Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
St000884: Permutations ⟶ ℤ
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,2] => 0
[1,1,0,0] => [2,1] => [2,1] => [2,1] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [1,3,2] => 1
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [2,1,3] => 1
[1,1,0,1,0,0] => [2,3,1] => [3,2,1] => [3,2,1] => 0
[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => [3,2,1] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => [1,4,3,2] => 0
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,2,3,1] => [4,3,2,1] => 0
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,3,2,1] => [4,3,2,1] => 0
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [4,2,3,1] => [4,3,2,1] => 0
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [4,3,2,1] => [4,3,2,1] => 0
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,2,3,1,5] => [4,3,2,1,5] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [5,4,3,2,1] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,2,4,3,1] => [5,4,3,2,1] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [5,3,2,4,1] => [5,4,3,2,1] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,2,3,1,5] => [4,3,2,1,5] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [5,2,3,4,1] => [5,4,3,2,1] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [5,2,4,3,1] => [5,4,3,2,1] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 0
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [5,3,2,4,1] => [5,4,3,2,1] => 0
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [5,3,2,4,1] => [5,4,3,2,1] => 0
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 0
>>> Load all 1216 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [1,3,2,7,6,5,4] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,7,5,6,4] => [1,3,2,7,6,5,4] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,7,3,5,4,6,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [1,7,3,6,5,4,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,7,3,6,5,4,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [1,7,6,4,5,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [1,7,6,4,5,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,7,3,5,4,6,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [1,7,3,6,5,4,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,7,3,6,5,4,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [7,2,5,4,3,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [7,2,6,4,5,3,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [7,2,6,4,5,3,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [7,2,5,4,3,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [7,2,6,5,4,3,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [7,2,6,5,4,3,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,2,6,5,4,3,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [7,5,3,4,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [7,6,3,4,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [7,6,3,4,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [7,5,3,4,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [7,6,3,5,4,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [7,6,3,5,4,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [7,6,3,5,4,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [7,6,4,3,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [7,6,4,3,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [7,2,5,4,3,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [7,2,6,4,5,3,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [7,2,6,4,5,3,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [7,2,5,4,3,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [7,2,6,5,4,3,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [7,2,6,5,4,3,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,2,6,5,4,3,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [7,5,3,4,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [7,6,3,4,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [7,6,3,4,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [7,5,3,4,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [7,6,3,5,4,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [7,6,3,5,4,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [7,6,3,5,4,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [7,6,4,3,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [7,6,4,3,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [7,5,3,4,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [7,6,3,4,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [7,6,3,4,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [7,5,3,4,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [7,6,3,5,4,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [7,6,3,5,4,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [7,6,3,5,4,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [7,6,4,3,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [7,6,4,3,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [7,6,4,3,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [7,6,4,3,5,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [1,8,7,4,5,6,3,2] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [1,8,3,4,7,6,5,2] => [1,8,7,4,6,5,3,2] => 0
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [1,8,3,4,7,6,5,2] => [1,8,7,4,6,5,3,2] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [1,8,3,5,4,6,7,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [1,8,3,7,5,6,4,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [1,8,3,6,5,4,7,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,8,6,5,7,2] => [1,8,3,7,6,5,4,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,8,6,7,5,2] => [1,8,3,7,6,5,4,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [1,8,3,7,6,5,4,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [1,8,4,3,5,6,7,2] => [1,8,7,4,5,6,3,2] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [1,8,4,3,6,5,7,2] => [1,8,7,4,6,5,3,2] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => [1,8,5,4,3,6,7,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [1,8,5,4,3,7,6,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [1,8,6,4,5,3,7,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [1,8,7,4,5,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [1,8,7,4,6,5,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => [1,8,7,4,6,5,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [1,8,5,4,3,7,6,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [1,8,7,5,4,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [1,8,7,5,4,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [1,8,7,4,5,6,3,2] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [1,8,3,4,7,6,5,2] => [1,8,7,4,6,5,3,2] => 0
