Identifier
-
Mp00254:
Permutations
—Inverse fireworks map⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000833: Permutations ⟶ ℤ
Values
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => [2,1] => 1
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => [3,1,2] => 2
[2,1,3] => [2,1,3] => [2,1,3] => [2,3,1] => 1
[2,3,1] => [1,3,2] => [1,3,2] => [3,1,2] => 2
[3,1,2] => [3,1,2] => [2,3,1] => [2,1,3] => 2
[3,2,1] => [3,2,1] => [3,2,1] => [3,2,1] => 3
[1,2,3,4] => [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] => [4,1,2,3] => 3
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 2
[1,3,4,2] => [1,2,4,3] => [1,2,4,3] => [4,1,2,3] => 3
[1,4,2,3] => [1,4,2,3] => [1,3,4,2] => [3,1,2,4] => 3
[1,4,3,2] => [1,4,3,2] => [1,4,3,2] => [4,3,1,2] => 5
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,3,4,1] => 1
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 2
[2,3,4,1] => [1,2,4,3] => [1,2,4,3] => [4,1,2,3] => 3
[2,4,1,3] => [2,4,1,3] => [3,1,4,2] => [3,1,4,2] => 4
[2,4,3,1] => [1,4,3,2] => [1,4,3,2] => [4,3,1,2] => 5
[3,1,2,4] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => 2
[3,1,4,2] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 4
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => [3,4,2,1] => 3
[3,2,4,1] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 4
[3,4,1,2] => [2,4,1,3] => [3,1,4,2] => [3,1,4,2] => 4
[3,4,2,1] => [1,4,3,2] => [1,4,3,2] => [4,3,1,2] => 5
[4,1,2,3] => [4,1,2,3] => [2,3,4,1] => [2,1,3,4] => 3
[4,1,3,2] => [4,1,3,2] => [2,4,3,1] => [4,2,1,3] => 5
[4,2,1,3] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => 4
[4,2,3,1] => [4,1,3,2] => [2,4,3,1] => [4,2,1,3] => 5
[4,3,1,2] => [4,3,1,2] => [3,4,2,1] => [3,2,1,4] => 5
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 6
[1,2,3,4,5] => [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] => [5,1,2,3,4] => 4
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,4,2,3,5] => 3
[1,2,4,5,3] => [1,2,3,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => 4
[1,2,5,3,4] => [1,2,5,3,4] => [1,2,4,5,3] => [4,1,2,3,5] => 4
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 7
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,4,2,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [3,1,5,2,4] => 6
[1,3,4,2,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,4,2,3,5] => 3
[1,3,4,5,2] => [1,2,3,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => 4
[1,3,5,2,4] => [1,3,5,2,4] => [1,4,2,5,3] => [4,1,5,2,3] => 6
[1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 7
[1,4,2,3,5] => [1,4,2,3,5] => [1,3,4,2,5] => [1,3,2,4,5] => 3
[1,4,2,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => [3,1,5,2,4] => 6
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 5
[1,4,3,5,2] => [1,3,2,5,4] => [1,3,2,5,4] => [3,1,5,2,4] => 6
[1,4,5,2,3] => [1,3,5,2,4] => [1,4,2,5,3] => [4,1,5,2,3] => 6
[1,4,5,3,2] => [1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 7
[1,5,2,3,4] => [1,5,2,3,4] => [1,3,4,5,2] => [3,1,2,4,5] => 4
[1,5,2,4,3] => [1,5,2,4,3] => [1,3,5,4,2] => [5,3,1,2,4] => 7
[1,5,3,2,4] => [1,5,3,2,4] => [1,4,3,5,2] => [4,1,3,2,5] => 6
[1,5,3,4,2] => [1,5,2,4,3] => [1,3,5,4,2] => [5,3,1,2,4] => 7
[1,5,4,2,3] => [1,5,4,2,3] => [1,4,5,3,2] => [4,3,1,2,5] => 7
[1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 9
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [2,3,4,5,1] => 1
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 5
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => [2,4,1,5,3] => 4
[2,1,4,5,3] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 5
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,4,5,3] => [2,1,4,5,3] => 5
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => [5,2,1,4,3] => 8
[2,3,1,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,4,2,5] => 2
[2,3,1,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [3,1,5,2,4] => 6
[2,3,4,1,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,4,2,3,5] => 3
[2,3,4,5,1] => [1,2,3,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => 4
[2,3,5,1,4] => [1,3,5,2,4] => [1,4,2,5,3] => [4,1,5,2,3] => 6
[2,3,5,4,1] => [1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 7
[2,4,1,3,5] => [2,4,1,3,5] => [3,1,4,2,5] => [3,4,1,5,2] => 4
[2,4,1,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => [3,1,5,2,4] => 6
[2,4,3,1,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 5
[2,4,3,5,1] => [1,3,2,5,4] => [1,3,2,5,4] => [3,1,5,2,4] => 6
[2,4,5,1,3] => [1,3,5,2,4] => [1,4,2,5,3] => [4,1,5,2,3] => 6
[2,4,5,3,1] => [1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 7
[2,5,1,3,4] => [2,5,1,3,4] => [3,1,4,5,2] => [3,1,4,5,2] => 5
[2,5,1,4,3] => [2,5,1,4,3] => [3,1,5,4,2] => [5,3,1,4,2] => 8
[2,5,3,1,4] => [1,5,3,2,4] => [1,4,3,5,2] => [4,1,3,2,5] => 6
[2,5,3,4,1] => [1,5,2,4,3] => [1,3,5,4,2] => [5,3,1,2,4] => 7
[2,5,4,1,3] => [2,5,4,1,3] => [4,1,5,3,2] => [4,3,1,5,2] => 8
[2,5,4,3,1] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 9
[3,1,2,4,5] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,4,1,5] => 2
[3,1,2,5,4] => [3,1,2,5,4] => [2,3,1,5,4] => [2,1,5,3,4] => 6
[3,1,4,2,5] => [2,1,4,3,5] => [2,1,4,3,5] => [2,4,1,5,3] => 4
[3,1,4,5,2] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 5
[3,1,5,2,4] => [3,1,5,2,4] => [2,4,1,5,3] => [2,1,4,3,5] => 6
[3,1,5,4,2] => [2,1,5,4,3] => [2,1,5,4,3] => [5,2,1,4,3] => 8
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [3,4,5,2,1] => 3
[3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,5,4,1] => 7
[3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => [2,4,1,5,3] => 4
[3,2,4,5,1] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 5
[3,2,5,1,4] => [3,2,5,1,4] => [4,2,1,5,3] => [4,2,5,3,1] => 7
[3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => [5,2,1,4,3] => 8
[3,4,1,2,5] => [2,4,1,3,5] => [3,1,4,2,5] => [3,4,1,5,2] => 4
[3,4,1,5,2] => [1,3,2,5,4] => [1,3,2,5,4] => [3,1,5,2,4] => 6
[3,4,2,1,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 5
[3,4,2,5,1] => [1,3,2,5,4] => [1,3,2,5,4] => [3,1,5,2,4] => 6
[3,4,5,1,2] => [1,3,5,2,4] => [1,4,2,5,3] => [4,1,5,2,3] => 6
[3,4,5,2,1] => [1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 7
[3,5,1,2,4] => [3,5,1,2,4] => [3,4,1,5,2] => [3,1,4,2,5] => 6
[3,5,1,4,2] => [2,5,1,4,3] => [3,1,5,4,2] => [5,3,1,4,2] => 8
[3,5,2,1,4] => [3,5,2,1,4] => [4,3,1,5,2] => [4,1,5,3,2] => 7
>>> Load all 980 entries. <<<[3,5,2,4,1] => [2,5,1,4,3] => [3,1,5,4,2] => [5,3,1,4,2] => 8
[3,5,4,1,2] => [2,5,4,1,3] => [4,1,5,3,2] => [4,3,1,5,2] => 8
[3,5,4,2,1] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 9
[4,1,2,3,5] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,1,4,5] => 3
[4,1,2,5,3] => [3,1,2,5,4] => [2,3,1,5,4] => [2,1,5,3,4] => 6
[4,1,3,2,5] => [4,1,3,2,5] => [2,4,3,1,5] => [2,4,3,1,5] => 5
[4,1,3,5,2] => [3,1,2,5,4] => [2,3,1,5,4] => [2,1,5,3,4] => 6
[4,1,5,2,3] => [3,1,5,2,4] => [2,4,1,5,3] => [2,1,4,3,5] => 6
[4,1,5,3,2] => [2,1,5,4,3] => [2,1,5,4,3] => [5,2,1,4,3] => 8
[4,2,1,3,5] => [4,2,1,3,5] => [3,2,4,1,5] => [3,4,2,5,1] => 4
[4,2,1,5,3] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,5,4,1] => 7
[4,2,3,1,5] => [4,1,3,2,5] => [2,4,3,1,5] => [2,4,3,1,5] => 5
[4,2,3,5,1] => [3,1,2,5,4] => [2,3,1,5,4] => [2,1,5,3,4] => 6
[4,2,5,1,3] => [3,2,5,1,4] => [4,2,1,5,3] => [4,2,5,3,1] => 7
[4,2,5,3,1] => [2,1,5,4,3] => [2,1,5,4,3] => [5,2,1,4,3] => 8
[4,3,1,2,5] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => 5
[4,3,1,5,2] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,5,4,1] => 7
[4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [4,5,3,2,1] => 6
[4,3,2,5,1] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,5,4,1] => 7
[4,3,5,1,2] => [3,2,5,1,4] => [4,2,1,5,3] => [4,2,5,3,1] => 7
[4,3,5,2,1] => [2,1,5,4,3] => [2,1,5,4,3] => [5,2,1,4,3] => 8
[4,5,1,2,3] => [3,5,1,2,4] => [3,4,1,5,2] => [3,1,4,2,5] => 6
[4,5,1,3,2] => [2,5,1,4,3] => [3,1,5,4,2] => [5,3,1,4,2] => 8
[4,5,2,1,3] => [3,5,2,1,4] => [4,3,1,5,2] => [4,1,5,3,2] => 7
[4,5,2,3,1] => [2,5,1,4,3] => [3,1,5,4,2] => [5,3,1,4,2] => 8
[4,5,3,1,2] => [2,5,4,1,3] => [4,1,5,3,2] => [4,3,1,5,2] => 8
[4,5,3,2,1] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 9
[5,1,2,3,4] => [5,1,2,3,4] => [2,3,4,5,1] => [2,1,3,4,5] => 4
[5,1,2,4,3] => [5,1,2,4,3] => [2,3,5,4,1] => [5,2,1,3,4] => 7
[5,1,3,2,4] => [5,1,3,2,4] => [2,4,3,5,1] => [4,2,3,1,5] => 6
[5,1,3,4,2] => [5,1,2,4,3] => [2,3,5,4,1] => [5,2,1,3,4] => 7
[5,1,4,2,3] => [5,1,4,2,3] => [2,4,5,3,1] => [4,2,1,3,5] => 7
[5,1,4,3,2] => [5,1,4,3,2] => [2,5,4,3,1] => [5,4,2,1,3] => 9
[5,2,1,3,4] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => 5
[5,2,1,4,3] => [5,2,1,4,3] => [3,2,5,4,1] => [3,2,1,5,4] => 8
[5,2,3,1,4] => [5,1,3,2,4] => [2,4,3,5,1] => [4,2,3,1,5] => 6
[5,2,3,4,1] => [5,1,2,4,3] => [2,3,5,4,1] => [5,2,1,3,4] => 7
[5,2,4,1,3] => [5,2,4,1,3] => [4,2,5,3,1] => [4,2,1,5,3] => 8
