TopCoder Statistics - Problem Statement

Problem Statement

You are given a matrix M consisting of zeros and ones. You are allowed to perform operations of the following type:

Choose a position (i, j) in the matrix.
Flip all the values but M(i, j) in the i-th row of M. By flipping, '0' becomes '1' and '1' becomes '0'. Note that M(i, j) does not get changed.
Flip all the values but M(i, j) in the j-th column of M. Note that M(i, j) does not get changed.

Output "possible" if it is possible to transform M to an all ones matrix by applying any number of these operations. Otherwise, output "impossible".

Definition

Class:: UniformingMatrix
Method:: isPossible
Parameters:: String[]
Returns:: String
Method signature:: String isPossible(String[] M)
(be sure your method is public)

Notes

Note that the return value is case-sensitive.

Constraints

M will contain between 1 and 100 elements, inclusive.
Each elements of M will contain between 1 and 100 characters, inclusive.
All the elements of M will contain the same number of characters.
Each character of each element of M will be '0' or '1'.

Examples

{"0"}

Returns: "impossible"

The only operation it is possible to apply here is on M(0, 0). However, this operation does not change the value M(0, 0), and hence there is no way to obtain all ones matrix.
{"1101", "0010"}

Returns: "possible"

One possibility here is to apply the operation on M(1, 2).
{"11111", "11111", "11111", "11111", "11111", "11111", "11111", "11111"}

Returns: "possible"

The input matrix is already in the required format, so there is no need to apply any operation in this case.
{"110", "001", "110"}

Returns: "possible"

It is possible to obtain the all ones matrix from the input by applying the operations on M(2, 1), M(2, 2) and M(1, 1). For instance, applying the operation on M(2, 1) leads to matrix 100 011 011
{"01010", "10101", "01010", "01010"}

Returns: "possible"
{"01011", "10100", "01011", "01011"}

Returns: "possible"
{"1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "0110000011011110010011011101011010100110111001101001100011100010100010000110010001111010000001101011", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100", "1001111100100001101100100010100101011001000110010110011100011101011101111001101110000101111110010100"}

Returns: "possible"
{"0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "1010011010100010011101111011100011001001010110011101010010010011101110110001001000001011001100111100", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011", "0101100101011101100010000100011100110110101001100010101101101100010001001110110111110100110011000011"}

Returns: "possible"
{"0100101010101010000011101101111100100001011011011011001001000100001000010000101101101101111011011111", "1011010101010101111100010010000011011110100100100100110110111011110111101111010010010010000100100000", "0100101010101010000011101101111100100001011011011011001001000100001000010000101101101101111011011111", "1011010101010101111100010010000011011110100100100100110110111011110111101111010010010010000100100000", "1011010101010101111100010010000011011110100100100100110110111011110111101111010010010010000100100000", "1011010101010101111100010010000011011110100100100100110110111011110111101111010010010010000100100000", "1011010101010101111100010010000011011110100100100100110110111011110111101111010010010010000100100000", "0100101010101010000011101101111100100001011011011011001001000100001000010000101101101101111011011111", "0100101010101010000011101101111100100001011011011011001001000100001000010000101101101101111011011111", "0100101010101010000011101101111100100001011011011011001001000100001000010000101101101101111011011111", "1011010101010101111100010010000011011110100100100100110110111011110111101111010010010010000100100000", "0100101010101010000011101101111100100001011011011011001001000100001000010000101101101101111011011111", "0100101010101010000011101101111100100001011011011011001001000100001000010000101101101101111011011111", "1011010101010101111100010010000011011110100100100100110110111011110111101111010010010010000100100000", "1011010101010101111100010010000011011110100100100100110110111011110111101111010010010010000100100000", "0100101010101010000011101101111100100001011011011011001001000100001000010000101101101101111011011111", "0100101010101010000011101101111100100001011011011011001001000100001000010000101101101101111011011111", "1011010101010101111100010010000011011110100100100100110110111011110111101111010010010010000100100000", 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"1011010101010101111100010010000011011110100100100100110110111011110111101111010010010010000100100000"}

Returns: "possible"
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"1111110001001100011100010101111111011111011101101101111010001010011111010110100111010000111100110110"}

