Identifier
Mp00030:
Dyck paths
—zeta map⟶
Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
[1,0] => [1,0] => [1] => [1] =>
[1,0,1,0] => [1,1,0,0] => [2,1] => [2,1] => 0
[1,1,0,0] => [1,0,1,0] => [1,2] => [1,2] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [3,2,1] => [3,2,1] => 00
[1,0,1,1,0,0] => [1,0,1,1,0,0] => [1,3,2] => [3,1,2] => 00
[1,1,0,0,1,0] => [1,1,0,1,0,0] => [2,3,1] => [2,3,1] => 00
[1,1,0,1,0,0] => [1,1,0,0,1,0] => [2,1,3] => [2,1,3] => 01
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [1,2,3] => [1,2,3] => 11
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => 000
[1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => [4,3,1,2] => 000
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,2,3,1] => 000
[1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [4,2,1,3] => 000
[1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => [4,1,2,3] => 000
[1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,4,3,1] => 000
[1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,3,4,1] => 000
[1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => 000
[1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => 001
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1,2,4] => 001
[1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1,4,2] => 000
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,3,1,4] => 001
[1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => 011
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => 111
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => 0000
[1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [5,4,3,1,2] => 0000
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,4,2,3,1] => 0000
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [5,4,2,1,3] => 0000
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [5,4,1,2,3] => 0000
[1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [5,2,4,3,1] => 0000
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,2,3,4,1] => 0000
[1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [5,3,2,4,1] => 0000
[1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [5,3,2,1,4] => 0000
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [5,3,1,2,4] => 0000
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [5,3,1,4,2] => 0000
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [5,2,3,1,4] => 0000
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [5,2,1,3,4] => 0000
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [5,1,2,3,4] => 0000
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [3,5,4,2,1] => 0000
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [2,5,3,4,1] => 0000
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,3,5,4,1] => 0000
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,2,4,5,1] => 0000
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [3,1,4,5,2] => 0000
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [3,5,2,4,1] => 0000
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [2,4,3,5,1] => 0000
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => 0000
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => 0001
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [4,3,1,2,5] => 0001
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [4,3,1,5,2] => 0000
[1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,2,3,1,5] => 0001
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [4,2,1,3,5] => 0001
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [4,1,2,3,5] => 0001
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [5,1,3,4,2] => 0000
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,3,4,5,1] => 0000
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [4,2,3,5,1] => 0000
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,4,3,1,5] => 0001
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,3,4,1,5] => 0001
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [4,2,1,5,3] => 0000
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,2,4,1,5] => 0001
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => 0011
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,1,2,4,5] => 0011
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [4,1,2,5,3] => 0000
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,1,4,2,5] => 0001
[1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,3,1,4,5] => 0011
[1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => 0111
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => 1111
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 00000
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 00000
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => 00000
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [6,5,4,2,1,3] => 00000
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 00000
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [6,5,2,4,3,1] => 00000
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => 00000
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,5,3,2,4,1] => 00000
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [6,5,3,2,1,4] => 00000
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [6,5,3,1,2,4] => 00000
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [6,5,3,1,4,2] => 00000
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [6,5,2,3,1,4] => 00000
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [6,5,2,1,3,4] => 00000
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 00000
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [6,3,5,4,2,1] => 00000
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [6,2,5,3,4,1] => 00000
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [6,2,3,5,4,1] => 00000
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [6,3,2,4,5,1] => 00000
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [6,3,1,4,5,2] => 00000
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [6,3,5,2,4,1] => 00000
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [6,2,4,3,5,1] => 00000
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [6,4,3,2,5,1] => 00000
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [6,4,3,2,1,5] => 00000
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [6,4,3,1,2,5] => 00000
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [6,4,3,1,5,2] => 00000
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [6,4,2,3,1,5] => 00000
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [6,4,2,1,3,5] => 00000
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [6,4,1,2,3,5] => 00000
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [6,5,1,3,4,2] => 00000
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => 00000
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [6,4,2,3,5,1] => 00000
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [6,2,4,3,1,5] => 00000
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [6,2,3,4,1,5] => 00000
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [6,4,2,1,5,3] => 00000
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [6,3,2,4,1,5] => 00000
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [6,3,2,1,4,5] => 00000
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [6,3,1,2,4,5] => 00000
>>> Load all 1513 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [6,4,1,2,5,3] => 00000
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [6,3,1,4,2,5] => 00000
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [6,2,3,1,4,5] => 00000
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [6,2,1,3,4,5] => 00000
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 00000
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => 00000
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [6,2,4,5,3,1] => 00000
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [4,2,6,5,3,1] => 00000
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,6,2,4,5,1] => 00000
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [6,1,3,4,5,2] => 00000
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => 00000
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,3,4,6,5,1] => 00000
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,2,6,4,5,1] => 00000
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => 00000
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,3,1,5,6,2] => 00000
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [3,1,6,4,5,2] => 00000
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => 00000
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [4,2,1,5,6,3] => 00000
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,1,2,5,6,3] => 00000
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [4,6,3,5,2,1] => 00000
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,6,4,3,5,1] => 00000
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [3,4,6,2,5,1] => 00000
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,5,2,4,6,1] => 00000
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [5,1,3,4,6,2] => 00000
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [4,6,3,2,5,1] => 00000
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => 00000
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => 00000
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 00001
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => 00001
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [5,4,3,1,6,2] => 00000
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => 00001
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [5,4,2,1,3,6] => 00001
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => 00001
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [4,6,3,1,5,2] => 00000
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [2,5,3,4,6,1] => 00000
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => 00000
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [5,2,4,3,1,6] => 00001
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => 00001
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [5,4,2,1,6,3] => 00000
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [5,3,2,4,1,6] => 00001
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [5,3,2,1,4,6] => 00001
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [5,3,1,2,4,6] => 00001
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [5,4,1,2,6,3] => 00000
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [5,3,1,4,2,6] => 00001
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [5,2,3,1,4,6] => 00001
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [5,2,1,3,4,6] => 00001
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 00001
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [6,4,1,5,3,2] => 00000
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [2,6,3,4,5,1] => 00000
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [2,3,6,4,5,1] => 00000
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [2,4,3,5,6,1] => 00000
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => 00000
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [4,6,2,3,5,1] => 00000
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,5,4,6,1] => 00000
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [5,2,4,3,6,1] => 00000
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => 00001
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [2,5,3,4,1,6] => 00001
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => 00000
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,3,5,4,1,6] => 00001
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => 00001
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => 00001
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [6,2,4,1,5,3] => 00000
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => 00000
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [5,3,2,4,6,1] => 00000
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,5,2,4,1,6] => 00001
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [2,4,3,5,1,6] => 00001
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [5,3,2,1,6,4] => 00000
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => 00001
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 00011
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => 00011
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [5,3,1,2,6,4] => 00000
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [4,3,1,5,2,6] => 00001
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => 00011
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [4,2,1,3,5,6] => 00011
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 00011
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [6,1,4,2,5,3] => 00000
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => 00000
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [5,3,1,4,6,2] => 00000
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [5,1,3,4,2,6] => 00001
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => 00001
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [5,2,3,1,6,4] => 00000
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => 00001
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => 00011
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => 00011
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [5,2,1,3,6,4] => 00000
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [4,2,1,5,3,6] => 00001
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => 00011
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 00111
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 00111
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [5,1,2,3,6,4] => 00000
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [4,1,2,5,3,6] => 00001
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => 00011
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => 00111
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 01111
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 11111
[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] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [7,6,5,4,3,1,2] => 000000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,6,5,4,2,3,1] => 000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [7,6,5,4,2,1,3] => 000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => 000000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [7,6,5,2,4,3,1] => 000000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,6,5,2,3,4,1] => 000000
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,6,5,3,2,4,1] => 000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [7,6,5,3,2,1,4] => 000000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [7,6,5,3,1,2,4] => 000000
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [7,6,5,3,1,4,2] => 000000
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [7,6,5,2,3,1,4] => 000000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [7,6,5,2,1,3,4] => 000000
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => 000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [7,6,3,5,4,2,1] => 000000
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [7,6,2,5,3,4,1] => 000000
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [7,6,2,3,5,4,1] => 000000
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,6,3,2,4,5,1] => 000000
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [7,6,3,1,4,5,2] => 000000
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [7,6,3,5,2,4,1] => 000000
