Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000340: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1] => [1,0] => 0
[1,0,1,0] => [2,1] => [1,2] => [1,0,1,0] => 0
[1,1,0,0] => [1,2] => [2,1] => [1,1,0,0] => 1
[1,0,1,0,1,0] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0] => 1
[1,1,0,0,1,0] => [3,1,2] => [1,3,2] => [1,0,1,1,0,0] => 1
[1,1,0,1,0,0] => [2,1,3] => [3,2,1] => [1,1,1,0,0,0] => 1
[1,1,1,0,0,0] => [1,2,3] => [2,3,1] => [1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [4,3,1,2] => [1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [4,1,3,2] => [1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [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] => [4,5,3,2,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [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] => [5,2,1,3,4] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [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] => [5,6,4,3,2,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [5,6,1,4,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
>>> Load all 886 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [5,6,4,1,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [5,4,6,1,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [4,5,6,1,3,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [5,6,4,3,2,1] => [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] => [6,3,4,2,1,5] => [1,5,6,4,3,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [5,6,3,4,2,1] => [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] => [6,3,2,4,1,5] => [1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [5,6,1,3,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [1,6,5,3,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [5,6,4,2,3,1] => [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] => [6,3,4,1,2,5] => [1,5,6,3,4,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [5,6,3,2,4,1] => [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] => [6,3,2,1,4,5] => [1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [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] => [6,7,5,4,3,2,1] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [1,2,7,3,4,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [7,1,6,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [1,7,6,2,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [6,7,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [6,5,7,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [1,2,3,7,4,5,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [7,1,2,6,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [7,6,1,5,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [6,7,1,5,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [1,2,7,6,3,4,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [7,1,6,5,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [1,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [6,7,5,4,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [1,6,7,5,2,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [7,5,6,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [6,5,7,4,1,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [1,2,6,7,3,4,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [7,1,5,6,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [1,7,5,6,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [6,7,4,5,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [1,6,5,7,2,3,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [7,5,4,6,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [6,5,4,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [5,6,4,7,1,2,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [1,5,6,7,2,3,4] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [7,4,5,6,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [6,4,5,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [5,4,6,7,1,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [4,5,6,7,1,2,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [1,2,3,4,7,5,6] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [7,1,2,3,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [7,6,1,2,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [6,7,1,2,5,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [1,2,7,3,6,4,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [7,1,6,2,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [1,7,6,2,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [7,6,5,1,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [6,7,5,1,4,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [7,5,6,1,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [6,5,7,1,4,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [5,6,7,1,4,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [1,2,3,7,6,4,5] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [7,1,2,6,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [1,7,2,6,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [7,6,1,5,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [6,7,1,5,4,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [1,2,7,6,5,3,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [7,1,6,5,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [1,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [1,6,7,5,4,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [7,5,6,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [6,5,7,4,3,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [5,6,7,4,3,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [1,2,6,7,5,3,4] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [7,1,5,6,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [1,7,5,6,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [7,6,4,5,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [6,7,4,5,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [1,6,5,7,4,2,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [7,5,4,6,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [6,5,4,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [5,6,4,7,3,1,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [1,5,6,7,4,2,3] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [7,4,5,6,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [6,4,5,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [5,4,6,7,3,1,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [4,5,6,7,3,1,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [1,2,3,6,7,4,5] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [7,1,2,5,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [7,6,1,4,5,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [6,7,1,4,5,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [1,2,7,5,6,3,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [7,1,6,4,5,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [1,7,6,4,5,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [7,6,5,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [6,7,5,3,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [1,6,7,4,5,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [7,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [6,5,7,3,4,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [5,6,7,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [1,2,6,5,7,3,4] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [7,1,5,4,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [1,7,5,4,6,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [7,6,4,3,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [1,6,5,4,7,