TopCoder Statistics - Problem Statement

Problem Statement

Let G=(V,E) be an undirected graph.

A spanning subgraph of G is a graph that can be created by removing some (possibly empty) subset of edges from G. Note that a spanning subgraph must still contain all vertices of the original graph G.

A spanning subgraph H is called a half of G if the degree of every vertex v in H is exactly half of its degree in G.

You are given String[] a: the adjacency matrix of the graph G. More precisely, a[i][j] is '1' if vertices i and j are connected by an edge, and it is '0' if they are not.

Find and return the adjacency matrix of any graph that is a half of G. If there are multiple answers, you may return any one of them. If there are no answers, output an empty String[] instead.

Definition

Class:: HalfGraph
Method:: compute
Parameters:: String[]
Returns:: String[]
Method signature:: String[] compute(String[] a)
(be sure your method is public)

Constraints

n will be between 1 and 50, inclusive.
a has exactly n elements.
Each element of a is a string of length n, consisting of characters '0' and '1' only.
The matrix is symmetric, i.e., for all i,j we have a[i][j] = a[j][i].
The main diagonal contains only characters '0'. In other words, the graph doesn't contain any loops.

Examples

{"000", "000", "000"}

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

An empty graph is its own half, because the half of zero is zero.
{"01111", "10111", "11011", "11101", "11110"}

Returns: {"00011", "00110", "01001", "11000", "10100" }

The input is a complete graph G on five vertices. In the graph G the degree of each vertex is 4. Thus, the output can be any subgraph of G that has 5 vertices and in which the degree of each vertex is 2.
{"010", "101", "010"}

Returns: { }

This graph contains the edges 0-1 and 1-2. It does not have any half, because you cannot have a vertex of degree 1/2.
{"01111", "10100", "11000", "10001", "10010"}

Returns: {"00011", "00100", "01000", "10000", "10000" }

Remember that the returned graph must be a subgraph of the original one. You are not allowed to add new edges, you may only erase the existing ones.
{"01111","10111","11011","11101","11110"}

Returns: {"00011", "00110", "01001", "11000", "10100" }
{"011","101","110"}

Returns: { }
{"0000000000","0010101001","0100000100","0000000000","0100000111","0000001001","0100010011","0010100011","0000101101","0100111110"}

Returns: { }
{"0011111111","0011111111","1101111101","1110111110","1111010111","1111101101","1111010111","1111111001","1101101001","1110111110"}

Returns: { }
{"01111110010111111111","10011111101111111101","10011111111111111111","11101111110111111111","11110111110111111111","11111011111011101101","11111101111111110111","01111110111111111111","01111111011111111111","10111111101111111111","01100111110100111111","11111011111011111010","11111111110101111111","11111111110110011101","11111111111110011111","11111011111111101111","11111101111111110111","11111111111011111011","10111011111110111101","11111111111011111110"}

Returns: {"00001010000111000111", "00010110100100101100", "00011001011010010110", "01100101100001011001", "10100110010010101001", "01011001010001100100", "11001000101100110001", "00110100001011011010", "01010010010111001001", "00101100101100100110", "00100011010000011001", "11000010110000110010", "10101001100001101100", "10010101100010010001", "01001110010110000110", "00110011001101000011", "01011001101010000110", "11100100010010101001", "10100001010100111000", "10011010101001010100" }
{"011101111111111111111101111101","101111110111111111111111111111","110111011111111111111111111111","111010111111111111111111111111","011101111111111111111111111111","111010111101111111111111011111","110111001111101111101111011111","111111001111111111111111111111","101111110111111011111100111011","111111111011111111111111111011","111110111101111111111111111111","111111111110111111111111110111","111111111111011111111111011111","111111011111101111111111111111","111111111111110101111111111111","111111110111111011111111111111","111111111111110101111111111111","111111111111111110111111111011","111111111111111111011011111111","111111011111111111101111111111","111111111111111111110111111101","111111111111111111011011111111","011111110111111111111101101111","111111110111111111111110111111","111110011111011111111111011111","111111111111111111111101101111","111111111110111111111111110111","111111110011111110111111111011","011111111111111111110111111100","111111111111111111111111111100"}

Returns: {"000001010111101010101001100100", "001100110100010101010110011010", "010011001010101010101001100101", "010010101001010101010110011010", "001100011010101010110001100101", "101000100101010101001100011010", "010101000100100101001010010101", "110010001001011010100111001010", "001110010011000010101000101001", "110001100010101101010101010010", "101010001100011001011010011001", "100101011000110010110100100110", "101010100101001110001011000101", "010101010011000101100101011010", "101010010110100001011010100101", "010101100100110010100101011010", "101010011001100100011010100101", "010101100110011000110100110010", "101010011001010101001001011001", "010110000111001011000110100110", "101001101010101010100011001001", "010101010101010101010001011001", "010100110010101010011000100110", "101010010100110100101100001101", "101010001001001011010010010110", "010101100110010101100100101001", "010101011010010100101101010010", "101010100001101010010011100001", "010101010101010101010010101000", "001010101010101010101101010100" }
{"0111111111111111111111110111111111111111","1011111111111111111111111111111111110111","1101111111111011011111101111111111111111","1110111101111111111110111101111111111111","1111011111111101111111111111111111111111","1111101111111111110111111111111111111111","1111110111110111111111111111111111111111","1111111011111111111111111111011111111111","1110111101110111111111111111111101111111","1111111110111011111101111111110111111111","1111111111011011111111111111111111111111","1111111111101111111111111111111110111111","1111110101110110111111111111111111111111","1101111110011011111111111111111111111111","1111011111111101111111111111111111111111","1111111111110110111111111111111111111111","1101111111111111011111111111111111111111","1111111111111111101111111111111111110111","1111101111111111110111111111111111111111","1111111111111111111011111111110111111111","1111111110111111111101111111111111111111","1110111111111111111110111111111110111110","1111111111111111111111010111111111111111","1101111111111111111111101111111111111111","0111111111111111111111010111111110111111","1111111111111111111111111011111111101111","1110111111111111111111111101101111011111","1111111111111111111111111110111111111011","1111111011111111111111111111011111111111","1111111111111111111111111101101111111111","1111111110111111111011111111110101111111","1111111111111111111111111111111011111011","1111111101111111111111111111110101110111","1111111111101111111110110111111110111111","1111111111111111111111111101111111011111","1111111111111111111111111011111111101111","1011111111111111101111111111111101110111","1111111111111111111111111110111011111001","1111111111111111111111111111111111111001","1111111111111111111110111111111111111110"}

Returns: {"0000101010101010101010100111100001010111", "0011010101010101010101010101001010100110", "0100010110100010011010101010010101101010", "0100101001011001100110011000100110010101", "1001011001001100011001101001011001101010", "0110100100110011000110010110100110010101", "1001100011000101110001101001011001101010", "0110010010110100101101010100010110010101", "1010001100010011010110010010101100101010", "0101101000101010101000101001100101010101", "1010010101011000100101100110011010101010", "0101010110100011011001000110110010010101", "1001100001100100010110011001011001101010", "0100101100001011001001100101100110010101", "1010010011010100100110010110011001101010", "0101011010010100011000111001100110010101", "1001001101100010010011100110011001101010", "0110101010011001100110001011001101010001", "1010100101010101000101011001100110010110", "0101010110101010011000101100110001101001", "1011010010001010110001010110010110010110", "0100101100110100101010100101101000101010", "1010101001100101100101010010010110101001", "0101010110001011001010101001101001010101", "0011101001001001011100010011000110101010", "1100010100110110100111000010011011000101", "1010010010110010110010101100101000011010", "1100101001001101011001011000110101010001", "1001010011010101001101010011000110100110", "0010101100111010100110100101001000101101", "0100101010101010110001010110010001011010", "0011010111000101011010101001100011010001", "0101010100110101001010101100100100100110", "1010101001001010110100010101001100110001", "0110101010101010100101101000110011001010", "1001010101010101011010010011001101000101", "0010101010101010100101101010011000100101", "1101010101010101001010010100110010011000", "1110101010101010101011001010101010100000", "1001010101010101010100110101010101011000" }
{"01111111111111111111111111111111111111110111111111","10111111101111111111111111111111111111111111111111","11011101111111111111111111111111111111111110111011","11101011111111111111111111111111111111111111111111","11110011111111111111111111111111111111111111111111","11100011111111011111111111111111111111111111101011","11011101111111111111111111111111111111111111111111","11111110111111111111101011111111111111111111111110","11111111011111111111111111111011111111111111111111","10111111101111111111111111111111111111111111111111","11111111110111111111111111111111111101110111110111","11111111111011111111111111110111111111001111111111","11111111111101111111111111111111111111111011111111","11111111111110111111111111011111111111111111111111","11111011111111011111111111111111111111111101011111","11111111111111101111111111111111101111111111111111","11111111111111110101111111111110101111111111111111","11111111111111111011011111111111111111111111111111","11111111111111110101111111101111111011111111111111","11111111111111111110111111111111111111111111111101","11111111111111111011011111111111111111111111111111","11111110111111111111101111111111111111111111111111","11111111111111111111110111111111111111111111011111","11111110111111111111111011111111111111111111111111","11111111111111111111111101111111011111111111111111","11111111111111111111111110111110111111111111111111","11111111111110111111111111011111111111111111111111","11111111111111111101111111101111111111111111111111","11111111111011111111111111110111111111111111111111","11111111011111111111111111111011111111111111111111","11111111111111111111111111111101111111111110111111","11111111111111110111111110111110111111111111111011","11111111111111111111111101111111011111111111111111","11111111111111100111111111111111101111110111111111","11111111111111111111111111111111110111111110111111","11111111111111111101111111111111111011111111111111","11111111110111111111111111111111111101111111111111","11111111111111111111111111111111111110111111011111","11111111111011111111111111111111111111011111111111","11111111111011111111111111111111111111101111111111","01111111110111111111111111111111101111110111111111","11111111111101111111111111111111111111111011111111","11111111111111011111111111111111111111111101111111","11011111111111111111111111111101110111111110111111","11111111111111011111110111111111111110111111011111","11111011111111111111111111111111111111111111101111","11111111110111111111111111111111111111111111110111","11011011111111111111111111111110111111111111111011","11111111111111111110111111111111111111111111111101","11111110111111111111111111111111111111111111111110"}

