Identifier
-
Mp00254:
Permutations
—Inverse fireworks map⟶
Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
St000035: Permutations ⟶ ℤ
Values
[1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => 1
[1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => 1
[2,1,3] => [2,1,3] => [2,1,3] => 1
[2,3,1] => [1,3,2] => [1,3,2] => 1
[3,1,2] => [3,1,2] => [2,3,1] => 1
[3,2,1] => [3,2,1] => [3,2,1] => 1
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,3,4,2] => [1,2,4,3] => [1,2,4,3] => 1
[1,4,2,3] => [1,4,2,3] => [1,3,4,2] => 1
[1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 1
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2
[2,3,1,4] => [1,3,2,4] => [1,3,2,4] => 1
[2,3,4,1] => [1,2,4,3] => [1,2,4,3] => 1
[2,4,1,3] => [2,4,1,3] => [3,4,1,2] => 1
[2,4,3,1] => [1,4,3,2] => [1,4,3,2] => 1
[3,1,2,4] => [3,1,2,4] => [2,3,1,4] => 1
[3,1,4,2] => [2,1,4,3] => [2,1,4,3] => 2
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 1
[3,2,4,1] => [2,1,4,3] => [2,1,4,3] => 2
[3,4,1,2] => [2,4,1,3] => [3,4,1,2] => 1
[3,4,2,1] => [1,4,3,2] => [1,4,3,2] => 1
[4,1,2,3] => [4,1,2,3] => [2,3,4,1] => 1
[4,1,3,2] => [4,1,3,2] => [3,2,4,1] => 2
[4,2,1,3] => [4,2,1,3] => [3,4,2,1] => 1
[4,2,3,1] => [4,1,3,2] => [3,2,4,1] => 2
[4,3,1,2] => [4,3,1,2] => [2,4,3,1] => 1
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 1
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,2,4,5,3] => [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,2,5,3,4] => [1,2,5,3,4] => [1,2,4,5,3] => 1
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 1
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[1,3,4,2,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,3,4,5,2] => [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,3,5,2,4] => [1,3,5,2,4] => [1,4,5,2,3] => 1
[1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 1
[1,4,2,3,5] => [1,4,2,3,5] => [1,3,4,2,5] => 1
[1,4,2,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 1
[1,4,3,5,2] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[1,4,5,2,3] => [1,3,5,2,4] => [1,4,5,2,3] => 1
[1,4,5,3,2] => [1,2,5,4,3] => [1,2,5,4,3] => 1
[1,5,2,3,4] => [1,5,2,3,4] => [1,3,4,5,2] => 1
[1,5,2,4,3] => [1,5,2,4,3] => [1,4,3,5,2] => 2
[1,5,3,2,4] => [1,5,3,2,4] => [1,4,5,3,2] => 1
[1,5,3,4,2] => [1,5,2,4,3] => [1,4,3,5,2] => 2
[1,5,4,2,3] => [1,5,4,2,3] => [1,3,5,4,2] => 1
[1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 2
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 2
[2,1,4,5,3] => [2,1,3,5,4] => [2,1,3,5,4] => 2
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,4,5,3] => 2
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => 2
[2,3,1,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[2,3,1,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[2,3,4,1,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[2,3,4,5,1] => [1,2,3,5,4] => [1,2,3,5,4] => 1
[2,3,5,1,4] => [1,3,5,2,4] => [1,4,5,2,3] => 1
[2,3,5,4,1] => [1,2,5,4,3] => [1,2,5,4,3] => 1
[2,4,1,3,5] => [2,4,1,3,5] => [3,4,1,2,5] => 1
[2,4,1,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[2,4,3,1,5] => [1,4,3,2,5] => [1,4,3,2,5] => 1
[2,4,3,5,1] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[2,4,5,1,3] => [1,3,5,2,4] => [1,4,5,2,3] => 1
[2,4,5,3,1] => [1,2,5,4,3] => [1,2,5,4,3] => 1
[2,5,1,3,4] => [2,5,1,3,4] => [3,4,5,1,2] => 1
[2,5,1,4,3] => [2,5,1,4,3] => [4,3,5,1,2] => 2
[2,5,3,1,4] => [1,5,3,2,4] => [1,4,5,3,2] => 1
[2,5,3,4,1] => [1,5,2,4,3] => [1,4,3,5,2] => 2
[2,5,4,1,3] => [2,5,4,1,3] => [3,5,4,1,2] => 1
[2,5,4,3,1] => [1,5,4,3,2] => [1,5,4,3,2] => 1
[3,1,2,4,5] => [3,1,2,4,5] => [2,3,1,4,5] => 1
[3,1,2,5,4] => [3,1,2,5,4] => [2,3,1,5,4] => 2
[3,1,4,2,5] => [2,1,4,3,5] => [2,1,4,3,5] => 2
[3,1,4,5,2] => [2,1,3,5,4] => [2,1,3,5,4] => 2
[3,1,5,2,4] => [3,1,5,2,4] => [4,5,2,3,1] => 2
[3,1,5,4,2] => [2,1,5,4,3] => [2,1,5,4,3] => 2
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 1
[3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 2
[3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => 2
[3,2,4,5,1] => [2,1,3,5,4] => [2,1,3,5,4] => 2
[3,2,5,1,4] => [3,2,5,1,4] => [4,5,1,3,2] => 2
[3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => 2
[3,4,1,2,5] => [2,4,1,3,5] => [3,4,1,2,5] => 1
[3,4,1,5,2] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[3,4,2,1,5] => [1,4,3,2,5] => [1,4,3,2,5] => 1
[3,4,2,5,1] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[3,4,5,1,2] => [1,3,5,2,4] => [1,4,5,2,3] => 1
[3,4,5,2,1] => [1,2,5,4,3] => [1,2,5,4,3] => 1
[3,5,1,2,4] => [3,5,1,2,4] => [2,4,5,1,3] => 1
[3,5,1,4,2] => [2,5,1,4,3] => [4,3,5,1,2] => 2
>>> Load all 1388 entries. <<<[3,5,2,1,4] => [3,5,2,1,4] => [4,5,2,1,3] => 1
[3,5,2,4,1] => [2,5,1,4,3] => [4,3,5,1,2] => 2
[3,5,4,1,2] => [2,5,4,1,3] => [3,5,4,1,2] => 1
[3,5,4,2,1] => [1,5,4,3,2] => [1,5,4,3,2] => 1
[4,1,2,3,5] => [4,1,2,3,5] => [2,3,4,1,5] => 1
[4,1,2,5,3] => [3,1,2,5,4] => [2,3,1,5,4] => 2
[4,1,3,2,5] => [4,1,3,2,5] => [3,2,4,1,5] => 2
[4,1,3,5,2] => [3,1,2,5,4] => [2,3,1,5,4] => 2
[4,1,5,2,3] => [3,1,5,2,4] => [4,5,2,3,1] => 2
[4,1,5,3,2] => [2,1,5,4,3] => [2,1,5,4,3] => 2
[4,2,1,3,5] => [4,2,1,3,5] => [3,4,2,1,5] => 1
[4,2,1,5,3] => [3,2,1,5,4] => [3,2,1,5,4] => 2
[4,2,3,1,5] => [4,1,3,2,5] => [3,2,4,1,5] => 2
[4,2,3,5,1] => [3,1,2,5,4] => [2,3,1,5,4] => 2
[4,2,5,1,3] => [3,2,5,1,4] => [4,5,1,3,2] => 2
[4,2,5,3,1] => [2,1,5,4,3] => [2,1,5,4,3] => 2
[4,3,1,2,5] => [4,3,1,2,5] => [2,4,3,1,5] => 1
[4,3,1,5,2] => [3,2,1,5,4] => [3,2,1,5,4] => 2
[4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1
[4,3,2,5,1] => [3,2,1,5,4] => [3,2,1,5,4] => 2
[4,3,5,1,2] => [3,2,5,1,4] => [4,5,1,3,2] => 2
[4,3,5,2,1] => [2,1,5,4,3] => [2,1,5,4,3] => 2
[4,5,1,2,3] => [3,5,1,2,4] => [2,4,5,1,3] => 1
[4,5,1,3,2] => [2,5,1,4,3] => [4,3,5,1,2] => 2
[4,5,2,1,3] => [3,5,2,1,4] => [4,5,2,1,3] => 1
[4,5,2,3,1] => [2,5,1,4,3] => [4,3,5,1,2] => 2
[4,5,3,1,2] => [2,5,4,1,3] => [3,5,4,1,2] => 1
[4,5,3,2,1] => [1,5,4,3,2] => [1,5,4,3,2] => 1
[5,1,2,3,4] => [5,1,2,3,4] => [2,3,4,5,1] => 1
[5,1,2,4,3] => [5,1,2,4,3] => [2,4,3,5,1] => 2
[5,1,3,2,4] => [5,1,3,2,4] => [3,2,4,5,1] => 2
[5,1,3,4,2] => [5,1,2,4,3] => [2,4,3,5,1] => 2
[5,1,4,2,3] => [5,1,4,2,3] => [3,4,2,5,1] => 2
[5,1,4,3,2] => [5,1,4,3,2] => [4,3,2,5,1] => 2
[5,2,1,3,4] => [5,2,1,3,4] => [3,4,5,2,1] => 1
[5,2,1,4,3] => [5,2,1,4,3] => [4,3,5,2,1] => 2
[5,2,3,1,4] => [5,1,3,2,4] => [3,2,4,5,1] => 2
[5,2,3,4,1] => [5,1,2,4,3] => [2,4,3,5,1] => 2
[5,2,4,1,3] => [5,2,4,1,3] => [3,4,1,5,2] => 2
[5,2,4,3,1] => [5,1,4,3,2] => [4,3,2,5,1] => 2
[5,3,1,2,4] => [5,3,1,2,4] => [2,4,5,3,1] => 1
[5,3,1,4,2] => [5,2,1,4,3] => [4,3,5,2,1] => 2
[5,3,2,1,4] => [5,3,2,1,4] => [4,5,3,2,1] => 1
[5,3,2,4,1] => [5,2,1,4,3] => [4,3,5,2,1] => 2
[5,3,4,1,2] => [5,2,4,1,3] => [3,4,1,5,2] => 2
[5,3,4,2,1] => [5,1,4,3,2] => [4,3,2,5,1] => 2
[5,4,1,2,3] => [5,4,1,2,3] => [2,3,5,4,1] => 1
[5,4,1,3,2] => [5,4,1,3,2] => [3,2,5,4,1] => 2
[5,4,2,1,3] => [5,4,2,1,3] => [3,5,4,2,1] => 1
[5,4,2,3,1] => [5,4,1,3,2] => [3,2,5,4,1] => 2
[5,4,3,1,2] => [5,4,3,1,2] => [2,5,4,3,1] => 1
[5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,2,3,6,4,5] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 1
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,2,4,5,6,3] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,2,4,6,3,5] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => 1
[1,2,4,6,5,3] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[1,2,5,3,4,6] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 1
[1,2,5,3,6,4] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 1
[1,2,5,4,6,3] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,2,5,6,3,4] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => 1
[1,2,5,6,4,3] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[1,2,6,3,4,5] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 1
[1,2,6,3,5,4] => [1,2,6,3,5,4] => [1,2,5,4,6,3] => 2
[1,2,6,4,3,5] => [1,2,6,4,3,5] => [1,2,5,6,4,3] => 1
[1,2,6,4,5,3] => [1,2,6,3,5,4] => [1,2,5,4,6,3] => 2
[1,2,6,5,3,4] => [1,2,6,5,3,4] => [1,2,4,6,5,3] => 1
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[1,3,2,6,4,5] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => 2
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[1,3,4,2,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 1
[1,3,4,2,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,3,4,5,2,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,3,4,5,6,2] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,3,4,6,2,5] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => 1
[1,3,4,6,5,2] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[1,3,5,2,4,6] => [1,3,5,2,4,6] => [1,4,5,2,3,6] => 1
[1,3,5,2,6,4] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,3,5,4,2,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 1
[1,3,5,4,6,2] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,3,5,6,2,4] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => 1
[1,3,5,6,4,2] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[1,3,6,2,4,5] => [1,3,6,2,4,5] => [1,4,5,6,2,3] => 1
[1,3,6,2,5,4] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[1,3,6,4,2,5] => [1,2,6,4,3,5] => [1,2,5,6,4,3] => 1
[1,3,6,4,5,2] => [1,2,6,3,5,4] => [1,2,5,4,6,3] => 2
[1,3,6,5,2,4] => [1,3,6,5,2,4] => [1,4,6,5,2,3] => 1
[1,3,6,5,4,2] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[1,4,2,3,5,6] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 1
[1,4,2,3,6,5] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 2
[1,4,2,5,3,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[1,4,2,5,6,3] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[1,4,2,6,3,5] => [1,4,2,6,3,5] => [1,5,6,3,4,2] => 2
[1,4,2,6,5,3] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 1
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[1,4,3,5,2,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[1,4,3,5,6,2] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[1,4,3,6,2,5] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[1,4,3,6,5,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[1,4,5,2,3,6] => [1,3,5,2,4,6] => [1,4,5,2,3,6] => 1
[1,4,5,2,6,3] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,4,5,3,2,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 1
