Statistics

Problem Statement for "AutomorphicTree"

Problem Statement

Consider a tree with V vertices labeled 0 through V-1. A bijective function f from {0, ..., V-1} to {0, ..., V-1} is called an automorphism of this tree if for any u and v, vertices u and v are directly connected by an edge if and only if vertices f(u) and f(v) are directly connected by an edge. In other words, an automorphism is any permutation of vertex labels such that after the permutation the tree looks the same as in the beginning. (Note that there is always at least one automorphism: the identity function.)

Cat Snuke became age years old today. You want to give him a birthday present that has something to do with his age. As he likes trees, you decided to give him a tree with exactly age automorphisms. Due to your budget you can only buy him a tree that contains between 1 and 200 vertices, inclusive.

You are given the long age. Find a tree that matches the above requirements and return a int[] with its description in the format specified below. If there are many such trees, you may return any of them. If there are no such trees, return an empty int[] instead.

Given that you want to return a tree with V vertices, you should return a int[] X with exactly 2V-1 elements: the number of vertices, followed by the list of edges. More precisely: X[0] should be V. For each edge in your tree, there must be an i between 0 and V-2, inclusive, such that X[2*i+1] and X[2*i+2] are the endpoints of that edge. Note that V must be between 1 and 200, inclusive.

Definition

Class:
AutomorphicTree
Method:
construct
Parameters:
long
Returns:
int[]
Method signature:
int[] construct(long age)
(be sure your method is public)

Constraints

  • age will be between 1 and 10^18, inclusive.

Examples

  1. 1

    Returns: {1 }

    A tree with only one vertex.

  2. 2

    Returns: {8, 0, 1, 0, 2, 0, 3, 3, 4, 4, 5, 0, 6, 6, 7 }

  3. 3

    Returns: { }

  4. 4

    Returns: {11, 0, 1, 0, 2, 3, 4, 3, 5, 0, 3, 0, 6, 6, 7, 7, 8, 3, 9, 9, 10 }

  5. 5

    Returns: { }

  6. 6

    Returns: {9, 0, 1, 0, 2, 0, 3, 0, 4, 4, 5, 5, 6, 0, 7, 7, 8 }

  7. 7

    Returns: { }

  8. 8

    Returns: {6, 0, 1, 1, 2, 3, 4, 4, 5, 4, 1 }

    The return value describes the following tree with 6 vertices: 0 3 | | | | 1------4 | | | | 2 5 We can easily verify that it has exactly 8 automorphisms.

  9. 9

    Returns: { }

  10. 10

    Returns: { }

  11. 11

    Returns: { }

  12. 12

    Returns: {12, 0, 1, 0, 2, 3, 4, 3, 5, 3, 6, 0, 3, 0, 7, 7, 8, 8, 9, 3, 10, 10, 11 }

  13. 13

    Returns: { }

  14. 14

    Returns: { }

  15. 15

    Returns: { }

  16. 16

    Returns: {17, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 0, 3, 3, 6, 6, 9, 0, 12, 12, 13, 13, 14, 9, 15, 15, 16 }

  17. 17

    Returns: { }

  18. 18

    Returns: { }

  19. 19

    Returns: { }

  20. 20

    Returns: { }

  21. 21

    Returns: { }

  22. 22

    Returns: { }

  23. 24

    Returns: {15, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 6, 9, 0, 3, 3, 6, 0, 10, 10, 11, 11, 12, 6, 13, 13, 14 }

  24. 25

    Returns: { }

  25. 26

    Returns: { }

  26. 27

    Returns: { }

  27. 28

    Returns: { }

  28. 30

    Returns: { }

  29. 32

    Returns: {20, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 0, 3, 3, 6, 6, 9, 9, 12, 0, 15, 15, 16, 16, 17, 12, 18, 18, 19 }

