Identifier
Identifier
Values
[1] => 1
[1,2] => 2
[2,1] => 2
[1,2,3] => 3
[1,3,2] => 1
[2,1,3] => 3
[2,3,1] => 1
[3,1,2] => 2
[3,2,1] => 2
[1,2,3,4] => 4
[1,2,4,3] => 4
[1,3,2,4] => 2
[1,3,4,2] => 3
[1,4,2,3] => 2
[1,4,3,2] => 3
[2,1,3,4] => 4
[2,1,4,3] => 4
[2,3,1,4] => 2
[2,3,4,1] => 3
[2,4,1,3] => 2
[2,4,3,1] => 3
[3,1,2,4] => 3
[3,1,4,2] => 4
[3,2,1,4] => 3
[3,2,4,1] => 4
[3,4,1,2] => 2
[3,4,2,1] => 2
[4,1,2,3] => 3
[4,1,3,2] => 4
[4,2,1,3] => 3
[4,2,3,1] => 4
[4,3,1,2] => 2
[4,3,2,1] => 2
[1,2,3,4,5] => 5
[1,2,3,5,4] => 3
[1,2,4,3,5] => 5
[1,2,4,5,3] => 3
[1,2,5,3,4] => 4
[1,2,5,4,3] => 4
[1,3,2,4,5] => 3
[1,3,2,5,4] => 1
[1,3,4,2,5] => 4
[1,3,4,5,2] => 2
[1,3,5,2,4] => 3
[1,3,5,4,2] => 3
[1,4,2,3,5] => 3
[1,4,2,5,3] => 1
[1,4,3,2,5] => 4
[1,4,3,5,2] => 2
[1,4,5,2,3] => 3
[1,4,5,3,2] => 3
[1,5,2,3,4] => 2
[1,5,2,4,3] => 2
[1,5,3,2,4] => 3
[1,5,3,4,2] => 3
[1,5,4,2,3] => 3
[1,5,4,3,2] => 3
[2,1,3,4,5] => 5
[2,1,3,5,4] => 3
[2,1,4,3,5] => 5
[2,1,4,5,3] => 3
[2,1,5,3,4] => 4
[2,1,5,4,3] => 4
[2,3,1,4,5] => 3
[2,3,1,5,4] => 1
[2,3,4,1,5] => 4
[2,3,4,5,1] => 2
[2,3,5,1,4] => 3
[2,3,5,4,1] => 3
[2,4,1,3,5] => 3
[2,4,1,5,3] => 1
[2,4,3,1,5] => 4
[2,4,3,5,1] => 2
[2,4,5,1,3] => 3
[2,4,5,3,1] => 3
[2,5,1,3,4] => 2
[2,5,1,4,3] => 2
[2,5,3,1,4] => 3
[2,5,3,4,1] => 3
[2,5,4,1,3] => 3
[2,5,4,3,1] => 3
[3,1,2,4,5] => 4
[3,1,2,5,4] => 2
[3,1,4,2,5] => 5
[3,1,4,5,2] => 3
[3,1,5,2,4] => 4
[3,1,5,4,2] => 4
[3,2,1,4,5] => 4
[3,2,1,5,4] => 2
[3,2,4,1,5] => 5
[3,2,4,5,1] => 3
[3,2,5,1,4] => 4
[3,2,5,4,1] => 4
[3,4,1,2,5] => 3
[3,4,1,5,2] => 1
[3,4,2,1,5] => 3
[3,4,2,5,1] => 1
[3,4,5,1,2] => 3
[3,4,5,2,1] => 3
[3,5,1,2,4] => 2
[3,5,1,4,2] => 2
[3,5,2,1,4] => 2
[3,5,2,4,1] => 2
[3,5,4,1,2] => 3
[3,5,4,2,1] => 3
[4,1,2,3,5] => 4
[4,1,2,5,3] => 2
[4,1,3,2,5] => 5
[4,1,3,5,2] => 3
[4,1,5,2,3] => 4
[4,1,5,3,2] => 4
[4,2,1,3,5] => 4
[4,2,1,5,3] => 2
[4,2,3,1,5] => 5
[4,2,3,5,1] => 3
[4,2,5,1,3] => 4
[4,2,5,3,1] => 4
[4,3,1,2,5] => 3
[4,3,1,5,2] => 1
[4,3,2,1,5] => 3
[4,3,2,5,1] => 1
[4,3,5,1,2] => 3
[4,3,5,2,1] => 3
[4,5,1,2,3] => 2
[4,5,1,3,2] => 2
[4,5,2,1,3] => 2
[4,5,2,3,1] => 2
[4,5,3,1,2] => 3
[4,5,3,2,1] => 3
[5,1,2,3,4] => 3
[5,1,2,4,3] => 3
[5,1,3,2,4] => 4
[5,1,3,4,2] => 4
[5,1,4,2,3] => 4
[5,1,4,3,2] => 4
[5,2,1,3,4] => 3
[5,2,1,4,3] => 3
[5,2,3,1,4] => 4
[5,2,3,4,1] => 4
[5,2,4,1,3] => 4
[5,2,4,3,1] => 4
[5,3,1,2,4] => 2
[5,3,1,4,2] => 2
[5,3,2,1,4] => 2
[5,3,2,4,1] => 2
[5,3,4,1,2] => 3
[5,3,4,2,1] => 3
[5,4,1,2,3] => 2
[5,4,1,3,2] => 2
[5,4,2,1,3] => 2
[5,4,2,3,1] => 2
[5,4,3,1,2] => 3
[5,4,3,2,1] => 3
[1,2,3,4,5,6] => 6
[1,2,3,4,6,5] => 6
[1,2,3,5,4,6] => 4
[1,2,3,5,6,4] => 5
[1,2,3,6,4,5] => 4
[1,2,3,6,5,4] => 5
[1,2,4,3,5,6] => 6
[1,2,4,3,6,5] => 6
[1,2,4,5,3,6] => 4
[1,2,4,5,6,3] => 5
[1,2,4,6,3,5] => 4
[1,2,4,6,5,3] => 5
[1,2,5,3,4,6] => 5
[1,2,5,3,6,4] => 6
[1,2,5,4,3,6] => 5
[1,2,5,4,6,3] => 6
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 4
[1,2,6,3,4,5] => 5
[1,2,6,3,5,4] => 6
[1,2,6,4,3,5] => 5
[1,2,6,4,5,3] => 6
