Identifier
-
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
St001465: Permutations ⟶ ℤ
Values
[1,0] => [1] => {{1}} => [1] => 0
[1,0,1,0] => [1,2] => {{1},{2}} => [1,2] => 0
[1,1,0,0] => [2,1] => {{1,2}} => [2,1] => 1
[1,0,1,0,1,0] => [1,2,3] => {{1},{2},{3}} => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => {{1},{2,3}} => [1,3,2] => 1
[1,1,0,0,1,0] => [2,1,3] => {{1,2},{3}} => [2,1,3] => 1
[1,1,0,1,0,0] => [2,3,1] => {{1,2,3}} => [2,3,1] => 0
[1,1,1,0,0,0] => [3,1,2] => {{1,2,3}} => [2,3,1] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => {{1},{2},{3},{4}} => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => {{1},{2},{3,4}} => [1,2,4,3] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => {{1},{2,3},{4}} => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => {{1},{2,3,4}} => [1,3,4,2] => 0
[1,0,1,1,1,0,0,0] => [1,4,2,3] => {{1},{2,3,4}} => [1,3,4,2] => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => {{1,2},{3},{4}} => [2,1,3,4] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => {{1,2},{3,4}} => [2,1,4,3] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => {{1,2,3},{4}} => [2,3,1,4] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => {{1,2,3,4}} => [2,3,4,1] => 0
[1,1,0,1,1,0,0,0] => [2,4,1,3] => {{1,2,3,4}} => [2,3,4,1] => 0
[1,1,1,0,0,0,1,0] => [3,1,2,4] => {{1,2,3},{4}} => [2,3,1,4] => 0
[1,1,1,0,0,1,0,0] => [3,1,4,2] => {{1,2,3,4}} => [2,3,4,1] => 0
[1,1,1,0,1,0,0,0] => [3,4,1,2] => {{1,3},{2,4}} => [3,4,1,2] => 0
[1,1,1,1,0,0,0,0] => [4,1,2,3] => {{1,2,3,4}} => [2,3,4,1] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => {{1},{2},{3},{4,5}} => [1,2,3,5,4] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => {{1},{2},{3,4},{5}} => [1,2,4,3,5] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => {{1},{2},{3,4,5}} => [1,2,4,5,3] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => {{1},{2},{3,4,5}} => [1,2,4,5,3] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => {{1},{2,3},{4},{5}} => [1,3,2,4,5] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}} => [1,3,2,5,4] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => {{1},{2,3,4},{5}} => [1,3,4,2,5] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => {{1},{2,3,4},{5}} => [1,3,4,2,5] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => {{1},{2,4},{3,5}} => [1,4,5,2,3] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => [2,1,3,4,5] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => {{1,2},{3},{4,5}} => [2,1,3,5,4] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => {{1,2},{3,4},{5}} => [2,1,4,3,5] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => {{1,2},{3,4,5}} => [2,1,4,5,3] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => {{1,2},{3,4,5}} => [2,1,4,5,3] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => [2,3,1,4,5] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => {{1,2,3},{4,5}} => [2,3,1,5,4] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => {{1,2,4},{3,5}} => [2,4,5,1,3] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => {{1,2,3},{4},{5}} => [2,3,1,4,5] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => {{1,2,3},{4,5}} => [2,3,1,5,4] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => {{1,3},{2,4},{5}} => [3,4,1,2,5] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => {{1,3},{2,4,5}} => [3,4,1,5,2] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => {{1,3},{2,4,5}} => [3,4,1,5,2] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => {{1,2,4},{3,5}} => [2,4,5,1,3] => 0
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => {{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => {{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => {{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => {{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => {{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => 0
>>> Load all 1014 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => {{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => {{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => {{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => {{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => {{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => {{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => {{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => {{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => {{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => {{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => {{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => {{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => {{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => {{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => {{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => {{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => {{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => {{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => {{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => {{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => {{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => {{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => {{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => {{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => {{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => {{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => {{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => {{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => {{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => {{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => {{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => {{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => {{1},{2,5},{3,6},{4,7}} => [1,5,6,7,2,3,4] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => {{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => {{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => {{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => {{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => {{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => {{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => {{1,3},{2,4},{5},{6},{7}} => [3,4,1,2,5,6,7] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,1,2,4,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => {{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => {{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => {{1,4},{2,5},{3,6},{7}} => [4,5,6,1,2,3,7] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,1,2,7,3,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}} => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}} => [1,2,3,4,5,6,8,7] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,4,7] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,4,8,6] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,4,6,7] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,4,7,8,5] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,4,8,5,7] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,4,5] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,4,5,8,6] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 0
