Identifier
-
Mp00223:
Permutations
—runsort⟶
Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
St001005: Permutations ⟶ ℤ
Values
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [1,2] => [1,2] => [1,2] => 0
[1,2,3] => [1,2,3] => [1,2,3] => [1,3,2] => 2
[1,3,2] => [1,3,2] => [2,3,1] => [2,3,1] => 3
[2,1,3] => [1,3,2] => [2,3,1] => [2,3,1] => 3
[2,3,1] => [1,2,3] => [1,2,3] => [1,3,2] => 2
[3,1,2] => [1,2,3] => [1,2,3] => [1,3,2] => 2
[3,2,1] => [1,2,3] => [1,2,3] => [1,3,2] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 2
[1,2,4,3] => [1,2,4,3] => [2,3,4,1] => [2,4,3,1] => 3
[1,3,2,4] => [1,3,2,4] => [2,3,1,4] => [2,4,1,3] => 4
[1,3,4,2] => [1,3,4,2] => [2,4,1,3] => [2,4,1,3] => 4
[1,4,2,3] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 4
[1,4,3,2] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 4
[2,1,3,4] => [1,3,4,2] => [2,4,1,3] => [2,4,1,3] => 4
[2,1,4,3] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 4
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 2
[2,4,1,3] => [1,3,2,4] => [2,3,1,4] => [2,4,1,3] => 4
[2,4,3,1] => [1,2,4,3] => [2,3,4,1] => [2,4,3,1] => 3
[3,1,2,4] => [1,2,4,3] => [2,3,4,1] => [2,4,3,1] => 3
[3,1,4,2] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 4
[3,2,1,4] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 4
[3,2,4,1] => [1,2,4,3] => [2,3,4,1] => [2,4,3,1] => 3
[3,4,1,2] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 2
[3,4,2,1] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 2
[4,1,2,3] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 2
[4,1,3,2] => [1,3,2,4] => [2,3,1,4] => [2,4,1,3] => 4
[4,2,1,3] => [1,3,2,4] => [2,3,1,4] => [2,4,1,3] => 4
[4,2,3,1] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 2
[4,3,1,2] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 2
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 2
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => [2,5,4,3,1] => 3
[1,2,4,3,5] => [1,2,4,3,5] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[1,2,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[1,2,5,3,4] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[1,2,5,4,3] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[1,3,2,4,5] => [1,3,2,4,5] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[1,3,2,5,4] => [1,3,2,5,4] => [3,4,2,5,1] => [3,5,2,4,1] => 3
[1,3,4,2,5] => [1,3,4,2,5] => [2,4,1,3,5] => [2,5,1,4,3] => 4
[1,3,4,5,2] => [1,3,4,5,2] => [2,5,1,3,4] => [2,5,1,4,3] => 4
[1,3,5,2,4] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 4
[1,3,5,4,2] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 4
[1,4,2,3,5] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[1,4,2,5,3] => [1,4,2,5,3] => [3,4,5,1,2] => [3,5,4,1,2] => 4
[1,4,3,2,5] => [1,4,2,5,3] => [3,4,5,1,2] => [3,5,4,1,2] => 4
[1,4,3,5,2] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[1,4,5,2,3] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 4
[1,4,5,3,2] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 4
[1,5,2,3,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[1,5,2,4,3] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => 3
[1,5,3,2,4] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => 3
[1,5,3,4,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[1,5,4,2,3] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[1,5,4,3,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[2,1,3,4,5] => [1,3,4,5,2] => [2,5,1,3,4] => [2,5,1,4,3] => 4
[2,1,3,5,4] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 4
[2,1,4,3,5] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[2,1,4,5,3] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 4
[2,1,5,3,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[2,1,5,4,3] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[2,3,1,4,5] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 4
[2,3,1,5,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[2,3,4,1,5] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[2,3,5,1,4] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[2,3,5,4,1] => [1,2,3,5,4] => [2,3,4,5,1] => [2,5,4,3,1] => 3
[2,4,1,3,5] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 4
[2,4,1,5,3] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => 3
[2,4,3,1,5] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => 3
[2,4,3,5,1] => [1,2,4,3,5] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[2,4,5,1,3] => [1,3,2,4,5] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[2,4,5,3,1] => [1,2,4,5,3] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[2,5,1,3,4] => [1,3,4,2,5] => [2,4,1,3,5] => [2,5,1,4,3] => 4
[2,5,1,4,3] => [1,4,2,5,3] => [3,4,5,1,2] => [3,5,4,1,2] => 4
[2,5,3,1,4] => [1,4,2,5,3] => [3,4,5,1,2] => [3,5,4,1,2] => 4
[2,5,3,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[2,5,4,1,3] => [1,3,2,5,4] => [3,4,2,5,1] => [3,5,2,4,1] => 3
[2,5,4,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[3,1,2,4,5] => [1,2,4,5,3] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[3,1,2,5,4] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[3,1,4,2,5] => [1,4,2,5,3] => [3,4,5,1,2] => [3,5,4,1,2] => 4
[3,1,4,5,2] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 4
[3,1,5,2,4] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => 3
[3,1,5,4,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[3,2,1,4,5] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 4
[3,2,1,5,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[3,2,4,1,5] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => 3
[3,2,4,5,1] => [1,2,4,5,3] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[3,2,5,1,4] => [1,4,2,5,3] => [3,4,5,1,2] => [3,5,4,1,2] => 4
[3,2,5,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[3,4,1,2,5] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[3,4,1,5,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[3,4,2,1,5] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[3,4,2,5,1] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[3,4,5,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[3,4,5,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[3,5,1,2,4] => [1,2,4,3,5] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[3,5,1,4,2] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[3,5,2,1,4] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
>>> Load all 872 entries. <<<[3,5,2,4,1] => [1,2,4,3,5] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[3,5,4,1,2] => [1,2,3,5,4] => [2,3,4,5,1] => [2,5,4,3,1] => 3
[3,5,4,2,1] => [1,2,3,5,4] => [2,3,4,5,1] => [2,5,4,3,1] => 3
[4,1,2,3,5] => [1,2,3,5,4] => [2,3,4,5,1] => [2,5,4,3,1] => 3
[4,1,2,5,3] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[4,1,3,2,5] => [1,3,2,5,4] => [3,4,2,5,1] => [3,5,2,4,1] => 3
[4,1,3,5,2] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 4
[4,1,5,2,3] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[4,1,5,3,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[4,2,1,3,5] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 4
[4,2,1,5,3] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[4,2,3,1,5] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[4,2,3,5,1] => [1,2,3,5,4] => [2,3,4,5,1] => [2,5,4,3,1] => 3
[4,2,5,1,3] => [1,3,2,5,4] => [3,4,2,5,1] => [3,5,2,4,1] => 3
