181013

Ruby


Expansion of Product_{d | ｋ} theta_3(q^d)

k <= 96 のとき、出力してみた。

def s(k, n)
  s = 0
  (1..n).each{|i| s += i if n % i == 0 && i % k == 0}
  s
end

def A(ary, n)
  a_ary = [1]
  a = [0] + (1..n).map{|i| ary.inject(0){|s, j| s + j[1] * s(j[0], i)}}
  (1..n).each{|i| a_ary << (1..i).inject(0){|s, j| s - a[j] * a_ary[-j]} / i}
  a_ary
end

def B(k, n)
  ary = []
  (1..k).select{|i| k % i == 0}.each{|i|
    ary << [2 * i, 5]
    ary << [i, -2]
    ary << [4 * i, -2]
  }
  A(ary, n)
end

n = 100
(1..96).each{|i| p [i, B(i, n)]}

出力結果
[1, [1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
[2, [1, 2, 2, 4, 2, 0, 4, 0, 2, 6, 0, 4, 4, 0, 0, 0, 2, 4, 6, 4, 0, 0, 4, 0, 4, 2, 0, 8, 0, 0, 0, 0, 2, 8, 4, 0, 6, 0, 4, 0, 0, 4, 0, 4, 4, 0, 0, 0, 4, 2, 2, 8, 0, 0, 8, 0, 0, 8, 0, 4, 0, 0, 0, 0, 2, 0, 8, 4, 4, 0, 0, 0, 6, 4, 0, 4, 4, 0, 0, 0, 0, 10, 4, 4, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 2, 12, 2]]
[3, [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 12, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 12, 0, 0, 4, 0, 2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 6]]
[4, [1, 2, 2, 4, 4, 4, 8, 8, 6, 6, 8, 4, 8, 12, 0, 8, 12, 8, 10, 12, 8, 8, 24, 8, 8, 14, 8, 16, 16, 4, 0, 16, 6, 16, 16, 8, 12, 20, 24, 8, 24, 8, 16, 20, 8, 20, 0, 16, 24, 18, 10, 8, 24, 12, 32, 24, 0, 16, 24, 12, 16, 20, 0, 24, 12, 8, 16, 28, 16, 16, 48, 8, 30, 32, 8, 20, 24, 16, 0, 16, 24, 18, 32, 20, 16, 24, 24, 24, 24, 16, 24, 24, 16, 24, 0, 8, 8, 40, 18, 20, 28]]
[5, [1, 2, 0, 0, 2, 2, 4, 0, 0, 6, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 8, 0, 0, 4, 2, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 6, 4, 0, 0, 6, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 10, 0, 0, 8, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 2]]
[6, [1, 2, 2, 6, 6, 4, 14, 8, 6, 26, 12, 16, 42, 12, 16, 44, 6, 20, 50, 16, 36, 56, 24, 16, 42, 30, 28, 78, 48, 36, 84, 40, 6, 80, 36, 48, 150, 44, 40, 100, 36, 36, 112, 48, 72, 148, 48, 48, 42, 50, 62, 124, 84, 52, 158, 64, 48, 144, 60, 64, 252, 60, 64, 200, 6, 88, 168, 64, 108, 176, 96, 80, 150, 84, 76, 218, 120, 96, 196, 72, 36, 242, 84, 80, 336, 104, 88, 204, 72, 84, 300, 112, 144, 216, 96, 128, 42, 100, 114, 304, 186]]
[7, [1, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 4, 0, 0, 8, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 10, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 2]]
