Identifier
-
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
St001279: Integer partitions ⟶ ℤ
Values
[1,0] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [2] => 2
[1,1,0,0] => [1,2] => [1,1] => 0
[1,0,1,0,1,0] => [2,3,1] => [3] => 3
[1,0,1,1,0,0] => [2,1,3] => [2,1] => 2
[1,1,0,0,1,0] => [1,3,2] => [2,1] => 2
[1,1,0,1,0,0] => [3,1,2] => [3] => 3
[1,1,1,0,0,0] => [1,2,3] => [1,1,1] => 0
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [4] => 4
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [3,1] => 3
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,2] => 4
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [4] => 4
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,1] => 2
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [3,1] => 3
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [2,1,1] => 2
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [4] => 4
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [2,2] => 4
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [3,1] => 3
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [2,1,1] => 2
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [3,1] => 3
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [4] => 4
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [5] => 5
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [4,1] => 4
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [3,2] => 5
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [5] => 5
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [3,1,1] => 3
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [3,2] => 5
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [2,2,1] => 4
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [5] => 5
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [3,2] => 5
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [4,1] => 4
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [2,2,1] => 4
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [3,2] => 5
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [5] => 5
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [2,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [4,1] => 4
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [3,1,1] => 3
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [2,2,1] => 4
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [4,1] => 4
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [2,1,1,1] => 2
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [5] => 5
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [4,1] => 4
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [3,2] => 5
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [5] => 5
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [2,2,1] => 4
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [3,2] => 5
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [5] => 5
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [3,2] => 5
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [3,1,1] => 3
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [3,1,1] => 3
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [2,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [4,1] => 4
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [2,2,1] => 4
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [3,1,1] => 3
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [5] => 5
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [3,2] => 5
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [5] => 5
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [4,1] => 4
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [2,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [3,1,1] => 3
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [4,1] => 4
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [5] => 5
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [6] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [5,1] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [4,2] => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [6] => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [4,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [3,3] => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [3,2,1] => 5
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [6] => 6
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [4,2] => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [5,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [3,2,1] => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [3,3] => 6
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [6] => 6
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [3,1,1,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [4,2] => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [3,2,1] => 5
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [2,2,2] => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [4,2] => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [2,2,1,1] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [6] => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [5,1] => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [3,3] => 6
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [6] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [3,2,1] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [4,2] => 6
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [6] => 6
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [3,3] => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [4,1,1] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [3,2,1] => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [2,2,1,1] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [4,2] => 6
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [2,2,2] => 6
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [3,2,1] => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [6] => 6
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [4,2] => 6
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [6] => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [5,1] => 5
>>> Load all 2391 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [2,2,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [3,2,1] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [4,2] => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [6] => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [5,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [4,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [3,2,1] => 5
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [5,1] => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [3,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [3,2,1] => 5
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [2,2,1,1] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [5,1] => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [3,2,1] => 5
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [4,1,1] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [2,2,1,1] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [3,2,1] => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [5,1] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [6] => 6
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [5,1] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [4,2] => 6
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [6] => 6
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [4,1,1] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [4,2] => 6
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [3,2,1] => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [6] => 6
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [3,3] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [5,1] => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [2,2,2] => 6
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [4,2] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [6] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [2,2,1,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [3,3] => 6
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [3,2,1] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [6] => 6
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [4,2] => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [5,1] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [4,2] => 6
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [2,2,2] => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [4,2] => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [3,2,1] => 5
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [3,2,1] => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [3,3] => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [6] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [4,2] => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [3,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [4,1,1] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [3,1,1,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [2,2,1,1] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [4,1,1] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [5,1] => 5
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [4,1,1] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [3,2,1] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [5,1] => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [2,2,1,1] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [3,2,1] => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [5,1] => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [3,2,1] => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [3,1,1,1] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [6] => 6
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [5,1] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [3,3] => 6
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [6] => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [3,2,1] => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [6] => 6
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [4,2] => 6
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [2,2,2] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [5,1] => 5
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [4,2] => 6
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [6] => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [3,3] => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [6] => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [4,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [3,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [4,1,1] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [2,2,1,1] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [3,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [5,1] => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [3,2,1] => 5
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [5,1] => 5
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [4,1,1] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [6] => 6
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [4,2] => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [6] => 6
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [3,3] => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [5,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [2,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [3,1,1,1] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [4,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [5,1] => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [6] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [7] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [6,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [5,2] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [7] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [5,1,1] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [4,3] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [4,2,1] => 6
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [7] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [5,2] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [6,1] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [4,2,1] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [4,3] => 7
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [7] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [4,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [4,3] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [3,3,1] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [3,2,2] => 7
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [4,3] => 7
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [3,2,1,1] => 5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [7] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [6,1] => 6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [4,3] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [7] => 7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [4,2,1] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [5,2] => 7
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [7] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [4,3] => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [5,1,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [3,3,1] => 6
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [3,2,1,1] => 5
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [4,3] => 7
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [3,2,2] => 7
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [3,3,1] => 6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [7] => 7
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [5,2] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [7] => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [6,1] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [3,2,1,1] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [3,3,1] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [4,3] => 7
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [7] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,1,1,1,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [5,2] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [4,2,1] => 6
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [3,2,2] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [5,2] => 7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [3,2,1,1] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [3,2,2] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [2,2,2,1] => 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [5,2] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [3,2,2] => 7
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [4,2,1] => 6
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [2,2,2,1] => 6
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [3,2,2] => 7
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [5,2] => 7
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [2,2,1,1,1] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [7] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [6,1] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [5,2] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [7] => 7
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [5,1,1] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [4,3] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [3,3,1] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [7] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [4,3] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [6,1] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [3,2,2] => 7
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [4,3] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [7] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [3,2,1,1] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [4,3] => 7
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [4,2,1] => 6
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [7] => 7
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [5,2] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [6,1] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [4,3] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [3,2,2] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [5,2] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [3,3,1] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [4,2,1] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [4,3] => 7
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [7] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [4,3] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [4,1,1,1] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [4,2,1] => 6
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [3,2,1,1] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,2,2,1] => 6
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [4,2,1] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [2,2,1,1,1] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [5,2] => 7
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [4,2,1] => 6
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [3,2,2] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [5,2] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [2,2,2,1] => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [3,2,2] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [5,2] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [3,2,2] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [3,2,1,1] => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [7] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [6,1] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [4,3] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [7] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [4,2,1] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [7] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [5,2] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [3,2,2] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [6,1] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [5,2] => 7
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [7] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [4,3] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [7] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [5,1,1] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [3,2,1,1] => 5
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [2,2,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [4,2,1] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [2,2,2,1] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [3,2,1,1] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [5,2] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [3,2,2] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [5,2] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [4,2,1] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [7] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [5,2] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [7] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [4,3] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [6,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,2,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [3,2,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [4,2,1] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [5,2] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [7] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [6,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [5,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [4,2,1] => 6
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [6,1] => 6
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [4,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [3,3,1] => 6
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [3,2,1,1] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [6,1] => 6
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [4,2,1] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [5,1,1] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [3,2,1,1] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [3,3,1] => 6
