Identifier
-
Mp00087:
Permutations
—inverse first fundamental transformation⟶
Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St000292: Binary words ⟶ ℤ
Values
[1] => [1] => [1,0] => 10 => 0
[1,2] => [1,2] => [1,0,1,0] => 1010 => 1
[2,1] => [2,1] => [1,1,0,0] => 1100 => 0
[1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 101010 => 2
[1,3,2] => [1,3,2] => [1,0,1,1,0,0] => 101100 => 1
[2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 110010 => 1
[2,3,1] => [3,1,2] => [1,1,1,0,0,0] => 111000 => 0
[3,1,2] => [3,2,1] => [1,1,1,0,0,0] => 111000 => 0
[3,2,1] => [2,3,1] => [1,1,0,1,0,0] => 110100 => 1
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 10101010 => 3
[1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 10101100 => 2
[1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 10110010 => 2
[1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 10111000 => 1
[1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 10111000 => 1
[1,4,3,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 10110100 => 2
[2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 11001010 => 2
[2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 11001100 => 1
[2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 11100010 => 1
[2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 11110000 => 0
[2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0] => 11110000 => 0
[2,4,3,1] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 11101000 => 1
[3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 11100010 => 1
[3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0] => 11110000 => 0
[3,2,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 11010010 => 2
[3,2,4,1] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => 11011000 => 1
[3,4,1,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 11100100 => 1
[3,4,2,1] => [4,1,3,2] => [1,1,1,1,0,0,0,0] => 11110000 => 0
[4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => 11110000 => 0
[4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 11101000 => 1
[4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0] => 11011000 => 1
[4,2,3,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 11010100 => 2
[4,3,1,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => 11110000 => 0
[4,3,2,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 11100100 => 1
[1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 1010101010 => 4
[1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 3
[1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 1010110010 => 3
[1,2,4,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 2
[1,2,5,3,4] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 2
[1,2,5,4,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 1010110100 => 3
[1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 1011001010 => 3
[1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 1011001100 => 2
[1,3,4,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => 2
[1,3,4,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 1
[1,3,5,2,4] => [1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 1
[1,3,5,4,2] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 2
[1,4,2,3,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => 2
[1,4,2,5,3] => [1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 1
[1,4,3,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 1011010010 => 3
[1,4,3,5,2] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 2
[1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 2
[1,4,5,3,2] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 1
[1,5,2,3,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 1
[1,5,2,4,3] => [1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 2
[1,5,3,2,4] => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 2
[1,5,3,4,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => 3
[1,5,4,2,3] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 1
[1,5,4,3,2] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 2
[2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 1100101010 => 3
[2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 1100101100 => 2
[2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 1100110010 => 2
[2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 1
[2,1,5,3,4] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 1
[2,1,5,4,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => 2
[2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => 2
[2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 1
[2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 1
[2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[2,3,5,1,4] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[2,3,5,4,1] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 1111010000 => 1
[2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 1
[2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[2,4,3,1,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 2
[2,4,3,5,1] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 1110110000 => 1
[2,4,5,1,3] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1111000100 => 1
[2,4,5,3,1] => [5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[2,5,1,4,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1111010000 => 1
[2,5,3,1,4] => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => 1110110000 => 1
[2,5,3,4,1] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 1110101000 => 2
[2,5,4,1,3] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[2,5,4,3,1] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 1111001000 => 1
[3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => 2
[3,1,2,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 1
[3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 1
[3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[3,1,5,4,2] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => 1111010000 => 1
[3,2,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 1101001010 => 3
[3,2,1,5,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => 2
[3,2,4,1,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 2
[3,2,4,5,1] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 1101110000 => 1
[3,2,5,1,4] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => 1101110000 => 1
[3,2,5,4,1] => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => 1101101000 => 2
[3,4,1,2,5] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 2
[3,4,1,5,2] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1110011000 => 1
[3,4,2,1,5] => [4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 1
[3,4,2,5,1] => [5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[3,4,5,1,2] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[3,4,5,2,1] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 1111001000 => 1
[3,5,1,2,4] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => 1110011000 => 1
[3,5,1,4,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 1110010100 => 2
>>> Load all 3141 entries. <<<[3,5,2,1,4] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[3,5,2,4,1] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => 1111010000 => 1
[3,5,4,1,2] => [4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1111000100 => 1
[3,5,4,2,1] => [5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 1
[4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 2
[4,1,3,5,2] => [3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => 1110110000 => 1
[4,1,5,2,3] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1111000100 => 1
[4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 2
[4,2,1,5,3] => [2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0] => 1101110000 => 1
[4,2,3,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 1101010010 => 3
[4,2,3,5,1] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => 1101011000 => 2
[4,2,5,1,3] => [2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => 1101100100 => 2
[4,2,5,3,1] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0] => 1101110000 => 1
[4,3,1,2,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 1
[4,3,1,5,2] => [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[4,3,2,1,5] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 2
[4,3,2,5,1] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 1110011000 => 1
[4,3,5,1,2] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 1111001000 => 1
[4,3,5,2,1] => [5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[4,5,1,2,3] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[4,5,1,3,2] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1111000100 => 1
[4,5,2,1,3] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0] => 1111001000 => 1
[4,5,2,3,1] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[4,5,3,1,2] => [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => 1110100100 => 2
[4,5,3,2,1] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => 1110110000 => 1
[5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 1111010000 => 1
[5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => 1110110000 => 1
[5,1,3,4,2] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 1110101000 => 2
[5,1,4,2,3] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 1111001000 => 1
[5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => 1101110000 => 1
[5,2,1,4,3] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 1101101000 => 2
[5,2,3,1,4] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 1101011000 => 2
[5,2,3,4,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 1101010100 => 3
[5,2,4,1,3] => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => 1101110000 => 1
[5,2,4,3,1] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 1101100100 => 2
[5,3,1,2,4] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[5,3,1,4,2] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 1111010000 => 1
[5,3,2,1,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => 1110011000 => 1
[5,3,2,4,1] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 1110010100 => 2
[5,3,4,1,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[5,3,4,2,1] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1111000100 => 1
[5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => 1111001000 => 1
[5,4,1,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[5,4,2,1,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0
[5,4,2,3,1] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1111000100 => 1
[5,4,3,1,2] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 1110110000 => 1
[5,4,3,2,1] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 1110100100 => 2
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 5
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 4
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 4
[1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 3
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 3
[1,2,3,6,5,4] => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 4
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 4
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 3
[1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 3
[1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 2
[1,2,4,6,3,5] => [1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 2
[1,2,4,6,5,3] => [1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 3
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 3
[1,2,5,3,6,4] => [1,2,6,4,3,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 2
[1,2,5,4,3,6] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 4
[1,2,5,4,6,3] => [1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 3
[1,2,5,6,3,4] => [1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 3
[1,2,5,6,4,3] => [1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 2
[1,2,6,3,4,5] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 2
[1,2,6,3,5,4] => [1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 3
[1,2,6,4,3,5] => [1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 3
[1,2,6,4,5,3] => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 4
[1,2,6,5,3,4] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 2
[1,2,6,5,4,3] => [1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 3
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 4
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 3
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 3
[1,3,2,5,6,4] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 2
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 2
[1,3,2,6,5,4] => [1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 3
[1,3,4,2,5,6] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 3
[1,3,4,2,6,5] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 2
[1,3,4,5,2,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 2
[1,3,4,5,6,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,3,4,6,2,5] => [1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,3,4,6,5,2] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 2
[1,3,5,2,4,6] => [1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 2
[1,3,5,2,6,4] => [1,6,4,2,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,3,5,4,2,6] => [1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 3
[1,3,5,4,6,2] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 2
[1,3,5,6,2,4] => [1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 2
[1,3,5,6,4,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,3,6,2,4,5] => [1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,3,6,2,5,4] => [1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 2
[1,3,6,4,2,5] => [1,4,6,5,2,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 2
[1,3,6,4,5,2] => [1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 3
[1,3,6,5,2,4] => [1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,3,6,5,4,2] => [1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 2
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 3
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 2
[1,4,2,5,3,6] => [1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 2
[1,4,2,5,6,3] => [1,6,3,2,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,4,2,6,3,5] => [1,6,5,3,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,4,2,6,5,3] => [1,5,6,3,2,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 2
[1,4,3,2,5,6] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 4
[1,4,3,2,6,5] => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 3
[1,4,3,5,2,6] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 3
[1,4,3,5,6,2] => [1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 2
[1,4,3,6,2,5] => [1,3,6,5,2,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 2
[1,4,3,6,5,2] => [1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 3
[1,4,5,2,3,6] => [1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 3
[1,4,5,2,6,3] => [1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 2
[1,4,5,3,2,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 2
[1,4,5,3,6,2] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,4,5,6,2,3] => [1,6,3,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,4,5,6,3,2] => [1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 2
[1,4,6,2,3,5] => [1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 2
[1,4,6,2,5,3] => [1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 3
[1,4,6,3,2,5] => [1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,4,6,3,5,2] => [1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 2
[1,4,6,5,2,3] => [1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 2
[1,4,6,5,3,2] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,5,2,3,4,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 2
[1,5,2,3,6,4] => [1,6,4,3,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,5,2,4,3,6] => [1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 3
[1,5,2,4,6,3] => [1,4,6,3,2,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 2
[1,5,2,6,3,4] => [1,5,3,2,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 2
[1,5,2,6,4,3] => [1,6,3,2,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,5,3,2,4,6] => [1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 3
[1,5,3,2,6,4] => [1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 2
[1,5,3,4,2,6] => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 4
[1,5,3,4,6,2] => [1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 3
[1,5,3,6,2,4] => [1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 3
[1,5,3,6,4,2] => [1,3,6,2,5,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 2
[1,5,4,2,3,6] => [1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 2
[1,5,4,2,6,3] => [1,6,3,4,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,5,4,3,2,6] => [1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 3
[1,5,4,3,6,2] => [1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 2
[1,5,4,6,2,3] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 2
[1,5,4,6,3,2] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,5,6,2,3,4] => [1,6,4,2,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,5,6,2,4,3] => [1,5,4,2,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 2
[1,5,6,3,2,4] => [1,5,2,6,4,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 2
[1,5,6,3,4,2] => [1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,5,6,4,2,3] => [1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 3
[1,5,6,4,3,2] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 2
[1,6,2,3,4,5] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,6,2,3,5,4] => [1,5,6,4,3,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 2
[1,6,2,4,3,5] => [1,4,6,5,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 2
[1,6,2,4,5,3] => [1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 3
[1,6,2,5,3,4] => [1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,6,2,5,4,3] => [1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 2
[1,6,3,2,4,5] => [1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 2
[1,6,3,2,5,4] => [1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 3
[1,6,3,4,2,5] => [1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 3
[1,6,3,4,5,2] => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 4
[1,6,3,5,2,4] => [1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 2
[1,6,3,5,4,2] => [1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 3
[1,6,4,2,3,5] => [1,6,5,3,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,6,4,2,5,3] => [1,5,6,3,4,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 2
[1,6,4,3,2,5] => [1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 2
[1,6,4,3,5,2] => [1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 3
[1,6,4,5,2,3] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,6,4,5,3,2] => [1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 2
[1,6,5,2,3,4] => [1,5,3,6,4,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 2
[1,6,5,2,4,3] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,6,5,3,2,4] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 1
[1,6,5,3,4,2] => [1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 2
[1,6,5,4,2,3] => [1,4,6,3,5,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 2
[1,6,5,4,3,2] => [1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 3
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 4
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 3
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 3
[2,1,3,5,6,4] => [2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 2
[2,1,3,6,4,5] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 2
[2,1,3,6,5,4] => [2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 3
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 3
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 2
[2,1,4,5,3,6] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 2
[2,1,4,5,6,3] => [2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 1
[2,1,4,6,3,5] => [2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 1
[2,1,4,6,5,3] => [2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 2
[2,1,5,3,4,6] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 2
[2,1,5,3,6,4] => [2,1,6,4,3,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 1
[2,1,5,4,3,6] => [2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 3
[2,1,5,4,6,3] => [2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 2
[2,1,5,6,3,4] => [2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 2
[2,1,5,6,4,3] => [2,1,6,3,5,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 1
[2,1,6,3,4,5] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 1
[2,1,6,3,5,4] => [2,1,5,6,4,3] => [1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 2
[2,1,6,4,3,5] => [2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 2
[2,1,6,4,5,3] => [2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 3
[2,1,6,5,3,4] => [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 1
[2,1,6,5,4,3] => [2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 2
[2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => 3
[2,3,1,4,6,5] => [3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 2
[2,3,1,5,4,6] => [3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 111000110010 => 2
[2,3,1,5,6,4] => [3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 1
[2,3,1,6,4,5] => [3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 1
[2,3,1,6,5,4] => [3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 2
[2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 2
[2,3,4,1,6,5] => [4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 1
[2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,3,4,6,1,5] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,3,4,6,5,1] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[2,3,5,1,4,6] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[2,3,5,1,6,4] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,3,5,4,1,6] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 2
[2,3,5,4,6,1] => [4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[2,3,5,6,1,4] => [5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[2,3,5,6,4,1] => [6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,3,6,1,4,5] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,3,6,1,5,4] => [5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[2,3,6,4,1,5] => [4,6,5,1,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[2,3,6,4,5,1] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 2
[2,3,6,5,1,4] => [6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,3,6,5,4,1] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 2
[2,4,1,3,6,5] => [4,3,1,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 1
[2,4,1,5,3,6] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,4,1,6,3,5] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,4,1,6,5,3] => [5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[2,4,3,1,5,6] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 3
[2,4,3,1,6,5] => [3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 2
[2,4,3,5,1,6] => [3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 2
[2,4,3,5,6,1] => [3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[2,4,3,6,1,5] => [3,6,5,1,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[2,4,3,6,5,1] => [3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 2
[2,4,5,1,3,6] => [4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 2
[2,4,5,1,6,3] => [4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[2,4,5,3,1,6] => [5,1,2,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[2,4,5,3,6,1] => [6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,4,5,6,1,3] => [6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,4,5,6,3,1] => [5,3,6,1,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[2,4,6,1,3,5] => [4,1,2,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[2,4,6,1,5,3] => [4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 2
[2,4,6,3,1,5] => [6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,4,6,3,5,1] => [5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[2,4,6,5,1,3] => [5,1,2,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[2,4,6,5,3,1] => [6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,5,1,3,4,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[2,5,1,3,6,4] => [6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,5,1,4,3,6] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 2
[2,5,1,4,6,3] => [4,6,3,1,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[2,5,1,6,3,4] => [5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[2,5,1,6,4,3] => [6,3,1,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,5,3,1,4,6] => [3,5,4,1,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 2
[2,5,3,1,6,4] => [3,6,4,1,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[2,5,3,4,1,6] => [3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 3
[2,5,3,4,6,1] => [3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 2
[2,5,3,6,1,4] => [3,5,1,2,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 2
[2,5,3,6,4,1] => [3,6,1,2,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[2,5,4,1,3,6] => [5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[2,5,4,1,6,3] => [6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,5,4,3,1,6] => [4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 2
[2,5,4,3,6,1] => [4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[2,5,4,6,1,3] => [5,1,2,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[2,5,4,6,3,1] => [6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,5,6,1,3,4] => [6,4,1,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,5,6,1,4,3] => [5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[2,5,6,3,1,4] => [5,1,2,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[2,5,6,3,4,1] => [6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,5,6,4,1,3] => [4,5,1,2,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 2
[2,5,6,4,3,1] => [4,6,1,2,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,6,1,3,5,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[2,6,1,4,3,5] => [4,6,5,3,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[2,6,1,4,5,3] => [4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 2
[2,6,1,5,3,4] => [6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,6,1,5,4,3] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[2,6,3,1,4,5] => [3,6,5,4,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[2,6,3,1,5,4] => [3,5,6,4,1,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 2
[2,6,3,4,1,5] => [3,4,6,5,1,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 2
[2,6,3,4,5,1] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 111010101000 => 3
[2,6,3,5,1,4] => [3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[2,6,3,5,4,1] => [3,5,4,6,1,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 2
[2,6,4,1,3,5] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,6,4,1,5,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[2,6,4,3,1,5] => [4,3,6,5,1,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[2,6,4,3,5,1] => [4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 2
[2,6,4,5,1,3] => [6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,6,4,5,3,1] => [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[2,6,5,1,3,4] => [5,3,6,4,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[2,6,5,1,4,3] => [6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,6,5,3,1,4] => [6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[2,6,5,3,4,1] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[2,6,5,4,1,3] => [4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[2,6,5,4,3,1] => [4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 2
[3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => 3
[3,1,2,4,6,5] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 2
[3,1,2,5,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 111000110010 => 2
[3,1,2,5,6,4] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 1
[3,1,2,6,4,5] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 1
[3,1,2,6,5,4] => [3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 2
[3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 2
[3,1,4,2,6,5] => [4,2,1,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 1
[3,1,4,5,2,6] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[3,1,4,5,6,2] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,1,4,6,2,5] => [6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,1,4,6,5,2] => [5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[3,1,5,2,4,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,1,5,4,2,6] => [4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 2
[3,1,5,4,6,2] => [4,6,2,1,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[3,1,5,6,2,4] => [5,2,1,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[3,1,5,6,4,2] => [6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,1,6,2,5,4] => [5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[3,1,6,4,2,5] => [4,6,5,2,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[3,1,6,4,5,2] => [4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 2
[3,1,6,5,2,4] => [6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,1,6,5,4,2] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[3,2,1,4,5,6] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 4
[3,2,1,4,6,5] => [2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 3
[3,2,1,5,4,6] => [2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 3
[3,2,1,5,6,4] => [2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 2
[3,2,1,6,4,5] => [2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 2
[3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 3
[3,2,4,1,5,6] => [2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => 3
[3,2,4,1,6,5] => [2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 2
[3,2,4,5,1,6] => [2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 2
[3,2,4,5,6,1] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[3,2,4,6,1,5] => [2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[3,2,4,6,5,1] => [2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 2
[3,2,5,1,4,6] => [2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 2
[3,2,5,1,6,4] => [2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[3,2,5,4,1,6] => [2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 3
[3,2,5,4,6,1] => [2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 2
[3,2,5,6,1,4] => [2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 2
[3,2,5,6,4,1] => [2,6,1,3,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[3,2,6,1,4,5] => [2,6,5,4,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[3,2,6,1,5,4] => [2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 2
[3,2,6,4,1,5] => [2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 2
[3,2,6,4,5,1] => [2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => 110110101000 => 3
[3,2,6,5,1,4] => [2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[3,2,6,5,4,1] => [2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 2
[3,4,1,2,5,6] => [3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 3
[3,4,1,2,6,5] => [3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 2
[3,4,1,5,2,6] => [3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 2
