Statistics

Problem Statement for "PigeonholeNim"

Problem Statement

We have a wooden cabinet. The whole cabinet is divided into pigeonholes: a vertical grid of R rows times C columns of rectangular spaces that can contain objects.


Each pigeonhole contains some nonnegative number of tokens.

If a pigeonhole is empty, all pigeonholes that are higher in the same column are also empty.

You are given the numbers of tokens in the int[] piles. The pile sizes are given in column-major order: first the leftmost column from top to bottom, then the next column from top to bottom, and so on.

Formally, if we number the rows 0 to R-1 top to bottom and the columns 0 to C-1 left to right, the number of tokens in cell (row r, column c) is piles[ R*c + r ].


We are going to play a version of the game of NIM with these pigeonholes. The rules are as follows:

  • This is a two-player game. The players take alternating turns.
  • Valid numbers are positive integers that do not contain the digits 4 and 7. (Some valid numbers are 1, 2, 3, 5, 6, 13, 290016, and so on. The numbers 0, 4, 7, 100402 and 2007407 are not valid.)
  • A valid move consists of selecting a non-empty column and making one of two things:
    1. You may remove a valid number of tokens from the topmost non-empty pigeonhole in the chosen column.
    2. If a move of the first type would clear a pigeonhole completely and the column is not empty yet, you may also remove exactly one token from the pigeonhole immediately below the one you just cleared.

Note that you cannot remove tokens from more than two pigeonholes in the same turn. For example, suppose there is a column with three pigeonholes, containing 5, 1 and 7 tokens from top to bottom. If we select this column, we have the following ways to make a move:

  • We may remove 1, 2, 3, or 5 tokens from the top pigeonhole.
  • We may remove 5 tokens from the top and 1 from the middle pigeonhole.

Note that removing 5 from the top, 1 from the middle and also 1 from the bottom is not a valid move: even if we clear the second pigeonhole along with the first, that's all we are allowed to do.


The game ends as soon as any one column becomes empty, even if there are still tokens in other columns.

There are two ways in which the winner can be determined:

  • If emptyWins = 1, whoever created the empty column wins.
  • If emptyWins = 0, whoever created (or, most likely and more precisely, whoever was forced to create) the empty column loses.

You are given the initial position of the game, as described above, and the value of emptyWins. It's your turn. Return the number of distinct winning moves you have in the given position.

Definition

Class:
PigeonholeNim
Method:
countWinningMoves
Parameters:
int, int, int[], int
Returns:
int
Method signature:
int countWinningMoves(int R, int C, int[] piles, int emptyWins)
(be sure your method is public)

Notes

  • We are using the standard meaning of "winning moves": A move is a winning move if after making the move you will have a strategy that guarantees that you can win the game regardless of how your opponent plays.
  • Two moves are distinct if they affect different columns, and also if they affect the same column and leave it in a different state.

Constraints

  • R will be between 1 and 20, inclusive.
  • C will be between 1 and 20, inclusive.
  • piles will have R*C elements.
  • Each element of piles will be between 0 and 200, inclusive.
  • Each column in the grid of pigeonholes will be non-empty.
  • In each column, if a pigeonhole is empty, all pigeonholes that are higher in the same column are also empty.
  • emptyWins will be either 0 or 1.

Examples

  1. 1

    1

    {9}

    1

    Returns: 2

    We can win simply by taking all 9 tokens from the only pigeonhole, as this creates an empty column. We can also win by taking 5 tokens. This leaves our opponent with 4 tokens, and they cannot take all of them. After their move we can take the rest.

  2. 1

    1

    {17}

    0

    Returns: 2

    Here we want to force our opponent to clear the only column. The most straightforward way of doing so is by taking 16 tokens, but we can also take just 12, leaving the opponent with 5 tokens.

  3. 4

    1

    {121, 1, 1, 123}

    1

    Returns: 2

    There is one column: +------+ | 121 | +------+ | 1 | +------+ | 1 | +------+ | 123 | +------+ Making a move of the second type wins us the game. (We take the 121+1 tokens from the top two pigeonholes. Our opponent can then either just take 1 token from the third pigeonhole, or 1+1 from the fourth. In either case, we can take all that remains in our next turn.) Perhaps surprisingly, taking 80 tokens from the top pile is also a winning move.

  4. 2

    4

    {2, 19, 2, 191, 2, 111, 2, 33}

    1

    Returns: 0

    This is a losing position. If our opponent is smart, we will eventually be forced to clear a cell in the topmost row, and once that happens, our opponent will clear the rest of the column. (Note that we cannot save ourselves by doing a move of the second type.)

  5. 2

    4

    {2, 19, 2, 5, 2, 111, 2, 33}

    1

    Returns: 1

    This seems to be a similar situation to the one in the previous example. However, now the bottom pigeonhole in the second column only contains 5 tokens. This changes the game quite significantly. There is exactly one winning move: to remove one token from the top pigeonhole in that column (turning it from {2,5} to {1,5} ). In this situation, there are exactly four independent moves that don't immediately lose the game: removing one token from one of the other columns, or removing 1+1 tokens from column 2 (leaving four tokens in the bottom pigeonhole). Our opponent will play the first of these moves, we play the second, they play the third, we play the fourth. (The order does not matter. If they do anything else, they lose.) Now we have columns {1, 19}, {0, 4}, {1, 111}, and {1, 33}. Regardless of what our opponent does next, we can win in our next turn.

  6. 3

    3

    {1, 1, 1, 1, 1, 1, 1, 1, 1}

    0

    Returns: 3

    Nobody wants to be the one who empties a column and loses. The three winning moves we have in this position are as follows: choose any column and remove 1+1 tokens from it.

  7. 5

    3

    {0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1}

    0

    Returns: 3

    The same example as the previous one but now with two empty pigeonholes on the top of each column. These don't change anything, the three winning moves remain the same.

  8. 20

    20

    {94, 94, 98, 93, 100, 98, 99, 96, 93, 91, 94, 90, 100, 98, 98, 95, 93, 94, 97, 97, 98, 96, 91, 94, 95, 94, 94, 99, 94, 99, 90, 91, 95, 94, 93, 90, 93, 95, 94, 92, 99, 90, 97, 94, 92, 98, 95, 99, 93, 97, 92, 95, 92, 96, 100, 92, 93, 93, 93, 93, 93, 96, 92, 92, 97, 92, 97, 96, 95, 100, 90, 92, 96, 95, 94, 94, 93, 97, 93, 93, 91, 97, 96, 97, 91, 90, 95, 93, 98, 91, 94, 91, 94, 97, 95, 90, 98, 97, 98, 98, 100, 94, 90, 92, 100, 98, 95, 99, 96, 94, 97, 95, 95, 96, 90, 90, 93, 92, 91, 96, 100, 98, 98, 90, 93, 91, 96, 90, 94, 98, 92, 98, 94, 95, 93, 91, 99, 99, 94, 94, 95, 96, 93, 96, 93, 92, 96, 96, 91, 100, 94, 97, 92, 91, 92, 91, 97, 90, 92, 98, 99, 100, 93, 96, 95, 97, 93, 92, 98, 98, 98, 100, 98, 91, 96, 92, 96, 96, 91, 90, 98, 92, 100, 92, 94, 98, 97, 94, 98, 94, 91, 100, 90, 99, 92, 94, 94, 94, 97, 90, 97, 93, 100, 97, 98, 99, 95, 99, 91, 99, 94, 98, 94, 92, 95, 99, 96, 97, 98, 93, 91, 98, 97, 99, 90, 98, 92, 100, 98, 95, 99, 99, 90, 97, 92, 96, 90, 93, 92, 96, 98, 96, 95, 92, 92, 90, 90, 90, 93, 90, 100, 94, 91, 96, 92, 93, 96, 97, 99, 92, 93, 93, 97, 91, 100, 96, 90, 95, 96, 93, 99, 95, 92, 95, 92, 92, 93, 90, 98, 98, 95, 100, 93, 94, 95, 96, 99, 99, 93, 100, 90, 93, 99, 98, 100, 94, 97, 91, 93, 94, 91, 96, 98, 95, 91, 92, 94, 100, 97, 92, 93, 100, 100, 96, 98, 96, 93, 95, 92, 100, 96, 96, 98, 97, 92, 94, 92, 93, 92, 96, 91, 93, 93, 90, 90, 96, 96, 96, 90, 96, 94, 92, 94, 94, 96, 91, 91, 100, 98, 95, 100, 91, 91, 97, 92, 97, 92, 95, 94, 91, 91, 99, 99, 98, 94, 100, 90, 96, 92, 94, 99, 94, 98, 98, 94, 93, 97, 95, 91, 96, 90, 96, 96, 92, 94, 95, 97, 99, 96, 99, 96, 97, 98, 90, 96, 94, 96, 91, 97, 92}

    1

    Returns: 14

  9. 20

    20

    {182, 184, 184, 185, 200, 194, 187, 195, 194, 188, 183, 181, 191, 185, 198, 184, 183, 198, 194, 184, 189, 194, 186, 191, 196, 192, 195, 187, 190, 195, 199, 196, 183, 182, 189, 191, 200, 193, 180, 198, 197, 189, 192, 188, 196, 200, 183, 190, 187, 183, 184, 188, 195, 184, 180, 188, 180, 186, 200, 187, 196, 185, 186, 188, 192, 194, 190, 192, 189, 187, 184, 184, 183, 190, 194, 181, 187, 194, 200, 197, 182, 188, 192, 198, 187, 193, 200, 194, 188, 196, 183, 192, 196, 183, 191, 197, 192, 190, 180, 196, 199, 183, 193, 193, 181, 194, 190, 182, 198, 183, 199, 189, 188, 189, 199, 183, 182, 193, 183, 185, 189, 191, 191, 182, 199, 196, 180, 190, 196, 200, 192, 180, 194, 200, 197, 184, 187, 200, 187, 182, 198, 191, 187, 185, 194, 183, 186, 185, 186, 198, 182, 184, 185, 188, 194, 192, 200, 183, 189, 186, 188, 183, 187, 193, 185, 200, 189, 200, 183, 193, 187, 180, 198, 200, 197, 187, 197, 193, 190, 192, 184, 184, 180, 198, 185, 195, 182, 182, 200, 191, 180, 183, 200, 187, 183, 197, 180, 188, 190, 189, 199, 190, 182, 186, 185, 183, 188, 184, 192, 200, 182, 187, 197, 192, 186, 180, 187, 194, 180, 183, 194, 197, 200, 181, 192, 200, 186, 200, 196, 185, 186, 198, 195, 198, 182, 196, 197, 189, 184, 191, 180, 197, 185, 180, 185, 186, 190, 193, 186, 194, 185, 199, 184, 181, 181, 198, 187, 199, 197, 200, 187, 200, 199, 195, 184, 198, 195, 196, 188, 181, 187, 190, 186, 180, 195, 192, 197, 194, 185, 180, 194, 198, 194, 193, 200, 197, 190, 200, 191, 186, 183, 188, 194, 188, 198, 199, 194, 190, 188, 185, 198, 198, 199, 192, 193, 186, 180, 180, 191, 194, 196, 195, 200, 184, 180, 200, 180, 182, 196, 190, 181, 200, 190, 195, 181, 200, 184, 189, 194, 180, 191, 196, 182, 200, 191, 198, 194, 191, 198, 193, 193, 180, 181, 181, 187, 183, 187, 183, 180, 195, 199, 186, 192, 194, 200, 190, 192, 183, 194, 194, 194, 182, 185, 185, 182, 186, 191, 193, 187, 191, 183, 199, 198, 191, 192, 185, 189, 190, 181, 191, 192, 180, 183, 194, 197, 191, 184, 183, 189, 181, 181, 185, 186, 198, 180, 200, 191, 198, 189, 198}

