8 4 3\\n3 9 4 4\\n3 10 4 1\\n3 11 3 20\\n3 12 4 3\\n3 13 3 20\\n3 14 4 1\\n3 15 3 24\\n3 16 3 21\\n3 17 3 21\\n3 18 4 3\\n3 19 4 1\\n3 20 3 22\\n3 21 4 3\\n3 22 4 4\\n3 23 4 4\\n3 24 4 2\\n4 2 4 3\\n4 3 4 4\\n'}, {'type': 'stdin_stdout', 'input': '1\\n4\\n4 2 3 1\\n', 'output': '1\\n1 1 1 4\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80557","program":"```python\nn = int(input())\nI = lambda : map(int,input().split())\nli = list (I())\ndd = {}\narr = [ [0 for i in range(51)] for j in range(51) ] \nl2 = [ ]\nc=0\nfor i in range (1,n+1) :\n l1 = list(I())\n l2 = l2 + l1\n c = c + len(l1)\n for j in range(li[i-1]) :\n arr[i][j+1] = l1[j]\n dd[l1[j]] = [i , j+1]\n#print(dd)\n#print(l2)\nl3 = l2[:]\nl3.sort()\n#print(l3)\nans= 0 \nd1 = {}\nfor i,j in enumerate(l2) :\n d1[j]=i\n#print(d1)\nanswer = [ ]\n#print(dd)\n#print(l2)\nfor i in range(c) :\n if l2[i]!=l3[i] :\n t1 = l2[i]\n t2 = i+1\n #print(t1,t2)\n #temp = dd[t1]\n #temp1 = dd[t2]\n answer = answer + [dd[t1] + dd[t2]]\n l2[i] = i+1\n l2[d1[t2]] = t1\n d1[t1] = d1[t2]\n d1[i+1] = i\n temp2 = dd[t1]\n dd[t1] = dd[t2]\n dd[t2] = temp2\n ans+=1\n #print(l2)\nprint(ans)\nfor i in range(ans) :\n print(*answer[i])\n\n```","inputs":"1\n4\n4 3 2 1\n","output":"2\n1 1 1 4\n1 2 1 3\n","actual_output":"2\n1 1 1 4\n1 2 1 3\n","execution_success":true,"sample_index":12826},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"285_E. Positions in Permutations","prompt":"Solve the following coding problem using the programming language python:\n\nPermutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as pi. We'll call number n the size or the length of permutation p1, p2, ..., pn.\n\nWe'll call position i (1 \u2264 i \u2264 n) in permutation p1, p2, ..., pn good, if |p[i] - i| = 1. Count the number of permutations of size n with exactly k good positions. Print the answer modulo 1000000007 (109 + 7).\n\nInput\n\nThe single line contains two space-separated integers n and k (1 \u2264 n \u2264 1000, 0 \u2264 k \u2264 n).\n\nOutput\n\nPrint the number of permutations of length n with exactly k good positions modulo 1000000007 (109 + 7).\n\nExamples\n\nInput\n\n1 0\n\n\nOutput\n\n1\n\n\nInput\n\n2 1\n\n\nOutput\n\n0\n\n\nInput\n\n3 2\n\n\nOutput\n\n4\n\n\nInput\n\n4 1\n\n\nOutput\n\n6\n\n\nInput\n\n7 4\n\n\nOutput\n\n328\n\nNote\n\nThe only permutation of size 1 has 0 good positions.\n\nPermutation (1, 2) has 0 good positions, and permutation (2, 1) has 2 positions.\n\nPermutations of size 3:\n\n 1. (1, 2, 3) \u2014 0 positions\n 2. \u2014 2 positions\n 3. \u2014 2 positions\n 4. \u2014 2 positions\n 5. \u2014 2 positions\n 6. (3, 2, 1) \u2014 0 positions\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nmod=10**9+7\nn,k=map(int,input().split())\n\nA=[0]*(n+1)\nB=[0]*(n+1)\nC=[0]*(n+1)\nF=[0]*(n+1)\nG=[0]*(n+1)\n\nF[0]=G[0]=1\nfor i in range(1,n+1):\n\tG[i]=F[i]=F[i-1]*i%mod\n\tG[i]=pow(F[i],(mod-2),mod)\n\nfor i in range(0,n):\n\tif i*2>n:\n\t\tbreak\n\tB[i]=(F[n-i]*G[i]*G[n-i*2])%mod\nfor i in range(0,n//2+1):\n\tfor j in range(0,n//2+1):\n\t\tA[i+j]=(A[i+j]+B[i]*B[j])%mod\nfor i in range(0,n+1):\n\tA[i]=A[i]*F[n-i]%mod\nfor i in range(0,n+1):\n\tfor j in range(0,i+1):\n\t\tC[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod\nprint(C[k]%mod)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 1\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 1\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n', 'output': '328\\n'}, 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'output': '320603049\\n'}], 'language': 'python'}","metadata":"{'difficulty': 11, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80565","program":"```python\nmod=10**9+7\nn,k=map(int,input().split())\n\nA=[0]*(n+1)\nB=[0]*(n+1)\nC=[0]*(n+1)\nF=[0]*(n+1)\nG=[0]*(n+1)\n\nF[0]=G[0]=1\nfor i in range(1,n+1):\n\tG[i]=F[i]=F[i-1]*i%mod\n\tG[i]=pow(F[i],(mod-2),mod)\n\nfor i in range(0,n):\n\tif i*2>n:\n\t\tbreak\n\tB[i]=(F[n-i]*G[i]*G[n-i*2])%mod\nfor i in range(0,n//2+1):\n\tfor j in range(0,n//2+1):\n\t\tA[i+j]=(A[i+j]+B[i]*B[j])%mod\nfor i in range(0,n+1):\n\tA[i]=A[i]*F[n-i]%mod\nfor i in range(0,n+1):\n\tfor j in range(0,i+1):\n\t\tC[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod\nprint(C[k]%mod)\n\n```","inputs":"2 1\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12827},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"356_C. Compartments","prompt":"Solve the following coding problem using the programming language python:\n\nA team of students from the city S is sent to the All-Berland Olympiad in Informatics. Traditionally, they go on the train. All students have bought tickets in one carriage, consisting of n compartments (each compartment has exactly four people). We know that if one compartment contain one or two students, then they get bored, and if one compartment contain three or four students, then the compartment has fun throughout the entire trip.\n\nThe students want to swap with other people, so that no compartment with students had bored students. To swap places with another person, you need to convince him that it is really necessary. The students can not independently find the necessary arguments, so they asked a sympathetic conductor for help. The conductor can use her life experience to persuade any passenger to switch places with some student.\n\nHowever, the conductor does not want to waste time persuading the wrong people, so she wants to know what is the minimum number of people necessary to persuade her to change places with the students. Your task is to find the number. \n\nAfter all the swaps each compartment should either have no student left, or have a company of three or four students. \n\nInput\n\nThe first line contains integer n (1 \u2264 n \u2264 106) \u2014 the number of compartments in the carriage. The second line contains n integers a1, a2, ..., an showing how many students ride in each compartment (0 \u2264 ai \u2264 4). It is guaranteed that at least one student is riding in the train.\n\nOutput\n\nIf no sequence of swapping seats with other people leads to the desired result, print number \"-1\" (without the quotes). In another case, print the smallest number of people you need to persuade to swap places.\n\nExamples\n\nInput\n\n5\n1 2 2 4 3\n\n\nOutput\n\n2\n\n\nInput\n\n3\n4 1 1\n\n\nOutput\n\n2\n\n\nInput\n\n4\n0 3 0 4\n\n\nOutput\n\n0\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\nA = [0, 0, 0, 0, 0]\nB = map(int, input().split(' '))\n\nfor i in B:\n\tA[i] += 1\n\nres = min(A[1], A[2])\nA[1] -= res\nA[2] -= res\nA[3] += res\n\nres += 2 * (A[1] // 3)\nA[3] += A[1] // 3\nA[1] %= 3\n\nres += 2 * (A[2] // 3)\nA[3] += 2 * (A[2] // 3)\nA[2] %= 3\n\nassert(A[1] == 0 or A[2] == 0)\n\nif (A[1] == 1):\n\tif (A[3] > 0):\n\t\tres += 1 #; A[1] = 0; A[3] -= 1; A[4] += 1\n\telif (A[4] > 1):\n\t\tres += 2 #; A[1] = 0; A[4] -= 2; A[3] += 3\n\telse:\n\t\tprint(-1)\n\t\texit()\nelif (A[1] == 2):\n\tif (A[4] > 0):\n\t\tres += 2 #; A[1] = 0; A[4] -= 1; A[3] += 1\n\telif (A[3] > 1):\n\t\tres += 2 #; A[1] = 0; A[3] -= 2; A[4] += 2\n\telse:\n\t\tprint(-1)\n\t\texit()\n\nif (A[2] == 1):\n\tif (A[4] > 0):\n\t\tres += 1 #; A[4] -= 1; A[2] = 0; A[3] += 1\n\telif (A[3] > 1):\n\t\tres += 2; #; A[2] = 0; A[3] -= 2; A[4] += 2\n\telse:\n\t\tprint(-1)\n\t\texit()\nelif (A[2] == 2):\n\tres += 2 #; A[2] = 0; A[4] += 1\n\t\nprint(res)\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n4 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n0 3 0 4\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n1 2 2 4 3\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '20\\n4 2 3 3 1 3 2 3 1 4 4 4 2 1 4 2 1 3 4 4\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '166\\n2 3 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 2 2 2 2 2 2 2 2 2 4 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 3 2 2 2 2 2 2 2 2 2 3 2 0 2 0 3 2 2 2 0 2 0 2 2 2 2 2 2 3 0 2 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'-1\\n'}, {'type': 'stdin_stdout', 'input': '15\\n1 2 2 1 2 3 2 1 2 2 1 1 2 1 1\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '10\\n2 3 3 1 3 1 0 2 2 4\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n1 1 1 2 1 2 4 1 2 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '10\\n4 4 2 2 1 1 3 1 1 2\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '20\\n4 1 1 1 4 2 3 3 2 1 1 4 4 3 1 0 2 4 2 3\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '11\\n2 2 0 2 0 2 2 2 2 2 2\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '20\\n4 4 2 4 4 2 3 1 4 1 1 4 1 4 3 4 4 3 3 3\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '20\\n1 1 4 4 2 1 4 3 2 3 1 1 2 2 2 4 4 2 4 2\\n', 'output': '7\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1 3\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '13\\n2 1 2 2 1 0 1 2 1 1 2 1 2\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '13\\n1 1 1 2 0 1 4 1 3 1 1 1 0\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '6\\n2 2 4 4 4 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '27\\n0 2 4 1 4 2 1 2 3 4 2 4 1 2 3 2 3 2 2 2 0 4 3 0 3 0 1\\n', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '11\\n1 1 1 2 1 1 1 1 1 1 1\\n', 'output': '7\\n'}], 'language': 'python'}","metadata":"{'difficulty': 9, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80577","program":"```python\nn = int(input())\nA = [0, 0, 0, 0, 0]\nB = map(int, input().split(' '))\n\nfor i in B:\n\tA[i] += 1\n\nres = min(A[1], A[2])\nA[1] -= res\nA[2] -= res\nA[3] += res\n\nres += 2 * (A[1] // 3)\nA[3] += A[1] // 3\nA[1] %= 3\n\nres += 2 * (A[2] // 3)\nA[3] += 2 * (A[2] // 3)\nA[2] %= 3\n\nassert(A[1] == 0 or A[2] == 0)\n\nif (A[1] == 1):\n\tif (A[3] > 0):\n\t\tres += 1 #; A[1] = 0; A[3] -= 1; A[4] += 1\n\telif (A[4] > 1):\n\t\tres += 2 #; A[1] = 0; A[4] -= 2; A[3] += 3\n\telse:\n\t\tprint(-1)\n\t\texit()\nelif (A[1] == 2):\n\tif (A[4] > 0):\n\t\tres += 2 #; A[1] = 0; A[4] -= 1; A[3] += 1\n\telif (A[3] > 1):\n\t\tres += 2 #; A[1] = 0; A[3] -= 2; A[4] += 2\n\telse:\n\t\tprint(-1)\n\t\texit()\n\nif (A[2] == 1):\n\tif (A[4] > 0):\n\t\tres += 1 #; A[4] -= 1; A[2] = 0; A[3] += 1\n\telif (A[3] > 1):\n\t\tres += 2; #; A[2] = 0; A[3] -= 2; A[4] += 2\n\telse:\n\t\tprint(-1)\n\t\texit()\nelif (A[2] == 2):\n\tres += 2 #; A[2] = 0; A[4] += 1\n\t\nprint(res)\n\n\n```","inputs":"3\n4 1 1\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12828},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"37_B. Computer Game","prompt":"Solve the following coding problem using the programming language python:\n\nVasya\u2019s elder brother Petya loves playing computer games. In one of his favourite computer games Petya reached the final level where a fight with the boss take place.\n\nWhile playing the game Petya found spell scrolls and now he is about to use them. Let\u2019s describe the way fighting goes on this level:\n\n1) The boss has two parameters: max \u2014 the initial amount of health and reg \u2014 regeneration rate per second.\n\n2) Every scroll also has two parameters: powi \u2014 spell power measured in percents \u2014 the maximal amount of health counted off the initial one, which allows to use the scroll (i.e. if the boss has more than powi percent of health the scroll cannot be used); and dmgi the damage per second inflicted upon the boss if the scroll is used. As soon as a scroll is used it disappears and another spell is cast upon the boss that inflicts dmgi of damage per second upon him until the end of the game.\n\nDuring the battle the actions per second are performed in the following order: first the boss gets the damage from all the spells cast upon him, then he regenerates reg of health (at the same time he can\u2019t have more than max of health), then the player may use another scroll (no more than one per second).\n\nThe boss is considered to be defeated if at the end of a second he has nonpositive ( \u2264 0) amount of health.\n\nHelp Petya to determine whether he can win with the set of scrolls available to him and if he can, determine the minimal number of seconds he needs to do it.\n\nInput\n\nThe first line contains three integers N, max and reg (1 \u2264 N, max, reg \u2264 1000) \u2013\u2013 the amount of scrolls and the parameters of the boss. The next N lines contain two integers powi and dmgi each \u2014 the parameters of the i-th scroll (0 \u2264 powi \u2264 100, 1 \u2264 dmgi \u2264 2000). \n\nOutput\n\nIn case Petya can\u2019t complete this level, output in the single line NO.\n\nOtherwise, output on the first line YES. On the second line output the minimal time after which the boss can be defeated and the number of used scrolls. In the next lines for each used scroll output space-separated number of seconds passed from the start of the battle to the moment the scroll was used and the number of the scroll. Scrolls are numbered starting from 1 in the input order. The first scroll is considered to be available to be used after 0 seconds.\n\nOutput scrolls in the order they were used. It is not allowed to use scrolls after the boss is defeated.