Identifier
-
Mp00080:
Set partitions
—to permutation⟶
Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
St000647: Permutations ⟶ ℤ
Values
{{1}} => [1] => [1] => [1] => 0
{{1,2}} => [2,1] => [1,2] => [1,2] => 0
{{1},{2}} => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}} => [2,3,1] => [1,2,3] => [1,2,3] => 0
{{1,2},{3}} => [2,1,3] => [1,2,3] => [1,2,3] => 0
{{1,3},{2}} => [3,2,1] => [1,3,2] => [3,1,2] => 1
{{1},{2,3}} => [1,3,2] => [1,2,3] => [1,2,3] => 0
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}} => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3},{4}} => [2,3,1,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,4},{3}} => [2,4,3,1] => [1,2,4,3] => [4,1,2,3] => 1
{{1,2},{3,4}} => [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2},{3},{4}} => [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}} => [3,2,4,1] => [1,3,4,2] => [2,4,1,3] => 1
{{1,3},{2,4}} => [3,4,1,2] => [1,3,2,4] => [3,1,2,4] => 1
{{1,3},{2},{4}} => [3,2,1,4] => [1,3,2,4] => [3,1,2,4] => 1
{{1,4},{2,3}} => [4,3,2,1] => [1,4,2,3] => [3,4,1,2] => 1
{{1},{2,3,4}} => [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3},{4}} => [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,4},{2},{3}} => [4,2,3,1] => [1,4,2,3] => [3,4,1,2] => 1
{{1},{2,4},{3}} => [1,4,3,2] => [1,2,4,3] => [4,1,2,3] => 1
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4},{5}} => [2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,5},{4}} => [2,3,5,4,1] => [1,2,3,5,4] => [5,1,2,3,4] => 1
{{1,2,3},{4,5}} => [2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,4,5},{3}} => [2,4,3,5,1] => [1,2,4,5,3] => [3,5,1,2,4] => 1
{{1,2,4},{3,5}} => [2,4,5,1,3] => [1,2,4,3,5] => [4,1,2,3,5] => 1
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [1,2,4,3,5] => [4,1,2,3,5] => 1
{{1,2,5},{3,4}} => [2,5,4,3,1] => [1,2,5,3,4] => [4,5,1,2,3] => 1
{{1,2},{3,4,5}} => [2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [1,2,5,3,4] => [4,5,1,2,3] => 1
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [1,2,3,5,4] => [5,1,2,3,4] => 1
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,3,4,5},{2}} => [3,2,4,5,1] => [1,3,4,5,2] => [2,3,5,1,4] => 1
{{1,3,4},{2,5}} => [3,5,4,1,2] => [1,3,4,2,5] => [2,4,1,3,5] => 1
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [1,3,4,2,5] => [2,4,1,3,5] => 1
{{1,3,5},{2,4}} => [3,4,5,2,1] => [1,3,5,2,4] => [2,4,5,1,3] => 1
{{1,3},{2,4,5}} => [3,4,1,5,2] => [1,3,2,4,5] => [3,1,2,4,5] => 1
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [1,3,2,4,5] => [3,1,2,4,5] => 1
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [1,3,5,2,4] => [2,4,5,1,3] => 1
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [1,3,2,5,4] => [2,5,1,3,4] => 1
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [1,3,2,4,5] => [3,1,2,4,5] => 1
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [1,3,2,4,5] => [3,1,2,4,5] => 1
{{1,4,5},{2,3}} => [4,3,2,5,1] => [1,4,5,2,3] => [4,2,5,1,3] => 2
{{1,4},{2,3,5}} => [4,3,5,1,2] => [1,4,2,3,5] => [3,4,1,2,5] => 1
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [1,4,2,3,5] => [3,4,1,2,5] => 1
{{1,5},{2,3,4}} => [5,3,4,2,1] => [1,5,2,3,4] => [3,4,5,1,2] => 1
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [1,5,2,3,4] => [3,4,5,1,2] => 1
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,2,3,5,4] => [5,1,2,3,4] => 1
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [1,4,5,2,3] => [4,2,5,1,3] => 2
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [1,4,2,5,3] => [5,3,1,2,4] => 2
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [1,4,2,3,5] => [3,4,1,2,5] => 1
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [1,4,2,3,5] => [3,4,1,2,5] => 1
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [1,5,2,4,3] => [5,3,4,1,2] => 2
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,2,4,5,3] => [3,5,1,2,4] => 1
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,2,4,3,5] => [4,1,2,3,5] => 1
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,2,4,3,5] => [4,1,2,3,5] => 1
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [1,5,2,3,4] => [3,4,5,1,2] => 1
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,2,5,3,4] => [4,5,1,2,3] => 1
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [1,5,2,3,4] => [3,4,5,1,2] => 1
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,2,5,3,4] => [4,5,1,2,3] => 1
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,3,5,4] => [5,1,2,3,4] => 1
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 1
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [1,2,3,5,6,4] => [4,6,1,2,3,5] => 1
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 1
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 1
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [1,2,3,6,4,5] => [5,6,1,2,3,4] => 1
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [1,2,3,6,4,5] => [5,6,1,2,3,4] => 1
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 1
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [1,2,4,5,6,3] => [3,4,6,1,2,5] => 1
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => [1,2,4,5,3,6] => [3,5,1,2,4,6] => 1
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [1,2,4,5,3,6] => [3,5,1,2,4,6] => 1
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [1,2,4,6,3,5] => [3,5,6,1,2,4] => 1
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 1
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 1
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [1,2,4,6,3,5] => [3,5,6,1,2,4] => 1
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [1,2,4,3,6,5] => [3,6,1,2,4,5] => 1
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 1
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 1
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [1,2,5,6,3,4] => [5,3,6,1,2,4] => 2
>>> Load all 1048 entries. <<<{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => [1,2,5,3,4,6] => [4,5,1,2,3,6] => 1
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [1,2,5,3,4,6] => [4,5,1,2,3,6] => 1
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [1,2,6,3,4,5] => [4,5,6,1,2,3] => 1
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [1,2,6,3,4,5] => [4,5,6,1,2,3] => 1
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 1
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [1,2,5,6,3,4] => [5,3,6,1,2,4] => 2
{{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => [1,2,5,3,6,4] => [6,4,1,2,3,5] => 2
{{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => [1,2,5,3,4,6] => [4,5,1,2,3,6] => 1
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [1,2,5,3,4,6] => [4,5,1,2,3,6] => 1
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [1,2,6,3,5,4] => [6,4,5,1,2,3] => 2
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [1,2,3,5,6,4] => [4,6,1,2,3,5] => 1
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 1
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 1
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [1,2,6,3,4,5] => [4,5,6,1,2,3] => 1
{{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [5,6,1,2,3,4] => 1
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [1,2,6,3,4,5] => [4,5,6,1,2,3] => 1
{{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => [1,2,3,6,4,5] => [5,6,1,2,3,4] => 1
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 1
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [1,3,4,5,6,2] => [2,3,4,6,1,5] => 1
{{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => [1,3,4,5,2,6] => [2,3,5,1,4,6] => 1
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [1,3,4,5,2,6] => [2,3,5,1,4,6] => 1
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [1,3,4,6,2,5] => [2,3,5,6,1,4] => 1
{{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => 1
{{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => 1
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [1,3,4,6,2,5] => [2,3,5,6,1,4] => 1
{{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => [1,3,4,2,6,5] => [2,3,6,1,4,5] => 1
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => 1
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => 1
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [1,3,5,6,2,4] => [5,2,3,6,1,4] => 2
{{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => [1,3,5,2,4,6] => [2,4,5,1,3,6] => 1
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [1,3,5,2,4,6] => [2,4,5,1,3,6] => 1
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [1,3,6,2,4,5] => [2,4,5,6,1,3] => 1
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 1
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 1
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [1,3,6,2,4,5] => [2,4,5,6,1,3] => 1
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [1,3,2,4,6,5] => [2,6,1,3,4,5] => 1
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 1
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 1
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [1,3,5,6,2,4] => [5,2,3,6,1,4] => 2
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [1,3,5,2,6,4] => [6,2,4,1,3,5] => 2
{{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => [1,3,5,2,4,6] => [2,4,5,1,3,6] => 1
{{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => [1,3,5,2,4,6] => [2,4,5,1,3,6] => 1
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [1,3,6,2,5,4] => [6,2,4,5,1,3] => 2
{{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => [1,3,2,5,6,4] => [2,4,6,1,3,5] => 1
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [1,3,2,5,4,6] => [2,5,1,3,4,6] => 1
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [1,3,2,5,4,6] => [2,5,1,3,4,6] => 1
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [1,3,6,2,4,5] => [2,4,5,6,1,3] => 1
{{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => [1,3,2,6,4,5] => [2,5,6,1,3,4] => 1
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 1
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 1
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [1,3,6,2,4,5] => [2,4,5,6,1,3] => 1
{{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => [1,3,2,6,4,5] => [2,5,6,1,3,4] => 1
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [2,6,1,3,4,5] => 1
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 1
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 1
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [1,4,5,6,2,3] => [2,5,3,6,1,4] => 2
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [1,4,5,2,3,6] => [4,2,5,1,3,6] => 2
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [1,4,5,2,3,6] => [4,2,5,1,3,6] => 2
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [1,4,6,2,3,5] => [4,2,5,6,1,3] => 2
{{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => [1,4,2,3,5,6] => [3,4,1,2,5,6] => 1