    1

    Returns: 31

  10. 3

    1

    {0, 0, 8}

    1

    Returns: 1

  11. 3

    4

    {0, 0, 1, 0, 1, 2, 1, 5, 8, 9, 1, 6}

    1

    Returns: 1

  12. 4

    2

    {0, 9, 6, 6, 0, 6, 9, 10}

    0

    Returns: 2

  13. 2

    3

    {0, 6, 10, 7, 9, 9}

    1

    Returns: 1

  14. 2

    4

    {0, 7, 10, 6, 0, 4, 0, 5}

    1

    Returns: 1

  15. 3

    2

    {0, 0, 4, 0, 0, 5}

    0

    Returns: 2

  16. 4

    1

    {0, 0, 2, 2}

    1

    Returns: 1

  17. 4

    3

    {0, 0, 0, 10, 0, 8, 6, 1, 0, 4, 4, 6}

    1

    Returns: 2

  18. 2

    2

    {0, 3, 10, 6}

    1

    Returns: 1

  19. 4

    1

    {2, 7, 2, 6}

    1

    Returns: 1

  20. 1

    2

    {3, 9}

    1

    Returns: 2

  21. 4

    1

    {0, 0, 3, 9}

    0

    Returns: 1

  22. 2

    1

    {7, 2}

    0

    Returns: 1

  23. 3

    1

    {0, 0, 4}

    0

    Returns: 1

  24. 3

    1

    {0, 0, 6}

    0

    Returns: 2

  25. 1

    4

    {7, 6, 5, 10}

    1

    Returns: 3

  26. 4

    1

    {0, 0, 9, 2}

    1

    Returns: 1

  27. 1

    2

    {6, 6}

    0

    Returns: 0

  28. 1

    4

    {8, 5, 9, 1}

    1

    Returns: 4

  29. 4

    1

    {0, 0, 0, 10}

    1

    Returns: 2

  30. 3

    4

    {0, 0, 2, 0, 5, 7, 0, 9, 6, 2, 2, 10}

    1

    Returns: 1

  31. 1

    4

    {5, 5, 4, 5}

    1

    Returns: 3

  32. 3

    1

    {3, 10, 8}

    0

    Returns: 1

  33. 4

    4

    {0, 0, 10, 5, 0, 0, 5, 2, 3, 7, 6, 8, 0, 0, 0, 10}

    1

    Returns: 1

  34. 2

    4

    {1, 3, 10, 3, 0, 2, 8, 7}

    1

    Returns: 1

  35. 1

    2

    {2, 9}

    1

    Returns: 2

  36. 4

    4

    {6, 2, 9, 7, 0, 0, 0, 7, 0, 0, 10, 3, 0, 0, 0, 10}

    0

    Returns: 0

  37. 3

    4

    {2, 3, 8, 0, 0, 5, 8, 2, 6, 0, 0, 10}

    0

    Returns: 2

  38. 3

    3

    {0, 10, 2, 0, 0, 5, 0, 8, 4}

    0

    Returns: 3

  39. 4

    2

    {0, 6, 2, 6, 0, 3, 10, 2}

    0

    Returns: 3

  40. 3

    1

    {111, 142, 117}

    1

    Returns: 4

  41. 13

    5

    {0, 0, 0, 0, 169, 7, 27, 1, 68, 124, 186, 140, 3, 0, 0, 0, 0, 0, 134, 132, 92, 114, 62, 9, 144, 96, 0, 0, 0, 0, 0, 0, 0, 0, 51, 62, 187, 10, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 59, 179, 86, 56, 121, 191, 29, 198, 107, 155, 91, 173, 74, 198, 62, 143}

    1

    Returns: 7

  42. 3

    13

    {200, 102, 67, 187, 133, 57, 156, 30, 161, 54, 98, 125, 65, 155, 143, 39, 114, 4, 44, 141, 161, 195, 22, 20, 69, 131, 160, 140, 122, 112, 94, 195, 9, 156, 68, 165, 156, 133, 173}

    0

    Returns: 19

  43. 19

    20

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 68, 11, 36, 47, 190, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 87, 163, 12, 160, 61, 183, 16, 97, 32, 6, 23, 78, 14, 141, 79, 62, 157, 188, 137, 39, 141, 149, 196, 0, 0, 0, 0, 0, 0, 88, 143, 14, 30, 106, 107, 91, 78, 145, 195, 126, 154, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 17, 74, 181, 126, 129, 30, 194, 63, 0, 85, 43, 119, 6, 151, 26, 172, 118, 118, 71, 164, 140, 176, 178, 177, 7, 144, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152, 154, 123, 138, 191, 93, 0, 0, 0, 198, 175, 53, 188, 162, 24, 27, 132, 79, 104, 86, 138, 93, 28, 24, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 170, 77, 114, 199, 0, 0, 0, 15, 40, 149, 123, 1, 8, 109, 118, 134, 113, 158, 66, 76, 27, 78, 32, 0, 0, 0, 128, 110, 61, 129, 146, 132, 68, 81, 143, 6, 156, 173, 98, 153, 151, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 47, 157, 47, 160, 20, 125, 106, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99, 128, 190, 117, 162, 96, 0, 32, 131, 103, 27, 23, 108, 106, 141, 27, 159, 45, 171, 128, 122, 113, 153, 24, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 183, 125, 86, 167, 167, 27, 65, 125, 24, 0, 0, 0, 0, 0, 154, 58, 133, 165, 54, 130, 66, 183, 196, 79, 129, 156, 30, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156, 61, 161, 142, 96, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 151, 101, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 85, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164, 113, 112, 174}

    0

    Returns: 28

  44. 2

    2

    {161, 7, 139, 127}

    1

    Returns: 3

  45. 2

    19

    {42, 199, 75, 19, 13, 192, 155, 77, 12, 165, 159, 172, 2, 66, 89, 50, 143, 56, 95, 95, 35, 52, 115, 158, 9, 190, 78, 155, 172, 77, 108, 29, 109, 108, 89, 194, 128, 66}

    0

    Returns: 17

  46. 19

    13

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 185, 160, 161, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109, 121, 51, 76, 2, 30, 155, 145, 4, 0, 0, 0, 0, 96, 121, 55, 86, 103, 10, 173, 166, 151, 107, 84, 138, 89, 2, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 71, 173, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 157, 114, 119, 105, 187, 185, 86, 185, 0, 0, 0, 96, 26, 182, 97, 97, 46, 76, 8, 8, 148, 174, 148, 49, 33, 144, 58, 0, 0, 0, 0, 107, 182, 109, 149, 188, 33, 40, 198, 185, 190, 190, 97, 138, 165, 118, 0, 0, 0, 0, 0, 11, 152, 62, 188, 151, 33, 19, 5, 36, 32, 133, 200, 33, 157, 0, 0, 0, 0, 0, 0, 0, 157, 149, 7, 43, 154, 139, 149, 163, 186, 38, 60, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125, 126, 188, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 135, 69, 37, 120, 101, 26, 198, 169, 0, 0, 0, 0, 0, 0, 170, 174, 147, 193, 38, 1, 67, 90, 41, 159, 11, 106, 124, 0, 0, 0, 0, 0, 0, 0, 169, 29, 53, 172, 46, 160, 60, 73, 171, 63, 118, 179}

    0

    Returns: 22

  47. 3

    5

    {194, 45, 126, 156, 188, 186, 44, 50, 104, 187, 172, 14, 121, 84, 141}

    1

    Returns: 2

  48. 13

    5

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75, 65, 156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 115, 198, 84, 0, 0, 0, 152, 47, 67, 88, 71, 25, 76, 54, 10, 196, 0, 0, 0, 0, 0, 0, 0, 0, 20, 98, 167, 6, 168, 0, 152, 39, 28, 108, 78, 57, 106, 193, 49, 23, 55, 165}

    1

    Returns: 6

  49. 3

    3

    {96, 31, 24, 178, 81, 117, 55, 197, 31}

    0

    Returns: 2

  50. 1

    3

    {79, 188, 189}

    1

    Returns: 2

  51. 3

    20

    {152, 16, 20, 66, 118, 130, 57, 132, 131, 125, 73, 82, 112, 133, 64, 157, 175, 180, 165, 85, 147, 163, 54, 147, 46, 49, 62, 193, 11, 8, 178, 156, 131, 156, 67, 189, 156, 76, 51, 88, 152, 155, 162, 144, 87, 130, 45, 192, 199, 84, 96, 48, 41, 170, 187, 127, 20, 10, 101, 119}

    1

    Returns: 15

  52. 1

    2

    {177, 148}

    1

    Returns: 3

  53. 1

    3

    {3, 162, 73}

    1

    Returns: 2

  54. 13

    5

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 114, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 140, 115, 139, 0, 0, 0, 41, 194, 62, 71, 172, 82, 50, 143, 173, 127, 0, 0, 0, 0, 0, 87, 135, 30, 57, 195, 66, 58, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 187, 141}

    0

    Returns: 9

  55. 20

    3

    {133, 41, 72, 93, 36, 192, 43, 21, 48, 15, 198, 131, 46, 155, 166, 143, 157, 158, 27, 74, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 127, 160, 185, 37, 198, 35, 63, 183, 0, 0, 0, 0, 0, 0, 0, 117, 7, 80, 49, 191, 7, 111, 45, 69, 179, 125, 49, 115}

    1

    Returns: 3

  56. 13

    2

    {0, 0, 0, 0, 56, 81, 157, 104, 168, 77, 188, 69, 161, 0, 0, 0, 0, 0, 0, 0, 61, 76, 117, 46, 46, 142}

    1

    Returns: 5

  57. 3

    13

    {190, 14, 79, 10, 169, 18, 157, 154, 103, 146, 130, 109, 38, 97, 99, 169, 139, 58, 136, 144, 106, 178, 114, 139, 47, 65, 103, 83, 86, 32, 97, 112, 36, 23, 189, 112, 64, 61, 1}

