Identifier
-
Mp00310:
Permutations
—toric promotion⟶
Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
St000018: Permutations ⟶ ℤ
Values
[1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => 1
[1,2,3] => [3,2,1] => [3,2,1] => 3
[1,3,2] => [2,3,1] => [2,3,1] => 2
[2,1,3] => [3,1,2] => [1,3,2] => 1
[2,3,1] => [1,3,2] => [3,1,2] => 2
[3,1,2] => [2,1,3] => [2,1,3] => 1
[3,2,1] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [4,2,3,1] => [2,4,3,1] => 4
[1,2,4,3] => [4,3,1,2] => [1,4,3,2] => 3
[1,3,2,4] => [2,4,1,3] => [2,1,4,3] => 2
[1,3,4,2] => [2,3,4,1] => [2,3,4,1] => 3
[1,4,2,3] => [3,4,1,2] => [1,3,4,2] => 2
[1,4,3,2] => [3,1,2,4] => [1,3,2,4] => 1
[2,1,3,4] => [4,1,2,3] => [1,2,4,3] => 1
[2,1,4,3] => [4,1,3,2] => [4,1,3,2] => 4
[2,3,1,4] => [1,4,2,3] => [1,4,2,3] => 2
[2,3,4,1] => [4,2,1,3] => [2,4,1,3] => 3
[2,4,1,3] => [4,3,2,1] => [4,3,2,1] => 6
[2,4,3,1] => [1,4,3,2] => [4,3,1,2] => 5
[3,1,2,4] => [2,4,3,1] => [4,2,3,1] => 5
[3,1,4,2] => [1,2,3,4] => [1,2,3,4] => 0
[3,2,1,4] => [1,2,4,3] => [4,1,2,3] => 3
[3,2,4,1] => [2,1,4,3] => [4,2,1,3] => 4
[3,4,1,2] => [2,3,1,4] => [2,3,1,4] => 2
[3,4,2,1] => [2,1,3,4] => [2,1,3,4] => 1
[4,1,2,3] => [3,4,2,1] => [3,4,2,1] => 5
[4,1,3,2] => [3,2,4,1] => [3,2,4,1] => 4
[4,2,1,3] => [1,3,4,2] => [3,1,4,2] => 3
[4,2,3,1] => [3,1,4,2] => [3,4,1,2] => 4
[4,3,1,2] => [3,2,1,4] => [3,2,1,4] => 3
[4,3,2,1] => [1,3,2,4] => [3,1,2,4] => 2
[1,2,3,4,5] => [5,2,3,4,1] => [2,3,5,4,1] => 5
[1,2,3,5,4] => [5,2,4,1,3] => [2,1,5,4,3] => 4
[1,2,4,3,5] => [5,3,1,2,4] => [1,3,5,2,4] => 3
[1,2,4,5,3] => [5,3,4,1,2] => [1,3,5,4,2] => 4
[1,2,5,3,4] => [5,4,1,2,3] => [1,2,5,4,3] => 3
[1,2,5,4,3] => [5,4,1,3,2] => [5,1,4,3,2] => 7
[1,3,2,4,5] => [2,5,1,3,4] => [2,1,3,5,4] => 2
[1,3,2,5,4] => [2,5,1,4,3] => [5,2,1,4,3] => 6
[1,3,4,2,5] => [2,3,5,1,4] => [2,3,1,5,4] => 3
[1,3,4,5,2] => [2,3,4,5,1] => [2,3,4,5,1] => 4
[1,3,5,2,4] => [2,4,5,1,3] => [2,1,4,5,3] => 3
[1,3,5,4,2] => [2,4,1,3,5] => [2,1,4,3,5] => 2
[1,4,2,3,5] => [3,5,1,2,4] => [1,3,2,5,4] => 2
[1,4,2,5,3] => [3,5,1,4,2] => [3,5,1,4,2] => 6
[1,4,3,2,5] => [3,1,2,5,4] => [5,1,3,2,4] => 5
[1,4,3,5,2] => [3,1,2,4,5] => [1,3,2,4,5] => 1
[1,4,5,2,3] => [3,4,5,1,2] => [1,3,4,5,2] => 3
[1,4,5,3,2] => [3,4,1,2,5] => [1,3,4,2,5] => 2
[1,5,2,3,4] => [4,5,1,2,3] => [1,2,4,5,3] => 2
[1,5,2,4,3] => [4,5,1,3,2] => [4,1,5,3,2] => 6
[1,5,3,2,4] => [4,1,2,5,3] => [4,1,5,2,3] => 5
[1,5,3,4,2] => [4,1,2,3,5] => [1,2,4,3,5] => 1
[1,5,4,2,3] => [4,1,3,5,2] => [4,1,3,5,2] => 5
[1,5,4,3,2] => [4,1,3,2,5] => [4,1,3,2,5] => 4
[2,1,3,4,5] => [5,1,2,3,4] => [1,2,3,5,4] => 1
[2,1,3,5,4] => [5,1,2,4,3] => [5,1,2,4,3] => 5
[2,1,4,3,5] => [5,1,3,2,4] => [1,5,3,2,4] => 4
[2,1,4,5,3] => [5,1,3,4,2] => [3,1,5,4,2] => 5
[2,1,5,3,4] => [5,1,4,2,3] => [1,5,2,4,3] => 4
[2,1,5,4,3] => [5,1,4,3,2] => [5,4,1,3,2] => 8
[2,3,1,4,5] => [1,5,2,3,4] => [1,2,5,3,4] => 2
[2,3,1,5,4] => [1,5,2,4,3] => [5,1,4,2,3] => 6
[2,3,4,1,5] => [5,2,1,3,4] => [2,1,5,3,4] => 3
[2,3,4,5,1] => [5,2,3,1,4] => [2,3,5,1,4] => 4
[2,3,5,1,4] => [5,2,4,3,1] => [5,2,4,3,1] => 8
[2,3,5,4,1] => [5,2,1,4,3] => [5,2,4,1,3] => 7
[2,4,1,3,5] => [5,3,2,4,1] => [3,5,2,4,1] => 7
[2,4,1,5,3] => [1,5,3,4,2] => [5,1,3,4,2] => 6
[2,4,3,1,5] => [1,5,3,2,4] => [3,5,1,2,4] => 5
[2,4,3,5,1] => [5,3,2,1,4] => [3,5,2,1,4] => 6
[2,4,5,1,3] => [5,3,4,2,1] => [3,5,4,2,1] => 8
[2,4,5,3,1] => [5,3,1,4,2] => [3,5,4,1,2] => 7
[2,5,1,3,4] => [5,4,2,3,1] => [2,5,4,3,1] => 7
[2,5,1,4,3] => [5,4,3,1,2] => [1,5,4,3,2] => 6
[2,5,3,1,4] => [1,5,4,2,3] => [1,5,4,2,3] => 5
[2,5,3,4,1] => [5,4,2,1,3] => [2,5,4,1,3] => 6
[2,5,4,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => 10
[2,5,4,3,1] => [1,5,4,3,2] => [5,4,3,1,2] => 9
[3,1,2,4,5] => [2,5,3,4,1] => [2,5,3,4,1] => 6
[3,1,2,5,4] => [2,5,4,1,3] => [2,5,1,4,3] => 5
[3,1,4,2,5] => [1,2,3,5,4] => [5,1,2,3,4] => 4
[3,1,4,5,2] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,1,5,2,4] => [1,2,4,5,3] => [4,1,2,5,3] => 4
[3,1,5,4,2] => [1,2,4,3,5] => [4,1,2,3,5] => 3
[3,2,1,4,5] => [1,2,5,3,4] => [1,5,2,3,4] => 3
[3,2,1,5,4] => [1,2,5,4,3] => [5,4,1,2,3] => 7
[3,2,4,1,5] => [2,1,5,3,4] => [2,5,1,3,4] => 4
[3,2,4,5,1] => [2,5,3,1,4] => [2,5,3,1,4] => 5
[3,2,5,1,4] => [2,5,4,3,1] => [5,4,2,3,1] => 9
[3,2,5,4,1] => [2,1,5,4,3] => [5,4,2,1,3] => 8
[3,4,1,2,5] => [2,3,5,4,1] => [5,2,3,4,1] => 7
[3,4,1,5,2] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[3,4,2,1,5] => [2,1,3,5,4] => [5,2,1,3,4] => 5
[3,4,2,5,1] => [2,3,1,5,4] => [5,2,3,1,4] => 6
[3,4,5,1,2] => [2,3,4,1,5] => [2,3,4,1,5] => 3
[3,4,5,2,1] => [2,3,1,4,5] => [2,3,1,4,5] => 2
[3,5,1,2,4] => [2,4,5,3,1] => [4,2,5,3,1] => 7
[3,5,1,4,2] => [2,4,3,5,1] => [4,2,3,5,1] => 6
>>> Load all 1245 entries. <<<[3,5,2,1,4] => [2,1,4,5,3] => [4,2,1,5,3] => 5
[3,5,2,4,1] => [2,4,1,5,3] => [4,2,5,1,3] => 6
[3,5,4,1,2] => [2,4,3,1,5] => [4,2,3,1,5] => 5
[3,5,4,2,1] => [2,1,4,3,5] => [4,2,1,3,5] => 4
[4,1,2,3,5] => [3,5,2,4,1] => [3,2,5,4,1] => 6
[4,1,2,5,3] => [3,5,4,1,2] => [1,5,3,4,2] => 5
[4,1,3,2,5] => [3,2,5,1,4] => [3,2,1,5,4] => 4
[4,1,3,5,2] => [3,2,4,5,1] => [3,2,4,5,1] => 5
[4,1,5,2,3] => [1,3,4,5,2] => [3,1,4,5,2] => 4
[4,1,5,3,2] => [1,3,4,2,5] => [3,1,4,2,5] => 3
[4,2,1,3,5] => [1,3,5,2,4] => [3,1,2,5,4] => 3
[4,2,1,5,3] => [1,3,5,4,2] => [5,3,1,4,2] => 7
[4,2,3,1,5] => [3,1,5,2,4] => [3,1,5,2,4] => 4
[4,2,3,5,1] => [3,5,2,1,4] => [3,2,5,1,4] => 5
[4,2,5,1,3] => [3,5,4,2,1] => [5,3,4,2,1] => 9
[4,2,5,3,1] => [3,1,5,4,2] => [5,3,4,1,2] => 8
[4,3,1,2,5] => [3,2,5,4,1] => [5,3,2,4,1] => 8
[4,3,1,5,2] => [1,3,2,4,5] => [3,1,2,4,5] => 2
[4,3,2,1,5] => [1,3,2,5,4] => [5,3,1,2,4] => 6
[4,3,2,5,1] => [3,2,1,5,4] => [5,3,2,1,4] => 7
[4,3,5,1,2] => [3,2,4,1,5] => [3,2,4,1,5] => 4
[4,3,5,2,1] => [3,2,1,4,5] => [3,2,1,4,5] => 3
[4,5,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => 7
[4,5,1,3,2] => [3,4,2,5,1] => [3,4,2,5,1] => 6
[4,5,2,1,3] => [3,1,4,5,2] => [3,4,1,5,2] => 5
[4,5,2,3,1] => [3,4,1,5,2] => [3,4,5,1,2] => 6
[4,5,3,1,2] => [3,4,2,1,5] => [3,4,2,1,5] => 5
[4,5,3,2,1] => [3,1,4,2,5] => [3,4,1,2,5] => 4
[5,1,2,3,4] => [4,5,2,3,1] => [2,4,5,3,1] => 6
[5,1,2,4,3] => [4,5,3,1,2] => [1,4,5,3,2] => 5
[5,1,3,2,4] => [4,2,5,1,3] => [2,4,1,5,3] => 4
[5,1,3,4,2] => [4,2,3,5,1] => [2,4,3,5,1] => 5
[5,1,4,2,3] => [4,3,5,1,2] => [1,4,3,5,2] => 4
[5,1,4,3,2] => [4,3,1,2,5] => [1,4,3,2,5] => 3
[5,2,1,3,4] => [1,4,5,2,3] => [1,4,2,5,3] => 3
[5,2,1,4,3] => [1,4,5,3,2] => [4,5,1,3,2] => 7
[5,2,3,1,4] => [4,1,5,2,3] => [1,4,5,2,3] => 4
[5,2,3,4,1] => [4,5,2,1,3] => [2,4,5,1,3] => 5
[5,2,4,1,3] => [4,5,3,2,1] => [4,5,3,2,1] => 9
[5,2,4,3,1] => [4,1,5,3,2] => [4,5,3,1,2] => 8
[5,3,1,2,4] => [4,2,5,3,1] => [4,5,2,3,1] => 8
[5,3,1,4,2] => [1,4,2,3,5] => [1,4,2,3,5] => 2
[5,3,2,1,4] => [1,4,2,5,3] => [4,5,1,2,3] => 6
[5,3,2,4,1] => [4,2,1,5,3] => [4,5,2,1,3] => 7
[5,3,4,1,2] => [4,2,3,1,5] => [2,4,3,1,5] => 4
[5,3,4,2,1] => [4,2,1,3,5] => [2,4,1,3,5] => 3
[5,4,1,2,3] => [4,3,5,2,1] => [4,3,5,2,1] => 8
[5,4,1,3,2] => [4,3,2,5,1] => [4,3,2,5,1] => 7
[5,4,2,1,3] => [1,4,3,5,2] => [4,3,1,5,2] => 6
[5,4,2,3,1] => [4,3,1,5,2] => [4,3,5,1,2] => 7
[5,4,3,1,2] => [4,3,2,1,5] => [4,3,2,1,5] => 6
[5,4,3,2,1] => [1,4,3,2,5] => [4,3,1,2,5] => 5
[1,2,3,4,5,6] => [6,2,3,4,5,1] => [2,3,4,6,5,1] => 6
[1,2,3,4,6,5] => [6,2,3,5,1,4] => [2,3,1,6,5,4] => 5
[1,2,3,5,4,6] => [6,2,4,1,3,5] => [2,1,4,6,3,5] => 4
[1,2,3,5,6,4] => [6,2,4,5,1,3] => [2,1,4,6,5,3] => 5
[1,2,3,6,4,5] => [6,2,5,1,3,4] => [2,1,3,6,5,4] => 4
[1,2,3,6,5,4] => [6,2,5,1,4,3] => [6,2,1,5,4,3] => 9
[1,2,4,3,5,6] => [6,3,1,2,4,5] => [1,3,2,6,4,5] => 3
[1,2,4,3,6,5] => [6,3,1,2,5,4] => [6,1,3,5,2,4] => 8
[1,2,4,5,3,6] => [6,3,4,1,2,5] => [1,3,4,6,2,5] => 4
[1,2,4,5,6,3] => [6,3,4,5,1,2] => [1,3,4,6,5,2] => 5
[1,2,4,6,3,5] => [6,3,5,1,2,4] => [1,3,2,6,5,4] => 4
[1,2,4,6,5,3] => [6,3,5,1,4,2] => [3,6,1,5,4,2] => 9
[1,2,5,3,4,6] => [6,4,1,2,3,5] => [1,2,4,6,3,5] => 3
[1,2,5,3,6,4] => [6,4,1,2,5,3] => [4,1,6,5,2,3] => 8
[1,2,5,4,3,6] => [6,4,1,3,2,5] => [1,6,4,3,2,5] => 7
[1,2,5,4,6,3] => [6,4,1,3,5,2] => [4,1,6,3,5,2] => 8
[1,2,5,6,3,4] => [6,4,5,1,2,3] => [1,2,4,6,5,3] => 4
[1,2,5,6,4,3] => [6,4,5,1,3,2] => [4,1,6,5,3,2] => 9
[1,2,6,3,4,5] => [6,5,1,2,3,4] => [1,2,3,6,5,4] => 3
[1,2,6,3,5,4] => [6,5,1,2,4,3] => [6,1,2,5,4,3] => 8
[1,2,6,4,3,5] => [6,5,1,3,2,4] => [1,6,3,5,2,4] => 7
[1,2,6,4,5,3] => [6,5,1,3,4,2] => [3,1,6,5,4,2] => 8
[1,2,6,5,3,4] => [6,5,1,4,2,3] => [1,6,2,5,4,3] => 7
[1,2,6,5,4,3] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 12
[1,3,2,4,5,6] => [2,6,1,3,4,5] => [2,1,3,4,6,5] => 2
[1,3,2,4,6,5] => [2,6,1,3,5,4] => [6,2,1,3,5,4] => 7
[1,3,2,5,4,6] => [2,6,1,4,3,5] => [2,6,1,4,3,5] => 6
[1,3,2,5,6,4] => [2,6,1,4,5,3] => [4,2,1,6,5,3] => 7
[1,3,2,6,4,5] => [2,6,1,5,3,4] => [2,6,1,3,5,4] => 6
[1,3,2,6,5,4] => [2,6,1,5,4,3] => [6,5,2,1,4,3] => 11
[1,3,4,2,5,6] => [2,3,6,1,4,5] => [2,3,1,4,6,5] => 3
[1,3,4,2,6,5] => [2,3,6,1,5,4] => [6,2,3,1,5,4] => 8
[1,3,4,5,2,6] => [2,3,4,6,1,5] => [2,3,4,1,6,5] => 4
[1,3,4,5,6,2] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => 5
[1,3,4,6,2,5] => [2,3,5,6,1,4] => [2,3,1,5,6,4] => 4
[1,3,4,6,5,2] => [2,3,5,1,4,6] => [2,3,1,5,4,6] => 3
[1,3,5,2,4,6] => [2,4,6,1,3,5] => [2,1,4,3,6,5] => 3