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [6,1] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [3,1,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [4,2,1] => 6
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [3,2,1,1] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [2,2,2,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [4,2,1] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [2,2,1,1,1] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [6,1] => 6
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [5,1,1] => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [3,3,1] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [6,1] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [3,2,1,1] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [4,2,1] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [6,1] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [3,3,1] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [4,1,1,1] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [3,2,1,1] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [2,2,1,1,1] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [4,2,1] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [2,2,2,1] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [3,2,1,1] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [6,1] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [4,2,1] => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [6,1] => 6
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [5,1,1] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [3,2,1,1] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [4,2,1] => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [6,1] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [7] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [6,1] => 6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [5,2] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [7] => 7
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [5,1,1] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [4,3] => 7
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [4,2,1] => 6
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [7] => 7
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [5,2] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [6,1] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [4,2,1] => 6
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [4,3] => 7
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [7] => 7
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [4,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [5,2] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [4,2,1] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [3,2,2] => 7
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [5,2] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [3,2,1,1] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [7] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [6,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [4,3] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [7] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [3,3,1] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [5,2] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [7] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [4,3] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [5,1,1] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [3,2,2] => 7
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [2,2,2,1] => 6
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [5,2] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [3,2,2] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [4,2,1] => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [7] => 7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [5,2] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [7] => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [6,1] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [2,2,2,1] => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [3,2,2] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [5,2] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [7] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [2,2,1,1,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [4,3] => 7
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [3,3,1] => 6
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [3,2,2] => 7
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [4,3] => 7
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [3,2,1,1] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [7] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [6,1] => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [4,3] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [7] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [4,2,1] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [5,2] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [7] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [4,3] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [5,1,1] => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [5,2] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [4,2,1] => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [3,2,2] => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [5,2] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [2,2,2,1] => 6
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [5,2] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [7] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [5,2] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [4,2,1] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [3,2,2] => 7
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [5,2] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [3,2,2] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [5,2] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [3,2,1,1] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [3,3,1] => 6
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [3,2,1,1] => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [4,3] => 7
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [3,2,2] => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [3,3,1] => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [7] => 7
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [5,2] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [7] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [6,1] => 6
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [5,2] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [3,2,2] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [5,2] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [7] => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [4,2,1] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [3,2,1,1] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [3,3,1] => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [4,3] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [7] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [5,2] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [3,1,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [5,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [4,1,1,1] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [3,2,1,1] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [5,1,1] => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [3,1,1,1,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [3,2,1,1] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [2,2,1,1,1] => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [5,1,1] => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [3,2,1,1] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [4,1,1,1] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [3,2,1,1] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [5,1,1] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [6,1] => 6
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [5,1,1] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [4,2,1] => 6
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [6,1] => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [4,1,1,1] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [4,2,1] => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [3,2,1,1] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [6,1] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [3,3,1] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [5,1,1] => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [2,2,2,1] => 6
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [4,2,1] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [6,1] => 6
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [2,2,1,1,1] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [3,3,1] => 6
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [3,2,1,1] => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [6,1] => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [4,2,1] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [5,1,1] => 5
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [4,2,1] => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [2,2,2,1] => 6
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [4,2,1] => 6
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [3,2,1,1] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [3,2,1,1] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [3,3,1] => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [6,1] => 6
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [4,2,1] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [3,1,1,1,1] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [7] => 7
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [6,1] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [5,2] => 7
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [7] => 7
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [5,1,1] => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [4,3] => 7
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [3,3,1] => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [7] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [4,3] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [6,1] => 6
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [3,2,2] => 7
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [4,3] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [7] => 7
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [3,2,1,1] => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [7] => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [6,1] => 6
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [5,2] => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [7] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [4,2,1] => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [3,2,2] => 7
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [5,2] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [7] => 7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [2,2,2,1] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [5,2] => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [7] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [5,2] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [3,2,2] => 7
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [5,1,1] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [4,3] => 7
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [4,2,1] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [7] => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [5,2] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [6,1] => 6
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [4,3] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [3,2,2] => 7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [5,2] => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [3,3,1] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [7] => 7
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [5,2] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [7] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [5,2] => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [6,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [4,2,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [4,3] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [7] => 7
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [4,3] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [7] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [4,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [4,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [3,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [2,2,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [4,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [5,1,1] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [4,1,1,1] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [3,2,1,1] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [5,1,1] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [2,2,1,1,1] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [3,2,1,1] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [5,1,1] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [3,2,1,1] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [3,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [6,1] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [5,1,1] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [3,3,1] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [6,1] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [3,2,1,1] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [6,1] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [4,2,1] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [2,2,2,1] => 6
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [5,1,1] => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [4,2,1] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [6,1] => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [3,3,1] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [6,1] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [4,1,1,1] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [7] => 7
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [6,1] => 6
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [4,3] => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [7] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [4,2,1] => 6
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [7] => 7
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [5,2] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [3,2,2] => 7
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [6,1] => 6
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [4,3] => 7
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [7] => 7
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [5,2] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [7] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [3,3,1] => 6
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [5,2] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [7] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [4,3] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [7] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [4,3] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [5,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [3,1,1,1,1] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [4,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [2,2,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [3,1,1,1,1] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [5,1,1] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [3,2,1,1] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [5,1,1] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [4,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [6,1] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [4,2,1] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [6,1] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [3,3,1] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [5,1,1] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [7] => 7
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [5,2] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [7] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [4,3] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [7] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [6,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [3,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [4,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [5,1,1] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [6,1] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [7] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [8] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [7,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [6,2] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [8] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [6,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6] => [5,3] => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,8] => [5,2,1] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => [8] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [6,2] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6,8] => [7,1] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => [5,2,1] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => [5,3] => 8
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [8] => 8
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [4,4] => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8] => [4,3,1] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [4,2,2] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,8,5,7] => [4,4] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => [4,2,1,1] => 6
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,6,1,7,8,5] => [8] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => [8] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => [5,2,1] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,8,5,7] => [8] => 8
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,4,6,8,1,5,7] => [5,3] => 8
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [6,1,1] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,1,5,7,8,6] => [4,3,1] => 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [4,2,1,1] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [4,4] => 8
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [4,2,2] => 8
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,4,1,7,5,6,8] => [4,3,1] => 7
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,4,7,1,5,8,6] => [8] => 8
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,4,7,1,8,5,6] => [6,2] => 8
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,7,8,1,5,6] => [8] => 8
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [7,1] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,1,5,6,8,7] => [4,2,1,1] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => [4,3,1] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [4,4] => 8
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [8] => 8
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [4,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,4] => [5,3] => 8
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,4,8] => [4,3,1] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,5,6,8,4,7] => [5,3] => 8
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,4,7,8] => [3,3,1,1] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,2,1] => 7
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,7,8,4,6] => [3,3,2] => 8
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,5,4,6,7,8] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,4] => [8] => 8
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,5,1,6,4,8,7] => [6,2] => 8
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,5,1,6,8,4,7] => [8] => 8
