Identifier
Values
[1,0,1,0] => [2,1] => 0 => 1 => 1
[1,1,0,0] => [1,2] => 1 => 0 => 0
[1,0,1,0,1,0] => [2,3,1] => 00 => 01 => 1
[1,0,1,1,0,0] => [2,1,3] => 01 => 10 => 1
[1,1,0,0,1,0] => [1,3,2] => 10 => 11 => 1
[1,1,0,1,0,0] => [3,1,2] => 00 => 01 => 1
[1,1,1,0,0,0] => [1,2,3] => 11 => 00 => 0
[1,0,1,0,1,0,1,0] => [2,3,4,1] => 000 => 001 => 1
[1,0,1,0,1,1,0,0] => [2,3,1,4] => 001 => 010 => 1
[1,0,1,1,0,0,1,0] => [2,1,4,3] => 010 => 101 => 2
[1,0,1,1,0,1,0,0] => [2,4,1,3] => 000 => 001 => 1
[1,0,1,1,1,0,0,0] => [2,1,3,4] => 011 => 100 => 1
[1,1,0,0,1,0,1,0] => [1,3,4,2] => 100 => 011 => 1
[1,1,0,0,1,1,0,0] => [1,3,2,4] => 101 => 110 => 1
[1,1,0,1,0,0,1,0] => [3,1,4,2] => 000 => 001 => 1
[1,1,0,1,0,1,0,0] => [3,4,1,2] => 000 => 001 => 1
[1,1,0,1,1,0,0,0] => [3,1,2,4] => 001 => 010 => 1
[1,1,1,0,0,0,1,0] => [1,2,4,3] => 110 => 111 => 1
[1,1,1,0,0,1,0,0] => [1,4,2,3] => 100 => 011 => 1
[1,1,1,0,1,0,0,0] => [4,1,2,3] => 000 => 001 => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => 111 => 000 => 0
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0000 => 0001 => 1
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => 0001 => 0010 => 1
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 0010 => 0101 => 2
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => 0000 => 0001 => 1
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => 0011 => 0100 => 1
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 0100 => 1001 => 2
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => 0101 => 1010 => 2
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 0000 => 0001 => 1
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => 0000 => 0001 => 1
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => 0001 => 0010 => 1
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => 0110 => 1011 => 2
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => 0100 => 1001 => 2
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => 0000 => 0001 => 1
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => 0111 => 1000 => 1
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 1000 => 0011 => 1
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => 1001 => 0110 => 1
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 1010 => 1101 => 2
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => 1000 => 0011 => 1
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => 1011 => 1100 => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => 0000 => 0001 => 1
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => 0001 => 0010 => 1
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => 0000 => 0001 => 1
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => 0000 => 0001 => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => 0001 => 0010 => 1
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => 0010 => 0101 => 2
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => 0000 => 0001 => 1
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => 0000 => 0001 => 1
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => 0011 => 0100 => 1
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 1100 => 0111 => 1
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => 1101 => 1110 => 1
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => 1000 => 0011 => 1
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => 1000 => 0011 => 1
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => 1001 => 0110 => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => 0000 => 0001 => 1
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => 0000 => 0001 => 1
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => 0000 => 0001 => 1
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => 0001 => 0010 => 1
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => 1110 => 1111 => 1
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => 1100 => 0111 => 1
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => 1000 => 0011 => 1
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => 0000 => 0001 => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 1111 => 0000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 00000 => 00001 => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => 00001 => 00010 => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => 00010 => 00101 => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => 00000 => 00001 => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => 00011 => 00100 => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => 00100 => 01001 => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => 00101 => 01010 => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => 00000 => 00001 => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => 00000 => 00001 => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => 00001 => 00010 => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => 00110 => 01011 => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => 00100 => 01001 => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => 00000 => 00001 => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => 00111 => 01000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => 01000 => 10001 => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => 01001 => 10010 => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => 01010 => 10101 => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => 01000 => 10001 => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => 01011 => 10100 => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => 00000 => 00001 => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => 00001 => 00010 => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => 00000 => 00001 => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => 00000 => 00001 => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => 00001 => 00010 => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => 00010 => 00101 => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => 00000 => 00001 => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => 00000 => 00001 => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => 00011 => 00100 => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => 01100 => 10011 => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => 01101 => 10110 => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => 01000 => 10001 => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => 01000 => 10001 => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => 01001 => 10010 => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 00000 => 00001 => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => 00000 => 00001 => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => 00000 => 00001 => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => 00001 => 00010 => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => 01110 => 10111 => 2
>>> Load all 2139 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => 01100 => 10011 => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => 01000 => 10001 => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => 00000 => 00001 => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => 01111 => 10000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => 10000 => 00011 => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => 10001 => 00110 => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => 10010 => 01101 => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => 10000 => 00011 => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => 10011 => 01100 => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => 10100 => 11001 => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => 10101 => 11010 => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => 10000 => 00011 => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => 10000 => 00011 => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => 10001 => 00110 => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => 10110 => 11011 => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => 10100 => 11001 => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => 10000 => 00011 => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => 10111 => 11000 => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => 00000 => 00001 => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => 00001 => 00010 => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => 00010 => 00101 => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => 00000 => 00001 => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => 00011 => 00100 => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => 00000 => 00001 => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => 00001 => 00010 => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => 00000 => 00001 => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => 00000 => 00001 => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => 00001 => 00010 => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 00010 => 00101 => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => 00000 => 00001 => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => 00000 => 00001 => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => 00011 => 00100 => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => 00100 => 01001 => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => 00101 => 01010 => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 00000 => 00001 => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => 00000 => 00001 => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => 00001 => 00010 => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 00000 => 00001 => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => 00000 => 00001 => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => 00000 => 00001 => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => 00001 => 00010 => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => 00110 => 01011 => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => 00100 => 01001 => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => 00000 => 00001 => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => 00000 => 00001 => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => 00111 => 01000 => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => 11000 => 00111 => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => 11001 => 01110 => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => 11010 => 11101 => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => 11000 => 00111 => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => 11011 => 11100 => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => 10000 => 00011 => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => 10001 => 00110 => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 10000 => 00011 => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => 10000 => 00011 => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => 10001 => 00110 => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 10010 => 01101 => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => 10000 => 00011 => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => 10000 => 00011 => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => 10011 => 01100 => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 00000 => 00001 => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => 00001 => 00010 => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 00000 => 00001 => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => 00000 => 00001 => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => 00001 => 00010 => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 00000 => 00001 => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => 00000 => 00001 => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => 00000 => 00001 => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => 00001 => 00010 => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => 00010 => 00101 => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => 00000 => 00001 => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => 00000 => 00001 => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => 00000 => 00001 => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => 00011 => 00100 => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 11100 => 01111 => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => 11101 => 11110 => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 11000 => 00111 => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => 11000 => 00111 => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => 11001 => 01110 => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 10000 => 00011 => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => 10000 => 00011 => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => 10000 => 00011 => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => 10001 => 00110 => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => 00000 => 00001 => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => 00000 => 00001 => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => 00000 => 00001 => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => 00000 => 00001 => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => 00001 => 00010 => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => 11110 => 11111 => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => 11100 => 01111 => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => 11000 => 00111 => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => 10000 => 00011 => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => 00000 => 00001 => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => 11111 => 00000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => 000000 => 000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => 000001 => 000010 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => 000010 => 000101 => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => 000000 => 000001 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => 000011 => 000100 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => 000100 => 001001 => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => 000101 => 001010 => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => 000000 => 000001 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => 000000 => 000001 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => 000001 => 000010 => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => 000110 => 001011 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => 000100 => 001001 => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => 000000 => 000001 => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => 000111 => 001000 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => 001000 => 010001 => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => 001001 => 010010 => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => 001010 => 010101 => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => 001000 => 010001 => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => 001011 => 010100 => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => 000000 => 000001 => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => 000001 => 000010 => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => 000000 => 000001 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => 000000 => 000001 => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => 000001 => 000010 => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => 000010 => 000101 => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => 000000 => 000001 => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => 000000 => 000001 => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => 000011 => 000100 => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => 001100 => 010011 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => 001101 => 010110 => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => 001000 => 010001 => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => 001000 => 010001 => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => 001001 => 010010 => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => 000000 => 000001 => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => 000000 => 000001 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => 000000 => 000001 => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => 000001 => 000010 => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => 001110 => 010111 => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => 001100 => 010011 => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => 001000 => 010001 => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => 000000 => 000001 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => 001111 => 010000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => 010000 => 100001 => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => 010001 => 100010 => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => 010010 => 100101 => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => 010000 => 100001 => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => 010011 => 100100 => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => 010100 => 101001 => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => 010101 => 101010 => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => 010000 => 100001 => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => 010000 => 100001 => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => 010001 => 100010 => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => 010110 => 101011 => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => 010100 => 101001 => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => 010000 => 100001 => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => 010111 => 101000 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => 000000 => 000001 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => 000001 => 000010 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => 000010 => 000101 => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => 000000 => 000001 => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => 000011 => 000100 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => 000000 => 000001 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => 000001 => 000010 => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => 000000 => 000001 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => 000000 => 000001 => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => 000001 => 000010 => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => 000010 => 000101 => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => 000000 => 000001 => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => 000000 => 000001 => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => 000011 => 000100 => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => 000100 => 001001 => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => 000101 => 001010 => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => 000000 => 000001 => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => 000000 => 000001 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => 000001 => 000010 => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => 000000 => 000001 => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => 000000 => 000001 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => 000000 => 000001 => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => 000001 => 000010 => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => 000110 => 001011 => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => 000100 => 001001 => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => 000000 => 000001 => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => 000000 => 000001 => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => 000111 => 001000 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => 011000 => 100011 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => 011001 => 100110 => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => 011010 => 101101 => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => 011000 => 100011 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => 011011 => 101100 => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => 010000 => 100001 => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => 010001 => 100010 => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => 010000 => 100001 => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => 010000 => 100001 => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => 010001 => 100010 => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => 010010 => 100101 => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => 010000 => 100001 => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => 010000 => 100001 => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => 010011 => 100100 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => 000000 => 000001 => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => 000001 => 000010 => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => 000000 => 000001 => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => 000000 => 000001 => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => 000001 => 000010 => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => 000000 => 000001 => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => 000000 => 000001 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => 000000 => 000001 => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => 000001 => 000010 => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => 000010 => 000101 => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => 000000 => 000001 => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => 000000 => 000001 => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => 000000 => 000001 => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => 000011 => 000100 => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => 011100 => 100111 => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => 011101 => 101110 => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => 011000 => 100011 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => 011000 => 100011 => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => 011001 => 100110 => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => 010000 => 100001 => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => 010000 => 100001 => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => 010000 => 100001 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => 010001 => 100010 => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => 000000 => 000001 => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => 000000 => 000001 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => 000000 => 000001 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => 000000 => 000001 => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => 000001 => 000010 => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => 011110 => 101111 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => 011100 => 100111 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => 011000 => 100011 => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => 010000 => 100001 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => 000000 => 000001 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => 011111 => 100000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => 100000 => 000011 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => 100001 => 000110 => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => 100010 => 001101 => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => 100000 => 000011 => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => 100011 => 001100 => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => 100100 => 011001 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => 100101 => 011010 => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => 100000 => 000011 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => 100000 => 000011 => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => 100001 => 000110 => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => 100110 => 011011 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => 100100 => 011001 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => 100000 => 000011 => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => 100111 => 011000 => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => 101000 => 110001 => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => 101001 => 110010 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => 101010 => 110101 => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => 101000 => 110001 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => 101011 => 110100 => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => 100000 => 000011 => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => 100001 => 000110 => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => 100000 => 000011 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => 100000 => 000011 => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => 100001 => 000110 => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => 100010 => 001101 => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => 100000 => 000011 => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => 100000 => 000011 => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => 100011 => 001100 => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => 101100 => 110011 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => 101101 => 110110 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => 101000 => 110001 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => 101000 => 110001 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => 101001 => 110010 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => 100000 => 000011 => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => 100000 => 000011 => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => 100000 => 000011 => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => 100001 => 000110 => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => 101110 => 110111 => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => 101100 => 110011 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => 101000 => 110001 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => 100000 => 000011 => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => 101111 => 110000 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => 000000 => 000001 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => 000001 => 000010 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => 000010 => 000101 => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => 000000 => 000001 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => 000011 => 000100 => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => 000100 => 001001 => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => 000101 => 001010 => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => 000000 => 000001 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => 000000 => 000001 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => 000001 => 000010 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => 000110 => 001011 => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => 000100 => 001001 => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => 000000 => 000001 => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => 000111 => 001000 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => 000000 => 000001 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => 000001 => 000010 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => 000010 => 000101 => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => 000000 => 000001 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => 000011 => 000100 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => 000000 => 000001 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => 000001 => 000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => 000000 => 000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => 000000 => 000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => 000001 => 000010 => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => 000010 => 000101 => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => 000000 => 000001 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => 000000 => 000001 => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => 000011 => 000100 => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => 000100 => 001001 => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => 000101 => 001010 => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => 000000 => 000001 => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => 000000 => 000001 => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => 000001 => 000010 => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => 000000 => 000001 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => 000000 => 000001 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => 000000 => 000001 => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => 000001 => 000010 => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => 000110 => 001011 => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => 000100 => 001001 => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => 000000 => 000001 => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => 000000 => 000001 => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => 000111 => 001000 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => 001000 => 010001 => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => 001001 => 010010 => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => 001010 => 010101 => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => 001000 => 010001 => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => 001011 => 010100 => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => 000000 => 000001 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => 000001 => 000010 => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => 000000 => 000001 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => 000000 => 000001 => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => 000001 => 000010 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => 000010 => 000101 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => 000000 => 000001 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => 000000 => 000001 => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => 000011 => 000100 => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => 000000 => 000001 => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => 000001 => 000010 => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => 000000 => 000001 => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => 000000 => 000001 => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => 000001 => 000010 => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => 000000 => 000001 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => 000000 => 000001 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => 000000 => 000001 => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => 000001 => 000010 => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => 000010 => 000101 => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => 000000 => 000001 => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => 000000 => 000001 => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => 000000 => 000001 => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => 000011 => 000100 => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => 001100 => 010011 => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => 001101 => 010110 => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => 001000 => 010001 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => 001000 => 010001 => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => 001001 => 010010 => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => 000000 => 000001 => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => 000000 => 000001 => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => 000000 => 000001 => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => 000001 => 000010 => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => 000000 => 000001 => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => 000000 => 000001 => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => 000000 => 000001 => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => 000000 => 000001 => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => 000001 => 000010 => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 001110 => 010111 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => 001100 => 010011 => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => 001000 => 010001 => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => 000000 => 000001 => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => 000000 => 000001 => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => 001111 => 010000 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => 110000 => 000111 => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => 110001 => 001110 => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => 110010 => 011101 => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => 110000 => 000111 => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => 110011 => 011100 => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => 110100 => 111001 => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => 110101 => 111010 => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => 110000 => 000111 => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => 110000 => 000111 => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => 110001 => 001110 => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => 110110 => 111011 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => 110100 => 111001 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => 110000 => 000111 => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => 110111 => 111000 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => 100000 => 000011 => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => 100001 => 000110 => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => 100010 => 001101 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => 100000 => 000011 => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => 100011 => 001100 => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => 100000 => 000011 => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => 100001 => 000110 => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => 100000 => 000011 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => 100000 => 000011 => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => 100001 => 000110 => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => 100010 => 001101 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => 100000 => 000011 => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => 100000 => 000011 => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => 100011 => 001100 => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => 100100 => 011001 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => 100101 => 011010 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => 100000 => 000011 => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => 100000 => 000011 => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => 100001 => 000110 => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => 100000 => 000011 => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => 100000 => 000011 => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => 100000 => 000011 => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => 100001 => 000110 => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => 100110 => 011011 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => 100100 => 011001 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => 100000 => 000011 => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => 100000 => 000011 => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => 100111 => 011000 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => 000000 => 000001 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => 000001 => 000010 => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => 000010 => 000101 => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => 000000 => 000001 => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => 000011 => 000100 => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => 000000 => 000001 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => 000001 => 000010 => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => 000000 => 000001 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => 000000 => 000001 => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => 000001 => 000010 => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => 000010 => 000101 => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => 000000 => 000001 => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => 000000 => 000001 => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => 000011 => 000100 => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => 000000 => 000001 => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => 000001 => 000010 => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => 000000 => 000001 => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => 000000 => 000001 => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => 000001 => 000010 => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => 000000 => 000001 => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => 000000 => 000001 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => 000000 => 000001 => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => 000001 => 000010 => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => 000010 => 000101 => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => 000000 => 000001 => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => 000000 => 000001 => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => 000000 => 000001 => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => 000011 => 000100 => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => 000100 => 001001 => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => 000101 => 001010 => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => 000000 => 000001 => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => 000000 => 000001 => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => 000001 => 000010 => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => 000000 => 000001 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => 000000 => 000001 => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => 000000 => 000001 => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => 000001 => 000010 => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 000000 => 000001 => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => 000000 => 000001 => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => 000000 => 000001 => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => 000000 => 000001 => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => 000001 => 000010 => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 000110 => 001011 => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => 000100 => 001001 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => 000000 => 000001 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => 000000 => 000001 => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => 000000 => 000001 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => 000111 => 001000 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => 111000 => 001111 => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => 111001 => 011110 => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => 111010 => 111101 => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => 111000 => 001111 => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => 111011 => 111100 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => 110000 => 000111 => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => 110001 => 001110 => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => 110000 => 000111 => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => 110000 => 000111 => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => 110001 => 001110 => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => 110010 => 011101 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => 110000 => 000111 => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => 110000 => 000111 => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => 110011 => 011100 => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => 100000 => 000011 => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => 100001 => 000110 => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => 100000 => 000011 => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => 100000 => 000011 => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => 100001 => 000110 => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => 100000 => 000011 => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => 100000 => 000011 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => 100000 => 000011 => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => 100001 => 000110 => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 100010 => 001101 => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => 100000 => 000011 => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => 100000 => 000011 => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => 100000 => 000011 => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => 100011 => 001100 => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => 000000 => 000001 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => 000001 => 000010 => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => 000000 => 000001 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => 000000 => 000001 => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => 000001 => 000010 => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 000000 => 000001 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => 000000 => 000001 => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => 000000 => 000001 => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => 000001 => 000010 => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 000000 => 000001 => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => 000000 => 000001 => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => 000000 => 000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => 000000 => 000001 => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => 000001 => 000010 => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 000010 => 000101 => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => 000000 => 000001 => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => 000000 => 000001 => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => 000000 => 000001 => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => 000000 => 000001 => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => 000011 => 000100 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => 111100 => 011111 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => 111101 => 111110 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 111000 => 001111 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => 111000 => 001111 => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => 111001 => 011110 => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 110000 => 000111 => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => 110000 => 000111 => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => 110000 => 000111 => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => 110001 => 001110 => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 100000 => 000011 => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => 100000 => 000011 => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => 100000 => 000011 => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => 100000 => 000011 => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => 100001 => 000110 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 000000 => 000001 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => 000000 => 000001 => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => 000000 => 000001 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => 000000 => 000001 => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => 000000 => 000001 => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => 000001 => 000010 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 111110 => 111111 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => 111100 => 011111 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => 111000 => 001111 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => 110000 => 000111 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => 100000 => 000011 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => 000000 => 000001 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => 111111 => 000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => 0000000 => 0000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => 0000001 => 0000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => 0000010 => 0000101 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => 0000000 => 0000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => 0000011 => 0000100 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6] => 0000100 => 0001001 => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,8] => 0000101 => 0001010 => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => 0000000 => 0000001 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => 0000000 => 0000001 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6,8] => 0000001 => 0000010 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => 0000110 => 0001011 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => 0000100 => 0001001 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => 0000000 => 0000001 => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => 0000111 => 0001000 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => 0001000 => 0010001 => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8] => 0001001 => 0010010 => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => 0001010 => 0010101 => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,8,5,7] => 0001000 => 0010001 => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => 0001011 => 0010100 => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,4,6,1,7,5,8] => 0000001 => 0000010 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => 0000000 => 0000001 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => 0000001 => 0000010 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,4,6,8,1,5,7] => 0000000 => 0000001 => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => 0000011 => 0000100 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => 0001000 => 0010001 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => 0001000 => 0010001 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,4,1,7,5,6,8] => 0001001 => 0010010 => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,4,7,1,8,5,6] => 0000000 => 0000001 => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => 0000001 => 0000010 => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,1,5,6,8,7] => 0001110 => 0010111 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => 0001100 => 0010011 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => 0001000 => 0010001 => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => 0000000 => 0000001 => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => 0001111 => 0010000 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,4] => 0010000 => 0100001 => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,4,8] => 0010001 => 0100010 => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,5,6,8,4,7] => 0010000 => 0100001 => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,4,7,8] => 0010011 => 0100100 => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => 0010101 => 0101010 => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,7,8,4,6] => 0010000 => 0100001 => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,5,4,6,7,8] => 0010111 => 0101000 => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,5,1,6,4,7,8] => 0000011 => 0000100 => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,6,1,8,4,7] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,8,1,4,7] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => 0000011 => 0000100 => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6,8] => 0000101 => 0001010 => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,7,1,4,8,6] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6,8] => 0000001 => 0000010 => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,5,1,4,8,6,7] => 0000100 => 0001001 => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,8,1,4,6,7] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,1,4,6,7,8] => 0000111 => 0001000 => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => 0011000 => 0100011 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7] => 0011010 => 0101101 => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => 0010001 => 0100010 => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,4,5] => 0010000 => 0100001 => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => 0010000 => 0100001 => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => 0010011 => 0100100 => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,1,4,7,8,5] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,1,4,7,5,8] => 0000001 => 0000010 => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,6,7,1,8,4,5] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,6,7,8,1,4,5] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,8,7] => 0000010 => 0000101 => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,6,1,4,5,7,8] => 0000011 => 0000100 => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6] => 0011100 => 0100111 => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8] => 0011101 => 0101110 => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => 0011000 => 0100011 => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,1,4,7,5,6,8] => 0011001 => 0100110 => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => 0010000 => 0100001 => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,1,4,5,8,6] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,1,4,8,5,6] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => 0011110 => 0101111 => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => 0011100 => 0100111 => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => 0010000 => 0100001 => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => 0000000 => 0000001 => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => 0011111 => 0100000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => 0100000 => 1000001 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,3,8] => 0100001 => 1000010 => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => 0100010 => 1000101 => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,4,5,6,8,3,7] => 0100000 => 1000001 => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => 0100000 => 1000001 => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4,5,8,3,6,7] => 0100000 => 1000001 => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => 0100111 => 1001000 => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,6,7,5,8] => 0101001 => 1010010 => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => 0101010 => 1010101 => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => 0101011 => 1010100 => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,6,3,7,8,5] => 0100000 => 1000001 => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,6,3,7,5,8] => 0100001 => 1000010 => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,7,3,8,5] => 0100000 => 1000001 => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,8,5,7] => 0100000 => 1000001 => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,6,3,5,7,8] => 0100011 => 1000100 => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => 0101100 => 1010011 => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => 0101000 => 1010001 => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => 0101000 => 1010001 => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,7,3,5,8,6] => 0100000 => 1000001 => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => 0101110 => 1010111 => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => 0101100 => 1010011 => 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => 0101000 => 1010001 => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,8,3,5,6,7] => 0100000 => 1000001 => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => 0101111 => 1010000 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,5,6,7,3,8] => 0000001 => 0000010 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,6,3,8,7] => 0000010 => 0000101 => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,5,6,8,3,7] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => 0000011 => 0000100 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,5,3,7,8,6] => 0000100 => 0001001 => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => 0000101 => 0001010 => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,4,1,5,7,3,8,6] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => 0000110 => 0001011 => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => 0000100 => 0001001 => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,3,6,7,8] => 0000111 => 0001000 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,4,5,1,6,3,8,7] => 0000010 => 0000101 => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,6,1,7,3,8] => 0000001 => 0000010 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,1,3] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,1,3,8] => 0000001 => 0000010 => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,6,8,1,3,7] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => 0000011 => 0000100 => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,4,5,1,3,7,8,6] => 0000100 => 0001001 => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6,8] => 0000101 => 0001010 => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,4,5,1,7,3,8,6] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,4,5,1,7,8,3,6] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,7,8,1,3,6] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => 0000111 => 0001000 => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => 0001010 => 0010101 => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,8,5,7] => 0001000 => 0010001 => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,6,5,7,8] => 0001011 => 0010100 => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => 0000001 => 0000010 => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,7,8,3,5] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,8,7] => 0000010 => 0000101 => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,6,3,5,7,8] => 0000011 => 0000100 => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,6,1,3,7,5,8] => 0000001 => 0000010 => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,6,7,1,3,8,5] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,6,7,8,1,3,5] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => 0000010 => 0000101 => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,8,5,7] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,6,1,3,5,7,8] => 0000011 => 0000100 => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,3,5,7,8,6] => 0001100 => 0010011 => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => 0001000 => 0010001 => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,3,7,8,5,6] => 0001000 => 0010001 => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,5,8,6] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,7,3,8,5,6] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,7,8,3,5,6] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,4,7,1,3,5,8,6] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => 0001000 => 0010001 => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,8,3,5,6,7] => 0000000 => 0000001 => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8] => 0001111 => 0010000 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,4] => 0110000 => 1000011 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,6,4,8,7] => 0110010 => 1001101 => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,8,4,7] => 0110000 => 1000011 => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,7,8,6] => 0110100 => 1011001 => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4,6,8,7] => 0110110 => 1011011 => 3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,1,3,5,8,4,6,7] => 0110000 => 1000011 => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8] => 0110111 => 1011000 => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,1,5,3,6,7,4,8] => 0100001 => 1000010 => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => 0100010 => 1000101 => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,1,5,3,6,8,4,7] => 0100000 => 1000001 => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,5,6,3,7,8,4] => 0100000 => 1000001 => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,1,5,6,3,7,4,8] => 0100001 => 1000010 => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,5,6,7,3,8,4] => 0100000 => 1000001 => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => 0100000 => 1000001 => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,1,5,6,7,3,4,8] => 0100001 => 1000010 => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => 0100010 => 1000101 => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,1,5,6,3,4,7,8] => 0100011 => 1000100 => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => 0100000 => 1000001 => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,5,3,7,8,4,6] => 0100000 => 1000001 => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,5,7,3,4,8,6] => 0100000 => 1000001 => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => 0100000 => 1000001 => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => 0100000 => 1000001 => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6,8] => 0100001 => 1000010 => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,1,5,3,8,4,6,7] => 0100000 => 1000001 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,4] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,1,3,6,4,8,7] => 0000010 => 0000101 => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,1,3,6,8,4,7] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,1,3,6,4,7,8] => 0000011 => 0000100 => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,5,1,6,3,7,8,4] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,1,6,3,7,4,8] => 0000001 => 0000010 => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,1,6,7,8,3,4] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,1,6,3,4,8,7] => 0000010 => 0000101 => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,1,6,3,4,7,8] => 0000011 => 0000100 => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,5,6,1,3,7,8,4] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,5,6,1,3,7,4,8] => 0000001 => 0000010 => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,5,6,1,7,8,3,4] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,5,6,1,7,3,4,8] => 0000001 => 0000010 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,5,6,7,1,3,8,4] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,5,6,7,1,8,3,4] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,5,6,1,3,8,4,7] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,7,4,8,6] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,7,8,4,6] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6,8] => 0000001 => 0000010 => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,5,1,7,8,3,4,6] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,5,7,1,3,4,8,6] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,5,7,1,8,3,4,6] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,5,1,8,3,4,6,7] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,5,8,1,3,4,6,7] => 0000000 => 0000001 => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,4,6,7,8] => 0000111 => 0001000 => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => 0111000 => 1000111 => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => 0111010 => 1011101 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => 0111011 => 1011100 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,6,7,4,8,5] => 0110000 => 1000011 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,6,7,8,4,5] => 0110000 => 1000011 => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,6,4,5,8,7] => 0110010 => 1001101 => 3
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,1,3,6,4,5,7,8] => 0110011 => 1001100 => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => 0100000 => 1000001 => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => 0100000 => 1000001 => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,6,3,7,8,4,5] => 0100000 => 1000001 => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,1,6,3,7,4,5,8] => 0100001 => 1000010 => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => 0100000 => 1000001 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => 0100010 => 1000101 => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => 0100000 => 1000001 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,1,6,3,8,4,5,7] => 0100000 => 1000001 => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,1,6,8,3,4,5,7] => 0100000 => 1000001 => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,1,3,4,7,8,5] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,1,3,4,7,5,8] => 0000001 => 0000010 => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,6,1,3,7,4,8,5] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,6,1,7,3,4,8,5] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,6,1,7,3,8,4,5] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,6,1,7,8,3,4,5] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,6,1,7,3,4,5,8] => 0000001 => 0000010 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,6,7,1,3,8,4,5] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,6,7,1,3,4,5,8] => 0000001 => 0000010 => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,6,1,8,3,4,5,7] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => 0000011 => 0000100 => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => 0111100 => 1001111 => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => 0111101 => 1011110 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,4,7,5,8,6] => 0111000 => 1000111 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,1,3,4,7,8,5,6] => 0111000 => 1000111 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => 0111001 => 1001110 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,1,3,7,4,8,5,6] => 0110000 => 1000011 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,3,7,8,4,5,6] => 0110000 => 1000011 => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,1,7,3,4,8,5,6] => 0100000 => 1000001 => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,7,8,3,4,5,6] => 0100000 => 1000001 => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => 0100001 => 1000010 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,7,1,3,4,5,8,6] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => 0000001 => 0000010 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => 0111110 => 1011111 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => 0111100 => 1001111 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => 0111000 => 1000111 => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => 0110000 => 1000011 => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => 0100000 => 1000001 => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => 0000000 => 0000001 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => 0111111 => 1000000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => 1000000 => 0000011 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,2,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,6,2,8,7] => 1000010 => 0001101 => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,8,2,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,2,7,8] => 1000011 => 0001100 => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,2,7,8,6] => 1000100 => 0011001 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,8] => 1000101 => 0011010 => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,5,2,8,6,7] => 1000100 => 0011001 => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,5,8,2,6,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => 1000111 => 0011000 => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => 1001001 => 0110010 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7] => 1001010 => 0110101 => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,6,2,7,5,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => 1000000 => 0000011 => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,8,7] => 1000010 => 0001101 => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,4,6,8,2,5,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => 1000011 => 0001100 => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,4,2,5,7,8,6] => 1001100 => 0110011 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,2,7,5,8,6] => 1001000 => 0110001 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,4,7,2,5,8,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,4,7,8,2,5,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7] => 1001110 => 0110111 => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,3,4,2,5,8,6,7] => 1001100 => 0110011 => 2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => 1001000 => 0110001 => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8] => 1001111 => 0110000 => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,6,4,8,7] => 1010010 => 1100101 => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => 1010100 => 1101001 => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => 1010101 => 1101010 => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,7,8,4,6] => 1010000 => 1100001 => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6,8] => 1010001 => 1100010 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => 1010100 => 1101001 => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => 1010000 => 1100001 => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => 1010111 => 1101000 => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,5,2,6,7,4,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,5,2,6,4,8,7] => 1000010 => 0001101 => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,5,2,6,8,4,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,6,7,2,4,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,5,6,2,4,8,7] => 1000010 => 0001101 => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,5,6,2,8,4,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,6,8,2,4,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => 1000011 => 0001100 => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6,8] => 1000101 => 0011010 => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,7,4,8,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,7,8,4,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,7,2,4,8,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,7,2,8,4,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,5,2,4,6,8,7] => 1000110 => 0011011 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,5,2,4,8,6,7] => 1000100 => 0011001 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,2,4,6,7,8] => 1000111 => 0011000 => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5] => 1011000 => 1100011 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7] => 1011010 => 1101101 => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,4,6,8,5,7] => 1011000 => 1100011 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => 1011011 => 1101100 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => 1010001 => 1100010 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,7,8,4,5] => 1010000 => 1100001 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => 1010000 => 1100001 => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => 1010011 => 1100100 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,6,2,4,7,8,5] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,2,4,7,5,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,2,7,4,8,5] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,7,4,5,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,6,7,2,4,8,5] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,6,7,8,2,4,5] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,8,7] => 1000010 => 0001101 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,6,2,4,8,5,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,6,2,4,5,7,8] => 1000011 => 0001100 => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => 1011100 => 1100111 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => 1011101 => 1101110 => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,3,2,4,7,5,8,6] => 1011000 => 1100011 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => 1010000 => 1100001 => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => 1010001 => 1100010 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,2,4,5,8,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,7,2,4,8,5,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6,8] => 1000001 => 0000110 => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => 1011110 => 1101111 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => 1011100 => 1100111 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => 1011000 => 1100011 => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => 1010000 => 1100001 => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => 1000000 => 0000011 => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => 1011111 => 1100000 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => 0000000 => 0000001 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => 0000001 => 0000010 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,8,2,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,5,2,7,8,6] => 0000100 => 0001001 => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4,5,7,8,2,6] => 0000000 => 0000001 => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => 0000111 => 0001000 => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => 0001000 => 0010001 => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,4,2,6,7,5,8] => 0001001 => 0010010 => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => 0001010 => 0010101 => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => 0001000 => 0010001 => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,1,4,2,6,5,7,8] => 0001011 => 0010100 => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,4,6,7,8,2,5] => 0000000 => 0000001 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,8,7] => 0000010 => 0000101 => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => 0001100 => 0010011 => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => 0001000 => 0010001 => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,4,2,7,8,5,6] => 0001000 => 0010001 => 2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,4,2,7,5,6,8] => 0001001 => 0010010 => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,2,5,8,6,7] => 0001100 => 0010011 => 2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => 0001000 => 0010001 => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,4,8,2,5,6,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => 0001111 => 0010000 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,5,6,7,2,8] => 0000001 => 0000010 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,5,6,8,2,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,4,1,5,6,2,7,8] => 0000011 => 0000100 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6,8] => 0000101 => 0001010 => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,7,8,2,6] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6,8] => 0000001 => 0000010 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,2,8,6,7] => 0000100 => 0001001 => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4,1,5,8,2,6,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,1,5,2,6,7,8] => 0000111 => 0001000 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,1,6,2,8,7] => 0000010 => 0000101 => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,1,6,2,7,8] => 0000011 => 0000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => 0000001 => 0000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => 0000001 => 0000010 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,1,2,8,7] => 0000010 => 0000101 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,6,1,8,2,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,8,1,2,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => 0000011 => 0000100 => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,5,1,2,7,8,6] => 0000100 => 0001001 => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,5,1,7,8,2,6] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,7,8,1,2,6] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => 0000001 => 0000010 => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,5,1,2,6,8,7] => 0000110 => 0001011 => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => 0000111 => 0001000 => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,5] => 0001000 => 0010001 => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,6,7,5,8] => 0001001 => 0010010 => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => 0001010 => 0010101 => 3
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,6,5,7,8] => 0001011 => 0010100 => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,4,1,6,2,7,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,6,2,7,5,8] => 0000001 => 0000010 => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,6,7,8,2,5] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,4,1,6,7,2,5,8] => 0000001 => 0000010 => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,8,7] => 0000010 => 0000101 => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,8,5,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,4,6,1,2,7,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,4,6,7,1,2,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,4,6,7,1,8,2,5] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,1,2,5] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => 0000001 => 0000010 => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,8,7] => 0000010 => 0000101 => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,4,1,2,5,7,8,6] => 0001100 => 0010011 => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => 0001000 => 0010001 => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => 0001000 => 0010001 => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,4,7,1,2,5,8,6] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1,2,5,6,8,7] => 0001110 => 0010111 => 2
