Statistics

Problem Statement

NOTE: This problem statement contains images that may not display properly if viewed outside of the applet.

"Twisted Matrix" is a strange game in which you are given a binary matrix (containing only '1' or '0') and must perform a series of twist operations in order to reach a certain goal matrix. A twist operation involves taking any 2x2 block inside the matrix and then rotating the elements within the block 90 degrees clockwise or counterclockwise.
The following image shows two consecutive twist operations performed on a initial matrix.


Little Johnny has won the first prize in a world wide Twisted Matrix tournament. Unfortunately, his friends do not believe him. The situation is not helped by the fact that little Johnny has a very bad memory and cannot clearly remember the last move he made in order to reach the goal matrix in the finals. He only partially remembers the last two matrices in the game. You are given matrices A and B. Each matrix is given as String[], the j-th character of the i-th element of each String[] describes the cell at row i, column j of the matrix. Each cell contains '0' or '1' if little Johnny remembers the number in that cell or '?' otherwise. Matrix B was the last matrix in the game and A was the matrix preceeding it, which means that performing one twist operation on A must transform it into B. Return a String[] representing the complete contents of the matrix B. If there are many valid solutions then return the lexicographically first solution. If no solution is possible then return an empty String[].

Definition

Class:

TwistedMatrix

Method:

solve

Parameters:

String[], String[]

Returns:

String[]

Method signature:

String[] solve(String[] A, String[] B)

(be sure your method is public)

Notes

• The lexicographically first of two matrices is the one with the lexicographically earlier row at the first row at which they differ.
• The lexicographically first of two rows is the one with the smaller cell at the first column at which they differ.

Constraints

• A and B will each contain N elements, where N is between 2 and 30, inclusive.
• Each element of A and B will contain M characters, where M is between 2 and 30, inclusive.
• Each character in each element of A and B will be '1', '0' or '?'.

Examples

1. {"1000", "0000", "0000", "0000"}

   {"0000", "?000", "0000", "0000"}

   Returns: {"0000", "1000", "0000", "0000" }

2. {"11", "01"}

   {"??", "??"}

   Returns: {"01", "11" }

   Another possibility is {"11","10"} but {"01","11"} comes earlier lexicographically.

3. {"000", "0?0", "000"}

   {"111", "1?1", "111"}

   Returns: { }

4. {"?1111", "11111", "11011", "10111"}

   {"?1111", "11111", "1??11", "1??11"}

   Returns: {"01111", "11111", "10011", "11111" }

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

   {"??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????"}

   Returns: {"000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000" }

6. {"?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?"}

   {"1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1"}

   Returns: { }

7. {"?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?"}

   {"?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?", "?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1", "1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?"}

   Returns: { }

8. {"?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?"}

   {"?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?", "?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0", "0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?"}

   Returns: {"000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000010000000000000000", "000000000000001000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000" }

9. {"101010100101001111100000000110", "001011001001000110001101011111", "000100101111010000000101111011", "000111110011100110101011011110", "011101010010101001000000001000", "101101000010101100101010011001", "010000000001000010100100000110", "111111101010011010011111011101", "101111010110010000010001011000", "001101111111010101110110110011", "011000100110110011111001110010", "111100011001001101010101001111", "101011000000111111010010110101", "101100001011110110101100010000", "101110101011001000100011000010", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????"}

   {"??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "000111110011111011110100111111", "010100011000001111000001011101", "110101111011001010110010111110", "010010100101100000011111110000", "000110001011110111010111001101", "011000000100001111100100001001", "100010100110111111111011110111", "101001111101101111111001101110", "000100000010000010110100010101", "111111100110111001001100000011", "000011101001000000001110000100", "011100010011101101000010000111", "111000100011100101011010011000", "001010010010111100001011001111", "101010000100000010010011111111"}

   Returns: {"001010100101001111100000000110", "101011001001000110001101011111", "000100101111010000000101111011", "000111110011100110101011011110", "011101010010101001000000001000", "101101000010101100101010011001", "010000000001000010100100000110", "111111101010011010011111011101", "101111010110010000010001011000", "001101111111010101110110110011", "011000100110110011111001110010", "111100011001001101010101001111", "101011000000111111010010110101", "101100001011110110101100010000", "101110101011001000100011000010", "000111110011111011110100111111", "010100011000001111000001011101", "110101111011001010110010111110", "010010100101100000011111110000", "000110001011110111010111001101", "011000000100001111100100001001", "100010100110111111111011110111", "101001111101101111111001101110", "000100000010000010110100010101", "111111100110111001001100000011", "000011101001000000001110000100", "011100010011101101000010000111", "111000100011100101011010011000", "001010010010111100001011001111", "101010000100000010010011111111" }

10. {"0000?0000101010011100","101??1?1010000000?111","01??101?0011101100101","0000100?1010?0?110100","10100110100010??00?1?","1?1000?11111010001?1?","1111?00010010010?0100","110101111001101001010","?001111001??100101010","11?011010?01?10111110","0?11?1011001010100010","00010?0111010100??011","0001111110011?00101?0"}

    {"000000000101010011100","?01110010100000000111","0111?111?01?101100101","0?0010001010000?10100","10100?101000100000011","11100011111101??01111","1111?0??10?1?01?00100","11010?111001101001010","100?111001001001?1010","11001101010?110?11110","011101011001010?00010","0?01?1011101010000011","000111111?011?00101?0"}

    Returns: {"000000000101010011100", "101110010100000000111", "011101110011101100101", "000010001010000110100", "101001101000100000011", "111000111111010001111", "111100001001001000100", "110101111001101001010", "100111100100100101010", "110011010101110111110", "011101011001010100010", "000101011101010000011", "000111111001100010100" }

11. {"101110110011100111111111?0111","00100111?1011?011011001011100","00110101?0001?1?0110110111101","01?01000000100?00111111001011","011?110?00011101110000110?0?0","00101001000111110111111110011","101011001111111100100?011?000","11111??1111010111101??10?0?11","111?1001101100?011?1?10110011","0?11111100101100000?11?1?1100","1010001110?100110110100010100","10?1001?00000?00111?011011010","11111?1?000?10010011110?01110","00111011000010011100001001?10"}

    {"?01110110?1?10011111111110?11","00100?1101?1110?1011001011100","0011010??000101?0110?10?111?1","0100100000?10000011111?001011","0???1101000111?1110?001100000","0?1?1001000111?10111111110011","10101100?11?1111001001?11000?","?11111111110101111010?100011?","11?11001101?00001111010110011","0111111100101?00?0001111?1100","?010001110010011011?100010100","101?0011?0000?00?111011011010","111111?000001?010011110001110","00111011000?10011100001001110"}

    Returns: {"10111011001110011111111110111", "00100111010111011011001011100", "00110100100010100110110111101", "01001000000100000111111001011", "01101101000111011100001100000", "00101001000111110111111110011", "10101100111111110010010110000", "11111111111010111101001000111", "11111001101100001111010110011", "01111111001011000000111101100", "10100011100100110110100010100", "10110011000000001111011011010", "11111110000010010011110001110", "00111011000010011100001001110" }

12. {"011000100","001100?00","0??110011","01??00?10"}

    {"0110001?0","00?1?0100","000110011","010001010"}

    Returns: {"011000100", "001100100", "000110011", "010001010" }

13. {"0110?0001?110","0101?00110101"}

    {"010000?010110","01?1000110101"}

    Returns: {"0100000010110", "0111000110101" }

14. {"00011?01010?01001","???0110?101001110","000100010110?000?","0?00?110?00?010?1","0100000110?01000?","0101100?0100101?0","1011000001110?100","110010101?0001111","111001?011111101?","00000010101001?10","100100110110?1?11","0?0110001?0000?01","10110101000000010","010?1100101000101"}

    {"0001100101010100?","00101?01101001?10","00010001?110100?1","00?01110000?01011","01000001?000100?0","0?0110000100??100","1011000010110?10?","110??010110001111","1110010011?111010","000000101010011?0","10010?11?11011111","0?01100010000000?","10110101000000?10","010111001010001??"}

    Returns: {"00011001010101001", "00101101101001110", "00010001011010001", "00001110000001011", "01000001100010000", "01011000010010100", "10110000101100100", "11001010110001111", "11100100111111010", "00000010101001110", "10010011011011111", "00011000100000001", "10110101000000010", "01011100101000101" }

15. {"?1","00","11","01","10","??","0?","01","00","00","00","10","01","1?","10","?0","?0","?1","00","?0","0?","01"}

    {"11","00","11","01","?0","11","00","01","00","00","00","10","0?","10","10","00","0?","01","00","10","01","?0"}

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

16. {"0101001?1?01?1110110111010010","011100??0110110100001001?1100","10011110101010000100010001100","110?1110110001001000000?10000","00?0101000011?100101101011001","0111101?111?1?1011?0111010011"}

    {"0101?01111011?1101101??010010","0111000?011011010000100?01100","10?11110101010000100010001?0?","110011?011000100100000001?0?0","00?10010000110100101101011001","01111??0111010101110111010?11"}

    Returns: {"01010011110111110110111010010", "01110000011011010000100101100", "10011110101010000100010001100", "11001110110001001000000010000", "00010010000110100101101011001", "01111010111010101110111010011" }