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [7,6,2,4,3,5,1] => 000000
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [7,6,4,3,2,5,1] => 000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [7,6,4,3,2,1,5] => 000000
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [7,6,4,3,1,2,5] => 000000
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [7,6,4,3,1,5,2] => 000000
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [7,6,4,2,3,1,5] => 000000
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [7,6,4,2,1,3,5] => 000000
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [7,6,4,1,2,3,5] => 000000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [7,6,5,1,3,4,2] => 000000
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,6,2,3,4,5,1] => 000000
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,6,4,2,3,5,1] => 000000
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [7,6,2,4,3,1,5] => 000000
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [7,6,2,3,4,1,5] => 000000
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [7,6,4,2,1,5,3] => 000000
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [7,6,3,2,4,1,5] => 000000
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [7,6,3,2,1,4,5] => 000000
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [7,6,3,1,2,4,5] => 000000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [7,6,4,1,2,5,3] => 000000
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [7,6,3,1,4,2,5] => 000000
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [7,6,2,3,1,4,5] => 000000
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [7,6,2,1,3,4,5] => 000000
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => 000000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [7,3,6,5,4,2,1] => 000000
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [7,6,2,4,5,3,1] => 000000
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [7,4,2,6,5,3,1] => 000000
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [7,3,6,2,4,5,1] => 000000
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [7,6,1,3,4,5,2] => 000000
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [7,3,4,6,5,2,1] => 000000
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [7,2,3,4,6,5,1] => 000000
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [7,3,2,6,4,5,1] => 000000
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [7,4,3,2,5,6,1] => 000000
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [7,4,3,1,5,6,2] => 000000
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [7,3,1,6,4,5,2] => 000000
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [7,4,2,3,5,6,1] => 000000
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [7,4,2,1,5,6,3] => 000000
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [7,4,1,2,5,6,3] => 000000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [7,4,6,3,5,2,1] => 000000
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [7,2,6,4,3,5,1] => 000000
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [7,3,4,6,2,5,1] => 000000
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [7,3,5,2,4,6,1] => 000000
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [7,5,1,3,4,6,2] => 000000
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [7,4,6,3,2,5,1] => 000000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [7,3,5,4,2,6,1] => 000000
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [7,5,4,3,2,6,1] => 000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [7,5,4,3,2,1,6] => 000000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [7,5,4,3,1,2,6] => 000000
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [7,5,4,3,1,6,2] => 000000
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [7,5,4,2,3,1,6] => 000000
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [7,5,4,2,1,3,6] => 000000
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [7,5,4,1,2,3,6] => 000000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [7,4,6,3,1,5,2] => 000000
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [7,2,5,3,4,6,1] => 000000
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [7,5,4,2,3,6,1] => 000000
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [7,5,2,4,3,1,6] => 000000
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [7,5,2,3,4,1,6] => 000000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [7,5,4,2,1,6,3] => 000000
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [7,5,3,2,4,1,6] => 000000
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [7,5,3,2,1,4,6] => 000000
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [7,5,3,1,2,4,6] => 000000
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [7,5,4,1,2,6,3] => 000000
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [7,5,3,1,4,2,6] => 000000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [7,5,2,3,1,4,6] => 000000
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [7,5,2,1,3,4,6] => 000000
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [7,5,1,2,3,4,6] => 000000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [7,6,4,1,5,3,2] => 000000
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [7,2,6,3,4,5,1] => 000000
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [7,2,3,6,4,5,1] => 000000
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [7,2,4,3,5,6,1] => 000000
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [7,2,3,4,5,6,1] => 000000
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [7,4,6,2,3,5,1] => 000000
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [7,2,3,5,4,6,1] => 000000
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [7,5,2,4,3,6,1] => 000000
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [7,3,5,4,2,1,6] => 000000
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [7,2,5,3,4,1,6] => 000000
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [7,5,2,3,4,6,1] => 000000
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [7,2,3,5,4,1,6] => 000000
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [7,3,2,4,5,1,6] => 000000
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [7,3,1,4,5,2,6] => 000000
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [7,6,2,4,1,5,3] => 000000
[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] => [3,2,4,5,7,6,1] => [7,3,2,4,5,6,1] => 000000
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [7,5,3,2,4,6,1] => 000000
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [7,3,5,2,4,1,6] => 000000
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [7,2,4,3,5,1,6] => 000000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [7,5,3,2,1,6,4] => 000000
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [7,4,3,2,5,1,6] => 000000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [7,4,3,2,1,5,6] => 000000
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [7,4,3,1,2,5,6] => 000000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [7,5,3,1,2,6,4] => 000000
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [7,4,3,1,5,2,6] => 000000
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [7,4,2,3,1,5,6] => 000000
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [7,4,2,1,3,5,6] => 000000
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [7,4,1,2,3,5,6] => 000000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [7,6,1,4,2,5,3] => 000000
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [7,3,1,4,5,6,2] => 000000
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [7,5,3,1,4,6,2] => 000000
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [7,5,1,3,4,2,6] => 000000
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [7,2,3,4,5,1,6] => 000000
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [7,5,2,3,1,6,4] => 000000
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [7,4,2,3,5,1,6] => 000000
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [7,2,4,3,1,5,6] => 000000
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [7,2,3,4,1,5,6] => 000000
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [7,5,2,1,3,6,4] => 000000
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [7,4,2,1,5,3,6] => 000000
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [7,3,2,4,1,5,6] => 000000
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [7,3,2,1,4,5,6] => 000000
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [7,3,1,2,4,5,6] => 000000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [7,5,1,2,3,6,4] => 000000
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [7,4,1,2,5,3,6] => 000000
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [7,3,1,4,2,5,6] => 000000
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [7,2,3,1,4,5,6] => 000000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [7,2,1,3,4,5,6] => 000000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [4,7,6,5,3,2,1] => 000000
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [7,2,6,4,5,3,1] => 000000
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [7,2,4,6,5,3,1] => 000000
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [7,3,5,2,6,4,1] => 000000
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [7,5,1,3,6,4,2] => 000000
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [3,7,4,6,5,2,1] => 000000
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [5,2,3,7,6,4,1] => 000000
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [7,3,2,5,6,4,1] => 000000
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [4,7,3,2,5,6,1] => 000000
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [4,7,3,1,5,6,2] => 000000
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [7,3,1,5,6,4,2] => 000000
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [4,7,2,3,5,6,1] => 000000
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [7,2,4,1,5,6,3] => 000000
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [7,1,4,2,5,6,3] => 000000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [3,4,7,6,5,2,1] => 000000
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,2,5,7,6,3,1] => 000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [3,4,5,7,6,2,1] => 000000
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [3,2,4,7,5,6,1] => 000000
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [3,1,4,7,5,6,2] => 000000
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [4,3,7,5,6,2,1] => 000000
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [3,4,2,7,5,6,1] => 000000
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [4,3,7,2,5,6,1] => 000000
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => 000000
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [5,4,3,1,6,7,2] => 000000
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [4,7,1,3,5,6,2] => 000000
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [5,4,2,3,6,7,1] => 000000
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [5,4,2,1,6,7,3] => 000000
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [5,4,1,2,6,7,3] => 000000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,7,1,5,6,3,2] => 000000
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [2,3,4,7,5,6,1] => 000000
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,2,7,3,5,6,1] => 000000
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [5,2,4,3,6,7,1] => 000000
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [5,2,3,4,6,7,1] => 000000
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [7,2,1,4,5,6,3] => 000000
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [5,3,2,4,6,7,1] => 000000
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [5,3,2,1,6,7,4] => 000000
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [5,3,1,2,6,7,4] => 000000
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [7,1,2,4,5,6,3] => 000000
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,3,1,4,6,7,2] => 000000
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [5,2,3,1,6,7,4] => 000000
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [5,2,1,3,6,7,4] => 000000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [5,1,2,3,6,7,4] => 000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [4,7,6,3,5,2,1] => 000000
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [7,2,5,4,6,3,1] => 000000
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [3,7,5,4,6,2,1] => 000000
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [3,7,5,2,4,6,1] => 000000
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [7,1,5,3,4,6,2] => 000000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,5,7,4,6,2,1] => 000000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [3,4,5,7,2,6,1] => 000000
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [4,3,7,5,2,6,1] => 000000
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [4,6,3,2,5,7,1] => 000000
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [4,6,3,1,5,7,2] => 000000
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [7,1,4,5,3,6,2] => 000000
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,6,2,3,5,7,1] => 000000
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [6,2,4,1,5,7,3] => 000000
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [6,1,4,2,5,7,3] => 000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [5,7,4,3,6,2,1] => 000000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [3,7,5,4,2,6,1] => 000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [3,5,7,4,2,6,1] => 000000
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [4,6,3,5,2,7,1] => 000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [6,4,1,5,3,7,2] => 000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [5,7,4,3,2,6,1] => 000000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,6,5,4,2,7,1] => 000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => 000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 000001
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [6,5,4,3,1,2,7] => 000001
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [6,5,4,3,1,7,2] => 000000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,5,4,2,3,1,7] => 000001
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [6,5,4,2,1,3,7] => 000001
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => 000001
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [5,7,4,3,1,6,2] => 000000
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [6,2,4,5,3,7,1] => 000000
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [6,5,4,2,3,7,1] => 000000
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [6,5,2,4,3,1,7] => 000001
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,5,2,3,4,1,7] => 000001
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [6,5,4,2,1,7,3] => 000000
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,5,3,2,4,1,7] => 000001
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [6,5,3,2,1,4,7] => 000001
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [6,5,3,1,2,4,7] => 000001
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [6,5,4,1,2,7,3] => 000000
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [6,5,3,1,4,2,7] => 000001
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [6,5,2,3,1,4,7] => 000001
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [6,5,2,1,3,4,7] => 000001
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => 000001
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [5,7,4,6,1,3,2] => 000000
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [2,7,5,3,4,6,1] => 000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [2,7,4,5,3,6,1] => 000000
