Identifier
-
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
St000001: Permutations ⟶ ℤ
Values
[1] => [1] => 1
[1,2] => [1,2] => 1
[2,1] => [2,1] => 1
[1,2,3] => [1,2,3] => 1
[1,3,2] => [1,3,2] => 1
[2,1,3] => [2,1,3] => 1
[2,3,1] => [3,2,1] => 2
[3,1,2] => [3,2,1] => 2
[3,2,1] => [3,2,1] => 2
[1,2,3,4] => [1,2,3,4] => 1
[1,2,4,3] => [1,2,4,3] => 1
[1,3,2,4] => [1,3,2,4] => 1
[1,3,4,2] => [1,4,3,2] => 2
[1,4,2,3] => [1,4,3,2] => 2
[1,4,3,2] => [1,4,3,2] => 2
[2,1,3,4] => [2,1,3,4] => 1
[2,1,4,3] => [2,1,4,3] => 2
[2,3,1,4] => [3,2,1,4] => 2
[2,3,4,1] => [4,2,3,1] => 6
[2,4,1,3] => [3,4,1,2] => 2
[2,4,3,1] => [4,3,2,1] => 16
[3,1,2,4] => [3,2,1,4] => 2
[3,1,4,2] => [4,2,3,1] => 6
[3,2,1,4] => [3,2,1,4] => 2
[3,2,4,1] => [4,2,3,1] => 6
[3,4,1,2] => [4,3,2,1] => 16
[3,4,2,1] => [4,3,2,1] => 16
[4,1,2,3] => [4,2,3,1] => 6
[4,1,3,2] => [4,2,3,1] => 6
[4,2,1,3] => [4,3,2,1] => 16
[4,2,3,1] => [4,3,2,1] => 16
[4,3,1,2] => [4,3,2,1] => 16
[4,3,2,1] => [4,3,2,1] => 16
[1,2,3,4,5] => [1,2,3,4,5] => 1
[1,2,3,5,4] => [1,2,3,5,4] => 1
[1,2,4,3,5] => [1,2,4,3,5] => 1
[1,2,4,5,3] => [1,2,5,4,3] => 2
[1,2,5,3,4] => [1,2,5,4,3] => 2
[1,2,5,4,3] => [1,2,5,4,3] => 2
[1,3,2,4,5] => [1,3,2,4,5] => 1
[1,3,2,5,4] => [1,3,2,5,4] => 2
[1,3,4,2,5] => [1,4,3,2,5] => 2
[1,3,4,5,2] => [1,5,3,4,2] => 6
[1,3,5,2,4] => [1,4,5,2,3] => 2
[1,3,5,4,2] => [1,5,4,3,2] => 16
[1,4,2,3,5] => [1,4,3,2,5] => 2
[1,4,2,5,3] => [1,5,3,4,2] => 6
[1,4,3,2,5] => [1,4,3,2,5] => 2
[1,4,3,5,2] => [1,5,3,4,2] => 6
[1,4,5,2,3] => [1,5,4,3,2] => 16
[1,4,5,3,2] => [1,5,4,3,2] => 16
[1,5,2,3,4] => [1,5,3,4,2] => 6
[1,5,2,4,3] => [1,5,3,4,2] => 6
[1,5,3,2,4] => [1,5,4,3,2] => 16
[1,5,3,4,2] => [1,5,4,3,2] => 16
[1,5,4,2,3] => [1,5,4,3,2] => 16
[1,5,4,3,2] => [1,5,4,3,2] => 16
[2,1,3,4,5] => [2,1,3,4,5] => 1
[2,1,3,5,4] => [2,1,3,5,4] => 2
[2,1,4,3,5] => [2,1,4,3,5] => 2
[2,1,4,5,3] => [2,1,5,4,3] => 8
[2,1,5,3,4] => [2,1,5,4,3] => 8
[2,1,5,4,3] => [2,1,5,4,3] => 8
[2,3,1,4,5] => [3,2,1,4,5] => 2
[2,3,1,5,4] => [3,2,1,5,4] => 8
[2,3,4,1,5] => [4,2,3,1,5] => 6
[2,3,4,5,1] => [5,2,3,4,1] => 20
[2,3,5,1,4] => [4,2,5,1,3] => 16
[2,3,5,4,1] => [5,2,4,3,1] => 90
[2,4,1,3,5] => [3,4,1,2,5] => 2
[2,4,1,5,3] => [3,5,1,4,2] => 16
[2,4,3,1,5] => [4,3,2,1,5] => 16
[2,4,3,5,1] => [5,3,2,4,1] => 90
[2,4,5,1,3] => [4,5,3,1,2] => 42
[2,4,5,3,1] => [5,4,3,2,1] => 768
[2,5,1,3,4] => [3,5,1,4,2] => 16
[2,5,1,4,3] => [3,5,1,4,2] => 16
[2,5,3,1,4] => [4,5,3,1,2] => 42
[2,5,3,4,1] => [5,4,3,2,1] => 768
[2,5,4,1,3] => [4,5,3,1,2] => 42
[2,5,4,3,1] => [5,4,3,2,1] => 768
[3,1,2,4,5] => [3,2,1,4,5] => 2
[3,1,2,5,4] => [3,2,1,5,4] => 8
[3,1,4,2,5] => [4,2,3,1,5] => 6
[3,1,4,5,2] => [5,2,3,4,1] => 20
[3,1,5,2,4] => [4,2,5,1,3] => 16
[3,1,5,4,2] => [5,2,4,3,1] => 90
[3,2,1,4,5] => [3,2,1,4,5] => 2
[3,2,1,5,4] => [3,2,1,5,4] => 8
[3,2,4,1,5] => [4,2,3,1,5] => 6
[3,2,4,5,1] => [5,2,3,4,1] => 20
[3,2,5,1,4] => [4,2,5,1,3] => 16
[3,2,5,4,1] => [5,2,4,3,1] => 90
[3,4,1,2,5] => [4,3,2,1,5] => 16
[3,4,1,5,2] => [5,3,2,4,1] => 90
[3,4,2,1,5] => [4,3,2,1,5] => 16
[3,4,2,5,1] => [5,3,2,4,1] => 90
[3,4,5,1,2] => [5,4,3,2,1] => 768
[3,4,5,2,1] => [5,4,3,2,1] => 768
[3,5,1,2,4] => [4,5,3,1,2] => 42
[3,5,1,4,2] => [5,4,3,2,1] => 768
>>> Load all 1733 entries. <<<[3,5,2,1,4] => [4,5,3,1,2] => 42
[3,5,2,4,1] => [5,4,3,2,1] => 768
[3,5,4,1,2] => [5,4,3,2,1] => 768
[3,5,4,2,1] => [5,4,3,2,1] => 768
[4,1,2,3,5] => [4,2,3,1,5] => 6
[4,1,2,5,3] => [5,2,3,4,1] => 20
[4,1,3,2,5] => [4,2,3,1,5] => 6
[4,1,3,5,2] => [5,2,3,4,1] => 20
[4,1,5,2,3] => [5,2,4,3,1] => 90
[4,1,5,3,2] => [5,2,4,3,1] => 90
[4,2,1,3,5] => [4,3,2,1,5] => 16
[4,2,1,5,3] => [5,3,2,4,1] => 90
[4,2,3,1,5] => [4,3,2,1,5] => 16
[4,2,3,5,1] => [5,3,2,4,1] => 90
[4,2,5,1,3] => [5,4,3,2,1] => 768
[4,2,5,3,1] => [5,4,3,2,1] => 768
[4,3,1,2,5] => [4,3,2,1,5] => 16
[4,3,1,5,2] => [5,3,2,4,1] => 90
[4,3,2,1,5] => [4,3,2,1,5] => 16
[4,3,2,5,1] => [5,3,2,4,1] => 90
[4,3,5,1,2] => [5,4,3,2,1] => 768
[4,3,5,2,1] => [5,4,3,2,1] => 768
[4,5,1,2,3] => [5,4,3,2,1] => 768
[4,5,1,3,2] => [5,4,3,2,1] => 768
[4,5,2,1,3] => [5,4,3,2,1] => 768
[4,5,2,3,1] => [5,4,3,2,1] => 768
[4,5,3,1,2] => [5,4,3,2,1] => 768
[4,5,3,2,1] => [5,4,3,2,1] => 768
[5,1,2,3,4] => [5,2,3,4,1] => 20
[5,1,2,4,3] => [5,2,3,4,1] => 20
[5,1,3,2,4] => [5,2,4,3,1] => 90
[5,1,3,4,2] => [5,2,4,3,1] => 90
[5,1,4,2,3] => [5,2,4,3,1] => 90
[5,1,4,3,2] => [5,2,4,3,1] => 90
[5,2,1,3,4] => [5,3,2,4,1] => 90
[5,2,1,4,3] => [5,3,2,4,1] => 90
[5,2,3,1,4] => [5,4,3,2,1] => 768
[5,2,3,4,1] => [5,4,3,2,1] => 768
[5,2,4,1,3] => [5,4,3,2,1] => 768
[5,2,4,3,1] => [5,4,3,2,1] => 768
[5,3,1,2,4] => [5,4,3,2,1] => 768
[5,3,1,4,2] => [5,4,3,2,1] => 768
[5,3,2,1,4] => [5,4,3,2,1] => 768
[5,3,2,4,1] => [5,4,3,2,1] => 768
[5,3,4,1,2] => [5,4,3,2,1] => 768
[5,3,4,2,1] => [5,4,3,2,1] => 768
[5,4,1,2,3] => [5,4,3,2,1] => 768
[5,4,1,3,2] => [5,4,3,2,1] => 768
[5,4,2,1,3] => [5,4,3,2,1] => 768
[5,4,2,3,1] => [5,4,3,2,1] => 768
[5,4,3,1,2] => [5,4,3,2,1] => 768
[5,4,3,2,1] => [5,4,3,2,1] => 768
[1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
[1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => [1,2,3,6,5,4] => 2
[1,2,3,6,4,5] => [1,2,3,6,5,4] => 2
[1,2,3,6,5,4] => [1,2,3,6,5,4] => 2
[1,2,4,3,5,6] => [1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => 2
[1,2,4,5,6,3] => [1,2,6,4,5,3] => 6
[1,2,4,6,3,5] => [1,2,5,6,3,4] => 2
[1,2,4,6,5,3] => [1,2,6,5,4,3] => 16
[1,2,5,3,4,6] => [1,2,5,4,3,6] => 2
[1,2,5,3,6,4] => [1,2,6,4,5,3] => 6
[1,2,5,4,3,6] => [1,2,5,4,3,6] => 2
[1,2,5,4,6,3] => [1,2,6,4,5,3] => 6
[1,2,5,6,3,4] => [1,2,6,5,4,3] => 16
[1,2,5,6,4,3] => [1,2,6,5,4,3] => 16
[1,2,6,3,4,5] => [1,2,6,4,5,3] => 6
[1,2,6,3,5,4] => [1,2,6,4,5,3] => 6
[1,2,6,4,3,5] => [1,2,6,5,4,3] => 16
[1,2,6,4,5,3] => [1,2,6,5,4,3] => 16
[1,2,6,5,3,4] => [1,2,6,5,4,3] => 16
[1,2,6,5,4,3] => [1,2,6,5,4,3] => 16
[1,3,2,4,5,6] => [1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => [1,3,2,6,5,4] => 8
[1,3,2,6,4,5] => [1,3,2,6,5,4] => 8
[1,3,2,6,5,4] => [1,3,2,6,5,4] => 8
[1,3,4,2,5,6] => [1,4,3,2,5,6] => 2
[1,3,4,2,6,5] => [1,4,3,2,6,5] => 8
[1,3,4,5,2,6] => [1,5,3,4,2,6] => 6
[1,3,4,5,6,2] => [1,6,3,4,5,2] => 20
[1,3,4,6,2,5] => [1,5,3,6,2,4] => 16
[1,3,4,6,5,2] => [1,6,3,5,4,2] => 90
[1,3,5,2,4,6] => [1,4,5,2,3,6] => 2
[1,3,5,2,6,4] => [1,4,6,2,5,3] => 16
[1,3,5,4,2,6] => [1,5,4,3,2,6] => 16
[1,3,5,4,6,2] => [1,6,4,3,5,2] => 90
[1,3,5,6,2,4] => [1,5,6,4,2,3] => 42
[1,3,5,6,4,2] => [1,6,5,4,3,2] => 768
[1,3,6,2,4,5] => [1,4,6,2,5,3] => 16
[1,3,6,2,5,4] => [1,4,6,2,5,3] => 16
[1,3,6,4,2,5] => [1,5,6,4,2,3] => 42
[1,3,6,4,5,2] => [1,6,5,4,3,2] => 768
[1,3,6,5,2,4] => [1,5,6,4,2,3] => 42
[1,3,6,5,4,2] => [1,6,5,4,3,2] => 768
[1,4,2,3,5,6] => [1,4,3,2,5,6] => 2
[1,4,2,3,6,5] => [1,4,3,2,6,5] => 8
[1,4,2,5,3,6] => [1,5,3,4,2,6] => 6
[1,4,2,5,6,3] => [1,6,3,4,5,2] => 20
[1,4,2,6,3,5] => [1,5,3,6,2,4] => 16
[1,4,2,6,5,3] => [1,6,3,5,4,2] => 90
[1,4,3,2,5,6] => [1,4,3,2,5,6] => 2
[1,4,3,2,6,5] => [1,4,3,2,6,5] => 8
[1,4,3,5,2,6] => [1,5,3,4,2,6] => 6
[1,4,3,5,6,2] => [1,6,3,4,5,2] => 20
[1,4,3,6,2,5] => [1,5,3,6,2,4] => 16
[1,4,3,6,5,2] => [1,6,3,5,4,2] => 90
[1,4,5,2,3,6] => [1,5,4,3,2,6] => 16
[1,4,5,2,6,3] => [1,6,4,3,5,2] => 90
[1,4,5,3,2,6] => [1,5,4,3,2,6] => 16
[1,4,5,3,6,2] => [1,6,4,3,5,2] => 90
[1,4,5,6,2,3] => [1,6,5,4,3,2] => 768
[1,4,5,6,3,2] => [1,6,5,4,3,2] => 768
[1,4,6,2,3,5] => [1,5,6,4,2,3] => 42
[1,4,6,2,5,3] => [1,6,5,4,3,2] => 768
[1,4,6,3,2,5] => [1,5,6,4,2,3] => 42
[1,4,6,3,5,2] => [1,6,5,4,3,2] => 768
[1,4,6,5,2,3] => [1,6,5,4,3,2] => 768
[1,4,6,5,3,2] => [1,6,5,4,3,2] => 768
[1,5,2,3,4,6] => [1,5,3,4,2,6] => 6
[1,5,2,3,6,4] => [1,6,3,4,5,2] => 20
[1,5,2,4,3,6] => [1,5,3,4,2,6] => 6
[1,5,2,4,6,3] => [1,6,3,4,5,2] => 20
[1,5,2,6,3,4] => [1,6,3,5,4,2] => 90
[1,5,2,6,4,3] => [1,6,3,5,4,2] => 90
[1,5,3,2,4,6] => [1,5,4,3,2,6] => 16
[1,5,3,2,6,4] => [1,6,4,3,5,2] => 90
[1,5,3,4,2,6] => [1,5,4,3,2,6] => 16
[1,5,3,4,6,2] => [1,6,4,3,5,2] => 90
[1,5,3,6,2,4] => [1,6,5,4,3,2] => 768
[1,5,3,6,4,2] => [1,6,5,4,3,2] => 768
[1,5,4,2,3,6] => [1,5,4,3,2,6] => 16
[1,5,4,2,6,3] => [1,6,4,3,5,2] => 90
[1,5,4,3,2,6] => [1,5,4,3,2,6] => 16
[1,5,4,3,6,2] => [1,6,4,3,5,2] => 90
[1,5,4,6,2,3] => [1,6,5,4,3,2] => 768
[1,5,4,6,3,2] => [1,6,5,4,3,2] => 768
[1,5,6,2,3,4] => [1,6,5,4,3,2] => 768
[1,5,6,2,4,3] => [1,6,5,4,3,2] => 768
[1,5,6,3,2,4] => [1,6,5,4,3,2] => 768
[1,5,6,3,4,2] => [1,6,5,4,3,2] => 768
[1,5,6,4,2,3] => [1,6,5,4,3,2] => 768
[1,5,6,4,3,2] => [1,6,5,4,3,2] => 768
[1,6,2,3,4,5] => [1,6,3,4,5,2] => 20
[1,6,2,3,5,4] => [1,6,3,4,5,2] => 20
[1,6,2,4,3,5] => [1,6,3,5,4,2] => 90
[1,6,2,4,5,3] => [1,6,3,5,4,2] => 90
[1,6,2,5,3,4] => [1,6,3,5,4,2] => 90
[1,6,2,5,4,3] => [1,6,3,5,4,2] => 90
[1,6,3,2,4,5] => [1,6,4,3,5,2] => 90
[1,6,3,2,5,4] => [1,6,4,3,5,2] => 90
[1,6,3,4,2,5] => [1,6,5,4,3,2] => 768
[1,6,3,4,5,2] => [1,6,5,4,3,2] => 768
[1,6,3,5,2,4] => [1,6,5,4,3,2] => 768
[1,6,3,5,4,2] => [1,6,5,4,3,2] => 768
[1,6,4,2,3,5] => [1,6,5,4,3,2] => 768
[1,6,4,2,5,3] => [1,6,5,4,3,2] => 768
[1,6,4,3,2,5] => [1,6,5,4,3,2] => 768
[1,6,4,3,5,2] => [1,6,5,4,3,2] => 768