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,4,5,6] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}} => [1,2,4,3,6,5,7,8] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,3,4,7,8] => {{1},{2},{3,5},{4,6},{7},{8}} => [1,2,5,6,3,4,7,8] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}} => [1,3,2,4,5,7,6,8] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}} => [1,3,2,5,4,7,6,8] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}} => [1,3,4,2,6,7,5,8] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => {{1},{2,3,5},{4,6,7},{8}} => [1,3,5,6,2,7,4,8] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,2,4,6,8] => {{1},{2,3,5},{4,6,7},{8}} => [1,3,5,6,2,7,4,8] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,2,3,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}} => [1,3,4,2,6,7,5,8] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}} => [1,3,4,2,6,7,5,8] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,2,3,8] => {{1},{2,4,6},{3,5,7},{8}} => [1,4,5,6,7,2,3,8] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4,8] => {{1},{2,3,5},{4,6,7},{8}} => [1,3,5,6,2,7,4,8] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,7,3,4,6,8] => {{1},{2,3,5},{4,6,7},{8}} => [1,3,5,6,2,7,4,8] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,2,3,4,5,8] => {{1},{2,4,6},{3,5,7},{8}} => [1,4,5,6,7,2,3,8] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,3,4,5,6,7,8] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}} => [2,1,3,4,5,6,8,7] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}} => [2,1,4,3,6,5,8,7] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => {{1,2},{3,4},{5,7},{6,8}} => [2,1,4,3,7,8,5,6] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => {{1,2},{3,5},{4,6},{7,8}} => [2,1,5,6,3,4,8,7] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,3,8,4,6] => {{1,2},{3,5},{4,7},{6,8}} => [2,1,5,7,3,8,4,6] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,3,4,5] => {{1,2},{3,6},{4,7},{5,8}} => [2,1,6,7,8,3,4,5] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => {{1,2,3},{4},{5},{6,7,8}} => [2,3,1,4,5,7,8,6] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,6,7] => {{1,2,3},{4},{5},{6,7,8}} => [2,3,1,4,5,7,8,6] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,5,7] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,8,6] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,5,6,7] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,1,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,1,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,1,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,1,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,1,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,1,7,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,1,7,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,1,8,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,1,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,1,5,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,1,5,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,1,8,5,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,1,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,1,5,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,1,4,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,1,6,4,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,1,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,3,5,1,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,1,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,1,7,8,4] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,1,8,4,7] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,1,4,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,1,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,1,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,1,4,8,6] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,1,4,6,7] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,1,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,1,4,5,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,6,1,4,7,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,1,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,1,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,1,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,1,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,1,4,8,5,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,1,3,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,1,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,3,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,1,5,6,3,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,1,5,6,7,3,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,3] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,1,5,6,8,3,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,1,5,8,3,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,1,6,3,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 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] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 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] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,1,6,7,8,3,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,1,7,3,5,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,8,5,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,1,7,8,3,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,1,8,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,1,3,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,4,5,6,1,3,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,1,7,3,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,1,7,8,3] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,1,8,3,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,1,8,3] => {{1,2,4,6},{3,5,7,8}} => [2,4,5,6,7,1,8,3] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,1,3] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,1,3,7] => {{1,2,4,6},{3,5,7,8}} => [2,4,5,6,7,1,8,3] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,4,5,7,1,8,3,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,1,3,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,1,7,3,8,5] => {{1,2,4},{3,6},{5,7,8}} => [2,4,6,1,7,3,8,5] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,1,8,3,5,7] => {{1,2,4},{3,6},{5,7,8}} => [2,4,6,1,7,3,8,5] => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,1,3,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,1,3,4,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,1,3,6,4,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,1,3,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,1,3,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,5,1,3,7,4,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,1,3,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,1,3,7,8,4,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,1,3,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,1,6,7,3,4,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,5,1,6,8,3,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,1,7,3,4,8,6] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,1,8,3,4,6,7] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,1,3,4,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,5,6,1,3,7,4,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,1,3,7,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,5,6,1,3,8,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,1,7,8,3,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,1,3,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,5,7,1,3,4,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,5,7,1,8,3,4,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,1,3,4,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,6,1,3,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,1,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1,3,4,7,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,1,3,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,1,3,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,1,3,7,8,4,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,6,1,7,3,4,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,1,7,3,4,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,1,8,3,4,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,6,7,1,3,4,8,5] => {{1,2,4,6},{3,5,7,8}} => [2,4,5,6,7,1,8,3] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,6,7,1,3,8,4,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,1,3,4,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => {{1,2,4,6},