Identifier
Mp00296:
Dyck paths
—Knuth-Krattenthaler⟶
Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
[1,0] => [1,0] => [1] =>
[1,0,1,0] => [1,1,0,0] => [1,2] => 1
[1,1,0,0] => [1,0,1,0] => [2,1] => 0
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [1,2,3] => 11
[1,0,1,1,0,0] => [1,1,0,1,0,0] => [2,1,3] => 01
[1,1,0,0,1,0] => [1,0,1,0,1,0] => [3,2,1] => 00
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [2,3,1] => 00
[1,1,1,0,0,0] => [1,1,0,0,1,0] => [3,1,2] => 00
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 111
[1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [2,1,3,4] => 011
[1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0] => [3,2,1,4] => 001
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [2,3,1,4] => 001
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => [3,1,2,4] => 001
[1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 000
[1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 000
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 000
[1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 000
[1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 000
[1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 000
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 000
[1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 000
[1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 000
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 1111
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => 0111
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => 0011
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => 0011
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => 0011
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => 0001
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => 0001
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => 0001
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => 0001
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => 0001
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => 0001
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => 0001
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => 0001
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => 0001
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 0000
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 0000
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 0000
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 0000
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 0000
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 0000
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 0000
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 0000
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0000
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 0000
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 0000
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 0000
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 0000
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 0000
[1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 0000
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 0000
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 0000
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 0000
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 0000
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 0000
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 0000
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 0000
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 0000
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 0000
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 0000
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 0000
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 0000
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 0000
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => 11111
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => 01111
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => 00111
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => 00111
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => 00111
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => 00011
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => 00011
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => 00011
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => 00011
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => 00011
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => 00011
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => 00011
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => 00011
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => 00011
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => 00001
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => 00001
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => 00001
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => 00001
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => 00001
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => 00001
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => 00001
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => 00001
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => 00001
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => 00001
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => 00001
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => 00001
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => 00001
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => 00001
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => 00001
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => 00001
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => 00001
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => 00001
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => 00001
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => 00001
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => 00001
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => 00001
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => 00001
>>> Load all 1577 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => 00001
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => 00001
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => 00001
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => 00001
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => 00001
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 00000
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => 00000
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => 00000
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => 00000
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => 00000
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 00000
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 00000
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => 00000
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 00000
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 00000
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => 00000
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 00000
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => 00000
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 00000
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 00000
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 00000
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 00000
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 00000
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 00000
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 00000
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 00000
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 00000
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 00000
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 00000
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 00000
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 00000
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 00000
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 00000
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 00000
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 00000
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 00000
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 00000
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 00000
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 00000
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 00000
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 00000
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 00000
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => 00000
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 00000
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => 00000
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 00000
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 00000
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => 00000
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => 00000
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => 00000
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => 00000
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => 00000
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => 00000
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => 00000
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => 00000
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => 00000
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => 00000
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => 00000
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => 00000
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => 00000
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => 00000
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => 00000
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => 00000
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => 00000
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => 00000
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => 00000
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => 00000
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 00000
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 00000
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 00000
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => 00000
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => 00000
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => 00000
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => 00000
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => 00000
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 00000
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => 00000
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => 00000
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => 00000
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => 00000
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => 00000
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => 00000
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => 00000
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => 00000
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => 00000
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => 00000
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => 00000
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 00000
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => 00000
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 00000
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 00000
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => 00000
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 00000
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 00000
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 00000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => 111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => 011111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => 001111
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => 001111
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => 001111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => 000111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => 000111
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => 000111
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => 000111
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => 000111
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => 000111
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => 000111
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => 000111
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => 000111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => 000011
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => 000011
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => 000011
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => 000011
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => 000011
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => 000011
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => 000011
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => 000011
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => 000011
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => 000011
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => 000011
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => 000011
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => 000011
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => 000011
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => 000011
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => 000011
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => 000011
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => 000011
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => 000011
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => 000011
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => 000011
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => 000011
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => 000011
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => 000011
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => 000011
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => 000011
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => 000011
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => 000011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => 000001
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => 000001
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => 000001
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => 000001
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => 000001
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => 000001
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => 000001
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => 000001
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => 000001
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => 000001
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => 000001
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => 000001
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => 000001
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => 000001
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => 000001
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => 000001
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => 000001
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => 000001
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => 000001
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => 000001
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => 000001
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => 000001
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => 000001
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => 000001
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => 000001
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => 000001
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => 000001
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => 000001
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => 000001
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => 000001
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => 000001
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => 000001
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => 000001
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => 000001
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => 000001
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => 000001
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => 000001
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => 000001
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => 000001
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => 000001
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => 000001
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => 000001
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => 000001
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => 000001
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => 000001
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => 000001
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => 000001
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => 000001
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => 000001
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => 000001
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => 000001
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => 000001
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => 000001
