Statistics

Problem Statement for "Clicountingd2"

Problem Statement

Hero has a simple undirected graph. I.e., the graph has no self-loops and each pair of vertices is connected by at most one edge. Hero would like to solve a standard problem: he wants to find the size of the largest clique in his graph. (A clique is a subset C of vertices such that each pair of vertices in C is connected by an edge. The size of a clique is the number of vertices in C.) However, Hero is facing an issue: for some (at most 20) pairs of vertices he does not remember whether they are connected by an edge or not. You are given the information Hero remembers: a String[] g with n elements, where n is the number of vertices in the graph. The vertices are numbered 0 through n-1. For each valid i and j, g[i][j] is one of '0', '1', and '?'. Here, '0' means that vertices i and j are not connected, '1' means that they are connected, and '?' means that Hero does not remember whether they are connected. Let there be k unordered pairs of vertices for which Hero does not remember whether they are connected or not. Then, there are exactly 2^k different graphs consistent with what Hero remembers. For each of those graphs find the size of the largest clique, and return the sum of those 2^k numbers.

Definition

Class:
Clicountingd2
Method:
count
Parameters:
String[]
Returns:
int
Method signature:
int count(String[] g)
(be sure your method is public)

Constraints

  • g will contain n elements.
  • n will be between 1 and 20, inclusive.
  • Each element in g will contain exactly n characters.
  • Each character in g will be either '0', '1' or '?'.
  • For each valid i and j, g[i][j] will be equal to g[j][i].
  • For each valid i, g[i][i] will be '0'.
  • Number of unknown edges (number of '?' characters divided by 2) will be between 0 and 20, inclusive.

Examples

  1. {"01","10"}

    Returns: 2

  2. {"0?","?0"}

    Returns: 3

    Here the maximum clique size is either 2 (if the unknown edge is present) or 1 (if the edge is absent).

  3. {"011","101","110"}

    Returns: 3

    This is a complete graph on 3 vertices. The size of the maximum clique is 3.

  4. {"0?1","?01","110"}

    Returns: 5

    Hero is not sure about a single edge. If the edge is in the graph, we get the situation from Example 2. If the edge is not there, we get a graph in which the size of the maximum clique is 2. The answer is therefore 3+2 = 5.

  5. {"0???","?0??","??0?","???0"}

    Returns: 151

  6. {"001?????","001?????","110?????","???0??0?","????0?01","?????0?0","???00?01","????1010"}

    Returns: 3534230

  7. {"00000000010010100011","00111111101011011110","01001101110000?00000","0100000110?011100010","01100011100110000100","011000?1111001001110","01001?0100000100110?","01111110110001111000","011111010001?0101100","10100101001101001001","010?01000100100?1101","00001000110010111001","11011000?0110001101?","01010111010000101000","10?10001100101010001","0100000100?110101110","01000111111111010010","01001110101000010000","11010100000010011000","100000?00111?0100000"}

    Returns: 704

  8. {"01?11111111111111111","10100111?11111111010","?100111101111011111?","1000101111100111??1?","10110111111??11?0101","111010001010?0??1111","111110001?1101111101","11111000111?11111101","1?01111100111101??11","111110?1001111111101","111111111101101011?0","1110?01?111010101111","1110??011111011?1110","11011011110010111111","11111?11011111011101","1111??111100?1101100","111?0111?11111110111","101?1111?1111111101?","1111010010?111001101","10??1111110101101?10"}

    Returns: 4810752

  9. {"0??????","?0????0","??001??","??00???","??1?0??","?????0?","?0????0"}

    Returns: 822732

  10. {"0????","?0???","??0??","???0?","????0"}

    Returns: 2750

  11. {"01??1?1011?1","101?00??1?1?","?1000??1101?","??0011111111","10010111??01","?0?11011?111","1??11101??00","0?1111101?11","1111???100?1","1?01?1??00?1","?1110101??00","1??111011100"}

    Returns: 5750784

  12. {"01111110101111","10111111111111","11011110?11111","11101111111111","11110111111111","11111011101111","1111110111?101","01011110111111","11?11111010111","01111011101?11","111111?1010?11","111111111??011","11111101111101","11111111111110"}

    Returns: 156

  13. {"010101?0","10?1?11?","0?0111??","1110111?","0?11011?","1111101?","?1?11101","0?????10"}

