Statistics

Problem Statement for "ReliefMeasuring"

Problem Statement

The relief of an area near Alone Hill was measured using an old machine which might be inaccurate. The area has a rectangular form, and it was split into a rectangular grid containing n rows and m columns of equal squares. The results are given as a String[] heights, where the j-th character of the i-th element is '1' (one) if the height of the point at the center of the square at row i, column j is greater than some constant value, and '0' (zero) otherwise. heights contains exactly n elements, each element of which contains exactly m characters. A cell is a neighbour of another cell if they share the side. The measured area has one special property: if point A is the center of some cell and point B is the center of the neighbour cell and point A is closer to the hill peak than point B, then the height of A is greater or equal than the height of B. Distance is measured using the euclidian distance along the horizontal plane. In other words, the distance between point (xa,ya) and point (xb,yb) is equal to sqrt((xa-xb)^2+(ya-yb)^2). It is known that one of the given measurements was taken at the peak of the hill, i.e., the hill coincides with the center of one of the squares.

Using that property, you can tell whether or not the given results might be accurate. For example, the relief map on the left might be accurate while the one on the right is definitely not:
{"0100", {"01010",
 "1110",  "10101",
 "0110",  "01010",
 "0110"}  "10101"}

Return the minimal number of characters you must replace in heights to make the results possibly accurate. If it is already possible that the results are accurate, return 0.

Definition

Class:
ReliefMeasuring
Method:
minValuesToFix
Parameters:
String[]
Returns:
int
Method signature:
int minValuesToFix(String[] heights)
(be sure your method is public)

Constraints

  • heights will contain between 1 and 25 elements, inclusive.
  • Each element of heights will contain between 1 and 25 characters, inclusive.
  • Each element of heights will contain the same number of characters as others.
  • Each element of heights will contain only '0' and '1' characters.

Examples

  1. {"0100","1110","0110","0110"}

    Returns: 0

    This is the example from the statement.

  2. {"101"}

    Returns: 1

    Replace the middle character.

  3. {"101", "010", "101"}

    Returns: 3

  4. {"0010", "0101", "0010"}

    Returns: 1

  5. {"1010", "0101", "1010", "0101"}

    Returns: 5

  6. {"011", "110"}

    Returns: 1

  7. {"0"}

    Returns: 0

  8. {"10", "11"}

    Returns: 0

  9. {"111", "111", "111"}

    Returns: 0

  10. {"0000", "0101", "1010", "1001"}

    Returns: 4

  11. {"00111", "11110", "11111", "11011", "00010"}

    Returns: 2

  12. {"111111", "111111", "111110", "111111", "011011", "100111"}

    Returns: 3

  13. {"0000010", "1001000", "0100000", "0000000", "0000000", "0000000", "0000001"}

    Returns: 4

  14. {"00100111", "10111111", "10110001", "01100100", "00000000", "00000010", "10100101", "11100010"}

    Returns: 15

  15. {"111111111", "111111110", "110111011", "011100001", "011101100", "111101101", "011111111", "011011100", "111100111"}

    Returns: 18

  16. {"0000000000", "1000010000", "0000000000", "0000000000", "0000000000", "0000010110", "0000000000", "0010010000", "1000000000", "0100000000"}

    Returns: 7

  17. {"00000111101", "11101101100", "01011001000", "00000000000", "00101010010", "11110001001", "01000011110", "00111110000", "00110011011", "11110001001", "00111101111"}

    Returns: 37

  18. {"111111111111", "111110110111", "011011100001", "000101000011", "101101011111", "011011011100", "111100111111", "100110110011", "111111110010", "011011111111", "111100011110", "001111100101"}

    Returns: 41

  19. {"0000000000000", "0000000000000", "0000000000000", "0000000000000", "0000000000000", "0000000000000", "0000000000000", "1000000000000", "0000000000000", "0000000000010", "0000000000000", "0000000000000", "0000000000000"}

    Returns: 1

  20. {"00000011100001", "01000100000001", "00000111000001", "10111100101000", "00001111001000", "00000100011001", "00000110000000", "00110100100000", "11110101001100", "00011000000100", "11011010100010", "10010000110101", "10010000100000", "01010001000001"}

