Identifier
Identifier
Values
[1] => 1
[1,2] => 2
[2,1] => 2
[1,2,3] => 3
[1,3,2] => 3
[2,1,3] => 3
[2,3,1] => 3
[3,1,2] => 3
[3,2,1] => 3
[1,2,3,4] => 5
[1,2,4,3] => 5
[1,3,2,4] => 5
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 3
[2,1,3,4] => 5
[2,1,4,3] => 5
[2,3,1,4] => 3
[2,3,4,1] => 3
[2,4,1,3] => 1
[2,4,3,1] => 3
[3,1,2,4] => 3
[3,1,4,2] => 1
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 5
[3,4,2,1] => 5
[4,1,2,3] => 3
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 5
[4,3,1,2] => 5
[4,3,2,1] => 5
[1,2,3,4,5] => 8
[1,2,3,5,4] => 8
[1,2,4,3,5] => 8
[1,2,4,5,3] => 6
[1,2,5,3,4] => 6
[1,2,5,4,3] => 6
[1,3,2,4,5] => 8
[1,3,2,5,4] => 8
[1,3,4,2,5] => 3
[1,3,4,5,2] => 3
[1,3,5,2,4] => 1
[1,3,5,4,2] => 3
[1,4,2,3,5] => 3
[1,4,2,5,3] => 1
[1,4,3,2,5] => 3
[1,4,3,5,2] => 3
[1,4,5,2,3] => 5
[1,4,5,3,2] => 5
[1,5,2,3,4] => 3
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 5
[1,5,4,2,3] => 5
[1,5,4,3,2] => 5
[2,1,3,4,5] => 8
[2,1,3,5,4] => 8
[2,1,4,3,5] => 8
[2,1,4,5,3] => 6
[2,1,5,3,4] => 6
[2,1,5,4,3] => 6
[2,3,1,4,5] => 6
[2,3,1,5,4] => 6
[2,3,4,1,5] => 3
[2,3,4,5,1] => 5
[2,3,5,1,4] => 2
[2,3,5,4,1] => 5
[2,4,1,3,5] => 1
[2,4,1,5,3] => 1
[2,4,3,1,5] => 3
[2,4,3,5,1] => 5
[2,4,5,1,3] => 2
[2,4,5,3,1] => 3
[2,5,1,3,4] => 2
[2,5,1,4,3] => 2
[2,5,3,1,4] => 1
[2,5,3,4,1] => 3
[2,5,4,1,3] => 2
[2,5,4,3,1] => 3
[3,1,2,4,5] => 6
[3,1,2,5,4] => 6
[3,1,4,2,5] => 1
[3,1,4,5,2] => 2
[3,1,5,2,4] => 1
[3,1,5,4,2] => 2
[3,2,1,4,5] => 6
[3,2,1,5,4] => 6
[3,2,4,1,5] => 3
[3,2,4,5,1] => 5
[3,2,5,1,4] => 2
[3,2,5,4,1] => 5
[3,4,1,2,5] => 5
[3,4,1,5,2] => 2
[3,4,2,1,5] => 5
[3,4,2,5,1] => 3
[3,4,5,1,2] => 6
[3,4,5,2,1] => 6
[3,5,1,2,4] => 2
[3,5,1,4,2] => 1
[3,5,2,1,4] => 2
[3,5,2,4,1] => 1
[3,5,4,1,2] => 6
[3,5,4,2,1] => 6
[4,1,2,3,5] => 3
[4,1,2,5,3] => 2
[4,1,3,2,5] => 3
[4,1,3,5,2] => 1
[4,1,5,2,3] => 2
[4,1,5,3,2] => 2
[4,2,1,3,5] => 3
[4,2,1,5,3] => 2
[4,2,3,1,5] => 5
[4,2,3,5,1] => 3
[4,2,5,1,3] => 1
[4,2,5,3,1] => 1
[4,3,1,2,5] => 5
[4,3,1,5,2] => 2
[4,3,2,1,5] => 5
[4,3,2,5,1] => 3
[4,3,5,1,2] => 6
[4,3,5,2,1] => 6
[4,5,1,2,3] => 6
[4,5,1,3,2] => 6
[4,5,2,1,3] => 6
[4,5,2,3,1] => 8
[4,5,3,1,2] => 8
[4,5,3,2,1] => 8
[5,1,2,3,4] => 5
[5,1,2,4,3] => 5
[5,1,3,2,4] => 5
[5,1,3,4,2] => 3
[5,1,4,2,3] => 3
[5,1,4,3,2] => 3
[5,2,1,3,4] => 5
[5,2,1,4,3] => 5
[5,2,3,1,4] => 3
[5,2,3,4,1] => 3
[5,2,4,1,3] => 1
[5,2,4,3,1] => 3
[5,3,1,2,4] => 3
[5,3,1,4,2] => 1
[5,3,2,1,4] => 3
[5,3,2,4,1] => 3
[5,3,4,1,2] => 8
[5,3,4,2,1] => 8
[5,4,1,2,3] => 6
[5,4,1,3,2] => 6
[5,4,2,1,3] => 6
[5,4,2,3,1] => 8
[5,4,3,1,2] => 8
[5,4,3,2,1] => 8
[1,2,3,4,5,6] => 13
[1,2,3,4,6,5] => 13
[1,2,3,5,4,6] => 13
[1,2,3,5,6,4] => 9
[1,2,3,6,4,5] => 9
[1,2,3,6,5,4] => 9
[1,2,4,3,5,6] => 13
[1,2,4,3,6,5] => 13
[1,2,4,5,3,6] => 6
[1,2,4,5,6,3] => 6
[1,2,4,6,3,5] => 2
[1,2,4,6,5,3] => 6
[1,2,5,3,4,6] => 6
[1,2,5,3,6,4] => 2
[1,2,5,4,3,6] => 6
[1,2,5,4,6,3] => 6
[1,2,5,6,3,4] => 10
[1,2,5,6,4,3] => 10
[1,2,6,3,4,5] => 6
[1,2,6,3,5,4] => 6
[1,2,6,4,3,5] => 6
[1,2,6,4,5,3] => 10
[1,2,6,5,3,4] => 10
[1,2,6,5,4,3] => 10
[1,3,2,4,5,6] => 13
