Identifier
-
Mp00090:
Permutations
—cycle-as-one-line notation⟶
Permutations
St000255: Permutations ⟶ ℤ
Values
[1] => [1] => 1
[1,2] => [1,2] => 1
[2,1] => [1,2] => 1
[1,2,3] => [1,2,3] => 1
[1,3,2] => [1,2,3] => 1
[2,1,3] => [1,2,3] => 1
[2,3,1] => [1,2,3] => 1
[3,1,2] => [1,3,2] => 2
[3,2,1] => [1,3,2] => 2
[1,2,3,4] => [1,2,3,4] => 1
[1,2,4,3] => [1,2,3,4] => 1
[1,3,2,4] => [1,2,3,4] => 1
[1,3,4,2] => [1,2,3,4] => 1
[1,4,2,3] => [1,2,4,3] => 3
[1,4,3,2] => [1,2,4,3] => 3
[2,1,3,4] => [1,2,3,4] => 1
[2,1,4,3] => [1,2,3,4] => 1
[2,3,1,4] => [1,2,3,4] => 1
[2,3,4,1] => [1,2,3,4] => 1
[2,4,1,3] => [1,2,4,3] => 3
[2,4,3,1] => [1,2,4,3] => 3
[3,1,2,4] => [1,3,2,4] => 2
[3,1,4,2] => [1,3,4,2] => 3
[3,2,1,4] => [1,3,2,4] => 2
[3,2,4,1] => [1,3,4,2] => 3
[3,4,1,2] => [1,3,2,4] => 2
[3,4,2,1] => [1,3,2,4] => 2
[4,1,2,3] => [1,4,3,2] => 5
[4,1,3,2] => [1,4,2,3] => 3
[4,2,1,3] => [1,4,3,2] => 5
[4,2,3,1] => [1,4,2,3] => 3
[4,3,1,2] => [1,4,2,3] => 3
[4,3,2,1] => [1,4,2,3] => 3
[1,2,3,4,5] => [1,2,3,4,5] => 1
[1,2,3,5,4] => [1,2,3,4,5] => 1
[1,2,4,3,5] => [1,2,3,4,5] => 1
[1,2,4,5,3] => [1,2,3,4,5] => 1
[1,2,5,3,4] => [1,2,3,5,4] => 4
[1,2,5,4,3] => [1,2,3,5,4] => 4
[1,3,2,4,5] => [1,2,3,4,5] => 1
[1,3,2,5,4] => [1,2,3,4,5] => 1
[1,3,4,2,5] => [1,2,3,4,5] => 1
[1,3,4,5,2] => [1,2,3,4,5] => 1
[1,3,5,2,4] => [1,2,3,5,4] => 4
[1,3,5,4,2] => [1,2,3,5,4] => 4
[1,4,2,3,5] => [1,2,4,3,5] => 3
[1,4,2,5,3] => [1,2,4,5,3] => 6
[1,4,3,2,5] => [1,2,4,3,5] => 3
[1,4,3,5,2] => [1,2,4,5,3] => 6
[1,4,5,2,3] => [1,2,4,3,5] => 3
[1,4,5,3,2] => [1,2,4,3,5] => 3
[1,5,2,3,4] => [1,2,5,4,3] => 14
[1,5,2,4,3] => [1,2,5,3,4] => 6
[1,5,3,2,4] => [1,2,5,4,3] => 14
[1,5,3,4,2] => [1,2,5,3,4] => 6
[1,5,4,2,3] => [1,2,5,3,4] => 6
[1,5,4,3,2] => [1,2,5,3,4] => 6
[2,1,3,4,5] => [1,2,3,4,5] => 1
[2,1,3,5,4] => [1,2,3,4,5] => 1
[2,1,4,3,5] => [1,2,3,4,5] => 1
[2,1,4,5,3] => [1,2,3,4,5] => 1
[2,1,5,3,4] => [1,2,3,5,4] => 4
[2,1,5,4,3] => [1,2,3,5,4] => 4
[2,3,1,4,5] => [1,2,3,4,5] => 1
[2,3,1,5,4] => [1,2,3,4,5] => 1
[2,3,4,1,5] => [1,2,3,4,5] => 1
[2,3,4,5,1] => [1,2,3,4,5] => 1
[2,3,5,1,4] => [1,2,3,5,4] => 4
[2,3,5,4,1] => [1,2,3,5,4] => 4
[2,4,1,3,5] => [1,2,4,3,5] => 3
[2,4,1,5,3] => [1,2,4,5,3] => 6
[2,4,3,1,5] => [1,2,4,3,5] => 3
[2,4,3,5,1] => [1,2,4,5,3] => 6
[2,4,5,1,3] => [1,2,4,3,5] => 3
[2,4,5,3,1] => [1,2,4,3,5] => 3
[2,5,1,3,4] => [1,2,5,4,3] => 14
[2,5,1,4,3] => [1,2,5,3,4] => 6
[2,5,3,1,4] => [1,2,5,4,3] => 14
[2,5,3,4,1] => [1,2,5,3,4] => 6
[2,5,4,1,3] => [1,2,5,3,4] => 6
[2,5,4,3,1] => [1,2,5,3,4] => 6
[3,1,2,4,5] => [1,3,2,4,5] => 2
[3,1,2,5,4] => [1,3,2,4,5] => 2
[3,1,4,2,5] => [1,3,4,2,5] => 3
[3,1,4,5,2] => [1,3,4,5,2] => 4
[3,1,5,2,4] => [1,3,5,4,2] => 11
[3,1,5,4,2] => [1,3,5,2,4] => 8
[3,2,1,4,5] => [1,3,2,4,5] => 2
[3,2,1,5,4] => [1,3,2,4,5] => 2
[3,2,4,1,5] => [1,3,4,2,5] => 3
[3,2,4,5,1] => [1,3,4,5,2] => 4
[3,2,5,1,4] => [1,3,5,4,2] => 11
[3,2,5,4,1] => [1,3,5,2,4] => 8
[3,4,1,2,5] => [1,3,2,4,5] => 2
[3,4,1,5,2] => [1,3,2,4,5] => 2
[3,4,2,1,5] => [1,3,2,4,5] => 2
[3,4,2,5,1] => [1,3,2,4,5] => 2
[3,4,5,1,2] => [1,3,5,2,4] => 8
[3,4,5,2,1] => [1,3,5,2,4] => 8
[3,5,1,2,4] => [1,3,2,5,4] => 8
[3,5,1,4,2] => [1,3,2,5,4] => 8
>>> Load all 1307 entries. <<<[3,5,2,1,4] => [1,3,2,5,4] => 8
[3,5,2,4,1] => [1,3,2,5,4] => 8
[3,5,4,1,2] => [1,3,4,2,5] => 3
[3,5,4,2,1] => [1,3,4,2,5] => 3
[4,1,2,3,5] => [1,4,3,2,5] => 5
[4,1,2,5,3] => [1,4,5,3,2] => 9
[4,1,3,2,5] => [1,4,2,3,5] => 3
[4,1,3,5,2] => [1,4,5,2,3] => 6
[4,1,5,2,3] => [1,4,2,3,5] => 3
[4,1,5,3,2] => [1,4,3,5,2] => 7
[4,2,1,3,5] => [1,4,3,2,5] => 5
[4,2,1,5,3] => [1,4,5,3,2] => 9
[4,2,3,1,5] => [1,4,2,3,5] => 3
[4,2,3,5,1] => [1,4,5,2,3] => 6
[4,2,5,1,3] => [1,4,2,3,5] => 3
[4,2,5,3,1] => [1,4,3,5,2] => 7
[4,3,1,2,5] => [1,4,2,3,5] => 3
[4,3,1,5,2] => [1,4,5,2,3] => 6
[4,3,2,1,5] => [1,4,2,3,5] => 3
[4,3,2,5,1] => [1,4,5,2,3] => 6
[4,3,5,1,2] => [1,4,2,3,5] => 3
[4,3,5,2,1] => [1,4,2,3,5] => 3
[4,5,1,2,3] => [1,4,2,5,3] => 8
[4,5,1,3,2] => [1,4,3,2,5] => 5
[4,5,2,1,3] => [1,4,2,5,3] => 8
[4,5,2,3,1] => [1,4,3,2,5] => 5
[4,5,3,1,2] => [1,4,2,5,3] => 8
[4,5,3,2,1] => [1,4,2,5,3] => 8
[5,1,2,3,4] => [1,5,4,3,2] => 14
[5,1,2,4,3] => [1,5,3,2,4] => 7
[5,1,3,2,4] => [1,5,4,2,3] => 9
[5,1,3,4,2] => [1,5,2,3,4] => 4
[5,1,4,2,3] => [1,5,3,4,2] => 10
[5,1,4,3,2] => [1,5,2,3,4] => 4
[5,2,1,3,4] => [1,5,4,3,2] => 14
[5,2,1,4,3] => [1,5,3,2,4] => 7
[5,2,3,1,4] => [1,5,4,2,3] => 9
[5,2,3,4,1] => [1,5,2,3,4] => 4
[5,2,4,1,3] => [1,5,3,4,2] => 10
[5,2,4,3,1] => [1,5,2,3,4] => 4
[5,3,1,2,4] => [1,5,4,2,3] => 9
[5,3,1,4,2] => [1,5,2,3,4] => 4
[5,3,2,1,4] => [1,5,4,2,3] => 9
[5,3,2,4,1] => [1,5,2,3,4] => 4
[5,3,4,1,2] => [1,5,2,3,4] => 4
[5,3,4,2,1] => [1,5,2,3,4] => 4
[5,4,1,2,3] => [1,5,3,2,4] => 7
[5,4,1,3,2] => [1,5,2,4,3] => 11
[5,4,2,1,3] => [1,5,3,2,4] => 7
[5,4,2,3,1] => [1,5,2,4,3] => 11
[5,4,3,1,2] => [1,5,2,4,3] => 11
[5,4,3,2,1] => [1,5,2,4,3] => 11
[1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
[1,2,3,4,6,5] => [1,2,3,4,5,6] => 1
[1,2,3,5,4,6] => [1,2,3,4,5,6] => 1
[1,2,3,5,6,4] => [1,2,3,4,5,6] => 1
[1,2,3,6,4,5] => [1,2,3,4,6,5] => 5
[1,2,3,6,5,4] => [1,2,3,4,6,5] => 5
[1,2,4,3,5,6] => [1,2,3,4,5,6] => 1
[1,2,4,3,6,5] => [1,2,3,4,5,6] => 1
[1,2,4,5,3,6] => [1,2,3,4,5,6] => 1
[1,2,4,5,6,3] => [1,2,3,4,5,6] => 1
[1,2,4,6,3,5] => [1,2,3,4,6,5] => 5
[1,2,4,6,5,3] => [1,2,3,4,6,5] => 5
[1,2,5,3,4,6] => [1,2,3,5,4,6] => 4
[1,2,5,3,6,4] => [1,2,3,5,6,4] => 10
[1,2,5,4,3,6] => [1,2,3,5,4,6] => 4
[1,2,5,4,6,3] => [1,2,3,5,6,4] => 10
[1,2,5,6,3,4] => [1,2,3,5,4,6] => 4
[1,2,5,6,4,3] => [1,2,3,5,4,6] => 4
[1,2,6,3,4,5] => [1,2,3,6,5,4] => 30
[1,2,6,3,5,4] => [1,2,3,6,4,5] => 10
[1,2,6,4,3,5] => [1,2,3,6,5,4] => 30
[1,2,6,4,5,3] => [1,2,3,6,4,5] => 10
[1,2,6,5,3,4] => [1,2,3,6,4,5] => 10
[1,2,6,5,4,3] => [1,2,3,6,4,5] => 10
[1,3,2,4,5,6] => [1,2,3,4,5,6] => 1
[1,3,2,4,6,5] => [1,2,3,4,5,6] => 1
[1,3,2,5,4,6] => [1,2,3,4,5,6] => 1
[1,3,2,5,6,4] => [1,2,3,4,5,6] => 1
[1,3,2,6,4,5] => [1,2,3,4,6,5] => 5
[1,3,2,6,5,4] => [1,2,3,4,6,5] => 5
[1,3,4,2,5,6] => [1,2,3,4,5,6] => 1
[1,3,4,2,6,5] => [1,2,3,4,5,6] => 1
[1,3,4,5,2,6] => [1,2,3,4,5,6] => 1
[1,3,4,5,6,2] => [1,2,3,4,5,6] => 1
[1,3,4,6,2,5] => [1,2,3,4,6,5] => 5
[1,3,4,6,5,2] => [1,2,3,4,6,5] => 5
[1,3,5,2,4,6] => [1,2,3,5,4,6] => 4
[1,3,5,2,6,4] => [1,2,3,5,6,4] => 10
[1,3,5,4,2,6] => [1,2,3,5,4,6] => 4
[1,3,5,4,6,2] => [1,2,3,5,6,4] => 10
[1,3,5,6,2,4] => [1,2,3,5,4,6] => 4
[1,3,5,6,4,2] => [1,2,3,5,4,6] => 4
