Identifier
-
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000052: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1] => [1,0] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,0,1,0] => 0
[1,1,0,0] => [2,1] => [2,1] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0] => 0
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 0
[1,1,0,1,0,0] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0] => 0
[1,1,1,0,0,0] => [3,1,2] => [2,3,1] => [1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [1,6,3,4,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [1,5,6,3,4,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [1,6,3,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
>>> Load all 837 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [1,4,6,3,5,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => 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] => [1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [4,6,2,3,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [4,6,2,5,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [2,6,3,4,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [3,5,2,4,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [3,6,2,4,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [2,6,3,5,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [3,6,2,5,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[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] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [1,2,3,6,7,4,5] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [1,2,3,7,5,6,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [1,2,3,5,7,4,6] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[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] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[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] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [1,2,6,7,3,4,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [1,2,5,6,3,4,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [1,2,7,5,6,3,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [1,2,5,7,3,4,6] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [1,2,5,6,7,3,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [1,2,6,4,5,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [1,2,7,4,5,3,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [1,2,6,7,4,5,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [1,2,4,6,3,5,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [1,2,7,4,6,3,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [1,2,4,7,3,5,6] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [1,2,4,6,7,3,5] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [1,2,4,7,5,6,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [1,2,5,7,4,6,3] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [1,2,4,5,7,3,6] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[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] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[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] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 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] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[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] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [1,3,2,6,7,4,5] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [1,3,2,7,5,6,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [1,3,2,5,7,4,6] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [1,3,2,5,6,7,4] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [1,4,2,3,6,7,5] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [1,5,6,2,3,4,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [1,7,5,6,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [1,5,7,2,3,4,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [1,5,6,7,2,3,4] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [1,4,5,2,3,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [1,4,5,2,3,7,6] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [1,6,4,5,2,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [1,7,4,5,2,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [1,6,7,4,5,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [1,4,6,2,3,5,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [1,7,4,6,2,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [1,4,7,2,3,5,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [1,4,5,6,2,3,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [1,4,7,5,6,2,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [1,5,7,4,6,2,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [1,4,5,7,2,3,6] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [1,4,5,6,7,2,3] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [1,3,4,2,7,5,6] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [1,3,4,2,6,7,5] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [1,5,3,4,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [1,5,3,4,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [1,6,3,4,2,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [1,7,3,4,2,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [1,6,7,3,4,2,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [1,5,6,3,4,2,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [1,5,7,3,4,2,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [1,5,6,7,3,4,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [1,3,5,2,4,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [1,3,5,2,4,7,6] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [1,6,3,5,2,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [1,7,3,5,2,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [1,6,7,3,5,2,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [1,3,6,2,4,5,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [1,7,3,6,2,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [1,3,7,2,4,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [1,3,6,7,2,4,5] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [1,3,5,6,2,4,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [1,3,7,5,6,2,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [1,5,7,3,6,2,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => [1,3,5,7,2,4,6] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [1,3,5,6,7,2,4] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [1,3,4,5,2,7,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [1,3,6,4,5,2,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [1,3,7,4,5,2,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [1,3,6,7,4,5,2] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [1,4,6,3,5,2,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [1,7,4,6,3,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [1,4,7,3,5,2,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [1,4,6,7,3,5,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [1,3,4,6,2,5,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [1,3,7,4,6,2,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => [1,4,7,3,6,2,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => [1,3,4,7,2,5,6] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [1,3,4,6,7,2,5] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [1,3,4,7,5,6,2] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [1,3,5,7,4,6,2] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [1,4,5,7,3,6,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [1,3,4,5,7,2,6] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 4
