Identifier
-
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000749: Integer partitions ⟶ ℤ
Values
[1,0,1,0] => [1,2] => [1,1] => [1] => 0
[1,0,1,0,1,0] => [1,2,3] => [1,1,1] => [1,1] => 0
[1,0,1,1,0,0] => [1,3,2] => [2,1] => [1] => 0
[1,1,0,0,1,0] => [2,1,3] => [2,1] => [1] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,1,1] => [1,1] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,1,1] => [1,1] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1] => [1] => 0
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [3,1] => [1] => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,1] => [1,1] => 0
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2] => [2] => 0
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1] => [1] => 0
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [3,1] => [1] => 0
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [2,2] => [2] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [3,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [3,1,1] => [1,1] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,1,1,1] => [1,1,1] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,1,1] => [1,1] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [4,1] => [1] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [4,1] => [1] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [3,1,1] => [1,1] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [4,1] => [1] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [2,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [4,1] => [1] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,2] => [2] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [3,2] => [2] => 0
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,1] => [1,1] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2] => [2] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1] => [1] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [4,1] => [1] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [3,2] => [2] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [3,1,1] => [1,1] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [3,2] => [2] => 0
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [4,1] => [1] => 0
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [2,2,1] => [2,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [3,2] => [2] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [3,2] => [2] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [4,1] => [1] => 0
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [3,2] => [2] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [3,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [3,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [3,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [4,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [3,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [4,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [2,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [4,1,1] => [1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,2,1] => [2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [3,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,1,1,1] => [1,1,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [4,1,1] => [1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [5,1] => [1] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [5,1] => [1] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [4,1,1] => [1,1] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [5,1] => [1] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [3,2,1] => [2,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [5,1] => [1] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [3,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [3,2,1] => [2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [4,1,1] => [1,1] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [5,1] => [1] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [5,1] => [1] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [2,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [3,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [5,1] => [1] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [3,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [4,1,1] => [1,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [5,1] => [1] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [3,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [5,1] => [1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [5,1] => [1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [3,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [3,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [3,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [4,2] => [2] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [4,2] => [2] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [3,2,1] => [2,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [4,2] => [2] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [2,2,2] => [2,2] => 2
>>> Load all 2191 entries. <<<[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [4,2] => [2] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,1,1] => [1,1,1] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1] => [2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1] => [2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,3] => [3] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [3,3] => [3] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,1] => [1,1] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2] => [2] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1] => [1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [5,1] => [1] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [4,2] => [2] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [4,1,1] => [1,1] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [4,2] => [2] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [5,1] => [1] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [3,2,1] => [2,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [3,3] => [3] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [3,3] => [3] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [5,1] => [1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [4,2] => [2] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [3,2,1] => [2,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [3,2,1] => [2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [3,3] => [3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [3,3] => [3] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [4,1,1] => [1,1] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [4,2] => [2] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [5,1] => [1] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [5,1] => [1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [4,2] => [2] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [2,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [3,2,1] => [2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [4,2] => [2] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [4,2] => [2] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [5,1] => [1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [3,3] => [3] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [3,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [4,2] => [2] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [2,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [4,2] => [2] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [4,2] => [2] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [4,2] => [2] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [5,1] => [1] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [3,2,1] => [2,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [3,3] => [3] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [3,3] => [3] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [5,1] => [1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [4,2] => [2] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [5,1] => [1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [4,2] => [2] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [3,3] => [3] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [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] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [5,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [5,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [5,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [5,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [5,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [5,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [5,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [5,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [5,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [5,1,1] => [1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [2,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [4,2,1] => [2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [4,2,1] => [2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [4,2,1] => [2,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [2,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [4,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [3,3,1] => [3,1] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [3,3,1] => [3,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [4,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [5,1,1] => [1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [6,1] => [1] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [6,1] => [1] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [5,1,1] => [1,1] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [6,1] => [1] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [4,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [6,1] => [1] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [4,2,1] => [2,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [5,1,1] => [1,1] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [6,1] => [1] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [6,1] => [1] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [3,3,1] => [3,1] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [6,1] => [1] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [3,3,1] => [3,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [5,1,1] => [1,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [6,1] => [1] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [4,2,1] => [2,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [6,1] => [1] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [6,1] => [1] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [3,3,1] => [3,1] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [3,3,1] => [3,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [4,2,1] => [2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [5,1,1] => [1,1] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [6,1] => [1] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [6,1] => [1] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [5,1,1] => [1,1] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [6,1] => [1] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [4,2,1] => [2,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [6,1] => [1] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [2,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [4,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [4,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [5,1,1] => [1,1] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [6,1] => [1] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [3,3,1] => [3,1] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [6,1] => [1] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [4,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [2,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => [4,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [4,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [4,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [5,1,1] => [1,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [6,1] => [1] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [6,1] => [1] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [3,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [3,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [6,1] => [1] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [3,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [5,1,1] => [1,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [6,1] => [1] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => [4,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => [2,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [6,1] => [1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [5,1,1] => [1,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [6,1] => [1] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [4,2,1] => [2,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [6,1] => [1] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [3,3,1] => [3,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [6,1] => [1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [3,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [3,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [4,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => [4,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => [4,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [2,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [4,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [3,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => [3,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [3,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [4,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [5,2] => [2] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [5,2] => [2] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => [4,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [5,2] => [2] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [3,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [5,2] => [2] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => [3,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => [4,2,1] => [2,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [5,2] => [2] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => [5,2] => [2] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [2,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [3,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [5,2] => [2] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => [3,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [4,2,1] => [2,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => [5,2] => [2] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => [3,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => [5,2] => [2] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [5,2] => [2] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,1] => [2,1,1] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,3,1] => [3,1] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [3,3,1] => [3,1] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,2,2] => [2,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,3,1] => [3,1] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [4,3] => [3] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [4,3] => [3] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [3,3,1] => [3,1] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [4,3] => [3] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [3,2,2] => [2,2] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [4,3] => [3] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,1,1,1] => [1,1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,3] => [3] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [4,3] => [3] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,1,1] => [1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2] => [2] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1] => [1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [6,1] => [1] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [5,2] => [2] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [5,1,1] => [1,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [5,2] => [2] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [6,1] => [1] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [4,2,1] => [2,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [4,3] => [3] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [4,3] => [3] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [6,1] => [1] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [5,2] => [2] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [4,1,1,1] => [1,1,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => [4,2,1] => [2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => [4,2,1] => [2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [4,3] => [3] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => [4,3] => [3] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [5,1,1] => [1,1] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [5,2] => [2] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [6,1] => [1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => [6,1] => [1] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [5,2] => [2] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [3,2,2] => [2,2] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [3,3,1] => [3,1] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [4,3] => [3] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [4,3] => [3] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [6,1] => [1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [4,3] => [3] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => [3,3,1] => [3,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [4,3] => [3] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [3,2,2] => [2,2] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [5,2] => [2] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [4,3] => [3] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [5,1,1] => [1,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [5,2] => [2] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => [6,1] => [1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [4,2,1] => [2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [4,3] => [3] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => [4,3] => [3] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [6,1] => [1] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [5,2] => [2] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [3,2,2] => [2,2] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [6,1] => [1] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => [5,2] => [2] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => [4,3] => [3] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [3,2,1,1] => [2,1,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [3,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => [3,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => [3,2,2] => [2,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [3,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [4,3] => [3] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => [4,3] => [3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [3,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => [4,3] => [3] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [3,2,2] => [2,2] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => [4,3] => [3] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [4,1,1,1] => [1,1,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => [4,2,1] => [2,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => [4,2,1] => [2,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [4,3] => [3] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => [4,3] => [3] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [5,1,1] => [1,1] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [5,2] => [2] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [6,1] => [1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => [6,1] => [1] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [5,2] => [2] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [5,1,1] => [1,1] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => [5,2] => [2] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => [6,1] => [1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [4,2,1] => [2,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [4,3] => [3] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => [4,3] => [3] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => [6,1] => [1] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => [5,2] => [2] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [2,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [2,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [3,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [3,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [3,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [4,2,1] => [2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [5,2] => [2] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [5,2] => [2] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [4,2,1] => [2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [5,2] => [2] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [3,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [5,2] => [2] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [5,1,1] => [1,1] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [5,2] => [2] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [6,1] => [1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [3,3,1] => [3,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [4,3] => [3] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [4,3] => [3] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [6,1] => [1] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [5,2] => [2] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [3,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [4,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [5,2] => [2] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => [5,2] => [2] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [2,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [3,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [5,2] => [2] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => [3,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => [4,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [5,2] => [2] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [5,2] => [2] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => [5,2] => [2] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => [4,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => [5,2] => [2] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [3,2,2] => [2,2] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [5,2] => [2] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6] => [5,2] => [2] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [4,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [4,2,1] => [2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [4,2,1] => [2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [4,3] => [3] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => [4,3] => [3] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [5,1,1] => [1,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => [5,2] => [2] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [6,1] => [1] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => [6,1] => [1] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [5,2] => [2] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [3,2,1,1] => [2,1,1] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => [3,2,2] => [2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => [3,3,1] => [3,1] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [4,3] => [3] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => [4,3] => [3] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [6,1] => [1] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [4,3] => [3] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => [3,3,1] => [3,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => [4,3] => [3] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => [3,2,2] => [2,2] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => [5,2] => [2] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [4,3] => [3] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => [5,1,1] => [1,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [5,2] => [2] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [6,1] => [1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [4,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [5,2] => [2] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => [5,2] => [2] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => [2,2,2,1] => [2,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [3,2,2] => [2,2] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [5,2] => [2] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6] => [3,2,2] => [2,2] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => [6,1] => [1] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [5,2] => [2] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,1,2,3,5] => [5,2] => [2] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [5,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [5,2] => [2] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [6,1] => [1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => [4,2,1] => [2,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => [4,3] => [3] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => [4,3] => [3] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [6,1] => [1] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => [5,2] => [2] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [3,2,2] => [2,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => [3,3,1] => [3,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => [4,3] => [3] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [5,2] => [2] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6] => [4,3] => [3] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [6,1] => [1] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => [5,2] => [2] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1,7,2,3,4,5] => [4,3] => [3] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,5,7] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,5,8,6] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,5,6] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,4,7] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,4,6,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,4,8,6] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,4,6] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,4,6,7] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,4,7,8,5] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,4,8,5,7] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,4,5,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,4,8,5] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,4,5] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,4,5,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,4,5,8,6] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,4,8,5,6] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,4,5,6] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,5,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,6,7] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,3,7] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,3,6,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,3,6] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,3,6,7] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,3,5,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,3,5,8,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,3,8,5,7] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,3,5] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,3,5,7] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,3,5,6,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,3,5,8,6] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,3,8,5,6] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,3,5,6] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,3,5,6,7] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,3,4,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,3,4,7,8,6] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,4,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,8,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,3,6,7,4,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,3,6,7,8,4] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,2,5,3,7,4,6,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,8,6] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,3,8,4,6,7] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,3,4,7,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,3,7,4,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,3,7,8,4] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,5,6,3,8,4,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,3,8,4] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,3,4] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,3,4,7] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,3,4,6,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,3,4,8,6] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,3,8,4,6] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,3,4,6] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,3,4,6,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,6,3,4,7,5,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,3,4,7,8,5] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,3,4,8,5,7] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,6,3,7,4,5,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,8,5] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,3,8,4,5,7] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,3,4,5,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,6,7,3,4,8,5] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,3,8,4,5] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,3,4,5] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,6,8,3,4,5,7] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,3,4,5,8,6] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,3,8,4,5,6] => [6,1,1] => [1,1] => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,3,4,5,6] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [6,1,1] => [1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,5,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,5,6] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,4,6,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,4,6] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,4,6,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,8,5,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,4,5,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,4,8,5] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,4,5] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,4,5,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,8,5,6] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,6,7] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,8,6] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,5,6] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,5,6,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,6,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [7,1] => [1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,2,7] => [7,1] => [1] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,2,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,2,6,7] => [7,1] => [1] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,2,5,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,2,5,8,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,2,7,5,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,2,5,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,2,8,5] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,8,2,5,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,3,4,7,2,5,6,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,2,5,8,6] => [7,1] => [1] => 0
