Identifier
-
Mp00070:
Permutations
—Robinson-Schensted recording tableau⟶
Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St001061: Permutations ⟶ ℤ
Values
[1,2] => [[1,2]] => [1,2] => 0
[2,1] => [[1],[2]] => [2,1] => 1
[1,2,3] => [[1,2,3]] => [1,2,3] => 0
[1,3,2] => [[1,2],[3]] => [3,1,2] => 0
[2,1,3] => [[1,3],[2]] => [2,1,3] => 1
[2,3,1] => [[1,2],[3]] => [3,1,2] => 0
[3,1,2] => [[1,3],[2]] => [2,1,3] => 1
[3,2,1] => [[1],[2],[3]] => [3,2,1] => 2
[1,2,3,4] => [[1,2,3,4]] => [1,2,3,4] => 0
[1,2,4,3] => [[1,2,3],[4]] => [4,1,2,3] => 0
[1,3,2,4] => [[1,2,4],[3]] => [3,1,2,4] => 0
[1,3,4,2] => [[1,2,3],[4]] => [4,1,2,3] => 0
[1,4,2,3] => [[1,2,4],[3]] => [3,1,2,4] => 0
[1,4,3,2] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[2,1,3,4] => [[1,3,4],[2]] => [2,1,3,4] => 1
[2,1,4,3] => [[1,3],[2,4]] => [2,4,1,3] => 0
[2,3,1,4] => [[1,2,4],[3]] => [3,1,2,4] => 0
[2,3,4,1] => [[1,2,3],[4]] => [4,1,2,3] => 0
[2,4,1,3] => [[1,2],[3,4]] => [3,4,1,2] => 1
[2,4,3,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[3,1,2,4] => [[1,3,4],[2]] => [2,1,3,4] => 1
[3,1,4,2] => [[1,3],[2,4]] => [2,4,1,3] => 0
[3,2,1,4] => [[1,4],[2],[3]] => [3,2,1,4] => 2
[3,2,4,1] => [[1,3],[2],[4]] => [4,2,1,3] => 1
[3,4,1,2] => [[1,2],[3,4]] => [3,4,1,2] => 1
[3,4,2,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[4,1,2,3] => [[1,3,4],[2]] => [2,1,3,4] => 1
[4,1,3,2] => [[1,3],[2],[4]] => [4,2,1,3] => 1
[4,2,1,3] => [[1,4],[2],[3]] => [3,2,1,4] => 2
[4,2,3,1] => [[1,3],[2],[4]] => [4,2,1,3] => 1
[4,3,1,2] => [[1,4],[2],[3]] => [3,2,1,4] => 2
[4,3,2,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 3
[1,2,3,4,5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 0
[1,2,4,3,5] => [[1,2,3,5],[4]] => [4,1,2,3,5] => 0
[1,2,4,5,3] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 0
[1,2,5,3,4] => [[1,2,3,5],[4]] => [4,1,2,3,5] => 0
[1,2,5,4,3] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 0
[1,3,2,4,5] => [[1,2,4,5],[3]] => [3,1,2,4,5] => 0
[1,3,2,5,4] => [[1,2,4],[3,5]] => [3,5,1,2,4] => 1
[1,3,4,2,5] => [[1,2,3,5],[4]] => [4,1,2,3,5] => 0
[1,3,4,5,2] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 0
[1,3,5,2,4] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 0
[1,3,5,4,2] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 0
[1,4,2,3,5] => [[1,2,4,5],[3]] => [3,1,2,4,5] => 0
[1,4,2,5,3] => [[1,2,4],[3,5]] => [3,5,1,2,4] => 1
[1,4,3,2,5] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => 1
[1,4,3,5,2] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => 1
[1,4,5,2,3] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 0
[1,4,5,3,2] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 0
[1,5,2,3,4] => [[1,2,4,5],[3]] => [3,1,2,4,5] => 0
[1,5,2,4,3] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => 1
[1,5,3,2,4] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => 1
[1,5,3,4,2] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => 1
[1,5,4,2,3] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => 1
[1,5,4,3,2] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 2
[2,1,3,4,5] => [[1,3,4,5],[2]] => [2,1,3,4,5] => 1
[2,1,3,5,4] => [[1,3,4],[2,5]] => [2,5,1,3,4] => 0
[2,1,4,3,5] => [[1,3,5],[2,4]] => [2,4,1,3,5] => 0
[2,1,4,5,3] => [[1,3,4],[2,5]] => [2,5,1,3,4] => 0
[2,1,5,3,4] => [[1,3,5],[2,4]] => [2,4,1,3,5] => 0
[2,1,5,4,3] => [[1,3],[2,4],[5]] => [5,2,4,1,3] => 2
[2,3,1,4,5] => [[1,2,4,5],[3]] => [3,1,2,4,5] => 0
[2,3,1,5,4] => [[1,2,4],[3,5]] => [3,5,1,2,4] => 1
[2,3,4,1,5] => [[1,2,3,5],[4]] => [4,1,2,3,5] => 0
[2,3,4,5,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 0
[2,3,5,1,4] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 0
[2,3,5,4,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 0
[2,4,1,3,5] => [[1,2,5],[3,4]] => [3,4,1,2,5] => 1
[2,4,1,5,3] => [[1,2,4],[3,5]] => [3,5,1,2,4] => 1
[2,4,3,1,5] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => 1
[2,4,3,5,1] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => 1
[2,4,5,1,3] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 0
[2,4,5,3,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 0
[2,5,1,3,4] => [[1,2,5],[3,4]] => [3,4,1,2,5] => 1
[2,5,1,4,3] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 0
[2,5,3,1,4] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => 1
[2,5,3,4,1] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => 1
[2,5,4,1,3] => [[1,2],[3,5],[4]] => [4,3,5,1,2] => 1
[2,5,4,3,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 2
[3,1,2,4,5] => [[1,3,4,5],[2]] => [2,1,3,4,5] => 1
[3,1,2,5,4] => [[1,3,4],[2,5]] => [2,5,1,3,4] => 0
[3,1,4,2,5] => [[1,3,5],[2,4]] => [2,4,1,3,5] => 0
[3,1,4,5,2] => [[1,3,4],[2,5]] => [2,5,1,3,4] => 0
[3,1,5,2,4] => [[1,3,5],[2,4]] => [2,4,1,3,5] => 0
[3,1,5,4,2] => [[1,3],[2,4],[5]] => [5,2,4,1,3] => 2
[3,2,1,4,5] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 2
[3,2,1,5,4] => [[1,4],[2,5],[3]] => [3,2,5,1,4] => 1
[3,2,4,1,5] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => 1
[3,2,4,5,1] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => 1
[3,2,5,1,4] => [[1,3],[2,5],[4]] => [4,2,5,1,3] => 2
[3,2,5,4,1] => [[1,3],[2,4],[5]] => [5,2,4,1,3] => 2
[3,4,1,2,5] => [[1,2,5],[3,4]] => [3,4,1,2,5] => 1
[3,4,1,5,2] => [[1,2,4],[3,5]] => [3,5,1,2,4] => 1
[3,4,2,1,5] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => 1
[3,4,2,5,1] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => 1
[3,4,5,1,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 0
[3,4,5,2,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 0
[3,5,1,2,4] => [[1,2,5],[3,4]] => [3,4,1,2,5] => 1
[3,5,1,4,2] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 0
[3,5,2,1,4] => [[1,2],[3,5],[4]] => [4,3,5,1,2] => 1
>>> Load all 873 entries. <<<[3,5,2,4,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 0
[3,5,4,1,2] => [[1,2],[3,5],[4]] => [4,3,5,1,2] => 1
[3,5,4,2,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 2
[4,1,2,3,5] => [[1,3,4,5],[2]] => [2,1,3,4,5] => 1
[4,1,2,5,3] => [[1,3,4],[2,5]] => [2,5,1,3,4] => 0
[4,1,3,2,5] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => 1
[4,1,3,5,2] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => 1
[4,1,5,2,3] => [[1,3,5],[2,4]] => [2,4,1,3,5] => 0
[4,1,5,3,2] => [[1,3],[2,4],[5]] => [5,2,4,1,3] => 2
[4,2,1,3,5] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 2
[4,2,1,5,3] => [[1,4],[2,5],[3]] => [3,2,5,1,4] => 1
[4,2,3,1,5] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => 1
[4,2,3,5,1] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => 1
[4,2,5,1,3] => [[1,3],[2,5],[4]] => [4,2,5,1,3] => 2
[4,2,5,3,1] => [[1,3],[2,4],[5]] => [5,2,4,1,3] => 2
[4,3,1,2,5] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 2
[4,3,1,5,2] => [[1,4],[2,5],[3]] => [3,2,5,1,4] => 1
[4,3,2,1,5] => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => 3
[4,3,2,5,1] => [[1,4],[2],[3],[5]] => [5,3,2,1,4] => 2
[4,3,5,1,2] => [[1,3],[2,5],[4]] => [4,2,5,1,3] => 2
[4,3,5,2,1] => [[1,3],[2],[4],[5]] => [5,4,2,1,3] => 2
[4,5,1,2,3] => [[1,2,5],[3,4]] => [3,4,1,2,5] => 1
[4,5,1,3,2] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 0
[4,5,2,1,3] => [[1,2],[3,5],[4]] => [4,3,5,1,2] => 1
[4,5,2,3,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 0
