Identifier
Identifier
Values
[1,2] => 4
[2,1] => 1
[1,2,3] => 8
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 2
[1,2,3,4] => 16
[1,2,4,3] => 4
[1,3,2,4] => 4
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 4
[2,1,3,4] => 4
[2,1,4,3] => 1
[2,3,1,4] => 2
[2,3,4,1] => 1
[2,4,1,3] => 1
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 1
[3,2,1,4] => 4
[3,2,4,1] => 2
[3,4,1,2] => 1
[3,4,2,1] => 1
[4,1,2,3] => 1
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 4
[4,3,1,2] => 1
[4,3,2,1] => 1
[1,2,3,4,5] => 32
[1,2,3,5,4] => 8
[1,2,4,3,5] => 8
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 8
[1,3,2,4,5] => 8
[1,3,2,5,4] => 2
[1,3,4,2,5] => 4
[1,3,4,5,2] => 2
[1,3,5,2,4] => 2
[1,3,5,4,2] => 4
[1,4,2,3,5] => 4
[1,4,2,5,3] => 2
[1,4,3,2,5] => 8
[1,4,3,5,2] => 4
[1,4,5,2,3] => 2
[1,4,5,3,2] => 2
[1,5,2,3,4] => 2
[1,5,2,4,3] => 4
[1,5,3,2,4] => 4
[1,5,3,4,2] => 8
[1,5,4,2,3] => 2
[1,5,4,3,2] => 2
[2,1,3,4,5] => 8
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 1
[2,1,5,3,4] => 1
[2,1,5,4,3] => 2
[2,3,1,4,5] => 4
[2,3,1,5,4] => 1
[2,3,4,1,5] => 2
[2,3,4,5,1] => 1
[2,3,5,1,4] => 1
[2,3,5,4,1] => 2
[2,4,1,3,5] => 2
[2,4,1,5,3] => 1
[2,4,3,1,5] => 4
[2,4,3,5,1] => 2
[2,4,5,1,3] => 1
[2,4,5,3,1] => 1
[2,5,1,3,4] => 1
[2,5,1,4,3] => 2
[2,5,3,1,4] => 2
[2,5,3,4,1] => 4
[2,5,4,1,3] => 1
[2,5,4,3,1] => 1
[3,1,2,4,5] => 4
[3,1,2,5,4] => 1
[3,1,4,2,5] => 2
[3,1,4,5,2] => 1
[3,1,5,2,4] => 1
[3,1,5,4,2] => 2
[3,2,1,4,5] => 8
[3,2,1,5,4] => 2
[3,2,4,1,5] => 4
[3,2,4,5,1] => 2
[3,2,5,1,4] => 2
[3,2,5,4,1] => 4
[3,4,1,2,5] => 2
[3,4,1,5,2] => 1
[3,4,2,1,5] => 2
[3,4,2,5,1] => 1
[3,4,5,1,2] => 1
[3,4,5,2,1] => 1
[3,5,1,2,4] => 1
[3,5,1,4,2] => 2
[3,5,2,1,4] => 1
[3,5,2,4,1] => 2
[3,5,4,1,2] => 1
[3,5,4,2,1] => 1
[4,1,2,3,5] => 2
[4,1,2,5,3] => 1
[4,1,3,2,5] => 4
[4,1,3,5,2] => 2
[4,1,5,2,3] => 1
[4,1,5,3,2] => 1
[4,2,1,3,5] => 4
[4,2,1,5,3] => 2
[4,2,3,1,5] => 8
[4,2,3,5,1] => 4
[4,2,5,1,3] => 2
[4,2,5,3,1] => 2
[4,3,1,2,5] => 2
[4,3,1,5,2] => 1
[4,3,2,1,5] => 2
[4,3,2,5,1] => 1
[4,3,5,1,2] => 1
[4,3,5,2,1] => 1
[4,5,1,2,3] => 1
[4,5,1,3,2] => 1
[4,5,2,1,3] => 1
[4,5,2,3,1] => 1
[4,5,3,1,2] => 2
[4,5,3,2,1] => 2
[5,1,2,3,4] => 1
[5,1,2,4,3] => 2
[5,1,3,2,4] => 2
[5,1,3,4,2] => 4
[5,1,4,2,3] => 1
[5,1,4,3,2] => 1
[5,2,1,3,4] => 2
[5,2,1,4,3] => 4
[5,2,3,1,4] => 4
[5,2,3,4,1] => 8
[5,2,4,1,3] => 2
[5,2,4,3,1] => 2
[5,3,1,2,4] => 1
[5,3,1,4,2] => 2
[5,3,2,1,4] => 1
[5,3,2,4,1] => 2
[5,3,4,1,2] => 1
[5,3,4,2,1] => 1
[5,4,1,2,3] => 1
[5,4,1,3,2] => 1
[5,4,2,1,3] => 1
[5,4,2,3,1] => 1
[5,4,3,1,2] => 2
[5,4,3,2,1] => 2
[1,2,3,4,5,6] => 64
[1,2,3,4,6,5] => 16
[1,2,3,5,4,6] => 16
[1,2,3,5,6,4] => 8
[1,2,3,6,4,5] => 8
[1,2,3,6,5,4] => 16
[1,2,4,3,5,6] => 16
[1,2,4,3,6,5] => 4
[1,2,4,5,3,6] => 8
[1,2,4,5,6,3] => 4
[1,2,4,6,3,5] => 4
[1,2,4,6,5,3] => 8
[1,2,5,3,4,6] => 8
[1,2,5,3,6,4] => 4
[1,2,5,4,3,6] => 16
[1,2,5,4,6,3] => 8
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 4
[1,2,6,3,4,5] => 4
[1,2,6,3,5,4] => 8
[1,2,6,4,3,5] => 8
[1,2,6,4,5,3] => 16
