Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000706: Integer partitions ⟶ ℤ
Values
[1,1,0,1,0,0] => [2,1,3] => [1,1,0,0,1,0] => [2] => 1
[1,1,1,0,0,0] => [1,2,3] => [1,0,1,0,1,0] => [2,1] => 1
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => [2] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => [3] => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => [3,1] => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => [3] => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [3,2] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 1
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => [2] => 1
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => [2] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [4,2] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
>>> Load all 959 entries. <<<[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 1
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 1
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,1,2,8] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,1,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,1,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8,6,7,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,7,8,5,4,3,2,1,9] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,7,5,6,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8,6,5,7,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7,6,5,8,4,3,2,1,9] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [6,7,5,8,4,3,2,1,9] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8,5,6,7,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,5,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,4,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,2,1,5,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,2,1,6,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,6,4,3,2,1,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8,7,4,5,3,2,1,6,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8,7,6,3,4,2,1,5,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,3,1,4,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [7,8,2,3,4,5,1,6,9] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [8,7,5,3,1,2,4,6,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,1,4,5,6,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,3,1,2,4,5,6,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,1,2,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,6,9,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,2,1,3,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,3,2,1,4,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,2,1,3,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,1,5,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,3,2,1,4,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,4,3,2,1,6,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9,8,6,5,4,3,2,1,7,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,5,4,3,2,1,6,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,7,6,5,4,3,2,1,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [10,9,8,6,5,4,3,2,1,7,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,4,3,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,3,2,1] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,3,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,3,4,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,2,3,1] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,5,1] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,3,1,2] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [7,8,9,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,3,4,5,6,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [8,9,10,6,7,4,5,2,3,1] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,4,5,6,2,3,1] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,2,3,4,1] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,2,3,4,5,1] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,3,4,1,2] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,3,4,5,6,1,2] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,4,5,6,1,2,3] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,5,6,1,2,3,4] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,3,1] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,2,1,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,1,3,4] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,1,3,4,5] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,5,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,5,2,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,5,3,2,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,9,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [7,8,9,5,4,3,2,1,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,8,9,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,3,2,1,5] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,3,2,1,4] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,8,9,2,1,3] => [1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [5,6,7,4,8,9,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,1,4,5,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,9,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [7,6,8,9,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,3,4,2,1] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,7,9,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,6,9,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,8,10,7,6,5,4,3,2,1,11] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,2,1,4] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [8,7,9,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,3,4,1,2,5] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,3,2,1,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,8,7,6,5,4,3,2,1,9,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [8,9,10,4,5,6,1,2,3,7] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,4,1,5,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,1,5] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [9,8,10,6,7,4,5,2,3,1] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,1,4,5] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,1,4] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,10,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,3,1,2,4,6,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,4,5,1,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [8,7,9,10,5,6,2,1,3,4] => [1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,2,3,1,4,6,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [7,8,9,3,4,5,1,2,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
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Description
The product of the factorials of the multiplicities of an integer partition.
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
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
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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