[4,5,3,1,2] => [[1,2],[3,5],[4]] => [4,3,5,1,2] => 1
[4,5,3,2,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 2
[5,1,2,3,4] => [[1,3,4,5],[2]] => [2,1,3,4,5] => 1
[5,1,2,4,3] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => 1
[5,1,3,2,4] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => 1
[5,1,3,4,2] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => 1
[5,1,4,2,3] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => 1
[5,1,4,3,2] => [[1,3],[2],[4],[5]] => [5,4,2,1,3] => 2
[5,2,1,3,4] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 2
[5,2,1,4,3] => [[1,4],[2,5],[3]] => [3,2,5,1,4] => 1
[5,2,3,1,4] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => 1
[5,2,3,4,1] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => 1
[5,2,4,1,3] => [[1,3],[2,5],[4]] => [4,2,5,1,3] => 2
[5,2,4,3,1] => [[1,3],[2],[4],[5]] => [5,4,2,1,3] => 2
[5,3,1,2,4] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 2
[5,3,1,4,2] => [[1,4],[2,5],[3]] => [3,2,5,1,4] => 1
[5,3,2,1,4] => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => 3
[5,3,2,4,1] => [[1,4],[2],[3],[5]] => [5,3,2,1,4] => 2
[5,3,4,1,2] => [[1,3],[2,5],[4]] => [4,2,5,1,3] => 2
[5,3,4,2,1] => [[1,3],[2],[4],[5]] => [5,4,2,1,3] => 2
[5,4,1,2,3] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 2
[5,4,1,3,2] => [[1,4],[2],[3],[5]] => [5,3,2,1,4] => 2
[5,4,2,1,3] => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => 3
[5,4,2,3,1] => [[1,4],[2],[3],[5]] => [5,3,2,1,4] => 2
[5,4,3,1,2] => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => 3
[5,4,3,2,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 4
[1,2,3,4,5,6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 0
[1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => 0
[1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 0
[1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => 0
[1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 0
[1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => 0
[1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 0
[1,2,4,5,3,6] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => 0
[1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 0
[1,2,4,6,3,5] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 0
[1,2,4,6,5,3] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 0
[1,2,5,3,4,6] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => 0
[1,2,5,3,6,4] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 0
[1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 0
[1,2,5,4,6,3] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 0
[1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 0
[1,2,5,6,4,3] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 0
[1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => 0
[1,2,6,3,5,4] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 0
[1,2,6,4,3,5] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 0
[1,2,6,4,5,3] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 0
[1,2,6,5,3,4] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 0
[1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1
[1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => 0
[1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 1
[1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 1
[1,3,2,5,6,4] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 1
[1,3,2,6,4,5] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 1
[1,3,2,6,5,4] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[1,3,4,2,5,6] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => 0
[1,3,4,2,6,5] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 0
[1,3,4,5,2,6] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => 0
[1,3,4,5,6,2] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 0
[1,3,4,6,2,5] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 0
[1,3,4,6,5,2] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 0
[1,3,5,2,4,6] => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 0
[1,3,5,2,6,4] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 0
[1,3,5,4,2,6] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 0
[1,3,5,4,6,2] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 0
[1,3,5,6,2,4] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 0
[1,3,5,6,4,2] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 0
[1,3,6,2,4,5] => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 0
[1,3,6,2,5,4] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[1,3,6,4,2,5] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 0
[1,3,6,4,5,2] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 0
[1,3,6,5,2,4] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[1,3,6,5,4,2] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1
[1,4,2,3,5,6] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => 0
[1,4,2,3,6,5] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 1
[1,4,2,5,3,6] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 1
[1,4,2,5,6,3] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 1
[1,4,2,6,3,5] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 1
[1,4,2,6,5,3] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 1
[1,4,3,2,6,5] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[1,4,3,5,2,6] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 1
[1,4,3,5,6,2] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 1
[1,4,3,6,2,5] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[1,4,3,6,5,2] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[1,4,5,2,3,6] => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 0
[1,4,5,2,6,3] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 0
[1,4,5,3,2,6] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 0
[1,4,5,3,6,2] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 0
[1,4,5,6,2,3] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 0
[1,4,5,6,3,2] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 0
[1,4,6,2,3,5] => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 0
[1,4,6,2,5,3] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[1,4,6,3,2,5] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[1,4,6,3,5,2] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[1,4,6,5,2,3] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[1,4,6,5,3,2] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1
[1,5,2,3,4,6] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => 0
[1,5,2,3,6,4] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 1
[1,5,2,4,3,6] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 1
[1,5,2,4,6,3] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 1
[1,5,2,6,3,4] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 1
[1,5,2,6,4,3] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[1,5,3,2,4,6] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 1
[1,5,3,2,6,4] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[1,5,3,4,2,6] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 1
[1,5,3,4,6,2] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 1
[1,5,3,6,2,4] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[1,5,3,6,4,2] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[1,5,4,2,3,6] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 1
