Identifier
-
Mp00223:
Permutations
—runsort⟶
Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
St001077: Permutations ⟶ ℤ
Values
[1,2] => [1,2] => [2,1] => [1,2] => 0
[2,1] => [1,2] => [2,1] => [1,2] => 0
[1,2,3] => [1,2,3] => [2,3,1] => [3,1,2] => 2
[1,3,2] => [1,3,2] => [2,1,3] => [3,2,1] => 1
[2,1,3] => [1,3,2] => [2,1,3] => [3,2,1] => 1
[2,3,1] => [1,2,3] => [2,3,1] => [3,1,2] => 2
[3,1,2] => [1,2,3] => [2,3,1] => [3,1,2] => 2
[3,2,1] => [1,2,3] => [2,3,1] => [3,1,2] => 2
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [3,4,1,2] => 4
[1,2,4,3] => [1,2,4,3] => [2,3,1,4] => [3,4,2,1] => 3
[1,3,2,4] => [1,3,2,4] => [2,4,3,1] => [3,1,2,4] => 2
[1,3,4,2] => [1,3,4,2] => [2,4,1,3] => [3,1,4,2] => 3
[1,4,2,3] => [1,4,2,3] => [2,1,4,3] => [3,2,1,4] => 1
[1,4,3,2] => [1,4,2,3] => [2,1,4,3] => [3,2,1,4] => 1
[2,1,3,4] => [1,3,4,2] => [2,4,1,3] => [3,1,4,2] => 3
[2,1,4,3] => [1,4,2,3] => [2,1,4,3] => [3,2,1,4] => 1
[2,3,1,4] => [1,4,2,3] => [2,1,4,3] => [3,2,1,4] => 1
[2,3,4,1] => [1,2,3,4] => [2,3,4,1] => [3,4,1,2] => 4
[2,4,1,3] => [1,3,2,4] => [2,4,3,1] => [3,1,2,4] => 2
[2,4,3,1] => [1,2,4,3] => [2,3,1,4] => [3,4,2,1] => 3
[3,1,2,4] => [1,2,4,3] => [2,3,1,4] => [3,4,2,1] => 3
[3,1,4,2] => [1,4,2,3] => [2,1,4,3] => [3,2,1,4] => 1
[3,2,1,4] => [1,4,2,3] => [2,1,4,3] => [3,2,1,4] => 1
[3,2,4,1] => [1,2,4,3] => [2,3,1,4] => [3,4,2,1] => 3
[3,4,1,2] => [1,2,3,4] => [2,3,4,1] => [3,4,1,2] => 4
[3,4,2,1] => [1,2,3,4] => [2,3,4,1] => [3,4,1,2] => 4
[4,1,2,3] => [1,2,3,4] => [2,3,4,1] => [3,4,1,2] => 4
[4,1,3,2] => [1,3,2,4] => [2,4,3,1] => [3,1,2,4] => 2
[4,2,1,3] => [1,3,2,4] => [2,4,3,1] => [3,1,2,4] => 2
[4,2,3,1] => [1,2,3,4] => [2,3,4,1] => [3,4,1,2] => 4
[4,3,1,2] => [1,2,3,4] => [2,3,4,1] => [3,4,1,2] => 4
[4,3,2,1] => [1,2,3,4] => [2,3,4,1] => [3,4,1,2] => 4
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [3,4,5,2,1] => 5
[1,2,4,3,5] => [1,2,4,3,5] => [2,3,5,4,1] => [3,4,1,2,5] => 4
[1,2,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => [3,4,1,5,2] => 5
[1,2,5,3,4] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[1,2,5,4,3] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[1,3,2,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => [3,5,4,1,2] => 5
[1,3,2,5,4] => [1,3,2,5,4] => [2,4,3,1,5] => [3,5,4,2,1] => 4
[1,3,4,2,5] => [1,3,4,2,5] => [2,4,5,3,1] => [3,5,1,2,4] => 5
[1,3,4,5,2] => [1,3,4,5,2] => [2,4,5,1,3] => [3,5,1,4,2] => 4
[1,3,5,2,4] => [1,3,5,2,4] => [2,4,1,5,3] => [3,5,2,1,4] => 4
[1,3,5,4,2] => [1,3,5,2,4] => [2,4,1,5,3] => [3,5,2,1,4] => 4
[1,4,2,3,5] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[1,4,2,5,3] => [1,4,2,5,3] => [2,5,3,1,4] => [3,1,5,4,2] => 3
[1,4,3,2,5] => [1,4,2,5,3] => [2,5,3,1,4] => [3,1,5,4,2] => 3
[1,4,3,5,2] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[1,4,5,2,3] => [1,4,5,2,3] => [2,5,1,4,3] => [3,1,4,2,5] => 3
[1,4,5,3,2] => [1,4,5,2,3] => [2,5,1,4,3] => [3,1,4,2,5] => 3
[1,5,2,3,4] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[1,5,2,4,3] => [1,5,2,4,3] => [2,1,4,3,5] => [3,2,5,4,1] => 2
[1,5,3,2,4] => [1,5,2,4,3] => [2,1,4,3,5] => [3,2,5,4,1] => 2
[1,5,3,4,2] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[1,5,4,2,3] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[1,5,4,3,2] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[2,1,3,4,5] => [1,3,4,5,2] => [2,4,5,1,3] => [3,5,1,4,2] => 4
[2,1,3,5,4] => [1,3,5,2,4] => [2,4,1,5,3] => [3,5,2,1,4] => 4
[2,1,4,3,5] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[2,1,4,5,3] => [1,4,5,2,3] => [2,5,1,4,3] => [3,1,4,2,5] => 3
[2,1,5,3,4] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[2,1,5,4,3] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[2,3,1,4,5] => [1,4,5,2,3] => [2,5,1,4,3] => [3,1,4,2,5] => 3
[2,3,1,5,4] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[2,3,4,1,5] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[2,3,4,5,1] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[2,3,5,1,4] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[2,3,5,4,1] => [1,2,3,5,4] => [2,3,4,1,5] => [3,4,5,2,1] => 5
[2,4,1,3,5] => [1,3,5,2,4] => [2,4,1,5,3] => [3,5,2,1,4] => 4
[2,4,1,5,3] => [1,5,2,4,3] => [2,1,4,3,5] => [3,2,5,4,1] => 2
[2,4,3,1,5] => [1,5,2,4,3] => [2,1,4,3,5] => [3,2,5,4,1] => 2
[2,4,3,5,1] => [1,2,4,3,5] => [2,3,5,4,1] => [3,4,1,2,5] => 4
[2,4,5,1,3] => [1,3,2,4,5] => [2,4,3,5,1] => [3,5,4,1,2] => 5
[2,4,5,3,1] => [1,2,4,5,3] => [2,3,5,1,4] => [3,4,1,5,2] => 5
[2,5,1,3,4] => [1,3,4,2,5] => [2,4,5,3,1] => [3,5,1,2,4] => 5
[2,5,1,4,3] => [1,4,2,5,3] => [2,5,3,1,4] => [3,1,5,4,2] => 3
[2,5,3,1,4] => [1,4,2,5,3] => [2,5,3,1,4] => [3,1,5,4,2] => 3
[2,5,3,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[2,5,4,1,3] => [1,3,2,5,4] => [2,4,3,1,5] => [3,5,4,2,1] => 4
[2,5,4,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[3,1,2,4,5] => [1,2,4,5,3] => [2,3,5,1,4] => [3,4,1,5,2] => 5
[3,1,2,5,4] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[3,1,4,2,5] => [1,4,2,5,3] => [2,5,3,1,4] => [3,1,5,4,2] => 3
[3,1,4,5,2] => [1,4,5,2,3] => [2,5,1,4,3] => [3,1,4,2,5] => 3
[3,1,5,2,4] => [1,5,2,4,3] => [2,1,4,3,5] => [3,2,5,4,1] => 2
[3,1,5,4,2] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[3,2,1,4,5] => [1,4,5,2,3] => [2,5,1,4,3] => [3,1,4,2,5] => 3
[3,2,1,5,4] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[3,2,4,1,5] => [1,5,2,4,3] => [2,1,4,3,5] => [3,2,5,4,1] => 2
[3,2,4,5,1] => [1,2,4,5,3] => [2,3,5,1,4] => [3,4,1,5,2] => 5
[3,2,5,1,4] => [1,4,2,5,3] => [2,5,3,1,4] => [3,1,5,4,2] => 3
[3,2,5,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[3,4,1,2,5] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[3,4,1,5,2] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[3,4,2,1,5] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[3,4,2,5,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[3,4,5,1,2] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[3,4,5,2,1] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[3,5,1,2,4] => [1,2,4,3,5] => [2,3,5,4,1] => [3,4,1,2,5] => 4
[3,5,1,4,2] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[3,5,2,1,4] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
>>> Load all 872 entries. <<<[3,5,2,4,1] => [1,2,4,3,5] => [2,3,5,4,1] => [3,4,1,2,5] => 4
[3,5,4,1,2] => [1,2,3,5,4] => [2,3,4,1,5] => [3,4,5,2,1] => 5
[3,5,4,2,1] => [1,2,3,5,4] => [2,3,4,1,5] => [3,4,5,2,1] => 5
[4,1,2,3,5] => [1,2,3,5,4] => [2,3,4,1,5] => [3,4,5,2,1] => 5
[4,1,2,5,3] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[4,1,3,2,5] => [1,3,2,5,4] => [2,4,3,1,5] => [3,5,4,2,1] => 4
[4,1,3,5,2] => [1,3,5,2,4] => [2,4,1,5,3] => [3,5,2,1,4] => 4
[4,1,5,2,3] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[4,1,5,3,2] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[4,2,1,3,5] => [1,3,5,2,4] => [2,4,1,5,3] => [3,5,2,1,4] => 4
[4,2,1,5,3] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[4,2,3,1,5] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[4,2,3,5,1] => [1,2,3,5,4] => [2,3,4,1,5] => [3,4,5,2,1] => 5
[4,2,5,1,3] => [1,3,2,5,4] => [2,4,3,1,5] => [3,5,4,2,1] => 4
[4,2,5,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[4,3,1,2,5] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[4,3,1,5,2] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[4,3,2,1,5] => [1,5,2,3,4] => [2,1,4,5,3] => [3,2,5,1,4] => 3
[4,3,2,5,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,4,2,1,5] => 3
[4,3,5,1,2] => [1,2,3,5,4] => [2,3,4,1,5] => [3,4,5,2,1] => 5