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => 000001
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => 000001
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => 000001
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => 000001
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => 000001
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => 000001
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => 000001
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => 000001
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => 000001
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => 000001
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => 000001
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => 000001
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => 000001
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => 000001
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => 000001
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => 000001
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => 000001
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => 000001
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => 000001
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => 000001
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => 000001
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => 000001
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => 000001
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => 000001
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => 000001
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => 000001
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => 000001
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => 000001
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => 000001
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => 000001
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => 000001
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => 000001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => 000001
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => 000001
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => 000001
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => 000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => 000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => 000000
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => 000000
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => 000000
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => 000000
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => 000000
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => 000000
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => 000000
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => 000000
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => 000000
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => 000000
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => 000000
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => 000000
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => 000000
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => 000000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => 000000
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => 000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 000000
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => 000000
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => 000000
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => 000000
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => 000000
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => 000000
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => 000000
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => 000000
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => 000000
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => 000000
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => 000000
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => 000000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => 000000
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => 000000
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => 000000
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => 000000
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => 000000
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => 000000
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => 000000
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => 000000
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => 000000
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => 000000
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => 000000
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => 000000
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => 000000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => 000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => 000000
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => 000000
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => 000000
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => 000000
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => 000000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => 000000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => 000000
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => 000000
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => 000000
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => 000000
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => 000000
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => 000000
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => 000000
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => 000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => 000000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => 000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => 000000
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => 000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => 000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => 000000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => 000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => 000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => 000000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => 000000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => 000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => 000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => 000000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => 000000
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => 000000
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => 000000
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => 000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => 000000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => 000000
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => 000000
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => 000000
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => 000000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => 000000
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => 000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => 000000
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => 000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => 000000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => 000000
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => 000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => 000000
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => 000000
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => 000000
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => 000000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => 000000
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => 000000
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => 000000
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => 000000
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => 000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => 000000
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => 000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => 000000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => 000000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => 000000
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => 000000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => 000000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => 000000
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => 000000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => 000000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => 000000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => 000000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => 000000
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => 000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => 000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => 000000
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => 000000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => 000000
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => 000000
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => 000000
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => 000000
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => 000000
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => 000000
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => 000000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => 000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => 000000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => 000000
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => 000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => 000000
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => 000000
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => 000000
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => 000000
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => 000000
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => 000000
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => 000000
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => 000000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => 000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => 000000
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => 000000
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => 000000
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => 000000
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => 000000
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => 000000
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => 000000
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => 000000
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => 000000
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => 000000
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => 000000
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => 000000
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => 000000
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => 000000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => 000000
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => 000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => 000000
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => 000000
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => 000000
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => 000000
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => 000000
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => 000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => 000000
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => 000000
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => 000000
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => 000000
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => 000000
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => 000000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => 000000
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => 000000
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => 000000
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => 000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => 000000
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => 000000
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => 000000
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => 000000
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => 000000
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => 000000
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => 000000
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => 000000
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => 000000
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => 000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => 000000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => 000000
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => 000000
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => 000000
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => 000000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => 000000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => 000000
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => 000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => 000000
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => 000000
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => 000000
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => 000000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => 000000
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => 000000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => 000000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => 000000
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => 000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => 000000
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => 000000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => 000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => 000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => 000000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => 000000
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => 000000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => 000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => 000000
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => 000000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => 000000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => 000000
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => 000000
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => 000000
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => 000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => 000000
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => 000000
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => 000000
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => 000000
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => 000000
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => 000000
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => 000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => 000000
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => 000000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => 000000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => 000000
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => 000000
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => 000000
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => 000000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => 000000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => 000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => 000000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => 000000
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => 000000
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => 000000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => 000000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => 000000
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => 000000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => 000000
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => 000000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => 000000
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => 000000
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => 000000
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => 000000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => 000000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => 000000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => 000000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => 000000
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => 000000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => 000000
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => 000000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => 000000
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => 000000
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => 000000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => 000000
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => 000000
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => 000000
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => 000000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => 000000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => 000000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => 000000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => 000000