[1,2,6,5,3,4] => 4
[1,2,6,5,4,3] => 4
[1,3,2,4,5,6] => 16
[1,3,2,4,6,5] => 4
[1,3,2,5,4,6] => 4
[1,3,2,5,6,4] => 2
[1,3,2,6,4,5] => 2
[1,3,2,6,5,4] => 4
[1,3,4,2,5,6] => 8
[1,3,4,2,6,5] => 2
[1,3,4,5,2,6] => 4
[1,3,4,5,6,2] => 2
[1,3,4,6,2,5] => 2
[1,3,4,6,5,2] => 4
[1,3,5,2,4,6] => 4
[1,3,5,2,6,4] => 2
[1,3,5,4,2,6] => 8
[1,3,5,4,6,2] => 4
[1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => 2
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 4
[1,3,6,4,2,5] => 4
[1,3,6,4,5,2] => 8
[1,3,6,5,2,4] => 2
[1,3,6,5,4,2] => 2
[1,4,2,3,5,6] => 8
[1,4,2,3,6,5] => 2
[1,4,2,5,3,6] => 4
[1,4,2,5,6,3] => 2
[1,4,2,6,3,5] => 2
[1,4,2,6,5,3] => 4
[1,4,3,2,5,6] => 16
[1,4,3,2,6,5] => 4
[1,4,3,5,2,6] => 8
[1,4,3,5,6,2] => 4
[1,4,3,6,2,5] => 4
[1,4,3,6,5,2] => 8
[1,4,5,2,3,6] => 4
[1,4,5,2,6,3] => 2
[1,4,5,3,2,6] => 4
[1,4,5,3,6,2] => 2
[1,4,5,6,2,3] => 2
[1,4,5,6,3,2] => 2
[1,4,6,2,3,5] => 2
[1,4,6,2,5,3] => 4
[1,4,6,3,2,5] => 2
[1,4,6,3,5,2] => 4
[1,4,6,5,2,3] => 2
[1,4,6,5,3,2] => 2
[1,5,2,3,4,6] => 4
[1,5,2,3,6,4] => 2
[1,5,2,4,3,6] => 8
[1,5,2,4,6,3] => 4
[1,5,2,6,3,4] => 2
[1,5,2,6,4,3] => 2
[1,5,3,2,4,6] => 8
[1,5,3,2,6,4] => 4
[1,5,3,4,2,6] => 16
[1,5,3,4,6,2] => 8
[1,5,3,6,2,4] => 4
[1,5,3,6,4,2] => 4
[1,5,4,2,3,6] => 4
[1,5,4,2,6,3] => 2
[1,5,4,3,2,6] => 4
[1,5,4,3,6,2] => 2
[1,5,4,6,2,3] => 2
[1,5,4,6,3,2] => 2
[1,5,6,2,3,4] => 2
[1,5,6,2,4,3] => 2
[1,5,6,3,2,4] => 2
[1,5,6,3,4,2] => 2
[1,5,6,4,2,3] => 4
[1,5,6,4,3,2] => 4
[1,6,2,3,4,5] => 2
[1,6,2,3,5,4] => 4
[1,6,2,4,3,5] => 4
[1,6,2,4,5,3] => 8
[1,6,2,5,3,4] => 2
[1,6,2,5,4,3] => 2
[1,6,3,2,4,5] => 4
[1,6,3,2,5,4] => 8
[1,6,3,4,2,5] => 8
[1,6,3,4,5,2] => 16
[1,6,3,5,2,4] => 4
[1,6,3,5,4,2] => 4
[1,6,4,2,3,5] => 2
[1,6,4,2,5,3] => 4
[1,6,4,3,2,5] => 2
[1,6,4,3,5,2] => 4
[1,6,4,5,2,3] => 2
[1,6,4,5,3,2] => 2
[1,6,5,2,3,4] => 2
[1,6,5,2,4,3] => 2
[1,6,5,3,2,4] => 2
[1,6,5,3,4,2] => 2
[1,6,5,4,2,3] => 4
[1,6,5,4,3,2] => 4
[2,1,3,4,5,6] => 16
[2,1,3,4,6,5] => 4
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 2
[2,1,3,6,4,5] => 2
[2,1,3,6,5,4] => 4
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 1
[2,1,4,5,3,6] => 2
[2,1,4,5,6,3] => 1
[2,1,4,6,3,5] => 1
[2,1,4,6,5,3] => 2
[2,1,5,3,4,6] => 2
[2,1,5,3,6,4] => 1
[2,1,5,4,3,6] => 4
[2,1,5,4,6,3] => 2
[2,1,5,6,3,4] => 1
[2,1,5,6,4,3] => 1
[2,1,6,3,4,5] => 1
[2,1,6,3,5,4] => 2
[2,1,6,4,3,5] => 2
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 1
[2,1,6,5,4,3] => 1
[2,3,1,4,5,6] => 8
[2,3,1,4,6,5] => 2
[2,3,1,5,4,6] => 2
[2,3,1,5,6,4] => 1
[2,3,1,6,4,5] => 1
[2,3,1,6,5,4] => 2
[2,3,4,1,5,6] => 4
[2,3,4,1,6,5] => 1
[2,3,4,5,1,6] => 2
[2,3,4,5,6,1] => 1
[2,3,4,6,1,5] => 1
[2,3,4,6,5,1] => 2
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 1
[2,3,5,4,1,6] => 4
[2,3,5,4,6,1] => 2
[2,3,5,6,1,4] => 1
[2,3,5,6,4,1] => 1
[2,3,6,1,4,5] => 1
[2,3,6,1,5,4] => 2
[2,3,6,4,1,5] => 2
[2,3,6,4,5,1] => 4
[2,3,6,5,1,4] => 1
[2,3,6,5,4,1] => 1
[2,4,1,3,5,6] => 4
[2,4,1,3,6,5] => 1
[2,4,1,5,3,6] => 2
[2,4,1,5,6,3] => 1
[2,4,1,6,3,5] => 1