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => [4,4] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,5,6,7,1,8,4] => [8] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => [5,3] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,6,7,1,4,8] => [7,1] => 7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,6,1,4,8,7] => [4,2,2] => 8
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,6,1,8,4,7] => [4,4] => 8
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,8,1,4,7] => [8] => 8
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [4,2,1,1] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6,8] => [5,2,1] => 7
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,7,4,8,6] => [8] => 8
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,7,1,4,8,6] => [4,4] => 8
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,7,1,8,4,6] => [4,2,2] => 8
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,7,8,1,4,6] => [6,2] => 8
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6,8] => [4,3,1] => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,5,1,4,8,6,7] => [5,3] => 8
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [8] => 8
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,8,1,4,6,7] => [4,4] => 8
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,1,4,6,7,8] => [5,1,1,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [4,3,1] => 7
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8] => [3,3,1,1] => 6
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7] => [3,2,2,1] => 7
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [4,3,1] => 7
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,4,5] => [5,3] => 8
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [5,3] => 8
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,4,5,7] => [3,3,2] => 8
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => [3,3,1,1] => 6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,1,4,7,8,5] => [8] => 8
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,1,4,7,5,8] => [7,1] => 7
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => [8] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,6,7,1,8,4,5] => [6,2] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,6,7,8,1,4,5] => [4,2,2] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,8,7] => [6,2] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,6,1,4,8,5,7] => [8] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => [5,3] => 8
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,6,1,4,5,7,8] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6] => [3,3,1,1] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [3,2,2,1] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,1,4,7,5,6,8] => [3,3,1,1] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,7,4,5,8,6] => [5,3] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,3,2] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,7,8,4,5,6] => [5,3] => 8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,1,4,5,8,6] => [8] => 8
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,1,4,8,5,6] => [6,2] => 8
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [5,3] => 8
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6,8] => [7,1] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [3,3,1,1] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [4,3,1] => 7
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => [5,3] => 8
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [8] => 8
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [3,1,1,1,1,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => [6,2] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,3,8] => [5,2,1] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [4,2,2] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,4,5,6,8,3,7] => [6,2] => 8
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => [6,2] => 8
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4,5,7,8,3,6] => [4,2,2] => 8
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,3,6,8,7] => [3,2,2,1] => 7
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4,5,8,3,6,7] => [6,2] => 8
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => [3,2,1,1,1] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [4,2,2] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,6,7,5,8] => [3,2,2,1] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [4,2,2] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => [2,2,2,1,1] => 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,6,3,7,8,5] => [6,2] => 8
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,6,3,7,5,8] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,7,3,8,5] => [3,3,2] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,6,7,8,3,5] => [6,2] => 8
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,8,7] => [4,2,2] => 8
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,8,5,7] => [6,2] => 8
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [3,3,2] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [3,2,2,1] => 7
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [4,2,2] => 8
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [2,2,2,2] => 8
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,7,3,5,8,6] => [6,2] => 8
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,4,7,8,3,5,6] => [6,2] => 8
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => [2,2,2,1,1] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [3,2,2,1] => 7
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [4,2,2] => 8
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,8,3,5,6,7] => [6,2] => 8
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [2,2,1,1,1,1] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,3] => [8] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,5,6,7,3,8] => [7,1] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,6,3,8,7] => [6,2] => 8
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,5,6,8,3,7] => [8] => 8
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => [6,1,1] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,5,3,7,8,6] => [5,3] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [5,2,1] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,4,1,5,7,3,8,6] => [8] => 8
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => [5,2,1] => 7
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [5,3] => 8
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,4,1,5,8,3,6,7] => [8] => 8
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,3,6,7,8] => [5,1,1,1] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,4,5,1,6,7,8,3] => [5,3] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,4,5,1,6,3,8,7] => [3,3,2] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,4,5,1,6,8,3,7] => [5,3] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,4,5,1,6,3,7,8] => [3,3,1,1] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => [8] => 8
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,6,1,7,3,8] => [7,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => [4,4] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,1,3] => [8] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,1,3,8] => [4,3,1] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,6,1,3,8,7] => [6,2] => 8
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,6,1,8,3,7] => [8] => 8
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,6,8,1,3,7] => [4,4] => 8
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [6,1,1] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,4,5,1,3,7,8,6] => [3,3,2] => 8
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6,8] => [3,2,2,1] => 7
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,4,5,1,7,3,8,6] => [5,3] => 8
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,4,5,1,7,8,3,6] => [3,3,2] => 8
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6,8] => [4,3,1] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,7,1,8,3,6] => [6,2] => 8
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,7,8,1,3,6] => [8] => 8
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [5,3] => 8
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [3,2,1,1,1] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,6,7,8,5] => [4,4] => 8
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => [4,2,2] => 8
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,8,5,7] => [4,4] => 8
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,6,5,7,8] => [4,2,1,1] => 6
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [8] => 8
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [7,1] => 7
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => [5,3] => 8
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,7,8,3,5] => [8] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,8,7] => [6,2] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [8] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => [5,3] => 8
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,6,1,3,7,5,8] => [4,3,1] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [3,3,2] => 8
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,6,7,1,3,8,5] => [6,2] => 8
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,6,7,8,1,3,5] => [6,2] => 8
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [5,2,1] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [3,3,2] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,8,5,7] => [5,3] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [3,3,2] => 8
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [6,2] => 8
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,6,1,3,5,7,8] => [3,3,1,1] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => [4,4] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,3,7,8,5,6] => [4,2,2] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,5,8,6] => [8] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,7,3,8,5,6] => [6,2] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,7,8,3,5,6] => [8] => 8
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => [5,3] => 8
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [8] => 8
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => [4,4] => 8
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,8,3,5,6,7] => [8] => 8
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [5,3] => 8
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8] => [4,1,1,1,1] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,4] => [5,2,1] => 7
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,6,4,8,7] => [3,2,2,1] => 7
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,8,4,7] => [5,2,1] => 7
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,7,8,6] => [3,2,2,1] => 7
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4,6,8,7] => [2,2,2,1,1] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,1,3,5,8,4,6,7] => [5,2,1] => 7
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8] => [2,2,1,1,1,1] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [6,2] => 8
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,1,5,3,6,7,4,8] => [5,2,1] => 7
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [4,2,2] => 8
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,1,5,3,6,8,4,7] => [6,2] => 8
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,5,6,3,7,8,4] => [4,2,2] => 8
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,1,5,6,3,7,4,8] => [3,2,2,1] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,5,6,7,3,8,4] => [6,2] => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => [3,3,2] => 8
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,1,5,6,7,3,4,8] => [5,2,1] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,2,2,2] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,1,5,6,8,3,4,7] => [6,2] => 8
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,1,5,6,3,4,7,8] => [2,2,2,1,1] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [6,2] => 8
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,5,3,7,8,4,6] => [4,2,2] => 8
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,5,7,3,4,8,6] => [4,2,2] => 8
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [2,2,2,2] => 8
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => [4,2,2] => 8
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6,8] => [3,2,2,1] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,5,3,4,6,8,7] => [3,2,2,1] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,1,5,3,8,4,6,7] => [6,2] => 8
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,1,5,8,3,4,6,7] => [4,2,2] => 8
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,5,3,4,6,7,8] => [3,2,1,1,1] => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,4] => [8] => 8
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,1,3,6,4,8,7] => [6,2] => 8
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,1,3,6,8,4,7] => [8] => 8
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,1,3,6,4,7,8] => [6,1,1] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,5,1,6,3,7,8,4] => [4,4] => 8
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,1,6,3,7,4,8] => [4,3,1] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => [8] => 8
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,1,6,7,8,3,4] => [5,3] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,1,6,3,4,8,7] => [4,2,2] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,1,6,8,3,4,7] => [8] => 8
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,1,6,3,4,7,8] => [4,2,1,1] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,5,6,1,3,7,8,4] => [8] => 8
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,5,6,1,3,7,4,8] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,5,6,1,7,8,3,4] => [8] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,5,6,1,7,3,4,8] => [5,2,1] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,5,6,7,1,3,8,4] => [3,3,2] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,5,6,7,1,8,3,4] => [5,3] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => [8] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,5,6,1,3,4,8,7] => [6,2] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,5,6,1,3,8,4,7] => [8] => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [3,3,2] => 8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,7,4,8,6] => [8] => 8
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,7,8,4,6] => [6,2] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => [4,4] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,5,1,7,8,3,4,6] => [6,2] => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,5,7,1,3,4,8,6] => [8] => 8
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,5,7,1,8,3,4,6] => [8] => 8
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [5,3] => 8
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,5,1,3,8,4,6,7] => [8] => 8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,5,1,8,3,4,6,7] => [4,4] => 8
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,5,8,1,3,4,6,7] => [8] => 8
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,4,6,7,8] => [5,1,1,1] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [4,2,1,1] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,2,2,1,1] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [2,2,1,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,6,7,4,8,5] => [3,2,2,1] => 7
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,6,7,8,4,5] => [5,2,1] => 7
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,6,4,5,8,7] => [3,2,2,1] => 7
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,1,3,6,4,5,7,8] => [3,2,1,1,1] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [6,2] => 8
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [3,3,2] => 8
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,6,3,7,8,4,5] => [6,2] => 8
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,1,6,3,7,4,5,8] => [3,2,2,1] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,6,7,3,4,8,5] => [6,2] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [2,2,2,2] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [4,2,2] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => [6,2] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,1,6,3,8,4,5,7] => [3,3,2] => 8
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,1,6,8,3,4,5,7] => [6,2] => 8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,1,3,4,7,8,5] => [8] => 8
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,1,3,4,7,5,8] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,6,1,3,7,4,8,5] => [5,3] => 8
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,1,3,7,8,4,5] => [8] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,6,1,7,3,4,8,5] => [8] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,6,1,7,8,3,4,5] => [4,2,2] => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => [4,4] => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,6,7,1,3,8,4,5] => [8] => 8
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,6,7,1,8,3,4,5] => [6,2] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [8] => 8
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,6,7,1,3,4,5,8] => [4,3,1] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,8,7] => [6,2] => 8
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,8,5,7] => [8] => 8
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,6,1,3,8,4,5,7] => [5,3] => 8
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [4,4] => 8
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => [6,1,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [3,2,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [2,2,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,4,7,5,8,6] => [4,2,1,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,1,3,4,7,8,5,6] => [2,2,2,1,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => [3,2,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,1,3,7,4,8,5,6] => [3,2,2,1] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,3,7,8,4,5,6] => [5,2,1] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,7,3,4,5,8,6] => [6,2] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,1,7,3,4,8,5,6] => [4,2,2] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,1,7,3,8,4,5,6] => [6,2] => 8
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,7,8,3,4,5,6] => [3,3,2] => 8
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => [5,2,1] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,7,1,3,4,5,8,6] => [8] => 8
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,7,1,3,8,4,5,6] => [8] => 8
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => [5,3] => 8
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [8] => 8
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => [7,1] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,2,1,1,1,1] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [3,2,1,1,1] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [4,2,1,1] => 6
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [5,2,1] => 7
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [6,2] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [8] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => [7,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,2,8] => [6,1,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,6,2,8,7] => [5,2,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,8,2,7] => [7,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,2,7,8] => [5,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,2,7,8,6] => [4,3,1] => 7
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,8] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => [5,2,1] => 7
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,5,2,8,6,7] => [4,3,1] => 7
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,5,8,2,6,7] => [7,1] => 7
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [4,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,5] => [4,3,1] => 7
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => [3,3,1,1] => 6
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7] => [3,2,2,1] => 7
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,6,2,7,5,8] => [6,1,1] => 6
