Statistics

Problem Statement for "BinaryCodes"

Problem Statement

Given a finite alphabet S, a binary code over this alphabet S is a function that maps each element of S to some (possibly empty) string over the alphabet {0,1}.

An example of such a code for S={a,b,c,d} is the function f defined by f(a)=1, f(b)=1010, f(c)=01, f(d)=10101.

Any binary code can be naturally extended to encode strings over the alphabet S simply by concatenating the codes of the string's letters, in order. For example, using the code mentioned above we can encode cac as f(cac)=01101.

A code is called ambiguous if there are two different strings over S that have the same encoding. Obviously, in practice we want to avoid using an ambiguous code.

A code is called really ambiguous if there are three different strings over S that have the same encoding. For example, the code from the above example is really ambiguous: the strings ba, acc, and d are all encoded to 10101.

You will be given a String[] code containing the strings over {0,1} used to encode letters of some alphabet S. Your method should check whether this code is really ambiguous. If it is really ambiguous, find a shortest string over {0,1} that is an encoding of (at least) three different strings over S, and return its length. If the given code is not really ambiguous, return -1.

Definition

Class:
BinaryCodes
Method:
ambiguous
Parameters:
String[]
Returns:
int
Method signature:
int ambiguous(String[] code)
(be sure your method is public)

Notes

  • Your method does not need to know the actual elements of S, and the size of S is obviously equal to the number of elements in code.

Constraints

  • code will contain between 2 and 30 elements, inclusive.
  • Each element of code will contain between 0 and 50 characters, inclusive.
  • Each element of code will only contain the characters '0' (zero) and '1' (one).

Examples

  1. {"1","1010","01","10101"}

    Returns: 5

    This is the example from the problem statement, and the string 10101 is the shortest string that can be decoded in three different ways.

  2. {"0","1"}

    Returns: -1

    This code is obviously not ambiguous.

  3. {"0","11","11","11"}

    Returns: 2

    This is clearly a really ambiguous code, as there are three different one letter strings over S that are encoded to 11.

  4. {"0000","001","01001","01010","01011"}

    Returns: -1

    This code is a prefix code, i.e., no code word is a prefix of another code word. If a code has this property, it is guaranteed that it is not ambiguous, but the other direction is not true.

  5. {"1","10","00"}

    Returns: -1

    This is not a prefix code, but it can easily be shown that this code is not ambiguous.

  6. {"","01101001001","111101011"}

    Returns: 0

    Having an empty code word is a great way how to design a really ambiguous code.

  7. {"00011011","000110","11","0001","1011","00","011011"}

    Returns: 8

    The shortest proof that this code is really ambiguous is 00011011. Note that this string can in fact be decoded in four different ways.

  8. {"00000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000"}

    Returns: 148

  9. {"000000000","110","1","10","00000","0000110"}

    Returns: 6

  10. {"000000","0000","000"}

    Returns: 9

  11. {"010","110111","1101","11","0101101"}

    Returns: 9

  12. {"01010101010101010101010101010101010101010101010101","0101010101010101010101010101010101010101010101010", "1010101010101010101010101010101010101010101010101"}

    Returns: 198

  13. {"01","001","01001"}

    Returns: 10

  14. {"00000000000000000000000000000000000000000000000001","0","1","01"}

    Returns: 4

  15. {"00000000000000000000000000000000000000000000000011","0","000000000000000000000000000011","0000000000000000000000000000011"}

    Returns: 50

  16. {"00000110111010111111111111100","01011100011010010010010000","11111101010111000001001101110","000001101110101111111111111001101","0010000011000001000000111111110111","110111001110100000000100011","10011010001011101111000010","000011000001000000111111110111","100010001000010110111000000101111","100000110111010111111111111100110","1101001111010001100010101010","110011010001011101111000010001000","0011000001000000111111110111","010100010100100000000100111111","10011110100011000101010100011110","00111101000110001010101000111101","111001110100000000100011100001","10001000100001011011100000010111","01101100110100010111011110000100010","0000100111111010101110000010011","10000101011100011010010010010000","01010111000001001101110110","0000001010110100110100110","1010100010100100000000100","0011110101010001010010000","00000010101101001101001100110","00000000101011010011010011001101","100001010111000110100100100100","01110110111001110100000000100011","100010001000010110111000000101111"}