17. {"101111?0?0001000110","110011?010?11010?11"}

    {"10111?1?10001000010","110011001011??10111"}

    Returns: {"1011111010001000010", "1100110010111010111" }

18. {"?011100?00111111111101111??","1?001?10100001011001000001?","0100001101?00000000101010?1","00?100101011110000000110001","1000101101000010100?0000111"}

    {"00?1?01000111111111?0111110","100??00110000101100100000?0","0?000011011000??00?10101001","00010?1010111100000001?0001","1000101101?0001010010000111"}

    Returns: {"001110100011111111110111110", "100010011000010110010000010", "010000110110000000010101001", "000100101011110000000110001", "100010110100001010010000111" }

19. {"111111010?1101?0010","0111??00010?1100000"}

    {"11?11001?0110110010","0111100?01001100000"}

    Returns: {"1111100100110110010", "0111100001001100000" }

20. {"0000?100111111","0110100110?001","1001111011?111","0111110111000?","11000010110111","10101?110?0100","10?000110111?1","11110101000000","10000000010100","?0?1?111001?10","0010100111100?","101?010010000?","0??100?1010100","10111?01111101","11110110011000","1001100100111?","11100010100000","10010?11?01?00","010000?10?1011","101?000010110?","1100000010100?","001001?0010011","10001000011101","1??10000010?01","01111001001101"}

    {"0?00010011?11?","?1?010011?1001","1001?110110111","?1?11101110000","110?0010110111","1010111100?1?0","?0000011011111","11110101000000","1?000000010100","100111?1001110","001????11110?0","101?0?00100001","00010011010100","1?11?001111101","11110110011000","10011001001111","1??00010100000","1001011?001100","01?00001000111","101100001?1100","1?000000101000","001?01100100?1","10001000011101","?111??00?10001","01111001001?01"}

    Returns: {"00000100111111", "01101001101001", "10011110110111", "01111101110000", "11000010110111", "10101111000100", "10000011011111", "11110101000000", "10000000010100", "10011111001110", "00101001111000", "10100100100001", "00010011010100", "10111001111101", "11110110011000", "10011001001111", "11100010100000", "10010111001100", "01000001000111", "10110000101100", "11000000101000", "00100110010011", "10001000011101", "11110000010001", "01111001001101" }

21. {"00011000110100","0110001001?111","000100?0011100","10111?11100111","00?00110001110","100?100?110100","01?00101111010","10100101011101","11010010?11110","01010101??1111","01100101010110","00?11011001101","?001?11010100?","0111??00101111","?0001000111101","001100?1011?0?","111101101?0110","1010000??0111?","00111110000011","11010110?00001","0110?000110010","11010100000?10"}

    {"00011000110100","?110001?0?011?","0?010010011100","10111111100111","?00??110001110","100010?0110100","01000101111010","10100101011101","110100100?1110","0101010110111?","0110010?0?0110","001110?1001?0?","1001110110100?","0111000010?111","?0001000111101","001?00010?1000","111101101101??","10100000101111","00?11110000011","1?01011000?001","011000?0?10?10","??010100000010"}

    Returns: {"00011000110100", "01100010010111", "00010010011100", "10111111100111", "00000110001110", "10001000110100", "01000101111010", "10100101011101", "11010010011110", "01010101101111", "01100101010110", "00111011001101", "10011101101000", "01110000101111", "00001000111101", "00110001011000", "11110110110110", "10100000101111", "00111110000011", "11010110000001", "01100000110010", "11010100000010" }

22. {"10","00","01","00","10","01","10","11","11","10","1?","?0","10"}

    {"?0","00","01","00","10","01","10","11","11","10","10","00","01"}

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

23. {"?1101?001?010010?00011101001","01110110101?11111100101?11?1","00010010?1?11101111011000111","000010111?0?0001000?001?0011","00000?11110001000001??1101?0","011100001110101001?001101010","0001110010001101101000101101","111?1?1100101??1??000001?1?1","0?00001001101001010101011100","100110000101001?001110001001","00010111010?11111010?01010?0","110011?101?000?100?0011??000","1110101100100101011?1?00?111","11101000010100001?1001001?10","0110011010??111010110110?10?","01010001100001?01011?101101?","00100?1111100110111110011?01","1110100?1100111100000001?100","?001001100010?0?100001000111","0001011100001001111111001110","000011101100011?010?11000011","0?0?1?001001110100101??00111","0001110001001?11??0000?01?00","00101?111111000?0011?01?1110","0011110?110?001100?1?0110110","001111110110??000110?01?11?0","0111010111101??01100?0110011"}

    {"111010001001001010001110?001","011101101011111111??10101111","00?10?1?11111?011?101?000?11","0000101110010?01000100110011","0?00011111000100000100110100","01110000111??010011001101010","000111001000110110100010?101","11111011001?1011??00000111?1","0100?0100?101001010?010?1100","1001100??10100110?11?0001001","0001?1110101111?1010001?1010","1100?10101100011000001110000","?11010?100?0010?011010001111","1110100001?10000111001?01010","01?00?1010111?1010110110??00","?101000110?001001011?1011011","0010011??1100110111?10011?01","11101001110011110000000?010?","1001?011000101001000??0?0111","00?1011?00001001111111001110","00001110110001110?0?11000011","0001100010011101?0?011100111","0?011100?10010?1110?0?0??000","?010111?11110001001100111110","?01111001?01001100??1011011?","?01111110110110001100011?100","01?101011110111011000?110011"}

    Returns: {"1110100010010010100011101001", "0111011010111111110010101111", "0001001011111001111011000111", "0000101110010101000100110011", "0000011111000100000100110100", "0111000011101010011001101010", "0001110010001101101000101101", "1111101100101011000000011101", "0100001001101001010101011100", "1001100001010011001110001001", "0001011101011111101000101010", "1100110101100011000001110000", "1110101100100101011010001111", "1110100001010000111001001010", "0110011010111110101101100100", "0101000110000100101101011011", "0010011111100110111110011001", "1110100111001111000000010100", "1001001100010100100001000111", "0001011100001001111111001110", "0000111011000111010011000011", "0001100010011101001011100111", "0001110001001011110000001000", "0010111111110001001100111110", "0011110011010011000110110110", "0011111101101100011000111100", "0111010111101110110000110011" }

24. {"101?01?11?1001??01101","011111001?0??01001111","0000010111?11101?1000","101010111100?0000?001","?1111?0000??101100001","011001?00?1000101?100"}

    {"10100?0110100111?1101","011111001000001001111","00000101111?110001000","101?10?1110010?101001","0?1110000010101100001","0110?10?0110001011100"}

    Returns: {"101001011010011101101", "011111001000001001111", "000001011111110001000", "101010111100100101001", "011110000010101100001", "011001000110001011100" }

25. {"11?10110?10000","0011?11?1?1111","01101111011010","11110100110100","101?00101101?1","10110?0?01?100","00?00?00011101","0110000?001111","000?1?0111?100","01?10000111010","?01?0110?0100?","11011010100110","1011?0001??101","0110010?101000","?011011?010100","11100101100110"}

    {"111101100?0?00","001101101111??","01?0111?011010","11110100110100","?01000?011?111","1?11010?01?100","00000?0?0?0101","01100001001111","00011?01110100","?10100?0111010","001001101010?0","1101?0101??110","10111000?0110?","011001001010?0","101101?0010100","?11?0101100110"}

    Returns: {"11110110010000", "00110110111111", "01101111011010", "11110100110100", "10100010110111", "10110100011100", "00000000010101", "01100001001111", "00011001110100", "01010000111010", "00100110101000", "11011010100110", "10111000101101", "01100100101000", "10110110010100", "11100101100110" }

26. {"00110","01100","??000","01?10","01001","011?0","11101","10101","1?1?0","10011","?01?1","1?101","01010","10110","11100","11110","001?0","01100","11000","00111","0101?","11101","10100","11111","10110","00001","0?000"}

    {"00110","?0100","01000","01?10","01001","01110","11?01","1?101","10?10","?0011","1?101","10101","0101?","10110","11100","11110","?01?0","?1100","11?00","00111","?1011","11101","10100","1111?","10110","00001","00000"}

    Returns: {"00110", "00100", "01000", "01010", "01001", "01110", "11101", "10101", "10110", "10011", "10101", "10101", "01010", "10110", "11100", "11110", "00100", "01100", "11000", "00111", "01011", "11101", "10100", "11111", "10110", "00001", "00000" }

27. {"110?100001100010001100010","?1?000100111?101110011001","11001?110001?111?00101001","01?10?1000100001001?10001","?0000001010?1001?000?000?","11000?00100?1?10110001111","110?0111?0011100001110100","1?111?10100100110001010?1","0001110101110010011011001","0110?10011100??111?10001?","0011011100100111101010000","1100111100110111000111000","0000111101111011000010110","101001100010??01100100000","110??01110010011000011010","0111111001011110110110101","0011110111110?0001?111110","1011001?000101?0011111001","1010??0011000001111100111","0000?10010001?000000010??","0011101000100?001?0001011","0101101110?0100?101110011"}

