Statistics

Problem Statement for "GameOnABoard"

Problem Statement

This problem statement contains superscripts and/or subscripts. These may not display properly outside the applet.

Alice and Bob are playing a game on a rectangular board. We use (i, j) to denote the j-th cell in the i-th row (0-based index). Each cell has a cost of either 0 or 1 and they are given by the String[] cost. The j-th character of i-th element in cost (0-based index) denotes the cost of cell (i, j). A path between two distinct cells (x1, y1) and (x2, y2) is a sequence of cells (c0, c1, ..., ck) such that c0=(x1, y1), ck=(x2, y2) and for each i from 0 to k-1, cells ci and ci+1 have a common side. Cost of a path is the total cost of cells on this path.

The game is played as follows: First Alice chooses a cell (x1,y1), then Bob chooses a cell (x2,y2) which is different from (x1, y1). Finally, they compute the value L: the minimum cost of a path between (x1,y1) and (x2,y2). Alice's goal is to minimize L, and Bob's goal is to maximize L. Compute and return the value L that will be achieved if both players play optimally.

Definition

Class:
GameOnABoard
Method:
optimalChoice
Parameters:
String[]
Returns:
int
Method signature:
int optimalChoice(String[] cost)
(be sure your method is public)

Notes

  • Two cells (x1, y1) and (x2, y2) have a common side if |x1-x2|+|y1-y2|=1.

Constraints

  • cost will contain between 2 and 40 elements, inclusive.
  • Each element of cost will be between 2 and 40 characters long, inclusive.
  • Each element of cost will be of the same length.
  • Each element of cost will consist of '0's and '1's only.

Examples

  1. {"11", "10"}

    Returns: 2

    Regardless of Alice's choice, Bob can always achieve L=2 by choosing the opposite corner. Sometimes he also has other optimal moves. For example, if Alice chooses (0,0), Bob can choose any of the other three cells to get L=2.

  2. {"01", "10"}

    Returns: 1

    Alice will not choose the cell (0,1), nor the cell (1,0). If she chooses one of those, Bob will choose the other one and L will be 2. Alice prefers the other option. If she chooses one of the cells (0,0) or (1,1), Bob can only achieve L=1.

  3. {"011","011"}

    Returns: 2

  4. {"00","11","00","10"}

    Returns: 1

  5. {"00", "11", "11"}

    Returns: 2

  6. {"0110011000","1000101110","1100111110","1110111101","0001111111","1100001101","1111011100","1010111111","1000001000","1010010110"}

    Returns: 4

  7. {"111001", "001000", "111111", "001111", "001100", "001011", "111001", "010011"}

    Returns: 3

  8. {"011001000","111010101","110011100","011111000","000001011","111001000","101100111","011001011"}

    Returns: 3

  9. {"11111100010","01101000100","10001101101","00110011001","11100110101","10000011001","01000000010","01000110011","01000111101","11100100110","00011010111","01110100111"}

    Returns: 4

  10. {"001001101011", "110011001101", "111111000001", "111101010001", "011100101111", "110010111000", "111111110101", "111011110111", "111100100011", "000000000110", "101011011110", "011111000111", "101111001011"}

    Returns: 5

  11. {"000000101110","011011110000","111100110101","001011010111","100001111011","000111100100","001111100101","000111010010","101101001100","111011111011","110010111001","101010001100","100101100011","010110111010","111010001100"}

    Returns: 5

  12. {"000110001010011010","001011001010100101","000100000100111111","000100010111000110","001011101100011001","001101111111101001","001110000010001000","000000011010001001","100001100001101100","101101111111110011","001110000101111001","111001001011010010","011100001100111101","111110000001011110","100111110010101101","000001010010110110","100011000110001110","110100001101101001","000000101010110101","100000111011011100"}

    Returns: 5

  13. {"00101100100101111011","00111110011001000000","10100011100111100100","00000101001111101110","10001011101011100111","00010001001001000101","10100011101011111000","10001011100010000001","00110111111100100110","00100100000001100011","10110000011101100101","01110011001010000111","11111100101100101011","11100110100110100000","11100101001011000100","01111010011100111001","11101010110011010110"}

    Returns: 4

  14. {"1111100010111010","0000110111001010","1000100011101111","0101010110100110","1100110110010100","1111101000000110","0110110111110010","1110110000100011","1010110011100000","0110000010101100","0010111010111110","0110110110101001","1100001111110110","1001011101000101","1001001100000001","1011001101101011","1111110111011110","0111101100111011","1000101001110101","1110101001100010"}

    Returns: 5

  15. {"1101110000011101000011","1110101101110110100111","0100100100010100001010","1001101000100001011010","1010011100000100101010","0101101001110101001000","0100100111011111100111","1011001010101110100011","0010110101010011100001","1101110010101010001110","0000101000110100001001","1101101011111101010111","1111101110110111100101","1010101111000101011011","0001101000101101111001","0101010011110101100011","1000111010111111100101","1111000111011110111111","0011100000111101010111","0101101111101000001100","1001001100010000110010","1101110001001000010011","1111000000001110100010"}

