/* mockturtle: C++ logic network library
 * Copyright (C) 2018-2019  EPFL
 *
 * Permission is hereby granted, free of charge, to any person
 * obtaining a copy of this software and associated documentation
 * files (the "Software"), to deal in the Software without
 * restriction, including without limitation the rights to use,
 * copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following
 * conditions:
 *
 * The above copyright notice and this permission notice shall be
 * included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
 * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 * OTHER DEALINGS IN THE SOFTWARE.
 */

/*!
  \file mig_npn.hpp
  \brief Replace with size-optimum MIGs from NPN

  \author Mathias Soeken
*/

#pragma once

#include <iostream>
#include <sstream>
#include <unordered_map>
#include <vector>

#include <kitty/dynamic_truth_table.hpp>
#include <kitty/npn.hpp>
#include <kitty/print.hpp>

#include "../../algorithms/cleanup.hpp"
#include "../../io/write_bench.hpp"
#include "../../networks/mig.hpp"
#include "../../traits.hpp"
#include "../../views/topo_view.hpp"

namespace mockturtle
{

/*! \brief Resynthesis function based on pre-computed size-optimum MIGs.
 *
 * This resynthesis function can be passed to ``node_resynthesis``,
 * ``cut_rewriting``, and ``refactoring``.  It will produce an MIG based on
 * pre-computed size-optimum MIGs with up to at most 4 variables.
 * Consequently, the nodes' fan-in sizes in the input network must not exceed
 * 4.
 *
   \verbatim embed:rst

   Example

   .. code-block:: c++

      const klut_network klut = ...;
      mig_npn_resynthesis resyn;
      const auto mig = node_resynthesis<mig_network>( klut, resyn );
   \endverbatim
 */
class mig_npn_resynthesis
{
public:
  /*! \brief Default constructor.
   *
   * \param use_multiple If true, up to 10 structures are tried for each
   *                     function.
   */
  mig_npn_resynthesis( bool use_multiple = false )
  {
    if ( use_multiple )
    {
      build_db10();
    }
    else
    {
      build_db();
    }
  }

  template<typename LeavesIterator, typename Fn>
  void operator()( mig_network& mig, kitty::dynamic_truth_table const& function, LeavesIterator begin, LeavesIterator end, Fn&& fn )
  {
    assert( function.num_vars() <= 4 );
    const auto fe = kitty::extend_to( function, 4 );
    const auto config = kitty::exact_npn_canonization( fe );

    const auto it = class2signal.find( static_cast<uint16_t>( std::get<0>( config )._bits[0] ) );

    std::vector<mig_network::signal> pis( 4, mig.get_constant( false ) );
    std::copy( begin, end, pis.begin() );

    std::vector<mig_network::signal> pis_perm( 4 );
    auto perm = std::get<2>( config );
    for ( auto i = 0; i < 4; ++i )
    {
      pis_perm[i] = pis[perm[i]];
    }

    const auto& phase = std::get<1>( config );
    for ( auto i = 0; i < 4; ++i )
    {
      if ( ( phase >> perm[i] ) & 1 )
      {
        pis_perm[i] = !pis_perm[i];
      }
    }

    for ( auto const& po : it->second )
    {
      topo_view topo{db, po};
      auto f = cleanup_dangling( topo, mig, pis_perm.begin(), pis_perm.end() ).front();

      if ( !fn( ( ( phase >> 4 ) & 1 ) ? !f : f ) )
      {
        return; /* quit */
      }
    }
  }

private:
  void build_db()
  {
    std::vector<mig_network::signal> signals;
    signals.push_back( db.get_constant( false ) );

    auto p = nodes.begin();
    for ( auto i = 0u; i < *p; ++i )
    {
      signals.push_back( db.create_pi() );
    }

    p++;         /* point to number of outputs */
    p += *p + 1; /* move past number of output */

    /* create nodes */
    while ( p != nodes.end() )
    {
      const auto c1 = signals[*p >> 1] ^ ( *p & 1 );
      ++p;
      const auto c2 = signals[*p >> 1] ^ ( *p & 1 );
      ++p;
      const auto c3 = signals[*p >> 1] ^ ( *p & 1 );
      ++p;

      signals.push_back( db.create_maj( c1, c2, c3 ) );
    }

    /* create POs */
    p = nodes.begin() + 2;
    for ( auto i = 0u; i < nodes[1]; ++i )
    {
      const auto driver = signals[*p >> 1] ^ ( *p & 1 );
      ++p;

      db.create_po( driver );
      class2signal[classes[i]].push_back( driver );
    }
  }

  void build_db10()
  {
    std::vector<mig_network::signal> signals;
    signals.push_back( db.get_constant( false ) );

    auto p = nodes10.begin();
    for ( auto i = 0u; i < *p; ++i )
    {
      signals.push_back( db.create_pi() );
    }

    p++;         /* point to number of outputs */
    const auto num_functions = *p++;

    for ( auto i = 0u; i < num_functions; ++i )
    {
      p += *p + 1;
    }

    /* create nodes */
    while ( p != nodes10.end() )
    {
      const auto c1 = signals[*p >> 1] ^ ( *p & 1 );
      ++p;
      const auto c2 = signals[*p >> 1] ^ ( *p & 1 );
      ++p;
      const auto c3 = signals[*p >> 1] ^ ( *p & 1 );
      ++p;

      signals.push_back( db.create_maj( c1, c2, c3 ) );
    }

    /* create PIs */
    p = nodes10.begin() + 2;
    for ( auto i = 0u; i < nodes10[1]; ++i )
    {
      const auto functions = *p++;
      for ( auto j = 0u; j < functions; ++j )
      {
        const auto driver = signals[*p >> 1] ^ ( *p & 1 );
        ++p;

        db.create_po( driver );
        class2signal[classes[i]].push_back( driver );
      }
    }
  }

  mig_network db;
  std::unordered_map<uint16_t, std::vector<mig_network::signal>> class2signal;

