Statistics

Problem Statement for "GraphWalkWithProbabilities"

Problem Statement

Hero is playing a game on a directed graph. The graph has N nodes, numbered 0 through N-1. Each node of the graph has two associated probabilities: winprob[i] and loseprob[i]. At the beginning of the game, Hero takes a token and places it onto the node start. The game then proceeds in turns. Each turn consists of the following steps:
  1. Let x be the node currently occupied by the token.
  2. Hero picks a node y. The node y must either be the current node (i.e., y=x), or there must be an edge from x to y.
  3. Hero moves the token from x to y.
  4. One of three outcomes is chosen at random: With probability winprob[y] percent the game ends and Hero wins. With probability loseprob[y] percent the game ends and Hero loses. In all other cases (i.e., with probability 100-winprob[y]-loseprob[y] percent) the game continues.
You are given a String[] graph that describes the graph. More precisely, for each valid i and j, graph[i][j] is '1' if there is an edge from i to j, and it is '0' otherwise. Note that for all i, graph[i][i] is '1' to indicate that it is always allowed to stay in a node. You are also given the int[]s winprob and loseprob, and the int start. Assuming that Hero plays the game optimally, return a real number between 0 and 1, inclusive: the probability that he wins the game.

Definition

Class:
GraphWalkWithProbabilities
Method:
findprob
Parameters:
String[], int[], int[], int
Returns:
double
Method signature:
double findprob(String[] graph, int[] winprob, int[] looseprob, int Start)
(be sure your method is public)

Notes

  • Your return value must have an absolute or a relative error less than 1e-9.
  • Note that the input probabilities (winprob, loseprob) are given in percents but the return value is not.
  • The constraints guarantee that with probability 1 the game will end.

Constraints

  • Number of elemets in graph is equal to number of nodes N.
  • N will be between 1 and 50, inclusive.
  • Each element of graph will contain exactly N characters.
  • Each character in graph will be either '0' or '1'.
  • graph[i][i] will be equal to '1' for all i between 0 and N-1, inclusive.
  • winprob and loseprob will contain exactly N elements.
  • Each element of winprob and loseprob will be between 0 and 100, inclusive.
  • For each i, the sum of winprob[i] and loseprob[i] will be at least 1.
  • start will be between 0 and N-1, inclusive.

Examples

  1. {"1"}

    {1}

    {1}

    0

    Returns: 0.5

    In each turn, Hero has to stay in the only node. After each turn, he wins the game with probability 1% and loses the game with probability 1%. By the symmetry of the situation, his overall probability of winning the game has to be 50%, hence the correct return value is 0.5. Note that as the number of turns increases, the probability that the game is still going on decreases towards zero. Specifically, the probability that the game still runs after k turns is 0.98^k. Therefore, the probability of Hero playing the game forever without winning or losing it is 0.

  2. {"11","11"}

    {60,40}

    {40,60}

    0

    Returns: 0.6

    At the first turn Hero can choose to stay at node 0 or to move token to node 1. After he made choice game will end at the end of turn. First node has better probability of winning, so optimal play is to stay at node 0 and win with probability of 60 percents.

  3. {"11","11"}

    {2,3}

    {3,4}

    0

    Returns: 0.4285714285714286

    Here optimal play is to move to node 1 at first turn and stay there until end of game, in this way answer is 3/7.

  4. {"110","011","001"}

    {2,1,10}

    {20,20,10}

    0

    Returns: 0.405

    Nodes number 0 and 1 have too weak probability of winning, so Hero moves to node number 1 at first turn, to node 2 at second turn, and waits for end.

  5. {"111","111","011"}

    {100,1,1}

    {0,50,50}

    2

    Returns: 0.5

  6. {"1001010000","1101000010","0110001110","0101010000","1110100100","0000011010","1000011000","0101001100","1100000011","0011001011"}

    {3,1,0,3,5,5,2,0,5,3}

    {5,27,36,11,48,32,49,15,18,39}

    1

    Returns: 0.375

  7. {"1001010000","1101000010","0110001110","0101010000","1110100100","0000011010","1000011000","0101001100","1100000011","0011001011"}

    {3,1,0,3,5,5,2,0,5,3}

    {5,27,36,11,48,32,49,15,18,39}

    9

    Returns: 0.33875

  8. {"1001010000","1101000010","0110001110","0101010000","1110100100","0000011010","1000011000","0101001100","1100000011","0011001011"}

    {3,1,0,3,5,5,2,0,5,3}

    {5,27,36,11,48,32,49,15,18,39}

    5

    Returns: 0.33875

  9. {"1001010000","1101000010","0110001110","0101010000","1110100100","0000011010","1000011000","0101001100","1100000011","0011001011"}

    {3,1,0,3,5,5,2,0,5,3}

    {5,27,36,11,48,32,49,15,18,39}

    3

    Returns: 0.28

  10. {"1011010000","1101000011","0110001110","0101010010","1111100100","0000011010","1100011000","0101001100","1100000011","0011001011"}

    {1,7,0,1,1,5,4,6,1,1}

    {5,27,36,11,48,32,49,15,18,39}

    7

    Returns: 0.2857142857142857

  11. {"101101000010010","010110110001110","011001001011110","001100000001010","110011000001010","011001100000011","001100101011001","101001010010001","000100001000010","110100000111010","101110100010100","000100101011000","010010101010101","111111110101011","110101000010111"}

    {0,2,4,1,6,5,6,4,3,1,7,0,7,2,7}

    {45,27,8,5,10,21,25,20,34,2,27,31,35,47,30}

    11

    Returns: 0.3233333333333333

  12. {"101101000010010","010110110001110","011001001011110","001100000001010","110011000001010","011001100000011","001100101011001","101001010010001","000100001000010","110100000111010","101110100010100","000100101011000","010010101010101","111111110101011","110101000010111"}

    {0,2,4,1,6,5,6,4,3,1,7,0,7,2,7}

    {45,27,8,5,10,21,25,20,34,2,27,31,35,47,30}

    14

    Returns: 0.3233333333333333

  13. {"101101000010010","010110110001110","011001001011110","001100000001010","110011000001010","011001100000011","001100101011001","101001010010001","000100001000010","110100000111010","101110100010100","000100101011000","010010101010101","111111110101011","110101000010111"}

    {0,2,4,1,6,5,6,4,3,1,7,0,7,2,7}

    {45,27,8,5,10,21,25,20,34,2,27,31,35,47,30}

    8

    Returns: 0.3233333333333333

  14. {"10110100001001000011","01100011100100010010","11110001000000001010","11010100000101001100","11001000110011001010","11001101001010010001","00010010100001011010","00000111101011101000","10100000100101010000","01001010111000111111","11101010011101010000","10110101000100100100","00000010011110100001","00010010100001011110","00100110000110110010","01001010010010010001","00000001010001111000","10001110101000000110","10000000010100010111","01001101111000100011"}

    {5,3,0,6,5,2,7,7,7,5,3,1,5,4,6,0,3,5,6,3}

    {38,16,11,14,28,19,24,37,35,3,45,2,26,40,23,46,47,17,49,29}

    1

    Returns: 0.4131562500000001

  15. {"10110100001001000011","01100011100100010010","11110001000000001010","11010100000101001100","11001000110011001010","11001101001010010001","00010010100001011010","00000111101011101000","10100000100101010000","01001010111000111111","11101010011101010000","10110101000100100100","00000010011110100001","00010010100001011110","00100110000110110010","01001010010010010001","00000001010001111000","10001110101000000110","10000000010100010111","01001101111000100011"}

    {5,3,0,6,5,2,7,7,7,5,3,1,5,4,6,0,3,5,6,3}

    {38,16,11,14,28,19,24,37,35,3,45,2,26,40,23,46,47,17,49,29}

    2

    Returns: 0.3925000000000001

  16. {"10110100001001000011","01100011100100010010","11110001000000001010","11010100000101001100","11001000110011001010","11001101001010010001","00010010100001011010","00000111101011101000","10100000100101010000","01001010111000111111","11101010011101010000","10110101000100100100","00000010011110100001","00010010100001011110","00100110000110110010","01001010010010010001","00000001010001111000","10001110101000000110","10000000010100010111","01001101111000100011"}

    {5,3,0,6,5,2,7,7,7,5,3,1,5,4,6,0,3,5,6,3}

    {38,16,11,14,28,19,24,37,35,3,45,2,26,40,23,46,47,17,49,29}

    3

    Returns: 0.41562500000000013

  17. {"10110100001001000011","01100011100100010010","11110001000000001010","11010100000101001100","11001000110011001010","11001101001010010001","00010010100001011010","00000111101011101000","10100000100101010000","01001010111000111111","11101010011101010000","10110101000100100100","00000010011110100001","00010010100001011110","00100110000110110010","01001010010010010001","00000001010001111000","10001110101000000110","10000000010100010111","01001101111000100011"}

    {5,3,0,6,5,2,7,7,7,5,3,1,5,4,6,0,3,5,6,3}

    {38,16,11,14,28,19,24,37,35,3,45,2,26,40,23,46,47,17,49,29}

    4

    Returns: 0.6250000000000002

  18. {"10110100001001000011","01100011100100010010","11110001000000001010","11010100000101001100","11001000110011001010","11001101001010010001","00010010100001011010","00000111101011101000","10100000100101010000","01001010111000111111","11101010011101010000","10110101000100100100","00000010011110100001","00010010100001011110","00100110000110110010","01001010010010010001","00000001010001111000","10001110101000000110","10000000010100010111","01001101111000100011"}

    {5,3,0,6,5,2,7,7,7,5,3,1,5,4,6,0,3,5,6,3}

    {38,16,11,14,28,19,24,37,35,3,45,2,26,40,23,46,47,17,49,29}

    5

    Returns: 0.4812500000000001

  19. {"10110100001001000011","01100011100100010010","11110001000000001010","11010100000101001100","11001000110011001010","11001101001010010001","00010010100001011010","00000111101011101000","10100000100101010000","01001010111000111111","11101010011101010000","10110101000100100100","00000010011110100001","00010010100001011110","00100110000110110010","01001010010010010001","00000001010001111000","10001110101000000110","10000000010100010111","01001101111000100011"}

