TopCoder Statistics - Problem Statement

Problem Statement

One-time pad (patented by Vernam in 1919) is one of the most widely known schemes to encrypt a binary string to achieve confidentiality. This scheme takes a binary string (a string consisting of only the digits 0 and 1) as input and outputs another binary string of the same length. The input is called the plaintext, and the output is called the ciphertext. The scheme uses a key which is another binary string of the same length as the input. The i-th bit of the ciphertext is defined as the XOR of the i-th bit of the plaintext and the key (see the notes for XOR definition). The ciphertext is sent to the receiving party.

In this problem, we will consider several messages, each of length N, encrypted using a single key of length N.

We would like to investigate how strong this cipher is. Suppose an adversary manages to find out the content of all the original messages (i.e., the plaintexts) and some of the encrypted messages (i.e., ciphertexts). These messages are given in the String[]s plaintexts and ciphertexts, respectively. Return the number of possible keys that are consistent with this data. The constraints will guarantee that there is at least one such key. A key is consistent if for all members of ciphertexts C, there exists a member of plaintexts P such that when P is encrypted using the specified key, it becomes C.

Definition

Class:: NetworkXOneTimePad
Method:: crack
Parameters:: String[], String[]
Returns:: int
Method signature:: int crack(String[] plaintexts, String[] ciphertexts)
(be sure your method is public)

Notes

XOR is a binary operation on bits defined as follows: 0 XOR 0 = 0, 0 XOR 1 = 1, 1 XOR 0 = 1, 1 XOR 1 = 0.

Constraints

plaintexts will contain between 1 and 50 elements, inclusive.
Each element of plaintexts will contain between 1 and 50 characters, inclusive.
All the elements of plaintexts will contain the same number of characters.
All the characters in plaintexts will be either '0' (zero) or '1' (one).
All the elements of plaintexts will be distinct.
ciphertexts will contain between 1 and 50 elements, inclusive.
All the elements of ciphertexts will contain the same number of characters as all the elements of plaintexts.
All the characters in ciphertexts will be either '0' (zero) or '1' (one).
All the elements of ciphertexts will be distinct.
There will exist at least one key that is consistent with the given plaintexts and ciphertexts.

Examples

{"110", "001"}

{"101", "010"}

Returns: 2

The two possible keys are "011" and "100".
{"00", "01", "10", "11"}

{"00", "01", "10", "11"}

Returns: 4
{"01", "10"}

{"00"}

Returns: 2
{"000", "111", "010", "101", "110", "001"}

{"011", "100"}

Returns: 6
{"0"}

{"1"}

Returns: 1
{"01011010011101000011001","00001001010101100010001","00111001110000011001100","00010100111110000001010","01100001001011010101010","01000101000111000101110","11000111010011110101010","10110000001011000001011","01111010011100011001010","00000011110001001110110","11101101110001001111011","01111101011100000011110","10101010011011100001000","01101001100101111110000","11111000010100010111000","01110101010111100100001","01000010000110111100011","11001011011000010011101","11110111111011001100011","00101000101010001010111","00000101010000000101110","01011001110010111110000","10101010001010111100000","11011100010000001001101","10010010010000110000010","00011010010000100101100","10000110110100000101101","01010110100011011101101","11100010110110001010110","01010110011001000010101","00111010111110000110000","01110101011010110000110","11001011101001111100101","11110100100110101001110","10110110010011011010000","10001100100000111000001","00101100000111001110001","00100010111010100110100","00110010001011010000100","11010011010000111000011","00111110101111100100001","01011010110100000001001","01001100011111111011111","11011011110010100101110","00100101101010000110001","11101000100111111101101","01101110100000011101111","11101100010100111010001","00110011111110101101000"}

{"11100101010111010110111","10010101010000110111000","10110101101010110100111","11001010110100110011111","10100011111110011111110","00000010010000000010100","11101101011100110001000","01100111111011111110101","11000110011001110000011","01001011110010010111000","10110010111010010100010"}

Returns: 1
{"11000111111100110111001000001101100011100100","01000001011101011100110010000010001000001010","11000001011111001010011001011101110000001100","01001001111110000110011101101100111111111101","10110111111110100000011010111100001110001001","01011101011011001010011111000000011011110010","01101100110000011110100110011100101100001111","00011111011000100010001001100101110100000001","11011001111101011101101110101011100110100110","10100010010110000100010100001001000010110110","01011100000110101110001011011011001100110011","01001001110110101111111111110110001100011001","00010001100011000101010001010110010110000110","00011100000101101011111010000001010111011101","10101111010000001001011010000001111000111110","11011100000100011111011010100111110011010111","11011100010111100100110010111110000110001111","00001100100101100101101100000011000011000000","10001011101001111110010100011001010100000011","10110110100111101011100010000001000110100110","10010111001101100110010000011001101011110010","10011001101011010001101100010010011011000011","10110111110100101010010100101110001000111011","01001111000101000101011111101101010111100111","00111100100101011101111100100001101111110001","00110111101011100011111001101010011010100011","11100110101010100000100110001111000000111000","01100011110111110011011011100011001101000101","11000001100100110011100010101001010001010010","11100010110111000011100010111001111010000011","00000111101011010000000011010011111010100100","10111110001011110011100100101100110101100101","00111000101100010011111011110001101100110111","00001111110011000011001111010010001111011011","01011010011000111001010000100011111101010110","00100000100010100110111000010000000010001110","01111110111101111101000010011011011100011111","10111001000010110100001110010111111001010110","10101001111011000101010110111111110010110100","11000110101001110100101111011010001010001111","00011010100111100010100010011110000100011000","10100110110110111110001010100111101100100000","11001110110010000000010101001011111000011111","01110011011100001011011110010000111011011111","11010000110111001101010101100000011010111111","10110000010010111011011011000111000001000001","00100100000001001100001111011010100101001000","10110010111010111011011111111101010100110100"}

{"01101010111110000110111000010010000000101100","10001101010101100100000000110111100100000110","11011101101011111101100011100011111010001010","01000111100001000110100110101100111000001111","11110100100100101011001001000100000000111011","10000101110110111110101111011001010011110001","11000011111011111011111101100111100011010111","10010110010000000001100010010110010001011010","10110010110101000101110000101110110000010011","00010000001100100111101000010010011111011011","01011011000101011110100010101100000111111110","11101100101010011110001010100101101110000010","01110010000011001011010110011001011001101001","11010110101111011010010000101011101000010100","00000010111010111000100111111110010100010011","01111110110010000011101101001000111000111000","01111011110110011000101000001001100010000101","10010001010011110010101101110101110111111110","10000101111110010111001101000011100000010101","01111010101111010011010000110100101010101010","00001101010111110010101011101000011100000000","01100101110011111101100100001010011110111000","01101110011110111100100110111100101110111010","10010000001110010110111001101110100000111111","00010000011111011100000000001011101010000011","11111011100011011011001011011111110110101111","11000000101101011101011110110110101111001100","01111100011010000011101001110010101101001101"}

Returns: 1
{"001101001001100111","001000111101100001","001111001110100001","000000111000010001","110110001110000100","000101100111101001","001111100101101111","100001011111011101","010101010010010111","110001011101000000","000110001000011010","111001110110000000","110111010101100111","100001011001101011","111001111110110101","001100111101011000","110100101111010111","111000010000111101","011110101111111011","101011100100100100","110000100101011001","101101011010011101","101001100011001011","111110111101110010","010000000110010001","011000011100101011","001110101111110101","110011010010110000","111101010010101000","110010111011010000","100110011111001010","101111011011011010","101010100010100111","110101110100100111","010110101101111001","111000010110001110","011011111011011001","011100100111101100","110011110001111100","101111100000111011","101111000000111101","101101001110110100","010011110110101011","001001000110110100"}

{"010000010110101110","100111100101001111","101111010110011000","010001011100110100","110000010011111010","010011001110011001","010110110101110101","000100001000011000","111110101100011100","001001011110111000","110110010000001010","101010000111100110","011010010100101000","001010100001010110","110000101000011011","110000110011111100","110010111101110101","101011011100010110","011001111011011011","101100000010111101","100001001110110011","100010100001101001"}

Returns: 1
{"00111110100110110001010110010100110000011","11010100010010001001111110100001100011111","11101111101111000011011110001101111101001","01010110100001100010000001011010011111110","11111001100110011100101100101000111000010","11011001111100010100101011010000001011100","01101101100000101101010001001111111111001","11111100001101100100001111111000101110010","00101011000101011101111110001110110101111","10101001010000101111110001000110010110011","01011111010101110011111111110111101111111","10110001110111010011011111110110010110010","11100001001111010101011111100101010010110","10011100001110000110111101011011111101100","11101010010011001011000011111001100100110","00001101001010011100110100100010011001101","01101111001101111100100001001011110111111","11000111010110111010011100001001010100010","11001111110010000000101100010010001101010","01000111101110101110100101100010010011110","00100110111111100111000010010100100001111","01011110101101010010110101110001101111111","01010010011100011110100100110111111100100","11111000111110101111001100011001100110010","00110110100001011011101011111100100001001","11011101111011001010110011011011111011010","01100011101001011011100001001010110000000","00101010111000100101100111010110000111011","10001111110110001010111001111101101100101","01111011000011111000001001001110110111101","00011101110010011010000000001001110010101","00000100100001001101010111000100001001101","00111000100111110111110111111011110000111","01010101000100000100101011011101001011010","00011101000001110100010110101110011011101","01100000111111001111001110101000111111001","00001100111110010010000011001010111001101","10111000001000000100000000010110101100010","10011101100111000000110010111111011000001","01101100101110101000011011110111001011010","01111100011110000001000000010000111110100","00101001011100000111111010110100101001101","10100000000000111101000101110110110100001","01000011001011101101000111010001101101011","11101111001001111001111000100101110001000","00111110001010011100111011111010110100011"}

{"10101110010101111101000110000000011100111","10110000001101101101110011101111001101111","01011100111000010011111010110101011110111","00100001111010110101110101010010101011011","01100111000101011001011010011001000000001","00010100100100011100111001001111000000100","01001111111100100000011000011101101001010","10000100010100001000000111011110000100101","10100001110110011101111110100000010100101","11101000010101010101001010111100000010001","01100010111001010001000111101101011001110","00000111011100010000111101101001010001101","11001011100001110111000011000101010000011","11011101101110011110101111001001110110010","01010101010001010000110111001111000110010","11001111000100110100100001110110101110110","01101001100101001111011011110001101111110","10111110001011000001101111101000011100001","11100100000100110010011111100011110110010","11110100110100011011000100000100000011100","10100010010010111111100011000010111010011","00110000100010011110000100000010010001010","00010101001101011010110110101011100101001","00111001011101001001011011100010101011010","10100011101111000111111010011010001000111","11101011000011000001100101011110001101000","01100111100011100011111100110001001100000","01000111011000011010101000000110110000010","11110011101001100010001101011010001010101","11010111111111101001111011100011010010111","11011010110110000100100000100011000001100","01010001010110001110101111000100110110100","01110001001100000110101000111100000101010","10000101100000000110110000110110100100101"}

Returns: 1
{"11101010000","00111111011","00011100000","01000111000","00000001000","00010100100","11011111100","11001110111","11100001101","00010101011","00000110001","11101000001","00001001101","11110101101","10001000100","01010001011","01001001011","00011001001","01011100001","01011010101"}

{"10011001110","00101110001","00010000010","11111001011","00010111011","11011111101","11111011010","11100100111","11110000111","01001101011","00000101110","00000100001","01000000001","00011000111"}

Returns: 1
{"11001101010001111010001","11101000101110110011010","01110100010001111100000","01100101101101001111100","01111110111100011111000","11101000000001101000100","01000010101101001000100","10100011100011001011101","10011111011100100101100","01100111011000100100001","01000011010101101001101","01010100101111110100100","00010001011100000011100","00011000100010001000111","11011001110101000011001","11111101010110000111001","00111000011111011000101"}