[4,2,5,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[4,3,1,2,5] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[4,3,1,5,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[4,3,2,1,5] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[4,3,2,5,1] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => 4
[4,3,5,1,2] => [1,2,3,5,4] => [2,3,4,5,1] => [2,5,4,3,1] => 3
[4,3,5,2,1] => [1,2,3,5,4] => [2,3,4,5,1] => [2,5,4,3,1] => 3
[4,5,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[4,5,1,3,2] => [1,3,2,4,5] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[4,5,2,1,3] => [1,3,2,4,5] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[4,5,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[4,5,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[4,5,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[5,1,2,3,4] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[5,1,2,4,3] => [1,2,4,3,5] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[5,1,3,2,4] => [1,3,2,4,5] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[5,1,3,4,2] => [1,3,4,2,5] => [2,4,1,3,5] => [2,5,1,4,3] => 4
[5,1,4,2,3] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[5,1,4,3,2] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[5,2,1,3,4] => [1,3,4,2,5] => [2,4,1,3,5] => [2,5,1,4,3] => 4
[5,2,1,4,3] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[5,2,3,1,4] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[5,2,3,4,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[5,2,4,1,3] => [1,3,2,4,5] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[5,2,4,3,1] => [1,2,4,3,5] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[5,3,1,2,4] => [1,2,4,3,5] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[5,3,1,4,2] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[5,3,2,1,4] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[5,3,2,4,1] => [1,2,4,3,5] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[5,3,4,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[5,3,4,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[5,4,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[5,4,1,3,2] => [1,3,2,4,5] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[5,4,2,1,3] => [1,3,2,4,5] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[5,4,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[5,4,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 2
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[1,2,3,5,6,4] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 4
[1,2,3,6,4,5] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[1,2,3,6,5,4] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => 3
[1,2,4,5,3,6] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 4
[1,2,4,5,6,3] => [1,2,4,5,6,3] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 4
[1,2,4,6,3,5] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[1,2,4,6,5,3] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[1,2,5,3,4,6] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[1,2,5,3,6,4] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[1,2,5,4,3,6] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[1,2,5,4,6,3] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[1,2,5,6,3,4] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[1,2,5,6,4,3] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[1,2,6,3,4,5] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[1,2,6,3,5,4] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[1,2,6,4,3,5] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[1,2,6,4,5,3] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[1,2,6,5,3,4] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[1,2,6,5,4,3] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => 3
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => [3,6,2,5,1,4] => 4
[1,3,2,5,6,4] => [1,3,2,5,6,4] => [3,4,2,6,1,5] => [3,6,2,5,1,4] => 4
[1,3,2,6,4,5] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[1,3,2,6,5,4] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[1,3,4,2,5,6] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 4
[1,3,4,2,6,5] => [1,3,4,2,6,5] => [3,5,2,4,6,1] => [3,6,2,5,4,1] => 3
[1,3,4,5,2,6] => [1,3,4,5,2,6] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 4
[1,3,4,5,6,2] => [1,3,4,5,6,2] => [2,6,1,3,4,5] => [2,6,1,5,4,3] => 4
[1,3,4,6,2,5] => [1,3,4,6,2,5] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => 4
[1,3,4,6,5,2] => [1,3,4,6,2,5] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => 4
[1,3,5,2,4,6] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[1,3,5,2,6,4] => [1,3,5,2,6,4] => [3,5,2,6,1,4] => [3,6,2,5,1,4] => 4
[1,3,5,4,2,6] => [1,3,5,2,6,4] => [3,5,2,6,1,4] => [3,6,2,5,1,4] => 4
[1,3,5,4,6,2] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[1,3,5,6,2,4] => [1,3,5,6,2,4] => [2,1,4,6,3,5] => [2,1,6,5,4,3] => 4
[1,3,5,6,4,2] => [1,3,5,6,2,4] => [2,1,4,6,3,5] => [2,1,6,5,4,3] => 4
[1,3,6,2,4,5] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[1,3,6,2,5,4] => [1,3,6,2,5,4] => [3,2,5,6,4,1] => [3,2,6,5,4,1] => 3
[1,3,6,4,2,5] => [1,3,6,2,5,4] => [3,2,5,6,4,1] => [3,2,6,5,4,1] => 3
[1,3,6,4,5,2] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[1,3,6,5,2,4] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[1,3,6,5,4,2] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[1,4,2,3,5,6] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[1,4,2,3,6,5] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[1,4,2,5,3,6] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[1,4,2,5,6,3] => [1,4,2,5,6,3] => [3,4,6,1,2,5] => [3,6,5,1,4,2] => 4
[1,4,2,6,3,5] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[1,4,2,6,5,3] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[1,4,3,2,5,6] => [1,4,2,5,6,3] => [3,4,6,1,2,5] => [3,6,5,1,4,2] => 4
[1,4,3,2,6,5] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[1,4,3,5,2,6] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[1,4,3,5,6,2] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[1,4,3,6,2,5] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[1,4,3,6,5,2] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[1,4,5,2,3,6] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[1,4,5,2,6,3] => [1,4,5,2,6,3] => [3,5,6,1,2,4] => [3,6,5,1,4,2] => 4
[1,4,5,3,2,6] => [1,4,5,2,6,3] => [3,5,6,1,2,4] => [3,6,5,1,4,2] => 4
[1,4,5,3,6,2] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[1,4,5,6,2,3] => [1,4,5,6,2,3] => [2,1,6,3,4,5] => [2,1,6,5,4,3] => 4
[1,4,5,6,3,2] => [1,4,5,6,2,3] => [2,1,6,3,4,5] => [2,1,6,5,4,3] => 4
[1,4,6,2,3,5] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[1,4,6,2,5,3] => [1,4,6,2,5,3] => [3,2,6,4,5,1] => [3,2,6,5,4,1] => 3
[1,4,6,3,2,5] => [1,4,6,2,5,3] => [3,2,6,4,5,1] => [3,2,6,5,4,1] => 3
[1,4,6,3,5,2] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[1,4,6,5,2,3] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[1,4,6,5,3,2] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[1,5,2,3,4,6] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[1,5,2,3,6,4] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[1,5,2,4,3,6] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[1,5,2,4,6,3] => [1,5,2,4,6,3] => [3,2,6,4,1,5] => [3,2,6,5,1,4] => 4
