Statistics

Problem Statement for "MaxOfMin"

Problem Statement

Nam has a permutation P = { P[1], P[2], ..., P[N] } of integers from 1 to N, inclusive.

For any such permutation we can define the following values:

  • pmin(k, i) is the minimum of k consecutive elements, starting at index i
  • f(k) is the maximum of pmin(k, i) over all valid choices of k consecutive elements

Formally:

  • for each k and i such that 1 <= k <= N and 1 <= i <= N-k+1: pmin(k, i) = min{ P[i], P[i+1], ..., P[i+k-1] }
  • f(k) = max{ pmin(k, 1), pmin(k, 2), ..., pmin(k, N-k+1) }

Nam has calculated all N values f(1), f(2), ..., f(N) and he has written them on a piece of paper. You are given these values in the int[] F of length N. For each valid i, F[i] = f(i + 1).

A few days later Nam totally forgot his permutation P. Luckily, he still kept the paper with the sequence F.

Please help him: count all permutations P that correspond to the given F and return that count modulo 998244353.

Definition

Class:
MaxOfMin
Method:
count
Parameters:
int[]
Returns:
int
Method signature:
int count(int[] F)
(be sure your method is public)

Constraints

  • F will have between 1 and 50 elements, inclusive.
  • Each element of F will be between 1 and 50, inclusive.

Examples

  1. {3, 1, 1}

    Returns: 2

    Let's examine all six permutations of the set {1, 2, 3}: P = {1, 2, 3} f(1) = max(1, 2, 3) = 3 f(2) = max(1, 2) = 2 f(3) = max(1) = 1 P = {1, 3, 2} f(1) = max(1, 3, 2) = 3 f(2) = max(1, 2) = 2 f(3) = max(1) = 1 P = {2, 1, 3} f(1) = max(2, 1, 3) = 3 f(2) = max(1, 1) = 1 f(3) = max(1) = 1 P = {2, 3, 1} f(1) = max(2, 3, 1) = 3 f(2) = max(2, 1) = 2 f(3) = max(1) = 1 P = {3, 1, 2} f(1) = max(3, 1, 2) = 3 f(2) = max(1, 1) = 1 f(3) = max(1) = 1 P = {3, 2, 1} f(1) = max(3, 2, 1) = 3 f(2) = max(2, 1) = 2 f(3) = max(1) = 1 We see that there are two permutations that match the given F: the permutations {2, 1, 3} and {3, 1, 2}.

  2. {3, 1, 3}

    Returns: 0

    As we saw above, for N = 3 there are no permutations with f(3) = 3.

  3. {5, 2, 2, 1, 1}

    Returns: 12

    The twelve permutations that match this F are precisely the permutations in which P[2] and P[4] are 1 and 2, in either order.

  4. {6, 5, 2, 1, 1, 1}

    Returns: 40

  5. {50, 45, 39, 33, 27, 19, 19, 19, 12, 12, 7, 7, 7, 6, 6, 4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 364866987

    Don't forget the modulo.