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [2,6,4,3,5,7,1] => 000000
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [2,6,3,4,5,7,1] => 000000
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [5,7,4,2,3,6,1] => 000000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [4,2,6,5,3,7,1] => 000000
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [6,5,2,4,3,7,1] => 000000
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [6,3,5,4,2,1,7] => 000001
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [6,2,5,3,4,1,7] => 000001
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [6,5,2,3,4,7,1] => 000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [6,2,3,5,4,1,7] => 000001
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [6,3,2,4,5,1,7] => 000001
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [6,3,1,4,5,2,7] => 000001
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [5,7,4,2,1,6,3] => 000000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [3,6,2,4,5,7,1] => 000000
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [6,5,3,2,4,7,1] => 000000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [6,3,5,2,4,1,7] => 000001
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [6,2,4,3,5,1,7] => 000001
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [6,5,3,2,1,7,4] => 000000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [6,4,3,2,5,1,7] => 000001
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [6,4,3,2,1,5,7] => 000001
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [6,4,3,1,2,5,7] => 000001
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [6,5,3,1,2,7,4] => 000000
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [6,4,3,1,5,2,7] => 000001
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [6,4,2,3,1,5,7] => 000001
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [6,4,2,1,3,5,7] => 000001
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [6,4,1,2,3,5,7] => 000001
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [5,7,4,1,2,6,3] => 000000
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [6,1,3,4,5,7,2] => 000000
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [6,5,3,1,4,7,2] => 000000
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [6,5,1,3,4,2,7] => 000001
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => 000001
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [6,5,2,3,1,7,4] => 000000
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [6,4,2,3,5,1,7] => 000001
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [6,2,4,3,1,5,7] => 000001
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [6,2,3,4,1,5,7] => 000001
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [6,5,2,1,3,7,4] => 000000
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [6,4,2,1,5,3,7] => 000001
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [6,3,2,4,1,5,7] => 000001
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [6,3,2,1,4,5,7] => 000001
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [6,3,1,2,4,5,7] => 000001
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [6,5,1,2,3,7,4] => 000000
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [6,4,1,2,5,3,7] => 000001
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [6,3,1,4,2,5,7] => 000001
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [6,2,3,1,4,5,7] => 000001
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [6,2,1,3,4,5,7] => 000001
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 000001
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [7,6,1,4,5,3,2] => 000000
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [7,2,5,3,6,4,1] => 000000
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [7,2,3,5,6,4,1] => 000000
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [2,7,4,3,5,6,1] => 000000
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [2,7,3,4,5,6,1] => 000000
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,2,7,5,6,3,1] => 000000
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [2,3,4,5,7,6,1] => 000000
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [2,4,7,3,5,6,1] => 000000
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [3,5,4,2,6,7,1] => 000000
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [2,5,3,4,6,7,1] => 000000
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [2,3,7,4,5,6,1] => 000000
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [2,3,5,4,6,7,1] => 000000
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => 000000
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [3,1,4,5,6,7,2] => 000000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [5,7,4,2,6,3,1] => 000000
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [2,7,3,5,4,6,1] => 000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [4,2,5,7,3,6,1] => 000000
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [3,4,6,2,5,7,1] => 000000
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [2,3,6,4,5,7,1] => 000000
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [5,7,2,4,3,6,1] => 000000
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [3,4,6,5,2,7,1] => 000000
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [6,3,5,4,2,7,1] => 000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [3,6,5,4,2,1,7] => 000001
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [6,2,4,5,3,1,7] => 000001
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [6,2,5,3,4,7,1] => 000000
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [4,2,6,5,3,1,7] => 000001
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [3,6,2,4,5,1,7] => 000001
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [6,1,3,4,5,2,7] => 000001
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [5,7,2,3,4,6,1] => 000000
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,6,5,7,1] => 000000
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [6,2,3,5,4,7,1] => 000000
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [3,4,6,5,2,1,7] => 000001
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [2,3,4,6,5,1,7] => 000001
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [6,3,2,4,5,7,1] => 000000
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [3,2,6,4,5,1,7] => 000001
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => 000001
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [4,3,1,5,6,2,7] => 000001
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [6,3,1,4,5,7,2] => 000000
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [3,1,6,4,5,2,7] => 000001
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [4,2,3,5,6,1,7] => 000001
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [4,2,1,5,6,3,7] => 000001
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => 000001
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [7,5,2,6,1,4,3] => 000000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [3,7,2,4,5,6,1] => 000000
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [3,2,7,4,5,6,1] => 000000
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => 000000
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => 000000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [5,7,3,2,4,6,1] => 000000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,6,4,5,7,1] => 000000
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [6,3,5,2,4,7,1] => 000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [4,6,3,5,2,1,7] => 000001
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [2,6,4,3,5,1,7] => 000001
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [6,2,4,3,5,7,1] => 000000
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [3,4,6,2,5,1,7] => 000001
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,5,2,4,6,1,7] => 000001
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [5,1,3,4,6,2,7] => 000001
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [7,3,5,2,1,6,4] => 000000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => 000000
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [6,4,3,2,5,7,1] => 000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [4,6,3,2,5,1,7] => 000001
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [3,5,4,2,6,1,7] => 000001
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [6,4,3,2,1,7,5] => 000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => 000001
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 000011
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [5,4,3,1,2,6,7] => 000011
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [6,4,3,1,2,7,5] => 000000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [5,4,3,1,6,2,7] => 000001
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,4,2,3,1,6,7] => 000011
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [5,4,2,1,3,6,7] => 000011
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => 000011
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [7,3,5,1,2,6,4] => 000000
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [4,3,1,5,6,7,2] => 000000
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [6,4,3,1,5,7,2] => 000000
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [4,6,3,1,5,2,7] => 000001
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [2,5,3,4,6,1,7] => 000001
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [6,4,2,3,1,7,5] => 000000
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [5,4,2,3,6,1,7] => 000001
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [5,2,4,3,1,6,7] => 000011
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => 000011
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [6,4,2,1,3,7,5] => 000000
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [5,4,2,1,6,3,7] => 000001
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [5,3,2,4,1,6,7] => 000011
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [5,3,2,1,4,6,7] => 000011
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [5,3,1,2,4,6,7] => 000011
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [6,4,1,2,3,7,5] => 000000
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [5,4,1,2,6,3,7] => 000001
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [5,3,1,4,2,6,7] => 000011
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [5,2,3,1,4,6,7] => 000011
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [5,2,1,3,4,6,7] => 000011
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 000011
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [7,5,1,6,2,4,3] => 000000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [7,1,3,4,5,6,2] => 000000
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [3,1,7,4,5,6,2] => 000000
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [5,1,3,4,6,7,2] => 000000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => 000000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [5,7,3,1,4,6,2] => 000000
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [3,1,6,4,5,7,2] => 000000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [6,5,1,3,4,7,2] => 000000
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [6,4,1,5,3,2,7] => 000001
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [2,6,3,4,5,1,7] => 000001
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [6,2,3,4,5,7,1] => 000000
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [2,3,6,4,5,1,7] => 000001
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [2,4,3,5,6,1,7] => 000001
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => 000001
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [7,2,5,3,1,6,4] => 000000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => 000000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [6,4,2,3,5,7,1] => 000000
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,6,2,3,5,1,7] => 000001
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [2,3,5,4,6,1,7] => 000001
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [6,2,4,3,1,7,5] => 000000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [5,2,4,3,6,1,7] => 000001
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [3,5,4,2,1,6,7] => 000011
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [2,5,3,4,1,6,7] => 000011
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [6,2,3,4,1,7,5] => 000000
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,2,3,4,6,1,7] => 000001
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [2,3,5,4,1,6,7] => 000011
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => 000011
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [3,1,4,5,2,6,7] => 000011
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [7,2,5,1,3,6,4] => 000000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [4,2,1,5,6,7,3] => 000000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [6,4,2,1,5,7,3] => 000000
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [6,2,4,1,5,3,7] => 000001
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => 000001
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [6,3,2,4,1,7,5] => 000000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [5,3,2,4,6,1,7] => 000001
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [3,5,2,4,1,6,7] => 000011
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [2,4,3,5,1,6,7] => 000011
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [6,3,2,1,4,7,5] => 000000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [5,3,2,1,6,4,7] => 000001
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => 000011
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 000111
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [4,3,1,2,5,6,7] => 000111
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [6,3,1,2,4,7,5] => 000000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [5,3,1,2,6,4,7] => 000001
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [4,3,1,5,2,6,7] => 000011
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => 000111
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [4,2,1,3,5,6,7] => 000111
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 000111
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [7,1,5,2,3,6,4] => 000000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [4,1,2,5,6,7,3] => 000000
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [6,4,1,2,5,7,3] => 000000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [6,1,4,2,5,3,7] => 000001
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [3,1,4,5,6,2,7] => 000001
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [6,3,1,4,2,7,5] => 000000
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [5,3,1,4,6,2,7] => 000001
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [5,1,3,4,2,6,7] => 000011
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => 000011
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [6,2,3,1,4,7,5] => 000000
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [5,2,3,1,6,4,7] => 000001
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [4,2,3,5,1,6,7] => 000011
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [2,4,3,1,5,6,7] => 000111
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => 000111
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [6,2,1,3,4,7,5] => 000000
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [5,2,1,3,6,4,7] => 000001
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [4,2,1,5,3,6,7] => 000011