    Returns: 66

  17. {"100111100010001010111001","00000010111110010100111111","00011111111101011000100000101","1001011101001111110001100111","1110110000100110000011100","00101110100111111000110011101100010","11101001000011101101001001101","0110111110110000100110000011100010001","00000010100000010111110010100111111","110100101110100111011011111011000","001011110000100101101001111","010011000001110001000110011110","10000100101101001111000100010","010100011111111101011000100000101","0010100000010111110010100111111","00100010101110010010111010","00010001010110100101110100111011011","010100111101000101001001101101","01000110011110001000101011100","00010010110100111100010001010","1000111111111010110001000001","011111100011001110110001010","0100111101000101001001101101001011110","11101001000011101101001001101010","111010010000111011010010011010101","10110100101110100111","10010011110100101011000","0110001010010011110100101011000000000101","01001111010001010010011011010010111","0100111101001010110000000"}

    Returns: 124

  18. {"00101100010101001","10101101010100111100100000010","1010001111110100100101111010000100","010100111100100000010100","11111000010100010001000","110110000010100011010010010101010","100011000001","1001000100100111011000001010001101001001010","1011000101010010011011","1010010001111111100001010001000100","0011110011101100100010010011","1110011100001011011010011001","1011000001010001101001001","0011011101011010101","001111110100100101111010000100100011000001","100111110101011111011000111001011000","1010000100100011000001","11011001100101001100100010110011110011101","001111001000000101001101100110010100110010001","0001000011100000","001101001000111","1001101100110010100110010001011","10001110010110001110011100001011011010011","0101100010101001001101110101101","000100001110000010011111010101111101","010101000111111010010010111","1001101001000111111110000101000100010000","011001111001110110010001001001","000100001110000010011111010101111","1011000111001011000111001110000101101101001"}

    Returns: 300

  19. {"00011001111110110001011110110100100","0000111010010001111010111","011100100011100101110","10111110010111101110001","01010000111110111001011111001011110111000101","0101111100101111011100010101111100011","111110111010111000010001101101110101110011","001010100111011100","0010001100111101000101101100","1000011010110101000111","011100001000110110","101000011111011100","01011111000110100001110101001101","100001101011010100011100001110100100011110101","100100000100011001111010001011011","1000011010110101000111000011101001000111101","0110011111101100010111101101001000","01000011101010011010001","00010001100111101000101101100101010011101110","0111110111010111000010001101101110101110011","11011100100011100101110","011101110010001110010111","011001111110110001011110110","101010011101110011111011101","10010111101101010001111001001000000","1110101110011","0001100101111011010100011110010010000","01111100011010000111010100110100011001011110","1101010001111001001000000","10100001111101110"}

    Returns: 110

  20. {"00110000011101100","110100110001011111001111010100111001","0100100110110000","1000010110101001010111111000100","000011000100001000101000010","00101110001111011010011000","1010111001000001101010010111000111101101001","10101001010111111000100","0001100010000110000011101","100011011111010011100101110","0110111110100111001011100001100101011100","110010100000100110110100010001110101110","0001100101011100101010100001111100110","1111111100011000100001","0110001000010001010000100100100110110000101","0111011011111000111111111100011000100","101011100100000110101","011101101111100011","10000011101100011011111","10111110011110101001110010001010000001000","100010111110011110101001110010001010000001","101010100001111100110","01110110111110001111111111","010011100101110000110010101110010101010000111","0000100010100001001001001101","10110101001010111111000100","00010100000010000110001","11001101100101000001001101101000100011","1100101000001001101101000100011","0100000110101001011100011110"}