[3,4,1,5,6,2] => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[3,4,1,6,2,5] => [3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[3,4,1,6,5,2] => [3,1,5,6,2,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => 2
[3,4,2,1,5,6] => [4,1,3,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 2
[3,4,2,1,6,5] => [4,1,3,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 1
[3,4,2,5,1,6] => [5,1,3,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[3,4,2,5,6,1] => [6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,4,2,6,1,5] => [6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,4,2,6,5,1] => [5,6,1,3,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[3,4,5,1,2,6] => [5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[3,4,5,1,6,2] => [6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,4,5,2,1,6] => [4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 2
[3,4,5,2,6,1] => [4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[3,4,5,6,1,2] => [5,1,3,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[3,4,5,6,2,1] => [6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,4,6,1,2,5] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,4,6,1,5,2] => [5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[3,4,6,2,1,5] => [4,2,6,5,1,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[3,4,6,2,5,1] => [4,2,5,6,1,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 2
[3,4,6,5,1,2] => [6,2,4,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,4,6,5,2,1] => [5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[3,5,1,2,4,6] => [3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 2
[3,5,1,2,6,4] => [3,1,6,4,2,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[3,5,1,4,2,6] => [3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 3
[3,5,1,4,6,2] => [3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 2
[3,5,1,6,2,4] => [3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 2
[3,5,1,6,4,2] => [3,1,6,2,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[3,5,2,1,4,6] => [5,4,1,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[3,5,2,1,6,4] => [6,4,1,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,5,2,4,1,6] => [4,5,1,3,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 2
[3,5,2,4,6,1] => [4,6,1,3,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[3,5,2,6,1,4] => [5,1,3,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[3,5,2,6,4,1] => [6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,5,4,1,2,6] => [4,1,3,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 2
[3,5,4,1,6,2] => [4,1,3,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[3,5,4,2,1,6] => [5,1,3,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[3,5,4,2,6,1] => [6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,5,4,6,1,2] => [6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,5,4,6,2,1] => [5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[3,5,6,1,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[3,5,6,1,4,2] => [6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,5,6,2,1,4] => [6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,5,6,2,4,1] => [5,4,2,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[3,5,6,4,1,2] => [4,6,2,5,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[3,5,6,4,2,1] => [4,5,2,6,1,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 2
[3,6,1,2,4,5] => [3,1,6,5,4,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[3,6,1,2,5,4] => [3,1,5,6,4,2] => [1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => 2
[3,6,1,4,2,5] => [3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 2
[3,6,1,4,5,2] => [3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => 111001010100 => 3
[3,6,1,5,2,4] => [3,1,6,4,5,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[3,6,1,5,4,2] => [3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 2
[3,6,2,1,4,5] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,6,2,1,5,4] => [5,6,4,1,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[3,6,2,4,1,5] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[3,6,2,4,5,1] => [4,5,6,1,3,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 2
[3,6,2,5,1,4] => [6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,6,2,5,4,1] => [5,4,6,1,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[3,6,4,1,2,5] => [4,1,3,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[3,6,4,1,5,2] => [4,1,3,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 2
[3,6,4,2,1,5] => [6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,6,4,2,5,1] => [5,6,1,3,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[3,6,4,5,1,2] => [5,1,3,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[3,6,4,5,2,1] => [6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,6,5,1,2,4] => [6,4,1,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,6,5,1,4,2] => [5,4,1,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[3,6,5,2,1,4] => [5,1,3,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[3,6,5,2,4,1] => [6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[3,6,5,4,1,2] => [4,5,1,3,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 2
[3,6,5,4,2,1] => [4,6,1,3,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 2
[4,1,2,3,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 1
[4,1,2,5,3,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[4,1,2,5,6,3] => [6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,1,2,6,5,3] => [5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 3
[4,1,3,2,6,5] => [3,4,2,1,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 2
[4,1,3,5,2,6] => [3,5,2,1,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 2
[4,1,3,5,6,2] => [3,6,2,1,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[4,1,3,6,2,5] => [3,6,5,2,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[4,1,3,6,5,2] => [3,5,6,2,1,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 2
[4,1,5,2,3,6] => [4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 2
[4,1,5,2,6,3] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[4,1,5,3,2,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[4,1,5,3,6,2] => [6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,1,5,6,2,3] => [6,3,5,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,1,5,6,3,2] => [5,3,6,2,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[4,1,6,2,3,5] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[4,1,6,2,5,3] => [4,2,1,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 2
[4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,1,6,3,5,2] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[4,1,6,5,2,3] => [5,2,1,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[4,1,6,5,3,2] => [6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,2,1,3,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => 3
[4,2,1,3,6,5] => [2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 2
[4,2,1,5,3,6] => [2,5,3,1,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 2
[4,2,1,5,6,3] => [2,6,3,1,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[4,2,1,6,3,5] => [2,6,5,3,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[4,2,1,6,5,3] => [2,5,6,3,1,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 2
[4,2,3,1,5,6] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 4
[4,2,3,1,6,5] => [2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 3
[4,2,3,5,1,6] => [2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 3
[4,2,3,5,6,1] => [2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 2
[4,2,3,6,1,5] => [2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 2
[4,2,3,6,5,1] => [2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => 110101101000 => 3
[4,2,5,1,3,6] => [2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 3
[4,2,5,1,6,3] => [2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => 2
[4,2,5,3,1,6] => [2,5,1,4,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 2
[4,2,5,3,6,1] => [2,6,1,4,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[4,2,5,6,1,3] => [2,6,3,5,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[4,2,5,6,3,1] => [2,5,3,6,1,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 2
[4,2,6,1,3,5] => [2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => 2
[4,2,6,1,5,3] => [2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => 110110010100 => 3
[4,2,6,3,1,5] => [2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[4,2,6,3,5,1] => [2,5,6,1,4,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 2
[4,2,6,5,1,3] => [2,5,1,4,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 2
[4,2,6,5,3,1] => [2,6,1,4,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[4,3,1,2,5,6] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 2
[4,3,1,2,6,5] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 1
[4,3,1,5,2,6] => [5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[4,3,1,5,6,2] => [6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,3,1,6,2,5] => [6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,3,1,6,5,2] => [5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[4,3,2,1,5,6] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 3
[4,3,2,1,6,5] => [3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 2
[4,3,2,5,1,6] => [3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 2
[4,3,2,5,6,1] => [3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[4,3,2,6,1,5] => [3,2,6,5,1,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[4,3,2,6,5,1] => [3,2,5,6,1,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => 2
[4,3,5,1,2,6] => [4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 2
[4,3,5,1,6,2] => [4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[4,3,5,2,1,6] => [5,1,4,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[4,3,5,2,6,1] => [6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,3,5,6,1,2] => [6,2,3,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,3,5,6,2,1] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[4,3,6,1,2,5] => [4,1,6,5,2,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[4,3,6,1,5,2] => [4,1,5,6,2,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 2
[4,3,6,2,1,5] => [6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,3,6,2,5,1] => [5,6,1,4,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[4,3,6,5,1,2] => [5,1,4,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[4,3,6,5,2,1] => [6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,5,1,2,3,6] => [5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[4,5,1,2,6,3] => [6,3,1,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,5,1,3,2,6] => [4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 2
[4,5,1,3,6,2] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[4,5,1,6,2,3] => [5,2,6,3,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[4,5,1,6,3,2] => [6,2,5,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,5,2,1,3,6] => [4,1,5,3,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 2
[4,5,2,1,6,3] => [4,1,6,3,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[4,5,2,3,1,6] => [5,1,4,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[4,5,2,3,6,1] => [6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,5,2,6,1,3] => [6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,5,2,6,3,1] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[4,5,3,1,2,6] => [3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 3
[4,5,3,1,6,2] => [3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => 2
[4,5,3,2,1,6] => [3,5,1,4,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 2
[4,5,3,2,6,1] => [3,6,1,4,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[4,5,3,6,1,2] => [3,6,2,5,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[4,5,3,6,2,1] => [3,5,2,6,1,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 2
[4,5,6,1,2,3] => [4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 2
[4,5,6,1,3,2] => [4,1,6,2,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[4,5,6,2,1,3] => [5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[4,5,6,2,3,1] => [6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,5,6,3,1,2] => [6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,5,6,3,2,1] => [5,2,6,1,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[4,6,1,2,3,5] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,6,1,2,5,3] => [5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[4,6,1,3,2,5] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[4,6,1,3,5,2] => [4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 2
[4,6,1,5,2,3] => [6,3,1,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,6,1,5,3,2] => [5,3,1,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[4,6,2,1,3,5] => [4,1,6,5,3,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[4,6,2,1,5,3] => [4,1,5,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 2
[4,6,2,3,1,5] => [6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,6,2,3,5,1] => [5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[4,6,2,5,1,3] => [5,1,4,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[4,6,2,5,3,1] => [6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,6,3,1,2,5] => [3,4,1,6,5,2] => [1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => 2
[4,6,3,1,5,2] => [3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => 3
[4,6,3,2,1,5] => [3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[4,6,3,2,5,1] => [3,5,6,1,4,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 2
[4,6,3,5,1,2] => [3,5,1,4,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 2
[4,6,3,5,2,1] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[4,6,5,1,2,3] => [4,1,6,3,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[4,6,5,1,3,2] => [4,1,5,3,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 2
[4,6,5,2,1,3] => [6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[4,6,5,2,3,1] => [5,3,6,1,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[4,6,5,3,1,2] => [5,1,4,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[4,6,5,3,2,1] => [6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 2
[5,1,2,4,6,3] => [4,6,3,2,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[5,1,2,6,3,4] => [5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,1,3,2,4,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 2
[5,1,3,2,6,4] => [3,6,4,2,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[5,1,3,4,2,6] => [3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 3
[5,1,3,4,6,2] => [3,4,6,2,1,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 2
[5,1,3,6,2,4] => [3,5,2,1,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 2
[5,1,3,6,4,2] => [3,6,2,1,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[5,1,4,2,3,6] => [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[5,1,4,2,6,3] => [6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,1,4,3,2,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 2
[5,1,4,3,6,2] => [4,3,6,2,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[5,1,4,6,2,3] => [5,2,1,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[5,1,4,6,3,2] => [6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,1,6,2,3,4] => [6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,1,6,2,4,3] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[5,1,6,3,2,4] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[5,1,6,3,4,2] => [6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,1,6,4,2,3] => [4,5,2,1,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 2
[5,1,6,4,3,2] => [4,6,2,1,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[5,2,1,3,4,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 2
[5,2,1,3,6,4] => [2,6,4,3,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[5,2,1,4,3,6] => [2,4,5,3,1,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 3
[5,2,1,4,6,3] => [2,4,6,3,1,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 2
[5,2,1,6,3,4] => [2,5,3,1,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 2
[5,2,1,6,4,3] => [2,6,3,1,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[5,2,3,1,4,6] => [2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 3
[5,2,3,1,6,4] => [2,3,6,4,1,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 2
[5,2,3,4,1,6] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 4
[5,2,3,4,6,1] => [2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => 110101011000 => 3
[5,2,3,6,1,4] => [2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => 110101100100 => 3
[5,2,3,6,4,1] => [2,3,6,1,5,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 2
[5,2,4,1,3,6] => [2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 2
[5,2,4,1,6,3] => [2,6,3,4,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[5,2,4,3,1,6] => [2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 3
[5,2,4,3,6,1] => [2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => 2
[5,2,4,6,1,3] => [2,5,1,6,3,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 2
[5,2,4,6,3,1] => [2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[5,2,6,1,3,4] => [2,6,4,1,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[5,2,6,1,4,3] => [2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 2
[5,2,6,3,1,4] => [2,5,1,6,4,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 2
[5,2,6,3,4,1] => [2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[5,2,6,4,1,3] => [2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => 110110100100 => 3
[5,2,6,4,3,1] => [2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 2
[5,3,1,2,4,6] => [5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[5,3,1,2,6,4] => [6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,3,1,4,2,6] => [4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 2
[5,3,1,4,6,2] => [4,6,2,3,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[5,3,1,6,2,4] => [5,2,3,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[5,3,1,6,4,2] => [6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,3,2,1,4,6] => [3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 2
[5,3,2,1,6,4] => [3,2,6,4,1,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[5,3,2,4,1,6] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 3
[5,3,2,4,6,1] => [3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 2
[5,3,2,6,1,4] => [3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 2
[5,3,2,6,4,1] => [3,2,6,1,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[5,3,4,1,2,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[5,3,4,1,6,2] => [6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,3,4,2,1,6] => [4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 2
[5,3,4,2,6,1] => [4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[5,3,4,6,1,2] => [5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[5,3,4,6,2,1] => [6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,3,6,1,2,4] => [6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,3,6,1,4,2] => [5,4,1,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[5,3,6,2,1,4] => [5,1,6,4,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[5,3,6,2,4,1] => [6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,3,6,4,1,2] => [4,5,1,6,2,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 2
[5,3,6,4,2,1] => [4,6,1,5,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[5,4,1,2,3,6] => [4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 2
[5,4,1,2,6,3] => [4,2,6,3,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[5,4,1,3,2,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[5,4,1,3,6,2] => [6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,4,1,6,2,3] => [6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,4,1,6,3,2] => [5,3,1,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[5,4,2,1,3,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 1
[5,4,2,1,6,3] => [6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,4,2,3,1,6] => [4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 2
[5,4,2,3,6,1] => [4,3,2,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[5,4,2,6,1,3] => [5,1,6,3,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[5,4,2,6,3,1] => [6,1,5,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,4,3,1,2,6] => [3,5,2,4,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 2
[5,4,3,1,6,2] => [3,6,2,4,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[5,4,3,2,1,6] => [3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 3
[5,4,3,2,6,1] => [3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => 2
[5,4,3,6,1,2] => [3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 2
[5,4,3,6,2,1] => [3,6,1,5,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[5,4,6,1,2,3] => [5,2,4,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[5,4,6,1,3,2] => [6,2,4,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,4,6,2,1,3] => [4,2,5,1,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 2
[5,4,6,2,3,1] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[5,4,6,3,1,2] => [5,1,6,2,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[5,4,6,3,2,1] => [6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,6,1,2,3,4] => [5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[5,6,1,2,4,3] => [6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,6,1,3,2,4] => [6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,6,1,3,4,2] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[5,6,1,4,2,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[5,6,1,4,3,2] => [4,5,3,1,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 2
[5,6,2,1,3,4] => [6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,6,2,1,4,3] => [5,4,1,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[5,6,2,3,1,4] => [5,1,6,4,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[5,6,2,3,4,1] => [6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,6,2,4,1,3] => [4,5,1,6,3,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 2
[5,6,2,4,3,1] => [4,6,1,5,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[5,6,3,1,2,4] => [3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[5,6,3,1,4,2] => [3,5,4,1,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 2
[5,6,3,2,1,4] => [3,5,1,6,4,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 2
[5,6,3,2,4,1] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[5,6,3,4,1,2] => [3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => 111010100100 => 3
[5,6,3,4,2,1] => [3,4,6,1,5,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 2
[5,6,4,1,2,3] => [6,3,4,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,6,4,1,3,2] => [5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[5,6,4,2,1,3] => [5,1,6,3,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[5,6,4,2,3,1] => [6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[5,6,4,3,1,2] => [4,3,5,1,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 2
[5,6,4,3,2,1] => [4,3,6,1,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[6,1,2,4,3,5] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 2
[6,1,2,5,3,4] => [6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,1,2,5,4,3] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[6,1,3,2,4,5] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[6,1,3,2,5,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 2
[6,1,3,4,2,5] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 2
[6,1,3,4,5,2] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 111010101000 => 3
[6,1,3,5,2,4] => [3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[6,1,3,5,4,2] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 2
[6,1,4,2,3,5] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,1,4,2,5,3] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[6,1,4,3,2,5] => [4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[6,1,4,3,5,2] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 2
[6,1,4,5,2,3] => [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,1,4,5,3,2] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[6,1,5,2,3,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[6,1,5,2,4,3] => [6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,1,5,3,2,4] => [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,1,5,3,4,2] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[6,1,5,4,2,3] => [4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[6,1,5,4,3,2] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 2
[6,2,1,3,4,5] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[6,2,1,3,5,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 2
[6,2,1,4,3,5] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 2
[6,2,1,4,5,3] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 110110101000 => 3
[6,2,1,5,3,4] => [2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[6,2,1,5,4,3] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 2
[6,2,3,1,4,5] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 2
[6,2,3,1,5,4] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 110101101000 => 3
[6,2,3,4,1,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 110101011000 => 3
[6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 110101010100 => 4
[6,2,3,5,1,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 2
[6,2,3,5,4,1] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 110101100100 => 3
[6,2,4,1,3,5] => [2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[6,2,4,1,5,3] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 2
[6,2,4,3,1,5] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => 2
[6,2,4,3,5,1] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 110110010100 => 3
[6,2,4,5,1,3] => [2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[6,2,4,5,3,1] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 2
[6,2,5,1,3,4] => [2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 2
[6,2,5,1,4,3] => [2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[6,2,5,3,1,4] => [2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 1
[6,2,5,3,4,1] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 2
[6,2,5,4,1,3] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 2
[6,2,5,4,3,1] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 110110100100 => 3
[6,3,1,2,4,5] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,3,1,2,5,4] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[6,3,1,4,2,5] => [4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[6,3,1,4,5,2] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 2
[6,3,1,5,2,4] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,3,1,5,4,2] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[6,3,2,1,4,5] => [3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[6,3,2,1,5,4] => [3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => 2
[6,3,2,4,1,5] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 2
[6,3,2,4,5,1] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 111001010100 => 3
[6,3,2,5,1,4] => [3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 1
[6,3,2,5,4,1] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 2
[6,3,4,1,2,5] => [6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,3,4,1,5,2] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[6,3,4,2,1,5] => [4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[6,3,4,2,5,1] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 2
[6,3,4,5,1,2] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,3,4,5,2,1] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[6,3,5,1,2,4] => [5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[6,3,5,1,4,2] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,3,5,2,1,4] => [6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,3,5,2,4,1] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[6,3,5,4,1,2] => [4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[6,3,5,4,2,1] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 2
[6,4,1,2,3,5] => [4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[6,4,1,2,5,3] => [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 2
[6,4,1,3,2,5] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,4,1,3,5,2] => [5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[6,4,1,5,2,3] => [5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[6,4,1,5,3,2] => [6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,4,2,1,3,5] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,4,2,1,5,3] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 1
[6,4,2,3,1,5] => [4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 1
[6,4,2,3,5,1] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 2
[6,4,2,5,1,3] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,4,2,5,3,1] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[6,4,3,1,2,5] => [3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[6,4,3,1,5,2] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 2
[6,4,3,2,1,5] => [3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => 2
[6,4,3,2,5,1] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => 3
[6,4,3,5,1,2] => [3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[6,4,3,5,2,1] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 2
[6,4,5,1,2,3] => [6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,4,5,1,3,2] => [5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[6,4,5,2,1,3] => [4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[6,4,5,2,3,1] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 2
[6,4,5,3,1,2] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,4,5,3,2,1] => [5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[6,5,1,2,3,4] => [6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,5,1,2,4,3] => [5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[6,5,1,3,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[6,5,1,3,4,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,5,1,4,2,3] => [4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 2
[6,5,1,4,3,2] => [4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[6,5,2,1,3,4] => [5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 1
[6,5,2,1,4,3] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,5,2,3,1,4] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,5,2,3,4,1] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[6,5,2,4,1,3] => [4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 1
[6,5,2,4,3,1] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 2
[6,5,3,1,2,4] => [3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 2
[6,5,3,1,4,2] => [3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[6,5,3,2,1,4] => [3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 1
[6,5,3,2,4,1] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 2
[6,5,3,4,1,2] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 2
[6,5,3,4,2,1] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 111010100100 => 3
[6,5,4,1,2,3] => [5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 1
[6,5,4,1,3,2] => [6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,5,4,2,1,3] => [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 0
[6,5,4,2,3,1] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 1
[6,5,4,3,1,2] => [4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 1
[6,5,4,3,2,1] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 2