[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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [2,1,3,4,6,7,5] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => [2,1,3,6,7,4,5] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [2,1,3,5,6,4,7] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => [2,1,3,7,5,6,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [2,1,3,5,7,4,6] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [2,1,3,5,6,7,4] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => [2,1,4,3,6,7,5] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [2,1,6,7,3,4,5] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => [2,1,5,6,3,4,7] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [2,1,7,5,6,3,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [2,1,5,7,3,4,6] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [2,1,5,6,7,3,4] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [2,1,4,5,3,6,7] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => [2,1,4,5,3,7,6] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => [2,1,6,4,5,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [2,1,7,4,5,3,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => [2,1,6,7,4,5,3] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [2,1,4,6,3,5,7] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [2,1,7,4,6,3,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [2,1,4,7,3,5,6] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => [2,1,4,6,7,3,5] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [2,1,4,5,6,3,7] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => [2,1,4,7,5,6,3] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => [2,1,5,7,4,6,3] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => [2,1,4,5,7,3,6] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [2,1,4,5,6,7,3] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [3,1,2,4,6,7,5] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [3,1,2,6,7,4,5] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [3,1,2,5,6,4,7] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [3,1,2,7,5,6,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [3,1,2,5,7,4,6] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [3,1,2,5,6,7,4] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [4,1,2,3,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [5,6,1,2,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [5,7,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [4,5,1,2,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [4,5,1,2,3,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [6,4,5,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [7,4,5,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => [6,7,4,5,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [4,6,1,2,3,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [7,4,6,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [4,7,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [4,6,7,1,2,3,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => [4,7,5,6,1,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [5,7,4,6,1,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [4,5,7,1,2,3,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => [4,5,6,7,1,2,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [3,4,1,2,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => [3,4,1,2,5,7,6] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => [3,4,1,2,6,5,7] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [3,4,1,2,7,5,6] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => [3,4,1,2,6,7,5] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [5,3,4,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [5,3,4,1,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [6,3,4,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [7,3,4,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => [6,7,3,4,1,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => [5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => [7,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [5,7,3,4,1,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => [5,6,7,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [3,5,1,2,4,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [3,5,1,2,4,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [6,3,5,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [7,3,5,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [6,7,3,5,1,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [3,6,1,2,4,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [7,3,6,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [3,7,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [3,6,7,1,2,4,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => [3,5,6,1,2,4,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [3,7,5,6,1,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [5,7,3,6,1,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [3,5,7,1,2,4,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [3,5,6,7,1,2,4] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [3,4,5,1,2,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [3,4,5,1,2,7,6] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => [3,6,4,5,1,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => [3,7,4,5,1,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => [3,6,7,4,5,1,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [4,6,3,5,1,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [7,4,6,3,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [4,7,3,5,1,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => [4,6,7,3,5,1,2] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [3,4,6,1,2,5,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [3,7,4,6,1,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [4,7,3,6,1,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [3,4,7,1,2,5,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => [3,4,6,7,1,2,5] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [3,4,5,6,1,2,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => [3,4,7,5,6,1,2] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => [3,5,7,4,6,1,2] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => [4,5,7,3,6,1,2] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => [3,4,5,7,1,2,6] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => [3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [2,3,1,4,5,7,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [2,3,1,4,6,5,7] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [2,3,1,4,7,5,6] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => [2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [2,3,1,5,4,6,7] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => [2,3,1,5,4,7,6] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [2,3,1,6,4,5,7] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [2,3,1,7,4,5,6] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => [2,3,1,6,7,4,5] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [2,3,1,5,6,4,7] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => [2,3,1,7,5,6,4] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [2,3,1,5,7,4,6] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => [2,3,1,5,6,7,4] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [4,2,3,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => [4,2,3,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => [4,2,3,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [4,2,3,1,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => [4,2,3,1,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [5,2,3,1,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [5,2,3,1,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [6,2,3,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [7,2,3,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => [6,7,2,3,1,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => [5,6,2,3,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => [7,5,6,2,3,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [5,7,2,3,1,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => [5,6,7,2,3,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [4,5,2,3,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => [4,5,2,3,1,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => [7,4,5,2,3,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => [6,7,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [4,6,2,3,1,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [7,4,6,2,3,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => [4,7,2,3,1,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => [4,6,7,2,3,1,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => [4,5,6,2,3,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => [4,7,5,6,2,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => [5,7,4,6,2,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => [4,5,7,2,3,1,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => [4,5,6,7,2,3,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [2,4,1,3,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [2,4,1,3,5,7,6] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [2,4,1,3,6,5,7] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [2,4,1,3,7,5,6] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [2,4,1,3,6,7,5] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [5,2,4,1,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [5,2,4,1,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [6,2,4,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [7,2,4,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [6,7,2,4,1,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [5,6,2,4,1,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [7,5,6,2,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [5,7,2,4,1,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [5,6,7,2,4,1,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [2,5,1,3,4,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [2,5,1,3,4,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [6,2,5,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [7,2,5,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => [6,7,2,5,1,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [2,6,1,3,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [7,2,6,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [2,6,7,1,3,4,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [2,5,6,1,3,4,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [2,7,5,6,1,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [5,7,2,6,1,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [2,5,7,1,3,4,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => [2,5,6,7,1,3,4] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => [2,4,5,1,3,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [2,4,5,1,3,7,6] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [2,6,4,5,1,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [2,7,4,5,1,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => [2,6,7,4,5,1,3] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [4,6,2,5,1,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [7,4,6,2,5,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [4,7,2,5,1,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => [4,6,7,2,5,1,3] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => [2,4,6,1,3,5,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [2,7,4,6,1,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [4,7,2,6,1,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [2,4,7,1,3,5,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => [2,4,6,7,1,3,5] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => [2,4,5,6,1,3,7] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => [2,4,7,5,6,1,3] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [2,5,7,4,6,1,3] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [4,5,7,2,6,1,3] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,1,2,4,5] => [2,4,5,7,1,3,6] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6] => [2,4,5,6,7,1,3] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [2,3,4,1,6,5,7] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [2,3,4,1,7,5,6] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => [2,3,4,1,6,7,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [2,5,3,4,1,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => [2,5,3,4,1,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [2,6,3,4,1,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => [2,7,3,4,1,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => [2,6,7,3,4,1,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => [2,5,6,3,4,1,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => [2,7,5,6,3,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [2,5,7,3,4,1,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => [2,5,6,7,3,4,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [3,5,2,4,1,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => [3,5,2,4,1,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => [6,3,5,2,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [7,3,5,2,4,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => [6,7,3,5,2,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [3,6,2,4,1,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => [7,3,6,2,4,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [3,7,2,4,1,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => [3,6,7,2,4,1,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => [3,5,6,2,4,1,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => [3,7,5,6,2,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => [5,7,3,6,2,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => [3,5,7,2,4,1,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [3,5,6,7,2,4,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => [2,3,5,1,4,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [2,3,5,1,4,7,6] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [2,6,3,5,1,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => [2,7,3,5,1,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => [2,6,7,3,5,1,4] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [3,6,2,5,1,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [7,3,6,2,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [3,7,2,5,1,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => [3,6,7,2,5,1,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => [2,3,6,1,4,5,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [2,7,3,6,1,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [3,7,2,6,1,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => [2,3,7,1,4,5,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6] => [2,3,6,7,1,4,5] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => [2,3,5,6,1,4,7] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => [2,3,7,5,6,1,4] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [2,5,7,3,6,1,4] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => [3,5,7,2,6,1,4] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,1,2,3,5] => [2,3,5,7,1,4,6] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6] => [2,3,5,6,7,1,4] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [2,3,6,4,5,1,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => [2,3,7,4,5,1,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => [2,3,6,7,4,5,1] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => [2,4,6,3,5,1,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => [2,7,4,6,3,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => [2,4,7,3,5,1,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => [2,4,6,7,3,5,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [3,4,6,2,5,1,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => [3,7,4,6,2,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => [4,7,3,6,2,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [3,4,7,2,5,1,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => [3,4,6,7,2,5,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => [2,3,4,6,1,5,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => [2,3,7,4,6,1,5] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,1,2,7,3,4] => [2,4,7,3,6,1,5] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [3,4,7,2,6,1,5] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => [2,3,4,7,1,5,6] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6] => [2,3,4,6,7,1,5] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => [2,3,4,7,5,6,1] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => [2,3,5,7,4,6,1] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => [2,4,5,7,3,6,1] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1,7,2,3,4,5] => [3,4,5,7,2,6,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => [2,3,4,5,7,1,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,7,8,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,3,4,6,7,8,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,3,4,5,6,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,3,6,7,8,4] => [1,2,8,4,5,3,6,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,7,8,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [1,4,2,3,8,5,6,7] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,2,6] => [1,6,8,2,3,4,5,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,2,8,5] => [1,8,5,7,2,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,2,6,7,4,8] => [1,7,4,5,2,3,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,6,8,4,7] => [1,7,8,4,5,2,3,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,8,6] => [1,8,6,7,4,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => [1,7,4,6,2,3,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => [1,5,8,4,6,2,3,7] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => [1,3,4,2,5,7,8,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,2,5,6,7,3,8] => [1,7,3,4,2,5,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,8,3] => [1,8,3,4,2,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [1,8,6,7,3,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,2,5,7,8,3,6] => [1,6,8,3,4,2,5,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,2,5,8,3,6,7] => [1,6,7,8,3,4,2,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,6,3,5,7,8] => [1,5,6,3,4,2,7,8] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5,8] => [1,7,5,6,3,4,2,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,8,5,7] => [1,7,8,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,8,5,6] => [1,6,8,5,7,3,4,2] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,2,6,3,7,8] => [1,6,3,5,2,4,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,8,7] => [1,6,3,5,2,4,8,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,8,6] => [1,8,6,7,3,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,2,7,3,8] => [1,7,3,6,2,4,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,2,7,3,8,5] => [1,8,5,7,3,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4,8] => [1,7,4,6,3,5,2,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,8,4,5] => [1,5,8,4,7,3,6,2] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [1,3,4,5,6,8,2,7] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 4
