Identifier
-
Mp00223:
Permutations
—runsort⟶
Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
St000495: Permutations ⟶ ℤ
Values
[1,2] => [1,2] => [2,1] => [2,1] => 1
[2,1] => [1,2] => [2,1] => [2,1] => 1
[1,2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 2
[1,3,2] => [1,3,2] => [2,1,3] => [2,1,3] => 1
[2,1,3] => [1,3,2] => [2,1,3] => [2,1,3] => 1
[2,3,1] => [1,2,3] => [2,3,1] => [2,3,1] => 2
[3,1,2] => [1,2,3] => [2,3,1] => [2,3,1] => 2
[3,2,1] => [1,2,3] => [2,3,1] => [2,3,1] => 2
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [2,4,3,1] => 3
[1,2,4,3] => [1,2,4,3] => [2,3,1,4] => [2,4,1,3] => 3
[1,3,2,4] => [1,3,2,4] => [2,4,3,1] => [2,4,3,1] => 3
[1,3,4,2] => [1,3,4,2] => [2,1,3,4] => [2,1,4,3] => 2
[1,4,2,3] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 3
[1,4,3,2] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 3
[2,1,3,4] => [1,3,4,2] => [2,1,3,4] => [2,1,4,3] => 2
[2,1,4,3] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 3
[2,3,1,4] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 3
[2,3,4,1] => [1,2,3,4] => [2,3,4,1] => [2,4,3,1] => 3
[2,4,1,3] => [1,3,2,4] => [2,4,3,1] => [2,4,3,1] => 3
[2,4,3,1] => [1,2,4,3] => [2,3,1,4] => [2,4,1,3] => 3
[3,1,2,4] => [1,2,4,3] => [2,3,1,4] => [2,4,1,3] => 3
[3,1,4,2] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 3
[3,2,1,4] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 3
[3,2,4,1] => [1,2,4,3] => [2,3,1,4] => [2,4,1,3] => 3
[3,4,1,2] => [1,2,3,4] => [2,3,4,1] => [2,4,3,1] => 3
[3,4,2,1] => [1,2,3,4] => [2,3,4,1] => [2,4,3,1] => 3
[4,1,2,3] => [1,2,3,4] => [2,3,4,1] => [2,4,3,1] => 3
[4,1,3,2] => [1,3,2,4] => [2,4,3,1] => [2,4,3,1] => 3
[4,2,1,3] => [1,3,2,4] => [2,4,3,1] => [2,4,3,1] => 3
[4,2,3,1] => [1,2,3,4] => [2,3,4,1] => [2,4,3,1] => 3
[4,3,1,2] => [1,2,3,4] => [2,3,4,1] => [2,4,3,1] => 3
[4,3,2,1] => [1,2,3,4] => [2,3,4,1] => [2,4,3,1] => 3
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[1,2,4,3,5] => [1,2,4,3,5] => [2,3,5,4,1] => [2,5,4,3,1] => 5
[1,2,4,5,3] => [1,2,4,5,3] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[1,2,5,3,4] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[1,2,5,4,3] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[1,3,2,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => [2,5,4,3,1] => 5
[1,3,2,5,4] => [1,3,2,5,4] => [2,4,3,1,5] => [2,5,4,1,3] => 4
[1,3,4,2,5] => [1,3,4,2,5] => [2,5,3,4,1] => [2,5,4,3,1] => 5
[1,3,4,5,2] => [1,3,4,5,2] => [2,1,3,4,5] => [2,1,5,4,3] => 4
[1,3,5,2,4] => [1,3,5,2,4] => [2,5,3,1,4] => [2,5,4,1,3] => 4
[1,3,5,4,2] => [1,3,5,2,4] => [2,5,3,1,4] => [2,5,4,1,3] => 4
[1,4,2,3,5] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[1,4,2,5,3] => [1,4,2,5,3] => [2,4,1,3,5] => [2,5,1,4,3] => 4
[1,4,3,2,5] => [1,4,2,5,3] => [2,4,1,3,5] => [2,5,1,4,3] => 4
[1,4,3,5,2] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[1,4,5,2,3] => [1,4,5,2,3] => [2,5,1,3,4] => [2,5,1,4,3] => 4
[1,4,5,3,2] => [1,4,5,2,3] => [2,5,1,3,4] => [2,5,1,4,3] => 4
[1,5,2,3,4] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[1,5,2,4,3] => [1,5,2,4,3] => [2,4,1,5,3] => [2,5,1,4,3] => 4
[1,5,3,2,4] => [1,5,2,4,3] => [2,4,1,5,3] => [2,5,1,4,3] => 4
[1,5,3,4,2] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[1,5,4,2,3] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[1,5,4,3,2] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[2,1,3,4,5] => [1,3,4,5,2] => [2,1,3,4,5] => [2,1,5,4,3] => 4
[2,1,3,5,4] => [1,3,5,2,4] => [2,5,3,1,4] => [2,5,4,1,3] => 4
[2,1,4,3,5] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[2,1,4,5,3] => [1,4,5,2,3] => [2,5,1,3,4] => [2,5,1,4,3] => 4
[2,1,5,3,4] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[2,1,5,4,3] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[2,3,1,4,5] => [1,4,5,2,3] => [2,5,1,3,4] => [2,5,1,4,3] => 4
[2,3,1,5,4] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[2,3,4,1,5] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[2,3,4,5,1] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[2,3,5,1,4] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[2,3,5,4,1] => [1,2,3,5,4] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[2,4,1,3,5] => [1,3,5,2,4] => [2,5,3,1,4] => [2,5,4,1,3] => 4
[2,4,1,5,3] => [1,5,2,4,3] => [2,4,1,5,3] => [2,5,1,4,3] => 4
[2,4,3,1,5] => [1,5,2,4,3] => [2,4,1,5,3] => [2,5,1,4,3] => 4
[2,4,3,5,1] => [1,2,4,3,5] => [2,3,5,4,1] => [2,5,4,3,1] => 5
[2,4,5,1,3] => [1,3,2,4,5] => [2,4,3,5,1] => [2,5,4,3,1] => 5
[2,4,5,3,1] => [1,2,4,5,3] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[2,5,1,3,4] => [1,3,4,2,5] => [2,5,3,4,1] => [2,5,4,3,1] => 5
[2,5,1,4,3] => [1,4,2,5,3] => [2,4,1,3,5] => [2,5,1,4,3] => 4
[2,5,3,1,4] => [1,4,2,5,3] => [2,4,1,3,5] => [2,5,1,4,3] => 4
[2,5,3,4,1] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[2,5,4,1,3] => [1,3,2,5,4] => [2,4,3,1,5] => [2,5,4,1,3] => 4
[2,5,4,3,1] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[3,1,2,4,5] => [1,2,4,5,3] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[3,1,2,5,4] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[3,1,4,2,5] => [1,4,2,5,3] => [2,4,1,3,5] => [2,5,1,4,3] => 4
[3,1,4,5,2] => [1,4,5,2,3] => [2,5,1,3,4] => [2,5,1,4,3] => 4
[3,1,5,2,4] => [1,5,2,4,3] => [2,4,1,5,3] => [2,5,1,4,3] => 4
[3,1,5,4,2] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[3,2,1,4,5] => [1,4,5,2,3] => [2,5,1,3,4] => [2,5,1,4,3] => 4
[3,2,1,5,4] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[3,2,4,1,5] => [1,5,2,4,3] => [2,4,1,5,3] => [2,5,1,4,3] => 4
[3,2,4,5,1] => [1,2,4,5,3] => [2,3,1,4,5] => [2,5,1,4,3] => 4
[3,2,5,1,4] => [1,4,2,5,3] => [2,4,1,3,5] => [2,5,1,4,3] => 4
[3,2,5,4,1] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[3,4,1,2,5] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[3,4,1,5,2] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[3,4,2,1,5] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[3,4,2,5,1] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[3,4,5,1,2] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[3,4,5,2,1] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[3,5,1,2,4] => [1,2,4,3,5] => [2,3,5,4,1] => [2,5,4,3,1] => 5
[3,5,1,4,2] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[3,5,2,1,4] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
>>> Load all 872 entries. <<<[3,5,2,4,1] => [1,2,4,3,5] => [2,3,5,4,1] => [2,5,4,3,1] => 5
[3,5,4,1,2] => [1,2,3,5,4] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[3,5,4,2,1] => [1,2,3,5,4] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[4,1,2,3,5] => [1,2,3,5,4] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[4,1,2,5,3] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[4,1,3,2,5] => [1,3,2,5,4] => [2,4,3,1,5] => [2,5,4,1,3] => 4
[4,1,3,5,2] => [1,3,5,2,4] => [2,5,3,1,4] => [2,5,4,1,3] => 4
[4,1,5,2,3] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[4,1,5,3,2] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[4,2,1,3,5] => [1,3,5,2,4] => [2,5,3,1,4] => [2,5,4,1,3] => 4
[4,2,1,5,3] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[4,2,3,1,5] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[4,2,3,5,1] => [1,2,3,5,4] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[4,2,5,1,3] => [1,3,2,5,4] => [2,4,3,1,5] => [2,5,4,1,3] => 4
[4,2,5,3,1] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[4,3,1,2,5] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[4,3,1,5,2] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[4,3,2,1,5] => [1,5,2,3,4] => [2,4,5,1,3] => [2,5,4,1,3] => 4