[1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,4,5,7,2,6] => [1,7,6,2,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,4,5,7,6,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,3,4,6,2,7,5] => [1,7,5,2,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,4,6,5,7,2] => [1,5,7,2,3,4,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,3,4,6,7,2,5] => [1,6,2,3,4,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,3,4,6,7,5,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,4,7,2,5,6] => [1,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,4,7,2,6,5] => [1,6,7,5,2,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,3,4,7,5,2,6] => [1,5,7,6,2,3,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,3,4,7,5,6,2] => [1,5,6,7,2,3,4] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 3
[1,3,4,7,6,2,5] => [1,7,5,6,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,4,7,6,5,2] => [1,6,5,7,2,3,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,3,5,2,6,7,4] => [1,7,4,2,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,5,2,7,4,6] => [1,7,6,4,2,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,5,2,7,6,4] => [1,6,7,4,2,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,3,5,4,6,7,2] => [1,4,7,2,3,5,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,3,5,4,7,2,6] => [1,4,7,6,2,3,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,3,5,4,7,6,2] => [1,4,6,7,2,3,5] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 3
[1,3,5,6,4,7,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,5,6,7,2,4] => [1,7,4,6,2,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,5,6,7,4,2] => [1,6,4,7,2,3,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,3,5,7,4,2,6] => [1,7,6,2,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,5,7,4,6,2] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,3,5,7,6,2,4] => [1,6,2,3,5,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,3,5,7,6,4,2] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,6,2,4,7,5] => [1,7,5,4,2,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,6,2,5,7,4] => [1,5,7,4,2,3,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,3,6,2,7,4,5] => [1,6,4,2,3,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,3,6,2,7,5,4] => [1,7,4,2,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,6,4,2,7,5] => [1,4,7,5,2,3,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,3,6,4,7,5,2] => [1,4,7,2,3,6,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,3,6,5,2,7,4] => [1,7,4,5,2,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,6,5,4,7,2] => [1,5,4,7,2,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,3,6,5,7,2,4] => [1,6,2,3,7,4,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,3,6,5,7,4,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,6,7,2,4,5] => [1,7,5,2,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,6,7,2,5,4] => [1,6,5,2,3,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,3,6,7,4,2,5] => [1,6,2,3,7,5,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,3,6,7,4,5,2] => [1,7,2,3,6,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,6,7,5,4,2] => [1,5,7,2,3,6,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,3,7,2,4,5,6] => [1,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,7,2,4,6,5] => [1,6,7,5,4,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,3,7,2,5,4,6] => [1,5,7,6,4,2,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,3,7,2,5,6,4] => [1,5,6,7,4,2,3] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 3
[1,3,7,2,6,4,5] => [1,7,5,6,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,7,2,6,5,4] => [1,6,5,7,4,2,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,3,7,4,2,5,6] => [1,4,7,6,5,2,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,3,7,4,2,6,5] => [1,4,6,7,5,2,3] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 3
[1,3,7,4,6,2,5] => [1,4,7,5,6,2,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,3,7,5,2,4,6] => [1,7,6,4,5,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,7,5,2,6,4] => [1,6,7,4,5,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,3,7,5,4,2,6] => [1,5,4,7,6,2,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,3,7,5,6,2,4] => [1,7,4,5,6,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,7,5,6,4,2] => [1,6,4,5,7,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,3,7,6,2,4,5] => [1,6,4,7,5,2,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,3,7,6,2,5,4] => [1,7,4,6,5,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,7,6,4,2,5] => [1,7,5,4,6,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,3,7,6,4,5,2] => [1,6,5,4,7,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,3,7,6,5,2,4] => [1,5,7,4,6,2,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,3,7,6,5,4,2] => [1,5,6,4,7,2,3] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 3
[1,4,2,5,6,7,3] => [1,7,3,2,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,2,5,7,3,6] => [1,7,6,3,2,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,2,5,7,6,3] => [1,6,7,3,2,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,4,2,6,3,7,5] => [1,7,5,3,2,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,2,6,5,7,3] => [1,5,7,3,2,4,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,4,2,6,7,3,5] => [1,6,3,2,4,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,4,2,6,7,5,3] => [1,7,3,2,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,2,7,3,5,6] => [1,7,6,5,3,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,2,7,3,6,5] => [1,6,7,5,3,2,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,4,2,7,5,3,6] => [1,5,7,6,3,2,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,4,2,7,5,6,3] => [1,5,6,7,3,2,4] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 3
[1,4,2,7,6,3,5] => [1,7,5,6,3,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,2,7,6,5,3] => [1,6,5,7,3,2,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,4,3,5,6,7,2] => [1,3,7,2,4,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,4,3,5,7,2,6] => [1,3,7,6,2,4,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,4,3,6,2,7,5] => [1,3,7,5,2,4,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,4,3,6,7,5,2] => [1,3,7,2,4,6,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,4,3,7,2,5,6] => [1,3,7,6,5,2,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,4,3,7,6,2,5] => [1,3,7,5,6,2,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,4,5,3,6,7,2] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,5,3,7,2,6] => [1,7,6,2,4,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,5,3,7,6,2] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,4,5,6,2,7,3] => [1,7,3,5,2,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,5,6,3,7,2] => [1,5,3,7,2,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,4,5,6,7,2,3] => [1,6,2,4,7,3,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,4,5,6,7,3,2] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,5,7,2,3,6] => [1,7,6,3,5,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,5,7,2,6,3] => [1,6,7,3,5,2,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,4,5,7,3,2,6] => [1,5,3,7,6,2,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,4,5,7,6,2,3] => [1,7,3,5,6,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,5,7,6,3,2] => [1,6,3,5,7,2,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,4,6,3,2,7,5] => [1,7,5,2,4,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,6,3,5,7,2] => [1,5,7,2,4,3,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,4,6,3,7,2,5] => [1,6,2,4,3,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,4,6,3,7,5,2] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,6,5,3,7,2] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,6,5,7,2,3] => [1,7,3,6,2,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,6,5,7,3,2] => [1,6,3,7,2,4,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,4,6,7,2,3,5] => [1,6,3,7,5,2,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,4,6,7,2,5,3] => [1,7,3,6,5,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,6,7,3,2,5] => [1,7,5,3,6,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,6,7,3,5,2] => [1,6,5,3,7,2,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,4,6,7,5,2,3] => [1,5,7,3,6,2,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,4,6,7,5,3,2] => [1,5,6,3,7,2,4] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 3
[1,4,7,3,2,5,6] => [1,7,6,5,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,7,3,2,6,5] => [1,6,7,5,2,4,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,4,7,3,5,2,6] => [1,5,7,6,2,4,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,4,7,3,5,6,2] => [1,5,6,7,2,4,3] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 3
[1,4,7,3,6,2,5] => [1,7,5,6,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,7,3,6,5,2] => [1,6,5,7,2,4,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,4,7,5,3,2,6] => [1,7,6,2,4,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,7,5,3,6,2] => [1,6,7,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,4,7,5,6,2,3] => [1,6,2,4,5,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,4,7,5,6,3,2] => [1,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,7,6,2,3,5] => [1,7,5,2,4,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,7,6,2,5,3] => [1,6,5,2,4,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,4,7,6,3,2,5] => [1,6,2,4,7,5,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,4,7,6,3,5,2] => [1,7,2,4,6,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,4,7,6,5,3,2] => [1,5,7,2,4,6,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,5,2,3,6,7,4] => [1,7,4,3,2,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,2,3,7,4,6] => [1,7,6,4,3,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,2,3,7,6,4] => [1,6,7,4,3,2,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,5,2,4,6,7,3] => [1,4,7,3,2,5,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,5,2,4,7,3,6] => [1,4,7,6,3,2,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,5,2,4,7,6,3] => [1,4,6,7,3,2,5] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 3
[1,5,2,6,4,7,3] => [1,7,3,2,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,2,6,7,3,4] => [1,7,4,6,3,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,2,6,7,4,3] => [1,6,4,7,3,2,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,5,2,7,4,3,6] => [1,7,6,3,2,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,2,7,4,6,3] => [1,6,7,3,2,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,5,2,7,6,3,4] => [1,6,3,2,5,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,5,2,7,6,4,3] => [1,7,3,2,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,3,2,6,7,4] => [1,3,7,4,2,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,5,3,2,7,4,6] => [1,3,7,6,4,2,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,5,3,6,4,7,2] => [1,3,7,2,5,4,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,5,3,6,7,2,4] => [1,3,7,4,6,2,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,5,3,7,4,2,6] => [1,3,7,6,2,5,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,5,3,7,6,4,2] => [1,3,7,2,5,6,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,5,4,2,6,7,3] => [1,7,3,4,2,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,4,2,7,3,6] => [1,7,6,3,4,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,4,2,7,6,3] => [1,6,7,3,4,2,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,5,4,6,2,7,3] => [1,5,2,7,3,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,5,4,6,3,7,2] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,4,6,7,2,3] => [1,7,3,4,6,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,4,6,7,3,2] => [1,6,3,4,7,2,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,5,4,7,2,3,6] => [1,5,2,7,6,3,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,5,4,7,3,2,6] => [1,7,6,2,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,4,7,3,6,2] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,5,4,7,6,2,3] => [1,6,2,5,7,3,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,5,4,7,6,3,2] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,6,2,3,7,4] => [1,7,4,2,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,6,2,7,3,4] => [1,6,3,7,4,2,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,5,6,2,7,4,3] => [1,7,3,6,4,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,6,3,2,7,4] => [1,5,2,7,4,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,5,6,3,4,7,2] => [1,7,2,5,4,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,6,3,7,2,4] => [1,7,4,3,6,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,6,3,7,4,2] => [1,6,4,3,7,2,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,5,6,4,3,7,2] => [1,4,7,2,5,3,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,5,6,4,7,2,3] => [1,4,7,3,6,2,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,5,6,7,2,4,3] => [1,5,2,7,3,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,5,6,7,3,2,4] => [1,6,2,5,3,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,5,6,7,3,4,2] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,6,7,4,2,3] => [1,7,3,6,2,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,6,7,4,3,2] => [1,6,3,7,2,5,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,5,7,2,3,4,6] => [1,7,6,4,2,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,7,2,3,6,4] => [1,6,7,4,2,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,5,7,2,6,3,4] => [1,7,4,2,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,7,2,6,4,3] => [1,6,4,2,5,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,5,7,3,2,4,6] => [1,5,2,7,6,4,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,5,7,3,4,2,6] => [1,7,6,2,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,7,3,4,6,2] => [1,6,7,2,5,4,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,5,7,3,6,2,4] => [1,6,2,5,7,4,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,5,7,3,6,4,2] => [1,7,2,5,6,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,7,4,3,2,6] => [1,4,7,6,2,5,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,5,7,4,3,6,2] => [1,4,6,7,2,5,3] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 3
[1,5,7,4,6,3,2] => [1,4,7,2,5,6,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,5,7,6,2,3,4] => [1,5,2,7,4,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,5,7,6,3,2,4] => [1,7,4,6,2,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,5,7,6,3,4,2] => [1,6,4,7,2,5,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,5,7,6,4,2,3] => [1,6,2,5,4,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,5,7,6,4,3,2] => [1,7,2,5,4,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,2,3,4,7,5] => [1,7,5,4,3,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,2,3,5,7,4] => [1,5,7,4,3,2,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,6,2,3,7,4,5] => [1,6,4,3,2,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,6,2,3,7,5,4] => [1,7,4,3,2,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,2,4,3,7,5] => [1,4,7,5,3,2,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,6,2,4,7,5,3] => [1,4,7,3,2,6,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,6,2,5,3,7,4] => [1,7,4,5,3,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,2,5,4,7,3] => [1,5,4,7,3,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,6,2,5,7,3,4] => [1,6,3,2,7,4,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,6,2,5,7,4,3] => [1,7,3,2,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,2,7,3,4,5] => [1,7,5,3,2,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,2,7,3,5,4] => [1,6,5,3,2,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,6,2,7,4,3,5] => [1,6,3,2,7,5,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,6,2,7,4,5,3] => [1,7,3,2,6,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,2,7,5,4,3] => [1,5,7,3,2,6,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,6,3,2,4,7,5] => [1,3,7,5,4,2,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,6,3,2,7,5,4] => [1,3,7,4,2,6,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,6,3,5,2,7,4] => [1,3,7,4,5,2,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,6,3,5,7,4,2] => [1,3,7,2,6,4,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,6,3,7,2,4,5] => [1,3,7,5,2,6,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,6,3,7,4,5,2] => [1,3,7,2,6,5,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,6,4,2,3,7,5] => [1,7,5,3,4,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,4,2,5,7,3] => [1,5,7,3,4,2,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,6,4,2,7,3,5] => [1,6,3,4,2,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,6,4,2,7,5,3] => [1,7,3,4,2,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,4,5,2,7,3] => [1,7,3,4,5,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,4,5,7,2,3] => [1,6,2,7,3,4,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,6,4,5,7,3,2] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,4,7,2,3,5] => [1,7,5,2,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,4,7,2,5,3] => [1,6,5,2,7,3,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,6,4,7,3,2,5] => [1,6,2,7,5,3,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,6,4,7,3,5,2] => [1,7,2,6,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,4,7,5,2,3] => [1,5,6,2,7,3,4] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 3
[1,6,4,7,5,3,2] => [1,5,7,2,6,3,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,6,5,2,3,7,4] => [1,5,3,7,4,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,6,5,2,4,7,3] => [1,7,3,5,4,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,5,2,7,3,4] => [1,7,4,2,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,5,2,7,4,3] => [1,6,4,2,7,3,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,6,5,3,2,7,4] => [1,7,4,3,5,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,5,3,7,2,4] => [1,6,2,7,4,3,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,6,5,3,7,4,2] => [1,7,2,6,4,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,5,4,2,7,3] => [1,4,7,3,5,2,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,6,5,4,7,3,2] => [1,4,7,2,6,3,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,6,5,7,2,3,4] => [1,6,3,5,2,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,6,5,7,2,4,3] => [1,7,3,5,2,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,5,7,3,4,2] => [1,5,3,7,2,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,6,5,7,4,2,3] => [1,6,2,7,3,5,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,6,5,7,4,3,2] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,7,2,3,4,5] => [1,6,4,2,7,5,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,6,7,2,3,5,4] => [1,7,4,2,6,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,7,2,4,3,5] => [1,7,5,4,2,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,7,2,4,5,3] => [1,6,5,4,2,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,6,7,2,5,3,4] => [1,5,7,4,2,6,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,6,7,3,2,4,5] => [1,7,5,2,6,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,7,3,2,5,4] => [1,6,5,2,7,4,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,6,7,3,4,2,5] => [1,6,2,7,5,4,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,6,7,3,4,5,2] => [1,7,2,6,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,7,3,5,2,4] => [1,5,6,2,7,4,3] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 3
[1,6,7,3,5,4,2] => [1,5,7,2,6,4,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,6,7,4,2,3,5] => [1,4,7,5,2,6,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,6,7,4,3,5,2] => [1,4,7,2,6,5,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,6,7,5,2,3,4] => [1,7,4,5,2,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,7,5,2,4,3] => [1,6,4,5,2,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,6,7,5,3,2,4] => [1,6,2,7,4,5,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,6,7,5,3,4,2] => [1,7,2,6,4,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,6,7,5,4,3,2] => [1,5,4,7,2,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,7,2,3,4,5,6] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,2,3,4,6,5] => [1,6,7,5,4,3,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,7,2,3,5,4,6] => [1,5,7,6,4,3,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,7,2,3,5,6,4] => [1,5,6,7,4,3,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 3
[1,7,2,3,6,4,5] => [1,7,5,6,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,2,3,6,5,4] => [1,6,5,7,4,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,7,2,4,3,5,6] => [1,4,7,6,5,3,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,7,2,4,3,6,5] => [1,4,6,7,5,3,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 3
[1,7,2,4,6,3,5] => [1,4,7,5,6,3,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,7,2,5,3,4,6] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,2,5,3,6,4] => [1,6,7,4,5,3,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,7,2,5,4,3,6] => [1,5,4,7,6,3,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,7,2,5,6,3,4] => [1,7,4,5,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,2,5,6,4,3] => [1,6,4,5,7,3,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,7,2,6,3,4,5] => [1,6,4,7,5,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,7,2,6,3,5,4] => [1,7,4,6,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,2,6,4,3,5] => [1,7,5,4,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,2,6,4,5,3] => [1,6,5,4,7,3,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,7,2,6,5,3,4] => [1,5,7,4,6,3,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,7,2,6,5,4,3] => [1,5,6,4,7,3,2] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 3
[1,7,3,2,4,5,6] => [1,3,7,6,5,4,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,7,3,2,6,4,5] => [1,3,7,5,6,4,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,7,3,5,2,4,6] => [1,3,7,6,4,5,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,7,3,5,6,2,4] => [1,3,7,4,5,6,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,7,3,6,2,5,4] => [1,3,7,4,6,5,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,7,3,6,4,2,5] => [1,3,7,5,4,6,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 2
[1,7,4,2,3,5,6] => [1,7,6,5,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,4,2,3,6,5] => [1,6,7,5,3,4,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,7,4,2,5,3,6] => [1,5,7,6,3,4,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,7,4,2,5,6,3] => [1,5,6,7,3,4,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 3
[1,7,4,2,6,3,5] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,4,2,6,5,3] => [1,6,5,7,3,4,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,7,4,5,2,3,6] => [1,7,6,3,4,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,4,5,2,6,3] => [1,6,7,3,4,5,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,7,4,5,6,2,3] => [1,7,3,4,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,4,5,6,3,2] => [1,6,3,4,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,7,4,6,2,3,5] => [1,6,3,4,7,5,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,7,4,6,2,5,3] => [1,7,3,4,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,4,6,3,2,5] => [1,7,5,3,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,4,6,3,5,2] => [1,6,5,3,4,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,7,4,6,5,2,3] => [1,5,7,3,4,6,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,7,5,2,3,4,6] => [1,5,3,7,6,4,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,7,5,2,4,3,6] => [1,7,6,3,5,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,5,2,4,6,3] => [1,6,7,3,5,4,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,7,5,2,6,3,4] => [1,6,3,5,7,4,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,7,5,2,6,4,3] => [1,7,3,5,6,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,5,3,2,4,6] => [1,7,6,4,3,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,5,3,2,6,4] => [1,6,7,4,3,5,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 2
[1,7,5,3,6,2,4] => [1,7,4,3,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,5,3,6,4,2] => [1,6,4,3,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,7,5,4,2,3,6] => [1,4,7,6,3,5,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,7,5,4,2,6,3] => [1,4,6,7,3,5,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 3
[1,7,5,4,6,2,3] => [1,4,7,3,5,6,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,7,5,6,2,3,4] => [1,7,4,6,3,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,5,6,2,4,3] => [1,6,4,7,3,5,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,7,5,6,3,2,4] => [1,5,3,7,4,6,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[1,7,5,6,4,2,3] => [1,7,3,5,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,5,6,4,3,2] => [1,6,3,5,4,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,7,6,2,3,4,5] => [1,7,5,3,6,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,6,2,3,5,4] => [1,6,5,3,7,4,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,7,6,2,4,3,5] => [1,6,3,7,5,4,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,7,6,2,4,5,3] => [1,7,3,6,5,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,6,2,5,3,4] => [1,5,6,3,7,4,2] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 3
[1,7,6,2,5,4,3] => [1,5,7,3,6,4,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,7,6,3,2,4,5] => [1,6,4,3,7,5,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 2
[1,7,6,3,2,5,4] => [1,7,4,3,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,6,3,4,2,5] => [1,7,5,4,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,6,3,4,5,2] => [1,6,5,4,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,7,6,3,5,2,4] => [1,5,7,4,3,6,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 2
[1,7,6,4,2,5,3] => [1,4,7,3,6,5,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,7,6,4,3,2,5] => [1,4,7,5,3,6,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 2
[1,7,6,5,2,3,4] => [1,6,3,7,4,5,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 2
[1,7,6,5,2,4,3] => [1,7,3,6,4,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,6,5,3,2,4] => [1,7,4,5,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 1
[1,7,6,5,3,4,2] => [1,6,4,5,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 2
[1,7,6,5,4,2,3] => [1,5,4,7,3,6,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 2
[2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,4,5,7,3,6] => [2,1,7,6,3,4,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,4,6,3,7,5] => [2,1,7,5,3,4,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,4,6,7,5,3] => [2,1,7,3,4,6,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,4,7,3,5,6] => [2,1,7,6,5,3,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,4,7,6,3,5] => [2,1,7,5,6,3,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,5,3,6,7,4] => [2,1,7,4,3,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,5,3,7,4,6] => [2,1,7,6,4,3,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,5,6,4,7,3] => [2,1,7,3,5,4,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,5,6,7,3,4] => [2,1,7,4,6,3,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,5,7,4,3,6] => [2,1,7,6,3,5,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,5,7,6,4,3] => [2,1,7,3,5,6,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,6,3,4,7,5] => [2,1,7,5,4,3,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,6,3,7,5,4] => [2,1,7,4,3,6,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,6,5,3,7,4] => [2,1,7,4,5,3,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,6,5,7,4,3] => [2,1,7,3,6,4,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,6,7,3,4,5] => [2,1,7,5,3,6,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,6,7,4,5,3] => [2,1,7,3,6,5,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,7,3,4,5,6] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,7,3,6,4,5] => [2,1,7,5,6,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,7,5,3,4,6] => [2,1,7,6,4,5,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,7,5,6,3,4] => [2,1,7,4,5,6,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,7,6,3,5,4] => [2,1,7,4,6,5,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,1,7,6,4,3,5] => [2,1,7,5,4,6,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 1
[2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,3,4,6,1,5,7] => [6,5,1,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,3,4,6,5,1,7] => [5,6,1,2,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[2,3,5,1,4,7,6] => [5,4,1,2,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[2,3,5,1,6,4,7] => [6,4,1,2,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,3,5,4,6,1,7] => [4,6,1,2,3,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[2,3,5,6,1,4,7] => [5,1,2,3,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[2,3,5,6,4,1,7] => [6,1,2,3,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,3,6,1,4,5,7] => [6,5,4,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,3,6,1,5,4,7] => [5,6,4,1,2,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[2,3,6,4,1,5,7] => [4,6,5,1,2,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[2,3,6,4,5,1,7] => [4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 3
[2,3,6,5,1,4,7] => [6,4,5,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,3,6,5,4,1,7] => [5,4,6,1,2,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[2,4,1,5,3,7,6] => [5,3,1,2,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[2,4,1,5,6,3,7] => [6,3,1,2,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,4,1,6,3,5,7] => [6,5,3,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,4,1,6,5,3,7] => [5,6,3,1,2,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[2,4,3,5,6,1,7] => [3,6,1,2,4,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[2,4,3,6,1,5,7] => [3,6,5,1,2,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[2,4,3,6,5,1,7] => [3,5,6,1,2,4,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 3
[2,4,5,3,1,7,6] => [5,1,2,4,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[2,4,5,3,6,1,7] => [6,1,2,4,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,4,5,6,1,3,7] => [6,3,5,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,4,5,6,3,1,7] => [5,3,6,1,2,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[2,4,6,3,1,5,7] => [6,5,1,2,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,4,6,3,5,1,7] => [5,6,1,2,4,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[2,4,6,5,1,3,7] => [5,1,2,4,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[2,4,6,5,3,1,7] => [6,1,2,4,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,5,1,3,4,7,6] => [5,4,3,1,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[2,5,1,3,6,4,7] => [6,4,3,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,5,1,4,6,3,7] => [4,6,3,1,2,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[2,5,1,6,3,4,7] => [5,3,1,2,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[2,5,1,6,4,3,7] => [6,3,1,2,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,5,3,1,6,4,7] => [3,6,4,1,2,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[2,5,3,6,4,1,7] => [3,6,1,2,5,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[2,5,4,1,3,7,6] => [5,3,4,1,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[2,5,4,1,6,3,7] => [6,3,4,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,5,4,3,6,1,7] => [4,3,6,1,2,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[2,5,4,6,1,3,7] => [5,1,2,6,3,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[2,5,4,6,3,1,7] => [6,1,2,5,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,5,6,1,3,4,7] => [6,4,1,2,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,5,6,1,4,3,7] => [5,4,1,2,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[2,5,6,3,1,4,7] => [5,1,2,6,4,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[2,5,6,3,4,1,7] => [6,1,2,5,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,5,6,4,3,1,7] => [4,6,1,2,5,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[2,6,1,3,4,5,7] => [6,5,4,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,6,1,3,5,4,7] => [5,6,4,3,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[2,6,1,4,3,5,7] => [4,6,5,3,1,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[2,6,1,4,5,3,7] => [4,5,6,3,1,2,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 3