\n\nExamples\n\nInput\n\n2 10 3\n100 3\n99 1\n\n\nOutput\n\nNO\n\n\nInput\n\n2 100 10\n100 11\n90 9\n\n\nOutput\n\nYES\n19 2\n0 1\n10 2\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nclass Scroll:\n\tdef __init__(self, id, power, damage):\n\t\tself.id = id\n\t\tself.power = power\n\t\tself.damage = damage\n\t\tself.active = False\n\nnum_scrolls, boss_max, regenerate = map(int, input().split())\nscrolls = [Scroll(i+1, *map(int, input().split())) for i in range(num_scrolls)]\nscrolls.sort(key = lambda scroll: -scroll.damage)\nboss_curr = boss_max\nscroll_damage = 0\nactive_scrolls = []\ntick = 0\nwhile True:\n\tboss_prev = boss_curr\n\tboss_curr -= scroll_damage\n\tboss_curr = min(boss_max, boss_curr + regenerate)\n\tif boss_curr <= 0:\n\t\tprint('YES')\n\t\tprint(tick, len(active_scrolls))\n\t\tfor scroll in active_scrolls:\n\t\t\tprint(scroll.start, scroll.id)\n\t\tbreak\n\tfound = False\n\tfor scroll in scrolls:\n\t\tif not scroll.active and 100*boss_curr <= scroll.power*boss_max:\n\t\t\tscroll.start = tick\n\t\t\tscroll.active = True\n\t\t\tactive_scrolls.append(scroll)\n\t\t\tscroll_damage += scroll.damage\n\t\t\tfound = True\n\t\t\tbreak\n\tif not found and boss_curr >= boss_prev:\n\t\tprint('NO')\n\t\tbreak\n\ttick += 1\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '2 100 10\\n100 11\\n90 9\\n', 'output': 'YES\\n19 2\\n0 1\\n10 2\\n'}, {'type': 'stdin_stdout', 'input': '2 10 3\\n100 3\\n99 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 328 249\\n62 265\\n32 271\\n72 237\\n28 99\\n22 364\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 337 873\\n62 81\\n87 481\\n39 1189\\n45 450\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 1000 1\\n100 1\\n100 1\\n', 'output': 'YES\\n1001 2\\n0 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '5 351 183\\n16 337\\n19 221\\n81 359\\n87 253\\n5 240\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 100 5\\n100 1\\n100 1\\n100 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10 1000 8\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n', 'output': 'YES\\n509 10\\n0 1\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n'}, {'type': 'stdin_stdout', 'input': '11 2 10\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n100 1\\n', 'output': 'YES\\n12 11\\n0 1\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n10 11\\n'}, {'type': 'stdin_stdout', 'input': '3 200 10\\n100 3\\n100 8\\n50 1000\\n', 'output': 'YES\\n102 3\\n0 2\\n1 1\\n101 3\\n'}, {'type': 'stdin_stdout', 'input': '2 100 2\\n100 2\\n100 2\\n', 'output': 'YES\\n51 2\\n0 1\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '3 100 2\\n100 1\\n100 1\\n100 1\\n', 'output': 'YES\\n102 3\\n0 1\\n1 2\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '3 100 4\\n100 1\\n100 1\\n100 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '29 634 982\\n60 1351\\n54 640\\n1 253\\n72 24\\n40 529\\n52 339\\n73 21\\n34 1284\\n32 1264\\n76 1346\\n92 320\\n11 1441\\n67 1215\\n69 1524\\n77 1672\\n83 412\\n48 241\\n25 894\\n91 1474\\n18 1743\\n98 1944\\n48 788\\n77 860\\n31 629\\n91 1042\\n36 1116\\n41 1162\\n63 129\\n15 1125\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 100 3\\n100 1\\n100 1\\n100 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 940 591\\n92 762\\n59 255\\n15 1061\\n53 1016\\n10 527\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '6 1000 53\\n100 10\\n100 10\\n100 10\\n100 10\\n100 10\\n100 10\\n', 'output': 'YES\\n148 6\\n0 1\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '20 1000 35\\n10 6\\n66 38\\n81 11\\n18 46\\n80 54\\n76 55\\n100 7\\n96 23\\n24 37\\n4 24\\n4 50\\n71 4\\n83 15\\n7 23\\n100 44\\n99 34\\n100 17\\n100 66\\n23 15\\n90 35\\n', 'output': 'YES\\n7 7\\n0 18\\n1 15\\n2 20\\n3 5\\n4 6\\n5 2\\n6 4\\n'}, {'type': 'stdin_stdout', 'input': '20 1000 100\\n49 26\\n46 36\\n1 114\\n80 4\\n80 125\\n100 17\\n6 184\\n100 20\\n59 60\\n47 92\\n52 20\\n44 50\\n3 15\\n10 192\\n6 13\\n60 3\\n63 102\\n78 17\\n0 124\\n31 100\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10 100 5\\n61 3\\n55 2\\n12 6\\n39 5\\n21 10\\n39 7\\n16 1\\n10 1\\n70 5\\n100 7\\n', 'output': 'YES\\n21 6\\n0 10\\n15 9\\n17 1\\n18 2\\n19 6\\n20 5\\n'}, {'type': 'stdin_stdout', 'input': '5 851 931\\n88 401\\n48 1196\\n86 1817\\n20 1575\\n30 1474\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '50 1000 17\\n26 1\\n96 22\\n100 27\\n99 30\\n97 5\\n39 14\\n100 17\\n100 8\\n98 21\\n100 17\\n100 34\\n75 11\\n68 31\\n100 13\\n3 5\\n74 4\\n100 12\\n100 25\\n100 32\\n3 14\\n100 10\\n100 2\\n75 28\\n24 16\\n27 20\\n34 13\\n64 29\\n50 19\\n90 22\\n42 7\\n48 12\\n97 34\\n22 1\\n57 33\\n100 13\\n100 31\\n61 12\\n100 18\\n64 19\\n29 24\\n100 33\\n87 10\\n35 33\\n77 28\\n100 15\\n87 34\\n68 2\\n44 29\\n55 3\\n41 5\\n', 'output': 'YES\\n8 8\\n0 11\\n1 41\\n2 32\\n3 46\\n4 19\\n5 13\\n6 34\\n7 43\\n'}, {'type': 'stdin_stdout', 'input': '4 660 722\\n67 360\\n96 778\\n6 1041\\n62 395\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '35 999 199\\n95 80\\n79 279\\n14 291\\n100 88\\n64 55\\n100 209\\n85 4\\n14 237\\n75 126\\n41 260\\n81 67\\n99 311\\n71 220\\n98 312\\n53 213\\n55 377\\n78 374\\n79 308\\n34 40\\n92 281\\n53 119\\n96 170\\n90 7\\n87 176\\n27 50\\n78 95\\n31 327\\n56 138\\n91 221\\n7 144\\n100 335\\n29 139\\n61 247\\n38 203\\n100 242\\n', 'output': 'YES\\n3 3\\n0 31\\n1 14\\n2 16\\n'}, {'type': 'stdin_stdout', 'input': '2 439 283\\n25 510\\n31 547\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '70 1000 1\\n91 2\\n43 1\\n100 1\\n79 2\\n26 1\\n68 2\\n4 2\\n64 1\\n100 1\\n80 2\\n20 2\\n70 1\\n25 1\\n99 1\\n64 1\\n35 2\\n60 1\\n63 2\\n93 1\\n40 2\\n100 1\\n54 1\\n100 1\\n15 2\\n72 1\\n28 1\\n5 1\\n93 1\\n100 2\\n39 2\\n54 2\\n100 1\\n55 1\\n43 1\\n20 1\\n28 2\\n21 1\\n100 2\\n98 1\\n35 1\\n12 2\\n50 2\\n7 2\\n7 2\\n12 2\\n100 2\\n44 1\\n40 2\\n56 2\\n5 1\\n100 1\\n94 2\\n100 2\\n74 1\\n83 2\\n100 2\\n81 2\\n37 2\\n29 1\\n100 2\\n99 1\\n39 2\\n83 2\\n96 2\\n30 2\\n39 1\\n38 1\\n51 1\\n11 1\\n100 2\\n', 'output': 'YES\\n34 34\\n0 29\\n1 38\\n2 46\\n3 53\\n4 56\\n5 60\\n6 70\\n7 64\\n8 52\\n9 3\\n10 1\\n11 9\\n12 14\\n13 19\\n14 55\\n15 4\\n16 10\\n17 57\\n18 63\\n19 6\\n20 8\\n21 18\\n22 12\\n23 31\\n24 42\\n25 49\\n26 20\\n27 16\\n28 30\\n29 36\\n30 11\\n31 24\\n32 41\\n33 7\\n'}, {'type': 'stdin_stdout', 'input': '5 328 249\\n62 265\\n32 271\\n72 237\\n28 99\\n22 116\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 1000 1\\n100 1\\n100 2\\n', 'output': 'YES\\n501 2\\n0 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '6 1000 53\\n100 10\\n100 10\\n100 16\\n100 10\\n100 10\\n100 10\\n', 'output': 'YES\\n82 6\\n0 3\\n1 1\\n2 2\\n3 4\\n4 5\\n5 6\\n'}, {'type': 'stdin_stdout', 'input': '20 1000 35\\n10 6\\n66 38\\n81 11\\n18 46\\n80 54\\n76 55\\n100 7\\n96 23\\n24 37\\n4 24\\n4 50\\n71 4\\n83 15\\n7 23\\n100 44\\n99 34\\n100 32\\n100 66\\n23 15\\n90 35\\n', 'output': 'YES\\n7 7\\n0 18\\n1 15\\n2 20\\n3 5\\n4 6\\n5 2\\n6 4\\n'}, {'type': 'stdin_stdout', 'input': '10 100 5\\n61 3\\n55 2\\n12 6\\n39 5\\n25 10\\n39 7\\n16 1\\n10 1\\n70 5\\n100 7\\n', 'output': 'YES\\n21 6\\n0 10\\n15 9\\n17 1\\n18 2\\n19 6\\n20 5\\n'}, {'type': 'stdin_stdout', 'input': '50 1000 17\\n26 1\\n96 22\\n100 27\\n99 30\\n97 5\\n39 14\\n100 17\\n100 8\\n98 21\\n100 17\\n100 34\\n75 11\\n68 31\\n100 13\\n3 5\\n74 4\\n100 12\\n100 25\\n100 42\\n3 14\\n100 10\\n100 2\\n75 28\\n24 16\\n27 20\\n34 13\\n64 29\\n50 19\\n90 22\\n42 7\\n48 12\\n97 34\\n22 1\\n57 33\\n100 13\\n100 31\\n61 12\\n100 18\\n64 19\\n29 24\\n100 33\\n87 10\\n35 33\\n77 28\\n100 15\\n87 34\\n68 2\\n44 29\\n55 3\\n41 5\\n', 'output': 'YES\\n8 8\\n0 19\\n1 11\\n2 32\\n3 46\\n4 41\\n5 34\\n6 43\\n7 13\\n'}, {'type': 'stdin_stdout', 'input': '35 999 199\\n95 80\\n79 279\\n14 291\\n100 88\\n64 55\\n100 209\\n85 4\\n14 237\\n75 126\\n41 260\\n81 67\\n99 311\\n71 220\\n98 312\\n53 213\\n55 377\\n78 374\\n79 308\\n34 40\\n92 281\\n53 119\\n96 170\\n90 7\\n87 176\\n27 50\\n78 95\\n31 327\\n56 138\\n91 221\\n7 144\\n100 335\\n29 139\\n61 244\\n38 203\\n100 242\\n', 'output': 'YES\\n3 3\\n0 31\\n1 14\\n2 16\\n'}, {'type': 'stdin_stdout', 'input': '70 1000 1\\n91 2\\n43 1\\n100 1\\n79 2\\n26 1\\n68 2\\n4 2\\n64 2\\n100 1\\n80 2\\n20 2\\n70 1\\n25 1\\n99 1\\n64 1\\n35 2\\n60 1\\n63 2\\n93 1\\n40 2\\n100 1\\n54 1\\n100 1\\n15 2\\n72 1\\n28 1\\n5 1\\n93 1\\n100 2\\n39 2\\n54 2\\n100 1\\n55 1\\n43 1\\n20 1\\n28 2\\n21 1\\n100 2\\n98 1\\n35 1\\n12 2\\n50 2\\n7 2\\n7 2\\n12 2\\n100 2\\n44 1\\n40 2\\n56 2\\n5 1\\n100 1\\n94 2\\n100 2\\n74 1\\n83 2\\n100 2\\n81 2\\n37 2\\n29 1\\n100 2\\n99 1\\n39 2\\n83 2\\n96 2\\n30 2\\n39 1\\n38 1\\n51 1\\n11 1\\n100 2\\n', 'output': 'YES\\n34 34\\n0 29\\n1 38\\n2 46\\n3 53\\n4 56\\n5 60\\n6 70\\n7 64\\n8 52\\n9 3\\n10 1\\n11 9\\n12 14\\n13 19\\n14 55\\n15 4\\n16 10\\n17 57\\n18 63\\n19 6\\n20 8\\n21 18\\n22 49\\n23 31\\n24 42\\n25 2\\n26 20\\n27 16\\n28 30\\n29 36\\n30 11\\n31 24\\n32 41\\n33 7\\n'}, {'type': 'stdin_stdout', 'input': '3 100 1\\n100 1\\n100 2\\n100 1\\n', 'output': 'YES\\n35 3\\n0 2\\n1 1\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '6 1000 53\\n000 10\\n100 10\\n100 16\\n100 10\\n100 10\\n100 10\\n', 'output': 'YES\\n338 5\\n0 3\\n1 2\\n2 4\\n3 5\\n4 6\\n'}, {'type': 'stdin_stdout', 'input': '35 999 199\\n95 80\\n79 279\\n14 291\\n100 88\\n64 55\\n100 209\\n85 4\\n14 237\\n75 126\\n41 260\\n81 67\\n99 313\\n71 220\\n98 312\\n53 213\\n55 377\\n78 374\\n79 308\\n34 40\\n92 281\\n53 119\\n96 170\\n90 7\\n87 176\\n27 50\\n78 95\\n31 327\\n56 138\\n91 221\\n7 144\\n100 335\\n29 139\\n61 244\\n38 203\\n100 242\\n', 'output': 'YES\\n3 3\\n0 31\\n1 12\\n2 16\\n'}, {'type': 'stdin_stdout', 'input': '3 100 2\\n100 1\\n100 2\\n100 1\\n', 'output': 'YES\\n52 3\\n0 2\\n1 1\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '20 1000 35\\n10 6\\n8 38\\n81 11\\n18 46\\n80 54\\n76 55\\n100 7\\n96 23\\n24 37\\n6 24\\n4 50\\n71 4\\n83 15\\n7 23\\n100 44\\n99 34\\n100 32\\n100 66\\n23 15\\n90 35\\n', 'output': 'YES\\n7 7\\n0 18\\n1 15\\n2 20\\n3 5\\n4 6\\n5 16\\n6 4\\n'}, {'type': 'stdin_stdout', 'input': '50 1000 17\\n26 1\\n96 22\\n100 27\\n99 30\\n97 5\\n39 14\\n100 17\\n100 8\\n98 21\\n100 17\\n100 34\\n75 11\\n68 31\\n100 13\\n3 5\\n74 4\\n100 12\\n100 25\\n100 42\\n3 14\\n100 10\\n100 2\\n75 28\\n24 16\\n27 33\\n34 13\\n64 29\\n50 19\\n90 22\\n42 7\\n48 12\\n97 34\\n22 1\\n57 33\\n100 13\\n100 31\\n61 12\\n100 18\\n64 19\\n29 24\\n100 33\\n87 10\\n35 33\\n77 28\\n000 15\\n87 34\\n68 2\\n44 29\\n55 3\\n41 5\\n', 'output': 'YES\\n8 8\\n0 19\\n1 11\\n2 32\\n3 46\\n4 41\\n5 34\\n6 43\\n7 25\\n'}, {'type': 'stdin_stdout', 'input': '2 1001 0\\n101 1\\n100 2\\n', 'output': 'YES\\n334 2\\n0 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '4 337 873\\n62 81\\n87 942\\n39 1189\\n45 450\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 351 183\\n16 229\\n19 221\\n81 359\\n87 253\\n5 240\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 100 4\\n100 1\\n100 2\\n100 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '29 634 982\\n60 1351\\n54 640\\n1 253\\n72 24\\n40 529\\n52 339\\n73 21\\n34 1284\\n32 1264\\n76 1346\\n92 320\\n11 1441\\n67 1215\\n45 1524\\n77 1672\\n83 412\\n48 241\\n25 894\\n91 1474\\n18 1743\\n98 1944\\n48 788\\n77 860\\n31 629\\n91 1042\\n36 1116\\n41 1162\\n63 129\\n15 1125\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '3 100 3\\n100 1\\n101 1\\n100 1\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 1099 591\\n92 762\\n59 255\\n15 1061\\n53 1016\\n10 527\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '20 1000 100\\n49 26\\n46 36\\n1 114\\n80 4\\n80 125\\n100 3\\n6 184\\n100 20\\n59 60\\n47 92\\n52 20\\n44 50\\n3 15\\n10 192\\n6 13\\n60 3\\n63 102\\n78 17\\n0 124\\n31 100\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 851 931\\n88 401\\n48 1196\\n86 1817\\n20 1575\\n30 1994\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 660 722\\n67 360\\n96 778\\n6 1102\\n62 395\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 439 283\\n25 510\\n31 34\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 328 249\\n62 265\\n32 271\\n72 237\\n28 99\\n25 116\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 337 873\\n62 81\\n87 942\\n39 1134\\n45 450\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 1000 1\\n101 1\\n100 2\\n', 'output': 'YES\\n501 2\\n0 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '5 351 183\\n16 229\\n25 221\\n81 359\\n87 253\\n5 240\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '29 634 982\\n60 1351\\n54 640\\n1 253\\n72 24\\n40 529\\n52 339\\n73 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'output': 'YES\\n21 6\\n0 10\\n15 9\\n17 1\\n18 2\\n19 6\\n20 5\\n'}, {'type': 'stdin_stdout', 'input': '5 851 931\\n88 627\\n48 1196\\n86 1817\\n20 1575\\n30 1994\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '50 1000 17\\n26 1\\n96 22\\n100 27\\n99 30\\n97 5\\n39 14\\n100 17\\n100 8\\n98 21\\n100 17\\n100 34\\n75 11\\n68 31\\n100 13\\n3 5\\n74 4\\n100 12\\n100 25\\n100 42\\n3 14\\n100 10\\n100 2\\n75 28\\n24 16\\n27 20\\n34 13\\n64 29\\n50 19\\n90 22\\n42 7\\n48 12\\n97 34\\n22 1\\n57 33\\n100 13\\n100 31\\n61 12\\n100 18\\n64 19\\n29 24\\n100 33\\n87 10\\n35 33\\n77 28\\n000 15\\n87 34\\n68 2\\n44 29\\n55 3\\n41 5\\n', 'output': 'YES\\n8 8\\n0 19\\n1 11\\n2 32\\n3 46\\n4 41\\n5 34\\n6 43\\n7 13\\n'}, {'type': 'stdin_stdout', 'input': '4 660 722\\n67 360\\n96 778\\n6 441\\n62 395\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 337 283\\n25 510\\n31 34\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '70 1000 1\\n91 2\\n43 1\\n100 1\\n79 2\\n26 1\\n68 2\\n4 2\\n64 2\\n100 1\\n80 2\\n20 2\\n70 1\\n25 1\\n99 1\\n64 1\\n35 2\\n60 1\\n63 2\\n93 1\\n40 2\\n100 1\\n54 1\\n100 1\\n15 2\\n72 1\\n28 1\\n5 1\\n93 1\\n100 2\\n39 2\\n54 2\\n100 1\\n55 1\\n43 1\\n20 1\\n28 2\\n21 1\\n100 2\\n98 1\\n35 1\\n12 2\\n50 2\\n7 2\\n7 2\\n12 2\\n100 2\\n44 1\\n40 2\\n56 2\\n5 1\\n100 1\\n94 2\\n100 2\\n74 1\\n83 2\\n100 2\\n81 2\\n37 2\\n29 1\\n100 2\\n99 1\\n39 2\\n83 2\\n96 2\\n30 2\\n3 1\\n38 1\\n51 1\\n11 1\\n100 2\\n', 'output': 'YES\\n34 34\\n0 29\\n1 38\\n2 46\\n3 53\\n4 56\\n5 60\\n6 70\\n7 64\\n8 52\\n9 3\\n10 1\\n11 9\\n12 14\\n13 19\\n14 55\\n15 4\\n16 10\\n17 57\\n18 63\\n19 6\\n20 8\\n21 18\\n22 49\\n23 31\\n24 42\\n25 2\\n26 20\\n27 16\\n28 30\\n29 36\\n30 11\\n31 24\\n32 41\\n33 7\\n'}, {'type': 'stdin_stdout', 'input': '5 328 249\\n62 265\\n32 271\\n72 237\\n28 99\\n25 61\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 337 873\\n62 81\\n87 942\\n39 1134\\n45 708\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '2 1001 1\\n101 1\\n100 2\\n', 'output': 'YES\\n501 2\\n0 2\\n1 1\\n'}, {'type': 'stdin_stdout', 'input': '5 494 183\\n16 229\\n25 221\\n81 359\\n87 253\\n5 240\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '29 634 982\\n60 1351\\n54 640\\n1 253\\n72 24\\n40 529\\n52 339\\n73 21\\n34 1284\\n32 1264\\n76 1346\\n92 320\\n11 1441\\n67 1215\\n45 1524\\n77 1672\\n83 412\\n48 241\\n25 894\\n91 1474\\n18 1743\\n98 1944\\n48 1506\\n77 860\\n31 629\\n91 1042\\n36 1116\\n41 1162\\n63 129\\n15 1920\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 1652 591\\n92 762\\n59 255\\n15 285\\n53 1016\\n10 527\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '20 1000 100\\n49 26\\n46 36\\n1 114\\n80 4\\n80 125\\n100 3\\n6 184\\n100 20\\n41 60\\n47 92\\n57 20\\n44 50\\n3 15\\n10 192\\n6 13\\n60 3\\n63 102\\n78 17\\n0 124\\n31 100\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '10 100 5\\n61 3\\n55 2\\n12 9\\n19 5\\n25 10\\n39 7\\n16 1\\n10 1\\n70 5\\n100 7\\n', 'output': 'YES\\n21 6\\n0 10\\n15 9\\n17 1\\n18 2\\n19 6\\n20 5\\n'}, {'type': 'stdin_stdout', 'input': '4 1164 722\\n67 360\\n96 778\\n6 441\\n62 395\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '35 999 199\\n95 80\\n79 279\\n14 291\\n110 88\\n64 55\\n100 209\\n85 4\\n14 237\\n75 126\\n41 260\\n81 67\\n99 313\\n71 220\\n98 312\\n53 213\\n55 377\\n78 374\\n79 308\\n34 40\\n92 281\\n53 119\\n96 170\\n90 7\\n87 176\\n27 50\\n78 95\\n31 327\\n56 138\\n91 221\\n7 144\\n100 335\\n29 139\\n61 244\\n38 203\\n100 242\\n', 'output': 'YES\\n3 3\\n0 31\\n1 12\\n2 16\\n'}, {'type': 'stdin_stdout', 'input': '2 337 283\\n25 510\\n52 34\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '70 1000 1\\n91 2\\n43 1\\n100 1\\n79 2\\n26 1\\n68 2\\n4 2\\n64 2\\n100 1\\n80 2\\n20 2\\n70 1\\n25 1\\n99 1\\n64 1\\n35 2\\n60 1\\n63 2\\n93 1\\n40 2\\n100 1\\n54 1\\n100 1\\n15 2\\n72 1\\n28 1\\n5 1\\n93 1\\n100 2\\n39 2\\n54 2\\n100 1\\n55 1\\n43 1\\n20 1\\n28 2\\n21 1\\n100 2\\n98 1\\n35 1\\n12 2\\n50 2\\n7 2\\n7 2\\n12 2\\n100 2\\n44 1\\n40 2\\n56 2\\n5 1\\n100 1\\n94 2\\n100 2\\n74 1\\n83 2\\n100 2\\n81 2\\n37 2\\n29 1\\n100 2\\n99 1\\n39 2\\n83 2\\n96 2\\n30 2\\n3 1\\n38 1\\n51 1\\n21 1\\n100 2\\n', 'output': 'YES\\n34 34\\n0 29\\n1 38\\n2 46\\n3 53\\n4 56\\n5 60\\n6 70\\n7 64\\n8 52\\n9 3\\n10 1\\n11 9\\n12 14\\n13 19\\n14 55\\n15 4\\n16 10\\n17 57\\n18 63\\n19 6\\n20 8\\n21 18\\n22 49\\n23 31\\n24 42\\n25 2\\n26 20\\n27 16\\n28 30\\n29 36\\n30 11\\n31 24\\n32 41\\n33 7\\n'}, {'type': 'stdin_stdout', 'input': '5 328 249\\n25 265\\n32 271\\n72 237\\n28 99\\n25 61\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '4 337 1185\\n62 81\\n87 942\\n39 1134\\n45 708\\n', 'output': 'NO\\n'}, {'type': 'stdin_stdout', 'input': '5 494 183\\n16 229\\n36 221\\n81 359\\n87 253\\n5 240\\n', 'output': 'NO\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80581","program":"```python\nclass Scroll:\n\tdef __init__(self, id, power, damage):\n\t\tself.id = id\n\t\tself.power = power\n\t\tself.damage = damage\n\t\tself.active = False\n\nnum_scrolls, boss_max, regenerate = map(int, input().split())\nscrolls = [Scroll(i+1, *map(int, input().split())) for i in range(num_scrolls)]\nscrolls.sort(key = lambda scroll: -scroll.damage)\nboss_curr = boss_max\nscroll_damage = 0\nactive_scrolls = []\ntick = 0\nwhile True:\n\tboss_prev = boss_curr\n\tboss_curr -= scroll_damage\n\tboss_curr = min(boss_max, boss_curr + regenerate)\n\tif boss_curr <= 0:\n\t\tprint('YES')\n\t\tprint(tick, len(active_scrolls))\n\t\tfor scroll in active_scrolls:\n\t\t\tprint(scroll.start, scroll.id)\n\t\tbreak\n\tfound = False\n\tfor scroll in scrolls:\n\t\tif not scroll.active and 100*boss_curr <= scroll.power*boss_max:\n\t\t\tscroll.start = tick\n\t\t\tscroll.active = True\n\t\t\tactive_scrolls.append(scroll)\n\t\t\tscroll_damage += scroll.damage\n\t\t\tfound = True\n\t\t\tbreak\n\tif not found and boss_curr >= boss_prev:\n\t\tprint('NO')\n\t\tbreak\n\ttick += 1\n\n```","inputs":"2 100 10\n100 11\n90 9\n","output":"YES\n19 2\n0 1\n10 2\n","actual_output":"YES\n19 2\n0 1\n10 2\n","execution_success":true,"sample_index":12829},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"427_B. Prison Transfer","prompt":"Solve the following coding problem using the programming language python:\n\nThe prison of your city has n prisoners. As the prison can't accommodate all of them, the city mayor has decided to transfer c of the prisoners to a prison located in another city.