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 8
[2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => 4
[2,4,3,5,6,1] => 2
[2,4,3,6,1,5] => 2
[2,4,3,6,5,1] => 4
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 1
[2,4,5,3,1,6] => 2
[2,4,5,3,6,1] => 1
[2,4,5,6,1,3] => 1
[2,4,5,6,3,1] => 1
[2,4,6,1,3,5] => 1
[2,4,6,1,5,3] => 2
[2,4,6,3,1,5] => 1
[2,4,6,3,5,1] => 2
[2,4,6,5,1,3] => 1
[2,4,6,5,3,1] => 1
[2,5,1,3,4,6] => 2
[2,5,1,3,6,4] => 1
[2,5,1,4,3,6] => 4
[2,5,1,4,6,3] => 2
[2,5,1,6,3,4] => 1
[2,5,1,6,4,3] => 1
[2,5,3,1,4,6] => 4
[2,5,3,1,6,4] => 2
[2,5,3,4,1,6] => 8
[2,5,3,4,6,1] => 4
[2,5,3,6,1,4] => 2
[2,5,3,6,4,1] => 2
[2,5,4,1,3,6] => 2
[2,5,4,1,6,3] => 1
[2,5,4,3,1,6] => 2
[2,5,4,3,6,1] => 1
[2,5,4,6,1,3] => 1
[2,5,4,6,3,1] => 1
[2,5,6,1,3,4] => 1
[2,5,6,1,4,3] => 1
[2,5,6,3,1,4] => 1
[2,5,6,3,4,1] => 1
[2,5,6,4,1,3] => 2
[2,5,6,4,3,1] => 2
[2,6,1,3,4,5] => 1
[2,6,1,3,5,4] => 2
[2,6,1,4,3,5] => 2
[2,6,1,4,5,3] => 4
[2,6,1,5,3,4] => 1
[2,6,1,5,4,3] => 1
[2,6,3,1,4,5] => 2
[2,6,3,1,5,4] => 4
[2,6,3,4,1,5] => 4
[2,6,3,4,5,1] => 8
[2,6,3,5,1,4] => 2
[2,6,3,5,4,1] => 2
[2,6,4,1,3,5] => 1
[2,6,4,1,5,3] => 2
[2,6,4,3,1,5] => 1
[2,6,4,3,5,1] => 2
[2,6,4,5,1,3] => 1
[2,6,4,5,3,1] => 1
[2,6,5,1,3,4] => 1
[2,6,5,1,4,3] => 1
[2,6,5,3,1,4] => 1
[2,6,5,3,4,1] => 1
[2,6,5,4,1,3] => 2
[2,6,5,4,3,1] => 2
[3,1,2,4,5,6] => 8
[3,1,2,4,6,5] => 2
[3,1,2,5,4,6] => 2
[3,1,2,5,6,4] => 1
[3,1,2,6,4,5] => 1
[3,1,2,6,5,4] => 2
[3,1,4,2,5,6] => 4
[3,1,4,2,6,5] => 1
[3,1,4,5,2,6] => 2
[3,1,4,5,6,2] => 1
[3,1,4,6,2,5] => 1
[3,1,4,6,5,2] => 2
[3,1,5,2,4,6] => 2
[3,1,5,2,6,4] => 1
[3,1,5,4,2,6] => 4
[3,1,5,4,6,2] => 2
[3,1,5,6,2,4] => 1
[3,1,5,6,4,2] => 1
[3,1,6,2,4,5] => 1
[3,1,6,2,5,4] => 2
[3,1,6,4,2,5] => 2
[3,1,6,4,5,2] => 4
[3,1,6,5,2,4] => 1
[3,1,6,5,4,2] => 1
[3,2,1,4,5,6] => 16
[3,2,1,4,6,5] => 4
[3,2,1,5,4,6] => 4
[3,2,1,5,6,4] => 2
[3,2,1,6,4,5] => 2
[3,2,1,6,5,4] => 4
[3,2,4,1,5,6] => 8
[3,2,4,1,6,5] => 2
[3,2,4,5,1,6] => 4
[3,2,4,5,6,1] => 2
[3,2,4,6,1,5] => 2
[3,2,4,6,5,1] => 4
[3,2,5,1,4,6] => 4
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 8
[3,2,5,4,6,1] => 4
[3,2,5,6,1,4] => 2
[3,2,5,6,4,1] => 2
[3,2,6,1,4,5] => 2
[3,2,6,1,5,4] => 4
[3,2,6,4,1,5] => 4
[3,2,6,4,5,1] => 8
[3,2,6,5,1,4] => 2
[3,2,6,5,4,1] => 2
[3,4,1,2,5,6] => 4
[3,4,1,2,6,5] => 1
[3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => 1
[3,4,1,6,2,5] => 1
[3,4,1,6,5,2] => 2
[3,4,2,1,5,6] => 4
[3,4,2,1,6,5] => 1
[3,4,2,5,1,6] => 2
[3,4,2,5,6,1] => 1
[3,4,2,6,1,5] => 1
[3,4,2,6,5,1] => 2
[3,4,5,1,2,6] => 2
[3,4,5,1,6,2] => 1
[3,4,5,2,1,6] => 2
[3,4,5,2,6,1] => 1
[3,4,5,6,1,2] => 1
[3,4,5,6,2,1] => 1
[3,4,6,1,2,5] => 1
[3,4,6,1,5,2] => 2
[3,4,6,2,1,5] => 1
[3,4,6,2,5,1] => 2
[3,4,6,5,1,2] => 1
[3,4,6,5,2,1] => 1
[3,5,1,2,4,6] => 2
[3,5,1,2,6,4] => 1
[3,5,1,4,2,6] => 4
[3,5,1,4,6,2] => 2
[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] => 1
[3,5,2,4,1,6] => 4
[3,5,2,4,6,1] => 2
[3,5,2,6,1,4] => 1
[3,5,2,6,4,1] => 1
[3,5,4,1,2,6] => 2
[3,5,4,1,6,2] => 1
[3,5,4,2,1,6] => 2
[3,5,4,2,6,1] => 1