[1,3,2,4,6,5] => 13
[1,3,2,5,4,6] => 13
[1,3,2,5,6,4] => 9
[1,3,2,6,4,5] => 9
[1,3,2,6,5,4] => 9
[1,3,4,2,5,6] => 6
[1,3,4,2,6,5] => 6
[1,3,4,5,2,6] => 3
[1,3,4,5,6,2] => 5
[1,3,4,6,2,5] => 2
[1,3,4,6,5,2] => 5
[1,3,5,2,4,6] => 1
[1,3,5,2,6,4] => 1
[1,3,5,4,2,6] => 3
[1,3,5,4,6,2] => 5
[1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => 3
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 2
[1,3,6,4,2,5] => 1
[1,3,6,4,5,2] => 3
[1,3,6,5,2,4] => 2
[1,3,6,5,4,2] => 3
[1,4,2,3,5,6] => 6
[1,4,2,3,6,5] => 6
[1,4,2,5,3,6] => 1
[1,4,2,5,6,3] => 2
[1,4,2,6,3,5] => 1
[1,4,2,6,5,3] => 2
[1,4,3,2,5,6] => 6
[1,4,3,2,6,5] => 6
[1,4,3,5,2,6] => 3
[1,4,3,5,6,2] => 5
[1,4,3,6,2,5] => 2
[1,4,3,6,5,2] => 5
[1,4,5,2,3,6] => 5
[1,4,5,2,6,3] => 2
[1,4,5,3,2,6] => 5
[1,4,5,3,6,2] => 3
[1,4,5,6,2,3] => 6
[1,4,5,6,3,2] => 6
[1,4,6,2,3,5] => 2
[1,4,6,2,5,3] => 1
[1,4,6,3,2,5] => 2
[1,4,6,3,5,2] => 1
[1,4,6,5,2,3] => 6
[1,4,6,5,3,2] => 6
[1,5,2,3,4,6] => 3
[1,5,2,3,6,4] => 2
[1,5,2,4,3,6] => 3
[1,5,2,4,6,3] => 1
[1,5,2,6,3,4] => 2
[1,5,2,6,4,3] => 2
[1,5,3,2,4,6] => 3
[1,5,3,2,6,4] => 2
[1,5,3,4,2,6] => 5
[1,5,3,4,6,2] => 3
[1,5,3,6,2,4] => 1
[1,5,3,6,4,2] => 1
[1,5,4,2,3,6] => 5
[1,5,4,2,6,3] => 2
[1,5,4,3,2,6] => 5
[1,5,4,3,6,2] => 3
[1,5,4,6,2,3] => 6
[1,5,4,6,3,2] => 6
[1,5,6,2,3,4] => 6
[1,5,6,2,4,3] => 6
[1,5,6,3,2,4] => 6
[1,5,6,3,4,2] => 8
[1,5,6,4,2,3] => 8
[1,5,6,4,3,2] => 8
[1,6,2,3,4,5] => 5
[1,6,2,3,5,4] => 5
[1,6,2,4,3,5] => 5
[1,6,2,4,5,3] => 3
[1,6,2,5,3,4] => 3
[1,6,2,5,4,3] => 3
[1,6,3,2,4,5] => 5
[1,6,3,2,5,4] => 5
[1,6,3,4,2,5] => 3
[1,6,3,4,5,2] => 3
[1,6,3,5,2,4] => 1
[1,6,3,5,4,2] => 3
[1,6,4,2,3,5] => 3
[1,6,4,2,5,3] => 1
[1,6,4,3,2,5] => 3
[1,6,4,3,5,2] => 3
[1,6,4,5,2,3] => 8
[1,6,4,5,3,2] => 8
[1,6,5,2,3,4] => 6
[1,6,5,2,4,3] => 6
[1,6,5,3,2,4] => 6
[1,6,5,3,4,2] => 8
[1,6,5,4,2,3] => 8
[1,6,5,4,3,2] => 8
[2,1,3,4,5,6] => 13
[2,1,3,4,6,5] => 13
[2,1,3,5,4,6] => 13
[2,1,3,5,6,4] => 9
[2,1,3,6,4,5] => 9
[2,1,3,6,5,4] => 9
[2,1,4,3,5,6] => 13
[2,1,4,3,6,5] => 13
[2,1,4,5,3,6] => 6
[2,1,4,5,6,3] => 6
[2,1,4,6,3,5] => 2
[2,1,4,6,5,3] => 6
[2,1,5,3,4,6] => 6
[2,1,5,3,6,4] => 2
[2,1,5,4,3,6] => 6
[2,1,5,4,6,3] => 6
[2,1,5,6,3,4] => 10
[2,1,5,6,4,3] => 10
[2,1,6,3,4,5] => 6
[2,1,6,3,5,4] => 6
[2,1,6,4,3,5] => 6
[2,1,6,4,5,3] => 10
[2,1,6,5,3,4] => 10
[2,1,6,5,4,3] => 10
[2,3,1,4,5,6] => 9
[2,3,1,4,6,5] => 9
[2,3,1,5,4,6] => 9
[2,3,1,5,6,4] => 9
[2,3,1,6,4,5] => 9
[2,3,1,6,5,4] => 9
[2,3,4,1,5,6] => 6
[2,3,4,1,6,5] => 6
[2,3,4,5,1,6] => 5
[2,3,4,5,6,1] => 8
[2,3,4,6,1,5] => 3
[2,3,4,6,5,1] => 8
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 2
[2,3,5,4,1,6] => 5
[2,3,5,4,6,1] => 8
[2,3,5,6,1,4] => 4
[2,3,5,6,4,1] => 6
[2,3,6,1,4,5] => 4
[2,3,6,1,5,4] => 4
[2,3,6,4,1,5] => 2
[2,3,6,4,5,1] => 6
[2,3,6,5,1,4] => 4
[2,3,6,5,4,1] => 6
[2,4,1,3,5,6] => 2
[2,4,1,3,6,5] => 2
[2,4,1,5,3,6] => 1
[2,4,1,5,6,3] => 2
[2,4,1,6,3,5] => 1
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 6
[2,4,3,1,6,5] => 6
[2,4,3,5,1,6] => 5
[2,4,3,5,6,1] => 8
[2,4,3,6,1,5] => 3
[2,4,3,6,5,1] => 8