    Returns: 7

  16. {"1100101111011001110110","0100010110111001011000","1000100010110101011111","1011001010110001010010","0100001010001000111011","0111001000100011101000","1111100100010111001001","0001100011111001110101","0100000011000110111101","1101000101101101110110","0110011100111101010101","1010010111100011110010","1010110100000010100101","0111010110100101100100","1101011010010010100011","1101111110111000011010","1100000001000100011001","0101111111101110010000","0101000100011100000010","1000010000111011010010","1100101000110010100101","0000101010111111101010","1011011001000101010010"}

    Returns: 5

  17. {"1101100000000010001001","1001001111111101000000","0100110011111111011000","0010100011111101100111","1011101011101010100110","1000000000101010111101","1000001111100011111110","1111101011000001010101","0000000001001100000010","1100011001111100011100","1000101111000011111000","1000011001010011011011","1100100100001000110101","0000000110110100110111","0010111101101110011001","1000001111011001111111","0010011100010010010100","0101110100110011111110","0101000110000110001010","0000010010101010101100","0100110111110110010011","0101101000110101001011","0001001001001011001101","1010110110100001100010","0110110011110000001110"}

    Returns: 5

  18. {"101001100001101011010110001010","100101010001001101011001010010","000100010000010001111110101111","111100010011111101010001000000","011110111101111111110111011011","010011101001001000101101010001","010101110111100000101110100011","110100011101111001010000101010","000010101000000111010101100101","110011011111010010000100010101","010010000000111011001001100000","100101000101001011111010001100","101000101111111001001010101011","100101001001001111110100101011","000010000101010010100011011100","001010101011100010101001010101","000111111100000010101100111100","000011100001100010001101110001","111000100001110001001101100110","111110000000101011011011001010","100010010010001011000000110111","111111010111001001111110110100","111000001110101001110000111010","001011101110000000000010111110","110101010100011011110101101001","111001010001001010010011011100","100000010111111100100111110101","001101110111100011101100001100","111000100001010110011010010110"}

    Returns: 5

  19. {"001011000010000100001101101","101010000011100101110111000","101101001110010111100101001","111110010010010110110010000","101000100001111110101110001","100111010011110110011101101","110101001101100010001011101","000011111100000111101010101","100011001010100011101010101","110011101000001101010000000","110011111001000000101011000","000111001100010110101101000","011001110101001110110001101","001001011100101000011001000","001010000011010110101110010","001010011100011110000110110","100011101000101011100111010","000010001001000000111101111","100111010010100110001101100","000110110011111100101100011","011111110001000011111001111","010101110001111110010100100","110111000101000001100101101","011000000011010000101111011","110000011010110010100111100","100000101011001110010100111","110011101010010100100111100"}

    Returns: 5

  20. {"111011101110110101011101001011","011110111100011011111011110010","101010110010111010010111111010","000001110101010010100101010111","000001001111001011111101100000","000011001101010000111011111011","100111101110100000110101101110","101001110101110101110001010101","111011101100010110101010010010","101000011010110000001111010011","101000000011111011010101111110","100010011110010100001101111101","101001111011110101100000011100","100111001101100001101011100010","011010000010111110100011110100","101110001100111010111010111101","101101001000111101010000110010","011001100011011100011001100000","111001100110000011110001001000","110110111000000100111001110111","001000100110100001101101101001","010111100000100001100001001001","100100110100101111011011010101","001111101100101100001100011010","101010000101110110110000010000","010001100010111001110010101100","000010011011000101110101011101","111110111001011001010101001101","010111110111000001000000100001","001111001101001011010111000100"}

    Returns: 7

  21. {"01100101000110000001001001111011001","10001000000001001100001011110011101","10011010011100011010000111011100101","11010011000010101000010100111001101","10001110001000000010001100000111100","10001001010010001111011011001010111","10000001001000101011101001001001001","01010000101110000101010011010110101","11100101101110000010110001101010110","11101001010000110100011011110101011","11011000011111100110011000010001100","11110010110010010001101001100001010","10000100010001100000001011101011011","11001001011111000111000101001010000","10110101000000101000010100101101011","01010110010101101000111010011111001","00000111001101101101101000101001001","00110011110100101010101010010000100","10010110110110001011011010100010101","11011000110010100000100100001001100","01011110011101010011001000011110001","11111010110100111110111011111001101","10111011100100110111010100001010100","01110010001010101011100100110000010","01101010101001100101000101110110100","00100100111110100101111000111001001","00111011011110101110100000011100111","10101110010101000011001000100101000","00010001100011000011000100000111011","01110011110000001110110101111101001","00011001001111110001001010000100100","01011011000011010110101111010111001","00000100101011101000110001111111010","00010000110000101001100111111001111","00101111100011001111100001010010110"}