[1,3,5,2,6,4] => [2,4,6,1,5,3] => [4,2,6,1,5,3] => 8
[1,3,5,4,2,6] => [2,4,1,3,6,5] => [6,2,1,4,3,5] => 7
[1,3,5,4,6,2] => [2,4,1,3,5,6] => [2,1,4,3,5,6] => 2
[1,3,5,6,2,4] => [2,4,5,6,1,3] => [2,1,4,5,6,3] => 4
[1,3,5,6,4,2] => [2,4,5,1,3,6] => [2,1,4,5,3,6] => 3
[1,3,6,2,4,5] => [2,5,6,1,3,4] => [2,1,3,5,6,4] => 3
[1,3,6,2,5,4] => [2,5,6,1,4,3] => [5,2,1,6,4,3] => 8
[1,3,6,4,2,5] => [2,5,1,3,6,4] => [5,2,1,6,3,4] => 7
[1,3,6,4,5,2] => [2,5,1,3,4,6] => [2,1,3,5,4,6] => 2
[1,3,6,5,2,4] => [2,5,1,4,6,3] => [5,2,1,4,6,3] => 7
[1,3,6,5,4,2] => [2,5,1,4,3,6] => [5,2,1,4,3,6] => 6
[1,4,2,3,5,6] => [3,6,1,2,4,5] => [1,3,2,4,6,5] => 2
[1,4,2,3,6,5] => [3,6,1,2,5,4] => [6,1,3,2,5,4] => 7
[1,4,2,5,3,6] => [3,6,1,4,2,5] => [3,1,6,4,2,5] => 6
[1,4,2,5,6,3] => [3,6,1,4,5,2] => [3,4,1,6,5,2] => 7
[1,4,2,6,3,5] => [3,6,1,5,2,4] => [3,1,6,2,5,4] => 6
[1,4,2,6,5,3] => [3,6,1,5,4,2] => [6,3,5,1,4,2] => 11
[1,4,3,2,5,6] => [3,1,2,6,4,5] => [1,6,3,2,4,5] => 5
[1,4,3,2,6,5] => [3,1,2,6,5,4] => [6,5,1,3,2,4] => 10
[1,4,3,5,2,6] => [3,1,2,4,6,5] => [6,1,3,2,4,5] => 6
[1,4,3,5,6,2] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => 1
[1,4,3,6,2,5] => [3,1,2,5,6,4] => [5,1,3,2,6,4] => 6
[1,4,3,6,5,2] => [3,1,2,5,4,6] => [5,1,3,2,4,6] => 5
[1,4,5,2,3,6] => [3,4,6,1,2,5] => [1,3,4,2,6,5] => 3
[1,4,5,2,6,3] => [3,4,6,1,5,2] => [3,4,6,1,5,2] => 8
[1,4,5,3,2,6] => [3,4,1,2,6,5] => [6,1,3,4,2,5] => 7
[1,4,5,3,6,2] => [3,4,1,2,5,6] => [1,3,4,2,5,6] => 2
[1,4,5,6,2,3] => [3,4,5,6,1,2] => [1,3,4,5,6,2] => 4
[1,4,5,6,3,2] => [3,4,5,1,2,6] => [1,3,4,5,2,6] => 3
[1,4,6,2,3,5] => [3,5,6,1,2,4] => [1,3,2,5,6,4] => 3
[1,4,6,2,5,3] => [3,5,6,1,4,2] => [3,5,1,6,4,2] => 8
[1,4,6,3,2,5] => [3,5,1,2,6,4] => [5,1,3,6,2,4] => 7
[1,4,6,3,5,2] => [3,5,1,2,4,6] => [1,3,2,5,4,6] => 2
[1,4,6,5,2,3] => [3,5,1,4,6,2] => [3,5,1,4,6,2] => 7
[1,4,6,5,3,2] => [3,5,1,4,2,6] => [3,5,1,4,2,6] => 6
[1,5,2,3,4,6] => [4,6,1,2,3,5] => [1,2,4,3,6,5] => 2
[1,5,2,3,6,4] => [4,6,1,2,5,3] => [4,1,6,2,5,3] => 7
[1,5,2,4,3,6] => [4,6,1,3,2,5] => [4,1,3,6,2,5] => 6
[1,5,2,4,6,3] => [4,6,1,3,5,2] => [4,1,3,6,5,2] => 7
[1,5,2,6,3,4] => [4,6,1,5,2,3] => [1,4,6,2,5,3] => 6
[1,5,2,6,4,3] => [4,6,1,5,3,2] => [4,6,5,1,3,2] => 11
[1,5,3,2,4,6] => [4,1,2,6,3,5] => [4,1,2,6,3,5] => 5
[1,5,3,2,6,4] => [4,1,2,6,5,3] => [6,4,1,5,2,3] => 10
[1,5,3,4,2,6] => [4,1,2,3,6,5] => [6,1,2,4,3,5] => 6
[1,5,3,4,6,2] => [4,1,2,3,5,6] => [1,2,4,3,5,6] => 1
[1,5,3,6,2,4] => [4,1,2,5,6,3] => [4,1,5,2,6,3] => 6
[1,5,3,6,4,2] => [4,1,2,5,3,6] => [4,1,5,2,3,6] => 5
[1,5,4,2,3,6] => [4,1,3,6,2,5] => [4,1,3,2,6,5] => 5
[1,5,4,2,6,3] => [4,1,3,6,5,2] => [6,4,1,3,5,2] => 10
[1,5,4,3,2,6] => [4,1,3,2,6,5] => [6,4,1,3,2,5] => 9
[1,5,4,3,6,2] => [4,1,3,2,5,6] => [4,1,3,2,5,6] => 4
[1,5,4,6,2,3] => [4,1,3,5,6,2] => [4,1,3,5,6,2] => 6
[1,5,4,6,3,2] => [4,1,3,5,2,6] => [4,1,3,5,2,6] => 5
[1,5,6,2,3,4] => [4,5,6,1,2,3] => [1,2,4,5,6,3] => 3
[1,5,6,2,4,3] => [4,5,6,1,3,2] => [4,1,5,6,3,2] => 8
[1,5,6,3,2,4] => [4,5,1,2,6,3] => [4,1,5,6,2,3] => 7
[1,5,6,3,4,2] => [4,5,1,2,3,6] => [1,2,4,5,3,6] => 2
[1,5,6,4,2,3] => [4,5,1,3,6,2] => [4,1,5,3,6,2] => 7
[1,5,6,4,3,2] => [4,5,1,3,2,6] => [4,1,5,3,2,6] => 6
[1,6,2,3,4,5] => [5,6,1,2,3,4] => [1,2,3,5,6,4] => 2
[1,6,2,3,5,4] => [5,6,1,2,4,3] => [5,1,2,6,4,3] => 7
[1,6,2,4,3,5] => [5,6,1,3,2,4] => [1,5,3,6,2,4] => 6
[1,6,2,4,5,3] => [5,6,1,3,4,2] => [3,1,5,6,4,2] => 7
[1,6,2,5,3,4] => [5,6,1,4,2,3] => [1,5,2,6,4,3] => 6
[1,6,2,5,4,3] => [5,6,1,4,3,2] => [5,6,1,4,3,2] => 11
[1,6,3,2,4,5] => [5,1,2,6,3,4] => [1,5,2,6,3,4] => 5
[1,6,3,2,5,4] => [5,1,2,6,4,3] => [5,6,1,4,2,3] => 10
[1,6,3,4,2,5] => [5,1,2,3,6,4] => [5,1,2,6,3,4] => 6
[1,6,3,4,5,2] => [5,1,2,3,4,6] => [1,2,3,5,4,6] => 1
[1,6,3,5,2,4] => [5,1,2,4,6,3] => [5,1,2,4,6,3] => 6
[1,6,3,5,4,2] => [5,1,2,4,3,6] => [5,1,2,4,3,6] => 5
[1,6,4,2,3,5] => [5,1,3,6,2,4] => [1,5,3,2,6,4] => 5
[1,6,4,2,5,3] => [5,1,3,6,4,2] => [5,6,1,3,4,2] => 10
[1,6,4,3,2,5] => [5,1,3,2,6,4] => [5,6,1,3,2,4] => 9
[1,6,4,3,5,2] => [5,1,3,2,4,6] => [1,5,3,2,4,6] => 4
[1,6,4,5,2,3] => [5,1,3,4,6,2] => [3,1,5,4,6,2] => 6
[1,6,4,5,3,2] => [5,1,3,4,2,6] => [3,1,5,4,2,6] => 5
[1,6,5,2,3,4] => [5,1,4,6,2,3] => [1,5,2,4,6,3] => 5
[1,6,5,2,4,3] => [5,1,4,6,3,2] => [5,4,1,6,3,2] => 10
[1,6,5,3,2,4] => [5,1,4,2,6,3] => [5,4,1,6,2,3] => 9
[1,6,5,3,4,2] => [5,1,4,2,3,6] => [1,5,2,4,3,6] => 4
[1,6,5,4,2,3] => [5,1,4,3,6,2] => [5,4,1,3,6,2] => 9
[1,6,5,4,3,2] => [5,1,4,3,2,6] => [5,4,1,3,2,6] => 8
[2,1,3,4,5,6] => [6,1,2,3,4,5] => [1,2,3,4,6,5] => 1
[2,1,3,4,6,5] => [6,1,2,3,5,4] => [6,1,2,3,5,4] => 6
[2,1,3,5,4,6] => [6,1,2,4,3,5] => [1,6,2,4,3,5] => 5
[2,1,3,5,6,4] => [6,1,2,4,5,3] => [4,1,2,6,5,3] => 6
[2,1,3,6,4,5] => [6,1,2,5,3,4] => [1,6,2,3,5,4] => 5
[2,1,3,6,5,4] => [6,1,2,5,4,3] => [6,5,1,2,4,3] => 10
[2,1,4,3,5,6] => [6,1,3,2,4,5] => [1,3,6,2,4,5] => 4
[2,1,4,3,6,5] => [6,1,3,2,5,4] => [6,1,5,3,2,4] => 9
[2,1,4,5,3,6] => [6,1,3,4,2,5] => [3,1,4,6,2,5] => 5
[2,1,4,5,6,3] => [6,1,3,4,5,2] => [3,1,4,6,5,2] => 6
[2,1,4,6,3,5] => [6,1,3,5,2,4] => [3,1,2,6,5,4] => 5
[2,1,4,6,5,3] => [6,1,3,5,4,2] => [6,3,1,5,4,2] => 10
[2,1,5,3,4,6] => [6,1,4,2,3,5] => [1,2,6,4,3,5] => 4
[2,1,5,3,6,4] => [6,1,4,2,5,3] => [6,1,4,5,2,3] => 9
[2,1,5,4,3,6] => [6,1,4,3,2,5] => [4,6,1,3,2,5] => 8
[2,1,5,4,6,3] => [6,1,4,3,5,2] => [6,1,4,3,5,2] => 9
[2,1,5,6,3,4] => [6,1,4,5,2,3] => [1,4,2,6,5,3] => 5
[2,1,5,6,4,3] => [6,1,4,5,3,2] => [4,6,1,5,3,2] => 10
[2,1,6,3,4,5] => [6,1,5,2,3,4] => [1,2,6,3,5,4] => 4
[2,1,6,3,5,4] => [6,1,5,2,4,3] => [6,1,5,2,4,3] => 9
[2,1,6,4,3,5] => [6,1,5,3,2,4] => [1,6,5,3,2,4] => 8
[2,1,6,4,5,3] => [6,1,5,3,4,2] => [6,1,3,5,4,2] => 9
[2,1,6,5,3,4] => [6,1,5,4,2,3] => [1,6,5,2,4,3] => 8
[2,1,6,5,4,3] => [6,1,5,4,3,2] => [6,5,4,1,3,2] => 13
[2,3,1,4,5,6] => [1,6,2,3,4,5] => [1,2,3,6,4,5] => 2
[2,3,1,4,6,5] => [1,6,2,3,5,4] => [6,1,2,5,3,4] => 7
[2,3,1,5,4,6] => [1,6,2,4,3,5] => [1,6,4,2,3,5] => 6
[2,3,1,5,6,4] => [1,6,2,4,5,3] => [6,1,2,4,5,3] => 7
[2,3,1,6,4,5] => [1,6,2,5,3,4] => [1,6,2,5,3,4] => 6
[2,3,1,6,5,4] => [1,6,2,5,4,3] => [6,5,1,4,2,3] => 11
[2,3,4,1,5,6] => [6,2,1,3,4,5] => [2,1,3,6,4,5] => 3
[2,3,4,1,6,5] => [6,2,1,3,5,4] => [6,2,1,5,3,4] => 8
[2,3,4,5,1,6] => [6,2,3,1,4,5] => [2,3,1,6,4,5] => 4
[2,3,4,5,6,1] => [6,2,3,4,1,5] => [2,3,4,6,1,5] => 5
[2,3,4,6,1,5] => [6,2,3,5,4,1] => [6,2,3,5,4,1] => 10
[2,3,4,6,5,1] => [6,2,3,1,5,4] => [6,2,3,5,1,4] => 9
[2,3,5,1,4,6] => [6,2,4,3,5,1] => [2,6,4,3,5,1] => 9
[2,3,5,1,6,4] => [6,2,1,4,5,3] => [6,2,1,4,5,3] => 8
[2,3,5,4,1,6] => [6,2,1,4,3,5] => [2,6,4,1,3,5] => 7
[2,3,5,4,6,1] => [6,2,4,3,1,5] => [2,6,4,3,1,5] => 8
[2,3,5,6,1,4] => [6,2,4,5,3,1] => [4,2,6,5,3,1] => 10
[2,3,5,6,4,1] => [6,2,4,1,5,3] => [4,2,6,5,1,3] => 9
[2,3,6,1,4,5] => [6,2,5,3,4,1] => [2,6,3,5,4,1] => 9
[2,3,6,1,5,4] => [6,2,5,4,1,3] => [2,6,1,5,4,3] => 8
[2,3,6,4,1,5] => [6,2,1,5,3,4] => [2,6,1,5,3,4] => 7
[2,3,6,4,5,1] => [6,2,5,3,1,4] => [2,6,3,5,1,4] => 8
[2,3,6,5,1,4] => [6,2,5,4,3,1] => [6,5,2,4,3,1] => 13
[2,3,6,5,4,1] => [6,2,1,5,4,3] => [6,5,2,4,1,3] => 12
[2,4,1,3,5,6] => [6,3,2,4,5,1] => [3,2,6,4,5,1] => 8
[2,4,1,3,6,5] => [6,3,2,5,1,4] => [3,2,6,1,5,4] => 7
[2,4,1,5,3,6] => [1,6,3,4,2,5] => [1,6,3,4,2,5] => 6
[2,4,1,5,6,3] => [1,6,3,4,5,2] => [3,1,6,4,5,2] => 7
[2,4,1,6,3,5] => [1,6,3,5,2,4] => [1,6,3,2,5,4] => 6
[2,4,1,6,5,3] => [1,6,3,5,4,2] => [6,5,1,3,4,2] => 11
[2,4,3,1,5,6] => [1,6,3,2,4,5] => [3,1,6,2,4,5] => 5
[2,4,3,1,6,5] => [1,6,3,2,5,4] => [6,3,5,1,2,4] => 10
[2,4,3,5,1,6] => [6,3,2,1,4,5] => [3,2,6,1,4,5] => 6
[2,4,3,5,6,1] => [6,3,2,4,1,5] => [3,2,6,4,1,5] => 7
[2,4,3,6,1,5] => [6,3,2,5,4,1] => [6,3,5,2,4,1] => 12
[2,4,3,6,5,1] => [6,3,2,1,5,4] => [6,3,5,2,1,4] => 11
[2,4,5,1,3,6] => [6,3,4,2,5,1] => [3,4,6,2,5,1] => 9
[2,4,5,1,6,3] => [6,3,1,4,5,2] => [3,6,1,4,5,2] => 8
[2,4,5,3,1,6] => [6,3,1,4,2,5] => [3,4,6,1,2,5] => 7
[2,4,5,3,6,1] => [6,3,4,2,1,5] => [3,4,6,2,1,5] => 8
[2,4,5,6,1,3] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => 10
[2,4,5,6,3,1] => [6,3,4,1,5,2] => [3,4,6,5,1,2] => 9
[2,4,6,1,3,5] => [6,3,5,2,4,1] => [3,2,6,5,4,1] => 9
[2,4,6,1,5,3] => [6,3,5,4,1,2] => [1,6,3,5,4,2] => 8
[2,4,6,3,1,5] => [6,3,1,5,2,4] => [3,1,6,5,2,4] => 7
[2,4,6,3,5,1] => [6,3,5,2,1,4] => [3,2,6,5,1,4] => 8
[2,4,6,5,1,3] => [6,3,5,4,2,1] => [6,3,5,4,2,1] => 13
[2,4,6,5,3,1] => [6,3,1,5,4,2] => [6,3,5,4,1,2] => 12
[2,5,1,3,4,6] => [6,4,2,3,5,1] => [2,4,6,3,5,1] => 8
[2,5,1,3,6,4] => [6,4,2,5,1,3] => [2,4,6,1,5,3] => 7
[2,5,1,4,3,6] => [6,4,3,1,2,5] => [1,4,6,3,2,5] => 6
[2,5,1,4,6,3] => [6,4,3,5,1,2] => [1,4,6,3,5,2] => 7
[2,5,1,6,3,4] => [1,6,4,5,2,3] => [1,6,2,4,5,3] => 6
[2,5,1,6,4,3] => [1,6,4,5,3,2] => [6,4,1,5,3,2] => 11
[2,5,3,1,4,6] => [1,6,4,2,3,5] => [1,4,6,2,3,5] => 5
[2,5,3,1,6,4] => [1,6,4,2,5,3] => [4,6,5,1,2,3] => 10
[2,5,3,4,1,6] => [6,4,2,1,3,5] => [2,4,6,1,3,5] => 6
[2,5,3,4,6,1] => [6,4,2,3,1,5] => [2,4,6,3,1,5] => 7
[2,5,3,6,1,4] => [6,4,2,5,3,1] => [4,6,5,2,3,1] => 12
[2,5,3,6,4,1] => [6,4,2,1,5,3] => [4,6,5,2,1,3] => 11
[2,5,4,1,3,6] => [6,4,3,2,5,1] => [4,6,3,2,5,1] => 11
[2,5,4,1,6,3] => [1,6,4,3,5,2] => [4,6,3,1,5,2] => 10
[2,5,4,3,1,6] => [1,6,4,3,2,5] => [4,6,3,1,2,5] => 9