  30. 33

    Returns: { }

  31. 94376581706246400

    Returns: { }

  32. 51326922240

    Returns: { }

  33. 431620120448766480

    Returns: { }

  34. 78933204590672250

    Returns: { }

  35. 5766853551513600

    Returns: { }

  36. 698962846982400

    Returns: { }

  37. 283461893000

    Returns: { }

  38. 1373350659912000

    Returns: { }

  39. 7719031406592

    Returns: { }

  40. 28692347580355200

    Returns: { }

  41. 164319083095326720

    Returns: { }

  42. 841362101204625

    Returns: { }

  43. 6766430249779200

    Returns: { }

  44. 64579998463402500

    Returns: { }

  45. 2889855095400000

    Returns: { }

  46. 151694107291155000

    Returns: { }

  47. 3769200833563116

    Returns: { }

  48. 53659632682656

    Returns: { }

  49. 85622172962485320

    Returns: { }

  50. 325618755338247525

    Returns: { }

  51. 47289252131550

    Returns: { }

  52. 541515795814743750

    Returns: { }

  53. 326037580227450000

    Returns: { }

  54. 71537790230156250

    Returns: { }

  55. 93812023433576448

    Returns: { }

  56. 249620992744748625

    Returns: { }

  57. 207779852048857088

    Returns: { }

  58. 30420119740294557

    Returns: { }

  59. 8104250880000

    Returns: { }

  60. 36961903979000000

    Returns: { }

  61. 1000000000000000000

    Returns: { }

  62. 397702619345604664

    Returns: { }

  63. 607505858809155393

    Returns: { }

  64. 923786070493167105

    Returns: { }

  65. 770972990481548020

    Returns: { }

  66. 609508546352094986

    Returns: { }

  67. 36

    Returns: {13, 0, 1, 0, 2, 0, 3, 4, 5, 4, 6, 4, 7, 0, 4, 0, 8, 8, 9, 9, 10, 4, 11, 11, 12 }

  68. 48

    Returns: {18, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 9, 12, 0, 3, 3, 6, 6, 9, 0, 13, 13, 14, 14, 15, 9, 16, 16, 17 }

  69. 64

    Returns: {23, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 0, 18, 18, 19, 19, 20, 15, 21, 21, 22 }

  70. 72

    Returns: {16, 0, 1, 0, 2, 3, 4, 3, 5, 3, 6, 7, 8, 7, 9, 7, 10, 0, 3, 3, 7, 0, 11, 11, 12, 12, 13, 7, 14, 14, 15 }

  71. 96

    Returns: {21, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 12, 15, 0, 3, 3, 6, 6, 9, 9, 12, 0, 16, 16, 17, 17, 18, 12, 19, 19, 20 }

  72. 120

    Returns: {11, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 6, 7, 7, 8, 0, 9, 9, 10 }

  73. 128

    Returns: {26, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 0, 21, 21, 22, 22, 23, 18, 24, 24, 25 }

  74. 144

    Returns: {19, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 6, 9, 10, 11, 10, 12, 10, 13, 0, 3, 3, 6, 6, 10, 0, 14, 14, 15, 15, 16, 10, 17, 17, 18 }

  75. 192

    Returns: {24, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 15, 18, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 0, 19, 19, 20, 20, 21, 15, 22, 22, 23 }

  76. 216

    Returns: {17, 0, 1, 0, 2, 0, 3, 4, 5, 4, 6, 4, 7, 8, 9, 8, 10, 8, 11, 0, 4, 4, 8, 0, 12, 12, 13, 13, 14, 8, 15, 15, 16 }

  77. 240

    Returns: {14, 0, 1, 0, 2, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 0, 3, 0, 9, 9, 10, 10, 11, 3, 12, 12, 13 }

  78. 256

    Returns: {29, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 0, 24, 24, 25, 25, 26, 21, 27, 27, 28 }

  79. 288

    Returns: {22, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 9, 12, 13, 14, 13, 15, 13, 16, 0, 3, 3, 6, 6, 9, 9, 13, 0, 17, 17, 18, 18, 19, 13, 20, 20, 21 }

  80. 384

    Returns: {27, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 18, 21, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 0, 22, 22, 23, 23, 24, 18, 25, 25, 26 }

  81. 432

    Returns: {20, 0, 1, 0, 2, 3, 4, 3, 5, 3, 6, 7, 8, 7, 9, 7, 10, 11, 12, 11, 13, 11, 14, 0, 3, 3, 7, 7, 11, 0, 15, 15, 16, 16, 17, 11, 18, 18, 19 }

  82. 480

    Returns: {17, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 6, 9, 6, 10, 6, 11, 0, 3, 3, 6, 0, 12, 12, 13, 13, 14, 6, 15, 15, 16 }

  83. 512

    Returns: {32, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 0, 27, 27, 28, 28, 29, 24, 30, 30, 31 }

  84. 576

    Returns: {25, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 12, 15, 16, 17, 16, 18, 16, 19, 0, 3, 3, 6, 6, 9, 9, 12, 12, 16, 0, 20, 20, 21, 21, 22, 16, 23, 23, 24 }

  85. 720

    Returns: {15, 0, 1, 0, 2, 0, 3, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 0, 4, 0, 10, 10, 11, 11, 12, 4, 13, 13, 14 }

  86. 768

    Returns: {30, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 21, 24, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 0, 25, 25, 26, 26, 27, 21, 28, 28, 29 }

  87. 864

    Returns: {23, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 6, 9, 10, 11, 10, 12, 10, 13, 14, 15, 14, 16, 14, 17, 0, 3, 3, 6, 6, 10, 10, 14, 0, 18, 18, 19, 19, 20, 14, 21, 21, 22 }

  88. 960

    Returns: {20, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 9, 12, 9, 13, 9, 14, 0, 3, 3, 6, 6, 9, 0, 15, 15, 16, 16, 17, 9, 18, 18, 19 }

  89. 1024

    Returns: {35, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 0, 30, 30, 31, 31, 32, 27, 33, 33, 34 }

