Statistics

Problem Statement for "AcyclicOrientation"

Problem Statement

You are given a simple undirected graph G on n vertices. The vertices are numbered 0 through n-1. You are given the int n and two int[]s u and v that contain the list of edges. More precisely, for each valid index i the graph contains an edge between the vertices u[i] and v[i].

An orientation of G is a directed graph that can be obtained from G by assigning one of the two possible directions to each edge of G. Let A(G) be the number of orientations of G that are acyclic. Compute and return the value A(G) modulo 6.

Definition

Class:
AcyclicOrientation
Method:
count
Parameters:
int, int[], int[]
Returns:
int
Method signature:
int count(int n, int[] u, int[] v)
(be sure your method is public)

Constraints

  • n will be between 1 and 100, inclusive.
  • u will contain between 0 and 100 elements, inslusive.
  • u and v will contain the same number of elements.
  • Each element of u will be between 0 and n-1, inclusive.
  • Each element of v will be between 0 and n-1, inclusive.
  • G will not contain loops.
  • G will not contain repeated edges.

Examples

  1. 3

    {0, 1, 0}

    {2, 2, 1}

    Returns: 0

    The given graph G is a triangle. A triangle has 8 orientations. Out of these, 2 are directed cycles and 6 are acyclic. The return value is (6 modulo 6) = 0.

  2. 5

    {0, 1, 2, 3}

    {1, 2, 3, 4}

    Returns: 4

    The given graph G is a line. There are 16 orientations, and obviously all 16 are acyclic. The return value is (16 modulo 6) = 4.

  3. 4

    {0, 3}

    {1, 1}

    Returns: 4

  4. 3

    {0, 1, 0}

    {2, 2, 1}

    Returns: 0

  5. 5

    {0, 3, 1, 2}

    {3, 1, 2, 4}

    Returns: 4

  6. 4

    {0, 3}

    {1, 1}

    Returns: 4

  7. 32

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

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

    Returns: 0

  8. 5

    {4, 3, 1, 2, 3}

    {0, 0, 2, 4, 1}

    Returns: 0

  9. 100

    {85, 85, 96, 97, 67, 9, 60, 94, 18, 99, 38, 84, 87, 97, 68, 63, 1, 29, 23, 23, 94, 73, 79, 24, 5, 23, 33, 64, 86, 21, 1, 77, 15, 49, 80, 95, 71, 37, 18, 99, 67, 79, 32, 2, 83, 56, 37, 95, 60, 35, 83, 63, 18, 21, 95, 23, 38, 94, 29, 77, 5, 84, 99, 45, 56, 5, 33, 45, 12, 23, 5, 67, 79, 73, 61, 56, 68, 63, 38, 87, 38, 87, 37, 5, 30, 32, 77, 45, 80, 50, 64, 43, 14, 86, 49, 86, 97, 12, 12, 85}

    {90, 76, 69, 16, 91, 57, 82, 40, 81, 57, 81, 0, 42, 72, 11, 31, 74, 89, 81, 8, 74, 98, 78, 8, 41, 91, 72, 48, 65, 13, 22, 10, 92, 19, 8, 54, 74, 26, 82, 42, 72, 25, 13, 19, 17, 20, 46, 6, 53, 69, 59, 3, 7, 89, 34, 19, 7, 34, 16, 76, 72, 3, 7, 44, 92, 90, 88, 69, 0, 48, 39, 55, 82, 57, 47, 59, 81, 16, 10, 20, 46, 41, 17, 26, 91, 74, 39, 25, 7, 16, 20, 25, 92, 91, 65, 47, 19, 69, 40, 19}

    Returns: 2

  10. 100

    {71, 61, 60, 98, 51, 84, 16, 71, 84, 33, 93, 82, 70, 35, 3, 43, 35, 4, 28, 67, 41, 16, 34, 50, 82, 34, 20, 56, 12, 66, 40, 66, 43, 25, 88, 76, 21, 40, 40, 66, 56, 75, 67, 60, 51, 71, 91, 21, 56, 33, 96, 20, 84, 59, 40, 88, 87, 52, 96, 37, 67, 82, 19, 25, 36, 25, 34, 24, 41, 1}