[1,5,4,2,6,3] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 2
[1,5,4,3,6,2] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 2
[1,5,4,6,2,3] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[1,5,4,6,3,2] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 1
[1,5,6,2,3,4] => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 0
[1,5,6,2,4,3] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[1,5,6,3,2,4] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[1,5,6,3,4,2] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[1,5,6,4,2,3] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[1,5,6,4,3,2] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1
[1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => 0
[1,6,2,3,5,4] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 1
[1,6,2,4,3,5] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 1
[1,6,2,4,5,3] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 1
[1,6,2,5,3,4] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 1
[1,6,2,5,4,3] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 1
[1,6,3,2,4,5] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 1
[1,6,3,2,5,4] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[1,6,3,4,2,5] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 1
[1,6,3,4,5,2] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 1
[1,6,3,5,2,4] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[1,6,3,5,4,2] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 1
[1,6,4,2,3,5] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 1
[1,6,4,2,5,3] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[1,6,4,3,2,5] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 2
[1,6,4,3,5,2] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 2
[1,6,4,5,2,3] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[1,6,4,5,3,2] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 1
[1,6,5,2,3,4] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 1
[1,6,5,2,4,3] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 2
[1,6,5,3,2,4] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 2
[1,6,5,3,4,2] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 2
[1,6,5,4,2,3] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 2
[1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 3
[2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 0
[2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 0
[2,1,3,5,6,4] => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 0
[2,1,3,6,4,5] => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 0
[2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 0
[2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 1
[2,1,4,5,3,6] => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 0
[2,1,4,5,6,3] => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 0
[2,1,4,6,3,5] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => 0
[2,1,4,6,5,3] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[2,1,5,3,4,6] => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 0
[2,1,5,3,6,4] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 1
[2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[2,1,5,4,6,3] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[2,1,5,6,3,4] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => 0
[2,1,5,6,4,3] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[2,1,6,3,4,5] => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 0
[2,1,6,3,5,4] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[2,1,6,4,3,5] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[2,1,6,4,5,3] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[2,1,6,5,3,4] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 2
[2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => 0
[2,3,1,4,6,5] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 1
[2,3,1,5,4,6] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 1
[2,3,1,5,6,4] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 1
[2,3,1,6,4,5] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 1
[2,3,1,6,5,4] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => 0
[2,3,4,1,6,5] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 0
[2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => 0
[2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 0
[2,3,4,6,1,5] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 0
[2,3,4,6,5,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 0
[2,3,5,1,4,6] => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 0
[2,3,5,1,6,4] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 0
[2,3,5,4,1,6] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 0
[2,3,5,4,6,1] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 0
[2,3,5,6,1,4] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 0
[2,3,5,6,4,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 0
[2,3,6,1,4,5] => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 0
[2,3,6,1,5,4] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[2,3,6,4,1,5] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 0
[2,3,6,4,5,1] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 0
[2,3,6,5,1,4] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[2,3,6,5,4,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1
[2,4,1,3,5,6] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 1
[2,4,1,3,6,5] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => 0
[2,4,1,5,3,6] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 1
[2,4,1,5,6,3] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 1
[2,4,1,6,3,5] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => 0
[2,4,1,6,5,3] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[2,4,3,1,5,6] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 1
[2,4,3,1,6,5] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[2,4,3,5,1,6] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 1
[2,4,3,5,6,1] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 1
[2,4,3,6,1,5] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[2,4,3,6,5,1] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[2,4,5,1,3,6] => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 0
[2,4,5,1,6,3] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 0
[2,4,5,3,1,6] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 0
[2,4,5,3,6,1] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 0
[2,4,5,6,1,3] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 0
[2,4,5,6,3,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 0
[2,4,6,1,3,5] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 1
[2,4,6,1,5,3] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[2,4,6,3,1,5] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[2,4,6,3,5,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[2,4,6,5,1,3] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[2,4,6,5,3,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1
[2,5,1,3,4,6] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 1
[2,5,1,3,6,4] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => 0
[2,5,1,4,3,6] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[2,5,1,4,6,3] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[2,5,1,6,3,4] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => 0