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => 000111
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 001111
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 001111
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [6,1,2,3,4,7,5] => 000000
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [5,1,2,3,6,4,7] => 000001
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [4,1,2,5,3,6,7] => 000011
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,1,4,2,5,6,7] => 000111
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => 001111
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 011111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 111111
[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] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [8,7,6,5,4,3,1,2] => 0000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [8,7,6,5,4,2,3,1] => 0000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [8,7,6,5,4,2,1,3] => 0000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [8,7,6,5,4,1,2,3] => 0000000
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [8,7,6,5,2,3,4,1] => 0000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [8,7,6,5,3,2,1,4] => 0000000
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [8,7,6,5,3,1,2,4] => 0000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [8,7,6,5,3,1,4,2] => 0000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [8,7,6,5,2,3,1,4] => 0000000
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [8,7,6,5,2,1,3,4] => 0000000
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [8,7,6,5,1,2,3,4] => 0000000
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [8,7,6,3,2,4,5,1] => 0000000
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [8,7,6,3,5,2,4,1] => 0000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [8,7,6,4,3,2,1,5] => 0000000
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [8,7,6,4,3,1,2,5] => 0000000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [8,7,6,4,3,1,5,2] => 0000000
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [8,7,6,4,2,3,1,5] => 0000000
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [8,7,6,4,2,1,3,5] => 0000000
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [8,7,6,4,1,2,3,5] => 0000000
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [8,7,6,2,3,4,5,1] => 0000000
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [8,7,6,2,4,3,1,5] => 0000000
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [8,7,6,2,3,4,1,5] => 0000000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [8,7,6,4,2,1,5,3] => 0000000
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [8,7,6,3,2,4,1,5] => 0000000
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [8,7,6,3,2,1,4,5] => 0000000
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [8,7,6,3,1,2,4,5] => 0000000
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [8,7,6,4,1,2,5,3] => 0000000
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [8,7,6,3,1,4,2,5] => 0000000
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [8,7,6,2,3,1,4,5] => 0000000
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [8,7,6,2,1,3,4,5] => 0000000
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [8,7,6,1,2,3,4,5] => 0000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [8,7,3,6,5,4,2,1] => 0000000
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,8,4,7,6,5,2] => [8,7,6,1,3,4,5,2] => 0000000
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [8,7,3,4,6,5,2,1] => 0000000
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => [8,7,3,2,6,4,5,1] => 0000000
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [8,7,4,3,2,5,6,1] => 0000000
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [8,7,3,1,6,4,5,2] => 0000000
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [8,7,4,2,1,5,6,3] => 0000000
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [8,7,4,1,2,5,6,3] => 0000000
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [8,7,4,6,3,5,2,1] => 0000000
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [8,7,4,6,3,2,5,1] => 0000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [8,7,5,4,3,2,1,6] => 0000000
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [8,7,5,4,3,1,2,6] => 0000000
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [8,7,5,4,3,1,6,2] => 0000000
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [8,7,5,4,1,2,3,6] => 0000000
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [8,7,5,4,2,3,6,1] => 0000000
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [8,7,5,4,2,1,6,3] => 0000000
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [8,7,5,3,2,4,1,6] => 0000000
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,1,5,4,8,7,6] => [8,7,5,3,2,1,4,6] => 0000000
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [8,7,5,2,1,3,4,6] => 0000000
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [8,7,5,1,2,3,4,6] => 0000000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [8,7,6,4,1,5,3,2] => 0000000
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [8,7,2,3,4,5,6,1] => 0000000
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [8,7,3,5,4,2,1,6] => 0000000
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [8,7,5,3,2,1,6,4] => 0000000
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [8,7,4,3,2,5,1,6] => 0000000
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [8,7,4,3,2,1,5,6] => 0000000
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [8,7,4,2,1,3,5,6] => 0000000
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [8,7,4,1,2,3,5,6] => 0000000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [8,7,6,1,4,2,5,3] => 0000000
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [8,7,5,3,1,4,6,2] => 0000000
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [8,7,2,3,4,5,1,6] => 0000000
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => [8,7,2,4,3,1,5,6] => 0000000
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [8,7,2,3,4,1,5,6] => 0000000
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [8,7,4,2,1,5,3,6] => 0000000
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [8,7,3,2,4,1,5,6] => 0000000
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [8,7,3,2,1,4,5,6] => 0000000
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [8,7,4,1,2,5,3,6] => 0000000
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [8,7,3,1,4,2,5,6] => 0000000
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [8,7,2,1,3,4,5,6] => 0000000
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [8,7,1,2,3,4,5,6] => 0000000
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [8,7,2,4,6,5,3,1] => 0000000
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [8,3,7,4,6,5,2,1] => 0000000
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [8,7,3,2,5,6,4,1] => 0000000
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [8,4,7,3,2,5,6,1] => 0000000
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => [8,4,7,2,3,5,6,1] => 0000000
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [8,7,2,4,1,5,6,3] => 0000000
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,8,5,7,6,3] => [8,7,1,4,2,5,6,3] => 0000000
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [8,3,4,5,7,6,2,1] => 0000000
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [8,4,3,7,5,6,2,1] => 0000000
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [8,4,3,7,2,5,6,1] => 0000000
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [8,5,4,3,2,6,7,1] => 0000000
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,8,4,5,7,6,3,2] => [8,4,7,1,5,6,3,2] => 0000000
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [8,4,2,7,3,5,6,1] => 0000000
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [8,7,2,1,4,5,6,3] => 0000000
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [8,5,3,2,1,6,7,4] => 0000000
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [8,5,3,1,2,6,7,4] => 0000000
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,8,4,5,7,6,3] => [8,7,1,2,4,5,6,3] => 0000000
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,4,6,8,7,2] => [8,5,3,1,4,6,7,2] => 0000000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [8,4,7,6,3,5,2,1] => 0000000
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [8,3,7,5,4,6,2,1] => 0000000
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [8,3,7,5,2,4,6,1] => 0000000
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => [8,4,3,7,5,2,6,1] => 0000000
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [8,6,2,4,1,5,7,3] => 0000000
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,6,4,5,8,7,3] => [8,6,1,4,2,5,7,3] => 0000000
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [8,5,7,4,3,6,2,1] => 0000000
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => [8,3,7,5,4,2,6,1] => 0000000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [8,3,5,7,4,2,6,1] => 0000000
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [8,5,7,4,3,2,6,1] => 0000000
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [6,5,3,4,2,8,7,1] => [8,3,6,5,4,2,7,1] => 0000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [8,6,5,4,3,2,7,1] => 0000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [8,6,5,4,3,2,1,7] => 0000000
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [8,6,5,4,3,1,2,7] => 0000000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [8,6,5,4,3,1,7,2] => 0000000
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [8,6,5,4,2,3,1,7] => 0000000
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [8,6,5,4,2,1,3,7] => 0000000
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,5,4,3,8,7] => [8,6,5,4,1,2,3,7] => 0000000
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,6,4,5,3,8,7,1] => [8,6,2,4,5,3,7,1] => 0000000
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [8,6,5,4,2,3,7,1] => 0000000
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [8,6,5,2,3,4,1,7] => 0000000
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [8,6,5,4,2,1,7,3] => 0000000
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [8,6,5,3,2,1,4,7] => 0000000
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [8,6,5,2,3,1,4,7] => 0000000
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [8,6,5,1,2,3,4,7] => 0000000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [8,5,7,4,6,1,3,2] => 0000000
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,2,4,5,3,8,7,1] => [8,4,2,6,5,3,7,1] => 0000000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [8,5,7,4,2,1,6,3] => 0000000
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [8,6,5,3,2,4,7,1] => 0000000
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [8,6,3,5,2,4,1,7] => 0000000
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [8,6,5,3,2,1,7,4] => 0000000
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [8,6,4,3,2,1,5,7] => 0000000
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [8,6,4,2,3,1,5,7] => 0000000
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [8,6,4,2,1,3,5,7] => 0000000
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => [8,5,7,4,1,2,6,3] => 0000000
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [8,6,1,3,4,5,7,2] => 0000000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [8,6,5,2,3,1,7,4] => 0000000
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [8,6,4,2,3,5,1,7] => 0000000
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [8,6,2,4,3,1,5,7] => 0000000
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [8,6,2,3,4,1,5,7] => 0000000
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [8,6,4,2,1,5,3,7] => 0000000
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [8,6,3,2,4,1,5,7] => 0000000
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,2,1,4,6,5,8,7] => [8,6,3,2,1,4,5,7] => 0000000
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,5,3,8,7] => [8,6,4,1,2,5,3,7] => 0000000
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [8,6,3,1,4,2,5,7] => 0000000
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [8,6,1,2,3,4,5,7] => 0000000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [8,7,6,1,4,5,3,2] => 0000000
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [8,2,7,3,4,5,6,1] => 0000000
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,2,3,4,6,8,7,1] => [8,2,3,5,4,6,7,1] => 0000000
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [8,3,2,4,5,6,7,1] => 0000000
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [8,3,1,4,5,6,7,2] => 0000000
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [8,5,7,4,2,6,3,1] => 0000000
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [8,4,2,5,7,3,6,1] => 0000000
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [8,5,7,2,4,3,6,1] => 0000000
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [8,3,6,5,4,2,1,7] => 0000000
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,4,5,3,1,8,7] => [8,6,2,4,5,3,1,7] => 0000000
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2,4,5,3,1,8,7] => [8,4,2,6,5,3,1,7] => 0000000
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [8,3,6,2,4,5,1,7] => 0000000
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,4,6,5,8,7,2] => [8,6,3,1,4,5,7,2] => 0000000
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [8,4,2,1,5,6,3,7] => 0000000
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [8,4,1,2,5,6,3,7] => 0000000
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [8,4,3,2,5,6,7,1] => 0000000
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [8,6,4,3,2,5,7,1] => 0000000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [8,6,4,3,2,1,7,5] => 0000000
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [8,5,4,3,2,6,1,7] => 0000000
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [8,5,4,3,2,1,6,7] => 0000000
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [8,5,4,2,1,3,6,7] => 0000000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [8,7,3,5,1,2,6,4] => 0000000
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,3,5,6,8,7,2] => [8,4,3,1,5,6,7,2] => 0000000
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [8,6,4,3,1,5,7,2] => 0000000
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [8,6,4,2,3,1,7,5] => 0000000
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [8,6,4,2,1,3,7,5] => 0000000
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [8,5,4,2,1,6,3,7] => 0000000
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [8,6,4,1,2,3,7,5] => 0000000
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,4,6,3,8,7] => [8,5,4,1,2,6,3,7] => 0000000
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [8,5,2,1,3,4,6,7] => 0000000
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [8,5,1,2,3,4,6,7] => 0000000
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [8,2,3,4,5,6,7,1] => 0000000
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [8,2,6,3,4,5,1,7] => 0000000
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [8,2,3,4,5,6,1,7] => 0000000
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [8,6,4,2,3,5,7,1] => 0000000
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [8,4,6,2,3,5,1,7] => 0000000
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [8,5,2,4,3,6,1,7] => 0000000
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [8,7,2,5,1,3,6,4] => 0000000
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [8,4,2,1,5,6,7,3] => 0000000
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [8,6,2,4,1,5,3,7] => 0000000