[2,5,4,3,6,1] => [6,4,3,2,1,5] => [4,6,3,2,1,5] => 10
[2,5,4,6,1,3] => [6,4,3,5,2,1] => [4,6,3,5,2,1] => 12
[2,5,4,6,3,1] => [6,4,3,1,5,2] => [4,6,3,5,1,2] => 11
[2,5,6,1,3,4] => [6,4,5,2,3,1] => [2,4,6,5,3,1] => 9
[2,5,6,1,4,3] => [6,4,5,3,1,2] => [1,4,6,5,3,2] => 8
[2,5,6,3,1,4] => [6,4,1,5,2,3] => [1,4,6,5,2,3] => 7
[2,5,6,3,4,1] => [6,4,5,2,1,3] => [2,4,6,5,1,3] => 8
[2,5,6,4,1,3] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => 13
[2,5,6,4,3,1] => [6,4,1,5,3,2] => [4,6,5,3,1,2] => 12
[2,6,1,3,4,5] => [6,5,2,3,4,1] => [2,3,6,5,4,1] => 8
[2,6,1,3,5,4] => [6,5,2,4,1,3] => [2,1,6,5,4,3] => 7
[2,6,1,4,3,5] => [6,5,3,1,2,4] => [1,3,6,5,2,4] => 6
[2,6,1,4,5,3] => [6,5,3,4,1,2] => [1,3,6,5,4,2] => 7
[2,6,1,5,3,4] => [6,5,4,1,2,3] => [1,2,6,5,4,3] => 6
[2,6,1,5,4,3] => [6,5,4,1,3,2] => [6,1,5,4,3,2] => 11
[2,6,3,1,4,5] => [1,6,5,2,3,4] => [1,2,6,5,3,4] => 5
[2,6,3,1,5,4] => [1,6,5,2,4,3] => [6,1,5,4,2,3] => 10
[2,6,3,4,1,5] => [6,5,2,1,3,4] => [2,1,6,5,3,4] => 6
[2,6,3,4,5,1] => [6,5,2,3,1,4] => [2,3,6,5,1,4] => 7
[2,6,3,5,1,4] => [6,5,2,4,3,1] => [6,2,5,4,3,1] => 12
[2,6,3,5,4,1] => [6,5,2,1,4,3] => [6,2,5,4,1,3] => 11
[2,6,4,1,3,5] => [6,5,3,2,4,1] => [3,6,5,2,4,1] => 11
[2,6,4,1,5,3] => [1,6,5,3,4,2] => [6,1,5,3,4,2] => 10
[2,6,4,3,1,5] => [1,6,5,3,2,4] => [3,6,5,1,2,4] => 9
[2,6,4,3,5,1] => [6,5,3,2,1,4] => [3,6,5,2,1,4] => 10
[2,6,4,5,1,3] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => 12
[2,6,4,5,3,1] => [6,5,3,1,4,2] => [3,6,5,4,1,2] => 11
[2,6,5,1,3,4] => [6,5,4,2,3,1] => [2,6,5,4,3,1] => 11
[2,6,5,1,4,3] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => 10
[2,6,5,3,1,4] => [1,6,5,4,2,3] => [1,6,5,4,2,3] => 9
[2,6,5,3,4,1] => [6,5,4,2,1,3] => [2,6,5,4,1,3] => 10
[2,6,5,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 15
[2,6,5,4,3,1] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 14
[3,1,2,4,5,6] => [2,6,3,4,5,1] => [2,3,6,4,5,1] => 7
[3,1,2,4,6,5] => [2,6,3,5,1,4] => [2,3,6,1,5,4] => 6
[3,1,2,5,4,6] => [2,6,4,1,3,5] => [2,1,6,4,3,5] => 5
[3,1,2,5,6,4] => [2,6,4,5,1,3] => [2,1,6,4,5,3] => 6
[3,1,2,6,4,5] => [2,6,5,1,3,4] => [2,1,6,3,5,4] => 5
[3,1,2,6,5,4] => [2,6,5,1,4,3] => [6,2,5,1,4,3] => 10
[3,1,4,2,5,6] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => 4
[3,1,4,2,6,5] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
[3,1,4,5,2,6] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 5
[3,1,4,5,6,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[3,1,4,6,2,5] => [1,2,3,5,6,4] => [5,1,2,3,6,4] => 5
[3,1,4,6,5,2] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 4
[3,1,5,2,4,6] => [1,2,4,6,3,5] => [4,1,2,3,6,5] => 4
[3,1,5,2,6,4] => [1,2,4,6,5,3] => [6,4,1,2,5,3] => 9
[3,1,5,4,2,6] => [1,2,4,3,6,5] => [6,4,1,2,3,5] => 8
[3,1,5,4,6,2] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 3
[3,1,5,6,2,4] => [1,2,4,5,6,3] => [4,1,2,5,6,3] => 5
[3,1,5,6,4,2] => [1,2,4,5,3,6] => [4,1,2,5,3,6] => 4
[3,1,6,2,4,5] => [1,2,5,6,3,4] => [1,5,2,3,6,4] => 4
[3,1,6,2,5,4] => [1,2,5,6,4,3] => [5,6,1,2,4,3] => 9
[3,1,6,4,2,5] => [1,2,5,3,6,4] => [5,6,1,2,3,4] => 8
[3,1,6,4,5,2] => [1,2,5,3,4,6] => [1,5,2,3,4,6] => 3
[3,1,6,5,2,4] => [1,2,5,4,6,3] => [5,4,1,2,6,3] => 8
[3,1,6,5,4,2] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => 7
[3,2,1,4,5,6] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 3
[3,2,1,4,6,5] => [1,2,6,3,5,4] => [6,1,5,2,3,4] => 8
[3,2,1,5,4,6] => [1,2,6,4,3,5] => [4,6,1,2,3,5] => 7
[3,2,1,5,6,4] => [1,2,6,4,5,3] => [6,1,4,2,5,3] => 8
[3,2,1,6,4,5] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => 7
[3,2,1,6,5,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 12
[3,2,4,1,5,6] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => 4
[3,2,4,1,6,5] => [2,1,6,3,5,4] => [6,2,5,1,3,4] => 9
[3,2,4,5,1,6] => [2,6,3,1,4,5] => [2,3,6,1,4,5] => 5
[3,2,4,5,6,1] => [2,6,3,4,1,5] => [2,3,6,4,1,5] => 6
[3,2,4,6,1,5] => [2,6,3,5,4,1] => [6,2,5,3,4,1] => 11
[3,2,4,6,5,1] => [2,6,3,1,5,4] => [6,2,5,3,1,4] => 10
[3,2,5,1,4,6] => [2,6,4,3,5,1] => [4,6,2,3,5,1] => 10
[3,2,5,1,6,4] => [2,1,6,4,5,3] => [6,2,4,1,5,3] => 9
[3,2,5,4,1,6] => [2,1,6,4,3,5] => [4,6,2,1,3,5] => 8
[3,2,5,4,6,1] => [2,6,4,3,1,5] => [4,6,2,3,1,5] => 9
[3,2,5,6,1,4] => [2,6,4,5,3,1] => [6,2,4,5,3,1] => 11
[3,2,5,6,4,1] => [2,6,4,1,5,3] => [6,2,4,5,1,3] => 10
[3,2,6,1,4,5] => [2,6,5,3,4,1] => [2,6,5,3,4,1] => 10
[3,2,6,1,5,4] => [2,6,5,4,1,3] => [2,6,5,1,4,3] => 9
[3,2,6,4,1,5] => [2,1,6,5,3,4] => [2,6,5,1,3,4] => 8
[3,2,6,4,5,1] => [2,6,5,3,1,4] => [2,6,5,3,1,4] => 9
[3,2,6,5,1,4] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => 14
[3,2,6,5,4,1] => [2,1,6,5,4,3] => [6,5,4,2,1,3] => 13
[3,4,1,2,5,6] => [2,3,6,4,5,1] => [2,6,3,4,5,1] => 8
[3,4,1,2,6,5] => [2,3,6,5,1,4] => [2,6,3,1,5,4] => 7
[3,4,1,5,2,6] => [2,1,3,4,6,5] => [6,2,1,3,4,5] => 6
[3,4,1,5,6,2] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[3,4,1,6,2,5] => [2,1,3,5,6,4] => [5,2,1,3,6,4] => 6
[3,4,1,6,5,2] => [2,1,3,5,4,6] => [5,2,1,3,4,6] => 5
[3,4,2,1,5,6] => [2,1,3,6,4,5] => [2,6,1,3,4,5] => 5
[3,4,2,1,6,5] => [2,1,3,6,5,4] => [6,5,2,1,3,4] => 10
[3,4,2,5,1,6] => [2,3,1,6,4,5] => [2,6,3,1,4,5] => 6
[3,4,2,5,6,1] => [2,3,6,4,1,5] => [2,6,3,4,1,5] => 7
[3,4,2,6,1,5] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => 12
[3,4,2,6,5,1] => [2,3,1,6,5,4] => [6,5,2,3,1,4] => 11
[3,4,5,1,2,6] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => 9
[3,4,5,1,6,2] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => 2
[3,4,5,2,1,6] => [2,3,1,4,6,5] => [6,2,3,1,4,5] => 7
[3,4,5,2,6,1] => [2,3,4,1,6,5] => [6,2,3,4,1,5] => 8
[3,4,5,6,1,2] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => 4
[3,4,5,6,2,1] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => 3
[3,4,6,1,2,5] => [2,3,5,6,4,1] => [5,2,3,6,4,1] => 9
[3,4,6,1,5,2] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => 8
[3,4,6,2,1,5] => [2,3,1,5,6,4] => [5,2,3,1,6,4] => 7
[3,4,6,2,5,1] => [2,3,5,1,6,4] => [5,2,3,6,1,4] => 8
[3,4,6,5,1,2] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => 7
[3,4,6,5,2,1] => [2,3,1,5,4,6] => [5,2,3,1,4,6] => 6
[3,5,1,2,4,6] => [2,4,6,3,5,1] => [4,2,3,6,5,1] => 8
[3,5,1,2,6,4] => [2,4,6,5,1,3] => [2,6,1,4,5,3] => 7
[3,5,1,4,2,6] => [2,4,3,6,1,5] => [4,2,3,1,6,5] => 6
[3,5,1,4,6,2] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => 7
[3,5,1,6,2,4] => [2,1,4,5,6,3] => [4,2,1,5,6,3] => 6
[3,5,1,6,4,2] => [2,1,4,5,3,6] => [4,2,1,5,3,6] => 5
[3,5,2,1,4,6] => [2,1,4,6,3,5] => [4,2,1,3,6,5] => 5
[3,5,2,1,6,4] => [2,1,4,6,5,3] => [6,4,2,1,5,3] => 10
[3,5,2,4,1,6] => [2,4,1,6,3,5] => [4,2,1,6,3,5] => 6
[3,5,2,4,6,1] => [2,4,6,3,1,5] => [4,2,3,6,1,5] => 7
[3,5,2,6,1,4] => [2,4,6,5,3,1] => [6,4,2,5,3,1] => 12
[3,5,2,6,4,1] => [2,4,1,6,5,3] => [6,4,2,5,1,3] => 11
[3,5,4,1,2,6] => [2,4,3,6,5,1] => [6,4,2,3,5,1] => 11
[3,5,4,1,6,2] => [2,1,4,3,5,6] => [4,2,1,3,5,6] => 4
[3,5,4,2,1,6] => [2,1,4,3,6,5] => [6,4,2,1,3,5] => 9
[3,5,4,2,6,1] => [2,4,3,1,6,5] => [6,4,2,3,1,5] => 10
[3,5,4,6,1,2] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => 6
[3,5,4,6,2,1] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => 5
[3,5,6,1,2,4] => [2,4,5,6,3,1] => [4,2,5,6,3,1] => 9
[3,5,6,1,4,2] => [2,4,5,3,6,1] => [4,2,5,3,6,1] => 8
[3,5,6,2,1,4] => [2,4,1,5,6,3] => [4,2,5,1,6,3] => 7
[3,5,6,2,4,1] => [2,4,5,1,6,3] => [4,2,5,6,1,3] => 8
[3,5,6,4,1,2] => [2,4,5,3,1,6] => [4,2,5,3,1,6] => 7
[3,5,6,4,2,1] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => 6
[3,6,1,2,4,5] => [2,5,6,3,4,1] => [2,5,3,6,4,1] => 8
[3,6,1,2,5,4] => [2,5,6,4,1,3] => [2,5,1,6,4,3] => 7
[3,6,1,4,2,5] => [2,5,3,6,1,4] => [2,5,3,1,6,4] => 6
[3,6,1,4,5,2] => [2,5,3,4,6,1] => [2,5,3,4,6,1] => 7
[3,6,1,5,2,4] => [2,5,4,6,1,3] => [2,5,1,4,6,3] => 6
[3,6,1,5,4,2] => [2,5,4,1,3,6] => [2,5,1,4,3,6] => 5
[3,6,2,1,4,5] => [2,1,5,6,3,4] => [2,5,1,3,6,4] => 5
[3,6,2,1,5,4] => [2,1,5,6,4,3] => [5,6,2,1,4,3] => 10
[3,6,2,4,1,5] => [2,5,1,6,3,4] => [2,5,1,6,3,4] => 6
[3,6,2,4,5,1] => [2,5,6,3,1,4] => [2,5,3,6,1,4] => 7
[3,6,2,5,1,4] => [2,5,6,4,3,1] => [5,6,2,4,3,1] => 12
[3,6,2,5,4,1] => [2,5,1,6,4,3] => [5,6,2,4,1,3] => 11
[3,6,4,1,2,5] => [2,5,3,6,4,1] => [5,6,2,3,4,1] => 11
[3,6,4,1,5,2] => [2,1,5,3,4,6] => [2,5,1,3,4,6] => 4
[3,6,4,2,1,5] => [2,1,5,3,6,4] => [5,6,2,1,3,4] => 9
[3,6,4,2,5,1] => [2,5,3,1,6,4] => [5,6,2,3,1,4] => 10
[3,6,4,5,1,2] => [2,5,3,4,1,6] => [2,5,3,4,1,6] => 6
[3,6,4,5,2,1] => [2,5,3,1,4,6] => [2,5,3,1,4,6] => 5
[3,6,5,1,2,4] => [2,5,4,6,3,1] => [5,4,2,6,3,1] => 11
[3,6,5,1,4,2] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => 10
[3,6,5,2,1,4] => [2,1,5,4,6,3] => [5,4,2,1,6,3] => 9
[3,6,5,2,4,1] => [2,5,4,1,6,3] => [5,4,2,6,1,3] => 10
[3,6,5,4,1,2] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => 9
[3,6,5,4,2,1] => [2,1,5,4,3,6] => [5,4,2,1,3,6] => 8
[4,1,2,3,5,6] => [3,6,2,4,5,1] => [3,2,4,6,5,1] => 7
[4,1,2,3,6,5] => [3,6,2,5,1,4] => [3,2,1,6,5,4] => 6
[4,1,2,5,3,6] => [3,6,4,1,2,5] => [1,3,6,4,2,5] => 5
[4,1,2,5,6,3] => [3,6,4,5,1,2] => [1,3,6,4,5,2] => 6
[4,1,2,6,3,5] => [3,6,5,1,2,4] => [1,3,6,2,5,4] => 5
[4,1,2,6,5,3] => [3,6,5,1,4,2] => [3,6,5,1,4,2] => 10
[4,1,3,2,5,6] => [3,2,6,1,4,5] => [3,2,1,4,6,5] => 4
[4,1,3,2,6,5] => [3,2,6,1,5,4] => [6,3,2,1,5,4] => 9
[4,1,3,5,2,6] => [3,2,4,6,1,5] => [3,2,4,1,6,5] => 5