[4,3,5,2,1] => [1,2,3,5,4] => [2,3,4,1,5] => [3,4,5,2,1] => 5
[4,5,1,2,3] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[4,5,1,3,2] => [1,3,2,4,5] => [2,4,3,5,1] => [3,5,4,1,2] => 5
[4,5,2,1,3] => [1,3,2,4,5] => [2,4,3,5,1] => [3,5,4,1,2] => 5
[4,5,2,3,1] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[4,5,3,1,2] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[4,5,3,2,1] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[5,1,2,3,4] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[5,1,2,4,3] => [1,2,4,3,5] => [2,3,5,4,1] => [3,4,1,2,5] => 4
[5,1,3,2,4] => [1,3,2,4,5] => [2,4,3,5,1] => [3,5,4,1,2] => 5
[5,1,3,4,2] => [1,3,4,2,5] => [2,4,5,3,1] => [3,5,1,2,4] => 5
[5,1,4,2,3] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[5,1,4,3,2] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[5,2,1,3,4] => [1,3,4,2,5] => [2,4,5,3,1] => [3,5,1,2,4] => 5
[5,2,1,4,3] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[5,2,3,1,4] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[5,2,3,4,1] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[5,2,4,1,3] => [1,3,2,4,5] => [2,4,3,5,1] => [3,5,4,1,2] => 5
[5,2,4,3,1] => [1,2,4,3,5] => [2,3,5,4,1] => [3,4,1,2,5] => 4
[5,3,1,2,4] => [1,2,4,3,5] => [2,3,5,4,1] => [3,4,1,2,5] => 4
[5,3,1,4,2] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[5,3,2,1,4] => [1,4,2,3,5] => [2,5,3,4,1] => [3,1,5,2,4] => 4
[5,3,2,4,1] => [1,2,4,3,5] => [2,3,5,4,1] => [3,4,1,2,5] => 4
[5,3,4,1,2] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[5,3,4,2,1] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[5,4,1,2,3] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[5,4,1,3,2] => [1,3,2,4,5] => [2,4,3,5,1] => [3,5,4,1,2] => 5
[5,4,2,1,3] => [1,3,2,4,5] => [2,4,3,5,1] => [3,5,4,1,2] => 5
[5,4,2,3,1] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[5,4,3,1,2] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[5,4,3,2,1] => [1,2,3,4,5] => [2,3,4,5,1] => [3,4,5,1,2] => 4
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[1,2,3,5,6,4] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [3,4,5,1,6,2] => 5
[1,2,3,6,4,5] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[1,2,3,6,5,4] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [3,4,6,5,2,1] => 6
[1,2,4,5,3,6] => [1,2,4,5,3,6] => [2,3,5,6,4,1] => [3,4,6,1,2,5] => 5
[1,2,4,5,6,3] => [1,2,4,5,6,3] => [2,3,5,6,1,4] => [3,4,6,1,5,2] => 4
[1,2,4,6,3,5] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[1,2,4,6,5,3] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[1,2,5,3,4,6] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[1,2,5,3,6,4] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[1,2,5,4,3,6] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[1,2,5,4,6,3] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[1,2,5,6,3,4] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[1,2,5,6,4,3] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[1,2,6,3,4,5] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[1,2,6,3,5,4] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[1,2,6,4,3,5] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[1,2,6,4,5,3] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[1,2,6,5,3,4] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[1,2,6,5,4,3] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [3,5,4,6,2,1] => 6
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [3,5,4,1,2,6] => 5
[1,3,2,5,6,4] => [1,3,2,5,6,4] => [2,4,3,6,1,5] => [3,5,4,1,6,2] => 6
[1,3,2,6,4,5] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[1,3,2,6,5,4] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[1,3,4,2,5,6] => [1,3,4,2,5,6] => [2,4,5,3,6,1] => [3,5,6,4,1,2] => 4
[1,3,4,2,6,5] => [1,3,4,2,6,5] => [2,4,5,3,1,6] => [3,5,6,4,2,1] => 5
[1,3,4,5,2,6] => [1,3,4,5,2,6] => [2,4,5,6,3,1] => [3,5,6,1,2,4] => 6
[1,3,4,5,6,2] => [1,3,4,5,6,2] => [2,4,5,6,1,3] => [3,5,6,1,4,2] => 5
[1,3,4,6,2,5] => [1,3,4,6,2,5] => [2,4,5,1,6,3] => [3,5,6,2,1,4] => 5
[1,3,4,6,5,2] => [1,3,4,6,2,5] => [2,4,5,1,6,3] => [3,5,6,2,1,4] => 5
[1,3,5,2,4,6] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[1,3,5,2,6,4] => [1,3,5,2,6,4] => [2,4,6,3,1,5] => [3,5,1,6,4,2] => 6
[1,3,5,4,2,6] => [1,3,5,2,6,4] => [2,4,6,3,1,5] => [3,5,1,6,4,2] => 6
[1,3,5,4,6,2] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[1,3,5,6,2,4] => [1,3,5,6,2,4] => [2,4,6,1,5,3] => [3,5,1,4,2,6] => 4
[1,3,5,6,4,2] => [1,3,5,6,2,4] => [2,4,6,1,5,3] => [3,5,1,4,2,6] => 4
[1,3,6,2,4,5] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[1,3,6,2,5,4] => [1,3,6,2,5,4] => [2,4,1,5,3,6] => [3,5,2,6,4,1] => 5
[1,3,6,4,2,5] => [1,3,6,2,5,4] => [2,4,1,5,3,6] => [3,5,2,6,4,1] => 5
[1,3,6,4,5,2] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[1,3,6,5,2,4] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[1,3,6,5,4,2] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[1,4,2,3,5,6] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[1,4,2,3,6,5] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[1,4,2,5,3,6] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[1,4,2,5,6,3] => [1,4,2,5,6,3] => [2,5,3,6,1,4] => [3,6,4,1,5,2] => 5
[1,4,2,6,3,5] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[1,4,2,6,5,3] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[1,4,3,2,5,6] => [1,4,2,5,6,3] => [2,5,3,6,1,4] => [3,6,4,1,5,2] => 5
[1,4,3,2,6,5] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[1,4,3,5,2,6] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[1,4,3,5,6,2] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[1,4,3,6,2,5] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[1,4,3,6,5,2] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[1,4,5,2,3,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[1,4,5,2,6,3] => [1,4,5,2,6,3] => [2,5,6,3,1,4] => [3,6,1,5,4,2] => 7
[1,4,5,3,2,6] => [1,4,5,2,6,3] => [2,5,6,3,1,4] => [3,6,1,5,4,2] => 7
[1,4,5,3,6,2] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[1,4,5,6,2,3] => [1,4,5,6,2,3] => [2,5,6,1,4,3] => [3,6,1,4,2,5] => 5
[1,4,5,6,3,2] => [1,4,5,6,2,3] => [2,5,6,1,4,3] => [3,6,1,4,2,5] => 5
[1,4,6,2,3,5] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[1,4,6,2,5,3] => [1,4,6,2,5,3] => [2,5,1,4,3,6] => [3,6,2,5,4,1] => 6
[1,4,6,3,2,5] => [1,4,6,2,5,3] => [2,5,1,4,3,6] => [3,6,2,5,4,1] => 6
[1,4,6,3,5,2] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[1,4,6,5,2,3] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[1,4,6,5,3,2] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[1,5,2,3,4,6] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[1,5,2,3,6,4] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[1,5,2,4,3,6] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[1,5,2,4,6,3] => [1,5,2,4,6,3] => [2,6,3,5,1,4] => [3,1,5,2,6,4] => 5
[1,5,2,6,3,4] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[1,5,2,6,4,3] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[1,5,3,2,4,6] => [1,5,2,4,6,3] => [2,6,3,5,1,4] => [3,1,5,2,6,4] => 5
[1,5,3,2,6,4] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[1,5,3,4,2,6] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[1,5,3,4,6,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[1,5,3,6,2,4] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[1,5,3,6,4,2] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[1,5,4,2,3,6] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[1,5,4,2,6,3] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[1,5,4,3,2,6] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[1,5,4,3,6,2] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[1,5,4,6,2,3] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[1,5,4,6,3,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[1,5,6,2,3,4] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[1,5,6,2,4,3] => [1,5,6,2,4,3] => [2,6,1,4,3,5] => [3,1,4,6,5,2] => 4