    {17, 15, 77, 5, 63, 9, 79, 81, 5, 38, 64, 44, 6, 78, 32, 31, 74, 55, 72, 48, 72, 38, 23, 42, 64, 13, 78, 79, 27, 77, 65, 18, 94, 64, 13, 57, 86, 6, 83, 83, 57, 32, 69, 74, 5, 58, 39, 64, 29, 77, 80, 23, 17, 17, 63, 78, 31, 55, 27, 80, 13, 7, 77, 17, 77, 29, 83, 6, 5, 69}

    Returns: 2

  11. 99

    {73, 59, 79, 85, 83, 82, 39, 0, 27, 5, 79, 85, 41, 62, 28, 61, 0, 67, 29, 18, 41, 85, 33, 35, 94, 27, 46, 29, 31, 59, 95, 59, 67, 93, 79, 93, 87, 10, 42, 33, 73, 88, 28, 4, 58, 87, 46, 0, 59, 53, 61, 5, 61, 8, 94, 36, 33, 52, 49, 36, 8, 81, 0, 3, 33, 91, 46, 83, 90, 46}

    {16, 98, 7, 32, 47, 34, 84, 22, 56, 68, 80, 1, 80, 68, 72, 92, 70, 37, 14, 2, 48, 75, 78, 14, 16, 47, 24, 13, 44, 6, 12, 75, 70, 24, 56, 2, 12, 54, 96, 98, 68, 76, 34, 97, 74, 44, 11, 34, 66, 12, 54, 13, 12, 60, 68, 1, 48, 77, 17, 70, 7, 78, 55, 50, 22, 1, 64, 77, 74, 54}

    Returns: 4

  12. 99

    {86, 17, 42, 76, 69, 48, 95, 15, 29, 19, 42, 60, 58, 58, 8, 7, 27, 58, 24, 46, 56, 19, 14}

    {68, 85, 51, 6, 50, 78, 5, 39, 3, 16, 79, 78, 92, 77, 37, 2, 5, 2, 84, 13, 5, 59, 89}

    Returns: 2

  13. 98

    {79, 24, 62, 93, 32, 7, 16, 18, 58, 34, 3, 72, 7, 9, 35, 18, 7, 31, 24, 18, 15, 19, 76, 35, 94, 60, 78, 32, 8, 79, 57, 33, 52, 82, 64, 44, 76, 1, 24, 50, 1, 72, 9, 8}

    {4, 23, 2, 42, 61, 26, 48, 26, 85, 29, 29, 55, 89, 68, 59, 43, 47, 20, 81, 4, 20, 11, 91, 89, 92, 66, 14, 67, 14, 27, 11, 26, 67, 56, 26, 22, 26, 87, 17, 30, 45, 30, 48, 55}

    Returns: 4

  14. 22

    {19, 19, 2, 19, 6, 2, 16, 14, 19, 19, 2, 20, 14, 19, 8, 5, 16, 8, 5, 2, 14, 8, 20, 8, 16, 2, 20, 8, 16, 16, 8, 6, 8, 16, 20, 19, 20, 19, 20, 19, 6, 8, 2, 8, 14, 6, 6, 6, 2, 19, 19, 20, 8, 5, 16, 2, 5, 20, 2, 6, 8, 2, 6, 20, 5, 16, 8, 6, 5, 5, 19, 14, 14, 6, 2, 14, 20, 6, 20, 5, 5, 5, 16, 6, 2, 14, 19, 14, 16, 20, 2, 5, 16, 5, 20, 8, 14, 16, 14, 8}

    {1, 18, 9, 11, 7, 12, 12, 4, 13, 21, 1, 12, 11, 3, 18, 3, 7, 15, 12, 0, 21, 0, 15, 4, 18, 3, 1, 21, 3, 0, 9, 10, 7, 17, 9, 15, 18, 7, 4, 4, 11, 3, 21, 12, 10, 1, 9, 0, 11, 17, 0, 7, 10, 0, 21, 15, 21, 17, 7, 15, 11, 18, 17, 10, 18, 9, 1, 21, 1, 11, 12, 18, 13, 3, 10, 1, 11, 18, 3, 4, 13, 9, 13, 4, 17, 7, 9, 17, 10, 13, 4, 10, 11, 17, 21, 17, 15, 4, 0, 13}