    Returns: 2598

  14. {"010011011101011","10?11?1101000?1","0?01?1?11111111","0110111111111?0","11?1011?1010110","1?111010000110?","01?1110111011?1","1111?01011111?1","101110110111111","1111001110111?1","001110011101110","101101111110101","001111111111001","1?1?10??1?10001","11100?111101110"}

    Returns: 16384

  15. {"0??11110?01111","?001?1111??111","?0001???111110","11001?111??111","1?11011111?111","11??10?11?1?11","11?11?01111111","01?11110111111","?1111111011111","0?1?1?11101111","1?1??1111101?1","11111?111110??","1111111111??0?","11011111111??0"}

    Returns: 8770636

  16. {"00??1?","00?11?","??00??","?10011","11?10?","???1?0"}

    Returns: 850

  17. {"001?01000??10000000","0001011?01010001001","100000010?0001000?1","?100010001?0?010000","00000100010000?0?10","11011000?100000001?","0100000010010000010","0?10000010000000000","00000?110?0?0010?0?","?1?11100?0010000001","?00?000000011?11100","11000010?1101001100","000?000000110000010","0010000000?00010011","0001?0001010010?010","01000000001100?00??","0000?000?0110000010","00?011100000111?100","01100?00?100010?000"}

    Returns: 4194304

  18. {"01010011","10?11010","0?011011","11100111","01100010","00010011","11111101","10110110"}

    Returns: 8

  19. {"01010011111110011110","10111100111110111000","01011111111011111101","11101111111001111111","01110111100111111111","01111011110110111100","10111101101011111111","10111110111011011111","111111110?1111111010","11110101?01111110111","11110011110100110011","11001100111010111011","11101111110100011111","00111011110000110110","01111110111101011001","11111111111111101101","11111111100110110111","10111111010011011011","10011011111111001101","00111011011110111110"}

    Returns: 18

  20. {"0?11?1111?","?01011101?","1101?11?11","10101111?1","?1?1010011","111110?111","11110?011?","10?10110??","111?111?01","??1111??10"}

    Returns: 12276

  21. {"0011?100011011110101","0000?11110?11000?001","1000?10?0100011?1111","10001101011001111110","???10011100100100010","111100?001?111?00000","01001?0?1101?0011000","01?110?0001?11000000","010010100000101?1101","1011011000101?101001","1?010?01010001111?1?","0100111?000000000000","110001?111000?100010","101101010?10?0011?00","10111?00111010010010","10?10010?01001100111","0?110010111001000100","1011000010?00?01100?","00111000001010110000","1110000011?000010?00"}

    Returns: 5799936

  22. {"01101110111011011011","10100111010111111011","1101111??01111110111","00100111011?11111111","10100100100111111111","1111101101?0?111110?","11110101011?1111111?","01?10110101111110111","10?010010110?1111111","11010110101111111111","10110?11110111111110","011?10?101101101?111","11111?11?11101101111","11111111111110011111","0111111111101001?111","11111111111101101111","11011110111?11?10001","00111111111111110011","11111011111111110101","11111??1110111111110"}

    Returns: 18112

  23. {"011?0100?0?001110","1000101?0000010?0","10000100110?111?0","?0001??0010011110","01010000000111111","101?001101?10000?","010?01000?0100010","0?0001000?0??0010","?0100000000000100","001101??00110111?","?0000?00010?01001","00?0111?01?00?00?","0011100?000000000","11111000011?001?1","10111000110001010","1??1101101000?100","00001?000?1?01000"}

    Returns: 4759552

  24. {"0000?11111110","000111?010111","0001110011001","0110100101011","?111010011011","1110100?1?110","1?00000111001","10010?1000110","1110111001111","10111?1010100","1100010111010","1101110110101","0111101010010"}

    Returns: 80

  25. {"0?11????","?0???1?1","1?0??1?0","1??0?11?","????0??1","?111?0??","???1??0?","?10?1??0"}

    Returns: 2092804

  26. {"0?111?1??1","?011?1??11","110?111???","11?01???1?","1?11011110","?11?10???1","1?1?1?0111","????1?10??","?1?11?1?01","11??011?10"}

    Returns: 5622237

  27. {"00000?0000100000","00?0??0000100011","0?0000100000?000","000000100001000?","0?00000000000?00","??0000000?000000","001100000000?000","00000000?0000000","0000000?00100100","00000?0000?0?100","110000001?00010?","0001000000000100","00?000?00?000000","0000?0001111000?","0100000000000001","010?000000?00?10"}