    Returns: 49

  21. {"011001111001010", "100010011111110", "100111001101101", "111001011101111", "111100111011110", "101111111111011", "101001001111110", "110010011110111", "011111101110001", "011101101101111", "001011111110110", "101101111101101", "100111000110001", "110011101001110", "001111111111010"}

    Returns: 62

  22. {"1111111111111111", "1111111111111111", "1111101101111111", "1111111111111111", "1011111111111111", "1111111111111111", "1111111111111111", "1111111111111111", "1111111111111111", "1111111110111111", "1111111111111111", "1111101111111111", "1111110111110111", "1111111111111111", "1111111111111111", "1111111101111111"}

    Returns: 8

  23. {"00000010100001000", "00100000001000001", "11000001101011001", "01000000011010010", "00000001000100000", "00001100000000011", "01001000001111010", "00011000001100000", "01001101101010001", "01001000010000010", "01000010000001010", "00100000000000101", "00001000100101111", "00101110000010100", "00101000000100001", "01101101111000010", "01100001000000000"}

    Returns: 72

  24. {"001001111000010100", "010010111110100111", "000101101111001010", "101111111100111001", "010101111111111011", "100000001111110110", "010011110111011111", "100110000011101101", "101111001010111100", "110101101111001100", "100111000100000110", "011101001010001011", "111110010111010001", "010100101101010100", "101111111011110100", "100111110100010100", "111000101110100111", "100011101100110010"}

    Returns: 107

  25. {"1111111111111111111", "1110111111110011101", "1111111111111111110", "1111110110111110111", "1110111111111111110", "1111111111111111111", "1111111011111101111", "1110111111001111111", "1111111111010111111", "1111111111111111111", "1111110110111111111", "1111111101111111111", "0111111111111111111", "1111111111111111111", "1111011101111111111", "1111111111111111111", "1111111111110111011", "1101111111111111111", "1101111111111011111"}

    Returns: 28

  26. {"00100000000011001010", "01000000010000010101", "00100100000000000000", "00000001000101001010", "00010110000000001000", "10111011000000100000", "00001101000100000000", "00000101000000000000", "00000000000001000001", "00001000010010000100", "10110011000000100000", "10001011000000000001", "10100110010001001000", "01000000010000010000", "00000100001000110010", "00101001010011000110", "00100000000010001010", "01010010000100000000", "01010000100000000100", "00000100000000011000"}

    Returns: 79

  27. {"011110110101110010111", "101111101100101011101", "101110100001010101011", "011011101011111100101", "011111110100100010111", "111100001101001101111", "110001100000111110010", "111011101100001010011", "110101011011010110110", "100110001001111101110", "011011101011101011010", "010011001101101101101", "110011111101001101000", "101111101010111101010", "111011011010110100110", "001110011101100001100", "111001110110011101000", "011010110101100010001", "111011110000010001110", "000000111111111000010", "101100011001101010000"}

    Returns: 157

  28. {"1111101111111111111111", "0111111110010101111111", "1111111111110111111011", "0111110111111011111111", "1111110111111011111111", "0111111111101111110101", "1111011111100111111111", "1111111101011111110111", "1111110111110101111001", "1011111011111111111011", "1111111101111101101111", "1111101101111011111101", "0011110111011111111101", "1111111111111111111111", "1101111101110111101110", "1111111111111101110111", "1110111111111011110111", "1101111111111111010111", "1110111111111111111001", "1011110101101110111111", "0111111110001001111111", "0110111111110111111010"}

    Returns: 72

  29. {"00100000000010001010000", "00000000000010101001001", "00000000000000000000010", "00001000010000101000000", "00000000001110010000001", "00000000001010001000000", "00000001010000000000000", "00000000000000000000000", "00000100100001001011000", "10000000000001000001100", "00000000001010011000000", "10010000000000001000001", "00000000010000100011001", "00010100101001100011000", "00000000000000101001010", "01000000000000001000000", "10000000000000000000000", "00001000000000000000001", "00000010000000100000000", "00000000000000000000001", "00000000000000000000000", "00010010000000000001000", "00000000000000000001000"}

