Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
St000119: Permutations ⟶ ℤ
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,2] => 0
[1,1,0,0] => [2,1] => [1,2] => [1,2] => 0
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => [1,2,3] => [1,2,3] => 0
[1,1,0,0,1,0] => [2,1,3] => [1,2,3] => [1,2,3] => 0
[1,1,0,1,0,0] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[1,1,1,0,0,0] => [3,2,1] => [1,3,2] => [1,3,2] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,2,4,3] => [1,2,4,3] => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [1,2,4,3] => [1,2,4,3] => 0
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [1,3,2,4] => [1,3,2,4] => 0
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [1,3,4,2] => [1,4,3,2] => 1
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [1,4,2,3] => [1,4,2,3] => 0
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,4,2,3] => [1,4,2,3] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,2,4,5,3] => [1,2,5,4,3] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [1,2,4,5,3] => [1,2,5,4,3] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [1,3,4,2,5] => [1,4,3,2,5] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [1,3,4,5,2] => [1,5,3,4,2] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,3,5,2,4] => [1,5,3,2,4] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [1,4,5,2,3] => [1,5,2,4,3] => 1
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,4,5,2,3] => [1,5,2,4,3] => 1
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,5,2,4,3] => [1,4,5,2,3] => 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] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,2,4,6,3,5] => [1,2,6,4,3,5] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [1,2,5,6,3,4] => [1,2,6,3,5,4] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 0
>>> Load all 905 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,2,5,6,3,4] => [1,2,6,3,5,4] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [1,2,5,6,3,4] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [1,2,4,6,3,5] => [1,2,6,4,3,5] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [1,2,5,6,3,4] => [1,2,6,3,5,4] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,2,5,6,3,4] => [1,2,6,3,5,4] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,2,6,3,5,4] => [1,2,5,6,3,4] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,3,4,6,2,5] => [1,6,3,4,2,5] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [1,3,5,2,4,6] => [1,5,3,2,4,6] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,3,5,6,2,4] => [1,6,3,2,5,4] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [1,3,6,2,4,5] => [1,6,3,2,4,5] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [1,3,6,2,4,5] => [1,6,3,2,4,5] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [1,4,5,2,3,6] => [1,5,2,4,3,6] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [1,4,5,6,2,3] => [1,6,2,4,5,3] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [1,4,6,2,3,5] => [1,6,2,4,3,5] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [1,5,6,2,3,4] => [1,6,2,3,5,4] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [1,5,6,2,3,4] => [1,6,2,3,5,4] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [1,5,2,6,3,4] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [1,4,5,2,3,6] => [1,5,2,4,3,6] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,4,5,6,2,3] => [1,6,2,4,5,3] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,4,6,2,3,5] => [1,6,2,4,3,5] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,5,6,2,3,4] => [1,6,2,3,5,4] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [1,5,6,2,3,4] => [1,6,2,3,5,4] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [1,6,2,3,5,4] => [1,5,2,6,3,4] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,4,5,2,3,6] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,5,6,2,4,3] => [1,4,6,2,5,3] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [1,4,6,2,3,5] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [1,6,2,4,5,3] => [1,5,6,2,4,3] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [1,5,6,2,3,4] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [1,5,6,2,3,4] => 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] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [1,7,2,3,4,6,5] => [1,6,2,3,7,4,5] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [1,7,2,3,4,6,5] => [1,6,2,3,7,4,5] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [1,7,2,3,5,4,6] => [1,5,2,7,3,4,6] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [1,7,2,3,6,4,5] => [1,6,2,7,3,4,5] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [1,7,2,3,6,4,5] => [1,6,2,7,3,4,5] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [1,7,2,3,4,6,5] => [1,6,2,3,7,4,5] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [1,7,2,3,4,6,5] => [1,6,2,3,7,4,5] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [1,7,2,3,5,4,6] => [1,5,2,7,3,4,6] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [1,7,2,3,6,4,5] => [1,6,2,7,3,4,5] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [1,7,2,3,6,4,5] => [1,6,2,7,3,4,5] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [1,7,2,4,3,5,6] => [1,4,7,2,3,5,6] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [1,7,2,4,3,5,6] => [1,4,7,2,3,5,6] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [1,7,2,5,3,4,6] => [1,5,7,2,3,4,6] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [1,7,2,6,3,4,5] => [1,6,7,2,3,4,5] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [1,7,2,6,3,4,5] => [1,6,7,2,3,4,5] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [1,7,2,5,3,4,6] => [1,5,7,2,3,4,6] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [1,7,2,6,3,4,5] => [1,6,7,2,3,4,5] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [1,7,2,6,3,4,5] => [1,6,7,2,3,4,5] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [1,7,2,6,3,5,4] => [1,5,6,7,2,3,4] => 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] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 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] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 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] => [1,2,3,6,8,4,5,7] => [1,2,3,8,4,6,5,7] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,8,4,5,7,6] => [1,2,3,7,4,8,5,6] => 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] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [1,2,3,6,8,4,5,7] => [1,2,3,8,4,6,5,7] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6,8] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 0