[1,5,6,3,2,4] => [1,5,6,2,4,3] => [2,6,1,4,3,5] => [3,1,4,6,5,2] => 4
[1,5,6,3,4,2] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[1,5,6,4,2,3] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[1,5,6,4,3,2] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[1,6,2,3,4,5] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[1,6,2,3,5,4] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[1,6,2,4,3,5] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[1,6,2,4,5,3] => [1,6,2,4,5,3] => [2,1,4,6,3,5] => [3,2,5,1,6,4] => 4
[1,6,2,5,3,4] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[1,6,2,5,4,3] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[1,6,3,2,4,5] => [1,6,2,4,5,3] => [2,1,4,6,3,5] => [3,2,5,1,6,4] => 4
[1,6,3,2,5,4] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[1,6,3,4,2,5] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[1,6,3,4,5,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[1,6,3,5,2,4] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[1,6,3,5,4,2] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[1,6,4,2,3,5] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[1,6,4,2,5,3] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[1,6,4,3,2,5] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[1,6,4,3,5,2] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[1,6,4,5,2,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[1,6,4,5,3,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[1,6,5,2,3,4] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[1,6,5,2,4,3] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[1,6,5,3,2,4] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[1,6,5,3,4,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[1,6,5,4,2,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[1,6,5,4,3,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[2,1,3,4,5,6] => [1,3,4,5,6,2] => [2,4,5,6,1,3] => [3,5,6,1,4,2] => 5
[2,1,3,4,6,5] => [1,3,4,6,2,5] => [2,4,5,1,6,3] => [3,5,6,2,1,4] => 5
[2,1,3,5,4,6] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[2,1,3,5,6,4] => [1,3,5,6,2,4] => [2,4,6,1,5,3] => [3,5,1,4,2,6] => 4
[2,1,3,6,4,5] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[2,1,3,6,5,4] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[2,1,4,3,5,6] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[2,1,4,3,6,5] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[2,1,4,5,3,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[2,1,4,5,6,3] => [1,4,5,6,2,3] => [2,5,6,1,4,3] => [3,6,1,4,2,5] => 5
[2,1,4,6,3,5] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[2,1,4,6,5,3] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[2,1,5,3,4,6] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[2,1,5,3,6,4] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[2,1,5,4,3,6] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[2,1,5,4,6,3] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[2,1,5,6,3,4] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[2,1,5,6,4,3] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[2,1,6,3,4,5] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[2,1,6,3,5,4] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[2,1,6,4,3,5] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[2,1,6,4,5,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[2,1,6,5,3,4] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[2,1,6,5,4,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[2,3,1,4,5,6] => [1,4,5,6,2,3] => [2,5,6,1,4,3] => [3,6,1,4,2,5] => 5
[2,3,1,4,6,5] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[2,3,1,5,4,6] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[2,3,1,5,6,4] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[2,3,1,6,4,5] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[2,3,1,6,5,4] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[2,3,4,1,5,6] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[2,3,4,1,6,5] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[2,3,4,5,1,6] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[2,3,4,6,1,5] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[2,3,4,6,5,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[2,3,5,1,4,6] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[2,3,5,1,6,4] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[2,3,5,4,1,6] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[2,3,5,4,6,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[2,3,5,6,1,4] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[2,3,5,6,4,1] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [3,4,5,1,6,2] => 5
[2,3,6,1,4,5] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[2,3,6,1,5,4] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[2,3,6,4,1,5] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[2,3,6,4,5,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[2,3,6,5,1,4] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[2,3,6,5,4,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[2,4,1,3,5,6] => [1,3,5,6,2,4] => [2,4,6,1,5,3] => [3,5,1,4,2,6] => 4
[2,4,1,3,6,5] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[2,4,1,5,3,6] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[2,4,1,5,6,3] => [1,5,6,2,4,3] => [2,6,1,4,3,5] => [3,1,4,6,5,2] => 4
[2,4,1,6,3,5] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[2,4,1,6,5,3] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[2,4,3,1,5,6] => [1,5,6,2,4,3] => [2,6,1,4,3,5] => [3,1,4,6,5,2] => 4
[2,4,3,1,6,5] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[2,4,3,5,1,6] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[2,4,3,5,6,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[2,4,3,6,1,5] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[2,4,3,6,5,1] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [3,4,6,5,2,1] => 6
[2,4,5,1,3,6] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[2,4,5,1,6,3] => [1,6,2,4,5,3] => [2,1,4,6,3,5] => [3,2,5,1,6,4] => 4
[2,4,5,3,1,6] => [1,6,2,4,5,3] => [2,1,4,6,3,5] => [3,2,5,1,6,4] => 4
[2,4,5,3,6,1] => [1,2,4,5,3,6] => [2,3,5,6,4,1] => [3,4,6,1,2,5] => 5
[2,4,5,6,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[2,4,5,6,3,1] => [1,2,4,5,6,3] => [2,3,5,6,1,4] => [3,4,6,1,5,2] => 4
[2,4,6,1,3,5] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[2,4,6,1,5,3] => [1,5,2,4,6,3] => [2,6,3,5,1,4] => [3,1,5,2,6,4] => 5
[2,4,6,3,1,5] => [1,5,2,4,6,3] => [2,6,3,5,1,4] => [3,1,5,2,6,4] => 5
[2,4,6,3,5,1] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[2,4,6,5,1,3] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [3,5,4,6,2,1] => 6
[2,4,6,5,3,1] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[2,5,1,3,4,6] => [1,3,4,6,2,5] => [2,4,5,1,6,3] => [3,5,6,2,1,4] => 5
[2,5,1,3,6,4] => [1,3,6,2,5,4] => [2,4,1,5,3,6] => [3,5,2,6,4,1] => 5
[2,5,1,4,3,6] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[2,5,1,4,6,3] => [1,4,6,2,5,3] => [2,5,1,4,3,6] => [3,6,2,5,4,1] => 6