[8, [1, 2, 2, 4, 4, 4, 8, 8, 8, 10, 12, 12, 16, 20, 16, 24, 24, 20, 26, 20, 24, 32, 24, 24, 32, 30, 28, 40, 32, 20, 48, 32, 24, 48, 36, 48, 52, 36, 40, 56, 48, 52, 64, 44, 48, 84, 48, 48, 96, 50, 62, 72, 56, 68, 80, 72, 64, 80, 60, 60, 96, 52, 64, 104, 24, 72, 96, 68, 72, 96, 96, 72, 104, 68, 76, 124, 80, 96, 112, 80, 144, 130, 84, 84, 128, 104, 88, 120, 96, 100, 156, 112, 96, 128, 96, 120, 96, 116, 114, 156, 124]]
[9, [1, 2, 0, 2, 6, 0, 0, 4, 0, 4, 4, 0, 10, 16, 0, 0, 14, 0, 4, 4, 0, 16, 8, 0, 0, 14, 0, 2, 20, 0, 8, 4, 0, 0, 4, 0, 12, 32, 0, 8, 20, 0, 0, 12, 0, 16, 8, 0, 26, 14, 0, 0, 32, 0, 0, 8, 0, 24, 12, 0, 0, 32, 0, 8, 30, 0, 8, 12, 0, 0, 8, 0, 20, 24, 0, 10, 20, 0, 0, 12, 0, 4, 12, 0, 32, 48, 0, 0, 40, 0, 8, 8, 0, 48, 8, 0, 0, 24, 0, 8, 42]]
[10, [1, 2, 2, 4, 2, 2, 8, 4, 10, 10, 2, 16, 8, 12, 16, 4, 26, 20, 26, 24, 2, 32, 24, 28, 40, 2, 28, 40, 16, 28, 8, 24, 58, 48, 36, 4, 26, 44, 40, 56, 10, 36, 64, 36, 24, 10, 48, 52, 104, 66, 2, 72, 28, 60, 80, 16, 80, 80, 60, 56, 8, 60, 64, 116, 122, 12, 96, 76, 36, 96, 16, 72, 130, 68, 76, 4, 40, 80, 112, 80, 26, 130, 84, 68, 64, 20, 88, 120, 120, 84, 26, 120, 48, 128, 96, 24, 232, 84, 114, 144, 2]]
[11, [1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 4, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 2, 6]]
[12, [1, 2, 2, 6, 8, 8, 18, 20, 18, 34, 40, 32, 56, 68, 44, 88, 108, 64, 122, 156, 96, 172, 232, 128, 234, 322, 180, 294, 400, 216, 344, 516, 234, 400, 608, 288, 488, 708, 364, 524, 864, 432, 620, 988, 480, 728, 1072, 576, 756, 1174, 594, 896, 1360, 680, 1050, 1424, 900, 1188, 1656, 896, 1248, 1892, 940, 1540, 1836, 1040, 1688, 2124, 1152, 1696, 2448, 1216, 2178, 2660, 1364, 2182, 2896, 1488, 2260, 3268, 1296, 2578, 3312, 1696, 2800, 3520, 1932, 2760, 4320, 1968, 3016, 4264, 2112, 3516, 4320, 2176, 3042, 4660, 2438, 3632, 4808]]
[13, [1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 4, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, 4, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2]]
[14, [1, 2, 2, 4, 2, 0, 4, 2, 6, 10, 8, 8, 4, 8, 2, 8, 18, 12, 18, 12, 8, 4, 16, 24, 28, 30, 16, 24, 2, 20, 32, 24, 38, 32, 28, 0, 18, 20, 28, 40, 40, 28, 4, 40, 16, 48, 32, 24, 68, 2, 38, 40, 16, 28, 56, 48, 6, 48, 36, 44, 32, 48, 40, 10, 82, 56, 64, 32, 28, 80, 8, 48, 86, 36, 52, 108, 28, 8, 80, 48, 104, 66, 60, 60, 4, 80, 64, 88, 80, 68, 104, 8, 32, 96, 56, 88, 156, 60, 2, 104, 38]]
