Identifier
Values
[1,0] => [2,1] => [2,1] => 1 => 1
[1,0,1,0] => [3,1,2] => [3,2,1] => 11 => 2
[1,1,0,0] => [2,3,1] => [3,1,2] => 10 => 2
[1,0,1,0,1,0] => [4,1,2,3] => [4,3,2,1] => 111 => 3
[1,0,1,1,0,0] => [3,1,4,2] => [4,2,1,3] => 110 => 3
[1,1,0,0,1,0] => [2,4,1,3] => [4,3,1,2] => 101 => 2
[1,1,0,1,0,0] => [4,3,1,2] => [4,2,3,1] => 110 => 3
[1,1,1,0,0,0] => [2,3,4,1] => [4,1,2,3] => 100 => 3
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [5,4,3,2,1] => 1111 => 4
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5,3,2,1,4] => 1110 => 4
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [5,4,2,1,3] => 1101 => 3
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [5,3,4,2,1] => 1110 => 4
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,2,1,3,4] => 1100 => 4
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [5,4,3,1,2] => 1011 => 3
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [5,3,1,2,4] => 1010 => 3
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [5,4,2,3,1] => 1101 => 3
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [4,2,5,3,1] => 1110 => 4
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [5,2,3,1,4] => 1100 => 4
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [5,4,1,2,3] => 1001 => 3
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [5,3,4,1,2] => 1010 => 3
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [5,2,3,4,1] => 1100 => 4
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => 1000 => 4
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => 11111 => 5
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => 11110 => 5
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => 11101 => 4
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [6,4,5,3,2,1] => 11110 => 5
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [6,3,2,1,4,5] => 11100 => 5
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => 11011 => 4
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => 11010 => 4
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [6,5,3,4,2,1] => 11101 => 4
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => 11110 => 5
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [6,3,4,2,1,5] => 11100 => 5
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [6,5,2,1,3,4] => 11001 => 4
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [6,4,5,2,1,3] => 11010 => 4
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [6,3,4,5,2,1] => 11100 => 5
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,2,1,3,4,5] => 11000 => 5
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => 10111 => 4
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [6,4,3,1,2,5] => 10110 => 4
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [6,5,3,1,2,4] => 10101 => 3
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [6,4,5,3,1,2] => 10110 => 4
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => 10100 => 4
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [6,5,4,2,3,1] => 11011 => 4
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [6,4,2,3,1,5] => 11010 => 4
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,2,6,5,3,1] => 11101 => 4
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [5,3,1,6,4,2] => 11110 => 5
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [4,2,6,3,1,5] => 11100 => 5
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [6,5,2,3,1,4] => 11001 => 4
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [6,4,5,2,3,1] => 11010 => 4
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [5,2,4,6,3,1] => 11100 => 5
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [6,2,3,1,4,5] => 11000 => 5
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [6,5,4,1,2,3] => 10011 => 4
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,4,1,2,3,5] => 10010 => 4
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [6,5,3,4,1,2] => 10101 => 3
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [5,3,6,4,1,2] => 10110 => 4
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [6,3,4,1,2,5] => 10100 => 4
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [6,5,2,3,4,1] => 11001 => 4
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [5,2,3,6,4,1] => 11010 => 4
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [5,2,6,3,4,1] => 11100 => 5
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [6,2,3,4,1,5] => 11000 => 5
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,5,1,2,3,4] => 10001 => 4
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [6,4,5,1,2,3] => 10010 => 4
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [6,3,4,5,1,2] => 10100 => 4
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [6,2,3,4,5,1] => 11000 => 5
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 10000 => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => 111111 => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [7,5,4,3,2,1,6] => 111110 => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [7,6,4,3,2,1,5] => 111101 => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [7,5,6,4,3,2,1] => 111110 => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [7,4,3,2,1,5,6] => 111100 => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [7,6,5,3,2,1,4] => 111011 => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [7,5,3,2,1,4,6] => 111010 => 5
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [7,6,4,5,3,2,1] => 111101 => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [6,4,7,5,3,2,1] => 111110 => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [7,4,5,3,2,1,6] => 111100 => 6
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [7,6,3,2,1,4,5] => 111001 => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [7,5,6,3,2,1,4] => 111010 => 5
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [7,4,5,6,3,2,1] => 111100 => 6
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [7,3,2,1,4,5,6] => 111000 => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [7,6,5,4,2,1,3] => 110111 => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [7,5,4,2,1,3,6] => 110110 => 5
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [7,6,4,2,1,3,5] => 110101 => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [7,5,6,4,2,1,3] => 110110 => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => 110100 => 5
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [7,6,5,3,4,2,1] => 111011 => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [7,5,3,4,2,1,6] => 111010 => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [5,3,7,6,4,2,1] => 111101 => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [6,4,2,1,7,5,3] => 111110 => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [5,3,7,4,2,1,6] => 111100 => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [7,6,3,4,2,1,5] => 111001 => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [7,5,6,3,4,2,1] => 111010 => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [6,3,5,7,4,2,1] => 111100 => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [7,3,4,2,1,5,6] => 111000 => 6
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [7,6,5,2,1,3,4] => 110011 => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => 110010 => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [7,6,4,5,2,1,3] => 110101 => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [6,4,7,5,2,1,3] => 110110 => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [7,4,5,2,1,3,6] => 110100 => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [7,6,3,4,5,2,1] => 111001 => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [6,3,4,7,5,2,1] => 111010 => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [6,3,7,4,5,2,1] => 111100 => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [7,3,4,5,2,1,6] => 111000 => 6
>>> Load all 728 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [7,6,2,1,3,4,5] => 110001 => 5
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [7,5,6,2,1,3,4] => 110010 => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [7,4,5,6,2,1,3] => 110100 => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [7,3,4,5,6,2,1] => 111000 => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,2,1,3,4,5,6] => 110000 => 6
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [7,6,5,4,3,1,2] => 101111 => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [7,5,4,3,1,2,6] => 101110 => 5
