Identifier
-
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St000374: Permutations ⟶ ℤ
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [2,1] => [1,2] => 0
[1,1,0,0] => [1,2] => [1,2] => [1,2] => 0
[1,0,1,0,1,0] => [2,3,1] => [3,1,2] => [1,3,2] => 1
[1,0,1,1,0,0] => [2,1,3] => [2,1,3] => [1,2,3] => 0
[1,1,0,0,1,0] => [1,3,2] => [1,3,2] => [1,2,3] => 0
[1,1,0,1,0,0] => [3,1,2] => [2,3,1] => [1,2,3] => 0
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [4,1,2,3] => [1,4,3,2] => 1
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [3,1,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,1,4,3] => [1,2,3,4] => 0
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [3,1,4,2] => [1,3,4,2] => 1
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [1,4,2,3] => [1,2,4,3] => 1
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [1,3,2,4] => [1,2,3,4] => 0
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [2,4,1,3] => [1,2,4,3] => 1
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [3,4,1,2] => [1,3,2,4] => 1
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [2,3,1,4] => [1,2,3,4] => 0
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [1,2,4,3] => [1,2,3,4] => 0
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,3,4,2] => [1,2,3,4] => 0
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [2,3,4,1] => [1,2,3,4] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [5,1,2,3,4] => [1,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [4,1,2,3,5] => [1,4,3,2,5] => 1
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [3,1,2,5,4] => [1,3,2,4,5] => 1
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [4,1,2,5,3] => [1,4,5,3,2] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [3,1,2,4,5] => [1,3,2,4,5] => 1
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [2,1,5,3,4] => [1,2,3,5,4] => 1
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 0
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [3,1,5,2,4] => [1,3,5,4,2] => 1
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [4,1,5,2,3] => [1,4,2,3,5] => 2
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [3,1,4,2,5] => [1,3,4,2,5] => 1
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [2,1,3,5,4] => [1,2,3,4,5] => 0
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => 0
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [3,1,4,5,2] => [1,3,4,5,2] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [1,5,2,3,4] => [1,2,5,4,3] => 1
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [1,4,2,3,5] => [1,2,4,3,5] => 1
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,3,2,5,4] => [1,2,3,4,5] => 0
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [1,4,2,5,3] => [1,2,4,5,3] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => [1,2,3,4,5] => 0
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [2,5,1,3,4] => [1,2,5,4,3] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [2,4,1,3,5] => [1,2,4,3,5] => 1
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [3,5,1,2,4] => [1,3,2,5,4] => 2
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [4,5,1,2,3] => [1,4,2,5,3] => 2
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [3,4,1,2,5] => [1,3,2,4,5] => 1
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [2,3,1,5,4] => [1,2,3,4,5] => 0
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [2,4,1,5,3] => [1,2,4,5,3] => 1
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [3,4,1,5,2] => [1,3,2,4,5] => 1
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [2,3,1,4,5] => [1,2,3,4,5] => 0
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [1,2,5,3,4] => [1,2,3,5,4] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,3,4,5] => 0
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,3,5,2,4] => [1,2,3,5,4] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [1,4,5,2,3] => [1,2,4,3,5] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [1,3,4,2,5] => [1,2,3,4,5] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [2,4,5,1,3] => [1,2,4,3,5] => 1
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [3,4,5,1,2] => [1,3,5,2,4] => 2
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [2,3,4,1,5] => [1,2,3,4,5] => 0
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,4,5] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [1,2,4,5,3] => [1,2,3,4,5] => 0
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [1,3,4,5,2] => [1,2,3,4,5] => 0
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,5,4,3,2,6] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [1,4,3,2,5,6] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [5,1,2,3,6,4] => [1,5,6,4,3,2] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,4,3,2,5,6] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [1,3,2,4,6,5] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [1,3,2,4,5,6] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [4,1,2,6,3,5] => [1,4,6,5,3,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [5,1,2,6,3,4] => [1,5,3,2,4,6] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [4,1,2,5,3,6] => [1,4,5,3,2,6] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [1,3,2,4,5,6] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [3,1,2,5,6,4] => [1,3,2,4,5,6] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [4,1,2,5,6,3] => [1,4,5,6,3,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [1,2,3,6,5,4] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [1,2,3,5,4,6] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => [1,2,3,5,6,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [3,1,6,2,4,5] => [1,3,6,5,4,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [3,1,5,2,4,6] => [1,3,5,4,2,6] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [4,1,6,2,3,5] => [1,4,2,3,6,5] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [5,1,6,2,3,4] => [1,5,3,6,4,2] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [4,1,5,2,3,6] => [1,4,2,3,5,6] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [1,3,4,2,5,6] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => [1,3,5,6,4,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [4,1,5,2,6,3] => [1,4,2,3,5,6] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [3,1,4,2,5,6] => [1,3,4,2,5,6] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [1,2,3,4,6,5] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [2,1,4,6,3,5] => [1,2,3,4,6,5] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [2,1,5,6,3,4] => [1,2,3,5,4,6] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [3,1,4,6,2,5] => [1,3,4,6,5,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [3,1,5,6,2,4] => [1,3,5,2,4,6] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [4,1,5,6,2,3] => [1,4,6,3,5,2] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [3,1,4,5,2,6] => [1,3,4,5,2,6] => 1
>>> Load all 1033 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,2,3,4,5,6] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => [1,2,3,4,5,6] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => [1,2,3,4,5,6] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [3,1,4,5,6,2] => [1,3,4,5,6,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [1,2,6,5,4,3] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [1,2,5,4,3,6] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [1,2,4,3,5,6] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [1,5,2,3,6,4] => [1,2,5,6,4,3] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [1,2,4,3,5,6] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [1,2,3,4,6,5] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [1,4,2,6,3,5] => [1,2,4,6,5,3] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [1,5,2,6,3,4] => [1,2,5,3,4,6] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => [1,2,4,5,3,6] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => [1,2,4,5,6,3] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [2,6,1,3,4,5] => [1,2,6,5,4,3] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [2,5,1,3,4,6] => [1,2,5,4,3,6] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [2,4,1,3,6,5] => [1,2,4,3,5,6] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [2,5,1,3,6,4] => [1,2,5,6,4,3] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [2,4,1,3,5,6] => [1,2,4,3,5,6] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [3,6,1,2,4,5] => [1,3,2,6,5,4] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [3,5,1,2,4,6] => [1,3,2,5,4,6] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [4,6,1,2,3,5] => [1,4,2,6,5,3] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [5,6,1,2,3,4] => [1,5,3,2,6,4] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [4,5,1,2,3,6] => [1,4,2,5,3,6] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [3,4,1,2,6,5] => [1,3,2,4,5,6] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [3,5,1,2,6,4] => [1,3,2,5,6,4] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [4,5,1,2,6,3] => [1,4,2,5,6,3] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [3,4,1,2,5,6] => [1,3,2,4,5,6] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [2,3,1,6,4,5] => [1,2,3,4,6,5] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [2,4,1,6,3,5] => [1,2,4,6,5,3] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [2,5,1,6,3,4] => [1,2,5,3,4,6] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [2,4,1,5,3,6] => [1,2,4,5,3,6] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [3,4,1,6,2,5] => [1,3,2,4,6,5] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [3,5,1,6,2,4] => [1,3,2,5,4,6] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [4,5,1,6,2,3] => [1,4,6,3,2,5] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [3,4,1,5,2,6] => [1,3,2,4,5,6] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => [1,2,3,4,5,6] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => [1,2,3,4,5,6] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [2,4,1,5,6,3] => [1,2,4,5,6,3] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [3,4,1,5,6,2] => [1,3,2,4,5,6] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,2,3,6,5,4] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,2,3,5,4,6] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => [1,2,3,5,6,4] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [1,3,6,2,4,5] => [1,2,3,6,5,4] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [1,3,5,2,4,6] => [1,2,3,5,4,6] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [1,4,6,2,3,5] => [1,2,4,3,6,5] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [1,5,6,2,3,4] => [1,2,5,3,6,4] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => [1,2,4,3,5,6] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => [1,2,3,4,5,6] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [1,3,5,2,6,4] => [1,2,3,5,6,4] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => [1,2,4,3,5,6] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => [1,2,3,4,5,6] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [2,3,6,1,4,5] => [1,2,3,6,5,4] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [2,3,5,1,4,6] => [1,2,3,5,4,6] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [2,4,6,1,3,5] => [1,2,4,3,6,5] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [2,5,6,1,3,4] => [1,2,5,3,6,4] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [2,4,5,1,3,6] => [1,2,4,3,5,6] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [3,4,6,1,2,5] => [1,3,6,5,2,4] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [3,5,6,1,2,4] => [1,3,6,4,2,5] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [4,5,6,1,2,3] => [1,4,2,5,3,6] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [3,4,5,1,2,6] => [1,3,5,2,4,6] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => [1,2,3,4,5,6] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [2,3,5,1,6,4] => [1,2,3,5,6,4] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [2,4,5,1,6,3] => [1,2,4,3,5,6] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [3,4,5,1,6,2] => [1,3,5,6,2,4] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [1,2,3,4,5,6] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,2,3,4,6,5] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [1,2,4,6,3,5] => [1,2,3,4,6,5] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => [1,2,3,5,4,6] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => [1,2,3,4,5,6] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [1,3,4,6,2,5] => [1,2,3,4,6,5] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [1,3,5,6,2,4] => [1,2,3,5,4,6] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => [1,2,4,6,3,5] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => [1,2,3,4,5,6] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [2,3,4,6,1,5] => [1,2,3,4,6,5] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [2,3,5,6,1,4] => [1,2,3,5,4,6] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [2,4,5,6,1,3] => [1,2,4,6,3,5] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [3,4,5,6,1,2] => [1,3,5,2,4,6] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [1,2,3,4,5,6] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => [1,2,3,4,5,6] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => [1,2,3,4,5,6] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => [1,2,3,4,5,6] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [6,1,2,3,4,7,5] => [1,6,7,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => [1,4,3,2,5,7,6] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => [1,4,3,2,5,6,7] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [5,1,2,3,7,4,6] => [1,5,7,6,4,3,2] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => [1,4,3,2,5,6,7] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [4,1,2,3,6,7,5] => [1,4,3,2,5,6,7] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [5,1,2,3,6,7,4] => [1,5,6,7,4,3,2] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [1,4,3,2,5,6,7] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => [1,3,2,4,7,6,5] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => [1,3,2,4,6,5,7] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [1,3,2,4,5,6,7] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [3,1,2,6,4,7,5] => [1,3,2,4,6,7,5] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [1,3,2,4,5,6,7] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [4,1,2,7,3,5,6] => [1,4,7,6,5,3,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [4,1,2,6,3,5,7] => [1,4,6,5,3,2,7] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [4,1,2,5,3,7,6] => [1,4,5,3,2,6,7] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [4,1,2,6,3,7,5] => [1,4,6,7,5,3,2] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [4,1,2,5,3,6,7] => [1,4,5,3,2,6,7] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => [1,3,2,4,5,7,6] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [1,3,2,4,5,6,7] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [3,1,2,5,7,4,6] => [1,3,2,4,5,7,6] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [3,1,2,6,7,4,5] => [1,3,2,4,6,5,7] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [3,1,2,5,6,4,7] => [1,3,2,4,5,6,7] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [4,1,2,5,7,3,6] => [1,4,5,7,6,3,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [4,1,2,6,7,3,5] => [1,4,6,3,2,5,7] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [4,1,2,5,6,3,7] => [1,4,5,6,3,2,7] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [1,3,2,4,5,6,7] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [3,1,2,4,6,7,5] => [1,3,2,4,5,6,7] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [3,1,2,5,6,7,4] => [1,3,2,4,5,6,7] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [4,1,2,5,6,7,3] => [1,4,5,6,7,3,2] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => [1,2,3,7,6,5,4] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => [1,2,3,6,5,4,7] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => [1,2,3,5,4,6,7] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [2,1,6,3,4,7,5] => [1,2,3,6,7,5,4] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => [1,2,3,5,4,6,7] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => [1,2,3,4,5,7,6] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,1,5,3,7,4,6] => [1,2,3,5,7,6,4] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [2,1,6,3,7,4,5] => [1,2,3,6,4,5,7] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [2,1,5,3,6,4,7] => [1,2,3,5,6,4,7] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [2,1,4,3,6,7,5] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [2,1,5,3,6,7,4] => [1,2,3,5,6,7,4] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [3,1,7,2,4,5,6] => [1,3,7,6,5,4,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [3,1,6,2,4,5,7] => [1,3,6,5,4,2,7] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [3,1,5,2,4,7,6] => [1,3,5,4,2,6,7] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [3,1,6,2,4,7,5] => [1,3,6,7,5,4,2] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [3,1,5,2,4,6,7] => [1,3,5,4,2,6,7] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [4,1,7,2,3,5,6] => [1,4,2,3,7,6,5] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [4,1,6,2,3,5,7] => [1,4,2,3,6,5,7] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [4,1,5,2,3,7,6] => [1,4,2,3,5,6,7] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [4,1,6,2,3,7,5] => [1,4,2,3,6,7,5] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [4,1,5,2,3,6,7] => [1,4,2,3,5,6,7] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [3,1,4,2,7,5,6] => [1,3,4,2,5,7,6] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [3,1,4,2,6,5,7] => [1,3,4,2,5,6,7] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [3,1,5,2,7,4,6] => [1,3,5,7,6,4,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [3,1,6,2,7,4,5] => [1,3,6,4,2,5,7] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [3,1,5,2,6,4,7] => [1,3,5,6,4,2,7] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [4,1,5,2,7,3,6] => [1,4,2,3,5,7,6] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [4,1,6,2,7,3,5] => [1,4,2,3,6,5,7] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [4,1,5,2,6,3,7] => [1,4,2,3,5,6,7] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [3,1,4,2,5,7,6] => [1,3,4,2,5,6,7] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [3,1,4,2,6,7,5] => [1,3,4,2,5,6,7] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [3,1,5,2,6,7,4] => [1,3,5,6,7,4,2] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [4,1,5,2,6,7,3] => [1,4,2,3,5,6,7] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [3,1,4,2,5,6,7] => [1,3,4,2,5,6,7] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => [1,2,3,4,7,6,5] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => [1,2,3,4,6,5,7] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [2,1,3,6,4,7,5] => [1,2,3,4,6,7,5] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,1,4,7,3,5,6] => [1,2,3,4,7,6,5] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [2,1,4,6,3,5,7] => [1,2,3,4,6,5,7] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,1,5,7,3,4,6] => [1,2,3,5,4,7,6] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [2,1,6,7,3,4,5] => [1,2,3,6,4,7,5] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [2,1,5,6,3,4,7] => [1,2,3,5,4,6,7] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [2,1,4,5,3,7,6] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [2,1,4,6,3,7,5] => [1,2,3,4,6,7,5] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [2,1,5,6,3,7,4] => [1,2,3,5,4,6,7] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [2,1,4,5,3,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [3,1,4,7,2,5,6] => [1,3,4,7,6,5,2] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [3,1,4,6,2,5,7] => [1,3,4,6,5,2,7] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [3,1,5,7,2,4,6] => [1,3,5,2,4,7,6] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [3,1,6,7,2,4,5] => [1,3,6,4,7,5,2] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [3,1,5,6,2,4,7] => [1,3,5,2,4,6,7] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [4,1,5,6,2,3,7] => [1,4,6,3,5,2,7] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [3,1,4,5,2,7,6] => [1,3,4,5,2,6,7] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [3,1,4,6,2,7,5] => [1,3,4,6,7,5,2] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [3,1,5,6,2,7,4] => [1,3,5,2,4,6,7] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [3,1,4,5,2,6,7] => [1,3,4,5,2,6,7] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6] => [1,2,3,4,5,7,6] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [2,1,3,5,7,4,6] => [1,2,3,4,5,7,6] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [2,1,3,6,7,4,5] => [1,2,3,4,6,5,7] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [2,1,3,5,6,4,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [2,1,4,5,7,3,6] => [1,2,3,4,5,7,6] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [2,1,4,6,7,3,5] => [1,2,3,4,6,5,7] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [2,1,5,6,7,3,4] => [1,2,3,5,7,4,6] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [2,1,4,5,6,3,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [3,1,4,5,7,2,6] => [1,3,4,5,7,6,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [3,1,4,6,7,2,5] => [1,3,4,6,2,5,7] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [3,1,5,6,7,2,4] => [1,3,5,7,4,6,2] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [4,1,5,6,7,2,3] => [1,4,6,2,3,5,7] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [3,1,4,5,6,2,7] => [1,3,4,5,6,2,7] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [2,1,3,4,6,7,5] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [2,1,3,5,6,7,4] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [2,1,4,5,6,7,3] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [3,1,4,5,6,7,2] => [1,3,4,5,6,7,2] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [1,2,7,6,5,4,3] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => [1,2,6,5,4,3,7] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => [1,2,5,4,3,6,7] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [1,6,2,3,4,7,5] => [1,2,6,7,5,4,3] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => [1,2,5,4,3,6,7] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => [1,2,4,3,5,7,6] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => [1,2,4,3,5,6,7] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [1,5,2,3,7,4,6] => [1,2,5,7,6,4,3] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [1,6,2,3,7,4,5] => [1,2,6,4,3,5,7] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [1,5,2,3,6,4,7] => [1,2,5,6,4,3,7] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => [1,2,4,3,5,6,7] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [1,4,2,3,6,7,5] => [1,2,4,3,5,6,7] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [1,5,2,3,6,7,4] => [1,2,5,6,7,4,3] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => [1,2,4,3,5,6,7] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => [1,2,3,4,7,6,5] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => [1,2,3,4,6,5,7] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,6,4,7,5] => [1,2,3,4,6,7,5] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [1,4,2,7,3,5,6] => [1,2,4,7,6,5,3] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [1,4,2,6,3,5,7] => [1,2,4,6,5,3,7] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [1,5,2,7,3,4,6] => [1,2,5,3,4,7,6] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [1,6,2,7,3,4,5] => [1,2,6,4,7,5,3] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [1,5,2,6,3,4,7] => [1,2,5,3,4,6,7] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [1,4,2,5,3,7,6] => [1,2,4,5,3,6,7] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [1,4,2,6,3,7,5] => [1,2,4,6,7,5,3] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [1,5,2,6,3,7,4] => [1,2,5,3,4,6,7] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [1,4,2,5,3,6,7] => [1,2,4,5,3,6,7] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => [1,2,3,4,5,7,6] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [1,3,2,5,7,4,6] => [1,2,3,4,5,7,6] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,6,7,4,5] => [1,2,3,4,6,5,7] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [1,4,2,5,7,3,6] => [1,2,4,5,7,6,3] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [1,4,2,6,7,3,5] => [1,2,4,6,3,5,7] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [1,5,2,6,7,3,4] => [1,2,5,7,4,6,3] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [1,4,2,5,6,3,7] => [1,2,4,5,6,3,7] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [1,3,2,5,6,7,4] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [1,4,2,5,6,7,3] => [1,2,4,5,6,7,3] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [2,7,1,3,4,5,6] => [1,2,7,6,5,4,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [2,6,1,3,4,5,7] => [1,2,6,5,4,3,7] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [2,5,1,3,4,7,6] => [1,2,5,4,3,6,7] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [2,6,1,3,4,7,5] => [1,2,6,7,5,4,3] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [2,5,1,3,4,6,7] => [1,2,5,4,3,6,7] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [2,4,1,3,7,5,6] => [1,2,4,3,5,7,6] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [2,4,1,3,6,5,7] => [1,2,4,3,5,6,7] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [2,5,1,3,7,4,6] => [1,2,5,7,6,4,3] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [2,6,1,3,7,4,5] => [1,2,6,4,3,5,7] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [2,5,1,3,6,4,7] => [1,2,5,6,4,3,7] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [2,4,1,3,5,7,6] => [1,2,4,3,5,6,7] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [2,4,1,3,6,7,5] => [1,2,4,3,5,6,7] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [2,5,1,3,6,7,4] => [1,2,5,6,7,4,3] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [2,4,1,3,5,6,7] => [1,2,4,3,5,6,7] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [3,7,1,2,4,5,6] => [1,3,2,7,6,5,4] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [3,6,1,2,4,5,7] => [1,3,2,6,5,4,7] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [3,5,1,2,4,7,6] => [1,3,2,5,4,6,7] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [3,6,1,2,4,7,5] => [1,3,2,6,7,5,4] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [3,5,1,2,4,6,7] => [1,3,2,5,4,6,7] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [4,7,1,2,3,5,6] => [1,4,2,7,6,5,3] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [4,6,1,2,3,5,7] => [1,4,2,6,5,3,7] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [4,5,1,2,3,7,6] => [1,4,2,5,3,6,7] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [4,6,1,2,3,7,5] => [1,4,2,6,7,5,3] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [4,5,1,2,3,6,7] => [1,4,2,5,3,6,7] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [3,4,1,2,7,5,6] => [1,3,2,4,5,7,6] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [3,4,1,2,6,5,7] => [1,3,2,4,5,6,7] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [3,5,1,2,7,4,6] => [1,3,2,5,7,6,4] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [3,6,1,2,7,4,5] => [1,3,2,6,4,5,7] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [3,5,1,2,6,4,7] => [1,3,2,5,6,4,7] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [4,5,1,2,7,3,6] => [1,4,2,5,7,6,3] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [4,6,1,2,7,3,5] => [1,4,2,6,3,5,7] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [4,5,1,2,6,3,7] => [1,4,2,5,6,3,7] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [3,4,1,2,5,7,6] => [1,3,2,4,5,6,7] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [3,4,1,2,6,7,5] => [1,3,2,4,5,6,7] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [3,5,1,2,6,7,4] => [1,3,2,5,6,7,4] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [4,5,1,2,6,7,3] => [1,4,2,5,6,7,3] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [3,4,1,2,5,6,7] => [1,3,2,4,5,6,7] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [2,3,1,7,4,5,6] => [1,2,3,4,7,6,5] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [2,3,1,6,4,5,7] => [1,2,3,4,6,5,7] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [2,3,1,6,4,7,5] => [1,2,3,4,6,7,5] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [2,4,1,7,3,5,6] => [1,2,4,7,6,5,3] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [2,4,1,6,3,5,7] => [1,2,4,6,5,3,7] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [2,5,1,7,3,4,6] => [1,2,5,3,4,7,6] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [2,6,1,7,3,4,5] => [1,2,6,4,7,5,3] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [2,5,1,6,3,4,7] => [1,2,5,3,4,6,7] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [2,4,1,5,3,7,6] => [1,2,4,5,3,6,7] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [2,4,1,6,3,7,5] => [1,2,4,6,7,5,3] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [2,5,1,6,3,7,4] => [1,2,5,3,4,6,7] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [2,4,1,5,3,6,7] => [1,2,4,5,3,6,7] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [3,4,1,7,2,5,6] => [1,3,2,4,7,6,5] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [3,4,1,6,2,5,7] => [1,3,2,4,6,5,7] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [3,5,1,7,2,4,6] => [1,3,2,5,4,7,6] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [3,6,1,7,2,4,5] => [1,3,2,6,4,7,5] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [3,5,1,6,2,4,7] => [1,3,2,5,4,6,7] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [4,5,1,6,2,3,7] => [1,4,6,3,2,5,7] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [3,4,1,5,2,7,6] => [1,3,2,4,5,6,7] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [3,4,1,6,2,7,5] => [1,3,2,4,6,7,5] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [3,5,1,6,2,7,4] => [1,3,2,5,4,6,7] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [3,4,1,5,2,6,7] => [1,3,2,4,5,6,7] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [2,3,1,4,7,5,6] => [1,2,3,4,5,7,6] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [2,3,1,5,7,4,6] => [1,2,3,4,5,7,6] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [2,3,1,6,7,4,5] => [1,2,3,4,6,5,7] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [2,4,1,5,7,3,6] => [1,2,4,5,7,6,3] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [2,4,1,6,7,3,5] => [1,2,4,6,3,5,7] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [2,5,1,6,7,3,4] => [1,2,5,7,4,6,3] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [2,4,1,5,6,3,7] => [1,2,4,5,6,3,7] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [3,4,1,5,7,2,6] => [1,3,2,4,5,7,6] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [3,4,1,6,7,2,5] => [1,3,2,4,6,5,7] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [3,5,1,6,7,2,4] => [1,3,2,5,7,4,6] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [4,5,1,6,7,2,3] => [1,4,6,2,5,7,3] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [3,4,1,5,6,2,7] => [1,3,2,4,5,6,7] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [2,4,1,5,6,7,3] => [1,2,4,5,6,7,3] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [3,4,1,5,6,7,2] => [1,3,2,4,5,6,7] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [1,2,3,7,6,5,4] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [1,2,3,6,5,4,7] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => [1,2,3,5,4,6,7] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [1,2,6,3,4,7,5] => [1,2,3,6,7,5,4] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => [1,2,3,5,4,6,7] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => [1,2,3,4,5,7,6] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [1,2,5,3,7,4,6] => [1,2,3,5,7,6,4] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [1,2,6,3,7,4,5] => [1,2,3,6,4,5,7] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [1,2,5,3,6,4,7] => [1,2,3,5,6,4,7] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,6,7,5] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [1,2,5,3,6,7,4] => [1,2,3,5,6,7,4] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [1,3,7,2,4,5,6] => [1,2,3,7,6,5,4] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [1,3,6,2,4,5,7] => [1,2,3,6,5,4,7] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [1,3,5,2,4,7,6] => [1,2,3,5,4,6,7] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [1,3,6,2,4,7,5] => [1,2,3,6,7,5,4] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [1,3,5,2,4,6,7] => [1,2,3,5,4,6,7] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [1,4,7,2,3,5,6] => [1,2,4,3,7,6,5] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [1,4,6,2,3,5,7] => [1,2,4,3,6,5,7] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [1,5,7,2,3,4,6] => [1,2,5,3,7,6,4] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [1,6,7,2,3,4,5] => [1,2,6,4,3,7,5] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [1,5,6,2,3,4,7] => [1,2,5,3,6,4,7] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [1,4,5,2,3,7,6] => [1,2,4,3,5,6,7] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [1,4,6,2,3,7,5] => [1,2,4,3,6,7,5] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [1,5,6,2,3,7,4] => [1,2,5,3,6,7,4] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [1,4,5,2,3,6,7] => [1,2,4,3,5,6,7] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [1,3,4,2,7,5,6] => [1,2,3,4,5,7,6] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [1,3,5,2,7,4,6] => [1,2,3,5,7,6,4] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [1,3,6,2,7,4,5] => [1,2,3,6,4,5,7] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [1,3,5,2,6,4,7] => [1,2,3,5,6,4,7] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [1,4,5,2,7,3,6] => [1,2,4,3,5,7,6] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [1,4,6,2,7,3,5] => [1,2,4,3,6,5,7] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [1,5,6,2,7,3,4] => [1,2,5,7,4,3,6] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [1,4,5,2,6,3,7] => [1,2,4,3,5,6,7] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,3,4,2,6,7,5] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [1,3,5,2,6,7,4] => [1,2,3,5,6,7,4] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [1,4,5,2,6,7,3] => [1,2,4,3,5,6,7] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [2,3,7,1,4,5,6] => [1,2,3,7,6,5,4] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [2,3,6,1,4,5,7] => [1,2,3,6,5,4,7] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [2,3,5,1,4,7,6] => [1,2,3,5,4,6,7] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [2,3,6,1,4,7,5] => [1,2,3,6,7,5,4] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [2,3,5,1,4,6,7] => [1,2,3,5,4,6,7] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [2,4,7,1,3,5,6] => [1,2,4,3,7,6,5] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [2,4,6,1,3,5,7] => [1,2,4,3,6,5,7] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [2,5,7,1,3,4,6] => [1,2,5,3,7,6,4] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [2,6,7,1,3,4,5] => [1,2,6,4,3,7,5] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [2,5,6,1,3,4,7] => [1,2,5,3,6,4,7] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [2,4,5,1,3,7,6] => [1,2,4,3,5,6,7] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [2,4,6,1,3,7,5] => [1,2,4,3,6,7,5] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [2,5,6,1,3,7,4] => [1,2,5,3,6,7,4] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [2,4,5,1,3,6,7] => [1,2,4,3,5,6,7] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [3,4,7,1,2,5,6] => [1,3,7,6,5,2,4] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [3,4,6,1,2,5,7] => [1,3,6,5,2,4,7] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [3,5,7,1,2,4,6] => [1,3,7,6,4,2,5] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [3,6,7,1,2,4,5] => [1,3,7,5,2,6,4] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [3,5,6,1,2,4,7] => [1,3,6,4,2,5,7] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [4,5,7,1,2