    Returns: 2

  15. 23

    {13, 17, 7, 22, 8, 16, 5, 9, 1, 22, 5, 2, 5, 20, 5, 14, 6, 6, 22, 7, 22, 20, 9, 17, 8, 10, 17, 6, 8, 17, 10, 7, 20, 14, 22, 2, 5, 6, 5, 14, 2, 16, 8, 22, 8, 16, 2, 9, 20, 13, 6, 20, 6, 17, 14, 6, 13, 20, 22, 5, 1, 2, 1, 14, 17, 7, 16, 10, 14, 2, 20, 16, 6, 13, 10, 13, 2, 8, 1, 1, 13, 7, 7, 22, 6, 7, 14, 9, 2, 9, 10, 20, 8, 1, 16, 22, 20}

    {11, 11, 19, 0, 0, 21, 18, 0, 3, 21, 3, 15, 0, 3, 4, 11, 3, 19, 19, 18, 18, 18, 12, 18, 12, 3, 19, 11, 3, 15, 4, 3, 15, 3, 12, 4, 15, 4, 19, 0, 18, 0, 11, 11, 19, 3, 19, 18, 4, 19, 15, 11, 12, 12, 12, 0, 21, 21, 15, 12, 19, 21, 12, 18, 3, 11, 11, 18, 19, 0, 19, 18, 21, 12, 11, 4, 3, 18, 11, 4, 18, 4, 15, 3, 18, 0, 21, 3, 12, 11, 0, 0, 21, 18, 12, 4, 12}

    Returns: 4

  16. 17

    {0, 2, 2, 2, 6, 6, 9, 4, 11, 3, 3, 9, 4, 4, 3, 0, 3, 4, 6, 0, 2, 6, 9, 6, 11, 4, 0, 0, 4, 3, 4, 2, 6, 9, 3, 11, 11, 2, 11, 3, 3, 6, 6, 0, 9, 3, 0, 9, 2, 9}

    {14, 1, 14, 16, 14, 16, 15, 7, 10, 8, 5, 16, 15, 13, 1, 13, 12, 10, 10, 1, 15, 12, 1, 13, 5, 1, 7, 12, 14, 15, 16, 8, 5, 14, 16, 14, 13, 10, 16, 13, 14, 7, 8, 8, 8, 10, 15, 12, 5, 13}

    Returns: 4

  17. 100

    {5, 39, 90, 62, 52, 6, 2, 6, 86, 9, 45, 24, 37, 47, 5, 90, 92, 19, 47, 6, 10, 65, 99, 49, 20, 19, 38, 87, 86, 74}

    {28, 29, 82, 79, 82, 67, 13, 14, 32, 73, 69, 33, 51, 75, 4, 34, 43, 26, 71, 28, 1, 36, 40, 4, 60, 43, 75, 12, 60, 27}

    Returns: 4

  18. 30

    {11, 11, 25, 25, 11, 19, 12, 27, 11, 12, 29, 1, 0, 26, 26, 0, 27, 2, 25, 2, 12, 29, 2, 0, 9, 24, 2, 12, 26, 19, 9, 3, 5, 3, 19, 24, 11, 29, 9, 20, 29, 9, 3, 5, 11, 26, 26, 19, 5, 1, 21, 24, 3, 21, 9, 19, 1, 9, 27, 1, 24, 25, 12, 1, 9, 24, 20, 29, 24, 27, 26, 2, 12, 5, 9, 2, 26, 21, 0, 9, 0, 11, 5, 5, 20, 11, 25, 20, 24, 27, 3, 5, 9, 0, 12, 29, 20, 21, 26, 0}

    {17, 23, 17, 4, 22, 6, 14, 4, 7, 16, 22, 28, 14, 4, 13, 22, 6, 28, 28, 16, 22, 16, 7, 6, 7, 28, 6, 4, 18, 15, 22, 15, 4, 4, 4, 16, 6, 28, 23, 22, 7, 13, 17, 6, 18, 7, 17, 17, 18, 7, 6, 6, 6, 22, 28, 18, 17, 6, 28, 13, 8, 14, 10, 8, 17, 7, 7, 17, 23, 23, 8, 22, 28, 13, 14, 15, 10, 13, 16, 4, 13, 14, 16, 22, 17, 13, 16, 18, 15, 14, 7, 10, 18, 28, 17, 8, 15, 15, 28, 8}