Returns: { }
{"00001000100010000000000000000100000000000000000000","00000000010000000001000000000000010000000001000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000100000000010","10000000001000000100001000000000010000000100101000","00000001000000000000000000000000100000000100100000","00000000000000000000001000000000000000000000010000","00000100000000000100000000001100000000000000000000","10000000000100000100101000000000010100000000001000","01000000000000001000000000000000010000010000000000","00001000000000000000000000000000000000001000000000","00000000100000000001000000000000000000010010000000","10000000000000000000000000000000000000000100000000","00000000000000000000000000010000010000000000101000","00000000000000000000000000000000000000100000001000","00000000000000000001100000000000000000000000000000","00000000010000000000000100101010000100000000001001","00001001100000000001100100000011000000000110000000","00000000000000000000000000000000000000000000000000","01000000000100010100001000000000100000000010100000","00000000100000010100001010000001010000011000000001","00000000000000000000000000100000000000000000001000","00001010100000000001100000001000010000001100000100","00000000000000001100000000010000000000010001100000","00000000000000000000100000000000000000100000000000","00000000000000000000000000000000000000000000000000","00000000000000001000010000000000000001000011001000","00000000000001000000000100000000000000000000000000","00000001000000001000001000000000110000100000000000","10000001000000000000000000000000000000000000000000","00000000000000001100000000000000000000000000000000","00000000000000000100100000000000000000000000000000","00000100000000000001000000001000010000000000000000","01001000110001000000101000001000100000010000000000","00000000000000000000000000000000000000000100100000","00000000100000001000000000000000000000000000000000","00000000000000000000000000000000000000000000100010","00000000000000000000000000100000000000010000000000","00010000000000100000000010001000000000000000001001","00000000010100000000100100000000010001000000100001","00000000001000000000101000000000000000000000000100","00001100000010000100001000000000001000000000010001","00000000000100000101000000100000000000000000000000","01000000000000000000000100100000000000000000000001","00001100000001000001000100000000001010010000000000","00000010000000000000000000000000000000000100000000","00001000100001101000010000100000000000100000000000","00000000000000000000001000000000000000001000000000","00010000000000000000000000000000000010000000000000","00000000000000001000100000000000000000110101000000"}

Returns: {"00001000000010000000000000000000000000000000000000", "00000000000000000001000000000000000000000001000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000010", "10000000000000000000000000000000010000000100100000", "00000000000000000000000000000000100000000100000000", "00000000000000000000000000000000000000000000010000", "00000000000000000100000000000100000000000000000000", "00000000000100000000101000000000000000000000001000", "00000000000000001000000000000000000000010000000000", "00000000000000000000000000000000000000001000000000", "00000000100000000000000000000000000000000010000000", "10000000000000000000000000000000000000000000000000", "00000000000000000000000000000000010000000000001000", "00000000000000000000000000000000000000000000001000", "00000000000000000001000000000000000000000000000000", "00000000010000000000000000001000000100000000000001", "00000001000000000000100100000010000000000010000000", "00000000000000000000000000000000000000000000000000", "01000000000000010000001000000000000000000000100000", "00000000100000000100000000000001010000010000000000", "00000000000000000000000000100000000000000000000000", "00000000100000000001000000001000000000001000000100", "00000000000000000100000000010000000000000000100000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000010000000000000001000001000000", "00000000000000000000000100000000000000000000000000", "00000000000000001000001000000000000000100000000000", "00000001000000000000000000000000000000000000000000", "00000000000000000100000000000000000000000000000000", "00000000000000000000100000000000000000000000000000", "00000100000000000000000000000000010000000000000000", "00001000000001000000100000000000100000010000000000", "00000000000000000000000000000000000000000100000000", "00000000000000001000000000000000000000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000100000000000000000000000", "00000000000000000000000010001000000000000000001000", "00000000010000000000100000000000010000000000000001", "00000000001000000000001000000000000000000000000000", "00001100000000000000000000000000001000000000000001", "00000000000100000100000000000000000000000000000000", "01000000000000000000000000100000000000000000000000", "00001000000000000001000100000000000010000000000000", "00000010000000000000000000000000000000000000000000", "00000000100001100000000000000000000000100000000000", "00000000000000000000001000000000000000000000000000", "00010000000000000000000000000000000000000000000000", "00000000000000001000000000000000000000010100000000" }
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Returns: { }
{"00010000111000100100000001100000000000000000100010","00000010000000000100001100000000101010000001000000","00000001001000000000001001000000000110000000000000","10000000001000000000000000110000001000000010011000","00000001010100000000000000000100000000000000010010","00000000000000000000000000000000000000001001000000","01000000000000000100100000000000001000000100011001","00101000000110100000000001011001000010000000000110","10000000000000000000000000100000000000000000000000","10001000000000000001001010100000010000000001000000","10110000000001000000000000000000000010000011001000","00001001000000000100000000100000000011000000000000","00000001000000000000000000000100011000000000000000","00000000001000000000000000010010000000100000000000","10000001000000000000001000000000000000000000001110","00000000000000000000000000000010000000000010000000","00000000000000000000000001000000010000000000000000","11000010000100000001001000000010010000000000000000","00000000000000000000100000000000000000000000000100","00000000010000000100100000100000000100100000000000","00000010000000000011000000010000000010000100000000","00000000000000000000000000101011000000001000000010","01100000010000100100000000100001000001000100000010","01000000000000000000000000010100010000100100000000","00000000010000000000000000000000000000100000100001","10100001000000001000000000000000000010100000000000","10010000110100000001011000010000000000001000000000","00010001000001000000100100100000000011101000100010","00000001000000000000010000000000000000101000000000","00001000000010000000000100000001001000010000000000","00000000000001010100010000000000000000000000000000","00000001000000000000011000000100000001000100000000","01000000000000000000000000000000000000000000001000","00000000010010001100000100000000001100000010000000","01010010000010000000000000000100010100100000100010","00100000000000000001000000000000011000000001000100","01100001001100000000100001010000000000000011000000","00000000000100000000001000010001000000000000000011","00000000000001000001000111011000001000000000000000","00000000000000000000000000000100000000000000001000","00000100000000000000010000111000000000000000000001","00000010000000000000101100000001000000000001000000","00010000001000010000000000000000010010000000010000","01000100011000000000000000000000000110000100000010","10000000000000000000000010010000001000000000000000","00011010000000000000000000000000000000000010000000","00010010001000100000000000000000100000010000000000","00000001000000100010000000000000000100000000000011","10001001000000100000011000010000001001000001000101","00000010000000000000000010000000000001001000000110"}