[1,6,4,5,2,3] => [1,6,5,4,3,2] => 768
[1,6,4,5,3,2] => [1,6,5,4,3,2] => 768
[1,6,5,2,3,4] => [1,6,5,4,3,2] => 768
[1,6,5,2,4,3] => [1,6,5,4,3,2] => 768
[1,6,5,3,2,4] => [1,6,5,4,3,2] => 768
[1,6,5,3,4,2] => [1,6,5,4,3,2] => 768
[1,6,5,4,2,3] => [1,6,5,4,3,2] => 768
[1,6,5,4,3,2] => [1,6,5,4,3,2] => 768
[2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => [2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => [2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => [2,1,3,6,5,4] => 8
[2,1,3,6,4,5] => [2,1,3,6,5,4] => 8
[2,1,3,6,5,4] => [2,1,3,6,5,4] => 8
[2,1,4,3,5,6] => [2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => [2,1,4,3,6,5] => 6
[2,1,4,5,3,6] => [2,1,5,4,3,6] => 8
[2,1,4,5,6,3] => [2,1,6,4,5,3] => 36
[2,1,4,6,3,5] => [2,1,5,6,3,4] => 10
[2,1,4,6,5,3] => [2,1,6,5,4,3] => 112
[2,1,5,3,4,6] => [2,1,5,4,3,6] => 8
[2,1,5,3,6,4] => [2,1,6,4,5,3] => 36
[2,1,5,4,3,6] => [2,1,5,4,3,6] => 8
[2,1,5,4,6,3] => [2,1,6,4,5,3] => 36
[2,1,5,6,3,4] => [2,1,6,5,4,3] => 112
[2,1,5,6,4,3] => [2,1,6,5,4,3] => 112
[2,1,6,3,4,5] => [2,1,6,4,5,3] => 36
[2,1,6,3,5,4] => [2,1,6,4,5,3] => 36
[2,1,6,4,3,5] => [2,1,6,5,4,3] => 112
[2,1,6,4,5,3] => [2,1,6,5,4,3] => 112
[2,1,6,5,3,4] => [2,1,6,5,4,3] => 112
[2,1,6,5,4,3] => [2,1,6,5,4,3] => 112
[2,3,1,4,5,6] => [3,2,1,4,5,6] => 2
[2,3,1,4,6,5] => [3,2,1,4,6,5] => 8
[2,3,1,5,4,6] => [3,2,1,5,4,6] => 8
[2,3,1,5,6,4] => [3,2,1,6,5,4] => 80
[2,3,1,6,4,5] => [3,2,1,6,5,4] => 80
[2,3,1,6,5,4] => [3,2,1,6,5,4] => 80
[2,3,4,1,5,6] => [4,2,3,1,5,6] => 6
[2,3,4,1,6,5] => [4,2,3,1,6,5] => 36
[2,3,4,5,1,6] => [5,2,3,4,1,6] => 20
[2,3,4,5,6,1] => [6,2,3,4,5,1] => 70
[2,3,4,6,1,5] => [5,2,3,6,1,4] => 90
[2,3,4,6,5,1] => [6,2,3,5,4,1] => 448
[2,3,5,1,4,6] => [4,2,5,1,3,6] => 16
[2,3,5,1,6,4] => [4,2,6,1,5,3] => 244
[2,3,5,4,1,6] => [5,2,4,3,1,6] => 90
[2,3,5,4,6,1] => [6,2,4,3,5,1] => 448
[2,3,5,6,1,4] => [5,2,6,4,1,3] => 768
[2,3,5,6,4,1] => [6,2,5,4,3,1] => 7700
[2,3,6,1,4,5] => [4,2,6,1,5,3] => 244
[2,3,6,1,5,4] => [4,2,6,1,5,3] => 244
[2,3,6,4,1,5] => [5,2,6,4,1,3] => 768
[2,3,6,4,5,1] => [6,2,5,4,3,1] => 7700
[2,3,6,5,1,4] => [5,2,6,4,1,3] => 768
[2,3,6,5,4,1] => [6,2,5,4,3,1] => 7700
[2,4,1,3,5,6] => [3,4,1,2,5,6] => 2
[2,4,1,3,6,5] => [3,4,1,2,6,5] => 10
[2,4,1,5,3,6] => [3,5,1,4,2,6] => 16
[2,4,1,5,6,3] => [3,6,1,4,5,2] => 90
[2,4,1,6,3,5] => [3,5,1,6,2,4] => 42
[2,4,1,6,5,3] => [3,6,1,5,4,2] => 432
[2,4,3,1,5,6] => [4,3,2,1,5,6] => 16
[2,4,3,1,6,5] => [4,3,2,1,6,5] => 112
[2,4,3,5,1,6] => [5,3,2,4,1,6] => 90
[2,4,3,5,6,1] => [6,3,2,4,5,1] => 448
[2,4,3,6,1,5] => [5,3,2,6,1,4] => 432
[2,4,3,6,5,1] => [6,3,2,5,4,1] => 3080
[2,4,5,1,3,6] => [4,5,3,1,2,6] => 42
[2,4,5,1,6,3] => [4,6,3,1,5,2] => 768
[2,4,5,3,1,6] => [5,4,3,2,1,6] => 768
[2,4,5,3,6,1] => [6,4,3,2,5,1] => 7700
[2,4,5,6,1,3] => [5,6,3,4,1,2] => 2640
[2,4,5,6,3,1] => [6,5,3,4,2,1] => 68640
[2,4,6,1,3,5] => [4,5,6,1,2,3] => 42
[2,4,6,1,5,3] => [4,6,5,1,3,2] => 1188
[2,4,6,3,1,5] => [5,4,6,2,1,3] => 1188
[2,4,6,3,5,1] => [6,4,5,2,3,1] => 16016
[2,4,6,5,1,3] => [5,6,4,3,1,2] => 8580
[2,4,6,5,3,1] => [6,5,4,3,2,1] => 292864
[2,5,1,3,4,6] => [3,5,1,4,2,6] => 16
[2,5,1,3,6,4] => [3,6,1,4,5,2] => 90
[2,5,1,4,3,6] => [3,5,1,4,2,6] => 16
[2,5,1,4,6,3] => [3,6,1,4,5,2] => 90
[2,5,1,6,3,4] => [3,6,1,5,4,2] => 432
[2,5,1,6,4,3] => [3,6,1,5,4,2] => 432
[2,5,3,1,4,6] => [4,5,3,1,2,6] => 42
[2,5,3,1,6,4] => [4,6,3,1,5,2] => 768
[2,5,3,4,1,6] => [5,4,3,2,1,6] => 768
[2,5,3,4,6,1] => [6,4,3,2,5,1] => 7700
[2,5,3,6,1,4] => [5,6,3,4,1,2] => 2640
[2,5,3,6,4,1] => [6,5,3,4,2,1] => 68640
[2,5,4,1,3,6] => [4,5,3,1,2,6] => 42
[2,5,4,1,6,3] => [4,6,3,1,5,2] => 768
[2,5,4,3,1,6] => [5,4,3,2,1,6] => 768
[2,5,4,3,6,1] => [6,4,3,2,5,1] => 7700
[2,5,4,6,1,3] => [5,6,3,4,1,2] => 2640
[2,5,4,6,3,1] => [6,5,3,4,2,1] => 68640
[2,5,6,1,3,4] => [4,6,5,1,3,2] => 1188
[2,5,6,1,4,3] => [4,6,5,1,3,2] => 1188
[2,5,6,3,1,4] => [5,6,4,3,1,2] => 8580
[2,5,6,3,4,1] => [6,5,4,3,2,1] => 292864
[2,5,6,4,1,3] => [5,6,4,3,1,2] => 8580
[2,5,6,4,3,1] => [6,5,4,3,2,1] => 292864
[2,6,1,3,4,5] => [3,6,1,4,5,2] => 90
[2,6,1,3,5,4] => [3,6,1,4,5,2] => 90
[2,6,1,4,3,5] => [3,6,1,5,4,2] => 432
[2,6,1,4,5,3] => [3,6,1,5,4,2] => 432
[2,6,1,5,3,4] => [3,6,1,5,4,2] => 432
[2,6,1,5,4,3] => [3,6,1,5,4,2] => 432
[2,6,3,1,4,5] => [4,6,3,1,5,2] => 768
[2,6,3,1,5,4] => [4,6,3,1,5,2] => 768
[2,6,3,4,1,5] => [5,6,3,4,1,2] => 2640
[2,6,3,4,5,1] => [6,5,3,4,2,1] => 68640
[2,6,3,5,1,4] => [5,6,3,4,1,2] => 2640
[2,6,3,5,4,1] => [6,5,3,4,2,1] => 68640
[2,6,4,1,3,5] => [4,6,5,1,3,2] => 1188
[2,6,4,1,5,3] => [4,6,5,1,3,2] => 1188
[2,6,4,3,1,5] => [5,6,4,3,1,2] => 8580
[2,6,4,3,5,1] => [6,5,4,3,2,1] => 292864
[2,6,4,5,1,3] => [5,6,4,3,1,2] => 8580
[2,6,4,5,3,1] => [6,5,4,3,2,1] => 292864
[2,6,5,1,3,4] => [4,6,5,1,3,2] => 1188
[2,6,5,1,4,3] => [4,6,5,1,3,2] => 1188
[2,6,5,3,1,4] => [5,6,4,3,1,2] => 8580
[2,6,5,3,4,1] => [6,5,4,3,2,1] => 292864
[2,6,5,4,1,3] => [5,6,4,3,1,2] => 8580
[2,6,5,4,3,1] => [6,5,4,3,2,1] => 292864
[3,1,2,4,5,6] => [3,2,1,4,5,6] => 2
[3,1,2,4,6,5] => [3,2,1,4,6,5] => 8
[3,1,2,5,4,6] => [3,2,1,5,4,6] => 8
[3,1,2,5,6,4] => [3,2,1,6,5,4] => 80
[3,1,2,6,4,5] => [3,2,1,6,5,4] => 80
[3,1,2,6,5,4] => [3,2,1,6,5,4] => 80
[3,1,4,2,5,6] => [4,2,3,1,5,6] => 6
[3,1,4,2,6,5] => [4,2,3,1,6,5] => 36
[3,1,4,5,2,6] => [5,2,3,4,1,6] => 20
[3,1,4,5,6,2] => [6,2,3,4,5,1] => 70
[3,1,4,6,2,5] => [5,2,3,6,1,4] => 90
[3,1,4,6,5,2] => [6,2,3,5,4,1] => 448
[3,1,5,2,4,6] => [4,2,5,1,3,6] => 16
[3,1,5,2,6,4] => [4,2,6,1,5,3] => 244
[3,1,5,4,2,6] => [5,2,4,3,1,6] => 90
[3,1,5,4,6,2] => [6,2,4,3,5,1] => 448
[3,1,5,6,2,4] => [5,2,6,4,1,3] => 768
[3,1,5,6,4,2] => [6,2,5,4,3,1] => 7700
[3,1,6,2,4,5] => [4,2,6,1,5,3] => 244
[3,1,6,2,5,4] => [4,2,6,1,5,3] => 244
[3,1,6,4,2,5] => [5,2,6,4,1,3] => 768
[3,1,6,4,5,2] => [6,2,5,4,3,1] => 7700
[3,1,6,5,2,4] => [5,2,6,4,1,3] => 768
[3,1,6,5,4,2] => [6,2,5,4,3,1] => 7700
[3,2,1,4,5,6] => [3,2,1,4,5,6] => 2
[3,2,1,4,6,5] => [3,2,1,4,6,5] => 8
[3,2,1,5,4,6] => [3,2,1,5,4,6] => 8
[3,2,1,5,6,4] => [3,2,1,6,5,4] => 80
[3,2,1,6,4,5] => [3,2,1,6,5,4] => 80
[3,2,1,6,5,4] => [3,2,1,6,5,4] => 80
[3,2,4,1,5,6] => [4,2,3,1,5,6] => 6
[3,2,4,1,6,5] => [4,2,3,1,6,5] => 36
[3,2,4,5,1,6] => [5,2,3,4,1,6] => 20
[3,2,4,5,6,1] => [6,2,3,4,5,1] => 70
[3,2,4,6,1,5] => [5,2,3,6,1,4] => 90
[3,2,4,6,5,1] => [6,2,3,5,4,1] => 448
[3,2,5,1,4,6] => [4,2,5,1,3,6] => 16
[3,2,5,1,6,4] => [4,2,6,1,5,3] => 244
[3,2,5,4,1,6] => [5,2,4,3,1,6] => 90
[3,2,5,4,6,1] => [6,2,4,3,5,1] => 448
[3,2,5,6,1,4] => [5,2,6,4,1,3] => 768
[3,2,5,6,4,1] => [6,2,5,4,3,1] => 7700
[3,2,6,1,4,5] => [4,2,6,1,5,3] => 244
[3,2,6,1,5,4] => [4,2,6,1,5,3] => 244
[3,2,6,4,1,5] => [5,2,6,4,1,3] => 768
[3,2,6,4,5,1] => [6,2,5,4,3,1] => 7700
[3,2,6,5,1,4] => [5,2,6,4,1,3] => 768
[3,2,6,5,4,1] => [6,2,5,4,3,1] => 7700
[3,4,1,2,5,6] => [4,3,2,1,5,6] => 16
[3,4,1,2,6,5] => [4,3,2,1,6,5] => 112
[3,4,1,5,2,6] => [5,3,2,4,1,6] => 90
[3,4,1,5,6,2] => [6,3,2,4,5,1] => 448
[3,4,1,6,2,5] => [5,3,2,6,1,4] => 432
[3,4,1,6,5,2] => [6,3,2,5,4,1] => 3080
[3,4,2,1,5,6] => [4,3,2,1,5,6] => 16
[3,4,2,1,6,5] => [4,3,2,1,6,5] => 112
[3,4,2,5,1,6] => [5,3,2,4,1,6] => 90
[3,4,2,5,6,1] => [6,3,2,4,5,1] => 448
[3,4,2,6,1,5] => [5,3,2,6,1,4] => 432
[3,4,2,6,5,1] => [6,3,2,5,4,1] => 3080
[3,4,5,1,2,6] => [5,4,3,2,1,6] => 768
[3,4,5,1,6,2] => [6,4,3,2,5,1] => 7700
[3,4,5,2,1,6] => [5,4,3,2,1,6] => 768
[3,4,5,2,6,1] => [6,4,3,2,5,1] => 7700
[3,4,5,6,1,2] => [6,5,3,4,2,1] => 68640
[3,4,5,6,2,1] => [6,5,3,4,2,1] => 68640
[3,4,6,1,2,5] => [5,4,6,2,1,3] => 1188
[3,4,6,1,5,2] => [6,4,5,2,3,1] => 16016
[3,4,6,2,1,5] => [5,4,6,2,1,3] => 1188
[3,4,6,2,5,1] => [6,4,5,2,3,1] => 16016
[3,4,6,5,1,2] => [6,5,4,3,2,1] => 292864
[3,4,6,5,2,1] => [6,5,4,3,2,1] => 292864
[3,5,1,2,4,6] => [4,5,3,1,2,6] => 42
[3,5,1,2,6,4] => [4,6,3,1,5,2] => 768
[3,5,1,4,2,6] => [5,4,3,2,1,6] => 768
[3,5,1,4,6,2] => [6,4,3,2,5,1] => 7700
[3,5,1,6,2,4] => [5,6,3,4,1,2] => 2640
[3,5,1,6,4,2] => [6,5,3,4,2,1] => 68640
[3,5,2,1,4,6] => [4,5,3,1,2,6] => 42
[3,5,2,1,6,4] => [4,6,3,1,5,2] => 768
[3,5,2,4,1,6] => [5,4,3,2,1,6] => 768
[3,5,2,4,6,1] => [6,4,3,2,5,1] => 7700
[3,5,2,6,1,4] => [5,6,3,4,1,2] => 2640
[3,5,2,6,4,1] => [6,5,3,4,2,1] => 68640
[3,5,4,1,2,6] => [5,4,3,2,1,6] => 768
[3,5,4,1,6,2] => [6,4,3,2,5,1] => 7700
[3,5,4,2,1,6] => [5,4,3,2,1,6] => 768
[3,5,4,2,6,1] => [6,4,3,2,5,1] => 7700
[3,5,4,6,1,2] => [6,5,3,4,2,1] => 68640
[3,5,4,6,2,1] => [6,5,3,4,2,1] => 68640
[3,5,6,1,2,4] => [5,6,4,3,1,2] => 8580
[3,5,6,1,4,2] => [6,5,4,3,2,1] => 292864
[3,5,6,2,1,4] => [5,6,4,3,1,2] => 8580
[3,5,6,2,4,1] => [6,5,4,3,2,1] => 292864
[3,5,6,4,1,2] => [6,5,4,3,2,1] => 292864
[3,5,6,4,2,1] => [6,5,4,3,2,1] => 292864
[3,6,1,2,4,5] => [4,6,3,1,5,2] => 768
[3,6,1,2,5,4] => [4,6,3,1,5,2] => 768
[3,6,1,4,2,5] => [5,6,3,4,1,2] => 2640
[3,6,1,4,5,2] => [6,5,3,4,2,1] => 68640
[3,6,1,5,2,4] => [5,6,3,4,1,2] => 2640
[3,6,1,5,4,2] => [6,5,3,4,2,1] => 68640
[3,6,2,1,4,5] => [4,6,3,1,5,2] => 768
[3,6,2,1,5,4] => [4,6,3,1,5,2] => 768
[3,6,2,4,1,5] => [5,6,3,4,1,2] => 2640
[3,6,2,4,5,1] => [6,5,3,4,2,1] => 68640
[3,6,2,5,1,4] => [5,6,3,4,1,2] => 2640
[3,6,2,5,4,1] => [6,5,3,4,2,1] => 68640