    Returns: 49152

  28. {"01101111111111111111","10?111111?11111111?1","1?0111?0111101101111","0110111111?10111?111","111101111111?1?11111","1111101111111101111?","11?11100111111111111","11011100111111101111","11111111011111111111","1?111111100110111?11","111?1111100?1111111?","1111111111?01?111101","1100?111111101111111","11111111101?10111111","1111?011111111011111","11011110111111101110","111?11111111111101?0","111111111?1111111011","1?11111111101111?101","11111?1111?111100110"}

    Returns: 195728

  29. {"011?1111?1111?1","101?11?11???111","110111111111111","??1011??11?1111","11110111111111?","11111011111?111","1?1?1101?111111","111?11101??1111","?11111?101111?1","1?11111?1011111","1?1?111?1101111","1?111?111110???","11111111111?011","?1111111?11?101","1111?111111?110"}

    Returns: 10572329

  30. {"011111110?11","101111111111","110111111111","111011?10111","111101111011","111110111010","111?11011111","111111101101","011011110111","?11100111011","111111101101","111110111110"}

    Returns: 30

  31. {"01001010?00111010001","1010011?10001?00?00?","0100?00?110010101001","0000100101110011?101","10?1000?1101?1101110","0100000???0010110000","110000000010110?1101","0??1??0001011100110?","?1101?00011011100100","00111?01100101?10011","00010010100011010010","10011001010010100011","1110?11110110?000101","1?0010111110?0?11000","001111001?010?00?111","100101?00110010001?0","0?1?1011000001?00111","00011011100010111001","000010000111001?1000","1?11001?010110101100"}

    Returns: 5209088

  32. {"01111101111110111111","101111?0111111111111","11001111011010101001","11001111101111110110","1111001101?100101111","11110010101000110111","0?11110111?011111111","10111010110111101110","11010111001111101101","11101011000101111110","1111?1?0100001110111","11011001110000111111","11110011100001110100","0101001111101011110?","11111111111111011111","11010110011111101110","11101011110101110110","11011111111111111001","11011111011100111000","1110111010110?100100"}

    Returns: 128

  33. {"000?000?0000000010?1","00000010100100000000","00000000010000?00000","?0000000000?0?000?00","00000000000000000000","00000000?0?000??0000","01000000000000000000","?000000000000?0000?0","01000?00000000001100","00100000000000000000","00000?00000000000011","010?0000000000010000","00000000000000000000","000?000?00000001?000","00?00?00000000000?00","00000?0000010100?0?0","1000000010000?0?000?","000?0000100000?000?0","?000000?0010000?0?0?","1000000000100000?0?0"}

    Returns: 2973696

  34. {"0?11?01111000","?0000?10000??","1000101101101","1000000000?10","?010010100111","0?001011?1111","1110010000000","1010110001000","10000?00000?0","1010010100011","001?110000011","0?011100?110?","0?101100011?0"}

    Returns: 2304

  35. {"0111010?110","1000?10?1?0","100?1001001","10?010?0??1","0?110?0?10?","1100?0?1?00","000?0?0?10?","??10?1?0000","110?1?1000?","1?0?0000001","0011?0?0?10"}

    Returns: 246688

  36. {"0??????","?00????","?00????","???0???","????0??","?????0?","??????0"}

    Returns: 3309747

  37. {"0011010?1011111","001111111111110","110100100101100","111011111111?10","010101111111???","110110111111101","011111011111011","?101111001111?1","110111100010011","011111110011100","110111111101111","111111110110101","111??1010111011","1101?01?101010?","1000?11110111?0"}

    Returns: 1152

  38. {"0001110111","0000110100","0000100000","1000000000","1110001110","1100001101","0000110000","1100110011","100010010?","10000101?0"}

    Returns: 8

  39. {"0?1111?11?111?1","?0?111111111111","1?011111111??11","1110111111?1111","11110111?111111","11111011?111111","?111110??1?11?1","111111?01111110","1111???1011?111","?1111111101???1","111?11?11101111","11?11111??10?1?","11?111111?1?011","?11111?11?11101","11111110111?110"}

