Identifier
-
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
Mp00310: Permutations —toric promotion⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St001667: Permutations ⟶ ℤ
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => [1,2] => 1
[2,1] => [2,1] => [2,1] => [2,1] => 1
[1,2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,3,2] => [1,3,2] => [2,3,1] => [2,1,3] => 1
[2,1,3] => [2,1,3] => [3,1,2] => [1,3,2] => 1
[2,3,1] => [3,2,1] => [1,2,3] => [1,2,3] => 1
[3,1,2] => [3,2,1] => [1,2,3] => [1,2,3] => 1
[3,2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 1
[1,2,3,4] => [1,2,3,4] => [4,2,3,1] => [4,2,3,1] => 2
[1,2,4,3] => [1,2,4,3] => [4,3,1,2] => [1,4,3,2] => 1
[1,3,2,4] => [1,3,2,4] => [2,4,1,3] => [2,4,1,3] => 2
[1,3,4,2] => [1,4,3,2] => [3,1,2,4] => [1,3,4,2] => 2
[1,4,2,3] => [1,4,3,2] => [3,1,2,4] => [1,3,4,2] => 2
[1,4,3,2] => [1,4,3,2] => [3,1,2,4] => [1,3,4,2] => 2
[2,1,3,4] => [2,1,3,4] => [4,1,2,3] => [1,2,4,3] => 2
[2,1,4,3] => [2,1,4,3] => [4,1,3,2] => [4,1,3,2] => 2
[2,3,1,4] => [3,2,1,4] => [1,2,4,3] => [4,1,2,3] => 1
[2,3,4,1] => [4,2,3,1] => [3,1,4,2] => [3,1,4,2] => 2
[2,4,1,3] => [3,4,1,2] => [2,3,1,4] => [2,3,1,4] => 2
[2,4,3,1] => [4,3,2,1] => [1,3,2,4] => [1,3,2,4] => 2
[3,1,2,4] => [3,2,1,4] => [1,2,4,3] => [4,1,2,3] => 1
[3,1,4,2] => [4,2,3,1] => [3,1,4,2] => [3,1,4,2] => 2
[3,2,1,4] => [3,2,1,4] => [1,2,4,3] => [4,1,2,3] => 1
[3,2,4,1] => [4,2,3,1] => [3,1,4,2] => [3,1,4,2] => 2
[3,4,1,2] => [4,3,2,1] => [1,3,2,4] => [1,3,2,4] => 2
[3,4,2,1] => [4,3,2,1] => [1,3,2,4] => [1,3,2,4] => 2
[4,1,2,3] => [4,2,3,1] => [3,1,4,2] => [3,1,4,2] => 2
[4,1,3,2] => [4,2,3,1] => [3,1,4,2] => [3,1,4,2] => 2
[4,2,1,3] => [4,3,2,1] => [1,3,2,4] => [1,3,2,4] => 2
[4,2,3,1] => [4,3,2,1] => [1,3,2,4] => [1,3,2,4] => 2
[4,3,1,2] => [4,3,2,1] => [1,3,2,4] => [1,3,2,4] => 2
[4,3,2,1] => [4,3,2,1] => [1,3,2,4] => [1,3,2,4] => 2
[1,2,3,4,5] => [1,2,3,4,5] => [5,2,3,4,1] => [5,2,3,4,1] => 2
[1,2,3,5,4] => [1,2,3,5,4] => [5,2,4,1,3] => [2,5,1,4,3] => 2
[1,2,4,3,5] => [1,2,4,3,5] => [5,3,1,2,4] => [1,3,5,4,2] => 2
[1,2,4,5,3] => [1,2,5,4,3] => [5,4,1,3,2] => [5,1,4,3,2] => 2
[1,2,5,3,4] => [1,2,5,4,3] => [5,4,1,3,2] => [5,1,4,3,2] => 2
[1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,3,2] => [5,1,4,3,2] => 2
[1,3,2,4,5] => [1,3,2,4,5] => [2,5,1,3,4] => [2,3,5,1,4] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [2,5,1,4,3] => [5,2,4,1,3] => 2
[1,3,4,2,5] => [1,4,3,2,5] => [3,1,2,5,4] => [3,1,2,5,4] => 2
[1,3,4,5,2] => [1,5,3,4,2] => [4,1,2,3,5] => [1,2,4,5,3] => 2
[1,3,5,2,4] => [1,4,5,2,3] => [3,4,5,1,2] => [3,4,1,2,5] => 2
[1,3,5,4,2] => [1,5,4,3,2] => [4,1,3,2,5] => [1,4,3,5,2] => 2
[1,4,2,3,5] => [1,4,3,2,5] => [3,1,2,5,4] => [3,1,2,5,4] => 2
[1,4,2,5,3] => [1,5,3,4,2] => [4,1,2,3,5] => [1,2,4,5,3] => 2
[1,4,3,2,5] => [1,4,3,2,5] => [3,1,2,5,4] => [3,1,2,5,4] => 2
[1,4,3,5,2] => [1,5,3,4,2] => [4,1,2,3,5] => [1,2,4,5,3] => 2
[1,4,5,2,3] => [1,5,4,3,2] => [4,1,3,2,5] => [1,4,3,5,2] => 2
[1,4,5,3,2] => [1,5,4,3,2] => [4,1,3,2,5] => [1,4,3,5,2] => 2
[1,5,2,3,4] => [1,5,3,4,2] => [4,1,2,3,5] => [1,2,4,5,3] => 2
[1,5,2,4,3] => [1,5,3,4,2] => [4,1,2,3,5] => [1,2,4,5,3] => 2
[1,5,3,2,4] => [1,5,4,3,2] => [4,1,3,2,5] => [1,4,3,5,2] => 2
[1,5,3,4,2] => [1,5,4,3,2] => [4,1,3,2,5] => [1,4,3,5,2] => 2
[1,5,4,2,3] => [1,5,4,3,2] => [4,1,3,2,5] => [1,4,3,5,2] => 2
[1,5,4,3,2] => [1,5,4,3,2] => [4,1,3,2,5] => [1,4,3,5,2] => 2
[2,1,3,4,5] => [2,1,3,4,5] => [5,1,2,3,4] => [1,2,3,5,4] => 2
[2,1,3,5,4] => [2,1,3,5,4] => [5,1,2,4,3] => [5,1,2,4,3] => 2
[2,1,4,3,5] => [2,1,4,3,5] => [5,1,3,2,4] => [1,5,3,4,2] => 2
[2,1,4,5,3] => [2,1,5,4,3] => [5,1,4,3,2] => [5,4,1,3,2] => 2
[2,1,5,3,4] => [2,1,5,4,3] => [5,1,4,3,2] => [5,4,1,3,2] => 2
[2,1,5,4,3] => [2,1,5,4,3] => [5,1,4,3,2] => [5,4,1,3,2] => 2
[2,3,1,4,5] => [3,2,1,4,5] => [1,2,5,3,4] => [1,5,2,3,4] => 2
[2,3,1,5,4] => [3,2,1,5,4] => [1,2,5,4,3] => [5,4,1,2,3] => 2
[2,3,4,1,5] => [4,2,3,1,5] => [3,1,5,2,4] => [1,3,2,5,4] => 2
[2,3,4,5,1] => [5,2,3,4,1] => [4,5,2,1,3] => [4,5,2,1,3] => 2
[2,3,5,1,4] => [4,2,5,1,3] => [3,5,4,2,1] => [5,3,2,1,4] => 2
[2,3,5,4,1] => [5,2,4,3,1] => [4,1,5,3,2] => [4,3,1,5,2] => 2
[2,4,1,3,5] => [3,4,1,2,5] => [2,3,5,4,1] => [5,2,1,3,4] => 2
[2,4,1,5,3] => [3,5,1,4,2] => [2,4,3,5,1] => [4,2,3,1,5] => 2
[2,4,3,1,5] => [4,3,2,1,5] => [1,3,2,5,4] => [3,1,5,2,4] => 2
[2,4,3,5,1] => [5,3,2,4,1] => [4,2,1,5,3] => [4,2,5,3,1] => 2
[2,4,5,1,3] => [4,5,3,1,2] => [3,4,2,1,5] => [3,4,2,1,5] => 2
[2,4,5,3,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[2,5,1,3,4] => [3,5,1,4,2] => [2,4,3,5,1] => [4,2,3,1,5] => 2
[2,5,1,4,3] => [3,5,1,4,2] => [2,4,3,5,1] => [4,2,3,1,5] => 2
[2,5,3,1,4] => [4,5,3,1,2] => [3,4,2,1,5] => [3,4,2,1,5] => 2
[2,5,3,4,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[2,5,4,1,3] => [4,5,3,1,2] => [3,4,2,1,5] => [3,4,2,1,5] => 2
[2,5,4,3,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[3,1,2,4,5] => [3,2,1,4,5] => [1,2,5,3,4] => [1,5,2,3,4] => 2
[3,1,2,5,4] => [3,2,1,5,4] => [1,2,5,4,3] => [5,4,1,2,3] => 2
[3,1,4,2,5] => [4,2,3,1,5] => [3,1,5,2,4] => [1,3,2,5,4] => 2
[3,1,4,5,2] => [5,2,3,4,1] => [4,5,2,1,3] => [4,5,2,1,3] => 2
[3,1,5,2,4] => [4,2,5,1,3] => [3,5,4,2,1] => [5,3,2,1,4] => 2
[3,1,5,4,2] => [5,2,4,3,1] => [4,1,5,3,2] => [4,3,1,5,2] => 2
[3,2,1,4,5] => [3,2,1,4,5] => [1,2,5,3,4] => [1,5,2,3,4] => 2
[3,2,1,5,4] => [3,2,1,5,4] => [1,2,5,4,3] => [5,4,1,2,3] => 2
[3,2,4,1,5] => [4,2,3,1,5] => [3,1,5,2,4] => [1,3,2,5,4] => 2
[3,2,4,5,1] => [5,2,3,4,1] => [4,5,2,1,3] => [4,5,2,1,3] => 2
[3,2,5,1,4] => [4,2,5,1,3] => [3,5,4,2,1] => [5,3,2,1,4] => 2
[3,2,5,4,1] => [5,2,4,3,1] => [4,1,5,3,2] => [4,3,1,5,2] => 2
[3,4,1,2,5] => [4,3,2,1,5] => [1,3,2,5,4] => [3,1,5,2,4] => 2
[3,4,1,5,2] => [5,3,2,4,1] => [4,2,1,5,3] => [4,2,5,3,1] => 2
[3,4,2,1,5] => [4,3,2,1,5] => [1,3,2,5,4] => [3,1,5,2,4] => 2
[3,4,2,5,1] => [5,3,2,4,1] => [4,2,1,5,3] => [4,2,5,3,1] => 2
[3,4,5,1,2] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[3,4,5,2,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[3,5,1,2,4] => [4,5,3,1,2] => [3,4,2,1,5] => [3,4,2,1,5] => 2
[3,5,1,4,2] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
>>> Load all 1062 entries. <<<[3,5,2,1,4] => [4,5,3,1,2] => [3,4,2,1,5] => [3,4,2,1,5] => 2
[3,5,2,4,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[3,5,4,1,2] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[3,5,4,2,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[4,1,2,3,5] => [4,2,3,1,5] => [3,1,5,2,4] => [1,3,2,5,4] => 2
[4,1,2,5,3] => [5,2,3,4,1] => [4,5,2,1,3] => [4,5,2,1,3] => 2
[4,1,3,2,5] => [4,2,3,1,5] => [3,1,5,2,4] => [1,3,2,5,4] => 2
[4,1,3,5,2] => [5,2,3,4,1] => [4,5,2,1,3] => [4,5,2,1,3] => 2
[4,1,5,2,3] => [5,2,4,3,1] => [4,1,5,3,2] => [4,3,1,5,2] => 2
[4,1,5,3,2] => [5,2,4,3,1] => [4,1,5,3,2] => [4,3,1,5,2] => 2
[4,2,1,3,5] => [4,3,2,1,5] => [1,3,2,5,4] => [3,1,5,2,4] => 2
[4,2,1,5,3] => [5,3,2,4,1] => [4,2,1,5,3] => [4,2,5,3,1] => 2
[4,2,3,1,5] => [4,3,2,1,5] => [1,3,2,5,4] => [3,1,5,2,4] => 2
[4,2,3,5,1] => [5,3,2,4,1] => [4,2,1,5,3] => [4,2,5,3,1] => 2
[4,2,5,1,3] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[4,2,5,3,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[4,3,1,2,5] => [4,3,2,1,5] => [1,3,2,5,4] => [3,1,5,2,4] => 2
[4,3,1,5,2] => [5,3,2,4,1] => [4,2,1,5,3] => [4,2,5,3,1] => 2
[4,3,2,1,5] => [4,3,2,1,5] => [1,3,2,5,4] => [3,1,5,2,4] => 2
[4,3,2,5,1] => [5,3,2,4,1] => [4,2,1,5,3] => [4,2,5,3,1] => 2
[4,3,5,1,2] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[4,3,5,2,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[4,5,1,2,3] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[4,5,1,3,2] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[4,5,2,1,3] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[4,5,2,3,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[4,5,3,1,2] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[4,5,3,2,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,1,2,3,4] => [5,2,3,4,1] => [4,5,2,1,3] => [4,5,2,1,3] => 2
[5,1,2,4,3] => [5,2,3,4,1] => [4,5,2,1,3] => [4,5,2,1,3] => 2
[5,1,3,2,4] => [5,2,4,3,1] => [4,1,5,3,2] => [4,3,1,5,2] => 2
[5,1,3,4,2] => [5,2,4,3,1] => [4,1,5,3,2] => [4,3,1,5,2] => 2
[5,1,4,2,3] => [5,2,4,3,1] => [4,1,5,3,2] => [4,3,1,5,2] => 2
[5,1,4,3,2] => [5,2,4,3,1] => [4,1,5,3,2] => [4,3,1,5,2] => 2
[5,2,1,3,4] => [5,3,2,4,1] => [4,2,1,5,3] => [4,2,5,3,1] => 2
[5,2,1,4,3] => [5,3,2,4,1] => [4,2,1,5,3] => [4,2,5,3,1] => 2