[2,5,1,6,4,3] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[2,5,3,1,4,6] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 1
[2,5,3,1,6,4] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[2,5,3,4,1,6] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 1
[2,5,3,4,6,1] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 1
[2,5,3,6,1,4] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[2,5,3,6,4,1] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[2,5,4,1,3,6] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[2,5,4,1,6,3] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[2,5,4,3,1,6] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 2
[2,5,4,3,6,1] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 2
[2,5,4,6,1,3] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[2,5,4,6,3,1] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 1
[2,5,6,1,3,4] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 1
[2,5,6,1,4,3] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[2,5,6,3,1,4] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[2,5,6,3,4,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[2,5,6,4,1,3] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[2,5,6,4,3,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1
[2,6,1,3,4,5] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 1
[2,6,1,3,5,4] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[2,6,1,4,3,5] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[2,6,1,4,5,3] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[2,6,1,5,3,4] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[2,6,1,5,4,3] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[2,6,3,1,4,5] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 1
[2,6,3,1,5,4] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[2,6,3,4,1,5] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 1
[2,6,3,4,5,1] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 1
[2,6,3,5,1,4] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[2,6,3,5,4,1] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 1
[2,6,4,1,3,5] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[2,6,4,1,5,3] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[2,6,4,3,1,5] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 2
[2,6,4,3,5,1] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 2
[2,6,4,5,1,3] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[2,6,4,5,3,1] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 1
[2,6,5,1,3,4] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[2,6,5,1,4,3] => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 1
[2,6,5,3,1,4] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 2
[2,6,5,3,4,1] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 2
[2,6,5,4,1,3] => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 2
[2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 3
[3,1,2,4,5,6] => [[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => 1
[3,1,2,4,6,5] => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 0
[3,1,2,5,4,6] => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 0
[3,1,2,5,6,4] => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 0
[3,1,2,6,4,5] => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 0
[3,1,2,6,5,4] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[3,1,4,2,5,6] => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 0
[3,1,4,2,6,5] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 1
[3,1,4,5,2,6] => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 0
[3,1,4,5,6,2] => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 0
[3,1,4,6,2,5] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => 0
[3,1,4,6,5,2] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[3,1,5,2,4,6] => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 0
[3,1,5,2,6,4] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 1
[3,1,5,4,2,6] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[3,1,5,4,6,2] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[3,1,5,6,2,4] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => 0
[3,1,5,6,4,2] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[3,1,6,2,4,5] => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 0
[3,1,6,2,5,4] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[3,1,6,4,2,5] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[3,1,6,4,5,2] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[3,1,6,5,2,4] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[3,1,6,5,4,2] => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 2
[3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[3,2,1,5,6,4] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[3,2,1,6,4,5] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => 2
[3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 1
[3,2,4,1,6,5] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 1
[3,2,4,5,6,1] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 1
[3,2,4,6,1,5] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[3,2,4,6,5,1] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[3,2,5,1,4,6] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[3,2,5,1,6,4] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[3,2,5,4,1,6] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[3,2,5,4,6,1] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[3,2,5,6,1,4] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[3,2,5,6,4,1] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[3,2,6,1,4,5] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[3,2,6,1,5,4] => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => 0
[3,2,6,4,1,5] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[3,2,6,4,5,1] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[3,2,6,5,1,4] => [[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => 1
[3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 2
[3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 1
[3,4,1,2,6,5] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => 0
[3,4,1,5,2,6] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 1
[3,4,1,5,6,2] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 1
[3,4,1,6,2,5] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => 0
[3,4,1,6,5,2] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[3,4,2,1,5,6] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 1
[3,4,2,1,6,5] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[3,4,2,5,1,6] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 1
[3,4,2,5,6,1] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 1
[3,4,2,6,1,5] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[3,4,2,6,5,1] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[3,4,5,1,2,6] => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 0
[3,4,5,1,6,2] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 0
[3,4,5,2,1,6] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 0
[3,4,5,2,6,1] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 0
[3,4,5,6,1,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 0
[3,4,5,6,2,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 0
[3,4,6,1,2,5] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 1
