Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00223: Permutations —runsort⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
St000157: Standard tableaux ⟶ ℤ
Values
[1,0] => [1] => [1] => [[1]] => 0
[1,0,1,0] => [2,1] => [1,2] => [[1,2]] => 0
[1,1,0,0] => [1,2] => [1,2] => [[1,2]] => 0
[1,0,1,0,1,0] => [3,2,1] => [1,2,3] => [[1,2,3]] => 0
[1,0,1,1,0,0] => [2,3,1] => [1,2,3] => [[1,2,3]] => 0
[1,1,0,0,1,0] => [3,1,2] => [1,2,3] => [[1,2,3]] => 0
[1,1,0,1,0,0] => [2,1,3] => [1,3,2] => [[1,2],[3]] => 1
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [[1,2,3]] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,2,3,4] => [[1,2,3,4]] => 0
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [1,2,3,4] => [[1,2,3,4]] => 0
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,2,3,4] => [[1,2,3,4]] => 0
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [1,2,4,3] => [[1,2,3],[4]] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => [[1,2,3,4]] => 0
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,2,3,4] => [[1,2,3,4]] => 0
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [1,2,3,4] => [[1,2,3,4]] => 0
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [1,3,2,4] => [[1,2,4],[3]] => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [1,4,2,3] => [[1,2,4],[3]] => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [1,4,2,3] => [[1,2,4],[3]] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,2,3,4] => [[1,2,3,4]] => 0
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,2,4,3] => [[1,2,3],[4]] => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [1,3,4,2] => [[1,2,3],[4]] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [[1,2,3,4]] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [1,2,3,5,4] => [[1,2,3,4],[5]] => 1
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,2,4,3,5] => [[1,2,3,5],[4]] => 1
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [1,2,5,3,4] => [[1,2,3,5],[4]] => 1
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [1,2,5,3,4] => [[1,2,3,5],[4]] => 1
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [1,2,3,5,4] => [[1,2,3,4],[5]] => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [1,2,4,5,3] => [[1,2,3,4],[5]] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [1,2,3,5,4] => [[1,2,3,4],[5]] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [1,3,2,4,5] => [[1,2,4,5],[3]] => 1
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [1,3,2,4,5] => [[1,2,4,5],[3]] => 1
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [1,4,2,3,5] => [[1,2,4,5],[3]] => 1
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [1,5,2,3,4] => [[1,2,4,5],[3]] => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [1,5,2,3,4] => [[1,2,4,5],[3]] => 1
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [1,4,2,3,5] => [[1,2,4,5],[3]] => 1
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [1,5,2,3,4] => [[1,2,4,5],[3]] => 1
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [1,5,2,4,3] => [[1,2,4],[3],[5]] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,5,2,3,4] => [[1,2,4,5],[3]] => 1
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,2,4,3,5] => [[1,2,3,5],[4]] => 1
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [1,2,5,3,4] => [[1,2,3,5],[4]] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [1,2,5,3,4] => [[1,2,3,5],[4]] => 1
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [1,3,4,2,5] => [[1,2,3,5],[4]] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [1,3,5,2,4] => [[1,2,3],[4,5]] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [1,4,5,2,3] => [[1,2,3],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,4,5,2,3] => [[1,2,3],[4,5]] => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [1,2,3,5,4] => [[1,2,3,4],[5]] => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [1,2,4,5,3] => [[1,2,3,4],[5]] => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,3,4,5,2] => [[1,2,3,4],[5]] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,2,5,3,4,6] => [[1,2,3,5,6],[4]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,2,5,3,4,6] => [[1,2,3,5,6],[4]] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [1,2,6,3,5,4] => [[1,2,3,5],[4],[6]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,2,4,5,3,6] => [[1,2,3,4,6],[5]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,2,4,6,3,5] => [[1,2,3,4],[5,6]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => 1