Returns: "possible"
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"1000101000001100000000001100000000000000010010100011110000000000000000010000000010000010000000000101", "0111010111110011111111110011111111111111101101011100001111111111111111101111111101111101111111111010", "1000101000001100000000001100000000000000010010100011110000000000000000010000000010000010000000000101", "1000101000001100000000001100000000000000010010100011110000000000000000010000000010000010000000000101", "0111010111110011111111110011111111111111101101011100001111111111111111101111111101111101111111111010", "0111010111110011111111110011111111111111101101011100001111111111111111101111111101111101111111111010", "0111010111110011111111110011111111111111101101011100001111111111111111101111111101111101111111111010", "1000101000001100000000001100000000000000010010100011110000000000000000010000000010000010000000000101", "0111010111110011111111110011111111111111101101011100001111111111111111101111111101111101111111111010", "0111010111110011111111110011111111111111101101011100001111111111111111101111111101111101111111111010"}

Returns: "possible"
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Returns: "possible"
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Returns: "possible"
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Returns: "impossible"
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Returns: "impossible"
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"101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "010100101011111010001100110010000010100111011101011011111000010010101100101000110001110001001011100", "010100101011111010001100110010000010100111011101011011111000010010101100101000110001110001001011100", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "101011010100000101110011001101111101011000100010100100000111101101010011010111001110001110110100011", "010100101011111010001100110010000010100111011101011011111000010010101100101000110001110001001011100", "010100101011111010001100110010000010100111011101011011111000010010101100101000110001110001001011100", "010100101011111010001100110010000010100111011101011011111000010010101100101000110001110001001011100", "010100101011111010001100110010000010100111011101011011111000010010101100101000110001110001001011100"}

Returns: "possible"
{"0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", 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"0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", 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"1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "1011100010001101110110100110111000110111101011011001011111111001101010111111101111111000111", "0100011101110010001001011001000111001000010100100110100000000110010101000000010000000111000"}

Returns: "impossible"
{"011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "100000110010000101100100011011011001100110000101010101111010101110101000011011000010101011000011", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "100000110010000101100100011011011001100110000101010101111010101110101000011011000010101011000011", "100000110010000101100100011011011001100110000101010101111010101110101000011011000010101011000011", "100000110010000101100100011011011001100110000101010101111010101110101000011011000010101011000011", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", 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"011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "100000110010000101100100011011011001100110000101010101111010101110101000011011000010101011000011", "100000110010000101100100011011011001100110000101010101111010101110101000011011000010101011000011", "100000110010000101100100011011011001100110000101010101111010101110101000011011000010101011000011", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", 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"011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100", "100000110010000101100100011011011001100110000101010101111010101110101000011011000010101011000011", "011111001101111010011011100100100110011001111010101010000101010001010111100100111101010100111100"}

Returns: "possible"
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"0011100110011010010010000000110100111010101100100110101010101001001110011010010001011010111100"}

Returns: "possible"
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Returns: "impossible"
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"0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "1000111110001101111011110111001010011100110110111110011001000111111000001110001111100100000", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "1000111110001101111011110111001010011100110110111110011001000111111000001110001111100100000", "1000111110001101111011110111001010011100110110111110011001000111111000001110001111100100000", "1000111110001101111011110111001010011100110110111110011001000111111000001110001111100100000", "1000111110001101111011110111001010011100110110111110011001000111111000001110001111100100000", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "1000111110001101111011110111001010011100110110111110011001000111111000001110001111100100000", "1000111110001101111011110111001010011100110110111110011001000111111000001110001111100100000", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "1000111110001101111011110111001010011100110110111110011001000111111000001110001111100100000", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "0111000001110010000100001000110101100011001001000001100110111000000111110001110000011011111", "1000111110001101111011110111001010011100110110111110011001000111111000001110001111100100000"}