[5,2,3,1,4] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,2,3,4,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,2,4,1,3] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,2,4,3,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,3,1,2,4] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,3,1,4,2] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,3,2,1,4] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,3,2,4,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,3,4,1,2] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,3,4,2,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,4,1,2,3] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,4,1,3,2] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,4,2,1,3] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,4,2,3,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,4,3,1,2] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[5,4,3,2,1] => [5,4,3,2,1] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 2
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,2,3,5,1,4] => [2,6,1,3,5,4] => 3
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [6,2,4,1,3,5] => [2,4,6,1,5,3] => 3
[1,2,3,5,6,4] => [1,2,3,6,5,4] => [6,2,5,1,4,3] => [6,2,5,1,4,3] => 3
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [6,2,5,1,4,3] => [6,2,5,1,4,3] => 3
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,2,5,1,4,3] => [6,2,5,1,4,3] => 3
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [6,3,1,2,4,5] => [1,3,4,6,5,2] => 3
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [6,3,1,2,5,4] => [3,1,2,6,5,4] => 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [6,4,1,3,2,5] => [1,6,4,5,3,2] => 3
[1,2,4,5,6,3] => [1,2,6,4,5,3] => [6,5,1,3,4,2] => [6,1,3,5,4,2] => 2
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [6,4,5,1,2,3] => [1,4,6,2,5,3] => 3
[1,2,4,6,5,3] => [1,2,6,5,4,3] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 3
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [6,4,1,3,2,5] => [1,6,4,5,3,2] => 3
[1,2,5,3,6,4] => [1,2,6,4,5,3] => [6,5,1,3,4,2] => [6,1,3,5,4,2] => 2
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [6,4,1,3,2,5] => [1,6,4,5,3,2] => 3
[1,2,5,4,6,3] => [1,2,6,4,5,3] => [6,5,1,3,4,2] => [6,1,3,5,4,2] => 2
[1,2,5,6,3,4] => [1,2,6,5,4,3] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 3
[1,2,5,6,4,3] => [1,2,6,5,4,3] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 3
[1,2,6,3,4,5] => [1,2,6,4,5,3] => [6,5,1,3,4,2] => [6,1,3,5,4,2] => 2
[1,2,6,3,5,4] => [1,2,6,4,5,3] => [6,5,1,3,4,2] => [6,1,3,5,4,2] => 2
[1,2,6,4,3,5] => [1,2,6,5,4,3] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 3
[1,2,6,4,5,3] => [1,2,6,5,4,3] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 3
[1,2,6,5,3,4] => [1,2,6,5,4,3] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 3
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 3
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [2,6,1,3,4,5] => [2,3,4,6,1,5] => 3
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [2,6,1,3,5,4] => [6,2,3,5,1,4] => 3
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [2,6,1,4,3,5] => [2,6,4,5,1,3] => 3
[1,3,2,5,6,4] => [1,3,2,6,5,4] => [2,6,1,5,4,3] => [6,5,2,4,1,3] => 3
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [2,6,1,5,4,3] => [6,5,2,4,1,3] => 3
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [2,6,1,5,4,3] => [6,5,2,4,1,3] => 3
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [3,1,2,6,4,5] => [1,3,2,4,6,5] => 3
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [3,1,2,6,5,4] => [6,3,1,2,5,4] => 3
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => 2
[1,3,4,5,6,2] => [1,6,3,4,5,2] => [5,1,2,3,4,6] => [1,2,3,5,6,4] => 3
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [4,1,2,5,6,3] => [4,1,2,5,6,3] => 3
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [5,1,2,4,3,6] => [1,5,2,4,6,3] => 3
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [3,4,6,1,2,5] => [3,4,6,1,2,5] => 3
[1,3,5,2,6,4] => [1,4,6,2,5,3] => [3,5,6,1,4,2] => [5,3,4,1,2,6] => 3
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [4,1,3,2,6,5] => [4,1,6,3,5,2] => 3
[1,3,5,4,6,2] => [1,6,4,3,5,2] => [5,1,3,2,4,6] => [1,3,5,4,6,2] => 3
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [4,5,1,3,6,2] => [4,3,5,6,1,2] => 3
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,3,6,2,4,5] => [1,4,6,2,5,3] => [3,5,6,1,4,2] => [5,3,4,1,2,6] => 3
[1,3,6,2,5,4] => [1,4,6,2,5,3] => [3,5,6,1,4,2] => [5,3,4,1,2,6] => 3
[1,3,6,4,2,5] => [1,5,6,4,2,3] => [4,5,1,3,6,2] => [4,3,5,6,1,2] => 3
[1,3,6,4,5,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,3,6,5,2,4] => [1,5,6,4,2,3] => [4,5,1,3,6,2] => [4,3,5,6,1,2] => 3
[1,3,6,5,4,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [3,1,2,6,4,5] => [1,3,2,4,6,5] => 3
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [3,1,2,6,5,4] => [6,3,1,2,5,4] => 3
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => 2
[1,4,2,5,6,3] => [1,6,3,4,5,2] => [5,1,2,3,4,6] => [1,2,3,5,6,4] => 3
[1,4,2,6,3,5] => [1,5,3,6,2,4] => [4,1,2,5,6,3] => [4,1,2,5,6,3] => 3
[1,4,2,6,5,3] => [1,6,3,5,4,2] => [5,1,2,4,3,6] => [1,5,2,4,6,3] => 3
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [3,1,2,6,4,5] => [1,3,2,4,6,5] => 3
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [3,1,2,6,5,4] => [6,3,1,2,5,4] => 3
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => 2
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [5,1,2,3,4,6] => [1,2,3,5,6,4] => 3
[1,4,3,6,2,5] => [1,5,3,6,2,4] => [4,1,2,5,6,3] => [4,1,2,5,6,3] => 3
[1,4,3,6,5,2] => [1,6,3,5,4,2] => [5,1,2,4,3,6] => [1,5,2,4,6,3] => 3
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [4,1,3,2,6,5] => [4,1,6,3,5,2] => 3
[1,4,5,2,6,3] => [1,6,4,3,5,2] => [5,1,3,2,4,6] => [1,3,5,4,6,2] => 3
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [4,1,3,2,6,5] => [4,1,6,3,5,2] => 3
[1,4,5,3,6,2] => [1,6,4,3,5,2] => [5,1,3,2,4,6] => [1,3,5,4,6,2] => 3
[1,4,5,6,2,3] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,4,5,6,3,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,4,6,2,3,5] => [1,5,6,4,2,3] => [4,5,1,3,6,2] => [4,3,5,6,1,2] => 3
[1,4,6,2,5,3] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,4,6,3,2,5] => [1,5,6,4,2,3] => [4,5,1,3,6,2] => [4,3,5,6,1,2] => 3
[1,4,6,3,5,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,4,6,5,2,3] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,4,6,5,3,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => 2
[1,5,2,3,6,4] => [1,6,3,4,5,2] => [5,1,2,3,4,6] => [1,2,3,5,6,4] => 3
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => 2
[1,5,2,4,6,3] => [1,6,3,4,5,2] => [5,1,2,3,4,6] => [1,2,3,5,6,4] => 3
[1,5,2,6,3,4] => [1,6,3,5,4,2] => [5,1,2,4,3,6] => [1,5,2,4,6,3] => 3
[1,5,2,6,4,3] => [1,6,3,5,4,2] => [5,1,2,4,3,6] => [1,5,2,4,6,3] => 3
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [4,1,3,2,6,5] => [4,1,6,3,5,2] => 3
[1,5,3,2,6,4] => [1,6,4,3,5,2] => [5,1,3,2,4,6] => [1,3,5,4,6,2] => 3
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [4,1,3,2,6,5] => [4,1,6,3,5,2] => 3
[1,5,3,4,6,2] => [1,6,4,3,5,2] => [5,1,3,2,4,6] => [1,3,5,4,6,2] => 3
[1,5,3,6,2,4] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,5,3,6,4,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [4,1,3,2,6,5] => [4,1,6,3,5,2] => 3
[1,5,4,2,6,3] => [1,6,4,3,5,2] => [5,1,3,2,4,6] => [1,3,5,4,6,2] => 3
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [4,1,3,2,6,5] => [4,1,6,3,5,2] => 3
[1,5,4,3,6,2] => [1,6,4,3,5,2] => [5,1,3,2,4,6] => [1,3,5,4,6,2] => 3
[1,5,4,6,2,3] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,5,4,6,3,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,5,6,2,3,4] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,5,6,2,4,3] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,5,6,3,2,4] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,5,6,3,4,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,5,6,4,2,3] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,5,6,4,3,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,2,3,4,5] => [1,6,3,4,5,2] => [5,1,2,3,4,6] => [1,2,3,5,6,4] => 3
[1,6,2,3,5,4] => [1,6,3,4,5,2] => [5,1,2,3,4,6] => [1,2,3,5,6,4] => 3
[1,6,2,4,3,5] => [1,6,3,5,4,2] => [5,1,2,4,3,6] => [1,5,2,4,6,3] => 3
[1,6,2,4,5,3] => [1,6,3,5,4,2] => [5,1,2,4,3,6] => [1,5,2,4,6,3] => 3
[1,6,2,5,3,4] => [1,6,3,5,4,2] => [5,1,2,4,3,6] => [1,5,2,4,6,3] => 3
[1,6,2,5,4,3] => [1,6,3,5,4,2] => [5,1,2,4,3,6] => [1,5,2,4,6,3] => 3
[1,6,3,2,4,5] => [1,6,4,3,5,2] => [5,1,3,2,4,6] => [1,3,5,4,6,2] => 3
[1,6,3,2,5,4] => [1,6,4,3,5,2] => [5,1,3,2,4,6] => [1,3,5,4,6,2] => 3
[1,6,3,4,2,5] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,3,4,5,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,3,5,2,4] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,3,5,4,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,4,2,3,5] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,4,2,5,3] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,4,3,2,5] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,4,3,5,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,4,5,2,3] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,4,5,3,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,5,2,3,4] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,5,2,4,3] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,5,3,2,4] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,5,3,4,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,5,4,2,3] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[1,6,5,4,3,2] => [1,6,5,4,3,2] => [5,1,4,3,2,6] => [1,5,4,3,6,2] => 3