    0

    Returns: 15

  58. 19

    5

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 136, 79, 48, 102, 72, 190, 152, 0, 0, 0, 0, 0, 0, 42, 82, 40, 72, 124, 26, 74, 178, 67, 39, 101, 173, 57, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 143, 57, 54, 28, 51, 128, 0, 0, 0, 0, 0, 86, 93, 108, 25, 23, 85, 67, 137, 60, 149, 185, 177, 36, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176, 94, 59, 63, 126}

    0

    Returns: 2

  59. 1

    20

    {105, 120, 60, 109, 197, 5, 109, 159, 132, 17, 126, 50, 101, 49, 186, 1, 62, 127, 134, 4}

    1

    Returns: 14

  60. 5

    3

    {79, 157, 180, 171, 133, 182, 178, 191, 161, 130, 0, 160, 57, 173, 14}

    1

    Returns: 3

  61. 5

    20

    {103, 140, 103, 36, 108, 0, 0, 179, 135, 87, 140, 191, 28, 196, 157, 0, 131, 99, 68, 40, 0, 56, 14, 145, 68, 0, 67, 46, 96, 158, 96, 60, 147, 149, 142, 0, 0, 28, 35, 93, 0, 38, 188, 45, 100, 0, 0, 178, 171, 70, 0, 0, 160, 188, 137, 0, 0, 83, 117, 133, 189, 182, 68, 25, 90, 0, 0, 3, 162, 142, 0, 0, 69, 120, 135, 0, 120, 39, 94, 35, 0, 0, 6, 26, 14, 99, 127, 53, 169, 173, 0, 173, 148, 41, 162, 0, 0, 15, 143, 191}

    1

    Returns: 18

  62. 2

    19

    {44, 44, 51, 86, 1, 152, 134, 189, 52, 141, 115, 42, 75, 134, 165, 112, 168, 121, 142, 112, 176, 6, 43, 150, 110, 103, 9, 143, 13, 16, 156, 177, 27, 54, 124, 49, 142, 9}

    0

    Returns: 19

  63. 1

    3

    {67, 123, 72}

    0

    Returns: 2

  64. 20

    19

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 110, 165, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 127, 132, 191, 28, 75, 198, 156, 164, 0, 0, 0, 0, 26, 126, 50, 10, 39, 189, 130, 194, 67, 38, 72, 96, 38, 86, 171, 137, 0, 33, 37, 110, 105, 147, 82, 174, 47, 155, 199, 97, 5, 27, 109, 191, 43, 175, 17, 26, 0, 27, 20, 56, 8, 47, 99, 25, 17, 143, 124, 192, 5, 32, 45, 86, 172, 188, 34, 180, 0, 0, 0, 0, 14, 100, 41, 108, 142, 8, 19, 63, 174, 179, 129, 110, 131, 161, 154, 17, 0, 0, 0, 0, 0, 49, 12, 79, 12, 46, 16, 135, 80, 79, 112, 184, 88, 13, 95, 191, 0, 0, 0, 0, 0, 134, 161, 42, 49, 159, 7, 137, 193, 120, 59, 67, 107, 123, 2, 194, 0, 14, 88, 159, 105, 24, 20, 160, 88, 54, 67, 88, 178, 31, 160, 39, 153, 116, 97, 149, 87, 52, 66, 71, 173, 118, 64, 124, 46, 148, 105, 100, 51, 10, 83, 12, 61, 18, 30, 71, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 146, 11, 68, 96, 96, 94, 41, 23, 0, 0, 0, 0, 0, 0, 120, 171, 88, 155, 100, 42, 76, 31, 115, 109, 150, 174, 68, 64, 185, 62, 195, 12, 41, 9, 196, 79, 166, 108, 127, 64, 55, 15, 178, 70, 149, 149, 55, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 101, 83, 69, 0, 0, 0, 0, 137, 70, 185, 46, 131, 3, 162, 132, 151, 79, 147, 77, 172, 105, 148, 150, 96, 85, 63, 73, 55, 175, 177, 87, 104, 179, 96, 176, 190, 55, 36, 196, 91, 132, 8, 119, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 172, 48, 44, 116, 18, 55, 94, 173, 99, 0, 0, 0, 0, 0, 0, 0, 0, 15, 6, 83, 144, 50, 98, 4, 36, 143, 172, 101, 95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 102, 108, 124, 9, 43, 40, 50, 91, 153, 200, 185}

    1

    Returns: 25

  65. 20

    20

    {0, 0, 0, 0, 114, 42, 170, 41, 136, 110, 4, 33, 47, 126, 33, 107, 95, 7, 3, 149, 0, 0, 78, 43, 72, 133, 186, 198, 79, 169, 157, 107, 48, 83, 26, 150, 95, 142, 169, 197, 0, 0, 0, 158, 118, 114, 48, 58, 168, 71, 7, 195, 162, 25, 102, 13, 94, 146, 163, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 51, 48, 87, 61, 100, 16, 171, 30, 0, 0, 0, 0, 0, 0, 94, 115, 125, 119, 127, 152, 44, 195, 10, 107, 152, 130, 140, 119, 0, 0, 0, 0, 0, 0, 0, 0, 59, 128, 106, 199, 192, 12, 90, 78, 160, 64, 121, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133, 58, 5, 102, 182, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 118, 160, 9, 148, 153, 48, 194, 25, 53, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176, 94, 185, 107, 67, 200, 91, 69, 178, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39, 80, 73, 12, 156, 112, 94, 140, 194, 158, 0, 0, 0, 0, 0, 0, 173, 113, 142, 160, 185, 1, 67, 73, 123, 66, 198, 144, 187, 169, 0, 0, 0, 0, 0, 0, 164, 120, 15, 76, 127, 25, 134, 161, 77, 183, 94, 133, 142, 63, 0, 0, 0, 0, 0, 0, 180, 81, 105, 23, 56, 159, 145, 74, 52, 87, 26, 139, 56, 198, 0, 0, 0, 0, 0, 13, 52, 17, 93, 10, 113, 18, 198, 185, 178, 144, 17, 124, 198, 185, 0, 0, 0, 0, 0, 49, 55, 48, 148, 192, 169, 56, 102, 192, 142, 121, 104, 10, 139, 44, 0, 0, 0, 0, 0, 0, 88, 24, 70, 130, 119, 114, 105, 58, 125, 54, 67, 160, 131, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 139, 165, 182, 49, 51, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 182, 120, 112, 23, 132, 195, 198, 199, 135, 0, 0, 0, 0, 0, 0, 0, 0, 0, 77, 103, 128, 23, 77, 73, 80, 127, 154, 145, 31, 0, 0, 0, 0, 0, 115, 52, 11, 157, 2, 7, 188, 127, 131, 119, 170, 142, 74, 110, 86}

    1

    Returns: 26

  66. 19

    3

    {0, 0, 30, 31, 108, 185, 2, 7, 52, 100, 44, 173, 181, 173, 173, 169, 124, 32, 10, 0, 0, 0, 0, 0, 0, 0, 177, 51, 57, 149, 36, 122, 144, 116, 200, 20, 41, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 175, 56, 91, 133, 95, 66, 20, 36, 140}

    1

    Returns: 3

  67. 5

    19

    {162, 43, 166, 130, 114, 156, 112, 26, 42, 181, 192, 142, 11, 38, 122, 0, 80, 157, 175, 105, 0, 0, 105, 170, 134, 130, 107, 129, 59, 130, 0, 0, 110, 155, 29, 0, 0, 197, 194, 81, 0, 0, 58, 103, 178, 0, 39, 17, 198, 156, 47, 95, 91, 167, 111, 73, 184, 155, 16, 116, 0, 184, 6, 183, 185, 0, 0, 10, 5, 179, 0, 156, 31, 11, 27, 140, 29, 138, 63, 4, 139, 37, 78, 130, 123, 0, 22, 129, 154, 140, 0, 147, 68, 199, 122}

    0

    Returns: 21

  68. 19

    20

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 198, 172, 124, 146, 64, 76, 117, 86, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 57, 31, 79, 21, 194, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 189, 164, 9, 15, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 119, 48, 72, 200, 0, 0, 0, 149, 176, 74, 63, 9, 75, 88, 7, 126, 146, 99, 178, 171, 71, 165, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 170, 177, 52, 146, 0, 0, 0, 0, 0, 0, 0, 171, 40, 63, 155, 91, 140, 123, 164, 199, 103, 96, 109, 0, 0, 0, 0, 0, 0, 0, 0, 159, 66, 108, 195, 92, 98, 68, 43, 102, 14, 153, 0, 12, 99, 138, 113, 84, 10, 71, 184, 172, 200, 99, 100, 58, 100, 58, 95, 7, 32, 76, 32, 138, 158, 182, 30, 184, 106, 161, 166, 102, 66, 95, 98, 94, 14, 88, 199, 176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 177, 16, 183, 145, 187, 125, 0, 158, 26, 80, 172, 144, 194, 19, 110, 125, 142, 136, 98, 91, 131, 50, 163, 148, 119, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 71, 12, 30, 115, 86, 119, 187, 62, 111, 146, 2, 72, 114, 100, 84, 41, 93, 83, 96, 194, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 70, 122, 0, 0, 0, 39, 74, 150, 44, 121, 134, 175, 99, 132, 169, 176, 22, 64, 127, 186, 81, 0, 0, 0, 0, 58, 76, 78, 31, 39, 125, 174, 18, 51, 133, 103, 124, 136, 109, 173, 0, 67, 65, 12, 98, 156, 97, 73, 166, 133, 136, 175, 169, 182, 44, 4, 106, 81, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 111, 69, 32, 73, 76, 0, 0, 0, 0, 0, 0, 0, 112, 5, 27, 138, 108, 193, 168, 44, 114, 75, 118, 188}