Returns: "impossible"
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"0000110100100110101000010010111111111010100011101100100100101100011110010010100110111000010010110", "1111001011011001010111101101000000000101011100010011011011010011100001101101011001000111101101001", "1111001011011001010111101101000000000101011100010011011011010011100001101101011001000111101101001", "1111001011011001010111101101000000000101011100010011011011010011100001101101011001000111101101001", "0000110100100110101000010010111111111010100011101100100100101100011110010010100110111000010010110", "0000110100100110101000010010111111111010100011101100100100101100011110010010100110111000010010110", "0000110100100110101000010010111111111010100011101100100100101100011110010010100110111000010010110", "0000110100100110101000010010111111111010100011101100100100101100011110010010100110111000010010110", "1111001011011001010111101101000000000101011100010011011011010011100001101101011001000111101101001", 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"1111001011011001010111101101000000000101011100010011011011010011100001101101011001000111101101001", "1111001011011001010111101101000000000101011100010011011011010011100001101101011001000111101101001", "1111001011011001010111101101000000000101011100010011011011010011100001101101011001000111101101001", "1111001011011001010111101101000000000101011100010011011011010011100001101101011001000111101101001", "1111001011011001010111101101000000000101011100010011011011010011100001101101011001000111101101001", "1111001011011001010111101101000000000101011100010011011011010011100001101101011001000111101101001"}

Returns: "possible"
{"1101100001010111010000111101000101111111111101001110100000001001101010111011110111100010101110101", "0010011110101000101111000010111010000000000010110001011111110110010101000100001000011101010001010", "0010011110101000101111000010111010000000000010110001011111110110010101000100001000011101010001010", "1101100001010111010000111101000101111111111101001110100000001001101010111011110111100010101110101", "0010011110101000101111000010111010000000000010110001011111110110010101000100001000011101010001010", "0010011110101000101111000010111010000000000010110001011111110110010101000100001000011101010001010", "0010011110101000101111000010111010000000000010110001011111110110010101000100001000011101010001010", "0010011110101000101111000010111010000000000010110001011111110110010101000100001000011101010001010", "0010011110101000101111000010111010000000000010110001011111110110010101000100001000011101010001010", 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"0010011110101000101111000010111010000000000010110001011111110110010101000100001000011101010001010", "0010011110101000101111000010111010000000000010110001011111110110010101000100001000011101010001010", "1101100001010111010000111101000101111111111101001110100000001001101010111011110111100010101110101"}

Returns: "impossible"
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Returns: "impossible"
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Returns: "possible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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"1111111111111111111111111111111111111111111101111111111111111111111111111111111111111111111", "1111111111111110111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111110111111111111111", "1111111111111111111111111111111111111111111111111111111101111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111101111111111111111111111", "0111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111110111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111101111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111101111111", "1111111111111111111111111111111111111110111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111101111111111111111111111111111", "1111111111111111111111011111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111011111", "1111111111111111111111111111111111111111111111111111111111111111011111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111110111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110", "1111111111111111111111111101111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111101111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111011111111111111111111111111111111111111", "1111111111111111111111111111110111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111011111111111111111", "1111111111111111111111111111111111111111011111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111110111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111110111111111111111111111111111", "1111111111011111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111101111111111111111"}

Returns: "impossible"
{"1111111111111111111111111111111111111111111111111111111111111111011111111111111111111111111", "1111111111111111111111111111111111111111111111111011111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111011111111111111111111111111111111111111111111", "1011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111110111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111101111111111111", "1111111111111111111111111111111111111111111111111111111111111111110111111111111111111111111", "1111111111111111111111111111111111011111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111011111111111111111111111111111111111111111111111111111111111111111", "1111111111011111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111011111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111101111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111011111111111111111111111111111", "1111111111111111111111011111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111110111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111110111111111111111111111111111111111111111111111111111111111111111111111111", "1111111110111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111101111111", "0111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111011111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111110111111111111111111111111111111", "1111111101111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111011111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111101111111111", "1111111111111111111111111111110111111111111111111111111111111111111111111111111111111111111", "1111011111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111101111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111011111111111111", "1111111111111111111111111111111111111111101111111111111111111111111111111111111111111111111", "1111111111111111111111111111101111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111101111", "1111111111111111111111111111111111111111111111111111111111111111111111011111111111111111111", "1111111111111111111111111111111111111111111111101111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111101111111111111111111111111111111", "1111111111111011111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111011111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111110111111111111111111111111111111111111111", "1111111111111111011111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111110111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111110111111", "1111111111111111111111111111111101111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111011111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111110111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111110111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111110111111111111111111111111111111111", "1111111111111111111111111111111111111111011111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111011111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111101111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111101111111111111111111111", "1111111111111111111111111111111111111111111111111101111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111101111111111111111111111111111111111", "1111111111111101111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111011", "1111110111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110", "1110111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111011111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111110111111111111111", "1111111111111111111111111111111111111111111101111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111101111111111111111111111111111", "1111111111111111111111111110111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111110111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111011111", "1111111111111111111111111111111111111111111111111111101111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111011111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111011111111111111111111111111111111111111", "1101111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111110111111111111111111111111111", "1111111111111111111111111111111111111111111110111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111110111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111101", "1111111111111111111111111111111111111111111111110111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111110111", "1111101111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111110111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111011111111111111111111111111111111111", "1111111111111111111111111111111011111111111111111111111111111111111111111111111111111111111", "1111111111111110111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111101111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111101111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111101111111111111111", "1111111111111111111111111111111111101111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111011111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111110111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111110111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111101111111111111111111", "1111111111111111111111111111111111111101111111111111111111111111111111111111111111111111111", "1111111111101111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111110111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111011111111", "1111111111110111111111111111111111111111111111111111111111111111111111111111111111111111111"}