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [6,1,2,3,4,5] => [1,2,3,4,6,5] => 3
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [6,1,2,3,5,4] => [6,1,2,3,5,4] => 2
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [6,1,2,4,3,5] => [1,6,2,4,5,3] => 3
[2,1,3,5,6,4] => [2,1,3,6,5,4] => [6,1,2,5,4,3] => [6,5,1,2,4,3] => 3
[2,1,3,6,4,5] => [2,1,3,6,5,4] => [6,1,2,5,4,3] => [6,5,1,2,4,3] => 3
[2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,1,2,5,4,3] => [6,5,1,2,4,3] => 3
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [6,1,3,2,4,5] => [1,3,6,4,5,2] => 3
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [6,1,3,2,5,4] => [3,1,6,2,5,4] => 3
[2,1,4,5,3,6] => [2,1,5,4,3,6] => [6,1,4,3,2,5] => [1,6,4,3,5,2] => 3
[2,1,4,5,6,3] => [2,1,6,4,5,3] => [6,1,5,3,4,2] => [6,1,5,3,4,2] => 3
[2,1,4,6,3,5] => [2,1,5,6,3,4] => [6,1,4,5,2,3] => [4,6,1,2,5,3] => 3
[2,1,4,6,5,3] => [2,1,6,5,4,3] => [6,1,5,4,3,2] => [6,5,4,1,3,2] => 3
[2,1,5,3,4,6] => [2,1,5,4,3,6] => [6,1,4,3,2,5] => [1,6,4,3,5,2] => 3
[2,1,5,3,6,4] => [2,1,6,4,5,3] => [6,1,5,3,4,2] => [6,1,5,3,4,2] => 3
[2,1,5,4,3,6] => [2,1,5,4,3,6] => [6,1,4,3,2,5] => [1,6,4,3,5,2] => 3
[2,1,5,4,6,3] => [2,1,6,4,5,3] => [6,1,5,3,4,2] => [6,1,5,3,4,2] => 3
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [6,1,5,4,3,2] => [6,5,4,1,3,2] => 3
[2,1,5,6,4,3] => [2,1,6,5,4,3] => [6,1,5,4,3,2] => [6,5,4,1,3,2] => 3
[2,1,6,3,4,5] => [2,1,6,4,5,3] => [6,1,5,3,4,2] => [6,1,5,3,4,2] => 3
[2,1,6,3,5,4] => [2,1,6,4,5,3] => [6,1,5,3,4,2] => [6,1,5,3,4,2] => 3
[2,1,6,4,3,5] => [2,1,6,5,4,3] => [6,1,5,4,3,2] => [6,5,4,1,3,2] => 3
[2,1,6,4,5,3] => [2,1,6,5,4,3] => [6,1,5,4,3,2] => [6,5,4,1,3,2] => 3
[2,1,6,5,3,4] => [2,1,6,5,4,3] => [6,1,5,4,3,2] => [6,5,4,1,3,2] => 3
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,1,5,4,3,2] => [6,5,4,1,3,2] => 3
[2,3,1,4,5,6] => [3,2,1,4,5,6] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 3
[2,3,1,4,6,5] => [3,2,1,4,6,5] => [1,2,6,3,5,4] => [6,1,5,2,3,4] => 3
[2,3,1,5,4,6] => [3,2,1,5,4,6] => [1,2,6,4,3,5] => [1,6,4,2,3,5] => 2
[2,3,1,5,6,4] => [3,2,1,6,5,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 2
[2,3,1,6,4,5] => [3,2,1,6,5,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 2
[2,3,1,6,5,4] => [3,2,1,6,5,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 2
[2,3,4,1,5,6] => [4,2,3,1,5,6] => [3,1,6,2,4,5] => [1,3,4,2,6,5] => 3
[2,3,4,1,6,5] => [4,2,3,1,6,5] => [3,1,6,2,5,4] => [6,1,3,2,5,4] => 3
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [4,6,2,1,3,5] => [2,4,6,3,1,5] => 3
[2,3,4,5,6,1] => [6,2,3,4,5,1] => [5,6,2,3,1,4] => [2,5,3,6,1,4] => 3
[2,3,4,6,1,5] => [5,2,3,6,1,4] => [4,6,2,5,3,1] => [6,4,2,5,1,3] => 3
[2,3,4,6,5,1] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[2,3,5,1,4,6] => [4,2,5,1,3,6] => [3,6,4,2,5,1] => [6,3,4,2,1,5] => 3
[2,3,5,1,6,4] => [4,2,6,1,5,3] => [3,6,5,4,1,2] => [3,6,5,4,1,2] => 2
[2,3,5,4,1,6] => [5,2,4,3,1,6] => [4,1,6,3,2,5] => [1,4,3,2,6,5] => 3
[2,3,5,4,6,1] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[2,3,5,6,1,4] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[2,3,5,6,4,1] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[2,3,6,1,4,5] => [4,2,6,1,5,3] => [3,6,5,4,1,2] => [3,6,5,4,1,2] => 2
[2,3,6,1,5,4] => [4,2,6,1,5,3] => [3,6,5,4,1,2] => [3,6,5,4,1,2] => 2
[2,3,6,4,1,5] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[2,3,6,4,5,1] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[2,3,6,5,1,4] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[2,3,6,5,4,1] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[2,4,1,3,5,6] => [3,4,1,2,5,6] => [2,3,6,4,5,1] => [6,2,3,1,4,5] => 3
[2,4,1,3,6,5] => [3,4,1,2,6,5] => [2,3,6,5,1,4] => [2,6,5,1,3,4] => 2
[2,4,1,5,3,6] => [3,5,1,4,2,6] => [2,4,3,6,1,5] => [4,6,2,3,1,5] => 3
[2,4,1,5,6,3] => [3,6,1,4,5,2] => [2,5,3,4,6,1] => [5,2,3,4,1,6] => 3
[2,4,1,6,3,5] => [3,5,1,6,2,4] => [2,1,4,5,6,3] => [2,1,4,5,6,3] => 2
[2,4,1,6,5,3] => [3,6,1,5,4,2] => [2,5,4,1,3,6] => [2,5,6,4,1,3] => 3
[2,4,3,1,5,6] => [4,3,2,1,5,6] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => 3
[2,4,3,1,6,5] => [4,3,2,1,6,5] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 3
[2,4,3,5,1,6] => [5,3,2,4,1,6] => [4,2,1,6,3,5] => [2,4,3,6,5,1] => 3
[2,4,3,5,6,1] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[2,4,3,6,1,5] => [5,3,2,6,1,4] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 3
[2,4,3,6,5,1] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[2,4,5,1,3,6] => [4,5,3,1,2,6] => [3,4,2,6,5,1] => [3,2,1,6,4,5] => 2
[2,4,5,1,6,3] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[2,4,5,3,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[2,4,5,6,1,3] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[2,4,5,6,3,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[2,4,6,1,3,5] => [4,5,6,1,2,3] => [3,4,5,6,2,1] => [3,2,1,4,5,6] => 2
[2,4,6,1,5,3] => [4,6,5,1,3,2] => [3,5,4,2,6,1] => [5,3,4,2,1,6] => 3
[2,4,6,3,1,5] => [5,4,6,2,1,3] => [4,3,1,5,6,2] => [4,1,5,6,3,2] => 3
[2,4,6,3,5,1] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[2,4,6,5,1,3] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[2,4,6,5,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[2,5,1,3,4,6] => [3,5,1,4,2,6] => [2,4,3,6,1,5] => [4,6,2,3,1,5] => 3
[2,5,1,3,6,4] => [3,6,1,4,5,2] => [2,5,3,4,6,1] => [5,2,3,4,1,6] => 3
[2,5,1,4,3,6] => [3,5,1,4,2,6] => [2,4,3,6,1,5] => [4,6,2,3,1,5] => 3
[2,5,1,4,6,3] => [3,6,1,4,5,2] => [2,5,3,4,6,1] => [5,2,3,4,1,6] => 3
[2,5,1,6,3,4] => [3,6,1,5,4,2] => [2,5,4,1,3,6] => [2,5,6,4,1,3] => 3
[2,5,1,6,4,3] => [3,6,1,5,4,2] => [2,5,4,1,3,6] => [2,5,6,4,1,3] => 3
[2,5,3,1,4,6] => [4,5,3,1,2,6] => [3,4,2,6,5,1] => [3,2,1,6,4,5] => 2
[2,5,3,1,6,4] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[2,5,3,4,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[2,5,3,6,1,4] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[2,5,3,6,4,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[2,5,4,1,3,6] => [4,5,3,1,2,6] => [3,4,2,6,5,1] => [3,2,1,6,4,5] => 2
[2,5,4,1,6,3] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[2,5,4,3,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[2,5,4,6,1,3] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[2,5,4,6,3,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[2,5,6,1,3,4] => [4,6,5,1,3,2] => [3,5,4,2,6,1] => [5,3,4,2,1,6] => 3
[2,5,6,1,4,3] => [4,6,5,1,3,2] => [3,5,4,2,6,1] => [5,3,4,2,1,6] => 3
[2,5,6,3,1,4] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[2,5,6,3,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[2,5,6,4,1,3] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[2,5,6,4,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[2,6,1,3,4,5] => [3,6,1,4,5,2] => [2,5,3,4,6,1] => [5,2,3,4,1,6] => 3
[2,6,1,3,5,4] => [3,6,1,4,5,2] => [2,5,3,4,6,1] => [5,2,3,4,1,6] => 3
[2,6,1,4,3,5] => [3,6,1,5,4,2] => [2,5,4,1,3,6] => [2,5,6,4,1,3] => 3
[2,6,1,4,5,3] => [3,6,1,5,4,2] => [2,5,4,1,3,6] => [2,5,6,4,1,3] => 3
[2,6,1,5,3,4] => [3,6,1,5,4,2] => [2,5,4,1,3,6] => [2,5,6,4,1,3] => 3
[2,6,1,5,4,3] => [3,6,1,5,4,2] => [2,5,4,1,3,6] => [2,5,6,4,1,3] => 3
[2,6,3,1,4,5] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[2,6,3,1,5,4] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[2,6,3,4,1,5] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[2,6,3,4,5,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[2,6,3,5,1,4] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[2,6,3,5,4,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[2,6,4,1,3,5] => [4,6,5,1,3,2] => [3,5,4,2,6,1] => [5,3,4,2,1,6] => 3
[2,6,4,1,5,3] => [4,6,5,1,3,2] => [3,5,4,2,6,1] => [5,3,4,2,1,6] => 3
[2,6,4,3,1,5] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[2,6,4,3,5,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[2,6,4,5,1,3] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[2,6,4,5,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[2,6,5,1,3,4] => [4,6,5,1,3,2] => [3,5,4,2,6,1] => [5,3,4,2,1,6] => 3
[2,6,5,1,4,3] => [4,6,5,1,3,2] => [3,5,4,2,6,1] => [5,3,4,2,1,6] => 3
[2,6,5,3,1,4] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[2,6,5,3,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[2,6,5,4,1,3] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[2,6,5,4,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 3
[3,1,2,4,6,5] => [3,2,1,4,6,5] => [1,2,6,3,5,4] => [6,1,5,2,3,4] => 3
[3,1,2,5,4,6] => [3,2,1,5,4,6] => [1,2,6,4,3,5] => [1,6,4,2,3,5] => 2