[1,5,2,6,3,4] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[1,5,2,6,4,3] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[1,5,3,2,4,6] => [1,5,2,4,6,3] => [3,2,6,4,1,5] => [3,2,6,5,1,4] => 4
[1,5,3,2,6,4] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[1,5,3,4,2,6] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[1,5,3,4,6,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[1,5,3,6,2,4] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[1,5,3,6,4,2] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[1,5,4,2,3,6] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[1,5,4,2,6,3] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[1,5,4,3,2,6] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[1,5,4,3,6,2] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[1,5,4,6,2,3] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[1,5,4,6,3,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[1,5,6,2,3,4] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[1,5,6,2,4,3] => [1,5,6,2,4,3] => [3,2,6,5,1,4] => [3,2,6,5,1,4] => 4
[1,5,6,3,2,4] => [1,5,6,2,4,3] => [3,2,6,5,1,4] => [3,2,6,5,1,4] => 4
[1,5,6,3,4,2] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[1,5,6,4,2,3] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[1,5,6,4,3,2] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[1,6,2,3,4,5] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[1,6,2,3,5,4] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[1,6,2,4,3,5] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[1,6,2,4,5,3] => [1,6,2,4,5,3] => [3,2,6,1,5,4] => [3,2,6,1,5,4] => 4
[1,6,2,5,3,4] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[1,6,2,5,4,3] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[1,6,3,2,4,5] => [1,6,2,4,5,3] => [3,2,6,1,5,4] => [3,2,6,1,5,4] => 4
[1,6,3,2,5,4] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[1,6,3,4,2,5] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[1,6,3,4,5,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[1,6,3,5,2,4] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[1,6,3,5,4,2] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[1,6,4,2,3,5] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[1,6,4,2,5,3] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[1,6,4,3,2,5] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[1,6,4,3,5,2] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[1,6,4,5,2,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[1,6,4,5,3,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[1,6,5,2,3,4] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[1,6,5,2,4,3] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[1,6,5,3,2,4] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[1,6,5,3,4,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[1,6,5,4,2,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[1,6,5,4,3,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[2,1,3,4,5,6] => [1,3,4,5,6,2] => [2,6,1,3,4,5] => [2,6,1,5,4,3] => 4
[2,1,3,4,6,5] => [1,3,4,6,2,5] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => 4
[2,1,3,5,4,6] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[2,1,3,5,6,4] => [1,3,5,6,2,4] => [2,1,4,6,3,5] => [2,1,6,5,4,3] => 4
[2,1,3,6,4,5] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[2,1,3,6,5,4] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[2,1,4,3,5,6] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[2,1,4,3,6,5] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[2,1,4,5,3,6] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[2,1,4,5,6,3] => [1,4,5,6,2,3] => [2,1,6,3,4,5] => [2,1,6,5,4,3] => 4
[2,1,4,6,3,5] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[2,1,4,6,5,3] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[2,1,5,3,4,6] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[2,1,5,3,6,4] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[2,1,5,4,3,6] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[2,1,5,4,6,3] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[2,1,5,6,3,4] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[2,1,5,6,4,3] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[2,1,6,3,4,5] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[2,1,6,3,5,4] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[2,1,6,4,3,5] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[2,1,6,4,5,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[2,1,6,5,3,4] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[2,1,6,5,4,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => [1,4,5,6,2,3] => [2,1,6,3,4,5] => [2,1,6,5,4,3] => 4
[2,3,1,4,6,5] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[2,3,1,5,4,6] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[2,3,1,5,6,4] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[2,3,1,6,4,5] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[2,3,1,6,5,4] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[2,3,4,1,5,6] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[2,3,4,1,6,5] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[2,3,4,5,1,6] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[2,3,4,6,1,5] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[2,3,4,6,5,1] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[2,3,5,1,4,6] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[2,3,5,1,6,4] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[2,3,5,4,1,6] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[2,3,5,4,6,1] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[2,3,5,6,1,4] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[2,3,5,6,4,1] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 4
[2,3,6,1,4,5] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[2,3,6,1,5,4] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[2,3,6,4,1,5] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[2,3,6,4,5,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[2,3,6,5,1,4] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[2,3,6,5,4,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[2,4,1,3,5,6] => [1,3,5,6,2,4] => [2,1,4,6,3,5] => [2,1,6,5,4,3] => 4
[2,4,1,3,6,5] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[2,4,1,5,3,6] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[2,4,1,5,6,3] => [1,5,6,2,4,3] => [3,2,6,5,1,4] => [3,2,6,5,1,4] => 4
[2,4,1,6,3,5] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[2,4,1,6,5,3] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[2,4,3,1,5,6] => [1,5,6,2,4,3] => [3,2,6,5,1,4] => [3,2,6,5,1,4] => 4
[2,4,3,1,6,5] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[2,4,3,5,1,6] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[2,4,3,5,6,1] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[2,4,3,6,1,5] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[2,4,3,6,5,1] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => 3
[2,4,5,1,3,6] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[2,4,5,1,6,3] => [1,6,2,4,5,3] => [3,2,6,1,5,4] => [3,2,6,1,5,4] => 4
[2,4,5,3,1,6] => [1,6,2,4,5,3] => [3,2,6,1,5,4] => [3,2,6,1,5,4] => 4
[2,4,5,3,6,1] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 4
[2,4,5,6,1,3] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[2,4,5,6,3,1] => [1,2,4,5,6,3] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 4