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => [4,3,1] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,7,2,5,8] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,8,7] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,4,6,8,2,5,7] => [4,3,1] => 7
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => [5,1,1,1] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,4,2,5,7,8,6] => [3,3,1,1] => 6
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,4,2,5,7,6,8] => [3,2,1,1,1] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,2,7,5,8,6] => [4,3,1] => 7
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,4,2,7,8,5,6] => [3,2,2,1] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,4,7,2,5,8,6] => [7,1] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,4,7,8,2,5,6] => [7,1] => 7
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [6,1,1] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7] => [3,2,1,1,1] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,3,4,2,5,8,6,7] => [3,3,1,1] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [4,3,1] => 7
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [7,1] => 7
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8] => [3,1,1,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,6,7,8,4] => [5,2,1] => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,5,6,7,4,8] => [4,2,1,1] => 6
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,6,4,8,7] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,5,6,4,7,8] => [3,2,1,1,1] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [2,2,2,1,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,7,8,4,6] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6,8] => [4,2,1,1] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [5,2,1] => 7
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,5,2,6,7,4,8] => [6,1,1] => 6
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,5,2,6,4,8,7] => [5,2,1] => 7
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,5,2,6,8,4,7] => [7,1] => 7
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,5,6,2,7,8,4] => [4,3,1] => 7
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => [3,3,1,1] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => [4,3,1] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,6,7,2,4,8] => [6,1,1] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,5,6,2,4,8,7] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,5,6,2,8,4,7] => [4,3,1] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,6,8,2,4,7] => [7,1] => 7
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [3,2,1,1,1] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6,8] => [4,2,1,1] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,7,4,8,6] => [7,1] => 7
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,7,8,4,6] => [5,2,1] => 7
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6,8] => [6,1,1] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,7,2,4,8,6] => [4,3,1] => 7
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,7,2,8,4,6] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => [5,2,1] => 7
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [3,3,1,1] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,5,2,4,6,8,7] => [4,2,1,1] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,5,2,4,8,6,7] => [4,3,1] => 7
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [7,1] => 7
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [4,3,1] => 7
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,2,4,6,7,8] => [4,1,1,1,1] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5] => [4,2,1,1] => 6
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7] => [2,2,2,1,1] => 6
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,4,6,8,5,7] => [4,2,1,1] => 6
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [4,2,1,1] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,2,6,7,4,8,5] => [3,2,2,1] => 7
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,7,8,4,5] => [5,2,1] => 7
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,2,6,7,4,5,8] => [2,2,2,1,1] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [5,2,1] => 7
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,6,8,4,5,7] => [3,2,2,1] => 7
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [3,2,1,1,1] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,6,2,4,7,8,5] => [7,1] => 7
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,2,4,7,5,8] => [6,1,1] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,2,7,4,8,5] => [4,3,1] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => [7,1] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,7,4,5,8] => [4,2,1,1] => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,6,7,2,4,8,5] => [7,1] => 7
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,6,7,8,2,4,5] => [3,2,2,1] => 7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,8,7] => [5,2,1] => 7
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,6,2,4,8,5,7] => [7,1] => 7
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,6,2,4,5,7,8] => [5,1,1,1] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => [3,2,1,1,1] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,3,2,4,7,5,8,6] => [4,2,1,1] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [2,2,2,1,1] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [3,2,2,1] => 7
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [4,2,1,1] => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,2,4,5,8,6] => [7,1] => 7
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,7,2,4,8,5,6] => [5,2,1] => 7
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [7,1] => 7
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [4,3,1] => 7
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6,8] => [6,1,1] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [3,2,1,1,1] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [4,2,1,1] => 6
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [5,2,1] => 7
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [7,1] => 7
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [8] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => [7,1] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,5,6,2,8,7] => [6,2] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,8,2,7] => [8] => 8
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,5,2,7,8,6] => [5,3] => 8
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6,8] => [5,2,1] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,5,7,2,8,6] => [8] => 8
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4,5,7,8,2,6] => [6,2] => 8
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4,5,8,2,6,7] => [8] => 8
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => [5,1,1,1] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [4,4] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,4,2,6,7,5,8] => [4,3,1] => 7
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [4,2,2] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [4,4] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,1,4,2,6,5,7,8] => [4,2,1,1] => 6
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,6,2,7,8,5] => [8] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,6,7,2,8,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,4,6,7,8,2,5] => [8] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,8,7] => [6,2] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,8,5,7] => [8] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => [5,3] => 8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => [4,3,1] => 7
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [4,4] => 8
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,4,2,7,8,5,6] => [4,2,2] => 8
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,4,2,7,5,6,8] => [4,3,1] => 7
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,7,2,5,8,6] => [8] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,2,5,8,6,7] => [4,3,1] => 7
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [4,4] => 8
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,4,8,2,5,6,7] => [8] => 8
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [4,1,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [6,2] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,5,6,7,2,8] => [5,2,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,4,1,5,6,2,8,7] => [4,2,2] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,5,6,8,2,7] => [6,2] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,4,1,5,6,2,7,8] => [4,2,1,1] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6,8] => [3,2,2,1] => 7
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,4,1,5,7,2,8,6] => [6,2] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,7,8,2,6] => [4,2,2] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6,8] => [5,2,1] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,2,8,6,7] => [3,3,2] => 8
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4,1,5,8,2,6,7] => [6,2] => 8
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,1,5,2,6,7,8] => [3,2,1,1,1] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [8] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,5,1,6,7,2,8] => [7,1] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,1,6,2,8,7] => [6,2] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,1,6,2,7,8] => [6,1,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => [5,3] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => [4,3,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [8] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => [4,4] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => [7,1] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,1,2,8,7] => [3,3,2] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,6,1,8,2,7] => [5,3] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,8,1,2,7] => [8] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [3,3,1,1] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,5,1,2,7,8,6] => [5,3] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,5,1,7,8,2,6] => [6,2] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,5,7,1,8,2,6] => [3,3,2] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,7,8,1,2,6] => [5,3] => 8
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => [4,3,1] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,5,1,2,6,8,7] => [5,2,1] => 7
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [5,3] => 8
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [5,1,1,1] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,5] => [4,2,2] => 8
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,6,7,5,8] => [3,2,2,1] => 7
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [2,2,2,2] => 8
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,8,5,7] => [4,2,2] => 8
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,6,5,7,8] => [2,2,2,1,1] => 6
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,4,1,6,2,7,8,5] => [6,2] => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,6,2,7,5,8] => [5,2,1] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => [3,3,2] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,6,7,8,2,5] => [6,2] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,8,7] => [4,2,2] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,8,5,7] => [6,2] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,8,2,5,7] => [3,3,2] => 8
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,4,6,1,2,7,8,5] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [5,3] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,4,6,7,1,8,2,5] => [5,3] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,1,2,5] => [3,3,2] => 8
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => [7,1] => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,8,7] => [6,2] => 8
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,4,1,2,5,7,8,6] => [3,2,2,1] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [2,2,2,1,1] => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => [4,2,2] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [2,2,2,2] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,4,1,2,7,5,6,8] => [3,2,2,1] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,4,7,1,2,5,8,6] => [8] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [8] => 8
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [4,4] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1,2,5,6,8,7] => [2,2,2,1,1] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,2,5,8,6,7] => [3,2,2,1] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [4,2,2] => 8
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1,8,2,5,6,7] => [6,2] => 8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [8] => 8
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [2,2,1,1,1,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,4] => [5,3] => 8
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,5,6,8,4,7] => [5,3] => 8
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => [3,2,2,1] => 7
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,7,4,8,6] => [5,3] => 8
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6,8] => [4,3,1] => 7
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,5,4,6,8,7] => [3,2,2,1] => 7
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,5,8,4,6,7] => [5,3] => 8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => [8] => 8
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [6,2] => 8
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,5,2,6,8,4,7] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,5,6,2,7,8,4] => [4,4] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,5,6,7,2,8,4] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,2,4] => [5,3] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,5,6,2,4,8,7] => [4,2,2] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => [4,4] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,5,6,8,2,4,7] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,5,6,2,4,7,8] => [4,2,1,1] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6,8] => [5,2,1] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,7,8,4,6] => [6,2] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => [7,1] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => [4,4] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,7,2,8,4,6] => [4,2,2] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,7,8,2,4,6] => [6,2] => 8
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6,8] => [4,3,1] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,5,2,4,8,6,7] => [5,3] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [8] => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,5,8,2,4,6,7] => [4,4] => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,5,1,2,6,7,8,4] => [6,2] => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [5,2,1] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7] => [4,2,2] => 8
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,1,2,6,8,4,7] => [6,2] => 8
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,5,1,6,2,7,8,4] => [4,2,2] => 8
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [3,2,2,1] => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,5,1,6,7,2,8,4] => [6,2] => 8
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,5,1,6,7,8,2,4] => [3,3,2] => 8
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,5,1,6,7,2,4,8] => [5,2,1] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [2,2,2,2] => 8
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,5,1,6,8,2,4,7] => [6,2] => 8
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => [2,2,2,1,1] => 6
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => [6,2] => 8
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,5,6,1,2,7,4,8] => [5,2,1] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,5,6,1,7,8,2,4] => [5,3] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,5,6,7,1,2,8,4] => [5,3] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,5,6,7,1,8,2,4] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,1,2,4] => [5,3] => 8
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [5,2,1] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [4,2,2] => 8
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [8] => 8
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [5,3] => 8
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,5,6,1,2,4,7,8] => [4,2,1,1] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,7,8,6] => [3,3,2] => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [3,2,2,1] => 7
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,7,4,8,6] => [6,2] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,7,8,4,6] => [4,2,2] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6,8] => [5,2,1] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [2,2,2,2] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,7,8,2,4,6] => [4,2,2] => 8
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6,8] => [3,2,2,1] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => [6,2] => 8
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [8] => 8
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => [5,2,1] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,5,1,2,4,6,8,7] => [3,2,2,1] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,5,1,2,8,4,6,7] => [6,2] => 8
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,5,1,8,2,4,6,7] => [4,2,2] => 8
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,5,1,2,4,6,7,8] => [3,2,1,1,1] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => [4,3,1] => 7
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,7,5,8] => [3,3,1,1] => 6
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [3,2,2,1] => 7
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,2,4,6,8,5,7] => [4,3,1] => 7
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,2,6,4,7,8,5] => [5,3] => 8
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [3,1,2,6,4,7,5,8] => [4,3,1] => 7
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [3,3,2] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,6,7,8,4,5] => [5,3] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,6,4,5,8,7] => [3,3,2] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [3,1,2,6,8,4,5,7] => [3,3,2] => 8
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [5,3] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [3,1,6,2,7,4,5,8] => [5,2,1] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,6,7,2,8,4,5] => [6,2] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [6,2] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [3,1,6,2,4,8,5,7] => [8] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [3,1,6,2,8,4,5,7] => [5,3] => 8
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => [8] => 8
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,6,2,4,5,7,8] => [6,1,1] => 6
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => [6,2] => 8
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [5,2,1] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,6,1,2,7,4,8,5] => [3,3,2] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [3,6,1,2,7,8,4,5] => [6,2] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [6,2] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [4,2,2] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [2,2,2,2] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => [4,4] => 8
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [6,2] => 8
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,6,7,1,2,4,5,8] => [7,1] => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,8,7] => [4,2,2] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,8,5,7] => [6,2] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [3,6,1,2,8,4,5,7] => [3,3,2] => 8
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,6,1,8,2,4,5,7] => [6,2] => 8
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,6,8,1,2,4,5,7] => [8] => 8
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,6,1,2,4,5,7,8] => [4,2,1,1] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,2,4,5,7,8,6] => [3,3,1,1] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [3,2,1,1,1] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => [4,3,1] => 7