[1,4,5,3,6,2] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,4,5,6,2,3] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => 1
[1,4,5,6,3,2] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[1,4,6,2,3,5] => [1,4,6,2,3,5] => [1,3,5,6,2,4] => 1
[1,4,6,2,5,3] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[1,4,6,3,2,5] => [1,4,6,3,2,5] => [1,5,6,3,2,4] => 1
[1,4,6,3,5,2] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[1,4,6,5,2,3] => [1,3,6,5,2,4] => [1,4,6,5,2,3] => 1
[1,4,6,5,3,2] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[1,5,2,3,4,6] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 1
[1,5,2,3,6,4] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 2
[1,5,2,4,3,6] => [1,5,2,4,3,6] => [1,4,3,5,2,6] => 2
[1,5,2,4,6,3] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 2
[1,5,2,6,3,4] => [1,4,2,6,3,5] => [1,5,6,3,4,2] => 2
[1,5,2,6,4,3] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[1,5,3,2,4,6] => [1,5,3,2,4,6] => [1,4,5,3,2,6] => 1
[1,5,3,2,6,4] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[1,5,3,4,2,6] => [1,5,2,4,3,6] => [1,4,3,5,2,6] => 2
[1,5,3,4,6,2] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 2
[1,5,3,6,2,4] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[1,5,3,6,4,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[1,5,4,2,3,6] => [1,5,4,2,3,6] => [1,3,5,4,2,6] => 1
[1,5,4,2,6,3] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 1
[1,5,4,3,6,2] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[1,5,4,6,2,3] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[1,5,4,6,3,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[1,5,6,2,3,4] => [1,4,6,2,3,5] => [1,3,5,6,2,4] => 1
[1,5,6,2,4,3] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[1,5,6,3,2,4] => [1,4,6,3,2,5] => [1,5,6,3,2,4] => 1
[1,5,6,3,4,2] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[1,5,6,4,2,3] => [1,3,6,5,2,4] => [1,4,6,5,2,3] => 1
[1,5,6,4,3,2] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[1,6,2,3,4,5] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 1
[1,6,2,3,5,4] => [1,6,2,3,5,4] => [1,3,5,4,6,2] => 2
[1,6,2,4,3,5] => [1,6,2,4,3,5] => [1,4,3,5,6,2] => 2
[1,6,2,4,5,3] => [1,6,2,3,5,4] => [1,3,5,4,6,2] => 2
[1,6,2,5,3,4] => [1,6,2,5,3,4] => [1,4,5,3,6,2] => 2
[1,6,2,5,4,3] => [1,6,2,5,4,3] => [1,5,4,3,6,2] => 2
[1,6,3,2,4,5] => [1,6,3,2,4,5] => [1,4,5,6,3,2] => 1
[1,6,3,2,5,4] => [1,6,3,2,5,4] => [1,5,4,6,3,2] => 2
[1,6,3,4,2,5] => [1,6,2,4,3,5] => [1,4,3,5,6,2] => 2
[1,6,3,4,5,2] => [1,6,2,3,5,4] => [1,3,5,4,6,2] => 2
[1,6,3,5,2,4] => [1,6,3,5,2,4] => [1,4,5,2,6,3] => 2
[1,6,3,5,4,2] => [1,6,2,5,4,3] => [1,5,4,3,6,2] => 2
[1,6,4,2,3,5] => [1,6,4,2,3,5] => [1,3,5,6,4,2] => 1
[1,6,4,2,5,3] => [1,6,3,2,5,4] => [1,5,4,6,3,2] => 2
[1,6,4,3,2,5] => [1,6,4,3,2,5] => [1,5,6,4,3,2] => 1
[1,6,4,3,5,2] => [1,6,3,2,5,4] => [1,5,4,6,3,2] => 2
[1,6,4,5,2,3] => [1,6,3,5,2,4] => [1,4,5,2,6,3] => 2
[1,6,4,5,3,2] => [1,6,2,5,4,3] => [1,5,4,3,6,2] => 2
[1,6,5,2,3,4] => [1,6,5,2,3,4] => [1,3,4,6,5,2] => 1
[1,6,5,2,4,3] => [1,6,5,2,4,3] => [1,4,3,6,5,2] => 2
[1,6,5,3,2,4] => [1,6,5,3,2,4] => [1,4,6,5,3,2] => 1
[1,6,5,3,4,2] => [1,6,5,2,4,3] => [1,4,3,6,5,2] => 2
[1,6,5,4,2,3] => [1,6,5,4,2,3] => [1,3,6,5,4,2] => 1
[1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 1
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 2
[2,1,3,6,4,5] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => 2
[2,1,3,6,5,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 2
[2,1,4,5,6,3] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 2
[2,1,4,6,3,5] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => 2
[2,1,4,6,5,3] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[2,1,5,3,4,6] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => 2
[2,1,5,3,6,4] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 2
[2,1,5,4,6,3] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[2,1,5,6,3,4] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => 2
[2,1,5,6,4,3] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[2,1,6,3,4,5] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => 2
[2,1,6,3,5,4] => [2,1,6,3,5,4] => [2,1,5,4,6,3] => 3
[2,1,6,4,3,5] => [2,1,6,4,3,5] => [2,1,5,6,4,3] => 2
[2,1,6,4,5,3] => [2,1,6,3,5,4] => [2,1,5,4,6,3] => 3
[2,1,6,5,3,4] => [2,1,6,5,3,4] => [2,1,4,6,5,3] => 2
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[2,3,1,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 1
[2,3,1,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[2,3,1,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[2,3,1,5,6,4] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[2,3,1,6,4,5] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => 2
[2,3,1,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[2,3,4,1,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 1
[2,3,4,1,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[2,3,4,5,1,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[2,3,4,5,6,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[2,3,4,6,1,5] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => 1
[2,3,4,6,5,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[2,3,5,1,4,6] => [1,3,5,2,4,6] => [1,4,5,2,3,6] => 1
[2,3,5,1,6,4] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[2,3,5,4,1,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 1
[2,3,5,4,6,1] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[2,3,5,6,1,4] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => 1
[2,3,5,6,4,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[2,3,6,1,4,5] => [1,3,6,2,4,5] => [1,4,5,6,2,3] => 1
[2,3,6,1,5,4] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[2,3,6,4,1,5] => [1,2,6,4,3,5] => [1,2,5,6,4,3] => 1
[2,3,6,4,5,1] => [1,2,6,3,5,4] => [1,2,5,4,6,3] => 2
[2,3,6,5,1,4] => [1,3,6,5,2,4] => [1,4,6,5,2,3] => 1
[2,3,6,5,4,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[2,4,1,3,5,6] => [2,4,1,3,5,6] => [3,4,1,2,5,6] => 1
[2,4,1,3,6,5] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => 2
[2,4,1,5,3,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[2,4,1,5,6,3] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[2,4,1,6,3,5] => [2,4,1,6,3,5] => [5,6,3,4,1,2] => 2
[2,4,1,6,5,3] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[2,4,3,1,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 1
[2,4,3,1,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[2,4,3,5,1,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[2,4,3,5,6,1] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[2,4,3,6,1,5] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[2,4,3,6,5,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[2,4,5,1,3,6] => [1,3,5,2,4,6] => [1,4,5,2,3,6] => 1
[2,4,5,1,6,3] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[2,4,5,3,1,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 1
[2,4,5,3,6,1] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[2,4,5,6,1,3] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => 1
[2,4,5,6,3,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[2,4,6,1,3,5] => [2,4,6,1,3,5] => [3,5,6,1,2,4] => 1
[2,4,6,1,5,3] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[2,4,6,3,1,5] => [1,4,6,3,2,5] => [1,5,6,3,2,4] => 1
[2,4,6,3,5,1] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[2,4,6,5,1,3] => [1,3,6,5,2,4] => [1,4,6,5,2,3] => 1
[2,4,6,5,3,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[2,5,1,3,4,6] => [2,5,1,3,4,6] => [3,4,5,1,2,6] => 1
[2,5,1,3,6,4] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => 2
[2,5,1,4,3,6] => [2,5,1,4,3,6] => [4,3,5,1,2,6] => 2
[2,5,1,4,6,3] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => 2
[2,5,1,6,3,4] => [2,4,1,6,3,5] => [5,6,3,4,1,2] => 2
[2,5,1,6,4,3] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[2,5,3,1,4,6] => [1,5,3,2,4,6] => [1,4,5,3,2,6] => 1
[2,5,3,1,6,4] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[2,5,3,4,1,6] => [1,5,2,4,3,6] => [1,4,3,5,2,6] => 2
[2,5,3,4,6,1] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 2
[2,5,3,6,1,4] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[2,5,3,6,4,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[2,5,4,1,3,6] => [2,5,4,1,3,6] => [3,5,4,1,2,6] => 1
[2,5,4,1,6,3] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[2,5,4,3,1,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 1
[2,5,4,3,6,1] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[2,5,4,6,1,3] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[2,5,4,6,3,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[2,5,6,1,3,4] => [2,4,6,1,3,5] => [3,5,6,1,2,4] => 1
[2,5,6,1,4,3] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[2,5,6,3,1,4] => [1,4,6,3,2,5] => [1,5,6,3,2,4] => 1
[2,5,6,3,4,1] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[2,5,6,4,1,3] => [1,3,6,5,2,4] => [1,4,6,5,2,3] => 1
[2,5,6,4,3,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[2,6,1,3,4,5] => [2,6,1,3,4,5] => [3,4,5,6,1,2] => 1
[2,6,1,3,5,4] => [2,6,1,3,5,4] => [3,5,4,6,1,2] => 2
[2,6,1,4,3,5] => [2,6,1,4,3,5] => [4,3,5,6,1,2] => 2
[2,6,1,4,5,3] => [2,6,1,3,5,4] => [3,5,4,6,1,2] => 2
[2,6,1,5,3,4] => [2,6,1,5,3,4] => [4,5,3,6,1,2] => 2
[2,6,1,5,4,3] => [2,6,1,5,4,3] => [5,4,3,6,1,2] => 2
[2,6,3,1,4,5] => [1,6,3,2,4,5] => [1,4,5,6,3,2] => 1
[2,6,3,1,5,4] => [1,6,3,2,5,4] => [1,5,4,6,3,2] => 2
[2,6,3,4,1,5] => [1,6,2,4,3,5] => [1,4,3,5,6,2] => 2
[2,6,3,4,5,1] => [1,6,2,3,5,4] => [1,3,5,4,6,2] => 2
[2,6,3,5,1,4] => [1,6,3,5,2,4] => [1,4,5,2,6,3] => 2
[2,6,3,5,4,1] => [1,6,2,5,4,3] => [1,5,4,3,6,2] => 2
[2,6,4,1,3,5] => [2,6,4,1,3,5] => [3,5,6,4,1,2] => 1
[2,6,4,1,5,3] => [1,6,3,2,5,4] => [1,5,4,6,3,2] => 2
[2,6,4,3,1,5] => [1,6,4,3,2,5] => [1,5,6,4,3,2] => 1
[2,6,4,3,5,1] => [1,6,3,2,5,4] => [1,5,4,6,3,2] => 2
[2,6,4,5,1,3] => [1,6,3,5,2,4] => [1,4,5,2,6,3] => 2
[2,6,4,5,3,1] => [1,6,2,5,4,3] => [1,5,4,3,6,2] => 2
[2,6,5,1,3,4] => [2,6,5,1,3,4] => [3,4,6,5,1,2] => 1
[2,6,5,1,4,3] => [2,6,5,1,4,3] => [4,3,6,5,1,2] => 2
[2,6,5,3,1,4] => [1,6,5,3,2,4] => [1,4,6,5,3,2] => 1
[2,6,5,3,4,1] => [1,6,5,2,4,3] => [1,4,3,6,5,2] => 2
[2,6,5,4,1,3] => [2,6,5,4,1,3] => [3,6,5,4,1,2] => 1
[2,6,5,4,3,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 1
