Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00069: Permutations —complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
[1,0] => [1] => [1] =>
[1,0,1,0] => [2,1] => [1,2] => 1
[1,1,0,0] => [1,2] => [2,1] => 0
[1,0,1,0,1,0] => [3,2,1] => [1,2,3] => 11
[1,0,1,1,0,0] => [2,3,1] => [2,1,3] => 01
[1,1,0,0,1,0] => [3,1,2] => [1,3,2] => 10
[1,1,0,1,0,0] => [2,1,3] => [2,3,1] => 00
[1,1,1,0,0,0] => [1,2,3] => [3,2,1] => 00
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,2,3,4] => 111
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [2,1,3,4] => 011
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,3,2,4] => 101
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [2,3,1,4] => 001
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [3,2,1,4] => 001
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,2,4,3] => 110
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,1,4,3] => 010
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [1,3,4,2] => 100
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [2,3,4,1] => 000
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [3,2,4,1] => 000
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,4,3,2] => 100
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [2,4,3,1] => 000
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [3,4,2,1] => 000
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4,3,2,1] => 000
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,2,3,4,5] => 1111
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [2,1,3,4,5] => 0111
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,3,2,4,5] => 1011
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [2,3,1,4,5] => 0011
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [3,2,1,4,5] => 0011
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,2,4,3,5] => 1101
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [2,1,4,3,5] => 0101
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,3,4,2,5] => 1001
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [2,3,4,1,5] => 0001
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [3,2,4,1,5] => 0001
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,4,3,2,5] => 1001
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [2,4,3,1,5] => 0001
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [3,4,2,1,5] => 0001
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [4,3,2,1,5] => 0001
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,2,3,5,4] => 1110
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [2,1,3,5,4] => 0110
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,3,2,5,4] => 1010
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [2,3,1,5,4] => 0010
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [3,2,1,5,4] => 0010
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [1,2,4,5,3] => 1100
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [2,1,4,5,3] => 0100
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [1,3,4,5,2] => 1000
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [2,3,4,5,1] => 0000
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,2,4,5,1] => 0000
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [1,4,3,5,2] => 1000
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [2,4,3,5,1] => 0000
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [3,4,2,5,1] => 0000
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [4,3,2,5,1] => 0000
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,2,5,4,3] => 1100
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [2,1,5,4,3] => 0100
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,3,5,4,2] => 1000
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [2,3,5,4,1] => 0000
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [3,2,5,4,1] => 0000
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [1,4,5,3,2] => 1000
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [2,4,5,3,1] => 0000
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,4,5,2,1] => 0000
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [4,3,5,2,1] => 0000
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,5,4,3,2] => 1000
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [2,5,4,3,1] => 0000
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,5,4,2,1] => 0000
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [4,5,3,2,1] => 0000
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5,4,3,2,1] => 0000
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => 11111
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [2,1,3,4,5,6] => 01111
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,3,2,4,5,6] => 10111
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [2,3,1,4,5,6] => 00111
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [3,2,1,4,5,6] => 00111
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => 11011
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [2,1,4,3,5,6] => 01011
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,3,4,2,5,6] => 10011
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [2,3,4,1,5,6] => 00011
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [3,2,4,1,5,6] => 00011
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,4,3,2,5,6] => 10011
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [2,4,3,1,5,6] => 00011
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [3,4,2,1,5,6] => 00011
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [4,3,2,1,5,6] => 00011
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,2,3,5,4,6] => 11101
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [2,1,3,5,4,6] => 01101
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => 10101
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [2,3,1,5,4,6] => 00101
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [3,2,1,5,4,6] => 00101
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,2,4,5,3,6] => 11001
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [2,1,4,5,3,6] => 01001
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,3,4,5,2,6] => 10001
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [2,3,4,5,1,6] => 00001
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [3,2,4,5,1,6] => 00001
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,4,3,5,2,6] => 10001
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [2,4,3,5,1,6] => 00001
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [3,4,2,5,1,6] => 00001
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,3,2,5,1,6] => 00001
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,2,5,4,3,6] => 11001
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [2,1,5,4,3,6] => 01001
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,3,5,4,2,6] => 10001
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [2,3,5,4,1,6] => 00001
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [3,2,5,4,1,6] => 00001
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,4,5,3,2,6] => 10001
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [2,4,5,3,1,6] => 00001
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [3,4,5,2,1,6] => 00001
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [4,3,5,2,1,6] => 00001
>>> Load all 1799 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => 10001
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,5,4,3,1,6] => 00001
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [3,5,4,2,1,6] => 00001
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [4,5,3,2,1,6] => 00001
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [5,4,3,2,1,6] => 00001
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [1,2,3,4,6,5] => 11110
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => 01110
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [1,3,2,4,6,5] => 10110
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [2,3,1,4,6,5] => 00110
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [3,2,1,4,6,5] => 00110
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [1,2,4,3,6,5] => 11010
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => 01010
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [1,3,4,2,6,5] => 10010
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [2,3,4,1,6,5] => 00010
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [3,2,4,1,6,5] => 00010
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [1,4,3,2,6,5] => 10010
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [2,4,3,1,6,5] => 00010
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [3,4,2,1,6,5] => 00010
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [4,3,2,1,6,5] => 00010
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [1,2,3,5,6,4] => 11100
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [2,1,3,5,6,4] => 01100
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [1,3,2,5,6,4] => 10100
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [2,3,1,5,6,4] => 00100
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [3,2,1,5,6,4] => 00100
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [1,2,4,5,6,3] => 11000
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [2,1,4,5,6,3] => 01000
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [1,3,4,5,6,2] => 10000
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [2,3,4,5,6,1] => 00000
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [3,2,4,5,6,1] => 00000
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [1,4,3,5,6,2] => 10000
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [2,4,3,5,6,1] => 00000
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [3,4,2,5,6,1] => 00000
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [4,3,2,5,6,1] => 00000
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [1,2,5,4,6,3] => 11000
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [2,1,5,4,6,3] => 01000
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [1,3,5,4,6,2] => 10000
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [2,3,5,4,6,1] => 00000
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [3,2,5,4,6,1] => 00000
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [1,4,5,3,6,2] => 10000
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [2,4,5,3,6,1] => 00000
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [3,4,5,2,6,1] => 00000
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [4,3,5,2,6,1] => 00000
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [1,5,4,3,6,2] => 10000
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,5,4,3,6,1] => 00000
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [3,5,4,2,6,1] => 00000
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [4,5,3,2,6,1] => 00000
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [5,4,3,2,6,1] => 00000
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [1,2,3,6,5,4] => 11100
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [2,1,3,6,5,4] => 01100
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [1,3,2,6,5,4] => 10100
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [2,3,1,6,5,4] => 00100
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => 00100
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [1,2,4,6,5,3] => 11000
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [2,1,4,6,5,3] => 01000
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [1,3,4,6,5,2] => 10000
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [2,3,4,6,5,1] => 00000
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [3,2,4,6,5,1] => 00000
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,4,3,6,5,2] => 10000
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [2,4,3,6,5,1] => 00000
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [3,4,2,6,5,1] => 00000
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [4,3,2,6,5,1] => 00000
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [1,2,5,6,4,3] => 11000
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [2,1,5,6,4,3] => 01000
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [1,3,5,6,4,2] => 10000
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [2,3,5,6,4,1] => 00000
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [3,2,5,6,4,1] => 00000
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [1,4,5,6,3,2] => 10000
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [2,4,5,6,3,1] => 00000
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [3,4,5,6,2,1] => 00000
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [4,3,5,6,2,1] => 00000
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [1,5,4,6,3,2] => 10000
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,5,4,6,3,1] => 00000
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [3,5,4,6,2,1] => 00000
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [4,5,3,6,2,1] => 00000
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [5,4,3,6,2,1] => 00000
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [1,2,6,5,4,3] => 11000
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [2,1,6,5,4,3] => 01000
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,3,6,5,4,2] => 10000
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [2,3,6,5,4,1] => 00000
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [3,2,6,5,4,1] => 00000
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [1,4,6,5,3,2] => 10000
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [2,4,6,5,3,1] => 00000
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [3,4,6,5,2,1] => 00000
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,3,6,5,2,1] => 00000
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [1,5,6,4,3,2] => 10000
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,5,6,4,3,1] => 00000
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [3,5,6,4,2,1] => 00000
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [4,5,6,3,2,1] => 00000
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [5,4,6,3,2,1] => 00000
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => 10000
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [2,6,5,4,3,1] => 00000
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,6,5,4,2,1] => 00000
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [4,6,5,3,2,1] => 00000
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [5,6,4,3,2,1] => 00000
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 00000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [2,1,3,4,5,6,7] => 011111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [1,3,2,4,5,6,7] => 101111
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [2,3,1,4,5,6,7] => 001111
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [3,2,1,4,5,6,7] => 001111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [1,2,4,3,5,6,7] => 110111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [2,1,4,3,5,6,7] => 010111
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [1,3,4,2,5,6,7] => 100111
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [2,3,4,1,5,6,7] => 000111
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [3,2,4,1,5,6,7] => 000111
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [1,4,3,2,5,6,7] => 100111
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [2,4,3,1,5,6,7] => 000111
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [3,4,2,1,5,6,7] => 000111
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,3,2,1,5,6,7] => 000111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [1,2,3,5,4,6,7] => 111011
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [2,1,3,5,4,6,7] => 011011
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [1,3,2,5,4,6,7] => 101011
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [2,3,1,5,4,6,7] => 001011
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [3,2,1,5,4,6,7] => 001011
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [1,2,4,5,3,6,7] => 110011
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [2,1,4,5,3,6,7] => 010011
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [1,3,4,5,2,6,7] => 100011
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [2,3,4,5,1,6,7] => 000011
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [3,2,4,5,1,6,7] => 000011
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [1,4,3,5,2,6,7] => 100011
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [2,4,3,5,1,6,7] => 000011
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [3,4,2,5,1,6,7] => 000011
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [4,3,2,5,1,6,7] => 000011
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => 110011
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [2,1,5,4,3,6,7] => 010011
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [1,3,5,4,2,6,7] => 100011
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [2,3,5,4,1,6,7] => 000011
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [3,2,5,4,1,6,7] => 000011
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [1,4,5,3,2,6,7] => 100011
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [2,4,5,3,1,6,7] => 000011
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [3,4,5,2,1,6,7] => 000011
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [4,3,5,2,1,6,7] => 000011
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [1,5,4,3,2,6,7] => 100011
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [2,5,4,3,1,6,7] => 000011
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [3,5,4,2,1,6,7] => 000011
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [4,5,3,2,1,6,7] => 000011
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [5,4,3,2,1,6,7] => 000011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [1,2,3,4,6,5,7] => 111101
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [2,1,3,4,6,5,7] => 011101
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => 101101
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [2,3,1,4,6,5,7] => 001101
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [3,2,1,4,6,5,7] => 001101
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [1,2,4,3,6,5,7] => 110101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [2,1,4,3,6,5,7] => 010101
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [1,3,4,2,6,5,7] => 100101
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [2,3,4,1,6,5,7] => 000101
