Identifier
Identifier
Values
[1] => 2
[1,2] => 3
[2,1] => 1
[1,2,3] => 4
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 2
[1,2,3,4] => 5
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 3
[2,1,3,4] => 3
[2,1,4,3] => 1
[2,3,1,4] => 3
[2,3,4,1] => 3
[2,4,1,3] => 1
[2,4,3,1] => 1
[3,1,2,4] => 3
[3,1,4,2] => 1
[3,2,1,4] => 3
[3,2,4,1] => 1
[3,4,1,2] => 3
[3,4,2,1] => 3
[4,1,2,3] => 3
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 3
[4,3,1,2] => 3
[4,3,2,1] => 1
[1,2,3,4,5] => 6
[1,2,3,5,4] => 4
[1,2,4,3,5] => 4
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 4
[1,3,2,4,5] => 4
[1,3,2,5,4] => 2
[1,3,4,2,5] => 4
[1,3,4,5,2] => 4
[1,3,5,2,4] => 2
[1,3,5,4,2] => 2
[1,4,2,3,5] => 4
[1,4,2,5,3] => 2
[1,4,3,2,5] => 4
[1,4,3,5,2] => 2
[1,4,5,2,3] => 4
[1,4,5,3,2] => 4
[1,5,2,3,4] => 4
[1,5,2,4,3] => 2
[1,5,3,2,4] => 2
[1,5,3,4,2] => 4
[1,5,4,2,3] => 4
[1,5,4,3,2] => 2
[2,1,3,4,5] => 4
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 2
[2,1,5,3,4] => 2
[2,1,5,4,3] => 2
[2,3,1,4,5] => 4
[2,3,1,5,4] => 2
[2,3,4,1,5] => 4
[2,3,4,5,1] => 4
[2,3,5,1,4] => 2
[2,3,5,4,1] => 2
[2,4,1,3,5] => 2
[2,4,1,5,3] => 2
[2,4,3,1,5] => 2
[2,4,3,5,1] => 2
[2,4,5,1,3] => 2
[2,4,5,3,1] => 2
[2,5,1,3,4] => 2
[2,5,1,4,3] => 2
[2,5,3,1,4] => 2
[2,5,3,4,1] => 2
[2,5,4,1,3] => 2
[2,5,4,3,1] => 2
[3,1,2,4,5] => 4
[3,1,2,5,4] => 2
[3,1,4,2,5] => 2
[3,1,4,5,2] => 2
[3,1,5,2,4] => 2
[3,1,5,4,2] => 2
[3,2,1,4,5] => 4
[3,2,1,5,4] => 2
[3,2,4,1,5] => 2
[3,2,4,5,1] => 2
[3,2,5,1,4] => 2
[3,2,5,4,1] => 2
[3,4,1,2,5] => 4
[3,4,1,5,2] => 2
[3,4,2,1,5] => 4
[3,4,2,5,1] => 2
[3,4,5,1,2] => 4
[3,4,5,2,1] => 4
[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] => 2
[3,5,4,2,1] => 2
[4,1,2,3,5] => 4
[4,1,2,5,3] => 2
[4,1,3,2,5] => 2
[4,1,3,5,2] => 2
[4,1,5,2,3] => 2
[4,1,5,3,2] => 2
[4,2,1,3,5] => 2
[4,2,1,5,3] => 2
[4,2,3,1,5] => 4
[4,2,3,5,1] => 2
[4,2,5,1,3] => 2
[4,2,5,3,1] => 2
[4,3,1,2,5] => 4
[4,3,1,5,2] => 2
[4,3,2,1,5] => 2
[4,3,2,5,1] => 2
[4,3,5,1,2] => 2
[4,3,5,2,1] => 2
[4,5,1,2,3] => 4
[4,5,1,3,2] => 2
[4,5,2,1,3] => 2
[4,5,2,3,1] => 4
[4,5,3,1,2] => 4
[4,5,3,2,1] => 2
[5,1,2,3,4] => 4
[5,1,2,4,3] => 2
[5,1,3,2,4] => 2
[5,1,3,4,2] => 2
[5,1,4,2,3] => 2
[5,1,4,3,2] => 2
[5,2,1,3,4] => 2
[5,2,1,4,3] => 2
[5,2,3,1,4] => 2
[5,2,3,4,1] => 4
[5,2,4,1,3] => 2
[5,2,4,3,1] => 2
[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] => 4
[5,3,4,2,1] => 2
[5,4,1,2,3] => 4
[5,4,1,3,2] => 2
[5,4,2,1,3] => 2
[5,4,2,3,1] => 2
[5,4,3,1,2] => 2
[5,4,3,2,1] => 2
[1,2,3,4,5,6] => 7
[1,2,3,4,6,5] => 5
[1,2,3,5,4,6] => 5
[1,2,3,5,6,4] => 5
[1,2,3,6,4,5] => 5
[1,2,3,6,5,4] => 5
[1,2,4,3,5,6] => 5
[1,2,4,3,6,5] => 3
[1,2,4,5,3,6] => 5
[1,2,4,5,6,3] => 5
[1,2,4,6,3,5] => 3
[1,2,4,6,5,3] => 3
[1,2,5,3,4,6] => 5
[1,2,5,3,6,4] => 3
[1,2,5,4,3,6] => 5
[1,2,5,4,6,3] => 3
[1,2,5,6,3,4] => 5
[1,2,5,6,4,3] => 5
[1,2,6,3,4,5] => 5
[1,2,6,3,5,4] => 3
[1,2,6,4,3,5] => 3
[1,2,6,4,5,3] => 5
[1,2,6,5,3,4] => 5
[1,2,6,5,4,3] => 3
[1,3,2,4,5,6] => 5
[1,3,2,4,6,5] => 3
[1,3,2,5,4,6] => 3
[1,3,2,5,6,4] => 3
[1,3,2,6,4,5] => 3
[1,3,2,6,5,4] => 3
[1,3,4,2,5,6] => 5
[1,3,4,2,6,5] => 3
[1,3,4,5,2,6] => 5
[1,3,4,5,6,2] => 5
[1,3,4,6,2,5] => 3
[1,3,4,6,5,2] => 3
[1,3,5,2,4,6] => 3
[1,3,5,2,6,4] => 3
[1,3,5,4,2,6] => 3
[1,3,5,4,6,2] => 3
[1,3,5,6,2,4] => 3
[1,3,5,6,4,2] => 3
[1,3,6,2,4,5] => 3
[1,3,6,2,5,4] => 3
[1,3,6,4,2,5] => 3
[1,3,6,4,5,2] => 3
[1,3,6,5,2,4] => 3
[1,3,6,5,4,2] => 3
[1,4,2,3,5,6] => 5
[1,4,2,3,6,5] => 3
[1,4,2,5,3,6] => 3
[1,4,2,5,6,3] => 3
[1,4,2,6,3,5] => 3
[1,4,2,6,5,3] => 3
[1,4,3,2,5,6] => 5
[1,4,3,2,6,5] => 3
[1,4,3,5,2,6] => 3
[1,4,3,5,6,2] => 3
[1,4,3,6,2,5] => 3
[1,4,3,6,5,2] => 3
[1,4,5,2,3,6] => 5
[1,4,5,2,6,3] => 3
[1,4,5,3,2,6] => 5
[1,4,5,3,6,2] => 3
[1,4,5,6,2,3] => 5
[1,4,5,6,3,2] => 5
[1,4,6,2,3,5] => 3
[1,4,6,2,5,3] => 3
[1,4,6,3,2,5] => 3
[1,4,6,3,5,2] => 3
[1,4,6,5,2,3] => 3
[1,4,6,5,3,2] => 3
[1,5,2,3,4,6] => 5
[1,5,2,3,6,4] => 3
[1,5,2,4,3,6] => 3
[1,5,2,4,6,3] => 3
[1,5,2,6,3,4] => 3
[1,5,2,6,4,3] => 3
[1,5,3,2,4,6] => 3
[1,5,3,2,6,4] => 3
[1,5,3,4,2,6] => 5
[1,5,3,4,6,2] => 3
[1,5,3,6,2,4] => 3
[1,5,3,6,4,2] => 3
[1,5,4,2,3,6] => 5
[1,5,4,2,6,3] => 3
[1,5,4,3,2,6] => 3
[1,5,4,3,6,2] => 3
[1,5,4,6,2,3] => 3
[1,5,4,6,3,2] => 3
[1,5,6,2,3,4] => 5
[1,5,6,2,4,3] => 3
[1,5,6,3,2,4] => 3
[1,5,6,3,4,2] => 5
[1,5,6,4,2,3] => 5
[1,5,6,4,3,2] => 3
[1,6,2,3,4,5] => 5
[1,6,2,3,5,4] => 3
[1,6,2,4,3,5] => 3
[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] => 3
[1,6,3,2,5,4] => 3
[1,6,3,4,2,5] => 3
[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] => 3
[1,6,4,2,5,3] => 3
[1,6,4,3,2,5] => 3
[1,6,4,3,5,2] => 3
[1,6,4,5,2,3] => 5
[1,6,4,5,3,2] => 3
[1,6,5,2,3,4] => 5
[1,6,5,2,4,3] => 3
[1,6,5,3,2,4] => 3
[1,6,5,3,4,2] => 3
[1,6,5,4,2,3] => 3
[1,6,5,4,3,2] => 3
[2,1,3,4,5,6] => 5
[2,1,3,4,6,5] => 3
[2,1,3,5,4,6] => 3
[2,1,3,5,6,4] => 3
[2,1,3,6,4,5] => 3
[2,1,3,6,5,4] => 3
[2,1,4,3,5,6] => 3
[2,1,4,3,6,5] => 1
[2,1,4,5,3,6] => 3
[2,1,4,5,6,3] => 3
[2,1,4,6,3,5] => 1
[2,1,4,6,5,3] => 1
[2,1,5,3,4,6] => 3
[2,1,5,3,6,4] => 1
[2,1,5,4,3,6] => 3
[2,1,5,4,6,3] => 1
[2,1,5,6,3,4] => 3
[2,1,5,6,4,3] => 3
[2,1,6,3,4,5] => 3
[2,1,6,3,5,4] => 1
[2,1,6,4,3,5] => 1
[2,1,6,4,5,3] => 3
[2,1,6,5,3,4] => 3
[2,1,6,5,4,3] => 1
[2,3,1,4,5,6] => 5
[2,3,1,4,6,5] => 3
[2,3,1,5,4,6] => 3
[2,3,1,5,6,4] => 3
[2,3,1,6,4,5] => 3