  90. 1152

    Returns: {28, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 15, 18, 19, 20, 19, 21, 19, 22, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 19, 0, 23, 23, 24, 24, 25, 19, 26, 26, 27 }

  91. 1296

    Returns: {21, 0, 1, 0, 2, 0, 3, 4, 5, 4, 6, 4, 7, 8, 9, 8, 10, 8, 11, 12, 13, 12, 14, 12, 15, 0, 4, 4, 8, 8, 12, 0, 16, 16, 17, 17, 18, 12, 19, 19, 20 }

  92. 1440

    Returns: {18, 0, 1, 0, 2, 3, 4, 3, 5, 3, 6, 7, 8, 7, 9, 7, 10, 7, 11, 7, 12, 0, 3, 3, 7, 0, 13, 13, 14, 14, 15, 7, 16, 16, 17 }

  93. 1536

    Returns: {33, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 24, 27, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 0, 28, 28, 29, 29, 30, 24, 31, 31, 32 }

  94. 1728

    Returns: {26, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 9, 12, 13, 14, 13, 15, 13, 16, 17, 18, 17, 19, 17, 20, 0, 3, 3, 6, 6, 9, 9, 13, 13, 17, 0, 21, 21, 22, 22, 23, 17, 24, 24, 25 }

  95. 1920

    Returns: {23, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 12, 15, 12, 16, 12, 17, 0, 3, 3, 6, 6, 9, 9, 12, 0, 18, 18, 19, 19, 20, 12, 21, 21, 22 }

  96. 2048

    Returns: {38, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 0, 33, 33, 34, 34, 35, 30, 36, 36, 37 }

  97. 141557760

    Returns: {64, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 45, 48, 49, 50, 49, 51, 49, 52, 53, 54, 53, 55, 53, 56, 53, 57, 53, 58, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 49, 49, 53, 0, 59, 59, 60, 60, 61, 53, 62, 62, 63 }

  98. 603979776

    Returns: {85, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 51, 52, 51, 53, 54, 55, 54, 56, 57, 58, 57, 59, 60, 61, 60, 62, 63, 64, 63, 65, 66, 67, 66, 68, 69, 70, 69, 71, 72, 73, 72, 74, 72, 75, 76, 77, 76, 78, 76, 79, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 69, 69, 72, 72, 76, 0, 80, 80, 81, 81, 82, 76, 83, 83, 84 }

  99. 836232702197760000

    Returns: {53, 0, 1, 0, 2, 0, 3, 4, 5, 4, 6, 4, 7, 8, 9, 8, 10, 8, 11, 12, 13, 12, 14, 12, 15, 16, 17, 16, 18, 16, 19, 16, 20, 16, 21, 16, 22, 16, 23, 24, 25, 24, 26, 24, 27, 24, 28, 24, 29, 24, 30, 24, 31, 32, 33, 32, 34, 32, 35, 32, 36, 32, 37, 32, 38, 32, 39, 40, 41, 40, 42, 40, 43, 40, 44, 40, 45, 40, 46, 40, 47, 0, 4, 4, 8, 8, 12, 12, 16, 16, 24, 24, 32, 32, 40, 0, 48, 48, 49, 49, 50, 40, 51, 51, 52 }

  100. 3799912185593856

    Returns: {149, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 51, 52, 51, 53, 54, 55, 54, 56, 57, 58, 57, 59, 60, 61, 60, 62, 63, 64, 63, 65, 66, 67, 66, 68, 69, 70, 69, 71, 72, 73, 72, 74, 75, 76, 75, 77, 78, 79, 78, 80, 81, 82, 81, 83, 84, 85, 84, 86, 87, 88, 87, 89, 90, 91, 90, 92, 93, 94, 93, 95, 96, 97, 96, 98, 99, 100, 99, 101, 102, 103, 102, 104, 105, 106, 105, 107, 108, 109, 108, 110, 111, 112, 111, 113, 114, 115, 114, 116, 117, 118, 117, 119, 120, 121, 120, 122, 123, 124, 123, 125, 126, 127, 126, 128, 129, 130, 129, 131, 132, 133, 132, 134, 132, 135, 136, 137, 136, 138, 136, 139, 140, 141, 140, 142, 140, 143, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 69, 69, 72, 72, 75, 75, 78, 78, 81, 81, 84, 84, 87, 87, 90, 90, 93, 93, 96, 96, 99, 99, 102, 102, 105, 105, 108, 108, 111, 111, 114, 114, 117, 117, 120, 120, 123, 123, 126, 126, 129, 129, 132, 132, 136, 136, 140, 0, 144, 144, 145, 145, 146, 140, 147, 147, 148 }

  101. 995328000

    Returns: {43, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 12, 15, 16, 17, 16, 18, 16, 19, 20, 21, 20, 22, 20, 23, 20, 24, 20, 25, 26, 27, 26, 28, 26, 29, 26, 30, 26, 31, 32, 33, 32, 34, 32, 35, 32, 36, 32, 37, 0, 3, 3, 6, 6, 9, 9, 12, 12, 16, 16, 20, 20, 26, 26, 32, 0, 38, 38, 39, 39, 40, 32, 41, 41, 42 }