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [3,2,4,1,6,5,7] => 000101
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [1,4,3,2,6,5,7] => 100101
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [2,4,3,1,6,5,7] => 000101
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [3,4,2,1,6,5,7] => 000101
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [4,3,2,1,6,5,7] => 000101
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [1,2,3,5,6,4,7] => 111001
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [2,1,3,5,6,4,7] => 011001
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [1,3,2,5,6,4,7] => 101001
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [2,3,1,5,6,4,7] => 001001
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [3,2,1,5,6,4,7] => 001001
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [1,2,4,5,6,3,7] => 110001
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [2,1,4,5,6,3,7] => 010001
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [1,3,4,5,6,2,7] => 100001
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [2,3,4,5,6,1,7] => 000001
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [3,2,4,5,6,1,7] => 000001
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [1,4,3,5,6,2,7] => 100001
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [2,4,3,5,6,1,7] => 000001
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [3,4,2,5,6,1,7] => 000001
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [4,3,2,5,6,1,7] => 000001
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [1,2,5,4,6,3,7] => 110001
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [2,1,5,4,6,3,7] => 010001
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [1,3,5,4,6,2,7] => 100001
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [2,3,5,4,6,1,7] => 000001
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [3,2,5,4,6,1,7] => 000001
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [1,4,5,3,6,2,7] => 100001
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [2,4,5,3,6,1,7] => 000001
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [3,4,5,2,6,1,7] => 000001
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [4,3,5,2,6,1,7] => 000001
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [1,5,4,3,6,2,7] => 100001
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [2,5,4,3,6,1,7] => 000001
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [3,5,4,2,6,1,7] => 000001
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [4,5,3,2,6,1,7] => 000001
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [5,4,3,2,6,1,7] => 000001
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [1,2,3,6,5,4,7] => 111001
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [2,1,3,6,5,4,7] => 011001
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [1,3,2,6,5,4,7] => 101001
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [2,3,1,6,5,4,7] => 001001
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [3,2,1,6,5,4,7] => 001001
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [1,2,4,6,5,3,7] => 110001
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [2,1,4,6,5,3,7] => 010001
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [1,3,4,6,5,2,7] => 100001
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [2,3,4,6,5,1,7] => 000001
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [3,2,4,6,5,1,7] => 000001
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [1,4,3,6,5,2,7] => 100001
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [2,4,3,6,5,1,7] => 000001
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [3,4,2,6,5,1,7] => 000001
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [4,3,2,6,5,1,7] => 000001
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [1,2,5,6,4,3,7] => 110001
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [2,1,5,6,4,3,7] => 010001
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [1,3,5,6,4,2,7] => 100001
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [2,3,5,6,4,1,7] => 000001
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [3,2,5,6,4,1,7] => 000001
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [1,4,5,6,3,2,7] => 100001
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [2,4,5,6,3,1,7] => 000001
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [3,4,5,6,2,1,7] => 000001
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [4,3,5,6,2,1,7] => 000001
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [1,5,4,6,3,2,7] => 100001
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [2,5,4,6,3,1,7] => 000001
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [3,5,4,6,2,1,7] => 000001
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [4,5,3,6,2,1,7] => 000001
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [5,4,3,6,2,1,7] => 000001
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [1,2,6,5,4,3,7] => 110001
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [2,1,6,5,4,3,7] => 010001
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [1,3,6,5,4,2,7] => 100001
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [2,3,6,5,4,1,7] => 000001
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [3,2,6,5,4,1,7] => 000001
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [1,4,6,5,3,2,7] => 100001
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [2,4,6,5,3,1,7] => 000001
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [3,4,6,5,2,1,7] => 000001
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [4,3,6,5,2,1,7] => 000001
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [1,5,6,4,3,2,7] => 100001
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [2,5,6,4,3,1,7] => 000001
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [3,5,6,4,2,1,7] => 000001
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [4,5,6,3,2,1,7] => 000001
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [5,4,6,3,2,1,7] => 000001
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [1,6,5,4,3,2,7] => 100001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,6,5,4,3,1,7] => 000001
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [3,6,5,4,2,1,7] => 000001
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [4,6,5,3,2,1,7] => 000001
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [5,6,4,3,2,1,7] => 000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [6,5,4,3,2,1,7] => 000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => 111110
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [2,1,3,4,5,7,6] => 011110
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [1,3,2,4,5,7,6] => 101110
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [2,3,1,4,5,7,6] => 001110
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [3,2,1,4,5,7,6] => 001110
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [1,2,4,3,5,7,6] => 110110
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [2,1,4,3,5,7,6] => 010110
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [1,3,4,2,5,7,6] => 100110
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [2,3,4,1,5,7,6] => 000110
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [3,2,4,1,5,7,6] => 000110
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [1,4,3,2,5,7,6] => 100110
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [2,4,3,1,5,7,6] => 000110
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [3,4,2,1,5,7,6] => 000110
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [4,3,2,1,5,7,6] => 000110
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [1,2,3,5,4,7,6] => 111010
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [2,1,3,5,4,7,6] => 011010
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [1,3,2,5,4,7,6] => 101010
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [2,3,1,5,4,7,6] => 001010
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [3,2,1,5,4,7,6] => 001010
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [1,2,4,5,3,7,6] => 110010
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [2,1,4,5,3,7,6] => 010010
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [1,3,4,5,2,7,6] => 100010
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [2,3,4,5,1,7,6] => 000010
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [3,2,4,5,1,7,6] => 000010
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [1,4,3,5,2,7,6] => 100010
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [2,4,3,5,1,7,6] => 000010
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [3,4,2,5,1,7,6] => 000010
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [4,3,2,5,1,7,6] => 000010
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [1,2,5,4,3,7,6] => 110010
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [2,1,5,4,3,7,6] => 010010
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [1,3,5,4,2,7,6] => 100010
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [2,3,5,4,1,7,6] => 000010
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [3,2,5,4,1,7,6] => 000010
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [1,4,5,3,2,7,6] => 100010
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [2,4,5,3,1,7,6] => 000010
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [3,4,5,2,1,7,6] => 000010
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [4,3,5,2,1,7,6] => 000010
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [1,5,4,3,2,7,6] => 100010
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [2,5,4,3,1,7,6] => 000010
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [3,5,4,2,1,7,6] => 000010
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [4,5,3,2,1,7,6] => 000010
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [5,4,3,2,1,7,6] => 000010
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [1,2,3,4,6,7,5] => 111100
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [2,1,3,4,6,7,5] => 011100
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [1,3,2,4,6,7,5] => 101100
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [2,3,1,4,6,7,5] => 001100
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [3,2,1,4,6,7,5] => 001100
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [1,2,4,3,6,7,5] => 110100
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [2,1,4,3,6,7,5] => 010100
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [1,3,4,2,6,7,5] => 100100
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [2,3,4,1,6,7,5] => 000100
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [3,2,4,1,6,7,5] => 000100
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [1,4,3,2,6,7,5] => 100100
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [2,4,3,1,6,7,5] => 000100
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [3,4,2,1,6,7,5] => 000100
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [4,3,2,1,6,7,5] => 000100
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [1,2,3,5,6,7,4] => 111000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [2,1,3,5,6,7,4] => 011000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [1,3,2,5,6,7,4] => 101000
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [2,3,1,5,6,7,4] => 001000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [3,2,1,5,6,7,4] => 001000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [1,2,4,5,6,7,3] => 110000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [2,1,4,5,6,7,3] => 010000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [1,3,4,5,6,7,2] => 100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [2,3,4,5,6,7,1] => 000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [3,2,4,5,6,7,1] => 000000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [1,4,3,5,6,7,2] => 100000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [2,4,3,5,6,7,1] => 000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [3,4,2,5,6,7,1] => 000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [4,3,2,5,6,7,1] => 000000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [1,2,5,4,6,7,3] => 110000
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [2,1,5,4,6,7,3] => 010000
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [1,3,5,4,6,7,2] => 100000
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [2,3,5,4,6,7,1] => 000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [3,2,5,4,6,7,1] => 000000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [1,4,5,3,6,7,2] => 100000
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [2,4,5,3,6,7,1] => 000000
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [3,4,5,2,6,7,1] => 000000
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [4,3,5,2,6,7,1] => 000000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [1,5,4,3,6,7,2] => 100000
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [2,5,4,3,6,7,1] => 000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [3,5,4,2,6,7,1] => 000000
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [4,5,3,2,6,7,1] => 000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [5,4,3,2,6,7,1] => 000000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [1,2,3,6,5,7,4] => 111000
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [2,1,3,6,5,7,4] => 011000
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [1,3,2,6,5,7,4] => 101000
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [2,3,1,6,5,7,4] => 001000
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [3,2,1,6,5,7,4] => 001000
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [1,2,4,6,5,7,3] => 110000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [2,1,4,6,5,7,3] => 010000
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [1,3,4,6,5,7,2] => 100000
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [2,3,4,6,5,7,1] => 000000
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [3,2,4,6,5,7,1] => 000000
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [1,4,3,6,5,7,2] => 100000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [2,4,3,6,5,7,1] => 000000
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [3,4,2,6,5,7,1] => 000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [4,3,2,6,5,7,1] => 000000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [1,2,5,6,4,7,3] => 110000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [2,1,5,6,4,7,3] => 010000
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [1,3,5,6,4,7,2] => 100000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [2,3,5,6,4,7,1] => 000000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [3,2,5,6,4,7,1] => 000000
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [1,4,5,6,3,7,2] => 100000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [2,4,5,6,3,7,1] => 000000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [3,4,5,6,2,7,1] => 000000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [4,3,5,6,2,7,1] => 000000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [1,5,4,6,3,7,2] => 100000
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [2,5,4,6,3,7,1] => 000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [3,5,4,6,2,7,1] => 000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [4,5,3,6,2,7,1] => 000000
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [5,4,3,6,2,7,1] => 000000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [1,2,6,5,4,7,3] => 110000
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [2,1,6,5,4,7,3] => 010000
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [1,3,6,5,4,7,2] => 100000
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [2,3,6,5,4,7,1] => 000000
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [3,2,6,5,4,7,1] => 000000
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [1,4,6,5,3,7,2] => 100000
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [2,4,6,5,3,7,1] => 000000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [3,4,6,5,2,7,1] => 000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [4,3,6,5,2,7,1] => 000000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [1,5,6,4,3,7,2] => 100000
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [2,5,6,4,3,7,1] => 000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [3,5,6,4,2,7,1] => 000000
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [4,5,6,3,2,7,1] => 000000
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [5,4,6,3,2,7,1] => 000000
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [1,6,5,4,3,7,2] => 100000
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [2,6,5,4,3,7,1] => 000000
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [3,6,5,4,2,7,1] => 000000
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [4,6,5,3,2,7,1] => 000000
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [5,6,4,3,2,7,1] => 000000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [6,5,4,3,2,7,1] => 000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [1,2,3,4,7,6,5] => 111100
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [2,1,3,4,7,6,5] => 011100
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [1,3,2,4,7,6,5] => 101100
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [2,3,1,4,7,6,5] => 001100
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [3,2,1,4,7,6,5] => 001100
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [1,2,4,3,7,6,5] => 110100
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [2,1,4,3,7,6,5] => 010100
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [1,3,4,2,7,6,5] => 100100
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [2,3,4,1,7,6,5] => 000100
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [3,2,4,1,7,6,5] => 000100
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [1,4,3,2,7,6,5] => 100100
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [2,4,3,1,7,6,5] => 000100
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [3,4,2,1,7,6,5] => 000100
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [4,3,2,1,7,6,5] => 000100
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [1,2,3,5,7,6,4] => 111000
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [2,1,3,5,7,6,4] => 011000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [1,3,2,5,7,6,4] => 101000
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [2,3,1,5,7,6,4] => 001000
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [3,2,1,5,7,6,4] => 001000