[3,1,2,5,6,4] => [3,2,1,6,5,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 2
[3,1,2,6,4,5] => [3,2,1,6,5,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 2
[3,1,2,6,5,4] => [3,2,1,6,5,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 2
[3,1,4,2,5,6] => [4,2,3,1,5,6] => [3,1,6,2,4,5] => [1,3,4,2,6,5] => 3
[3,1,4,2,6,5] => [4,2,3,1,6,5] => [3,1,6,2,5,4] => [6,1,3,2,5,4] => 3
[3,1,4,5,2,6] => [5,2,3,4,1,6] => [4,6,2,1,3,5] => [2,4,6,3,1,5] => 3
[3,1,4,5,6,2] => [6,2,3,4,5,1] => [5,6,2,3,1,4] => [2,5,3,6,1,4] => 3
[3,1,4,6,2,5] => [5,2,3,6,1,4] => [4,6,2,5,3,1] => [6,4,2,5,1,3] => 3
[3,1,4,6,5,2] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[3,1,5,2,4,6] => [4,2,5,1,3,6] => [3,6,4,2,5,1] => [6,3,4,2,1,5] => 3
[3,1,5,2,6,4] => [4,2,6,1,5,3] => [3,6,5,4,1,2] => [3,6,5,4,1,2] => 2
[3,1,5,4,2,6] => [5,2,4,3,1,6] => [4,1,6,3,2,5] => [1,4,3,2,6,5] => 3
[3,1,5,4,6,2] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[3,1,5,6,2,4] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[3,1,5,6,4,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[3,1,6,2,4,5] => [4,2,6,1,5,3] => [3,6,5,4,1,2] => [3,6,5,4,1,2] => 2
[3,1,6,2,5,4] => [4,2,6,1,5,3] => [3,6,5,4,1,2] => [3,6,5,4,1,2] => 2
[3,1,6,4,2,5] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[3,1,6,4,5,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[3,1,6,5,2,4] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[3,1,6,5,4,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 3
[3,2,1,4,6,5] => [3,2,1,4,6,5] => [1,2,6,3,5,4] => [6,1,5,2,3,4] => 3
[3,2,1,5,4,6] => [3,2,1,5,4,6] => [1,2,6,4,3,5] => [1,6,4,2,3,5] => 2
[3,2,1,5,6,4] => [3,2,1,6,5,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 2
[3,2,1,6,4,5] => [3,2,1,6,5,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 2
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 2
[3,2,4,1,5,6] => [4,2,3,1,5,6] => [3,1,6,2,4,5] => [1,3,4,2,6,5] => 3
[3,2,4,1,6,5] => [4,2,3,1,6,5] => [3,1,6,2,5,4] => [6,1,3,2,5,4] => 3
[3,2,4,5,1,6] => [5,2,3,4,1,6] => [4,6,2,1,3,5] => [2,4,6,3,1,5] => 3
[3,2,4,5,6,1] => [6,2,3,4,5,1] => [5,6,2,3,1,4] => [2,5,3,6,1,4] => 3
[3,2,4,6,1,5] => [5,2,3,6,1,4] => [4,6,2,5,3,1] => [6,4,2,5,1,3] => 3
[3,2,4,6,5,1] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[3,2,5,1,4,6] => [4,2,5,1,3,6] => [3,6,4,2,5,1] => [6,3,4,2,1,5] => 3
[3,2,5,1,6,4] => [4,2,6,1,5,3] => [3,6,5,4,1,2] => [3,6,5,4,1,2] => 2
[3,2,5,4,1,6] => [5,2,4,3,1,6] => [4,1,6,3,2,5] => [1,4,3,2,6,5] => 3
[3,2,5,4,6,1] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[3,2,5,6,1,4] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[3,2,5,6,4,1] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[3,2,6,1,4,5] => [4,2,6,1,5,3] => [3,6,5,4,1,2] => [3,6,5,4,1,2] => 2
[3,2,6,1,5,4] => [4,2,6,1,5,3] => [3,6,5,4,1,2] => [3,6,5,4,1,2] => 2
[3,2,6,4,1,5] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[3,2,6,4,5,1] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[3,2,6,5,1,4] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[3,2,6,5,4,1] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[3,4,1,2,5,6] => [4,3,2,1,5,6] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => 3
[3,4,1,2,6,5] => [4,3,2,1,6,5] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 3
[3,4,1,5,2,6] => [5,3,2,4,1,6] => [4,2,1,6,3,5] => [2,4,3,6,5,1] => 3
[3,4,1,5,6,2] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[3,4,1,6,2,5] => [5,3,2,6,1,4] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 3
[3,4,1,6,5,2] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[3,4,2,1,5,6] => [4,3,2,1,5,6] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => 3
[3,4,2,1,6,5] => [4,3,2,1,6,5] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 3
[3,4,2,5,1,6] => [5,3,2,4,1,6] => [4,2,1,6,3,5] => [2,4,3,6,5,1] => 3
[3,4,2,5,6,1] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[3,4,2,6,1,5] => [5,3,2,6,1,4] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 3
[3,4,2,6,5,1] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[3,4,5,1,2,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[3,4,5,1,6,2] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[3,4,5,2,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[3,4,5,2,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[3,4,5,6,1,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[3,4,5,6,2,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[3,4,6,1,2,5] => [5,4,6,2,1,3] => [4,3,1,5,6,2] => [4,1,5,6,3,2] => 3
[3,4,6,1,5,2] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[3,4,6,2,1,5] => [5,4,6,2,1,3] => [4,3,1,5,6,2] => [4,1,5,6,3,2] => 3
[3,4,6,2,5,1] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[3,4,6,5,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,4,6,5,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,5,1,2,4,6] => [4,5,3,1,2,6] => [3,4,2,6,5,1] => [3,2,1,6,4,5] => 2
[3,5,1,2,6,4] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[3,5,1,4,6,2] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[3,5,1,6,2,4] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[3,5,1,6,4,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[3,5,2,1,4,6] => [4,5,3,1,2,6] => [3,4,2,6,5,1] => [3,2,1,6,4,5] => 2
[3,5,2,1,6,4] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[3,5,2,4,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[3,5,2,6,1,4] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[3,5,2,6,4,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[3,5,4,1,6,2] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[3,5,4,2,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[3,5,4,6,1,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[3,5,4,6,2,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[3,5,6,1,2,4] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[3,5,6,1,4,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,5,6,2,1,4] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[3,5,6,2,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,5,6,4,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,5,6,4,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,6,1,2,4,5] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[3,6,1,2,5,4] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[3,6,1,4,2,5] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[3,6,1,4,5,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[3,6,1,5,2,4] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[3,6,1,5,4,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[3,6,2,1,4,5] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[3,6,2,1,5,4] => [4,6,3,1,5,2] => [3,1,5,2,4,6] => [1,3,5,2,6,4] => 3
[3,6,2,4,1,5] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[3,6,2,4,5,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[3,6,2,5,1,4] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[3,6,2,5,4,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[3,6,4,1,2,5] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[3,6,4,1,5,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,6,4,2,1,5] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[3,6,4,2,5,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,6,4,5,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,6,4,5,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,6,5,1,2,4] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[3,6,5,1,4,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,6,5,2,1,4] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[3,6,5,2,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,6,5,4,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[3,6,5,4,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,1,2,3,5,6] => [4,2,3,1,5,6] => [3,1,6,2,4,5] => [1,3,4,2,6,5] => 3
[4,1,2,3,6,5] => [4,2,3,1,6,5] => [3,1,6,2,5,4] => [6,1,3,2,5,4] => 3
[4,1,2,5,3,6] => [5,2,3,4,1,6] => [4,6,2,1,3,5] => [2,4,6,3,1,5] => 3
[4,1,2,5,6,3] => [6,2,3,4,5,1] => [5,6,2,3,1,4] => [2,5,3,6,1,4] => 3
[4,1,2,6,3,5] => [5,2,3,6,1,4] => [4,6,2,5,3,1] => [6,4,2,5,1,3] => 3
[4,1,2,6,5,3] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[4,1,3,2,5,6] => [4,2,3,1,5,6] => [3,1,6,2,4,5] => [1,3,4,2,6,5] => 3
[4,1,3,2,6,5] => [4,2,3,1,6,5] => [3,1,6,2,5,4] => [6,1,3,2,5,4] => 3
[4,1,3,5,2,6] => [5,2,3,4,1,6] => [4,6,2,1,3,5] => [2,4,6,3,1,5] => 3
[4,1,3,5,6,2] => [6,2,3,4,5,1] => [5,6,2,3,1,4] => [2,5,3,6,1,4] => 3
[4,1,3,6,2,5] => [5,2,3,6,1,4] => [4,6,2,5,3,1] => [6,4,2,5,1,3] => 3
[4,1,3,6,5,2] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[4,1,5,2,3,6] => [5,2,4,3,1,6] => [4,1,6,3,2,5] => [1,4,3,2,6,5] => 3
[4,1,5,2,6,3] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[4,1,5,3,2,6] => [5,2,4,3,1,6] => [4,1,6,3,2,5] => [1,4,3,2,6,5] => 3
[4,1,5,3,6,2] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[4,1,5,6,2,3] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[4,1,5,6,3,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[4,1,6,2,3,5] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[4,1,6,2,5,3] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[4,1,6,3,2,5] => [5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 2