    Returns: 146

  21. {"0001010011010110000101101000010110011","000101001101011","1111111101001001001","111100110011011111","00010100110101100001011010000101100","111111011111111010010010011010","11101101101110010110011000001010","10010110011000001010","010100011010111101000100001001110100","11100100100101000110000","11001101011111101100010000","1110010001101100000111011011011","111001000000010100","10111010111001001001010001100001010110011","111111001000000","0101100111111110","101010101011111000011111001100010","01000110110000011101101101110010110011000001010","00111010010111010111001001001010001100001","00010100110010100111100110011011","0101111110110001000","10101100111111110111111110100100100110","101010111110000111110011000101000101001110","0000101001100101001111001100110","11111111001000000010100011010111101000100001","1000101001110010001101100000","1010101011111000011111001100010100010100","0000101101000010","01101011110100010000100111010010111010","110101111110110001000000010100110010100"}

    Returns: 300

  22. {"11000","11","100000","101000","110000","111000","100001","101001","110001","111001","100010","101010","110010","111010","100011","101011","110011","111011","000100","001100","010100","011100","000101","001101","010101","011101","000111","001111","010111","011111"}

    Returns: 13

  23. {"111111111000","111111111","100000","101000","110000","111000","100001","101001","110001","111001","100010","101010","110010","111010","100011","101011","110011","111011","000100","001100","010100","011100","000101","001101","010101","011101","000111","001111","010111","011111"}

    Returns: 42

  24. {"11111111101000","11111111101","100000","101000","110000","111000","100001","101001","110001","111001","100010","101010","110010","111010","100011","101011","110011","111011","000100","001100","010100","011100","000101","001101","010101","011101","000110","001110","010110","011110"}

    Returns: -1

  25. {"110","110"}

    Returns: 6

  26. {"00000000000000000000000000000000000000000000000001","00000000000000000000000000000000000000000000000010","00000000000000000000000000000000000000000000000011","00000000000000000000000000000000000000000000000100","00000000000000000000000000000000000000000000000101","00000000000000000000000000000000000000000000000110","00000000000000000000000000000000000000000000000111","00000000000000000000000000000000000000000000001000","00000000000000000000000000000000000000000000001001","00000000000000000000000000000000000000000000001010","00000000000000000000000000000000000000000000001011","00000000000000000000000000000000000000000000001100","00000000000000000000000000000000000000000000001101","00000000000000000000000000000000000000000000001110","00000000000000000000000000000000000000000000001111","00000000000000000000000000000000000000000000010000","00000000000000000000000000000000000000000000010001","00000000000000000000000000000000000000000000010010","00000000000000000000000000000000000000000000010011","00000000000000000000000000000000000000000000010100","00000000000000000000000000000000000000000000010101","00000000000000000000000000000000000000000000010110","00000000000000000000000000000000000000000000010111","00000000000000000000000000000000000000000000011000","00000000000000000000000000000000000000000000011001","00000000000000000000000000000000000000000000011010","00000000000000000000000000000000000000000000011011","00000000000000000000000000000000000000000000011100","00000000000000000000000000000000000000000000011101","0"}

    Returns: 52

  27. {"00000000000000000000000000000000000000000000000001","00000000000000000000000000000000000000000000000010","00000000000000000000000000000000000000000000000011","00000000000000000000000000000000000000000000000100","00000000000000000000000000000000000000000000000101","00000000000000000000000000000000000000000000000110","00000000000000000000000000000000000000000000000111","00000000000000000000000000000000000000000000001000","00000000000000000000000000000000000000000000001001","00000000000000000000000000000000000000000000001010","00000000000000000000000000000000000000000000001011","00000000000000000000000000000000000000000000001100","00000000000000000000000000000000000000000000001101","00000000000000000000000000000000000000000000001110","00000000000000000000000000000000000000000000001111","00000000000000000000000000000000000000000000010000","00000000000000000000000000000000000000000000010001","00000000000000000000000000000000000000000000010010","00000000000000000000000000000000000000000000010011","00000000000000000000000000000000000000000000010100","00000000000000000000000000000000000000000000010101","00000000000000000000000000000000000000000000010110","00000000000000000000000000000000000000000000010111","00000000000000000000000000000000000000000000011000","00000000000000000000000000000000000000000000011001","00000000000000000000000000000000000000000000011010","00000000000000000000000000000000000000000000011011","00000000000000000000000000000000000000000000011100","00000000000000000000000000000000000000000000011101","00000000000000000000000000000000000000000000011110"}