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,2,4,7,8,5,6] => [3,2,2,1] => 7
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [3,3,1,1] => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [3,1,2,7,4,8,5,6] => [3,3,2] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,2,7,8,4,5,6] => [5,3] => 8
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,2,7,4,5,6,8] => [4,3,1] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,7,2,4,5,8,6] => [8] => 8
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [3,1,7,2,8,4,5,6] => [8] => 8
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => [5,3] => 8
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6,8] => [7,1] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => [6,2] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [3,7,1,2,4,8,5,6] => [4,2,2] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [3,7,1,2,8,4,5,6] => [6,2] => 8
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,7,1,8,2,4,5,6] => [3,3,2] => 8
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [5,3] => 8
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => [5,2,1] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [3,2,1,1,1] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [3,3,1,1] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [4,3,1] => 7
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => [5,3] => 8
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [8] => 8
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [6,2] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [3,1,1,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [6,1,1] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,7,3,8] => [5,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,4,5,6,3,8,7] => [4,2,1,1] => 6
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,6,8,3,7] => [6,1,1] => 6
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,3,7,8] => [4,1,1,1,1] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,5,3,7,8,6] => [3,3,1,1] => 6
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6,8] => [3,2,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,7,8,3,6] => [4,2,1,1] => 6
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6,8] => [5,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,4,5,3,8,6,7] => [3,3,1,1] => 6
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,4,5,8,3,6,7] => [6,1,1] => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [4,2,1,1] => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,6,7,5,8] => [3,2,1,1,1] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [2,2,2,1,1] => 6
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,8,5,7] => [4,2,1,1] => 6
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [2,2,1,1,1,1] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,6,7,8,3,5] => [6,1,1] => 6
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,8,7] => [4,2,1,1] => 6
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,8,5,7] => [6,1,1] => 6
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => [3,3,1,1] => 6
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [4,1,1,1,1] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [3,2,1,1,1] => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => [2,2,1,1,1,1] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,4,3,7,8,5,6] => [2,2,2,1,1] => 6
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => [3,2,1,1,1] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,7,3,5,8,6] => [6,1,1] => 6
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,4,7,3,8,5,6] => [4,2,1,1] => 6
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,4,7,8,3,5,6] => [6,1,1] => 6
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [5,1,1,1] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [2,2,1,1,1,1] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [3,2,1,1,1] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [4,2,1,1] => 6
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [6,1,1] => 6
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [7,1] => 7
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => [6,1,1] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [4,2,1,1] => 6
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [7,1] => 7
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,4,2,5,7,8,3,6] => [5,2,1] => 7
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6,8] => [6,1,1] => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,4,2,5,3,6,8,7] => [4,2,1,1] => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [4,3,1] => 7
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [4,1,1,1,1] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [5,2,1] => 7
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,5,2,6,7,3,8] => [4,2,1,1] => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,5,2,6,3,8,7] => [3,2,2,1] => 7
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,5,2,6,8,3,7] => [5,2,1] => 7
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [3,2,1,1,1] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,4,5,6,2,7,3,8] => [6,1,1] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,2,8,3] => [4,3,1] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,2,3] => [7,1] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => [3,3,1,1] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,6,8,2,3,7] => [4,3,1] => 7
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [5,1,1,1] => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,4,5,2,3,7,8,6] => [3,2,2,1] => 7
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6,8] => [2,2,2,1,1] => 6
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [5,2,1] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,4,5,2,7,8,3,6] => [3,2,2,1] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6,8] => [4,2,1,1] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [7,1] => 7
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,7,8,2,3,6] => [7,1] => 7
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [6,1,1] => 6
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,5,2,3,8,6,7] => [3,2,2,1] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [5,2,1] => 7
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,2,3,6,7,8] => [2,2,1,1,1,1] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,6,7,8,5] => [4,3,1] => 7
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,6,7,5,8] => [3,3,1,1] => 6
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [3,2,2,1] => 7
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,6,5,7,8] => [3,2,1,1,1] => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [6,1,1] => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => [7,1] => 7
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,6,7,3,5,8] => [4,2,1,1] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,8,7] => [5,2,1] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [7,1] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,8,3,5,7] => [4,3,1] => 7
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => [5,1,1,1] => 5
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,4,6,2,3,7,8,5] => [5,2,1] => 7
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [3,2,2,1] => 7
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => [5,2,1] => 7
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,7,3,5,8] => [2,2,2,1,1] => 6
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => [7,1] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,4,6,7,8,2,3,5] => [5,2,1] => 7
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [4,2,1,1] => 6
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,8,7] => [3,2,2,1] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,8,5,7] => [5,2,1] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [3,2,2,1] => 7
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [5,2,1] => 7
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,6,2,3,5,7,8] => [3,2,1,1,1] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,4,2,3,5,7,8,6] => [3,3,1,1] => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [3,2,1,1,1] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,4,2,3,7,5,8,6] => [4,3,1] => 7
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,3,7,8,5,6] => [3,2,2,1] => 7
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [3,3,1,1] => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,4,2,7,3,5,8,6] => [7,1] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [5,2,1] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [7,1] => 7
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [6,1,1] => 6
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,4,7,2,3,5,8,6] => [5,2,1] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,7,2,3,8,5,6] => [3,2,2,1] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => [5,2,1] => 7
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => [7,1] => 7
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6,8] => [4,2,1,1] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => [3,2,1,1,1] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [3,3,1,1] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [4,3,1] => 7
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [7,1] => 7
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [5,2,1] => 7
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [3,1,1,1,1,1] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [8] => 8
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,5,6,7,3,8] => [7,1] => 7
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [6,2] => 8
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,5,6,8,3,7] => [8] => 8
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3,7,8] => [6,1,1] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => [5,3] => 8
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => [5,2,1] => 7
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,5,7,3,8,6] => [8] => 8
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,5,7,8,3,6] => [6,2] => 8
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6,8] => [7,1] => 7
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,5,3,8,6,7] => [5,3] => 8
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,1,2,5,8,3,6,7] => [8] => 8
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => [5,1,1,1] => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [5,3] => 8
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [3,3,2] => 8
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [5,3] => 8
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,1,5,2,6,3,7,8] => [3,3,1,1] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,5,6,7,2,8,3] => [4,4] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,2,3] => [8] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,1,5,6,7,2,3,8] => [4,3,1] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,5,6,2,3,8,7] => [6,2] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [4,1,5,6,2,8,3,7] => [8] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => [4,4] => 8
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,1,5,6,2,3,7,8] => [6,1,1] => 6
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [3,3,2] => 8
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6,8] => [3,2,2,1] => 7
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [5,3] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [3,3,2] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6,8] => [4,3,1] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,5,7,2,8,3,6] => [6,2] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,1,5,2,3,8,6,7] => [3,3,2] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,5,2,8,3,6,7] => [5,3] => 8
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,5,2,3,6,7,8] => [3,2,1,1,1] => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,3] => [8] => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [7,1] => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [6,2] => 8
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,5,1,2,6,8,3,7] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,5,1,6,2,7,8,3] => [6,2] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [5,2,1] => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,5,1,6,7,8,2,3] => [5,3] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [4,5,1,6,7,2,3,8] => [7,1] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,5,1,6,2,3,8,7] => [4,2,2] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [4,5,1,6,2,8,3,7] => [6,2] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [4,5,1,6,8,2,3,7] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,1,6,2,3,7,8] => [4,2,1,1] => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,1,2,7,8,3] => [4,2,2] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,1,2,7,3,8] => [3,2,2,1] => 7
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => [6,2] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,6,1,7,8,2,3] => [3,3,2] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,6,1,7,2,3,8] => [5,2,1] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,1,2,8,3] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => [5,3] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [7,1] => 7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [2,2,2,2] => 8
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,6,1,2,8,3,7] => [4,2,2] => 8
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [6,2] => 8
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [8] => 8
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [2,2,2,1,1] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6,8] => [5,2,1] => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,5,1,2,7,3,8,6] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [4,5,1,2,7,8,3,6] => [6,2] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,5,1,7,2,3,8,6] => [6,2] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [4,5,1,7,2,8,3,6] => [4,2,2] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [4,5,1,7,8,2,3,6] => [4,4] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [2,2,2,2] => 8
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [6,2] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [4,5,1,2,3,8,6,7] => [5,3] => 8
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,5,1,8,2,3,6,7] => [6,2] => 8
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [4,2,2] => 8
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [5,1,1,1] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [4,4] => 8
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [4,3,1] => 7
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [4,2,2] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,8,5,7] => [4,4] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [4,2,1,1] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,6,3,7,8,5] => [8] => 8
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5,8] => [7,1] => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,6,7,3,8,5] => [5,3] => 8
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,6,7,3,5,8] => [5,2,1] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,8,7] => [6,2] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [5,3] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,6,2,3,7,5,8] => [4,3,1] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [3,3,2] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,6,2,7,3,5,8] => [3,2,2,1] => 7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,6,7,2,3,8,5] => [6,2] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,6,7,8,2,3,5] => [6,2] => 8
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,6,7,2,3,5,8] => [5,2,1] => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => [3,3,2] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,8,5,7] => [5,3] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => [3,3,2] => 8
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,8,2,3,5,7] => [6,2] => 8
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,6,2,3,5,7,8] => [3,3,1,1] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [7,1] => 7
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,6,1,2,7,8,3,5] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [4,6,1,2,7,3,5,8] => [5,2,1] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [4,6,1,7,2,8,3,5] => [4,4] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [4,6,1,7,8,2,3,5] => [4,2,2] => 8
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => [7,1] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [4,6,7,1,2,8,3,5] => [4,2,2] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [2,2,2,2] => 8
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [4,2,2] => 8
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,6,7,1,2,3,5,8] => [5,2,1] => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,8,7] => [6,2] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,8,5,7] => [8] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,8,3,5,7] => [5,3] => 8
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => [8] => 8
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [6,2] => 8
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [4,6,1,2,3,5,7,8] => [6,1,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [4,3,1] => 7
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [4,2,1,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [4,4] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [4,2,2] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [4,3,1] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,7,3,5,8,6] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,1,2,7,3,5,6,8] => [7,1] => 7
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,7,2,3,5,8,6] => [5,3] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,7,2,3,8,5,6] => [3,3,2] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [4,1,7,2,8,3,5,6] => [5,3] => 8
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => [8] => 8
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6,8] => [4,3,1] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [4,7,1,2,3,5,8,6] => [8] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [4,7,1,2,3,8,5,6] => [6,2] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [4,7,1,2,8,3,5,6] => [8] => 8
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => [5,3] => 8
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6,8] => [7,1] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [4,2,1,1] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [4,3,1] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [4,4] => 8
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,8,3,5,6,7] => [8] => 8
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [5,3] => 8
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [8] => 8
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [4,1,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [5,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,4,8] => [4,1,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,5,6,4,8,7] => [3,2,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,8,4,7] => [5,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,4,7,8] => [3,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [3,2,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [2,2,1,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => [5,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => [3,2,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => [4,1,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [2,2,1,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [3,2,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,5,8,4,6,7] => [5,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [6,1,1] => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,2,5,3,6,7,4,8] => [5,1,1,1] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,5,3,6,4,8,7] => [4,2,1,1] => 6
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [4,1,1,1,1] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [4,2,1,1] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => [3,2,1,1,1] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [6,1,1] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => [3,3,1,1] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,5,6,3,8,4,7] => [4,2,1,1] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,2,5,6,8,3,4,7] => [6,1,1] => 6