    Returns: 9805556

  40. {"0????","?0???","??0??","???0?","????0"}

    Returns: 2750

  41. {"011?0011110011110?11","1011?110101100010010","110001?011110?010110","?100101?1011011?1011","0?010100010110111101","0110101111?011010111","11?1010111?001100001","100?01100111111111?0","11110110011?11000101","10101111100111101101","01110??1100010111111","01111001?10010111010","10001101111101010001","10?10111110010001001","10011011011100010?01","111?1101001110101111","00011001011101010011","?0101101111000?10011","1111010?001100011101","10011110111011111110"}

    Returns: 24576

  42. {"0110100111101110000","1011100?01110111?0?","11011001101?11?111?","01100?010011010001?","1110011110011111111","000?10101111111??10","0000110001101111111","1?111000?0?1111?1?0","1010110?00110111010","1100011000111101110","1111011?1101101001?","01?1110111100010111","10101111011001?1101","11111111110010111??","11?011111011?101001","01101?1?11001110011","0?101?1101011100011","0011111?11110?01101","0???101000?11?11110"}

    Returns: 1743872

  43. {"01???11??","10110?1?1","?10??1?1?","?1?0??01?","?0??0??1?","1?1??0111","11?0?10??","??1111?0?","?1???1??0"}

    Returns: 4790194

  44. {"0?11?0??","?0?10111","1?011111","11101???","?0110?1?","011??001","?11?100?","?11??1?0"}

    Returns: 8922

  45. {"01111111111?10111111","10111111111111111111","11011111110111111111","11101011?11111111111","11110?11111111111111","1110?0?1111111110111","11111?01111111111111","1111111011111111?111","111?1111011111111111","11111111101111111111","11011111110111111111","?1111111111011111111","11111111111101110111","01111111111110111111","1111111111111101111?","11111111111111101111","1111101?111101110111","11111111111111111011","11111111111111111101","11111111111111?11110"}

    Returns: 968

  46. {"0??????","?0?????","??0????","???0???","????0??","?????01","?????10"}

    Returns: 3493492

  47. {"0"}

    Returns: 1

  48. {"0????","?0???","??0??","???0?","????0"}

    Returns: 2750

  49. {"00000000000000000","000?00?00?0000?0?","000?00000000?0000","0??0?0?0000?00??0","000?00000000000?0","0000000?00000000?","0?0?00000000?000?","00000?00?000?1000","0000000?000000000","0?000000001000100","000000000100000?0","000?0000000000000","00?000??000000000","00000001000000000","0?0?0000010000000","000??00000?000000","0?000??0000000000"}

    Returns: 2647552

  50. {"00000??0000?0000","000000??00000000","00000?0000?00000","0000000000?01?00","0000000?0?000??0","?0?0000000000?00","??00000000?000?0","0?00?00000000000","000000000000?000","0000?000000?0?00","00??00?000000100","?00000000?000000","00010000?0000000","000???000?1000?0","0000?0?000000?00","0000000000000000"}

    Returns: 2531328

  51. {"0?????","?0????","??0???","???0??","????0?","?????0"}

    Returns: 97829

  52. {"00?1011011101000","0011011?1?11?110","?1001?1??0101001","11000010?1110111","001001111111?111","11?0100111?11101","111110011?11101?","0??0111010111011","11??111101111011","1?0111?010111101","11111?11110?11?1","0101111111?01?11","1?10?1111111010?","01011100011?101?","0101101110?10101","001111?11111??10"}

    Returns: 921344

  53. {"0????","?0???","??0??","???0?","????0"}

    Returns: 2750

  54. {"011101?1","10111011","11011110","111011?1","011101?1","10111011","?11??101","11011110"}

    Returns: 35

  55. {"0?????1","?0?????","??0????","???0???","????0??","?????0?","1?????0"}

    Returns: 3493492

  56. {"01??10?1??","10??101?11","??0111?011","??101?1?1?","11110111??","001?10010?","?1?1100110","1?0?1110??","?111?01?0?","?11???0??0"}

    Returns: 1298296

  57. {"000001010","000001101","000?00100","00?001100","000000110","110100000","011110000","100010000","010000000"}

    Returns: 5

  58. {"0?0?1","?01??","010??","???0?","1???0"}

    Returns: 351

  59. {"01111??110","1010?1????","11011??111","1010?1?111","1?1?0?00?1","?1?1?0??1?","????0?001?","1?110?001?","1?11?11100","0?111???00"}