[3,1,2,4,5,6] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => 1
[3,1,2,4,6,5] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => 2
[3,1,2,5,4,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => 2
[3,1,2,5,6,4] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => 2
[3,1,2,6,4,5] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => 2
[3,1,2,6,5,4] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[3,1,4,2,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 2
[3,1,4,2,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[3,1,4,5,2,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 2
[3,1,4,5,6,2] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 2
[3,1,4,6,2,5] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => 2
[3,1,4,6,5,2] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[3,1,5,2,4,6] => [3,1,5,2,4,6] => [4,5,2,3,1,6] => 2
[3,1,5,2,6,4] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[3,1,5,4,2,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 2
[3,1,5,4,6,2] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[3,1,5,6,2,4] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => 2
[3,1,5,6,4,2] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[3,1,6,2,4,5] => [3,1,6,2,4,5] => [4,5,6,2,3,1] => 2
[3,1,6,2,5,4] => [3,1,6,2,5,4] => [5,4,6,2,3,1] => 3
[3,1,6,4,2,5] => [2,1,6,4,3,5] => [2,1,5,6,4,3] => 2
[3,1,6,4,5,2] => [2,1,6,3,5,4] => [2,1,5,4,6,3] => 3
[3,1,6,5,2,4] => [3,1,6,5,2,4] => [4,6,5,2,3,1] => 2
[3,1,6,5,4,2] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 2
[3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 2
[3,2,1,5,6,4] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 2
[3,2,1,6,4,5] => [3,2,1,6,4,5] => [3,2,1,5,6,4] => 2
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[3,2,4,1,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 2
[3,2,4,1,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[3,2,4,5,1,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 2
[3,2,4,5,6,1] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 2
[3,2,4,6,1,5] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => 2
[3,2,4,6,5,1] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[3,2,5,1,4,6] => [3,2,5,1,4,6] => [4,5,1,3,2,6] => 2
[3,2,5,1,6,4] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[3,2,5,4,1,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 2
[3,2,5,4,6,1] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[3,2,5,6,1,4] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => 2
[3,2,5,6,4,1] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[3,2,6,1,4,5] => [3,2,6,1,4,5] => [4,5,6,1,3,2] => 2
[3,2,6,1,5,4] => [3,2,6,1,5,4] => [5,4,6,1,3,2] => 3
[3,2,6,4,1,5] => [2,1,6,4,3,5] => [2,1,5,6,4,3] => 2
[3,2,6,4,5,1] => [2,1,6,3,5,4] => [2,1,5,4,6,3] => 3
[3,2,6,5,1,4] => [3,2,6,5,1,4] => [4,6,5,1,3,2] => 2
[3,2,6,5,4,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[3,4,1,2,5,6] => [2,4,1,3,5,6] => [3,4,1,2,5,6] => 1
[3,4,1,2,6,5] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => 2
[3,4,1,5,2,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[3,4,1,5,6,2] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[3,4,1,6,2,5] => [2,4,1,6,3,5] => [5,6,3,4,1,2] => 2
[3,4,1,6,5,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[3,4,2,1,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 1
[3,4,2,1,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[3,4,2,5,1,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[3,4,2,5,6,1] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[3,4,2,6,1,5] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[3,4,2,6,5,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[3,4,5,1,2,6] => [1,3,5,2,4,6] => [1,4,5,2,3,6] => 1
[3,4,5,1,6,2] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[3,4,5,2,1,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 1
[3,4,5,2,6,1] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[3,4,5,6,1,2] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => 1
[3,4,5,6,2,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[3,4,6,1,2,5] => [2,4,6,1,3,5] => [3,5,6,1,2,4] => 1
[3,4,6,1,5,2] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[3,4,6,2,1,5] => [1,4,6,3,2,5] => [1,5,6,3,2,4] => 1
[3,4,6,2,5,1] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[3,4,6,5,1,2] => [1,3,6,5,2,4] => [1,4,6,5,2,3] => 1
[3,4,6,5,2,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[3,5,1,2,4,6] => [3,5,1,2,4,6] => [2,4,5,1,3,6] => 1
[3,5,1,2,6,4] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => 2
[3,5,1,4,2,6] => [2,5,1,4,3,6] => [4,3,5,1,2,6] => 2
[3,5,1,4,6,2] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => 2
[3,5,1,6,2,4] => [2,4,1,6,3,5] => [5,6,3,4,1,2] => 2
[3,5,1,6,4,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[3,5,2,1,4,6] => [3,5,2,1,4,6] => [4,5,2,1,3,6] => 1
[3,5,2,1,6,4] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[3,5,2,4,1,6] => [2,5,1,4,3,6] => [4,3,5,1,2,6] => 2
[3,5,2,4,6,1] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => 2
[3,5,2,6,1,4] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[3,5,2,6,4,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[3,5,4,1,2,6] => [2,5,4,1,3,6] => [3,5,4,1,2,6] => 1
[3,5,4,1,6,2] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[3,5,4,2,1,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 1
[3,5,4,2,6,1] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[3,5,4,6,1,2] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[3,5,4,6,2,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[3,5,6,1,2,4] => [2,4,6,1,3,5] => [3,5,6,1,2,4] => 1
[3,5,6,1,4,2] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[3,5,6,2,1,4] => [1,4,6,3,2,5] => [1,5,6,3,2,4] => 1
[3,5,6,2,4,1] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[3,5,6,4,1,2] => [1,3,6,5,2,4] => [1,4,6,5,2,3] => 1
[3,5,6,4,2,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[3,6,1,2,4,5] => [3,6,1,2,4,5] => [2,4,5,6,1,3] => 1
[3,6,1,2,5,4] => [3,6,1,2,5,4] => [2,5,4,6,1,3] => 2
[3,6,1,4,2,5] => [2,6,1,4,3,5] => [4,3,5,6,1,2] => 2
[3,6,1,4,5,2] => [2,6,1,3,5,4] => [3,5,4,6,1,2] => 2
[3,6,1,5,2,4] => [3,6,1,5,2,4] => [4,5,2,6,1,3] => 2
[3,6,1,5,4,2] => [2,6,1,5,4,3] => [5,4,3,6,1,2] => 2
[3,6,2,1,4,5] => [3,6,2,1,4,5] => [4,5,6,2,1,3] => 1
[3,6,2,1,5,4] => [3,6,2,1,5,4] => [5,4,6,2,1,3] => 2
[3,6,2,4,1,5] => [2,6,1,4,3,5] => [4,3,5,6,1,2] => 2
[3,6,2,4,5,1] => [2,6,1,3,5,4] => [3,5,4,6,1,2] => 2
[3,6,2,5,1,4] => [3,6,2,5,1,4] => [4,5,1,6,2,3] => 2
[3,6,2,5,4,1] => [2,6,1,5,4,3] => [5,4,3,6,1,2] => 2
[3,6,4,1,2,5] => [2,6,4,1,3,5] => [3,5,6,4,1,2] => 1
[3,6,4,1,5,2] => [1,6,3,2,5,4] => [1,5,4,6,3,2] => 2
[3,6,4,2,1,5] => [1,6,4,3,2,5] => [1,5,6,4,3,2] => 1
[3,6,4,2,5,1] => [1,6,3,2,5,4] => [1,5,4,6,3,2] => 2
[3,6,4,5,1,2] => [1,6,3,5,2,4] => [1,4,5,2,6,3] => 2
[3,6,4,5,2,1] => [1,6,2,5,4,3] => [1,5,4,3,6,2] => 2
[3,6,5,1,2,4] => [3,6,5,1,2,4] => [2,4,6,5,1,3] => 1
[3,6,5,1,4,2] => [2,6,5,1,4,3] => [4,3,6,5,1,2] => 2
[3,6,5,2,1,4] => [3,6,5,2,1,4] => [4,6,5,2,1,3] => 1
[3,6,5,2,4,1] => [2,6,5,1,4,3] => [4,3,6,5,1,2] => 2
[3,6,5,4,1,2] => [2,6,5,4,1,3] => [3,6,5,4,1,2] => 1
[3,6,5,4,2,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 1
[4,1,2,3,5,6] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => 1
[4,1,2,3,6,5] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => 2
[4,1,2,5,3,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => 2
[4,1,2,5,6,3] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => 2
[4,1,2,6,3,5] => [4,1,2,6,3,5] => [2,5,6,3,4,1] => 2
[4,1,2,6,5,3] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[4,1,3,2,5,6] => [4,1,3,2,5,6] => [3,2,4,1,5,6] => 2
[4,1,3,2,6,5] => [4,1,3,2,6,5] => [3,2,4,1,6,5] => 3
[4,1,3,5,2,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => 2
[4,1,3,5,6,2] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => 2
[4,1,3,6,2,5] => [4,1,3,6,2,5] => [5,6,2,3,4,1] => 2
[4,1,3,6,5,2] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[4,1,5,2,3,6] => [3,1,5,2,4,6] => [4,5,2,3,1,6] => 2
[4,1,5,2,6,3] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[4,1,5,3,2,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 2
[4,1,5,3,6,2] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[4,1,5,6,2,3] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => 2
[4,1,5,6,3,2] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[4,1,6,2,3,5] => [4,1,6,2,3,5] => [3,5,6,2,4,1] => 2
[4,1,6,2,5,3] => [3,1,6,2,5,4] => [5,4,6,2,3,1] => 3
[4,1,6,3,2,5] => [4,1,6,3,2,5] => [5,6,3,2,4,1] => 2
[4,1,6,3,5,2] => [3,1,6,2,5,4] => [5,4,6,2,3,1] => 3
[4,1,6,5,2,3] => [3,1,6,5,2,4] => [4,6,5,2,3,1] => 2
[4,1,6,5,3,2] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[4,2,1,3,5,6] => [4,2,1,3,5,6] => [3,4,2,1,5,6] => 1
[4,2,1,3,6,5] => [4,2,1,3,6,5] => [3,4,2,1,6,5] => 2
[4,2,1,5,3,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 2
[4,2,1,5,6,3] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 2
[4,2,1,6,3,5] => [4,2,1,6,3,5] => [5,6,3,4,2,1] => 2
[4,2,1,6,5,3] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[4,2,3,1,5,6] => [4,1,3,2,5,6] => [3,2,4,1,5,6] => 2
[4,2,3,1,6,5] => [4,1,3,2,6,5] => [3,2,4,1,6,5] => 3
[4,2,3,5,1,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => 2
[4,2,3,5,6,1] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => 2
[4,2,3,6,1,5] => [4,1,3,6,2,5] => [5,6,2,3,4,1] => 2
[4,2,3,6,5,1] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[4,2,5,1,3,6] => [3,2,5,1,4,6] => [4,5,1,3,2,6] => 2
[4,2,5,1,6,3] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[4,2,5,3,1,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 2
[4,2,5,3,6,1] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[4,2,5,6,1,3] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => 2
[4,2,5,6,3,1] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[4,2,6,1,3,5] => [4,2,6,1,3,5] => [3,5,6,1,4,2] => 2
[4,2,6,1,5,3] => [3,2,6,1,5,4] => [5,4,6,1,3,2] => 3
[4,2,6,3,1,5] => [4,1,6,3,2,5] => [5,6,3,2,4,1] => 2
[4,2,6,3,5,1] => [3,1,6,2,5,4] => [5,4,6,2,3,1] => 3
[4,2,6,5,1,3] => [3,2,6,5,1,4] => [4,6,5,1,3,2] => 2
[4,2,6,5,3,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[4,3,1,2,5,6] => [4,3,1,2,5,6] => [2,4,3,1,5,6] => 1