    {5,3,0,6,5,2,7,7,7,5,3,1,5,4,6,0,3,5,6,3}

    {38,16,11,14,28,19,24,37,35,3,45,2,26,40,23,46,47,17,49,29}

    6

    Returns: 0.3925000000000001

  20. {"10110100001001000011","01100011100100010010","11110001000000001010","11010100000101001100","11001000110011001010","11001101001010010001","00010010100001011010","00000111101011101000","10100000100101010000","01001010111000111111","11101010011101010000","10110101000100100100","00000010011110100001","00010010100001011110","00100110000110110010","01001010010010010001","00000001010001111000","10001110101000000110","10000000010100010111","01001101111000100011"}

    {5,3,0,6,5,2,7,7,7,5,3,1,5,4,6,0,3,5,6,3}

    {38,16,11,14,28,19,24,37,35,3,45,2,26,40,23,46,47,17,49,29}

    7

    Returns: 0.4812500000000001

  21. {"100101000010010000100110001110","010001000011100001000000001010","101001000001010011001100000001","001100101001001001001010010001","000010000000010010100000011010","101011100010100000100001010000","000010101010001111111100101001","110101010010110101000000100100","000000101110001000000001001010","000001111100100110000110000010","010010000110100100010000000101","000011100011001100101000000110","000000000101100101010100110111","000000001000010010111011011000","101010001001001000001000000001","110001000000101110011001010001","000000111111101010010011011010","010100000111000101001001011010","010010110000100110100000011110","001110000000000000011010000010","010001101010000100001001000110","000010100000010011101100000000","000100000001001101000011001010","101010110001100000001111101000","001101100100110000001001100010","000001101100000011111010110000","100000101000000001000001001110","100000111101000100010000110111","110000001000000010001100000010","101000101001111110100000100111"}

    {1,2,2,2,7,6,0,3,1,0,5,2,2,5,5,4,7,3,1,2,3,5,3,2,4,2,5,4,4,7}

    {9,36,27,38,40,12,26,15,40,50,17,30,22,35,12,16,16,24,3,12,50,48,12,30,14,16,4,39,31,13}

    23

    Returns: 0.5555555555555557

  22. {"100101000010010000100110001110","010001000011100001000000001010","101001000001010011001100000001","001100101001001001001010010001","000010000000010010100000011010","101011100010100000100001010000","000010101010001111111100101001","110101010010110101000000100100","000000101110001000000001001010","000001111100100110000110000010","010010000110100100010000000101","000011100011001100101000000110","000000000101100101010100110111","000000001000010010111011011000","101010001001001000001000000001","110001000000101110011001010001","000000111111101010010011011010","010100000111000101001001011010","010010110000100110100000011110","001110000000000000011010000010","010001101010000100001001000110","000010100000010011101100000000","000100000001001101000011001010","101010110001100000001111101000","001101100100110000001001100010","000001101100000011111010110000","100000101000000001000001001110","100000111101000100010000110111","110000001000000010001100000010","101000101001111110100000100111"}

    {1,2,2,2,7,6,0,3,1,0,5,2,2,5,5,4,7,3,1,2,3,5,3,2,4,2,5,4,4,7}

    {9,36,27,38,40,12,26,15,40,50,17,30,22,35,12,16,16,24,3,12,50,48,12,30,14,16,4,39,31,13}

    24

    Returns: 0.5055333333333334

  23. {"100101000010010000100110001110","010001000011100001000000001010","101001000001010011001100000001","001100101001001001001010010001","000010000000010010100000011010","101011100010100000100001010000","000010101010001111111100101001","110101010010110101000000100100","000000101110001000000001001010","000001111100100110000110000010","010010000110100100010000000101","000011100011001100101000000110","000000000101100101010100110111","000000001000010010111011011000","101010001001001000001000000001","110001000000101110011001010001","000000111111101010010011011010","010100000111000101001001011010","010010110000100110100000011110","001110000000000000011010000010","010001101010000100001001000110","000010100000010011101100000000","000100000001001101000011001010","101010110001100000001111101000","001101100100110000001001100010","000001101100000011111010110000","100000101000000001000001001110","100000111101000100010000110111","110000001000000010001100000010","101000101001111110100000100111"}

    {1,2,2,2,7,6,0,3,1,0,5,2,2,5,5,4,7,3,1,2,3,5,3,2,4,2,5,4,4,7}

    {9,36,27,38,40,12,26,15,40,50,17,30,22,35,12,16,16,24,3,12,50,48,12,30,14,16,4,39,31,13}

    25

    Returns: 0.5433333333333334

  24. {"100101000010010000100110001110","010001000011100001000000001010","101001000001010011001100000001","001100101001001001001010010001","000010000000010010100000011010","101011100010100000100001010000","000010101010001111111100101001","110101010010110101000000100100","000000101110001000000001001010","000001111100100110000110000010","010010000110100100010000000101","000011100011001100101000000110","000000000101100101010100110111","000000001000010010111011011000","101010001001001000001000000001","110001000000101110011001010001","000000111111101010010011011010","010100000111000101001001011010","010010110000100110100000011110","001110000000000000011010000010","010001101010000100001001000110","000010100000010011101100000000","000100000001001101000011001010","101010110001100000001111101000","001101100100110000001001100010","000001101100000011111010110000","100000101000000001000001001110","100000111101000100010000110111","110000001000000010001100000010","101000101001111110100000100111"}

    {1,2,2,2,7,6,0,3,1,0,5,2,2,5,5,4,7,3,1,2,3,5,3,2,4,2,5,4,4,7}

    {9,36,27,38,40,12,26,15,40,50,17,30,22,35,12,16,16,24,3,12,50,48,12,30,14,16,4,39,31,13}

    26

    Returns: 0.5555555555555557

  25. {"100101000010010000100110001110","010001000011100001000000001010","101001000001010011001100000001","001100101001001001001010010001","000010000000010010100000011010","101011100010100000100001010000","000010101010001111111100101001","110101010010110101000000100100","000000101110001000000001001010","000001111100100110000110000010","010010000110100100010000000101","000011100011001100101000000110","000000000101100101010100110111","000000001000010010111011011000","101010001001001000001000000001","110001000000101110011001010001","000000111111101010010011011010","010100000111000101001001011010","010010110000100110100000011110","001110000000000000011010000010","010001101010000100001001000110","000010100000010011101100000000","000100000001001101000011001010","101010110001100000001111101000","001101100100110000001001100010","000001101100000011111010110000","100000101000000001000001001110","100000111101000100010000110111","110000001000000010001100000010","101000101001111110100000100111"}

    {1,2,2,2,7,6,0,3,1,0,5,2,2,5,5,4,7,3,1,2,3,5,3,2,4,2,5,4,4,7}

    {9,36,27,38,40,12,26,15,40,50,17,30,22,35,12,16,16,24,3,12,50,48,12,30,14,16,4,39,31,13}

    27

    Returns: 0.5100000000000001

  26. {"100101000010010000100110001110","010001000011100001000000001010","101001000001010011001100000001","001100101001001001001010010001","000010000000010010100000011010","101011100010100000100001010000","000010101010001111111100101001","110101010010110101000000100100","000000101110001000000001001010","000001111100100110000110000010","010010000110100100010000000101","000011100011001100101000000110","000000000101100101010100110111","000000001000010010111011011000","101010001001001000001000000001","110001000000101110011001010001","000000111111101010010011011010","010100000111000101001001011010","010010110000100110100000011110","001110000000000000011010000010","010001101010000100001001000110","000010100000010011101100000000","000100000001001101000011001010","101010110001100000001111101000","001101100100110000001001100010","000001101100000011111010110000","100000101000000001000001001110","100000111101000100010000110111","110000001000000010001100000010","101000101001111110100000100111"}

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

    {27,21,19,36,57,24,41,41,54,38,37,51,45,20,57,21,32,64,43,3,65,27,5,57,36,37,49,66,66,9}

    29

    Returns: 0.435

  27. {"100101000010010000100110001110","010001000011100001000000001010","101001000001010011001100000001","001100101001001001001010010001","000010000000010010100000011010","101011100010100000100001010000","000010101010001111111100101001","110101010010110101000000100100","000000101110001000000001001010","000001111100100110000110000010","010010000110100100010000000101","000011100011001100101000000110","000000000101100101010100110111","000000001000010010111011011000","101010001001001000001000000001","110001000000101110011001010001","000000111111101010010011011010","010100000111000101001001011010","010010110000100110100000011110","001110000000000000011010000010","010001101010000100001001000110","000010100000010011101100000000","000100000001001101000011001010","101010110001100000001111101000","001101100100110000001001100010","000001101100000011111010110000","100000101000000001000001001110","100000111101000100010000110111","110000001000000010001100000010","101000101001111110100000100111"}

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

    {27,21,19,36,57,24,41,41,54,38,37,51,45,20,57,21,32,64,43,3,65,27,5,57,36,37,49,66,66,9}

    13

    Returns: 0.5

  28. {"100101000010010000100110001110","010001000011100001000000001010","101001000001010011001100000001","001100101001001001001010010001","000010000000010010100000011010","101011100010100000100001010000","000010101010001111111100101001","110101010010110101000000100100","000000101110001000000001001010","000001111100100110000110000010","010010000110100100010000000101","000011100011001100101000000110","000000000101100101010100110111","000000001000010010111011011000","101010001001001000001000000001","110001000000101110011001010001","000000111111101010010011011010","010100000111000101001001011010","010010110000100110100000011110","001110000000000000011010000010","010001101010000100001001000110","000010100000010011101100000000","000100000001001101000011001010","101010110001100000001111101000","001101100100110000001001100010","000001101100000011111010110000","100000101000000001000001001110","100000111101000100010000110111","110000001000000010001100000010","101000101001111110100000100111"}