[5,2,4,3,1] => [5,1,4,3,2] => [2,5,4,3,1] => [5,4,2,1,3] => 9
[5,3,1,2,4] => [5,3,1,2,4] => [3,4,2,5,1] => [3,2,4,1,5] => 6
[5,3,1,4,2] => [5,2,1,4,3] => [3,2,5,4,1] => [3,2,1,5,4] => 8
[5,3,2,1,4] => [5,3,2,1,4] => [4,3,2,5,1] => [4,3,5,2,1] => 7
[5,3,2,4,1] => [5,2,1,4,3] => [3,2,5,4,1] => [3,2,1,5,4] => 8
[5,3,4,1,2] => [5,2,4,1,3] => [4,2,5,3,1] => [4,2,1,5,3] => 8
[5,3,4,2,1] => [5,1,4,3,2] => [2,5,4,3,1] => [5,4,2,1,3] => 9
[5,4,1,2,3] => [5,4,1,2,3] => [3,4,5,2,1] => [3,2,1,4,5] => 7
[5,4,1,3,2] => [5,4,1,3,2] => [3,5,4,2,1] => [5,3,2,1,4] => 9
[5,4,2,1,3] => [5,4,2,1,3] => [4,3,5,2,1] => [4,3,2,5,1] => 8
[5,4,2,3,1] => [5,4,1,3,2] => [3,5,4,2,1] => [5,3,2,1,4] => 9
[5,4,3,1,2] => [5,4,3,1,2] => [4,5,3,2,1] => [4,3,2,1,5] => 9
[5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 10
[1,2,3,4,5,6] => [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] => [6,1,2,3,4,5] => 5
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,5,2,3,4,6] => 4
[1,2,3,5,6,4] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 5
[1,2,3,6,4,5] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => [5,1,2,3,4,6] => 5
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 3
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[1,2,4,5,3,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,5,2,3,4,6] => 4
[1,2,4,5,6,3] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 5
[1,2,4,6,3,5] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => [5,1,6,2,3,4] => 8
[1,2,4,6,5,3] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[1,2,5,3,4,6] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => [1,4,2,3,5,6] => 4
[1,2,5,3,6,4] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,5,4,2,3,6] => 7
[1,2,5,4,6,3] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[1,2,5,6,3,4] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => [5,1,6,2,3,4] => 8
[1,2,5,6,4,3] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[1,2,6,3,4,5] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => [4,1,2,3,5,6] => 5
[1,2,6,3,5,4] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => [6,4,1,2,3,5] => 9
[1,2,6,4,3,5] => [1,2,6,4,3,5] => [1,2,5,4,6,3] => [5,1,4,2,3,6] => 8
[1,2,6,4,5,3] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => [6,4,1,2,3,5] => 9
[1,2,6,5,3,4] => [1,2,6,5,3,4] => [1,2,5,6,4,3] => [5,4,1,2,3,6] => 9
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,4,5,2,6] => 2
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 7
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 6
[1,3,2,5,6,4] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 7
[1,3,2,6,4,5] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => [3,1,2,5,4,6] => 7
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[1,3,4,2,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 3
[1,3,4,2,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[1,3,4,5,2,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,5,2,3,4,6] => 4
[1,3,4,5,6,2] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 5
[1,3,4,6,2,5] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => [5,1,6,2,3,4] => 8
[1,3,4,6,5,2] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[1,3,5,2,4,6] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => [1,4,2,5,3,6] => 6
[1,3,5,2,6,4] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[1,3,5,4,2,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,5,4,2,3,6] => 7
[1,3,5,4,6,2] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[1,3,5,6,2,4] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => [5,1,6,2,3,4] => 8
[1,3,5,6,4,2] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[1,3,6,2,4,5] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => [4,1,2,5,3,6] => 7
[1,3,6,2,5,4] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[1,3,6,4,2,5] => [1,2,6,4,3,5] => [1,2,5,4,6,3] => [5,1,4,2,3,6] => 8
[1,3,6,4,5,2] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => [6,4,1,2,3,5] => 9
[1,3,6,5,2,4] => [1,3,6,5,2,4] => [1,5,2,6,4,3] => [5,4,1,6,2,3] => 11
[1,3,6,5,4,2] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[1,4,2,3,5,6] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => [1,3,4,2,5,6] => 3
[1,4,2,3,6,5] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => [3,1,6,2,4,5] => 8
[1,4,2,5,3,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 6
[1,4,2,5,6,3] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 7
[1,4,2,6,3,5] => [1,4,2,6,3,5] => [1,3,5,2,6,4] => [3,1,5,2,4,6] => 8
[1,4,2,6,5,3] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,5,3,2,6] => 5
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[1,4,3,5,2,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 6
[1,4,3,5,6,2] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 7
[1,4,3,6,2,5] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[1,4,3,6,5,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[1,4,5,2,3,6] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => [1,4,2,5,3,6] => 6
[1,4,5,2,6,3] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[1,4,5,3,2,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,5,4,2,3,6] => 7
[1,4,5,3,6,2] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[1,4,5,6,2,3] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => [5,1,6,2,3,4] => 8
[1,4,5,6,3,2] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[1,4,6,2,3,5] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => [4,1,5,2,3,6] => 8
[1,4,6,2,5,3] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[1,4,6,3,2,5] => [1,4,6,3,2,5] => [1,5,4,2,6,3] => [5,1,6,4,2,3] => 10
[1,4,6,3,5,2] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[1,4,6,5,2,3] => [1,3,6,5,2,4] => [1,5,2,6,4,3] => [5,4,1,6,2,3] => 11
[1,4,6,5,3,2] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[1,5,2,3,4,6] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => [1,3,2,4,5,6] => 4
[1,5,2,3,6,4] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => [3,1,6,2,4,5] => 8
[1,5,2,4,3,6] => [1,5,2,4,3,6] => [1,3,5,4,2,6] => [1,5,3,2,4,6] => 7
[1,5,2,4,6,3] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => [3,1,6,2,4,5] => 8
[1,5,2,6,3,4] => [1,4,2,6,3,5] => [1,3,5,2,6,4] => [3,1,5,2,4,6] => 8
[1,5,2,6,4,3] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[1,5,3,2,4,6] => [1,5,3,2,4,6] => [1,4,3,5,2,6] => [1,4,3,5,2,6] => 6
[1,5,3,2,6,4] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[1,5,3,4,2,6] => [1,5,2,4,3,6] => [1,3,5,4,2,6] => [1,5,3,2,4,6] => 7
[1,5,3,4,6,2] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => [3,1,6,2,4,5] => 8
[1,5,3,6,2,4] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[1,5,3,6,4,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[1,5,4,2,3,6] => [1,5,4,2,3,6] => [1,4,5,3,2,6] => [1,4,3,2,5,6] => 7
[1,5,4,2,6,3] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 9
[1,5,4,3,6,2] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[1,5,4,6,2,3] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[1,5,4,6,3,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[1,5,6,2,3,4] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => [4,1,5,2,3,6] => 8
[1,5,6,2,4,3] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[1,5,6,3,2,4] => [1,4,6,3,2,5] => [1,5,4,2,6,3] => [5,1,6,4,2,3] => 10
[1,5,6,3,4,2] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[1,5,6,4,2,3] => [1,3,6,5,2,4] => [1,5,2,6,4,3] => [5,4,1,6,2,3] => 11
[1,5,6,4,3,2] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[1,6,2,3,4,5] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => [3,1,2,4,5,6] => 5
[1,6,2,3,5,4] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => [6,3,1,2,4,5] => 9
[1,6,2,4,3,5] => [1,6,2,4,3,5] => [1,3,5,4,6,2] => [5,1,3,2,4,6] => 8
[1,6,2,4,5,3] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => [6,3,1,2,4,5] => 9
[1,6,2,5,3,4] => [1,6,2,5,3,4] => [1,3,5,6,4,2] => [5,3,1,2,4,6] => 9
[1,6,2,5,4,3] => [1,6,2,5,4,3] => [1,3,6,5,4,2] => [6,5,3,1,2,4] => 12
[1,6,3,2,4,5] => [1,6,3,2,4,5] => [1,4,3,5,6,2] => [4,1,3,5,2,6] => 7
[1,6,3,2,5,4] => [1,6,3,2,5,4] => [1,4,3,6,5,2] => [4,3,1,6,2,5] => 11
[1,6,3,4,2,5] => [1,6,2,4,3,5] => [1,3,5,4,6,2] => [5,1,3,2,4,6] => 8
[1,6,3,4,5,2] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => [6,3,1,2,4,5] => 9
[1,6,3,5,2,4] => [1,6,3,5,2,4] => [1,5,3,6,4,2] => [5,3,1,6,2,4] => 11
[1,6,3,5,4,2] => [1,6,2,5,4,3] => [1,3,6,5,4,2] => [6,5,3,1,2,4] => 12
[1,6,4,2,3,5] => [1,6,4,2,3,5] => [1,4,5,3,6,2] => [4,1,3,2,5,6] => 8
[1,6,4,2,5,3] => [1,6,3,2,5,4] => [1,4,3,6,5,2] => [4,3,1,6,2,5] => 11
[1,6,4,3,2,5] => [1,6,4,3,2,5] => [1,5,4,3,6,2] => [5,1,4,3,2,6] => 10
[1,6,4,3,5,2] => [1,6,3,2,5,4] => [1,4,3,6,5,2] => [4,3,1,6,2,5] => 11
[1,6,4,5,2,3] => [1,6,3,5,2,4] => [1,5,3,6,4,2] => [5,3,1,6,2,4] => 11
[1,6,4,5,3,2] => [1,6,2,5,4,3] => [1,3,6,5,4,2] => [6,5,3,1,2,4] => 12
[1,6,5,2,3,4] => [1,6,5,2,3,4] => [1,4,5,6,3,2] => [4,3,1,2,5,6] => 9