[4,3,2,5,1] => [1,2,5,3,4] => [2,3,5,1,4] => [2,5,4,1,3] => 4
[4,3,5,1,2] => [1,2,3,5,4] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[4,3,5,2,1] => [1,2,3,5,4] => [2,3,4,1,5] => [2,5,4,1,3] => 4
[4,5,1,2,3] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[4,5,1,3,2] => [1,3,2,4,5] => [2,4,3,5,1] => [2,5,4,3,1] => 5
[4,5,2,1,3] => [1,3,2,4,5] => [2,4,3,5,1] => [2,5,4,3,1] => 5
[4,5,2,3,1] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[4,5,3,1,2] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[4,5,3,2,1] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[5,1,2,3,4] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[5,1,2,4,3] => [1,2,4,3,5] => [2,3,5,4,1] => [2,5,4,3,1] => 5
[5,1,3,2,4] => [1,3,2,4,5] => [2,4,3,5,1] => [2,5,4,3,1] => 5
[5,1,3,4,2] => [1,3,4,2,5] => [2,5,3,4,1] => [2,5,4,3,1] => 5
[5,1,4,2,3] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[5,1,4,3,2] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[5,2,1,3,4] => [1,3,4,2,5] => [2,5,3,4,1] => [2,5,4,3,1] => 5
[5,2,1,4,3] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[5,2,3,1,4] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[5,2,3,4,1] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[5,2,4,1,3] => [1,3,2,4,5] => [2,4,3,5,1] => [2,5,4,3,1] => 5
[5,2,4,3,1] => [1,2,4,3,5] => [2,3,5,4,1] => [2,5,4,3,1] => 5
[5,3,1,2,4] => [1,2,4,3,5] => [2,3,5,4,1] => [2,5,4,3,1] => 5
[5,3,1,4,2] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[5,3,2,1,4] => [1,4,2,3,5] => [2,4,5,3,1] => [2,5,4,3,1] => 5
[5,3,2,4,1] => [1,2,4,3,5] => [2,3,5,4,1] => [2,5,4,3,1] => 5
[5,3,4,1,2] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[5,3,4,2,1] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[5,4,1,2,3] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[5,4,1,3,2] => [1,3,2,4,5] => [2,4,3,5,1] => [2,5,4,3,1] => 5
[5,4,2,1,3] => [1,3,2,4,5] => [2,4,3,5,1] => [2,5,4,3,1] => 5
[5,4,2,3,1] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[5,4,3,1,2] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[5,4,3,2,1] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 5
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[1,2,3,5,6,4] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 5
[1,2,3,6,4,5] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[1,2,3,6,5,4] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [2,6,5,4,1,3] => 6
[1,2,4,5,3,6] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [2,6,5,4,3,1] => 7
[1,2,4,5,6,3] => [1,2,4,5,6,3] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 6
[1,2,4,6,3,5] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[1,2,4,6,5,3] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[1,2,5,3,4,6] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[1,2,5,3,6,4] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[1,2,5,4,3,6] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[1,2,5,4,6,3] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[1,2,5,6,3,4] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[1,2,5,6,4,3] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[1,2,6,3,4,5] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[1,2,6,3,5,4] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[1,2,6,4,3,5] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[1,2,6,4,5,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[1,2,6,5,3,4] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[1,2,6,5,4,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [2,6,5,4,1,3] => 6
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [2,6,5,4,3,1] => 7
[1,3,2,5,6,4] => [1,3,2,5,6,4] => [2,4,3,1,5,6] => [2,6,5,1,4,3] => 5
[1,3,2,6,4,5] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[1,3,2,6,5,4] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[1,3,4,2,5,6] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [2,6,5,4,3,1] => 7
[1,3,4,2,6,5] => [1,3,4,2,6,5] => [2,5,3,4,1,6] => [2,6,5,4,1,3] => 6
[1,3,4,5,2,6] => [1,3,4,5,2,6] => [2,6,3,4,5,1] => [2,6,5,4,3,1] => 7
[1,3,4,5,6,2] => [1,3,4,5,6,2] => [2,1,3,4,5,6] => [2,1,6,5,4,3] => 6
[1,3,4,6,2,5] => [1,3,4,6,2,5] => [2,6,3,4,1,5] => [2,6,5,4,1,3] => 6
[1,3,4,6,5,2] => [1,3,4,6,2,5] => [2,6,3,4,1,5] => [2,6,5,4,1,3] => 6
[1,3,5,2,4,6] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[1,3,5,2,6,4] => [1,3,5,2,6,4] => [2,5,3,1,4,6] => [2,6,5,1,4,3] => 5
[1,3,5,4,2,6] => [1,3,5,2,6,4] => [2,5,3,1,4,6] => [2,6,5,1,4,3] => 5
[1,3,5,4,6,2] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[1,3,5,6,2,4] => [1,3,5,6,2,4] => [2,6,3,1,4,5] => [2,6,5,1,4,3] => 5
[1,3,5,6,4,2] => [1,3,5,6,2,4] => [2,6,3,1,4,5] => [2,6,5,1,4,3] => 5
[1,3,6,2,4,5] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[1,3,6,2,5,4] => [1,3,6,2,5,4] => [2,5,3,1,6,4] => [2,6,5,1,4,3] => 5
[1,3,6,4,2,5] => [1,3,6,2,5,4] => [2,5,3,1,6,4] => [2,6,5,1,4,3] => 5
[1,3,6,4,5,2] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[1,3,6,5,2,4] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[1,3,6,5,4,2] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[1,4,2,3,5,6] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[1,4,2,3,6,5] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[1,4,2,5,3,6] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[1,4,2,5,6,3] => [1,4,2,5,6,3] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 6
[1,4,2,6,3,5] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[1,4,2,6,5,3] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[1,4,3,2,5,6] => [1,4,2,5,6,3] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 6
[1,4,3,2,6,5] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[1,4,3,5,2,6] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[1,4,3,5,6,2] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[1,4,3,6,2,5] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[1,4,3,6,5,2] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[1,4,5,2,3,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[1,4,5,2,6,3] => [1,4,5,2,6,3] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 6
[1,4,5,3,2,6] => [1,4,5,2,6,3] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 6
[1,4,5,3,6,2] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[1,4,5,6,2,3] => [1,4,5,6,2,3] => [2,6,1,3,4,5] => [2,6,1,5,4,3] => 6
[1,4,5,6,3,2] => [1,4,5,6,2,3] => [2,6,1,3,4,5] => [2,6,1,5,4,3] => 6
[1,4,6,2,3,5] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[1,4,6,2,5,3] => [1,4,6,2,5,3] => [2,5,1,3,6,4] => [2,6,1,5,4,3] => 6
[1,4,6,3,2,5] => [1,4,6,2,5,3] => [2,5,1,3,6,4] => [2,6,1,5,4,3] => 6
[1,4,6,3,5,2] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[1,4,6,5,2,3] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[1,4,6,5,3,2] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[1,5,2,3,4,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[1,5,2,3,6,4] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[1,5,2,4,3,6] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[1,5,2,4,6,3] => [1,5,2,4,6,3] => [2,4,1,5,3,6] => [2,6,1,5,4,3] => 6
[1,5,2,6,3,4] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[1,5,2,6,4,3] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[1,5,3,2,4,6] => [1,5,2,4,6,3] => [2,4,1,5,3,6] => [2,6,1,5,4,3] => 6