[1,3,6,2,4,5] => [1,2,3,6,5,4] => 30
[1,3,6,2,5,4] => [1,2,3,6,4,5] => 10
[1,3,6,4,2,5] => [1,2,3,6,5,4] => 30
[1,3,6,4,5,2] => [1,2,3,6,4,5] => 10
[1,3,6,5,2,4] => [1,2,3,6,4,5] => 10
[1,3,6,5,4,2] => [1,2,3,6,4,5] => 10
[1,4,2,3,5,6] => [1,2,4,3,5,6] => 3
[1,4,2,3,6,5] => [1,2,4,3,5,6] => 3
[1,4,2,5,3,6] => [1,2,4,5,3,6] => 6
[1,4,2,5,6,3] => [1,2,4,5,6,3] => 10
[1,4,2,6,3,5] => [1,2,4,6,5,3] => 35
[1,4,2,6,5,3] => [1,2,4,6,3,5] => 20
[1,4,3,2,5,6] => [1,2,4,3,5,6] => 3
[1,4,3,2,6,5] => [1,2,4,3,5,6] => 3
[1,4,3,5,2,6] => [1,2,4,5,3,6] => 6
[1,4,3,5,6,2] => [1,2,4,5,6,3] => 10
[1,4,3,6,2,5] => [1,2,4,6,5,3] => 35
[1,4,3,6,5,2] => [1,2,4,6,3,5] => 20
[1,4,5,2,3,6] => [1,2,4,3,5,6] => 3
[1,4,5,2,6,3] => [1,2,4,3,5,6] => 3
[1,4,5,3,2,6] => [1,2,4,3,5,6] => 3
[1,4,5,3,6,2] => [1,2,4,3,5,6] => 3
[1,4,5,6,2,3] => [1,2,4,6,3,5] => 20
[1,4,5,6,3,2] => [1,2,4,6,3,5] => 20
[1,4,6,2,3,5] => [1,2,4,3,6,5] => 15
[1,4,6,2,5,3] => [1,2,4,3,6,5] => 15
[1,4,6,3,2,5] => [1,2,4,3,6,5] => 15
[1,4,6,3,5,2] => [1,2,4,3,6,5] => 15
[1,4,6,5,2,3] => [1,2,4,5,3,6] => 6
[1,4,6,5,3,2] => [1,2,4,5,3,6] => 6
[1,5,2,3,4,6] => [1,2,5,4,3,6] => 14
[1,5,2,3,6,4] => [1,2,5,6,4,3] => 40
[1,5,2,4,3,6] => [1,2,5,3,4,6] => 6
[1,5,2,4,6,3] => [1,2,5,6,3,4] => 20
[1,5,2,6,3,4] => [1,2,5,3,4,6] => 6
[1,5,2,6,4,3] => [1,2,5,4,6,3] => 25
[1,5,3,2,4,6] => [1,2,5,4,3,6] => 14
[1,5,3,2,6,4] => [1,2,5,6,4,3] => 40
[1,5,3,4,2,6] => [1,2,5,3,4,6] => 6
[1,5,3,4,6,2] => [1,2,5,6,3,4] => 20
[1,5,3,6,2,4] => [1,2,5,3,4,6] => 6
[1,5,3,6,4,2] => [1,2,5,4,6,3] => 25
[1,5,4,2,3,6] => [1,2,5,3,4,6] => 6
[1,5,4,2,6,3] => [1,2,5,6,3,4] => 20
[1,5,4,3,2,6] => [1,2,5,3,4,6] => 6
[1,5,4,3,6,2] => [1,2,5,6,3,4] => 20
[1,5,4,6,2,3] => [1,2,5,3,4,6] => 6
[1,5,4,6,3,2] => [1,2,5,3,4,6] => 6
[1,5,6,2,3,4] => [1,2,5,3,6,4] => 20
[1,5,6,2,4,3] => [1,2,5,4,3,6] => 14
[1,5,6,3,2,4] => [1,2,5,3,6,4] => 20
[1,5,6,3,4,2] => [1,2,5,4,3,6] => 14
[1,5,6,4,2,3] => [1,2,5,3,6,4] => 20
[1,5,6,4,3,2] => [1,2,5,3,6,4] => 20
[1,6,2,3,4,5] => [1,2,6,5,4,3] => 84
[1,6,2,3,5,4] => [1,2,6,4,3,5] => 25
[1,6,2,4,3,5] => [1,2,6,5,3,4] => 40
[1,6,2,4,5,3] => [1,2,6,3,4,5] => 10
[1,6,2,5,3,4] => [1,2,6,4,5,3] => 46
[1,6,2,5,4,3] => [1,2,6,3,4,5] => 10
[1,6,3,2,4,5] => [1,2,6,5,4,3] => 84
[1,6,3,2,5,4] => [1,2,6,4,3,5] => 25
[1,6,3,4,2,5] => [1,2,6,5,3,4] => 40
[1,6,3,4,5,2] => [1,2,6,3,4,5] => 10
[1,6,3,5,2,4] => [1,2,6,4,5,3] => 46
[1,6,3,5,4,2] => [1,2,6,3,4,5] => 10
[1,6,4,2,3,5] => [1,2,6,5,3,4] => 40
[1,6,4,2,5,3] => [1,2,6,3,4,5] => 10
[1,6,4,3,2,5] => [1,2,6,5,3,4] => 40
[1,6,4,3,5,2] => [1,2,6,3,4,5] => 10
[1,6,4,5,2,3] => [1,2,6,3,4,5] => 10
[1,6,4,5,3,2] => [1,2,6,3,4,5] => 10
[1,6,5,2,3,4] => [1,2,6,4,3,5] => 25
[1,6,5,2,4,3] => [1,2,6,3,5,4] => 35
[1,6,5,3,2,4] => [1,2,6,4,3,5] => 25
[1,6,5,3,4,2] => [1,2,6,3,5,4] => 35
[1,6,5,4,2,3] => [1,2,6,3,5,4] => 35
[1,6,5,4,3,2] => [1,2,6,3,5,4] => 35
[2,1,3,4,5,6] => [1,2,3,4,5,6] => 1
[2,1,3,4,6,5] => [1,2,3,4,5,6] => 1
[2,1,3,5,4,6] => [1,2,3,4,5,6] => 1
[2,1,3,5,6,4] => [1,2,3,4,5,6] => 1
[2,1,3,6,4,5] => [1,2,3,4,6,5] => 5
[2,1,3,6,5,4] => [1,2,3,4,6,5] => 5
[2,1,4,3,5,6] => [1,2,3,4,5,6] => 1
[2,1,4,3,6,5] => [1,2,3,4,5,6] => 1
[2,1,4,5,3,6] => [1,2,3,4,5,6] => 1
[2,1,4,5,6,3] => [1,2,3,4,5,6] => 1
[2,1,4,6,3,5] => [1,2,3,4,6,5] => 5
[2,1,4,6,5,3] => [1,2,3,4,6,5] => 5
[2,1,5,3,4,6] => [1,2,3,5,4,6] => 4
[2,1,5,3,6,4] => [1,2,3,5,6,4] => 10
[2,1,5,4,3,6] => [1,2,3,5,4,6] => 4
[2,1,5,4,6,3] => [1,2,3,5,6,4] => 10
[2,1,5,6,3,4] => [1,2,3,5,4,6] => 4
[2,1,5,6,4,3] => [1,2,3,5,4,6] => 4
[2,1,6,3,4,5] => [1,2,3,6,5,4] => 30
[2,1,6,3,5,4] => [1,2,3,6,4,5] => 10
[2,1,6,4,3,5] => [1,2,3,6,5,4] => 30
[2,1,6,4,5,3] => [1,2,3,6,4,5] => 10
[2,1,6,5,3,4] => [1,2,3,6,4,5] => 10
[2,1,6,5,4,3] => [1,2,3,6,4,5] => 10
[2,3,1,4,5,6] => [1,2,3,4,5,6] => 1
[2,3,1,4,6,5] => [1,2,3,4,5,6] => 1
[2,3,1,5,4,6] => [1,2,3,4,5,6] => 1
[2,3,1,5,6,4] => [1,2,3,4,5,6] => 1
[2,3,1,6,4,5] => [1,2,3,4,6,5] => 5
[2,3,1,6,5,4] => [1,2,3,4,6,5] => 5
[2,3,4,1,5,6] => [1,2,3,4,5,6] => 1
[2,3,4,1,6,5] => [1,2,3,4,5,6] => 1
[2,3,4,5,1,6] => [1,2,3,4,5,6] => 1
[2,3,4,5,6,1] => [1,2,3,4,5,6] => 1
[2,3,4,6,1,5] => [1,2,3,4,6,5] => 5
[2,3,4,6,5,1] => [1,2,3,4,6,5] => 5
[2,3,5,1,4,6] => [1,2,3,5,4,6] => 4
[2,3,5,1,6,4] => [1,2,3,5,6,4] => 10
[2,3,5,4,1,6] => [1,2,3,5,4,6] => 4
[2,3,5,4,6,1] => [1,2,3,5,6,4] => 10
[2,3,5,6,1,4] => [1,2,3,5,4,6] => 4
[2,3,5,6,4,1] => [1,2,3,5,4,6] => 4
[2,3,6,1,4,5] => [1,2,3,6,5,4] => 30
[2,3,6,1,5,4] => [1,2,3,6,4,5] => 10
[2,3,6,4,1,5] => [1,2,3,6,5,4] => 30
[2,3,6,4,5,1] => [1,2,3,6,4,5] => 10
[2,3,6,5,1,4] => [1,2,3,6,4,5] => 10
[2,3,6,5,4,1] => [1,2,3,6,4,5] => 10
[2,4,1,3,5,6] => [1,2,4,3,5,6] => 3
[2,4,1,3,6,5] => [1,2,4,3,5,6] => 3
[2,4,1,5,3,6] => [1,2,4,5,3,6] => 6
[2,4,1,5,6,3] => [1,2,4,5,6,3] => 10
[2,4,1,6,3,5] => [1,2,4,6,5,3] => 35
[2,4,1,6,5,3] => [1,2,4,6,3,5] => 20
[2,4,3,1,5,6] => [1,2,4,3,5,6] => 3
[2,4,3,1,6,5] => [1,2,4,3,5,6] => 3
[2,4,3,5,1,6] => [1,2,4,5,3,6] => 6
[2,4,3,5,6,1] => [1,2,4,5,6,3] => 10
[2,4,3,6,1,5] => [1,2,4,6,5,3] => 35
[2,4,3,6,5,1] => [1,2,4,6,3,5] => 20
[2,4,5,1,3,6] => [1,2,4,3,5,6] => 3
[2,4,5,1,6,3] => [1,2,4,3,5,6] => 3
[2,4,5,3,1,6] => [1,2,4,3,5,6] => 3
[2,4,5,3,6,1] => [1,2,4,3,5,6] => 3
[2,4,5,6,1,3] => [1,2,4,6,3,5] => 20
[2,4,5,6,3,1] => [1,2,4,6,3,5] => 20
[2,4,6,1,3,5] => [1,2,4,3,6,5] => 15
[2,4,6,1,5,3] => [1,2,4,3,6,5] => 15
[2,4,6,3,1,5] => [1,2,4,3,6,5] => 15
[2,4,6,3,5,1] => [1,2,4,3,6,5] => 15
[2,4,6,5,1,3] => [1,2,4,5,3,6] => 6
[2,4,6,5,3,1] => [1,2,4,5,3,6] => 6
[2,5,1,3,4,6] => [1,2,5,4,3,6] => 14
[2,5,1,3,6,4] => [1,2,5,6,4,3] => 40
[2,5,1,4,3,6] => [1,2,5,3,4,6] => 6
[2,5,1,4,6,3] => [1,2,5,6,3,4] => 20
[2,5,1,6,3,4] => [1,2,5,3,4,6] => 6
[2,5,1,6,4,3] => [1,2,5,4,6,3] => 25
[2,5,3,1,4,6] => [1,2,5,4,3,6] => 14
[2,5,3,1,6,4] => [1,2,5,6,4,3] => 40
[2,5,3,4,1,6] => [1,2,5,3,4,6] => 6
[2,5,3,4,6,1] => [1,2,5,6,3,4] => 20
[2,5,3,6,1,4] => [1,2,5,3,4,6] => 6
[2,5,3,6,4,1] => [1,2,5,4,6,3] => 25
[2,5,4,1,3,6] => [1,2,5,3,4,6] => 6
[2,5,4,1,6,3] => [1,2,5,6,3,4] => 20
[2,5,4,3,1,6] => [1,2,5,3,4,6] => 6
[2,5,4,3,6,1] => [1,2,5,6,3,4] => 20
[2,5,4,6,1,3] => [1,2,5,3,4,6] => 6
[2,5,4,6,3,1] => [1,2,5,3,4,6] => 6
[2,5,6,1,3,4] => [1,2,5,3,6,4] => 20
[2,5,6,1,4,3] => [1,2,5,4,3,6] => 14
[2,5,6,3,1,4] => [1,2,5,3,6,4] => 20
[2,5,6,3,4,1] => [1,2,5,4,3,6] => 14
[2,5,6,4,1,3] => [1,2,5,3,6,4] => 20
[2,5,6,4,3,1] => [1,2,5,3,6,4] => 20
[2,6,1,3,4,5] => [1,2,6,5,4,3] => 84