    Returns: 1350752

  60. {"0101011101011?100?","10111010?101001010","010001111011011011","1100110101100010?0","010100101111011010","101100111011100110","1110110?1111001110","101101?0100000?000","0?1011110110100110","110110101011110011","001111101100001000","111011100100?01101","10000100110?001111","?0101000010000111?","1111101?0011110101","000001101001111010","011?11101100110100","?010000001011?1000"}

    Returns: 1408

  61. {"010111111101","100111101011","000111111110","111011111101","111101111111","111110110101","111111000111","101111001111","111110010011","101111110001","011010111001","110111111110"}

    Returns: 7

  62. {"000111100101001","000000010100001","000010000?10000","1000000001010?0","101000001100110","100000111101001","100001001110011","01000100000??11","0000111000110?0","11?111100000010","001000101001010","1001010?1010011","0000100?0000000","000?1011?111000","110001110001000"}

    Returns: 128

  63. {"000001?0110100100?0","0000000000?11100000","00000000?0000000000","0000?0010001?000100","000?000?0000?10100?","100000010?00?000000","?0000001010?0100100","0001?1100010010?001","10?000000010000000?","10000?10000???00001","0?00000110000000000","110100?00?0000?1000","010???000?000000000","010010110?00000000?","10000000000?0000000","0000100?00010000001","00010010000000000?0","?000000000000000?01","0000?001?1000?01010"}

    Returns: 3448832

  64. {"01111111101111?11?","101110111111?11111","110111111111101111","11100?1?0?1?11?111","11100011101?1111?1","101?00101111111101","111111001111101111","111?10000111110111","111011100101111111","011?01111011110?11","111111110101101001","111??11111100111?1","1?1111111110011011","110111011101101110","?11?1110101111011?","111111111?01011011","1111?011110?111100","?1111111111110?100"}

    Returns: 71772

  65. {"0????","?0???","??0??","???0?","????0"}

    Returns: 2750

  66. {"0000000000?0000?00","0000000?0000110001","0000000?0?10000000","00000?000000000000","000000000000000000","000?0000000010?000","00000001000?0000?0","0??0001000000?0000","0000000000?0000010","00?00000000000000?","?0100000?000000010","000000?0000000000?","010001000000000?0?","0100000?0000000000","00000?00000000000?","?00000000000?00000","000000?01010000000","010000000?0??0?000"}

    Returns: 184320

  67. {"010101010?1?10110001","1010??100?0011000001","010??10?1001?01110??","10?01010010001101010","0??1000011110?1?0001","1?1000?0011001010000","01010?01111010011010","10?00010?0?011110111","0010101?010000000001","??011110100101101001","1000111?0000001?01?0","?0101000010010100110","11?00011000100110011","0101?101010000101101","10111001011111010111","1010?11100?01010111?","00110010010001010110","00000001001101111010","00?1001100?110111101","11?010011100111?0010"}

    Returns: 2961408

  68. {"0011111111001?","00101011101111","11001010010010","10001111111101","11110101111101","10011011111111","11110101111011","11011110111011","11011111011111","10111111100110","01011111100011","01011100110000","11100111111000","?1011111101000"}

    Returns: 14

  69. {"01101111?1??1111?110","1010110111111?0?111?","11001111110?111?1?11","00001111111111111111","11110011??1111111110","11110011111111111111","10111101111111111110","111111101?11111111?1","?111?11101?111111111","1111?11?101?11111111","?1011111?10111111110","?1?111111?101?11?111","11111111111100111111","1?111111111?00?01011","1011111111111?0?1111","1??11111111110?01111","?1111111111?11110111","11?11111111110111011","1111111?111111111101","0?110101110111111110"}

    Returns: 12176000

  70. {"0?1110?10111001110?1","?001011111?111111101","10011111001011101??1","11100?100111111?1?11","10100111110111100111","011?1010001011111101","?1111101?1?111110111","1110101011111?1110?1","010010?101101111111?","11011011101111001111","1?1101?1110111111111","11011011011001101010","0111111111100?110110","0111111?1111?001?110","11111111101110011011","110?0111101011100111","1111010111110?10011?","01??1110111011011001","?0?1101?111111111001","11111111?1100011?110"}

    Returns: 981648

  71. {"01001101011111101101","10111111110101011111","01011111111?11010110","011011001111100?1111","11110111111111111110","11111011111111111110","01101100111111011111","11101100011001101110","01111110011111001111","11111111101110111111","10111111110111111111","11?11110111000111111","10111110111001111111","11101111101010111111","10001101011111001110","011?1110011111001110","11011111111111110001","11111111111111110011","01111111111111110101","11010010111111001110"}