    Returns: 6

  22. {"1000101011001001100001111000000011","0100111001011111010100001000010011","0101111001001100111000110101011001","1000010111001000110101110101010110","0011110010010001000100011100100000","0000111111100101101101001100001010","0010010011111011111001110010010010","0010011110100110101000011100001110","1010110010010101010011010100111011","0100011010110011000100100111000111","1000110110111101100110100000011110","0110111111011010001011100000011100","1000110010001100010010110101110001","1000101100000110011110101000011101","1100000110011110011111100101110011","0010001001100110101111010100001011","0010100100100110011101011101000100","1100111010011111011110101110101011","1010101001111010011110101111011001","1101111011010001110100100000010100","1011001110110100000011110000000111","1001001001010100110001100111101111","0000101111110111110010000001010110","0110110100101010101011000111111110","1101011011111110111100111001100110","1000101100000000110001000110001101","1100011111010110111110111110000001","1001010001011000011111000000110001","0010011011110010110010000000001001","1110111110010101110110011100001010","1110100111101001010001101111101111","1011100101100111100101001110010111","0000100001110001001001000000011101"}

    Returns: 7

  23. {"1110110111101001011010111011011000","0100111101001011101110011111111101","0000100000010100100110010000001111","1100111110000000011000010001100100","1001000010000010110010010010000101","0101100111001000110101000111110111","0011101110111010111110000100111110","0101100110110111011101111010011000","0011000010110111110011111001111101","1101111010100011010100000010100110","1101010011110101100001110101111011","1000100000100011011110000111101111","1100101111001101001100111010000101","1100001001011011111001111011100101","0001101101111110001100101000111011","1001110110011001111001110110010111","0010001100001011010001101010010100","0101110000001000111111100100010100","1011110101111010100001011010101100","1110010100010100100010001000011101","0010011110111000111010101100000011","1100011011110010001110101000000000","0100110111100100000000000101000100","1001110101101101111110001101111110","1101111111110101010110111001110010","1110000110111001111000001111001100","0100111111100000001001111011111110","0000000010111100010101110100000100","1000111101000101011100111001011000","0100011010001110001111101110101001","0000101111000101011111001000101101","1000011111011011100100010100111010","0101110100011110111010100111000101"}

    Returns: 6

  24. {"0111101000100010001011100100111110000010","1110000111010000001000001101110010001001","0101010111100000101111101111110000010110","1111110100000110010111010001101111101000","0110101000000010101111010110110100110000","0011011101000110101110010000000101101011","1000101011110100010001001001011000000000","1011110010010101111110000100001000111000","0101100011001000111000010001110011101100","0101010000011011000011000111110110100001","0111000011100111001111011001001101101111","0010011010100101011111101101110001001100","0110100111001001110101010000010001111100","0001000011101011101101110011101010001110","1000010000110110100110111001001101110000","0000110000000100111100010111011011111110","0110100110100111001100100000010010011010","1100100110101111000110100110011001010011","1110100101010100001100000010110001111000","1111011100101111011011111011100101010000","1010110001010101001101000011001101011110","0001101001101101111100000001110011110100","0100100100111111010100110001000111011101","0011111100000100101101110011110100011100","1010101100001001011101011001001010010000","0010010100010001001100100001000111011001","1101001101011011110110110000111111100110","0010110111011101010010101110100110110100","0111110001010110011000001100110110101111","1011110110111111111110000010001101101100","1110001100010011001010110100100010110000","1010111011001100100000010010111011000010","0010100101111101001101001111100101010100","0111000100100100001000010001100100000011","0101001000100100101101011010001100001101","0011110010010100010010111100011011010010"}

    Returns: 7

  25. {"110100010100100100001100001111111011","001001000110100000011111101010010000","100100011000110011100101010111110010","110111110010000110111000110110100010","110100001011101101001000101000010001","100101100111001101001010100001001011","001111101010000111100100001000000110","111001101100000010100100010000000100","101101100110000001110101000010011101","011010011001001110110110000110111010","100001000111110000011111100101100111","100100001000010010110101111111000111","011011110011010000110100001110111111","110010101111010010110111100110101100","111100010011010101100111000011000010","000010101011001011100010111001011000","011111110000110110000100101010010110","000001010111100101011011000101101011","000100010100000001100100010110101101","001100111110110101011101011010101111","010110110110001110010000100010000000","011100011111011010101001110100001100","010110111000101000001010010010100011","101111011101001010000110001101101110","100000100100111000101011101011010111","011001111110010000000101011101000011","101111011111100011000100111100001010","011111100100101001110111011010010011","100010110001001111000111111100101101","010001101100000111001010110001011001","101011111001111110111000010101001111","011001111001101101010010001000000011","101110101100010100001000001011010000","011110011010110010011011011000110011","001100101001001100100110100111000100","101011110001101011011001101111000000","100111000101011000010001111000101010","110011111110001110110011111111101011"}

    Returns: 7

  26. {"110010100101010110100010001100111011", "001000000110100011010100000001001000", "011000110111101001011101110111000100", "111001011000100101111010100110110011", "111000011101001010000100001010000010", "111001110010100101000001001100011011", "111110100111010101100000100111000111", "011111111100100111111110000001110111", "110000010101001111100011110000001000", "010010110111111100011101100000011010", "110001100001111001101000101110110001", "110010000111011110000010110111010101", "100100110101001001101000001101101101", "001011101101001100111110101111001110", "111010111111111100110100000011111100", "110101101000001001000100101011100000", "011011001011010001001000100000110101", "011111111100000011010111010011010100", "111001111110001110001110010100111010", "000001111000001100101010000001101110", "010000110000010010111110111000010101", "100010010100110011000111101001101011", "111010110001101011010001111101111100", "000111110000110000000101100101000110", "110000010111001001110001101010111100", "011111101101001011011010011111100010", "110101111101010100110010000011001101", "101101111001010100101111100001110001", "000110010100101111011011110010010010", "110101010011101000111011100000010011", "110001010001110011010100110000010001", "111010101100111100100011001101010100", "011000000000100001011010000100010001", "100000110110000001010001001111010000", "100011111110010011011011001110011111", "101100001111100101001101100000100001", "010000111011010110011001110011111000", "100010100111110111001010100101111010", "000110011110111011111000101000001000"}