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [7,6,4,3,1,2,5] => 101101 => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [7,5,6,4,3,1,2] => 101110 => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [7,4,3,1,2,5,6] => 101100 => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [7,6,5,3,1,2,4] => 101011 => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => 101010 => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [7,6,4,5,3,1,2] => 101101 => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [6,4,7,5,3,1,2] => 101110 => 5
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [7,4,5,3,1,2,6] => 101100 => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [7,6,3,1,2,4,5] => 101001 => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [7,5,6,3,1,2,4] => 101010 => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [7,4,5,6,3,1,2] => 101100 => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => 101000 => 5
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [7,6,5,4,2,3,1] => 110111 => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [7,5,4,2,3,1,6] => 110110 => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [7,6,4,2,3,1,5] => 110101 => 4
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [7,5,6,4,2,3,1] => 110110 => 5
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [7,4,2,3,1,5,6] => 110100 => 5
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [4,2,7,6,5,3,1] => 111011 => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [4,2,7,5,3,1,6] => 111010 => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [5,3,1,7,6,4,2] => 111101 => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [6,4,2,7,5,3,1] => 111110 => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [5,3,1,7,4,2,6] => 111100 => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [4,2,7,6,3,1,5] => 111001 => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [4,2,7,5,6,3,1] => 111010 => 5
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [6,3,1,5,7,4,2] => 111100 => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [4,2,7,3,1,5,6] => 111000 => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [7,6,5,2,3,1,4] => 110011 => 5
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [7,5,2,3,1,4,6] => 110010 => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [7,6,4,5,2,3,1] => 110101 => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [6,4,7,5,2,3,1] => 110110 => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [7,4,5,2,3,1,6] => 110100 => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [5,2,4,7,6,3,1] => 111001 => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [7,5,2,4,6,3,1] => 111010 => 5
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [6,3,1,7,4,5,2] => 111100 => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [5,2,4,7,3,1,6] => 111000 => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [7,6,2,3,1,4,5] => 110001 => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [7,5,6,2,3,1,4] => 110010 => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [7,4,5,6,2,3,1] => 110100 => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [6,2,4,5,7,3,1] => 111000 => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [7,2,3,1,4,5,6] => 110000 => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [7,6,5,4,1,2,3] => 100111 => 5
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [7,5,4,1,2,3,6] => 100110 => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [7,6,4,1,2,3,5] => 100101 => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [7,5,6,4,1,2,3] => 100110 => 5
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => 100100 => 5
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [7,6,5,3,4,1,2] => 101011 => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [7,5,3,4,1,2,6] => 101010 => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [5,3,7,6,4,1,2] => 101101 => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [6,4,1,2,7,5,3] => 101110 => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [5,3,7,4,1,2,6] => 101100 => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [7,6,3,4,1,2,5] => 101001 => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [7,5,6,3,4,1,2] => 101010 => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [6,3,5,7,4,1,2] => 101100 => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [7,3,4,1,2,5,6] => 101000 => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [7,6,5,2,3,4,1] => 110011 => 5
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [7,5,2,3,4,1,6] => 110010 => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [5,2,3,7,6,4,1] => 110101 => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [6,4,1,7,5,2,3] => 110110 => 5
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [5,2,3,7,4,1,6] => 110100 => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [5,2,7,6,3,4,1] => 111001 => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [6,3,4,1,7,5,2] => 111010 => 5
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [7,4,1,6,3,5,2] => 111100 => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [5,2,7,3,4,1,6] => 111000 => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [7,6,2,3,4,1,5] => 110001 => 5
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [7,5,6,2,3,4,1] => 110010 => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [6,2,3,5,7,4,1] => 110100 => 5
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [6,2,5,7,3,4,1] => 111000 => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [7,2,3,4,1,5,6] => 110000 => 6
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [7,6,5,1,2,3,4] => 100011 => 5
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [7,5,1,2,3,4,6] => 100010 => 5
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [7,6,4,5,1,2,3] => 100101 => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [6,4,7,5,1,2,3] => 100110 => 5
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [7,4,5,1,2,3,6] => 100100 => 5
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [7,6,3,4,5,1,2] => 101001 => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [6,3,4,7,5,1,2] => 101010 => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [6,3,7,4,5,1,2] => 101100 => 5
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [7,3,4,5,1,2,6] => 101000 => 5
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [7,6,2,3,4,5,1] => 110001 => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [6,2,3,4,7,5,1] => 110010 => 5
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [6,2,3,7,4,5,1] => 110100 => 5
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [6,2,7,3,4,5,1] => 111000 => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [7,2,3,4,5,1,6] => 110000 => 6
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [7,6,1,2,3,4,5] => 100001 => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [7,5,6,1,2,3,4] => 100010 => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [7,4,5,6,1,2,3] => 100100 => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [7,3,4,5,6,1,2] => 101000 => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [7,2,3,4,5,6,1] => 110000 => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => 100000 => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [8,7,6,5,4,3,2,1] => 1111111 => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [8,6,5,4,3,2,1,7] => 1111110 => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [8,7,5,4,3,2,1,6] => 1111101 => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => [8,6,7,5,4,3,2,1] => 1111110 => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [8,5,4,3,2,1,6,7] => 1111100 => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [8,7,6,4,3,2,1,5] => 1111011 => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [8,6,4,3,2,1,5,7] => 1111010 => 6
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7] => [8,7,5,6,4,3,2,1] => 1111101 => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => [7,5,8,6,4,3,2,1] => 1111110 => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => [8,5,6,4,3,2,1,7] => 1111100 => 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [8,7,4,3,2,1,5,6] => 1111001 => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6] => [8,6,7,4,3,2,1,5] => 1111010 => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5] => [8,5,6,7,4,3,2,1] => 1111100 => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [8,4,3,2,1,5,6,7] => 1111000 => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [8,7,6,5,3,2,1,4] => 1110111 => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [8,6,5,3,2,1,4,7] => 1110110 => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [8,7,5,3,2,1,4,6] => 1110101 => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [4,1,2,8,3,7,5,6] => [8,6,7,5,3,2,1,4] => 1110110 => 6