[2,5,1,6,3,4] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[2,5,1,6,4,3] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[2,5,3,1,4,6] => [1,4,6,2,5,3] => [2,5,1,4,3,6] => [3,6,2,5,4,1] => 6
[2,5,3,1,6,4] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[2,5,3,4,1,6] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[2,5,3,4,6,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[2,5,3,6,1,4] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[2,5,3,6,4,1] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[2,5,4,1,3,6] => [1,3,6,2,5,4] => [2,4,1,5,3,6] => [3,5,2,6,4,1] => 5
[2,5,4,1,6,3] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[2,5,4,3,1,6] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[2,5,4,3,6,1] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[2,5,4,6,1,3] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [3,5,4,1,2,6] => 5
[2,5,4,6,3,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[2,5,6,1,3,4] => [1,3,4,2,5,6] => [2,4,5,3,6,1] => [3,5,6,4,1,2] => 4
[2,5,6,1,4,3] => [1,4,2,5,6,3] => [2,5,3,6,1,4] => [3,6,4,1,5,2] => 5
[2,5,6,3,1,4] => [1,4,2,5,6,3] => [2,5,3,6,1,4] => [3,6,4,1,5,2] => 5
[2,5,6,3,4,1] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[2,5,6,4,1,3] => [1,3,2,5,6,4] => [2,4,3,6,1,5] => [3,5,4,1,6,2] => 6
[2,5,6,4,3,1] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[2,6,1,3,4,5] => [1,3,4,5,2,6] => [2,4,5,6,3,1] => [3,5,6,1,2,4] => 6
[2,6,1,3,5,4] => [1,3,5,2,6,4] => [2,4,6,3,1,5] => [3,5,1,6,4,2] => 6
[2,6,1,4,3,5] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[2,6,1,4,5,3] => [1,4,5,2,6,3] => [2,5,6,3,1,4] => [3,6,1,5,4,2] => 7
[2,6,1,5,3,4] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[2,6,1,5,4,3] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[2,6,3,1,4,5] => [1,4,5,2,6,3] => [2,5,6,3,1,4] => [3,6,1,5,4,2] => 7
[2,6,3,1,5,4] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[2,6,3,4,1,5] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[2,6,3,4,5,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[2,6,3,5,1,4] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[2,6,3,5,4,1] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[2,6,4,1,3,5] => [1,3,5,2,6,4] => [2,4,6,3,1,5] => [3,5,1,6,4,2] => 6
[2,6,4,1,5,3] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[2,6,4,3,1,5] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[2,6,4,3,5,1] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[2,6,4,5,1,3] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[2,6,4,5,3,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[2,6,5,1,3,4] => [1,3,4,2,6,5] => [2,4,5,3,1,6] => [3,5,6,4,2,1] => 5
[2,6,5,1,4,3] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[2,6,5,3,1,4] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[2,6,5,3,4,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[2,6,5,4,1,3] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[2,6,5,4,3,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[3,1,2,4,5,6] => [1,2,4,5,6,3] => [2,3,5,6,1,4] => [3,4,6,1,5,2] => 4
[3,1,2,4,6,5] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[3,1,2,5,4,6] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[3,1,2,5,6,4] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[3,1,2,6,4,5] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[3,1,2,6,5,4] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[3,1,4,2,5,6] => [1,4,2,5,6,3] => [2,5,3,6,1,4] => [3,6,4,1,5,2] => 5
[3,1,4,2,6,5] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[3,1,4,5,2,6] => [1,4,5,2,6,3] => [2,5,6,3,1,4] => [3,6,1,5,4,2] => 7
[3,1,4,5,6,2] => [1,4,5,6,2,3] => [2,5,6,1,4,3] => [3,6,1,4,2,5] => 5
[3,1,4,6,2,5] => [1,4,6,2,5,3] => [2,5,1,4,3,6] => [3,6,2,5,4,1] => 6
[3,1,4,6,5,2] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[3,1,5,2,4,6] => [1,5,2,4,6,3] => [2,6,3,5,1,4] => [3,1,5,2,6,4] => 5
[3,1,5,2,6,4] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[3,1,5,4,2,6] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[3,1,5,4,6,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[3,1,5,6,2,4] => [1,5,6,2,4,3] => [2,6,1,4,3,5] => [3,1,4,6,5,2] => 4
[3,1,5,6,4,2] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[3,1,6,2,4,5] => [1,6,2,4,5,3] => [2,1,4,6,3,5] => [3,2,5,1,6,4] => 4
[3,1,6,2,5,4] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[3,1,6,4,2,5] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[3,1,6,4,5,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[3,1,6,5,2,4] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[3,1,6,5,4,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[3,2,1,4,5,6] => [1,4,5,6,2,3] => [2,5,6,1,4,3] => [3,6,1,4,2,5] => 5
[3,2,1,4,6,5] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[3,2,1,5,4,6] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[3,2,1,5,6,4] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[3,2,1,6,4,5] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[3,2,1,6,5,4] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[3,2,4,1,5,6] => [1,5,6,2,4,3] => [2,6,1,4,3,5] => [3,1,4,6,5,2] => 4
[3,2,4,1,6,5] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[3,2,4,5,1,6] => [1,6,2,4,5,3] => [2,1,4,6,3,5] => [3,2,5,1,6,4] => 4
[3,2,4,5,6,1] => [1,2,4,5,6,3] => [2,3,5,6,1,4] => [3,4,6,1,5,2] => 4
[3,2,4,6,1,5] => [1,5,2,4,6,3] => [2,6,3,5,1,4] => [3,1,5,2,6,4] => 5
[3,2,4,6,5,1] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[3,2,5,1,4,6] => [1,4,6,2,5,3] => [2,5,1,4,3,6] => [3,6,2,5,4,1] => 6
[3,2,5,1,6,4] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[3,2,5,4,1,6] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[3,2,5,4,6,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[3,2,5,6,1,4] => [1,4,2,5,6,3] => [2,5,3,6,1,4] => [3,6,4,1,5,2] => 5
[3,2,5,6,4,1] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[3,2,6,1,4,5] => [1,4,5,2,6,3] => [2,5,6,3,1,4] => [3,6,1,5,4,2] => 7
[3,2,6,1,5,4] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[3,2,6,4,1,5] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[3,2,6,4,5,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[3,2,6,5,1,4] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[3,2,6,5,4,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[3,4,1,2,5,6] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[3,4,1,2,6,5] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[3,4,1,5,2,6] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[3,4,1,5,6,2] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[3,4,1,6,2,5] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[3,4,1,6,5,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[3,4,2,1,5,6] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[3,4,2,1,6,5] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[3,4,2,5,1,6] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[3,4,2,5,6,1] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[3,4,2,6,1,5] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[3,4,2,6,5,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[3,4,5,1,2,6] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[3,4,5,1,6,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[3,4,5,2,1,6] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[3,4,5,2,6,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[3,4,5,6,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[3,4,5,6,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[3,4,6,1,2,5] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[3,4,6,1,5,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