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [8,6,3,2,4,1,7,5] => 0000000
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [8,5,3,2,4,6,1,7] => 0000000
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [8,3,5,2,4,1,6,7] => 0000000
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,5,6,4,8,7] => [8,5,3,2,1,6,4,7] => 0000000
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [8,4,3,2,1,5,6,7] => 0000000
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [8,4,1,2,3,5,6,7] => 0000000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [8,7,1,5,2,3,6,4] => 0000000
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [8,6,4,1,2,5,7,3] => 0000000
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [8,2,3,4,5,1,6,7] => 0000000
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,6,4,8,7] => [8,5,2,3,1,6,4,7] => 0000000
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [8,2,3,4,1,5,6,7] => 0000000
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [8,4,2,1,5,3,6,7] => 0000000
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [8,3,2,1,4,5,6,7] => 0000000
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [8,3,1,2,4,5,6,7] => 0000000
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [8,2,3,1,4,5,6,7] => 0000000
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [8,2,1,3,4,5,6,7] => 0000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 0000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [4,8,7,6,5,3,2,1] => 0000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [8,7,2,5,6,4,3,1] => 0000000
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [8,3,7,5,2,6,4,1] => 0000000
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [8,3,5,7,6,4,2,1] => 0000000
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,3,8,6,7,5,1] => [8,4,6,2,3,7,5,1] => 0000000
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,8,6,7,5,3] => [8,6,1,4,2,7,5,3] => 0000000
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [5,3,8,7,6,4,2,1] => 0000000
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [8,3,2,4,6,7,5,1] => 0000000
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [5,8,4,2,1,6,7,3] => 0000000
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => [5,8,4,1,2,6,7,3] => 0000000
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [8,4,2,6,3,7,5,1] => 0000000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [4,5,8,7,6,3,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [4,2,8,5,7,6,3,1] => 0000000
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [5,3,2,8,6,7,4,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [3,4,5,8,7,6,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [3,4,5,6,8,7,2,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [4,3,2,8,5,6,7,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [4,3,1,8,5,6,7,2] => 0000000
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [4,5,1,8,6,7,3,2] => 0000000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [4,2,3,8,5,6,7,1] => 0000000
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [4,2,1,8,5,6,7,3] => 0000000
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [4,1,2,8,5,6,7,3] => 0000000
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [4,3,8,7,5,6,2,1] => 0000000
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [4,1,8,5,3,6,7,2] => 0000000
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [6,5,4,3,2,7,8,1] => 0000000
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [6,5,4,3,1,7,8,2] => 0000000
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [6,5,4,2,3,7,8,1] => 0000000
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [6,5,4,2,1,7,8,3] => 0000000
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [6,5,4,1,2,7,8,3] => 0000000
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [5,8,4,1,6,7,3,2] => 0000000
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,2,5,4,3,7,8,1] => [6,5,2,4,3,7,8,1] => 0000000
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [6,5,2,3,4,7,8,1] => 0000000
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [5,8,2,4,1,6,7,3] => 0000000
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [6,5,3,2,1,7,8,4] => 0000000
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [6,5,3,1,2,7,8,4] => 0000000
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,5,7,8,4] => [6,5,2,3,1,7,8,4] => 0000000
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [6,5,2,1,3,7,8,4] => 0000000
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [6,5,1,2,3,7,8,4] => 0000000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [4,8,1,7,5,6,3,2] => 0000000
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [2,3,4,8,5,6,7,1] => 0000000
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8,2,4,5,3,6,7,1] => [4,2,5,3,8,6,7,1] => 0000000
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => [5,2,8,4,3,6,7,1] => 0000000
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [6,3,1,4,5,7,8,2] => 0000000
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [8,5,2,1,6,7,4,3] => 0000000
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [5,3,8,2,4,6,7,1] => 0000000
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [6,4,3,2,1,7,8,5] => 0000000
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [6,4,3,1,2,7,8,5] => 0000000
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [6,4,3,1,5,7,8,2] => 0000000
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [6,4,2,1,3,7,8,5] => 0000000
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [6,2,3,4,5,7,8,1] => 0000000
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [8,2,3,5,1,6,7,4] => 0000000
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [6,2,3,4,1,7,8,5] => 0000000
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [6,3,2,1,4,7,8,5] => 0000000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [8,1,2,5,3,6,7,4] => 0000000
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [6,3,1,4,2,7,8,5] => 0000000
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [6,1,2,3,4,7,8,5] => 0000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [5,8,7,4,6,3,2,1] => 0000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [8,2,7,5,4,6,3,1] => 0000000
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => [3,8,7,5,4,6,2,1] => 0000000
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [3,8,5,7,4,6,2,1] => 0000000
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [8,2,6,4,1,5,7,3] => 0000000
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8,3,6,4,5,7,2,1] => [3,4,8,6,5,7,2,1] => 0000000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8,6,3,4,5,7,2,1] => [3,4,6,8,5,7,2,1] => 0000000
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [4,6,8,3,5,7,2,1] => 0000000
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [5,7,4,2,3,6,8,1] => 0000000
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,7,5,4,6,8,3] => [5,7,4,1,2,6,8,3] => 0000000
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,2,5,4,3,6,8,1] => [5,7,2,4,3,6,8,1] => 0000000
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [8,2,5,6,1,4,7,3] => 0000000
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [7,3,5,2,1,6,8,4] => 0000000
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,7,5,6,8,4] => [7,2,5,1,3,6,8,4] => 0000000
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [7,1,5,2,3,6,8,4] => 0000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [5,8,7,4,3,6,2,1] => 0000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [6,8,3,5,4,7,2,1] => 0000000
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [6,8,4,1,5,3,7,2] => 0000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8,6,4,5,3,7,2,1] => [4,6,8,5,3,7,2,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => [3,4,6,8,5,2,7,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [4,6,8,3,5,2,7,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [5,7,4,3,6,2,8,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7,5,4,6,3,8,2] => [5,7,4,6,1,3,8,2] => 0000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [5,7,4,2,6,3,8,1] => 0000000
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,7,5,6,4,8,3] => [7,5,1,6,2,4,8,3] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [6,8,5,4,3,7,2,1] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [4,7,6,3,5,2,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7,6,4,5,3,8,2] => [7,6,1,4,5,3,8,2] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [6,8,5,4,3,2,7,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [4,7,6,5,3,2,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1] => 0000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0000001
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [7,6,5,4,3,1,2,8] => 0000001
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [7,6,5,4,3,1,8,2] => 0000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [7,6,5,4,2,3,1,8] => 0000001
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [7,6,5,4,2,1,3,8] => 0000001
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [7,6,5,4,1,2,3,8] => 0000001
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [6,8,5,4,3,1,7,2] => 0000000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [7,6,5,4,2,3,8,1] => 0000000
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [7,6,5,2,3,4,1,8] => 0000001
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [7,6,5,4,2,1,8,3] => 0000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,6,5,3,2,4,1,8] => 0000001
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [7,6,5,3,2,1,4,8] => 0000001
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [7,6,5,4,1,2,8,3] => 0000000
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,7,6,5,4,8] => [7,6,5,2,3,1,4,8] => 0000001
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,7,6,5,4,8] => [7,6,5,2,1,3,4,8] => 0000001
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [7,6,5,1,2,3,4,8] => 0000001
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [6,8,5,4,7,1,3,2] => 0000000
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [6,8,2,4,5,3,7,1] => 0000000
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [7,6,3,5,4,2,1,8] => 0000001
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => [7,6,2,5,3,4,1,8] => 0000001
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [7,6,5,2,3,4,8,1] => 0000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [7,6,2,3,5,4,1,8] => 0000001
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,2,4,7,6,5,1,8] => [7,6,3,2,4,5,1,8] => 0000001
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [6,8,5,4,2,1,7,3] => 0000000
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [4,2,3,7,6,5,1,8] => [7,6,2,4,3,5,1,8] => 0000001
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [7,6,5,3,2,1,8,4] => 0000000
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,2,7,6,5,1,8] => [7,6,4,3,2,5,1,8] => 0000001
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [7,6,4,3,2,1,5,8] => 0000001
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [7,6,4,3,1,2,5,8] => 0000001
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [7,6,5,3,1,2,8,4] => 0000000
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,3,7,6,5,2,8] => [7,6,4,3,1,5,2,8] => 0000001
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,7,6,5,8] => [7,6,4,2,1,3,5,8] => 0000001
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [6,8,5,4,1,2,7,3] => 0000000
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => [7,6,5,1,3,4,2,8] => 0000001
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [7,6,2,3,4,5,1,8] => 0000001
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,4,3,7,6,5,1,8] => [7,6,4,2,3,5,1,8] => 0000001
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => [7,6,2,4,3,1,5,8] => 0000001
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [7,6,2,3,4,1,5,8] => 0000001
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,7,6,5,3,8] => [7,6,4,2,1,5,3,8] => 0000001
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [7,6,3,2,4,1,5,8] => 0000001
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [7,6,3,2,1,4,5,8] => 0000001
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [7,6,5,1,2,3,8,4] => 0000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,6,5,3,8] => [7,6,4,1,2,5,3,8] => 0000001
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,6,5,8] => [7,6,3,1,4,2,5,8] => 0000001
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [7,6,1,2,3,4,5,8] => 0000001
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [5,8,7,4,6,1,3,2] => 0000000
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,8,4,6,5,7,3,1] => [8,2,6,4,5,7,3,1] => 0000000
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [2,8,6,4,3,5,7,1] => 0000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,8,6,4,5,7,3,1] => [6,2,8,4,5,7,3,1] => 0000000
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => [2,8,5,3,6,4,7,1] => 0000000
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [6,8,5,2,4,3,7,1] => 0000000
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [7,6,3,5,4,2,8,1] => 0000000
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [7,3,6,5,4,2,1,8] => 0000001
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => [7,6,2,4,5,3,1,8] => 0000001
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => [6,8,5,2,3,4,7,1] => 0000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => [7,3,4,6,5,2,1,8] => 0000001
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => [7,2,3,4,6,5,1,8] => 0000001
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [7,4,3,1,5,6,2,8] => 0000001
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,7,3,4,6,5,2,8] => [7,3,1,6,4,5,2,8] => 0000001
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,6,3,8] => [7,4,2,1,5,6,3,8] => 0000001
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,6,3,8] => [7,4,1,2,5,6,3,8] => 0000001
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [6,8,5,7,2,1,4,3] => 0000000
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [3,8,6,2,4,5,7,1] => 0000000
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [2,7,4,3,5,6,8,1] => 0000000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [7,3,2,6,5,4,8,1] => [7,6,3,5,2,4,8,1] => 0000000
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [7,4,6,3,5,2,1,8] => 0000001
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [7,3,5,2,4,6,1,8] => 0000001
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [4,7,3,2,5,6,8,1] => 0000000
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [7,3,5,4,2,6,1,8] => 0000001
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [7,6,4,3,2,1,8,5] => 0000000
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [7,5,4,3,2,6,1,8] => 0000001
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [7,5,4,3,2,1,6,8] => 0000001
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [7,5,4,3,1,2,6,8] => 0000001
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [7,6,4,3,1,2,8,5] => 0000000
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [7,5,4,2,3,1,6,8] => 0000001
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [6,8,5,3,1,2,7,4] => 0000000
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,3,4,7,6,1,8] => [7,2,5,3,4,6,1,8] => 0000001
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [7,6,4,2,3,1,8,5] => 0000000
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => [7,5,2,4,3,1,6,8] => 0000001
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [7,5,2,3,4,1,6,8] => 0000001