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

    {27,21,19,36,57,24,41,41,54,38,37,51,45,20,57,21,32,64,43,3,65,27,5,57,36,37,49,66,66,9}

    2

    Returns: 0.435

  29. {"1001010000100000000001100011100000010000","1110000100000000100010000100000100001100","0110000001000100100001001001001010000001","0001000000000100101000000110101010101000","1010100010000101000000001010000000111111","1100111001110101000010110101000000100100","0000001001100000000000010010100000011110","0010011100001000001000000000010010010000","0000000111000011100010001100101000000100","0000000001010001010101001001110000000010","0000001010100001100010100000100100100000","1000000001110001000000101010001001000001","0000000000111010000000110010100101000000","1100010100100101101000001011000010010000","0000011110001010000000000000001010000010","0100001000100001000000010001100000101000","0001001110100000100000010000000100100100","0000000010101010110000000000001110101000","0011011001001100001010010000100000011011","0000001110101000000110000010100000000100","0000000010100000101011000100010000010011","0100000010000000100001000000001010001010","0111101010000010011000100111000011010010","0100100100100010000100110100100001000100","1010000000110010000100001000000000100010","0000110110000000101011101100101011110100","1100000000100101001100000110000000010000","0011000100000010000010001001001000000000","0010000001101000100001000100110000001000","0101010010000000000000010100111010110000","1100000000001100100000001000011000100000","0100010011110010100101000000010100001010","1100001000000000000000011010100011100100","0000001000001000010001010000010001000010","0001000011000000100000100000000000100000","1000000000100001000010011010000100010000","0000000001000000010010000000100000001000","1001010101001110000010000100011000000101","1000010110010000001000000000010001000010","0000010100010001000000000000000010000011"}

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

    {28,70,43,20,29,26,37,54,33,57,18,6,64,61,57,34,37,40,32,62,7,66,30,25,59,11,31,2,47,70,6,23,56,62,26,67,47,33,70,22}

    17

    Returns: 0.5774400000000002

  30. {"1001010000100000000001100011100000010000","1110000100000000100010000100000100001100","0110000001000100100001001001001010000001","0001000000000100101000000110101010101000","1010100010000101000000001010000000111111","1100111001110101000010110101000000100100","0000001001100000000000010010100000011110","0010011100001000001000000000010010010000","0000000111000011100010001100101000000100","0000000001010001010101001001110000000010","0000001010100001100010100000100100100000","1000000001110001000000101010001001000001","0000000000111010000000110010100101000000","1100010100100101101000001011000010010000","0000011110001010000000000000001010000010","0100001000100001000000010001100000101000","0001001110100000100000010000000100100100","0000000010101010110000000000001110101000","0011011001001100001010010000100000011011","0000001110101000000110000010100000000100","0000000010100000101011000100010000010011","0100000010000000100001000000001010001010","0111101010000010011000100111000011010010","0100100100100010000100110100100001000100","1010000000110010000100001000000000100010","0000110110000000101011101100101011110100","1100000000100101001100000110000000010000","0011000100000010000010001001001000000000","0010000001101000100001000100110000001000","0101010010000000000000010100111010110000","1100000000001100100000001000011000100000","0100010011110010100101000000010100001010","1100001000000000000000011010100011100100","0000001000001000010001010000010001000010","0001000011000000100000100000000000100000","1000000000100001000010011010000100010000","0000000001000000010010000000100000001000","1001010101001110000010000100011000000101","1000010110010000001000000000010001000010","0000010100010001000000000000000010000011"}

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

    {28,70,43,20,29,26,37,54,33,57,18,6,64,61,57,34,37,40,32,62,7,66,30,25,59,11,31,2,47,70,6,23,56,62,26,67,47,33,70,22}

    22

    Returns: 0.8

  31. {"1001010000100000000001100011100000010000","1110000100000000100010000100000100001100","0110000001000100100001001001001010000001","0001000000000100101000000110101010101000","1010100010000101000000001010000000111111","1100111001110101000010110101000000100100","0000001001100000000000010010100000011110","0010011100001000001000000000010010010000","0000000111000011100010001100101000000100","0000000001010001010101001001110000000010","0000001010100001100010100000100100100000","1000000001110001000000101010001001000001","0000000000111010000000110010100101000000","1100010100100101101000001011000010010000","0000011110001010000000000000001010000010","0100001000100001000000010001100000101000","0001001110100000100000010000000100100100","0000000010101010110000000000001110101000","0011011001001100001010010000100000011011","0000001110101000000110000010100000000100","0000000010100000101011000100010000010011","0100000010000000100001000000001010001010","0111101010000010011000100111000011010010","0100100100100010000100110100100001000100","1010000000110010000100001000000000100010","0000110110000000101011101100101011110100","1100000000100101001100000110000000010000","0011000100000010000010001001001000000000","0010000001101000100001000100110000001000","0101010010000000000000010100111010110000","1100000000001100100000001000011000100000","0100010011110010100101000000010100001010","1100001000000000000000011010100011100100","0000001000001000010001010000010001000010","0001000011000000100000100000000000100000","1000000000100001000010011010000100010000","0000000001000000010010000000100000001000","1001010101001110000010000100011000000101","1000010110010000001000000000010001000010","0000010100010001000000000000000010000011"}

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

    {28,70,43,20,29,26,37,54,33,57,18,6,64,61,57,34,37,40,32,62,7,66,30,25,59,11,31,2,47,70,6,23,56,62,26,67,47,33,70,22}

    31

    Returns: 0.6060000000000001

  32. {"1001010000100000000001100011100000010000","1110000100000000100010000100000100001100","0110000001000100100001001001001010000001","0001000000000100101000000110101010101000","1010100010000101000000001010000000111111","1100111001110101000010110101000000100100","0000001001100000000000010010100000011110","0010011100001000001000000000010010010000","0000000111000011100010001100101000000100","0000000001010001010101001001110000000010","0000001010100001100010100000100100100000","1000000001110001000000101010001001000001","0000000000111010000000110010100101000000","1100010100100101101000001011000010010000","0000011110001010000000000000001010000010","0100001000100001000000010001100000101000","0001001110100000100000010000000100100100","0000000010101010110000000000001110101000","0011011001001100001010010000100000011011","0000001110101000000110000010100000000100","0000000010100000101011000100010000010011","0100000010000000100001000000001010001010","0111101010000010011000100111000011010010","0100100100100010000100110100100001000100","1010000000110010000100001000000000100010","0000110110000000101011101100101011110100","1100000000100101001100000110000000010000","0011000100000010000010001001001000000000","0010000001101000100001000100110000001000","0101010010000000000000010100111010110000","1100000000001100100000001000011000100000","0100010011110010100101000000010100001010","1100001000000000000000011010100011100100","0000001000001000010001010000010001000010","0001000011000000100000100000000000100000","1000000000100001000010011010000100010000","0000000001000000010010000000100000001000","1001010101001110000010000100011000000101","1000010110010000001000000000010001000010","0000010100010001000000000000000010000011"}

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

    {28,70,43,20,29,26,37,54,33,57,18,6,64,61,57,34,37,40,32,62,7,66,30,25,59,11,31,2,47,70,6,23,56,62,26,67,47,33,70,22}

    39

    Returns: 0.6060000000000001

  33. {"1001000000100000000001100011100000010000","1100000100000000000010000100000100001100","0010000001000000100001001001001000000001","0001000000000000101000000110100010101000","1000100010000101000000001010000000111111","1100111001010101000000110101000000100000","0000001001100000000000010000100000011110","0010001100001000001000000000010010000000","0000000111000011100010001100101000000000","0000000001010001000101001001100000000010","0000001010100000000010100000000100100000","1000000000110001000000101010001001000001","0000000000011000000000110010100100000000","1100010100100101101000001011000000010000","0000001110000010000000000000001010000000","0100001000100001000000010001100000100000","0001001110100000100000010000000100100100","0000000010101010010000000000001110101000","0011011001001000001010010000100000011010","0000001100101000000110000010100000000100","0000000000000000101011000100010000010011","0100000010000000100001000000001010001010","0011101010000010011000100110000011010010","0100000100100010000100110100100001000100","1010000000110000000100001000000000100010","0000110110000000101011100100001011110100","1100000000100101000100000010000000000000","0011000100000010000010001001001000000000","0010000001101000100000000000110000001000","0101000010000000000000010100111010110000","1100000000001000100000001000011000100000","0100010011100010100101000000010100000010","1100000000000000000000011010100011100100","0000001000001000010000000000010001000010","0001000011000000100000100000000000100000","1000000000100001000010011000000100010000","0000000001000000010010000000100000001000","0001010101000110000010000100011000000101","1000000110010000001000000000010001000010","0000010100010001000000000000000010000011"}

    {5,7,6,5,6,7,0,2,2,7,1,1,7,0,4,5,2,7,6,5,4,5,2,5,0,0,5,3,6,0,3,2,2,3,1,3,6,2,1,7}

    {48,8,49,18,19,43,19,2,12,52,13,11,49,8,17,44,7,15,41,4,59,44,11,24,22,51,55,40,46,5,49,42,21,35,56,10,58,39,47,11}

    19

    Returns: 0.5555555555555557

  34. {"1001000000100000000001100011100000010000","1100000100000000000010000100000100001100","0010000001000000100001001001001000000001","0001000000000000101000000110100010101000","1000100010000101000000001010000000111111","1100111001010101000000110101000000100000","0000001001100000000000010000100000011110","0010001100001000001000000000010010000000","0000000111000011100010001100101000000000","0000000001010001000101001001100000000010","0000001010100000000010100000000100100000","1000000000110001000000101010001001000001","0000000000011000000000110010100100000000","1100010100100101101000001011000000010000","0000001110000010000000000000001010000000","0100001000100001000000010001100000100000","0001001110100000100000010000000100100100","0000000010101010010000000000001110101000","0011011001001000001010010000100000011010","0000001100101000000110000010100000000100","0000000000000000101011000100010000010011","0100000010000000100001000000001010001010","0011101010000010011000100110000011010010","0100000100100010000100110100100001000100","1010000000110000000100001000000000100010","0000110110000000101011100100001011110100","1100000000100101000100000010000000000000","0011000100000010000010001001001000000000","0010000001101000100000000000110000001000","0101000010000000000000010100111010110000","1100000000001000100000001000011000100000","0100010011100010100101000000010100000010","1100000000000000000000011010100011100100","0000001000001000010000000000010001000010","0001000011000000100000100000000000100000","1000000000100001000010011000000100010000","0000000001000000010010000000100000001000","0001010101000110000010000100011000000101","1000000110010000001000000000010001000010","0000010100010001000000000000000010000011"}