[3,5,4,6,1,2] => 1
[3,5,4,6,2,1] => 1
[3,5,6,1,2,4] => 1
[3,5,6,1,4,2] => 1
[3,5,6,2,1,4] => 1
[3,5,6,2,4,1] => 1
[3,5,6,4,1,2] => 2
[3,5,6,4,2,1] => 2
[3,6,1,2,4,5] => 1
[3,6,1,2,5,4] => 2
[3,6,1,4,2,5] => 2
[3,6,1,4,5,2] => 4
[3,6,1,5,2,4] => 1
[3,6,1,5,4,2] => 1
[3,6,2,1,4,5] => 1
[3,6,2,1,5,4] => 2
[3,6,2,4,1,5] => 2
[3,6,2,4,5,1] => 4
[3,6,2,5,1,4] => 1
[3,6,2,5,4,1] => 1
[3,6,4,1,2,5] => 1
[3,6,4,1,5,2] => 2
[3,6,4,2,1,5] => 1
[3,6,4,2,5,1] => 2
[3,6,4,5,1,2] => 1
[3,6,4,5,2,1] => 1
[3,6,5,1,2,4] => 1
[3,6,5,1,4,2] => 1
[3,6,5,2,1,4] => 1
[3,6,5,2,4,1] => 1
[3,6,5,4,1,2] => 2
[3,6,5,4,2,1] => 2
[4,1,2,3,5,6] => 4
[4,1,2,3,6,5] => 1
[4,1,2,5,3,6] => 2
[4,1,2,5,6,3] => 1
[4,1,2,6,3,5] => 1
[4,1,2,6,5,3] => 2
[4,1,3,2,5,6] => 8
[4,1,3,2,6,5] => 2
[4,1,3,5,2,6] => 4
[4,1,3,5,6,2] => 2
[4,1,3,6,2,5] => 2
[4,1,3,6,5,2] => 4
[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] => 1
[4,1,5,6,3,2] => 1
[4,1,6,2,3,5] => 1
[4,1,6,2,5,3] => 2
[4,1,6,3,2,5] => 1
[4,1,6,3,5,2] => 2
[4,1,6,5,2,3] => 1
[4,1,6,5,3,2] => 1
[4,2,1,3,5,6] => 8
[4,2,1,3,6,5] => 2
[4,2,1,5,3,6] => 4
[4,2,1,5,6,3] => 2
[4,2,1,6,3,5] => 2
[4,2,1,6,5,3] => 4
[4,2,3,1,5,6] => 16
[4,2,3,1,6,5] => 4
[4,2,3,5,1,6] => 8
[4,2,3,5,6,1] => 4
[4,2,3,6,1,5] => 4
[4,2,3,6,5,1] => 8
[4,2,5,1,3,6] => 4
[4,2,5,1,6,3] => 2
[4,2,5,3,1,6] => 4
[4,2,5,3,6,1] => 2
[4,2,5,6,1,3] => 2
[4,2,5,6,3,1] => 2
[4,2,6,1,3,5] => 2
[4,2,6,1,5,3] => 4
[4,2,6,3,1,5] => 2
[4,2,6,3,5,1] => 4
[4,2,6,5,1,3] => 2
[4,2,6,5,3,1] => 2
[4,3,1,2,5,6] => 4
[4,3,1,2,6,5] => 1
[4,3,1,5,2,6] => 2
[4,3,1,5,6,2] => 1
[4,3,1,6,2,5] => 1
[4,3,1,6,5,2] => 2
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 1
[4,3,2,5,1,6] => 2
[4,3,2,5,6,1] => 1
[4,3,2,6,1,5] => 1
[4,3,2,6,5,1] => 2
[4,3,5,1,2,6] => 2
[4,3,5,1,6,2] => 1
[4,3,5,2,1,6] => 2
[4,3,5,2,6,1] => 1
[4,3,5,6,1,2] => 1
[4,3,5,6,2,1] => 1
[4,3,6,1,2,5] => 1
[4,3,6,1,5,2] => 2
[4,3,6,2,1,5] => 1
[4,3,6,2,5,1] => 2
[4,3,6,5,1,2] => 1
[4,3,6,5,2,1] => 1
[4,5,1,2,3,6] => 2
[4,5,1,2,6,3] => 1
[4,5,1,3,2,6] => 2
[4,5,1,3,6,2] => 1
[4,5,1,6,2,3] => 1
[4,5,1,6,3,2] => 1
[4,5,2,1,3,6] => 2
[4,5,2,1,6,3] => 1
[4,5,2,3,1,6] => 2
[4,5,2,3,6,1] => 1
[4,5,2,6,1,3] => 1
[4,5,2,6,3,1] => 1
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 2
[4,5,3,2,1,6] => 4
[4,5,3,2,6,1] => 2
[4,5,3,6,1,2] => 2
[4,5,3,6,2,1] => 2
[4,5,6,1,2,3] => 1
[4,5,6,1,3,2] => 1
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 1
[4,5,6,3,1,2] => 1
[4,5,6,3,2,1] => 1
[4,6,1,2,3,5] => 1
[4,6,1,2,5,3] => 2
[4,6,1,3,2,5] => 1
[4,6,1,3,5,2] => 2
[4,6,1,5,2,3] => 1
[4,6,1,5,3,2] => 1
[4,6,2,1,3,5] => 1
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 1
[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] => 2
[4,6,3,1,5,2] => 4
[4,6,3,2,1,5] => 2
[4,6,3,2,5,1] => 4
[4,6,3,5,1,2] => 2
[4,6,3,5,2,1] => 2
[4,6,5,1,2,3] => 1
[4,6,5,1,3,2] => 1
[4,6,5,2,1,3] => 1
[4,6,5,2,3,1] => 1
[4,6,5,3,1,2] => 1
[4,6,5,3,2,1] => 1
[5,1,2,3,4,6] => 2
[5,1,2,3,6,4] => 1
[5,1,2,4,3,6] => 4
[5,1,2,4,6,3] => 2
[5,1,2,6,3,4] => 1