[4,1,3,5,6,2] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => 6
[4,1,3,6,2,5] => [3,2,5,6,1,4] => [3,2,1,5,6,4] => 5
[4,1,3,6,5,2] => [3,2,5,1,4,6] => [3,2,1,5,4,6] => 4
[4,1,5,2,3,6] => [1,3,4,6,2,5] => [3,1,4,2,6,5] => 4
[4,1,5,2,6,3] => [1,3,4,6,5,2] => [6,3,1,4,5,2] => 9
[4,1,5,3,2,6] => [1,3,4,2,6,5] => [6,3,1,4,2,5] => 8
[4,1,5,3,6,2] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => 3
[4,1,5,6,2,3] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => 5
[4,1,5,6,3,2] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => 4
[4,1,6,2,3,5] => [1,3,5,6,2,4] => [3,1,2,5,6,4] => 4
[4,1,6,2,5,3] => [1,3,5,6,4,2] => [5,3,1,6,4,2] => 9
[4,1,6,3,2,5] => [1,3,5,2,6,4] => [5,3,1,6,2,4] => 8
[4,1,6,3,5,2] => [1,3,5,2,4,6] => [3,1,2,5,4,6] => 3
[4,1,6,5,2,3] => [1,3,5,4,6,2] => [5,3,1,4,6,2] => 8
[4,1,6,5,3,2] => [1,3,5,4,2,6] => [5,3,1,4,2,6] => 7
[4,2,1,3,5,6] => [1,3,6,2,4,5] => [3,1,2,4,6,5] => 3
[4,2,1,3,6,5] => [1,3,6,2,5,4] => [6,3,1,2,5,4] => 8
[4,2,1,5,3,6] => [1,3,6,4,2,5] => [3,6,1,4,2,5] => 7
[4,2,1,5,6,3] => [1,3,6,4,5,2] => [6,1,3,4,5,2] => 8
[4,2,1,6,3,5] => [1,3,6,5,2,4] => [3,6,1,2,5,4] => 7
[4,2,1,6,5,3] => [1,3,6,5,4,2] => [6,5,3,1,4,2] => 12
[4,2,3,1,5,6] => [3,1,6,2,4,5] => [3,1,2,6,4,5] => 4
[4,2,3,1,6,5] => [3,1,6,2,5,4] => [6,3,1,5,2,4] => 9
[4,2,3,5,1,6] => [3,6,2,1,4,5] => [3,2,1,6,4,5] => 5
[4,2,3,5,6,1] => [3,6,2,4,1,5] => [3,2,4,6,1,5] => 6
[4,2,3,6,1,5] => [3,6,2,5,4,1] => [6,3,2,5,4,1] => 11
[4,2,3,6,5,1] => [3,6,2,1,5,4] => [6,3,2,5,1,4] => 10
[4,2,5,1,3,6] => [3,6,4,2,5,1] => [3,6,4,2,5,1] => 10
[4,2,5,1,6,3] => [3,1,6,4,5,2] => [3,6,4,1,5,2] => 9
[4,2,5,3,1,6] => [3,1,6,4,2,5] => [3,6,4,1,2,5] => 8
[4,2,5,3,6,1] => [3,6,4,2,1,5] => [3,6,4,2,1,5] => 9
[4,2,5,6,1,3] => [3,6,4,5,2,1] => [3,6,4,5,2,1] => 11
[4,2,5,6,3,1] => [3,6,4,1,5,2] => [3,6,4,5,1,2] => 10
[4,2,6,1,3,5] => [3,6,5,2,4,1] => [3,6,2,5,4,1] => 10
[4,2,6,1,5,3] => [3,6,5,4,1,2] => [1,6,5,3,4,2] => 9
[4,2,6,3,1,5] => [3,1,6,5,2,4] => [3,6,1,5,2,4] => 8
[4,2,6,3,5,1] => [3,6,5,2,1,4] => [3,6,2,5,1,4] => 9
[4,2,6,5,1,3] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => 14
[4,2,6,5,3,1] => [3,1,6,5,4,2] => [6,5,3,4,1,2] => 13
[4,3,1,2,5,6] => [3,2,6,4,5,1] => [3,6,2,4,5,1] => 9
[4,3,1,2,6,5] => [3,2,6,5,1,4] => [3,6,2,1,5,4] => 8
[4,3,1,5,2,6] => [1,3,2,4,6,5] => [6,3,1,2,4,5] => 7
[4,3,1,5,6,2] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 2
[4,3,1,6,2,5] => [1,3,2,5,6,4] => [5,3,1,2,6,4] => 7
[4,3,1,6,5,2] => [1,3,2,5,4,6] => [5,3,1,2,4,6] => 6
[4,3,2,1,5,6] => [1,3,2,6,4,5] => [3,6,1,2,4,5] => 6
[4,3,2,1,6,5] => [1,3,2,6,5,4] => [6,5,3,1,2,4] => 11
[4,3,2,5,1,6] => [3,2,1,6,4,5] => [3,6,2,1,4,5] => 7
[4,3,2,5,6,1] => [3,2,6,4,1,5] => [3,6,2,4,1,5] => 8
[4,3,2,6,1,5] => [3,2,6,5,4,1] => [6,5,3,2,4,1] => 13
[4,3,2,6,5,1] => [3,2,1,6,5,4] => [6,5,3,2,1,4] => 12
[4,3,5,1,2,6] => [3,2,4,6,5,1] => [6,3,2,4,5,1] => 10
[4,3,5,1,6,2] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 3
[4,3,5,2,1,6] => [3,2,1,4,6,5] => [6,3,2,1,4,5] => 8
[4,3,5,2,6,1] => [3,2,4,1,6,5] => [6,3,2,4,1,5] => 9
[4,3,5,6,1,2] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => 5
[4,3,5,6,2,1] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => 4
[4,3,6,1,2,5] => [3,2,5,6,4,1] => [5,3,2,6,4,1] => 10
[4,3,6,1,5,2] => [3,2,5,4,6,1] => [5,3,2,4,6,1] => 9
[4,3,6,2,1,5] => [3,2,1,5,6,4] => [5,3,2,1,6,4] => 8
[4,3,6,2,5,1] => [3,2,5,1,6,4] => [5,3,2,6,1,4] => 9
[4,3,6,5,1,2] => [3,2,5,4,1,6] => [5,3,2,4,1,6] => 8
[4,3,6,5,2,1] => [3,2,1,5,4,6] => [5,3,2,1,4,6] => 7
[4,5,1,2,3,6] => [3,4,6,2,5,1] => [3,4,2,6,5,1] => 8
[4,5,1,2,6,3] => [3,4,6,5,1,2] => [1,6,3,4,5,2] => 7
[4,5,1,3,2,6] => [3,4,2,6,1,5] => [3,4,2,1,6,5] => 6
[4,5,1,3,6,2] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => 7
[4,5,1,6,2,3] => [3,1,4,5,6,2] => [3,4,1,5,6,2] => 6
[4,5,1,6,3,2] => [3,1,4,5,2,6] => [3,4,1,5,2,6] => 5
[4,5,2,1,3,6] => [3,1,4,6,2,5] => [3,4,1,2,6,5] => 5
[4,5,2,1,6,3] => [3,1,4,6,5,2] => [6,3,4,1,5,2] => 10
[4,5,2,3,1,6] => [3,4,1,6,2,5] => [3,4,1,6,2,5] => 6
[4,5,2,3,6,1] => [3,4,6,2,1,5] => [3,4,2,6,1,5] => 7
[4,5,2,6,1,3] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => 12
[4,5,2,6,3,1] => [3,4,1,6,5,2] => [6,3,4,5,1,2] => 11
[4,5,3,1,2,6] => [3,4,2,6,5,1] => [6,3,4,2,5,1] => 11
[4,5,3,1,6,2] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => 4
[4,5,3,2,1,6] => [3,1,4,2,6,5] => [6,3,4,1,2,5] => 9
[4,5,3,2,6,1] => [3,4,2,1,6,5] => [6,3,4,2,1,5] => 10
[4,5,3,6,1,2] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => 6
[4,5,3,6,2,1] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => 5
[4,5,6,1,2,3] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => 9
[4,5,6,1,3,2] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => 8
[4,5,6,2,1,3] => [3,4,1,5,6,2] => [3,4,5,1,6,2] => 7
[4,5,6,2,3,1] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => 8
[4,5,6,3,1,2] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => 7
[4,5,6,3,2,1] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => 6
[4,6,1,2,3,5] => [3,5,6,2,4,1] => [3,2,5,6,4,1] => 8
[4,6,1,2,5,3] => [3,5,6,4,1,2] => [1,5,3,6,4,2] => 7
[4,6,1,3,2,5] => [3,5,2,6,1,4] => [3,2,5,1,6,4] => 6
[4,6,1,3,5,2] => [3,5,2,4,6,1] => [3,2,5,4,6,1] => 7
[4,6,1,5,2,3] => [3,5,4,6,1,2] => [1,5,3,4,6,2] => 6
[4,6,1,5,3,2] => [3,5,4,1,2,6] => [1,5,3,4,2,6] => 5
[4,6,2,1,3,5] => [3,1,5,6,2,4] => [3,1,5,2,6,4] => 5
[4,6,2,1,5,3] => [3,1,5,6,4,2] => [5,3,6,1,4,2] => 10
[4,6,2,3,1,5] => [3,5,1,6,2,4] => [3,1,5,6,2,4] => 6
[4,6,2,3,5,1] => [3,5,6,2,1,4] => [3,2,5,6,1,4] => 7
[4,6,2,5,1,3] => [3,5,6,4,2,1] => [5,3,6,4,2,1] => 12
[4,6,2,5,3,1] => [3,5,1,6,4,2] => [5,3,6,4,1,2] => 11
[4,6,3,1,2,5] => [3,5,2,6,4,1] => [5,3,6,2,4,1] => 11
[4,6,3,1,5,2] => [3,1,5,2,4,6] => [3,1,5,2,4,6] => 4
[4,6,3,2,1,5] => [3,1,5,2,6,4] => [5,3,6,1,2,4] => 9
[4,6,3,2,5,1] => [3,5,2,1,6,4] => [5,3,6,2,1,4] => 10
[4,6,3,5,1,2] => [3,5,2,4,1,6] => [3,2,5,4,1,6] => 6
[4,6,3,5,2,1] => [3,5,2,1,4,6] => [3,2,5,1,4,6] => 5
[4,6,5,1,2,3] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => 11
[4,6,5,1,3,2] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => 10
[4,6,5,2,1,3] => [3,1,5,4,6,2] => [5,3,4,1,6,2] => 9
[4,6,5,2,3,1] => [3,5,4,1,6,2] => [5,3,4,6,1,2] => 10
[4,6,5,3,1,2] => [3,5,4,2,1,6] => [5,3,4,2,1,6] => 9
[4,6,5,3,2,1] => [3,1,5,4,2,6] => [5,3,4,1,2,6] => 8
[5,1,2,3,4,6] => [4,6,2,3,5,1] => [2,4,3,6,5,1] => 7
[5,1,2,3,6,4] => [4,6,2,5,1,3] => [2,4,1,6,5,3] => 6
[5,1,2,4,3,6] => [4,6,3,1,2,5] => [1,4,3,6,2,5] => 5
[5,1,2,4,6,3] => [4,6,3,5,1,2] => [1,4,3,6,5,2] => 6
[5,1,2,6,3,4] => [4,6,5,1,2,3] => [1,2,6,4,5,3] => 5
[5,1,2,6,4,3] => [4,6,5,1,3,2] => [6,1,4,5,3,2] => 10
[5,1,3,2,4,6] => [4,2,6,1,3,5] => [2,4,1,3,6,5] => 4
[5,1,3,2,6,4] => [4,2,6,1,5,3] => [4,6,2,1,5,3] => 9
[5,1,3,4,2,6] => [4,2,3,6,1,5] => [2,4,3,1,6,5] => 5
[5,1,3,4,6,2] => [4,2,3,5,6,1] => [2,4,3,5,6,1] => 6
[5,1,3,6,2,4] => [4,2,5,6,1,3] => [2,4,1,5,6,3] => 5
[5,1,3,6,4,2] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => 4
[5,1,4,2,3,6] => [4,3,6,1,2,5] => [1,4,3,2,6,5] => 4
[5,1,4,2,6,3] => [4,3,6,1,5,2] => [4,3,6,1,5,2] => 9
[5,1,4,3,2,6] => [4,3,1,2,6,5] => [6,1,4,3,2,5] => 8
[5,1,4,3,6,2] => [4,3,1,2,5,6] => [1,4,3,2,5,6] => 3
[5,1,4,6,2,3] => [4,3,5,6,1,2] => [1,4,3,5,6,2] => 5
[5,1,4,6,3,2] => [4,3,5,1,2,6] => [1,4,3,5,2,6] => 4
[5,1,6,2,3,4] => [1,4,5,6,2,3] => [1,4,2,5,6,3] => 4
[5,1,6,2,4,3] => [1,4,5,6,3,2] => [4,5,1,6,3,2] => 9
[5,1,6,3,2,4] => [1,4,5,2,6,3] => [4,5,1,6,2,3] => 8
[5,1,6,3,4,2] => [1,4,5,2,3,6] => [1,4,2,5,3,6] => 3
[5,1,6,4,2,3] => [1,4,5,3,6,2] => [4,5,1,3,6,2] => 8
[5,1,6,4,3,2] => [1,4,5,3,2,6] => [4,5,1,3,2,6] => 7
[5,2,1,3,4,6] => [1,4,6,2,3,5] => [1,4,2,3,6,5] => 3
[5,2,1,3,6,4] => [1,4,6,2,5,3] => [4,6,1,2,5,3] => 8
[5,2,1,4,3,6] => [1,4,6,3,2,5] => [4,1,6,3,2,5] => 7
[5,2,1,4,6,3] => [1,4,6,3,5,2] => [4,3,1,6,5,2] => 8
[5,2,1,6,3,4] => [1,4,6,5,2,3] => [1,6,4,2,5,3] => 7
[5,2,1,6,4,3] => [1,4,6,5,3,2] => [6,4,5,1,3,2] => 12
[5,2,3,1,4,6] => [4,1,6,2,3,5] => [1,4,2,6,3,5] => 4
[5,2,3,1,6,4] => [4,1,6,2,5,3] => [4,6,1,5,2,3] => 9
[5,2,3,4,1,6] => [4,6,2,1,3,5] => [2,4,1,6,3,5] => 5
[5,2,3,4,6,1] => [4,6,2,3,1,5] => [2,4,3,6,1,5] => 6
[5,2,3,6,1,4] => [4,6,2,5,3,1] => [4,6,2,5,3,1] => 11
[5,2,3,6,4,1] => [4,6,2,1,5,3] => [4,6,2,5,1,3] => 10
[5,2,4,1,3,6] => [4,6,3,2,5,1] => [4,3,6,2,5,1] => 10
[5,2,4,1,6,3] => [4,1,6,3,5,2] => [4,6,1,3,5,2] => 9
[5,2,4,3,1,6] => [4,1,6,3,2,5] => [4,3,6,1,2,5] => 8
[5,2,4,3,6,1] => [4,6,3,2,1,5] => [4,3,6,2,1,5] => 9
[5,2,4,6,1,3] => [4,6,3,5,2,1] => [4,3,6,5,2,1] => 11
[5,2,4,6,3,1] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 10
[5,2,6,1,3,4] => [4,6,5,2,3,1] => [2,6,4,5,3,1] => 10
[5,2,6,1,4,3] => [4,6,5,3,1,2] => [1,6,4,5,3,2] => 9
[5,2,6,3,1,4] => [4,1,6,5,2,3] => [1,6,4,5,2,3] => 8
[5,2,6,3,4,1] => [4,6,5,2,1,3] => [2,6,4,5,1,3] => 9
[5,2,6,4,1,3] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => 14
[5,2,6,4,3,1] => [4,1,6,5,3,2] => [6,4,5,3,1,2] => 13
[5,3,1,2,4,6] => [4,2,6,3,5,1] => [4,2,6,3,5,1] => 9
[5,3,1,2,6,4] => [4,2,6,5,1,3] => [2,6,4,1,5,3] => 8
[5,3,1,4,2,6] => [1,4,2,3,6,5] => [6,1,4,2,3,5] => 7
[5,3,1,4,6,2] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => 2