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 2
[2,4,5,3,1,6] => 3
[2,4,5,3,6,1] => 3
[2,4,5,6,1,3] => 3
[2,4,5,6,3,1] => 3
[2,4,6,1,3,5] => 1
[2,4,6,1,5,3] => 1
[2,4,6,3,1,5] => 1
[2,4,6,3,5,1] => 1
[2,4,6,5,1,3] => 3
[2,4,6,5,3,1] => 3
[2,5,1,3,4,6] => 2
[2,5,1,3,6,4] => 1
[2,5,1,4,3,6] => 2
[2,5,1,4,6,3] => 1
[2,5,1,6,3,4] => 2
[2,5,1,6,4,3] => 2
[2,5,3,1,4,6] => 1
[2,5,3,1,6,4] => 1
[2,5,3,4,1,6] => 3
[2,5,3,4,6,1] => 3
[2,5,3,6,1,4] => 1
[2,5,3,6,4,1] => 1
[2,5,4,1,3,6] => 2
[2,5,4,1,6,3] => 2
[2,5,4,3,1,6] => 3
[2,5,4,3,6,1] => 3
[2,5,4,6,1,3] => 3
[2,5,4,6,3,1] => 3
[2,5,6,1,3,4] => 4
[2,5,6,1,4,3] => 4
[2,5,6,3,1,4] => 2
[2,5,6,3,4,1] => 5
[2,5,6,4,1,3] => 3
[2,5,6,4,3,1] => 5
[2,6,1,3,4,5] => 3
[2,6,1,3,5,4] => 3
[2,6,1,4,3,5] => 3
[2,6,1,4,5,3] => 3
[2,6,1,5,3,4] => 3
[2,6,1,5,4,3] => 3
[2,6,3,1,4,5] => 2
[2,6,3,1,5,4] => 2
[2,6,3,4,1,5] => 2
[2,6,3,4,5,1] => 3
[2,6,3,5,1,4] => 1
[2,6,3,5,4,1] => 3
[2,6,4,1,3,5] => 1
[2,6,4,1,5,3] => 1
[2,6,4,3,1,5] => 2
[2,6,4,3,5,1] => 3
[2,6,4,5,1,3] => 3
[2,6,4,5,3,1] => 5
[2,6,5,1,3,4] => 4
[2,6,5,1,4,3] => 4
[2,6,5,3,1,4] => 2
[2,6,5,3,4,1] => 5
[2,6,5,4,1,3] => 3
[2,6,5,4,3,1] => 5
[3,1,2,4,5,6] => 9
[3,1,2,4,6,5] => 9
[3,1,2,5,4,6] => 9
[3,1,2,5,6,4] => 9
[3,1,2,6,4,5] => 9
[3,1,2,6,5,4] => 9
[3,1,4,2,5,6] => 2
[3,1,4,2,6,5] => 2
[3,1,4,5,2,6] => 2
[3,1,4,5,6,2] => 3
[3,1,4,6,2,5] => 1
[3,1,4,6,5,2] => 3
[3,1,5,2,4,6] => 1
[3,1,5,2,6,4] => 1
[3,1,5,4,2,6] => 2
[3,1,5,4,6,2] => 3
[3,1,5,6,2,4] => 2
[3,1,5,6,4,2] => 3
[3,1,6,2,4,5] => 2
[3,1,6,2,5,4] => 2
[3,1,6,4,2,5] => 1
[3,1,6,4,5,2] => 3
[3,1,6,5,2,4] => 2
[3,1,6,5,4,2] => 3
[3,2,1,4,5,6] => 9
[3,2,1,4,6,5] => 9
[3,2,1,5,4,6] => 9
[3,2,1,5,6,4] => 9
[3,2,1,6,4,5] => 9
[3,2,1,6,5,4] => 9
[3,2,4,1,5,6] => 6
[3,2,4,1,6,5] => 6
[3,2,4,5,1,6] => 5
[3,2,4,5,6,1] => 8
[3,2,4,6,1,5] => 3
[3,2,4,6,5,1] => 8
[3,2,5,1,4,6] => 2
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 5
[3,2,5,4,6,1] => 8
[3,2,5,6,1,4] => 4
[3,2,5,6,4,1] => 6
[3,2,6,1,4,5] => 4
[3,2,6,1,5,4] => 4
[3,2,6,4,1,5] => 2
[3,2,6,4,5,1] => 6
[3,2,6,5,1,4] => 4
[3,2,6,5,4,1] => 6
[3,4,1,2,5,6] => 10
[3,4,1,2,6,5] => 10
[3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => 4
[3,4,1,6,2,5] => 2
[3,4,1,6,5,2] => 4
[3,4,2,1,5,6] => 10
[3,4,2,1,6,5] => 10
[3,4,2,5,1,6] => 3
[3,4,2,5,6,1] => 6
[3,4,2,6,1,5] => 3
[3,4,2,6,5,1] => 6
[3,4,5,1,2,6] => 6
[3,4,5,1,6,2] => 3
[3,4,5,2,1,6] => 6
[3,4,5,2,6,1] => 3
[3,4,5,6,1,2] => 10
[3,4,5,6,2,1] => 10
[3,4,6,1,2,5] => 4
[3,4,6,1,5,2] => 2
[3,4,6,2,1,5] => 4
[3,4,6,2,5,1] => 2
[3,4,6,5,1,2] => 10
[3,4,6,5,2,1] => 10
[3,5,1,2,4,6] => 2
[3,5,1,2,6,4] => 2
[3,5,1,4,2,6] => 1
[3,5,1,4,6,2] => 1
[3,5,1,6,2,4] => 1
[3,5,1,6,4,2] => 1
[3,5,2,1,4,6] => 2
[3,5,2,1,6,4] => 2
[3,5,2,4,1,6] => 1
[3,5,2,4,6,1] => 1
[3,5,2,6,1,4] => 1
[3,5,2,6,4,1] => 1
[3,5,4,1,2,6] => 6
[3,5,4,1,6,2] => 3
[3,5,4,2,1,6] => 6
[3,5,4,2,6,1] => 3
[3,5,4,6,1,2] => 10
[3,5,4,6,2,1] => 10
[3,5,6,1,2,4] => 4
[3,5,6,1,4,2] => 2
[3,5,6,2,1,4] => 4
[3,5,6,2,4,1] => 2
[3,5,6,4,1,2] => 6
[3,5,6,4,2,1] => 6
[3,6,1,2,4,5] => 4
[3,6,1,2,5,4] => 4