[2,3,1,6,5,4] => 3
[2,3,4,1,5,6] => 5
[2,3,4,1,6,5] => 3
[2,3,4,5,1,6] => 5
[2,3,4,5,6,1] => 5
[2,3,4,6,1,5] => 3
[2,3,4,6,5,1] => 3
[2,3,5,1,4,6] => 3
[2,3,5,1,6,4] => 3
[2,3,5,4,1,6] => 3
[2,3,5,4,6,1] => 3
[2,3,5,6,1,4] => 3
[2,3,5,6,4,1] => 3
[2,3,6,1,4,5] => 3
[2,3,6,1,5,4] => 3
[2,3,6,4,1,5] => 3
[2,3,6,4,5,1] => 3
[2,3,6,5,1,4] => 3
[2,3,6,5,4,1] => 3
[2,4,1,3,5,6] => 3
[2,4,1,3,6,5] => 1
[2,4,1,5,3,6] => 3
[2,4,1,5,6,3] => 3
[2,4,1,6,3,5] => 1
[2,4,1,6,5,3] => 1
[2,4,3,1,5,6] => 3
[2,4,3,1,6,5] => 1
[2,4,3,5,1,6] => 3
[2,4,3,5,6,1] => 3
[2,4,3,6,1,5] => 1
[2,4,3,6,5,1] => 1
[2,4,5,1,3,6] => 3
[2,4,5,1,6,3] => 3
[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] => 1
[2,4,6,5,3,1] => 1
[2,5,1,3,4,6] => 3
[2,5,1,3,6,4] => 1
[2,5,1,4,3,6] => 3
[2,5,1,4,6,3] => 1
[2,5,1,6,3,4] => 3
[2,5,1,6,4,3] => 3
[2,5,3,1,4,6] => 3
[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] => 3
[2,5,4,1,6,3] => 1
[2,5,4,3,1,6] => 3
[2,5,4,3,6,1] => 3
[2,5,4,6,1,3] => 1
[2,5,4,6,3,1] => 1
[2,5,6,1,3,4] => 3
[2,5,6,1,4,3] => 3
[2,5,6,3,1,4] => 3
[2,5,6,3,4,1] => 3
[2,5,6,4,1,3] => 3
[2,5,6,4,3,1] => 3
[2,6,1,3,4,5] => 3
[2,6,1,3,5,4] => 1
[2,6,1,4,3,5] => 1
[2,6,1,4,5,3] => 3
[2,6,1,5,3,4] => 3
[2,6,1,5,4,3] => 1
[2,6,3,1,4,5] => 3
[2,6,3,1,5,4] => 1
[2,6,3,4,1,5] => 3
[2,6,3,4,5,1] => 3
[2,6,3,5,1,4] => 1
[2,6,3,5,4,1] => 1
[2,6,4,1,3,5] => 1
[2,6,4,1,5,3] => 3
[2,6,4,3,1,5] => 1
[2,6,4,3,5,1] => 1
[2,6,4,5,1,3] => 3
[2,6,4,5,3,1] => 3
[2,6,5,1,3,4] => 3
[2,6,5,1,4,3] => 1
[2,6,5,3,1,4] => 3
[2,6,5,3,4,1] => 3
[2,6,5,4,1,3] => 1
[2,6,5,4,3,1] => 1
[3,1,2,4,5,6] => 5
[3,1,2,4,6,5] => 3
[3,1,2,5,4,6] => 3
[3,1,2,5,6,4] => 3
[3,1,2,6,4,5] => 3
[3,1,2,6,5,4] => 3
[3,1,4,2,5,6] => 3
[3,1,4,2,6,5] => 1
[3,1,4,5,2,6] => 3
[3,1,4,5,6,2] => 3
[3,1,4,6,2,5] => 1
[3,1,4,6,5,2] => 1
[3,1,5,2,4,6] => 3
[3,1,5,2,6,4] => 1
[3,1,5,4,2,6] => 3
[3,1,5,4,6,2] => 1
[3,1,5,6,2,4] => 3
[3,1,5,6,4,2] => 3
[3,1,6,2,4,5] => 3
[3,1,6,2,5,4] => 1
[3,1,6,4,2,5] => 1
[3,1,6,4,5,2] => 3
[3,1,6,5,2,4] => 3
[3,1,6,5,4,2] => 1
[3,2,1,4,5,6] => 5
[3,2,1,4,6,5] => 3
[3,2,1,5,4,6] => 3
[3,2,1,5,6,4] => 3
[3,2,1,6,4,5] => 3
[3,2,1,6,5,4] => 3
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 1
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 3
[3,2,4,6,1,5] => 1
[3,2,4,6,5,1] => 1
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 1
[3,2,5,4,1,6] => 3
[3,2,5,4,6,1] => 1
[3,2,5,6,1,4] => 3
[3,2,5,6,4,1] => 3
[3,2,6,1,4,5] => 3
[3,2,6,1,5,4] => 1
[3,2,6,4,1,5] => 1
[3,2,6,4,5,1] => 3
[3,2,6,5,1,4] => 3
[3,2,6,5,4,1] => 1
[3,4,1,2,5,6] => 5
[3,4,1,2,6,5] => 3
[3,4,1,5,2,6] => 3
[3,4,1,5,6,2] => 3
[3,4,1,6,2,5] => 3
[3,4,1,6,5,2] => 3
[3,4,2,1,5,6] => 5
[3,4,2,1,6,5] => 3
[3,4,2,5,1,6] => 3
[3,4,2,5,6,1] => 3
[3,4,2,6,1,5] => 3
[3,4,2,6,5,1] => 3
[3,4,5,1,2,6] => 5
[3,4,5,1,6,2] => 3
[3,4,5,2,1,6] => 5
[3,4,5,2,6,1] => 3
[3,4,5,6,1,2] => 5
[3,4,5,6,2,1] => 5
[3,4,6,1,2,5] => 3
[3,4,6,1,5,2] => 3
[3,4,6,2,1,5] => 3
[3,4,6,2,5,1] => 3
[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] => 3
[3,5,1,4,2,6] => 3
[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] => 3
[3,5,2,1,6,4] => 3
[3,5,2,4,1,6] => 3
[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] => 3
[3,5,4,1,6,2] => 1
[3,5,4,2,1,6] => 3
[3,5,4,2,6,1] => 1
[3,5,4,6,1,2] => 3
[3,5,4,6,2,1] => 3
[3,5,6,1,2,4] => 3
[3,5,6,1,4,2] => 3
[3,5,6,2,1,4] => 3
[3,5,6,2,4,1] => 3
[3,5,6,4,1,2] => 3
[3,5,6,4,2,1] => 3
[3,6,1,2,4,5] => 3
[3,6,1,2,5,4] => 3
[3,6,1,4,2,5] => 1
[3,6,1,4,5,2] => 3
[3,6,1,5,2,4] => 1
[3,6,1,5,4,2] => 3
[3,6,2,1,4,5] => 3
[3,6,2,1,5,4] => 3
[3,6,2,4,1,5] => 1
[3,6,2,4,5,1] => 3
[3,6,2,5,1,4] => 1
[3,6,2,5,4,1] => 3
[3,6,4,1,2,5] => 3
[3,6,4,1,5,2] => 1
[3,6,4,2,1,5] => 3
[3,6,4,2,5,1] => 1
[3,6,4,5,1,2] => 3
[3,6,4,5,2,1] => 3
[3,6,5,1,2,4] => 3
[3,6,5,1,4,2] => 1
[3,6,5,2,1,4] => 3
[3,6,5,2,4,1] => 1
[3,6,5,4,1,2] => 3
[3,6,5,4,2,1] => 3
[4,1,2,3,5,6] => 5
[4,1,2,3,6,5] => 3
[4,1,2,5,3,6] => 3
[4,1,2,5,6,3] => 3
[4,1,2,6,3,5] => 3
[4,1,2,6,5,3] => 3
[4,1,3,2,5,6] => 3
[4,1,3,2,6,5] => 1
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 3
[4,1,3,6,2,5] => 1
[4,1,3,6,5,2] => 1
[4,1,5,2,3,6] => 3
[4,1,5,2,6,3] => 1
[4,1,5,3,2,6] => 3
[4,1,5,3,6,2] => 1
[4,1,5,6,2,3] => 3
[4,1,5,6,3,2] => 3
[4,1,6,2,3,5] => 3
[4,1,6,2,5,3] => 1
[4,1,6,3,2,5] => 1
[4,1,6,3,5,2] => 3
[4,1,6,5,2,3] => 3
[4,1,6,5,3,2] => 1
[4,2,1,3,5,6] => 3
[4,2,1,3,6,5] => 1
[4,2,1,5,3,6] => 3
[4,2,1,5,6,3] => 3
[4,2,1,6,3,5] => 1
[4,2,1,6,5,3] => 1
[4,2,3,1,5,6] => 5
[4,2,3,1,6,5] => 3
[4,2,3,5,1,6] => 3
[4,2,3,5,6,1] => 3
[4,2,3,6,1,5] => 3
[4,2,3,6,5,1] => 3
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 1
[4,2,5,3,1,6] => 3
[4,2,5,3,6,1] => 1
[4,2,5,6,1,3] => 3
[4,2,5,6,3,1] => 3
[4,2,6,1,3,5] => 1
[4,2,6,1,5,3] => 3
[4,2,6,3,1,5] => 3
[4,2,6,3,5,1] => 1
[4,2,6,5,1,3] => 1
[4,2,6,5,3,1] => 3
[4,3,1,2,5,6] => 5
[4,3,1,2,6,5] => 3
[4,3,1,5,2,6] => 3
[4,3,1,5,6,2] => 3
[4,3,1,6,2,5] => 3
[4,3,1,6,5,2] => 3
[4,3,2,1,5,6] => 3
[4,3,2,1,6,5] => 1
[4,3,2,5,1,6] => 3
[4,3,2,5,6,1] => 3
[4,3,2,6,1,5] => 1
[4,3,2,6,5,1] => 1
[4,3,5,1,2,6] => 3
[4,3,5,1,6,2] => 1
[4,3,5,2,1,6] => 3
[4,3,5,2,6,1] => 1
[4,3,5,6,1,2] => 3
[4,3,5,6,2,1] => 3
[4,3,6,1,2,5] => 3
[4,3,6,1,5,2] => 1
[4,3,6,2,1,5] => 1
[4,3,6,2,5,1] => 3
[4,3,6,5,1,2] => 3
[4,3,6,5,2,1] => 1
[4,5,1,2,3,6] => 5
[4,5,1,2,6,3] => 3