Returns: "impossible"
{"1111111111111111111111111111111011111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111110111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111011111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111101111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111011111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111101", "1111111111111111111111111111111111111111111111111111111111111111111101111111111111111111111", "1110111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111110111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111101111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111110111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111101111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111110111111", "1101111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111110111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111110111111111111", "1111111111111111111111111111110111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111101111111111111111111111111111111", "1111111111111111111111111111111111110111111111111111111111111111111111111111111111111111111", "1011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111011", "1111111111111111111111111111111111111111111111111111111111111111111111111110111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111011111", "1111111111111111111111111111111111111111111111111111011111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111011111111111111111111111111111", "1111111111111111111111111111111110111111111111111111111111111111111111111111111111111111111", "1111110111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111101111111111111111", "1111111111111011111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111101111111111111111111111111111111111111111111111111111111111111", "0111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111110111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110", "1111111111111111111111111111111111111111111111111111111011111111111111111111111111111111111", "1111111011111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111011111111111111", "1111111111111111111111111111111111111111111111111011111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111101111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111011111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111110111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111110111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111110111111111", "1111111111111111111111111111111111111111111110111111111111111111111111111111111111111111111", "1111111101111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111110111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111101111", "1111111111111111111111111111111111111111111111111111111111110111111111111111111111111111111", "1111111111111101111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111110111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111011111111", "1111111111111111111111111111111111111111011111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111110111111111111111111111", "1111111111111111111111111111111111111111111111110111111111111111111111111111111111111111111", "1111111111111111111111111111111111111011111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111101111111111111111111111111111111111", "1111111111111111111111111111111111111111101111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111110111111111111111111", "1111111111111111111101111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111011111111111111111111111111111111", "1111111111111111111111111111111101111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111101111111111", "1111111111111111111111111111111111111111111011111111111111111111111111111111111111111111111", "1111111111111111111111111111111111011111111111111111111111111111111111111111111111111111111", "1111111111011111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111011111111111111111111", "1111111111111111111011111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111011111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111101111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111101111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111101111111111111111111111111111111111111111111111", "1111111111111111111111111101111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111101111111111111", "1111111111111111111111111111111111111111111111111111111111111111111011111111111111111111111", "1111111111111111111111111111111111111111111111111101111111111111111111111111111111111111111", "1111111111111111111111111011111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111011111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111110111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111110111", "1111111111111111111111111110111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111101111111", "1111111111111111111111110111111111111111111111111111111111111111111111111111111111111111111", "1111111111111110111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111101111111111111111111", "1111111111110111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111011111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111011111111111111111", "1111111111111111111111111111111111111101111111111111111111111111111111111111111111111111111", "1111111111111111111111011111111111111111111111111111111111111111111111111111111111111111111", "1111111111101111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111101111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111101111111111111111111111111111111111111111111111111111111111111111111111111"}