{{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => [1,4,2,3,5,6] => [3,4,1,2,5,6] => 1
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [1,4,6,2,3,5] => [4,2,5,6,1,3] => 2
{{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => [1,4,2,3,6,5] => [6,3,1,2,4,5] => 2
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [3,4,1,2,5,6] => 1
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [3,4,1,2,5,6] => 1
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [1,5,6,2,3,4] => [4,5,2,6,1,3] => 2
{{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => [1,5,2,3,4,6] => [3,4,5,1,2,6] => 1
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [1,5,2,3,4,6] => [3,4,5,1,2,6] => 1
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [1,6,2,3,4,5] => [3,4,5,6,1,2] => 1
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [1,6,2,3,4,5] => [3,4,5,6,1,2] => 1
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 1
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [1,5,6,2,3,4] => [4,5,2,6,1,3] => 2
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [1,5,2,3,6,4] => [6,3,4,1,2,5] => 2
{{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => [1,5,2,3,4,6] => [3,4,5,1,2,6] => 1
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [3,4,5,1,2,6] => 1
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [1,6,2,3,5,4] => [6,3,4,5,1,2] => 2
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [1,2,3,5,6,4] => [4,6,1,2,3,5] => 1
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 1
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 1
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [3,4,5,6,1,2] => 1
{{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => [1,2,3,6,4,5] => [5,6,1,2,3,4] => 1
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [3,4,5,6,1,2] => 1
{{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => [1,2,3,6,4,5] => [5,6,1,2,3,4] => 1
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 1
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [1,4,5,6,2,3] => [2,5,3,6,1,4] => 2
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [1,4,5,2,6,3] => [2,6,4,1,3,5] => 2
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [1,4,5,2,3,6] => [4,2,5,1,3,6] => 2
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [1,4,5,2,3,6] => [4,2,5,1,3,6] => 2
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [1,4,6,2,5,3] => [2,6,4,5,1,3] => 2
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [1,4,2,5,6,3] => [4,2,6,1,3,5] => 2
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [1,4,2,5,3,6] => [5,3,1,2,4,6] => 2
{{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => [1,4,2,5,3,6] => [5,3,1,2,4,6] => 2
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [1,4,6,2,3,5] => [4,2,5,6,1,3] => 2
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [1,4,2,6,3,5] => [5,2,6,1,3,4] => 2
{{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => [1,4,2,3,5,6] => [3,4,1,2,5,6] => 1
{{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => [1,4,2,3,5,6] => [3,4,1,2,5,6] => 1
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [1,4,6,2,3,5] => [4,2,5,6,1,3] => 2
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,2,6,1,3,4] => 2
{{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [6,3,1,2,4,5] => 2
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [1,4,2,3,5,6] => [3,4,1,2,5,6] => 1
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [1,4,2,3,5,6] => [3,4,1,2,5,6] => 1
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [1,5,6,2,4,3] => [6,4,2,5,1,3] => 3
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [1,5,2,4,6,3] => [4,6,3,1,2,5] => 2
{{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => [1,5,2,4,3,6] => [5,3,4,1,2,6] => 2
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [5,3,4,1,2,6] => 2
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [1,6,2,4,5,3] => [4,6,3,5,1,2] => 2
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [1,2,4,5,6,3] => [3,4,6,1,2,5] => 1
{{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => [1,2,4,5,3,6] => [3,5,1,2,4,6] => 1
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [1,2,4,5,3,6] => [3,5,1,2,4,6] => 1
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,6,1,2] => 2
{{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => [1,2,4,6,3,5] => [3,5,6,1,2,4] => 1
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 1
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 1
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,6,1,2] => 2
{{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => [1,2,4,6,3,5] => [3,5,6,1,2,4] => 1
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [1,2,4,3,6,5] => [3,6,1,2,4,5] => 1
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 1
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 1
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [1,5,6,2,3,4] => [4,5,2,6,1,3] => 2
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [5,6,3,1,2,4] => 2
{{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => [1,5,2,3,4,6] => [3,4,5,1,2,6] => 1
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [3,4,5,1,2,6] => 1
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [5,6,3,4,1,2] => 2
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [1,2,5,6,3,4] => [5,3,6,1,2,4] => 2
{{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => [1,2,5,3,4,6] => [4,5,1,2,3,6] => 1
{{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [4,5,1,2,3,6] => 1
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [1,6,2,3,4,5] => [3,4,5,6,1,2] => 1
{{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => [1,2,6,3,4,5] => [4,5,6,1,2,3] => 1
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [3,4,5,6,1,2] => 1
{{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [4,5,6,1,2,3] => 1
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 1
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [1,5,6,2,3,4] => [4,5,2,6,1,3] => 2
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [5,6,3,1,2,4] => 2
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [6,3,4,1,2,5] => 2
{{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => [1,5,2,3,4,6] => [3,4,5,1,2,6] => 1
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [3,4,5,1,2,6] => 1
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [5,6,3,4,1,2] => 2
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [1,2,5,6,3,4] => [5,3,6,1,2,4] => 2
{{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => [1,2,5,3,6,4] => [6,4,1,2,3,5] => 2
{{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => [1,2,5,3,4,6] => [4,5,1,2,3,6] => 1
{{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [4,5,1,2,3,6] => 1
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [6,3,4,5,1,2] => 2
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [6,4,5,1,2,3] => 2
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [1,2,3,5,6,4] => [4,6,1,2,3,5] => 1
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 1
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 1
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [3,4,5,6,1,2] => 1
{{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [4,5,6,1,2,3] => 1
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [5,6,1,2,3,4] => 1
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [3,4,5,6,1,2] => 1
{{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [4,5,6,1,2,3] => 1
{{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => [1,2,3,6,4,5] => [5,6,1,2,3,4] => 1
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 1
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,4,5,7},{6}} => [2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,2,3,4,6},{5},{7}} => [2,3,4,6,5,1,7] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,2,3,4,7},{5,6}} => [2,3,4,7,6,5,1] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1,2,3,4},{5,6,7}} => [2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,4},{5,6},{7}} => [2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,4,7},{5},{6}} => [2,3,4,7,5,6,1] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1,2,3,4},{5,7},{6}} => [2,3,4,1,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,5,6},{4,7}} => [2,3,5,7,6,1,4] => [1,2,3,5,6,4,7] => [4,6,1,2,3,5,7] => 1
{{1,2,3,5,6},{4},{7}} => [2,3,5,4,6,1,7] => [1,2,3,5,6,4,7] => [4,6,1,2,3,5,7] => 1
{{1,2,3,5},{4,6,7}} => [2,3,5,6,1,7,4] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1,2,3,5},{4,6},{7}} => [2,3,5,6,1,4,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1,2,3,5},{4},{6,7}} => [2,3,5,4,1,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1,2,3,5},{4},{6},{7}} => [2,3,5,4,1,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1,2,3,6},{4,5,7}} => [2,3,6,5,7,1,4] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1,2,3,6},{4,5},{7}} => [2,3,6,5,4,1,7] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1,2,3,7},{4,5,6}} => [2,3,7,5,6,4,1] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1,2,3},{4,5,6,7}} => [2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3},{4,5,6},{7}} => [2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,7},{4,5},{6}} => [2,3,7,5,4,6,1] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1,2,3},{4,5,7},{6}} => [2,3,1,5,7,6,4] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1,2,3},{4,5},{6,7}} => [2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3},{4,5},{6},{7}} => [2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,6},{4,7},{5}} => [2,3,6,7,5,1,4] => [1,2,3,6,4,7,5] => [7,5,1,2,3,4,6] => 2
{{1,2,3,6},{4},{5,7}} => [2,3,6,4,7,1,5] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1,2,3,6},{4},{5},{7}} => [2,3,6,4,5,1,7] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1,2,3,7},{4,6},{5}} => [2,3,7,6,5,4,1] => [1,2,3,7,4,6,5] => [7,5,6,1,2,3,4] => 2
{{1,2,3},{4,6},{5,7}} => [2,3,1,6,7,4,5] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,2,3},{4,6},{5},{7}} => [2,3,1,6,5,4,7] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,2,3,7},{4},{5,6}} => [2,3,7,4,6,5,1] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1,2,3},{4,7},{5,6}} => [2,3,1,7,6,5,4] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1,2,3},{4},{5,6,7}} => [2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3},{4},{5,6},{7}} => [2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3,7},{4},{5},{6}} => [2,3,7,4,5,6,1] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1,2,3},{4,7},{5},{6}} => [2,3,1,7,5,6,4] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1,2,3},{4},{5,7},{6}} => [2,3,1,4,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1,2,3},{4},{5},{6,7}} => [2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,4,6,7},{3,5}} => [2,4,5,6,3,7,1] => [1,2,4,6,7,3,5] => [6,3,4,7,1,2,5] => 2