    Returns: 2

  19. 10

    {0, 9, 6, 6, 9, 4, 4, 8}

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

    Returns: 4

  20. 100

    {54, 14, 89, 12, 62, 82, 20, 96, 18, 7, 42, 93, 91, 50, 5, 63, 57, 22, 3, 8, 13, 90, 21, 67, 36, 81, 13, 31, 35, 80, 52, 45, 70, 19, 71, 97, 69, 87, 73, 98, 39, 20, 16, 11, 26, 10, 57, 93, 99, 35, 94, 32, 14, 84, 64, 40, 47, 26, 66, 97, 55, 48, 85, 79, 27, 88, 3, 66, 60, 99, 76, 5, 17, 63, 52, 37, 58, 1, 87, 96, 1, 50, 41, 41, 48, 90, 31, 43, 0, 34, 30, 85, 44, 12, 53, 92, 83, 19, 6, 69}

    {74, 86, 34, 92, 51, 46, 78, 6, 74, 24, 86, 43, 8, 53, 33, 94, 30, 11, 49, 32, 29, 72, 76, 75, 23, 4, 9, 91, 0, 47, 49, 70, 25, 80, 38, 38, 56, 82, 68, 2, 40, 54, 28, 60, 68, 7, 83, 33, 65, 58, 78, 98, 77, 18, 55, 44, 25, 21, 46, 51, 61, 2, 4, 71, 61, 77, 79, 10, 24, 45, 15, 56, 95, 28, 37, 23, 42, 17, 9, 59, 62, 88, 36, 59, 81, 67, 73, 15, 89, 64, 95, 27, 65, 75, 84, 16, 39, 72, 29, 22}

    Returns: 2

  21. 99

    {48, 73, 76, 38, 5, 44, 25, 33, 12, 75, 98, 56, 35, 33, 62, 45, 80, 66, 61, 24, 21, 42, 53, 16, 83, 47, 48, 74, 63, 81, 68, 35, 92, 47, 17, 61, 27, 57, 23, 44, 9, 0, 52, 78, 82, 86, 24, 55, 95, 53, 21, 32, 41, 83, 59, 42, 3, 97, 1, 13, 34, 34, 8, 94, 7, 77, 6, 65, 79, 85, 87, 2, 89, 36, 54, 71, 68, 69, 49, 71, 88, 40, 97, 74, 19, 39, 43, 39, 41, 31, 19, 54, 84, 8, 2, 81, 89, 62, 87}

    {93, 15, 63, 45, 14, 40, 9, 80, 60, 52, 86, 90, 64, 32, 96, 66, 94, 51, 43, 30, 23, 58, 29, 57, 12, 11, 26, 75, 64, 98, 18, 59, 25, 76, 69, 58, 93, 31, 46, 96, 0, 20, 67, 72, 37, 50, 92, 79, 13, 7, 60, 49, 28, 95, 82, 50, 6, 37, 91, 51, 27, 5, 72, 67, 78, 46, 16, 11, 88, 20, 65, 22, 3, 15, 36, 18, 56, 4, 29, 70, 38, 1, 77, 90, 17, 84, 28, 10, 73, 85, 55, 14, 70, 91, 10, 30, 4, 26, 22}

    Returns: 0

  22. 98

    {66, 8, 75, 41, 31, 94, 7, 90, 26, 19, 31, 33, 43, 45, 48, 49, 89, 70, 17, 56, 46, 83, 32, 58, 92, 78, 78, 82, 95, 56, 2, 32, 77, 11, 28, 84, 57, 9, 52, 22, 76, 12, 80, 59, 51, 73, 14, 7, 42, 34, 30, 51, 30, 90, 42, 73, 35, 77, 54, 66, 41, 61, 10, 10, 47, 21, 33, 24, 93, 72, 97, 67, 28, 16, 85, 23, 44, 1, 35, 55, 55, 18, 0, 87, 64, 37, 3, 61, 67, 38, 64, 54, 97, 69, 29, 75, 63, 95}