    Returns: 7

  27. {"0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000"}

    Returns: 0

  28. {"11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111","11111111111111111111111111111111111111"}

    Returns: 40

  29. {"101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010","101010101010101010101010101010101010101","010101010101010101010101010101010101010"}

    Returns: 19

  30. {"000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111","000000000000000000000000000000000000000","111111111111111111111111111111111111111"}

    Returns: 9

  31. {"011101110111011101110111011101110111011","111011101110111011101110111011101110111","110111011101110111011101110111011101110","101110111011101110111011101110111011101","011101110111011101110111011101110111011","111011101110111011101110111011101110111","110111011101110111011101110111011101110","101110111011101110111011101110111011101","011101110111011101110111011101110111011","111011101110111011101110111011101110111","110111011101110111011101110111011101110","101110111011101110111011101110111011101","011101110111011101110111011101110111011","111011101110111011101110111011101110111","110111011101110111011101110111011101110","101110111011101110111011101110111011101","011101110111011101110111011101110111011","111011101110111011101110111011101110111","110111011101110111011101110111011101110","101110111011101110111011101110111011101","011101110111011101110111011101110111011","111011101110111011101110111011101110111","110111011101110111011101110111011101110","101110111011101110111011101110111011101","011101110111011101110111011101110111011","111011101110111011101110111011101110111","110111011101110111011101110111011101110","101110111011101110111011101110111011101","011101110111011101110111011101110111011","111011101110111011101110111011101110111","110111011101110111011101110111011101110","101110111011101110111011101110111011101","011101110111011101110111011101110111011","111011101110111011101110111011101110111","110111011101110111011101110111011101110","101110111011101110111011101110111011101"}

    Returns: 28

  32. {"1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010","1010101010101010101010101010101010101","0101010101010101010101010101010101010"}

    Returns: 18

  33. {"0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111","0000000000000000000000000000000000000","1111111111111111111111111111111111111"}

    Returns: 9

  34. {"0111011101110111011101110111011101110","1110111011101110111011101110111011101","1101110111011101110111011101110111011","1011101110111011101110111011101110111","0111011101110111011101110111011101110","1110111011101110111011101110111011101","1101110111011101110111011101110111011","1011101110111011101110111011101110111","0111011101110111011101110111011101110","1110111011101110111011101110111011101","1101110111011101110111011101110111011","1011101110111011101110111011101110111","0111011101110111011101110111011101110","1110111011101110111011101110111011101","1101110111011101110111011101110111011","1011101110111011101110111011101110111","0111011101110111011101110111011101110","1110111011101110111011101110111011101","1101110111011101110111011101110111011","1011101110111011101110111011101110111","0111011101110111011101110111011101110","1110111011101110111011101110111011101","1101110111011101110111011101110111011","1011101110111011101110111011101110111","0111011101110111011101110111011101110","1110111011101110111011101110111011101","1101110111011101110111011101110111011","1011101110111011101110111011101110111","0111011101110111011101110111011101110","1110111011101110111011101110111011101","1101110111011101110111011101110111011","1011101110111011101110111011101110111","0111011101110111011101110111011101110","1110111011101110111011101110111011101","1101110111011101110111011101110111011","1011101110111011101110111011101110111"}

    Returns: 27

  35. {"10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010","01010101010101010101010101010101","10101010101010101010101010101010"}

    Returns: 17

  36. {"00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000","11111111111111111111111111111111","00000000000000000000000000000000"}

    Returns: 9

  37. {"01110111011101110111011101110111","11101110111011101110111011101110","11011101110111011101110111011101","10111011101110111011101110111011","01110111011101110111011101110111","11101110111011101110111011101110","11011101110111011101110111011101","10111011101110111011101110111011","01110111011101110111011101110111","11101110111011101110111011101110","11011101110111011101110111011101","10111011101110111011101110111011","01110111011101110111011101110111","11101110111011101110111011101110","11011101110111011101110111011101","10111011101110111011101110111011","01110111011101110111011101110111","11101110111011101110111011101110","11011101110111011101110111011101","10111011101110111011101110111011","01110111011101110111011101110111","11101110111011101110111011101110","11011101110111011101110111011101","10111011101110111011101110111011","01110111011101110111011101110111","11101110111011101110111011101110","11011101110111011101110111011101","10111011101110111011101110111011","01110111011101110111011101110111","11101110111011101110111011101110","11011101110111011101110111011101","10111011101110111011101110111011","01110111011101110111011101110111","11101110111011101110111011101110","11011101110111011101110111011101"}