[3,6,1,4,2,5] => 1
[3,6,1,4,5,2] => 2
[3,6,1,5,2,4] => 1
[3,6,1,5,4,2] => 2
[3,6,2,1,4,5] => 4
[3,6,2,1,5,4] => 4
[3,6,2,4,1,5] => 1
[3,6,2,4,5,1] => 2
[3,6,2,5,1,4] => 1
[3,6,2,5,4,1] => 2
[3,6,4,1,2,5] => 2
[3,6,4,1,5,2] => 1
[3,6,4,2,1,5] => 2
[3,6,4,2,5,1] => 1
[3,6,4,5,1,2] => 6
[3,6,4,5,2,1] => 6
[3,6,5,1,2,4] => 4
[3,6,5,1,4,2] => 2
[3,6,5,2,1,4] => 4
[3,6,5,2,4,1] => 2
[3,6,5,4,1,2] => 6
[3,6,5,4,2,1] => 6
[4,1,2,3,5,6] => 6
[4,1,2,3,6,5] => 6
[4,1,2,5,3,6] => 2
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 2
[4,1,2,6,5,3] => 4
[4,1,3,2,5,6] => 6
[4,1,3,2,6,5] => 6
[4,1,3,5,2,6] => 1
[4,1,3,5,6,2] => 2
[4,1,3,6,2,5] => 1
[4,1,3,6,5,2] => 2
[4,1,5,2,3,6] => 2
[4,1,5,2,6,3] => 1
[4,1,5,3,2,6] => 2
[4,1,5,3,6,2] => 1
[4,1,5,6,2,3] => 4
[4,1,5,6,3,2] => 4
[4,1,6,2,3,5] => 2
[4,1,6,2,5,3] => 1
[4,1,6,3,2,5] => 2
[4,1,6,3,5,2] => 1
[4,1,6,5,2,3] => 4
[4,1,6,5,3,2] => 4
[4,2,1,3,5,6] => 6
[4,2,1,3,6,5] => 6
[4,2,1,5,3,6] => 2
[4,2,1,5,6,3] => 4
[4,2,1,6,3,5] => 2
[4,2,1,6,5,3] => 4
[4,2,3,1,5,6] => 10
[4,2,3,1,6,5] => 10
[4,2,3,5,1,6] => 3
[4,2,3,5,6,1] => 6
[4,2,3,6,1,5] => 3
[4,2,3,6,5,1] => 6
[4,2,5,1,3,6] => 1
[4,2,5,1,6,3] => 1
[4,2,5,3,1,6] => 1
[4,2,5,3,6,1] => 1
[4,2,5,6,1,3] => 2
[4,2,5,6,3,1] => 2
[4,2,6,1,3,5] => 1
[4,2,6,1,5,3] => 1
[4,2,6,3,1,5] => 1
[4,2,6,3,5,1] => 1
[4,2,6,5,1,3] => 2
[4,2,6,5,3,1] => 2
[4,3,1,2,5,6] => 10
[4,3,1,2,6,5] => 10
[4,3,1,5,2,6] => 2
[4,3,1,5,6,2] => 4
[4,3,1,6,2,5] => 2
[4,3,1,6,5,2] => 4
[4,3,2,1,5,6] => 10
[4,3,2,1,6,5] => 10
[4,3,2,5,1,6] => 3
[4,3,2,5,6,1] => 6
[4,3,2,6,1,5] => 3
[4,3,2,6,5,1] => 6
[4,3,5,1,2,6] => 6
[4,3,5,1,6,2] => 3
[4,3,5,2,1,6] => 6
[4,3,5,2,6,1] => 3
[4,3,5,6,1,2] => 10
[4,3,5,6,2,1] => 10
[4,3,6,1,2,5] => 4
[4,3,6,1,5,2] => 2
[4,3,6,2,1,5] => 4
[4,3,6,2,5,1] => 2
[4,3,6,5,1,2] => 10
[4,3,6,5,2,1] => 10
[4,5,1,2,3,6] => 6
[4,5,1,2,6,3] => 4
[4,5,1,3,2,6] => 6
[4,5,1,3,6,2] => 2
[4,5,1,6,2,3] => 4
[4,5,1,6,3,2] => 4
[4,5,2,1,3,6] => 6
[4,5,2,1,6,3] => 4
[4,5,2,3,1,6] => 8
[4,5,2,3,6,1] => 5
[4,5,2,6,1,3] => 2
[4,5,2,6,3,1] => 2
[4,5,3,1,2,6] => 8
[4,5,3,1,6,2] => 3
[4,5,3,2,1,6] => 8
[4,5,3,2,6,1] => 5
[4,5,3,6,1,2] => 6
[4,5,3,6,2,1] => 6
[4,5,6,1,2,3] => 9
[4,5,6,1,3,2] => 9
[4,5,6,2,1,3] => 9
[4,5,6,2,3,1] => 9
[4,5,6,3,1,2] => 9
[4,5,6,3,2,1] => 9
[4,6,1,2,3,5] => 3
[4,6,1,2,5,3] => 2
[4,6,1,3,2,5] => 3
[4,6,1,3,5,2] => 1
[4,6,1,5,2,3] => 2
[4,6,1,5,3,2] => 2
[4,6,2,1,3,5] => 3
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 3
[4,6,2,3,5,1] => 2
[4,6,2,5,1,3] => 1
[4,6,2,5,3,1] => 1
[4,6,3,1,2,5] => 3
[4,6,3,1,5,2] => 1
[4,6,3,2,1,5] => 3
[4,6,3,2,5,1] => 2
[4,6,3,5,1,2] => 2
[4,6,3,5,2,1] => 2
[4,6,5,1,2,3] => 9
[4,6,5,1,3,2] => 9
[4,6,5,2,1,3] => 9
[4,6,5,2,3,1] => 9
[4,6,5,3,1,2] => 9
[4,6,5,3,2,1] => 9
[5,1,2,3,4,6] => 5
[5,1,2,3,6,4] => 3
[5,1,2,4,3,6] => 5
[5,1,2,4,6,3] => 2
[5,1,2,6,3,4] => 4
[5,1,2,6,4,3] => 4
[5,1,3,2,4,6] => 5
[5,1,3,2,6,4] => 3
[5,1,3,4,2,6] => 3
[5,1,3,4,6,2] => 2
[5,1,3,6,2,4] => 1
[5,1,3,6,4,2] => 1
[5,1,4,2,3,6] => 3
[5,1,4,2,6,3] => 1
[5,1,4,3,2,6] => 3
[5,1,4,3,6,2] => 2