    Returns: 66

  30. {"010110010001101010000101", "100100100010000000011010", "000010101101101011000100", "101011010010110011110011", "011000001101010001011100", "000010100110100010110010", "101001011000001000100111", "000000111001100000100000", "000100011011000111000110", "100011110100100001010010", "000100100011010010011011", "010110011000000100001000", "101010110111000001010011", "001101010100000000010011", "000001101100011011110000", "011010101000011100000101", "111110001100000110000101", "011010111001111010110000", "010100101010001111011100", "011011010001011011001111", "010110001010011101001000", "111100010000001111111001", "000111001000011011010000", "100110101001011011001101"}

    Returns: 210

  31. {"1111111110111010110011011", "1010011111110001101111111", "0110111101111111001111111", "1111111101101111100111110", "0100110111001101110110111", "1100111111010110010101011", "0111000111111101110111101", "1101111010110101101111101", "1111110111100110101111111", "1101111110110111011111101", "1111001111111111111111100", "0001111101010111110111111", "0001010111111011111111010", "1010101101110110110111011", "1111111011111111111001011", "1111101011111110111011001", "1100111101111111101111101", "1111010110101101111011111", "1111111111110111010111110", "1111101111101111101110100", "1101111101110011111111111", "1111001110011000111111111", "1110111111110111101100111", "1100110111011110111011001", "1010111100001111110111111"}

    Returns: 154

  32. {"1"}

    Returns: 0

  33. {"10"}

    Returns: 0

  34. {"10", "11", "01"}

    Returns: 1

  35. {"1111", "1111"}

    Returns: 0

  36. {"00000", "00000"}

    Returns: 0

  37. {"000000", "100000", "101011"}

    Returns: 2

  38. {"1011011", "0000010", "1011110"}

    Returns: 5

  39. {"00000", "01000", "00101", "01110", "00011", "10100", "01010", "00001"}

    Returns: 8

  40. {"000000000", "000000000", "000000100", "000000000"}

    Returns: 0

  41. {"0000001000", "0010101110", "0000110100", "0100000001"}

    Returns: 5

  42. {"10101000101", "00100111111", "00000101100", "11100110111"}

    Returns: 11

  43. {"111110001011", "011111111100", "001101110111", "011111111111", "111111101111"}

    Returns: 8

  44. {"1000000", "0100001", "0001000", "0000000", "0000011", "1000101", "1000000", "1001000", "1010000", "0000010", "0000001", "0000000", "1100000"}

    Returns: 14

  45. {"10000000100001", "00010000000000", "00000111000101", "10000001001000", "10100000000010"}

    Returns: 11

  46. {"100010001010010", "001010100000101", "100111001101101", "000011010001010", "010101001001100", "110000100111100"}

    Returns: 27

  47. {"1111111110011010", "1011111011110111", "1111101001111111", "0111111000011101", "0010111010111000", "0111101110011101"}

    Returns: 23

  48. {"11111111100111101", "11111111111111111", "11111111111111011", "11111101111111111", "11101111110111111", "01110011101011111"}

    Returns: 11

  49. {"0001000000", "0100000000", "0000100000", "0000000000", "0000100000", "0000000000", "0000000000", "0000100000", "0000000000", "0000010010", "0001000000", "0100000000", "1000000010", "1000000000", "0000000000", "0110000000", "0000000000", "0000000000"}

    Returns: 12

  50. {"1001101110010000100", "1011011000000011010", "1000001101010010100", "0011000000001001010", "0000001110100001010", "1001111010010010110", "1000101010100010100"}

    Returns: 41

  51. {"10111011100110101011", "11101111000001101010", "00011111010111100001", "11000010111010111000", "01111010000111010011", "11011011010110100111", "11111100111000111110"}

    Returns: 48

  52. {"111111111001111010111", "111111101111111111001", "111111011111111001111", "111111110101111010111", "101110011101011111011", "111011110100111111111", "001111011111101111111", "111111111110111111100"}