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [2,2,1,1,1,1] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => [3,3,1,1] => 6
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => [3,2,1,1,1] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,2,5,3,7,4,8,6] => [6,1,1] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,2,5,3,7,8,4,6] => [4,2,1,1] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6,8] => [5,1,1,1] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,2,5,7,3,4,8,6] => [4,2,1,1] => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => [2,2,2,1,1] => 6
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,2,5,7,8,3,4,6] => [4,2,1,1] => 6
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [3,2,1,1,1] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,2,5,3,4,6,8,7] => [3,2,1,1,1] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => [3,3,1,1] => 6
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [6,1,1] => 6
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [4,2,1,1] => 6
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => [3,1,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => [7,1] => 7
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,5,2,3,6,7,4,8] => [6,1,1] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => [5,2,1] => 7
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,5,2,3,6,8,4,7] => [7,1] => 7
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => [5,1,1,1] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => [4,3,1] => 7
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [3,3,1,1] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,7,8,3,4] => [4,3,1] => 7
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,2,6,7,3,4,8] => [6,1,1] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,5,2,6,3,4,8,7] => [3,2,2,1] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [4,3,1] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,2,6,8,3,4,7] => [7,1] => 7
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [3,2,1,1,1] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => [7,1] => 7
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,6,2,7,8,3,4] => [7,1] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,5,6,7,2,3,8,4] => [3,2,2,1] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,6,7,2,8,3,4] => [5,2,1] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => [7,1] => 7
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => [2,2,2,1,1] => 6
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,5,6,2,3,4,8,7] => [5,2,1] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => [7,1] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => [5,2,1] => 7
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [3,2,2,1] => 7
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,5,6,2,3,4,7,8] => [5,1,1,1] => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [4,3,1] => 7
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [4,2,1,1] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,7,4,8,6] => [7,1] => 7
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,7,8,4,6] => [5,2,1] => 7
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => [6,1,1] => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,5,2,7,3,4,8,6] => [4,3,1] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [3,2,2,1] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,5,2,7,8,3,4,6] => [5,2,1] => 7
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [3,3,1,1] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,5,7,2,3,4,8,6] => [7,1] => 7
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,2,3,8,4,6] => [5,2,1] => 7
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [7,1] => 7
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => [5,2,1] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,5,2,3,4,6,8,7] => [4,2,1,1] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [4,3,1] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,5,2,3,8,4,6,7] => [7,1] => 7
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [4,3,1] => 7
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [7,1] => 7
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [4,1,1,1,1] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [8] => 8
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,6,7,4,8] => [7,1] => 7
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,6,8,4,7] => [8] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => [6,1,1] => 6
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,2,6,3,7,8,4] => [4,4] => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,1,2,6,3,7,4,8] => [4,3,1] => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,7,3,8,4] => [8] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,2,6,7,8,3,4] => [5,3] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,1,2,6,7,3,4,8] => [7,1] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,1,2,6,3,8,4,7] => [4,4] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,1,2,6,8,3,4,7] => [8] => 8
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => [4,2,1,1] => 6
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,1,6,2,3,7,4,8] => [7,1] => 7
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [6,2] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,1,6,2,7,3,4,8] => [5,2,1] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,6,7,2,3,8,4] => [3,3,2] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [5,1,6,7,2,8,3,4] => [5,3] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,2,3,4] => [8] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [5,1,6,2,3,4,8,7] => [6,2] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => [8] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,1,6,2,8,3,4,7] => [6,2] => 8
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [5,1,6,2,3,4,7,8] => [6,1,1] => 6
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [5,3] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => [4,4] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => [5,3] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,6,1,7,8,2,3,4] => [6,2] => 8
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,1,7,2,3,4,8] => [5,2,1] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => [8] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => [6,2] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [4,2,2] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [2,2,2,2] => 8
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [7,1] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,8,7] => [3,3,2] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => [5,3] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,6,1,2,8,3,4,7] => [8] => 8
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,6,1,8,2,3,4,7] => [5,3] => 8
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [5,3] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,7,4,8,6] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,7,8,4,6] => [6,2] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [4,4] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,7,3,8,4,6] => [4,2,2] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,7,8,3,4,6] => [6,2] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,7,2,3,4,8,6] => [8] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [8] => 8
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,1,7,8,2,3,4,6] => [5,3] => 8
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6,8] => [7,1] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,7,1,2,3,4,8,6] => [5,3] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => [5,3] => 8
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,7,1,8,2,3,4,6] => [8] => 8
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [5,3] => 8
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => [4,3,1] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [5,2,1] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [5,3] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [8] => 8
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [4,4] => 8
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [5,3] => 8
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [5,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [4,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => [3,1,1,1,1,1] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [2,2,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,6,8,5,7] => [4,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [5,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [4,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [3,2,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,2,3,6,7,8,4,5] => [5,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,6,7,4,5,8] => [2,2,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => [3,2,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => [5,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,6,8,4,5,7] => [3,2,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [3,1,1,1,1,1] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [6,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,2,6,3,4,7,5,8] => [5,1,1,1] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => [3,3,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,2,6,3,7,8,4,5] => [6,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,2,6,3,7,4,5,8] => [3,2,1,1,1] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => [6,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,2,6,7,3,8,4,5] => [4,2,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => [2,2,2,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [5,1,1,1] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => [4,2,1,1] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,2,6,3,4,8,5,7] => [6,1,1] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [3,3,1,1] => 6
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [6,1,1] => 6
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => [4,1,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,6,2,3,4,7,8,5] => [7,1] => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [6,1,1] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => [4,3,1] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,3,7,8,4,5] => [7,1] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,2,3,7,4,5,8] => [4,2,1,1] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,6,2,7,3,4,8,5] => [7,1] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [5,2,1] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,6,2,7,8,3,4,5] => [3,2,2,1] => 7
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [6,1,1] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,7,2,3,8,4,5] => [7,1] => 7
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => [5,2,1] => 7
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [7,1] => 7
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => [3,3,1,1] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => [5,2,1] => 7
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [7,1] => 7
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,6,2,3,8,4,5,7] => [4,3,1] => 7
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => [7,1] => 7
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [4,3,1] => 7
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [5,1,1,1] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [7,1] => 7
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => [5,3] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,1,2,3,7,8,4,5] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [6,1,2,3,7,4,5,8] => [5,2,1] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,7,3,4,8,5] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,1,2,7,3,8,4,5] => [6,2] => 8
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => [7,1] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,7,2,3,4,8,5] => [4,4] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,1,7,2,3,8,4,5] => [8] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,1,7,2,8,3,4,5] => [6,2] => 8
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => [8] => 8
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => [4,3,1] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => [8] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,7,1,2,3,8,4,5] => [5,3] => 8
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => [5,3] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [8] => 8
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => [7,1] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [6,2] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,8,5,7] => [8] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,8,4,5,7] => [5,3] => 8
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => [8] => 8
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [4,4] => 8
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [8] => 8
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [6,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [3,1,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [4,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [2,2,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [3,1,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [5,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [3,2,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,3,7,8,4,5,6] => [5,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [4,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [6,1,1] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,2,7,3,4,8,5,6] => [4,2,1,1] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [6,1,1] => 6
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [3,3,1,1] => 6
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => [5,1,1,1] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [7,1] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [5,2,1] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [7,1] => 7
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [4,3,1] => 7
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [7,1] => 7
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [6,1,1] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [8] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [6,2] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => [8] => 8
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => [5,3] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [8] => 8
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [4,4] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [7,1] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [3,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [4,1,1,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [5,1,1,1] => 5
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [6,1,1] => 6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [7,1] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [8] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => [2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [9] => 9
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [9] => 9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => [2,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [10] => 10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => [8,1] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [7,2] => 9
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [7,2] => 9
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7,9] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [10] => 10
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,11,9] => [11] => 11
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [8,2] => 10
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [1,2,8,3,4,5,6,9,7] => [7,1,1] => 7
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,8,1,2,3,4,5,9,6] => [5,4] => 9
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,1,3,4,5,6,7] => [5,4] => 9
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => [8,2] => 10
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,11,1,3,4,5,6,7,8,9,10] => [11] => 11
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,12,10] => [12] => 12
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [1,2,9,3,4,5,6,7,10,8] => [8,1,1] => 8
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [8,9,1,2,3,4,5,6,10,7] => [10] => 10
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,9,8] => [6,2,1] => 8
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7,9] => [6,2,1] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,9,10,1,3,4,5,6,7,8] => [10] => 10
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,12,1,3,4,5,6,7,8,9,10,11] => [12] => 12
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,8,5,6,9,7] => [5,1,1,1,1] => 5
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [6,7,1,2,3,4,5,9,8] => [7,2] => 9
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,1,3,4,5,9,6,7,8] => [4,2,1,1,1] => 6
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [2,8,1,3,9,4,5,6,7] => [6,3] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,1,8,9,3,4,5,6,7] => [7,2] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7] => [4,1,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,8,1,2,3,4,9,5] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,9,8] => [3,2,1,1,1,1] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,9,7,8] => [3,2,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,7,8,9,1,3,4,5,6] => [9] => 9
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9] => [4,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,5,9,6,7,10,8] => [5,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => [3,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,3,4,8,5,9,6] => [6,3] => 9
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [5,1,2,8,3,4,6,9,7] => [5,4] => 9
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,8,6,9] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,10,1,3,4,5,6,7] => [4,3,3] => 10
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,9,2,4,5,6,7,8] => [8,1] => 8
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [3,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,6,9,7,10,8] => [4,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,8,9,6] => [9] => 9
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [2,8,1,3,4,5,6,9,7] => [9] => 9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,7,10,8,9] => [3,2,1,1,1,1,1] => 5
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,9,1,4,5,6,7,8] => [9] => 9
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => [3,1,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1,2,3,4,5,9,6,10,7] => [7,3] => 10
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,1,7,8,9,3,4,5,6] => [7,2] => 9
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,1,9,4,5,6,7,8] => [6,3] => 9
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,1,2] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,1,2,9] => [4,4,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,6,7,1,9,2,8] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,7,9,1,2,8] => [5,4] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => [7,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,5,6,1,8,9,2,7] => [4,3,2] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,5,6,8,1,9,2,7] => [7,2] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,6,8,9,1,2,7] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,6,8,1,2,7,9] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,5,6,1,2,9,7,8] => [3,3,3] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,6,9,1,2,7,8] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7,8,9] => [3,3,1,1,1] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,7,8,9,1,2,6] => [7,2] => 9
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,8,9,1,2,6,7] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8,9] => [5,1,1,1,1] => 5
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,4,7,8,9,1,2,5,6] => [9] => 9