[5,3,1,6,2,4] => [1,4,2,5,6,3] => [4,5,1,2,6,3] => 7
[5,3,1,6,4,2] => [1,4,2,5,3,6] => [4,5,1,2,3,6] => 6
[5,3,2,1,4,6] => [1,4,2,6,3,5] => [4,1,6,2,3,5] => 6
[5,3,2,1,6,4] => [1,4,2,6,5,3] => [6,4,5,1,2,3] => 11
[5,3,2,4,1,6] => [4,2,1,6,3,5] => [4,2,6,1,3,5] => 7
[5,3,2,4,6,1] => [4,2,6,3,1,5] => [4,2,6,3,1,5] => 8
[5,3,2,6,1,4] => [4,2,6,5,3,1] => [6,4,5,2,3,1] => 13
[5,3,2,6,4,1] => [4,2,1,6,5,3] => [6,4,5,2,1,3] => 12
[5,3,4,1,2,6] => [4,2,3,6,5,1] => [6,2,4,3,5,1] => 10
[5,3,4,1,6,2] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => 3
[5,3,4,2,1,6] => [4,2,1,3,6,5] => [6,2,4,1,3,5] => 8
[5,3,4,2,6,1] => [4,2,3,1,6,5] => [6,2,4,3,1,5] => 9
[5,3,4,6,1,2] => [4,2,3,5,1,6] => [2,4,3,5,1,6] => 5
[5,3,4,6,2,1] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => 4
[5,3,6,1,2,4] => [4,2,5,6,3,1] => [4,5,2,6,3,1] => 10
[5,3,6,1,4,2] => [4,2,5,3,6,1] => [4,5,2,3,6,1] => 9
[5,3,6,2,1,4] => [4,2,1,5,6,3] => [4,5,2,1,6,3] => 8
[5,3,6,2,4,1] => [4,2,5,1,6,3] => [4,5,2,6,1,3] => 9
[5,3,6,4,1,2] => [4,2,5,3,1,6] => [4,5,2,3,1,6] => 8
[5,3,6,4,2,1] => [4,2,1,5,3,6] => [4,5,2,1,3,6] => 7
[5,4,1,2,3,6] => [4,3,6,2,5,1] => [4,3,2,6,5,1] => 9
[5,4,1,2,6,3] => [4,3,6,5,1,2] => [1,6,4,3,5,2] => 8
[5,4,1,3,2,6] => [4,3,2,6,1,5] => [4,3,2,1,6,5] => 7
[5,4,1,3,6,2] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => 8
[5,4,1,6,2,3] => [1,4,3,5,6,2] => [4,3,1,5,6,2] => 7
[5,4,1,6,3,2] => [1,4,3,5,2,6] => [4,3,1,5,2,6] => 6
[5,4,2,1,3,6] => [1,4,3,6,2,5] => [4,3,1,2,6,5] => 6
[5,4,2,1,6,3] => [1,4,3,6,5,2] => [6,4,3,1,5,2] => 11
[5,4,2,3,1,6] => [4,3,1,6,2,5] => [4,3,1,6,2,5] => 7
[5,4,2,3,6,1] => [4,3,6,2,1,5] => [4,3,2,6,1,5] => 8
[5,4,2,6,1,3] => [4,3,6,5,2,1] => [6,4,3,5,2,1] => 13
[5,4,2,6,3,1] => [4,3,1,6,5,2] => [6,4,3,5,1,2] => 12
[5,4,3,1,2,6] => [4,3,2,6,5,1] => [6,4,3,2,5,1] => 12
[5,4,3,1,6,2] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => 5
[5,4,3,2,1,6] => [1,4,3,2,6,5] => [6,4,3,1,2,5] => 10
[5,4,3,2,6,1] => [4,3,2,1,6,5] => [6,4,3,2,1,5] => 11
[5,4,3,6,1,2] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => 7
[5,4,3,6,2,1] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 6
[5,4,6,1,2,3] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => 10
[5,4,6,1,3,2] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => 9
[5,4,6,2,1,3] => [4,3,1,5,6,2] => [4,3,5,1,6,2] => 8
[5,4,6,2,3,1] => [4,3,5,1,6,2] => [4,3,5,6,1,2] => 9
[5,4,6,3,1,2] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => 8
[5,4,6,3,2,1] => [4,3,1,5,2,6] => [4,3,5,1,2,6] => 7
[5,6,1,2,3,4] => [4,5,6,2,3,1] => [2,4,5,6,3,1] => 8
[5,6,1,2,4,3] => [4,5,6,3,1,2] => [1,4,5,6,3,2] => 7
[5,6,1,3,2,4] => [4,5,2,6,1,3] => [2,4,5,1,6,3] => 6
[5,6,1,3,4,2] => [4,5,2,3,6,1] => [2,4,5,3,6,1] => 7
[5,6,1,4,2,3] => [4,5,3,6,1,2] => [1,4,5,3,6,2] => 6
[5,6,1,4,3,2] => [4,5,3,1,2,6] => [1,4,5,3,2,6] => 5
[5,6,2,1,3,4] => [4,1,5,6,2,3] => [1,4,5,2,6,3] => 5
[5,6,2,1,4,3] => [4,1,5,6,3,2] => [4,5,6,1,3,2] => 10
[5,6,2,3,1,4] => [4,5,1,6,2,3] => [1,4,5,6,2,3] => 6
[5,6,2,3,4,1] => [4,5,6,2,1,3] => [2,4,5,6,1,3] => 7
[5,6,2,4,1,3] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => 12
[5,6,2,4,3,1] => [4,5,1,6,3,2] => [4,5,6,3,1,2] => 11
[5,6,3,1,2,4] => [4,5,2,6,3,1] => [4,5,6,2,3,1] => 11
[5,6,3,1,4,2] => [4,1,5,2,3,6] => [1,4,5,2,3,6] => 4
[5,6,3,2,1,4] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => 9
[5,6,3,2,4,1] => [4,5,2,1,6,3] => [4,5,6,2,1,3] => 10
[5,6,3,4,1,2] => [4,5,2,3,1,6] => [2,4,5,3,1,6] => 6
[5,6,3,4,2,1] => [4,5,2,1,3,6] => [2,4,5,1,3,6] => 5
[5,6,4,1,2,3] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => 11
[5,6,4,1,3,2] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => 10
[5,6,4,2,1,3] => [4,1,5,3,6,2] => [4,5,3,1,6,2] => 9
[5,6,4,2,3,1] => [4,5,3,1,6,2] => [4,5,3,6,1,2] => 10
[5,6,4,3,1,2] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 9
[5,6,4,3,2,1] => [4,1,5,3,2,6] => [4,5,3,1,2,6] => 8
[6,1,2,3,4,5] => [5,6,2,3,4,1] => [2,3,5,6,4,1] => 7
[6,1,2,3,5,4] => [5,6,2,4,1,3] => [2,1,5,6,4,3] => 6
[6,1,2,4,3,5] => [5,6,3,1,2,4] => [1,3,5,6,2,4] => 5
[6,1,2,4,5,3] => [5,6,3,4,1,2] => [1,3,5,6,4,2] => 6
[6,1,2,5,3,4] => [5,6,4,1,2,3] => [1,2,5,6,4,3] => 5
[6,1,2,5,4,3] => [5,6,4,1,3,2] => [5,1,6,4,3,2] => 10
[6,1,3,2,4,5] => [5,2,6,1,3,4] => [2,1,5,3,6,4] => 4
[6,1,3,2,5,4] => [5,2,6,1,4,3] => [5,2,6,1,4,3] => 9
[6,1,3,4,2,5] => [5,2,3,6,1,4] => [2,3,5,1,6,4] => 5
[6,1,3,4,5,2] => [5,2,3,4,6,1] => [2,3,5,4,6,1] => 6
[6,1,3,5,2,4] => [5,2,4,6,1,3] => [2,1,5,4,6,3] => 5
[6,1,3,5,4,2] => [5,2,4,1,3,6] => [2,1,5,4,3,6] => 4
[6,1,4,2,3,5] => [5,3,6,1,2,4] => [1,3,5,2,6,4] => 4
[6,1,4,2,5,3] => [5,3,6,1,4,2] => [3,5,6,1,4,2] => 9
[6,1,4,3,2,5] => [5,3,1,2,6,4] => [5,1,6,3,2,4] => 8
[6,1,4,3,5,2] => [5,3,1,2,4,6] => [1,3,5,2,4,6] => 3
[6,1,4,5,2,3] => [5,3,4,6,1,2] => [1,3,5,4,6,2] => 5
[6,1,4,5,3,2] => [5,3,4,1,2,6] => [1,3,5,4,2,6] => 4
[6,1,5,2,3,4] => [5,4,6,1,2,3] => [1,2,5,4,6,3] => 4
[6,1,5,2,4,3] => [5,4,6,1,3,2] => [5,1,4,6,3,2] => 9
[6,1,5,3,2,4] => [5,4,1,2,6,3] => [5,1,4,6,2,3] => 8
[6,1,5,3,4,2] => [5,4,1,2,3,6] => [1,2,5,4,3,6] => 3
[6,1,5,4,2,3] => [5,4,1,3,6,2] => [5,1,4,3,6,2] => 8
[6,1,5,4,3,2] => [5,4,1,3,2,6] => [5,1,4,3,2,6] => 7
[6,2,1,3,4,5] => [1,5,6,2,3,4] => [1,2,5,3,6,4] => 3
[6,2,1,3,5,4] => [1,5,6,2,4,3] => [5,1,6,2,4,3] => 8
[6,2,1,4,3,5] => [1,5,6,3,2,4] => [1,5,6,3,2,4] => 7
[6,2,1,4,5,3] => [1,5,6,3,4,2] => [5,1,3,6,4,2] => 8
[6,2,1,5,3,4] => [1,5,6,4,2,3] => [1,5,6,2,4,3] => 7
[6,2,1,5,4,3] => [1,5,6,4,3,2] => [5,6,4,1,3,2] => 12
[6,2,3,1,4,5] => [5,1,6,2,3,4] => [1,2,5,6,3,4] => 4
[6,2,3,1,5,4] => [5,1,6,2,4,3] => [5,1,6,4,2,3] => 9
[6,2,3,4,1,5] => [5,6,2,1,3,4] => [2,1,5,6,3,4] => 5
[6,2,3,4,5,1] => [5,6,2,3,1,4] => [2,3,5,6,1,4] => 6
[6,2,3,5,1,4] => [5,6,2,4,3,1] => [5,2,6,4,3,1] => 11
[6,2,3,5,4,1] => [5,6,2,1,4,3] => [5,2,6,4,1,3] => 10
[6,2,4,1,3,5] => [5,6,3,2,4,1] => [3,5,6,2,4,1] => 10
[6,2,4,1,5,3] => [5,1,6,3,4,2] => [5,1,6,3,4,2] => 9
[6,2,4,3,1,5] => [5,1,6,3,2,4] => [3,5,6,1,2,4] => 8
[6,2,4,3,5,1] => [5,6,3,2,1,4] => [3,5,6,2,1,4] => 9
[6,2,4,5,1,3] => [5,6,3,4,2,1] => [3,5,6,4,2,1] => 11
[6,2,4,5,3,1] => [5,6,3,1,4,2] => [3,5,6,4,1,2] => 10
[6,2,5,1,3,4] => [5,6,4,2,3,1] => [2,5,6,4,3,1] => 10
[6,2,5,1,4,3] => [5,6,4,3,1,2] => [1,5,6,4,3,2] => 9
[6,2,5,3,1,4] => [5,1,6,4,2,3] => [1,5,6,4,2,3] => 8
[6,2,5,3,4,1] => [5,6,4,2,1,3] => [2,5,6,4,1,3] => 9
[6,2,5,4,1,3] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => 14
[6,2,5,4,3,1] => [5,1,6,4,3,2] => [5,6,4,3,1,2] => 13
[6,3,1,2,4,5] => [5,2,6,3,4,1] => [2,5,6,3,4,1] => 9
[6,3,1,2,5,4] => [5,2,6,4,1,3] => [2,5,6,1,4,3] => 8
[6,3,1,4,2,5] => [1,5,2,3,6,4] => [5,1,6,2,3,4] => 7
[6,3,1,4,5,2] => [1,5,2,3,4,6] => [1,2,5,3,4,6] => 2
[6,3,1,5,2,4] => [1,5,2,4,6,3] => [5,1,4,2,6,3] => 7
[6,3,1,5,4,2] => [1,5,2,4,3,6] => [5,1,4,2,3,6] => 6
[6,3,2,1,4,5] => [1,5,2,6,3,4] => [1,5,6,2,3,4] => 6
[6,3,2,1,5,4] => [1,5,2,6,4,3] => [5,6,4,1,2,3] => 11
[6,3,2,4,1,5] => [5,2,1,6,3,4] => [2,5,6,1,3,4] => 7
[6,3,2,4,5,1] => [5,2,6,3,1,4] => [2,5,6,3,1,4] => 8
[6,3,2,5,1,4] => [5,2,6,4,3,1] => [5,6,4,2,3,1] => 13
[6,3,2,5,4,1] => [5,2,1,6,4,3] => [5,6,4,2,1,3] => 12
[6,3,4,1,2,5] => [5,2,3,6,4,1] => [5,2,6,3,4,1] => 10
[6,3,4,1,5,2] => [5,2,1,3,4,6] => [2,1,5,3,4,6] => 3
[6,3,4,2,1,5] => [5,2,1,3,6,4] => [5,2,6,1,3,4] => 8
[6,3,4,2,5,1] => [5,2,3,1,6,4] => [5,2,6,3,1,4] => 9
[6,3,4,5,1,2] => [5,2,3,4,1,6] => [2,3,5,4,1,6] => 5
[6,3,4,5,2,1] => [5,2,3,1,4,6] => [2,3,5,1,4,6] => 4
[6,3,5,1,2,4] => [5,2,4,6,3,1] => [5,2,4,6,3,1] => 10
[6,3,5,1,4,2] => [5,2,4,3,6,1] => [5,2,4,3,6,1] => 9
[6,3,5,2,1,4] => [5,2,1,4,6,3] => [5,2,4,1,6,3] => 8
[6,3,5,2,4,1] => [5,2,4,1,6,3] => [5,2,4,6,1,3] => 9
[6,3,5,4,1,2] => [5,2,4,3,1,6] => [5,2,4,3,1,6] => 8
[6,3,5,4,2,1] => [5,2,1,4,3,6] => [5,2,4,1,3,6] => 7
[6,4,1,2,3,5] => [5,3,6,2,4,1] => [3,5,2,6,4,1] => 9
[6,4,1,2,5,3] => [5,3,6,4,1,2] => [1,5,6,3,4,2] => 8
[6,4,1,3,2,5] => [5,3,2,6,1,4] => [3,5,2,1,6,4] => 7
[6,4,1,3,5,2] => [5,3,2,4,6,1] => [3,5,2,4,6,1] => 8
[6,4,1,5,2,3] => [1,5,3,4,6,2] => [5,1,3,4,6,2] => 7
[6,4,1,5,3,2] => [1,5,3,4,2,6] => [5,1,3,4,2,6] => 6
[6,4,2,1,3,5] => [1,5,3,6,2,4] => [3,5,1,2,6,4] => 6
[6,4,2,1,5,3] => [1,5,3,6,4,2] => [5,6,3,1,4,2] => 11
[6,4,2,3,1,5] => [5,3,1,6,2,4] => [3,5,1,6,2,4] => 7
[6,4,2,3,5,1] => [5,3,6,2,1,4] => [3,5,2,6,1,4] => 8
[6,4,2,5,1,3] => [5,3,6,4,2,1] => [5,6,3,4,2,1] => 13
[6,4,2,5,3,1] => [5,3,1,6,4,2] => [5,6,3,4,1,2] => 12
[6,4,3,1,2,5] => [5,3,2,6,4,1] => [5,6,3,2,4,1] => 12
[6,4,3,1,5,2] => [1,5,3,2,4,6] => [3,5,1,2,4,6] => 5
[6,4,3,2,1,5] => [1,5,3,2,6,4] => [5,6,3,1,2,4] => 10
[6,4,3,2,5,1] => [5,3,2,1,6,4] => [5,6,3,2,1,4] => 11
[6,4,3,5,1,2] => [5,3,2,4,1,6] => [3,5,2,4,1,6] => 7
[6,4,3,5,2,1] => [5,3,2,1,4,6] => [3,5,2,1,4,6] => 6
[6,4,5,1,2,3] => [5,3,4,6,2,1] => [3,5,4,6,2,1] => 10
[6,4,5,1,3,2] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => 9
[6,4,5,2,1,3] => [5,3,1,4,6,2] => [3,5,4,1,6,2] => 8
[6,4,5,2,3,1] => [5,3,4,1,6,2] => [3,5,4,6,1,2] => 9
[6,4,5,3,1,2] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => 8
[6,4,5,3,2,1] => [5,3,1,4,2,6] => [3,5,4,1,2,6] => 7
[6,5,1,2,3,4] => [5,4,6,2,3,1] => [2,5,4,6,3,1] => 9