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => 1110100 => 6
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => [8,7,6,4,5,3,2,1] => 1111011 => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,1,2,5,3,4,8,6] => [8,6,4,5,3,2,1,7] => 1111010 => 6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7] => [6,4,8,7,5,3,2,1] => 1111101 => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [7,5,3,2,1,8,6,4] => 1111110 => 7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [7,1,2,6,3,4,8,5] => [6,4,8,5,3,2,1,7] => 1111100 => 7
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,1,2,5,3,8,4,7] => [8,7,4,5,3,2,1,6] => 1111001 => 6
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [8,1,2,5,3,7,4,6] => [8,6,7,4,5,3,2,1] => 1111010 => 6
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5] => [7,4,6,8,5,3,2,1] => 1111100 => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,1,2,5,3,7,8,4] => [8,4,5,3,2,1,6,7] => 1111000 => 7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [8,7,6,3,2,1,4,5] => 1110011 => 6
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => 1110010 => 6
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [4,1,2,8,6,3,5,7] => [8,7,5,6,3,2,1,4] => 1110101 => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [4,1,2,8,7,3,5,6] => [7,5,8,6,3,2,1,4] => 1110110 => 6
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5] => [8,5,6,3,2,1,4,7] => 1110100 => 6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7] => [8,7,4,5,6,3,2,1] => 1111001 => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [8,1,2,5,7,3,4,6] => [7,4,5,8,6,3,2,1] => 1111010 => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5] => [7,4,8,5,6,3,2,1] => 1111100 => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [7,1,2,5,6,3,8,4] => [8,4,5,6,3,2,1,7] => 1111000 => 7
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [8,7,3,2,1,4,5,6] => 1110001 => 6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => [8,6,7,3,2,1,4,5] => 1110010 => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,1,2,8,6,7,3,5] => [8,5,6,7,3,2,1,4] => 1110100 => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [8,4,5,6,7,3,2,1] => 1111000 => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [8,3,2,1,4,5,6,7] => 1110000 => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [8,7,6,5,4,2,1,3] => 1101111 => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [8,6,5,4,2,1,3,7] => 1101110 => 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,1,8,2,4,7,5,6] => [8,6,7,5,4,2,1,3] => 1101110 => 6
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [8,5,4,2,1,3,6,7] => 1101100 => 6
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [8,7,6,4,2,1,3,5] => 1101011 => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => 1101010 => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7] => [8,7,5,6,4,2,1,3] => 1101101 => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,1,8,2,7,4,5,6] => [7,5,8,6,4,2,1,3] => 1101110 => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,1,7,2,6,4,8,5] => [8,5,6,4,2,1,3,7] => 1101100 => 6
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => 1101001 => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,8,7,4,6] => [8,6,7,4,2,1,3,5] => 1101010 => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => 1101000 => 6
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => [8,7,6,5,3,4,2,1] => 1110111 => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6] => [8,6,5,3,4,2,1,7] => 1110110 => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,1,4,2,3,8,5,7] => [8,7,5,3,4,2,1,6] => 1110101 => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [8,1,4,2,3,7,5,6] => [8,6,7,5,3,4,2,1] => 1110110 => 6
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => [5,3,8,7,6,4,2,1] => 1111011 => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [6,4,2,1,8,7,5,3] => 1111101 => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6] => [7,5,3,8,6,4,2,1] => 1111110 => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => [6,4,2,1,8,5,3,7] => 1111100 => 7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => [5,3,8,7,4,2,1,6] => 1111001 => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5] => [7,4,2,1,6,8,5,3] => 1111100 => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4] => [5,3,8,4,2,1,6,7] => 1111000 => 7
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7] => [8,7,6,3,4,2,1,5] => 1110011 => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6] => [8,6,3,4,2,1,5,7] => 1110010 => 6
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7] => [8,7,5,6,3,4,2,1] => 1110101 => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [8,1,4,2,7,3,5,6] => [7,5,8,6,3,4,2,1] => 1110110 => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => [8,5,6,3,4,2,1,7] => 1110100 => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [8,1,5,2,7,3,4,6] => [8,6,3,5,7,4,2,1] => 1111010 => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5] => [7,4,2,1,8,5,6,3] => 1111100 => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => [6,3,5,8,4,2,1,7] => 1111000 => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,4,2,6,8,3,7] => [8,7,3,4,2,1,5,6] => 1110001 => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [8,1,4,2,6,7,3,5] => [8,5,6,7,3,4,2,1] => 1110100 => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [8,1,5,2,6,7,3,4] => [7,3,5,6,8,4,2,1] => 1111000 => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3] => [8,3,4,2,1,5,6,7] => 1110000 => 7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => [8,7,6,5,2,1,3,4] => 1100111 => 6
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [8,6,5,2,1,3,4,7] => 1100110 => 6
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => 1100101 => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => 1100100 => 6
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,8,5,2,4,6,7] => [8,7,6,4,5,2,1,3] => 1101011 => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,7,5,2,4,8,6] => [8,6,4,5,2,1,3,7] => 1101010 => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => [6,4,8,7,5,2,1,3] => 1101101 => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,7,8,2,4,5,6] => [7,5,2,1,3,8,6,4] => 1101110 => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6] => [8,6,7,4,5,2,1,3] => 1101010 => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => [8,7,6,3,4,5,2,1] => 1110011 => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6] => [7,5,2,1,8,6,3,4] => 1110110 => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,1,6,5,2,3,4,7] => [6,3,8,7,4,5,2,1] => 1111001 => 6
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,1,8,5,2,3,4,6] => [7,4,5,2,1,8,6,3] => 1111010 => 6
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => [8,5,2,1,7,4,6,3] => 1111100 => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4] => [6,3,8,4,5,2,1,7] => 1111000 => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,1,4,5,2,8,3,7] => [8,7,3,4,5,2,1,6] => 1110001 => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6] => [8,6,7,3,4,5,2,1] => 1110010 => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [8,1,6,5,2,7,3,4] => [7,3,6,8,4,5,2,1] => 1111000 => 7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [6,1,4,5,2,7,8,3] => [8,3,4,5,2,1,6,7] => 1110000 => 7
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [8,7,6,2,1,3,4,5] => 1100011 => 6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,8,6,2,5,7] => [8,7,5,6,2,1,3,4] => 1100101 => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,8,7,2,5,6] => [7,5,8,6,2,1,3,4] => 1100110 => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,1,4,7,6,2,8,5] => [8,5,6,2,1,3,4,7] => 1100100 => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,8,5,6,2,4,7] => [8,7,4,5,6,2,1,3] => 1101001 => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6] => [7,4,5,8,6,2,1,3] => 1101010 => 5