[2,6,1,3,5,4] => [1,2,6,4,3,5] => 25
[2,6,1,4,3,5] => [1,2,6,5,3,4] => 40
[2,6,1,4,5,3] => [1,2,6,3,4,5] => 10
[2,6,1,5,3,4] => [1,2,6,4,5,3] => 46
[2,6,1,5,4,3] => [1,2,6,3,4,5] => 10
[2,6,3,1,4,5] => [1,2,6,5,4,3] => 84
[2,6,3,1,5,4] => [1,2,6,4,3,5] => 25
[2,6,3,4,1,5] => [1,2,6,5,3,4] => 40
[2,6,3,4,5,1] => [1,2,6,3,4,5] => 10
[2,6,3,5,1,4] => [1,2,6,4,5,3] => 46
[2,6,3,5,4,1] => [1,2,6,3,4,5] => 10
[2,6,4,1,3,5] => [1,2,6,5,3,4] => 40
[2,6,4,1,5,3] => [1,2,6,3,4,5] => 10
[2,6,4,3,1,5] => [1,2,6,5,3,4] => 40
[2,6,4,3,5,1] => [1,2,6,3,4,5] => 10
[2,6,4,5,1,3] => [1,2,6,3,4,5] => 10
[2,6,4,5,3,1] => [1,2,6,3,4,5] => 10
[2,6,5,1,3,4] => [1,2,6,4,3,5] => 25
[2,6,5,1,4,3] => [1,2,6,3,5,4] => 35
[2,6,5,3,1,4] => [1,2,6,4,3,5] => 25
[2,6,5,3,4,1] => [1,2,6,3,5,4] => 35
[2,6,5,4,1,3] => [1,2,6,3,5,4] => 35
[2,6,5,4,3,1] => [1,2,6,3,5,4] => 35
[3,1,2,4,5,6] => [1,3,2,4,5,6] => 2
[3,1,2,4,6,5] => [1,3,2,4,5,6] => 2
[3,1,2,5,4,6] => [1,3,2,4,5,6] => 2
[3,1,2,5,6,4] => [1,3,2,4,5,6] => 2
[3,1,2,6,4,5] => [1,3,2,4,6,5] => 10
[3,1,2,6,5,4] => [1,3,2,4,6,5] => 10
[3,1,4,2,5,6] => [1,3,4,2,5,6] => 3
[3,1,4,2,6,5] => [1,3,4,2,5,6] => 3
[3,1,4,5,2,6] => [1,3,4,5,2,6] => 4
[3,1,4,5,6,2] => [1,3,4,5,6,2] => 5
[3,1,4,6,2,5] => [1,3,4,6,5,2] => 19
[3,1,4,6,5,2] => [1,3,4,6,2,5] => 15
[3,1,5,2,4,6] => [1,3,5,4,2,6] => 11
[3,1,5,2,6,4] => [1,3,5,6,4,2] => 26
[3,1,5,4,2,6] => [1,3,5,2,4,6] => 8
[3,1,5,4,6,2] => [1,3,5,6,2,4] => 20
[3,1,5,6,2,4] => [1,3,5,2,4,6] => 8
[3,1,5,6,4,2] => [1,3,5,4,6,2] => 14
[3,1,6,2,4,5] => [1,3,6,5,4,2] => 58
[3,1,6,2,5,4] => [1,3,6,4,2,5] => 21
[3,1,6,4,2,5] => [1,3,6,5,2,4] => 44
[3,1,6,4,5,2] => [1,3,6,2,4,5] => 15
[3,1,6,5,2,4] => [1,3,6,4,5,2] => 27
[3,1,6,5,4,2] => [1,3,6,2,4,5] => 15
[3,2,1,4,5,6] => [1,3,2,4,5,6] => 2
[3,2,1,4,6,5] => [1,3,2,4,5,6] => 2
[3,2,1,5,4,6] => [1,3,2,4,5,6] => 2
[3,2,1,5,6,4] => [1,3,2,4,5,6] => 2
[3,2,1,6,4,5] => [1,3,2,4,6,5] => 10
[3,2,1,6,5,4] => [1,3,2,4,6,5] => 10
[3,2,4,1,5,6] => [1,3,4,2,5,6] => 3
[3,2,4,1,6,5] => [1,3,4,2,5,6] => 3
[3,2,4,5,1,6] => [1,3,4,5,2,6] => 4
[3,2,4,5,6,1] => [1,3,4,5,6,2] => 5
[3,2,4,6,1,5] => [1,3,4,6,5,2] => 19
[3,2,4,6,5,1] => [1,3,4,6,2,5] => 15
[3,2,5,1,4,6] => [1,3,5,4,2,6] => 11
[3,2,5,1,6,4] => [1,3,5,6,4,2] => 26
[3,2,5,4,1,6] => [1,3,5,2,4,6] => 8
[3,2,5,4,6,1] => [1,3,5,6,2,4] => 20
[3,2,5,6,1,4] => [1,3,5,2,4,6] => 8
[3,2,5,6,4,1] => [1,3,5,4,6,2] => 14
[3,2,6,1,4,5] => [1,3,6,5,4,2] => 58
[3,2,6,1,5,4] => [1,3,6,4,2,5] => 21
[3,2,6,4,1,5] => [1,3,6,5,2,4] => 44
[3,2,6,4,5,1] => [1,3,6,2,4,5] => 15
[3,2,6,5,1,4] => [1,3,6,4,5,2] => 27
[3,2,6,5,4,1] => [1,3,6,2,4,5] => 15
[3,4,1,2,5,6] => [1,3,2,4,5,6] => 2
[3,4,1,2,6,5] => [1,3,2,4,5,6] => 2
[3,4,1,5,2,6] => [1,3,2,4,5,6] => 2
[3,4,1,5,6,2] => [1,3,2,4,5,6] => 2
[3,4,1,6,2,5] => [1,3,2,4,6,5] => 10
[3,4,1,6,5,2] => [1,3,2,4,6,5] => 10
[3,4,2,1,5,6] => [1,3,2,4,5,6] => 2
[3,4,2,1,6,5] => [1,3,2,4,5,6] => 2
[3,4,2,5,1,6] => [1,3,2,4,5,6] => 2
[3,4,2,5,6,1] => [1,3,2,4,5,6] => 2
[3,4,2,6,1,5] => [1,3,2,4,6,5] => 10
[3,4,2,6,5,1] => [1,3,2,4,6,5] => 10
[3,4,5,1,2,6] => [1,3,5,2,4,6] => 8
[3,4,5,1,6,2] => [1,3,5,6,2,4] => 20
[3,4,5,2,1,6] => [1,3,5,2,4,6] => 8
[3,4,5,2,6,1] => [1,3,5,6,2,4] => 20
[3,4,5,6,1,2] => [1,3,5,2,4,6] => 8
[3,4,5,6,2,1] => [1,3,5,2,4,6] => 8
[3,4,6,1,2,5] => [1,3,6,5,2,4] => 44
[3,4,6,1,5,2] => [1,3,6,2,4,5] => 15
[3,4,6,2,1,5] => [1,3,6,5,2,4] => 44
[3,4,6,2,5,1] => [1,3,6,2,4,5] => 15
[3,4,6,5,1,2] => [1,3,6,2,4,5] => 15
[3,4,6,5,2,1] => [1,3,6,2,4,5] => 15
[3,5,1,2,4,6] => [1,3,2,5,4,6] => 8
[3,5,1,2,6,4] => [1,3,2,5,6,4] => 20
[3,5,1,4,2,6] => [1,3,2,5,4,6] => 8
[3,5,1,4,6,2] => [1,3,2,5,6,4] => 20
[3,5,1,6,2,4] => [1,3,2,5,4,6] => 8
[3,5,1,6,4,2] => [1,3,2,5,4,6] => 8
[3,5,2,1,4,6] => [1,3,2,5,4,6] => 8
[3,5,2,1,6,4] => [1,3,2,5,6,4] => 20
[3,5,2,4,1,6] => [1,3,2,5,4,6] => 8
[3,5,2,4,6,1] => [1,3,2,5,6,4] => 20
[3,5,2,6,1,4] => [1,3,2,5,4,6] => 8
[3,5,2,6,4,1] => [1,3,2,5,4,6] => 8
[3,5,4,1,2,6] => [1,3,4,2,5,6] => 3
[3,5,4,1,6,2] => [1,3,4,2,5,6] => 3
[3,5,4,2,1,6] => [1,3,4,2,5,6] => 3
[3,5,4,2,6,1] => [1,3,4,2,5,6] => 3
[3,5,4,6,1,2] => [1,3,4,6,2,5] => 15
[3,5,4,6,2,1] => [1,3,4,6,2,5] => 15
[3,5,6,1,2,4] => [1,3,6,4,2,5] => 21
[3,5,6,1,4,2] => [1,3,6,2,5,4] => 51
[3,5,6,2,1,4] => [1,3,6,4,2,5] => 21
[3,5,6,2,4,1] => [1,3,6,2,5,4] => 51
[3,5,6,4,1,2] => [1,3,6,2,5,4] => 51
[3,5,6,4,2,1] => [1,3,6,2,5,4] => 51
[3,6,1,2,4,5] => [1,3,2,6,5,4] => 60
[3,6,1,2,5,4] => [1,3,2,6,4,5] => 20
[3,6,1,4,2,5] => [1,3,2,6,5,4] => 60
[3,6,1,4,5,2] => [1,3,2,6,4,5] => 20
[3,6,1,5,2,4] => [1,3,2,6,4,5] => 20
[3,6,1,5,4,2] => [1,3,2,6,4,5] => 20
[3,6,2,1,4,5] => [1,3,2,6,5,4] => 60
[3,6,2,1,5,4] => [1,3,2,6,4,5] => 20
[3,6,2,4,1,5] => [1,3,2,6,5,4] => 60
[3,6,2,4,5,1] => [1,3,2,6,4,5] => 20
[3,6,2,5,1,4] => [1,3,2,6,4,5] => 20
[3,6,2,5,4,1] => [1,3,2,6,4,5] => 20
[3,6,4,1,2,5] => [1,3,4,2,6,5] => 15
[3,6,4,1,5,2] => [1,3,4,2,6,5] => 15
[3,6,4,2,1,5] => [1,3,4,2,6,5] => 15
[3,6,4,2,5,1] => [1,3,4,2,6,5] => 15
[3,6,4,5,1,2] => [1,3,4,5,2,6] => 4
[3,6,4,5,2,1] => [1,3,4,5,2,6] => 4
[3,6,5,1,2,4] => [1,3,5,2,6,4] => 25
[3,6,5,1,4,2] => [1,3,5,4,2,6] => 11
[3,6,5,2,1,4] => [1,3,5,2,6,4] => 25
[3,6,5,2,4,1] => [1,3,5,4,2,6] => 11
[3,6,5,4,1,2] => [1,3,5,2,6,4] => 25
[3,6,5,4,2,1] => [1,3,5,2,6,4] => 25
[4,1,2,3,5,6] => [1,4,3,2,5,6] => 5
[4,1,2,3,6,5] => [1,4,3,2,5,6] => 5
[4,1,2,5,3,6] => [1,4,5,3,2,6] => 9
[4,1,2,5,6,3] => [1,4,5,6,3,2] => 14
[4,1,2,6,3,5] => [1,4,6,5,3,2] => 37
[4,1,2,6,5,3] => [1,4,6,3,2,5] => 23
[4,1,3,2,5,6] => [1,4,2,3,5,6] => 3
[4,1,3,2,6,5] => [1,4,2,3,5,6] => 3
[4,1,3,5,2,6] => [1,4,5,2,3,6] => 6
[4,1,3,5,6,2] => [1,4,5,6,2,3] => 10
[4,1,3,6,2,5] => [1,4,6,5,2,3] => 26
[4,1,3,6,5,2] => [1,4,6,2,3,5] => 15
[4,1,5,2,3,6] => [1,4,2,3,5,6] => 3
[4,1,5,2,6,3] => [1,4,2,3,5,6] => 3
[4,1,5,3,2,6] => [1,4,3,5,2,6] => 7
[4,1,5,3,6,2] => [1,4,3,5,6,2] => 9
[4,1,5,6,2,3] => [1,4,6,3,5,2] => 31
[4,1,5,6,3,2] => [1,4,6,2,3,5] => 15
[4,1,6,2,3,5] => [1,4,2,3,6,5] => 15
[4,1,6,2,5,3] => [1,4,2,3,6,5] => 15
[4,1,6,3,2,5] => [1,4,3,6,5,2] => 34
[4,1,6,3,5,2] => [1,4,3,6,2,5] => 26
[4,1,6,5,2,3] => [1,4,5,2,3,6] => 6
[4,1,6,5,3,2] => [1,4,5,3,6,2] => 12
[4,2,1,3,5,6] => [1,4,3,2,5,6] => 5
[4,2,1,3,6,5] => [1,4,3,2,5,6] => 5
[4,2,1,5,3,6] => [1,4,5,3,2,6] => 9
[4,2,1,5,6,3] => [1,4,5,6,3,2] => 14
[4,2,1,6,3,5] => [1,4,6,5,3,2] => 37
[4,2,1,6,5,3] => [1,4,6,3,2,5] => 23
[4,2,3,1,5,6] => [1,4,2,3,5,6] => 3
[4,2,3,1,6,5] => [1,4,2,3,5,6] => 3