Returns: { }
{"01000101000000000000001000100010000000010000100011","10001000000000100000000000000011010010000000001000","00001000000000000100001000000000000000000000001000","00000000000110001000101001000000000001011010000011","01100001100000000000000000101000010000001010000001","10000000001000010000010010000001000010000100000000","00000000000010000010000000000000000000000000000000","10001000000000000000000100000011000000011000000010","00001000000000000100000000000000000010000000100000","00000000000000000000000000000000000000000000000000","00000100000000010010000001110100000000000100000000","00010000000001100000010000010000000000000000001000","00010010000001100000110000000001000001000000000000","00000000000110010001000100101100100000010000000000","01000000000110000100100110100000100000000000110100","00000100001001000000000101011111000100010100010000","00010000000000000000000000001100000000000000100000","00100000100000100000000000100001010000000000000000","00000010001000000001000000010000100000000101010000","00000000000001000010000000010000001000010001000000","00010000000010100000010001101101000001001000000010","00000100000110000000100010000000000000000000001000","10110000000000000000000000000100011000000000001010","00000001000001110000000000010000010000001001000000","00000100000000100000010000000100000000010010010010","00010000001000010000100000000110010000011010000000","10001000001001100100100000000001010000000010100100","00000000001100010011000100000001000011101000001000","00001000000001011000100000000100010000000000000010","00000000001001011000101011001000001010000101100110","11000001000000010000000001000000010000001011000010","01000101000010010100100000110000000110011010000000","00000000000001100010000000000000000000000000001000","01001000000000000100001101101010001100010000000000","00000000000000000001001000000100010001000000000001","00000000000000010000000000000001010000000000000010","01000100100000000000000000010101000000000010000100","00010000000010000000100000010000001000000010000000","00000000000000000000000000010000000000000000000001","10010001000001010001000011000001010000000000000000","00011001000000000000100101010011000000000100000110","00000100001000010010000000000100000000001001011001","00011000000000000000000011100011000011000001000000","00000000000000000011000100000110000000000110001000","10000000100000101000000000100100000000000000010001","00000000000000110010000010000000000000000100100000","01100000000100000000011000010000100000000101000010","00000000000000100000000000100100000010001000000001","10010001000000000000101010001110000100001000001000","10011000000000000000000000000000001000100100100100"}

Returns: { }
{"00001001000000010000001100000001000100000000111000","00001000001001000000011000000000100010000000000001","00000000000000100000000100011000101000010000000100","00000000101111100110111111000101000000000000010010","11000100100000001001000000001001110000000000010111","00001000010000001100010010100000000000000000111000","00000000011000001000000101100011000010000001001010","10000000000000000100000001001011001011000000000010","00011000000010000000000000000000000000110010000000","00000110000001000000000001011010000010000000101000","01010010000001100010000000000010010100000001000000","00010000000000100001100000101010001110000000000000","00010000100000000000000100001010010000101000000101","01010000011000000100001000000010000001010001001010","00110000001100001000001000001000100000000100000100","10000000000000000000000100000011001101001001000100","00001110000000100001000000101000100100110000000010","00010101000001000001101000010110101010000010000110","00010000001000000000000101111000000100000101100010","00001000000100001100000100000000000000010000000110","00010000000100000100011101010010100001100100001000","01010100000000000000100000100100001000000000000100","11010000000001100100100010010000000000101000000100","10110010000010010011100000100000010000010100000001","00010100000000000000001000000000100100000000001000","00010011010000000010100000100000011100000001000010","00000110000100001010010101001011000010000000001100","00100000010000000110101000000000001001000000110000","00101001010110101010000000100101000110010100001010","00010000000000000100010000001001110100100001000000","00000011011111010100100000100001000001000000000010","10011011000000010000000000101110000001100001010000","01101000000000101100100010000100000000100010111110","00001000001010000000000101000100000000100000000010","00100001000100010100010001010000000000000000000000","10000000001100011010000011001100000010000000110111","01000011010100000100000000101000000100000000010000","00000001000001010000100000010011000000000000001000","00000000100010001000101000000101110000000100000000","00100000100001001001000100001000000000000011000010","00000000000010010000001000000000000000000000100000","00000000000000100010100100001000000000100000000000","00000000100000000100000000000000100000010000000000","00000010001001010010000001000101000000010000100101","10000100010000000010000000010000100100001001001000","10011100000000000000000000010001100110000000000100","10000110010001000000100010101000100001000000100000","00101000000010110101011000100000100100000001010000","00011011000001001111000001001010110100010000000000","01001000000010000000000100000000000100000001000000"}

Returns: { }
{"01001000010010000000000011001000001101000110100001","10100011101100000100001100000000000100100010000010","01010001100110000111001000000100100111000000001101","00101111000001100110110000100110000100101000000111","10010001000011100001000100000000010010001001000101","00010001000000100000000001100000000010100000010000","01010001001000110000101000000000000000100010010010","01111110000000001100000111000100001010100101110111","01100000000010010100100000000000000000000010001000","10000000000000010111100001001001010000111100000000","01000010000000010110111100100010001100001100000111","01100000000001000001100100000000000100101000001000","10101000100000110000000100000001100001001001000000","00011000000100110001000010000100010100000000000000","00011110000011010110001010010001010000100001000011","00000010111011100100001010011010000000000100100010","00000001000000000010000001010000000000001101001000","01110001111000110000101001000000001010001000100000","00110000011000101000001000001100001000010000010000","00101000010101000000000010001100010011100000010010","00010010111100000100010010111100101000110011001101","00010000001000000000100000000001100100000100011010","01100010001000110110000110110100000010000001000111","01001001001110000000001000000000001000110000000110","10000001000001110001101000000001010100000000000010","10000101010000001100000000000000000010000000001000","00010100001000000000101000000001000100000000010101","00000000000000111000101000000011110000001100000001","10000000010000010011100000000000001000001000000110","00110001000001000011101000000010000011011100000000","00010000001000010000000000010100000000000000110001","00000000010010100000010010110000000000011100000000","00100000000010000000110000010000001110000000001111","00001000010001100001000010010000001000000000000011","10000001001000000110100100001000110000100001000101","11110000001101000000010010100000100001110111000100","00101101000000000101001001000100100000010100110000","10100000000010000001000000000100000100000000000000","01010111010100100001100100000000001100000110000010","00000000010000000010100100000101000110000000001100","00011000011110001100000000011101000000000000101101","10000001011000011000010000010101000110100000000010","11000010100000000000100000000000000100100000000100","00001001000010101000101000000000001100000000001000","10000001000000010100000000000010000010001000010000","00000111000000000011010000100010000010000000100000","00100000100100001000110001000000100000011001000010","00111001001000000000101100101000101100011010000000","01010011001000110001011110001000110000100100001000","10111001001000100000101000110010111000001000000000"}