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,1,8,7,6,2,4,5] => [7,4,8,5,6,2,1,3] => 1101100 => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,1,7,5,6,2,8,4] => [8,4,5,6,2,1,3,7] => 1101000 => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,1,4,5,6,2,3,7] => [8,7,3,4,5,6,2,1] => 1110001 => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6] => [7,3,4,5,8,6,2,1] => 1110010 => 6
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5] => [7,3,4,8,5,6,2,1] => 1110100 => 6
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4] => [7,3,8,4,5,6,2,1] => 1111000 => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [7,1,4,5,6,2,8,3] => [8,3,4,5,6,2,1,7] => 1110000 => 7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [8,7,2,1,3,4,5,6] => 1100001 => 6
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,1,4,5,8,7,2,6] => [8,6,7,2,1,3,4,5] => 1100010 => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,1,4,8,6,7,2,5] => [8,5,6,7,2,1,3,4] => 1100100 => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,8,5,6,7,2,4] => [8,4,5,6,7,2,1,3] => 1101000 => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3] => [8,3,4,5,6,7,2,1] => 1110000 => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,2,1,3,4,5,6,7] => 1100000 => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [8,7,6,5,4,3,1,2] => 1011111 => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [8,6,5,4,3,1,2,7] => 1011110 => 6
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => [8,7,5,4,3,1,2,6] => 1011101 => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6] => [8,6,7,5,4,3,1,2] => 1011110 => 6
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => [8,7,6,4,3,1,2,5] => 1011011 => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [8,6,4,3,1,2,5,7] => 1011010 => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,8,1,3,6,4,5,7] => [8,7,5,6,4,3,1,2] => 1011101 => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [8,7,6,5,3,1,2,4] => 1010111 => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => 1010101 => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,8,3,7,5,6] => [8,6,7,5,3,1,2,4] => 1010110 => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => 1010100 => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,8,1,5,3,4,6,7] => [8,7,6,4,5,3,1,2] => 1011011 => 5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,7,1,5,3,4,8,6] => [8,6,4,5,3,1,2,7] => 1011010 => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,8,1,6,3,4,5,7] => [6,4,8,7,5,3,1,2] => 1011101 => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [7,5,3,1,2,8,6,4] => 1011110 => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,7,1,6,3,4,8,5] => [6,4,8,5,3,1,2,7] => 1011100 => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,8,1,5,3,7,4,6] => [8,6,7,4,5,3,1,2] => 1011010 => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,8,1,6,3,7,4,5] => [7,4,6,8,5,3,1,2] => 1011100 => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [8,7,6,3,1,2,4,5] => 1010011 => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7] => [8,7,5,6,3,1,2,4] => 1010101 => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6] => [7,5,8,6,3,1,2,4] => 1010110 => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,4,1,7,6,3,8,5] => [8,5,6,3,1,2,4,7] => 1010100 => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => [7,4,8,5,6,3,1,2] => 1011100 => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,8,7,3,6] => [8,6,7,3,1,2,4,5] => 1010010 => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => 1010000 => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [8,7,6,5,4,2,3,1] => 1101111 => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => [8,6,5,4,2,3,1,7] => 1101110 => 6
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6] => [8,6,7,5,4,2,3,1] => 1101110 => 6
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,3,1,2,8,4,6,7] => [8,7,6,4,2,3,1,5] => 1101011 => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,3,1,2,7,4,8,6] => [8,6,4,2,3,1,5,7] => 1101010 => 5
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,3,1,2,6,4,5,7] => [8,7,5,6,4,2,3,1] => 1101101 => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5] => [8,5,6,4,2,3,1,7] => 1101100 => 6
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,1,2,8,7,4,6] => [8,6,7,4,2,3,1,5] => 1101010 => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [8,3,1,2,6,7,4,5] => [8,5,6,7,4,2,3,1] => 1101100 => 6
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,1,2,6,7,8,4] => [8,4,2,3,1,5,6,7] => 1101000 => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [4,2,8,7,6,5,3,1] => 1110111 => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,1,2,3,8,5,7] => [4,2,8,7,5,3,1,6] => 1110101 => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,4,1,2,3,7,5,6] => [4,2,8,6,7,5,3,1] => 1110110 => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => [5,3,1,8,7,6,4,2] => 1111011 => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [5,3,1,8,6,4,2,7] => 1111010 => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [6,4,2,8,7,5,3,1] => 1111101 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => [8,6,4,2,7,5,3,1] => 1111110 => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => [6,4,2,8,5,3,1,7] => 1111100 => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7] => [5,3,1,8,7,4,2,6] => 1111001 => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => [5,3,1,8,6,7,4,2] => 1111010 => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5] => [7,4,2,6,8,5,3,1] => 1111100 => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => [5,3,1,8,4,2,6,7] => 1111000 => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,2,8,3,6,7] => [4,2,8,7,6,3,1,5] => 1110011 => 6
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,4,1,2,7,3,8,6] => [4,2,8,6,3,1,5,7] => 1110010 => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => [4,2,7,5,8,6,3,1] => 1110110 => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => [4,2,8,5,6,3,1,7] => 1110100 => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => [8,6,3,1,5,7,4,2] => 1111010 => 6
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,1,2,6,3,4,5] => [7,4,2,8,5,6,3,1] => 1111100 => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => [6,3,1,5,8,4,2,7] => 1111000 => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [5,4,1,2,6,8,3,7] => [4,2,8,7,3,1,5,6] => 1110001 => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,4,1,2,8,7,3,6] => [4,2,8,6,7,3,1,5] => 1110010 => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5] => [4,2,8,5,6,7,3,1] => 1110100 => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => [7,3,1,5,6,8,4,2] => 1111000 => 7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3] => [4,2,8,3,1,5,6,7] => 1110000 => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,3,1,8,2,5,6,7] => [8,7,6,5,2,3,1,4] => 1100111 => 6
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,3,1,7,2,5,8,6] => [8,6,5,2,3,1,4,7] => 1100110 => 6
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,3,1,6,2,8,5,7] => [8,7,5,2,3,1,4,6] => 1100101 => 5
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => [8,6,7,5,2,3,1,4] => 1100110 => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,3,1,5,2,4,6,7] => [8,7,6,4,5,2,3,1] => 1101011 => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,3,1,5,2,4,8,6] => [8,6,4,5,2,3,1,7] => 1101010 => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,3,1,6,2,4,5,7] => [6,4,8,7,5,2,3,1] => 1101101 => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => [7,5,2,3,1,8,6,4] => 1101110 => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => [6,4,8,5,2,3,1,7] => 1101100 => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,1,5,2,8,4,7] => [8,7,4,5,2,3,1,6] => 1101001 => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => [8,6,7,4,5,2,3,1] => 1101010 => 5
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8,3,1,6,2,7,4,5] => [7,4,6,8,5,2,3,1] => 1101100 => 6
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [6,3,1,5,2,7,8,4] => [8,4,5,2,3,1,6,7] => 1101000 => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,4,1,6,2,3,5,7] => [8,7,5,2,4,6,3,1] => 1110101 => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => [8,6,3,1,7,5,2,4] => 1110110 => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5] => [8,5,2,4,6,3,1,7] => 1110100 => 6
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,8,1,5,2,3,4,7] => [6,3,1,8,7,4,5,2] => 1111001 => 6
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => [7,4,5,2,8,6,3,1] => 1111010 => 6