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [2,2,1,1,1,1,1] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,9,2,4] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,9,6,8] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,9,1,2,4] => [6,3] => 9
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,9,1,2,4,6,8] => [9] => 9
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [3,1,2,6,9,4,5,7,8] => [4,3,2] => 9
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,9,1,2,4,5] => [5,2,2] => 9
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [3,8,1,2,4,5,9,6,7] => [5,2,2] => 9
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,1,2,4,5,6,9,7,8] => [3,3,1,1,1] => 6
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => [6,3] => 9
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,9,2,4,5,6,7,8] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,9,1,2,4,5,6,7,8] => [7,2] => 9
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [3,1,1,1,1,1,1] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,9,2,3] => [4,4,1] => 8
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8,9] => [3,1,1,1,1,1,1] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,9,2,3] => [5,4] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,5,6,1,7,8,9,2,3] => [7,2] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,8,1,9,2,3] => [6,3] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,1,2,3] => [3,3,3] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => [8,1] => 8
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,6,7,1,9,2,3,8] => [5,4] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,7,9,1,2,3,8] => [9] => 9
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [2,2,2,1,1,1] => 6
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,5,1,2,3,9,6,7,8] => [5,4] => 9
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,6,7,8,9,2,3,5] => [5,4] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,8,3,9,5,7] => [3,2,2,2] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,8,3,5,7,9] => [3,3,2,1] => 8
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,9,1,2,3,5] => [7,2] => 9
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,6,7,8,1,2,3,5,9] => [4,2,2,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [4,1,2,3,8,9,5,6,7] => [5,4] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [4,1,2,3,5,9,6,7,8] => [4,4,1] => 8
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => [5,4] => 9
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,9,1,2,3,5,6,7,8] => [9] => 9
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [4,1,1,1,1,1] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,5,2,6,7,8,9,3,4] => [8,1] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,9,2,3,4] => [8,1] => 8
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,7,8,9,2,3,4,6] => [4,2,2,1] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,1,6,2,7,3,9,4,8] => [7,2] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [5,1,6,7,8,2,9,3,4] => [6,3] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,9,2,3,4] => [9] => 9
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,6,1,7,8,9,2,3,4] => [5,4] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,7,1,8,2,3,4,9] => [4,2,2,1] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,8,1,9,2,3,4] => [7,2] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [2,2,2,2,1] => 8
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,7,9,1,2,3,4,8] => [3,2,2,2] => 9
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,6,1,2,3,4,9,7,8] => [3,3,3] => 9
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,7,8,9,1,2,3,4,6] => [7,2] => 9
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,8,1,2,9,3,4,6,7] => [9] => 9
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [5,8,9,1,2,3,4,6,7] => [9] => 9
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5,1,2,3,4,9,6,7,8] => [5,4] => 9
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,9,4,6,7,8] => [9] => 9
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [5,9,1,2,3,4,6,7,8] => [6,3] => 9
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [5,1,1,1,1] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [1,6,7,8,2,9,3,4,5] => [4,2,2,1] => 8
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,9,2,3,4,5] => [2,2,2,2,1] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,1,7,2,8,3,9,4,5] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [6,1,7,8,9,2,3,4,5] => [3,2,2,2] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,8,1,9,2,3,4,5] => [7,2] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => [8,1] => 8
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [6,7,1,9,2,3,4,5,8] => [6,3] => 9
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [6,7,9,1,2,3,4,5,8] => [9] => 9
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,8,9,2,3,4,5,7] => [6,3] => 9
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [6,8,1,9,2,3,4,5,7] => [3,3,3] => 9
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [6,8,9,1,2,3,4,5,7] => [6,3] => 9
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7,9] => [8,1] => 8
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,9,7,8] => [6,3] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,9,5,7,8] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [6,1,2,9,3,4,5,7,8] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [6,9,1,2,3,4,5,7,8] => [9] => 9
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [6,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,4,7,8,5,6,9] => [2,2,1,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,4,7,9,5,6,8] => [3,2,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,7,8,9,2,3,4,5,6] => [8,1] => 8
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,7,9,2,3,4,5,6,8] => [8,1] => 8
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8,9] => [6,1,1,1] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [7,1,8,2,3,9,4,5,6] => [4,3,2] => 9
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [7,1,8,2,9,3,4,5,6] => [5,4] => 9
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [7,1,8,9,2,3,4,5,6] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6,9] => [8,1] => 8
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [7,8,1,9,2,3,4,5,6] => [6,3] => 9
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [3,3,3] => 9
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6,9] => [4,4,1] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,9,6,8] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [7,1,9,2,3,4,5,6,8] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [7,9,1,2,3,4,5,6,8] => [5,4] => 9
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9] => [7,1,1] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,8,9,6,7] => [2,2,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [1,2,3,4,8,5,9,6,7] => [3,2,1,1,1,1] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [1,2,3,4,8,9,5,6,7] => [5,1,1,1,1] => 5
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [1,2,3,8,4,5,9,6,7] => [4,2,1,1,1] => 6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,9,6,7] => [6,2,1] => 8
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,8,2,9,3,4,5,6,7] => [8,1] => 8
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [4,4,1] => 8
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7,9] => [7,1,1] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,9,6,7] => [7,2] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,9,5,6,7] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [8,1,2,3,9,4,5,6,7] => [6,3] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [8,1,2,9,3,4,5,6,7] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [8,1,9,2,3,4,5,6,7] => [5,4] => 9
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [9] => 9
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => [8,1] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,9,7,8] => [3,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,9,6,7,8] => [4,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [5,1,1,1,1] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [6,1,1,1] => 6
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => [7,1,1] => 7
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [8,1] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [9] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,1,9] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,1,7] => [7,2] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,7,8,9,1,6] => [9] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,9,1,5] => [6,3] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,1,4] => [9] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,1,3] => [5,4] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [10] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,1,8,9] => [7,1,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => [10] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,6,1,9,7,8] => [6,3] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,7,9,10,1,8] => [8,2] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,5,1,8,9,6,7] => [5,2,2] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,10,1,7] => [10] => 10
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,1,7,8,9,5,6] => [5,4] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,7,8,9,10,1,6] => [7,3] => 10
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,9,4,5] => [3,3,3] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,9,10,1,5] => [10] => 10
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,9,3,4] => [7,2] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,10,1,4] => [6,4] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,10,1,3] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,1,2] => [5,5] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11] => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => [10,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [8,1,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => [11] => 11
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,9,1,7,8] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,10,11,1,9] => [9,2] => 11
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [6,1,1,1] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,9,10,2,3] => [9,1] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,10,11,1,3] => [6,5] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [11] => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => [10] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,5,8,9,1,6,7] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [7,1,1,1] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,3,6,7,1,8,9,4,5] => [9] => 9
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,1,6,7,8] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,7,8,11,1,9,10] => [11] => 11
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,9,10,1,7,8] => [10] => 10
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,7,8,9,1,5,6] => [5,2,2] => 9
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,10,1,7,8,9] => [10] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,8,9,10,1,6,7] => [6,2,2] => 10
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,6,7,8,9,1,4,5] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [6,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,7,11,1,8,9,10] => [11] => 11
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,5,6,7,8,1,9,3,4] => [6,3] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,5,6,1,7,8,9,10,2,3] => [4,4,2] => 10
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,7,8,9,10,1,5,6] => [10] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,9,1,3,4] => [9] => 9
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,9,1,5,6,7,8] => [9] => 9
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [4,1,1,1,1,1] => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,9,1,3,4,5] => [3,2,2,2] => 9
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,6,7,8,9,10,1,4,5] => [10] => 10
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,10,1,6,7,8,9] => [10] => 10
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [5,1,1,1,1,1] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,9,10,1,3,4] => [4,3,3] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,11,1,7,8,9,10] => [11] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,8,9,1,10,2,3] => [7,3] => 10
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,9,10,1,3,4,5] => [10] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8] => [7,2] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,6,1,8,9,7] => [6,3] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,9] => [6,2,1] => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,7,8,9,6] => [5,4] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8] => [5,2,2] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,7,6,8,9] => [5,2,1,1] => 7
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,5,1,6,7,9,8] => [5,2,1,1] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,9,5] => [5,4] => 9
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,9] => [4,2,2,1] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,6,5,7,8,9] => [4,2,1,1,1] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,9,4] => [6,3] => 9
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8] => [3,2,2,2] => 9
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,5,4,6,7,8,9] => [3,2,1,1,1,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7,9] => [3,2,2,1,1] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,1,4,5,6,8,9,7] => [3,3,1,1,1] => 6
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,1,4,5,6,7,9,8] => [3,2,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,3] => [7,2] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,8,3,9] => [6,2,1] => 8
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,5,3,6,7,8,9] => [3,2,1,1,1,1] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,9,5] => [5,2,2] => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9] => [2,2,2,2,1] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,7,8,9] => [2,2,2,1,1,1] => 6
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9] => [2,2,1,1,1,1,1] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,9,4] => [6,2,1] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,6,8,9,7] => [3,2,1,1,1,1] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,8,7,9] => [2,2,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,2] => [8,1] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,8,2,9] => [7,1,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,6,7,2,9,8] => [6,2,1] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,7,2,8,9] => [6,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,5,2,6,7,8,9] => [4,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,9] => [3,2,2,1,1] => 7
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9] => [3,1,1,1,1,1,1] => 3
[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] => [2,2,2,2,1] => 8
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,5,4,6,7,8,9] => [2,2,1,1,1,1,1] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,3,2,4,5,6,8,9,7] => [3,2,1,1,1,1] => 5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,3] => [7,1,1] => 7
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,5,3,6,7,8,9] => [3,1,1,1,1,1,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,9] => [2,2,2,1,1,1] => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,3,5,7,8,9,6] => [4,2,1,1,1] => 6
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,4] => [6,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,8,4,9] => [5,1,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8] => [2,2,2,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,5] => [5,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [2,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,6] => [4,1,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,5,7,8,6,9] => [3,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,9,8] => [2,2,1,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,8,1,10,9] => [8,2] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,9,10,8] => [7,3] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8,10] => [7,2,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,8,9,10,7] => [6,4] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,10,9] => [6,2,2] => 10
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,7,8,9,10,6] => [5,5] => 10
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8,10] => [5,2,2,1] => 9
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,9,10,5] => [6,4] => 10
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,5,8,9,10,7] => [4,4,2] => 10
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,10,9] => [4,2,2,2] => 10
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,9,10,4] => [7,3] => 10
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,2,2,1] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,10,3] => [8,2] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,7,8,3,10,9] => [6,2,2] => 10
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,9,10,5] => [6,2,2] => 10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,9,10,7] => [4,2,2,2] => 10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,2,2,2,2] => 10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,8,7,9,10] => [2,2,2,2,1,1] => 8
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,8,9,10,7] => [4,2,2,1,1] => 8
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9,10] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,7,8,9,10,6] => [5,2,1,1,1] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,6,7,9,10,8] => [3,2,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,2] => [9,1] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,8,9,2,10] => [8,1,1] => 8
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,4,7,8,6,10,9] => [3,2,2,2,1] => 9
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => [3,2,2,2,1] => 9
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [2,2,2,2,1,1] => 8
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,8,9,10,7] => [4,2,2,1,1] => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,10,3] => [8,1,1] => 8
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,10,4] => [7,1,1,1] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8,10] => [2,2,2,1,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,10,5] => [6,1,1,1,1] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,10,6] => [5,1,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,8,9,6,10] => [4,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,7,8,6,9,10] => [3,1,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,6,8,9,10,7] => [4,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,9,7,10] => [3,1,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,2] => [9] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,2] => [7,2] => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,9,2] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,1,8,9,2] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,1,9,2] => [5,4] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [10] => 10
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,9,4] => [6,3] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,10,2] => [8,2] => 10
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,10,2] => [7,3] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,7,1,2,9,8] => [7,2] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,1,10,2] => [10] => 10
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => [9,1] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,7,8,9,10,2,3,4,5,6] => [9,1] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5,11] => [2,2,2,2,2,1] => 10
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => [9,1] => 9
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,9,10,2,3,4,5] => [9,1] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,7,8,9,10,11,2,3,4,5,6] => [2,2,2,2,2,1] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,11,2] => [10,1] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,7,9,2,8] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => [9,1] => 9
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => [9,1] => 9
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [9,1] => 9