  6. {1}

    Returns: 1

  7. {2, 1}

    Returns: 2

  8. {3, 2, 1}

    Returns: 4

  9. {4, 3, 2, 1}

    Returns: 8

  10. {4, 2, 2, 1}

    Returns: 4

  11. {4, 3, 1, 1}

    Returns: 4

  12. {4, 2, 1, 1}

    Returns: 8

  13. {5, 4, 3, 2, 1}

    Returns: 16

  14. {5, 3, 3, 2, 1}

    Returns: 8

  15. {5, 4, 2, 2, 1}

    Returns: 8

  16. {5, 3, 2, 2, 1}

    Returns: 16

  17. {5, 4, 3, 1, 1}

    Returns: 8

  18. {5, 3, 3, 1, 1}

    Returns: 4

  19. {5, 4, 1, 1, 1}

    Returns: 8

  20. {5, 3, 2, 1, 1}

    Returns: 16

  21. {5, 3, 1, 1, 1}

    Returns: 16

  22. {5, 4, 2, 1, 1}

    Returns: 8

  23. {6, 5, 4, 3, 2, 1}

    Returns: 32

  24. {6, 4, 4, 3, 2, 1}

    Returns: 16

  25. {6, 5, 3, 3, 2, 1}

    Returns: 16

  26. {6, 4, 3, 3, 2, 1}

    Returns: 32

  27. {6, 5, 4, 2, 2, 1}

    Returns: 16

  28. {6, 4, 4, 2, 2, 1}

    Returns: 8

  29. {6, 5, 2, 2, 2, 1}

    Returns: 16

  30. {6, 4, 3, 2, 2, 1}

    Returns: 32

  31. {6, 4, 2, 2, 2, 1}

    Returns: 32

  32. {6, 5, 3, 2, 2, 1}

    Returns: 16

  33. {6, 3, 3, 2, 2, 1}

    Returns: 24

  34. {6, 5, 4, 3, 1, 1}

    Returns: 16

  35. {6, 4, 4, 3, 1, 1}

    Returns: 8

  36. {6, 5, 3, 3, 1, 1}

    Returns: 8

  37. {6, 4, 3, 3, 1, 1}

    Returns: 16

  38. {6, 5, 4, 1, 1, 1}

    Returns: 16

  39. {6, 4, 4, 1, 1, 1}

    Returns: 8

  40. {6, 4, 3, 2, 1, 1}

    Returns: 32

  41. {6, 4, 2, 1, 1, 1}

    Returns: 80

  42. {6, 5, 3, 2, 1, 1}

    Returns: 16

  43. {6, 5, 3, 1, 1, 1}

    Returns: 16

  44. {6, 3, 3, 1, 1, 1}

    Returns: 24

  45. {6, 3, 3, 2, 1, 1}

    Returns: 24

  46. {6, 5, 4, 2, 1, 1}

    Returns: 16

  47. {6, 4, 3, 1, 1, 1}

    Returns: 32

  48. {6, 4, 4, 2, 1, 1}

    Returns: 8

  49. {6, 5, 2, 2, 1, 1}

    Returns: 16

  50. {6, 4, 2, 2, 1, 1}

    Returns: 32

  51. {6, 3, 2, 1, 1, 1}

    Returns: 24

  52. {6, 3, 2, 2, 1, 1}

    Returns: 48

  53. {7, 6, 5, 4, 3, 2, 1}

    Returns: 64

  54. {7, 5, 5, 4, 3, 2, 1}

    Returns: 32

  55. {7, 6, 4, 4, 3, 2, 1}

    Returns: 32

  56. {7, 5, 4, 4, 3, 2, 1}

    Returns: 64

  57. {7, 6, 5, 3, 3, 2, 1}

    Returns: 32

  58. {7, 5, 5, 3, 3, 2, 1}

    Returns: 16

  59. {7, 6, 3, 3, 3, 2, 1}

    Returns: 32

  60. {7, 5, 4, 3, 3, 2, 1}

    Returns: 64

  61. {7, 5, 3, 3, 3, 2, 1}

    Returns: 64

  62. {7, 6, 4, 3, 3, 2, 1}

    Returns: 32

  63. {7, 4, 4, 3, 3, 2, 1}

    Returns: 48

  64. {7, 6, 5, 4, 2, 2, 1}

    Returns: 32

  65. {7, 5, 5, 4, 2, 2, 1}

    Returns: 16

  66. {7, 6, 4, 4, 2, 2, 1}

    Returns: 16

  67. {7, 5, 4, 4, 2, 2, 1}

    Returns: 32

  68. {7, 6, 5, 2, 2, 2, 1}

    Returns: 32

  69. {7, 5, 5, 2, 2, 2, 1}

    Returns: 16

  70. {7, 6, 3, 2, 2, 2, 1}

    Returns: 80

  71. {7, 5, 4, 3, 2, 2, 1}

    Returns: 64

  72. {7, 5, 3, 2, 2, 2, 1}

    Returns: 160

  73. {7, 6, 4, 3, 2, 2, 1}

    Returns: 32

  74. {7, 6, 4, 2, 2, 2, 1}

    Returns: 32

  75. {7, 4, 4, 2, 2, 2, 1}

    Returns: 48

  76. {7, 4, 4, 3, 2, 2, 1}

    Returns: 48

  77. {7, 6, 5, 3, 2, 2, 1}

    Returns: 32

  78. {7, 5, 4, 2, 2, 2, 1}

    Returns: 64

  79. {7, 5, 5, 3, 2, 2, 1}

    Returns: 16

  80. {7, 6, 3, 3, 2, 2, 1}

    Returns: 32

  81. {7, 5, 3, 3, 2, 2, 1}

    Returns: 64

  82. {50, 44, 40, 40, 24, 24, 16, 16, 16, 16, 13, 7, 6, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 362394381

  83. {50, 44, 36, 28, 24, 24, 23, 23, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 635000275

  84. {50, 48, 36, 36, 24, 24, 24, 19, 19, 11, 8, 8, 8, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 844397046