[3,6,4,1,2,5] => [5,6,4,3,1,2] => 8580
[3,6,4,1,5,2] => [6,5,4,3,2,1] => 292864
[3,6,4,2,1,5] => [5,6,4,3,1,2] => 8580
[3,6,4,2,5,1] => [6,5,4,3,2,1] => 292864
[3,6,4,5,1,2] => [6,5,4,3,2,1] => 292864
[3,6,4,5,2,1] => [6,5,4,3,2,1] => 292864
[3,6,5,1,2,4] => [5,6,4,3,1,2] => 8580
[3,6,5,1,4,2] => [6,5,4,3,2,1] => 292864
[3,6,5,2,1,4] => [5,6,4,3,1,2] => 8580
[3,6,5,2,4,1] => [6,5,4,3,2,1] => 292864
[3,6,5,4,1,2] => [6,5,4,3,2,1] => 292864
[3,6,5,4,2,1] => [6,5,4,3,2,1] => 292864
[4,1,2,3,5,6] => [4,2,3,1,5,6] => 6
[4,1,2,3,6,5] => [4,2,3,1,6,5] => 36
[4,1,2,5,3,6] => [5,2,3,4,1,6] => 20
[4,1,2,5,6,3] => [6,2,3,4,5,1] => 70
[4,1,2,6,3,5] => [5,2,3,6,1,4] => 90
[4,1,2,6,5,3] => [6,2,3,5,4,1] => 448
[4,1,3,2,5,6] => [4,2,3,1,5,6] => 6
[4,1,3,2,6,5] => [4,2,3,1,6,5] => 36
[4,1,3,5,2,6] => [5,2,3,4,1,6] => 20
[4,1,3,5,6,2] => [6,2,3,4,5,1] => 70
[4,1,3,6,2,5] => [5,2,3,6,1,4] => 90
[4,1,3,6,5,2] => [6,2,3,5,4,1] => 448
[4,1,5,2,3,6] => [5,2,4,3,1,6] => 90
[4,1,5,2,6,3] => [6,2,4,3,5,1] => 448
[4,1,5,3,2,6] => [5,2,4,3,1,6] => 90
[4,1,5,3,6,2] => [6,2,4,3,5,1] => 448
[4,1,5,6,2,3] => [6,2,5,4,3,1] => 7700
[4,1,5,6,3,2] => [6,2,5,4,3,1] => 7700
[4,1,6,2,3,5] => [5,2,6,4,1,3] => 768
[4,1,6,2,5,3] => [6,2,5,4,3,1] => 7700
[4,1,6,3,2,5] => [5,2,6,4,1,3] => 768
[4,1,6,3,5,2] => [6,2,5,4,3,1] => 7700
[4,1,6,5,2,3] => [6,2,5,4,3,1] => 7700
[4,1,6,5,3,2] => [6,2,5,4,3,1] => 7700
[4,2,1,3,5,6] => [4,3,2,1,5,6] => 16
[4,2,1,3,6,5] => [4,3,2,1,6,5] => 112
[4,2,1,5,3,6] => [5,3,2,4,1,6] => 90
[4,2,1,5,6,3] => [6,3,2,4,5,1] => 448
[4,2,1,6,3,5] => [5,3,2,6,1,4] => 432
[4,2,1,6,5,3] => [6,3,2,5,4,1] => 3080
[4,2,3,1,5,6] => [4,3,2,1,5,6] => 16
[4,2,3,1,6,5] => [4,3,2,1,6,5] => 112
[4,2,3,5,1,6] => [5,3,2,4,1,6] => 90
[4,2,3,5,6,1] => [6,3,2,4,5,1] => 448
[4,2,3,6,1,5] => [5,3,2,6,1,4] => 432
[4,2,3,6,5,1] => [6,3,2,5,4,1] => 3080
[4,2,5,1,3,6] => [5,4,3,2,1,6] => 768
[4,2,5,1,6,3] => [6,4,3,2,5,1] => 7700
[4,2,5,3,1,6] => [5,4,3,2,1,6] => 768
[4,2,5,3,6,1] => [6,4,3,2,5,1] => 7700
[4,2,5,6,1,3] => [6,5,3,4,2,1] => 68640
[4,2,5,6,3,1] => [6,5,3,4,2,1] => 68640
[4,2,6,1,3,5] => [5,4,6,2,1,3] => 1188
[4,2,6,1,5,3] => [6,4,5,2,3,1] => 16016
[4,2,6,3,1,5] => [5,4,6,2,1,3] => 1188
[4,2,6,3,5,1] => [6,4,5,2,3,1] => 16016
[4,2,6,5,1,3] => [6,5,4,3,2,1] => 292864
[4,2,6,5,3,1] => [6,5,4,3,2,1] => 292864
[4,3,1,2,5,6] => [4,3,2,1,5,6] => 16
[4,3,1,2,6,5] => [4,3,2,1,6,5] => 112
[4,3,1,5,2,6] => [5,3,2,4,1,6] => 90
[4,3,1,5,6,2] => [6,3,2,4,5,1] => 448
[4,3,1,6,2,5] => [5,3,2,6,1,4] => 432
[4,3,1,6,5,2] => [6,3,2,5,4,1] => 3080
[4,3,2,1,5,6] => [4,3,2,1,5,6] => 16
[4,3,2,1,6,5] => [4,3,2,1,6,5] => 112
[4,3,2,5,1,6] => [5,3,2,4,1,6] => 90
[4,3,2,5,6,1] => [6,3,2,4,5,1] => 448
[4,3,2,6,1,5] => [5,3,2,6,1,4] => 432
[4,3,2,6,5,1] => [6,3,2,5,4,1] => 3080
[4,3,5,1,2,6] => [5,4,3,2,1,6] => 768
[4,3,5,1,6,2] => [6,4,3,2,5,1] => 7700
[4,3,5,2,1,6] => [5,4,3,2,1,6] => 768
[4,3,5,2,6,1] => [6,4,3,2,5,1] => 7700
[4,3,5,6,1,2] => [6,5,3,4,2,1] => 68640
[4,3,5,6,2,1] => [6,5,3,4,2,1] => 68640
[4,3,6,1,2,5] => [5,4,6,2,1,3] => 1188
[4,3,6,1,5,2] => [6,4,5,2,3,1] => 16016
[4,3,6,2,1,5] => [5,4,6,2,1,3] => 1188
[4,3,6,2,5,1] => [6,4,5,2,3,1] => 16016
[4,3,6,5,1,2] => [6,5,4,3,2,1] => 292864
[4,3,6,5,2,1] => [6,5,4,3,2,1] => 292864
[4,5,1,2,3,6] => [5,4,3,2,1,6] => 768
[4,5,1,2,6,3] => [6,4,3,2,5,1] => 7700
[4,5,1,3,2,6] => [5,4,3,2,1,6] => 768
[4,5,1,3,6,2] => [6,4,3,2,5,1] => 7700
[4,5,1,6,2,3] => [6,5,3,4,2,1] => 68640
[4,5,1,6,3,2] => [6,5,3,4,2,1] => 68640
[4,5,2,1,3,6] => [5,4,3,2,1,6] => 768
[4,5,2,1,6,3] => [6,4,3,2,5,1] => 7700
[4,5,2,3,1,6] => [5,4,3,2,1,6] => 768
[4,5,2,3,6,1] => [6,4,3,2,5,1] => 7700
[4,5,2,6,1,3] => [6,5,3,4,2,1] => 68640
[4,5,2,6,3,1] => [6,5,3,4,2,1] => 68640
[4,5,3,1,2,6] => [5,4,3,2,1,6] => 768
[4,5,3,1,6,2] => [6,4,3,2,5,1] => 7700
[4,5,3,2,1,6] => [5,4,3,2,1,6] => 768
[4,5,3,2,6,1] => [6,4,3,2,5,1] => 7700
[4,5,3,6,1,2] => [6,5,3,4,2,1] => 68640
[4,5,3,6,2,1] => [6,5,3,4,2,1] => 68640
[4,5,6,1,2,3] => [6,5,4,3,2,1] => 292864
[4,5,6,1,3,2] => [6,5,4,3,2,1] => 292864
[4,5,6,2,1,3] => [6,5,4,3,2,1] => 292864
[4,5,6,2,3,1] => [6,5,4,3,2,1] => 292864
[4,5,6,3,1,2] => [6,5,4,3,2,1] => 292864
[4,5,6,3,2,1] => [6,5,4,3,2,1] => 292864
[4,6,1,2,3,5] => [5,6,3,4,1,2] => 2640
[4,6,1,2,5,3] => [6,5,3,4,2,1] => 68640
[4,6,1,3,2,5] => [5,6,3,4,1,2] => 2640
[4,6,1,3,5,2] => [6,5,3,4,2,1] => 68640
[4,6,1,5,2,3] => [6,5,3,4,2,1] => 68640
[4,6,1,5,3,2] => [6,5,3,4,2,1] => 68640
[4,6,2,1,3,5] => [5,6,4,3,1,2] => 8580
[4,6,2,1,5,3] => [6,5,4,3,2,1] => 292864
[4,6,2,3,1,5] => [5,6,4,3,1,2] => 8580
[4,6,2,3,5,1] => [6,5,4,3,2,1] => 292864
[4,6,2,5,1,3] => [6,5,4,3,2,1] => 292864
[4,6,2,5,3,1] => [6,5,4,3,2,1] => 292864
[4,6,3,1,2,5] => [5,6,4,3,1,2] => 8580
[4,6,3,1,5,2] => [6,5,4,3,2,1] => 292864
[4,6,3,2,1,5] => [5,6,4,3,1,2] => 8580
[4,6,3,2,5,1] => [6,5,4,3,2,1] => 292864
[4,6,3,5,1,2] => [6,5,4,3,2,1] => 292864
[4,6,3,5,2,1] => [6,5,4,3,2,1] => 292864
[4,6,5,1,2,3] => [6,5,4,3,2,1] => 292864
[4,6,5,1,3,2] => [6,5,4,3,2,1] => 292864
[4,6,5,2,1,3] => [6,5,4,3,2,1] => 292864
[4,6,5,2,3,1] => [6,5,4,3,2,1] => 292864
[4,6,5,3,1,2] => [6,5,4,3,2,1] => 292864
[4,6,5,3,2,1] => [6,5,4,3,2,1] => 292864
[5,1,2,3,4,6] => [5,2,3,4,1,6] => 20
[5,1,2,3,6,4] => [6,2,3,4,5,1] => 70
[5,1,2,4,3,6] => [5,2,3,4,1,6] => 20
[5,1,2,4,6,3] => [6,2,3,4,5,1] => 70
[5,1,2,6,3,4] => [6,2,3,5,4,1] => 448
[5,1,2,6,4,3] => [6,2,3,5,4,1] => 448
[5,1,3,2,4,6] => [5,2,4,3,1,6] => 90
[5,1,3,2,6,4] => [6,2,4,3,5,1] => 448
[5,1,3,4,2,6] => [5,2,4,3,1,6] => 90
[5,1,3,4,6,2] => [6,2,4,3,5,1] => 448
[5,1,3,6,2,4] => [6,2,5,4,3,1] => 7700
[5,1,3,6,4,2] => [6,2,5,4,3,1] => 7700
[5,1,4,2,3,6] => [5,2,4,3,1,6] => 90
[5,1,4,2,6,3] => [6,2,4,3,5,1] => 448
[5,1,4,3,2,6] => [5,2,4,3,1,6] => 90
[5,1,4,3,6,2] => [6,2,4,3,5,1] => 448
[5,1,4,6,2,3] => [6,2,5,4,3,1] => 7700
[5,1,4,6,3,2] => [6,2,5,4,3,1] => 7700
[5,1,6,2,3,4] => [6,2,5,4,3,1] => 7700
[5,1,6,2,4,3] => [6,2,5,4,3,1] => 7700
[5,1,6,3,2,4] => [6,2,5,4,3,1] => 7700
[5,1,6,3,4,2] => [6,2,5,4,3,1] => 7700
[5,1,6,4,2,3] => [6,2,5,4,3,1] => 7700
[5,1,6,4,3,2] => [6,2,5,4,3,1] => 7700
[5,2,1,3,4,6] => [5,3,2,4,1,6] => 90
[5,2,1,3,6,4] => [6,3,2,4,5,1] => 448
[5,2,1,4,3,6] => [5,3,2,4,1,6] => 90
[5,2,1,4,6,3] => [6,3,2,4,5,1] => 448
[5,2,1,6,3,4] => [6,3,2,5,4,1] => 3080
[5,2,1,6,4,3] => [6,3,2,5,4,1] => 3080
[5,2,3,1,4,6] => [5,4,3,2,1,6] => 768
[5,2,3,1,6,4] => [6,4,3,2,5,1] => 7700
[5,2,3,4,1,6] => [5,4,3,2,1,6] => 768
[5,2,3,4,6,1] => [6,4,3,2,5,1] => 7700
[5,2,3,6,1,4] => [6,5,3,4,2,1] => 68640
[5,2,3,6,4,1] => [6,5,3,4,2,1] => 68640
[5,2,4,1,3,6] => [5,4,3,2,1,6] => 768
[5,2,4,1,6,3] => [6,4,3,2,5,1] => 7700
[5,2,4,3,1,6] => [5,4,3,2,1,6] => 768
[5,2,4,3,6,1] => [6,4,3,2,5,1] => 7700
[5,2,4,6,1,3] => [6,5,3,4,2,1] => 68640
[5,2,4,6,3,1] => [6,5,3,4,2,1] => 68640
[5,2,6,1,3,4] => [6,4,5,2,3,1] => 16016
[5,2,6,1,4,3] => [6,4,5,2,3,1] => 16016
[5,2,6,3,1,4] => [6,5,4,3,2,1] => 292864
[5,2,6,3,4,1] => [6,5,4,3,2,1] => 292864
[5,2,6,4,1,3] => [6,5,4,3,2,1] => 292864
[5,2,6,4,3,1] => [6,5,4,3,2,1] => 292864
[5,3,1,2,4,6] => [5,4,3,2,1,6] => 768
[5,3,1,2,6,4] => [6,4,3,2,5,1] => 7700
[5,3,1,4,2,6] => [5,4,3,2,1,6] => 768
[5,3,1,4,6,2] => [6,4,3,2,5,1] => 7700
[5,3,1,6,2,4] => [6,5,3,4,2,1] => 68640
[5,3,1,6,4,2] => [6,5,3,4,2,1] => 68640
[5,3,2,1,4,6] => [5,4,3,2,1,6] => 768
[5,3,2,1,6,4] => [6,4,3,2,5,1] => 7700
[5,3,2,4,1,6] => [5,4,3,2,1,6] => 768
[5,3,2,4,6,1] => [6,4,3,2,5,1] => 7700
[5,3,2,6,1,4] => [6,5,3,4,2,1] => 68640
[5,3,2,6,4,1] => [6,5,3,4,2,1] => 68640
[5,3,4,1,2,6] => [5,4,3,2,1,6] => 768
[5,3,4,1,6,2] => [6,4,3,2,5,1] => 7700
[5,3,4,2,1,6] => [5,4,3,2,1,6] => 768
[5,3,4,2,6,1] => [6,4,3,2,5,1] => 7700
[5,3,4,6,1,2] => [6,5,3,4,2,1] => 68640
[5,3,4,6,2,1] => [6,5,3,4,2,1] => 68640
[5,3,6,1,2,4] => [6,5,4,3,2,1] => 292864
[5,3,6,1,4,2] => [6,5,4,3,2,1] => 292864
[5,3,6,2,1,4] => [6,5,4,3,2,1] => 292864
[5,3,6,2,4,1] => [6,5,4,3,2,1] => 292864
[5,3,6,4,1,2] => [6,5,4,3,2,1] => 292864
[5,3,6,4,2,1] => [6,5,4,3,2,1] => 292864
[5,4,1,2,3,6] => [5,4,3,2,1,6] => 768
[5,4,1,2,6,3] => [6,4,3,2,5,1] => 7700
[5,4,1,3,2,6] => [5,4,3,2,1,6] => 768
[5,4,1,3,6,2] => [6,4,3,2,5,1] => 7700
[5,4,1,6,2,3] => [6,5,3,4,2,1] => 68640
[5,4,1,6,3,2] => [6,5,3,4,2,1] => 68640
[5,4,2,1,3,6] => [5,4,3,2,1,6] => 768
[5,4,2,1,6,3] => [6,4,3,2,5,1] => 7700
[5,4,2,3,1,6] => [5,4,3,2,1,6] => 768
[5,4,2,3,6,1] => [6,4,3,2,5,1] => 7700
[5,4,2,6,1,3] => [6,5,3,4,2,1] => 68640
[5,4,2,6,3,1] => [6,5,3,4,2,1] => 68640
[5,4,3,1,2,6] => [5,4,3,2,1,6] => 768
[5,4,3,1,6,2] => [6,4,3,2,5,1] => 7700
[5,4,3,2,1,6] => [5,4,3,2,1,6] => 768
[5,4,3,2,6,1] => [6,4,3,2,5,1] => 7700
[5,4,3,6,1,2] => [6,5,3,4,2,1] => 68640
[5,4,3,6,2,1] => [6,5,3,4,2,1] => 68640
[5,4,6,1,2,3] => [6,5,4,3,2,1] => 292864
[5,4,6,1,3,2] => [6,5,4,3,2,1] => 292864
[5,4,6,2,1,3] => [6,5,4,3,2,1] => 292864
[5,4,6,2,3,1] => [6,5,4,3,2,1] => 292864
[5,4,6,3,1,2] => [6,5,4,3,2,1] => 292864
[5,4,6,3,2,1] => [6,5,4,3,2,1] => 292864
[5,6,1,2,3,4] => [6,5,3,4,2,1] => 68640
[5,6,1,2,4,3] => [6,5,3,4,2,1] => 68640
[5,6,1,3,2,4] => [6,5,3,4,2,1] => 68640