[5,1,2,6,4,3] => 1
[5,1,3,2,4,6] => 4
[5,1,3,2,6,4] => 2
[5,1,3,4,2,6] => 8
[5,1,3,4,6,2] => 4
[5,1,3,6,2,4] => 2
[5,1,3,6,4,2] => 2
[5,1,4,2,3,6] => 2
[5,1,4,2,6,3] => 1
[5,1,4,3,2,6] => 2
[5,1,4,3,6,2] => 1
[5,1,4,6,2,3] => 1
[5,1,4,6,3,2] => 1
[5,1,6,2,3,4] => 1
[5,1,6,2,4,3] => 1
[5,1,6,3,2,4] => 1
[5,1,6,3,4,2] => 1
[5,1,6,4,2,3] => 2
[5,1,6,4,3,2] => 2
[5,2,1,3,4,6] => 4
[5,2,1,3,6,4] => 2
[5,2,1,4,3,6] => 8
[5,2,1,4,6,3] => 4
[5,2,1,6,3,4] => 2
[5,2,1,6,4,3] => 2
[5,2,3,1,4,6] => 8
[5,2,3,1,6,4] => 4
[5,2,3,4,1,6] => 16
[5,2,3,4,6,1] => 8
[5,2,3,6,1,4] => 4
[5,2,3,6,4,1] => 4
[5,2,4,1,3,6] => 4
[5,2,4,1,6,3] => 2
[5,2,4,3,1,6] => 4
[5,2,4,3,6,1] => 2
[5,2,4,6,1,3] => 2
[5,2,4,6,3,1] => 2
[5,2,6,1,3,4] => 2
[5,2,6,1,4,3] => 2
[5,2,6,3,1,4] => 2
[5,2,6,3,4,1] => 2
[5,2,6,4,1,3] => 4
[5,2,6,4,3,1] => 4
[5,3,1,2,4,6] => 2
[5,3,1,2,6,4] => 1
[5,3,1,4,2,6] => 4
[5,3,1,4,6,2] => 2
[5,3,1,6,2,4] => 1
[5,3,1,6,4,2] => 1
[5,3,2,1,4,6] => 2
[5,3,2,1,6,4] => 1
[5,3,2,4,1,6] => 4
[5,3,2,4,6,1] => 2
[5,3,2,6,1,4] => 1
[5,3,2,6,4,1] => 1
[5,3,4,1,2,6] => 2
[5,3,4,1,6,2] => 1
[5,3,4,2,1,6] => 2
[5,3,4,2,6,1] => 1
[5,3,4,6,1,2] => 1
[5,3,4,6,2,1] => 1
[5,3,6,1,2,4] => 1
[5,3,6,1,4,2] => 1
[5,3,6,2,1,4] => 1
[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] => 2
[5,4,1,2,6,3] => 1
[5,4,1,3,2,6] => 2
[5,4,1,3,6,2] => 1
[5,4,1,6,2,3] => 1
[5,4,1,6,3,2] => 1
[5,4,2,1,3,6] => 2
[5,4,2,1,6,3] => 1
[5,4,2,3,1,6] => 2
[5,4,2,3,6,1] => 1
[5,4,2,6,1,3] => 1
[5,4,2,6,3,1] => 1
[5,4,3,1,2,6] => 4
[5,4,3,1,6,2] => 2
[5,4,3,2,1,6] => 4
[5,4,3,2,6,1] => 2
[5,4,3,6,1,2] => 2
[5,4,3,6,2,1] => 2
[5,4,6,1,2,3] => 1
[5,4,6,1,3,2] => 1
[5,4,6,2,1,3] => 1
[5,4,6,2,3,1] => 1
[5,4,6,3,1,2] => 1
[5,4,6,3,2,1] => 1
[5,6,1,2,3,4] => 1
[5,6,1,2,4,3] => 1
[5,6,1,3,2,4] => 1
[5,6,1,3,4,2] => 1
[5,6,1,4,2,3] => 2
[5,6,1,4,3,2] => 2
[5,6,2,1,3,4] => 1
[5,6,2,1,4,3] => 1
[5,6,2,3,1,4] => 1
[5,6,2,3,4,1] => 1
[5,6,2,4,1,3] => 2
[5,6,2,4,3,1] => 2
[5,6,3,1,2,4] => 2
[5,6,3,1,4,2] => 2
[5,6,3,2,1,4] => 2
[5,6,3,2,4,1] => 2
[5,6,3,4,1,2] => 4
[5,6,3,4,2,1] => 4
[5,6,4,1,2,3] => 1
[5,6,4,1,3,2] => 1
[5,6,4,2,1,3] => 1
[5,6,4,2,3,1] => 1
[5,6,4,3,1,2] => 1
[5,6,4,3,2,1] => 1
[6,1,2,3,4,5] => 1
[6,1,2,3,5,4] => 2
[6,1,2,4,3,5] => 2
[6,1,2,4,5,3] => 4
[6,1,2,5,3,4] => 1
[6,1,2,5,4,3] => 1
[6,1,3,2,4,5] => 2
[6,1,3,2,5,4] => 4
[6,1,3,4,2,5] => 4
[6,1,3,4,5,2] => 8
[6,1,3,5,2,4] => 2
[6,1,3,5,4,2] => 2
[6,1,4,2,3,5] => 1
[6,1,4,2,5,3] => 2
[6,1,4,3,2,5] => 1
[6,1,4,3,5,2] => 2
[6,1,4,5,2,3] => 1
[6,1,4,5,3,2] => 1
[6,1,5,2,3,4] => 1
[6,1,5,2,4,3] => 1
[6,1,5,3,2,4] => 1
[6,1,5,3,4,2] => 1
[6,1,5,4,2,3] => 2
[6,1,5,4,3,2] => 2
[6,2,1,3,4,5] => 2
[6,2,1,3,5,4] => 4
[6,2,1,4,3,5] => 4
[6,2,1,4,5,3] => 8
[6,2,1,5,3,4] => 2
[6,2,1,5,4,3] => 2
[6,2,3,1,4,5] => 4
[6,2,3,1,5,4] => 8
[6,2,3,4,1,5] => 8
[6,2,3,4,5,1] => 16
[6,2,3,5,1,4] => 4
[6,2,3,5,4,1] => 4
[6,2,4,1,3,5] => 2
[6,2,4,1,5,3] => 4
[6,2,4,3,1,5] => 2
[6,2,4,3,5,1] => 4
[6,2,4,5,1,3] => 2
[6,2,4,5,3,1] => 2
[6,2,5,1,3,4] => 2
[6,2,5,1,4,3] => 2