{3,5,7,8}} => [2,4,5,6,7,1,8,3] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,1,3,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,1,3,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,1,3,8,4,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,2,4,5,7,8,6] => {{1,2,3},{4},{5},{6,7,8}} => [2,3,1,4,5,7,8,6] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => {{1,2,3},{4},{5},{6,7,8}} => [2,3,1,4,5,7,8,6] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,2,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,2,6,8,5,7] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,8,5,6,7] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,2,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,6,2,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,2,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,2] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,6,8,2,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,4,5,7,2,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,4,5,7,8,2,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,4,5,8,2,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,5,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,4,6,2,7,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,4,6,2,8,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,4,6,7,8,2,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,4,7,2,5,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4,8,2,5,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,2,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,2,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,2,7,8,4,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,1,5,6,2,7,8,4] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,1,5,6,2,8,4,7] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,1,5,6,7,2,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,1,5,6,8,2,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,1,5,7,2,4,8,6] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,1,5,8,2,4,6,7] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,6,2,4,5,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,6,2,4,7,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,6,2,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,6,2,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,6,7,2,4,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,1,6,8,2,4,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,7,2,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,7,2,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,8,4,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8] => {{1,3},{2,4},{5},{6},{7},{8}} => [3,4,1,2,5,6,7,8] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => {{1,3},{2,4},{5,6},{7,8}} => [3,4,1,2,6,5,8,7] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,1,2,7,8,5,6] => {{1,3},{2,4},{5,7},{6,8}} => [3,4,1,2,7,8,5,6] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,1,2,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,1,6,2,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,1,6,7,2,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,2] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,1,7,8,2,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,1,2,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,1,8,2] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,1,2] => {{1,3,5,7},{2,4,6,8}} => [3,4,5,6,7,8,1,2] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,1,2,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,1,2,5,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,1,2,7,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,1,2,7,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,1,7,8,2,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,4,6,7,1,2,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,1,2,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,1,2,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,1,2,5,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,1,8,2,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,1,2,5,6] => {{1,3,5,7},{2,4,6,8}} => [3,4,5,6,7,8,1,2] => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,1,6,2,4,8,7] => {{1,3},{2,5},{4,6},{7,8}} => [3,5,1,6,2,4,8,7] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,8,4,6] => {{1,3},{2,5},{4,7},{6,8}} => [3,5,1,7,2,8,4,6] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,1,7,2,4,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,1,7,2,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,5,6,1,8,2,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,1,8,2,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,1,2,4,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,1,7,8,2,4,5] => {{1,3},{2,6},{4,7},{5,8}} => [3,6,1,7,8,2,4,5] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,6,7,1,2,4,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,6,7,1,2,4,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,1,2,8,4,5] => {{1,3,4,7},{2,5,6,8}} => [3,5,4,7,6,8,1,2] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,1,2,4,5] => {{1,3,4,5,7,8},{2,6}} => [3,6,4,5,7,2,8,1] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,1,2,4,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,3,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,3,6,8,5,7] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,3,7,5,8,6] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,2,5,3,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,2,5,6,3,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,2,5,6,3,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,6,7,3,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,3] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,2,5,6,8,3,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,5,7,3,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,5,7,8,3,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,2,5,8,3,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,1,2,6,3,5,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,1,2,6,3,7,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,1,2,6,3,8,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,7,3,5,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,1,2,7,3,5,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,1,2,7,8,3,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,2,8,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,5,6,2,3,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,5,6,2,3,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,5,6,2,8,3,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,5,6,7,2,8,3] => {{1,2,4,6},{3,5,7,8}} => [2,4,5,6,7,1,8,3] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,8,2,3] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,5,6,8,2,3,7] => {{1,2,4,6},{3,5,7,8}} => [2,4,5,6,7,1,8,3] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,5,7,2,8,3,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5] => {{1,2,4},{3,6},{5,7,8}} => [2,4,6,1,7,3,8,5] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,8,3,5,7] => {{1,2,4},{3,6},{5,7,8}} => [2,4,6,1,7,3,8,5] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,1,7,8,2,3,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,1,2,3,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,5,1,2,6,7,3,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,1,2,6,7,8,3] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,1,2,6,8,3,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,1,2,7,3,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,5,1,2,7,3,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,5,1,2,7,8,3,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,1,2,8,3,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,5,1,6,7,2,3,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,1,6,7,2,8,3] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,1,6,8,2,3,