[1,2,6,5,3,4] => 4
[1,2,6,5,4,3] => 4
[1,3,2,4,5,6] => 4
[1,3,2,4,6,5] => 4
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 3
[1,3,2,6,4,5] => 2
[1,3,2,6,5,4] => 3
[1,3,4,2,5,6] => 5
[1,3,4,2,6,5] => 5
[1,3,4,5,2,6] => 3
[1,3,4,5,6,2] => 4
[1,3,4,6,2,5] => 3
[1,3,4,6,5,2] => 4
[1,3,5,2,4,6] => 4
[1,3,5,2,6,4] => 5
[1,3,5,4,2,6] => 4
[1,3,5,4,6,2] => 5
[1,3,5,6,2,4] => 3
[1,3,5,6,4,2] => 3
[1,3,6,2,4,5] => 4
[1,3,6,2,5,4] => 5
[1,3,6,4,2,5] => 4
[1,3,6,4,5,2] => 5
[1,3,6,5,2,4] => 3
[1,3,6,5,4,2] => 3
[1,4,2,3,5,6] => 4
[1,4,2,3,6,5] => 4
[1,4,2,5,3,6] => 2
[1,4,2,5,6,3] => 3
[1,4,2,6,3,5] => 2
[1,4,2,6,5,3] => 3
[1,4,3,2,5,6] => 5
[1,4,3,2,6,5] => 5
[1,4,3,5,2,6] => 3
[1,4,3,5,6,2] => 4
[1,4,3,6,2,5] => 3
[1,4,3,6,5,2] => 4
[1,4,5,2,3,6] => 4
[1,4,5,2,6,3] => 5
[1,4,5,3,2,6] => 4
[1,4,5,3,6,2] => 5
[1,4,5,6,2,3] => 3
[1,4,5,6,3,2] => 3
[1,4,6,2,3,5] => 4
[1,4,6,2,5,3] => 5
[1,4,6,3,2,5] => 4
[1,4,6,3,5,2] => 5
[1,4,6,5,2,3] => 3
[1,4,6,5,3,2] => 3
[1,5,2,3,4,6] => 3
[1,5,2,3,6,4] => 4
[1,5,2,4,3,6] => 3
[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] => 4
[1,5,3,2,6,4] => 5
[1,5,3,4,2,6] => 4
[1,5,3,4,6,2] => 5
[1,5,3,6,2,4] => 3
[1,5,3,6,4,2] => 3
[1,5,4,2,3,6] => 4
[1,5,4,2,6,3] => 5
[1,5,4,3,2,6] => 4
[1,5,4,3,6,2] => 5
[1,5,4,6,2,3] => 3
[1,5,4,6,3,2] => 3
[1,5,6,2,3,4] => 4
[1,5,6,2,4,3] => 4
[1,5,6,3,2,4] => 4
[1,5,6,3,4,2] => 4
[1,5,6,4,2,3] => 4
[1,5,6,4,3,2] => 4
[1,6,2,3,4,5] => 3
[1,6,2,3,5,4] => 4
[1,6,2,4,3,5] => 3
[1,6,2,4,5,3] => 4
[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] => 5
[1,6,3,4,2,5] => 4
[1,6,3,4,5,2] => 5
[1,6,3,5,2,4] => 3
[1,6,3,5,4,2] => 3
[1,6,4,2,3,5] => 4
[1,6,4,2,5,3] => 5
[1,6,4,3,2,5] => 4
[1,6,4,3,5,2] => 5
[1,6,4,5,2,3] => 3
[1,6,4,5,3,2] => 3
[1,6,5,2,3,4] => 4
[1,6,5,2,4,3] => 4
[1,6,5,3,2,4] => 4
[1,6,5,3,4,2] => 4
[1,6,5,4,2,3] => 4
[1,6,5,4,3,2] => 4
[2,1,3,4,5,6] => 6
[2,1,3,4,6,5] => 6
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 5
[2,1,3,6,4,5] => 4
[2,1,3,6,5,4] => 5
[2,1,4,3,5,6] => 6
[2,1,4,3,6,5] => 6
[2,1,4,5,3,6] => 4
[2,1,4,5,6,3] => 5
[2,1,4,6,3,5] => 4
[2,1,4,6,5,3] => 5
[2,1,5,3,4,6] => 5
[2,1,5,3,6,4] => 6
[2,1,5,4,3,6] => 5
[2,1,5,4,6,3] => 6
[2,1,5,6,3,4] => 4
[2,1,5,6,4,3] => 4
[2,1,6,3,4,5] => 5
[2,1,6,3,5,4] => 6
[2,1,6,4,3,5] => 5
[2,1,6,4,5,3] => 6
[2,1,6,5,3,4] => 4
[2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => 4
[2,3,1,4,6,5] => 4
[2,3,1,5,4,6] => 2
[2,3,1,5,6,4] => 3
[2,3,1,6,4,5] => 2
[2,3,1,6,5,4] => 3
[2,3,4,1,5,6] => 5
[2,3,4,1,6,5] => 5
[2,3,4,5,1,6] => 3
[2,3,4,5,6,1] => 4
[2,3,4,6,1,5] => 3
[2,3,4,6,5,1] => 4
[2,3,5,1,4,6] => 4
[2,3,5,1,6,4] => 5
[2,3,5,4,1,6] => 4
[2,3,5,4,6,1] => 5
[2,3,5,6,1,4] => 3
[2,3,5,6,4,1] => 3
[2,3,6,1,4,5] => 4
[2,3,6,1,5,4] => 5
[2,3,6,4,1,5] => 4
[2,3,6,4,5,1] => 5
[2,3,6,5,1,4] => 3
[2,3,6,5,4,1] => 3
[2,4,1,3,5,6] => 4
[2,4,1,3,6,5] => 4
[2,4,1,5,3,6] => 2
[2,4,1,5,6,3] => 3
[2,4,1,6,3,5] => 2
[2,4,1,6,5,3] => 3
[2,4,3,1,5,6] => 5
[2,4,3,1,6,5] => 5