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [1,8,3,4,7,6,5,2] => [1,8,7,4,6,5,3,2] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [1,8,3,5,4,6,7,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [1,8,3,5,4,7,6,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [1,8,3,7,5,6,4,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [1,8,3,7,5,6,4,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [1,8,3,7,6,5,4,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [1,8,3,7,6,5,4,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [1,8,3,7,6,5,4,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [1,8,4,3,5,6,7,2] => [1,8,7,4,5,6,3,2] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [1,8,5,4,3,7,6,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [1,8,6,4,5,3,7,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [1,8,7,4,5,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => [1,8,7,4,6,5,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [1,8,7,4,6,5,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [1,8,5,4,3,7,6,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [1,8,7,5,4,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => [1,8,7,5,4,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [1,8,6,5,4,3,7,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [1,8,4,3,5,6,7,2] => [1,8,7,4,5,6,3,2] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [1,8,4,3,5,7,6,2] => [1,8,7,4,5,6,3,2] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [1,8,5,4,3,7,6,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [1,8,7,4,5,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => [1,8,7,4,5,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [1,8,6,4,5,3,7,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [1,8,7,4,6,5,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => [1,8,7,4,6,5,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => [1,8,5,4,3,7,6,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [1,8,6,5,4,3,7,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [1,8,7,5,4,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [1,8,6,5,4,3,7,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,8,4,5,6,3,7,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [1,8,5,4,3,6,7,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,8,5,4,3,7,6,2] => [1,8,7,5,4,6,3,2] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => [1,8,6,5,4,3,7,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [1,8,7,5,4,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [1,8,7,5,4,6,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [1,8,6,5,4,3,7,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,6,7,5] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [2,1,8,4,7,6,5,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [2,1,8,4,7,6,5,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [2,1,8,7,5,6,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [2,1,8,7,5,6,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [2,1,8,6,5,4,7,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,6,4,5,3,8,7] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,8,4,6,5,7,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [2,1,8,4,7,6,5,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [2,1,8,4,7,6,5,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [2,1,8,7,5,6,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [2,1,8,7,5,6,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [2,1,8,6,5,4,7,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,7,5,4,6,8,3] => [2,1,8,6,5,4,7,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [2,1,8,7,5,6,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [2,1,8,7,5,6,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [2,1,8,6,5,4,7,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [2,1,8,6,5,4,7,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [3,2,1,8,6,5,7,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,8,6,7,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,2,1,8,5,7,6,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [3,2,1,8,6,5,7,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,2,3,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,2,3,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [4,2,3,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,3,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,2,3,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [7,6,3,4,5,2,1,8] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [7,2,3,4,6,5,1,8] => [7,6,3,4,5,2,1,8] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [7,2,3,5,4,6,1,8] => [7,6,3,5,4,2,1,8] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [7,2,3,6,5,4,1,8] => [7,6,3,5,4,2,1,8] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [7,2,3,6,5,4,1,8] => [7,6,3,5,4,2,1,8] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [5,2,4,3,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [5,2,4,3,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [8,2,4,3,6,5,7,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [8,2,4,3,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [8,2,4,3,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [6,2,5,4,3,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [6,2,5,4,3,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [8,2,6,4,5,3,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [8,2,7,4,5,6,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [8,2,6,4,5,3,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [8,2,7,4,6,5,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [6,2,5,4,3,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [6,2,5,4,3,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [7,2,6,5,4,3,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => [8,2,6,5,4,3,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => [8,2,7,5,4,6,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [7,2,6,5,4,3,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [8,2,6,5,4,3,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [7,2,6,5,4,3,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [8,2,6,5,4,3,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [4,3,2,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [4,3,2,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [5,3,2,4,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [5,3,2,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [5,3,2,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [7,3,2,5,4,6,1,8] => [7,6,3,5,4,2,1,8] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [8,4,3,2,6,5,7,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [6,5,3,4,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [7,6,3,4,5,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [8,7,3,4,5,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [8,7,3,4,5,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,6,3,5,4,1,7,8] => [6,5,3,4,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [6,5,3,4,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => [8,6,3,5,4,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [8,7,3,5,4,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => [8,6,3,5,4,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => [7,6,3,5,4,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [6,4,3,2,5,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [8,4,3,2,6,5,7,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [8,6,4,3,5,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [8,7,4,3,5,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [8,7,4,3,5,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [8,6,4,3,5,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,4,5,3,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [3,2,1,8,5,7,6,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [3,2,1,8,6,5,7,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [3,2,1,8,5,6,7,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,2,1,8,5,7,6,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [3,2,1,8,6,5,7,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [3,2,1,8,6,5,7,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [4,2,3,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [4,2,3,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [4,2,3,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [4,2,3,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [5,2,3,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [7,6,3,4,5,2,1,8] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [5,2,4,3,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [5,2,4,3,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [5,2,4,3,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [6,2,4,3,5,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [7,2,4,3,6,5,1,8] => [7,6,4,3,5,2,1,8] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [8,2,4,3,6,5,7,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [8,2,4,3,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,6,4,5,1,7,8] => [6,2,5,4,3,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [6,2,5,4,3,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,6,4,5,7,1,8] => [7,2,5,4,3,6,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [7,2,6,4,5,3,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [8,2,7,4,5,6,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [7,2,6,4,5,3,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [8,2,6,4,5,3,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [8,2,7,4,6,5,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [6,2,5,4,3,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [7,2,5,4,3,6,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [7,2,6,5,4,3,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [8,2,7,5,4,6,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => [8,2,7,5,4,6,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [7,2,6,5,4,3,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [8,2,6,5,4,3,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,2,6,5,4,3,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [8,2,6,5,4,3,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,8,6,5,7,4,1] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [4,3,2,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [4,3,2,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [5,3,2,4,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => [5,3,2,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [5,3,2,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [6,4,3,2,5,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => [6,4,3,2,5,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [7,4,3,2,6,5,1,8] => [7,6,4,3,5,2,1,8] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [6,5,3,4,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [6,5,3,4,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [7,5,3,4,2,6,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [7,6,3,4,5,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [8,6,3,4,5,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [8,7,3,4,5,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [8,7,3,4,5,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => [7,6,3,4,5,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => [8,7,3,4,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => [6,5,3,4,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [6,5,3,4,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => [7,5,3,4,2,6,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [7,6,3,5,4,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [8,7,3,5,4,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => [8,7,3,5,4,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [7,6,3,5,4,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [7,6,3,5,4,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => [6,4,3,2,5,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [6,4,3,2,5,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => [7,4,3,2,6,5,1,8] => [7,6,4,3,5,2,1,8] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [8,4,3,2,6,5,7,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,2,4,3,8,7,6,1] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [7,6,4,3,5,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [8,6,4,3,5,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8,2,4,3,7,6,5,1] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2,4,5,3,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8,2,4,5,6,3,7,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [7,5,4,3,2,6,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8,2,5,4,7,6,3,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,6,5,4,3,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [4,3,2,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [4,3,2,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [5,3,2,4,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [5,3,2,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [5,3,2,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [7,3,2,5,4,6,1,8] => [7,6,3,5,4,2,1