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [10,1] => 10
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [9,1] => 9
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [9,1] => 9
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [10,1] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,7,8,10,2,9] => [9,1] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,7,9,2,8] => [9] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,4,5,6,7,9,3,8] => [7,2] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,8,2,9] => [8,1] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,8,1,2,9,3] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,7,1,2,8,9,3] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,6,1,2,7,8,9,3] => [5,2,2] => 9
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,9,3] => [9] => 9
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,9,3] => [9] => 9
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,10,8,9] => [3,1,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [3,1,1,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,10,7,8] => [8,2] => 10
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,4,7,5,8,9,6] => [5,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,3,6,4,7,8,9,5] => [6,1,1,1] => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,9,4] => [7,1,1] => 7
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,9,3] => [8,1] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [10] => 10
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [8,1,1] => 8
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [7,1,1,1] => 7
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [6,1,1,1,1] => 6
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [5,1,1,1,1,1] => 5
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,7,1,2,8,3,9] => [8,1] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,6,7,8,9,2,4,5] => [8,1] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,5,6,7,8,1,2,9,4] => [6,3] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,9,10,1,2,4] => [7,3] => 10
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [11] => 11
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,2,5,6,7,8,9] => [4,1,1,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,3,6,7,8,9] => [5,1,1,1,1] => 5
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,4,7,8,9] => [6,1,1,1] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,7,5,8,9] => [7,1,1] => 7
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,5,1,6,7,8,9,3] => [6,3] => 9
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,9,4] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,8,1,9,10,7] => [10] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,8,9,1,10,7] => [7,3] => 10
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,5,1,6,7,8,2,9] => [8,1] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,5,2,6,7,8,9,4] => [8,1] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,5,6,1,7,8,9,10,2,4] => [6,4] => 10
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,6,1,7,8,9,10,2,5] => [10] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,1,7,8,9,10,2,6] => [7,3] => 10
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => [10] => 10
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,9,3,4,5] => [7,2] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,8,2,9,3] => [8,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,8,1,3,9] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,6,1,7,2,8,9] => [4,3,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,7,8,1,2,9,10] => [4,4,1,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,1,6,2,7,8,9] => [6,1,1,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,6,7,10,1,2,8,9] => [6,4] => 10
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1,5,9,2,6,7,8] => [7,2] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,9,10,1,2,7,8] => [5,5] => 10
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,1,4,8,9,2,5,6,7] => [6,3] => 9
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,4,5,8,9,10,1,2,6,7] => [7,3] => 10
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,7,8,9,2,4,5,6] => [8,1] => 8
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,4,7,8,9,10,1,2,5,6] => [3,3,2,2] => 10
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,9,10,1,2,4,5] => [7,3] => 10
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [5,5] => 10
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,2,4,6,7,8,9] => [4,1,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,6,8,7,9] => [4,2,1,1,1] => 6
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,7,3,5,6,8,9] => [5,1,1,1,1] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,7,6,8,9] => [5,2,1,1] => 7
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [6,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,7,9,6,8] => [4,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [4,1,1,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,4,6,9,5,7,8] => [5,1,1,1,1] => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [5,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [6,1,1,1,1] => 6
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [7,1,1] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [7,1,1,1] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [8,1,1] => 8
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,8,9,4,7] => [4,3,2] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,4,7,5,8,6,9] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,4,5,7,8,1,9,6] => [6,3] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,5,7,1,8,9,6] => [9] => 9
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,9,10,4] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,8,9,10,1,2,7] => [4,4,2] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,11,8,9] => [9,2] => 11
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,6,1,7,2,9,8] => [4,3,2] => 9
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [3,2,2,2] => 9
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,9,8] => [5,2,2] => 9
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,9] => [6,2,1] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,9] => [4,2,2,1] => 8
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8,10] => [3,2,2,2,1] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,9,6,10,8] => [10] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,8,6,10,9] => [8,2] => 10
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7,10,9] => [6,2,2] => 10
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [4,2,2,2] => 10
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [2,2,1,1,1,1,1,1] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,9,10,1,2,11] => [5,5,1] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,9,10,11,1,2,8] => [9,2] => 11
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,9,10,11,1,2,5] => [4,4,3] => 11
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,9,10,2,3,4] => [3,3,3,1] => 9
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8,10] => [8,1,1] => 8
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [10] => 10
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [10] => 10
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,4,6,8,10,12,1,3,5,7,9,11] => [12] => 12
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => [12] => 12
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [8,10,1,2,3,4,5,6,7,9] => [10] => 10
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,10,1,2,4,5,6,7,8,9] => [8,2] => 10
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [3,1,1,1,1,1,1,1,1] => 3
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => [3,1,1,1,1,1,1,1,1,1] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11] => 11
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,4,6,7,8,9] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,6,1,5,7,8,9] => [6,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,5,7,1,6,8,9] => [7,1,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7,9] => [8,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [2,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [2,2,2,2,2] => 10
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [1,8,9,10,2,3,4,5,6,7] => [3,3,3,1] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => [10] => 10
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [3,7,8,9,10,1,2,4,5,6] => [8,2] => 10
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,10,1,4,5,6,7,8,9] => [10] => 10
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,10,1,5,6,7,8,9] => [10] => 10
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,7,8,9,5] => [9] => 9
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,9,4] => [9] => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [6,1,2,3,4,7,9,5,8] => [9] => 9
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [5,10,1,2,3,4,6,7,8,9] => [7,3] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,4,5,8,1,6,9,7] => [9] => 9
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,9,3] => [9] => 9
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [5,5] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [11] => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,11,10] => [9,2] => 11
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,8,1,9,7] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,7,9,1,10,8] => [10] => 10
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [5,5] => 10
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [10] => 10
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,4,6,9,8] => [4,2,2,1] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,9] => [4,2,2,1] => 8
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,9,2,5,6,7,8] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [2,2,2,2,1,1] => 8
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [2,2,2,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,11,1,6,7,8,9,10] => [11] => 11
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => [7,3] => 10
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => [5,5] => 10
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,7,8,9,10,1,2,3,4,6] => [4,2,2,2] => 10
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,7,8,9,10,1,2,3,5,6] => [6,2,2] => 10
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [1,9,2,10,3,4,5,6,7,8] => [5,4,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,10,1,11,9] => [11] => 11
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,5,6,8,2,9,7] => [9] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,9,1,6,8] => [6,3] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,6,7,8,9,1,3,5] => [5,4] => 9
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,9,10,3] => [10] => 10
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,7,8,9,10,5] => [10] => 10
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,2,3,7,4,8,9,5] => [5,4] => 9
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,8,9,10,6] => [10] => 10
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,7,8,10,1,2,3,4,9] => [10] => 10
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,4,9,3,5,6,7,8] => [7,2] => 9
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7,9] => [3,3,2,1] => 8
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6,9,8] => [5,2,2] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,8,10,11,9] => [3,1,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,6,1,7,8,9,5] => [9] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,7,1,8,9,10,6] => [10] => 10
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,6,1,7,8,9,10,5] => [10] => 10
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,6,8,9,2,7] => [6,2,1] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,9,10,3] => [10] => 10
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,5,6,1,7,8,9,10,3] => [10] => 10
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,5,6,1,7,8,9,10,4] => [6,4] => 10
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,6,7,8,9,2,3,4,5,10] => [2,2,2,2,1,1] => 8
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,8,9,10,1,2,3,4,5,11,6] => [6,5] => 11
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,10,11,1,3,4,5,6,7] => [6,5] => 11
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,1,3,4,5,8,6,7,9] => [3,2,1,1,1,1] => 5
[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] => [4,2,2,1] => 8
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,6,3,7,5,9,8] => [6,2,1] => 8
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,9] => [3,2,2,1,1] => 7
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,9,8,10] => [4,2,2,1,1] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,10,7,9] => [9,1] => 9
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,10,9] => [3,2,2,2,1] => 9
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => [4,2,2,1] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,4,1,2,5,6,8,9,7] => [3,2,2,1,1] => 7
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,7,8,9,4,5,6] => [3,2,2,2] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,5,6,7,9,2,8] => [7,2] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,7,1,8,2,9,3] => [5,4] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,9,10,7] => [10] => 10
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,9,8] => [3,2,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,5,1,8,6,9,7] => [5,4] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,7,8,10,1,2,3,9] => [4,3,3] => 10
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,9,10,2,3,4] => [4,3,3] => 10
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [4,10,1,2,3,5,6,7,8,9] => [10] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,6,9,10,7,8] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [10] => 10
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,5,1,9,6,7,8] => [5,4] => 9
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,9,5,8] => [5,1,1,1,1] => 5
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [7,8,10,1,2,3,4,5,6,9] => [4,3,3] => 10
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,4,7,6,9,8] => [5,2,2] => 9
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7,9] => [6,2,1] => 8
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,4,6,8,10,1,2,5,7,9] => [7,3] => 10
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,6,8,10,1,2,3,5,7,9] => [8,2] => 10
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,1,8,2,9,3,10,4,5,6] => [8,2] => 10
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,3,8,1,4,5,6,9,7] => [9] => 9
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [2,7,1,3,4,5,8,9,6] => [9] => 9
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,4,1,7,5,8,6,9] => [4,4,1] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,10,7,12,9,11] => [11,1] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,6,7,1,8,2,10,9] => [8,2] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,6,7,8,1,9,2,11,10] => [5,4,2] => 11
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10,11] => [3,1,1,1,1,1,1,1,1] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,9,4] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [1,2,3,4,5,9,6,10,7,8] => [3,2,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [12] => 12
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1,10,2,3,4,5,6,7,9] => [5,5] => 10
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,1,2,4,7,6,9,8] => [3,2,2,2] => 9
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [5,2,2,1] => 9
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [3,1,8,9,10,2,4,5,6,7] => [10] => 10
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,7,3,8,4,9,5,10,6] => [6,2,2] => 10
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,8,3,9,4,10,5,11,6,12,7] => [10,2] => 12
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,8,9,2,3,10] => [4,4,1,1] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,10,7,9] => [4,1,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,10,11,12,3] => [10,2] => 12
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,9,8] => [4,2,2,1] => 8
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,5,2,4,7,6,9,8,10] => [4,2,2,1,1] => 8
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,5,2,3,7,6,9,8] => [2,2,2,2,1] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [2,9,1,3,4,5,6,7,10,8] => [10] => 10
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,3,11,1,4,5,6,7,8,9,10] => [11] => 11
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7,9] => [8,1] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,4,1,7,3,8,5,6,9] => [6,2,1] => 8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7,10,9] => [4,2,2,2] => 10
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [3,1,4,2,9,5,10,6,11,7,12,8] => [6,4,2] => 12
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,5,6,9,10,1,2,3,7,8] => [10] => 10
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,5,8,9,10,1,2,3,6,7] => [4,4,2] => 10
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,5,7,2,4,6,9,8,10] => [3,3,2,1,1] => 8
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,5,7,2,9,4,6,8,10] => [3,3,2,1,1] => 8
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,5,7,9,1,2,4,6,8,10] => [9,1] => 9
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,9] => [6,2,1] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8] => [5,2,2] => 9
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,10,9] => [4,2,2,2] => 10
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,6,1,2,3,7,8,9,4] => [6,3] => 9
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,2,6,4,7,5,9,8] => [4,2,2,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,9,1,10,11,8] => [11] => 11
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,8,3,9,5,10,7] => [3,3,2,2] => 10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,2,2,2,2,2] => 12
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,6,8,9,10,1,3,4,5,7] => [7,3] => 10
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,10,11,12,1,3,4,5,6,7] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,2,7,3,8,4,9,5] => [6,2,1] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,9] => [6,2,1] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,7,3,8,6,9] => [5,3,1] => 8
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5,8,9,10] => [2,2,1,1,1,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6,9,8] => [3,2,2,2] => 9
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,5,1,6,2,8,7,9] => [6,2,1] => 8
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [1,2,6,3,4,7,5,9,8] => [5,2,1,1] => 7
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [8,1,9,2,10,3,4,5,6,7] => [7,3] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [11,1] => 11
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7,9] => [2,2,2,2,1] => 8
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,11,1,5,6,7,8,9,10] => [11] => 11
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,2,7,4,6,9,8] => [6,2,1] => 8
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7,10] => [4,4,1,1] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,5,6,7,9,2,10,8] => [10] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,12,11] => [10,2] => 12
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,7,2,8,3,9,4,10,6] => [5,5] => 10
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,6,1,3,5,7,8,9] => [3,3,1,1,1] => 6
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,6,1,3,5,7,8,9,10] => [3,3,1,1,1,1] => 6
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,4,6,8,1,3,5,7,9,10] => [6,2,1,1] => 8
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,0,1 1,0,2,2 1,0,3,4,6 1,0,4,6,13,18 1,0,5,8,21,40,57 1,0,6,10,30,66,130,186
$F_{1} = 1$
$F_{2} = 1 + q^{2}$
$F_{3} = 1 + 2\ q^{2} + 2\ q^{3}$
$F_{4} = 1 + 3\ q^{2} + 4\ q^{3} + 6\ q^{4}$
$F_{5} = 1 + 4\ q^{2} + 6\ q^{3} + 13\ q^{4} + 18\ q^{5}$
$F_{6} = 1 + 5\ q^{2} + 8\ q^{3} + 21\ q^{4} + 40\ q^{5} + 57\ q^{6}$
$F_{7} = 1 + 6\ q^{2} + 10\ q^{3} + 30\ q^{4} + 66\ q^{5} + 130\ q^{6} + 186\ q^{7}$
Description
The sum of the parts of an integer partition that are at least two.
Map
cycle type
Description
The cycle type of a permutation as a partition.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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