[2,4,3,5,1,6] => 3
[2,4,3,5,6,1] => 4
[2,4,3,6,1,5] => 3
[2,4,3,6,5,1] => 4
[2,4,5,1,3,6] => 4
[2,4,5,1,6,3] => 5
[2,4,5,3,1,6] => 4
[2,4,5,3,6,1] => 5
[2,4,5,6,1,3] => 3
[2,4,5,6,3,1] => 3
[2,4,6,1,3,5] => 4
[2,4,6,1,5,3] => 5
[2,4,6,3,1,5] => 4
[2,4,6,3,5,1] => 5
[2,4,6,5,1,3] => 3
[2,4,6,5,3,1] => 3
[2,5,1,3,4,6] => 3
[2,5,1,3,6,4] => 4
[2,5,1,4,3,6] => 3
[2,5,1,4,6,3] => 4
[2,5,1,6,3,4] => 2
[2,5,1,6,4,3] => 2
[2,5,3,1,4,6] => 4
[2,5,3,1,6,4] => 5
[2,5,3,4,1,6] => 4
[2,5,3,4,6,1] => 5
[2,5,3,6,1,4] => 3
[2,5,3,6,4,1] => 3
[2,5,4,1,3,6] => 4
[2,5,4,1,6,3] => 5
[2,5,4,3,1,6] => 4
[2,5,4,3,6,1] => 5
[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] => 4
[2,5,6,3,4,1] => 4
[2,5,6,4,1,3] => 4
[2,5,6,4,3,1] => 4
[2,6,1,3,4,5] => 3
[2,6,1,3,5,4] => 4
[2,6,1,4,3,5] => 3
[2,6,1,4,5,3] => 4
[2,6,1,5,3,4] => 2
[2,6,1,5,4,3] => 2
[2,6,3,1,4,5] => 4
[2,6,3,1,5,4] => 5
[2,6,3,4,1,5] => 4
[2,6,3,4,5,1] => 5
[2,6,3,5,1,4] => 3
[2,6,3,5,4,1] => 3
[2,6,4,1,3,5] => 4
[2,6,4,1,5,3] => 5
[2,6,4,3,1,5] => 4
[2,6,4,3,5,1] => 5
[2,6,4,5,1,3] => 3
[2,6,4,5,3,1] => 3
[2,6,5,1,3,4] => 4
[2,6,5,1,4,3] => 4
[2,6,5,3,1,4] => 4
[2,6,5,3,4,1] => 4
[2,6,5,4,1,3] => 4
[2,6,5,4,3,1] => 4
[3,1,2,4,5,6] => 5
[3,1,2,4,6,5] => 5
[3,1,2,5,4,6] => 3
[3,1,2,5,6,4] => 4
[3,1,2,6,4,5] => 3
[3,1,2,6,5,4] => 4
[3,1,4,2,5,6] => 6
[3,1,4,2,6,5] => 6
[3,1,4,5,2,6] => 4
[3,1,4,5,6,2] => 5
[3,1,4,6,2,5] => 4
[3,1,4,6,5,2] => 5
[3,1,5,2,4,6] => 5
[3,1,5,2,6,4] => 6
[3,1,5,4,2,6] => 5
[3,1,5,4,6,2] => 6
[3,1,5,6,2,4] => 4
[3,1,5,6,4,2] => 4
[3,1,6,2,4,5] => 5
[3,1,6,2,5,4] => 6
[3,1,6,4,2,5] => 5
[3,1,6,4,5,2] => 6
[3,1,6,5,2,4] => 4
[3,1,6,5,4,2] => 4
[3,2,1,4,5,6] => 5
[3,2,1,4,6,5] => 5
[3,2,1,5,4,6] => 3
[3,2,1,5,6,4] => 4
[3,2,1,6,4,5] => 3
[3,2,1,6,5,4] => 4
[3,2,4,1,5,6] => 6
[3,2,4,1,6,5] => 6
[3,2,4,5,1,6] => 4
[3,2,4,5,6,1] => 5
[3,2,4,6,1,5] => 4
[3,2,4,6,5,1] => 5
[3,2,5,1,4,6] => 5
[3,2,5,1,6,4] => 6
[3,2,5,4,1,6] => 5
[3,2,5,4,6,1] => 6
[3,2,5,6,1,4] => 4
[3,2,5,6,4,1] => 4
[3,2,6,1,4,5] => 5
[3,2,6,1,5,4] => 6
[3,2,6,4,1,5] => 5
[3,2,6,4,5,1] => 6
[3,2,6,5,1,4] => 4
[3,2,6,5,4,1] => 4
[3,4,1,2,5,6] => 4
[3,4,1,2,6,5] => 4
[3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => 3
[3,4,1,6,2,5] => 2
[3,4,1,6,5,2] => 3
[3,4,2,1,5,6] => 4
[3,4,2,1,6,5] => 4
[3,4,2,5,1,6] => 2
[3,4,2,5,6,1] => 3
[3,4,2,6,1,5] => 2
[3,4,2,6,5,1] => 3
[3,4,5,1,2,6] => 4
[3,4,5,1,6,2] => 5
[3,4,5,2,1,6] => 4
[3,4,5,2,6,1] => 5
[3,4,5,6,1,2] => 3
[3,4,5,6,2,1] => 3
[3,4,6,1,2,5] => 4
[3,4,6,1,5,2] => 5
[3,4,6,2,1,5] => 4
[3,4,6,2,5,1] => 5
[3,4,6,5,1,2] => 3
[3,4,6,5,2,1] => 3
[3,5,1,2,4,6] => 3
[3,5,1,2,6,4] => 4
[3,5,1,4,2,6] => 3
[3,5,1,4,6,2] => 4
[3,5,1,6,2,4] => 2
[3,5,1,6,4,2] => 2
[3,5,2,1,4,6] => 3
[3,5,2,1,6,4] => 4
[3,5,2,4,1,6] => 3
[3,5,2,4,6,1] => 4
[3,5,2,6,1,4] => 2
[3,5,2,6,4,1] => 2
[3,5,4,1,2,6] => 4
[3,5,4,1,6,2] => 5
[3,5,4,2,1,6] => 4
[3,5,4,2,6,1] => 5
[3,5,4,6,1,2] => 3
[3,5,4,6,2,1] => 3
[3,5,6,1,2,4] => 4
[3,5,6,1,4,2] => 4
[3,5,6,2,1,4] => 4