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [1,2,4,5,7,6,3] => 110000
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [2,1,4,5,7,6,3] => 010000
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [1,3,4,5,7,6,2] => 100000
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [2,3,4,5,7,6,1] => 000000
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [3,2,4,5,7,6,1] => 000000
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [1,4,3,5,7,6,2] => 100000
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [2,4,3,5,7,6,1] => 000000
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [3,4,2,5,7,6,1] => 000000
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [4,3,2,5,7,6,1] => 000000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [1,2,5,4,7,6,3] => 110000
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [2,1,5,4,7,6,3] => 010000
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [1,3,5,4,7,6,2] => 100000
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [2,3,5,4,7,6,1] => 000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [3,2,5,4,7,6,1] => 000000
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [1,4,5,3,7,6,2] => 100000
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [2,4,5,3,7,6,1] => 000000
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [3,4,5,2,7,6,1] => 000000
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [4,3,5,2,7,6,1] => 000000
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,5,4,3,7,6,2] => 100000
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [2,5,4,3,7,6,1] => 000000
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [3,5,4,2,7,6,1] => 000000
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [4,5,3,2,7,6,1] => 000000
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [5,4,3,2,7,6,1] => 000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [1,2,3,6,7,5,4] => 111000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [2,1,3,6,7,5,4] => 011000
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [1,3,2,6,7,5,4] => 101000
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [2,3,1,6,7,5,4] => 001000
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [3,2,1,6,7,5,4] => 001000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [1,2,4,6,7,5,3] => 110000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [2,1,4,6,7,5,3] => 010000
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [1,3,4,6,7,5,2] => 100000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [2,3,4,6,7,5,1] => 000000
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [3,2,4,6,7,5,1] => 000000
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [1,4,3,6,7,5,2] => 100000
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [2,4,3,6,7,5,1] => 000000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [3,4,2,6,7,5,1] => 000000
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [4,3,2,6,7,5,1] => 000000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [1,2,5,6,7,4,3] => 110000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [2,1,5,6,7,4,3] => 010000
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [1,3,5,6,7,4,2] => 100000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [2,3,5,6,7,4,1] => 000000
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [3,2,5,6,7,4,1] => 000000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [1,4,5,6,7,3,2] => 100000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [2,4,5,6,7,3,1] => 000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [3,4,5,6,7,2,1] => 000000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [4,3,5,6,7,2,1] => 000000
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [1,5,4,6,7,3,2] => 100000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [2,5,4,6,7,3,1] => 000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [3,5,4,6,7,2,1] => 000000
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [4,5,3,6,7,2,1] => 000000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [5,4,3,6,7,2,1] => 000000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [1,2,6,5,7,4,3] => 110000
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [2,1,6,5,7,4,3] => 010000
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [1,3,6,5,7,4,2] => 100000
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [2,3,6,5,7,4,1] => 000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [3,2,6,5,7,4,1] => 000000
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [1,4,6,5,7,3,2] => 100000
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [2,4,6,5,7,3,1] => 000000
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [3,4,6,5,7,2,1] => 000000
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [4,3,6,5,7,2,1] => 000000
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [1,5,6,4,7,3,2] => 100000
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [2,5,6,4,7,3,1] => 000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [3,5,6,4,7,2,1] => 000000
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [4,5,6,3,7,2,1] => 000000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [5,4,6,3,7,2,1] => 000000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [1,6,5,4,7,3,2] => 100000
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [2,6,5,4,7,3,1] => 000000
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [3,6,5,4,7,2,1] => 000000
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [4,6,5,3,7,2,1] => 000000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [5,6,4,3,7,2,1] => 000000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [6,5,4,3,7,2,1] => 000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => 111000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [2,1,3,7,6,5,4] => 011000
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [1,3,2,7,6,5,4] => 101000
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [2,3,1,7,6,5,4] => 001000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [3,2,1,7,6,5,4] => 001000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [1,2,4,7,6,5,3] => 110000
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [2,1,4,7,6,5,3] => 010000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [1,3,4,7,6,5,2] => 100000
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [2,3,4,7,6,5,1] => 000000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [3,2,4,7,6,5,1] => 000000
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [1,4,3,7,6,5,2] => 100000
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [2,4,3,7,6,5,1] => 000000
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [3,4,2,7,6,5,1] => 000000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [4,3,2,7,6,5,1] => 000000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [1,2,5,7,6,4,3] => 110000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [2,1,5,7,6,4,3] => 010000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [1,3,5,7,6,4,2] => 100000
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [2,3,5,7,6,4,1] => 000000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [3,2,5,7,6,4,1] => 000000
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [1,4,5,7,6,3,2] => 100000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [2,4,5,7,6,3,1] => 000000
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [3,4,5,7,6,2,1] => 000000
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [4,3,5,7,6,2,1] => 000000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [1,5,4,7,6,3,2] => 100000
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [2,5,4,7,6,3,1] => 000000
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [3,5,4,7,6,2,1] => 000000
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [4,5,3,7,6,2,1] => 000000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [5,4,3,7,6,2,1] => 000000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [1,2,6,7,5,4,3] => 110000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [2,1,6,7,5,4,3] => 010000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [1,3,6,7,5,4,2] => 100000
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [2,3,6,7,5,4,1] => 000000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [3,2,6,7,5,4,1] => 000000
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [1,4,6,7,5,3,2] => 100000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [2,4,6,7,5,3,1] => 000000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [3,4,6,7,5,2,1] => 000000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [4,3,6,7,5,2,1] => 000000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [1,5,6,7,4,3,2] => 100000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [2,5,6,7,4,3,1] => 000000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [3,5,6,7,4,2,1] => 000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [4,5,6,7,3,2,1] => 000000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [5,4,6,7,3,2,1] => 000000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [1,6,5,7,4,3,2] => 100000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [2,6,5,7,4,3,1] => 000000
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [3,6,5,7,4,2,1] => 000000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [4,6,5,7,3,2,1] => 000000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [5,6,4,7,3,2,1] => 000000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [6,5,4,7,3,2,1] => 000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [1,2,7,6,5,4,3] => 110000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [2,1,7,6,5,4,3] => 010000
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [1,3,7,6,5,4,2] => 100000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [2,3,7,6,5,4,1] => 000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [3,2,7,6,5,4,1] => 000000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [1,4,7,6,5,3,2] => 100000
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [2,4,7,6,5,3,1] => 000000
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [3,4,7,6,5,2,1] => 000000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [4,3,7,6,5,2,1] => 000000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [1,5,7,6,4,3,2] => 100000
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [2,5,7,6,4,3,1] => 000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [3,5,7,6,4,2,1] => 000000
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [4,5,7,6,3,2,1] => 000000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [5,4,7,6,3,2,1] => 000000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [1,6,7,5,4,3,2] => 100000
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [2,6,7,5,4,3,1] => 000000
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [3,6,7,5,4,2,1] => 000000
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [4,6,7,5,3,2,1] => 000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [5,6,7,4,3,2,1] => 000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [6,5,7,4,3,2,1] => 000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => 100000
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [2,7,6,5,4,3,1] => 000000
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [3,7,6,5,4,2,1] => 000000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [4,7,6,5,3,2,1] => 000000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [5,7,6,4,3,2,1] => 000000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [6,7,5,4,3,2,1] => 000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => 000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 1111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [2,1,3,4,5,6,7,8] => 0111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [1,3,2,4,5,6,7,8] => 1011111
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [2,3,1,4,5,6,7,8] => 0011111
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [3,2,1,4,5,6,7,8] => 0011111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [1,2,4,3,5,6,7,8] => 1101111
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [2,1,4,3,5,6,7,8] => 0101111
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [1,3,4,2,5,6,7,8] => 1001111
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [2,3,4,1,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [3,2,4,1,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [1,4,3,2,5,6,7,8] => 1001111
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [2,4,3,1,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [3,4,2,1,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [4,3,2,1,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [1,2,3,5,4,6,7,8] => 1110111
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [2,1,3,5,4,6,7,8] => 0110111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [1,3,2,5,4,6,7,8] => 1010111
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [2,3,1,5,4,6,7,8] => 0010111
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,2,1] => [3,2,1,5,4,6,7,8] => 0010111
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,3,2,1] => [2,1,4,5,3,6,7,8] => 0100111
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [1,3,4,5,2,6,7,8] => 1000111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [2,3,4,5,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [3,2,4,5,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [2,4,3,5,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [3,4,2,5,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [4,3,2,5,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [1,2,5,4,3,6,7,8] => 1100111
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,2,1] => [2,1,5,4,3,6,7,8] => 0100111
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [2,3,5,4,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [3,2,5,4,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [2,4,5,3,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [3,4,5,2,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [4,3,5,2,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [2,5,4,3,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [3,5,4,2,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [4,5,3,2,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [5,4,3,2,1,6,7,8] => 0000111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [1,2,3,4,6,5,7,8] => 1111011
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [2,1,3,4,6,5,7,8] => 0111011
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [1,3,2,4,6,5,7,8] => 1011011
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [1,2,4,3,6,5,7,8] => 1101011
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [2,1,4,3,6,5,7,8] => 0101011
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [2,3,4,1,6,5,7,8] => 0001011
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [3,2,4,1,6,5,7,8] => 0001011
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,2,1] => [2,4,3,1,6,5,7,8] => 0001011
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [4,3,2,1,6,5,7,8] => 0001011
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [1,2,3,5,6,4,7,8] => 1110011
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [2,3,1,5,6,4,7,8] => 0010011
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [3,2,1,5,6,4,7,8] => 0010011
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [1,2,4,5,6,3,7,8] => 1100011
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [1,3,4,5,6,2,7,8] => 1000011
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [2,3,4,5,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [3,2,4,5,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,7,2,1] => [1,4,3,5,6,2,7,8] => 1000011
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [3,4,2,5,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [4,3,2,5,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,2,1] => [2,3,5,4,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,2,1] => [1,4,5,3,6,2,7,8] => 1000011
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [3,4,5,2,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,7,2,1] => [1,5,4,3,6,2,7,8] => 1000011
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [3,5,4,2,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [4,5,3,2,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [5,4,3,2,6,1,7,8] => 0000011
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [1,2,3,6,5,4,7,8] => 1110011
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [1,3,2,6,5,4,7,8] => 1010011
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [2,3,1,6,5,4,7,8] => 0010011
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [3,2,1,6,5,4,7,8] => 0010011
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [2,1,4,6,5,3,7,8] => 0100011
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [2,3,4,6,5,1,7,8] => 0000011
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,7,2,1] => [1,4,3,6,5,2,7,8] => 1000011
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,2,1] => [2,4,3,6,5,1,7,8] => 0000011
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,2,1] => [4,3,2,6,5,1,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [1,2,5,6,4,3,7,8] => 1100011
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,2,1] => [2,1,5,6,4,3,7,8] => 0100011
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [1,3,5,6,4,2,7,8] => 1000011
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [1,4,5,6,3,2,7,8] => 1000011
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [2,4,5,6,3,1,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [3,4,5,6,2,1,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,7,2,1] => [1,5,4,6,3,2,7,8] => 1000011
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,2,1] => [5,4,3,6,2,1,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [1,2,6,5,4,3,7,8] => 1100011
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [1,4,6,5,3,2,7,8] => 1000011
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [2,4,6,5,3,1,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,2,1] => [4,3,6,5,2,1,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [1,5,6,4,3,2,7,8] => 1000011
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [4,5,6,3,2,1,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,2,1] => [5,4,6,3,2,1,7,8] => 0000011
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [1,6,5,4,3,2,7,8] => 1000011
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [3,6,5,4,2,1,7,8] => 0000011
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [5,6,4,3,2,1,7,8] => 0000011