  inline static const std::vector<uint16_t> classes{{0x1ee1, 0x1be4, 0x1bd8, 0x18e7, 0x17e8, 0x17ac, 0x1798, 0x1796, 0x178e, 0x177e, 0x16e9, 0x16bc, 0x169e, 0x003f, 0x0359, 0x0672, 0x07e9, 0x0693, 0x0358, 0x01bf, 0x6996, 0x0356, 0x01bd, 0x001f, 0x01ac, 0x001e, 0x0676, 0x01ab, 0x01aa, 0x001b, 0x07e1, 0x07e0, 0x0189, 0x03de, 0x035a, 0x1686, 0x0186, 0x03db, 0x0357, 0x01be, 0x1683, 0x0368, 0x0183, 0x03d8, 0x07e6, 0x0182, 0x03d7, 0x0181, 0x03d6, 0x167e, 0x016a, 0x007e, 0x0169, 0x006f, 0x0069, 0x0168, 0x0001, 0x019a, 0x036b, 0x1697, 0x0369, 0x0199, 0x0000, 0x169b, 0x003d, 0x036f, 0x0666, 0x019b, 0x0187, 0x03dc, 0x0667, 0x0003, 0x168e, 0x06b6, 0x01eb, 0x07e2, 0x017e, 0x07b6, 0x007f, 0x19e3, 0x06b7, 0x011a, 0x077e, 0x018b, 0x00ff, 0x0673, 0x01a8, 0x000f, 0x1696, 0x036a, 0x011b, 0x0018, 0x0117, 0x1698, 0x036c, 0x01af, 0x0016, 0x067a, 0x0118, 0x0017, 0x067b, 0x0119, 0x169a, 0x003c, 0x036e, 0x07e3, 0x017f, 0x03d4, 0x06f0, 0x011e, 0x037c, 0x012c, 0x19e6, 0x01ef, 0x16a9, 0x037d, 0x006b, 0x012d, 0x012f, 0x01fe, 0x0019, 0x03fc, 0x179a, 0x013c, 0x016b, 0x06f2, 0x03c0, 0x033c, 0x1668, 0x0669, 0x019e, 0x013d, 0x0006, 0x019f, 0x013e, 0x0776, 0x013f, 0x016e, 0x03c3, 0x3cc3, 0x033f, 0x166b, 0x016f, 0x011f, 0x035e, 0x0690, 0x0180, 0x03d5, 0x06f1, 0x06b0, 0x037e, 0x03c1, 0x03c5, 0x03c6, 0x01a9, 0x166e, 0x03cf, 0x03d9, 0x07bc, 0x01bc, 0x1681, 0x03dd, 0x03c7, 0x06f9, 0x0660, 0x0196, 0x0661, 0x0197, 0x0662, 0x07f0, 0x0198, 0x0663, 0x07f1, 0x0007, 0x066b, 0x033d, 0x1669, 0x066f, 0x01ad, 0x0678, 0x01ae, 0x0679, 0x067e, 0x168b, 0x035f, 0x0691, 0x0696, 0x0697, 0x06b1, 0x0778, 0x16ac, 0x06b2, 0x0779, 0x16ad, 0x01e8, 0x06b3, 0x0116, 0x077a, 0x01e9, 0x06b4, 0x19e1, 0x01ea, 0x06b5, 0x01ee, 0x06b9, 0x06bd, 0x06f6, 0x07b0, 0x07b1, 0x07b4, 0x07b5, 0x07f2, 0x07f8, 0x018f, 0x0ff0, 0x166a, 0x035b, 0x1687, 0x1689, 0x036d, 0x069f, 0x1699}};
  inline static const std::vector<uint16_t> nodes{{4, 222, 17, 24, 34, 41, 46, 56, 68, 76, 84, 96, 109, 116, 122, 127, 137, 142, 151, 157, 166, 173, 182, 188, 193, 199, 208, 214, 220, 227, 232, 239, 247, 256, 259, 264, 272, 278, 286, 293, 297, 300, 307, 312, 321, 328, 336, 344, 351, 355, 362, 372, 378, 384, 387, 389, 393, 398, 401, 408, 417, 421, 425, 433, 0, 439, 445, 451, 454, 459, 467, 472, 475, 477, 482, 486, 491, 498, 502, 506, 509, 517, 523, 526, 532, 537, 9, 545, 548, 335, 554, 560, 563, 568, 573, 576, 580, 583, 586, 594, 596, 599, 603, 605, 612, 616, 622, 627, 629, 630, 634, 638, 640, 644, 650, 657, 665, 669, 675, 677, 679, 686, 691, 696, 702, 708, 713, 718, 722, 728, 738, 747, 750, 755, 756, 761, 766, 770, 773, 778, 785, 789, 159, 797, 801, 803, 810, 812, 820, 827, 831, 836, 844, 853, 857, 862, 869, 876, 879, 887, 892, 900, 911, 915, 921, 927, 930, 938, 941, 951, 954, 960, 966, 971, 975, 977, 985, 991, 1003, 1007, 1011, 1014, 1020, 1027, 1030, 1037, 1039, 1041, 1044, 1049, 1053, 1060, 1066, 1070, 1073, 1077, 1082, 1093, 1096, 1100, 1107, 1112, 1119, 1124, 1135, 1138, 1141, 1147, 1148, 1152, 1159, 1166, 1175, 1178, 1186, 1191, 1194, 1202, 1205, 1213, 1221, 1229, 1231, 1237, 1, 2, 4, 6, 8, 11, 9, 10, 12, 7, 12, 14, 0, 2, 7, 8, 10, 19, 8, 10, 21, 18, 20, 23, 5, 6, 8, 2, 4, 6, 0, 26, 28, 1, 26, 28, 0, 31, 32, 6, 9, 28, 8, 29, 36, 7, 36, 38, 0, 8, 28, 0, 8, 43, 28, 43, 44, 0, 5, 8, 4, 7, 48, 0, 2, 8, 2, 6, 48, 50, 53, 54, 0, 4, 9, 0, 2, 59, 0, 2, 58, 7, 8, 62, 2, 5, 6, 61, 64, 66, 0, 6, 9, 1, 4, 8, 2, 71, 72, 29, 70, 74, 0, 4, 8, 2, 4, 7, 0, 3, 8, 79, 80, 82, 0, 7, 8, 2, 7, 86, 4, 6, 87, 0, 6, 8, 2, 4, 92, 88, 90, 95, 0, 2, 4, 1, 6, 98, 2, 4, 99, 8, 100, 103, 101, 102, 104, 9, 104, 106, 1, 4, 6, 0, 9, 110, 2, 8, 110, 29, 112, 114, 0, 3, 6, 4, 52, 118, 80, 118, 121, 0, 4, 6, 1, 8, 124, 0, 2, 9, 0, 4, 128, 6, 9, 130, 4, 6, 131, 128, 133, 134, 0, 2, 5, 3, 6, 78, 93, 138, 140, 0, 9, 28, 2, 4, 9, 0, 6, 147, 145, 146, 148, 4, 8, 71, 2, 4, 8, 28, 152, 155, 4, 6, 8, 0, 8, 159, 2, 5, 158, 2, 6, 83, 160, 163, 164, 1, 2, 6, 0, 3, 4, 8, 168, 170, 3, 6, 18, 1, 18, 174, 4, 9, 176, 5, 8, 176, 177, 178, 180, 2, 82, 110, 2, 83, 110, 82, 185, 186, 2, 7, 78, 99, 158, 190, 0, 5, 6, 0, 3, 194, 6, 8, 197, 4, 8, 52, 4, 7, 8, 2, 6, 200, 1, 202, 204, 0, 201, 206, 0, 6, 10, 6, 9, 10, 0, 211, 212, 6, 9, 98, 1, 80, 216, 0, 99, 218, 4, 6, 53, 3, 52, 222, 1, 52, 224, 3, 6, 170, 2, 8, 228, 8, 128, 231, 2, 6, 8, 3, 4, 8, 1, 234, 236, 1, 6, 146, 6, 146, 241, 0, 9, 242, 0, 240, 245, 2, 5, 8, 4, 6, 248, 1, 8, 250, 0, 9, 252, 251, 252, 254, 10, 131, 194, 4, 7, 248, 0, 6, 249, 79, 260, 262, 0, 4, 7, 6, 8, 266, 3, 6, 8, 18, 269, 270, 2, 7, 8, 4, 82, 275, 5, 80, 276, 2, 8, 266, 4, 8, 281, 2, 7, 282, 0, 281, 284, 5, 8, 28, 0, 4, 29, 110, 288, 290, 0, 2, 110, 8, 110, 294, 1, 6, 236, 128, 159, 298, 4, 6, 83, 2, 4, 303, 274, 302, 305, 6, 58, 128, 8, 159, 308, 129, 308, 310, 5, 6, 170, 2, 7, 170, 4, 8, 316, 1, 314, 318, 2, 6, 9, 0, 249, 322, 0, 110, 325, 8, 324, 327, 2, 9, 170, 4, 6, 171, 1, 6, 8, 330, 333, 334, 2, 5, 266, 6, 8, 338, 2, 8, 267, 0, 341, 342, 3, 4, 6, 0, 8, 110, 110, 347, 348, 4, 8, 170, 125, 168, 352, 0, 9, 346, 1, 2, 8, 4, 194, 358, 356, 358, 361, 3, 6, 266, 1, 2, 266, 0, 2, 6, 4, 8, 368, 364, 366, 371, 7, 26, 128, 3, 6, 374, 27, 374, 376, 4, 9, 66, 0, 67, 380, 5, 380, 382, 2, 145, 346, 8, 66, 139, 7, 66, 346, 1, 8, 390, 6, 8, 80, 0, 28, 395, 8, 395, 396, 1, 10, 12, 0, 3, 26, 2, 9, 402, 0, 6, 26, 402, 404, 407, 4, 6, 129, 8, 128, 410, 4, 7, 412, 5, 410, 414, 2, 8, 158, 8, 28, 419, 4, 71, 128, 5, 410, 422, 1, 6, 10, 3, 8, 10, 0, 5, 10, 426, 428, 430, 3, 4, 86, 2, 26, 434, 87, 434, 436, 2, 7, 266, 8, 267, 440, 4, 267, 442, 4, 6, 369, 8, 368, 446, 5, 446, 448, 2, 4, 93, 3, 138, 452, 2, 8, 194, 3, 10, 456, 0, 8, 154, 6, 155, 460, 0, 7, 154, 1, 462, 464, 4, 9, 196, 4, 194, 469, 8, 468, 471, 1, 12, 98, 1, 4, 334, 1, 6, 80, 2, 8, 479, 48, 80, 481, 2, 29, 70, 10, 29, 484, 0, 4, 70, 52, 346, 489, 0, 8, 93, 2, 93, 492, 4, 7, 92, 170, 494, 497, 3, 6, 160, 146, 159, 500, 1, 2, 202, 29, 70, 504, 8, 98, 334, 4, 6, 78, 4, 6, 9, 3, 78, 512, 154, 511, 514, 0, 2, 67, 8, 171, 