    Returns: -1

  28. {"0011100","01110","0010000","001000","0010","0100000","1101000","11110","1001100","01","111","1010","110000","0100","1011100","001100000","111000","0000000","0111100","1111100","11100000","101100000","0101000","0001100","0110","1000000","011","1010000","011000","101100"}

    Returns: -1

  29. {"0011100","01110","0000100","000100","0100","0000010","0001011","01111","0011001","10","111","0101","000011","0010","0011101","000001100","000111","0000000","0011110","0011111","00000111","000001101","0001010","0011000","0110","0000001","110","0000101","000110","001101"}

    Returns: -1

  30. {"111000100","1001010","10110","010100","11010","010010","01110","1101","001","011000100","11110","00000100","0010001010","110100","110001010","00001010","101010","11","00010","00110","00101","1100","110010","100100","10101","001000100","101000100","10000100","000","1010001010"}

    Returns: -1

  31. {"111000100","1001010","10110","010100","11010","010010","01110","1101","001","011000100","11110","00000100","0010001010","110100","110001010","00001010","101010","11","00010","00110","00101","1100","110010","100100","10101","001000100","101000100","10000100","0001010111000000111110111110","111111111111111111000000010111111000"}

    Returns: -1

  32. {"011110","001","000111","010","010111","100","1101111","100011","0101","001011","001111","0101111","00110","100111","11111","01110","1000","1101","011011","010011","110111","111110","10110","000011","0000","110011","111011","101011","10010010100010100100001010010101110101"}

    Returns: 79

  33. {"000000000000000000000","0000000000000000000000","00000000000000000000000","000000000000000000000000","0000000000000000000000000","00000000000000000000000000","000000000000000000000000000","0000000000000000000000000000","00000000000000000000000000000","000000000000000000000000000000","0000000000000000000000000000000","00000000000000000000000000000000","000000000000000000000000000000000","0000000000000000000000000000000000","00000000000000000000000000000000000","000000000000000000000000000000000000","0000000000000000000000000000000000000","00000000000000000000000000000000000000","000000000000000000000000000000000000000","0000000000000000000000000000000000000000","00000000000000000000000000000000000000000","000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000","000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000"}

    Returns: 43

  34. {"010","01010101010101","0101010101010101","010101010101010101","01010101010101010101","0101010101010101010101","010101010101010101010101","01010101010101010101010101","0101010101010101010101010101","010101010101010101010101010101","01010101010101010101010101010101","0101010101010101010101010101010101","010101010101010101010101010101010101","01010101010101010101010101010101010101","0101010101010101010101010101010101010101","010101010101010101010101010101010101010101","01010101010101010101010101010101010101010101","0101010101010101010101010101010101010101010101","010101010101010101010101010101010101010101010101","01010101010101010101010101010101010101010101010101"}

    Returns: 30

  35. {"010","01010","0101010","010101010","01010101010","0101010101010","010101010101010","01010101010101010","0101010101010101010","010101010101010101010","01010101010101010101010","0101010101010101010101010","010101010101010101010101010","01010101010101010101010101010","0101010101010101010101010101010","010101010101010101010101010101010","01010101010101010101010101010101010","0101010101010101010101010101010101010","010101010101010101010101010101010101010","01010101010101010101010101010101010101010","0101010101010101010101010101010101010101010","010101010101010101010101010101010101010101010","01010101010101010101010101010101010101010101010","0101010101010101010101010101010101010101010101010"}