Returns: "impossible"
{"1111111111111111111111111111110111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111101111111111111111111", "1111111111111111111111111111111111111111111111111111111111111110111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111101111111", "1101111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111011111111111111111", "1111111111111111110111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111011111111111111111111111111111", "1111111111111111111111111111111101111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111110111111111111111111111111111111111111111111111111", "1111011111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111110111111111111111111111111111111111111111111111111111111111", "1111111111111111111111101111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111011111111111111111111", "1110111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111011111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111101111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111110111", "1111111111111111111111111111101111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111011111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110", "1111111111111111111111111111111111111111111111111101111111111111111111111111111111111111111", "1111111111111111011111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111101111111111111111111111111", "1111111111111111111111111111011111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111110111111111111111111111111", "1111111111111111111111111111111111111111111111111011111111111111111111111111111111111111111", "1111111111111101111111111111111111111111111111111111111111111111111111111111111111111111111", "1111110111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111011111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111011111111", "1111111111111111111111011111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111101111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111110111111111111111111111111111111", "1111101111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111101111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111110111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111011111", "1111111111111111111111111111111111111111111111111111111111111111111110111111111111111111111", "1111111111111111111111111111111111111111111111111111111101111111111111111111111111111111111", "1111111111111111111111111111111111101111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111101111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111101", "1111111111111011111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111011111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111101111", "1111111111111111111111111111111111111111111111111111101111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111011111111111111111111111111", "0111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111110111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111011111111111111111111111111111111111111111111111111", "1111111111101111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111110111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111110111111111111111111111111111111111111", "1111111111111111111101111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111110111111111111111", "1111111110111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111110111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111101111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111101111111111111111111111111111111111111111111111111111", "1111111101111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111011111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111101111111111111", "1111111111111111111111110111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111101111111111111111", "1011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111011111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111011111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111110111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111011111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111011111111111111111111111111111111111", "1111111111111111111111111111111111111011111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111110111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111110111111111111111111", "1111111111111111111111111111111111111111111111111111111111111101111111111111111111111111111", "1111111111111111111011111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111011111111111111111111111111111111111111111111111111111111111", "1111111111111111111110111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111110111111111111111111111111111111111111111", "1111111111011111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111011111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111110111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111110111111111", "1111111111111111111111111111111111111111101111111111111111111111111111111111111111111111111", "1111111111111111101111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111011111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111011", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111110111111", "1111111111111111111111111111111111111111111101111111111111111111111111111111111111111111111", "1111111111111110111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111110111111111111111111111111111111111111111111111111111111111111111111111111111111"}

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

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

Returns: "impossible"
{"1"}

Returns: "possible"
{"00", "00"}

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

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

Returns: "impossible"
{"11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111"}

Returns: "possible"
{"1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111"}

Returns: "possible"
{"1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", 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"1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111"}

Returns: "possible"
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Returns: "possible"
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"1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111"}

Returns: "possible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "possible"
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Returns: "possible"
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Returns: "possible"
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"0000001000000000010000001000001010001101100000000000000000100000000000000000000100000000010"}

Returns: "impossible"
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"0000001100010000100000000100000000100001000000000100000000000000001000000010000000000000000000000", "1000001000000000000000100000000000000000000000000000011000100000000100000000000000000000000000000", "0000000100000000000000000101000000000000101000000000000000000000000010000000000010000010000000001"}

Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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Returns: "impossible"
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"00000000001000000000010000101000000000000001000000010110000000010000010000000000010000010000100"}

Returns: "impossible"
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Returns: "impossible"
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"011110100111101111110010101001001110101101111111111110101000101101110101001101111100111010000", "011110110001101001011110111000011100000101110101110111010000100110011100100010010100011110011", "001001110111100101011111111110100011111110101001100000011111100101111110111110110100100111011", "000101111001111111110010111011111101000110001110110111011101110100101111101100010101110101101", "101000001011011001000010110000011111101111111100000001110000100111111011101110110011010111011", "001010010111001011001011010100100110011101000011011010001101111100111011110101010101111111111", "000100001101001101000110101011001100000001000101111011001110100110011101101110100101100001001", "001000001010010001011011111011111011111000011101001001011001110100011100100111000101011111011", "000000100101000000011001001111101001011010111100101001111100100101011101010111111100111111111", "010111110101011110011011111111110101001101100100110011001100100110011101101110110110011110101", "001000000010011111100000100010001110111101110001011010110101101100001001001011000100111011111", "110100111101011111010110110010101111000100111011001010001110010110001101110101101111000011100", "101011100011011011010111010100111101111010011100110010100011111000011001111011111100101011101", "000011010111111101011011111001111111001011110011011010101011100011100111010111011101101010011", "011110111110011111110110001010100111000010010011111001000000010101001111001111111011011111101", "101100001111000100010011000110111111010000111110100011101110110111100001101110100100100111101", "001010111101000101010010101010100001000101110000110111000010100100101111111111100111111101001", "010010000001000010101011001000101110111111110001110000000000000100111110101110100011011000101", "101001111101110100100110101111100111011101111000110001001100011100011001100110101101111111111", "011110011010100011000010011110011110001111010111110111000100101110100101101111100101011010000", "001111011111010010010110000101111100000011111001011011101011000000111001111111111110101111101", "001001111111110001101111110100110101011101111111001001100001000101101101101101100101010010010", "100100111111011110101000011010101011111010110100111111000111000101010011100010111101101110111", "000000110111011000011100100010000111001001000001110011001001100000101001011011011111100111101", "010010011111010011100100101010010101010111101100011000001100011111101100011101000100100111101", "010011111000011011000011111010111110011100110111001010001100100111011010011101010001111010100", "001110011111001011010110011011011101101101110001011010001100010110111100100110010000111110100"}