[6,2,5,3,1,4] => 2
[6,2,5,3,4,1] => 2
[6,2,5,4,1,3] => 4
[6,2,5,4,3,1] => 4
[6,3,1,2,4,5] => 1
[6,3,1,2,5,4] => 2
[6,3,1,4,2,5] => 2
[6,3,1,4,5,2] => 4
[6,3,1,5,2,4] => 1
[6,3,1,5,4,2] => 1
[6,3,2,1,4,5] => 1
[6,3,2,1,5,4] => 2
[6,3,2,4,1,5] => 2
[6,3,2,4,5,1] => 4
[6,3,2,5,1,4] => 1
[6,3,2,5,4,1] => 1
[6,3,4,1,2,5] => 1
[6,3,4,1,5,2] => 2
[6,3,4,2,1,5] => 1
[6,3,4,2,5,1] => 2
[6,3,4,5,1,2] => 1
[6,3,4,5,2,1] => 1
[6,3,5,1,2,4] => 1
[6,3,5,1,4,2] => 1
[6,3,5,2,1,4] => 1
[6,3,5,2,4,1] => 1
[6,3,5,4,1,2] => 2
[6,3,5,4,2,1] => 2
[6,4,1,2,3,5] => 1
[6,4,1,2,5,3] => 2
[6,4,1,3,2,5] => 1
[6,4,1,3,5,2] => 2
[6,4,1,5,2,3] => 1
[6,4,1,5,3,2] => 1
[6,4,2,1,3,5] => 1
[6,4,2,1,5,3] => 2
[6,4,2,3,1,5] => 1
[6,4,2,3,5,1] => 2
[6,4,2,5,1,3] => 1
[6,4,2,5,3,1] => 1
[6,4,3,1,2,5] => 2
[6,4,3,1,5,2] => 4
[6,4,3,2,1,5] => 2
[6,4,3,2,5,1] => 4
[6,4,3,5,1,2] => 2
[6,4,3,5,2,1] => 2
[6,4,5,1,2,3] => 1
[6,4,5,1,3,2] => 1
[6,4,5,2,1,3] => 1
[6,4,5,2,3,1] => 1
[6,4,5,3,1,2] => 1
[6,4,5,3,2,1] => 1
[6,5,1,2,3,4] => 1
[6,5,1,2,4,3] => 1
[6,5,1,3,2,4] => 1
[6,5,1,3,4,2] => 1
[6,5,1,4,2,3] => 2
[6,5,1,4,3,2] => 2
[6,5,2,1,3,4] => 1
[6,5,2,1,4,3] => 1
[6,5,2,3,1,4] => 1
[6,5,2,3,4,1] => 1
[6,5,2,4,1,3] => 2
[6,5,2,4,3,1] => 2
[6,5,3,1,2,4] => 2
[6,5,3,1,4,2] => 2
[6,5,3,2,1,4] => 2
[6,5,3,2,4,1] => 2
[6,5,3,4,1,2] => 4
[6,5,3,4,2,1] => 4
[6,5,4,1,2,3] => 1
[6,5,4,1,3,2] => 1
[6,5,4,2,1,3] => 1
[6,5,4,2,3,1] => 1
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 1
[1,2,3,4,5,6,7] => 128
[1,2,3,4,5,7,6] => 32
[1,2,3,4,6,5,7] => 32
[1,2,3,4,6,7,5] => 16
[1,2,3,4,7,5,6] => 16
[1,2,3,4,7,6,5] => 32
[1,2,3,5,4,6,7] => 32
[1,2,3,5,4,7,6] => 8
[1,2,3,5,6,4,7] => 16
[1,2,3,5,6,7,4] => 8
[1,2,3,5,7,4,6] => 8
[1,2,3,5,7,6,4] => 16
[1,2,3,6,4,5,7] => 16
[1,2,3,6,4,7,5] => 8
[1,2,3,6,5,4,7] => 32
[1,2,3,6,5,7,4] => 16
[1,2,3,6,7,4,5] => 8
[1,2,3,6,7,5,4] => 8
[1,2,3,7,4,5,6] => 8
[1,2,3,7,4,6,5] => 16
[1,2,3,7,5,4,6] => 16
[1,2,3,7,5,6,4] => 32
[1,2,3,7,6,4,5] => 8
[1,2,3,7,6,5,4] => 8
[1,2,4,3,5,6,7] => 32
[1,2,4,3,5,7,6] => 8
[1,2,4,3,6,5,7] => 8
[1,2,4,3,6,7,5] => 4
[1,2,4,3,7,5,6] => 4
[1,2,4,3,7,6,5] => 8
[1,2,4,5,3,6,7] => 16
[1,2,4,5,3,7,6] => 4
[1,2,4,5,6,3,7] => 8
[1,2,4,5,6,7,3] => 4
[1,2,4,5,7,3,6] => 4
[1,2,4,5,7,6,3] => 8
[1,2,4,6,3,5,7] => 8
[1,2,4,6,3,7,5] => 4
[1,2,4,6,5,3,7] => 16
[1,2,4,6,5,7,3] => 8
[1,2,4,6,7,3,5] => 4
[1,2,4,6,7,5,3] => 4
[1,2,4,7,3,5,6] => 4
[1,2,4,7,3,6,5] => 8
[1,2,4,7,5,3,6] => 8
[1,2,4,7,5,6,3] => 16
[1,2,4,7,6,3,5] => 4
[1,2,4,7,6,5,3] => 4
[1,2,5,3,4,6,7] => 16
[1,2,5,3,4,7,6] => 4
[1,2,5,3,6,4,7] => 8
[1,2,5,3,6,7,4] => 4
[1,2,5,3,7,4,6] => 4
[1,2,5,3,7,6,4] => 8
[1,2,5,4,3,6,7] => 32
[1,2,5,4,3,7,6] => 8
[1,2,5,4,6,3,7] => 16
[1,2,5,4,6,7,3] => 8
[1,2,5,4,7,3,6] => 8
[1,2,5,4,7,6,3] => 16
[1,2,5,6,3,4,7] => 8
[1,2,5,6,3,7,4] => 4
[1,2,5,6,4,3,7] => 8
[1,2,5,6,4,7,3] => 4
[1,2,5,6,7,3,4] => 4
[1,2,5,6,7,4,3] => 4
[1,2,5,7,3,4,6] => 4
[1,2,5,7,3,6,4] => 8
[1,2,5,7,4,3,6] => 4
[1,2,5,7,4,6,3] => 8
[1,2,5,7,6,3,4] => 4
[1,2,5,7,6,4,3] => 4