\n\nFor this reason, he made the n prisoners to stand in a line, with a number written on their chests. The number is the severity of the crime he/she has committed. The greater the number, the more severe his/her crime was.\n\nThen, the mayor told you to choose the c prisoners, who will be transferred to the other prison. He also imposed two conditions. They are,\n\n * The chosen c prisoners has to form a contiguous segment of prisoners. \n * Any of the chosen prisoner's crime level should not be greater then t. Because, that will make the prisoner a severe criminal and the mayor doesn't want to take the risk of his running away during the transfer. \n\n\n\nFind the number of ways you can choose the c prisoners.\n\nInput\n\nThe first line of input will contain three space separated integers n (1 \u2264 n \u2264 2\u00b7105), t (0 \u2264 t \u2264 109) and c (1 \u2264 c \u2264 n). The next line will contain n space separated integers, the ith integer is the severity ith prisoner's crime. The value of crime severities will be non-negative and will not exceed 109. \n\nOutput\n\nPrint a single integer \u2014 the number of ways you can choose the c prisoners.\n\nExamples\n\nInput\n\n4 3 3\n2 3 1 1\n\n\nOutput\n\n2\n\n\nInput\n\n1 1 1\n2\n\n\nOutput\n\n0\n\n\nInput\n\n11 4 2\n2 2 0 7 3 2 2 4 9 1 4\n\n\nOutput\n\n6\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\na=list(map(int,input().split()[1:]))\nb=list(map(int,input().split()))\nm=0\nc=0\nfor i in b:\n if i>a[0]:\n if not c=a[1]else m)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 1 1\\n2\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '4 3 3\\n2 3 1 1\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '11 4 2\\n2 2 0 7 3 2 2 4 9 1 4\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '4 2 2\\n1 3 3 2\\n', 'output': '0\\n'}, {'type': 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'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80589","program":"```python\na=list(map(int,input().split()[1:]))\nb=list(map(int,input().split()))\nm=0\nc=0\nfor i in b:\n if i>a[0]:\n if not c=a[1]else m)\n\n```","inputs":"1 1 1\n2\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12830},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"472_A. Design Tutorial: Learn from Math","prompt":"Solve the following coding problem using the programming language python:\n\nOne way to create a task is to learn from math. You can generate some random math statement or modify some theorems to get something new and build a new task from that.\n\nFor example, there is a statement called the \"Goldbach's conjecture\". It says: \"each even number no less than four can be expressed as the sum of two primes\". Let's modify it. How about a statement like that: \"each integer no less than 12 can be expressed as the sum of two composite numbers.\" Not like the Goldbach's conjecture, I can prove this theorem.\n\nYou are given an integer n no less than 12, express it as a sum of two composite numbers.\n\nInput\n\nThe only line contains an integer n (12 \u2264 n \u2264 106).\n\nOutput\n\nOutput two composite integers x and y (1 < x, y < n) such that x + y = n. If there are multiple solutions, you can output any of them.\n\nExamples\n\nInput\n\n12\n\n\nOutput\n\n4 8\n\n\nInput\n\n15\n\n\nOutput\n\n6 9\n\n\nInput\n\n23\n\n\nOutput\n\n8 15\n\n\nInput\n\n1000000\n\n\nOutput\n\n500000 500000\n\nNote\n\nIn the first example, 12 = 4 + 8 and both 4, 8 are composite numbers. You can output \"6 6\" or \"8 4\" as well.\n\nIn the second example, 15 = 6 + 9. Note that you can't output \"1 14\" because 1 is not a composite number.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef isprime(k):\n m=0\n for j in range(2,k):\n if k%j==0:\n m=m+1\n if m==0:\n return 0\n else:\n return 1\n\nn=int(input())\nfor i in range(4,n-3):\n if isprime(i)==1 and isprime(n-i)==1:\n print(i,n-i)\n exit()\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1000000\\n', 'output': '4 999996\\n'}, {'type': 'stdin_stdout', 'input': '23\\n', 'output': '8 15\\n'}, {'type': 'stdin_stdout', 'input': '15\\n', 'output': '6 9\\n'}, {'type': 'stdin_stdout', 'input': '12\\n', 'output': '4 8\\n'}, {'type': 'stdin_stdout', 'input': '738457\\n', 'output': '4 738453\\n'}, {'type': 'stdin_stdout', 'input': '46220\\n', 'output': '4 46216\\n'}, {'type': 'stdin_stdout', 'input': '59\\n', 'output': '4 55\\n'}, {'type': 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Secret Combination","prompt":"Solve the following coding problem using the programming language python:\n\nYou got a box with a combination lock. The lock has a display showing n digits. There are two buttons on the box, each button changes digits on the display. You have quickly discovered that the first button adds 1 to all the digits (all digits 9 become digits 0), and the second button shifts all the digits on the display one position to the right (the last digit becomes the first one). For example, if the display is currently showing number 579, then if we push the first button, the display will show 680, and if after that we push the second button, the display will show 068.\n\nYou know that the lock will open if the display is showing the smallest possible number that can be obtained by pushing the buttons in some order. The leading zeros are ignored while comparing numbers. Now your task is to find the desired number.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 1000) \u2014 the number of digits on the display.\n\nThe second line contains n digits \u2014 the initial state of the display.\n\nOutput\n\nPrint a single line containing n digits \u2014 the desired state of the display containing the smallest possible number.\n\nExamples\n\nInput\n\n3\n579\n\n\nOutput\n\n024\n\n\nInput\n\n4\n2014\n\n\nOutput\n\n0142\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\ns = input()\ni = 0\nmin_ = int(s)\ns1 = s\ni = 0\nwhile (i <= n):\n s = s[1::] + s[0]\n if (int(s[0]) != 0):\n g = (9 - int(s[0])) + 1\n s2 = ''\n for j in range(len(s)):\n h = int(s[j]) + g\n if (h >= 10):\n h = abs(10 - h)\n s2 = s2 + str(h)\n s = s2\n if (int(s) < min_):\n min_ = int(s)\n s1 = s\n i = i + 1\nprint(s1)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n2014\\n', 'output': '0142\\n'}, {'type': 'stdin_stdout', 'input': '3\\n579\\n', 'output': '024\\n'}, {'type': 'stdin_stdout', 'input': '100\\n6669666666666666666866266666666666666666666666666666666666666666626666666666666966666766665667666656\\n', 'output': '0000000000000000000000000000000000000000006000000000000030000010000900100009000030000000000000002006\\n'}, {'type': 'stdin_stdout', 'input': '200\\n79025531557298703099245700860027432585447902553155729870309924570086002743258544790255315572987030992457008600274325854479025531557298703099245700860027432585447902553155729870309924570086002743258544\\n', 'output': '00274325854479025531557298703099245700860027432585447902553155729870309924570086002743258544790255315572987030992457008600274325854479025531557298703099245700860027432585447902553155729870309924570086\\n'}, {'type': 'stdin_stdout', 'input': 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n):\n s = s[1::] + s[0]\n if (int(s[0]) != 0):\n g = (9 - int(s[0])) + 1\n s2 = ''\n for j in range(len(s)):\n h = int(s[j]) + g\n if (h >= 10):\n h = abs(10 - h)\n s2 = s2 + str(h)\n s = s2\n if (int(s) < min_):\n min_ = int(s)\n s1 = s\n i = i + 1\nprint(s1)\n```","inputs":"4\n2014\n","output":"0142\n","actual_output":"0142\n","execution_success":true,"sample_index":12832},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"547_A. Mike and Frog","prompt":"Solve the following coding problem using the programming language python:\n\nMike has a frog and a flower. His frog is named Xaniar and his flower is named Abol. Initially(at time 0), height of Xaniar is h1 and height of Abol is h2. Each second, Mike waters Abol and Xaniar.\n\n\n\nSo, if height of Xaniar is h1 and height of Abol is h2, after one second height of Xaniar will become and height of Abol will become where x1, y1, x2 and y2 are some integer numbers and denotes the remainder of a modulo b.\n\nMike is a competitive programmer fan. He wants to know the minimum time it takes until height of Xania is a1 and height of Abol is a2.\n\nMike has asked you for your help. Calculate the minimum time or say it will never happen.\n\nInput\n\nThe first line of input contains integer m (2 \u2264 m \u2264 106).\n\nThe second line of input contains integers h1 and a1 (0 \u2264 h1, a1 < m).\n\nThe third line of input contains integers x1 and y1 (0 \u2264 x1, y1 < m).\n\nThe fourth line of input contains integers h2 and a2 (0 \u2264 h2, a2 < m).\n\nThe fifth line of input contains integers x2 and y2 (0 \u2264 x2, y2 < m).\n\nIt is guaranteed that h1 \u2260 a1 and h2 \u2260 a2.\n\nOutput\n\nPrint the minimum number of seconds until Xaniar reaches height a1 and Abol reaches height a2 or print -1 otherwise.\n\nExamples\n\nInput\n\n5\n4 2\n1 1\n0 1\n2 3\n\n\nOutput\n\n3\n\n\nInput\n\n1023\n1 2\n1 0\n1 2\n1 1\n\n\nOutput\n\n-1\n\nNote\n\nIn the first sample, heights sequences are following:\n\nXaniar: \n\nAbol: \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef main():\n m, tt = int(input()), [0] * 4\n for i in 0, 2:\n h, a = map(int, input().split())\n x, y = map(int, input().split())\n ha = (h, a)\n for t in range(1, m * 2):\n h = (h * x + y) % m\n if h in ha:\n if h == ha[0]:\n if tt[i]:\n tt[i] = t - tt[i]\n break\n else:\n tt[i] = t\n else:\n if tt[i + 1]:\n tt[i] = t - tt[i + 1]\n break\n else:\n tt[i + 1] = t\n step1, shift1, step2, shift2 = tt if tt[0] > tt[2] else tt[2:] + tt[:2]\n if shift1 == shift2 != 0:\n print(shift1)\n return\n if step1 and not step2 and shift1 and shift1 <= shift2 and not (shift2 - shift1) % step1:\n print(shift2)\n return\n if all(tt):\n if step2 == 1:\n print(shift1 if shift1 >= shift2 else shift2 + (shift2 - shift1) % step1)\n return\n for t in range(shift1 - shift2, shift1 - shift2 + step1 * step2, step1):\n if not t % step2:\n print(t + shift2)\n return\n print(-1)\n\n\nif __name__ == '__main__':\n main()\n\n```","verification_info":"{'test_cases': [{'type': 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tt = int(input()), [0] * 4\n for i in 0, 2:\n h, a = map(int, input().split())\n x, y = map(int, input().split())\n ha = (h, a)\n for t in range(1, m * 2):\n h = (h * x + y) % m\n if h in ha:\n if h == ha[0]:\n if tt[i]:\n tt[i] = t - tt[i]\n break\n else:\n tt[i] = t\n else:\n if tt[i + 1]:\n tt[i] = t - tt[i + 1]\n break\n else:\n tt[i + 1] = t\n step1, shift1, step2, shift2 = tt if tt[0] > tt[2] else tt[2:] + tt[:2]\n if shift1 == shift2 != 0:\n print(shift1)\n return\n if step1 and not step2 and shift1 and shift1 <= shift2 and not (shift2 - shift1) % step1:\n print(shift2)\n return\n if all(tt):\n if step2 == 1:\n print(shift1 if shift1 >= shift2 else shift2 + (shift2 - shift1) % step1)\n return\n for t in range(shift1 - shift2, shift1 - shift2 + step1 * step2, step1):\n if not t % step2:\n print(t + shift2)\n return\n print(-1)\n\n\nif __name__ == '__main__':\n main()\n\n```","inputs":"1023\n1 2\n1 0\n1 2\n1 1\n","output":"-1\n","actual_output":"-1\n","execution_success":true,"sample_index":12833},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"595_A. Vitaly and Night","prompt":"Solve the following coding problem using the programming language python:\n\nOne day Vitaly was going home late at night and wondering: how many people aren't sleeping at that moment? To estimate, Vitaly decided to look which windows are lit in the house he was passing by at that moment.\n\nVitaly sees a building of n floors and 2\u00b7m windows on each floor. On each floor there are m flats numbered from 1 to m, and two consecutive windows correspond to each flat. If we number the windows from 1 to 2\u00b7m from left to right, then the j-th flat of the i-th floor has windows 2\u00b7j - 1 and 2\u00b7j in the corresponding row of windows (as usual, floors are enumerated from the bottom). Vitaly thinks that people in the flat aren't sleeping at that moment if at least one of the windows corresponding to this flat has lights on.\n\nGiven the information about the windows of the given house, your task is to calculate the number of flats where, according to Vitaly, people aren't sleeping.\n\nInput\n\nThe first line of the input contains two integers n and m (1 \u2264 n, m \u2264 100) \u2014 the number of floors in the house and the number of flats on each floor respectively.\n\nNext n lines describe the floors from top to bottom and contain 2\u00b7m characters each. If the i-th window of the given floor has lights on, then the i-th character of this line is '1', otherwise it is '0'.\n\nOutput\n\nPrint a single integer \u2014 the number of flats that have lights on in at least one window, that is, the flats where, according to Vitaly, people aren't sleeping.