518, 6, 67, 520, 0, 2, 27, 26, 235, 524, 6, 8, 524, 5, 26, 524, 4, 529, 530, 3, 4, 194, 1, 456, 534, 1, 4, 270, 5, 6, 538, 0, 8, 540, 271, 538, 542, 1, 2, 110, 112, 358, 547, 4, 9, 82, 2, 6, 29, 29, 550, 552, 4, 128, 202, 4, 202, 557, 128, 557, 558, 3, 10, 234, 0, 5, 346, 4, 9, 346, 347, 564, 566, 4, 6, 358, 1, 234, 570, 0, 6, 29, 43, 154, 574, 5, 86, 368, 4, 371, 578, 6, 129, 190, 4, 9, 168, 0, 29, 584, 6, 8, 98, 2, 118, 589, 4, 8, 98, 589, 590, 592, 130, 159, 270, 1, 8, 28, 0, 4, 271, 8, 465, 600, 10, 248, 346, 0, 2, 249, 6, 8, 249, 1, 2, 608, 29, 606, 610, 6, 8, 195, 4, 194, 615, 5, 8, 128, 8, 128, 158, 4, 618, 621, 0, 147, 240, 202, 240, 624, 2, 8, 346, 1, 160, 356, 8, 81, 98, 8, 70, 633, 3, 4, 26, 159, 524, 636, 26, 58, 589, 0, 28, 159, 159, 236, 642, 5, 8, 18, 2, 8, 18, 146, 646, 649, 4, 6, 139, 4, 8, 138, 5, 652, 654, 3, 8, 110, 2, 111, 658, 0, 8, 513, 658, 660, 663, 2, 6, 73, 71, 158, 666, 0, 6, 67, 3, 4, 66, 8, 671, 672, 66, 158, 369, 6, 129, 154, 0, 4, 169, 8, 169, 680, 8, 680, 683, 168, 682, 685, 4, 8, 19, 2, 99, 688, 1, 8, 110, 0, 9, 692, 111, 692, 694, 7, 8, 128, 0, 4, 129, 346, 698, 701, 9, 194, 202, 2, 5, 202, 3, 704, 706, 2, 9, 124, 2, 346, 711, 4, 8, 70, 1, 2, 714, 29, 70, 716, 6, 26, 407, 0, 407, 720, 0, 4, 159, 7, 8, 724, 6, 159, 726, 6, 8, 159, 2, 4, 730, 1, 158, 732, 158, 732, 735, 0, 734, 737, 2, 4, 335, 2, 5, 334, 3, 740, 742, 1, 92, 744, 2, 7, 72, 9, 402, 748, 0, 2, 29, 1, 158, 752, 0, 29, 146, 4, 7, 358, 8, 10, 759, 4, 8, 66, 8, 66, 763, 266, 763, 764, 5, 6, 274, 93, 170, 768, 2, 129, 158, 0, 4, 235, 2, 9, 774, 235, 248, 776, 5, 6, 78, 1, 4, 780, 7, 780, 782, 5, 6, 202, 9, 202, 786, 0, 3, 158, 6, 202, 791, 2, 159, 790, 0, 792, 795, 0, 9, 146, 2, 346, 799, 6, 8, 10, 4, 8, 92, 4, 6, 805, 0, 3, 806, 274, 805, 808, 29, 70, 154, 6, 8, 81, 1, 6, 814, 0, 7, 816, 815, 816, 818, 4, 8, 269, 2, 266, 823, 1, 268, 824, 0, 8, 81, 71, 146, 828, 0, 2, 71, 4, 6, 832, 70, 154, 835, 5, 6, 128, 4, 8, 839, 4, 8, 838, 838, 840, 843, 0, 4, 202, 2, 6, 203, 1, 4, 848, 5, 846, 850, 0, 9, 18, 59, 110, 854, 0, 4, 275, 4, 93, 274, 5, 858, 860, 1, 4, 66, 0, 7, 66, 129, 864, 866, 6, 8, 791, 0, 4, 870, 2, 4, 159, 790, 873, 874, 1, 78, 194, 2, 8, 99, 4, 7, 98, 1, 86, 98, 880, 882, 885, 8, 111, 170, 6, 111, 170, 112, 888, 891, 3, 8, 512, 0, 4, 894, 0, 7, 894, 512, 897, 898, 2, 4, 147, 6, 8, 903, 7, 146, 904, 0, 8, 903, 904, 906, 909, 2, 8, 98, 2, 268, 913, 1, 8, 18, 4, 194, 916, 1, 194, 918, 2, 4, 155, 0, 7, 922, 8, 465, 924, 2, 4, 334, 0, 95, 928, 3, 6, 72, 0, 9, 932, 4, 6, 935, 128, 932, 937, 1, 12, 740, 1, 2, 170, 5, 170, 942, 6, 8, 944, 7, 942, 946, 945, 946, 948, 2, 93, 158, 0, 95, 952, 6, 8, 93, 8, 92, 98, 0, 956, 959, 4, 8, 195, 2, 9, 194, 11, 962, 964, 4, 270, 539, 92, 538, 969, 0, 7, 146, 1, 92, 972, 1, 334, 928, 6, 8, 589, 3, 4, 978, 0, 4, 978, 588, 980, 983, 1, 4, 274, 4, 8, 159, 158, 986, 989, 2, 8, 155, 4, 6, 992, 1, 154, 994, 4, 992, 997, 0, 155, 996, 6, 998, 1001, 0, 99, 102, 6, 8, 1005, 2, 6, 266, 168, 268, 1009, 0, 6, 155, 154, 589, 1012, 1, 8, 158, 3, 4, 1016, 128, 159, 1018, 1, 6, 154, 2, 4, 1023, 8, 465, 1024, 4, 7, 18, 6, 589, 1028, 6, 124, 237, 4, 6, 82, 236, 1032, 1035, 8, 110, 368, 87, 236, 706, 3, 4, 70, 2, 29, 1042, 2, 6, 138, 28, 248, 1047, 3, 6, 48, 71, 146, 1050, 7, 8, 98, 0, 6, 99, 8, 99, 1056, 9, 1054, 1058, 4, 52, 81, 1, 4, 234, 0, 1063, 1064, 0, 3, 154, 66, 93, 1068, 99, 588, 740, 2, 8, 111, 49, 1050, 1074, 3, 358, 570, 0, 9, 570, 571, 1078, 1080, 2, 8, 124, 7, 124, 1084, 4, 8, 1086, 4, 1084, 1089, 8, 1089, 1090, 159, 248, 346, 0, 235, 1094, 0, 358, 589, 6, 589, 1098, 0, 8, 478, 2, 4, 81, 478, 1102, 1105, 4, 8, 81, 0, 3, 80, 334, 1109, 1110, 4, 71, 138, 5, 6, 1114, 235, 1114, 1116, 1, 6, 26, 2, 6, 26, 128, 1120, 1123, 3, 4, 52, 6, 52, 1127, 5, 8, 52, 2, 6, 53, 1129, 1130, 1132, 1, 4, 698, 128, 155, 1136, 87, 236, 646, 3, 6, 52, 5, 6, 52, 248, 1142, 1145, 10, 29, 70, 70, 147, 358, 7, 70, 1150, 2, 4, 86, 4, 18, 1155, 8, 87, 1156, 0, 8, 237, 6, 52, 236, 6, 236, 1161, 1160, 1163, 1164, 0, 3, 146, 6, 8, 1168, 6, 1168, 1171, 146, 1170, 1173, 0, 29, 274, 9, 334, 1176, 7, 8, 28, 0, 29, 1180, 1, 6, 1180, 9, 1182, 1184, 2, 8, 170, 1, 314, 1188, 0, 8, 87, 6, 86, 1193, 2, 6, 158, 0, 154, 1197, 1, 2, 158, 155, 1198, 1200, 19, 234, 266, 4, 8, 235, 0, 6, 234, 3, 4, 1208, 6, 1206, 1211, 1, 6, 922, 8, 154, 1215, 9, 1214, 1216, 155, 1216, 1218, 2, 9, 368, 4, 7, 1222, 4, 9, 368, 6, 1224, 1227, 3, 28, 288, 4, 86, 237, 2, 4, 1233, 86, 1233, 1234}};
  inline static const std::vector<uint16_t> nodes10{{4, 222, 10, 17, 21, 25, 29, 33, 35, 17, 29, 21, 37, 10, 46, 56, 66, 70, 74, 78, 82, 84, 88, 90, 10, 100, 108, 112, 116, 118, 122, 126, 130, 140, 144, 10, 153, 159, 163, 167, 171, 175, 177, 181, 185, 189, 10, 194, 198, 198, 204, 206, 208, 212, 204, 214, 206, 2, 224, 230, 10, 240, 250, 258, 264, 276, 280, 286, 294, 296, 300, 10, 308, 316, 320, 326, 330, 334, 336, 340, 344, 350, 4, 352, 360, 362, 364, 10, 374, 384, 390, 392, 398, 404, 414, 398, 392, 422, 10, 431, 439, 443, 453, 463, 473, 481, 489, 499, 443, 2, 506, 510, 10, 514, 518, 526, 530, 536, 538, 542, 546, 550, 552, 4, 557, 559, 561, 563, 9, 571, 579, 587, 593, 599, 607, 613, 617, 623, 2, 626, 632, 10, 639, 643, 639, 643, 649, 651, 653, 655, 655, 649, 10, 663, 673, 679, 685, 689, 693, 697, 701, 705, 709, 10, 718, 728, 738, 744, 754, 758, 764, 768, 776, 780, 2, 783, 785, 10, 792, 800, 804, 812, 804, 816, 824, 824, 832, 840, 10, 846, 852, 856, 860, 864, 868, 872, 876, 878, 882, 10, 889, 893, 899, 903, 909, 913, 917, 923, 929, 935, 10, 937, 941, 943, 945, 949, 953, 955, 957, 961, 965, 10, 970, 980, 988, 996, 1000, 1006, 1014, 1024, 1032, 1038, 10, 1044, 1046, 1050, 1052, 1056, 1060, 1062, 1064, 1068, 1062, 10, 1070, 1074, 1080, 1070, 1082, 1084, 1088, 1096, 1102, 1108, 10, 1111, 1115, 1119, 1123, 1129, 1131, 1135, 1141, 1145, 1149, 10, 1156, 1164, 1168, 1170, 1174, 1178, 1180, 1182, 1184, 1186, 2, 1191, 1193, 10, 1197, 1203, 1205, 1209, 1211, 1203, 1215, 1217, 1221, 1223, 10, 1228, 