[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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => [2,1,3,4,6,7,8,5] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => [2,1,3,5,6,7,8,4] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,5,6,7] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,8,5,6] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,8,6,7,5] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,6,3,4,5,8,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,8,3,4,5,6,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,3,8,6] => [2,1,8,6,7,3,4,5] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,3,6,7] => [2,1,6,7,8,3,4,5] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,5,8,7] => [2,1,5,6,3,4,8,7] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,3,8,5,7] => [2,1,7,8,5,6,3,4] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7] => [2,1,6,4,5,3,8,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,8,6] => [2,1,8,6,7,4,5,3] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,3,8,4,6] => [2,1,6,8,4,7,3,5] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,8,5] => [2,1,8,5,7,4,6,3] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,3,7,8,4,5] => [2,1,5,8,4,6,3,7] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [2,1,4,5,6,7,8,3] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [3,1,2,7,4,5,6,8] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,1,2,3,8,5,6,7] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,5,7] => [4,1,2,3,7,8,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,8,6] => [4,1,2,3,8,6,7,5] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,1,2,3,4,5,8,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7] => [7,8,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,1,8,6] => [8,6,7,1,2,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,1,6] => [6,8,1,2,3,4,5,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,1,6,7] => [6,7,8,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,1,7,5,8] => [7,5,6,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,1,5] => [5,8,1,2,3,4,6,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,1,8,5,6] => [6,8,5,7,1,2,3,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,1,5,6,7] => [5,6,7,8,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,1,6,7,8,4] => [8,4,5,1,2,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,7,4,5,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,1,4] => [4,8,1,2,3,5,6,7] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,1,4,5,8,7] => [4,5,6,1,2,3,8,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => [5,8,4,6,1,2,3,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,1,4,8,5,6] => [4,6,8,5,7,1,2,3] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [3,4,1,2,6,5,8,7] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,1,3,6,7,8,5] => [3,4,1,2,8,5,6,7] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => [3,4,1,2,7,8,5,6] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => [3,4,1,2,8,6,7,5] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,1,5,6,3,8,7] => [6,3,4,1,2,5,8,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,3] => [8,3,4,1,2,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7] => [5,6,3,4,1,2,8,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5,8] => [7,5,6,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => [8,5,6,3,4,1,2,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7] => [7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,1,6,7,8,3,5] => [5,8,3,4,1,2,6,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,1,6,8,3,5,7] => [5,7,8,3,4,1,2,6] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,1,8,3,6,7] => [6,7,8,3,5,1,2,4] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,1,8,3] => [8,3,7,1,2,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,1,3] => [3,8,1,2,4,5,6,7] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [3,7,8,5,6,1,2,4] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,1,8,3,5,7] => [5,7,8,3,6,1,2,4] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,1,8,3,5] => [5,8,3,7,1,2,4,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,1,6,7,3,4,8] => [4,7,3,5,1,2,6,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => [8,4,7,3,5,1,2,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,1,7,3,4,8,6] => [4,8,6,7,3,5,1,2] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,5,7,1,8,3,4,6] => [4,6,8,3,7,1,2,5] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,6,1,3,4,5,7,8] => [3,4,5,6,1,2,7,8] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,6,1,3,7,4,8,5] => [3,8,5,7,4,6,1,2] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,6,1,7,3,8,4,5] => [5,8,4,7,3,6,1,2] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,1,3,4,5,6,8] => [3,4,5,6,7,1,2,8] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [3,4,5,6,8,1,2,7] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => [2,3,1,4,5,7,8,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7] => [4,2,3,1,6,5,8,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,2,6,7,8,5] => [4,2,3,1,8,5,6,7] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,2,6,8,5,7] => [4,2,3,1,7,8,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => [4,2,3,1,8,6,7,5] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,2] => [8,2,3,1,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,4,6,8,2,5,7] => [5,7,8,2,3,1,4,6] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7] => [6,4,5,2,3,1,8,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,6,8] => [6,7,4,5,2,3,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,7,4,5,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,8,4,6,7] => [6,7,8,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,1,5,6,2,8,4,7] => [7,8,4,6,2,3,1,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,1,5,7,2,4,8,6] => [4,8,6,7,2,3,1,5] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,1,5,7,2,8,4,6] => [6,8,4,7,2,3,1,5] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,6,2,4,5,8,7] => [4,5,6,2,3,1,8,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,7,4,5,8] => [5,7,4,6,2,3,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,8,5] => [8,5,7,4,6,