{"01101010000111001000110","00010101111101100100000"}

Returns: 2
{"01001010101100111011011","01100010101010001010000","10100110010011101011001","10010100001000111001101","00110101111011101011110","10001001000001010110111","00101100110101111100010","00011001110011110010110","11011000011101111000100","01011010011001111111101","11000100001111101111001","11111001100001011010001","01000011000000101101100","01011000001000000000011","11111010001000101001110","01110011011111010000101","11111000110001011101001","11011001010000001111001","01101010110010110110111","01111011011010110001001","11010011000000101110110","00000100011001000100010","01101101000011100110001","01010001011001000101111"}

{"00111000101011111100000","10001000001111101110101","11011011010000100111000","11101110010110101001100","11110111011000111110000","00000110101100111010111","00010001100011111011000","10111001111001100100111","11000110111010010001100","10011010101011010101101","10101000010001100011001","10000001100011111000010","10011000111010101010011","10010011111010010000001","10101111100000110011111","10100000001001011111110","01010110101011101100011","10110001111100000101011","00111010010010001000111","01001011100010000011001","00011010111110101101010","01100100110000111110111","00111011000010001111111","00011011110011011010111"}

Returns: 1
{"0","1"}

{"0","1"}

Returns: 2
{"00","10","01","11"}

{"00","11","10","01"}

Returns: 4
{"111","101","011","010","100","001","110","000"}

{"001","110","111","101","100","011","010","000"}

Returns: 8
{"0000","1011","0100","0010","0111","0101","1001","1010","1000","0011","0110","1100","0001","1101","1110","1111"}

{"0110","1111","0101","1100","1010","0100","0010","1011","0011","0000","1110","0111","1000","1001","0001","1101"}

Returns: 16
{"10100","10010","01111","01000","00011","11110","00110","00111","11100","00001","10000","10101","01100","10001","11101","00100","00000","11000","11010","10110","10111","10011","01110","11011","11111","00101","11001","01101","01011","01010","01001","00010"}

{"00101","10001","10011","11110","01111","11001","10110","11111","10111","00000","00100","01000","01011","00110","01001","11101","10010","11011","01110","10000","10101","01101","01010","10100","11010","00011","11000","00111","00010","01100","00001","11100"}

Returns: 32
{"11110000011011100101011101010110111111111100000000","11100111101011011111100110010100000111010010000001","11100111010110010110010111010010111111101010011001","11000000000100001110011101010010101000101001001010","10101011001111110100001110101101111100101001100011","11000110011110110110101100100110110101000110000111","01110000001111001110010001101101011010110010011010","00001010010010100011111001000010110011111111111111","11011111111100011111111010100001010000000000101100","01000001110001010011010010001101100001001100010101","00101010011100011111010010011101011101000111001110","00101000110101110101101100111011111101100010111110","00111011110011000000010001011000000001000100001110","11001111010110110101011010010111001110010111011100","11001101011010010011100000111111001111010011000100","11010010000101010011011001011100101011010110101010","00001101001011110011111111110001000000101011000110","00101101011101010111010111010011011111111000000011","10101110101111000100011100000011010111100010101101","10001110110010001111101101110101001111000111001110","01111011110110100110111000010101110101011001100110","00011010000110101100111000001100011101001011010101","10100011111111110101111100100110011100011101001110","00100001110110000110111001011011010001000011010111","10101001001010110010001011110011011000000101110111","01111101100010000011010110101101000010001000110011","01001010101000011101001110000000011010000100111010","11010011001111111101110010011010011101111001000011","10100000101000100010000100110110111001000100101000","11110111110000111110110000111001011010110101100111","11100111110001011101011010011110001111000101100011","00011011011011001110100001110010010110000001101000","00111011101000111100011010011010000000101111101000","10010101111111111101001011000010101100010011101001","10110000101000110010001001111001000101101110010110","00000001110101111110111110110100010001101000110111","01100011001110000111000010010111100000010111111110","11100110011001010111000011110001110011010011111111","11010011001100010101011111000110111110111011000100","00111000011100010111110001010001100001100101101011","00001010100101001011101011100000100111010001101101","00100110101000101100000000011000001101011000101110","00010011101101100100110010000001100000110000001000","10111110100100001011001010010011100110011100111001","10000101000010101110110001001011000101111110111101","00000100011001010011101010100010001101111001010011","01111001010011000010000101001111100111000100110011","00001100111100001100010110100101000111001100101011","00110000011010010110010000000101010101100011000010","00110011100111100100010111010111100011111010001001"}

{"11110000011011100101011101010110111111111100000000","11100111101011011111100110010100000111010010000001","11100111010110010110010111010010111111101010011001","11000000000100001110011101010010101000101001001010","10101011001111110100001110101101111100101001100011","11000110011110110110101100100110110101000110000111","01110000001111001110010001101101011010110010011010","00001010010010100011111001000010110011111111111111","11011111111100011111111010100001010000000000101100","01000001110001010011010010001101100001001100010101","00101010011100011111010010011101011101000111001110","00101000110101110101101100111011111101100010111110","00111011110011000000010001011000000001000100001110","11001111010110110101011010010111001110010111011100","11001101011010010011100000111111001111010011000100","11010010000101010011011001011100101011010110101010","00001101001011110011111111110001000000101011000110","00101101011101010111010111010011011111111000000011","10101110101111000100011100000011010111100010101101","10001110110010001111101101110101001111000111001110","01111011110110100110111000010101110101011001100110","00011010000110101100111000001100011101001011010101","10100011111111110101111100100110011100011101001110","00100001110110000110111001011011010001000011010111","10101001001010110010001011110011011000000101110111","01111101100010000011010110101101000010001000110011","01001010101000011101001110000000011010000100111010","11010011001111111101110010011010011101111001000011","10100000101000100010000100110110111001000100101000","11110111110000111110110000111001011010110101100111","11100111110001011101011010011110001111000101100011","00011011011011001110100001110010010110000001101000","00111011101000111100011010011010000000101111101000","10010101111111111101001011000010101100010011101001","10110000101000110010001001111001000101101110010110","00000001110101111110111110110100010001101000110111","01100011001110000111000010010111100000010111111110","11100110011001010111000011110001110011010011111111","11010011001100010101011111000110111110111011000100","00111000011100010111110001010001100001100101101011","00001010100101001011101011100000100111010001101101","00100110101000101100000000011000001101011000101110","00010011101101100100110010000001100000110000001000","10111110100100001011001010010011100110011100111001","10000101000010101110110001001011000101111110111101","00000100011001010011101010100010001101111001010011","01111001010011000010000101001111100111000100110011","00001100111100001100010110100101000111001100101011","00110000011010010110010000000101010101100011000010","00110011100111100100010111010111100011111010001001"}

Returns: 1
{"111001","111000","010100","010010","000101","010000","101011","011011","110001","111100","000000","010001","100010","001011","000111","110111","011110","001101","110100","111010","100100","001010","011100","110011","110101","110110","011000","010011","100111","110010","100101","100000","001111","101000","001001","101110","000010","111101","000001","001000","101101","111011","000100","110000","100001","011101","111111","001110","100110","101111"}

{"111001","111000","010100","010010","000101","010000","101011","011011","110001","111100","000000","010001","100010","001011","000111","110111","011110","001101","110100","111010","100100","001010","011100","110011","110101","110110","011000","010011","100111","110010","100101","100000","001111","101000","001001","101110","000010","111101","000001","001000","101101","111011","000100","110000","100001","011101","111111","001110","100110","101111"}

Returns: 1
{"00110001101100001110010101001111010110011111011000","00001000101010100110000000110101100010000011001101","00011100111011001101100110010100010100010100000110","11000101110010001010101110000110001111100010100110","00010101110000011110011100110110110111111000111100","01000110011101111110011111111000000010000101011101","11000000001101010001011011111111010110101000000011","00011010001110110110010100111001010100111010000111","11011001010100010010000010111000011100010111000101","11100010110111101110100100011100110110000010110011","11011001100111110011110010010101110000001110011010","11111011011111111100011111101010100011001001001111","11000101001010001001011011010110001110000110101101","10110011110001001100111101011001101000101101111100","10100011101010100101100101010010111010100010011111","11101000000001000010001101011010011010011101010100","11110101110000100010010100110110100011111001000110","00110000101111011000111110011101001100101101110000","00010110010111001001111001001010110001110100101010","11001000101000100110000100010000111001010101000001","01111010000101111101111001111001101110010011101111","01011110111010111110000110111000000101000100100000","01010111010011011011000110011011001010010100000011","00111111011111100011100011011001110101101101000101","00010100000101001101001010100001101011110001101101","10011000000110010010111011000001001111111010000011","11101011111010001111011101100111110001111111111100","00011010011011010000010011010111110001001000100111","10001000011101111011100011001010011101110101100000","00100011011101111000000110101101000101010100110010","00110001111001101000010010100001110011101101111000","11110010100011001100000100100000111011000000111010","11110010010000101101110100001101010111011001100101","11011110000111111100010010101110000100101110111001","11000011110110011100001011000010111101001010101011","00111111110010010011001100111001001100100110010010","11100011011111111000000010001000011110000010111110","00011011011000000110111000000101101011111010001111","01010001110010100011111111100001001001000100010000","11101110111101010111011101001110101001010001010010","11010000101000100010011001110010000100011110110000","01110101001101100000000000100000100010010011011111","00111110000111000000011010101110010000101111000011","01111100100100000101000000000011101101000011111100","00110111001100010011100000001100110011000011111001","00111101100000010111111111010010010110100011010101","00010100101000111101100101000001010010111010111010","11101110000101010100101000011110101000110101011001","01101101101010100000011001100000100101010010100010","11001001000000110000100010000100010001010101001100"}

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Returns: 2
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Returns: 1
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{"00101010111011010110000010101110001011011011111110","10001111100011010101000010101010111111010011000000","01111111101101011000011000100000111011011100011001","11000101000110101111111110100111011101110011000000","10100110011111101011011010111110100110110000011100","00010000111011001001101001010011000101101101110111","11110011110010110101110011010110000011111101010001","00000101111001111100101001101100110000101011101110","01001101110011101110001111001010010101100001001111","10011111110000100000100000101101001100111110110111","01110110001100111100001111011001101011100111110111","10110111000010110001001101000010001100111001010001","01111110101010111000111111101101011110000011101011","01110101111010101100100101100010100000110110011111","10110111111010110001101110100011110011010000110010","11010001101001110100100101100000010001110000000110"}

Returns: 3
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Returns: 2
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Returns: 1
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Returns: 1
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Returns: 4
{"11001001011001111100101100110001010110011000011000","11010001000110111110100000100010001000011100001111","10001110010101000110111000101010101111010000111011","01111011100000101110110100110111011000011111111001","11110110001001000110111000110010010011011101000111","11010110000001000110100100001010010100111010000100","01111100010100100001011001001001000110010110111011","00010010011100100010001010111100111011001100101100","00101100000101110000101100000011001100001010101011","01011110110011100101010101100111100111000110001000","01110111110111101101100110110100000111010010010100","01010111111010001110011000100011011100000010001110","11010111101111100001110011001101111001110100000111","01110101111111010111100111100100011010101110010111","01001011100110000101000001011011101101101000010000","00101110001101001010101101010011010001110110101000","00001110000000101001010011000100001010100110110010","00100101101110000110010010101110010000110010000111","10101111110011100001110011010101000101111001111011","10010000100011011011100111010110000000111100100100","10001000111100011001101011000101011110111000110011","00000111001001000010011110000000110001100010110100","00100010011010001001111111010000001110111011000101","10001111111011100001101111101101000010011110111000","10010100111111010111110000001101000011001111101110","10111101111011011111000011011110100011011011110010","11001111001101001010111010111010001000010111010001","11110001010100011000011100000101111111010001010110","10110100110010110100001110011010011000011111110100","00110101001001111100110010110011010000100111111110","10011000101000010100100010001110011100000010000011","10011111011100011011001111110000000010001011000001","01101101011101111100101110010011101011001101000001","00110010001110000100110110011011001100000001110101","00010101000001111100101110001011010111000000111101","00101010010001000110111010001000010010000101100010","00011110101011111100111000110011010001011001000000","00010101001000110000000111001110010000011101101111","11110100001000100111111101100110011010110111001110","10111000011010101111111110100101011110010111011011","10011111010101010111100110110101000101010110010011","00110111101111110100001011100000110001001101011100","00111110100110011111000110100100001010001001011010","00010010111100111111101010110000001110010100101101","10100000000101101101110010110110000000010011001100","01000101011001100001110010000100011010000001111111","01111011000000110011010100111011101101000111111000","11100111001001010111100110101101111001011011101111"}