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,7,8,2,5,6] => [7,1] => [1] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,2,5,6,7] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,2,4,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,2,4,6,8,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,8,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,2,6,7,4,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,6,8,4,7] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,2,7,4,6,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,8,6] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,2,8,4,6,7] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,2,4,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,5,6,2,4,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,2,7,8,4] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,6,2,8,4,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,2,4,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,2,4] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,2,4,7] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,2,4,6,8] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,2,4,8,6] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,2,8,4,6] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,2,4,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,2,4,6,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,2,4,5,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,2,4,5,8,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,2,4,7,5,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,6,2,4,7,8,5] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,2,7,4,5,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,2,7,4,8,5] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,6,7,2,4,8,5] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,2,4,5] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,2,4,5,6,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,7,2,4,5,8,6] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,2,4,8,5,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,2,8,4,5,6] => [7,1] => [1] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,2,4,5,6] => [4,3,1] => [3,1] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [7,1] => [1] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,2,3,5,7,8,6] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,2,3,6,7,5,8] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,2,3,6,7,8,5] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,2,3,7,5,8,6] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,2,3,7,8,5,6] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,3,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,3,6,8,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,8,6,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,2,5,6,7,3,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,8,3] => [7,1] => [1] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,2,5,7,3,6,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [7,1] => [1] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,2,5,7,8,3,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,6,3,5,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,6,3,5,8,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,8,5,7] => [7,1] => [1] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,2,6,7,3,5,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,2,6,7,8,3,5] => [7,1] => [1] => 0
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,2,6,8,3,5,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,7,3,5,6,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,7,3,5,8,6] => [7,1] => [1] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,8,5,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,2,7,8,3,5,6] => [7,1] => [1] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,8,3,5,6,7] => [7,1] => [1] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,2,3,6,7,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,2,3,7,6,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,2,3,7,8,6] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,2,6,3,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,7,3,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,2,6,7,8,3] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,6,8,3,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,4,5,2,7,3,6,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,8,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,7,8,3,6] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,2,8,3,6,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,2,3,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,2,7,3,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,2,3,8] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,2,8,3] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,2,3] => [7,1] => [1] => 0
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,4,5,6,8,2,3,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,2,3,6,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,2,3,8,6] => [7,1] => [1] => 0
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,2,3,6] => [7,1] => [1] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,2,3,5,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,4,6,2,3,5,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,2,3,7,8,5] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,2,7,3,5,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,2,7,3,8,5] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,2,8,3,5,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,2,3,5,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,2,8,3,5] => [7,1] => [1] => 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,2,3,5] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,2,3,5,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,2,3,5,6,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,2,3,5,8,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,2,3,8,5,6] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,2,8,3,5,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,2,3,5,6] => [7,1] => [1] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,2,3,4,7,8,6] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,2,3,6,4,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2,3,6,4,8,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,2,3,6,7,4,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,3,6,7,8,4] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,2,3,6,8,4,7] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,5,2,3,7,4,6,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,2,3,7,8,4,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,2,3,8,4,6,7] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,6,3,4,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,6,3,4,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4,8] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,8,4,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,2,6,7,3,4,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,2,6,7,8,3,4] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,2,6,8,3,4,7] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,7,3,4,6,8] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,7,3,4,8,6] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,8,4,6] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,2,7,8,3,4,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,8,3,4,6,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,2,3,4,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,2,3,4,8,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,6,2,3,7,8,4] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,5,6,2,8,3,4,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,2,3,4,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,2,3,8,4] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,5,6,7,2,8,3,4] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,2,3,4] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,5,6,8,2,3,4,7] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,2,3,4,8,6] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,5,7,2,3,8,4,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,2,8,3,4,6] => [7,1] => [1] => 0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,5,7,8,2,3,4,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,2,3,4,7,5,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,3,4,7,8,5] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,2,3,4,8,5,7] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,2,3,7,4,5,8] => [4,2,1,1] => [2,1,1] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,2,3,7,8,4,5] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,6,2,3,8,4,5,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,7,3,4,5,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,7,3,4,8,5] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,8,4,5] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,2,7,8,3,4,5] => [3,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,8,3,4,5,7] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,2,3,4,5,8] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,6,7,2,3,8,4,5] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,2,8,3,4,5] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,2,3,4,5] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => [6,1,1] => [1,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,2,3,4,8,5,6] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,2,3,8,4,5,6] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,8,3,4,5,6] => [4,3,1] => [3,1] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [7,1] => [1] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [7,1] => [1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [4,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,5,8,6] => [4,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,5,6] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => [4,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,3,5,6,8,4,7] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,4,6,7] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,4,5,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,6,7,4,8,5] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,4,5] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,7,4,8,5,6] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,4,5,6] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,5,7] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => [2,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [6,2] => [2] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,3,7] => [6,2] => [2] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,3,8,6] => [6,2] => [2] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,3,6] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,3,6,7] => [6,2] => [2] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,5,8,7] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,4,6,3,7,5,8] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,3,7,8,5] => [6,2] => [2] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,3,8,5,7] => [6,2] => [2] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,3,8,5] => [3,3,2] => [3,2] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,3,5] => [6,2] => [2] => 0
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,3,5,7] => [3,3,2] => [3,2] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,3,5,8,6] => [6,2] => [2] => 0
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,3,5,6] => [6,2] => [2] => 0
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,3,5,6,7] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,3,6,7,4,8] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,3,6,7,8,4] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,3,6,8,4,7] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,8,6] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,3,7,8,4,6] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,8,4,6,7] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,3,4,7,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => [2,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,4,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,3,7,8,4] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,4,8] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,3,8,4] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,3,4] => [3,3,2] => [3,2] => 0
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,3,4,7] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,5,7,3,4,6,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,3,4,8,6] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,3,8,4,6] => [2,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,3,4,6] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,3,4,6,7] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,3,4,7,8,5] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,3,4,8,5,7] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,7,4,5,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,8,5] => [3,3,2] => [3,2] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,3,7,8,4,5] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,8,4,5,7] => [3,3,2] => [3,2] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,3,4,8,5] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,3,4,5] => [2,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,3,4,5,7] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => [5,2,1] => [2,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,3,4,5,8,6] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,3,4,8,5,6] => [4,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,8,4,5,6] => [6,2] => [2] => 0
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,3,4,5,6] => [3,3,2] => [3,2] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [6,2] => [2] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,6,7] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [4,3,1] => [3,1] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,7,5,6,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,5,6] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,5,6,7] => [4,3,1] => [3,1] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [4,3,1] => [3,1] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [5,3] => [3] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,4,7] => [5,3] => [3] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,4,6] => [3,3,2] => [3,2] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,4,5,7,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5,8] => [4,3,1] => [3,1] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,8,5,7] => [5,3] => [3] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,4,5] => [5,3] => [3] => 0
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,4,5,7] => [3,3,2] => [3,2] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,4,5,8,6] => [5,3] => [3] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,8,5,6] => [3,3,2] => [3,2] => 0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,4,5,6] => [5,3] => [3] => 0
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,4,5,6,7] => [5,3] => [3] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [4,2,1,1] => [2,1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,3,1] => [3,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,6,7] => [4,3,1] => [3,1] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,2,2] => [2,2] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,3,1] => [3,1] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,4] => [4] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,5,7] => [4,4] => [4] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,5,6,8] => [4,3,1] => [3,1] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,8,6] => [4,4] => [4] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => [4,2,2] => [2,2] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,5,6,7] => [4,4] => [4] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [5,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,3] => [3] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,6,7] => [5,3] => [3] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,1,1] => [1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,2] => [2] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,1] => [1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,1,6,8] => [7,1] => [1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,1,6] => [6,2] => [2] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,1,5,7,8] => [6,1,1] => [1,1] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,1,5,8] => [5,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,1,5,7] => [5,3] => [3] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,1,5,6,8] => [7,1] => [1] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,1,8,5,6] => [6,2] => [2] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,1,4,6,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,4,7,6,8] => [5,2,1] => [2,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,4,8,6,7] => [5,3] => [3] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,8,7] => [6,2] => [2] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,1,4,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,1,4,8,7] => [4,2,2] => [2,2] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,1,7,8,4] => [4,4] => [4] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,1,8,4,7] => [4,4] => [4] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,1,4,8] => [7,1] => [1] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,1,4] => [5,3] => [3] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,1,4,6,8] => [4,3,1] => [3,1] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,1,4,8,6] => [4,4] => [4] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,1,8,4,6] => [4,2,2] => [2,2] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,1,4,6] => [6,2] => [2] => 0