Returns: "impossible"
{"1111011100000001111111001101111100110101111111111100010100011010011111001001110010110101011", "1000111011100111011011111001010001110000101111100010100100101010111111100000110111111101000", "1000100000011011110010000000001000010000001000001100001000101110000000000110010100100100101", "0111110010010100101011001001101001010111110010010111111111010111000000110111011110100100010", "0101001011011000011010010100000001100011101101111110101110111000100111100000110101110111101", "0110111111010110001010001101000010110101101010100110011011110100101010000001010100000101010", "1110100110011100101101001011110111001111001101111111111011100110010110101110110001010110111", "1111011011011110111111011011010110001100100111001000101111011000110110110000111111110101011", "1101101101111111011111100011111111110100111110111111110001111001111001100001110001001111101", "1001101110010100101110101111001110010101111101111010110110111101011010101111110111001001111", 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"1001100101010100010100011011110011111000000100000010101101101001011000101011011000101100001", "1010011110110001010000100000010111000111110100110111111111001011010111100010011011100001111", "0010111001110110001010001010111110011111111110100101110010010110111010111010001111111110010", "1110111101110111011110101101010111010111111011111011110101110001010111110001011100100001010", "1100011110101011011000001111010001101111110001010100110101110011111100000101101111010011000", "1001100111111100100011110011100011111001010111011111110111101100111111100110111011011101011", "1110010111111111101010110101110110110110111100111011101001011111111100100011010101101100110", "0101100100000100000100001111000000110001111000111101000010110100111010110000000111111101000", "0111111101010110111001000001111001010111101000111111000111011010001000110111010100100111111", "0110011111001000010100110001000100100111100100001000101011010001111000010010100000110001100", 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Returns: "impossible"
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"100110110111110001111001111111100101110101110111011101000001111111101111111110011110101110111", "111010111110101111110101010001110111000011010111111111000010111011001011111100110111100111101", "111000001000011011010000000101010000001100100101100111101111010100001110010001101110000011001", "000001110001010010000001010000001001011001110001000000001000000100001101000100000000000000000", "101111001011110110110010101101101110110001111100011001000101111001111100011101110110101100111", "010111101011010010111111011101110010101110101101011110101111111011101111101111101101111111000", "001010001100001000011101100010001110100100000000010110001100010001001101100110001001110101000", "011111010111101011110101111101011101110010010101111100101110101111001011111000111111000101101", "101111011010111110111101101010101111010111010111111011111011100011001111011111100111110100011", "100010110011111011101111100111110100110110111010110101110100111011111111101100100111111111101", 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Returns: "impossible"
{"0100000010001110110001100010110011101101010100001010000010101000110100100100111101000100010", "1111111001111010110110100111010110111110101101110110110111111110000000100001110111101010110", "1001001010100010000010000100000000011000001110000011001000010000010011100100100000000100000", "1001110101100000101110010100010101111101111110011011001001011111010001110111001101011011011", "0110001100100100101010100010000110011101000111111100010110101000100011101000010001000000100", "1111111110101110110101111110111001111011011110011010111101110010010101101000010101100001101", "1101101100111000001101100111001001001111111011001100011000111011111110101011010111010111100", "1111100011101101011110100010110101111100101110010101111111010101110011110111110100110101100", "1110101101101010110011111111111101111111111100111100011111111111111111111111101011101111111", "1111110110110101011000001000010011100111001011010100101100110010100110110001000100011010011", 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"1101111101011111011010111011111110111111111111010111111111101110111011101100110101111110111", "1111100101111011111111111111111111111111111011011010101111101110001111110111011111100101101", "0010000111000010111101100101101111101010110000101100101011010000000001001100100100010010101", "0000001000000000000110000000001000000000000000000000100100001100010000001000000000000000001", "1111011101101111011111110101101011111111111111111011111111110111111111111011010001111111111", "1111111001110011011111111001111101111111111101111111011000011111011100110100101000111011111", "1011001001111101111010111001111111011111111011101111111111011101111111111111111101110011111", "1011110011001111101011010111111110101011100111100111100000010010110111000110101011000011011", "1011101101111111111111111111100011110111111111111010010111101101111110111011111110011010111", "0001101100110001011001110110100010000111110111010110001111011010110001000010010000101010111", "0111100111101011111111111011101111101011101111111011101110101011101111110111111100110111111", "1011101011110011110010111011101011110000100010001010111010110010100011001110111000110010001", "1110011111110111011111111011101111111111110110111111001111100011101010011111011111000111111", "1110101110100101111010010010101101001111100110001000011101111101101111101000100100011000111", "1111111111111110111011101111111111111011111110111111110111111101111101101111110101110111110", "1111111111111101101010111101010011111111110111110011111100110101100011101111110100110110110", "1111111111110