>>> Load all 1049 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [1,4,2,3,5,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [1,4,2,3,5,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [1,5,2,3,4,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [1,5,2,3,4,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [1,6,2,3,5,4] => [[1,2,4,5],[3],[6]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [1,4,2,3,5,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [1,4,2,3,5,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [1,5,2,3,4,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [1,5,2,4,3,6] => [[1,2,4,6],[3],[5]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [1,6,2,4,3,5] => [[1,2,4,6],[3],[5]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [1,6,2,5,3,4] => [[1,2,4,6],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [1,6,2,5,3,4] => [[1,2,4,6],[3],[5]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [1,5,2,3,4,6] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [1,6,2,3,5,4] => [[1,2,4,5],[3],[6]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [1,6,2,4,5,3] => [[1,2,4,5],[3],[6]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [1,2,5,3,4,6] => [[1,2,3,5,6],[4]] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,2,5,3,4,6] => [[1,2,3,5,6],[4]] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [1,2,6,3,5,4] => [[1,2,3,5],[4],[6]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [1,3,4,2,5,6] => [[1,2,3,5,6],[4]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [1,3,4,2,5,6] => [[1,2,3,5,6],[4]] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [1,3,5,2,4,6] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [1,3,6,2,4,5] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [1,3,6,2,4,5] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [1,4,5,2,3,6] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [1,4,6,2,3,5] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [1,5,6,2,3,4] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [1,5,6,2,3,4] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [1,4,5,2,3,6] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [1,4,6,2,3,5] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [1,5,6,2,3,4] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [1,5,6,2,4,3] => [[1,2,3],[4,5],[6]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,5,6,2,3,4] => [[1,2,3,6],[4,5]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [1,2,4,5,3,6] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [1,2,4,6,3,5] => [[1,2,3,4],[5,6]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [1,3,4,5,2,6] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [1,3,4,6,2,5] => [[1,2,3,4],[5,6]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [1,3,5,6,2,4] => [[1,2,3,4],[5,6]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [1,4,5,6,2,3] => [[1,2,3,4],[5,6]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,4,5,6,2,3] => [[1,2,3,4],[5,6]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => [[1,2,3,4,5],[6]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [1,2,3,7,4,6,5] => [[1,2,3,4,6],[5],[7]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [1,2,3,5,6,4,7] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [1,2,3,5,7,4,6] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [1,2,7,3,4,6,5] => [[1,2,3,5,6],[4],[7]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [1,2,6,3,5,4,7] => [[1,2,3,5,7],[4],[6]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [1,2,7,3,5,4,6] => [[1,2,3,5,7],[4],[6]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [1,2,7,3,6,4,5] => [[1,2,3,5,7],[4],[6]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [1,2,7,3,6,4,5] => [[1,2,3,5,7],[4],[6]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [1,2,7,3,4,6,5] => [[1,2,3,5,6],[4],[7]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [1,2,7,3,5,6,4] => [[1,2,3,5,6],[4],[7]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [1,2,3,7,4,6,5] => [[1,2,3,4,6],[5],[7]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [1,2,4,6,3,5,7] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [1,2,4,7,3,5,6] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [1,2,4,7,3,5,6] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [1,2,5,7,3,4,6] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,2,5,7,3,4,6] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [1,2,6,7,3,5,4] => [[1,2,3,4],[5,6],[7]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [1,2,3,5,6,4,7] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [1,2,3,5,7,4,6] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [1,2,4,5,6,3,7] => [[1,2,3,4,5,7],[6]] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,2,4,5,7,3,6] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [1,2,4,6,7,3,5] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [1,2,5,6,7,3,4] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [1,2,5,6,7,3,4] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [1,2,4,5,6,7,3] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [1,2,3,7,4,6,5] => [[1,2,3,4,6],[5],[7]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [1,2,3,5,6,4,7] => [[1,2,3,4,5,7],[6]] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [1,2,3,5,7,4,6] => [[1,2,3,4,5],[6,7]] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [1,3,2,4,7,5,6] => [[1,2,4,5,7],[3,6]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [1,3,2,4,7,5,6] => [[1,2,4,5,7],[3,6]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [1,3,2,4,6,7,5] => [[1,2,4,5,6],[3,7]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [1,4,2,3,5,7,6] => [[1,2,4,5,6],[3,7]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [1,7,2,3,4,6,5] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [1,6,2,3,5,4,7] => [[1,2,4,5,7],[3],[6]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [1,7,2,3,5,4,6] => [[1,2,4,5,7],[3],[6]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [1,7,2,3,6,4,5] => [[1,2,4,5,7],[3],[6]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [1,7,2,3,6,4,5] => [[1,2,4,5,7],[3],[6]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [1,7,2,3,4,6,5] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [1,7,2,3,5,6,4] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [1,4,2,3,5,7,6] => [[1,2,4,5,6],[3,7]] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [1,7,2,3,4,6,5] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [1,5,2,4,3,6,7] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [1,5,2,4,3,6,7] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [1,6,2,4,3,5,7] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [1,7,2,4,3,5,6] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [1,7,2,4,3,5,6] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [1,6,2,5,3,4,7] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [1,7,2,5,3,4,6] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [1,7,2,6,3,4,5] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [1,7,2,6,3,4,5] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [1,6,2,5,3,4,7] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [1,7,2,5,3,4,6] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [1,7,2,6,3,4,5] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [1,7,2,6,3,5,4] => [[1,2,4,6],[3],[5],[7]] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [1,7,2,6,3,4,5] => [[1,2,4,6,7],[3],[5]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [1,6,2,3,5,4,7] => [[1,2,4,5,7],[3],[6]] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [1,7,2,3,5,4,6] => [[1,2,4,5,7],[3],[6]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [1,7,2,3,6,4,5] => [[1,2,4,5,7],[3],[6]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [1,7,2,3,6,4,5] => [[1,2,4,5,7],[3],[6]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [1,6,2,4,5,3,7] => [[1,2,4,5,7],[3],[6]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [1,7,2,4,5,3,6] => [[1,2,4,5,7],[3],[6]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [1,7,2,4,6,3,5] => [[1,2,4,5],[3,7],[6]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [1,7,2,5,6,3,4] => [[1,2,4,5],[3,7],[6]] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [1,7,2,5,6,3,4] => [[1,2,4,5],[3,7],[6]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [1,7,2,3,4,6,5] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [1,7,2,3,5,6,4] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [1,7,2,4,5,6,3] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [1,2,7,3,4,6,5] => [[1,2,3,5,6],[4],[7]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [1,2,6,3,5,4,7] => [[1,2,3,5,7],[4],[6]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [1,2,7,3,5,4,6] => [[1,2,3,5,7],[4],[6]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [1,2,7,3,6,4,5] => [[1,2,3,5,7],[4],[6]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [1,2,7,3,6,4,5] => [[1,2,3,5,7],[4],[6]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [1,2,7,3,4,6,5] => [[1,2,3,5,6],[4],[7]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [1,2,7,3,5,6,4] => [[1,2,3,5,6],[4],[7]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [1,3,4,2,5,7,6] => [[1,2,3,5,6],[4,7]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [1,3,5,2,4,6,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [1,3,5,2,4,6,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [1,3,6,2,4,5,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [1,3,7,2,4,5,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [1,3,7,2,4,5,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [1,3,6,2,4,5,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [1,3,7,2,4,5,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [1,3,7,2,4,6,5] => [[1,2,3,6],[4,5],[7]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [1,3,7,2,4,5,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [1,4,6,2,3,5,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [1,4,7,2,3,5,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [1,4,7,2,3,5,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [1,5,6,2,3,4,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [1,5,7,2,3,4,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [1,5,6,2,3,4,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [1,5,7,2,3,4,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [1,6,7,2,3,5,4] => [[1,2,3,6],[4,5],[7]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [1,4,6,2,3,5,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [1,4,7,2,3,5,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [1,4,7,2,3,5,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [1,5,6,2,3,4,