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,1,4,6,7] => [4,4] => [4] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,1,4,5,7,8] => [6,1,1] => [1,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,1,4,5,8,7] => [6,2] => [2] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,6,1,4,7,5,8] => [7,1] => [1] => 0
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,1,8,4,5,7] => [5,3] => [3] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,1,8,4,5] => [6,2] => [2] => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,1,4,5] => [4,2,2] => [2,2] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,1,4,5,6,8] => [7,1] => [1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,1,4,8,5,6] => [6,2] => [2] => 0
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,7,8,1,4,5,6] => [5,3] => [3] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,1,3,6,5,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [4,2,2] => [2,2] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,1,3,6,7,8,5] => [4,4] => [4] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => [4,4] => [4] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => [4,4] => [4] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,1,3,7,8,5,6] => [4,2,2] => [2,2] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,1,3,8,5,6,7] => [4,4] => [4] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,3,6,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,3,6,8,7] => [5,2,1] => [2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,8] => [5,2,1] => [2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,3,7,8,6] => [5,3] => [3] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,8,6,7] => [5,3] => [3] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3,7,8] => [6,1,1] => [1,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,1,5,6,3,8,7] => [6,2] => [2] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,1,5,6,7,3,8] => [7,1] => [1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7] => [6,2] => [2] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5,8] => [7,1] => [1] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => [5,3] => [3] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,1,6,8,3,5,7] => [5,3] => [3] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,8,5,6] => [6,2] => [2] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,1,3,6,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,1,3,7,6,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,1,3,7,8,6] => [3,3,2] => [3,2] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,4,5,1,6,3,7,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,8,7] => [3,3,2] => [3,2] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,1,6,7,8,3] => [5,3] => [3] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,1,6,8,3,7] => [5,3] => [3] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,4,5,1,7,3,6,8] => [4,3,1] => [3,1] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,8,6] => [5,3] => [3] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,1,7,8,3,6] => [3,3,2] => [3,2] => 0
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,1,8,3,6,7] => [5,3] => [3] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,1,3,7,8] => [6,1,1] => [1,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,4,5,6,1,3,8,7] => [6,2] => [2] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,1,7,3,8] => [7,1] => [1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,1,3,8] => [4,3,1] => [3,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,1,8,3] => [4,4] => [4] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,1,3,7] => [4,4] => [4] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,4,5,7,1,8,3,6] => [6,2] => [2] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,1,3,5,7,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,1,3,5,8,7] => [3,3,2] => [3,2] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,4,6,1,3,7,5,8] => [4,3,1] => [3,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [5,3] => [3] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,1,7,3,8,5] => [3,3,2] => [3,2] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,1,8,3,5,7] => [3,3,2] => [3,2] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,1,3,5,8] => [5,2,1] => [2,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,1,3,8,5] => [6,2] => [2] => 0
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,1,3,5] => [6,2] => [2] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7] => [6,2] => [2] => 0
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,4,7,1,8,3,5,6] => [5,3] => [3] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [5,3] => [3] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,1,3,4,6,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,1,3,6,4,7,8] => [6,1,1] => [1,1] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [6,2] => [2] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,1,3,7,8,4,6] => [6,2] => [2] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,1,6,3,4,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,5,1,6,3,4,8,7] => [4,2,2] => [2,2] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4,8] => [4,3,1] => [3,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => [4,4] => [4] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,1,6,7,8,3,4] => [5,3] => [3] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,1,7,3,4,8,6] => [4,4] => [4] => 0
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,1,7,8,3,4,6] => [6,2] => [2] => 0
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,1,8,3,4,6,7] => [4,4] => [4] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,1,3,4,8,7] => [6,2] => [2] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,5,6,1,3,7,4,8] => [7,1] => [1] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,1,7,3,4,8] => [5,2,1] => [2,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,1,3,8,4] => [3,3,2] => [3,2] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,1,8,3,4] => [5,3] => [3] => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,1,3,4,7] => [3,3,2] => [3,2] => 0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,5,7,8,1,3,4,6] => [5,3] => [3] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,6,1,3,4,5,7,8] => [6,1,1] => [1,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,1,3,4,5,8,7] => [6,2] => [2] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1,3,4,7,5,8] => [7,1] => [1] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,6,1,3,7,4,8,5] => [5,3] => [3] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,1,3,8,4,5,7] => [5,3] => [3] => 0
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,1,7,8,3,4,5] => [4,2,2] => [2,2] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,1,3,4,5,8] => [4,3,1] => [3,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,6,7,1,3,4,8,5] => [4,4] => [4] => 0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,1,8,3,4,5] => [6,2] => [2] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [4,4] => [4] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,1,3,4,5,6,8] => [7,1] => [1] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,1,8,3,4,5,6] => [5,3] => [3] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,8,7] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,2,4,5,7,6,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,2,4,5,7,8,6] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,4,6,5,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,4,6,7,5,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,4,6,7,8,5] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,4,6,8,5,7] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,2,4,7,5,8,6] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,2,4,7,8,5,6] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,5,6,7,8,4] => [5,3] => [3] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,1,2,5,6,8,4,7] => [5,3] => [3] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,2,5,7,4,8,6] => [5,3] => [3] => 0
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,2,5,8,4,6,7] => [5,3] => [3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => [3,3,2] => [3,2] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5,8] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,2,6,4,7,8,5] => [5,3] => [3] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,2,6,7,4,8,5] => [3,3,2] => [3,2] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,1,2,6,7,8,4,5] => [5,3] => [3] => 0
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,1,2,6,8,4,5,7] => [3,3,2] => [3,2] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,2,7,4,8,5,6] => [3,3,2] => [3,2] => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,2,7,8,4,5,6] => [5,3] => [3] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => [5,3] => [3] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,2,5,7,8,6] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,2,5,8,6,7] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,5,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7] => [4,2,2] => [2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,2,6,7,5,8] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,2,6,7,8,5] => [4,4] => [4] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,2,6,8,5,7] => [4,4] => [4] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,7,5,6,8] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => [4,4] => [4] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,2,7,8,5,6] => [4,2,2] => [2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,8,5,6,7] => [4,4] => [4] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,2,6,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,5,2,7,8,6] => [5,3] => [3] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,6,2,8,7] => [6,2] => [2] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,2,8] => [7,1] => [1] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,4,5,7,8,2,6] => [6,2] => [2] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,5,8,7] => [6,2] => [2] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,4,6,7,2,8,5] => [5,3] => [3] => 0
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,4,6,8,2,5,7] => [5,3] => [3] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,5,2,4,8,6,7] => [5,3] => [3] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7] => [6,2] => [2] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,6,8] => [7,1] => [1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,2,7,8,4,6] => [6,2] => [2] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,5,6,2,4,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,1,5,6,2,4,8,7] => [4,2,2] => [2,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,1,5,6,2,7,8,4] => [4,4] => [4] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,1,5,6,2,8,4,7] => [4,4] => [4] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,1,5,6,7,8,2,4] => [5,3] => [3] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,5,7,2,4,6,8] => [4,3,1] => [3,1] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,1,5,7,2,4,8,6] => [4,4] => [4] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,1,5,7,2,8,4,6] => [4,2,2] => [2,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,1,5,7,8,2,4,6] => [6,2] => [2] => 0
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,1,5,8,2,4,6,7] => [4,4] => [4] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => [6,1,1] => [1,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,6,2,4,5,8,7] => [6,2] => [2] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,7,4,5,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,8,5] => [5,3] => [3] => 0
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,8,4,5,7] => [5,3] => [3] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,1,6,7,2,8,4,5] => [6,2] => [2] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,7,2,4,5,6,8] => [7,1] => [1] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,7,8,2,4,5,6] => [5,3] => [3] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,5,6,8,7] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,4,1,2,5,7,6,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,4,1,2,5,7,8,6] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,1,2,5,8,6,7] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,4,1,2,6,5,7,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [2,2,2,2] => [2,2,2] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,4,1,2,6,7,5,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,1,2,6,7,8,5] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,1,2,6,8,5,7] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,4,1,2,7,5,6,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,1,2,7,5,8,6] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,1,2,7,8,5,6] => [2,2,2,2] => [2,2,2] => 0
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,1,2,8,5,6,7] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,2,6,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,8,6,7] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,6,2,8,7] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,1,5,6,7,2,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,2] => [6,2] => [2] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,1,5,6,8,2,7] => [6,2] => [2] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,1,5,7,2,6,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,8,6] => [6,2] => [2] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,1,5,7,8,2,6] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,1,5,8,2,6,7] => [6,2] => [2] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,1,6,2,5,8,7] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,2,7,8,5] => [6,2] => [2] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,8,5,7] => [6,2] => [2] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,1,6,7,2,8,5] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,4,1,6,7,8,2,5] => [6,2] => [2] => 0