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1,8,2,5,6,7] => 0000000 => 0000001 => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => 0001111 => 0010000 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,4] => 0010000 => 0100001 => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,5,6,7,4,8] => 0010001 => 0100010 => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,5,6,8,4,7] => 0010000 => 0100001 => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => 0010101 => 0101010 => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,7,4,8,6] => 0010000 => 0100001 => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6,8] => 0010001 => 0100010 => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,5,4,6,8,7] => 0010110 => 0101011 => 3
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,5,8,4,6,7] => 0010000 => 0100001 => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => 0000010 => 0000101 => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,5,6,2,7,8,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,5,6,7,2,8,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,2,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,5,6,2,4,8,7] => 0000010 => 0000101 => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,5,6,8,2,4,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,5,6,2,4,7,8] => 0000011 => 0000100 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6,8] => 0000101 => 0001010 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,7,8,4,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,7,2,8,4,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,7,8,2,4,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,5,2,4,8,6,7] => 0000100 => 0001001 => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,5,8,2,4,6,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,5,1,2,6,7,8,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7] => 0000010 => 0000101 => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,1,2,6,8,4,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,5,1,6,2,7,8,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,5,1,6,7,2,8,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,5,1,6,7,8,2,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,5,1,6,7,2,4,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => 0000010 => 0000101 => 2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,5,1,6,8,2,4,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => 0000011 => 0000100 => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,5,6,1,2,7,4,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,5,6,1,7,8,2,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,5,6,7,1,2,8,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,5,6,7,1,8,2,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,1,2,4] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,5,6,1,2,8,4,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,7,8,6] => 0000100 => 0001001 => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => 0000101 => 0001010 => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,7,4,8,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,7,8,4,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,7,2,4,8,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,7,8,2,4,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,5,1,2,4,6,8,7] => 0000110 => 0001011 => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,5,1,2,4,8,6,7] => 0000100 => 0001001 => 2
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,5,1,2,8,4,6,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,5,1,8,2,4,6,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,5,1,2,4,6,7,8] => 0000111 => 0001000 => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => 0011000 => 0100011 => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,7,5,8] => 0011001 => 0100110 => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => 0011010 => 0101101 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,2,4,6,8,5,7] => 0011000 => 0100011 => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,2,6,4,7,8,5] => 0010000 => 0100001 => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [3,1,2,6,4,7,5,8] => 0010001 => 0100010 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => 0010000 => 0100001 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,6,7,8,4,5] => 0010000 => 0100001 => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,6,4,5,8,7] => 0010010 => 0100101 => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,1,6,2,4,7,5,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [3,1,6,2,7,4,5,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,6,7,2,8,4,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => 0000010 => 0000101 => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [3,1,6,2,4,8,5,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [3,1,6,2,8,4,5,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,6,2,4,5,7,8] => 0000011 => 0000100 => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,6,1,2,7,4,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,6,7,1,2,4,8,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,6,7,1,2,4,5,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,8,5,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,6,1,8,2,4,5,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,6,1,2,4,5,7,8] => 0000011 => 0000100 => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,2,4,5,7,8,6] => 0011100 => 0100111 => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => 0011101 => 0101110 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => 0011000 => 0100011 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,2,4,7,8,5,6] => 0011000 => 0100011 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => 0011001 => 0100110 => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [3,1,2,7,4,8,5,6] => 0010000 => 0100001 => 2
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [3,7,1,2,4,8,5,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [3,7,1,2,8,4,5,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => 0000001 => 0000010 => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => 0011110 => 0101111 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => 0011100 => 0100111 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => 0011000 => 0100011 => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => 0010000 => 0100001 => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => 0000000 => 0000001 => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => 0011111 => 0100000 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,7,3,8] => 1100001 => 0001110 => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,4,5,6,3,8,7] => 1100010 => 0011101 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,6,8,3,7] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,3,7,8] => 1100011 => 0011100 => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,5,3,7,8,6] => 1100100 => 0111001 => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6,8] => 1100101 => 0111010 => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,7,8,3,6] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6,8] => 1100001 => 0001110 => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,4,5,8,3,6,7] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => 1101000 => 1110001 => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,6,7,5,8] => 1101001 => 1110010 => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => 1101010 => 1110101 => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,8,5,7] => 1101000 => 1110001 => 2
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => 1101011 => 1110100 => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,6,7,8,3,5] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,8,7] => 1100010 => 0011101 => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,8,5,7] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => 1100011 => 0011100 => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => 1101100 => 1110011 => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => 1101101 => 1110110 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => 1101000 => 1110001 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,4,3,7,8,5,6] => 1101000 => 1110001 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => 1101001 => 1110010 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,7,3,5,8,6] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,4,7,3,8,5,6] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,4,7,8,3,5,6] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => 1100001 => 0001110 => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => 1101110 => 1110111 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => 1101100 => 1110011 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => 1101000 => 1110001 => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => 1100000 => 0000111 => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => 1101111 => 1110000 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,4,2,5,6,8,3,7] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => 1000101 => 0011010 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,4,2,5,7,8,3,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,4,2,5,3,6,8,7] => 1000110 => 0011011 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => 1000100 => 0011001 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,4,2,5,8,3,6,7] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => 1000111 => 0011000 => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,5,2,6,3,8,7] => 1000010 => 0001101 => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,5,2,6,8,3,7] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => 1000011 => 0001100 => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,4,5,6,2,7,8,3] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,2,8,3] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,2,3] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,6,8,2,3,7] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,4,5,2,3,7,8,6] => 1000100 => 0011001 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,4,5,2,7,8,3,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,7,8,2,3,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,5,2,3,8,6,7] => 1000100 => 0011001 => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,2,3,6,7,8] => 1000111 => 0011000 => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,6,7,8,5] => 1001000 => 0110001 => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,6,7,5,8] => 1001001 => 0110010 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => 1001010 => 0110101 => 3
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,6,5,7,8] => 1001011 => 0110100 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,6,7,3,5,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,8,7] => 1000010 => 0001101 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,8,3,5,7] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => 1000011 => 0001100 => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,4,6,2,3,7,8,5] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,7,3,5,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,8,7] => 1000010 => 0001101 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,8,5,7] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,6,2,3,5,7,8] => 1000011 => 0001100 => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,4,2,3,5,7,8,6] => 1001100 => 0110011 => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => 1001101 => 0110110 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,4,2,3,7,5,8,6] => 1001000 => 0110001 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,3,7,8,5,6] => 1001000 => 0110001 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => 1001001 => 0110010 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,4,2,7,3,5,8,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,4,7,2,3,5,8,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,7,2,3,8,5,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6,8] => 1000001 => 0000110 => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => 1001110 => 0110111 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => 1001100 => 0110011 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => 1001000 => 0110001 => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => 1000000 => 0000011 => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => 1001111 => 0110000 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,5,6,7,3,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => 0000010 => 0000101 => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,5,6,8,3,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3,7,8] => 0000011 => 0000100 => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => 0000100 => 0001001 => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => 0000101 => 0001010 => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,5,7,3,8,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,5,3,8,6,7] => 0000100 => 0001001 => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,1,2,5,8,3,6,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => 0000111 => 0001000 => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => 0000010 => 0000101 => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,1,5,2,6,3,7,8] => 0000011 => 0000100 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,5,6,7,2,8,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,2,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,1,5,6,7,2,3,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,5,6,2,3,8,7] => 0000010 => 0000101 => 2
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => 0000100 => 0001001 => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6,8] => 0000101 => 0001010 => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,5,7,2,8,3,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,1,5,2,3,8,6,7] => 0000100 => 0001001 => 2
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,5,2,8,3,6,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => 0000010 => 0000101 => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,5,1,2,6,8,3,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,5,1,6,2,7,8,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,5,1,6,7,8,2,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [4,5,1,6,7,2,3,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,5,1,6,2,3,8,7] => 0000010 => 0000101 => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [4,5,1,6,2,8,3,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,1,2,7,8,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,1,2,7,3,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,6,1,7,8,2,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,6,1,7,2,3,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,1,2,8,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => 0000010 => 0000101 => 2
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => 0000011 => 0000100 => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6,8] => 0000101 => 0001010 => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,5,1,2,7,3,8,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [4,5,1,2,7,8,3,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,5,1,7,2,3,8,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [4,5,1,7,2,8,3,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [4,5,1,7,8,2,3,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [4,5,1,2,3,8,6,7] => 0000100 => 0001001 => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,5,1,8,2,3,6,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => 0000111 => 0001000 => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => 0001000 => 0010001 => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => 0001010 => 0010101 => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,6,3,7,8,5] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,6,7,3,8,5] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,6,7,3,5,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,6,2,7,3,5,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,6,7,2,3,5,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => 0000010 => 0000101 => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,8,2,3,5,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,6,2,3,5,7,8] => 0000011 => 0000100 => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [4,6,1,2,7,3,5,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,6,7,1,2,3,8,5] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,8,7] => 0000010 => 0000101 => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,8,5,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,8,3,5,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [4,6,1,2,3,5,7,8] => 0000011 => 0000100 => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => 0001100 => 0010011 => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => 0001101 => 0010110 => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => 0001000 => 0010001 => 2