[2,6,1,5,3,4,7] => [6,4,5,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,6,1,5,4,3,7] => [5,4,6,3,1,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[2,6,3,1,4,5,7] => [3,6,5,4,1,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[2,6,3,1,5,4,7] => [3,5,6,4,1,2,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 3
[2,6,3,5,1,4,7] => [3,6,4,5,1,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[2,6,4,1,3,5,7] => [6,5,3,4,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,6,4,1,5,3,7] => [5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[2,6,4,3,1,5,7] => [4,3,6,5,1,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[2,6,4,5,1,3,7] => [6,3,4,5,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,6,4,5,3,1,7] => [5,3,4,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[2,6,5,1,3,4,7] => [5,3,6,4,1,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[2,6,5,1,4,3,7] => [6,3,5,4,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,6,5,3,1,4,7] => [6,4,3,5,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[2,6,5,3,4,1,7] => [5,4,3,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[2,6,5,4,1,3,7] => [4,6,3,5,1,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[2,6,5,4,3,1,7] => [4,5,3,6,1,2,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 3
[3,1,4,5,2,7,6] => [5,2,1,3,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[3,1,4,5,6,2,7] => [6,2,1,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,1,4,6,2,5,7] => [6,5,2,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,1,4,6,5,2,7] => [5,6,2,1,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[3,1,5,2,4,7,6] => [5,4,2,1,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[3,1,5,2,6,4,7] => [6,4,2,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,1,5,4,6,2,7] => [4,6,2,1,3,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[3,1,5,6,2,4,7] => [5,2,1,3,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[3,1,5,6,4,2,7] => [6,2,1,3,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,1,6,2,4,5,7] => [6,5,4,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,1,6,2,5,4,7] => [5,6,4,2,1,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[3,1,6,4,2,5,7] => [4,6,5,2,1,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[3,1,6,4,5,2,7] => [4,5,6,2,1,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 3
[3,1,6,5,2,4,7] => [6,4,5,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,1,6,5,4,2,7] => [5,4,6,2,1,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[3,2,4,5,6,1,7] => [2,6,1,3,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[3,2,4,6,1,5,7] => [2,6,5,1,3,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[3,2,5,1,6,4,7] => [2,6,4,1,3,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[3,2,5,6,4,1,7] => [2,6,1,3,5,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[3,2,6,1,4,5,7] => [2,6,5,4,1,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[3,2,6,5,1,4,7] => [2,6,4,5,1,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[3,4,2,5,1,7,6] => [5,1,3,2,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[3,4,2,5,6,1,7] => [6,1,3,2,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,4,2,6,1,5,7] => [6,5,1,3,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,4,2,6,5,1,7] => [5,6,1,3,2,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[3,4,5,1,2,7,6] => [5,2,4,1,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[3,4,5,1,6,2,7] => [6,2,4,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,4,5,2,6,1,7] => [4,2,6,1,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[3,4,5,6,1,2,7] => [5,1,3,6,2,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[3,4,5,6,2,1,7] => [6,1,3,5,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,4,6,1,2,5,7] => [6,5,2,4,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,4,6,1,5,2,7] => [5,6,2,4,1,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[3,4,6,2,1,5,7] => [4,2,6,5,1,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[3,4,6,5,1,2,7] => [6,2,4,5,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,4,6,5,2,1,7] => [5,2,4,6,1,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[3,5,2,1,4,7,6] => [5,4,1,3,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[3,5,2,1,6,4,7] => [6,4,1,3,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,5,2,4,6,1,7] => [4,6,1,3,2,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[3,5,2,6,1,4,7] => [5,1,3,2,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[3,5,2,6,4,1,7] => [6,1,3,2,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,5,4,2,1,7,6] => [5,1,3,4,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[3,5,4,2,6,1,7] => [6,1,3,4,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,5,4,6,1,2,7] => [6,2,5,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,5,4,6,2,1,7] => [5,2,6,1,3,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[3,5,6,1,2,4,7] => [5,2,6,4,1,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[3,5,6,1,4,2,7] => [6,2,5,4,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,5,6,2,1,4,7] => [6,4,2,5,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,5,6,2,4,1,7] => [5,4,2,6,1,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[3,5,6,4,1,2,7] => [4,6,2,5,1,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[3,5,6,4,2,1,7] => [4,5,2,6,1,3,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 3
[3,6,2,1,4,5,7] => [6,5,4,1,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,6,2,1,5,4,7] => [5,6,4,1,3,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[3,6,2,4,1,5,7] => [4,6,5,1,3,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[3,6,2,4,5,1,7] => [4,5,6,1,3,2,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 3
[3,6,2,5,1,4,7] => [6,4,5,1,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,6,2,5,4,1,7] => [5,4,6,1,3,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[3,6,4,2,1,5,7] => [6,5,1,3,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,6,4,2,5,1,7] => [5,6,1,3,4,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[3,6,4,5,1,2,7] => [5,1,3,4,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[3,6,4,5,2,1,7] => [6,1,3,4,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,6,5,1,2,4,7] => [6,4,1,3,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,6,5,1,4,2,7] => [5,4,1,3,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[3,6,5,2,1,4,7] => [5,1,3,6,4,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[3,6,5,2,4,1,7] => [6,1,3,5,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[3,6,5,4,2,1,7] => [4,6,1,3,5,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[4,1,2,5,3,7,6] => [5,3,2,1,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[4,1,2,5,6,3,7] => [6,3,2,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,1,2,6,3,5,7] => [6,5,3,2,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,1,2,6,5,3,7] => [5,6,3,2,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[4,1,3,5,6,2,7] => [3,6,2,1,4,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[4,1,3,6,2,5,7] => [3,6,5,2,1,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[4,1,3,6,5,2,7] => [3,5,6,2,1,4,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 3
[4,1,5,3,2,7,6] => [5,2,1,4,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[4,1,5,3,6,2,7] => [6,2,1,4,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,1,5,6,2,3,7] => [6,3,5,2,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,1,5,6,3,2,7] => [5,3,6,2,1,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[4,1,6,3,2,5,7] => [6,5,2,1,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,1,6,3,5,2,7] => [5,6,2,1,4,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[4,1,6,5,2,3,7] => [5,2,1,4,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[4,1,6,5,3,2,7] => [6,2,1,4,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,2,1,5,6,3,7] => [2,6,3,1,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[4,2,1,6,3,5,7] => [2,6,5,3,1,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[4,2,5,3,6,1,7] => [2,6,1,4,3,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[4,2,5,6,1,3,7] => [2,6,3,5,1,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[4,2,6,3,1,5,7] => [2,6,5,1,4,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[4,2,6,5,3,1,7] => [2,6,1,4,5,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[4,3,1,5,2,7,6] => [5,2,3,1,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[4,3,1,5,6,2,7] => [6,2,3,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,3,1,6,2,5,7] => [6,5,2,3,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,3,1,6,5,2,7] => [5,6,2,3,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[4,3,5,1,6,2,7] => [4,1,6,2,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[4,3,5,2,1,7,6] => [5,1,4,2,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[4,3,5,2,6,1,7] => [6,1,4,2,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,3,5,6,1,2,7] => [6,2,3,5,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,3,5,6,2,1,7] => [5,2,3,6,1,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[4,3,6,1,2,5,7] => [4,1,6,5,2,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[4,3,6,2,1,5,7] => [6,5,1,4,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,3,6,2,5,1,7] => [5,6,1,4,2,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[4,3,6,5,1,2,7] => [5,1,4,6,2,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[4,3,6,5,2,1,7] => [6,1,4,5,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,5,1,2,3,7,6] => [5,3,1,4,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[4,5,1,2,6,3,7] => [6,3,1,4,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,5,1,6,2,3,7] => [5,2,6,3,1,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[4,5,1,6,3,2,7] => [6,2,5,3,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,5,2,1,6,3,7] => [4,1,6,3,2,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[4,5,2,3,1,7,6] => [5,1,4,3,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[4,5,2,3,6,1,7] => [6,1,4,3,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,5,2,6,1,3,7] => [6,3,2,5,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,5,2,6,3,1,7] => [5,3,2,6,1,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[4,5,3,2,6,1,7] => [3,6,1,4,2,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[4,5,3,6,1,2,7] => [3,6,2,5,1,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[4,5,6,1,3,2,7] => [4,1,6,2,5,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[4,5,6,2,1,3,7] => [5,1,4,2,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[4,5,6,2,3,1,7] => [6,1,4,2,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,5,6,3,1,2,7] => [6,2,5,1,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,5,6,3,2,1,7] => [5,2,6,1,4,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[4,6,1,2,3,5,7] => [6,5,3,1,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,6,1,2,5,3,7] => [5,6,3,1,4,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[4,6,1,5,2,3,7] => [6,3,1,4,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,6,1,5,3,2,7] => [5,3,1,4,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[4,6,2,1,3,5,7] => [4,1,6,5,3,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[4,6,2,3,1,5,7] => [6,5,1,4,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,6,2,3,5,1,7] => [5,6,1,4,3,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[4,6,2,5,1,3,7] => [5,1,4,6,3,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[4,6,2,5,3,1,7] => [6,1,4,5,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,6,3,2,1,5,7] => [3,6,5,1,4,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[4,6,3,2,5,1,7] => [3,5,6,1,4,2,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 3
[4,6,3,5,2,1,7] => [3,6,1,4,5,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[4,6,5,1,2,3,7] => [4,1,6,3,5,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[4,6,5,2,1,3,7] => [6,3,5,1,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[4,6,5,2,3,1,7] => [5,3,6,1,4,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[4,6,5,3,1,2,7] => [5,1,4,3,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[4,6,5,3,2,1,7] => [6,1,4,3,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,1,2,3,4,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[5,1,2,3,6,4,7] => [6,4,3,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,1,2,4,6,3,7] => [4,6,3,2,1,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[5,1,2,6,3,4,7] => [5,3,2,1,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[5,1,2,6,4,3,7] => [6,3,2,1,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,1,3,2,6,4,7] => [3,6,4,2,1,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[5,1,3,6,4,2,7] => [3,6,2,1,5,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[5,1,4,2,3,7,6] => [5,3,4,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[5,1,4,2,6,3,7] => [6,3,4,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,1,4,3,6,2,7] => [4,3,6,2,1,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[5,1,4,6,2,3,7] => [5,2,1,6,3,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[5,1,4,6,3,2,7] => [6,2,1,5,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,1,6,2,3,4,7] => [6,4,2,1,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,1,6,2,4,3,7] => [5,4,2,1,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[5,1,6,3,2,4,7] => [5,2,1,6,4,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[5,1,6,3,4,2,7] => [6,2,1,5,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,1,6,4,3,2,7] => [4,6,2,1,5,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[5,2,1,3,6,4,7] => [2,6,4,3,1,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[5,2,1,6,4,3,7] => [2,6,3,1,5,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[5,2,4,1,6,3,7] => [2,6,3,4,1,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[5,2,4,6,3,1,7] => [2,6,1,5,3,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[5,2,6,1,3,4,7] => [2,6,4,1,5,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[5,2,6,3,4,1,7] => [2,6,1,5,4,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[5,3,1,2,4,7,6] => [5,4,2,3,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[5,3,1,2,6,4,7] => [6,4,2,3,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,3,1,4,6,2,7] => [4,6,2,3,1,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[5,3,1,6,2,4,7] => [5,2,3,1,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[5,3,1,6,4,2,7] => [6,2,3,1,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,3,4,1,2,7,6] => [5,2,3,4,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[5,3,4,1,6,2,7] => [6,2,3,4,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,3,4,6,1,2,7] => [5,1,6,2,3,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[5,3,4,6,2,1,7] => [6,1,5,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,3,6,1,2,4,7] => [6,4,1,5,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,3,6,1,4,2,7] => [5,4,1,6,2,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[5,3,6,2,1,4,7] => [5,1,6,4,2,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[5,3,6,2,4,1,7] => [6,1,5,4,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,3,6,4,1,2,7] => [4,5,1,6,2,3,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 3
[5,3,6,4,2,1,7] => [4,6,1,5,2,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[5,4,1,2,6,3,7] => [4,2,6,3,1,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[5,4,1,3,2,7,6] => [5,2,4,3,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[5,4,1,3,6,2,7] => [6,2,4,3,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,4,1,6,2,3,7] => [6,3,1,5,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,4,1,6,3,2,7] => [5,3,1,6,2,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[5,4,2,1,3,7,6] => [5,3,2,4,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 1
[5,4,2,1,6,3,7] => [6,3,2,4,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,4,2,6,1,3,7] => [5,1,6,3,2,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[5,4,2,6,3,1,7] => [6,1,5,3,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,4,3,1,6,2,7] => [3,6,2,4,1,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[5,4,3,6,2,1,7] => [3,6,1,5,2,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[5,4,6,1,2,3,7] => [5,2,4,1,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[5,4,6,1,3,2,7] => [6,2,4,1,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,4,6,2,3,1,7] => [4,2,6,1,5,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[5,4,6,3,1,2,7] => [5,1,6,2,4,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[5,4,6,3,2,1,7] => [6,1,5,2,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,6,1,2,3,4,7] => [5,3,1,6,4,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[5,6,1,2,4,3,7] => [6,3,1,5,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,6,1,3,2,4,7] => [6,4,3,1,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,6,1,3,4,2,7] => [5,4,3,1,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[5,6,1,4,2,3,7] => [4,6,3,1,5,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[5,6,2,1,3,4,7] => [6,4,1,5,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,6,2,1,4,3,7] => [5,4,1,6,3,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[5,6,2,3,1,4,7] => [5,1,6,4,3,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[5,6,2,3,4,1,7] => [6,1,5,4,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,6,2,4,1,3,7] => [4,5,1,6,3,2,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 3
[5,6,2,4,3,1,7] => [4,6,1,5,3,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[5,6,3,1,2,4,7] => [3,6,4,1,5,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[5,6,3,2,4,1,7] => [3,6,1,5,4,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[5,6,4,1,2,3,7] => [6,3,4,1,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,6,4,1,3,2,7] => [5,3,4,1,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[5,6,4,2,1,3,7] => [5,1,6,3,4,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[5,6,4,2,3,1,7] => [6,1,5,3,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[5,6,4,3,2,1,7] => [4,3,6,1,5,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[6,1,2,3,4,5,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,1,2,3,5,4,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[6,1,2,4,3,5,7] => [4,6,5,3,2,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[6,1,2,4,5,3,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 3
[6,1,2,5,3,4,7] => [6,4,5,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,1,2,5,4,3,7] => [5,4,6,3,2,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[6,1,3,2,4,5,7] => [3,6,5,4,2,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[6,1,3,2,5,4,7] => [3,5,6,4,2,1,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 3
[6,1,3,5,2,4,7] => [3,6,4,5,2,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[6,1,4,2,3,5,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,1,4,2,5,3,7] => [5,6,3,4,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[6,1,4,3,2,5,7] => [4,3,6,5,2,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[6,1,4,5,2,3,7] => [6,3,4,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,1,4,5,3,2,7] => [5,3,4,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[6,1,5,2,3,4,7] => [5,3,6,4,2,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[6,1,5,2,4,3,7] => [6,3,5,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,1,5,3,2,4,7] => [6,4,3,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,1,5,3,4,2,7] => [5,4,3,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[6,1,5,4,2,3,7] => [4,6,3,5,2,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[6,1,5,4,3,2,7] => [4,5,3,6,2,1,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 3
[6,2,1,3,4,5,7] => [2,6,5,4,3,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[6,2,1,5,3,4,7] => [2,6,4,5,3,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[6,2,4,1,3,5,7] => [2,6,5,3,4,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[6,2,4,5,1,3,7] => [2,6,3,4,5,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[6,2,5,1,4,3,7] => [2,6,3,5,4,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[6,2,5,3,1,4,7] => [2,6,4,3,5,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 2
[6,3,1,2,4,5,7] => [6,5,4,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,3,1,2,5,4,7] => [5,6,4,2,3,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[6,3,1,4,2,5,7] => [4,6,5,2,3,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[6,3,1,4,5,2,7] => [4,5,6,2,3,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 3
[6,3,1,5,2,4,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,3,1,5,4,2,7] => [5,4,6,2,3,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[6,3,4,1,2,5,7] => [6,5,2,3,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,3,4,1,5,2,7] => [5,6,2,3,4,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[6,3,4,5,1,2,7] => [6,2,3,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,3,4,5,2,1,7] => [5,2,3,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[6,3,5,1,2,4,7] => [5,2,3,6,4,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[6,3,5,1,4,2,7] => [6,2,3,5,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,3,5,2,1,4,7] => [6,4,2,3,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,3,5,2,4,1,7] => [5,4,2,3,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[6,3,5,4,1,2,7] => [4,6,2,3,5,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[6,4,1,2,3,5,7] => [4,2,6,5,3,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[6,4,1,3,2,5,7] => [6,5,2,4,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,4,1,3,5,2,7] => [5,6,2,4,3,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[6,4,1,5,2,3,7] => [5,2,4,6,3,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[6,4,1,5,3,2,7] => [6,2,4,5,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,4,2,1,3,5,7] => [6,5,3,2,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,4,2,1,5,3,7] => [5,6,3,2,4,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 2
[6,4,2,5,1,3,7] => [6,3,2,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,4,2,5,3,1,7] => [5,3,2,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[6,4,3,1,2,5,7] => [3,6,5,2,4,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[6,4,3,1,5,2,7] => [3,5,6,2,4,1,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 3
[6,4,3,5,1,2,7] => [3,6,2,4,5,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[6,4,5,1,2,3,7] => [6,3,5,2,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,4,5,1,3,2,7] => [5,3,6,2,4,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[6,4,5,2,1,3,7] => [4,2,6,3,5,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[6,4,5,3,1,2,7] => [6,2,4,3,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,4,5,3,2,1,7] => [5,2,4,3,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[6,5,1,2,3,4,7] => [6,4,2,5,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,5,1,2,4,3,7] => [5,4,2,6,3,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[6,5,1,3,2,4,7] => [5,2,6,4,3,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[6,5,1,3,4,2,7] => [6,2,5,4,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,5,1,4,2,3,7] => [4,5,2,6,3,1,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 3
[6,5,1,4,3,2,7] => [4,6,2,5,3,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[6,5,2,1,3,4,7] => [5,3,2,6,4,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 2
[6,5,2,1,4,3,7] => [6,3,2,5,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,5,2,3,1,4,7] => [6,4,3,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,5,2,3,4,1,7] => [5,4,3,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[6,5,2,4,1,3,7] => [4,6,3,2,5,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 2
[6,5,3,1,4,2,7] => [3,6,2,5,4,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[6,5,3,2,1,4,7] => [3,6,4,2,5,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 2
[6,5,4,1,2,3,7] => [5,2,6,3,4,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 2
[6,5,4,1,3,2,7] => [6,2,5,3,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,5,4,2,1,3,7] => [6,3,4,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 1
[6,5,4,2,3,1,7] => [5,3,4,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 2
[6,5,4,3,1,2,7] => [4,3,6,2,5,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 2
[6,5,7,4,3,2,1,8] => [4,7,1,6,2,5,3,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[6,5,4,7,3,2,1,8] => [7,1,6,2,5,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,4,6,7,3,2,1,8] => [7,1,5,3,6,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,5,7,3,4,2,1,8] => [7,1,6,2,5,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,6,7,3,4,2,1,8] => [6,2,7,1,5,4,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[4,5,6,3,7,2,1,8] => [7,1,4,3,6,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,3,4,5,7,2,1,8] => [7,1,6,2,3,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,7,5,4,2,3,1,8] => [4,7,1,6,3,5,2,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[5,6,7,4,2,3,1,8] => [4,7,1,5,2,6,3,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[5,6,4,7,2,3,1,8] => [7,1,5,2,6,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,4,6,7,2,3,1,8] => [6,3,7,1,5,2,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[5,6,7,3,2,4,1,8] => [7,1,5,2,6,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,5,7,2,3,4,1,8] => [7,1,6,4,2,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,6,7,2,3,4,1,8] => [6,4,2,7,1,5,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[6,7,2,3,4,5,1,8] => [7,1,6,5,4,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,4,5,6,2,7,1,8] => [7,1,3,5,2,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,5,6,2,3,7,1,8] => [7,1,4,2,5,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,3,5,2,6,7,1,8] => [7,1,4,2,3,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,5,2,3,6,7,1,8] => [7,1,4,3,2,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,4,2,5,6,7,1,8] => [7,1,3,2,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,6,4,3,1,2,8] => [4,7,2,5,3,6,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[7,5,4,6,3,1,2,8] => [7,2,5,3,4,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,6,3,4,1,2,8] => [7,2,5,4,3,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,6,7,3,4,1,2,8] => [7,2,6,1,5,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,4,5,6,1,2,8] => [7,2,3,4,5,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,3,4,5,7,1,2,8] => [6,1,7,2,3,4,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[3,4,5,6,7,1,2,8] => [7,2,4,6,1,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,6,5,4,2,1,3,8] => [4,7,3,5,2,6,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[7,4,5,6,2,1,3,8] => [7,3,5,2,4,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,4,6,7,2,1,3,8] => [7,3,6,1,5,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,7,5,4,1,2,3,8] => [4,7,3,5,1,6,2,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[7,5,6,4,1,2,3,8] => [4,7,3,6,2,5,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[7,6,4,5,1,2,3,8] => [6,2,7,3,4,5,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[7,4,5,6,1,2,3,8] => [6,2,4,7,3,5,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[6,4,5,7,1,2,3,8] => [7,3,5,1,6,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,5,6,7,1,2,3,8] => [7,3,6,2,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,6,5,3,2,1,4,8] => [7,4,3,5,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,6,2,3,1,4,8] => [7,4,2,5,3,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,5,7,2,3,1,4,8] => [6,1,7,4,2,5,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[5,6,7,2,3,1,4,8] => [7,4,2,6,1,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,7,5,3,1,2,4,8] => [7,4,3,5,1,6,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,6,5,2,1,3,4,8] => [7,4,2,6,3,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,7,5,1,2,3,4,8] => [7,4,1,6,3,5,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,6,7,1,2,3,4,8] => [7,4,1,5,2,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,6,4,2,3,1,5,8] => [7,5,3,4,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,6,2,3,4,1,5,8] => [7,5,4,3,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,7,2,3,1,4,5,8] => [7,5,1,6,4,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,7,2,1,3,4,5,8] => [6,4,1,7,5,3,2,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,6,1,2,3,4,5,8] => [6,4,2,7,5,3,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[6,7,1,2,3,4,5,8] => [7,5,3,1,6,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,4,5,3,1,2,6,8] => [7,6,2,4,3,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,4,5,1,2,6,8] => [7,6,2,3,4,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,4,5,1,2,3,6,8] => [7,6,3,5,2,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,2,3,1,4,6,8] => [7,6,4,3,2,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,1,2,3,4,6,8] => [7,6,4,2,5,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,4,1,2,5,6,8] => [7,6,5,2,3,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,4,2,1,3,5,6,8] => [7,6,5,3,2,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,1,2,4,5,6,8] => [7,6,5,4,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,2,3,4,5,6,8] => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,8,7,5,4,3,2] => [1,5,8,2,6,4,7,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,7,6,8,5,4,3,2] => [1,5,8,2,7,3,6,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,8,7,6,4,3,2] => [1,8,2,5,6,4,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,5,8,7,4,3,2] => [1,7,3,5,8,2,6,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,7,6,5,8,4,3,2] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,7,5,8,4,3,2] => [1,7,3,8,2,6,4,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,7,6,8,5,3,2] => [1,7,3,8,2,4,6,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,6,7,8,5,3,2] => [1,8,2,4,7,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,6,7,4,8,3,2] => [1,8,2,5,4,7,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,6,7,5,8,3,2] => [1,5,8,2,4,7,3,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,4,7,6,8,3,2] => [1,7,3,4,8,2,5,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,5,4,6,7,8,3,2] => [1,8,2,5,7,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,8,7,5,4,2] => [1,8,2,3,6,5,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,8,7,6,4,2] => [1,6,8,2,3,5,7,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,7,6,5,8,4,2] => [1,5,8,2,3,7,4,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,3,5,6,7,8,4,2] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,7,8,6,5,2] => [1,6,8,2,3,4,7,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,4,6,8,7,5,2] => [1,8,2,3,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,7,6,8,5,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,6,7,8,5,2] => [1,7,5,8,2,3,4,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,5,3,8,7,6,2] => [1,7,6,8,2,4,3,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,4,5,8,7,6,2] => [1,7,6,8,2,3,4,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,4,5,7,8,6,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,6,5,3,8,7,2] => [1,7,8,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,5,4,6,3,8,7,2] => [1,7,8,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,5,3,6,8,7,2] => [1,7,8,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,3,4,5,6,8,7,2] => [1,7,8,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,6,5,7,4,3,8,2] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,6,5,3,8,2] => [1,5,8,2,4,6,3,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,4,7,6,3,8,2] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,6,7,3,8,2] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,7,6,4,8,2] => [1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,5,7,4,8,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,6,7,5,8,2] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,5,7,6,8,2] => [1,6,8,2,3,4,5,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,5,4,6,3,7,8,2] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,6,4,7,8,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,3,6,7,8,2] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,7,6,4,3,2,1,8] => [4,7,1,5,3,6,2,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[4,7,6,5,3,2,1,8] => [7,1,4,5,3,6,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,6,7,5,3,2,1,8] => [6,2,7,1,4,5,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[3,5,6,7,4,2,1,8] => [7,1,3,6,2,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,5,4,7,6,2,1,8] => [6,2,5,7,1,3,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[4,6,5,3,7,2,1,8] => [6,2,7,1,4,3,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[4,3,6,5,7,2,1,8] => [6,2,3,7,1,4,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[2,5,7,6,4,3,1,8] => [7,1,2,5,4,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,6,5,7,4,3,1,8] => [7,1,2,6,3,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,4,5,7,6,3,1,8] => [6,3,5,7,1,2,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[2,3,6,7,5,4,1,8] => [5,7,1,2,3,6,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[2,3,5,7,6,4,1,8] => [7,1,2,3,5,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,6,5,7,4,1,8] => [7,1,2,3,6,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,5,6,7,4,1,8] => [6,4,7,1,2,3,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[2,3,4,7,6,5,1,8] => [6,5,7,1,2,3,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[2,3,4,6,7,5,1,8] => [7,1,2,3,4,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,3,5,2,7,6,1,8] => [6,7,1,4,2,3,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[2,3,4,5,7,6,1,8] => [6,7,1,2,3,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[3,6,5,4,2,7,1,8] => [4,7,1,3,5,2,6,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[4,3,6,5,2,7,1,8] => [7,1,4,5,2,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,5,4,6,3,7,1,8] => [7,1,2,5,3,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,5,6,4,7,1,8] => [7,1,2,3,5,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,4,2,6,5,7,1,8] => [5,7,1,3,2,4,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[2,3,4,6,5,7,1,8] => [5,7,1,2,3,4,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[2,4,5,3,6,7,1,8] => [7,1,2,4,3,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,4,5,8,6,7,2] => [1,6,7,8,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[2,3,4,7,5,6,1,8] => [5,6,7,1,2,3,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 3