[5,6,1,3,4,2] => [6,5,3,4,2,1] => 68640
[5,6,1,4,2,3] => [6,5,3,4,2,1] => 68640
[5,6,1,4,3,2] => [6,5,3,4,2,1] => 68640
[5,6,2,1,3,4] => [6,5,4,3,2,1] => 292864
[5,6,2,1,4,3] => [6,5,4,3,2,1] => 292864
[5,6,2,3,1,4] => [6,5,4,3,2,1] => 292864
[5,6,2,3,4,1] => [6,5,4,3,2,1] => 292864
[5,6,2,4,1,3] => [6,5,4,3,2,1] => 292864
[5,6,2,4,3,1] => [6,5,4,3,2,1] => 292864
[5,6,3,1,2,4] => [6,5,4,3,2,1] => 292864
[5,6,3,1,4,2] => [6,5,4,3,2,1] => 292864
[5,6,3,2,1,4] => [6,5,4,3,2,1] => 292864
[5,6,3,2,4,1] => [6,5,4,3,2,1] => 292864
[5,6,3,4,1,2] => [6,5,4,3,2,1] => 292864
[5,6,3,4,2,1] => [6,5,4,3,2,1] => 292864
[5,6,4,1,2,3] => [6,5,4,3,2,1] => 292864
[5,6,4,1,3,2] => [6,5,4,3,2,1] => 292864
[5,6,4,2,1,3] => [6,5,4,3,2,1] => 292864
[5,6,4,2,3,1] => [6,5,4,3,2,1] => 292864
[5,6,4,3,1,2] => [6,5,4,3,2,1] => 292864
[5,6,4,3,2,1] => [6,5,4,3,2,1] => 292864
[6,1,2,3,4,5] => [6,2,3,4,5,1] => 70
[6,1,2,3,5,4] => [6,2,3,4,5,1] => 70
[6,1,2,4,3,5] => [6,2,3,5,4,1] => 448
[6,1,2,4,5,3] => [6,2,3,5,4,1] => 448
[6,1,2,5,3,4] => [6,2,3,5,4,1] => 448
[6,1,2,5,4,3] => [6,2,3,5,4,1] => 448
[6,1,3,2,4,5] => [6,2,4,3,5,1] => 448
[6,1,3,2,5,4] => [6,2,4,3,5,1] => 448
[6,1,3,4,2,5] => [6,2,5,4,3,1] => 7700
[6,1,3,4,5,2] => [6,2,5,4,3,1] => 7700
[6,1,3,5,2,4] => [6,2,5,4,3,1] => 7700
[6,1,3,5,4,2] => [6,2,5,4,3,1] => 7700
[6,1,4,2,3,5] => [6,2,5,4,3,1] => 7700
[6,1,4,2,5,3] => [6,2,5,4,3,1] => 7700
[6,1,4,3,2,5] => [6,2,5,4,3,1] => 7700
[6,1,4,3,5,2] => [6,2,5,4,3,1] => 7700
[6,1,4,5,2,3] => [6,2,5,4,3,1] => 7700
[6,1,4,5,3,2] => [6,2,5,4,3,1] => 7700
[6,1,5,2,3,4] => [6,2,5,4,3,1] => 7700
[6,1,5,2,4,3] => [6,2,5,4,3,1] => 7700
[6,1,5,3,2,4] => [6,2,5,4,3,1] => 7700
[6,1,5,3,4,2] => [6,2,5,4,3,1] => 7700
[6,1,5,4,2,3] => [6,2,5,4,3,1] => 7700
[6,1,5,4,3,2] => [6,2,5,4,3,1] => 7700
[6,2,1,3,4,5] => [6,3,2,4,5,1] => 448
[6,2,1,3,5,4] => [6,3,2,4,5,1] => 448
[6,2,1,4,3,5] => [6,3,2,5,4,1] => 3080
[6,2,1,4,5,3] => [6,3,2,5,4,1] => 3080
[6,2,1,5,3,4] => [6,3,2,5,4,1] => 3080
[6,2,1,5,4,3] => [6,3,2,5,4,1] => 3080
[6,2,3,1,4,5] => [6,4,3,2,5,1] => 7700
[6,2,3,1,5,4] => [6,4,3,2,5,1] => 7700
[6,2,3,4,1,5] => [6,5,3,4,2,1] => 68640
[6,2,3,4,5,1] => [6,5,3,4,2,1] => 68640
[6,2,3,5,1,4] => [6,5,3,4,2,1] => 68640
[6,2,3,5,4,1] => [6,5,3,4,2,1] => 68640
[6,2,4,1,3,5] => [6,4,5,2,3,1] => 16016
[6,2,4,1,5,3] => [6,4,5,2,3,1] => 16016
[6,2,4,3,1,5] => [6,5,4,3,2,1] => 292864
[6,2,4,3,5,1] => [6,5,4,3,2,1] => 292864
[6,2,4,5,1,3] => [6,5,4,3,2,1] => 292864
[6,2,4,5,3,1] => [6,5,4,3,2,1] => 292864
[6,2,5,1,3,4] => [6,4,5,2,3,1] => 16016
[6,2,5,1,4,3] => [6,4,5,2,3,1] => 16016
[6,2,5,3,1,4] => [6,5,4,3,2,1] => 292864
[6,2,5,3,4,1] => [6,5,4,3,2,1] => 292864
[6,2,5,4,1,3] => [6,5,4,3,2,1] => 292864
[6,2,5,4,3,1] => [6,5,4,3,2,1] => 292864
[6,3,1,2,4,5] => [6,4,3,2,5,1] => 7700
[6,3,1,2,5,4] => [6,4,3,2,5,1] => 7700
[6,3,1,4,2,5] => [6,5,3,4,2,1] => 68640
[6,3,1,4,5,2] => [6,5,3,4,2,1] => 68640
[6,3,1,5,2,4] => [6,5,3,4,2,1] => 68640
[6,3,1,5,4,2] => [6,5,3,4,2,1] => 68640
[6,3,2,1,4,5] => [6,4,3,2,5,1] => 7700
[6,3,2,1,5,4] => [6,4,3,2,5,1] => 7700
[6,3,2,4,1,5] => [6,5,3,4,2,1] => 68640
[6,3,2,4,5,1] => [6,5,3,4,2,1] => 68640
[6,3,2,5,1,4] => [6,5,3,4,2,1] => 68640
[6,3,2,5,4,1] => [6,5,3,4,2,1] => 68640
[6,3,4,1,2,5] => [6,5,4,3,2,1] => 292864
[6,3,4,1,5,2] => [6,5,4,3,2,1] => 292864
[6,3,4,2,1,5] => [6,5,4,3,2,1] => 292864
[6,3,4,2,5,1] => [6,5,4,3,2,1] => 292864
[6,3,4,5,1,2] => [6,5,4,3,2,1] => 292864
[6,3,4,5,2,1] => [6,5,4,3,2,1] => 292864
[6,3,5,1,2,4] => [6,5,4,3,2,1] => 292864
[6,3,5,1,4,2] => [6,5,4,3,2,1] => 292864
[6,3,5,2,1,4] => [6,5,4,3,2,1] => 292864
[6,3,5,2,4,1] => [6,5,4,3,2,1] => 292864
[6,3,5,4,1,2] => [6,5,4,3,2,1] => 292864
[6,3,5,4,2,1] => [6,5,4,3,2,1] => 292864
[6,4,1,2,3,5] => [6,5,3,4,2,1] => 68640
[6,4,1,2,5,3] => [6,5,3,4,2,1] => 68640
[6,4,1,3,2,5] => [6,5,3,4,2,1] => 68640
[6,4,1,3,5,2] => [6,5,3,4,2,1] => 68640
[6,4,1,5,2,3] => [6,5,3,4,2,1] => 68640
[6,4,1,5,3,2] => [6,5,3,4,2,1] => 68640
[6,4,2,1,3,5] => [6,5,4,3,2,1] => 292864
[6,4,2,1,5,3] => [6,5,4,3,2,1] => 292864
[6,4,2,3,1,5] => [6,5,4,3,2,1] => 292864
[6,4,2,3,5,1] => [6,5,4,3,2,1] => 292864
[6,4,2,5,1,3] => [6,5,4,3,2,1] => 292864
[6,4,2,5,3,1] => [6,5,4,3,2,1] => 292864
[6,4,3,1,2,5] => [6,5,4,3,2,1] => 292864
[6,4,3,1,5,2] => [6,5,4,3,2,1] => 292864
[6,4,3,2,1,5] => [6,5,4,3,2,1] => 292864
[6,4,3,2,5,1] => [6,5,4,3,2,1] => 292864
[6,4,3,5,1,2] => [6,5,4,3,2,1] => 292864
[6,4,3,5,2,1] => [6,5,4,3,2,1] => 292864
[6,4,5,1,2,3] => [6,5,4,3,2,1] => 292864
[6,4,5,1,3,2] => [6,5,4,3,2,1] => 292864
[6,4,5,2,1,3] => [6,5,4,3,2,1] => 292864
[6,4,5,2,3,1] => [6,5,4,3,2,1] => 292864
[6,4,5,3,1,2] => [6,5,4,3,2,1] => 292864
[6,4,5,3,2,1] => [6,5,4,3,2,1] => 292864
[6,5,1,2,3,4] => [6,5,3,4,2,1] => 68640
[6,5,1,2,4,3] => [6,5,3,4,2,1] => 68640
[6,5,1,3,2,4] => [6,5,3,4,2,1] => 68640
[6,5,1,3,4,2] => [6,5,3,4,2,1] => 68640
[6,5,1,4,2,3] => [6,5,3,4,2,1] => 68640
[6,5,1,4,3,2] => [6,5,3,4,2,1] => 68640
[6,5,2,1,3,4] => [6,5,4,3,2,1] => 292864
[6,5,2,1,4,3] => [6,5,4,3,2,1] => 292864
[6,5,2,3,1,4] => [6,5,4,3,2,1] => 292864
[6,5,2,3,4,1] => [6,5,4,3,2,1] => 292864
[6,5,2,4,1,3] => [6,5,4,3,2,1] => 292864
[6,5,2,4,3,1] => [6,5,4,3,2,1] => 292864
[6,5,3,1,2,4] => [6,5,4,3,2,1] => 292864
[6,5,3,1,4,2] => [6,5,4,3,2,1] => 292864
[6,5,3,2,1,4] => [6,5,4,3,2,1] => 292864
[6,5,3,2,4,1] => [6,5,4,3,2,1] => 292864
[6,5,3,4,1,2] => [6,5,4,3,2,1] => 292864
[6,5,3,4,2,1] => [6,5,4,3,2,1] => 292864
[6,5,4,1,2,3] => [6,5,4,3,2,1] => 292864
[6,5,4,1,3,2] => [6,5,4,3,2,1] => 292864
[6,5,4,2,1,3] => [6,5,4,3,2,1] => 292864
[6,5,4,2,3,1] => [6,5,4,3,2,1] => 292864
[6,5,4,3,1,2] => [6,5,4,3,2,1] => 292864
[6,5,4,3,2,1] => [6,5,4,3,2,1] => 292864
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 1
[1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1
[1,3,4,6,7,5,2] => [1,7,3,6,5,4,2] => 7700
[1,3,4,7,5,6,2] => [1,7,3,6,5,4,2] => 7700
[1,3,4,7,6,5,2] => [1,7,3,6,5,4,2] => 7700
[1,3,5,4,7,6,2] => [1,7,4,3,6,5,2] => 3080
[1,3,5,6,4,7,2] => [1,7,5,4,3,6,2] => 7700
[1,3,5,6,7,4,2] => [1,7,6,4,5,3,2] => 68640
[1,3,5,7,2,4,6] => [1,5,6,7,2,3,4] => 42
[1,3,5,7,6,4,2] => [1,7,6,5,4,3,2] => 292864
[1,3,6,4,5,7,2] => [1,7,5,4,3,6,2] => 7700
[1,3,6,4,7,5,2] => [1,7,6,4,5,3,2] => 68640
[1,3,6,5,4,7,2] => [1,7,5,4,3,6,2] => 7700
[1,3,6,5,7,4,2] => [1,7,6,4,5,3,2] => 68640
[1,3,6,7,4,5,2] => [1,7,6,5,4,3,2] => 292864
[1,3,6,7,5,4,2] => [1,7,6,5,4,3,2] => 292864
[1,3,7,4,5,6,2] => [1,7,6,4,5,3,2] => 68640
[1,3,7,4,6,5,2] => [1,7,6,4,5,3,2] => 68640
[1,3,7,5,4,6,2] => [1,7,6,5,4,3,2] => 292864
[1,3,7,5,6,4,2] => [1,7,6,5,4,3,2] => 292864
[1,3,7,6,4,5,2] => [1,7,6,5,4,3,2] => 292864
[1,3,7,6,5,4,2] => [1,7,6,5,4,3,2] => 292864
[1,4,2,6,7,5,3] => [1,7,3,6,5,4,2] => 7700
[1,4,2,7,5,6,3] => [1,7,3,6,5,4,2] => 7700
[1,4,2,7,6,5,3] => [1,7,3,6,5,4,2] => 7700
[1,4,3,6,7,5,2] => [1,7,3,6,5,4,2] => 7700
[1,4,3,7,5,6,2] => [1,7,3,6,5,4,2] => 7700
[1,4,3,7,6,5,2] => [1,7,3,6,5,4,2] => 7700
[1,4,5,2,7,6,3] => [1,7,4,3,6,5,2] => 3080
[1,4,5,3,7,6,2] => [1,7,4,3,6,5,2] => 3080
[1,4,5,6,2,7,3] => [1,7,5,4,3,6,2] => 7700
[1,4,5,6,3,7,2] => [1,7,5,4,3,6,2] => 7700
[1,4,5,6,7,2,3] => [1,7,6,4,5,3,2] => 68640
[1,4,5,6,7,3,2] => [1,7,6,4,5,3,2] => 68640
[1,4,5,7,6,2,3] => [1,7,6,5,4,3,2] => 292864
[1,4,5,7,6,3,2] => [1,7,6,5,4,3,2] => 292864
[1,4,6,2,5,7,3] => [1,7,5,4,3,6,2] => 7700
[1,4,6,2,7,5,3] => [1,7,6,4,5,3,2] => 68640
[1,4,6,3,5,7,2] => [1,7,5,4,3,6,2] => 7700
[1,4,6,3,7,5,2] => [1,7,6,4,5,3,2] => 68640
[1,4,6,5,2,7,3] => [1,7,5,4,3,6,2] => 7700
[1,4,6,5,3,7,2] => [1,7,5,4,3,6,2] => 7700
[1,4,6,5,7,2,3] => [1,7,6,4,5,3,2] => 68640
[1,4,6,5,7,3,2] => [1,7,6,4,5,3,2] => 68640
[1,4,6,7,2,5,3] => [1,7,6,5,4,3,2] => 292864
[1,4,6,7,3,5,2] => [1,7,6,5,4,3,2] => 292864
[1,4,6,7,5,2,3] => [1,7,6,5,4,3,2] => 292864
[1,4,6,7,5,3,2] => [1,7,6,5,4,3,2] => 292864
[1,4,7,2,5,6,3] => [1,7,6,4,5,3,2] => 68640
[1,4,7,2,6,5,3] => [1,7,6,4,5,3,2] => 68640
[1,4,7,3,5,6,2] => [1,7,6,4,5,3,2] => 68640
[1,4,7,3,6,5,2] => [1,7,6,4,5,3,2] => 68640
[1,4,7,5,2,6,3] => [1,7,6,5,4,3,2] => 292864
[1,4,7,5,3,6,2] => [1,7,6,5,4,3,2] => 292864
[1,4,7,5,6,2,3] => [1,7,6,5,4,3,2] => 292864
[1,4,7,5,6,3,2] => [1,7,6,5,4,3,2] => 292864
[1,4,7,6,2,5,3] => [1,7,6,5,4,3,2] => 292864
[1,4,7,6,3,5,2] => [1,7,6,5,4,3,2] => 292864
[1,4,7,6,5,2,3] => [1,7,6,5,4,3,2] => 292864
[1,4,7,6,5,3,2] => [1,7,6,5,4,3,2] => 292864
[1,5,2,6,7,3,4] => [1,7,3,6,5,4,2] => 7700
[1,5,2,6,7,4,3] => [1,7,3,6,5,4,2] => 7700
[1,5,2,7,3,6,4] => [1,7,3,6,5,4,2] => 7700
[1,5,2,7,4,6,3] => [1,7,3,6,5,4,2] => 7700
[1,5,2,7,6,3,4] => [1,7,3,6,5,4,2] => 7700
[1,5,2,7,6,4,3] => [1,7,3,6,5,4,2] => 7700
[1,5,3,2,7,6,4] => [1,7,4,3,6,5,2] => 3080
[1,5,3,4,7,6,2] => [1,7,4,3,6,5,2] => 3080
[1,5,3,6,2,7,4] => [1,7,5,4,3,6,2] => 7700
[1,5,3,6,4,7,2] => [1,7,5,4,3,6,2] => 7700
[1,5,3,6,7,2,4] => [1,7,6,4,5,3,2] => 68640
[1,5,3,6,7,4,2] => [1,7,6,4,5,3,2] => 68640
[1,5,3,7,6,2,4] => [1,7,6,5,4,3,2] => 292864
[1,5,3,7,6,4,2] => [1,7,6,5,4,3,2] => 292864
[1,5,4,2,7,6,3] => [1,7,4,3,6,5,2] => 3080
[1,5,4,3,7,6,2] => [1,7,4,3,6,5,2] => 3080