[3,5,6,2,4,1] => 4
[3,5,6,4,1,2] => 4
[3,5,6,4,2,1] => 4
[3,6,1,2,4,5] => 3
[3,6,1,2,5,4] => 4
[3,6,1,4,2,5] => 3
[3,6,1,4,5,2] => 4
[3,6,1,5,2,4] => 2
[3,6,1,5,4,2] => 2
[3,6,2,1,4,5] => 3
[3,6,2,1,5,4] => 4
[3,6,2,4,1,5] => 3
[3,6,2,4,5,1] => 4
[3,6,2,5,1,4] => 2
[3,6,2,5,4,1] => 2
[3,6,4,1,2,5] => 4
[3,6,4,1,5,2] => 5
[3,6,4,2,1,5] => 4
[3,6,4,2,5,1] => 5
[3,6,4,5,1,2] => 3
[3,6,4,5,2,1] => 3
[3,6,5,1,2,4] => 4
[3,6,5,1,4,2] => 4
[3,6,5,2,1,4] => 4
[3,6,5,2,4,1] => 4
[3,6,5,4,1,2] => 4
[3,6,5,4,2,1] => 4
[4,1,2,3,5,6] => 5
[4,1,2,3,6,5] => 5
[4,1,2,5,3,6] => 3
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 3
[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] => 4
[4,1,3,5,6,2] => 5
[4,1,3,6,2,5] => 4
[4,1,3,6,5,2] => 5
[4,1,5,2,3,6] => 5
[4,1,5,2,6,3] => 6
[4,1,5,3,2,6] => 5
[4,1,5,3,6,2] => 6
[4,1,5,6,2,3] => 4
[4,1,5,6,3,2] => 4
[4,1,6,2,3,5] => 5
[4,1,6,2,5,3] => 6
[4,1,6,3,2,5] => 5
[4,1,6,3,5,2] => 6
[4,1,6,5,2,3] => 4
[4,1,6,5,3,2] => 4
[4,2,1,3,5,6] => 5
[4,2,1,3,6,5] => 5
[4,2,1,5,3,6] => 3
[4,2,1,5,6,3] => 4
[4,2,1,6,3,5] => 3
[4,2,1,6,5,3] => 4
[4,2,3,1,5,6] => 6
[4,2,3,1,6,5] => 6
[4,2,3,5,1,6] => 4
[4,2,3,5,6,1] => 5
[4,2,3,6,1,5] => 4
[4,2,3,6,5,1] => 5
[4,2,5,1,3,6] => 5
[4,2,5,1,6,3] => 6
[4,2,5,3,1,6] => 5
[4,2,5,3,6,1] => 6
[4,2,5,6,1,3] => 4
[4,2,5,6,3,1] => 4
[4,2,6,1,3,5] => 5
[4,2,6,1,5,3] => 6
[4,2,6,3,1,5] => 5
[4,2,6,3,5,1] => 6
[4,2,6,5,1,3] => 4
[4,2,6,5,3,1] => 4
[4,3,1,2,5,6] => 4
[4,3,1,2,6,5] => 4
[4,3,1,5,2,6] => 2
[4,3,1,5,6,2] => 3
[4,3,1,6,2,5] => 2
[4,3,1,6,5,2] => 3
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 4
[4,3,2,5,1,6] => 2
[4,3,2,5,6,1] => 3
[4,3,2,6,1,5] => 2
[4,3,2,6,5,1] => 3
[4,3,5,1,2,6] => 4
[4,3,5,1,6,2] => 5
[4,3,5,2,1,6] => 4
[4,3,5,2,6,1] => 5
[4,3,5,6,1,2] => 3
[4,3,5,6,2,1] => 3
[4,3,6,1,2,5] => 4
[4,3,6,1,5,2] => 5
[4,3,6,2,1,5] => 4
[4,3,6,2,5,1] => 5
[4,3,6,5,1,2] => 3
[4,3,6,5,2,1] => 3
[4,5,1,2,3,6] => 3
[4,5,1,2,6,3] => 4
[4,5,1,3,2,6] => 3
[4,5,1,3,6,2] => 4
[4,5,1,6,2,3] => 2
[4,5,1,6,3,2] => 2
[4,5,2,1,3,6] => 3
[4,5,2,1,6,3] => 4
[4,5,2,3,1,6] => 3
[4,5,2,3,6,1] => 4
[4,5,2,6,1,3] => 2
[4,5,2,6,3,1] => 2
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 5
[4,5,3,2,1,6] => 4
[4,5,3,2,6,1] => 5
[4,5,3,6,1,2] => 3
[4,5,3,6,2,1] => 3
[4,5,6,1,2,3] => 4
[4,5,6,1,3,2] => 4
[4,5,6,2,1,3] => 4
[4,5,6,2,3,1] => 4
[4,5,6,3,1,2] => 4
[4,5,6,3,2,1] => 4
[4,6,1,2,3,5] => 3
[4,6,1,2,5,3] => 4
[4,6,1,3,2,5] => 3
[4,6,1,3,5,2] => 4
[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] => 4
[4,6,2,3,1,5] => 3
[4,6,2,3,5,1] => 4
[4,6,2,5,1,3] => 2
[4,6,2,5,3,1] => 2
[4,6,3,1,2,5] => 4
[4,6,3,1,5,2] => 5
[4,6,3,2,1,5] => 4
[4,6,3,2,5,1] => 5
[4,6,3,5,1,2] => 3
[4,6,3,5,2,1] => 3
[4,6,5,1,2,3] => 4
[4,6,5,1,3,2] => 4
[4,6,5,2,1,3] => 4
[4,6,5,2,3,1] => 4
[4,6,5,3,1,2] => 4
[4,6,5,3,2,1] => 4
[5,1,2,3,4,6] => 4
[5,1,2,3,6,4] => 5
[5,1,2,4,3,6] => 4
[5,1,2,4,6,3] => 5
[5,1,2,6,3,4] => 3
[5,1,2,6,4,3] => 3
[5,1,3,2,4,6] => 5
[5,1,3,2,6,4] => 6