[2,4,1,6,3,7,5,8] => [7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,4,1,5,6,7,3,8] => [7,3,1,2,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,4,5,6,1,7,3,8] => [7,3,5,1,2,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,5,1,3,6,7,4,8] => [7,4,3,1,2,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,5,1,6,7,3,4,8] => [7,4,6,3,1,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,5,6,1,7,3,4,8] => [6,3,7,4,1,2,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[2,5,1,3,7,4,6,8] => [7,6,4,3,1,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,5,1,6,7,4,8] => [7,4,1,2,3,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,5,6,7,1,4,8] => [7,4,6,1,2,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,6,1,3,4,7,5,8] => [7,5,4,3,1,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,4,6,1,7,5,8] => [7,5,1,2,3,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,7,1,3,4,5,6,8] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,7,1,4,5,6,8] => [7,6,5,4,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,4,7,1,5,6,8] => [7,6,5,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,4,5,7,1,6,8] => [7,6,1,2,3,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,4,6,7,1,2,5,8] => [7,5,1,3,6,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,1,4,7,2,5,6,8] => [7,6,5,2,1,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,1,4,5,6,7,2,8] => [7,2,1,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,5,6,1,7,2,4,8] => [7,4,1,3,6,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,1,5,2,7,4,6,8] => [7,6,4,2,1,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,5,2,7,4,8,6] => [1,8,6,4,2,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,7,8,2,4,6] => [1,7,4,8,6,2,3,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,5,2,8,4,6,7] => [1,8,7,6,4,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,2,6,8,4,7] => [1,8,7,4,2,3,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,6,8,2,4,7] => [1,8,7,4,6,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,2,6,7,8,4] => [1,8,4,2,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,1,6,7,2,4,5,8] => [7,5,2,1,3,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,6,7,1,2,4,5,8] => [7,5,2,6,4,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,6,2,4,7,8,5] => [1,8,5,4,2,3,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,7,2,4,8,5] => [1,8,5,2,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,2,7,8,4,5] => [1,8,5,7,4,2,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,7,2,8,4,5] => [1,7,4,8,5,2,3,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,4,6,2,8,5,7] => [1,8,7,5,2,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,6,7,8,2,5] => [1,8,5,7,2,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,2,8,4,5,6] => [1,8,6,4,2,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,2,4,5,8,6] => [1,8,6,5,4,2,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,1,7,2,4,5,6,8] => [7,6,5,4,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,4,5,7,2,8,6] => [1,8,6,2,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,2,4,5,6,7] => [1,8,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,8,2,5,6,7] => [1,8,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,5,8,2,6,7] => [1,8,7,6,2,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,5,6,8,2,7] => [1,8,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,1,5,6,2,7,3,8] => [7,3,5,2,1,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,5,1,6,7,2,3,8] => [7,3,1,4,6,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,5,1,2,7,3,6,8] => [7,6,3,1,4,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,1,2,5,7,3,6,8] => [7,6,3,2,1,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,2,5,7,3,8,6] => [1,8,6,3,2,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,7,8,2,3,6] => [1,8,6,2,4,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,5,8,3,6,7] => [1,8,7,6,3,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,8,2,3,6,7] => [1,8,7,6,3,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,5,6,8,3,7] => [1,8,7,3,2,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,1,2,5,6,7,3,8] => [7,3,2,1,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,2,5,6,7,8,3] => [1,8,3,2,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,6,7,8,2,3] => [1,8,3,5,7,2,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,1,6,7,2,3,5,8] => [6,3,7,5,2,1,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[4,6,1,7,2,3,5,8] => [7,5,2,6,3,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,6,1,2,3,7,5,8] => [7,5,3,1,4,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,1,2,6,3,7,5,8] => [7,5,3,2,1,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,2,6,3,7,8,5] => [1,8,5,3,2,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,6,7,8,3,5] => [1,8,5,7,3,2,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,6,3,8,5,7] => [1,8,7,5,3,2,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,7,8,3,5,6] => [1,8,6,3,2,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,8,2,3,5,6] => [1,8,6,3,7,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,7,3,5,8,6] => [1,8,6,5,3,2,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,7,1,2,3,5,6,8] => [7,6,5,3,1,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,1,2,7,3,5,6,8] => [7,6,5,3,2,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,2,8,3,5,6,7] => [1,8,7,6,5,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,6,2,3,7,8,4] => [1,8,4,2,5,3,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,6,2,7,8,3,4] => [1,8,4,2,5,7,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,6,7,8,2,3,4] => [1,8,4,7,3,6,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,6,2,3,8,4,7] => [1,8,7,4,2,5,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,6,8,3,4,7] => [1,8,7,4,6,3,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,3,6,8,4,7] => [1,8,7,4,3,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,1,2,3,6,7,4,8] => [7,4,3,2,1,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,2,3,6,7,8,4] => [1,8,4,3,2,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,7,8,3,4,6] => [1,7,4,8,6,3,2,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,5,7,2,8,3,4,6] => [1,8,6,3,7,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,2,3,4,8,6] => [1,8,6,4,2,5,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,1,7,2,3,4,6,8] => [7,6,4,2,1,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,1,2,3,7,4,6,8] => [7,6,4,3,2,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,8,2,3,4,6,7] => [1,8,7,6,4,2,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,3,8,4,6,7] => [1,8,7,6,4,3,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,7,3,8,4,5] => [1,7,4,8,5,3,2,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,6,7,2,3,8,4,5] => [1,8,5,3,7,4,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,7,8,2,3,4,5] => [1,8,5,2,6,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,7,3,4,8,5] => [1,8,5,3,2,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,3,7,8,4,5] => [1,8,5,7,4,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,1,2,7,3,4,5,8] => [7,5,3,2,1,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,1,2,3,4,7,5,8] => [7,5,4,3,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,2,3,4,7,8,5] => [1,8,5,4,3,2,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,8,3,4,5,7] => [1,8,7,5,3,2,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,3,4,8,5,7] => [1,8,7,5,4,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,2,3,4,5,6] => [1,8,6,4,2,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,3,8,4,5,6] => [1,8,6,4,3,2,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,3,4,5,8,6] => [1,8,6,5,4,3,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,3,7,1,2,4,6,8] => [7,6,4,1,5,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,3,7,1,2,4,5,8] => [6,4,1,7,5,2,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,4,6,1,2,3,5,8] => [6,3,7,5,2,4,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[4,3,5,7,1,2,6,8] => [7,6,2,3,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,3,6,7,1,2,5,8] => [6,2,3,7,5,1,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,3,5,6,1,2,4,8] => [7,4,6,2,3,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,7,2,6,1,4,5,8] => [6,4,7,5,1,3,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[6,4,2,7,1,3,5,8] => [7,5,1,6,3,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,4,2,5,1,3,6,8] => [7,6,3,2,4,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,4,7,3,6,1,2,8] => [6,1,5,7,2,4,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,4,6,3,5,1,2,8] => [5,7,2,4,3,6,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[6,5,4,2,7,1,3,8] => [6,1,7,3,4,2,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[7,6,4,2,5,1,3,8] => [5,7,3,4,2,6,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[7,6,5,2,4,1,3,8] => [7,3,5,4,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,4,2,7,6,1,3,8] => [6,1,5,7,3,2,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[5,4,2,6,7,1,3,8] => [7,3,2,4,6,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,3,7,2,1,5,4,8] => [6,5,1,7,4,2,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[6,3,7,2,1,4,5,8] => [7,5,1,6,4,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,8,2,3,7,5,4] => [1,8,4,2,6,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,8,7,2,6,3] => [1,8,3,5,7,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,4,7,8,3,5,2] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,6,7,8,4,3] => [1,8,3,2,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,4,7,8,5,2,3] => [1,8,3,4,7,2,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,5,2,3,7,6,1,8] => [6,7,1,4,3,2,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,5,6,3,4,8,7,2] => [1,7,8,2,5,4,3,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[4,7,2,6,5,3,1,8] => [5,7,1,4,6,3,2,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[5,7,6,2,4,3,1,8] => [6,3,7,1,5,4,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,6,7,8,3,4,5,2] => [1,7,5,3,8,2,6,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,5,8,3,7,6,4,2] => [1,6,8,2,5,7,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,8,7,3,5,4,2] => [1,7,4,8,2,6,5,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,8,6,5,3,4,2] => [1,5,8,2,7,4,6,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[6,4,1,7,2,3,5,8] => [6,3,1,7,5,2,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,7,5,3,8,4,6,2] => [1,8,2,7,6,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,4,1,6,2,3,5,8] => [7,5,2,4,6,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,6,8,3,4,5,2] => [1,8,2,7,5,3,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,1,7,6,2,4,5,8] => [6,4,7,5,2,1,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,5,8,3,7,4,6,2] => [1,8,2,5,7,6,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,7,3,4,5,2] => [1,8,2,6,4,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,7,6,1,2,3,4,8] => [6,3,7,4,1,5,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,4,6,7,3,2,8,5] => [1,8,5,3,6,2,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,8,6,3,5,2] => [1,8,2,7,5,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,7,5,8,2,4] => [1,5,8,4,7,2,3,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,7,2,5,8,6,4,3] => [1,6,8,3,2,7,4,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,4,7,5,8,3,2,6] => [1,8,6,3,7,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,4,8,7,3,6,2] => [1,8,2,5,7,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,6,3,7,4,2] => [1,7,4,6,8,2,5,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[6,4,2,7,3,5,1,8] => [7,1,6,5,3,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,7,2,6,3,5,1,8] => [7,1,4,6,5,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,7,6,2,3,4,1,8] => [7,1,5,3,6,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,5,2,8,3,4,6] => [1,7,4,2,8,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,5,2,7,3,4,6] => [1,8,6,3,5,7,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,8,7,3,5,6] => [1,7,5,8,6,3,2,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,6,8,7,2,3,4,5] => [1,7,4,8,5,2,6,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,8,6,2,3,4,5] => [1,8,5,2,7,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,5,7,6,1,4,2,8] => [6,4,7,2,5,1,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[5,1,6,7,4,3,2,8] => [6,3,7,2,1,5,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[4,1,6,5,7,3,2,8] => [6,3,7,2,1,4,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,3,8,2,6,4,7,5] => [1,7,8,5,6,4,2,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,3,7,6,4,2,8,5] => [1,8,5,4,6,2,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 1
[2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11111111100000000010 => 1
[1,8,6,3,7,2,4,5] => [1,8,5,7,4,3,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,7,3,4,5,6] => [1,8,6,4,7,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,7,2,4,5,6] => [1,8,6,4,7,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,3,6,2,4,5] => [1,8,5,6,2,7,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,5,3,4,6,7] => [1,8,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,7,3,5,4,6] => [1,7,4,8,6,5,3,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,2,8,3,5,4,6] => [1,8,6,5,3,2,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,8,3,6,5,7] => [1,6,8,7,5,3,2,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,8,2,6,3,5,4,7] => [1,8,7,4,6,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,5,3,6,4,7] => [1,6,8,7,4,5,3,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,8,2,3,4,6,5,7] => [1,6,8,7,5,4,3,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,8,2,3,4,7,5,6] => [1,8,6,7,5,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,5,3,8,4,7] => [1,8,7,4,5,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,5,3,7,4,6] => [1,8,6,7,4,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,6,3,7,4,5] => [1,7,4,6,8,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,7,2,6,3,8,4,5] => [1,8,5,3,2,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,8,3,7,5,6] => [1,8,6,7,5,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,8,3,7,4,5] => [1,8,5,3,2,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,8,3,6,4,5] => [1,6,8,5,3,2,7,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[5,6,7,2,4,3,1,8] => [7,1,5,4,2,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,4,1,2,6,5,8] => [6,7,5,2,3,4,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,8,4,5,2,3,7,6] => [1,7,8,6,3,4,5,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[7,4,6,5,1,3,2,8] => [6,3,7,2,4,5,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,8,5,6,7,2,3,4] => [1,7,3,5,8,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,4,7,2,6,5,3] => [1,6,8,3,4,7,5,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,8,5,7,6,2,4,3] => [1,7,4,8,3,5,6,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,8,6,7,5,4,2,3] => [1,5,8,3,6,4,7,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,4,2,6,7,5,3] => [1,7,5,6,8,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,7,6,2,5,8,3,4] => [1,5,8,4,2,7,3,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,2,3,7,6,8,4] => [1,6,8,4,3,2,5,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,8,3,7,4,5,2] => [1,7,5,8,2,6,4,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,6,8,3,4,7,5,2] => [1,8,2,6,7,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,6,1,2,5,7,3,8] => [5,7,3,1,4,2,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[7,1,4,2,5,3,6,8] => [5,7,6,3,4,2,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[7,3,1,6,4,5,2,8] => [6,5,4,7,2,3,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,4,2,6,5,1,3,8] => [5,7,3,2,4,6,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[7,4,6,3,1,5,2,8] => [7,2,4,3,6,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,7,2,3,8,6,4] => [1,8,4,2,5,3,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,6,4,1,5,7,3,8] => [5,7,3,4,1,2,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,4,2,7,5,8,6,3] => [1,5,8,3,2,4,7,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[4,5,1,2,7,6,3,8] => [6,7,3,1,4,2,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[3,1,4,7,5,6,2,8] => [5,6,7,2,1,3,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 3
[1,3,7,2,4,8,6,5] => [1,8,5,4,2,3,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,7,4,1,6,2,3,8] => [7,3,4,1,5,6,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,4,7,2,5,3,6] => [1,7,3,4,8,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,4,2,6,5,8,3,7] => [1,5,8,7,3,2,4,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,4,2,6,8,3,7] => [1,8,7,3,4,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,6,4,8,3,7] => [1,8,7,3,2,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,5,2,7,3,8,4] => [1,8,4,2,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,8,7,3,6,5] => [1,8,5,7,6,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,7,3,8,5,4] => [1,8,4,7,5,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,7,1,6,2,4,3,8] => [6,4,7,3,1,5,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,8,2,3,4,5,6,9,7] => [1,9,7,6,5,4,3,2,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 1
[2,8,1,3,4,5,6,7,9] => [8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 1
[1,8,6,5,2,7,3,4] => [1,7,3,6,8,4,5,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[6,1,7,5,3,2,4,8] => [6,2,1,7,4,5,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,1,6,5,2,4,3,8] => [7,3,6,4,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,7,1,3,2,6,4,8] => [6,7,4,3,1,5,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[6,7,1,2,4,5,3,8] => [7,3,1,6,5,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,2,3,4,6,5,8] => [6,7,5,4,3,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,8,2,3,4,5,7,6] => [1,7,8,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,6,7,8,4,5,3,2] => [1,7,3,8,2,6,5,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,6,7,8,4,3,5,2] => [1,8,2,6,3,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,7,8,3,5,4,2] => [1,8,2,6,5,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,5,2,8,3,4,7] => [1,8,7,4,2,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,6,3,7,5,2,4] => [1,8,4,3,6,5,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,8,5,3,4,6] => [1,5,8,6,3,2,7,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,3,8,7,4,6,2,5] => [1,6,8,5,4,7,2,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,8,6,7,4,5,2,3] => [1,8,3,6,5,4,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,6,2,7,3,4] => [1,8,4,6,7,3,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 1
[1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 1
[1,4,7,6,2,8,3,5] => [1,7,3,8,5,2,4,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,2,8,6,7,3,5] => [1,8,5,6,7,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,7,3,8,6,5] => [1,8,5,3,2,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,6,4,7,2,5,1,8] => [6,5,2,7,1,3,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[4,5,2,3,7,1,6,8] => [7,6,1,4,3,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,5,1,7,3,2,6,8] => [7,6,2,5,3,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,3,1,5,7,2,6,8] => [7,6,2,3,1,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,3,1,7,5,2,6,8] => [5,7,6,2,3,1,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[6,3,4,1,2,7,5,8] => [7,5,2,3,4,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,6,2,1,4,7,5,8] => [7,5,4,1,3,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,5,2,7,4,6,1,8] => [6,7,1,3,2,5,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[3,6,2,1,5,7,4,8] => [5,7,4,1,3,2,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[7,3,1,5,2,6,4,8] => [6,7,4,5,2,3,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[3,6,5,1,2,7,4,8] => [7,4,1,3,5,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,5,6,2,7,1,4,8] => [6,1,3,7,4,2,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,8,4,6,3,7,2,5] => [1,8,5,3,4,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,6,7,3,2,4] => [1,8,4,6,3,5,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,6,2,7,5,3] => [1,8,3,4,6,7,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,6,7,2,4,3] => [1,8,3,5,7,4,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,5,6,7,1,3,2,8] => [6,3,7,2,5,1,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[6,5,1,7,4,2,3,8] => [7,3,1,6,2,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,3,7,2,1,5,6,8] => [7,6,5,1,4,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,8,7,3,6,2,4] => [1,6,8,4,7,2,5,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,7,2,8,4,6,5,3] => [1,6,8,3,2,7,5,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,7,8,4,6,5,2] => [1,6,8,2,3,7,5,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,4,2,8,5,3,6,7] => [1,5,8,7,6,3,2,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,4,2,5,3,6,7] => [1,5,8,7,6,3,4,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,2,8,4,3,6,7] => [1,8,7,6,3,2,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,7,8,4,3,6] => [1,8,6,4,7,3,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,8,4,5,3,6] => [1,7,3,2,8,6,5,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,5,7,3,6,8,4,2] => [1,7,4,3,8,2,5,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,4,2,7,8,6,5,3] => [1,6,8,3,2,4,7,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,5,7,2,8,6,4,3] => [1,6,8,3,7,4,2,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,4,7,3,8,2,5] => [1,8,5,3,4,7,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,3,4,8,2,5] => [1,7,2,8,5,4,3,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[6,1,5,7,4,3,2,8] => [7,2,1,6,3,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,8,6,4,3,2,7] => [1,8,7,2,5,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,7,4,3,2,5] => [1,8,5,4,7,2,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,6,1,7,4,3,2,8] => [7,2,6,3,1,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,1,7,6,4,3,2,8] => [7,2,1,5,4,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,7,6,4,3,2,5] => [1,8,5,4,6,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,4,6,1,3,7,2,8] => [7,2,4,1,5,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,5,8,4,3,2,7] => [1,8,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,5,6,7,8,9,3] => [1,9,3,2,4,5,6,7,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 1
[1,4,6,3,7,5,8,2] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,5,4,1,6,7,3,8] => [7,3,4,1,2,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,6,7,2,5,3,4] => [1,8,4,7,3,6,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,7,3,8,5,2,4] => [1,8,4,3,7,2,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[8,1,2,3,4,5,6,7,9] => [8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 1
[1,9,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 1
[9,1,2,3,4,5,6,7,8,10] => [9,8,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11111111100000000010 => 1
[1,10,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 1
[10,1,2,3,4,5,6,7,8,9,11] => [10,9,8,7,6,5,4,3,2,1,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1111111111000000000010 => 1
[8,9,1,2,3,4,5,6,7,10] => [9,7,5,3,1,8,6,4,2,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11111111100000000010 => 1
[7,1,8,2,3,4,5,6,9] => [8,6,4,2,1,7,5,3,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 1
[6,8,1,2,3,4,5,7,9] => [8,7,5,3,1,6,4,2,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 1
[1,8,2,9,3,4,5,6,7] => [1,9,7,5,3,2,8,6,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 1
[1,7,9,2,3,4,5,6,8] => [1,9,8,6,4,2,7,5,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 1
[1,9,10,2,3,4,5,6,7,8] => [1,10,8,6,4,2,9,7,5,3] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 1
[1,11,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 1
[1,7,5,8,2,6,4,3] => [1,6,8,3,5,2,7,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,4,7,5,8,2,3] => [1,5,8,3,4,7,2,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,4,2,8,3,6,7] => [1,8,7,6,3,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,3,8,4,2,6] => [1,8,6,4,3,7,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,5,3,7,4,2] => [1,8,2,6,7,4,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,2,6,7,4,3] => [1,8,3,5,6,7,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,3,5,2,6,1,4,8] => [7,4,2,3,5,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,5,1,6,4,2,8] => [7,2,3,5,6,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,6,7,3,8,2,5] => [1,7,2,4,8,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,3,6,2,7,8,5,4] => [1,7,5,8,4,2,3,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,5,6,7,8,2,4,3] => [1,7,4,8,3,6,2,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,5,6,7,8,4,2,3] => [1,8,3,6,4,7,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,4,1,6,3,8,5,7,9] => [8,7,5,3,1,2,4,6,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 1
[2,4,1,6,3,8,5,9,7,10] => [9,7,5,3,1,2,4,6,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11111111100000000010 => 1
[1,5,4,8,3,7,2,6] => [1,8,6,7,2,5,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,3,8,4,7,6] => [1,7,8,6,4,3,2,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,8,3,7,2,6,5] => [1,8,5,7,6,2,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,5,8,7,6,3] => [1,7,6,8,3,2,4,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,5,2,8,7,4,6] => [1,8,6,7,4,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,8,7,2,6,5] => [1,8,5,7,6,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,3,6,2,4,7,1,8] => [7,1,5,4,2,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,6,5,3,8,4,2] => [1,8,2,7,4,5,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,5,2,4,8,3] => [1,8,3,6,4,5,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,5,2,8,3,4] => [1,8,4,5,2,7,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,5,3,2,8,4] => [1,8,4,5,3,6,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,6,8,3,5,4] => [1,8,4,6,3,2,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,7,6,5,2,4,1,8] => [7,1,3,6,4,5,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,6,5,8,2,4,3] => [1,8,3,6,2,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,2,4,8,3,5] => [1,8,5,4,2,7,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,6,3,2,7,5,4] => [1,8,4,3,6,7,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,8,4,7,5,2] => [1,8,2,3,6,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,4,6,1,5,2,3,8] => [5,7,3,6,2,4,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[7,1,4,2,6,3,5,8] => [7,5,6,3,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,2,3,6,5,4,8] => [6,5,7,4,3,2,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,6,2,3,8,5,4,7] => [1,8,7,4,3,2,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,2,7,6,3,4] => [1,6,8,4,2,5,7,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,4,8,7,6,2,5] => [1,6,8,5,7,2,3,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,4,6,8,2,7,5,3] => [1,8,3,6,7,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,1,7,5,6,2,4,8] => [7,4,5,6,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,7,6,1,5,4,3,8] => [5,7,3,6,4,1,2,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[5,1,4,2,7,3,6,8] => [7,6,3,4,2,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,6,3,1,4,2,8] => [6,4,3,7,2,5,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[5,3,7,6,4,2,1,8] => [7,1,5,4,6,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,6,2,8,4,5,3] => [1,8,3,6,4,2,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,3,7,8,5,4] => [1,7,5,8,4,3,2,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[5,7,2,6,4,3,1,8] => [7,1,5,4,6,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,7,6,5,2,4,3] => [1,5,8,3,7,4,6,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,7,2,5,4,6,3] => [1,5,8,3,7,6,4,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,5,3,7,2,6,4] => [1,8,4,3,5,7,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,6,2,4,7,5,1,8] => [4,7,1,3,2,6,5,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,8,7,6,3,5,2,4] => [1,8,4,6,5,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,5,1,7,4,3,6,8] => [7,6,3,1,2,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,3,5,2,1,7,4,8] => [7,4,2,3,5,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,5,8,2,4,3,7] => [1,8,7,3,5,2,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,2,4,3,7,5] => [1,7,8,5,4,2,6,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,6,7,2,4,3,8,5] => [1,8,5,4,2,6,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,7,3,2,4,6] => [1,7,4,8,6,2,5,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,4,2,8,6,5,3] => [1,6,8,3,4,2,7,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,7,5,2,3,8,4] => [1,8,4,5,2,6,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,5,2,8,4,3,6] => [1,8,6,4,2,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,6,2,8,3,5] => [1,8,5,2,7,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,4,2,3,8,5,7] => [1,8,7,5,3,4,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,4,2,3,8,7,5] => [1,7,8,5,3,4,2,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,7,3,8,2,5,6] => [1,8,6,2,4,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,7,3,6,2,5,4] => [1,8,4,3,7,5,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,4,7,6,8,2,3] => [1,8,3,4,7,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,7,5,8,3,4] => [1,5,8,4,7,3,2,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,4,6,5,7,2,3] => [1,5,8,3,4,6,7,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,2,6,5,7,3,4] => [1,5,8,4,6,7,3,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,2,7,6,8,3,4] => [1,8,4,7,3,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,8,4,5,2,3] => [1,7,2,8,3,6,5,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,6,8,2,4,3,5] => [1,8,5,2,7,3,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,5,2,6,8,4] => [1,6,8,4,5,2,3,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,7,5,3,2,8,6,4] => [1,8,4,3,5,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,4,1,5,3,2,6,8] => [7,6,2,4,5,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,4,1,5,3,6,2,8] => [6,7,2,4,5,3,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[2,6,4,7,3,5,1,8] => [7,1,2,6,5,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,4,2,7,5,6,1,8] => [5,6,7,1,3,2,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 3