[1,5,4,6,2,7,3] => [1,7,5,4,3,6,2] => 7700
[1,5,4,6,3,7,2] => [1,7,5,4,3,6,2] => 7700
[1,5,4,6,7,2,3] => [1,7,6,4,5,3,2] => 68640
[1,5,4,6,7,3,2] => [1,7,6,4,5,3,2] => 68640
[1,5,4,7,6,2,3] => [1,7,6,5,4,3,2] => 292864
[1,5,4,7,6,3,2] => [1,7,6,5,4,3,2] => 292864
[1,5,6,2,3,7,4] => [1,7,5,4,3,6,2] => 7700
[1,5,6,2,4,7,3] => [1,7,5,4,3,6,2] => 7700
[1,5,6,2,7,3,4] => [1,7,6,4,5,3,2] => 68640
[1,5,6,2,7,4,3] => [1,7,6,4,5,3,2] => 68640
[1,5,6,3,2,7,4] => [1,7,5,4,3,6,2] => 7700
[1,5,6,3,4,7,2] => [1,7,5,4,3,6,2] => 7700
[1,5,6,3,7,2,4] => [1,7,6,4,5,3,2] => 68640
[1,5,6,3,7,4,2] => [1,7,6,4,5,3,2] => 68640
[1,5,6,4,2,7,3] => [1,7,5,4,3,6,2] => 7700
[1,5,6,4,3,7,2] => [1,7,5,4,3,6,2] => 7700
[1,5,6,4,7,2,3] => [1,7,6,4,5,3,2] => 68640
[1,5,6,4,7,3,2] => [1,7,6,4,5,3,2] => 68640
[1,5,6,7,2,3,4] => [1,7,6,5,4,3,2] => 292864
[1,5,6,7,2,4,3] => [1,7,6,5,4,3,2] => 292864
[1,5,6,7,3,2,4] => [1,7,6,5,4,3,2] => 292864
[1,5,6,7,3,4,2] => [1,7,6,5,4,3,2] => 292864
[1,5,6,7,4,2,3] => [1,7,6,5,4,3,2] => 292864
[1,5,6,7,4,3,2] => [1,7,6,5,4,3,2] => 292864
[1,5,7,2,3,6,4] => [1,7,6,4,5,3,2] => 68640
[1,5,7,2,4,6,3] => [1,7,6,4,5,3,2] => 68640
[1,5,7,2,6,3,4] => [1,7,6,4,5,3,2] => 68640
[1,5,7,2,6,4,3] => [1,7,6,4,5,3,2] => 68640
[1,5,7,3,2,6,4] => [1,7,6,5,4,3,2] => 292864
[1,5,7,3,4,6,2] => [1,7,6,5,4,3,2] => 292864
[1,5,7,3,6,2,4] => [1,7,6,5,4,3,2] => 292864
[1,5,7,3,6,4,2] => [1,7,6,5,4,3,2] => 292864
[1,5,7,4,2,6,3] => [1,7,6,5,4,3,2] => 292864
[1,5,7,4,3,6,2] => [1,7,6,5,4,3,2] => 292864
[1,5,7,4,6,2,3] => [1,7,6,5,4,3,2] => 292864
[1,5,7,4,6,3,2] => [1,7,6,5,4,3,2] => 292864
[1,5,7,6,2,3,4] => [1,7,6,5,4,3,2] => 292864
[1,5,7,6,2,4,3] => [1,7,6,5,4,3,2] => 292864
[1,5,7,6,3,2,4] => [1,7,6,5,4,3,2] => 292864
[1,5,7,6,3,4,2] => [1,7,6,5,4,3,2] => 292864
[1,5,7,6,4,2,3] => [1,7,6,5,4,3,2] => 292864
[1,5,7,6,4,3,2] => [1,7,6,5,4,3,2] => 292864
[1,6,2,4,7,3,5] => [1,7,3,6,5,4,2] => 7700
[1,6,2,4,7,5,3] => [1,7,3,6,5,4,2] => 7700
[1,6,2,5,7,3,4] => [1,7,3,6,5,4,2] => 7700
[1,6,2,5,7,4,3] => [1,7,3,6,5,4,2] => 7700
[1,6,2,7,3,4,5] => [1,7,3,6,5,4,2] => 7700
[1,6,2,7,3,5,4] => [1,7,3,6,5,4,2] => 7700
[1,6,2,7,4,3,5] => [1,7,3,6,5,4,2] => 7700
[1,6,2,7,4,5,3] => [1,7,3,6,5,4,2] => 7700
[1,6,2,7,5,3,4] => [1,7,3,6,5,4,2] => 7700
[1,6,2,7,5,4,3] => [1,7,3,6,5,4,2] => 7700
[1,6,3,2,7,4,5] => [1,7,4,3,6,5,2] => 3080
[1,6,3,2,7,5,4] => [1,7,4,3,6,5,2] => 3080
[1,6,3,4,2,7,5] => [1,7,5,4,3,6,2] => 7700
[1,6,3,4,5,7,2] => [1,7,5,4,3,6,2] => 7700
[1,6,3,4,7,2,5] => [1,7,6,4,5,3,2] => 68640
[1,6,3,4,7,5,2] => [1,7,6,4,5,3,2] => 68640
[1,6,3,5,2,7,4] => [1,7,5,4,3,6,2] => 7700
[1,6,3,5,4,7,2] => [1,7,5,4,3,6,2] => 7700
[1,6,3,5,7,2,4] => [1,7,6,4,5,3,2] => 68640
[1,6,3,5,7,4,2] => [1,7,6,4,5,3,2] => 68640
[1,6,3,7,4,2,5] => [1,7,6,5,4,3,2] => 292864
[1,6,3,7,4,5,2] => [1,7,6,5,4,3,2] => 292864
[1,6,3,7,5,2,4] => [1,7,6,5,4,3,2] => 292864
[1,6,3,7,5,4,2] => [1,7,6,5,4,3,2] => 292864
[1,6,4,2,3,7,5] => [1,7,5,4,3,6,2] => 7700
[1,6,4,2,5,7,3] => [1,7,5,4,3,6,2] => 7700
[1,6,4,2,7,3,5] => [1,7,6,4,5,3,2] => 68640
[1,6,4,2,7,5,3] => [1,7,6,4,5,3,2] => 68640
[1,6,4,3,2,7,5] => [1,7,5,4,3,6,2] => 7700
[1,6,4,3,5,7,2] => [1,7,5,4,3,6,2] => 7700
[1,6,4,3,7,2,5] => [1,7,6,4,5,3,2] => 68640
[1,6,4,3,7,5,2] => [1,7,6,4,5,3,2] => 68640
[1,6,4,5,2,7,3] => [1,7,5,4,3,6,2] => 7700
[1,6,4,5,3,7,2] => [1,7,5,4,3,6,2] => 7700
[1,6,4,5,7,2,3] => [1,7,6,4,5,3,2] => 68640
[1,6,4,5,7,3,2] => [1,7,6,4,5,3,2] => 68640
[1,6,4,7,2,3,5] => [1,7,6,5,4,3,2] => 292864
[1,6,4,7,2,5,3] => [1,7,6,5,4,3,2] => 292864
[1,6,4,7,3,2,5] => [1,7,6,5,4,3,2] => 292864
[1,6,4,7,3,5,2] => [1,7,6,5,4,3,2] => 292864
[1,6,4,7,5,2,3] => [1,7,6,5,4,3,2] => 292864
[1,6,4,7,5,3,2] => [1,7,6,5,4,3,2] => 292864
[1,6,5,2,3,7,4] => [1,7,5,4,3,6,2] => 7700
[1,6,5,2,4,7,3] => [1,7,5,4,3,6,2] => 7700
[1,6,5,2,7,3,4] => [1,7,6,4,5,3,2] => 68640
[1,6,5,2,7,4,3] => [1,7,6,4,5,3,2] => 68640
[1,6,5,3,2,7,4] => [1,7,5,4,3,6,2] => 7700
[1,6,5,3,4,7,2] => [1,7,5,4,3,6,2] => 7700
[1,6,5,3,7,2,4] => [1,7,6,4,5,3,2] => 68640
[1,6,5,3,7,4,2] => [1,7,6,4,5,3,2] => 68640
[1,6,5,4,2,7,3] => [1,7,5,4,3,6,2] => 7700
[1,6,5,4,3,7,2] => [1,7,5,4,3,6,2] => 7700
[1,6,5,4,7,2,3] => [1,7,6,4,5,3,2] => 68640
[1,6,5,4,7,3,2] => [1,7,6,4,5,3,2] => 68640
[1,6,5,7,2,3,4] => [1,7,6,5,4,3,2] => 292864
[1,6,5,7,2,4,3] => [1,7,6,5,4,3,2] => 292864
[1,6,5,7,3,2,4] => [1,7,6,5,4,3,2] => 292864
[1,6,5,7,3,4,2] => [1,7,6,5,4,3,2] => 292864
[1,6,5,7,4,2,3] => [1,7,6,5,4,3,2] => 292864
[1,6,5,7,4,3,2] => [1,7,6,5,4,3,2] => 292864
[1,6,7,2,3,4,5] => [1,7,6,4,5,3,2] => 68640
[1,6,7,2,3,5,4] => [1,7,6,4,5,3,2] => 68640
[1,6,7,2,4,3,5] => [1,7,6,4,5,3,2] => 68640
[1,6,7,2,4,5,3] => [1,7,6,4,5,3,2] => 68640
[1,6,7,2,5,3,4] => [1,7,6,4,5,3,2] => 68640
[1,6,7,2,5,4,3] => [1,7,6,4,5,3,2] => 68640
[1,6,7,3,2,4,5] => [1,7,6,5,4,3,2] => 292864
[1,6,7,3,2,5,4] => [1,7,6,5,4,3,2] => 292864
[1,6,7,3,4,2,5] => [1,7,6,5,4,3,2] => 292864
[1,6,7,3,4,5,2] => [1,7,6,5,4,3,2] => 292864
[1,6,7,3,5,2,4] => [1,7,6,5,4,3,2] => 292864
[1,6,7,3,5,4,2] => [1,7,6,5,4,3,2] => 292864
[1,6,7,4,2,3,5] => [1,7,6,5,4,3,2] => 292864
[1,6,7,4,2,5,3] => [1,7,6,5,4,3,2] => 292864
[1,6,7,4,3,2,5] => [1,7,6,5,4,3,2] => 292864
[1,6,7,4,3,5,2] => [1,7,6,5,4,3,2] => 292864
[1,6,7,4,5,2,3] => [1,7,6,5,4,3,2] => 292864
[1,6,7,4,5,3,2] => [1,7,6,5,4,3,2] => 292864
[1,6,7,5,2,3,4] => [1,7,6,5,4,3,2] => 292864
[1,6,7,5,2,4,3] => [1,7,6,5,4,3,2] => 292864
[1,6,7,5,3,2,4] => [1,7,6,5,4,3,2] => 292864
[1,6,7,5,3,4,2] => [1,7,6,5,4,3,2] => 292864
[1,6,7,5,4,2,3] => [1,7,6,5,4,3,2] => 292864
[1,6,7,5,4,3,2] => [1,7,6,5,4,3,2] => 292864
[1,7,2,4,5,3,6] => [1,7,3,6,5,4,2] => 7700
[1,7,2,4,5,6,3] => [1,7,3,6,5,4,2] => 7700
[1,7,2,4,6,3,5] => [1,7,3,6,5,4,2] => 7700
[1,7,2,4,6,5,3] => [1,7,3,6,5,4,2] => 7700
[1,7,2,5,3,4,6] => [1,7,3,6,5,4,2] => 7700
[1,7,2,5,3,6,4] => [1,7,3,6,5,4,2] => 7700
[1,7,2,5,4,3,6] => [1,7,3,6,5,4,2] => 7700
[1,7,2,5,4,6,3] => [1,7,3,6,5,4,2] => 7700
[1,7,2,5,6,3,4] => [1,7,3,6,5,4,2] => 7700
[1,7,2,5,6,4,3] => [1,7,3,6,5,4,2] => 7700
[1,7,2,6,3,4,5] => [1,7,3,6,5,4,2] => 7700
[1,7,2,6,3,5,4] => [1,7,3,6,5,4,2] => 7700
[1,7,2,6,4,3,5] => [1,7,3,6,5,4,2] => 7700
[1,7,2,6,4,5,3] => [1,7,3,6,5,4,2] => 7700
[1,7,2,6,5,3,4] => [1,7,3,6,5,4,2] => 7700
[1,7,2,6,5,4,3] => [1,7,3,6,5,4,2] => 7700
[1,7,3,2,5,4,6] => [1,7,4,3,6,5,2] => 3080
[1,7,3,2,5,6,4] => [1,7,4,3,6,5,2] => 3080
[1,7,3,2,6,4,5] => [1,7,4,3,6,5,2] => 3080
[1,7,3,2,6,5,4] => [1,7,4,3,6,5,2] => 3080
[1,7,3,4,2,5,6] => [1,7,5,4,3,6,2] => 7700
[1,7,3,4,2,6,5] => [1,7,5,4,3,6,2] => 7700
[1,7,3,4,5,2,6] => [1,7,6,4,5,3,2] => 68640
[1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => 68640
[1,7,3,4,6,2,5] => [1,7,6,4,5,3,2] => 68640
[1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => 68640
[1,7,3,5,4,2,6] => [1,7,6,5,4,3,2] => 292864
[1,7,3,5,4,6,2] => [1,7,6,5,4,3,2] => 292864
[1,7,3,5,6,2,4] => [1,7,6,5,4,3,2] => 292864
[1,7,3,5,6,4,2] => [1,7,6,5,4,3,2] => 292864
[1,7,3,6,4,2,5] => [1,7,6,5,4,3,2] => 292864
[1,7,3,6,4,5,2] => [1,7,6,5,4,3,2] => 292864
[1,7,3,6,5,2,4] => [1,7,6,5,4,3,2] => 292864
[1,7,3,6,5,4,2] => [1,7,6,5,4,3,2] => 292864
[1,7,4,2,3,5,6] => [1,7,5,4,3,6,2] => 7700
[1,7,4,2,3,6,5] => [1,7,5,4,3,6,2] => 7700
[1,7,4,2,5,3,6] => [1,7,6,4,5,3,2] => 68640
[1,7,4,2,5,6,3] => [1,7,6,4,5,3,2] => 68640
[1,7,4,2,6,3,5] => [1,7,6,4,5,3,2] => 68640
[1,7,4,2,6,5,3] => [1,7,6,4,5,3,2] => 68640
[1,7,4,3,2,5,6] => [1,7,5,4,3,6,2] => 7700
[1,7,4,3,2,6,5] => [1,7,5,4,3,6,2] => 7700
[1,7,4,3,5,2,6] => [1,7,6,4,5,3,2] => 68640
[1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => 68640
[1,7,4,3,6,2,5] => [1,7,6,4,5,3,2] => 68640
[1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => 68640
[1,7,4,5,2,3,6] => [1,7,6,5,4,3,2] => 292864
[1,7,4,5,2,6,3] => [1,7,6,5,4,3,2] => 292864
[1,7,4,5,3,2,6] => [1,7,6,5,4,3,2] => 292864
[1,7,4,5,3,6,2] => [1,7,6,5,4,3,2] => 292864
[1,7,4,5,6,2,3] => [1,7,6,5,4,3,2] => 292864
[1,7,4,5,6,3,2] => [1,7,6,5,4,3,2] => 292864
[1,7,4,6,2,3,5] => [1,7,6,5,4,3,2] => 292864
[1,7,4,6,2,5,3] => [1,7,6,5,4,3,2] => 292864
[1,7,4,6,3,2,5] => [1,7,6,5,4,3,2] => 292864
[1,7,4,6,3,5,2] => [1,7,6,5,4,3,2] => 292864
[1,7,4,6,5,2,3] => [1,7,6,5,4,3,2] => 292864
[1,7,4,6,5,3,2] => [1,7,6,5,4,3,2] => 292864
[1,7,5,2,3,4,6] => [1,7,6,4,5,3,2] => 68640
[1,7,5,2,3,6,4] => [1,7,6,4,5,3,2] => 68640
[1,7,5,2,4,3,6] => [1,7,6,4,5,3,2] => 68640
[1,7,5,2,4,6,3] => [1,7,6,4,5,3,2] => 68640
[1,7,5,2,6,3,4] => [1,7,6,4,5,3,2] => 68640
[1,7,5,2,6,4,3] => [1,7,6,4,5,3,2] => 68640
[1,7,5,3,2,4,6] => [1,7,6,5,4,3,2] => 292864
[1,7,5,3,2,6,4] => [1,7,6,5,4,3,2] => 292864
[1,7,5,3,4,2,6] => [1,7,6,5,4,3,2] => 292864
[1,7,5,3,4,6,2] => [1,7,6,5,4,3,2] => 292864
[1,7,5,3,6,2,4] => [1,7,6,5,4,3,2] => 292864
[1,7,5,3,6,4,2] => [1,7,6,5,4,3,2] => 292864
[1,7,5,4,2,3,6] => [1,7,6,5,4,3,2] => 292864
[1,7,5,4,2,6,3] => [1,7,6,5,4,3,2] => 292864
[1,7,5,4,3,2,6] => [1,7,6,5,4,3,2] => 292864
[1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => 292864
[1,7,5,4,6,2,3] => [1,7,6,5,4,3,2] => 292864
[1,7,5,4,6,3,2] => [1,7,6,5,4,3,2] => 292864