    {12, 18, 25, 53, 39, 52, 74, 76, 15, 96, 43, 34, 9, 1, 5, 79, 81, 83, 72, 49, 14, 4, 40, 22, 58, 93, 40, 91, 27, 36, 3, 62, 86, 96, 70, 88, 92, 48, 65, 36, 46, 15, 19, 23, 37, 4, 86, 57, 60, 65, 44, 91, 20, 69, 59, 88, 68, 68, 50, 53, 45, 38, 89, 63, 24, 80, 62, 82, 2, 94, 16, 6, 85, 8, 11, 21, 60, 17, 29, 79, 27, 6, 26, 20, 84, 71, 74, 50, 25, 71, 47, 0, 81, 87, 13, 5, 13, 39}

    Returns: 2

  23. 97

    {36, 92, 49, 20, 40, 84, 77, 42, 90, 18, 30, 2, 19, 73, 32, 62, 68, 28, 12, 31, 35, 42, 5, 93, 83, 68, 52, 9, 67, 72, 37, 4, 41, 35, 23, 79, 12, 94, 24, 14, 59, 26, 92, 24, 85, 46, 33, 9, 4, 59, 58, 26, 11, 51, 51, 14, 47, 89, 95, 38, 55, 5, 34, 13, 17, 19, 53, 61, 23, 74, 53, 87, 50, 29, 11, 65, 13, 40, 78, 78, 76, 64, 60, 17, 86, 0, 10, 75, 18, 7, 48, 86, 15, 6, 50, 36, 66}

    {6, 31, 82, 7, 28, 96, 80, 55, 71, 1, 54, 63, 1, 25, 71, 20, 47, 57, 33, 16, 74, 43, 56, 73, 3, 89, 94, 46, 3, 70, 90, 77, 84, 66, 44, 25, 37, 88, 82, 41, 32, 54, 85, 72, 0, 38, 52, 43, 21, 10, 44, 8, 65, 95, 81, 69, 27, 69, 45, 61, 45, 30, 22, 15, 64, 75, 29, 88, 27, 56, 16, 58, 39, 76, 21, 22, 96, 39, 80, 79, 2, 57, 83, 63, 67, 91, 62, 49, 93, 87, 8, 91, 60, 81, 34, 48, 70}

    Returns: 0

  24. 96

    {88, 24, 10, 45, 72, 60, 31, 66, 29, 44, 60, 56, 43, 53, 67, 26, 68, 39, 34, 22, 14, 49, 47, 13, 94, 88, 95, 20, 30, 32, 9, 50, 32, 71, 45, 8, 38, 58, 81, 89, 12, 55, 53, 25, 18, 74, 5, 75, 5, 92, 16, 50, 17, 91, 93, 63, 82, 15, 24, 72, 79, 73, 77, 41, 33, 85, 37, 58, 44, 54, 15, 23, 65, 55, 13, 85, 42, 35, 52, 43, 80, 82, 7, 12, 67, 30, 16, 80, 35, 77, 62, 62, 21, 40, 52, 57}

    {26, 1, 66, 78, 23, 11, 48, 0, 54, 36, 93, 57, 17, 10, 29, 42, 61, 31, 69, 20, 90, 81, 14, 79, 84, 71, 25, 83, 3, 64, 76, 94, 61, 0, 22, 19, 39, 51, 9, 69, 28, 86, 92, 59, 27, 68, 11, 36, 33, 64, 56, 40, 2, 89, 7, 86, 4, 87, 46, 65, 21, 18, 28, 2, 51, 38, 70, 78, 41, 75, 6, 90, 70, 74, 1, 84, 48, 95, 63, 6, 19, 46, 34, 4, 91, 47, 59, 73, 8, 76, 37, 87, 83, 3, 27, 49}

    Returns: 2

  25. 95

    {61, 12, 78, 7, 15, 90, 53, 61, 57, 51, 10, 33, 44, 94, 73, 28, 23, 52, 3, 17, 57, 41, 4, 6, 48, 86, 54, 13, 7, 63, 46, 60, 42, 77, 20, 10, 86, 91, 38, 63, 14, 33, 43, 74, 31, 27, 15, 76, 9, 67, 73, 5, 45, 83, 72, 30, 70, 59, 85, 34, 28, 1, 35, 0, 9, 11, 39, 38, 35, 50, 67, 50, 56, 80, 83, 26, 25, 60, 89, 74, 40, 23, 8, 17, 64, 2, 0, 62, 18, 2, 59, 51, 64, 32, 24}