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8] => [2,4,1,3,5,6,7,8] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,2] => [8,2,4,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,1,5,8,2,6,7] => [6,7,8,2,4,1,3,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,1,2] => [2,8,1,3,4,5,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,1,7,2,8,5] => [8,5,7,2,6,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,1,2,8,5] => [2,8,5,7,1,3,4,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,1,8,2,5] => [5,8,2,7,1,3,4,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,1,2,6,8,4,7] => [2,7,8,4,5,1,3,6] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,1,6,2,4,8,7] => [4,6,2,5,1,3,8,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,8,4,6] => [6,8,4,7,2,5,1,3] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,1,7,8,2,4,6] => [4,6,8,2,5,1,3,7] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,1,7,2,8,4] => [8,4,7,2,6,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [4,8,2,6,1,3,5,7] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,5,6,1,8,2,4,7] => [4,7,8,2,6,1,3,5] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,6,1,7,2,4,8,5] => [4,8,5,7,2,6,1,3] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,6,1,7,2,8,4,5] => [5,8,4,7,2,6,1,3] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,1,7,8,2,4,5] => [4,5,8,2,6,1,3,7] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,3] => [2,8,3,4,1,5,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,1,2,6,3,8,5,7] => [2,7,8,5,6,3,4,1] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,1,2,6,7,3,8,5] => [2,8,5,7,3,4,1,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7] => [6,3,5,2,4,1,8,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,2,6,8,3,7] => [7,8,3,5,2,4,1,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,8,6] => [8,6,7,3,5,2,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,2,7,8,3,6] => [6,8,3,5,2,4,1,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,5,6,8,2,3,7] => [3,7,8,2,4,1,5,6] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,5,7,2,8,3,6] => [6,8,3,7,2,4,1,5] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,1,6,2,3,7,8,5] => [3,8,5,6,2,4,1,7] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5] => [8,5,7,3,6,2,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,8,3,5,6] => [5,6,8,3,7,2,4,1] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [2,6,3,5,1,4,8,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3,8] => [7,3,6,2,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,8,3,7] => [7,8,3,6,2,5,1,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,1,7,2,3,8,6] => [3,8,6,7,2,5,1,4] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,8,3,6] => [6,8,3,7,2,5,1,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => [2,7,8,3,6,1,4,5] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,5,6,1,7,2,3,8] => [3,7,2,6,1,4,5,8] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,1,8,2,3] => [3,8,2,7,1,4,5,6] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8] => [2,3,4,5,1,6,7,8] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,4,6,8,7] => [2,3,4,5,1,6,8,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,6,2,3,8,4,7] => [3,7,8,4,6,2,5,1] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,8,4] => [8,4,7,3,6,2,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,8,3,4,6] => [4,6,8,3,7,2,5,1] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,7,8] => [2,3,4,5,6,1,7,8] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => [2,3,4,5,6,1,8,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [2,3,4,5,8,1,6,7] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [2,3,4,5,6,7,1,8] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,8,6] => [2,3,4,5,8,6,7,1] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [3,4,5,6,8,2,7,1] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [2,3,4,5,6,8,1,7] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => [2,3,4,5,6,7,8,1,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => [2,3,4,5,6,7,8,9,1,10] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,3,4,5,6,7,9,2,8] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,1,3,4,5,6,7,9] => [3,4,5,6,7,8,1,2,9] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => [2,3,4,5,6,7,1,9,8] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [2,1,4,5,6,7,8,9,3] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9] => [2,3,4,5,6,7,1,8,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,1,8] => [8,9,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,1,7] => [7,9,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,1,3] => [3,9,1,2,4,5,6,7,8] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [3,4,5,6,7,8,9,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,3,1,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,1,2] => [2,9,1,3,4,5,6,7,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [2,3,4,5,6,7,9,1,8] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,3,4,5,6,7,8] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,8,9,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,3,4,5,6,7,8,9] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,3,1,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,1,9] => [9,10,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [3,4,5,6,7,8,9,10,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 7
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,10,1,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,8,5,7,9] => [7,8,5,6,3,4,1,2,9] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,10,7,9] => [9,10,7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [2,10,1,3,4,5,6,7,8,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,11,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
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:
4,1 9,4,1 21,15,5,1 51,50,24,6,1 127,161,98,35,7,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 9 + 4\ q + q^{2}$
$F_{5} = 21 + 15\ q + 5\ q^{2} + q^{3}$
$F_{6} = 51 + 50\ q + 24\ q^{2} + 6\ q^{3} + q^{4}$
$F_{7} = 127 + 161\ q + 98\ q^{2} + 35\ q^{3} + 7\ q^{4} + q^{5}$
Description
The number of valleys of a Dyck path not on the x-axis.
That is, the number of valleys of nonminimal height. This corresponds to the number of -1's in an inclusion of Dyck paths into alternating sign matrices.
That is, the number of valleys of nonminimal height. This corresponds to the number of -1's in an inclusion of Dyck paths into alternating sign matrices.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
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!