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => 0001001 => 0010010 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,7,3,5,8,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,1,2,7,3,5,6,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,7,2,3,5,8,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,7,2,3,8,5,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [4,1,7,2,8,3,5,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6,8] => 0000001 => 0000010 => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [4,7,1,2,3,8,5,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => 0001100 => 0010011 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => 0001000 => 0010001 => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => 0000000 => 0000001 => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => 0001111 => 0010000 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => 1110000 => 0001111 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,4,8] => 1110001 => 0011110 => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,5,6,4,8,7] => 1110010 => 0111101 => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,8,4,7] => 1110000 => 0001111 => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,4,7,8] => 1110011 => 0111100 => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => 1110100 => 1111001 => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => 1110101 => 1111010 => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => 1110000 => 0001111 => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => 1110000 => 0001111 => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => 1110001 => 0011110 => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => 1110110 => 1111011 => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => 1110100 => 1111001 => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,5,8,4,6,7] => 1110000 => 0001111 => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => 1110111 => 1111000 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,2,5,3,6,7,4,8] => 1100001 => 0001110 => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,5,3,6,4,8,7] => 1100010 => 0011101 => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => 1100001 => 0001110 => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,2,5,6,3,4,8,7] => 1100010 => 0011101 => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,5,6,3,8,4,7] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,2,5,6,8,3,4,7] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => 1100011 => 0011100 => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => 1100100 => 0111001 => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => 1100101 => 0111010 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,2,5,3,7,4,8,6] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,2,5,3,7,8,4,6] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6,8] => 1100001 => 0001110 => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,2,5,7,3,4,8,6] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,2,5,7,8,3,4,6] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => 1100001 => 0001110 => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,2,5,3,4,6,8,7] => 1100110 => 0111011 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => 1100100 => 0111001 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => 1100000 => 0000111 => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => 1100111 => 0111000 => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,5,2,3,6,7,4,8] => 1000001 => 0000110 => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => 1000010 => 0001101 => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,5,2,3,6,8,4,7] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => 1000011 => 0001100 => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => 1000001 => 0000110 => 1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,2,6,7,3,4,8] => 1000001 => 0000110 => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,5,2,6,3,4,8,7] => 1000010 => 0001101 => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,2,6,8,3,4,7] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => 1000011 => 0001100 => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,5,6,7,2,3,8,4] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,6,7,2,8,3,4] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => 1000001 => 0000110 => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,5,6,2,3,4,8,7] => 1000010 => 0001101 => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,5,6,2,3,4,7,8] => 1000011 => 0001100 => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => 1000100 => 0011001 => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => 1000101 => 0011010 => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,7,4,8,6] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,7,8,4,6] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => 1000001 => 0000110 => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,5,2,7,3,4,8,6] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,5,2,7,8,3,4,6] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => 1000001 => 0000110 => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,5,7,2,3,4,8,6] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,2,3,8,4,6] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,5,2,3,4,6,8,7] => 1000110 => 0011011 => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => 1000100 => 0011001 => 2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,5,2,3,8,4,6,7] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => 1000000 => 0000011 => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => 1000111 => 0011000 => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,6,8,4,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => 0000011 => 0000100 => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,2,6,3,7,8,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,1,2,6,3,7,4,8] => 0000001 => 0000010 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,7,3,8,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,2,6,7,8,3,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,1,2,6,7,3,4,8] => 0000001 => 0000010 => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,1,2,6,3,8,4,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,1,2,6,8,3,4,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => 0000011 => 0000100 => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,1,6,2,3,7,4,8] => 0000001 => 0000010 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,1,6,2,7,3,4,8] => 0000001 => 0000010 => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [5,1,6,7,2,8,3,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,2,3,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,1,6,2,8,3,4,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [5,1,6,2,3,4,7,8] => 0000011 => 0000100 => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,6,1,7,8,2,3,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => 0000001 => 0000010 => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,6,1,2,8,3,4,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,6,1,8,2,3,4,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,7,4,8,6] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,7,8,4,6] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,7,3,8,4,6] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,7,8,3,4,6] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,1,7,8,2,3,4,6] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6,8] => 0000001 => 0000010 => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => 0000001 => 0000010 => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 0000110 => 0001011 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => 0000100 => 0001001 => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => 0000000 => 0000001 => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => 0000111 => 0001000 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => 1111000 => 0011111 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => 1111001 => 0111110 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => 1111010 => 1111101 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,6,8,5,7] => 1111000 => 0011111 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => 1111011 => 1111100 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => 1110000 => 0001111 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => 1110001 => 0011110 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => 1110000 => 0001111 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,2,3,6,7,8,4,5] => 1110000 => 0001111 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,6,7,4,5,8] => 1110001 => 0011110 => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => 1110010 => 0111101 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => 1110000 => 0001111 => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,6,8,4,5,7] => 1110000 => 0001111 => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => 1110011 => 0111100 => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => 1100000 => 0000111 => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,2,6,3,4,7,5,8] => 1100001 => 0001110 => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => 1100000 => 0000111 => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,2,6,3,7,8,4,5] => 1100000 => 0000111 => 1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,2,6,3,7,4,5,8] => 1100001 => 0001110 => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => 1100000 => 0000111 => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,2,6,7,3,8,4,5] => 1100000 => 0000111 => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => 1100000 => 0000111 => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => 1100001 => 0001110 => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => 1100010 => 0011101 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,2,6,3,4,8,5,7] => 1100000 => 0000111 => 1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => 1100000 => 0000111 => 1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => 1100000 => 0000111 => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => 1100011 => 0011100 => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,6,2,3,4,7,8,5] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => 1000001 => 0000110 => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,3,7,8,4,5] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,2,3,7,4,5,8] => 1000001 => 0000110 => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,6,2,7,3,4,8,5] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,6,2,7,8,3,4,5] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => 1000001 => 0000110 => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,6,7,2,3,4,8,5] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,7,2,3,8,4,5] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => 1000001 => 0000110 => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => 1000010 => 0001101 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,6,2,3,8,4,5,7] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => 1000000 => 0000011 => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => 1000011 => 0001100 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => 0000001 => 0000010 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,1,2,3,7,8,4,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,7,3,4,8,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,1,2,7,3,8,4,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,1,2,7,8,3,4,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => 0000001 => 0000010 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,7,2,3,4,8,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,1,7,2,3,8,4,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,1,7,2,8,3,4,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => 0000001 => 0000010 => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,7,1,2,3,8,4,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,7,1,2,8,3,4,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => 0000001 => 0000010 => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 0000010 => 0000101 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,8,5,7] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,8,4,5,7] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => 0000000 => 0000001 => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => 0000011 => 0000100 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => 1111100 => 0111111 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => 1111101 => 1111110 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => 1111000 => 0011111 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => 1111000 => 0011111 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => 1111001 => 0111110 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => 1110000 => 0001111 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => 1110000 => 0001111 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,3,7,8,4,5,6] => 1110000 => 0001111 => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => 1110001 => 0011110 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 1100000 => 0000111 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,2,7,3,4,8,5,6] => 1100000 => 0000111 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => 1100000 => 0000111 => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => 1100000 => 0000111 => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => 1100001 => 0001110 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 1000000 => 0000011 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => 1000000 => 0000011 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => 1000000 => 0000011 => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => 1000000 => 0000011 => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => 1000000 => 0000011 => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => 1000001 => 0000110 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 0000000 => 0000001 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => 0000000 => 0000001 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => 0000000 => 0000001 => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => 0000000 => 0000001 => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => 0000000 => 0000001 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => 0000000 => 0000001 => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => 0000001 => 0000010 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1111110 => 1111111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => 1111100 => 0111111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => 1111000 => 0011111 => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => 1110000 => 0001111 => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => 1100000 => 0000111 => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => 1000000 => 0000011 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => 0000000 => 0000001 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => 1111111 => 0000000 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 11111110 => 11111111 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => 01111111 => 10000000 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 111111110 => 111111111 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 00000000 => 00000001 => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => 00000000 => 00000001 => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => 011111111 => 100000000 => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 10000000 => 00000011 => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 00000010 => 00000101 => 2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => 01000000 => 10000001 => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7,9] => 00000001 => 00000010 => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => 000000000 => 000000001 => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => 0111111111 => 1000000000 => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [1,2,8,3,4,5,6,9,7] => 11000000 => 00000111 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,8,1,2,3,4,5,9,6] => 00000000 => 00000001 => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,1,3,4,5,6,7] => 00000000 => 00000001 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => 010000000 => 100000001 => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [1,2,9,3,4,5,6,7,10,8] => 110000000 => 000000111 => 1
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,9,10,1,3,4,5,6,7,8] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,8,5,6,9,7] => 11110000 => 00011111 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,1,3,4,5,9,6,7,8] => 01111000 => 10001111 => 2
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,1,8,9,3,4,5,6,7] => 01000000 => 10000001 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7] => 11111000 => 00111111 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,8,1,2,3,4,9,5] => 00000000 => 00000001 => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,9,8] => 00111110 => 01011111 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => 11111101 => 11111110 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,9,7,8] => 01111100 => 10011111 => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,7,8,9,1,3,4,5,6] => 00000000 => 00000001 => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => 10111111 => 11000000 => 1
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9] => 00011111 => 00100000 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,5,9,6,7,10,8] => 111110000 => 000111111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => 11111100 => 01111111 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,3,4,8,5,9,6] => 00000000 => 00000001 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => 01111110 => 10111111 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,8,6,9] => 00000001 => 00000010 => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,10,1,3,4,5,6,7] => 000000000 => 000000001 => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => 00111111 => 01000000 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,6,9,7,10,8] => 111111000 => 001111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => 111111101 => 111111110 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,8,9,6] => 00000000 => 00000001 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,7,10,8,9] => 011111100 => 100111111 => 2
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => 101111111 => 110000000 => 1
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9,10] => 000111111 => 001000000 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => 111111100 => 011111111 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1,2,3,4,5,9,6,10,7] => 000000000 => 000000001 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => 011111110 => 101111111 => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,1,7,8,9,3,4,5,6] => 01000000 => 10000001 => 2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => 001111111 => 010000000 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,1,2] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,1,2,9] => 00000001 => 00000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,6,7,1,9,2,8] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,7,9,1,2,8] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => 00000011 => 00000100 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,5,6,1,8,9,2,7] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,5,6,8,1,9,2,7] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,6,8,9,1,2,7] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,6,8,1,2,7,9] => 00000001 => 00000010 => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,5,6,1,2,9,7,8] => 00000100 => 00001001 => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,6,9,1,2,7,8] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7,8,9] => 00000111 => 00001000 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,7,8,9,1,2,6] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,8,9,1,2,6,7] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,4,7,8,9,1,2,5,6] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => 00011111 => 00100000 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,9,2,4] => 00000000 => 00000001 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,9,6,8] => 00000000 => 00000001 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,9,1,2,4] => 00000000 => 00000001 => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,9,1,2,4,6,8] => 00000000 => 00000001 => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,9,1,2,4,5] => 00000000 => 00000001 => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,1,2,4,5,6,9,7,8] => 00111100 => 01001111 => 2