[4,2,3,5,1,6] => [1,4,5,2,3,6] => 6
[4,2,3,5,6,1] => [1,4,5,6,2,3] => 10
[4,2,3,6,1,5] => [1,4,6,5,2,3] => 26
[4,2,3,6,5,1] => [1,4,6,2,3,5] => 15
[4,2,5,1,3,6] => [1,4,2,3,5,6] => 3
[4,2,5,1,6,3] => [1,4,2,3,5,6] => 3
[4,2,5,3,1,6] => [1,4,3,5,2,6] => 7
[4,2,5,3,6,1] => [1,4,3,5,6,2] => 9
[4,2,5,6,1,3] => [1,4,6,3,5,2] => 31
[4,2,5,6,3,1] => [1,4,6,2,3,5] => 15
[4,2,6,1,3,5] => [1,4,2,3,6,5] => 15
[4,2,6,1,5,3] => [1,4,2,3,6,5] => 15
[4,2,6,3,1,5] => [1,4,3,6,5,2] => 34
[4,2,6,3,5,1] => [1,4,3,6,2,5] => 26
[4,2,6,5,1,3] => [1,4,5,2,3,6] => 6
[4,2,6,5,3,1] => [1,4,5,3,6,2] => 12
[4,3,1,2,5,6] => [1,4,2,3,5,6] => 3
[4,3,1,2,6,5] => [1,4,2,3,5,6] => 3
[4,3,1,5,2,6] => [1,4,5,2,3,6] => 6
[4,3,1,5,6,2] => [1,4,5,6,2,3] => 10
[4,3,1,6,2,5] => [1,4,6,5,2,3] => 26
[4,3,1,6,5,2] => [1,4,6,2,3,5] => 15
[4,3,2,1,5,6] => [1,4,2,3,5,6] => 3
[4,3,2,1,6,5] => [1,4,2,3,5,6] => 3
[4,3,2,5,1,6] => [1,4,5,2,3,6] => 6
[4,3,2,5,6,1] => [1,4,5,6,2,3] => 10
[4,3,2,6,1,5] => [1,4,6,5,2,3] => 26
[4,3,2,6,5,1] => [1,4,6,2,3,5] => 15
[4,3,5,1,2,6] => [1,4,2,3,5,6] => 3
[4,3,5,1,6,2] => [1,4,2,3,5,6] => 3
[4,3,5,2,1,6] => [1,4,2,3,5,6] => 3
[4,3,5,2,6,1] => [1,4,2,3,5,6] => 3
[4,3,5,6,1,2] => [1,4,6,2,3,5] => 15
[4,3,5,6,2,1] => [1,4,6,2,3,5] => 15
[4,3,6,1,2,5] => [1,4,2,3,6,5] => 15
[4,3,6,1,5,2] => [1,4,2,3,6,5] => 15
[4,3,6,2,1,5] => [1,4,2,3,6,5] => 15
[4,3,6,2,5,1] => [1,4,2,3,6,5] => 15
[4,3,6,5,1,2] => [1,4,5,2,3,6] => 6
[4,3,6,5,2,1] => [1,4,5,2,3,6] => 6
[4,5,1,2,3,6] => [1,4,2,5,3,6] => 8
[4,5,1,2,6,3] => [1,4,2,5,6,3] => 15
[4,5,1,3,2,6] => [1,4,3,2,5,6] => 5
[4,5,1,3,6,2] => [1,4,3,2,5,6] => 5
[4,5,1,6,2,3] => [1,4,6,3,2,5] => 23
[4,5,1,6,3,2] => [1,4,6,2,5,3] => 38
[4,5,2,1,3,6] => [1,4,2,5,3,6] => 8
[4,5,2,1,6,3] => [1,4,2,5,6,3] => 15
[4,5,2,3,1,6] => [1,4,3,2,5,6] => 5
[4,5,2,3,6,1] => [1,4,3,2,5,6] => 5
[4,5,2,6,1,3] => [1,4,6,3,2,5] => 23
[4,5,2,6,3,1] => [1,4,6,2,5,3] => 38
[4,5,3,1,2,6] => [1,4,2,5,3,6] => 8
[4,5,3,1,6,2] => [1,4,2,5,6,3] => 15
[4,5,3,2,1,6] => [1,4,2,5,3,6] => 8
[4,5,3,2,6,1] => [1,4,2,5,6,3] => 15
[4,5,3,6,1,2] => [1,4,6,2,5,3] => 38
[4,5,3,6,2,1] => [1,4,6,2,5,3] => 38
[4,5,6,1,2,3] => [1,4,2,5,3,6] => 8
[4,5,6,1,3,2] => [1,4,2,5,3,6] => 8
[4,5,6,2,1,3] => [1,4,2,5,3,6] => 8
[4,5,6,2,3,1] => [1,4,2,5,3,6] => 8
[4,5,6,3,1,2] => [1,4,3,6,2,5] => 26
[4,5,6,3,2,1] => [1,4,3,6,2,5] => 26
[4,6,1,2,3,5] => [1,4,2,6,5,3] => 51
[4,6,1,2,5,3] => [1,4,2,6,3,5] => 25
[4,6,1,3,2,5] => [1,4,3,2,6,5] => 25
[4,6,1,3,5,2] => [1,4,3,2,6,5] => 25
[4,6,1,5,2,3] => [1,4,5,2,6,3] => 15
[4,6,1,5,3,2] => [1,4,5,3,2,6] => 9
[4,6,2,1,3,5] => [1,4,2,6,5,3] => 51
[4,6,2,1,5,3] => [1,4,2,6,3,5] => 25
[4,6,2,3,1,5] => [1,4,3,2,6,5] => 25
[4,6,2,3,5,1] => [1,4,3,2,6,5] => 25
[4,6,2,5,1,3] => [1,4,5,2,6,3] => 15
[4,6,2,5,3,1] => [1,4,5,3,2,6] => 9
[4,6,3,1,2,5] => [1,4,2,6,5,3] => 51
[4,6,3,1,5,2] => [1,4,2,6,3,5] => 25
[4,6,3,2,1,5] => [1,4,2,6,5,3] => 51
[4,6,3,2,5,1] => [1,4,2,6,3,5] => 25
[4,6,3,5,1,2] => [1,4,5,2,6,3] => 15
[4,6,3,5,2,1] => [1,4,5,2,6,3] => 15
[4,6,5,1,2,3] => [1,4,2,6,3,5] => 25
[4,6,5,1,3,2] => [1,4,2,6,3,5] => 25
[4,6,5,2,1,3] => [1,4,2,6,3,5] => 25
[4,6,5,2,3,1] => [1,4,2,6,3,5] => 25
[4,6,5,3,1,2] => [1,4,3,5,2,6] => 7
[4,6,5,3,2,1] => [1,4,3,5,2,6] => 7
[5,1,2,3,4,6] => [1,5,4,3,2,6] => 14
[5,1,2,3,6,4] => [1,5,6,4,3,2] => 28
[5,1,2,4,3,6] => [1,5,3,2,4,6] => 7
[5,1,2,4,6,3] => [1,5,6,3,2,4] => 16
[5,1,2,6,3,4] => [1,5,3,2,4,6] => 7
[5,1,2,6,4,3] => [1,5,4,6,3,2] => 23
[5,1,3,2,4,6] => [1,5,4,2,3,6] => 9
[5,1,3,2,6,4] => [1,5,6,4,2,3] => 19
[5,1,3,4,2,6] => [1,5,2,3,4,6] => 4
[5,1,3,4,6,2] => [1,5,6,2,3,4] => 10
[5,1,3,6,2,4] => [1,5,2,3,4,6] => 4
[5,1,3,6,4,2] => [1,5,4,6,2,3] => 16
[5,1,4,2,3,6] => [1,5,3,4,2,6] => 10
[5,1,4,2,6,3] => [1,5,6,3,4,2] => 22
[5,1,4,3,2,6] => [1,5,2,3,4,6] => 4
[5,1,4,3,6,2] => [1,5,6,2,3,4] => 10
[5,1,4,6,2,3] => [1,5,2,3,4,6] => 4
[5,1,4,6,3,2] => [1,5,3,4,6,2] => 13
[5,1,6,2,3,4] => [1,5,3,6,4,2] => 32
[5,1,6,2,4,3] => [1,5,4,2,3,6] => 9
[5,1,6,3,2,4] => [1,5,2,3,6,4] => 15
[5,1,6,3,4,2] => [1,5,4,3,6,2] => 19
[5,1,6,4,2,3] => [1,5,2,3,6,4] => 15
[5,1,6,4,3,2] => [1,5,3,6,2,4] => 24
[5,2,1,3,4,6] => [1,5,4,3,2,6] => 14
[5,2,1,3,6,4] => [1,5,6,4,3,2] => 28
[5,2,1,4,3,6] => [1,5,3,2,4,6] => 7
[5,2,1,4,6,3] => [1,5,6,3,2,4] => 16
[5,2,1,6,3,4] => [1,5,3,2,4,6] => 7
[5,2,1,6,4,3] => [1,5,4,6,3,2] => 23
[5,2,3,1,4,6] => [1,5,4,2,3,6] => 9
[5,2,3,1,6,4] => [1,5,6,4,2,3] => 19
[5,2,3,4,1,6] => [1,5,2,3,4,6] => 4
[5,2,3,4,6,1] => [1,5,6,2,3,4] => 10
[5,2,3,6,1,4] => [1,5,2,3,4,6] => 4
[5,2,3,6,4,1] => [1,5,4,6,2,3] => 16
[5,2,4,1,3,6] => [1,5,3,4,2,6] => 10
[5,2,4,1,6,3] => [1,5,6,3,4,2] => 22
[5,2,4,3,1,6] => [1,5,2,3,4,6] => 4
[5,2,4,3,6,1] => [1,5,6,2,3,4] => 10
[5,2,4,6,1,3] => [1,5,2,3,4,6] => 4
[5,2,4,6,3,1] => [1,5,3,4,6,2] => 13
[5,2,6,1,3,4] => [1,5,3,6,4,2] => 32
[5,2,6,1,4,3] => [1,5,4,2,3,6] => 9
[5,2,6,3,1,4] => [1,5,2,3,6,4] => 15
[5,2,6,3,4,1] => [1,5,4,3,6,2] => 19
[5,2,6,4,1,3] => [1,5,2,3,6,4] => 15
[5,2,6,4,3,1] => [1,5,3,6,2,4] => 24
[5,3,1,2,4,6] => [1,5,4,2,3,6] => 9
[5,3,1,2,6,4] => [1,5,6,4,2,3] => 19
[5,3,1,4,2,6] => [1,5,2,3,4,6] => 4
[5,3,1,4,6,2] => [1,5,6,2,3,4] => 10
[5,3,1,6,2,4] => [1,5,2,3,4,6] => 4
[5,3,1,6,4,2] => [1,5,4,6,2,3] => 16
[5,3,2,1,4,6] => [1,5,4,2,3,6] => 9
[5,3,2,1,6,4] => [1,5,6,4,2,3] => 19
[5,3,2,4,1,6] => [1,5,2,3,4,6] => 4
[5,3,2,4,6,1] => [1,5,6,2,3,4] => 10
[5,3,2,6,1,4] => [1,5,2,3,4,6] => 4
[5,3,2,6,4,1] => [1,5,4,6,2,3] => 16
[5,3,4,1,2,6] => [1,5,2,3,4,6] => 4
[5,3,4,1,6,2] => [1,5,6,2,3,4] => 10
[5,3,4,2,1,6] => [1,5,2,3,4,6] => 4
[5,3,4,2,6,1] => [1,5,6,2,3,4] => 10
[5,3,4,6,1,2] => [1,5,2,3,4,6] => 4
[5,3,4,6,2,1] => [1,5,2,3,4,6] => 4
[5,3,6,1,2,4] => [1,5,2,3,6,4] => 15
[5,3,6,1,4,2] => [1,5,4,2,3,6] => 9
[5,3,6,2,1,4] => [1,5,2,3,6,4] => 15
[5,3,6,2,4,1] => [1,5,4,2,3,6] => 9
[5,3,6,4,1,2] => [1,5,2,3,6,4] => 15
[5,3,6,4,2,1] => [1,5,2,3,6,4] => 15
[5,4,1,2,3,6] => [1,5,3,2,4,6] => 7
[5,4,1,2,6,3] => [1,5,6,3,2,4] => 16
[5,4,1,3,2,6] => [1,5,2,4,3,6] => 11
[5,4,1,3,6,2] => [1,5,6,2,4,3] => 26
[5,4,1,6,2,3] => [1,5,2,4,6,3] => 21
[5,4,1,6,3,2] => [1,5,3,2,4,6] => 7
[5,4,2,1,3,6] => [1,5,3,2,4,6] => 7
[5,4,2,1,6,3] => [1,5,6,3,2,4] => 16
[5,4,2,3,1,6] => [1,5,2,4,3,6] => 11
[5,4,2,3,6,1] => [1,5,6,2,4,3] => 26
[5,4,2,6,1,3] => [1,5,2,4,6,3] => 21
[5,4,2,6,3,1] => [1,5,3,2,4,6] => 7
[5,4,3,1,2,6] => [1,5,2,4,3,6] => 11
[5,4,3,1,6,2] => [1,5,6,2,4,3] => 26
[5,4,3,2,1,6] => [1,5,2,4,3,6] => 11