  102. 1564380905472000

    Returns: {45, 0, 1, 0, 2, 0, 3, 4, 5, 4, 6, 4, 7, 8, 9, 8, 10, 8, 11, 12, 13, 12, 14, 12, 15, 16, 17, 16, 18, 16, 19, 20, 21, 20, 22, 20, 23, 20, 24, 20, 25, 20, 26, 20, 27, 28, 29, 28, 30, 28, 31, 28, 32, 28, 33, 28, 34, 28, 35, 28, 36, 28, 37, 28, 38, 28, 39, 0, 4, 4, 8, 8, 12, 12, 16, 16, 20, 20, 28, 0, 40, 40, 41, 41, 42, 28, 43, 43, 44 }

  103. 2006581248000

    Returns: {58, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 21, 24, 25, 26, 25, 27, 25, 28, 29, 30, 29, 31, 29, 32, 33, 34, 33, 35, 33, 36, 33, 37, 33, 38, 39, 40, 39, 41, 39, 42, 39, 43, 39, 44, 45, 46, 45, 47, 45, 48, 45, 49, 45, 50, 45, 51, 45, 52, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 25, 25, 29, 29, 33, 33, 39, 39, 45, 0, 53, 53, 54, 54, 55, 45, 56, 56, 57 }

  104. 8358844170240000

    Returns: {71, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 6, 9, 10, 11, 10, 12, 10, 13, 14, 15, 14, 16, 14, 17, 18, 19, 18, 20, 18, 21, 22, 23, 22, 24, 22, 25, 26, 27, 26, 28, 26, 29, 30, 31, 30, 32, 30, 33, 34, 35, 34, 36, 34, 37, 38, 39, 38, 40, 38, 41, 42, 43, 42, 44, 42, 45, 42, 46, 42, 47, 48, 49, 48, 50, 48, 51, 48, 52, 48, 53, 54, 55, 54, 56, 54, 57, 54, 58, 54, 59, 60, 61, 60, 62, 60, 63, 60, 64, 60, 65, 0, 3, 3, 6, 6, 10, 10, 14, 14, 18, 18, 22, 22, 26, 26, 30, 30, 34, 34, 38, 38, 42, 42, 48, 48, 54, 54, 60, 0, 66, 66, 67, 67, 68, 60, 69, 69, 70 }

  105. 12189981081600

    Returns: {58, 0, 1, 0, 2, 3, 4, 3, 5, 3, 6, 7, 8, 7, 9, 7, 10, 11, 12, 11, 13, 11, 14, 15, 16, 15, 17, 15, 18, 19, 20, 19, 21, 19, 22, 23, 24, 23, 25, 23, 26, 27, 28, 27, 29, 27, 30, 31, 32, 31, 33, 31, 34, 35, 36, 35, 37, 35, 38, 39, 40, 39, 41, 39, 42, 39, 43, 39, 44, 45, 46, 45, 47, 45, 48, 45, 49, 45, 50, 45, 51, 45, 52, 0, 3, 3, 7, 7, 11, 11, 15, 15, 19, 19, 23, 23, 27, 27, 31, 31, 35, 35, 39, 39, 45, 0, 53, 53, 54, 54, 55, 45, 56, 56, 57 }

  106. 2354388664320000

    Returns: {65, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 36, 39, 36, 40, 36, 41, 42, 43, 42, 44, 42, 45, 42, 46, 42, 47, 48, 49, 48, 50, 48, 51, 48, 52, 48, 53, 48, 54, 48, 55, 48, 56, 48, 57, 48, 58, 48, 59, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 42, 42, 48, 0, 60, 60, 61, 61, 62, 48, 63, 63, 64 }

  107. 615585774066204672

    Returns: {156, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 51, 52, 51, 53, 54, 55, 54, 56, 57, 58, 57, 59, 60, 61, 60, 62, 63, 64, 63, 65, 66, 67, 66, 68, 69, 70, 69, 71, 72, 73, 72, 74, 75, 76, 75, 77, 78, 79, 78, 80, 81, 82, 81, 83, 84, 85, 84, 86, 87, 88, 87, 89, 90, 91, 90, 92, 93, 94, 93, 95, 96, 97, 96, 98, 99, 100, 99, 101, 102, 103, 102, 104, 105, 106, 105, 107, 108, 109, 108, 110, 111, 112, 111, 113, 114, 115, 114, 116, 117, 118, 117, 119, 120, 121, 120, 122, 123, 124, 123, 125, 123, 126, 127, 128, 127, 129, 127, 130, 131, 132, 131, 133, 131, 134, 135, 136, 135, 137, 135, 138, 139, 140, 139, 141, 139, 142, 143, 144, 143, 145, 143, 146, 147, 148, 147, 149, 147, 150, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 69, 69, 72, 72, 75, 75, 78, 78, 81, 81, 84, 84, 87, 87, 90, 90, 93, 93, 96, 96, 99, 99, 102, 102, 105, 105, 108, 108, 111, 111, 114, 114, 117, 117, 120, 120, 123, 123, 127, 127, 131, 131, 135, 135, 139, 139, 143, 143, 147, 0, 151, 151, 152, 152, 153, 147, 154, 154, 155 }