\n\nExamples\n\nInput\n\n2 2\n0 0 0 1\n1 0 1 1\n\n\nOutput\n\n3\n\n\nInput\n\n1 3\n1 1 0 1 0 0\n\n\nOutput\n\n2\n\nNote\n\nIn the first test case the house has two floors, two flats on each floor. That is, in total there are 4 flats. The light isn't on only on the second floor in the left flat. That is, in both rooms of the flat the light is off.\n\nIn the second test case the house has one floor and the first floor has three flats. The light is on in the leftmost flat (in both windows) and in the middle flat (in one window). In the right flat the light is off.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\netaj, kvart = map(int, input().split())\nOkna = []\n\nnotsleep = 0\n\nfor i in range(0, etaj):\n Okna.append(list(map(int, input().split())))\n\nfor i in range(0, etaj):\n for j in range(0, (kvart*2)-1, 2):\n if Okna[i][j] or Okna[i][j+1] == 1:\n notsleep += 1\n \nprint(notsleep)\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '1 3\\n1 1 0 1 0 0\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2 2\\n0 0 0 1\\n1 0 1 1\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n0 0\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1 1\\n0 1\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1 100\\n0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 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Longest k-Good Segment","prompt":"Solve the following coding problem using the programming language python:\n\nThe array a with n integers is given. Let's call the sequence of one or more consecutive elements in a segment. Also let's call the segment k-good if it contains no more than k different values.\n\nFind any longest k-good segment.\n\nAs the input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use scanf/printf instead of cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.\n\nInput\n\nThe first line contains two integers n, k (1 \u2264 k \u2264 n \u2264 5\u00b7105) \u2014 the number of elements in a and the parameter k.\n\nThe second line contains n integers ai (0 \u2264 ai \u2264 106) \u2014 the elements of the array a.\n\nOutput\n\nPrint two integers l, r (1 \u2264 l \u2264 r \u2264 n) \u2014 the index of the left and the index of the right ends of some k-good longest segment. If there are several longest segments you can print any of them. The elements in a are numbered from 1 to n from left to right.\n\nExamples\n\nInput\n\n5 5\n1 2 3 4 5\n\n\nOutput\n\n1 5\n\n\nInput\n\n9 3\n6 5 1 2 3 2 1 4 5\n\n\nOutput\n\n3 7\n\n\nInput\n\n3 1\n1 2 3\n\n\nOutput\n\n1 1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport re\nimport sys\nexit=sys.exit\nfrom bisect import bisect_left as bsl,bisect_right as bsr\nfrom collections import Counter,defaultdict as ddict,deque\nfrom functools import lru_cache\ncache=lru_cache(None)\nfrom heapq import *\nfrom itertools import *\nfrom math import inf\nfrom pprint import pprint as pp\nenum=enumerate\nri=lambda:int(rln())\nris=lambda:list(map(int,rfs()))\nrln=sys.stdin.readline\nrl=lambda:rln().rstrip('\\n')\nrfs=lambda:rln().split()\ncat=''.join\ncatn='\\n'.join\nmod=1000000007\nd4=[(0,-1),(1,0),(0,1),(-1,0)]\nd8=[(-1,-1),(0,-1),(1,-1),(-1,0),(1,0),(-1,1),(0,1),(1,1)]\n########################################################################\n\nn,k=ris()\na=ris()\nbeg=end=i=0\nocc=ddict(int)\nfor j in range(n):\n occ[a[j]]+=1\n while len(occ)>k:\n occ[a[i]]-=1\n if occ[a[i]]==0:\n del occ[a[i]]\n i+=1\n if end-begk:\n occ[a[i]]-=1\n if occ[a[i]]==0:\n del occ[a[i]]\n i+=1\n if end-beg units of energy.\n\nOf course, walking would be boring if there were no shortcuts. A shortcut is a special path that allows Mike walking from one intersection to another requiring only 1 unit of energy. There are exactly n shortcuts in Mike's city, the ith of them allows walking from intersection i to intersection ai (i \u2264 ai \u2264 ai + 1) (but not in the opposite direction), thus there is exactly one shortcut starting at each intersection. Formally, if Mike chooses a sequence p1 = 1, p2, ..., pk then for each 1 \u2264 i < k satisfying pi + 1 = api and api \u2260 pi Mike will spend only 1 unit of energy instead of |pi - pi + 1| walking from the intersection pi to intersection pi + 1. For example, if Mike chooses a sequence p1 = 1, p2 = ap1, p3 = ap2, ..., pk = apk - 1, he spends exactly k - 1 units of total energy walking around them.\n\nBefore going on his adventure, Mike asks you to find the minimum amount of energy required to reach each of the intersections from his home. Formally, for each 1 \u2264 i \u2264 n Mike is interested in finding minimum possible total energy of some sequence p1 = 1, p2, ..., pk = i.\n\nInput\n\nThe first line contains an integer n (1 \u2264 n \u2264 200 000) \u2014 the number of Mike's city intersection.\n\nThe second line contains n integers a1, a2, ..., an (i \u2264 ai \u2264 n , , describing shortcuts of Mike's city, allowing to walk from intersection i to intersection ai using only 1 unit of energy. Please note that the shortcuts don't allow walking in opposite directions (from ai to i).\n\nOutput\n\nIn the only line print n integers m1, m2, ..., mn, where mi denotes the least amount of total energy required to walk from intersection 1 to intersection i.\n\nExamples\n\nInput\n\n3\n2 2 3\n\n\nOutput\n\n0 1 2 \n\n\nInput\n\n5\n1 2 3 4 5\n\n\nOutput\n\n0 1 2 3 4 \n\n\nInput\n\n7\n4 4 4 4 7 7 7\n\n\nOutput\n\n0 1 2 1 2 3 3 \n\nNote\n\nIn the first sample case desired sequences are:\n\n1: 1; m1 = 0;\n\n2: 1, 2; m2 = 1;\n\n3: 1, 3; m3 = |3 - 1| = 2.\n\nIn the second sample case the sequence for any intersection 1 < i is always 1, i and mi = |1 - i|.\n\nIn the third sample case \u2014 consider the following intersection sequences:\n\n1: 1; m1 = 0;\n\n2: 1, 2; m2 = |2 - 1| = 1;\n\n3: 1, 4, 3; m3 = 1 + |4 - 3| = 2;\n\n4: 1, 4; m4 = 1;\n\n5: 1, 4, 5; m5 = 1 + |4 - 5| = 2;\n\n6: 1, 4, 6; m6 = 1 + |4 - 6| = 3;\n\n7: 1, 4, 5, 7; m7 = 1 + |4 - 5| + 1 = 3.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\ndef amount_of_total_energy(n, a):\n dist = [-1] * n\n dist[0] = 0\n pos = [0]\n\n for u in pos:\n\t for v in [u - 1, u + 1, a[u] - 1]:\n\t\t if v >= 0 and v < n and dist[v] == -1:\n\t\t\t dist[v] = dist[u] + 1\n\t\t\t pos.append(v)\t\n \n return dist\n\nn = int(input())\na = list(map(int,input().split()))\n\nprint(*amount_of_total_energy(n, a))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '5\\n1 2 3 4 5\\n', 'output': '0 1 2 3 4\\n'}, {'type': 'stdin_stdout', 'input': '7\\n4 4 4 4 7 7 7\\n', 'output': '0 1 2 1 2 3 3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n2 2 3\\n', 'output': '0 1 2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 3 3 4\\n', 'output': '0 1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '91\\n4 6 23 23 23 23 23 28 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 47 47 47 54 54 54 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'input': '3\\n3 1 1\\n', 'output': '0 1 1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 4 1 4\\n', 'output': '0 1 2 2\\n'}, {'type': 'stdin_stdout', 'input': '7\\n4 3 2 4 7 3 7\\n', 'output': '0 1 2 1 2 3 3\\n'}, {'type': 'stdin_stdout', 'input': '4\\n2 4 2 2\\n', 'output': '0 1 2 2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 3, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80633","program":"```python\ndef amount_of_total_energy(n, a):\n dist = [-1] * n\n dist[0] = 0\n pos = [0]\n\n for u in pos:\n\t for v in [u - 1, u + 1, a[u] - 1]:\n\t\t if v >= 0 and v < n and dist[v] == -1:\n\t\t\t dist[v] = dist[u] + 1\n\t\t\t pos.append(v)\t\n \n return dist\n\nn = int(input())\na = list(map(int,input().split()))\n\nprint(*amount_of_total_energy(n, a))\n```","inputs":"5\n1 2 3 4 5\n","output":"0 1 2 3 4\n","actual_output":"0 1 2 3 4\n","execution_success":true,"sample_index":12836},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"731_F. Video Cards","prompt":"Solve the following coding problem using the programming language python:\n\nLittle Vlad is fond of popular computer game Bota-2. Recently, the developers announced the new add-on named Bota-3. Of course, Vlad immediately bought only to find out his computer is too old for the new game and needs to be updated.\n\nThere are n video cards in the shop, the power of the i-th video card is equal to integer value ai. As Vlad wants to be sure the new game will work he wants to buy not one, but several video cards and unite their powers using the cutting-edge technology. To use this technology one of the cards is chosen as the leading one and other video cards are attached to it as secondary. For this new technology to work it's required that the power of each of the secondary video cards is divisible by the power of the leading video card. In order to achieve that the power of any secondary video card can be reduced to any integer value less or equal than the current power. However, the power of the leading video card should remain unchanged, i.e. it can't be reduced.\n\nVlad has an infinite amount of money so he can buy any set of video cards. Help him determine which video cards he should buy such that after picking the leading video card and may be reducing some powers of others to make them work together he will get the maximum total value of video power.\n\nInput\n\nThe first line of the input contains a single integer n (1 \u2264 n \u2264 200 000) \u2014 the number of video cards in the shop.\n\nThe second line contains n integers a1, a2, ..., an (1 \u2264 ai \u2264 200 000) \u2014 powers of video cards.\n\nOutput\n\nThe only line of the output should contain one integer value \u2014 the maximum possible total power of video cards working together.\n\nExamples\n\nInput\n\n4\n3 2 15 9\n\n\nOutput\n\n27\n\n\nInput\n\n4\n8 2 2 7\n\n\nOutput\n\n18\n\nNote\n\nIn the first sample, it would be optimal to buy video cards with powers 3, 15 and 9. The video card with power 3 should be chosen as the leading one and all other video cards will be compatible with it. Thus, the total power would be 3 + 15 + 9 = 27. If he buys all the video cards and pick the one with the power 2 as the leading, the powers of all other video cards should be reduced by 1, thus the total power would be 2 + 2 + 14 + 8 = 26, that is less than 27. Please note, that it's not allowed to reduce the power of the leading video card, i.e. one can't get the total power 3 + 1 + 15 + 9 = 28.\n\nIn the second sample, the optimal answer is to buy all video cards and pick the one with the power 2 as the leading. The video card with the power 7 needs it power to be reduced down to 6. The total power would be 8 + 2 + 2 + 6 = 18.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\ns = list(map(int, input().split()))\nh = max(s)\nss = [0] * (h + 1)\nfor i in s:\n ss[i] += 1\nf, x = [0] * h, 0\nfor j in reversed(ss):\n x += j\n f.append(x)\nf.reverse()\nres = []\nfor i, x in enumerate(ss):\n if x:\n summ, x = 0, f[i]\n for j in range(i, h + 1, i):\n o = f[j + i]\n summ += (x - o) * j\n x = o\n res.append(summ)\nprint(max(res))\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n8 2 2 7\\n', 'output': '18\\n'}, {'type': 'stdin_stdout', 'input': '4\\n3 2 15 9\\n', 'output': '27\\n'}, {'type': 'stdin_stdout', 'input': '100\\n881 479 355 759 257 497 690 598 275 446 439 787 257 326 584 713 322 5 253 781 434 307 164 154 241 381 38 942 680 906 240 11 431 478 628 959 346 74 493 964 455 746 950 41 585 549 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h, 0\nfor j in reversed(ss):\n x += j\n f.append(x)\nf.reverse()\nres = []\nfor i, x in enumerate(ss):\n if x:\n summ, x = 0, f[i]\n for j in range(i, h + 1, i):\n o = f[j + i]\n summ += (x - o) * j\n x = o\n res.append(summ)\nprint(max(res))\n```","inputs":"4\n8 2 2 7\n","output":"18\n","actual_output":"18\n","execution_success":true,"sample_index":12837},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"756_A. Pavel and barbecue","prompt":"Solve the following coding problem using the programming language python:\n\nPavel cooks barbecue. There are n skewers, they lay on a brazier in a row, each on one of n positions. Pavel wants each skewer to be cooked some time in every of n positions in two directions: in the one it was directed originally and in the reversed direction.\n\nPavel has a plan: a permutation p and a sequence b1, b2, ..., bn, consisting of zeros and ones. Each second Pavel move skewer on position i to position pi, and if bi equals 1 then he reverses it. So he hope that every skewer will visit every position in both directions.\n\nUnfortunately, not every pair of permutation p and sequence b suits Pavel. What is the minimum total number of elements in the given permutation p and the given sequence b he needs to change so that every skewer will visit each of 2n placements? Note that after changing the permutation should remain a permutation as well.\n\nThere is no problem for Pavel, if some skewer visits some of the placements several times before he ends to cook. In other words, a permutation p and a sequence b suit him if there is an integer k (k \u2265 2n), so that after k seconds each skewer visits each of the 2n placements.\n\nIt can be shown that some suitable pair of permutation p and sequence b exists for any n.\n\nInput\n\nThe first line contain the integer n (1 \u2264 n \u2264 2\u00b7105) \u2014 the number of skewers.\n\nThe second line contains a sequence of integers p1, p2, ..., pn (1 \u2264 pi \u2264 n) \u2014 the permutation, according to which Pavel wants to move the skewers.\n\nThe third line contains a sequence b1, b2, ..., bn consisting of zeros and ones, according to which Pavel wants to reverse the skewers.\n\nOutput\n\nPrint single integer \u2014 the minimum total number of elements in the given permutation p and the given sequence b he needs to change so that every skewer will visit each of 2n placements.\n\nExamples\n\nInput\n\n4\n4 3 2 1\n0 1 1 1\n\n\nOutput\n\n2\n\n\nInput\n\n3\n2 3 1\n0 0 0\n\n\nOutput\n\n1\n\nNote\n\nIn the first example Pavel can change the permutation to 4, 3, 1, 2.\n\nIn the second example Pavel can change any element of b to 1.