    Returns: 29

  53. {"0001000000010000000000", "0010000000000000000000", "1000000000000000000000", "0000000010000000000000", "0000000100100001000000", "0100000000100000001010", "0000000000000000000110", "0000000000000000000000"}

    Returns: 11

  54. {"111111111001", "111011111111", "111111111111", "111111111111", "011111111011", "111111111110", "111111011111", "101110011101", "011111111111", "011110110111", "111111111111", "011111101111", "111111111111", "110111111101", "110111101111", "111011111111", "111011111111", "111111111111", "111111111111", "101111111111", "111111111111", "010111111100", "111011111111"}

    Returns: 28

  55. {"101100001011011110001111", "001011010110001101101000", "011010011010110110010010", "111011111011100111101110", "110110011111000100100100", "001000110100111110110000", "101000101111010111010000", "010111000010001000101101", "001101101100011111100100"}

    Returns: 71

  56. {"1011110111111111101111110", "0101111011100111111100001", "1110011110110110110111111", "1111111111011111011111101", "1111111101110110110101100", "1110110111110110010101100", "1111111101111111000111111", "1101101111110111111111110", "1100011111100101001001111"}

    Returns: 51

  57. {"0"}

    Returns: 0

  58. {"00"}

    Returns: 0

  59. {"1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111110111111111111111111", "1111100011111111111111111", "1111000001111111111111111", "1110000000111111111111111", "1100000000011111111111111", "1000000000001111111111111", "0000000000000111111111111", "0000000000000011111111111", "0000000000000001111111111", "0000000000000011111111111", "0000000000000111111111111", "1000000000001111111111111", "1100000000011111111111111", "1110000000111111111111111"}

    Returns: 30

  60. {"0000", "0000"}

    Returns: 0

  61. {"00000", "00000"}

    Returns: 0

  62. {"000000", "000000", "000000"}

    Returns: 0

  63. {"0000000", "0000000", "0000000"}

    Returns: 0

  64. {"0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000001", "0000000000000000000000011", "0000000000000000000000111", "0000000000000000000001111", "0000000000000000000011111", "0000000000000000000111111", "0000000000000000001111111", "0000000000000000011111111", "0000000000000000111111111", "0000000000000001111111111", "0000000000000011111111111", "0000000000000111111111111", "0000000000001111111111111", "0000000000011111111111111", "0000000000111111111111111", "0000000001111111111111111", "0000000011111111111111111", "0000000111111111111111111", "1000001111111111111111111", "1100011111111111111111111"}

    Returns: 3

  65. {"100000000", "110000000", "111000000", "111100000"}

    Returns: 0

  66. {"0000000000", "0000000000", "0000000000", "0000000000"}

    Returns: 0

  67. {"00000000000", "00000000000", "00000000000", "10000000000"}

    Returns: 0

  68. {"000000000111", "000000000011", "000000000001", "000000000011", "000000000111"}

    Returns: 2

  69. {"0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000001", "0000000000000000000000011", "0000000000000000000000111", "0000000000000000000001111", "0000000000000000000011111"}

    Returns: 0

  70. {"00000000000000", "00000000000000", "00000000000000", "00000000000000", "00000000000000"}

    Returns: 0

  71. {"111110000000000", "111100000000000", "111000000000000", "110000000000000", "100000000000000", "110000000000000"}

    Returns: 1

  72. {"1111111111100000", "1111111111000000", "1111111110000000", "1111111100000000", "1111111000000000", "1111111100000000"}

    Returns: 1

  73. {"00000000000000001", "00000000000000000", "00000000000000000", "00000000000000000", "00000000000000000", "00000000000000000"}

    Returns: 0

  74. {"0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000"}

    Returns: 0

  75. {"1111111111111000000", "1111111111110000000", "1111111111100000000", "1111111111000000000", "1111111110000000000", "1111111111000000000", "1111111111100000000"}

    Returns: 2

  76. {"00000000000000000000", "00000000000000000000", "00000000000000000000", "00000000000000000000", "00000000000000000000", "00000000000000000000", "00000000000000000000"}