[3,4,6,2,1,5] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[3,4,6,2,5,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[3,4,6,5,1,2] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[3,4,6,5,2,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[3,5,1,2,4,6] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[3,5,1,2,6,4] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[3,5,1,4,2,6] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[3,5,1,4,6,2] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[3,5,1,6,2,4] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[3,5,1,6,4,2] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[3,5,2,1,4,6] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[3,5,2,1,6,4] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[3,5,2,4,1,6] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[3,5,2,4,6,1] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[3,5,2,6,1,4] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[3,5,2,6,4,1] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[3,5,4,1,2,6] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[3,5,4,1,6,2] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[3,5,4,2,1,6] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[3,5,4,2,6,1] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[3,5,4,6,1,2] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[3,5,4,6,2,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[3,5,6,1,2,4] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[3,5,6,1,4,2] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[3,5,6,2,1,4] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[3,5,6,2,4,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[3,5,6,4,1,2] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [3,4,5,1,6,2] => 5
[3,5,6,4,2,1] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [3,4,5,1,6,2] => 5
[3,6,1,2,4,5] => [1,2,4,5,3,6] => [2,3,5,6,4,1] => [3,4,6,1,2,5] => 5
[3,6,1,2,5,4] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[3,6,1,4,2,5] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[3,6,1,4,5,2] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[3,6,1,5,2,4] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[3,6,1,5,4,2] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[3,6,2,1,4,5] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[3,6,2,1,5,4] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[3,6,2,4,1,5] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[3,6,2,4,5,1] => [1,2,4,5,3,6] => [2,3,5,6,4,1] => [3,4,6,1,2,5] => 5
[3,6,2,5,1,4] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[3,6,2,5,4,1] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[3,6,4,1,2,5] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[3,6,4,1,5,2] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[3,6,4,2,1,5] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[3,6,4,2,5,1] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[3,6,4,5,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[3,6,4,5,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[3,6,5,1,2,4] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [3,4,6,5,2,1] => 6
[3,6,5,1,4,2] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[3,6,5,2,1,4] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[3,6,5,2,4,1] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [3,4,6,5,2,1] => 6
[3,6,5,4,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[3,6,5,4,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[4,1,2,3,5,6] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [3,4,5,1,6,2] => 5
[4,1,2,3,6,5] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[4,1,2,5,3,6] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[4,1,2,5,6,3] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[4,1,2,6,3,5] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[4,1,2,6,5,3] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[4,1,3,2,5,6] => [1,3,2,5,6,4] => [2,4,3,6,1,5] => [3,5,4,1,6,2] => 6
[4,1,3,2,6,5] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[4,1,3,5,2,6] => [1,3,5,2,6,4] => [2,4,6,3,1,5] => [3,5,1,6,4,2] => 6
[4,1,3,5,6,2] => [1,3,5,6,2,4] => [2,4,6,1,5,3] => [3,5,1,4,2,6] => 4
[4,1,3,6,2,5] => [1,3,6,2,5,4] => [2,4,1,5,3,6] => [3,5,2,6,4,1] => 5
[4,1,3,6,5,2] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[4,1,5,2,3,6] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[4,1,5,2,6,3] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[4,1,5,3,2,6] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[4,1,5,3,6,2] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[4,1,5,6,2,3] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[4,1,5,6,3,2] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[4,1,6,2,3,5] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[4,1,6,2,5,3] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[4,1,6,3,2,5] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[4,1,6,3,5,2] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[4,1,6,5,2,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,1,6,5,3,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,2,1,3,5,6] => [1,3,5,6,2,4] => [2,4,6,1,5,3] => [3,5,1,4,2,6] => 4
[4,2,1,3,6,5] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[4,2,1,5,3,6] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[4,2,1,5,6,3] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[4,2,1,6,3,5] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[4,2,1,6,5,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,2,3,1,5,6] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[4,2,3,1,6,5] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,2,3,5,1,6] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[4,2,3,5,6,1] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [3,4,5,1,6,2] => 5
[4,2,3,6,1,5] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[4,2,3,6,5,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[4,2,5,1,3,6] => [1,3,6,2,5,4] => [2,4,1,5,3,6] => [3,5,2,6,4,1] => 5
[4,2,5,1,6,3] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[4,2,5,3,1,6] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[4,2,5,3,6,1] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[4,2,5,6,1,3] => [1,3,2,5,6,4] => [2,4,3,6,1,5] => [3,5,4,1,6,2] => 6
[4,2,5,6,3,1] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[4,2,6,1,3,5] => [1,3,5,2,6,4] => [2,4,6,3,1,5] => [3,5,1,6,4,2] => 6
[4,2,6,1,5,3] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[4,2,6,3,1,5] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[4,2,6,3,5,1] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[4,2,6,5,1,3] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[4,2,6,5,3,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[4,3,1,2,5,6] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[4,3,1,2,6,5] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[4,3,1,5,2,6] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[4,3,1,5,6,2] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[4,3,1,6,2,5] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[4,3,1,6,5,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,3,2,1,5,6] => [1,5,6,2,3,4] => [2,6,1,4,5,3] => [3,1,4,6,2,5] => 5
[4,3,2,1,6,5] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,3,2,5,1,6] => [1,6,2,5,3,4] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 2
[4,3,2,5,6,1] => [1,2,5,6,3,4] => [2,3,6,1,5,4] => [3,4,1,5,2,6] => 5