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,1,7,8,2,3,6] => {{1,3,4,7},{2,5,6,8}} => [3,5,4,7,6,8,1,2] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,1,2,3,7,8] => {{1,4},{2,5},{3,6},{7},{8}} => [4,5,6,1,2,3,7,8] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,1,2,3,8,7] => {{1,4},{2,5},{3,6},{7,8}} => [4,5,6,1,2,3,8,7] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,1,2,3,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,1,2,8,3] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,1,2,3] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,1,2,3,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,1,2,8,3,6] => {{1,4},{2,5},{3,7},{6,8}} => [4,5,7,1,2,8,3,6] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,6,1,2,3,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,6,1,2,3,7,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,1,2,3,8,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,6,1,2,7,8,3,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,1,7,2,3,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,6,1,7,2,8,3,5] => {{1,3,4,7},{2,5,6,8}} => [3,5,4,7,6,8,1,2] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,1,8,2,3,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,1,8,2,3,5] => {{1,4},{2,6},{3,7},{5,8}} => [4,6,7,1,8,2,3,5] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,1,2,3,5,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,1,2,3,5,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,1,2,3,8,5,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,1,2,8,3,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,2,3,6,4,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,2,3,6,7,4,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2,3,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,1,2,3,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,1,2,3,7,8,4,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,1,2,3,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,2,6,3,7,8,4] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2,6,3,8,4,7] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,4,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,2,6,7,3,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2,6,8,3,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,1,2,7,3,4,8,6] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,1,2,8,3,4,6,7] => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,6,2,3,4,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,6,2,3,7,4,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,6,2,3,7,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,6,2,3,8,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,6,7,8,2,3,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,1,7,2,3,4,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,1,7,2,3,4,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,1,7,2,3,8,4,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,8,3,4,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,1,2,7,3,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,1,2,7,8,3,4] => {{1,3,5,7},{2,4,6,8}} => [3,4,5,6,7,8,1,2] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,1,2,8,3,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,1,7,8,2,3,4] => {{1,3,4,5,7,8},{2,6}} => [3,6,4,5,7,2,8,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,1,2,3,4,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,1,2,3,8,4] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => {{1,5},{2,6},{3,7},{4,8}} => [5,6,7,8,1,2,3,4] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,1,8,2,3,4,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,2,3,4,7,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,2,3,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2,3,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,2,3,7,8,4,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,2,7,3,4,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,2,7,3,4,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2,8,3,4,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,7,2,3,4,8,5] => {{1,2,4,6},{3,5,7,8}} => [2,4,5,6,7,1,8,3] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,7,2,3,8,4,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,7,8,2,3,4,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => {{1,2,4,6},{3,5,7,8}} => [2,4,5,6,7,1,8,3] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,1,2,3,4,5,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,1,2,3,4,8,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,8,5,6] => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1,2,3,8,4,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => {{1,3,5,7},{2,4,6,8}} => [3,4,5,6,7,8,1,2] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,1,2,3,4,5,6,7,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,8,2,3,4,5,6,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,1,2,3,4,5,7,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,1,2,3,4,5,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,2,3,4,5,8,6,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,1,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,9,1,2,3,4,5,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,1,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,1,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,1,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,7,1,8,9,6] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,1,6] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,5,8,1,6,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,8,9,1,6,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,9,1,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,6,1,7,8,9,5] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,9,1,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,5,1,6,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,6,7,9,4,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,1,4] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,6,7,1,8,9,4,5] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,9,1,4,5] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,8,1,4,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,1,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,9,3] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,1,5,6,7,9,3,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,8,1,9,3] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [2,5,1,3,6,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,9,1,3,4] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [2,6,1,3,4,9,5,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [2,7,1,3,4,5,8,9,6] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,7,1,3,4,5,9,6,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,7,8,9,1,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,1,3,4,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,8,1,9,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,9,2] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,6,7,9,2,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,4,5,6,8,2,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,4,5,6,9,2,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,9,2,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,9,6,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,5,6,7,8,9,2,4] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,8,2,4,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,9,2,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,9,2] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,7,1,8,9,2] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,7,1,9,2,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,1,2] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,6,8,9,1,2,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,6,9,1,2,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,5,8,9,1,2,6,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