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [6,5,4,3,2,1,7,8] => 0000011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [1,2,3,4,5,7,6,8] => 1111101
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [2,1,3,4,5,7,6,8] => 0111101
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [1,3,2,4,5,7,6,8] => 1011101
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [2,3,1,4,5,7,6,8] => 0011101
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,3,1] => [3,2,1,4,5,7,6,8] => 0011101
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [1,2,4,3,5,7,6,8] => 1101101
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [1,4,3,2,5,7,6,8] => 1001101
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [4,3,2,1,5,7,6,8] => 0001101
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [1,2,3,5,4,7,6,8] => 1110101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,8] => 1010101
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [2,3,1,5,4,7,6,8] => 0010101
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [3,2,1,5,4,7,6,8] => 0010101
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [1,2,4,5,3,7,6,8] => 1100101
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [1,3,4,5,2,7,6,8] => 1000101
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => [2,3,4,5,1,7,6,8] => 0000101
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [1,4,3,5,2,7,6,8] => 1000101
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [2,4,3,5,1,7,6,8] => 0000101
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [3,4,2,5,1,7,6,8] => 0000101
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [2,1,5,4,3,7,6,8] => 0100101
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [1,3,5,4,2,7,6,8] => 1000101
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,3,1] => [2,3,5,4,1,7,6,8] => 0000101
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [3,2,5,4,1,7,6,8] => 0000101
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,3,1] => [2,4,5,3,1,7,6,8] => 0000101
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,2,3,1] => [3,4,5,2,1,7,6,8] => 0000101
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,2,3,1] => [3,5,4,2,1,7,6,8] => 0000101
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [5,4,3,2,1,7,6,8] => 0000101
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [1,2,3,4,6,7,5,8] => 1111001
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [1,2,4,3,6,7,5,8] => 1101001
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,4,1] => [2,1,4,3,6,7,5,8] => 0101001
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [1,3,4,2,6,7,5,8] => 1001001
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [2,3,4,1,6,7,5,8] => 0001001
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [1,4,3,2,6,7,5,8] => 1001001
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [4,3,2,1,6,7,5,8] => 0001001
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [1,2,3,5,6,7,4,8] => 1110001
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [2,3,1,5,6,7,4,8] => 0010001
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [1,2,4,5,6,7,3,8] => 1100001
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [2,1,4,5,6,7,3,8] => 0100001
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [1,3,4,5,6,7,2,8] => 1000001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [2,3,4,5,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [3,2,4,5,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [3,4,2,5,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => [4,3,2,5,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,6,1] => [1,2,5,4,6,7,3,8] => 1100001
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,6,1] => [2,1,5,4,6,7,3,8] => 0100001
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [1,4,5,3,6,7,2,8] => 1000001
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [2,5,4,3,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [3,5,4,2,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [5,4,3,2,6,7,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [1,2,3,6,5,7,4,8] => 1110001
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [1,3,2,6,5,7,4,8] => 1010001
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [2,3,1,6,5,7,4,8] => 0010001
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [3,2,1,6,5,7,4,8] => 0010001
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [2,3,4,6,5,7,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [1,4,3,6,5,7,2,8] => 1000001
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [2,4,3,6,5,7,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [3,4,2,6,5,7,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,8,1] => [4,3,2,6,5,7,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [1,2,5,6,4,7,3,8] => 1100001
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [1,3,5,6,4,7,2,8] => 1000001
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [3,4,5,6,2,7,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [1,5,4,6,3,7,2,8] => 1000001
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [2,5,4,6,3,7,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [3,5,4,6,2,7,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [4,5,3,6,2,7,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [5,4,3,6,2,7,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [1,3,6,5,4,7,2,8] => 1000001
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,2,8,1] => [3,2,6,5,4,7,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [3,4,6,5,2,7,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [5,4,6,3,2,7,1,8] => 0000001
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => [5,6,4,3,2,7,1,8] => 0000001
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [6,5,4,3,2,7,1,8] => 0000001
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [1,2,3,4,7,6,5,8] => 1111001
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [1,3,2,4,7,6,5,8] => 1011001
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [3,2,1,4,7,6,5,8] => 0011001
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [2,3,4,1,7,6,5,8] => 0001001
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [1,4,3,2,7,6,5,8] => 1001001
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [4,3,2,1,7,6,5,8] => 0001001
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,5,1] => [1,2,3,5,7,6,4,8] => 1110001
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,5,1] => [1,3,2,5,7,6,4,8] => 1010001
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [3,2,1,5,7,6,4,8] => 0010001
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [2,3,4,5,7,6,1,8] => 0000001
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => [1,4,3,5,7,6,2,8] => 1000001
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,7,1] => [1,3,5,4,7,6,2,8] => 1000001
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [3,2,5,4,7,6,1,8] => 0000001
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [3,4,5,2,7,6,1,8] => 0000001
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [4,3,5,2,7,6,1,8] => 0000001
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [3,5,4,2,7,6,1,8] => 0000001
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [4,5,3,2,7,6,1,8] => 0000001
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [5,4,3,2,7,6,1,8] => 0000001
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [1,2,3,6,7,5,4,8] => 1110001
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [2,1,3,6,7,5,4,8] => 0110001
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [1,2,4,6,7,5,3,8] => 1100001
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [1,3,4,6,7,5,2,8] => 1000001
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [3,2,4,6,7,5,1,8] => 0000001
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [1,2,5,6,7,4,3,8] => 1100001
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [2,1,5,6,7,4,3,8] => 0100001
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => [1,3,5,6,7,4,2,8] => 1000001
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,8,1] => [2,3,5,6,7,4,1,8] => 0000001
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [3,2,5,6,7,4,1,8] => 0000001
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [3,4,5,6,7,2,1,8] => 0000001
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [5,4,3,6,7,2,1,8] => 0000001
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,5,8,1] => [2,3,6,5,7,4,1,8] => 0000001
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,8,1] => [3,2,6,5,7,4,1,8] => 0000001
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [1,4,6,5,7,3,2,8] => 1000001
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,8,1] => [4,3,6,5,7,2,1,8] => 0000001
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,7,1] => [1,5,6,4,7,3,2,8] => 1000001
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [2,5,6,4,7,3,1,8] => 0000001
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,8,1] => [5,4,6,3,7,2,1,8] => 0000001
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [3,6,5,4,7,2,1,8] => 0000001
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [5,6,4,3,7,2,1,8] => 0000001
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [6,5,4,3,7,2,1,8] => 0000001
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [1,2,3,7,6,5,4,8] => 1110001
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [3,2,1,7,6,5,4,8] => 0010001
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [2,3,4,7,6,5,1,8] => 0000001
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,3,5,6,1] => [1,2,5,7,6,4,3,8] => 1100001
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [1,3,5,7,6,4,2,8] => 1000001
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [2,3,5,7,6,4,1,8] => 0000001
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,8,1] => [3,2,5,7,6,4,1,8] => 0000001
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => [4,3,5,7,6,2,1,8] => 0000001
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [3,5,4,7,6,2,1,8] => 0000001
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => [4,5,3,7,6,2,1,8] => 0000001
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,5,6,1] => [1,2,6,7,5,4,3,8] => 1100001
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [2,1,6,7,5,4,3,8] => 0100001
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [2,3,6,7,5,4,1,8] => 0000001
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [3,2,6,7,5,4,1,8] => 0000001
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [2,4,6,7,5,3,1,8] => 0000001
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [1,5,6,7,4,3,2,8] => 1000001
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [2,5,6,7,4,3,1,8] => 0000001
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,7,8,1] => [3,5,6,7,4,2,1,8] => 0000001
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [4,5,6,7,3,2,1,8] => 0000001
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [5,4,6,7,3,2,1,8] => 0000001
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [1,6,5,7,4,3,2,8] => 1000001
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [4,6,5,7,3,2,1,8] => 0000001
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [5,6,4,7,3,2,1,8] => 0000001
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [6,5,4,7,3,2,1,8] => 0000001
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [1,2,7,6,5,4,3,8] => 1100001
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [2,1,7,6,5,4,3,8] => 0100001
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [2,3,7,6,5,4,1,8] => 0000001
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [3,2,7,6,5,4,1,8] => 0000001
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [3,4,7,6,5,2,1,8] => 0000001
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,7,8,1] => [4,3,7,6,5,2,1,8] => 0000001
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,8,1] => [2,5,7,6,4,3,1,8] => 0000001
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,8,1] => [3,5,7,6,4,2,1,8] => 0000001
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [4,5,7,6,3,2,1,8] => 0000001
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [5,4,7,6,3,2,1,8] => 0000001
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [1,6,7,5,4,3,2,8] => 1000001
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [2,6,7,5,4,3,1,8] => 0000001
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [4,6,7,5,3,2,1,8] => 0000001
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [5,6,7,4,3,2,1,8] => 0000001
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [6,5,7,4,3,2,1,8] => 0000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [1,7,6,5,4,3,2,8] => 1000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,7,6,5,4,3,1,8] => 0000001
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [4,7,6,5,3,2,1,8] => 0000001
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [5,7,6,4,3,2,1,8] => 0000001
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [6,7,5,4,3,2,1,8] => 0000001
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [7,6,5,4,3,2,1,8] => 0000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,8,7] => 1111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7] => 0111110
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [1,3,2,4,5,6,8,7] => 1011110
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [2,3,1,4,5,6,8,7] => 0011110
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [3,2,1,4,5,6,8,7] => 0011110
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [1,2,4,3,5,6,8,7] => 1101110
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [2,1,4,3,5,6,8,7] => 0101110
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [1,3,4,2,5,6,8,7] => 1001110
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [2,3,4,1,5,6,8,7] => 0001110
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,1,2] => [1,4,3,2,5,6,8,7] => 1001110
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [4,3,2,1,5,6,8,7] => 0001110
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [1,2,3,5,4,6,8,7] => 1110110
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [2,1,3,5,4,6,8,7] => 0110110
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [2,3,4,5,1,6,8,7] => 0000110
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [2,4,3,5,1,6,8,7] => 0000110
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,1,2] => [1,2,5,4,3,6,8,7] => 1100110
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [2,1,5,4,3,6,8,7] => 0100110
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [1,3,5,4,2,6,8,7] => 1000110
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [2,3,5,4,1,6,8,7] => 0000110
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [3,2,5,4,1,6,8,7] => 0000110
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [1,4,5,3,2,6,8,7] => 1000110
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,1,2] => [2,4,5,3,1,6,8,7] => 0000110
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [3,4,5,2,1,6,8,7] => 0000110
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [4,3,5,2,1,6,8,7] => 0000110
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,1,2] => [2,5,4,3,1,6,8,7] => 0000110
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [4,5,3,2,1,6,8,7] => 0000110
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [5,4,3,2,1,6,8,7] => 0000110
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [1,2,3,4,6,5,8,7] => 1111010
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [2,1,3,4,6,5,8,7] => 0111010
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,1,2] => [1,3,2,4,6,5,8,7] => 1011010
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [2,3,1,4,6,5,8,7] => 0011010
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [1,2,4,3,6,5,8,7] => 1101010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => 0101010
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [1,3,4,2,6,5,8,7] => 1001010
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [2,3,4,1,6,5,8,7] => 0001010
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [3,2,4,1,6,5,8,7] => 0001010
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [3,4,2,1,6,5,8,7] => 0001010
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [4,3,2,1,6,5,8,7] => 0001010
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,1,2] => [1,2,3,5,6,4,8,7] => 1110010
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,1,2] => [2,1,3,5,6,4,8,7] => 0110010
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,1,2] => [1,3,2,5,6,4,8,7] => 1010010
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,1,2] => [1,2,4,5,6,3,8,7] => 1100010
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [2,1,4,5,6,3,8,7] => 0100010
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [1,3,4,5,6,2,8,7] => 1000010
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [2,3,4,5,6,1,8,7] => 0000010
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => [2,4,3,5,6,1,8,7] => 0000010
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [4,3,2,5,6,1,8,7] => 0000010
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [2,1,5,4,6,3,8,7] => 0100010
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [3,2,5,4,6,1,8,7] => 0000010
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,1,2] => [3,5,4,2,6,1,8,7] => 0000010
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [4,5,3,2,6,1,8,7] => 0000010
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [5,4,3,2,6,1,8,7] => 0000010
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [1,2,3,6,5,4,8,7] => 1110010
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => [2,1,3,6,5,4,8,7] => 0110010
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [1,3,2,6,5,4,8,7] => 1010010
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,1,2] => [2,3,1,6,5,4,8,7] => 0010010
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => [3,2,1,6,5,4,8,7] => 0010010
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,1,2] => [4,3,2,6,5,1,8,7] => 0000010
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [2,1,5,6,4,3,8,7] => 0100010
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [3,4,5,6,2,1,8,7] => 0000010
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,7,1,2] => [1,5,4,6,3,2,8,7] => 1000010
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [2,1,6,5,4,3,8,7] => 0100010
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,7,1,2] => [1,3,6,5,4,2,8,7] => 1000010
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [4,3,6,5,2,1,8,7] => 0000010
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [1,5,6,4,3,2,8,7] => 1000010