[5,4,3,2,6,1] => [1,5,6,2,4,3] => 26
[5,4,3,6,1,2] => [1,5,2,4,6,3] => 21
[5,4,3,6,2,1] => [1,5,2,4,6,3] => 21
[5,4,6,1,2,3] => [1,5,2,4,3,6] => 11
[5,4,6,1,3,2] => [1,5,3,6,2,4] => 24
[5,4,6,2,1,3] => [1,5,2,4,3,6] => 11
[5,4,6,2,3,1] => [1,5,3,6,2,4] => 24
[5,4,6,3,1,2] => [1,5,2,4,3,6] => 11
[5,4,6,3,2,1] => [1,5,2,4,3,6] => 11
[5,6,1,2,3,4] => [1,5,3,2,6,4] => 26
[5,6,1,2,4,3] => [1,5,4,2,6,3] => 23
[5,6,1,3,2,4] => [1,5,2,6,4,3] => 44
[5,6,1,3,4,2] => [1,5,4,3,2,6] => 14
[5,6,1,4,2,3] => [1,5,2,6,3,4] => 20
[5,6,1,4,3,2] => [1,5,3,2,6,4] => 26
[5,6,2,1,3,4] => [1,5,3,2,6,4] => 26
[5,6,2,1,4,3] => [1,5,4,2,6,3] => 23
[5,6,2,3,1,4] => [1,5,2,6,4,3] => 44
[5,6,2,3,4,1] => [1,5,4,3,2,6] => 14
[5,6,2,4,1,3] => [1,5,2,6,3,4] => 20
[5,6,2,4,3,1] => [1,5,3,2,6,4] => 26
[5,6,3,1,2,4] => [1,5,2,6,4,3] => 44
[5,6,3,1,4,2] => [1,5,4,2,6,3] => 23
[5,6,3,2,1,4] => [1,5,2,6,4,3] => 44
[5,6,3,2,4,1] => [1,5,4,2,6,3] => 23
[5,6,3,4,1,2] => [1,5,2,6,3,4] => 20
[5,6,3,4,2,1] => [1,5,2,6,3,4] => 20
[5,6,4,1,2,3] => [1,5,2,6,3,4] => 20
[5,6,4,1,3,2] => [1,5,3,4,2,6] => 10
[5,6,4,2,1,3] => [1,5,2,6,3,4] => 20
[5,6,4,2,3,1] => [1,5,3,4,2,6] => 10
[5,6,4,3,1,2] => [1,5,2,6,3,4] => 20
[5,6,4,3,2,1] => [1,5,2,6,3,4] => 20
[6,1,2,3,4,5] => [1,6,5,4,3,2] => 42
[6,1,2,3,5,4] => [1,6,4,3,2,5] => 19
[6,1,2,4,3,5] => [1,6,5,3,2,4] => 23
[6,1,2,4,5,3] => [1,6,3,2,4,5] => 9
[6,1,2,5,3,4] => [1,6,4,5,3,2] => 32
[6,1,2,5,4,3] => [1,6,3,2,4,5] => 9
[6,1,3,2,4,5] => [1,6,5,4,2,3] => 28
[6,1,3,2,5,4] => [1,6,4,2,3,5] => 12
[6,1,3,4,2,5] => [1,6,5,2,3,4] => 14
[6,1,3,4,5,2] => [1,6,2,3,4,5] => 5
[6,1,3,5,2,4] => [1,6,4,5,2,3] => 22
[6,1,3,5,4,2] => [1,6,2,3,4,5] => 5
[6,1,4,2,3,5] => [1,6,5,3,4,2] => 32
[6,1,4,2,5,3] => [1,6,3,4,2,5] => 13
[6,1,4,3,2,5] => [1,6,5,2,3,4] => 14
[6,1,4,3,5,2] => [1,6,2,3,4,5] => 5
[6,1,4,5,2,3] => [1,6,3,4,5,2] => 17
[6,1,4,5,3,2] => [1,6,2,3,4,5] => 5
[6,1,5,2,3,4] => [1,6,4,2,3,5] => 12
[6,1,5,2,4,3] => [1,6,3,5,4,2] => 43
[6,1,5,3,2,4] => [1,6,4,3,5,2] => 26
[6,1,5,3,4,2] => [1,6,2,3,5,4] => 19
[6,1,5,4,2,3] => [1,6,3,5,2,4] => 32
[6,1,5,4,3,2] => [1,6,2,3,5,4] => 19
[6,2,1,3,4,5] => [1,6,5,4,3,2] => 42
[6,2,1,3,5,4] => [1,6,4,3,2,5] => 19
[6,2,1,4,3,5] => [1,6,5,3,2,4] => 23
[6,2,1,4,5,3] => [1,6,3,2,4,5] => 9
[6,2,1,5,3,4] => [1,6,4,5,3,2] => 32
[6,2,1,5,4,3] => [1,6,3,2,4,5] => 9
[6,2,3,1,4,5] => [1,6,5,4,2,3] => 28
[6,2,3,1,5,4] => [1,6,4,2,3,5] => 12
[6,2,3,4,1,5] => [1,6,5,2,3,4] => 14
[6,2,3,4,5,1] => [1,6,2,3,4,5] => 5
[6,2,3,5,1,4] => [1,6,4,5,2,3] => 22
[6,2,3,5,4,1] => [1,6,2,3,4,5] => 5
[6,2,4,1,3,5] => [1,6,5,3,4,2] => 32
[6,2,4,1,5,3] => [1,6,3,4,2,5] => 13
[6,2,4,3,1,5] => [1,6,5,2,3,4] => 14
[6,2,4,3,5,1] => [1,6,2,3,4,5] => 5
[6,2,4,5,1,3] => [1,6,3,4,5,2] => 17
[6,2,4,5,3,1] => [1,6,2,3,4,5] => 5
[6,2,5,1,3,4] => [1,6,4,2,3,5] => 12
[6,2,5,1,4,3] => [1,6,3,5,4,2] => 43
[6,2,5,3,1,4] => [1,6,4,3,5,2] => 26
[6,2,5,3,4,1] => [1,6,2,3,5,4] => 19
[6,2,5,4,1,3] => [1,6,3,5,2,4] => 32
[6,2,5,4,3,1] => [1,6,2,3,5,4] => 19
[6,3,1,2,4,5] => [1,6,5,4,2,3] => 28
[6,3,1,2,5,4] => [1,6,4,2,3,5] => 12
[6,3,1,4,2,5] => [1,6,5,2,3,4] => 14
[6,3,1,4,5,2] => [1,6,2,3,4,5] => 5
[6,3,1,5,2,4] => [1,6,4,5,2,3] => 22
[6,3,1,5,4,2] => [1,6,2,3,4,5] => 5
[6,3,2,1,4,5] => [1,6,5,4,2,3] => 28
[6,3,2,1,5,4] => [1,6,4,2,3,5] => 12
[6,3,2,4,1,5] => [1,6,5,2,3,4] => 14
[6,3,2,4,5,1] => [1,6,2,3,4,5] => 5
[6,3,2,5,1,4] => [1,6,4,5,2,3] => 22
[6,3,2,5,4,1] => [1,6,2,3,4,5] => 5
[6,3,4,1,2,5] => [1,6,5,2,3,4] => 14
[6,3,4,1,5,2] => [1,6,2,3,4,5] => 5
[6,3,4,2,1,5] => [1,6,5,2,3,4] => 14
[6,3,4,2,5,1] => [1,6,2,3,4,5] => 5
[6,3,4,5,1,2] => [1,6,2,3,4,5] => 5
[6,3,4,5,2,1] => [1,6,2,3,4,5] => 5
[6,3,5,1,2,4] => [1,6,4,2,3,5] => 12
[6,3,5,1,4,2] => [1,6,2,3,5,4] => 19
[6,3,5,2,1,4] => [1,6,4,2,3,5] => 12
[6,3,5,2,4,1] => [1,6,2,3,5,4] => 19
[6,3,5,4,1,2] => [1,6,2,3,5,4] => 19
[6,3,5,4,2,1] => [1,6,2,3,5,4] => 19
[6,4,1,2,3,5] => [1,6,5,3,2,4] => 23
[6,4,1,2,5,3] => [1,6,3,2,4,5] => 9
[6,4,1,3,2,5] => [1,6,5,2,4,3] => 37
[6,4,1,3,5,2] => [1,6,2,4,3,5] => 14
[6,4,1,5,2,3] => [1,6,3,2,4,5] => 9
[6,4,1,5,3,2] => [1,6,2,4,5,3] => 27
[6,4,2,1,3,5] => [1,6,5,3,2,4] => 23
[6,4,2,1,5,3] => [1,6,3,2,4,5] => 9
[6,4,2,3,1,5] => [1,6,5,2,4,3] => 37
[6,4,2,3,5,1] => [1,6,2,4,3,5] => 14
[6,4,2,5,1,3] => [1,6,3,2,4,5] => 9
[6,4,2,5,3,1] => [1,6,2,4,5,3] => 27
[6,4,3,1,2,5] => [1,6,5,2,4,3] => 37
[6,4,3,1,5,2] => [1,6,2,4,3,5] => 14
[6,4,3,2,1,5] => [1,6,5,2,4,3] => 37
[6,4,3,2,5,1] => [1,6,2,4,3,5] => 14
[6,4,3,5,1,2] => [1,6,2,4,5,3] => 27
[6,4,3,5,2,1] => [1,6,2,4,5,3] => 27
[6,4,5,1,2,3] => [1,6,3,5,2,4] => 32
[6,4,5,1,3,2] => [1,6,2,4,3,5] => 14
[6,4,5,2,1,3] => [1,6,3,5,2,4] => 32
[6,4,5,2,3,1] => [1,6,2,4,3,5] => 14
[6,4,5,3,1,2] => [1,6,2,4,3,5] => 14
[6,4,5,3,2,1] => [1,6,2,4,3,5] => 14
[6,5,1,2,3,4] => [1,6,4,2,5,3] => 31
[6,5,1,2,4,3] => [1,6,3,2,5,4] => 34
[6,5,1,3,2,4] => [1,6,4,3,2,5] => 19
[6,5,1,3,4,2] => [1,6,2,5,4,3] => 58
[6,5,1,4,2,3] => [1,6,3,2,5,4] => 34
[6,5,1,4,3,2] => [1,6,2,5,3,4] => 26
[6,5,2,1,3,4] => [1,6,4,2,5,3] => 31
[6,5,2,1,4,3] => [1,6,3,2,5,4] => 34
[6,5,2,3,1,4] => [1,6,4,3,2,5] => 19
[6,5,2,3,4,1] => [1,6,2,5,4,3] => 58
[6,5,2,4,1,3] => [1,6,3,2,5,4] => 34
[6,5,2,4,3,1] => [1,6,2,5,3,4] => 26
[6,5,3,1,2,4] => [1,6,4,2,5,3] => 31
[6,5,3,1,4,2] => [1,6,2,5,4,3] => 58
[6,5,3,2,1,4] => [1,6,4,2,5,3] => 31
[6,5,3,2,4,1] => [1,6,2,5,4,3] => 58
[6,5,3,4,1,2] => [1,6,2,5,3,4] => 26
[6,5,3,4,2,1] => [1,6,2,5,3,4] => 26
[6,5,4,1,2,3] => [1,6,3,4,2,5] => 13
[6,5,4,1,3,2] => [1,6,2,5,3,4] => 26
[6,5,4,2,1,3] => [1,6,3,4,2,5] => 13
[6,5,4,2,3,1] => [1,6,2,5,3,4] => 26
[6,5,4,3,1,2] => [1,6,2,5,3,4] => 26
[6,5,4,3,2,1] => [1,6,2,5,3,4] => 26
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 1
[1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => 1
[1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => 1
[1,2,3,4,6,7,5] => [1,2,3,4,5,6,7] => 1
[1,2,3,4,7,5,6] => [1,2,3,4,5,7,6] => 6
[1,2,3,4,7,6,5] => [1,2,3,4,5,7,6] => 6
[1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => 1
[1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => 1
[1,2,3,5,6,4,7] => [1,2,3,4,5,6,7] => 1
[1,2,3,5,6,7,4] => [1,2,3,4,5,6,7] => 1
[1,2,3,5,7,4,6] => [1,2,3,4,5,7,6] => 6
[1,2,3,5,7,6,4] => [1,2,3,4,5,7,6] => 6
[1,2,3,6,4,5,7] => [1,2,3,4,6,5,7] => 5
[1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => 5
[1,2,3,6,7,4,5] => [1,2,3,4,6,5,7] => 5
[1,2,3,6,7,5,4] => [1,2,3,4,6,5,7] => 5