,3,6] => [1,4,2,5,3,7,6] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [4,6,7,1,2,3,5] => [1,4,2,6,3,7,5] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [4,5,6,1,2,3,7] => [1,4,2,5,3,6,7] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [3,4,5,1,2,7,6] => [1,3,5,2,4,6,7] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [3,4,6,1,2,7,5] => [1,3,6,7,5,2,4] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [3,5,6,1,2,7,4] => [1,3,6,7,4,2,5] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [4,5,6,1,2,7,3] => [1,4,2,5,3,6,7] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [3,4,5,1,2,6,7] => [1,3,5,2,4,6,7] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [2,3,4,1,7,5,6] => [1,2,3,4,5,7,6] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [2,3,5,1,7,4,6] => [1,2,3,5,7,6,4] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [2,3,6,1,7,4,5] => [1,2,3,6,4,5,7] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [2,3,5,1,6,4,7] => [1,2,3,5,6,4,7] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [2,4,5,1,7,3,6] => [1,2,4,3,5,7,6] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [2,4,6,1,7,3,5] => [1,2,4,3,6,5,7] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [2,5,6,1,7,3,4] => [1,2,5,7,4,3,6] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [2,4,5,1,6,3,7] => [1,2,4,3,5,6,7] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [3,4,5,1,7,2,6] => [1,3,5,7,6,2,4] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [3,4,6,1,7,2,5] => [1,3,6,2,4,5,7] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [3,5,6,1,7,2,4] => [1,3,6,2,5,7,4] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [4,5,6,1,7,2,3] => [1,4,2,5,7,3,6] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [3,4,5,1,6,2,7] => [1,3,5,6,2,4,7] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [2,3,5,1,6,7,4] => [1,2,3,5,6,7,4] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [2,4,5,1,6,7,3] => [1,2,4,3,5,6,7] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [3,4,5,1,6,7,2] => [1,3,5,6,7,2,4] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [1,2,3,4,7,6,5] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => [1,2,3,4,6,5,7] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [1,2,3,6,4,7,5] => [1,2,3,4,6,7,5] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [1,2,4,7,3,5,6] => [1,2,3,4,7,6,5] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [1,2,4,6,3,5,7] => [1,2,3,4,6,5,7] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [1,2,5,7,3,4,6] => [1,2,3,5,4,7,6] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [1,2,6,7,3,4,5] => [1,2,3,6,4,7,5] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [1,2,5,6,3,4,7] => [1,2,3,5,4,6,7] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [1,2,4,5,3,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [1,2,4,6,3,7,5] => [1,2,3,4,6,7,5] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [1,2,5,6,3,7,4] => [1,2,3,5,4,6,7] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [1,3,4,7,2,5,6] => [1,2,3,4,7,6,5] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [1,3,4,6,2,5,7] => [1,2,3,4,6,5,7] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [1,3,5,7,2,4,6] => [1,2,3,5,4,7,6] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [1,3,6,7,2,4,5] => [1,2,3,6,4,7,5] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [1,3,5,6,2,4,7] => [1,2,3,5,4,6,7] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [1,4,5,7,2,3,6] => [1,2,4,7,6,3,5] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [1,4,6,7,2,3,5] => [1,2,4,7,5,3,6] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [1,5,6,7,2,3,4] => [1,2,5,3,6,4,7] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [1,4,5,6,2,3,7] => [1,2,4,6,3,5,7] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [1,3,4,5,2,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,3,4,6,2,7,5] => [1,2,3,4,6,7,5] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [1,3,5,6,2,7,4] => [1,2,3,5,4,6,7] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [1,4,5,6,2,7,3] => [1,2,4,6,7,3,5] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [2,3,4,7,1,5,6] => [1,2,3,4,7,6,5] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [2,3,4,6,1,5,7] => [1,2,3,4,6,5,7] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [2,3,5,7,1,4,6] => [1,2,3,5,4,7,6] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [2,3,6,7,1,4,5] => [1,2,3,6,4,7,5] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [2,3,5,6,1,4,7] => [1,2,3,5,4,6,7] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [2,4,5,7,1,3,6] => [1,2,4,7,6,3,5] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [2,4,6,7,1,3,5] => [1,2,4,7,5,3,6] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [2,5,6,7,1,3,4] => [1,2,5,3,6,4,7] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [2,4,5,6,1,3,7] => [1,2,4,6,3,5,7] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [3,4,5,7,1,2,6] => [1,3,5,2,4,7,6] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [3,4,6,7,1,2,5] => [1,3,6,2,4,7,5] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [3,5,6,7,1,2,4] => [1,3,6,2,5,4,7] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [3,4,5,6,1,2,7] => [1,3,5,2,4,6,7] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [2,3,4,6,1,7,5] => [1,2,3,4,6,7,5] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [2,3,5,6,1,7,4] => [1,2,3,5,4,6,7] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [2,4,5,6,1,7,3] => [1,2,4,6,7,3,5] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [3,4,5,6,1,7,2] => [1,3,5,2,4,6,7] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => [1,2,3,4,5,7,6] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [1,2,3,5,7,4,6] => [1,2,3,4,5,7,6] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => [1,2,3,4,6,5,7] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [1,2,4,5,7,3,6] => [1,2,3,4,5,7,6] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [1,2,4,6,7,3,5] => [1,2,3,4,6,5,7] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => [1,2,3,5,7,4,6] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [1,3,4,5,7,2,6] => [1,2,3,4,5,7,6] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,3,4,6,7,2,5] => [1,2,3,4,6,5,7] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [1,3,5,6,7,2,4] => [1,2,3,5,7,4,6] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => [1,2,4,6,3,5,7] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [2,3,4,5,7,1,6] => [1,2,3,4,5,7,6] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [2,3,4,6,7,1,5] => [1,2,3,4,6,5,7] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [2,3,5,6,7,1,4] => [1,2,3,5,7,4,6] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [2,4,5,6,7,1,3] => [1,2,4,6,3,5,7] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [3,4,5,6,7,1,2] => [1,3,5,7,2,4,6] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [7,1,2,3,4,5,8,6] => [1,7,8,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => [6,1,2,3,4,8,5,7] => [1,6,8,7,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [6,1,2,3,4,7,8,5] => [1,6,7,8,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,6,1,7,8,5] => [5,1,2,3,8,4,6,7] => [1,5,8,7,6,4,3,2] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,5,4,6,8,7] => [3,1,2,5,4,6,8,7] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8] => [3,1,2,4,7,5,6,8] => [1,3,2,4,5,7,6,8] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7] => [3,1,2,4,6,5,8,7] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [3,1,2,5,7,4,6,8] => [1,3,2,4,5,7,6,8] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => [3,1,2,5,6,4,7,8] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8] => [3,1,2,4,5,7,6,8] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [3,1,2,4,7,8,5,6] => [1,3,2,4,5,7,6,8] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,1,4,7,5,6,8] => [3,1,2,4,6,7,5,8] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,1,2,5,7,8,4,6] => [1,3,2,4,5,7,6,8] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,1,7,4,5,6,8] => [3,1,2,5,6,7,4,8] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [3,1,2,4,5,6,8,7] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [3,1,2,4,5,7,8,6] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [3,1,2,4,6,7,8,5] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => [3,1,2,5,6,7,8,4] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,3,6,8,7] => [2,1,5,3,4,6,8,7] => [1,2,3,5,4,6,7,8] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => [2,1,5,3,4,6,7,8] => [1,2,3,5,4,6,7,8] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [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] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [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] => [2,1,4,6,7,3,5,8] => [2,1,6,3,7,4,5,8] => [1,2,3,6,4,5,7,8] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [2,1,6,3,7,4,8,5] => [1,2,3,6,4,5,7,8] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,6,8,5,7] => [1,2,3,4,5,6,8,7] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [2,1,4,3,7,8,5,6] => [1,2,3,4,5,7,6,8] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,4,3,7,5,6,8] => [2,1,4,3,6,7,5,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [2,1,4,3,5,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [2,1,4,3,6,7,8,5] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,8,3,5,6,7] => [2,1,5,3,6,7,8,4] => [1,2,3,5,6,7,8,4] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6,8] => [4,1,5,2,3,7,6,8] => [1,4,2,3,5,6,7,8] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,4,5,1,7,8,3,6] => [4,1,7,2,3,8,5,6] => [1,4,2,3,7,5,6,8] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,7,8,1,3,6] => [6,1,7,2,3,8,4,5] => [1,6,8,5,3,7,4,2] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,4,5,1,3,8,6,7] => [4,1,5,2,3,7,8,6] => [1,4,2,3,5,6,7,8] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [4,1,5,2,3,6,7,8] => [1,4,2,3,5,6,7,8] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [3,1,5,2,7,4,8,6] => [1,3,5,7,8,6,4,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,6,1,3,7,5,8] => [4,1,5,2,7,3,6,8] => [1,4,2,3,5,7,6,8] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [4,1,5,2,6,3,8,7] => [1,4,2,3,5,6,7,8] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,6,1,3,5,7,8] => [4,1,5,2,6,3,7,8] => [1,4,2,3,5,6,7,8] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,4,7,1,3,8,5,6] => [4,1,5,2,7,8,3,6] => [1,4,2,3,5,7,6,8] => 3
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [4,1,5,2,6,7,8,3] => [1,4,2,3,5,6,7,8] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,1,3,5,4,8,6,7] => [2,1,3,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,1,5,6,3,7,4,8] => [2,1,5,7,3,4,6,8] => [1,2,3,5,4,7,6,8] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,1,5,6,3,4,8,7] => [1,2,3,5,4,6,7,8] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,1,5,6,3,4,7,8] => [2,1,5,6,3,4,7,8] => [1,2,3,5,4,6,7,8] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [2,1,5,7,3,8,4,6] => [1,2,3,5,4,7,6,8] => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6,8] => [2,1,5,6,3,7,4,8] => [1,2,3,5,4,6,7,8] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,5,3,4,6,8,7] => [2,1,4,5,3,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,1,5,8,3,4,6,7] => [2,1,5,6,3,7,8,4] => [1,2,3,5,4,6,7,8] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,5,3,4,6,7,8] => [2,1,4,5,3,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,1,3,4,6,7,5,8] => [2,1,3,4,7,5,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,6,4,5,8,7] => [2,1,3,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [2,1,6,7,8,3,4,5] => [1,2,3,6,4,7,5,8] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [2,1,4,5,6,3,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,1,3,4,7,8,5,6] => [2,1,3,4,7,8,5,6] => [1,2,3,4,5,7,6,8] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => [2,1,3,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,7,4,5,8,6] => [2,1,3,5,6,8,4,7] => [1,2,3,4,5,6,8,7] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,7,3,4,5,8,6] => [2,1,4,5,6,8,3,7] => [1,2,3,4,5,6,8,7] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,1,7,3,4,8,5,6] => [2,1,4,5,7,8,3,6] => [1,2,3,4,5,7,6,8] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => [2,1,4,5,6,7,3,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [2,1,3,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [2,1,3,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [2,1,3,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [2,1,4,5,6,7,8,3] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [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] => [1,3,4,5,8,2,6,7] => [1,6,2,3,4,7,8,5] => [1,2,6,7,8,5,4,3] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [1,3,2,5,7,4,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,6,4,5,8,7] => [1,3,2,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [1,3,2,5,6,4,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,3,2,4,7,5,8,6] => [1,3,2,4,6,8,5,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,3,2,4,7,8,5,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,3,2,4,7,5,6,8] => [1,3,2,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,3,2,5,7,8,4,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [1,3,2,5,6,7,4,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [1,3,2,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [1,3,2,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4,5,8,2,6,7] => [2,6,1,3,4,7,8,5] => [1,2,6,7,8,5,4,3] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6,8] => [3,5,1,2,4,7,6,8] => [1,3,2,5,4,6,7,8] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,4,1,5,2,6,8,7] => [3,5,1,2,4,6,8,7] => [1,3,2,5,4,6,7,8] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,2,8,6,7] => [3,5,1,2,4,7,8,6] => [1,3,2,5,4,6,7,8] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,1,5,2,6,7,8] => [3,5,1,2,4,6,7,8] => [1,3,2,5,4,6,7,8] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6,8] => [4,5,1,2,3,7,6,8] => [1,4,2,5,3,6,7,8] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,5,1,2,6,8,7] => [4,5,1,2,3,6,8,7] => [1,4,2,5,3,6,7,8] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [4,5,1,2,3,6,7,8] => [1,4,2,5,3,6,7,8] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,6,7,5,8] => [3,4,1,2,7,5,6,8] => [1,3,2,4,5,7,6,8] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [3,4,1,2,6,5,8,7] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,6,5,7,8] => [3,4,1,2,6,5,7,8] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,8,2,5,7] => [3,6,1,2,7,4,8,5] => [1,3,2,6,4,5,7,8] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,4,6,1,7,2,5,8] => [4,6,1,2,7,3,5,8] => [1,4,2,6,3,5,7,8] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [3,4,1,2,5,7,6,8] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [3,4,1,2,7,8,5,6] => [1,3,2,4,5,7,6,8] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,4,1,2,7,5,6,8] => [3,4,1,2,6,7,5,8] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1,2,5,6,8,7] => [3,4,1,2,5,6,8,7] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,2,5,8,6,7] => [3,4,1,2,5,7,8,6] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [3,4,1,2,6,7,8,5] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,5,4,6,7,8] => [2,3,1,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [3,5,1,7,2,4,6,8] => [1,3,2,5,4,7,6,8] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [3,5,1,6,2,4,8,7] => [1,3,2,5,4,6,7,8] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => [3,5,1,6,2,4,7,8] => [1,3,2,5,4,6,7,8] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [5,6,1,7,2,3,4,8] => [1,5,2,6,3,4,7,8] => 3
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [5,6,1,7,2,3,8,4] => [1,5,2,6,3,4,7,8] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [3,4,1,5,2,7,6,8] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [3,5,1,7,2,8,4,6] => [1,3,2,5,4,7,6,8] => 3
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6,8] => [3,5,1,6,2,7,4,8] => [1,3,2,5,4,6,7,8] => 2
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,5,1,8,2,4,6,7] => [3,5,1,6,2,7,8,4] => [1,3,2,5,4,6,7,8] => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,5,1,2,4,6,7,8] => [3,4,1,5,2,6,7,8] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,7,5,8] => [2,3,1,4,7,5,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [2,3,1,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,1,2,6,4,5,7,8] => [2,3,1,5,6,4,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [3,4,1,5,7,2,6,8] => [1,3,2,4,5,7,6,8] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [3,6,1,7,8,2,4,5] => [1,3,2,6,4,7,5,8] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,8,7] => [3,4,1,5,6,2,8,7] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,6,1,2,4,5,7,8] => [3,4,1,5,6,2,7,8] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,2,4,5,7,8,6] => [2,3,1,4,5,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [2,3,1,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,2,4,7,8,5,6] => [2,3,1,4,7,8,5,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [2,3,1,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,7,4,5,8,6] => [2,3,1,5,6,8,4,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [3,1,2,7,4,8,5,6] => [2,3,1,5,7,8,4,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,2,7,4,5,6,8] => [2,3,1,5,6,7,4,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [3,7,1,2,4,8,5,6] => [3,4,1,5,7,8,2,6] => [1,3,2,4,5,7,6,8] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => [3,4,1,5,6,7,2,8] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [2,3,1,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [2,3,1,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => [2,3,1,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [3,4,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6,8] => [1,2,5,3,4,7,6,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