,8] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [6,4,3,2,5,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [6,4,3,2,5,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [7,4,3,2,6,5,1,8] => [7,6,4,3,5,2,1,8] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => [7,5,3,4,2,6,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [8,6,3,4,5,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [8,7,3,4,5,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => [8,7,3,4,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [8,7,3,4,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => [8,7,3,4,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => [6,5,3,4,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [6,5,3,4,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [7,5,3,4,2,6,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [7,6,3,5,4,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [8,7,3,5,4,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [8,6,3,5,4,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [6,4,3,2,5,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [7,4,3,2,6,5,1,8] => [7,6,4,3,5,2,1,8] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [8,4,3,2,6,5,7,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [8,7,4,3,5,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,2,6,5,1,8] => [7,6,4,3,5,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [8,6,4,3,5,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,3,4,5,2,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [7,5,4,3,2,6,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [7,5,4,3,2,6,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8,3,6,4,5,7,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [6,4,3,2,5,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [6,4,3,2,5,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [7,4,3,2,6,5,1,8] => [7,6,4,3,5,2,1,8] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [8,4,3,2,6,5,7,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [8,6,4,3,5,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [8,7,4,3,5,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [8,7,4,3,5,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => [7,6,4,3,5,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [8,6,4,3,5,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8,6,3,5,4,7,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [7,5,4,3,2,6,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8,6,4,5,3,7,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,7,6,4,5,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 0
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,9,8,7,5,6,4,3,2] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,8,7,5,6,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,7,5,4,6,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,7,4,6,5,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 0
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,9,8,6,5,7,4,3,2] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9,8,5,7,6,4,3,2] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,10,9,8,6,7,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [1,11,10,9,8,7,6,5,4,3,2] => [1,11,10,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,9,8,5,6,7,4,3,2] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,10,9,8,6,5,7,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,10,9,8,5,6,7,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,9,8,5,4,6,7,3,2] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,10,9,6,5,8,7,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,9,8,4,5,6,7,3,2] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => 0
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,10,9,5,6,7,8,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => 1
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,4,5,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,9,5,4,6,7,8,3,2] => [1,9,8,7,5,6,4,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,10,9,8,6,7,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => 1
[] => [] => [] => [] => 0
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [9,2,8,7,6,5,4,3,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,9,4,3,5,6,7,8,1] => [9,8,4,3,5,6,7,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,9,4,5,6,7,8,3,1] => [9,8,7,4,5,6,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [9,7,6,5,4,3,2,8,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,8,6,5,7,4,3,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,8,7,5,6,4,3,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [9,2,8,7,6,5,4,3,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9,2,4,5,6,8,7,3,1] => [9,8,7,4,5,6,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [9,2,7,4,5,6,3,8,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9,2,7,6,5,4,3,8,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,2,8,7,6,5,4,3,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9,3,4,2,5,6,7,8,1] => [9,8,4,3,5,6,7,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => [9,8,7,4,5,6,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9,3,4,5,6,8,7,2,1] => [9,8,7,4,5,6,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9,3,7,6,5,4,8,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,3,8,7,6,5,4,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9,4,3,2,5,6,7,8,1] => [9,8,4,3,5,6,7,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [9,4,3,5,6,7,2,8,1] => [9,8,7,4,5,6,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [9,4,3,5,6,7,8,2,1] => [9,8,7,4,5,6,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [9,8,3,4,5,7,6,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9,8,3,5,7,6,4,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [9,8,3,6,5,4,7,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [9,8,3,7,6,5,4,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [9,8,4,3,5,6,7,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [9,8,4,3,6,7,5,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9,8,4,5,3,7,6,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9,8,4,5,7,6,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [8,7,4,6,5,3,2,9,1] => [9,7,6,5,4,3,2,8,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [9,8,4,6,5,7,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9,8,4,7,6,5,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [9,7,6,5,4,3,2,8,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,7,5,4,6,3,2,9,1] => [9,7,6,5,4,3,2,8,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [9,8,5,4,6,3,7,