[4,1,6,3,5,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[4,1,6,5,2,3] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[4,1,6,5,3,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[4,2,1,3,5,6] => [4,3,2,1,5,6] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => 3
[4,2,1,3,6,5] => [4,3,2,1,6,5] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 3
[4,2,1,5,3,6] => [5,3,2,4,1,6] => [4,2,1,6,3,5] => [2,4,3,6,5,1] => 3
[4,2,1,5,6,3] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[4,2,1,6,3,5] => [5,3,2,6,1,4] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 3
[4,2,1,6,5,3] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[4,2,3,1,5,6] => [4,3,2,1,5,6] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => 3
[4,2,3,1,6,5] => [4,3,2,1,6,5] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 3
[4,2,3,5,1,6] => [5,3,2,4,1,6] => [4,2,1,6,3,5] => [2,4,3,6,5,1] => 3
[4,2,3,5,6,1] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[4,2,3,6,1,5] => [5,3,2,6,1,4] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 3
[4,2,3,6,5,1] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[4,2,5,1,6,3] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[4,2,5,3,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[4,2,5,6,1,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,2,5,6,3,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,2,6,1,3,5] => [5,4,6,2,1,3] => [4,3,1,5,6,2] => [4,1,5,6,3,2] => 3
[4,2,6,1,5,3] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[4,2,6,3,1,5] => [5,4,6,2,1,3] => [4,3,1,5,6,2] => [4,1,5,6,3,2] => 3
[4,2,6,3,5,1] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[4,2,6,5,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,2,6,5,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,3,1,2,5,6] => [4,3,2,1,5,6] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => 3
[4,3,1,2,6,5] => [4,3,2,1,6,5] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 3
[4,3,1,5,2,6] => [5,3,2,4,1,6] => [4,2,1,6,3,5] => [2,4,3,6,5,1] => 3
[4,3,1,5,6,2] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[4,3,1,6,2,5] => [5,3,2,6,1,4] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 3
[4,3,1,6,5,2] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => 3
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 3
[4,3,2,5,1,6] => [5,3,2,4,1,6] => [4,2,1,6,3,5] => [2,4,3,6,5,1] => 3
[4,3,2,5,6,1] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[4,3,2,6,1,5] => [5,3,2,6,1,4] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 3
[4,3,2,6,5,1] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[4,3,5,1,6,2] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[4,3,5,2,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[4,3,5,6,1,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,3,5,6,2,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,3,6,1,2,5] => [5,4,6,2,1,3] => [4,3,1,5,6,2] => [4,1,5,6,3,2] => 3
[4,3,6,1,5,2] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[4,3,6,2,1,5] => [5,4,6,2,1,3] => [4,3,1,5,6,2] => [4,1,5,6,3,2] => 3
[4,3,6,2,5,1] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[4,3,6,5,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,3,6,5,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[4,5,1,2,6,3] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[4,5,1,3,6,2] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[4,5,1,6,2,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,5,1,6,3,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[4,5,2,1,6,3] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[4,5,2,3,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[4,5,2,6,1,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,5,2,6,3,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[4,5,3,1,6,2] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[4,5,3,2,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[4,5,3,6,1,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,5,3,6,2,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,5,6,1,2,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,5,6,1,3,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,5,6,2,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,5,6,2,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,5,6,3,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,5,6,3,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,1,2,3,5] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[4,6,1,2,5,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,6,1,3,2,5] => [5,6,3,4,1,2] => [4,5,2,3,1,6] => [4,5,2,6,1,3] => 3
[4,6,1,3,5,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,6,1,5,2,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,6,1,5,3,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[4,6,2,1,3,5] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[4,6,2,1,5,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,2,3,1,5] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[4,6,2,3,5,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,2,5,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,2,5,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,3,1,2,5] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[4,6,3,1,5,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,3,2,1,5] => [5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[4,6,3,2,5,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,3,5,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,3,5,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,5,1,2,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,5,1,3,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,5,2,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,5,2,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,5,3,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[4,6,5,3,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,1,2,3,4,6] => [5,2,3,4,1,6] => [4,6,2,1,3,5] => [2,4,6,3,1,5] => 3
[5,1,2,3,6,4] => [6,2,3,4,5,1] => [5,6,2,3,1,4] => [2,5,3,6,1,4] => 3
[5,1,2,4,3,6] => [5,2,3,4,1,6] => [4,6,2,1,3,5] => [2,4,6,3,1,5] => 3
[5,1,2,4,6,3] => [6,2,3,4,5,1] => [5,6,2,3,1,4] => [2,5,3,6,1,4] => 3
[5,1,2,6,3,4] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[5,1,2,6,4,3] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[5,1,3,2,4,6] => [5,2,4,3,1,6] => [4,1,6,3,2,5] => [1,4,3,2,6,5] => 3
[5,1,3,2,6,4] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[5,1,3,4,2,6] => [5,2,4,3,1,6] => [4,1,6,3,2,5] => [1,4,3,2,6,5] => 3
[5,1,3,4,6,2] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[5,1,3,6,2,4] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[5,1,3,6,4,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[5,1,4,2,3,6] => [5,2,4,3,1,6] => [4,1,6,3,2,5] => [1,4,3,2,6,5] => 3
[5,1,4,2,6,3] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[5,1,4,3,2,6] => [5,2,4,3,1,6] => [4,1,6,3,2,5] => [1,4,3,2,6,5] => 3
[5,1,4,3,6,2] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[5,1,4,6,2,3] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[5,1,4,6,3,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[5,1,6,2,3,4] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[5,1,6,2,4,3] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[5,1,6,3,2,4] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[5,1,6,3,4,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[5,1,6,4,2,3] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[5,1,6,4,3,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[5,2,1,3,4,6] => [5,3,2,4,1,6] => [4,2,1,6,3,5] => [2,4,3,6,5,1] => 3
[5,2,1,3,6,4] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[5,2,1,4,3,6] => [5,3,2,4,1,6] => [4,2,1,6,3,5] => [2,4,3,6,5,1] => 3