[1,5,3,2,6,4] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[1,5,3,4,2,6] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[1,5,3,4,6,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[1,5,3,6,2,4] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[1,5,3,6,4,2] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[1,5,4,2,3,6] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[1,5,4,2,6,3] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[1,5,4,3,2,6] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[1,5,4,3,6,2] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[1,5,4,6,2,3] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[1,5,4,6,3,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[1,5,6,2,3,4] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[1,5,6,2,4,3] => [1,5,6,2,4,3] => [2,5,1,6,3,4] => [2,6,1,5,4,3] => 6
[1,5,6,3,2,4] => [1,5,6,2,4,3] => [2,5,1,6,3,4] => [2,6,1,5,4,3] => 6
[1,5,6,3,4,2] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[1,5,6,4,2,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[1,5,6,4,3,2] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[1,6,2,3,4,5] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[1,6,2,3,5,4] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[1,6,2,4,3,5] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[1,6,2,4,5,3] => [1,6,2,4,5,3] => [2,4,1,5,6,3] => [2,6,1,5,4,3] => 6
[1,6,2,5,3,4] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[1,6,2,5,4,3] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[1,6,3,2,4,5] => [1,6,2,4,5,3] => [2,4,1,5,6,3] => [2,6,1,5,4,3] => 6
[1,6,3,2,5,4] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[1,6,3,4,2,5] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[1,6,3,4,5,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[1,6,3,5,2,4] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[1,6,3,5,4,2] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[1,6,4,2,3,5] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[1,6,4,2,5,3] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[1,6,4,3,2,5] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[1,6,4,3,5,2] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[1,6,4,5,2,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[1,6,4,5,3,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[1,6,5,2,3,4] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[1,6,5,2,4,3] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[1,6,5,3,2,4] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[1,6,5,3,4,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[1,6,5,4,2,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[1,6,5,4,3,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[2,1,3,4,5,6] => [1,3,4,5,6,2] => [2,1,3,4,5,6] => [2,1,6,5,4,3] => 6
[2,1,3,4,6,5] => [1,3,4,6,2,5] => [2,6,3,4,1,5] => [2,6,5,4,1,3] => 6
[2,1,3,5,4,6] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[2,1,3,5,6,4] => [1,3,5,6,2,4] => [2,6,3,1,4,5] => [2,6,5,1,4,3] => 5
[2,1,3,6,4,5] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[2,1,3,6,5,4] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[2,1,4,3,5,6] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[2,1,4,3,6,5] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[2,1,4,5,3,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[2,1,4,5,6,3] => [1,4,5,6,2,3] => [2,6,1,3,4,5] => [2,6,1,5,4,3] => 6
[2,1,4,6,3,5] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[2,1,4,6,5,3] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[2,1,5,3,4,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[2,1,5,3,6,4] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[2,1,5,4,3,6] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[2,1,5,4,6,3] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[2,1,5,6,3,4] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[2,1,5,6,4,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[2,1,6,3,4,5] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[2,1,6,3,5,4] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[2,1,6,4,3,5] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[2,1,6,4,5,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[2,1,6,5,3,4] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[2,1,6,5,4,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[2,3,1,4,5,6] => [1,4,5,6,2,3] => [2,6,1,3,4,5] => [2,6,1,5,4,3] => 6
[2,3,1,4,6,5] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[2,3,1,5,4,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[2,3,1,5,6,4] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[2,3,1,6,4,5] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[2,3,1,6,5,4] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[2,3,4,1,5,6] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[2,3,4,1,6,5] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[2,3,4,5,1,6] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[2,3,4,6,1,5] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[2,3,4,6,5,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[2,3,5,1,4,6] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[2,3,5,1,6,4] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[2,3,5,4,1,6] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[2,3,5,4,6,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[2,3,5,6,1,4] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[2,3,5,6,4,1] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 5
[2,3,6,1,4,5] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[2,3,6,1,5,4] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[2,3,6,4,1,5] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[2,3,6,4,5,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[2,3,6,5,1,4] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[2,3,6,5,4,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[2,4,1,3,5,6] => [1,3,5,6,2,4] => [2,6,3,1,4,5] => [2,6,5,1,4,3] => 5
[2,4,1,3,6,5] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[2,4,1,5,3,6] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[2,4,1,5,6,3] => [1,5,6,2,4,3] => [2,5,1,6,3,4] => [2,6,1,5,4,3] => 6
[2,4,1,6,3,5] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[2,4,1,6,5,3] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[2,4,3,1,5,6] => [1,5,6,2,4,3] => [2,5,1,6,3,4] => [2,6,1,5,4,3] => 6
[2,4,3,1,6,5] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[2,4,3,5,1,6] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[2,4,3,5,6,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[2,4,3,6,1,5] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[2,4,3,6,5,1] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [2,6,5,4,1,3] => 6
[2,4,5,1,3,6] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[2,4,5,1,6,3] => [1,6,2,4,5,3] => [2,4,1,5,6,3] => [2,6,1,5,4,3] => 6
[2,4,5,3,1,6] => [1,6,2,4,5,3] => [2,4,1,5,6,3] => [2,6,1,5,4,3] => 6
[2,4,5,3,6,1] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [2,6,5,4,3,1] => 7
[2,4,5,6,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[2,4,5,6,3,1] => [1,2,4,5,6,3] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 6
[2,4,6,1,3,5] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[2,4,6,1,5,3] => [1,5,2,4,6,3] => [2,4,1,5,3,6] => [2,6,1,5,4,3] => 6
[2,4,6,3,1,5] => [1,5,2,4,6,3] => [2,4,1,5,3,6] => [2,6,1,5,4,3] => 6
[2,4,6,3,5,1] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[2,4,6,5,1,3] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [2,6,5,4,1,3] => 6