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,4,1,6,8,2,5,7] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,1,8,2,5,6,7] => [6,2] => [2] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,1,2,6,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,1,2,6,8,7] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,1,2,7,8,6] => [5,3] => [3] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,1,6,2,7,8] => [6,1,1] => [1,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,8,7] => [6,2] => [2] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,1,6,7,2,8] => [7,1] => [1] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,1,7,8,2,6] => [6,2] => [2] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,1,2,7,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,1,2,8,7] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,1,7,2,8] => [4,3,1] => [3,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,1,7,8,2] => [5,3] => [3] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,1,8,2,7] => [5,3] => [3] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,1,2,8] => [7,1] => [1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,1,2] => [4,4] => [4] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,5,7,1,2,6,8] => [4,3,1] => [3,1] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,1,8,2,6] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,1,2,6] => [5,3] => [3] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,1,2,6,7] => [5,3] => [3] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,1,2,5,8,7] => [6,2] => [2] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,1,7,2,8,5] => [5,3] => [3] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,4,6,7,1,2,5,8] => [7,1] => [1] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,1,8,2,5] => [5,3] => [3] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,1,2,5] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,1,2,5,6] => [4,4] => [4] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,1,2,4,6,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,1,2,4,6,8,7] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,1,2,4,7,6,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,1,2,4,7,8,6] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,1,2,6,7,4,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,1,2,6,7,8,4] => [6,2] => [2] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,1,2,6,8,4,7] => [6,2] => [2] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,1,2,7,4,6,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,1,2,7,4,8,6] => [6,2] => [2] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,1,2,7,8,4,6] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,5,1,2,8,4,6,7] => [6,2] => [2] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,5,1,6,2,4,7,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,1,6,2,4,8,7] => [2,2,2,2] => [2,2,2] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,5,1,6,7,2,4,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => [6,2] => [2] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,1,6,7,8,2,4] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,5,1,6,8,2,4,7] => [6,2] => [2] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,1,7,2,4,6,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,8,4,6] => [2,2,2,2] => [2,2,2] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,1,7,8,2,4,6] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,5,1,8,2,4,6,7] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,5,6,1,2,4,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,1,2,4,8,7] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,1,2,7,4,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,1,2,7,8,4] => [6,2] => [2] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [5,3] => [3] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,1,2,4,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,1,2,8,4] => [5,3] => [3] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,1,2,4] => [5,3] => [3] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,1,2,4,7] => [5,3] => [3] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,1,2,4,6,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,1,2,4,8,6] => [6,2] => [2] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,1,2,4,5,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,1,2,4,5,8,7] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,1,2,4,7,5,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,1,2,4,7,8,5] => [6,2] => [2] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,1,2,4,8,5,7] => [6,2] => [2] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,1,2,7,4,8,5] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,1,2,7,8,4,5] => [6,2] => [2] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,1,2,8,4,5,7] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,6,1,7,2,4,8,5] => [6,2] => [2] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,6,1,7,2,8,4,5] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,1,7,8,2,4,5] => [2,2,2,2] => [2,2,2] => 0
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,1,8,2,4,5,7] => [6,2] => [2] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,6,7,1,2,4,5,8] => [7,1] => [1] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,1,2,8,4,5] => [4,4] => [4] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,1,2,4,5] => [6,2] => [2] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,1,2,4,5,6,8] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,7,1,2,4,5,8,6] => [6,2] => [2] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,1,2,4,8,5,6] => [4,2,2] => [2,2] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,1,2,8,4,5,6] => [6,2] => [2] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,1,8,2,4,5,6] => [3,3,2] => [3,2] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [5,3] => [3] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [6,2] => [2] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,3,5,6,8,7] => [4,2,1,1] => [2,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,3,5,7,6,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,3,5,7,8,6] => [4,3,1] => [3,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,3,5,8,6,7] => [4,3,1] => [3,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => [4,2,2] => [2,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,3,6,7,5,8] => [4,3,1] => [3,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,3,6,7,8,5] => [4,4] => [4] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,3,6,8,5,7] => [4,4] => [4] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [4,3,1] => [3,1] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,3,7,5,8,6] => [4,4] => [4] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,1,2,3,7,8,5,6] => [4,2,2] => [2,2] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => [4,4] => [4] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,2,5,3,6,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,5,3,7,8,6] => [5,3] => [3] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,2,5,3,8,6,7] => [5,3] => [3] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,2,5,6,3,7,8] => [6,1,1] => [1,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,2,5,6,3,8,7] => [6,2] => [2] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,6,7,3,8] => [7,1] => [1] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6,8] => [7,1] => [1] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,5,7,8,3,6] => [6,2] => [2] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,1,2,6,3,5,8,7] => [6,2] => [2] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => [7,1] => [1] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,1,2,6,7,3,8,5] => [5,3] => [3] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,7,3,5,6,8] => [7,1] => [1] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,5,2,3,7,6,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,5,2,3,7,8,6] => [3,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,5,2,3,8,6,7] => [3,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,3,7,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7] => [3,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,2,6,7,8,3] => [5,3] => [3] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,2,6,8,3,7] => [5,3] => [3] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,7,3,6,8] => [4,3,1] => [3,1] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,8,6] => [5,3] => [3] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,2,7,8,3,6] => [3,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,8,3,6,7] => [5,3] => [3] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,5,6,2,3,7,8] => [6,1,1] => [1,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,5,6,2,3,8,7] => [6,2] => [2] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,5,6,7,2,3,8] => [4,3,1] => [3,1] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,5,6,7,2,8,3] => [4,4] => [4] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,5,6,8,2,3,7] => [4,4] => [4] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,5,7,2,8,3,6] => [6,2] => [2] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,1,6,2,3,5,8,7] => [3,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,1,6,2,3,7,5,8] => [4,3,1] => [3,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,1,6,2,3,7,8,5] => [5,3] => [3] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,1,6,2,3,8,5,7] => [5,3] => [3] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,7,3,5,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5] => [3,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,8,3,5,7] => [3,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,1,6,7,2,3,5,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,1,6,7,2,3,8,5] => [6,2] => [2] => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,1,6,7,8,2,3,5] => [6,2] => [2] => 0
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,1,6,8,2,3,5,7] => [6,2] => [2] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,1,7,2,3,5,6,8] => [4,3,1] => [3,1] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,1,7,2,3,5,8,6] => [5,3] => [3] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,1,7,2,3,8,5,6] => [3,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,8,3,5,6] => [5,3] => [3] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [5,3] => [3] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,1,2,3,6,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,1,2,3,7,6,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,1,2,3,8,6,7] => [5,3] => [3] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [6,2] => [2] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,5,1,2,6,7,3,8] => [7,1] => [1] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,5,1,2,7,8,3,6] => [6,2] => [2] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,5,1,6,2,3,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,1,6,2,3,8,7] => [4,2,2] => [2,2] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,5,1,6,2,7,8,3] => [6,2] => [2] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,8,3,7] => [6,2] => [2] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,5,1,6,7,2,3,8] => [7,1] => [1] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,1,6,7,8,2,3] => [5,3] => [3] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,1,7,2,3,8,6] => [6,2] => [2] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,8,3,6] => [4,2,2] => [2,2] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,1,7,8,2,3,6] => [4,4] => [4] => 0
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,1,8,2,3,6,7] => [6,2] => [2] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,1,2,3,7,8] => [2,2,2,1,1] => [2,2,1,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,1,2,3,8,7] => [2,2,2,2] => [2,2,2] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,5,6,1,2,7,3,8] => [3,2,2,1] => [2,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,1,2,7,8,3] => [4,2,2] => [2,2] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => [4,2,2] => [2,2] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,5,6,1,7,2,3,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,1,7,2,8,3] => [6,2] => [2] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => [3,3,2] => [3,2] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,1,8,2,3,7] => [6,2] => [2] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,1,2,3,8] => [7,1] => [1] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,1,8,2,3] => [5,3] => [3] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,1,2,8,3,6] => [2,2,2,2] => [2,2,2] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,1,2,3,6] => [6,2] => [2] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [4,2,2] => [2,2] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,6,1,2,3,5,7,8] => [6,1,1] => [1,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => [6,2] => [2] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,6,1,2,3,7,5,8] => [7,1] => [1] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,6,1,2,7,3,5,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,1,2,8,3,5,7] => [5,3] => [3] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,1,7,2,3,5,8] => [7,1] => [1] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,6,1,7,2,8,3,5] => [4,4] => [4] => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,1,7,8,2,3,5] => [4,2,2] => [2,2] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,1,2,3,5,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,6,7,1,2,8,3,5] => [4,2,2] => [2,2] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,1,8,2,3,5] => [2,2,2,2] => [2,2,2] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,1,2,3,5] => [4,2,2] => [2,2] => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [6,2] => [2] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,1,2,3,5,6,8] => [7,1] => [1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,1,2,3,8,5,6] => [6,2] => [2] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,1,8,2,3,5,6] => [5,3] => [3] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8] => [5,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,4,6,8,7] => [5,2,1] => [2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,4,7,8,6] => [5,3] => [3] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => [5,3] => [3] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,2,3,6,4,7,8] => [6,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,2,3,6,7,4,8] => [7,1] => [1] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,1,2,3,7,8,4,6] => [6,2] => [2] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,2,6,3,4,7,8] => [4,2,1,1] => [2,1,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [4,3,1] => [3,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,2,6,3,7,8,4] => [4,4] => [4] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2,6,3,8,4,7] => [4,4] => [4] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,4,8] => [7,1] => [1] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,2,6,7,8,3,4] => [5,3] => [3] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,1,2,7,3,4,8,6] => [4,4] => [4] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,1,2,7,3,8,4,6] => [4,2,2] => [2,2] => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,1,2,7,8,3,4,6] => [6,2] => [2] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,1,2,8,3,4,6,7] => [4,4] => [4] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => [6,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,6,2,3,4,8,7] => [6,2] => [2] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,6,2,3,7,4,8] => [7,1] => [1] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,7,3,4,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,8,4] => [6,2] => [2] => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,8,3,4,7] => [6,2] => [2] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,6,7,2,3,8,4] => [3,3,2] => [3,2] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,6,7,2,8,3,4] => [5,3] => [3] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,1,7,2,3,4,6,8] => [7,1] => [1] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,1,7,8,2,3,4,6] => [5,3] => [3] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4,8,7] => [3,3,2] => [3,2] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,6,1,2,3,7,8,4] => [5,3] => [3] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,8,4,7] => [5,3] => [3] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,1,2,7,8,3,4] => [4,4] => [4] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,1,7,2,3,4,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,6,1,7,2,3,8,4] => [5,3] => [3] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,1,7,8,2,3,4] => [6,2] => [2] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,1,8,2,3,4,7] => [5,3] => [3] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,1,2,3,4,8] => [7,1] => [1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,1,2,8,3,4] => [6,2] => [2] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,1,8,2,3,4] => [4,2,2] => [2,2] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => [2,2,2,2] => [2,2,2] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,1,2,3,4,6,8] => [4,3,1] => [3,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,1,2,3,4,8,6] => [5,3] => [3] => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,1,2,8,3,4,6] => [5,3] => [3] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [5,3] => [3] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [5,3] => [3] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,7,8] => [6,1,1] => [1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => [6,2] => [2] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,2,3,4,7,5,8] => [7,1] => [1] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => [5,2,1] => [2,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,2,3,7,4,8,5] => [5,3] => [3] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,1,2,3,8,4,5,7] => [5,3] => [3] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,2,7,3,4,5,8] => [7,1] => [1] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,2,7,3,8,4,5] => [6,2] => [2] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,7,2,3,4,5,8] => [4,3,1] => [3,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,7,2,3,4,8,5] => [4,4] => [4] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,7,2,8,3,4,5] => [6,2] => [2] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [4,4] => [4] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,1,2,3,4,5,8] => [7,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,1,2,3,8,4,5] => [5,3] => [3] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,1,8,2,3,4,5] => [5,3] => [3] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [7,1] => [1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,8,5,6] => [6,2] => [2] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1,2,8,3,4,5,6] => [5,3] => [3] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [4,4] => [4] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => [8,1] => [1] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [8,1] => [1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => [9,1] => [1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,1,2,3,4,5,6,9] => [4,4,1] => [4,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [4,4,1] => [4,1] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [9,1] => [1] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9,11] => [10,1] => [1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,1,2,3,4,5,6,7,10] => [9,1] => [1] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,8,2,3,4,5,6,9] => [8,1] => [1] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,1,2,3,4,5,7,9] => [8,1] => [1] => 0