[5,1,3,4,2,6] => 5
[5,1,3,4,6,2] => 6
[5,1,3,6,2,4] => 4
[5,1,3,6,4,2] => 4
[5,1,4,2,3,6] => 5
[5,1,4,2,6,3] => 6
[5,1,4,3,2,6] => 5
[5,1,4,3,6,2] => 6
[5,1,4,6,2,3] => 4
[5,1,4,6,3,2] => 4
[5,1,6,2,3,4] => 5
[5,1,6,2,4,3] => 5
[5,1,6,3,2,4] => 5
[5,1,6,3,4,2] => 5
[5,1,6,4,2,3] => 5
[5,1,6,4,3,2] => 5
[5,2,1,3,4,6] => 4
[5,2,1,3,6,4] => 5
[5,2,1,4,3,6] => 4
[5,2,1,4,6,3] => 5
[5,2,1,6,3,4] => 3
[5,2,1,6,4,3] => 3
[5,2,3,1,4,6] => 5
[5,2,3,1,6,4] => 6
[5,2,3,4,1,6] => 5
[5,2,3,4,6,1] => 6
[5,2,3,6,1,4] => 4
[5,2,3,6,4,1] => 4
[5,2,4,1,3,6] => 5
[5,2,4,1,6,3] => 6
[5,2,4,3,1,6] => 5
[5,2,4,3,6,1] => 6
[5,2,4,6,1,3] => 4
[5,2,4,6,3,1] => 4
[5,2,6,1,3,4] => 5
[5,2,6,1,4,3] => 5
[5,2,6,3,1,4] => 5
[5,2,6,3,4,1] => 5
[5,2,6,4,1,3] => 5
[5,2,6,4,3,1] => 5
[5,3,1,2,4,6] => 3
[5,3,1,2,6,4] => 4
[5,3,1,4,2,6] => 3
[5,3,1,4,6,2] => 4
[5,3,1,6,2,4] => 2
[5,3,1,6,4,2] => 2
[5,3,2,1,4,6] => 3
[5,3,2,1,6,4] => 4
[5,3,2,4,1,6] => 3
[5,3,2,4,6,1] => 4
[5,3,2,6,1,4] => 2
[5,3,2,6,4,1] => 2
[5,3,4,1,2,6] => 4
[5,3,4,1,6,2] => 5
[5,3,4,2,1,6] => 4
[5,3,4,2,6,1] => 5
[5,3,4,6,1,2] => 3
[5,3,4,6,2,1] => 3
[5,3,6,1,2,4] => 4
[5,3,6,1,4,2] => 4
[5,3,6,2,1,4] => 4
[5,3,6,2,4,1] => 4
[5,3,6,4,1,2] => 4
[5,3,6,4,2,1] => 4
[5,4,1,2,3,6] => 3
[5,4,1,2,6,3] => 4
[5,4,1,3,2,6] => 3
[5,4,1,3,6,2] => 4
[5,4,1,6,2,3] => 2
[5,4,1,6,3,2] => 2
[5,4,2,1,3,6] => 3
[5,4,2,1,6,3] => 4
[5,4,2,3,1,6] => 3
[5,4,2,3,6,1] => 4
[5,4,2,6,1,3] => 2
[5,4,2,6,3,1] => 2
[5,4,3,1,2,6] => 4
[5,4,3,1,6,2] => 5
[5,4,3,2,1,6] => 4
[5,4,3,2,6,1] => 5
[5,4,3,6,1,2] => 3
[5,4,3,6,2,1] => 3
[5,4,6,1,2,3] => 4
[5,4,6,1,3,2] => 4
[5,4,6,2,1,3] => 4
[5,4,6,2,3,1] => 4
[5,4,6,3,1,2] => 4
[5,4,6,3,2,1] => 4
[5,6,1,2,3,4] => 3
[5,6,1,2,4,3] => 3
[5,6,1,3,2,4] => 3
[5,6,1,3,4,2] => 3
[5,6,1,4,2,3] => 3
[5,6,1,4,3,2] => 3
[5,6,2,1,3,4] => 3
[5,6,2,1,4,3] => 3
[5,6,2,3,1,4] => 3
[5,6,2,3,4,1] => 3
[5,6,2,4,1,3] => 3
[5,6,2,4,3,1] => 3
[5,6,3,1,2,4] => 4
[5,6,3,1,4,2] => 4
[5,6,3,2,1,4] => 4
[5,6,3,2,4,1] => 4
[5,6,3,4,1,2] => 4
[5,6,3,4,2,1] => 4
[5,6,4,1,2,3] => 4
[5,6,4,1,3,2] => 4
[5,6,4,2,1,3] => 4
[5,6,4,2,3,1] => 4
[5,6,4,3,1,2] => 4
[5,6,4,3,2,1] => 4
[6,1,2,3,4,5] => 4
[6,1,2,3,5,4] => 5
[6,1,2,4,3,5] => 4
[6,1,2,4,5,3] => 5
[6,1,2,5,3,4] => 3
[6,1,2,5,4,3] => 3
[6,1,3,2,4,5] => 5
[6,1,3,2,5,4] => 6
[6,1,3,4,2,5] => 5
[6,1,3,4,5,2] => 6
[6,1,3,5,2,4] => 4
[6,1,3,5,4,2] => 4
[6,1,4,2,3,5] => 5
[6,1,4,2,5,3] => 6
[6,1,4,3,2,5] => 5
[6,1,4,3,5,2] => 6
[6,1,4,5,2,3] => 4
[6,1,4,5,3,2] => 4
[6,1,5,2,3,4] => 5
[6,1,5,2,4,3] => 5
[6,1,5,3,2,4] => 5
[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] => 4
[6,2,1,3,5,4] => 5
[6,2,1,4,3,5] => 4
[6,2,1,4,5,3] => 5
[6,2,1,5,3,4] => 3
[6,2,1,5,4,3] => 3
[6,2,3,1,4,5] => 5
[6,2,3,1,5,4] => 6
[6,2,3,4,1,5] => 5
[6,2,3,4,5,1] => 6
[6,2,3,5,1,4] => 4
[6,2,3,5,4,1] => 4
[6,2,4,1,3,5] => 5
[6,2,4,1,5,3] => 6
[6,2,4,3,1,5] => 5
[6,2,4,3,5,1] => 6
[6,2,4,5,1,3] => 4
[6,2,4,5,3,1] => 4
[6,2,5,1,3,4] => 5
[6,2,5,1,4,3] => 5
[6,2,5,3,1,4] => 5