111101101110111011111101111111101011001011111111111111111111101111101010111110", "0110101110100000000111000010100100111011001001010000011111101101010010110101001100100011110", "0100001110010001001100011110100100111001010001000111001001010010001000101111110101010001000", "1011111110011110111111101111111111111110111010101111111110111111001111101111110000101011101", "0111000001010010101111010001000000000001110000100001001000100100100010000100001100000000000", "0111011011000111110011010101000110001010100010011010000111000000000010000100000110110011010", "0111111101111111001111110111011110011111111111101111011011111101110111111001111101101011111", "1111111011111110111110111110101111110111111111111111110111101111110111101111110101110110110", "1110100101111111110110001110010011111110101110101010011010111011111111001001100101110010001", "1011111110111101110111110110001011111111001110010011110101011010111110011010001101100111111", "1001001111111101001001111101111111110111111110111110110111111101101101100011101101011011011", "0111111101101001111110110011101101110110111110111011011101110100100101001011011100000001011", "0111110101101101100101010111001110101010111111111110011111010011111111111111110100010011111", "1110111111111011101101011111111101111111010110011111111111111010010010111111011000011110011", "1110111100111001101111101110010100111010011011011111111000100010100011011101000000101111101", "1000011110000011010010110000110111011100110011111111111110101001110011011111011000001110111", "1010001000000110110110101101000011000101001010101010111100001111000101000111011100010100000", "1010111010001100111010111010101110101011001010000100010000111110100001011001010110111111101", "0010000010100000000100000001011001000000100010101100000011001011100000010111010000000000100", "1110101010110111111101100010101110111010100110111000101011101100100110100000110100111101010", "1111001111110011111011111111001111110111011001011010111101010111111111101111110100111110111", "1111101101011110011110101111110101111111111101011110111111111111110111111011111101111110101", "0111111111011000111011010001011001111111111101011010100111110101101101011111111000100011111", "1111110100111010110101001101101010111101100110011101110001101101100010000111101110101011101", "1110111111111011011011110111110111110111111110100000111010111111101111111111111101110100111", "0111011111110010100000100011001001010001010000110001001000100000010111101111010000001000001", "1110110110110001100000100000001000000000000100001010101000000110010110000010000000000100001", "1111110011111111101111010111101101111110101111111110111111110101100111110111000110111001011", "1111111111111011111111111111011111011111101111110111111001111011110010111111011101111111111", "1101110011110101010010101110010101111111101101100000111111011110101101111111111011111101101", "1110101010010010101110100000010000110010011100010010011010111001111111101111001010011001111", "1111010001011000100011011111001100100111101111000011010001110101010010110111110111101110100", "0011111110100111110101100001001100010110110111101011100111011110111110100101000010111011111", "0110111101111011111001100111100111111111111111011100110110001000101011010010100110010011100", "0010000010110000011000100010000100101100001000010010110001100001000110011010000101100010100", "0000000000010011100010000100001011100000000101000011001110000100110001101000100010001110100", "0110111011010000011010010011011101111110011101000100001101011010010111101111100000001010111", "0101011101111010110111100100011110011101001001100101110100010111011110111111010110101100111", "1011111101111001101011100111001001111111011011011111111110110110011101111111101000100010110", "0111001110011110111011110001100001101001011101111110110101011110110100110011111100110110111", "1110111101111110110110100101001111011011010110111011001110011011101111100100111011110100011", "0000100000100000100000011001000100010101011000010010001000111010100000000110000010001010101", "1101111111110101100111101011110111101011111101111111010111111100101111111111111001010010111", "1101001000101000001001011101101010100000101110111000011110110100110001000001010110010100001", "1000111101111101101011100111001101110011111111110000101111010111111110111011010100111101010", "1001111111111011011111111111111011101111111111111111111111011101011111111111101111111100111", "1011011111111111011001111111110101111111110011111010110001111000011111111111111111111110111", "1111011111010010111111110111101110101001111111111110101100111010111011110110110101001111100", "1001100010111110010111101011011101110100011111110110011001010110110011001110101100101110011", "1100111111111111111111101010110011011111111010011111011111111111110111111111100110111111111", "1111100110000110000001111000101110111111010010011000110101001000110111101001100101000110000", "1101011011011001111000110001101101011111101101011011101100110001100011010011101101001111111", "0111101111111111111011010111001101111111111111111111000111110111111110101101111110100100110", "0110111111010010000000101000100100011110010110011011101100011111011101111111010010111001111", "1111011111101111110001101101111111111101111111011100111101111111111111011111010111110111010", "1011101000000011000000100011000100000111101100000001000100000100100111111101110001111111010", "0100001110010100010001010010000001000110001110100001011110110000010010100000000110000001100", "0010001101111101111011100111100010100111001110011010111101101110110000011100011110011000011", "0111101011101011111110111000101011100000011111010010111001001111110101100111110100111010101", "1111110111010111111111110010111101111111111111111111111101010111110111101111100101111111111"}