[4,3,1,2,6,5] => [4,3,1,2,6,5] => [2,4,3,1,6,5] => 2
[4,3,1,5,2,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 2
[4,3,1,5,6,2] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 2
[4,3,1,6,2,5] => [4,3,1,6,2,5] => [5,6,2,4,3,1] => 2
[4,3,1,6,5,2] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 1
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 2
[4,3,2,5,1,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 2
[4,3,2,5,6,1] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 2
[4,3,2,6,1,5] => [4,3,2,6,1,5] => [5,6,1,4,3,2] => 2
[4,3,2,6,5,1] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[4,3,5,1,2,6] => [3,2,5,1,4,6] => [4,5,1,3,2,6] => 2
[4,3,5,1,6,2] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[4,3,5,2,1,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 2
[4,3,5,2,6,1] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[4,3,5,6,1,2] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => 2
[4,3,5,6,2,1] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[4,3,6,1,2,5] => [4,3,6,1,2,5] => [2,5,6,1,4,3] => 2
[4,3,6,1,5,2] => [3,2,6,1,5,4] => [5,4,6,1,3,2] => 3
[4,3,6,2,1,5] => [4,3,6,2,1,5] => [5,6,2,1,4,3] => 2
[4,3,6,2,5,1] => [3,2,6,1,5,4] => [5,4,6,1,3,2] => 3
[4,3,6,5,1,2] => [3,2,6,5,1,4] => [4,6,5,1,3,2] => 2
[4,3,6,5,2,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[4,5,1,2,3,6] => [3,5,1,2,4,6] => [2,4,5,1,3,6] => 1
[4,5,1,2,6,3] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => 2
[4,5,1,3,2,6] => [2,5,1,4,3,6] => [4,3,5,1,2,6] => 2
[4,5,1,3,6,2] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => 2
[4,5,1,6,2,3] => [2,4,1,6,3,5] => [5,6,3,4,1,2] => 2
[4,5,1,6,3,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[4,5,2,1,3,6] => [3,5,2,1,4,6] => [4,5,2,1,3,6] => 1
[4,5,2,1,6,3] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[4,5,2,3,1,6] => [2,5,1,4,3,6] => [4,3,5,1,2,6] => 2
[4,5,2,3,6,1] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => 2
[4,5,2,6,1,3] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[4,5,2,6,3,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[4,5,3,1,2,6] => [2,5,4,1,3,6] => [3,5,4,1,2,6] => 1
[4,5,3,1,6,2] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[4,5,3,2,1,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 1
[4,5,3,2,6,1] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[4,5,3,6,1,2] => [1,4,3,6,2,5] => [1,5,6,2,4,3] => 2
[4,5,3,6,2,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[4,5,6,1,2,3] => [2,4,6,1,3,5] => [3,5,6,1,2,4] => 1
[4,5,6,1,3,2] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[4,5,6,2,1,3] => [1,4,6,3,2,5] => [1,5,6,3,2,4] => 1
[4,5,6,2,3,1] => [1,3,6,2,5,4] => [1,5,4,6,2,3] => 2
[4,5,6,3,1,2] => [1,3,6,5,2,4] => [1,4,6,5,2,3] => 1
[4,5,6,3,2,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[4,6,1,2,3,5] => [4,6,1,2,3,5] => [2,3,5,6,1,4] => 1
[4,6,1,2,5,3] => [3,6,1,2,5,4] => [2,5,4,6,1,3] => 2
[4,6,1,3,2,5] => [4,6,1,3,2,5] => [3,2,5,6,1,4] => 2
[4,6,1,3,5,2] => [3,6,1,2,5,4] => [2,5,4,6,1,3] => 2
[4,6,1,5,2,3] => [3,6,1,5,2,4] => [4,5,2,6,1,3] => 2
[4,6,1,5,3,2] => [2,6,1,5,4,3] => [5,4,3,6,1,2] => 2
[4,6,2,1,3,5] => [4,6,2,1,3,5] => [3,5,6,2,1,4] => 1
[4,6,2,1,5,3] => [3,6,2,1,5,4] => [5,4,6,2,1,3] => 2
[4,6,2,3,1,5] => [4,6,1,3,2,5] => [3,2,5,6,1,4] => 2
[4,6,2,3,5,1] => [3,6,1,2,5,4] => [2,5,4,6,1,3] => 2
[4,6,2,5,1,3] => [3,6,2,5,1,4] => [4,5,1,6,2,3] => 2
[4,6,2,5,3,1] => [2,6,1,5,4,3] => [5,4,3,6,1,2] => 2
[4,6,3,1,2,5] => [4,6,3,1,2,5] => [2,5,6,3,1,4] => 1
[4,6,3,1,5,2] => [3,6,2,1,5,4] => [5,4,6,2,1,3] => 2
[4,6,3,2,1,5] => [4,6,3,2,1,5] => [5,6,3,2,1,4] => 1
[4,6,3,2,5,1] => [3,6,2,1,5,4] => [5,4,6,2,1,3] => 2
[4,6,3,5,1,2] => [3,6,2,5,1,4] => [4,5,1,6,2,3] => 2
[4,6,3,5,2,1] => [2,6,1,5,4,3] => [5,4,3,6,1,2] => 2
[4,6,5,1,2,3] => [3,6,5,1,2,4] => [2,4,6,5,1,3] => 1
[4,6,5,1,3,2] => [2,6,5,1,4,3] => [4,3,6,5,1,2] => 2
[4,6,5,2,1,3] => [3,6,5,2,1,4] => [4,6,5,2,1,3] => 1
[4,6,5,2,3,1] => [2,6,5,1,4,3] => [4,3,6,5,1,2] => 2
[4,6,5,3,1,2] => [2,6,5,4,1,3] => [3,6,5,4,1,2] => 1
[4,6,5,3,2,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 1
[5,1,2,3,4,6] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => 1
[5,1,2,3,6,4] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => 2
[5,1,2,4,3,6] => [5,1,2,4,3,6] => [2,4,3,5,1,6] => 2
[5,1,2,4,6,3] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => 2
[5,1,2,6,3,4] => [4,1,2,6,3,5] => [2,5,6,3,4,1] => 2
[5,1,2,6,4,3] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[5,1,3,2,4,6] => [5,1,3,2,4,6] => [3,2,4,5,1,6] => 2
[5,1,3,2,6,4] => [4,1,3,2,6,5] => [3,2,4,1,6,5] => 3
[5,1,3,4,2,6] => [5,1,2,4,3,6] => [2,4,3,5,1,6] => 2
[5,1,3,4,6,2] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => 2
[5,1,3,6,2,4] => [4,1,3,6,2,5] => [5,6,2,3,4,1] => 2
[5,1,3,6,4,2] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[5,1,4,2,3,6] => [5,1,4,2,3,6] => [3,4,2,5,1,6] => 2
[5,1,4,2,6,3] => [4,1,3,2,6,5] => [3,2,4,1,6,5] => 3
[5,1,4,3,2,6] => [5,1,4,3,2,6] => [4,3,2,5,1,6] => 2
[5,1,4,3,6,2] => [4,1,3,2,6,5] => [3,2,4,1,6,5] => 3
[5,1,4,6,2,3] => [4,1,3,6,2,5] => [5,6,2,3,4,1] => 2
[5,1,4,6,3,2] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[5,1,6,2,3,4] => [4,1,6,2,3,5] => [3,5,6,2,4,1] => 2
[5,1,6,2,4,3] => [3,1,6,2,5,4] => [5,4,6,2,3,1] => 3
[5,1,6,3,2,4] => [4,1,6,3,2,5] => [5,6,3,2,4,1] => 2
[5,1,6,3,4,2] => [3,1,6,2,5,4] => [5,4,6,2,3,1] => 3
[5,1,6,4,2,3] => [3,1,6,5,2,4] => [4,6,5,2,3,1] => 2
[5,1,6,4,3,2] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[5,2,1,3,4,6] => [5,2,1,3,4,6] => [3,4,5,2,1,6] => 1
[5,2,1,3,6,4] => [4,2,1,3,6,5] => [3,4,2,1,6,5] => 2
[5,2,1,4,3,6] => [5,2,1,4,3,6] => [4,3,5,2,1,6] => 2
[5,2,1,4,6,3] => [4,2,1,3,6,5] => [3,4,2,1,6,5] => 2
[5,2,1,6,3,4] => [4,2,1,6,3,5] => [5,6,3,4,2,1] => 2
[5,2,1,6,4,3] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[5,2,3,1,4,6] => [5,1,3,2,4,6] => [3,2,4,5,1,6] => 2
[5,2,3,1,6,4] => [4,1,3,2,6,5] => [3,2,4,1,6,5] => 3
[5,2,3,4,1,6] => [5,1,2,4,3,6] => [2,4,3,5,1,6] => 2
[5,2,3,4,6,1] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => 2
[5,2,3,6,1,4] => [4,1,3,6,2,5] => [5,6,2,3,4,1] => 2
[5,2,3,6,4,1] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[5,2,4,1,3,6] => [5,2,4,1,3,6] => [3,4,1,5,2,6] => 2
[5,2,4,1,6,3] => [4,1,3,2,6,5] => [3,2,4,1,6,5] => 3
[5,2,4,3,1,6] => [5,1,4,3,2,6] => [4,3,2,5,1,6] => 2
[5,2,4,3,6,1] => [4,1,3,2,6,5] => [3,2,4,1,6,5] => 3
[5,2,4,6,1,3] => [4,1,3,6,2,5] => [5,6,2,3,4,1] => 2
[5,2,4,6,3,1] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[5,2,6,1,3,4] => [4,2,6,1,3,5] => [3,5,6,1,4,2] => 2
[5,2,6,1,4,3] => [3,2,6,1,5,4] => [5,4,6,1,3,2] => 3
[5,2,6,3,1,4] => [4,1,6,3,2,5] => [5,6,3,2,4,1] => 2
[5,2,6,3,4,1] => [3,1,6,2,5,4] => [5,4,6,2,3,1] => 3
[5,2,6,4,1,3] => [3,2,6,5,1,4] => [4,6,5,1,3,2] => 2
[5,2,6,4,3,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[5,3,1,2,4,6] => [5,3,1,2,4,6] => [2,4,5,3,1,6] => 1
[5,3,1,2,6,4] => [4,3,1,2,6,5] => [2,4,3,1,6,5] => 2
[5,3,1,4,2,6] => [5,2,1,4,3,6] => [4,3,5,2,1,6] => 2
[5,3,1,4,6,2] => [4,2,1,3,6,5] => [3,4,2,1,6,5] => 2
[5,3,1,6,2,4] => [4,3,1,6,2,5] => [5,6,2,4,3,1] => 2
[5,3,1,6,4,2] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[5,3,2,1,4,6] => [5,3,2,1,4,6] => [4,5,3,2,1,6] => 1
[5,3,2,1,6,4] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 2
[5,3,2,4,1,6] => [5,2,1,4,3,6] => [4,3,5,2,1,6] => 2
[5,3,2,4,6,1] => [4,2,1,3,6,5] => [3,4,2,1,6,5] => 2
[5,3,2,6,1,4] => [4,3,2,6,1,5] => [5,6,1,4,3,2] => 2
[5,3,2,6,4,1] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[5,3,4,1,2,6] => [5,2,4,1,3,6] => [3,4,1,5,2,6] => 2
[5,3,4,1,6,2] => [4,1,3,2,6,5] => [3,2,4,1,6,5] => 3
[5,3,4,2,1,6] => [5,1,4,3,2,6] => [4,3,2,5,1,6] => 2
[5,3,4,2,6,1] => [4,1,3,2,6,5] => [3,2,4,1,6,5] => 3
[5,3,4,6,1,2] => [4,1,3,6,2,5] => [5,6,2,3,4,1] => 2
[5,3,4,6,2,1] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[5,3,6,1,2,4] => [4,3,6,1,2,5] => [2,5,6,1,4,3] => 2
[5,3,6,1,4,2] => [3,2,6,1,5,4] => [5,4,6,1,3,2] => 3
[5,3,6,2,1,4] => [4,3,6,2,1,5] => [5,6,2,1,4,3] => 2
[5,3,6,2,4,1] => [3,2,6,1,5,4] => [5,4,6,1,3,2] => 3
[5,3,6,4,1,2] => [3,2,6,5,1,4] => [4,6,5,1,3,2] => 2
[5,3,6,4,2,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[5,4,1,2,3,6] => [5,4,1,2,3,6] => [2,3,5,4,1,6] => 1
[5,4,1,2,6,3] => [4,3,1,2,6,5] => [2,4,3,1,6,5] => 2
[5,4,1,3,2,6] => [5,4,1,3,2,6] => [3,2,5,4,1,6] => 2
[5,4,1,3,6,2] => [4,3,1,2,6,5] => [2,4,3,1,6,5] => 2
[5,4,1,6,2,3] => [4,3,1,6,2,5] => [5,6,2,4,3,1] => 2
[5,4,1,6,3,2] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[5,4,2,1,3,6] => [5,4,2,1,3,6] => [3,5,4,2,1,6] => 1
[5,4,2,1,6,3] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 2
[5,4,2,3,1,6] => [5,4,1,3,2,6] => [3,2,5,4,1,6] => 2
[5,4,2,3,6,1] => [4,3,1,2,6,5] => [2,4,3,1,6,5] => 2
[5,4,2,6,1,3] => [4,3,2,6,1,5] => [5,6,1,4,3,2] => 2
[5,4,2,6,3,1] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[5,4,3,1,2,6] => [5,4,3,1,2,6] => [2,5,4,3,1,6] => 1
[5,4,3,1,6,2] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 2
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 2
[5,4,3,6,1,2] => [4,3,2,6,1,5] => [5,6,1,4,3,2] => 2
[5,4,3,6,2,1] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[5,4,6,1,2,3] => [4,3,6,1,2,5] => [2,5,6,1,4,3] => 2
[5,4,6,1,3,2] => [3,2,6,1,5,4] => [5,4,6,1,3,2] => 3
[5,4,6,2,1,3] => [4,3,6,2,1,5] => [5,6,2,1,4,3] => 2
[5,4,6,2,3,1] => [3,2,6,1,5,4] => [5,4,6,1,3,2] => 3
[5,4,6,3,1,2] => [3,2,6,5,1,4] => [4,6,5,1,3,2] => 2
[5,4,6,3,2,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[5,6,1,2,3,4] => [4,6,1,2,3,5] => [2,3,5,6,1,4] => 1
[5,6,1,2,4,3] => [3,6,1,2,5,4] => [2,5,4,6,1,3] => 2
[5,6,1,3,2,4] => [4,6,1,3,2,5] => [3,2,5,6,1,4] => 2
[5,6,1,3,4,2] => [3,6,1,2,5,4] => [2,5,4,6,1,3] => 2
[5,6,1,4,2,3] => [3,6,1,5,2,4] => [4,5,2,6,1,3] => 2
[5,6,1,4,3,2] => [2,6,1,5,4,3] => [5,4,3,6,1,2] => 2
[5,6,2,1,3,4] => [4,6,2,1,3,5] => [3,5,6,2,1,4] => 1
[5,6,2,1,4,3] => [3,6,2,1,5,4] => [5,4,6,2,1,3] => 2
[5,6,2,3,1,4] => [4,6,1,3,2,5] => [3,2,5,6,1,4] => 2
[5,6,2,3,4,1] => [3,6,1,2,5,4] => [2,5,4,6,1,3] => 2
[5,6,2,4,1,3] => [3,6,2,5,1,4] => [4,5,1,6,2,3] => 2
[5,6,2,4,3,1] => [2,6,1,5,4,3] => [5,4,3,6,1,2] => 2