    1

    Returns: 26

  69. 5

    3

    {0, 0, 96, 18, 171, 0, 0, 114, 139, 70, 0, 0, 84, 3, 126}

    1

    Returns: 3

  70. 19

    18

    {177, 185, 179, 186, 171, 166, 182, 174, 175, 189, 152, 200, 176, 192, 151, 156, 150, 166, 200, 180, 196, 184, 150, 170, 186, 177, 164, 165, 183, 182, 172, 178, 165, 152, 185, 173, 195, 194, 172, 188, 171, 185, 186, 198, 162, 165, 200, 196, 152, 158, 171, 156, 173, 187, 174, 182, 184, 166, 156, 191, 164, 194, 171, 163, 180, 197, 157, 199, 176, 188, 172, 193, 168, 199, 165, 185, 166, 172, 184, 186, 152, 180, 169, 186, 199, 175, 166, 196, 183, 164, 188, 157, 190, 163, 174, 181, 166, 188, 185, 159, 178, 150, 160, 185, 190, 198, 155, 154, 167, 182, 189, 184, 180, 200, 177, 173, 198, 152, 188, 166, 191, 188, 183, 193, 180, 195, 190, 170, 151, 186, 165, 163, 172, 177, 194, 161, 161, 180, 162, 158, 156, 158, 196, 200, 186, 172, 183, 175, 156, 167, 178, 150, 191, 157, 176, 154, 173, 151, 166, 152, 158, 161, 197, 182, 181, 162, 200, 199, 181, 183, 179, 186, 186, 150, 194, 154, 161, 159, 184, 171, 190, 152, 189, 165, 195, 153, 174, 157, 151, 155, 169, 153, 185, 169, 165, 189, 196, 184, 159, 185, 187, 198, 167, 189, 186, 155, 186, 181, 171, 185, 153, 157, 176, 176, 172, 169, 186, 198, 181, 188, 158, 154, 182, 157, 179, 191, 200, 179, 151, 177, 186, 183, 198, 154, 200, 200, 168, 200, 195, 181, 182, 157, 198, 165, 172, 200, 171, 160, 179, 151, 187, 156, 192, 179, 179, 167, 190, 184, 193, 194, 194, 151, 185, 162, 193, 168, 152, 199, 166, 184, 180, 174, 154, 196, 200, 156, 183, 195, 187, 188, 180, 184, 197, 200, 173, 187, 169, 176, 199, 193, 163, 196, 190, 155, 156, 182, 169, 175, 171, 184, 173, 156, 155, 189, 197, 177, 173, 153, 172, 187, 153, 175, 190, 167, 166, 163, 168, 163, 179, 192, 169, 178, 199, 178, 170, 193, 153, 159, 187, 180, 150, 151, 177, 179, 183, 178, 189, 166, 168, 156, 169, 157}

    0

    Returns: 10

  71. 19

    19

    {181, 177, 165, 182, 186, 182, 166, 170, 185, 151, 188, 193, 174, 188, 187, 194, 188, 194, 189, 179, 189, 185, 161, 193, 194, 174, 152, 161, 189, 161, 189, 154, 181, 176, 153, 164, 179, 161, 188, 175, 150, 189, 158, 197, 154, 185, 174, 150, 174, 181, 197, 179, 190, 173, 196, 157, 182, 175, 156, 155, 200, 176, 176, 185, 156, 189, 161, 192, 181, 180, 178, 188, 155, 175, 183, 182, 170, 177, 197, 162, 170, 175, 154, 158, 195, 181, 171, 191, 191, 156, 166, 181, 200, 155, 172, 151, 175, 189, 155, 188, 164, 183, 191, 163, 182, 166, 195, 198, 169, 182, 188, 157, 185, 153, 168, 196, 161, 181, 194, 165, 175, 189, 180, 150, 187, 175, 188, 165, 190, 185, 173, 200, 156, 171, 154, 160, 187, 156, 165, 161, 155, 159, 182, 160, 196, 160, 154, 155, 158, 187, 175, 172, 157, 176, 168, 185, 190, 164, 193, 172, 199, 155, 191, 170, 156, 152, 162, 185, 158, 171, 155, 170, 199, 195, 192, 177, 182, 184, 186, 198, 199, 193, 172, 183, 183, 177, 190, 178, 177, 193, 176, 196, 181, 151, 162, 170, 153, 188, 177, 156, 178, 199, 187, 157, 156, 171, 177, 197, 153, 171, 200, 198, 161, 192, 176, 180, 197, 183, 180, 194, 183, 157, 164, 162, 190, 151, 184, 181, 170, 159, 193, 160, 199, 168, 154, 153, 197, 188, 169, 152, 191, 189, 192, 150, 166, 172, 162, 185, 163, 173, 173, 158, 162, 178, 189, 152, 200, 197, 169, 188, 192, 169, 176, 157, 177, 176, 172, 198, 181, 166, 152, 196, 186, 196, 194, 181, 164, 167, 175, 153, 151, 175, 162, 199, 176, 173, 183, 155, 172, 196, 189, 190, 171, 178, 154, 154, 180, 167, 154, 160, 163, 164, 177, 180, 200, 162, 168, 150, 157, 188, 186, 150, 166, 184, 163, 184, 173, 180, 163, 171, 175, 152, 193, 191, 187, 176, 170, 184, 172, 150, 156, 151, 169, 200, 153, 188, 163, 183, 189, 150, 152, 185, 187, 153, 174, 198, 179, 162, 155, 167, 193, 190, 175, 182, 172, 152, 154, 169, 188, 195, 169}

    0

    Returns: 49

  72. 20

    19

    {179, 176, 196, 196, 171, 196, 155, 166, 176, 173, 156, 195, 174, 174, 161, 168, 151, 151, 186, 193, 186, 162, 158, 185, 164, 155, 150, 177, 177, 176, 195, 177, 187, 196, 158, 159, 199, 196, 197, 197, 174, 184, 191, 179, 166, 190, 191, 159, 154, 152, 187, 165, 196, 187, 158, 154, 151, 158, 157, 183, 199, 158, 189, 168, 186, 188, 176, 185, 197, 181, 189, 187, 151, 160, 200, 188, 184, 187, 190, 196, 159, 164, 157, 159, 168, 189, 180, 191, 181, 179, 188, 169, 176, 198, 178, 188, 161, 150, 177, 200, 181, 181, 196, 176, 171, 173, 185, 169, 169, 175, 174, 152, 189, 198, 183, 167, 159, 179, 175, 156, 199, 192, 156, 187, 152, 173, 190, 171, 192, 193, 186, 198, 159, 150, 166, 172, 160, 189, 152, 176, 180, 195, 170, 159, 167, 166, 171, 176, 192, 157, 163, 192, 161, 189, 164, 168, 192, 165, 179, 194, 199, 183, 171, 159, 183, 173, 157, 159, 161, 186, 164, 184, 186, 200, 183, 199, 170, 190, 200, 190, 184, 163, 200, 190, 165, 152, 173, 174, 198, 161, 181, 188, 196, 196, 160, 162, 175, 196, 192, 153, 180, 170, 185, 184, 154, 166, 156, 158, 192, 182, 197, 187, 192, 163, 167, 188, 174, 157, 166, 185, 172, 157, 174, 173, 191, 184, 164, 168, 166, 188, 193, 194, 191, 170, 186, 152, 198, 189, 163, 168, 178, 199, 170, 198, 157, 159, 187, 161, 166, 171, 167, 156, 168, 163, 152, 198, 167, 189, 191, 163, 162, 193, 181, 181, 154, 174, 191, 151, 191, 199, 187, 159, 156, 176, 169, 164, 176, 198, 162, 155, 163, 191, 190, 192, 164, 185, 155, 185, 176, 169, 170, 173, 157, 155, 194, 170, 179, 163, 199, 157, 191, 155, 184, 192, 171, 198, 186, 194, 180, 200, 164, 153, 170, 169, 200, 196, 197, 192, 200, 174, 166, 199, 187, 153, 154, 166, 179, 182, 164, 182, 182, 181, 168, 170, 177, 183, 165, 189, 193, 194, 191, 171, 186, 190, 163, 186, 161, 162, 165, 198, 152, 151, 194, 188, 182, 188, 166, 197, 188, 168, 162, 171, 187, 188, 190, 185, 171, 182, 161, 197, 199, 170, 173, 161, 160, 192, 196, 181, 154, 152}

    1

    Returns: 44

  73. 19

    20

    {178, 168, 189, 156, 200, 190, 194, 181, 190, 167, 171, 168, 194, 163, 194, 177, 154, 166, 189, 174, 170, 179, 168, 160, 165, 161, 173, 164, 169, 152, 163, 194, 186, 180, 151, 172, 150, 190, 168, 167, 185, 176, 198, 183, 165, 179, 179, 153, 155, 196, 158, 196, 175, 178, 161, 165, 152, 175, 193, 178, 184, 183, 156, 185, 151, 184, 178, 184, 181, 187, 160, 160, 200, 198, 165, 167, 192, 170, 162, 185, 193, 181, 182, 197, 167, 179, 166, 171, 183, 157, 164, 198, 166, 200, 164, 152, 200, 158, 165, 194, 197, 195, 178, 197, 195, 199, 155, 170, 196, 185, 197, 191, 191, 163, 170, 190, 156, 200, 166, 183, 160, 167, 173, 158, 197, 160, 155, 161, 153, 199, 182, 161, 188, 191, 185, 189, 189, 156, 168, 152, 170, 161, 155, 178, 167, 156, 169, 162, 187, 198, 198, 181, 189, 196, 159, 199, 158, 165, 195, 184, 165, 188, 169, 166, 193, 197, 179, 151, 169, 162, 197, 151, 177, 161, 167, 194, 181, 162, 178, 150, 173, 190, 165, 175, 182, 161, 200, 161, 161, 188, 153, 163, 170, 189, 175, 191, 169, 196, 167, 190, 155, 169, 164, 152, 185, 180, 169, 165, 168, 179, 161, 161, 185, 169, 200, 179, 168, 168, 189, 197, 153, 169, 152, 192, 154, 189, 188, 175, 186, 182, 177, 159, 174, 174, 192, 184, 164, 183, 185, 176, 194, 178, 184, 161, 166, 175, 170, 171, 157, 174, 177, 158, 155, 197, 177, 165, 165, 150, 166, 184, 151, 171, 175, 184, 169, 195, 162, 166, 154, 193, 153, 165, 161, 189, 172, 172, 155, 193, 181, 166, 167, 199, 188, 173, 163, 153, 166, 181, 164, 192, 156, 183, 169, 161, 175, 167, 197, 187, 195, 162, 183, 167, 198, 160, 160, 170, 159, 167, 180, 156, 168, 194, 166, 159, 175, 193, 164, 164, 198, 200, 161, 155, 168, 183, 159, 179, 199, 168, 152, 156, 193, 185, 164, 163, 156, 162, 181, 174, 169, 195, 166, 150, 171, 173, 176, 156, 155, 171, 166, 184, 164, 187, 196, 194, 158, 165, 193, 181, 185, 194, 190, 162, 199, 152, 197, 160, 151, 186, 170, 164, 193, 173, 164, 165, 181, 173, 162, 177, 161, 179}