[6,5,1,2,4,3] => [5,4,6,3,1,2] => [1,5,4,6,3,2] => 8
[6,5,1,3,2,4] => [5,4,2,6,1,3] => [2,5,4,1,6,3] => 7
[6,5,1,3,4,2] => [5,4,2,3,6,1] => [2,5,4,3,6,1] => 8
[6,5,1,4,2,3] => [5,4,3,6,1,2] => [1,5,4,3,6,2] => 7
[6,5,1,4,3,2] => [5,4,3,1,2,6] => [1,5,4,3,2,6] => 6
[6,5,2,1,3,4] => [1,5,4,6,2,3] => [1,5,4,2,6,3] => 6
[6,5,2,1,4,3] => [1,5,4,6,3,2] => [5,4,6,1,3,2] => 11
[6,5,2,3,1,4] => [5,4,1,6,2,3] => [1,5,4,6,2,3] => 7
[6,5,2,3,4,1] => [5,4,6,2,1,3] => [2,5,4,6,1,3] => 8
[6,5,2,4,1,3] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => 13
[6,5,2,4,3,1] => [5,4,1,6,3,2] => [5,4,6,3,1,2] => 12
[6,5,3,1,2,4] => [5,4,2,6,3,1] => [5,4,6,2,3,1] => 12
[6,5,3,1,4,2] => [1,5,4,2,3,6] => [1,5,4,2,3,6] => 5
[6,5,3,2,1,4] => [1,5,4,2,6,3] => [5,4,6,1,2,3] => 10
[6,5,3,2,4,1] => [5,4,2,1,6,3] => [5,4,6,2,1,3] => 11
[6,5,3,4,1,2] => [5,4,2,3,1,6] => [2,5,4,3,1,6] => 7
[6,5,3,4,2,1] => [5,4,2,1,3,6] => [2,5,4,1,3,6] => 6
[6,5,4,1,2,3] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => 12
[6,5,4,1,3,2] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => 11
[6,5,4,2,1,3] => [1,5,4,3,6,2] => [5,4,3,1,6,2] => 10
[6,5,4,2,3,1] => [5,4,3,1,6,2] => [5,4,3,6,1,2] => 11
[6,5,4,3,1,2] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 10
[6,5,4,3,2,1] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => 9
[1,3,4,5,2,6,7] => [2,3,4,7,1,5,6] => [2,3,4,1,5,7,6] => 4
[1,3,4,5,6,2,7] => [2,3,4,5,7,1,6] => [2,3,4,5,1,7,6] => 5
[1,3,4,5,6,7,2] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => 6
[1,4,3,2,5,6,7] => [3,1,2,7,4,5,6] => [1,3,7,2,4,5,6] => 5
[1,4,3,5,6,7,2] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1
[1,6,3,4,2,5,7] => [5,1,2,3,7,4,6] => [5,1,2,3,7,4,6] => 6
[1,6,3,4,7,5,2] => [5,1,2,3,6,4,7] => [5,1,2,6,3,4,7] => 6
[1,7,3,4,2,5,6] => [6,1,2,3,7,4,5] => [1,6,2,3,7,4,5] => 6
[1,7,3,4,5,2,6] => [6,1,2,3,4,7,5] => [6,1,2,3,7,4,5] => 7
[1,7,3,4,5,6,2] => [6,1,2,3,4,5,7] => [1,2,3,4,6,5,7] => 1
[2,1,3,4,5,6,7] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => 1
[2,3,1,5,4,6,7] => [1,7,2,4,3,5,6] => [1,4,7,2,3,5,6] => 6
[2,3,4,1,5,6,7] => [7,2,1,3,4,5,6] => [2,1,3,4,7,5,6] => 3
[2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => [2,3,4,5,7,1,6] => 6
[2,5,7,6,1,4,3] => [7,4,6,5,3,1,2] => [1,7,4,6,5,3,2] => 13
[2,6,7,5,1,4,3] => [7,5,6,4,3,1,2] => [1,5,7,6,4,3,2] => 13
[2,7,4,6,1,5,3] => [7,6,3,5,4,1,2] => [1,7,3,6,5,4,2] => 12
[2,7,5,6,1,4,3] => [7,6,4,5,3,1,2] => [1,4,7,6,5,3,2] => 12
[2,7,6,1,3,5,4] => [7,6,5,2,4,1,3] => [2,1,7,6,5,4,3] => 11
[2,7,6,1,4,5,3] => [7,6,5,3,4,1,2] => [1,3,7,6,5,4,2] => 11
[2,7,6,5,1,4,3] => [7,6,5,4,3,1,2] => [1,7,6,5,4,3,2] => 15
[2,7,6,5,4,1,3] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 21
[2,7,6,5,4,3,1] => [1,7,6,5,4,3,2] => [7,6,5,4,3,1,2] => 20
[3,1,4,2,7,6,5] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => 15
[3,1,4,5,2,6,7] => [1,2,3,4,7,5,6] => [1,7,2,3,4,5,6] => 5
[3,1,4,5,2,7,6] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => 11
[3,1,4,5,6,2,7] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 6
[3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[3,1,4,5,7,2,6] => [1,2,3,4,6,7,5] => [6,1,2,3,4,7,5] => 6
[3,1,4,5,7,6,2] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 5
[3,1,4,6,2,5,7] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => 5
[3,1,4,6,5,2,7] => [1,2,3,5,4,7,6] => [7,5,1,2,3,4,6] => 10
[3,1,4,6,5,7,2] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 4
[3,1,4,6,7,2,5] => [1,2,3,5,6,7,4] => [5,1,2,3,6,7,4] => 6
[3,1,4,6,7,5,2] => [1,2,3,5,6,4,7] => [5,1,2,3,6,4,7] => 5
[3,1,4,7,2,5,6] => [1,2,3,6,7,4,5] => [1,6,2,3,4,7,5] => 5
[3,1,4,7,5,2,6] => [1,2,3,6,4,7,5] => [6,7,1,2,3,4,5] => 10
[3,1,5,2,4,6,7] => [1,2,4,7,3,5,6] => [4,1,2,3,5,7,6] => 4
[3,1,5,4,6,2,7] => [1,2,4,3,5,7,6] => [7,4,1,2,3,5,6] => 9
[3,1,5,4,6,7,2] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 3
[3,1,6,2,4,5,7] => [1,2,5,7,3,4,6] => [1,5,2,3,4,7,6] => 4
[3,1,6,4,2,7,5] => [1,2,5,3,7,6,4] => [7,5,6,1,2,3,4] => 14
[3,1,6,4,7,2,5] => [1,2,5,3,6,7,4] => [5,6,1,2,3,7,4] => 9
[3,1,6,4,7,5,2] => [1,2,5,3,6,4,7] => [5,6,1,2,3,4,7] => 8
[3,1,7,2,4,5,6] => [1,2,6,7,3,4,5] => [1,2,6,3,4,7,5] => 4
[3,1,7,4,2,5,6] => [1,2,6,3,7,4,5] => [1,6,7,2,3,4,5] => 8
[3,1,7,5,2,4,6] => [1,2,6,4,7,3,5] => [4,6,1,2,3,7,5] => 8
[3,1,7,5,4,6,2] => [1,2,6,4,3,5,7] => [4,6,1,2,3,5,7] => 7
[3,2,1,6,4,5,7] => [1,2,7,5,3,4,6] => [1,5,7,2,3,4,6] => 7
[3,2,1,7,6,5,4] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => 18
[3,2,4,1,5,6,7] => [2,1,7,3,4,5,6] => [2,1,3,7,4,5,6] => 4
[3,2,4,5,6,1,7] => [2,7,3,4,1,5,6] => [2,3,4,7,1,5,6] => 6
[3,2,6,4,1,5,7] => [2,1,7,5,3,4,6] => [2,5,7,1,3,4,6] => 8
[3,4,1,5,2,6,7] => [2,1,3,4,7,5,6] => [2,7,1,3,4,5,6] => 6
[3,4,1,5,6,2,7] => [2,1,3,4,5,7,6] => [7,2,1,3,4,5,6] => 7
[3,4,1,5,6,7,2] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 1
[3,4,1,7,5,6,2] => [2,1,3,6,4,5,7] => [2,6,1,3,4,5,7] => 5
[3,4,2,1,5,6,7] => [2,1,3,7,4,5,6] => [2,1,7,3,4,5,6] => 5
[3,4,5,1,6,2,7] => [2,3,1,4,5,7,6] => [7,2,3,1,4,5,6] => 8
[3,4,5,1,6,7,2] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => 2
[3,4,5,6,1,7,2] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => 3
[3,4,5,6,2,1,7] => [2,3,4,1,5,7,6] => [7,2,3,4,1,5,6] => 9
[3,4,5,6,2,7,1] => [2,3,4,5,1,7,6] => [7,2,3,4,5,1,6] => 10
[3,4,5,6,7,1,2] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => 5
[3,4,5,6,7,2,1] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => 4
[3,4,5,7,1,6,2] => [2,3,4,6,5,7,1] => [6,2,3,4,5,7,1] => 10
[3,4,6,1,5,7,2] => [2,3,5,4,6,7,1] => [5,2,3,4,6,7,1] => 9
[3,5,1,4,6,7,2] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => 8
[3,5,4,1,6,2,7] => [2,1,4,3,5,7,6] => [7,4,2,1,3,5,6] => 10
[3,5,6,4,1,7,2] => [2,4,1,5,3,6,7] => [4,2,5,1,3,6,7] => 6
[3,6,4,1,5,7,2] => [2,1,5,3,4,6,7] => [2,5,1,3,4,6,7] => 4
[3,7,4,1,5,6,2] => [2,1,6,3,4,5,7] => [2,1,6,3,4,5,7] => 4
[3,7,4,2,1,5,6] => [2,1,6,3,7,4,5] => [2,6,7,1,3,4,5] => 9
[3,7,5,6,4,1,2] => [2,6,4,5,3,1,7] => [6,2,4,5,3,1,7] => 11
[4,1,3,5,6,7,2] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => 7
[4,2,1,3,5,6,7] => [1,3,7,2,4,5,6] => [3,1,2,4,5,7,6] => 3
[4,2,6,7,1,5,3] => [3,7,5,6,4,1,2] => [1,7,3,5,6,4,2] => 11
[4,2,7,6,5,3,1] => [3,1,7,6,5,4,2] => [7,6,5,3,4,1,2] => 19
[4,3,1,5,6,2,7] => [1,3,2,4,5,7,6] => [7,3,1,2,4,5,6] => 8
[4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 2
[4,3,1,7,5,6,2] => [1,3,2,6,4,5,7] => [3,6,1,2,4,5,7] => 6
[4,3,5,1,6,2,7] => [3,2,1,4,5,7,6] => [7,3,2,1,4,5,6] => 9
[4,3,5,1,6,7,2] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 3
[4,3,5,6,2,1,7] => [3,2,4,1,5,7,6] => [7,3,2,4,1,5,6] => 10
[4,3,6,1,5,7,2] => [3,2,5,4,6,7,1] => [5,3,2,4,6,7,1] => 10
[4,3,6,7,5,2,1] => [3,2,5,1,6,4,7] => [5,3,2,6,1,4,7] => 9
[4,5,1,3,6,7,2] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => 8
[4,5,3,1,6,2,7] => [3,1,4,2,5,7,6] => [7,3,4,1,2,5,6] => 10
[4,5,3,1,6,7,2] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => 4
[4,5,3,7,6,1,2] => [3,4,2,6,5,1,7] => [6,3,4,2,5,1,7] => 11
[4,5,6,1,3,7,2] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => 9
[4,5,6,7,1,3,2] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => 10
[4,5,6,7,2,3,1] => [3,4,5,6,1,7,2] => [3,4,5,6,7,1,2] => 10
[4,5,7,6,3,1,2] => [3,4,6,5,2,1,7] => [6,3,4,5,2,1,7] => 12
[4,7,3,6,5,1,2] => [3,6,2,5,4,1,7] => [6,3,2,5,4,1,7] => 11
[4,7,6,5,3,1,2] => [3,6,5,4,2,1,7] => [6,5,3,4,2,1,7] => 14
[5,1,6,3,7,4,2] => [1,4,5,2,6,3,7] => [4,5,1,6,2,3,7] => 8
[5,2,4,7,1,6,3] => [4,7,3,6,5,1,2] => [1,7,4,3,6,5,2] => 11
[5,2,7,6,1,4,3] => [4,7,6,5,3,1,2] => [1,7,6,4,5,3,2] => 14
[5,3,1,7,4,6,2] => [1,4,2,6,3,5,7] => [4,1,6,2,3,5,7] => 6
[5,3,2,1,7,6,4] => [1,4,2,7,6,5,3] => [7,6,4,5,1,2,3] => 17
[5,3,4,1,6,7,2] => [4,2,1,3,5,6,7] => [2,4,1,3,5,6,7] => 3
[5,3,6,1,4,7,2] => [4,2,5,3,6,7,1] => [4,5,2,3,6,7,1] => 10
[5,3,7,2,6,4,1] => [4,2,6,1,7,5,3] => [6,4,7,2,5,1,3] => 15
[5,4,1,3,6,7,2] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => 9
[5,4,3,6,1,7,2] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 6
[5,4,3,7,2,6,1] => [4,3,2,6,1,7,5] => [6,4,3,2,7,1,5] => 13
[5,4,3,7,6,1,2] => [4,3,2,6,5,1,7] => [6,4,3,2,5,1,7] => 12
[5,4,6,1,3,7,2] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1] => 10
[5,4,7,6,3,1,2] => [4,3,6,5,2,1,7] => [6,4,3,5,2,1,7] => 13
[5,6,2,7,1,4,3] => [4,5,7,6,3,1,2] => [1,7,4,5,6,3,2] => 12
[5,6,3,1,7,4,2] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => 9
[5,6,3,2,1,7,4] => [4,1,5,2,7,6,3] => [7,4,5,6,1,2,3] => 15
[5,6,4,1,2,7,3] => [4,5,3,7,6,1,2] => [1,7,4,5,3,6,2] => 11
[5,6,4,7,3,1,2] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1,7] => 11
[5,6,7,4,3,1,2] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => 12
[5,7,4,6,3,1,2] => [4,6,3,5,2,1,7] => [4,3,6,5,2,1,7] => 11
[6,1,7,3,2,4,5] => [1,5,6,2,7,3,4] => [1,5,6,2,7,3,4] => 8
[6,2,5,7,1,4,3] => [5,7,4,6,3,1,2] => [1,5,4,7,6,3,2] => 11
[6,3,1,4,7,2,5] => [1,5,2,3,6,7,4] => [5,1,6,2,3,7,4] => 8
[6,3,1,4,7,5,2] => [1,5,2,3,6,4,7] => [5,1,6,2,3,4,7] => 7
[6,3,1,7,4,2,5] => [1,5,2,6,3,7,4] => [5,6,7,1,2,3,4] => 12
[6,3,2,1,4,5,7] => [1,5,2,7,3,4,6] => [1,5,2,7,3,4,6] => 6
[6,4,2,7,5,3,1] => [5,3,1,7,6,4,2] => [7,5,6,3,4,1,2] => 18