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => 000000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => 000000
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => 000000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => 000000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => 000000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => 000000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => 000000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => 000000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => 000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => 000000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => 000000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => 000000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => 000000
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => 000000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => 000000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => 000000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => 000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => 000000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => 000000
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => 000000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => 000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => 000000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => 000000
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => 000000
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => 000000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => 000000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => 000000
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => 000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => 000000
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => 000000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => 000000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => 000000
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => 000000
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => 000000
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => 000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => 000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => 000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => 000000
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => 000000
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => 000000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => 000000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => 000000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => 000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => 000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => 1111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [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] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => 0011111
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [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] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => 0011111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [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] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => 0001111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [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] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => 0000111
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => 0000111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => 0000011
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => 0000011
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => 0000011
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => 0000011
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [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] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => 0000011
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => 0000011
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => 0000011
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => 0000011
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => 0000011
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => 0000011
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => 0000011
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => 0000011
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => 0000011
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => 0000011
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => 0000011
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => 0000011
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => 0000011
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => 0000011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => 0000001
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => 0000001
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => 0000001
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => 0000001
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => 0000001
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => 0000001
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => 0000001
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => 0000001
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => 0000001
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => 0000001
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => 0000001
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => 0000001
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => 0000001
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => 0000001
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => 0000001
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => 0000001
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => 0000001
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => 0000001
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => 0000001
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => 0000001
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => 0000001
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => 0000001
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => 0000001
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => 0000001
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => 0000001
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => 0000001
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => 0000001
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => 0000001
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => 0000001
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => 0000001
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => 0000001
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => 0000001
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => 0000001
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => 0000001
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => 0000001
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => 0000001
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => 0000001
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => 0000001
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => 0000001
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => 0000001
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => 0000001
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => 0000001
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => 0000001
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => 0000001
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => 0000001
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => 0000001
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => 0000001
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => 0000001
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => 0000001
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => 0000001
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => 0000001
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => 0000001
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => 0000001
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => 0000001
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => 0000001
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => 0000001
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => 0000001
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => 0000001
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => 0000001
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => 0000001
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => 0000001
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => 0000001
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => 0000001
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => 0000001
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => 0000001
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => 0000001
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => 0000001
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => 0000001
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => 0000001
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => 0000001
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => 0000001
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => 0000001
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => 0000001
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => 0000001
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => 0000001
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => 0000001
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => 0000001
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => 0000001
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => 0000001
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => 0000001
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => 0000001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => 0000001
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => 0000001
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => 0000001
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => 0000001
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => 0000001
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => 0000001
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => 0000001
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => 0000001
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => 0000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => 0000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => 0000001
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => 0000001
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => 0000001
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => 0000001
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => 0000001
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => 0000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => 0000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => 0000000
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => 0000000
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => 0000000
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => 0000000
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => 0000000
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => 0000000
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => 0000000
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => 0000000
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => 0000000
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => 0000000
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => 0000000
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => 0000000
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => 0000000
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => 0000000
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => 0000000
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => 0000000
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => 0000000
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => 0000000
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => 0000000
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => 0000000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => 0000000
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => 0000000
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => 0000000
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => 0000000
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => 0000000
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => 0000000
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => 0000000
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => 0000000
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => 0000000
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => 0000000
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => 0000000
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => 0000000
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => 0000000
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => 0000000
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => 0000000
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => 0000000
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => 0000000
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => 0000000
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => 0000000
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => 0000000
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => 0000000
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => 0000000
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => 0000000
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => 0000000
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => 0000000
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => 0000000
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => 0000000
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => 0000000
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => 0000000
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => 0000000
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => 0000000
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => 0000000
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => 0000000
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => 0000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => 0000000
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => 0000000
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => 0000000
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => 0000000
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => 0000000
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => 0000000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => 0000000
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => 0000000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => 0000000
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => 0000000
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => 0000000
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => 0000000
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => 0000000
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => 0000000
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => 0000000
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => 0000000
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => 0000000
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => 0000000
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => 0000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => 0000000
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => 0000000
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => 0000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => 0000000
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => 0000000
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => 0000000
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => 0000000
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => 0000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => 0000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => 0000000
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => 0000000
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => 0000000
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => 0000000
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => 0000000
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => 0000000
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => 0000000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => 0000000
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => 0000000
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => 0000000
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => 0000000
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => 0000000
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => 0000000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => 0000000
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => 0000000
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => 0000000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => 0000000
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => 0000000
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => 0000000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => 0000000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => 0000000
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => 0000000
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => 0000000
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => 0000000
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => 0000000
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => 0000000
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => 0000000