[2,4,6,5,3,1] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[2,5,1,3,4,6] => [1,3,4,6,2,5] => [2,6,3,4,1,5] => [2,6,5,4,1,3] => 6
[2,5,1,3,6,4] => [1,3,6,2,5,4] => [2,5,3,1,6,4] => [2,6,5,1,4,3] => 5
[2,5,1,4,3,6] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[2,5,1,4,6,3] => [1,4,6,2,5,3] => [2,5,1,3,6,4] => [2,6,1,5,4,3] => 6
[2,5,1,6,3,4] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[2,5,1,6,4,3] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[2,5,3,1,4,6] => [1,4,6,2,5,3] => [2,5,1,3,6,4] => [2,6,1,5,4,3] => 6
[2,5,3,1,6,4] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[2,5,3,4,1,6] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[2,5,3,4,6,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[2,5,3,6,1,4] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[2,5,3,6,4,1] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[2,5,4,1,3,6] => [1,3,6,2,5,4] => [2,5,3,1,6,4] => [2,6,5,1,4,3] => 5
[2,5,4,1,6,3] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[2,5,4,3,1,6] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[2,5,4,3,6,1] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[2,5,4,6,1,3] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [2,6,5,4,3,1] => 7
[2,5,4,6,3,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[2,5,6,1,3,4] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [2,6,5,4,3,1] => 7
[2,5,6,1,4,3] => [1,4,2,5,6,3] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 6
[2,5,6,3,1,4] => [1,4,2,5,6,3] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 6
[2,5,6,3,4,1] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[2,5,6,4,1,3] => [1,3,2,5,6,4] => [2,4,3,1,5,6] => [2,6,5,1,4,3] => 5
[2,5,6,4,3,1] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[2,6,1,3,4,5] => [1,3,4,5,2,6] => [2,6,3,4,5,1] => [2,6,5,4,3,1] => 7
[2,6,1,3,5,4] => [1,3,5,2,6,4] => [2,5,3,1,4,6] => [2,6,5,1,4,3] => 5
[2,6,1,4,3,5] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[2,6,1,4,5,3] => [1,4,5,2,6,3] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 6
[2,6,1,5,3,4] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[2,6,1,5,4,3] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[2,6,3,1,4,5] => [1,4,5,2,6,3] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 6
[2,6,3,1,5,4] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[2,6,3,4,1,5] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[2,6,3,4,5,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[2,6,3,5,1,4] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[2,6,3,5,4,1] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[2,6,4,1,3,5] => [1,3,5,2,6,4] => [2,5,3,1,4,6] => [2,6,5,1,4,3] => 5
[2,6,4,1,5,3] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[2,6,4,3,1,5] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[2,6,4,3,5,1] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[2,6,4,5,1,3] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[2,6,4,5,3,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[2,6,5,1,3,4] => [1,3,4,2,6,5] => [2,5,3,4,1,6] => [2,6,5,4,1,3] => 6
[2,6,5,1,4,3] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[2,6,5,3,1,4] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[2,6,5,3,4,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[2,6,5,4,1,3] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[2,6,5,4,3,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[3,1,2,4,5,6] => [1,2,4,5,6,3] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 6
[3,1,2,4,6,5] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[3,1,2,5,4,6] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[3,1,2,5,6,4] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[3,1,2,6,4,5] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[3,1,2,6,5,4] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[3,1,4,2,5,6] => [1,4,2,5,6,3] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 6
[3,1,4,2,6,5] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[3,1,4,5,2,6] => [1,4,5,2,6,3] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 6
[3,1,4,5,6,2] => [1,4,5,6,2,3] => [2,6,1,3,4,5] => [2,6,1,5,4,3] => 6
[3,1,4,6,2,5] => [1,4,6,2,5,3] => [2,5,1,3,6,4] => [2,6,1,5,4,3] => 6
[3,1,4,6,5,2] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[3,1,5,2,4,6] => [1,5,2,4,6,3] => [2,4,1,5,3,6] => [2,6,1,5,4,3] => 6
[3,1,5,2,6,4] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[3,1,5,4,2,6] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[3,1,5,4,6,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[3,1,5,6,2,4] => [1,5,6,2,4,3] => [2,5,1,6,3,4] => [2,6,1,5,4,3] => 6
[3,1,5,6,4,2] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[3,1,6,2,4,5] => [1,6,2,4,5,3] => [2,4,1,5,6,3] => [2,6,1,5,4,3] => 6
[3,1,6,2,5,4] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[3,1,6,4,2,5] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[3,1,6,4,5,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[3,1,6,5,2,4] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[3,1,6,5,4,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[3,2,1,4,5,6] => [1,4,5,6,2,3] => [2,6,1,3,4,5] => [2,6,1,5,4,3] => 6
[3,2,1,4,6,5] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[3,2,1,5,4,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[3,2,1,5,6,4] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[3,2,1,6,4,5] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[3,2,1,6,5,4] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[3,2,4,1,5,6] => [1,5,6,2,4,3] => [2,5,1,6,3,4] => [2,6,1,5,4,3] => 6
[3,2,4,1,6,5] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[3,2,4,5,1,6] => [1,6,2,4,5,3] => [2,4,1,5,6,3] => [2,6,1,5,4,3] => 6
[3,2,4,5,6,1] => [1,2,4,5,6,3] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 6
[3,2,4,6,1,5] => [1,5,2,4,6,3] => [2,4,1,5,3,6] => [2,6,1,5,4,3] => 6
[3,2,4,6,5,1] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[3,2,5,1,4,6] => [1,4,6,2,5,3] => [2,5,1,3,6,4] => [2,6,1,5,4,3] => 6
[3,2,5,1,6,4] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[3,2,5,4,1,6] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[3,2,5,4,6,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[3,2,5,6,1,4] => [1,4,2,5,6,3] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 6
[3,2,5,6,4,1] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[3,2,6,1,4,5] => [1,4,5,2,6,3] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 6