[1,3,8,2,6,4,5,7] => [1,8,7,5,6,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,3,5,4,8,6] => [1,5,8,6,4,3,2,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,3,8,2,4,5,7,6] => [1,7,8,6,5,4,2,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,8,2,3,5,4,6,7] => [1,5,8,7,6,4,3,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,7,8,2,5,3,6,4] => [1,5,8,4,2,7,6,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,2,3,6,4,5,7] => [1,8,7,5,6,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,3,4,6,7,5] => [1,6,7,8,5,4,3,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,7,8,2,4,3,6,5] => [1,8,5,4,2,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,6,5,3,7,4,1,8] => [7,1,2,6,4,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,2,8,7,3,4,6] => [1,8,6,3,2,5,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,2,7,3,5,6] => [1,7,5,8,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[2,6,5,7,1,4,3,8] => [7,3,5,1,2,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,1,2,6,7,5,3,8] => [7,3,2,1,4,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,1,6,7,5,2,3,8] => [5,7,3,6,2,1,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,3,8,6,2,7,5,4] => [1,8,4,6,7,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,7,4,3,8,6] => [1,8,6,3,2,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,2,6,8,5,3] => [1,8,3,4,2,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,3,5,2,7,1,6,8] => [7,6,1,4,2,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,4,1,3,7,2,6,8] => [7,6,2,4,3,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,8,7,3,5,2,6] => [1,7,2,4,8,6,5,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,4,8,3,7,5,6,2] => [1,7,6,5,8,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,3,4,8,2,6,5,7] => [1,6,8,7,5,2,3,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,4,7,2,3,8,5] => [1,8,5,2,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,4,7,3,2,1,6,8] => [7,6,1,5,2,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,3,7,6,2,1,4,8] => [7,4,6,1,5,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,5,2,7,1,4,3,8] => [7,3,2,5,1,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,7,8,4,6,2,3] => [1,6,8,3,7,2,5,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,5,7,8,6,2,4] => [1,6,8,4,7,2,3,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,5,2,7,8,6,3,4] => [1,6,8,4,7,3,2,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,7,5,2,8,3,4] => [1,7,3,8,4,5,2,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,5,6,8,3,2,7] => [1,8,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,6,5,8,2,7] => [1,5,8,7,2,3,4,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,7,8,3,5,4,6,2] => [1,5,8,2,7,6,4,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,7,6,5,3,2,4] => [1,5,8,4,6,3,7,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,7,6,3,2,5,8,4] => [1,8,4,3,6,5,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,3,6,2,7,4] => [1,7,8,4,3,5,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,2,5,8,3,7,6] => [1,7,8,6,3,2,4,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,2,5,8,7,3,6] => [1,8,6,7,3,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,2,6,7,4,5] => [1,8,5,6,7,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,7,8,4,6,3] => [1,7,6,4,8,3,2,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,3,6,2,4,8,7,5] => [1,7,8,5,4,2,3,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,3,7,6,2,8,4,5] => [1,8,5,2,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,7,2,6,1,5,4,8] => [7,4,6,5,1,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,2,3,6,4,8,5] => [1,8,5,6,4,3,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,5,3,4,7,6] => [1,7,8,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,8,2,3,6,4,7,5] => [1,7,8,5,6,4,3,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,3,5,2,8,4,7,6] => [1,7,8,6,4,2,3,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,8,2,7,3,4,6,5] => [1,7,6,4,8,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,5,8,2,3,7,4,6] => [1,8,6,7,4,2,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,2,3,5,4,7] => [1,8,7,4,2,6,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,5,2,8,4,7] => [1,8,7,4,5,2,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,3,6,2,4,7] => [1,8,7,4,3,5,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,3,2,7,4,5] => [1,8,5,2,6,7,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,2,5,7,8,4] => [1,5,8,4,2,3,6,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,4,6,3,5,7,8,2] => [1,5,8,2,4,3,6,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,3,6,5,2,7,8,4] => [1,8,4,5,2,3,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,5,6,8,2,4] => [1,7,2,3,8,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[7,1,6,2,3,4,5,8] => [7,5,3,6,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,8,3,4,5,6,2] => [1,8,2,7,6,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,8,4,5,7,3] => [1,7,8,3,2,6,5,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[2,7,6,1,3,4,5,8] => [7,5,3,6,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,6,2,3,4,5,7] => [1,8,7,5,3,6,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,3,5,1,7,4,2,8] => [6,4,1,7,2,3,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,1,6,3,4,2,5,8] => [7,5,4,3,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,5,3,6,8,4,2] => [1,8,2,7,4,3,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,7,5,2,6,3,1,8] => [6,3,5,7,1,4,2,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,3,4,7,6,2,8,5] => [1,8,5,6,2,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,3,8,6,5,4] => [1,6,8,4,3,2,7,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[6,5,4,2,7,3,1,8] => [7,1,6,3,4,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,4,1,7,2,6,3,8] => [6,7,3,1,5,2,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[7,1,6,2,5,4,3,8] => [5,7,3,6,4,2,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,7,6,8,3,2,4,5] => [1,8,5,3,6,2,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,6,5,3,2,4,7] => [1,8,7,4,5,3,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,5,4,7,1,6,2,8] => [6,7,2,5,1,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,8,2,7,4,3,5,6] => [1,7,5,4,8,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,4,2,6,3,5,7] => [1,8,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,1,7,3,2,5,6,8] => [7,6,5,2,1,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,6,7,1,3,5,4,8] => [7,4,1,2,6,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,1,5,7,6,2,3,8] => [7,3,5,6,2,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,6,7,2,1,4,5,8] => [6,4,2,7,5,1,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[5,1,4,6,7,2,3,8] => [7,3,4,6,2,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,5,4,6,7,1,3,8] => [7,3,4,6,1,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,6,5,2,1,4,3,8] => [6,4,2,7,3,5,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,3,4,1,6,2,5,8] => [7,5,6,2,3,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,4,1,6,5,2,8] => [6,5,7,2,3,4,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[7,3,4,1,5,6,2,8] => [5,6,7,2,3,4,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 3
[7,6,5,4,1,3,2,8] => [4,7,2,6,3,5,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[7,3,4,1,5,2,6,8] => [5,7,6,2,3,4,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,7,4,6,2,8,5,3] => [1,7,5,2,8,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,3,4,5,8,7,2,6] => [1,8,6,7,2,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,6,5,8,3,2] => [1,5,8,2,7,3,4,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,3,4,5,8,6,2,7] => [1,6,8,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,4,5,8,2,7,6] => [1,7,8,6,2,3,4,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,8,7,2,4,5,6,3] => [1,8,3,7,6,5,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,1,6,3,2,5,4,8] => [7,4,3,6,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,4,2,1,6,5,3,8] => [6,5,7,3,2,4,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[7,4,1,3,5,2,6,8] => [5,7,6,2,4,3,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[7,3,1,2,4,6,5,8] => [6,7,5,4,2,3,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,8,6,7,4,2,5,3] => [1,7,5,4,8,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,2,7,4,3,6,5] => [1,8,5,4,7,6,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,3,2,7,6,4] => [1,7,6,8,4,3,5,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,8,4,5,2,6,7,3] => [1,6,7,8,3,4,5,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,8,5,2,4,6,3,7] => [1,6,8,7,3,5,4,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,8,4,2,3,5,7,6] => [1,7,8,6,5,3,4,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[2,3,4,5,6,7,8,9,10,1,11] => [10,1,2,3,4,5,6,7,8,9,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1111111111000000000010 => 1
[1,3,4,5,6,7,8,9,10,11,2] => [1,11,2,3,4,5,6,7,8,9,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 1
[1,3,4,8,2,7,5,6] => [1,8,6,7,5,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,7,5,2,6,1,3,8] => [7,3,5,6,1,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,2,7,4,8,3,5] => [1,8,5,4,7,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,6,5,1,4,2,3,8] => [6,2,7,3,5,4,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[7,6,5,1,2,4,3,8] => [7,3,5,2,6,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,7,4,2,5,3,1,8] => [5,7,1,6,3,4,2,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,8,2,5,3,7,6,4] => [1,7,6,8,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[3,1,5,2,7,4,8,6,9] => [8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 1
[3,6,7,2,5,1,4,8] => [5,7,4,2,6,1,3,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,6,5,2,4,8,7,3] => [1,7,8,3,5,4,2,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[2,7,6,1,3,5,4,8] => [6,5,3,7,4,1,2,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,4,6,3,8,5,7,2] => [1,7,8,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,6,2,5,8,4,3,7] => [1,8,7,3,2,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,7,6,3,2,5,4] => [1,7,5,3,8,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,7,6,3,2,4,5] => [1,8,5,3,7,4,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,3,5,1,7,2,4,8] => [7,4,1,6,2,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,4,7,6,1,5,8] => [7,5,6,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,4,5,2,7,3,6] => [1,8,6,7,3,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,5,2,7,6,3] => [1,7,6,8,3,4,5,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[6,3,5,4,7,2,1,8] => [4,7,1,6,2,3,5,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,8,4,5,2,6,3,7] => [1,6,8,7,3,4,5,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[2,3,4,7,5,1,6,8] => [5,7,6,1,2,3,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[2,3,4,7,1,6,5,8] => [6,7,5,1,2,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,8,4,5,2,3,6,7] => [1,8,7,6,3,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,6,1,7,3,5,2,8] => [7,2,6,5,3,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,1,6,7,4,2,3,8] => [7,3,6,2,1,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,7,2,1,5,3,4,8] => [5,7,4,1,6,3,2,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[2,7,4,1,6,5,3,8] => [6,5,7,3,4,1,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[2,6,4,1,7,5,3,8] => [7,3,4,1,2,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,4,5,2,8,7,3] => [1,7,8,3,4,5,2,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,7,4,8,6,3,2,5] => [1,7,2,8,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,8,3,6,7,5,2] => [1,7,5,6,8,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[2,7,1,5,6,3,4,8] => [7,4,5,6,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,6,7,5,2,1,4,8] => [7,4,5,2,6,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,5,6,4,2,3,8] => [7,3,5,4,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,4,6,2,5,3,7] => [1,8,7,3,4,6,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,3,1,5,6,2,4,8] => [7,4,5,6,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,7,5,1,6,2,4,8] => [7,4,1,3,5,6,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,4,2,3,5,6,8] => [7,6,5,3,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,5,1,2,3,7,4,8] => [7,4,2,5,3,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,7,4,1,2,5,3,8] => [7,3,4,1,6,5,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,8,2,5,7,4,6] => [1,5,8,6,7,4,2,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,4,8,3,2,5,7,6] => [1,7,8,6,5,2,4,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[3,6,2,7,1,4,5,8] => [7,5,1,3,2,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,6,7,3,4,8,2] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,5,8,6,4,2] => [1,6,8,2,3,7,4,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,5,4,8,3,7,6,2] => [1,7,6,8,2,5,3,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[3,1,6,5,2,7,4,8] => [7,4,5,2,1,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,7,4,2,1,5,6,8] => [7,6,5,1,3,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,1,7,5,6,3,2,8] => [7,2,1,4,5,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,7,2,3,5,4,6] => [1,8,6,5,3,7,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,7,2,5,3,4,6] => [1,5,8,6,3,7,4,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[5,6,2,1,3,7,4,8] => [7,4,1,5,3,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,3,6,1,2,7,4,8] => [7,4,1,5,2,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,7,6,1,5,2,4,8] => [5,7,4,1,3,6,2,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,6,4,8,7,5,3,2] => [1,8,2,6,5,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,7,6,2,5,4] => [1,8,4,7,5,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,6,2,3,4,7] => [1,8,7,4,6,3,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,4,7,2,8,3,5] => [1,7,3,4,8,5,2,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,5,7,2,3,4,6] => [1,7,4,8,6,3,5,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[2,4,1,7,5,3,6,8] => [5,7,6,3,1,2,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[6,3,7,2,4,5,1,8] => [7,1,6,5,4,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,3,7,2,5,4,1,8] => [5,7,1,6,4,2,3,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,7,6,3,4,2,8,5] => [1,8,5,4,3,6,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,6,3,2,5,7,4] => [1,7,8,4,3,6,5,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[4,1,6,3,7,5,2,8] => [7,2,1,4,3,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,6,7,8,5,2,4] => [1,8,4,7,2,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,7,6,8,2,4] => [1,8,4,7,2,3,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,7,4,6,8,2] => [1,6,8,2,3,5,4,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,5,7,8,4,6,2] => [1,7,6,4,8,2,3,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,3,5,7,8,4,2,6] => [1,8,6,4,7,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,2,7,8,6,4] => [1,8,4,2,3,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,7,8,2,6,4] => [1,8,4,7,6,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,2,5,4,8,6] => [1,5,8,6,4,2,3,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,4,7,3,5,2,8,6] => [1,5,8,6,2,4,3,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,3,7,5,2,4,8,6] => [1,8,6,4,5,2,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,2,8,7,6,4] => [1,7,6,8,4,2,3,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,6,2,8,7,5,4] => [1,8,4,2,3,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,2,8,6,5,4] => [1,6,8,4,2,3,7,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,4,8,7,3,5,2] => [1,7,5,8,2,6,3,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[5,4,7,6,2,3,1,8] => [7,1,5,2,4,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,7,2,3,6,5,1,8] => [6,5,7,1,4,3,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[4,6,2,3,5,7,1,8] => [5,7,1,4,3,2,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,5,7,2,8,4,3,6] => [1,7,3,8,6,4,2,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,5,8,2,7,4,3,6] => [1,8,6,4,2,5,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,3,4,8,6,5] => [1,8,5,4,3,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,3,4,7,6,5] => [1,7,6,8,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,8,7,3,5,4,2,6] => [1,5,8,6,4,3,7,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,7,2,3,4,6,8,5] => [1,6,8,5,4,3,2,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,2,3,4,8,7,5] => [1,7,8,5,4,3,2,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,8,7,6,4,2,3,5] => [1,7,3,8,5,4,6,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,7,2,6,8,5,4] => [1,8,4,2,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,3,7,2,6,5,1,8] => [6,5,7,1,4,2,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[3,4,6,1,5,7,2,8] => [5,7,2,4,1,3,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,3,6,5,7,8,2,4] => [1,8,4,5,7,2,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,7,2,6,8,3] => [1,6,8,3,5,2,4,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,5,8,7,3,2,6,4] => [1,8,4,7,6,2,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,6,1,2,7,5,3,8] => [7,3,1,4,2,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,1,4,2,7,5,3,8] => [7,3,4,2,1,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,6,4,2,1,5,3,8] => [7,3,4,2,6,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,8,5,6,3,4,2] => [1,8,2,7,4,5,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,8,6,3,4,2] => [1,8,2,5,6,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,8,3,6,4,2] => [1,6,8,2,5,3,7,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,7,8,5,3,6,4,2] => [1,6,8,2,7,4,5,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,4,2,8,7,5,3] => [1,8,3,4,2,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,2,4,7,6,5] => [1,7,6,8,5,4,2,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,6,2,3,8,7,5,4] => [1,8,4,3,2,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,3,8,7,6,4] => [1,7,6,8,4,3,2,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[7,5,2,6,4,1,3,8] => [7,3,2,5,4,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,5,2,8,3,7,4] => [1,7,8,4,2,6,3,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[2,7,6,3,1,4,5,8] => [6,4,3,7,5,1,2,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,8,2,7,3,6,5,4] => [1,6,8,4,7,5,3,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[3,4,2,7,1,5,6,8] => [7,6,5,1,3,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,2,5,8,6,7,3] => [1,6,7,8,3,2,4,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[2,6,4,5,7,1,3,8] => [6,1,2,7,3,4,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,8,4,2,3,5,6,7] => [1,8,7,6,5,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,6,7,5,2,4] => [1,8,4,6,5,7,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,8,4,7,5,3] => [1,8,3,2,6,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,5,7,2,6,4] => [1,8,4,5,7,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,7,2,3,6,4,5] => [1,6,8,5,3,7,4,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,5,2,8,6,7,4,3] => [1,8,3,2,5,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,2,3,6,5,4] => [1,6,8,4,2,7,5,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,7,4,8,6,2,3,5] => [1,8,5,6,2,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,5,2,8,6,3,4] => [1,6,8,4,2,7,3,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[6,7,1,3,2,5,4,8] => [7,4,3,1,6,5,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,7,2,4,3,5,1,8] => [4,7,1,6,5,3,2,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[6,7,2,3,1,5,4,8] => [6,5,1,7,4,3,2,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[2,4,1,6,5,7,3,8] => [5,7,3,1,2,4,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[2,5,1,6,4,7,3,8] => [7,3,1,2,5,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,6,2,4,3,7,1,8] => [4,7,1,5,3,2,6,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[4,5,2,6,1,7,3,8] => [7,3,2,5,1,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,6,5,7,1,3,2,8] => [7,2,6,3,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,5,2,6,4,7,1,8] => [7,1,3,2,5,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,4,2,6,1,7,5,8] => [7,5,1,3,2,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,7,2,8,5,6,4] => [1,8,4,2,3,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,8,4,2,6,3] => [1,8,3,7,6,2,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,3,6,2,1,7,5,8] => [7,5,1,4,2,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,6,1,4,7,5,3,8] => [4,7,3,1,2,6,5,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[5,1,6,3,7,4,2,8] => [6,4,3,7,2,1,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[2,6,1,3,7,5,4,8] => [7,4,3,1,2,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,4,1,6,2,7,3,8] => [7,3,1,5,2,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,4,2,1,5,6,3,8] => [5,6,7,3,2,4,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 3
[4,3,7,2,5,6,1,8] => [5,6,7,1,4,2,3,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 3
[6,7,1,4,3,2,5,8] => [4,7,5,3,1,6,2,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[2,5,6,4,7,1,3,8] => [4,7,3,6,1,2,5,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,7,5,3,8,2,6,4] => [1,7,6,2,8,4,3,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,2,7,4,5,3,6] => [1,8,6,5,4,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,6,2,7,1,5,3,8] => [7,3,2,6,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,7,1,6,2,5,3,8] => [7,3,1,4,6,5,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,5,6,4,7,2,3] => [1,8,3,5,4,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,2,7,3,6,4] => [1,8,4,2,5,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,8,7,2,3,6] => [1,7,3,5,8,6,2,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,4,5,8,6,2,3,7] => [1,8,7,3,5,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,8,6,2,7,3] => [1,7,8,3,5,6,2,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,6,7,2,3,5,8,4] => [1,8,4,2,6,5,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,2,3,5,7,4] => [1,7,8,4,2,6,5,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,5,7,6,2,8,3] => [1,8,3,5,6,2,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,7,2,3,8,5,4] => [1,7,5,3,8,4,2,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,7,2,8,4,5,6,3] => [1,8,3,2,7,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,6,1,7,3,2,5,8] => [6,2,7,5,3,1,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[6,1,2,3,7,5,4,8] => [7,4,3,2,1,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,8,3,4,7,6,2] => [1,7,6,8,2,5,4,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[7,1,2,3,5,6,4,8] => [5,6,7,4,3,2,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 3
[5,1,2,3,7,6,4,8] => [6,7,4,3,2,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,8,2,5,6,3,4,7] => [1,8,7,4,5,6,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,5,3,6,7,4] => [1,6,7,8,4,5,3,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,5,2,6,4,7,8,3] => [1,8,3,2,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,7,6,2,5,4,3] => [1,8,3,7,4,6,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,5,6,2,1,7,4,8] => [7,4,2,5,1,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,6,2,4,7,3,5] => [1,7,3,6,8,5,4,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,6,3,4,7,2,5] => [1,8,5,4,3,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,4,2,5,1,6,3,8] => [6,7,3,2,4,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[7,3,6,5,2,1,4,8] => [7,4,5,2,3,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,3,7,5,2,1,4,8] => [6,1,7,4,5,2,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[2,5,7,6,3,1,4,8] => [7,4,6,1,2,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,5,2,1,4,6,8] => [7,6,4,2,3,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,4,2,3,6,7,5] => [1,6,7,8,5,3,4,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[4,7,5,2,1,6,3,8] => [6,7,3,5,1,4,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[4,3,1,6,2,7,5,8] => [7,5,2,3,1,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,4,2,7,3,1,5,8] => [6,1,7,5,3,2,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,4,7,5,6,8,2,3] => [1,8,3,7,2,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,5,8,2,4,6] => [1,8,6,2,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,2,6,7,3,5] => [1,8,5,6,7,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,5,3,8,2,4,6] => [1,8,6,2,7,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,5,8,3,2,6] => [1,7,2,8,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,5,8,3,7,4,2,6] => [1,7,2,5,8,6,4,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,7,4,2,5,3,8,6] => [1,5,8,6,3,4,2,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,6,5,3,7,2,4] => [1,8,4,5,3,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,4,6,7,8,2,3] => [1,7,2,5,8,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[2,6,5,1,4,7,3,8] => [7,3,5,4,1,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,7,8,3,4,6,2] => [1,8,2,5,3,7,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,6,3,4,8,2,7] => [1,8,7,2,5,4,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,8,7,5,3,6] => [1,8,6,5,7,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,1,6,5,3,2,4,8] => [7,4,5,3,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,6,4,2,5,3,8] => [4,7,3,6,5,2,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,7,4,2,5,8,6,3] => [1,5,8,3,4,2,7,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,5,2,7,4,6,3] => [1,8,3,5,7,6,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,6,3,8,5,2] => [1,8,2,7,5,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,7,5,6,2,3,4] => [1,7,3,8,4,5,6,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,8,6,7,5,2,3,4] => [1,5,8,4,7,3,6,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,7,4,2,6,3,8,5] => [1,8,5,6,3,4,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,7,6,2,4,5,1,8] => [7,1,3,6,5,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,3,6,1,7,2,4,8] => [6,2,3,7,4,1,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[6,1,2,7,5,4,3,8] => [5,7,3,2,1,6,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[5,7,4,1,2,6,3,8] => [6,7,3,4,1,5,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,3,4,8,7,5,2,6] => [1,8,6,5,7,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,3,6,2,8,5] => [1,8,5,6,2,4,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,3,1,2,5,7,4,8] => [5,7,4,2,3,1,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[7,1,4,2,6,5,3,8] => [6,5,7,3,4,2,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[3,5,2,7,6,4,1,8] => [7,1,3,2,5,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,3,7,6,2,4,1,8] => [6,4,7,1,5,2,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[3,5,7,2,6,1,4,8] => [7,4,2,5,6,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,5,7,2,1,6,4,8] => [6,7,4,2,5,1,3,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[5,3,7,1,6,2,4,8] => [7,4,1,5,6,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,5,7,1,4,6,2,8] => [6,7,2,5,4,1,3,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[3,5,4,2,7,1,6,8] => [7,6,1,3,4,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,1,4,5,6,7,8,2,9] => [8,2,1,3,4,5,6,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 1
[7,3,1,2,5,4,6,8] => [5,7,6,4,2,3,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[5,3,1,2,7,4,6,8] => [7,6,4,2,3,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,1,5,2,4,6,8] => [7,6,4,5,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,7,1,3,2,4,6,8] => [7,6,4,3,1,5,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,1,7,2,5,4,6,8] => [5,7,6,4,2,1,3,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[3,1,7,5,2,4,6,8] => [7,6,4,5,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,5,3,2,4,6,8] => [7,6,4,3,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,9,2,4,5,6,7,8] => [1,9,8,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 1