    {"110110?001100010001100010","1110001001110101110?1100?","1100111100011111000101001","01010110001?0001001?10001","0?00000101001??11?00?0001","11?00?0010011110110001111","1011011110011100001110100","11011?10100100110001010?1","0001110101110010?11011001","0110110011?00?0?1?1?0001?","00??01110?1001111010100?0","1100?11100110??100011?0?0","00001?1101?11011?00010110","1010?11000?0?101100100000","1101101110010011?0?01101?","??11111001?1?110110110101","001111011111010???01?1110","10?10011??010100011?11001","1010010011000001111100111","0000010010001000000001?10","00?110100010000?110001011","010110?110001??11011?0011"}

    Returns: {"1101100001100010001100010", "1110001001110101110011001", "1100111100011111000101001", "0101011000100001001010001", "0000000101001001100000001", "1100000010011110110001111", "1011011110011100001110100", "1101101010010011000101001", "0001110101110010011011001", "0110110011100001111100010", "0011011100100111101010000", "1100111100110111000111000", "0000111101111011000010110", "1010011000100101100100000", "1101101110010011000011010", "0111111001011110110110101", "0011110111110100010111110", "1011001100010100011111001", "1010010011000001111100111", "0000010010001000000001010", "0011101000100000110001011", "0101101110001001101110011" }

28. {"00","?0","00","00","?0","10"}

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

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

29. {"00?01111101","11101011000","110111?101?","0100001111?","00110000000","1011001?000","00111000111","1100100?1?1","10000000011","00101100010","01001000110","11001110101","00101110011","10001010100","0?110011100","11?11010101","0?000?01111","11101111011","?1101101110","10100000110","001011?1000","100111000?1","00?01111100","00111100110","1000100?010","0?0000010?0"}

    {"0010?111001","111?1011100","11011???0?0","01000011110","00110000000","10110??1000","00?11000111","1?0?10011?1","1000?000011","00101100010","?1001000110","11?01110?01","?01011?0011","100?101?100","?0110?1?100","11011010101","0000010?111","11101111011","0110?101110","1010000?110","001?1111000","100111?0?11","00101111100","001111?0110","10001000010","00000001000"}

    Returns: {"00101111001", "11101011100", "11011101010", "01000011110", "00110000000", "10110011000", "00111000111", "11001001101", "10000000011", "00101100010", "01001000110", "11001110101", "00101110011", "10001010100", "00110011100", "11011010101", "00000101111", "11101111011", "01101101110", "10100000110", "00101111000", "10011100011", "00101111100", "00111100110", "10001000010", "00000001000" }

30. {"111101??00111?00111","1001001001?011?10??","0001?10011010011010","0000?111?001011?1?0","?100??1011?0?10???1","0?100?1000011?01101","1??0???000110100110","0001111010110110011","01101110010101?10?0","00?011101?1?0?00001"}

    {"11110111001?1?0?111","1001001001??11?10?1","00???10011??00?10?0","000??11100010110110","?1001110??011101111","??1?0??00000100?101","1010???00?11?100?10","0?0111101011????0?1","01101110?1010?11??0","0?101110?111000?0?1"}

    Returns: {"1111011100111000111", "1001001001001101001", "0001010011010011010", "0000011100010110110", "0100111011011101111", "0010001000001001101", "1010000000110100110", "0001111010110110011", "0110111001010111000", "0010111011110000001" }

31. {"01001?0100100??00111??00???0","111?01?11100?0010101?0?110?1","00?11??01?0??00111?0001?0001","0011110010??010011?1?1101???","10????00?001?01000010?010100","0?00111001?11?1???1110?10111","1??1?11010000??1?000??0?0101","10??100111001101010110?00100","1?01001?0??1?101?1?1011111?1","?00?1111000?0011001?11?1?010","11010?1111010110110111110101","0101?101100101111?100??11?11","000??01001000101?1?1?0101???","00?11?00100?01111??10?0011?1","11100?000110001?110?10101010","0?1??11101101?1?1?11??111011","111001?1111??110101010110111","100?0??1100?0100?11000101010","01??000?00?11?0010100????0?0","0?111000??100?010111?11011?0"}

    {"010011010?10?11001?1???0110?","111001??110010?101010?011?11","00111000?101?0011?0000110001","001?1100?0?0?10011111?101101","101100001?0?1010?00100010100","?00011?001011111001110010?11","110101101?000?11100?110?0101","100?1?011100?101?101100?010?","10?100?0011111010101011?1?0?","00001?11??0?00110?1111010010","11010011?1010110??0111?1010?","010111011?0101111010?10??011","000110100?000?011101??101?10","00?1100?10?0?11111?1?0001111","111000?001?00011?100101?1010","00101?110110101?1011?111101?","111?01?11?101110101010110???","100100111?1?0?0?01100?10101?","?1000?0??0111?00??100010??10","011?1?0000100001?11111101110"}

    Returns: {"0100110100100110011100001100", "1110010111001001010100011011", "0011100011010001110000110001", "0011110010000100111111101101", "1011000010011010000100010100", "0000111001011111001110010111", "1101011010000011100011000101", "1000100111001101010110000100", "1001001001111101010101111101", "0000111100000011001111010010", "1101001111010110110111110101", "0101110110010111101001011011", "0001101001000101110100101010", "0001100010000111110100001111", "1110000001100011110010101010", "0010111101101010101101111011", "1110010110101110101010110111", "1001001110100100011000101010", "0100000000111000101000100010", "0111100000100001011111101110" }

32. {"0?1011100?","1000?10011","100?0111?1","01?0110100","1??1110000","10?1000001","0??0111010","1?011??110","000?011100","1?1?10?0?1","0001100010","10101?000?","1?0?110?11","1100100100"}

    {"??101?1?01","10?00100?1","?001?111?1","0??0110100","10011?000?","100100000?","?110?11?10","1001?1?010","00010?1100","11?0?01001","0001100?1?","10?0110001","1100110?11","11?0100?00"}

    Returns: {"0010111001", "1000010011", "1001011101", "0100110100", "1001110000", "1001000001", "0110111010", "1001111010", "0001011100", "1110101001", "0001100010", "1010110001", "1100110011", "1100100100" }

33. {"1001?10?01??","100000111?01","?1?00001?001","00110110??10","010?001?111?","?101?1??00?1","1??1?10??111","000111101011","10010001??10","000111?1??01","100001001101","1?0?11100101","0??010001011","01000110?000","1100?0001111","1?1?10??0?11","0?0010?01001","00?100?0?01?","0?000?100010","00?101001101","?10100010?11","00?0?10?1???","?1?110000001","0?1110110000","10?110111001","0111101?1011","111010100010"}

    {"100?110?0?00","?00?0011100?","?1?000011001","0011?1100110","0101001011?0","??0???000?0?","10?10?001111","000??1101?11","10?1000?1110","0?0111011?01","?000?1001101","100011100101","010010001011","01?001?000?0","110?1?00111?","101110000?11","010010??1??1","?00100?000??","0100001?1010","00?101001?01","?1?1??010011","0000010?1001","1111??00?0?1","001110?10000","1001101?1?01","011?10???011","1110101?00?0"}

    Returns: {"100111000100", "100000111001", "010000011001", "001101100110", "010100101110", "010101000001", "100101001111", "000111101011", "100100011110", "000111011001", "100001001101", "100011100101", "010010001011", "010001100000", "110010001111", "101110000011", "010010001001", "000100000010", "010000101010", "000101001001", "010100010011", "000001001001", "111110000001", "001110110000", "100110111001", "011110101011", "111010100010" }

34. {"0000?00111001?110111","11?00100000?0?00?10?","1??11?0?11000001?001","0100001?0110??01?001","?1?1100?00?01101??10","?0?00110?01011111010","000?010100?10??1?01?","01110101111?111011?0","?100?11110110011100?","1100?011?00?101?0000","100?0101??0001??0?00","0?1111?0?0?100??1?11","1110???011?00?010101","00111101?0?01110?1?0","1101?101?011?1110?11","1001011??1000?101?00","1001110101100?010100","?0011101?0110?1?1111","0011101011111?101110","010010101000100010?0","?1?000?00110?0?0?010","00010000111010?1110?","01?10?1101001?110100","1111?000100?01000010","011?01??1?011?10?000","10?0?1?01?011?110?10","0?000?10?0111?00?011","?1?01001?0001?110?10"}

    {"000?0?011?0010110??1","110?01000??00??01?01","?????00?11000?0110?1","0?00001?0???10010001","110??00100001101011?","00100??0111011111010","000?0101001?010?0011","011?010??1?0?11011?0","0100111110?100111001","1??0?0110?011011??00","1??0010?1?0?01000100","01111?000?0100?11011","1??0110?11100?01010?","001?1?0?000011101100","1?01?101001111110011","100101101100??101100","1?011?01?1?0010?01?0","100?110100???0??1111","0011?0101111101011?0","0100101010?0?00??000","?11000000?10?0101??0","000?0?00?110100111?1","01?1011101?01111??00","111110?01000010?0010","0?10??1110??1?10?000","10?01?1011?11?110110","010?0??0101?100?0011","?1001001??001?110010"}

    Returns: {"00000001110010110111", "11000100000000001101", "10011000110000011001", "01000010011010010001", "11011001000011010110", "00100110111011111010", "00000101001101010011", "01110101111011101100", "01001111101100111001", "11000011000110110000", "10000101100001000100", "01111100000100011011", "11101100111000010101", "00111101000011101100", "11010101001111110011", "10010110110000101100", "10011101011001010100", "10011101001100101111", "00111010111110101110", "01001010100010001000", "01100000011000101010", "00010000111010011101", "01010111010011110100", "11111000100001000010", "01100111100110100000", "10001110110110110110", "01000010101110000011", "01001001000010110010" }