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 0
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 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] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => [1,2,3,6,7,4,5,8] => [1,2,3,7,4,6,5,8] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [1,2,3,6,8,4,5,7] => [1,2,3,8,4,6,5,7] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6,8] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 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] => [1,2,3,6,7,4,5,8] => [1,2,3,7,4,6,5,8] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [1,2,3,6,8,4,5,7] => [1,2,3,8,4,6,5,7] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [1,2,3,8,4,5,7,6] => [1,2,3,7,4,8,5,6] => 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] => [1,2,6,3,5,4,7,8] => [1,2,5,6,3,4,7,8] => 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] => [1,2,6,3,5,4,7,8] => [1,2,5,6,3,4,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 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] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 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] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 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] => [1,2,3,6,8,4,5,7] => [1,2,3,8,4,6,5,7] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [1,2,3,8,4,5,7,6] => [1,2,3,7,4,8,5,6] => 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] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 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] => [1,2,3,6,8,4,5,7] => [1,2,3,8,4,6,5,7] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [1,2,3,8,4,5,7,6] => [1,2,3,7,4,8,5,6] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,8,6,7,4] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 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] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 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] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 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] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 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] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => [1,2,3,6,8,4,5,7] => [1,2,3,8,4,6,5,7] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 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] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6,8] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 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] => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6,8] => 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] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [1,2,3,8,4,5,7,6] => [1,2,3,7,4,8,5,6] => 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] => [1,2,6,3,5,4,7,8] => [1,2,5,6,3,4,7,8] => 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] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 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] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 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] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 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] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 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] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,6,7] => 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] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,6,7] => 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] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 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] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 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] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 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] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,6,7] => 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] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,6,7] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,7,6,8] => [1,4,2,3,5,7,6,8] => 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] => [1,4,2,3,5,8,6,7] => [1,4,2,3,5,8,6,7] => 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] => [1,4,2,3,5,8,6,7] => [1,4,2,3,5,8,6,7] => 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] => [1,4,5,2,3,6,7,8] => [1,5,2,4,3,6,7,8] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => [1,4,5,2,3,6,7,8] => [1,5,2,4,3,6,7,8] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => [1,4,5,2,3,6,7,8] => [1,5,2,4,3,6,7,8] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,2,3,6,5,1,7,8] => [1,4,6,2,3,5,7,8] => [1,6,2,4,3,5,7,8] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,2,3,6,5,1,8,7] => [1,4,6,2,3,5,7,8] => [1,6,2,4,3,5,7,8] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [1,4,6,8,2,3,5,7] => [1,8,2,4,3,6,5,7] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => [1,4,7,2,3,5,6,8] => [1,7,2,4,3,5,6,8] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [1,4,8,2,3,5,6,7] => [1,8,2,4,3,5,6,7] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [1,4,8,2,3,5,6,7] => [1,8,2,4,3,5,6,7] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,2,3,8,6,7,5,1] => [1,4,8,2,3,5,6,7] => [1,8,2,4,3,5,6,7] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => [1,4,8,2,3,5,7,6] => [1,7,2,4,3,8,5,6] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 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] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 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] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 