[1,7,2,3,6,8,5,4] => [1,8,4,3,2,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,4,5,8,3,2,7] => [1,8,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,6,2,7,1,3,5,8] => [6,3,2,7,5,1,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,5,4,7,3,6,8,2] => [1,6,8,2,5,3,4,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[4,6,2,7,3,1,5,8] => [7,5,3,2,6,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,4,6,7,2,5,3] => [1,7,5,8,3,4,6,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,8,2,7,6,4,3,5] => [1,8,5,6,4,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,7,5,3,6,4] => [1,5,8,4,7,6,3,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[7,4,1,6,3,5,2,8] => [7,2,4,6,5,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,4,7,5,3,8,2] => [1,5,8,2,6,3,4,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[6,3,5,2,7,4,1,8] => [7,1,6,4,2,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,5,7,2,6,3,1,8] => [7,1,4,2,5,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,5,8,2,7,3,6] => [1,8,6,7,3,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,7,4,2,6,3] => [1,8,3,5,4,7,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,8,7,3,5,6,2] => [1,8,2,4,7,6,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,6,7,2,5,3,1,8] => [5,7,1,4,2,6,3,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,4,7,8,2,6,5,3] => [1,6,8,3,7,5,2,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,7,8,3,5,2,4,6] => [1,5,8,6,2,7,4,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,6,4,2,7,8,3,5] => [1,8,5,7,3,4,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,6,5,8,4,3] => [1,5,8,3,2,7,4,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,2,8,4,6,7,3] => [1,6,7,8,3,2,5,4] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,5,2,7,4,6,8,3] => [1,6,8,3,2,5,4,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[6,1,7,2,3,5,4,8] => [7,4,2,1,6,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,6,2,4,5,7,3] => [1,7,8,3,6,5,4,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,8,6,2,4,5,3,7] => [1,8,7,3,6,5,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,1,6,2,3,5,4,8] => [6,5,3,7,4,2,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,3,4,8,7,5,6,2] => [1,7,6,5,8,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,5,6,8,3,7,4,2] => [1,8,2,5,3,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,5,2,4,6,7] => [1,8,7,6,4,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,7,8,5,3,4] => [1,8,4,7,3,2,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,7,6,3,2,4,1,8] => [6,4,3,7,1,5,2,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,7,8,2,3,5,6,4] => [1,8,4,2,7,6,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,3,2,8,4,5] => [1,8,5,2,7,4,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,4,2,1,7,3,6,8] => [7,6,3,2,4,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,7,2,1,4,5,6,8] => [7,6,5,4,1,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,6,5,8,4,2,3] => [1,7,2,8,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[5,7,2,3,6,1,4,8] => [6,1,5,7,4,3,2,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[4,7,2,3,1,5,6,8] => [7,6,5,1,4,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,2,3,8,6,4,7] => [1,6,8,7,4,3,2,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,8,7,5,2,3,6,4] => [1,7,6,3,8,4,5,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,4,5,3,8,2,6,7] => [1,8,7,6,2,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,7,4,8,5,3] => [1,7,5,4,8,3,2,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,6,5,7,4,8,2,3] => [1,8,3,5,4,7,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,6,8,2,3,4] => [1,7,3,8,4,6,2,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,2,5,3,8,6,4] => [1,8,4,5,3,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,6,2,7,4,3,1,8] => [6,3,2,7,1,5,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,5,8,7,4,3,6,2] => [1,8,2,5,4,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,6,2,3,5,4] => [1,7,5,2,8,4,6,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[8,3,1,2,4,5,6,7,9] => [8,7,6,5,4,2,3,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 1
[1,8,5,2,4,7,6,3] => [1,7,6,8,3,5,4,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,6,8,5,2,3,7] => [1,5,8,7,3,6,2,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,7,4,8,2,5,3,6] => [1,8,6,5,2,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,4,7,3,2,5,1,8] => [7,1,6,5,2,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,4,8,6,3,7,2] => [1,7,8,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[3,1,6,4,7,5,2,8] => [4,7,2,1,3,6,5,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[3,6,2,7,5,4,1,8] => [5,7,1,3,2,6,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[2,5,7,3,4,1,6,8] => [7,6,1,2,5,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,8,5,2,7,4,6] => [1,8,6,7,4,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,6,7,2,4,5] => [1,8,5,7,4,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,7,6,2,4,5] => [1,7,4,8,5,6,2,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,7,8,6,2,3,5] => [1,7,3,8,5,6,2,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,5,6,8,2,3,4] => [1,8,4,6,2,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,6,8,7,2,3,5] => [1,8,5,7,3,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,5,7,3,2,4] => [1,8,4,5,7,2,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,7,4,1,5,3,6,8] => [5,7,6,3,4,1,2,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[2,5,7,4,3,1,6,8] => [4,7,6,1,2,5,3,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[5,3,4,1,7,2,6,8] => [7,6,2,3,4,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,5,3,2,6,4,8] => [6,7,4,3,5,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[7,1,6,3,5,2,4,8] => [5,7,4,3,6,2,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[2,3,7,6,1,5,4,8] => [7,4,6,5,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,4,1,7,2,5,3,8] => [7,3,1,6,5,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,6,7,5,1,2,4,8] => [6,2,7,4,5,1,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,6,2,5,3,8,7,4] => [1,7,8,4,5,3,2,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,8,2,6,3,7,5,4] => [1,8,4,6,7,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,6,4,8,5,3] => [1,8,3,2,7,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,7,4,8,6,3] => [1,8,3,2,5,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,8,4,7,6,3] => [1,7,6,8,3,2,5,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,4,8,3,6,5,2] => [1,6,8,2,7,5,3,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,5,6,3,8,2,4,7] => [1,8,7,4,3,6,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,8,3,2,6,5] => [1,7,6,2,8,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,7,4,5,6,8,2,3] => [1,7,2,8,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,4,5,6,7,9,8,2] => [1,8,9,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 2
[1,8,7,2,3,4,5,6] => [1,7,5,3,8,6,4,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,2,3,7,4,5,6] => [1,7,5,8,6,4,3,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,5,8,2,3,4,6] => [1,8,6,3,5,2,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,7,5,2,3,4,6] => [1,8,6,3,7,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,9,1,3,4,5,6,7,8,10] => [9,8,7,6,5,4,3,1,2,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11111111100000000010 => 1
[7,4,6,1,3,2,5,8] => [7,5,3,6,2,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,7,4,5,6,2,1,8] => [7,1,3,4,5,6,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,5,2,6,7,3,1,8] => [7,1,4,6,3,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,2,5,6,3,4,8] => [7,4,5,6,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,6,3,5,7,2,4] => [1,5,8,4,3,6,7,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,7,6,8,5,2,4,3] => [1,5,8,3,6,2,7,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,4,8,6,3,2,7] => [1,8,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,3,6,7,4,2] => [1,8,2,5,6,7,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,5,6,7,3,4] => [1,8,4,5,6,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,4,8,7,2,3,6] => [1,8,6,2,5,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,8,5,4,2,7] => [1,5,8,7,2,3,6,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,2,3,6,7,5,4] => [1,7,5,6,8,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,5,4,8,3,6,2,7] => [1,6,8,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,6,8,4,5,2,7] => [1,8,7,2,3,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,3,2,6,8,5] => [1,6,8,5,2,4,3,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,4,5,7,8,2,3] => [1,8,3,4,5,7,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,4,2,7,6,3,1,8] => [7,1,5,6,3,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,6,7,3,8,2,4] => [1,8,4,7,2,5,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,6,4,8,5,2] => [1,8,2,3,7,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,5,6,1,4,3,2,8] => [6,3,7,2,5,4,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,8,6,3,4,2,5,7] => [1,8,7,5,4,3,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,6,3,4,2,7,5] => [1,7,8,5,4,3,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[5,3,1,7,4,6,2,8] => [6,7,2,3,1,5,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[2,7,5,1,4,6,3,8] => [6,7,3,5,4,1,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,7,2,8,4,3,5,6] => [1,8,6,3,2,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,6,3,7,8,2,4] => [1,7,2,5,8,4,3,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[7,3,1,2,5,6,4,8] => [5,6,7,4,2,3,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 3
[1,8,5,3,2,6,4,7] => [1,6,8,7,4,3,5,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[3,6,7,1,5,4,2,8] => [5,7,2,6,4,1,3,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,4,7,6,3,8,5,2] => [1,7,5,3,8,2,4,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,4,2,7,6,3,5] => [1,6,8,5,7,3,4,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[2,6,1,7,5,4,3,8] => [5,7,3,1,2,6,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[6,4,7,1,5,3,2,8] => [5,7,2,4,1,6,3,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,8,2,6,7,3,4,5] => [1,8,5,7,4,6,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,8,6,4,7,2] => [1,7,8,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[5,1,7,6,3,4,2,8] => [6,4,7,2,1,5,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,5,6,8,4,2,3,7] => [1,8,7,3,6,2,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,4,2,6,8,7,3] => [1,7,8,3,4,2,5,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,7,2,3,5,8,6,4] => [1,5,8,4,3,2,7,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,2,3,7,5,6,4] => [1,7,6,5,8,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,6,7,8,2,4,3,5] => [1,7,3,8,5,2,6,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,2,5,6,8,3,4] => [1,7,3,2,8,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,5,8,2,6,7,3,4] => [1,8,4,2,5,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,3,6,7,4,5] => [1,8,5,6,7,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,8,2,6,7,5] => [1,6,7,8,5,2,3,4] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,7,5,6,2,3,8,4] => [1,8,4,6,3,5,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,7,4,1,6,3,5,8] => [7,5,6,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,6,5,3,2,7,4] => [1,7,8,4,5,3,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,8,6,2,3,7,4,5] => [1,8,5,3,6,7,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,8,2,7,4,5] => [1,8,5,2,3,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,8,5,4,3,7] => [1,5,8,7,3,2,6,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,4,8,3,2,5,6,7] => [1,8,7,6,5,2,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,5,8,3,4,6] => [1,8,6,3,2,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,6,4,5,7,3,1,8] => [7,1,2,6,3,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,6,7,4,5,8,2] => [1,8,2,3,6,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,5,6,8,3,4,2] => [1,8,2,7,4,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,5,2,8,6,4] => [1,8,4,5,2,3,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,3,6,4,8,2] => [1,8,2,5,6,4,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,6,8,4,2,7,3] => [1,7,8,3,6,2,5,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[4,7,1,2,6,3,5,8] => [7,5,6,3,1,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,5,7,2,3,6,1,8] => [6,7,1,4,2,5,3,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,7,5,8,4,2,6,3] => [1,7,6,2,8,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[3,6,7,1,2,5,4,8] => [6,5,2,7,4,1,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,3,8,2,4,7,5,6] => [1,8,6,7,5,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,4,2,1,7,6,3,8] => [6,7,3,2,4,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,6,7,3,5,4,8,2] => [1,5,8,2,6,4,3,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,2,8,4,3,7,6] => [1,7,8,6,3,2,5,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,6,7,2,5,8,4,3] => [1,5,8,3,7,4,2,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,2,7,6,4,8,3] => [1,8,3,2,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,5,3,2,8,7,4] => [1,7,8,4,3,5,2,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[5,3,1,7,6,4,2,8] => [7,2,3,1,5,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,2,6,4,3,5,7] => [1,8,7,5,4,6,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[8,1,2,3,4,5,7,6,9] => [7,8,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 111111101000000010 => 2
[7,1,2,3,5,4,6,8] => [5,7,6,4,3,2,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,9,2,3,4,5,6,8,7] => [1,8,9,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 2
[9,1,2,3,4,5,6,8,7,10] => [8,9,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 11111111010000000010 => 2
[7,1,2,6,4,5,3,8] => [6,5,4,7,3,2,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,1,2,4,3,5,6,8] => [4,7,6,5,3,2,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,9,2,3,4,5,7,6,8] => [1,7,9,8,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 101111110110000000 => 2
[1,5,7,3,6,8,2,4] => [1,8,4,3,7,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,8,6,7,3,2,5] => [1,8,5,7,2,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,7,5,4,2,6] => [1,5,8,6,4,7,2,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[4,7,2,5,3,6,1,8] => [6,7,1,4,5,3,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[7,1,2,5,3,4,6,8] => [7,6,4,5,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,7,3,2,8,4,5] => [1,7,4,3,8,5,2,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,5,7,3,8,2,4,6] => [1,7,4,3,8,6,2,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,6,2,7,4,5,3] => [1,7,5,8,3,6,4,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,5,6,2,8,4,3,7] => [1,8,7,3,6,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,4,6,3,1,7,5,8] => [7,5,1,2,4,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,8,5,6,7,3,2] => [1,8,2,4,5,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,2,7,5,6,4] => [1,7,6,5,8,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,5,8,7,3,4,6,2] => [1,7,6,4,8,2,5,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,7,8,5,2,6,3,4] => [1,6,8,4,5,2,7,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,7,6,8,4,2,5,3] => [1,8,3,6,2,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,3,8,6,2,4] => [1,6,8,4,3,7,2,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,5,7,8,4,2,3,6] => [1,7,3,8,6,2,5,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,5,7,8,3,6,2] => [1,8,2,4,7,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,6,3,2,7,5] => [1,7,8,5,3,4,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[2,5,7,1,6,3,4,8] => [7,4,1,2,5,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,7,3,2,6,5,4] => [1,6,8,4,3,7,5,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,7,2,5,8,4,3,6] => [1,7,3,2,8,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,7,2,8,6,4,5,3] => [1,8,3,2,7,5,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,6,4,7,2,5] => [1,8,5,4,6,7,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,7,8,4,5,2,3] => [1,8,3,7,2,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,5,8,4,7,2,3] => [1,7,2,6,8,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[7,5,2,6,1,4,3,8] => [6,4,7,3,2,5,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,5,8,6,3,7,2,4] => [1,8,4,6,7,2,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,6,3,2,8,4] => [1,8,4,6,2,5,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,4,6,3,8,2,7] => [1,8,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,4,7,5,6,3,1,8] => [7,1,2,4,5,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,1,6,3,4,2,8] => [6,4,7,2,5,3,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,4,7,3,6,8,5,2] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,7,5,3,2,6] => [1,5,8,6,3,4,7,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[5,3,7,2,6,4,1,8] => [7,1,5,6,4,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,6,1,3,4,2,8] => [7,2,5,3,6,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,1,3,4,2,6,8] => [7,6,2,5,4,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,7,3,8,2,6,4] => [1,8,4,3,7,6,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,3,5,6,4,1,2,8] => [7,2,3,5,4,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,5,7,4,6,3,1,8] => [4,7,1,2,5,6,3,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,7,8,5,3,2,6,4] => [1,7,6,2,8,4,5,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,5,3,2,6,7,4] => [1,6,7,8,4,3,5,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,7,8,5,6,3,2,4] => [1,7,2,8,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,5,2,4,8,6,3] => [1,8,3,5,4,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,2,4,6,7,3] => [1,6,7,8,3,5,4,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,4,8,6,2,3,5,7] => [1,8,7,5,2,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,3,2,4,5,6] => [1,7,5,2,8,6,4,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,4,5,8,6,7,2,3] => [1,8,3,5,6,7,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,5,6,7,2,3] => [1,8,3,4,5,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,7,8,3,4,2,5] => [1,8,5,3,7,2,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,5,6,2,3,4] => [1,8,4,5,6,2,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,5,2,3,8,6] => [1,8,6,3,4,5,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,5,6,2,3,7] => [1,8,7,3,4,5,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,7,5,2,8,6] => [1,5,8,6,2,3,4,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[7,5,4,2,1,6,3,8] => [6,7,3,4,2,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,6,2,5,8,7,4,3] => [1,8,3,2,6,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,6,2,8,7,4,3] => [1,8,3,6,7,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,3,4,7,1,5,2,8] => [6,5,1,7,2,3,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[3,6,5,2,7,1,4,8] => [7,4,2,6,1,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,5,2,6,7,1,4,8] => [7,4,6,1,3,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,7,1,2,6,4,3,8] => [7,3,1,5,6,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,2,5,7,4,3,6] => [1,8,6,4,5,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,7,2,6,4,3,5] => [1,7,3,8,5,6,4,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,2,7,3,6,8,5] => [1,6,8,5,3,2,4,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,8,2,7,4,5,6] => [1,7,5,8,6,4,2,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,6,8,4,5,7,2] => [1,7,8,2,3,6,5,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[3,7,6,5,2,1,4,8] => [6,1,3,7,4,5,2,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,1,5,2,6,4,3,8] => [7,3,5,6,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,5,6,2,7,4,3] => [1,7,4,6,8,3,5,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,6,7,8,5,4,2,3] => [1,5,8,3,7,2,6,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,4,7,5,6,8,3,2] => [1,7,3,8,2,4,5,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,7,6,5,2,8,4] => [1,5,8,4,6,2,3,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,8,7,4,6,3,2] => [1,6,8,2,5,4,7,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,6,5,3,7,4,8,2] => [1,8,2,6,4,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,4,5,7,3,8,2] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,4,7,3,5,8,2] => [1,8,2,6,5,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,5,3,4,6,2] => [1,8,2,7,6,4,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,5,1,6,3,2,4,8] => [7,4,6,2,5,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,2,6,3,4,5,8] => [6,4,7,5,3,2,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[7,3,1,4,6,2,5,8] => [4,7,5,6,2,3,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,4,8,6,5,7,3,2] => [1,5,8,2,4,6,7,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,7,2,4,3,5,6] => [1,8,6,3,7,5,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,8,5,7,4,2] => [1,5,8,2,3,6,7,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[3,7,5,2,6,4,1,8] => [7,1,3,5,6,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,6,3,5,2,4,7] => [1,5,8,7,4,3,6,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[7,4,2,6,3,1,5,8] => [7,5,3,2,4,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,8,3,6,4,2,5] => [1,7,2,8,5,6,4,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,8,3,2,4,6,5] => [1,8,5,2,7,6,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,4,1,6,7,5,3,8] => [7,3,1,2,4,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,3,7,1,5,2,4,8] => [5,7,4,1,6,2,3,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,4,5,3,8,6,7,2] => [1,6,7,8,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,6,5,3,2,8,4,7] => [1,8,7,4,3,5,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,8,7,6,4,3] => [1,6,8,3,2,5,7,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,7,8,3,2,5,4,6] => [1,8,6,5,2,7,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,8,5,2,4,6] => [1,5,8,6,2,3,7,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,3,7,8,5,4,6,2] => [1,5,8,2,3,7,6,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,7,6,8,3,2,4] => [1,8,4,6,3,7,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,8,3,6,7,2,5] => [1,8,5,6,7,2,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,8,2,3,6,5] => [1,7,6,3,8,5,2,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[3,6,7,4,1,5,2,8] => [4,7,2,6,5,1,3,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,3,8,5,7,4,2,6] => [1,8,6,4,5,7,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,5,6,3,7,4,1,8] => [6,4,3,7,1,2,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[4,3,1,7,5,6,2,8] => [5,6,7,2,3,1,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 3
[1,4,8,5,3,2,6,7] => [1,8,7,6,2,4,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,6,4,2,7,5] => [1,7,8,5,4,6,2,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,3,5,8,4,2,7,6] => [1,7,8,6,2,3,5,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,7,5,8,4,2,3,6] => [1,8,6,2,7,3,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,5,6,2,7,3] => [1,7,8,3,4,5,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,8,6,3,7,5,2] => [1,8,2,4,6,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,3,7,4,2,6] => [1,8,6,4,3,5,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,8,5,2,3,6] => [1,5,8,6,2,7,3,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,5,2,7,4,3,6] => [1,7,3,5,8,6,4,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,6,8,7,5,3,2,4] => [1,5,8,4,7,2,6,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,4,2,6,8,7,5,3] => [1,8,3,2,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,6,3,2,7,4] => [1,7,8,4,6,2,5,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,7,4,6,3,2,8,5] => [1,8,5,3,4,6,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,6,4,2,5,7] => [1,8,7,5,4,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,3,4,7,2,1,5,8] => [6,1,7,5,2,3,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[5,3,6,7,2,4,1,8] => [7,1,5,2,3,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,1,5,6,7,3,2,8] => [7,2,1,4,6,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,1,2,6,4,5,8] => [7,5,6,4,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,1,7,4,2,3,5,8] => [4,7,5,2,1,6,3,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[6,1,7,2,5,3,4,8] => [5,7,4,2,1,6,3,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[5,1,7,2,6,3,4,8] => [7,4,2,1,5,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,6,1,4,2,3,5,8] => [4,7,5,2,6,3,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[4,6,1,5,2,7,3,8] => [7,3,1,4,5,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,6,3,2,4,5,8] => [6,4,3,7,5,2,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[5,6,1,2,4,7,3,8] => [7,3,1,5,4,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,2,6,4,7,3,5] => [1,8,5,4,6,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,1,4,7,3,6,2,8] => [6,7,2,1,5,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[4,7,6,3,5,2,1,8] => [5,7,1,4,3,6,2,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,6,5,8,7,4,2,3] => [1,8,3,5,7,2,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,5,2,8,6,3] => [1,8,3,4,5,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,6,1,3,4,2,5,8] => [6,2,7,5,4,3,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[3,6,2,1,7,5,4,8] => [7,4,1,3,2,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,8,3,2,4,7,5] => [1,7,8,5,2,6,4,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,7,2,6,3,5,8,4] => [1,8,4,6,5,3,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,4,2,7,1,6,5,8] => [6,7,5,1,3,2,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,4,2,6,8,5,3,7] => [1,8,7,3,2,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,3,5,4,2,7] => [1,5,8,7,2,6,4,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,7,5,2,4,6,3] => [1,8,3,7,6,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,7,5,2,6,3] => [1,5,8,3,4,7,6,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[7,6,1,3,2,5,4,8] => [6,5,2,7,4,3,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[4,7,1,5,2,6,3,8] => [6,7,3,1,4,5,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[6,4,1,3,2,7,5,8] => [7,5,2,4,3,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,7,3,4,5,2,6] => [1,8,6,5,4,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,9,3,4,5,6,7,2] => [1,9,2,8,7,6,5,4,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 1
[1,3,7,8,4,5,6,2] => [1,8,2,3,7,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,6,3,8,2,5] => [1,7,2,8,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,6,8,7,2,3,5,4] => [1,8,4,7,5,2,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,2,3,6,7,4] => [1,6,7,8,4,2,5,3] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,8,4,2,3,6,5,7] => [1,6,8,7,5,3,4,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,8,4,7,3,2,6,5] => [1,8,5,3,4,7,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,5,2,1,4,3,6,8] => [7,6,3,2,5,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,7,5,6,1,4,8] => [7,4,5,6,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,7,6,2,4,1,3,8] => [7,3,6,1,5,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,7,1,3,6,4,5,8] => [7,5,6,4,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,6,3,2,5,4,7] => [1,8,7,4,3,6,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,8,6,7,2,5] => [1,8,5,6,7,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,7,3,5,2,4] => [1,8,4,7,2,6,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,6,3,5,8,2,7] => [1,5,8,7,2,4,3,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,4,7,8,3,5,2,6] => [1,8,6,5,3,7,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,3,5,8,4,2] => [1,5,8,2,7,4,3,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[6,1,5,3,2,7,4,8] => [7,4,3,5,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,6,3,8,2,7,4] => [1,7,8,4,3,6,2,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,5,6,3,7,2,8,4] => [1,8,4,3,6,2,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,3,4,2,7,6] => [1,7,8,6,2,5,4,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,5,3,7,2,8,6] => [1,8,6,2,4,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,3,8,2,7,6] => [1,7,8,6,2,4,3,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,3,7,2,6,4,8,5] => [1,8,5,6,4,2,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,7,2,3,6,4] => [1,8,4,7,6,3,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,1,2,3,4,5,8,6,9] => [8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 1
[1,4,2,5,7,6,8,3] => [1,6,8,3,2,4,5,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,4,6,8,5,2,7] => [1,8,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,8,6,4,3,7] => [1,8,7,3,2,5,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,3,5,7,8,4] => [1,5,8,4,3,2,6,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,3,4,8,5,2,6,7] => [1,5,8,7,6,2,3,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,7,2,3,6,8,4] => [1,6,8,4,2,5,3,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[7,1,5,4,6,2,3,8] => [4,7,3,5,6,2,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[5,6,1,7,4,2,3,8] => [6,2,7,3,1,5,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[2,3,7,1,6,4,5,8] => [7,5,6,4,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,5,6,2,8,4,3] => [1,8,3,5,2,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,4,7,3,5,2,1,8] => [5,7,1,6,2,4,3,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[6,1,7,2,4,3,5,8] => [7,5,4,2,1,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,5,7,8,3,2,6] => [1,7,2,4,8,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,5,4,2,8,6,3,7] => [1,6,8,7,3,4,2,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,7,4,8,3,5,2,6] => [1,7,2,8,6,5,3,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,8,4,2,7,5,3,6] => [1,8,6,5,7,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,5,2,7,1,6,3,8] => [6,7,3,2,5,1,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[3,6,4,5,7,2,1,8] => [6,2,7,1,3,4,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,4,8,7,5,2,3,6] => [1,5,8,6,2,4,7,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,6,2,5,3,7,8,4] => [1,8,4,5,3,2,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,6,7,3,5,4] => [1,7,5,8,4,6,3,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,8,2,7,3,5,6,4] => [1,8,4,7,6,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,3,7,4,6,5] => [1,8,5,7,6,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,4,2,7,5,1,6,8] => [5,7,6,1,3,2,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,8,4,5,7,6,2,3] => [1,6,8,3,4,5,7,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[6,4,1,7,3,2,5,8] => [7,5,3,1,6,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,6,7,8,2,5,3] => [1,8,3,6,2,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[5,3,4,1,6,7,2,8] => [7,2,3,4,1,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,8,2,5,7,3,4] => [1,5,8,4,2,6,7,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,4,2,7,6,8,3] => [1,6,8,3,4,2,5,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,8,5,6,2,4,7] => [1,8,7,4,5,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,3,6,4,2,7] => [1,8,7,2,5,6,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,3,1,7,2,4,5,8] => [7,5,2,3,1,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,6,3,7,8,5,2] => [1,7,5,8,2,4,3,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[7,1,5,4,2,3,6,8] => [4,7,6,3,5,2,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[4,1,5,7,6,3,2,8] => [6,3,5,7,2,1,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,3,6,1,4,5,2,8] => [7,2,3,6,5,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,6,5,7,2,8,3] => [1,8,3,6,2,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,10,2,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 1