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Returns: 3
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{"00011001110110001100000010010101101111101001111111","10011000001000100111011100010011111011100110101100","10010011101011101011100011101110111010100010000011","00111001111110001100011110101101101000001110111100","00100110100110110110010110010110101010101100100000","10110001001100101111101111000000011011110010110000","01100001101010001100000010001101010011100100000011","11000011111010111010010110100100110000111110010011","10111000000101000100100010000100100000110110110110","10010100011111100100001110010000100100101011000001","00111110111001110100011010000101110100101000110111","11111101100011101000110000011011000111111000010100"}

Returns: 2
{"11001001011001111100101100110001010110011000011000","11010001000110111110100000100010001000011100001111","10001110010101000110111000101010101111010000111011","01111011100000101110110100110111011000011111111001","11110110001001000110111000110010010011011101000111","11010110000001000110100100001010010100111010000100","01111100010100100001011001001001000110010110111011","00010010011100100010001010111100111011001100101100","00101100000101110000101100000011001100001010101011","01011110110011100101010101100111100111000110001000","01110111110111101101100110110100000111010010010100","01010111111010001110011000100011011100000010001110","11010111101111100001110011001101111001110100000111","01110101111111010111100111100100011010101110010111","01001011100110000101000001011011101101101000010000","00101110001101001010101101010011010001110110101000","00001110000000101001010011000100001010100110110010","00100101101110000110010010101110010000110010000111","10101111110011100001110011010101000101111001111011","10011110101101010001011001101100010010101001101011","10001000111100011001101011000101011110111000110011","00000111001001000010011110000000110001100010110100","10101111110011001001100111000110010010110101110001","10001111111011100001101111101101000010011110111000","10010100111111010111110000001101000011001111101110","10111101111011011111000011011110100011011011110010","11001111001101001010111010111010001000010111010001","11110001010100011000011100000101111111010001010110","10110100110010110100001110011010011000011111110100","00110101001001111100110010110011010000100111111110","10011000101000010100100010001110011100000010000011","10011111011100011011001111110000000010001011000001","01101101011101111100101110010011101011001101000001","00110010001110000100110110011011001100000001110101","00010101000001111100101110001011010111000000111101","00101010010001000110111010001000010010000101100010","00011110101011111100111000110011010001011001000000","00010101001000110000000111001110010000011101101111","11110100001000100111111101100110011010110111001110","10111000011010101111111110100101011110010111011011","10011111010101010111100110110101000101010110010011","00110111101111110100001011100000110001001101011100","00111110100110011111000110100100001010001001011010","00010010111100111111101010110000001110010100101101","10100000000101101101110010110110000000010011001100","01000101011001100001110010000100011010000001111111","01111011000000110011010100111011101101000111111000","11100111001001010111100110101101111001011011101111"}

{"00011001110110001100000010010101101111101001111111","10011000001000100111011100010011111011100110101100","10010011101011101011100011101110111010100010000011","00111001111110001100011110101101101000001110111100","00100110100110110110010110010110101010101100100000","10110001001100101111101111000000011011110010110000","01100001101010001100000010001101010011100100000011","11000011111010111010010110100100110000111110010011","10111000000101000100100010000100100000110110110110","10010100011111100100001110010000100100101011000001","00111110111001110100011010000101110100101000110111","11111101100011101000110000011011000111111000010100"}

Returns: 2
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{"11101000011001001100100011101110001001111000010111","11101110111000101001010000110010010101000101100000","00001010100001110010111110000110110101100110110101","10010110011100110000010010001011000010001100010101","01100010010111010110000110000011100000101011001110","01111110100000100000010011010100100011100000010011","11100011010111010111010001110100100001011100111001","01101100111011011110010100001111110111000111100010","00100000000101111110011110111111010110010011101000","10001011011100110001101110001111000100010010111000"}

Returns: 5
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{"11101000011001001100100011101110001001111000010111","11101110111000101001010000110010010101000101100000","00001010100001110010111110000110110101100110110101","10010110011100110000010010001011000010001100010101","01100010010111010110000110000011100000101011001110","01111110100000100000010011010100100011100000010011","11100011010111010111010001110100100001011100111001","01101100111011011110010100001111110111000111100010","00100000000101111110011110111111010110010011101000","10001011011100110001101110001111000100010010111000"}

Returns: 4
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{"11101000011001001100100011101110001001111000010111","11101110111000101001010000110010010101000101100000","00001010100001110010111110000110110101100110110101","10010110011100110000010010001011000010001100010101","01100010010111010110000110000011100000101011001110","01111110100000100000010011010100100011100000010011","11100011010111010111010001110100100001011100111001","01101100111011011110010100001111110111000111100010","00100000000101111110011110111111010110010011101000","10001011011100110001101110001111000100010010111000"}

Returns: 3
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{"11101000011001001100100011101110001001111000010111","11101110111000101001010000110010010101000101100000","00001010100001110010111110000110110101100110110101","10010110011100110000010010001011000010001100010101","01100010010111010110000110000011100000101011001110","01111110100000100000010011010100100011100000010011","11100011010111010111010001110100100001011100111001","01101100111011011110010100001111110111000111100010","00100000000101111110011110111111010110010011101000","10001011011100110001101110001111000100010010111000"}

Returns: 3
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{"11011100001100100100100111001001110111011000000011","10010100011101010111010110101110111010010110101000","11000101011101001111101001011001010001000111100110","01100111100011111001000100011101000100100110101001","11111001010010001010100001111000111101000111010000"}

Returns: 10
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{"11011100001100100100100111001001110111011000000011","10010100011101010111010110101110111010010110101000","11000101011101001111101001011001010001000111100110","01100111100011111001000100011101000100100110101001","11111001010010001010100001111000111101000111010000"}

Returns: 9
{"00110110111001110101010010100111110010100000110000","11000101000111011011000000010100001100010000110001","10001101010110101000110001110011000001011110011010","10010100000111000011111111100011100111000001111111","10101000001000000110110111000010001011000001001001","11101101100111111101101110111001100100000100111011","11010001101000111000100110011000001000000100001101","01001111011001001011000011111101110001100101110100","10111100100111100101010001001110001111010101110101","11110100110110010110100000101001000010011011011110","01000100101000010001101010101110011001110011001001","11100110010110100111000111101010001100010010000110","00010101101000001001010101011001110010100010000111","01011101111001111010100100111110111111101100101100","01111000100111010100100010001111110101110011111111","10001001010101001000101111100011001011011001011111","11000001000100111011011110000100000110010111110100","00110010111010010101001100110111111000100111110101","10011111011010111000110011111011000101001001011011","10010000000100100011100001110011101101000110111010","10000111001100101000000111000110011100010000100100","10111011000011101101001111100111110000010000010010","10100010010010000110000001110111010110001111110111","00011001111101011011100010100011100101110001011101","11101010000011110101110000010000011011000001011100","01101001001001010101100000100100001001010011101011","00000100000110001000010111110010001110000010010011","11110111111000100110000101000001110000110010010010","01001100010111111011100110010101000011001100111000","01010101000110010000101000000101100101010011011101","00101000100100101111001011011101011010000010010001","00101000010000111011110010010111101100101111110101","00110001000001010000111100000111001010110000010000","10010011111111100110010001000011011111010001011111","01100000000001001000000011110000100001100001011110","01011001111000011110101011111101010000111110100110","11100010010111000011001000101001100011000000001100","11000111001001101101001110011000101001011111011111","11111011000110101000000110111001000101011111101001","10101010000110110000111001001110101110001110100111","11010000011110010110101010101011110101011110110000","10111101010001001011011101111101110010001111001000","10011000001111100101011011001100111000010000011011","10000001011110001110010101011100011110001111111110","00100011100000111000111000011000001011101110110001","10110001110111011011111101001111000001001001101001","00010011001001101101010000001011010100101000100110","10001101111000011110110101101110101101001001011111","11100000110111000011000010111000101010011000100111","10101000100110110000110011011111100111010110001100"}

{"11011100001100100100100111001001110111011000000011","10010100011101010111010110101110111010010110101000","11000101011101001111101001011001010001000111100110","01100111100011111001000100011101000100100110101001","11111001010010001010100001111000111101000111010000"}

Returns: 8
{"00110110111001110101010010100111110010100000110000","11000101000111011011000000010100001100010000110001","10001101010110101000110001110011000001011110011010","10010100000111000011111111100011100111000001111111","10101000001000000110110111000010001011000001001001","11101101100111111101101110111001100100000100111011","11010001101000111000100110011000001000000100001101","01001111011001001011000011111101110001100101110100","10111100100111100101010001001110001111010101110101","11110100110110010110100000101001000010011011011110","01000100101000010001101010101110011001110011001001","11100110010110100111000111101010001100010010000110","00010101101000001001010101011001110010100010000111","01011101111001111010100100111110111111101100101100","01111000100111010100100010001111110101110011111111","10001001010101001000101111100011001011011001011111","11000001000100111011011110000100000110010111110100","00110010111010010101001100110111111000100111110101","10011111011010111000110011111011000101001001011011","10010000000100100011100001110011101101000110111010","10000111001100101000000111000110011100010000100100","10111011000011101101001111100111110000010000010010","10100010010010000110000001110111010110001111110111","11011101000001001001111100010101111110100000010110","11101010000011110101110000010000011011000001011100","01101001001001010101100000100100001001010011101011","00000100000110001000010111110010001110000010010011","11110111111000100110000101000001110000110010010010","01001100010111111011100110010101000011001100111000","01010101000110010000101000000101100101010011011101","00101000100100101111001011011101011010000010010001","00101000010000111011110010010111101100101111110101","00110001000001010000111100000111001010110000010000","10010011111111100110010001000011011111010001011111","01100000000001001000000011110000100001100001011110","01011001111000011110101011111101010000111110100110","11100010010111000011001000101001100011000000001100","11000111001001101101001110011000101001011111011111","11111011000110101000000110111001000101011111101001","10101010000110110000111001001110101110001110100111","11010000011110010110101010101011110101011110110000","10111101010001001011011101111101110010001111001000","10011000001111100101011011001100111000010000011011","10000001011110001110010101011100011110001111111110","00100011100000111000111000011000001011101110110001","10110001110111011011111101001111000001001001101001","00010011001001101101010000001011010100101000100110","10001101111000011110110101101110101101001001011111","11100000110111000011000010111000101010011000100111","10101000100110110000110011011111100111010110001100"}

{"11011100001100100100100111001001110111011000000011","10010100011101010111010110101110111010010110101000","11000101011101001111101001011001010001000111100110","01100111100011111001000100011101000100100110101001","11111001010010001010100001111000111101000111010000"}