[15, [1, 2, 0, 2, 6, 2, 4, 4, 4, 14, 0, 0, 14, 4, 4, 2, 10, 12, 12, 16, 6, 28, 8, 12, 48, 2, 8, 38, 20, 12, 4, 16, 40, 48, 8, 4, 66, 4, 8, 52, 4, 36, 28, 28, 16, 14, 12, 36, 106, 18, 0, 60, 28, 12, 40, 0, 52, 64, 16, 24, 14, 28, 16, 100, 62, 4, 40, 52, 52, 84, 4, 24, 160, 52, 24, 2, 64, 48, 48, 40, 10, 122, 16, 60, 140, 12, 20, 108, 88, 36, 12, 56, 60, 112, 20, 16, 204, 52, 32, 144, 6]]
[16, [1, 2, 2, 4, 4, 4, 8, 8, 8, 10, 12, 12, 16, 20, 16, 24, 26, 24, 30, 28, 32, 40, 40, 40, 48, 50, 52, 64, 64, 60, 80, 80, 72, 88, 88, 88, 100, 100, 88, 104, 112, 112, 120, 124, 112, 124, 144, 112, 144, 146, 134, 168, 160, 140, 160, 184, 160, 184, 188, 148, 192, 220, 160, 200, 218, 176, 224, 220, 192, 240, 272, 232, 248, 248, 220, 268, 304, 240, 272, 336, 240, 314, 328, 260, 320, 360, 328, 312, 368, 296, 364, 440, 320, 360, 416, 344, 432, 472, 354, 420, 484]]
[17, [1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 2]]
[18, [1, 2, 2, 6, 6, 4, 14, 8, 6, 28, 16, 20, 54, 24, 24, 72, 22, 32, 104, 44, 72, 152, 60, 56, 158, 58, 80, 234, 112, 148, 304, 136, 86, 308, 140, 168, 512, 224, 252, 560, 224, 152, 560, 220, 316, 856, 320, 376, 718, 322, 242, 764, 384, 444, 1170, 480, 448, 900, 464, 332, 1184, 560, 584, 1672, 550, 576, 1276, 556, 580, 1712, 672, 776, 1960, 572, 768, 1446, 748, 832, 1968, 952, 800, 2240, 844, 884, 2224, 1032, 956, 2696, 1020, 944, 3056, 880, 1232, 3048, 1184, 1328, 2846, 1180, 1266, 3440, 1318]]
[19, [1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 4, 2, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6]]
[20, [1, 2, 2, 4, 4, 6, 12, 12, 14, 14, 18, 24, 28, 32, 20, 36, 44, 48, 62, 40, 60, 80, 96, 92, 72, 98, 104, 152, 140, 84, 132, 160, 198, 208, 144, 172, 236, 304, 288, 208, 262, 284, 400, 404, 224, 330, 356, 460, 508, 318, 394, 416, 624, 608, 424, 520, 456, 752, 724, 472, 588, 508, 768, 884, 572, 640, 640, 916, 1024, 752, 860, 656, 1114, 1168, 744, 1044, 672, 1104, 1344, 832, 1044, 866, 1324, 1364, 1168, 1328, 860, 1640, 1584, 1092, 1518, 1072, 1484, 1792, 1172, 1464, 1304, 1776, 1902, 1448, 1908]]
[21, [1, 2, 0, 2, 6, 0, 0, 6, 4, 2, 4, 12, 6, 4, 8, 0, 10, 0, 0, 16, 8, 6, 4, 12, 4, 14, 8, 2, 34, 12, 4, 16, 40, 12, 12, 48, 6, 28, 8, 4, 44, 24, 8, 16, 44, 0, 12, 24, 10, 58, 16, 0, 28, 36, 0, 24, 100, 16, 16, 48, 8, 28, 16, 6, 62, 48, 4, 40, 24, 12, 44, 36, 4, 28, 16, 14, 64, 84, 8, 16, 96, 2, 20, 24, 34, 72, 24, 12, 68, 24, 4, 108, 60, 16, 24, 48, 40, 76, 56, 12, 74]]