    {5,7,6,5,6,7,0,2,2,7,1,1,7,0,4,5,2,7,6,5,4,5,2,5,0,0,5,3,6,0,3,2,2,3,1,3,6,2,1,7}

    {48,8,49,18,19,43,19,2,12,52,13,11,49,8,17,44,7,15,41,4,59,44,11,24,22,51,55,40,46,5,49,42,21,35,56,10,58,39,47,11}

    27

    Returns: 0.5

  35. {"1001000000100000000001100011100000010000","1100000100000000000010000100000100001100","0010000001000000100001001001001000000001","0001000000000000101000000110100010101000","1000100010000101000000001010000000111111","1100111001010101000000110101000000100000","0000001001100000000000010000100000011110","0010001100001000001000000000010010000000","0000000111000011100010001100101000000000","0000000001010001000101001001100000000010","0000001010100000000010100000000100100000","1000000000110001000000101010001001000001","0000000000011000000000110010100100000000","1100010100100101101000001011000000010000","0000001110000010000000000000001010000000","0100001000100001000000010001100000100000","0001001110100000100000010000000100100100","0000000010101010010000000000001110101000","0011011001001000001010010000100000011010","0000001100101000000110000010100000000100","0000000000000000101011000100010000010011","0100000010000000100001000000001010001010","0011101010000010011000100110000011010010","0100000100100010000100110100100001000100","1010000000110000000100001000000000100010","0000110110000000101011100100001011110100","1100000000100101000100000010000000000000","0011000100000010000010001001001000000000","0010000001101000100000000000110000001000","0101000010000000000000010100111010110000","1100000000001000100000001000011000100000","0100010011100010100101000000010100000010","1100000000000000000000011010100011100100","0000001000001000010000000000010001000010","0001000011000000100000100000000000100000","1000000000100001000010011000000100010000","0000000001000000010010000000100000001000","0001010101000110000010000100011000000101","1000000110010000001000000000010001000010","0000010100010001000000000000000010000011"}

    {5,7,6,5,6,7,0,2,2,7,1,1,7,0,4,5,2,7,6,5,4,5,2,5,0,0,5,3,6,0,3,2,2,3,1,3,6,2,1,7}

    {48,8,49,18,19,43,19,2,12,52,13,11,49,8,17,44,7,15,41,4,59,44,11,24,22,51,55,40,46,5,49,42,21,35,56,10,58,39,47,11}

    31

    Returns: 0.5555555555555557

  36. {"1001000000100000000001100011100000010000","1100000100000000000010000100000100001100","0010000001000000100001001001001000000001","0001000000000000101000000110100010101000","1000100010000101000000001010000000111111","1100111001010101000000110101000000100000","0000001001100000000000010000100000011110","0010001100001000001000000000010010000000","0000000111000011100010001100101000000000","0000000001010001000101001001100000000010","0000001010100000000010100000000100100000","1000000000110001000000101010001001000001","0000000000011000000000110010100100000000","1100010100100101101000001011000000010000","0000001110000010000000000000001010000000","0100001000100001000000010001100000100000","0001001110100000100000010000000100100100","0000000010101010010000000000001110101000","0011011001001000001010010000100000011010","0000001100101000000110000010100000000100","0000000000000000101011000100010000010011","0100000010000000100001000000001010001010","0011101010000010011000100110000011010010","0100000100100010000100110100100001000100","1010000000110000000100001000000000100010","0000110110000000101011100100001011110100","1100000000100101000100000010000000000000","0011000100000010000010001001001000000000","0010000001101000100000000000110000001000","0101000010000000000000010100111010110000","1100000000001000100000001000011000100000","0100010011100010100101000000010100000010","1100000000000000000000011010100011100100","0000001000001000010000000000010001000010","0001000011000000100000100000000000100000","1000000000100001000010011000000100010000","0000000001000000010010000000100000001000","0001010101000110000010000100011000000101","1000000110010000001000000000010001000010","0000010100010001000000000000000010000011"}

    {5,7,6,5,6,7,0,2,2,7,1,1,7,0,4,5,2,7,6,5,4,5,2,5,0,0,5,3,6,0,3,2,2,3,1,3,6,2,1,7}

    {48,8,49,18,19,43,19,2,12,52,13,11,49,8,17,44,7,15,41,4,59,44,11,24,22,51,55,40,46,5,49,42,21,35,56,10,58,39,47,11}

    33

    Returns: 0.47025

  37. {"10010000001000000000011000111000000100001100000100","01000000001000010000010000110000000000010000001000","01101001001000000001000000000000000010100000011010","00111010001000000010000101000000001010000000111111","11001010010101010000001101010000001000000000001001","10000100000001000010000001111000100010000010000010","00000010010010000000000000010100001110001000110010","10000001000000000000010001000101001001100000000010","00000010101000000000101000000001001000001000000000","10000100010010101000100100000100000000000110000000","00110010101100000000110001010010000110100000101100","00000100000100001110000000000000000000001010000000","01000010001010010000000100011000001000000001001110","10000000000001000000010010010000000000101010100100","00000000001110101000001101100100100000001001000010","00000110100000011100101000000010000010100000000100","00000000000000001010010001000100000100110100000010","00000010000100000100101000101000111010100000100110","00000110000011010010010000010010001000010011010010","00010001001010000001110000000100000000000000100010","00001101100000001010111000000010111101001100000000","10010100010000001000010000000000110001000000100000","10001000001000000000001000000110100010000000000001","00000010000101000010000100000000010100101010110000","11000000000010001000000010000100001000000100010011","10001010010100000001000001001011000000000000000000","00011010100001100100000000100000100001000000000001","00000000100001000011000000110000100000000000000000","10000000001000010000100110001001000100000000000001","00000001001000000010000000100100010101010001100000","10000100011000000001100000011011000000100000000001","00010000000000010100010001000001000000000010000010","00000000101000001000101000100000100010000100000101","00100010000000000000000001000010010000000100000100","00010001000010010000100010001100011010000011011010","00000100000000001101001100000000000101100001000100","01000000110010000000000000100000010010100000000110","00000000000011000000100110000010101011000000100010","00000000001110000000100000000001001000100100000000","00001110000000010000001001100000101010110010100000","10010000001000000000000011000000100100101000010001","00000000010010000001000001001000000000000100001100","00000011000000000000001110000011100001000010000000","01000000001100010000000100100000010101000001010000","00010000100000000100100001000000000000010100110110","00000000010000000100010000000000010000100110010000","10100000011000000010100000000100001000000000001010","00100001010000000010100001000000100100110000000101","00000000001000000001000000000101000000000000000010","00000010100100000001100010001000100010000101000001"}

    {3,3,5,2,3,0,5,0,0,5,6,6,5,4,2,7,7,6,3,6,1,6,4,0,1,1,5,5,1,5,3,2,7,7,5,2,5,3,0,0,1,0,5,6,6,1,6,2,2,5}

    {3,14,27,20,35,4,57,27,39,32,27,25,37,43,26,19,7,45,38,17,38,26,34,16,19,52,15,57,25,30,48,10,20,55,22,58,59,24,48,14,4,49,25,59,21,57,5,55,49,42}

    7

    Returns: 0.5

  38. {"10010000001000000000011000111000000100001100000100","01000000001000010000010000110000000000010000001000","01101001001000000001000000000000000010100000011010","00111010001000000010000101000000001010000000111111","11001010010101010000001101010000001000000000001001","10000100000001000010000001111000100010000010000010","00000010010010000000000000010100001110001000110010","10000001000000000000010001000101001001100000000010","00000010101000000000101000000001001000001000000000","10000100010010101000100100000100000000000110000000","00110010101100000000110001010010000110100000101100","00000100000100001110000000000000000000001010000000","01000010001010010000000100011000001000000001001110","10000000000001000000010010010000000000101010100100","00000000001110101000001101100100100000001001000010","00000110100000011100101000000010000010100000000100","00000000000000001010010001000100000100110100000010","00000010000100000100101000101000111010100000100110","00000110000011010010010000010010001000010011010010","00010001001010000001110000000100000000000000100010","00001101100000001010111000000010111101001100000000","10010100010000001000010000000000110001000000100000","10001000001000000000001000000110100010000000000001","00000010000101000010000100000000010100101010110000","11000000000010001000000010000100001000000100010011","10001010010100000001000001001011000000000000000000","00011010100001100100000000100000100001000000000001","00000000100001000011000000110000100000000000000000","10000000001000010000100110001001000100000000000001","00000001001000000010000000100100010101010001100000","10000100011000000001100000011011000000100000000001","00010000000000010100010001000001000000000010000010","00000000101000001000101000100000100010000100000101","00100010000000000000000001000010010000000100000100","00010001000010010000100010001100011010000011011010","00000100000000001101001100000000000101100001000100","01000000110010000000000000100000010010100000000110","00000000000011000000100110000010101011000000100010","00000000001110000000100000000001001000100100000000","00001110000000010000001001100000101010110010100000","10010000001000000000000011000000100100101000010001","00000000010010000001000001001000000000000100001100","00000011000000000000001110000011100001000010000000","01000000001100010000000100100000010101000001010000","00010000100000000100100001000000000000010100110110","00000000010000000100010000000000010000100110010000","10100000011000000010100000000100001000000000001010","00100001010000000010100001000000100100110000000101","00000000001000000001000000000101000000000000000010","00000010100100000001100010001000100010000101000001"}