,4,5,3,6,8,7] => [1,2,5,3,4,6,8,7] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,4,5,3,8,6,7] => [1,2,5,3,4,7,8,6] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,2,5,3,4,6,7,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,6,7,5,8] => [1,2,4,3,7,5,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,6,7,3,5,8] => [1,2,6,3,7,4,5,8] => [1,2,3,6,4,5,7,8] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => [1,2,6,3,7,4,8,5] => [1,2,3,6,4,5,7,8] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => [1,2,4,3,6,8,5,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,4,3,7,8,5,6] => [1,2,4,3,7,8,5,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => [1,2,4,3,6,7,5,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [1,2,4,3,6,7,8,5] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,2,5,3,6,7,8,4] => [1,2,3,5,6,7,8,4] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [1,3,5,2,4,7,6,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,4,2,5,3,6,8,7] => [1,3,5,2,4,6,8,7] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,3,5,2,4,7,8,6] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [1,3,5,2,4,6,7,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,5,2,6,3,8,7] => [1,4,6,2,3,5,8,7] => [1,2,4,3,6,5,7,8] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,4,6,2,3,5,7,8] => [1,2,4,3,6,5,7,8] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [1,3,4,2,6,5,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,6,7,3,5,8] => [1,3,6,2,7,4,5,8] => [1,2,3,6,4,5,7,8] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,8,3,5,7] => [1,3,6,2,7,4,8,5] => [1,2,3,6,4,5,7,8] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,7,3,5,8] => [1,4,6,2,7,3,5,8] => [1,2,4,3,6,5,7,8] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [1,4,6,2,7,3,8,5] => [1,2,4,3,6,5,7,8] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,4,2,3,5,7,8,6] => [1,3,4,2,5,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [1,3,4,2,5,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,3,7,8,5,6] => [1,3,4,2,7,8,5,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [1,3,4,2,6,7,5,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => [1,3,4,2,5,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,3,4,2,5,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [1,3,4,2,6,7,8,5] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [1,3,5,2,6,7,8,4] => [1,2,3,5,6,7,8,4] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [1,3,4,2,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => [2,3,5,1,4,7,6,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => [2,3,5,1,4,6,7,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [2,4,6,1,3,5,8,7] => [1,2,4,3,6,5,7,8] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,1,5,2,6,3,7,8] => [2,4,6,1,3,5,7,8] => [1,2,4,3,6,5,7,8] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,6,1,7,2,3,8] => [4,6,7,1,2,3,5,8] => [1,4,2,6,3,7,5,8] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [5,6,7,1,2,3,4,8] => [1,5,2,6,3,7,4,8] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [4,5,6,1,2,3,8,7] => [1,4,2,5,3,6,7,8] => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [4,5,6,1,2,3,7,8] => [1,4,2,5,3,6,7,8] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [4,5,7,1,2,8,3,6] => [1,4,2,5,3,7,6,8] => 3
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6,8] => [4,5,6,1,2,7,3,8] => [1,4,2,5,3,6,7,8] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [4,5,6,1,2,7,8,3] => [1,4,2,5,3,6,7,8] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [2,3,4,1,7,5,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [2,3,4,1,6,5,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [2,3,4,1,6,5,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => [2,4,6,1,7,3,8,5] => [1,2,4,3,6,5,7,8] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [4,6,7,1,8,2,3,5] => [1,4,2,6,3,7,5,8] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [2,3,4,1,5,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [2,3,4,1,5,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [2,3,4,1,6,8,5,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [2,3,4,1,7,8,5,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [2,3,4,1,6,7,5,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [2,3,4,1,5,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [2,3,4,1,5,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [2,3,4,1,6,7,8,5] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,8,3,5,6,7] => [2,3,5,1,6,7,8,4] => [1,2,3,5,6,7,8,4] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [2,3,4,1,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => [1,2,5,7,3,4,6,8] => [1,2,3,5,4,7,6,8] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,2,5,6,7,3,4,8] => [1,2,6,7,3,4,5,8] => [1,2,3,6,4,7,5,8] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,2,5,6,3,4,8,7] => [1,2,5,6,3,4,8,7] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,2,5,6,3,4,7,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => [1,2,4,5,3,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => [1,2,4,5,3,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => [1,2,5,7,3,8,4,6] => [1,2,3,5,4,7,6,8] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [1,2,5,6,3,7,4,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => [1,2,4,5,3,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [1,2,5,6,3,7,8,4] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => [1,2,4,5,3,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [1,3,5,7,2,4,6,8] => [1,2,3,5,4,7,6,8] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,5,2,6,3,4,8,7] => [1,3,5,6,2,4,8,7] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [1,3,5,6,2,4,7,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [1,3,4,5,2,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [1,3,4,5,2,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,3,5,7,2,8,4,6] => [1,2,3,5,4,7,6,8] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [1,3,5,6,2,7,4,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,5,2,3,4,6,8,7] => [1,3,4,5,2,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,3,4,5,2,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [1,3,5,6,2,7,8,4] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [1,3,4,5,2,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,1,2,6,3,7,4,8] => [2,3,5,7,1,4,6,8] => [1,2,3,5,4,7,6,8] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,1,2,6,7,3,4,8] => [2,3,6,7,1,4,5,8] => [1,2,3,6,4,7,5,8] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,3,4,8,7] => [2,3,5,6,1,4,8,7] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => [2,3,5,6,1,4,7,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [5,6,7,8,1,2,3,4] => [1,5,2,6,3,7,4,8] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [2,3,4,5,1,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6,8] => [2,3,4,5,1,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,7,3,8,4,6] => [2,3,5,7,1,8,4,6] => [1,2,3,5,4,7,6,8] => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6,8] => [2,3,5,6,1,7,4,8] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [2,3,4,5,1,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [2,3,4,5,1,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [2,3,5,6,1,7,8,4] => [1,2,3,5,4,6,7,8] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [2,3,4,5,1,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,5,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [1,2,3,5,7,4,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => [1,2,3,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [1,2,3,5,6,4,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,2,6,3,4,7,5,8] => [1,2,4,5,7,3,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => [1,2,6,7,8,3,4,5] => [1,2,3,6,4,7,5,8] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => [1,2,4,5,6,3,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => [1,2,4,5,6,3,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [1,3,4,5,7,2,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,6,2,7,8,3,4,5] => [1,3,6,7,8,2,4,5] => [1,2,3,6,4,7,5,8] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => [1,3,4,5,6,2,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [1,3,4,5,6,2,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [2,3,4,5,7,1,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,1,2,7,8,3,4,5] => [2,3,6,7,8,1,4,5] => [1,2,3,6,4,7,5,8] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [2,3,4,5,6,1,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [2,3,4,5,6,1,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [1,2,3,4,6,8,5,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [1,2,3,4,7,8,5,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [1,2,3,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [1,2,3,5,6,8,4,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [1,2,3,5,7,8,4,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