  108. 44030125670400

    Returns: {89, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 48, 51, 52, 53, 52, 54, 52, 55, 56, 57, 56, 58, 56, 59, 60, 61, 60, 62, 60, 63, 64, 65, 64, 66, 64, 67, 68, 69, 68, 70, 68, 71, 72, 73, 72, 74, 72, 75, 72, 76, 72, 77, 78, 79, 78, 80, 78, 81, 78, 82, 78, 83, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 52, 52, 56, 56, 60, 60, 64, 64, 68, 68, 72, 72, 78, 0, 84, 84, 85, 85, 86, 78, 87, 87, 88 }

  109. 19237055439568896

    Returns: {141, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 51, 52, 51, 53, 54, 55, 54, 56, 57, 58, 57, 59, 60, 61, 60, 62, 63, 64, 63, 65, 66, 67, 66, 68, 69, 70, 69, 71, 72, 73, 72, 74, 75, 76, 75, 77, 78, 79, 78, 80, 81, 82, 81, 83, 84, 85, 84, 86, 87, 88, 87, 89, 90, 91, 90, 92, 93, 94, 93, 95, 96, 97, 96, 98, 99, 100, 99, 101, 102, 103, 102, 104, 105, 106, 105, 107, 108, 109, 108, 110, 108, 111, 112, 113, 112, 114, 112, 115, 116, 117, 116, 118, 116, 119, 120, 121, 120, 122, 120, 123, 124, 125, 124, 126, 124, 127, 128, 129, 128, 130, 128, 131, 132, 133, 132, 134, 132, 135, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 69, 69, 72, 72, 75, 75, 78, 78, 81, 81, 84, 84, 87, 87, 90, 90, 93, 93, 96, 96, 99, 99, 102, 102, 105, 105, 108, 108, 112, 112, 116, 116, 120, 120, 124, 124, 128, 128, 132, 0, 136, 136, 137, 137, 138, 132, 139, 139, 140 }

  110. 60183678025728

    Returns: {86, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 21, 24, 25, 26, 25, 27, 25, 28, 29, 30, 29, 31, 29, 32, 33, 34, 33, 35, 33, 36, 37, 38, 37, 39, 37, 40, 41, 42, 41, 43, 41, 44, 45, 46, 45, 47, 45, 48, 49, 50, 49, 51, 49, 52, 53, 54, 53, 55, 53, 56, 57, 58, 57, 59, 57, 60, 61, 62, 61, 63, 61, 64, 65, 66, 65, 67, 65, 68, 69, 70, 69, 71, 69, 72, 73, 74, 73, 75, 73, 76, 77, 78, 77, 79, 77, 80, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 25, 25, 29, 29, 33, 33, 37, 37, 41, 41, 45, 45, 49, 49, 53, 53, 57, 57, 61, 61, 65, 65, 69, 69, 73, 73, 77, 0, 81, 81, 82, 82, 83, 77, 84, 84, 85 }

  111. 37614798766080

    Returns: {73, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 6, 9, 10, 11, 10, 12, 10, 13, 14, 15, 14, 16, 14, 17, 18, 19, 18, 20, 18, 21, 22, 23, 22, 24, 22, 25, 26, 27, 26, 28, 26, 29, 30, 31, 30, 32, 30, 33, 34, 35, 34, 36, 34, 37, 38, 39, 38, 40, 38, 41, 42, 43, 42, 44, 42, 45, 46, 47, 46, 48, 46, 49, 50, 51, 50, 52, 50, 53, 54, 55, 54, 56, 54, 57, 58, 59, 58, 60, 58, 61, 62, 63, 62, 64, 62, 65, 62, 66, 62, 67, 0, 3, 3, 6, 6, 10, 10, 14, 14, 18, 18, 22, 22, 26, 26, 30, 30, 34, 34, 38, 38, 42, 42, 46, 46, 50, 50, 54, 54, 58, 58, 62, 0, 68, 68, 69, 69, 70, 62, 71, 71, 72 }

  112. 47194790952960000

    Returns: {66, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 27, 30, 31, 32, 31, 33, 31, 34, 31, 35, 31, 36, 37, 38, 37, 39, 37, 40, 37, 41, 37, 42, 37, 43, 37, 44, 45, 46, 45, 47, 45, 48, 45, 49, 45, 50, 45, 51, 45, 52, 53, 54, 53, 55, 53, 56, 53, 57, 53, 58, 53, 59, 53, 60, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 31, 31, 37, 37, 45, 45, 53, 0, 61, 61, 62, 62, 63, 53, 64, 64, 65 }