[5,1,4,6,2,3] => 2
[5,1,4,6,3,2] => 2
[5,1,6,2,3,4] => 3
[5,1,6,2,4,3] => 3
[5,1,6,3,2,4] => 3
[5,1,6,3,4,2] => 3
[5,1,6,4,2,3] => 3
[5,1,6,4,3,2] => 3
[5,2,1,3,4,6] => 5
[5,2,1,3,6,4] => 3
[5,2,1,4,3,6] => 5
[5,2,1,4,6,3] => 2
[5,2,1,6,3,4] => 4
[5,2,1,6,4,3] => 4
[5,2,3,1,4,6] => 3
[5,2,3,1,6,4] => 3
[5,2,3,4,1,6] => 3
[5,2,3,4,6,1] => 3
[5,2,3,6,1,4] => 2
[5,2,3,6,4,1] => 2
[5,2,4,1,3,6] => 1
[5,2,4,1,6,3] => 1
[5,2,4,3,1,6] => 3
[5,2,4,3,6,1] => 3
[5,2,4,6,1,3] => 1
[5,2,4,6,3,1] => 1
[5,2,6,1,3,4] => 2
[5,2,6,1,4,3] => 2
[5,2,6,3,1,4] => 1
[5,2,6,3,4,1] => 2
[5,2,6,4,1,3] => 1
[5,2,6,4,3,1] => 2
[5,3,1,2,4,6] => 3
[5,3,1,2,6,4] => 3
[5,3,1,4,2,6] => 1
[5,3,1,4,6,2] => 1
[5,3,1,6,2,4] => 1
[5,3,1,6,4,2] => 1
[5,3,2,1,4,6] => 3
[5,3,2,1,6,4] => 3
[5,3,2,4,1,6] => 3
[5,3,2,4,6,1] => 3
[5,3,2,6,1,4] => 2
[5,3,2,6,4,1] => 2
[5,3,4,1,2,6] => 8
[5,3,4,1,6,2] => 3
[5,3,4,2,1,6] => 8
[5,3,4,2,6,1] => 5
[5,3,4,6,1,2] => 6
[5,3,4,6,2,1] => 6
[5,3,6,1,2,4] => 2
[5,3,6,1,4,2] => 1
[5,3,6,2,1,4] => 2
[5,3,6,2,4,1] => 1
[5,3,6,4,1,2] => 2
[5,3,6,4,2,1] => 2
[5,4,1,2,3,6] => 6
[5,4,1,2,6,3] => 4
[5,4,1,3,2,6] => 6
[5,4,1,3,6,2] => 2
[5,4,1,6,2,3] => 4
[5,4,1,6,3,2] => 4
[5,4,2,1,3,6] => 6
[5,4,2,1,6,3] => 4
[5,4,2,3,1,6] => 8
[5,4,2,3,6,1] => 5
[5,4,2,6,1,3] => 2
[5,4,2,6,3,1] => 2
[5,4,3,1,2,6] => 8
[5,4,3,1,6,2] => 3
[5,4,3,2,1,6] => 8
[5,4,3,2,6,1] => 5
[5,4,3,6,1,2] => 6
[5,4,3,6,2,1] => 6
[5,4,6,1,2,3] => 9
[5,4,6,1,3,2] => 9
[5,4,6,2,1,3] => 9
[5,4,6,2,3,1] => 9
[5,4,6,3,1,2] => 9
[5,4,6,3,2,1] => 9
[5,6,1,2,3,4] => 10
[5,6,1,2,4,3] => 10
[5,6,1,3,2,4] => 10
[5,6,1,3,4,2] => 6
[5,6,1,4,2,3] => 6
[5,6,1,4,3,2] => 6
[5,6,2,1,3,4] => 10
[5,6,2,1,4,3] => 10
[5,6,2,3,1,4] => 6
[5,6,2,3,4,1] => 6
[5,6,2,4,1,3] => 2
[5,6,2,4,3,1] => 6
[5,6,3,1,2,4] => 6
[5,6,3,1,4,2] => 2
[5,6,3,2,1,4] => 6
[5,6,3,2,4,1] => 6
[5,6,3,4,1,2] => 13
[5,6,3,4,2,1] => 13
[5,6,4,1,2,3] => 9
[5,6,4,1,3,2] => 9
[5,6,4,2,1,3] => 9
[5,6,4,2,3,1] => 13
[5,6,4,3,1,2] => 13
[5,6,4,3,2,1] => 13
[6,1,2,3,4,5] => 8
[6,1,2,3,5,4] => 8
[6,1,2,4,3,5] => 8
[6,1,2,4,5,3] => 6
[6,1,2,5,3,4] => 6
[6,1,2,5,4,3] => 6
[6,1,3,2,4,5] => 8
[6,1,3,2,5,4] => 8
[6,1,3,4,2,5] => 3
[6,1,3,4,5,2] => 3
[6,1,3,5,2,4] => 1
[6,1,3,5,4,2] => 3
[6,1,4,2,3,5] => 3
[6,1,4,2,5,3] => 1
[6,1,4,3,2,5] => 3
[6,1,4,3,5,2] => 3
[6,1,4,5,2,3] => 5
[6,1,4,5,3,2] => 5
[6,1,5,2,3,4] => 3
[6,1,5,2,4,3] => 3
[6,1,5,3,2,4] => 3
[6,1,5,3,4,2] => 5
[6,1,5,4,2,3] => 5
[6,1,5,4,3,2] => 5
[6,2,1,3,4,5] => 8
[6,2,1,3,5,4] => 8
[6,2,1,4,3,5] => 8
[6,2,1,4,5,3] => 6
[6,2,1,5,3,4] => 6
[6,2,1,5,4,3] => 6
[6,2,3,1,4,5] => 6
[6,2,3,1,5,4] => 6
[6,2,3,4,1,5] => 3
[6,2,3,4,5,1] => 5
[6,2,3,5,1,4] => 2
[6,2,3,5,4,1] => 5
[6,2,4,1,3,5] => 1
[6,2,4,1,5,3] => 1
[6,2,4,3,1,5] => 3
[6,2,4,3,5,1] => 5
[6,2,4,5,1,3] => 2
[6,2,4,5,3,1] => 3
[6,2,5,1,3,4] => 2
[6,2,5,1,4,3] => 2
[6,2,5,3,1,4] => 1
[6,2,5,3,4,1] => 3
[6,2,5,4,1,3] => 2
[6,2,5,4,3,1] => 3
[6,3,1,2,4,5] => 6
[6,3,1,2,5,4] => 6
[6,3,1,4,2,5] => 1
[6,3,1,4,5,2] => 2
[6,3,1,5,2,4] => 1
[6,3,1,5,4,2] => 2
[6,3,2,1,4,5] => 6
[6,3,2,1,5,4] => 6
[6,3,2,4,1,5] => 3