{{1,2,4,6},{3,5,7}} => [2,4,5,6,7,1,3] => [1,2,4,6,3,5,7] => [3,5,6,1,2,4,7] => 1
{{1,2,4,6},{3,5},{7}} => [2,4,5,6,3,1,7] => [1,2,4,6,3,5,7] => [3,5,6,1,2,4,7] => 1
{{1,2,4},{3,5,6,7}} => [2,4,5,1,6,7,3] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1,2,4},{3,5,6},{7}} => [2,4,5,1,6,3,7] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1,2,4},{3,5},{6,7}} => [2,4,5,1,3,7,6] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1,2,4},{3,5},{6},{7}} => [2,4,5,1,3,6,7] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1,2,4,6,7},{3},{5}} => [2,4,3,6,5,7,1] => [1,2,4,6,7,3,5] => [6,3,4,7,1,2,5] => 2
{{1,2,4,6},{3},{5,7}} => [2,4,3,6,7,1,5] => [1,2,4,6,3,5,7] => [3,5,6,1,2,4,7] => 1
{{1,2,4,6},{3},{5},{7}} => [2,4,3,6,5,1,7] => [1,2,4,6,3,5,7] => [3,5,6,1,2,4,7] => 1
{{1,2,4},{3,6},{5,7}} => [2,4,6,1,7,3,5] => [1,2,4,3,6,5,7] => [3,6,1,2,4,5,7] => 1
{{1,2,4},{3,6},{5},{7}} => [2,4,6,1,5,3,7] => [1,2,4,3,6,5,7] => [3,6,1,2,4,5,7] => 1
{{1,2,4},{3},{5,6,7}} => [2,4,3,1,6,7,5] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1,2,4},{3},{5,6},{7}} => [2,4,3,1,6,5,7] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1,2,4},{3},{5},{6,7}} => [2,4,3,1,5,7,6] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1,2,4},{3},{5},{6},{7}} => [2,4,3,1,5,6,7] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1,2,5,7},{3,4,6}} => [2,5,4,6,7,3,1] => [1,2,5,7,3,4,6] => [5,3,6,7,1,2,4] => 2
{{1,2,5,7},{3,4},{6}} => [2,5,4,3,7,6,1] => [1,2,5,7,3,4,6] => [5,3,6,7,1,2,4] => 2
{{1,2,5},{3,4,7},{6}} => [2,5,4,7,1,6,3] => [1,2,5,3,4,7,6] => [7,4,1,2,3,5,6] => 2
{{1,2,6},{3,4,5,7}} => [2,6,4,5,7,1,3] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1,2,6},{3,4,5},{7}} => [2,6,4,5,3,1,7] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1,2},{3,4,5,6,7}} => [2,1,4,5,6,7,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3,4,5,6},{7}} => [2,1,4,5,6,3,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3,4,5,7},{6}} => [2,1,4,5,7,6,3] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1,2},{3,4,5},{6,7}} => [2,1,4,5,3,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3,4,5},{6},{7}} => [2,1,4,5,3,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,6},{3,4},{5,7}} => [2,6,4,3,7,1,5] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1,2,6},{3,4},{5},{7}} => [2,6,4,3,5,1,7] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1,2,7},{3,4,6},{5}} => [2,7,4,6,5,3,1] => [1,2,7,3,4,6,5] => [7,4,5,6,1,2,3] => 2
{{1,2},{3,4,6},{5,7}} => [2,1,4,6,7,3,5] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,2},{3,4,6},{5},{7}} => [2,1,4,6,5,3,7] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,2},{3,4,7},{5,6}} => [2,1,4,7,6,5,3] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1,2},{3,4},{5,6,7}} => [2,1,4,3,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3,4},{5,6},{7}} => [2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3,4,7},{5},{6}} => [2,1,4,7,5,6,3] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1,2},{3,4},{5,7},{6}} => [2,1,4,3,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1,2},{3,4},{5},{6,7}} => [2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3,4},{5},{6},{7}} => [2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,5,7},{3},{4,6}} => [2,5,3,6,7,4,1] => [1,2,5,7,3,4,6] => [5,3,6,7,1,2,4] => 2
{{1,2,5,7},{3},{4},{6}} => [2,5,3,4,7,6,1] => [1,2,5,7,3,4,6] => [5,3,6,7,1,2,4] => 2
{{1,2,5},{3},{4,7},{6}} => [2,5,3,7,1,6,4] => [1,2,5,3,4,7,6] => [7,4,1,2,3,5,6] => 2
{{1,2},{3,5,6},{4,7}} => [2,1,5,7,6,3,4] => [1,2,3,5,6,4,7] => [4,6,1,2,3,5,7] => 1
{{1,2},{3,5,6},{4},{7}} => [2,1,5,4,6,3,7] => [1,2,3,5,6,4,7] => [4,6,1,2,3,5,7] => 1
{{1,2,7},{3,5},{4,6}} => [2,7,5,6,3,4,1] => [1,2,7,3,5,4,6] => [6,4,5,7,1,2,3] => 2
{{1,2},{3,5},{4,6,7}} => [2,1,5,6,3,7,4] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1,2},{3,5},{4,6},{7}} => [2,1,5,6,3,4,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1,2,7},{3,5},{4},{6}} => [2,7,5,4,3,6,1] => [1,2,7,3,5,4,6] => [6,4,5,7,1,2,3] => 2
{{1,2},{3,5},{4},{6,7}} => [2,1,5,4,3,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1,2},{3,5},{4},{6},{7}} => [2,1,5,4,3,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1,2,6},{3},{4,5,7}} => [2,6,3,5,7,1,4] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1,2,6},{3},{4,5},{7}} => [2,6,3,5,4,1,7] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1,2,7},{3,6},{4,5}} => [2,7,6,5,4,3,1] => [1,2,7,3,6,4,5] => [6,7,4,5,1,2,3] => 2
{{1,2},{3,6},{4,5,7}} => [2,1,6,5,7,3,4] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1,2},{3,6},{4,5},{7}} => [2,1,6,5,4,3,7] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1,2},{3,7},{4,5,6}} => [2,1,7,5,6,4,3] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1,2},{3},{4,5,6,7}} => [2,1,3,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3},{4,5,6},{7}} => [2,1,3,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3,7},{4,5},{6}} => [2,1,7,5,4,6,3] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1,2},{3},{4,5,7},{6}} => [2,1,3,5,7,6,4] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1,2},{3},{4,5},{6,7}} => [2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3},{4,5},{6},{7}} => [2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2,6},{3},{4},{5,7}} => [2,6,3,4,7,1,5] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1,2,6},{3},{4},{5},{7}} => [2,6,3,4,5,1,7] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1,2,7},{3,6},{4},{5}} => [2,7,6,4,5,3,1] => [1,2,7,3,6,4,5] => [6,7,4,5,1,2,3] => 2
{{1,2},{3,6},{4,7},{5}} => [2,1,6,7,5,3,4] => [1,2,3,6,4,7,5] => [7,5,1,2,3,4,6] => 2
{{1,2},{3,6},{4},{5,7}} => [2,1,6,4,7,3,5] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1,2},{3,6},{4},{5},{7}} => [2,1,6,4,5,3,7] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1,2,7},{3},{4,6},{5}} => [2,7,3,6,5,4,1] => [1,2,7,3,4,6,5] => [7,4,5,6,1,2,3] => 2
{{1,2},{3,7},{4,6},{5}} => [2,1,7,6,5,4,3] => [1,2,3,7,4,6,5] => [7,5,6,1,2,3,4] => 2
{{1,2},{3},{4,6},{5,7}} => [2,1,3,6,7,4,5] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,2},{3},{4,6},{5},{7}} => [2,1,3,6,5,4,7] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,2},{3,7},{4},{5,6}} => [2,1,7,4,6,5,3] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1,2},{3},{4,7},{5,6}} => [2,1,3,7,6,5,4] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1,2},{3},{4},{5,6,7}} => [2,1,3,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3},{4},{5,6},{7}} => [2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3,7},{4},{5},{6}} => [2,1,7,4,5,6,3] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1,2},{3},{4,7},{5},{6}} => [2,1,3,7,5,6,4] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1,2},{3},{4},{5,7},{6}} => [2,1,3,4,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1,2},{3},{4},{5},{6,7}} => [2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => [1,3,4,5,6,7,2] => [2,3,4,5,7,1,6] => 1
{{1,3,4,5,7},{2,6}} => [3,6,4,5,7,2,1] => [1,3,4,5,7,2,6] => [2,3,4,6,7,1,5] => 1
{{1,3,4,5,7},{2},{6}} => [3,2,4,5,7,6,1] => [1,3,4,5,7,2,6] => [2,3,4,6,7,1,5] => 1
{{1,3,4,5},{2,7},{6}} => [3,7,4,5,1,6,2] => [1,3,4,5,2,7,6] => [2,3,4,7,1,5,6] => 1
{{1,3,4,7},{2,5,6}} => [3,5,4,7,6,2,1] => [1,3,4,7,2,5,6] => [2,3,5,6,7,1,4] => 1
{{1,3,4},{2,5,6,7}} => [3,5,4,1,6,7,2] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
{{1,3,4},{2,5,6},{7}} => [3,5,4,1,6,2,7] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
{{1,3,4,7},{2,5},{6}} => [3,5,4,7,2,6,1] => [1,3,4,7,2,5,6] => [2,3,5,6,7,1,4] => 1
{{1,3,4},{2,5},{6,7}} => [3,5,4,1,2,7,6] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
{{1,3,4},{2,5},{6},{7}} => [3,5,4,1,2,6,7] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
{{1,3,4,7},{2},{5,6}} => [3,2,4,7,6,5,1] => [1,3,4,7,2,5,6] => [2,3,5,6,7,1,4] => 1
{{1,3,4},{2},{5,6,7}} => [3,2,4,1,6,7,5] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
{{1,3,4},{2},{5,6},{7}} => [3,2,4,1,6,5,7] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
{{1,3,4,7},{2},{5},{6}} => [3,2,4,7,5,6,1] => [1,3,4,7,2,5,6] => [2,3,5,6,7,1,4] => 1
{{1,3,4},{2},{5},{6,7}} => [3,2,4,1,5,7,6] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
{{1,3,4},{2},{5},{6},{7}} => [3,2,4,1,5,6,7] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
{{1,3},{2,4,5,6,7}} => [3,4,1,5,6,7,2] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2,4,5,6},{7}} => [3,4,1,5,6,2,7] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2,4,5,7},{6}} => [3,4,1,5,7,6,2] => [1,3,2,4,5,7,6] => [2,7,1,3,4,5,6] => 1
{{1,3},{2,4,5},{6,7}} => [3,4,1,5,2,7,6] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2,4,5},{6},{7}} => [3,4,1,5,2,6,7] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2,4,6,7},{5}} => [3,4,1,6,5,7,2] => [1,3,2,4,6,7,5] => [2,5,7,1,3,4,6] => 1
{{1,3},{2,4,6},{5,7}} => [3,4,1,6,7,2,5] => [1,3,2,4,6,5,7] => [2,6,1,3,4,5,7] => 1
{{1,3},{2,4,6},{5},{7}} => [3,4,1,6,5,2,7] => [1,3,2,4,6,5,7] => [2,6,1,3,4,5,7] => 1
{{1,3},{2,4,7},{5,6}} => [3,4,1,7,6,5,2] => [1,3,2,4,7,5,6] => [2,6,7,1,3,4,5] => 1
{{1,3},{2,4},{5,6,7}} => [3,4,1,2,6,7,5] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2,4},{5,6},{7}} => [3,4,1,2,6,5,7] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2,4,7},{5},{6}} => [3,4,1,7,5,6,2] => [1,3,2,4,7,5,6] => [2,6,7,1,3,4,5] => 1
{{1,3},{2,4},{5,7},{6}} => [3,4,1,2,7,6,5] => [1,3,2,4,5,7,6] => [2,7,1,3,4,5,6] => 1
{{1,3},{2,4},{5},{6,7}} => [3,4,1,2,5,7,6] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2,4},{5},{6},{7}} => [3,4,1,2,5,6,7] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2,5},{4,6,7}} => [3,5,1,6,2,7,4] => [1,3,2,5,4,6,7] => [2,5,1,3,4,6,7] => 1
{{1,3},{2,5},{4,6},{7}} => [3,5,1,6,2,4,7] => [1,3,2,5,4,6,7] => [2,5,1,3,4,6,7] => 1
{{1,3},{2,5},{4},{6,7}} => [3,5,1,4,2,7,6] => [1,3,2,5,4,6,7] => [2,5,1,3,4,6,7] => 1
{{1,3},{2,5},{4},{6},{7}} => [3,5,1,4,2,6,7] => [1,3,2,5,4,6,7] => [2,5,1,3,4,6,7] => 1
{{1,3},{2},{4,5,6,7}} => [3,2,1,5,6,7,4] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2},{4,5,6},{7}} => [3,2,1,5,6,4,7] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2},{4,5,7},{6}} => [3,2,1,5,7,6,4] => [1,3,2,4,5,7,6] => [2,7,1,3,4,5,6] => 1
{{1,3},{2},{4,5},{6,7}} => [3,2,1,5,4,7,6] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2},{4,5},{6},{7}} => [3,2,1,5,4,6,7] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2},{4,6,7},{5}} => [3,2,1,6,5,7,4] => [1,3,2,4,6,7,5] => [2,5,7,1,3,4,6] => 1
{{1,3},{2},{4,6},{5,7}} => [3,2,1,6,7,4,5] => [1,3,2,4,6,5,7] => [2,6,1,3,4,5,7] => 1
{{1,3},{2},{4,6},{5},{7}} => [3,2,1,6,5,4,7] => [1,3,2,4,6,5,7] => [2,6,1,3,4,5,7] => 1