[1,2,6,3,4,5,7] => 8
[1,2,6,3,4,7,5] => 4
[1,2,6,3,5,4,7] => 16
[1,2,6,3,5,7,4] => 8
[1,2,6,3,7,4,5] => 4
[1,2,6,3,7,5,4] => 4
[1,2,6,4,3,5,7] => 16
[1,2,6,4,3,7,5] => 8
[1,2,6,4,5,3,7] => 32
[1,2,6,4,5,7,3] => 16
[1,2,6,4,7,3,5] => 8
[1,2,6,4,7,5,3] => 8
[1,2,6,5,3,4,7] => 8
[1,2,6,5,3,7,4] => 4
[1,2,6,5,4,3,7] => 8
[1,2,6,5,4,7,3] => 4
[1,2,6,5,7,3,4] => 4
[1,2,6,5,7,4,3] => 4
[1,2,6,7,3,4,5] => 4
[1,2,6,7,3,5,4] => 4
[1,2,6,7,4,3,5] => 4
[1,2,6,7,4,5,3] => 4
[1,2,6,7,5,3,4] => 8
[1,2,6,7,5,4,3] => 8
[1,2,7,3,4,5,6] => 4
[1,2,7,3,4,6,5] => 8
[1,2,7,3,5,4,6] => 8
[1,2,7,3,5,6,4] => 16
[1,2,7,3,6,4,5] => 4
[1,2,7,3,6,5,4] => 4
[1,2,7,4,3,5,6] => 8
[1,2,7,4,3,6,5] => 16
[1,2,7,4,5,3,6] => 16
[1,2,7,4,5,6,3] => 32
[1,2,7,4,6,3,5] => 8
[1,2,7,4,6,5,3] => 8
[1,2,7,5,3,4,6] => 4
[1,2,7,5,3,6,4] => 8
[1,2,7,5,4,3,6] => 4
[1,2,7,5,4,6,3] => 8
[1,2,7,5,6,3,4] => 4
[1,2,7,5,6,4,3] => 4
[1,2,7,6,3,4,5] => 4
[1,2,7,6,3,5,4] => 4
[1,2,7,6,4,3,5] => 4
[1,2,7,6,4,5,3] => 4
[1,2,7,6,5,3,4] => 8
[1,2,7,6,5,4,3] => 8
[1,3,2,4,5,6,7] => 32
[1,3,2,4,5,7,6] => 8
[1,3,2,4,6,5,7] => 8
[1,3,2,4,6,7,5] => 4
[1,3,2,4,7,5,6] => 4
[1,3,2,4,7,6,5] => 8
[1,3,2,5,4,6,7] => 8
[1,3,2,5,4,7,6] => 2
[1,3,2,5,6,4,7] => 4
[1,3,2,5,6,7,4] => 2
[1,3,2,5,7,4,6] => 2
[1,3,2,5,7,6,4] => 4
[1,3,2,6,4,5,7] => 4
[1,3,2,6,4,7,5] => 2
[1,3,2,6,5,4,7] => 8
[1,3,2,6,5,7,4] => 4
[1,3,2,6,7,4,5] => 2
[1,3,2,6,7,5,4] => 2
[1,3,2,7,4,5,6] => 2
[1,3,2,7,4,6,5] => 4
[1,3,2,7,5,4,6] => 4
[1,3,2,7,5,6,4] => 8
[1,3,2,7,6,4,5] => 2
[1,3,2,7,6,5,4] => 2
[1,3,4,2,5,6,7] => 16
[1,3,4,2,5,7,6] => 4
[1,3,4,2,6,5,7] => 4
[1,3,4,2,6,7,5] => 2
[1,3,4,2,7,5,6] => 2
[1,3,4,2,7,6,5] => 4
[1,3,4,5,2,6,7] => 8
[1,3,4,5,2,7,6] => 2
[1,3,4,5,6,2,7] => 4
[1,3,4,5,6,7,2] => 2
[1,3,4,5,7,2,6] => 2
[1,3,4,5,7,6,2] => 4
[1,3,4,6,2,5,7] => 4
[1,3,4,6,2,7,5] => 2
[1,3,4,6,5,2,7] => 8
[1,3,4,6,5,7,2] => 4
[1,3,4,6,7,2,5] => 2
[1,3,4,6,7,5,2] => 2
[1,3,4,7,2,5,6] => 2
[1,3,4,7,2,6,5] => 4
[1,3,4,7,5,2,6] => 4
[1,3,4,7,5,6,2] => 8
[1,3,4,7,6,2,5] => 2
[1,3,4,7,6,5,2] => 2
[1,3,5,2,4,6,7] => 8
[1,3,5,2,4,7,6] => 2
[1,3,5,2,6,4,7] => 4
[1,3,5,2,6,7,4] => 2
[1,3,5,2,7,4,6] => 2
[1,3,5,2,7,6,4] => 4
[1,3,5,4,2,6,7] => 16
[1,3,5,4,2,7,6] => 4
[1,3,5,4,6,2,7] => 8
[1,3,5,4,6,7,2] => 4
[1,3,5,4,7,2,6] => 4
[1,3,5,4,7,6,2] => 8
[1,3,5,6,2,4,7] => 4
[1,3,5,6,2,7,4] => 2
[1,3,5,6,4,2,7] => 4
[1,3,5,6,4,7,2] => 2
[1,3,5,6,7,2,4] => 2
[1,3,5,6,7,4,2] => 2
[1,3,5,7,2,4,6] => 2
[1,3,5,7,2,6,4] => 4
[1,3,5,7,4,2,6] => 2
[1,3,5,7,4,6,2] => 4
[1,3,5,7,6,2,4] => 2
[1,3,5,7,6,4,2] => 2
[1,3,6,2,4,5,7] => 4
[1,3,6,2,4,7,5] => 2
[1,3,6,2,5,4,7] => 8
[1,3,6,2,5,7,4] => 4
[1,3,6,2,7,4,5] => 2
[1,3,6,2,7,5,4] => 2
[1,3,6,4,2,5,7] => 8
[1,3,6,4,2,7,5] => 4
[1,3,6,4,5,2,7] => 16
[1,3,6,4,5,7,2] => 8
[1,3,6,4,7,2,5] => 4
[1,3,6,4,7,5,2] => 4
[1,3,6,5,2,4,7] => 4
[1,3,6,5,2,7,4] => 2
[1,3,6,5,4,2,7] => 4
[1,3,6,5,4,7,2] => 2
[1,3,6,5,7,2,4] => 2
[1,3,6,5,7,4,2] => 2
[1,3,6,7,2,4,5] => 2
[1,3,6,7,2,5,4] => 2
[1,3,6,7,4,2,5] => 2
[1,3,6,7,4,5,2] => 2
[1,3,6,7,5,2,4] => 4