    {84, 68, 47, 34, 79, 47, 30, 75, 92, 66, 71, 5, 75, 70, 58, 37, 3, 41, 22, 18, 79, 66, 49, 68, 62, 72, 39, 4, 65, 21, 11, 25, 24, 89, 36, 88, 54, 65, 82, 44, 20, 81, 92, 31, 29, 14, 26, 46, 32, 55, 93, 90, 93, 91, 37, 1, 48, 22, 42, 77, 29, 52, 69, 82, 87, 16, 88, 53, 6, 85, 19, 8, 45, 40, 13, 87, 58, 19, 94, 27, 56, 76, 43, 55, 21, 69, 36, 80, 81, 16, 49, 12, 71, 78, 84}

    Returns: 0

  26. 94

    {54, 82, 68, 5, 6, 77, 2, 11, 73, 55, 13, 11, 74, 61, 31, 79, 18, 34, 10, 40, 2, 19, 24, 89, 60, 90, 4, 27, 39, 1, 12, 42, 93, 38, 43, 88, 53, 28, 0, 51, 17, 70, 90, 80, 58, 9, 52, 26, 78, 46, 64, 59, 31, 89, 16, 4, 21, 19, 7, 72, 91, 35, 30, 23, 71, 39, 81, 57, 5, 48, 59, 17, 49, 69, 28, 49, 15, 25, 36, 15, 76, 20, 72, 25, 45, 52, 65, 36, 34, 53, 87, 83, 84, 67}

    {73, 67, 30, 65, 93, 8, 63, 85, 80, 47, 29, 58, 79, 82, 8, 85, 0, 57, 60, 32, 56, 91, 7, 22, 50, 26, 33, 3, 87, 66, 62, 45, 92, 9, 54, 64, 20, 37, 42, 55, 61, 68, 84, 81, 14, 10, 38, 69, 40, 77, 75, 56, 44, 75, 43, 16, 70, 23, 71, 83, 44, 22, 41, 78, 12, 13, 66, 21, 18, 46, 76, 32, 62, 51, 74, 33, 48, 47, 3, 29, 24, 37, 50, 86, 1, 63, 14, 41, 6, 88, 27, 86, 92, 35}

    Returns: 2

  27. 100

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

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

    Returns: 2

  28. 99

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

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

    Returns: 4

  29. 98

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

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

    Returns: 2

  30. 97

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

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

    Returns: 4

  31. 96

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

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

    Returns: 2

  32. 95

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

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

    Returns: 4

  33. 100

    {81, 80, 36, 77, 63, 7, 88, 86, 65, 14, 99, 91, 20, 19, 12, 40, 40, 15, 86, 2, 79, 99, 69, 71, 37, 44, 70, 75, 80, 58, 38, 91, 48, 52, 58, 73, 91, 41, 43, 81, 6, 11, 2, 36, 45, 83, 97, 20, 62, 61, 63, 29, 57, 32, 7, 64, 4, 43, 84, 67, 99, 8, 77, 38, 76, 68, 54, 86, 36, 84, 59, 4, 39, 41, 51, 42, 15, 63, 34, 45, 48, 48, 9, 4, 52, 90, 73, 86, 16, 47, 39, 47, 8, 67, 81, 25, 94, 26, 56, 2}

    {50, 13, 16, 91, 14, 85, 7, 76, 9, 11, 24, 46, 77, 62, 48, 35, 78, 86, 68, 75, 59, 48, 58, 7, 70, 96, 13, 53, 3, 45, 28, 2, 21, 98, 51, 30, 42, 22, 8, 46, 39, 8, 54, 84, 21, 51, 40, 76, 16, 90, 42, 12, 18, 56, 13, 84, 67, 0, 50, 6, 46, 48, 78, 86, 66, 61, 23, 41, 72, 80, 25, 37, 83, 46, 89, 83, 74, 44, 37, 47, 26, 87, 48, 6, 2, 24, 33, 82, 49, 60, 92, 59, 49, 88, 62, 39, 49, 52, 30, 63}