[6,2,5,3,4,1] => 5
[6,2,5,4,1,3] => 5
[6,2,5,4,3,1] => 5
[6,3,1,2,4,5] => 3
[6,3,1,2,5,4] => 4
[6,3,1,4,2,5] => 3
[6,3,1,4,5,2] => 4
[6,3,1,5,2,4] => 2
[6,3,1,5,4,2] => 2
[6,3,2,1,4,5] => 3
[6,3,2,1,5,4] => 4
[6,3,2,4,1,5] => 3
[6,3,2,4,5,1] => 4
[6,3,2,5,1,4] => 2
[6,3,2,5,4,1] => 2
[6,3,4,1,2,5] => 4
[6,3,4,1,5,2] => 5
[6,3,4,2,1,5] => 4
[6,3,4,2,5,1] => 5
[6,3,4,5,1,2] => 3
[6,3,4,5,2,1] => 3
[6,3,5,1,2,4] => 4
[6,3,5,1,4,2] => 4
[6,3,5,2,1,4] => 4
[6,3,5,2,4,1] => 4
[6,3,5,4,1,2] => 4
[6,3,5,4,2,1] => 4
[6,4,1,2,3,5] => 3
[6,4,1,2,5,3] => 4
[6,4,1,3,2,5] => 3
[6,4,1,3,5,2] => 4
[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] => 4
[6,4,2,3,1,5] => 3
[6,4,2,3,5,1] => 4
[6,4,2,5,1,3] => 2
[6,4,2,5,3,1] => 2
[6,4,3,1,2,5] => 4
[6,4,3,1,5,2] => 5
[6,4,3,2,1,5] => 4
[6,4,3,2,5,1] => 5
[6,4,3,5,1,2] => 3
[6,4,3,5,2,1] => 3
[6,4,5,1,2,3] => 4
[6,4,5,1,3,2] => 4
[6,4,5,2,1,3] => 4
[6,4,5,2,3,1] => 4
[6,4,5,3,1,2] => 4
[6,4,5,3,2,1] => 4
[6,5,1,2,3,4] => 3
[6,5,1,2,4,3] => 3
[6,5,1,3,2,4] => 3
[6,5,1,3,4,2] => 3
[6,5,1,4,2,3] => 3
[6,5,1,4,3,2] => 3
[6,5,2,1,3,4] => 3
[6,5,2,1,4,3] => 3
[6,5,2,3,1,4] => 3
[6,5,2,3,4,1] => 3
[6,5,2,4,1,3] => 3
[6,5,2,4,3,1] => 3
[6,5,3,1,2,4] => 4
[6,5,3,1,4,2] => 4
[6,5,3,2,1,4] => 4
[6,5,3,2,4,1] => 4
[6,5,3,4,1,2] => 4
[6,5,3,4,2,1] => 4
[6,5,4,1,2,3] => 4
[6,5,4,1,3,2] => 4
[6,5,4,2,1,3] => 4
[6,5,4,2,3,1] => 4
[6,5,4,3,1,2] => 4
[6,5,4,3,2,1] => 4
[1,2,3,4,5,6,7] => 7
[1,2,3,4,5,7,6] => 5
[1,2,3,4,6,5,7] => 7
[1,2,3,4,6,7,5] => 5
[1,2,3,4,7,5,6] => 6
[1,2,3,4,7,6,5] => 6
[1,2,3,5,4,6,7] => 5
[1,2,3,5,4,7,6] => 3
[1,2,3,5,6,4,7] => 6
[1,2,3,5,6,7,4] => 4
[1,2,3,5,7,4,6] => 5
[1,2,3,5,7,6,4] => 5
[1,2,3,6,4,5,7] => 5
[1,2,3,6,4,7,5] => 3
[1,2,3,6,5,4,7] => 6
[1,2,3,6,5,7,4] => 4
[1,2,3,6,7,4,5] => 5
[1,2,3,6,7,5,4] => 5
[1,2,3,7,4,5,6] => 4
[1,2,3,7,4,6,5] => 4
[1,2,3,7,5,4,6] => 5
[1,2,3,7,5,6,4] => 5
[1,2,3,7,6,4,5] => 5
[1,2,3,7,6,5,4] => 5
[1,2,4,3,5,6,7] => 7
[1,2,4,3,5,7,6] => 5
[1,2,4,3,6,5,7] => 7
[1,2,4,3,6,7,5] => 5
[1,2,4,3,7,5,6] => 6
[1,2,4,3,7,6,5] => 6
[1,2,4,5,3,6,7] => 5
[1,2,4,5,3,7,6] => 3
[1,2,4,5,6,3,7] => 6
[1,2,4,5,6,7,3] => 4
[1,2,4,5,7,3,6] => 5
[1,2,4,5,7,6,3] => 5
[1,2,4,6,3,5,7] => 5
[1,2,4,6,3,7,5] => 3
[1,2,4,6,5,3,7] => 6
[1,2,4,6,5,7,3] => 4
[1,2,4,6,7,3,5] => 5
[1,2,4,6,7,5,3] => 5
[1,2,4,7,3,5,6] => 4
[1,2,4,7,3,6,5] => 4
[1,2,4,7,5,3,6] => 5
[1,2,4,7,5,6,3] => 5
[1,2,4,7,6,3,5] => 5
[1,2,4,7,6,5,3] => 5
[1,2,5,3,4,6,7] => 6
[1,2,5,3,4,7,6] => 4
[1,2,5,3,6,4,7] => 7
[1,2,5,3,6,7,4] => 5
[1,2,5,3,7,4,6] => 6
[1,2,5,3,7,6,4] => 6
[1,2,5,4,3,6,7] => 6
[1,2,5,4,3,7,6] => 4
[1,2,5,4,6,3,7] => 7
[1,2,5,4,6,7,3] => 5
[1,2,5,4,7,3,6] => 6
[1,2,5,4,7,6,3] => 6
[1,2,5,6,3,4,7] => 5
[1,2,5,6,3,7,4] => 3
[1,2,5,6,4,3,7] => 5
[1,2,5,6,4,7,3] => 3
[1,2,5,6,7,3,4] => 5
[1,2,5,6,7,4,3] => 5
[1,2,5,7,3,4,6] => 4
[1,2,5,7,3,6,4] => 4
[1,2,5,7,4,3,6] => 4
[1,2,5,7,4,6,3] => 4
[1,2,5,7,6,3,4] => 5
[1,2,5,7,6,4,3] => 5
[1,2,6,3,4,5,7] => 6
[1,2,6,3,4,7,5] => 4