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,9,3,4,5,6,7] => [8,1] => [1] => 0
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,2,3,4,5,6,8] => [8,1] => [1] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [9,1] => [1] => 0
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [10,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,1,2,3,4,5,9] => [8,1] => [1] => 0
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,2,3,4,5,6] => [8,1] => [1] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,10,3,4,5,6,7,8] => [5,4,1] => [4,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,8,9,10,2,3,4,5,6,7] => [3,3,3,1] => [3,3,1] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,8,2,3,4,5,9,6,7] => [6,2,1] => [2,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,2,8,9,3,4,5,6] => [8,1] => [1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,2,3,4,5,8,6,9] => [8,1] => [1] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,8,1,2,3,4,9] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,1,3,4,5,6,7,9] => [8,1] => [1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => [7,2] => [2] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => [8,1] => [1] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,2,3,4,5] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [7,2] => [2] => 0
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,2,4,5,6,7,8] => [8,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,9,1,2,3,4,5,10] => [9,1] => [1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9] => [7,1,1] => [1,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,7,1,8,2,3,4,9] => [4,2,2,1] => [2,2,1] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [4,6,7,8,1,2,3,5,9] => [4,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,7,9] => [7,1,1] => [1,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5,9,8] => [7,2] => [2] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,6,7,8,2,9,3,4,5] => [4,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,5,7,8,9,2,3,4,6] => [4,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,10,2,3,4,5,6] => [9,1] => [1] => 0
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,8,9,3,4,5,6,7] => [7,2] => [2] => 0
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => [7,1,1] => [1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,1,2,3,4,5,6,7,10,9] => [8,2] => [2] => 0
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => [8,2] => [2] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,7,9,10] => [8,1,1] => [1,1] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,8,10] => [8,1,1] => [1,1] => 0
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,2,7,8,9,3,4,5] => [8,1] => [1] => 0
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1,7,8,9,3,4,5,6] => [7,2] => [2] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,3,7,8,9,2,4,5,6] => [8,1] => [1] => 0
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [8,1,1] => [1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,1,7] => [7,2] => [2] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,7,8,1,9,6] => [6,3] => [3] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,5,7,9,1,6,8] => [6,3] => [3] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,1,5] => [6,3] => [3] => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,7,8,9,1,5,6] => [5,2,2] => [2,2] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,3,8,9,5,7] => [7,2] => [2] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,5,1,6,7,8,9,3] => [6,3] => [3] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,1,3] => [5,4] => [4] => 0
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,9,1,3,5] => [5,4] => [4] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,8,1,9,3,4] => [6,3] => [3] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,6,1,7,3,8,4,9,5] => [7,2] => [2] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,9,1,3,4,5] => [3,2,2,2] => [2,2,2] => 0
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,6,9,1,3,4,5,7,8] => [5,4] => [4] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,8,1,3,9,4,5,6,7] => [6,3] => [3] => 0
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,8,9,1,3,4,5,6,7] => [5,4] => [4] => 0
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,8,9,2,5,6,7] => [6,3] => [3] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,9,2] => [7,2] => [2] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,1,5,6,7,9,2,8] => [7,2] => [2] => 0
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,5,9,2,6,7,8] => [7,2] => [2] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,1,9,2] => [5,4] => [4] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,7,9,1,2,8] => [5,4] => [4] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,6,8,1,9,2,7] => [7,2] => [2] => 0
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,5,7,8,9,1,2,6] => [7,2] => [2] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,8,1,2,9,4] => [6,3] => [3] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,9,1,2,4] => [6,3] => [3] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,7,9,1,2,4,8] => [6,3] => [3] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,9,1,2,4,5] => [5,2,2] => [2,2] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,8,1,2,4,5,6,9,7] => [7,2] => [2] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [3,8,1,2,4,5,9,6,7] => [5,2,2] => [2,2] => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,1,2,4,5,6,7,8] => [7,2] => [2] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,1,2,8,9,3,5,6,7] => [6,3] => [3] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,8,9,2,3] => [5,4] => [4] => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,6,7,8,9,2,3,5] => [5,4] => [4] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,6,1,2,7,8,9,3] => [5,2,2] => [2,2] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,6,1,7,8,9,2,3] => [7,2] => [2] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,9,3] => [5,4] => [4] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,7,1,9,2,3,8] => [5,4] => [4] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,8,1,9,2,3] => [6,3] => [3] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [3,3,3] => [3,3] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,9,1,2,3,5] => [7,2] => [2] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [5,1,6,7,8,2,9,3,4] => [6,3] => [3] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0] => [5,6,1,2,3,7,8,9,4] => [6,3] => [3] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,6,1,7,8,9,2,3,4] => [5,4] => [4] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,8,1,9,2,3,4] => [7,2] => [2] => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,9,1,2,3,4,8] => [3,2,2,2] => [2,2,2] => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,7,8,9,1,2,3,4,6] => [7,2] => [2] => 0
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [5,7,9,1,2,3,4,6,8] => [5,4] => [4] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [5,8,1,2,3,4,6,9,7] => [6,3] => [3] => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,1,2,3,4,6,7,8] => [6,3] => [3] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [6,1,2,3,7,4,8,9,5] => [5,4] => [4] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,1,7,8,9,2,3,4,5] => [3,2,2,2] => [2,2,2] => 0
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [6,1,8,9,2,3,4,5,7] => [6,3] => [3] => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [6,7,1,9,2,3,4,5,8] => [6,3] => [3] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,7,8,1,9,2,3,4,5] => [7,2] => [2] => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,8,1,9,2,3,4,5,7] => [3,3,3] => [3,3] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,8,9,1,2,3,4,5,7] => [6,3] => [3] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,1,2,3,4,8,5,9,6] => [6,3] => [3] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,1,2,8,3,4,5,9,6] => [5,4] => [4] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [7,1,8,2,3,9,4,5,6] => [4,3,2] => [3,2] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,9,3,4,5,6] => [5,4] => [4] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,1,2,3,4,5,9,6] => [5,4] => [4] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [7,8,1,9,2,3,4,5,6] => [6,3] => [3] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [3,3,3] => [3,3] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,1,2,3,4,5,6,8] => [5,4] => [4] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,9,6,7] => [7,2] => [2] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,1,2,3,9,4,5,6,7] => [6,3] => [3] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1,9,2,3,4,5,6,7] => [5,4] => [4] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [6,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [7,1,1] => [1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [8,1] => [1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,6,9,7] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,5,8,9,6] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,4,7,8,9,5] => [6,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [6,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,3,6,7,8,9,4] => [7,1,1] => [1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [7,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,8,9,3] => [8,1] => [1] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [8,1,1] => [1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [9,1] => [1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,6,7] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,6,9,7,10,8] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,4,7,8,5,9,6] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,4,8,5,6,9,7] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [10,1] => [1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,6,9,10,7,8] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,4,7,9,5,6,8] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,7,3,8,9,4] => [7,1,1] => [1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,4,8,9,5,6,7] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,9,10,2] => [8,2] => [2] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [11,1] => [1] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,9,10,11,2] => [9,2] => [2] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,8,2,9,3] => [8,1] => [1] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,7,8,9,10,2] => [7,3] => [3] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,2,3] => [4,4,1] => [4,1] => 1
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [6,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,2,3,4] => [8,1] => [1] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [6,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,10,2,3] => [9,1] => [1] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,10,2,3,4] => [3,3,3,1] => [3,3,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [2,1,1,1,1,1,1,1] => [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] => [1,2,3,4,5,7,6,9,8] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,4,7,5,6,9,8] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,7,8] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => [3,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,2,3,4,5,6,8,9] => [6,1,1,1] => [1,1,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => [6,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,7,8] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5,8,6,7,9] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5,9,6,7,8] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => [6,2,1] => [2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,7,9,8] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,6,9,7,8] => [3,3,1,1,1] => [3,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7,9] => [3,2,2,1,1] => [2,2,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => [3,2,2,2] => [2,2,2] => 0
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => [6,3] => [3] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,3,5,9,6,7,8] => [4,4,1] => [4,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => [4,2,2,1] => [2,2,1] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => [5,4] => [4] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8,9] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,2,3,4,7,6,8,9] => [5,2,1,1] => [2,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => [5,4] => [4] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,5,7,8,9] => [6,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => [6,3] => [3] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [7,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [2,2,2,2,1,1] => [2,2,2,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,7,10,8,9] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9,10] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => [2,2,2,2,1,1] => [2,2,2,1,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,2,2,2,2] => [2,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,7,8,9] => [4,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => [4,4,2] => [4,2] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,3,4,5,6,7,10,9] => [6,2,2] => [2,2] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => [7,3] => [3] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => [4,2,2,2] => [2,2,2] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,6,5,10,7,8,9] => [4,4,2] => [4,2] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => [4,4,2] => [4,2] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => [6,4] => [4] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8,9,10] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => [5,5] => [5] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5,7,8,9,10] => [6,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => [6,4] => [4] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9,10] => [7,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => [7,3] => [3] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [6,1,1,1] => [1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,1,1] => [1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [8,1] => [1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,5,1,4,6,7,8,9] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,4,6,1,5,7,8,9] => [6,1,1,1] => [1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [6,1,1,1,1] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,1,6,8,9] => [7,1,1] => [1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [7,1,1,1] => [1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,1,7,9] => [8,1] => [1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [8,1,1] => [1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [9,1] => [1] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,9,11,1,2,3,4,10] => [6,5] => [5] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,8,10,1,2,3,9] => [4,3,3] => [3,3] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,1,6,7,8,9,10,2,3,4] => [4,3,3] => [3,3] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,1,7,8,9,10,11,2,3,4,5] => [6,5] => [5] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [9,11,1,2,3,4,5,6,7,8,10] => [6,5] => [5] => 0
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [7,8,10,1,2,3,4,5,6,9] => [4,3,3] => [3,3] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [8,1,9,10,2,3,4,5,6,7] => [4,3,3] => [3,3] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [10,1,11,2,3,4,5,6,7,8,9] => [6,5] => [5] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => [3,3,1,1,1] => [3,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,1,2,9] => [4,4,1] => [4,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,7,1,2,8,9] => [7,1,1] => [1,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,6,1,2,7,8,9] => [3,3,1,1,1] => [3,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,5,1,2,6,7,8,9] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8,9] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,1,2,3,4,7,5,8,9] => [7,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,2,3,6,4,7,8,9] => [6,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,3,6,7,8,9] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9] => [4,1,1,1,1,1] => [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] => [9,10,1,2,3,4,5,6,7,8] => [5,5] => [5] => 0