[1,7,5,6,2,3,4] => [1,7,6,5,4,3,2] => 292864
[1,7,5,6,2,4,3] => [1,7,6,5,4,3,2] => 292864
[1,7,5,6,3,2,4] => [1,7,6,5,4,3,2] => 292864
[1,7,5,6,3,4,2] => [1,7,6,5,4,3,2] => 292864
[1,7,5,6,4,2,3] => [1,7,6,5,4,3,2] => 292864
[1,7,5,6,4,3,2] => [1,7,6,5,4,3,2] => 292864
[1,7,6,2,3,4,5] => [1,7,6,4,5,3,2] => 68640
[1,7,6,2,3,5,4] => [1,7,6,4,5,3,2] => 68640
[1,7,6,2,4,3,5] => [1,7,6,4,5,3,2] => 68640
[1,7,6,2,4,5,3] => [1,7,6,4,5,3,2] => 68640
[1,7,6,2,5,3,4] => [1,7,6,4,5,3,2] => 68640
[1,7,6,2,5,4,3] => [1,7,6,4,5,3,2] => 68640
[1,7,6,3,2,4,5] => [1,7,6,5,4,3,2] => 292864
[1,7,6,3,2,5,4] => [1,7,6,5,4,3,2] => 292864
[1,7,6,3,4,2,5] => [1,7,6,5,4,3,2] => 292864
[1,7,6,3,4,5,2] => [1,7,6,5,4,3,2] => 292864
[1,7,6,3,5,2,4] => [1,7,6,5,4,3,2] => 292864
[1,7,6,3,5,4,2] => [1,7,6,5,4,3,2] => 292864
[1,7,6,4,2,3,5] => [1,7,6,5,4,3,2] => 292864
[1,7,6,4,2,5,3] => [1,7,6,5,4,3,2] => 292864
[1,7,6,4,3,2,5] => [1,7,6,5,4,3,2] => 292864
[1,7,6,4,3,5,2] => [1,7,6,5,4,3,2] => 292864
[1,7,6,4,5,2,3] => [1,7,6,5,4,3,2] => 292864
[1,7,6,4,5,3,2] => [1,7,6,5,4,3,2] => 292864
[1,7,6,5,2,3,4] => [1,7,6,5,4,3,2] => 292864
[1,7,6,5,2,4,3] => [1,7,6,5,4,3,2] => 292864
[1,7,6,5,3,2,4] => [1,7,6,5,4,3,2] => 292864
[1,7,6,5,3,4,2] => [1,7,6,5,4,3,2] => 292864
[1,7,6,5,4,2,3] => [1,7,6,5,4,3,2] => 292864
[1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 292864
[2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 1
[2,1,4,6,7,5,3] => [2,1,7,6,5,4,3] => 8448
[2,1,4,7,5,6,3] => [2,1,7,6,5,4,3] => 8448
[2,1,4,7,6,5,3] => [2,1,7,6,5,4,3] => 8448
[2,1,5,6,7,3,4] => [2,1,7,6,5,4,3] => 8448
[2,1,5,6,7,4,3] => [2,1,7,6,5,4,3] => 8448
[2,1,5,7,3,6,4] => [2,1,7,6,5,4,3] => 8448
[2,1,5,7,4,6,3] => [2,1,7,6,5,4,3] => 8448
[2,1,5,7,6,3,4] => [2,1,7,6,5,4,3] => 8448
[2,1,5,7,6,4,3] => [2,1,7,6,5,4,3] => 8448
[2,1,6,4,7,3,5] => [2,1,7,6,5,4,3] => 8448
[2,1,6,4,7,5,3] => [2,1,7,6,5,4,3] => 8448
[2,1,6,5,7,3,4] => [2,1,7,6,5,4,3] => 8448
[2,1,6,5,7,4,3] => [2,1,7,6,5,4,3] => 8448
[2,1,6,7,3,4,5] => [2,1,7,6,5,4,3] => 8448
[2,1,6,7,3,5,4] => [2,1,7,6,5,4,3] => 8448
[2,1,6,7,4,3,5] => [2,1,7,6,5,4,3] => 8448
[2,1,6,7,4,5,3] => [2,1,7,6,5,4,3] => 8448
[2,1,6,7,5,3,4] => [2,1,7,6,5,4,3] => 8448
[2,1,6,7,5,4,3] => [2,1,7,6,5,4,3] => 8448
[2,1,7,4,5,3,6] => [2,1,7,6,5,4,3] => 8448
[2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => 8448
[2,1,7,4,6,3,5] => [2,1,7,6,5,4,3] => 8448
[2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => 8448
[2,1,7,5,3,4,6] => [2,1,7,6,5,4,3] => 8448
[2,1,7,5,3,6,4] => [2,1,7,6,5,4,3] => 8448
[2,1,7,5,4,3,6] => [2,1,7,6,5,4,3] => 8448
[2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => 8448
[2,1,7,5,6,3,4] => [2,1,7,6,5,4,3] => 8448
[2,1,7,5,6,4,3] => [2,1,7,6,5,4,3] => 8448
[2,1,7,6,3,4,5] => [2,1,7,6,5,4,3] => 8448
[2,1,7,6,3,5,4] => [2,1,7,6,5,4,3] => 8448
[2,1,7,6,4,3,5] => [2,1,7,6,5,4,3] => 8448
[2,1,7,6,4,5,3] => [2,1,7,6,5,4,3] => 8448
[2,1,7,6,5,3,4] => [2,1,7,6,5,4,3] => 8448
[2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 8448
[2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => 2
[2,3,5,1,4,6,7] => [4,2,5,1,3,6,7] => 16
[2,3,5,6,4,1,7] => [6,2,5,4,3,1,7] => 7700
[2,3,5,7,1,4,6] => [5,2,6,7,1,3,4] => 1188
[2,3,6,4,5,1,7] => [6,2,5,4,3,1,7] => 7700
[2,3,6,5,4,1,7] => [6,2,5,4,3,1,7] => 7700
[2,4,1,3,5,6,7] => [3,4,1,2,5,6,7] => 2
[2,4,3,1,5,6,7] => [4,3,2,1,5,6,7] => 16
[2,4,3,6,1,5,7] => [5,3,2,6,1,4,7] => 432
[2,4,3,6,5,1,7] => [6,3,2,5,4,1,7] => 3080
[2,4,5,3,1,6,7] => [5,4,3,2,1,6,7] => 768
[2,4,5,3,1,7,6] => [5,4,3,2,1,7,6] => 8448
[2,4,5,3,6,1,7] => [6,4,3,2,5,1,7] => 7700
[2,4,5,3,7,1,6] => [6,4,3,2,7,1,5] => 58916
[2,4,5,6,1,3,7] => [5,6,3,4,1,2,7] => 2640
[2,4,5,6,3,1,7] => [6,5,3,4,2,1,7] => 68640
[2,4,6,1,3,5,7] => [4,5,6,1,2,3,7] => 42
[2,4,6,3,7,1,5] => [6,4,7,2,5,1,3] => 292864
[2,4,6,5,3,1,7] => [6,5,4,3,2,1,7] => 292864
[2,4,7,3,5,1,6] => [6,4,7,2,5,1,3] => 292864
[2,4,7,3,6,1,5] => [6,4,7,2,5,1,3] => 292864
[2,5,3,4,1,6,7] => [5,4,3,2,1,6,7] => 768
[2,5,3,4,1,7,6] => [5,4,3,2,1,7,6] => 8448
[2,5,3,4,6,1,7] => [6,4,3,2,5,1,7] => 7700
[2,5,3,4,7,1,6] => [6,4,3,2,7,1,5] => 58916
[2,5,3,6,1,4,7] => [5,6,3,4,1,2,7] => 2640
[2,5,3,6,4,1,7] => [6,5,3,4,2,1,7] => 68640
[2,5,4,3,1,6,7] => [5,4,3,2,1,6,7] => 768
[2,5,4,3,1,7,6] => [5,4,3,2,1,7,6] => 8448
[2,5,4,3,6,1,7] => [6,4,3,2,5,1,7] => 7700
[2,5,4,3,7,1,6] => [6,4,3,2,7,1,5] => 58916
[2,5,4,6,1,3,7] => [5,6,3,4,1,2,7] => 2640
[2,5,4,6,3,1,7] => [6,5,3,4,2,1,7] => 68640
[2,5,6,3,4,1,7] => [6,5,4,3,2,1,7] => 292864
[2,5,6,4,3,1,7] => [6,5,4,3,2,1,7] => 292864
[2,6,3,4,1,5,7] => [5,6,3,4,1,2,7] => 2640
[2,6,3,4,5,1,7] => [6,5,3,4,2,1,7] => 68640
[2,6,3,5,1,4,7] => [5,6,3,4,1,2,7] => 2640
[2,6,3,5,4,1,7] => [6,5,3,4,2,1,7] => 68640
[2,6,4,3,5,1,7] => [6,5,4,3,2,1,7] => 292864
[2,6,4,5,3,1,7] => [6,5,4,3,2,1,7] => 292864
[2,6,5,3,4,1,7] => [6,5,4,3,2,1,7] => 292864
[2,6,5,4,3,1,7] => [6,5,4,3,2,1,7] => 292864
[3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => 2
[3,1,5,2,4,6,7] => [4,2,5,1,3,6,7] => 16
[3,1,5,6,4,2,7] => [6,2,5,4,3,1,7] => 7700
[3,1,5,7,2,4,6] => [5,2,6,7,1,3,4] => 1188
[3,1,6,4,5,2,7] => [6,2,5,4,3,1,7] => 7700
[3,1,6,5,4,2,7] => [6,2,5,4,3,1,7] => 7700
[3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 2
[3,2,5,1,4,6,7] => [4,2,5,1,3,6,7] => 16
[3,2,5,6,4,1,7] => [6,2,5,4,3,1,7] => 7700
[3,2,5,7,1,4,6] => [5,2,6,7,1,3,4] => 1188
[3,2,6,4,5,1,7] => [6,2,5,4,3,1,7] => 7700
[3,2,6,5,4,1,7] => [6,2,5,4,3,1,7] => 7700
[3,4,1,2,5,6,7] => [4,3,2,1,5,6,7] => 16
[3,4,1,6,2,5,7] => [5,3,2,6,1,4,7] => 432
[3,4,1,6,5,2,7] => [6,3,2,5,4,1,7] => 3080
[3,4,2,1,5,6,7] => [4,3,2,1,5,6,7] => 16
[3,4,2,6,1,5,7] => [5,3,2,6,1,4,7] => 432
[3,4,2,6,5,1,7] => [6,3,2,5,4,1,7] => 3080
[3,4,5,1,2,6,7] => [5,4,3,2,1,6,7] => 768
[3,4,5,1,2,7,6] => [5,4,3,2,1,7,6] => 8448
[3,4,5,1,6,2,7] => [6,4,3,2,5,1,7] => 7700
[3,4,5,1,7,2,6] => [6,4,3,2,7,1,5] => 58916
[3,4,5,2,1,6,7] => [5,4,3,2,1,6,7] => 768
[3,4,5,2,1,7,6] => [5,4,3,2,1,7,6] => 8448
[3,4,5,2,6,1,7] => [6,4,3,2,5,1,7] => 7700
[3,4,5,2,7,1,6] => [6,4,3,2,7,1,5] => 58916
[3,4,5,6,1,2,7] => [6,5,3,4,2,1,7] => 68640
[3,4,5,6,2,1,7] => [6,5,3,4,2,1,7] => 68640
[3,4,6,1,7,2,5] => [6,4,7,2,5,1,3] => 292864
[3,4,6,2,7,1,5] => [6,4,7,2,5,1,3] => 292864
[3,4,6,5,1,2,7] => [6,5,4,3,2,1,7] => 292864
[3,4,6,5,2,1,7] => [6,5,4,3,2,1,7] => 292864
[3,4,7,1,5,2,6] => [6,4,7,2,5,1,3] => 292864
[3,4,7,1,6,2,5] => [6,4,7,2,5,1,3] => 292864
[3,4,7,2,5,1,6] => [6,4,7,2,5,1,3] => 292864
[3,4,7,2,6,1,5] => [6,4,7,2,5,1,3] => 292864
[3,5,1,4,2,6,7] => [5,4,3,2,1,6,7] => 768
[3,5,1,4,2,7,6] => [5,4,3,2,1,7,6] => 8448
[3,5,1,4,6,2,7] => [6,4,3,2,5,1,7] => 7700
[3,5,1,4,7,2,6] => [6,4,3,2,7,1,5] => 58916
[3,5,1,6,2,4,7] => [5,6,3,4,1,2,7] => 2640
[3,5,1,6,4,2,7] => [6,5,3,4,2,1,7] => 68640
[3,5,2,4,1,6,7] => [5,4,3,2,1,6,7] => 768
[3,5,2,4,1,7,6] => [5,4,3,2,1,7,6] => 8448
[3,5,2,4,6,1,7] => [6,4,3,2,5,1,7] => 7700
[3,5,2,4,7,1,6] => [6,4,3,2,7,1,5] => 58916
[3,5,2,6,1,4,7] => [5,6,3,4,1,2,7] => 2640
[3,5,2,6,4,1,7] => [6,5,3,4,2,1,7] => 68640
[3,5,4,1,2,6,7] => [5,4,3,2,1,6,7] => 768
[3,5,4,1,2,7,6] => [5,4,3,2,1,7,6] => 8448
[3,5,4,1,6,2,7] => [6,4,3,2,5,1,7] => 7700
[3,5,4,1,7,2,6] => [6,4,3,2,7,1,5] => 58916
[3,5,4,2,1,6,7] => [5,4,3,2,1,6,7] => 768
[3,5,4,2,1,7,6] => [5,4,3,2,1,7,6] => 8448
[3,5,4,2,6,1,7] => [6,4,3,2,5,1,7] => 7700
[3,5,4,2,7,1,6] => [6,4,3,2,7,1,5] => 58916
[3,5,4,6,1,2,7] => [6,5,3,4,2,1,7] => 68640
[3,5,4,6,2,1,7] => [6,5,3,4,2,1,7] => 68640
[3,5,6,1,4,2,7] => [6,5,4,3,2,1,7] => 292864
[3,5,6,2,4,1,7] => [6,5,4,3,2,1,7] => 292864
[3,5,6,4,1,2,7] => [6,5,4,3,2,1,7] => 292864
[3,5,6,4,2,1,7] => [6,5,4,3,2,1,7] => 292864
[3,6,1,4,2,5,7] => [5,6,3,4,1,2,7] => 2640
[3,6,1,4,5,2,7] => [6,5,3,4,2,1,7] => 68640
[3,6,1,5,2,4,7] => [5,6,3,4,1,2,7] => 2640
[3,6,1,5,4,2,7] => [6,5,3,4,2,1,7] => 68640
[3,6,2,4,1,5,7] => [5,6,3,4,1,2,7] => 2640
[3,6,2,4,5,1,7] => [6,5,3,4,2,1,7] => 68640
[3,6,2,5,1,4,7] => [5,6,3,4,1,2,7] => 2640
[3,6,2,5,4,1,7] => [6,5,3,4,2,1,7] => 68640
[3,6,4,1,5,2,7] => [6,5,4,3,2,1,7] => 292864
[3,6,4,2,5,1,7] => [6,5,4,3,2,1,7] => 292864
[3,6,4,5,1,2,7] => [6,5,4,3,2,1,7] => 292864
[3,6,4,5,2,1,7] => [6,5,4,3,2,1,7] => 292864
[3,6,5,1,4,2,7] => [6,5,4,3,2,1,7] => 292864
[3,6,5,2,4,1,7] => [6,5,4,3,2,1,7] => 292864
[3,6,5,4,1,2,7] => [6,5,4,3,2,1,7] => 292864
[3,6,5,4,2,1,7] => [6,5,4,3,2,1,7] => 292864
[4,1,5,6,2,3,7] => [6,2,5,4,3,1,7] => 7700
[4,1,5,6,3,2,7] => [6,2,5,4,3,1,7] => 7700
[4,1,6,2,5,3,7] => [6,2,5,4,3,1,7] => 7700
[4,1,6,3,5,2,7] => [6,2,5,4,3,1,7] => 7700
[4,1,6,5,2,3,7] => [6,2,5,4,3,1,7] => 7700
[4,1,6,5,3,2,7] => [6,2,5,4,3,1,7] => 7700
[4,2,1,3,5,6,7] => [4,3,2,1,5,6,7] => 16
[4,2,1,6,3,5,7] => [5,3,2,6,1,4,7] => 432
[4,2,1,6,5,3,7] => [6,3,2,5,4,1,7] => 3080
[4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => 16
[4,2,3,6,1,5,7] => [5,3,2,6,1,4,7] => 432
[4,2,3,6,5,1,7] => [6,3,2,5,4,1,7] => 3080
[4,2,5,1,3,6,7] => [5,4,3,2,1,6,7] => 768
[4,2,5,1,3,7,6] => [5,4,3,2,1,7,6] => 8448
[4,2,5,1,6,3,7] => [6,4,3,2,5,1,7] => 7700
[4,2,5,1,7,3,6] => [6,4,3,2,7,1,5] => 58916
[4,2,5,3,1,6,7] => [5,4,3,2,1,6,7] => 768