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => [8,5,2,7,4,6,3,1] => 1111100 => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => [6,3,1,8,4,5,2,7] => 1111000 => 7
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7] => [5,2,4,8,7,3,1,6] => 1110001 => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8,4,1,5,2,7,3,6] => [5,2,4,8,6,7,3,1] => 1110010 => 6
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => [8,5,2,4,6,7,3,1] => 1110100 => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => [7,3,1,6,8,4,5,2] => 1111000 => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3] => [5,2,4,8,3,1,6,7] => 1110000 => 7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7] => [8,7,6,2,3,1,4,5] => 1100011 => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [4,3,1,8,6,2,5,7] => [8,7,5,6,2,3,1,4] => 1100101 => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => [7,5,8,6,2,3,1,4] => 1100110 => 6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,1,7,6,2,8,5] => [8,5,6,2,3,1,4,7] => 1100100 => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7] => [8,7,4,5,6,2,3,1] => 1101001 => 5
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => [7,4,5,8,6,2,3,1] => 1101010 => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => [7,4,8,5,6,2,3,1] => 1101100 => 6
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4] => [8,4,5,6,2,3,1,7] => 1101000 => 6
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7] => [6,2,4,5,8,7,3,1] => 1110001 => 6
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => [8,6,2,4,5,7,3,1] => 1110010 => 6
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => [8,5,6,2,4,7,3,1] => 1110100 => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [7,3,1,8,4,5,6,2] => 1111000 => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3] => [6,2,4,5,8,3,1,7] => 1110000 => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7] => [8,7,2,3,1,4,5,6] => 1100001 => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [4,3,1,5,8,7,2,6] => [8,6,7,2,3,1,4,5] => 1100010 => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => [8,5,6,7,2,3,1,4] => 1100100 => 6
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4] => [8,4,5,6,7,2,3,1] => 1101000 => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => [7,2,4,5,6,8,3,1] => 1110000 => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [8,2,3,1,4,5,6,7] => 1100000 => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [8,7,6,5,4,1,2,3] => 1001111 => 6
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => [8,6,5,4,1,2,3,7] => 1001110 => 6
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => [8,7,5,4,1,2,3,6] => 1001101 => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [8,5,4,1,2,3,6,7] => 1001100 => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [8,7,6,4,1,2,3,5] => 1001011 => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6] => [7,5,8,6,4,1,2,3] => 1001110 => 6
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,3,7,1,6,4,8,5] => [8,5,6,4,1,2,3,7] => 1001100 => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => 1001001 => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,3,8,1,6,7,4,5] => [8,5,6,7,4,1,2,3] => 1001100 => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => 1001000 => 6
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => [8,7,6,5,3,4,1,2] => 1010111 => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,7,4,1,3,5,8,6] => [8,6,5,3,4,1,2,7] => 1010110 => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => [8,7,5,3,4,1,2,6] => 1010101 => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,4,1,3,7,8,5] => [8,5,3,4,1,2,6,7] => 1010100 => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,8,5,1,3,4,6,7] => [5,3,8,7,6,4,1,2] => 1011011 => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,8,1,3,4,5,7] => [6,4,1,2,8,7,5,3] => 1011101 => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => [7,5,3,8,6,4,1,2] => 1011110 => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [6,4,1,2,8,5,3,7] => 1011100 => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7] => [5,3,8,7,4,1,2,6] => 1011001 => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => [5,3,8,6,7,4,1,2] => 1011010 => 5
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => [7,4,1,2,6,8,5,3] => 1011100 => 6
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,6,5,1,3,7,8,4] => [5,3,8,4,1,2,6,7] => 1011000 => 6
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,5,4,1,8,3,6,7] => [8,7,6,3,4,1,2,5] => 1010011 => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,5,4,1,7,3,8,6] => [8,6,3,4,1,2,5,7] => 1010010 => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => [8,7,5,6,3,4,1,2] => 1010101 => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => [7,5,8,6,3,4,1,2] => 1010110 => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,7,4,1,6,3,8,5] => [8,5,6,3,4,1,2,7] => 1010100 => 5
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,8,5,1,6,3,4,7] => [6,3,5,8,7,4,1,2] => 1011001 => 5
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => [8,6,3,5,7,4,1,2] => 1011010 => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => [7,4,1,2,8,5,6,3] => 1011100 => 6
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,7,5,1,6,3,8,4] => [6,3,5,8,4,1,2,7] => 1011000 => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,5,4,1,6,8,3,7] => [8,7,3,4,1,2,5,6] => 1010001 => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,5,4,1,8,7,3,6] => [8,6,7,3,4,1,2,5] => 1010010 => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5] => [8,5,6,7,3,4,1,2] => 1010100 => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4] => [7,3,5,6,8,4,1,2] => 1011000 => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3] => [8,3,4,1,2,5,6,7] => 1010000 => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7] => [8,7,6,5,2,3,4,1] => 1100111 => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,3,4,1,2,5,8,6] => [8,6,5,2,3,4,1,7] => 1100110 => 6
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [8,3,4,1,2,7,5,6] => [8,6,7,5,2,3,4,1] => 1100110 => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6] => [7,5,2,3,8,6,4,1] => 1101110 => 6
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => [6,4,1,8,5,2,3,7] => 1101100 => 6
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7] => [5,2,3,8,7,4,1,6] => 1101001 => 5
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8,3,5,1,2,7,4,6] => [5,2,3,8,6,7,4,1] => 1101010 => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => [7,4,1,6,8,5,2,3] => 1101100 => 6
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [6,3,5,1,2,7,8,4] => [5,2,3,8,4,1,6,7] => 1101000 => 6
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => [6,3,4,1,8,7,5,2] => 1110101 => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => [7,5,2,8,6,3,4,1] => 1110110 => 6
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => [6,3,4,1,8,5,2,7] => 1110100 => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => [8,7,4,1,6,3,5,2] => 1111001 => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => [8,6,3,5,2,7,4,1] => 1111010 => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => [8,5,2,7,4,1,6,3] => 1111100 => 7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => [8,4,1,6,3,5,2,7] => 1111000 => 7
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,5,4,1,2,8,3,7] => [5,2,8,7,3,4,1,6] => 1110001 => 6
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => [5,2,8,6,7,3,4,1] => 1110010 => 6
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => [7,3,4,1,6,8,5,2] => 1110100 => 6
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => [8,4,1,6,7,3,5,2] => 1111000 => 7
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3] => [5,2,8,3,4,1,6,7] => 1110000 => 7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,3,4,1,8,2,6,7] => [8,7,6,2,3,4,1,5] => 1100011 => 6
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,3,4,1,7,2,8,6] => [8,6,2,3,4,1,5,7] => 1100010 => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7] => [8,7,5,6,2,3,4,1] => 1100101 => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => [7,5,8,6,2,3,4,1] => 1100110 => 6
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7,3,4,1,6,2,8,5] => [8,5,6,2,3,4,1,7] => 1100100 => 6
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6] => [8,6,2,3,5,7,4,1] => 1101010 => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => [7,4,1,8,5,6,2,3] => 1101100 => 6