[4,5,1,3,2,6] => 3
[4,5,1,3,6,2] => 3
[4,5,1,6,2,3] => 3
[4,5,1,6,3,2] => 3
[4,5,2,1,3,6] => 3
[4,5,2,1,6,3] => 3
[4,5,2,3,1,6] => 5
[4,5,2,3,6,1] => 3
[4,5,2,6,1,3] => 3
[4,5,2,6,3,1] => 3
[4,5,3,1,2,6] => 5
[4,5,3,1,6,2] => 3
[4,5,3,2,1,6] => 3
[4,5,3,2,6,1] => 3
[4,5,3,6,1,2] => 3
[4,5,3,6,2,1] => 3
[4,5,6,1,2,3] => 5
[4,5,6,1,3,2] => 3
[4,5,6,2,1,3] => 3
[4,5,6,2,3,1] => 5
[4,5,6,3,1,2] => 5
[4,5,6,3,2,1] => 3
[4,6,1,2,3,5] => 3
[4,6,1,2,5,3] => 3
[4,6,1,3,2,5] => 1
[4,6,1,3,5,2] => 1
[4,6,1,5,2,3] => 3
[4,6,1,5,3,2] => 1
[4,6,2,1,3,5] => 1
[4,6,2,1,5,3] => 1
[4,6,2,3,1,5] => 3
[4,6,2,3,5,1] => 3
[4,6,2,5,1,3] => 1
[4,6,2,5,3,1] => 3
[4,6,3,1,2,5] => 3
[4,6,3,1,5,2] => 3
[4,6,3,2,1,5] => 1
[4,6,3,2,5,1] => 1
[4,6,3,5,1,2] => 3
[4,6,3,5,2,1] => 1
[4,6,5,1,2,3] => 3
[4,6,5,1,3,2] => 1
[4,6,5,2,1,3] => 1
[4,6,5,2,3,1] => 3
[4,6,5,3,1,2] => 3
[4,6,5,3,2,1] => 1
[5,1,2,3,4,6] => 5
[5,1,2,3,6,4] => 3
[5,1,2,4,3,6] => 3
[5,1,2,4,6,3] => 3
[5,1,2,6,3,4] => 3
[5,1,2,6,4,3] => 3
[5,1,3,2,4,6] => 3
[5,1,3,2,6,4] => 1
[5,1,3,4,2,6] => 3
[5,1,3,4,6,2] => 3
[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] => 1
[5,1,4,6,2,3] => 3
[5,1,4,6,3,2] => 3
[5,1,6,2,3,4] => 3
[5,1,6,2,4,3] => 1
[5,1,6,3,2,4] => 1
[5,1,6,3,4,2] => 3
[5,1,6,4,2,3] => 3
[5,1,6,4,3,2] => 1
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 1
[5,2,1,4,3,6] => 3
[5,2,1,4,6,3] => 1
[5,2,1,6,3,4] => 3
[5,2,1,6,4,3] => 3
[5,2,3,1,4,6] => 3
[5,2,3,1,6,4] => 3
[5,2,3,4,1,6] => 5
[5,2,3,4,6,1] => 3
[5,2,3,6,1,4] => 3
[5,2,3,6,4,1] => 3
[5,2,4,1,3,6] => 3
[5,2,4,1,6,3] => 3
[5,2,4,3,1,6] => 3
[5,2,4,3,6,1] => 1
[5,2,4,6,1,3] => 1
[5,2,4,6,3,1] => 1
[5,2,6,1,3,4] => 3
[5,2,6,1,4,3] => 1
[5,2,6,3,1,4] => 1
[5,2,6,3,4,1] => 3
[5,2,6,4,1,3] => 3
[5,2,6,4,3,1] => 1
[5,3,1,2,4,6] => 3
[5,3,1,2,6,4] => 3
[5,3,1,4,2,6] => 3
[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] => 1
[5,3,2,4,1,6] => 3
[5,3,2,4,6,1] => 1
[5,3,2,6,1,4] => 3
[5,3,2,6,4,1] => 3
[5,3,4,1,2,6] => 5
[5,3,4,1,6,2] => 3
[5,3,4,2,1,6] => 3
[5,3,4,2,6,1] => 3
[5,3,4,6,1,2] => 3
[5,3,4,6,2,1] => 3
[5,3,6,1,2,4] => 3
[5,3,6,1,4,2] => 1
[5,3,6,2,1,4] => 1
[5,3,6,2,4,1] => 3
[5,3,6,4,1,2] => 3
[5,3,6,4,2,1] => 1
[5,4,1,2,3,6] => 5
[5,4,1,2,6,3] => 3
[5,4,1,3,2,6] => 3
[5,4,1,3,6,2] => 3
[5,4,1,6,2,3] => 3
[5,4,1,6,3,2] => 3
[5,4,2,1,3,6] => 3
[5,4,2,1,6,3] => 1
[5,4,2,3,1,6] => 3
[5,4,2,3,6,1] => 3
[5,4,2,6,1,3] => 1
[5,4,2,6,3,1] => 1
[5,4,3,1,2,6] => 3
[5,4,3,1,6,2] => 1
[5,4,3,2,1,6] => 3
[5,4,3,2,6,1] => 1
[5,4,3,6,1,2] => 3
[5,4,3,6,2,1] => 3
[5,4,6,1,2,3] => 3
[5,4,6,1,3,2] => 1
[5,4,6,2,1,3] => 1
[5,4,6,2,3,1] => 3
[5,4,6,3,1,2] => 3
[5,4,6,3,2,1] => 1
[5,6,1,2,3,4] => 5
[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] => 5
[5,6,2,4,1,3] => 3
[5,6,2,4,3,1] => 3
[5,6,3,1,2,4] => 3
[5,6,3,1,4,2] => 3
[5,6,3,2,1,4] => 3
[5,6,3,2,4,1] => 3
[5,6,3,4,1,2] => 5
[5,6,3,4,2,1] => 3
[5,6,4,1,2,3] => 5
[5,6,4,1,3,2] => 3
[5,6,4,2,1,3] => 3
[5,6,4,2,3,1] => 3
[5,6,4,3,1,2] => 3
[5,6,4,3,2,1] => 3
[6,1,2,3,4,5] => 5
[6,1,2,3,5,4] => 3
[6,1,2,4,3,5] => 3
[6,1,2,4,5,3] => 3
[6,1,2,5,3,4] => 3
[6,1,2,5,4,3] => 3
[6,1,3,2,4,5] => 3
[6,1,3,2,5,4] => 1
[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] => 1
[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] => 1
[6,1,4,5,2,3] => 3
[6,1,4,5,3,2] => 3
[6,1,5,2,3,4] => 3
[6,1,5,2,4,3] => 1
[6,1,5,3,2,4] => 1
[6,1,5,3,4,2] => 3
[6,1,5,4,2,3] => 3
[6,1,5,4,3,2] => 1
[6,2,1,3,4,5] => 3
[6,2,1,3,5,4] => 1
[6,2,1,4,3,5] => 1
[6,2,1,4,5,3] => 3
[6,2,1,5,3,4] => 3
[6,2,1,5,4,3] => 1
[6,2,3,1,4,5] => 3
[6,2,3,1,5,4] => 3
[6,2,3,4,1,5] => 3
[6,2,3,4,5,1] => 5
[6,2,3,5,1,4] => 3
[6,2,3,5,4,1] => 3
[6,2,4,1,3,5] => 1
[6,2,4,1,5,3] => 1
[6,2,4,3,1,5] => 1
[6,2,4,3,5,1] => 3
[6,2,4,5,1,3] => 3
[6,2,4,5,3,1] => 3
[6,2,5,1,3,4] => 3
[6,2,5,1,4,3] => 3
[6,2,5,3,1,4] => 1
[6,2,5,3,4,1] => 3
[6,2,5,4,1,3] => 1
[6,2,5,4,3,1] => 3
[6,3,1,2,4,5] => 3
[6,3,1,2,5,4] => 3
[6,3,1,4,2,5] => 1
[6,3,1,4,5,2] => 3
[6,3,1,5,2,4] => 1
[6,3,1,5,4,2] => 3
[6,3,2,1,4,5] => 3
[6,3,2,1,5,4] => 1
[6,3,2,4,1,5] => 1
[6,3,2,4,5,1] => 3
[6,3,2,5,1,4] => 3
[6,3,2,5,4,1] => 1
[6,3,4,1,2,5] => 3
[6,3,4,1,5,2] => 3
[6,3,4,2,1,5] => 3
[6,3,4,2,5,1] => 3
[6,3,4,5,1,2] => 5
[6,3,4,5,2,1] => 3
[6,3,5,1,2,4] => 3
[6,3,5,1,4,2] => 3
[6,3,5,2,1,4] => 1
[6,3,5,2,4,1] => 1
[6,3,5,4,1,2] => 3
[6,3,5,4,2,1] => 1
[6,4,1,2,3,5] => 3
[6,4,1,2,5,3] => 3
[6,4,1,3,2,5] => 1
[6,4,1,3,5,2] => 1
[6,4,1,5,2,3] => 3
[6,4,1,5,3,2] => 1
[6,4,2,1,3,5] => 1
[6,4,2,1,5,3] => 3
[6,4,2,3,1,5] => 3
[6,4,2,3,5,1] => 3
[6,4,2,5,1,3] => 3
[6,4,2,5,3,1] => 1
[6,4,3,1,2,5] => 3
[6,4,3,1,5,2] => 1
[6,4,3,2,1,5] => 1
[6,4,3,2,5,1] => 3
[6,4,3,5,1,2] => 3
[6,4,3,5,2,1] => 1
[6,4,5,1,2,3] => 5
[6,4,5,1,3,2] => 3
[6,4,5,2,1,3] => 3
[6,4,5,2,3,1] => 3
[6,4,5,3,1,2] => 3
[6,4,5,3,2,1] => 3
[6,5,1,2,3,4] => 5
[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] => 1
[6,5,2,3,1,4] => 3
[6,5,2,3,4,1] => 3
[6,5,2,4,1,3] => 1
[6,5,2,4,3,1] => 1
[6,5,3,1,2,4] => 3
[6,5,3,1,4,2] => 1
[6,5,3,2,1,4] => 3
[6,5,3,2,4,1] => 1
[6,5,3,4,1,2] => 3
[6,5,3,4,2,1] => 3
[6,5,4,1,2,3] => 3
[6,5,4,1,3,2] => 1
[6,5,4,2,1,3] => 1
[6,5,4,2,3,1] => 3
[6,5,4,3,1,2] => 3
[6,5,4,3,2,1] => 1
[1,2,3,4,5,6,7] => 8
[1,2,3,4,5,7,6] => 6
[1,2,3,4,6,5,7] => 6
[1,2,3,4,6,7,5] => 6
[1,2,3,4,7,5,6] => 6
[1,2,3,4,7,6,5] => 6
