""" Largest product in a grid
In the 20x20 grid below, four numbers along a diagonal line have been marked
in red.
The product of these numbers is 26 x 63 x 78 x 14 = 1788696.
What is the greatest product of four adjacent numbers in the same direction
(up, down, left, right, or diagonally) in the 20x20 grid?
"""

def main():
    """ Iretating over our matrix, we compute the horizonal, vertical, and
    diagonals products and gets their maximum each irritation.
    """
    matrix = [[8,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,8]]
    matrix += [[49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00]]
    matrix += [[81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65]]
    matrix += [[52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91]]
    matrix += [[22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80]]
    matrix += [[24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50]]
    matrix += [[32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70]]
    matrix += [[67,26,20,68,02,62,12,20,95,63,94,39,63,8,40,91,66,49,94,21]]
    matrix += [[24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72]]
    matrix += [[21,36,23,9,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95]]
    matrix += [[78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,9,53,56,92]]
    matrix += [[16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57]]
    matrix += [[86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58]]
    matrix += [[19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40]]
    matrix += [[04,52,8,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66]]
    matrix += [[88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69]]
    matrix += [[04,42,16,73,38,25,39,11,24,94,72,18,8,46,29,32,40,62,76,36]]
    matrix += [[20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16]]
    matrix += [[20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54]]
    matrix += [[01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48]]
    result, n_of_nums = 0, 4 # n is number of numbers required
    for i in xrange(0, len(matrix)-n_of_nums):
        for j in xrange(0, len(matrix)-n_of_nums):
            horizontal, vertical, m_diagonal, c_diagonal = 1, 1, 1, 1
            for k in xrange(n_of_nums):
                horizontal *= matrix[i][j+k]
                vertical *= matrix[i+k][j]
                m_diagonal *= matrix[i+k][j+k] # main diagonal
                c_diagonal *= matrix[i+n_of_nums-1-k][j+k] # counter diagonal
            result = max(horizontal, vertical, m_diagonal, c_diagonal, result)
    print result

if __name__ == '__main__':
    main()

## test