[1,6,5,2,4,3] => [1,6,5,2,4,3] => [1,4,6,5,3,2] => [6,4,3,1,2,5] => 12
[1,6,5,3,2,4] => [1,6,5,3,2,4] => [1,5,4,6,3,2] => [5,4,1,3,2,6] => 11
[1,6,5,3,4,2] => [1,6,5,2,4,3] => [1,4,6,5,3,2] => [6,4,3,1,2,5] => 12
[1,6,5,4,2,3] => [1,6,5,4,2,3] => [1,5,6,4,3,2] => [5,4,3,1,2,6] => 12
[1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 14
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,3,4,5,6,1] => 1
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 6
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,3,1,5,6,4] => 5
[2,1,3,5,6,4] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 6
[2,1,3,6,4,5] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => [2,1,3,5,6,4] => 6
[2,1,3,6,5,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 10
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,4,5,1,6,3] => 4
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[2,1,4,5,3,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,3,1,5,6,4] => 5
[2,1,4,5,6,3] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 6
[2,1,4,6,3,5] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => [2,1,5,3,6,4] => 9
[2,1,4,6,5,3] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 10
[2,1,5,3,4,6] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => [2,4,1,5,6,3] => 5
[2,1,5,3,6,4] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,5,4,1,6,3] => 8
[2,1,5,4,6,3] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[2,1,5,6,3,4] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => [2,1,5,3,6,4] => 9
[2,1,5,6,4,3] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 10
[2,1,6,3,4,5] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => [2,1,4,5,6,3] => 6
[2,1,6,3,5,4] => [2,1,6,3,5,4] => [2,1,4,6,5,3] => [6,2,1,4,5,3] => 10
[2,1,6,4,3,5] => [2,1,6,4,3,5] => [2,1,5,4,6,3] => [5,2,4,1,6,3] => 9
[2,1,6,4,5,3] => [2,1,6,3,5,4] => [2,1,4,6,5,3] => [6,2,1,4,5,3] => 10
[2,1,6,5,3,4] => [2,1,6,5,3,4] => [2,1,5,6,4,3] => [5,2,1,4,6,3] => 10
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 13
[2,3,1,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,4,5,2,6] => 2
[2,3,1,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 7
[2,3,1,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 6
[2,3,1,5,6,4] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 7
[2,3,1,6,4,5] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => [3,1,2,5,4,6] => 7
[2,3,1,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[2,3,4,1,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 3
[2,3,4,1,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[2,3,4,5,1,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,5,2,3,4,6] => 4
[2,3,4,5,6,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 5
[2,3,4,6,1,5] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => [5,1,6,2,3,4] => 8
[2,3,4,6,5,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[2,3,5,1,4,6] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => [1,4,2,5,3,6] => 6
[2,3,5,1,6,4] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[2,3,5,4,1,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,5,4,2,3,6] => 7
[2,3,5,4,6,1] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[2,3,5,6,1,4] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => [5,1,6,2,3,4] => 8
[2,3,5,6,4,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[2,3,6,1,4,5] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => [4,1,2,5,3,6] => 7
[2,3,6,1,5,4] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[2,3,6,4,1,5] => [1,2,6,4,3,5] => [1,2,5,4,6,3] => [5,1,4,2,3,6] => 8
[2,3,6,4,5,1] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => [6,4,1,2,3,5] => 9
[2,3,6,5,1,4] => [1,3,6,5,2,4] => [1,5,2,6,4,3] => [5,4,1,6,2,3] => 11
[2,3,6,5,4,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[2,4,1,3,5,6] => [2,4,1,3,5,6] => [3,1,4,2,5,6] => [3,4,5,1,6,2] => 4
[2,4,1,3,6,5] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [3,1,4,2,6,5] => 9
[2,4,1,5,3,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 6
[2,4,1,5,6,3] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 7
[2,4,1,6,3,5] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => [3,1,5,2,6,4] => 9
[2,4,1,6,5,3] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[2,4,3,1,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,5,3,2,6] => 5
[2,4,3,1,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[2,4,3,5,1,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 6
[2,4,3,5,6,1] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 7
[2,4,3,6,1,5] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[2,4,3,6,5,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[2,4,5,1,3,6] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => [1,4,2,5,3,6] => 6
[2,4,5,1,6,3] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[2,4,5,3,1,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,5,4,2,3,6] => 7
[2,4,5,3,6,1] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[2,4,5,6,1,3] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => [5,1,6,2,3,4] => 8
[2,4,5,6,3,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[2,4,6,1,3,5] => [2,4,6,1,3,5] => [4,1,5,2,6,3] => [4,1,5,2,6,3] => 9
[2,4,6,1,5,3] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[2,4,6,3,1,5] => [1,4,6,3,2,5] => [1,5,4,2,6,3] => [5,1,6,4,2,3] => 10
[2,4,6,3,5,1] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[2,4,6,5,1,3] => [1,3,6,5,2,4] => [1,5,2,6,4,3] => [5,4,1,6,2,3] => 11
[2,4,6,5,3,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[2,5,1,3,4,6] => [2,5,1,3,4,6] => [3,1,4,5,2,6] => [3,4,1,5,6,2] => 5
[2,5,1,3,6,4] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [3,1,4,2,6,5] => 9
[2,5,1,4,3,6] => [2,5,1,4,3,6] => [3,1,5,4,2,6] => [3,5,4,1,6,2] => 8
[2,5,1,4,6,3] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [3,1,4,2,6,5] => 9
[2,5,1,6,3,4] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => [3,1,5,2,6,4] => 9
[2,5,1,6,4,3] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[2,5,3,1,4,6] => [1,5,3,2,4,6] => [1,4,3,5,2,6] => [1,4,3,5,2,6] => 6
[2,5,3,1,6,4] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[2,5,3,4,1,6] => [1,5,2,4,3,6] => [1,3,5,4,2,6] => [1,5,3,2,4,6] => 7
[2,5,3,4,6,1] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => [3,1,6,2,4,5] => 8
[2,5,3,6,1,4] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[2,5,3,6,4,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[2,5,4,1,3,6] => [2,5,4,1,3,6] => [4,1,5,3,2,6] => [4,5,3,1,6,2] => 8
[2,5,4,1,6,3] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[2,5,4,3,1,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 9
[2,5,4,3,6,1] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[2,5,4,6,1,3] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[2,5,4,6,3,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[2,5,6,1,3,4] => [2,4,6,1,3,5] => [4,1,5,2,6,3] => [4,1,5,2,6,3] => 9
[2,5,6,1,4,3] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[2,5,6,3,1,4] => [1,4,6,3,2,5] => [1,5,4,2,6,3] => [5,1,6,4,2,3] => 10
[2,5,6,3,4,1] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[2,5,6,4,1,3] => [1,3,6,5,2,4] => [1,5,2,6,4,3] => [5,4,1,6,2,3] => 11
[2,5,6,4,3,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[2,6,1,3,4,5] => [2,6,1,3,4,5] => [3,1,4,5,6,2] => [3,1,4,5,6,2] => 6
[2,6,1,3,5,4] => [2,6,1,3,5,4] => [3,1,4,6,5,2] => [6,3,1,4,5,2] => 10
[2,6,1,4,3,5] => [2,6,1,4,3,5] => [3,1,5,4,6,2] => [5,3,4,1,6,2] => 9
[2,6,1,4,5,3] => [2,6,1,3,5,4] => [3,1,4,6,5,2] => [6,3,1,4,5,2] => 10
[2,6,1,5,3,4] => [2,6,1,5,3,4] => [3,1,5,6,4,2] => [5,3,1,4,6,2] => 10
[2,6,1,5,4,3] => [2,6,1,5,4,3] => [3,1,6,5,4,2] => [6,5,3,1,4,2] => 13
[2,6,3,1,4,5] => [1,6,3,2,4,5] => [1,4,3,5,6,2] => [4,1,3,5,2,6] => 7
[2,6,3,1,5,4] => [1,6,3,2,5,4] => [1,4,3,6,5,2] => [4,3,1,6,2,5] => 11
[2,6,3,4,1,5] => [1,6,2,4,3,5] => [1,3,5,4,6,2] => [5,1,3,2,4,6] => 8
[2,6,3,4,5,1] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => [6,3,1,2,4,5] => 9
[2,6,3,5,1,4] => [1,6,3,5,2,4] => [1,5,3,6,4,2] => [5,3,1,6,2,4] => 11
[2,6,3,5,4,1] => [1,6,2,5,4,3] => [1,3,6,5,4,2] => [6,5,3,1,2,4] => 12
[2,6,4,1,3,5] => [2,6,4,1,3,5] => [4,1,5,3,6,2] => [4,3,5,1,6,2] => 9
[2,6,4,1,5,3] => [1,6,3,2,5,4] => [1,4,3,6,5,2] => [4,3,1,6,2,5] => 11
[2,6,4,3,1,5] => [1,6,4,3,2,5] => [1,5,4,3,6,2] => [5,1,4,3,2,6] => 10
[2,6,4,3,5,1] => [1,6,3,2,5,4] => [1,4,3,6,5,2] => [4,3,1,6,2,5] => 11
[2,6,4,5,1,3] => [1,6,3,5,2,4] => [1,5,3,6,4,2] => [5,3,1,6,2,4] => 11
[2,6,4,5,3,1] => [1,6,2,5,4,3] => [1,3,6,5,4,2] => [6,5,3,1,2,4] => 12
[2,6,5,1,3,4] => [2,6,5,1,3,4] => [4,1,5,6,3,2] => [4,3,1,5,6,2] => 10
[2,6,5,1,4,3] => [2,6,5,1,4,3] => [4,1,6,5,3,2] => [6,4,3,1,5,2] => 13
[2,6,5,3,1,4] => [1,6,5,3,2,4] => [1,5,4,6,3,2] => [5,4,1,3,2,6] => 11
[2,6,5,3,4,1] => [1,6,5,2,4,3] => [1,4,6,5,3,2] => [6,4,3,1,2,5] => 12
[2,6,5,4,1,3] => [2,6,5,4,1,3] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 13