[5,6,3,1,2,4] => [4,6,3,1,2,5] => [2,5,6,3,1,4] => 1
[5,6,3,1,4,2] => [3,6,2,1,5,4] => [5,4,6,2,1,3] => 2
[5,6,3,2,1,4] => [4,6,3,2,1,5] => [5,6,3,2,1,4] => 1
[5,6,3,2,4,1] => [3,6,2,1,5,4] => [5,4,6,2,1,3] => 2
[5,6,3,4,1,2] => [3,6,2,5,1,4] => [4,5,1,6,2,3] => 2
[5,6,3,4,2,1] => [2,6,1,5,4,3] => [5,4,3,6,1,2] => 2
[5,6,4,1,2,3] => [3,6,5,1,2,4] => [2,4,6,5,1,3] => 1
[5,6,4,1,3,2] => [2,6,5,1,4,3] => [4,3,6,5,1,2] => 2
[5,6,4,2,1,3] => [3,6,5,2,1,4] => [4,6,5,2,1,3] => 1
[5,6,4,2,3,1] => [2,6,5,1,4,3] => [4,3,6,5,1,2] => 2
[5,6,4,3,1,2] => [2,6,5,4,1,3] => [3,6,5,4,1,2] => 1
[5,6,4,3,2,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 1
[6,1,2,3,4,5] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => 1
[6,1,2,3,5,4] => [6,1,2,3,5,4] => [2,3,5,4,6,1] => 2
[6,1,2,4,3,5] => [6,1,2,4,3,5] => [2,4,3,5,6,1] => 2
[6,1,2,4,5,3] => [6,1,2,3,5,4] => [2,3,5,4,6,1] => 2
[6,1,2,5,3,4] => [6,1,2,5,3,4] => [2,4,5,3,6,1] => 2
[6,1,2,5,4,3] => [6,1,2,5,4,3] => [2,5,4,3,6,1] => 2
[6,1,3,2,4,5] => [6,1,3,2,4,5] => [3,2,4,5,6,1] => 2
[6,1,3,2,5,4] => [6,1,3,2,5,4] => [3,2,5,4,6,1] => 3
[6,1,3,4,2,5] => [6,1,2,4,3,5] => [2,4,3,5,6,1] => 2
[6,1,3,4,5,2] => [6,1,2,3,5,4] => [2,3,5,4,6,1] => 2
[6,1,3,5,2,4] => [6,1,3,5,2,4] => [4,5,2,3,6,1] => 2
[6,1,3,5,4,2] => [6,1,2,5,4,3] => [2,5,4,3,6,1] => 2
[6,1,4,2,3,5] => [6,1,4,2,3,5] => [3,4,2,5,6,1] => 2
[6,1,4,2,5,3] => [6,1,3,2,5,4] => [3,2,5,4,6,1] => 3
[6,1,4,3,2,5] => [6,1,4,3,2,5] => [4,3,2,5,6,1] => 2
[6,1,4,3,5,2] => [6,1,3,2,5,4] => [3,2,5,4,6,1] => 3
[6,1,4,5,2,3] => [6,1,3,5,2,4] => [4,5,2,3,6,1] => 2
[6,1,4,5,3,2] => [6,1,2,5,4,3] => [2,5,4,3,6,1] => 2
[6,1,5,2,3,4] => [6,1,5,2,3,4] => [3,4,5,2,6,1] => 2
[6,1,5,2,4,3] => [6,1,5,2,4,3] => [4,3,5,2,6,1] => 3
[6,1,5,3,2,4] => [6,1,5,3,2,4] => [4,5,3,2,6,1] => 2
[6,1,5,3,4,2] => [6,1,5,2,4,3] => [4,3,5,2,6,1] => 3
[6,1,5,4,2,3] => [6,1,5,4,2,3] => [3,5,4,2,6,1] => 2
[6,1,5,4,3,2] => [6,1,5,4,3,2] => [5,4,3,2,6,1] => 2
[6,2,1,3,4,5] => [6,2,1,3,4,5] => [3,4,5,6,2,1] => 1
[6,2,1,3,5,4] => [6,2,1,3,5,4] => [3,5,4,6,2,1] => 2
[6,2,1,4,3,5] => [6,2,1,4,3,5] => [4,3,5,6,2,1] => 2
[6,2,1,4,5,3] => [6,2,1,3,5,4] => [3,5,4,6,2,1] => 2
[6,2,1,5,3,4] => [6,2,1,5,3,4] => [4,5,3,6,2,1] => 2
[6,2,1,5,4,3] => [6,2,1,5,4,3] => [5,4,3,6,2,1] => 2
[6,2,3,1,4,5] => [6,1,3,2,4,5] => [3,2,4,5,6,1] => 2
[6,2,3,1,5,4] => [6,1,3,2,5,4] => [3,2,5,4,6,1] => 3
[6,2,3,4,1,5] => [6,1,2,4,3,5] => [2,4,3,5,6,1] => 2
[6,2,3,4,5,1] => [6,1,2,3,5,4] => [2,3,5,4,6,1] => 2
[6,2,3,5,1,4] => [6,1,3,5,2,4] => [4,5,2,3,6,1] => 2
[6,2,3,5,4,1] => [6,1,2,5,4,3] => [2,5,4,3,6,1] => 2
[6,2,4,1,3,5] => [6,2,4,1,3,5] => [3,4,1,5,6,2] => 2
[6,2,4,1,5,3] => [6,1,3,2,5,4] => [3,2,5,4,6,1] => 3
[6,2,4,3,1,5] => [6,1,4,3,2,5] => [4,3,2,5,6,1] => 2
[6,2,4,3,5,1] => [6,1,3,2,5,4] => [3,2,5,4,6,1] => 3
[6,2,4,5,1,3] => [6,1,3,5,2,4] => [4,5,2,3,6,1] => 2
[6,2,4,5,3,1] => [6,1,2,5,4,3] => [2,5,4,3,6,1] => 2
[6,2,5,1,3,4] => [6,2,5,1,3,4] => [3,4,5,1,6,2] => 2
[6,2,5,1,4,3] => [6,2,5,1,4,3] => [4,3,5,1,6,2] => 3
[6,2,5,3,1,4] => [6,1,5,3,2,4] => [4,5,3,2,6,1] => 2
[6,2,5,3,4,1] => [6,1,5,2,4,3] => [4,3,5,2,6,1] => 3
[6,2,5,4,1,3] => [6,2,5,4,1,3] => [3,5,4,1,6,2] => 2
[6,2,5,4,3,1] => [6,1,5,4,3,2] => [5,4,3,2,6,1] => 2
[6,3,1,2,4,5] => [6,3,1,2,4,5] => [2,4,5,6,3,1] => 1
[6,3,1,2,5,4] => [6,3,1,2,5,4] => [2,5,4,6,3,1] => 2
[6,3,1,4,2,5] => [6,2,1,4,3,5] => [4,3,5,6,2,1] => 2
[6,3,1,4,5,2] => [6,2,1,3,5,4] => [3,5,4,6,2,1] => 2
[6,3,1,5,2,4] => [6,3,1,5,2,4] => [4,5,2,6,3,1] => 2
[6,3,1,5,4,2] => [6,2,1,5,4,3] => [5,4,3,6,2,1] => 2
[6,3,2,1,4,5] => [6,3,2,1,4,5] => [4,5,6,3,2,1] => 1
[6,3,2,1,5,4] => [6,3,2,1,5,4] => [5,4,6,3,2,1] => 2
[6,3,2,4,1,5] => [6,2,1,4,3,5] => [4,3,5,6,2,1] => 2
[6,3,2,4,5,1] => [6,2,1,3,5,4] => [3,5,4,6,2,1] => 2
[6,3,2,5,1,4] => [6,3,2,5,1,4] => [4,5,1,6,3,2] => 2
[6,3,2,5,4,1] => [6,2,1,5,4,3] => [5,4,3,6,2,1] => 2
[6,3,4,1,2,5] => [6,2,4,1,3,5] => [3,4,1,5,6,2] => 2
[6,3,4,1,5,2] => [6,1,3,2,5,4] => [3,2,5,4,6,1] => 3
[6,3,4,2,1,5] => [6,1,4,3,2,5] => [4,3,2,5,6,1] => 2
[6,3,4,2,5,1] => [6,1,3,2,5,4] => [3,2,5,4,6,1] => 3
[6,3,4,5,1,2] => [6,1,3,5,2,4] => [4,5,2,3,6,1] => 2
[6,3,4,5,2,1] => [6,1,2,5,4,3] => [2,5,4,3,6,1] => 2
[6,3,5,1,2,4] => [6,3,5,1,2,4] => [2,4,5,1,6,3] => 2
[6,3,5,1,4,2] => [6,2,5,1,4,3] => [4,3,5,1,6,2] => 3
[6,3,5,2,1,4] => [6,3,5,2,1,4] => [4,5,2,1,6,3] => 2
[6,3,5,2,4,1] => [6,2,5,1,4,3] => [4,3,5,1,6,2] => 3
[6,3,5,4,1,2] => [6,2,5,4,1,3] => [3,5,4,1,6,2] => 2
[6,3,5,4,2,1] => [6,1,5,4,3,2] => [5,4,3,2,6,1] => 2
[6,4,1,2,3,5] => [6,4,1,2,3,5] => [2,3,5,6,4,1] => 1
[6,4,1,2,5,3] => [6,3,1,2,5,4] => [2,5,4,6,3,1] => 2
[6,4,1,3,2,5] => [6,4,1,3,2,5] => [3,2,5,6,4,1] => 2
[6,4,1,3,5,2] => [6,3,1,2,5,4] => [2,5,4,6,3,1] => 2
[6,4,1,5,2,3] => [6,3,1,5,2,4] => [4,5,2,6,3,1] => 2
[6,4,1,5,3,2] => [6,2,1,5,4,3] => [5,4,3,6,2,1] => 2
[6,4,2,1,3,5] => [6,4,2,1,3,5] => [3,5,6,4,2,1] => 1
[6,4,2,1,5,3] => [6,3,2,1,5,4] => [5,4,6,3,2,1] => 2
[6,4,2,3,1,5] => [6,4,1,3,2,5] => [3,2,5,6,4,1] => 2
[6,4,2,3,5,1] => [6,3,1,2,5,4] => [2,5,4,6,3,1] => 2
[6,4,2,5,1,3] => [6,3,2,5,1,4] => [4,5,1,6,3,2] => 2
[6,4,2,5,3,1] => [6,2,1,5,4,3] => [5,4,3,6,2,1] => 2
[6,4,3,1,2,5] => [6,4,3,1,2,5] => [2,5,6,4,3,1] => 1
[6,4,3,1,5,2] => [6,3,2,1,5,4] => [5,4,6,3,2,1] => 2
[6,4,3,2,1,5] => [6,4,3,2,1,5] => [5,6,4,3,2,1] => 1
[6,4,3,2,5,1] => [6,3,2,1,5,4] => [5,4,6,3,2,1] => 2
[6,4,3,5,1,2] => [6,3,2,5,1,4] => [4,5,1,6,3,2] => 2
[6,4,3,5,2,1] => [6,2,1,5,4,3] => [5,4,3,6,2,1] => 2
[6,4,5,1,2,3] => [6,3,5,1,2,4] => [2,4,5,1,6,3] => 2
[6,4,5,1,3,2] => [6,2,5,1,4,3] => [4,3,5,1,6,2] => 3
[6,4,5,2,1,3] => [6,3,5,2,1,4] => [4,5,2,1,6,3] => 2
[6,4,5,2,3,1] => [6,2,5,1,4,3] => [4,3,5,1,6,2] => 3
[6,4,5,3,1,2] => [6,2,5,4,1,3] => [3,5,4,1,6,2] => 2
[6,4,5,3,2,1] => [6,1,5,4,3,2] => [5,4,3,2,6,1] => 2
[6,5,1,2,3,4] => [6,5,1,2,3,4] => [2,3,4,6,5,1] => 1
[6,5,1,2,4,3] => [6,5,1,2,4,3] => [2,4,3,6,5,1] => 2
[6,5,1,3,2,4] => [6,5,1,3,2,4] => [3,2,4,6,5,1] => 2
[6,5,1,3,4,2] => [6,5,1,2,4,3] => [2,4,3,6,5,1] => 2
[6,5,1,4,2,3] => [6,5,1,4,2,3] => [3,4,2,6,5,1] => 2
[6,5,1,4,3,2] => [6,5,1,4,3,2] => [4,3,2,6,5,1] => 2
[6,5,2,1,3,4] => [6,5,2,1,3,4] => [3,4,6,5,2,1] => 1
[6,5,2,1,4,3] => [6,5,2,1,4,3] => [4,3,6,5,2,1] => 2
[6,5,2,3,1,4] => [6,5,1,3,2,4] => [3,2,4,6,5,1] => 2
[6,5,2,3,4,1] => [6,5,1,2,4,3] => [2,4,3,6,5,1] => 2
[6,5,2,4,1,3] => [6,5,2,4,1,3] => [3,4,1,6,5,2] => 2
[6,5,2,4,3,1] => [6,5,1,4,3,2] => [4,3,2,6,5,1] => 2
[6,5,3,1,2,4] => [6,5,3,1,2,4] => [2,4,6,5,3,1] => 1
[6,5,3,1,4,2] => [6,5,2,1,4,3] => [4,3,6,5,2,1] => 2
[6,5,3,2,1,4] => [6,5,3,2,1,4] => [4,6,5,3,2,1] => 1
[6,5,3,2,4,1] => [6,5,2,1,4,3] => [4,3,6,5,2,1] => 2
[6,5,3,4,1,2] => [6,5,2,4,1,3] => [3,4,1,6,5,2] => 2
[6,5,3,4,2,1] => [6,5,1,4,3,2] => [4,3,2,6,5,1] => 2
[6,5,4,1,2,3] => [6,5,4,1,2,3] => [2,3,6,5,4,1] => 1
[6,5,4,1,3,2] => [6,5,4,1,3,2] => [3,2,6,5,4,1] => 2
[6,5,4,2,1,3] => [6,5,4,2,1,3] => [3,6,5,4,2,1] => 1
[6,5,4,2,3,1] => [6,5,4,1,3,2] => [3,2,6,5,4,1] => 2
[6,5,4,3,1,2] => [6,5,4,3,1,2] => [2,6,5,4,3,1] => 1
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 1
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[1,2,3,4,6,7,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,2,3,5,6,4,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[1,2,3,5,6,7,4] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,2,4,5,6,3,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[1,2,4,5,6,7,3] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1
[1,3,4,5,6,2,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[1,3,4,5,6,7,2] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,3,5,7,2,4,6] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[1,3,6,7,2,4,5] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[1,4,5,7,2,3,6] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[1,4,6,7,2,3,5] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[1,4,7,3,6,2,5] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[1,5,6,7,2,3,4] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[1,5,7,3,6,2,4] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[1,5,7,4,6,2,3] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[1,6,7,3,5,2,4] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[1,6,7,4,5,2,3] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[1,7,2,6,5,4,3] => [1,7,2,6,5,4,3] => [1,6,5,4,3,7,2] => 2
[1,7,3,2,6,4,5] => [1,7,3,2,6,4,5] => [1,5,6,4,7,3,2] => 2
[1,7,3,2,6,5,4] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[1,7,3,6,5,4,2] => [1,7,2,6,5,4,3] => [1,6,5,4,3,7,2] => 2
[1,7,4,2,6,5,3] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[1,7,4,3,2,5,6] => [1,7,4,3,2,5,6] => [1,5,6,7,4,3,2] => 1
[1,7,4,3,2,6,5] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[1,7,4,3,6,5,2] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[1,7,4,6,5,3,2] => [1,7,2,6,5,4,3] => [1,6,5,4,3,7,2] => 2
[1,7,5,2,6,4,3] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[1,7,5,3,2,4,6] => [1,7,5,3,2,4,6] => [1,4,6,7,5,3,2] => 1
[1,7,5,3,2,6,4] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[1,7,5,3,6,4,2] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[1,7,5,4,2,6,3] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[1,7,5,4,3,2,6] => [1,7,5,4,3,2,6] => [1,6,7,5,4,3,2] => 1
[1,7,5,4,3,6,2] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[1,7,5,4,6,3,2] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[1,7,5,6,4,3,2] => [1,7,2,6,5,4,3] => [1,6,5,4,3,7,2] => 2
[1,7,6,3,2,5,4] => [1,7,6,3,2,5,4] => [1,5,4,7,6,3,2] => 2
[1,7,6,4,2,5,3] => [1,7,6,3,2,5,4] => [1,5,4,7,6,3,2] => 2
[1,7,6,4,3,2,5] => [1,7,6,4,3,2,5] => [1,5,7,6,4,3,2] => 1
[1,7,6,4,3,5,2] => [1,7,6,3,2,5,4] => [1,5,4,7,6,3,2] => 2
[1,7,6,5,3,2,4] => [1,7,6,5,3,2,4] => [1,4,7,6,5,3,2] => 1
[1,7,6,5,4,2,3] => [1,7,6,5,4,2,3] => [1,3,7,6,5,4,2] => 1
[1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 1
[2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[2,3,1,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1
[2,3,4,5,6,1,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[2,3,4,5,6,7,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[2,3,5,7,1,4,6] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[2,3,6,7,1,4,5] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[2,4,1,3,5,6,7] => [2,4,1,3,5,6,7] => [3,4,1,2,5,6,7] => 1