  113. 197522841600

    Returns: {41, 0, 1, 0, 2, 0, 3, 4, 5, 4, 6, 4, 7, 8, 9, 8, 10, 8, 11, 12, 13, 12, 14, 12, 15, 16, 17, 16, 18, 16, 19, 20, 21, 20, 22, 20, 23, 20, 24, 20, 25, 20, 26, 20, 27, 28, 29, 28, 30, 28, 31, 28, 32, 28, 33, 28, 34, 28, 35, 0, 4, 4, 8, 8, 12, 12, 16, 16, 20, 20, 28, 0, 36, 36, 37, 37, 38, 28, 39, 39, 40 }

  114. 15655155793920

    Returns: {103, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 51, 52, 51, 53, 54, 55, 54, 56, 57, 58, 57, 59, 60, 61, 60, 62, 63, 64, 63, 65, 66, 67, 66, 68, 69, 70, 69, 71, 72, 73, 72, 74, 72, 75, 76, 77, 76, 78, 76, 79, 80, 81, 80, 82, 80, 83, 84, 85, 84, 86, 84, 87, 88, 89, 88, 90, 88, 91, 92, 93, 92, 94, 92, 95, 92, 96, 92, 97, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 69, 69, 72, 72, 76, 76, 80, 80, 84, 84, 88, 88, 92, 0, 98, 98, 99, 99, 100, 92, 101, 101, 102 }

  115. 608672457267609600

    Returns: {119, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 51, 52, 51, 53, 54, 55, 54, 56, 57, 58, 57, 59, 60, 61, 60, 62, 63, 64, 63, 65, 66, 67, 66, 68, 66, 69, 70, 71, 70, 72, 70, 73, 74, 75, 74, 76, 74, 77, 78, 79, 78, 80, 78, 81, 82, 83, 82, 84, 82, 85, 86, 87, 86, 88, 86, 89, 90, 91, 90, 92, 90, 93, 94, 95, 94, 96, 94, 97, 98, 99, 98, 100, 98, 101, 102, 103, 102, 104, 102, 105, 102, 106, 102, 107, 108, 109, 108, 110, 108, 111, 108, 112, 108, 113, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 70, 70, 74, 74, 78, 78, 82, 82, 86, 86, 90, 90, 94, 94, 98, 98, 102, 102, 108, 0, 114, 114, 115, 115, 116, 108, 117, 117, 118 }

  116. 81749606400

    Returns: {50, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 33, 36, 33, 37, 33, 38, 33, 39, 33, 40, 33, 41, 33, 42, 33, 43, 33, 44, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 0, 45, 45, 46, 46, 47, 33, 48, 48, 49 }

  117. 639106080130990080

    Returns: {116, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 51, 52, 51, 53, 54, 55, 54, 56, 57, 58, 57, 59, 60, 61, 60, 62, 63, 64, 63, 65, 63, 66, 67, 68, 67, 69, 67, 70, 71, 72, 71, 73, 71, 74, 75, 76, 75, 77, 75, 78, 79, 80, 79, 81, 79, 82, 83, 84, 83, 85, 83, 86, 87, 88, 87, 89, 87, 90, 91, 92, 91, 93, 91, 94, 95, 96, 95, 97, 95, 98, 99, 100, 99, 101, 99, 102, 103, 104, 103, 105, 103, 106, 103, 107, 103, 108, 103, 109, 103, 110, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 67, 67, 71, 71, 75, 75, 79, 79, 83, 83, 87, 87, 91, 91, 95, 95, 99, 99, 103, 0, 111, 111, 112, 112, 113, 103, 114, 114, 115 }

  118. 589800044652134400

    Returns: {83, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 18, 21, 22, 23, 22, 24, 22, 25, 26, 27, 26, 28, 26, 29, 30, 31, 30, 32, 30, 33, 34, 35, 34, 36, 34, 37, 38, 39, 38, 40, 38, 41, 42, 43, 42, 44, 42, 45, 46, 47, 46, 48, 46, 49, 50, 51, 50, 52, 50, 53, 54, 55, 54, 56, 54, 57, 58, 59, 58, 60, 58, 61, 62, 63, 62, 64, 62, 65, 62, 66, 62, 67, 62, 68, 62, 69, 70, 71, 70, 72, 70, 73, 70, 74, 70, 75, 70, 76, 70, 77, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 22, 22, 26, 26, 30, 30, 34, 34, 38, 38, 42, 42, 46, 46, 50, 50, 54, 54, 58, 58, 62, 62, 70, 0, 78, 78, 79, 79, 80, 70, 81, 81, 82 }

  119. 34279898952499200

    Returns: {72, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 48, 51, 52, 53, 52, 54, 52, 55, 52, 56, 52, 57, 52, 58, 52, 59, 52, 60, 52, 61, 52, 62, 52, 63, 52, 64, 52, 65, 52, 66, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 52, 0, 67, 67, 68, 68, 69, 52, 70, 70, 71 }