[2,6,5,4,3,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 14
[3,1,2,4,5,6] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,4,5,1,6] => 2
[3,1,2,4,6,5] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => [2,1,3,6,4,5] => 7
[3,1,2,5,4,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => [2,3,1,5,4,6] => 6
[3,1,2,5,6,4] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => [2,1,3,6,4,5] => 7
[3,1,2,6,4,5] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => [2,1,3,5,4,6] => 7
[3,1,2,6,5,4] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,1,5,3,4] => 11
[3,1,4,2,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,4,5,1,6,3] => 4
[3,1,4,2,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[3,1,4,5,2,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,3,1,5,6,4] => 5
[3,1,4,5,6,2] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 6
[3,1,4,6,2,5] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => [2,1,5,3,6,4] => 9
[3,1,4,6,5,2] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 10
[3,1,5,2,4,6] => [3,1,5,2,4,6] => [2,4,1,5,3,6] => [2,4,1,5,3,6] => 6
[3,1,5,2,6,4] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[3,1,5,4,2,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,5,4,1,6,3] => 8
[3,1,5,4,6,2] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[3,1,5,6,2,4] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => [2,1,5,3,6,4] => 9
[3,1,5,6,4,2] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 10
[3,1,6,2,4,5] => [3,1,6,2,4,5] => [2,4,1,5,6,3] => [2,1,4,5,3,6] => 7
[3,1,6,2,5,4] => [3,1,6,2,5,4] => [2,4,1,6,5,3] => [6,2,1,4,3,5] => 11
[3,1,6,4,2,5] => [2,1,6,4,3,5] => [2,1,5,4,6,3] => [5,2,4,1,6,3] => 9
[3,1,6,4,5,2] => [2,1,6,3,5,4] => [2,1,4,6,5,3] => [6,2,1,4,5,3] => 10
[3,1,6,5,2,4] => [3,1,6,5,2,4] => [2,5,1,6,4,3] => [5,2,1,4,3,6] => 11
[3,1,6,5,4,2] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 13
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,4,5,6,2,1] => 3
[3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,4,6,5,1] => 8
[3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,5,2,6,4,1] => 7
[3,2,1,5,6,4] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,4,6,5,1] => 8
[3,2,1,6,4,5] => [3,2,1,6,4,5] => [3,2,1,5,6,4] => [3,2,5,6,4,1] => 8
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[3,2,4,1,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,4,5,1,6,3] => 4
[3,2,4,1,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[3,2,4,5,1,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,3,1,5,6,4] => 5
[3,2,4,5,6,1] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 6
[3,2,4,6,1,5] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => [2,1,5,3,6,4] => 9
[3,2,4,6,5,1] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 10
[3,2,5,1,4,6] => [3,2,5,1,4,6] => [4,2,1,5,3,6] => [4,5,2,6,3,1] => 7
[3,2,5,1,6,4] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[3,2,5,4,1,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,5,4,1,6,3] => 8
[3,2,5,4,6,1] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[3,2,5,6,1,4] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => [2,1,5,3,6,4] => 9
[3,2,5,6,4,1] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 10
[3,2,6,1,4,5] => [3,2,6,1,4,5] => [4,2,1,5,6,3] => [4,2,5,6,3,1] => 8
[3,2,6,1,5,4] => [3,2,6,1,5,4] => [4,2,1,6,5,3] => [4,2,1,6,5,3] => 12
[3,2,6,4,1,5] => [2,1,6,4,3,5] => [2,1,5,4,6,3] => [5,2,4,1,6,3] => 9
[3,2,6,4,5,1] => [2,1,6,3,5,4] => [2,1,4,6,5,3] => [6,2,1,4,5,3] => 10
[3,2,6,5,1,4] => [3,2,6,5,1,4] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 12
[3,2,6,5,4,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 13
[3,4,1,2,5,6] => [2,4,1,3,5,6] => [3,1,4,2,5,6] => [3,4,5,1,6,2] => 4
[3,4,1,2,6,5] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [3,1,4,2,6,5] => 9
[3,4,1,5,2,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 6
[3,4,1,5,6,2] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 7
[3,4,1,6,2,5] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => [3,1,5,2,6,4] => 9
[3,4,1,6,5,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[3,4,2,1,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,5,3,2,6] => 5
[3,4,2,1,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[3,4,2,5,1,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 6
[3,4,2,5,6,1] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 7
[3,4,2,6,1,5] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[3,4,2,6,5,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[3,4,5,1,2,6] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => [1,4,2,5,3,6] => 6
[3,4,5,1,6,2] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[3,4,5,2,1,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,5,4,2,3,6] => 7
[3,4,5,2,6,1] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 8
[3,4,5,6,1,2] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => [5,1,6,2,3,4] => 8
[3,4,5,6,2,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[3,4,6,1,2,5] => [2,4,6,1,3,5] => [4,1,5,2,6,3] => [4,1,5,2,6,3] => 9
[3,4,6,1,5,2] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[3,4,6,2,1,5] => [1,4,6,3,2,5] => [1,5,4,2,6,3] => [5,1,6,4,2,3] => 10
[3,4,6,2,5,1] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[3,4,6,5,1,2] => [1,3,6,5,2,4] => [1,5,2,6,4,3] => [5,4,1,6,2,3] => 11
[3,4,6,5,2,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[3,5,1,2,4,6] => [3,5,1,2,4,6] => [3,4,1,5,2,6] => [3,4,1,5,2,6] => 6
[3,5,1,2,6,4] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [3,1,4,2,6,5] => 9
[3,5,1,4,2,6] => [2,5,1,4,3,6] => [3,1,5,4,2,6] => [3,5,4,1,6,2] => 8
[3,5,1,4,6,2] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [3,1,4,2,6,5] => 9
[3,5,1,6,2,4] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => [3,1,5,2,6,4] => 9
[3,5,1,6,4,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[3,5,2,1,4,6] => [3,5,2,1,4,6] => [4,3,1,5,2,6] => [4,5,1,6,3,2] => 7
[3,5,2,1,6,4] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[3,5,2,4,1,6] => [2,5,1,4,3,6] => [3,1,5,4,2,6] => [3,5,4,1,6,2] => 8
[3,5,2,4,6,1] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [3,1,4,2,6,5] => 9
[3,5,2,6,1,4] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[3,5,2,6,4,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[3,5,4,1,2,6] => [2,5,4,1,3,6] => [4,1,5,3,2,6] => [4,5,3,1,6,2] => 8
[3,5,4,1,6,2] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[3,5,4,2,1,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 9
[3,5,4,2,6,1] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[3,5,4,6,1,2] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[3,5,4,6,2,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[3,5,6,1,2,4] => [2,4,6,1,3,5] => [4,1,5,2,6,3] => [4,1,5,2,6,3] => 9
[3,5,6,1,4,2] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[3,5,6,2,1,4] => [1,4,6,3,2,5] => [1,5,4,2,6,3] => [5,1,6,4,2,3] => 10
[3,5,6,2,4,1] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[3,5,6,4,1,2] => [1,3,6,5,2,4] => [1,5,2,6,4,3] => [5,4,1,6,2,3] => 11
[3,5,6,4,2,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[3,6,1,2,4,5] => [3,6,1,2,4,5] => [3,4,1,5,6,2] => [3,1,4,5,2,6] => 7
[3,6,1,2,5,4] => [3,6,1,2,5,4] => [3,4,1,6,5,2] => [6,3,1,4,2,5] => 11
[3,6,1,4,2,5] => [2,6,1,4,3,5] => [3,1,5,4,6,2] => [5,3,4,1,6,2] => 9
[3,6,1,4,5,2] => [2,6,1,3,5,4] => [3,1,4,6,5,2] => [6,3,1,4,5,2] => 10
[3,6,1,5,2,4] => [3,6,1,5,2,4] => [3,5,1,6,4,2] => [5,3,1,4,2,6] => 11
[3,6,1,5,4,2] => [2,6,1,5,4,3] => [3,1,6,5,4,2] => [6,5,3,1,4,2] => 13
[3,6,2,1,4,5] => [3,6,2,1,4,5] => [4,3,1,5,6,2] => [4,1,5,6,3,2] => 8
[3,6,2,1,5,4] => [3,6,2,1,5,4] => [4,3,1,6,5,2] => [4,3,1,6,5,2] => 12
[3,6,2,4,1,5] => [2,6,1,4,3,5] => [3,1,5,4,6,2] => [5,3,4,1,6,2] => 9
[3,6,2,4,5,1] => [2,6,1,3,5,4] => [3,1,4,6,5,2] => [6,3,1,4,5,2] => 10
[3,6,2,5,1,4] => [3,6,2,5,1,4] => [5,3,1,6,4,2] => [5,3,1,6,4,2] => 12
[3,6,2,5,4,1] => [2,6,1,5,4,3] => [3,1,6,5,4,2] => [6,5,3,1,4,2] => 13
[3,6,4,1,2,5] => [2,6,4,1,3,5] => [4,1,5,3,6,2] => [4,3,5,1,6,2] => 9
[3,6,4,1,5,2] => [1,6,3,2,5,4] => [1,4,3,6,5,2] => [4,3,1,6,2,5] => 11
[3,6,4,2,1,5] => [1,6,4,3,2,5] => [1,5,4,3,6,2] => [5,1,4,3,2,6] => 10
[3,6,4,2,5,1] => [1,6,3,2,5,4] => [1,4,3,6,5,2] => [4,3,1,6,2,5] => 11
[3,6,4,5,1,2] => [1,6,3,5,2,4] => [1,5,3,6,4,2] => [5,3,1,6,2,4] => 11
[3,6,4,5,2,1] => [1,6,2,5,4,3] => [1,3,6,5,4,2] => [6,5,3,1,2,4] => 12
[3,6,5,1,2,4] => [3,6,5,1,2,4] => [4,5,1,6,3,2] => [4,3,1,5,2,6] => 11
[3,6,5,1,4,2] => [2,6,5,1,4,3] => [4,1,6,5,3,2] => [6,4,3,1,5,2] => 13
[3,6,5,2,1,4] => [3,6,5,2,1,4] => [5,4,1,6,3,2] => [5,4,1,6,3,2] => 12
[3,6,5,2,4,1] => [2,6,5,1,4,3] => [4,1,6,5,3,2] => [6,4,3,1,5,2] => 13
[3,6,5,4,1,2] => [2,6,5,4,1,3] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 13
[3,6,5,4,2,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 14