[2,4,1,6,3,5,7] => [2,4,1,6,3,5,7] => [5,6,3,4,1,2,7] => 2
[2,4,1,7,3,6,5] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[2,4,5,7,1,3,6] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[2,4,6,1,3,5,7] => [2,4,6,1,3,5,7] => [3,5,6,1,2,4,7] => 1
[2,4,6,7,1,3,5] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[2,4,7,3,6,1,5] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[2,5,1,6,3,4,7] => [2,4,1,6,3,5,7] => [5,6,3,4,1,2,7] => 2
[2,5,1,7,3,6,4] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[2,5,1,7,4,6,3] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[2,5,6,1,3,4,7] => [2,4,6,1,3,5,7] => [3,5,6,1,2,4,7] => 1
[2,5,6,7,1,3,4] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[2,5,7,3,6,1,4] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[2,5,7,4,6,1,3] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[2,6,1,7,3,5,4] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[2,6,1,7,4,5,3] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[2,6,7,3,5,1,4] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[2,6,7,4,5,1,3] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[2,7,1,3,4,5,6] => [2,7,1,3,4,5,6] => [3,4,5,6,7,1,2] => 1
[2,7,3,1,6,4,5] => [1,7,3,2,6,4,5] => [1,5,6,4,7,3,2] => 2
[2,7,3,1,6,5,4] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[2,7,3,6,5,4,1] => [1,7,2,6,5,4,3] => [1,6,5,4,3,7,2] => 2
[2,7,4,1,6,5,3] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[2,7,4,3,1,5,6] => [1,7,4,3,2,5,6] => [1,5,6,7,4,3,2] => 1
[2,7,4,3,1,6,5] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[2,7,4,3,6,5,1] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[2,7,4,6,5,3,1] => [1,7,2,6,5,4,3] => [1,6,5,4,3,7,2] => 2
[2,7,5,1,6,4,3] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[2,7,5,3,1,4,6] => [1,7,5,3,2,4,6] => [1,4,6,7,5,3,2] => 1
[2,7,5,3,1,6,4] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[2,7,5,3,6,4,1] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[2,7,5,4,1,6,3] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[2,7,5,4,3,1,6] => [1,7,5,4,3,2,6] => [1,6,7,5,4,3,2] => 1
[2,7,5,4,3,6,1] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[2,7,5,4,6,3,1] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[2,7,5,6,4,3,1] => [1,7,2,6,5,4,3] => [1,6,5,4,3,7,2] => 2
[2,7,6,3,1,5,4] => [1,7,6,3,2,5,4] => [1,5,4,7,6,3,2] => 2
[2,7,6,4,1,5,3] => [1,7,6,3,2,5,4] => [1,5,4,7,6,3,2] => 2
[2,7,6,4,3,1,5] => [1,7,6,4,3,2,5] => [1,5,7,6,4,3,2] => 1
[2,7,6,4,3,5,1] => [1,7,6,3,2,5,4] => [1,5,4,7,6,3,2] => 2
[2,7,6,5,3,1,4] => [1,7,6,5,3,2,4] => [1,4,7,6,5,3,2] => 1
[2,7,6,5,4,3,1] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[3,1,7,6,5,4,2] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 1
[3,2,7,6,5,4,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[3,4,1,2,5,6,7] => [2,4,1,3,5,6,7] => [3,4,1,2,5,6,7] => 1
[3,4,1,6,2,5,7] => [2,4,1,6,3,5,7] => [5,6,3,4,1,2,7] => 2
[3,4,1,7,2,6,5] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[3,4,5,7,1,2,6] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[3,4,6,1,2,5,7] => [2,4,6,1,3,5,7] => [3,5,6,1,2,4,7] => 1
[3,4,6,7,1,2,5] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[3,4,7,2,6,1,5] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[3,5,1,6,2,4,7] => [2,4,1,6,3,5,7] => [5,6,3,4,1,2,7] => 2
[3,5,1,7,2,6,4] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[3,5,1,7,4,6,2] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[3,5,2,7,4,6,1] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[3,5,6,1,2,4,7] => [2,4,6,1,3,5,7] => [3,5,6,1,2,4,7] => 1
[3,5,6,7,1,2,4] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[3,5,7,2,6,1,4] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[3,5,7,4,6,1,2] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[3,6,1,7,2,5,4] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[3,6,1,7,4,5,2] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[3,6,2,5,1,4,7] => [3,6,2,5,1,4,7] => [4,5,1,6,2,3,7] => 2
[3,6,2,7,4,5,1] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[3,6,7,2,5,1,4] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[3,6,7,4,5,1,2] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[3,7,4,1,6,5,2] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[3,7,4,2,1,5,6] => [1,7,4,3,2,5,6] => [1,5,6,7,4,3,2] => 1
[3,7,4,2,1,6,5] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[3,7,4,2,6,5,1] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[3,7,4,6,5,2,1] => [1,7,2,6,5,4,3] => [1,6,5,4,3,7,2] => 2
[3,7,5,1,6,4,2] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[3,7,5,2,1,6,4] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[3,7,5,2,6,4,1] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[3,7,5,4,1,6,2] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[3,7,5,4,2,1,6] => [1,7,5,4,3,2,6] => [1,6,7,5,4,3,2] => 1
[3,7,5,4,2,6,1] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[3,7,5,4,6,2,1] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[3,7,5,6,4,2,1] => [1,7,2,6,5,4,3] => [1,6,5,4,3,7,2] => 2
[3,7,6,4,1,5,2] => [1,7,6,3,2,5,4] => [1,5,4,7,6,3,2] => 2
[3,7,6,4,2,1,5] => [1,7,6,4,3,2,5] => [1,5,7,6,4,3,2] => 1
[3,7,6,4,2,5,1] => [1,7,6,3,2,5,4] => [1,5,4,7,6,3,2] => 2
[3,7,6,5,4,2,1] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => 1
[4,1,2,3,5,7,6] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => 2
[4,1,2,3,6,7,5] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => 2
[4,1,7,6,5,3,2] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[4,2,7,6,5,3,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 1
[4,3,7,6,5,2,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[4,5,1,6,2,3,7] => [2,4,1,6,3,5,7] => [5,6,3,4,1,2,7] => 2
[4,5,1,7,2,6,3] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[4,5,1,7,3,6,2] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[4,5,2,7,3,6,1] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[4,5,6,1,2,3,7] => [2,4,6,1,3,5,7] => [3,5,6,1,2,4,7] => 1
[4,5,6,7,1,2,3] => [1,3,5,7,2,4,6] => [1,4,6,7,2,3,5] => 1
[4,5,7,2,6,1,3] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[4,5,7,3,6,1,2] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[4,6,1,7,2,5,3] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[4,6,1,7,3,5,2] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[4,6,2,5,1,3,7] => [3,6,2,5,1,4,7] => [4,5,1,6,2,3,7] => 2
[4,6,2,7,3,5,1] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[4,6,3,5,1,2,7] => [3,6,2,5,1,4,7] => [4,5,1,6,2,3,7] => 2
[4,6,7,2,5,1,3] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[4,6,7,3,5,1,2] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[4,7,1,2,3,5,6] => [4,7,1,2,3,5,6] => [2,3,5,6,7,1,4] => 1
[4,7,5,1,6,3,2] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[4,7,5,2,1,6,3] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[4,7,5,2,6,3,1] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[4,7,5,3,1,6,2] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[4,7,5,3,2,1,6] => [1,7,5,4,3,2,6] => [1,6,7,5,4,3,2] => 1
[4,7,5,3,2,6,1] => [1,7,4,3,2,6,5] => [1,6,5,7,4,3,2] => 2
[4,7,5,3,6,2,1] => [1,7,3,2,6,5,4] => [1,6,5,4,7,3,2] => 2
[4,7,5,6,3,2,1] => [1,7,2,6,5,4,3] => [1,6,5,4,3,7,2] => 2
[4,7,6,5,3,2,1] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => 1
[5,1,2,3,4,7,6] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => 2
[5,1,2,3,6,7,4] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => 2
[5,1,2,4,6,7,3] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => 2
[5,1,3,4,6,7,2] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => 2
[5,1,7,6,4,3,2] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[5,2,3,4,6,7,1] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => 2
[5,2,7,6,4,3,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[5,3,7,6,4,2,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 1
[5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 2
[5,4,7,6,3,2,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[5,6,1,7,2,4,3] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[5,6,1,7,3,4,2] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[5,6,2,4,1,3,7] => [3,6,2,5,1,4,7] => [4,5,1,6,2,3,7] => 2
[5,6,2,7,3,4,1] => [2,4,1,7,3,6,5] => [6,5,7,3,4,1,2] => 3
[5,6,3,4,1,2,7] => [3,6,2,5,1,4,7] => [4,5,1,6,2,3,7] => 2
[5,6,7,2,4,1,3] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[5,6,7,3,4,1,2] => [1,4,7,3,6,2,5] => [1,5,6,2,7,3,4] => 2
[5,7,1,2,3,4,6] => [5,7,1,2,3,4,6] => [2,3,4,6,7,1,5] => 1
[5,7,6,4,3,2,1] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => 1
[6,1,2,3,4,7,5] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => 2
[6,1,2,3,5,7,4] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => 2
[6,1,2,4,5,7,3] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => 2
[6,1,3,4,5,7,2] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => 2
[6,1,5,4,3,2,7] => [6,1,5,4,3,2,7] => [5,4,3,2,6,1,7] => 2
[6,1,7,5,4,3,2] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[6,2,1,5,3,4,7] => [6,2,1,5,3,4,7] => [4,5,3,6,2,1,7] => 2
[6,2,1,5,4,3,7] => [6,2,1,5,4,3,7] => [5,4,3,6,2,1,7] => 2
[6,2,3,4,5,7,1] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => 2
[6,2,5,4,3,1,7] => [6,1,5,4,3,2,7] => [5,4,3,2,6,1,7] => 2
[6,2,7,5,4,3,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[6,3,1,5,4,2,7] => [6,2,1,5,4,3,7] => [5,4,3,6,2,1,7] => 2
[6,3,2,1,4,5,7] => [6,3,2,1,4,5,7] => [4,5,6,3,2,1,7] => 1
[6,3,2,1,5,4,7] => [6,3,2,1,5,4,7] => [5,4,6,3,2,1,7] => 2
[6,3,2,5,4,1,7] => [6,2,1,5,4,3,7] => [5,4,3,6,2,1,7] => 2
[6,3,5,4,2,1,7] => [6,1,5,4,3,2,7] => [5,4,3,2,6,1,7] => 2
[6,3,7,5,4,2,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[6,4,1,5,3,2,7] => [6,2,1,5,4,3,7] => [5,4,3,6,2,1,7] => 2
[6,4,2,1,3,5,7] => [6,4,2,1,3,5,7] => [3,5,6,4,2,1,7] => 1
[6,4,2,1,5,3,7] => [6,3,2,1,5,4,7] => [5,4,6,3,2,1,7] => 2
[6,4,2,5,3,1,7] => [6,2,1,5,4,3,7] => [5,4,3,6,2,1,7] => 2
[6,4,3,1,5,2,7] => [6,3,2,1,5,4,7] => [5,4,6,3,2,1,7] => 2
[6,4,3,2,1,5,7] => [6,4,3,2,1,5,7] => [5,6,4,3,2,1,7] => 1
[6,4,3,2,1,7,5] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 2
[6,4,3,2,5,1,7] => [6,3,2,1,5,4,7] => [5,4,6,3,2,1,7] => 2
