Statistics

Problem Statement for "ChristmasTreeDecoration"

Problem Statement

Christmas is just around the corner, and Alice just decorated her Christmas tree. There are N stars on the tree. The stars are numbered 1 through N. Additionally, each star has some color. You are given the colors of stars as a int[] col with N elements. For each i, col[i] is the color of star i+1. (Different integers represent different colors.)

Alice has prepared N-1 ribbons and she is now going to attach them to the tree. Each ribbon will connect two of the stars. The ribbons have to be placed in such a way that all stars and ribbons will hold together. (In other words, in the resulting arrangement the stars and ribbons will correspond to vertices and edges of a tree.)

Only some pairs of stars can be connected by a ribbon. You are given a list of all such pairs of stars in two int[]s: x and y. For each valid i, it is possible to add a ribbon that connects the stars with numbers x[i] and y[i].

According to Alice, a ribbon that connects two stars that share the same color is less beautiful than a ribbon that connects two stars with different colors. Therefore, she would like to minimize the number of ribbons that connect two same-colored stars. Compute and return the smallest possible number of such ribbons.

Definition

Class:
ChristmasTreeDecoration
Method:
solve
Parameters:
int[], int[], int[]
Returns:
int
Method signature:
int solve(int[] col, int[] x, int[] y)
(be sure your method is public)

Constraints

  • N will be between 2 and 50, inclusive.
  • The number of elements in col will be N exactly.
  • The number of elements in x will be between 1 and 200, inclusive.
  • The number of elements in y will be the same as the number of elements in x.
  • All elements of x and y will be between 1 and N, inclusive.
  • For each i, the numbers x[i] and y[i] will be different.
  • All unordered pairs (x[i], y[i]) will be distinct.
  • There will be at least one way to choose N-1 ribbons that form a connected graph.

Examples

  1. {1,1,2,2}

    {1,2,3,4}

    {2,3,4,1}

    Returns: 1

    We have four stars. Stars 1 and 2 have the same color, and stars 3 a 4 have the same color. There are four pairs of stars we may connect: 1-2, 2-3, 3-4, and 4-1. One optimal solution is to use the following ribbons: 2-3, 3-4, and 4-1. Two of these are beautiful (2-3 and 4-1) and only one (3-4) is not beautiful.

  2. {1,1,2,2}

    {1,2,3,4,1,2}

    {2,3,4,1,3,4}

    Returns: 0

    Now we can have three beautiful ribbons.

  3. {50,50,50,50}

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

    {2,3,4,4,3,4}

    Returns: 3

    All stars have the same color. Regardless of how we attach the ribbons, none of them will be beautiful.

  4. {1,4,2,3}

    {1,2,3}

    {2,3,4}

    Returns: 0

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

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

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

    Returns: 5

  6. {13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13}

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

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

    Returns: 49

  7. {49,11,11,11,11,49,49,49,11,11,49,49,11,32,11,11,32,11,11,32,11,11,32,49,32,32,32,11,49,49,11,11,11,49,49,49,49,11,32,32,32,49,49,11,49,49,49,32,32,11}

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

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

    Returns: 4

  8. {36,36,49,49,49,49,46,46,49,49,46,50,50,49,50,36,46,36,49,50,46,21,36,21,50,46,50,46,50,49,36,46,36,50,50,46,21,21,21,36,46,50,46,50,46,50,36,36,46,36}

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

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

    Returns: 1

  9. {2,18,37,1,48,15,15,18,1,18,2,3,48,37,48,15,15,15,3,2,3,37,2,37,3,15,18,15,37,37,18,3,48,15,3,37,3,3,3,3,1,3,2,3,18,37,37,2,48,18}

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

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

    Returns: 1

  10. {2,35,1,40,35,13,13,45,35,13,48,40,13,8,45,31,35,40,31,1,2,13,13,48,45,45,1,35,13,48,13,8,35,2,48,2,1,40,2,8,48,2,31,45,1,45,40,35,40,8}