[4,1,2,3,5,6] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => 3
[4,1,2,3,6,5] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => [2,1,6,3,4,5] => 8
[4,1,2,5,3,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => [2,3,1,5,4,6] => 6
[4,1,2,5,6,3] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => [2,1,3,6,4,5] => 7
[4,1,2,6,3,5] => [4,1,2,6,3,5] => [2,3,5,1,6,4] => [2,1,5,3,4,6] => 8
[4,1,2,6,5,3] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,1,5,3,4] => 11
[4,1,3,2,5,6] => [4,1,3,2,5,6] => [2,4,3,1,5,6] => [2,4,5,3,1,6] => 5
[4,1,3,2,6,5] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,6,3,1,5] => 10
[4,1,3,5,2,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => [2,3,1,5,4,6] => 6
[4,1,3,5,6,2] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => [2,1,3,6,4,5] => 7
[4,1,3,6,2,5] => [4,1,3,6,2,5] => [2,5,3,1,6,4] => [5,2,6,3,1,4] => 10
[4,1,3,6,5,2] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,1,5,3,4] => 11
[4,1,5,2,3,6] => [3,1,5,2,4,6] => [2,4,1,5,3,6] => [2,4,1,5,3,6] => 6
[4,1,5,2,6,3] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[4,1,5,3,2,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,5,4,1,6,3] => 8
[4,1,5,3,6,2] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[4,1,5,6,2,3] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => [2,1,5,3,6,4] => 9
[4,1,5,6,3,2] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 10
[4,1,6,2,3,5] => [4,1,6,2,3,5] => [2,4,5,1,6,3] => [2,1,4,3,5,6] => 8
[4,1,6,2,5,3] => [3,1,6,2,5,4] => [2,4,1,6,5,3] => [6,2,1,4,3,5] => 11
[4,1,6,3,2,5] => [4,1,6,3,2,5] => [2,5,4,1,6,3] => [2,1,5,4,3,6] => 10
[4,1,6,3,5,2] => [3,1,6,2,5,4] => [2,4,1,6,5,3] => [6,2,1,4,3,5] => 11
[4,1,6,5,2,3] => [3,1,6,5,2,4] => [2,5,1,6,4,3] => [5,2,1,4,3,6] => 11
[4,1,6,5,3,2] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 13
[4,2,1,3,5,6] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [3,4,5,2,6,1] => 4
[4,2,1,3,6,5] => [4,2,1,3,6,5] => [3,2,4,1,6,5] => [3,2,6,4,5,1] => 9
[4,2,1,5,3,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,5,2,6,4,1] => 7
[4,2,1,5,6,3] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,4,6,5,1] => 8
[4,2,1,6,3,5] => [4,2,1,6,3,5] => [3,2,5,1,6,4] => [3,2,5,4,6,1] => 9
[4,2,1,6,5,3] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[4,2,3,1,5,6] => [4,1,3,2,5,6] => [2,4,3,1,5,6] => [2,4,5,3,1,6] => 5
[4,2,3,1,6,5] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,6,3,1,5] => 10
[4,2,3,5,1,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => [2,3,1,5,4,6] => 6
[4,2,3,5,6,1] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => [2,1,3,6,4,5] => 7
[4,2,3,6,1,5] => [4,1,3,6,2,5] => [2,5,3,1,6,4] => [5,2,6,3,1,4] => 10
[4,2,3,6,5,1] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,1,5,3,4] => 11
[4,2,5,1,3,6] => [3,2,5,1,4,6] => [4,2,1,5,3,6] => [4,5,2,6,3,1] => 7
[4,2,5,1,6,3] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[4,2,5,3,1,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,5,4,1,6,3] => 8
[4,2,5,3,6,1] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[4,2,5,6,1,3] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => [2,1,5,3,6,4] => 9
[4,2,5,6,3,1] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 10
[4,2,6,1,3,5] => [4,2,6,1,3,5] => [4,2,5,1,6,3] => [4,2,5,3,6,1] => 9
[4,2,6,1,5,3] => [3,2,6,1,5,4] => [4,2,1,6,5,3] => [4,2,1,6,5,3] => 12
[4,2,6,3,1,5] => [4,1,6,3,2,5] => [2,5,4,1,6,3] => [2,1,5,4,3,6] => 10
[4,2,6,3,5,1] => [3,1,6,2,5,4] => [2,4,1,6,5,3] => [6,2,1,4,3,5] => 11
[4,2,6,5,1,3] => [3,2,6,5,1,4] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 12
[4,2,6,5,3,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 13
[4,3,1,2,5,6] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [3,4,5,2,1,6] => 5
[4,3,1,2,6,5] => [4,3,1,2,6,5] => [3,4,2,1,6,5] => [3,2,6,4,1,5] => 10
[4,3,1,5,2,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,5,2,6,4,1] => 7
[4,3,1,5,6,2] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,4,6,5,1] => 8
[4,3,1,6,2,5] => [4,3,1,6,2,5] => [3,5,2,1,6,4] => [3,2,5,4,1,6] => 10
[4,3,1,6,5,2] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,5,6,3,2,1] => 6
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 11
[4,3,2,5,1,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,5,2,6,4,1] => 7
[4,3,2,5,6,1] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,4,6,5,1] => 8
[4,3,2,6,1,5] => [4,3,2,6,1,5] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 11
[4,3,2,6,5,1] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[4,3,5,1,2,6] => [3,2,5,1,4,6] => [4,2,1,5,3,6] => [4,5,2,6,3,1] => 7
[4,3,5,1,6,2] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[4,3,5,2,1,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,5,4,1,6,3] => 8
[4,3,5,2,6,1] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[4,3,5,6,1,2] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => [2,1,5,3,6,4] => 9
[4,3,5,6,2,1] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 10
[4,3,6,1,2,5] => [4,3,6,1,2,5] => [4,5,2,1,6,3] => [4,2,5,3,1,6] => 10
[4,3,6,1,5,2] => [3,2,6,1,5,4] => [4,2,1,6,5,3] => [4,2,1,6,5,3] => 12
[4,3,6,2,1,5] => [4,3,6,2,1,5] => [5,4,2,1,6,3] => [5,2,6,4,3,1] => 11
[4,3,6,2,5,1] => [3,2,6,1,5,4] => [4,2,1,6,5,3] => [4,2,1,6,5,3] => 12
[4,3,6,5,1,2] => [3,2,6,5,1,4] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 12
[4,3,6,5,2,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 13
[4,5,1,2,3,6] => [3,5,1,2,4,6] => [3,4,1,5,2,6] => [3,4,1,5,2,6] => 6
[4,5,1,2,6,3] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [3,1,4,2,6,5] => 9
[4,5,1,3,2,6] => [2,5,1,4,3,6] => [3,1,5,4,2,6] => [3,5,4,1,6,2] => 8
[4,5,1,3,6,2] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [3,1,4,2,6,5] => 9
[4,5,1,6,2,3] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => [3,1,5,2,6,4] => 9
[4,5,1,6,3,2] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[4,5,2,1,3,6] => [3,5,2,1,4,6] => [4,3,1,5,2,6] => [4,5,1,6,3,2] => 7
[4,5,2,1,6,3] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[4,5,2,3,1,6] => [2,5,1,4,3,6] => [3,1,5,4,2,6] => [3,5,4,1,6,2] => 8
[4,5,2,3,6,1] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => [3,1,4,2,6,5] => 9
[4,5,2,6,1,3] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[4,5,2,6,3,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[4,5,3,1,2,6] => [2,5,4,1,3,6] => [4,1,5,3,2,6] => [4,5,3,1,6,2] => 8
[4,5,3,1,6,2] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[4,5,3,2,1,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 9
[4,5,3,2,6,1] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 10
[4,5,3,6,1,2] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => [5,1,6,3,2,4] => 10
[4,5,3,6,2,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 11
[4,5,6,1,2,3] => [2,4,6,1,3,5] => [4,1,5,2,6,3] => [4,1,5,2,6,3] => 9
[4,5,6,1,3,2] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[4,5,6,2,1,3] => [1,4,6,3,2,5] => [1,5,4,2,6,3] => [5,1,6,4,2,3] => 10
[4,5,6,2,3,1] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => [6,4,1,5,2,3] => 11
[4,5,6,3,1,2] => [1,3,6,5,2,4] => [1,5,2,6,4,3] => [5,4,1,6,2,3] => 11
[4,5,6,3,2,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[4,6,1,2,3,5] => [4,6,1,2,3,5] => [3,4,5,1,6,2] => [3,1,4,2,5,6] => 8
[4,6,1,2,5,3] => [3,6,1,2,5,4] => [3,4,1,6,5,2] => [6,3,1,4,2,5] => 11
[4,6,1,3,2,5] => [4,6,1,3,2,5] => [3,5,4,1,6,2] => [3,1,5,4,2,6] => 10
[4,6,1,3,5,2] => [3,6,1,2,5,4] => [3,4,1,6,5,2] => [6,3,1,4,2,5] => 11
[4,6,1,5,2,3] => [3,6,1,5,2,4] => [3,5,1,6,4,2] => [5,3,1,4,2,6] => 11
[4,6,1,5,3,2] => [2,6,1,5,4,3] => [3,1,6,5,4,2] => [6,5,3,1,4,2] => 13
[4,6,2,1,3,5] => [4,6,2,1,3,5] => [4,3,5,1,6,2] => [4,1,5,3,6,2] => 9
[4,6,2,1,5,3] => [3,6,2,1,5,4] => [4,3,1,6,5,2] => [4,3,1,6,5,2] => 12
[4,6,2,3,1,5] => [4,6,1,3,2,5] => [3,5,4,1,6,2] => [3,1,5,4,2,6] => 10
[4,6,2,3,5,1] => [3,6,1,2,5,4] => [3,4,1,6,5,2] => [6,3,1,4,2,5] => 11
[4,6,2,5,1,3] => [3,6,2,5,1,4] => [5,3,1,6,4,2] => [5,3,1,6,4,2] => 12
[4,6,2,5,3,1] => [2,6,1,5,4,3] => [3,1,6,5,4,2] => [6,5,3,1,4,2] => 13
[4,6,3,1,2,5] => [4,6,3,1,2,5] => [4,5,3,1,6,2] => [4,1,5,3,2,6] => 10
[4,6,3,1,5,2] => [3,6,2,1,5,4] => [4,3,1,6,5,2] => [4,3,1,6,5,2] => 12
[4,6,3,2,1,5] => [4,6,3,2,1,5] => [5,4,3,1,6,2] => [5,1,6,4,3,2] => 11
[4,6,3,2,5,1] => [3,6,2,1,5,4] => [4,3,1,6,5,2] => [4,3,1,6,5,2] => 12
[4,6,3,5,1,2] => [3,6,2,5,1,4] => [5,3,1,6,4,2] => [5,3,1,6,4,2] => 12
[4,6,3,5,2,1] => [2,6,1,5,4,3] => [3,1,6,5,4,2] => [6,5,3,1,4,2] => 13
[4,6,5,1,2,3] => [3,6,5,1,2,4] => [4,5,1,6,3,2] => [4,3,1,5,2,6] => 11
[4,6,5,1,3,2] => [2,6,5,1,4,3] => [4,1,6,5,3,2] => [6,4,3,1,5,2] => 13
[4,6,5,2,1,3] => [3,6,5,2,1,4] => [5,4,1,6,3,2] => [5,4,1,6,3,2] => 12
[4,6,5,2,3,1] => [2,6,5,1,4,3] => [4,1,6,5,3,2] => [6,4,3,1,5,2] => 13
[4,6,5,3,1,2] => [2,6,5,4,1,3] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 13
[4,6,5,3,2,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 14