[4,2,5,3,1,7,6] => [5,4,3,2,1,7,6] => 8448
[4,2,5,3,6,1,7] => [6,4,3,2,5,1,7] => 7700
[4,2,5,3,7,1,6] => [6,4,3,2,7,1,5] => 58916
[4,2,5,6,1,3,7] => [6,5,3,4,2,1,7] => 68640
[4,2,5,6,3,1,7] => [6,5,3,4,2,1,7] => 68640
[4,2,6,1,7,3,5] => [6,4,7,2,5,1,3] => 292864
[4,2,6,3,7,1,5] => [6,4,7,2,5,1,3] => 292864
[4,2,6,5,1,3,7] => [6,5,4,3,2,1,7] => 292864
[4,2,6,5,3,1,7] => [6,5,4,3,2,1,7] => 292864
[4,2,7,1,5,3,6] => [6,4,7,2,5,1,3] => 292864
[4,2,7,1,6,3,5] => [6,4,7,2,5,1,3] => 292864
[4,2,7,3,5,1,6] => [6,4,7,2,5,1,3] => 292864
[4,2,7,3,6,1,5] => [6,4,7,2,5,1,3] => 292864
[4,3,1,2,5,6,7] => [4,3,2,1,5,6,7] => 16
[4,3,1,6,2,5,7] => [5,3,2,6,1,4,7] => 432
[4,3,1,6,5,2,7] => [6,3,2,5,4,1,7] => 3080
[4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 16
[4,3,2,6,1,5,7] => [5,3,2,6,1,4,7] => 432
[4,3,2,6,5,1,7] => [6,3,2,5,4,1,7] => 3080
[4,3,5,1,2,6,7] => [5,4,3,2,1,6,7] => 768
[4,3,5,1,2,7,6] => [5,4,3,2,1,7,6] => 8448
[4,3,5,1,6,2,7] => [6,4,3,2,5,1,7] => 7700
[4,3,5,1,7,2,6] => [6,4,3,2,7,1,5] => 58916
[4,3,5,2,1,6,7] => [5,4,3,2,1,6,7] => 768
[4,3,5,2,1,7,6] => [5,4,3,2,1,7,6] => 8448
[4,3,5,2,6,1,7] => [6,4,3,2,5,1,7] => 7700
[4,3,5,2,7,1,6] => [6,4,3,2,7,1,5] => 58916
[4,3,5,6,1,2,7] => [6,5,3,4,2,1,7] => 68640
[4,3,5,6,2,1,7] => [6,5,3,4,2,1,7] => 68640
[4,3,6,1,7,2,5] => [6,4,7,2,5,1,3] => 292864
[4,3,6,2,7,1,5] => [6,4,7,2,5,1,3] => 292864
[4,3,6,5,1,2,7] => [6,5,4,3,2,1,7] => 292864
[4,3,6,5,2,1,7] => [6,5,4,3,2,1,7] => 292864
[4,3,7,1,5,2,6] => [6,4,7,2,5,1,3] => 292864
[4,3,7,1,6,2,5] => [6,4,7,2,5,1,3] => 292864
[4,3,7,2,5,1,6] => [6,4,7,2,5,1,3] => 292864
[4,3,7,2,6,1,5] => [6,4,7,2,5,1,3] => 292864
[4,5,1,2,3,6,7] => [5,4,3,2,1,6,7] => 768
[4,5,1,2,3,7,6] => [5,4,3,2,1,7,6] => 8448
[4,5,1,2,6,3,7] => [6,4,3,2,5,1,7] => 7700
[4,5,1,2,7,3,6] => [6,4,3,2,7,1,5] => 58916
[4,5,1,3,2,6,7] => [5,4,3,2,1,6,7] => 768
[4,5,1,3,2,7,6] => [5,4,3,2,1,7,6] => 8448
[4,5,1,3,6,2,7] => [6,4,3,2,5,1,7] => 7700
[4,5,1,3,7,2,6] => [6,4,3,2,7,1,5] => 58916
[4,5,1,6,2,3,7] => [6,5,3,4,2,1,7] => 68640
[4,5,1,6,3,2,7] => [6,5,3,4,2,1,7] => 68640
[4,5,2,1,3,6,7] => [5,4,3,2,1,6,7] => 768
[4,5,2,1,3,7,6] => [5,4,3,2,1,7,6] => 8448
[4,5,2,1,6,3,7] => [6,4,3,2,5,1,7] => 7700
[4,5,2,1,7,3,6] => [6,4,3,2,7,1,5] => 58916
[4,5,2,3,1,6,7] => [5,4,3,2,1,6,7] => 768
[4,5,2,3,1,7,6] => [5,4,3,2,1,7,6] => 8448
[4,5,2,3,6,1,7] => [6,4,3,2,5,1,7] => 7700
[4,5,2,3,7,1,6] => [6,4,3,2,7,1,5] => 58916
[4,5,2,6,1,3,7] => [6,5,3,4,2,1,7] => 68640
[4,5,2,6,3,1,7] => [6,5,3,4,2,1,7] => 68640
[4,5,3,1,2,6,7] => [5,4,3,2,1,6,7] => 768
[4,5,3,1,2,7,6] => [5,4,3,2,1,7,6] => 8448
[4,5,3,1,6,2,7] => [6,4,3,2,5,1,7] => 7700
[4,5,3,1,7,2,6] => [6,4,3,2,7,1,5] => 58916
[4,5,3,2,1,6,7] => [5,4,3,2,1,6,7] => 768
[4,5,3,2,1,7,6] => [5,4,3,2,1,7,6] => 8448
[4,5,3,2,6,1,7] => [6,4,3,2,5,1,7] => 7700
[4,5,3,2,7,1,6] => [6,4,3,2,7,1,5] => 58916
[4,5,3,6,1,2,7] => [6,5,3,4,2,1,7] => 68640
[4,5,3,6,2,1,7] => [6,5,3,4,2,1,7] => 68640
[4,5,6,1,2,3,7] => [6,5,4,3,2,1,7] => 292864
[4,5,6,1,3,2,7] => [6,5,4,3,2,1,7] => 292864
[4,5,6,2,1,3,7] => [6,5,4,3,2,1,7] => 292864
[4,5,6,2,3,1,7] => [6,5,4,3,2,1,7] => 292864
[4,5,6,3,1,2,7] => [6,5,4,3,2,1,7] => 292864
[4,5,6,3,2,1,7] => [6,5,4,3,2,1,7] => 292864
[4,6,1,2,3,5,7] => [5,6,3,4,1,2,7] => 2640
[4,6,1,2,5,3,7] => [6,5,3,4,2,1,7] => 68640
[4,6,1,3,2,5,7] => [5,6,3,4,1,2,7] => 2640
[4,6,1,3,5,2,7] => [6,5,3,4,2,1,7] => 68640
[4,6,1,5,2,3,7] => [6,5,3,4,2,1,7] => 68640
[4,6,1,5,3,2,7] => [6,5,3,4,2,1,7] => 68640
[4,6,2,1,5,3,7] => [6,5,4,3,2,1,7] => 292864
[4,6,2,3,5,1,7] => [6,5,4,3,2,1,7] => 292864
[4,6,2,5,1,3,7] => [6,5,4,3,2,1,7] => 292864
[4,6,2,5,3,1,7] => [6,5,4,3,2,1,7] => 292864
[4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => 292864
[4,6,3,2,5,1,7] => [6,5,4,3,2,1,7] => 292864
[4,6,3,5,1,2,7] => [6,5,4,3,2,1,7] => 292864
[4,6,3,5,2,1,7] => [6,5,4,3,2,1,7] => 292864
[4,6,5,1,2,3,7] => [6,5,4,3,2,1,7] => 292864
[4,6,5,1,3,2,7] => [6,5,4,3,2,1,7] => 292864
[4,6,5,2,1,3,7] => [6,5,4,3,2,1,7] => 292864
[4,6,5,2,3,1,7] => [6,5,4,3,2,1,7] => 292864
[4,6,5,3,1,2,7] => [6,5,4,3,2,1,7] => 292864
[4,6,5,3,2,1,7] => [6,5,4,3,2,1,7] => 292864
[5,1,3,6,2,4,7] => [6,2,5,4,3,1,7] => 7700
[5,1,3,6,4,2,7] => [6,2,5,4,3,1,7] => 7700
[5,1,4,6,2,3,7] => [6,2,5,4,3,1,7] => 7700
[5,1,4,6,3,2,7] => [6,2,5,4,3,1,7] => 7700
[5,1,6,2,3,4,7] => [6,2,5,4,3,1,7] => 7700
[5,1,6,2,4,3,7] => [6,2,5,4,3,1,7] => 7700
[5,1,6,3,2,4,7] => [6,2,5,4,3,1,7] => 7700
[5,1,6,3,4,2,7] => [6,2,5,4,3,1,7] => 7700
[5,1,6,4,2,3,7] => [6,2,5,4,3,1,7] => 7700
[5,1,6,4,3,2,7] => [6,2,5,4,3,1,7] => 7700
[5,2,1,6,3,4,7] => [6,3,2,5,4,1,7] => 3080
[5,2,1,6,4,3,7] => [6,3,2,5,4,1,7] => 3080
[5,2,3,1,4,6,7] => [5,4,3,2,1,6,7] => 768
[5,2,3,1,4,7,6] => [5,4,3,2,1,7,6] => 8448
[5,2,3,1,6,4,7] => [6,4,3,2,5,1,7] => 7700
[5,2,3,1,7,4,6] => [6,4,3,2,7,1,5] => 58916
[5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => 768
[5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => 8448
[5,2,3,4,6,1,7] => [6,4,3,2,5,1,7] => 7700
[5,2,3,4,7,1,6] => [6,4,3,2,7,1,5] => 58916
[5,2,3,6,1,4,7] => [6,5,3,4,2,1,7] => 68640
[5,2,3,6,4,1,7] => [6,5,3,4,2,1,7] => 68640
[5,2,4,1,3,6,7] => [5,4,3,2,1,6,7] => 768
[5,2,4,1,3,7,6] => [5,4,3,2,1,7,6] => 8448
[5,2,4,1,6,3,7] => [6,4,3,2,5,1,7] => 7700
[5,2,4,1,7,3,6] => [6,4,3,2,7,1,5] => 58916
[5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => 768
[5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => 8448
[5,2,4,3,6,1,7] => [6,4,3,2,5,1,7] => 7700
[5,2,4,3,7,1,6] => [6,4,3,2,7,1,5] => 58916
[5,2,4,6,1,3,7] => [6,5,3,4,2,1,7] => 68640
[5,2,4,6,3,1,7] => [6,5,3,4,2,1,7] => 68640
[5,2,6,3,1,4,7] => [6,5,4,3,2,1,7] => 292864
[5,2,6,3,4,1,7] => [6,5,4,3,2,1,7] => 292864
[5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => 292864
[5,2,6,4,3,1,7] => [6,5,4,3,2,1,7] => 292864
[5,2,7,1,3,4,6] => [6,4,7,2,5,1,3] => 292864
[5,2,7,1,4,3,6] => [6,4,7,2,5,1,3] => 292864
[5,3,1,2,4,6,7] => [5,4,3,2,1,6,7] => 768
[5,3,1,2,4,7,6] => [5,4,3,2,1,7,6] => 8448
[5,3,1,2,6,4,7] => [6,4,3,2,5,1,7] => 7700
[5,3,1,2,7,4,6] => [6,4,3,2,7,1,5] => 58916
[5,3,1,4,2,6,7] => [5,4,3,2,1,6,7] => 768
[5,3,1,4,2,7,6] => [5,4,3,2,1,7,6] => 8448
[5,3,1,4,6,2,7] => [6,4,3,2,5,1,7] => 7700
[5,3,1,4,7,2,6] => [6,4,3,2,7,1,5] => 58916
[5,3,1,6,2,4,7] => [6,5,3,4,2,1,7] => 68640
[5,3,1,6,4,2,7] => [6,5,3,4,2,1,7] => 68640
[5,3,2,1,4,6,7] => [5,4,3,2,1,6,7] => 768
[5,3,2,1,4,7,6] => [5,4,3,2,1,7,6] => 8448
[5,3,2,1,6,4,7] => [6,4,3,2,5,1,7] => 7700
[5,3,2,1,7,4,6] => [6,4,3,2,7,1,5] => 58916
[5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => 768
[5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => 8448
[5,3,2,4,6,1,7] => [6,4,3,2,5,1,7] => 7700
[5,3,2,4,7,1,6] => [6,4,3,2,7,1,5] => 58916
[5,3,2,6,1,4,7] => [6,5,3,4,2,1,7] => 68640
[5,3,2,6,4,1,7] => [6,5,3,4,2,1,7] => 68640
[5,3,4,1,2,6,7] => [5,4,3,2,1,6,7] => 768
[5,3,4,1,2,7,6] => [5,4,3,2,1,7,6] => 8448
[5,3,4,1,6,2,7] => [6,4,3,2,5,1,7] => 7700
[5,3,4,1,7,2,6] => [6,4,3,2,7,1,5] => 58916
[5,3,4,2,1,6,7] => [5,4,3,2,1,6,7] => 768
[5,3,4,2,1,7,6] => [5,4,3,2,1,7,6] => 8448
[5,3,4,2,6,1,7] => [6,4,3,2,5,1,7] => 7700
[5,3,4,2,7,1,6] => [6,4,3,2,7,1,5] => 58916
[5,3,4,6,1,2,7] => [6,5,3,4,2,1,7] => 68640
[5,3,4,6,2,1,7] => [6,5,3,4,2,1,7] => 68640
[5,3,6,1,2,4,7] => [6,5,4,3,2,1,7] => 292864
[5,3,6,1,4,2,7] => [6,5,4,3,2,1,7] => 292864
[5,3,6,2,1,4,7] => [6,5,4,3,2,1,7] => 292864
[5,3,6,2,4,1,7] => [6,5,4,3,2,1,7] => 292864
[5,3,6,4,1,2,7] => [6,5,4,3,2,1,7] => 292864
[5,3,6,4,2,1,7] => [6,5,4,3,2,1,7] => 292864
[5,4,1,2,3,6,7] => [5,4,3,2,1,6,7] => 768
[5,4,1,2,3,7,6] => [5,4,3,2,1,7,6] => 8448
[5,4,1,2,6,3,7] => [6,4,3,2,5,1,7] => 7700
[5,4,1,2,7,3,6] => [6,4,3,2,7,1,5] => 58916
[5,4,1,3,2,6,7] => [5,4,3,2,1,6,7] => 768
[5,4,1,3,2,7,6] => [5,4,3,2,1,7,6] => 8448
[5,4,1,3,6,2,7] => [6,4,3,2,5,1,7] => 7700
[5,4,1,3,7,2,6] => [6,4,3,2,7,1,5] => 58916
[5,4,1,6,2,3,7] => [6,5,3,4,2,1,7] => 68640
[5,4,1,6,3,2,7] => [6,5,3,4,2,1,7] => 68640
[5,4,2,1,3,6,7] => [5,4,3,2,1,6,7] => 768
[5,4,2,1,3,7,6] => [5,4,3,2,1,7,6] => 8448
[5,4,2,1,6,3,7] => [6,4,3,2,5,1,7] => 7700
[5,4,2,1,7,3,6] => [6,4,3,2,7,1,5] => 58916
[5,4,2,3,1,6,7] => [5,4,3,2,1,6,7] => 768
[5,4,2,3,1,7,6] => [5,4,3,2,1,7,6] => 8448
[5,4,2,3,6,1,7] => [6,4,3,2,5,1,7] => 7700
[5,4,2,3,7,1,6] => [6,4,3,2,7,1,5] => 58916
[5,4,2,6,1,3,7] => [6,5,3,4,2,1,7] => 68640
[5,4,2,6,3,1,7] => [6,5,3,4,2,1,7] => 68640
[5,4,3,1,2,6,7] => [5,4,3,2,1,6,7] => 768
[5,4,3,1,2,7,6] => [5,4,3,2,1,7,6] => 8448
[5,4,3,1,6,2,7] => [6,4,3,2,5,1,7] => 7700
[5,4,3,1,7,2,6] => [6,4,3,2,7,1,5] => 58916
[5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 768
[5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 8448
[5,4,3,2,6,1,7] => [6,4,3,2,5,1,7] => 7700
[5,4,3,2,7,1,6] => [6,4,3,2,7,1,5] => 58916
[5,4,3,6,1,2,7] => [6,5,3,4,2,1,7] => 68640
[5,4,3,6,2,1,7] => [6,5,3,4,2,1,7] => 68640
[5,4,6,1,2,3,7] => [6,5,4,3,2,1,7] => 292864
[5,4,6,1,3,2,7] => [6,5,4,3,2,1,7] => 292864
[5,4,6,2,1,3,7] => [6,5,4,3,2,1,7] => 292864
[5,4,6,2,3,1,7] => [6,5,4,3,2,1,7] => 292864
[5,4,6,3,1,2,7] => [6,5,4,3,2,1,7] => 292864