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [7,5,4,3,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [6,5,4,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [5,6,4,3,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [1,5,6,4,7,2,3] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [7,4,5,3,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [6,4,5,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [5,4,6,3,7,1,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [4,5,6,3,7,1,2] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [1,2,5,6,7,3,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [7,1,4,5,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [1,7,4,5,6,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [7,6,3,4,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [6,7,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [1,6,4,5,7,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [7,5,3,4,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [6,5,3,4,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [5,6,3,4,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [1,5,4,6,7,2,3] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [7,4,3,5,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [6,4,3,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [5,4,3,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [4,5,3,6,7,1,2] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [1,4,5,6,7,2,3] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [7,3,4,5,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [6,3,4,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [5,3,4,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [4,3,5,6,7,1,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [7,1,2,3,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [7,6,1,2,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [6,7,1,2,3,5,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [1,2,7,3,4,6,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [7,1,6,2,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [1,7,6,2,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [7,6,5,1,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [6,7,5,1,2,4,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [7,5,6,1,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [6,5,7,1,2,4,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [5,6,7,1,2,4,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [1,2,3,7,4,6,5] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [7,1,2,6,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [7,6,1,5,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [6,7,1,5,2,4,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [1,2,7,6,3,5,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [7,1,6,5,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [1,7,6,5,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [7,6,5,4,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [6,7,5,4,1,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [1,6,7,5,2,4,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [7,5,6,4,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [6,5,7,4,1,3,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [5,6,7,4,1,3,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [1,2,6,7,3,5,4] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [7,1,5,6,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [1,7,5,6,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [7,6,4,5,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [6,7,4,5,1,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [1,6,5,7,2,4,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [7,5,4,6,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [6,5,4,7,1,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [5,6,4,7,1,3,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [1,5,6,7,2,4,3] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [7,4,5,6,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [6,4,5,7,1,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [5,4,6,7,1,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [4,5,6,7,1,3,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [1,2,3,4,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [7,1,2,3,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [1,7,2,3,6,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [7,6,1,2,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [6,7,1,2,5,4,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [1,2,7,3,6,5,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [7,1,6,2,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [1,7,6,2,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [7,6,5,1,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [6,7,5,1,4,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [1,6,7,2,5,4,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [7,5,6,1,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [6,5,7,1,4,3,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [5,6,7,1,4,3,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [7,1,2,6,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [1,7,2,6,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [7,6,1,5,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [6,7,1,5,4,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [7,1,6,5,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [6,7,5,4,3,2,1] => [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] => [7,4,5,3,2,1,6] => [1,6,7,5,4,3,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [7,5,6,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [1,2,6,7,5,4,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [7,1,5,6,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [1,7,5,6,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [7,6,4,5,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [6,7,4,5,3,2,1] => [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] => [7,4,3,5,2,1,6] => [1,6,5,7,4,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [7,5,4,6,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [6,5,4,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [5,6,4,7,3,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [1,5,6,7,4,3,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [7,4,5,6,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [6,4,5,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [5,4,6,7,3,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [4,5,6,7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [1,2,3,6,7,5,4] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [7,1,2,5,6,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [1,7,2,5,6,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [7,6,1,4,5,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [6,7,1,4,5,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [1,2,7,5,6,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [7,1,6,4,5,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [7,6,5,3,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [6,7,5,3,4,2,1] => [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] => [7,4,5,2,3,1,6] => [1,6,7,4,5,3,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [7,5,6,3,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [6,5,7,3,4,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [5,6,7,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [1,2,6,5,7,4,3] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [7,1,5,4,6,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [1,