35. {"?101?11010??1?01?11","100?111?1??011???11","1?11110??0001?011?0","?1000?0??10000?010?","010?0010100010011?1","001?1010010?000?1?0","0?11110?1??00??0001","0010?1?0001?010?111","011?0?0?0??110?0??0","00?1??11001?0?0?011","0100?0?001?10000?1?","110??00010010010?1?","10??1111??00?001101","?0??1001011010??000","??10??0?100?11001?1","11101?01?0?10111100","0?011?001?00001001?"}

    {"01?101??1?1?11??11?","10???1?11110?1?111?","????110?1?00110?110","0100??01010?000?1?0","01010?10?0?010??111","00111??0??000?00?00","0?11?10011??0110001","001011000???0100111","01?10101011110?011?","00????1?00?10100?11","01?0001?0101?00?011","110?100010010010???","10101??1?0?0??0??01","0000?00101?01?1?00?","??1?01?010??1100??1","11?0?0011??1?111100","??0111?0?10?001001?"}

    Returns: {"0101010010101101111", "1000111111101101111", "1011110010001101110", "0100000101000000100", "0101001010001001111", "0011101001000000100", "0011110011000110001", "0010110000100100111", "0111010101111000110", "0001001100110100011", "0100001001010000011", "1100100010010010010", "1010111100000001101", "0000100101101010000", "0010010010001100101", "1110100110010111100", "0001110011000010010" }

36. {"01?????01?0100?11110??11?0?10","11?1?10??1?1000??10??110?1011","00?1?110011101???000010010011","1000?001?0?0000011?01?00?1?10","1?010?1??1?0110?01???0??110??","0?100000110010?011?1100??00?0","0011??011010?01?10?0?00?11??0","0?1??00100?1?0?1??10011?10100","?100011?0100???11000010?0000?","1?00000011??00???101101001001","0011??0?000?0110?1?0?111???11","111?111??01??001??011??100?1?","??0??1?10?0??1??01??01?01000?","???1100?011?1000000??100001?1","??0?11??0?1011?111101?10?1???","?000?10?001?01?1??00001??0110","0??0?0??1?1?0101101?0???00?1?","?1??01?00100???1??1?100000?0?","00?010000111?1?1?100??10??01?","0111?010??0?0?11100101??01111","0110??10001?001?0?1?010011?11","1?011?0?1001?1?10?00?11?11101","10?0?11100?00?0100?011??????1","001?11110?1??101??111?00?001?","?1001?10??1010?0?10?0?110000?","0011??110??1111?1111111101010","?00?00111111111111110?0??11?0","1001100???001?01??1001??11?11"}

    {"?10?1010?10?00?111?00?1?101??","11111??001?10?0??1?00110110?1","?001011?0???0??110?0?1?????11","10001?0100000?0011?010?0?1?1?","110100?10?10110101??1?0?110?1","011?000??10?101?1?0???01110?0","?011??011??010?0?01?0?0??001?","011?0?0??01??0?11??0011??0100","11?0???1010011?1??00010????01","1???000?1???0?011101?010010??","0011??010001?11001?001??0?01?","111?1??0?01?00?10?01101??0110","100?11??0?0??10001?0010010?00","111??00101101000????01000?1?1","???????0001?11?????0?01???011","1?0?11?00?11?1011?00001?00?10","000????11?1?010110?0000??011?","???101100100011?001?1?0000?0?","0010??0??11101??110001101?011","0?110010?000?01?10?1??100?1??","?110??10?010001001??01?0111?1","100?1?0?1?01??1?0?001111??101","1?00011?001?00010?10110010001","0010?1?1?1?0??0???11100010010","???0??100?1????01?0?0?110??01","00?????101011???111?1?1?01010","00?00?1?1??1111111??0?0111110","?001100?1100???11?10?1?1?11??"}

    Returns: {"01001010110100011110001110110", "11111100010100000100011011011", "00010110011101011000010010011", "10001001000000001100100001010", "11010011011011010100100011001", "01100000110010101101100111000", "00110001101010101010000010010", "01100001001100011010011010100", "11000111010011011000010000001", "10000000110000011101101001001", "00110001000101100100011100011", "11101110001000010001101100110", "10001101000001000100010010000", "11111001011010000000010000101", "00001100001011011110101001011", "10001100001101011000001000110", "00000001101001011010000000110", "01010110010001110010100000000", "00101000011101011100011010011", "01110010000000111001011001111", "01100010001000100110010011111", "10011000100101110000111111101", "10000111001000010010110010001", "00101111011001010011100010010", "01001010001010001100001100001", "00110011010111101111111101010", "00000011111111111111000111110", "10011000110010011010010111111" }

37. {"11?1","1?01","00?0","000?","00?1","110?","01?0","101?","???1","00?1","??00","1?01","0100","1001","100?","1000","?1??","?1??","10??","?100","10??","0110","?11?","001?"}

    {"??01","?101","?00?","00?1","00??","?10?","??10","??11","00?1","00?1","01?0","1?0?","0?00","?001","100?","1?0?","0111","010?","?01?","1100","101?","0?10","1111","???0"}

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

38. {"?0?1","11?0","110?","??00","1?10","0?11"}

    {"??11","??10","1101","000?","1???","0?11"}

    Returns: {"0011", "1010", "1101", "0000", "1010", "0011" }

39. {"0??01?111?1","111?1???1?0","?10?0101101","00?11110?0?","011100??010","?00?00?1?01","01?0111???0","?1111?1?001","???11?10000","10010000??0","1101????010","0?010?10?0?","11?0???00?1","1001?000011","??1100?1110","00?11010001","?1000?1?110","??011100010","0??0???11?0","?0010??1110","11?00?0101?","?1?1?1?010?","11111010??1","??100?01100","101??1?0?11","0??????1101","1?010100111","?0000?1?101"}

    {"01?0?111101","?11?11??100","?1?0??0??0?","00??111??0?","01110?1001?","0000001101?","?100??1?001","011?1111001","01?1101?000","?001??00000","?101001???0","0101??10?00","1?1?1??0011","100?1000011","0111??1?110","00??1???001","110001??11?","10?11??00??","0??0000111?","?0?1??0111?","1100???1?1?","01??01?010?","?1??101??1?","0?1?01?110?","10101?1?011","0001????101","1101?100?11","??000??01??"}

    Returns: {"01001111101", "11101100100", "01000101101", "00011110000", "01110010010", "00000011010", "01001110001", "01111111001", "01011010000", "10010000000", "11010010010", "01010010000", "11101000011", "10011000011", "01110011110", "00011010001", "11000110110", "10011100010", "00000001110", "00010001110", "11000001010", "01010100100", "11111010011", "00100101100", "10101110011", "00010001101", "11010100111", "00000010101" }

40. {"10","01","01","0?","1?","1?","11"}

    {"0?","10","0?","0?","?1","?0","11"}

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

41. {"00??1?1000","0?1?00?10?","010???1101","10111101?0","01101???01","?1111101?0","0110011??1","1001?11001","1?001?110?","001101001?","??1001?010","?011?1000?","01101?1101","?1?1??1?10","?1100111?1","00101??1?1","1100111?0?","1001110001","100??00?10","?11000?01?","?0???000?1","1110010?01"}

    {"00?0111???","0?1100110?","01?0011101","1??1110??0","???0??0001","??1111??00","?1010111?1","?0101?1?01","100?10?1??","0011010???","?01?01101?","?0?101?001","?1????1101","1101??1110","?1?0???10?","0?101?1111","110?1??10?","?001??0?01","1?01100??0","1????01?11","101?0000??","1?1?010??1"}

    Returns: {"0000111000", "0011001100", "0100011101", "1011110100", "0110100001", "0111110100", "0101011101", "1010111001", "1000101100", "0011010010", "0010011010", "0011010001", "0110101101", "1101001110", "0110011101", "0010101111", "1100111100", "1001110001", "1001100010", "1110001011", "1010000001", "1110010001" }

42. {"0?1","001","11?","00?","1?1","101","?10","111","0??","?10","011","110","100","?00","?10","11?","100","101","11?","10?","000","010","011","1??","111"}

    {"0?1","???","110","?00","111","1?1","?1?","111","??1","??1","011","?1?","1?0","0?0","110","1?1","100","?01","111","100","?00","?10","011","10?","1?1"}

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

43. {"110","1?0","0?0","??0","?01","?11","000","11?","100","110","??0","1?0","10?"}

    {"?10","110","?00","11?","?01","1?1","000","?11","1?0","11?","?00","1?1","100"}

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

44. {"0111","0111","?001","011?","0111","?000","01?0","1?11","10??","1101","011?","010?","0?00","101?","0111","?011","0?00","1010","1?0?","?110","10??","1001","00?0","111?","1?0?","11?0"}

    {"?111","01??","?00?","0111","??11","0?0?","?100","1??1","?0??","?101","??11","?100","0000","?011","01??","0?11","00?0","?0?0","??00","1110","1011","10?1","??00","1101","1???","1100"}