[22, [1, 2, 2, 4, 2, 0, 4, 0, 2, 6, 0, 6, 8, 4, 8, 4, 2, 12, 6, 8, 12, 0, 14, 12, 8, 10, 4, 12, 16, 12, 12, 12, 2, 28, 20, 16, 26, 8, 24, 24, 12, 20, 24, 8, 46, 28, 12, 24, 8, 34, 26, 32, 28, 12, 20, 48, 16, 24, 20, 12, 48, 12, 28, 16, 2, 32, 60, 28, 36, 44, 24, 36, 26, 20, 24, 32, 40, 64, 32, 24, 12, 34, 28, 40, 64, 24, 16, 48, 46, 16, 60, 16, 48, 44, 32, 24, 8, 40, 34, 98, 62]]
[23, [1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 0, 0, 2]]
[24, [1, 2, 2, 6, 8, 8, 18, 20, 20, 38, 44, 44, 72, 84, 80, 128, 144, 132, 202, 220, 208, 308, 320, 304, 452, 454, 428, 618, 608, 576, 844, 812, 744, 1124, 1060, 976, 1448, 1324, 1248, 1852, 1656, 1564, 2320, 2068, 1984, 2896, 2528, 2408, 3600, 3066, 2926, 4396, 3696, 3600, 5274, 4376, 4288, 6276, 5148, 5052, 7376, 5996, 5904, 8612, 6840, 6816, 10048, 7748, 7760, 11456, 8832, 8944, 12980, 9940, 10140, 14786, 11200, 11312, 16652, 12556, 12960, 18674, 13716, 14468, 20960, 15360, 16096, 23160, 17136, 18060, 25628, 18744, 19648, 28476, 20640, 21720, 30984, 22540, 24178, 33844, 24504]]
[25, [1, 2, 0, 0, 2, 2, 4, 0, 0, 6, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 8, 0, 0, 4, 4, 4, 0, 0, 8, 8, 8, 0, 0, 12, 0, 6, 0, 0, 8, 0, 8, 0, 0, 0, 10, 20, 0, 0, 14, 4, 0, 0, 0, 16, 8, 4, 0, 0, 0, 0, 16, 0, 0, 2, 0, 8, 0, 0, 8, 16, 8, 0, 0, 12, 0, 0, 0, 0, 16, 2, 18, 0, 0, 8, 0, 12, 0, 0, 8, 0, 0, 0, 0, 20, 8, 4, 0, 0, 0, 4]]
[26, [1, 2, 2, 4, 2, 0, 4, 0, 2, 6, 0, 4, 4, 2, 4, 4, 10, 8, 6, 12, 0, 4, 16, 0, 12, 10, 2, 12, 4, 12, 12, 12, 18, 8, 8, 20, 6, 16, 16, 4, 24, 12, 20, 20, 16, 28, 16, 16, 36, 14, 26, 36, 2, 20, 20, 16, 28, 40, 28, 20, 12, 36, 16, 28, 42, 0, 40, 28, 8, 16, 36, 16, 46, 20, 16, 32, 16, 40, 4, 40, 48, 34, 28, 36, 20, 36, 28, 40, 32, 36, 60, 0, 16, 48, 36, 32, 76, 20, 30, 28, 26]]
[27, [1, 2, 0, 2, 6, 0, 0, 4, 0, 4, 4, 0, 10, 16, 0, 0, 14, 0, 4, 4, 0, 16, 8, 0, 0, 14, 0, 4, 24, 0, 12, 16, 0, 0, 12, 0, 20, 40, 0, 28, 52, 0, 0, 40, 0, 24, 16, 0, 58, 30, 0, 0, 60, 0, 4, 48, 0, 40, 20, 0, 0, 40, 0, 32, 94, 0, 24, 52, 0, 0, 32, 0, 52, 40, 0, 62, 48, 0, 0, 76, 0, 4, 28, 0, 80, 72, 0, 0, 104, 0, 24, 68, 0, 64, 32, 0, 0, 40, 0, 48, 90]]