    Returns: 25

  38. {"1000110001111100011111100101111111111","1001110101111011111100011001110011111","1111111011111011000001101101010011110","1111100011110111111111101010110101111","1101110110111011110110010001111101001","1111100110111001101111101011111111101","1001011101011110110101101000101101110","0111100100110111111111101111000111111","1111110011111111001110111111111010011","1110111101111010111111111111111101010","1110110001011011010001011011110011100","1111110111101110011111111110001011011","0100111011111111111110101110111000001","1111101011110101100010111001101110111","0111111110011001111100111111110111110","0000110010101111101101111001101111010","0100011111110011100111010101101111101","0011110010011110100011111111111111011","1110110111011111110011111001111110111","1011011001111101111001110011111111111","1111011111111110111110000111110011101","0101110111011110111110010100111110100","1010011111011111111101111111011101010","1111111110001101110001011111110101100","0000110011111110110111111010101101011","1100111111011110001111110111011111110","0011001100111111111101111111011001111","1111010111000111100010011000110111111","1101100100100111110111101110101101101","0011111011111110111110101111110111101","1111011111111110101100110111000011111","1111110110111111011111101111000111011","0111010100110101101110110011110111011","0101111101101110101011100011110111111"}

    Returns: 15

  39. {"11000111010101000110111011111101","01010101101001010101110111111111","11011101111111111011101110110110","00011001111110111001111001010111","10111011111011110111111110101010","11111111111101110001101100101011","10110110111011010111110111101100","01111111011010011010100100101111","11011011110111011110111111000111","01110101110110011111110011111110","10111011110001111110101101101101","11001011001111101011011110111110","10001101111110101111111110101011","01111011101011010111010001110111","11011111110011011110101100110011","01101111111011111111111001100011","11111111111011101011100001110111","11111110111100010110001101111110","11101011000110010110000011011100","10111100111111101011111111111101","00111110010101111101111111110011","11100110101111001111101100110111","11110011000111110010110111100110","11110010110101111110101111111110","11100111011101011111100110101101","11011110111010010010111101101011","11001111010010110110111011101111","11011000111011011001111110011110","01110011011110001110111001100111","11100110101111010011111011010101","10011101111111111101110010100101","11111111111101101110111110011111","10011111100101010110111011011101","11111001001010011111100101111111","11110110111011110111110111010011","10101111110111110111111111101010"}

    Returns: 13

  40. {"011111100100111101101100011111100111","101001111110111101110011111111011100","111111111111111011110101111111111110","010111111111111101101110001111110111","111011111111110110001100101111101011","111101101101010100110111101110110011","111100010111100011111111001111011111","010011111111101101011011111011111100","101111011111101111110111110011010111","001101011111111110111001010101101011","110111111111100111100111111011011110","110011101111111111110010001111010111","111011111110101011011011110110110110","111100110001100111111110111101101111","100001111111100011111101100111101101","111011101101110111110111111110001110","110110000111010010111011100011101100","111101000101111111100111111110100111","110101011010111110011111111111111110","011100111111011111111110010011111111","111011010111101111111011111110110111","011111111011101111101111111011111110","111110011100110111101010011011100111","111010010110111111110101011110110010","001111010110111110011111110111010111","011000111111110111001110111111110101","110111111111101101110001111011111111","010010111111111110111001010111111110","111011111010110010110101000111110111","101011111011001110111011001110100011","110111010011010111110111101011011111","011000111101011101011011111110100011","101100111110011000011111010110001001"}

    Returns: 15

  41. {"111110001111111110111110101101101111111","101001011111010100110111001101100111110","011101100111010110011011010111111111110","011111010110001100110111111111001111011","010111011110110000111111100101111111101","111110101111110101111111101011111111010","011111110111111110011110110010111100111","001101111101111011011011111101011100111","111110111010111101001001110101111011111","111010100101110001101010001111111010100","110111101010011111011010001111001111110","111111111000110101101111111111111010110","001001111101110111000100110110100111111","111011001011010111111101101011111111111","100111111001111101101111100001110111001","101101010110011110110011111111010111011","110111110101111111111111111100011101110","110111101111111110101111001011001111100","111111001101011110100001101011101010101","111100111010000010111011111110101101011","011101111001111101101011011010110111011","001111101001100011111011110101110111011","110101000111111111010101110111110111101","011001011111111000111001101111011101101","000110010010001100101011111101111111101","000111110100110101110111111110111111101","111111110110111101111111111001011011101","011110010001000010111111111110111111011","111111110000011111100100011101110101111","011111111011111011000000111011111110111","111011111000101100110111111011101111111","111000010010000101001100101011111111101","000111000111111111110111101101110101110","001101110111110110111111111111111110111","010111011110000101111011010100101100011"}