[2,4,6,1,3,5] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[2,4,6,1,5,3] => [1,5,2,4,6,3] => [3,2,6,4,1,5] => [3,2,6,5,1,4] => 4
[2,4,6,3,1,5] => [1,5,2,4,6,3] => [3,2,6,4,1,5] => [3,2,6,5,1,4] => 4
[2,4,6,3,5,1] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[2,4,6,5,1,3] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => 3
[2,4,6,5,3,1] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[2,5,1,3,4,6] => [1,3,4,6,2,5] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => 4
[2,5,1,3,6,4] => [1,3,6,2,5,4] => [3,2,5,6,4,1] => [3,2,6,5,4,1] => 3
[2,5,1,4,3,6] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[2,5,1,4,6,3] => [1,4,6,2,5,3] => [3,2,6,4,5,1] => [3,2,6,5,4,1] => 3
[2,5,1,6,3,4] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[2,5,1,6,4,3] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[2,5,3,1,4,6] => [1,4,6,2,5,3] => [3,2,6,4,5,1] => [3,2,6,5,4,1] => 3
[2,5,3,1,6,4] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[2,5,3,4,1,6] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[2,5,3,4,6,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[2,5,3,6,1,4] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[2,5,3,6,4,1] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[2,5,4,1,3,6] => [1,3,6,2,5,4] => [3,2,5,6,4,1] => [3,2,6,5,4,1] => 3
[2,5,4,1,6,3] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[2,5,4,3,1,6] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[2,5,4,3,6,1] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[2,5,4,6,1,3] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => [3,6,2,5,1,4] => 4
[2,5,4,6,3,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[2,5,6,1,3,4] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 4
[2,5,6,1,4,3] => [1,4,2,5,6,3] => [3,4,6,1,2,5] => [3,6,5,1,4,2] => 4
[2,5,6,3,1,4] => [1,4,2,5,6,3] => [3,4,6,1,2,5] => [3,6,5,1,4,2] => 4
[2,5,6,3,4,1] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[2,5,6,4,1,3] => [1,3,2,5,6,4] => [3,4,2,6,1,5] => [3,6,2,5,1,4] => 4
[2,5,6,4,3,1] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[2,6,1,3,4,5] => [1,3,4,5,2,6] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 4
[2,6,1,3,5,4] => [1,3,5,2,6,4] => [3,5,2,6,1,4] => [3,6,2,5,1,4] => 4
[2,6,1,4,3,5] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[2,6,1,4,5,3] => [1,4,5,2,6,3] => [3,5,6,1,2,4] => [3,6,5,1,4,2] => 4
[2,6,1,5,3,4] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[2,6,1,5,4,3] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[2,6,3,1,4,5] => [1,4,5,2,6,3] => [3,5,6,1,2,4] => [3,6,5,1,4,2] => 4
[2,6,3,1,5,4] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[2,6,3,4,1,5] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[2,6,3,4,5,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[2,6,3,5,1,4] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[2,6,3,5,4,1] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[2,6,4,1,3,5] => [1,3,5,2,6,4] => [3,5,2,6,1,4] => [3,6,2,5,1,4] => 4
[2,6,4,1,5,3] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[2,6,4,3,1,5] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[2,6,4,3,5,1] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[2,6,4,5,1,3] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[2,6,4,5,3,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[2,6,5,1,3,4] => [1,3,4,2,6,5] => [3,5,2,4,6,1] => [3,6,2,5,4,1] => 3
[2,6,5,1,4,3] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[2,6,5,3,1,4] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[2,6,5,3,4,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[2,6,5,4,1,3] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[2,6,5,4,3,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[3,1,2,4,5,6] => [1,2,4,5,6,3] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 4
[3,1,2,4,6,5] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[3,1,2,5,4,6] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[3,1,2,5,6,4] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[3,1,2,6,4,5] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[3,1,2,6,5,4] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[3,1,4,2,5,6] => [1,4,2,5,6,3] => [3,4,6,1,2,5] => [3,6,5,1,4,2] => 4
[3,1,4,2,6,5] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[3,1,4,5,2,6] => [1,4,5,2,6,3] => [3,5,6,1,2,4] => [3,6,5,1,4,2] => 4
[3,1,4,5,6,2] => [1,4,5,6,2,3] => [2,1,6,3,4,5] => [2,1,6,5,4,3] => 4
[3,1,4,6,2,5] => [1,4,6,2,5,3] => [3,2,6,4,5,1] => [3,2,6,5,4,1] => 3
[3,1,4,6,5,2] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[3,1,5,2,4,6] => [1,5,2,4,6,3] => [3,2,6,4,1,5] => [3,2,6,5,1,4] => 4
[3,1,5,2,6,4] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[3,1,5,4,2,6] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[3,1,5,4,6,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[3,1,5,6,2,4] => [1,5,6,2,4,3] => [3,2,6,5,1,4] => [3,2,6,5,1,4] => 4
[3,1,5,6,4,2] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[3,1,6,2,4,5] => [1,6,2,4,5,3] => [3,2,6,1,5,4] => [3,2,6,1,5,4] => 4
[3,1,6,2,5,4] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,1,6,4,2,5] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,1,6,4,5,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[3,1,6,5,2,4] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[3,1,6,5,4,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[3,2,1,4,5,6] => [1,4,5,6,2,3] => [2,1,6,3,4,5] => [2,1,6,5,4,3] => 4
[3,2,1,4,6,5] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[3,2,1,5,4,6] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[3,2,1,5,6,4] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[3,2,1,6,4,5] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[3,2,1,6,5,4] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[3,2,4,1,5,6] => [1,5,6,2,4,3] => [3,2,6,5,1,4] => [3,2,6,5,1,4] => 4
[3,2,4,1,6,5] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[3,2,4,5,1,6] => [1,6,2,4,5,3] => [3,2,6,1,5,4] => [3,2,6,1,5,4] => 4
[3,2,4,5,6,1] => [1,2,4,5,6,3] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 4
[3,2,4,6,1,5] => [1,5,2,4,6,3] => [3,2,6,4,1,5] => [3,2,6,5,1,4] => 4
[3,2,4,6,5,1] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[3,2,5,1,4,6] => [1,4,6,2,5,3] => [3,2,6,4,5,1] => [3,2,6,5,4,1] => 3
[3,2,5,1,6,4] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,2,5,4,1,6] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,2,5,4,6,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[3,2,5,6,1,4] => [1,4,2,5,6,3] => [3,4,6,1,2,5] => [3,6,5,1,4,2] => 4
[3,2,5,6,4,1] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[3,2,6,1,4,5] => [1,4,5,2,6,3] => [3,5,6,1,2,4] => [3,6,5,1,4,2] => 4