    Returns: {"0111", "0111", "0001", "0111", "0111", "0000", "0100", "1011", "1000", "1101", "0111", "0100", "0000", "1011", "0111", "0011", "0000", "1010", "1000", "1110", "1011", "1001", "0000", "1101", "1000", "1100" }

45. {"???1010??1?11?10?1?0??0?0111","0?100?10110?010??0?10?10?1??","?01000??10100??10?1????????0","011?00?01100111010??11?01110","??0?1?0101?01001?101?1001101","????001?011??1?1?11??????011","01??1?010?0??01???0?10???1?0","??0??101111100??????1011110?","1001?0??1??1?0?0?0010?11????","?1??0????10001?111001?01111?","000110?0?0?11101????0010?1?1","??1110100?1?1?0?11?1??100??0","?100001?01?1???0??01101???0?","1?0?0001??01?1011?10?11???10","0?0??11??01001?01???10?0?0?1","000000?1?11?1?0000?0??10?000","??101?0?100?????01111?010010"}

    {"0001010?????10?001?0??010?11","???0011?1?000?001??100?001?1","?11???1?101000110?1??0??1?10","01?0?01?11??1??0?0001?0??110","?001?00???1??00111010?001101","1101?01??11????1011?1?00??1?","??0010010?0?00100?0??00?????","??0111?1???100??010????1110?","??01?01?101100?01?0??01?1??0","????00???1?001??11?011?1?1?0","0001?000???1110101?1??1001?1","?01?1??000111101111111?0?1?0","?1?00?1101?10???0101?0?1110?","100??00111?1?1?????001110??0","01??0?110010??10???010001?11","000?0?0???11???000?0011?0?0?","1???1?0?100?0?1?0??????1?0?0"}

    Returns: {"0001010001011010010000010111", "0000011011000100100100100101", "0110001010100011001000001010", "0110001011001110100011001110", "0001100101101001110101001101", "1101001001100101011010000011", "0100100100000010000010000100", "0001110111110000010010111100", "1001001010110000100100111000", "0100000001000101110011011110", "0001100000011101010100100101", "0011101000111101111111100100", "0100001101010000010110111100", "1000000111010101101001110010", "0100011100100110100010001011", "0000000101111000000001100000", "1010100010000010011110010010" }

46. {"11???01?0??11??0????10001??","0?1?00?10???0?0?111?01?0010","111??1?1????10??0101?100?10","?10?1?01???0000100001??????","????1?000????10?1??110?1??0","??1101010???00???1??10?101?","11??00??1?0111111?1?011???1","?1?110101??11?11?0?1?1?1101","01000?0110???1????10?01000?","???0??0???100?11??0?0100111","0?01?1001??011??10??10??0?0","1?1??0010??0??01001?0??1001","111111?0?0?111?100???1?100?","1?1?1?0??00?????0110000??00","???0?1?10?01000?0000?11000?","?0??11?01?01??0100??1?00???","?001???0?0?????01?1???0?0?0","1?1100?????10?000???1111010","???110?00?100?1?1?1?0?100?0","1???1??10?010000000??1?0?11","1110?101?0011????010?1?1???","1?0100000001010???00?10?011","?10110110?110?01?1111??0?0?","???01?1??0??1110?10?1011?01","?11??0???11?010111?100?1?1?","???110??1?010???100??001001","?1?011?????11???1????1?00?1"}

    {"?10???10?1011000?11?1??01?1","00??????010????1???001?001?","1?11?1?1?00?1??101?1110011?","01?0110?00??0001???0?1?????","11?11?0?0?0011001?11??010?0","0????1?1000000?011?010?10?0","?101000111011111?0?0??1100?","0???1?101?11111110?1?1011?1","???00001?01??1???110?0?0?00","11000??00?1?00?10??0?100???","010101001?0??110???1?01???0","?1??0?010100??01???1??0?00?","11?11????0??11?1?001111?00?","???11001?0?10??0011?0????0?","???0???1??01?0??0?0??11?000","?01?1??0??0?00?100?111???1?","1???0?0??001001?1110??00000","1?????01000?0??0????1??1?1?","1001?0100?1000???0??00100?0","??01??01??0?????0?00??1?1??","11101101??0??001?0?0?1?1?10","11????000???01??01??0?0001?","??0?1?1??0?1???10?111000??0","?1001?101011???011?11?1??01","?1??10?0?11001?1??1?????111","0?0??001?10?001110?0?????01","11??1110001?11101??1?1??01?"}

    Returns: {"110000100101100001101000101", "000000010100000111100100010", "111101010000100101011100110", "010011010000000100001100000", "110110000000110010111001000", "001101010000000011001001010", "110100011101111110100111001", "010110101011111110010101101", "010000011010010001100010000", "110000000010001100000100111", "010101001000111010011010000", "111000010100000100110001001", "111111000001110100011111000", "101110010001000001100000000", "000001010001000000000110000", "001011001001000100011100010", "100100000001001011100000000", "101100010001000000001111010", "100110100010001010100010000", "100110010001000000000110111", "111011010001100100100101010", "110100000001010001000100011", "010110110011000101111000000", "010010101011111011011011001", "011010000110010111110001111", "000110011101001110000001001", "110011100011111010010100011" }

47. {"?1?0100101?","10??100????","1?1?1?1?010","1?1???01?11","1111?1??1??","111??1011?0","10?0111?0??","1??1???01??","???10110??0","0??1?10110?","?0???10?10?","????1??10?1","1100010?01?","110010???00","?1?0?11?0??","00000011?11","1??00?0?1?0","?1?1?01?1??","1????001000","00??000?10?","01??11111?0","000??000011"}

    {"0?0?1?01?1?","10111?0?000","1???1110??0","1?11000??11","?1???110?1?","1?1????111?","1???11?10??","?111??0?11?","?1?101?011?","???10?01?01","????11?110?","01??111??11","?100?101010","??1010101?0","01??011??10","??00??1??1?","?1?0?1?0??0","11??00?010?","1??00?????0","00010?0110?","011???1???0","000??0000?1"}

    Returns: {"01001001010", "10111000000", "10101110010", "10110001011", "11110110110", "11100101110", "10001111000", "11110000110", "01010110110", "00010101101", "00001101100", "01001111011", "11000101010", "10101010100", "01100110010", "00000011011", "11000100100", "11010010100", "10000001000", "00010001100", "01101111100", "00000000011" }

48. {"10??10000101?1?0?01101?","??001??1??110?00???0101","?11??111???????0?1???1?"}

    {"1?10??0001??????0??1?11","?100111101?101001??010?","???111110???011?11?0?11"}

    Returns: {"10100000010101000011011", "01001111011101001000101", "01111111000001101100011" }

49. {"??0??1??0100100?1?10?110?","???000?0?0???11?1100?1???","0???00?10?001??0??0101?11","0?011110?0??001?1?0?1000?","?1??0?1???011110?10??1??0","0100010?00?1?11??1?010??0","1?01??0?0?00?1?01111?1101","01101?110111?0?11000?11?0","?110?0?11?0??101??011001?","00??01?1????1100101?0????","000???1?10?0?01?11?1?100?","0?0?00?0?1??01?1?00101?00","11?0?111??1?11?11?1??11?1","???000???0?1?1011??0?00?1","10???00??11???1?011110??0","??1?10?00????1?0110000110","1101??1100100?0?010??11??","?0?100?10?0?0?110000?1001","10???1??0011010??1101?100","??10?1??101?1?101??1?10??","10?????111011?1????1?1100","?1?10??0001110??0?10?1?1?","?010?1000??1?0111??111010","1??10?1?001??01?01??1?110","?0?1????1????1??10?0??000","00?0010?????11100??000101","001?0?011?00??110??00?1?1","1???111??1?0?0?001110?00?"}

    {"00?001??0???1?0?1????1??0","0100?0??1??1?1???1000?0??","0010????000?1000?1?1??1?1","0???1???0??1001??00??00?0","?100??11??011110010?0?100","??0?010??001?????10?1?00?","??0??10?0?00110????11?10?","01?0???1??111???1?0?????0","?11000?1?00????1???11?0?0","?0?10??10?11??00??1?00?0?","00?1?11010?01010?10?11???","?0???000010?011100?1??000","?1?01111001??101???011?0?","10??0?11?0?1110110??10011","10?0??01???1?0?10111??0?0","????1??000?10??0??0?001?0","110?0111?0?0?????1001????","?0110?0?0?000????0?0?1?01","10?00?10?0??01?0??1010??0","010101??1010?1101101????0","?01011111?011011?00??1100","11110???0?1??001?0?00?1?0","0???01??0?110???1?01??010","10?10??????00??1010111?10","101???01110?0?0?1000???00","001?0?01?0?01?10?1?00010?","0?100?011??01?1?010?001??","1?0011??1100?????11??1??1"}

    Returns: {"0000010001001000101001100", "0100000010010110110001000", "0010000100001000010101111", "0001111000010010100010000", "0100001100011110010001100", "0100010000010110010010000", "1001010000001100111111101", "0110101101111001100001100", "0110000110000101000110010", "0001010100111100101000000", "0001011010001010110111000", "0000000001000111000101000", "1100111100101101101011101", "1000001100011101100010011", "1000000101110011011110000", "0010100000010100110000110", "1101011100100000010011100", "0011000100000011000001001", "1000011000110100011010100", "0101010010101110110101000", "1010111111011011000101100", "1111000000111001001001110", "0010010000110011100111010", "1001001000100011010111110", "1011000111000100100000000", "0010010100001110010000101", "0010000110001011010000101", "1000111011000000011101001" }

