Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000668: Integer partitions ⟶ ℤ
Values
[1,1,1,0,0,0] => [1,2,3] => [1,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [2,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [2,1,1] => [1,1] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [2,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [2,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [3,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [3,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [3,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [3,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [3,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [3,1,1] => [1,1] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [3,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [3,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [3,1,1] => [1,1] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [2,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [3,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [3,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [3,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [3,1,1] => [1,1] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [3,1,1] => [1,1] => 1
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [3,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [3,1,1] => [1,1] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [3,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [4,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [4,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [4,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [4,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [4,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [4,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [4,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [4,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [4,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [4,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [4,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [4,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [4,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [4,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [4,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [4,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [4,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [4,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [4,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [4,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [4,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [4,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [4,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [4,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [4,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [4,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [4,1,1] => [1,1] => 1
>>> Load all 1994 entries. <<<[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [4,1,1] => [1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [4,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [4,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [4,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [4,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [4,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [4,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [4,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [4,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [4,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [5,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [5,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [5,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [5,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [5,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [5,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [5,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [5,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [5,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [5,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [5,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [5,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [5,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [5,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [5,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [5,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [5,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [5,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [5,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [5,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [5,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [5,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [5,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [5,1,1] => [1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [5,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [5,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [5,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [5,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [5,1,1,1] => [1,1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,7,2,1] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [5,1,1,1] => [1,1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,5,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,5,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,5,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,7,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [6,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [5,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,7,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [6,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [6,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [6,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [6,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [6,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [6,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [6,1,1] => [1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,1,3] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,1,3] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,1,3] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,1,3] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [6,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [6,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [6,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [6,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [6,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [6,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,1,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [6,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [6,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,1,5] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,1,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [6,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [6,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [6,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,1,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [6,1,1] => [1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [6,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [6,1,1] => [1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [6,1,1] => [1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,1,2,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [6,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [6,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,1,3,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [6,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [6,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [6,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [6,1,1] => [1,1] => 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] => [6,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [6,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,1,4,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [5,1,1,1] => [1,1,1] => 