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => 0000000
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => 0000000
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => 0000000
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => 0000000
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => 0000000
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => 0000000
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => 0000000
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => 0000000
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => 0000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => 0000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => 0000000
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => 0000000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => 0000000
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => 0000000
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => 0000000
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => 0000000
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => 0000000
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => 0000000
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => 0000000
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => 0000000
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => 0000000
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => 0000000
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => 0000000
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => 0000000
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => 0000000
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => 0000000
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => 0000000
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => 0000000
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => 0000000
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => 0000000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => 0000000
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => 0000000
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => 0000000
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => 0000000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => 0000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => 0000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => 0000000
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => 0000000
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => 0000000
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => 0000000
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => 0000000
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => 0000000
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => 0000000
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => 0000000
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => 0000000
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => 0000000
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => 0000000
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => 0000000
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => 0000000
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => 0000000
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => 0000000
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => 0000000
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => 0000000
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => 0000000
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => 0000000
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => 0000000
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => 0000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => 0000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => 0000000
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => 0000000
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => 0000000
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => 0000000
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => 0000000
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => 0000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => 0000000
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => 0000000
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => 0000000
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => 0000000
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => 0000000
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => 0000000
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => 0000000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => 0000000
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => 0000000
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => 0000000
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => 0000000
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => 0000000
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => 0000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => 0000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => 0000000
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => 0000000
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => 0000000
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => 0000000
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => 0000000
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => 0000000
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => 0000000
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => 0000000
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => 0000000
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => 0000000
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => 0000000
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => 0000000
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => 0000000
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => 0000000
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => 0000000
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => 0000000
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => 0000000
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => 0000000
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => 0000000
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => 0000000
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => 0000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => 0000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => 0000000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => 0000000
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => 0000000
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => 0000000
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => 0000000
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => 0000000
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => 0000000
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => 0000000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => 0000000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => 0000000
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => 0000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => 0000000
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => 0000000
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => 0000000
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => 0000000
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => 0000000
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => 0000000
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => 0000000
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => 0000000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => 0000000
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => 0000000
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => 0000000
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => 0000000
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => 0000000
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => 0000000
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => 0000000
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => 0000000
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => 0000000
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => 0000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => 0000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => 0000000
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => 0000000
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => 0000000
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => 0000000
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => 0000000
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => 0000000
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => 0000000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => 0000000
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => 0000000
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => 0000000
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => 0000000
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => 0000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => 0000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => 0000000
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => 0000000
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => 0000000
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => 0000000
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => 0000000
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => 0000000
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => 0000000
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => 0000000
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => 0000000
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => 0000000
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => 0000000
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => 0000000
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => 0000000
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => 0000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => 0000000
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => 0000000
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => 0000000
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => 0000000
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => 0000000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => 0000000
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => 0000000
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => 0000000
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => 0000000
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => 0000000
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => 0000000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => 0000000
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => 0000000
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => 0000000
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => 0000000
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => 0000000
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => 0000000
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => 0000000
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => 0000000
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => 0000000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => 0000000
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => 0000000
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => 0000000
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => 0000000
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => 0000000
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => 0000000
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => 0000000
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => 0000000
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => 0000000
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => 0000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => 0000000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => 0000000
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => 0000000
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => 0000000
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => 0000000
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => 0000000
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => 0000000
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => 0000000
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => 0000000
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => 0000000
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => 0000000
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => 0000000
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => 0000000
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => 0000000
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => 0000000
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => 0000000
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => 0000000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => 0000000
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => 0000000
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => 0000000
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => 0000000
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => 0000000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => 0000000
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => 0000000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => 0000000
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => 0000000
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => 0000000
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => 0000000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => 0000000
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => 0000000
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => 0000000
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => 0000000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => 0000000
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => 0000000
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => 0000000
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => 0000000
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => 0000000
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => 0000000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => 0000000
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => 0000000
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => 0000000
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => 0000000
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => 0000000
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => 0000000
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => 0000000
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => 0000000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => 0000000
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => 0000000
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => 0000000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => 0000000
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => 0000000
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => 0000000
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => 0000000
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => 0000000
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => 0000000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => 0000000
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => 0000000
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => 0000000
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => 0000000
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => 0000000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => 0000000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => 0000000
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => 0000000
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => 0000000
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => 0000000
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => 0000000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => 0000000
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => 0000000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => 0000000
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => 0000000
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => 0000000
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => 0000000
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => 0000000
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => 0000000
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => 0000000
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => 0000000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => 0000000
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => 0000000
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => 0000000
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => 0000000
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => 0000000
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => 0000000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => 0000000
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => 0000000
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => 0000000
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => 0000000
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => 0000000
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => 0000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => 0000000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => 0000000
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => 0000000
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => 0000000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => 0000000
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => 0000000
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => 0000000