    Returns: 14

  42. {"11001001111111011111100011010111101","11011100110010001111100111111001110","11011000101111110111101111110101000","01101111011110101101111011010101111","00111011110111111101001011111110101","01110111101100111111011011010101100","11101011110111011101111111101110111","00111110011010111011101110110111101","11111111111111010101111111111000011","11101110011111101110111101011100111","11010000011011010111011110011011110","11101001110111011111111011011001000","01011101101001110101110110101110111","10111111110101100001100011111111011","11111100110011010010011111011101011","11011110001011101101111111110111111","11001110101001110111110111101011001","01111111001001110101000111111111110","10110010100100110110100111101111111","11111111111111101001111101011110111","10010111111111001110110001010011101","11101101010111111100011001111011111","11101101011011111100111011111101011","00100111111001010101010101110111100","11001111011100101111111111100111110","11011100010110011010111111111010111","11011111111110010101100101110111100","11101101101111111011111110111111101","11111111001111100011011111111111101","00111111111110011111101101001011101","11101110101111110010111001011101101","11011010111111000110111011010010110","11111110001011111111111111110111101","11101111111111100001001011011100111","00001111001111011111011011111001101"}

    Returns: 14

  43. {"0100101011011110001100110111111111","1111101011111111111100110111010011","1011011111100001011001111101001001","1111101111111111111011100101101111","0110110111111111001110001100111011","0101111001111010110011111011101001","1101001001101011110111111111010010","1111010111001111111000010101111111","1110101100101111111000010110110111","1101100101111111101101111000011001","0010110110101011010100110101111110","1011011110001111001101111111001111","1001001001111110111001000110111111","1011101100110011110111111011101111","0111111100000111110111110101011101","1110011111011111111101110111011111","1100110001010111110001111110111111","1001001000111111111101011000100010","0111111011001110011101011111101100","1111100011111001111001111111110000","1111111111011111010001011111010101","1111011011011101111000110101101111","1011011010011001111111101110011000","1011101011101111101101011101010010","0110111101111100100010111011101110","1111111011111111111100111110011001","0011011011111000101010111110010101","0011101011011011011111100001011011","1101011010111110110011100100101111","1111000011101100111111111001001111","1111011111110011111111001111100100","1101101001011101101101101111111110","1111111000011110111101011111111100","1111110101110110011101100111011110","0110011011001110111110111111011010","0111011001111110110101011101101001","1111111011011111110011111011111101","1111001111000110100111100111110101","1011110011011111101011101110101011"}

    Returns: 13

  44. {"100100111111111111111110111001111110111","101011010110111111111101111011111101110","011101101010111111101010001101111000011","011100101011111011011011100011101101010","010100111001101010011111010111111111111","111111111111111011101010011100111111111","111011001111110011101100110111011111111","110001111011110101110111110010111110111","111111111110010001110010011111011110111","111010100111101010101100100010111101111","111111111011110100011001001101111011110","111100111011110110011101110011000101011","010111010001111110110101100111110111110","111101011011110111111111111111110110011","101011110011001101001011010101111111101","001010100001111011011100011101100011011","111101110111101111110101110000011111101","001111111011101111011000011010111101111","110111100111111111100101111111110100110","110101111101100101011110101110110111110","101010011100100011111011110110001101100","100111010111111111101011111111101101100","101110011111000111100101000011111110110","111011101111000011101111101100001111111","101101101111111111111110111100111111101","011100111000000110100001111111111111011","111101101111111111100010011000111101011","011010001101111100111111011011111101111","100111101111111110110011000110010000000","111110111001010110110101100100010010110","011010111111011110110111110010110110011","110111111101011101001111001111001001100","111110111110010111111111111101110111100","011111011011111101111111111001011110011","100100100001001100011111100111111110111","110101111110111111111010111100111111110","111011111101110111111001111010110110101","101111011111011111110111110111111111111","111110110110110011101101111110111000010","001011111111111011111111110111100100111"}

    Returns: 14

  45. {"101010111000000111110111110011011","001011111111101110110001111111111","110011011110110011110100110110111","110110001000111111100111111010111","011101111101001101011101111101011","111111111101111100101011101001001","101011000101101010111101110100011","101111101111111111100111111101101","010111110111111111100011110111000","111111110011111100111011111101001","100111111110011111110111111001011","011011101111111111111111110111011","100111111111001111101110110101000","011111111111011110001111111001111","110111111111111001011101011110110","010011110110001001111111100011101","111111111010011111111001011110111","101011111101110101111111011110111","111101110110011111111111110001111","011100101111111011110011111111111","110111010111110110111111101111001","111111101010110110111011111111111","110111001111111111111000101110111","110111100111100101011011111111001","100010111110110110101111110100110","111011111010101110001100011100111","011011101111110111011011011110111","110101010110010101110111111111111","111111111110101010011111111101101","111101111111100001110001100010011","101111001001010110111011110011111","011111111010111011010011011111111","011101011001111111111110111101111","001110111111111111111101101111001","001110111110001111101110111110000","111111111100001011100111111111100"}

    Returns: 16

  46. {"111111011111111000101110101010111111001","101101011101111111111100111101111111111","111110011111001111111111101000101011111","111110011101110111100110111111011111111","111111111011011111101111011010011101111","100100100001111111111111111011011101110","101011110111111101111011101001011111011","010111101011111111001101111101111010101","111111010000011011001110111011111100111","100101010111111111110111010110111111110","110110110100000111101100101101111101011","111011011010111111110111111111110101111","111011010101111011100110010010000101111","111110011111111011111111100110100000110","111111101101100110110110111101111111111","000001100111111110011001110111011111111","101101111110111111000101011101110011111","111011001100110011100110010011110111111","110010101101011110110111111111010111101","111110010011011101111111110011010111110","011110111010011110100010011111111111010","011111111110101111111100101111111111110","001111111110111001111100011100101100111","101111011100011011011111101011111111101","101011101111011111111111100000101111110","111110110101100110110111100011101111001","111111001110111100110110111111101000110","111111110111001111110001110011111111111","010110111111111111011101101101110100011","100111100111101011000111101111001000001","010111111010111011111110111111101100101"}