1236, 1240, 1244, 1252, 1256, 1264, 1268, 1274, 1278, 10, 1283, 1287, 1293, 1297, 1305, 1311, 1319, 1323, 1325, 1327, 8, 1332, 1338, 1344, 1350, 1358, 1364, 1368, 1374, 10, 1378, 1380, 1384, 1388, 1394, 1396, 1402, 1406, 1410, 1412, 10, 1418, 1422, 1428, 1432, 1436, 1440, 1442, 1444, 1448, 1452, 2, 1458, 1462, 10, 1469, 1473, 1477, 1483, 1487, 1489, 1493, 1487, 1497, 1501, 7, 875, 1503, 1507, 1509, 845, 1511, 1513, 8, 1516, 1524, 1530, 1538, 1542, 1550, 1558, 1566, 10, 1573, 1577, 1581, 1589, 1593, 1597, 1601, 1607, 1611, 1615, 10, 1620, 1630, 1636, 1642, 1648, 1654, 1658, 1664, 1668, 1674, 10, 1681, 1685, 1691, 1697, 1701, 1707, 1711, 1713, 1717, 1719, 10, 1724, 1728, 1732, 1734, 1738, 1744, 1750, 1752, 1760, 1764, 2, 1768, 1772, 10, 1778, 1782, 1786, 1790, 1798, 1806, 1810, 1812, 1816, 1822, 6, 1825, 1829, 1833, 1837, 1841, 1843, 10, 1845, 1849, 1853, 1859, 1863, 1865, 1869, 1875, 1879, 1885, 10, 1888, 1892, 1898, 1904, 1908, 1912, 1920, 1926, 1934, 1938, 10, 1944, 1948, 1956, 1962, 1962, 1972, 1976, 1986, 1990, 1994, 10, 2002, 2006, 2010, 2016, 2020, 2024, 2016, 2028, 2032, 2036, 10, 2042, 2044, 2046, 2048, 2050, 2052, 2054, 2056, 2058, 2060, 9, 2063, 2063, 2067, 2069, 2071, 2073, 2069, 2077, 2071, 2, 2079, 2081, 10, 2085, 809, 809, 2089, 2085, 789, 2093, 797, 797, 2097, 10, 2100, 2104, 2108, 2114, 2120, 2124, 2130, 2134, 2136, 2140, 10, 2143, 2145, 2147, 2151, 2153, 2155, 2159, 2161, 2165, 2167, 10, 2172, 2176, 2172, 2182, 2186, 2190, 2190, 2194, 2186, 2200, 10, 2207, 2211, 2217, 2225, 2227, 2231, 2233, 2237, 2239, 2241, 10, 2245, 2249, 2251, 2253, 2255, 2259, 2263, 2267, 2269, 2271, 10, 2277, 2281, 2283, 2285, 2287, 2289, 2293, 2297, 2301, 2303, 10, 2309, 2315, 2321, 2329, 2331, 2335, 2331, 2337, 2343, 2345, 1, 0, 10, 2351, 2355, 2359, 2363, 2371, 2375, 2379, 2381, 2383, 2387, 10, 2391, 2395, 2399, 2403, 2407, 2411, 2413, 2417, 2419, 2425, 10, 2431, 2435, 2441, 2445, 2447, 2447, 2445, 2453, 2459, 2465, 10, 2468, 2474, 2478, 2482, 2484, 2486, 2490, 2492, 2494, 2498, 7, 2503, 2505, 2507, 2511, 2513, 2515, 2521, 10, 2527, 2533, 2535, 2541, 2543, 2545, 2549, 2551, 2555, 2557, 10, 2560, 2564, 2566, 2568, 2570, 2578, 2584, 2590, 2594, 2596, 10, 2601, 2603, 2607, 2609, 2611, 2603, 2615, 2617, 2619, 2617, 4, 2621, 2623, 1535, 1547, 5, 2626, 2632, 2636, 2640, 2632, 10, 2644, 2650, 2656, 2660, 2662, 2666, 2670, 2672, 2674, 2678, 10, 2683, 2687, 2693, 2697, 2701, 2707, 2711, 2717, 2721, 2729, 10, 2732, 2738, 2746, 2752, 2758, 2764, 2772, 2780, 2786, 2790, 10, 2794, 2800, 2806, 2808, 2810, 2814, 2816, 2822, 2828, 2830, 8, 2832, 2834, 2832, 2834, 2834, 2832, 2832, 2834, 10, 2837, 2841, 2845, 2847, 2849, 2851, 2855, 2857, 2859, 2861, 10, 2867, 2877, 2885, 2889, 2893, 2897, 2905, 2911, 2915, 2919, 10, 2923, 2931, 2937, 2941, 2947, 2953, 2959, 2963, 2969, 2971, 10, 2972, 2978, 2980, 2982, 2972, 2986, 2988, 2994, 2998, 2982, 10, 3006, 3014, 3018, 3022, 3026, 3030, 3034, 3038, 3042, 3046, 5, 3049, 3051, 3053, 3057, 3059, 1, 9, 10, 3065, 3069, 3077, 3069, 3081, 3087, 3095, 3099, 3081, 3103, 10, 3104, 3112, 3114, 3120, 3122, 3128, 3136, 3138, 3142, 3144, 1, 657, 10, 3146, 3154, 3160, 3164, 3172, 3180, 3186, 3190, 3192, 3194, 10, 3196, 3200, 3202, 3204, 3206, 3214, 3218, 3220, 3222, 3228, 6, 3233, 3235, 3237, 3239, 3241, 3243, 10, 3246, 3248, 3250, 3252, 3254, 3256, 3260, 3262, 3268, 3270, 10, 3273, 3277, 487, 3281, 3283, 3285, 3287, 3291, 3293, 441, 2, 3294, 3294, 10, 3296, 3302, 3306, 3310, 3314, 3296, 3318, 3324, 3330, 3332, 10, 3335, 3339, 3341, 3345, 3349, 3351, 3355, 3359, 3361, 3365, 10, 3366, 3368, 3370, 3372, 3376, 3378, 3366, 3378, 3380, 3370, 10, 3386, 3392, 3396, 3400, 3410, 3414, 3418, 3426, 3432, 3436, 10, 3440, 3442, 3446, 3452, 3454, 3458, 3462, 3464, 3468, 3474, 1, 191, 6, 3477, 3479, 3477, 3485, 3477, 3491, 10, 3493, 3495, 3497, 3499, 3503, 3507, 3511, 3513, 3515, 3519, 10, 3524, 3530, 3534, 3540, 3548, 3556, 3562, 3570, 3574, 3582, 10, 3584, 3586, 3588, 3590, 3584, 3592, 3594, 3596, 3598, 3600, 10, 3604, 3608, 3612, 3616, 3618, 3622, 3628, 3634, 3640, 3646, 10, 3653, 3653, 3657, 3663, 3665, 3667, 3669, 3671, 3673, 3679, 4, 1997, 1425, 2133, 2041, 10, 3680, 3682, 3684, 3688, 3690, 3694, 3696, 3700, 3702, 3704, 10, 3706, 3712, 3716, 3720, 3724, 3728, 3706, 3734, 3736, 3740, 10, 3744, 3748, 3752, 3756, 3760, 3764, 3766, 3772, 3776, 3782, 10, 3788, 3792, 3796, 3800, 3802, 3806, 3792, 3808, 3814, 3800, 10, 3820, 3824, 3830, 3834, 3836, 3838, 3844, 3848, 3852, 3860, 10, 3868, 3872, 3880, 3884, 3892, 3900, 3908, 3916, 3922, 3926, 10, 3929, 3933, 3939, 3941, 3943, 3947, 3949, 3951, 3953, 3957, 10, 3963, 3973, 3981, 3989, 3995, 4001, 4009, 4013, 4019, 4025, 10, 4027, 4033, 4027, 4039, 4047, 4051, 4055, 4061, 4065, 4067, 10, 4071, 4075, 4077, 4081, 4083, 4087, 4091, 4087, 4077, 4097, 3, 4099, 4101, 4103, 2, 4105, 4107, 10, 4108, 4110, 4112, 4116, 4120, 4124, 4130, 4136, 4142, 4148, 10, 4153, 4157, 4161, 4165, 4169, 4173, 4177, 4179, 4181, 4187, 10, 4188, 4192, 4194, 4196, 4198, 4200, 4204, 4206, 4198, 4200, 1, 4210, 10, 4214, 4216, 4222, 4226, 4230, 4234, 4238, 4242, 4246, 4252, 6, 4257, 4259, 4261, 4265, 4267, 4269, 10, 4270, 4276, 4280, 4284, 4288, 4294, 4294, 4270, 4288, 4300, 10, 4302, 4304, 4306, 4308, 4310, 4316, 4320, 4324, 4326, 4330, 10, 4332, 4336, 4340, 4346, 4350, 4356, 4360, 4364, 4368, 4374, 10, 4382, 4388, 4394, 4400, 4404, 4408, 4414, 4416, 4418, 4422, 10, 4433, 4437, 4447, 4453, 4457, 4459, 4465, 4467, 4471, 4475, 5, 4480, 4486, 4490, 4496, 4498, 10, 4501, 4505, 4507, 4509, 4511, 4513, 4517, 4519, 4525, 4529, 2, 4530, 4532, 10, 4537, 4539, 4541, 4543, 4545, 4549, 4551, 4555, 4559, 4563, 10, 4568, 4574, 4578, 4582, 4588, 4594, 4602, 4608, 4588, 4594, 10, 4610, 4612, 4614, 4616, 4618, 4622, 4624, 4626, 4628, 4630, 10, 4635, 4637, 4639, 4641, 4643, 4645, 4649, 4651, 4653, 4655, 10, 4660, 4664, 4666, 4672, 4678, 4682, 4688, 4692, 4696, 4700, 10, 4705, 4707, 4709, 4711, 4715, 4719, 4723, 4727, 4729, 4731, 10, 4735, 4737, 4739, 