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [4,5,6,3,2,1,8,7] => 0000010
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [5,4,6,3,2,1,8,7] => 0000010
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [1,6,5,4,3,2,8,7] => 1000010
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [2,6,5,4,3,1,8,7] => 0000010
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [3,6,5,4,2,1,8,7] => 0000010
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [4,6,5,3,2,1,8,7] => 0000010
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [5,6,4,3,2,1,8,7] => 0000010
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [6,5,4,3,2,1,8,7] => 0000010
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [1,2,3,4,5,7,8,6] => 1111100
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [2,1,3,4,5,7,8,6] => 0111100
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [1,3,2,4,5,7,8,6] => 1011100
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [2,3,1,4,5,7,8,6] => 0011100
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [3,2,1,4,5,7,8,6] => 0011100
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [1,2,4,3,5,7,8,6] => 1101100
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [2,1,4,3,5,7,8,6] => 0101100
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => [1,3,4,2,5,7,8,6] => 1001100
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,1,3] => [1,4,3,2,5,7,8,6] => 1001100
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [4,3,2,1,5,7,8,6] => 0001100
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [1,2,3,5,4,7,8,6] => 1110100
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,2,1,3] => [2,1,3,5,4,7,8,6] => 0110100
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,1,3] => [1,3,2,5,4,7,8,6] => 1010100
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,1,3] => [1,2,4,5,3,7,8,6] => 1100100
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,1,3] => [1,3,4,5,2,7,8,6] => 1000100
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [2,3,4,5,1,7,8,6] => 0000100
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,1,3] => [1,2,5,4,3,7,8,6] => 1100100
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,1,3] => [1,3,5,4,2,7,8,6] => 1000100
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,1,3] => [3,2,5,4,1,7,8,6] => 0000100
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [2,4,5,3,1,7,8,6] => 0000100
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [1,5,4,3,2,7,8,6] => 1000100
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,2,1,3] => [3,5,4,2,1,7,8,6] => 0000100
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [5,4,3,2,1,7,8,6] => 0000100
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [1,2,3,4,6,7,8,5] => 1111000
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [2,1,3,4,6,7,8,5] => 0111000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [1,3,2,4,6,7,8,5] => 1011000
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [2,3,1,4,6,7,8,5] => 0011000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [1,2,4,3,6,7,8,5] => 1101000
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [2,3,4,1,6,7,8,5] => 0001000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [1,4,3,2,6,7,8,5] => 1001000
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [3,4,2,1,6,7,8,5] => 0001000
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [4,3,2,1,6,7,8,5] => 0001000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [1,2,3,5,6,7,8,4] => 1110000
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [2,1,3,5,6,7,8,4] => 0110000
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [2,3,1,5,6,7,8,4] => 0010000
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [3,2,1,5,6,7,8,4] => 0010000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [1,2,4,5,6,7,8,3] => 1100000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [2,1,4,5,6,7,8,3] => 0100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [1,3,4,5,6,7,8,2] => 1000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [3,2,4,5,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [1,4,3,5,6,7,8,2] => 1000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [2,4,3,5,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [3,4,2,5,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [4,3,2,5,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [1,2,5,4,6,7,8,3] => 1100000
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [2,1,5,4,6,7,8,3] => 0100000
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [2,3,5,4,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [3,2,5,4,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,1,7] => [1,4,5,3,6,7,8,2] => 1000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [2,4,5,3,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [3,4,5,2,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [1,5,4,3,6,7,8,2] => 1000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [2,5,4,3,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,1,8] => [3,5,4,2,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [5,4,3,2,6,7,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [1,2,3,6,5,7,8,4] => 1110000
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [3,2,1,6,5,7,8,4] => 0010000
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [1,3,4,6,5,7,8,2] => 1000000
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [2,3,4,6,5,7,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [1,4,3,6,5,7,8,2] => 1000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [2,4,3,6,5,7,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [4,3,2,6,5,7,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [2,3,5,6,4,7,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [2,4,5,6,3,7,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [3,4,5,6,2,7,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [4,3,5,6,2,7,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,1,8] => [5,4,3,6,2,7,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [1,2,6,5,4,7,8,3] => 1100000
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [2,3,6,5,4,7,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,1,8] => [2,4,6,5,3,7,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,1,8] => [3,4,6,5,2,7,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,6,2,1,8] => [2,5,6,4,3,7,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,1,8] => [5,4,6,3,2,7,8,1] => 0000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [2,6,5,4,3,7,8,1] => 0000000
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [6,5,4,3,2,7,8,1] => 0000000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [1,2,3,4,7,6,8,5] => 1111000
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [3,2,4,1,7,6,8,5] => 0001000
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [1,4,3,2,7,6,8,5] => 1001000
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [2,4,3,1,7,6,8,5] => 0001000
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [4,3,2,1,7,6,8,5] => 0001000
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [1,2,3,5,7,6,8,4] => 1110000
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [3,2,1,5,7,6,8,4] => 0010000
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [2,3,4,5,7,6,8,1] => 0000000
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [3,2,4,5,7,6,8,1] => 0000000
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [2,4,3,5,7,6,8,1] => 0000000
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [4,3,2,5,7,6,8,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [1,2,5,4,7,6,8,3] => 1100000
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [2,1,5,4,7,6,8,3] => 0100000
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [2,3,5,4,7,6,8,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [3,2,5,4,7,6,8,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [4,3,5,2,7,6,8,1] => 0000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [2,5,4,3,7,6,8,1] => 0000000
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [5,4,3,2,7,6,8,1] => 0000000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [1,2,3,6,7,5,8,4] => 1110000
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [3,2,1,6,7,5,8,4] => 0010000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [1,3,4,6,7,5,8,2] => 1000000
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [2,3,4,6,7,5,8,1] => 0000000
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,4,1,8] => [2,4,3,6,7,5,8,1] => 0000000
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [3,4,2,6,7,5,8,1] => 0000000
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [1,2,5,6,7,4,8,3] => 1100000
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [2,1,5,6,7,4,8,3] => 0100000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,1,7] => [1,3,5,6,7,4,8,2] => 1000000
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [2,3,5,6,7,4,8,1] => 0000000
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [2,4,5,6,7,3,8,1] => 0000000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [3,4,5,6,7,2,8,1] => 0000000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,1,7] => [1,5,4,6,7,3,8,2] => 1000000
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,1,8] => [5,4,3,6,7,2,8,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [2,4,6,5,7,3,8,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,1,8] => [3,4,6,5,7,2,8,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [4,3,6,5,7,2,8,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,1,8] => [3,5,6,4,7,2,8,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [5,4,6,3,7,2,8,1] => 0000000
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [3,6,5,4,7,2,8,1] => 0000000
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [4,6,5,3,7,2,8,1] => 0000000
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [6,5,4,3,7,2,8,1] => 0000000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [1,2,3,7,6,5,8,4] => 1110000
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [1,3,2,7,6,5,8,4] => 1010000
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [3,2,1,7,6,5,8,4] => 0010000
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,4,1,6] => [1,2,4,7,6,5,8,3] => 1100000
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [2,1,4,7,6,5,8,3] => 0100000
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [1,3,4,7,6,5,8,2] => 1000000
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [2,3,4,7,6,5,8,1] => 0000000
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [3,2,4,7,6,5,8,1] => 0000000
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [2,4,3,7,6,5,8,1] => 0000000
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [3,4,2,7,6,5,8,1] => 0000000
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [4,3,2,7,6,5,8,1] => 0000000
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,1,6] => [2,1,5,7,6,4,8,3] => 0100000
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [2,3,5,7,6,4,8,1] => 0000000
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,1,8] => [3,4,5,7,6,2,8,1] => 0000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [2,5,4,7,6,3,8,1] => 0000000
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,1,8] => [3,5,4,7,6,2,8,1] => 0000000
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,1,8] => [5,4,3,7,6,2,8,1] => 0000000
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,1,6] => [2,1,6,7,5,4,8,3] => 0100000
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [3,2,6,7,5,4,8,1] => 0000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [1,4,6,7,5,3,8,2] => 1000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [2,4,6,7,5,3,8,1] => 0000000
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,7,1,8] => [4,3,6,7,5,2,8,1] => 0000000
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [4,5,6,7,3,2,8,1] => 0000000
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7,3,4,2,5,6,1,8] => [2,6,5,7,4,3,8,1] => 0000000
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,1,8] => [4,6,5,7,3,2,8,1] => 0000000
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [2,1,7,6,5,4,8,3] => 0100000
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [2,3,7,6,5,4,8,1] => 0000000
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [3,2,7,6,5,4,8,1] => 0000000
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [3,5,7,6,4,2,8,1] => 0000000
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,1,8] => [4,6,7,5,3,2,8,1] => 0000000
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [6,5,7,4,3,2,8,1] => 0000000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [1,7,6,5,4,3,8,2] => 1000000
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [2,7,6,5,4,3,8,1] => 0000000
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [4,7,6,5,3,2,8,1] => 0000000
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [5,7,6,4,3,2,8,1] => 0000000
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [6,7,5,4,3,2,8,1] => 0000000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [7,6,5,4,3,2,8,1] => 0000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [1,2,3,4,5,8,7,6] => 1111100
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [2,1,3,4,5,8,7,6] => 0111100
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,1,2,3] => [1,3,2,4,5,8,7,6] => 1011100
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [3,2,1,4,5,8,7,6] => 0011100
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,1,2,3] => [1,2,4,3,5,8,7,6] => 1101100
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [2,1,4,3,5,8,7,6] => 0101100
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [3,2,4,1,5,8,7,6] => 0001100
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [1,4,3,2,5,8,7,6] => 1001100
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [2,4,3,1,5,8,7,6] => 0001100
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [4,3,2,1,5,8,7,6] => 0001100
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [1,2,3,5,4,8,7,6] => 1110100
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,1,2,3] => [2,1,3,5,4,8,7,6] => 0110100
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [1,3,2,5,4,8,7,6] => 1010100
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [1,2,4,5,3,8,7,6] => 1100100
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [2,1,4,5,3,8,7,6] => 0100100
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => [1,3,4,5,2,8,7,6] => 1000100
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [2,3,4,5,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [3,2,4,5,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => [2,4,3,5,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [3,4,2,5,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => [4,3,2,5,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [1,2,5,4,3,8,7,6] => 1100100
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [2,1,5,4,3,8,7,6] => 0100100
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => [2,3,5,4,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [3,2,5,4,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [2,4,5,3,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [3,4,5,2,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [4,3,5,2,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [1,5,4,3,2,8,7,6] => 1000100
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,1,2,3] => [2,5,4,3,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,1,2,3] => [3,5,4,2,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [4,5,3,2,1,8,7,6] => 0000100
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [5,4,3,2,1,8,7,6] => 0000100
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [1,2,3,4,6,8,7,5] => 1111000
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [1,3,2,4,6,8,7,5] => 1011000
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,1,2,4] => [3,2,1,4,6,8,7,5] => 0011000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [1,2,4,3,6,8,7,5] => 1101000
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [2,1,4,3,6,8,7,5] => 0101000
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => [1,3,4,2,6,8,7,5] => 1001000
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [3,2,4,1,6,8,7,5] => 0001000
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,1,2,4] => [1,4,3,2,6,8,7,5] => 1001000
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [4,3,2,1,6,8,7,5] => 0001000
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [1,2,3,5,6,8,7,4] => 1110000
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,1,2,5] => [1,3,2,5,6,8,7,4] => 1010000
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [3,2,1,5,6,8,7,4] => 0010000
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [1,2,4,5,6,8,7,3] => 1100000
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [2,1,4,5,6,8,7,3] => 0100000
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [1,3,4,5,6,8,7,2] => 1000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [2,3,4,5,6,8,7,1] => 0000000
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [2,4,3,5,6,8,7,1] => 0000000
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,1,2,8] => [3,4,2,5,6,8,7,1] => 0000000
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,1,2,8] => [4,3,2,5,6,8,7,1] => 0000000
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,1,2,6] => [1,2,5,4,6,8,7,3] => 1100000
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,1,2,6] => [2,1,5,4,6,8,7,3] => 0100000
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,1,2,7] => [1,4,5,3,6,8,7,2] => 1000000
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,1,2,8] => [2,4,5,3,6,8,7,1] => 0000000
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,1,2,7] => [1,5,4,3,6,8,7,2] => 1000000
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => [2,5,4,3,6,8,7,1] => 0000000
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [5,4,3,2,6,8,7,1] => 0000000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [1,2,3,6,5,8,7,4] => 1110000
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [2,1,3,6,5,8,7,4] => 0110000
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [1,3,2,6,5,8,7,4] => 1010000
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,1,2,5] => [2,3,1,6,5,8,7,4] => 0010000
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [3,2,1,6,5,8,7,4] => 0010000
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [1,2,4,6,5,8,7,3] => 1100000
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,1,2,6] => [2,1,4,6,5,8,7,3] => 0100000