Returns: 7
{"10110000001011010010010101011110001101010010110111","10010000011110001101101011110001011001001111001001","00101110000110011010000100001011101010010011001101","00001110010011000101111010100100111110001110110011","00100110101111011111000101000010110001000110001010","00000110111010000000111011101101100101011011110100","01111101010100111010001010111110100010010011100100","01011101000001100101110100010001110110001110011010","00111101001011111001111101111011010101100100100111","00011101011110100110000011010100000001111001011001","11110001110000010110110111111011010011010001010011","11010001100101001001001001010100000111001100101101","10101100100101010110101100110100111110010010010011","10001100110000001001010010011011101010001111101101","10010101001001001100000011011110010101011100010010","10110101011100010011111101110001000001000001101100","10111000010101000011100101101001010000101100000110","10011000000000011100011011000110000100110001111000","10100011110000110011110010101000110001011011000011","10000011100101101100001100000111100101000110111101","00110111100001110010011100110101100100001100111000","00010111110100101101100010011010110000010001000110","11100001110010000000000001110111101111101100001011","11000001100111011111111111011000111011110001110101","01100011010101001101111011100111001111100111110101","01000011000000010010000101001000011011111010001011","11111010010001100000101110011111000011100010010111","11011010000100111111010000110000010111111111101001","00111000100011000000100001100011101100010001100111","00011000110110011111011111001100111000001100011001","10110000101110101101101000001011001110011001111101","10010000111011110010010110100100011010000100000011","00000000001010000100100010100011100100100100011001","00100000011111011011011100001100110000111001100111","10100010000100110011001110110000001100010101101010","10000010010001101100110000011111011000001000010100","00011100100001001001101100001001111010100110001101","00111100110100010110010010100110101110111011110011","01000101011011011011001110011001100111010000111000","01100101001110000100110000110110110011001101000110","00000010001110100010001110010110111000110011000010","00100010011011111101110000111001101100101110111100","10000000010110101011010001011000101110110000101111","10100000000011110100101111110111111010101101010001","01000001110010111001111000100101111000111011110101","01100001100111100110000110001010101100100110001011","00101111010000100011111011011010101110110111000100","00001111000101111100000101110101111010101010111010","00101000110111110111100110100010000011001011110001","00001000100010101000011000001101010111010110001111"}

{"01010011101010101010000100001101001111111000111010","01110011111111110101111010100010011011100101000100"}

Returns: 50
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{"01010011101010101010000100001101001111111000111010","01110011111111110101111010100010011011100101000100"}

Returns: 48
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{"01010011101010101010000100001101001111111000111010","01110011111111110101111010100010011011100101000100"}

Returns: 46
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{"01010011101010101010000100001101001111111000111010","01110011111111110101111010100010011011100101000100"}

Returns: 44
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{"01010101110100000100001101101111111100011011111110"}

Returns: 50
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{"01010101110100000100001101101111111100011011111110"}

Returns: 50
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{"01010101110100000100001101101111111100011011111110"}

Returns: 50
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{"01010101110100000100001101101111111100011011111110"}

Returns: 50
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Returns: 2
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{"00000000000000000000101101110010000101100000101001","00000000000000000000010101010001001000001100111110","00000000000000000000010110100000100001101001010111","00000000000000000000101011010110100011111010110010","00000000000000000000110110101111001010110111010011","00000000000000000000111011110001001010010000100001","00000000000000000000101101000001100101011110111011","00000000000000000000111011101110111100001101111010","00000000000000000000001000001001011111101111100011","00000000000000000000110111111011100111000111110000","00000000000000000000000101110100010110001110010101","00000000000000000000001111000001101010010011001100","00000000000000000000000101010010001111100000110100","00000000000000000000000110100001110011111000100000","00000000000000000000011011100110000110100010011010","00000000000000000000111010110000100110010111011110"}

Returns: 3
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Returns: 4
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Returns: 5
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{"00000000000000000000000110101000011101111100001010","00000000000000000000000111001001110010110101111001","00000000000000000000010110011010101001100011110011","00000000000000000000100001011000100001010010001100","00000000000000000000001110110011110001011100001110"}

Returns: 10
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{"00000000000000000000000010011111111111101100011011","00000000000000000000011111110100100011111000000100"}

Returns: 50
{"01000111100101011001100101101000011110000110010011","10110110110111001010100101101000011110000110010011","11000100110100110110100101101000011110000110010011","00111101011111110011100101101000011110000110010011","01001011001101100011100101101000011110000110010011","01010110011010110010100101101000011110000110010011","10011100100011000011100101101000011110000110010011","11111000001011011111100101101000011110000110010011","00001010100011011010100101101000011110000110010011","10011111000010111011100101101000011110000110010011","01100001001111011110100101101000011110000110010011","01111100010101100110100101101000011110000110010011","01101001110011100000100101101000011110000110010011","11101100100001010110100101101000011110000110010011","01110100101011010000100101101000011110000110010011","10100000101110001110100101101000011110000110010011","11100101101000101100100101101000011110000110010011","00011010010011111110100101101000011110000110010011","10101000101011111011100101101000011110000110010011","11110000111110011100100101101000011110000110010011","00111110111111000111100101101000011110000110010011","01001111010111000001100101101000011110000110010011","11011110110100010001100101101000011110000110010011","01011000011011110111100101101000011110000110010011","00000001000100010000100101101000011110000110010011","10011110101000111011100101101000011110000110010011","10010100111111011111100101101000011110000110010011","10010111101101010100100101101000011110000110010011","10000011000111111110100101101000011110000110010011","10101110110100111101100101101000011110000110010011","00110011010011000011100101101000011110000110010011","01010001011101000101100101101000011110000110010011","00000101010000111001100101101000011110000110010011","11111110101100110001100101101000011110000110010011","11101010110010100011100101101000011110000110010011","00001001001101111100100101101000011110000110010011","01001101001110110100100101101000011110000110010011","00010011100101000100100101101000011110000110010011","11100111110011100011100101101000011110000110010011","00010110111010110100100101101000011110000110010011","01011110011011011001100101101000011110000110010011","00111000101000010011100101101000011110000110010011","00110111110101010100100101101000011110000110010011","10010110001000001010100101101000011110000110010011","00011010111111000001100101101000011110000110010011","00010010000000111000100101101000011110000110010011","10111110001000010001100101101000011110000110010011","10110000110100000001100101101000011110000110010011","11011011111001001110100101101000011110000110010011","00000010011000110111100101101000011110000110010011"}

{"00000000000000000000100000010111011000111101011011"}

Returns: 50
{"11011010101000100111100101001100111010010110101010", "11010101100001101000111011101000111001111110100010", "00101110100000110101000001000100000111101101110101", "01111101101111110011100100101110001111100001110101", "01000001001001011000000011000010110111101001100000", "01101011011010100111101110111011100011011110010001", "11100001111110111001010100000001111100111000101000", "10110100001000110111111110110011001001101001011010", "10111111001111100111111101110001010100000111110101", "00011100000000000000100001100010001111010000100101", "11110101101101111011111110111001100111111000011110", "00110001011001010001110110011111110110110000101001", "11110010101111000101100111101001110010010000100110", "10111001001010110111001000001100011110000101000010", "11001001000000000100100010010110010111011001101111", "11111011000100101011001000011111000110010000010100", "00000000001110111010110011100101101111111100110001", "01111001000010101001110101001010001111011101111011", "10111101100000111000111100000110101010000010001101", "11001101111010101001101001010000110001010111101010", "10000110000101000010111000101000001010000010111110", "10000011001001111001001111000100100011111100011011", "10011100101101011100001000110111110000011001100011", "00100100001110000001111010010000010000010100110010", "11001101001101010110000001101100000110000011110101", "00101110111011000001011100000110110001100000000000", "10101110111110011000010010111110011100101010111011", "00000111001001110110100001111111110111111011101100", "11100111110001101010000101010010100101110111101011", "01100110010010011010110001101011101100001001010011", "01101110100011101101101010110010101110111010101011", "11111010010110101010100100110110001110111100111010", "11010011000100111010100101010011110100000110101110", "10010010010101100101100001010110011000001111000110", "00100111100000010001010110011111001001111011010110", "01001101000110011000110001000110110000100110011111", "10001011010111011010000000111100100001100001100110", "11011011100111110111111111010111011010101110001010", "01010100001000110111100100101101000011101001010000", "10011100111101000111111100110110111001110010011000", "10101000110011100001101011101000001101010011100100", "00000110110010001001101001000101101100111111111111", "00000011010001010000011101100010110111011011101001", "00010101101010010110101010000110100110001000001000", "11001000011010010100110111001010110011000101001011", "00011101111000001111111111101011010000110100100010", "01110000010101011010011011001101010100101100001110", "01011101100111100101100101010110010110000000110100", "01011001100110011111001001100101010110010001000100", "00000011010000100100011001011011011010110110011001" }

{"11011010101000100111100101001100111010010110101010", "11010101100001101000111011101000111001111110100010", "00101110100000110101000001000100000111101101110101", "01111101101111110011100100101110001111100001110101", "01000001001001011000000011000010110111101001100000", "01101011011010100111101110111011100011011110010001", "11100001111110111001010100000001111100111000101000", "10110100001000110111111110110011001001101001011010", "10111111001111100111111101110001010100000111110101", "00011100000000000000100001100010001111010000100101", "11110101101101111011111110111001100111111000011110", "00110001011001010001110110011111110110110000101001", "11110010101111000101100111101001110010010000100110", "10111001001010110111001000001100011110000101000010", "11001001000000000100100010010110010111011001101111", "11111011000100101011001000011111000110010000010100", "00000000001110111010110011100101101111111100110001", "01111001000010101001110101001010001111011101111011", "10111101100000111000111100000110101010000010001101", "11001101111010101001101001010000110001010111101010", "10000110000101000010111000101000001010000010111110", "10000011001001111001001111000100100011111100011011", "10011100101101011100001000110111110000011001100011", "00100100001110000001111010010000010000010100110010", "11001101001101010110000001101100000110000011110101", "00101110111011000001011100000110110001100000000000", "10101110111110011000010010111110011100101010111011", "00000111001001110110100001111111110111111011101100", "11100111110001101010000101010010100101110111101011", "01100110010010011010110001101011101100001001010011", "01101110100011101101101010110010101110111010101011", "11111010010110101010100100110110001110111100111010", "11010011000100111010100101010011110100000110101110", "10010010010101100101100001010110011000001111000110", "00100111100000010001010110011111001001111011010110", "01001101000110011000110001000110110000100110011111", "10001011010111011010000000111100100001100001100110", "11011011100111110111111111010111011010101110001010", "01010100001000110111100100101101000011101001010000", "10011100111101000111111100110110111001110010011000", "10101000110011100001101011101000001101010011100100", "00000110110010001001101001000101101100111111111111", "00000011010001010000011101100010110111011011101001", "00010101101010010110101010000110100110001000001000", "11001000011010010100110111001010110011000101001011", "00011101111000001111111111101011010000110100100010", "01110000010101011010011011001101010100101100001110", "01011101100111100101100101010110010110000000110100", "01011001100110011111001001100101010110010001000100", "00000011010000100100011001011011011010110110011001" }