[6,3,2,4,5,1] => 5
[6,3,2,5,1,4] => 2
[6,3,2,5,4,1] => 5
[6,3,4,1,2,5] => 5
[6,3,4,1,5,2] => 2
[6,3,4,2,1,5] => 5
[6,3,4,2,5,1] => 3
[6,3,4,5,1,2] => 6
[6,3,4,5,2,1] => 6
[6,3,5,1,2,4] => 2
[6,3,5,1,4,2] => 1
[6,3,5,2,1,4] => 2
[6,3,5,2,4,1] => 1
[6,3,5,4,1,2] => 6
[6,3,5,4,2,1] => 6
[6,4,1,2,3,5] => 3
[6,4,1,2,5,3] => 2
[6,4,1,3,2,5] => 3
[6,4,1,3,5,2] => 1
[6,4,1,5,2,3] => 2
[6,4,1,5,3,2] => 2
[6,4,2,1,3,5] => 3
[6,4,2,1,5,3] => 2
[6,4,2,3,1,5] => 5
[6,4,2,3,5,1] => 3
[6,4,2,5,1,3] => 1
[6,4,2,5,3,1] => 1
[6,4,3,1,2,5] => 5
[6,4,3,1,5,2] => 2
[6,4,3,2,1,5] => 5
[6,4,3,2,5,1] => 3
[6,4,3,5,1,2] => 6
[6,4,3,5,2,1] => 6
[6,4,5,1,2,3] => 9
[6,4,5,1,3,2] => 9
[6,4,5,2,1,3] => 9
[6,4,5,2,3,1] => 13
[6,4,5,3,1,2] => 13
[6,4,5,3,2,1] => 13
[6,5,1,2,3,4] => 10
[6,5,1,2,4,3] => 10
[6,5,1,3,2,4] => 10
[6,5,1,3,4,2] => 6
[6,5,1,4,2,3] => 6
[6,5,1,4,3,2] => 6
[6,5,2,1,3,4] => 10
[6,5,2,1,4,3] => 10
[6,5,2,3,1,4] => 6
[6,5,2,3,4,1] => 6
[6,5,2,4,1,3] => 2
[6,5,2,4,3,1] => 6
[6,5,3,1,2,4] => 6
[6,5,3,1,4,2] => 2
[6,5,3,2,1,4] => 6
[6,5,3,2,4,1] => 6
[6,5,3,4,1,2] => 13
[6,5,3,4,2,1] => 13
[6,5,4,1,2,3] => 9
[6,5,4,1,3,2] => 9
[6,5,4,2,1,3] => 9
[6,5,4,2,3,1] => 13
[6,5,4,3,1,2] => 13
[6,5,4,3,2,1] => 13
[1,2,3,4,5,6,7] => 21
[1,2,3,4,5,7,6] => 21
[1,2,3,4,6,5,7] => 21
[1,2,3,4,6,7,5] => 15
[1,2,3,4,7,5,6] => 15
[1,2,3,4,7,6,5] => 15
[1,2,3,5,4,6,7] => 21
[1,2,3,5,4,7,6] => 21
[1,2,3,5,6,4,7] => 9
[1,2,3,5,6,7,4] => 9
[1,2,3,5,7,4,6] => 3
[1,2,3,5,7,6,4] => 9
[1,2,3,6,4,5,7] => 9
[1,2,3,6,4,7,5] => 3
[1,2,3,6,5,4,7] => 9
[1,2,3,6,5,7,4] => 9
[1,2,3,6,7,4,5] => 15
[1,2,3,6,7,5,4] => 15
[1,2,3,7,4,5,6] => 9
[1,2,3,7,4,6,5] => 9
[1,2,3,7,5,4,6] => 9
[1,2,3,7,5,6,4] => 15
[1,2,3,7,6,4,5] => 15
[1,2,3,7,6,5,4] => 15
[1,2,4,3,5,6,7] => 21
[1,2,4,3,5,7,6] => 21
[1,2,4,3,6,5,7] => 21
[1,2,4,3,6,7,5] => 15
[1,2,4,3,7,5,6] => 15
[1,2,4,3,7,6,5] => 15
[1,2,4,5,3,6,7] => 12
[1,2,4,5,3,7,6] => 12
[1,2,4,5,6,3,7] => 6
[1,2,4,5,6,7,3] => 10
[1,2,4,5,7,3,6] => 4
[1,2,4,5,7,6,3] => 10
[1,2,4,6,3,5,7] => 2
[1,2,4,6,3,7,5] => 2
[1,2,4,6,5,3,7] => 6
[1,2,4,6,5,7,3] => 10
[1,2,4,6,7,3,5] => 4
[1,2,4,6,7,5,3] => 6
[1,2,4,7,3,5,6] => 4
[1,2,4,7,3,6,5] => 4
[1,2,4,7,5,3,6] => 2
[1,2,4,7,5,6,3] => 6
[1,2,4,7,6,3,5] => 4
[1,2,4,7,6,5,3] => 6
[1,2,5,3,4,6,7] => 12
[1,2,5,3,4,7,6] => 12
[1,2,5,3,6,4,7] => 2
[1,2,5,3,6,7,4] => 4
[1,2,5,3,7,4,6] => 2
[1,2,5,3,7,6,4] => 4
[1,2,5,4,3,6,7] => 12
[1,2,5,4,3,7,6] => 12
[1,2,5,4,6,3,7] => 6
[1,2,5,4,6,7,3] => 10
[1,2,5,4,7,3,6] => 4
[1,2,5,4,7,6,3] => 10
[1,2,5,6,3,4,7] => 10
[1,2,5,6,3,7,4] => 4
[1,2,5,6,4,3,7] => 10
[1,2,5,6,4,7,3] => 6
[1,2,5,6,7,3,4] => 12
[1,2,5,6,7,4,3] => 12
[1,2,5,7,3,4,6] => 4
[1,2,5,7,3,6,4] => 2
[1,2,5,7,4,3,6] => 4
[1,2,5,7,4,6,3] => 2
[1,2,5,7,6,3,4] => 12
[1,2,5,7,6,4,3] => 12
[1,2,6,3,4,5,7] => 6
[1,2,6,3,4,7,5] => 4
[1,2,6,3,5,4,7] => 6
[1,2,6,3,5,7,4] => 2
[1,2,6,3,7,4,5] => 4
[1,2,6,3,7,5,4] => 4
[1,2,6,4,3,5,7] => 6
[1,2,6,4,3,7,5] => 4
[1,2,6,4,5,3,7] => 10
[1,2,6,4,5,7,3] => 6
[1,2,6,4,7,3,5] => 2
[1,2,6,4,7,5,3] => 2
[1,2,6,5,3,4,7] => 10
[1,2,6,5,3,7,4] => 4