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,9,2,4,5,6,7,8] => 00000000 => 00000001 => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,9,1,2,4,5,6,7,8] => 00000000 => 00000001 => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => 00111111 => 01000000 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,9,2,3] => 10000000 => 00000011 => 1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8,9] => 10011111 => 01100000 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,9,2,3] => 00000000 => 00000001 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,8,1,9,2,3] => 00000000 => 00000001 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,1,2,3] => 00000000 => 00000001 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => 00000001 => 00000010 => 1
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => 00000111 => 00001000 => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,8,3,9,5,7] => 00000000 => 00000001 => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,8,3,5,7,9] => 00000001 => 00000010 => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,9,1,2,3,5] => 00000000 => 00000001 => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [4,1,2,3,5,9,6,7,8] => 00011000 => 00100011 => 2
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,9,1,2,3,5,6,7,8] => 00000000 => 00000001 => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => 00011111 => 00100000 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,9,2,3,4] => 10000000 => 00000011 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,1,6,2,7,3,9,4,8] => 00000000 => 00000001 => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,6,1,7,8,9,2,3,4] => 00000000 => 00000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,8,1,9,2,3,4] => 00000000 => 00000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => 00000000 => 00000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => 00000001 => 00000010 => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,7,8,9,1,2,3,4,6] => 00000000 => 00000001 => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [5,8,9,1,2,3,4,6,7] => 00000000 => 00000001 => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,9,4,6,7,8] => 00000000 => 00000001 => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => 00001111 => 00010000 => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,9,2,3,4,5] => 10000000 => 00000011 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,1,7,2,8,3,9,4,5] => 00000000 => 00000001 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,8,1,9,2,3,4,5] => 00000000 => 00000001 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => 00000000 => 00000001 => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [6,8,9,1,2,3,4,5,7] => 00000000 => 00000001 => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [6,1,2,9,3,4,5,7,8] => 00000000 => 00000001 => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => 00000111 => 00001000 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,4,7,8,5,6,9] => 11110001 => 00111110 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,4,7,9,5,6,8] => 11110000 => 00011111 => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,7,8,9,2,3,4,5,6] => 10000000 => 00000011 => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8,9] => 10000011 => 00001100 => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [7,1,8,2,3,9,4,5,6] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [7,1,8,2,9,3,4,5,6] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [7,8,1,9,2,3,4,5,6] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,9,6,8] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [7,1,9,2,3,4,5,6,8] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [7,9,1,2,3,4,5,6,8] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9] => 00000011 => 00000100 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,8,9,6,7] => 11111000 => 00111111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [1,2,3,4,8,5,9,6,7] => 11110000 => 00011111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [1,2,3,4,8,9,5,6,7] => 11110000 => 00011111 => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [1,2,3,8,4,5,9,6,7] => 11100000 => 00001111 => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,9,6,7] => 10000000 => 00000011 => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => 10000000 => 00000011 => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7,9] => 10000001 => 00000110 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,9,6,7] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,9,5,6,7] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [8,1,2,9,3,4,5,6,7] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [8,1,9,2,3,4,5,6,7] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => 00000001 => 00000010 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,9,7,8] => 11111100 => 01111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,9,6,7,8] => 11111000 => 00111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => 11110000 => 00011111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => 11100000 => 00001111 => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => 11000000 => 00000111 => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => 10000000 => 00000011 => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => 11111111 => 00000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => 00000000 => 00000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,1,9] => 00000001 => 00000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => 00000000 => 00000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,1,7] => 00000000 => 00000001 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,7,8,9,1,6] => 00000000 => 00000001 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,9,1,5] => 00000000 => 00000001 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,1,4] => 00000000 => 00000001 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,1,3] => 00000000 => 00000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => 000000000 => 000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,10] => 000000001 => 000000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,1,8,9] => 00000011 => 00000100 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => 000000000 => 000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,6,1,9,7,8] => 00000100 => 00001001 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,7,9,10,1,8] => 000000000 => 000000001 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,5,1,8,9,6,7] => 00001000 => 00010001 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,10,1,7] => 000000000 => 000000001 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,1,7,8,9,5,6] => 00010000 => 00100001 => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,7,8,9,10,1,6] => 000000000 => 000000001 => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,9,4,5] => 00100000 => 01000001 => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,9,10,1,5] => 000000000 => 000000001 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,9,3,4] => 01000000 => 10000001 => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,10,1,4] => 000000000 => 000000001 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,10,1,3] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,1,2] => 000000000 => 000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000000 => 0000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => 0000000001 => 0000000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => 000000011 => 000000100 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => 0000000000 => 0000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => 00000111 => 00001000 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,9,10,2,3] => 100000000 => 000000011 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,10,11,1,3] => 0000000000 => 0000000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => 0000000000 => 0000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => 000000111 => 000001000 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,3,6,7,1,8,9,4,5] => 00000000 => 00000001 => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => 00001111 => 00010000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => 000001111 => 000010000 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,5,6,7,8,1,9,3,4] => 00000000 => 00000001 => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,5,6,1,7,8,9,10,2,3] => 000000000 => 000000001 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,9,1,3,4] => 00000000 => 00000001 => 1
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => 00011111 => 00100000 => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,9,1,3,4,5] => 00000000 => 00000001 => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => 000011111 => 000100000 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,9,10,1,3,4] => 000000000 => 000000001 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,8,9,1,10,2,3] => 000000000 => 000000001 => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,9,10,1,3,4,5] => 000000000 => 000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8] => 00000010 => 00000101 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,6,1,8,9,7] => 00000100 => 00001001 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,9] => 00000101 => 00001010 => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,7,8,9,6] => 00001000 => 00010001 => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8] => 00001010 => 00010101 => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,7,6,8,9] => 00001011 => 00010100 => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,5,1,6,7,9,8] => 00001110 => 00010111 => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,9,5] => 00010000 => 00100001 => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,9] => 00010101 => 00101010 => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,6,5,7,8,9] => 00010111 => 00101000 => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,9,4] => 00100000 => 01000001 => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8] => 00101010 => 01010101 => 4
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,5,4,6,7,8,9] => 00101111 => 01010000 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7,9] => 00110101 => 01011010 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,1,4,5,6,8,9,7] => 00111100 => 01001111 => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,1,4,5,6,7,9,8] => 00111110 => 01011111 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,3] => 01000000 => 10000001 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,8,3,9] => 01000001 => 10000010 => 2
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,5,3,6,7,8,9] => 01001111 => 10010000 => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,9,5] => 01010000 => 10100001 => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9] => 01010101 => 10101010 => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,7,8,9] => 01010111 => 10101000 => 3
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9] => 01011111 => 10100000 => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,9,4] => 01100000 => 10000011 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,6,8,9,7] => 01111100 => 10011111 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,8,7,9] => 01111101 => 10111110 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,2] => 10000000 => 00000011 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,8,2,9] => 10000001 => 00000110 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,6,7,2,9,8] => 10000010 => 00001101 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,7,2,8,9] => 10000011 => 00001100 => 1
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,5,2,6,7,8,9] => 10001111 => 00110000 => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,9] => 10010101 => 01101010 => 3
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9] => 10011111 => 01100000 => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8] => 10101010 => 11010101 => 4
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,5,4,6,7,8,9] => 10101111 => 11010000 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,3,2,4,5,6,8,9,7] => 10111100 => 11001111 => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,9,8] => 10111110 => 11011111 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,3] => 11000000 => 00000111 => 1
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,5,3,6,7,8,9] => 11001111 => 01110000 => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,9] => 11010101 => 11101010 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,3,5,7,8,9,6] => 11011000 => 11100011 => 2
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9] => 11011111 => 11100000 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,4] => 11100000 => 00001111 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,8,4,9] => 11100001 => 00011110 => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8] => 11101010 => 11110101 => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => 11101111 => 11110000 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,5] => 11110000 => 00011111 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => 11110111 => 11111000 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,6] => 11111000 => 00111111 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,5,7,8,6,9] => 11111001 => 01111110 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,9,8] => 11111010 => 11111101 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9] => 11111011 => 11111100 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,8,1,10,9] => 000000010 => 000000101 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,9,10,8] => 000000100 => 000001001 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8,10] => 000000101 => 000001010 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,8,9,10,7] => 000001000 => 000010001 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,10,9] => 000001010 => 000010101 => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,7,8,9,10,6] => 000010000 => 000100001 => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8,10] => 000010101 => 000101010 => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,9,10,5] => 000100000 => 001000001 => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,10,9] => 000101010 => 001010101 => 4
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => 000111111 => 001000000 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,9,10,4] => 001000000 => 010000001 => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => 001010101 => 010101010 => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,10,3] => 010000000 => 100000001 => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => 010101010 => 101010101 => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,8,7,9,10] => 010101011 => 101010100 => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,8,9,10,7] => 010111000 => 101000111 => 3
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9,10] => 010111111 => 101000000 => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,7,8,9,10,6] => 011110000 => 100001111 => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,6,7,9,10,8] => 011111100 => 100111111 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,2] => 100000000 => 000000011 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,8,9,2,10] => 100000001 => 000000110 => 1
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9,10] => 100111111 => 011000000 => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,4,7,8,6,10,9] => 101010010 => 110100101 => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => 101010100 => 110101001 => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => 101010101 => 110101010 => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,8,9,10,7] => 101011000 => 110100011 => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,10,3] => 110000000 => 000000111 => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,10,9] => 110101010 => 111010101 => 4