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,3,5,1,6,2,8,4] => [6,2,3,5,8,4,1,7] => 1101000 => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => [6,2,5,8,7,3,4,1] => 1110001 => 6
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => [8,6,2,5,7,3,4,1] => 1110010 => 6
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => [7,3,4,1,8,5,6,2] => 1110100 => 6
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => [8,4,1,7,3,5,6,2] => 1111000 => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3] => [6,2,5,8,3,4,1,7] => 1110000 => 7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [5,3,4,1,6,8,2,7] => [8,7,2,3,4,1,5,6] => 1100001 => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,3,4,1,8,7,2,6] => [8,6,7,2,3,4,1,5] => 1100010 => 6
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => [8,5,6,7,2,3,4,1] => 1100100 => 6
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => [7,2,3,5,6,8,4,1] => 1101000 => 6
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => [7,2,5,6,8,3,4,1] => 1110000 => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2] => [8,2,3,4,1,5,6,7] => 1100000 => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [8,7,6,5,1,2,3,4] => 1000111 => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => [8,6,5,1,2,3,4,7] => 1000110 => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [8,7,5,1,2,3,4,6] => 1000101 => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,4,8,1,7,5,6] => [8,6,7,5,1,2,3,4] => 1000110 => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => 1000100 => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,8,5,1,4,6,7] => [8,7,6,4,5,1,2,3] => 1001011 => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,7,5,1,4,8,6] => [8,6,4,5,1,2,3,7] => 1001010 => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,8,6,1,4,5,7] => [6,4,8,7,5,1,2,3] => 1001101 => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,7,8,1,4,5,6] => [7,5,1,2,3,8,6,4] => 1001110 => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5] => [6,4,8,5,1,2,3,7] => 1001100 => 6
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,6,5,1,8,4,7] => [8,7,4,5,1,2,3,6] => 1001001 => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6] => [8,6,7,4,5,1,2,3] => 1001010 => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,8,6,1,7,4,5] => [7,4,6,8,5,1,2,3] => 1001100 => 6
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4] => [8,4,5,1,2,3,6,7] => 1001000 => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => [8,7,6,3,4,5,1,2] => 1010011 => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,4,5,1,3,8,6] => [8,6,3,4,5,1,2,7] => 1010010 => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => [6,3,4,8,7,5,1,2] => 1010101 => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => [7,5,1,2,8,6,3,4] => 1010110 => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,7,4,6,1,3,8,5] => [6,3,4,8,5,1,2,7] => 1010100 => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => [6,3,8,7,4,5,1,2] => 1011001 => 5
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => [7,4,5,1,2,8,6,3] => 1011010 => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => [8,5,1,2,7,4,6,3] => 1011100 => 6
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => [6,3,8,4,5,1,2,7] => 1011000 => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,6,4,5,1,8,3,7] => [8,7,3,4,5,1,2,6] => 1010001 => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,6,7,3,4,5,1,2] => 1010010 => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => [7,3,4,6,8,5,1,2] => 1010100 => 5
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => [7,3,6,8,4,5,1,2] => 1011000 => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3] => [8,3,4,5,1,2,6,7] => 1010000 => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,3,4,5,1,2,6,7] => [8,7,6,2,3,4,5,1] => 1100011 => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => [7,5,1,8,6,2,3,4] => 1100110 => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7,3,4,6,1,2,8,5] => [6,2,3,4,8,5,1,7] => 1100100 => 6
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => [6,2,3,8,7,4,5,1] => 1101001 => 5
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => [7,4,5,1,8,6,2,3] => 1101010 => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => [8,5,1,7,4,6,2,3] => 1101100 => 6
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,6,5,1,2,8,4] => [6,2,3,8,4,5,1,7] => 1101000 => 6
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => [6,2,8,7,3,4,5,1] => 1110001 => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => [7,3,4,5,1,8,6,2] => 1110010 => 6
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5] => [8,5,1,7,3,4,6,2] => 1110100 => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => [8,4,5,1,7,3,6,2] => 1111000 => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3] => [6,2,8,3,4,5,1,7] => 1110000 => 7
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,4,5,1,8,2,7] => [8,7,2,3,4,5,1,6] => 1100001 => 6
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6] => [8,6,7,2,3,4,5,1] => 1100010 => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5] => [7,2,3,4,6,8,5,1] => 1100100 => 6
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => [7,2,3,6,8,4,5,1] => 1101000 => 6
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3] => [7,2,6,8,3,4,5,1] => 1110000 => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2] => [8,2,3,4,5,1,6,7] => 1100000 => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [8,7,6,1,2,3,4,5] => 1000011 => 6
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [8,6,1,2,3,4,5,7] => 1000010 => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7] => [8,7,5,6,1,2,3,4] => 1000101 => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6] => [7,5,8,6,1,2,3,4] => 1000110 => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,4,7,6,1,8,5] => [8,5,6,1,2,3,4,7] => 1000100 => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,3,8,5,6,1,4,7] => [8,7,4,5,6,1,2,3] => 1001001 => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6] => [7,4,5,8,6,1,2,3] => 1001010 => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => [7,4,8,5,6,1,2,3] => 1001100 => 6
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4] => [8,4,5,6,1,2,3,7] => 1001000 => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7] => [8,7,3,4,5,6,1,2] => 1010001 => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => [7,3,4,5,8,6,1,2] => 1010010 => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => [7,3,4,8,5,6,1,2] => 1010100 => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [7,3,8,4,5,6,1,2] => 1011000 => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7,4,5,6,1,8,3] => [8,3,4,5,6,1,2,7] => 1010000 => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [8,7,2,3,4,5,6,1] => 1100001 => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => [7,2,3,4,5,8,6,1] => 1100010 => 6
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => [7,2,3,4,8,5,6,1] => 1100100 => 6
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => [7,2,3,8,4,5,6,1] => 1101000 => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => [7,2,8,3,4,5,6,1] => 1110000 => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => [8,2,3,4,5,6,1,7] => 1100000 => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [8,7,1,2,3,4,5,6] => 1000001 => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => [8,6,7,1,2,3,4,5] => 1000010 => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5] => [8,5,6,7,1,2,3,4] => 1000100 => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4] => [8,4,5,6,7,1,2,3] => 1001000 => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => [8,3,4,5,6,7,1,2] => 1010000 => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => [8,2,3,4,5,6,7,1] => 1100000 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => 1000000 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => [9,8,7,6,5,4,3,2,1] => 11111111 => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [9,7,6,5,4,3,2,1,8] => 11111110 => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [9,8,6,5,4,3,2,1,7] => 11111101 => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,1,2,3,4,5,8,6,7] => [9,7,8,6,5,4,3,2,1] => 11111110 => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [9,6,5,4,3,2,1,7,8] => 11111100 => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,1,2,3,4,9,5,7,8] => [9,8,7,5,4,3,2,1,6] => 11111011 => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,1,2,3,4,8,5,6,7] => [8,6,9,7,5,4,3,2,1] => 11111110 => 8