[3,2,6,1,5,4] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[3,2,6,4,1,5] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[3,2,6,4,5,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[3,2,6,5,1,4] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[3,2,6,5,4,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[3,4,1,2,5,6] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[3,4,1,2,6,5] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[3,4,1,5,2,6] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[3,4,1,5,6,2] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[3,4,1,6,2,5] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[3,4,1,6,5,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[3,4,2,1,5,6] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[3,4,2,1,6,5] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[3,4,2,5,1,6] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[3,4,2,5,6,1] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[3,4,2,6,1,5] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[3,4,2,6,5,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[3,4,5,1,2,6] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[3,4,5,1,6,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[3,4,5,2,1,6] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[3,4,5,2,6,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[3,4,5,6,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[3,4,5,6,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[3,4,6,1,2,5] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[3,4,6,1,5,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[3,4,6,2,1,5] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[3,4,6,2,5,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[3,4,6,5,1,2] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[3,4,6,5,2,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[3,5,1,2,4,6] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[3,5,1,2,6,4] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[3,5,1,4,2,6] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[3,5,1,4,6,2] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[3,5,1,6,2,4] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[3,5,1,6,4,2] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[3,5,2,1,4,6] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[3,5,2,1,6,4] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[3,5,2,4,1,6] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[3,5,2,4,6,1] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[3,5,2,6,1,4] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[3,5,2,6,4,1] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[3,5,4,1,2,6] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[3,5,4,1,6,2] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[3,5,4,2,1,6] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[3,5,4,2,6,1] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[3,5,4,6,1,2] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[3,5,4,6,2,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[3,5,6,1,2,4] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[3,5,6,1,4,2] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[3,5,6,2,1,4] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[3,5,6,2,4,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[3,5,6,4,1,2] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 5
[3,5,6,4,2,1] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 5
[3,6,1,2,4,5] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [2,6,5,4,3,1] => 7
[3,6,1,2,5,4] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[3,6,1,4,2,5] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[3,6,1,4,5,2] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[3,6,1,5,2,4] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[3,6,1,5,4,2] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[3,6,2,1,4,5] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[3,6,2,1,5,4] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[3,6,2,4,1,5] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[3,6,2,4,5,1] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [2,6,5,4,3,1] => 7
[3,6,2,5,1,4] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[3,6,2,5,4,1] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[3,6,4,1,2,5] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[3,6,4,1,5,2] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[3,6,4,2,1,5] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[3,6,4,2,5,1] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[3,6,4,5,1,2] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[3,6,4,5,2,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[3,6,5,1,2,4] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [2,6,5,4,1,3] => 6
[3,6,5,1,4,2] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[3,6,5,2,1,4] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[3,6,5,2,4,1] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [2,6,5,4,1,3] => 6
[3,6,5,4,1,2] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[3,6,5,4,2,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[4,1,2,3,5,6] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 5
[4,1,2,3,6,5] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[4,1,2,5,3,6] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[4,1,2,5,6,3] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[4,1,2,6,3,5] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[4,1,2,6,5,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[4,1,3,2,5,6] => [1,3,2,5,6,4] => [2,4,3,1,5,6] => [2,6,5,1,4,3] => 5
[4,1,3,2,6,5] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[4,1,3,5,2,6] => [1,3,5,2,6,4] => [2,5,3,1,4,6] => [2,6,5,1,4,3] => 5
[4,1,3,5,6,2] => [1,3,5,6,2,4] => [2,6,3,1,4,5] => [2,6,5,1,4,3] => 5
[4,1,3,6,2,5] => [1,3,6,2,5,4] => [2,5,3,1,6,4] => [2,6,5,1,4,3] => 5
[4,1,3,6,5,2] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[4,1,5,2,3,6] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[4,1,5,2,6,3] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[4,1,5,3,2,6] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[4,1,5,3,6,2] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[4,1,5,6,2,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[4,1,5,6,3,2] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[4,1,6,2,3,5] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[4,1,6,2,5,3] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[4,1,6,3,2,5] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[4,1,6,3,5,2] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[4,1,6,5,2,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,1,6,5,3,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,2,1,3,5,6] => [1,3,5,6,2,4] => [2,6,3,1,4,5] => [2,6,5,1,4,3] => 5
[4,2,1,3,6,5] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[4,2,1,5,3,6] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[4,2,1,5,6,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[4,2,1,6,3,5] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[4,2,1,6,5,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,2,3,1,5,6] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[4,2,3,1,6,5] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,2,3,5,1,6] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[4,2,3,5,6,1] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 5
[4,2,3,6,1,5] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[4,2,3,6,5,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[4,2,5,1,3,6] => [1,3,6,2,5,4] => [2,5,3,1,6,4] => [2,6,5,1,4,3] => 5
[4,2,5,1,6,3] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[4,2,5,3,1,6] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[4,2,5,3,6,1] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[4,2,5,6,1,3] => [1,3,2,5,6,4] => [2,4,3,1,5,6] => [2,6,5,1,4,3] => 5
[4,2,5,6,3,1] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[4,2,6,1,3,5] => [1,3,5,2,6,4] => [2,5,3,1,4,6] => [2,6,5,1,4,3] => 5