[3,2,6,1,5,4] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[3,2,6,4,1,5] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[3,2,6,4,5,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[3,2,6,5,1,4] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[3,2,6,5,4,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[3,4,1,2,5,6] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[3,4,1,2,6,5] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[3,4,1,5,2,6] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[3,4,1,5,6,2] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[3,4,1,6,2,5] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,4,1,6,5,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[3,4,2,1,5,6] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[3,4,2,1,6,5] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[3,4,2,5,1,6] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,4,2,5,6,1] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[3,4,2,6,1,5] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[3,4,2,6,5,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[3,4,5,1,2,6] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[3,4,5,1,6,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[3,4,5,2,1,6] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[3,4,5,2,6,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[3,4,5,6,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[3,4,5,6,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[3,4,6,1,2,5] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[3,4,6,1,5,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[3,4,6,2,1,5] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[3,4,6,2,5,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[3,4,6,5,1,2] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[3,4,6,5,2,1] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[3,5,1,2,4,6] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[3,5,1,2,6,4] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[3,5,1,4,2,6] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[3,5,1,4,6,2] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[3,5,1,6,2,4] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[3,5,1,6,4,2] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[3,5,2,1,4,6] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[3,5,2,1,6,4] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[3,5,2,4,1,6] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[3,5,2,4,6,1] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[3,5,2,6,1,4] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[3,5,2,6,4,1] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[3,5,4,1,2,6] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[3,5,4,1,6,2] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[3,5,4,2,1,6] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[3,5,4,2,6,1] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[3,5,4,6,1,2] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[3,5,4,6,2,1] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[3,5,6,1,2,4] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[3,5,6,1,4,2] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[3,5,6,2,1,4] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[3,5,6,2,4,1] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[3,5,6,4,1,2] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 4
[3,5,6,4,2,1] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 4
[3,6,1,2,4,5] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 4
[3,6,1,2,5,4] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[3,6,1,4,2,5] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[3,6,1,4,5,2] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[3,6,1,5,2,4] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[3,6,1,5,4,2] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[3,6,2,1,4,5] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[3,6,2,1,5,4] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[3,6,2,4,1,5] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[3,6,2,4,5,1] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 4
[3,6,2,5,1,4] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[3,6,2,5,4,1] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[3,6,4,1,2,5] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[3,6,4,1,5,2] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[3,6,4,2,1,5] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[3,6,4,2,5,1] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[3,6,4,5,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[3,6,4,5,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[3,6,5,1,2,4] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => 3
[3,6,5,1,4,2] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[3,6,5,2,1,4] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[3,6,5,2,4,1] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => 3
[3,6,5,4,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[3,6,5,4,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[4,1,2,3,5,6] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 4
[4,1,2,3,6,5] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[4,1,2,5,3,6] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[4,1,2,5,6,3] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[4,1,2,6,3,5] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[4,1,2,6,5,3] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[4,1,3,2,5,6] => [1,3,2,5,6,4] => [3,4,2,6,1,5] => [3,6,2,5,1,4] => 4
[4,1,3,2,6,5] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[4,1,3,5,2,6] => [1,3,5,2,6,4] => [3,5,2,6,1,4] => [3,6,2,5,1,4] => 4
[4,1,3,5,6,2] => [1,3,5,6,2,4] => [2,1,4,6,3,5] => [2,1,6,5,4,3] => 4
[4,1,3,6,2,5] => [1,3,6,2,5,4] => [3,2,5,6,4,1] => [3,2,6,5,4,1] => 3
[4,1,3,6,5,2] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[4,1,5,2,3,6] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[4,1,5,2,6,3] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[4,1,5,3,2,6] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[4,1,5,3,6,2] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[4,1,5,6,2,3] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[4,1,5,6,3,2] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[4,1,6,2,3,5] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[4,1,6,2,5,3] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[4,1,6,3,2,5] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[4,1,6,3,5,2] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[4,1,6,5,2,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,1,6,5,3,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,2,1,3,5,6] => [1,3,5,6,2,4] => [2,1,4,6,3,5] => [2,1,6,5,4,3] => 4
[4,2,1,3,6,5] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[4,2,1,5,3,6] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[4,2,1,5,6,3] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[4,2,1,6,3,5] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[4,2,1,6,5,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,2,3,1,5,6] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[4,2,3,1,6,5] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,2,3,5,1,6] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[4,2,3,5,6,1] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 4
[4,2,3,6,1,5] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[4,2,3,6,5,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[4,2,5,1,3,6] => [1,3,6,2,5,4] => [3,2,5,6,4,1] => [3,2,6,5,4,1] => 3
[4,2,5,1,6,3] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[4,2,5,3,1,6] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[4,2,5,3,6,1] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[4,2,5,6,1,3] => [1,3,2,5,6,4] => [3,4,2,6,1,5] => [3,6,2,5,1,4] => 4