[1,2,6,5,4,3,7] => 10
[1,2,6,5,4,7,3] => 6
[1,2,6,5,7,3,4] => 12
[1,2,6,5,7,4,3] => 12
[1,2,6,7,3,4,5] => 12
[1,2,6,7,3,5,4] => 12
[1,2,6,7,4,3,5] => 12
[1,2,6,7,4,5,3] => 16
[1,2,6,7,5,3,4] => 16
[1,2,6,7,5,4,3] => 16
[1,2,7,3,4,5,6] => 10
[1,2,7,3,4,6,5] => 10
[1,2,7,3,5,4,6] => 10
[1,2,7,3,5,6,4] => 6
[1,2,7,3,6,4,5] => 6
[1,2,7,3,6,5,4] => 6
[1,2,7,4,3,5,6] => 10
[1,2,7,4,3,6,5] => 10
[1,2,7,4,5,3,6] => 6
[1,2,7,4,5,6,3] => 6
[1,2,7,4,6,3,5] => 2
[1,2,7,4,6,5,3] => 6
[1,2,7,5,3,4,6] => 6
[1,2,7,5,3,6,4] => 2
[1,2,7,5,4,3,6] => 6
[1,2,7,5,4,6,3] => 6
[1,2,7,5,6,3,4] => 16
[1,2,7,5,6,4,3] => 16
[1,2,7,6,3,4,5] => 12
[1,2,7,6,3,5,4] => 12
[1,2,7,6,4,3,5] => 12
[1,2,7,6,4,5,3] => 16
[1,2,7,6,5,3,4] => 16
[1,2,7,6,5,4,3] => 16
[1,3,2,4,5,6,7] => 21
[1,3,2,4,5,7,6] => 21
[1,3,2,4,6,5,7] => 21
[1,3,2,4,6,7,5] => 15
[1,3,2,4,7,5,6] => 15
[1,3,2,4,7,6,5] => 15
[1,3,2,5,4,6,7] => 21
[1,3,2,5,4,7,6] => 21
[1,3,2,5,6,4,7] => 9
[1,3,2,5,6,7,4] => 9
[1,3,2,5,7,4,6] => 3
[1,3,2,5,7,6,4] => 9
[1,3,2,6,4,5,7] => 9
[1,3,2,6,4,7,5] => 3
[1,3,2,6,5,4,7] => 9
[1,3,2,6,5,7,4] => 9
[1,3,2,6,7,4,5] => 15
[1,3,2,6,7,5,4] => 15
[1,3,2,7,4,5,6] => 9
[1,3,2,7,4,6,5] => 9
[1,3,2,7,5,4,6] => 9
[1,3,2,7,5,6,4] => 15
[1,3,2,7,6,4,5] => 15
[1,3,2,7,6,5,4] => 15
[1,3,4,2,5,6,7] => 9
[1,3,4,2,5,7,6] => 9
[1,3,4,2,6,5,7] => 9
[1,3,4,2,6,7,5] => 9
[1,3,4,2,7,5,6] => 9
[1,3,4,2,7,6,5] => 9
[1,3,4,5,2,6,7] => 6
[1,3,4,5,2,7,6] => 6
[1,3,4,5,6,2,7] => 5
[1,3,4,5,6,7,2] => 8
[1,3,4,5,7,2,6] => 3
[1,3,4,5,7,6,2] => 8
[1,3,4,6,2,5,7] => 2
[1,3,4,6,2,7,5] => 2
[1,3,4,6,5,2,7] => 5
[1,3,4,6,5,7,2] => 8
[1,3,4,6,7,2,5] => 4
[1,3,4,6,7,5,2] => 6
[1,3,4,7,2,5,6] => 4
[1,3,4,7,2,6,5] => 4
[1,3,4,7,5,2,6] => 2
[1,3,4,7,5,6,2] => 6
[1,3,4,7,6,2,5] => 4
[1,3,4,7,6,5,2] => 6
[1,3,5,2,4,6,7] => 2
[1,3,5,2,4,7,6] => 2
[1,3,5,2,6,4,7] => 1
[1,3,5,2,6,7,4] => 2
[1,3,5,2,7,4,6] => 1
[1,3,5,2,7,6,4] => 2
[1,3,5,4,2,6,7] => 6
[1,3,5,4,2,7,6] => 6
[1,3,5,4,6,2,7] => 5
[1,3,5,4,6,7,2] => 8
[1,3,5,4,7,2,6] => 3
[1,3,5,4,7,6,2] => 8
[1,3,5,6,2,4,7] => 2
[1,3,5,6,2,7,4] => 2
[1,3,5,6,4,2,7] => 3
[1,3,5,6,4,7,2] => 3
[1,3,5,6,7,2,4] => 3
[1,3,5,6,7,4,2] => 3
[1,3,5,7,2,4,6] => 1
[1,3,5,7,2,6,4] => 1
[1,3,5,7,4,2,6] => 1
[1,3,5,7,4,6,2] => 1
[1,3,5,7,6,2,4] => 3
[1,3,5,7,6,4,2] => 3
[1,3,6,2,4,5,7] => 2
[1,3,6,2,4,7,5] => 1
[1,3,6,2,5,4,7] => 2
[1,3,6,2,5,7,4] => 1
[1,3,6,2,7,4,5] => 2
[1,3,6,2,7,5,4] => 2
[1,3,6,4,2,5,7] => 1
[1,3,6,4,2,7,5] => 1
[1,3,6,4,5,2,7] => 3
[1,3,6,4,5,7,2] => 3
[1,3,6,4,7,2,5] => 1
[1,3,6,4,7,5,2] => 1
[1,3,6,5,2,4,7] => 2
[1,3,6,5,2,7,4] => 2
[1,3,6,5,4,2,7] => 3
[1,3,6,5,4,7,2] => 3
[1,3,6,5,7,2,4] => 3
[1,3,6,5,7,4,2] => 3
[1,3,6,7,2,4,5] => 4
[1,3,6,7,2,5,4] => 4
[1,3,6,7,4,2,5] => 2
[1,3,6,7,4,5,2] => 5
[1,3,6,7,5,2,4] => 3
[1,3,6,7,5,4,2] => 5
[1,3,7,2,4,5,6] => 3
[1,3,7,2,4,6,5] => 3
[1,3,7,2,5,4,6] => 3
[1,3,7,2,5,6,4] => 3
[1,3,7,2,6,4,5] => 3
[1,3,7,2,6,5,4] => 3
[1,3,7,4,2,5,6] => 2
[1,3,7,4,2,6,5] => 2
[1,3,7,4,5,2,6] => 2
[1,3,7,4,5,6,2] => 3
[1,3,7,4,6,2,5] => 1
[1,3,7,4,6,5,2] => 3
[1,3,7,5,2,4,6] => 1
[1,3,7,5,2,6,4] => 1