[1,2,3,5,4,6,7] => 6
[1,2,3,5,4,7,6] => 4
[1,2,3,5,6,4,7] => 6
[1,2,3,5,6,7,4] => 6
[1,2,3,5,7,4,6] => 4
[1,2,3,5,7,6,4] => 4
[1,2,3,6,4,5,7] => 6
[1,2,3,6,4,7,5] => 4
[1,2,3,6,5,4,7] => 6
[1,2,3,6,5,7,4] => 4
[1,2,3,6,7,4,5] => 6
[1,2,3,6,7,5,4] => 6
[1,2,3,7,4,5,6] => 6
[1,2,3,7,4,6,5] => 4
[1,2,3,7,5,4,6] => 4
[1,2,3,7,5,6,4] => 6
[1,2,3,7,6,4,5] => 6
[1,2,3,7,6,5,4] => 4
[1,2,4,3,5,6,7] => 6
[1,2,4,3,5,7,6] => 4
[1,2,4,3,6,5,7] => 4
[1,2,4,3,6,7,5] => 4
[1,2,4,3,7,5,6] => 4
[1,2,4,3,7,6,5] => 4
[1,2,4,5,3,6,7] => 6
[1,2,4,5,3,7,6] => 4
[1,2,4,5,6,3,7] => 6
[1,2,4,5,6,7,3] => 6
[1,2,4,5,7,3,6] => 4
[1,2,4,5,7,6,3] => 4
[1,2,4,6,3,5,7] => 4
[1,2,4,6,3,7,5] => 4
[1,2,4,6,5,3,7] => 4
[1,2,4,6,5,7,3] => 4
[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] => 4
[1,2,4,7,5,3,6] => 4
[1,2,4,7,5,6,3] => 4
[1,2,4,7,6,3,5] => 4
[1,2,4,7,6,5,3] => 4
[1,2,5,3,4,6,7] => 6
[1,2,5,3,4,7,6] => 4
[1,2,5,3,6,4,7] => 4
[1,2,5,3,6,7,4] => 4
[1,2,5,3,7,4,6] => 4
[1,2,5,3,7,6,4] => 4
[1,2,5,4,3,6,7] => 6
[1,2,5,4,3,7,6] => 4
[1,2,5,4,6,3,7] => 4
[1,2,5,4,6,7,3] => 4
[1,2,5,4,7,3,6] => 4
[1,2,5,4,7,6,3] => 4
[1,2,5,6,3,4,7] => 6
[1,2,5,6,3,7,4] => 4
[1,2,5,6,4,3,7] => 6
[1,2,5,6,4,7,3] => 4
[1,2,5,6,7,3,4] => 6
[1,2,5,6,7,4,3] => 6
[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] => 4
[1,2,5,7,6,4,3] => 4
[1,2,6,3,4,5,7] => 6
[1,2,6,3,4,7,5] => 4
[1,2,6,3,5,4,7] => 4
[1,2,6,3,5,7,4] => 4
[1,2,6,3,7,4,5] => 4
[1,2,6,3,7,5,4] => 4
[1,2,6,4,3,5,7] => 4
[1,2,6,4,3,7,5] => 4
[1,2,6,4,5,3,7] => 6
[1,2,6,4,5,7,3] => 4
[1,2,6,4,7,3,5] => 4
[1,2,6,4,7,5,3] => 4
[1,2,6,5,3,4,7] => 6
[1,2,6,5,3,7,4] => 4
[1,2,6,5,4,3,7] => 4
[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] => 6
[1,2,6,7,3,5,4] => 4
[1,2,6,7,4,3,5] => 4
[1,2,6,7,4,5,3] => 6
[1,2,6,7,5,3,4] => 6
[1,2,6,7,5,4,3] => 4
[1,2,7,3,4,5,6] => 6
[1,2,7,3,4,6,5] => 4
[1,2,7,3,5,4,6] => 4
[1,2,7,3,5,6,4] => 4
[1,2,7,3,6,4,5] => 4
[1,2,7,3,6,5,4] => 4
[1,2,7,4,3,5,6] => 4
[1,2,7,4,3,6,5] => 4
[1,2,7,4,5,3,6] => 4
[1,2,7,4,5,6,3] => 6
[1,2,7,4,6,3,5] => 4
[1,2,7,4,6,5,3] => 4
[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] => 6
[1,2,7,5,6,4,3] => 4
[1,2,7,6,3,4,5] => 6
[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] => 4
[1,2,7,6,5,4,3] => 4
[1,3,2,4,5,6,7] => 6
[1,3,2,4,5,7,6] => 4
[1,3,2,4,6,5,7] => 4
[1,3,2,4,6,7,5] => 4
[1,3,2,4,7,5,6] => 4
[1,3,2,4,7,6,5] => 4
[1,3,2,5,4,6,7] => 4
[1,3,2,5,4,7,6] => 2
[1,3,2,5,6,4,7] => 4
[1,3,2,5,6,7,4] => 4
[1,3,2,5,7,4,6] => 2
[1,3,2,5,7,6,4] => 2
[1,3,2,6,4,5,7] => 4
[1,3,2,6,4,7,5] => 2
[1,3,2,6,5,4,7] => 4
[1,3,2,6,5,7,4] => 2
[1,3,2,6,7,4,5] => 4
[1,3,2,6,7,5,4] => 4
[1,3,2,7,4,5,6] => 4
[1,3,2,7,4,6,5] => 2
[1,3,2,7,5,4,6] => 2
[1,3,2,7,5,6,4] => 4
[1,3,2,7,6,4,5] => 4
[1,3,2,7,6,5,4] => 2
[1,3,4,2,5,6,7] => 6
[1,3,4,2,5,7,6] => 4
[1,3,4,2,6,5,7] => 4
[1,3,4,2,6,7,5] => 4
[1,3,4,2,7,5,6] => 4
[1,3,4,2,7,6,5] => 4
[1,3,4,5,2,6,7] => 6
[1,3,4,5,2,7,6] => 4
[1,3,4,5,6,2,7] => 6
[1,3,4,5,6,7,2] => 6
[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] => 4
[1,3,4,6,5,2,7] => 4
[1,3,4,6,5,7,2] => 4
[1,3,4,6,7,2,5] => 4
[1,3,4,6,7,5,2] => 4
[1,3,4,7,2,5,6] => 4
[1,3,4,7,2,6,5] => 4
[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] => 4
[1,3,5,2,4,7,6] => 2
[1,3,5,2,6,4,7] => 4
[1,3,5,2,6,7,4] => 4
[1,3,5,2,7,4,6] => 2
[1,3,5,2,7,6,4] => 2
[1,3,5,4,2,6,7] => 4
[1,3,5,4,2,7,6] => 2
[1,3,5,4,6,2,7] => 4
[1,3,5,4,6,7,2] => 4
[1,3,5,4,7,2,6] => 2
[1,3,5,4,7,6,2] => 2
[1,3,5,6,2,4,7] => 4
[1,3,5,6,2,7,4] => 4
[1,3,5,6,4,2,7] => 4
[1,3,5,6,4,7,2] => 4
[1,3,5,6,7,2,4] => 4
[1,3,5,6,7,4,2] => 4
[1,3,5,7,2,4,6] => 2
[1,3,5,7,2,6,4] => 2
[1,3,5,7,4,2,6] => 2
[1,3,5,7,4,6,2] => 2
[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] => 4
[1,3,6,2,5,7,4] => 2
[1,3,6,2,7,4,5] => 4
[1,3,6,2,7,5,4] => 4
[1,3,6,4,2,5,7] => 4
[1,3,6,4,2,7,5] => 2
[1,3,6,4,5,2,7] => 4
[1,3,6,4,5,7,2] => 4
[1,3,6,4,7,2,5] => 2
[1,3,6,4,7,5,2] => 2
[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] => 4
[1,3,6,5,7,2,4] => 2
[1,3,6,5,7,4,2] => 2
[1,3,6,7,2,4,5] => 4
[1,3,6,7,2,5,4] => 4
[1,3,6,7,4,2,5] => 4
[1,3,6,7,4,5,2] => 4
[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] => 2
[1,3,7,2,5,4,6] => 2
[1,3,7,2,5,6,4] => 4
[1,3,7,2,6,4,5] => 4
[1,3,7,2,6,5,4] => 2
[1,3,7,4,2,5,6] => 4
[1,3,7,4,2,6,5] => 2
[1,3,7,4,5,2,6] => 4
[1,3,7,4,5,6,2] => 4
[1,3,7,4,6,2,5] => 2
[1,3,7,4,6,5,2] => 2
[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] => 2
[1,3,7,5,6,2,4] => 4
[1,3,7,5,6,4,2] => 4
[1,3,7,6,2,4,5] => 4
[1,3,7,6,2,5,4] => 2
[1,3,7,6,4,2,5] => 4
[1,3,7,6,4,5,2] => 4
[1,3,7,6,5,2,4] => 2
[1,3,7,6,5,4,2] => 2
[1,4,2,3,5,6,7] => 6
[1,4,2,3,5,7,6] => 4
[1,4,2,3,6,5,7] => 4
[1,4,2,3,6,7,5] => 4
[1,4,2,3,7,5,6] => 4
[1,4,2,3,7,6,5] => 4
[1,4,2,5,3,6,7] => 4
[1,4,2,5,3,7,6] => 2
[1,4,2,5,6,3,7] => 4
[1,4,2,5,6,7,3] => 4
[1,4,2,5,7,3,6] => 2
[1,4,2,5,7,6,3] => 2
[1,4,2,6,3,5,7] => 4
[1,4,2,6,3,7,5] => 2
[1,4,2,6,5,3,7] => 4
[1,4,2,6,5,7,3] => 2
[1,4,2,6,7,3,5] => 4
[1,4,2,6,7,5,3] => 4
[1,4,2,7,3,5,6] => 4
[1,4,2,7,3,6,5] => 2
[1,4,2,7,5,3,6] => 2
[1,4,2,7,5,6,3] => 4
[1,4,2,7,6,3,5] => 4
[1,4,2,7,6,5,3] => 2
[1,4,3,2,5,6,7] => 6
[1,4,3,2,5,7,6] => 4
[1,4,3,2,6,5,7] => 4
[1,4,3,2,6,7,5] => 4
[1,4,3,2,7,5,6] => 4
[1,4,3,2,7,6,5] => 4
[1,4,3,5,2,6,7] => 4
[1,4,3,5,2,7,6] => 2
[1,4,3,5,6,2,7] => 4
[1,4,3,5,6,7,2] => 4