[6,4,7,5,3,2,1] => [5,3,1,6,4,2,7] => [5,6,3,4,1,2,7] => 12
[6,5,2,7,1,4,3] => [5,4,7,6,3,1,2] => [1,7,5,4,6,3,2] => 13
[6,5,4,1,2,7,3] => [5,4,3,7,6,1,2] => [1,7,5,4,3,6,2] => 12
[6,5,4,1,3,2,7] => [5,4,3,2,7,1,6] => [5,4,3,2,1,7,6] => 11
[6,5,4,3,7,1,2] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => 11
[6,5,4,3,7,2,1] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 10
[6,5,4,7,3,1,2] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1,7] => 12
[6,5,7,4,3,1,2] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1,7] => 13
[6,7,2,3,4,5,1] => [5,6,7,2,3,1,4] => [2,3,5,6,7,1,4] => 8
[6,7,2,5,1,4,3] => [5,6,7,4,3,1,2] => [1,5,6,7,4,3,2] => 12
[6,7,3,2,1,4,5] => [5,1,6,2,7,3,4] => [1,5,6,7,2,3,4] => 9
[6,7,3,4,2,1,5] => [5,6,2,1,3,7,4] => [5,2,6,7,1,3,4] => 11
[6,7,4,3,1,5,2] => [5,1,6,3,2,4,7] => [3,5,6,1,2,4,7] => 8
[6,7,4,5,3,1,2] => [5,6,3,4,2,1,7] => [3,5,6,4,2,1,7] => 11
[6,7,5,1,2,4,3] => [5,6,4,7,3,1,2] => [1,5,6,4,7,3,2] => 11
[6,7,5,4,3,1,2] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1,7] => 14
[7,1,3,4,5,2,6] => [6,2,3,4,7,1,5] => [2,3,4,6,1,7,5] => 6
[7,2,1,3,4,5,6] => [1,6,7,2,3,4,5] => [1,2,3,6,4,7,5] => 3
[7,2,3,4,5,6,1] => [6,7,2,3,4,1,5] => [2,3,4,6,7,1,5] => 7
[7,2,5,3,1,4,6] => [6,1,7,4,2,3,5] => [1,4,6,7,2,3,5] => 8
[7,2,5,6,1,4,3] => [6,7,4,5,3,1,2] => [1,4,6,7,5,3,2] => 11
[7,2,6,5,1,4,3] => [6,7,5,4,3,1,2] => [1,6,7,5,4,3,2] => 14
[7,3,1,4,2,5,6] => [1,6,2,3,7,4,5] => [1,6,2,7,3,4,5] => 7
[7,3,1,4,5,2,6] => [1,6,2,3,4,7,5] => [6,1,2,7,3,4,5] => 8
[7,3,4,2,1,5,6] => [6,2,1,3,7,4,5] => [2,6,1,7,3,4,5] => 8
[7,4,6,5,3,1,2] => [6,3,5,4,2,1,7] => [6,3,5,4,2,1,7] => 13
[7,5,3,2,1,6,4] => [1,6,4,2,7,5,3] => [6,7,4,5,1,2,3] => 16
[7,5,6,4,3,1,2] => [6,4,5,3,2,1,7] => [4,6,5,3,2,1,7] => 13
[7,6,2,5,1,4,3] => [6,5,7,4,3,1,2] => [1,6,5,7,4,3,2] => 13
[7,6,3,5,4,1,2] => [6,5,2,4,3,1,7] => [6,2,5,4,3,1,7] => 12
[7,6,4,5,3,1,2] => [6,5,3,4,2,1,7] => [3,6,5,4,2,1,7] => 12
[7,6,5,1,2,4,3] => [6,5,4,7,3,1,2] => [1,6,5,4,7,3,2] => 12
[7,6,5,1,4,2,3] => [6,5,4,3,7,1,2] => [1,6,5,4,3,7,2] => 11
[7,6,5,3,4,1,2] => [6,5,4,2,3,1,7] => [2,6,5,4,3,1,7] => 11
[7,6,5,4,3,1,2] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 15
[7,6,5,4,3,8,2,1] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 15
[4,5,6,7,8,2,3,1] => [3,4,5,6,7,1,8,2] => [3,4,5,6,7,8,1,2] => 12
[7,6,5,4,3,2,8,1] => [6,5,4,3,2,1,8,7] => [8,6,5,4,3,2,1,7] => 22
[2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,1,7] => [2,3,4,5,6,8,1,7] => 7
[8,7,6,5,4,3,1,2] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 21
[7,8,6,5,4,3,1,2] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1,8] => 20
[8,6,7,5,4,3,1,2] => [7,5,6,4,3,2,1,8] => [5,7,6,4,3,2,1,8] => 19
[8,7,5,6,4,3,1,2] => [7,6,4,5,3,2,1,8] => [4,7,6,5,3,2,1,8] => 18
[7,8,4,3,5,6,1,2] => [6,7,3,2,4,5,1,8] => [3,2,6,7,4,5,1,8] => 11
[3,4,5,6,7,8,1,2] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1,8] => 6
[8,7,6,5,2,3,1,4] => [7,6,5,4,1,8,2,3] => [1,7,6,5,4,8,2,3] => 16
[8,7,6,4,2,3,1,5] => [7,6,5,3,1,8,2,4] => [3,7,6,5,1,8,2,4] => 16
[8,7,6,2,3,4,1,5] => [7,6,5,8,2,1,3,4] => [2,1,7,6,5,8,3,4] => 12
[7,8,4,3,2,1,5,6] => [6,1,7,3,2,8,4,5] => [3,6,7,8,1,2,4,5] => 14
[7,8,3,2,4,1,5,6] => [6,7,2,1,8,3,4,5] => [2,1,6,7,8,3,4,5] => 10
[8,7,3,2,1,4,5,6] => [1,7,6,2,8,3,4,5] => [1,2,7,6,8,3,4,5] => 10
[7,6,5,4,3,2,1,8] => [1,6,5,4,3,2,8,7] => [8,6,5,4,3,1,2,7] => 21
[3,4,1,2,5,6,7,8] => [2,3,8,4,5,6,7,1] => [2,3,4,8,5,6,7,1] => 10
[2,1,3,4,5,6,7,8] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,7] => 1
[5,4,3,2,8,7,6,1] => [4,3,2,1,8,7,6,5] => [8,7,6,4,3,2,1,5] => 24
[1,4,3,5,6,7,8,2] => [3,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 1
[1,3,4,5,6,7,8,2] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => 7
[3,2,1,8,7,6,5,4] => [1,2,8,7,6,5,4,3] => [8,7,6,5,4,1,2,3] => 25
[2,3,1,8,7,6,5,4] => [1,8,2,7,6,5,4,3] => [8,7,6,5,1,4,2,3] => 24
[1,3,2,8,7,6,5,4] => [2,8,1,7,6,5,4,3] => [8,7,6,5,2,1,4,3] => 24
[3,4,2,1,6,8,7,5] => [2,1,3,8,5,7,6,4] => [8,7,2,5,1,3,6,4] => 18
[3,2,4,1,7,6,8,5] => [2,1,8,3,6,5,7,4] => [8,2,6,5,1,3,7,4] => 16
[3,5,4,2,1,8,7,6] => [2,1,4,3,8,7,6,5] => [8,7,6,4,2,1,3,5] => 22
[3,2,7,6,5,4,1,8] => [2,1,8,6,5,4,3,7] => [6,8,5,4,2,1,3,7] => 19
[1,3,2,4,5,6,7,8] => [2,8,1,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 2
[1,8,4,3,5,6,7,2] => [7,1,3,2,4,5,6,8] => [1,3,2,7,4,5,6,8] => 4
[2,6,7,8,1,3,4,5] => [8,5,6,7,2,3,4,1] => [2,3,5,6,8,7,4,1] => 12
[2,1,6,3,4,8,5,7] => [8,1,5,2,3,7,4,6] => [1,8,2,5,3,7,4,6] => 10
[3,1,4,2,5,6,7,8] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 4
[3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[3,4,1,5,6,7,8,2] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 1
[3,4,5,6,7,1,8,2] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => 4
[3,5,6,1,7,2,4,8] => [2,4,1,5,6,8,3,7] => [4,2,5,1,6,3,8,7] => 8
[1,3,4,5,7,8,2,6] => [2,3,4,6,7,8,1,5] => [2,3,4,1,6,7,8,5] => 6
[1,3,2,4,5,8,6,7] => [2,8,1,3,4,7,5,6] => [2,8,1,3,4,5,7,6] => 8
[4,1,5,2,7,3,8,6] => [1,3,4,8,6,2,7,5] => [8,3,6,1,4,7,2,5] => 16
[1,4,5,2,7,3,8,6] => [3,4,8,1,6,2,7,5] => [8,3,4,1,6,7,2,5] => 15
[4,6,1,7,2,3,5,8] => [3,1,5,6,8,2,4,7] => [3,1,5,2,6,4,8,7] => 6
[4,1,2,3,5,7,8,6] => [3,8,2,4,6,7,1,5] => [3,2,4,1,6,8,7,5] => 8
[4,1,2,3,8,5,6,7] => [3,8,2,7,1,4,5,6] => [3,2,1,4,5,8,7,6] => 6
[1,5,2,3,4,7,6,8] => [4,8,1,2,3,6,5,7] => [1,8,2,4,3,6,5,7] => 8
[1,6,7,8,2,3,4,5] => [5,6,7,8,1,2,3,4] => [1,2,3,5,6,7,8,4] => 4
[6,8,5,7,3,1,4,2] => [5,7,4,1,6,2,3,8] => [1,5,4,7,6,2,3,8] => 10
[7,3,2,8,6,5,1,4] => [6,2,8,7,5,4,3,1] => [8,6,7,5,4,2,3,1] => 26
[5,7,2,4,8,1,3,6] => [4,6,8,3,7,2,5,1] => [4,3,6,2,8,7,5,1] => 15
[8,7,6,5,2,4,1,3] => [7,6,5,4,8,3,2,1] => [7,6,5,4,8,3,2,1] => 24
[2,6,8,1,3,7,4,5] => [8,5,7,2,6,1,3,4] => [2,1,5,3,8,7,6,4] => 9
[2,3,8,5,1,7,4,6] => [8,2,1,7,4,6,3,5] => [2,8,1,7,4,3,6,5] => 13
[3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,9,1,8] => 8
[3,5,2,7,4,8,1,6] => [2,4,8,6,3,7,5,1] => [8,4,6,2,7,3,5,1] => 20
[2,1,5,7,4,8,6,3] => [8,1,4,6,3,7,5,2] => [6,4,8,1,7,3,5,2] => 18
[5,6,7,8,3,1,4,2] => [4,5,6,1,7,2,3,8] => [1,4,5,6,7,2,3,8] => 8
[5,6,7,8,1,3,2,4] => [4,5,6,7,2,8,1,3] => [2,4,5,6,7,1,8,3] => 10
[3,5,2,7,1,8,4,6] => [2,4,1,8,6,7,3,5] => [2,8,4,1,6,3,7,5] => 12
[7,8,3,2,1,6,5,4] => [6,1,7,2,8,5,4,3] => [6,7,8,5,4,1,2,3] => 22
[6,5,4,1,2,3,8,7] => [5,4,3,8,2,7,1,6] => [5,4,3,2,1,8,7,6] => 13
[7,8,3,2,1,5,4,6] => [6,1,7,2,8,4,3,5] => [4,6,7,8,1,2,3,5] => 15
[6,3,8,2,1,4,5,7] => [5,2,1,7,8,3,4,6] => [2,5,1,7,3,4,8,6] => 8
[2,6,8,4,7,1,5,3] => [8,5,7,3,6,4,1,2] => [1,5,8,3,7,6,4,2] => 15
[3,1,4,2,8,7,6,5] => [1,2,3,8,7,6,5,4] => [8,7,6,5,1,2,3,4] => 22
[6,1,5,2,8,3,7,4] => [5,4,8,1,7,2,6,3] => [5,4,8,1,7,2,6,3] => 16
[5,3,6,2,4,8,1,7] => [4,2,5,8,3,7,6,1] => [8,4,5,2,3,7,6,1] => 18
[5,3,7,8,1,4,2,6] => [4,2,6,7,3,8,1,5] => [4,2,6,3,7,1,8,5] => 11
[6,4,7,8,5,2,3,1] => [5,3,6,7,4,1,8,2] => [5,6,3,7,4,8,1,2] => 17
[4,6,1,7,8,5,2,3] => [3,1,5,6,7,4,8,2] => [5,3,6,1,7,4,8,2] => 13
[8,7,6,1,4,3,2,5] => [7,6,5,3,1,2,8,4] => [7,1,6,5,8,3,2,4] => 17
[7,6,8,1,3,2,4,5] => [6,5,7,2,8,1,3,4] => [2,1,6,5,7,3,8,4] => 9
[3,2,6,8,4,1,5,7] => [2,8,5,1,7,3,4,6] => [2,1,8,5,3,7,4,6] => 10
[3,2,7,1,8,4,6,5] => [2,1,8,6,7,3,5,4] => [8,2,6,1,7,3,5,4] => 16
[6,5,1,2,3,8,7,4] => [5,4,8,2,7,1,6,3] => [5,4,8,2,1,7,6,3] => 16
[7,3,8,4,2,6,1,5] => [6,2,7,3,8,5,4,1] => [6,7,8,5,2,3,4,1] => 22
[3,4,8,1,5,6,7,2] => [2,3,7,4,5,6,8,1] => [2,3,7,4,5,6,8,1] => 10
[4,6,3,5,8,2,7,1] => [3,5,2,4,7,1,8,6] => [7,3,2,5,4,8,1,6] => 14
[1,4,7,5,8,3,2,6] => [3,6,1,4,7,2,8,5] => [6,3,7,1,4,8,2,5] => 14
[6,2,8,7,5,4,3,1] => [5,1,8,7,6,4,3,2] => [8,7,5,6,4,3,1,2] => 26
[3,2,1,8,7,4,5,6] => [1,2,8,7,6,3,4,5] => [1,2,8,7,6,3,4,5] => 12
[4,3,7,2,6,8,5,1] => [3,2,6,8,5,1,7,4] => [6,5,3,2,8,7,1,4] => 17
[3,1,4,5,6,8,7,2] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 6
[5,8,3,7,4,2,6,1] => [4,7,2,6,3,1,8,5] => [7,4,6,2,8,3,1,5] => 18
[3,1,4,8,6,5,7,2] => [1,2,3,7,5,4,6,8] => [5,7,1,2,3,4,6,8] => 9
[4,1,2,3,6,8,7,5] => [3,8,2,5,7,1,6,4] => [5,3,2,8,1,7,6,4] => 14
[3,8,2,1,4,6,5,7] => [2,1,7,8,3,5,4,6] => [2,7,1,8,3,5,4,6] => 11
[5,1,2,6,4,8,7,3] => [4,8,5,1,3,7,6,2] => [8,4,1,7,5,3,6,2] => 18
[7,4,8,5,2,6,1,3] => [6,3,7,4,8,5,2,1] => [6,7,8,3,4,5,2,1] => 22
[6,3,7,4,8,5,1,2] => [5,2,6,3,7,4,1,8] => [5,6,7,2,3,4,1,8] => 15
[4,3,8,7,1,2,5,6] => [3,2,7,6,8,4,5,1] => [3,7,6,2,4,8,5,1] => 16
[3,4,5,6,7,8,9,1,2] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1,9] => 7
[3,4,5,6,7,8,9,10,1,2] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1,10] => 8
[3,7,8,1,6,2,4,5] => [2,6,7,5,8,1,3,4] => [2,1,6,3,7,5,8,4] => 8
[8,1,4,3,2,7,6,5] => [7,3,1,2,8,6,5,4] => [7,8,6,1,5,3,2,4] => 21
[6,4,3,8,2,5,1,7] => [5,3,2,7,1,8,4,6] => [5,3,7,2,1,8,4,6] => 13
[6,5,3,7,8,2,1,4] => [5,4,2,6,1,7,8,3] => [5,4,6,2,7,1,8,3] => 14
[5,3,7,8,2,1,4,6] => [4,2,6,1,7,8,3,5] => [4,2,6,1,7,3,8,5] => 10
[6,1,8,3,2,4,5,7] => [1,5,7,2,8,3,4,6] => [1,5,2,7,3,8,4,6] => 8
[1,8,2,4,3,5,6,7] => [7,8,1,3,2,4,5,6] => [1,3,2,7,4,8,5,6] => 6
[1,6,2,5,3,4,7,8] => [5,8,1,4,2,3,6,7] => [1,5,2,4,3,8,6,7] => 6
[5,6,8,3,2,1,4,7] => [4,5,1,7,2,8,3,6] => [4,5,1,7,8,2,3,6] => 12
[5,6,3,2,7,8,1,4] => [4,5,2,8,6,7,3,1] => [4,8,5,6,2,7,3,1] => 19