[1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => 1
[1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => 1
[1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => 1
[1,2,4,3,6,7,5] => [1,2,3,4,5,6,7] => 1
[1,2,4,3,7,5,6] => [1,2,3,4,5,7,6] => 6
[1,2,4,3,7,6,5] => [1,2,3,4,5,7,6] => 6
[1,2,4,5,3,6,7] => [1,2,3,4,5,6,7] => 1
[1,2,4,5,3,7,6] => [1,2,3,4,5,6,7] => 1
[1,2,4,5,6,3,7] => [1,2,3,4,5,6,7] => 1
[1,2,4,5,6,7,3] => [1,2,3,4,5,6,7] => 1
[1,2,4,5,7,3,6] => [1,2,3,4,5,7,6] => 6
[1,2,4,5,7,6,3] => [1,2,3,4,5,7,6] => 6
[1,2,4,6,3,5,7] => [1,2,3,4,6,5,7] => 5
[1,2,4,6,5,3,7] => [1,2,3,4,6,5,7] => 5
[1,2,4,6,7,3,5] => [1,2,3,4,6,5,7] => 5
[1,2,4,6,7,5,3] => [1,2,3,4,6,5,7] => 5
[1,2,6,7,3,4,5] => [1,2,3,6,4,7,5] => 40
[1,2,6,7,4,3,5] => [1,2,3,6,4,7,5] => 40
[1,2,6,7,5,3,4] => [1,2,3,6,4,7,5] => 40
[1,2,6,7,5,4,3] => [1,2,3,6,4,7,5] => 40
[1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => 1
[1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => 1
[1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => 1
[1,3,2,4,6,7,5] => [1,2,3,4,5,6,7] => 1
[1,3,2,4,7,5,6] => [1,2,3,4,5,7,6] => 6
[1,3,2,4,7,6,5] => [1,2,3,4,5,7,6] => 6
[1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => 1
[1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => 1
[1,3,2,5,6,4,7] => [1,2,3,4,5,6,7] => 1
[1,3,2,5,6,7,4] => [1,2,3,4,5,6,7] => 1
[1,3,2,5,7,4,6] => [1,2,3,4,5,7,6] => 6
[1,3,2,5,7,6,4] => [1,2,3,4,5,7,6] => 6
[1,3,2,6,4,5,7] => [1,2,3,4,6,5,7] => 5
[1,3,2,6,5,4,7] => [1,2,3,4,6,5,7] => 5
[1,3,2,6,7,4,5] => [1,2,3,4,6,5,7] => 5
[1,3,2,6,7,5,4] => [1,2,3,4,6,5,7] => 5
[1,3,4,2,5,6,7] => [1,2,3,4,5,6,7] => 1
[1,3,4,2,5,7,6] => [1,2,3,4,5,6,7] => 1
[1,3,4,2,6,5,7] => [1,2,3,4,5,6,7] => 1
[1,3,4,2,6,7,5] => [1,2,3,4,5,6,7] => 1
[1,3,4,2,7,5,6] => [1,2,3,4,5,7,6] => 6
[1,3,4,2,7,6,5] => [1,2,3,4,5,7,6] => 6
[1,3,4,5,2,6,7] => [1,2,3,4,5,6,7] => 1
[1,3,4,5,2,7,6] => [1,2,3,4,5,6,7] => 1
[1,3,4,5,6,2,7] => [1,2,3,4,5,6,7] => 1
[1,3,4,5,6,7,2] => [1,2,3,4,5,6,7] => 1
[1,3,4,5,7,2,6] => [1,2,3,4,5,7,6] => 6
[1,3,4,5,7,6,2] => [1,2,3,4,5,7,6] => 6
[1,3,4,6,2,5,7] => [1,2,3,4,6,5,7] => 5
[1,3,4,6,5,2,7] => [1,2,3,4,6,5,7] => 5
[1,3,4,6,7,2,5] => [1,2,3,4,6,5,7] => 5
[1,3,4,6,7,5,2] => [1,2,3,4,6,5,7] => 5
[1,3,6,7,2,4,5] => [1,2,3,6,4,7,5] => 40
[1,3,6,7,4,2,5] => [1,2,3,6,4,7,5] => 40
[1,3,6,7,5,2,4] => [1,2,3,6,4,7,5] => 40
[1,3,6,7,5,4,2] => [1,2,3,6,4,7,5] => 40
[1,6,2,7,4,3,5] => [1,2,6,3,4,7,5] => 45
[1,6,2,7,5,3,4] => [1,2,6,3,4,7,5] => 45
[1,6,3,7,4,2,5] => [1,2,6,3,4,7,5] => 45
[1,6,3,7,5,2,4] => [1,2,6,3,4,7,5] => 45
[1,6,4,7,2,3,5] => [1,2,6,3,4,7,5] => 45
[1,6,4,7,3,2,5] => [1,2,6,3,4,7,5] => 45
[1,6,4,7,5,2,3] => [1,2,6,3,4,7,5] => 45
[1,6,4,7,5,3,2] => [1,2,6,3,4,7,5] => 45
[2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => 1
[2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => 1
[2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => 1
[2,1,3,4,6,7,5] => [1,2,3,4,5,6,7] => 1
[2,1,3,4,7,5,6] => [1,2,3,4,5,7,6] => 6
[2,1,3,4,7,6,5] => [1,2,3,4,5,7,6] => 6
[2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => 1
[2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => 1
[2,1,3,5,6,4,7] => [1,2,3,4,5,6,7] => 1
[2,1,3,5,6,7,4] => [1,2,3,4,5,6,7] => 1
[2,1,3,5,7,4,6] => [1,2,3,4,5,7,6] => 6
[2,1,3,5,7,6,4] => [1,2,3,4,5,7,6] => 6
[2,1,3,6,4,5,7] => [1,2,3,4,6,5,7] => 5
[2,1,3,6,5,4,7] => [1,2,3,4,6,5,7] => 5
[2,1,3,6,7,4,5] => [1,2,3,4,6,5,7] => 5
[2,1,3,6,7,5,4] => [1,2,3,4,6,5,7] => 5
[2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => 1
[2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => 1
[2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => 1
[2,1,4,3,6,7,5] => [1,2,3,4,5,6,7] => 1
[2,1,4,3,7,5,6] => [1,2,3,4,5,7,6] => 6
[2,1,4,3,7,6,5] => [1,2,3,4,5,7,6] => 6
[2,1,4,5,3,6,7] => [1,2,3,4,5,6,7] => 1
[2,1,4,5,3,7,6] => [1,2,3,4,5,6,7] => 1
[2,1,4,5,6,3,7] => [1,2,3,4,5,6,7] => 1
[2,1,4,5,6,7,3] => [1,2,3,4,5,6,7] => 1
[2,1,4,5,7,3,6] => [1,2,3,4,5,7,6] => 6
[2,1,4,5,7,6,3] => [1,2,3,4,5,7,6] => 6
[2,1,4,6,3,5,7] => [1,2,3,4,6,5,7] => 5
[2,1,4,6,5,3,7] => [1,2,3,4,6,5,7] => 5
[2,1,4,6,7,3,5] => [1,2,3,4,6,5,7] => 5
[2,1,4,6,7,5,3] => [1,2,3,4,6,5,7] => 5
[2,1,6,7,3,4,5] => [1,2,3,6,4,7,5] => 40
[2,1,6,7,4,3,5] => [1,2,3,6,4,7,5] => 40
[2,1,6,7,5,3,4] => [1,2,3,6,4,7,5] => 40
[2,1,6,7,5,4,3] => [1,2,3,6,4,7,5] => 40
[2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => 1
[2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => 1
[2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => 1
[2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => 1
[2,3,1,4,7,5,6] => [1,2,3,4,5,7,6] => 6
[2,3,1,4,7,6,5] => [1,2,3,4,5,7,6] => 6
[2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => 1
[2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => 1
[2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => 1
[2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => 1
[2,3,1,5,7,4,6] => [1,2,3,4,5,7,6] => 6
[2,3,1,5,7,6,4] => [1,2,3,4,5,7,6] => 6
[2,3,1,6,4,5,7] => [1,2,3,4,6,5,7] => 5
[2,3,1,6,5,4,7] => [1,2,3,4,6,5,7] => 5
[2,3,1,6,7,4,5] => [1,2,3,4,6,5,7] => 5
[2,3,1,6,7,5,4] => [1,2,3,4,6,5,7] => 5
[2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => 1
[2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => 1
[2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => 1
[2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => 1
[2,3,4,1,7,5,6] => [1,2,3,4,5,7,6] => 6
[2,3,4,1,7,6,5] => [1,2,3,4,5,7,6] => 6
[2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => 1
[2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => 1
[2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => 1
[2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => 1
[2,3,4,5,7,1,6] => [1,2,3,4,5,7,6] => 6
[2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => 6
[2,3,4,6,1,5,7] => [1,2,3,4,6,5,7] => 5
[2,3,4,6,5,1,7] => [1,2,3,4,6,5,7] => 5
[2,3,4,6,7,1,5] => [1,2,3,4,6,5,7] => 5
[2,3,4,6,7,5,1] => [1,2,3,4,6,5,7] => 5
[2,3,6,7,1,4,5] => [1,2,3,6,4,7,5] => 40
[2,3,6,7,4,1,5] => [1,2,3,6,4,7,5] => 40
[2,3,6,7,5,1,4] => [1,2,3,6,4,7,5] => 40
[2,3,6,7,5,4,1] => [1,2,3,6,4,7,5] => 40
[2,6,1,7,4,3,5] => [1,2,6,3,4,7,5] => 45
[2,6,1,7,5,3,4] => [1,2,6,3,4,7,5] => 45
[2,6,3,7,4,1,5] => [1,2,6,3,4,7,5] => 45
[2,6,3,7,5,1,4] => [1,2,6,3,4,7,5] => 45
[2,6,4,7,1,3,5] => [1,2,6,3,4,7,5] => 45
[2,6,4,7,3,1,5] => [1,2,6,3,4,7,5] => 45
[2,6,4,7,5,1,3] => [1,2,6,3,4,7,5] => 45