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [7,6,4,2,1,3,8,5] => 0000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,4,7,6,3,8] => [7,5,4,2,1,6,3,8] => 0000001
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [7,5,3,2,4,1,6,8] => 0000001
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [7,5,3,2,1,4,6,8] => 0000001
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [7,5,3,1,2,4,6,8] => 0000001
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [7,5,3,1,4,2,6,8] => 0000001
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [7,5,2,3,1,4,6,8] => 0000001
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [7,5,1,2,3,4,6,8] => 0000001
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [6,8,5,7,1,2,4,3] => 0000000
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [8,1,6,3,4,5,7,2] => 0000000
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [7,6,5,1,3,4,8,2] => 0000000
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [7,6,2,3,4,5,8,1] => 0000000
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [7,2,3,4,5,6,1,8] => 0000001
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,8,6,5,7,4] => [6,8,5,2,3,1,7,4] => 0000000
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [7,6,4,2,3,5,8,1] => 0000000
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,7,4,3,6,5,1,8] => [7,4,6,2,3,5,1,8] => 0000001
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [7,2,3,5,4,6,1,8] => 0000001
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,3,4,1,7,6,8] => [7,2,5,3,4,1,6,8] => 0000001
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [7,6,2,3,4,1,8,5] => 0000000
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,3,4,1,7,6,8] => [7,2,3,5,4,1,6,8] => 0000001
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [7,3,1,4,5,2,6,8] => 0000001
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [7,6,4,2,1,5,8,3] => 0000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [7,6,3,2,4,1,8,5] => 0000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [7,5,3,2,4,6,1,8] => 0000001
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [7,3,5,2,4,1,6,8] => 0000001
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [7,4,3,2,1,5,6,8] => 0000001
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [7,4,3,1,2,5,6,8] => 0000001
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [7,4,1,2,3,5,6,8] => 0000001
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [6,8,5,1,2,3,7,4] => 0000000
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [7,6,4,1,2,5,8,3] => 0000000
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [7,3,1,4,5,6,2,8] => 0000001
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [7,2,3,4,5,1,6,8] => 0000001
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [7,2,3,4,1,5,6,8] => 0000001
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [7,3,2,1,4,5,6,8] => 0000001
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [7,3,1,2,4,5,6,8] => 0000001
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [7,6,1,2,3,4,8,5] => 0000000
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [7,2,3,1,4,5,6,8] => 0000001
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [7,2,1,3,4,5,6,8] => 0000001
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 0000001
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [8,7,5,1,6,4,3,2] => 0000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,7,5,6,4,1] => [8,2,7,5,3,6,4,1] => 0000000
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,2,3,8,6,7,5,1] => [8,2,6,4,3,7,5,1] => 0000000
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [8,2,6,3,4,7,5,1] => 0000000
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [8,2,4,6,3,7,5,1] => 0000000
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [8,2,3,6,4,7,5,1] => 0000000
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [3,8,2,4,5,6,7,1] => 0000000
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [8,1,3,4,5,6,7,2] => 0000000
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => [4,2,5,6,8,7,3,1] => 0000000
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [3,4,2,5,8,6,7,1] => 0000000
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [2,3,4,5,8,6,7,1] => 0000000
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8,2,5,4,6,7,3,1] => [5,2,8,4,6,7,3,1] => 0000000
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,8,3,5,4,6,7,1] => [2,5,8,3,4,6,7,1] => 0000000
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,8,7,1] => 0000000
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [2,3,8,5,4,6,7,1] => 0000000
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [3,4,6,5,2,7,8,1] => 0000000
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [2,3,4,6,5,7,8,1] => 0000000
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [3,2,8,4,5,6,7,1] => 0000000
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,8,1] => 0000000
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [4,3,1,5,6,7,8,2] => 0000000
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [3,1,8,4,5,6,7,2] => 0000000
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [4,2,3,5,6,7,8,1] => 0000000
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [4,2,1,5,6,7,8,3] => 0000000
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [4,1,2,5,6,7,8,3] => 0000000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [5,8,7,4,2,6,3,1] => 0000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [4,2,8,6,5,7,3,1] => 0000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [3,4,5,6,8,2,7,1] => 0000000
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [4,2,5,7,3,6,8,1] => 0000000
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [3,1,7,4,5,6,8,2] => 0000000
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [4,2,7,5,6,3,8,1] => 0000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [7,3,6,5,4,2,8,1] => 0000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [4,7,6,5,3,2,1,8] => 0000001
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => [7,2,4,6,5,3,1,8] => 0000001
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [7,3,5,2,6,4,1,8] => 0000001
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [7,2,4,5,6,3,8,1] => [4,2,5,7,6,3,8,1] => 0000000
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [7,3,6,2,4,5,8,1] => 0000000
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,7,5,6,1,8] => [4,7,3,2,5,6,1,8] => 0000001
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,3,7,5,6,2,8] => [4,7,3,1,5,6,2,8] => 0000001
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,8,6,5,7,4,1] => [6,8,5,2,3,7,4,1] => 0000000
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,3,4,5,7,6,8,1] => 0000000
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => [6,8,2,3,5,4,7,1] => 0000000
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [3,4,5,7,6,2,8,1] => 0000000
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [3,4,7,6,5,2,1,8] => 0000001
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,2,4,5,6,3,1,8] => [4,2,5,7,6,3,1,8] => 0000001
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => [3,1,4,7,5,6,2,8] => 0000001
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [7,4,3,2,5,6,8,1] => 0000000
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1,8] => [4,3,7,2,5,6,1,8] => 0000001
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1,8] => 0000001
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [5,4,3,1,6,7,2,8] => 0000001
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,3,5,7,6,8,2] => [7,4,3,1,5,6,8,2] => 0000000
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [5,4,2,3,6,7,1,8] => 0000001
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [5,4,2,1,6,7,3,8] => 0000001
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [5,4,1,2,6,7,3,8] => 0000001
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,7,4,5,6,3,2,8] => [4,7,1,5,6,3,2,8] => 0000001
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => [5,2,4,3,6,7,1,8] => 0000001
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [5,2,3,4,6,7,1,8] => 0000001
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,7,4,5,6,3,8] => [7,2,1,4,5,6,3,8] => 0000001
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,7,4,5,6,3,8] => [7,1,2,4,5,6,3,8] => 0000001
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [8,7,2,5,6,1,4,3] => 0000000
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [3,2,4,5,8,6,7,1] => 0000000
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8,3,2,5,4,6,7,1] => [3,5,8,2,4,6,7,1] => 0000000
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,4,3,5,2,7,8,1] => [4,6,3,5,2,7,8,1] => 0000000
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [2,4,8,3,5,6,7,1] => 0000000
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [5,1,3,4,6,7,8,2] => 0000000
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,2,4,3,5,6,8,1] => [2,4,7,3,5,6,8,1] => 0000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [4,7,6,3,5,2,1,8] => 0000001
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [7,2,6,4,3,5,8,1] => 0000000
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [3,7,5,2,4,6,1,8] => 0000001
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [4,3,7,5,2,6,1,8] => 0000001
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [8,6,3,7,2,1,5,4] => 0000000
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [3,5,4,2,6,7,8,1] => 0000000
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [4,3,7,2,5,6,8,1] => 0000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [5,7,4,3,6,2,1,8] => 0000001
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [3,5,7,4,2,6,1,8] => 0000001
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,4,3,5,2,7,1,8] => [4,6,3,5,2,7,1,8] => 0000001
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [8,4,6,3,2,1,7,5] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,8,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [7,5,4,3,2,6,8,1] => 0000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [5,7,4,3,2,6,1,8] => 0000001
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [7,5,4,3,2,1,8,6] => 0000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [6,5,4,3,2,7,1,8] => 0000001
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0000011
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [6,5,4,3,1,2,7,8] => 0000011
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [6,5,4,1,2,3,7,8] => 0000011
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [5,4,3,1,6,7,8,2] => 0000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [7,5,4,2,3,1,8,6] => 0000000
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [6,5,2,3,4,1,7,8] => 0000011
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,6,5,4,7,3,8] => [6,5,4,2,1,7,3,8] => 0000001
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [6,5,3,2,1,4,7,8] => 0000011
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,5,4,2,7,8] => [6,5,3,1,4,2,7,8] => 0000011
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [4,8,3,1,5,6,7,2] => 0000000
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [4,8,1,3,5,6,7,2] => 0000000
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [2,5,3,4,6,7,8,1] => 0000000
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [6,8,4,3,1,5,7,2] => 0000000
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [8,4,6,2,3,1,7,5] => 0000000
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [5,4,2,3,6,7,8,1] => 0000000
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => [6,2,3,5,4,1,7,8] => 0000011
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [8,4,6,2,1,3,7,5] => 0000000
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [5,4,2,1,6,7,8,3] => 0000000
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [7,5,4,2,1,6,8,3] => 0000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [7,5,3,2,4,1,8,6] => 0000000
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [6,4,3,2,5,1,7,8] => 0000011
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [6,4,3,2,1,5,7,8] => 0000011
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,3,2,6,5,7,8] => [6,4,3,1,2,5,7,8] => 0000011
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [6,5,3,1,2,7,4,8] => 0000001
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [6,4,3,1,5,2,7,8] => 0000011
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [6,4,2,1,3,5,7,8] => 0000011
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [6,4,1,2,3,5,7,8] => 0000011
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [5,4,1,2,6,7,8,3] => 0000000
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [7,5,4,1,2,6,8,3] => 0000000
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [6,5,3,1,4,7,2,8] => 0000001
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [6,5,1,3,4,2,7,8] => 0000011
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [6,2,3,4,5,1,7,8] => 0000011
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,4,7,8,6] => [7,5,2,3,1,4,8,6] => 0000000
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => [6,2,4,3,1,5,7,8] => 0000011
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [6,4,2,1,5,3,7,8] => 0000011
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [6,3,1,2,4,5,7,8] => 0000011
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [6,4,1,2,5,3,7,8] => 0000011
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 0000011
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [8,7,1,5,6,2,4,3] => 0000000
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [2,8,3,4,5,6,7,1] => 0000000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [3,1,4,5,8,6,7,2] => 0000000
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => [2,6,3,4,5,7,8,1] => 0000000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [2,3,8,4,5,6,7,1] => 0000000
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [2,3,6,4,5,7,8,1] => 0000000
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [2,4,3,5,6,7,8,1] => 0000000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => 0000000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [6,8,5,3,1,7,4,2] => 0000000
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [8,1,3,5,6,4,7,2] => 0000000
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [2,3,7,4,5,6,8,1] => 0000000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [6,8,5,1,3,4,7,2] => 0000000
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [7,6,1,4,5,3,2,8] => 0000001
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [7,2,5,3,6,4,1,8] => 0000001
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [7,2,6,3,4,5,8,1] => 0000000
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,7,3,5,6,4,1,8] => [7,2,3,5,6,4,1,8] => 0000001
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [4,2,7,5,6,3,1,8] => 0000001
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [2,3,4,5,7,6,1,8] => 0000001
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,3,4,2,6,7,1,8] => [3,5,4,2,6,7,1,8] => 0000001
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [2,5,3,4,6,7,1,8] => 0000001
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [7,2,3,4,5,6,8,1] => 0000000
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1,8] => 0000001
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [3,1,4,5,6,7,2,8] => 0000001
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [8,6,2,7,3,1,5,4] => 0000000
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [4,8,2,3,5,6,7,1] => 0000000
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [2,3,5,4,6,7,8,1] => 0000000