[4,2,6,1,5,3] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[4,2,6,3,1,5] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[4,2,6,3,5,1] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[4,2,6,5,1,3] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[4,2,6,5,3,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[4,3,1,2,5,6] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[4,3,1,2,6,5] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[4,3,1,5,2,6] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[4,3,1,5,6,2] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[4,3,1,6,2,5] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[4,3,1,6,5,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,3,2,1,5,6] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 5
[4,3,2,1,6,5] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,3,2,5,1,6] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 5
[4,3,2,5,6,1] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 5
[4,3,2,6,1,5] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 5
[4,3,2,6,5,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[4,3,5,1,2,6] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[4,3,5,1,6,2] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[4,3,5,2,1,6] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 5
[4,3,5,2,6,1] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 5
[4,3,5,6,1,2] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 5
[4,3,5,6,2,1] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 5
[4,3,6,1,2,5] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[4,3,6,1,5,2] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[4,3,6,2,1,5] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 5
[4,3,6,2,5,1] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 5
[4,3,6,5,1,2] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[4,3,6,5,2,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[4,5,1,2,3,6] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[4,5,1,2,6,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[4,5,1,3,2,6] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[4,5,1,3,6,2] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[4,5,1,6,2,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,5,1,6,3,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,5,2,1,3,6] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[4,5,2,1,6,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,5,2,3,1,6] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,5,2,3,6,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[4,5,2,6,1,3] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[4,5,2,6,3,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[4,5,3,1,2,6] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[4,5,3,1,6,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,5,3,2,1,6] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[4,5,3,2,6,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[4,5,3,6,1,2] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[4,5,3,6,2,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[4,5,6,1,2,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[4,5,6,1,3,2] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[4,5,6,2,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[4,5,6,2,3,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[4,5,6,3,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[4,5,6,3,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[4,6,1,2,3,5] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[4,6,1,2,5,3] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[4,6,1,3,2,5] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [2,6,5,4,3,1] => 7
[4,6,1,3,5,2] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[4,6,1,5,2,3] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[4,6,1,5,3,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[4,6,2,1,3,5] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[4,6,2,1,5,3] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[4,6,2,3,1,5] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[4,6,2,3,5,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[4,6,2,5,1,3] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [2,6,5,4,3,1] => 7
[4,6,2,5,3,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[4,6,3,1,2,5] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[4,6,3,1,5,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[4,6,3,2,1,5] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[4,6,3,2,5,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[4,6,3,5,1,2] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[4,6,3,5,2,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[4,6,5,1,2,3] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[4,6,5,1,3,2] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [2,6,5,4,1,3] => 6
[4,6,5,2,1,3] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [2,6,5,4,1,3] => 6
[4,6,5,2,3,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[4,6,5,3,1,2] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[4,6,5,3,2,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[5,1,2,3,4,6] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[5,1,2,3,6,4] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[5,1,2,4,3,6] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [2,6,5,4,1,3] => 6
[5,1,2,4,6,3] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[5,1,2,6,3,4] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,1,2,6,4,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,1,3,2,4,6] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [2,6,5,4,1,3] => 6
[5,1,3,2,6,4] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[5,1,3,4,2,6] => [1,3,4,2,6,5] => [2,5,3,4,1,6] => [2,6,5,4,1,3] => 6
[5,1,3,4,6,2] => [1,3,4,6,2,5] => [2,6,3,4,1,5] => [2,6,5,4,1,3] => 6
[5,1,3,6,2,4] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[5,1,3,6,4,2] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[5,1,4,2,3,6] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[5,1,4,2,6,3] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[5,1,4,3,2,6] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[5,1,4,3,6,2] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[5,1,4,6,2,3] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[5,1,4,6,3,2] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[5,1,6,2,3,4] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,1,6,2,4,3] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[5,1,6,3,2,4] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[5,1,6,3,4,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,1,6,4,2,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,1,6,4,3,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,2,1,3,4,6] => [1,3,4,6,2,5] => [2,6,3,4,1,5] => [2,6,5,4,1,3] => 6
[5,2,1,3,6,4] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[5,2,1,4,3,6] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[5,2,1,4,6,3] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[5,2,1,6,3,4] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,2,1,6,4,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,2,3,1,4,6] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[5,2,3,1,6,4] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,2,3,4,1,6] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,2,3,4,6,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[5,2,3,6,1,4] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[5,2,3,6,4,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[5,2,4,1,3,6] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[5,2,4,1,6,3] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[5,2,4,3,1,6] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[5,2,4,3,6,1] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [2,6,5,4,1,3] => 6