    Returns: 0

  77. {"000000000000000111111", "000000000000000011111", "000000000000000111111", "000000000000001111111", "000000000000011111111", "000000000000111111111", "000000000001111111111", "000000000011111111111"}

    Returns: 1

  78. {"1111111111111000000000", "1111111111110000000000", "1111111111111000000000", "1111111111111100000000", "1111111111111110000000", "1111111111111111000000", "1111111111111111100000", "1111111111111111110000"}

    Returns: 1

  79. {"1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111"}

    Returns: 0

  80. {"000000000011111111111111", "000000000001111111111111", "000000000000111111111111", "000000000000011111111111", "000000000000001111111111", "000000000000011111111111", "000000000000111111111111", "000000000001111111111111", "000000000011111111111111"}

    Returns: 7

  81. {"1111000000000001111111111", "1110000000000000111111111", "1100000000000000011111111", "1000000000000000001111111", "0000000000000000000111111", "1000000000000000001111111", "1100000000000000011111111", "1110000000000000111111111", "1111000000000001111111111"}

    Returns: 27

  82. {"1"}

    Returns: 0

  83. {"11", "11"}

    Returns: 0

  84. {"01", "00"}

    Returns: 0

  85. {"111", "111", "111", "010"}

    Returns: 0

  86. {"11", "11", "11", "01", "00"}

    Returns: 0

  87. {"0111"}

    Returns: 0

  88. {"111", "111", "010", "000"}

    Returns: 0

  89. {"111", "111", "111", "111", "111", "111", "111", "111"}

    Returns: 0

  90. {"111", "111"}

    Returns: 0

  91. {"001111111", "000111111", "000011111", "000001111", "000000111"}

    Returns: 0

  92. {"1111", "1111", "1111", "1111", "1111", "1111", "1111"}

    Returns: 0

  93. {"00001111", "00011111", "00111111", "01111111", "11111111", "01111111", "00111111", "00011111", "00001111"}

    Returns: 0

  94. {"11111111", "11111111", "11111111", "11111111", "11111111", "01111111", "00111111", "00011111"}

    Returns: 0

  95. {"111111110000", "111111111000", "111111110000", "111111100000", "111111000000", "111110000000"}

    Returns: 0

  96. {"111111111111111", "111111111111111"}

    Returns: 0

  97. {"111111111111110", "111111111111111", "111111111111111", "111111111111111", "111111111111111", "111111111111111", "111111111111111", "111111111111111", "111111111111111", "111111111111111", "111111111111111"}

    Returns: 0

  98. {"0000000000000", "0000000000000", "0000000000000", "1000000000000", "1100000000000", "1110000000000", "1111000000000", "1111100000000", "1111110000000", "1111111000000", "1111111100000", "1111111000000", "1111110000000", "1111100000000", "1111000000000"}

    Returns: 0

  99. {"000000010000000000", "000000111000000000", "000001111100000000", "000011111110000000", "000111111111000000", "000011111110000000", "000001111100000000"}

    Returns: 0

  100. {"111111111110", "111111111111", "111111111110", "111111111100", "111111111000", "111111110000", "111111100000", "111111000000", "111110000000", "111100000000", "111000000000", "010000000000", "000000000000", "000000000000", "000000000000", "000000000000", "000000000000"}

    Returns: 0

  101. {"01111", "11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111"}

    Returns: 0

  102. {"0000000", "0000000", "0000000", "0000000", "0000000", "0000000", "0000000", "0000000", "0100000", "1110000", "1111000", "1111100", "1111110", "1111111", "1111110", "1111100", "1111000", "1110000"}

    Returns: 0

  103. {"000000000000000", "000010000000000", "000111000000000", "001111100000000", "011111110000000", "111111111000000", "011111110000000", "001111100000000", "000111000000000", "000010000000000"}

    Returns: 0

  104. {"000000111", "000001111", "000011111", "000111111", "001111111", "011111111", "111111111", "111111111", "111111111", "111111111", "111111111", "111111111", "111111111", "111111111"}

    Returns: 0

  105. {"111110000000", "111111000000", "111111100000", "111111110000", "111111111000", "111111110000", "111111100000"}