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [7,10,1,2,3,4,5,6,8,9] => [6,4] => [4] => 0
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,1,2,3,4,6,7,8,9] => [7,3] => [3] => 0
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,10,1,2,4,5,6,7,8,9] => [8,2] => [2] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,7,1,2,9,8] => [7,2] => [2] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,9,3,4] => [7,2] => [2] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,8,1,3,9] => [8,1] => [1] => 0
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,4,5,6,7,8] => [6,3] => [3] => 0
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,1,2,9,5,6,7,8] => [5,2,2] => [2,2] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,5,1,2,3,9,6,7,8] => [5,4] => [4] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [5,6,1,2,3,4,9,7,8] => [3,3,3] => [3,3] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [5,2,1,1] => [2,1,1] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,1,7,8,9,10,4] => [6,4] => [4] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,10,2,3,4,5] => [9,1] => [1] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,2,6,7,8,9,3,4] => [8,1] => [1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,8,2,9] => [8,1] => [1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,2,8] => [8,1] => [1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [7,2] => [2] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [7,2] => [2] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,7,8] => [6,3] => [3] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,9,6,7,8] => [5,4] => [4] => 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,1,8,9,5,6,7] => [5,4] => [4] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,8,9,10,1,6,7] => [6,2,2] => [2,2] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,7,8,9,4,5,6] => [3,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,9,3,4,5] => [7,2] => [2] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,9,10,1,3,4] => [4,3,3] => [3,3] => 0
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,9,3,5,6,7,8] => [7,2] => [2] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6,9,8] => [5,2,2] => [2,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,1,2,6,9,4,5,7,8] => [4,3,2] => [3,2] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [4,6,1,2,3,5,9,7,8] => [6,3] => [3] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,1,2,3,8,9,5,6,7] => [5,4] => [4] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,1,2,3,4,5,6,10,7,8] => [8,2] => [2] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,1,2,3,4,10,5,6,7,8] => [7,3] => [3] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,3,5,7,8,9,6] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,10,1,6] => [7,3] => [3] => 0
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,8,9,10,1,3,4,5,6,7] => [4,3,3] => [3,3] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [6,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => [5,2,1,1] => [2,1,1] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,5,7,8,9] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8,9] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,9] => [4,2,2,1] => [2,2,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5,8,7,9] => [6,2,1] => [2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,8,5,7,9] => [8,1] => [1] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,9,8] => [7,2] => [2] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8] => [5,2,2] => [2,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [3,2,2,2] => [2,2,2] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => [4,2,2,2] => [2,2,2] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [2,5,1,6,3,4,8,7,9] => [4,2,2,1] => [2,2,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => [6,2,2] => [2,2] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,8,5,6,9] => [6,2,1] => [2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => [8,2] => [2] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,5,8,9] => [7,1,1] => [1,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,8,5,9,7,10] => [9,1] => [1] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,9,7] => [5,4] => [4] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,7,5,9,8,10] => [7,2,1] => [2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,9,8] => [4,3,2] => [3,2] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8,10] => [5,2,2,1] => [2,2,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,9,8] => [4,2,2,1] => [2,2,1] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,9,10,1,8] => [8,2] => [2] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,10,1,4] => [6,4] => [4] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [5,5] => [5] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,8,10,11,1,9] => [9,2] => [2] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,11,1,3] => [6,5] => [5] => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [8,1,10,2,3,4,5,6,7,9] => [5,5] => [5] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,9,1,2,10] => [9,1] => [1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,8,1,2,3,9] => [8,1] => [1] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,8,9,1,2,3,4,10] => [9,1] => [1] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,5,6,8,1,2,7,9] => [8,1] => [1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10,11] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [7,1,1] => [1,1] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [6,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,5,7,8] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,6,8] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,1,2,5,6,7,8,9,4] => [6,3] => [3] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [5,5] => [5] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,4,7,8,5,6,9] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [8,2] => [2] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [6,3] => [3] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => [6,4] => [4] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => [6,2,1] => [2,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [2,2,2,2,2] => [2,2,2,2] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [5,5] => [5] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [10,1] => [1] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6,9,8] => [3,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,7,9,3,8] => [7,2] => [2] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [7,1,1] => [1,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,6,1,2,9,7,8] => [3,3,3] => [3,3] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,9,10,1,2,4,5] => [7,3] => [3] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => [6,2,1] => [2,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [8,1,9,2,10,3,4,5,6,7] => [7,3] => [3] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,7,8,1,2,9,10] => [4,4,1,1] => [4,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8,9,10] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [8,2] => [2] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [6,3] => [3] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [2,2,2,2,2,1] => [2,2,2,2,1] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6,9,8] => [3,2,2,2] => [2,2,2] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7,9] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7,10,9] => [2,2,2,2,2] => [2,2,2,2] => 2
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,7,8,9,10,1,2,3,5,6] => [6,2,2] => [2,2] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,9,10,1,2,11] => [5,5,1] => [5,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,4,6,8,5,7,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,5,2,4,6,7,8,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [8,1,1] => [1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [5,4] => [4] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,7,9] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,3,6,7,8,9] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [5,6,7,9,10,1,2,3,4,8] => [8,2] => [2] => 0
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,6,8,9,10,1,2,3,4,7] => [6,2,2] => [2,2] => 2
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,7,8,9,10,1,2,3,4,6] => [4,2,2,2] => [2,2,2] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,6,8,9,2,7] => [6,2,1] => [2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,9,10,1,2,3,4,5,11] => [2,2,2,2,2,1] => [2,2,2,2,1] => 3
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,10,11,2,3,4,5,6] => [2,2,2,2,2,1] => [2,2,2,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,5,6,7,1,2,8,3,9] => [8,1] => [1] => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,9,2,4,5] => [8,1] => [1] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,9] => [4,2,2,1] => [2,2,1] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7,9] => [6,2,1] => [2,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,4,7,6,9,8] => [5,2,2] => [2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,10,9] => [4,2,2,2] => [2,2,2] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7,9] => [4,2,2,1] => [2,2,1] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,10,9] => [6,2,2] => [2,2] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6,10,9] => [8,2] => [2] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,5,2,4,7,6,9,8] => [4,2,2,1] => [2,2,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,2,7,8,9] => [6,1,1,1] => [1,1,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,2,8,9] => [4,3,1,1] => [3,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6,9] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7,10] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => [5,1,2,3,4,8,6,9,7] => [5,4] => [4] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,2,9] => [9,1] => [1] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => [6,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,7,10,8] => [4,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,5,9,6,10,8] => [6,2,2] => [2,2] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,9,6,10,8] => [8,2] => [2] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,4,8,5,9,6,7] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,5,2,6,7,8,9,4] => [8,1] => [1] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => [5,2,2] => [2,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [6,1,1,1] => [1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,5,8] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,7,8,2,9] => [8,1] => [1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,11,12,1,2] => [6,6] => [6] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,8,9,10,1,2,7] => [4,4,2] => [4,2] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,9,10,1,2,4] => [7,3] => [3] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,6,7,10,1,2,8,9] => [6,4] => [4] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,5,6,9,10,1,2,7,8] => [5,5] => [5] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,8,5,10,7,9] => [9,1] => [1] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,9,8] => [4,2,2,1] => [2,2,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,4,5,7,8,9,10,6] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,3,5,7,4,6,9,8] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,9,8] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,3,4,6,8,5,7,10,9] => [4,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,3,4,7,5,8,6,10,9] => [4,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,8,5,7,10,9,11] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,3,5,7,4,6,9,8,10] => [4,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,5,7,3,6,9,8] => [5,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,9,8] => [3,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,6,3,4,7,5,9,8] => [5,2,1,1] => [2,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,2,3,6,4,7,5,9,8,10] => [4,2,1,1,1,1] => [2,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,2,3,4,7,5,8,6,10,9,11] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,8,9,2,3,10] => [4,4,1,1] => [4,1,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9,10,11] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,7,8,9,5,6] => [5,4] => [4] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7,10,9] => [3,3,2,2] => [3,2,2] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7,10,9] => [4,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,6,3,7,4,8,5,10,9] => [3,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,1,6,2,7,4,8,5,10,9] => [5,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,6,2,7,3,8,5,10,9] => [3,3,2,2] => [3,2,2] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,10,9] => [6,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,5,8,6,10,9] => [4,2,2,2] => [2,2,2] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,7,5,8,6,10,9] => [4,4,2] => [4,2] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,7,3,8,6,10,9] => [5,3,2] => [3,2] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,7,4,8,6,10,9] => [6,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,8,5,9,6,10,7] => [3,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,4,2,8,5,9,6,10,7] => [4,3,3] => [3,3] => 0
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,8,3,9,6,10,7] => [4,3,3] => [3,3] => 0
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,3,8,4,9,6,10,7] => [5,3,2] => [3,2] => 0
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,5,2,8,4,9,6,10,7] => [7,3] => [3] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,8,3,9,5,10,7] => [3,3,2,2] => [3,2,2] => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,1,6,2,8,3,9,4,10,7] => [5,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,1,7,2,8,3,9,5,10,6] => [5,3,2] => [3,2] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,7,2,8,3,9,4,10,6] => [5,5] => [5] => 0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,8,4,9,5,10,7] => [3,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,8,4,9,5,10,7] => [5,3,2] => [3,2] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,7,3,8,4,9,5,10,6] => [6,2,2] => [2,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,1,7,2,8,4,9,5,10,6] => [8,2] => [2] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,6,5,9,7,10,8] => [4,4,2] => [4,2] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,1,5,2,6,3,9,7,10,8] => [4,3,3] => [3,3] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4,9,7,10,8] => [4,4,2] => [4,2] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,6,4,9,7,10,8] => [6,4] => [4] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,6,3,7,4,9,5,10,8] => [5,3,2] => [3,2] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,1,6,2,7,4,9,5,10,8] => [5,5] => [5] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,6,2,7,3,9,5,10,8] => [5,3,2] => [3,2] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,1,6,2,7,3,9,4,10,8] => [8,2] => [2] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,4,2,7,5,9,6,10,8] => [6,4] => [4] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,9,6,10,8] => [7,3] => [3] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,2,2,2,2,2] => [2,2,2,2,2] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,10,9,12,11] => [4,2,2,2,2] => [2,2,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7,10,9,12,11] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7,10,9,12,11] => [4,2,2,2,2] => [2,2,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,10,9,12,11] => [6,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,6,3,7,4,8,5,10,9,12,11] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,6,2,7,4,8,5,10,9,12,11] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,6,2,7,3,8,5,10,9,12,11] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,10,9,12,11] => [6,2,2,2] => [2,2,2] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,7,5,8,6,10,9,12,11] => [4,2,2,2,2] => [2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,7,5,8,6,10,9,12,11] => [4,4,2,2] => [4,2,2] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,5,2,7,3,8,6,10,9,12,11] => [5,3,2,2] => [3,2,2] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,3,7,4,8,6,10,9,12,11] => [6,2,2,2] => [2,2,2] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6,10,9,12,11] => [8,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,8,5,9,6,10,7,12,11] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,8,5,9,6,10,7,12,11] => [4,3,3,2] => [3,3,2] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,8,3,9,6,10,7,12,11] => [4,3,3,2] => [3,3,2] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,8,4,9,6,10,7,12,11] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,8,4,9,6,10,7,12,11] => [7,3,2] => [3,2] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,6,2,8,3,9,5,10,7,12,11] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,8,3,9,4,10,7,12,11] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,7,2,8,3,9,5,10,6,12,11] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,7,2,8,3,9,4,10,6,12,11] => [5,5,2] => [5,2] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,6,3,8,4,9,5,10,7,12,11] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,1,6,2,8,4,9,5,10,7,12,11] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [6,1,7,2,8,3,9,4,10,5,12,11] => [10,2] => [2] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,7,3,8,4,9,5,10,6,12,11] => [6,2,2,2] => [2,2,2] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,1,7,2,8,4,9,5,10,6,12,11] => [8,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,6,5,9,7,10,8,12,11] => [4,2,2,2,2] => [2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5,9,7,10,8,12,11] => [4,4,2,2] => [4,2,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,9,7,10,8,12,11] => [4,3,3,2] => [3,3,2] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,9,7,10,8,12,11] => [4,4,2,2] => [4,2,2] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,9,7,10,8,12,11] => [6,4,2] => [4,2] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,6,3,7,4,9,5,10,8,12,11] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,6,2,7,4,9,5,10,8,12,11] => [5,5,2] => [5,2] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,1,6,2,7,3,9,5,10,8,12,11] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,9,4,10,8,12,11] => [8,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,5,9,6,10,8,12,11] => [6,2,2,2] => [2,2,2] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,7,5,9,6,10,8,12,11] => [6,4,2] => [4,2] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,7,3,9,6,10,8,12,11] => [7,3,2] => [3,2] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,7,4,9,6,10,8,12,11] => [8,2,2] => [2,2] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8,12,11] => [10,2] => [2] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,6,5,10,7,11,8,12,9] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,4,2,6,5,10,7,11,8,12,9] => [4,3,3,2] => [3,3,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3,10,7,11,8,12,9] => [3,3,3,3] => [3,3,3] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,3,6,4,10,7,11,8,12,9] => [4,3,3,2] => [3,3,2] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,5,2,6,4,10,7,11,8,12,9] => [6,3,3] => [3,3] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,10,5,11,8,12,9] => [4,3,3,2] => [3,3,2] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,10,5,11,8,12,9] => [5,4,3] => [4,3] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,10,5,11,8,12,9] => [4,3,3,2] => [3,3,2] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,10,4,11,8,12,9] => [7,3,2] => [3,2] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,7,5,10,6,11,8,12,9] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,4,2,7,5,10,6,11,8,12,9] => [5,4,3] => [4,3] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,7,3,10,6,11,8,12,9] => [6,3,3] => [3,3] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,3,7,4,10,6,11,8,12,9] => [7,3,2] => [3,2] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,5,2,7,4,10,6,11,8,12,9] => [9,3] => [3] => 0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,8,4,10,5,11,7,12,9] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,8,4,10,5,11,7,12,9] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,1,7,2,8,3,10,4,11,5,12,9] => [9,3] => [3] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,7,3,8,4,10,5,11,6,12,9] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,1,7,2,8,4,10,5,11,6,12,9] => [7,3,2] => [3,2] => 0
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,6,3,9,4,10,5,11,7,12,8] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,1,6,2,9,4,10,5,11,7,12,8] => [5,5,2] => [5,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,7,3,9,4,10,5,11,6,12,8] => [5,5,2] => [5,2] => 1
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,1,7,2,9,4,10,5,11,6,12,8] => [7,5] => [5] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,8,3,10,5,11,7,12,9] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,7,2,8,3,10,5,11,6,12,9] => [4,3,3,2] => [3,3,2] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,1,6,2,8,3,10,4,11,7,12,9] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,1,7,2,8,3,10,4,11,6,12,9] => [5,4,3] => [4,3] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,1,8,2,9,3,10,4,11,5,12,7] => [6,6] => [6] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,1,6,2,9,3,10,5,11,7,12,8] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,1,7,2,9,3,10,5,11,6,12,8] => [5,4,3] => [4,3] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,9,3,10,4,11,7,12,8] => [8,2,2] => [2,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,7,2,9,3,10,4,11,6,12,8] => [8,4] => [4] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,8,5,10,6,11,7,12,9] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,1,4,2,8,5,10,6,11,7,12,9] => [4,3,3,2] => [3,3,2] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,8,3,10,6,11,7,12,9] => [4,3,3,2] => [3,3,2] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,5,3,8,4,10,6,11,7,12,9] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,1,5,2,8,4,10,6,11,7,12,9] => [7,3,2] => [3,2] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,8,3,9,4,10,5,11,6,12,7] => [10,2] => [2] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [4,1,8,2,9,3,10,5,11,6,12,7] => [9,3] => [3] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,4,3,9,5,10,6,11,7,12,8] => [6,2,2,2] => [2,2,2] => 0
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,1,4,2,9,5,10,6,11,7,12,8] => [6,4,2] => [4,2] => 0
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,1,5,2,9,3,10,6,11,7,12,8] => [7,3,2] => [3,2] => 0
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,5,3,9,4,10,6,11,7,12,8] => [8,2,2] => [2,2] => 2
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,1,5,2,9,4,10,6,11,7,12,8] => [10,2] => [2] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,8,7,11,9,12,10] => [4,2,2,2,2] => [2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,6,5,8,7,11,9,12,10] => [4,4,2,2] => [4,2,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,1,5,2,6,3,8,7,11,9,12,10] => [4,3,3,2] => [3,3,2] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4,8,7,11,9,12,10] => [4,4,2,2] => [4,2,2] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,6,4,8,7,11,9,12,10] => [6,4,2] => [4,2] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,6,3,7,4,8,5,11,9,12,10] => [4,3,3,2] => [3,3,2] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,6,2,7,4,8,5,11,9,12,10] => [5,4,3] => [4,3] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5,11,9,12,10] => [4,3,3,2] => [3,3,2] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,1,6,2,7,3,8,4,11,9,12,10] => [6,4,2] => [4,2] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6,11,9,12,10] => [4,4,2,2] => [4,2,2] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6,11,9,12,10] => [4,4,4] => [4,4] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,1,5,2,7,3,8,6,11,9,12,10] => [5,4,3] => [4,3] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,7,4,8,6,11,9,12,10] => [6,4,2] => [4,2] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,7,4,8,6,11,9,12,10] => [8,4] => [4] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,8,5,9,6,11,7,12,10] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,1,4,2,8,5,9,6,11,7,12,10] => [5,4,3] => [4,3] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,8,3,9,6,11,7,12,10] => [5,4,3] => [4,3] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,8,4,9,6,11,7,12,10] => [5,5,2] => [5,2] => 1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,8,4,9,6,11,7,12,10] => [7,5] => [5] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,6,2,8,3,9,5,11,7,12,10] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,1,6,2,8,3,9,4,11,7,12,10] => [5,5,2] => [5,2] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,7,2,8,3,9,5,11,6,12,10] => [7,3,2] => [3,2] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,1,7,2,8,3,9,4,11,6,12,10] => [7,5] => [5] => 0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,6,3,8,4,9,5,11,7,12,10] => [5,3,2,2] => [3,2,2] => 0
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,1,6,2,8,4,9,5,11,7,12,10] => [5,5,2] => [5,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,7,3,8,4,9,5,11,6,12,10] => [8,2,2] => [2,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,1,7,2,8,4,9,5,11,6,12,10] => [10,2] => [2] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,7,11,8,12,10] => [6,2,2,2] => [2,2,2] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,4,2,6,5,9,7,11,8,12,10] => [6,4,2] => [4,2] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,6,3,9,7,11,8,12,10] => [6,3,3] => [3,3] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,6,4,9,7,11,8,12,10] => [6,4,2] => [4,2] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4,9,7,11,8,12,10] => [6,6] => [6] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,6,3,7,4,9,5,11,8,12,10] => [7,3,2] => [3,2] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,6,2,7,4,9,5,11,8,12,10] => [7,5] => [5] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,1,6,2,7,3,9,5,11,8,12,10] => [7,3,2] => [3,2] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [5,1,6,2,7,3,9,4,11,8,12,10] => [10,2] => [2] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,5,9,6,11,8,12,10] => [8,2,2] => [2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,4,2,7,5,9,6,11,8,12,10] => [8,4] => [4] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,9,6,11,8,12,10] => [9,3] => [3] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,9,6,11,8,12,10] => [10,2] => [2] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8,10] => [7,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6,9] => [4,4,1] => [4,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [3,5,1,6,2,4,8,7,9] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,8,3,10,5,7,9] => [3,3,2,2] => [3,2,2] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,9,12,11] => [10,2] => [2] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [8,1,2,3,4,5,9,6,10,7] => [7,3] => [3] => 0
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => [6,6] => [6] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [3,9,1,2,4,5,6,7,10,8] => [8,2] => [2] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5,8,7,10,9,11] => [6,2,2,1] => [2,2,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,6,2,3,5,8,7,9] => [3,3,2,1] => [3,2,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [2,4,6,1,3,5,8,7,9] => [3,3,2,1] => [3,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7,9] => [3,3,2,1] => [3,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,10,9,11] => [4,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,8,9,1,10,2,3] => [7,3] => [3] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0] => [10,1,2,3,4,5,6,7,11,8,9] => [9,2] => [2] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [2,8,9,10,11,1,3,4,5,6,7] => [6,5] => [5] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,11,10] => [9,2] => [2] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => [5,4] => [4] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,9,11,2,10] => [10,1] => [1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7,9] => [6,2,1] => [2,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,8,9,2,3,4,5,6,7,10] => [4,4,1,1] => [4,1,1] => 2
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [6,8,10,1,2,3,4,5,7,9] => [7,3] => [3] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,6,1,2,3,7,8,9,10] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,9,8] => [6,2,1] => [2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,9,8,10] => [4,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,2,7,3,8,4,9,5,10,6] => [6,2,1,1] => [2,1,1] => 0
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,4,6,9,10,1,3,5,7,8] => [7,3] => [3] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [2,4,6,8,1,3,5,7,9,10] => [6,2,1,1] => [2,1,1] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,1,6,8,3,5,7,9] => [5,3,1] => [3,1] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,4,5,8,9,10,1,2,6,7] => [7,3] => [3] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,4,7,8,9,10,1,2,5,6] => [3,3,2,2] => [3,2,2] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [5,1,2,3,9,10,4,6,7,8] => [7,3] => [3] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,7,4,6,9,8] => [6,2,1] => [2,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => [3,2,2,1,1] => [2,2,1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,9,8,10] => [4,2,2,1,1] => [2,2,1,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,6,1,2,3,7,8,9] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,10,9,11] => [4,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,2,5,7,4,6,9,8] => [4,2,2,1] => [2,2,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => [7,3] => [3] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,5,8,9,10,7] => [4,4,2] => [4,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,6,8,9,1,10,7] => [7,3] => [3] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,9,8] => [4,3,2] => [3,2] => 0
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,5,8,9,10,1,2,3,6,7] => [4,4,2] => [4,2] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4,9] => [6,2,1] => [2,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,9,5] => [6,2,1] => [2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,10,5] => [6,2,2] => [2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,5,8,9,10,7] => [4,2,2,2] => [2,2,2] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,8,5,7,9] => [4,4,1] => [4,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,9] => [4,2,2,1] => [2,2,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8,10] => [5,2,2,1] => [2,2,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => [4,2,2,1] => [2,2,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => [5,2,2] => [2,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => [4,2,2,1,1] => [2,2,1,1] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7,9] => [3,2,2,1,1] => [2,2,1,1] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,6,7,8,10,1,2,3,5,9] => [7,3] => [3] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,4,7,6,9,8] => [5,2,2] => [2,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,9,8] => [5,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,1,5,6,7,8,10,2,9] => [8,2] => [2] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,9,7] => [5,4] => [4] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => [6,2,2] => [2,2] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => [4,2,2,2] => [2,2,2] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,3,6,8,7,9] => [5,2,1,1] => [2,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => [3,2,2,2,2,1] => [2,2,2,2,1] => 3
search for individual values
searching the database for the individual values of this statistic
Description
The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree.
For example, restricting $S_{(6,3)}$ to $\mathfrak S_8$ yields $$S_{(5,3)}\oplus S_{(6,2)}$$ of degrees (number of standard Young tableaux) 28 and 20, none of which are odd. Restricting to $\mathfrak S_7$ yields $$S_{(4,3)}\oplus 2S_{(5,2)}\oplus S_{(6,1)}$$ of degrees 14, 14 and 6. However, restricting to $\mathfrak S_6$ yields
$$S_{(3,3)}\oplus 3S_{(4,2)}\oplus 3S_{(5,1)}\oplus S_6$$ of degrees 5,9,5 and 1. Therefore, the statistic on the partition $(6,3)$ gives 3.
This is related to $2$-saturations of Welter's game, see [1, Corollary 1.2].
For example, restricting $S_{(6,3)}$ to $\mathfrak S_8$ yields $$S_{(5,3)}\oplus S_{(6,2)}$$ of degrees (number of standard Young tableaux) 28 and 20, none of which are odd. Restricting to $\mathfrak S_7$ yields $$S_{(4,3)}\oplus 2S_{(5,2)}\oplus S_{(6,1)}$$ of degrees 14, 14 and 6. However, restricting to $\mathfrak S_6$ yields
$$S_{(3,3)}\oplus 3S_{(4,2)}\oplus 3S_{(5,1)}\oplus S_6$$ of degrees 5,9,5 and 1. Therefore, the statistic on the partition $(6,3)$ gives 3.
This is related to $2$-saturations of Welter's game, see [1, Corollary 1.2].
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
cycle type
Description
The cycle type of a permutation as a partition.
searching the database
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