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => 110111111 => 111000000 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,10,4] => 111000000 => 000001111 => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8,10] => 111010101 => 111101010 => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => 111011111 => 111100000 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,10,5] => 111100000 => 000011111 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,10,9] => 111101010 => 111110101 => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => 111101111 => 111110000 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,10,6] => 111110000 => 000111111 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,8,9,6,10] => 111110001 => 001111110 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,7,8,6,9,10] => 111110011 => 011111100 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => 111110111 => 111111000 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,6,8,9,10,7] => 111111000 => 001111111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,9,7,10] => 111111001 => 011111110 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,10,9] => 111111010 => 111111101 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => 111111011 => 111111100 => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => 111111111 => 000000000 => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,2] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,2] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,9,2] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,2] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,1,8,9,2] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,1,9,2] => 00000000 => 00000001 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => 000000000 => 000000001 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,9,4] => 00100000 => 01000001 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,10,2] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,9,5] => 00010000 => 00100001 => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,9,10,2] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,5,1,2,7,8,9,6] => 00001000 => 00010001 => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,10,2] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,5,6,1,2,8,9,7] => 00000100 => 00001001 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,6,7,1,8,9,10,2] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,7,1,2,9,8] => 00000010 => 00000101 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,8,1,9,10,2] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,1,10,2] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,7,8,9,10,2,3,4,5,6] => 100000000 => 000000011 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,11,2] => 1000000000 => 0000000011 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,7,9,2,8] => 10000000 => 00000011 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => 000000001 => 000000010 => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => 000000001 => 000000010 => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => 100000000 => 000000011 => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => 0000000001 => 0000000010 => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => 1000000000 => 0000000011 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,7,8,10,2,9] => 100000000 => 000000011 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,7,9,2,8] => 00000000 => 00000001 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,4,5,6,7,9,3,8] => 01000000 => 10000001 => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,8,2,9] => 00000001 => 00000010 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,8,1,2,9,3] => 00000000 => 00000001 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,7,1,2,8,9,3] => 00000000 => 00000001 => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,6,1,2,7,8,9,3] => 00000000 => 00000001 => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,9,3] => 00000000 => 00000001 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,9,3] => 00000000 => 00000001 => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => 001111111 => 010000000 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,10,8,9] => 111111100 => 011111111 => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,10,7,8] => 000000000 => 000000001 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,9,3] => 10000000 => 00000011 => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => 000000011 => 000000100 => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => 000000111 => 000001000 => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => 000001111 => 000010000 => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => 000011111 => 000100000 => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => 000111111 => 001000000 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,7,1,2,8,3,9] => 00000001 => 00000010 => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,6,7,8,9,2,4,5] => 10000000 => 00000011 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,5,6,7,8,1,2,9,4] => 00000000 => 00000001 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,9,10,1,2,4] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000000 => 0000000001 => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,2,5,6,7,8,9] => 00011111 => 00100000 => 1
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,3,6,7,8,9] => 00001111 => 00010000 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,4,7,8,9] => 00000111 => 00001000 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,7,5,8,9] => 00000011 => 00000100 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,5,1,6,7,8,9,3] => 00000000 => 00000001 => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,9,4] => 00000000 => 00000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,8,1,9,10,7] => 000000000 => 000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,8,9,1,10,7] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,5,1,6,7,8,2,9] => 00000001 => 00000010 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,5,2,6,7,8,9,4] => 10000000 => 00000011 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,5,6,1,7,8,9,10,2,4] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,6,1,7,8,9,10,2,5] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,1,7,8,9,10,2,6] => 000000000 => 000000001 => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => 000000000 => 000000001 => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,9,3,4,5] => 01000000 => 10000001 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,8,2,9,3] => 10000000 => 00000011 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,6,1,7,2,8,9] => 00000011 => 00000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,7,8,1,2,9,10] => 000000011 => 000000100 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,1,6,2,7,8,9] => 00000111 => 00001000 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,6,7,10,1,2,8,9] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1,5,9,2,6,7,8] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,9,10,1,2,7,8] => 000000000 => 000000001 => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,1,4,8,9,2,5,6,7] => 00000000 => 00000001 => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,4,5,8,9,10,1,2,6,7] => 000000000 => 000000001 => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,7,8,9,2,4,5,6] => 10000000 => 00000011 => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,4,7,8,9,10,1,2,5,6] => 000000000 => 000000001 => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,9,10,1,2,4,5] => 000000000 => 000000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => 000000000 => 000000001 => 1
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,2,4,6,7,8,9] => 10001111 => 00110000 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,6,8,7,9] => 00011101 => 00101110 => 2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,7,3,5,6,8,9] => 11000011 => 00011100 => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,7,6,8,9] => 00001011 => 00010100 => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => 11100000 => 00001111 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,7,9,6,8] => 11111000 => 00111111 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => 111111000 => 001111111 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => 111110000 => 000111111 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => 111100000 => 000011111 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => 111000000 => 000001111 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => 110000000 => 000000111 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,8,9,4,7] => 00100000 => 01000001 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,4,7,5,8,6,9] => 11110001 => 00111110 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,8,9,10,1,2,7] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,11,8,9] => 0000000000 => 0000000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,6,1,7,2,9,8] => 00000010 => 00000101 => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => 00101010 => 01010101 => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,9,8] => 00001010 => 00010101 => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,9] => 00000101 => 00001010 => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,9] => 00010101 => 00101010 => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8,10] => 001010101 => 010101010 => 4
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,9,6,10,8] => 000000000 => 000000001 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,8,6,10,9] => 000000010 => 000000101 => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7,10,9] => 000001010 => 000010101 => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => 000101010 => 001010101 => 4
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => 000111111 => 001000000 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,9,10,1,2,11] => 0000000001 => 0000000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,9,10,11,1,2,8] => 0000000000 => 0000000001 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,9,10,11,1,2,5] => 0000000000 => 0000000001 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,9,10,2,3,4] => 100000000 => 000000011 => 1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8,10] => 100000001 => 000000110 => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => 000000000 => 000000001 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => 000000000 => 000000001 => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,4,6,8,10,12,1,3,5,7,9,11] => 00000000000 => 00000000001 => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => 00000000000 => 00000000001 => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => 1111111111 => 0000000000 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,8,9,1,2,10,3] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [8,10,1,2,3,4,5,6,7,9] => 000000000 => 000000001 => 1
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,4,6,7,8,9] => 00001111 => 00010000 => 1
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,6,1,5,7,8,9] => 00000111 => 00001000 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,5,7,1,6,8,9] => 00000011 => 00000100 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7,9] => 00000001 => 00000010 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => 1111111101 => 1111111110 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => 000000000 => 000000001 => 1
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [3,7,8,9,10,1,2,4,5,6] => 000000000 => 000000001 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,7,8,9,5] => 00000000 => 00000001 => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,9,4] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => 000000000 => 000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,11,10] => 0000000010 => 0000000101 => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,10,1,11,2] => 0000000000 => 0000000001 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,4,6,9,8] => 10100010 => 11000101 => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,9] => 00010101 => 00101010 => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,1,9,3] => 00000000 => 00000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => 000000011 => 000000100 => 1
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => 000001111 => 000010000 => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,7,8,9,10,1,2,3,4,6] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [7,8,9,1,10,2,3,4,5,6] => 000000000 => 000000001 => 1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,7,8,9,10,1,2,3,5,6] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [7,8,1,9,10,2,3,4,5,6] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [7,1,8,9,10,2,3,4,5,6] => 000000000 => 000000001 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,6,7,8,9,1,3,5] => 00000000 => 00000001 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,9,10,3] => 000000000 => 000000001 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,7,8,9,10,5] => 000000000 => 000000001 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,2,3,7,4,8,9,5] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,8,9,10,6] => 000000000 => 000000001 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,7,8,10,1,2,3,4,9] => 000000000 => 000000001 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7,9] => 00000101 => 00001010 => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6,9,8] => 00001010 => 00010101 => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [7,8,9,1,2,10,3,4,5,6] => 000000000 => 000000001 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,9,1,10,3] => 000000000 => 000000001 => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,6,7,8,9,2,3,4,5,10] => 100000001 => 000000110 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,1,3,4,5,8,6,7,9] => 01111001 => 10011110 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,9,8] => 10001010 => 00110101 => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,6,3,7,5,9,8] => 10000010 => 00001101 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,9] => 10010101 => 01101010 => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,9,8,10] => 100010101 => 001101010 => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,10,9] => 100101010 => 011010101 => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => 00010101 => 00101010 => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,4,1,2,5,6,8,9,7] => 00011100 => 00100111 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,7,1,8,2,9,3] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,9,10,7] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,9,8] => 11110010 => 01111101 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,5,1,8,6,9,7] => 00001000 => 00010001 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,6,9,10,7,8] => 111111000 => 001111111 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => 000000000 => 000000001 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,9,5,8] => 11110000 => 00011111 => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,4,7,6,9,8] => 00001010 => 00010101 => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7,9] => 00000001 => 00000010 => 1
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,4,6,8,10,1,2,5,7,9] => 000000000 => 000000001 => 1
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,6,8,10,1,2,3,5,7,9] => 000000000 => 000000001 => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,1,8,2,9,3,10,4,5,6] => 000000000 => 000000001 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,4,1,7,5,8,6,9] => 00010001 => 00100010 => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,7,2,8,3,9,4,10,5,6] => 100000000 => 000000011 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,6,7,1,8,2,10,9] => 000000010 => 000000101 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,6,7,8,1,9,2,11,10] => 0000000010 => 0000000101 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,9,4] => 00000000 => 00000001 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [1,2,3,4,5,9,6,10,7,8] => 111110000 => 000111111 => 1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1,10,2,3,4,5,6,7,9] => 000000000 => 000000001 => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,1,2,4,7,6,9,8] => 00001010 => 00010101 => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,8,9,1,2,3,4,10,5,6] => 000000000 => 000000001 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => 000010101 => 000101010 => 3
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,7,3,8,4,9,5,10,6] => 010000000 => 100000001 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,8,9,2,3,10] => 100000001 => 000000110 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,10,7,9] => 111111000 => 001111111 => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,9,8] => 10001010 => 00110101 => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,5,2,4,7,6,9,8,10] => 100010101 => 001101010 => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7,9] => 00000001 => 00000010 => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,4,1,7,3,8,5,6,9] => 00000001 => 00000010 => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,6,1,2,3,7,8,9,10,4] => 000000000 => 000000001 => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7,10,9] => 010001010 => 100010101 => 4
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,1,2,8,3,9,4,10,5,6] => 000000000 => 000000001 => 1
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,5,6,9,10,1,2,3,7,8] => 000000000 => 000000001 => 1
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,5,8,9,10,1,2,3,6,7] => 000000000 => 000000001 => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,5,7,2,4,6,9,8,10] => 100000101 => 000011010 => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,5,7,2,9,4,6,8,10] => 100000001 => 000000110 => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,5,7,9,1,2,4,6,8,10] => 000000001 => 000000010 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,9] => 00000101 => 00001010 => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8] => 00001010 => 00010101 => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,10,9] => 000101010 => 001010101 => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,6,1,2,3,7,8,9,4] => 00000000 => 00000001 => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,2,6,4,7,5,9,8] => 10100010 => 11000101 => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,8,3,9,5,10,7] => 000000000 => 000000001 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 01010101010 => 10101010101 => 6
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,6,8,9,10,1,3,4,5,7] => 000000000 => 000000001 => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,10,11,12,1,3,4,5,6,7] => 00000000000 => 00000000001 => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,2,7,3,8,4,9,5] => 10000000 => 00000011 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,9] => 00000001 => 00000010 => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,7,3,8,6,9] => 00000001 => 00000010 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5,8,9,10] => 111000111 => 001111000 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,7,8,1,9,2,10,3] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6,9,8] => 00001010 => 00010101 => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,5,1,6,2,8,7,9] => 00000101 => 00001010 => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [1,2,6,3,4,7,5,9,8] => 11000010 => 00011101 => 2
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [8,1,9,2,10,3,4,5,6,7] => 000000000 => 000000001 => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7,9] => 00010101 => 00101010 => 3
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,7,8,9,2,10,3,4,5,6] => 100000000 => 000000011 => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,2,7,4,6,9,8] => 10000010 => 00001101 => 2
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7,10] => 100000001 => 000000110 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,12,11] => 00000000010 => 00000000101 => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,7,2,8,3,9,4,10,6] => 000000000 => 000000001 => 1
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,6,1,3,5,7,8,9] => 00000111 => 00001000 => 1
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,6,1,3,5,7,8,9,10] => 000001111 => 000010000 => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,4,6,8,1,3,5,7,9,10] => 000000011 => 000000100 => 1
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Description
The number of runs of ones in a binary word.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
path rowmotion
Description
Return the rowmotion of the binary word, regarded as a lattice path.
Consider the binary word of length $n$ as a lattice path with $n$ steps, where a 1 corresponds to an up step and a 0 corresponds to a down step.
This map returns the path whose peaks are the valleys of the original path with an up step appended.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.