    Returns: -1

  36. { "01101001100101101001011001101001100101100110100101", "0110100110010110100101100110100110010110011010010", "011010011001011010010110011010011001011001101001", "01101001100101101001011001101001100101100110100", "0110100110010110100101100110100110010110011010", "110011010010101101001100101101", "011010011001011010010110011010011001011001101", "01101001100101101001011001101001100101100110", "0110100110010110100101100110100110010110011", "011010011001011010010110011010011001011001", "01101001100101101001011001101001100101100", "0110100110010110100101100110100110010110", "011010011001011010010110011010011001011", "01101001100101101001011001101001100101", "0110100110010110100101100110100110010", "011010011001011010010110011010011001", "01101001100101101001011001101001100", "0110100110010110100101100110100110", "011010011001011010010110011010011", "01101001100101101001011001101001", "001011001101001100101100110100101", "0110100110010110100101100110100", "011010011001011010010110011010", "01101001100101101001011001101", "0110100110010110100101100110", "011010011001011010010110011", "01101001100101101001011001", "0110100110010110100101100", "011010011001011010010110", "01101001100101101001011"}

    Returns: 150

  37. {"10100000000100101011110101011111","11110010000110001011001001100010101000000001001010","1111010101111110111111111100111100001011","10111111111100111100001011","11110010000110001","11110010000110001011001001100010","0110010011000101010000000010","010101111010101111110111111111100111100001011","11111011010110110010001011101011000101000110101100","11000111101100111101001111001111111100000110","1111001111111100000110","0111101100111101001111001111111100000110","1111101101011011001000101110101100010100011010","111110110101101100100010","11101011000101000110101100011110110011110100","11000111011010110100111110110101001010111000011100","1110011101000001111010111100000010011111","101001010111000011100111001","11000111011010110100111110110","1110011101000001111010111100000010011111","11000111011010110100111110110101001010111000011100","1101000001111010111100000010011111"}

    Returns: 80

  38. {"00000101111000111011110110100100011001010111100001","00000101111100100110001101001011011110","101011110000101","0100000101111100100110001101001011011110","0000010111100011101111011010010001100101011110","00010100000101111100100110001101001011011110","0000010111100011101111011010010001100","10000100011111101011101101101101101","0110110110110111100111","100001000111111010111","01110101010111101000011101100100011000111100010","1101100100011000111100010","111001110111010101011110100001","10000100011111101011101101101101101111001110111010","1010111101000011101100100011000111100010","1110110111100101001111000011110001011100","01111000011110001011100","00001110010100111110110000011011001110111111100101","00001110010100111110110000011011001110111111100101","000001101100111011111110010111101101111001010","1110110111100101001111000011110001011100","0000111001010011111011"}

    Returns: 80

  39. {"011011111001001101010010100101000100011","0100110101001010010100010001101111001","00100111100000000011100010010100010000110010011000","00001100101000011011100010110100001101110110111110","1100100110101001010010100010001101111001","110010001101000001","0011001001100011011111010000001","0000110010100001101110001011010000110111","00010000011111111110010001101000001","00101101011110111010110101011011000100100001110011","01111001","1101111101000000100000011010010100011001","00000011010010100011001","00101101011110111010110101011011000100100001110011","001001111000000000111000100101000100","00100111100000000011100010010100010000110010011","00101101011110111010110101011","00001100101000011011100010110100001101110110111","00010000011111111110010001101000001","01100010010000111001100010000011111111","0001101111101000000100000011010010100011001"}

    Returns: 70

  40. {"101100110000110000","1100101001100011010011110001010100111111","110011111111101001111111101110101110001","001110010001011111100100110010010111111111010011","11001010011000110100111100010101001111110011010100","110101001111111111010101010001010100010100011110","101110101110001","101101101010011010000000101100110000110000","1110100111110011111011001111111110100111","1111101110101110001","110010100110001101001111000101010011111100","11100111100110111100001010100","1111111111010101010001010100010100011110","11100111100110111100001010100011101001111100111110","011101001111100111110110011111111101001111111","00110101001111111111010101010001010100010100011110","10110110101001101000000010110011000011000000111001","101101101010011010000000","001110010001011111100100110010010111111111010011","111001111001101111000010101000","0001011111100100110010010111111111010011"}