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => 0000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => 0000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => 0000000
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => 0000000
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => 0000000
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => 0000000
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => 0000000
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => 0000000
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => 0000000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => 0000000
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => 0000000
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => 0000000
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => 0000000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => 0000000
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => 0000000
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => 0000000
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => 0000000
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => 0000000
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => 0000000
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => 0000000
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => 0000000
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => 0000000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => 0000000
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => 0000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => 0000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => 0000000
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => 0000000
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => 0000000
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => 0000000
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => 0000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => 0000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => 0000000
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => 0000000
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => 0000000
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => 0000000
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => 0000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => 0000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => 0000000
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => 0000000
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => 0000000
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => 0000000
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => 0000000
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => 0000000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => 0000000
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => 0000000
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => 0000000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => 0000000
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => 0000000
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => 0000000
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => 0000000
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => 0000000
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => 0000000
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => 0000000
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => 0000000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => 0000000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => 0000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => 0000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => 00000000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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] => 00000001
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => 000000000
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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] => 000000001
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [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] => 0000000001
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,3,1,2,4,5,6,7,9] => 00000001
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [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] => 00000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => 00000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => 00000001
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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] => 00000011
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,2,1,3,4,5,6,7,8,10] => 000000001
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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] => 000000011
[] => [] => [] =>
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [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] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [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] => 00000000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => 00000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [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] => 00000000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => 00000000
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [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] => 00000000
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [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] => 00000000
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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] => 00000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => 00000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,1,2] => 00000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => 00000000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [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] => 00000000
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,1,6,7] => 00000000
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [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] => 00000000
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [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] => 00000000
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,1,3,4,5,6] => 00000000
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [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] => 00000000
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [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] => 00000000
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [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] => 00000000
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,1,3,4,5,6,7] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [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] => 00000000
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [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] => 00000000
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [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] => 00000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => 11111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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] => 01111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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] => 00111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [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] => 00011111
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [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] => 00001111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [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] => 00000111
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => 00000011
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => 00000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => 111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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] => 011111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [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] => 00111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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] => 001111111
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => 00011111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [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] => 000111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [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] => 000011111
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [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] => 000001111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => 000000111
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => 000000011
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => 000000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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] => 0111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [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] => 001111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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] => 0011111111
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [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] => 00011111
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [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] => 00011111
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => 0000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [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] => 000111111
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [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] => 00001111
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => 00000011
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [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] => 000011111
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => 00000001
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [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] => 00000111
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => 00000001
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [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] => 000001111
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => 000000001
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,3,5,6,7,8,9,10,1,2] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [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] => 00111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [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] => 00011111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [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] => 00011111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [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] => 00001111
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [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] => 00001111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [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] => 00000111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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] => 00000111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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] => 00000011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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] => 00000001
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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] => 00000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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] => 00000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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] => 00000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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] => 00000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,1,8] => 00000000
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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] => 00000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,1,7,8] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [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] => 001111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [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] => 000111111
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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] => 000001111
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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] => 000000111
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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] => 000000011
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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] => 000000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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] => 000000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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] => 000000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,1,9] => 000000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [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] => 000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,10,1] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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] => 000000000
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [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] => 000000000
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [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] => 000000000
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [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] => 000000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [4,5,3,6,7,8,9,1,2] => 00000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [8,9,3,4,5,6,7,1,2] => 00000000
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [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] => 000000000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [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] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,3,6,7,8,9,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,10,1] => 000000000
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [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] => 000000000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [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] => 000000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,1,6,7,8,9] => 00001111
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,7,8,9,1] => 00000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [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] => 00000000
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [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] => 00000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [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] => 00000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [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] => 00000000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [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] => 00000000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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] => 00000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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] => 000000000
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,3,1] => 00000000
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [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] => 000000000
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,3,4,2,1] => 00000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [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] => 000000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [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] => 000000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => 00000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [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] => 000000000
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => 00000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [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] => 000000000
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => 00000000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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] => 000000000
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [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] => 00000001
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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] => 000000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => 000000000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => 0000000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => 0000000000
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [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] => 0000000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9] => 00011111
Map
Knuth-Krattenthaler
Description
The map that sends the Dyck path to a 321-avoiding permutation, then applies the Robinson-Schensted correspondence and finally interprets the first row of the insertion tableau and the second row of the recording tableau as up steps.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and $321$-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and $321$-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.
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
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
Sorry, this map was not found in the database.