    Returns: 14

  47. {"110001111001111010011010010000110","110111101101101101011011100010011","110110111111011011011110100011101","111111110011111111100111110100100","111110010101110111111011111010111","000110011010111111111110110010111","011011111101111010111100010111011","011111111111101111011111111110111","010110001111100101101111010111101","111011011011011111010111010001111","111110111111011111101101111011111","110001110111111111100101110011111","001101111001111111111111100110111","110111101111111111001111101111011","101011111111111101110111111001101","011111111110011110111101110110001","001111111111111010011011111111111","011001011011111111111101011110111","111010100111010101111111110010111","110010011011111111011110110111111","011010011101111111111011011111101","111111011111011101011101111111111","111101111110110011010110011101001","110011010111111101111110111111011","111110111011110011111111100111100","001101011110111011111110100101111","111111111111100110111101111111111","100111000111111100110111111101011","100111001010111011110110110111011","111101110101011001111111110111111","011110011011100111011111010011111","011110101111111001111111011111011","110100011100001100011111101011011","011000111111111111111111111101100","111011111110010110111011111011011","100111011010011101011111110011000","101111111111011011111111011110011","111101111000111000111111101101111","111111111111101111111010110110111","100011111100010100000110101101111"}

    Returns: 18

  48. {"000110100111110010110101111101011","101110111011011001001111001010100","111010111101111011111111100011110","001110110110101101011111011011001","111110111000101011111111100000110","101110100011111011111111111111111","111011001110111101111111100111101","001110011011101110000101111101111","010111011010110110111001111110011","100101111101110111010101111111110","110110111100100011110101110101110","111001101101111111110111111111110","010011111101011111000101110111011","110101111110111111111111101111011","001111111011111000110001010111111","110111101101111110111011101011111","111111011110111101111100111000001","111111001111111001001111101011001","011011001110110110111111011010111","111101011111100011111101011111011","111101111110010111001111101111010","101000101010100010000001011001010","110011111111011011011101111001110","101111111011001111011101011011010","110110001001110011100111100011111","111001111111011111111001100111101","110110111011101111111100111101111","100111011100110111011100011110111","111001011111111111011111011110011","110101011111110110110111110111111","010011011101101110101110011011001","011111001001101100101110101011110","011100110101111001101111111111100","100011101110111111010011111101011","000101010111001111010111110011010"}

    Returns: 11

  49. {"1111111000011011100111111010111110101101","1010111110101010111111110101100111011011","0110111111101110001100001010111101110001","1111011111111111000101101111100110110101","1011001110110111111111111111111011101110","1110111111001111111000011101011111010111","1111001001101111010101111001011111111101","0011000101111111000111001110011010101111","0101110110110011100111011001000110101011","0110110011100101011111011100111101000011","0011110111110111111111111001111110100111","1110110111111110111001011011111011111111","1111111101110101100010011010010111010101","1101100111101100110101001101111101111111","1101111110110110011010111110111111011011","1111110011101111111101101101100111100010","0111101011111001111101101110110110101111","1111111111101000111110010100100011010111","0000110011111011001110111101111100100001","0101111011110100111100111110001001010001","1011100110100001111011101110011111101011","0101111011011111011101111111111111011100","1101011111111011111001010111111110111111","0011111111111110011111110100001111111011","1000001011100111110011000011111111101111","0110001110111011010111110101111101111111","1011101010001101001100110110100101101101","1001111111111101110111001101110111111101","1110111110111010111101111110110111011110","1101011010111110000101001100110110110100","1110110111010101111111110101100110110101","1101101011100001101000101111110111101111","1000111011011111111011101010101011111111","1111111011001111111011010011110110000101","1001011111111101011101111010101001001110","1010111010101011010101000110110011101111","0111010101110111111101101111100111111110","1111011111111011011110110110111010101011","0110111111100111001101111111101110110111","0000111101011001011111111010100111000011"}

    Returns: 14

  50. {"1100011111011000100110101001111111111111","0011101101110111011101001011111100101011","0101011110111111111110011110111111111001","1110111101011010101000011010001100101111","1011111111101110111111111110011100101011","1111011111010011111110101011101111111111","1101001101011010101101101100001101110110","1111111111001111110101111100001010101111","1010111100101110011111111111111110001110","1110111111110011101110111111101011111111","1110100111111100111101111111001100110001","1001011001011110011111011011111111101111","1111101101110101111011111010110001110011","0111111111110111100001111101111001001111","1000001101011110110111111001100111111011","1111111110101010110111111100011111100011","1111011100100111111011111110100011011111","1101101110001001101010110010101111101111","1111010101111110110101111011111111111110","0110001111110111111011101100010011000101","0101111111010111111110101101111110000101","1010111111010111110011110001001111110110","0001101111011110111111010111110110101011","1100110011111011001001010101010010010111","1111101000111000011111111001011111011101","0110010110110111110110110111110101111100","0111111110111011001101101110111010110111","1110001110101011101111110110010101101110","0010111100101110111101110111111111011101","1011010101101110011101011111101111101011","0111110110111111111100101010111111001100","0101101010001101111101101110101110111110","1110110111101011111010111111111000111010","0100111010111011111011101010010101011000","1010110110110101001111011100111110111011","0011011111111100010110011011011011010001","1101011110110100011110101111101010111111","1110011100111111010110111111111110111100","1011111100111111001111001111000000111010"}