[4,2,5,6,3,1] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[4,2,6,1,3,5] => [1,3,5,2,6,4] => [3,5,2,6,1,4] => [3,6,2,5,1,4] => 4
[4,2,6,1,5,3] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[4,2,6,3,1,5] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[4,2,6,3,5,1] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[4,2,6,5,1,3] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[4,2,6,5,3,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[4,3,1,2,5,6] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[4,3,1,2,6,5] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[4,3,1,5,2,6] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[4,3,1,5,6,2] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[4,3,1,6,2,5] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[4,3,1,6,5,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,3,2,1,5,6] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 4
[4,3,2,1,6,5] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,3,2,5,1,6] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[4,3,2,5,6,1] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 4
[4,3,2,6,1,5] => [1,5,2,6,3,4] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 4
[4,3,2,6,5,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[4,3,5,1,2,6] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[4,3,5,1,6,2] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[4,3,5,2,1,6] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 3
[4,3,5,2,6,1] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 3
[4,3,5,6,1,2] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 4
[4,3,5,6,2,1] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 4
[4,3,6,1,2,5] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[4,3,6,1,5,2] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[4,3,6,2,1,5] => [1,5,2,3,6,4] => [3,2,5,6,1,4] => [3,2,6,5,1,4] => 4
[4,3,6,2,5,1] => [1,2,5,3,6,4] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 4
[4,3,6,5,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[4,3,6,5,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[4,5,1,2,3,6] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[4,5,1,2,6,3] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[4,5,1,3,2,6] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[4,5,1,3,6,2] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[4,5,1,6,2,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,5,1,6,3,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,5,2,1,3,6] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[4,5,2,1,6,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,5,2,3,1,6] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,5,2,3,6,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[4,5,2,6,1,3] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[4,5,2,6,3,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[4,5,3,1,2,6] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[4,5,3,1,6,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,5,3,2,1,6] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[4,5,3,2,6,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[4,5,3,6,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[4,5,3,6,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[4,5,6,1,2,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[4,5,6,1,3,2] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[4,5,6,2,1,3] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[4,5,6,2,3,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[4,5,6,3,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[4,5,6,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[4,6,1,2,3,5] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[4,6,1,2,5,3] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[4,6,1,3,2,5] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => [3,6,2,5,1,4] => 4
[4,6,1,3,5,2] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[4,6,1,5,2,3] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[4,6,1,5,3,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[4,6,2,1,3,5] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[4,6,2,1,5,3] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[4,6,2,3,1,5] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[4,6,2,3,5,1] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[4,6,2,5,1,3] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => [3,6,2,5,1,4] => 4
[4,6,2,5,3,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[4,6,3,1,2,5] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[4,6,3,1,5,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[4,6,3,2,1,5] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[4,6,3,2,5,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[4,6,3,5,1,2] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[4,6,3,5,2,1] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[4,6,5,1,2,3] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[4,6,5,1,3,2] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => 3
[4,6,5,2,1,3] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => 3
[4,6,5,2,3,1] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[4,6,5,3,1,2] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[4,6,5,3,2,1] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[5,1,2,3,4,6] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[5,1,2,3,6,4] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[5,1,2,4,3,6] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => 3
[5,1,2,4,6,3] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[5,1,2,6,3,4] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,1,2,6,4,3] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,1,3,2,4,6] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => 3
[5,1,3,2,6,4] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[5,1,3,4,2,6] => [1,3,4,2,6,5] => [3,5,2,4,6,1] => [3,6,2,5,4,1] => 3
[5,1,3,4,6,2] => [1,3,4,6,2,5] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => 4
[5,1,3,6,2,4] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[5,1,3,6,4,2] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[5,1,4,2,3,6] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[5,1,4,2,6,3] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[5,1,4,3,2,6] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[5,1,4,3,6,2] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[5,1,4,6,2,3] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[5,1,4,6,3,2] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[5,1,6,2,3,4] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,1,6,2,4,3] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[5,1,6,3,2,4] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[5,1,6,3,4,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,1,6,4,2,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,1,6,4,3,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,2,1,3,4,6] => [1,3,4,6,2,5] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => 4