Returns: 1
{"01111111111111111111111111111111111111111111111111", "10111111111111111111111111111111111111111111111111", "11011111111111111111111111111111111111111111111111", "11101111111111111111111111111111111111111111111111", "11110111111111111111111111111111111111111111111111", "11111011111111111111111111111111111111111111111111", "11111101111111111111111111111111111111111111111111", "11111110111111111111111111111111111111111111111111", "11111111011111111111111111111111111111111111111111", "11111111101111111111111111111111111111111111111111", "11111111110111111111111111111111111111111111111111", "11111111111011111111111111111111111111111111111111", "11111111111101111111111111111111111111111111111111", "11111111111110111111111111111111111111111111111111", "11111111111111011111111111111111111111111111111111", "11111111111111101111111111111111111111111111111111", "11111111111111110111111111111111111111111111111111", "11111111111111111011111111111111111111111111111111", "11111111111111111101111111111111111111111111111111", "11111111111111111110111111111111111111111111111111", "11111111111111111111011111111111111111111111111111", "11111111111111111111101111111111111111111111111111", "11111111111111111111110111111111111111111111111111", "11111111111111111111111011111111111111111111111111", "11111111111111111111111101111111111111111111111111", "11111111111111111111111110111111111111111111111111", "11111111111111111111111111011111111111111111111111", "11111111111111111111111111101111111111111111111111", "11111111111111111111111111110111111111111111111111", "11111111111111111111111111111011111111111111111111", "11111111111111111111111111111101111111111111111111", "11111111111111111111111111111110111111111111111111", "11111111111111111111111111111111011111111111111111", "11111111111111111111111111111111101111111111111111", "11111111111111111111111111111111110111111111111111", "11111111111111111111111111111111111011111111111111", "11111111111111111111111111111111111101111111111111", "11111111111111111111111111111111111110111111111111", "11111111111111111111111111111111111111011111111111", "11111111111111111111111111111111111111101111111111", "11111111111111111111111111111111111111110111111111", "11111111111111111111111111111111111111111011111111", "11111111111111111111111111111111111111111101111111", "11111111111111111111111111111111111111111110111111", "11111111111111111111111111111111111111111111011111", "11111111111111111111111111111111111111111111101111", "11111111111111111111111111111111111111111111110111", "11111111111111111111111111111111111111111111111011", "11111111111111111111111111111111111111111111111101", "11111111111111111111111111111111111111111111111110" }

{"01111111111111111111111111111111111111111111111111", "10111111111111111111111111111111111111111111111111", "11011111111111111111111111111111111111111111111111", "11101111111111111111111111111111111111111111111111", "11110111111111111111111111111111111111111111111111", "11111011111111111111111111111111111111111111111111", "11111101111111111111111111111111111111111111111111", "11111110111111111111111111111111111111111111111111", "11111111011111111111111111111111111111111111111111", "11111111101111111111111111111111111111111111111111", "11111111110111111111111111111111111111111111111111", "11111111111011111111111111111111111111111111111111", "11111111111101111111111111111111111111111111111111", "11111111111110111111111111111111111111111111111111", "11111111111111011111111111111111111111111111111111", "11111111111111101111111111111111111111111111111111", "11111111111111110111111111111111111111111111111111", "11111111111111111011111111111111111111111111111111", "11111111111111111101111111111111111111111111111111", "11111111111111111110111111111111111111111111111111", "11111111111111111111011111111111111111111111111111", "11111111111111111111101111111111111111111111111111", "11111111111111111111110111111111111111111111111111", "11111111111111111111111011111111111111111111111111", "11111111111111111111111101111111111111111111111111", "11111111111111111111111110111111111111111111111111", "11111111111111111111111111011111111111111111111111", "11111111111111111111111111101111111111111111111111", "11111111111111111111111111110111111111111111111111", "11111111111111111111111111111011111111111111111111", "11111111111111111111111111111101111111111111111111", "11111111111111111111111111111110111111111111111111", "11111111111111111111111111111111011111111111111111", "11111111111111111111111111111111101111111111111111", "11111111111111111111111111111111110111111111111111", "11111111111111111111111111111111111011111111111111", "11111111111111111111111111111111111101111111111111", "11111111111111111111111111111111111110111111111111", "11111111111111111111111111111111111111011111111111", "11111111111111111111111111111111111111101111111111", "11111111111111111111111111111111111111110111111111", "11111111111111111111111111111111111111111011111111", "11111111111111111111111111111111111111111101111111", "11111111111111111111111111111111111111111110111111", "11111111111111111111111111111111111111111111011111", "11111111111111111111111111111111111111111111101111", "11111111111111111111111111111111111111111111110111", "11111111111111111111111111111111111111111111111011", "11111111111111111111111111111111111111111111111101", "11111111111111111111111111111111111111111111111110" }

Returns: 1
{"00", "10", "11" }

{"10", "01" }

Returns: 2
{"110", "001" }

{"101", "010" }

Returns: 2
{"111", "011", "101" }

{"010", "000" }

Returns: 2
{"00", "01", "10" }

{"00", "01", "10" }

Returns: 1
{"110", "001", "010", "011" }

{"101", "010" }

Returns: 2
{"00", "01", "11" }

{"00", "11" }

Returns: 2
{"01011100110110100100000100110100100001000010001100", "00101010111101111100011000110110000101100001110110", "10010100110101100111111010111111010101011111111100", "11110001101000110001110011100000000011101001101000", "11100010000111010010110001011100001100111000010111", "01001110110111001111111010110011000101000100010011", "00100010001000110001000100001110000100100101010111", "11101111010111000110101101110111000100011010110100", "10000000001110110110111111010110010101100000010010", "00010001000111100101101001111110101100100100110011", "10101000010100110110011010011110101111101111111100", "00010001101100111000011110001010010011101110011001", "11010010100110100100110101110010001010101100110001", "01010011010001101110101001011100101111010001100000", "01000100111001011001000101010011010000110010010110", "00011000110101010100000101010100101011001100101000", "00110010011000101111100100110111010001000110101011", "10110101101101001100001100000001010001011000101111", "11110100100011000110001010011101100010111111000101", "11011101000001001101000111110111000110001000111001", "11100110001100011101011101101100100011010011100011", "11100111110010110100010111110110000101101010110111", "01000010100111000110100011101010001001010110100110", "00010011010101110111111001111100000101011011101011", "01000010000111000110101111100110011010001100001100", "11010110111001101100110001010100001011010001000000", "11111001110110111011001110111001100011101111111110", "01001011001000011011001111001010110101011001011110", "11000011100100110111110001000110110101011011110101", "00001110100001100111100000000100100011100011000111", "00110011111100110010001111001010101011010000100010", "01110101100111100000001001100010110101000101010101", "10110000001000010001010111001010100100001001001010", "01010110010011111000011001010011011000111011000011", "10110001000111011100111100110001001001001000010101", "11001110110011011011100101011100010011100001000110", "01100001101111011000110110111000010100000101111100", "01110000010010101011011101001101011110000110111100", "11100111110011101010000001110111110111011110010110", "00101110110100111011111000100000111000000100101011", "11001011111101001111111111010010011000111011001010", "10001010111100001000111111011011010001001101101100", "00000100110101100011101001101000110011011101001100", "11100010010110100110101010010111110011010001001011", "10011011111000101101100111011001101010011001110011", "10010110000001101100011111011011110111010111000011", "00111101010001111101000001101011010000010010111101", "00000011111000100001110101011110010000010100110100", "10111101101011101001001100011010110010001101110111", "01010011010011100001110011000010010010001111010000" }

{"01011100110110100100000100110100100001000010001100", "00101010111101111100011000110110000101100001110110", "10010100110101100111111010111111010101011111111100", "11110001101000110001110011100000000011101001101000", "11100010000111010010110001011100001100111000010111", "01001110110111001111111010110011000101000100010011", "00100010001000110001000100001110000100100101010111", "11101111010111000110101101110111000100011010110100", "10000000001110110110111111010110010101100000010010", "00010001000111100101101001111110101100100100110011", "10101000010100110110011010011110101111101111111100", "00010001101100111000011110001010010011101110011001", "11010010100110100100110101110010001010101100110001", "01010011010001101110101001011100101111010001100000", "01000100111001011001000101010011010000110010010110", "00011000110101010100000101010100101011001100101000", "00110010011000101111100100110111010001000110101011", "10110101101101001100001100000001010001011000101111", "11110100100011000110001010011101100010111111000101", "11011101000001001101000111110111000110001000111001", "11100110001100011101011101101100100011010011100011", "11100111110010110100010111110110000101101010110111", "01000010100111000110100011101010001001010110100110", "00010011010101110111111001111100000101011011101011", "01000010000111000110101111100110011010001100001100", "11010110111001101100110001010100001011010001000000", "11111001110110111011001110111001100011101111111110", "01001011001000011011001111001010110101011001011110", "11000011100100110111110001000110110101011011110101", "00001110100001100111100000000100100011100011000111", "00110011111100110010001111001010101011010000100010", "01110101100111100000001001100010110101000101010101", "10110000001000010001010111001010100100001001001010", "01010110010011111000011001010011011000111011000011", "10110001000111011100111100110001001001001000010101", "11001110110011011011100101011100010011100001000110", "01100001101111011000110110111000010100000101111100", "01110000010010101011011101001101011110000110111100", "11100111110011101010000001110111110111011110010110", "00101110110100111011111000100000111000000100101011", "11001011111101001111111111010010011000111011001010", "10001010111100001000111111011011010001001101101100", "00000100110101100011101001101000110011011101001100", "11100010010110100110101010010111110011010001001011", "10011011111000101101100111011001101010011001110011", "10010110000001101100011111011011110111010111000011", "00111101010001111101000001101011010000010010111101", "00000011111000100001110101011110010000010100110100", "10111101101011101001001100011010110010001101110111", "01010011010011100001110011000010010010001111010000" }

Returns: 1
{"0111", "1010", "1111" }

{"1111", "0010", "0111" }

Returns: 1
{"10", "01", "11" }

{"11", "00" }

Returns: 2
{"00", "01", "10" }

{"11", "00" }

Returns: 2
{"11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111110111111111", "11111111111111111111111110111111111111111111011111", "11111111111111111111110111111111111111111110111011" }

{"11111111111111111111111011111111111111111011111111" }

Returns: 4
{"011", "111", "010" }

{"010", "110" }

Returns: 2
{"11001000001111111010100100100110101011101101110110", "11001000001111111010100100100110101011101101111100", "11001000001111111010100100100110101011101110010111", "11001000001111111010100100100110101011101110011011", "11001000001111111010100100100110101011101110011110", "11001000001111111010100100100110101011101110101110", "11001000001111111010100100100110101011101110110011", "11001000001111111010100100100110101011101110110101", "11001000001111111010100100100110101011101110111001", "11001000001111111010100100100110101011101111001101", "11001000001111111010100100100110101011101111001110", "11001000001111111010100100100110101011101111010101", "11001000001111111010100100100110101011101111011010", "11001000001111111010100100100110101011101111100110", "11001000001111111010100100100110101011101111101100", "11001000001111111010100100100110101011101111110100", "11001000001111111010100100100110101011110001011111", "11001000001111111010100100100110101011110001101111", "11001000001111111010100100100110101011110001111011", "11001000001111111010100100100110101011110010011111", "11001000001111111010100100100110101011110010110111", "11001000001111111010100100100110101011110010111101", "11001000001111111010100100100110101011110010111110", "11001000001111111010100100100110101011110011011011", "11001000001111111010100100100110101011110011100111", "11001000001111111010100100100110101011110011101101", "11001000001111111010100100100110101011110011110101", "11001000001111111010100100100110101011110011111001", "11001000001111111010100100100110101011110100011111", "11001000001111111010100100100110101011110100110111", "11001000001111111010100100100110101011110100111011", "11001000001111111010100100100110101011110100111110", "11001000001111111010100100100110101011110101010111", "11001000001111111010100100100110101011110101011110", "11001000001111111010100100100110101011110101101011", "11001000001111111010100100100110101011110101101110", "11001000001111111010100100100110101011110101110110", "11001000001111111010100100100110101011110110001111", "11001000001111111010100100100110101011110110100111", "11001000001111111010100100100110101011110110101011", "11001000001111111010100100100110101011110110110101", "11001000001111111010100100100110101011110110111010", "11001000001111111010100100100110101011110111001110", "11001000001111111010100100100110101011110111010101", "11001000001111111010100100100110101011110111011001", "11001000001111111010100100100110101011110111100110", "11001000001111111010100100100110101011110111101010", "11001000001111111010100100100110101011110111110100", "11001000001111111010100100100110101011111000101111", "11001000001111111010100100100110101011111000111011" }