,4,7,8,9,1,2,5,6] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,9,3] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0] => [4,1,2,5,6,7,9,3,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,1,2,5,9,3,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [4,1,2,8,3,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,5,1,2,6,7,8,9,3] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,7,1,2,8,9,3] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,8,1,2,9,3] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,9,1,2,3,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,8,1,2,3,9,5,6,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,9,1,2,3,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,1,2,3,9,4,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,1,6,7,8,9,2,3,4] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,9,3,4,6,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,1,7,2,8,3,9,4] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,8,1,2,9,3,4,6,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [5,8,9,1,2,3,4,6,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,1,2,3,4,7,8,9,5] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,1,2,3,4,7,9,5,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [6,1,2,3,4,8,5,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,1,2,3,4,9,5,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [6,1,2,9,3,4,5,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,1,7,2,8,3,9,4,5] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [6,7,1,2,3,4,8,9,5] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [6,7,8,1,2,3,4,9,5] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,1,2,3,4,5,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [6,8,1,2,3,4,5,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,9,1,2,3,4,5,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,1,2,3,4,5,8,9,6] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,1,2,3,4,5,9,6,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,1,8,2,3,4,5,9,6] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,1,8,9,2,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,1,9,2,3,4,5,6,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,1,2,3,4,9,5,6,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,1,2,9,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => [1,2,3,4,5,6,7,9,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [1,2,3,4,5,6,7,8,10,9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,9,10,2] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,9,10,2] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,8,9,10,2] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,1,2,3,4,7,8,9,10,5] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,1,10,2] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,3,4,5,6,7,8,9] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,3,4,5,6,7,8,9,10] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => [2,1,4,3,6,5,8,7,10,9] => 5
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,1,6,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,1,7,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,10,1,2,3,4,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,1,7,8,9,10,2,3,4,5] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => [2,1,3,4,5,6,7,8,9,10,11] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,1,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,10,1,2,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,7,1,2,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => 0
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,9,1,2,3,4,5,6,10,7] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,1,2,3,4,7,5,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => 0
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,10,1,2,3,4,5,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,10,1,2,3,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,8,1,3,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,1,3] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,7,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,1,7,8,9,10,5] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,8,2,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,9,10,1,7,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,7,8,9,10,1,5,6] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,9,10,1,4,5] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,5,7,1,8,9,10,6] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,8,5,7,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,10,7,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,5,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,8,5,9,7,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 0
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,10,1,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,10,1,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,10,1,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,10,1,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,8,9,10,1,7] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,10,1,5] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,9,1,2,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,8,1,2,3,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,8,9,1,2,3,4,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,5,6,8,1,2,7,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,9,10,1,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [7,1,8,9,10,2,3,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,9,10,1,3,4,5] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,1,6,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,6,8,1,9,10,7] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => {{1,6},{2,7},{3,8},{4,9},{5,10}} => [6,7,8,9,10,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,1,2,3,10,4,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,10,3,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,5,6,7,1,2,8,3,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,9,6,8,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,7,9,1,10,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,1,2,3,4,5,6,9,10,7] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,1,2,3,4,5,8,9,10,6] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,5,7,9,10,1,2,4,6,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,7,8,2,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,5,1,3,6,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,9,1,3,4,5,6,7,10,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,1,7,2,8,3,9,4,10,5] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [2,8,1,3,4,5,6,10,7,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [2,8,1,9,10,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,6,7,8,10,2,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,5,6,9,10,1,2,3,7,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,1,8,9,10,2,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,10,2,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,4,5,6,7,9,2,10,8] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,7,10,1,2,3,4,5,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,1,5,6,7,8,10,3,9] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 0
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searching the database for statistics with the same generating function
Generating function
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Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,2 10,3,1 31,8,3 98,27,6,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 3 + 2\ q$
$F_{4} = 10 + 3\ q + q^{2}$
$F_{5} = 31 + 8\ q + 3\ q^{2}$
$F_{6} = 98 + 27\ q + 6\ q^{2} + q^{3}$
Description
The number of adjacent transpositions in the cycle decomposition of a permutation.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
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