Returns: {"00000000000010000000000011001000000100000110000000", "00100010100000000100000100000000000000100000000010", "01000001000100000010001000000000100011000000001000", "00001101000000100000110000000010000100000000000101", "00010000000001000001000100000000010000001000000001", "00010000000000100000000000000000000010000000010000", "01000001001000000000001000000000000000100000000010", "00110010000000001100000000000100001000100001100100", "01000000000010000100000000000000000000000010000000", "00000000000000010011000001000001000000010100000000", "00000010000000010010100000100000001000001000000101", "00100000000001000000100000000000000000100000001000", "10000000100000100000000100000000000001001000000000", "00001000000100010000000000000100000100000000000000", "00010100000010000100001000010000010000100000000001", "00000000011001000100000010001000000000000100000010", "00000001000000000000000000010000000000001001000000", "01000001100000110000100001000000000000000000100000", "00100000011000000000001000000000001000000000010000", "00001000010000000000000010001100000010000000000010", "00010000001100000100000010000100101000010011000000", "00010000000000000000000000000001000100000000011000", "00100010000000100010000100100000000010000000000011", "01001000000010000000001000000000000000100000000100", "10000000000000010001100000000000010000000000000010", "10000000010000000100000000000000000000000000001000", "00000000001000000000001000000001000000000000010100", "00000000000000101000000000000011010000000100000000", "10000000000000010001000000000000000000001000000010", "00000001000001000001100000000000000010011000000000", "00010000000000000000000000010000000000000000100001", "00000000010000000000010000110000000000000100000000", "00100000000000000000100000000000001110000000000100", "00001000000000100000000010010000000000000000000001", "00000001001000000010100000000000100000000001000001", "10010000000001000000010000000000100001010010000100", "00100100000000000001001000000100100000000000010000", "00100000000010000000000000000000000100000000000000", "01000011000100100000000100000000000000000100000010", "00000000010000000000100000000100000100000000001000", "00001000001010001000000000001100000000000000100100", "10000000010000010000000000010001000000100000000010", "10000000100000000000100000000000000100000000000000", "00000001000000001000100000000000001000000000001000", "00000001000000000100000000000010000000001000000000", "00000100000000000010010000100000000010000000000000", "00100000000100000000010001000000000000010001000000", "00010001001000000000000100100000100100001000000000", "01000010000000010001001010001000000000100100000000", "00011000001000100000001000000010011000000000000000" }
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Returns: {"00000000010000000000000100000000000000000101100000", "00001000000000011000000000110000000000000010000000", "00000011000000001000101000000000000000000000000000", "00000000000100010000001000000000001000001000000001", "01000010000010000100000011000100000010000000100000", "00000000001100000001000000000011000101000000001000", "00101000000000000000010000000000010000110000001000", "00100000010000000100000001010010000000000000000010", "00000000000000000010000010000001000000000000000100", "10000001000000000000001000000000101100010000000100", "00000100000001100000101001000000010000000000100100", "00010100000001000000000000101001001000000010000000", "00001000000000000011010000010000010000100100010100", "00000000001100000000000001100100000000010010000000", "00000000001000001100000100000010000000001000100000", "01010000000000000000100000000001000000100000000000", "01100000000000100000001000000001000110000000011000", "00001001000000100000101000000000100000000100100000", "00000000100010000000000000000001000100000000000000", "00000100000010000000100010000100100001000010001000", "00100000001000010101000000000100000000000000010000", "00000010000010000000000100110000000000010000100010", "00110000011000001100000000000000001000001000000100", "10000000000000100000010000000001000000010010001000", "00001000100000000001000001001000000000000001001000", "00001001001001000000000010000000110000100000100000", "01000000000101000000010000000000000010000000000000", "01000001000010000000010000000000000000001000010000", "00000000000100000000000010000000010000000100000000", "00001000000001000001100000000010000000000000000100", "00000101000000100000000000000101001000000100000100", "00000100100100011010000100000010100000000010101000", "00000000010000000101000001000001000100001001010000", "00000010001010000000000001001000000010010000001000", "00010000010100000000001000000010000000000000000000", "00000100010000001010000000000000100000000010010000", "00001000000000001000000000100000010000000001100001", "00000100000000000001000000000000000000000000000000", "00000010000010010000000001000000000000000100101010", "00000010010001000000010100000000010000001000000001", "00010000000000100000001000010000100000010110001000", "10000000000010000100000000001010000000101000000001", "01000000000101000001000100000001000100001000001010", "10000000000000000000000010000000100010000000000000", "10001000001000100100010001000001000010100000010000", "00000000000010001000100000010000100100000000100000", "00000110000000001001000110000001010000101010000000", "00000000111010000000001000000110000000000000000001", "00000001000000000000010000000000000000100010000000", "00010000000000000000000000000000000010010100000100" }
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Returns: {"00001001001000100000000000100001000000001001000110", "00110010110100000010000010000000000001000010001000", "01000100000000000100001100000010000000110000100100", "01000000000001010000000100000000010000000000000001", "10000000000000001010100000010000000100000000000001", "00100000001010010001000001000011000000011000000000", "01000000000100000000000100000000001010000000000010", "10000000000000110000000100000000100000000011001000", "01000000001000000100010000010100000000000000000010", "01000000000100000000010000011100100000000001101001", "10000100100001001000100010100001001000000000000010", "01000010010000001000001000010001000100100001010000", "00000100000000001001000000000000001100000000100000", "00010000001000100000010100000000010001010000100000", "10000001000001000000000010100010001000101000100000", "00010101000000000100000000100000010100010010000000", "00001000001110000001000000001100001010000001000000", "00100000100000010000001000100100000100100000000100", "01001000000000000000000110001010000100010000000000", "00000100000010001000000000000100000000010000011000", "00001000001000000000000000000000100100000000000010", "00000000110001000000000001101000000000100000000010", "00100000000100000100000000000000110000000001110000", "00110011000001000010000000010000100100100010000100", "01000000001000100010000000010000000000011001001000", "00000100000000000000010000100001010000000000000100", "10000000001000110100010001000001000101000000010010", "00001000110100000000000110000000000000000010000001", "00000000010000001010010000000011000010000000101100", "00000000110000001101000000000000001101000000000000", "00100100000000100010000000001000000000100000110010", "10000100001100000000000001101000000000011000001010", "00000001010000000000101100000000010100000010001000", "00010000000001010000001001000000100010001000010000", "00000010001010101000000000000100000000010000000001", "00001000000110010110100100100100100010000001000001", "00000010000000001000000000001000010100000010000100", "01000000000001000000000000100100000000011000000000", "00100000000100100100010100000010000000000000000100", "00100100000001010011000010000001001001000010000001", "10000100000000100000000010000001010001000000000010", "00000000000000000000000000000000000000000000000001", "01000001000000010000000100010000100010010000000000", "10000001010100001000001010000000000100000000010000", "00100000010011100000001000001010000000000000000001", "00000000000100000001001000100010010000000001000000", "01000001010000000001000010001001100000000000000000", "10100000000000000100000101001000000010100000000000", "10000010101000000000110000100011000000001000000000", "00011000010000000000000000010000001100010100100000" }
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Returns: { }
{"00010001101011110000111000100100101100100111000101","00110111101000001100101010101110011000011011010111","01001011110010110011111000011011110110111010010100","11000011010111001110111110111100011000110010101100","00100010011101101110101010111000111010010010010001","01000010100111110100101000100001111010110101011100","01111100111000011011000010110001101101110100011100","11110000101111001110100010111110110000010001001101","11100111011011101010000000111001111111110110111011","00111010100001000111100100111001111111011111111111","11001011100001001001111001101001011000000100011010","00011101000010100001001001110110110010111100110110","10110101100101100001111000100100100100101110010110","10011101111010110111111000001111100110101011101101","10101100100111001110111100100111110011010010110111","10100110000001000011010100000001101110000111111000","01011011101000100000100000110011000100011000101011","01011101010001100011111001101111101001010111000011","00111011110001110100000000001111111100100110001001","00100010011111010100100110001000100100000011101010","11111101011011101101001001001111101011110001001010","10110000001011110100000000100111100010000110100011","11111100001111100100100010011111100010101110111011","00010000010000110001000010000001111000110000110011","01011011000000000001001100011101111000110111010001","00000000001100000100100000000000100000000100001001","11011111111110101100010000010111111100101101011101","00111011110100001000001010100110011111010001011111","01111001111001000111101010000101100110111001001100","11010001000111100110111010111011110111010111111111","01100001000101101110111000110100101010100001110110","00100110111001111110111110101100001110110010001111","10101111110111110111111111101110000111100111011010","01111101111100100010000110110100000010100110100110","11011110111000010110100110110011000010101010100011","10100010110011011011000000111101100000011010000011","00101100110101110000111000011111111001110010110011","00000010110000100100100000010100100010010000000001","10110110100111000010101110101011111010000101110110","01111111110100101100100110011101000111000101100000","01100000010111001000001000101000001100000111000001","10000110111110010110011011100100110000111011111100","11111000110011110111011010000101111110001101110010","11000101010001010101100010111110100000111110010111","00010000110101111001011100000110011010110110010000","01101110111110110000001110110110100010100111100011","00010111111001011011101001111101100000000100000011","11110111010111100000000000111111010000100101000011","01000000111110101101111100010111111110100011011101","11001001110001101110011111110101001111001001011110"}