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] => [1,6,7,2,3,4,5,8] => [1,7,2,3,4,6,5,8] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [1,6,8,2,3,4,5,7] => [1,8,2,3,4,6,5,7] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 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] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => [1,8,2,3,4,5,7,6] => [1,7,2,3,4,8,5,6] => 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] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 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] => [1,6,7,2,3,4,5,8] => [1,7,2,3,4,6,5,8] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => [1,8,2,3,4,5,7,6] => [1,7,2,3,4,8,5,6] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [1,8,2,3,4,7,5,6] => [1,7,2,3,8,4,5,6] => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [1,8,2,3,4,7,5,6] => [1,7,2,3,8,4,5,6] => 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] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 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] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8,2,4,3,7,6,5,1] => [1,8,2,3,4,5,7,6] => [1,7,2,3,4,8,5,6] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 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] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 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] => [1,6,8,2,3,4,5,7] => [1,8,2,3,4,6,5,7] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8,2,4,5,6,3,7,1] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [1,8,2,3,4,5,7,6] => [1,7,2,3,4,8,5,6] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [1,8,2,3,4,7,5,6] => [1,7,2,3,8,4,5,6] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [1,8,2,3,4,7,5,6] => [1,7,2,3,8,4,5,6] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [1,6,7,2,3,5,4,8] => [1,5,2,7,3,6,4,8] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [1,7,2,3,5,4,6,8] => [1,5,2,7,3,4,6,8] => 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] => [1,8,2,3,5,4,6,7] => [1,5,2,8,3,4,6,7] => 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] => [1,8,2,3,5,4,6,7] => [1,5,2,8,3,4,6,7] => 0
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8,2,5,4,7,6,3,1] => [1,8,2,3,5,7,4,6] => [1,7,2,8,3,5,4,6] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => [1,7,2,3,6,4,5,8] => [1,6,2,7,3,4,5,8] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [1,8,2,3,6,4,5,7] => [1,6,2,8,3,4,5,7] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => [1,7,2,3,6,4,5,8] => [1,6,2,7,3,4,5,8] => 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] => [1,8,2,3,6,4,5,7] => [1,6,2,8,3,4,5,7] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 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] => [1,4,2,3,5,7,6,8] => [1,4,2,3,5,7,6,8] => 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] => [1,4,2,3,5,8,6,7] => [1,4,2,3,5,8,6,7] => 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] => [1,4,2,3,5,8,6,7] => [1,4,2,3,5,8,6,7] => 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] => [1,4,5,2,3,6,7,8] => [1,5,2,4,3,6,7,8] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [1,4,5,2,3,6,7,8] => [1,5,2,4,3,6,7,8] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [1,4,6,2,3,5,7,8] => [1,6,2,4,3,5,7,8] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [1,4,6,2,3,5,7,8] => [1,6,2,4,3,5,7,8] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [1,4,6,7,2,3,5,8] => [1,7,2,4,3,6,5,8] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [1,4,6,8,2,3,5,7] => [1,8,2,4,3,6,5,7] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [1,4,8,2,3,5,6,7] => [1,8,2,4,3,5,6,7] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [1,4,8,2,3,5,6,7] => [1,8,2,4,3,5,6,7] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [1,4,8,2,3,5,6,7] => [1,8,2,4,3,5,6,7] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [1,4,8,2,3,5,7,6] => [1,7,2,4,3,8,5,6] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 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] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 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] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => [1,6,7,2,3,4,5,8] => [1,7,2,3,4,6,5,8] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 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] => [1,8,2,3,4,5,7,6] => [1,7,2,3,4,8,5,6] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 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] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [1,6,7,2,3,4,5,8] => [1,7,2,3,4,6,5,8] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,3,2,5,4,8,7,1] => [1,6,8,2,3,4,5,7] => [1,8,2,3,4,6,5,7] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 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] => [1,8,2,3,4,5,7,6] => [1,7,2,3,4,8,5,6] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [1,8,2,3,4,7,5,6] => [1,7,2,3,8,4,5,6] => 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] => [1,8,2,3,4,7,5,6] => [1,7,2,3,8,4,5,6] => 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] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 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] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,2,6,5,1,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,3,4,5,2,1,7,8] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 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] => [1,6,7,2,3,4,5,8] => [1,7,2,3,4,6,5,8] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [1,6,8,2,3,4,5,7] => [1,8,2,3,4,6,5,7] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 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] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 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] => [1,8,2,3,4,5,7,6] => [1,7,2,3,4,8,5,6] => 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] => [1,8,2,3,4,7,5,6] => [1,7,2,3,8,4,5,6] => 