4741, 4743, 4743, 4739, 4737, 4745, 4745, 1, 927, 10, 4751, 4755, 4757, 4763, 4765, 4769, 4773, 4775, 4773, 4775, 10, 4777, 4781, 4785, 4787, 4789, 4793, 4795, 4797, 4799, 4803, 1, 19, 10, 4808, 4812, 4816, 4824, 4830, 4834, 4838, 4842, 4850, 4858, 4, 4860, 4862, 4864, 4866, 10, 4870, 4876, 4880, 4886, 4888, 4894, 4896, 4902, 4908, 4914, 10, 4921, 4927, 4931, 4935, 4937, 4927, 4943, 4949, 4953, 4959, 7, 4963, 4967, 4971, 4973, 4967, 4975, 4979, 2, 4982, 4984, 10, 4990, 4994, 4996, 5002, 5004, 5010, 5014, 5018, 5024, 5028, 10, 5031, 5039, 5043, 5051, 5055, 5059, 5061, 5063, 5067, 5071, 10, 5077, 5081, 5085, 5089, 5085, 5089, 5093, 5097, 5101, 5105, 10, 5110, 5114, 5118, 5110, 5122, 5128, 5132, 5136, 5138, 5144, 10, 5149, 5155, 5157, 5161, 5163, 5167, 5171, 5173, 5177, 5181, 10, 5186, 5192, 5198, 5186, 5204, 5208, 5212, 5218, 5224, 5204, 10, 5227, 5229, 5231, 5233, 5235, 5237, 5239, 5241, 5243, 5239, 10, 5249, 5255, 5259, 5267, 5271, 5277, 5283, 5287, 5297, 5305, 10, 5312, 5314, 5318, 5322, 5330, 5336, 5340, 5344, 5348, 5352, 3, 5358, 5362, 5366, 10, 5373, 5381, 5387, 5391, 5393, 5397, 5397, 5407, 5417, 5421, 10, 5423, 5427, 5429, 5435, 5441, 5445, 5449, 5455, 5457, 5461, 10, 5463, 5467, 5473, 5479, 5485, 5489, 5493, 5497, 5505, 5509, 10, 5515, 5517, 5521, 5521, 5527, 5531, 5535, 5539, 5545, 5549, 10, 5550, 5556, 5560, 5564, 5564, 5560, 5566, 5570, 5572, 5576, 10, 5580, 5590, 5594, 5600, 5604, 5608, 5612, 5620, 5626, 5630, 5, 5635, 5639, 5635, 5639, 5641, 10, 5647, 5653, 5657, 5661, 5663, 5669, 5675, 5681, 5689, 5695, 8, 5696, 5698, 5696, 5702, 5706, 5698, 5710, 5714, 10, 5718, 5722, 5724, 5728, 5734, 5740, 5746, 5752, 5758, 5764, 10, 5770, 5774, 5778, 5784, 5788, 5790, 5794, 5798, 5800, 5806, 10, 5809, 5811, 5811, 5809, 5815, 5819, 5823, 5825, 5829, 5815, 10, 5833, 5835, 5835, 5839, 5841, 1207, 5843, 5845, 5847, 5845, 10, 5849, 5851, 5853, 5855, 5857, 5859, 5863, 5865, 5867, 5869, 10, 5875, 5883, 5887, 5893, 5897, 5901, 5907, 5913, 5915, 5917, 10, 5919, 5923, 5929, 5935, 5941, 5947, 5955, 5961, 5967, 5973, 10, 5979, 5985, 5991, 5997, 6003, 6009, 6015, 6021, 6025, 6025, 10, 6029, 6033, 6033, 6037, 6037, 5977, 829, 829, 6029, 821, 10, 6039, 6045, 6047, 6051, 6057, 6063, 6065, 6069, 6071, 6073, 9, 6078, 6084, 6086, 6088, 6092, 6094, 6096, 6098, 6102, 10, 6106, 6110, 6112, 6118, 6122, 6126, 6134, 6138, 6142, 6144, 7, 6151, 6155, 6157, 6157, 6161, 6163, 6155, 10, 6166, 6170, 6172, 6178, 6180, 6184, 6186, 6192, 6194, 6196, 10, 6207, 6211, 6217, 6221, 6231, 6237, 6241, 6249, 6253, 6259, 2, 1387, 4837, 10,
                                                     6265, 6269, 6273, 6277, 6283, 6285, 6287, 6291, 6293, 6295, 10, 6296, 6298, 6300, 6304, 6306, 6308, 6310, 6296, 6312, 6314, 10, 6319, 6323, 6327, 6331, 6335, 6339, 6341, 6343, 6349, 6353, 2, 6357, 6361, 10, 6362, 6366, 6370, 6376, 6380, 6386, 6390, 6394, 6398, 6402, 10, 6408, 6414, 6420, 6426, 6432, 6438, 6442, 6450, 6456, 6460, 10, 6462, 6464, 6462, 6468, 6472, 6474, 6462, 6478, 6462, 6482, 10, 6489, 6493, 6495, 6497, 6499, 6503, 6505, 6507, 6499, 6509, 10, 6515, 6517, 6521, 6523, 6525, 6529, 6531, 6537, 6539, 6545, 1, 6550, 10, 6555, 6559, 6563, 6567, 6573, 6577, 6581, 6583, 6585, 6589, 10, 6592, 6594, 6602, 6608, 6614, 6618, 6620, 6626, 6632, 6636, 10, 6640, 6646, 6652, 6658, 6662, 6664, 6668, 6672, 6676, 6680, 10, 6683, 6689, 6691, 6697, 6703, 6709, 6715, 6721, 6723, 6725, 2, 6728, 6728, 10, 6731, 6737, 6741, 6749, 6755, 6759, 6763, 6769, 6775, 6781, 10, 6784, 6788, 6794, 6798, 6784, 6802, 6804, 6810, 6812, 6816, 10, 6823, 6831, 6837, 6845, 6851, 6857, 6865, 6869, 6879, 6885, 10, 6886, 6892, 6898, 6902, 6906, 6910, 6912, 6914, 6916, 6920, 6, 6925, 6929, 6933, 6935, 6937, 6941, 4, 6945, 6947, 6949, 6953, 4, 6954, 6956, 6958, 6960, 10, 6964, 6968, 6970, 6974, 6980, 6984, 6988, 6990, 6994, 6998, 10, 7003, 7009, 7011, 7015, 7023, 7027, 7029, 7031, 7035, 7039, 10, 7046, 7054, 7060, 7064, 7068, 7072, 7076, 7082, 7088, 7096, 10, 7103, 7107, 7115, 7119, 7123, 7127, 7131, 7133, 7135, 7139, 10, 7142, 7144, 7148, 7154, 7158, 7162, 7166, 7172, 7176, 7180, 10, 7186, 7190, 7196, 7200, 7206, 7208, 7214, 7218, 7222, 7226, 10, 7229, 7231, 7233, 7235, 7237, 7239, 7241, 7243, 7245, 7247, 10, 7248, 7250, 7252, 7254, 7250, 7254, 7252, 5760, 5760, 7256, 10, 7262, 7268, 7272, 7276, 7280, 7284, 7286, 7288, 7290, 7292, 5, 7295, 7297, 7299, 7301, 7303, 9, 7305, 7307, 7311, 7317, 7319, 7323, 7329, 7333, 7339, 10, 7343, 7349, 7349, 7355, 7359, 7363, 7367, 7371, 7349, 7375, 7, 7381, 7383, 7387, 7391, 7393, 7399, 7403, 10, 7405, 7407, 7405, 7411, 7413, 7415, 7417, 7419, 7413, 7421, 10, 7425, 7431, 7437, 7441, 7443, 7447, 7453, 7459, 7463, 7467, 1, 2, 4, 7, 8, 10, 6, 8, 11, 9, 12, 14, 6, 8, 10, 6, 12, 19, 8, 10, 13, 6, 12, 23, 6, 9, 10, 7, 14, 26, 7, 8, 26, 11, 26, 30, 11, 12, 26, 10, 14, 19, 0, 4, 7, 2, 4, 6, 9, 38, 40, 8, 38, 40, 8, 42, 45, 0, 3, 4, 0, 2, 6, 9, 48, 50, 8, 48, 50, 8, 52, 55, 0, 5, 6, 3, 4, 6, 9, 58, 60, 8, 58, 60, 8, 62, 65, 48, 50, 53, 8, 52, 69, 58, 60, 63, 8, 62, 73, 8, 49, 50, 48, 55, 76, 8, 59, 60, 58, 65, 80, 51, 52, 76, 9, 48, 76, 51, 76, 86, 61, 62, 80, 2, 4, 8, 3, 6, 8, 0, 93, 94, 0, 92, 94, 92, 96, 99, 5, 6, 8, 0, 40, 103, 0, 41, 102, 1, 104, 106, 0, 92, 95, 1, 96, 110, 1, 40, 102, 41, 104, 114, 103, 106, 114, 1, 40, 106, 103, 106, 120, 1, 92, 94, 95, 96, 124, 1, 92, 96, 95, 96, 128, 2, 5, 8, 2, 6, 9, 0, 132, 135, 0, 133, 134, 1, 136, 138, 1, 132, 134, 135, 138, 142, 2, 5, 6, 3, 8, 146, 2, 8, 146, 2, 148, 151, 7, 8, 40, 6, 8, 40, 6, 154, 157, 6, 8, 41, 9, 154, 160, 6, 9, 40, 41, 154, 164, 6, 9, 154, 41, 154, 168, 2, 9, 146, 147, 148, 172, 7, 160, 164, 2, 8, 147, 3, 172, 178, 8, 146, 149, 2, 148, 183, 8, 40, 155, 6, 154, 187, 1, 8, 40, 8, 40, 191, 0, 190, 193, 0, 8, 40, 0, 190, 197, 0, 8, 41, 0, 9, 40, 1, 200, 202, 9, 190, 200, 41, 190, 202, 0, 9, 190, 41, 190, 210, 40, 197, 200, 0, 2, 8, 0, 5, 8, 2, 6, 218, 4, 7, 218, 217, 220, 222, 3, 6, 216, 4, 6, 217, 218, 227, 228, 0, 7, 8, 2, 4, 232, 