    {3,3,5,2,3,0,5,0,0,5,6,6,5,4,2,7,7,6,3,6,1,6,4,0,1,1,5,5,1,5,3,2,7,7,5,2,5,3,0,0,1,0,5,6,6,1,6,2,2,5}

    {3,14,27,20,35,4,57,27,39,32,27,25,37,43,26,19,7,45,38,17,38,26,34,16,19,52,15,57,25,30,48,10,20,55,22,58,59,24,48,14,4,49,25,59,21,57,5,55,49,42}

    21

    Returns: 0.5

  39. {"10010000001000000000011000111000000100001100000100","01000000001000010000010000110000000000010000001000","01101001001000000001000000000000000010100000011010","00111010001000000010000101000000001010000000111111","11001010010101010000001101010000001000000000001001","10000100000001000010000001111000100010000010000010","00000010010010000000000000010100001110001000110010","10000001000000000000010001000101001001100000000010","00000010101000000000101000000001001000001000000000","10000100010010101000100100000100000000000110000000","00110010101100000000110001010010000110100000101100","00000100000100001110000000000000000000001010000000","01000010001010010000000100011000001000000001001110","10000000000001000000010010010000000000101010100100","00000000001110101000001101100100100000001001000010","00000110100000011100101000000010000010100000000100","00000000000000001010010001000100000100110100000010","00000010000100000100101000101000111010100000100110","00000110000011010010010000010010001000010011010010","00010001001010000001110000000100000000000000100010","00001101100000001010111000000010111101001100000000","10010100010000001000010000000000110001000000100000","10001000001000000000001000000110100010000000000001","00000010000101000010000100000000010100101010110000","11000000000010001000000010000100001000000100010011","10001010010100000001000001001011000000000000000000","00011010100001100100000000100000100001000000000001","00000000100001000011000000110000100000000000000000","10000000001000010000100110001001000100000000000001","00000001001000000010000000100100010101010001100000","10000100011000000001100000011011000000100000000001","00010000000000010100010001000001000000000010000010","00000000101000001000101000100000100010000100000101","00100010000000000000000001000010010000000100000100","00010001000010010000100010001100011010000011011010","00000100000000001101001100000000000101100001000100","01000000110010000000000000100000010010100000000110","00000000000011000000100110000010101011000000100010","00000000001110000000100000000001001000100100000000","00001110000000010000001001100000101010110010100000","10010000001000000000000011000000100100101000010001","00000000010010000001000001001000000000000100001100","00000011000000000000001110000011100001000010000000","01000000001100010000000100100000010101000001010000","00010000100000000100100001000000000000010100110110","00000000010000000100010000000000010000100110010000","10100000011000000010100000000100001000000000001010","00100001010000000010100001000000100100110000000101","00000000001000000001000000000101000000000000000010","00000010100100000001100010001000100010000101000001"}

    {3,3,5,2,3,0,5,0,0,5,6,6,5,4,2,7,7,6,3,6,1,6,4,0,1,1,5,5,1,5,3,2,7,7,5,2,5,3,0,0,1,0,5,6,6,1,6,2,2,5}

    {3,14,27,20,35,4,57,27,39,32,27,25,37,43,26,19,7,45,38,17,38,26,34,16,19,52,15,57,25,30,48,10,20,55,22,58,59,24,48,14,4,49,25,59,21,57,5,55,49,42}

    45

    Returns: 0.4

  40. {"10010000001000000000011000111000000100001100000100","01000000001000010000010000110000000000010000001000","01101001001000000001000000000000000010100000011010","00111010001000000010000101000000001010000000111111","11001010010101010000001101010000001000000000001001","10000100000001000010000001111000100010000010000010","00000010010010000000000000010100001110001000110010","10000001000000000000010001000101001001100000000010","00000010101000000000101000000001001000001000000000","10000100010010101000100100000100000000000110000000","00110010101100000000110001010010000110100000101100","00000100000100001110000000000000000000001010000000","01000010001010010000000100011000001000000001001110","10000000000001000000010010010000000000101010100100","00000000001110101000001101100100100000001001000010","00000110100000011100101000000010000010100000000100","00000000000000001010010001000100000100110100000010","00000010000100000100101000101000111010100000100110","00000110000011010010010000010010001000010011010010","00010001001010000001110000000100000000000000100010","00001101100000001010111000000010111101001100000000","10010100010000001000010000000000110001000000100000","10001000001000000000001000000110100010000000000001","00000010000101000010000100000000010100101010110000","11000000000010001000000010000100001000000100010011","10001010010100000001000001001011000000000000000000","00011010100001100100000000100000100001000000000001","00000000100001000011000000110000100000000000000000","10000000001000010000100110001001000100000000000001","00000001001000000010000000100100010101010001100000","10000100011000000001100000011011000000100000000001","00010000000000010100010001000001000000000010000010","00000000101000001000101000100000100010000100000101","00100010000000000000000001000010010000000100000100","00010001000010010000100010001100011010000011011010","00000100000000001101001100000000000101100001000100","01000000110010000000000000100000010010100000000110","00000000000011000000100110000010101011000000100010","00000000001110000000100000000001001000100100000000","00001110000000010000001001100000101010110010100000","10010000001000000000000011000000100100101000010001","00000000010010000001000001001000000000000100001100","00000011000000000000001110000011100001000010000000","01000000001100010000000100100000010101000001010000","00010000100000000100100001000000000000010100110110","00000000010000000100010000000000010000100110010000","10100000011000000010100000000100001000000000001010","00100001010000000010100001000000100100110000000101","00000000001000000001000000000101000000000000000010","00000010100100000001100010001000100010000101000001"}

    {3,3,5,2,3,0,5,0,0,5,6,6,5,4,2,7,7,6,3,6,1,6,4,0,1,1,5,5,1,5,3,2,7,7,5,2,5,3,0,0,1,0,5,6,6,1,6,2,2,5}

    {3,14,27,20,35,4,57,27,39,32,27,25,37,43,26,19,7,45,38,17,38,26,34,16,19,52,15,57,25,30,48,10,20,55,22,58,59,24,48,14,4,49,25,59,21,57,5,55,49,42}

    49

    Returns: 0.435

  41. {"10010000001000000000011000000000000100001100000100","01000000000000010000010000110000000000010000000000","00101001000000000001000000000000000010100000011000","00111010001000000010000000000000000010000000101011","10001000010101010000001101000000001000000000000001","10000100000000000000000001111000100010000000000000","00000010010000000000000000000100001100001000110010","00000001000000000000010001000001001001100000000000","00000010101000000000101000000001001000001000000000","00000100010000001000100000000100000000000010000000","00100010101000000000110001010010000110100000101100","00000000000100000100000000000000000000001010000000","01000000001010010000000100011000001000000001000100","10000000000001000000010010010000000000101000100100","00000000001100101000000101000100100000001001000000","00000100100000011100100000000010000010000000000000","00000000000000001010010000000100000100110100000010","00000000000100000100001000101000011010000000100110","00000010000010010010010000010010000000010000000010","00010000000010000001110000000100000000000000100000","00000100000000000000101000000010011101001100000000","10010100010000000000010000000000110001000000000000","00000000000000000000001000000000000010000000000001","00000010000101000010000100000000000100001000010000","11000000000010001000000010000000001000000100010010","10001000010100000000000001000001000000000000000000","00011010100001100100000000100000100001000000000001","00000000100001000001000000110000100000000000000000","10000000001000010000000110001001000000000000000001","00000001001000000000000000000100010101010001000000","00000100001000000000100000010010000000100000000001","00010000000000000000010000000001000000000010000010","00000000101000001000100000100000100010000100000100","00000000000000000000000001000000010000000100000100","00010000000010010000000010000000011000000001010000","00000100000000001101001100000000000100100001000000","01000000110000000000000000000000010010100000000110","00000000000011000000000110000000100001000000100010","00000000000100000000100000000001000000100100000000","00001110000000000000001001100000100000110010000000","10010000001000000000000010000000100100001000010000","00000000000000000001000001000000000000000100001100","00000000000000000000001110000011000001000010000000","01000000001000010000000100000000010000000001010000","00010000100000000100100001000000000000010100110110","00000000000000000100010000000000010000000000010000","10000000000000000000100000000100001000000000001010","00100000010000000010100000000000100100010000000101","00000000000000000001000000000101000000000000000010","00000000100100000001100010001000100000000101000001"}

    {3,3,5,2,3,0,5,0,0,5,6,6,5,4,2,7,7,6,3,6,1,6,4,0,1,1,5,5,1,5,3,2,7,7,5,2,5,3,0,0,1,0,5,6,6,1,6,2,2,5}

    {3,14,27,20,35,4,57,27,39,32,27,25,37,43,26,19,7,45,38,17,38,26,34,16,19,52,15,57,25,30,48,10,20,55,22,58,59,24,48,14,4,49,25,59,21,57,5,55,49,42}