[1,4,3,5,7,2,6] => 2
[1,4,3,5,7,6,2] => 2
[1,4,3,6,2,5,7] => 4
[1,4,3,6,2,7,5] => 2
[1,4,3,6,5,2,7] => 4
[1,4,3,6,5,7,2] => 2
[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] => 2
[1,4,3,7,5,2,6] => 2
[1,4,3,7,5,6,2] => 4
[1,4,3,7,6,2,5] => 4
[1,4,3,7,6,5,2] => 2
[1,4,5,2,3,6,7] => 6
[1,4,5,2,3,7,6] => 4
[1,4,5,2,6,3,7] => 4
[1,4,5,2,6,7,3] => 4
[1,4,5,2,7,3,6] => 4
[1,4,5,2,7,6,3] => 4
[1,4,5,3,2,6,7] => 6
[1,4,5,3,2,7,6] => 4
[1,4,5,3,6,2,7] => 4
[1,4,5,3,6,7,2] => 4
[1,4,5,3,7,2,6] => 4
[1,4,5,3,7,6,2] => 4
[1,4,5,6,2,3,7] => 6
[1,4,5,6,2,7,3] => 4
[1,4,5,6,3,2,7] => 6
[1,4,5,6,3,7,2] => 4
[1,4,5,6,7,2,3] => 6
[1,4,5,6,7,3,2] => 6
[1,4,5,7,2,3,6] => 4
[1,4,5,7,2,6,3] => 4
[1,4,5,7,3,2,6] => 4
[1,4,5,7,3,6,2] => 4
[1,4,5,7,6,2,3] => 4
[1,4,5,7,6,3,2] => 4
[1,4,6,2,3,5,7] => 4
[1,4,6,2,3,7,5] => 4
[1,4,6,2,5,3,7] => 4
[1,4,6,2,5,7,3] => 2
[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] => 4
[1,4,6,3,5,2,7] => 4
[1,4,6,3,5,7,2] => 2
[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
[1,4,6,7,2,3,5] => 4
[1,4,6,7,5,3,2] => 4
[1,4,7,2,3,5,6] => 4
[1,4,7,6,5,3,2] => 4
[1,5,2,3,4,7,6] => 4
[1,5,2,7,3,4,6] => 4
[1,5,4,7,6,3,2] => 2
[1,5,6,2,7,3,4] => 4
[1,5,6,4,7,3,2] => 4
[1,5,6,7,2,3,4] => 6
[1,5,6,7,4,3,2] => 4
[1,5,7,2,3,4,6] => 4
[1,5,7,6,4,3,2] => 2
[1,6,2,3,4,7,5] => 4
[1,6,2,3,7,4,5] => 4
[1,6,2,7,3,4,5] => 4
[1,6,5,4,3,7,2] => 2
[1,6,5,4,7,3,2] => 4
[1,6,5,7,4,3,2] => 2
[1,6,7,2,3,4,5] => 6
[1,6,7,5,4,3,2] => 4
[1,7,2,3,4,5,6] => 6
[1,7,3,5,6,4,2] => 4
[1,7,3,6,5,4,2] => 4
[1,7,4,3,6,5,2] => 2
[1,7,4,5,3,6,2] => 4
[1,7,4,5,6,3,2] => 4
[1,7,4,6,5,3,2] => 2
[1,7,5,4,3,6,2] => 4
[1,7,5,4,6,3,2] => 2
[1,7,6,4,5,3,2] => 4
[1,7,6,5,4,3,2] => 2
[2,1,3,4,5,6,7] => 6
[2,1,3,4,7,5,6] => 4
[2,1,3,7,4,5,6] => 4
[2,1,6,3,4,5,7] => 4
[2,1,7,3,4,5,6] => 4
[2,1,7,6,5,4,3] => 2
[2,3,1,4,5,6,7] => 6
[2,3,4,1,5,6,7] => 6
[2,3,4,1,5,7,6] => 4
[2,3,4,5,1,6,7] => 6
[2,3,4,5,1,7,6] => 4
[2,3,4,5,6,1,7] => 6
[2,3,4,5,6,7,1] => 6
[2,3,4,5,7,1,6] => 4
[2,3,4,6,1,7,5] => 4
[2,3,4,6,7,1,5] => 4
[2,3,4,7,1,5,6] => 4
[2,3,5,6,7,1,4] => 4
[2,4,1,3,5,6,7] => 4
[2,5,1,3,4,6,7] => 4
[2,5,7,1,3,4,6] => 2
[2,6,1,3,4,5,7] => 4
[2,6,1,7,3,4,5] => 4
[2,6,5,4,3,1,7] => 2
[2,6,7,1,3,4,5] => 4
[2,7,1,3,4,5,6] => 4
[3,1,2,4,5,6,7] => 6
[3,1,2,4,5,7,6] => 4
[3,2,1,4,5,6,7] => 6
[3,2,4,5,6,7,1] => 4
[3,4,1,2,5,6,7] => 6
[3,4,2,5,6,7,1] => 4
[3,4,5,2,6,7,1] => 4
[3,4,5,6,2,7,1] => 4
[3,4,5,6,7,1,2] => 6
[3,5,6,1,2,4,7] => 4
[3,5,6,4,2,1,7] => 4
[3,6,1,2,4,5,7] => 4
[3,6,5,4,2,1,7] => 4
[4,1,2,3,5,6,7] => 6
[4,1,2,3,5,7,6] => 4
[4,1,6,2,3,5,7] => 4
[4,2,3,5,6,7,1] => 4
[4,2,5,1,3,6,7] => 4
[4,3,2,1,5,6,7] => 4
[4,3,2,5,6,7,1] => 4
[4,3,5,2,6,7,1] => 2
[4,3,6,5,2,1,7] => 2
[4,5,1,6,2,3,7] => 4
[4,5,2,3,6,7,1] => 4
[4,5,3,6,2,1,7] => 4
[4,5,6,1,2,3,7] => 6
[4,5,6,3,2,1,7] => 4
[4,6,1,2,3,5,7] => 4
[4,6,1,2,3,7,5] => 4
[4,6,5,3,2,1,7] => 2
[5,1,2,3,4,6,7] => 6
[5,1,2,3,4,7,6] => 4
[5,1,2,3,6,4,7] => 4
[5,1,2,3,6,7,4] => 4
[5,1,2,3,7,4,6] => 4
[5,1,2,6,3,4,7] => 4
[5,1,6,2,3,4,7] => 4
[5,1,6,2,3,7,4] => 2
[5,2,3,4,6,7,1] => 4
[5,2,6,7,1,3,4] => 4
[5,3,2,4,6,7,1] => 2
[5,3,2,6,1,4,7] => 4
[5,4,3,2,1,6,7] => 4
[5,4,3,2,1,7,6] => 2
[5,4,3,2,6,1,7] => 2
[5,4,3,6,2,1,7] => 4
[5,4,6,3,2,1,7] => 2
[5,6,1,2,3,4,7] => 6
[5,6,1,2,3,7,4] => 4
[5,6,3,4,1,2,7] => 6
[5,6,4,3,2,1,7] => 4
[5,6,7,1,2,3,4] => 6
[6,1,2,3,4,5,7] => 6
[6,1,2,3,4,7,5] => 4
[6,1,2,3,7,4,5] => 4
[6,1,2,7,3,4,5] => 4
[6,2,3,4,5,7,1] => 4
[6,2,4,5,3,1,7] => 4
[6,2,5,4,3,1,7] => 4
[6,3,2,5,4,1,7] => 2
[6,3,4,2,5,1,7] => 4
[6,3,4,5,2,1,7] => 4
[6,3,5,4,2,1,7] => 2
[6,4,3,2,5,1,7] => 4
[6,4,3,2,7,1,5] => 2
[6,4,3,5,2,1,7] => 2
[6,4,7,2,5,1,3] => 2
[6,5,3,4,2,1,7] => 4
[6,5,4,3,2,1,7] => 2
[6,7,1,2,3,4,5] => 6
[6,7,4,5,1,2,3] => 6
[7,1,2,3,4,5,6] => 6
[7,2,1,3,4,5,6] => 4
[7,2,3,1,4,5,6] => 4
[7,2,3,4,1,5,6] => 4
[7,2,3,4,5,1,6] => 4
[7,3,1,2,4,5,6] => 4
[7,3,2,1,4,5,6] => 4
[7,3,2,4,1,5,6] => 2
[7,3,4,1,2,5,6] => 4
[7,4,1,2,3,5,6] => 4
[7,4,2,1,3,5,6] => 2
[7,4,5,6,1,2,3] => 6
[7,5,1,2,3,4,6] => 4
[7,5,6,1,2,3,4] => 6
[7,5,6,3,4,1,2] => 4
[7,6,1,2,3,4,5] => 6
[7,6,4,5,1,2,3] => 4
[7,6,5,1,2,3,4] => 4
[7,6,5,3,4,1,2] => 4
[7,6,5,4,1,2,3] => 4
[7,6,5,4,3,1,2] => 2
[7,6,5,4,3,2,1] => 2
[8,7,6,5,4,3,2,1] => 1
[7,6,8,5,4,3,2,1] => 1
[7,8,5,6,4,3,2,1] => 3
[7,8,6,4,5,3,2,1] => 3
[8,6,7,4,5,3,2,1] => 3
[7,6,5,4,8,3,2,1] => 1
[6,5,7,4,8,3,2,1] => 1
[7,8,6,5,3,4,2,1] => 3
[8,6,7,5,3,4,2,1] => 3
[8,7,5,6,3,4,2,1] => 3
[6,7,8,3,4,5,2,1] => 5
[7,8,6,5,4,2,3,1] => 3
[8,6,7,5,4,2,3,1] => 3
[8,7,5,6,4,2,3,1] => 3
[8,7,6,4,5,2,3,1] => 3
[8,6,5,7,3,2,4,1] => 1
[6,7,8,5,2,3,4,1] => 5
[8,5,6,7,2,3,4,1] => 5
[7,8,3,2,4,5,6,1] => 5
[7,6,5,4,3,2,8,1] => 1
[6,5,7,4,3,2,8,1] => 1
[6,5,4,3,7,2,8,1] => 1
[5,4,6,3,7,2,8,1] => 1
[3,4,5,2,6,7,8,1] => 5
[5,2,3,4,6,7,8,1] => 5
[4,3,2,5,6,7,8,1] => 5
[3,4,2,5,6,7,8,1] => 5
[4,2,3,5,6,7,8,1] => 5
[3,2,4,5,6,7,8,1] => 5
[2,3,4,5,6,7,8,1] => 7
[8,7,6,5,4,3,1,2] => 3
[7,8,6,5,4,3,1,2] => 3
[8,6,7,5,4,3,1,2] => 3
[8,7,5,6,4,3,1,2] => 3
[8,7,6,4,5,3,1,2] => 3
[8,7,6,5,3,4,1,2] => 3
[8,7,5,6,3,4,1,2] => 5
[7,8,5,6,3,4,1,2] => 5
[5,6,7,8,3,4,1,2] => 7
[7,8,3,4,5,6,1,2] => 7
[3,4,5,6,7,8,1,2] => 7
[8,7,6,5,4,2,1,3] => 1
[7,6,8,5,4,2,1,3] => 1
[8,7,6,5,4,1,2,3] => 3
[6,7,8,5,4,1,2,3] => 5
[8,5,6,7,4,1,2,3] => 5
[8,7,6,4,5,1,2,3] => 5
[8,6,7,4,5,1,2,3] => 5