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] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [4,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,4,5,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,3,4,5,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,1,3,4,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,1,4,5,6,7,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [9,4,1,2,3,5,6,7,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,1,5,6,7,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [12,2,1,3,4,5,6,7,8,9,10,11] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [11,3,1,2,4,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [10,4,1,2,3,5,6,7,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,1,5,6,7,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,4,1,2,5,6,7,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,1,6,7,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,10,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,1,6,7,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [9,6,1,2,3,4,5,7,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,1,7,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [6,2,3,4,5,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,3,6,7,8,9,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [10,6,1,2,3,4,5,7,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,1,7,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,1,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,7,8,9,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [10,7,1,2,3,4,5,6,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,1,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,6,7,8,9,10,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,1,2] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,1,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,4,5,6,7,8,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [5,3,4,6,7,8,9,1,2] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [4,5,3,6,7,8,9,1,2] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [9,4,2,3,5,6,7,8,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [9,3,4,2,5,6,7,8,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [6,5,4,2,3,7,8,9,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,6,7,2,3,4,8,9,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,3,5,6,7,8,9,10,1,2] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [6,1,1,1] => [1,1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [6,1,1,1] => [1,1,1] => 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] => [6,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [6,5,7,8,4,3,2,1,9] => [6,1,1,1] => [1,1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1,9] => [6,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,8,2,1,9] => [7,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,8,2,1,9] => [6,1,1,1] => [1,1,1] => 1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,1,9] => [7,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,1,9] => [6,1,1,1] => [1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [7,1,1] => [1,1] => 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] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,3,4,5,6,8,1,2,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [7,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,4,3,2,1,8,9] => [6,1,1,1] => [1,1,1] => 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] => [6,1,1,1] => [1,1,1] => 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] => [6,1,1,1] => [1,1,1] => 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] => [6,1,1,1] => [1,1,1] => 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] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,1,8,9] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,7,1,8,9] => [5,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,2,3,4,5,6,1,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,1,2,8,9] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,6,5,3,2,1,4,8,9] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [6,7,4,3,2,1,5,8,9] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,1,7,8,9] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,2,6,1,7,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,1,2,6,8,9] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,2,7,8,9] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,5,3,2,1,6,7,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,1,6,7,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1,2,4,6,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1,2,6,7,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,1,2,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,1,3,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1,2,3,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1,2,4,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [8,1,1] => [1,1] => 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] => [6,1,1,1] => [1,1,1] => 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] => [8,1,1] => [1,1] => 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] => [7,1,1,1] => [1,1,1] => 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] => [8,1,1] => [1,1] => 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] => [5,1,1,1,1] => [1,1,1,1] => 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] => [8,1,1] => [1,1] => 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] => [9,1,1] => [1,1] => 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] => [6,1,1,1,1] => [1,1,1,1] => 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] => [7,1,1] => [1,1] => 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] => [8,1,1] => [1,1] => 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] => [9,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,9,1] => [7,1,1] => [1,1] => 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] => [8,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,9,1] => [6,1,1,1] => [1,1,1] => 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] => [8,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 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] => [9,1,1] => [1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,1,2,3,4,5,10] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,10,1] => [8,1,1] => [1,1] => 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] => [8,1,1] => [1,1] => 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] => [9,1,1] => [1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,10,1] => [7,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,9,6,7,5,4,3,2,1] => [7,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [9,6,7,8,5,4,3,2,1] => [7,1,1] => [1,1] => 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] => [6,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,3,2,1] => [6,1,1,1] => [1,1,1] => 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] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,3,2,1] => [7,1,1] => [1,1] => 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] => [5,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,2,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,2,3,1] => [7,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,3,1] => [5,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1,1] => [1,1,1,1,1] => 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] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,3,4,5,6,7,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,1,2] => [7,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,1,2] => [7,1,1] => [1,1] => 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] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,1,2] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => [7,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => [6,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => [5,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [9,8,3,4,5,6,7,1,2] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [8,9,3,4,5,6,7,1,2] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [7,1,1] => [1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [5,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [5,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [9,10,7,8,6,5,4,3,2,1] => [8,1,1] => [1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,4,3,2,1] => [7,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,2,1] => [6,1,1,1,1] => [1,1,1,1] => 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] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,2,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,3,1] => [6,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1,1,1] => [1,1,1,1,1] => 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] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,2,3,4,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,3,4,5,6,7,8,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,1,2] => [8,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => [8,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => [7,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => [6,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => [5,1,1,1,1,1] => [1,1,1,1,1] => 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] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [10,9,3,4,5,6,7,8,1,2] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [9,10,3,4,5,6,7,8,1,2] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,1,2] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => [8,1,1] => [1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => [7,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [7,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [6,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,6,7,5,4,3,2,1,8] => [7,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9,10] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,1,2,7,8,9,10] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1,8,9,10,11] => [6,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,7,5,4,3,2,1,8,9,10] => [6,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,1,2,8,9,10] => [6,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [7,6,5,4,3,1,2,8,9,10,11] => [6,1,1,1,1,1] => [1,1,1,1,1] => 