    Returns: 84

  41. {"00110110100001011011101000","001101001011110000000010000111111001001","0000101011001000100","0011110010011001111011010010111111","010101110100100100101000001101001011","010011110110110110100","0000000010011011100010011110110110110100","11011110000000010011011100010011110110110110100","0011011010000101101110100001010111010010","111111000011011110000000010011011100","00110110100001011011101000010101110100100100101000","010100110011011010111","1111001111001001100111101101001011111100000100010","0010101011101111010110110001010101111110000","01010011001101101011100001010110010001001111001111","0000000010000111111001001","110000000010000111111001001","001001100111101101001011111100000100010","01010011001101101011100001010110010001001111","001010101110111101011011000101010","00101010111011110101101100010101011111100001101111","010010100000110100101111","00000100010"}

    Returns: 89

  42. {"10100100001111101011110111011001001011011010100010","000011010010100000110101010011111110011101111111","111011111111110011000011111001101000111011100101","1110011000011111001101000111011100101","00010010101111011000111110010011100101101111010010","01000010011001011111111011010110100101101001001100","101111100001000000111000000010000001110","10011000011111001101000111011100101","1100001000000111000000010000001110","00110001110000100101110101110110001001111111","00010011001011111111011010110100101101001","10100100001111101011110111011001001011011010100010","00110001110000100101110101110110001001111111","01001001100111111000010000001011111000110001110010","101111100001000000111000000010000001110","101000101001101010110111101010001101111000110","0001001010111101100011111001001110010110","00010101000101001101010110111101010001101111000110","00010011001011111111011010110100101101001","00010010101111011000111110010011100101101111010010","11110100100000110100101000001101010100111111100","01001001100111111000010000001011111000110001110","10100010100110101011011110101000110111100011010111","00001101001010000011010101001111111001110111111111","01110000100101110101110110001001111111","01001001100111111000010000001011111000110001110010","101001000011111010111101110110010010110110101"}

    Returns: 78

  43. {"00011101111100101000100101110011010101110000011011","1011010111101010110111110101101000100101","00011101111100101000100101110011010101110000011011","0001111000100110011100000111111111100000000111","10001011010111101010110111110101101000100101011110","10010101111100100101101110011011010000101011100110","00111100010110101111010101101111101011010001001010","1110111001101100110111001110110000111010","01100101001111001010110100010001111111010","11001010100100000010011110111011001","011110101000111101011111001011100010010110100","1101100110111001110110000111010","0011011001010100100000010011110111011001","00011101111100101000100101110011010101110000011011","00011110001001100111000001111111111000000","00011110001001100111000001111111111000000001111000","00011011111000000000000011010000001001100100100110","000110111110000000000000110100000010","100101011111001001011011100110110100001010111","10111001101100110111001110110000111010","0110010010011011001010100100000010011110111011001","101000111101011111001011100010010110100","01100101001111001010110100010001111111010111011100","0110010100111100101011010001000111111101011","11110101000111101011111001011100010010110100","10010101111100100101101110011011010000101011100110","00110000110111110000000000000110100000010011001001"}

    Returns: 50

  44. {"000011100001010111000111101001011011101111010001","00011110010111010010000011111001","10110101000001110001000000000101101111111111011","010100111011010100011001000110111101110011","10110000000111010001100010001100111111110101","111111110010111010001111000001010101000100101000","01110011110000110110011110001111001010101101101010","111100011110010101011011010100111011010100","11001010001010001100100111111011","0100010010101101010000011100010000000","0110010001101111011100111111111100101110100","01110110101000110010001101111011100111","011010101100101000101000110","111011000000011101000110001000110011111111","11111110010111010001111000001010101000100101000","00011110010111010010000011111001010001001010110101","000111100101110100100000111110010100010010","00000111000100000000010110111111111101111","01001111110110111111111101100000100000111000010","100100111111011011111111110110000010","01111000001010101000100101000","000000111010001100010001100111111110101","0101","001011011111111110111110110","011100111100001101100","101001001001100101010110001101010","1010010010011001010101100","10100100100110010101011000110101011001010001010001","10111000111101001011011101111010001","0111111111101100000100000111000010101"}