[1,3,6,7,5,4,2] => 4
[1,3,7,2,4,5,6] => 2
[1,3,7,2,4,6,5] => 4
[1,3,7,2,5,4,6] => 4
[1,3,7,2,5,6,4] => 8
[1,3,7,2,6,4,5] => 2
[1,3,7,2,6,5,4] => 2
[1,3,7,4,2,5,6] => 4
[1,3,7,4,2,6,5] => 8
[1,3,7,4,5,2,6] => 8
[1,3,7,4,5,6,2] => 16
[1,3,7,4,6,2,5] => 4
[1,3,7,4,6,5,2] => 4
[1,3,7,5,2,4,6] => 2
[1,3,7,5,2,6,4] => 4
[1,3,7,5,4,2,6] => 2
[1,3,7,5,4,6,2] => 4
[1,3,7,5,6,2,4] => 2
[1,3,7,5,6,4,2] => 2
[1,3,7,6,2,4,5] => 2
[1,3,7,6,2,5,4] => 2
[1,3,7,6,4,2,5] => 2
[1,3,7,6,4,5,2] => 2
[1,3,7,6,5,2,4] => 4
[1,3,7,6,5,4,2] => 4
[1,4,2,3,5,6,7] => 16
[1,4,2,3,5,7,6] => 4
[1,4,2,3,6,5,7] => 4
[1,4,2,3,6,7,5] => 2
[1,4,2,3,7,5,6] => 2
[1,4,2,3,7,6,5] => 4
[1,4,2,5,3,6,7] => 8
[1,4,2,5,3,7,6] => 2
[1,4,2,5,6,3,7] => 4
[1,4,2,5,6,7,3] => 2
[1,4,2,5,7,3,6] => 2
[1,4,2,5,7,6,3] => 4
[1,4,2,6,3,5,7] => 4
[1,4,2,6,3,7,5] => 2
[1,4,2,6,5,3,7] => 8
[1,4,2,6,5,7,3] => 4
[1,4,2,6,7,3,5] => 2
[1,4,2,6,7,5,3] => 2
[1,4,2,7,3,5,6] => 2
[1,4,2,7,3,6,5] => 4
[1,4,2,7,5,3,6] => 4
[1,4,2,7,5,6,3] => 8
[1,4,2,7,6,3,5] => 2
[1,4,2,7,6,5,3] => 2
[1,4,3,2,5,6,7] => 32
[1,4,3,2,5,7,6] => 8
[1,4,3,2,6,5,7] => 8
[1,4,3,2,6,7,5] => 4
[1,4,3,2,7,5,6] => 4
[1,4,3,2,7,6,5] => 8
[1,4,3,5,2,6,7] => 16
[1,4,3,5,2,7,6] => 4
[1,4,3,5,6,2,7] => 8
[1,4,3,5,6,7,2] => 4
[1,4,3,5,7,2,6] => 4
[1,4,3,5,7,6,2] => 8
[1,4,3,6,2,5,7] => 8
[1,4,3,6,2,7,5] => 4
[1,4,3,6,5,2,7] => 16
[1,4,3,6,5,7,2] => 8
[1,4,3,6,7,2,5] => 4
[1,4,3,6,7,5,2] => 4
[1,4,3,7,2,5,6] => 4
[1,4,3,7,2,6,5] => 8
[1,4,3,7,5,2,6] => 8
[1,4,3,7,5,6,2] => 16
[1,4,3,7,6,2,5] => 4
[1,4,3,7,6,5,2] => 4
[1,4,5,2,3,6,7] => 8
[1,4,5,2,3,7,6] => 2
[1,4,5,2,6,3,7] => 4
[1,4,5,2,6,7,3] => 2
[1,4,5,2,7,3,6] => 2
[1,4,5,2,7,6,3] => 4
[1,4,5,3,2,6,7] => 8
[1,4,5,3,2,7,6] => 2
[1,4,5,3,6,2,7] => 4
[1,4,5,3,6,7,2] => 2
[1,4,5,3,7,2,6] => 2
[1,4,5,3,7,6,2] => 4
[1,4,5,6,2,3,7] => 4
[1,4,5,6,2,7,3] => 2
[1,4,5,6,3,2,7] => 4
[1,4,5,6,3,7,2] => 2
[1,4,5,6,7,2,3] => 2
[1,4,5,6,7,3,2] => 2
[1,4,5,7,2,3,6] => 2
[1,4,5,7,2,6,3] => 4
[1,4,5,7,3,2,6] => 2
[1,4,5,7,3,6,2] => 4
[1,4,5,7,6,2,3] => 2
[1,4,5,7,6,3,2] => 2
[1,4,6,2,3,5,7] => 4
[1,4,6,2,3,7,5] => 2
[1,4,6,2,5,3,7] => 8
[1,4,6,2,5,7,3] => 4
[1,4,6,2,7,3,5] => 2
[1,4,6,2,7,5,3] => 2
[1,4,6,3,2,5,7] => 4
[1,4,6,3,2,7,5] => 2
[1,4,6,3,5,2,7] => 8
[1,4,6,3,5,7,2] => 4
[1,4,6,3,7,2,5] => 2
[1,4,6,3,7,5,2] => 2
[1,4,6,5,2,3,7] => 4
[1,4,6,5,2,7,3] => 2
[1,4,6,5,3,2,7] => 4
[1,4,6,5,3,7,2] => 2
click to show generating function       
Description
The number of affine bounded permutations that project to a given permutation.
As affine bounded permutations are in bijection with usual permutations where fix-points come in two colors, this statistic is $2^k$ where $k$ is the number of fixed points St000022The number of fixed points of a permutation..
References
[1] Lam, T. Totally nonnegative Grassmannian and Grassmann polytopes arXiv:1506.00603
Code
def statistic(pi):
    return 2^pi.number_of_fixed_points()

Created
Feb 03, 2017 at 11:11 by Christian Stump
Updated
Feb 03, 2017 at 11:11 by Christian Stump