    20

    Returns: 0.485

  42. {"10010000001000000000011000000000000100001100000100","01000000000000010000010000110000000000010000000000","00101001000000000001000000000000000010100000011000","00111010001000000010000000000000000010000000101011","10001000010101010000001101000000001000000000000001","10000100000000000000000001111000100010000000000000","00000010010000000000000000000100001100001000110010","00000001000000000000010001000001001001100000000000","00000010101000000000101000000001001000001000000000","00000100010000001000100000000100000000000010000000","00100010101000000000110001010010000110100000101100","00000000000100000100000000000000000000001010000000","01000000001010010000000100011000001000000001000100","10000000000001000000010010010000000000101000100100","00000000001100101000000101000100100000001001000000","00000100100000011100100000000010000010000000000000","00000000000000001010010000000100000100110100000010","00000000000100000100001000101000011010000000100110","00000010000010010010010000010010000000010000000010","00010000000010000001110000000100000000000000100000","00000100000000000000101000000010011101001100000000","10010100010000000000010000000000110001000000000000","00000000000000000000001000000000000010000000000001","00000010000101000010000100000000000100001000010000","11000000000010001000000010000000001000000100010010","10001000010100000000000001000001000000000000000000","00011010100001100100000000100000100001000000000001","00000000100001000001000000110000100000000000000000","10000000001000010000000110001001000000000000000001","00000001001000000000000000000100010101010001000000","00000100001000000000100000010010000000100000000001","00010000000000000000010000000001000000000010000010","00000000101000001000100000100000100010000100000100","00000000000000000000000001000000010000000100000100","00010000000010010000000010000000011000000001010000","00000100000000001101001100000000000100100001000000","01000000110000000000000000000000010010100000000110","00000000000011000000000110000000100001000000100010","00000000000100000000100000000001000000100100000000","00001110000000000000001001100000100000110010000000","10010000001000000000000010000000100100001000010000","00000000000000000001000001000000000000000100001100","00000000000000000000001110000011000001000010000000","01000000001000010000000100000000010000000001010000","00010000100000000100100001000000000000010100110110","00000000000000000100010000000000010000000000010000","10000000000000000000100000000100001000000000001010","00100000010000000010100000000000100100010000000101","00000000000000000001000000000101000000000000000010","00000000100100000001100010001000100000000101000001"}

    {3,3,5,2,3,0,5,0,0,5,6,6,5,4,2,7,7,6,3,6,1,6,4,0,1,1,5,5,1,5,3,2,7,7,5,2,5,3,0,0,1,0,5,6,6,1,6,2,2,5}

    {3,14,27,20,35,4,57,27,39,32,27,25,37,43,26,19,7,45,38,17,38,26,34,16,19,52,15,57,25,30,48,10,20,55,22,58,59,24,48,14,4,49,25,59,21,57,5,55,49,42}

    30

    Returns: 0.48

  43. {"10010000001000000000011000000000000100001100000100","01000000000000010000010000110000000000010000000000","00101001000000000001000000000000000010100000011000","00111010001000000010000000000000000010000000101011","10001000010101010000001101000000001000000000000001","10000100000000000000000001111000100010000000000000","00000010010000000000000000000100001100001000110010","00000001000000000000010001000001001001100000000000","00000010101000000000101000000001001000001000000000","00000100010000001000100000000100000000000010000000","00100010101000000000110001010010000110100000101100","00000000000100000100000000000000000000001010000000","01000000001010010000000100011000001000000001000100","10000000000001000000010010010000000000101000100100","00000000001100101000000101000100100000001001000000","00000100100000011100100000000010000010000000000000","00000000000000001010010000000100000100110100000010","00000000000100000100001000101000011010000000100110","00000010000010010010010000010010000000010000000010","00010000000010000001110000000100000000000000100000","00000100000000000000101000000010011101001100000000","10010100010000000000010000000000110001000000000000","00000000000000000000001000000000000010000000000001","00000010000101000010000100000000000100001000010000","11000000000010001000000010000000001000000100010010","10001000010100000000000001000001000000000000000000","00011010100001100100000000100000100001000000000001","00000000100001000001000000110000100000000000000000","10000000001000010000000110001001000000000000000001","00000001001000000000000000000100010101010001000000","00000100001000000000100000010010000000100000000001","00010000000000000000010000000001000000000010000010","00000000101000001000100000100000100010000100000100","00000000000000000000000001000000010000000100000100","00010000000010010000000010000000011000000001010000","00000100000000001101001100000000000100100001000000","01000000110000000000000000000000010010100000000110","00000000000011000000000110000000100001000000100010","00000000000100000000100000000001000000100100000000","00001110000000000000001001100000100000110010000000","10010000001000000000000010000000100100001000010000","00000000000000000001000001000000000000000100001100","00000000000000000000001110000011000001000010000000","01000000001000010000000100000000010000000001010000","00010000100000000100100001000000000000010100110110","00000000000000000100010000000000010000000000010000","10000000000000000000100000000100001000000000001010","00100000010000000010100000000000100100010000000101","00000000000000000001000000000101000000000000000010","00000000100100000001100010001000100000000101000001"}

    {3,3,5,2,3,0,5,0,0,5,6,6,5,4,2,7,7,6,3,6,1,6,4,0,1,1,5,5,1,5,3,2,7,7,5,2,5,3,0,0,1,0,5,6,6,1,6,2,2,5}

    {3,14,27,20,35,4,57,27,39,32,27,25,37,43,26,19,7,45,38,17,38,26,34,16,19,52,15,57,25,30,48,10,20,55,22,58,59,24,48,14,4,49,25,59,21,57,5,55,49,42}

    12

    Returns: 0.44

  44. {"10010000001000000000011000000000000100001100000100","01000000000000010000010000110000000000010000000000","00101001000000000001000000000000000010100000011000","00111010001000000010000000000000000010000000101011","10001000010101010000001101000000001000000000000001","10000100000000000000000001111000100010000000000000","00000010010000000000000000000100001100001000110010","00000001000000000000010001000001001001100000000000","00000010101000000000101000000001001000001000000000","00000100010000001000100000000100000000000010000000","00100010101000000000110001010010000110100000101100","00000000000100000100000000000000000000001010000000","01000000001010010000000100011000001000000001000100","10000000000001000000010010010000000000101000100100","00000000001100101000000101000100100000001001000000","00000100100000011100100000000010000010000000000000","00000000000000001010010000000100000100110100000010","00000000000100000100001000101000011010000000100110","00000010000010010010010000010010000000010000000010","00010000000010000001110000000100000000000000100000","00000100000000000000101000000010011101001100000000","10010100010000000000010000000000110001000000000000","00000000000000000000001000000000000010000000000001","00000010000101000010000100000000000100001000010000","11000000000010001000000010000000001000000100010010","10001000010100000000000001000001000000000000000000","00011010100001100100000000100000100001000000000001","00000000100001000001000000110000100000000000000000","10000000001000010000000110001001000000000000000001","00000001001000000000000000000100010101010001000000","00000100001000000000100000010010000000100000000001","00010000000000000000010000000001000000000010000010","00000000101000001000100000100000100010000100000100","00000000000000000000000001000000010000000100000100","00010000000010010000000010000000011000000001010000","00000100000000001101001100000000000100100001000000","01000000110000000000000000000000010010100000000110","00000000000011000000000110000000100001000000100010","00000000000100000000100000000001000000100100000000","00001110000000000000001001100000100000110010000000","10010000001000000000000010000000100100001000010000","00000000000000000001000001000000000000000100001100","00000000000000000000001110000011000001000010000000","01000000001000010000000100000000010000000001010000","00010000100000000100100001000000000000010100110110","00000000000000000100010000000000010000000000010000","10000000000000000000100000000100001000000000001010","00100000010000000010100000000000100100010000000101","00000000000000000001000000000101000000000000000010","00000000100100000001100010001000100000000101000001"}

    {3,3,5,2,3,0,5,0,0,5,6,6,5,4,2,7,7,6,3,6,1,6,4,0,1,1,5,5,1,5,3,2,7,7,5,2,5,3,0,0,1,0,5,6,6,1,6,2,2,5}

    {3,14,27,20,35,4,57,27,39,32,27,25,37,43,26,19,7,45,38,17,38,26,34,16,19,52,15,57,25,30,48,10,20,55,22,58,59,24,48,14,4,49,25,59,21,57,5,55,49,42}

    42

    Returns: 0.412

  45. {"11000000000000000000000000000000000000000000000000","11100000000000000000000000000000000000000000000000","01110000000000000000000000000000000000000000000000","00111000000000000000000000000000000000000000000000","00011100000000000000000000000000000000000000000000","00001110000000000000000000000000000000000000000000","00000111000000000000000000000000000000000000000000","00000011100000000000000000000000000000000000000000","00000001110000000000000000000000000000000000000000","00000000111000000000000000000000000000000000000000","00000000011100000000000000000000000000000000000000","00000000001110000000000000000000000000000000000000","00000000000111000000000000000000000000000000000000","00000000000011100000000000000000000000000000000000","00000000000001110000000000000000000000000000000000","00000000000000111000000000000000000000000000000000","00000000000000011100000000000000000000000000000000","00000000000000001110000000000000000000000000000000","00000000000000000111000000000000000000000000000000","00000000000000000011100000000000000000000000000000","00000000000000000001110000000000000000000000000000","00000000000000000000111000000000000000000000000000","00000000000000000000011100000000000000000000000000","00000000000000000000001110000000000000000000000000","00000000000000000000000111000000000000000000000000","00000000000000000000000011100000000000000000000000","00000000000000000000000001110000000000000000000000","00000000000000000000000000111000000000000000000000","00000000000000000000000000011100000000000000000000","00000000000000000000000000001110000000000000000000","00000000000000000000000000000111000000000000000000","00000000000000000000000000000011100000000000000000","00000000000000000000000000000001110000000000000000","00000000000000000000000000000000111000000000000000","00000000000000000000000000000000011100000000000000","00000000000000000000000000000000001110000000000000","00000000000000000000000000000000000111000000000000","00000000000000000000000000000000000011100000000000","00000000000000000000000000000000000001110000000000","00000000000000000000000000000000000000111000000000","00000000000000000000000000000000000000011100000000","00000000000000000000000000000000000000001110000000","00000000000000000000000000000000000000000111000000","00000000000000000000000000000000000000000011100000","00000000000000000000000000000000000000000001110000","00000000000000000000000000000000000000000000111000","00000000000000000000000000000000000000000000011100","00000000000000000000000000000000000000000000001110","00000000000000000000000000000000000000000000000111","00000000000000000000000000000000000000000000000011"}

    {1,6,1,6,2,1,1,1,3,3,7,6,4,5,6,7,3,5,3,3,7,2,1,5,5,3,6,5,3,1,4,6,0,0,0,6,2,2,6,1,5,4,4,6,3,0,2,1,6,1}