[5,1,2,3,4,6] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,1,4,5,6] => 4
[5,1,2,3,6,4] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => [2,1,6,3,4,5] => 8
[5,1,2,4,3,6] => [5,1,2,4,3,6] => [2,3,5,4,1,6] => [2,5,3,1,4,6] => 7
[5,1,2,4,6,3] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => [2,1,6,3,4,5] => 8
[5,1,2,6,3,4] => [4,1,2,6,3,5] => [2,3,5,1,6,4] => [2,1,5,3,4,6] => 8
[5,1,2,6,4,3] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,1,5,3,4] => 11
[5,1,3,2,4,6] => [5,1,3,2,4,6] => [2,4,3,5,1,6] => [2,4,3,5,1,6] => 6
[5,1,3,2,6,4] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,6,3,1,5] => 10
[5,1,3,4,2,6] => [5,1,2,4,3,6] => [2,3,5,4,1,6] => [2,5,3,1,4,6] => 7
[5,1,3,4,6,2] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => [2,1,6,3,4,5] => 8
[5,1,3,6,2,4] => [4,1,3,6,2,5] => [2,5,3,1,6,4] => [5,2,6,3,1,4] => 10
[5,1,3,6,4,2] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,1,5,3,4] => 11
[5,1,4,2,3,6] => [5,1,4,2,3,6] => [2,4,5,3,1,6] => [2,4,3,1,5,6] => 7
[5,1,4,2,6,3] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,6,3,1,5] => 10
[5,1,4,3,2,6] => [5,1,4,3,2,6] => [2,5,4,3,1,6] => [2,5,4,3,1,6] => 9
[5,1,4,3,6,2] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,6,3,1,5] => 10
[5,1,4,6,2,3] => [4,1,3,6,2,5] => [2,5,3,1,6,4] => [5,2,6,3,1,4] => 10
[5,1,4,6,3,2] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,1,5,3,4] => 11
[5,1,6,2,3,4] => [4,1,6,2,3,5] => [2,4,5,1,6,3] => [2,1,4,3,5,6] => 8
[5,1,6,2,4,3] => [3,1,6,2,5,4] => [2,4,1,6,5,3] => [6,2,1,4,3,5] => 11
[5,1,6,3,2,4] => [4,1,6,3,2,5] => [2,5,4,1,6,3] => [2,1,5,4,3,6] => 10
[5,1,6,3,4,2] => [3,1,6,2,5,4] => [2,4,1,6,5,3] => [6,2,1,4,3,5] => 11
[5,1,6,4,2,3] => [3,1,6,5,2,4] => [2,5,1,6,4,3] => [5,2,1,4,3,6] => 11
[5,1,6,4,3,2] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 13
[5,2,1,3,4,6] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [3,4,2,5,6,1] => 5
[5,2,1,3,6,4] => [4,2,1,3,6,5] => [3,2,4,1,6,5] => [3,2,6,4,5,1] => 9
[5,2,1,4,3,6] => [5,2,1,4,3,6] => [3,2,5,4,1,6] => [3,5,2,1,6,4] => 8
[5,2,1,4,6,3] => [4,2,1,3,6,5] => [3,2,4,1,6,5] => [3,2,6,4,5,1] => 9
[5,2,1,6,3,4] => [4,2,1,6,3,5] => [3,2,5,1,6,4] => [3,2,5,4,6,1] => 9
[5,2,1,6,4,3] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[5,2,3,1,4,6] => [5,1,3,2,4,6] => [2,4,3,5,1,6] => [2,4,3,5,1,6] => 6
[5,2,3,1,6,4] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,6,3,1,5] => 10
[5,2,3,4,1,6] => [5,1,2,4,3,6] => [2,3,5,4,1,6] => [2,5,3,1,4,6] => 7
[5,2,3,4,6,1] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => [2,1,6,3,4,5] => 8
[5,2,3,6,1,4] => [4,1,3,6,2,5] => [2,5,3,1,6,4] => [5,2,6,3,1,4] => 10
[5,2,3,6,4,1] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,1,5,3,4] => 11
[5,2,4,1,3,6] => [5,2,4,1,3,6] => [4,2,5,3,1,6] => [4,5,2,1,6,3] => 8
[5,2,4,1,6,3] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,6,3,1,5] => 10
[5,2,4,3,1,6] => [5,1,4,3,2,6] => [2,5,4,3,1,6] => [2,5,4,3,1,6] => 9
[5,2,4,3,6,1] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,6,3,1,5] => 10
[5,2,4,6,1,3] => [4,1,3,6,2,5] => [2,5,3,1,6,4] => [5,2,6,3,1,4] => 10
[5,2,4,6,3,1] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,1,5,3,4] => 11
[5,2,6,1,3,4] => [4,2,6,1,3,5] => [4,2,5,1,6,3] => [4,2,5,3,6,1] => 9
[5,2,6,1,4,3] => [3,2,6,1,5,4] => [4,2,1,6,5,3] => [4,2,1,6,5,3] => 12
[5,2,6,3,1,4] => [4,1,6,3,2,5] => [2,5,4,1,6,3] => [2,1,5,4,3,6] => 10
[5,2,6,3,4,1] => [3,1,6,2,5,4] => [2,4,1,6,5,3] => [6,2,1,4,3,5] => 11
[5,2,6,4,1,3] => [3,2,6,5,1,4] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 12
[5,2,6,4,3,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 13
[5,3,1,2,4,6] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => 6
[5,3,1,2,6,4] => [4,3,1,2,6,5] => [3,4,2,1,6,5] => [3,2,6,4,1,5] => 10
[5,3,1,4,2,6] => [5,2,1,4,3,6] => [3,2,5,4,1,6] => [3,5,2,1,6,4] => 8
[5,3,1,4,6,2] => [4,2,1,3,6,5] => [3,2,4,1,6,5] => [3,2,6,4,5,1] => 9
[5,3,1,6,2,4] => [4,3,1,6,2,5] => [3,5,2,1,6,4] => [3,2,5,4,1,6] => 10
[5,3,1,6,4,2] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[5,3,2,1,4,6] => [5,3,2,1,4,6] => [4,3,2,5,1,6] => [4,5,3,6,2,1] => 7
[5,3,2,1,6,4] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 11
[5,3,2,4,1,6] => [5,2,1,4,3,6] => [3,2,5,4,1,6] => [3,5,2,1,6,4] => 8
[5,3,2,4,6,1] => [4,2,1,3,6,5] => [3,2,4,1,6,5] => [3,2,6,4,5,1] => 9
[5,3,2,6,1,4] => [4,3,2,6,1,5] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 11
[5,3,2,6,4,1] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[5,3,4,1,2,6] => [5,2,4,1,3,6] => [4,2,5,3,1,6] => [4,5,2,1,6,3] => 8
[5,3,4,1,6,2] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,6,3,1,5] => 10
[5,3,4,2,1,6] => [5,1,4,3,2,6] => [2,5,4,3,1,6] => [2,5,4,3,1,6] => 9
[5,3,4,2,6,1] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,6,3,1,5] => 10
[5,3,4,6,1,2] => [4,1,3,6,2,5] => [2,5,3,1,6,4] => [5,2,6,3,1,4] => 10
[5,3,4,6,2,1] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,1,5,3,4] => 11
[5,3,6,1,2,4] => [4,3,6,1,2,5] => [4,5,2,1,6,3] => [4,2,5,3,1,6] => 10
[5,3,6,1,4,2] => [3,2,6,1,5,4] => [4,2,1,6,5,3] => [4,2,1,6,5,3] => 12
[5,3,6,2,1,4] => [4,3,6,2,1,5] => [5,4,2,1,6,3] => [5,2,6,4,3,1] => 11
[5,3,6,2,4,1] => [3,2,6,1,5,4] => [4,2,1,6,5,3] => [4,2,1,6,5,3] => 12
[5,3,6,4,1,2] => [3,2,6,5,1,4] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 12
[5,3,6,4,2,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 13
[5,4,1,2,3,6] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [3,4,2,1,5,6] => 7
[5,4,1,2,6,3] => [4,3,1,2,6,5] => [3,4,2,1,6,5] => [3,2,6,4,1,5] => 10
[5,4,1,3,2,6] => [5,4,1,3,2,6] => [3,5,4,2,1,6] => [3,5,4,2,1,6] => 9
[5,4,1,3,6,2] => [4,3,1,2,6,5] => [3,4,2,1,6,5] => [3,2,6,4,1,5] => 10
[5,4,1,6,2,3] => [4,3,1,6,2,5] => [3,5,2,1,6,4] => [3,2,5,4,1,6] => 10
[5,4,1,6,3,2] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[5,4,2,1,3,6] => [5,4,2,1,3,6] => [4,3,5,2,1,6] => [4,5,3,2,6,1] => 8
[5,4,2,1,6,3] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 11
[5,4,2,3,1,6] => [5,4,1,3,2,6] => [3,5,4,2,1,6] => [3,5,4,2,1,6] => 9
[5,4,2,3,6,1] => [4,3,1,2,6,5] => [3,4,2,1,6,5] => [3,2,6,4,1,5] => 10
[5,4,2,6,1,3] => [4,3,2,6,1,5] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 11
[5,4,2,6,3,1] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[5,4,3,1,2,6] => [5,4,3,1,2,6] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 9
[5,4,3,1,6,2] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 11
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 10
[5,4,3,2,6,1] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 11
[5,4,3,6,1,2] => [4,3,2,6,1,5] => [5,3,2,1,6,4] => [5,3,6,4,2,1] => 11
[5,4,3,6,2,1] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[5,4,6,1,2,3] => [4,3,6,1,2,5] => [4,5,2,1,6,3] => [4,2,5,3,1,6] => 10
[5,4,6,1,3,2] => [3,2,6,1,5,4] => [4,2,1,6,5,3] => [4,2,1,6,5,3] => 12
[5,4,6,2,1,3] => [4,3,6,2,1,5] => [5,4,2,1,6,3] => [5,2,6,4,3,1] => 11
[5,4,6,2,3,1] => [3,2,6,1,5,4] => [4,2,1,6,5,3] => [4,2,1,6,5,3] => 12
[5,4,6,3,1,2] => [3,2,6,5,1,4] => [5,2,1,6,4,3] => [5,2,1,6,4,3] => 12
[5,4,6,3,2,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 13
[5,6,1,2,3,4] => [4,6,1,2,3,5] => [3,4,5,1,6,2] => [3,1,4,2,5,6] => 8
[5,6,1,2,4,3] => [3,6,1,2,5,4] => [3,4,1,6,5,2] => [6,3,1,4,2,5] => 11
[5,6,1,3,2,4] => [4,6,1,3,2,5] => [3,5,4,1,6,2] => [3,1,5,4,2,6] => 10
[5,6,1,3,4,2] => [3,6,1,2,5,4] => [3,4,1,6,5,2] => [6,3,1,4,2,5] => 11
[5,6,1,4,2,3] => [3,6,1,5,2,4] => [3,5,1,6,4,2] => [5,3,1,4,2,6] => 11
[5,6,1,4,3,2] => [2,6,1,5,4,3] => [3,1,6,5,4,2] => [6,5,3,1,4,2] => 13
[5,6,2,1,3,4] => [4,6,2,1,3,5] => [4,3,5,1,6,2] => [4,1,5,3,6,2] => 9
[5,6,2,1,4,3] => [3,6,2,1,5,4] => [4,3,1,6,5,2] => [4,3,1,6,5,2] => 12
[5,6,2,3,1,4] => [4,6,1,3,2,5] => [3,5,4,1,6,2] => [3,1,5,4,2,6] => 10
[5,6,2,3,4,1] => [3,6,1,2,5,4] => [3,4,1,6,5,2] => [6,3,1,4,2,5] => 11
[5,6,2,4,1,3] => [3,6,2,5,1,4] => [5,3,1,6,4,2] => [5,3,1,6,4,2] => 12
[5,6,2,4,3,1] => [2,6,1,5,4,3] => [3,1,6,5,4,2] => [6,5,3,1,4,2] => 13
[5,6,3,1,2,4] => [4,6,3,1,2,5] => [4,5,3,1,6,2] => [4,1,5,3,2,6] => 10
[5,6,3,1,4,2] => [3,6,2,1,5,4] => [4,3,1,6,5,2] => [4,3,1,6,5,2] => 12
[5,6,3,2,1,4] => [4,6,3,2,1,5] => [5,4,3,1,6,2] => [5,1,6,4,3,2] => 11
[5,6,3,2,4,1] => [3,6,2,1,5,4] => [4,3,1,6,5,2] => [4,3,1,6,5,2] => 12
[5,6,3,4,1,2] => [3,6,2,5,1,4] => [5,3,1,6,4,2] => [5,3,1,6,4,2] => 12
[5,6,3,4,2,1] => [2,6,1,5,4,3] => [3,1,6,5,4,2] => [6,5,3,1,4,2] => 13
[5,6,4,1,2,3] => [3,6,5,1,2,4] => [4,5,1,6,3,2] => [4,3,1,5,2,6] => 11
[5,6,4,1,3,2] => [2,6,5,1,4,3] => [4,1,6,5,3,2] => [6,4,3,1,5,2] => 13
[5,6,4,2,1,3] => [3,6,5,2,1,4] => [5,4,1,6,3,2] => [5,4,1,6,3,2] => 12
[5,6,4,2,3,1] => [2,6,5,1,4,3] => [4,1,6,5,3,2] => [6,4,3,1,5,2] => 13
[5,6,4,3,1,2] => [2,6,5,4,1,3] => [5,1,6,4,3,2] => [5,4,3,1,6,2] => 13
[5,6,4,3,2,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 14