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

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

    Returns: 1

  11. {14,7,35,28,15,49,3,46,8,2,49,42,38,2,28,7,38,15,8,31,48,48,31,12,2,49,48,44,28,12,7,20,49,3,3,3,2,46,19,49,19,46,28,28,3,3,35,7,50,28}

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

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

    Returns: 1

  12. {36,27,1,23,5,14,16,12,16,43,49,12,21,32,37,46,15,32,23,43,17,12,15,4,50,33,23,1,26,45,14,4,43,38,28,31,24,26,50,28,26,34,13,3,22,44,25,34,13,12}

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

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

    Returns: 1

  13. {13,2,13,13,2,2,2,2,2,2,13,13,2,13,13,13,13,13,13,13,13,13,2,13,2,13,13,13,2,2,13,2,2,13,13,13,13,13,13,2,13,13,2,13,2,2,13,13,13,2}

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

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

    Returns: 9

  14. {32,6,32,11,6,6,32,49,32,6,49,6,6,32,6,11,6,11,11,6,49,6,32,11,11,49,11,49,32,11,11,32,49,49,11,49,32,11,32,11,6,6,6,6,11,49,32,32,32,6}

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

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

    Returns: 10

  15. {50,49,30,36,50,50,46,30,50,50,21,30,30,30,30,30,36,36,50,46,49,46,36,30,50,46,49,46,49,49,36,46,49,50,46,30,21,36,21,36,50,21,46,49,50,46,30,30,50,30}

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

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

    Returns: 11

  16. {3,37,27,2,2,27,48,37,48,15,37,15,3,18,18,48,15,15,3,15,2,27,15,48,27,15,2,2,18,2,48,3,15,15,2,27,27,2,15,27,18,1,48,3,27,15,37,48,48,18}

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

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

    Returns: 16

  17. {2,1,40,31,35,8,40,19,2,8,1,8,2,19,2,19,19,8,35,13,48,2,8,13,45,31,48,45,48,2,1,40,48,35,31,13,13,35,13,8,19,1,1,35,2,31,13,8,13,40}

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

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

    Returns: 2

  18. {15,30,20,36,22,19,37,9,20,50,50,44,36,28,22,50,44,36,15,15,20,22,15,9,9,9,30,15,9,44,28,9,22,30,37,12,30,37,15,20,22,19,30,9,15,37,19,20,50,20}

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

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

    Returns: 1

  19. {39,33,36,36,22,38,36,38,33,12,13,38,50,35,23,36,12,2,36,13,1,33,13,36,35,39,38,2,33,23,12,35,36,28,36,28,28,23,22,35,1,2,13,13,23,50,12,50,28,33}

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

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

    Returns: 2

  20. {43,33,36,15,13,20,36,24,18,39,39,45,16,33,45,33,39,15,24,43,24,45,16,29,43,43,20,33,36,27,38,13,15,29,15,36,20,27,33,37,43,33,43,13,7,33,13,43,37,15}

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

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

    Returns: 0

  21. {10,47,18,32,30,35,4,15,10,45,45,41,41,47,12,47,4,9,10,23,18,41,41,30,41,32,45,11,15,11,10,47,11,9,45,24,23,21,35,11,32,21,41,47,23,41,4,12,21,35}

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

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

    Returns: 0

  22. {49,7,8,13,20,38,3,49,13,15,3,38,7,8,14,50,31,7,28,31,8,42,35,2,28,2,50,38,7,31,2,28,44,3,50,13,49,44,7,42,2,46,42,38,49,35,2,28,8,42}

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

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

    Returns: 0

  23. {48,43,5,10,33,48,3,49,3,48,15,43,12,12,14,46,7,10,49,20,46,9,6,48,43,46,12,44,31,14,6,9,33,35,14,12,34,48,10,7,44,7,8,12,14,14,34,35,9,12}

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

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

    Returns: 0

  24. {32,5,23,17,16,32,47,17,10,22,47,22,7,31,2,45,11,21,11,11,5,37,30,37,10,39,45,39,31,7,11,17,35,10,47,32,23,5,32,12,35,13,39,13,45,47,12,12,7,35}