7,5,4,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [7,6,4,3,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [6,7,4,3,5,2,1] => [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] => [7,4,3,2,5,1,6] => [1,6,5,4,7,3,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [7,5,4,3,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [6,5,4,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [5,6,4,3,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [1,5,6,4,7,3,2] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [7,4,5,3,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [6,4,5,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [5,4,6,3,7,2,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [4,5,6,3,7,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [1,2,5,6,7,4,3] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [7,1,4,5,6,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [1,7,4,5,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [7,6,3,4,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [6,7,3,4,5,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [1,6,4,5,7,3,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [7,5,3,4,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [6,5,3,4,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [5,6,3,4,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [1,5,4,6,7,3,2] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [7,4,3,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [6,4,3,5,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [5,4,3,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [4,5,3,6,7,2,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [1,4,5,6,7,3,2] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [7,3,4,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [6,3,4,5,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [5,3,4,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [4,3,5,6,7,2,1] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [3,4,5,6,7,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [7,1,2,3,5,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [7,6,1,2,4,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [6,7,1,2,4,5,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [1,2,7,3,5,6,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [7,1,6,2,4,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [1,7,6,2,4,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [7,6,5,1,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [6,7,5,1,3,4,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [1,6,7,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [7,5,6,1,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [6,5,7,1,3,4,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [5,6,7,1,3,4,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [1,2,3,7,5,6,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [7,1,2,6,4,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [1,7,2,6,4,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [7,6,1,5,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [6,7,1,5,3,4,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [1,2,7,6,4,5,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [7,1,6,5,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [1,7,6,5,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [6,7,5,4,2,3,1] => [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] => [7,4,5,3,1,2,6] => [1,6,7,5,3,4,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [7,5,6,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [6,5,7,4,2,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [5,6,7,4,2,3,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [1,2,6,7,4,5,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [7,1,5,6,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [7,6,4,5,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [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] => [7,4,3,5,1,2,6] => [1,6,5,7,3,4,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [7,5,4,6,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [6,5,4,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [5,6,4,7,2,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,5,6,7,3,4,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [7,4,5,6,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [6,4,5,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [5,4,6,7,2,3,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [4,5,6,7,2,3,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [1,2,3,6,5,7,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [7,1,2,5,4,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [1,7,2,5,4,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [7,6,1,4,3,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [6,7,1,4,3,5,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [1,2,7,5,4,6,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [7,1,6,4,3,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [1,7,6,4,3,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [7,6,5,3,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [6,7,5,3,2,4,1] => [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] => [7,4,5,2,1,3,6] => [1,6,7,4,3,5,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [7,5,6,3,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [6,5,7,3,2,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [5,6,7,3,2,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [1,2,6,5,4,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [7,1,5,4,3,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [1,7,5,4,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [7,6,4,3,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [6,7,4,3,2,5,1] => [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] => [7,4,3,2,1,5,6] => [1,6,5,4,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [7,5,4,3,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [6,5,4,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [5,6,4,3,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [1,5,6,4,3,7,2] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [7,4,5,3,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [6,4,5,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [5,4,6,3,2,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [4,5,6,3,2,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [1,2,5,6,4,7,3] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [7,1,4,5,3,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [1,7,4,5,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [7,6,3,4,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [6,7,3,4,2,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [1,6,4,5,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [7,5,3,4,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [6,5,3,4,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [5,6,3,4,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [1,5,4,6,3,7,2] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [7,4,3,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [6,4,3,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [5,4,3,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [4,5,3,6,2,7,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [1,4,5,6,3,7,2] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [7,3,4,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [6,3,4,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [5,3,4,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [4,3,5,