[2,6,4,7,5,3,1] => [1,2,6,3,4,7,5] => 45
[3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => 2
[3,1,2,4,5,7,6] => [1,3,2,4,5,6,7] => 2
[3,1,2,4,6,5,7] => [1,3,2,4,5,6,7] => 2
[3,1,2,4,6,7,5] => [1,3,2,4,5,6,7] => 2
[3,1,2,5,4,6,7] => [1,3,2,4,5,6,7] => 2
[3,1,2,5,4,7,6] => [1,3,2,4,5,6,7] => 2
[3,1,2,5,6,4,7] => [1,3,2,4,5,6,7] => 2
[3,1,2,5,6,7,4] => [1,3,2,4,5,6,7] => 2
[3,1,7,2,4,5,6] => [1,3,7,6,5,4,2] => 378
[3,1,7,4,5,6,2] => [1,3,7,2,4,5,6] => 24
[3,1,7,4,6,5,2] => [1,3,7,2,4,5,6] => 24
[3,1,7,5,4,6,2] => [1,3,7,2,4,5,6] => 24
[3,1,7,5,6,4,2] => [1,3,7,2,4,5,6] => 24
[3,2,1,4,5,6,7] => [1,3,2,4,5,6,7] => 2
[3,2,1,4,5,7,6] => [1,3,2,4,5,6,7] => 2
[3,2,1,4,6,5,7] => [1,3,2,4,5,6,7] => 2
[3,2,1,4,6,7,5] => [1,3,2,4,5,6,7] => 2
[3,2,1,5,4,6,7] => [1,3,2,4,5,6,7] => 2
[3,2,1,5,4,7,6] => [1,3,2,4,5,6,7] => 2
[3,2,1,5,6,4,7] => [1,3,2,4,5,6,7] => 2
[3,2,1,5,6,7,4] => [1,3,2,4,5,6,7] => 2
[3,2,7,1,4,5,6] => [1,3,7,6,5,4,2] => 378
[3,2,7,4,5,6,1] => [1,3,7,2,4,5,6] => 24
[3,2,7,4,6,5,1] => [1,3,7,2,4,5,6] => 24
[3,2,7,5,4,6,1] => [1,3,7,2,4,5,6] => 24
[3,2,7,5,6,4,1] => [1,3,7,2,4,5,6] => 24
[3,4,1,2,5,6,7] => [1,3,2,4,5,6,7] => 2
[3,4,1,2,5,7,6] => [1,3,2,4,5,6,7] => 2
[3,4,1,2,6,5,7] => [1,3,2,4,5,6,7] => 2
[3,4,1,2,6,7,5] => [1,3,2,4,5,6,7] => 2
[3,4,1,5,2,6,7] => [1,3,2,4,5,6,7] => 2
[3,4,1,5,2,7,6] => [1,3,2,4,5,6,7] => 2
[3,4,1,5,6,2,7] => [1,3,2,4,5,6,7] => 2
[3,4,1,5,6,7,2] => [1,3,2,4,5,6,7] => 2
[3,4,2,1,5,6,7] => [1,3,2,4,5,6,7] => 2
[3,4,2,1,5,7,6] => [1,3,2,4,5,6,7] => 2
[3,4,2,1,6,5,7] => [1,3,2,4,5,6,7] => 2
[3,4,2,1,6,7,5] => [1,3,2,4,5,6,7] => 2
[3,4,2,5,1,6,7] => [1,3,2,4,5,6,7] => 2
[3,4,2,5,1,7,6] => [1,3,2,4,5,6,7] => 2
[3,4,2,5,6,1,7] => [1,3,2,4,5,6,7] => 2
[3,4,2,5,6,7,1] => [1,3,2,4,5,6,7] => 2
[3,4,7,1,5,6,2] => [1,3,7,2,4,5,6] => 24
[3,4,7,1,6,5,2] => [1,3,7,2,4,5,6] => 24
[3,4,7,2,5,6,1] => [1,3,7,2,4,5,6] => 24
[3,4,7,2,6,5,1] => [1,3,7,2,4,5,6] => 24
[3,4,7,5,1,6,2] => [1,3,7,2,4,5,6] => 24
[3,4,7,5,2,6,1] => [1,3,7,2,4,5,6] => 24
[3,4,7,5,6,1,2] => [1,3,7,2,4,5,6] => 24
[3,4,7,5,6,2,1] => [1,3,7,2,4,5,6] => 24
[4,1,2,6,3,7,5] => [1,4,6,7,5,3,2] => 97
[4,1,2,7,3,5,6] => [1,4,7,6,5,3,2] => 211
[4,1,3,6,5,7,2] => [1,4,6,7,2,3,5] => 45
[4,1,3,7,5,6,2] => [1,4,7,2,3,5,6] => 27
[4,1,3,7,6,5,2] => [1,4,7,2,3,5,6] => 27
[4,1,5,6,3,7,2] => [1,4,6,7,2,3,5] => 45
[4,1,5,7,3,6,2] => [1,4,7,2,3,5,6] => 27
[4,1,5,7,6,3,2] => [1,4,7,2,3,5,6] => 27
[4,2,1,6,3,7,5] => [1,4,6,7,5,3,2] => 97
[4,2,1,7,3,5,6] => [1,4,7,6,5,3,2] => 211
[4,2,3,6,5,7,1] => [1,4,6,7,2,3,5] => 45
[4,2,3,7,5,6,1] => [1,4,7,2,3,5,6] => 27
[4,2,3,7,6,5,1] => [1,4,7,2,3,5,6] => 27
[4,2,5,6,3,7,1] => [1,4,6,7,2,3,5] => 45
[4,2,5,7,3,6,1] => [1,4,7,2,3,5,6] => 27
[4,2,5,7,6,3,1] => [1,4,7,2,3,5,6] => 27
[4,3,1,6,5,7,2] => [1,4,6,7,2,3,5] => 45
[4,3,1,7,5,6,2] => [1,4,7,2,3,5,6] => 27
[4,3,1,7,6,5,2] => [1,4,7,2,3,5,6] => 27
[4,3,2,6,5,7,1] => [1,4,6,7,2,3,5] => 45
[4,3,2,7,5,6,1] => [1,4,7,2,3,5,6] => 27
[4,3,2,7,6,5,1] => [1,4,7,2,3,5,6] => 27
[4,3,5,6,1,7,2] => [1,4,6,7,2,3,5] => 45
[4,3,5,6,2,7,1] => [1,4,6,7,2,3,5] => 45
[4,3,5,7,1,6,2] => [1,4,7,2,3,5,6] => 27
[4,3,5,7,2,6,1] => [1,4,7,2,3,5,6] => 27
[4,3,5,7,6,1,2] => [1,4,7,2,3,5,6] => 27
[4,3,5,7,6,2,1] => [1,4,7,2,3,5,6] => 27
[5,1,2,3,6,7,4] => [1,5,6,7,4,3,2] => 48
[5,1,2,3,7,4,6] => [1,5,7,6,4,3,2] => 124
[5,1,2,7,4,3,6] => [1,5,4,7,6,3,2] => 125
[5,1,2,7,6,4,3] => [1,5,6,4,7,3,2] => 43
[5,1,3,4,6,7,2] => [1,5,6,7,2,3,4] => 20
[5,1,3,4,7,6,2] => [1,5,7,2,3,4,6] => 24
[5,1,3,6,7,4,2] => [1,5,7,2,3,4,6] => 24
[5,1,3,7,2,4,6] => [1,5,2,3,4,7,6] => 24
[5,1,3,7,2,6,4] => [1,5,2,3,4,7,6] => 24
[5,1,4,3,6,7,2] => [1,5,6,7,2,3,4] => 20
[5,1,4,3,7,6,2] => [1,5,7,2,3,4,6] => 24
[5,1,4,6,7,3,2] => [1,5,7,2,3,4,6] => 24
[5,1,4,7,2,3,6] => [1,5,2,3,4,7,6] => 24
[5,1,4,7,2,6,3] => [1,5,2,3,4,7,6] => 24
[5,2,1,3,6,7,4] => [1,5,6,7,4,3,2] => 48
[5,2,1,3,7,4,6] => [1,5,7,6,4,3,2] => 124
[5,2,1,7,4,3,6] => [1,5,4,7,6,3,2] => 125
[5,2,1,7,6,4,3] => [1,5,6,4,7,3,2] => 43
[5,2,3,4,6,7,1] => [1,5,6,7,2,3,4] => 20
[5,2,3,4,7,6,1] => [1,5,7,2,3,4,6] => 24
[5,2,3,6,7,4,1] => [1,5,7,2,3,4,6] => 24
[5,2,3,7,1,4,6] => [1,5,2,3,4,7,6] => 24
[5,2,3,7,1,6,4] => [1,5,2,3,4,7,6] => 24
[5,2,4,3,6,7,1] => [1,5,6,7,2,3,4] => 20
[5,2,4,3,7,6,1] => [1,5,7,2,3,4,6] => 24
[5,2,4,6,7,3,1] => [1,5,7,2,3,4,6] => 24
[5,2,4,7,1,3,6] => [1,5,2,3,4,7,6] => 24
[5,2,4,7,1,6,3] => [1,5,2,3,4,7,6] => 24
[5,3,1,4,6,7,2] => [1,5,6,7,2,3,4] => 20
[5,3,1,4,7,6,2] => [1,5,7,2,3,4,6] => 24
[5,3,1,6,7,4,2] => [1,5,7,2,3,4,6] => 24
[5,3,1,7,2,4,6] => [1,5,2,3,4,7,6] => 24
[5,3,1,7,2,6,4] => [1,5,2,3,4,7,6] => 24
[5,3,2,4,6,7,1] => [1,5,6,7,2,3,4] => 20
[5,3,2,4,7,6,1] => [1,5,7,2,3,4,6] => 24
[5,3,2,6,7,4,1] => [1,5,7,2,3,4,6] => 24
[5,3,2,7,1,4,6] => [1,5,2,3,4,7,6] => 24
[5,3,2,7,1,6,4] => [1,5,2,3,4,7,6] => 24
[5,3,4,1,6,7,2] => [1,5,6,7,2,3,4] => 20
[5,3,4,1,7,6,2] => [1,5,7,2,3,4,6] => 24
[5,3,4,2,6,7,1] => [1,5,6,7,2,3,4] => 20
[5,3,4,2,7,6,1] => [1,5,7,2,3,4,6] => 24
[5,3,4,6,7,1,2] => [1,5,7,2,3,4,6] => 24
[5,3,4,6,7,2,1] => [1,5,7,2,3,4,6] => 24
[5,3,4,7,1,2,6] => [1,5,2,3,4,7,6] => 24
[5,3,4,7,1,6,2] => [1,5,2,3,4,7,6] => 24
[5,3,4,7,2,1,6] => [1,5,2,3,4,7,6] => 24
[5,3,4,7,2,6,1] => [1,5,2,3,4,7,6] => 24
[5,7,1,4,2,6,3] => [1,5,2,7,3,4,6] => 56
[5,7,1,4,6,2,3] => [1,5,6,2,7,3,4] => 45
[5,7,1,6,2,4,3] => [1,5,2,7,3,4,6] => 56
[5,7,2,4,1,6,3] => [1,5,2,7,3,4,6] => 56
[5,7,2,4,6,1,3] => [1,5,6,2,7,3,4] => 45
[5,7,2,6,1,4,3] => [1,5,2,7,3,4,6] => 56
[5,7,3,4,1,6,2] => [1,5,2,7,3,4,6] => 56
[5,7,3,4,2,6,1] => [1,5,2,7,3,4,6] => 56
[5,7,3,4,6,1,2] => [1,5,6,2,7,3,4] => 45
[5,7,3,4,6,2,1] => [1,5,6,2,7,3,4] => 45
[5,7,3,6,1,4,2] => [1,5,2,7,3,4,6] => 56
[5,7,3,6,2,4,1] => [1,5,2,7,3,4,6] => 56
[5,7,4,1,2,6,3] => [1,5,2,7,3,4,6] => 56
[5,7,4,1,6,2,3] => [1,5,6,2,7,3,4] => 45
[5,7,4,2,1,6,3] => [1,5,2,7,3,4,6] => 56
[5,7,4,2,6,1,3] => [1,5,6,2,7,3,4] => 45
[5,7,4,3,1,6,2] => [1,5,2,7,3,4,6] => 56
[5,7,4,3,2,6,1] => [1,5,2,7,3,4,6] => 56
[5,7,4,3,6,1,2] => [1,5,6,2,7,3,4] => 45
[5,7,4,3,6,2,1] => [1,5,6,2,7,3,4] => 45
[5,7,4,6,1,2,3] => [1,5,2,7,3,4,6] => 56
[5,7,4,6,1,3,2] => [1,5,2,7,3,4,6] => 56
[5,7,4,6,2,1,3] => [1,5,2,7,3,4,6] => 56
[5,7,4,6,2,3,1] => [1,5,2,7,3,4,6] => 56
[6,1,2,3,4,7,5] => [1,6,7,5,4,3,2] => 90
[6,1,2,3,7,5,4] => [1,6,5,7,4,3,2] => 76
[6,1,2,7,4,5,3] => [1,6,5,4,7,3,2] => 66
[6,1,3,4,5,7,2] => [1,6,7,2,3,4,5] => 15
[6,1,3,5,4,7,2] => [1,6,7,2,3,4,5] => 15