    Returns: 15

  51. {"1011110011100111110101111110111111111","1101111110010010111001001101110011101","0101011111010111111110100110111111101","1001100110101110011111111101000001111","1111001110111010011111011110011010111","1101111101101101111011111011111001111","0000001111000100111111001101111000111","1111100011010111101011111110101011100","1100110111111010110111011111111011110","1111111110010100111101011111111101111","0101101011111110110001100111101101111","0010111111100100100111011111111101101","1111101111011110111110010011100100110","0011111111111011001111100111000111111","1110111011111111111111011111101001001","1000111111110100101101111111011101111","1111111111110111111010111011100101001","1111011111111100000001010110010010011","1011011100111111100111110101101101101","1111101101111110001101001101101110111","0101111110010111100111110101100110101","1110100011111111011001110001101111111","1010111111110011101110111001111011111","1101101000111101100110000111010010111","1100001111110001111111110110111111110","1111111011101011000101110111101100011","1110111100011000110110011110111111110","1111101010101101101010111100101000110","1111111110101111010111110000101111110","1101010111001111101011101101010010111","1011100111111111111111110010001111011","0110110111001111111101101111011011011","0011101110110111111111111111110111100","1111010111111110111100111011110101010","1011110010101111100111001111011101111","1111101111111111010011011111111000111","1001101100011111110010011011001001111","1111011101100111101111111110101110111","1111101111001110010011001110010111011"}

    Returns: 14

  52. {"1111111111101111111101100111011110","0111111100011111011111111111111111","1011001111010101101110111111100111","1110101100111110010101111111111011","0111100111011101001111111110111110","1111111110100011111011001011111111","0111110111111001101011111111110100","0101110011111111101010111111111111","0110101111110100011001011011101110","1001111011010110111011011001001101","1111111011110010110011111111110111","1100111101111010111011100100001110","0001101111110101011101011111111001","1111100111110011100111111001011101","1101111010111111111110101011111111","1111011111110111001011110111100111","1111100111010111011101001110111111","1001101111111111011101101111111111","0101101110011100110101011110110101","0110100011011101111111011110111110","1001111111101111111101110111011011","1101011111001001110000001101001100","0101110111011001101111100001111000","0011110101111011100011111111101011","1110101101010111100001111111011111","0011111100111101111011101111111101","1101111110101111011111101101000111","1101111101001100110111010111010011","1011100100100111110111111101111111","1111111111100011110010111101010000","0101111111101101001101101111011110","1001111111000111111000110001100111"}

    Returns: 14

  53. {"110010100101010110100010001100111011", "001000000110100011010100000001001000", "011000110111101001011101110111000100", "111001011000100101111010100110110011", "111000011101001010000100001010000010", "111001110010100101000001001100011011", "111110100111010101100000100111000111", "011111111100100111111110000001110111", "110000010101001111100011110000001000", "010010110111111100011101100000011010", "110001100001111001101000101110110001", "110010000111011110000010110111010101", "100100110101001001101000001101101101", "001011101101001100111110101111001110", "111010111111111100110100000011111100", "110101101000001001000100101011100000", "011011001011010001001000100000110101", "011111111100000011010111010011010100", "111001111110001110001110010100111010", "000001111000001100101010000001101110", "010000110000010010111110111000010101", "100010010100110011000111101001101011", "111010110001101011010001111101111100", "000111110000110000000101100101000110", "110000010111001001110001101010111100", "011111101101001011011010011111100010", "110101111101010100110010000011001101", "101101111001010100101111100001110001", "000110010100101111011011110010010010", "110101010011101000111011100000010011", "110001010001110011010100110000010001", "111010101100111100100011001101010100", "011000000000100001011010000100010001", "100000110110000001010001001111010000", "100011111110010011011011001110011111", "101100001111100101001101100000100001", "010000111011010110011001110011111000", "100010100111110111001010100101111010", "000110011110111011111000101000001000" }

    Returns: 7

  54. {"1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111", "1111111111111111111111111111111111111111" }

    Returns: 41

  55. {"10011100110111011100", "10110011011100100100", "10110100101001000110", "11010101010101010101", "01001101101110011011", "11010101101011011001", "01101001010101101101", "01011100101101010110", "10110101101011010110", "01110011010101010111", "11101111011011011010", "01110111010110111010", "01101101010101011010", "10101101001100110011", "10101100111010101101", "10110010101010101100", "10110110010110011100", "10001110010111000110", "01011010110011100110", "00101001101101010110" }

    Returns: 6

  56. {"101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101", "101010101010101010101010101010101010101" }

    Returns: 10

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