50. {"???00","????0","0??01","0?110","?1?01","?11??","??011","010?1","0???0","01???","01?11","1????","??000","????1","00???","1?00?","?1??0","?1001","1000?","????1","10??1","?11?0","1??11","??00?","???01","?????"}

    {"??0?0","???0?","0?1?1","01010","????1","???0?","11?11","??001","???1?","0110?","?1?11","???00","1?0??","1???1","????1","?1???","??1?0","?1???","?0???","0??11","?0???","011??","??0??","0000?","00???","1?1??"}

    Returns: {"00000", "00000", "00101", "01010", "00101", "01100", "11011", "01001", "00010", "01100", "01011", "10000", "10000", "10001", "00001", "11000", "01100", "01001", "10000", "00011", "10001", "01100", "10011", "00000", "00001", "10100" }

51. {"?01?1?1011??1??","110?10?0??01?01","0?00?1??0?1?0??","1010?1????1??11","??1???00?????00","1?10?0??00?????"}

    {"?011?????110111","??011?10110????","000????1011????","1010?1001??0101","1?1??0?010?101?","????0??1?001?0?"}

    Returns: {"001110101110111", "110110101101001", "000001010110000", "101001001010101", "101000001001010", "101000010001000" }

52. {"?110?0?00??01????0??1?0","0?01??1?0?1??10?001111?","1011110??01?1?10?1?????","???0?111?1?0001?11?1?0?","???????0?01??10?????0??","1??10?????????00?0??0?1","?00?010??????0???1?????","?1??1100???1011??1??1??","?1??00?11??11111?10????","1?11?0??0??11?1?????00?","????101????0111?101?111","1?1?10??11?0?00?1??10?1","??11?0??1??1010?01?00??","00???1??00?10???0?100??","?1?01?001?00?0??00??0??","0?1????0??111?1???0?0??","??01?01?1???01??0?0?010","???0??1??0?0?1?????0??1","100?0???1??1?0???00????","?1?0????1??0011????0110","??11101?0?1?00???10010?","?0110?0??0?????1?0?0?1?"}

    {"?110?0?0?????0?1??0????","01?1???101??1?????1111?","1??111??0????1?011??101","00?0?1?1?110001011???00","??10?1??????0?00??000??","???10?1101?0??0??0???0?","10?0?10?1???????0?11?1?","???1?1??0??1?11??1?1??0","???0?01?1?0111111????1?","1?1??01????11????10??00","1??????0100011??10?0?1?","101?1?0?110000?01?010?1","???11?0??1?1????0100??1","0??10??0???????????00??","??00??0??0??1??0?0010??","??1?????0?111?1??0010?1","??010?111?01??0?0???010","????101?1??01110????0??","???101???0011???1???101","11?0??1??0?0????1?0?110","1011?0?1?010???0??0?10?","1???0001?01?10??0?00?10"}

    Returns: {"01100000000000010000100", "01010011011011000011110", "10111100001011101100101", "00000111011000101101000", "00100100001001000000000", "10010011010000000000001", "10000100100000000111010", "01011100000101100101100", "01000011100111111100010", "10110010000110100100000", "10001010100011101010111", "10101000110000001001001", "00111000110101000100001", "00010100000100000010000", "01001000100010000001000", "00100000001110100001001", "00010011100101000000010", "00001010100011100000001", "10010100100110001000101", "11000010100001101000110", "10111011001000000100100", "10110001001010010000010" }

53. {"?1??1??1??01??????10?0????1??0","10??0?0??100?101?111????0??1??","??10110??????10111?1?0?10??100","?0??????10?1110??10??1????1?0?","????1??100?0??11??1?1010??1?1?","1??1??????11?00??????000??1???","?1?0?1???110110?10?0?10??00???","1??0???0??10??0??0?0??011??0??","11?0??00?11?010??1????00?1?01?","1111??0001??1???01???1?10?01?0","?0?1011010?010?00?0?0???1?10??","1?1????11?01??1??????0?001?1??","?00?01??1?01?0?110??1??0??1110","???101??1110??0?1?1?1?10??10??","1?101?0?10??110010??0??001??0?","?0?1?1??01?1?0?01?1?01??11??0?","???1??00?????????101?0?01?0110","???101??1?0?0??01??0??0?0110?1","??0101???00??00110??01?00011??","??1?0????1???1??0?0010??0????1","???1111??010??????100?10??1?00","01??00?????00?11?????1?10?1??1"}

    {"?1?0?111?1????????1???00?010?0","?00??1?00??001??01?10?11????0?","1?1??101??1011?111??00?1001?00","??????1?1?11??0??1???1101?????","?0?0?111???0?01?01??1?10?1????","?01?10?0???11????1?00?0?0?1?0?","?1?0?1?1111?11?1?0???10????11?","1???110??1?0?1??1010?00?1000??","??10?100?1??0??0110?1?????1??0","?1????00010?10??0??0110?01010?","?0??01??10?0?0?0????0?111???1?","1011????10?100??100?00?00?11??","?0?1????1?0110?1?0??1???1111?0","0??101?0111?0101??101?1011??00","??1?1?00????11??10100?10??0100","?0?1???1?111??0????0?11??100??","?1?1??????0?????01??10???1?1??","00??01?11101??1?1??0??0????0??","100101001???10??1??10?0000?11?","?110??0?1?0??1?0010?1?000?1?1?","???1?111?010010??1???11?01??00","0111?0?0???0?0110010?1010????1"}

    Returns: {"010001110101000000100000001000", "100001000100010101110011000100", "101011010010110111010001001100", "000000101011110001000110101000", "000011110000001101101010011010", "101110000011100001000000001000", "010001011110110110000100000110", "100011000110010010100001100000", "111001000110010011001000011010", "111100000100100001001101010100", "000101101000100000000011101010", "101100011001001010000000011100", "000101001001100110001000111110", "000101001110010110101010111000", "101010001000110010100010010100", "000101010111000010100110110000", "010100000000000001011000110110", "000101011101001010000000011001", "100101001000100110010100001110", "011000001100010001001000001011", "000111110010010001100110011000", "011100000000001100100101001001" }

54. {"0?00??0","?011110","?1?011?","????000","???1?00","1??1010","?0??001","?011?0?","??1???0","???1001","?00?111","1110???","???0000","1??1??1","?1???1?","0?0?1??","000?1?1","0100?11","0?1????","10?0000","???000?","?0????0","0???111","000?1?1","?0??1??"}

    {"010??00","0??1110","1?1??1?","0??0?0?","?0??100","1101010","10??0??","001?10?","1??1?00","?1?10?1","0??01??","?1101?1","???0?00","0?11??1","??01??0","?00???0","0?01???","?1?0?1?","011??00","?00???0","??10?0?","?0110??","?0011??","?00?101","?0???1?"}

    Returns: {"0100000", "0011110", "1110110", "0000000", "0001100", "1101010", "1000001", "0011100", "1011000", "0101001", "0000111", "1110101", "0000000", "0111001", "0101010", "0000100", "0001101", "0100011", "0110000", "1000000", "0010000", "0011000", "0001111", "0000101", "0000110" }

55. {"01???1?0?0?1?","???0011?10?11","??1?1??0????1","?0?0?01?1??10","?0??0????110?","011??1?????01","01100?001??0?","??1110????0??","?0??01?11??01","???0??????0??","??10?1111????","10??0010??0??","0??1??0??00??","?1?10???0?110","???????1010??","??????0???11?","??1??010?????","???????10????"}

    {"??01????0??1?","??0??1???????","101?11?01?10?","??10?01???0??","??????1??11??","?11?1?1?10?0?","??1??1???010?","01??????0?00?","?01????1?1?0?","?1???0????0?1","?010??11??1?1","?0010???0???1","00?1000?1?0??","01??0?11?0?10","??0??1??01???","??????0??0??1","?0???0?0????1","?01??0??0?0??"}

    Returns: {"0001010000010", "0100011010011", "1010110010101", "0010001010010", "0000001001100", "0110111010001", "0110010010100", "0111100000000", "0010010111001", "0100000000001", "0010011110101", "1001001000001", "0001000010000", "0101001100110", "0000010101000", "0000000000111", "0010001000001", "0010000100000" }

56. {"?1?011??1???01??1??????0","?1??1??0?0?1????????0?01","1?001?0??01?0101??0?110?","???????????0??0?1???11??","0011?1?0??1???0?1????10?","?100????0???1??1??????0?","?1???1?000?????0?00100??","01??0????1011?00????010?","001?0????00?0??1?1????0?","?0?????1????10?1?00??00?","??1?1??1?00?1???0?0?0?10","000?1?01?1??0???????????","?1?1???0??1???0???110?00","01??10?0???1????1?0?0?01","1???1?1??0?1???1?1????01","??????1??1???0?0???1????","??1??0?0?0?1???1??0????1","1?1??1???0??10???00???0?","111???01110?1?1?1????010","10?01?1000??00?11?????01","0???????1??11??1??????1?","?0?0??1?01??0?10?????011","1???1???1??111??????0???","?0?????00???0??????001??","?001?1?????01??1?1?1???0","??0?010???00??1?111?11?1","0???????0?00?1???11??01?","0?1?????1??0?0?1??????01","1?1110?1?????11???11010?","???01???11?0?1?11?11??01"}