[8,7,4,5,6,1,2,3] => 5
[7,8,4,5,6,1,2,3] => 7
[7,6,5,8,3,2,1,4] => 3
[7,5,6,8,2,3,1,4] => 3
[6,7,5,8,3,1,2,4] => 3
[6,5,7,8,2,1,3,4] => 3
[8,7,6,5,1,2,3,4] => 5
[8,7,5,6,1,2,3,4] => 5
[7,8,5,6,1,2,3,4] => 7
[8,5,6,7,1,2,3,4] => 7
[5,6,7,8,1,2,3,4] => 7
[8,7,6,4,3,2,1,5] => 1
[8,7,6,4,2,1,3,5] => 1
[8,7,6,1,2,3,4,5] => 5
[8,6,7,1,2,3,4,5] => 7
[6,7,8,1,2,3,4,5] => 7
[7,8,5,4,2,1,3,6] => 3
[7,8,5,4,1,2,3,6] => 5
[8,7,1,2,3,4,5,6] => 7
[7,8,1,2,3,4,5,6] => 7
[8,6,5,4,3,2,1,7] => 1
[8,6,5,4,3,1,2,7] => 3
[8,5,6,3,4,1,2,7] => 5
[8,6,5,4,2,1,3,7] => 1
[8,6,4,3,2,1,5,7] => 1
[8,6,4,2,1,3,5,7] => 1
[8,2,3,4,1,5,6,7] => 5
[8,4,1,2,3,5,6,7] => 5
[8,3,2,1,4,5,6,7] => 5
[8,2,3,1,4,5,6,7] => 5
[8,3,1,2,4,5,6,7] => 5
[8,2,1,3,4,5,6,7] => 5
[8,1,2,3,4,5,6,7] => 7
[7,6,5,4,3,2,1,8] => 3
[6,7,5,4,3,2,1,8] => 3
[6,5,7,4,3,2,1,8] => 3
[5,6,7,4,3,2,1,8] => 5
[7,6,4,5,3,2,1,8] => 3
[6,5,4,7,3,2,1,8] => 3
[7,5,6,3,4,2,1,8] => 5
[7,6,4,3,5,2,1,8] => 3
[7,6,3,4,5,2,1,8] => 5
[7,5,4,3,6,2,1,8] => 3
[6,7,5,4,2,3,1,8] => 5
[6,5,7,3,2,4,1,8] => 3
[5,6,7,2,3,4,1,8] => 7
[2,3,4,5,6,7,1,8] => 7
[5,6,7,1,2,3,4,8] => 7
[6,7,1,2,3,4,5,8] => 7
[7,1,2,3,4,5,6,8] => 7
[6,5,4,3,2,1,7,8] => 3
[2,3,4,5,6,1,7,8] => 7
[5,6,3,4,1,2,7,8] => 7
[4,5,6,1,2,3,7,8] => 7
[6,1,2,3,4,5,7,8] => 7
[5,4,3,2,1,6,7,8] => 5
[2,3,4,5,1,6,7,8] => 7
[5,1,2,3,4,6,7,8] => 7
[4,3,2,1,5,6,7,8] => 5
[3,4,1,2,5,6,7,8] => 7
[3,2,1,4,5,6,7,8] => 7
[2,1,3,4,5,6,7,8] => 7
[1,2,3,4,5,6,7,8] => 9
[6,5,8,7,4,3,2,1] => 1
[3,5,8,7,6,4,2,1] => 3
[4,3,6,5,8,7,2,1] => 1
[2,6,8,7,5,4,3,1] => 1
[2,3,5,6,8,7,4,1] => 3
[3,2,6,5,4,8,7,1] => 1
[4,3,6,5,7,2,8,1] => 1
[3,2,6,5,7,4,8,1] => 1
[4,3,5,2,7,6,8,1] => 1
[3,2,5,4,7,6,8,1] => 1
[1,8,7,6,5,4,3,2] => 3
[1,7,8,6,5,4,3,2] => 3
[1,6,8,7,5,4,3,2] => 3
[1,7,6,8,5,4,3,2] => 3
[1,6,7,8,5,4,3,2] => 5
[1,5,8,7,6,4,3,2] => 3
[1,7,6,5,8,4,3,2] => 3
[1,3,5,7,8,6,4,2] => 3
[1,4,3,8,7,6,5,2] => 3
[1,6,5,4,3,8,7,2] => 3
[1,4,3,6,5,8,7,2] => 3
[2,1,8,7,6,5,4,3] => 1
[2,1,6,5,7,4,8,3] => 1
[2,1,5,4,7,6,8,3] => 1
[1,2,6,7,8,5,4,3] => 5
[3,2,1,8,7,6,5,4] => 3
[3,2,1,6,5,8,7,4] => 3
[1,2,3,5,6,7,8,4] => 7
[4,3,2,1,8,7,6,5] => 1
[3,4,2,1,7,8,6,5] => 5
[2,4,3,1,6,8,7,5] => 1
[2,4,3,1,7,6,8,5] => 1
[3,2,4,1,6,8,7,5] => 1
[3,2,4,1,7,6,8,5] => 1
[2,3,4,1,6,7,8,5] => 5
[2,1,4,3,8,7,6,5] => 1
[2,1,4,3,6,8,7,5] => 1
[2,1,4,3,7,6,8,5] => 1
[5,4,3,2,1,8,7,6] => 3
[3,2,5,4,1,8,7,6] => 3
[3,2,1,4,5,8,7,6] => 5
[2,3,1,4,5,7,8,6] => 5
[6,5,4,3,2,1,8,7] => 1
[4,3,5,2,6,1,8,7] => 1
[3,2,5,4,6,1,8,7] => 1
[2,3,4,5,6,1,8,7] => 5
[2,1,6,5,4,3,8,7] => 1
[2,1,4,6,5,3,8,7] => 1
[2,1,5,4,6,3,8,7] => 1
[4,3,2,1,6,5,8,7] => 1
[2,4,3,1,6,5,8,7] => 1
[3,2,4,1,6,5,8,7] => 1
[2,1,4,3,6,5,8,7] => 1
[2,1,3,4,5,6,8,7] => 5
[1,2,3,4,5,6,8,7] => 7
[5,7,6,4,3,2,1,8] => 3
[4,7,6,5,3,2,1,8] => 3
[3,2,7,6,5,4,1,8] => 3
[5,4,3,2,7,6,1,8] => 3
[3,2,5,4,7,6,1,8] => 3
[1,4,3,2,7,6,5,8] => 5
[1,3,4,2,6,7,5,8] => 5
[1,3,2,5,4,7,6,8] => 3
[1,2,3,5,4,7,6,8] => 5
[1,3,2,4,5,7,6,8] => 5
[1,2,3,4,5,7,6,8] => 7
[1,2,4,3,6,5,7,8] => 5
[1,3,2,5,4,6,7,8] => 5
[1,2,3,5,4,6,7,8] => 7
[1,3,2,4,5,6,7,8] => 7
[1,8,4,7,6,5,3,2] => 3
[1,8,5,4,7,6,3,2] => 3
[1,8,7,4,5,6,3,2] => 5
[1,8,7,4,6,5,3,2] => 3
[1,8,6,5,4,7,3,2] => 3
[1,8,7,5,4,6,3,2] => 3
[1,8,7,5,6,4,3,2] => 3
[2,1,4,5,8,6,7,3] => 3
[2,1,8,5,4,7,6,3] => 1
[2,3,4,8,5,6,7,1] => 5
[2,3,6,4,5,1,8,7] => 3
[2,3,7,4,5,6,8,1] => 5
[2,8,4,3,5,7,6,1] => 1
[4,2,3,1,8,6,7,5] => 5
[8,2,7,4,6,5,3,1] => 3
[4,3,2,7,5,6,8,1] => 3
[4,3,2,8,5,7,6,1] => 1
[6,3,2,5,4,1,8,7] => 1
[8,3,2,5,4,7,6,1] => 1
[8,3,2,7,6,5,4,1] => 1
[8,3,7,4,6,5,2,1] => 1
[7,3,6,5,4,2,1,8] => 3
[7,4,3,6,5,2,1,8] => 3
[7,6,3,5,4,2,1,8] => 3
[8,5,4,3,2,7,6,1] => 1
[8,7,4,3,6,5,2,1] => 1
[2,4,6,8,1,3,5,7] => 1
[2,4,6,1,7,3,8,5] => 3
[2,1,4,3,7,5,8,6] => 1
[2,4,1,3,7,5,8,6] => 1
[2,1,4,3,7,8,5,6] => 3
[2,4,7,8,1,3,5,6] => 3
[2,1,4,3,8,5,6,7] => 3
[2,4,5,6,7,1,8,3] => 5
[2,1,5,3,6,4,8,7] => 1
[2,1,5,6,3,4,8,7] => 3
[2,5,6,8,1,3,4,7] => 3
[2,1,5,3,7,4,8,6] => 1
[2,5,1,7,3,4,8,6] => 3
[2,1,5,7,3,8,4,6] => 1
[2,5,7,8,1,3,4,6] => 3
[2,3,5,6,1,7,8,4] => 5
[2,1,6,3,7,4,8,5] => 1
[2,6,7,1,3,4,8,5] => 3
[2,1,6,7,8,3,4,5] => 5
[2,6,7,8,1,3,4,5] => 5
[2,1,6,3,4,7,8,5] => 3
[2,1,6,3,4,5,8,7] => 3
[2,6,1,3,4,5,7,8] => 5
[2,7,8,1,3,4,5,6] => 5
[2,7,1,3,4,5,6,8] => 5
[2,3,4,5,7,8,1,6] => 5
[2,1,8,3,4,5,6,7] => 5
[2,8,1,3,4,5,6,7] => 5
[2,1,3,8,4,5,6,7] => 5
[2,3,4,5,6,8,1,7] => 5
[3,1,4,2,6,5,8,7] => 1
[3,4,1,2,6,5,8,7] => 3
[3,1,4,2,6,8,5,7] => 1
[3,4,6,8,1,2,5,7] => 3
[3,1,4,2,7,5,8,6] => 1
[3,4,1,2,7,8,5,6] => 5
[3,4,7,8,1,2,5,6] => 5
[3,1,5,2,6,4,8,7] => 1
[3,5,1,6,2,4,8,7] => 1
[3,1,5,6,2,8,4,7] => 3
[3,5,6,8,1,2,4,7] => 3
[3,1,5,2,7,4,8,6] => 1
[3,5,1,7,2,8,4,6] => 1
[3,5,7,8,1,2,4,6] => 3
[1,3,2,5,4,8,6,7] => 3
[1,3,5,8,2,4,6,7] => 3
[1,3,5,6,2,7,4,8] => 5
[3,1,6,2,7,4,8,5] => 1
[3,6,7,1,2,8,4,5] => 5
[3,6,1,7,8,2,4,5] => 3
[3,6,7,8,1,2,4,5] => 5
[1,3,2,6,4,7,5,8] => 3
[3,1,2,6,7,4,8,5] => 3
[1,3,2,6,4,8,5,7] => 3
[1,3,2,6,4,5,7,8] => 5
[1,3,2,7,4,8,5,6] => 3
[1,3,2,7,4,5,6,8] => 5
[1,3,2,8,4,5,6,7] => 5
[3,1,2,4,5,8,6,7] => 5
[1,3,2,4,5,8,6,7] => 5
[4,1,5,2,6,3,8,7] => 1
[4,5,6,1,2,3,8,7] => 5
[4,1,5,6,8,2,3,7] => 3
[4,5,6,8,1,2,3,7] => 5
[4,1,5,2,7,3,8,6] => 1
[4,1,5,2,7,8,3,6] => 3
[4,5,7,1,2,8,3,6] => 3
[4,5,1,7,8,2,3,6] => 5
[4,5,7,8,1,2,3,6] => 5
[1,4,2,5,3,7,6,8] => 3
[1,4,2,5,3,8,6,7] => 3