Returns: { }
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Returns: {"01000000000001010010001000001001111010001011000000", "10000000001000000000000101000100001000100000010000", "00010000110100101000100010110000000101001000001001", "00100001010001010000001001000000100100010100010100", "00000110101000000001100000001100000000010100000001", "00001000101010000001000011000001000010101001000100", "00001001010001000010011000010100010000100010110010", "00010010000101000010000000001000011000000010101000", "00101100001000000010000100110000000010000000100100", "00110010000000110000100000100001000010010100011001", "01001100100000000010010000000000000010000000000100", "00100001000010101100101001001010100101000100000110", "00000100000101000001100010001100001001010001000001", "10010011000010011000000000110010001010010000100000", "00100000010100000100001001001001010000100001000100", "10010000010001000010100000000000100010001000001000", "00100000000101000000001000010000000100001000010000", "00000000000100100011000000000000010010000101000000", "10000011101000010100010000100000100010000111000000", "00001100000010000100001010100100010010110001100010", "00101000010110010000001101010010000100011001000100", "00000010001000000010000100100010000000000000010010", "10010010000100101001100001001000001000100100101000", "01000000100000000000110000000001100001010001001101", "00100100000010000001000000010000010010000100111000", "01010100000100100000101000010011001000100100010100", "00100000110001000011010000000001010101001001000011", "00100010100001001000100011000000011000100000010100", "10001001000110100000001000000001100000010010010000", "01001010000010000001000000000000000011000000100000", "00000000000101000000110001000000001000000000000000", "10000100010000100000000101101000100010001101000001", "10010000000100010010000100001001000000101000100000", "10000011000000100101000010110000000011000110001000", "11000001000011000000001001010010000010010000000101", "00110000000100001000100000100000000010010100001001", "10000100111001010111000010000101011100001110000100", "00100000000110000000000100100100010000110000010000", "01000110000000100001001001010000100001000000000011", "00011000010011000001100100001000001101000000101000", "10100100000000011000100000100001100010000001100010", "00011000010100000110001011000001010110000001000101", "10000011000000000010000000001000010010000001000000", "10000100000010100111100100100001000000001110110000", "00000011100001000001001010000100100000011001000001", "01010010010000001000010011011000000001000001001000", "00100001010000010000001110000000010100010000010101", "00010100101100100000100101010000001010000100001000", "00000010000100000001010000100000000000101000000000", "00101000010010000000000100100001001100100100101000" }
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Returns: {"00010010100100001111000000000000010010010010010010", "00000001010001101000001000001101000101000000010001", "00000110001000010000010010001000011000001001101010", "10000000001001000100011001000011000000100110010100", "00000001001000001000000000100110001100010000100001", "00100000010101000000100110001100000010000000010000", "10100000000010110001000010011000011000100011000010", "01001000011000000000000001000001101010000000000100", "10000000010000010100100100100010010001010000000000", "01000101100100001000011010100000001001101101100001", "00111001000000100010100001001100100000100100010001", "10000100010001000000001100000010010000000010001000", "00000010000001100000110010000100000010000101000100", "01010100000110001000001001001011000001000001001000", "01000010001010001001010001001100000101101000000010", "00100010100000000110001010110010010000011100010000", "11001000010001100001000010100000000110001011000001", "10010000100000010000000010000100100000000010001010", "10000000001000010001101000101000100001010000100100", "10000010000000101010010001010001000010100000010001", "00000100101010000010010000001000011100000100100000", "00110000010010100001100000001110001000011001000000", "01010000010101010010000101100011010000010010000110", "00000100100100000000001010100000100001100000001001", "00100110010010011100000101000100100010000100010100", "00010001001001100001001010001001001000000001010001", "00001000110000011010001100000110010101011001001010", "00000010000000010001000000000000010100000000000100", "01100110001001100010110001000011000110101000010000", "01001100001010100100010010100000011001000111001001", "00011000100101010000011000101001100010001000010100", "01010001000001000001001001001010000000000000100010", "00000001001000000110000110000010000100111001000001", "10100010100100010000101000110100001001000110000100", "00101011010000000000110001000100010010100100001000", "01001000000000101000100000111000100001010000100010", "10000101000010001001000010001010001000001010000001", "01000000110001100010000100100100010100111001000010", "00010010011000100001000100001000101001000000100001", "10001000100000010010011000100000100101000000100000", "00100000010000111000010000101010100011000000001010", "00010000011010010000100010000100011000000001000010", "10010010000100001100001000000100010010000000001000", "00100010010011001000010001100100100001000100000100", "00101000010000000010100000000001000100110000000001", "11010100001000010001000011001010000000000000000000", "00100000000101000100000100100100001000001010000000", "00010001000010000010001010010010010000000001000000", "10100010000000100100001000100001000101001100000000", "01001000011000001001000101000100100010100000100000" }
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Returns: {"01000010000010001100100100100001000100000000011011", "10010000010100000010010001010100100010001100000000", "00010110000100110010000000010010010000110000001000", "01100010000011000000000010100001000000010000010000", "00000101010001001001011001001010001000100110000100", "00101000101000110001001100101010101000010001110100", "10110001000100110000100001010010001100011010100000", "00001010001101001000010000000100000100000001000011", "00000100001000000100000001010001000011100100011010", "01001000001000000000010000001000110000001010101000", "00000101110000110000001000101010101000000011000001", "01100011000010000011000101001000010010101000010100", "10010000000100001000001010010011000000010001011000", "00011001000000100010100100101001001000100000100001", "00100110001001000001000100100100000011000101000001", "00100110001000000101011000000000110000001010000100", "10001001000010000000010001010000100010001000100000", "10000000100000010000100000000010011100000100010100", "01100000000101000000100001010000000010110001001000", "00001100000100110000010000010100010000000010100001", "10000010000001000110000010101010100000110000010000", "01001001010000011001000100010101001010101000000010", "00001100001010010000000010000001000011000001000010", "10000100000101100000010001000000001000001100010100", "00010000000010000000101000000001001000000000100001", "01001010100100001010000100001010110100000000001110", "10010100001001100000100000000000011000001110001010", "01100010100010001011010000001001100010001000100001", "00001100011101000000100001010000000000010000100100", "01000001000000100001010000000010100000100001100010", "00101110001010000100100001000100010010000010000001", "10010000100011000000011010010000110001000000011001", "01000100011000011000100001010101000000000010100101", "00100000010100010101000001100011000101000001100000", "00001110001001000100010110100000000000001110010100", "10000011000000000100000001000000010000010010001000", "01000000100100101010011000010010000000001001001100", "00000000100000100000001000000001010000000010000000", "00101000100101000010110000000100000000010100110000", "00110110000010000010100000001000000100100011000100", "01000010010100011000010100110000001010000100110000", "01001000100000100100000100100000001000101001001000", "00001010011000010001000000100010101101010001000001", "00000101001010100010001000000100010010010110000100", "00000110010001001001000010011100110000101000000001", "10010100100110000100100100000001001000101000000100", "10100000110010000010000001100001000110000100000100", "00001100000100010100000101001000101010010001011000", "10000001100000000000011001100100000000000000000001", "10000001001001100001000010010011100000000010100010" }
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Returns: {"00000010101010100100011000000111001010110000000100", "00110000100101001010000001001000000001000100100001", "01001100010010000001100110001001010100001010010110", "01000011000011001101011001100110100010000101000010", "00100100110000010010100011000001101000100100100100", "00101010001100100011001000000010001001100000110100", "10010100010000011000010010110001010010110000001011", "00010000100010101000110000010010001101001001000001", "11001001000000100010001101000001001001010000000110", "00101010001101000000101000100110100010001101010001", "10000100010010010101000010011000100110000011010010", "01000100010011000010000001011000000001110100100001", "10110001001100101010100101000101010100101010101010", "01010000010100010000000000000000001110000111000010", "10000101100010000001010010001000000001100100100001", "00001010001001000110100010000001011010010001000010", "01010011000010000100010000101000000100011001010100", "10010000001000011001010001000011100001101000100010", "01001100100110010001000100110000011011000110000101", "00110100001000100110001001100010100100000011010010", "00101001010010010000011000001011010001001000100101", "10010011000000101100100100000001001000010100100100", "10010100110000000001100000101100001100110010001010", "00100000100010000010010001010100000011010001000010", "00101010001000110000000000001000000110001001000100", "01011000100110000101000100000010110100101100010010", "00010010010000001011001000010000000011010010100100", "00000011001100000010000100100001001000100100010001", "01100000001100101000101010000000110110001000011000", "10010000010010000000001100000011100000100000001000", "10010101010000000101100001000100001100000011000010", "10101010100010010100110000010100010001010001100010", "00011000011000000101000001001100001000100100011000", "00100010000010010010100001001001000001001010100010", "10001101100001010010011000010010100010001010000101", "00100001001011001001001011001010000010100001000100", "10010010011001010010000110101000001100000101000110", "01000101100100100110100100100001010000001001100001", "10001110000110100100001001010100100100010110011100", "10000010100100011000011100100001000000100000100010", "00100001010010001100100011001000011001000110000010", "01011000010101100010010001010000100010101001000110", "00100000001011000011001000100010011000101000110000", "00010001011001011001000110000011000111000100010101", "01001100000110100100110000100001010001010010000001", "00100100011000001001000001011000100000100011000000", "00000010000010000000001000001100100000100000000110", "10101100100000001010110010100000001110100101001000", "00110010101011010101001101000011010010011100001000", "01000011010100100010100000010000001001000001100000" }
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Returns: {"00001010100100100100100000101010010001110001010110", "00000101000011011000000001010100010000100011100010", "00011000000001010010110011000001001001001100001000", "00100010100100000011000001000000101000010100000001", "10100000011001000000001000011000000111001100010000", "01000000010010000100011100010100010000100000101001", "10010000100101100000000010100010101001100010000001", "01000000010010010001001000001101000010000001000100", "10010010000001010001100000001000100110001000010000", "00001101001100000101000100010100001001100100100110", "00001000010010101010010001110110010010010001001001", "10010010010001000010101001000000100101010000101001", "01000101001000110000011010001001000001101001010100", "01101010100100101010000100100010100100001100010110", "10000010001011000101100001000000000100110010001001", "01100001100010001100101000110000010010100000101010", "01000000001001010000010011000110100001010010010001", "10000100010000110000010000100100000010001001000010", "00110000001101000001000001100001101000100010000101", "00010001110000100010000101001000011000001100011000", "10100000100100110000000010011000010100000000100000", "00100100001010001100000110100100001011010101000010", "00001101000110010000000000010100000000110001011000", "00000100010001000001010001011001000000101000100100", "00100010000010001000110001100000010101001000000101", "01110000001100101011000110010100001000100101100010", "10000010001001010110010010000100101010010010010100", "01001100011000010000101101000010000000100100000000", "10001001100010000001100100000010010010010001110100", "01000101011000001100011001100001100110010010000001", "10000010001001001000000000011000010001101000001100", "00100001000010000010000100000100100100001100000000", "00010010100101001010000000100101000101100100110010", "11000100001000010001100010001010001100010011000100", "00110010010000000011010001100000010001010001010001", "00001000100101100000100010000101110000100000100010", "00001001101000010100010000101100000001001010100000", "10101010010110001000010010000010101010011100000110", "11000110010010110010001101010010100100010001001001", "10010000001100101000011000101100011001100000101001", "00101000100011000101000110000011000011000110001000", "00111000010001000001010001010001100001001000011000", "01000010000000101010000000100100010010001001000001", "11000001001010000100011001001000011000100010000010", "01000100010100010000100101001000100110010000000001", "10001000100011001001001000101000101000000100001100", "00100100001100110001001000000010000000111100010010", "10000001010011000010000110101010010001000000010001", "11000000010001010100010001000000100101000001001000", "00010110001100101010000010000100001000110010100100" }
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Returns: { }
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Returns: { }
{"01111111101111101101111111100101111111111111101111","10111100101101100111010011000111110111111111111111","11001111111111110001011111101111111011110011100111","11001111101010011111110101100110101111101111110111","11110111101100111111111110100111101111001111111111","11111011111111111111111111110111010110001101111111","10111100111101110111111111111111111111111100111011","10111100101101110111101111100111111101100000001110","11111111011100011111111110110111001111111011111101","00100110100000111011111001000111111111001111111100","11111111100101101001111011101101111101011011011110","11101111101011001010111110011111111111111010010101","10110100000100111101110111110110101111110111101111","11100111001100101111011100010011111111101111111111","11101111011011011111111110111111110111111101010110","00111111110010101111111111101111111101011111110111","10011100111111110111011111000111111110011111101111","11011111100011111011100110101000101001111111110111","01011111110101111101101111100101111110111110100101","11111111111011111110001011110101011011111010000111","10011111111110110110010111000111111111101111110010","11111110111111111000101101101111101111111011100011","10101111111101111011010101011111001011111110011101","10111111100111111110111000101101011111011110001111","11101111101110111111100001111011001111101111010011","11110111011010011011111010101111111010111101101011","10111111101010110111010111011011111111101111010111","00000110100111100001001010101101010001111111000011","00100010001100110100011111110110101011111111100111","11111111111110111011111101011011111111011111111111","01111111110111111000111011101101111011011010011110","11101111111101111011111111110110111111111111011111","11111011011111111110110001101111011101001110001111","11100111011101111011100101110111100001011111101110","10111011111111011111111111101111100110110111011101","11011111111111111010110110100101101011111111111100","11111110110111101011111111101111001101111110011010","11111011111111110101111110111111110110111110110100","11110011100111100111111011111001001111011111111010","11100010101110111111011101011111011111101110111111","11011110111101111111111111111111110111110111111110","11011110010011111110101111111101111111111001010111","11111000111111011111111110111111111111111000101011","11111100111011111100110011111101011100101100100001","11111110110011011110110001001100010101111011001111","01011110111101110100101010100111001111111100001111","11001111111011001000001101000111111110111010110111","11111101111111111111001100101111111101011100111010","11111111001011111101110111111111110010111110111101","11111110100111011111011111111101101000010111111010"}