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [8,1,2,3,4,7,5,9,6] => [9,6,7,5,4,3,2,1,8] => 11111100 => 8
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,1,2,3,4,7,9,5,8] => [9,8,5,4,3,2,1,6,7] => 11111001 => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,1,2,3,4,9,8,5,7] => [9,7,8,5,4,3,2,1,6] => 11111010 => 7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [9,1,2,3,4,7,8,5,6] => [9,6,7,8,5,4,3,2,1] => 11111100 => 8
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [9,5,4,3,2,1,6,7,8] => 11111000 => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [5,1,2,3,9,4,6,7,8] => [9,8,7,6,4,3,2,1,5] => 11110111 => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [9,1,2,3,6,4,5,7,8] => [9,8,7,5,6,4,3,2,1] => 11111011 => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,1,2,3,9,4,5,6,7] => [8,6,4,3,2,1,9,7,5] => 11111110 => 8
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,1,2,3,9,8,4,6,7] => [8,6,9,7,4,3,2,1,5] => 11110110 => 7
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [9,1,2,3,6,8,4,5,7] => [8,5,6,9,7,4,3,2,1] => 11111010 => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,1,2,3,6,9,8,4,7] => [9,7,8,4,3,2,1,5,6] => 11110010 => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [9,1,2,5,3,4,6,7,8] => [9,8,7,6,4,5,3,2,1] => 11110111 => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,1,2,8,3,4,5,6,7] => [8,6,4,9,7,5,3,2,1] => 11111110 => 8
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,9,3,6,7,8] => [9,8,7,6,3,2,1,4,5] => 11100111 => 7
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [4,1,2,8,9,3,5,6,7] => [8,6,3,2,1,4,9,7,5] => 11101110 => 7
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [8,1,2,5,9,3,4,6,7] => [8,6,3,2,1,9,7,4,5] => 11110110 => 7
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,9,8,3,6,7] => [8,6,9,7,3,2,1,4,5] => 11100110 => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8] => [9,8,7,6,5,4,2,1,3] => 11011111 => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,1,4,2,3,5,6,7,8] => [9,8,7,6,5,3,4,2,1] => 11101111 => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,8,2,3,4,5,6,7] => [9,7,5,3,8,6,4,2,1] => 11111110 => 8
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,4,9,2,5,6,7,8] => [9,8,7,6,5,2,1,3,4] => 11001111 => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,9,8,2,4,5,6,7] => [8,6,4,9,7,5,2,1,3] => 11011110 => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9,1,4,8,2,3,5,6,7] => [8,6,3,4,9,7,5,2,1] => 11101110 => 7
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,4,8,9,2,5,6,7] => [8,6,2,1,3,4,9,7,5] => 11001110 => 7
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,1,4,5,6,2,8,9,3] => [9,3,4,5,6,2,1,7,8] => 11100000 => 8
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [9,1,8,5,6,7,2,3,4] => [8,3,9,4,5,6,7,2,1] => 11110000 => 8
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8,1,4,5,6,7,2,9,3] => [9,3,4,5,6,7,2,1,8] => 11100000 => 8
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,4,9,6,7,8,2,5] => [9,5,6,7,8,2,1,3,4] => 11001000 => 7
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,9,5,6,7,8,2,4] => [9,4,5,6,7,8,2,1,3] => 11010000 => 7
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9,1,4,5,6,7,8,2,3] => [9,3,4,5,6,7,8,2,1] => 11100000 => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,1,3,4,5,6,7,8] => 11000000 => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => [9,8,7,6,5,4,3,1,2] => 10111111 => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,8,1,3,4,5,6,9,7] => [9,7,6,5,4,3,1,2,8] => 10111110 => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,9,1,3,4,5,8,6,7] => [9,7,8,6,5,4,3,1,2] => 10111110 => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,9,3,5,6,7,8] => [9,8,7,6,5,3,1,2,4] => 10101111 => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => 10101010 => 5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => 10100000 => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,3,1,2,4,5,6,7,8] => [9,8,7,6,5,4,2,3,1] => 11011111 => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,4,1,2,3,5,6,7,8] => [4,2,9,8,7,6,5,3,1] => 11101111 => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,9,1,2,3,4,6,7,8] => [5,3,1,9,8,7,6,4,2] => 11110111 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => [9,7,5,3,1,8,6,4,2] => 11111110 => 8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,3,1,9,2,5,6,7,8] => [9,8,7,6,5,2,3,1,4] => 11001111 => 7
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,3,1,6,2,8,5,9,7] => [9,7,5,2,3,1,4,6,8] => 11001010 => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [9,3,1,5,2,4,6,7,8] => [9,8,7,6,4,5,2,3,1] => 11010111 => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9,3,1,8,2,4,5,6,7] => [8,6,4,9,7,5,2,3,1] => 11011110 => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [9,3,1,5,2,8,4,6,7] => [8,6,9,7,4,5,2,3,1] => 11010110 => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,3,1,5,2,7,4,9,6] => [9,6,7,4,5,2,3,1,8] => 11010100 => 6
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,3,1,5,8,7,2,9,6] => [9,6,7,2,3,1,4,5,8] => 11000100 => 7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,2] => [9,2,3,1,4,5,6,7,8] => 11000000 => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,9,1,4,5,6,7,8] => [9,8,7,6,5,4,1,2,3] => 10011111 => 7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => 10010001 => 6
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => 10010000 => 7
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,9,4,1,3,5,6,7,8] => [9,8,7,6,5,3,4,1,2] => 10101111 => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,9,8,1,3,4,5,6,7] => [9,7,5,3,8,6,4,1,2] => 10111110 => 7
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,5,4,1,6,7,8,9,3] => [9,3,4,1,2,5,6,7,8] => 10100000 => 7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [9,3,4,1,2,5,6,7,8] => [9,8,7,6,5,2,3,4,1] => 11001111 => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,3,8,1,2,4,5,6,7] => [9,7,5,2,3,8,6,4,1] => 11011110 => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,7,8,1,2,3,4,5,6] => [9,6,3,8,5,2,7,4,1] => 11111100 => 8
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [5,3,4,1,6,7,8,9,2] => [9,2,3,4,1,5,6,7,8] => 11000000 => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,9,1,5,6,7,8] => [9,8,7,6,5,1,2,3,4] => 10001111 => 7
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [2,3,9,5,1,4,6,7,8] => [9,8,7,6,4,5,1,2,3] => 10010111 => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [2,3,9,8,1,4,5,6,7] => [8,6,4,9,7,5,1,2,3] => 10011110 => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [6,3,4,5,1,7,9,2,8] => [9,8,2,3,4,5,1,6,7] => 11000001 => 7
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [6,3,4,5,1,7,8,9,2] => [9,2,3,4,5,1,6,7,8] => 11000000 => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,9,1,6,7,8] => [9,8,7,6,1,2,3,4,5] => 10000111 => 7
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => 10000100 => 7
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [2,3,4,9,6,1,5,7,8] => [9,8,7,5,6,1,2,3,4] => 10001011 => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [2,3,9,5,6,1,4,7,8] => [9,8,7,4,5,6,1,2,3] => 10010011 => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [2,3,8,5,6,1,4,9,7] => [9,7,4,5,6,1,2,3,8] => 10010010 => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [9,7,4,5,6,1,2,3,8] => [7,2,9,8,3,4,5,6,1] => 11100001 => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,3,4,5,6,1,9,2,8] => [9,8,2,3,4,5,6,1,7] => 11000001 => 7
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,2] => [9,2,3,4,5,6,1,7,8] => 11000000 => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,9,1,7,8] => [9,8,7,1,2,3,4,5,6] => 10000011 => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [9,7,1,2,3,4,5,6,8] => 10000010 => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [2,3,4,5,9,7,1,6,8] => [9,8,6,7,1,2,3,4,5] => 10000101 => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [2,3,4,9,6,7,1,5,8] => [9,8,5,6,7,1,2,3,4] => 10001001 => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [2,3,9,5,6,7,1,4,8] => [9,8,4,5,6,7,1,2,3] => 10010001 => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [2,9,4,5,6,7,1,3,8] => [9,8,3,4,5,6,7,1,2] => 10100001 => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,8,4,5,6,7,1,9,3] => [9,3,4,5,6,7,1,2,8] => 10100000 => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [9,8,2,3,4,5,6,7,1] => 11000001 => 7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,2] => [9,2,3,4,5,6,7,1,8] => 11000000 => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => [9,8,1,2,3,4,5,6,7] => 10000001 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,9,8,1,7] => [9,7,8,1,2,3,4,5,6] => 10000010 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,5,9,7,8,1,6] => [9,6,7,8,1,2,3,4,5] => 10000100 => 7