[1,2,6,3,5,4,7] => 7
[1,2,6,3,5,7,4] => 5
[1,2,6,3,7,4,5] => 6
[1,2,6,3,7,5,4] => 6
[1,2,6,4,3,5,7] => 6
[1,2,6,4,3,7,5] => 4
[1,2,6,4,5,3,7] => 7
[1,2,6,4,5,7,3] => 5
[1,2,6,4,7,3,5] => 6
[1,2,6,4,7,5,3] => 6
[1,2,6,5,3,4,7] => 5
[1,2,6,5,3,7,4] => 3
[1,2,6,5,4,3,7] => 5
[1,2,6,5,4,7,3] => 3
[1,2,6,5,7,3,4] => 5
[1,2,6,5,7,4,3] => 5
[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] => 5
[1,2,6,7,5,4,3] => 5
[1,2,7,3,4,5,6] => 5
[1,2,7,3,4,6,5] => 5
[1,2,7,3,5,4,6] => 6
[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] => 5
[1,2,7,4,3,6,5] => 5
[1,2,7,4,5,3,6] => 6
[1,2,7,4,5,6,3] => 6
[1,2,7,4,6,3,5] => 6
[1,2,7,4,6,5,3] => 6
[1,2,7,5,3,4,6] => 4
[1,2,7,5,3,6,4] => 4
[1,2,7,5,4,3,6] => 4
[1,2,7,5,4,6,3] => 4
[1,2,7,5,6,3,4] => 5
[1,2,7,5,6,4,3] => 5
[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] => 5
[1,2,7,6,5,4,3] => 5
[1,3,2,4,5,6,7] => 5
[1,3,2,4,5,7,6] => 3
[1,3,2,4,6,5,7] => 5
[1,3,2,4,6,7,5] => 3
[1,3,2,4,7,5,6] => 4
[1,3,2,4,7,6,5] => 4
[1,3,2,5,4,6,7] => 3
[1,3,2,5,4,7,6] => 1
[1,3,2,5,6,4,7] => 4
[1,3,2,5,6,7,4] => 2
[1,3,2,5,7,4,6] => 3
[1,3,2,5,7,6,4] => 3
[1,3,2,6,4,5,7] => 3
[1,3,2,6,4,7,5] => 1
[1,3,2,6,5,4,7] => 4
[1,3,2,6,5,7,4] => 2
[1,3,2,6,7,4,5] => 3
[1,3,2,6,7,5,4] => 3
[1,3,2,7,4,5,6] => 2
[1,3,2,7,4,6,5] => 2
[1,3,2,7,5,4,6] => 3
[1,3,2,7,5,6,4] => 3
[1,3,2,7,6,4,5] => 3
[1,3,2,7,6,5,4] => 3
[1,3,4,2,5,6,7] => 6
[1,3,4,2,5,7,6] => 4
[1,3,4,2,6,5,7] => 6
[1,3,4,2,6,7,5] => 4
[1,3,4,2,7,5,6] => 5
[1,3,4,2,7,6,5] => 5
[1,3,4,5,2,6,7] => 4
[1,3,4,5,2,7,6] => 2
[1,3,4,5,6,2,7] => 5
[1,3,4,5,6,7,2] => 3
[1,3,4,5,7,2,6] => 4
[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] => 5
[1,3,4,6,5,7,2] => 3
[1,3,4,6,7,2,5] => 4
[1,3,4,6,7,5,2] => 4
[1,3,4,7,2,5,6] => 3
[1,3,4,7,2,6,5] => 3
[1,3,4,7,5,2,6] => 4
[1,3,4,7,5,6,2] => 4
[1,3,4,7,6,2,5] => 4
[1,3,4,7,6,5,2] => 4
[1,3,5,2,4,6,7] => 5
[1,3,5,2,4,7,6] => 3
[1,3,5,2,6,4,7] => 6
[1,3,5,2,6,7,4] => 4
[1,3,5,2,7,4,6] => 5
[1,3,5,2,7,6,4] => 5
[1,3,5,4,2,6,7] => 5
[1,3,5,4,2,7,6] => 3
[1,3,5,4,6,2,7] => 6
[1,3,5,4,6,7,2] => 4
[1,3,5,4,7,2,6] => 5
[1,3,5,4,7,6,2] => 5
[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] => 4
[1,3,5,6,7,4,2] => 4
[1,3,5,7,2,4,6] => 3
[1,3,5,7,2,6,4] => 3
[1,3,5,7,4,2,6] => 3
[1,3,5,7,4,6,2] => 3
[1,3,5,7,6,2,4] => 4
[1,3,5,7,6,4,2] => 4
[1,3,6,2,4,5,7] => 5
[1,3,6,2,4,7,5] => 3
[1,3,6,2,5,4,7] => 6
[1,3,6,2,5,7,4] => 4
[1,3,6,2,7,4,5] => 5
[1,3,6,2,7,5,4] => 5
[1,3,6,4,2,5,7] => 5
[1,3,6,4,2,7,5] => 3
[1,3,6,4,5,2,7] => 6
[1,3,6,4,5,7,2] => 4
[1,3,6,4,7,2,5] => 5
[1,3,6,4,7,5,2] => 5
[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] => 4
[1,3,6,5,7,4,2] => 4
[1,3,6,7,2,4,5] => 3
[1,3,6,7,2,5,4] => 3
[1,3,6,7,4,2,5] => 3
[1,3,6,7,4,5,2] => 3
[1,3,6,7,5,2,4] => 4
[1,3,6,7,5,4,2] => 4
[1,3,7,2,4,5,6] => 4
[1,3,7,2,4,6,5] => 4
[1,3,7,2,5,4,6] => 5
[1,3,7,2,5,6,4] => 5
[1,3,7,2,6,4,5] => 5
[1,3,7,2,6,5,4] => 5
[1,3,7,4,2,5,6] => 4
[1,3,7,4,2,6,5] => 4
[1,3,7,4,5,2,6] => 5
[1,3,7,4,5,6,2] => 5