{{1,3},{2},{4,7},{5,6}} => [3,2,1,7,6,5,4] => [1,3,2,4,7,5,6] => [2,6,7,1,3,4,5] => 1
{{1,3},{2},{4},{5,6,7}} => [3,2,1,4,6,7,5] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2},{4},{5,6},{7}} => [3,2,1,4,6,5,7] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2},{4,7},{5},{6}} => [3,2,1,7,5,6,4] => [1,3,2,4,7,5,6] => [2,6,7,1,3,4,5] => 1
{{1,3},{2},{4},{5,7},{6}} => [3,2,1,4,7,6,5] => [1,3,2,4,5,7,6] => [2,7,1,3,4,5,6] => 1
{{1,3},{2},{4},{5},{6,7}} => [3,2,1,4,5,7,6] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,3},{2},{4},{5},{6},{7}} => [3,2,1,4,5,6,7] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
{{1,4,5},{2,3,6,7}} => [4,3,6,5,1,7,2] => [1,4,5,2,3,6,7] => [4,2,5,1,3,6,7] => 2
{{1,4,5},{2,3,6},{7}} => [4,3,6,5,1,2,7] => [1,4,5,2,3,6,7] => [4,2,5,1,3,6,7] => 2
{{1,4,5},{2,3},{6,7}} => [4,3,2,5,1,7,6] => [1,4,5,2,3,6,7] => [4,2,5,1,3,6,7] => 2
{{1,4,5},{2,3},{6},{7}} => [4,3,2,5,1,6,7] => [1,4,5,2,3,6,7] => [4,2,5,1,3,6,7] => 2
{{1,4},{2,3,5,6,7}} => [4,3,5,1,6,7,2] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2,3,5,6},{7}} => [4,3,5,1,6,2,7] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2,3,5,7},{6}} => [4,3,5,1,7,6,2] => [1,4,2,3,5,7,6] => [7,3,1,2,4,5,6] => 2
{{1,4},{2,3,5},{6,7}} => [4,3,5,1,2,7,6] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2,3,5},{6},{7}} => [4,3,5,1,2,6,7] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2,3},{5,6,7}} => [4,3,2,1,6,7,5] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2,3},{5,6},{7}} => [4,3,2,1,6,5,7] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2,3},{5,7},{6}} => [4,3,2,1,7,6,5] => [1,4,2,3,5,7,6] => [7,3,1,2,4,5,6] => 2
{{1,4},{2,3},{5},{6,7}} => [4,3,2,1,5,7,6] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2,3},{5},{6},{7}} => [4,3,2,1,5,6,7] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,5},{2,3,4,7},{6}} => [5,3,4,7,1,6,2] => [1,5,2,3,4,7,6] => [7,3,4,1,2,5,6] => 2
{{1,7},{2,3,4,5,6}} => [7,3,4,5,6,2,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,7},{2,3,4,5},{6}} => [7,3,4,5,2,6,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,7},{2,3,4},{5,6}} => [7,3,4,2,6,5,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2,3,4,7},{5,6}} => [1,3,4,7,6,5,2] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,7},{2,3,4},{5},{6}} => [7,3,4,2,5,6,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2,3,4,7},{5},{6}} => [1,3,4,7,5,6,2] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1},{2,3,4},{5,7},{6}} => [1,3,4,2,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,5},{2,3},{4,7},{6}} => [5,3,2,7,1,6,4] => [1,5,2,3,4,7,6] => [7,3,4,1,2,5,6] => 2
{{1},{2,3,5,6},{4,7}} => [1,3,5,7,6,2,4] => [1,2,3,5,6,4,7] => [4,6,1,2,3,5,7] => 1
{{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => [1,2,3,5,6,4,7] => [4,6,1,2,3,5,7] => 1
{{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1,6},{2,3,7},{4,5}} => [6,3,7,5,4,1,2] => [1,6,2,3,7,4,5] => [6,7,3,4,1,2,5] => 2
{{1},{2,3,6},{4,5,7}} => [1,3,6,5,7,2,4] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1},{2,3,6},{4,5},{7}} => [1,3,6,5,4,2,7] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1,7},{2,3},{4,5,6}} => [7,3,2,5,6,4,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2,3,7},{4,5,6}} => [1,3,7,5,6,4,2] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,7},{2,3},{4,5},{6}} => [7,3,2,5,4,6,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2,3,7},{4,5},{6}} => [1,3,7,5,4,6,2] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,6},{2,3,7},{4},{5}} => [6,3,7,4,5,1,2] => [1,6,2,3,7,4,5] => [6,7,3,4,1,2,5] => 2
{{1},{2,3,6},{4,7},{5}} => [1,3,6,7,5,2,4] => [1,2,3,6,4,7,5] => [7,5,1,2,3,4,6] => 2
{{1},{2,3,6},{4},{5,7}} => [1,3,6,4,7,2,5] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1},{2,3,6},{4},{5},{7}} => [1,3,6,4,5,2,7] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1},{2,3,7},{4,6},{5}} => [1,3,7,6,5,4,2] => [1,2,3,7,4,6,5] => [7,5,6,1,2,3,4] => 2
{{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1},{2,3},{4,6},{5},{7}} => [1,3,2,6,5,4,7] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,7},{2,3},{4},{5,6}} => [7,3,2,4,6,5,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2,3,7},{4},{5,6}} => [1,3,7,4,6,5,2] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1},{2,3},{4,7},{5,6}} => [1,3,2,7,6,5,4] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,7},{2,3},{4},{5},{6}} => [7,3,2,4,5,6,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2,3,7},{4},{5},{6}} => [1,3,7,4,5,6,2] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1},{2,3},{4,7},{5},{6}} => [1,3,2,7,5,6,4] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1},{2,3},{4},{5,7},{6}} => [1,3,2,4,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,4,5},{2},{3,6,7}} => [4,2,6,5,1,7,3] => [1,4,5,2,3,6,7] => [4,2,5,1,3,6,7] => 2
{{1,4,5},{2},{3,6},{7}} => [4,2,6,5,1,3,7] => [1,4,5,2,3,6,7] => [4,2,5,1,3,6,7] => 2
{{1,4,5},{2},{3},{6,7}} => [4,2,3,5,1,7,6] => [1,4,5,2,3,6,7] => [4,2,5,1,3,6,7] => 2
{{1,4,5},{2},{3},{6},{7}} => [4,2,3,5,1,6,7] => [1,4,5,2,3,6,7] => [4,2,5,1,3,6,7] => 2
{{1,4},{2,7},{3,5,6}} => [4,7,5,1,6,3,2] => [1,4,2,7,3,5,6] => [5,2,6,7,1,3,4] => 2
{{1,4},{2},{3,5,6,7}} => [4,2,5,1,6,7,3] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2},{3,5,6},{7}} => [4,2,5,1,6,3,7] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2,7},{3,5},{6}} => [4,7,5,1,3,6,2] => [1,4,2,7,3,5,6] => [5,2,6,7,1,3,4] => 2
{{1,4},{2},{3,5,7},{6}} => [4,2,5,1,7,6,3] => [1,4,2,3,5,7,6] => [7,3,1,2,4,5,6] => 2
{{1,4},{2},{3,5},{6,7}} => [4,2,5,1,3,7,6] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2},{3,5},{6},{7}} => [4,2,5,1,3,6,7] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2,7},{3},{5,6}} => [4,7,3,1,6,5,2] => [1,4,2,7,3,5,6] => [5,2,6,7,1,3,4] => 2
{{1,4},{2},{3},{5,6,7}} => [4,2,3,1,6,7,5] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2},{3},{5,6},{7}} => [4,2,3,1,6,5,7] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2,7},{3},{5},{6}} => [4,7,3,1,5,6,2] => [1,4,2,7,3,5,6] => [5,2,6,7,1,3,4] => 2
{{1,4},{2},{3},{5,7},{6}} => [4,2,3,1,7,6,5] => [1,4,2,3,5,7,6] => [7,3,1,2,4,5,6] => 2
{{1,4},{2},{3},{5},{6,7}} => [4,2,3,1,5,7,6] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1,4},{2},{3},{5},{6},{7}} => [4,2,3,1,5,6,7] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => 1
{{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => [1,2,4,6,7,3,5] => [6,3,4,7,1,2,5] => 2
{{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => [1,2,4,6,3,5,7] => [3,5,6,1,2,4,7] => 1
{{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => [1,2,4,6,3,5,7] => [3,5,6,1,2,4,7] => 1
{{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => [1,2,4,6,7,3,5] => [6,3,4,7,1,2,5] => 2
{{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => [1,2,4,6,3,5,7] => [3,5,6,1,2,4,7] => 1
{{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => [1,2,4,6,3,5,7] => [3,5,6,1,2,4,7] => 1
{{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => [1,2,4,3,6,5,7] => [3,6,1,2,4,5,7] => 1
{{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => [1,2,4,3,6,5,7] => [3,6,1,2,4,5,7] => 1
{{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 1
{{1,5},{2},{3,4,7},{6}} => [5,2,4,7,1,6,3] => [1,5,2,3,4,7,6] => [7,3,4,1,2,5,6] => 2
{{1,6},{2,5},{3,4,7}} => [6,5,4,7,2,1,3] => [1,6,2,5,3,4,7] => [5,6,3,4,1,2,7] => 2
{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [1,6,2,5,3,4,7] => [5,6,3,4,1,2,7] => 2
{{1,7},{2,5,6},{3,4}} => [7,5,4,3,6,2,1] => [1,7,2,5,6,3,4] => [6,4,7,3,5,1,2] => 3
{{1},{2,5,7},{3,4,6}} => [1,5,4,6,7,3,2] => [1,2,5,7,3,4,6] => [5,3,6,7,1,2,4] => 2
{{1},{2,5,7},{3,4},{6}} => [1,5,4,3,7,6,2] => [1,2,5,7,3,4,6] => [5,3,6,7,1,2,4] => 2
{{1},{2,5},{3,4,7},{6}} => [1,5,4,7,2,6,3] => [1,2,5,3,4,7,6] => [7,4,1,2,3,5,6] => 2
{{1},{2,6},{3,4,5,7}} => [1,6,4,5,7,2,3] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1},{2,6},{3,4,5},{7}} => [1,6,4,5,3,2,7] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,7},{2},{3,4,5},{6}} => [7,2,4,5,3,6,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2,6},{3,4},{5,7}} => [1,6,4,3,7,2,5] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1},{2,6},{3,4},{5},{7}} => [1,6,4,3,5,2,7] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => [1,2,7,3,4,6,5] => [7,4,5,6,1,2,3] => 2
{{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,7},{2},{3,4},{5,6}} => [7,2,4,3,6,5,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2},{3,4,7},{5,6}} => [1,2,4,7,6,5,3] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,7},{2},{3,4},{5},{6}} => [7,2,4,3,5,6,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => [1,5,2,3,4,7,6] => [7,3,4,1,2,5,6] => 2
{{1,6},{2,5},{3},{4,7}} => [6,5,3,7,2,1,4] => [1,6,2,5,3,4,7] => [5,6,3,4,1,2,7] => 2
{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [1,6,2,5,3,4,7] => [5,6,3,4,1,2,7] => 2
{{1,7},{2,5,6},{3},{4}} => [7,5,3,4,6,2,1] => [1,7,2,5,6,3,4] => [6,4,7,3,5,1,2] => 3
{{1},{2,5,7},{3},{4,6}} => [1,5,3,6,7,4,2] => [1,2,5,7,3,4,6] => [5,3,6,7,1,2,4] => 2
{{1},{2,5,7},{3},{4},{6}} => [1,5,3,4,7,6,2] => [1,2,5,7,3,4,6] => [5,3,6,7,1,2,4] => 2
{{1},{2,5},{3},{4,7},{6}} => [1,5,3,7,2,6,4] => [1,2,5,3,4,7,6] => [7,4,1,2,3,5,6] => 2
{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [1,7,2,6,3,5,4] => [7,5,6,3,4,1,2] => 3
{{1},{2},{3,5,6},{4,7}} => [1,2,5,7,6,3,4] => [1,2,3,5,6,4,7] => [4,6,1,2,3,5,7] => 1
{{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => [1,2,3,5,6,4,7] => [4,6,1,2,3,5,7] => 1
{{1},{2,7},{3,5},{4,6}} => [1,7,5,6,3,4,2] => [1,2,7,3,5,4,6] => [6,4,5,7,1,2,3] => 2
{{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => [1,2,7,3,5,4,6] => [6,4,5,7,1,2,3] => 2
{{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 1
{{1,6},{2},{3,7},{4,5}} => [6,2,7,5,4,1,3] => [1,6,2,3,7,4,5] => [6,7,3,4,1,2,5] => 2
{{1},{2,6},{3},{4,5,7}} => [1,6,3,5,7,2,4] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1},{2,6},{3},{4,5},{7}} => [1,6,3,5,4,2,7] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [1,2,7,3,6,4,5] => [6,7,4,5,1,2,3] => 2
{{1},{2},{3,6},{4,5,7}} => [1,2,6,5,7,3,4] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2},{3,7},{4,5,6}} => [1,2,7,5,6,4,3] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,7},{2},{3},{4,5},{6}} => [7,2,3,5,4,6,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2},{3,7},{4,5},{6}} => [1,2,7,5,4,6,3] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,6},{2},{3,7},{4},{5}} => [6,2,7,4,5,1,3] => [1,6,2,3,7,4,5] => [6,7,3,4,1,2,5] => 2
{{1},{2,6},{3},{4},{5,7}} => [1,6,3,4,7,2,5] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1},{2,6},{3},{4},{5},{7}} => [1,6,3,4,5,2,7] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => 1
{{1},{2,7},{3,6},{4},{5}} => [1,7,6,4,5,3,2] => [1,2,7,3,6,4,5] => [6,7,4,5,1,2,3] => 2