  85. {50, 41, 35, 23, 23, 23, 23, 16, 16, 7, 7, 7, 7, 5, 5, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 636554883

  86. {50, 46, 44, 39, 28, 23, 23, 23, 18, 18, 18, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1}

    Returns: 61968324

  87. {50, 39, 31, 28, 28, 21, 21, 16, 16, 16, 16, 16, 16, 5, 5, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 959769113

  88. {50, 47, 33, 27, 19, 19, 19, 10, 10, 10, 10, 7, 7, 7, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 2156243

  89. {50, 46, 37, 26, 25, 21, 20, 20, 14, 14, 14, 7, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 203474160

  90. {50, 44, 32, 29, 29, 29, 26, 26, 15, 15, 15, 7, 7, 5, 5, 5, 5, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 308248720

  91. {50, 47, 39, 38, 21, 17, 17, 17, 17, 13, 13, 13, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1}

    Returns: 715753460

  92. {50, 43, 41, 39, 31, 26, 17, 17, 17, 17, 17, 17, 15, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 595987394

  93. {50, 42, 38, 31, 25, 25, 22, 22, 22, 22, 7, 7, 7, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1}

    Returns: 553840734

  94. {50, 43, 31, 29, 29, 21, 13, 13, 12, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 642104638

  95. {50, 47, 36, 33, 24, 23, 23, 23, 23, 12, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1}

    Returns: 67726504

  96. {50, 40, 37, 34, 18, 14, 14, 14, 11, 11, 10, 9, 9, 6, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 804036240

  97. {50, 48, 47, 36, 21, 17, 17, 9, 9, 9, 9, 9, 9, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 418365676

  98. {50, 40, 39, 26, 26, 26, 20, 20, 8, 8, 8, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1}

    Returns: 449321145

  99. {50, 42, 33, 32, 29, 29, 23, 23, 23, 18, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 988094594

  100. {50, 46, 43, 37, 37, 18, 18, 18, 18, 18, 12, 12, 12, 8, 7, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 162208323

  101. {50, 45, 42, 41, 21, 20, 17, 12, 12, 8, 7, 7, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 36384098

  102. {30, 24, 19, 14, 14, 14, 13, 9, 5, 5, 5, 5, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1}

    Returns: 924348611

  103. {31, 28, 21, 19, 19, 17, 15, 11, 11, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 399870760

  104. {32, 30, 18, 15, 14, 11, 11, 11, 11, 11, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1}

    Returns: 805701930

  105. {33, 30, 23, 22, 12, 10, 10, 10, 10, 10, 9, 9, 9, 9, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1}

    Returns: 246348861

  106. {34, 28, 21, 21, 11, 9, 9, 9, 9, 7, 7, 7, 7, 4, 4, 4, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 392202765

  107. {35, 28, 26, 21, 18, 16, 16, 16, 12, 10, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1}

    Returns: 5687370

  108. {36, 30, 27, 20, 20, 20, 10, 10, 10, 10, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1}

    Returns: 269213591

  109. {37, 30, 24, 21, 19, 14, 13, 13, 11, 9, 9, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 596884536

  110. {38, 29, 19, 18, 17, 16, 11, 11, 11, 11, 11, 9, 7, 7, 6, 6, 6, 6, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 795558420

  111. {39, 34, 24, 22, 22, 22, 20, 19, 9, 9, 9, 9, 9, 9, 8, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 995111097

  112. {40, 37, 32, 29, 17, 17, 17, 17, 17, 16, 16, 11, 9, 9, 8, 8, 8, 7, 7, 7, 7, 6, 6, 6, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 152408571

  113. {41, 35, 31, 29, 20, 15, 15, 10, 10, 10, 10, 10, 10, 10, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 603596086

  114. {42, 37, 35, 29, 29, 26, 20, 20, 20, 20, 8, 8, 8, 8, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 487915121

  115. {43, 39, 26, 26, 21, 21, 15, 11, 11, 11, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 1, 1, 1, 1, 1, 1}

    Returns: 400153262

  116. {44, 42, 36, 23, 23, 20, 20, 20, 16, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 278352692

  117. {45, 39, 30, 30, 24, 19, 19, 19, 16, 16, 16, 16, 16, 10, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1}

    Returns: 189363579

  118. {46, 40, 34, 34, 24, 16, 13, 13, 13, 10, 10, 10, 10, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1}

    Returns: 754248377

  119. {47, 43, 40, 40, 27, 20, 20, 19, 10, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1}

    Returns: 535196289

  120. {48, 47, 33, 30, 22, 22, 17, 17, 17, 17, 7, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 291077856