  120. 42467328000

    Returns: {63, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 36, 39, 40, 41, 40, 42, 40, 43, 40, 44, 40, 45, 46, 47, 46, 48, 46, 49, 46, 50, 46, 51, 52, 53, 52, 54, 52, 55, 52, 56, 52, 57, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 40, 40, 46, 46, 52, 0, 58, 58, 59, 59, 60, 52, 61, 61, 62 }

  121. 8957952

    Returns: {48, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 15, 18, 19, 20, 19, 21, 19, 22, 23, 24, 23, 25, 23, 26, 27, 28, 27, 29, 27, 30, 31, 32, 31, 33, 31, 34, 35, 36, 35, 37, 35, 38, 39, 40, 39, 41, 39, 42, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 19, 19, 23, 23, 27, 27, 31, 31, 35, 35, 39, 0, 43, 43, 44, 44, 45, 39, 46, 46, 47 }

  122. 41561539529932800

    Returns: {127, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 51, 52, 51, 53, 54, 55, 54, 56, 57, 58, 57, 59, 60, 61, 60, 62, 63, 64, 63, 65, 66, 67, 66, 68, 69, 70, 69, 71, 72, 73, 72, 74, 75, 76, 75, 77, 78, 79, 78, 80, 81, 82, 81, 83, 84, 85, 84, 86, 87, 88, 87, 89, 90, 91, 90, 92, 93, 94, 93, 95, 96, 97, 96, 98, 99, 100, 99, 101, 102, 103, 102, 104, 105, 106, 105, 107, 108, 109, 108, 110, 108, 111, 108, 112, 108, 113, 114, 115, 114, 116, 114, 117, 114, 118, 114, 119, 114, 120, 114, 121, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 69, 69, 72, 72, 75, 75, 78, 78, 81, 81, 84, 84, 87, 87, 90, 90, 93, 93, 96, 96, 99, 99, 102, 102, 105, 105, 108, 108, 114, 0, 122, 122, 123, 123, 124, 114, 125, 125, 126 }

  123. 159776520032747520

    Returns: {110, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 51, 52, 51, 53, 54, 55, 54, 56, 57, 58, 57, 59, 57, 60, 61, 62, 61, 63, 61, 64, 65, 66, 65, 67, 65, 68, 69, 70, 69, 71, 69, 72, 73, 74, 73, 75, 73, 76, 77, 78, 77, 79, 77, 80, 81, 82, 81, 83, 81, 84, 85, 86, 85, 87, 85, 88, 89, 90, 89, 91, 89, 92, 93, 94, 93, 95, 93, 96, 97, 98, 97, 99, 97, 100, 97, 101, 97, 102, 97, 103, 97, 104, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 61, 61, 65, 65, 69, 69, 73, 73, 77, 77, 81, 81, 85, 85, 89, 89, 93, 93, 97, 0, 105, 105, 106, 106, 107, 97, 108, 108, 109 }

  124. 653996851200

    Returns: {59, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 42, 45, 42, 46, 42, 47, 42, 48, 42, 49, 42, 50, 42, 51, 42, 52, 42, 53, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 0, 54, 54, 55, 55, 56, 42, 57, 57, 58 }

  125. 1755758592000

    Returns: {47, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 12, 15, 16, 17, 16, 18, 16, 19, 20, 21, 20, 22, 20, 23, 20, 24, 20, 25, 26, 27, 26, 28, 26, 29, 26, 30, 26, 31, 26, 32, 26, 33, 34, 35, 34, 36, 34, 37, 34, 38, 34, 39, 34, 40, 34, 41, 0, 3, 3, 6, 6, 9, 9, 12, 12, 16, 16, 20, 20, 26, 26, 34, 0, 42, 42, 43, 43, 44, 34, 45, 45, 46 }

  126. 28894769971200000

    Returns: {70, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 21, 24, 25, 26, 25, 27, 25, 28, 29, 30, 29, 31, 29, 32, 33, 34, 33, 35, 33, 36, 33, 37, 33, 38, 39, 40, 39, 41, 39, 42, 39, 43, 39, 44, 45, 46, 45, 47, 45, 48, 45, 49, 45, 50, 51, 52, 51, 53, 51, 54, 51, 55, 51, 56, 57, 58, 57, 59, 57, 60, 57, 61, 57, 62, 57, 63, 57, 64, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 25, 25, 29, 29, 33, 33, 39, 39, 45, 45, 51, 51, 57, 0, 65, 65, 66, 66, 67, 57, 68, 68, 69 }