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [9,8,5,4,6,7,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,7,6,4,5,3,2,9,1] => [9,7,6,5,4,3,2,8,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9,8,7,4,5,6,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,8,7,4,6,5,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,7,6,5,4,3,2,8,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9,7,6,5,4,3,8,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [9,8,6,5,4,3,7,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [9,8,6,5,4,7,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9,8,7,5,4,6,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9,3,4,5,6,7,8,2] => [1,9,8,4,5,6,7,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9,4,5,6,7,8,3,2] => [1,9,8,7,5,6,4,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,10,3,4,5,6,7,8,9,2] => [1,10,9,4,5,6,7,8,3,2] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,10,4,5,6,7,8,9,3,2] => [1,10,9,8,5,6,7,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,10,9,8,7] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [2,1,6,5,4,3,10,9,8,7] => [2,1,6,5,4,3,10,9,8,7] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [2,1,8,7,6,5,4,3,10,9] => [2,1,8,7,6,5,4,3,10,9] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => [4,3,2,1,6,5,10,9,8,7] => [4,3,2,1,6,5,10,9,8,7] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [4,3,2,1,10,9,8,7,6,5] => [4,3,2,1,10,9,8,7,6,5] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,3,2,1,10,9,8,7] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [10,9,3,4,5,6,8,7,2,1] => [10,9,8,7,5,6,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10,9,4,3,5,6,7,8,2,1] => [10,9,8,7,5,6,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [10,9,8,5,7,6,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [10,9,8,6,5,7,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [10,9,8,4,5,7,6,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [10,9,8,5,4,6,7,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => 0
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,8,7,6,5,4,3,2,9,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,8,7,5,6,4,3,2,10,1] => [10,8,7,6,5,4,3,2,9,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,9,8,7,5,6,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,8,4,7,6,5,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,4,8,7,6,5,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,3,8,7,6,5,4,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,3,9,8,7,6,5,4,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,2,9,8,7,6,5,4,3,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,10,9,4,5,6,7,8,3,2] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,9,4,3,5,6,7,8,2] => [1,9,8,4,5,6,7,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [10,8,7,6,5,4,3,2,9,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [10,8,7,6,5,4,3,9,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [10,9,7,6,5,4,3,8,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [10,9,7,6,5,4,8,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [10,9,8,6,5,4,7,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => 3
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [10,9,8,5,4,7,6,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [10,7,6,5,4,3,2,9,8,1] => [10,9,7,6,5,4,3,8,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => [10,2,9,8,7,6,5,4,3,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,9,4,5,6,7,8,2] => [1,9,8,4,5,6,7,3,2] => [1,9,8,7,6,5,4,3,2] => 0
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10,3,2,9,8,7,6,5,4,1] => [10,9,3,8,7,6,5,4,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => [2,1,6,5,4,3,8,7,10,9] => [2,1,6,5,4,3,8,7,10,9] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,8,7,6,5,10,9] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,10,9,8,7] => 3
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,3,11,10,9,8,7,6,5,4,2] => [1,11,10,9,8,7,6,5,4,3,2] => [1,11,10,9,8,7,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,10,9,7] => [2,1,6,5,4,3,10,9,8,7] => [2,1,6,5,4,3,10,9,8,7] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,10,9,7] => [4,3,2,1,6,5,10,9,8,7] => [4,3,2,1,6,5,10,9,8,7] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,7,10,12,11,9] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,12,11,10,9] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5,10,12,11,9] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,8,7,6,5,12,11,10,9] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,7,10,12,11,9] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,6,5,4,3,8,7,12,11,10,9] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,10,9,7,12,11] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,6,5,4,3,10,9,8,7,12,11] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9,12,11] => [4,3,2,1,6,5,8,7,10,9,12,11] => [4,3,2,1,6,5,8,7,10,9,12,11] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,7,10,12,11,9] => [4,3,2,1,6,5,8,7,12,11,10,9] => [4,3,2,1,6,5,8,7,12,11,10,9] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5,8,10,9,7,12,11] => [4,3,2,1,6,5,10,9,8,7,12,11] => [4,3,2,1,6,5,10,9,8,7,12,11] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9,12,11] => [4,3,2,1,8,7,6,5,10,9,12,11] => [4,3,2,1,8,7,6,5,10,9,12,11] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5,10,12,11,9] => [4,3,2,1,8,7,6,5,12,11,10,9] => [4,3,2,1,8,7,6,5,12,11,10,9] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [10,9,6,5,4,3,8,7,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 0
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,2 10,3,1 31,8,3 98,27,6,1
F1=1
F2=1+q
F3=3+2 q
F4=10+3 q+q2
F5=31+8 q+3 q2
F6=98+27 q+6 q2+q3
Description
The number of isolated descents of a permutation.
A descent i is isolated if neither i+1 nor i−1 are descents. If a permutation has only isolated descents, then it is called primitive in [1].
A descent i is isolated if neither i+1 nor i−1 are descents. If a permutation has only isolated descents, then it is called primitive in [1].
Map
to non-crossing permutation
Description
Sends a Dyck path D with valley at positions {(i1,j1),…,(ik,jk)} to the unique non-crossing permutation π having descents {i1,…,ik} and whose inverse has descents {j1,…,jk}.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to n(n−1) minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to n(n−1) minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
Demazure product with inverse
Description
This map sends a permutation π to π−1⋆π where ⋆ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!