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nimport sys\ninput = sys.stdin.readline\n\nn = int(input())\npermutation = list(map(int, input().split()))\n\ngo = set(range(1,n+1))\nreached = set()\nans = 0\nwhile go:\n x = go.pop()\n while x not in reached:\n reached.add(x)\n x = permutation[x-1]\n if x in go:\n go.remove(x)\n ans += 1\nif ans == 1:\n ans = 0\n\npermutation = input().split()\nif permutation.count('1') % 2 == 0:\n ans += 1\nprint(ans)#\n \t\t \t\t\t\t \t \t \t \t\t \t\t \t\t \t\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n2 3 1\\n0 0 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 3 2 1\\n0 1 1 1\\n', 'output': '2\\n'}, 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{'type': 'stdin_stdout', 'input': '5\\n2 1 3 4 5\\n1 1 1 0 1\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 3 2 1\\n0 1 1 0\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '20\\n10 15 20 17 8 1 14 6 3 13 19 2 16 12 4 5 11 7 9 18\\n0 0 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '4\\n4 3 2 1\\n0 0 0 0\\n', 'output': '3\\n'}], 'language': 'python'}","metadata":"{'difficulty': 7, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80645","program":"```python\nimport sys\ninput = sys.stdin.readline\n\nn = int(input())\npermutation = list(map(int, input().split()))\n\ngo = set(range(1,n+1))\nreached = set()\nans = 0\nwhile go:\n x = go.pop()\n while x not in reached:\n reached.add(x)\n x = permutation[x-1]\n if x in go:\n go.remove(x)\n ans += 1\nif ans == 1:\n ans = 0\n\npermutation = input().split()\nif permutation.count('1') % 2 == 0:\n ans += 1\nprint(ans)#\n \t\t \t\t\t\t \t \t \t \t\t \t\t \t\t \t\n```","inputs":"3\n2 3 1\n0 0 0\n","output":"1\n","actual_output":"1\n","execution_success":true,"sample_index":12838},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"777_B. Game of Credit Cards","prompt":"Solve the following coding problem using the programming language python:\n\nAfter the fourth season Sherlock and Moriary have realized the whole foolishness of the battle between them and decided to continue their competitions in peaceful game of Credit Cards.\n\nRules of this game are simple: each player bring his favourite n-digit credit card. Then both players name the digits written on their cards one by one. If two digits are not equal, then the player, whose digit is smaller gets a flick (knock in the forehead usually made with a forefinger) from the other player. For example, if n = 3, Sherlock's card is 123 and Moriarty's card has number 321, first Sherlock names 1 and Moriarty names 3 so Sherlock gets a flick. Then they both digit 2 so no one gets a flick. Finally, Sherlock names 3, while Moriarty names 1 and gets a flick.\n\nOf course, Sherlock will play honestly naming digits one by one in the order they are given, while Moriary, as a true villain, plans to cheat. He is going to name his digits in some other order (however, he is not going to change the overall number of occurences of each digit). For example, in case above Moriarty could name 1, 2, 3 and get no flicks at all, or he can name 2, 3 and 1 to give Sherlock two flicks.\n\nYour goal is to find out the minimum possible number of flicks Moriarty will get (no one likes flicks) and the maximum possible number of flicks Sherlock can get from Moriarty. Note, that these two goals are different and the optimal result may be obtained by using different strategies.\n\nInput\n\nThe first line of the input contains a single integer n (1 \u2264 n \u2264 1000) \u2014 the number of digits in the cards Sherlock and Moriarty are going to use.\n\nThe second line contains n digits \u2014 Sherlock's credit card number.\n\nThe third line contains n digits \u2014 Moriarty's credit card number.\n\nOutput\n\nFirst print the minimum possible number of flicks Moriarty will get. Then print the maximum possible number of flicks that Sherlock can get from Moriarty.\n\nExamples\n\nInput\n\n3\n123\n321\n\n\nOutput\n\n0\n2\n\n\nInput\n\n2\n88\n00\n\n\nOutput\n\n2\n0\n\nNote\n\nFirst sample is elaborated in the problem statement. In the second sample, there is no way Moriarty can avoid getting two flicks.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\ns = list(map(int, list(input())))\nm = map(int, list(input()))\n\nma = [0] * 10\nfor dig in m:\n ma[dig] += 1\n\nma2 = list(ma)\n\nmin_f = 0\nfor nu in s:\n for x in range(nu, 10):\n if ma[x] > 0:\n ma[x] -= 1\n break\n else:\n min_f += 1\n for z in range(len(ma)):\n if ma[z] > 0:\n ma[z] -= 1\n break\n\nprint(min_f)\n\nma = ma2\n\nmax_f = 0\nfor nu in s:\n for x in range(nu+1, 10):\n if ma[x] > 0:\n ma[x] -= 1\n max_f += 1\n break\n else:\n for z in range(len(ma)):\n if ma[z] > 0:\n ma[z] -= 1\n break\n\nprint(max_f)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n123\\n321\\n', 'output': '0\\n2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n88\\n00\\n', 'output': '2\\n0\\n'}, 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'3\\n000\\n111\\n', 'output': '0 3\\n'}, {'type': 'stdin_stdout', 'input': '3\\n010\\n101\\n', 'output': '0 2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n010\\n001\\n', 'output': '0 1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n010\\n000\\n', 'output': '1 0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n011\\n100\\n', 'output': '1 1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80649","program":"```python\nn = int(input())\ns = list(map(int, list(input())))\nm = map(int, list(input()))\n\nma = [0] * 10\nfor dig in m:\n ma[dig] += 1\n\nma2 = list(ma)\n\nmin_f = 0\nfor nu in s:\n for x in range(nu, 10):\n if ma[x] > 0:\n ma[x] -= 1\n break\n else:\n min_f += 1\n for z in range(len(ma)):\n if ma[z] > 0:\n ma[z] -= 1\n break\n\nprint(min_f)\n\nma = ma2\n\nmax_f = 0\nfor nu in s:\n for x in range(nu+1, 10):\n if ma[x] > 0:\n ma[x] -= 1\n max_f += 1\n break\n else:\n for z in range(len(ma)):\n if ma[z] > 0:\n ma[z] -= 1\n break\n\nprint(max_f)\n```","inputs":"3\n123\n321\n","output":"0\n2\n","actual_output":"0\n2\n","execution_success":true,"sample_index":12839},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"822_B. Crossword solving","prompt":"Solve the following coding problem using the programming language python:\n\nErelong Leha was bored by calculating of the greatest common divisor of two factorials. Therefore he decided to solve some crosswords. It's well known that it is a very interesting occupation though it can be very difficult from time to time. In the course of solving one of the crosswords, Leha had to solve a simple task. You are able to do it too, aren't you?\n\nLeha has two strings s and t. The hacker wants to change the string s at such way, that it can be found in t as a substring. All the changes should be the following: Leha chooses one position in the string s and replaces the symbol in this position with the question mark \"?\". The hacker is sure that the question mark in comparison can play the role of an arbitrary symbol. For example, if he gets string s=\"ab?b\" as a result, it will appear in t=\"aabrbb\" as a substring.\n\nGuaranteed that the length of the string s doesn't exceed the length of the string t. Help the hacker to replace in s as few symbols as possible so that the result of the replacements can be found in t as a substring. The symbol \"?\" should be considered equal to any other symbol.\n\nInput\n\nThe first line contains two integers n and m (1 \u2264 n \u2264 m \u2264 1000) \u2014 the length of the string s and the length of the string t correspondingly.\n\nThe second line contains n lowercase English letters \u2014 string s.\n\nThe third line contains m lowercase English letters \u2014 string t.\n\nOutput\n\nIn the first line print single integer k \u2014 the minimal number of symbols that need to be replaced.\n\nIn the second line print k distinct integers denoting the positions of symbols in the string s which need to be replaced. Print the positions in any order. If there are several solutions print any of them. The numbering of the positions begins from one.\n\nExamples\n\nInput\n\n3 5\nabc\nxaybz\n\n\nOutput\n\n2\n2 3 \n\n\nInput\n\n4 10\nabcd\nebceabazcd\n\n\nOutput\n\n1\n2 \n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, m = map(int, input().split())\ns = input()\nt = input()\n\nres = 1001\nres_ind = []\n\nb = 0\ne = len(s)\nwhile b <= len(t)-len(s):\n sr = t[b:e]\n k = 0\n ind = []\n for i in range(len(s)):\n if s[i] != sr[i]:\n k += 1\n else:\n ind.append(i+1)\n if k < res:\n res = k\n res_ind = ind\n b += 1\n e += 1\nprint(res)\nres_ind = [x for x in range(1, len(s)+1) if x not in res_ind]\nprint(*res_ind)\n \n \n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4 10\\nabcd\\nebceabazcd\\n', 'output': '1\\n2 \\n'}, {'type': 'stdin_stdout', 'input': '3 5\\nabc\\nxaybz\\n', 'output': '2\\n2 3 \\n'}, {'type': 'stdin_stdout', 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{'type': 'stdin_stdout', 'input': '3 3\\nbbc\\ncb{\\n', 'output': '2\\n1 3\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\ncpefs\\neorcd\\n', 'output': '5\\n1 2 3 4 5\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\nbbb\\n{ab\\n', 'output': '2\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '5 5\\nsofgc\\neorcd\\n', 'output': '4\\n1 3 4 5\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\nbaa\\nzba\\n', 'output': '2\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\naaa\\nvabae\\n', 'output': '1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '10 15\\nsdkjeaafww\\nefykkffnkddkfej\\n', 'output': '9\\n1 2 4 5 6 7 8 9 10\\n'}, {'type': 'stdin_stdout', 'input': '3 10\\nass\\nbdcbefssss\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\naaa\\nbcbbb\\n', 'output': '3\\n1 2 3\\n'}, {'type': 'stdin_stdout', 'input': '4 10\\ndcba\\nebdeabazcd\\n', 'output': '2\\n1 2\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\nbac\\nxabyz\\n', 'output': '2\\n1 3\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\ng\\nsu\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '2 5\\n`a\\n`vbca\\n', 'output': '1\\n2\\n'}, {'type': 'stdin_stdout', 'input': '3 5\\naa_\\nbabvd\\n', 'output': '2\\n1 3\\n'}, {'type': 'stdin_stdout', 'input': '3 3\\nabd\\naxxx\\n', 'output': '2\\n2 3\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\ng\\nss\\n', 'output': '1\\n1\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\nz`\\nza`\\n', 'output': '1\\n2\\n'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80657","program":"```python\nn, m = map(int, input().split())\ns = input()\nt = input()\n\nres = 1001\nres_ind = []\n\nb = 0\ne = len(s)\nwhile b <= len(t)-len(s):\n sr = t[b:e]\n k = 0\n ind = []\n for i in range(len(s)):\n if s[i] != sr[i]:\n k += 1\n else:\n ind.append(i+1)\n if k < res:\n res = k\n res_ind = ind\n b += 1\n e += 1\nprint(res)\nres_ind = [x for x in range(1, len(s)+1) if x not in res_ind]\nprint(*res_ind)\n \n \n\n```","inputs":"4 10\nabcd\nebceabazcd\n","output":"1\n2 \n","actual_output":"1\n2\n","execution_success":true,"sample_index":12840},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"847_G. University Classes","prompt":"Solve the following coding problem using the programming language python:\n\nThere are n student groups at the university. During the study day, each group can take no more than 7 classes. Seven time slots numbered from 1 to 7 are allocated for the classes.\n\nThe schedule on Monday is known for each group, i. e. time slots when group will have classes are known.\n\nYour task is to determine the minimum number of rooms needed to hold classes for all groups on Monday. Note that one room can hold at most one group class in a single time slot.\n\nInput\n\nThe first line contains a single integer n (1 \u2264 n \u2264 1000) \u2014 the number of groups. \n\nEach of the following n lines contains a sequence consisting of 7 zeroes and ones \u2014 the schedule of classes on Monday for a group. If the symbol in a position equals to 1 then the group has class in the corresponding time slot. In the other case, the group has no class in the corresponding time slot.\n\nOutput\n\nPrint minimum number of rooms needed to hold all groups classes on Monday.\n\nExamples\n\nInput\n\n2\n0101010\n1010101\n\n\nOutput\n\n1\n\n\nInput\n\n3\n0101011\n0011001\n0110111\n\n\nOutput\n\n3\n\nNote\n\nIn the first example one room is enough. It will be occupied in each of the seven time slot by the first group or by the second group.\n\nIn the second example three rooms is enough, because in the seventh time slot all three groups have classes.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\n\nschedules = []\n\nfor i in range(n):\n schedules.append(input())\n \nminimum = 0\n\nfor i in range(7):\n activeSlots = 0\n for j in range(n):\n activeSlots += int(schedules[j][i])\n if activeSlots > minimum:\n minimum = activeSlots\n\nprint(minimum)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n0101011\\n0011001\\n0110111\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0101010\\n1010101\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1101110\\n1111011\\n1101110\\n0100011\\n1110110\\n1110100\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0111000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20\\n1111111\\n1101011\\n1111011\\n0111111\\n1111111\\n1110111\\n1111111\\n1111111\\n1111111\\n1111111\\n1110111\\n1111111\\n0111111\\n1011111\\n1111111\\n1111111\\n1101110\\n1111111\\n1111111\\n1111111\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0100101\\n0000001\\n0110000\\n0010000\\n0011110\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1111111\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0000000\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0000000\\n0010000\\n0000000\\n0000010\\n0000000\\n0100001\\n1000000\\n0000000\\n0000000\\n0000000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0101111\\n1101011\\n1010011\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1000000\\n0101000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1101110\\n1111001\\n1101110\\n0100011\\n1110110\\n1110100\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0111100\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20\\n1111111\\n1101011\\n1111011\\n0111111\\n1111111\\n1110111\\n1101111\\n1111111\\n1111111\\n1111111\\n1110111\\n1111111\\n0111111\\n1011111\\n1111111\\n1111111\\n1101110\\n1111111\\n1111111\\n1111111\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0100101\\n0000001\\n0010000\\n0010000\\n0011110\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0000000\\n0010000\\n0000000\\n0000000\\n0000000\\n0100001\\n1000000\\n1000000\\n0000000\\n0000000\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1101110\\n1111001\\n1101100\\n0100011\\n1010110\\n1100100\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '20\\n1101111\\n1101011\\n1111011\\n0111111\\n1111111\\n1110111\\n1101101\\n1111111\\n1111111\\n1110111\\n1110111\\n1111111\\n0111111\\n1011111\\n1111111\\n1111111\\n1101110\\n1111111\\n1111111\\n1111111\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1110111\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0001000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0000000\\n0010000\\n0000000\\n0000000\\n0000000\\n0100001\\n1000000\\n0000000\\n0000000\\n0000000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0101111\\n1001011\\n1010011\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0000000\\n0101000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0101011\\n0011001\\n0010111\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0101010\\n1000101\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1101110\\n1111001\\n1101100\\n0100011\\n1110110\\n1110100\\n', 'output': '6\\n'}, 