[4,3,2,6,1,5] => [1,5,2,6,3,4] => [2,6,3,1,5,4] => [3,1,5,4,2,6] => 3
[4,3,2,6,5,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[4,3,5,1,2,6] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[4,3,5,1,6,2] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[4,3,5,2,1,6] => [1,6,2,3,5,4] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 4
[4,3,5,2,6,1] => [1,2,6,3,5,4] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 4
[4,3,5,6,1,2] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [3,4,5,1,6,2] => 5
[4,3,5,6,2,1] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => [3,4,5,1,6,2] => 5
[4,3,6,1,2,5] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[4,3,6,1,5,2] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[4,3,6,2,1,5] => [1,5,2,3,6,4] => [2,6,3,4,1,5] => [3,1,5,6,4,2] => 5
[4,3,6,2,5,1] => [1,2,5,3,6,4] => [2,3,6,4,1,5] => [3,4,1,6,5,2] => 5
[4,3,6,5,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[4,3,6,5,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[4,5,1,2,3,6] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[4,5,1,2,6,3] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[4,5,1,3,2,6] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[4,5,1,3,6,2] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[4,5,1,6,2,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,5,1,6,3,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,5,2,1,3,6] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[4,5,2,1,6,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,5,2,3,1,6] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,5,2,3,6,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[4,5,2,6,1,3] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[4,5,2,6,3,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[4,5,3,1,2,6] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[4,5,3,1,6,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,5,3,2,1,6] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[4,5,3,2,6,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[4,5,3,6,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[4,5,3,6,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[4,5,6,1,2,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[4,5,6,1,3,2] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[4,5,6,2,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[4,5,6,2,3,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[4,5,6,3,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[4,5,6,3,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[4,6,1,2,3,5] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[4,6,1,2,5,3] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[4,6,1,3,2,5] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [3,5,4,1,2,6] => 5
[4,6,1,3,5,2] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[4,6,1,5,2,3] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[4,6,1,5,3,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[4,6,2,1,3,5] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[4,6,2,1,5,3] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[4,6,2,3,1,5] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[4,6,2,3,5,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[4,6,2,5,1,3] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [3,5,4,1,2,6] => 5
[4,6,2,5,3,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[4,6,3,1,2,5] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[4,6,3,1,5,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[4,6,3,2,1,5] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[4,6,3,2,5,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[4,6,3,5,1,2] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[4,6,3,5,2,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[4,6,5,1,2,3] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[4,6,5,1,3,2] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [3,5,4,6,2,1] => 6
[4,6,5,2,1,3] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [3,5,4,6,2,1] => 6
[4,6,5,2,3,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[4,6,5,3,1,2] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[4,6,5,3,2,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[5,1,2,3,4,6] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[5,1,2,3,6,4] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[5,1,2,4,3,6] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [3,4,6,5,2,1] => 6
[5,1,2,4,6,3] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[5,1,2,6,3,4] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,1,2,6,4,3] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,1,3,2,4,6] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [3,5,4,6,2,1] => 6
[5,1,3,2,6,4] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[5,1,3,4,2,6] => [1,3,4,2,6,5] => [2,4,5,3,1,6] => [3,5,6,4,2,1] => 5
[5,1,3,4,6,2] => [1,3,4,6,2,5] => [2,4,5,1,6,3] => [3,5,6,2,1,4] => 5
[5,1,3,6,2,4] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[5,1,3,6,4,2] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[5,1,4,2,3,6] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[5,1,4,2,6,3] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[5,1,4,3,2,6] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[5,1,4,3,6,2] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[5,1,4,6,2,3] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[5,1,4,6,3,2] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[5,1,6,2,3,4] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,1,6,2,4,3] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[5,1,6,3,2,4] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[5,1,6,3,4,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,1,6,4,2,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,1,6,4,3,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,2,1,3,4,6] => [1,3,4,6,2,5] => [2,4,5,1,6,3] => [3,5,6,2,1,4] => 5
[5,2,1,3,6,4] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[5,2,1,4,3,6] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[5,2,1,4,6,3] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[5,2,1,6,3,4] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,2,1,6,4,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,2,3,1,4,6] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[5,2,3,1,6,4] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,2,3,4,1,6] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,2,3,4,6,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[5,2,3,6,1,4] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[5,2,3,6,4,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[5,2,4,1,3,6] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[5,2,4,1,6,3] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[5,2,4,3,1,6] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[5,2,4,3,6,1] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [3,4,6,5,2,1] => 6
[5,2,4,6,1,3] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [3,5,4,6,2,1] => 6
[5,2,4,6,3,1] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[5,2,6,1,3,4] => [1,3,4,2,6,5] => [2,4,5,3,1,6] => [3,5,6,4,2,1] => 5