[5,2,1,3,6,4] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[5,2,1,4,3,6] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[5,2,1,4,6,3] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[5,2,1,6,3,4] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,2,1,6,4,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,2,3,1,4,6] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[5,2,3,1,6,4] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,2,3,4,1,6] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,2,3,4,6,1] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[5,2,3,6,1,4] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[5,2,3,6,4,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[5,2,4,1,3,6] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[5,2,4,1,6,3] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[5,2,4,3,1,6] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[5,2,4,3,6,1] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => 3
[5,2,4,6,1,3] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => 3
[5,2,4,6,3,1] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[5,2,6,1,3,4] => [1,3,4,2,6,5] => [3,5,2,4,6,1] => [3,6,2,5,4,1] => 3
[5,2,6,1,4,3] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[5,2,6,3,1,4] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[5,2,6,3,4,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,2,6,4,1,3] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[5,2,6,4,3,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,3,1,2,4,6] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[5,3,1,2,6,4] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,3,1,4,2,6] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[5,3,1,4,6,2] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[5,3,1,6,2,4] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[5,3,1,6,4,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,3,2,1,4,6] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 4
[5,3,2,1,6,4] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,3,2,4,1,6] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 4
[5,3,2,4,6,1] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[5,3,2,6,1,4] => [1,4,2,6,3,5] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 4
[5,3,2,6,4,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,3,4,1,2,6] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,3,4,1,6,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,3,4,2,1,6] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,3,4,2,6,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,3,4,6,1,2] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[5,3,4,6,2,1] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[5,3,6,1,2,4] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => 3
[5,3,6,1,4,2] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[5,3,6,2,1,4] => [1,4,2,3,6,5] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 3
[5,3,6,2,4,1] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => 3
[5,3,6,4,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[5,3,6,4,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[5,4,1,2,3,6] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[5,4,1,2,6,3] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,4,1,3,2,6] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[5,4,1,3,6,2] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[5,4,1,6,2,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,4,1,6,3,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,4,2,1,3,6] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 4
[5,4,2,1,6,3] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,4,2,3,1,6] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,4,2,3,6,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[5,4,2,6,1,3] => [1,3,2,6,4,5] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[5,4,2,6,3,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,4,3,1,2,6] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,4,3,1,6,2] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,4,3,2,1,6] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 4
[5,4,3,2,6,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[5,4,3,6,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[5,4,3,6,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[5,4,6,1,2,3] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[5,4,6,1,3,2] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => 3
[5,4,6,2,1,3] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => 3
[5,4,6,2,3,1] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[5,4,6,3,1,2] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[5,4,6,3,2,1] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 3
[5,6,1,2,3,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[5,6,1,2,4,3] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[5,6,1,3,2,4] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[5,6,1,3,4,2] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 4
[5,6,1,4,2,3] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[5,6,1,4,3,2] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[5,6,2,1,3,4] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 4
[5,6,2,1,4,3] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[5,6,2,3,1,4] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[5,6,2,3,4,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[5,6,2,4,1,3] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[5,6,2,4,3,1] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[5,6,3,1,2,4] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[5,6,3,1,4,2] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[5,6,3,2,1,4] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[5,6,3,2,4,1] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[5,6,3,4,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[5,6,3,4,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[5,6,4,1,2,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[5,6,4,1,3,2] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[5,6,4,2,1,3] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[5,6,4,2,3,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[5,6,4,3,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[5,6,4,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,1,2,3,4,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,1,2,3,5,4] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[6,1,2,4,3,5] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[6,1,2,4,5,3] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 4
[6,1,2,5,3,4] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,1,2,5,4,3] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,1,3,2,4,5] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[6,1,3,2,5,4] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => [3,6,2,5,1,4] => 4
[6,1,3,4,2,5] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 4
[6,1,3,4,5,2] => [1,3,4,5,2,6] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 4