[6,4,3,5,2,1,7] => [6,2,1,5,4,3,7] => [5,4,3,6,2,1,7] => 2
[6,4,5,3,2,1,7] => [6,1,5,4,3,2,7] => [5,4,3,2,6,1,7] => 2
[6,4,7,5,3,2,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[6,5,2,1,4,3,7] => [6,5,2,1,4,3,7] => [4,3,6,5,2,1,7] => 2
[6,5,3,1,4,2,7] => [6,5,2,1,4,3,7] => [4,3,6,5,2,1,7] => 2
[6,5,3,2,1,4,7] => [6,5,3,2,1,4,7] => [4,6,5,3,2,1,7] => 1
[6,5,3,2,1,7,4] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 2
[6,5,3,2,4,1,7] => [6,5,2,1,4,3,7] => [4,3,6,5,2,1,7] => 2
[6,5,4,2,1,3,7] => [6,5,4,2,1,3,7] => [3,6,5,4,2,1,7] => 1
[6,5,4,2,1,7,3] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 2
[6,5,4,3,1,2,7] => [6,5,4,3,1,2,7] => [2,6,5,4,3,1,7] => 1
[6,5,4,3,1,7,2] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 2
[6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 1
[6,5,4,3,2,7,1] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 2
[6,5,7,4,3,2,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[6,7,1,2,3,4,5] => [5,7,1,2,3,4,6] => [2,3,4,6,7,1,5] => 1
[6,7,5,4,3,2,1] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => 1
[7,1,3,2,4,5,6] => [7,1,3,2,4,5,6] => [3,2,4,5,6,7,1] => 2
[7,1,3,5,2,4,6] => [7,1,3,5,2,4,6] => [4,5,2,3,6,7,1] => 2
[7,1,4,2,3,5,6] => [7,1,4,2,3,5,6] => [3,4,2,5,6,7,1] => 2
[7,1,4,3,2,5,6] => [7,1,4,3,2,5,6] => [4,3,2,5,6,7,1] => 2
[7,1,4,5,2,3,6] => [7,1,3,5,2,4,6] => [4,5,2,3,6,7,1] => 2
[7,1,5,2,3,4,6] => [7,1,5,2,3,4,6] => [3,4,5,2,6,7,1] => 2
[7,1,5,2,4,3,6] => [7,1,5,2,4,3,6] => [4,3,5,2,6,7,1] => 3
[7,1,5,3,4,2,6] => [7,1,5,2,4,3,6] => [4,3,5,2,6,7,1] => 3
[7,1,6,2,3,4,5] => [7,1,6,2,3,4,5] => [3,4,5,6,2,7,1] => 2
[7,2,3,1,4,5,6] => [7,1,3,2,4,5,6] => [3,2,4,5,6,7,1] => 2
[7,2,3,5,1,4,6] => [7,1,3,5,2,4,6] => [4,5,2,3,6,7,1] => 2
[7,2,4,3,1,5,6] => [7,1,4,3,2,5,6] => [4,3,2,5,6,7,1] => 2
[7,2,4,5,1,3,6] => [7,1,3,5,2,4,6] => [4,5,2,3,6,7,1] => 2
[7,2,5,3,4,1,6] => [7,1,5,2,4,3,6] => [4,3,5,2,6,7,1] => 3
[7,3,4,2,1,5,6] => [7,1,4,3,2,5,6] => [4,3,2,5,6,7,1] => 2
[7,3,4,5,1,2,6] => [7,1,3,5,2,4,6] => [4,5,2,3,6,7,1] => 2
[7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 1
[8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 1
[5,4,6,3,7,2,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 1
[7,6,5,8,3,2,1,4] => [6,5,4,8,3,2,1,7] => [7,8,3,2,1,6,5,4] => 2
[5,6,7,8,1,2,3,4] => [2,4,6,8,1,3,5,7] => [3,5,7,8,1,2,4,6] => 1
[8,7,6,4,2,1,3,5] => [8,7,6,4,2,1,3,5] => [3,5,8,7,6,4,2,1] => 1
[8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => 1
[7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 1
[4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 1
[1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[4,3,6,5,7,2,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,6,5,7,4,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,5,2,7,6,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,5,4,7,6,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 1
[2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 2
[2,1,6,5,7,4,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,5,4,7,6,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,4,5,6,7,8,3] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => 2
[3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 2
[1,2,3,5,6,7,8,4] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 1
[4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 2
[4,3,2,1,7,6,8,5] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 3
[3,2,4,1,8,7,6,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 3
[3,2,4,1,7,6,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 3
[2,1,4,3,7,6,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 2
[3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => 2
[6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 2
[4,3,5,2,6,1,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,5,4,6,1,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 3
[2,1,5,4,6,3,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 3
[3,2,4,1,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => 2
[1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => 2
[1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => 2
[1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => 2
[4,2,3,1,8,6,7,5] => [4,1,3,2,8,5,7,6] => [3,2,4,1,7,6,8,5] => 4
[2,4,6,8,1,3,5,7] => [2,4,6,8,1,3,5,7] => [3,5,7,8,1,2,4,6] => 1
[2,1,4,3,7,5,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,4,1,3,7,5,8,6] => [2,4,1,3,6,5,8,7] => [3,4,1,2,6,5,8,7] => 3
[2,1,4,3,7,8,5,6] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,8,5,6] => 3
[2,1,5,3,6,4,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,5,6,3,4,8,7] => [2,1,4,6,3,5,8,7] => [2,1,5,6,3,4,8,7] => 3
[2,1,5,3,7,4,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,6,3,7,4,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,4,2,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,4,1,2,6,5,8,7] => [2,4,1,3,6,5,8,7] => [3,4,1,2,6,5,8,7] => 3
[3,1,4,2,6,8,5,7] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,8,5,6] => 3
[3,1,4,2,7,5,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,4,1,2,7,8,5,6] => [2,4,1,3,6,8,5,7] => [3,4,1,2,7,8,5,6] => 2
[3,1,5,2,6,4,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,5,2,7,4,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,5,1,7,2,8,4,6] => [2,4,1,6,3,8,5,7] => [7,8,5,6,3,4,1,2] => 3
[1,3,5,6,2,7,4,8] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => 2
[3,1,6,2,7,4,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,6,1,7,2,8,4,5] => [2,4,1,6,3,8,5,7] => [7,8,5,6,3,4,1,2] => 3
[3,1,2,4,5,8,6,7] => [3,1,2,4,5,8,6,7] => [2,3,1,4,5,7,8,6] => 2
[4,1,5,2,6,3,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,1,5,2,6,8,3,7] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,8,5,6] => 3
[4,1,5,2,7,3,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,1,5,2,7,8,3,6] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,8,5,6] => 3
[4,1,6,2,7,3,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[1,4,2,3,7,5,6,8] => [1,4,2,3,7,5,6,8] => [1,3,4,2,6,7,5,8] => 2
[4,1,2,3,8,5,6,7] => [4,1,2,3,8,5,6,7] => [2,3,4,1,6,7,8,5] => 2
[5,1,6,2,7,3,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[6,1,2,3,4,5,8,7] => [6,1,2,3,4,5,8,7] => [2,3,4,5,6,1,8,7] => 2
[6,4,5,2,3,1,8,7] => [6,2,5,1,4,3,8,7] => [4,3,5,1,6,2,8,7] => 4
[3,6,1,5,4,2,8,7] => [2,6,1,5,4,3,8,7] => [5,4,3,6,1,2,8,7] => 3
[2,1,8,6,7,4,5,3] => [2,1,8,4,7,3,6,5] => [2,1,6,5,7,3,8,4] => 4
[4,3,2,1,7,8,5,6] => [4,3,2,1,6,8,5,7] => [4,3,2,1,7,8,5,6] => 2
[3,4,1,2,8,7,6,5] => [2,4,1,3,8,7,6,5] => [3,4,1,2,8,7,6,5] => 2
[2,1,5,8,3,7,6,4] => [2,1,4,8,3,7,6,5] => [2,1,7,6,5,8,3,4] => 3
[6,5,8,7,2,1,4,3] => [4,3,8,7,2,1,6,5] => [6,5,8,7,2,1,4,3] => 3
[5,1,4,2,7,3,8,6] => [4,1,3,2,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
[7,1,4,2,6,3,8,5] => [6,1,3,2,5,4,8,7] => [3,2,5,4,6,1,8,7] => 4
[7,1,5,2,6,3,8,4] => [6,1,3,2,5,4,8,7] => [3,2,5,4,6,1,8,7] => 4
[4,3,1,2,8,7,5,6] => [4,3,1,2,8,7,5,6] => [2,4,3,1,6,8,7,5] => 2
[4,3,1,2,6,5,8,7] => [4,3,1,2,6,5,8,7] => [2,4,3,1,6,5,8,7] => 3
[6,3,1,5,2,4,8,7] => [6,3,1,5,2,4,8,7] => [4,5,2,6,3,1,8,7] => 3
[8,4,5,1,2,7,3,6] => [8,3,5,1,2,7,4,6] => [2,6,7,4,5,1,8,3] => 3
[2,1,6,5,3,4,8,7] => [2,1,6,5,3,4,8,7] => [2,1,4,6,5,3,8,7] => 3
[2,1,8,5,3,7,4,6] => [2,1,8,5,3,7,4,6] => [2,1,6,7,4,8,5,3] => 3
[2,1,4,3,8,7,5,6] => [2,1,4,3,8,7,5,6] => [2,1,4,3,6,8,7,5] => 3
[4,3,2,1,6,8,5,7] => [4,3,2,1,6,8,5,7] => [4,3,2,1,7,8,5,6] => 2
[5,4,2,8,7,1,3,6] => [5,4,2,8,7,1,3,6] => [3,6,8,7,1,5,4,2] => 2
[4,3,2,1,7,5,8,6] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 3
[2,4,1,3,8,7,6,5] => [2,4,1,3,8,7,6,5] => [3,4,1,2,8,7,6,5] => 2
[3,1,5,8,2,7,6,4] => [2,1,4,8,3,7,6,5] => [2,1,7,6,5,8,3,4] => 3
[3,1,4,2,8,7,6,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 3
[3,2,5,8,1,7,6,4] => [2,1,4,8,3,7,6,5] => [2,1,7,6,5,8,3,4] => 3
[4,1,3,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
[5,1,3,2,6,4,8,7] => [4,1,3,2,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
[6,1,3,2,5,4,8,7] => [6,1,3,2,5,4,8,7] => [3,2,5,4,6,1,8,7] => 4
[7,1,3,2,5,4,8,6] => [6,1,3,2,5,4,8,7] => [3,2,5,4,6,1,8,7] => 4
[8,1,3,2,5,4,7,6] => [8,1,3,2,5,4,7,6] => [3,2,5,4,7,6,8,1] => 4
[8,1,4,2,5,3,7,6] => [8,1,3,2,5,4,7,6] => [3,2,5,4,7,6,8,1] => 4
[7,1,4,2,5,3,8,6] => [6,1,3,2,5,4,8,7] => [3,2,5,4,6,1,8,7] => 4
[6,1,4,2,5,3,8,7] => [6,1,3,2,5,4,8,7] => [3,2,5,4,6,1,8,7] => 4
[5,1,4,2,6,3,8,7] => [4,1,3,2,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
[2,1,6,3,5,4,8,7] => [2,1,6,3,5,4,8,7] => [2,1,5,4,6,3,8,7] => 4
[6,2,5,1,4,3,8,7] => [6,2,5,1,4,3,8,7] => [4,3,5,1,6,2,8,7] => 4
[7,2,6,1,4,3,8,5] => [6,2,5,1,4,3,8,7] => [4,3,5,1,6,2,8,7] => 4
[7,2,5,1,4,3,8,6] => [6,2,5,1,4,3,8,7] => [4,3,5,1,6,2,8,7] => 4
[2,1,7,3,5,4,8,6] => [2,1,6,3,5,4,8,7] => [2,1,5,4,6,3,8,7] => 4
[2,1,8,3,5,4,7,6] => [2,1,8,3,5,4,7,6] => [2,1,5,4,7,6,8,3] => 4
[8,2,5,1,4,3,7,6] => [8,2,5,1,4,3,7,6] => [4,3,5,1,7,6,8,2] => 4
[8,2,6,1,4,3,7,5] => [8,2,5,1,4,3,7,6] => [4,3,5,1,7,6,8,2] => 4
[8,2,6,1,5,3,7,4] => [8,2,5,1,4,3,7,6] => [4,3,5,1,7,6,8,2] => 4
[2,1,8,3,6,4,7,5] => [2,1,8,3,5,4,7,6] => [2,1,5,4,7,6,8,3] => 4
[2,1,7,3,6,4,8,5] => [2,1,6,3,5,4,8,7] => [2,1,5,4,6,3,8,7] => 4
[7,2,6,1,5,3,8,4] => [6,2,5,1,4,3,8,7] => [4,3,5,1,6,2,8,7] => 4
[8,1,5,2,6,3,7,4] => [8,1,3,2,5,4,7,6] => [3,2,5,4,7,6,8,1] => 4
[6,1,5,2,7,3,8,4] => [4,1,3,2,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
[6,1,4,2,7,3,8,5] => [4,1,3,2,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
[8,1,4,2,6,3,7,5] => [8,1,3,2,5,4,7,6] => [3,2,5,4,7,6,8,1] => 4
[8,1,3,2,6,4,7,5] => [8,1,3,2,5,4,7,6] => [3,2,5,4,7,6,8,1] => 4
[7,1,3,2,6,4,8,5] => [6,1,3,2,5,4,8,7] => [3,2,5,4,6,1,8,7] => 4
[6,1,3,2,7,4,8,5] => [4,1,3,2,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
[5,1,3,2,7,4,8,6] => [4,1,3,2,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
[4,1,3,2,7,5,8,6] => [4,1,3,2,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
[2,1,4,3,8,5,7,6] => [2,1,4,3,8,5,7,6] => [2,1,4,3,7,6,8,5] => 4
[3,1,4,2,8,5,7,6] => [2,1,4,3,8,5,7,6] => [2,1,4,3,7,6,8,5] => 4
[4,1,3,2,8,5,7,6] => [4,1,3,2,8,5,7,6] => [3,2,4,1,7,6,8,5] => 4
[8,4,7,1,3,2,6,5] => [8,4,7,1,3,2,6,5] => [3,2,6,5,7,1,8,4] => 4