{{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => [1,2,3,6,4,7,5] => [7,5,1,2,3,4,6] => 2
{{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => 1
{{1},{2,7},{3},{4,6},{5}} => [1,7,3,6,5,4,2] => [1,2,7,3,4,6,5] => [7,4,5,6,1,2,3] => 2
{{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => [1,2,3,7,4,6,5] => [7,5,6,1,2,3,4] => 2
{{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 1
{{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2},{3,7},{4},{5,6}} => [1,2,7,4,6,5,3] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => 1
{{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => 1
{{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => 1
{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 1
{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
{{1,2},{3,4},{5,6},{7,8}} => [2,1,4,3,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,4},{2,3},{5,6},{7,8}} => [4,3,2,1,6,5,8,7] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,8},{2,3},{4,5},{6,7}} => [8,3,2,5,4,7,6,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,2},{3,5},{4,6},{7,8}} => [2,1,5,6,3,4,8,7] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1,6},{2,5},{3,4},{7,8}} => [6,5,4,3,2,1,8,7] => [1,6,2,5,3,4,7,8] => [5,6,3,4,1,2,7,8] => 2
{{1,4},{2,7},{3,5},{6,8}} => [4,7,5,1,3,8,2,6] => [1,4,2,7,3,5,6,8] => [5,2,6,7,1,3,4,8] => 2
{{1,2},{3,7},{4,5},{6,8}} => [2,1,7,5,4,8,3,6] => [1,2,3,7,4,5,6,8] => [5,6,7,1,2,3,4,8] => 1
{{1,2},{3,8},{4,5},{6,7}} => [2,1,8,5,4,7,6,3] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1,8},{2,7},{3,4},{5,6}} => [8,7,4,3,6,5,2,1] => [1,8,2,7,3,4,5,6] => [5,6,7,8,3,4,1,2] => 2
{{1,2},{3,5},{4,7},{6,8}} => [2,1,5,7,3,8,4,6] => [1,2,3,5,4,7,6,8] => [4,7,1,2,3,5,6,8] => 1
{{1,3},{2,4},{5,7},{6,8}} => [3,4,1,2,7,8,5,6] => [1,3,2,4,5,7,6,8] => [2,7,1,3,4,5,6,8] => 1
{{1,2},{3,4},{5,7},{6,8}} => [2,1,4,3,7,8,5,6] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1,2},{3,4},{5,8},{6,7}} => [2,1,4,3,8,7,6,5] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1,3},{2,4},{5,8},{6,7}} => [3,4,1,2,8,7,6,5] => [1,3,2,4,5,8,6,7] => [2,7,8,1,3,4,5,6] => 1
{{1,8},{2,3},{4,7},{5,6}} => [8,3,2,7,6,5,4,1] => [1,8,2,3,4,7,5,6] => [7,8,3,4,5,6,1,2] => 2
{{1,5},{2,4},{3,8},{6,7}} => [5,4,8,2,1,7,6,3] => [1,5,2,4,3,8,6,7] => [4,7,2,8,1,3,5,6] => 2
{{1,3},{2,5},{4,8},{6,7}} => [3,5,1,8,2,7,6,4] => [1,3,2,5,4,8,6,7] => [2,4,7,8,1,3,5,6] => 1
{{1,2},{3,8},{4,7},{5,6}} => [2,1,8,7,6,5,4,3] => [1,2,3,8,4,7,5,6] => [7,8,5,6,1,2,3,4] => 2
{{1,8},{2,7},{3,6},{4,5}} => [8,7,6,5,4,3,2,1] => [1,8,2,7,3,6,4,5] => [7,8,5,6,3,4,1,2] => 3
{{1,2},{3,4},{5,6},{7,8},{9,10}} => [2,1,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 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] => [1,2,3,4,5,6,7,8] => 0
{{1},{2},{3},{4},{5},{6},{7,8}} => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2},{3},{4},{5},{6,8},{7}} => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1},{2},{3},{4},{5},{6,7,8}} => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2},{3},{4},{5,8},{6},{7}} => [1,2,3,4,8,6,7,5] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2},{3},{4},{5,8},{6,7}} => [1,2,3,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2},{3},{4},{5,6,8},{7}} => [1,2,3,4,6,8,7,5] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1},{2},{3},{4},{5,6,7,8}} => [1,2,3,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2},{3},{4,8},{5},{6},{7}} => [1,2,3,8,5,6,7,4] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1},{2},{3},{4,5,8},{6},{7}} => [1,2,3,5,8,6,7,4] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2},{3},{4,8},{5,6,7}} => [1,2,3,8,6,7,5,4] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1},{2},{3},{4,5,6,8},{7}} => [1,2,3,5,6,8,7,4] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2},{3,4},{5,6},{7},{8}} => [1,2,4,3,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2},{3,4},{5,8},{6,7}} => [1,2,4,3,8,7,6,5] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2},{3,4},{5,6,7,8}} => [1,2,4,3,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2},{3,5},{4},{6,7,8}} => [1,2,5,4,3,7,8,6] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1},{2},{3,8},{4},{5},{6},{7}} => [1,2,8,4,5,6,7,3] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1},{2},{3,5,8},{4},{6},{7}} => [1,2,5,4,8,6,7,3] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1},{2},{3,8},{4},{5,6,7}} => [1,2,8,4,6,7,5,3] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1},{2},{3,5,8},{4},{6,7}} => [1,2,5,4,8,7,6,3] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1},{2},{3,5,6,7,8},{4}} => [1,2,5,4,6,7,8,3] => [1,2,3,5,6,7,8,4] => [4,5,6,8,1,2,3,7] => 1
{{1},{2},{3,4,5},{6,7,8}} => [1,2,4,5,3,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2},{3,4,8},{5},{6},{7}} => [1,2,4,8,5,6,7,3] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1},{2},{3,4,5,6},{7,8}} => [1,2,4,5,6,3,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2},{3,8},{4,7},{5,6}} => [1,2,8,7,6,5,4,3] => [1,2,3,8,4,7,5,6] => [7,8,5,6,1,2,3,4] => 2
{{1},{2},{3,4,5,8},{6},{7}} => [1,2,4,5,8,6,7,3] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2},{3,4,5,6,7},{8}} => [1,2,4,5,6,7,3,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2},{3,8},{4,5,6,7}} => [1,2,8,5,6,7,4,3] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1},{2},{3,4,5,8},{6,7}} => [1,2,4,5,8,7,6,3] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2},{3,4,5,6,8},{7}} => [1,2,4,5,6,8,7,3] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1},{2},{3,4,5,6,7,8}} => [1,2,4,5,6,7,8,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2,3},{4},{5},{6,7},{8}} => [1,3,2,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2,3},{4},{5,8},{6,7}} => [1,3,2,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2,3},{4},{5,6,7,8}} => [1,3,2,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2,3},{4,5},{6,7},{8}} => [1,3,2,5,4,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2,3},{4,5},{6,8},{7}} => [1,3,2,5,4,8,7,6] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1},{2,3},{4,5},{6,7,8}} => [1,3,2,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2,3},{4,6,7},{5},{8}} => [1,3,2,6,5,7,4,8] => [1,2,3,4,6,7,5,8] => [5,7,1,2,3,4,6,8] => 1
{{1},{2,3},{4,5,6},{7,8}} => [1,3,2,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2,3},{4,7},{5,6},{8}} => [1,3,2,7,6,5,4,8] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => 1
{{1},{2,3},{4,8},{5,6},{7}} => [1,3,2,8,6,5,7,4] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1},{2,3},{4,8},{5,7},{6}} => [1,3,2,8,7,6,5,4] => [1,2,3,4,8,5,7,6] => [8,6,7,1,2,3,4,5] => 2
{{1},{2,3},{4,8},{5,6,7}} => [1,3,2,8,6,7,5,4] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1},{2,3},{4,5,8},{6,7}} => [1,3,2,5,8,7,6,4] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2,3},{4,5,6,8},{7}} => [1,3,2,5,6,8,7,4] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1},{2,3},{4,5,6,7,8}} => [1,3,2,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2,5},{3},{4},{6,8},{7}} => [1,5,3,4,2,8,7,6] => [1,2,5,3,4,6,8,7] => [8,4,1,2,3,5,6,7] => 2
{{1},{2,3,4},{5},{6,7,8}} => [1,3,4,2,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2,3,4},{5,6},{7,8}} => [1,3,4,2,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2,3,4},{5,6,7},{8}} => [1,3,4,2,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1},{2,3,4},{5,8},{6,7}} => [1,3,4,2,8,7,6,5] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2,3,4},{5,6,8},{7}} => [1,3,4,2,6,8,7,5] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1},{2,5},{3,4},{6,8},{7}} => [1,5,4,3,2,8,7,6] => [1,2,5,3,4,6,8,7] => [8,4,1,2,3,5,6,7] => 2
{{1},{2,3,5},{4},{6,7,8}} => [1,3,5,4,2,7,8,6] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1},{2,3,8},{4},{5},{6},{7}} => [1,3,8,4,5,6,7,2] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1},{2,3,8},{4},{5,6,7}} => [1,3,8,4,6,7,5,2] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1},{2,3,5,8},{4},{6,7}} => [1,3,5,4,8,7,6,2] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1},{2,3,5,6,7,8},{4}} => [1,3,5,4,6,7,8,2] => [1,2,3,5,6,7,8,4] => [4,5,6,8,1,2,3,7] => 1
{{1},{2,8},{3,6},{4,5},{7}} => [1,8,6,5,4,3,7,2] => [1,2,8,3,6,4,5,7] => [6,7,4,5,8,1,2,3] => 2
{{1},{2,3,8},{4,5},{6},{7}} => [1,3,8,5,4,6,7,2] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1},{2,3,8},{4,5},{6,7}} => [1,3,8,5,4,7,6,2] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1},{2,8},{3,7},{4,6},{5}} => [1,8,7,6,5,4,3,2] => [1,2,8,3,7,4,6,5] => [8,6,7,4,5,1,2,3] => 3
{{1},{2,3,4,8},{5},{6},{7}} => [1,3,4,8,5,6,7,2] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1},{2,3,8},{4,7},{5,6}} => [1,3,8,7,6,5,4,2] => [1,2,3,8,4,7,5,6] => [7,8,5,6,1,2,3,4] => 2
{{1},{2,3,4,8},{5,6},{7}} => [1,3,4,8,6,5,7,2] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1},{2,3,4,5,7},{6},{8}} => [1,3,4,5,7,6,2,8] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1},{2,3,8},{4,5,7},{6}} => [1,3,8,5,7,6,4,2] => [1,2,3,8,4,5,7,6] => [8,5,6,7,1,2,3,4] => 2
{{1},{2,3,4,8},{5,7},{6}} => [1,3,4,8,7,6,5,2] => [1,2,3,4,8,5,7,6] => [8,6,7,1,2,3,4,5] => 2
{{1},{2,3,4,5,8},{6},{7}} => [1,3,4,5,8,6,7,2] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2,3,4,5,8},{6,7}} => [1,3,4,5,8,7,6,2] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1},{2,3,4,5,6,8},{7}} => [1,3,4,5,6,8,7,2] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1},{2,3,4,5,6,7,8}} => [1,3,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3},{4},{5},{6},{7,8}} => [2,1,3,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3},{4},{5,6},{7},{8}} => [2,1,3,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3},{4},{5,8},{6,7}} => [2,1,3,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1,2},{3},{4},{5,6,7,8}} => [2,1,3,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3},{4,5},{6},{7},{8}} => [2,1,3,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3},{4,5},{6,7,8}} => [2,1,3,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3},{4,5,6},{7,8}} => [2,1,3,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3,4},{5},{6},{7},{8}} => [2,1,4,3,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3,4},{5},{6,7,8}} => [2,1,4,3,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3,4},{5,6},{7},{8}} => [2,1,4,3,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3,4},{5,6,8},{7}} => [2,1,4,3,6,8,7,5] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1,2},{3,4},{5,6,7,8}} => [2,1,4,3,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3,5},{4},{6},{7},{8}} => [2,1,5,4,3,6,7,8] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1,2},{3,8},{4},{5,6,7}} => [2,1,8,4,6,7,5,3] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1,2},{3,5,8},{4},{6,7}} => [2,1,5,4,8,7,6,3] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1,2},{3,5,6,8},{4},{7}} => [2,1,5,4,6,8,7,3] => [1,2,3,5,6,8,4,7] => [4,5,7,8,1,2,3,6] => 1