[2,5,8,7,6,1,4,3] => [8,4,7,6,5,3,1,2] => [1,8,7,4,6,5,3,2] => 19
[3,4,5,2,7,8,1,6] => [2,3,4,8,6,7,5,1] => [8,2,6,3,4,7,5,1] => 17
[8,2,5,4,7,1,6,3] => [7,8,4,3,6,5,1,2] => [1,7,4,8,6,3,5,2] => 16
[1,8,7,3,4,5,6,2] => [7,1,6,2,3,4,5,8] => [1,2,3,7,4,6,5,8] => 4
[8,5,2,3,7,1,6,4] => [7,4,8,2,6,5,1,3] => [2,7,4,8,1,6,5,3] => 15
[8,3,2,7,6,5,1,4] => [7,2,8,6,5,4,3,1] => [7,8,6,5,4,2,3,1] => 26
[8,7,6,5,4,1,3,2] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1] => 22
[2,1,8,7,6,3,5,4] => [8,1,7,6,5,2,4,3] => [8,1,7,6,5,2,4,3] => 20
[5,3,2,1,8,7,6,4] => [1,4,2,8,7,6,5,3] => [8,7,6,4,5,1,2,3] => 24
[3,1,8,6,7,4,5,2] => [1,2,7,5,6,3,4,8] => [1,7,2,5,3,6,4,8] => 8
[7,4,8,5,6,2,3,1] => [6,3,7,4,5,1,8,2] => [3,6,7,4,5,8,1,2] => 16
[5,1,6,2,8,4,7,3] => [1,4,5,8,7,3,6,2] => [4,8,5,1,3,7,6,2] => 16
[3,1,7,4,8,5,6,2] => [1,2,6,3,7,4,5,8] => [1,6,7,2,3,4,5,8] => 8
[2,4,8,5,3,1,6,7] => [8,3,1,7,4,2,5,6] => [3,4,8,1,7,2,5,6] => 12
[3,6,1,8,4,2,5,7] => [2,1,5,7,3,8,4,6] => [5,2,7,1,3,8,4,6] => 11
[5,8,2,3,7,6,4,1] => [4,7,8,2,1,6,5,3] => [7,4,8,2,6,5,1,3] => 20
[6,2,8,1,3,7,4,5] => [5,8,7,2,6,1,3,4] => [2,1,5,8,3,7,6,4] => 10
[3,1,4,5,8,6,7,2] => [1,2,3,4,7,5,6,8] => [1,7,2,3,4,5,6,8] => 5
[1,4,2,8,7,6,5,3] => [3,8,1,7,6,5,4,2] => [8,7,6,3,5,1,4,2] => 24
[1,4,5,2,8,7,3,6] => [3,4,8,1,7,6,2,5] => [3,8,4,1,7,2,6,5] => 14
[6,3,5,8,2,1,7,4] => [5,2,4,1,7,8,6,3] => [7,5,2,4,8,1,6,3] => 17
[2,1,3,4,5,6,7,8,9] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,9,8] => 1
[2,1,3,4,5,6,7,8,9,10] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,10,9] => 1
[2,1,3,4,5,6,7,8,9,10,11] => [11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[7,1,6,5,2,4,3,8] => [6,5,1,4,8,3,2,7] => [6,5,1,4,3,8,2,7] => 14
[8,1,6,5,2,3,7,4] => [7,5,1,4,8,2,6,3] => [7,1,5,4,8,2,6,3] => 15
[6,5,1,4,3,2,7,8] => [5,4,3,1,2,8,6,7] => [1,8,5,4,3,2,6,7] => 12
[5,6,3,2,1,8,7,4] => [4,1,5,2,8,7,6,3] => [8,7,4,5,6,1,2,3] => 22
[6,7,3,8,2,1,5,4] => [5,6,2,1,7,8,4,3] => [5,6,7,8,2,1,4,3] => 18
[6,2,7,8,5,4,1,3] => [5,8,6,7,4,3,2,1] => [5,8,6,7,4,3,2,1] => 24
[2,8,1,7,3,5,6,4] => [8,7,6,1,2,4,5,3] => [4,1,2,8,7,6,5,3] => 13
[6,7,3,1,8,4,2,5] => [5,1,6,2,7,3,8,4] => [5,6,7,8,1,2,3,4] => 16
[7,3,1,5,8,4,2,6] => [1,6,2,4,7,3,8,5] => [6,7,1,4,2,8,3,5] => 14
[2,8,6,7,4,5,1,3] => [8,7,5,6,3,4,2,1] => [3,5,8,7,6,4,2,1] => 20
[2,8,4,7,3,6,1,5] => [8,7,3,6,2,5,4,1] => [8,3,2,7,6,5,4,1] => 20
[5,8,6,7,2,4,1,3] => [4,7,5,6,8,3,2,1] => [4,7,5,6,8,3,2,1] => 20
[1,3,4,5,6,7,8,9,2] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1] => 8
[1,3,4,5,6,7,8,9,10,2] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1] => 9
[4,6,3,8,2,5,1,7] => [3,5,2,7,1,8,4,6] => [5,3,2,7,1,8,4,6] => 12
[7,8,4,6,2,3,1,5] => [6,7,3,5,1,8,2,4] => [3,1,6,7,5,8,2,4] => 12
[5,7,8,6,2,3,1,4] => [4,6,7,5,1,8,2,3] => [1,6,4,7,5,8,2,3] => 13
[7,1,4,3,5,6,8,2] => [6,3,1,2,4,5,7,8] => [1,3,2,6,4,5,7,8] => 3
[3,1,8,6,4,2,7,5] => [1,2,7,5,3,8,6,4] => [7,8,5,6,1,2,3,4] => 20
[8,7,6,5,4,3,9,2,1] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => 21
[9,8,7,6,5,4,3,10,2,1] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => 28
[1,2,8,4,3,5,6,7] => [8,7,1,3,2,4,5,6] => [1,3,2,8,4,7,5,6] => 7
[1,6,3,8,2,4,7,5] => [5,1,2,7,8,3,6,4] => [5,7,1,2,8,3,6,4] => 13
[1,8,3,2,4,5,6,7] => [7,1,2,8,3,4,5,6] => [1,2,3,7,4,8,5,6] => 5
[1,8,7,3,4,2,5,6] => [7,1,6,2,3,8,4,5] => [1,7,2,6,3,8,4,5] => 10
[4,7,8,3,2,1,5,6] => [3,6,1,7,2,8,4,5] => [3,6,1,7,8,2,4,5] => 12
[4,6,3,1,5,2,7,8] => [3,1,5,2,4,8,6,7] => [3,8,1,5,2,4,6,7] => 10
[4,6,7,2,3,1,5,8] => [3,5,6,1,8,2,4,7] => [3,1,5,6,2,8,4,7] => 8
[3,2,5,1,6,8,7,4] => [2,1,8,4,5,7,6,3] => [8,7,2,1,4,5,6,3] => 17
[6,5,1,7,8,4,2,3] => [1,5,4,6,7,3,8,2] => [5,4,6,1,7,3,8,2] => 14
[3,2,5,8,1,6,7,4] => [2,8,4,7,5,6,1,3] => [2,1,8,4,7,5,6,3] => 12
[4,3,7,2,6,8,1,5] => [3,2,6,8,5,7,4,1] => [6,5,3,2,8,7,4,1] => 18
[2,4,1,7,3,8,6,5] => [1,8,3,6,2,7,5,4] => [8,6,1,7,3,5,2,4] => 19
[3,5,8,2,1,7,4,6] => [2,4,1,7,8,6,3,5] => [4,7,2,1,8,3,6,5] => 13
[3,5,2,8,1,7,4,6] => [2,4,8,7,6,1,3,5] => [2,1,8,7,4,3,6,5] => 12
[8,3,7,4,6,1,5,2] => [7,2,6,3,5,4,8,1] => [7,2,6,3,5,4,8,1] => 16
[6,3,1,8,4,5,7,2] => [1,5,2,7,3,4,6,8] => [1,5,2,7,3,4,6,8] => 6
[3,1,6,8,4,5,7,2] => [1,2,5,7,3,4,6,8] => [1,5,2,3,4,7,6,8] => 4
[5,7,1,8,3,4,6,2] => [4,1,6,7,2,3,5,8] => [1,4,2,6,3,7,5,8] => 5
[3,7,8,1,5,2,4,6] => [2,6,7,4,8,1,3,5] => [2,1,6,4,7,3,8,5] => 8
[7,1,2,8,6,4,3,5] => [6,8,7,1,5,3,2,4] => [1,8,6,3,7,5,2,4] => 16
[3,7,4,8,1,6,2,5] => [2,6,3,7,5,8,1,4] => [2,6,7,3,1,5,8,4] => 12
[8,7,3,5,1,4,2,6] => [7,6,2,4,3,8,1,5] => [2,7,4,6,3,1,8,5] => 13
[3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[6,7,1,8,4,5,2,3] => [5,1,6,7,3,4,8,2] => [5,1,6,3,7,4,8,2] => 12
[3,6,2,1,4,8,7,5] => [2,1,5,8,3,7,6,4] => [8,5,7,2,1,3,6,4] => 18
[7,4,1,2,3,8,6,5] => [6,3,8,2,7,1,5,4] => [6,3,8,2,1,7,5,4] => 16
[2,4,3,6,5,8,1,7] => [8,3,2,5,4,7,6,1] => [8,3,7,5,2,4,6,1] => 20
[6,4,2,8,7,5,3,1] => [5,3,1,8,7,6,4,2] => [8,7,5,6,3,4,1,2] => 25
[6,4,2,8,7,5,1,3] => [5,3,8,7,6,4,2,1] => [8,7,5,6,3,4,2,1] => 26
[6,1,7,3,4,8,2,5] => [1,5,6,2,3,7,8,4] => [5,1,6,2,7,3,8,4] => 10
[3,7,2,1,4,5,8,6] => [2,1,6,8,3,4,7,5] => [6,2,8,1,3,4,7,5] => 12
[3,7,2,1,5,8,4,6] => [2,1,6,8,4,7,3,5] => [4,6,2,1,3,8,7,5] => 11
[1,6,8,7,4,3,2,5] => [5,7,1,6,3,2,8,4] => [5,7,6,8,1,3,2,4] => 18
[5,4,6,1,3,7,2,8] => [4,3,5,2,6,8,1,7] => [4,3,5,2,6,1,8,7] => 10
[7,1,5,8,4,3,2,6] => [6,4,7,1,3,2,8,5] => [6,7,1,4,8,3,2,5] => 16
[9,8,7,6,5,4,3,1,2] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 28
[10,9,8,7,6,5,4,3,1,2] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => 36
[2,5,4,1,6,3,8,7] => [1,8,4,3,5,2,7,6] => [8,4,3,7,1,5,2,6] => 17
[5,3,8,2,1,6,4,7] => [4,2,1,7,8,5,3,6] => [4,7,2,8,1,5,3,6] => 14
[2,7,6,4,1,8,5,3] => [1,8,6,5,3,7,4,2] => [6,8,5,7,3,1,4,2] => 22
[7,3,5,6,8,1,4,2] => [6,2,4,5,7,3,8,1] => [4,2,6,5,7,3,8,1] => 13
[7,8,2,6,1,5,3,4] => [6,7,8,5,4,1,2,3] => [1,2,6,7,8,5,4,3] => 12
[2,8,4,7,5,6,1,3] => [8,7,3,6,4,5,2,1] => [3,8,4,7,6,5,2,1] => 20
[7,5,2,8,6,4,1,3] => [6,4,8,7,5,3,2,1] => [8,6,7,4,5,3,2,1] => 26
[7,3,1,8,4,2,5,6] => [1,6,2,7,3,8,4,5] => [1,6,7,8,2,3,4,5] => 12
[2,5,3,7,8,1,6,4] => [8,4,2,6,7,5,1,3] => [2,8,4,1,6,7,5,3] => 14
[5,8,1,3,6,2,7,4] => [4,7,2,5,8,1,6,3] => [4,5,2,7,8,1,6,3] => 14
[7,8,5,2,4,6,3,1] => [6,7,4,8,3,1,5,2] => [4,6,7,3,8,5,1,2] => 18
[2,4,8,6,1,3,5,7] => [8,3,7,5,2,4,6,1] => [3,2,8,5,7,4,6,1] => 15
[4,6,8,2,1,3,5,7] => [3,5,1,7,8,2,4,6] => [3,1,5,2,7,4,8,6] => 7
[8,1,6,3,7,2,5,4] => [7,5,1,2,6,8,4,3] => [5,7,1,6,8,2,4,3] => 16
[3,2,7,1,8,5,6,4] => [2,1,8,6,7,4,5,3] => [8,2,6,1,4,7,5,3] => 16
[2,1,7,3,8,5,6,4] => [8,1,6,2,7,4,5,3] => [8,1,6,2,7,4,5,3] => 16
[6,5,7,4,8,1,3,2] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,8,1] => 16
[3,4,6,1,5,7,8,2] => [2,3,5,4,6,7,8,1] => [5,2,3,4,6,7,8,1] => 10
[5,8,7,6,4,3,1,2] => [4,7,6,5,3,2,1,8] => [7,6,4,5,3,2,1,8] => 20
[1,4,3,7,2,6,5,8] => [3,1,2,6,8,5,4,7] => [6,1,8,3,2,5,4,7] => 12
[8,2,7,6,5,1,4,3] => [7,8,6,5,4,3,1,2] => [1,7,8,6,5,4,3,2] => 20
[4,3,8,7,6,2,1,5] => [3,2,1,7,6,5,8,4] => [7,6,5,3,2,1,8,4] => 19
[2,8,7,6,5,4,1,3] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 28
[2,1,7,3,4,8,6,5] => [8,1,6,2,3,7,5,4] => [8,6,1,2,7,5,3,4] => 17
[1,5,8,2,7,6,3,4] => [4,7,8,1,6,5,2,3] => [1,7,4,8,2,6,5,3] => 14
[1,2,5,3,8,7,4,6] => [8,4,1,2,7,6,3,5] => [4,8,1,2,7,6,3,5] => 14
[4,2,8,7,6,5,3,1] => [3,1,8,7,6,5,4,2] => [8,7,6,5,3,4,1,2] => 26
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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 1,2,2,1 1,3,5,6,5,3,1 1,4,9,15,20,22,20,15,9,4,1 1,5,14,29,49,71,90,101,101,90,71,49,29,14,5,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + 2\ q^{2} + q^{3}$
$F_{4} = 1 + 3\ q + 5\ q^{2} + 6\ q^{3} + 5\ q^{4} + 3\ q^{5} + q^{6}$
$F_{5} = 1 + 4\ q + 9\ q^{2} + 15\ q^{3} + 20\ q^{4} + 22\ q^{5} + 20\ q^{6} + 15\ q^{7} + 9\ q^{8} + 4\ q^{9} + q^{10}$
$F_{6} = 1 + 5\ q + 14\ q^{2} + 29\ q^{3} + 49\ q^{4} + 71\ q^{5} + 90\ q^{6} + 101\ q^{7} + 101\ q^{8} + 90\ q^{9} + 71\ q^{10} + 49\ q^{11} + 29\ q^{12} + 14\ q^{13} + 5\ q^{14} + q^{15}$
Description
The number of inversions of a permutation.
This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$.
This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$.
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
toric promotion
Description
Toric promotion of a permutation.
Let $\sigma\in\mathfrak S_n$ be a permutation and let
$ \tau_{i, j}(\sigma) = \begin{cases} \sigma & \text{if $|\sigma^{-1}(i) - \sigma^{-1}(j)| = 1$}\\ (i, j)\circ\sigma & \text{otherwise}. \end{cases} $
The toric promotion operator is the product $\tau_{n,1}\tau_{n-1,n}\dots\tau_{1,2}$.
This is the special case of toric promotion on graphs for the path graph. Its order is $n-1$.
Let $\sigma\in\mathfrak S_n$ be a permutation and let
$ \tau_{i, j}(\sigma) = \begin{cases} \sigma & \text{if $|\sigma^{-1}(i) - \sigma^{-1}(j)| = 1$}\\ (i, j)\circ\sigma & \text{otherwise}. \end{cases} $
The toric promotion operator is the product $\tau_{n,1}\tau_{n-1,n}\dots\tau_{1,2}$.
This is the special case of toric promotion on graphs for the path graph. Its order is $n-1$.
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