  121. {49, 42, 36, 30, 26, 26, 24, 24, 24, 10, 10, 10, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 247737303

  122. {43, 41, 37, 36, 33, 31, 30, 30, 29, 26, 25, 24, 23, 23, 23, 22, 22, 20, 19, 19, 17, 16, 15, 14, 14, 13, 12, 10, 7, 7, 5, 5, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1}

    Returns: 866126678

  123. {44, 37, 32, 32, 32, 30, 26, 25, 23, 22, 21, 21, 21, 20, 20, 20, 19, 19, 19, 18, 17, 14, 13, 13, 12, 11, 11, 10, 9, 9, 7, 7, 7, 6, 4, 3, 3, 3, 3, 2, 2, 2, 1, 1}

    Returns: 299824595

  124. {45, 37, 36, 36, 33, 32, 32, 30, 30, 30, 28, 27, 25, 22, 22, 20, 20, 19, 19, 18, 17, 17, 16, 16, 16, 13, 12, 12, 12, 11, 11, 8, 7, 6, 6, 4, 4, 4, 2, 2, 2, 2, 1, 1, 1}

    Returns: 410815134

  125. {46, 44, 38, 38, 37, 36, 34, 33, 32, 26, 25, 24, 24, 24, 23, 22, 21, 20, 20, 19, 19, 19, 19, 17, 15, 15, 14, 12, 11, 11, 11, 10, 10, 9, 8, 8, 8, 7, 5, 4, 3, 2, 1, 1, 1, 1}

    Returns: 571409833

  126. {47, 32, 32, 28, 24, 24, 24, 20, 20, 19, 18, 17, 17, 17, 16, 15, 15, 15, 15, 14, 14, 13, 13, 12, 10, 9, 9, 8, 8, 7, 7, 7, 7, 6, 5, 5, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1}

    Returns: 547744114

  127. {48, 44, 40, 37, 37, 36, 35, 34, 34, 34, 32, 32, 31, 30, 28, 27, 26, 26, 25, 25, 24, 21, 20, 19, 18, 17, 17, 16, 15, 15, 15, 14, 14, 13, 10, 9, 9, 8, 7, 7, 7, 6, 6, 5, 5, 2, 1, 1}

    Returns: 0

  128. {49, 46, 45, 38, 37, 36, 34, 34, 33, 33, 32, 31, 30, 29, 28, 26, 26, 24, 22, 21, 21, 20, 20, 18, 17, 17, 15, 15, 14, 14, 13, 12, 12, 12, 11, 10, 8, 8, 8, 7, 6, 6, 6, 5, 2, 1, 1, 1, 1}

    Returns: 710821452

  129. {50, 41, 39, 38, 35, 35, 34, 33, 29, 29, 29, 27, 24, 23, 22, 22, 21, 20, 17, 17, 17, 16, 15, 14, 13, 11, 11, 10, 10, 10, 10, 9, 9, 9, 8, 7, 7, 7, 5, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1}

    Returns: 408362258

  130. {7, 6, 6, 4, 3, 1, 1}

    Returns: 0

  131. {8, 6, 5, 5, 3, 3, 2, 1}

    Returns: 64

  132. {9, 8, 4, 4, 3, 2, 1, 1, 1}

    Returns: 384

  133. {10, 10, 9, 5, 4, 3, 3, 2, 1, 1}

    Returns: 0

  134. {11, 11, 6, 5, 5, 5, 3, 3, 1, 1, 1}

    Returns: 0

  135. {12, 9, 7, 6, 5, 5, 4, 4, 3, 2, 2, 1}

    Returns: 4608

  136. {13, 9, 9, 7, 4, 3, 3, 2, 2, 1, 1, 1, 1}

    Returns: 41472

  137. {14, 14, 11, 11, 8, 8, 7, 5, 5, 5, 4, 1, 1, 1}

    Returns: 0

  138. {15, 11, 8, 7, 7, 6, 5, 4, 4, 3, 3, 1, 1, 1, 1}

    Returns: 589824

  139. {8, 7, 5, 3, 2, 2, 1, 1}

    Returns: 64

  140. {9, 9, 6, 5, 3, 2, 2, 1, 1}

    Returns: 0

  141. {10, 8, 6, 4, 4, 1, 1, 1, 1, 1}

    Returns: 2880

  142. {11, 10, 7, 6, 6, 5, 4, 3, 2, 1, 1}

    Returns: 512

  143. {12, 12, 10, 10, 5, 3, 3, 3, 2, 1, 1, 1}

    Returns: 0

  144. {50, 45, 41, 31, 24, 24, 24, 22, 22, 18, 11, 11, 4, 4, 4, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 643776487

  145. {50, 45, 41, 36, 27, 22, 14, 14, 14, 11, 8, 7, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 528435376

  146. {50, 43, 35, 35, 27, 24, 19, 19, 19, 17, 15, 15, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 512373941

  147. {50, 44, 33, 33, 25, 25, 25, 25, 11, 6, 6, 6, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 103835856

  148. {50, 46, 42, 36, 34, 34, 33, 30, 24, 23, 22, 22, 20, 20, 16, 16, 16, 13, 13, 13, 13, 13, 10, 10, 9, 8, 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 69562187

  149. {50, 46, 43, 43, 42, 41, 40, 37, 32, 26, 26, 23, 23, 23, 22, 19, 17, 13, 13, 13, 13, 13, 11, 11, 11, 10, 8, 8, 8, 8, 8, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1}

    Returns: 333470845

  150. {50, 44, 41, 29, 28, 28, 28, 27, 27, 27, 27, 26, 24, 23, 18, 18, 18, 17, 15, 10, 10, 10, 10, 9, 9, 9, 9, 9, 9, 7, 7, 6, 5, 5, 5, 5, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1}

    Returns: 948953533

  151. {50, 40, 39, 34, 28, 22, 22, 21, 19, 19, 19, 15, 15, 14, 14, 14, 14, 12, 11, 11, 10, 10, 9, 9, 7, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 3, 3, 2, 1, 1, 1, 1}

    Returns: 860331120

  152. {50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}

    Returns: 32990492

    Don't forget the modulo

  153. {50, 25, 25, 24, 24, 23, 23, 22, 22, 21, 21, 20, 20, 19, 19, 18, 18, 17, 17, 16, 16, 15, 15, 14, 14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1}

    Returns: 859741917

  154. {50, 49, 47, 46, 42, 40, 38, 36, 34, 33, 31, 29, 28, 27, 26, 25, 24, 22, 21, 20, 19, 18, 17, 14, 12, 11, 9, 8, 7, 6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 316722453

  155. {50, 49, 48, 47, 46, 44, 42, 41, 39, 37, 36, 35, 34, 31, 29, 28, 25, 23, 19, 18, 17, 14, 13, 12, 10, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 744432434

  156. {50, 48, 46, 41, 39, 37, 33, 32, 28, 27, 26, 25, 22, 20, 15, 11, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 5, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1}

    Returns: 265416870

  157. {50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 35, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 12, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}

    Returns: 8247623

  158. {50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 31, 31, 30, 29, 28, 27, 26, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 8, 8, 7, 6, 5, 4, 3, 2, 1}

    Returns: 503245988

  159. {50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 36, 36, 36, 35, 34, 33, 32, 30, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 19, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}

    Returns: 503245988

  160. {50, 49, 48, 47, 46, 45, 44, 43, 41, 41, 39, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 28, 28, 27, 26, 25, 24, 23, 22, 21, 20, 18, 17, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}

    Returns: 251622994

  161. {50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 32, 32, 32, 31, 30, 29, 28, 27, 25, 25, 24, 23, 22, 20, 20, 19, 18, 17, 16, 15, 14, 13, 12, 10, 10, 9, 8, 6, 6, 5, 4, 3, 2, 1}

    Returns: 125811497

  162. {50, 49, 48, 47, 46, 45, 44, 42, 42, 40, 40, 39, 37, 37, 35, 35, 34, 33, 31, 31, 29, 29, 28, 26, 26, 25, 23, 23, 22, 21, 20, 19, 18, 17, 15, 15, 14, 12, 12, 11, 10, 8, 8, 7, 6, 5, 3, 3, 2, 1}

    Returns: 679477111

  163. {50, 49, 47, 46, 46, 45, 44, 43, 42, 41, 40, 39, 37, 37, 36, 35, 33, 33, 32, 31, 30, 29, 28, 27, 23, 23, 23, 22, 22, 20, 20, 19, 17, 17, 16, 15, 14, 13, 12, 11, 10, 8, 8, 7, 4, 4, 4, 3, 2, 1}

    Returns: 335541016

  164. {50, 42, 36, 32, 32, 31, 31, 28, 26, 24, 24, 24, 23, 23, 21, 20, 20, 20, 18, 17, 17, 16, 15, 15, 15, 15, 15, 14, 13, 13, 12, 12, 11, 11, 11, 9, 8, 7, 6, 5, 5, 5, 3, 4, 3, 3, 2, 2, 2, 1}

    Returns: 0

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