[8,3,7,1,4,2,6,5] => [8,2,7,1,4,3,6,5] => [4,3,6,5,7,1,8,2] => 4
[8,3,7,1,5,2,6,4] => [8,2,7,1,4,3,6,5] => [4,3,6,5,7,1,8,2] => 4
[8,3,7,2,6,1,5,4] => [8,3,7,2,6,1,5,4] => [5,4,6,1,7,2,8,3] => 4
[3,1,8,4,7,2,6,5] => [2,1,8,4,7,3,6,5] => [2,1,6,5,7,3,8,4] => 4
[2,1,8,4,7,3,6,5] => [2,1,8,4,7,3,6,5] => [2,1,6,5,7,3,8,4] => 4
[6,4,7,8,2,5,3,1] => [2,1,4,8,3,7,6,5] => [2,1,7,6,5,8,3,4] => 3
[4,1,5,3,7,2,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[6,4,7,8,3,5,2,1] => [2,1,4,8,3,7,6,5] => [2,1,7,6,5,8,3,4] => 3
[5,1,6,2,4,8,7,3] => [3,1,5,2,4,8,7,6] => [4,5,2,3,1,8,7,6] => 3
[1,5,8,3,7,6,4,2] => [1,3,8,2,7,6,5,4] => [1,7,6,5,4,8,2,3] => 2
[3,1,6,2,4,8,7,5] => [3,1,5,2,4,8,7,6] => [4,5,2,3,1,8,7,6] => 3
[3,1,5,2,4,8,7,6] => [3,1,5,2,4,8,7,6] => [4,5,2,3,1,8,7,6] => 3
[3,2,5,1,6,4,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,5,4,7,1,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,5,3,7,6,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,5,3,7,1,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,5,3,6,1,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,5,1,6,3,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,5,4,6,2,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,1,5,3,6,2,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,5,1,6,2,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,5,2,7,1,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,6,2,7,5,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,6,2,7,1,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,6,1,7,2,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,5,1,7,2,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,5,4,7,2,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,5,4,7,3,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,5,4,7,6,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,1,5,3,7,6,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,5,1,7,6,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,6,1,7,5,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,3,6,5,7,1,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,3,6,4,7,2,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,3,6,4,7,1,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,3,6,1,7,4,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,1,6,3,7,4,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,1,6,3,7,5,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,6,4,7,5,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,6,4,7,5,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,6,4,7,3,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,6,4,7,2,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,1,6,3,7,2,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,1,6,3,7,2,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,3,6,1,7,2,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,3,6,2,7,1,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,3,6,2,7,4,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,2,6,3,7,4,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,2,6,3,7,1,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,2,6,1,7,3,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,5,1,7,3,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,6,1,7,3,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,6,3,7,1,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,6,3,7,5,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,6,4,7,5,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,6,4,7,1,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,6,1,7,4,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,5,1,7,4,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,4,1,7,5,8,6] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,4,2,7,6,8,5] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,5,1,7,6,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,6,1,7,5,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,2,6,5,7,1,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,6,5,7,3,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,6,5,7,1,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,6,1,7,5,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,2,5,1,7,6,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,1,5,2,7,6,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,5,2,7,6,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,5,3,7,6,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,6,3,7,5,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,6,2,7,5,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,1,6,2,7,5,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,1,6,2,7,4,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,2,6,1,7,4,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,2,6,4,7,1,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,2,6,4,7,3,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,4,6,2,7,3,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,4,6,2,7,1,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,4,6,1,7,2,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,1,6,4,7,2,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,1,6,5,7,2,8,3] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,6,5,7,2,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,6,5,7,3,8,4] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[3,1,6,5,7,4,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[4,1,6,5,7,3,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,1,6,4,7,3,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,4,6,1,7,3,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[5,4,6,3,7,1,8,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[2,1,6,5,7,8,3,4] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,8,5,6] => 3
[2,1,7,8,5,6,4,3] => [2,1,4,8,3,7,6,5] => [2,1,7,6,5,8,3,4] => 3
[3,1,6,4,5,2,8,7] => [2,1,6,3,5,4,8,7] => [2,1,5,4,6,3,8,7] => 4
[3,5,8,4,7,6,2,1] => [1,3,8,2,7,6,5,4] => [1,7,6,5,4,8,2,3] => 2
[2,1,5,3,8,6,7,4] => [2,1,4,3,8,5,7,6] => [2,1,4,3,7,6,8,5] => 4
[6,3,7,4,5,8,2,1] => [3,1,5,2,4,8,7,6] => [4,5,2,3,1,8,7,6] => 3
[5,1,7,4,8,6,3,2] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 3
[3,2,5,1,6,8,4,7] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,8,5,6] => 3
[3,5,2,4,7,1,8,6] => [2,4,1,3,6,5,8,7] => [3,4,1,2,6,5,8,7] => 3
[4,2,5,8,3,7,6,1] => [2,1,4,8,3,7,6,5] => [2,1,7,6,5,8,3,4] => 3
[5,4,2,1,6,8,3,7] => [4,3,2,1,6,8,5,7] => [4,3,2,1,7,8,5,6] => 2
[5,4,3,2,7,1,8,6] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 3
[4,3,6,2,8,7,5,1] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 3
[4,3,7,6,2,1,8,5] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 3
[6,4,3,1,7,2,8,5] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 3
[4,3,7,1,8,6,5,2] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 3
[5,3,8,7,6,4,2,1] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 2
[7,5,3,1,8,6,4,2] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 2
[5,7,1,6,3,2,8,4] => [2,6,1,5,4,3,8,7] => [5,4,3,6,1,2,8,7] => 3
[6,1,7,5,3,2,8,4] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 3
[7,6,5,3,2,1,8,4] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 2
[6,5,3,2,8,7,4,1] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 2
[5,2,6,3,8,7,4,1] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 3
[5,2,7,6,3,1,8,4] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 3
[6,5,2,1,7,3,8,4] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 3
[4,7,2,6,3,1,8,5] => [2,6,1,5,4,3,8,7] => [5,4,3,6,1,2,8,7] => 3
[7,3,6,2,4,1,8,5] => [6,2,5,1,4,3,8,7] => [4,3,5,1,6,2,8,7] => 4
[4,2,6,8,1,7,5,3] => [2,1,4,8,3,7,6,5] => [2,1,7,6,5,8,3,4] => 3
[5,1,6,8,2,7,4,3] => [2,1,4,8,3,7,6,5] => [2,1,7,6,5,8,3,4] => 3
[5,2,7,1,8,6,4,3] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 3
[6,2,8,7,5,4,3,1] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 2
[7,6,2,1,8,5,4,3] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 2
[6,1,7,2,8,5,4,3] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 3
[7,1,8,6,5,4,3,2] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 2
[3,2,1,6,4,8,5,7] => [3,2,1,6,4,8,5,7] => [3,2,1,7,8,5,6,4] => 3
[4,3,5,6,1,2,8,7] => [2,1,4,6,3,5,8,7] => [2,1,5,6,3,4,8,7] => 3
[8,5,2,7,4,1,3,6] => [8,5,2,7,4,1,3,6] => [3,6,7,4,1,8,5,2] => 2
[2,6,1,5,4,3,8,7] => [2,6,1,5,4,3,8,7] => [5,4,3,6,1,2,8,7] => 3
[2,1,4,8,3,7,6,5] => [2,1,4,8,3,7,6,5] => [2,1,7,6,5,8,3,4] => 3
[4,3,8,7,2,1,6,5] => [4,3,8,7,2,1,6,5] => [6,5,8,7,2,1,4,3] => 3
[8,3,6,1,4,2,7,5] => [8,2,5,1,4,3,7,6] => [4,3,5,1,7,6,8,2] => 4
[6,7,3,5,2,1,8,4] => [2,6,1,5,4,3,8,7] => [5,4,3,6,1,2,8,7] => 3
[7,3,5,4,6,1,8,2] => [6,1,3,2,5,4,8,7] => [3,2,5,4,6,1,8,7] => 4
[3,1,6,5,4,2,8,7] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 3
[2,1,5,3,8,7,6,4] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 3
[2,1,5,8,4,6,3,7] => [2,1,4,8,3,6,5,7] => [2,1,6,5,7,8,3,4] => 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:
1,1 1,5 1,18,5 1,58,61 1,179,479,61
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 5\ q$
$F_{4} = 1 + 18\ q + 5\ q^{2}$
$F_{5} = 1 + 58\ q + 61\ q^{2}$
$F_{6} = 1 + 179\ q + 479\ q^{2} + 61\ q^{3}$
Description
The number of left outer peaks of a permutation.
A left outer peak in a permutation $w = [w_1,..., w_n]$ is either a position $i$ such that $w_{i-1} < w_i > w_{i+1}$ or $1$ if $w_1 > w_2$.
In other words, it is a peak in the word $[0,w_1,..., w_n]$.
This appears in [1, def.3.1]. The joint distribution with St000366The number of double descents of a permutation. is studied in [3], where left outer peaks are called exterior peaks.
A left outer peak in a permutation $w = [w_1,..., w_n]$ is either a position $i$ such that $w_{i-1} < w_i > w_{i+1}$ or $1$ if $w_1 > w_2$.
In other words, it is a peak in the word $[0,w_1,..., w_n]$.
This appears in [1, def.3.1]. The joint distribution with St000366The number of double descents of a permutation. is studied in [3], where left outer peaks are called exterior peaks.
Map
Inverse fireworks map
Description
Sends a permutation to an inverse fireworks permutation.
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
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