[5,4,6,3,2,1,7] => [6,5,4,3,2,1,7] => 292864
[5,6,1,2,3,4,7] => [6,5,3,4,2,1,7] => 68640
[5,6,1,2,4,3,7] => [6,5,3,4,2,1,7] => 68640
[5,6,1,3,2,4,7] => [6,5,3,4,2,1,7] => 68640
[5,6,1,3,4,2,7] => [6,5,3,4,2,1,7] => 68640
[5,6,1,4,2,3,7] => [6,5,3,4,2,1,7] => 68640
[5,6,1,4,3,2,7] => [6,5,3,4,2,1,7] => 68640
[5,6,2,1,3,4,7] => [6,5,4,3,2,1,7] => 292864
[5,6,2,1,4,3,7] => [6,5,4,3,2,1,7] => 292864
[5,6,2,3,1,4,7] => [6,5,4,3,2,1,7] => 292864
[5,6,2,3,4,1,7] => [6,5,4,3,2,1,7] => 292864
[5,6,2,4,1,3,7] => [6,5,4,3,2,1,7] => 292864
[5,6,2,4,3,1,7] => [6,5,4,3,2,1,7] => 292864
[5,6,3,1,2,4,7] => [6,5,4,3,2,1,7] => 292864
[5,6,3,1,4,2,7] => [6,5,4,3,2,1,7] => 292864
[5,6,3,2,1,4,7] => [6,5,4,3,2,1,7] => 292864
[5,6,3,2,4,1,7] => [6,5,4,3,2,1,7] => 292864
[5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => 292864
[5,6,3,4,2,1,7] => [6,5,4,3,2,1,7] => 292864
[5,6,4,1,2,3,7] => [6,5,4,3,2,1,7] => 292864
[5,6,4,1,3,2,7] => [6,5,4,3,2,1,7] => 292864
[5,6,4,2,1,3,7] => [6,5,4,3,2,1,7] => 292864
[5,6,4,2,3,1,7] => [6,5,4,3,2,1,7] => 292864
[5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => 292864
[5,6,4,3,2,1,7] => [6,5,4,3,2,1,7] => 292864
[6,1,3,4,2,5,7] => [6,2,5,4,3,1,7] => 7700
[6,1,3,4,5,2,7] => [6,2,5,4,3,1,7] => 7700
[6,1,3,5,2,4,7] => [6,2,5,4,3,1,7] => 7700
[6,1,3,5,4,2,7] => [6,2,5,4,3,1,7] => 7700
[6,1,4,2,3,5,7] => [6,2,5,4,3,1,7] => 7700
[6,1,4,2,5,3,7] => [6,2,5,4,3,1,7] => 7700
[6,1,4,3,2,5,7] => [6,2,5,4,3,1,7] => 7700
[6,1,4,3,5,2,7] => [6,2,5,4,3,1,7] => 7700
[6,1,4,5,2,3,7] => [6,2,5,4,3,1,7] => 7700
[6,1,4,5,3,2,7] => [6,2,5,4,3,1,7] => 7700
[6,1,5,2,3,4,7] => [6,2,5,4,3,1,7] => 7700
[6,1,5,2,4,3,7] => [6,2,5,4,3,1,7] => 7700
[6,1,5,3,2,4,7] => [6,2,5,4,3,1,7] => 7700
[6,1,5,3,4,2,7] => [6,2,5,4,3,1,7] => 7700
[6,1,5,4,2,3,7] => [6,2,5,4,3,1,7] => 7700
[6,1,5,4,3,2,7] => [6,2,5,4,3,1,7] => 7700
[6,2,1,4,3,5,7] => [6,3,2,5,4,1,7] => 3080
[6,2,1,4,5,3,7] => [6,3,2,5,4,1,7] => 3080
[6,2,1,5,3,4,7] => [6,3,2,5,4,1,7] => 3080
[6,2,1,5,4,3,7] => [6,3,2,5,4,1,7] => 3080
[6,2,3,1,4,5,7] => [6,4,3,2,5,1,7] => 7700
[6,2,3,1,5,4,7] => [6,4,3,2,5,1,7] => 7700
[6,2,3,4,1,5,7] => [6,5,3,4,2,1,7] => 68640
[6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => 68640
[6,2,3,5,1,4,7] => [6,5,3,4,2,1,7] => 68640
[6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => 68640
[6,2,4,3,1,5,7] => [6,5,4,3,2,1,7] => 292864
[6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => 292864
[6,2,4,5,1,3,7] => [6,5,4,3,2,1,7] => 292864
[6,2,4,5,3,1,7] => [6,5,4,3,2,1,7] => 292864
[6,2,5,3,1,4,7] => [6,5,4,3,2,1,7] => 292864
[6,2,5,3,4,1,7] => [6,5,4,3,2,1,7] => 292864
[6,2,5,4,1,3,7] => [6,5,4,3,2,1,7] => 292864
[6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => 292864
[6,3,1,2,4,5,7] => [6,4,3,2,5,1,7] => 7700
[6,3,1,2,5,4,7] => [6,4,3,2,5,1,7] => 7700
[6,3,1,4,2,5,7] => [6,5,3,4,2,1,7] => 68640
[6,3,1,4,5,2,7] => [6,5,3,4,2,1,7] => 68640
[6,3,1,5,2,4,7] => [6,5,3,4,2,1,7] => 68640
[6,3,1,5,4,2,7] => [6,5,3,4,2,1,7] => 68640
[6,3,2,1,4,5,7] => [6,4,3,2,5,1,7] => 7700
[6,3,2,1,5,4,7] => [6,4,3,2,5,1,7] => 7700
[6,3,2,4,1,5,7] => [6,5,3,4,2,1,7] => 68640
[6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => 68640
[6,3,2,5,1,4,7] => [6,5,3,4,2,1,7] => 68640
[6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => 68640
[6,3,4,1,2,5,7] => [6,5,4,3,2,1,7] => 292864
[6,3,4,1,5,2,7] => [6,5,4,3,2,1,7] => 292864
[6,3,4,2,1,5,7] => [6,5,4,3,2,1,7] => 292864
[6,3,4,2,5,1,7] => [6,5,4,3,2,1,7] => 292864
[6,3,4,5,1,2,7] => [6,5,4,3,2,1,7] => 292864
[6,3,4,5,2,1,7] => [6,5,4,3,2,1,7] => 292864
[6,3,5,1,2,4,7] => [6,5,4,3,2,1,7] => 292864
[6,3,5,1,4,2,7] => [6,5,4,3,2,1,7] => 292864
[6,3,5,2,1,4,7] => [6,5,4,3,2,1,7] => 292864
[6,3,5,2,4,1,7] => [6,5,4,3,2,1,7] => 292864
[6,3,5,4,1,2,7] => [6,5,4,3,2,1,7] => 292864
[6,3,5,4,2,1,7] => [6,5,4,3,2,1,7] => 292864
[6,4,1,2,3,5,7] => [6,5,3,4,2,1,7] => 68640
[6,4,1,2,5,3,7] => [6,5,3,4,2,1,7] => 68640
[6,4,1,3,2,5,7] => [6,5,3,4,2,1,7] => 68640
[6,4,1,3,5,2,7] => [6,5,3,4,2,1,7] => 68640
[6,4,1,5,2,3,7] => [6,5,3,4,2,1,7] => 68640
[6,4,1,5,3,2,7] => [6,5,3,4,2,1,7] => 68640
[6,4,2,1,3,5,7] => [6,5,4,3,2,1,7] => 292864
[6,4,2,1,5,3,7] => [6,5,4,3,2,1,7] => 292864
[6,4,2,3,1,5,7] => [6,5,4,3,2,1,7] => 292864
[6,4,2,3,5,1,7] => [6,5,4,3,2,1,7] => 292864
[6,4,2,5,1,3,7] => [6,5,4,3,2,1,7] => 292864
[6,4,2,5,3,1,7] => [6,5,4,3,2,1,7] => 292864
[6,4,3,1,2,5,7] => [6,5,4,3,2,1,7] => 292864
[6,4,3,1,5,2,7] => [6,5,4,3,2,1,7] => 292864
[6,4,3,2,1,5,7] => [6,5,4,3,2,1,7] => 292864
[6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => 292864
[6,4,3,5,1,2,7] => [6,5,4,3,2,1,7] => 292864
[6,4,3,5,2,1,7] => [6,5,4,3,2,1,7] => 292864
[6,4,5,1,2,3,7] => [6,5,4,3,2,1,7] => 292864
[6,4,5,1,3,2,7] => [6,5,4,3,2,1,7] => 292864
[6,4,5,2,1,3,7] => [6,5,4,3,2,1,7] => 292864
[6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => 292864
[6,4,5,3,1,2,7] => [6,5,4,3,2,1,7] => 292864
[6,4,5,3,2,1,7] => [6,5,4,3,2,1,7] => 292864
[6,5,1,2,3,4,7] => [6,5,3,4,2,1,7] => 68640
[6,5,1,2,4,3,7] => [6,5,3,4,2,1,7] => 68640
[6,5,1,3,2,4,7] => [6,5,3,4,2,1,7] => 68640
[6,5,1,3,4,2,7] => [6,5,3,4,2,1,7] => 68640
[6,5,1,4,2,3,7] => [6,5,3,4,2,1,7] => 68640
[6,5,1,4,3,2,7] => [6,5,3,4,2,1,7] => 68640
[6,5,2,1,3,4,7] => [6,5,4,3,2,1,7] => 292864
[6,5,2,1,4,3,7] => [6,5,4,3,2,1,7] => 292864
[6,5,2,3,1,4,7] => [6,5,4,3,2,1,7] => 292864
[6,5,2,3,4,1,7] => [6,5,4,3,2,1,7] => 292864
[6,5,2,4,1,3,7] => [6,5,4,3,2,1,7] => 292864
[6,5,2,4,3,1,7] => [6,5,4,3,2,1,7] => 292864
[6,5,3,1,2,4,7] => [6,5,4,3,2,1,7] => 292864
[6,5,3,1,4,2,7] => [6,5,4,3,2,1,7] => 292864
[6,5,3,2,1,4,7] => [6,5,4,3,2,1,7] => 292864
[6,5,3,2,4,1,7] => [6,5,4,3,2,1,7] => 292864
[6,5,3,4,1,2,7] => [6,5,4,3,2,1,7] => 292864
[6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => 292864
[6,5,4,1,2,3,7] => [6,5,4,3,2,1,7] => 292864
[6,5,4,1,3,2,7] => [6,5,4,3,2,1,7] => 292864
[6,5,4,2,1,3,7] => [6,5,4,3,2,1,7] => 292864
[6,5,4,2,3,1,7] => [6,5,4,3,2,1,7] => 292864
[6,5,4,3,1,2,7] => [6,5,4,3,2,1,7] => 292864
[6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 292864
[1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 1
[1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 1
[1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => 80
[1,4,3,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => 80
[1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => 80
[1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => 6
[1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => 2
[1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => 2
[1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 1
[1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => 2
[1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => 2
[1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 1
[1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 1
[1,3,5,6,7,2,4,8] => [1,6,7,4,5,2,3,8] => 2640
[1,3,4,6,2,7,5,8] => [1,5,3,7,2,6,4,8] => 244
[1,3,4,7,2,5,6,8] => [1,5,3,7,2,6,4,8] => 244
[1,4,2,6,3,7,5,8] => [1,5,3,7,2,6,4,8] => 244
[1,4,6,2,7,3,5,8] => [1,6,7,4,5,2,3,8] => 2640
[1,2,4,6,3,5,7,8] => [1,2,5,6,3,4,7,8] => 2
[1,4,2,3,6,7,5,8] => [1,4,3,2,7,6,5,8] => 80
[1,4,2,7,3,5,6,8] => [1,5,3,7,2,6,4,8] => 244
[1,4,2,3,7,5,6,8] => [1,4,3,2,7,6,5,8] => 80
[1,5,7,2,3,4,6,8] => [1,6,7,4,5,2,3,8] => 2640
[] => [] => 1
[1,4,2,7,3,6,5,8] => [1,5,3,7,2,6,4,8] => 244
[1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 1
[1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 1
[1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 1
[1,4,3,7,2,5,6,8] => [1,5,3,7,2,6,4,8] => 244
[1,4,3,7,2,6,5,8] => [1,5,3,7,2,6,4,8] => 244
[1,4,7,2,6,3,5,8] => [1,6,7,4,5,2,3,8] => 2640
[1,4,6,3,7,2,5,8] => [1,6,7,4,5,2,3,8] => 2640
[1,3,7,4,6,2,5,8] => [1,6,7,4,5,2,3,8] => 2640
[1,4,7,3,6,2,5,8] => [1,6,7,4,5,2,3,8] => 2640
[1,3,6,4,7,2,5,8] => [1,6,7,4,5,2,3,8] => 2640
[1,4,3,6,2,7,5,8] => [1,5,3,7,2,6,4,8] => 244
[1,4,7,3,5,2,6,8] => [1,6,7,4,5,2,3,8] => 2640
[1,5,7,2,4,3,6,8] => [1,6,7,4,5,2,3,8] => 2640
[1,3,4,7,2,6,5,8] => [1,5,3,7,2,6,4,8] => 244
[1,4,7,2,5,3,6,8] => [1,6,7,4,5,2,3,8] => 2640
[1,3,6,5,7,2,4,8] => [1,6,7,4,5,2,3,8] => 2640
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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:
3,3 4,8,0,0,0,5,0,0,0,0,0,0,0,0,0,7
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 3\ q + 3\ q^{2}$
$F_{4} = 4\ q + 8\ q^{2} + 5\ q^{6} + 7\ q^{16}$
$F_{5} = 5\ q + 14\ q^{2} + 10\ q^{6} + 6\ q^{8} + 20\ q^{16} + 7\ q^{20} + 5\ q^{42} + 18\ q^{90} + 35\ q^{768}$
$F_{6} = 6\ q + 21\ q^{2} + 16\ q^{6} + 18\ q^{8} + 2\ q^{10} + 33\ q^{16} + 14\ q^{20} + 10\ q^{36} + 12\ q^{42} + 9\ q^{70} + 9\ q^{80} + 46\ q^{90} + 14\ q^{112} + 9\ q^{244} + 14\ q^{432} + 33\ q^{448} + 92\ q^{768} + 14\ q^{1188} + 13\ q^{2640} + 13\ q^{3080} + 82\ q^{7700} + 17\ q^{8580} + 13\ q^{16016} + 75\ q^{68640} + 135\ q^{292864}$
Description
The number of reduced words for a permutation.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
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