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'1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0101011\\n0001001\\n0010110\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1001010\\n1000101\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0110001\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0100101\\n0000001\\n0010000\\n0110010\\n0111110\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1000110\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1011001\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0000000\\n0010000\\n0000000\\n0000000\\n0000000\\n0100001\\n1000100\\n1001000\\n0000000\\n0000000\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0111101\\n1000011\\n1010011\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1000100\\n0101010\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0101011\\n0001001\\n1010110\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1001010\\n1000100\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1101111\\n1111001\\n1101100\\n0100011\\n1010110\\n1100100\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0110011\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20\\n1101111\\n1101011\\n1111011\\n0111111\\n1111111\\n1110111\\n1101101\\n1111111\\n1111111\\n1110111\\n1110111\\n1111111\\n0111111\\n1011111\\n1111111\\n1111111\\n1101110\\n1111111\\n1111110\\n1111111\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0100101\\n1000001\\n0010000\\n0110010\\n0111110\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1001110\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0011001\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0000000\\n0010010\\n0000000\\n0000000\\n0000000\\n0100001\\n1000100\\n1001000\\n0000000\\n0000000\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0111101\\n1000001\\n1010011\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1000110\\n0101010\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0101011\\n0001001\\n1010111\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1001010\\n1001100\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1101111\\n1111001\\n1001100\\n0100011\\n1010110\\n1100100\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0110111\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20\\n1101111\\n1101011\\n1111111\\n0111111\\n1111111\\n1110111\\n1101101\\n1111111\\n1111111\\n1110111\\n1110111\\n1111111\\n0111111\\n1011111\\n1111111\\n1111111\\n1101110\\n1111111\\n1111110\\n1111111\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0100101\\n1000001\\n0010000\\n1110010\\n0111110\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1001010\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0010001\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0000000\\n0010010\\n0000000\\n0000010\\n0000000\\n0100001\\n1000100\\n1001000\\n0000000\\n0000000\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0111101\\n1000001\\n1010010\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1000010\\n0101010\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0001011\\n0001001\\n1010111\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1001000\\n1001100\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1101111\\n1111001\\n1001100\\n0100011\\n1010100\\n1100100\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n0100111\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20\\n1101111\\n1101011\\n1111111\\n0111111\\n1111111\\n1110111\\n1101101\\n1111111\\n1111111\\n1110111\\n1110111\\n1111111\\n0111111\\n1011111\\n1111111\\n1111111\\n0101110\\n1111111\\n1111110\\n1111111\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0100101\\n1000001\\n0010000\\n1110010\\n0101110\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1101110\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1111101\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0000000\\n0010010\\n0000000\\n0000010\\n0000000\\n0100001\\n1000100\\n1001000\\n0000000\\n0000001\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0111101\\n0000001\\n1010010\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1000010\\n0101000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0000011\\n0001001\\n1010111\\n', 'output': '3\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1001001\\n1001100\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1101111\\n1111001\\n1000100\\n0100011\\n1010100\\n1100100\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1100011\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20\\n1101111\\n1101011\\n1111111\\n0111111\\n1111111\\n1110111\\n1101101\\n1111111\\n1111111\\n1110111\\n1110011\\n1111111\\n0111111\\n1011111\\n1111111\\n1111111\\n0101110\\n1111111\\n1111110\\n1111111\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0000101\\n1000001\\n0010000\\n1110010\\n0101110\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1001111\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1110101\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0000000\\n0010010\\n0010000\\n0000010\\n0000000\\n0100001\\n1000100\\n1001000\\n0000000\\n0000001\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0111101\\n0000001\\n1011010\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n0000010\\n0101000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '3\\n0000011\\n0001000\\n1010111\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '2\\n1001001\\n0001100\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '6\\n1101111\\n1111001\\n1000100\\n0100011\\n1010100\\n1110100\\n', 'output': '5\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1100001\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '20\\n1101111\\n1101011\\n1111111\\n0111111\\n1111111\\n1110111\\n1101101\\n1110111\\n1111111\\n1110111\\n1110011\\n1111111\\n0111111\\n1011111\\n1111111\\n1111111\\n0101110\\n1111111\\n1111110\\n1111111\\n', 'output': '19\\n'}, {'type': 'stdin_stdout', 'input': '5\\n0000101\\n1001001\\n0010000\\n1110010\\n0101110\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1\\n1000111\\n', 'output': '1\\n'}], 'language': 'python'}","metadata":"{'difficulty': 13, 'time_limit': {'seconds': 1, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80661","program":"```python\nn = int(input())\n\nschedules = []\n\nfor i in range(n):\n schedules.append(input())\n \nminimum = 0\n\nfor i in range(7):\n activeSlots = 0\n for j in range(n):\n activeSlots += int(schedules[j][i])\n if activeSlots > minimum:\n minimum = activeSlots\n\nprint(minimum)\n```","inputs":"3\n0101011\n0011001\n0110111\n","output":"3\n","actual_output":"3\n","execution_success":true,"sample_index":12841},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"869_B. The Eternal Immortality","prompt":"Solve the following coding problem using the programming language python:\n\nEven if the world is full of counterfeits, I still regard it as wonderful.\n\nPile up herbs and incense, and arise again from the flames and ashes of its predecessor \u2014 as is known to many, the phoenix does it like this.\n\nThe phoenix has a rather long lifespan, and reincarnates itself once every a! years. Here a! denotes the factorial of integer a, that is, a! = 1 \u00d7 2 \u00d7 ... \u00d7 a. Specifically, 0! = 1.\n\nKoyomi doesn't care much about this, but before he gets into another mess with oddities, he is interested in the number of times the phoenix will reincarnate in a timespan of b! years, that is, . Note that when b \u2265 a this value is always integer.\n\nAs the answer can be quite large, it would be enough for Koyomi just to know the last digit of the answer in decimal representation. And you're here to provide Koyomi with this knowledge.\n\nInput\n\nThe first and only line of input contains two space-separated integers a and b (0 \u2264 a \u2264 b \u2264 1018).\n\nOutput\n\nOutput one line containing a single decimal digit \u2014 the last digit of the value that interests Koyomi.\n\nExamples\n\nInput\n\n2 4\n\n\nOutput\n\n2\n\n\nInput\n\n0 10\n\n\nOutput\n\n0\n\n\nInput\n\n107 109\n\n\nOutput\n\n2\n\nNote\n\nIn the first example, the last digit of is 2;\n\nIn the second example, the last digit of is 0;\n\nIn the third example, the last digit of is 2.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# Main maut ko takiya, aur kafan ko chaadar banakkar audhta hoon!\n\na,b=input().split()\n\nif a[:-1]!=b[:-1]:\n\tprint(\"0\")\n\t\nelse:\n\tans=1\n\t\n\tfor i in range(int(a[-1])+1,int(b[-1])+1):\n\t\tans*=i\n\t\tans=ans%10\n\tprint(ans)\n\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '107 109\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '0 10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 4\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '1 3\\n', 'output': '6\\n'}, {'type': 'stdin_stdout', 'input': '998244355 998244359\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1 22\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1230 1232\\n', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '0 0\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '0 4\\n', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '1000000000000000000 1000000000000000000\\n', 'output': '1\\n'}, {'type': 'stdin_stdout', 'input': '0 11\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '101 1002\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '2 3\\n', 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kafan ko chaadar banakkar audhta hoon!\n\na,b=input().split()\n\nif a[:-1]!=b[:-1]:\n\tprint(\"0\")\n\t\nelse:\n\tans=1\n\t\n\tfor i in range(int(a[-1])+1,int(b[-1])+1):\n\t\tans*=i\n\t\tans=ans%10\n\tprint(ans)\n\n\n```","inputs":"107 109\n","output":"2\n","actual_output":"2\n","execution_success":true,"sample_index":12842},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"895_A. Pizza Separation","prompt":"Solve the following coding problem using the programming language python:\n\nStudents Vasya and Petya are studying at the BSU (Byteland State University). At one of the breaks they decided to order a pizza. In this problem pizza is a circle of some radius. The pizza was delivered already cut into n pieces. The i-th piece is a sector of angle equal to ai. Vasya and Petya want to divide all pieces of pizza into two continuous sectors in such way that the difference between angles of these sectors is minimal. Sector angle is sum of angles of all pieces in it. Pay attention, that one of sectors can be empty.\n\nInput\n\nThe first line contains one integer n (1 \u2264 n \u2264 360) \u2014 the number of pieces into which the delivered pizza was cut.\n\nThe second line contains n integers ai (1 \u2264 ai \u2264 360) \u2014 the angles of the sectors into which the pizza was cut. The sum of all ai is 360.\n\nOutput\n\nPrint one integer \u2014 the minimal difference between angles of sectors that will go to Vasya and Petya.\n\nExamples\n\nInput\n\n4\n90 90 90 90\n\n\nOutput\n\n0\n\n\nInput\n\n3\n100 100 160\n\n\nOutput\n\n40\n\n\nInput\n\n1\n360\n\n\nOutput\n\n360\n\n\nInput\n\n4\n170 30 150 10\n\n\nOutput\n\n0\n\nNote\n\nIn first sample Vasya can take 1 and 2 pieces, Petya can take 3 and 4 pieces. Then the answer is |(90 + 90) - (90 + 90)| = 0.\n\nIn third sample there is only one piece of pizza that can be taken by only one from Vasya and Petya. So the answer is |360 - 0| = 360.\n\nIn fourth sample Vasya can take 1 and 4 pieces, then Petya will take 2 and 3 pieces. So the answer is |(170 + 10) - (30 + 150)| = 0.\n\nPicture explaning fourth sample:\n\n\n\nBoth red and green sectors consist of two adjacent pieces of pizza. So Vasya can take green sector, then Petya will take red sector.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn=int(input())\na=list(map(int,input().split()))\nprint(2*min(abs(180-sum(a[l:r])) for l in range(n) for r in range(l,n)))\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '4\\n170 30 150 10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '3\\n100 100 160\\n', 'output': '40\\n'}, {'type': 'stdin_stdout', 'input': '4\\n90 90 90 90\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '1\\n360\\n', 'output': '360\\n'}, {'type': 'stdin_stdout', 'input': '4\\n70 80 110 100\\n', 'output': '20\\n'}, {'type': 'stdin_stdout', 'input': '8\\n10 10 70 70 90 90 10 10\\n', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '5\\n211 113 25 9 2\\n', 'output': '62\\n'}, {'type': 'stdin_stdout', 'input': '9\\n40 20 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10\n","output":"0\n","actual_output":"0\n","execution_success":true,"sample_index":12843},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"916_B. Jamie and Binary Sequence (changed after round)","prompt":"Solve the following coding problem using the programming language python:\n\nJamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:\n\nFind k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one. \n\nTo be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with . Give a value to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.\n\nFor definitions of powers and lexicographical order see notes.\n\nInput\n\nThe first line consists of two integers n and k (1 \u2264 n \u2264 1018, 1 \u2264 k \u2264 105) \u2014 the required sum and the length of the sequence.\n\nOutput\n\nOutput \"No\" (without quotes) in a single line if there does not exist such sequence. Otherwise, output \"Yes\" (without quotes) in the first line, and k numbers separated by space in the second line \u2014 the required sequence.\n\nIt is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].\n\nExamples\n\nInput\n\n23 5\n\n\nOutput\n\nYes\n3 3 2 1 0 \n\n\nInput\n\n13 2\n\n\nOutput\n\nNo\n\n\nInput\n\n1 2\n\n\nOutput\n\nYes\n-1 -1 \n\nNote\n\nSample 1:\n\n23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23\n\nAnswers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.\n\nAnswers like (4, 1, 1, 1, 0) do not have the minimum y value.\n\nSample 2:\n\nIt can be shown there does not exist a sequence with length 2.\n\nSample 3:\n\n\n\nPowers of 2:\n\nIf x > 0, then 2x = 2\u00b72\u00b72\u00b7...\u00b72 (x times).\n\nIf x = 0, then 2x = 1.\n\nIf x < 0, then .