5, 6, 232, 2, 216, 236, 234, 236, 239, 1, 2, 8, 5, 8, 242, 0, 6, 245, 8, 41, 246, 242, 245, 248, 0, 9, 92, 7, 8, 252, 6, 41, 254, 1, 252, 256, 2, 4, 255, 6, 254, 261, 1, 252, 262, 0, 2, 4, 0, 9, 266, 7, 8, 268, 2, 4, 271, 6, 270, 273, 1, 268, 274, 6, 41, 270, 1, 268, 278, 0, 6, 9, 8, 41, 282, 1, 252, 284, 0, 9, 234, 2, 4, 233, 6, 232, 291, 1, 288, 292, 1, 252, 292, 6, 41, 232, 1, 252, 298, 0, 4, 9, 7, 242, 302, 2, 4, 305, 6, 304, 307, 1, 4, 8, 0, 2, 9, 6, 311, 312, 41, 310, 314, 7, 310, 312, 5, 60, 318, 1, 8, 60, 5, 312, 322, 7, 60, 324, 7, 312, 322, 5, 60, 328, 6, 243, 302, 41, 242, 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8, 235, 2, 232, 2346, 4, 235, 2348, 2, 102, 232, 3, 290, 2352, 3, 4, 232, 102, 290, 2356, 3, 232, 290, 102, 290, 2360, 2, 5, 232, 6, 8, 2364, 2, 232, 2367, 4, 2364, 2369, 2, 103, 232, 4, 2364, 2373, 2, 102, 233, 102, 290, 2377, 233, 2352, 2356, 4, 2352, 2373, 3, 4, 2352, 233, 2352, 2384, 2, 4, 58, 2, 560, 2389, 1, 4, 906, 6, 906, 2392, 1, 4, 900, 6, 900, 2396, 1, 4, 910, 6, 910, 2400, 1, 4, 914, 6, 914, 2404, 1, 4, 890, 6, 890, 2408, 4, 890, 1328, 4, 7, 1328, 8, 1328, 2414, 8, 103, 1328, 2, 6, 39, 5, 6, 38, 8, 2420, 2423, 4, 7, 50, 4, 9, 50, 6, 2426, 2429, 5, 8, 346, 312, 346, 2432, 4, 6, 51, 5, 8, 2436, 50, 2436, 2438, 5, 6, 50, 8, 2436, 2442, 8, 346, 602, 0, 9, 10, 2, 6, 11, 4, 2449, 2450, 4, 8, 50, 5, 6, 2454, 51, 2454, 2456, 4, 8, 312, 5, 6, 2460, 313, 2460, 2462, 2, 4, 628, 0, 10, 2467, 2, 4, 629, 0, 3, 2470, 5, 2470, 2472, 2, 377, 628, 4, 376, 2477, 4, 49, 628, 2, 48, 2481, 3, 376, 2470, 5, 48, 2470, 2, 4, 14, 0, 10, 2489, 48, 376, 629, 0, 2467, 2470, 2, 5, 628, 48, 629, 2496, 2, 8, 1854, 1, 48, 2500, 1, 48, 1478, 3, 10, 1478, 3, 8, 10, 10, 58, 2508, 10, 58, 2193, 4, 267, 1478, 0, 6, 267, 2, 8, 2516, 4, 267, 2518, 1, 6, 1460, 2, 4, 2523, 1460, 2522, 2525, 0, 93, 1172, 6, 9, 2528, 1172, 2528, 2531, 500, 523, 1188, 3, 6, 1876, 4, 8, 1876, 1, 2536, 2538, 267, 424, 1460, 267, 424, 574, 3, 6, 376, 1, 1460, 2546, 1, 1460, 1854, 5, 6, 746, 1, 1460, 2552, 1, 574, 2546, 5, 8, 746, 302, 629, 2558, 0, 9, 1514, 310, 927, 2562, 310, 927, 1838, 232, 357, 1298, 357, 1030, 1838, 4, 9, 58, 0, 3, 2572, 5, 8, 2574, 59, 2572, 2576, 0, 5, 1030, 1, 60, 1030, 9, 2580, 2582, 0, 5, 322, 4, 7, 322, 9, 2586, 2588, 4, 9, 2170, 59, 2168, 2592, 302, 322, 927, 6, 8, 1979, 1, 266, 2598, 4, 14, 49, 6, 8, 2339, 4, 49, 2604, 4, 14, 465, 2, 14, 377, 1, 2, 14, 4, 14, 2612, 1, 14, 266, 1, 14, 444, 1, 8, 904, 1, 8, 500, 0, 5, 1424, 217, 358, 2624, 6, 8, 216, 0, 5, 2628, 217, 358, 2630, 4, 8, 521, 354, 358, 2635, 0, 3, 1424, 357, 358, 2638, 0, 9, 146, 267, 358, 2642, 1, 4, 282, 2, 7, 2646, 5, 1886, 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2039,
                                                     2, 61, 2796, 3, 2038, 2798, 9, 60, 1876, 3, 8, 2802, 61, 2802, 2804, 61, 1150, 2802, 0, 2041, 2142, 1, 6, 408, 0, 1425, 2812, 0, 1997, 2158, 8, 358, 1425, 0, 7, 2818, 6, 1425, 2820, 8, 146, 1997, 0, 5, 2824, 4, 1997, 2826, 94, 927, 2448, 146, 629, 1544, 41, 282, 1552, 8, 377, 1702, 0, 7, 266, 8, 266, 2839, 0, 7, 92, 8, 92, 2843, 8, 242, 554, 4, 8, 1348, 6, 8, 1336, 0, 6, 266, 1, 8, 2852, 8, 60, 242, 8, 266, 656, 8, 242, 926, 0, 2, 102, 4, 283, 2862, 102, 133, 2864, 3, 4, 134, 1, 2, 2868, 0, 7, 2868, 5, 2870, 2872, 8, 2868, 2874, 1, 2, 1366, 0, 7, 1366, 5, 2878, 2880, 8, 1366, 2882, 8, 38, 2878, 5, 1366, 2886, 8, 2878, 2880, 5, 1366, 2890, 8, 38, 2870, 5, 2868, 2894, 4, 9, 60, 0, 7, 2898, 8, 10, 2900, 5, 2898, 2902, 3, 4, 26, 8, 10, 38, 5, 2906, 2908, 9, 10, 160, 38, 160, 2912, 9, 10, 1066, 38, 1066, 2916, 10, 41, 50, 8, 40, 2921, 5, 8, 554, 3, 6, 2924, 2, 555, 2924, 4, 2926, 2928, 3, 4, 702, 2, 501, 702, 6, 2932, 2934, 8, 10, 50, 8, 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8, 3974, 500, 3131, 3976, 2, 3130, 3979, 4, 6, 3106, 1, 2, 3982, 9, 500, 3984, 3, 3106, 3986, 1, 2, 2218, 9, 500, 3990, 3, 3106, 3992, 1, 2, 904, 9, 500, 3996, 3, 3106, 3998, 1, 4, 3106, 9, 500, 3106, 6, 4002, 4004, 3, 3106, 4006, 4, 3958, 4004, 3, 3106, 4010, 1, 4, 4004, 6, 4004, 4014, 3, 3106, 4016, 3, 8, 3966, 3964, 3966, 4021, 2, 4020, 4023, 303, 926, 2984, 6, 8, 303, 0, 2, 4029, 303, 926, 4030, 1, 4, 2984, 5, 6, 2984, 8, 4034, 4036, 0, 2, 1031, 1, 6, 4040, 4, 7, 4040, 8, 4042, 4044, 2, 38, 103, 39, 576, 4048, 6, 8, 4048, 39, 4048, 4052, 4, 8, 59, 2, 6, 4057, 59, 1726, 4058, 4, 8, 4058, 59, 4058, 4062, 39, 576, 3810, 0, 3, 40, 8, 1950, 4069, 0, 3, 338, 8, 60, 4073, 8, 60, 4069, 0, 3, 926, 8, 60, 4079, 8, 60, 3071, 0, 6, 660, 8, 60, 4085, 0, 6, 48, 8, 60, 4089, 2, 5, 60, 0, 6, 4093, 8, 60, 4095, 60, 490, 905, 51, 146, 926, 41, 490, 926, 8, 60, 490, 6, 92, 313, 217, 502, 3106, 312, 1150, 1835, 312, 1731, 3130, 3, 8, 346, 312, 3687, 4114, 2, 9, 500, 217, 1914, 4118, 0, 8, 61, 217, 2038, 4122, 0, 8, 3931, 0, 9, 3930, 1, 4126, 4128, 0, 8, 433, 0, 9, 432, 1, 4132, 4134, 0, 8, 1147, 0, 9, 1146, 1, 4138, 4140, 0, 8, 521, 0, 9, 520, 1, 4144, 4146, 4, 6, 48, 1, 132, 4150, 3, 4, 50, 1, 132, 4154, 1, 4, 132, 60, 132, 4158, 0, 133, 1188, 4, 132, 4163, 4, 6, 491, 1, 132, 4166, 0, 2, 1030, 8, 10, 4171, 0, 4, 972, 8, 10, 4175, 1, 132, 3258, 132, 1189, 4158, 2, 7, 376, 4, 8, 4183, 1, 376, 4184, 0, 1731, 2622, 8, 38, 611, 6, 610, 4191, 8, 577, 734, 302, 656, 927, 9, 610, 730, 39, 610, 734, 6, 9, 610, 39, 610, 4202, 7, 730, 734, 4, 8, 243, 60, 1340, 4209, 0, 8, 3275, 500, 927, 4212, 927, 3584, 3854, 0, 3, 906, 5, 6, 4218, 7, 904, 4220, 0, 5, 1578, 4, 927, 4224, 0, 5, 3174, 4, 927, 4228, 0, 7, 2102, 6, 927, 4232, 1, 4, 1578, 0, 927, 4236, 1, 6, 2102, 0, 927, 4240, 1, 4, 3174, 0, 927, 4244, 0, 8, 3997, 5, 6, 4248, 7, 904, 4250, 2, 9, 554, 4, 146, 4255, 6, 358, 4255, 2, 60, 4255, 2, 8, 554, 60, 555, 4262, 60, 555, 2040, 8, 60, 1583, 282, 358, 3067, 3, 8, 282, 0, 4, 4273, 282, 358,