[28, [1, 2, 2, 4, 4, 4, 8, 10, 10, 10, 16, 12, 16, 28, 18, 24, 28, 32, 26, 36, 48, 28, 60, 52, 56, 58, 64, 88, 68, 100, 72, 96, 86, 104, 144, 92, 132, 116, 152, 120, 168, 184, 136, 220, 168, 228, 172, 240, 280, 234, 282, 208, 336, 212, 352, 408, 266, 360, 324, 444, 288, 492, 464, 338, 512, 392, 528, 380, 576, 568, 512, 556, 426, 680, 452, 724, 720, 604, 600, 588, 840, 506, 896, 756, 688, 720, 684, 968, 612, 1016, 896, 932, 840, 784, 1136, 712, 1176, 1168, 994, 844, 964]]
[29, [1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 4, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2]]
[30, [1, 2, 2, 6, 6, 6, 18, 12, 18, 38, 22, 48, 62, 36, 80, 82, 78, 132, 122, 136, 178, 196, 208, 212, 298, 290, 340, 474, 312, 428, 582, 424, 642, 688, 572, 868, 934, 772, 872, 1068, 1078, 1292, 1568, 1124, 1344, 1906, 1400, 1676, 2038, 1658, 2386, 2860, 1996, 2068, 2922, 2672, 3160, 3992, 2676, 3416, 4826, 3284, 3744, 4516, 3902, 5484, 6544, 4748, 4404, 6460, 6000, 6072, 8450, 5924, 6772, 10598, 6648, 6976, 9076, 7088, 10378, 12674, 8900, 8612, 12024, 10828, 10640, 14436, 10784, 11796, 18878, 12344, 11264, 15416, 12072, 16248, 21210, 14916, 13826, 21040, 17638]]
[31, [1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2]]
[32, [1, 2, 2, 4, 4, 4, 8, 8, 8, 10, 12, 12, 16, 20, 16, 24, 26, 24, 30, 28, 32, 40, 40, 40, 48, 50, 52, 64, 64, 60, 80, 80, 74, 92, 92, 96, 108, 108, 104, 120, 128, 132, 144, 148, 144, 164, 176, 160, 196, 194, 194, 224, 224, 220, 240, 264, 256, 284, 292, 276, 320, 340, 320, 360, 362, 352, 400, 396, 392, 440, 448, 440, 472, 472, 460, 516, 528, 488, 560, 560, 528, 606, 596, 596, 640, 640, 648, 680, 688, 664, 740, 736, 704, 800, 736, 744, 868, 824, 802, 860, 868]]
[33, [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 2, 10, 4, 4, 12, 6, 0, 8, 4, 4, 4, 0, 12, 8, 2, 0, 14, 12, 0, 8, 4, 8, 2, 4, 0, 14, 16, 4, 28, 8, 0, 12, 4, 6, 24, 8, 24, 50, 18, 8, 24, 20, 12, 16, 0, 36, 28, 4, 12, 52, 28, 0, 52, 14, 24, 0, 4, 8, 24, 8, 12, 88, 4, 8, 38, 20, 4, 16, 4, 44, 62, 12, 24, 36, 24, 12, 48, 0, 24, 32, 8, 40, 64, 8, 24, 96, 16, 16, 2, 18]]
[34, [1, 2, 2, 4, 2, 0, 4, 0, 2, 6, 0, 4, 4, 0, 0, 0, 2, 6, 10, 8, 8, 4, 4, 8, 4, 6, 12, 8, 8, 8, 0, 0, 2, 12, 14, 16, 18, 8, 8, 8, 8, 12, 8, 16, 20, 8, 8, 0, 4, 6, 22, 28, 20, 28, 24, 16, 8, 24, 16, 16, 32, 24, 16, 16, 2, 8, 16, 32, 46, 28, 32, 24, 18, 20, 24, 28, 24, 20, 40, 8, 8, 14, 12, 32, 48, 48, 16, 32, 20, 32, 16, 16, 32, 20, 16, 32, 4, 4, 26, 36, 38]]
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