    {"???????11?1??1?1?0?11?10","??10??0???1??010?1??0???","1??01??0?????101??011?00","??????0???1?0?0?1?1?????","?011??00??11?????0?0???0","??0?001???0?1?11??????0?","1?01???00??1???0000?????","?1??01?00?0????0???00??1","0?????0?10??0?0??1????0?","1??1?0???1???????0??100?","??1???????????01??01??10","0??111?1?1??????0?111???","?10??00????1????????0?00","01??1?00000??0?0???0???1","1?????11100??11?01??0?0?","??0?0??111?0?????10??0??","?????????????0?????11??1","?01?????0?01???100?0???0","1?1?1?0???0010??1???1???","?0?0??1??00?00?11?0?????","0000?11?100?1??1?01?1?1?","?0??1?100????0?????0????","1?1??11?1?0?1??0?????0??","00??01??0?????1?0???01??","?00????11??0??1???010???","0???01????0?????1?????1?","0??11??00????????1??10?1","????????1?1???1?11???00?","1???10??????1?1???110???","0?0010011?000?01?11??1??"}

    Returns: {"000011011010010110011010", "011010000011001001000001", "100010000010010100011100", "000000000010000010101100", "001101000011000010000100", "010000100000101100000000", "110101000001000000010000", "010001000101100000000101", "001000001000000101000000", "100100010100100100001000", "001010010000100100010010", "000111010100000000111000", "010100000011000000110000", "010010000001000010000001", "100010111001011101000001", "000000111100000001010000", "001000000001000100011001", "101001000001100100000000", "111010011100101010001010", "100010100000000110000001", "000001101001100100101010", "000010100100001000000011", "101011101001110000000000", "000001000000001000000100", "000101011000101101010000", "000001000000001011101111", "000110000000010001101011", "001000001010001111000001", "101110010000111000110100", "000010011100010111110101" }

57. {"0???00???0?","1??10?0?1??","11?0100?1?0","1????1??1??","1?10?1??0??","??11??01??0","0?001?1?0?0","?101????11?","?001????1?0","00???0?????","???1??0010?","??0?????10?","0???111??0?","????0??????","1?0???0???1","1001??1?10?","01???1?????","??01?0??01?"}

    {"??0??0?00?0","1??1???11?1","???01??????","??10?1???11","?1?0?1??0??","?01????10?0","??0???10?1?","11??????1??","?0??????1?0","??1?0???1??","???1?????0?","???1???11?0","????????0??","?0?10110??0","1??0??01?0?","??00???110?","?10?0????0?","10???0???1?"}

    Returns: {"00000000000", "10010001101", "11001000100", "10100100111", "11100100000", "00110001000", "00001010010", "11010000110", "00010000100", "00100000100", "00010000100", "00010001100", "00001110000", "00010110000", "10000001001", "10000011100", "01010100000", "10010000010" }

58. {"?0??????1??1?1????0???0???0?","0?????1???1?11???0100???1???","0?01??01?0??0???????1?1?????"}

    {"??1?????11?????1??0?????000?","?00??0?????11???1????01??1??","??0?1??1?001?110??1?1011?100"}

    Returns: {"0010000011001101000000000000", "0000001000111100101000101100", "0001100100010110001010110100" }

59. {"?011??????1??01??0???1????1","?0?1???110??11?001?0???1???","00111?????00?10??1????11??0","10????0??10??100?0?1?1?????","0??01??1????1??11111??00???","??????1?00?001?0?????01?0??","0?01???????1?0???1????0?001","?1?1??001?11?1??1???00110?0","???????1????10?101??0???01?","?1??0?0?110???001??00?011?1","01?1??1?1010??1??10???0011?","0??11???1?01?111????001??0?","?001?0?1?????0??0?0????1???","?1???1???00?????????0???0?1","??1??0????10??11???0?1??1?1","00??10???01??011??010??101?","0???101??0101??011??00?0???"}

    {"?011??10?0??10???0??1?1??1?","10??1????????1????1?11???0?","0?1111?1??????0???0011????0","1??1????0????1?000???10?1??","??10?0??????????1?111??0??1","?1?1??1???0?????????1?10?10","????0????????00??1110?0???1","??11??0??1?111??1???00?10??","????????0?0?1??????1???1???","????0??01??0?00?11??0???101","0?0?1???10???11??1?1???????","?11??110?0?111??0?0??0??00?","??0???0??0?0?0??0??1?0?11??","?11?11?????1????011??1??0??","0??1?0???01????1001?1?101?1","?0???0?1?0?000?111????0?0??","?????010?0???????10?????0??"}

    Returns: {"001100100000101000001110011", "100110011010110001101101000", "001111010000010001001111000", "100100000100010000010100100", "001010010000100111111000001", "010100100000010000001010010", "000100000001000001110000001", "011100001111110010000011000", "000000010000100101010001010", "010000001100000011000001101", "010110101010011001010000110", "011111101001111100000010000", "000100010000000000010001100", "011011000001000001100100001", "001100000010001100101110101", "000010010010001111010001010", "000010100010100011000000000" }

60. {"?1?1?0100","???1?????"}

    {"?1????1??","?00??10??"}

    Returns: {"010000100", "000111000" }

61. {"????0?","0???1?","0?0?1?","?1?1?0","?0??10","1?????","???0??","?????1","?1????","?????1"}

    {"?10?0?","?01?1?","?1???0","?????0","1?????","????0?","???0??","0??10?","??????","1???1?"}

    Returns: {"010000", "001010", "010000", "010110", "100010", "100000", "000000", "000101", "010000", "100011" }

62. {"01???0?0??0????????0?1????1??","???1????0??1???01????????????","????111???0??1??1???????????0","?0???1???0??1???????????001?0","???????????????11??0????1?00?","1?1???1?111?????000??0???0???","???1???0?????00?0?0??0?0??000","1????1?11????1???00??0??0??0?","??????1?????????0????1?1?1?00","????0???1??1?00??1?0????01?1?","??0??1???11???11?11?????0????","?0?????00??0??????1????00?01?","?10?1100???1????11???1??0?11?","???0??????100?1??1???????????","?????0?00???0?1?01?????0???1?","?0??1?00????0????10??1???1???","?0????00?1???0??11?????????10","001??????00?1111????????0???0","??????10????1????????1??1?0??","?0??0????1??00?10????1?0??1??","?0101???????0??1?111??1?101??","0???????011?01????0??01??????","?1??0???0??1?1?????1???0???1?","??0?1111?1??00?0??1??????????","0??101????0???????????10?????","?0???1?10????1????01?????1?0?"}

    {"0?1?1???0??????00?0?0?01?1???","1?1?0?0???1????????11?1?1?0?0","???0???10????????0?110???????","???????01????01?????1??1?0???","???0???0???000??1?0??????1???","1?11?11?1??0???????????????1?","??11??1?0????????????0100?0??","?????1??1???11??1?01??1??0???","???1?????0??11??????0??1????0","???1??????01????0?1??00?0?0??","??????????1?0????1????1?0?0??","???0??1??0??0??11????0?0?1?11","1?????000?11??0????????????1?","????1?011??0??10??1??????????","0????0?????????1??1??0?0?1???","????1?0?????00?1?1??01???1??1","0??????01??11?1???10??000?1?0","0???1??0000?1??????10????????","?0??0??00?101???0???????110?1","?0?0????01?1????0???0100?????","1?10?001?11???????111??????1?","010????????1?11??100?????????","???0???1??01??01??????0???0??","??0?1??101?????0?1?1?1?000??1","??????1??????0??00???????011?","??0???????0??1??1?0?1??1?????"}

    Returns: {"00101000000000000000010101100", "10110000001100001001101010000", "00001111000001001001100000000", "00000100100010100000100100100", "00000000000000011000000011000", "10110110111000000000000000010", "00110010000000000000001000000", "10000101100011001001001000000", "00010010000011000000010101000", "00010000100100000110000001010", "00000100011000110110001000000", "00000010000000011010000001011", "11001100001100001100010000110", "00001001101000100110000000000", "00000000000000110110000001010", "00001000000000010100010001001", "00000000110110101110000000110", "00101000000011110001000000000", "00000010001010000000010011001", "00000000010100010000010000100", "10101001011000010111101010110", "01000000011101100100001000000", "01000001000101010001000000010", "00001111010000000111010000001", "00010110000000000000001000110", "00000101000001001001100101000" }

63. {"1??","?0?","???","0??","?1?","0??","???","?1?"}

    {"???","00?","?01","00?","???","0??","???","0?1"}

    Returns: {"010", "000", "001", "000", "010", "000", "000", "011" }

64. {"??????1?","??0???0?","1??0???0","???????0","??1?????","1??1?0??","????????","??101?0?","1?1?1?1?"}

    {"?0?0??11","?1?0????","?0??1?0?","0??1????","??1?0??1","????0?0?","??1?0?1?","?11??100","????1??1"}