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [4,2,5,7,3,6,1,8] => 0000001
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [8,2,6,4,3,1,7,5] => 0000000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [7,5,2,4,3,6,8,1] => 0000000
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [5,7,2,4,3,6,1,8] => 0000001
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [3,4,6,5,2,7,1,8] => 0000001
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [7,3,5,4,2,1,8,6] => 0000000
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [6,3,5,4,2,7,1,8] => 0000001
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [3,6,5,4,2,1,7,8] => 0000011
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => [6,2,4,5,3,1,7,8] => 0000011
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [5,2,3,4,6,7,8,1] => 0000000
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [2,3,4,6,5,7,1,8] => 0000001
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [7,2,3,5,4,1,8,6] => 0000000
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => [6,2,3,5,4,7,1,8] => 0000001
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [2,3,4,6,5,1,7,8] => 0000011
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,2,4,5,1,7,8,6] => [7,3,2,4,5,1,8,6] => 0000000
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,2,4,6,5,7,1,8] => [6,3,2,4,5,7,1,8] => 0000001
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [4,3,2,5,6,1,7,8] => 0000011
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,3,5,6,1,7,8] => [4,2,3,5,6,1,7,8] => 0000011
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [4,1,2,5,6,3,7,8] => 0000011
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [8,6,2,7,1,3,5,4] => 0000000
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [8,2,4,1,5,6,7,3] => 0000000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [8,2,1,4,5,6,7,3] => 0000000
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1] => 0000000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [6,8,4,2,1,5,7,3] => 0000000
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [7,6,2,4,1,5,8,3] => 0000000
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [3,2,7,4,5,6,1,8] => 0000001
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [8,3,6,2,4,1,7,5] => 0000000
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [5,3,2,4,6,7,8,1] => 0000000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [7,5,3,2,4,6,8,1] => 0000000
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [5,7,3,2,4,6,1,8] => 0000001
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,3,4,6,2,7,8] => [5,1,3,4,6,2,7,8] => 0000011
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [5,3,2,1,6,7,8,4] => 0000000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [7,5,3,2,1,6,8,4] => 0000000
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => [7,3,5,2,1,6,4,8] => 0000001
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [4,3,2,5,6,7,1,8] => 0000001
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [4,6,3,2,5,1,7,8] => 0000011
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,3,4,2,6,1,7,8] => [3,5,4,2,6,1,7,8] => 0000011
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [7,4,3,2,1,5,8,6] => 0000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [6,4,3,2,1,7,5,8] => 0000001
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7,8] => 0000011
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0000111
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [5,4,3,1,2,6,7,8] => 0000111
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [6,4,3,1,2,7,5,8] => 0000001
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [5,4,3,1,6,2,7,8] => 0000011
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [5,4,2,3,1,6,7,8] => 0000111
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [5,4,2,1,3,6,7,8] => 0000111
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [5,4,1,2,3,6,7,8] => 0000111
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [6,4,3,1,5,7,2,8] => 0000001
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [4,6,3,1,5,2,7,8] => 0000011
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [5,2,4,3,1,6,7,8] => 0000111
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [5,2,3,4,1,6,7,8] => 0000111
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,4,6,3,7,8] => [5,4,2,1,6,3,7,8] => 0000011
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [5,3,2,4,1,6,7,8] => 0000111
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [5,3,2,1,4,6,7,8] => 0000111
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [5,3,1,2,4,6,7,8] => 0000111
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [5,3,1,4,2,6,7,8] => 0000111
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [5,2,3,1,4,6,7,8] => 0000111
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [5,2,1,3,4,6,7,8] => 0000111
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 0000111
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [8,6,1,7,2,3,5,4] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [8,1,4,2,5,6,7,3] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [8,1,2,4,5,6,7,3] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [6,1,4,2,5,7,8,3] => 0000000
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [3,1,4,5,6,7,8,2] => 0000000
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => [6,8,4,1,2,5,7,3] => 0000000
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [7,1,2,4,5,6,8,3] => 0000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [3,1,7,4,5,6,2,8] => 0000001
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => [5,1,3,4,6,7,2,8] => 0000001
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1,8] => 0000001
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [8,3,6,1,4,2,7,5] => 0000000
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [5,3,1,4,6,7,8,2] => 0000000
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [7,5,3,1,4,6,8,2] => 0000000
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [6,4,1,5,3,2,7,8] => 0000011
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [7,2,3,4,5,1,8,6] => 0000000
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [6,2,3,4,5,7,1,8] => 0000001
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7,8] => 0000011
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [5,2,3,1,6,7,8,4] => 0000000
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [7,5,2,3,1,6,8,4] => 0000000
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [7,2,5,3,1,6,4,8] => 0000001
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [4,2,3,5,6,7,1,8] => 0000001
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [7,4,2,3,5,1,8,6] => 0000000
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [2,3,5,4,6,1,7,8] => 0000011
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,2,3,1,6,7,5,8] => [6,2,4,3,1,7,5,8] => 0000001
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => [5,2,4,3,6,1,7,8] => 0000011
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [3,5,4,2,1,6,7,8] => 0000111
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [2,5,3,4,1,6,7,8] => 0000111
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [5,2,3,4,6,1,7,8] => 0000011
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [2,3,5,4,1,6,7,8] => 0000111
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [3,2,4,5,1,6,7,8] => 0000111
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [3,1,4,5,2,6,7,8] => 0000111
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [5,2,1,3,6,7,8,4] => 0000000
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [4,2,1,5,6,7,3,8] => 0000001
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,4,6,5,7,3,8] => [6,4,2,1,5,7,3,8] => 0000001
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,4,5,3,7,8] => [6,2,4,1,5,3,7,8] => 0000011
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [3,2,4,5,6,1,7,8] => 0000011
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,5,4,6,1,7,8] => [5,3,2,4,6,1,7,8] => 0000011
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [3,5,2,4,1,6,7,8] => 0000111
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [2,4,3,5,1,6,7,8] => 0000111
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,2,1,4,6,7,5,8] => [6,3,2,1,4,7,5,8] => 0000001
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [5,3,2,1,6,4,7,8] => 0000011
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [4,3,2,5,1,6,7,8] => 0000111
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 0001111
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [4,3,1,2,5,6,7,8] => 0001111
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [7,3,1,2,4,5,8,6] => 0000000
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => 0001111
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [4,2,1,3,5,6,7,8] => 0001111
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => 0001111
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [8,1,6,2,3,4,7,5] => 0000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [5,1,2,3,6,7,8,4] => 0000000
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [4,1,2,5,6,7,3,8] => 0000001
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [6,4,1,2,5,7,3,8] => 0000001
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => [6,1,4,2,5,3,7,8] => 0000011
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [7,3,1,4,2,5,8,6] => 0000000
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [6,3,1,4,2,7,5,8] => 0000001
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => [5,3,1,4,6,2,7,8] => 0000011
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [5,1,3,4,2,6,7,8] => 0000111
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => 0000111
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [7,2,3,1,4,5,8,6] => 0000000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [4,2,3,5,1,6,7,8] => 0000111
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [2,4,3,1,5,6,7,8] => 0001111
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => 0001111
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [4,2,1,5,3,6,7,8] => 0000111
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => 0001111
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => 0011111
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => 0011111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [7,1,2,3,4,5,8,6] => 0000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [6,1,2,3,4,7,5,8] => 0000001
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [5,1,2,3,6,4,7,8] => 0000011
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [4,1,2,5,3,6,7,8] => 0000111
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => 0001111
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => 0011111
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 0111111
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 1111111
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [8,1,2,3,4,5,6,9,7] => 00000000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => 00000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [9,1,2,3,4,5,6,7,10,8] => 000000000
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [9,2,1,3,4,5,6,7,8] => 00000000
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => 000000000
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [9,2,3,1,4,5,6,7,8] => 00000000
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [9,3,1,2,4,5,6,7,8] => 00000000
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [10,2,1,3,4,5,6,7,8,9] => 000000000
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [8,7,1,2,3,4,5,9,6] => 00000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [6,1,2,3,4,7,8,9,5] => 00000000
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [7,1,2,3,4,5,8,9,6] => 00000000
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [9,7,1,2,3,4,5,6,8] => 00000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,9,7,8,6] => [9,1,7,2,3,4,5,8,6] => 00000000
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [9,8,1,2,3,4,5,6,7] => 00000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [7,1,2,3,4,5,8,9,10,6] => 000000000
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [8,1,2,3,4,5,6,9,10,7] => 000000000
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [10,9,1,2,3,4,5,6,7,8] => 000000000
[] => [] => [] => [] =>
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 00000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [8,7,6,5,4,3,1,2,9] => 00000001
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [8,7,6,5,4,2,1,3,9] => 00000001
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,8,7,6,5,4,3,9] => [8,7,6,5,4,1,2,3,9] => 00000001
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,8,7,6,5,9] => [8,7,6,4,3,2,1,5,9] => 00000001
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,4,3,2,1,8,7,6,9] => [8,7,5,4,3,2,1,6,9] => 00000001
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,7,4,6,5,3,2,1,9] => [8,4,7,6,5,3,2,1,9] => 00000001
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => [8,6,5,4,3,2,1,7,9] => 00000001
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [8,6,4,2,1,3,5,7,9] => 00000001
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [8,2,3,4,5,6,7,1,9] => 00000001
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,6,8,7,9] => [8,3,1,2,4,5,6,7,9] => 00000001
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [8,2,1,3,4,5,6,7,9] => 00000001
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => 00000001
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,7,6,4,5,3,2,1,9] => [4,8,7,6,5,3,2,1,9] => 00000001
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,7,5,4,6,3,2,1,9] => [5,8,7,4,6,3,2,1,9] => 00000001
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => [7,6,5,4,3,2,8,1,9] => 00000001
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => 00000011
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,6,1,8,9] => [7,2,3,4,5,6,1,8,9] => 00000011
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [7,1,2,3,4,5,6,8,9] => 00000011
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,5,4,3,2,7,1,8,9] => [6,5,4,3,2,7,1,8,9] => 00000011
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => 00000111
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,4,6,5,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => 00000111
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => 00000111
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1,9] => 00000001
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [3,2,4,5,6,7,8,1,9] => 00000001
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,4,3,2,6,1,7,8,9] => [5,4,3,2,6,1,7,8,9] => 00000111
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => 00001111
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => 00001111
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [5,3,1,2,4,6,7,8,9] => 00001111
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => 00001111
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [3,1,4,5,6,7,8,2,9] => 00000001
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8,9] => 00000011
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => 00000111
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => [4,3,2,5,1,6,7,8,9] => 00001111
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => 00001111
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => [4,2,1,5,3,6,7,8,9] => 00001111
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => 00111111
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => 00111111