[6,1,2,3,4,5] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,1,3,4,5,6] => 5
[6,1,2,3,5,4] => [6,1,2,3,5,4] => [2,3,4,6,5,1] => [6,2,1,3,4,5] => 9
[6,1,2,4,3,5] => [6,1,2,4,3,5] => [2,3,5,4,6,1] => [5,2,3,1,4,6] => 8
[6,1,2,4,5,3] => [6,1,2,3,5,4] => [2,3,4,6,5,1] => [6,2,1,3,4,5] => 9
[6,1,2,5,3,4] => [6,1,2,5,3,4] => [2,3,5,6,4,1] => [5,2,1,3,4,6] => 9
[6,1,2,5,4,3] => [6,1,2,5,4,3] => [2,3,6,5,4,1] => [6,5,2,1,3,4] => 12
[6,1,3,2,4,5] => [6,1,3,2,4,5] => [2,4,3,5,6,1] => [4,2,3,5,1,6] => 7
[6,1,3,2,5,4] => [6,1,3,2,5,4] => [2,4,3,6,5,1] => [4,2,1,6,3,5] => 11
[6,1,3,4,2,5] => [6,1,2,4,3,5] => [2,3,5,4,6,1] => [5,2,3,1,4,6] => 8
[6,1,3,4,5,2] => [6,1,2,3,5,4] => [2,3,4,6,5,1] => [6,2,1,3,4,5] => 9
[6,1,3,5,2,4] => [6,1,3,5,2,4] => [2,5,3,6,4,1] => [5,2,1,6,3,4] => 11
[6,1,3,5,4,2] => [6,1,2,5,4,3] => [2,3,6,5,4,1] => [6,5,2,1,3,4] => 12
[6,1,4,2,3,5] => [6,1,4,2,3,5] => [2,4,5,3,6,1] => [4,2,3,1,5,6] => 8
[6,1,4,2,5,3] => [6,1,3,2,5,4] => [2,4,3,6,5,1] => [4,2,1,6,3,5] => 11
[6,1,4,3,2,5] => [6,1,4,3,2,5] => [2,5,4,3,6,1] => [5,2,4,3,1,6] => 10
[6,1,4,3,5,2] => [6,1,3,2,5,4] => [2,4,3,6,5,1] => [4,2,1,6,3,5] => 11
[6,1,4,5,2,3] => [6,1,3,5,2,4] => [2,5,3,6,4,1] => [5,2,1,6,3,4] => 11
[6,1,4,5,3,2] => [6,1,2,5,4,3] => [2,3,6,5,4,1] => [6,5,2,1,3,4] => 12
[6,1,5,2,3,4] => [6,1,5,2,3,4] => [2,4,5,6,3,1] => [4,2,1,3,5,6] => 9
[6,1,5,2,4,3] => [6,1,5,2,4,3] => [2,4,6,5,3,1] => [6,4,2,1,3,5] => 12
[6,1,5,3,2,4] => [6,1,5,3,2,4] => [2,5,4,6,3,1] => [5,4,2,3,1,6] => 11
[6,1,5,3,4,2] => [6,1,5,2,4,3] => [2,4,6,5,3,1] => [6,4,2,1,3,5] => 12
[6,1,5,4,2,3] => [6,1,5,4,2,3] => [2,5,6,4,3,1] => [5,4,2,1,3,6] => 12
[6,1,5,4,3,2] => [6,1,5,4,3,2] => [2,6,5,4,3,1] => [6,5,4,2,1,3] => 14
[6,2,1,3,4,5] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => 6
[6,2,1,3,5,4] => [6,2,1,3,5,4] => [3,2,4,6,5,1] => [3,2,1,4,6,5] => 10
[6,2,1,4,3,5] => [6,2,1,4,3,5] => [3,2,5,4,6,1] => [3,2,5,1,6,4] => 9
[6,2,1,4,5,3] => [6,2,1,3,5,4] => [3,2,4,6,5,1] => [3,2,1,4,6,5] => 10
[6,2,1,5,3,4] => [6,2,1,5,3,4] => [3,2,5,6,4,1] => [3,2,1,5,6,4] => 10
[6,2,1,5,4,3] => [6,2,1,5,4,3] => [3,2,6,5,4,1] => [6,3,2,1,5,4] => 13
[6,2,3,1,4,5] => [6,1,3,2,4,5] => [2,4,3,5,6,1] => [4,2,3,5,1,6] => 7
[6,2,3,1,5,4] => [6,1,3,2,5,4] => [2,4,3,6,5,1] => [4,2,1,6,3,5] => 11
[6,2,3,4,1,5] => [6,1,2,4,3,5] => [2,3,5,4,6,1] => [5,2,3,1,4,6] => 8
[6,2,3,4,5,1] => [6,1,2,3,5,4] => [2,3,4,6,5,1] => [6,2,1,3,4,5] => 9
[6,2,3,5,1,4] => [6,1,3,5,2,4] => [2,5,3,6,4,1] => [5,2,1,6,3,4] => 11
[6,2,3,5,4,1] => [6,1,2,5,4,3] => [2,3,6,5,4,1] => [6,5,2,1,3,4] => 12
[6,2,4,1,3,5] => [6,2,4,1,3,5] => [4,2,5,3,6,1] => [4,2,5,1,6,3] => 9
[6,2,4,1,5,3] => [6,1,3,2,5,4] => [2,4,3,6,5,1] => [4,2,1,6,3,5] => 11
[6,2,4,3,1,5] => [6,1,4,3,2,5] => [2,5,4,3,6,1] => [5,2,4,3,1,6] => 10
[6,2,4,3,5,1] => [6,1,3,2,5,4] => [2,4,3,6,5,1] => [4,2,1,6,3,5] => 11
[6,2,4,5,1,3] => [6,1,3,5,2,4] => [2,5,3,6,4,1] => [5,2,1,6,3,4] => 11
[6,2,4,5,3,1] => [6,1,2,5,4,3] => [2,3,6,5,4,1] => [6,5,2,1,3,4] => 12
[6,2,5,1,3,4] => [6,2,5,1,3,4] => [4,2,5,6,3,1] => [4,2,1,5,6,3] => 10
[6,2,5,1,4,3] => [6,2,5,1,4,3] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 13
[6,2,5,3,1,4] => [6,1,5,3,2,4] => [2,5,4,6,3,1] => [5,4,2,3,1,6] => 11
[6,2,5,3,4,1] => [6,1,5,2,4,3] => [2,4,6,5,3,1] => [6,4,2,1,3,5] => 12
[6,2,5,4,1,3] => [6,2,5,4,1,3] => [5,2,6,4,3,1] => [5,4,2,1,6,3] => 13
[6,2,5,4,3,1] => [6,1,5,4,3,2] => [2,6,5,4,3,1] => [6,5,4,2,1,3] => 14
[6,3,1,2,4,5] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,2,4,5,1,6] => 7
[6,3,1,2,5,4] => [6,3,1,2,5,4] => [3,4,2,6,5,1] => [3,2,1,6,4,5] => 11
[6,3,1,4,2,5] => [6,2,1,4,3,5] => [3,2,5,4,6,1] => [3,2,5,1,6,4] => 9
[6,3,1,4,5,2] => [6,2,1,3,5,4] => [3,2,4,6,5,1] => [3,2,1,4,6,5] => 10
[6,3,1,5,2,4] => [6,3,1,5,2,4] => [3,5,2,6,4,1] => [3,2,1,5,4,6] => 11
[6,3,1,5,4,2] => [6,2,1,5,4,3] => [3,2,6,5,4,1] => [6,3,2,1,5,4] => 13
[6,3,2,1,4,5] => [6,3,2,1,4,5] => [4,3,2,5,6,1] => [4,3,5,6,2,1] => 8
[6,3,2,1,5,4] => [6,3,2,1,5,4] => [4,3,2,6,5,1] => [4,3,2,6,5,1] => 12
[6,3,2,4,1,5] => [6,2,1,4,3,5] => [3,2,5,4,6,1] => [3,2,5,1,6,4] => 9
[6,3,2,4,5,1] => [6,2,1,3,5,4] => [3,2,4,6,5,1] => [3,2,1,4,6,5] => 10
[6,3,2,5,1,4] => [6,3,2,5,1,4] => [5,3,2,6,4,1] => [5,3,2,6,4,1] => 12
[6,3,2,5,4,1] => [6,2,1,5,4,3] => [3,2,6,5,4,1] => [6,3,2,1,5,4] => 13
[6,3,4,1,2,5] => [6,2,4,1,3,5] => [4,2,5,3,6,1] => [4,2,5,1,6,3] => 9
[6,3,4,1,5,2] => [6,1,3,2,5,4] => [2,4,3,6,5,1] => [4,2,1,6,3,5] => 11
[6,3,4,2,1,5] => [6,1,4,3,2,5] => [2,5,4,3,6,1] => [5,2,4,3,1,6] => 10
[6,3,4,2,5,1] => [6,1,3,2,5,4] => [2,4,3,6,5,1] => [4,2,1,6,3,5] => 11
[6,3,4,5,1,2] => [6,1,3,5,2,4] => [2,5,3,6,4,1] => [5,2,1,6,3,4] => 11
[6,3,4,5,2,1] => [6,1,2,5,4,3] => [2,3,6,5,4,1] => [6,5,2,1,3,4] => 12
[6,3,5,1,2,4] => [6,3,5,1,2,4] => [4,5,2,6,3,1] => [4,2,1,5,3,6] => 11
[6,3,5,1,4,2] => [6,2,5,1,4,3] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 13
[6,3,5,2,1,4] => [6,3,5,2,1,4] => [5,4,2,6,3,1] => [5,4,2,6,3,1] => 12
[6,3,5,2,4,1] => [6,2,5,1,4,3] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 13
[6,3,5,4,1,2] => [6,2,5,4,1,3] => [5,2,6,4,3,1] => [5,4,2,1,6,3] => 13
[6,3,5,4,2,1] => [6,1,5,4,3,2] => [2,6,5,4,3,1] => [6,5,4,2,1,3] => 14
[6,4,1,2,3,5] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,2,4,1,5,6] => 8
[6,4,1,2,5,3] => [6,3,1,2,5,4] => [3,4,2,6,5,1] => [3,2,1,6,4,5] => 11
[6,4,1,3,2,5] => [6,4,1,3,2,5] => [3,5,4,2,6,1] => [5,3,4,2,1,6] => 10
[6,4,1,3,5,2] => [6,3,1,2,5,4] => [3,4,2,6,5,1] => [3,2,1,6,4,5] => 11
[6,4,1,5,2,3] => [6,3,1,5,2,4] => [3,5,2,6,4,1] => [3,2,1,5,4,6] => 11
[6,4,1,5,3,2] => [6,2,1,5,4,3] => [3,2,6,5,4,1] => [6,3,2,1,5,4] => 13
[6,4,2,1,3,5] => [6,4,2,1,3,5] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => 9
[6,4,2,1,5,3] => [6,3,2,1,5,4] => [4,3,2,6,5,1] => [4,3,2,6,5,1] => 12
[6,4,2,3,1,5] => [6,4,1,3,2,5] => [3,5,4,2,6,1] => [5,3,4,2,1,6] => 10
[6,4,2,3,5,1] => [6,3,1,2,5,4] => [3,4,2,6,5,1] => [3,2,1,6,4,5] => 11
[6,4,2,5,1,3] => [6,3,2,5,1,4] => [5,3,2,6,4,1] => [5,3,2,6,4,1] => 12
[6,4,2,5,3,1] => [6,2,1,5,4,3] => [3,2,6,5,4,1] => [6,3,2,1,5,4] => 13
[6,4,3,1,2,5] => [6,4,3,1,2,5] => [4,5,3,2,6,1] => [4,3,5,2,1,6] => 10
[6,4,3,1,5,2] => [6,3,2,1,5,4] => [4,3,2,6,5,1] => [4,3,2,6,5,1] => 12
[6,4,3,2,1,5] => [6,4,3,2,1,5] => [5,4,3,2,6,1] => [5,4,6,3,2,1] => 11
[6,4,3,2,5,1] => [6,3,2,1,5,4] => [4,3,2,6,5,1] => [4,3,2,6,5,1] => 12
[6,4,3,5,1,2] => [6,3,2,5,1,4] => [5,3,2,6,4,1] => [5,3,2,6,4,1] => 12
[6,4,3,5,2,1] => [6,2,1,5,4,3] => [3,2,6,5,4,1] => [6,3,2,1,5,4] => 13
[6,4,5,1,2,3] => [6,3,5,1,2,4] => [4,5,2,6,3,1] => [4,2,1,5,3,6] => 11
[6,4,5,1,3,2] => [6,2,5,1,4,3] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 13
[6,4,5,2,1,3] => [6,3,5,2,1,4] => [5,4,2,6,3,1] => [5,4,2,6,3,1] => 12
[6,4,5,2,3,1] => [6,2,5,1,4,3] => [4,2,6,5,3,1] => [6,4,2,1,5,3] => 13
[6,4,5,3,1,2] => [6,2,5,4,1,3] => [5,2,6,4,3,1] => [5,4,2,1,6,3] => 13
[6,4,5,3,2,1] => [6,1,5,4,3,2] => [2,6,5,4,3,1] => [6,5,4,2,1,3] => 14
[6,5,1,2,3,4] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [3,2,1,4,5,6] => 9
[6,5,1,2,4,3] => [6,5,1,2,4,3] => [3,4,6,5,2,1] => [6,3,2,1,4,5] => 12
[6,5,1,3,2,4] => [6,5,1,3,2,4] => [3,5,4,6,2,1] => [5,3,2,4,1,6] => 11
[6,5,1,3,4,2] => [6,5,1,2,4,3] => [3,4,6,5,2,1] => [6,3,2,1,4,5] => 12
[6,5,1,4,2,3] => [6,5,1,4,2,3] => [3,5,6,4,2,1] => [5,3,2,1,4,6] => 12
[6,5,1,4,3,2] => [6,5,1,4,3,2] => [3,6,5,4,2,1] => [6,5,3,2,1,4] => 14
[6,5,2,1,3,4] => [6,5,2,1,3,4] => [4,3,5,6,2,1] => [4,3,2,5,6,1] => 10
[6,5,2,1,4,3] => [6,5,2,1,4,3] => [4,3,6,5,2,1] => [4,3,2,1,6,5] => 13
[6,5,2,3,1,4] => [6,5,1,3,2,4] => [3,5,4,6,2,1] => [5,3,2,4,1,6] => 11
[6,5,2,3,4,1] => [6,5,1,2,4,3] => [3,4,6,5,2,1] => [6,3,2,1,4,5] => 12
[6,5,2,4,1,3] => [6,5,2,4,1,3] => [5,3,6,4,2,1] => [5,3,2,1,6,4] => 13
[6,5,2,4,3,1] => [6,5,1,4,3,2] => [3,6,5,4,2,1] => [6,5,3,2,1,4] => 14
[6,5,3,1,2,4] => [6,5,3,1,2,4] => [4,5,3,6,2,1] => [4,3,2,5,1,6] => 11
[6,5,3,1,4,2] => [6,5,2,1,4,3] => [4,3,6,5,2,1] => [4,3,2,1,6,5] => 13
[6,5,3,2,1,4] => [6,5,3,2,1,4] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => 12
[6,5,3,2,4,1] => [6,5,2,1,4,3] => [4,3,6,5,2,1] => [4,3,2,1,6,5] => 13
[6,5,3,4,1,2] => [6,5,2,4,1,3] => [5,3,6,4,2,1] => [5,3,2,1,6,4] => 13
[6,5,3,4,2,1] => [6,5,1,4,3,2] => [3,6,5,4,2,1] => [6,5,3,2,1,4] => 14
[6,5,4,1,2,3] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => [4,3,2,1,5,6] => 12
[6,5,4,1,3,2] => [6,5,4,1,3,2] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 14
[6,5,4,2,1,3] => [6,5,4,2,1,3] => [5,4,6,3,2,1] => [5,4,3,2,6,1] => 13
[6,5,4,2,3,1] => [6,5,4,1,3,2] => [4,6,5,3,2,1] => [6,4,3,2,1,5] => 14
[6,5,4,3,1,2] => [6,5,4,3,1,2] => [5,6,4,3,2,1] => [5,4,3,2,1,6] => 14
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 15
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,5,3,4,6,7] => 4
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,5,3,6,7] => 3