Returns: { }
{"00011111010100111111111111111011111111101111110111","00111011111011111011111111011101111101111111110110","01011100011011111111111011101111111111110101011011","11101001110111111111111111010101011100111111011101","11110111111011111111011010110111111111111111111111","10101011101111110110101011111110101101111110111111","11001101011111111101101110101101110010111110111011","11011110111001111111001111011111111111101110110001","01011101011111110011111111001010110111110101111110","11111011101111110111111001111001111101111110011111","01101111110101110111101111111101011111100111111111","10010110111011110011111111111111110101011111111111","01111110110101110111111101111101101110110111111111","01111111111110111010111111110011011001011011110111","11111111111111011111100001011110110111111100111111","11111111111111101101101011111111111111111111011110","11111011000001110101011101100101011101111111101001","10111111011010111010110111111111111111011111100111","11111101111111100101111101111011111111110111011111","11111011111110111010111111111001101111011111111010","11110110111111110111010111111111101111101110111111","11111000110111001111101011010011101010101111001110","11111111111111011011010111101011111111110111101111","11010011101111001111101010101001111101111111101100","11111111101101010101111101110110111111010111111111","11110101111111111111111010111101111111111001101111","10101110011111011111101111011111010111111111010101","11011101011111110111110011101111011111011101111100","11100111111110110111101101110100011111001101011111","01111111001110111100100011111011111111111111101011","10101101100101110110111010110101101111101111100111","11111011011111011111111101110110111111110111111110","11101111110110110111111111000111011111010011011111","11111011111101111110001111111101101111111111010110","11111101011011011111111111011111110000111101111111","11111101111110111111101111111111110011011101101111","10101011101010110111111011111111110101110111111110","11101101111101111111101111111111110110111110011111","11111111111010111010111101100111011011011111011011","01111110110111111111001111110101111111100110101101","11011111010101111101110101111110011101100111111111","11111111111110111111111110111111011111111011111111","11011111011111011111111110100111110011111101111110","11111000101111011111011111111111111110101110110111","11001111101111101101101111010111001110011111001111","11111111111111110011100010111001111011101111001111","00111110111110111011111111011101101111111110110111","11011100111111110110111111111011111111011111111011","11101110111111110111111011001111111111101111111101","10111111011111101110101011101110101101111101111110"}

Returns: { }
{"01111111110011001111111011110111100111111111001110","10111111111111111111011101101101111111011111111111","11011101111111011111111111111111111111111110111111","11100110001101011100011111011111000010111111110101","11100111101101110011100110111111111000011111111011","11111011111111111111111011111111111110111111011111","11011101111111111111111111111001111111101001101111","11101110111110111111101111111111111001101101111001","11101111011111111111111100111111111111101101101011","11100111101110101111111111111111111101111101010011","01111111110111111101111101011111101111101110111111","01111111111011111111100110111011111111111011111101","11100111111100111101110111111111111111101111101111","11111110101100111111111111111111111111111011110111","01001111111111011111111100111111111011111111111011","01111111101111101011111101100111111011101111111110","11110111111111110111111111111111101111101101111110","11110111111111101011111101011111111011111011111011","11101111110101111101111011111101001101101010110101","11101111111111111110111111111111101101111111101011","10101111111111111111011011111101111111111101111111","11110110111011111111101011101111111101101011111011","11110111111001111111110111111101111111111111111110","01111011111111111101001011011111111011110111111101","10111111010111001011111101110011111110111110101111","11110111011011011111111110111011011000100111011110","11101111110111111011111011011011011110111001111111","10111111111111101111101111101111111111111011101111","01111111111111101111111101110110010111111110110101","11111101111011111111111100011011011111011111011011","10111101111111111101010111111100111110111011110111","11111111111111111111111111110100110111111111110011","11101111111111111101111110010011000111111011111111","01101111110111110100111111111111001011111110011011","01101111111111111111111111110110010110111101111111","11100110111111001011111010111111101001111100110111","11110110101111111100101110111111111001001011010111","11100011111111111111111100011101110110111110010111","10110111111111111111111111111011111101011111100011","11111100010101100101101110111111111101101111111111","11111111111111111111111010111111111111110111111011","11111101111010111001101111001101011101111011111010","11111100001111110111011111011111110011111101100111","11011111110111111101111101110111101010111110111110","01111011101111111111111110111011101100111111011011","01111101011101111110111101101111111111011101101111","11101111101110111101111111110100111000011101110110","11110110001111011010101111111010101111010011011011","11101110111011111101111011110111111111111111111100","01111111111111100111110110111111111111111010110100"}