6,2,7,1] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [3,4,5,6,2,7,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [7,1,2,4,5,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [1,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [7,6,1,3,4,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [6,7,1,3,4,5,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [1,2,7,4,5,6,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [7,1,6,3,4,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [1,7,6,3,4,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [7,6,5,2,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [6,7,5,2,3,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [1,6,7,3,4,5,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [7,5,6,2,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [6,5,7,2,3,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [5,6,7,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [1,2,6,4,5,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [7,1,5,3,4,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [1,7,5,3,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [7,6,4,2,3,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [6,7,4,2,3,5,1] => [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] => [7,4,3,1,2,5,6] => [1,6,5,3,4,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [7,5,4,2,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [6,5,4,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [5,6,4,2,3,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [1,5,6,3,4,7,2] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [7,4,5,2,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [6,4,5,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [5,4,6,2,3,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [4,5,6,2,3,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [1,2,5,4,6,7,3] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [7,1,4,3,5,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [1,7,4,3,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [7,6,3,2,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [6,7,3,2,4,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [1,6,4,3,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [7,5,3,2,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [6,5,3,2,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [5,6,3,2,4,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [1,5,4,3,6,7,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [7,4,3,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [6,4,3,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [5,4,3,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [4,5,3,2,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [1,4,5,3,6,7,2] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [7,3,4,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [6,3,4,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [5,3,4,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [4,3,5,2,6,7,1] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [3,4,5,2,6,7,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [7,1,3,4,5,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [1,7,3,4,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [7,6,2,3,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [6,7,2,3,4,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [1,6,3,4,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [7,5,2,3,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [6,5,2,3,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [5,6,2,3,4,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [1,5,3,4,6,7,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [7,4,2,3,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [6,4,2,3,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [5,4,2,3,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [4,5,2,3,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [1,4,3,5,6,7,2] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [7,3,2,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [6,3,2,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [5,3,2,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [4,3,2,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,4,2,5,6,7,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [7,2,3,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [6,2,3,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [5,2,3,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [4,2,3,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [3,2,4,5,6,7,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [1,2,8,3,4,5,6,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [1,8,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [1,7,8,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [1,2,3,8,4,5,6,7] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => [1,2,8,7,3,4,5,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [1,8,7,6,2,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [1,7,8,6,2,3,4,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [1,2,7,8,3,4,5,6] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [1,8,6,7,2,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,2,1] => [1,7,6,8,2,3,4,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [1,6,7,8,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [1,2,3,4,8,5,6,7] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [1,2,8,3,7,4,5,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [1,2,3,8,7,4,5,6] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [1,8,2,7,6,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [1,2,8,7,6,3,4,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [1,8,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => [1,2,7,8,6,3,4,5] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,7,2,1] => [1,8,6,7,5,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [1,2,3,7,8,4,5,6] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [1,2,7,6,8,3,4,5] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [1,8,6,5,7,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [1,7,6,5,8,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [1,2,6,7,8,3,4,5] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [1,6,5,7,8,2,3,4] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [1,5,6,7,8,2,3,4] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [1,2,3,4,5,8,6,7] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [1,8,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [1,7,8,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [1,2,3,8,4,7,5,6] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [1,2,7,8,3,6,4,5] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [1,8,6,7,2,5,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [1,6,7,8,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [1,2,3,4,8,7,5,6] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [1,8,2,3,7,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [1,2,8,3,7,6,4,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [1,8,7,2,6,5,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [1,2,3,8,7,6,4,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [1,2,8,7,6,5,3,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [1,8,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => [1,7,8,6,5,4,2,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => [1,8,6,7,5,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [1,7,6,8,5,4,2,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [1,2,3,7,8,6,