    0

    Returns: 29

  74. 18

    19

    {179, 164, 177, 199, 151, 177, 189, 182, 154, 181, 162, 175, 162, 196, 150, 165, 181, 183, 150, 185, 168, 180, 170, 169, 189, 194, 192, 183, 195, 194, 197, 190, 182, 174, 189, 164, 193, 153, 163, 163, 198, 181, 187, 178, 181, 175, 184, 175, 158, 176, 172, 150, 194, 183, 171, 184, 197, 156, 198, 189, 173, 182, 174, 166, 159, 153, 163, 153, 186, 166, 194, 166, 161, 173, 189, 173, 164, 186, 187, 185, 158, 165, 156, 158, 173, 153, 159, 196, 161, 174, 199, 199, 194, 192, 167, 183, 154, 189, 196, 184, 159, 165, 170, 179, 183, 197, 195, 166, 156, 172, 198, 166, 150, 190, 185, 167, 184, 167, 179, 183, 189, 179, 159, 173, 158, 192, 163, 151, 156, 153, 174, 181, 163, 192, 193, 183, 193, 186, 160, 190, 194, 173, 153, 185, 197, 161, 185, 165, 180, 199, 180, 177, 153, 194, 181, 194, 194, 194, 199, 164, 182, 186, 170, 182, 164, 174, 197, 179, 158, 190, 160, 160, 162, 171, 150, 187, 183, 197, 162, 185, 178, 160, 168, 183, 191, 177, 191, 180, 185, 177, 193, 151, 160, 187, 177, 175, 152, 185, 153, 153, 188, 194, 156, 163, 180, 162, 185, 152, 200, 184, 199, 157, 151, 171, 166, 180, 167, 156, 198, 197, 192, 157, 172, 180, 150, 167, 186, 179, 178, 161, 157, 166, 173, 179, 153, 181, 194, 152, 177, 191, 155, 194, 198, 194, 163, 173, 162, 164, 196, 187, 159, 163, 181, 182, 197, 156, 168, 199, 188, 190, 197, 193, 184, 198, 156, 200, 181, 162, 152, 159, 197, 182, 198, 166, 159, 167, 173, 159, 171, 200, 192, 184, 173, 158, 159, 177, 176, 186, 170, 193, 161, 188, 199, 174, 151, 156, 177, 197, 160, 193, 154, 156, 158, 156, 200, 154, 163, 151, 161, 174, 156, 154, 185, 180, 197, 151, 157, 161, 171, 192, 196, 158, 194, 158, 167, 164, 158, 153, 174, 160, 176, 185, 151, 154, 165, 193, 194, 182, 177, 182, 190, 188}

    0

    Returns: 52

  75. 19

    18

    {172, 167, 162, 152, 169, 152, 161, 153, 183, 169, 169, 177, 195, 171, 153, 173, 197, 200, 191, 188, 166, 190, 161, 183, 200, 200, 190, 160, 162, 189, 151, 184, 198, 200, 179, 164, 200, 166, 176, 180, 150, 198, 191, 153, 171, 189, 176, 155, 154, 189, 171, 163, 166, 171, 194, 157, 189, 159, 188, 178, 174, 187, 171, 162, 166, 167, 193, 179, 165, 180, 161, 186, 176, 174, 162, 152, 170, 152, 165, 154, 157, 167, 165, 180, 178, 198, 158, 189, 156, 194, 150, 187, 171, 168, 186, 152, 166, 173, 173, 173, 160, 155, 197, 166, 155, 180, 184, 182, 179, 192, 171, 188, 174, 160, 168, 157, 178, 177, 187, 193, 166, 165, 196, 165, 198, 152, 160, 152, 198, 169, 191, 176, 181, 165, 163, 153, 194, 167, 200, 187, 187, 163, 182, 152, 170, 167, 158, 176, 157, 157, 164, 183, 161, 194, 196, 189, 198, 161, 188, 157, 175, 170, 167, 150, 194, 194, 182, 184, 167, 196, 161, 182, 150, 190, 182, 187, 169, 186, 169, 192, 176, 186, 187, 173, 171, 165, 168, 163, 193, 194, 171, 175, 200, 194, 173, 193, 197, 163, 158, 198, 172, 182, 151, 179, 159, 184, 172, 175, 155, 155, 154, 185, 176, 200, 200, 182, 159, 192, 161, 160, 178, 154, 163, 173, 193, 174, 162, 181, 194, 154, 190, 185, 181, 162, 153, 151, 170, 185, 162, 174, 150, 158, 185, 192, 175, 173, 164, 156, 165, 162, 174, 166, 187, 179, 196, 200, 175, 176, 180, 152, 160, 159, 162, 172, 188, 199, 196, 184, 172, 159, 194, 153, 191, 152, 158, 190, 161, 161, 153, 150, 194, 172, 163, 151, 182, 158, 151, 196, 171, 197, 166, 169, 176, 197, 159, 178, 196, 178, 160, 192, 160, 183, 177, 150, 158, 161, 181, 158, 176, 173, 151, 150, 187, 179, 163, 169, 160, 167, 183, 196, 199, 169, 192, 189, 176, 161, 170, 156, 187, 173, 185, 192, 199, 164, 196, 163, 189, 179, 178, 161, 164, 200}

    1

    Returns: 21

  76. 18

    20

    {156, 175, 153, 173, 186, 190, 153, 178, 152, 156, 166, 171, 192, 163, 173, 150, 172, 164, 163, 162, 161, 171, 165, 174, 153, 192, 157, 158, 200, 189, 182, 189, 176, 170, 173, 178, 181, 179, 200, 181, 187, 160, 198, 152, 176, 187, 182, 184, 179, 170, 173, 177, 160, 183, 191, 185, 184, 164, 181, 176, 199, 197, 152, 172, 169, 189, 165, 180, 165, 163, 155, 181, 192, 174, 187, 163, 181, 151, 170, 165, 162, 171, 196, 187, 183, 164, 151, 175, 195, 152, 182, 187, 171, 185, 184, 170, 172, 190, 182, 179, 200, 189, 152, 186, 188, 161, 198, 156, 163, 154, 166, 186, 167, 174, 187, 200, 192, 151, 156, 183, 182, 199, 193, 173, 196, 176, 166, 199, 172, 167, 194, 159, 181, 199, 185, 192, 190, 158, 189, 189, 184, 159, 169, 168, 152, 188, 177, 173, 184, 198, 189, 174, 195, 189, 198, 186, 190, 200, 193, 200, 178, 185, 189, 196, 150, 166, 168, 180, 166, 199, 185, 196, 192, 174, 160, 162, 175, 176, 195, 190, 179, 153, 168, 181, 156, 183, 190, 169, 195, 173, 183, 185, 165, 155, 186, 154, 152, 158, 167, 194, 170, 176, 155, 163, 189, 186, 168, 162, 171, 156, 184, 163, 199, 180, 199, 161, 154, 181, 153, 162, 154, 173, 152, 178, 154, 199, 196, 194, 185, 154, 180, 199, 196, 163, 160, 154, 160, 154, 162, 163, 161, 186, 200, 197, 192, 163, 175, 197, 185, 180, 175, 152, 184, 160, 162, 199, 185, 189, 153, 192, 171, 155, 167, 182, 179, 178, 176, 164, 181, 163, 166, 189, 182, 160, 192, 199, 174, 169, 186, 189, 161, 196, 187, 160, 169, 151, 152, 198, 184, 184, 191, 195, 162, 162, 187, 155, 191, 177, 185, 164, 185, 150, 182, 159, 165, 195, 179, 177, 155, 182, 198, 199, 199, 183, 153, 189, 188, 200, 160, 192, 196, 174, 168, 171, 169, 175, 181, 155, 169, 168, 169, 181, 188, 186, 157, 197, 170, 183, 171, 171, 178, 162, 152, 189, 150, 151, 196, 181, 182, 179, 192, 185, 168, 177, 171, 190, 158, 191, 154, 193}

    0

    Returns: 15

  77. 19

    18

    {167, 181, 196, 168, 188, 173, 196, 170, 163, 162, 163, 161, 160, 163, 180, 173, 188, 169, 160, 175, 192, 170, 187, 174, 157, 157, 176, 196, 150, 151, 162, 174, 160, 193, 195, 193, 193, 192, 180, 157, 152, 165, 192, 151, 163, 154, 177, 176, 194, 162, 164, 187, 158, 180, 185, 178, 199, 154, 160, 200, 169, 155, 192, 177, 193, 187, 200, 175, 168, 183, 161, 159, 193, 163, 172, 183, 173, 166, 154, 158, 184, 192, 155, 165, 188, 169, 173, 179, 196, 190, 160, 191, 182, 178, 188, 177, 156, 160, 195, 197, 185, 152, 159, 180, 200, 188, 169, 189, 193, 176, 179, 182, 176, 192, 183, 182, 176, 182, 164, 182, 167, 161, 177, 188, 157, 157, 196, 199, 198, 170, 174, 162, 164, 175, 194, 200, 152, 159, 154, 199, 188, 161, 173, 172, 191, 177, 168, 195, 188, 153, 178, 177, 195, 151, 195, 196, 199, 185, 152, 151, 194, 153, 188, 157, 152, 156, 184, 157, 184, 165, 150, 184, 159, 169, 182, 180, 150, 155, 182, 188, 184, 189, 186, 166, 199, 180, 161, 163, 163, 171, 194, 199, 155, 192, 188, 187, 181, 157, 151, 179, 193, 178, 151, 152, 181, 179, 163, 197, 199, 157, 187, 175, 170, 177, 173, 197, 199, 160, 168, 176, 199, 192, 180, 186, 165, 168, 179, 171, 174, 183, 169, 177, 189, 198, 171, 178, 150, 159, 196, 165, 189, 172, 164, 157, 169, 200, 155, 198, 194, 180, 170, 156, 170, 150, 175, 162, 199, 183, 167, 184, 165, 158, 197, 200, 190, 152, 153, 169, 158, 188, 181, 200, 183, 169, 156, 181, 177, 162, 196, 176, 157, 173, 190, 175, 179, 161, 167, 199, 168, 152, 187, 187, 193, 168, 165, 152, 168, 171, 151, 181, 186, 174, 194, 192, 167, 191, 176, 188, 161, 192, 157, 187, 150, 174, 191, 184, 198, 185, 173, 196, 155, 185, 192, 194, 162, 186, 178, 182, 184, 199, 183, 195, 197, 192, 159, 165, 188, 172, 184, 180, 190, 199}