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

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

    Returns: 0

  25. {20,9,42,17,18,49,7,17,13,42,7,10,47,15,11,20,16,48,10,19,16,11,17,3,48,20,20,48,48,6,20,10,49,11,47,32,48,42,16,26,47,42,28,19,18,2,28,28,22,16}

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

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

    Returns: 0

  26. {39,29,26,27,21,23,7,47,46,17,12,28,35,47,22,33,11,34,19,9,9,46,12,4,32,31,39,39,5,32,44,37,12,25,33,1,26,44,23,40,36,27,29,14,29,10,31,19,12,45}

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

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

    Returns: 1

  27. {50,10,1,10,10,10,1,50,2,1,50,2,13,13,10,50,2,13,10,1,50,2,13,13,1,13,13,2,2,50,50,1,50,1,1,2,13,2,2,2}

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

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

    Returns: 2

  28. {22,43,35,31,35,31,31,42,22,35,31,22,43,31,35,43,42,22,22,43,22,43,43,43,31,42,35,22,22,22,43,22,43,35,42,42,42,31,22,42}

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

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

    Returns: 4

  29. {24,6,14,43,6,14,14,24,43,9,43,6,9,6,24,24,6,14,43,14,9,43,14,43,9,14,9,24,43,24,14,14,24,24,14,9,6,6,14,9}

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

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

    Returns: 5

  30. {35,35,26,1,35,26,35,47,1,35,26,35,35,47,1,26,1,47,26,1,47,1,1,47,1,47,47,35,1,1,37,35,37,1,37,47,35,47,1,37}

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

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

    Returns: 9

  31. {25,2,29,25,25,29,29,20,2,20,2,29,29,25,2,20,2,21,25,29,2,21,21,20,25,21,29,21,29,2,25,2,20,25,2,21,25,29,2,2}

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

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

    Returns: 6

  32. {23,23,29,50,23,10,10,20,23,20,20,20,29,20,10,29,29,23,29,10,20,10,29,50,10,23,10,23,10,20,50,50,29,23,29,23,10,10,10,50}

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

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

    Returns: 4

  33. {32,45,32,35,32,32,32,23,32,32,45,35,23,23,22,32,22,22,23,35,35,35,22,22,35,35,35,32,23,35,35,45,23,23,22,35,45,23,22,35}

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

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

    Returns: 4

  34. {12,12,12,26,27,39,12,23,23,26,39,27,12,39,26,23,12,27,12,39,39,26,26,12,12,39,23,26,23,12,39,12,39,39,26,39,27,12,27,12}

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

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

    Returns: 11

  35. {18,23,23,37,30,37,37,18,37,30,30,37,30,46,18,23,18,30,46,30,18,37,37,46,37,18,46,23,23,23,37,37,18,30,23,37,46,18,37,23}

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

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

    Returns: 4

  36. {8,8,24,23,40,8,23,8,23,38,40,38,24,23,8,38,8,23,40,24,24,24,40,40,24,40,40,38,38,23,8,38,38,40,38,40,40,23,8,8}

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

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

    Returns: 1

  37. {2, 3, 4, 1, 1 }

    {1, 1, 1, 2, 2, 3, 4 }

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

    Returns: 1

  38. {1, 2, 3, 3 }

    {1, 2, 3, 3 }

    {2, 3, 1, 4 }

    Returns: 1

  39. {2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2 }

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

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

    Returns: 1

  40. {1, 2, 3, 1 }

    {1, 1, 2, 1 }

    {2, 3, 3, 4 }

    Returns: 1

  41. {2, 3, 4, 3 }

    {1, 1, 2, 4 }

    {2, 3, 3, 2 }

    Returns: 1

  42. {1, 2, 3, 4, 5, 6, 1 }

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

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

    Returns: 1

  43. {1, 3, 2, 2 }

    {1, 1, 2, 3 }

    {2, 3, 3, 4 }

    Returns: 1

  44. {1, 1, 2, 3, 4 }

    {1, 2, 2, 2, 3, 3, 4 }

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

    Returns: 1

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.
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