    Returns: {"00000011", "01000000", "10001000", "00010000", "00100001", "00010000", "10100010", "01101100", "10101011" }

65. {"0???????0??1????????","????0????????????1??","0??????01??0????10??","?01???1????0????????","???1??1??0??1???????","0?????????0?????????","???0???????????1?0?0","??0????????00???0??0","?????0????00??1?????","1?0????????????1?11?","???????0?0?1????????","??????????1?1???????","?????????1???????0??","?10???????????????0?","????????1?0?1???????","???0??1?11?????11???","???????1????????0???","?0???1?0????1?10??1?","???????1??????101?0?"}

    {"??????1?????1???0???","?????01??????????111","?????1??????10??????","0????1???1???0??1??0","???1?0??1??1????0??0","0??????????????0????","?1????1?0???????????","??0??????1?????0????","?00??0????????1?1???","??????1?????????01??","?????0??0???1???1???","???????1????????????","????????1?1?????0???","?????0??????????????","???0?????00??????0??","?01???????????1????0","?1?????????11??1??1?","????????0????0?0????","????0???01??0?1??1??"}

    Returns: {"00000010000010000000", "00000010000000000111", "00000100100010001000", "00100110010000001000", "00010010100110000000", "00000000000000000000", "01000010000000010000", "00000000010000000000", "00000000000000101000", "10000010000000010110", "00000000000110001000", "00000001001010000000", "00000000111000000000", "01000000000000000000", "00000000100010000000", "00100010110000111000", "01000001000110010010", "00000100000010100010", "00000001010000101100" }

66. {"1???????????","??1??0????0?","?????0?0????","0????????1?0","?00??????1??","??????0?1???","????1???????","???0????????","??1???0??0??","????????????","???????????1","?1?1?0????0?","0??0????1???","????0???????","?0????1?????","?????0??????","?111?1?1?1??","???0??111???","???????1?100","?0?00?0?????","????0???????","?????0????01","0???1???10??","?????0??????","??11??0?10??","?0??01?????0","001???1?????","?????1??????","?????1??1??0"}

    {"?0????0?????","???0????110?","?0?1?0?????1","???0????????","???0????????","?1???????1??","????????0???","???????????1","??1??0?????0","????????????","????0011??1?","?????????0?1","????????????","?100?00?0???","?????0???1??","1??00?0???01","111??1?1???1","????????????","10?????11???","??????0?????","??????1??0??","1?0?1?0?????","???????????0","0???????????","1?????00????","????????0???","?0?0???????1","??1?1???????","???????1????"}

    Returns: {"000000000000", "101000001100", "000100000001", "000000000100", "000000000100", "010000001100", "000010000000", "000000000001", "001000000000", "000000000000", "000000110011", "010100000001", "000000001000", "010000000000", "000000100100", "100000000001", "111101010101", "000000111000", "100000011100", "000000000000", "000000100000", "100010000001", "000010001000", "000000000000", "101100001000", "000001000000", "001000100001", "001011000000", "000001011000" }

67. {"?????0???110????0??","?1??0???01???1?00?1","1?1??0??1?????1???1","?00????1????????1??","???1?????1???????1?","???0????1??????????","1????????????0?????","?????????01????????","??????????111???0??","????1??????????????","????????01?????0???","?????????0?????00??"}

    {"??0?10???1??01??0??","???0??????0?1????0?","??1???????????1?0??","00???01??10????1??1","??1?1??????1???????","0???????1????0???1?","??????0???????????1","??00???????????01??","0??????0??11???1??1","????11??1???0??????","????1????????1?????","1????1?1???????????"}

    Returns: {"0000100001010100000", "0100000001001100001", "1010000010000010001", "0000001101000001101", "0011100001010000010", "0000000010000000010", "1000000000000000001", "0000000000100000100", "0000000000111001001", "0000110010000000000", "0000100001000100000", "1000010100000000000" }

68. {"0??1?","?????","?????","????0","?????","1??0?","?1???","1????","?0??1","???0?","?00?0","?????"}

    {"????1","????1","????0","?????","0?0?1","????1","????1","?????","????0","1????","0????","?????"}

    Returns: {"00011", "00001", "00000", "00000", "00001", "10001", "01001", "10000", "00000", "10001", "00000", "00000" }

69. {"???????1????????1","?0?????????1?????","???????????1???0?","??101???1?11????1","??????1???01?0???","0??????1???????01","?????0?111???????","????????1???1????"}

    {"??????????????1??","???????????1???11","??????00??0?0??00","???0?1??1????11?1","????????0??1?????","???11???1??????01","00?00???1?????0??","?0???????????????"}

    Returns: {"00000000000000101", "00000001000100011", "00000000000100000", "00101100101101101", "00000010000100000", "00011001100000001", "00000001110000000", "00000000100010000" }

70. {"????0??????????","??????0?0??????","????0?????0????","????1?????????1","??????????1????","???0?????????1?"}

    {"??????????0?0??","?????1?0?1?????","???1?????0?????","???01????????1?","??????0????????","???????????1???"}

    Returns: {"000000000000000", "000001000100000", "000100000000000", "000010000000010", "000000000010000", "000000000001010" }

71. {"1????0?????0?????","?????????????????","????????0????????"}

    {"?0???????????0???","??????01????0?1??","????????????????1"}

    Returns: {"00000000000000000", "10000001000000100", "00000000000000001" }

72. {"??????????????????","0????????0????????"}

    {"?1????????????????","?????0???0????????"}

    Returns: {"010000000000000000", "000000000000000000" }

73. {"?????0??1???0???","???????????????0","?11?????????????","0??1???????????0","??????????110?0?","????????????????","?????1??????????","??????????0?????","????????????????","?????????????1??","??0?1??11??0????","????0???0?0?1???","?????0???????0?1","??0????0??????0?","???????1??1?????","???0??????1??11?"}

    {"????????????????","??????0????????0","?????????01?????","??0????1????????","0???????????????","????1????????0??","?????10???????0?","????????????????","?????11???????0?","??????1?????????","?1????1?????????","????????????????","???????0?????0??","???????0????????","??10???1??????1?","????????????????"}

    Returns: {"0000000000000000", "0000000010000000", "0110000000100000", "0001000100000000", "0000000000110000", "0000100000000000", "0000010000000000", "0000000000000000", "0000011000000000", "0000001000000100", "0100101110000000", "0000000000001000", "0000000000000001", "0000000000000000", "0010000100100010", "0000000000100110" }

74. {"0???????","????0???","???001??","????????","1???????","?1??????","????????","????????","??1?????","????????","?0??????"}

    {"????????","?100?01?","??????0?","1???????","??01????","??1?????","??????1?","??00????","????????","????????","???????0"}

    Returns: {"00000000", "01000010", "00000000", "10000100", "10010000", "01100000", "00000010", "00000000", "00100000", "00000000", "00000000" }

75. {"1???????","????0???","???0011?","????????","1???????","?1??????","????????","????????","??1?????","????????","?0??????"}

    {"0???????","?101?01?","??????0?","1???????","??01????","??1?????","??????1?","??00????","????????","????????","???????0"}

    Returns: { }

76. {"00111", "00111", "11111", "11111"}

    {"??1??", "??1??", "?????", "?????"}

    Returns: {"00111", "00111", "11111", "11111" }

    In order to get the lexicographically earliest solution, you must rotate the 2x2 block containing only zeros. Note that this movement does not modify the matrix, but it is still valid.

77. {"?1111", "11100", "11011", "10111" }

    {"?1100", "11111", "1??11", "1??11" }

    Returns: { }

78. {"10", "00" }

    {"00", "01" }

    Returns: { }

79. {"?1111", "11111", "11011", "10111" }

    {"?1111", "11111", "1??11", "1??11" }

    Returns: {"01111", "11111", "10011", "11111" }

80. {"?1", "1?" }

    {"??", "1?" }

    Returns: {"10", "11" }

81. {"1?", "11" }

    {"11", "11" }

    Returns: {"11", "11" }

82. {"?11", "1??" }

    {"???", "1??" }

    Returns: {"001", "101" }

83. {"01", "00" }

    {"00", "10" }

    Returns: { }

84. {"?1", "??" }

    {"?1", "11" }

    Returns: {"01", "11" }

85. {"00?", "???", "???" }

    {"000", "000", "00?" }

    Returns: {"000", "000", "000" }

86. {"1?", "??" }

    {"0?", "??" }

    Returns: {"00", "10" }

87. {"??10000", "1000100", "??10000", "1000000", "0000000", "0000000", "1000000" }

    {"0000000", "0000000", "0000000", "0000100", "???????", "1000000", "0000100" }

    Returns: { }

88. {"??", "??" }

    {"??", "1?" }

    Returns: {"00", "10" }

89. {"????????", "????????" }

    {"?????1??", "????????" }

    Returns: {"00000100", "00000000" }

90. {"??", "??" }

    {"??", "??" }

    Returns: {"00", "00" }

91. {"0?", "00" }

    {"00", "01" }

    Returns: {"00", "01" }

92. {"??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????" }

    {"??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????", "??????????????????????????????" }

    Returns: {"000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000", "000000000000000000000000000000" }

93. {"1101", "1101", "1100", "1100" }

    {"0101", "1101", "1100", "0111" }

    Returns: { }