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [2,3,4,6,5,8,7,1] => 0000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [1,4,3,6,5,8,7,2] => 1000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,1,2,8] => [2,4,3,6,5,8,7,1] => 0000000
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [3,4,2,6,5,8,7,1] => 0000000
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,1,2,8] => [4,3,2,6,5,8,7,1] => 0000000
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [1,4,5,6,3,8,7,2] => 1000000
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,1,2,8] => [2,4,5,6,3,8,7,1] => 0000000
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [1,2,6,5,4,8,7,3] => 1100000
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [1,3,6,5,4,8,7,2] => 1000000
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [3,2,6,5,4,8,7,1] => 0000000
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [1,4,6,5,3,8,7,2] => 1000000
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,1,2,8] => [2,4,6,5,3,8,7,1] => 0000000
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [4,3,6,5,2,8,7,1] => 0000000
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [1,5,6,4,3,8,7,2] => 1000000
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,1,2,8] => [4,5,6,3,2,8,7,1] => 0000000
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,1,2,8] => [5,4,6,3,2,8,7,1] => 0000000
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [1,6,5,4,3,8,7,2] => 1000000
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,1,2,8] => [2,6,5,4,3,8,7,1] => 0000000
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,1,2,8] => [4,6,5,3,2,8,7,1] => 0000000
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [6,5,4,3,2,8,7,1] => 0000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [1,2,3,4,7,8,6,5] => 1111000
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [2,1,3,4,7,8,6,5] => 0111000
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [2,3,1,4,7,8,6,5] => 0011000
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [3,2,1,4,7,8,6,5] => 0011000
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [1,2,4,3,7,8,6,5] => 1101000
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [2,1,4,3,7,8,6,5] => 0101000
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [1,3,4,2,7,8,6,5] => 1001000
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [3,2,4,1,7,8,6,5] => 0001000
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [3,4,2,1,7,8,6,5] => 0001000
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [4,3,2,1,7,8,6,5] => 0001000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [1,2,3,5,7,8,6,4] => 1110000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [1,3,2,5,7,8,6,4] => 1010000
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [3,2,1,5,7,8,6,4] => 0010000
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,1,3,6] => [1,2,4,5,7,8,6,3] => 1100000
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [2,1,4,5,7,8,6,3] => 0100000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [1,3,4,5,7,8,6,2] => 1000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [2,3,4,5,7,8,6,1] => 0000000
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [1,4,3,5,7,8,6,2] => 1000000
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,1,3,6] => [1,2,5,4,7,8,6,3] => 1100000
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [2,4,5,3,7,8,6,1] => 0000000
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [2,5,4,3,7,8,6,1] => 0000000
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [5,4,3,2,7,8,6,1] => 0000000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [1,2,3,6,7,8,5,4] => 1110000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [1,3,2,6,7,8,5,4] => 1010000
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [2,3,1,6,7,8,5,4] => 0010000
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [3,2,1,6,7,8,5,4] => 0010000
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [1,2,4,6,7,8,5,3] => 1100000
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [2,1,4,6,7,8,5,3] => 0100000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [1,3,4,6,7,8,5,2] => 1000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [2,3,4,6,7,8,5,1] => 0000000
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [1,4,3,6,7,8,5,2] => 1000000
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,1,4,8] => [2,4,3,6,7,8,5,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [1,2,5,6,7,8,4,3] => 1100000
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [2,1,5,6,7,8,4,3] => 0100000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [1,3,5,6,7,8,4,2] => 1000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [2,3,5,6,7,8,4,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [3,2,5,6,7,8,4,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [1,4,5,6,7,8,3,2] => 1000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [2,4,5,6,7,8,3,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [3,4,5,6,7,8,2,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [4,3,5,6,7,8,2,1] => 0000000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [1,5,4,6,7,8,3,2] => 1000000
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [5,4,3,6,7,8,2,1] => 0000000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [1,3,6,5,7,8,4,2] => 1000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,1,6,8] => [2,4,6,5,7,8,3,1] => 0000000
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [3,4,6,5,7,8,2,1] => 0000000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [1,6,5,4,7,8,3,2] => 1000000
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [2,6,5,4,7,8,3,1] => 0000000
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,1,7,8] => [3,6,5,4,7,8,2,1] => 0000000
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [6,5,4,3,7,8,2,1] => 0000000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [1,2,3,7,6,8,5,4] => 1110000
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [2,3,1,7,6,8,5,4] => 0010000
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [3,2,1,7,6,8,5,4] => 0010000
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [1,3,4,7,6,8,5,2] => 1000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [1,4,3,7,6,8,5,2] => 1000000
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [2,1,5,7,6,8,4,3] => 0100000
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,1,5,8] => [3,2,5,7,6,8,4,1] => 0000000
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,1,7,8] => [4,3,5,7,6,8,2,1] => 0000000
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [4,5,3,7,6,8,2,1] => 0000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [2,4,6,7,5,8,3,1] => 0000000
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [4,5,6,7,3,8,2,1] => 0000000
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [5,4,6,7,3,8,2,1] => 0000000
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [6,5,4,7,3,8,2,1] => 0000000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [1,2,7,6,5,8,4,3] => 1100000
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [1,4,7,6,5,8,3,2] => 1000000
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [2,4,7,6,5,8,3,1] => 0000000
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [3,4,7,6,5,8,2,1] => 0000000
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [4,3,7,6,5,8,2,1] => 0000000
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,1,7,8] => [5,4,7,6,3,8,2,1] => 0000000
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [5,6,7,4,3,8,2,1] => 0000000
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [3,7,6,5,4,8,2,1] => 0000000
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [6,7,5,4,3,8,2,1] => 0000000
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [7,6,5,4,3,8,2,1] => 0000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [1,2,3,4,8,7,6,5] => 1111000
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [2,1,3,4,8,7,6,5] => 0111000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [1,3,2,4,8,7,6,5] => 1011000
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [2,3,1,4,8,7,6,5] => 0011000
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [3,2,1,4,8,7,6,5] => 0011000
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [1,2,4,3,8,7,6,5] => 1101000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [2,1,4,3,8,7,6,5] => 0101000
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [1,3,4,2,8,7,6,5] => 1001000
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [2,3,4,1,8,7,6,5] => 0001000
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [3,2,4,1,8,7,6,5] => 0001000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [1,4,3,2,8,7,6,5] => 1001000
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [2,4,3,1,8,7,6,5] => 0001000
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [3,4,2,1,8,7,6,5] => 0001000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => 0001000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [1,2,3,5,8,7,6,4] => 1110000
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,1,2,3,5] => [1,3,2,5,8,7,6,4] => 1010000
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [3,2,1,5,8,7,6,4] => 0010000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [1,2,4,5,8,7,6,3] => 1100000
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [2,1,4,5,8,7,6,3] => 0100000
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [2,3,4,5,8,7,6,1] => 0000000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [1,4,3,5,8,7,6,2] => 1000000
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [4,3,2,5,8,7,6,1] => 0000000
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => [1,2,5,4,8,7,6,3] => 1100000
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [2,1,5,4,8,7,6,3] => 0100000
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [1,3,5,4,8,7,6,2] => 1000000
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,1,2,3,8] => [2,3,5,4,8,7,6,1] => 0000000
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,1,2,3,8] => [2,4,5,3,8,7,6,1] => 0000000
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [4,3,5,2,8,7,6,1] => 0000000
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [2,5,4,3,8,7,6,1] => 0000000
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [4,5,3,2,8,7,6,1] => 0000000
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [5,4,3,2,8,7,6,1] => 0000000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [1,2,3,6,8,7,5,4] => 1110000
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [2,1,3,6,8,7,5,4] => 0110000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [1,3,2,6,8,7,5,4] => 1010000
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [2,3,1,6,8,7,5,4] => 0010000
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [3,2,1,6,8,7,5,4] => 0010000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [1,2,4,6,8,7,5,3] => 1100000
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [2,1,4,6,8,7,5,3] => 0100000
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,1,2,4,8] => [2,3,4,6,8,7,5,1] => 0000000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [1,4,3,6,8,7,5,2] => 1000000
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,1,2,4,8] => [2,4,3,6,8,7,5,1] => 0000000
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [4,3,2,6,8,7,5,1] => 0000000
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,1,2,5,6] => [1,2,5,6,8,7,4,3] => 1100000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [1,3,5,6,8,7,4,2] => 1000000
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [2,3,5,6,8,7,4,1] => 0000000
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [3,4,5,6,8,7,2,1] => 0000000
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [4,3,5,6,8,7,2,1] => 0000000
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [4,5,3,6,8,7,2,1] => 0000000
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,1,2,7,8] => [5,4,3,6,8,7,2,1] => 0000000
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [2,1,6,5,8,7,4,3] => 0100000
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [1,4,6,5,8,7,3,2] => 1000000
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,1,2,6,8] => [2,4,6,5,8,7,3,1] => 0000000
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [4,3,6,5,8,7,2,1] => 0000000
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,1,2,6,8] => [2,5,6,4,8,7,3,1] => 0000000
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [4,5,6,3,8,7,2,1] => 0000000
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,1,2,6,8] => [2,6,5,4,8,7,3,1] => 0000000
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [5,6,4,3,8,7,2,1] => 0000000
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [6,5,4,3,8,7,2,1] => 0000000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [1,2,3,7,8,6,5,4] => 1110000
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [2,1,3,7,8,6,5,4] => 0110000
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [3,2,1,7,8,6,5,4] => 0010000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [1,2,4,7,8,6,5,3] => 1100000
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [2,1,4,7,8,6,5,3] => 0100000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [1,4,3,7,8,6,5,2] => 1000000
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,1,3,4,8] => [3,4,2,7,8,6,5,1] => 0000000
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [4,3,2,7,8,6,5,1] => 0000000
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [2,1,5,7,8,6,4,3] => 0100000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [1,3,5,7,8,6,4,2] => 1000000
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,1,3,6,8] => [2,4,5,7,8,6,3,1] => 0000000
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [4,3,5,7,8,6,2,1] => 0000000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,1,3,6,7] => [1,5,4,7,8,6,3,2] => 1000000
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [4,5,3,7,8,6,2,1] => 0000000
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [5,4,3,7,8,6,2,1] => 0000000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [1,2,6,7,8,5,4,3] => 1100000
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [2,1,6,7,8,5,4,3] => 0100000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [1,3,6,7,8,5,4,2] => 1000000
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [2,3,6,7,8,5,4,1] => 0000000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [1,4,6,7,8,5,3,2] => 1000000
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [2,4,6,7,8,5,3,1] => 0000000
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [3,4,6,7,8,5,2,1] => 0000000
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [4,3,6,7,8,5,2,1] => 0000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [1,5,6,7,8,4,3,2] => 1000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [2,5,6,7,8,4,3,1] => 0000000
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [3,5,6,7,8,4,2,1] => 0000000
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [4,5,6,7,8,3,2,1] => 0000000
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [5,4,6,7,8,3,2,1] => 0000000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [1,6,5,7,8,4,3,2] => 1000000
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [4,6,5,7,8,3,2,1] => 0000000
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [5,6,4,7,8,3,2,1] => 0000000
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [6,5,4,7,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [1,5,7,6,8,4,3,2] => 1000000
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [4,5,7,6,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [5,4,7,6,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,1,5,6,7] => [1,6,7,5,8,4,3,2] => 1000000
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [4,6,7,5,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [5,6,7,4,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [6,5,7,4,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [1,7,6,5,8,4,3,2] => 1000000
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [4,7,6,5,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [5,7,6,4,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [6,7,5,4,8,3,2,1] => 0000000
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [7,6,5,4,8,3,2,1] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [1,2,3,8,7,6,5,4] => 1110000
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [2,1,3,8,7,6,5,4] => 0110000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [1,3,2,8,7,6,5,4] => 1010000
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [2,3,1,8,7,6,5,4] => 0010000
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [3,2,1,8,7,6,5,4] => 0010000
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [1,2,4,8,7,6,5,3] => 1100000
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [2,1,4,8,7,6,5,3] => 0100000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [1,3,4,8,7,6,5,2] => 1000000
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [2,3,4,8,7,6,5,1] => 0000000
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [3,2,4,8,7,6,5,1] => 0000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [1,4,3,8,7,6,5,2] => 1000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [2,4,3,8,7,6,5,1] => 0000000
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [3,4,2,8,7,6,5,1] => 0000000
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [4,3,2,8,7,6,5,1] => 0000000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [1,2,5,8,7,6,4,3] => 1100000
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [1,3,5,8,7,6,4,2] => 1000000
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [7,6,4,1,2,3,5,8] => [2,3,5,8,7,6,4,1] => 0000000
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [1,4,5,8,7,6,3,2] => 1000000
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [3,4,5,8,7,6,2,1] => 0000000
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [2,5,4,8,7,6,3,1] => 0000000
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [5,4,3,8,7,6,2,1] => 0000000
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [8,6,3,1,2,4,5,7] => [1,3,6,8,7,5,4,2] => 1000000
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [3,2,6,8,7,5,4,1] => 0000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [1,4,6,8,7,5,3,2] => 1000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [2,4,6,8,7,5,3,1] => 0000000
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [3,5,6,8,7,4,2,1] => 0000000