    Returns: 0

  106. {"00000010000000000000", "00000111000000000000", "00001111100000000000", "00011111110000000000", "00111111111000000000", "01111111111100000000", "11111111111110000000", "11111111111111000000", "11111111111111100000", "11111111111111000000", "11111111111110000000", "01111111111100000000", "00111111111000000000", "00011111110000000000", "00001111100000000000", "00000111000000000000", "00000010000000000000"}

    Returns: 0

  107. {"1010101010101010101010101"}

    Returns: 12

  108. {"1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1"}

    Returns: 12

  109. {"1010101010101010101010101", "0101010101010101010101010"}

    Returns: 23

  110. {"10", "01", "10", "01", "10", "01", "10", "01", "10", "01", "10", "01", "10", "01", "10", "01", "10", "01", "10", "01", "10", "01", "10", "01", "10"}

    Returns: 23

  111. {"1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101", "0101010101010101010101010", "1010101010101010101010101"}

    Returns: 288

  112. {"0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000"}

    Returns: 0

  113. {"0100000100000000100001001", "0000001000000000000010000", "0000000000000000000000100", "0010000000001000000000000", "0000000000100001000000000", "0100000000000001000000000", "0000000000000100010010000", "0000001010000000110000000", "0000000000000001000100000", "0100000000000000000000000", "0000000000010000000010000", "0001000000010000010000000", "0000001000000000000000000", "0000000000000010001100100", "0000000000000000100000000", "0000010000000000000000100", "0000100001010000000010100", "0000000000100001000000001", "0000000000000001000000000", "1010100000000000000000000", "0000000011000000000000001", "0000000001010000000000000", "0000000000010000010000000", "0000000000000000001000000", "0000000000000000000101000"}

    Returns: 56

  114. {"0100000001000001011100000", "0000001001001000100110010", "0010000000000000000111010", "1000000000000100000001000", "1000000100010001001001001", "0000100000001010010000100", "0000100110001000011100000", "0000000100001100000010000", "0100100010100011000010011", "0100010001011000010000110", "0001010000100000010000000", "0011000100000001100000000", "0001010000000000000000000", "0100000001000001000001000", "0100001000000100000000100", "0000000000001010100101000", "0010001100000010001010000", "1000001000000000000001001", "1000000000000010000000000", "0000001000001001000110100", "0110000000000001000100000", "0000100000010010001011101", "0001000000000000010000001", "1000110100010000000111111", "0000000000101011000010001"}

    Returns: 126

  115. {"0100100101000001011100010", "0000001001101000101110011", "0010000000000000000111010", "1001000000000100000001100", "1001000100010001001011001", "0100100010001010010000100", "0000100110011000011100000", "0000000100011100100011000", "0100100011111011000011011", "0100111001111000010000110", "0001010000100000010000000", "0011000100000001110000000", "0011110000100000100001000", "0100000001000001000001000", "1100101000000100000100110", "0000000010011010100101101", "0010001111110010001010000", "1000001110000000000001001", "1000000000000011000000000", "0001001000001101000110100", "0110100000001001010100000", "0000100010011010001011101", "0001000000000000010100001", "1001110100110000011111111", "0000010000101011000010101"}

    Returns: 177

  116. {"1100100101000001011101010", "0100001001101000101110011", "0011100000000000000111010", "1001001000101110000001100", "1001101101010001001011001", "0100100010101010110000110", "0000100110011000011100000", "0000110101011110100011000", "0100100111111011000011011", "0101111001111000010000110", "0001010000100000110000000", "0011000100000001110010010", "0011111000100001100011100", "0100000001000001000101000", "1110101001000110000100110", "0000000010111010100101101", "0010001111110010001010001", "1010101110000001010001001", "1000000100000011000001000", "0001001000001101100110100", "0110101000001001010110100", "0010100010011110001011101", "0001100010000011010100001", "1001110100110000111111111", "1010010000101011100010101"}