                                                     4275, 2, 7, 3420, 267, 282, 4278, 2, 7, 3576, 267, 282, 4282, 1, 2, 3576, 41, 282, 4286, 4, 8, 40, 1, 2, 4290, 41, 282, 4292, 2, 9, 10, 4, 6, 4296, 10, 282, 4299, 218, 554, 629, 302, 501, 656, 282, 310, 501, 59, 218, 282, 39, 232, 302, 0, 9, 926, 1, 8, 4312, 927, 4312, 4314, 1, 6, 1382, 103, 1382, 4318, 1, 4, 2580, 1031, 2580, 4322, 0, 558, 577, 6, 8, 311, 0, 3692, 4329, 38, 102, 927, 0, 5, 1546, 9, 1030, 4334, 0, 9, 1546, 5, 1030, 4338, 0, 4, 103, 6, 9, 4342, 7, 102, 4344, 0, 7, 1534, 9, 102, 4348, 0, 6, 1031, 5, 8, 4352, 9, 1030, 4354, 4, 9, 4352, 5, 1030, 4358, 0, 9, 1534, 7, 102, 4362, 7, 8, 4342, 9, 102, 4366, 6, 8, 927, 1, 4, 4370, 0, 927, 4372, 2, 8, 1950, 1, 40, 4376, 0, 41, 4376, 4377, 4378, 4380, 0, 338, 2040, 0, 338, 2041, 2040, 4385, 4386, 1, 40, 2132, 0, 40, 2132, 0, 4390, 4393, 1, 40, 1424, 0, 40, 1424, 0, 4396, 4399, 0, 41, 2132, 40, 4393, 4402, 0, 41, 1424, 40, 4399, 4406, 1, 338, 2040, 338, 2040, 4411, 0, 4410, 4413, 2133, 4390, 4402, 1425, 4396, 4406, 0, 41, 4390, 2133, 4390, 4420, 1, 8, 282, 2, 4, 4425, 2, 4, 4424, 7, 282, 4428, 4424, 4426, 4431, 1, 628, 3008, 5, 1808, 4434, 6, 8, 629, 3, 4, 4438, 2, 4, 4439, 1, 628, 4442, 5, 4440, 4444, 3, 4, 4424, 6, 283, 4426, 5, 4448, 4450, 2, 5, 4424, 3, 4450, 4454, 4, 4431, 4454, 2, 5, 656, 7, 282, 3708, 4, 4460, 4463, 2, 4431, 4448, 2, 5, 4438, 3, 4444, 4468, 4439, 4440, 4468, 1, 628, 4472, 0, 3, 4460, 4, 7, 4460, 9, 4476, 4478, 1, 2, 3448, 4, 7, 4482, 9, 3448, 4484, 0, 5, 1454, 9, 1336, 4488, 0, 5, 1808, 2, 7, 1808, 9, 4492, 4494, 9, 1336, 3448, 2, 926, 2389, 2, 6, 266, 2, 926, 4503, 2, 926, 3141, 2, 926, 1117, 2, 926, 3841, 905, 926, 3996, 4, 6, 3997, 905, 3996, 4514, 1, 926, 1916, 2, 6, 267, 4, 7, 4520, 8, 4520, 4522, 4, 7, 3850, 8, 3850, 4526, 0, 93, 358, 0, 41, 634, 1, 4, 376, 8, 2546, 4534, 8, 10, 2546, 8, 10, 2516, 8, 10, 1854, 8, 10, 2552, 5, 6, 464, 8, 10, 4546, 8, 10, 406, 0, 6, 93, 8, 10, 4552, 0, 6, 445, 8, 10, 4556, 3, 6, 454, 8, 10, 4560, 0, 5, 2162, 8, 359, 4564, 7, 2162, 4566, 7, 312, 660, 5, 6, 4570, 9, 4570, 4572, 3, 38, 972, 9, 2990, 4576, 3, 58, 132, 9, 1372, 4580, 8, 38, 147, 9, 38, 146, 5, 4584, 4586, 8, 58, 359, 9, 58, 358, 7, 4590, 4592, 2, 4, 59, 8, 58, 4597, 9, 58, 4596, 7, 4598, 4600, 8, 38, 2421, 9, 38, 2420, 5, 4604, 4606, 48, 629, 2156, 376, 629, 1562, 376, 629, 1150, 232, 267, 1042, 267, 282, 1372, 2, 7, 660, 267, 282, 4620, 232, 267, 2038, 267, 282, 408, 267, 282, 1054, 232, 267, 2162, 1, 4, 216, 6, 8, 4632, 4, 8, 3850, 4, 8, 2420, 4, 8, 4520, 6, 8, 4596, 8, 926, 3274, 5, 6, 10, 4, 8, 4646, 6, 8, 884, 1, 216, 926, 8, 10, 926, 4, 8, 93, 0, 2, 4657, 2133, 4656, 4658, 8, 927, 2722, 3, 634, 4662, 4, 93, 4662, 0, 2, 2133, 8, 2133, 4668, 4, 93, 4670, 0, 4, 665, 8, 665, 4674, 5, 634, 4676, 0, 665, 1254, 5, 634, 4680, 0, 8, 635, 3, 4, 4684, 634, 927, 4686, 0, 927, 1254, 3, 634, 4690, 4, 665, 4684, 5, 634, 4694, 5, 972, 3148, 9, 660, 4698, 0, 9, 554, 0, 500, 4703, 1, 58, 2730, 58, 1030, 2581, 6, 38, 4703, 0, 5, 500, 500, 1030, 4712, 0, 7, 500, 102, 500, 4716, 1, 6, 38, 38, 102, 4720, 5, 6, 356, 1, 38, 4724, 8, 500, 559, 38, 303, 500, 6, 8, 103, 4, 102, 4733, 4, 102, 927, 6, 927, 1030, 9, 102, 1030, 8, 904, 927, 5, 904, 1030, 6, 1030, 4079, 0, 3, 4746, 926, 4746, 4748, 3, 2722, 3274, 6, 1030, 4753, 2723, 3402, 4738, 1, 2, 4738, 0, 3, 4758, 926, 4758, 4760, 3, 3402, 4758, 0, 3, 4738, 1, 3402, 4766, 6, 1030, 3275, 1, 3402, 4770, 3, 3402, 4746, 2, 346, 635, 0, 4, 2041, 60, 2040, 4779, 0, 2, 1997, 146, 1996, 4783, 5, 92, 346, 8, 146, 3934, 2, 5, 346, 8, 346, 4790, 49, 60, 420, 49, 60, 2040, 92, 313, 602, 5, 6, 92, 92, 313, 4800, 4, 8, 1346, 242, 904, 4805, 0, 1347, 4806, 0, 3, 2622, 1188, 1731, 4810, 0, 1189, 3130, 1188, 1731, 4814, 1, 242, 500, 6, 8, 500, 0, 243, 4820, 4818, 4821, 4822, 0, 4, 2039, 2, 6, 4826, 2038, 4122, 4829, 51, 904, 972, 5, 302, 4832, 8, 50, 500, 0, 4818, 4837, 5, 310, 746, 7, 2162, 4840, 1, 4, 1348, 9, 1348, 4844, 6, 242, 4847, 0, 4844, 4849, 0, 3, 904, 4, 6, 972, 0, 8, 4854, 972, 4852, 4857, 133, 146, 232, 282, 358, 635, 60, 232, 661, 41, 92, 282, 1, 2, 346, 312, 348, 4869, 0, 7, 1574, 1, 6, 4872, 1575, 4872, 4874, 0, 4, 973, 49, 974, 4878, 0, 5, 2102, 1, 4, 4882, 2103, 4882, 4884, 354, 1112, 1835, 0, 2, 1602, 0, 8, 1602, 354, 4890, 4893, 354, 4079, 4312, 0, 3, 1602, 0, 9, 1602, 354, 4899, 4900, 0, 9, 1996, 1, 8, 4904, 1997, 4904, 4906, 0, 147, 2156, 1, 146, 4910, 2157, 4910, 4912, 4, 242, 1031, 0, 5, 4916, 1030, 4916, 4918, 8, 927, 3274, 9, 926, 3274, 0, 4922, 4924, 0, 2, 559, 1, 576, 4928, 0, 2, 561, 1, 1726, 4932, 9, 576, 1830, 0, 927, 3208, 1, 8, 4938, 926, 4938, 4940, 1, 8, 2722, 0, 9, 4944, 926, 4944, 4946, 0, 9, 4922, 926, 4922, 4950, 2, 8, 4313, 0, 9, 4954, 926, 4954, 4956, 0, 358, 656, 8, 3008, 4961, 0, 358, 635, 8, 640, 4965, 6, 10, 635, 8, 644, 4969, 283, 634, 1090, 14, 283, 634, 6, 10, 232, 8, 290, 4977, 2, 8, 2646, 41, 282, 4980, 282, 635, 2648, 6, 8, 2278, 6, 8, 2279, 2278, 4987, 4988, 6, 313, 1030, 9, 1670, 4992, 604, 927, 1622, 2, 4, 354, 2, 7, 354, 904, 4999, 5000, 904, 1340, 1505, 9, 312, 346, 8, 313, 346, 347, 5006, 5008, 8, 313, 5006, 347, 5006, 5012, 4, 7, 3216, 9, 3636, 5016, 6, 9, 2278, 7, 8, 5020, 2279, 5020, 5022, 7, 312, 1622, 9, 1624, 5026, 58, 283, 1498, 2, 4, 103, 0, 7, 5032, 1, 6, 5032, 102, 5034, 5036, 1, 6, 5034, 102, 5034, 5040, 2, 6, 1031, 0, 5, 5044, 1, 4, 5044, 1030, 5046, 5048, 1, 4, 5046, 1030, 5046, 5052, 5, 6, 640, 1, 3658, 5056, 356, 555, 644, 555, 628, 1498, 1, 4, 2192, 58, 283, 5064, 0, 5, 4118, 283, 500, 5068, 0, 103, 972, 1, 6, 5072, 102, 5072, 5074, 7, 312, 356, 1, 4724, 5078, 0, 2, 657, 303, 500, 5082, 1, 102, 972, 6, 5072, 5086, 9, 356, 972, 1, 4724, 5090, 9, 356, 624, 1, 4724, 5094, 0, 6, 5086, 103, 5086, 5098, 9, 58, 1188, 1, 1726, 5102, 1, 4, 972, 4, 628, 972, 0, 5106, 5109, 0, 5, 972, 629, 4878, 5112, 4, 629, 972, 5, 4878, 5116, 4, 628, 4879, 972, 4878, 5121, 6, 8, 5107, 4, 972, 5124, 0, 5106, 5127, 5, 972, 4878, 629, 4878, 5130, 5, 628, 972, 629, 4878, 5134, 0, 4175, 5116, 6, 8, 4174, 4, 972, 5141, 0, 4175, 5142, 4, 58, 312, 2, 1166, 5147, 3, 216, 228, 1, 2, 5150, 229, 5150, 5152, 2, 3117, 5150, 8, 501, 1126, 1124, 