    1

    Returns: 22

  78. 19

    19

    {168, 175, 160, 161, 163, 181, 172, 184, 189, 166, 176, 198, 172, 174, 166, 160, 175, 153, 188, 198, 152, 174, 184, 178, 170, 152, 167, 195, 192, 199, 174, 174, 164, 174, 164, 173, 151, 157, 168, 157, 184, 189, 195, 157, 195, 176, 190, 191, 175, 166, 173, 174, 173, 153, 171, 199, 193, 177, 160, 191, 182, 160, 176, 195, 195, 199, 151, 166, 166, 172, 194, 153, 195, 186, 196, 181, 165, 189, 156, 169, 192, 185, 198, 154, 177, 181, 185, 183, 174, 172, 182, 162, 190, 186, 179, 163, 174, 180, 171, 165, 174, 167, 185, 195, 175, 174, 156, 173, 150, 195, 150, 164, 167, 152, 157, 178, 171, 179, 196, 165, 177, 186, 150, 167, 178, 174, 170, 160, 173, 170, 173, 198, 172, 164, 171, 196, 195, 166, 176, 152, 196, 162, 168, 197, 200, 185, 153, 188, 161, 175, 155, 167, 180, 157, 153, 153, 159, 168, 187, 160, 180, 183, 193, 174, 182, 192, 193, 155, 165, 181, 196, 170, 177, 183, 186, 164, 164, 168, 169, 157, 159, 181, 193, 154, 162, 183, 175, 180, 183, 177, 193, 163, 166, 166, 152, 174, 188, 174, 168, 191, 183, 183, 193, 192, 200, 195, 160, 150, 176, 170, 154, 161, 198, 166, 176, 160, 159, 194, 158, 178, 162, 163, 199, 200, 185, 174, 177, 167, 157, 168, 168, 191, 179, 181, 153, 151, 162, 150, 177, 151, 156, 184, 176, 198, 191, 160, 178, 168, 179, 196, 170, 176, 179, 178, 198, 157, 188, 181, 185, 164, 166, 153, 198, 150, 186, 175, 153, 191, 192, 182, 200, 151, 192, 182, 156, 198, 158, 188, 152, 186, 179, 165, 170, 179, 173, 197, 178, 173, 154, 192, 198, 176, 178, 184, 167, 157, 194, 170, 150, 181, 186, 183, 183, 193, 170, 185, 179, 157, 192, 162, 178, 154, 165, 162, 186, 190, 167, 161, 199, 181, 194, 178, 163, 179, 170, 167, 189, 196, 182, 161, 194, 178, 173, 164, 153, 183, 150, 168, 161, 180, 161, 181, 168, 182, 159, 191, 196, 184, 191, 190, 194, 178, 194, 195, 173, 181, 190, 198, 162, 197, 200}

    0

    Returns: 52

  79. 20

    20

    {165, 176, 183, 156, 195, 165, 170, 192, 150, 153, 183, 182, 170, 156, 153, 188, 153, 178, 171, 183, 181, 196, 173, 158, 157, 165, 158, 153, 154, 165, 166, 189, 158, 158, 165, 157, 173, 170, 175, 176, 188, 175, 175, 162, 165, 175, 176, 166, 194, 199, 186, 158, 176, 190, 161, 193, 195, 181, 164, 161, 178, 195, 199, 151, 200, 158, 195, 191, 193, 151, 152, 191, 190, 153, 162, 170, 191, 194, 197, 161, 172, 194, 175, 171, 163, 157, 177, 172, 160, 155, 170, 174, 156, 195, 198, 182, 196, 162, 156, 197, 169, 185, 167, 184, 160, 189, 172, 191, 169, 167, 194, 174, 150, 167, 150, 188, 169, 176, 159, 167, 155, 171, 177, 178, 180, 183, 198, 171, 158, 193, 172, 156, 157, 161, 197, 194, 197, 171, 168, 175, 190, 154, 197, 192, 189, 157, 188, 196, 151, 188, 180, 183, 180, 173, 184, 159, 160, 175, 186, 196, 199, 196, 188, 171, 161, 175, 200, 184, 163, 165, 150, 178, 163, 185, 155, 200, 184, 170, 154, 187, 150, 154, 164, 182, 156, 180, 174, 199, 185, 190, 158, 188, 172, 195, 169, 150, 183, 170, 177, 180, 159, 198, 151, 188, 157, 168, 200, 197, 166, 184, 183, 154, 153, 174, 189, 154, 157, 153, 187, 190, 184, 156, 169, 157, 178, 200, 180, 187, 190, 170, 163, 179, 171, 197, 165, 160, 172, 153, 157, 160, 150, 155, 166, 186, 179, 165, 180, 169, 183, 200, 177, 193, 159, 168, 186, 170, 198, 177, 190, 166, 154, 186, 179, 173, 161, 198, 173, 153, 173, 191, 182, 163, 153, 151, 150, 164, 182, 169, 187, 193, 167, 193, 197, 198, 156, 193, 200, 151, 162, 183, 179, 199, 191, 165, 165, 174, 176, 191, 200, 172, 172, 183, 167, 178, 166, 169, 166, 186, 192, 161, 191, 169, 164, 184, 187, 183, 198, 152, 195, 167, 159, 198, 185, 182, 170, 200, 152, 178, 196, 197, 155, 150, 186, 154, 168, 165, 192, 197, 193, 163, 164, 157, 195, 155, 171, 161, 182, 183, 192, 167, 160, 167, 176, 155, 175, 176, 197, 168, 156, 154, 151, 162, 185, 188, 161, 182, 181, 172, 185, 172, 170, 177, 150, 166, 153, 171, 188, 152, 152, 156, 176, 169, 181, 176, 175, 200, 174, 166, 193, 185, 196, 168, 189, 159, 168, 164, 165, 197, 175, 194}

    1

    Returns: 26

  80. 19

    18

    {177, 185, 179, 186, 171, 166, 182, 174, 175, 189, 152, 200, 176, 192, 151, 156, 150, 166, 200, 180, 196, 184, 150, 170, 186, 177, 164, 165, 183, 182, 172, 178, 165, 152, 185, 173, 195, 194, 172, 188, 171, 185, 186, 198, 162, 165, 200, 196, 152, 158, 171, 156, 173, 187, 174, 182, 184, 166, 156, 191, 164, 194, 171, 163, 180, 197, 157, 199, 176, 188, 172, 193, 168, 199, 165, 185, 166, 172, 184, 186, 152, 180, 169, 186, 199, 175, 166, 196, 183, 164, 188, 157, 190, 163, 174, 181, 166, 188, 185, 159, 178, 150, 160, 185, 190, 198, 155, 154, 167, 182, 189, 184, 180, 200, 177, 173, 198, 152, 188, 166, 191, 188, 183, 193, 180, 195, 190, 170, 151, 186, 165, 163, 172, 177, 194, 161, 161, 180, 162, 158, 156, 158, 196, 200, 186, 172, 183, 175, 156, 167, 178, 150, 191, 157, 176, 154, 173, 151, 166, 152, 158, 161, 197, 182, 181, 162, 200, 199, 181, 183, 179, 186, 186, 150, 194, 154, 161, 159, 184, 171, 190, 152, 189, 165, 195, 153, 174, 157, 151, 155, 169, 153, 185, 169, 165, 189, 196, 184, 159, 185, 187, 198, 167, 189, 186, 155, 186, 181, 171, 185, 153, 157, 176, 176, 172, 169, 186, 198, 181, 188, 158, 154, 182, 157, 179, 191, 200, 179, 151, 177, 186, 183, 198, 154, 200, 200, 168, 200, 195, 181, 182, 157, 198, 165, 172, 200, 171, 160, 179, 151, 187, 156, 192, 179, 179, 167, 190, 184, 193, 194, 194, 151, 185, 162, 193, 168, 152, 199, 166, 184, 180, 174, 154, 196, 200, 156, 183, 195, 187, 188, 180, 184, 197, 200, 173, 187, 169, 176, 199, 193, 163, 196, 190, 155, 156, 182, 169, 175, 171, 184, 173, 156, 155, 189, 197, 177, 173, 153, 172, 187, 153, 175, 190, 167, 166, 163, 168, 163, 179, 192, 169, 178, 199, 178, 170, 193, 153, 159, 187, 180, 150, 151, 177, 179, 183, 178, 189, 166, 168, 156, 169, 157}

    0

    Returns: 10

  81. 19

    19

    {181, 177, 165, 182, 186, 182, 166, 170, 185, 151, 188, 193, 174, 188, 187, 194, 188, 194, 189, 179, 189, 185, 161, 193, 194, 174, 152, 161, 189, 161, 189, 154, 181, 176, 153, 164, 179, 161, 188, 175, 150, 189, 158, 197, 154, 185, 174, 150, 174, 181, 197, 179, 190, 173, 196, 157, 182, 175, 156, 155, 200, 176, 176, 185, 156, 189, 161, 192, 181, 180, 178, 188, 155, 175, 183, 182, 170, 177, 197, 162, 170, 175, 154, 158, 195, 181, 171, 191, 191, 156, 166, 181, 200, 155, 172, 151, 175, 189, 155, 188, 164, 183, 191, 163, 182, 166, 195, 198, 169, 182, 188, 157, 185, 153, 168, 196, 161, 181, 194, 165, 175, 189, 180, 150, 187, 175, 188, 165, 190, 185, 173, 200, 156, 171, 154, 160, 187, 156, 165, 161, 155, 159, 182, 160, 196, 160, 154, 155, 158, 187, 175, 172, 157, 176, 168, 185, 190, 164, 193, 172, 199, 155, 191, 170, 156, 152, 162, 185, 158, 171, 155, 170, 199, 195, 192, 177, 182, 184, 186, 198, 199, 193, 172, 183, 183, 177, 190, 178, 177, 193, 176, 196, 181, 151, 162, 170, 153, 188, 177, 156, 178, 199, 187, 157, 156, 171, 177, 197, 153, 171, 200, 198, 161, 192, 176, 180, 197, 183, 180, 194, 183, 157, 164, 162, 190, 151, 184, 181, 170, 159, 193, 160, 199, 168, 154, 153, 197, 188, 169, 152, 191, 189, 192, 150, 166, 172, 162, 185, 163, 173, 173, 158, 162, 178, 189, 152, 200, 197, 169, 188, 192, 169, 176, 157, 177, 176, 172, 198, 181, 166, 152, 196, 186, 196, 194, 181, 164, 167, 175, 153, 151, 175, 162, 199, 176, 173, 183, 155, 172, 196, 189, 190, 171, 178, 154, 154, 180, 167, 154, 160, 163, 164, 177, 180, 200, 162, 168, 150, 157, 188, 186, 150, 166, 184, 163, 184, 173, 180, 163, 171, 175, 152, 193, 191, 187, 176, 170, 184, 172, 150, 156, 151, 169, 200, 153, 188, 163, 183, 189, 150, 152, 185, 187, 153, 174, 198, 179, 162, 155, 167, 193, 190, 175, 182, 172, 152, 154, 169, 188, 195, 169}