\n\nLexicographical order:\n\nGiven two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn, k = map(int, input().split())\ncnt = [0] * 200010\nans = ''\nfor i in range(64):\n if (n >> i)&1:\n k -= 1\n cnt[i] = 1;\nif k < 0:\n print(\"No\")\nelse:\n print(\"Yes\")\n for i in range(64, -64, -1):\n if k >= cnt[i]:\n cnt[i - 1] += cnt[i] * 2\n k -= cnt[i]\n cnt[i] = 0\n else: break\n for i in range(-64, 64):\n if cnt[i]:\n while k:\n cnt[i] -= 1\n cnt[i - 1] += 2 \n i -= 1\n k-= 1\n break\n for i in range(64, -100010, -1): ans += (str(i) + ' ') * cnt[i] \n print(ans)\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '23 5\\n', 'output': 'Yes\\n3 3 2 1 0\\n'}, {'type': 'stdin_stdout', 'input': '1 2\\n', 'output': 'Yes\\n-1 -1\\n'}, {'type': 'stdin_stdout', 'input': '13 2\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '513703875844698663 50\\n', 'output': 'Yes\\n55 55 55 55 55 55 55 55 55 55 55 55 55 55 53 48 43 41 39 38 37 36 34 27 26 25 24 22 21 20 18 17 15 14 13 12 9 5 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -9\\n'}, {'type': 'stdin_stdout', 'input': '337790572680259391 29\\n', 'output': 'Yes\\n58 55 53 52 44 41 39 37 36 35 34 30 29 28 26 24 20 18 16 13 10 9 8 5 4 3 2 1 0\\n'}, {'type': 'stdin_stdout', 'input': '923065764876596469 30\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '281474976710656 5\\n', 'output': 'Yes\\n46 46 46 45 45\\n'}, {'type': 'stdin_stdout', 'input': '288318372649779720 50\\n', 'output': 'Yes\\n53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 46 44 35 30 27 17 14 9 2 1 0 -1 -2 -3 -4 -5 -6 -6\\n'}, {'type': 'stdin_stdout', 'input': '19228 8\\n', 'output': 'Yes\\n13 13 11 9 8 4 3 2\\n'}, {'type': 'stdin_stdout', 'input': '7 4\\n', 'output': 'Yes\\n1 1 1 0\\n'}, {'type': 'stdin_stdout', 'input': '374585535361966567 30\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '36029346774812736 5\\n', 'output': 'Yes\\n55 39 15 11 6\\n'}, {'type': 'stdin_stdout', 'input': '855969764271400156 30\\n', 'output': 'No\\n'}, {'type': 'stdin_stdout', 'input': '23 35482\\n', 'output': 'Yes\\n-10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 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'19228 2\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '60081541776781920 5\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '846113779983498737 1\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '1383018767644920138 9\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '506625956819403088 19\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '1420779811309713115 30\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '521325125150442808 11\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '864691128455135231 55\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '922239521698513045 17\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '3480380926206 20\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '348636123221290143 9\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '734 5\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '1100585377792 0\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '2145934811 14\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '57421517433081233 18\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '836609510626614769 30\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '901283150305558530 2\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '478818723873062027 1\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '188382 10\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '84735259 12\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '7 1\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '9458089490805340 19\\n', 'output': 'No'}, {'type': 'stdin_stdout', 'input': '2838181084884567 9\\n', 'output': 'No'}], 'language': 'python'}","metadata":"{'difficulty': 8, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 256000000}","problem_id":"vfc_80673","program":"```python\nn, k = map(int, input().split())\ncnt = [0] * 200010\nans = ''\nfor i in range(64):\n if (n >> i)&1:\n k -= 1\n cnt[i] = 1;\nif k < 0:\n print(\"No\")\nelse:\n print(\"Yes\")\n for i in range(64, -64, -1):\n if k >= cnt[i]:\n cnt[i - 1] += cnt[i] * 2\n k -= cnt[i]\n cnt[i] = 0\n else: break\n for i in range(-64, 64):\n if cnt[i]:\n while k:\n cnt[i] -= 1\n cnt[i - 1] += 2 \n i -= 1\n k-= 1\n break\n for i in range(64, -100010, -1): ans += (str(i) + ' ') * cnt[i] \n print(ans)\n```","inputs":"23 5\n","output":"Yes\n3 3 2 1 0\n","actual_output":"Yes\n3 3 2 1 0 \n","execution_success":true,"sample_index":12844},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"939_C. Convenient For Everybody","prompt":"Solve the following coding problem using the programming language python:\n\nIn distant future on Earth day lasts for n hours and that's why there are n timezones. Local times in adjacent timezones differ by one hour. For describing local time, hours numbers from 1 to n are used, i.e. there is no time \"0 hours\", instead of it \"n hours\" is used. When local time in the 1-st timezone is 1 hour, local time in the i-th timezone is i hours.\n\nSome online programming contests platform wants to conduct a contest that lasts for an hour in such a way that its beginning coincides with beginning of some hour (in all time zones). The platform knows, that there are ai people from i-th timezone who want to participate in the contest. Each person will participate if and only if the contest starts no earlier than s hours 00 minutes local time and ends not later than f hours 00 minutes local time. Values s and f are equal for all time zones. If the contest starts at f hours 00 minutes local time, the person won't participate in it.\n\nHelp platform select such an hour, that the number of people who will participate in the contest is maximum. \n\nInput\n\nThe first line contains a single integer n (2 \u2264 n \u2264 100 000) \u2014 the number of hours in day.\n\nThe second line contains n space-separated integers a1, a2, ..., an (1 \u2264 ai \u2264 10 000), where ai is the number of people in the i-th timezone who want to participate in the contest.\n\nThe third line contains two space-separated integers s and f (1 \u2264 s < f \u2264 n).\n\nOutput\n\nOutput a single integer \u2014 the time of the beginning of the contest (in the first timezone local time), such that the number of participants will be maximum possible. If there are many answers, output the smallest among them.\n\nExamples\n\nInput\n\n3\n1 2 3\n1 3\n\n\nOutput\n\n3\n\n\nInput\n\n5\n1 2 3 4 1\n1 3\n\n\nOutput\n\n4\n\nNote\n\nIn the first example, it's optimal to start competition at 3 hours (in first timezone). In this case, it will be 1 hour in the second timezone and 2 hours in the third timezone. Only one person from the first timezone won't participate.\n\nIn second example only people from the third and the fourth timezones will participate.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\n# Problem D \nn = int(input())\ninp = input().split(\" \")\npeople = [ int(x) for x in inp ]\ninp = input().split(\" \")\ns, f = int(inp[0]), int(inp[1])\nr = f-s#+1 # tama\u00f1o de la ventana\nmax_s, idx_max = sum( people[i] for i in range(r) ), 0\nsum_ac = max_s\nres = (n-idx_max+s)%n if (n-idx_max+s)%n else n\nfor j in range(n):\n # print(sum_ac, idx_max, res)\n sum_ac = sum_ac - people[j] + people[(r+j)%n]\n if sum_ac>max_s:\n max_s, idx_max = sum_ac, (j+1)%n\n res = (n-(j+1)+s)%n if (n-(j+1)+s)%n else n\n elif sum_ac==max_s:\n res_1 = (n-(j+1)+s)%n if (n-(j+1)+s)%n else n\n if res_1max_s:\n max_s, idx_max = sum_ac, (j+1)%n\n res = (n-(j+1)+s)%n if (n-(j+1)+s)%n else n\n elif sum_ac==max_s:\n res_1 = (n-(j+1)+s)%n if (n-(j+1)+s)%n else n\n if res_1 du + d:\n D[v] = du + d\n heappush(H, (D[v], v))\n return D\n\n\nD1 = dijkstra(N, G1, S - 1)\nD2 = dijkstra(N, G2, T - 1)\n\nD = [10**15 - sum(_) for _ in zip(D1, D2)]\nfor i in range(N - 1, 0, -1):\n D[i - 1] = max(D[i - 1], D[i])\nprint(*D, sep='\\n')\n\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '8 12 3 8\\n2 8 685087149 857180777\\n6 7 298270585 209942236\\n2 4 346080035 234079976\\n2 5 131857300 22507157\\n4 8 30723332 173476334\\n2 6 480845267 448565596\\n1 4 181424400 548830121\\n4 5 57429995 195056405\\n7 8 160277628 479932440\\n1 6 475692952 203530153\\n3 5 336869679 160714712\\n2 7 389775999 199123879', 'output': '999999574976994\\n999999574976994\\n999999574976994\\n999999574976994\\n999999574976994\\n999999574976994\\n999999574976994\\n999999574976994'}, {'type': 'stdin_stdout', 'input': '4 3 2 3\\n1 4 1 100\\n1 2 1 10\\n1 3 20 1', 'output': '999999999999998\\n999999999999989\\n999999999999979\\n999999999999897'}, {'type': 'stdin_stdout', 'input': '8 12 3 8\\n2 8 685087149 857180777\\n6 7 298270585 209942236\\n2 4 346080035 234079976\\n2 5 131857300 22507157\\n4 8 30723332 173476334\\n2 6 480845267 706415811\\n1 4 181424400 548830121\\n4 5 57429995 195056405\\n7 8 160277628 479932440\\n1 6 475692952 203530153\\n3 5 336869679 160714712\\n2 7 389775999 199123879', 'output': '999999574976994\\n999999574976994\\n999999574976994\\n999999574976994\\n999999574976994\\n999999574976994\\n999999574976994\\n999999574976994\\n'}, {'type': 'stdin_stdout', 'input': '4 3 2 3\\n1 4 1 100\\n1 2 0 10\\n1 3 20 1', 'output': '999999999999999\\n999999999999989\\n999999999999980\\n999999999999898\\n'}, {'type': 'stdin_stdout', 'input': '8 12 4 8\\n2 8 685087149 857180777\\n6 7 298270585 209942236\\n2 4 346080035 234079976\\n2 5 131857300 22507157\\n4 8 30723332 173476334\\n2 6 480845267 706415811\\n1 4 181424400 548830121\\n4 5 57429995 195056405\\n7 8 160277628 479932440\\n1 6 475692952 203530153\\n3 5 336869679 160714712\\n2 7 389775999 199123879', 'output': '999999969276668\\n999999969276668\\n999999969276668\\n999999969276668\\n999999969276668\\n999999969276668\\n999999969276668\\n999999969276668\\n'}, {'type': 'stdin_stdout', 'input': '4 3 2 3\\n1 4 1 000\\n1 2 0 10\\n1 3 20 1', 'output': '999999999999999\\n999999999999998\\n999999999999998\\n999999999999998\\n'}, {'type': 'stdin_stdout', 'input': '4 3 2 3\\n1 4 1 000\\n1 2 0 10\\n1 3 20 0', 'output': '1000000000000000\\n999999999999999\\n999999999999999\\n999999999999999\\n'}, {'type': 'stdin_stdout', 'input': '4 3 2 3\\n1 4 1 100\\n1 2 0 10\\n2 3 20 1', 'output': '999999999999999\\n999999999999999\\n999999999999980\\n999999999999888\\n'}, {'type': 'stdin_stdout', 'input': '4 3 2 2\\n1 4 1 000\\n1 2 0 10\\n1 3 18 0', 'output': '1000000000000000\\n1000000000000000\\n999999999999989\\n999999999999989\\n'}, {'type': 'stdin_stdout', 'input': '4 3 2 2\\n1 4 1 000\\n1 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203530153\\n3 7 283198998 115858230\\n2 7 389775999 199123879', 'output': '999999485668631\\n999999393942742\\n999999393942742\\n999999393942742\\n999999393942742\\n999999342915629\\n999999342915629\\n999999342915629\\n'}, {'type': 'stdin_stdout', 'input': '8 12 3 5\\n2 8 685087149 1569714306\\n6 1 298270585 209942236\\n2 4 346080035 234079976\\n1 5 131857300 16126114\\n1 8 30723332 173476334\\n2 6 447829832 706415811\\n1 4 181424400 548830121\\n4 6 57429995 195056405\\n7 8 160277628 479932440\\n1 6 127300821 212520115\\n3 5 336869679 115858230\\n2 3 239468450 199123879', 'output': '999999884141770\\n999999884141770\\n999999884141770\\n999999663130321\\n999999663130321\\n999999310947241\\n999999310947241\\n999999310947241\\n'}, {'type': 'stdin_stdout', 'input': '8 12 3 5\\n2 8 685087149 1569714306\\n6 1 298270585 79271435\\n2 4 346080035 234079976\\n1 5 131857300 40131411\\n1 8 30723332 173476334\\n2 6 447829832 706415811\\n1 4 181424400 548830121\\n4 6 57429995 195056405\\n7 8 160277628 479932440\\n1 6 127300821 203530153\\n3 2 388016357 115858230\\n4 4 389775999 199123879', 'output': '999999335602543\\n999999335602543\\n999999335602543\\n999999089070767\\n999999089070767\\n999999089070767\\n999998840148131\\n999998840148131\\n'}, {'type': 'stdin_stdout', 'input': '8 12 5 8\\n2 8 685087149 857180777\\n6 7 298270585 209942236\\n2 4 346080035 234079976\\n2 5 131857300 22507157\\n4 8 30723332 173476334\\n2 6 480845267 448565596\\n1 4 89589077 38650304\\n4 5 57429995 195056405\\n7 8 160277628 479932440\\n1 6 475692952 203530153\\n3 5 336869679 160714712\\n2 7 704986659 199123879', 'output': '999999911846673\\n999999911846673\\n999999911846673\\n999999911846673\\n999999911846673\\n999999911846673\\n999999911846673\\n999999911846673\\n'}, {'type': 'stdin_stdout', 'input': '8 12 4 8\\n2 7 685087149 857180777\\n6 7 298270585 209942236\\n2 4 346080035 409099689\\n2 7 131857300 6418512\\n2 8 30723332 173476334\\n2 6 342572618 706415811\\n1 4 181424400 548830121\\n4 5 57429995 195056405\\n7 8 160277628 479932440\\n1 6 830590082 203530153\\n3 5 130018211 160714712\\n2 7 389775999 199123879', 'output': '999999623196633\\n999999623196633\\n999999623196633\\n999999623196633\\n999999623196633\\n999999623196633\\n999999623196633\\n999999623196633\\n'}, {'type': 'stdin_stdout', 'input': '8 12 3 8\\n2 8 685087149 1569714306\\n6 1 298270585 209942236\\n2 4 299739955 234079976\\n2 5 131857300 22507157\\n6 8 30723332 173476334\\n2 6 447829832 706415811\\n1 4 181424400 548830121\\n4 6 57429995 195056405\\n7 8 160277628 479932440\\n1 6 127300821 203530153\\n3 5 349798532 115858230\\n1 7 389775999 199123879', 'output': '999999259021898\\n999999259021898\\n999999259021898\\n999999130450886\\n999999130450886\\n999999130450886\\n999999130450886\\n999999130450886\\n'}, {'type': 'stdin_stdout', 'input': '8 12 3 5\\n2 8 685087149 1569714306\\n6 1 298270585 209942236\\n2 4 346080035 234079976\\n1 7 131857300 40131411\\n1 8 30723332 173476334\\n2 6 447829832 706415811\\n1 4 181424400 548830121\\n4 6 57429995 290626940\\n7 8 160277628 479932440\\n1 6 127300821 212520115\\n3 5 336869679 115858230\\n2 3 239468450 199123879', 'output': '999999884141770\\n999999884141770\\n999999884141770\\n999999663130321\\n999999663130321\\n999998517332495\\n999998011407143\\n999997979196188\\n'}, {'type': 'stdin_stdout', 'input': '8 12 3 5\\n2 8 685087149 1569714306\\n6 1 298270585 209942236\\n2 4 346080035 234079976\\n1 5 230638026 40131411\\n1 8 40870410 173476334\\n2 6 447829832 706415811\\n1 4 181424400 548830121\\n4 6 57429995 195056405\\n7 8 160277628 306666626\\n1 6 127300821 203530153\\n3 1 336869679 115858230\\n2 3 389775999 230712147', 'output': '999999844010359\\n999999844010359\\n999999844010359\\n999999432492295\\n999999432492295\\n999999408652166\\n999999408652166\\n999999408652166\\n'}, {'type': 'stdin_stdout', 'input': '8 12 3 5\\n2 3 685087149 1569714306\\n6 1 298270585 209942236\\n2 4 346080035 234079976\\n2 5 131857300 40131411\\n1 8 30723332 173476334\\n2 6 447829832 706415811\\n1 4 164631518 548830121\\n4 6 107728420 195056405\\n7 8 160277628 479932440\\n1 6 127300821 203530153\\n3 1 336869679 115858230\\n4 3 389775999 199123879', 'output': '999999526664734\\n999999526664734\\n999999526664734\\n999999336012614\\n999999183055551\\n999999066561708\\n999998869737159\\n999998869737159\\n'}, {'type': 'stdin_stdout', 'input': '8 12 3 5\\n2 8 685087149 1569714306\\n6 1 298270585 209942236\\n2 4 346080035 234079976\\n1 5 83783748 40131411\\n1 8 30723332 173476334\\n2 6 447829832 706415811\\n1 4 181424400 548830121\\n4 6 30593148 195056405\\n7 1 160277628 732388223\\n1 6 127300821 203530153\\n3 1 336869679 115858230\\n8 4 389775999 199123879', 'output': '999999844010359\\n999999844010359\\n999999844010359\\n999999579346573\\n999999579346573\\n999999418799244\\n999999418799244\\n999999418799244\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 1073741824}","problem_id":"vfc_80749","program":"```python\nimport math, string, itertools, fractions, collections, re, array, bisect, sys, random, time, copy, functools\nfrom heapq import heappush, heappop, heappushpop, heapify, heapreplace\n\nN, M, S, T = [int(_) for _ in input().split()]\nUVAB = [[int(_) for _ in input().split()] for _ in range(M)]\nG1 = collections.defaultdict(lambda: collections.defaultdict(int))\nG2 = collections.defaultdict(lambda: collections.defaultdict(int))\n\nfor u, v, a, b in UVAB:\n u -= 1\n v -= 1\n G1[u][v] = G1[v][u] = a\n G2[u][v] = G2[v][u] = b\n\n\ndef dijkstra(V, G, start):\n INF = float('inf')\n D = [INF for _ in range(V)]\n D[start] = 0\n H = [(0, start)]\n while H:\n du, u = heappop(H)\n if D[u] < du:\n continue\n for v, d in G[u].items():\n if D[v] > du + d:\n D[v] = du + d\n heappush(H, (D[v], v))\n return D\n\n\nD1 = dijkstra(N, G1, S - 1)\nD2 = dijkstra(N, G2, T - 1)\n\nD = [10**15 - sum(_) for _ in zip(D1, D2)]\nfor i in range(N - 1, 0, -1):\n D[i - 1] = max(D[i - 1], D[i])\nprint(*D, sep='\\n')\n\n```","inputs":"8 12 3 8\n2 8 685087149 857180777\n6 7 298270585 209942236\n2 4 346080035 234079976\n2 5 131857300 22507157\n4 8 30723332 173476334\n2 6 480845267 448565596\n1 4 181424400 548830121\n4 5 57429995 195056405\n7 8 160277628 479932440\n1 6 475692952 203530153\n3 5 336869679 160714712\n2 7 389775999 199123879","output":"999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994","actual_output":"999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n","execution_success":true,"sample_index":12852},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03465 AtCoder Grand Contest 020 - Median Sum","prompt":"Solve the following coding problem using the programming language python:\n\nYou are given N integers A_1, A_2, ..., A_N.