[5,2,1,4,6,3] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[5,2,1,6,3,4] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[5,2,1,6,4,3] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,2,3,1,6,4] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,2,3,4,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,2,3,6,1,4] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,2,3,6,4,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,2,4,1,6,3] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,2,4,3,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,2,4,6,1,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,2,4,6,3,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,2,6,1,3,4] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[5,2,6,1,4,3] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[5,2,6,3,1,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,2,6,3,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,2,6,4,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,2,6,4,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,3,1,2,6,4] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,3,1,4,6,2] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,3,1,6,2,4] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,3,1,6,4,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,3,2,1,6,4] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,3,2,4,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,3,2,6,1,4] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,3,2,6,4,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,3,4,1,6,2] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,3,4,2,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,3,4,6,1,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,3,4,6,2,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,3,6,1,2,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,3,6,1,4,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,3,6,2,1,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,3,6,2,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,3,6,4,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,3,6,4,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,4,1,2,6,3] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,4,1,3,6,2] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,4,1,6,2,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,4,1,6,3,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,4,2,1,6,3] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,4,2,3,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,4,2,6,1,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,4,2,6,3,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,4,3,1,6,2] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 3
[5,4,3,2,6,1] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[5,4,3,6,1,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,4,3,6,2,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,4,6,1,2,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,4,6,1,3,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,4,6,2,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,4,6,2,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,4,6,3,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,4,6,3,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,1,2,3,4] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,6,1,2,4,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,6,1,3,2,4] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,6,1,3,4,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,6,1,4,2,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,6,1,4,3,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[5,6,2,1,3,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,2,1,4,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,2,3,1,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,2,3,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,2,4,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,2,4,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,3,1,2,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,3,1,4,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,3,2,1,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,3,2,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,3,4,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,3,4,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,4,1,2,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,4,1,3,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,4,2,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,4,2,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,4,3,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[5,6,4,3,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,1,2,3,4,5] => [6,2,3,4,5,1] => [5,6,2,3,1,4] => [2,5,3,6,1,4] => 3
[6,1,2,3,5,4] => [6,2,3,4,5,1] => [5,6,2,3,1,4] => [2,5,3,6,1,4] => 3
[6,1,2,4,3,5] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[6,1,2,4,5,3] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[6,1,2,5,3,4] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[6,1,2,5,4,3] => [6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 3
[6,1,3,2,4,5] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[6,1,3,2,5,4] => [6,2,4,3,5,1] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[6,1,3,4,2,5] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,3,4,5,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,3,5,2,4] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,3,5,4,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,4,2,3,5] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,4,2,5,3] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,4,3,2,5] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,4,3,5,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,4,5,2,3] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,4,5,3,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,5,2,3,4] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,5,2,4,3] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,5,3,2,4] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,5,3,4,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,5,4,2,3] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,1,5,4,3,2] => [6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 3
[6,2,1,3,4,5] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[6,2,1,3,5,4] => [6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,3,1,6,4] => 3
[6,2,1,4,3,5] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[6,2,1,4,5,3] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[6,2,1,5,3,4] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[6,2,1,5,4,3] => [6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 3
[6,2,3,1,4,5] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[6,2,3,1,5,4] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[6,2,3,4,1,5] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,2,3,4,5,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,2,3,5,1,4] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,2,3,5,4,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,2,4,1,3,5] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[6,2,4,1,5,3] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[6,2,4,3,1,5] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,2,4,3,5,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,2,4,5,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,2,4,5,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,2,5,1,3,4] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[6,2,5,1,4,3] => [6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,1,5,4,6,2] => 3
[6,2,5,3,1,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,2,5,3,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,2,5,4,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,2,5,4,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,1,2,4,5] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[6,3,1,2,5,4] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[6,3,1,4,2,5] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,3,1,4,5,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,3,1,5,2,4] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,3,1,5,4,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,3,2,1,4,5] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[6,3,2,1,5,4] => [6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 3
[6,3,2,4,1,5] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,3,2,4,5,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,3,2,5,1,4] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,3,2,5,4,1] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,3,4,1,2,5] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,4,1,5,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,4,2,1,5] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,4,2,5,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,4,5,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,4,5,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,5,1,2,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,5,1,4,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,5,2,1,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,5,2,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,5,4,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,3,5,4,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,1,2,3,5] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,4,1,2,5,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,4,1,3,2,5] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,4,1,3,5,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,4,1,5,2,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,4,1,5,3,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