    0

    Returns: 49

  82. 20

    19

    {179, 176, 196, 196, 171, 196, 155, 166, 176, 173, 156, 195, 174, 174, 161, 168, 151, 151, 186, 193, 186, 162, 158, 185, 164, 155, 150, 177, 177, 176, 195, 177, 187, 196, 158, 159, 199, 196, 197, 197, 174, 184, 191, 179, 166, 190, 191, 159, 154, 152, 187, 165, 196, 187, 158, 154, 151, 158, 157, 183, 199, 158, 189, 168, 186, 188, 176, 185, 197, 181, 189, 187, 151, 160, 200, 188, 184, 187, 190, 196, 159, 164, 157, 159, 168, 189, 180, 191, 181, 179, 188, 169, 176, 198, 178, 188, 161, 150, 177, 200, 181, 181, 196, 176, 171, 173, 185, 169, 169, 175, 174, 152, 189, 198, 183, 167, 159, 179, 175, 156, 199, 192, 156, 187, 152, 173, 190, 171, 192, 193, 186, 198, 159, 150, 166, 172, 160, 189, 152, 176, 180, 195, 170, 159, 167, 166, 171, 176, 192, 157, 163, 192, 161, 189, 164, 168, 192, 165, 179, 194, 199, 183, 171, 159, 183, 173, 157, 159, 161, 186, 164, 184, 186, 200, 183, 199, 170, 190, 200, 190, 184, 163, 200, 190, 165, 152, 173, 174, 198, 161, 181, 188, 196, 196, 160, 162, 175, 196, 192, 153, 180, 170, 185, 184, 154, 166, 156, 158, 192, 182, 197, 187, 192, 163, 167, 188, 174, 157, 166, 185, 172, 157, 174, 173, 191, 184, 164, 168, 166, 188, 193, 194, 191, 170, 186, 152, 198, 189, 163, 168, 178, 199, 170, 198, 157, 159, 187, 161, 166, 171, 167, 156, 168, 163, 152, 198, 167, 189, 191, 163, 162, 193, 181, 181, 154, 174, 191, 151, 191, 199, 187, 159, 156, 176, 169, 164, 176, 198, 162, 155, 163, 191, 190, 192, 164, 185, 155, 185, 176, 169, 170, 173, 157, 155, 194, 170, 179, 163, 199, 157, 191, 155, 184, 192, 171, 198, 186, 194, 180, 200, 164, 153, 170, 169, 200, 196, 197, 192, 200, 174, 166, 199, 187, 153, 154, 166, 179, 182, 164, 182, 182, 181, 168, 170, 177, 183, 165, 189, 193, 194, 191, 171, 186, 190, 163, 186, 161, 162, 165, 198, 152, 151, 194, 188, 182, 188, 166, 197, 188, 168, 162, 171, 187, 188, 190, 185, 171, 182, 161, 197, 199, 170, 173, 161, 160, 192, 196, 181, 154, 152}

    1

    Returns: 44

  83. 19

    20

    {178, 168, 189, 156, 200, 190, 194, 181, 190, 167, 171, 168, 194, 163, 194, 177, 154, 166, 189, 174, 170, 179, 168, 160, 165, 161, 173, 164, 169, 152, 163, 194, 186, 180, 151, 172, 150, 190, 168, 167, 185, 176, 198, 183, 165, 179, 179, 153, 155, 196, 158, 196, 175, 178, 161, 165, 152, 175, 193, 178, 184, 183, 156, 185, 151, 184, 178, 184, 181, 187, 160, 160, 200, 198, 165, 167, 192, 170, 162, 185, 193, 181, 182, 197, 167, 179, 166, 171, 183, 157, 164, 198, 166, 200, 164, 152, 200, 158, 165, 194, 197, 195, 178, 197, 195, 199, 155, 170, 196, 185, 197, 191, 191, 163, 170, 190, 156, 200, 166, 183, 160, 167, 173, 158, 197, 160, 155, 161, 153, 199, 182, 161, 188, 191, 185, 189, 189, 156, 168, 152, 170, 161, 155, 178, 167, 156, 169, 162, 187, 198, 198, 181, 189, 196, 159, 199, 158, 165, 195, 184, 165, 188, 169, 166, 193, 197, 179, 151, 169, 162, 197, 151, 177, 161, 167, 194, 181, 162, 178, 150, 173, 190, 165, 175, 182, 161, 200, 161, 161, 188, 153, 163, 170, 189, 175, 191, 169, 196, 167, 190, 155, 169, 164, 152, 185, 180, 169, 165, 168, 179, 161, 161, 185, 169, 200, 179, 168, 168, 189, 197, 153, 169, 152, 192, 154, 189, 188, 175, 186, 182, 177, 159, 174, 174, 192, 184, 164, 183, 185, 176, 194, 178, 184, 161, 166, 175, 170, 171, 157, 174, 177, 158, 155, 197, 177, 165, 165, 150, 166, 184, 151, 171, 175, 184, 169, 195, 162, 166, 154, 193, 153, 165, 161, 189, 172, 172, 155, 193, 181, 166, 167, 199, 188, 173, 163, 153, 166, 181, 164, 192, 156, 183, 169, 161, 175, 167, 197, 187, 195, 162, 183, 167, 198, 160, 160, 170, 159, 167, 180, 156, 168, 194, 166, 159, 175, 193, 164, 164, 198, 200, 161, 155, 168, 183, 159, 179, 199, 168, 152, 156, 193, 185, 164, 163, 156, 162, 181, 174, 169, 195, 166, 150, 171, 173, 176, 156, 155, 171, 166, 184, 164, 187, 196, 194, 158, 165, 193, 181, 185, 194, 190, 162, 199, 152, 197, 160, 151, 186, 170, 164, 193, 173, 164, 165, 181, 173, 162, 177, 161, 179}

    0

    Returns: 29

  84. 18

    19

    {179, 164, 177, 199, 151, 177, 189, 182, 154, 181, 162, 175, 162, 196, 150, 165, 181, 183, 150, 185, 168, 180, 170, 169, 189, 194, 192, 183, 195, 194, 197, 190, 182, 174, 189, 164, 193, 153, 163, 163, 198, 181, 187, 178, 181, 175, 184, 175, 158, 176, 172, 150, 194, 183, 171, 184, 197, 156, 198, 189, 173, 182, 174, 166, 159, 153, 163, 153, 186, 166, 194, 166, 161, 173, 189, 173, 164, 186, 187, 185, 158, 165, 156, 158, 173, 153, 159, 196, 161, 174, 199, 199, 194, 192, 167, 183, 154, 189, 196, 184, 159, 165, 170, 179, 183, 197, 195, 166, 156, 172, 198, 166, 150, 190, 185, 167, 184, 167, 179, 183, 189, 179, 159, 173, 158, 192, 163, 151, 156, 153, 174, 181, 163, 192, 193, 183, 193, 186, 160, 190, 194, 173, 153, 185, 197, 161, 185, 165, 180, 199, 180, 177, 153, 194, 181, 194, 194, 194, 199, 164, 182, 186, 170, 182, 164, 174, 197, 179, 158, 190, 160, 160, 162, 171, 150, 187, 183, 197, 162, 185, 178, 160, 168, 183, 191, 177, 191, 180, 185, 177, 193, 151, 160, 187, 177, 175, 152, 185, 153, 153, 188, 194, 156, 163, 180, 162, 185, 152, 200, 184, 199, 157, 151, 171, 166, 180, 167, 156, 198, 197, 192, 157, 172, 180, 150, 167, 186, 179, 178, 161, 157, 166, 173, 179, 153, 181, 194, 152, 177, 191, 155, 194, 198, 194, 163, 173, 162, 164, 196, 187, 159, 163, 181, 182, 197, 156, 168, 199, 188, 190, 197, 193, 184, 198, 156, 200, 181, 162, 152, 159, 197, 182, 198, 166, 159, 167, 173, 159, 171, 200, 192, 184, 173, 158, 159, 177, 176, 186, 170, 193, 161, 188, 199, 174, 151, 156, 177, 197, 160, 193, 154, 156, 158, 156, 200, 154, 163, 151, 161, 174, 156, 154, 185, 180, 197, 151, 157, 161, 171, 192, 196, 158, 194, 158, 167, 164, 158, 153, 174, 160, 176, 185, 151, 154, 165, 193, 194, 182, 177, 182, 190, 188}

    0

    Returns: 52

  85. 19

    18

    {172, 167, 162, 152, 169, 152, 161, 153, 183, 169, 169, 177, 195, 171, 153, 173, 197, 200, 191, 188, 166, 190, 161, 183, 200, 200, 190, 160, 162, 189, 151, 184, 198, 200, 179, 164, 200, 166, 176, 180, 150, 198, 191, 153, 171, 189, 176, 155, 154, 189, 171, 163, 166, 171, 194, 157, 189, 159, 188, 178, 174, 187, 171, 162, 166, 167, 193, 179, 165, 180, 161, 186, 176, 174, 162, 152, 170, 152, 165, 154, 157, 167, 165, 180, 178, 198, 158, 189, 156, 194, 150, 187, 171, 168, 186, 152, 166, 173, 173, 173, 160, 155, 197, 166, 155, 180, 184, 182, 179, 192, 171, 188, 174, 160, 168, 157, 178, 177, 187, 193, 166, 165, 196, 165, 198, 152, 160, 152, 198, 169, 191, 176, 181, 165, 163, 153, 194, 167, 200, 187, 187, 163, 182, 152, 170, 167, 158, 176, 157, 157, 164, 183, 161, 194, 196, 189, 198, 161, 188, 157, 175, 170, 167, 150, 194, 194, 182, 184, 167, 196, 161, 182, 150, 190, 182, 187, 169, 186, 169, 192, 176, 186, 187, 173, 171, 165, 168, 163, 193, 194, 171, 175, 200, 194, 173, 193, 197, 163, 158, 198, 172, 182, 151, 179, 159, 184, 172, 175, 155, 155, 154, 185, 176, 200, 200, 182, 159, 192, 161, 160, 178, 154, 163, 173, 193, 174, 162, 181, 194, 154, 190, 185, 181, 162, 153, 151, 170, 185, 162, 174, 150, 158, 185, 192, 175, 173, 164, 156, 165, 162, 174, 166, 187, 179, 196, 200, 175, 176, 180, 152, 160, 159, 162, 172, 188, 199, 196, 184, 172, 159, 194, 153, 191, 152, 158, 190, 161, 161, 153, 150, 194, 172, 163, 151, 182, 158, 151, 196, 171, 197, 166, 169, 176, 197, 159, 178, 196, 178, 160, 192, 160, 183, 177, 150, 158, 161, 181, 158, 176, 173, 151, 150, 187, 179, 163, 169, 160, 167, 183, 196, 199, 169, 192, 189, 176, 161, 170, 156, 187, 173, 185, 192, 199, 164, 196, 163, 189, 179, 178, 161, 164, 200}