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,9,6,7,8,1,5] => [9,5,6,7,8,1,2,3,4] => 10001000 => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,4,5,6,7,8,1,3] => [9,3,4,5,6,7,8,1,2] => 10100000 => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,2] => [9,2,3,4,5,6,7,8,1] => 11000000 => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => 10000000 => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,10,1,9] => [10,9,1,2,3,4,5,6,7,8] => 100000001 => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,1,3,4,5,6,7,8,9] => 110000000 => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,1,2,9] => [10,9,2,3,4,5,6,7,8,1] => 110000001 => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [10,1,4,5,6,7,8,9,2,3] => [10,3,4,5,6,7,8,9,2,1] => 111000000 => 9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [2,10,4,5,6,7,8,1,3,9] => [10,9,3,4,5,6,7,8,1,2] => 101000001 => 7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,10,2,9] => [10,9,2,3,4,5,6,7,1,8] => 110000001 => 8
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,10,5,6,7,8,9,2,4] => [10,4,5,6,7,8,9,2,1,3] => 110100000 => 8
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9,1,4,5,6,7,8,2,10,3] => [10,3,4,5,6,7,8,2,1,9] => 111000000 => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [2,3,4,5,6,10,8,1,7,9] => [10,9,7,8,1,2,3,4,5,6] => 100000101 => 7
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => 101000000 => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,10,1,8,9] => [10,9,8,1,2,3,4,5,6,7] => 100000011 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,1,2,3,4,5,6,7,8] => [10,8,6,4,2,9,7,5,3,1] => 111111110 => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10,3,1,5,2,7,4,9,6,8] => [10,8,9,6,7,4,5,2,3,1] => 110101010 => 6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,10,2] => [10,2,3,1,4,5,6,7,8,9] => 110000000 => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,9,10,1,3,4,5,6,7,8] => [10,8,6,4,1,2,9,7,5,3] => 101111110 => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,3,10,1,2,4,5,6,7,8] => [10,8,6,4,1,9,7,5,2,3] => 110111110 => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,9,8,1,2,3,4,5,6,7] => [9,6,3,8,5,2,10,7,4,1] => 111111100 => 9
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,3,4,1,6,7,8,9,10,2] => [10,2,3,4,1,5,6,7,8,9] => 110000000 => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [9,5,1,7,3,10,6,2,8,4] => 111111000 => 9
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [6,3,4,5,1,7,8,9,10,2] => [10,2,3,4,5,1,6,7,8,9] => 110000000 => 9
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0] => [8,3,4,9,10,1,2,5,6,7] => [10,7,2,3,4,9,6,1,8,5] => 110011100 => 8
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,10,2] => [10,2,3,4,5,6,1,7,8,9] => 110000000 => 9
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,10,2] => [10,2,3,4,5,6,7,1,8,9] => 110000000 => 9
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,10,2] => [10,2,3,4,5,6,7,8,1,9] => 110000000 => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,10,9,1,8] => [10,8,9,1,2,3,4,5,6,7] => 100000010 => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [2,3,4,5,6,10,8,9,1,7] => [10,7,8,9,1,2,3,4,5,6] => 100000100 => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,10,7,8,9,1,6] => [10,6,7,8,9,1,2,3,4,5] => 100001000 => 8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,10,4,5,6,7,8,9,1,3] => [10,3,4,5,6,7,8,9,1,2] => 101000000 => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10,3,4,5,6,7,8,9,1,2] => [10,2,3,4,5,6,7,8,9,1] => 110000000 => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => 100000000 => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [10,8,7,6,5,4,3,2,1,9] => 111111110 => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,1,2,3,4,5,6,9,7,8] => [10,8,9,7,6,5,4,3,2,1] => 111111110 => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [10,1,2,3,4,5,9,6,7,8] => [9,7,10,8,6,5,4,3,2,1] => 111111110 => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,1,2,3,4,10,5,6,7,8] => [9,7,5,4,3,2,1,10,8,6] => 111111110 => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,3,9,4,5,6,7,8] => [9,7,5,10,8,6,4,3,2,1] => 111111110 => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,9,3,4,5,6,7,8] => [10,8,6,4,9,7,5,3,2,1] => 111111110 => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,10,2,3,4,5,6,7,8] => [10,8,6,4,2,1,9,7,5,3] => 111111110 => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => [10,7,6,5,4,3,2,1,8,9] => 111111100 => 9
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,1,2,3,4,5,10,9,6,8] => [10,8,9,6,5,4,3,2,1,7] => 111111010 => 8
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,1,2,3,4,10,9,5,7,8] => [9,7,10,8,5,4,3,2,1,6] => 111110110 => 8
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,1,2,3,9,10,4,6,7,8] => [9,7,4,3,2,1,5,10,8,6] => 111101110 => 8
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,10,9,3,5,6,7,8] => [9,7,5,10,8,6,3,2,1,4] => 111011110 => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,10,9,2,4,5,6,7,8] => [10,8,6,4,9,7,5,2,1,3] => 110111110 => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,1,2,3,4,5,6,10,7,9] => [10,9,7,6,5,4,3,2,1,8] => 111111101 => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => [10,8,6,5,4,3,2,1,7,9] => 111111010 => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,10,4,6,7,8,9] => [10,9,8,7,6,4,3,2,1,5] => 111101111 => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => 111101010 => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,10,3,5,6,7,8,9] => [10,9,8,7,6,5,3,2,1,4] => 111011111 => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,10,2,4,5,6,7,8,9] => [10,9,8,7,6,5,4,2,1,3] => 110111111 => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => [10,8,7,6,5,4,2,1,3,9] => 110111110 => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => [10,9,8,7,6,4,2,1,3,5] => 110101111 => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => 110101010 => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,10,1,3,4,5,6,7,8,9] => [10,9,8,7,6,5,4,3,1,2] => 101111111 => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,9,1,3,4,5,6,7,10,8] => [10,8,7,6,5,4,3,1,2,9] => 101111110 => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => 101010101 => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,10,1,4,5,6,7,8,9] => [10,9,8,7,6,5,4,1,2,3] => 100111111 => 8
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => 100100000 => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,10,1,5,6,7,8,9] => [10,9,8,7,6,5,1,2,3,4] => 100011111 => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,10,1,6,7,8,9] => [10,9,8,7,6,1,2,3,4,5] => 100001111 => 8
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => 100001000 => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,10,1,7,8,9] => [10,9,8,7,1,2,3,4,5,6] => 100000111 => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => 100000100 => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => [10,9,8,7,6,5,4,2,3,1] => 110111111 => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,10,1,2,3,4,6,7,8,9] => [5,3,1,10,9,8,7,6,4,2] => 111101111 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,10,1,2,3,4,5,6,7,9] => [10,9,7,5,3,1,8,6,4,2] => 111111101 => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [2,3,4,5,10,7,1,6,8,9] => [10,9,8,6,7,1,2,3,4,5] => 100001011 => 7
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [2,3,4,10,6,1,5,7,8,9] => [10,9,8,7,5,6,1,2,3,4] => 100010111 => 7
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,10,5,1,4,6,7,8,9] => [10,9,8,7,6,4,5,1,2,3] => 100101111 => 7
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,10,4,1,3,5,6,7,8,9] => [10,9,8,7,6,5,3,4,1,2] => 101011111 => 7
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Description
The number of strictly increasing runs in a binary word.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.