{"00110111110000000101011011011001010100010010001001", "00110111110000000101011011011001010100010010000011", "00110111110000000101011011011001010100010001101000", "00110111110000000101011011011001010100010001100100", "00110111110000000101011011011001010100010001100001", "00110111110000000101011011011001010100010001010001", "00110111110000000101011011011001010100010001001100", "00110111110000000101011011011001010100010001001010", "00110111110000000101011011011001010100010001000110", "00110111110000000101011011011001010100010000110010", "00110111110000000101011011011001010100010000110001", "00110111110000000101011011011001010100010000101010", "00110111110000000101011011011001010100010000100101", "00110111110000000101011011011001010100010000011001", "00110111110000000101011011011001010100010000010011", "00110111110000000101011011011001010100010000001011", "00110111110000000101011011011001010100001110100000", "00110111110000000101011011011001010100001110010000", "00110111110000000101011011011001010100001110000100", "00110111110000000101011011011001010100001101100000", "00110111110000000101011011011001010100001101001000", "00110111110000000101011011011001010100001101000010", "00110111110000000101011011011001010100001101000001", "00110111110000000101011011011001010100001100100100", "00110111110000000101011011011001010100001100011000", "00110111110000000101011011011001010100001100010010", "00110111110000000101011011011001010100001100001010", "00110111110000000101011011011001010100001100000110", "00110111110000000101011011011001010100001011100000", "00110111110000000101011011011001010100001011001000", "00110111110000000101011011011001010100001011000100", "00110111110000000101011011011001010100001011000001", "00110111110000000101011011011001010100001010101000", "00110111110000000101011011011001010100001010100001", "00110111110000000101011011011001010100001010010100", "00110111110000000101011011011001010100001010010001", "00110111110000000101011011011001010100001010001001", "00110111110000000101011011011001010100001001110000", "00110111110000000101011011011001010100001001011000", "00110111110000000101011011011001010100001001010100", "00110111110000000101011011011001010100001001001010", "00110111110000000101011011011001010100001001000101", "00110111110000000101011011011001010100001000110001", "00110111110000000101011011011001010100001000101010", "00110111110000000101011011011001010100001000100110", "00110111110000000101011011011001010100001000011001", "00110111110000000101011011011001010100001000010101", "00110111110000000101011011011001010100001000001011", "00110111110000000101011011011001010100000111010000", "00110111110000000101011011011001010100000111000100" }

Returns: 1
{"00", "01", "11" }

{"00", "01" }

Returns: 2
{"01", "10", "11" }

{"01", "10", "00" }

Returns: 1
{"11", "00", "10" }

{"00", "11" }

Returns: 2
{"01", "10", "11" }

{"00", "01", "10" }

Returns: 1
{"001000101111000110111110100110110", "000111001010110010001110100110110", "001110010010111101010111101001110", "101111010100100100101111111110100", "010100100111011111010001000101010", "110111100110000111100001010011000", "000001110110010000001001101000111", "101101010001101001011110010111010", "011000101111000001101010010000000", "101000100011011110001111101100000", "001011100001111101011001001110011", "111000010111111001001110101010100", "111010111000010111010001100110010", "001011011000111011101000011011110", "110010001010000001000111001010001", "111110100011001110101101100111101", "110010100101100001001100100010010", "110011110001100011000110000010111", "010000001101101001000011101010000", "001110100010011100001100100011100", "011000111011000011111000010110001", "100000011010110101111101101101111", "110001000101000000111000110100000", "101001010111011110101110000111001", "011100110100111111011001101000010", "001111010100111000110101011001010", "000011110001111111010111101010110", "111100011001010111100101011110100", "111011011000011110111000000011001", "011011101000110101111001000000100", "011010100000111001110100111110000", "110110010110011111111011111001011", "100101101100010010110010010010001" }

{"001000101111000110111110100110110", "000111001010110010001110100110110", "001110010010111101010111101001110", "101111010100100100101111111110100", "010100100111011111010001000101010", "110111100110000111100001010011000", "000001110110010000001001101000111", "101101010001101001011110010111010", "011000101111000001101010010000000", "101000100011011110001111101100000", "001011100001111101011001001110011", "111000010111111001001110101010100", "111010111000010111010001100110010", "001011011000111011101000011011110", "110010001010000001000111001010001", "111110100011001110101101100111101", "110010100101100001001100100010010", "110011110001100011000110000010111", "010000001101101001000011101010000", "001110100010011100001100100011100", "011000111011000011111000010110001", "100000011010110101111101101101111", "110001000101000000111000110100000", "101001010111011110101110000111001", "011100110100111111011001101000010", "001111010100111000110101011001010", "000011110001111111010111101010110", "111100011001010111100101011110100", "111011011000011110111000000011001", "011011101000110101111001000000100", "011010100000111001110100111110000", "110110010110011111111011111001011", "100101101100010010110010010010001" }

Returns: 1
{"00", "10", "11" }

{"11", "10", "01" }

Returns: 1
{"00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000000000000000000000010000", "00000000000000000000000000000000000000000000110000", "00000000000000000000000000000000000000000000001000", "00000000000000000000000000000000000000000000101000", "00000000000000000000000000000000000000000000011000", "00000000000000000000000000000000000000000000111000", "00000000000000000000000000000000000000000000000100", "00000000000000000000000000000000000000000000100100", "00000000000000000000000000000000000000000000010100", "00000000000000000000000000000000000000000000110100", "00000000000000000000000000000000000000000000001100", "00000000000000000000000000000000000000000000101100", "00000000000000000000000000000000000000000000011100", "00000000000000000000000000000000000000000000111100", "00000000000000000000000000000000000000000000000010", "00000000000000000000000000000000000000000000100010", "00000000000000000000000000000000000000000000010010", "00000000000000000000000000000000000000000000110010" }

{"00000000000000000000000000000000000000000000011011", "00000000000000000000000000000000000000000000111011", "00000000000000000000000000000000000000000000000111", "00000000000000000000000000000000000000000000100111", "00000000000000000000000000000000000000000000010111", "00000000000000000000000000000000000000000000110111", "00000000000000000000000000000000000000000000001111", "00000000000000000000000000000000000000000000101111", "00000000000000000000000000000000000000000000011111", "00000000000000000000000000000000000000000000111111" }

Returns: 16
{"00000000000000000000000000000000000000000000000001", "00000000000000000000000000000000000000000000000010", "10000000000000000000000000000000000000000000000000", "01000000000000000000000000000000000000000000000000" }

{"00000000000000000000000000000000000000000000000001", "00000000000000000000000000000000000000000000000010" }

Returns: 2
{"11", "01", "00" }

{"00", "10", "11" }

Returns: 1
{"000000000000000000000000000000000000", "010000000000000000000000000000000000", "100000000000000000000000000000000001", "110000000000000000000000000000000001" }

{"000000000000000000000000000000000000", "010000000000000000000000000000000000", "100000000000000000000000000000000001", "110000000000000000000000000000000001" }

Returns: 4
{"000", "001", "010", "100" }

{"000", "001", "010", "100" }

Returns: 1
{"101", "010", "001" }

{"000", "111", "011" }

Returns: 1
{"1001", "0000", "0001" }

{"0101", "1100" }

Returns: 2
{"11000001110011110000101110110100000001110111011000", "10000011011110010001100000000000110010101111111110", "11011111100110010000010001101111000010011010101001", "11011101001100111100100010000000110110010011111110", "00001101110001100100101000000000000001101100001010", "10001101000000101000100011111000010111101011010100", "10000001101001100100010000111101110000100000000001", "10001110000010011001110001100001000111000011101100", "01011110011011010101010011101001010100011110001111", "00011010101011000001110011111101000010010010001100", "11001011100011101001001101110001100011101010011011", "10011010100111101100011001101111100011011101111100", "11001100101001010100010111011010100111001011001110", "01011101111110110101100001101000100101011110101000", "01010011110110110100000111111001110101110001110110", "10001011010010001000000110011011110101000100111100", "11011011000100010001100010100100010000101011111111", "01001100000011111100000100111000110101100110011110", "10001000100100111101101100010101100110110100010001", "10000000011100101001111111101001100100111111000101", "11010001000001110000111101001011010001011001100001", "10011000111110000000110010101000100111010000001001", "01001011111111000100011100001101110010011101110000", "01001001001110000001011000110011010000101010111100", "01011100001001111101110100100000010010001000110101", "01010110100111111100000110000100100110110000111010", "00010010110111001000010110100101000101010001011010", "11010101111100011100001001001110000000100101010110", "01011010011001000101001111000101000110111101001001", "00001000110011010100010001101000110010011101000010", "00001001011000111101110000101100100110011100010011", "10001110011011011000000001001011000100101010111110", "00011010111010110100001100010011110111001101110100", "11010100111111001001101101100110110010111111100001", "00000001001001010100100000000000110100101001011010", "00000110010110101001001000110011000010001011000011", "11001100111000101001001010101001100101100001110101", "01000101100101011100110111101110110000011100011100", "11010010011100000001110111001010010100110001010001", "01010010010000111101101000001010000110100110100001", "11001101010111010100011110010100100001110111100001", "01000000000100010000000011010010110000101001100010", "10010000101011011100000000001101000101011011001101", "11000010110010000000100011101101000001010011111110", "10000100101101111000011111100110110110101010001001", "01010101010001111000010100001001000011010010110000", "10010111111101000100000001111111010001001110110011", "00011101110100100101010111101001100111011011010000", "10011101100111111101000101101101110111101010011100", "11010101011001010100010000100101000001000010100100" }

{"00010101000010011000111110110101100010000011100000", "01000010100011000000110011010011100010010011111111", "10000001111001000001010000000001100000010101100011", "01010001010110001101010011011110010101100111001100", "00001100101010000101001101000111110001001011100000", "10001010000010010101001111011110100010100001110001", "00010100000001001101011010011101010000011001010111", "11011011010110010000100000101110010010101110001101", "10001101111110101101010111101011100101011010011111", "10010011101101101100111011011001010110011010100000", "10000100011000001101100100111101100000100000011101", "10010100101100101001000111011010010011101110110001", "00010011100001010000100100011001000100001101010000", "10010111011010101101010101010111110110001100111011", "00001101010100000101000100001001110111110111001111", "01001100111101111001110000101011000111010111010101", "11001100001100110101111011010011010001010000001011", "10011011100100010100011100010110010110000001001000", "10011100000011100100110010111011110101100010101001", "01001111111111001000100010110010010111111111101101", "00011010111001000000110001110111000000010111111110", "01011001000011010001100001111011110111101100001000", "01000000010100110101000011101110100000011100000000", "01010110000000010101010010101100000001110010110010", "11000000110100000101110011010011100100010101011011", "00011110011011000001000010111100010010100110101000", "01001010101111011001010101001000100101111000111101", "01000101010000101001001100110101100110010110001000", "00010000111100100001101110011000000001100101100000", "10010010001011100101010100101010100101001101110111", "01001111100110001001010010011000010100010110111111", "11001001001110000101000010111011100010100001000011", "11011011000111100101011111000000100111110001110101", "00000011001111010001110000111110010001101111111111", "10011111100110000100000000111010000100100010001110", "01011100011010101100010110111110100111010110011101", "00001010011110111000011110100010110011010110011010", "11010011001010011001000101110110010101101101011011", "11000111101011111000011011100000010010110111000010", "01001001011001101100111111000110110110001000010000" }