,2,3,5,6,7,4,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [1,2,4,5,6,8,3,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,2,7,3,4,8,5,6] => [1,2,4,5,7,8,3,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => [1,2,4,5,6,7,3,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [1,3,4,5,6,8,2,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,3,4,5,7,8,2,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [1,3,4,5,6,7,2,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [2,3,4,5,6,8,1,7] => [1,2,3,4,5,6,8,7] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [2,3,4,5,7,8,1,6] => [1,2,3,4,5,7,6,8] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [2,3,4,5,6,7,1,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,3,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,4,5,6,7,8,3] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [1,3,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [2,3,4,5,6,7,9,1,8] => [1,2,3,4,5,6,7,9,8] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [2,3,4,5,6,7,8,10,1,9] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => [1,3,4,5,6,7,9,2,8] => [1,2,3,4,5,6,7,9,8] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [2,3,4,5,6,7,1,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [2,1,4,5,6,7,8,9,3] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,11,9] => [2,3,4,5,6,7,8,9,11,1,10] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,10,8] => [1,3,4,5,6,7,8,10,2,9] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [2,3,4,5,6,7,8,1,10,9] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,1,3,9,4,5,6,7,8] => [2,1,3,5,6,7,8,9,4] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => [2,1,4,5,6,7,8,9,10,3] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [1,10,2,3,4,5,6,7,8,11,9] => [1,3,4,5,6,7,8,9,11,2,10] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,9,8] => [1,3,4,5,6,7,2,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,9,8] => [2,3,4,5,1,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7,9] => [2,1,4,5,6,7,8,3,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,8,5,6,9,7] => [1,2,3,4,6,7,9,5,8] => [1,2,3,4,5,6,7,9,8] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7] => [1,2,3,4,5,7,9,6,8] => [1,2,3,4,5,6,7,9,8] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,9,8] => [2,3,1,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,9,7,8] => [2,1,3,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [2,1,3,4,5,10,6,7,8,9] => [2,1,3,4,5,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,7,9,8] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,6,9,7,10,8] => [1,2,3,4,5,6,8,10,7,9] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,7,10,8,9] => [2,1,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7,9] => [2,3,4,5,6,1,8,7,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,8,9,7] => [2,3,4,5,6,1,9,7,8] => [1,2,3,4,5,6,7,9,8] => 1
[] => [] => [] => [] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,1,2,4,5,6,9,7,8] => [2,3,1,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => [2,3,1,5,6,7,8,9,4] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => [2,3,4,1,6,7,8,9,5] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,5,3,4,6,7,8,9] => [1,2,4,5,3,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8,9] => [1,3,4,5,2,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5,1,2,3,4,9,6,7,8] => [2,3,4,5,1,7,8,9,6] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,6,3,4,5,7,8,9] => [1,2,4,5,6,3,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,9,7,8] => [2,3,4,5,6,1,8,9,7] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [2,3,4,5,6,1,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8,9] => [1,3,4,5,6,7,2,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9] => [2,3,4,5,6,7,1,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,5,8,6,7,9] => [1,2,3,4,5,7,8,6,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7,9] => [1,2,3,5,6,7,8,4,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7,9] => [1,3,4,5,6,7,8,2,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => [2,3,4,5,6,7,8,1,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,9,6,7,8] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [1,2,3,5,6,7,8,9,4] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => [1,2,4,5,6,7,8,9,3] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [1,3,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [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] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => [8,1,2,3,4,5,6,9,7] => [1,8,9,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => [9,1,2,3,4,5,6,7,10,8] => [1,9,10,8,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,9,7] => [2,1,4,3,6,5,9,7,8] => [1,2,3,4,5,6,7,9,8] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,7,8,9] => [2,1,4,3,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,6,8,9,7] => [2,1,3,4,5,6,9,7,8] => [1,2,3,4,5,6,7,9,8] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => [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] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,7,8] => [1,2,3,4,5,6,7,9,8] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [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] => [2,1,4,3,6,5,8,7,9,10] => [2,1,4,3,6,5,8,7,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,6,7,9,10,8] => [2,1,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,8,9] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => [2,3,4,5,6,7,8,9,1,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [2,3,4,5,6,7,8,1,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,7,6,8,9] => [2,3,4,5,1,7,6,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [1,2,4,5,6,7,8,9,10,3] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [2,3,1,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8,10] => [2,3,1,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8,10] => [1,3,4,5,6,7,8,9,2,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,8,4,5,6,7,9,10] => [1,2,3,5,6,7,8,4,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,4,5,8,6,7,9,10] => [1,2,3,4,5,7,8,6,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,5,3,4,6,7,8,9] => [2,1,4,5,3,6,7,8,9] => [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] => [2,3,4,5,6,8,1,9,7] => [7,1,2,3,4,5,9,6,8] => [1,7,9,8,6,5,4,3,2] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,9] => [2,3,4,1,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8,10] => [1,2,3,4,5,6,8,9,7,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8,9,10] => [1,3,4,2,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => [2,3,1,5,6,7,8,9,10,4] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => [2,3,4,5,1,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,9,10] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,9] => [1,3,4,2,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,10,9] => [1,3,4,2,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [1,3,2,5,4,7,6,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,6,5,7,8,9] => [2,3,4,1,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8,10] => [2,3,4,5,6,7,1,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,5,4,8,6,9,7] => [1,3,2,5,4,7,9,6,8] => [1,2,3,4,5,6,7,9,8] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,22,4 32,70,29,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 6\ q$
$F_{5} = 16 + 22\ q + 4\ q^{2}$
$F_{6} = 32 + 70\ q + 29\ q^{2} + q^{3}$
Description
The number of exclusive right-to-left minima of a permutation.
This is the number of right-to-left minima that are not left-to-right maxima.
This is also the number of non weak exceedences of a permutation that are also not mid-points of a decreasing subsequence of length 3.
Given a permutation $\pi = [\pi_1,\ldots,\pi_n]$, this statistic counts the number of position $j$ such that $\pi_j < j$ and there do not exist indices $i,k$ with $i < j < k$ and $\pi_i > \pi_j > \pi_k$.
See also St000213The number of weak exceedances (also weak excedences) of a permutation. and St000119The number of occurrences of the pattern 321 in a permutation..
This is the number of right-to-left minima that are not left-to-right maxima.
This is also the number of non weak exceedences of a permutation that are also not mid-points of a decreasing subsequence of length 3.
Given a permutation $\pi = [\pi_1,\ldots,\pi_n]$, this statistic counts the number of position $j$ such that $\pi_j < j$ and there do not exist indices $i,k$ with $i < j < k$ and $\pi_i > \pi_j > \pi_k$.
See also St000213The number of weak exceedances (also weak excedences) of a permutation. and St000119The number of occurrences of the pattern 321 in a permutation..
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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
inverse
Description
Sends a permutation to its inverse.
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