[1,3,7,5,4,2,6] => 2
[1,3,7,5,4,6,2] => 3
[1,3,7,5,6,2,4] => 3
[1,3,7,5,6,4,2] => 5
[1,3,7,6,2,4,5] => 4
[1,3,7,6,2,5,4] => 4
[1,3,7,6,4,2,5] => 2
[1,3,7,6,4,5,2] => 5
[1,3,7,6,5,2,4] => 3
[1,3,7,6,5,4,2] => 5
[1,4,2,3,5,6,7] => 9
[1,4,2,3,5,7,6] => 9
[1,4,2,3,6,5,7] => 9
[1,4,2,3,6,7,5] => 9
[1,4,2,3,7,5,6] => 9
[1,4,2,3,7,6,5] => 9
[1,4,2,5,3,6,7] => 2
[1,4,2,5,3,7,6] => 2
[1,4,2,5,6,3,7] => 2
[1,4,2,5,6,7,3] => 3
[1,4,2,5,7,3,6] => 1
[1,4,2,5,7,6,3] => 3
[1,4,2,6,3,5,7] => 1
[1,4,2,6,3,7,5] => 1
[1,4,2,6,5,3,7] => 2
[1,4,2,6,5,7,3] => 3
[1,4,2,6,7,3,5] => 2
[1,4,2,6,7,5,3] => 3
[1,4,2,7,3,5,6] => 2
[1,4,2,7,3,6,5] => 2
[1,4,2,7,5,3,6] => 1
[1,4,2,7,5,6,3] => 3
[1,4,2,7,6,3,5] => 2
[1,4,2,7,6,5,3] => 3
[1,4,3,2,5,6,7] => 9
[1,4,3,2,5,7,6] => 9
[1,4,3,2,6,5,7] => 9
[1,4,3,2,6,7,5] => 9
[1,4,3,2,7,5,6] => 9
[1,4,3,2,7,6,5] => 9
[1,4,3,5,2,6,7] => 6
[1,4,3,5,2,7,6] => 6
[1,4,3,5,6,2,7] => 5
[1,4,3,5,6,7,2] => 8
[1,4,3,5,7,2,6] => 3
[1,4,3,5,7,6,2] => 8
[1,4,3,6,2,5,7] => 2
[1,4,3,6,2,7,5] => 2
[1,4,3,6,5,2,7] => 5
[1,4,3,6,5,7,2] => 8
[1,4,3,6,7,2,5] => 4
[1,4,3,6,7,5,2] => 6
[1,4,3,7,2,5,6] => 4
[1,4,3,7,2,6,5] => 4
[1,4,3,7,5,2,6] => 2
[1,4,3,7,5,6,2] => 6
[1,4,3,7,6,2,5] => 4
[1,4,3,7,6,5,2] => 6
[1,4,5,2,3,6,7] => 10
[1,4,5,2,3,7,6] => 10
[1,4,5,2,6,3,7] => 2
[1,4,5,2,6,7,3] => 4
[1,4,5,2,7,3,6] => 2
[1,4,5,2,7,6,3] => 4
[1,4,5,3,2,6,7] => 10
[1,4,5,3,2,7,6] => 10
[1,4,5,3,6,2,7] => 3
[1,4,5,3,6,7,2] => 6
[1,4,5,3,7,2,6] => 3
[1,4,5,3,7,6,2] => 6
[1,4,5,6,2,3,7] => 6
[1,4,5,6,2,7,3] => 3
[1,4,5,6,3,2,7] => 6
[1,4,5,6,3,7,2] => 3
[1,4,5,6,7,2,3] => 10
[1,4,5,6,7,3,2] => 10
[1,4,5,7,2,3,6] => 4
[1,4,5,7,2,6,3] => 2
[1,4,5,7,3,2,6] => 4
[1,4,5,7,3,6,2] => 2
[1,4,5,7,6,2,3] => 10
[1,4,5,7,6,3,2] => 10
[1,4,6,2,3,5,7] => 2
[1,4,6,2,3,7,5] => 2
[1,4,6,2,5,3,7] => 1
[1,4,6,2,5,7,3] => 1
[1,4,6,2,7,3,5] => 1
[1,4,6,2,7,5,3] => 1
[1,4,6,3,2,5,7] => 2
[1,4,6,3,2,7,5] => 2
[1,4,6,3,5,2,7] => 1
[1,4,6,3,5,7,2] => 1
[1,4,6,3,7,2,5] => 1
[1,4,6,3,7,5,2] => 1
[1,4,6,5,2,3,7] => 6
[1,4,6,5,2,7,3] => 3
[1,4,6,5,3,2,7] => 6
[1,4,6,5,3,7,2] => 3
click to show generating function       
Description
The number of permutations obtained by switching adjacencies or successions.
For a permutation $\pi$, this statistic is the size of its equivalence class of the equivalence relation generated by the interchange of any two adjacent elements $\pi_i$ and $\pi_{i+1}$ such that $|\pi_i - \pi_{i+1}| = 1$.
References
[1] Stanley, R. P. An equivalence relation on the symmetric group and multiplicity-free flag $h$-vectors MathSciNet:3029438 arXiv:1208.3540
[2] Amdeberhan, T. "flavored" equivalence classes of permutations MathOverflow:256673
Code
def statistic(pi):
    def children(a):
        for i in range(len(a)-1):
            d = a[i] - a[i+1]
            if d == 1 or d == -1:
                yield Permutation(a[:i] + [a[i+1], a[i]] + a[i+2:])

    return len([1 for pi in RecursivelyEnumeratedSet([Permutation(pi)], children)])

Created
Apr 05, 2016 at 17:34 by Jiang Zeng
Updated
May 10, 2019 at 17:36 by Henning Ulfarsson