Returns: 1
{"00", "01", "10" }

{"00", "01", "11" }

Returns: 1
{"111", "101", "100", "000", "110", "001" }

{"000", "111", "010" }

Returns: 2
{"1111111111111111111111111111111111111111" }

{"1111111111111111111111111111111111111111" }

Returns: 1
{"110", "001", "111" }

{"101", "010" }

Returns: 2
{"111", "110", "100" }

{"000", "010" }

Returns: 2
{"000", "111", "010", "101", "110", "001" }

{"011", "100", "111" }

Returns: 4
{"000", "111", "010", "101", "110" }

{"011", "100" }

Returns: 4
{"110", "001", "000" }

{"101", "010", "011" }

Returns: 1
{"000", "111", "010" }

{"000", "111", "101" }

Returns: 1
{"110", "010", "111" }

{"101", "000", "001" }

Returns: 1
{"0000", "1010", "0101" }

{"0101", "1010" }

Returns: 2
{"000", "010", "001" }

{"000", "001" }

Returns: 2
{"11", "01", "10" }

{"00", "11" }

Returns: 2
{"000", "001", "010" }

{"000", "001", "010" }

Returns: 1
{"000", "111", "010", "101", "110", "001" }

{"011", "100", "101", "110" }

Returns: 2
{"00", "01", "10" }

{"00", "01" }

Returns: 2
{"111", "110", "100" }

{"010", "001" }

Returns: 2
{"00000110001001100101001001000110100111001111000001", "00110101100101111000011010010110101110110011101000", "01011111110110101100010011101101110111000001100010", "01000011000100111100001010101000100000110100111001", "01010101110110101000110101100101100100000110000100", "10110011101001001110010100101000111001111011001011", "10101111001010101000100100101111011010111111110110", "01010111100000000100100110001000010001110101100010", "11101100010101010100001000000010000101110011100000", "00011011000111100010111011010100111111010111011010", "01011110101100100001101110010001100100110010001101", "11000011010111101110010111111000110010110101010111", "11011110001000100110010001100010100010010011000000", "11011010101110011011110101100110000101010001100000", "10000101010000101010101000100110010011111001101110", "11101000010100010001101001100011101110110101011010", "11100100011000111001111100110001011011010010100110", "00001001000110011010011010110010000001011011111100", "01001111010101101101101010011001110001001110101100", "11011110100111001000111001101111001001100010000000", "10000100111110111110010011110000110101110001011100", "10011010110111000100011010100100111001011100011011", "10110001101110111101110010011100000001101001011010", "01011101001110001110010001000001111110000110110100", "11011010101010000101000010001101110110101010111101", "00010001100011101011000110110111010110011110110010", "10011001100011110111111101100010100110110000100100", "10001010101010001010101100010111100100100111000100", "00100001110000000001010011100010101111010011101100", "01111101001011000011010011010110010011101111101110", "10001010100111100000101001101001101100111110000111", "11100001001011000001100011111111001000110010110100", "10100100101000011111110010000100101011001101100111", "11110100011100100000000011100100100001110110110000", "10010000001011010001100011111101101011010001000001", "00100011000010110110111111001000101001110000110001", "00010000001011110101000111110111111100001110101111", "11111110100110111110011011000111100110011010101011", "11101010111101110101000110000111100100011000100011", "01010101110010001101100101100111001011011010100001", "10100011110110010101100100101001010000011101110111", "01010111111001110001111110011001100100100000001000", "11110000110100111001000110100110010111000101110010", "10101000000011000101110100110110000111001100010010", "00011011011010010110111101011010101110000000000011", "11000010111011110001111001100100011100010100100110", "00011010100010011100100010001101101110101011110011", "10011101111101110111101100000111010011111000000110", "01101001011100001010110010111101011001010110010011", "11000101110011010111001101111000011110010010010111" }

{"00101000111010111010000000010000110101110010011001", "00011011010110100111010011000000111100001110110000", "01110001000101110011011010111011100101111100111010", "01101101110111100011000011111110110010001001100001", "01111011000101110111111100110011110110111011011100", "10011101011010010001011101111110101011000110010011", "10000001111001110111101101111001001000000010101110", "01111001010011011011101111011110000011001000111010", "11000010100110001011000001010100010111001110111000", "00110101110100111101110010000010101101101010000010", "01110000011111111110100111000111110110001111010101", "11101101100100110001011110101110100000001000001111", "11110000111011111001011000110100110000101110011000", "11110100011101000100111100110000010111101100111000", "10101011100011110101100001110000000001000100110110", "11000110100111001110100000110101111100001000000010", "11001010101011100110110101100111001001101111111110", "00100111110101000101010011100100010011100110100100", "01100001100110110010100011001111100011110011110100", "11110000010100010111110000111001011011011111011000", "10101010001101100001011010100110100111001100000100", "10110100000100011011010011110010101011100001000011", "10011111011101100010111011001010010011010100000010", "01110011111101010001011000010111101100111011101100", "11110100011001011010001011011011100100010111100101", "00111111010000110100001111100001000100100011101010", "10110111010000101000110100110100110100001101111100", "10100100011001010101100101000001110110011010011100", "00001111000011011110011010110100111101101110110100", "01010011111000011100011010000000000001010010110110", "10100100010100111111100000111111111110000011011111", "11001111111000011110101010101001011010001111101100", "10001010011011000000111011010010111001110000111111", "11011010101111111111001010110010110011001011101000", "10111110111000001110101010101011111001101100011001", "00001101110001101001110110011110111011001101101001", "00111110111000101010001110100001101110110011110111", "11010000010101100001010010010001110100100111110011", "11000100001110101010001111010001110110100101111011", "01111011000001010010101100110001011001100111111001", "10001101000101001010101101111111000010100000101111", "01111001001010101110110111001111110110011101010000", "11011110000111100110001111110000000101111000101010", "10000110110000011010111101100000010101110001001010", "00110101101001001001110100001100111100111101011011", "11101100001000101110110000110010001110101001111110", "00110100010001000011101011011011111100010110101011", "10110011001110101000100101010001000001000101011110", "01000111101111010101111011101011001011101011001011", "11101011000000001000000100101110001100101111001111" }

Returns: 1
{"000", "110", "011" }

{"111", "001" }

Returns: 2
{"00000000000000000000000000000000000000000000000000", "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", "00000000000000000000000000000000000000000000011111", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000000000000000000000100001", "00000000000000000000000000000000000000000000100010", "00000000000000000000000000000000000000000000100011", "00000000000000000000000000000000000000000000100100", "00000000000000000000000000000000000000000000100101", "00000000000000000000000000000000000000000000100110", "00000000000000000000000000000000000000000000100111", "00000000000000000000000000000000000000000000101000", "00000000000000000000000000000000000000000000101001", "00000000000000000000000000000000000000000000101010", "00000000000000000000000000000000000000000000101011", "00000000000000000000000000000000000000000000101100", "00000000000000000000000000000000000000000000101101", "00000000000000000000000000000000000000000000101110", "00000000000000000000000000000000000000000000101111", "00000000000000000000000000000000000000000000110000", "00000000000000000000000000000000000000000000110001" }

{"00000000000000000000000000000000000000000000000000", "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", "00000000000000000000000000000000000000000000011111", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000000000000000000000100001", "00000000000000000000000000000000000000000000100010", "00000000000000000000000000000000000000000000100011", "00000000000000000000000000000000000000000000100100", "00000000000000000000000000000000000000000000100101", "00000000000000000000000000000000000000000000100110", "00000000000000000000000000000000000000000000100111", "00000000000000000000000000000000000000000000101000", "00000000000000000000000000000000000000000000101001", "00000000000000000000000000000000000000000000101010", "00000000000000000000000000000000000000000000101011", "00000000000000000000000000000000000000000000101100", "00000000000000000000000000000000000000000000101101", "00000000000000000000000000000000000000000000101110", "00000000000000000000000000000000000000000000101111", "00000000000000000000000000000000000000000000110000", "00000000000000000000000000000000000000000000110001" }

Returns: 2
{"00", "01", "10" }

{"11", "10" }

Returns: 2
{"000", "111", "010" }

{"000", "111" }

Returns: 2
{"001", "010", "110" }

{"101", "001", "010" }

Returns: 1
{"0000001111111111111111111111111111111111", "1000001111111111111111111111111111111111" }

{"0111111111111111111111111111111111111111", "1111111111111111111111111111111111111111" }

Returns: 2
{"000", "110", "111" }

{"000", "001" }

Returns: 2
{"000", "111", "010", "101", "110", "001", "011" }

{"011", "100" }

Returns: 6
{"001", "010", "111", "101" }

{"100", "110" }

Returns: 2
{"111111111111111111111111111111111111111" }

{"111111111111111111111111111111111111111" }

Returns: 1
{"110", "001", "010" }

{"101", "010" }

Returns: 2
{"01", "00", "10" }

{"10", "11" }

Returns: 2
{"010", "100", "001" }

{"010", "100", "001" }

Returns: 1
{"0" }

{"0" }

Returns: 1
{"1111", "0000", "0001" }

{"0000", "0001" }

Returns: 2
{"00", "01", "11" }

{"11", "10" }

Returns: 2
{"1000", "1001", "1010", "1100" }

{"1000", "1001" }

Returns: 2
{"00", "01", "11" }

{"00", "01", "11" }

Returns: 1
{"000", "111", "010", "101", "110", "100" }

{"011", "100" }

Returns: 4
{"11111111111111111111111111111111111111111111111111" }

{"11111111111111111111111111111111111111111111111111" }

Returns: 1
{"100", "010", "000" }

{"011", "101", "111" }

Returns: 1
{"000", "111", "110" }

{"100", "011", "010" }

Returns: 1
{"110101110101110101110101", "111111111111111111111111" }

{"100010100010100010100010", "101000101000101000101000" }

Returns: 2
{"11111111111111111111111111111111111111111111111111", "00000000000000000000000000000000000000000000000000" }

{"11111111111111111111111111111111111111111111111111" }

Returns: 2
{"000", "111", "010", "101", "110", "001", "100" }

{"011", "100" }

Returns: 6
{"000", "100", "010" }

{"001", "101" }

Returns: 2
{"00", "11", "01" }

{"00", "11" }

Returns: 2
{"10000000000000000000000000000000000000000000000000", "01000000000000000000000000000000000000000000000000" }

{"11000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000" }

Returns: 2
{"000", "101", "100", "111" }

{"110", "011", "010", "001" }

Returns: 1
{"111", "010", "011" }

{"111", "010" }

Returns: 2
{"11111111111111111111111111111111111111111111111", "10000000000000000000000000000000000000000000000", "11101111111111111111111111111111111111111111111" }

{"00000000000000000000000000000000000000000000000" }

Returns: 3
{"00", "01", "10" }

{"01", "10" }

Returns: 2
{"00101", "11110", "10110" }

{"10110", "01101", "00101" }

Returns: 1
{"10101010101010101010101010101010101010101010101010", "01010101010101010101010101010101010101010101010101", "01010101010101010101010101010101010101010101010100" }

{"00000000000000000000000000000000000000000000000000", "11111111111111111111111111111111111111111111111111" }