[5,2,6,1,4,3] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[5,2,6,3,1,4] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[5,2,6,3,4,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,2,6,4,1,3] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[5,2,6,4,3,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,3,1,2,4,6] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[5,3,1,2,6,4] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,3,1,4,2,6] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[5,3,1,4,6,2] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[5,3,1,6,2,4] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[5,3,1,6,4,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,3,2,1,4,6] => [1,4,6,2,3,5] => [2,5,1,4,6,3] => [3,6,2,5,1,4] => 5
[5,3,2,1,6,4] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,3,2,4,1,6] => [1,6,2,4,3,5] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 3
[5,3,2,4,6,1] => [1,2,4,6,3,5] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 6
[5,3,2,6,1,4] => [1,4,2,6,3,5] => [2,5,3,1,6,4] => [3,6,4,2,1,5] => 5
[5,3,2,6,4,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,3,4,1,2,6] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,3,4,1,6,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,3,4,2,1,6] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,3,4,2,6,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,3,4,6,1,2] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[5,3,4,6,2,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[5,3,6,1,2,4] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [3,4,6,5,2,1] => 6
[5,3,6,1,4,2] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[5,3,6,2,1,4] => [1,4,2,3,6,5] => [2,5,3,4,1,6] => [3,6,4,5,2,1] => 5
[5,3,6,2,4,1] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [3,4,6,5,2,1] => 6
[5,3,6,4,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[5,3,6,4,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[5,4,1,2,3,6] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[5,4,1,2,6,3] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,4,1,3,2,6] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[5,4,1,3,6,2] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[5,4,1,6,2,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,4,1,6,3,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,4,2,1,3,6] => [1,3,6,2,4,5] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 6
[5,4,2,1,6,3] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,4,2,3,1,6] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,4,2,3,6,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[5,4,2,6,1,3] => [1,3,2,6,4,5] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 4
[5,4,2,6,3,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,4,3,1,2,6] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,4,3,1,6,2] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,4,3,2,1,6] => [1,6,2,3,4,5] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 5
[5,4,3,2,6,1] => [1,2,6,3,4,5] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 5
[5,4,3,6,1,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[5,4,3,6,2,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 5
[5,4,6,1,2,3] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[5,4,6,1,3,2] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [3,5,4,6,2,1] => 6
[5,4,6,2,1,3] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [3,5,4,6,2,1] => 6
[5,4,6,2,3,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[5,4,6,3,1,2] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[5,4,6,3,2,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 5
[5,6,1,2,3,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[5,6,1,2,4,3] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[5,6,1,3,2,4] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[5,6,1,3,4,2] => [1,3,4,2,5,6] => [2,4,5,3,6,1] => [3,5,6,4,1,2] => 4
[5,6,1,4,2,3] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[5,6,1,4,3,2] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[5,6,2,1,3,4] => [1,3,4,2,5,6] => [2,4,5,3,6,1] => [3,5,6,4,1,2] => 4
[5,6,2,1,4,3] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[5,6,2,3,1,4] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[5,6,2,3,4,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[5,6,2,4,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[5,6,2,4,3,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[5,6,3,1,2,4] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[5,6,3,1,4,2] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[5,6,3,2,1,4] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[5,6,3,2,4,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[5,6,3,4,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[5,6,3,4,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[5,6,4,1,2,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[5,6,4,1,3,2] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[5,6,4,2,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[5,6,4,2,3,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[5,6,4,3,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[5,6,4,3,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,1,2,3,4,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,1,2,3,5,4] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[6,1,2,4,3,5] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[6,1,2,4,5,3] => [1,2,4,5,3,6] => [2,3,5,6,4,1] => [3,4,6,1,2,5] => 5
[6,1,2,5,3,4] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,1,2,5,4,3] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,1,3,2,4,5] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[6,1,3,2,5,4] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [3,5,4,1,2,6] => 5
[6,1,3,4,2,5] => [1,3,4,2,5,6] => [2,4,5,3,6,1] => [3,5,6,4,1,2] => 4
[6,1,3,4,5,2] => [1,3,4,5,2,6] => [2,4,5,6,3,1] => [3,5,6,1,2,4] => 6
[6,1,3,5,2,4] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[6,1,3,5,4,2] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[6,1,4,2,3,5] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,1,4,2,5,3] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[6,1,4,3,2,5] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[6,1,4,3,5,2] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,1,4,5,2,3] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[6,1,4,5,3,2] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[6,1,5,2,3,4] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,1,5,2,4,3] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[6,1,5,3,2,4] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[6,1,5,3,4,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,1,5,4,2,3] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,1,5,4,3,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,2,1,3,4,5] => [1,3,4,5,2,6] => [2,4,5,6,3,1] => [3,5,6,1,2,4] => 6
[6,2,1,3,5,4] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[6,2,1,4,3,5] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,2,1,4,5,3] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[6,2,1,5,3,4] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,2,1,5,4,3] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,2,3,1,4,5] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[6,2,3,1,5,4] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,2,3,4,1,5] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,2,3,4,5,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,2,3,5,1,4] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,2,3,5,4,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[6,2,4,1,3,5] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[6,2,4,1,5,3] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[6,2,4,3,1,5] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[6,2,4,3,5,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[6,2,4,5,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[6,2,4,5,3,1] => [1,2,4,5,3,6] => [2,3,5,6,4,1] => [3,4,6,1,2,5] => 5