[6,1,3,5,2,4] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[6,1,3,5,4,2] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[6,1,4,2,3,5] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,1,4,2,5,3] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[6,1,4,3,2,5] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[6,1,4,3,5,2] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,1,4,5,2,3] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[6,1,4,5,3,2] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[6,1,5,2,3,4] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,1,5,2,4,3] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[6,1,5,3,2,4] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[6,1,5,3,4,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,1,5,4,2,3] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,1,5,4,3,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,2,1,3,4,5] => [1,3,4,5,2,6] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 4
[6,2,1,3,5,4] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[6,2,1,4,3,5] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,2,1,4,5,3] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[6,2,1,5,3,4] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,2,1,5,4,3] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,2,3,1,4,5] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[6,2,3,1,5,4] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,2,3,4,1,5] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,2,3,4,5,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,2,3,5,1,4] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,2,3,5,4,1] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[6,2,4,1,3,5] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[6,2,4,1,5,3] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[6,2,4,3,1,5] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[6,2,4,3,5,1] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[6,2,4,5,1,3] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[6,2,4,5,3,1] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 4
[6,2,5,1,3,4] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 4
[6,2,5,1,4,3] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[6,2,5,3,1,4] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[6,2,5,3,4,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,2,5,4,1,3] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => [3,6,2,5,1,4] => 4
[6,2,5,4,3,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,3,1,2,4,5] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 4
[6,3,1,2,5,4] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,3,1,4,2,5] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[6,3,1,4,5,2] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[6,3,1,5,2,4] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[6,3,1,5,4,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,3,2,1,4,5] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 4
[6,3,2,1,5,4] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,3,2,4,1,5] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[6,3,2,4,5,1] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 4
[6,3,2,5,1,4] => [1,4,2,5,3,6] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 4
[6,3,2,5,4,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,3,4,1,2,5] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,3,4,1,5,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,3,4,2,1,5] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,3,4,2,5,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,3,4,5,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,3,4,5,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,3,5,1,2,4] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[6,3,5,1,4,2] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,3,5,2,1,4] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,3,5,2,4,1] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[6,3,5,4,1,2] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[6,3,5,4,2,1] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[6,4,1,2,3,5] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[6,4,1,2,5,3] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,4,1,3,2,5] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => [3,6,2,5,1,4] => 4
[6,4,1,3,5,2] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[6,4,1,5,2,3] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,4,1,5,3,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,4,2,1,3,5] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 4
[6,4,2,1,5,3] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,4,2,3,1,5] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,4,2,3,5,1] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[6,4,2,5,1,3] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => [3,6,2,5,1,4] => 4
[6,4,2,5,3,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,4,3,1,2,5] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,4,3,1,5,2] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,4,3,2,1,5] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 4
[6,4,3,2,5,1] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[6,4,3,5,1,2] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[6,4,3,5,2,1] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[6,4,5,1,2,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,4,5,1,3,2] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[6,4,5,2,1,3] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[6,4,5,2,3,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,4,5,3,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,4,5,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,5,1,2,3,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,5,1,2,4,3] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[6,5,1,3,2,4] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[6,5,1,3,4,2] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 4
[6,5,1,4,2,3] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,5,1,4,3,2] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,5,2,1,3,4] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 4
[6,5,2,1,4,3] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,5,2,3,1,4] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,5,2,3,4,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,5,2,4,1,3] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[6,5,2,4,3,1] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[6,5,3,1,2,4] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[6,5,3,1,4,2] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,5,3,2,1,4] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 4
[6,5,3,2,4,1] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[6,5,3,4,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,5,3,4,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,5,4,1,2,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,5,4,1,3,2] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[6,5,4,2,1,3] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[6,5,4,2,3,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,5,4,3,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
[6,5,4,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,2 8,4,12 16,18,86 32,90,598
$F_{2} = 2$
$F_{3} = 4\ q^{2} + 2\ q^{3}$
$F_{4} = 8\ q^{2} + 4\ q^{3} + 12\ q^{4}$
$F_{5} = 16\ q^{2} + 18\ q^{3} + 86\ q^{4}$
$F_{6} = 32\ q^{2} + 90\ q^{3} + 598\ q^{4}$
Description
The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both.
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
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