Returns: 2
{"10001110110000110000000001000011000100001110001011", "11101011010100100010011111110001100100101001110011", "00110001000101110010110010010110001010010011011001", "01110100100011100110001111001011110011010011110101", "11110000111111011101011001110010011000001011111110", "11101001010010101101111011010110011010010111110111", "11001101100000101011110111100110001100001010100111", "01010010100110000010001111111010011110001010100110", "10110100110101111111111100001101101011001110101111", "00011001011011100111100011000001001010000110010001", "00101101101011110010101001001010111010111101010110", "11111111001000111011110100110111011000100111101000", "00111001111100001001011100100011110010000001111011", "11111010001101000011001111011000000101111111100001", "01011100100110100101110100000010100010111001011011", "00110010101111100000001100010100000011011111100100", "10011000111101111101110001101010011011100000001010", "10111001100010010000011111101011101000100010001101", "00111110101100011101010010010011000010011011110110", "10100010101111101000100110001001001000111010010101", "10101011011001111111100111000000010101001000011100", "10001011010100011111010101000110010101011110010111", "01111100001111000100001010111010110111011101101010", "00001010111000111110010110100100010011010100010001", "10001000010101011011100101001110000000100111011000", "10111011010110000000101101100100101000000010011000", "11100111101101000011111001010000001101001010010110", "10110111011110010111111100100110100101100001110101", "10001001111001110001110010001111101101101111101100", "01000111011111101010101000111011000001011011000101", "00000101111110100101101110001011100111110100001110", "01010101011111111000001111110000110010000110010100", "01001001000101100010001101011010111001000010100110", "00100010001001000010110110000000111010111011111011", "11101001101101011101011101001001110101111011001010", "11111010111110010101010000000101010011100000011000", "01101100110001001010010111101001010010010111011001", "10101100110110101111000100111110100010010111010100", "01100000001110101001111100110011010010100011001010", "00101100000000011100000111011011111001111010111000", "11001111110011110001010000110101110011000001100010", "01000011001000011111010100000011101100110000010010", "01100111000000110101011010110011100110000000011011", "11101100101110111011000010011111110011000110111001", "01110101011000010000110100100010100100001010100100", "01001110100001000101010010111001001011011000000011", "10000110110010010011011011010101101100100110110100", "11101000001010110000000110110000011101111000011111", "10010110110001111101001011000010100100110100000100", "00100011110101001001111100111101110000010011001011" }

{"01110100100011100110001111001011110011010011110101", "01000111011111101010101000111011000001011011000101" }

Returns: 2
{"000", "111", "001" }

{"000", "111" }

Returns: 2
{"110", "001", "010" }

{"001", "110", "101" }

Returns: 1
{"01", "10", "11" }

{"00", "11" }

Returns: 2
{"0011", "0101" }

{"1100", "1010" }

Returns: 2
{"01110101000100010001110010111110011111011001011101", "11100000010001010010001001000110101111001001011101", "10110111100011001101111011010110101010101001100000", "00010011011010110000110110001111011001100110111110", "11101010010010001010101111001101100110100010100110", "11001100001111000100011110110110100011110010011101", "11100001001100001111010000001100101111011001100001", "11001101101011010010101011101011010010001101110111", "11001110011111100001110000101011100100111100010000", "00110010001001101110101110110111010010011011011111", "10111110001100010101010010001110101000010010100011", "11001101010111100110000001000001001000001101110011", "10100011010001011000110010101010101100000001111100", "11000011001111101111010100001100110100000010000111", "00100000100000100011110011010111100101111010110110", "10100100000001111110101001111100011001110101011000", "00100010000011100101111101011101101000100110110011", "01010110110100100001000100101000111111100011011101", "11100110101100101000011110110010100001110110000000", "01010101001010101111101100001110000111000111010110", "11010000000010010010010001111000101001111001001110", "01100000000101001010111101110110111111011001101111", "00111011110010011111101110100111001011100101001001", "11011010000011001101000111100011101100010100100110", "01011111010111010010010001011000010101011000100011", "10101010111111011010000111110100011110000110010100", "10011110011101001000110001101010001111010000110011", "10101101001111110000011010110100100010110001101001", "00101001110000101001101000101100001010110010110000", "00001110000011000011101111101101001100011000010001", "10010000000101000001011100011110011011000001001100", "10111101000111101010101110111010010100100100100011", "00110101110110000110101101010000011101010010100000", "00011001010111111111011001111001111001000100110001", "10110100111111011111010000110101000010010110111010", "00101111011101101000000110110111110100010001000010", "01010100111101111111010000100001011101001110001100", "00100100010010111101100110001100011001000000100100", "00101110001111010011001100111100110010000010111110", "10100000110100010101001010101101100001000111001000", "00110010011001100101010000010110110100011001101101", "01110011110110011101011011011110101010011011000010", "00100011001000000000110110101110110010000001110101", "11011101111101010100101110110001100110000101001011", "11011100001011011011011101010111110111001110011010", "00010111010100010011110100110110011010000110110001", "10001111000100100001011111101100111001000111111101", "01010110011000111100011111110100100000000000111000", "10001001110100100111001100100000000111111010110111", "00101111101100011111110001100011111000100010000110" }

{"01101010001101110000110011111110011110011110010010", "11111111011000110011001000000110101110001110010010", "10101000101010101100111010010110101011101110101111", "00001100010011010001110111001111011000100001110001", "11110101011011101011101110001101100111100101101001", "11010011000110100101011111110110100010110101010010", "11111110000101101110010001001100101110011110101110", "11010010100010110011101010101011010011001010111000", "11010001010110000000110001101011100101111011011111", "00101101000000001111101111110111010011011100010000", "10100001000101110100010011001110101001010101101100", "11010010011110000111000000000001001001001010111100", "10111100011000111001110011101010101101000110110011", "11011100000110001110010101001100110101000101001000", "00111111101001000010110010010111100100111101111001", "10111011001000011111101000111100011000110010010111", "00111101001010000100111100011101101001100001111100", "01001001111101000000000101101000111110100100010010", "11111001100101001001011111110010100000110001001111", "01001010000011001110101101001110000110000000011001", "11001111001011110011010000111000101000111110000001", "01111111001100101011111100110110111110011110100000", "00100100111011111110101111100111001010100010000110", "11000101001010101100000110100011101101010011101001", "01000000011110110011010000011000010100011111101100", "10110101110110111011000110110100011111000001011011", "10000001010100101001110000101010001110010111111100", "10110010000110010001011011110100100011110110100110", "00110110111001001000101001101100001011110101111111", "00010001001010100010101110101101001101011111011110", "10001111001100100000011101011110011010000110000011", "10100010001110001011101111111010010101100011101100", "00101010111111100111101100010000011100010101101111", "00000110011110011110011000111001111000000011111110", "10101011110110111110010001110101000011010001110101", "00110000010100001001000111110111110101010110001101", "01001011110100011110010001100001011100001001000011", "00111011011011011100100111001100011000000111101011", "00110001000110110010001101111100110011000101110001", "10111111111101110100001011101101100000000000000111", "00101101010000000100010001010110110101011110100010", "01101100111111111100011010011110101011011100001101", "00111100000001100001110111101110110011000110111010", "11000010110100110101101111110001100111000010000100", "11000011000010111010011100010111110110001001010101", "00001000011101110010110101110110011011000001111110", "10010000001101000000011110101100111000000000110010", "01001001010001011101011110110100100001000111110111", "10010110111101000110001101100000000110111101111000", "00110000100101111110110000100011111001100101001001" }

Returns: 1
{"000", "111", "100" }

{"000", "111", "100" }

Returns: 1
{"00", "01", "10" }

{"10", "01" }

Returns: 2
{"10111100110101100000101100011110001110101111010010", "10100100011101010111010101001010000011010000100001", "10001110100010011101011111111110110101100101110001", "01010101111000101000001011111001101101011111001101", "00111000000011100101010100110010001110010011000010", "11100100000100000100000110011110100111101110010000", "00000110101000110001011011111011011010000001010000", "00110100010000111001001110010010111101100100000100", "01000000101110001001000110111110010010110001000100", "00011110010110111010110110111110011110011010001100", "10011111010110000100100000000001001010111100010001", "01101101100000010011111011101111101011010010011110", "01111100111000011111011111100001100011000001000111", "00011110111000011101101110101010001010010110011101", "01000101111110110010110000111111011001101110101101", "10010010001100010010001100101010010001000010011010", "00011111101011111100100000100101110000110011100101", "11110011010001110111010111010001100101101101100111", "00101001101001000001011000011001010110110010111011", "11001000110010111110011100010100000101100101110101", "10101111010010000011011010011011101010010011111110", "00010100011100100000101000111101101111010111101111", "00011010101110100010001110101011110011011001001001", "00111011011100110001101011000010100001100101110010", "11001111011100001010101111011110000111011011011110", "00011101011011011111101010101001111001011110010101", "11101000001010100000111010111100111011111001011011", "10000001101000110111001011010101011010000100100111", "11100100001011100000101110111000011001001110100111", "10101001111101111101011110111000000000101011000100", "10101000011011011110101001100111101011010111100011", "10000011010111001100001100101000000101000101000010", "01010000110111110100101100100000101011000011100110", "00110111110111111001010101111011100110001011010110", "10111001111000111010100010110101110010100110101100", "11110001000011110111110000011100011011011010011001", "11000000011010100000011101011000010010011010001011", "11000011001001111110010010000111001100000111100011", "00000000010000001001111000000011001000001001101010", "00110110110000000001111100001101110101110011001101", "01011001010001100111011000011001000110011001111110", "01001001010000101011101100111001101101000010001100", "01011010000001010011111000011010111001001001001000", "11111111001101101110100100111110101000001101011000", "01100111000101100100011010100110000011111100110110", "11001100101001011100001000001100001111110010101010", "00010000011001110001101110100000000100101111000101", "00101000110111010011110001010000010101110001101110", "00110000100101010000100011000110101101111000111111", "11111001101010000101011110000111001111100001001011" }

{"10111100110101100000101100011110001110101111010010", "10100100011101010111010101001010000011010000100001", "10001110100010011101011111111110110101100101110001", "01010101111000101000001011111001101101011111001101", "00111000000011100101010100110010001110010011000010", "11100100000100000100000110011110100111101110010000", "00000110101000110001011011111011011010000001010000", "00110100010000111001001110010010111101100100000100", "01000000101110001001000110111110010010110001000100", "00011110010110111010110110111110011110011010001100", "10011111010110000100100000000001001010111100010001", "01101101100000010011111011101111101011010010011110", "01111100111000011111011111100001100011000001000111", "00011110111000011101101110101010001010010110011101", "01000101111110110010110000111111011001101110101101", "10010010001100010010001100101010010001000010011010", "00011111101011111100100000100101110000110011100101", "11110011010001110111010111010001100101101101100111", "00101001101001000001011000011001010110110010111011", "11001000110010111110011100010100000101100101110101", "10101111010010000011011010011011101010010011111110", "00010100011100100000101000111101101111010111101111", "00011010101110100010001110101011110011011001001001", "00111011011100110001101011000010100001100101110010", "11001111011100001010101111011110000111011011011110", "00011101011011011111101010101001111001011110010101", "11101000001010100000111010111100111011111001011011", "10000001101000110111001011010101011010000100100111", "11100100001011100000101110111000011001001110100111", "10101001111101111101011110111000000000101011000100", "10101000011011011110101001100111101011010111100011", "10000011010111001100001100101000000101000101000010", "01010000110111110100101100100000101011000011100110", "00110111110111111001010101111011100110001011010110", "10111001111000111010100010110101110010100110101100", "11110001000011110111110000011100011011011010011001", "11000000011010100000011101011000010010011010001011", "11000011001001111110010010000111001100000111100011", "00000000010000001001111000000011001000001001101010", "00110110110000000001111100001101110101110011001101", "01011001010001100111011000011001000110011001111110", "01001001010000101011101100111001101101000010001100", "01011010000001010011111000011010111001001001001000", "11111111001101101110100100111110101000001101011000", "01100111000101100100011010100110000011111100110110", "11001100101001011100001000001100001111110010101010", "00010000011001110001101110100000000100101111000101", "00101000110111010011110001010000010101110001101110", "00110000100101010000100011000110101101111000111111", "11111001101010000101011110000111001111100001001011" }

Returns: 1

Statistics

Problem Statement for "NetworkXOneTimePad"

Problem Statement

Definition

Notes

Constraints

Examples