[3,4,6,1,5,2] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[3,4,6,2,1,5] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[3,4,6,2,5,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[3,4,6,5,1,2] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[3,4,6,5,2,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1
[3,5,1,2,4,6] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 1
[3,5,1,2,6,4] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => 0
[3,5,1,4,2,6] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[3,5,1,4,6,2] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[3,5,1,6,2,4] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => 0
[3,5,1,6,4,2] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[3,5,2,1,4,6] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[3,5,2,1,6,4] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[3,5,2,4,1,6] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[3,5,2,4,6,1] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[3,5,2,6,1,4] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[3,5,2,6,4,1] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[3,5,4,1,2,6] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[3,5,4,1,6,2] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[3,5,4,2,1,6] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 2
[3,5,4,2,6,1] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 2
[3,5,4,6,1,2] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[3,5,4,6,2,1] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 1
[3,5,6,1,2,4] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 1
[3,5,6,1,4,2] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[3,5,6,2,1,4] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[3,5,6,2,4,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[3,5,6,4,1,2] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[3,5,6,4,2,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1
[3,6,1,2,4,5] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 1
[3,6,1,2,5,4] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[3,6,1,4,2,5] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[3,6,1,4,5,2] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[3,6,1,5,2,4] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[3,6,1,5,4,2] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[3,6,2,1,4,5] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[3,6,2,1,5,4] => [[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => 1
[3,6,2,4,1,5] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[3,6,2,4,5,1] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[3,6,2,5,1,4] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 2
[3,6,2,5,4,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[3,6,4,1,2,5] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[3,6,4,1,5,2] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[3,6,4,2,1,5] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 2
[3,6,4,2,5,1] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 2
[3,6,4,5,1,2] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[3,6,4,5,2,1] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 1
[3,6,5,1,2,4] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[3,6,5,1,4,2] => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 1
[3,6,5,2,1,4] => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 2
[3,6,5,2,4,1] => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 1
[3,6,5,4,1,2] => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 2
[3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 3
[4,1,2,3,5,6] => [[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => 1
[4,1,2,3,6,5] => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 0
[4,1,2,5,3,6] => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 0
[4,1,2,5,6,3] => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 0
[4,1,2,6,3,5] => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 0
[4,1,2,6,5,3] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[4,1,3,2,5,6] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 1
[4,1,3,2,6,5] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[4,1,3,5,2,6] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 1
[4,1,3,5,6,2] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 1
[4,1,3,6,2,5] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[4,1,3,6,5,2] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[4,1,5,2,3,6] => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 0
[4,1,5,2,6,3] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 1
[4,1,5,3,2,6] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[4,1,5,3,6,2] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[4,1,5,6,2,3] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => 0
[4,1,5,6,3,2] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[4,1,6,2,3,5] => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 0
[4,1,6,2,5,3] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[4,1,6,3,2,5] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[4,1,6,3,5,2] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[4,1,6,5,2,3] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[4,1,6,5,3,2] => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 2
[4,2,1,3,5,6] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[4,2,1,3,6,5] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[4,2,1,5,3,6] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[4,2,1,5,6,3] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[4,2,1,6,3,5] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[4,2,1,6,5,3] => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => 2
[4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 1
[4,2,3,1,6,5] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[4,2,3,5,1,6] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 1
[4,2,3,5,6,1] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 1
[4,2,3,6,1,5] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[4,2,3,6,5,1] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[4,2,5,1,3,6] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[4,2,5,1,6,3] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[4,2,5,3,1,6] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[4,2,5,3,6,1] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[4,2,5,6,1,3] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[4,2,5,6,3,1] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[4,2,6,1,3,5] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[4,2,6,1,5,3] => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => 0
[4,2,6,3,1,5] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[4,2,6,3,5,1] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[4,2,6,5,1,3] => [[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => 1
[4,2,6,5,3,1] => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 2
[4,3,1,2,5,6] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[4,3,1,2,6,5] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[4,3,1,5,2,6] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[4,3,1,5,6,2] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[4,3,1,6,2,5] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[4,3,1,6,5,2] => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => 2