[6,2,5,1,3,4] => [1,3,4,2,5,6] => [2,4,5,3,6,1] => [3,5,6,4,1,2] => 4
[6,2,5,1,4,3] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[6,2,5,3,1,4] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[6,2,5,3,4,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,2,5,4,1,3] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [3,5,4,1,2,6] => 5
[6,2,5,4,3,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,3,1,2,4,5] => [1,2,4,5,3,6] => [2,3,5,6,4,1] => [3,4,6,1,2,5] => 5
[6,3,1,2,5,4] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,3,1,4,2,5] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[6,3,1,4,5,2] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[6,3,1,5,2,4] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[6,3,1,5,4,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,3,2,1,4,5] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,5,2,4] => 6
[6,3,2,1,5,4] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,3,2,4,1,5] => [1,5,2,4,3,6] => [2,6,3,5,4,1] => [3,1,5,2,4,6] => 4
[6,3,2,4,5,1] => [1,2,4,5,3,6] => [2,3,5,6,4,1] => [3,4,6,1,2,5] => 5
[6,3,2,5,1,4] => [1,4,2,5,3,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => 6
[6,3,2,5,4,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,3,4,1,2,5] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,3,4,1,5,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,3,4,2,1,5] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,3,4,2,5,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,3,4,5,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,3,4,5,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,3,5,1,2,4] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[6,3,5,1,4,2] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,3,5,2,1,4] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,3,5,2,4,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[6,3,5,4,1,2] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[6,3,5,4,2,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[6,4,1,2,3,5] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[6,4,1,2,5,3] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,4,1,3,2,5] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [3,5,4,1,2,6] => 5
[6,4,1,3,5,2] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[6,4,1,5,2,3] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,4,1,5,3,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,4,2,1,3,5] => [1,3,5,2,4,6] => [2,4,6,3,5,1] => [3,5,1,6,2,4] => 7
[6,4,2,1,5,3] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,4,2,3,1,5] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,4,2,3,5,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[6,4,2,5,1,3] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [3,5,4,1,2,6] => 5
[6,4,2,5,3,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,4,3,1,2,5] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,4,3,1,5,2] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,4,3,2,1,5] => [1,5,2,3,4,6] => [2,6,3,4,5,1] => [3,1,5,6,2,4] => 6
[6,4,3,2,5,1] => [1,2,5,3,4,6] => [2,3,6,4,5,1] => [3,4,1,6,2,5] => 6
[6,4,3,5,1,2] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[6,4,3,5,2,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 4
[6,4,5,1,2,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,4,5,1,3,2] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[6,4,5,2,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[6,4,5,2,3,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,4,5,3,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,4,5,3,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,5,1,2,3,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,5,1,2,4,3] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[6,5,1,3,2,4] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[6,5,1,3,4,2] => [1,3,4,2,5,6] => [2,4,5,3,6,1] => [3,5,6,4,1,2] => 4
[6,5,1,4,2,3] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,5,1,4,3,2] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,5,2,1,3,4] => [1,3,4,2,5,6] => [2,4,5,3,6,1] => [3,5,6,4,1,2] => 4
[6,5,2,1,4,3] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,5,2,3,1,4] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,5,2,3,4,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,5,2,4,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[6,5,2,4,3,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[6,5,3,1,2,4] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[6,5,3,1,4,2] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,5,3,2,1,4] => [1,4,2,3,5,6] => [2,5,3,4,6,1] => [3,6,4,5,1,2] => 6
[6,5,3,2,4,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,5,1,2] => 5
[6,5,3,4,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,5,3,4,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,5,4,1,2,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,5,4,1,3,2] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[6,5,4,2,1,3] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,4,6,1,2] => 5
[6,5,4,2,3,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,5,4,3,1,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
[6,5,4,3,2,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 6
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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 6,4,6,8 6,42,48,24 24,42,100,330,206,18
$F_{2} = 2$
$F_{3} = 2\ q + 4\ q^{2}$
$F_{4} = 6\ q + 4\ q^{2} + 6\ q^{3} + 8\ q^{4}$
$F_{5} = 6\ q^{2} + 42\ q^{3} + 48\ q^{4} + 24\ q^{5}$
$F_{6} = 24\ q^{2} + 42\ q^{3} + 100\ q^{4} + 330\ q^{5} + 206\ q^{6} + 18\ q^{7}$
Description
The prefix exchange distance of a permutation.
This is the number of star transpositions needed to write a permutation.
In symbols, for a permutation $\pi\in\mathfrak S_n$ this is
$$\min\{ k \mid \pi = \tau_{i_1} \cdots \tau_{i_k}, 2 \leq i_1,\ldots,i_k \leq n\},$$
where $\tau_a = (1,a)$ for $2 \leq a \leq n$.
[1, Lem. 2.1] shows that the this length is $n+m-a-1$, where $m$ is the number of non-trival cycles not containing the element $1$, and $a$ is the number of fixed points different from $1$.
One may find in [2] explicit formulas for its generating function and a combinatorial proof that it is asymptotically normal.
This is the number of star transpositions needed to write a permutation.
In symbols, for a permutation $\pi\in\mathfrak S_n$ this is
$$\min\{ k \mid \pi = \tau_{i_1} \cdots \tau_{i_k}, 2 \leq i_1,\ldots,i_k \leq n\},$$
where $\tau_a = (1,a)$ for $2 \leq a \leq n$.
[1, Lem. 2.1] shows that the this length is $n+m-a-1$, where $m$ is the number of non-trival cycles not containing the element $1$, and $a$ is the number of fixed points different from $1$.
One may find in [2] explicit formulas for its generating function and a combinatorial proof that it is asymptotically normal.
Map
Lehmer code rotation
Description
Sends a permutation $\pi$ to the unique permutation $\tau$ (of the same length) such that every entry in the Lehmer code of $\tau$ is cyclically one larger than the Lehmer code of $\pi$.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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