[5,2,4,6,1,3] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [2,6,5,4,1,3] => 6
[5,2,4,6,3,1] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[5,2,6,1,3,4] => [1,3,4,2,6,5] => [2,5,3,4,1,6] => [2,6,5,4,1,3] => 6
[5,2,6,1,4,3] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[5,2,6,3,1,4] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[5,2,6,3,4,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,2,6,4,1,3] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[5,2,6,4,3,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,3,1,2,4,6] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[5,3,1,2,6,4] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,3,1,4,2,6] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[5,3,1,4,6,2] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[5,3,1,6,2,4] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[5,3,1,6,4,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,3,2,1,4,6] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [2,6,5,4,1,3] => 6
[5,3,2,1,6,4] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,3,2,4,1,6] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [2,6,5,4,1,3] => 6
[5,3,2,4,6,1] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [2,6,5,4,1,3] => 6
[5,3,2,6,1,4] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [2,6,5,4,1,3] => 6
[5,3,2,6,4,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,3,4,1,2,6] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,3,4,1,6,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,3,4,2,1,6] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,3,4,2,6,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,3,4,6,1,2] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[5,3,4,6,2,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[5,3,6,1,2,4] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [2,6,5,4,1,3] => 6
[5,3,6,1,4,2] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[5,3,6,2,1,4] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 6
[5,3,6,2,4,1] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [2,6,5,4,1,3] => 6
[5,3,6,4,1,2] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[5,3,6,4,2,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[5,4,1,2,3,6] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[5,4,1,2,6,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,4,1,3,2,6] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[5,4,1,3,6,2] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[5,4,1,6,2,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,4,1,6,3,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,4,2,1,3,6] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [2,6,5,4,1,3] => 6
[5,4,2,1,6,3] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,4,2,3,1,6] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,4,2,3,6,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[5,4,2,6,1,3] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [2,6,5,4,1,3] => 6
[5,4,2,6,3,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,4,3,1,2,6] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,4,3,1,6,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,4,3,2,1,6] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 6
[5,4,3,2,6,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 6
[5,4,3,6,1,2] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[5,4,3,6,2,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 6
[5,4,6,1,2,3] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[5,4,6,1,3,2] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [2,6,5,4,1,3] => 6
[5,4,6,2,1,3] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [2,6,5,4,1,3] => 6
[5,4,6,2,3,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[5,4,6,3,1,2] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[5,4,6,3,2,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 6
[5,6,1,2,3,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,1,2,4,3] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[5,6,1,3,2,4] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,1,3,4,2] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [2,6,5,4,3,1] => 7
[5,6,1,4,2,3] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[5,6,1,4,3,2] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[5,6,2,1,3,4] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [2,6,5,4,3,1] => 7
[5,6,2,1,4,3] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[5,6,2,3,1,4] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[5,6,2,3,4,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,2,4,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,2,4,3,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[5,6,3,1,2,4] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[5,6,3,1,4,2] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[5,6,3,2,1,4] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[5,6,3,2,4,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[5,6,3,4,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,3,4,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,4,1,2,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,4,1,3,2] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,4,2,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,4,2,3,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,4,3,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[5,6,4,3,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,1,2,3,4,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,1,2,3,5,4] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[6,1,2,4,3,5] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[6,1,2,4,5,3] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [2,6,5,4,3,1] => 7
[6,1,2,5,3,4] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,1,2,5,4,3] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,1,3,2,4,5] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[6,1,3,2,5,4] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [2,6,5,4,3,1] => 7
[6,1,3,4,2,5] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [2,6,5,4,3,1] => 7
[6,1,3,4,5,2] => [1,3,4,5,2,6] => [2,6,3,4,5,1] => [2,6,5,4,3,1] => 7
[6,1,3,5,2,4] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[6,1,3,5,4,2] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[6,1,4,2,3,5] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,1,4,2,5,3] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[6,1,4,3,2,5] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[6,1,4,3,5,2] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,1,4,5,2,3] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[6,1,4,5,3,2] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[6,1,5,2,3,4] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,1,5,2,4,3] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[6,1,5,3,2,4] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[6,1,5,3,4,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,1,5,4,2,3] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,1,5,4,3,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,2,1,3,4,5] => [1,3,4,5,2,6] => [2,6,3,4,5,1] => [2,6,5,4,3,1] => 7