[1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[1,2,4,5,3,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,5,3,4,6,7] => 4
[1,2,5,3,4,6,7] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => [1,2,4,3,5,6,7] => 4
[1,2,5,3,6,4,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 7
[1,2,5,4,6,3,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[1,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => [1,4,2,3,5,6,7] => 5
[1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => 2
[1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => 6
[1,3,2,5,6,4,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[1,3,2,6,4,5,7] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7] => [1,3,2,5,6,4,7] => 7
[1,3,4,2,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,5,3,6,7] => 3
[1,3,4,2,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[1,3,4,5,2,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,5,3,4,6,7] => 4
[1,3,5,2,4,6,7] => [1,3,5,2,4,6,7] => [1,4,2,5,3,6,7] => [1,4,5,2,6,3,7] => 6
[1,3,5,2,6,4,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[1,3,5,4,2,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 7
[1,3,5,4,6,2,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[1,3,6,2,4,5,7] => [1,3,6,2,4,5,7] => [1,4,2,5,6,3,7] => [1,4,2,5,6,3,7] => 7
[1,4,2,3,5,6,7] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => [1,3,4,5,2,6,7] => 3
[1,4,2,3,6,5,7] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => [1,3,2,6,4,5,7] => 8
[1,4,2,5,3,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => 6
[1,4,2,5,6,3,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[1,4,2,6,3,5,7] => [1,4,2,6,3,5,7] => [1,3,5,2,6,4,7] => [1,3,2,5,4,6,7] => 8
[1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,5,6,3,2,7] => 5
[1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[1,4,3,5,2,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => 6
[1,4,3,5,6,2,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[1,4,5,2,3,6,7] => [1,3,5,2,4,6,7] => [1,4,2,5,3,6,7] => [1,4,5,2,6,3,7] => 6
[1,4,5,2,6,3,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[1,4,5,3,2,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 7
[1,4,5,3,6,2,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[1,4,6,2,3,5,7] => [1,4,6,2,3,5,7] => [1,4,5,2,6,3,7] => [1,4,2,5,3,6,7] => 8
[1,5,2,3,4,6,7] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => [1,3,4,2,5,6,7] => 4
[1,5,2,3,6,4,7] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => [1,3,2,6,4,5,7] => 8
[1,5,2,4,3,6,7] => [1,5,2,4,3,6,7] => [1,3,5,4,2,6,7] => [1,3,5,4,2,6,7] => 7
[1,5,2,4,6,3,7] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => [1,3,2,6,4,5,7] => 8
[1,5,2,6,3,4,7] => [1,4,2,6,3,5,7] => [1,3,5,2,6,4,7] => [1,3,2,5,4,6,7] => 8
[1,5,3,2,4,6,7] => [1,5,3,2,4,6,7] => [1,4,3,5,2,6,7] => [1,4,5,3,6,2,7] => 6
[1,5,3,2,6,4,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[1,5,3,4,2,6,7] => [1,5,2,4,3,6,7] => [1,3,5,4,2,6,7] => [1,3,5,4,2,6,7] => 7
[1,5,3,4,6,2,7] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => [1,3,2,6,4,5,7] => 8
[1,5,4,2,3,6,7] => [1,5,4,2,3,6,7] => [1,4,5,3,2,6,7] => [1,4,5,3,2,6,7] => 7
[1,5,4,2,6,3,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[1,5,4,3,6,2,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[1,5,6,2,3,4,7] => [1,4,6,2,3,5,7] => [1,4,5,2,6,3,7] => [1,4,2,5,3,6,7] => 8
[1,6,2,3,4,5,7] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => [1,3,2,4,5,6,7] => 5
[1,6,3,2,4,5,7] => [1,6,3,2,4,5,7] => [1,4,3,5,6,2,7] => [1,4,3,5,6,2,7] => 7
[1,6,3,2,5,4,7] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7] => [1,4,3,2,6,5,7] => 11
[1,6,4,2,3,5,7] => [1,6,4,2,3,5,7] => [1,4,5,3,6,2,7] => [1,4,3,5,2,6,7] => 8
[1,6,4,2,5,3,7] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7] => [1,4,3,2,6,5,7] => 11
[1,6,4,3,5,2,7] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7] => [1,4,3,2,6,5,7] => 11
[1,6,5,2,3,4,7] => [1,6,5,2,3,4,7] => [1,4,5,6,3,2,7] => [1,4,3,2,5,6,7] => 9
[2,3,1,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => 2
[2,3,1,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[2,3,1,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => 6
[2,3,1,5,6,4,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[2,3,1,6,4,5,7] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7] => [1,3,2,5,6,4,7] => 7
[2,3,4,1,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,5,3,6,7] => 3
[2,3,4,1,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[2,3,4,5,1,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,5,3,4,6,7] => 4
[2,3,5,1,4,6,7] => [1,3,5,2,4,6,7] => [1,4,2,5,3,6,7] => [1,4,5,2,6,3,7] => 6
[2,3,5,1,6,4,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[2,3,5,4,1,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 7
[2,3,5,4,6,1,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[2,3,6,1,4,5,7] => [1,3,6,2,4,5,7] => [1,4,2,5,6,3,7] => [1,4,2,5,6,3,7] => 7
[2,4,1,5,3,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => 6
[2,4,1,5,6,3,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[2,4,3,1,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,5,6,3,2,7] => 5
[2,4,3,1,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[2,4,3,5,1,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => 6
[2,4,3,5,6,1,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[2,4,5,1,3,6,7] => [1,3,5,2,4,6,7] => [1,4,2,5,3,6,7] => [1,4,5,2,6,3,7] => 6
[2,4,5,1,6,3,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[2,4,5,3,1,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 7
[2,4,5,3,6,1,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[2,5,3,1,4,6,7] => [1,5,3,2,4,6,7] => [1,4,3,5,2,6,7] => [1,4,5,3,6,2,7] => 6
[2,5,3,1,6,4,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[2,5,3,4,1,6,7] => [1,5,2,4,3,6,7] => [1,3,5,4,2,6,7] => [1,3,5,4,2,6,7] => 7
[2,5,3,4,6,1,7] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => [1,3,2,6,4,5,7] => 8
[2,5,4,1,6,3,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[2,5,4,3,6,1,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[2,6,3,1,4,5,7] => [1,6,3,2,4,5,7] => [1,4,3,5,6,2,7] => [1,4,3,5,6,2,7] => 7
[2,6,3,1,5,4,7] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7] => [1,4,3,2,6,5,7] => 11
[2,6,4,1,5,3,7] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7] => [1,4,3,2,6,5,7] => 11
[2,6,4,3,5,1,7] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7] => [1,4,3,2,6,5,7] => 11
[3,4,1,5,2,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => 6
[3,4,1,5,6,2,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[3,4,2,1,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,5,6,3,2,7] => 5
[3,4,2,1,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[3,4,2,5,1,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => 6
[3,4,2,5,6,1,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[3,4,5,1,2,6,7] => [1,3,5,2,4,6,7] => [1,4,2,5,3,6,7] => [1,4,5,2,6,3,7] => 6
[3,4,5,1,6,2,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[3,4,5,2,1,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 7
[3,4,5,2,6,1,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 8
[3,5,2,1,6,4,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[3,5,4,1,6,2,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[3,5,4,2,6,1,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[3,6,4,1,5,2,7] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7] => [1,4,3,2,6,5,7] => 11
[3,6,4,2,5,1,7] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7] => [1,4,3,2,6,5,7] => 11
[4,5,2,1,6,3,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[4,5,3,1,6,2,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
[4,5,3,2,6,1,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 10
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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 1,1,3,1 1,1,3,6,6,6,1 1,1,3,6,13,13,27,25,20,10,1 1,1,3,6,13,22,36,52,85,107,109,134,85,50,15,1
$F_{2} = 1 + q$
$F_{3} = 1 + q + 3\ q^{2} + q^{3}$
$F_{4} = 1 + q + 3\ q^{2} + 6\ q^{3} + 6\ q^{4} + 6\ q^{5} + q^{6}$
$F_{5} = 1 + q + 3\ q^{2} + 6\ q^{3} + 13\ q^{4} + 13\ q^{5} + 27\ q^{6} + 25\ q^{7} + 20\ q^{8} + 10\ q^{9} + q^{10}$
$F_{6} = 1 + q + 3\ q^{2} + 6\ q^{3} + 13\ q^{4} + 22\ q^{5} + 36\ q^{6} + 52\ q^{7} + 85\ q^{8} + 107\ q^{9} + 109\ q^{10} + 134\ q^{11} + 85\ q^{12} + 50\ q^{13} + 15\ q^{14} + q^{15}$
Description
The comajor index of a permutation.
This is, $\operatorname{comaj}(\pi) = \sum_{i \in \operatorname{Des}(\pi)} (n-i)$ for a permutation $\pi$ of length $n$.
This is, $\operatorname{comaj}(\pi) = \sum_{i \in \operatorname{Des}(\pi)} (n-i)$ for a permutation $\pi$ of length $n$.
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
inverse
Description
Sends a permutation to its inverse.
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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