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import matplotlib.pyplot as plt
import numpy as np
hm1 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 390, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 61462, 1530, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 1890, 3420, 3420], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 750, 2640, 6060, 9480], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 6060, 15540], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm2 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 3420, 3420], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 31342, 6060, 9480], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 6060, 15540], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm3 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 284212, 3420], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 6060, 9480], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 6060, 15540], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm4 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 3420], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 364646, 9480], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 6060, 15540], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm5 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 194530], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 9480], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 6060, 15540], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm6 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 87568], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 202936, 15540], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm7 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 87568], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 702936, 15540], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm8 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 556515], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 15540], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm9 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1056515], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 15540], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm10 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 349892], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm11 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 849892], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm12 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1349892], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm13 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1849892], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm14 = np.array([[0, 1, 1, 2, 4, 7, 11, 16, 22, 22, 0, 0, 0, 0, 0], [0, 1, 4, 11, 25, 49, 86, 139, 210, 0, 0, 0, 0, 0, 0], [0, 2, 8, 28, 78, 179, 271, 417, 683, 767, 942, 1145, 1376, 1635, 0], [0, 0, 9, 52, 179, 463, 0, 84, 795, 1590, 2763, 3936, 5340, 7262, 7717], [0, 0, 12, 85, 346, 1008, 1238, 1322, 0, 287, 3337, 0, 455, 7885, 15602], [0, 0, 15, 112, 564, 1923, 3999, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 90, 790, 2790, 6789, 6789, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 105, 1000, 0, 1525, 8314, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 120, 1240, 649, 2174, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 135, 1375, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 177111], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
hm15 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 1145, 1376, 1635, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 6363, 3936, 5340, 7262, 7717], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 3337, 0, 455, 7885, 15602], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 371, 4079, 4534, 4989, 0, 910], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 455, 5073, 11574, 0, 0, 910], [0, 0, 0, 1007, 7253, 0, 18807, 17253, 6789, 7328, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 19456, 0, 138, 7688, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 1960, 12075, 0, 1525, 0, 138, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm16 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 13327, 7717], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 7885, 15602], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 38331, 4989, 0, 910], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 11574, 0, 0, 910], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 13246, 27854, 31278, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 37771, 21324, 52992, 96211, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm17 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 7717], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 33342, 15602], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 17574, 0, 910], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 910], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 27854, 31278, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 91638, 52992, 96211, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm18 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 41059], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 910], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 910], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 181305, 31278, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 52992, 96211, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 4174, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm19 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 41059], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 910], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 910], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 31278, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 191548, 96211, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm20 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 910], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 31278, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 545203, 96211, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 4924, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm21 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 910], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 117591, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 96211, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 62480, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm22 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 910], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 96211, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 175339, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm23 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 910], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 285862, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 485688, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm24 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 331802, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 914291, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm25 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 604075, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm26 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1104075, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm27 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1604075, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 69294, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm28 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 38655, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 507080, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm29 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 229273, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 177836, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 816462, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm30 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 190297, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 816462, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm31 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 155324, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 690297, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 816462, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm32 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 383417, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 962204, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 816462, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm33 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 390915, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 962204, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1308964, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm34 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 390915, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 1298376, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm35 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 390915, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 1798376, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm36 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 390915, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 2298376, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm37 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 390915, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 2798376, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm38 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 390915, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3298376, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm39 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 625445, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm40 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 1125445, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm41 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 1625445, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm42 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 2125445, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm43 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 2625445, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 250550, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm44 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 313637, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm45 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 813637, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm46 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 1313637, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm47 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 374653, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 1813637, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm48 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 606219, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 2082071, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm49 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 1106219, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 2082071, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm50 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 1394612, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 2293678, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm51 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 1394612, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 2793678, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm52 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 1394612, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 3293678, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm53 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 1394612, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 3793678, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm54 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 1394612, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 4293678, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm55 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 1394612, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 4793678, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm56 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 1394612, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5293678, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm57 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 1848247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm58 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 2348247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm59 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 2848247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm60 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 3348247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm61 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 3848247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm62 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 4348247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm63 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 4848247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm64 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 5348247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm65 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 5848247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm66 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 6348247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm67 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 6848247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm68 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 7348247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm69 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 7848247, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 50973, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm70 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 199987, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm71 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 699987, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm72 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 1199987, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm73 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 1699987, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm74 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 673536, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2199987, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm75 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm76 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 1446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm77 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 1946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm78 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 2446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm79 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 2946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm80 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 3446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm81 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 3946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm82 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 4446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm83 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 4946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm84 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 5446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm85 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 5946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm86 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 6446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm87 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 6946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm88 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 7446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm89 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 7946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm90 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 8446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm91 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 8946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm92 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 9446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm93 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 9946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm94 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 10446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm95 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 10946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm96 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 11446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm97 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 11946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm98 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 12446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm99 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 12946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm100 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 13446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm101 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 13946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm102 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 14446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm103 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 14946554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm104 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 419566], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15446554, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm105 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 605512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm106 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 1105512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm107 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 1605512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm108 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 2105512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm109 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 2605512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm110 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 3105512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm111 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 3605512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm112 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 4105512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm113 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 4605512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm114 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 5105512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm115 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 5605512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm116 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 6105512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm117 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 6605512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm118 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 7105512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm119 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 7605512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm120 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 8105512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm121 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 8605512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm122 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 9105512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm123 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 9605512], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 733989, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm124 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 10075667], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 763834, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm125 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 10075667], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 1263834, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm126 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 10075667], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 1763834, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm127 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 10075667], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 2263834, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hm128 = np.array([[0, 1, 1, 2, 4, 8, 16, 31, 57, 57, 0, 0, 0, 0, 0], [0, 1, 4, 12, 32, 79, 181, 384, 735, 0, 0, 0, 0, 0, 0], [0, 2, 10, 42, 144, 417, 694, 1232, 2415, 3427, 5549, 8438, 12269, 17245, 0], [0, 0, 18, 115, 474, 1328, 0, 1012, 4047, 8241, 17621, 27204, 40849, 64446, 77486], [0, 0, 34, 266, 1266, 3716, 5436, 6448, 0, 5218, 28057, 0, 13040, 84461, 161947], [0, 0, 59, 484, 2762, 9668, 22224, 0, 0, 7750, 43557, 54126, 67166, 0, 26367], [0, 0, 0, 673, 5239, 17596, 39820, 39820, 0, 10569, 67885, 166328, 0, 0, 26367], [0, 0, 0, 1007, 7253, 0, 18807, 58627, 39820, 53579, 150191, 399997, 504732, 716812, 0], [0, 0, 0, 1431, 10115, 4153, 22960, 0, 6789, 70802, 242250, 771273, 1666289, 3062358, 0], [0, 0, 0, 1960, 12075, 0, 18807, 0, 6789, 0, 146926, 1142018, 3563846, 8199233, 10075667], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 192541, 1472792, 5340043, 15760608, 1222163], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 2426969, 2763834, 1956152], [0, 0, 0, 0, 7922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216629]])
hms = [hm10, hm20, hm30, hm40, hm50, hm60, hm70, hm80, hm90, hm100, hm110, hm120]
n = max(np.max(hm) for hm in hms)
fig, axs = plt.subplots(nrows=3, ncols=4)
i = 1
for hm, ax in zip(hms, np.concatenate(axs)):
ax.imshow(hm, vmax=n)
ax.set_title(f"hm{i}")
i += 1
ax1.imshow(hm0, vmax=n)
ax1.set_title("hm0")
ax2.imshow(hm, vmax=n)
ax2.set_title("hm")