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [4,5,6,8,7,3,2,1] => 0000000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [1,6,5,8,7,4,3,2] => 1000000
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => [4,6,5,8,7,3,2,1] => 0000000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [1,2,7,8,6,5,4,3] => 1100000
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [8,6,2,1,3,4,5,7] => [1,3,7,8,6,5,4,2] => 1000000
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [1,4,7,8,6,5,3,2] => 1000000
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,2,1,3,4,6,8] => [2,4,7,8,6,5,3,1] => 0000000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [3,5,7,8,6,4,2,1] => 0000000
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [4,5,7,8,6,3,2,1] => 0000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [1,6,7,8,5,4,3,2] => 1000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [2,6,7,8,5,4,3,1] => 0000000
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [4,6,7,8,5,3,2,1] => 0000000
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [5,6,7,8,4,3,2,1] => 0000000
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [6,5,7,8,4,3,2,1] => 0000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [1,7,6,8,5,4,3,2] => 1000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [2,7,6,8,5,4,3,1] => 0000000
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [4,7,6,8,5,3,2,1] => 0000000
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [5,7,6,8,4,3,2,1] => 0000000
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [6,7,5,8,4,3,2,1] => 0000000
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [7,6,5,8,4,3,2,1] => 0000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [1,2,8,7,6,5,4,3] => 1100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [2,1,8,7,6,5,4,3] => 0100000
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [1,3,8,7,6,5,4,2] => 1000000
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [2,3,8,7,6,5,4,1] => 0000000
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [3,2,8,7,6,5,4,1] => 0000000
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [1,4,8,7,6,5,3,2] => 1000000
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [2,4,8,7,6,5,3,1] => 0000000
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,2,3,4,7,8] => [3,4,8,7,6,5,2,1] => 0000000
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,6,1,2,3,4,7,8] => [4,3,8,7,6,5,2,1] => 0000000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [1,5,8,7,6,4,3,2] => 1000000
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [2,5,8,7,6,4,3,1] => 0000000
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [3,5,8,7,6,4,2,1] => 0000000
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [4,5,8,7,6,3,2,1] => 0000000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [1,6,8,7,5,4,3,2] => 1000000
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [2,6,8,7,5,4,3,1] => 0000000
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [3,6,8,7,5,4,2,1] => 0000000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [4,6,8,7,5,3,2,1] => 0000000
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [6,5,8,7,4,3,2,1] => 0000000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [1,7,8,6,5,4,3,2] => 1000000
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [2,7,8,6,5,4,3,1] => 0000000
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,3,4,5,7,8] => [3,7,8,6,5,4,2,1] => 0000000
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [4,7,8,6,5,3,2,1] => 0000000
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [5,7,8,6,4,3,2,1] => 0000000
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [6,7,8,5,4,3,2,1] => 0000000
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [7,6,8,5,4,3,2,1] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => 1000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [2,8,7,6,5,4,3,1] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [3,8,7,6,5,4,2,1] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [4,8,7,6,5,3,2,1] => 0000000
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [5,8,7,6,4,3,2,1] => 0000000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [6,8,7,5,4,3,2,1] => 0000000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [7,8,6,5,4,3,2,1] => 0000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => 0000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 10000000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [8,7,6,5,4,3,2,1,9] => 00000001
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 100000000
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [7,8,6,5,4,3,2,1,9] => 00000001
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [9,8,7,6,5,4,3,2,1,10] => 000000001
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => 1000000000
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => [7,6,8,5,4,3,2,1,9] => 00000001
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [8,9,7,6,5,4,3,2,1,10] => 000000001
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [10,9,8,7,6,5,4,3,2,1,11] => 0000000001
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [1,12,11,10,9,8,7,6,5,4,3,2] => 10000000000
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => [6,7,8,5,4,3,2,1,9] => 00000001
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,1] => [7,6,5,8,4,3,2,1,9] => 00000001
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,10,1] => [8,7,9,6,5,4,3,2,1,10] => 000000001
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,7,8,9,1] => [4,8,7,6,5,3,2,1,9] => 00000001
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,1] => [6,5,8,7,4,3,2,1,9] => 00000001
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,10,1] => [7,8,9,6,5,4,3,2,1,10] => 000000001
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,10,1] => [8,7,6,9,5,4,3,2,1,10] => 000000001
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,10,11,1] => [9,8,10,7,6,5,4,3,2,1,11] => 0000000001
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [6,2,3,4,5,7,8,9,10,1] => [5,9,8,7,6,4,3,2,1,10] => 000000001
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [4,5,3,2,6,7,8,9,1] => [6,5,7,8,4,3,2,1,9] => 00000001
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,1] => [7,6,5,4,3,8,2,1,9] => 00000001
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,10,11,1] => [9,8,7,10,6,5,4,3,2,1,11] => 0000000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [1,3,9,8,7,6,5,4,2] => 10000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [2,1,9,8,7,6,5,4,3] => 01000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [2,8,7,6,5,4,3,1,9] => 00000001
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [7,6,5,4,3,2,1,9,8] => 00000010
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,1] => [7,6,5,4,3,2,8,1,9] => 00000001
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,10,1] => [8,7,6,5,4,9,3,2,1,10] => 000000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [1,2,9,8,7,6,5,4,3] => 11000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2,9] => 10000001
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [7,6,5,4,3,2,1,8,9] => 00000011
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,10,1] => [8,7,6,5,4,3,9,2,1,10] => 000000001
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,10,11,1] => [9,8,7,6,5,10,4,3,2,1,11] => 0000000001
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [10,8,1,2,3,4,5,6,7,9] => [1,3,10,9,8,7,6,5,4,2] => 100000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [2,1,10,9,8,7,6,5,4,3] => 010000000
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,4,5,6,7,8,1] => [1,7,8,6,5,4,3,2,9] => 10000001
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,2,1] => [6,7,5,4,3,2,1,8,9] => 00000011
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [8,7,6,5,4,3,2,1,10,9] => 000000010
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,10,1] => [8,7,6,5,4,3,2,9,1,10] => 000000001
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,10,11,1] => [9,8,7,6,5,4,10,3,2,1,11] => 0000000001
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [1,2,10,9,8,7,6,5,4,3] => 110000000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2,10] => 100000001
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [8,7,6,5,4,3,2,1,9,10] => 000000011
[] => [] => [] =>
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [3,2,4,5,6,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8,6,7,5,4,3,2,1,9] => [2,4,3,5,6,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => [3,4,2,5,6,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,7,8,5,4,3,2,1,9] => [4,3,2,5,6,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1,9] => [5,4,3,2,6,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [2,3,4,6,5,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => [2,3,5,6,4,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,3,2,1,9] => [6,5,4,3,2,7,8,9,1] => 00000000
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,2,1,9] => [2,3,4,5,7,6,8,9,1] => 00000000
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1,9] => [7,6,5,4,3,2,8,9,1] => 00000000
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,1,9] => [2,3,4,5,6,8,7,9,1] => 00000000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,1,9] => [3,4,5,6,7,8,2,9,1] => 00000000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,1,9] => [2,8,7,6,5,4,3,9,1] => 00000000
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1,9] => [7,8,6,5,4,3,2,9,1] => 00000000
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [8,7,6,5,4,3,2,9,1] => 00000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [2,3,4,5,6,7,9,8,1] => 00000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => [3,2,5,4,7,6,9,8,1] => 00000000
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [7,6,5,4,3,2,9,8,1] => 00000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => [2,3,4,5,6,8,9,7,1] => 00000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [3,4,5,6,7,8,9,2,1] => 00000000
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,2,3,4,5,6,1,8,9] => [3,8,7,6,5,4,9,2,1] => 00000000
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [8,7,6,5,4,3,9,2,1] => 00000000
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1,2,3,9] => [2,3,4,5,6,9,8,7,1] => 00000000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [4,5,6,7,8,9,3,2,1] => 00000000
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,1,7,8,9] => [4,8,7,6,5,9,3,2,1] => 00000000
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [8,7,6,5,4,9,3,2,1] => 00000000
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [5,4,3,2,9,8,7,6,1] => 00000000
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => [5,4,7,6,9,8,3,2,1] => 00000000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [5,6,7,8,9,4,3,2,1] => 00000000
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,3,4,1,6,7,8,9] => [5,8,7,6,9,4,3,2,1] => 00000000
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [8,7,6,5,9,4,3,2,1] => 00000000
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [6,5,4,9,8,7,3,2,1] => 00000000
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [6,7,8,9,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => [6,8,7,9,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [8,7,6,9,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => [3,2,9,8,7,6,5,4,1] => 00000000
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [7,6,9,8,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [7,8,9,6,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [8,7,9,6,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [2,9,8,7,6,5,4,3,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [3,9,8,7,6,5,4,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [4,9,8,7,6,5,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [5,9,8,7,6,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [6,9,8,7,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [7,9,8,6,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [8,9,7,6,5,4,3,2,1] => 00000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => 11111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => [2,1,3,4,5,6,7,8,9] => 01111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [2,3,1,4,5,6,7,8,9] => 00111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [2,3,4,1,5,6,7,8,9] => 00011111
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [2,3,4,5,1,6,7,8,9] => 00001111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [2,3,4,5,6,1,7,8,9] => 00000111
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [2,3,4,5,6,7,1,8,9] => 00000011
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [2,3,4,5,6,7,8,1,9] => 00000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [2,1,3,4,5,6,7,8,9,10] => 011111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [3,2,1,4,5,6,7,8,9] => 00111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [2,3,1,4,5,6,7,8,9,10] => 001111111
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [2,4,3,1,5,6,7,8,9] => 00011111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [2,3,4,1,5,6,7,8,9,10] => 000111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [2,3,4,5,1,6,7,8,9,10] => 000011111
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [2,3,4,5,6,1,7,8,9,10] => 000001111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [2,3,4,5,6,7,1,8,9,10] => 000000111
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [2,3,4,5,6,7,8,1,9,10] => 000000011
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [2,3,4,5,6,7,8,9,1,10] => 000000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,10,1] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10,11] => 1111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [2,1,3,4,5,6,7,8,9,10,11] => 0111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [3,2,1,4,5,6,7,8,9,10] => 001111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => [2,3,1,4,5,6,7,8,9,10,11] => 0011111111
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [7,6,8,9,5,4,3,2,1] => [3,4,2,1,5,6,7,8,9] => 00011111
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [4,3,2,1,5,6,7,8,9] => 00011111
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,1,2,10] => [2,3,4,5,6,7,8,10,9,1] => 000000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [2,3,4,5,6,7,8,9,10,1,11] => 0000000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [4,3,2,1,5,6,7,8,9,10] => 000111111
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [4,5,3,2,1,6,7,8,9] => 00001111
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,1,2,11] => [2,3,4,5,6,7,8,9,11,10,1] => 0000000000
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [5,4,3,2,1,6,7,8,9] => 00001111
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [5,4,3,2,1,6,7,8,9,10] => 000011111
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [5,6,4,3,2,1,7,8,9] => 00000111
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [6,5,4,3,2,1,7,8,9] => 00000111
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [6,5,4,3,2,1,7,8,9,10] => 000001111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,2,1] => [1,3,2,4,5,6,7,8,9] => 10111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [9,8,6,7,5,4,3,2,1] => [1,2,4,3,5,6,7,8,9] => 11011111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,9,6,7,5,4,3,2,1] => [2,1,4,3,5,6,7,8,9] => 01011111
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [9,6,7,8,5,4,3,2,1] => [1,4,3,2,5,6,7,8,9] => 10011111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,4,3,2,1] => [1,2,3,5,4,6,7,8,9] => 11101111
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,4,3,2,1] => [1,3,2,5,4,6,7,8,9] => 10101111
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,4,3,2,1] => [3,2,1,5,4,6,7,8,9] => 00101111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,3,2,1] => [1,2,3,4,6,5,7,8,9] => 11110111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,3,2,1] => [2,1,4,3,6,5,7,8,9] => 01010111
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,3,2,1] => [4,3,2,1,6,5,7,8,9] => 00010111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,2,1] => [1,2,3,4,5,7,6,8,9] => 11111011
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,2,1] => [5,4,3,2,1,7,6,8,9] => 00001011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,8,7,9] => 11111101
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,3,1] => [2,1,3,4,5,6,8,7,9] => 01111101
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,2,3,1] => [1,2,3,4,6,5,8,7,9] => 11110101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,4,5,2,3,1] => [1,2,4,3,6,5,8,7,9] => 11010101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,3,1] => [2,1,4,3,6,5,8,7,9] => 01010101
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [6,5,4,3,2,1,8,7,9] => 00000101
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,4,1] => [5,4,3,2,1,8,7,6,9] => 00001001
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,5,1] => [4,3,2,1,8,7,6,5,9] => 00010001
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => [2,1,8,7,6,5,4,3,9] => 01000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,9,8] => 11111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,9,8] => 01111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,1,2] => [1,3,2,4,5,6,7,9,8] => 10111110
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => [1,2,3,4,5,7,6,9,8] => 11111010
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => [1,2,3,5,4,7,6,9,8] => 11101010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => [1,3,2,5,4,7,6,9,8] => 10101010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,3,4,1,2] => [3,2,1,5,4,7,6,9,8] => 00101010
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,1,2] => [5,4,3,2,1,7,6,9,8] => 00001010
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => [1,7,6,5,4,3,2,9,8] => 10000010
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,9,8,7] => 11111100
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [1,2,3,4,6,5,9,8,7] => 11110100
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [2,1,4,3,6,5,9,8,7] => 01010100
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [1,2,3,6,5,4,9,8,7] => 11100100
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [3,2,1,6,5,4,9,8,7] => 00100100
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [6,5,4,3,2,1,9,8,7] => 00000100
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,9,8,7,6] => 11111000