[4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 2
[4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 2
[4,3,2,5,6,1] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 2
[4,3,2,6,1,5] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 3
[4,3,2,6,5,1] => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 3
[4,3,5,1,2,6] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[4,3,5,1,6,2] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[4,3,5,2,1,6] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 2
[4,3,5,2,6,1] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 2
[4,3,5,6,1,2] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[4,3,5,6,2,1] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 1
[4,3,6,1,2,5] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[4,3,6,1,5,2] => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => 0
[4,3,6,2,1,5] => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 2
[4,3,6,2,5,1] => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 1
[4,3,6,5,1,2] => [[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => 1
[4,3,6,5,2,1] => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 2
[4,5,1,2,3,6] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 1
[4,5,1,2,6,3] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => 0
[4,5,1,3,2,6] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[4,5,1,3,6,2] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[4,5,1,6,2,3] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => 0
[4,5,1,6,3,2] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[4,5,2,1,3,6] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[4,5,2,1,6,3] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[4,5,2,3,1,6] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[4,5,2,3,6,1] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[4,5,2,6,1,3] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[4,5,2,6,3,1] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 0
[4,5,3,1,2,6] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[4,5,3,1,6,2] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 1
[4,5,3,2,1,6] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 2
[4,5,3,2,6,1] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 2
[4,5,3,6,1,2] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 0
[4,5,3,6,2,1] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 1
[4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 1
[4,5,6,1,3,2] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[4,5,6,2,1,3] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[4,5,6,2,3,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1
[4,5,6,3,1,2] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 1
[4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1
[4,6,1,2,3,5] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 1
[4,6,1,2,5,3] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[4,6,1,3,2,5] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[4,6,1,3,5,2] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[4,6,1,5,2,3] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[4,6,1,5,3,2] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[4,6,2,1,3,5] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[4,6,2,1,5,3] => [[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => 1
[4,6,2,3,1,5] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[4,6,2,3,5,1] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[4,6,2,5,1,3] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 2
[4,6,2,5,3,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[4,6,3,1,2,5] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[4,6,3,1,5,2] => [[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => 1
[4,6,3,2,1,5] => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 2
[4,6,3,2,5,1] => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 1
[4,6,3,5,1,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 2
[4,6,3,5,2,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[4,6,5,1,2,3] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[4,6,5,1,3,2] => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 1
[4,6,5,2,1,3] => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 2
[4,6,5,2,3,1] => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 1
[4,6,5,3,1,2] => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 2
[4,6,5,3,2,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 3
[5,1,2,3,4,6] => [[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => 1
[5,1,2,3,6,4] => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 0
[5,1,2,4,3,6] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 1
[5,1,2,4,6,3] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 1
[5,1,2,6,3,4] => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 0
[5,1,2,6,4,3] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[5,1,3,2,4,6] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 1
[5,1,3,2,6,4] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[5,1,3,4,2,6] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 1
[5,1,3,4,6,2] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 1
[5,1,3,6,2,4] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[5,1,3,6,4,2] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[5,1,4,2,3,6] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 1
[5,1,4,2,6,3] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[5,1,4,3,2,6] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 2
[5,1,4,3,6,2] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 2
[5,1,4,6,2,3] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[5,1,4,6,3,2] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 1
[5,1,6,2,3,4] => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 0
[5,1,6,2,4,3] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[5,1,6,3,2,4] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[5,1,6,3,4,2] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[5,1,6,4,2,3] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[5,1,6,4,3,2] => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 2
[5,2,1,3,4,6] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[5,2,1,3,6,4] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[5,2,1,4,3,6] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[5,2,1,4,6,3] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[5,2,1,6,3,4] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[5,2,1,6,4,3] => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => 2
[5,2,3,1,4,6] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 1
[5,2,3,1,6,4] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 1
[5,2,3,4,6,1] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 1
[5,2,3,6,1,4] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[5,2,3,6,4,1] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 1
[5,2,4,1,3,6] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[5,2,4,1,6,3] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[5,2,4,3,1,6] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 2
[5,2,4,3,6,1] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 2