,4,2,1,3,5] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,2,1,5,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,2,3,1,5] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,2,3,5,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,2,5,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,2,5,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,3,1,2,5] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,3,1,5,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,3,2,1,5] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,3,2,5,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,3,5,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,3,5,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,5,1,2,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,5,1,3,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,5,2,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,5,2,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,5,3,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,4,5,3,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,1,2,3,4] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,5,1,2,4,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,5,1,3,2,4] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,5,1,3,4,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,5,1,4,2,3] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,5,1,4,3,2] => [6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,6,4,3,1] => 3
[6,5,2,1,3,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,2,1,4,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,2,3,1,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,2,3,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,2,4,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,2,4,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,3,1,2,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,3,1,4,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,3,2,1,4] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,3,2,4,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,3,4,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,3,4,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,4,1,2,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,4,1,3,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,4,2,1,3] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,4,2,3,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,4,3,1,2] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [7,3,1,2,4,5,6] => [1,3,4,5,7,6,2] => 3
[1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [7,3,1,2,5,4,6] => [1,3,2,5,7,6,4] => 3
[1,2,4,6,3,5,7] => [1,2,5,6,3,4,7] => [7,4,5,1,2,3,6] => [1,4,5,7,2,6,3] => 3
[1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [3,1,2,7,4,5,6] => [1,3,4,2,5,7,6] => 3
[1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [4,1,2,3,7,5,6] => [1,4,2,3,5,7,6] => 3
[1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [6,1,2,3,4,5,7] => [1,2,3,4,6,7,5] => 3
[1,3,4,6,5,7,2] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,3,5,4,2,6,7] => [1,5,4,3,2,6,7] => [4,1,3,2,7,5,6] => [1,4,3,7,5,6,2] => 3
[1,3,5,4,6,7,2] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,3,5,4,7,6,2] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,3,5,7,4,6,2] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,4,2,3,5,6,7] => [1,4,3,2,5,6,7] => [3,1,2,7,4,5,6] => [1,3,4,2,5,7,6] => 3
[1,4,2,5,3,6,7] => [1,5,3,4,2,6,7] => [4,1,2,3,7,5,6] => [1,4,2,3,5,7,6] => 3
[1,4,2,5,6,7,3] => [1,7,3,4,5,6,2] => [6,1,2,3,4,5,7] => [1,2,3,4,6,7,5] => 3
[1,4,2,6,5,7,3] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [3,1,2,7,4,5,6] => [1,3,4,2,5,7,6] => 3
[1,4,3,5,2,6,7] => [1,5,3,4,2,6,7] => [4,1,2,3,7,5,6] => [1,4,2,3,5,7,6] => 3
[1,4,3,5,6,7,2] => [1,7,3,4,5,6,2] => [6,1,2,3,4,5,7] => [1,2,3,4,6,7,5] => 3
[1,4,3,6,5,7,2] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,4,5,2,3,6,7] => [1,5,4,3,2,6,7] => [4,1,3,2,7,5,6] => [1,4,3,7,5,6,2] => 3
[1,4,5,2,6,7,3] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,4,5,2,7,6,3] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,4,5,3,2,6,7] => [1,5,4,3,2,6,7] => [4,1,3,2,7,5,6] => [1,4,3,7,5,6,2] => 3
[1,4,5,3,6,7,2] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,4,5,3,7,6,2] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,4,5,7,2,6,3] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,4,5,7,3,6,2] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,5,2,3,4,6,7] => [1,5,3,4,2,6,7] => [4,1,2,3,7,5,6] => [1,4,2,3,5,7,6] => 3
[1,5,2,3,6,7,4] => [1,7,3,4,5,6,2] => [6,1,2,3,4,5,7] => [1,2,3,4,6,7,5] => 3
[1,5,2,4,3,6,7] => [1,5,3,4,2,6,7] => [4,1,2,3,7,5,6] => [1,4,2,3,5,7,6] => 3
[1,5,2,4,6,7,3] => [1,7,3,4,5,6,2] => [6,1,2,3,4,5,7] => [1,2,3,4,6,7,5] => 3
[1,5,2,6,3,7,4] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,5,2,6,4,7,3] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,5,3,2,4,6,7] => [1,5,4,3,2,6,7] => [4,1,3,2,7,5,6] => [1,4,3,7,5,6,2] => 3
[1,5,3,2,6,7,4] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,5,3,2,7,6,4] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,5,3,4,2,6,7] => [1,5,4,3,2,6,7] => [4,1,3,2,7,5,6] => [1,4,3,7,5,6,2] => 3
[1,5,3,4,6,7,2] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,5,3,4,7,6,2] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,5,3,7,2,6,4] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,5,3,7,4,6,2] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,5,4,2,3,6,7] => [1,5,4,3,2,6,7] => [4,1,3,2,7,5,6] => [1,4,3,7,5,6,2] => 3
[1,5,4,2,6,7,3] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,5,4,2,7,6,3] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [4,1,3,2,7,5,6] => [1,4,3,7,5,6,2] => 3
[1,5,4,3,6,7,2] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,5,4,3,7,6,2] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,5,4,7,2,6,3] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,5,4,7,3,6,2] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,6,2,3,4,7,5] => [1,7,3,4,5,6,2] => [6,1,2,3,4,5,7] => [1,2,3,4,6,7,5] => 3
[1,6,2,3,5,7,4] => [1,7,3,4,5,6,2] => [6,1,2,3,4,5,7] => [1,2,3,4,6,7,5] => 3
[1,6,2,4,3,7,5] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,6,2,4,5,7,3] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,6,2,5,3,7,4] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,6,2,5,4,7,3] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,6,3,2,4,7,5] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,6,3,2,5,7,4] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,6,3,2,7,4,5] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,6,3,2,7,5,4] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,6,3,7,2,4,5] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,6,3,7,2,5,4] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,7,2,3,4,5,6] => [1,7,3,4,5,6,2] => [6,1,2,3,4,5,7] => [1,2,3,4,6,7,5] => 3
[1,7,2,3,4,6,5] => [1,7,3,4,5,6,2] => [6,1,2,3,4,5,7] => [1,2,3,4,6,7,5] => 3
[1,7,2,4,3,5,6] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,7,2,4,3,6,5] => [1,7,3,5,4,6,2] => [6,1,2,4,3,5,7] => [1,2,6,4,5,7,3] => 3
[1,7,3,2,4,5,6] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,7,3,2,4,6,5] => [1,7,4,3,5,6,2] => [6,1,3,2,4,5,7] => [1,3,4,6,5,7,2] => 3
[1,7,3,2,5,4,6] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,7,3,2,5,6,4] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,7,3,2,6,4,5] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,7,3,2,6,5,4] => [1,7,4,3,6,5,2] => [6,1,3,2,5,4,7] => [1,3,2,6,5,7,4] => 3
[1,7,3,5,2,4,6] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,7,3,5,2,6,4] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,7,3,6,2,4,5] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[1,7,3,6,2,5,4] => [1,7,5,6,3,4,2] => [6,1,4,5,2,3,7] => [1,4,6,2,5,7,3] => 3
[2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => 3
[2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [7,1,2,4,3,5,6] => [1,2,7,4,5,6,3] => 3
[2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [7,1,3,2,4,5,6] => [1,3,4,7,5,6,2] => 3
[2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [7,1,3,2,5,4,6] => [1,3,2,7,5,6,4] => 3
[2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,2,7,3,4,5,6] => [1,2,3,7,4,5,6] => 3
[2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [1,2,7,4,3,5,6] => [1,2,7,4,3,5,6] => 3
[2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [3,1,7,2,4,5,6] => [1,3,4,5,2,7,6] => 3
[2,3,5,4,1,6,7] => [5,2,4,3,1,6,7] => [4,1,7,3,2,5,6] => [1,4,5,3,2,7,6] => 3
[2,4,3,1,5,6,7] => [4,3,2,1,5,6,7] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => 3