    Returns: 40

  72. {"01?100111101111111","101011010?0111?111","?10101001101110110","101010011110010110","010101111001110111","011010011110001111","100010010111011100","110111100000010011","101111000111?01101","1?110110100?111101","00010110100000010?","111010101?00?10111","11101000?10?011111","111110110101101100","1?0001101100110111","111111101111111011","111111010001101100","1100110111?1101100"}

    Returns: 874

  73. {"0001111111100001","00110001011?1101","0100111110111110","1100110110101111","1011010010?11101","1011101011111111","1010010111111111","1111001011111111","1011111101100011","1100011110001110","1111?11110011101","0?10111100100?10","0111111101100111","01111111011?1011","0011011111011101","1101111110101110"}

    Returns: 56

  74. {"000??0???0000000","000000??10000000","0000?000?0000000","?000000000000001","?0?001000000?01?","0000101000100000","??0001000?000000","??00000000000?00","?1?0000000?10000","000000?000?00000","00000100??000010","0000000010000100","0000?00000000000","0000000?00010000","0000100000100001","0001?00000000010"}

    Returns: 81920

  75. {"0010???1?","00011??1?","100??1???","01?0?1?10","?1??011??","??1110?1?","????1?0??","11?1?1?01","???0???10"}

    Returns: 4479825

  76. {"0????","?0???","??0??","???0?","????0"}

    Returns: 2750

  77. {"0??100","?01111","?10010","1100?1","011?01","010110"}

    Returns: 28

  78. {"01010010001011111101","10111101?111110010??","01010011111101010110","111011110011?011?111","01010111?11101110011","01011011111101?1??11","10111101111?01100111","01111110111111101?11","0?10?11101011?111011","0110111110111011??11","11111111010?1011111?","011111?111?001010110","110?00011110011110?1","11101111?00110110111","10011?11111011001110","10111100111111001111","110?0?011?1010110?1?","10110?1?0?110111?011","0?1111111111?111110?","1?01111111?01101?1?0"}

    Returns: 8225536

  79. {"0????","?0???","??0??","???0?","????0"}

    Returns: 2750

  80. {"00110110111111?01","00101101111111111","11011110111???11?","1010011101?110011","01100100111011111","11111001101010111","1011000000?100111","0101010000?11101?","11101100001101111","11111000001110111","111?11??11000111?","11?10011110010101","11?11101010101001","11?01001101010100","?1101110111101011","01111111111000101","11?1111?11?110110"}

    Returns: 8448

  81. {"0110?111111?11","10111100010110","1101?010111?11","01100??1010111","?1?001111?1111","110?10101?1?1?","101?1101110111","10011010110111","10101111001010","1111??1100001?","10101100100100","?1?11?11001011","11111111110100","10111?110?0100"}

    Returns: 11264

  82. {"0????1?","?0?????","??0????","???0???","????0??","1????0?","??????0"}

    Returns: 3493492

  83. {"0111101110111","10?111111?1?1","1?0?1101111?1","11?011?111111","1111011?11111","0111101111111","110?1101?1111","1111?1101?111","111111?101111","0?11111?10111","1111111111011","1??1111111101","1111111111110"}

    Returns: 4608

  84. {"0??????","?0?????","??0????","???0???","????01?","????10?","??????0"}

    Returns: 3493492

  85. {"01000100111111","10011111111101","00011100110101","01100111110110","01100111010111","11111001001100","01011001110?10","01011110111110","11110011000101","1111101100?011","110001010?0111","111111?1101001","10011011011001","11101000111110"}

    Returns: 22

  86. {"0110110100100100?1?1", "1000?0101?0100001?10", "1000?011111101?10000", "0000001011011011?010", "1??00?10001111?10?10", "1000?010110111110101", "011111001100100?1000", "10100000111?11111111", "011101110010?001110?", "0?1101110011010111?0", "10101001110011010111", "0111110?010001001110", "00011111?010011100?1", "101011010111101?1000", "00?1?1010000110?0010", "001111?111101??0?011", "?10?00111101010?0000", "1?00?101111100000010", "?10110010?11?0110100", "10000101?01010010000" }

    Returns: 5898240

  87. {"0?1", "?01", "110" }

    Returns: 5

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