    {45,26,47,17,3,24,52,3,47,7,25,31,60,50,9,10,9,26,8,12,21,16,28,25,36,11,0,49,42,46,46,12,33,36,17,15,19,39,52,10,57,7,6,56,17,48,38,5,8,10}

    49

    Returns: 0.42857142857142855

  46. {"11000000000000000000000000000000000000000000000000","11100000000000000000000000000000000000000000000000","01110000000000000000000000000000000000000000000000","00111000000000000000000000000000000000000000000000","00011100000000000000000000000000000000000000000000","00001110000000000000000000000000000000000000000000","00000111000000000000000000000000000000000000000000","00000011100000000000000000000000000000000000000000","00000001110000000000000000000000000000000000000000","00000000111000000000000000000000000000000000000000","00000000011100000000000000000000000000000000000000","00000000001110000000000000000000000000000000000000","00000000000111000000000000000000000000000000000000","00000000000011100000000000000000000000000000000000","00000000000001110000000000000000000000000000000000","00000000000000111000000000000000000000000000000000","00000000000000011100000000000000000000000000000000","00000000000000001110000000000000000000000000000000","00000000000000000111000000000000000000000000000000","00000000000000000011100000000000000000000000000000","00000000000000000001110000000000000000000000000000","00000000000000000000111000000000000000000000000000","00000000000000000000011100000000000000000000000000","00000000000000000000001110000000000000000000000000","00000000000000000000000111000000000000000000000000","00000000000000000000000011100000000000000000000000","00000000000000000000000001110000000000000000000000","00000000000000000000000000111000000000000000000000","00000000000000000000000000011100000000000000000000","00000000000000000000000000001110000000000000000000","00000000000000000000000000000111000000000000000000","00000000000000000000000000000011100000000000000000","00000000000000000000000000000001110000000000000000","00000000000000000000000000000000111000000000000000","00000000000000000000000000000000011100000000000000","00000000000000000000000000000000001110000000000000","00000000000000000000000000000000000111000000000000","00000000000000000000000000000000000011100000000000","00000000000000000000000000000000000001110000000000","00000000000000000000000000000000000000111000000000","00000000000000000000000000000000000000011100000000","00000000000000000000000000000000000000001110000000","00000000000000000000000000000000000000000111000000","00000000000000000000000000000000000000000011100000","00000000000000000000000000000000000000000001110000","00000000000000000000000000000000000000000000111000","00000000000000000000000000000000000000000000011100","00000000000000000000000000000000000000000000001110","00000000000000000000000000000000000000000000000111","00000000000000000000000000000000000000000000000011"}

    {1,6,1,6,2,1,1,1,3,3,7,6,4,5,6,7,3,5,3,3,7,2,1,5,5,3,6,5,3,1,4,6,0,0,0,6,2,2,6,1,5,4,4,6,3,0,2,1,6,1}

    {45,26,47,17,3,24,52,3,47,7,25,31,60,50,9,10,9,26,8,12,21,16,28,25,36,11,0,49,42,46,46,12,33,36,17,15,19,39,52,10,57,7,6,56,17,48,38,5,8,10}

    0

    Returns: 0.19692480000000004

  47. {"11000000000000000000000000000000000000000000000000","11100000000000000000000000000000000000000000000000","01110000000000000000000000000000000000000000000000","00111000000000000000000000000000000000000000000000","00011100000000000000000000000000000000000000000000","00001110000000000000000000000000000000000000000000","00000111000000000000000000000000000000000000000000","00000011100000000000000000000000000000000000000000","00000001110000000000000000000000000000000000000000","00000000111000000000000000000000000000000000000000","00000000011100000000000000000000000000000000000000","00000000001110000000000000000000000000000000000000","00000000000111000000000000000000000000000000000000","00000000000011100000000000000000000000000000000000","00000000000001110000000000000000000000000000000000","00000000000000111000000000000000000000000000000000","00000000000000011100000000000000000000000000000000","00000000000000001110000000000000000000000000000000","00000000000000000111000000000000000000000000000000","00000000000000000011100000000000000000000000000000","00000000000000000001110000000000000000000000000000","00000000000000000000111000000000000000000000000000","00000000000000000000011100000000000000000000000000","00000000000000000000001110000000000000000000000000","00000000000000000000000111000000000000000000000000","00000000000000000000000011100000000000000000000000","00000000000000000000000001110000000000000000000000","00000000000000000000000000111000000000000000000000","00000000000000000000000000011100000000000000000000","00000000000000000000000000001110000000000000000000","00000000000000000000000000000111000000000000000000","00000000000000000000000000000011100000000000000000","00000000000000000000000000000001110000000000000000","00000000000000000000000000000000111000000000000000","00000000000000000000000000000000011100000000000000","00000000000000000000000000000000001110000000000000","00000000000000000000000000000000000111000000000000","00000000000000000000000000000000000011100000000000","00000000000000000000000000000000000001110000000000","00000000000000000000000000000000000000111000000000","00000000000000000000000000000000000000011100000000","00000000000000000000000000000000000000001110000000","00000000000000000000000000000000000000000111000000","00000000000000000000000000000000000000000011100000","00000000000000000000000000000000000000000001110000","00000000000000000000000000000000000000000000111000","00000000000000000000000000000000000000000000011100","00000000000000000000000000000000000000000000001110","00000000000000000000000000000000000000000000000111","00000000000000000000000000000000000000000000000011"}

    {1,6,1,6,2,1,1,1,3,3,7,6,4,5,6,7,3,5,3,3,7,2,1,5,5,3,6,5,3,1,4,6,0,0,0,6,2,2,6,1,5,4,4,6,3,0,2,1,6,1}

    {22,26,7,1,5,28,25,26,7,11,3,29,13,23,24,26,6,10,11,5,3,15,14,23,17,23,21,25,7,3,28,13,5,14,18,28,2,5,8,14,6,21,29,29,20,13,8,24,5,18}

    24

    Returns: 0.42501199999999995

  48. {"11000000000000000000000000000000000000000000000000","11100000000000000000000000000000000000000000000000","01110000000000000000000000000000000000000000000000","00111000000000000000000000000000000000000000000000","00011100000000000000000000000000000000000000000000","00001110000000000000000000000000000000000000000000","00000111000000000000000000000000000000000000000000","00000011100000000000000000000000000000000000000000","00000001110000000000000000000000000000000000000000","00000000111000000000000000000000000000000000000000","00000000011100000000000000000000000000000000000000","00000000001110000000000000000000000000000000000000","00000000000111000000000000000000000000000000000000","00000000000011100000000000000000000000000000000000","00000000000001110000000000000000000000000000000000","00000000000000111000000000000000000000000000000000","00000000000000011100000000000000000000000000000000","00000000000000001110000000000000000000000000000000","00000000000000000111000000000000000000000000000000","00000000000000000011100000000000000000000000000000","00000000000000000001110000000000000000000000000000","00000000000000000000111000000000000000000000000000","00000000000000000000011100000000000000000000000000","00000000000000000000001110000000000000000000000000","00000000000000000000000111000000000000000000000000","00000000000000000000000011100000000000000000000000","00000000000000000000000001110000000000000000000000","00000000000000000000000000111000000000000000000000","00000000000000000000000000011100000000000000000000","00000000000000000000000000001110000000000000000000","00000000000000000000000000000111000000000000000000","00000000000000000000000000000011100000000000000000","00000000000000000000000000000001110000000000000000","00000000000000000000000000000000111000000000000000","00000000000000000000000000000000011100000000000000","00000000000000000000000000000000001110000000000000","00000000000000000000000000000000000111000000000000","00000000000000000000000000000000000011100000000000","00000000000000000000000000000000000001110000000000","00000000000000000000000000000000000000111000000000","00000000000000000000000000000000000000011100000000","00000000000000000000000000000000000000001110000000","00000000000000000000000000000000000000000111000000","00000000000000000000000000000000000000000011100000","00000000000000000000000000000000000000000001110000","00000000000000000000000000000000000000000000111000","00000000000000000000000000000000000000000000011100","00000000000000000000000000000000000000000000001110","00000000000000000000000000000000000000000000000111","00000000000000000000000000000000000000000000000011"}

    {1,6,1,6,2,1,1,1,3,3,7,6,4,5,6,7,3,5,3,3,7,2,1,5,5,3,6,5,3,1,4,6,0,0,0,6,2,2,6,1,5,4,4,6,3,0,2,1,6,1}

    {22,26,7,1,5,28,25,26,7,11,3,29,13,23,24,26,6,10,11,5,3,15,14,23,17,23,21,25,7,3,28,13,5,14,18,28,2,5,8,14,6,21,29,29,20,13,8,24,5,18}

    49

    Returns: 0.5454545454545454

  49. {"11000000000000000000000000000000000000000000000000","11100000000000000000000000000000000000000000000000","01110000000000000000000000000000000000000000000000","00111000000000000000000000000000000000000000000000","00011100000000000000000000000000000000000000000000","00001110000000000000000000000000000000000000000000","00000111000000000000000000000000000000000000000000","00000011100000000000000000000000000000000000000000","00000001110000000000000000000000000000000000000000","00000000111000000000000000000000000000000000000000","00000000011100000000000000000000000000000000000000","00000000001110000000000000000000000000000000000000","00000000000111000000000000000000000000000000000000","00000000000011100000000000000000000000000000000000","00000000000001110000000000000000000000000000000000","00000000000000111000000000000000000000000000000000","00000000000000011100000000000000000000000000000000","00000000000000001110000000000000000000000000000000","00000000000000000111000000000000000000000000000000","00000000000000000011100000000000000000000000000000","00000000000000000001110000000000000000000000000000","00000000000000000000111000000000000000000000000000","00000000000000000000011100000000000000000000000000","00000000000000000000001110000000000000000000000000","00000000000000000000000111000000000000000000000000","00000000000000000000000011100000000000000000000000","00000000000000000000000001110000000000000000000000","00000000000000000000000000111000000000000000000000","00000000000000000000000000011100000000000000000000","00000000000000000000000000001110000000000000000000","00000000000000000000000000000111000000000000000000","00000000000000000000000000000011100000000000000000","00000000000000000000000000000001110000000000000000","00000000000000000000000000000000111000000000000000","00000000000000000000000000000000011100000000000000","00000000000000000000000000000000001110000000000000","00000000000000000000000000000000000111000000000000","00000000000000000000000000000000000011100000000000","00000000000000000000000000000000000001110000000000","00000000000000000000000000000000000000111000000000","00000000000000000000000000000000000000011100000000","00000000000000000000000000000000000000001110000000","00000000000000000000000000000000000000000111000000","00000000000000000000000000000000000000000011100000","00000000000000000000000000000000000000000001110000","00000000000000000000000000000000000000000000111000","00000000000000000000000000000000000000000000011100","00000000000000000000000000000000000000000000001110","00000000000000000000000000000000000000000000000111","00000000000000000000000000000000000000000000000011"}