4,5] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [1,2,8,6,7,5,3,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => [1,8,7,5,6,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [1,7,8,5,6,4,2,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [1,7,6,5,8,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [1,6,7,5,8,4,2,3] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [1,8,5,6,7,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => [1,5,6,7,8,4,2,3] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [1,2,3,4,7,8,5,6] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [1,2,8,3,6,7,4,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [1,8,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [1,7,8,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,5,1] => [1,2,3,8,6,7,4,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,5,1] => [1,8,2,7,5,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => [1,2,8,7,5,6,3,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [1,8,7,6,4,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,7,1] => [1,8,6,7,4,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [1,2,3,7,6,8,4,5] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [1,8,2,6,5,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [1,2,8,6,5,7,3,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [1,8,7,5,4,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [1,2,7,6,5,8,3,4] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [1,7,6,5,4,8,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [1,6,7,5,4,8,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [1,7,5,6,4,8,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [1,5,6,7,4,8,2,3] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [1,2,3,6,7,8,4,5] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [1,8,2,5,6,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [1,8,6,4,5,7,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [1,2,5,6,7,8,3,4] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,7,1] => [1,7,4,5,6,8,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [1,6,4,5,7,8,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [1,5,4,6,7,8,2,3] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [1,4,5,6,7,8,2,3] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,8,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [1,2,8,3,4,5,7,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [1,8,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [1,2,3,8,4,5,7,6] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [1,2,8,7,3,4,6,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => [1,7,8,6,2,3,5,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [1,7,6,8,2,3,5,4] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [1,2,3,4,8,5,7,6] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [1,2,8,3,7,4,6,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [1,8,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [1,8,7,6,5,2,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [1,2,7,8,6,3,5,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [1,7,6,8,5,2,4,3] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [1,2,3,7,8,4,6,5] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => [1,2,7,6,8,3,5,4] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [1,7,6,5,8,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [1,2,6,7,8,3,5,4] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => [1,7,5,6,8,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [1,6,5,7,8,2,4,3] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [1,5,6,7,8,2,4,3] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [1,2,3,4,5,8,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [1,8,2,3,4,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [1,2,8,3,4,7,6,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => [1,8,7,2,3,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [1,2,3,8,4,7,6,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,1,3] => [1,8,2,7,3,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,1,3] => [1,8,7,6,2,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,1,3] => [1,2,7,8,3,6,5,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,1,3] => [1,8,6,7,2,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [1,2,3,4,8,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [1,8,2,3,7,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [1,2,8,3,7,6,5,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [1,8,7,2,6,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [1,2,3,8,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [1,8,2,7,6,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [1,2,8,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [1,8,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [1,7,8,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [1,2,7,8,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [1,8,6,7,5,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,1,7] => [1,7,6,8,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [1,6,7,8,5,4,3,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [1,2,3,7,8,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [1,2,8,6,7,5,4,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [1,8,7,5,6,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [1,7,8,5,6,4,3,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [1,6,7,5,8,4,3,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [1,2,6,7,8,5,4,3] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [1,6,5,7,8,4,3,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [1,5,6,7,8,4,3,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [1,2,3,4,7,8,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [1,8,2,3,6,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [1,8,7,2,5,6,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [1,2,3,8,6,7,5,4] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [1,8,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [1,7,8,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [1,2,7,8,5,6,4,3] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,1,7] => [1,8,6,7,4,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [1,6,7,8,4,5,3,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [1,2,3,7,6,8,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [1,2,8,6,5,7,4,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [1,8,7,5,4,6,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [1,2,7,6,5,8,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,1,7] => [1,8,6,5,4,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [1,7,6,5,4,8,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [1,2,3,6,7,8,5,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [1,8,2,5,6,7,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [1,8,7,4,5,6,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [1,8,6,4,5,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [1,7,6,4,5,8,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [1,8,5,4,6,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [1,2,5,6,7,8,4,3] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [1,7,4,5,6,8,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [1,5,4,6,7,8,3,2] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [1,4,5,6,7,8,3,2] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [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