Returns: {"00001010100011001101100000010010100010111101000100", "00110101010100110010010100100101000111001010011010", "01001001011010010110001011001100011101010010100110", "01000100001001001000011001010011000000100101010001", "10100010100101000001000100101100110000010100101001", "01010011010100101010110010101001101010001011001010", "10001100101010010101101001011000101100100000100101", "01100100100110010101000110100011010001001100010001", "10001011001001101010001100010110101100100001001010", "01100100001100001010110011010101010001011001000001", "00110010110001100101001001001101001010001100110010", "01001101010010011001100000110010011010100010101001", "10100011000100100100010110101001100101100101001100", "10011000101000011010010101101010011100011000100101", "01000100101010010101101000010101100011001011010010", "01100011000101100010010101000010110001100010110010", "10010100110101000101101010110101000010100101001100", "10100011001010101000101100001011001010011000110010", "01100100110001010001011010010100000101000010010001", "10001011001100101010100101101010001001101001001001", "10000110010100101101010010100100111000101100101010", "01010100010011010010101001001001100101000011010001", "00110010101000101110010010011100101000111000101010", "01001001100011010101000001010011010010010011010100", "00100101010010001010101001100000100110100100100101", "00110010011001010001010110001001001000000110001010", "01001101000111001001100010010010010100101000101100", "10010010110100101010001100100011011001010011000110", "00101110001011000101011001000100010011100100010001", "01101000111000101010101000001010001100011001010001", "10010001100101010101000100110100010010010010100110", "01010101011010101100010101010000100110100101010001", "10001110100010110000111010000001000101011000101010", "00101001010101010000100100111010001000101010010001", "00100110101101000101101001010100010010010001101010", "01100010100011000010010010100101100001001100000101", "11000100001100101100000110001011001000001010010010", "01100001010010110011010000011000100100110010000101", "10010010100110011001101010101001010001001100100010", "10101000010001000100001100010110101001000101011001", "11000101011001100101101000100100110110100011010010", "10011001001010001000100011001001000100110010101000", "01100100000100110010010101010010010011001100000110", "10010100110010101001010100010101001000011000110100", "00101010001101010100101010100010101000100101001001", "01010001001000110110010100001101010010011001000110", "01001100100110001001101001100000101000010100100010", "10100010000011001000000110110010000101000011010001", "01100100101000110100101001010010101010101010011000", "00011011010101000011010010001101010101010000100100" }
{"01111111111111111111111111111111111111111101111111","10110111100011110111111100010111111010011111111101","11011110111111111111111111111111111111111101111101","11101111111111111111111110011111111111111111111011","10110101111011111011111111111110111111101111010110","11111001110111111111111011110101111111111111111111","11110001110111111111111111010111101001101111111100","11011110111011111101111111101110111111111111111111","11111111001110101111111111111100111111111101110001","10111111001111111001111110001110111010111111111011","10111001110111111111100011111111101011011101110111","10110110111010011110111111101111111101011111111111","11111111111101011111111111111111111110111101111111","11111111011010111011011111111111111100110101011111","11111111111001011111111101101111111111111111111110","11111111011111100011101011110111111111111111011111","10111111111111100110111111011101111010111111111111","11110111101110101011111101111110111110111011111011","11111110101111111101110110100111111110111111100111","11111111111011110110111111111111111110110100111101","11111111111110111111011111111110111011111111111111","11111111110111101111101111111111111011011111111011","11111111110111111101110111011110111111111011111111","11111011110111101111111011011111111111110111101101","10111111111111011011111101001111111110111111011111","10101111101111111101111110111011111111111101111011","10101101101111110111110001011110010011111111111011","11111110101011011101111101100111111111111011111011","10111001111111101101111111100111111111011111111111","11111111111111111111111110111011011111111111110111","11111011011111110111111111111101111111111111111111","11110110001111111011010111011110111110011011111111","11111111111111111111111111011011011111111101011110","11111101110111111111111111111111101110111111111111","11111111111111111111111111011111110111111111111111","10111101100111110111001111011111111011101110111011","11111101111010111111111111111111111101111111111111","10111111101100110000111101111110101110101111101010","10111111110011111111101111110110111111011111011111","11110101111111111111111111111111111010101111101111","11111111111110111110111011111111111111110111111111","11111111111111111011110111101110111111111011111110","01011111010100111110111110111111011111111101111111","11111111111111111110111111111111111011111110101111","11110111111110101111111101111111011111011111011101","11111111111111111101111011111111111110101110101010","11110111010111111101111111111011111111111111110111","11101111001111111011101110001111111010111111101011","10011101011111111110111011111111111111111111011101","11110101111111011111111111111111011110111011101110"}

Returns: { }
{"01111111111111110110011110111111111111111101111111","10111110111111111110111111110110111111100011111111","11011111110111110101111011111111111011111111111010","11101110111111111111111111110111111101111111111111","11110111111111111111111101110111111111011111111111","11111011111110111111111111110111011111111111111111","11111101111111111111111111110011111011111111111111","10101110101111111111111111111111011010111111110111","11111111001111111101111111111111111111111011111111","11111110001111111111111111111111110111111111111111","11011111110011111111111111111101101111011011110111","11111111110011111111111111010111111111111111111111","11111111111101111111111111101111111111111111110110","11111011111110111111101111111111101111011111011111","11111111111111010111110111111011001011111111111101","11111111111111101110111110111011111111111111111111","01011111111111010111011111111111101111011111111110","11111111111111111011111111111111111111111111111110","11011111011111111101110111111111011111111110111111","00111111111111101110101011101111101101011011111110","01111111111111110111001111101111101111111111111111","11111111111110111110001111101101111111111111111111","11111111111111011101110111111111111111111111111110","11011111111111111110111010011111111111101111111111","11110111111111111111111101111111101111111101111111","01111111111111101111111010111111111111111111101011","11111111111011111111111011011111111111111011111111","11111111111101111110001111101111110111111111111111","10100001111011111111111111110111111100111110111111","11111101111111001111111111111011111111110111101111","11111111110111111111101111111101111111011111111111","10111111111111111111111111111110111111111111111111","11111010111111011101111111111111011111111111110111","11111111110110010110011101111111101111111111111111","11111111101111111111111111101111110110111111111111","11011100111111011111111111111111111000111111111011","11101111111111111110111111110111111001011111011110","11111110111111111111111111110111110010111111110111","11110111110110110110111111111101111101001110111111","10111111111111111111111011111111111111001011101111","10111111111111111111111111111011111111110001111011","10111111010111111110111111011111111111100001111011","01111111111111111111111101111111111111110001111011","11111111111111111101111111110111111111011110111111","11111111111110111111111111111111111101111111010111","11111111111111111111111110111011111111101111101111","11111110110101111111111111111111011110111111010101","11011111111111111111111110111111111011110001111001","11111111111111011111111111111111111111111111110001","11011111111101110010110111111111111101111111111110"}

Returns: { }
{"01111111111111011111111111111111111111111111111111","10111111101111111111111111111111111111111111111111","11010111111111111111111111111111111111111111111111","11101111111111111111111111111111011111111111111111","11010111111111111111111111111110111111101101111110","11111011111111111011011111111101111111111111111111","11111101111111111111111111111111101111111111111111","11111110101111111101011110111111111011111111111111","11111111011111111111111111111111111111111011111111","10111110101111011011111111111111111110111111111111","11111111110111111101111111111111111111111111111111","11111111111011111011110111011111111111111111111111","11111111111101111111111111101110111111111111111011","11111111111110111111111111111111111111111011111111","01111111101111010111011111111111111111111011111111","11111111111111101111111111111111111111111111111011","11111111111111010111111111111111110111101111111111","11111011101011111011111111111111111111111111111111","11111110110111111101011111111111111111010011011111","11111111111111111110111111111111011111111111111111","11111010111111011101011111111111111111111111011111","11111111111111111111101111111111111011111100111111","11111111111011111111110111101111111111101111111111","11111111111111111111111011101110011111111111111111","11111111111111111111111101110111111111111111111111","11111110111111111111111110011111111111011111111111","11111111111011111111111110011110111111111111111111","11111111111101111111110011101111111111111111111111","11111111111111111111111101110111111111111111101101","11111111111111111111111111111010111111111111110110","11111011111111111111111111111101111111111111111111","11110111111101111111111011011010111111111001111111","11101111111111111110111011111111011111111111111111","11111101111111111111111111111111101111111111111111","11111111111111110111111111111111110111111111111111","11111110111111111111101111111111111010100111111111","11111111111111111111111111111111111101011111111111","11111111101111111111111111111111111010111111011111","11111111111111111101111110111111111101001111011111","11110111111111110111110111111111111011001111111111","11111111111111111101111111111111111011110111111101","11111111011110011101111111111110111111111011111111","11110111111111111111101111111110111111111101110101","11111111111111111111101111111111111111111110111111","11111111111111111101011111111111111110011111010111","11111111111111111111111111110111111111111111101111","11111111111111111111111111111011111111111101010111","11111111111101101111111111111111111111111111111001","11111111111111111111111111110111111111110101111000","11110111111111111111111111111011111111111111111100"}