{{1,2},{3,5,6,7,8},{4}} => [2,1,5,4,6,7,8,3] => [1,2,3,5,6,7,8,4] => [4,5,6,8,1,2,3,7] => 1
{{1,2},{3,4,5},{6},{7},{8}} => [2,1,4,5,3,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3,4,6},{5},{7,8}} => [2,1,4,6,5,3,8,7] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1
{{1,2},{3,4,8},{5},{6,7}} => [2,1,4,8,5,7,6,3] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1,2},{3,4,5,6},{7,8}} => [2,1,4,5,6,3,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2},{3,8},{4,5,6},{7}} => [2,1,8,5,6,4,7,3] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1,2},{3,4,8},{5,6},{7}} => [2,1,4,8,6,5,7,3] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1,2},{3,8},{4,5,7},{6}} => [2,1,8,5,7,6,4,3] => [1,2,3,8,4,5,7,6] => [8,5,6,7,1,2,3,4] => 2
{{1,2},{3,4,8},{5,7},{6}} => [2,1,4,8,7,6,5,3] => [1,2,3,4,8,5,7,6] => [8,6,7,1,2,3,4,5] => 2
{{1,2},{3,4,5,8},{6},{7}} => [2,1,4,5,8,6,7,3] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1,2},{3,4,8},{5,6,7}} => [2,1,4,8,6,7,5,3] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1,2},{3,4,5,8},{6,7}} => [2,1,4,5,8,7,6,3] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1,2},{3,4,5,6,8},{7}} => [2,1,4,5,6,8,7,3] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1,2},{3,4,5,6,7,8}} => [2,1,4,5,6,7,8,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,3},{2},{4},{5},{6,8},{7}} => [3,2,1,4,5,8,7,6] => [1,3,2,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => 1
{{1,3},{2},{4},{5,8},{6,7}} => [3,2,1,4,8,7,6,5] => [1,3,2,4,5,8,6,7] => [2,7,8,1,3,4,5,6] => 1
{{1,3},{2},{4,6},{5},{7,8}} => [3,2,1,6,5,4,8,7] => [1,3,2,4,6,5,7,8] => [2,6,1,3,4,5,7,8] => 1
{{1,3},{2},{4,8},{5},{6,7}} => [3,2,1,8,5,7,6,4] => [1,3,2,4,8,5,6,7] => [2,6,7,8,1,3,4,5] => 1
{{1,3},{2},{4,6,8},{5},{7}} => [3,2,1,6,5,8,7,4] => [1,3,2,4,6,8,5,7] => [2,5,7,8,1,3,4,6] => 1
{{1,3},{2},{4,6,7,8},{5}} => [3,2,1,6,5,7,8,4] => [1,3,2,4,6,7,8,5] => [2,5,6,8,1,3,4,7] => 1
{{1,3},{2},{4,8},{5,6},{7}} => [3,2,1,8,6,5,7,4] => [1,3,2,4,8,5,6,7] => [2,6,7,8,1,3,4,5] => 1
{{1,3},{2},{4,8},{5,6,7}} => [3,2,1,8,6,7,5,4] => [1,3,2,4,8,5,6,7] => [2,6,7,8,1,3,4,5] => 1
{{1,3},{2},{4,5,8},{6,7}} => [3,2,1,5,8,7,6,4] => [1,3,2,4,5,8,6,7] => [2,7,8,1,3,4,5,6] => 1
{{1,3},{2},{4,5,6,8},{7}} => [3,2,1,5,6,8,7,4] => [1,3,2,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => 1
{{1,4},{2},{3},{5},{6},{7},{8}} => [4,2,3,1,5,6,7,8] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4},{2},{3},{5},{6,8},{7}} => [4,2,3,1,5,8,7,6] => [1,4,2,3,5,6,8,7] => [8,3,1,2,4,5,6,7] => 2
{{1,4},{2},{3},{5,6},{7,8}} => [4,2,3,1,6,5,8,7] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4},{2},{3},{5,6,7,8}} => [4,2,3,1,6,7,8,5] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,8},{2},{3},{4},{5},{6},{7}} => [8,2,3,4,5,6,7,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,8},{2},{3},{4},{5},{6,7}} => [8,2,3,4,5,7,6,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,4,5},{2},{3},{6,7,8}} => [4,2,3,5,1,7,8,6] => [1,4,5,2,3,6,7,8] => [4,2,5,1,3,6,7,8] => 2
{{1,8},{2},{3},{4,5},{6},{7}} => [8,2,3,5,4,6,7,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,8},{2},{3,4},{5,6,7}} => [8,2,4,3,6,7,5,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,8},{2},{3,4,5},{6,7}} => [8,2,4,5,3,7,6,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,8},{2},{3,4,5,6},{7}} => [8,2,4,5,6,3,7,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,8},{2},{3,4,7},{5,6}} => [8,2,4,7,6,5,3,1] => [1,8,2,3,4,7,5,6] => [7,8,3,4,5,6,1,2] => 2
{{1,8},{2},{3,4,5,6,7}} => [8,2,4,5,6,7,3,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,3,4,5,6,8},{2},{7}} => [3,2,4,5,6,8,7,1] => [1,3,4,5,6,8,2,7] => [2,3,4,5,7,8,1,6] => 1
{{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => [1,3,4,5,6,7,8,2] => [2,3,4,5,6,8,1,7] => 1
{{1,2,3},{4},{5},{6},{7},{8}} => [2,3,1,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3},{4},{5},{6,7,8}} => [2,3,1,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3},{4},{5,6},{7,8}} => [2,3,1,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3},{4},{5,8},{6,7}} => [2,3,1,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1,2,3},{4,5},{6},{7},{8}} => [2,3,1,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3},{4,5},{6,7},{8}} => [2,3,1,5,4,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3},{4,6},{5},{7,8}} => [2,3,1,6,5,4,8,7] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1
{{1,2,3},{4,6,7},{5},{8}} => [2,3,1,6,5,7,4,8] => [1,2,3,4,6,7,5,8] => [5,7,1,2,3,4,6,8] => 1
{{1,2,3},{4,5,6},{7},{8}} => [2,3,1,5,6,4,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3},{4,8},{5,7},{6}} => [2,3,1,8,7,6,5,4] => [1,2,3,4,8,5,7,6] => [8,6,7,1,2,3,4,5] => 2
{{1,2,3},{4,5,6,7},{8}} => [2,3,1,5,6,7,4,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3},{4,8},{5,6,7}} => [2,3,1,8,6,7,5,4] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1,2,3},{4,5,6,7,8}} => [2,3,1,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,4},{2,3},{5},{6},{7},{8}} => [4,3,2,1,5,6,7,8] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4},{2,3},{5},{6},{7,8}} => [4,3,2,1,5,6,8,7] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4},{2,3},{5},{6,7},{8}} => [4,3,2,1,5,7,6,8] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4},{2,3},{5},{6,8},{7}} => [4,3,2,1,5,8,7,6] => [1,4,2,3,5,6,8,7] => [8,3,1,2,4,5,6,7] => 2
{{1,4},{2,3},{5},{6,7,8}} => [4,3,2,1,5,7,8,6] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4},{2,3},{5,6},{7},{8}} => [4,3,2,1,6,5,7,8] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4},{2,3},{5,6,7},{8}} => [4,3,2,1,6,7,5,8] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4},{2,3},{5,6,8},{7}} => [4,3,2,1,6,8,7,5] => [1,4,2,3,5,6,8,7] => [8,3,1,2,4,5,6,7] => 2
{{1,4},{2,3},{5,6,7,8}} => [4,3,2,1,6,7,8,5] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,8},{2,3},{4},{5},{6},{7}} => [8,3,2,4,5,6,7,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,8},{2,3},{4},{5,6,7}} => [8,3,2,4,6,7,5,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,2,6},{3},{4,5},{7,8}} => [2,6,3,5,4,1,8,7] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => 1
{{1,2,4,7,8},{3},{5},{6}} => [2,4,3,7,5,6,8,1] => [1,2,4,7,8,3,5,6] => [6,7,3,4,8,1,2,5] => 2
{{1,8},{2,7},{3},{4,5,6}} => [8,7,3,5,6,4,2,1] => [1,8,2,7,3,4,5,6] => [5,6,7,8,3,4,1,2] => 2
{{1,2,4,7,8},{3},{5,6}} => [2,4,3,7,6,5,8,1] => [1,2,4,7,8,3,5,6] => [6,7,3,4,8,1,2,5] => 2
{{1,2,3,4},{5},{6},{7},{8}} => [2,3,4,1,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3,4},{5},{6,7},{8}} => [2,3,4,1,5,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3,4},{5,6},{7},{8}} => [2,3,4,1,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3,4},{5,6},{7,8}} => [2,3,4,1,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3,4},{5,6,7},{8}} => [2,3,4,1,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3,4},{5,8},{6,7}} => [2,3,4,1,8,7,6,5] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1,2,3,4},{5,6,8},{7}} => [2,3,4,1,6,8,7,5] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,8},{2,3,4},{5},{6},{7}} => [8,3,4,2,5,6,7,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,8},{2,3,4},{5,6},{7}} => [8,3,4,2,6,5,7,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,2,5},{3,4},{6,8},{7}} => [2,5,4,3,1,8,7,6] => [1,2,5,3,4,6,8,7] => [8,4,1,2,3,5,6,7] => 2
{{1,2,6},{3,4},{5},{7,8}} => [2,6,4,3,5,1,8,7] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => 1
{{1,2,3,5},{4},{6},{7,8}} => [2,3,5,4,1,6,8,7] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1,2,3,8},{4},{5},{6},{7}} => [2,3,8,4,5,6,7,1] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1,2,3,5,8},{4},{6},{7}} => [2,3,5,4,8,6,7,1] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1,2,3,8},{4},{5,6,7}} => [2,3,8,4,6,7,5,1] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1,2,3,5,6,7,8},{4}} => [2,3,5,4,6,7,8,1] => [1,2,3,5,6,7,8,4] => [4,5,6,8,1,2,3,7] => 1
{{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3,4,5},{6,7},{8}} => [2,3,4,5,1,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3,4,5},{6,8},{7}} => [2,3,4,5,1,8,7,6] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1,2,3,4,5},{6,7,8}} => [2,3,4,5,1,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,6},{3,4,5},{7},{8}} => [2,6,4,5,3,1,7,8] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => 1
{{1,2,6},{3,4,5},{7,8}} => [2,6,4,5,3,1,8,7] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => 1
{{1,8},{2,7},{3,4,5},{6}} => [8,7,4,5,3,6,2,1] => [1,8,2,7,3,4,5,6] => [5,6,7,8,3,4,1,2] => 2
{{1,2,3,7},{4,5},{6},{8}} => [2,3,7,5,4,6,1,8] => [1,2,3,7,4,5,6,8] => [5,6,7,1,2,3,4,8] => 1
{{1,2,3,8},{4,5},{6},{7}} => [2,3,8,5,4,6,7,1] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1,2,3,4,6},{5},{7},{8}} => [2,3,4,6,5,1,7,8] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1
{{1,2,8},{3,7},{4,6},{5}} => [2,8,7,6,5,4,3,1] => [1,2,8,3,7,4,6,5] => [8,6,7,4,5,1,2,3] => 3
{{1,2,3,4,7},{5},{6},{8}} => [2,3,4,7,5,6,1,8] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => 1
{{1,2,3,4,8},{5},{6},{7}} => [2,3,4,8,5,6,7,1] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1,2,3,4,6,7},{5},{8}} => [2,3,4,6,5,7,1,8] => [1,2,3,4,6,7,5,8] => [5,7,1,2,3,4,6,8] => 1
{{1,2,3,4,8},{5},{6,7}} => [2,3,4,8,5,7,6,1] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,2,3,8},{4,5,6},{7}} => [2,3,8,5,6,4,7,1] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1,2,3,4,7},{5,6},{8}} => [2,3,4,7,6,5,1,8] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => 1
{{1,8},{2,3,4,7},{5,6}} => [8,3,4,7,6,5,2,1] => [1,8,2,3,4,7,5,6] => [7,8,3,4,5,6,1,2] => 2
{{1,2,3,8},{4,7},{5,6}} => [2,3,8,7,6,5,4,1] => [1,2,3,8,4,7,5,6] => [7,8,5,6,1,2,3,4] => 2
{{1,2,3,4,8},{5,6},{7}} => [2,3,4,8,6,5,7,1] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1,2,3,4,5,7},{6},{8}} => [2,3,4,5,7,6,1,8] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1,2,3,8},{4,5,7},{6}} => [2,3,8,5,7,6,4,1] => [1,2,3,8,4,5,7,6] => [8,5,6,7,1,2,3,4] => 2
{{1,2,3,4,8},{5,7},{6}} => [2,3,4,8,7,6,5,1] => [1,2,3,4,8,5,7,6] => [8,6,7,1,2,3,4,5] => 2
{{1,2,3,4,5,8},{6},{7}} => [2,3,4,5,8,6,7,1] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,8},{2,3,4,5,6,7}} => [8,3,4,5,6,7,2,1] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => 1
{{1,2,3,8},{4,5,6,7}} => [2,3,8,5,6,7,4,1] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => 1
{{1,2,3,4,8},{5,6,7}} => [2,3,4,8,6,7,5,1] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => 1