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => [1,8,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [1,7,8,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [1,2,3,8,4,6,7,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => [1,8,7,6,2,4,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [1,2,7,8,3,5,6,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [1,6,7,8,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [1,2,3,4,8,6,7,5] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => [1,8,7,2,6,4,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [1,2,3,8,7,5,6,4] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [1,8,7,6,5,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [1,8,6,7,5,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [1,2,3,7,8,5,6,4] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [1,8,2,6,7,4,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [1,8,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [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
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [1,7,6,5,8,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => [1,6,7,5,8,3,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [1,2,6,7,8,4,5,3] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [1,8,5,6,7,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [1,7,5,6,8,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [1,6,5,7,8,3,4,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [1,5,6,7,8,3,4,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [1,2,3,4,7,6,8,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [1,2,8,3,6,5,7,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [1,8,7,2,5,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [1,2,3,8,6,5,7,4] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [1,8,2,7,5,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [1,8,7,6,4,3,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [1,6,7,8,4,3,5,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [1,2,3,7,6,5,8,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [1,2,8,6,5,4,7,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [1,8,7,5,4,3,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [1,7,8,5,4,3,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [1,2,7,6,5,4,8,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [1,8,6,5,4,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [1,7,6,5,4,3,8,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [1,6,7,5,4,3,8,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [1,8,5,6,4,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [1,6,5,7,4,3,8,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [1,2,3,6,7,5,8,4] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [1,8,2,5,6,4,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,1,4,6] => [1,2,8,5,6,4,7,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [1,8,7,4,5,3,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [1,7,8,4,5,3,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [1,8,6,4,5,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => [1,6,7,4,5,3,8,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [1,8,5,4,6,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [1,2,5,6,7,4,8,3] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [1,7,4,5,6,3,8,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [1,6,4,5,7,3,8,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [1,4,5,6,7,3,8,2] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [1,2,3,4,6,7,8,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [1,8,2,3,5,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [1,2,8,3,5,6,7,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [1,8,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [1,7,8,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [1,2,3,8,5,6,7,4] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [1,2,8,7,4,5,6,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [1,8,7,6,3,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [1,7,8,6,3,4,5,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => [1,2,7,8,4,5,6,3] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [1,8,6,7,3,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [1,6,7,8,3,4,5,2] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [1,2,3,7,5,6,8,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [1,2,8,6,4,5,7,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [1,7,8,5,3,4,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [1,2,6,7,4,5,8,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [1,7,5,6,3,4,8,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [1,5,6,7,3,4,8,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [1,2,3,6,5,7,8,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [1,8,2,5,4,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [1,2,8,5,4,6,7,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [1,8,7,4,3,5,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [1,7,8,4,3,5,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [1,2,7,5,4,6,8,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [1,8,6,4,3,5,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [1,7,6,4,3,5,8,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [1,2,6,5,4,7,8,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [1,8,5,4,3,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [1,7,5,4,3,6,8,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [1,6,5,4,3,7,8,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [1,2,3,5,6,7,8,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [1,8,2,4,5,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [1,2,8,4,5,6,7,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [1,8,7,3,4,5,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [1,7,8,3,4,5,6,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [1,2,7,4,5,6,8,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [1,7,6,3,4,5,8,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => [1,6,7,3,4,5,8,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [1,7,5,3,4,6,8,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [1,5,6,3,4,7,8,2] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [1,2,5,4,6,7,8,3] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [1,5,4,3,6,7,8,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [1,4,5,3,6,7,8,2] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [1,2,4,5,6,7,8,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [1,8,3,4,5,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [1,7,3,4,5,6,8,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [1,5,3,4,6,7,8,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [1,4,3,5,6,7,8,2] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [1,3,4,5,6,7,8,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,4 1,12,1 1,34,7 1,98,32,1 1,294,124,10
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 4\ q$
$F_{4} = 1 + 12\ q + q^{2}$
$F_{5} = 1 + 34\ q + 7\ q^{2}$
$F_{6} = 1 + 98\ q + 32\ q^{2} + q^{3}$
$F_{7} = 1 + 294\ q + 124\ q^{2} + 10\ q^{3}$
Description
The number of non-final maximal constant sub-paths of length greater than one.
This is the total number of occurrences of the patterns $110$ and $001$.
This is the total number of occurrences of the patterns $110$ and $001$.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
Lehmer code rotation
Description
Sends a permutation $\pi$ to the unique permutation $\tau$ (of the same length) such that every entry in the Lehmer code of $\tau$ is cyclically one larger than the Lehmer code of $\pi$.
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.
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