    Returns: 135

  45. {"011110000101010011001000100","11100111110101111011110100101100010101010100","00111001111110011110110111100000111011101010101010","00110101100101101010100001001000001011001011101011","00100000101100101110101100100001","11110101111011110100101100010101010100","00010111000111111010011110001011","011011000110100101111001001","111011000100100000111010100111110011110","110100111111110110100010101","001111010011111111011010001010110000101011100110","10011111111011010001010","111111000100100101100011010","0011100111111001111011011110000011101110","1000010101110011001111000010101001100","00100001011011000110100101111001001","01111100110000110101010101000100101011000000000010","110101100111110011000","11101100010010000011101010011111","101010101000110101100101101010100001","1000100111111000100100101100011010","0110101010101000100101011000000000010111001","11000010101110011001111000010101001100100","0001011100011111101001111000101111010110","111011000100100000111010100111110011","0100111111000100100101100011010"}

    Returns: 134

  46. {"01100110010110010100","10001111011101011110001100100100100","000010100000101000011011100100","1111100111000001100111000001111000101010100100001","00011100110011111101111111111001110000011001110000","0110001111000010010010010100001","00001010000010100001101110010001011010010110100000","10000001000001011101011100001100110010110010100","1001010000100110101000100000001101100100","00110101101110010001010010011100111100100011111101","11000100000000010101100011110000100100","00110101000100000001101100100","11010011101110001010110001101011010000110","0101011011011101110011011101011001","10010000100010111110011100100001100111101000011111","01111000101010100100001010111011100010","0000111110101011011011101110011011101011001","010111011100010100000010000010111010111000","01011010010110100000100","00110101010010000100010111110011100100001100111101","000111001100111111011111","011110111010111100011001001001000011010110111001","1000110110001000000000101","0110010000101100001111110010111100000000000110011","011001000010110000111111001011","0001010010011100111100100011111101","11000000000001100111000110","11010011101110001010110001101011010000110001101010"}

    Returns: 268

  47. {"1100000", "1100001", "1100010", "1100011", "1100100", "1100101", "00000000000000000000000000000000000000000000000", "1100110", "1100111", "1101000", "1101001", "1101010", "1101011", "1101100", "1101101", "1101110", "1101111", "1110000", "1110001", "1110010", "1110011", "1110100", "000000000000000000000000000000000000000000000000", "1110101", "1110110", "1110111", "1111000", "1111001", "1111010", "1111011" }

    Returns: 142

  48. {"00010101110101", "10101010101110101", "1011111111111101110101", "1000000000000101110101", "101011111101110101", "10101010101110101", "10100101110101", "10101110101", "10101010101110101", "10101000001110101", "10101010101110101", "10101010101110101", "101010111110101", "101111110101", "10101010101110101", "10101010101110101", "10101010101110101", "1010000101110101", "10101010101110101", "10101010101110101", "101001110101", "10101010101110101", "1010111101110101", "10101110101", "10010101011001101010", "010001101101101", "100011011010101" }

    Returns: 17

  49. {"00000000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000000", "1101010101010", "1110101010101", "111110101010101", "111111010101101" }

    Returns: 148

  50. {"0001101", "001011110111", "001111101011101111", "1110011111001", "000110100101", "111011", "1001111101011101111111", "0011111001", "0001101001", "01111011100111", "1101011101111111001", "1111001" }

    Returns: 34

  51. {"0", "0" }

    Returns: 2

  52. {"1", "10", "100", "1000", "10000", "100000", "1000000", "10000000", "100000000", "1000000000", "10000000000", "100000000000", "1000000000000", "10000000000000", "100000000000000", "1000000000000000", "10000000000000000", "100000000000000000", "1000000000000000000", "10000000000000000000", "100000000000000000000", "1000000000000000000000", "10000000000000000000000", "100000000000000000000000", "1000000000000000000000000", "10000000000000000000000000", "100000000000000000000000000", "1000000000000000000000000000", "10000000000000000000000000000", "100000000000000000000000000000" }

    Returns: -1

  53. {"111111", "00000", "1111111" }

    Returns: 19

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