    Returns: 0

  34. 100

    {93, 22, 21, 64, 47, 14, 31, 37, 5, 94, 72, 47, 26, 9, 19, 17, 33, 35, 85, 62, 1, 70, 28, 96, 49, 76, 64, 68, 47, 59}

    {87, 59, 36, 36, 60, 15, 39, 26, 1, 24, 53, 46, 92, 51, 51, 61, 45, 21, 26, 90, 63, 55, 72, 32, 84, 80, 12, 37, 2, 1}

    Returns: 4

  35. 100

    {71, 4, 32, 93, 6, 14, 32, 31, 53, 89, 80, 35, 98, 29, 64, 31, 30, 30, 53, 15}

    {9, 90, 51, 92, 54, 51, 38, 17, 49, 42, 89, 10, 87, 34, 29, 35, 72, 74, 91, 27}

    Returns: 4

  36. 100

    {56, 94, 39, 34, 64, 3, 33, 37, 1, 92}

    {23, 34, 59, 57, 36, 94, 45, 7, 5, 52}

    Returns: 4

  37. 99

    {67, 52, 29, 39, 51, 89, 3, 83, 68, 50}

    {14, 69, 69, 80, 26, 75, 36, 47, 49, 3}

    Returns: 4

  38. 44

    {14, 4, 25, 12, 43, 28, 3, 14, 33, 40, 2, 36, 10, 4, 28, 15, 21, 14, 25, 3, 9, 37, 39, 43, 29, 5, 7, 6, 4, 24, 9, 22, 42, 5, 17, 1, 26, 1, 32, 15, 22, 34, 34, 43, 17, 32, 18, 7, 36, 19}

    {18, 13, 33, 14, 40, 20, 33, 30, 10, 23, 34, 19, 20, 11, 36, 4, 16, 17, 5, 25, 31, 42, 13, 21, 6, 3, 24, 5, 33, 37, 38, 11, 35, 33, 39, 4, 12, 35, 42, 0, 23, 24, 35, 8, 35, 38, 1, 6, 30, 22}

    Returns: 0

  39. 35

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

    {25, 23, 16, 30, 17, 22, 30, 14, 11, 11, 3, 29, 28, 26, 1, 6, 24, 11, 24, 4, 10, 3, 23, 28, 30, 23, 2, 16, 29, 20, 23, 30, 6, 17, 4, 26, 19, 32, 13, 21, 13, 19, 13, 20, 19, 6, 27, 21, 5, 18, 11, 3, 25, 14, 5, 16, 20, 31, 17, 23, 34, 6, 7, 34, 22, 21, 16, 3, 4, 11}

    Returns: 0

  40. 10

    {}

    {}

    Returns: 1

  41. 17

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

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

    Returns: 0

  42. 17

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

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

    Returns: 0

  43. 100

    {}

    {}

    Returns: 1

  44. 10

    {0, 6, 1, 6, 0, 4, 0, 8, 0, 6}

    {8, 5, 3, 7, 2, 2, 9, 3, 3, 8}

    Returns: 0

  45. 2

    {1}

    {0}

    Returns: 2

  46. 3

    {2, 0}

    {1, 2}

    Returns: 4

  47. 4

    {0, 2, 1, 2}

    {1, 0, 2, 3}

    Returns: 0

  48. 4

    {0, 1, 3, 3, 1, 2}

    {2, 3, 0, 2, 0, 1}

    Returns: 0

  49. 8

    {0, 1, 1, 5, 6, 1, 0, 7}

    {6, 4, 0, 4, 5, 7, 4, 5}

    Returns: 0

  50. 8

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

    {1, 2, 4, 0, 3, 7, 3, 6, 2, 7, 1, 1, 3, 0, 4, 3}

    Returns: 0

  51. 1

    { }

    { }

    Returns: 1

  52. 31

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

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

    Returns: 0

  53. 7

    { }

    { }

    Returns: 1

  54. 4

    {0, 1, 2, 3 }

    {1, 2, 3, 0 }

    Returns: 2

  55. 5

    {0, 1, 2, 3, 4 }

    {1, 2, 3, 4, 0 }

    Returns: 0

  56. 4

    {0, 2 }

    {1, 3 }

    Returns: 4

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