    Returns: 223

  117. {"1100100111000001011101010", "0100001011101000101110011", "1011100011000000000111010", "1001001010111111010001110", "1001111101110101001011101", "0100100110101010110001111", "0001100110011000011100000", "0001110111011110110011000", "0100100111111011000011111", "0101111001111010010000110", "1101010000100000111000001", "0011100100001001110010010", "1111111000100001100011100", "1101100001000001000111001", "1110101001010110000100110", "0010000010111011100101101", "0010001111111010001010001", "1010111110000101110001101", "1010000110001111001101000", "0001001001001111100110110", "0110101000001101010110100", "0010100110011110101011101", "0001100010010011010100001", "1111110110110011111111111", "1010010001101011100010101"}

    Returns: 253

  118. {"1100100111000001111101110", "1101001011111100101110011", "1011100011000110000111110", "1011001010111111011001110", "1101111101110101001011101", "1100100111101110110101111", "0011110110011011011101000", "0011110111011111110011000", "0100100111111011001111111", "0101111101111010010000111", "1101010010100001111000001", "0111101100101001110010010", "1111111000100101100011101", "1111110001100011000111001", "1110101001010110011100110", "0011010010111011100101101", "0110001111111010001011001", "1010111110000111110011101", "1010100110001111011111000", "1101001001011111100110111", "0110101000001101010111100", "0010100110011110101011101", "0001100110010111010100011", "1111111111110011111111111", "1110010001101011100110101"}

    Returns: 241

  119. {"1111111000101111011111111", "1110101111111011111111111", "1011011111001111011010001", "1111111110111010010111110", "1111101110011111100000110", "1010111111111111111101111", "1110110010111110111101110", "1110011111101110111110011", "1011011111001011011011101", "1101111110001100101000111", "1011101100000011111111011", "1110111100110011011101000", "0001111111111100010111110", "1011111011111110001111111", "1011111001111110110111101", "1110101111111011101101101", "1100110111101111110010001", "1011011111101111111111111", "1100111011110111110011110", "1100101111111011011011001", "0001101101010100010101111", "0010111011000110111111110", "1001101111110010110111111", "1011111011111011011111111", "0111011111111101111101101"}

    Returns: 170

  120. {"1111111001111111111111111", "1110101111111111111111111", "1111111111011111011010011", "1111111111111010110111111", "1111101110011111111001111", "1111111111111111111101111", "1110111011111110111101110", "1110011111101111111111011", "1011111111101011011111101", "1101111110011100111000111", "1011101101101011111111011", "1111111111110011011111010", "0111111111111100011111110", "1011111011111110011111111", "1011111101111110110111101", "1111111111111011111111101", "1101111111101111110110101", "1111111111101111111111111", "1100111011111111110111111", "1100101111111011011111011", "1011101101010111011111111", "0010111111010110111111110", "1001101111110010110111111", "1011111111111111011111111", "1111111111111101111101101"}

    Returns: 108

  121. {"1111111111111111111111111", "1111101111111111111111111", "1111111111011111111011111", "1111111111111110111111111", "1111111110011111111101111", "1111111111111111111101111", "1110111111111110111101111", "1110111111101111111111011", "1011111111111011111111101", "1101111110011110111000111", "1111101111111011111111111", "1111111111111111011111011", "1111111111111110011111111", "1111111111111111011111111", "1011111111111110111111101", "1111111111111011111111111", "1101111111111111110111101", "1111111111111111111111111", "1100111111111111110111111", "1100101111111011011111011", "1111101111110111111111111", "0111111111110110111111110", "1001101111110010111111111", "1011111111111111111111111", "1111111111111101111101111"}

    Returns: 62

  122. {"1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111", "1111111111111111111111111"}

    Returns: 0

  123. {"1110000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000010000000000000000", "0001111111111111100000000", "0011111111111111110000000", "0001111111111111000000000", "0000001111111000000000000", "0000000011000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000000000000000", "0000000000000111000000000", "0000000000011111110000000", "0000000001111111110000000", "0000001111111111111110000", "0000000011111111111000000", "0000000000001111000000000", "0000000000000000000000000", "0000000000000000000000000", "0001111111000000000000000", "0000011111000000000000000", "0000001100000000000000000", "0000000000000000000000000", "0000000000000000110000000" }

    Returns: 68

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