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] => [7,1,1] => [1,1] => 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] => [8,1,1] => [1,1] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => [7,1,1] => [1,1] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 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] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [9,8,6,1,2,3,4,5,7] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,1,2,3,4,6] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,1,2,3,5] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,1,2,4] => [7,1,1] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [8,9,5,4,3,2,1,6,7] => [6,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,8,9,1,2] => [6,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,7,1,8] => [7,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,1,10] => [8,1,1] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,1,3] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [8,9,7,6,4,3,2,1,5] => [7,1,1] => [1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,5,1,2] => [7,1,1] => [1,1] => 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] => [8,1,1] => [1,1] => 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] => [8,1,1] => [1,1] => 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] => [8,1,1] => [1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,7,8,9,10,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,2,3,8,9,1] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,1,2,8] => [7,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,9,6,5,4,3,2,1,7] => [7,1,1] => [1,1] => 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] => [7,1,1] => [1,1] => 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] => [6,1,1,1] => [1,1,1] => 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] => [7,1,1,1] => [1,1,1] => 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] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7,6,8,9,5,4,3,2,1,10] => [7,1,1,1] => [1,1,1] => 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] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,6,5,8,9,4,3,2,1,10] => [7,1,1,1] => [1,1,1] => 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] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,8,9,3,2,1,10] => [7,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,8,9,1,2] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,8,9,2,1,10] => [7,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,1,10] => [7,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [7,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,1,6,7] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,1,2,3] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 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] => [8,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [9,7,8,5,4,3,2,1,6] => [7,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [9,6,7,4,5,2,3,1,8] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [9,10,6,7,4,5,2,3,1,8] => [5,1,1,1,1,1] => [1,1,1,1,1] => 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] => [8,1,1] => [1,1] => 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] => [8,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,9,3,2,1,10] => [8,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1,10] => [8,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [8,1,1] => [1,1] => 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] => [9,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,8,7,10,6,5,4,3,2,1,11] => [9,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,10,4,3,2,1,11] => [9,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,10,3,2,1,11] => [9,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,10,1,11] => [9,1,1] => [1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,1,10,11] => [9,1,1] => [1,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [6,5,7,4,8,3,9,2,10,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [10,8,6,4,2,1,3,5,7,9] => [6,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => [7,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,6,5,4,3,2,1,8,9] => [8,1,1] => [1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,5,4,3,2,1,6,7,8] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [6,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,1,10] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 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] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,4,3,2,1,5,9] => [8,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,10,7,6,5,4,3,2,1,8] => [8,1,1] => [1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,1,2,3,4,7] => [5,1,1,1,1] => [1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [8,9,4,5,6,3,2,1,7] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [11,10,1,2,3,4,5,6,7,8,9] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [9,8,4,1,2,3,5,6,7] => [4,1,1,1,1,1] => [1,1,1,1,1] => 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] => [9,1,1] => [1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,10,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [8,9,5,6,3,4,1,2,7] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [10,7,8,5,6,3,4,1,2,9] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,1,2,9] => [8,1,1] => [1,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,2,1,8] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,6,7,3,2,1] => [7,1,1] => [1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,6,3,7,2,1] => [7,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9,10] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [10,7,8,6,5,4,3,2,1,9] => [8,1,1] => [1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [9,4,3,5,6,7,8,2,1] => [5,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 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] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [11,12,9,10,7,8,5,6,3,4,1,2] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [10,8,9,6,5,4,3,2,1,7] => [8,1,1] => [1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [8,9,5,6,4,3,2,1,7] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [9,4,5,6,7,8,2,1,3] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,2,1,3,4] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [11,3,4,5,6,7,8,9,10,1,2] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [10,4,5,6,7,8,9,2,1,3] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [11,8,9,10,1,2,3,4,5,6,7] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [9,7,8,4,3,2,1,5,6] => [6,1,1,1] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [10,4,3,5,6,7,8,9,2,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,2,4,5,6,7,8,9,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2,11] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5,11] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => [5,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,2,1,3,9] => [8,1,1] => [1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [9,8,4,3,5,6,7,2,1] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [10,8,6,5,4,3,2,1,7,9] => [8,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [8,9,4,5,6,2,3,1,7] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [6,4,5,7,3,8,2,9,1,10] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [9,7,5,2,3,1,4,6,8] => [5,1,1,1,1] => [1,1,1,1] => 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] => [5,1,1,1,1,1] => [1,1,1,1,1] => 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] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
search for individual values
searching the database for the individual values of this statistic
Description
The least common multiple of the parts of the 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
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence u=(u1,u2,…) is an index i such that ui<ui+1. Let asc(u) denote the number of ascents of u, and let
asc∗(u):={0if u is empty,1+asc(u)otherwise.
Given a permutation w in the symmetric group Sn, define
A′k:=max
where the maximum is taken over disjoint subsequences {u_i} of w.
Then A'_1, A'_2-A'_1, A'_3-A'_2,\dots is a partition of n. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence u=(u1,u2,…) is an index i such that ui<ui+1. Let asc(u) denote the number of ascents of u, and let
asc∗(u):={0if u is empty,1+asc(u)otherwise.
Given a permutation w in the symmetric group Sn, define
A′k:=max
where the maximum is taken over disjoint subsequences {u_i} of w.
Then A'_1, A'_2-A'_1, A'_3-A'_2,\dots is a partition of n. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
Map
first row removal
Description
Removes the first entry of an integer partition
searching the database
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