[5,2,4,6,1,3] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[5,2,4,6,3,1] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 1
[5,2,6,1,3,4] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[5,2,6,1,4,3] => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => 0
[5,2,6,3,1,4] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 2
[5,2,6,3,4,1] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 2
[5,2,6,4,1,3] => [[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => 1
[5,2,6,4,3,1] => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 2
[5,3,1,2,4,6] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[5,3,1,2,6,4] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[5,3,1,4,2,6] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[5,3,1,4,6,2] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[5,3,1,6,2,4] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[5,3,1,6,4,2] => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => 2
[5,3,2,1,4,6] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[5,3,2,1,6,4] => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 2
[5,3,2,4,1,6] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 2
[5,3,2,4,6,1] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 2
[5,3,2,6,1,4] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 3
[5,3,2,6,4,1] => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 3
[5,3,4,1,2,6] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[5,3,4,1,6,2] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[5,3,4,2,1,6] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 2
[5,3,4,2,6,1] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 2
[5,3,4,6,1,2] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[5,3,4,6,2,1] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 1
[5,3,6,1,2,4] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[5,3,6,1,4,2] => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => 0
[5,3,6,2,1,4] => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 2
[5,3,6,2,4,1] => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 1
[5,3,6,4,1,2] => [[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => 1
[5,3,6,4,2,1] => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 2
[5,4,1,2,3,6] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[5,4,1,2,6,3] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[5,4,1,3,2,6] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 2
[5,4,1,3,6,2] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 2
[5,4,1,6,2,3] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[5,4,1,6,3,2] => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 3
[5,4,2,1,3,6] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[5,4,2,1,6,3] => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 2
[5,4,2,3,1,6] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 2
[5,4,2,3,6,1] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 2
[5,4,2,6,1,3] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 3
[5,4,2,6,3,1] => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 3
[5,4,3,1,2,6] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[5,4,3,1,6,2] => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 2
[5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => 4
[5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => 3
[5,4,3,6,1,2] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 3
[5,4,3,6,2,1] => [[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => 3
[5,4,6,1,2,3] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[5,4,6,1,3,2] => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 1
[5,4,6,2,1,3] => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 2
[5,4,6,2,3,1] => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 1
[5,4,6,3,1,2] => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 2
[5,4,6,3,2,1] => [[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => 3
[5,6,1,2,3,4] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 1
[5,6,1,2,4,3] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[5,6,1,3,2,4] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[5,6,1,3,4,2] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[5,6,1,4,2,3] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[5,6,1,4,3,2] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[5,6,2,1,3,4] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[5,6,2,1,4,3] => [[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => 1
[5,6,2,3,1,4] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 0
[5,6,2,3,4,1] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 0
[5,6,2,4,1,3] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 2
[5,6,2,4,3,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[5,6,3,1,2,4] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[5,6,3,1,4,2] => [[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => 1
[5,6,3,2,1,4] => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 2
[5,6,3,2,4,1] => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 1
[5,6,3,4,1,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 2
[5,6,3,4,2,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[5,6,4,1,2,3] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 1
[5,6,4,1,3,2] => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 1
[5,6,4,2,1,3] => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 2
[5,6,4,2,3,1] => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 1
[5,6,4,3,1,2] => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 2
[5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 3
[6,1,2,3,4,5] => [[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => 1
[6,1,2,3,5,4] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 1
[6,1,2,4,3,5] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 1
[6,1,2,4,5,3] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 1
[6,1,2,5,3,4] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 1
[6,1,2,5,4,3] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 1
[6,1,3,2,4,5] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 1
[6,1,3,2,5,4] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[6,1,3,4,2,5] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 1
[6,1,3,4,5,2] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 1
[6,1,3,5,2,4] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[6,1,3,5,4,2] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 1
[6,1,4,2,3,5] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 1
[6,1,4,2,5,3] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[6,1,4,3,2,5] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 2
[6,1,4,3,5,2] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 2
[6,1,4,5,2,3] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[6,1,4,5,3,2] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 1
[6,1,5,2,3,4] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 1
[6,1,5,2,4,3] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 2
[6,1,5,3,2,4] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 2
[6,1,5,3,4,2] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 2
[6,1,5,4,2,3] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 2
[6,1,5,4,3,2] => [[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => 3