Returns: "impossible"
{"10101", "01010", "01010", "10101", "10101"}

Returns: "possible"
{"00110", "00110", "11001", "00110", "00110"}

Returns: "possible"
{"110101", "001010", "110101", "110101", "110101"}

Returns: "possible"
{"111001", "000110", "000110", "111001", "111001", "000110"}

Returns: "impossible"
{"011110", "100001", "011110", "011110", "011110", "100001"}

Returns: "possible"
{"0110010", "0011011", "0111110", "1101111", "1001100", "0100011", "1001111"}

Returns: "impossible"
{"011111", "111010", "001010", "101011", "110100", "101110", "001111"}

Returns: "impossible"
{"110011", "110110", "111111", "110011", "111011", "111111"}

Returns: "impossible"
{"011001", "001011", "101111", "100110", "101101", "001001", "001101"}

Returns: "impossible"
{"0110011", "1011000", "0101000", "0010001", "1010011", "1011011", "0111100"}

Returns: "impossible"
{"01", "01" }

Returns: "impossible"
{"0110011", "1011000", "0101000", "0010001", "1010011", "1011011", "0111100" }

Returns: "impossible"
{"011", "111" }

Returns: "impossible"
{"10", "10" }

Returns: "impossible"
{"0" }

Returns: "impossible"
{"11", "11", "00", "11" }

Returns: "impossible"
{"01", "01", "01", "01" }

Returns: "impossible"
{"100", "010" }

Returns: "impossible"
{"1100", "1111", "1111", "1111" }

Returns: "impossible"
{"010101011011101", "010101011011111", "010101011001101", "010101011011101" }

Returns: "impossible"
{"111", "110" }

Returns: "impossible"
{"1011", "1010", "1101", "1111", "0010", "0000", "1111", "1101" }

Returns: "impossible"
{"01010", "10101", "01010", "01010" }

Returns: "possible"
{"00", "11" }

Returns: "impossible"
{"01" }

Returns: "possible"
{"10" }

Returns: "possible"
{"000", "111", "111" }

Returns: "impossible"
{"00000", "00000", "00000", "00000", "00000" }

Returns: "impossible"
{"00" }

Returns: "possible"
{"00", "00", "11" }

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

Returns: "impossible"
{"0000", "1111" }

Returns: "impossible"

Statistics

Problem Statement for "UniformingMatrix"

Problem Statement

Definition

Notes

Constraints

Examples