[2,4,5,1,6,7,3] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[2,4,5,3,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[2,4,6,5,1,7,3] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[2,5,3,1,6,7,4] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[2,5,3,4,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[2,5,4,1,6,7,3] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[2,5,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[2,5,6,3,1,7,4] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[2,5,6,4,1,7,3] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[2,6,3,1,4,7,5] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[2,6,3,1,5,7,4] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[2,6,4,3,1,7,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[2,6,4,5,1,7,3] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[2,6,5,3,1,7,4] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[2,6,5,4,1,7,3] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[2,7,3,1,4,5,6] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[2,7,3,1,4,6,5] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[2,7,4,3,1,5,6] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[2,7,4,3,1,6,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [1,2,7,3,4,5,6] => [1,2,3,7,4,5,6] => 3
[3,1,2,5,4,6,7] => [3,2,1,5,4,6,7] => [1,2,7,4,3,5,6] => [1,2,7,4,3,5,6] => 3
[3,1,4,2,5,6,7] => [4,2,3,1,5,6,7] => [3,1,7,2,4,5,6] => [1,3,4,5,2,7,6] => 3
[3,1,5,4,2,6,7] => [5,2,4,3,1,6,7] => [4,1,7,3,2,5,6] => [1,4,5,3,2,7,6] => 3
[3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,2,7,3,4,5,6] => [1,2,3,7,4,5,6] => 3
[3,2,1,5,4,6,7] => [3,2,1,5,4,6,7] => [1,2,7,4,3,5,6] => [1,2,7,4,3,5,6] => 3
[3,2,4,1,5,6,7] => [4,2,3,1,5,6,7] => [3,1,7,2,4,5,6] => [1,3,4,5,2,7,6] => 3
[3,2,5,4,1,6,7] => [5,2,4,3,1,6,7] => [4,1,7,3,2,5,6] => [1,4,5,3,2,7,6] => 3
[3,4,1,2,5,6,7] => [4,3,2,1,5,6,7] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => 3
[3,4,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => 3
[3,4,5,1,2,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[3,4,5,2,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[3,5,1,2,6,7,4] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[3,5,1,4,2,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[3,5,2,1,6,7,4] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[3,5,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[3,5,4,1,2,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[3,5,4,2,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[3,5,6,1,2,7,4] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[3,5,6,2,1,7,4] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[3,6,1,2,4,7,5] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[3,6,1,2,5,7,4] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[3,6,2,1,4,7,5] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[3,6,2,1,5,7,4] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[3,6,4,1,2,7,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[3,6,4,2,1,7,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[3,6,5,1,2,7,4] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[3,6,5,2,1,7,4] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[3,7,1,2,4,5,6] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[3,7,1,2,4,6,5] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[3,7,2,1,4,5,6] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[3,7,2,1,4,6,5] => [4,7,3,1,5,6,2] => [3,1,6,2,4,5,7] => [1,3,4,6,2,7,5] => 3
[3,7,4,1,2,5,6] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[3,7,4,1,2,6,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[3,7,4,2,1,5,6] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[3,7,4,2,1,6,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,1,2,3,5,6,7] => [4,2,3,1,5,6,7] => [3,1,7,2,4,5,6] => [1,3,4,5,2,7,6] => 3
[4,1,3,2,5,6,7] => [4,2,3,1,5,6,7] => [3,1,7,2,4,5,6] => [1,3,4,5,2,7,6] => 3
[4,1,5,2,3,6,7] => [5,2,4,3,1,6,7] => [4,1,7,3,2,5,6] => [1,4,5,3,2,7,6] => 3
[4,1,5,3,2,6,7] => [5,2,4,3,1,6,7] => [4,1,7,3,2,5,6] => [1,4,5,3,2,7,6] => 3
[4,2,1,3,5,6,7] => [4,3,2,1,5,6,7] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => 3
[4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => 3
[4,2,5,1,3,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[4,2,5,3,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[4,3,1,2,5,6,7] => [4,3,2,1,5,6,7] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => 3
[4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => 3
[4,3,5,1,2,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[4,3,5,2,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[4,5,1,2,3,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[4,5,1,3,2,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[4,5,2,1,3,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[4,5,2,3,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[4,5,3,1,2,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[4,5,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[4,6,2,1,3,7,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,6,2,3,1,7,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,6,3,1,2,7,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,6,3,2,1,7,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,7,2,1,3,5,6] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,7,2,1,3,6,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,7,2,3,1,5,6] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,7,2,3,1,6,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,7,3,1,2,5,6] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,7,3,1,2,6,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,7,3,2,1,5,6] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[4,7,3,2,1,6,5] => [5,7,4,3,1,6,2] => [4,1,6,3,2,5,7] => [1,4,6,3,2,7,5] => 3
[5,1,3,2,4,6,7] => [5,2,4,3,1,6,7] => [4,1,7,3,2,5,6] => [1,4,5,3,2,7,6] => 3
[5,1,3,4,2,6,7] => [5,2,4,3,1,6,7] => [4,1,7,3,2,5,6] => [1,4,5,3,2,7,6] => 3
[5,1,4,2,3,6,7] => [5,2,4,3,1,6,7] => [4,1,7,3,2,5,6] => [1,4,5,3,2,7,6] => 3
[5,1,4,3,2,6,7] => [5,2,4,3,1,6,7] => [4,1,7,3,2,5,6] => [1,4,5,3,2,7,6] => 3
[5,2,3,1,4,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,2,4,1,3,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,3,1,2,4,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,3,1,4,2,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,3,2,1,4,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,3,4,1,2,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,3,4,2,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,4,1,2,3,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,4,1,3,2,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,4,2,1,3,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,4,2,3,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,4,3,1,2,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
[5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,4,3,2,7,5,6] => [1,4,3,7,5,2,6] => 3
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,20 216,504
$F_{1} = 1$
$F_{2} = 2\ q$
$F_{3} = 6\ q$
$F_{4} = 4\ q + 20\ q^{2}$
$F_{5} = 120\ q^{2}$
$F_{6} = 216\ q^{2} + 504\ q^{3}$
Description
The maximal size of a pair of weak twins for a permutation.
A pair of weak twins in a permutation is a pair of two disjoint subsequences of the same length with the same descent pattern. More formally, a pair of weak twins of size $k$ for a permutation $\pi$ of length $n$ are two disjoint lists $1 \leq i_1 < \dots < i_k \leq n$ and $1 \leq j_1 < \dots < j_k \leq n$ such that $\pi(i_a) < \pi(i_{a+1})$ if and only if $\pi(j_a) < \pi(j_{a+1})$ for all $1 \leq a < k$.
A pair of weak twins in a permutation is a pair of two disjoint subsequences of the same length with the same descent pattern. More formally, a pair of weak twins of size $k$ for a permutation $\pi$ of length $n$ are two disjoint lists $1 \leq i_1 < \dots < i_k \leq n$ and $1 \leq j_1 < \dots < j_k \leq n$ such that $\pi(i_a) < \pi(i_{a+1})$ if and only if $\pi(j_a) < \pi(j_{a+1})$ for all $1 \leq a < k$.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
Map
toric promotion
Description
Toric promotion of a permutation.
Let $\sigma\in\mathfrak S_n$ be a permutation and let
$ \tau_{i, j}(\sigma) = \begin{cases} \sigma & \text{if $|\sigma^{-1}(i) - \sigma^{-1}(j)| = 1$}\\ (i, j)\circ\sigma & \text{otherwise}. \end{cases} $
The toric promotion operator is the product $\tau_{n,1}\tau_{n-1,n}\dots\tau_{1,2}$.
This is the special case of toric promotion on graphs for the path graph. Its order is $n-1$.
Let $\sigma\in\mathfrak S_n$ be a permutation and let
$ \tau_{i, j}(\sigma) = \begin{cases} \sigma & \text{if $|\sigma^{-1}(i) - \sigma^{-1}(j)| = 1$}\\ (i, j)\circ\sigma & \text{otherwise}. \end{cases} $
The toric promotion operator is the product $\tau_{n,1}\tau_{n-1,n}\dots\tau_{1,2}$.
This is the special case of toric promotion on graphs for the path graph. Its order is $n-1$.
Map
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
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