{{1,2,3,4,5,8},{6,7}} => [2,3,4,5,8,7,6,1] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => 1
{{1,2,3,4,5,6,8},{7}} => [2,3,4,5,6,8,7,1] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1
{{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
{{1,3,4,5,6,8},{2,7}} => [3,7,4,5,6,8,2,1] => [1,3,4,5,6,8,2,7] => [2,3,4,5,7,8,1,6] => 1
{{1,2,3,5,6,8},{4,7}} => [2,3,5,7,6,8,4,1] => [1,2,3,5,6,8,4,7] => [4,5,7,8,1,2,3,6] => 1
{{1,2,3,4,6,7},{5,8}} => [2,3,4,6,8,7,1,5] => [1,2,3,4,6,7,5,8] => [5,7,1,2,3,4,6,8] => 1
{{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1,2,3,5,8},{4,6,7}} => [2,3,5,6,8,7,4,1] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1,2,3,4,7},{5,6,8}} => [2,3,4,7,6,8,1,5] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => 1
{{1,2,3,4,6},{5,7},{8}} => [2,3,4,6,7,1,5,8] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1
{{1,2,3,7},{4,5,6,8}} => [2,3,7,5,6,8,1,4] => [1,2,3,7,4,5,6,8] => [5,6,7,1,2,3,4,8] => 1
{{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1,2,4,5},{3,7,8},{6}} => [2,4,7,5,1,6,8,3] => [1,2,4,5,3,7,8,6] => [3,4,6,8,1,2,5,7] => 1
{{1,2,3,5},{4,6,7},{8}} => [2,3,5,6,1,7,4,8] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1,2,3,5},{4,7},{6,8}} => [2,3,5,7,1,8,4,6] => [1,2,3,5,4,7,6,8] => [4,7,1,2,3,5,6,8] => 1
{{1,2,3,4},{5,7},{6,8}} => [2,3,4,1,7,8,5,6] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1,2,3,5},{4,6},{7,8}} => [2,3,5,6,1,4,8,7] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1,2,4,5},{3,8},{6},{7}} => [2,4,8,5,1,6,7,3] => [1,2,4,5,3,8,6,7] => [3,4,7,8,1,2,5,6] => 1
{{1,2,3,5},{4,7},{6},{8}} => [2,3,5,7,1,6,4,8] => [1,2,3,5,4,7,6,8] => [4,7,1,2,3,5,6,8] => 1
{{1,2,3,5},{4,6},{7},{8}} => [2,3,5,6,1,4,7,8] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1,2,4},{3,6,8},{5},{7}} => [2,4,6,1,5,8,7,3] => [1,2,4,3,6,8,5,7] => [3,5,7,8,1,2,4,6] => 1
{{1},{2,3,5,8},{4,6},{7}} => [1,3,5,6,8,4,7,2] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1},{2,6},{3,4},{5,7,8}} => [1,6,4,3,7,2,8,5] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => 1
{{1},{2,4},{3,8},{5,6,7}} => [1,4,8,2,6,7,5,3] => [1,2,4,3,8,5,6,7] => [3,6,7,8,1,2,4,5] => 1
{{1,6},{2,3,7,8},{4},{5}} => [6,3,7,4,5,1,8,2] => [1,6,2,3,7,8,4,5] => [7,5,8,3,1,2,4,6] => 3
{{1,7},{2,6},{3,4,8},{5}} => [7,6,4,8,5,2,1,3] => [1,7,2,6,3,4,8,5] => [8,5,6,3,4,1,2,7] => 3
{{1,3},{2,4,6,8},{5},{7}} => [3,4,1,6,5,8,7,2] => [1,3,2,4,6,8,5,7] => [2,5,7,8,1,3,4,6] => 1
{{1,3},{2},{4,6,8},{5,7}} => [3,2,1,6,7,8,5,4] => [1,3,2,4,6,8,5,7] => [2,5,7,8,1,3,4,6] => 1
{{1,2,4},{3,8},{5},{6,7}} => [2,4,8,1,5,7,6,3] => [1,2,4,3,8,5,6,7] => [3,6,7,8,1,2,4,5] => 1
{{1,4},{2,7},{3},{5,6,8}} => [4,7,3,1,6,8,2,5] => [1,4,2,7,3,5,6,8] => [5,2,6,7,1,3,4,8] => 2
{{1,2,8},{3,6},{4},{5,7}} => [2,8,6,4,7,3,5,1] => [1,2,8,3,6,4,5,7] => [6,7,4,5,8,1,2,3] => 2
{{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] => [1,2,3,4,5,6,7,8,9] => 0
{{1},{2},{3},{4},{5},{6},{7},{8,9}} => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1},{2},{3},{4},{5},{6},{7,9},{8}} => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => 1
{{1},{2},{3},{4},{5},{6,9},{7},{8}} => [1,2,3,4,5,9,7,8,6] => [1,2,3,4,5,6,9,7,8] => [8,9,1,2,3,4,5,6,7] => 1
{{1},{2},{3},{4},{5,9},{6},{7},{8}} => [1,2,3,4,9,6,7,8,5] => [1,2,3,4,5,9,6,7,8] => [7,8,9,1,2,3,4,5,6] => 1
{{1},{2},{3},{4,9},{5},{6},{7},{8}} => [1,2,3,9,5,6,7,8,4] => [1,2,3,4,9,5,6,7,8] => [6,7,8,9,1,2,3,4,5] => 1
{{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] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1},{2},{3},{4},{5},{6},{7,8,9}} => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => 1
{{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} => [1,2,3,4,5,6,10,8,9,7] => [1,2,3,4,5,6,7,10,8,9] => [9,10,1,2,3,4,5,6,7,8] => 1
{{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} => [1,2,3,4,5,10,7,8,9,6] => [1,2,3,4,5,6,10,7,8,9] => [8,9,10,1,2,3,4,5,6,7] => 1
{{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => [1,2,3,4,10,6,7,8,9,5] => [1,2,3,4,5,10,6,7,8,9] => [7,8,9,10,1,2,3,4,5,6] => 1
{{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} => [1,2,3,10,5,6,7,8,9,4] => [1,2,3,4,10,5,6,7,8,9] => [6,7,8,9,10,1,2,3,4,5] => 1
{{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1},{2,3,4,5,6,7,8,9}} => [1,3,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5,6,8},{7},{9}} => [2,3,4,5,6,8,7,1,9] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => 1
{{1},{2,3,4,5,6,7,9},{8}} => [1,3,4,5,6,7,9,8,2] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => 1
{{1},{2,3,4,5,6,7,8,9,10}} => [1,3,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5,6,7,9},{8},{10}} => [2,3,4,5,6,7,9,8,1,10] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => 1
{{1,2,3,4,5,7,8},{6},{9}} => [2,3,4,5,7,6,8,1,9] => [1,2,3,4,5,7,8,6,9] => [6,8,1,2,3,4,5,7,9] => 1
{{1},{2,3,4,5,6,7,8,10},{9}} => [1,3,4,5,6,7,8,10,9,2] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => 1
{{1,4},{2,3,5,6},{7,8}} => [4,3,5,1,6,2,8,7] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,3},{2,4,5,7},{6,8}} => [3,4,1,5,7,8,2,6] => [1,3,2,4,5,7,6,8] => [2,7,1,3,4,5,6,8] => 1
{{1,2},{3,4,5,7},{6,8}} => [2,1,4,5,7,8,3,6] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1,4},{2,3,5,6,7,8}} => [4,3,5,1,6,7,8,2] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,2},{3,4,6,7},{5,8}} => [2,1,4,6,8,7,3,5] => [1,2,3,4,6,7,5,8] => [5,7,1,2,3,4,6,8] => 1
{{1,2},{3,5},{4,6,7,8}} => [2,1,5,6,3,7,8,4] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1,2},{3,5,6,8},{4,7}} => [2,1,5,7,6,8,4,3] => [1,2,3,5,6,8,4,7] => [4,5,7,8,1,2,3,6] => 1
{{1,4},{2},{3,5,6},{7,8}} => [4,2,5,1,6,3,8,7] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4,5},{2},{3,6},{7,8}} => [4,2,6,5,1,3,8,7] => [1,4,5,2,3,6,7,8] => [4,2,5,1,3,6,7,8] => 2
{{1,2},{3,7},{4},{5,6,8}} => [2,1,7,4,6,8,3,5] => [1,2,3,7,4,5,6,8] => [5,6,7,1,2,3,4,8] => 1
{{1},{2},{3,5},{4,6,7,8}} => [1,2,5,6,3,7,8,4] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1},{2,4},{3,6,8},{5,7}} => [1,4,6,2,7,8,5,3] => [1,2,4,3,6,8,5,7] => [3,5,7,8,1,2,4,6] => 1
{{1},{2},{3,7},{4,5,6,8}} => [1,2,7,5,6,8,3,4] => [1,2,3,7,4,5,6,8] => [5,6,7,1,2,3,4,8] => 1
{{1},{2,6},{3},{4,5,7,8}} => [1,6,3,5,7,2,8,4] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => 1
{{1,6},{2},{3,7,8},{4,5}} => [6,2,7,5,4,1,8,3] => [1,6,2,3,7,8,4,5] => [7,5,8,3,1,2,4,6] => 3
{{1,2},{3,4,7},{5},{6,8}} => [2,1,4,7,5,8,3,6] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => 1
{{1,2,5},{3},{4,6,8},{7}} => [2,5,3,6,1,8,7,4] => [1,2,5,3,4,6,8,7] => [8,4,1,2,3,5,6,7] => 2
{{1,3},{2,4},{5,6,8},{7}} => [3,4,1,2,6,8,7,5] => [1,3,2,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => 1
{{1,2},{3,5,8},{4,6},{7}} => [2,1,5,6,8,4,7,3] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1},{2,3,4,7},{5},{6,8}} => [1,3,4,7,5,8,2,6] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => 1
{{1},{2,3,4},{5,7},{6,8}} => [1,3,4,2,7,8,5,6] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1},{2,3,5},{4,7},{6,8}} => [1,3,5,7,2,8,4,6] => [1,2,3,5,4,7,6,8] => [4,7,1,2,3,5,6,8] => 1
{{1},{2,3,5},{4,6},{7,8}} => [1,3,5,6,2,4,8,7] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1,2,3,4,5},{6,7,8,9,10}} => [2,3,4,5,1,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,6},{2,5},{3,4,7,8}} => [6,5,4,7,2,1,8,3] => [1,6,2,5,3,4,7,8] => [5,6,3,4,1,2,7,8] => 2
{{1},{2,8},{3,6},{4,5,7}} => [1,8,6,5,7,3,4,2] => [1,2,8,3,6,4,5,7] => [6,7,4,5,8,1,2,3] => 2
{{1},{2,3,5},{4,6,7},{8}} => [1,3,5,6,2,7,4,8] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1},{2},{3,5},{4,6},{7},{8}} => [1,2,5,6,3,4,7,8] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1},{2,3},{4,5,7},{6,8}} => [1,3,2,5,7,8,4,6] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1,4},{2},{3,5,6,8},{7}} => [4,2,5,1,6,8,7,3] => [1,4,2,3,5,6,8,7] => [8,3,1,2,4,5,6,7] => 2
{{1,4},{2,7},{3,5,6,8}} => [4,7,5,1,6,8,2,3] => [1,4,2,7,3,5,6,8] => [5,2,6,7,1,3,4,8] => 2
{{1,2},{3},{4,6},{5,7,8}} => [2,1,3,6,7,4,8,5] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1
{{1},{2},{3,5,6,8},{4,7}} => [1,2,5,7,6,8,4,3] => [1,2,3,5,6,8,4,7] => [4,5,7,8,1,2,3,6] => 1
{{1},{2,3},{4,7},{5,6,8}} => [1,3,2,7,6,8,4,5] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => 1
{{1,3},{2},{4,6},{5,7,8}} => [3,2,1,6,7,4,8,5] => [1,3,2,4,6,5,7,8] => [2,6,1,3,4,5,7,8] => 1
{{1,3},{2,4,5},{6,8},{7}} => [3,4,1,5,2,8,7,6] => [1,3,2,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => 1
{{1},{2,4,5},{3,7,8},{6}} => [1,4,7,5,2,6,8,3] => [1,2,4,5,3,7,8,6] => [3,4,6,8,1,2,5,7] => 1
{{1,3},{2,5},{4,7,8},{6}} => [3,5,1,7,2,6,8,4] => [1,3,2,5,4,7,8,6] => [2,4,6,8,1,3,5,7] => 1
{{1,4},{2,3,5},{6,7},{8}} => [4,3,5,1,2,7,6,8] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4},{2,3,5},{6,8},{7}} => [4,3,5,1,2,8,7,6] => [1,4,2,3,5,6,8,7] => [8,3,1,2,4,5,6,7] => 2
{{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,4},{2},{3},{5},{6},{7},{8},{9}} => [4,2,3,1,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => 1
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3},{4},{5},{6},{7},{8},{9}} => [2,3,1,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,3},{2,4,8},{5},{6,7}} => [3,4,1,8,5,7,6,2] => [1,3,2,4,8,5,6,7] => [2,6,7,8,1,3,4,5] => 1
{{1,4,5},{2,3,6},{7},{8}} => [4,3,6,5,1,2,7,8] => [1,4,5,2,3,6,7,8] => [4,2,5,1,3,6,7,8] => 2
{{1,2,4},{3,8},{5,6},{7}} => [2,4,8,1,6,5,7,3] => [1,2,4,3,8,5,6,7] => [3,6,7,8,1,2,4,5] => 1