    1

    Returns: 21

  86. 18

    20

    {156, 175, 153, 173, 186, 190, 153, 178, 152, 156, 166, 171, 192, 163, 173, 150, 172, 164, 163, 162, 161, 171, 165, 174, 153, 192, 157, 158, 200, 189, 182, 189, 176, 170, 173, 178, 181, 179, 200, 181, 187, 160, 198, 152, 176, 187, 182, 184, 179, 170, 173, 177, 160, 183, 191, 185, 184, 164, 181, 176, 199, 197, 152, 172, 169, 189, 165, 180, 165, 163, 155, 181, 192, 174, 187, 163, 181, 151, 170, 165, 162, 171, 196, 187, 183, 164, 151, 175, 195, 152, 182, 187, 171, 185, 184, 170, 172, 190, 182, 179, 200, 189, 152, 186, 188, 161, 198, 156, 163, 154, 166, 186, 167, 174, 187, 200, 192, 151, 156, 183, 182, 199, 193, 173, 196, 176, 166, 199, 172, 167, 194, 159, 181, 199, 185, 192, 190, 158, 189, 189, 184, 159, 169, 168, 152, 188, 177, 173, 184, 198, 189, 174, 195, 189, 198, 186, 190, 200, 193, 200, 178, 185, 189, 196, 150, 166, 168, 180, 166, 199, 185, 196, 192, 174, 160, 162, 175, 176, 195, 190, 179, 153, 168, 181, 156, 183, 190, 169, 195, 173, 183, 185, 165, 155, 186, 154, 152, 158, 167, 194, 170, 176, 155, 163, 189, 186, 168, 162, 171, 156, 184, 163, 199, 180, 199, 161, 154, 181, 153, 162, 154, 173, 152, 178, 154, 199, 196, 194, 185, 154, 180, 199, 196, 163, 160, 154, 160, 154, 162, 163, 161, 186, 200, 197, 192, 163, 175, 197, 185, 180, 175, 152, 184, 160, 162, 199, 185, 189, 153, 192, 171, 155, 167, 182, 179, 178, 176, 164, 181, 163, 166, 189, 182, 160, 192, 199, 174, 169, 186, 189, 161, 196, 187, 160, 169, 151, 152, 198, 184, 184, 191, 195, 162, 162, 187, 155, 191, 177, 185, 164, 185, 150, 182, 159, 165, 195, 179, 177, 155, 182, 198, 199, 199, 183, 153, 189, 188, 200, 160, 192, 196, 174, 168, 171, 169, 175, 181, 155, 169, 168, 169, 181, 188, 186, 157, 197, 170, 183, 171, 171, 178, 162, 152, 189, 150, 151, 196, 181, 182, 179, 192, 185, 168, 177, 171, 190, 158, 191, 154, 193}

    0

    Returns: 15

  87. 19

    18

    {167, 181, 196, 168, 188, 173, 196, 170, 163, 162, 163, 161, 160, 163, 180, 173, 188, 169, 160, 175, 192, 170, 187, 174, 157, 157, 176, 196, 150, 151, 162, 174, 160, 193, 195, 193, 193, 192, 180, 157, 152, 165, 192, 151, 163, 154, 177, 176, 194, 162, 164, 187, 158, 180, 185, 178, 199, 154, 160, 200, 169, 155, 192, 177, 193, 187, 200, 175, 168, 183, 161, 159, 193, 163, 172, 183, 173, 166, 154, 158, 184, 192, 155, 165, 188, 169, 173, 179, 196, 190, 160, 191, 182, 178, 188, 177, 156, 160, 195, 197, 185, 152, 159, 180, 200, 188, 169, 189, 193, 176, 179, 182, 176, 192, 183, 182, 176, 182, 164, 182, 167, 161, 177, 188, 157, 157, 196, 199, 198, 170, 174, 162, 164, 175, 194, 200, 152, 159, 154, 199, 188, 161, 173, 172, 191, 177, 168, 195, 188, 153, 178, 177, 195, 151, 195, 196, 199, 185, 152, 151, 194, 153, 188, 157, 152, 156, 184, 157, 184, 165, 150, 184, 159, 169, 182, 180, 150, 155, 182, 188, 184, 189, 186, 166, 199, 180, 161, 163, 163, 171, 194, 199, 155, 192, 188, 187, 181, 157, 151, 179, 193, 178, 151, 152, 181, 179, 163, 197, 199, 157, 187, 175, 170, 177, 173, 197, 199, 160, 168, 176, 199, 192, 180, 186, 165, 168, 179, 171, 174, 183, 169, 177, 189, 198, 171, 178, 150, 159, 196, 165, 189, 172, 164, 157, 169, 200, 155, 198, 194, 180, 170, 156, 170, 150, 175, 162, 199, 183, 167, 184, 165, 158, 197, 200, 190, 152, 153, 169, 158, 188, 181, 200, 183, 169, 156, 181, 177, 162, 196, 176, 157, 173, 190, 175, 179, 161, 167, 199, 168, 152, 187, 187, 193, 168, 165, 152, 168, 171, 151, 181, 186, 174, 194, 192, 167, 191, 176, 188, 161, 192, 157, 187, 150, 174, 191, 184, 198, 185, 173, 196, 155, 185, 192, 194, 162, 186, 178, 182, 184, 199, 183, 195, 197, 192, 159, 165, 188, 172, 184, 180, 190, 199}

    1

    Returns: 22

  88. 19

    19

    {168, 175, 160, 161, 163, 181, 172, 184, 189, 166, 176, 198, 172, 174, 166, 160, 175, 153, 188, 198, 152, 174, 184, 178, 170, 152, 167, 195, 192, 199, 174, 174, 164, 174, 164, 173, 151, 157, 168, 157, 184, 189, 195, 157, 195, 176, 190, 191, 175, 166, 173, 174, 173, 153, 171, 199, 193, 177, 160, 191, 182, 160, 176, 195, 195, 199, 151, 166, 166, 172, 194, 153, 195, 186, 196, 181, 165, 189, 156, 169, 192, 185, 198, 154, 177, 181, 185, 183, 174, 172, 182, 162, 190, 186, 179, 163, 174, 180, 171, 165, 174, 167, 185, 195, 175, 174, 156, 173, 150, 195, 150, 164, 167, 152, 157, 178, 171, 179, 196, 165, 177, 186, 150, 167, 178, 174, 170, 160, 173, 170, 173, 198, 172, 164, 171, 196, 195, 166, 176, 152, 196, 162, 168, 197, 200, 185, 153, 188, 161, 175, 155, 167, 180, 157, 153, 153, 159, 168, 187, 160, 180, 183, 193, 174, 182, 192, 193, 155, 165, 181, 196, 170, 177, 183, 186, 164, 164, 168, 169, 157, 159, 181, 193, 154, 162, 183, 175, 180, 183, 177, 193, 163, 166, 166, 152, 174, 188, 174, 168, 191, 183, 183, 193, 192, 200, 195, 160, 150, 176, 170, 154, 161, 198, 166, 176, 160, 159, 194, 158, 178, 162, 163, 199, 200, 185, 174, 177, 167, 157, 168, 168, 191, 179, 181, 153, 151, 162, 150, 177, 151, 156, 184, 176, 198, 191, 160, 178, 168, 179, 196, 170, 176, 179, 178, 198, 157, 188, 181, 185, 164, 166, 153, 198, 150, 186, 175, 153, 191, 192, 182, 200, 151, 192, 182, 156, 198, 158, 188, 152, 186, 179, 165, 170, 179, 173, 197, 178, 173, 154, 192, 198, 176, 178, 184, 167, 157, 194, 170, 150, 181, 186, 183, 183, 193, 170, 185, 179, 157, 192, 162, 178, 154, 165, 162, 186, 190, 167, 161, 199, 181, 194, 178, 163, 179, 170, 167, 189, 196, 182, 161, 194, 178, 173, 164, 153, 183, 150, 168, 161, 180, 161, 181, 168, 182, 159, 191, 196, 184, 191, 190, 194, 178, 194, 195, 173, 181, 190, 198, 162, 197, 200}

    0

    Returns: 52

  89. 20

    20

    {165, 176, 183, 156, 195, 165, 170, 192, 150, 153, 183, 182, 170, 156, 153, 188, 153, 178, 171, 183, 181, 196, 173, 158, 157, 165, 158, 153, 154, 165, 166, 189, 158, 158, 165, 157, 173, 170, 175, 176, 188, 175, 175, 162, 165, 175, 176, 166, 194, 199, 186, 158, 176, 190, 161, 193, 195, 181, 164, 161, 178, 195, 199, 151, 200, 158, 195, 191, 193, 151, 152, 191, 190, 153, 162, 170, 191, 194, 197, 161, 172, 194, 175, 171, 163, 157, 177, 172, 160, 155, 170, 174, 156, 195, 198, 182, 196, 162, 156, 197, 169, 185, 167, 184, 160, 189, 172, 191, 169, 167, 194, 174, 150, 167, 150, 188, 169, 176, 159, 167, 155, 171, 177, 178, 180, 183, 198, 171, 158, 193, 172, 156, 157, 161, 197, 194, 197, 171, 168, 175, 190, 154, 197, 192, 189, 157, 188, 196, 151, 188, 180, 183, 180, 173, 184, 159, 160, 175, 186, 196, 199, 196, 188, 171, 161, 175, 200, 184, 163, 165, 150, 178, 163, 185, 155, 200, 184, 170, 154, 187, 150, 154, 164, 182, 156, 180, 174, 199, 185, 190, 158, 188, 172, 195, 169, 150, 183, 170, 177, 180, 159, 198, 151, 188, 157, 168, 200, 197, 166, 184, 183, 154, 153, 174, 189, 154, 157, 153, 187, 190, 184, 156, 169, 157, 178, 200, 180, 187, 190, 170, 163, 179, 171, 197, 165, 160, 172, 153, 157, 160, 150, 155, 166, 186, 179, 165, 180, 169, 183, 200, 177, 193, 159, 168, 186, 170, 198, 177, 190, 166, 154, 186, 179, 173, 161, 198, 173, 153, 173, 191, 182, 163, 153, 151, 150, 164, 182, 169, 187, 193, 167, 193, 197, 198, 156, 193, 200, 151, 162, 183, 179, 199, 191, 165, 165, 174, 176, 191, 200, 172, 172, 183, 167, 178, 166, 169, 166, 186, 192, 161, 191, 169, 164, 184, 187, 183, 198, 152, 195, 167, 159, 198, 185, 182, 170, 200, 152, 178, 196, 197, 155, 150, 186, 154, 168, 165, 192, 197, 193, 163, 164, 157, 195, 155, 171, 161, 182, 183, 192, 167, 160, 167, 176, 155, 175, 176, 197, 168, 156, 154, 151, 162, 185, 188, 161, 182, 181, 172, 185, 172, 170, 177, 150, 166, 153, 171, 188, 152, 152, 156, 176, 169, 181, 176, 175, 200, 174, 166, 193, 185, 196, 168, 189, 159, 168, 164, 165, 197, 175, 194}

    1

    Returns: 26

  90. 3

    4

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

    1

    Returns: 3

    +---+---+---+---+ | 0| 3| 6| 9| +---+---+---+---+ | 1| 4| 7| 10| +---+---+---+---+ | 2| 5| 8| 11| +---+---+---+---+

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