[1,7,6,3,8,2,5,4] => [1,8,4,3,6,2,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,7,8,4,5,3] => [1,8,3,2,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,6,4,2,3,5] => [1,8,5,4,6,2,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,4,7,3,2,8,6] => [1,8,6,2,5,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,7,5,2,4,3,1,8] => [7,1,6,3,5,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,4,2,7,6,1,5,8] => [7,5,6,1,3,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,3,4,1,7,5,2,8] => [7,2,3,4,1,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,7,6,8,2,4,3] => [1,8,3,7,4,6,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,3,8,5,4,2] => [1,8,2,7,4,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,6,3,8,4,2] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,6,3,5,4,2] => [1,8,2,7,4,6,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,3,5,4,6,1,2,8] => [4,7,2,3,5,6,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[5,7,6,1,3,2,4,8] => [7,4,1,5,3,6,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,4,6,5,1,7,2,8] => [7,2,4,5,1,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,8,5,3,6,7,2] => [1,6,7,8,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,3,5,8,6,4,2,7] => [1,8,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,7,8,6,4,2,3] => [1,8,3,7,2,5,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,6,5,3,4,7] => [1,5,8,7,4,6,3,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[4,3,1,5,6,7,2,8] => [7,2,3,1,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,8,5,6,3,2,7] => [1,8,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,5,2,7,3,4] => [1,8,4,5,2,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,7,2,8,5,4] => [1,8,4,7,5,2,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,3,6,5,1,7,4,8] => [7,4,5,1,2,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,6,8,4,7,2,3] => [1,8,3,6,7,2,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,8,4,7,6,2] => [1,7,6,8,2,3,5,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[6,3,7,5,2,4,1,8] => [7,1,6,4,5,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,1,7,3,4,2,5,8] => [6,2,1,7,5,4,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,3,4,9,2,5,6,7,8] => [1,9,8,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 1
[7,6,2,5,3,1,4,8] => [7,4,5,3,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,3,1,7,6,2,5,8] => [7,5,6,2,3,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,4,1,3,2,6,8] => [7,6,2,5,3,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,7,2,6,8,4,3] => [1,8,3,7,4,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,4,2,8,7,3,6] => [1,8,6,7,3,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,6,5,2,4,7] => [1,5,8,7,4,6,2,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,6,5,2,4,7,3] => [1,7,8,3,6,4,5,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[7,1,4,5,2,3,6,8] => [7,6,3,4,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,7,5,8,3,4,2] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,3,1,2,4,7,5,8] => [7,5,4,2,3,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,8,5,2,7,6,4] => [1,7,6,8,4,5,2,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[2,6,1,5,7,4,3,8] => [7,3,1,2,6,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,5,2,7,6,1,3,8] => [7,3,2,5,6,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,4,2,6,3,7,1,8] => [7,1,5,3,2,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,6,5,2,7,3,1,8] => [7,1,4,2,6,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,6,5,2,1,7,3,8] => [7,3,5,1,4,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,4,2,6,3,7,5] => [1,7,8,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[3,1,7,4,2,5,6,8] => [4,7,6,5,2,1,3,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,3,8,7,6,4,2,5] => [1,8,5,6,4,7,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,4,1,6,3,2,5,8] => [6,2,4,7,5,3,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,7,2,8,6,4,3,5] => [1,7,3,2,8,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[6,4,2,1,5,7,3,8] => [5,7,3,2,4,1,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[7,5,4,1,3,6,2,8] => [6,7,2,5,3,4,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,8,4,2,3,7,5,6] => [1,8,6,7,5,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,2,3,8,6,7,4] => [1,6,7,8,4,3,2,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,4,8,3,2,7,6,5] => [1,7,6,8,5,2,4,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,4,6,8,2,5,7,3] => [1,7,8,3,6,5,2,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,5,2,6,8,3,7,4] => [1,7,8,4,6,3,2,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,7,8,6,2,5,3] => [1,8,3,7,5,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,6,2,1,5,4,3,8] => [5,7,3,2,6,4,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[3,7,5,6,2,4,1,8] => [6,4,7,1,3,5,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,7,5,8,4,3,2,6] => [1,7,2,8,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[2,5,6,7,4,1,3,8] => [7,3,6,1,2,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,4,7,3,8,6,2] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,6,4,2,5,7,1,8] => [5,7,1,3,4,2,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[4,5,2,7,1,3,6,8] => [7,6,3,2,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,4,7,1,3,5,2,8] => [7,2,4,1,6,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,4,7,5,8,6,2] => [1,5,8,2,3,4,7,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,2,3,7,8,6,4] => [1,8,4,3,2,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,5,8,3,6,2] => [1,7,6,3,8,2,4,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[5,6,4,1,2,7,3,8] => [7,3,4,1,5,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,4,5,1,2,7,3,8] => [7,3,5,2,4,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,6,4,1,3,7,5,8] => [7,5,3,4,1,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,8,3,4,2,6,7] => [1,8,7,6,2,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,6,8,2,7,4] => [1,7,8,4,6,2,3,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[3,1,4,7,2,6,5,8] => [6,7,5,2,1,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[2,7,5,6,1,4,3,8] => [6,4,7,3,5,1,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,4,8,7,6,3,2,5] => [1,7,2,4,8,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,3,5,8,6,7,4,2] => [1,8,2,3,5,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,3,8,5,6,2] => [1,8,2,4,3,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,8,2,5,6,3] => [1,8,3,7,6,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,5,2,8,7,3,4] => [1,8,4,2,6,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,8,3,5,7,6] => [1,7,8,6,5,3,2,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,3,6,2,7,5,8,4] => [1,8,4,2,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,6,4,2,7,3] => [1,7,8,3,5,4,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,5,4,2,8,6,7,3] => [1,6,7,8,3,4,2,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,3,5,2,8,6,7,4] => [1,6,7,8,4,2,3,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,3,8,5,6,2,7,4] => [1,7,8,4,5,6,2,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,6,8,7,4,3,5,2] => [1,7,5,4,8,2,6,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[2,6,7,3,4,5,1,8] => [7,1,2,6,5,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,5,7,2,8,3,4] => [1,8,4,7,3,5,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,5,7,2,8,4,3] => [1,7,4,8,3,5,2,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[5,4,1,7,6,2,3,8] => [7,3,1,5,6,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,5,7,3,1,4,2,8] => [7,2,5,1,6,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,6,5,3,8,2,4] => [1,7,2,8,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[6,3,5,2,7,1,4,8] => [6,1,7,4,2,3,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[3,1,4,7,6,2,5,8] => [7,5,6,2,1,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,1,6,5,2,4,8] => [5,7,4,6,2,3,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[6,1,4,5,2,7,3,8] => [7,3,4,5,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,2,3,6,4,5,8] => [7,5,6,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,4,1,3,6,5,2,8] => [6,5,7,2,4,3,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,5,2,7,6,8,4,3] => [1,7,4,8,3,2,5,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,8,6,3,5,2,4] => [1,7,2,8,4,6,5,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,5,6,8,7,2,4] => [1,8,4,6,7,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,2,6,3,4,5] => [1,7,4,2,8,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[4,3,1,7,2,5,6,8] => [7,6,5,2,3,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,6,1,5,3,4,2,8] => [7,2,6,4,5,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,6,1,3,5,4,2,8] => [5,7,2,6,4,3,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[7,6,2,3,1,5,4,8] => [7,4,3,2,6,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,8,2,5,3,4,7] => [1,5,8,7,4,2,6,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,7,6,2,3,5,4] => [1,8,4,6,3,7,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,6,3,2,5,4] => [1,8,4,6,2,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,4,6,7,2,1,5,8] => [6,1,3,7,5,2,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[7,4,6,1,3,5,2,8] => [6,5,3,7,2,4,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,8,5,2,4,3,7,6] => [1,7,8,6,3,5,4,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,8,4,2,7,5,6,3] => [1,7,6,5,8,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[4,6,7,3,2,5,1,8] => [6,5,2,7,1,4,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,3,8,7,2,5,6,4] => [1,8,4,7,6,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,8,3,5,2,6,7] => [1,5,8,7,6,2,4,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,4,2,5,7,3,6] => [1,5,8,6,7,3,4,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,4,2,8,3,7,6] => [1,7,8,6,3,4,2,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,3,7,6,4,8,2,5] => [1,7,2,3,8,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,6,5,7,2,4,3] => [1,7,4,5,8,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,4,7,8,6,3,2,5] => [1,8,5,6,3,7,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,2,5,8,4,7] => [1,5,8,7,4,2,3,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,6,3,7,2,5,4] => [1,7,5,8,4,3,6,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,2,6,8,5,3,4] => [1,7,3,2,8,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,5,3,2,4,6,7] => [1,8,7,6,4,3,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,7,5,3,4,2,6] => [1,8,6,4,5,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,8,6,4,3,2,5] => [1,7,2,8,5,4,6,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[6,4,1,5,3,7,2,8] => [7,2,4,5,3,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,5,8,4,6,7,2] => [1,6,7,8,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[5,4,1,7,2,3,6,8] => [7,6,3,1,5,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,6,2,3,4,8,5] => [1,8,5,3,6,4,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,8,3,4,6,5] => [1,8,5,3,2,7,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,5,2,6,8,3,4] => [1,8,4,2,7,3,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,5,7,1,6,2,4,8] => [6,2,5,7,4,1,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,7,4,8,2,6,3,5] => [1,6,8,5,2,7,3,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[7,1,6,2,4,5,3,8] => [7,3,6,5,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,6,7,2,1,5,4,8] => [7,4,2,6,5,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,7,1,6,2,3,4,8] => [7,4,6,3,1,5,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,3,6,7,1,5,2,8] => [7,2,3,6,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,3,6,7,4,5,1,8] => [7,1,2,3,6,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,4,8,5,3,6,2] => [1,5,8,2,7,6,3,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[6,5,2,7,4,3,1,8] => [7,1,6,3,2,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,1,5,7,2,4,3,8] => [7,3,5,2,1,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,2,3,5,8,4,7] => [1,5,8,7,4,3,2,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,6,5,3,8,4,7,2] => [1,7,8,2,6,4,3,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[7,6,2,3,5,1,4,8] => [5,7,4,3,2,6,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[2,3,7,6,4,1,5,8] => [7,5,4,6,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,2,3,1,6,4,8] => [6,7,4,3,2,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[4,3,1,7,6,5,2,8] => [6,5,7,2,3,1,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[3,6,5,2,7,4,1,8] => [6,4,2,7,1,3,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,4,7,5,8,6,2,3] => [1,6,8,3,7,2,4,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[6,5,2,4,7,3,1,8] => [4,7,1,6,3,2,5,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,4,7,6,8,5,2,3] => [1,8,3,7,2,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,5,8,3,6,2] => [1,8,2,7,6,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,2,3,8,5,6,4] => [1,8,4,3,2,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,5,7,8,6,3] => [1,8,3,2,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,1,5,3,6,7,2,8] => [7,2,1,4,3,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,1,6,3,7,2,4,8] => [7,4,3,6,2,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,3,1,4,7,2,6,8] => [4,7,6,2,3,1,5,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[5,1,7,3,4,2,6,8] => [7,6,2,1,5,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[8,1,2,3,4,5,6,9,7,10] => [9,7,6,5,4,3,2,1,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11111111100000000010 => 1
[1,7,6,2,3,8,4,5] => [1,7,4,2,8,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,8,2,3,7,6,4,5] => [1,6,8,5,7,4,3,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,6,2,8,5,4,7] => [1,8,7,4,2,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,5,6,4,8,2,7] => [1,8,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,8,3,7,2,5,6] => [1,7,5,8,6,2,4,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,5,4,7,8,3,2,6] => [1,8,6,3,4,7,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,2,5,4,8,3] => [1,5,8,3,6,4,2,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[6,7,1,5,2,4,3,8] => [7,3,1,6,4,5,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,1,3,6,4,2,8] => [7,2,5,6,4,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,7,8,2,6,4,5] => [1,6,8,5,2,3,7,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,3,7,8,6,2,4,5] => [1,8,5,6,2,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,2,7,6,8,5,3] => [1,8,3,2,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,7,5,6,4,2,1,8] => [7,1,3,5,4,6,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,7,1,5,3,4,6,8] => [7,6,4,5,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,8,7,4,2,3,6] => [1,8,6,2,5,4,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,5,2,4,8,3,7] => [1,8,7,3,5,4,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,2,3,6,4,7] => [1,6,8,7,4,2,5,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[6,5,2,1,4,7,3,8] => [7,3,2,5,4,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,7,8,2,4,5,3] => [1,8,3,7,5,2,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,1,2,5,3,7,4,8] => [7,4,5,3,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,4,7,8,5,6,2] => [1,8,2,3,4,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,6,5,8,4,7,2] => [1,7,8,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[6,4,1,3,7,5,2,8] => [7,2,4,3,1,6,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,8,7,2,5,3,6] => [1,8,6,5,2,4,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,3,7,6,2,4] => [1,6,8,4,3,5,7,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,8,5,7,6,4,2,3] => [1,8,3,5,6,4,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,4,1,7,5,6,3,8] => [5,6,7,3,1,2,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 3
[1,5,4,2,7,3,8,6] => [1,8,6,3,4,2,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,7,2,4,8,3,5] => [1,7,3,8,5,4,2,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[5,1,2,4,6,7,3,8] => [4,7,3,2,1,5,6,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,7,6,2,8,5,3,4] => [1,8,4,2,7,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,6,7,3,4,1,5,8] => [6,1,2,7,5,4,3,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[3,4,5,7,2,1,6,8] => [7,6,1,3,5,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,5,2,6,8,7,4] => [1,7,8,4,2,3,5,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,8,6,7,3,5,2] => [1,7,5,8,2,4,6,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[4,6,1,5,7,2,3,8] => [6,2,7,3,1,4,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[6,5,1,2,7,3,4,8] => [6,3,1,7,4,2,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[4,7,1,6,5,2,3,8] => [5,7,3,1,4,6,2,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,7,5,3,6,8,2,4] => [1,7,2,8,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,8,4,6,3,2,5,7] => [1,8,7,5,3,4,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,6,4,2,3,7] => [1,8,7,3,5,4,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,5,6,4,8,2,3] => [1,7,2,8,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[2,5,7,3,4,6,1,8] => [6,7,1,2,5,4,3,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,3,6,7,4,8,2,5] => [1,8,5,4,7,2,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,4,1,5,7,6,3,8] => [6,7,3,1,2,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,8,6,5,7,4,2,3] => [1,8,3,6,4,5,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,8,3,2,6,5,7] => [1,6,8,7,5,2,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[7,6,4,1,2,5,3,8] => [6,5,2,7,3,4,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[6,5,7,1,3,2,4,8] => [7,4,1,6,2,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,5,2,4,1,7,3,8] => [4,7,3,2,5,1,6,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[5,7,2,3,6,4,1,8] => [7,1,5,6,4,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,6,2,5,7,1,3,8] => [7,3,2,6,1,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,2,5,8,6,3,7] => [1,6,8,7,3,2,4,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[5,1,7,3,6,4,2,8] => [7,2,1,5,6,4,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,3,1,7,5,4,2,8] => [5,7,2,3,1,6,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,6,7,2,5,3,8,4] => [1,5,8,4,2,6,3,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,7,5,6,8,3,2,4] => [1,7,2,8,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,3,5,8,4,6,2,7] => [1,6,8,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,5,6,2,8,7,3,4] => [1,7,3,6,8,4,2,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,3,7,8,2,4,6,5] => [1,8,5,2,3,7,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,7,4,6,3,1,5,8] => [7,5,3,4,6,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,5,7,1,3,6,4,8] => [6,7,4,1,2,5,3,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[7,3,5,1,4,2,6,8] => [7,6,2,3,5,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,3,5,2,1,6,4,8] => [6,7,4,2,3,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,7,8,2,4,6,3,5] => [1,6,8,5,4,2,7,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,8,2,6,7,5,3,4] => [1,8,4,6,5,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,1,5,6,2,3,4,8] => [7,4,6,3,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,8,2,7,3,4,5] => [1,8,5,7,4,2,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,5,6,3,7,1,4,8] => [7,4,3,6,1,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,6,7,2,4,5,3] => [1,8,3,6,4,7,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,8,5,7,3,6,2] => [1,8,2,4,5,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,6,5,8,2,7,3] => [1,7,8,3,6,2,4,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[3,7,5,4,6,2,1,8] => [4,7,1,3,5,6,2,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,5,4,8,7,3,2,6] => [1,7,2,5,8,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[7,3,6,5,1,2,4,8] => [6,2,3,7,4,5,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[3,5,2,1,6,7,4,8] => [7,4,1,3,2,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,6,2,8,5,4,3] => [1,7,4,2,8,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,7,6,8,3,4,2,5] => [1,7,2,8,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,8,7,3,5,2,6,4] => [1,5,8,4,3,7,6,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,5,8,3,4,6,2,7] => [1,6,8,7,2,5,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,4,7,6,2,3,8,5] => [1,8,5,2,4,6,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,4,6,7,2,3,5] => [1,8,5,7,3,4,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,4,8,6,2,5,7] => [1,8,7,5,6,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,8,3,4,7,2,6] => [1,8,6,7,2,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,6,2,5,7,4,3] => [1,5,8,3,6,7,4,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,4,6,5,8,7,2,3] => [1,8,3,6,7,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,8,3,2,6,5] => [1,8,5,3,7,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,6,2,3,8,5,4] => [1,8,4,2,7,5,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,4,5,8,2,3,6] => [1,8,6,2,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,7,5,8,4,6,2] => [1,8,2,3,7,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,7,8,5,4,3] => [1,7,4,8,3,2,6,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[1,7,2,6,4,3,8,5] => [1,8,5,4,6,3,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,8,7,2,3,6,5] => [1,8,5,2,4,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,6,5,2,7,4,3] => [1,8,3,6,7,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,6,2,7,4,3,5] => [1,8,5,7,3,6,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,7,5,8,4,2,3] => [1,8,3,7,2,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,5,7,8,3,2,4] => [1,8,4,7,2,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,8,3,2,5,6] => [1,7,5,3,8,6,2,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[3,7,6,1,2,5,4,8] => [7,4,1,3,6,5,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,7,6,2,3,1,5,8] => [7,5,3,6,1,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,4,7,2,8,6,5] => [1,8,5,2,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,6,2,8,7,3] => [1,7,8,3,5,2,4,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,5,2,6,8,7,4,3] => [1,7,4,6,8,3,2,5] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[2,3,6,1,5,7,4,8] => [5,7,4,1,2,3,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[6,1,4,7,3,2,5,8] => [6,2,1,7,5,3,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,5,6,7,3,8,4,2] => [1,7,4,8,2,5,3,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[4,1,6,7,2,5,3,8] => [7,3,6,5,2,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,2,8,5,4,6,3] => [1,5,8,3,2,7,6,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[2,6,4,7,5,3,1,8] => [5,7,1,2,6,3,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[4,6,2,5,7,3,1,8] => [6,3,2,7,1,4,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,4,6,5,8,2,3,7] => [1,8,7,3,6,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,8,5,3,4,7,2] => [1,7,8,2,6,4,5,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[7,4,2,1,5,3,6,8] => [5,7,6,3,2,4,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[5,3,1,2,7,6,4,8] => [6,7,4,2,3,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,8,7,3,6,4,2,5] => [1,8,5,6,4,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,5,8,2,6,3] => [1,8,3,7,6,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,5,4,1,7,6,3,8] => [6,7,3,4,1,2,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[5,4,7,1,3,6,2,8] => [6,7,2,4,1,5,3,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[4,1,2,6,5,7,3,8] => [5,7,3,2,1,4,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,3,6,2,8,5,7,4] => [1,7,8,4,2,3,6,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[7,1,2,6,4,3,5,8] => [7,5,4,6,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,2,6,5,3,4,8] => [5,7,4,6,3,2,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,5,6,8,3,4,7,2] => [1,7,8,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[4,6,5,7,1,2,3,8] => [6,2,7,3,5,1,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,4,7,3,8,6,5,2] => [1,6,8,2,4,3,7,5] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[4,1,2,5,7,6,3,8] => [6,7,3,2,1,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[1,6,7,3,4,8,2,5] => [1,8,5,4,3,7,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,9,2,3,4,5,6,7,10,8] => [1,10,8,7,6,5,4,3,2,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 1
[2,7,4,1,3,5,6,8] => [7,6,5,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,5,6,1,4,2,3,8] => [7,3,6,2,5,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,4,7,5,1,3,2,8] => [7,2,4,5,1,6,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,4,5,7,6,1,3,8] => [7,3,5,6,1,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,8,3,4,7,2,5] => [1,7,2,6,8,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,4,6,5,3,8,2,7] => [1,8,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,7,2,6,4,5,3] => [1,8,3,7,5,6,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,6,5,4,1,7,3,8] => [4,7,3,5,1,2,6,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,7,4,2,8,5,6,3] => [1,8,3,4,2,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,6,7,2,5,4] => [1,7,5,8,4,6,2,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[5,3,4,7,6,2,1,8] => [7,1,5,6,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,8,6,5,7,2,4] => [1,5,8,4,6,7,2,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,4,8,5,7,6,3,2] => [1,6,8,2,4,5,7,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 2
[1,4,5,3,8,7,2,6] => [1,8,6,7,2,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,3,1,6,2,4,5,8] => [6,4,7,5,2,3,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[6,3,5,4,1,7,2,8] => [4,7,2,3,5,1,6,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[5,4,1,3,7,6,2,8] => [6,7,2,4,3,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[4,3,1,5,7,6,2,8] => [6,7,2,3,1,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[6,4,2,1,3,7,5,8] => [7,5,3,2,4,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,2,5,7,8,4,3] => [1,7,4,5,8,3,2,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[1,6,4,5,2,7,8,3] => [1,8,3,4,5,2,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,6,2,3,4,7,5] => [1,7,8,5,3,6,4,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,7,6,2,8,5,3] => [1,8,3,7,5,2,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,5,8,4,3,6,2] => [1,8,2,7,6,3,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,5,2,6,4,7,3] => [1,7,8,3,5,6,4,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,7,8,5,2,6,3] => [1,5,8,3,7,6,2,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,6,4,8,2,3,5,7] => [1,8,7,5,2,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,7,3,5,8,6,2] => [1,5,8,2,4,3,7,6] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[5,1,2,6,4,7,3,8] => [7,3,2,1,5,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[7,1,4,5,6,2,3,8] => [7,3,4,5,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,4,6,8,5,3,2] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,5,4,7,8,2,6,3] => [1,8,3,4,7,6,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,7,2,5,6,1,4,8] => [7,4,5,6,1,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[3,7,2,5,1,6,4,8] => [6,7,4,5,1,3,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 2
[5,1,2,7,4,3,6,8] => [7,6,3,2,1,5,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,1,2,7,6,4,3,8] => [7,3,2,1,5,6,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[5,1,7,6,3,2,4,8] => [7,4,6,2,1,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,3,6,8,7,4,5,2] => [1,7,5,8,2,3,6,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 2
[5,7,1,3,6,2,4,8] => [7,4,3,1,5,6,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,10,2,3,4,7,5,6,8,9] => [1,10,9,8,6,7,5,4,3,2] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 1
[1,7,5,8,6,2,4,3] => [1,8,3,5,6,2,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,5,4,1,7,2,3,8] => [7,3,4,1,6,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,6,7,2,3,5,1,8] => [7,1,4,2,6,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[2,5,7,6,3,4,1,8] => [6,4,7,1,2,5,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[4,7,2,5,3,1,6,8] => [7,6,1,4,5,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,8,6,2,4,7,5,3] => [1,8,3,6,7,5,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[6,7,5,2,1,4,3,8] => [7,3,5,1,6,4,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,7,6,8,4,5,3,2] => [1,8,2,7,3,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,8,2,6,4,3,7,5] => [1,7,8,5,4,6,3,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 2
[1,4,7,6,8,3,5,2] => [1,8,2,4,6,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,7,5,2,4,3,8,6] => [1,8,6,3,5,4,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,7,2,3,5,1,6,8] => [5,7,6,1,4,3,2,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[1,6,5,3,8,7,4,2] => [1,8,2,6,7,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[4,7,2,3,6,1,5,8] => [7,5,6,1,4,3,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,4,8,7,6,3,5,2] => [1,8,2,4,7,5,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,4,5,8,7,3,2] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,3,8,7,5,2,6,4] => [1,5,8,4,7,6,2,3] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[7,1,2,4,6,3,5,8] => [4,7,5,6,3,2,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[1,7,2,5,8,4,6,3] => [1,8,3,2,7,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[3,1,6,4,2,7,5,8] => [4,7,5,2,1,3,6,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[6,7,1,2,4,3,5,8] => [6,3,1,7,5,4,2,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[6,1,5,7,4,2,3,8] => [6,2,1,7,3,5,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[1,6,4,5,2,8,3,7] => [1,8,7,3,4,5,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,6,2,5,7,4,8,3] => [1,8,3,2,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[1,4,5,7,6,8,2,3] => [1,7,2,4,8,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 2
[4,1,6,7,3,5,2,8] => [6,5,3,7,2,1,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 2
[6,3,4,5,1,7,2,8] => [7,2,3,4,5,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,5,4,8,3,6,7,2] => [1,6,7,8,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 3
[1,4,8,7,6,2,3,5] => [1,8,5,6,2,4,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,5,1,4,6,3,2,8] => [4,7,2,5,6,3,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[7,5,1,2,6,3,4,8] => [7,4,2,5,6,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,7,1,5,6,2,3,8] => [7,3,1,4,5,6,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[1,6,2,8,5,7,4,3] => [1,5,8,3,2,6,7,4] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 2
[1,8,4,7,2,5,6,3] => [1,8,3,4,7,6,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[7,6,1,5,2,3,4,8] => [7,4,5,2,6,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[6,1,2,4,7,5,3,8] => [4,7,3,2,1,6,5,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 2
[4,3,6,2,5,7,1,8] => [5,7,1,4,2,3,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 2
[5,6,7,1,3,2,4,8] => [6,2,7,4,1,5,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 2
[1,7,6,8,2,5,4,3] => [1,8,3,6,5,2,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1
[2,6,7,5,3,4,1,8] => [7,1,2,6,4,5,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
[4,3,7,6,2,5,1,8] => [7,1,4,6,5,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,3,1 6,11,6,1 24,50,35,10,1 120,274,225,85,15,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 2 + 3\ q + q^{2}$
$F_{4} = 6 + 11\ q + 6\ q^{2} + q^{3}$
$F_{5} = 24 + 50\ q + 35\ q^{2} + 10\ q^{3} + q^{4}$
$F_{6} = 120 + 274\ q + 225\ q^{2} + 85\ q^{3} + 15\ q^{4} + q^{5}$
Description
The number of ascents of 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.
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
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
to binary word
Description
Return the Dyck word as binary word.
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