1126, 5158, 1124, 1126, 3106, 8, 500, 1125, 8, 1126, 5165, 9, 500, 1124, 1124, 1126, 5169, 503, 1124, 1126, 0, 2, 735, 1, 1132, 5174, 0, 2, 2573, 1, 1166, 5178, 0, 3, 664, 0, 4, 664, 2470, 5182, 5185, 1, 2, 382, 0, 4, 383, 1975, 5188, 5190, 0, 3, 382, 0, 4, 382, 3508, 5194, 5197, 4, 376, 382, 4, 376, 383, 382, 5201, 5202, 2, 48, 383, 382, 1993, 5206, 1, 2, 628, 2467, 4674, 5210, 6, 8, 5210, 0, 4, 5215, 2467, 5210, 5216, 6, 8, 2466, 0, 4, 5221, 2467, 5210, 5222, 4, 58, 303, 6, 38, 303, 0, 303, 500, 8, 311, 500, 8, 58, 219, 6, 356, 555, 6, 303, 356, 1, 58, 356, 5, 356, 500, 4, 9, 588, 0, 7, 5244, 582, 588, 5246, 6, 132, 134, 1, 4, 5250, 132, 1484, 5252, 5, 628, 634, 135, 1498, 5256, 4, 135, 628, 5, 134, 628, 0, 2, 5262, 1, 5260, 5264, 7, 500, 580, 267, 1730, 5268, 2, 9, 1730, 7, 500, 5272, 267, 1730, 5274, 2, 9, 576, 1, 38, 5278, 267, 576, 5280, 0, 2, 310, 572, 576, 5285, 6, 9, 132, 2, 4, 5289, 0, 3, 5290, 1, 4, 5288, 132, 5292, 5294, 0, 6, 581, 4, 267, 5298, 9, 266, 5298, 580, 5300, 5303, 4, 7, 200, 1, 2, 5306, 8, 40, 5309, 6, 5306, 5311, 512, 656, 927, 8, 40, 2735, 4, 236, 5317, 8, 40, 1553, 0, 1546, 5321, 4, 243, 1188, 7, 8, 5324, 6, 8, 5324, 6, 5326, 5329, 0, 2, 905, 6, 660, 5332, 0, 2620, 5335, 8, 5324, 5327, 6, 5326, 5339, 6, 8, 5325, 5324, 5329, 5342, 4, 216, 746, 232, 904, 5347, 4, 8, 746, 228, 232, 5351, 0, 5, 3854, 0, 6, 3854, 904, 5354, 5357, 0, 5, 660, 904, 4085, 5360, 0, 4, 3854, 904, 3856, 5365, 5, 6, 660, 6, 634, 5361, 7, 5368, 5370, 7, 8, 92, 6, 9, 92, 1, 634, 5376, 93, 5374, 5378, 6, 9, 5374, 1, 634, 5382, 93, 5374, 5384, 8, 93, 644, 7, 5376, 5388, 201, 408, 3174, 9, 40, 520, 7, 3174, 5394, 3, 8, 634, 4, 7, 5398, 6, 5399, 5400, 1, 634, 5402, 5, 5400, 5404, 5, 8, 634, 2, 7, 5408, 6, 5409, 5410, 1, 634, 5412, 3, 5410, 5414, 9, 92, 644, 7, 1578, 5418, 0, 1352, 1915, 0, 2, 311, 1, 1730, 5424, 1, 1726, 5424, 2, 9, 2304, 1, 4, 5430, 5, 2304, 5432, 2, 9, 1726, 1, 4, 5436, 5, 1726, 5438, 1, 356, 5430, 5, 2304, 5442, 5, 356, 5430, 1, 2304, 5446, 2, 9, 356, 5, 628, 5450, 1, 356, 5452, 1, 356, 5256, 2, 4, 219, 5, 2304, 5458, 356, 500, 4151, 4, 8, 5082, 5, 500, 5464, 7, 8, 242, 0, 4, 5468, 5, 500, 5470, 7, 8, 490, 0, 4, 5474, 5, 500, 5476, 2, 8, 51, 0, 4, 5480, 5, 500, 5482, 4, 61, 1726, 1, 58, 5486, 4, 61, 1834, 1, 58, 5490, 4, 61, 64, 1, 58, 5494, 5, 8, 500, 1, 2, 5498, 7, 5498, 5500, 0, 500, 5502, 6, 40, 357, 356, 555, 5506, 8, 10, 41, 8, 10, 40, 40, 5510, 5513, 358, 3719, 3726, 9, 266, 358, 267, 3726, 5518, 8, 11, 40, 9, 10, 40, 41, 5522, 5524, 9, 10, 5522, 41, 5522, 5528, 8, 267, 358, 359, 5518, 5532, 9, 266, 5532, 359, 5532, 5536, 8, 38, 1189, 9, 38, 1188, 39, 5540, 5542, 9, 1188, 5540, 39, 5540, 5546, 0, 2467, 3708, 0, 665, 926, 0, 664, 926, 664, 5552, 5555, 0, 664, 927, 1, 5552, 5558, 0, 359, 634, 1, 4964, 5562, 0, 18, 383, 1, 358, 634, 359, 4964, 5568, 635, 5562, 5568, 1, 358, 5562, 635, 5562, 5574, 0, 9, 1348, 1526, 3699, 5578, 1, 8, 312, 4, 6, 5583, 3, 5582, 5584, 7, 312, 5586, 5, 5584, 5588, 5, 312, 5586, 7, 5584, 5592, 3, 242, 1342, 5, 312, 5596, 7, 1342, 5598, 5, 312, 1454, 243, 1336, 5602, 7, 312, 5596, 5, 1342, 5606, 7, 312, 1526, 243, 1348, 5610, 5, 6, 5582, 3, 4, 5582, 7, 312, 5616, 5583, 5614, 5618, 2, 6, 3078, 5, 6, 3078, 522, 5623, 5624, 0, 9, 3078, 5623, 5624, 5628, 2, 4, 19, 1, 14, 5632, 6, 8, 3709, 1, 3008, 5636, 1, 14, 3008, 2, 8, 2853, 6, 216, 2853, 4, 5642, 5644, 9, 60, 216, 4, 6, 5649, 216, 1113, 5650, 4, 7, 930, 102, 932, 5654, 4, 7, 48, 102, 932, 5658, 932, 1030, 1854, 4, 8, 1854, 1, 2, 5664, 1030, 1854, 5666, 4, 8, 2546, 1, 2, 5670, 1030, 2546, 5672, 8, 48, 1854, 1, 2, 5676, 1030, 1854, 5678, 0, 3, 482, 4, 7, 5682, 1, 376, 5684, 8, 482, 5686, 3, 216, 3274, 4, 6, 3274, 927, 5690, 5692, 376, 629, 3070, 376, 629, 4078, 2, 267, 926, 0, 383, 5700, 5, 10, 94, 0, 15, 5704, 2, 629, 926, 0, 2467, 5708, 4, 95, 628, 0, 2470, 5713, 8, 629, 1258, 282, 1259, 5716, 1, 6,
                                                     2740, 9, 2740, 5720, 9, 232, 5720, 1, 6, 3536, 9, 232, 5726, 8, 282, 1259, 0, 7, 5730, 1, 282, 5732, 0, 40, 232, 8, 233, 5736, 6, 232, 5739, 0, 232, 634, 8, 233, 5742, 6, 232, 5745, 0, 232, 290, 8, 233, 5748, 6, 232, 5751, 5, 60, 232, 1, 6, 5754, 9, 232, 5756, 1, 232, 282, 2, 5, 282, 3, 5760, 5762, 2, 8, 395, 4, 9, 394, 11, 5766, 5768, 3, 8, 746, 266, 5351, 5772, 3, 8, 58, 266, 1727, 5776, 3, 8, 2516, 4, 8, 2516, 266, 5780, 5783, 2, 8, 746, 266, 2558, 5787, 266, 1479, 2168, 5, 8, 2516, 266, 2519, 5792, 2, 8, 747, 11, 1298, 5796, 11, 1800, 2572, 2, 9, 746, 4, 8, 747, 11, 5802, 5804, 628, 3071, 3088, 102, 3000, 3088, 4, 94, 628, 628, 3088, 5813, 0, 94, 102, 4, 3071, 5816, 6, 8, 3448, 4, 3071, 5820, 1, 3000, 5820, 5, 94, 628, 1, 3000, 5826, 1, 6, 640, 8, 640, 5830, 8, 640, 644, 0, 7, 644, 8, 644, 5836, 628, 634, 959, 1, 628, 640, 283, 628, 634, 283, 634, 636, 1, 6, 590, 1, 40, 160, 1, 266, 614, 1, 6, 178, 1, 8, 482, 1, 8, 474, 4, 8, 61, 1, 6, 5860, 1, 6, 154, 1, 8, 492, 1, 266, 656, 1, 2, 94, 4, 664, 5871, 1, 3448, 5872, 0, 4, 4733, 3, 102, 5876, 1, 2, 5878, 4732, 5878, 5880, 2, 94, 3288, 664, 3088, 5885, 0, 2, 4733, 2, 103, 5876, 102, 5889, 5890, 4, 927, 2984, 102, 2723, 5894, 4, 628, 3742, 628, 1808, 5899, 0, 3, 3708, 4, 656, 3709, 628, 5903, 5904, 6, 8, 657, 2, 658, 5908, 659, 1808, 5910, 664, 3088, 3275, 664, 3088, 3709, 926, 2863, 3470, 1, 8, 5332, 9, 926, 5920, 7, 926, 3274, 5, 8, 5924, 9, 926, 5926, 5, 926, 3274, 7, 8, 5930, 9, 926, 5932, 2, 905, 926, 1, 8, 5936, 9, 926, 5938, 5, 6, 3208, 0, 7, 5942, 1, 926, 5944, 2, 7, 926, 4, 9, 5948, 0, 5, 5950, 1, 926, 5952, 6, 9, 3470, 0, 7, 5956, 1, 926, 5958, 9, 926, 3470, 0, 7, 5962, 1, 926, 5964, 9, 926, 5948, 0, 5, 5968, 1, 926, 5970, 0, 10, 267, 6, 8, 5975, 10, 441, 5976, 7, 10, 828, 8, 826, 5980, 9, 828, 5982, 7, 10, 836, 8, 834, 5986, 9, 836, 5988, 6, 191, 358, 1, 8, 5992, 787, 5992, 5994, 4, 146, 191, 1, 8, 5998, 807, 5998, 6000, 0, 201, 806, 1, 8, 6004, 807, 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};

} /* namespace mockturtle */