[6,2,1,3,5,4] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[6,2,1,4,3,5] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,2,1,4,5,3] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[6,2,1,5,3,4] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,2,1,5,4,3] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,2,3,1,4,5] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[6,2,3,1,5,4] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,2,3,4,1,5] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,2,3,4,5,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,2,3,5,1,4] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,2,3,5,4,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[6,2,4,1,3,5] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[6,2,4,1,5,3] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[6,2,4,3,1,5] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[6,2,4,3,5,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[6,2,4,5,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[6,2,4,5,3,1] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [2,6,5,4,3,1] => 7
[6,2,5,1,3,4] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [2,6,5,4,3,1] => 7
[6,2,5,1,4,3] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[6,2,5,3,1,4] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[6,2,5,3,4,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,2,5,4,1,3] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [2,6,5,4,3,1] => 7
[6,2,5,4,3,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,3,1,2,4,5] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [2,6,5,4,3,1] => 7
[6,3,1,2,5,4] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,3,1,4,2,5] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[6,3,1,4,5,2] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[6,3,1,5,2,4] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[6,3,1,5,4,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,3,2,1,4,5] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 7
[6,3,2,1,5,4] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,3,2,4,1,5] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 7
[6,3,2,4,5,1] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [2,6,5,4,3,1] => 7
[6,3,2,5,1,4] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [2,6,5,4,3,1] => 7
[6,3,2,5,4,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,3,4,1,2,5] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,3,4,1,5,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,3,4,2,1,5] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,3,4,2,5,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,3,4,5,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,3,4,5,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,3,5,1,2,4] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[6,3,5,1,4,2] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,3,5,2,1,4] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,3,5,2,4,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[6,3,5,4,1,2] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[6,3,5,4,2,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[6,4,1,2,3,5] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[6,4,1,2,5,3] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,4,1,3,2,5] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [2,6,5,4,3,1] => 7
[6,4,1,3,5,2] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[6,4,1,5,2,3] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,4,1,5,3,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,4,2,1,3,5] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [2,6,5,4,3,1] => 7
[6,4,2,1,5,3] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,4,2,3,1,5] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,4,2,3,5,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[6,4,2,5,1,3] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [2,6,5,4,3,1] => 7
[6,4,2,5,3,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,4,3,1,2,5] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,4,3,1,5,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,4,3,2,1,5] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 7
[6,4,3,2,5,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 7
[6,4,3,5,1,2] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[6,4,3,5,2,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 7
[6,4,5,1,2,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,4,5,1,3,2] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[6,4,5,2,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[6,4,5,2,3,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,4,5,3,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,4,5,3,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,1,2,3,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,1,2,4,3] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[6,5,1,3,2,4] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,1,3,4,2] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [2,6,5,4,3,1] => 7
[6,5,1,4,2,3] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,5,1,4,3,2] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,5,2,1,3,4] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [2,6,5,4,3,1] => 7
[6,5,2,1,4,3] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,5,2,3,1,4] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,5,2,3,4,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,2,4,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,2,4,3,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[6,5,3,1,2,4] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[6,5,3,1,4,2] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,5,3,2,1,4] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 7
[6,5,3,2,4,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 7
[6,5,3,4,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,3,4,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,4,1,2,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,4,1,3,2] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,4,2,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,4,2,3,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,4,3,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
[6,5,4,3,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 7
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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:
2,4 2,22 72,48 168,312,240
F2=2 q
F3=2 q+4 q2
F4=2 q2+22 q3
F5=72 q4+48 q5
F6=168 q5+312 q6+240 q7
Description
The number of inversions of distance at most 2 of a permutation.
An inversion of a permutation π is a pair i<j such that σ(i)>σ(j). Let j−i be the distance of such an inversion. Then inversions of distance at most 1 are then exactly the descents of π, see St000021The number of descents of a permutation.. This statistic counts the number of inversions of distance at most 2.
An inversion of a permutation π is a pair i<j such that σ(i)>σ(j). Let j−i be the distance of such an inversion. Then inversions of distance at most 1 are then exactly the descents of π, see St000021The number of descents of a permutation.. This statistic counts the number of inversions of distance at most 2.
Map
Kreweras complement
Description
Sends the permutation π∈Sn to the permutation π−1c where c=(1,…,n) is the long cycle.
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.
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