[1,3,7,4,6,2,5] => 5
[1,3,7,4,6,5,2] => 5
[1,3,7,5,2,4,6] => 3
[1,3,7,5,2,6,4] => 3
[1,3,7,5,4,2,6] => 3
[1,3,7,5,4,6,2] => 3
[1,3,7,5,6,2,4] => 4
[1,3,7,5,6,4,2] => 4
[1,3,7,6,2,4,5] => 3
[1,3,7,6,2,5,4] => 3
[1,3,7,6,4,2,5] => 3
[1,3,7,6,4,5,2] => 3
[1,3,7,6,5,2,4] => 4
[1,3,7,6,5,4,2] => 4
[1,4,2,3,5,6,7] => 5
[1,4,2,3,5,7,6] => 3
[1,4,2,3,6,5,7] => 5
[1,4,2,3,6,7,5] => 3
[1,4,2,3,7,5,6] => 4
[1,4,2,3,7,6,5] => 4
[1,4,2,5,3,6,7] => 3
[1,4,2,5,3,7,6] => 1
[1,4,2,5,6,3,7] => 4
[1,4,2,5,6,7,3] => 2
[1,4,2,5,7,3,6] => 3
[1,4,2,5,7,6,3] => 3
[1,4,2,6,3,5,7] => 3
[1,4,2,6,3,7,5] => 1
[1,4,2,6,5,3,7] => 4
[1,4,2,6,5,7,3] => 2
[1,4,2,6,7,3,5] => 3
[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] => 3
[1,4,2,7,5,6,3] => 3
[1,4,2,7,6,3,5] => 3
[1,4,2,7,6,5,3] => 3
[1,4,3,2,5,6,7] => 6
[1,4,3,2,5,7,6] => 4
[1,4,3,2,6,5,7] => 6
[1,4,3,2,6,7,5] => 4
[1,4,3,2,7,5,6] => 5
[1,4,3,2,7,6,5] => 5
[1,4,3,5,2,6,7] => 4
[1,4,3,5,2,7,6] => 2
[1,4,3,5,6,2,7] => 5
[1,4,3,5,6,7,2] => 3
[1,4,3,5,7,2,6] => 4
[1,4,3,5,7,6,2] => 4
[1,4,3,6,2,5,7] => 4
[1,4,3,6,2,7,5] => 2
[1,4,3,6,5,2,7] => 5
[1,4,3,6,5,7,2] => 3
[1,4,3,6,7,2,5] => 4
[1,4,3,6,7,5,2] => 4
[1,4,3,7,2,5,6] => 3
[1,4,3,7,2,6,5] => 3
[1,4,3,7,5,2,6] => 4
[1,4,3,7,5,6,2] => 4
[1,4,3,7,6,2,5] => 4
[1,4,3,7,6,5,2] => 4
[1,4,5,2,3,6,7] => 5
[1,4,5,2,3,7,6] => 3
[1,4,5,2,6,3,7] => 6
[1,4,5,2,6,7,3] => 4
[1,4,5,2,7,3,6] => 5
[1,4,5,2,7,6,3] => 5
[1,4,5,3,2,6,7] => 5
[1,4,5,3,2,7,6] => 3
[1,4,5,3,6,2,7] => 6
[1,4,5,3,6,7,2] => 4
[1,4,5,3,7,2,6] => 5
[1,4,5,3,7,6,2] => 5
[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] => 4
[1,4,5,6,7,3,2] => 4
[1,4,5,7,2,3,6] => 3
[1,4,5,7,2,6,3] => 3
[1,4,5,7,3,2,6] => 3
[1,4,5,7,3,6,2] => 3
[1,4,5,7,6,2,3] => 4
[1,4,5,7,6,3,2] => 4
[1,4,6,2,3,5,7] => 5
[1,4,6,2,3,7,5] => 3
[1,4,6,2,5,3,7] => 6
[1,4,6,2,5,7,3] => 4
[1,4,6,2,7,3,5] => 5
[1,4,6,2,7,5,3] => 5
[1,4,6,3,2,5,7] => 5
[1,4,6,3,2,7,5] => 3
[1,4,6,3,5,2,7] => 6
[1,4,6,3,5,7,2] => 4
[1,4,6,3,7,2,5] => 5
[1,4,6,3,7,5,2] => 5
[1,4,6,5,2,3,7] => 4
[1,4,6,5,2,7,3] => 2
[1,4,6,5,3,2,7] => 4
click to show generating function       
Description
The number of even deficiencies and of odd exceedences.
For a permutation $\sigma$, this is the number of indices $i$ such that $\sigma(i) \leq i$ if $i$ is even and $\sigma(i) \geq i$ if $i$ is odd.
According to [1], $\sigma$ is a D-permutation if all indices have this property and the coefficients of the characteristic polynomial of the homogenized linial arrangement are given by the number of D-permutations with a given number of cycles.
References
[1] Alexander Lazar and Michelle L. Wachs - On the homogenized linial arrangement: intersection lattice and Genocchi numbers http://fpsac2019.fmf.uni-lj.si/resources/Proceedings/169.pdf
Code
def statistic(pi):
    return sum(1 for i in [1 .. len(pi)] if ( pi(i) <= i if is_even(i) else pi(i) >= i))
Created
Jul 02, 2019 at 10:51 by Christian Stump
Updated
Jul 02, 2019 at 10:51 by Christian Stump