\n\nConsider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.\n\nLet the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.\n\nFind the median of this list, S_{2^{N-1}}.\n\nConstraints\n\n* 1 \\leq N \\leq 2000\n* 1 \\leq A_i \\leq 2000\n* All input values are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nA_1 A_2 ... A_N\n\n\nOutput\n\nPrint the median of the sorted list of the sums of all non-empty subsequences of A.\n\nExamples\n\nInput\n\n3\n1 2 1\n\n\nOutput\n\n2\n\n\nInput\n\n1\n58\n\n\nOutput\n\n58\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nn = int(input())\na = list(map(int, input().split()))\nd = (sum(a)+1)//2\nc = 1\nfor x in a:\n c |= c << x\nc >>= d\nfor i in range(d+5):\n if c & (1 << i):\n print(d+i)\n break\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '3\\n1 2 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '1\\n58', 'output': '58'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 0', 'output': '2'}, {'type': 'stdin_stdout', 'input': '1\\n32', 'output': '32'}, {'type': 'stdin_stdout', 'input': '1\\n62', 'output': '62'}, {'type': 'stdin_stdout', 'input': '1\\n26', 'output': '26'}, {'type': 'stdin_stdout', 'input': '3\\n1 2 -1', 'output': '1'}, {'type': 'stdin_stdout', 'input': '1\\n4', 'output': '4'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 -1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '1\\n7', 'output': '7'}, {'type': 'stdin_stdout', 'input': '1\\n0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3\\n3 5 -1', 'output': '5'}, {'type': 'stdin_stdout', 'input': '3\\n3 9 -1', 'output': '9'}, {'type': 'stdin_stdout', 'input': '3\\n-3 6 1', 'output': '6'}, {'type': 'stdin_stdout', 'input': '3\\n-3 14 3', 'output': '14'}, {'type': 'stdin_stdout', 'input': '3\\n-2 8 0', 'output': '8'}, {'type': 'stdin_stdout', 'input': '3\\n-2 16 0', 'output': '16'}, {'type': 'stdin_stdout', 'input': '3\\n-2 13 0', 'output': '13'}, {'type': 'stdin_stdout', 'input': '3\\n0 11 2', 'output': '11'}, {'type': 'stdin_stdout', 'input': '3\\n0 19 3', 'output': '19'}, {'type': 'stdin_stdout', 'input': '3\\n0 31 2', 'output': '31'}, {'type': 'stdin_stdout', 'input': '3\\n0 42 3', 'output': '42'}, {'type': 'stdin_stdout', 'input': '3\\n0 10 3', 'output': '10'}, {'type': 'stdin_stdout', 'input': '3\\n0 12 2', 'output': '12'}, {'type': 'stdin_stdout', 'input': '3\\n2 24 2', 'output': '24'}, {'type': 'stdin_stdout', 'input': '3\\n0 28 3', 'output': '28'}, {'type': 'stdin_stdout', 'input': '3\\n-1 43 3', 'output': '43'}, {'type': 'stdin_stdout', 'input': '3\\n0 50 5', 'output': '50'}, {'type': 'stdin_stdout', 'input': '3\\n0 85 5', 'output': '85'}, {'type': 'stdin_stdout', 'input': '3\\n-2 59 1', 'output': '59'}, {'type': 'stdin_stdout', 'input': '3\\n-1 71 -1', 'output': '71'}, {'type': 'stdin_stdout', 'input': '3\\n-1 34 -1', 'output': '34'}, {'type': 'stdin_stdout', 'input': '3\\n-1 36 -1', 'output': '36'}, {'type': 'stdin_stdout', 'input': '3\\n-1 18 -2', 'output': '18'}, {'type': 'stdin_stdout', 'input': '3\\n-1 35 0', 'output': '35'}, {'type': 'stdin_stdout', 'input': '3\\n-1 45 0', 'output': '45'}, {'type': 'stdin_stdout', 'input': '3\\n-1 23 0', 'output': '23'}, {'type': 'stdin_stdout', 'input': '3\\n-1 30 -1', 'output': '30'}, {'type': 'stdin_stdout', 'input': '3\\n-1 40 -1', 'output': '40'}, {'type': 'stdin_stdout', 'input': '3\\n0 20 5', 'output': '20'}, {'type': 'stdin_stdout', 'input': '3\\n-2 15 3', 'output': '15'}, {'type': 'stdin_stdout', 'input': '3\\n6 79 22', 'output': '79'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 66', 'output': '66'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 68', 'output': '68'}, {'type': 'stdin_stdout', 'input': '1\\n94', 'output': '94'}, {'type': 'stdin_stdout', 'input': '1\\n55', 'output': '55'}, {'type': 'stdin_stdout', 'input': '3\\n1 17 -1', 'output': '17'}, {'type': 'stdin_stdout', 'input': '3\\n1 25 3', 'output': '25'}, {'type': 'stdin_stdout', 'input': '3\\n0 22 3', 'output': '22'}, {'type': 'stdin_stdout', 'input': '3\\n2 47 2', 'output': '47'}, {'type': 'stdin_stdout', 'input': '3\\n0 80 3', 'output': '80'}, {'type': 'stdin_stdout', 'input': '3\\n0 83 5', 'output': '83'}, {'type': 'stdin_stdout', 'input': '3\\n0 82 5', 'output': '82'}, {'type': 'stdin_stdout', 'input': '3\\n0 41 5', 'output': '41'}, {'type': 'stdin_stdout', 'input': '3\\n1 107 5', 'output': '107'}, {'type': 'stdin_stdout', 'input': '3\\n-1 84 -1', 'output': '84'}, {'type': 'stdin_stdout', 'input': '3\\n-1 89 -1', 'output': '89'}, {'type': 'stdin_stdout', 'input': '3\\n0 70 -2', 'output': '70'}, {'type': 'stdin_stdout', 'input': '3\\n-1 64 -2', 'output': '64'}, {'type': 'stdin_stdout', 'input': '3\\n0 33 -1', 'output': '33'}, {'type': 'stdin_stdout', 'input': '3\\n-1 39 -1', 'output': '39'}, {'type': 'stdin_stdout', 'input': '3\\n-1 51 -1', 'output': '51'}, {'type': 'stdin_stdout', 'input': '3\\n-1 56 -1', 'output': '56'}, {'type': 'stdin_stdout', 'input': '3\\n4 100 34', 'output': '100'}, {'type': 'stdin_stdout', 'input': '3\\n1 125 34', 'output': '125'}, {'type': 'stdin_stdout', 'input': '3\\n-1 -1 67', 'output': '67'}, {'type': 'stdin_stdout', 'input': '1\\n21', 'output': '21'}, {'type': 'stdin_stdout', 'input': '3\\n0 57 3', 'output': '57'}, {'type': 'stdin_stdout', 'input': '3\\n0 29 5', 'output': '29'}, {'type': 'stdin_stdout', 'input': '3\\n-1 46 2', 'output': '46'}, {'type': 'stdin_stdout', 'input': '3\\n0 106 3', 'output': '106'}, {'type': 'stdin_stdout', 'input': '3\\n-1 95 1', 'output': '95'}, {'type': 'stdin_stdout', 'input': '3\\n-4 44 1', 'output': '44'}, {'type': 'stdin_stdout', 'input': '3\\n0 122 -2', 'output': '122'}, {'type': 'stdin_stdout', 'input': '3\\n-1 38 0', 'output': '38'}, {'type': 'stdin_stdout', 'input': '3\\n0 63 0', 'output': '63'}, {'type': 'stdin_stdout', 'input': '3\\n-2 27 8', 'output': '27'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 0', 'output': '2'}, {'type': 'stdin_stdout', 'input': '3\\n0 2 -1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '3\\n1 3 0', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 -1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '1\\n-1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3\\n2 3 0', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3\\n4 3 -1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3\\n3 3 -1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3\\n0 9 -1', 'output': '9'}, {'type': 'stdin_stdout', 'input': '3\\n1 9 -1', 'output': '9'}, {'type': 'stdin_stdout', 'input': '3\\n1 5 -1', 'output': '5'}, {'type': 'stdin_stdout', 'input': '3\\n0 5 -1', 'output': '5'}, {'type': 'stdin_stdout', 'input': '3\\n0 3 -1', 'output': '3'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 -1', 'output': '4'}, {'type': 'stdin_stdout', 'input': '3\\n0 4 0', 'output': '4'}, {'type': 'stdin_stdout', 'input': '3\\n0 5 0', 'output': '5'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 0', 'output': '1'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 0', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3\\n1 0 0', 'output': '1'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 1', 'output': '1'}, {'type': 'stdin_stdout', 'input': '3\\n0 -1 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3\\n0 -2 1', 'output': '0'}, {'type': 'stdin_stdout', 'input': '3\\n0 0 2', 'output': '2'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 2', 'output': '2'}, {'type': 'stdin_stdout', 'input': '3\\n0 1 1', 'output': '1'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 536870912}","problem_id":"vfc_80753","program":"```python\nn = int(input())\na = list(map(int, input().split()))\nd = (sum(a)+1)//2\nc = 1\nfor x in a:\n c |= c << x\nc >>= d\nfor i in range(d+5):\n if c & (1 << i):\n print(d+i)\n break\n```","inputs":"3\n1 2 1","output":"2","actual_output":"2\n","execution_success":true,"sample_index":12853},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03625 AtCoder Beginner Contest 071 - Make a Rectangle","prompt":"Solve the following coding problem using the programming language python:\n\nWe have N sticks with negligible thickness. The length of the i-th stick is A_i.\n\nSnuke wants to select four different sticks from these sticks and form a rectangle (including a square), using the sticks as its sides. Find the maximum possible area of the rectangle.\n\nConstraints\n\n* 4 \\leq N \\leq 10^5\n* 1 \\leq A_i \\leq 10^9\n* A_i is an integer.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nA_1 A_2 ... A_N\n\n\nOutput\n\nPrint the maximum possible area of the rectangle. If no rectangle can be formed, print 0.\n\nExamples\n\nInput\n\n6\n3 1 2 4 2 1\n\n\nOutput\n\n2\n\n\nInput\n\n4\n1 2 3 4\n\n\nOutput\n\n0\n\n\nInput\n\n10\n3 3 3 3 4 4 4 5 5 5\n\n\nOutput\n\n20\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN = int(input())\nA = sorted([int(_) for _ in input().split()], reverse=True)\n\ne = []\npre = 0\nfor i in range(N):\n if pre == A[i]:\n e.append(A[i])\n if len(e) >= 2: break\n pre = 0\n else:\n pre = A[i]\nif len(e) < 2: print(0)\nelse: print(e[0] * e[1])\n```","verification_info":"{'test_cases': [{'type': 'stdin_stdout', 'input': '10\\n3 3 3 3 4 4 4 5 5 5', 'output': '20'}, {'type': 'stdin_stdout', 'input': '6\\n3 1 2 4 2 1', 'output': '2'}, {'type': 'stdin_stdout', 'input': '4\\n1 2 3 4', 'output': '0'}, {'type': 'stdin_stdout', 'input': '10\\n3 3 3 3 4 4 2 5 5 5', 'output': '20\\n'}, {'type': 'stdin_stdout', 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{'type': 'stdin_stdout', 'input': '10\\n0 2 12 15 3 1 0 18 1 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-1 2 12 15 3 1 0 18 1 1', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-1 2 12 2 3 1 1 18 1 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-1 2 12 2 3 2 1 18 1 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-1 2 12 2 4 2 1 18 1 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-1 2 12 2 4 2 1 23 1 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-1 2 12 2 4 2 1 41 1 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-2 2 12 2 4 2 1 41 1 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-2 2 12 1 4 2 1 41 1 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-2 2 12 1 4 2 1 41 0 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-2 2 12 1 4 2 1 41 -1 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-2 2 1 1 4 2 1 41 -1 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-2 2 1 2 4 2 1 41 -1 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-2 2 1 2 4 2 1 41 0 1', 'output': '2\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-2 2 1 2 4 2 1 41 0 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-2 2 1 2 4 2 1 15 0 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-2 2 1 2 4 2 2 15 0 2', 'output': '4\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 2 1 2 4 2 4 15 0 2', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 2 1 2 4 2 4 15 0 0', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 1 2 4 2 4 15 0 0', 'output': '8\\n'}, {'type': 'stdin_stdout', 'input': '10\\n0 0 1 3 4 2 4 15 0 0', 'output': '0\\n'}, {'type': 'stdin_stdout', 'input': '10\\n-1 0 1 3 4 2 4 15 0 0', 'output': '0\\n'}], 'language': 'python'}","metadata":"{'difficulty': 0, 'time_limit': {'seconds': 2, 'nanos': 0}, 'memory_limit_bytes': 268435456}","problem_id":"vfc_80757","program":"```python\nN = int(input())\nA = sorted([int(_) for _ in input().split()], reverse=True)\n\ne = []\npre = 0\nfor i in range(N):\n if pre == A[i]:\n e.append(A[i])\n if len(e) >= 2: break\n pre = 0\n else:\n pre = A[i]\nif len(e) < 2: print(0)\nelse: print(e[0] * e[1])\n```","inputs":"10\n3 3 3 3 4 4 4 5 5 5","output":"20","actual_output":"20\n","execution_success":true,"sample_index":12854},{"source":"code_contests","task_type":"verifiable_code","in_source_id":"p03785 AtCoder Grand Contest 011 - Airport Bus","prompt":"Solve the following coding problem using the programming language python:\n\nEvery day, N passengers arrive at Takahashi Airport. The i-th passenger arrives at time T_i.\n\nEvery passenger arrived at Takahashi airport travels to the city by bus. Each bus can accommodate up to C passengers. Naturally, a passenger cannot take a bus that departs earlier than the airplane arrives at the airport. Also, a passenger will get angry if he/she is still unable to take a bus K units of time after the arrival of the airplane. For that reason, it is necessary to arrange buses so that the i-th passenger can take a bus departing at time between T_i and T_i + K (inclusive).\n\nWhen setting the departure times for buses under this condition, find the minimum required number of buses. Here, the departure time for each bus does not need to be an integer, and there may be multiple buses that depart at the same time.\n\nConstraints\n\n* 2 \\leq N \\leq 100000\n* 1 \\leq C \\leq 10^9\n* 1 \\leq K \\leq 10^9\n* 1 \\leq T_i \\leq 10^9\n* C, K and T_i are integers.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN C K\nT_1\nT_2\n:\nT_N\n\n\nOutput\n\nPrint the minimum required number of buses.\n\nExamples\n\nInput\n\n5 3 5\n1\n2\n3\n6\n12\n\n\nOutput\n\n3\n\n\nInput\n\n6 3 3\n7\n6\n2\n8\n10\n6\n\n\nOutput\n\n3\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code.","gold_standard_solution":"```python\nN,C,K=map(int,input().split())\nT=[int(input()) for i in range(N)]\nT.sort()\nS=[[T[0]]]\nt=T[0]\nk=0\nfor i in range(1,N):\n if T[i]<=t+K and len(S[k])