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] => [1,6,7,2,3,5,4,8] => [1,5,2,7,3,6,4,8] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => [1,6,8,2,3,5,4,7] => [1,5,2,8,3,6,4,7] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [1,7,2,3,5,4,6,8] => [1,5,2,7,3,4,6,8] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [1,8,2,3,5,4,6,7] => [1,5,2,8,3,4,6,7] => 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] => [1,8,2,3,5,4,6,7] => [1,5,2,8,3,4,6,7] => 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] => [1,8,2,3,5,7,4,6] => [1,7,2,8,3,5,4,6] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => [1,7,2,3,6,4,5,8] => [1,6,2,7,3,4,5,8] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [1,8,2,3,6,4,5,7] => [1,6,2,8,3,4,5,7] => 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] => [1,7,2,3,6,4,5,8] => [1,6,2,7,3,4,5,8] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [1,8,2,3,6,4,5,7] => [1,6,2,8,3,4,5,7] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [1,8,2,5,3,4,6,7] => [1,5,8,2,3,4,6,7] => 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] => [1,8,2,5,3,4,6,7] => [1,5,8,2,3,4,6,7] => 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] => [1,7,2,6,3,4,5,8] => [1,6,7,2,3,4,5,8] => 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] => [1,8,2,6,3,4,5,7] => [1,6,8,2,3,4,5,7] => 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] => [1,8,2,7,3,4,5,6] => [1,7,8,2,3,4,5,6] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [1,8,2,7,3,4,5,6] => [1,7,8,2,3,4,5,6] => 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] => [1,7,2,6,3,4,5,8] => [1,6,7,2,3,4,5,8] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [1,8,2,6,3,4,5,7] => [1,6,8,2,3,4,5,7] => 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] => [1,8,2,7,3,4,5,6] => [1,7,8,2,3,4,5,6] => 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] => [1,8,2,7,3,4,5,6] => [1,7,8,2,3,4,5,6] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [1,8,2,5,3,4,6,7] => [1,5,8,2,3,4,6,7] => 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] => [1,8,2,5,3,4,6,7] => [1,5,8,2,3,4,6,7] => 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] => [1,7,2,6,3,4,5,8] => [1,6,7,2,3,4,5,8] => 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] => [1,8,2,6,3,4,5,7] => [1,6,8,2,3,4,5,7] => 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] => [1,8,2,7,3,4,5,6] => [1,7,8,2,3,4,5,6] => 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] => [1,8,2,7,3,4,5,6] => [1,7,8,2,3,4,5,6] => 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] => [1,7,2,6,3,4,5,8] => [1,6,7,2,3,4,5,8] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => [1,8,2,6,3,4,5,7] => [1,6,8,2,3,4,5,7] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [1,8,2,7,3,4,5,6] => [1,7,8,2,3,4,5,6] => 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] => [1,8,2,7,3,4,5,6] => [1,7,8,2,3,4,5,6] => 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] => [1,8,2,7,3,6,4,5] => [1,6,7,8,2,3,4,5] => 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] => [1,8,2,7,3,6,4,5] => [1,6,7,8,2,3,4,5] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 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] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,3,2,4,5,6,7,8,1] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [9,3,2,5,6,7,8,4,1] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9,3,4,2,5,6,7,8,1] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9,3,4,5,2,6,7,8,1] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [9,3,4,5,6,2,8,7,1] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => 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] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,9,8,7] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,3,4,5,6,7,8,9,2,1] => [1,10,2,3,4,5,6,7,8,9] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,3,5,7,8,9,6] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,10,2,3,4,5,6,7,8,9] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,3,2,4,5,6,7,8,9,1] => [1,10,2,3,4,5,6,7,8,9] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [11,2,3,4,5,6,7,8,9,10,1] => [1,11,2,3,4,5,6,7,8,9,10] => [1,11,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,7,9,8,4] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [11,3,4,5,6,7,8,9,10,2,1] => [1,11,2,3,4,5,6,7,8,9,10] => [1,11,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,9,7] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,8,5] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,4,5,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10,3,2,5,4,7,6,9,8,1] => [1,10,2,3,4,5,6,7,8,9] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,5,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,8,10,9,5] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,5,7,8,10,9,6] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,10,5] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,5,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
13,1 35,6,1 97,26,8,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 5$
$F_{4} = 13 + q$
$F_{5} = 35 + 6\ q + q^{2}$
$F_{6} = 97 + 26\ q + 8\ q^{2} + q^{3}$
Description
The number of occurrences of the pattern 321 in a permutation.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
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
Clarke-Steingrimsson-Zeng
Description
The Clarke-Steingrimsson-Zeng map sending descents to excedances.
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
- $des$ is the number of descents, St000021The number of descents of a permutation.,
- $exc$ is the number of (strict) excedances, St000155The number of exceedances (also excedences) of a permutation.,
- $Dbot$ is the sum of the descent bottoms, St000154The sum of the descent bottoms of a permutation.,
- $Ebot$ is the sum of the excedance bottoms,
- $Ddif$ is the sum of the descent differences, St000030The sum of the descent differences of a permutations.,
- $Edif$ is the sum of the excedance differences (or depth), St000029The depth of a permutation.,
- $Res$ is the sum of the (right) embracing numbers,
- $Ine$ is the sum of the side numbers.
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