{{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5,6,7},{8,9}} => [2,3,4,5,6,7,1,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5,6},{7,8,9}} => [2,3,4,5,6,1,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5,6},{7,8},{9}} => [2,3,4,5,6,1,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5,6},{7},{8},{9}} => [2,3,4,5,6,1,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5},{6,7,8,9}} => [2,3,4,5,1,7,8,9,6] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5},{6,7},{8,9}} => [2,3,4,5,1,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5},{6,7},{8},{9}} => [2,3,4,5,1,7,6,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5},{6},{7},{8},{9}} => [2,3,4,5,1,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4},{5,6},{7,8},{9}} => [2,3,4,1,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4},{5,6},{7},{8},{9}} => [2,3,4,1,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4},{5},{6},{7},{8},{9}} => [2,3,4,1,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3},{4,5},{6,7},{8,9}} => [2,3,1,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3},{4,5},{6},{7},{8},{9}} => [2,3,1,5,4,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2},{3,4},{5,6},{7,8},{9}} => [2,1,4,3,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2},{3,4},{5,6},{7},{8},{9}} => [2,1,4,3,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2},{3,4},{5},{6},{7},{8},{9}} => [2,1,4,3,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5,6,7,8},{9,10}} => [2,3,4,5,6,7,8,1,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5,6,7,8},{9},{10}} => [2,3,4,5,6,7,8,1,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5,6,7},{8,9,10}} => [2,3,4,5,6,7,1,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5,6,7},{8,9},{10}} => [2,3,4,5,6,7,1,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5,6,7},{8},{9},{10}} => [2,3,4,5,6,7,1,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5,6},{7,8,9,10}} => [2,3,4,5,6,1,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5,6},{7,8},{9,10}} => [2,3,4,5,6,1,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5,6},{7},{8},{9},{10}} => [2,3,4,5,6,1,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5},{6,7},{8,9},{10}} => [2,3,4,5,1,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4,5},{6},{7},{8},{9},{10}} => [2,3,4,5,1,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4},{5,6,7,8},{9,10}} => [2,3,4,1,6,7,8,5,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4},{5,6},{7,8},{9,10}} => [2,3,4,1,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3,4},{5},{6},{7},{8},{9},{10}} => [2,3,4,1,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3},{4,5},{6,7},{8,9},{10}} => [2,3,1,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => [2,3,1,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2},{3,4},{5,6},{7,8},{9},{10}} => [2,1,4,3,6,5,8,7,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2},{3,4},{5,6},{7},{8},{9},{10}} => [2,1,4,3,6,5,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,2},{3,4},{5},{6},{7},{8},{9},{10}} => [2,1,4,3,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
{{1,4},{2,3},{5},{6},{7},{8},{9}} => [4,3,2,1,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => 1
{{1,2,3},{4,7},{5},{6,8}} => [2,3,1,7,5,8,4,6] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => 1
{{1,2,6},{3},{4,5,7},{8}} => [2,6,3,5,7,1,4,8] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => 1
{{1},{2,3,7},{4},{5,6,8}} => [1,3,7,4,6,8,2,5] => [1,2,3,7,4,5,6,8] => [5,6,7,1,2,3,4,8] => 1
{{1},{2,3},{4,6,7},{5,8}} => [1,3,2,6,8,7,4,5] => [1,2,3,4,6,7,5,8] => [5,7,1,2,3,4,6,8] => 1
{{1},{2,3},{4,6},{5,7,8}} => [1,3,2,6,7,4,8,5] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1
{{1},{2,6},{3,4,5,7},{8}} => [1,6,4,5,7,2,3,8] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => 1
{{1,4},{2},{3,5},{6,8},{7}} => [4,2,5,1,3,8,7,6] => [1,4,2,3,5,6,8,7] => [8,3,1,2,4,5,6,7] => 2
{{1},{2,5},{3,4,6,8},{7}} => [1,5,4,6,2,8,7,3] => [1,2,5,3,4,6,8,7] => [8,4,1,2,3,5,6,7] => 2
{{1},{2},{3,5,8},{4,6,7}} => [1,2,5,6,8,7,4,3] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1,3,4,5,6,7,8,9},{2}} => [3,2,4,5,6,7,8,9,1] => [1,3,4,5,6,7,8,9,2] => [2,3,4,5,6,7,9,1,8] => 1
{{1,2,3,4,9},{5,6,7,8}} => [2,3,4,9,6,7,8,5,1] => [1,2,3,4,9,5,6,7,8] => [6,7,8,9,1,2,3,4,5] => 1
{{1},{2,3,5},{4,6,7,8}} => [1,3,5,6,2,7,8,4] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1
{{1,4},{2},{3,5,6,7,8}} => [4,2,5,1,6,7,8,3] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1,4},{2,3,5,6,8},{7}} => [4,3,5,1,6,8,7,2] => [1,4,2,3,5,6,8,7] => [8,3,1,2,4,5,6,7] => 2
{{1},{2,3,5,6,8},{4,7}} => [1,3,5,7,6,8,4,2] => [1,2,3,5,6,8,4,7] => [4,5,7,8,1,2,3,6] => 1
{{1},{2,3,7},{4,5},{6,8}} => [1,3,7,5,4,8,2,6] => [1,2,3,7,4,5,6,8] => [5,6,7,1,2,3,4,8] => 1
{{1,3},{2},{4,5,7},{6,8}} => [3,2,1,5,7,8,4,6] => [1,3,2,4,5,7,6,8] => [2,7,1,3,4,5,6,8] => 1
{{1},{2},{3,4,6},{5,7,8}} => [1,2,4,6,7,3,8,5] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1
{{1},{2},{3,4,7},{5,6,8}} => [1,2,4,7,6,8,3,5] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => 1
{{1,2},{3},{4,6,7},{5,8}} => [2,1,3,6,8,7,4,5] => [1,2,3,4,6,7,5,8] => [5,7,1,2,3,4,6,8] => 1
{{1,4},{2},{3,5},{6,7,8}} => [4,2,5,1,3,7,8,6] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1},{2,3,4,6},{5,7},{8}} => [1,3,4,6,7,2,5,8] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1
{{1,2,6},{3,4,5,7,8}} => [2,6,4,5,7,1,8,3] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => 1
{{1},{2},{3},{4},{5,7},{6,8}} => [1,2,3,4,7,8,5,6] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1},{2,4},{3,8},{5},{6},{7}} => [1,4,8,2,5,6,7,3] => [1,2,4,3,8,5,6,7] => [3,6,7,8,1,2,4,5] => 1
{{1},{2},{3},{4},{5},{6,8},{7,9}} => [1,2,3,4,5,8,9,6,7] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => 1
{{1},{2},{3},{4,6,7},{5,8}} => [1,2,3,6,8,7,4,5] => [1,2,3,4,6,7,5,8] => [5,7,1,2,3,4,6,8] => 1
{{1},{2,4,5},{3,8},{6},{7}} => [1,4,8,5,2,6,7,3] => [1,2,4,5,3,8,6,7] => [3,4,7,8,1,2,5,6] => 1
{{1},{2,3,4,5,7},{6,8}} => [1,3,4,5,7,8,2,6] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1},{2,3,5,8},{4,6,7}} => [1,3,5,6,8,7,4,2] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1},{2,4,7,8},{3,5},{6}} => [1,4,5,7,3,6,8,2] => [1,2,4,7,8,3,5,6] => [6,7,3,4,8,1,2,5] => 2
{{1},{2,3,4,5,6,8},{7,9}} => [1,3,4,5,6,8,9,2,7] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => 1
{{1,3},{2,4,5,6,8},{7}} => [3,4,1,5,6,8,7,2] => [1,3,2,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => 1
{{1,2},{3,4,6},{5,7,8}} => [2,1,4,6,7,3,8,5] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1
{{1,2,3},{4,7},{5,6,8}} => [2,3,1,7,6,8,4,5] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => 1
{{1},{2},{3},{4},{5},{6,7,9},{8}} => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => 1
{{1},{2,6},{3,4,5,7,8}} => [1,6,4,5,7,2,8,3] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => 1
{{1},{2,3,4,6},{5,7,8}} => [1,3,4,6,7,2,8,5] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1
{{1,4,5},{2},{3,6,7,8}} => [4,2,6,5,1,7,8,3] => [1,4,5,2,3,6,7,8] => [4,2,5,1,3,6,7,8] => 2
{{1},{2},{3,5,8},{4,6},{7}} => [1,2,5,6,8,4,7,3] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => 1
{{1,2},{3,7},{4,5,6,8}} => [2,1,7,5,6,8,3,4] => [1,2,3,7,4,5,6,8] => [5,6,7,1,2,3,4,8] => 1
{{1,4},{2,3,5,6},{7},{8}} => [4,3,5,1,6,2,7,8] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1
{{1},{2},{3,4,5,7},{6,8}} => [1,2,4,5,7,8,3,6] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1
{{1,4,5},{2},{3,6,7},{8}} => [4,2,6,5,1,7,3,8] => [1,4,5,2,3,6,7,8] => [4,2,5,1,3,6,7,8] => 2
{{1},{2,5},{3},{4,6,8},{7}} => [1,5,3,6,2,8,7,4] => [1,2,5,3,4,6,8,7] => [8,4,1,2,3,5,6,7] => 2
{{1,4,5},{2,3,6,7,8}} => [4,3,6,5,1,7,8,2] => [1,4,5,2,3,6,7,8] => [4,2,5,1,3,6,7,8] => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,7 16,32,4 32,121,49,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 7\ q$
$F_{5} = 16 + 32\ q + 4\ q^{2}$
$F_{6} = 32 + 121\ q + 49\ q^{2} + q^{3}$
Description
The number of big descents of a permutation.
For a permutation $\pi$, this is the number of indices $i$ such that $\pi(i)-\pi(i+1) > 1$.
The generating functions of big descents is equal to the generating function of (normal) descents after sending a permutation from cycle to one-line notation Mp00090cycle-as-one-line notation, see [Theorem 2.5, 1].
For the number of small descents, see St000214The number of adjacencies of a permutation..
For a permutation $\pi$, this is the number of indices $i$ such that $\pi(i)-\pi(i+1) > 1$.
The generating functions of big descents is equal to the generating function of (normal) descents after sending a permutation from cycle to one-line notation Mp00090cycle-as-one-line notation, see [Theorem 2.5, 1].
For the number of small descents, see St000214The number of adjacencies of a permutation..
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
Lehmer-code to major-code bijection
Description
Sends a permutation to the unique permutation such that the Lehmer code is sent to the major code.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation $\sigma$ is given by $L(\sigma) = l_1 \ldots l_n$ with $l_i = \# \{ j > i : \sigma_j < \sigma_i \}$. In particular, $l_i$ is the number of boxes in the $i$-th column of the Rothe diagram. For example, the Lehmer code of $\sigma = [4,3,1,5,2]$ is $32010$. The Lehmer code $L : \mathfrak{S}_n\ \tilde\longrightarrow\ S_n$ is a bijection between permutations of size $n$ and sequences $l_1\ldots l_n \in \mathbf{N}^n$ with $l_i \leq i$.
* The major code $M(\sigma)$ of a permutation $\sigma \in \mathfrak{S}_n$ is a way to encode a permutation as a sequence $m_1 m_2 \ldots m_n$ with $m_i \geq i$. To define $m_i$, let $\operatorname{del}_i(\sigma)$ be the normalized permutation obtained by removing all $\sigma_j < i$ from the one-line notation of $\sigma$. The $i$-th index is then given by
$$m_i = \operatorname{maj}(\operatorname{del}_i(\sigma)) - \operatorname{maj}(\operatorname{del}_{i-1}(\sigma)).$$
For example, the permutation $[9,3,5,7,2,1,4,6,8]$ has major code $[5, 0, 1, 0, 1, 2, 0, 1, 0]$ since
$$\operatorname{maj}([8,2,4,6,1,3,5,7]) = 5, \quad \operatorname{maj}([7,1,3,5,2,4,6]) = 5, \quad \operatorname{maj}([6,2,4,1,3,5]) = 4,$$
$$\operatorname{maj}([5,1,3,2,4]) = 4, \quad \operatorname{maj}([4,2,1,3]) = 3, \quad \operatorname{maj}([3,1,2]) = 1, \quad \operatorname{maj}([2,1]) = 1.$$
Observe that the sum of the major code of $\sigma$ equals the major index of $\sigma$.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation $\sigma$ is given by $L(\sigma) = l_1 \ldots l_n$ with $l_i = \# \{ j > i : \sigma_j < \sigma_i \}$. In particular, $l_i$ is the number of boxes in the $i$-th column of the Rothe diagram. For example, the Lehmer code of $\sigma = [4,3,1,5,2]$ is $32010$. The Lehmer code $L : \mathfrak{S}_n\ \tilde\longrightarrow\ S_n$ is a bijection between permutations of size $n$ and sequences $l_1\ldots l_n \in \mathbf{N}^n$ with $l_i \leq i$.
* The major code $M(\sigma)$ of a permutation $\sigma \in \mathfrak{S}_n$ is a way to encode a permutation as a sequence $m_1 m_2 \ldots m_n$ with $m_i \geq i$. To define $m_i$, let $\operatorname{del}_i(\sigma)$ be the normalized permutation obtained by removing all $\sigma_j < i$ from the one-line notation of $\sigma$. The $i$-th index is then given by
$$m_i = \operatorname{maj}(\operatorname{del}_i(\sigma)) - \operatorname{maj}(\operatorname{del}_{i-1}(\sigma)).$$
For example, the permutation $[9,3,5,7,2,1,4,6,8]$ has major code $[5, 0, 1, 0, 1, 2, 0, 1, 0]$ since
$$\operatorname{maj}([8,2,4,6,1,3,5,7]) = 5, \quad \operatorname{maj}([7,1,3,5,2,4,6]) = 5, \quad \operatorname{maj}([6,2,4,1,3,5]) = 4,$$
$$\operatorname{maj}([5,1,3,2,4]) = 4, \quad \operatorname{maj}([4,2,1,3]) = 3, \quad \operatorname{maj}([3,1,2]) = 1, \quad \operatorname{maj}([2,1]) = 1.$$
Observe that the sum of the major code of $\sigma$ equals the major index of $\sigma$.
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