[6,1,3,7,4,2,5] => [1,6,2,3,4,7,5] => 24
[6,1,3,7,5,2,4] => [1,6,2,3,4,7,5] => 24
[6,1,4,3,5,7,2] => [1,6,7,2,3,4,5] => 15
[6,1,4,5,3,7,2] => [1,6,7,2,3,4,5] => 15
[6,1,4,7,3,2,5] => [1,6,2,3,4,7,5] => 24
[6,1,4,7,5,2,3] => [1,6,2,3,4,7,5] => 24
[6,1,7,3,4,5,2] => [1,6,5,4,3,7,2] => 56
[6,1,7,3,5,2,4] => [1,6,2,3,7,4,5] => 45
[6,1,7,4,5,2,3] => [1,6,2,3,7,4,5] => 45
[6,1,7,5,3,2,4] => [1,6,2,3,7,4,5] => 45
[6,1,7,5,4,2,3] => [1,6,2,3,7,4,5] => 45
[6,2,1,3,4,7,5] => [1,6,7,5,4,3,2] => 90
[6,2,1,3,7,5,4] => [1,6,5,7,4,3,2] => 76
[6,2,1,7,4,5,3] => [1,6,5,4,7,3,2] => 66
[6,2,3,4,5,7,1] => [1,6,7,2,3,4,5] => 15
[6,2,3,5,4,7,1] => [1,6,7,2,3,4,5] => 15
[6,2,3,7,4,1,5] => [1,6,2,3,4,7,5] => 24
[6,2,3,7,5,1,4] => [1,6,2,3,4,7,5] => 24
[6,2,4,3,5,7,1] => [1,6,7,2,3,4,5] => 15
[6,2,4,5,3,7,1] => [1,6,7,2,3,4,5] => 15
[6,2,4,7,3,1,5] => [1,6,2,3,4,7,5] => 24
[6,2,4,7,5,1,3] => [1,6,2,3,4,7,5] => 24
[6,2,7,3,4,5,1] => [1,6,5,4,3,7,2] => 56
[6,2,7,3,5,1,4] => [1,6,2,3,7,4,5] => 45
[6,2,7,4,5,1,3] => [1,6,2,3,7,4,5] => 45
[6,2,7,5,3,1,4] => [1,6,2,3,7,4,5] => 45
[6,2,7,5,4,1,3] => [1,6,2,3,7,4,5] => 45
[6,3,1,4,5,7,2] => [1,6,7,2,3,4,5] => 15
[6,3,1,5,4,7,2] => [1,6,7,2,3,4,5] => 15
[6,3,1,7,4,2,5] => [1,6,2,3,4,7,5] => 24
[6,3,1,7,5,2,4] => [1,6,2,3,4,7,5] => 24
[6,3,2,4,5,7,1] => [1,6,7,2,3,4,5] => 15
[6,3,2,5,4,7,1] => [1,6,7,2,3,4,5] => 15
[6,3,2,7,4,1,5] => [1,6,2,3,4,7,5] => 24
[6,3,2,7,5,1,4] => [1,6,2,3,4,7,5] => 24
[6,3,4,1,5,7,2] => [1,6,7,2,3,4,5] => 15
[6,3,4,2,5,7,1] => [1,6,7,2,3,4,5] => 15
[6,3,4,5,1,7,2] => [1,6,7,2,3,4,5] => 15
[6,3,4,5,2,7,1] => [1,6,7,2,3,4,5] => 15
[6,3,4,7,1,2,5] => [1,6,2,3,4,7,5] => 24
[6,3,4,7,2,1,5] => [1,6,2,3,4,7,5] => 24
[6,3,4,7,5,1,2] => [1,6,2,3,4,7,5] => 24
[6,3,4,7,5,2,1] => [1,6,2,3,4,7,5] => 24
[6,3,7,1,5,2,4] => [1,6,2,3,7,4,5] => 45
[6,3,7,2,5,1,4] => [1,6,2,3,7,4,5] => 45
[6,3,7,4,5,1,2] => [1,6,2,3,7,4,5] => 45
[6,3,7,4,5,2,1] => [1,6,2,3,7,4,5] => 45
[6,3,7,5,1,2,4] => [1,6,2,3,7,4,5] => 45
[6,3,7,5,2,1,4] => [1,6,2,3,7,4,5] => 45
[6,3,7,5,4,1,2] => [1,6,2,3,7,4,5] => 45
[6,3,7,5,4,2,1] => [1,6,2,3,7,4,5] => 45
[6,7,1,4,5,2,3] => [1,6,2,7,3,4,5] => 40
[6,7,1,5,4,2,3] => [1,6,2,7,3,4,5] => 40
[6,7,2,4,5,1,3] => [1,6,2,7,3,4,5] => 40
[6,7,2,5,4,1,3] => [1,6,2,7,3,4,5] => 40
[6,7,3,4,5,1,2] => [1,6,2,7,3,4,5] => 40
[6,7,3,4,5,2,1] => [1,6,2,7,3,4,5] => 40
[6,7,3,5,4,1,2] => [1,6,2,7,3,4,5] => 40
[6,7,3,5,4,2,1] => [1,6,2,7,3,4,5] => 40
[6,7,4,1,5,2,3] => [1,6,2,7,3,4,5] => 40
[6,7,4,2,5,1,3] => [1,6,2,7,3,4,5] => 40
[6,7,4,3,5,1,2] => [1,6,2,7,3,4,5] => 40
[6,7,4,3,5,2,1] => [1,6,2,7,3,4,5] => 40
[6,7,4,5,1,2,3] => [1,6,2,7,3,4,5] => 40
[6,7,4,5,2,1,3] => [1,6,2,7,3,4,5] => 40
[6,7,4,5,3,1,2] => [1,6,2,7,3,4,5] => 40
[6,7,4,5,3,2,1] => [1,6,2,7,3,4,5] => 40
[7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => 132
[7,1,2,5,3,4,6] => [1,7,6,4,5,3,2] => 107
[7,1,2,5,6,3,4] => [1,7,4,5,6,3,2] => 62
[7,1,2,6,3,5,4] => [1,7,4,6,5,3,2] => 151
[7,1,2,6,4,3,5] => [1,7,5,4,6,3,2] => 89
[7,1,3,4,5,6,2] => [1,7,2,3,4,5,6] => 6
[7,1,3,4,6,5,2] => [1,7,2,3,4,5,6] => 6
[7,1,3,5,4,6,2] => [1,7,2,3,4,5,6] => 6
[7,1,3,5,6,4,2] => [1,7,2,3,4,5,6] => 6
[7,1,4,3,5,6,2] => [1,7,2,3,4,5,6] => 6
[7,1,4,3,6,5,2] => [1,7,2,3,4,5,6] => 6
[7,1,4,5,3,6,2] => [1,7,2,3,4,5,6] => 6
[7,1,4,5,6,3,2] => [1,7,2,3,4,5,6] => 6
[7,1,5,2,6,4,3] => [1,7,3,5,6,4,2] => 122
[7,1,6,2,4,5,3] => [1,7,3,6,5,4,2] => 251
[7,1,6,3,2,5,4] => [1,7,4,3,6,5,2] => 150
[7,1,6,3,4,2,5] => [1,7,5,4,3,6,2] => 75
[7,1,6,5,3,2,4] => [1,7,4,5,3,6,2] => 54
[7,2,1,3,4,5,6] => [1,7,6,5,4,3,2] => 132
[7,2,1,5,3,4,6] => [1,7,6,4,5,3,2] => 107
[7,2,1,5,6,3,4] => [1,7,4,5,6,3,2] => 62
[7,2,1,6,3,5,4] => [1,7,4,6,5,3,2] => 151
[7,2,1,6,4,3,5] => [1,7,5,4,6,3,2] => 89
[7,2,3,4,5,6,1] => [1,7,2,3,4,5,6] => 6
[7,2,3,4,6,5,1] => [1,7,2,3,4,5,6] => 6
[7,2,3,5,4,6,1] => [1,7,2,3,4,5,6] => 6
[7,2,3,5,6,4,1] => [1,7,2,3,4,5,6] => 6
[7,2,4,3,5,6,1] => [1,7,2,3,4,5,6] => 6
[7,2,4,3,6,5,1] => [1,7,2,3,4,5,6] => 6
[7,2,4,5,3,6,1] => [1,7,2,3,4,5,6] => 6
[7,2,4,5,6,3,1] => [1,7,2,3,4,5,6] => 6
[7,2,5,1,6,4,3] => [1,7,3,5,6,4,2] => 122
[7,2,6,1,4,5,3] => [1,7,3,6,5,4,2] => 251
[7,2,6,3,1,5,4] => [1,7,4,3,6,5,2] => 150
[7,2,6,3,4,1,5] => [1,7,5,4,3,6,2] => 75
[7,2,6,5,3,1,4] => [1,7,4,5,3,6,2] => 54
[7,3,1,4,5,6,2] => [1,7,2,3,4,5,6] => 6
[7,3,1,4,6,5,2] => [1,7,2,3,4,5,6] => 6
[7,3,1,5,4,6,2] => [1,7,2,3,4,5,6] => 6
[7,3,1,5,6,4,2] => [1,7,2,3,4,5,6] => 6
[7,3,2,4,5,6,1] => [1,7,2,3,4,5,6] => 6
[7,3,2,4,6,5,1] => [1,7,2,3,4,5,6] => 6
[7,3,2,5,4,6,1] => [1,7,2,3,4,5,6] => 6
[7,3,2,5,6,4,1] => [1,7,2,3,4,5,6] => 6
[7,3,4,1,5,6,2] => [1,7,2,3,4,5,6] => 6
[7,3,4,1,6,5,2] => [1,7,2,3,4,5,6] => 6
[7,3,4,2,5,6,1] => [1,7,2,3,4,5,6] => 6
[7,3,4,2,6,5,1] => [1,7,2,3,4,5,6] => 6
[7,3,4,5,1,6,2] => [1,7,2,3,4,5,6] => 6
[7,3,4,5,2,6,1] => [1,7,2,3,4,5,6] => 6
[7,3,4,5,6,1,2] => [1,7,2,3,4,5,6] => 6
[7,3,4,5,6,2,1] => [1,7,2,3,4,5,6] => 6
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,2 8,4,10,0,2 16,8,20,18,4,16,6,12,6,2,6,0,0,6
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q + 2\ q^{2}$
$F_{4} = 8\ q + 4\ q^{2} + 10\ q^{3} + 2\ q^{5}$
$F_{5} = 16\ q + 8\ q^{2} + 20\ q^{3} + 18\ q^{4} + 4\ q^{5} + 16\ q^{6} + 6\ q^{7} + 12\ q^{8} + 6\ q^{9} + 2\ q^{10} + 6\ q^{11} + 6\ q^{14}$
$F_{6} = 32\ q + 16\ q^{2} + 40\ q^{3} + 36\ q^{4} + 42\ q^{5} + 32\ q^{6} + 12\ q^{7} + 24\ q^{8} + 22\ q^{9} + 68\ q^{10} + 12\ q^{11} + 10\ q^{12} + 6\ q^{13} + 32\ q^{14} + 56\ q^{15} + 8\ q^{16} + 2\ q^{17} + 20\ q^{19} + 48\ q^{20} + 8\ q^{21} + 6\ q^{22} + 14\ q^{23} + 4\ q^{24} + 28\ q^{25} + 28\ q^{26} + 6\ q^{27} + 6\ q^{28} + 8\ q^{30} + 6\ q^{31} + 10\ q^{32} + 6\ q^{34} + 12\ q^{35} + 6\ q^{37} + 4\ q^{38} + 12\ q^{40} + 2\ q^{42} + 2\ q^{43} + 8\ q^{44} + 4\ q^{46} + 8\ q^{51} + 6\ q^{58} + 4\ q^{60} + 4\ q^{84}$
Description
The number of reduced Kogan faces with the permutation as type.
This is equivalent to finding the number of ways to represent the permutation $\pi \in S_{n+1}$ as a reduced subword of $s_n (s_{n-1} s_n) (s_{n-2} s_{n-1} s_n) \dotsm (s_1 \dotsm s_n)$, or the number of reduced pipe dreams for $\pi$.
This is equivalent to finding the number of ways to represent the permutation $\pi \in S_{n+1}$ as a reduced subword of $s_n (s_{n-1} s_n) (s_{n-2} s_{n-1} s_n) \dotsm (s_1 \dotsm s_n)$, or the number of reduced pipe dreams for $\pi$.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
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