  127. 998603250204672000

    Returns: {96, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 39, 42, 43, 44, 43, 45, 43, 46, 47, 48, 47, 49, 47, 50, 51, 52, 51, 53, 51, 54, 55, 56, 55, 57, 55, 58, 59, 60, 59, 61, 59, 62, 63, 64, 63, 65, 63, 66, 67, 68, 67, 69, 67, 70, 71, 72, 71, 73, 71, 74, 71, 75, 71, 76, 77, 78, 77, 79, 77, 80, 77, 81, 77, 82, 83, 84, 83, 85, 83, 86, 83, 87, 83, 88, 83, 89, 83, 90, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 43, 43, 47, 47, 51, 51, 55, 55, 59, 59, 63, 63, 67, 67, 71, 71, 77, 77, 83, 0, 91, 91, 92, 92, 93, 83, 94, 94, 95 }

  128. 121645100408832000

    Returns: {25, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 12, 0, 13, 0, 14, 0, 15, 0, 16, 0, 17, 0, 18, 0, 19, 0, 20, 20, 21, 21, 22, 0, 23, 23, 24 }

  129. 576460752303423488

    Returns: {182, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 27, 28, 27, 29, 30, 31, 30, 32, 33, 34, 33, 35, 36, 37, 36, 38, 39, 40, 39, 41, 42, 43, 42, 44, 45, 46, 45, 47, 48, 49, 48, 50, 51, 52, 51, 53, 54, 55, 54, 56, 57, 58, 57, 59, 60, 61, 60, 62, 63, 64, 63, 65, 66, 67, 66, 68, 69, 70, 69, 71, 72, 73, 72, 74, 75, 76, 75, 77, 78, 79, 78, 80, 81, 82, 81, 83, 84, 85, 84, 86, 87, 88, 87, 89, 90, 91, 90, 92, 93, 94, 93, 95, 96, 97, 96, 98, 99, 100, 99, 101, 102, 103, 102, 104, 105, 106, 105, 107, 108, 109, 108, 110, 111, 112, 111, 113, 114, 115, 114, 116, 117, 118, 117, 119, 120, 121, 120, 122, 123, 124, 123, 125, 126, 127, 126, 128, 129, 130, 129, 131, 132, 133, 132, 134, 135, 136, 135, 137, 138, 139, 138, 140, 141, 142, 141, 143, 144, 145, 144, 146, 147, 148, 147, 149, 150, 151, 150, 152, 153, 154, 153, 155, 156, 157, 156, 158, 159, 160, 159, 161, 162, 163, 162, 164, 165, 166, 165, 167, 168, 169, 168, 170, 171, 172, 171, 173, 174, 175, 174, 176, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 69, 69, 72, 72, 75, 75, 78, 78, 81, 81, 84, 84, 87, 87, 90, 90, 93, 93, 96, 96, 99, 99, 102, 102, 105, 105, 108, 108, 111, 111, 114, 114, 117, 117, 120, 120, 123, 123, 126, 126, 129, 129, 132, 132, 135, 135, 138, 138, 141, 141, 144, 144, 147, 147, 150, 150, 153, 153, 156, 156, 159, 159, 162, 162, 165, 165, 168, 168, 171, 171, 174, 0, 177, 177, 178, 178, 179, 174, 180, 180, 181 }

  130. 990677827584000000

    Returns: {81, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 19, 18, 20, 21, 22, 21, 23, 24, 25, 24, 26, 24, 27, 28, 29, 28, 30, 28, 31, 32, 33, 32, 34, 32, 35, 36, 37, 36, 38, 36, 39, 40, 41, 40, 42, 40, 43, 40, 44, 40, 45, 46, 47, 46, 48, 46, 49, 46, 50, 46, 51, 52, 53, 52, 54, 52, 55, 52, 56, 52, 57, 58, 59, 58, 60, 58, 61, 58, 62, 58, 63, 64, 65, 64, 66, 64, 67, 64, 68, 64, 69, 70, 71, 70, 72, 70, 73, 70, 74, 70, 75, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 28, 28, 32, 32, 36, 36, 40, 40, 46, 46, 52, 52, 58, 58, 64, 64, 70, 0, 76, 76, 77, 77, 78, 70, 79, 79, 80 }

  131. 1694745980928000

    Returns: {37, 0, 1, 0, 2, 0, 3, 4, 5, 4, 6, 4, 7, 8, 9, 8, 10, 8, 11, 12, 13, 12, 14, 12, 15, 16, 17, 16, 18, 16, 19, 16, 20, 16, 21, 16, 22, 16, 23, 16, 24, 16, 25, 16, 26, 16, 27, 16, 28, 16, 29, 16, 30, 16, 31, 0, 4, 4, 8, 8, 12, 12, 16, 0, 32, 32, 33, 33, 34, 16, 35, 35, 36 }

  132. 120960

    Returns: {23, 0, 1, 0, 2, 3, 4, 3, 5, 6, 7, 6, 8, 6, 9, 10, 11, 10, 12, 10, 13, 10, 14, 10, 15, 10, 16, 10, 17, 0, 3, 3, 6, 6, 10, 0, 18, 18, 19, 19, 20, 10, 21, 21, 22 }

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: