Statistics

Problem Statement for "CentaurCompanyDiv2"

Problem Statement

The Centaur company has N servers, numbered 1 through N. These servers are currently connected into a network. The topology of the network is a tree. In other words, there are exactly N-1 bidirectional cables, each connecting some two servers in such a way that the entire network is connected.


The Centaur company is about to split into two new companies: the Human company and the Horse company. When this happens, the companies will divide the servers somehow. Once they divide their servers, they will cut each cable that connects a server of the Horse company and a server of the Human company.


While the Horse company has a lot of cables, the Human company does not have any. Therefore, when dividing the servers, the Human company must get a set of servers that will remain connected after the cables are cut.


You are given two int[]s a and b, each containing N-1 elements. These two arrays describe the original cables: for each i, there is a cable that connects the servers a[i] and b[i].


Compute and return the number of different ways in which the two companies may divide the servers. (It is possible that one of the companies will get no servers at all.)

Definition

Class:
CentaurCompanyDiv2
Method:
count
Parameters:
int[], int[]
Returns:
long
Method signature:
long count(int[] a, int[] b)
(be sure your method is public)

Notes

  • N can be determined as (1 + the length of a).

Constraints

  • N will be between 2 and 51, inclusive.
  • a and b will contain exactly N-1 elements.
  • Each element of a and b will be between 1 and N, inclusive.
  • The network defined by a and b will be a tree (as explained in the problem statement).

Examples

  1. {1}

    {2}

    Returns: 4

    There are 2^2 = 4 ways to divide the servers between two companies. For any division, the Human company's servers will remain connected.

  2. {2,2}

    {1,3}

    Returns: 7

    There are 2^3 = 8 ways to divide the servers between two companies. However, if the Human company gets server 1 and server 3, and the Horse company gets server 2, the Human company's servers will not be connected. Therefore the number of valid ways is 8 - 1 = 7.

  3. {1,2,3,4,5,6,7,8,9}

    {2,3,4,5,6,7,8,9,10}

    Returns: 56

  4. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

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

    Returns: 1125899906842675

    The answer overflows a 32-bit integer data type.

  5. {51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51,51}

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

    Returns: 1125899906842675

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

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

    Returns: 1327

  7. {2}

    {1}

    Returns: 4

  8. {1, 1}

    {2, 3}

    Returns: 7

  9. {1, 1, 4}

    {3, 2, 1}

    Returns: 12

  10. {1, 4, 1, 5}

    {4, 3, 2, 4}

    Returns: 18

  11. {6, 2, 2, 5, 4}

    {5, 1, 5, 3, 2}

    Returns: 29

  12. {3, 7, 5, 3, 3, 5}

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

    Returns: 41

  13. {6, 8, 6, 8, 7, 1, 8}

    {8, 3, 4, 2, 8, 3, 5}

    Returns: 82

  14. {1, 5, 1, 3, 1, 2, 2, 9}

    {8, 2, 5, 1, 6, 7, 4, 3}

    Returns: 89

  15. {10, 7, 2, 5, 6, 2, 4, 9, 7}

    {8, 10, 10, 4, 1, 6, 2, 2, 3}

    Returns: 144

  16. {1, 1, 1, 10, 6, 2, 7, 3, 4, 11}

    {5, 8, 9, 5, 3, 8, 1, 5, 5, 5}

    Returns: 336

  17. {5, 11, 8, 5, 9, 2, 6, 10, 11, 6, 11}

    {12, 1, 6, 11, 12, 3, 7, 1, 6, 4, 3}

    Returns: 348

  18. {6, 6, 12, 4, 10, 8, 1, 3, 7, 9, 13, 6}

    {1, 8, 2, 6, 4, 5, 11, 10, 8, 10, 10, 12}

    Returns: 483

  19. {9, 10, 3, 11, 9, 6, 4, 3, 5, 12, 5, 3, 12}

    {2, 2, 1, 2, 7, 2, 6, 6, 10, 14, 13, 8, 2}

    Returns: 823

  20. {5, 7, 6, 1, 12, 2, 6, 5, 7, 6, 1, 1, 9, 10}

    {8, 14, 2, 2, 3, 15, 13, 12, 2, 11, 4, 12, 1, 1}

    Returns: 1790

  21. {10, 3, 15, 15, 10, 4, 13, 11, 4, 16, 14, 14, 8, 2, 14}

    {4, 8, 8, 1, 6, 5, 3, 10, 8, 9, 7, 9, 12, 9, 11}

    Returns: 1030

  22. {16, 6, 6, 10, 9, 3, 1, 8, 4, 14, 2, 2, 13, 7, 15, 4}

    {13, 1, 5, 3, 2, 11, 17, 2, 1, 3, 1, 12, 1, 14, 13, 3}

    Returns: 3832

  23. {12, 11, 14, 17, 6, 6, 5, 8, 17, 8, 18, 2, 2, 1, 15, 11, 10}

    {7, 18, 15, 16, 7, 10, 4, 5, 2, 10, 14, 1, 18, 13, 9, 3, 18}

    Returns: 2093

  24. {11, 15, 13, 6, 1, 19, 15, 15, 7, 6, 12, 17, 16, 5, 15, 17, 12, 17}

    {12, 18, 14, 1, 9, 3, 10, 14, 2, 12, 8, 12, 19, 17, 2, 2, 19, 4}

    Returns: 8889

  25. {1, 8, 5, 12, 19, 11, 14, 13, 5, 17, 2, 8, 18, 2, 18, 19, 16, 13, 8}

    {13, 13, 1, 4, 9, 12, 13, 18, 7, 19, 5, 11, 10, 20, 16, 6, 15, 3, 6}

    Returns: 5671

  26. {12, 2, 17, 12, 18, 19, 13, 16, 3, 2, 12, 5, 7, 12, 5, 14, 19, 11, 13, 9}

    {11, 14, 15, 1, 7, 8, 20, 12, 6, 8, 18, 6, 10, 4, 12, 1, 21, 17, 12, 11}

    Returns: 9457

  27. {12, 20, 20, 3, 16, 21, 6, 9, 14, 22, 2, 7, 1, 2, 4, 4, 14, 8, 15, 5, 21}

    {18, 11, 16, 4, 4, 4, 18, 10, 13, 17, 21, 16, 18, 19, 9, 22, 16, 2, 21, 4, 6}

    Returns: 41836

  28. {2, 8, 16, 16, 1, 7, 15, 23, 13, 13, 12, 18, 9, 3, 18, 5, 1, 8, 7, 3, 3, 2}

    {15, 21, 19, 1, 2, 10, 22, 4, 6, 16, 17, 20, 3, 23, 8, 2, 12, 9, 14, 11, 14, 14}

    Returns: 19794

  29. {6, 5, 12, 1, 9, 14, 19, 22, 12, 17, 19, 17, 21, 13, 23, 2, 23, 11, 9, 5, 17, 11, 8}

    {17, 18, 20, 19, 17, 23, 15, 7, 23, 11, 11, 18, 24, 12, 3, 23, 16, 23, 4, 10, 21, 22, 2}

    Returns: 132722

  30. {7, 5, 20, 15, 21, 5, 10, 6, 13, 9, 14, 19, 17, 15, 5, 5, 3, 11, 15, 1, 3, 5, 13, 3}

    {18, 25, 22, 2, 23, 7, 8, 5, 24, 24, 22, 3, 2, 21, 22, 4, 12, 7, 8, 6, 21, 15, 7, 16}

    Returns: 175683

  31. {18, 13, 18, 8, 4, 12, 20, 5, 21, 9, 26, 3, 19, 2, 2, 15, 24, 16, 19, 1, 8, 21, 8, 18, 5}

    {1, 25, 3, 14, 5, 26, 16, 11, 6, 26, 4, 17, 7, 26, 10, 16, 8, 18, 23, 23, 22, 8, 18, 4, 25}

    Returns: 172668

  32. {7, 22, 11, 1, 27, 16, 23, 5, 17, 21, 9, 24, 20, 2, 3, 10, 14, 27, 5, 3, 25, 26, 7, 11, 8, 24}

    {20, 5, 17, 17, 23, 3, 25, 21, 20, 19, 21, 22, 19, 10, 15, 14, 18, 20, 14, 17, 13, 24, 12, 6, 20, 4}

    Returns: 82132

  33. {9, 5, 19, 22, 16, 28, 17, 2, 6, 12, 25, 8, 9, 14, 15, 19, 8, 17, 26, 20, 22, 26, 27, 12, 20, 17, 13}

    {15, 27, 7, 24, 17, 2, 11, 11, 11, 1, 2, 21, 19, 6, 6, 23, 4, 10, 9, 6, 18, 18, 17, 3, 4, 12, 18}

    Returns: 129018

  34. {11, 20, 18, 7, 11, 10, 22, 10, 27, 6, 19, 24, 14, 28, 19, 20, 27, 10, 28, 28, 17, 29, 26, 25, 7, 20, 4, 19}

    {24, 2, 8, 5, 20, 27, 19, 11, 21, 26, 9, 13, 12, 6, 14, 16, 14, 8, 23, 11, 16, 13, 1, 27, 10, 15, 29, 3}

    Returns: 406840

  35. {29, 16, 12, 20, 15, 15, 24, 28, 23, 24, 13, 10, 15, 6, 15, 11, 11, 18, 2, 11, 4, 25, 12, 24, 16, 2, 14, 17, 18}

    {24, 30, 10, 3, 22, 13, 11, 26, 21, 7, 27, 16, 14, 4, 17, 14, 5, 11, 12, 8, 3, 27, 6, 9, 15, 19, 23, 28, 1}

    Returns: 367907

  36. {24, 31, 11, 16, 8, 19, 3, 1, 15, 2, 31, 9, 19, 16, 17, 30, 11, 5, 22, 3, 28, 16, 10, 17, 18, 29, 14, 5, 8, 9}

    {21, 1, 27, 9, 6, 11, 28, 4, 11, 18, 22, 23, 21, 12, 25, 20, 28, 14, 15, 29, 13, 7, 15, 12, 9, 26, 20, 15, 21, 14}

    Returns: 242746

  37. {11, 6, 25, 24, 10, 18, 5, 10, 23, 22, 13, 31, 28, 10, 16, 28, 1, 3, 25, 19, 12, 29, 22, 27, 10, 22, 18, 2, 24, 30, 16}

    {24, 9, 7, 21, 22, 16, 28, 32, 7, 24, 15, 22, 16, 14, 9, 20, 10, 9, 10, 3, 18, 14, 15, 18, 4, 8, 17, 18, 26, 24, 25}

    Returns: 8804538

  38. {30, 6, 25, 17, 21, 10, 22, 8, 4, 25, 22, 14, 22, 31, 10, 5, 30, 18, 4, 33, 15, 33, 28, 17, 2, 31, 12, 12, 33, 14, 30, 21}

    {7, 24, 23, 1, 4, 20, 2, 10, 3, 10, 15, 32, 29, 19, 9, 19, 15, 26, 30, 16, 33, 18, 17, 14, 11, 13, 15, 10, 31, 31, 27, 6}

    Returns: 2714414

  39. {6, 1, 5, 26, 13, 27, 17, 31, 30, 17, 7, 11, 4, 33, 25, 18, 12, 32, 12, 11, 18, 25, 20, 21, 27, 27, 24, 9, 29, 12, 12, 10, 24}

    {8, 9, 9, 10, 1, 34, 19, 20, 16, 22, 34, 12, 2, 12, 2, 8, 20, 8, 9, 3, 19, 8, 30, 20, 28, 15, 15, 14, 19, 25, 15, 9, 23}

    Returns: 6349453

  40. {34, 24, 28, 24, 20, 30, 5, 31, 30, 30, 14, 16, 30, 3, 8, 1, 22, 23, 3, 26, 13, 10, 34, 31, 8, 35, 1, 28, 12, 22, 2, 9, 25, 25}

    {8, 11, 4, 26, 3, 21, 8, 34, 12, 15, 12, 31, 5, 12, 29, 7, 17, 2, 33, 21, 30, 3, 6, 32, 27, 5, 13, 29, 19, 20, 34, 20, 18, 3}

    Returns: 6807613

  41. {24, 13, 35, 30, 13, 6, 28, 19, 11, 11, 13, 12, 7, 36, 11, 11, 13, 14, 8, 14, 15, 28, 34, 11, 25, 11, 31, 22, 21, 15, 25, 9, 32, 25, 12}

    {6, 15, 11, 24, 2, 18, 13, 1, 33, 4, 27, 5, 25, 20, 8, 24, 16, 26, 23, 12, 19, 3, 15, 22, 9, 25, 12, 17, 2, 29, 31, 10, 30, 15, 20}

    Returns: 38502686

  42. {29, 3, 10, 21, 17, 10, 15, 15, 36, 28, 23, 9, 31, 15, 26, 7, 27, 27, 20, 30, 23, 3, 13, 16, 2, 3, 18, 32, 29, 19, 9, 14, 10, 15, 4, 15}

    {8, 20, 34, 5, 14, 6, 21, 30, 24, 24, 30, 21, 6, 25, 15, 24, 14, 1, 11, 3, 24, 33, 34, 11, 29, 10, 28, 3, 23, 27, 12, 10, 35, 22, 24, 37}

    Returns: 45351732

  43. {38, 13, 10, 31, 36, 1, 6, 25, 22, 14, 26, 11, 3, 12, 16, 15, 30, 6, 29, 37, 28, 30, 13, 16, 8, 26, 21, 33, 18, 30, 27, 33, 11, 20, 8, 38, 7}

    {34, 25, 6, 11, 13, 20, 16, 5, 7, 37, 17, 8, 37, 16, 20, 30, 26, 30, 16, 2, 30, 35, 19, 13, 2, 9, 26, 32, 17, 2, 13, 15, 23, 38, 4, 24, 15}

    Returns: 64154825

  44. {28, 31, 11, 33, 21, 20, 4, 6, 30, 28, 35, 15, 33, 12, 33, 33, 23, 15, 14, 10, 28, 4, 26, 16, 27, 29, 9, 2, 38, 2, 1, 2, 22, 36, 37, 38, 25, 36}

    {24, 33, 24, 29, 24, 2, 3, 32, 23, 32, 39, 5, 8, 4, 16, 17, 16, 7, 31, 23, 8, 22, 29, 39, 6, 34, 2, 15, 29, 18, 29, 8, 25, 13, 28, 19, 24, 24}

    Returns: 67041622

  45. {39, 13, 5, 26, 39, 3, 14, 3, 35, 35, 37, 27, 22, 18, 7, 37, 7, 22, 21, 36, 38, 40, 26, 34, 30, 8, 13, 35, 3, 31, 28, 7, 24, 20, 6, 9, 17, 39, 22}

    {8, 10, 36, 5, 16, 24, 31, 32, 15, 37, 7, 24, 28, 40, 31, 29, 3, 31, 12, 12, 25, 24, 34, 1, 17, 22, 12, 11, 4, 38, 19, 33, 23, 35, 40, 28, 28, 2, 5}

    Returns: 49924987

  46. {10, 17, 40, 1, 40, 36, 40, 10, 34, 40, 4, 10, 28, 11, 25, 32, 8, 21, 2, 7, 4, 17, 27, 40, 8, 7, 14, 19, 20, 14, 24, 7, 2, 34, 3, 36, 5, 23, 23, 13}

    {37, 33, 16, 29, 31, 32, 35, 32, 41, 18, 12, 21, 24, 7, 39, 38, 15, 24, 25, 1, 8, 13, 32, 17, 34, 40, 8, 41, 37, 32, 26, 30, 23, 9, 26, 16, 32, 6, 32, 22}

    Returns: 57897579

  47. {21, 27, 31, 34, 14, 28, 6, 37, 27, 6, 9, 11, 22, 4, 27, 10, 35, 21, 30, 13, 23, 35, 29, 22, 36, 35, 42, 37, 7, 21, 26, 32, 17, 42, 26, 36, 38, 30, 14, 23, 24}

    {16, 28, 2, 31, 6, 12, 27, 39, 1, 3, 6, 27, 19, 25, 32, 25, 40, 5, 26, 39, 40, 27, 14, 27, 42, 18, 20, 28, 1, 26, 8, 34, 30, 25, 35, 28, 26, 33, 41, 15, 36}

    Returns: 282868056

  48. {25, 5, 29, 26, 8, 12, 10, 2, 21, 11, 8, 42, 28, 10, 23, 29, 36, 7, 2, 22, 38, 35, 13, 42, 18, 29, 28, 32, 19, 33, 11, 41, 32, 19, 26, 9, 32, 28, 6, 38, 6, 41}

    {35, 19, 2, 24, 6, 35, 29, 15, 38, 15, 19, 16, 41, 40, 11, 35, 4, 28, 9, 2, 17, 43, 2, 17, 29, 34, 39, 3, 20, 29, 27, 30, 14, 1, 8, 31, 39, 15, 36, 22, 34, 37}

    Returns: 170555975

  49. {16, 16, 37, 14, 14, 21, 33, 22, 24, 23, 34, 18, 9, 13, 5, 30, 12, 34, 29, 16, 40, 32, 43, 42, 23, 40, 39, 22, 13, 1, 6, 31, 19, 7, 11, 3, 34, 25, 23, 14, 7, 24, 20}

    {38, 15, 40, 3, 41, 34, 4, 34, 34, 29, 44, 27, 43, 10, 44, 26, 39, 28, 7, 37, 2, 44, 42, 8, 42, 17, 34, 37, 29, 15, 14, 22, 18, 32, 29, 35, 18, 37, 36, 13, 4, 30, 24}

    Returns: 292563133

  50. {24, 3, 31, 11, 4, 24, 14, 8, 28, 27, 8, 2, 43, 21, 6, 45, 27, 27, 7, 44, 41, 15, 45, 41, 25, 30, 6, 40, 6, 11, 11, 35, 24, 34, 10, 37, 7, 30, 29, 1, 24, 34, 35, 19}

    {13, 23, 13, 23, 35, 34, 13, 17, 8, 20, 32, 30, 2, 6, 26, 34, 11, 33, 14, 22, 11, 7, 22, 16, 10, 24, 30, 34, 38, 42, 34, 30, 12, 29, 29, 12, 5, 8, 36, 18, 1, 9, 39, 20}

    Returns: 2023834862

  51. {11, 11, 37, 43, 36, 10, 31, 11, 29, 18, 7, 17, 30, 29, 19, 42, 36, 14, 15, 23, 3, 45, 3, 1, 32, 1, 36, 5, 21, 10, 16, 27, 36, 11, 45, 44, 8, 39, 41, 42, 11, 3, 39, 44, 13}

    {37, 29, 33, 28, 26, 9, 46, 41, 40, 15, 11, 24, 2, 38, 4, 17, 35, 11, 25, 22, 36, 34, 31, 46, 44, 12, 17, 36, 29, 41, 46, 30, 11, 28, 5, 37, 3, 20, 15, 22, 6, 30, 17, 4, 37}

    Returns: 3247390452

  52. {17, 22, 32, 39, 14, 7, 41, 28, 26, 40, 39, 35, 19, 8, 46, 10, 15, 41, 15, 28, 26, 23, 4, 47, 45, 33, 28, 30, 18, 46, 13, 45, 25, 12, 16, 30, 47, 19, 20, 2, 38, 19, 39, 19, 26, 5}

    {4, 36, 41, 27, 34, 18, 45, 9, 34, 22, 40, 44, 26, 18, 22, 26, 38, 19, 25, 30, 42, 44, 43, 18, 21, 32, 11, 40, 29, 1, 17, 6, 23, 38, 9, 20, 15, 24, 31, 30, 4, 39, 37, 15, 3, 18}

    Returns: 1306690255

  53. {16, 48, 43, 5, 22, 44, 21, 32, 16, 43, 5, 7, 31, 45, 41, 21, 9, 32, 28, 33, 42, 9, 9, 44, 39, 27, 39, 6, 6, 34, 5, 25, 22, 22, 23, 21, 30, 40, 46, 25, 38, 39, 1, 29, 1, 32, 19}

    {5, 34, 37, 9, 28, 10, 18, 22, 20, 33, 19, 36, 14, 35, 7, 45, 14, 2, 4, 47, 37, 24, 26, 43, 25, 30, 41, 44, 14, 8, 13, 11, 3, 15, 21, 30, 19, 28, 22, 8, 43, 5, 5, 8, 12, 9, 17}

    Returns: 1624095678

  54. {33, 35, 42, 23, 11, 19, 24, 39, 5, 49, 41, 34, 25, 26, 31, 29, 49, 25, 21, 33, 40, 18, 32, 27, 33, 12, 48, 32, 16, 8, 6, 17, 1, 38, 26, 13, 13, 20, 47, 22, 24, 43, 47, 8, 32, 22, 40, 36}

    {3, 4, 36, 37, 40, 8, 2, 24, 35, 14, 44, 24, 34, 33, 48, 24, 34, 22, 30, 34, 10, 37, 36, 12, 4, 35, 22, 23, 44, 10, 27, 22, 46, 44, 10, 22, 9, 27, 15, 1, 44, 14, 46, 30, 28, 45, 7, 24}

    Returns: 1033510347

  55. {19, 15, 14, 23, 27, 8, 46, 31, 3, 12, 21, 6, 33, 41, 10, 41, 29, 44, 5, 34, 35, 31, 22, 35, 38, 22, 7, 15, 41, 45, 24, 28, 34, 4, 20, 22, 43, 25, 30, 8, 5, 24, 14, 18, 37, 11, 13, 22, 35}

    {33, 25, 18, 45, 35, 50, 45, 44, 30, 33, 4, 4, 34, 18, 23, 36, 33, 13, 47, 49, 26, 22, 8, 22, 47, 33, 36, 17, 37, 9, 2, 36, 32, 22, 3, 42, 35, 16, 9, 48, 23, 8, 35, 1, 40, 45, 39, 9, 16}

    Returns: 5404328604

  56. {35, 33, 5, 4, 10, 14, 45, 31, 25, 32, 11, 45, 46, 14, 28, 7, 6, 35, 5, 50, 17, 50, 30, 46, 29, 37, 30, 21, 22, 29, 23, 13, 30, 1, 21, 14, 4, 34, 9, 5, 36, 21, 39, 7, 16, 7, 51, 44, 33, 37}

    {16, 40, 12, 42, 40, 31, 30, 24, 4, 51, 25, 26, 18, 37, 49, 31, 50, 30, 41, 3, 4, 4, 20, 51, 43, 15, 44, 28, 44, 14, 3, 15, 2, 48, 5, 19, 7, 36, 20, 7, 38, 27, 47, 33, 39, 36, 37, 36, 8, 48}

    Returns: 9751544877

  57. {7, 22, 30, 41, 39, 48, 9, 38, 4, 43, 35, 9, 1, 14, 39, 3, 23, 16, 10, 6, 32, 17, 12, 24, 18, 24, 28, 29, 29, 51, 2, 5, 22, 19, 42, 21, 20, 28, 45, 37, 51, 49, 39, 35, 35, 40, 25, 46, 12, 45}

    {35, 31, 9, 47, 16, 25, 47, 24, 14, 44, 5, 21, 9, 45, 13, 43, 46, 27, 44, 12, 5, 47, 15, 50, 29, 27, 44, 21, 11, 22, 46, 23, 46, 33, 3, 12, 27, 25, 33, 9, 26, 31, 5, 28, 36, 29, 45, 8, 5, 34}

    Returns: 4382134804

  58. {37, 36, 30, 51, 10, 13, 35, 3, 29, 22, 48, 40, 43, 50, 29, 43, 17, 42, 9, 39, 46, 37, 40, 36, 12, 7, 13, 24, 1, 37, 12, 31, 41, 35, 49, 11, 50, 17, 16, 21, 45, 25, 48, 51, 48, 1, 26, 19, 2, 48}

    {32, 26, 50, 4, 1, 48, 43, 47, 38, 29, 40, 44, 20, 33, 40, 23, 22, 2, 29, 6, 34, 18, 36, 50, 6, 4, 3, 46, 51, 34, 22, 6, 48, 13, 48, 49, 8, 5, 25, 3, 10, 1, 1, 14, 37, 19, 15, 28, 11, 27}

    Returns: 8637218556

  59. {19, 36, 45, 40, 30, 14, 27, 46, 2, 13, 4, 28, 43, 2, 5, 10, 16, 30, 27, 17, 24, 50, 1, 17, 37, 22, 5, 19, 8, 34, 37, 2, 30, 2, 25, 21, 17, 3, 27, 18, 23, 47, 36, 47, 15, 38, 16, 13, 51, 39}

    {38, 5, 41, 49, 42, 32, 44, 5, 4, 1, 11, 45, 31, 47, 17, 22, 9, 14, 18, 21, 14, 41, 26, 22, 2, 12, 49, 29, 21, 40, 43, 27, 1, 21, 48, 25, 20, 41, 45, 6, 46, 19, 35, 1, 43, 7, 27, 33, 38, 22}

    Returns: 10582000358

  60. {51, 12, 33, 27, 19, 11, 39, 25, 40, 7, 22, 43, 2, 19, 46, 21, 24, 45, 11, 32, 7, 50, 13, 32, 8, 1, 4, 51, 6, 15, 30, 26, 32, 47, 51, 14, 21, 10, 34, 31, 16, 19, 20, 32, 8, 49, 19, 8, 41, 25}

    {5, 24, 48, 6, 41, 47, 47, 28, 26, 29, 39, 46, 6, 50, 10, 48, 25, 16, 42, 18, 41, 38, 28, 3, 2, 25, 44, 19, 35, 32, 14, 37, 36, 32, 25, 7, 32, 4, 23, 41, 43, 49, 14, 34, 17, 10, 47, 47, 9, 40}

    Returns: 7618399589

  61. {51, 12, 18, 10, 6, 51, 4, 8, 3, 13, 20, 45, 19, 28, 5, 11, 30, 23, 31, 50, 30, 3, 28, 47, 44, 14, 15, 37, 28, 43, 41, 10, 48, 15, 39, 39, 49, 17, 15, 12, 13, 16, 22, 16, 27, 33, 25, 36, 10, 24}

    {38, 30, 3, 13, 28, 35, 6, 11, 25, 51, 12, 29, 31, 46, 40, 21, 3, 26, 11, 11, 1, 32, 5, 7, 25, 25, 30, 40, 29, 8, 50, 28, 14, 13, 37, 34, 30, 33, 31, 42, 7, 9, 31, 39, 23, 31, 26, 6, 2, 28}

    Returns: 8351873539

  62. {35, 42, 29, 12, 27, 26, 6, 39, 26, 19, 38, 46, 20, 47, 24, 21, 24, 12, 38, 47, 9, 6, 37, 29, 9, 17, 40, 9, 47, 49, 33, 16, 30, 29, 26, 3, 36, 41, 35, 4, 18, 28, 36, 19, 36, 7, 32, 10, 19, 47}

    {24, 2, 33, 49, 36, 24, 32, 15, 38, 27, 29, 23, 38, 34, 43, 23, 51, 33, 45, 50, 34, 44, 21, 37, 22, 11, 38, 10, 29, 13, 17, 12, 38, 28, 14, 51, 31, 51, 6, 36, 26, 25, 1, 42, 39, 35, 5, 48, 28, 8}

    Returns: 5587593633

  63. {13, 28, 23, 39, 22, 28, 21, 2, 47, 39, 7, 44, 4, 4, 9, 41, 15, 13, 13, 6, 38, 3, 18, 14, 18, 4, 10, 39, 15, 25, 3, 49, 36, 26, 13, 11, 39, 30, 13, 5, 51, 2, 31, 45, 37, 27, 28, 12, 13, 23}

    {24, 33, 16, 3, 4, 39, 43, 29, 1, 20, 51, 23, 40, 46, 34, 13, 17, 39, 48, 12, 49, 30, 21, 35, 51, 50, 13, 19, 34, 4, 34, 9, 12, 21, 1, 15, 42, 32, 8, 1, 3, 4, 23, 44, 51, 48, 2, 2, 14, 10}

    Returns: 42138251037

  64. {16, 30, 1, 23, 35, 13, 23, 48, 23, 44, 13, 31, 2, 13, 2, 17, 17, 45, 31, 5, 28, 32, 34, 15, 31, 43, 22, 25, 4, 25, 23, 41, 49, 19, 11, 32, 13, 14, 9, 26, 41, 8, 41, 7, 41, 12, 12, 11, 38, 37}

    {31, 21, 50, 13, 17, 18, 10, 40, 21, 50, 12, 12, 24, 11, 27, 36, 6, 50, 46, 36, 50, 49, 13, 13, 47, 13, 39, 11, 26, 51, 42, 22, 12, 41, 28, 33, 40, 6, 22, 13, 28, 21, 3, 20, 36, 20, 27, 29, 25, 43}

    Returns: 53228779547

  65. {14, 32, 4, 13, 23, 29, 4, 12, 37, 25, 7, 22, 17, 29, 20, 14, 42, 12, 45, 33, 42, 24, 18, 28, 23, 11, 19, 4, 15, 25, 11, 31, 11, 16, 5, 44, 30, 1, 31, 36, 10, 31, 33, 39, 10, 48, 29, 29, 10, 34}

    {41, 2, 1, 9, 20, 31, 25, 17, 29, 6, 25, 21, 47, 9, 40, 43, 8, 29, 12, 9, 19, 11, 29, 12, 9, 46, 41, 32, 45, 27, 35, 22, 50, 51, 37, 49, 45, 12, 44, 8, 41, 11, 3, 22, 29, 45, 38, 51, 26, 8}

    Returns: 16246658063

  66. {21, 12, 40, 48, 2, 7, 2, 7, 37, 33, 17, 1, 41, 29, 42, 45, 33, 46, 5, 48, 21, 39, 35, 9, 14, 13, 21, 29, 8, 28, 11, 21, 35, 32, 16, 32, 33, 37, 31, 51, 47, 46, 11, 50, 41, 49, 29, 6, 23, 15}

    {10, 16, 20, 19, 47, 6, 36, 28, 3, 31, 29, 21, 18, 4, 7, 46, 25, 49, 48, 50, 7, 13, 26, 50, 23, 48, 30, 46, 22, 12, 38, 29, 33, 2, 43, 22, 27, 33, 19, 13, 48, 31, 46, 24, 7, 34, 44, 40, 47, 31}

    Returns: 14478703472

  67. {16, 46, 40, 49, 44, 32, 29, 1, 45, 20, 50, 25, 36, 15, 4, 37, 1, 10, 34, 35, 40, 2, 45, 50, 13, 6, 42, 17, 24, 22, 14, 48, 49, 17, 25, 12, 32, 26, 39, 14, 30, 4, 11, 27, 51, 41, 23, 47, 33, 5}

    {38, 41, 36, 3, 33, 13, 3, 31, 6, 27, 28, 39, 37, 5, 22, 9, 21, 7, 8, 34, 26, 30, 29, 38, 19, 42, 43, 24, 47, 16, 20, 8, 35, 31, 12, 7, 28, 19, 18, 23, 21, 10, 18, 46, 2, 11, 44, 43, 51, 9}

    Returns: 1327

  68. {10, 10, 10, 13, 10, 42, 9, 50, 10, 36, 5, 10, 10, 49, 28, 10, 47, 10, 10, 29, 10, 10, 21, 10, 10, 48, 10, 24, 33, 10, 39, 10, 10, 45, 40, 11, 44, 51, 30, 10, 10, 32, 46, 10, 41, 37, 22, 10, 10, 16}

    {4, 19, 14, 10, 2, 10, 10, 10, 20, 10, 10, 1, 23, 10, 10, 43, 10, 15, 31, 10, 8, 25, 10, 17, 38, 10, 27, 10, 10, 18, 10, 6, 26, 10, 10, 10, 10, 10, 10, 34, 12, 10, 10, 7, 10, 10, 10, 35, 3, 10}

    Returns: 1125899906842675

  69. {1, 2, 3, 4, 5, 6, 7, 8, 9 }

    {2, 3, 4, 5, 6, 7, 8, 9, 10 }

    Returns: 56

  70. {1 }

    {2 }

    Returns: 4

  71. {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, 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 }

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

    Returns: 1125899906842675

  72. {10, 7, 2, 5, 6, 2, 4, 9, 7 }

    {8, 10, 10, 4, 1, 6, 2, 2, 3 }

    Returns: 144

  73. {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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 32, 14, 15, 16 }

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

    Returns: 356241767399479

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