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [1,2,3,5,4,9,8,7,6] => 11101000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [1,3,2,5,4,9,8,7,6] => 10101000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [1,2,5,4,3,9,8,7,6] => 11001000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [2,1,5,4,3,9,8,7,6] => 01001000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [1,5,4,3,2,9,8,7,6] => 10001000
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [5,4,3,2,1,9,8,7,6] => 00001000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [1,2,3,4,9,8,7,6,5] => 11110000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [1,2,4,3,9,8,7,6,5] => 11010000
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [1,4,3,2,9,8,7,6,5] => 10010000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [4,3,2,1,9,8,7,6,5] => 00010000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [1,2,3,9,8,7,6,5,4] => 11100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [1,3,2,9,8,7,6,5,4] => 10100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [3,2,1,9,8,7,6,5,4] => 00100000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [10,8,9,7,6,5,4,3,2,1] => [1,3,2,4,5,6,7,8,9,10] => 101111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [10,9,7,8,6,5,4,3,2,1] => [1,2,4,3,5,6,7,8,9,10] => 110111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [9,10,7,8,6,5,4,3,2,1] => [2,1,4,3,5,6,7,8,9,10] => 010111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [10,9,8,6,7,5,4,3,2,1] => [1,2,3,5,4,6,7,8,9,10] => 111011111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,4,3,2,1] => [1,2,3,4,6,5,7,8,9,10] => 111101111
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,4,3,2,1] => [2,1,4,3,6,5,7,8,9,10] => 010101111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,3,2,1] => [1,2,3,4,5,7,6,8,9,10] => 111110111
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [7,6,5,4,3,2,1,8,9,10] => 000000111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,2,1] => [1,2,3,4,5,6,8,7,9,10] => 111111011
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,2,1] => [2,1,4,3,6,5,8,7,9,10] => 010101011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,7,9,8,10] => 111111101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [10,9,8,6,7,4,5,2,3,1] => [1,2,3,5,4,7,6,9,8,10] => 111010101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8,10] => 101010101
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => [7,6,5,4,3,2,1,9,8,10] => 000000101
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,2,3,4,1] => [3,2,1,6,5,4,9,8,7,10] => 001001001
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,2,3,4,1] => [6,5,4,3,2,1,9,8,7,10] => 000001001
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,2,3,4,5,1] => [5,4,3,2,1,9,8,7,6,10] => 000010001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,10,9] => 111111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,10,9] => 011111110
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,8,7,10,9] => 111111010
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => [1,2,3,4,6,5,8,7,10,9] => 111101010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => [1,2,4,3,6,5,8,7,10,9] => 110101010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9] => 010101010
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [9,10,3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3,10,9] => 010000010
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,10,9,8] => 111111100
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => [1,2,3,4,5,7,6,10,9,8] => 111110100
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => [1,3,2,5,4,7,6,10,9,8] => 101010100
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [2,1,4,3,7,6,5,10,9,8] => 010100100
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [7,6,5,4,3,2,1,10,9,8] => 000000100
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,10,9,8,7] => 111111000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [2,1,4,3,6,5,10,9,8,7] => 010101000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,5,6,1,2,3,4] => [4,3,2,1,6,5,10,9,8,7] => 000101000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [3,2,1,6,5,4,10,9,8,7] => 001001000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [1,2,6,5,4,3,10,9,8,7] => 110001000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [2,1,6,5,4,3,10,9,8,7] => 010001000
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [6,5,4,3,2,1,10,9,8,7] => 000001000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [1,2,3,4,5,10,9,8,7,6] => 111110000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [1,3,2,5,4,10,9,8,7,6] => 101010000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [1,5,4,3,2,10,9,8,7,6] => 100010000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => 000010000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [1,2,3,4,10,9,8,7,6,5] => 111100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => [1,4,3,2,10,9,8,7,6,5] => 100100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [4,3,2,1,10,9,8,7,6,5] => 000100000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [1,2,3,10,9,8,7,6,5,4] => 111000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => [1,3,2,10,9,8,7,6,5,4] => 101000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [3,2,1,10,9,8,7,6,5,4] => 001000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1] => 000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,1,3] => [1,2,3,4,5,6,8,9,7] => 11111100
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,1,4] => [1,2,3,4,5,7,8,9,6] => 11111000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,1,5] => [1,2,3,4,6,7,8,9,5] => 11110000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,3,2,1,6] => [1,2,3,5,6,7,8,9,4] => 11100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,2,1,7] => [1,2,4,5,6,7,8,9,3] => 11000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1,8] => [1,3,4,5,6,7,8,9,2] => 10000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,1,3] => [1,2,3,4,5,6,7,9,10,8] => 111111100
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,1,4] => [1,2,3,4,5,8,7,9,6] => 11111000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,1,4] => [1,2,3,4,5,6,8,9,10,7] => 111111000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,4,2,1,5] => [1,2,3,4,7,6,8,9,5] => 11110000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,1,5] => [1,2,3,4,5,7,8,9,10,6] => 111110000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,3,2,1,6] => [1,2,3,6,5,7,8,9,4] => 11100000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,4,3,2,1,6] => [1,2,3,4,6,7,8,9,10,5] => 111100000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [9,8,5,6,4,3,2,1,7] => [1,2,5,4,6,7,8,9,3] => 11000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,4,3,2,1,7] => [1,2,3,5,6,7,8,9,10,4] => 111000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,6,7,5,4,3,2,1,8] => [1,4,3,5,6,7,8,9,2] => 10000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,2,1,8] => [1,2,4,5,6,7,8,9,10,3] => 110000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,1,9] => [1,3,4,5,6,7,8,9,10,2] => 100000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,9,11,10] => 1111111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,1,2] => [2,3,1,4,5,6,7,9,8] => 00111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [3,2,4,5,6,7,8,9,10,1] => 000000000
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [9,8,10,7,6,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [8,10,9,7,6,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10,11] => [10,9,11,8,7,6,5,4,3,2,1] => 0000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,1,3] => [2,3,1,4,5,6,8,9,7] => 00111100
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,1,3] => [2,1,3,4,5,6,8,9,7] => 01111100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => [1,4,5,6,7,8,9,3,2] => 10000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,1,3,4] => [1,2,3,4,5,8,9,7,6] => 11111000
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,8,7,6,5,4,3,2,10,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [2,10,9,8,7,6,5,4,3,1] => 000000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [2,11,10,9,8,7,6,5,4,3,1] => 0000000000
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [9,8,6,1,2,3,4,5,7] => [1,2,4,9,8,7,6,5,3] => 11000000
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,1,2,3,4,6] => [1,2,3,5,9,8,7,6,4] => 11100000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,1,2,3,5] => [1,2,3,4,6,9,8,7,5] => 11110000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,1,2,4] => [1,2,3,4,5,7,9,8,6] => 11111000
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [9,10,8,7,6,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [9,8,7,10,6,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [9,8,7,6,10,5,4,3,2,1] => 000000000
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [9,8,7,6,5,10,4,3,2,1] => 000000000
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [9,8,7,6,5,4,10,3,2,1] => 000000000
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [9,8,7,6,5,4,3,10,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [10,11,9,8,7,6,5,4,3,2,1] => 0000000000
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,1,3] => [6,5,4,3,2,1,8,9,7] => 00000100
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,9,1] => [3,2,4,5,6,7,8,1,9] => 00000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,9,6,5,4,3,2,1,7] => [2,1,4,5,6,7,8,9,3] => 01000000
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,1,2] => [2,3,4,5,6,7,1,9,8] => 00000010
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [7,8,9,5,4,3,2,1,6] => [3,2,1,5,6,7,8,9,4] => 00100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,8,9,6,5,4,3,2,1,10] => [4,3,2,5,6,7,8,9,10,1] => 000000000
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,3,2,1,5] => [4,3,2,1,6,7,8,9,5] => 00010000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [4,5,6,7,8,9,10,3,2,1] => 000000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,9,1,2,3,4,5,6] => [2,3,1,9,8,7,6,5,4] => 00100000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [3,10,9,8,7,6,5,4,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [4,10,9,8,7,6,5,3,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [5,10,9,8,7,6,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [6,10,9,8,7,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [7,10,9,8,6,5,4,3,2,1] => 000000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [9,8,6,5,7,4,3,2,1] => [1,2,4,5,3,6,7,8,9] => 11001111
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,5,1] => [1,2,3,4,5,7,8,9,6,10] => 111110001
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,1,2] => [2,3,4,5,1,6,7,9,8] => 00001110
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [8,9,6,5,7,4,3,2,1] => [2,1,4,5,3,6,7,8,9] => 01001111
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [2,3,4,6,5,7,8,9,10,1] => 000000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [9,6,7,4,5,2,3,1,8] => [1,4,3,6,5,8,7,9,2] => 10000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,1,10] => [3,2,5,4,7,6,9,8,10,1] => 000000000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,1,3] => [1,3,2,5,4,7,6,9,10,8] => 101010100
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1,10] => [8,7,6,5,4,3,2,9,10,1] => 000000000
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1,10] => [7,6,5,4,3,2,8,9,10,1] => 000000000
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1,10] => [6,5,4,3,2,7,8,9,10,1] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1,10] => [5,4,3,2,6,7,8,9,10,1] => 000000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [3,4,5,6,7,8,9,10,2,1] => 000000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,1,10,11] => [3,4,5,6,7,8,9,10,11,2,1] => 0000000000
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [8,7,10,9,6,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [7,6,5,10,9,8,4,3,2,1] => 000000000
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [6,5,4,3,10,9,8,7,2,1] => 000000000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [10,8,6,4,2,1,3,5,7,9] => [1,3,5,7,9,10,8,6,4,2] => 100000000
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [11,10,9,8,7,6,5,4,3,2,1] => 0000000000
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [9,8,7,6,5,4,3,2,1,11,10] => 0000000010
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => [10,9,8,7,6,5,4,3,2,11,1] => 0000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,2,1,3] => [1,2,3,4,5,6,7,8,10,11,9] => 1111111100
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,2,1,3] => [2,1,3,4,5,6,7,9,10,8] => 011111100
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,3,9,2,1] => [6,5,4,3,2,7,1,8,9] => 00000011
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,4,9,3,2,1] => [5,4,3,2,6,1,7,8,9] => 00000111
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,7,8,5,9,4,3,2,1] => [4,3,2,5,1,6,7,8,9] => 00001111
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,8,6,9,5,4,3,2,1] => [3,2,4,1,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [2,1,11,10,9,8,7,6,5,4,3] => 0100000000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [5,6,7,8,9,10,4,3,2,1] => 000000000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,4,1] => [1,2,3,4,5,7,8,6,9] => 11111001
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,1,2] => [2,3,4,5,6,7,8,1,10,9] => 000000010
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,2,1,3] => [2,3,4,5,6,1,8,9,7] => 00000100
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [8,9,10,7,6,5,4,3,2,1] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [9,8,7,10,5,4,3,2,1,6] => [2,3,4,1,6,7,8,9,10,5] => 000100000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [9,7,6,8,5,4,3,2,1] => [1,3,4,2,5,6,7,8,9] => 10011111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [10,8,7,9,6,5,4,3,2,1] => [1,3,4,2,5,6,7,8,9,10] => 100111111
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,4,3,2,1,5] => [2,1,3,4,5,7,8,9,10,6] => 011110000
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [6,7,8,9,10,5,4,3,2,1] => 000000000
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [7,8,9,10,6,5,4,3,2,1] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,8,7,6,5,4,3,2,1,10] => [1,3,4,5,6,7,8,9,10,11,2] => 1000000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,8,1] => [1,3,4,5,6,7,8,2,9] => 10000001
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8,10,9,11] => 1111111101
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [3,2,10,9,8,7,6,5,4,1] => 000000000
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => [8,7,6,5,4,3,2,10,9,1] => 000000000
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [7,6,8,5,9,4,3,2,1] => [3,4,2,5,1,6,7,8,9] => 00001111
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,10,7,6,5,4,3,2,1,8] => [2,1,4,5,6,7,8,9,10,3] => 010000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,7,9,5,4,3,2,1,6] => [2,3,1,5,6,7,8,9,4] => 00100000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,1,2,3,4,7] => [1,2,4,5,9,8,7,6,3] => 11000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [8,7,9,5,6,3,4,1,2] => [2,3,1,5,4,7,6,9,8] => 00101010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [10,8,7,9,5,6,3,4,1,2] => [1,3,4,2,6,5,8,7,10,9] => 100101010
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [11,10,1,2,3,4,5,6,7,8,9] => [1,2,11,10,9,8,7,6,5,4,3] => 1100000000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,4,1] => [1,2,3,4,5,6,8,9,7,10] => 111111001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,9,1] => [1,3,4,5,6,7,8,9,2,10] => 100000001
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,3,2,1,4] => [2,3,4,5,1,7,8,9,6] => 00001000
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,7,3,2,1] => [1,2,4,5,6,3,7,8,9] => 11000111
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9,7,8,5,6,3,4,1,2,10] => [2,4,3,6,5,8,7,10,9,1] => 000000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [10,7,8,5,6,3,4,1,2,9] => [1,4,3,6,5,8,7,10,9,2] => 100000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,2,1] => [1,3,4,5,6,7,2,8,9] => 10000011
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [1,7,6,5,4,3,9,8,2] => 10000000
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,1,2] => [1,3,4,5,6,7,2,9,8] => 10000010
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [9,8,10,6,7,4,5,2,3,1] => [2,3,1,5,4,7,6,9,8,10] => 001010101
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,2,3,1] => [2,3,4,5,6,1,8,7,9] => 00000101
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,1,2,4] => [1,2,3,4,5,6,8,10,9,7] => 111111000
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,10,1] => [3,2,5,4,7,6,9,8,1,10] => 000000001
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8,11,10,9] => 1111111100
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9,12,11] => 01010101010
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => [4,3,6,5,8,7,10,9,2,1] => 000000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 01000000000
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [9,8,7,6,5,4,3,2,1,10,11] => 0000000011
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [8,7,6,9,4,3,2,1,5] => [2,3,4,1,6,7,8,9,5] => 00010000
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [9,10,7,8,6,4,3,5,1,2] => [2,1,4,3,5,7,8,6,10,9] => 010110010
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,11,1] => [9,8,7,6,5,4,3,2,10,1,11] => 0000000001
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => [4,3,2,7,6,5,10,9,8,1] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [9,8,10,6,5,4,3,2,1,7] => [2,3,1,5,6,7,8,9,10,4] => 001000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => [1,3,5,7,9,8,6,4,2] => 10000000
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,3,4,1,2] => [2,3,4,5,6,1,8,7,10,9] => 000001010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [9,8,7,10,5,6,3,4,1,2] => [2,3,4,1,6,5,8,7,10,9] => 000101010
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [9,8,6,4,2,1,3,5,7] => [1,2,4,6,8,9,7,5,3] => 11000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [12,10,9,8,7,6,5,4,3,2,1,11] => [1,3,4,5,6,7,8,9,10,11,12,2] => 10000000000
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
searching the database
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