Returns: { }
{"01111111111111111111111110111111111111111111111111","10111111111111111111111011111111111111111111111111","11011011111111111111111111111101111111111111111110","11100111111111111111111111111111111111111111111111","11100111111111111101111111111111011111111111111111","11011011111111111111111111111111111111111111111111","11111101111111111111111111111111101111111111111111","11111110111111111111110111111111111111111111111111","11111111011111111111111111111111111111111111111110","11111111101111111111111111111110111111111110111011","11111111110111111111111110111111111111111111111111","11111111111011111111110011111111111110111111111111","11111111111101011111111111111111111111111111111111","11111111111110111111111111111111111111110111111111","11111111111101011111111111101111111111111111011111","11111111111111101111111111111111111111110111111111","11111111111111110110111111111111111111111111111111","11111111111111111011111111111111111111011111111111","11110111111111111101110101111111111111111111111111","11111111111111110110111111111111111111111111111111","11111111111111111111010111111111111111111111111111","11111111111111111111101111111111111111111111111110","11111110111011111101010111111111111111111011111111","10111111111011111111111011111111111111101111111111","11111111111111111101111101111111111111111111111111","01111111110111111111111110111111111111111111110111","11111111111111111111111111011111111111111110111111","11111111111111011111111111101111111111111111111111","11111111111111111111111111110111111111111011111111","11111111111111111111111111111011111111111111011111","11011111111111111111111111111101111111111111111111","11111111101111111111111111111110111111111111111111","11110111111111111111111111111111011011111111011111","11111101111111111111111111111111101111111111111111","11111111111111111111111111111111110111111111111101","11111111111111111111111111111111011011111111111111","11111111111111111111111111111111111101111111101111","11111111111011111111111111111111111110111111111111","11111111111111111011111111111111111111011010111111","11111111111111111111111011111111111111101111111111","11111111111110101111111111111111111111110101111111","11111111111111111111110111110111111111011011111111","11111111111111111111111111111111111111110101111111","11111111101111111111111111011111111111011110111111","11111111111111011111111111111011011111111111011111","11111111111111111111111111111111111101111111101111","11111111111111111111111110111111111111111111110111","11111111101111111111111111111111111111111111111011","11111111111111111111111111111111110111111111111101","11011111011111111111101111111111111111111111111110"}

Returns: { }
{"000101110000000","000000000000000","000101100000100","101000000010010","000000000001010","101000001000010","101000000100010","100000001001010","000001010000000","000000100000010","000100000000010","000010010000000","001000000000010","000111110110100","000000000000000"}

Returns: {"000100100000000", "000000000000000", "000001100000000", "100000000010000", "000000000000010", "001000001000000", "101000000000000", "000000000001010", "000001000000000", "000000000000010", "000100000000000", "000000010000000", "000000000000010", "000010010100100", "000000000000000" }
{"010000101010011","101010001001100","010000001001010","000010001011011","010101101001110","000010010011011","100010011000101","000001101001011","111110110001011","000000000000000","100101000000111","011111011000111","010010100011010","101111011011100","100101111011000"}

Returns: { }
{"001100111101100","000100111111111","100111010101001","111001111111101","001000010011101","001100000110101","110100011010000","111110101011111","110100110111011","111101001011011","010111111100101","111110011100011","110111010010001","010000011101001","011111011111110"}

Returns: { }
{"000111111011101","000111111110110","000110111001011","111011111111111","111100111110111","110100011110111","111110010101110","111111101111111","111111010110010","010111111010101","110111011101111","101100110010101","110111110111011","011111111010100","101111010111100"}

Returns: {"000101010010100", "000010101100010", "000100100001001", "101010010010110", "010100101000101", "100000010110010", "011010000001010", "100101001100101", "010010010110000", "010001011000100", "100101001001001", "001000100010001", "100110010100010", "010101100000100", "001010010011000" }
{"011011110111111","101111111111111","110111111111111","011011110111111","111101111111111","111110111111111","111111011111111","111111101111111","011011110111111","111111111011111","111111111101111","111111111110111","111111111111011","111111111111101","111111111111110"}

Returns: {"000001010010111", "001010101101010", "010101010010110", "001010100101001", "010101101010100", "101010010101001", "010110000101011", "101001001010110", "010010010110100", "010101101001001", "101010011000011", "010101100100110", "101010011001001", "111000110011000", "100101100110100" }
{"0000000000","0000000000","0000000000","0000000000","0000000000","0000000000","0000000000","0000000000","0000000000","0000000000"}

Returns: {"0000000000", "0000000000", "0000000000", "0000000000", "0000000000", "0000000000", "0000000000", "0000000000", "0000000000", "0000000000" }
{"0000","0000","0000","0000"}

Returns: {"0000", "0000", "0000", "0000" }
{"00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000"}

Returns: {"00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000" }
{"00000000000000000000001000000000000100000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000001000000000000000000000001","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","10000000000000000000000000000000000000001000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000100000000000000000000000000000000001000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","10000000000000000000000000000000000000000000000001","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000001001000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000100000000000000000000000000000100000000000000"}

Returns: { }
{"00000000000000101000000000000000100000000000000010","00010000001000000000010000100000000000000000000000","00000000000110001000000100000000000101000000000000","01000000000010001000000010000000000000000100000010","00000000000000000000000000001000100000000000000000","00000000001000000000000000000000100000000000000000","00000000000010000000000000100000110001100000000000","00000000000000100000101000000010011010101000010000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","01000100000000000000000100000000100000000000000000","00100000000000000000000010000000000000000000000000","00110010000000000001000000000000000000000100000001","00000000000000000001000000000001000100000000010000","10000001000000000100000000000111100000000010000000","00000000000000000000000000000000001000000010000000","10110000000000000010000011000000000000000000000000","00000000000000100000000000001000000000000000000000","00000000000000001000000100000000010000000000001000","00000000000011000000000000000000000000000000000000","00000001000000000000000000000000000000000000010000","01000000000000000000000000001000000001000100011000","00000001000000000000000000000000000000100000000000","00100000001000000010000000000000000000001100001000","00010000000100001000000001000011010100000000000000","00000000000000001000000010000000101000000000000101","01000010000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00001000000000000100010000000101100000000000000000","00000000000000100000000000001000100110100000000000","00000001000000100000000010000000000000000010000000","00000000000001100000000010001000000000000000000000","10001110001000100000000001001100000000000000000100","00000011000000000010000010000000000000000000000000","00000001000000010000000001000000000000000000001000","00100000000001000000000010000100000000000000000000","00000001000000000000000000000100000000000000000000","00100010000000000000010000000000000000100000000000","00000011000000000000001000000100000001000110000010","00000000000000000000000000000000000000000000000000","00000001000000000000000100000000000000000000000000","00010000000010000000010100000000000000100000000010","00000000000000110000000000000010000000100000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000001000001000000110000000000000000000000000000","00000000000000000010010100000000001000000000000000","00000000000000000000000001000000100000000000000000","10010000000000000000000000000000000000100100000000","00000000000010000000000001000000000000000000000000"}

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{"0110","1010","1100","0000"}

Returns: { }
{"011011","101011","110101","001010","110101","111010"}

Returns: { }
{"0111111","1011111","1101111","1110111","1111011","1111101","1111110"}

Returns: { }
{"00101110","00111111","11001111","01000001","11100111","11101011","11101101","01111110"}

Returns: { }
{"011111111","101111111","110111111","111011111","111101111","111110111","111111011","111111101","111111110"}

Returns: {"000010111", "001101010", "010110100", "011001001", "101000011", "010100110", "101001001", "110011000", "100110100" }
{"01111", "10100", "11000", "10001", "10010" }

Returns: {"00011", "00100", "01000", "10000", "10000" }
{"01111", "10111", "11011", "11101", "11110" }

Returns: {"00011", "00110", "01001", "11000", "10100" }
{"011", "101", "110" }

Returns: { }

Statistics

Problem Statement for "HalfGraph"

Problem Statement

Definition

Constraints

Examples