[6,2,1,3,4,5] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[6,2,1,3,5,4] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[6,2,1,4,3,5] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[6,2,1,4,5,3] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[6,2,1,5,3,4] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[6,2,1,5,4,3] => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 3
[6,2,3,1,4,5] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 1
[6,2,3,1,5,4] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[6,2,3,4,1,5] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 1
[6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 1
[6,2,3,5,1,4] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[6,2,3,5,4,1] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 1
[6,2,4,1,3,5] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[6,2,4,1,5,3] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[6,2,4,3,1,5] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 2
[6,2,4,3,5,1] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 2
[6,2,4,5,1,3] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[6,2,4,5,3,1] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 1
[6,2,5,1,3,4] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[6,2,5,1,4,3] => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 1
[6,2,5,3,1,4] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 2
[6,2,5,3,4,1] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 2
[6,2,5,4,1,3] => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 2
[6,2,5,4,3,1] => [[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => 3
[6,3,1,2,4,5] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[6,3,1,2,5,4] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[6,3,1,4,2,5] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[6,3,1,4,5,2] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[6,3,1,5,2,4] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[6,3,1,5,4,2] => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 3
[6,3,2,1,4,5] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[6,3,2,1,5,4] => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 2
[6,3,2,4,1,5] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 2
[6,3,2,4,5,1] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 2
[6,3,2,5,1,4] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 3
[6,3,2,5,4,1] => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 3
[6,3,4,1,2,5] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[6,3,4,1,5,2] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 2
[6,3,4,2,1,5] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 2
[6,3,4,2,5,1] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 2
[6,3,4,5,1,2] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 1
[6,3,4,5,2,1] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 1
[6,3,5,1,2,4] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[6,3,5,1,4,2] => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 1
[6,3,5,2,1,4] => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 2
[6,3,5,2,4,1] => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 1
[6,3,5,4,1,2] => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 2
[6,3,5,4,2,1] => [[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => 3
[6,4,1,2,3,5] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[6,4,1,2,5,3] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 1
[6,4,1,3,2,5] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 2
[6,4,1,3,5,2] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 2
[6,4,1,5,2,3] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 1
[6,4,1,5,3,2] => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 3
[6,4,2,1,3,5] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[6,4,2,1,5,3] => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 2
[6,4,2,3,1,5] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 2
[6,4,2,3,5,1] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 2
[6,4,2,5,1,3] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 3
[6,4,2,5,3,1] => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 3
[6,4,3,1,2,5] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[6,4,3,1,5,2] => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 2
[6,4,3,2,1,5] => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => 4
[6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => 3
[6,4,3,5,1,2] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 3
[6,4,3,5,2,1] => [[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => 3
[6,4,5,1,2,3] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[6,4,5,1,3,2] => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 1
[6,4,5,2,1,3] => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 2
[6,4,5,2,3,1] => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 1
[6,4,5,3,1,2] => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 2
[6,4,5,3,2,1] => [[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => 3
[6,5,1,2,3,4] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[6,5,1,2,4,3] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 2
[6,5,1,3,2,4] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 2
[6,5,1,3,4,2] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 2
[6,5,1,4,2,3] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 2
[6,5,1,4,3,2] => [[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => 3
[6,5,2,1,3,4] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[6,5,2,1,4,3] => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 2
[6,5,2,3,1,4] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 2
[6,5,2,3,4,1] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 2
[6,5,2,4,1,3] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 3
[6,5,2,4,3,1] => [[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => 3
[6,5,3,1,2,4] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[6,5,3,1,4,2] => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 2
[6,5,3,2,1,4] => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => 4
[6,5,3,2,4,1] => [[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => 3
[6,5,3,4,1,2] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 3
[6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => 3
[6,5,4,1,2,3] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[6,5,4,1,3,2] => [[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => 3
[6,5,4,2,1,3] => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => 4
[6,5,4,2,3,1] => [[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => 3
[6,5,4,3,1,2] => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => 4
[6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 5
[1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,2,1 9,11,3,1 39,48,28,4,1 189,288,189,48,5,1
$F_{2} = 1 + q$
$F_{3} = 3 + 2\ q + q^{2}$
$F_{4} = 9 + 11\ q + 3\ q^{2} + q^{3}$
$F_{5} = 39 + 48\ q + 28\ q^{2} + 4\ q^{3} + q^{4}$
$F_{6} = 189 + 288\ q + 189\ q^{2} + 48\ q^{3} + 5\ q^{4} + q^{5}$
Description
The number of indices that are both descents and recoils of a permutation.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
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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