[1,4,2,5,3,6,7,8] => 5
[1,4,5,6,7,2,3,8] => 7
[4,1,6,2,7,3,8,5] => 1
[4,6,7,1,8,2,3,5] => 3
[4,6,7,8,1,2,3,5] => 5
[1,4,2,6,3,7,5,8] => 3
[1,4,2,6,7,8,3,5] => 5
[1,4,2,6,3,8,5,7] => 3
[4,1,2,3,6,5,8,7] => 3
[1,4,2,6,3,5,7,8] => 5
[1,4,2,7,3,8,5,6] => 3
[4,7,1,2,3,5,6,8] => 5
[1,4,2,7,3,5,6,8] => 5
[1,4,2,3,7,5,6,8] => 5
[1,4,2,3,5,7,6,8] => 5
[1,4,2,8,3,5,6,7] => 5
[4,1,2,3,8,5,6,7] => 5
[1,4,2,3,5,8,6,7] => 5
[1,4,2,3,5,6,7,8] => 7
[5,1,6,2,7,3,8,4] => 1
[1,5,2,6,3,7,4,8] => 3
[1,5,2,6,3,8,4,7] => 3
[1,5,2,6,3,4,7,8] => 5
[1,2,5,6,3,4,7,8] => 7
[1,5,2,7,3,8,4,6] => 3
[5,7,1,2,3,4,6,8] => 5
[1,5,2,7,3,4,6,8] => 5
[1,5,2,3,4,7,6,8] => 5
[5,1,2,8,3,4,6,7] => 5
[1,5,2,8,3,4,6,7] => 5
[1,5,8,2,3,4,6,7] => 5
[1,5,2,3,4,8,6,7] => 5
[1,2,3,5,4,8,6,7] => 5
[5,1,2,3,4,6,8,7] => 5
[1,5,2,3,4,6,7,8] => 7
[1,6,2,7,3,8,4,5] => 3
[1,6,7,8,2,3,4,5] => 7
[6,7,1,2,3,4,8,5] => 5
[6,1,7,2,3,4,5,8] => 5
[6,1,2,7,3,4,5,8] => 5
[1,6,2,7,3,4,5,8] => 5
[1,6,7,2,3,4,5,8] => 7
[1,6,2,3,4,7,5,8] => 5
[1,2,3,6,4,7,5,8] => 5
[6,1,8,2,3,4,5,7] => 5
[1,6,2,8,3,4,5,7] => 5
[1,6,8,2,3,4,5,7] => 5
[1,6,2,3,4,8,5,7] => 5
[1,2,3,6,4,8,5,7] => 5
[6,1,2,3,4,5,8,7] => 5
[1,6,2,3,4,5,7,8] => 7
[1,2,3,6,4,5,7,8] => 7
[1,7,2,8,3,4,5,6] => 5
[1,7,8,2,3,4,5,6] => 7
[1,7,2,3,8,4,5,6] => 5
[7,1,2,3,4,8,5,6] => 5
[1,7,2,3,4,8,5,6] => 5
[1,2,3,7,4,8,5,6] => 5
[7,1,2,3,4,5,8,6] => 5
[1,7,2,3,4,5,8,6] => 5
[1,2,7,3,4,5,8,6] => 5
[1,7,2,3,4,5,6,8] => 7
[1,2,3,7,4,5,6,8] => 7
[1,8,2,3,4,5,6,7] => 7
[1,2,3,8,4,5,6,7] => 7
[1,2,3,4,5,8,6,7] => 7
[5,3,2,6,1,4,8,7] => 3
[7,3,2,5,4,8,1,6] => 3
[8,4,5,2,3,7,6,1] => 3
[7,4,5,2,3,8,1,6] => 5
[6,4,5,2,3,1,8,7] => 3
[5,4,6,2,1,3,8,7] => 1
[3,6,1,5,4,2,8,7] => 3
[4,6,5,1,3,2,8,7] => 1
[5,6,4,3,1,2,8,7] => 3
[7,5,4,3,2,8,1,6] => 3
[8,6,4,3,7,2,5,1] => 3
[7,6,4,3,8,2,1,5] => 1
[6,7,4,3,8,1,2,5] => 5
[5,7,4,3,1,8,2,6] => 1
[4,7,5,1,3,8,2,6] => 1
[3,7,1,5,4,8,2,6] => 1
[2,1,7,5,4,8,3,6] => 3
[3,8,1,5,4,7,6,2] => 3
[4,8,5,1,3,7,6,2] => 1
[5,8,4,3,1,7,6,2] => 3
[6,8,4,3,7,1,5,2] => 1
[7,8,4,3,6,5,1,2] => 3
[6,8,5,7,3,1,4,2] => 1
[5,8,6,7,1,3,4,2] => 3
[4,8,6,1,7,3,5,2] => 1
[3,8,1,6,7,4,5,2] => 5
[2,1,8,6,7,4,5,3] => 3
[2,1,7,6,8,4,3,5] => 1
[3,7,1,6,8,4,2,5] => 1
[4,7,6,1,8,3,2,5] => 1
[5,7,6,8,1,3,2,4] => 3
[5,4,7,2,1,8,3,6] => 3
[6,4,7,2,8,1,3,5] => 3
[7,4,6,2,8,3,1,5] => 1
[8,4,6,2,7,3,5,1] => 1
[8,3,2,6,7,4,5,1] => 3
[7,3,2,6,8,4,1,5] => 1
[6,3,2,7,8,1,4,5] => 5
[5,3,2,7,1,8,4,6] => 1
[4,3,2,1,7,8,5,6] => 3
[3,4,1,2,8,7,6,5] => 3
[5,3,2,8,1,7,6,4] => 3
[6,3,2,8,7,1,5,4] => 1
[7,3,2,8,6,5,1,4] => 3
[8,4,7,2,6,5,3,1] => 3
[7,4,8,2,6,5,1,3] => 1
[6,4,8,2,7,1,5,3] => 1
[5,4,8,2,1,7,6,3] => 1
[4,5,8,1,2,7,6,3] => 5
[3,5,1,8,2,7,6,4] => 1
[2,1,5,8,3,7,6,4] => 3
[2,1,6,8,7,3,5,4] => 1
[3,6,1,8,7,2,5,4] => 3
[4,6,8,1,7,2,5,3] => 3
[5,6,8,7,1,2,4,3] => 3
[6,5,8,7,2,1,4,3] => 1
[7,5,8,6,2,4,1,3] => 1
[8,5,7,6,2,4,3,1] => 1
[5,7,8,6,1,4,2,3] => 3
[4,7,8,1,6,5,2,3] => 5
[3,7,1,8,6,5,2,4] => 1
[2,1,7,8,6,5,3,4] => 3
[3,8,1,7,6,5,4,2] => 3
[4,8,7,1,6,5,3,2] => 1
[5,8,7,6,1,4,3,2] => 3
[6,8,7,5,4,1,3,2] => 1
[4,2,5,1,3,6,7,8] => 5
[5,2,6,7,1,3,4,8] => 5
[3,2,7,8,1,4,5,6] => 5
[5,3,2,6,1,4,7,8] => 5
[7,4,3,8,1,2,5,6] => 5
[4,7,3,6,8,1,2,5] => 3
[6,7,3,4,8,1,2,5] => 5
[5,4,2,7,8,1,3,6] => 3
[6,4,7,2,5,1,3,8] => 3
[6,4,3,2,7,1,5,8] => 3
[5,4,3,2,8,1,6,7] => 3
[7,5,3,8,2,6,1,4] => 3
[8,5,4,7,2,6,1,3] => 1
[8,5,4,7,3,6,1,2] => 3
[7,5,3,1,8,6,4,2] => 3
[8,7,1,3,6,2,4,5] => 3
[5,4,1,3,8,2,6,7] => 3
[4,8,5,7,1,6,2,3] => 3
[8,7,6,5,1,4,2,3] => 3
[3,2,1,5,8,4,6,7] => 3
[1,8,2,7,3,6,4,5] => 3
[2,5,3,4,1,8,6,7] => 3
[2,4,8,3,5,7,6,1] => 1
[8,7,2,6,3,5,4,1] => 1
[5,4,3,2,1,8,6,7] => 3
[3,8,4,7,6,5,2,1] => 3
[3,6,7,4,5,8,1,2] => 5
[7,8,1,4,5,2,3,6] => 5
[1,6,7,4,5,2,3,8] => 7
[8,5,7,4,2,1,6,3] => 1
[8,6,3,5,2,4,1,7] => 1
[8,3,7,5,2,4,6,1] => 1
[8,7,6,3,5,2,4,1] => 1
[8,5,7,4,3,2,6,1] => 1
[8,4,7,6,3,5,2,1] => 1
[6,5,8,4,2,7,3,1] => 1
[7,5,3,6,4,2,8,1] => 1
[8,5,3,6,2,7,4,1] => 1
[8,6,4,7,5,3,2,1] => 1
[8,6,5,4,2,7,3,1] => 1
[8,7,5,2,6,4,3,1] => 1
[2,1,8,7,4,3,6,5] => 1
[6,5,2,1,4,3,8,7] => 1
[8,5,2,7,4,1,6,3] => 3
[8,7,2,1,4,5,6,3] => 3
[8,7,2,3,4,1,6,5] => 3
[8,1,6,3,2,5,4,7] => 3
[1,2,3,8,4,7,5,6] => 5
[1,8,2,3,4,7,5,6] => 5
[1,6,2,5,3,4,7,8] => 5
[1,8,2,5,3,4,6,7] => 5
[1,8,2,7,3,4,5,6] => 5
[8,7,2,1,4,3,6,5] => 1
[8,2,1,5,4,3,7,6] => 1
[8,7,6,5,2,1,4,3] => 1
[8,7,6,3,2,5,4,1] => 1
[8,5,4,7,6,3,2,1] => 1
[5,4,3,8,7,6,1,2] => 3
[8,1,2,4,5,6,3,7] => 5
[1,8,2,6,3,5,4,7] => 3
[1,7,2,6,3,5,4,8] => 3
[1,7,2,6,3,4,5,8] => 5
[8,7,6,1,4,3,2,5] => 3
[7,1,8,6,5,4,3,2] => 1
[1,8,7,6,5,4,2,3] => 3
[3,2,1,4,8,5,6,7] => 5
[1,8,2,3,4,6,5,7] => 5
[1,6,2,7,3,5,4,8] => 3
[1,6,2,5,3,7,4,8] => 3
[1,5,3,7,2,6,4,8] => 5
[2,8,4,1,6,3,7,5] => 1
[5,3,6,4,7,1,8,2] => 1
[8,1,6,7,5,4,3,2] => 3
[8,1,6,7,4,5,2,3] => 5
[1,8,2,7,3,5,4,6] => 3
[1,7,2,8,3,5,4,6] => 3
[5,4,3,2,7,1,8,6] => 1
[3,5,2,7,1,8,6,4] => 1
[2,6,7,3,1,4,8,5] => 3
[5,4,1,8,7,2,3,6] => 5
[8,4,3,1,7,6,2,5] => 3
[5,7,4,3,2,1,8,6] => 3
[3,2,6,1,4,7,8,5] => 3
[3,6,7,2,1,8,5,4] => 5
[1,7,6,5,4,8,2,3] => 3
[1,5,4,2,8,3,6,7] => 5
[6,7,2,3,4,8,5,1] => 5
[4,6,2,5,8,3,7,1] => 1
[4,3,5,2,7,1,8,6] => 1
[3,2,6,1,7,4,8,5] => 1
[1,7,2,5,3,4,6,8] => 5
[1,6,2,4,3,5,7,8] => 5
[1,5,2,4,3,6,7,8] => 5
[1,6,2,4,3,7,5,8] => 3
[8,1,2,5,6,7,4,3] => 5
[7,8,3,2,1,6,5,4] => 3
[1,2,3,8,4,6,5,7] => 5