    {1,6,1,6,2,1,1,1,3,3,7,6,4,5,6,7,3,5,3,3,7,2,1,5,5,3,6,5,3,1,4,6,0,0,0,6,2,2,6,1,5,4,4,6,3,0,2,1,6,1}

    {22,26,7,1,5,28,25,26,7,11,3,29,13,23,24,26,6,10,11,5,3,15,14,23,17,23,21,25,7,3,28,13,5,14,18,28,2,5,8,14,6,21,29,29,20,13,8,24,5,18}

    0

    Returns: 0.6030285714285715

  50. {"11000000000000000000000000000000000000000000000000","11100000000000000000000000000000000000000000000000","01110000000000000000000000000000000000000000000000","00111000000000000000000000000000000000000000000000","00011100000000000000000000000000000000000000000000","00001110000000000000000000000000000000000000000000","00000111000000000000000000000000000000000000000000","00000011100000000000000000000000000000000000000000","00000001110000000000000000000000000000000000000000","00000000111000000000000000000000000000000000000000","00000000011100000000000000000000000000000000000000","00000000001110000000000000000000000000000000000000","00000000000111000000000000000000000000000000000000","00000000000011100000000000000000000000000000000000","00000000000001110000000000000000000000000000000000","00000000000000111000000000000000000000000000000000","00000000000000011100000000000000000000000000000000","00000000000000001110000000000000000000000000000000","00000000000000000111000000000000000000000000000000","00000000000000000011100000000000000000000000000000","00000000000000000001110000000000000000000000000000","00000000000000000000111000000000000000000000000000","00000000000000000000011100000000000000000000000000","00000000000000000000001110000000000000000000000000","00000000000000000000000111000000000000000000000000","00000000000000000000000011100000000000000000000000","00000000000000000000000001110000000000000000000000","00000000000000000000000000111000000000000000000000","00000000000000000000000000011100000000000000000000","00000000000000000000000000001110000000000000000000","00000000000000000000000000000111000000000000000000","00000000000000000000000000000011100000000000000000","00000000000000000000000000000001110000000000000000","00000000000000000000000000000000111000000000000000","00000000000000000000000000000000011100000000000000","00000000000000000000000000000000001110000000000000","00000000000000000000000000000000000111000000000000","00000000000000000000000000000000000011100000000000","00000000000000000000000000000000000001110000000000","00000000000000000000000000000000000000111000000000","00000000000000000000000000000000000000011100000000","00000000000000000000000000000000000000001110000000","00000000000000000000000000000000000000000111000000","00000000000000000000000000000000000000000011100000","00000000000000000000000000000000000000000001110000","00000000000000000000000000000000000000000000111000","00000000000000000000000000000000000000000000011100","00000000000000000000000000000000000000000000001110","00000000000000000000000000000000000000000000000111","00000000000000000000000000000000000000000000000011"}

    {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,50}

    {22,26,7,1,5,28,25,26,7,11,3,29,13,23,24,26,6,10,11,5,3,15,14,23,17,23,21,25,7,3,28,13,5,14,18,28,2,5,8,14,6,21,29,29,20,13,8,24,5,18}

    10

    Returns: 0.0010106770810557099

  51. {"11000000000000000000000000000000000000000000000000","11100000000000000000000000000000000000000000000000","01110000000000000000000000000000000000000000000000","00111000000000000000000000000000000000000000000000","00011100000000000000000000000000000000000000000000","00001110000000000000000000000000000000000000000000","00000111000000000000000000000000000000000000000000","00000011100000000000000000000000000000000000000000","00000001110000000000000000000000000000000000000000","00000000111000000000000000000000000000000000000000","00000000011100000000000000000000000000000000000000","00000000001110000000000000000000000000000000000000","00000000000111000000000000000000000000000000000000","00000000000011100000000000000000000000000000000000","00000000000001110000000000000000000000000000000000","00000000000000111000000000000000000000000000000000","00000000000000011100000000000000000000000000000000","00000000000000001110000000000000000000000000000000","00000000000000000111000000000000000000000000000000","00000000000000000011100000000000000000000000000000","00000000000000000001110000000000000000000000000000","00000000000000000000111000000000000000000000000000","00000000000000000000011100000000000000000000000000","00000000000000000000001110000000000000000000000000","00000000000000000000000111000000000000000000000000","00000000000000000000000011100000000000000000000000","00000000000000000000000001110000000000000000000000","00000000000000000000000000111000000000000000000000","00000000000000000000000000011100000000000000000000","00000000000000000000000000001110000000000000000000","00000000000000000000000000000111000000000000000000","00000000000000000000000000000011100000000000000000","00000000000000000000000000000001110000000000000000","00000000000000000000000000000000111000000000000000","00000000000000000000000000000000011100000000000000","00000000000000000000000000000000001110000000000000","00000000000000000000000000000000000111000000000000","00000000000000000000000000000000000011100000000000","00000000000000000000000000000000000001110000000000","00000000000000000000000000000000000000111000000000","00000000000000000000000000000000000000011100000000","00000000000000000000000000000000000000001110000000","00000000000000000000000000000000000000000111000000","00000000000000000000000000000000000000000011100000","00000000000000000000000000000000000000000001110000","00000000000000000000000000000000000000000000111000","00000000000000000000000000000000000000000000011100","00000000000000000000000000000000000000000000001110","00000000000000000000000000000000000000000000000111","00000000000000000000000000000000000000000000000011"}

    {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,50}

    {22,26,7,1,5,28,25,26,7,11,3,29,13,23,24,26,6,10,11,5,3,15,14,23,17,23,21,25,7,3,28,13,5,14,18,28,2,5,8,14,6,21,29,29,20,13,8,24,5,18}

    0

    Returns: 2.0987275067148604E-4

  52. {"11000000000000000000000000000000000000000000000000","11100000000000000000000000000000000000000000000000","01110000000000000000000000000000000000000000000000","00111000000000000000000000000000000000000000000000","00011100000000000000000000000000000000000000000000","00001110000000000000000000000000000000000000000000","00000111000000000000000000000000000000000000000000","00000011100000000000000000000000000000000000000000","00000001110000000000000000000000000000000000000000","00000000111000000000000000000000000000000000000000","00000000011100000000000000000000000000000000000000","00000000001110000000000000000000000000000000000000","00000000000111000000000000000000000000000000000000","00000000000011100000000000000000000000000000000000","00000000000001110000000000000000000000000000000000","00000000000000111000000000000000000000000000000000","00000000000000011100000000000000000000000000000000","00000000000000001110000000000000000000000000000000","00000000000000000111000000000000000000000000000000","00000000000000000011100000000000000000000000000000","00000000000000000001110000000000000000000000000000","00000000000000000000111000000000000000000000000000","00000000000000000000011100000000000000000000000000","00000000000000000000001110000000000000000000000000","00000000000000000000000111000000000000000000000000","00000000000000000000000011100000000000000000000000","00000000000000000000000001110000000000000000000000","00000000000000000000000000111000000000000000000000","00000000000000000000000000011100000000000000000000","00000000000000000000000000001110000000000000000000","00000000000000000000000000000111000000000000000000","00000000000000000000000000000011100000000000000000","00000000000000000000000000000001110000000000000000","00000000000000000000000000000000111000000000000000","00000000000000000000000000000000011100000000000000","00000000000000000000000000000000001110000000000000","00000000000000000000000000000000000111000000000000","00000000000000000000000000000000000011100000000000","00000000000000000000000000000000000001110000000000","00000000000000000000000000000000000000111000000000","00000000000000000000000000000000000000011100000000","00000000000000000000000000000000000000001110000000","00000000000000000000000000000000000000000111000000","00000000000000000000000000000000000000000011100000","00000000000000000000000000000000000000000001110000","00000000000000000000000000000000000000000000111000","00000000000000000000000000000000000000000000011100","00000000000000000000000000000000000000000000001110","00000000000000000000000000000000000000000000000111","00000000000000000000000000000000000000000000000011"}

    {2,1,2,0,1,2,1,1,1,0,0,2,1,0,2,2,2,0,2,1,2,2,0,0,2,2,1,0,2,1,1,2,0,1,1,2,2,1,0,0,0,0,0,1,2,0,2,2,2,50}

    {22,26,7,1,5,28,25,26,7,11,3,29,13,23,24,26,6,10,11,5,3,15,14,23,17,23,21,25,7,3,28,13,5,14,18,28,2,5,8,14,6,21,29,29,20,13,8,24,5,18}

    0

    Returns: 0.17222222222222222

  53. {"1"}

    {1}

    {0}

    0

    Returns: 1.0

  54. {"110", "011", "001" }

    {2, 1, 10 }

    {20, 20, 10 }

    0

    Returns: 0.405

  55. {"11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111" }

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

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

    5

    Returns: 1.0

  56. {"11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111" }

    {40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30 }

    {20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 30, 30, 30, 30, 30, 30, 30, 30, 30, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 }

    5

    Returns: 0.75

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