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [7,1,2,3,4,5,8,6,9] => 00000001
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,6,7,5,8,9] => [6,1,2,3,4,7,5,8,9] => 00000011
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => [4,1,2,5,3,6,7,8,9] => 00001111
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [3,1,4,2,5,6,7,8,9] => 00011111
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => 00111111
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 01111111
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 11111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,1,2] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [9,8,7,6,5,4,2,1,3] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [9,8,7,6,5,3,2,1,4] => 00000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [9,8,7,6,4,3,2,1,5] => 00000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [9,8,7,5,4,3,2,1,6] => 00000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [9,8,6,5,4,3,2,1,7] => 00000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [9,7,6,5,4,3,2,1,8] => 00000000
[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] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [10,9,8,7,6,5,4,3,1,2] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [9,8,7,6,5,4,1,2,3] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,4,2,1,3] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [9,8,7,6,5,2,3,1,4] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [10,9,8,7,6,5,3,2,1,4] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [10,9,8,7,6,4,3,2,1,5] => 000000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [10,9,8,7,5,4,3,2,1,6] => 000000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [10,9,8,6,5,4,3,2,1,7] => 000000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [10,9,7,6,5,4,3,2,1,8] => 000000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [10,8,7,6,5,4,3,2,1,9] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => 000000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,2,1] => 0000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [11,10,9,8,7,6,5,4,3,1,2] => 0000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,4,1,2,3] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [9,8,7,6,5,1,2,3,4] => 00000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,8,7,5,6,4,3,2,1,10] => [5,9,8,7,6,4,3,2,1,10] => 000000001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [11,9,8,7,6,5,4,3,2,1,10] => 0000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => 0000000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [10,9,8,7,6,5,1,2,3,4] => 000000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [12,10,9,8,7,6,5,4,3,2,1,11] => 00000000000
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [9,8,7,6,1,2,3,4,5] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [10,9,8,7,6,1,2,3,4,5] => 000000000
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [9,8,7,1,2,3,4,5,6] => 00000000
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [10,9,8,7,1,2,3,4,5,6] => 000000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => [8,7,6,5,4,3,2,9,1,10] => 000000001
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [9,8,7,6,5,3,1,4,2] => 00000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9,8,4,7,6,5,3,2,1] => [9,8,4,7,6,5,3,2,1] => 00000000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9,8,5,7,6,4,3,2] => [9,8,7,5,1,6,4,3,2] => 00000000
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [9,2,3,4,5,6,7,8,1] => 00000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => [5,9,8,7,6,4,3,2,1] => 00000000
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,9,5,6,7,8,1] => [2,3,4,9,5,6,7,8,1] => 00000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,9,8,7,5,6,4,3,2] => [9,8,7,1,5,6,4,3,2] => 00000000
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,9,8,1] => 00000000
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [5,1,2,3,6,7,8,9,4] => 00000000
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => [2,9,3,4,5,6,7,8,1] => 00000000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,9,6,7,8,1] => [2,3,9,4,5,6,7,8,1] => 00000000
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [3,1,4,5,6,7,8,9,2] => 00000000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1] => 00000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [4,1,2,5,6,7,8,9,3] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => [10,9,8,7,6,5,3,1,4,2] => 000000000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,4,8,7,6,5,3,2,1] => [10,9,8,4,7,6,5,3,2,1] => 000000000
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [10,9,8,1,2,3,4,5,6,7] => 000000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,8,4,7,6,5,3,2,1] => [10,9,4,8,7,6,5,3,2,1] => 000000000
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [10,2,3,4,5,6,7,8,9,1] => 000000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,9,8,7,5,6,4,3,2,1] => [5,10,9,8,7,6,4,3,2,1] => 000000000
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,10,6,7,8,9,1] => [2,3,4,10,5,6,7,8,9,1] => 000000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,10,9,8,6,7,5,4,3,2] => [10,9,8,6,1,7,5,4,3,2] => 000000000
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,10,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,10,8,9,1] => 000000000
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [6,1,2,3,4,7,8,9,10,5] => 000000000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,10,5,6,7,8,9,1] => [2,3,4,5,10,6,7,8,9,1] => 000000000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,10,9,1] => 000000000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,10,4,5,6,7,8,9,1] => [2,3,4,5,6,10,7,8,9,1] => 000000000
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [4,1,2,5,6,7,8,9,10,3] => 000000000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,10,7,8,9,1] => [2,3,10,4,5,6,7,8,9,1] => 000000000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1] => 000000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [3,1,4,5,6,7,8,9,10,2] => 000000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [5,1,2,3,6,7,8,9,10,4] => 000000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 111111111
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9,8,7,5,4,6,3,2,1] => [5,9,8,7,4,6,3,2,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => [7,9,6,5,4,3,2,8,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,9,1] => 00000000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,9,8,6,5,7,4,3,2] => [6,9,8,5,7,4,1,3,2] => 00000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [9,8,7,6,5,4,3,2,10,1] => 000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [9,8,7,6,5,4,3,1,2,10] => 000000001
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => 001111111
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => 001111111
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => 0011111111
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10,11] => [2,3,1,4,5,6,7,8,9,10,11] => 0011111111
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [8,6,5,4,3,2,1,9,7] => 00000000
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => 000000001
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => 011111111
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => 000111111
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => 000011111
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => 000001111
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => 000000111
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => 000000011
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => [6,5,4,3,2,7,8,9,1] => 00000000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => [9,7,6,5,4,3,2,1,8,10] => 000000001
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => 0111111111
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => [2,4,3,5,6,7,8,9,1] => 00000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10,3,2,9,8,7,6,5,4,1] => [10,9,8,7,6,3,5,2,4,1] => 000000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [9,7,6,5,4,3,1,2,8] => 00000000
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [7,6,5,4,3,2,8,9,1] => 00000000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => 000000111
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [7,6,1,2,3,4,8,9,5] => 00000000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [6,5,1,2,3,7,8,9,4] => 00000000
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [5,4,1,2,6,7,8,9,3] => 00000000
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [4,3,1,5,6,7,8,9,2] => 00000000
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,1] => 00000000
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [3,1,4,2,5,6,7,8,9,10] => 000111111
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,3,2,1,9,8,7,6,10] => [9,8,7,5,4,3,2,1,6,10] => 000000001
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,5,4,3,2,1,9,8,7,10] => [9,8,6,5,4,3,2,1,7,10] => 000000001
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => 000000011
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1,10,11] => [9,8,7,6,5,4,3,2,1,10,11] => 0000000011
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => 000111111
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => 000011111
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => 000001111
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => 000000111
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [2,3,4,5,6,7,8,1,9,10] => 000000011
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1,10] => 000000001
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [10,8,6,4,2,1,3,5,7,9] => 000000000
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [12,10,8,6,4,2,1,3,5,7,9,11] => 00000000000
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => 1111111111
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,5,4,3,2,1,9,10,8] => [9,7,6,5,4,3,2,1,10,8] => 000000000
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => 0000000001
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => [9,8,7,6,5,3,1,2,4] => 00000000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => 000001111
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [8,7,6,5,4,3,2,9,10,1] => 000000000
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => 001111111
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [10,7,6,5,4,3,2,9,8,1] => [10,7,9,6,5,4,3,2,8,1] => 000000000
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => 000011111
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => 000111111
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [10,9,8,7,6,5,4,3,2,11,1] => 0000000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => [9,7,6,5,4,3,2,8,1] => 00000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [8,7,6,5,4,2,3,9,1] => 00000000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [10,9,8,5,4,7,6,3,2,1] => [10,5,9,8,7,4,6,3,2,1] => 000000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000000
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [4,2,3,5,6,7,8,9,1] => 00000000
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [10,9,6,5,4,3,8,7,2,1] => [10,6,9,8,5,4,3,7,2,1] => 000000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [10,5,4,3,2,9,8,7,6,1] => [10,9,8,5,7,4,3,2,6,1] => 000000000
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [4,3,2,5,6,7,8,9,1] => 00000000
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [9,7,5,3,1,2,4,6,8] => 00000000
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [10,8,7,6,4,3,2,1,5,9] => 000000000
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [5,4,3,2,6,7,8,9,1] => 00000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => [7,6,5,4,3,2,8,9,10,1] => 000000000
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,2,3,4,9,6,7,8,1] => [2,3,9,5,4,6,7,8,1] => 00000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [10,8,7,6,5,4,2,1,3,9] => 000000000
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [2,3,4,5,6,7,8,9,10,1,11] => 0000000001
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,10,1] => [5,4,3,2,6,7,8,9,10,1] => 000000000
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [9,7,5,3,1,2,4,6,8,10] => 000000001
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10,11,12] => [3,1,2,4,5,6,7,8,9,10,11,12] => 00111111111
Map
zeta map
Description
The zeta map on Dyck paths.
The zeta map ζ is a bijection on Dyck paths of semilength n.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path D with corresponding area sequence a=(a1,…,an) to a Dyck path as follows:
The zeta map ζ is a bijection on Dyck paths of semilength n.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path D with corresponding area sequence a=(a1,…,an) to a Dyck path as follows:
- First, build an intermediate Dyck path consisting of d1 north steps, followed by d1 east steps, followed by d2 north steps and d2 east steps, and so on, where di is the number of i−1's within the sequence a.
For example, given a=(0,1,2,2,2,3,1,2), we build the path
NE NNEE NNNNEEEE NE. - Next, the rectangles between two consecutive peaks are filled. Observe that such the rectangle between the kth and the (k+1)st peak must be filled by dk east steps and dk+1 north steps. In the above example, the rectangle between the second and the third peak must be filled by 2 east and 4 north steps, the 2 being the number of 1's in a, and 4 being the number of 2's. To fill such a rectangle, scan through the sequence a from left to right, and add east or north steps whenever you see a k−1 or k, respectively. So to fill the 2×4 rectangle, we look for 1's and 2's in the sequence and see 122212, so this rectangle gets filled with ENNNEN.
The complete path we obtain in thus
NENNENNNENEEENEE.
Map
to non-crossing permutation
Description
Sends a Dyck path D with valley at positions {(i1,j1),…,(ik,jk)} to the unique non-crossing permutation π having descents {i1,…,ik} and whose inverse has descents {j1,…,jk}.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to n(n−1) minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to n(n−1) minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection ϕ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word w1w2...wn, compute the image inductively by starting with ϕ(w1)=w1.
At the i-th step, if ϕ(w1w2...wi)=v1v2...vi, define ϕ(w1w2...wiwi+1) by placing wi+1 on the end of the word v1v2...vi and breaking the word up into blocks as follows.
To compute ϕ([1,4,2,5,3]), the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection ϕ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word w1w2...wn, compute the image inductively by starting with ϕ(w1)=w1.
At the i-th step, if ϕ(w1w2...wi)=v1v2...vi, define ϕ(w1w2...wiwi+1) by placing wi+1 on the end of the word v1v2...vi and breaking the word up into blocks as follows.
- If wi+1≥vi, place a vertical line to the right of each vk for which wi+1≥vk.
- If wi+1<vi, place a vertical line to the right of each vk for which wi+1<vk.
To compute ϕ([1,4,2,5,3]), the sequence of words is
- 1
- |1|4→14
- |14|2→412
- |4|1|2|5→4125
- |4|125|3→45123.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
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(π)={i∈[n−1]|∀1≤j≤i<k≤n:π(j)<π(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(π)={i∈[n−1]|∀1≤j≤i<k≤n:π(j)<π(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.
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