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [1,5,7,2,3,4,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [1,5,6,2,4,3,7] => [[1,2,3,7],[4,5],[6]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [1,5,7,2,4,3,6] => [[1,2,3,7],[4,5],[6]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [1,6,7,2,4,3,5] => [[1,2,3,7],[4,5],[6]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [1,6,7,2,5,3,4] => [[1,2,3,7],[4,5],[6]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [1,6,7,2,5,3,4] => [[1,2,3,7],[4,5],[6]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [1,5,6,2,3,4,7] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [1,5,7,2,3,4,6] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [1,6,7,2,3,5,4] => [[1,2,3,6],[4,5],[7]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [1,6,7,2,4,5,3] => [[1,2,3,6],[4,5],[7]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [1,2,3,7,4,6,5] => [[1,2,3,4,6],[5],[7]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [1,2,4,6,3,5,7] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [1,2,4,7,3,5,6] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [1,2,4,7,3,5,6] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [1,2,5,7,3,4,6] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [1,2,5,7,3,4,6] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [1,2,6,7,3,5,4] => [[1,2,3,4],[5,6],[7]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [1,3,4,5,2,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [1,3,4,5,2,6,7] => [[1,2,3,4,6,7],[5]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [1,3,4,6,2,5,7] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [1,3,4,7,2,5,6] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [1,3,4,7,2,5,6] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [1,3,5,6,2,4,7] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [1,3,5,7,2,4,6] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [1,3,6,7,2,4,5] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [1,3,6,7,2,4,5] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [1,4,5,6,2,3,7] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [1,4,5,7,2,3,6] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [1,4,6,7,2,3,5] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [1,4,5,6,2,3,7] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [1,4,5,7,2,3,6] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [1,4,6,7,2,3,5] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [1,5,6,7,2,4,3] => [[1,2,3,4],[5,6],[7]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [1,2,3,5,6,4,7] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [1,2,3,5,7,4,6] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [1,2,4,5,6,3,7] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [1,2,4,5,7,3,6] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [1,2,4,6,7,3,5] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [1,2,5,6,7,3,4] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [1,2,5,6,7,3,4] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [1,3,4,5,6,2,7] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [1,3,4,5,7,2,6] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [1,3,4,6,7,2,5] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [1,3,5,6,7,2,4] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [1,4,5,6,7,2,3] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,4,5,6,7,2,3] => [[1,2,3,4,5],[6,7]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [1,2,4,5,6,7,3] => [[1,2,3,4,5,6],[7]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [1,3,4,5,6,7,2] => [[1,2,3,4,5,6],[7]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [1,2,3,4,8,5,6,7] => [[1,2,3,4,5,7,8],[6]] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [1,2,3,4,8,5,7,6] => [[1,2,3,4,5,7],[6],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [1,2,3,4,6,8,5,7] => [[1,2,3,4,5,6],[7,8]] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [1,2,3,6,4,5,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [1,2,3,8,4,5,7,6] => [[1,2,3,4,6,7],[5],[8]] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [1,2,3,8,4,6,7,5] => [[1,2,3,4,6,7],[5],[8]] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [1,2,3,4,8,5,6,7] => [[1,2,3,4,5,7,8],[6]] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [1,2,3,5,8,4,6,7] => [[1,2,3,4,5,8],[6,7]] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [1,2,8,3,4,5,6,7] => [[1,2,3,5,6,7,8],[4]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [1,2,8,3,4,5,6,7] => [[1,2,3,5,6,7,8],[4]] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [1,2,8,3,4,5,7,6] => [[1,2,3,5,6,7],[4],[8]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [1,2,8,3,4,5,7,6] => [[1,2,3,5,6,7],[4],[8]] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [1,2,8,3,4,5,6,7] => [[1,2,3,5,6,7,8],[4]] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [1,2,8,3,7,4,5,6] => [[1,2,3,5,7,8],[4],[6]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [1,2,8,3,7,4,6,5] => [[1,2,3,5,7],[4],[6],[8]] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [1,2,3,8,4,5,7,6] => [[1,2,3,4,6,7],[5],[8]] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [1,2,4,8,3,5,6,7] => [[1,2,3,4,7,8],[5,6]] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [1,2,3,4,8,5,6,7] => [[1,2,3,4,5,7,8],[6]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [1,2,4,5,6,3,7,8] => [[1,2,3,4,5,7,8],[6]] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [1,2,6,7,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [1,2,6,7,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [1,2,5,6,7,8,3,4] => [[1,2,3,4,5,6],[7,8]] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [1,2,5,6,7,8,3,4] => [[1,2,3,4,5,6],[7,8]] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [1,2,4,5,6,7,8,3] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [1,2,3,6,4,5,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => [1,2,3,8,4,5,7,6] => [[1,2,3,4,6,7],[5],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [1,2,3,6,4,5,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [1,2,3,8,4,7,5,6] => [[1,2,3,4,6,8],[5],[7]] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [1,2,3,8,4,6,7,5] => [[1,2,3,4,6,7],[5],[8]] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [1,2,3,5,6,4,7,8] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [1,2,3,7,8,4,6,5] => [[1,2,3,4,5],[6,7],[8]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [1,2,3,4,7,8,5,6] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [1,2,3,5,6,7,4,8] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [1,2,3,5,7,8,4,6] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [1,2,3,6,7,8,4,5] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [1,2,3,6,7,8,4,5] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [1,4,2,3,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [1,4,2,3,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [1,4,2,3,5,8,6,7] => [[1,2,4,5,6,8],[3,7]] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [1,4,2,3,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [1,5,2,3,4,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [1,5,2,3,4,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [1,6,2,3,4,5,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [1,7,2,3,4,5,6,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [1,8,2,3,4,5,7,6] => [[1,2,4,5,6,7],[3],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [1,8,2,3,4,7,5,6] => [[1,2,4,5,6,8],[3],[7]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [1,7,2,3,4,5,6,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [1,5,2,3,4,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [1,5,2,3,4,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [1,8,2,3,5,4,6,7] => [[1,2,4,5,7,8],[3],[6]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [1,8,2,3,6,4,5,7] => [[1,2,4,5,7,8],[3],[6]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [1,4,2,3,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [1,4,2,3,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [1,4,2,3,5,8,6,7] => [[1,2,4,5,6,8],[3,7]] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [1,4,2,3,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [1,4,2,3,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [1,5,2,3,4,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [1,5,2,3,4,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [1,6,2,3,4,5,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [1,8,2,3,4,7,5,6] => [[1,2,4,5,6,8],[3],[7]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [1,5,2,4,3,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [1,5,2,4,3,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [1,8,2,4,3,5,6,7] => [[1,2,4,6,7,8],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [1,6,2,5,3,4,7,8] => [[1,2,4,6,7,8],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [1,8,2,5,3,4,6,7] => [[1,2,4,6,7,8],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [1,8,2,7,3,4,5,6] => [[1,2,4,6,7,8],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [1,8,2,7,3,6,4,5] => [[1,2,4,6,8],[3],[5],[7]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [1,5,2,3,4,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [1,5,2,3,4,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [1,8,2,3,4,5,7,6] => [[1,2,4,5,6,7],[3],[8]] => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [1,8,2,3,6,4,5,7] => [[1,2,4,5,7,8],[3],[6]] => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [1,8,2,6,7,3,4,5] => [[1,2,4,5,8],[3,7],[6]] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [1,8,2,4,5,6,7,3] => [[1,2,4,5,6,7],[3],[8]] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [1,2,3,4,7,8,5,6] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [1,2,4,3,5,8,6,7] => [[1,2,3,5,6,8],[4,7]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [1,2,5,3,4,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [1,2,5,3,4,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [1,2,7,3,4,5,6,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [1,2,8,3,4,5,6,7] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [1,2,8,3,4,5,6,7] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => [1,2,8,3,4,5,6,7] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [1,2,8,3,4,5,6,7] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [1,2,5,3,4,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [1,2,5,3,4,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [1,2,7,3,4,5,6,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [1,2,7,3,4,5,6,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [1,3,4,2,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [1,3,4,2,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [1,3,4,2,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [1,3,5,2,4,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [1,3,5,2,4,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [1,3,6,2,4,5,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [1,3,7,2,4,5,6,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [1,3,8,2,4,5,6,7] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [1,3,8,2,4,5,7,6] => [[1,2,3,6,7],[4,5],[8]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [1,3,8,2,4,6,5,7] => [[1,2,3,6,8],[4,5],[7]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [1,3,8,2,4,5,6,7] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [1,3,8,2,4,5,6,7] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [1,4,5,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [1,4,5,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [1,5,6,2,3,4,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [1,5,6,2,3,4,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [1,5,8,2,3,4,6,7] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [1,7,8,2,3,4,5,6] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [1,4,5,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [1,4,5,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [1,4,7,2,3,5,6,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [1,4,7,2,3,5,6,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [1,5,6,2,3,4,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [1,7,8,2,3,5,6,4] => [[1,2,3,6,7],[4,5],[8]] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [1,7,8,2,3,4,5,6] => [[1,2,3,6,7,8],[4,5]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [1,2,3,6,4,5,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [1,2,3,6,4,5,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [1,2,3,7,4,5,6,8] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [1,2,3,8,4,7,5,6] => [[1,2,3,4,6,8],[5],[7]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [1,2,3,8,4,6,7,5] => [[1,2,3,4,6,7],[5],[8]] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [1,2,4,8,3,5,6,7] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [1,2,5,8,3,4,6,7] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [1,2,7,8,3,4,5,6] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [1,2,7,8,3,4,6,5] => [[1,2,3,4,7],[5,6],[8]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [1,2,5,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [1,2,7,8,3,4,5,6] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [1,2,7,8,3,6,4,5] => [[1,2,3,4,8],[5,6],[7]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [1,3,4,5,2,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [1,3,4,5,2,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [1,3,4,6,2,5,7,8] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [1,3,4,6,2,5,7,8] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [1,3,4,7,2,5,6,8] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [1,3,4,8,2,5,6,7] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [1,3,5,6,2,4,7,8] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [1,3,5,7,2,4,6,8] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [1,3,7,8,2,4,5,6] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [1,4,5,6,2,3,7,8] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [1,4,5,6,2,3,7,8] => [[1,2,3,4,7,8],[5,6]] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [1,4,7,8,2,3,5,6] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [1,5,6,7,2,3,4,8] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [1,5,6,8,2,3,4,7] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [1,5,7,8,2,3,4,6] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [1,6,7,8,2,3,4,5] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [1,6,7,8,2,3,4,5] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [1,5,6,7,2,3,4,8] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [1,6,7,8,2,3,4,5] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [1,6,7,8,2,3,4,5] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [1,2,3,4,7,5,6,8] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [1,2,3,4,7,5,6,8] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [1,2,3,4,8,5,7,6] => [[1,2,3,4,5,7],[6],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [1,2,3,5,6,4,7,8] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [1,2,3,7,8,4,5,6] => [[1,2,3,4,5,8],[6,7]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [1,2,4,6,8,3,5,7] => [[1,2,3,4,5],[6,7,8]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [1,2,5,7,8,3,4,6] => [[1,2,3,4,5],[6,7,8]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [1,3,4,5,6,2,7,8] => [[1,2,3,4,5,7,8],[6]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [1,4,5,6,7,2,3,8] => [[1,2,3,4,5,8],[6,7]] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [1,5,6,7,8,2,3,4] => [[1,2,3,4,5],[6,7,8]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [1,4,5,6,7,2,3,8] => [[1,2,3,4,5,8],[6,7]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [1,4,5,7,8,2,3,6] => [[1,2,3,4,5],[6,7,8]] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [1,5,6,7,8,2,4,3] => [[1,2,3,4,5],[6,7],[8]] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [1,5,6,7,8,2,3,4] => [[1,2,3,4,5],[6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [1,2,3,4,6,8,5,7] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [1,2,3,5,6,7,4,8] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [1,2,3,5,7,8,4,6] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [1,2,4,5,6,7,3,8] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [1,2,4,5,6,8,3,7] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [1,2,4,6,7,8,3,5] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [1,2,5,6,7,8,3,4] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [1,3,4,5,6,7,2,8] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [1,3,4,5,6,8,2,7] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [1,4,5,6,7,8,2,3] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [1,2,4,5,6,7,8,3] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [1,2,4,5,6,7,8,9,3] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,2,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [1,2,3,5,6,7,8,9,4] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [1,2,4,5,6,7,8,9,10,3] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [1,9,2,3,4,5,6,7,8] => [[1,2,4,5,6,7,8,9],[3]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [1,9,2,3,4,5,6,7,8] => [[1,2,4,5,6,7,8,9],[3]] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [1,9,2,3,4,5,6,7,8] => [[1,2,4,5,6,7,8,9],[3]] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [1,9,2,3,4,5,6,7,8] => [[1,2,4,5,6,7,8,9],[3]] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [1,6,7,8,9,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [1,5,6,7,8,9,2,3,4] => [[1,2,3,4,5,6],[7,8,9]] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [1,4,5,6,7,8,9,2,3] => [[1,2,3,4,5,6,7],[8,9]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [1,2,3,4,5,6,8,9,7] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,2] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,8,9] => [[1,2,3,4,5,6,7,8,10],[9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [1,2,3,4,5,6,10,7,8,9] => [[1,2,3,4,5,6,7,9,10],[8]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [1,2,3,4,5,10,6,7,8,9] => [[1,2,3,4,5,6,8,9,10],[7]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [1,2,3,4,10,5,6,7,8,9] => [[1,2,3,4,5,7,8,9,10],[6]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [1,2,3,10,4,5,6,7,8,9] => [[1,2,3,4,6,7,8,9,10],[5]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [1,2,10,3,4,5,6,7,8,9] => [[1,2,3,5,6,7,8,9,10],[4]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [1,10,2,3,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9,10],[3]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [1,10,2,3,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9,10],[3]] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [1,10,2,3,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9,10],[3]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [1,3,4,5,6,7,8,9,10,2] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [1,10,2,3,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9,10],[3]] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [1,4,5,6,7,8,9,10,2,3] => [[1,2,3,4,5,6,7,8],[9,10]] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [1,6,7,8,9,10,2,3,4,5] => [[1,2,3,4,5,6],[7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [1,5,6,7,8,9,10,2,3,4] => [[1,2,3,4,5,6,7],[8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [1,2,3,4,5,6,7,10,8,9] => [[1,2,3,4,5,6,7,8,10],[9]] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => [1,2,3,10,4,5,6,7,8,9] => [[1,2,3,4,6,7,8,9,10],[5]] => 1
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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 8,6 16,25,1 32,89,11 64,290,74,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 6\ q$
$F_{5} = 16 + 25\ q + q^{2}$
$F_{6} = 32 + 89\ q + 11\ q^{2}$
$F_{7} = 64 + 290\ q + 74\ q^{2} + q^{3}$
Description
The number of descents of a standard tableau.
Entry $i$ of a standard Young tableau is a descent if $i+1$ appears in a row below the row of $i$.
Entry $i$ of a standard Young tableau is a descent if $i+1$ appears in a row below the row of $i$.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
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