[8,7,1,6,4,5,3,2] => 3
[8,7,6,1,5,3,4,2] => 3
[4,8,7,5,6,3,2,1] => 3
[4,3,7,6,2,1,8,5] => 1
[4,7,6,3,2,8,1,5] => 1
[7,1,6,5,8,3,2,4] => 1
[7,1,6,5,4,8,2,3] => 3
[5,1,7,3,8,4,6,2] => 3
[4,3,6,2,7,1,8,5] => 1
[8,7,5,4,1,3,2,6] => 3
[6,4,3,8,2,1,5,7] => 1
[5,3,8,7,6,4,2,1] => 1
[8,4,7,6,5,1,3,2] => 3
[2,3,8,7,4,5,6,1] => 5
[7,6,5,3,2,1,8,4] => 1
[1,7,2,8,3,6,4,5] => 3
[1,5,2,8,3,7,4,6] => 3
[3,2,4,1,7,5,8,6] => 1
[4,3,6,1,7,2,8,5] => 1
[3,7,5,6,8,4,2,1] => 3
[5,4,6,3,7,1,8,2] => 1
[1,2,8,7,4,5,6,3] => 5
[2,8,6,3,7,4,5,1] => 3
[5,4,6,1,7,3,8,2] => 1
[1,8,2,6,3,4,5,7] => 5
[6,3,8,4,2,5,7,1] => 1
[8,7,1,6,2,5,4,3] => 3
[8,2,7,6,3,5,4,1] => 3
[1,2,3,7,4,6,5,8] => 5
[4,5,2,3,8,1,6,7] => 5
[8,1,7,6,5,4,2,3] => 3
[1,8,6,7,5,4,3,2] => 3
[6,2,8,7,5,4,3,1] => 3
[7,1,3,5,8,2,4,6] => 1
[4,6,2,7,3,5,1,8] => 3
[1,5,7,3,8,4,6,2] => 3
[8,1,7,6,5,2,4,3] => 1
[1,3,2,8,4,7,5,6] => 3
[5,2,3,8,1,6,7,4] => 5
[1,8,2,4,3,5,6,7] => 5
[2,4,1,8,7,6,5,3] => 1
[1,8,5,4,3,2,6,7] => 3
[8,2,6,1,7,3,5,4] => 1
[7,1,8,6,5,3,2,4] => 1
[1,7,2,5,3,6,4,8] => 3
[1,8,2,6,3,7,4,5] => 3
[5,1,2,4,8,3,6,7] => 3
[1,6,2,8,3,7,4,5] => 3
[2,8,7,6,5,3,4,1] => 3
[2,1,8,4,7,5,6,3] => 3
[5,7,3,8,4,6,2,1] => 1
[8,7,3,5,1,6,2,4] => 1
[6,4,8,1,7,2,3,5] => 3
[6,1,7,2,8,5,4,3] => 1
[7,1,2,8,3,5,4,6] => 3
[1,6,2,5,8,3,4,7] => 3
[8,1,7,5,6,4,3,2] => 3
[1,7,2,8,4,5,3,6] => 3
[1,7,3,4,2,5,8,6] => 3
[8,2,5,1,3,6,4,7] => 1
[7,1,2,8,5,3,4,6] => 3
[5,2,6,3,7,4,8,1] => 1
[1,6,2,8,3,5,4,7] => 3
[8,1,5,3,2,4,6,7] => 3
[7,8,5,6,2,1,4,3] => 3
[7,8,4,2,6,1,5,3] => 5
[8,6,1,3,4,2,5,7] => 3
[8,3,1,5,6,2,4,7] => 3
[6,5,8,7,3,4,1,2] => 3
[6,4,8,3,7,5,1,2] => 5
[3,6,4,5,7,2,8,1] => 3
[5,2,4,7,3,6,8,1] => 1
[4,2,5,1,6,3,8,7] => 1
[5,4,3,6,1,2,8,7] => 3
[4,5,2,3,7,6,1,8] => 5
[4,1,2,6,5,8,7,3] => 3
[5,1,6,2,4,8,7,3] => 1
[7,6,2,1,8,5,4,3] => 1
[2,7,6,8,5,4,1,3] => 1
[8,7,1,6,5,3,2,4] => 3
[2,8,1,3,4,5,7,6] => 3
[3,1,8,2,4,7,6,5] => 3
[5,4,8,1,7,2,6,3] => 1
[5,4,6,2,7,1,8,3] => 1
[1,7,6,8,5,4,2,3] => 3
[6,8,5,4,2,1,3,7] => 1
[1,7,2,6,3,8,4,5] => 3
[8,5,7,3,2,1,6,4] => 3
[4,2,5,3,7,6,8,1] => 1
[3,2,6,4,7,5,8,1] => 1
[4,2,6,3,7,5,8,1] => 1
[2,7,6,5,3,4,8,1] => 3
[5,8,6,7,4,3,2,1] => 3
[4,2,5,1,7,6,8,3] => 1
[4,2,6,1,7,3,8,5] => 1
[4,3,1,2,8,7,5,6] => 5
[4,1,5,2,7,6,8,3] => 1
[4,1,6,2,7,5,8,3] => 1
[1,7,2,4,3,5,6,8] => 5
[6,2,8,4,5,1,7,3] => 5
[8,1,4,2,6,3,5,7] => 3
[4,3,5,1,6,2,8,7] => 1
[3,1,5,4,7,6,8,2] => 1
[4,1,5,3,7,6,8,2] => 1
[4,1,6,3,7,5,8,2] => 1
[8,3,6,1,4,7,2,5] => 1
[1,7,2,3,4,6,5,8] => 5
[6,3,7,1,4,8,2,5] => 1
[2,1,7,5,6,8,3,4] => 3
[2,1,5,3,8,7,6,4] => 1
[1,6,7,8,3,4,5,2] => 7
[1,8,4,2,5,3,6,7] => 3
[3,1,6,5,4,2,8,7] => 1
[5,6,1,2,3,8,7,4] => 5
[1,3,2,7,4,6,5,8] => 3
[1,2,7,6,8,3,4,5] => 5
[8,7,1,5,6,4,3,2] => 3
[3,8,7,6,4,5,2,1] => 3
[4,8,2,3,5,1,6,7] => 3
[5,1,6,4,7,3,8,2] => 1
[6,1,8,7,2,5,4,3] => 3
[1,8,2,5,3,7,4,6] => 3
[2,6,8,4,3,7,5,1] => 1
[4,2,6,8,7,3,5,1] => 1
[8,5,1,3,7,2,6,4] => 3
[8,3,1,2,4,7,5,6] => 3
[1,8,2,4,3,7,5,6] => 3
[1,8,2,4,3,6,5,7] => 3
[4,7,2,5,8,3,6,1] => 1
[5,4,6,2,7,3,8,1] => 1
[6,1,8,3,2,5,4,7] => 1
[1,7,2,5,3,8,4,6] => 3
[8,4,1,5,7,2,6,3] => 3
[8,7,6,3,5,1,4,2] => 3
[3,4,8,5,6,7,2,1] => 5
[2,7,8,4,5,3,6,1] => 3
[3,1,6,5,7,4,8,2] => 1
[4,1,2,8,7,6,5,3] => 3
[5,8,1,2,7,6,3,4] => 5
[5,3,1,8,2,7,4,6] => 1
[4,1,2,3,6,8,7,5] => 3
[7,5,1,3,8,2,6,4] => 1
[3,6,8,5,7,2,4,1] => 1
[8,2,1,7,3,5,6,4] => 3
[2,8,4,1,6,7,5,3] => 3
[3,6,8,7,1,5,4,2] => 3
[8,3,6,7,2,1,5,4] => 3
[4,6,8,2,1,7,5,3] => 1
[3,7,6,8,4,5,2,1] => 3
[2,7,6,8,5,3,4,1] => 3
[2,4,8,6,7,3,5,1] => 3
[6,8,2,4,3,5,1,7] => 3
[7,5,2,8,3,4,6,1] => 3
[5,6,2,8,4,3,1,7] => 3
[5,7,8,6,3,4,1,2] => 5
[4,1,6,5,7,3,8,2] => 1
[3,2,5,1,7,6,8,4] => 1
[3,2,6,1,7,5,8,4] => 1
[4,2,6,1,7,5,8,3] => 1
[5,1,8,2,7,6,4,3] => 1
[6,4,3,1,2,8,7,5] => 3
[7,4,3,1,8,2,6,5] => 1
[3,2,8,1,7,6,4,5] => 3
[3,2,8,7,1,5,4,6] => 3
[4,8,2,7,1,5,3,6] => 1
[1,4,2,8,3,7,5,6] => 3
[1,6,2,4,3,8,5,7] => 3
[6,3,8,2,1,7,5,4] => 1
[7,5,1,3,8,4,2,6] => 1
[8,1,6,2,7,4,5,3] => 3
[6,8,1,7,2,5,3,4] => 3
[4,2,1,3,8,5,7,6] => 1
[3,2,5,1,6,4,8,7] => 1
[5,8,7,2,1,4,3,6] => 3
[3,2,8,6,5,1,4,7] => 3
[6,1,5,8,7,4,2,3] => 3
[3,8,6,7,1,5,2,4] => 3
[3,2,6,1,4,8,7,5] => 3
[5,7,2,8,4,3,6,1] => 1
[3,7,4,1,8,5,2,6] => 1
[5,2,6,1,7,3,8,4] => 1
[7,8,1,3,2,5,4,6] => 3
[6,1,2,8,4,3,5,7] => 3
[3,2,5,1,7,4,8,6] => 1
[5,4,6,1,7,2,8,3] => 1
[1,6,8,5,3,7,4,2] => 3
[8,6,1,7,4,2,5,3] => 1
[3,2,8,5,7,4,6,1] => 1
[3,6,5,8,7,4,1,2] => 3
[4,3,6,1,5,8,2,7] => 1
[1,3,6,7,5,8,2,4] => 3
[3,8,1,5,2,4,6,7] => 3
[3,7,8,1,5,2,4,6] => 3
[1,2,7,5,8,3,4,6] => 5
[6,7,1,4,2,8,3,5] => 3
[1,6,7,2,8,4,3,5] => 3
[5,4,2,8,7,1,6,3] => 1
[4,7,2,1,3,5,8,6] => 1
[5,2,7,1,3,8,4,6] => 1
[5,3,1,7,8,2,4,6] => 3
[4,3,5,2,1,8,6,7] => 3
[5,6,2,1,4,8,3,7] => 3
[4,1,3,2,8,5,6,7] => 3
[2,6,1,4,5,8,3,7] => 3
[2,1,7,6,5,8,3,4] => 3
[5,7,3,6,1,8,2,4] => 1
[6,4,3,5,8,1,7,2] => 1
[2,7,6,4,5,8,1,3] => 3
[7,3,5,4,8,6,1,2] => 3
[3,2,5,4,8,1,6,7] => 3
[3,2,6,7,4,5,1,8] => 5
[3,2,6,8,4,1,5,7] => 1
[4,6,2,8,3,1,5,7] => 3
[4,7,2,8,1,3,5,6] => 3
[5,6,8,2,3,1,4,7] => 3
[5,7,8,2,1,3,4,6] => 3
[1,4,3,7,8,5,6,2] => 5
[1,5,6,3,4,8,7,2] => 5
[4,1,2,7,8,5,6,3] => 5
[5,1,7,2,8,4,6,3] => 3
[6,1,7,8,2,4,5,3] => 3
[5,7,1,2,8,3,6,4] => 3
[6,7,1,8,2,3,5,4] => 3
[1,8,6,5,3,7,4,2] => 3
[5,8,7,3,2,6,1,4] => 3
[2,5,3,7,1,6,8,4] => 1
[2,6,1,3,5,4,8,7] => 1
[1,5,2,4,3,7,6,8] => 3
[1,3,2,8,4,6,5,7] => 3
[1,7,2,4,3,6,5,8] => 3
[2,8,3,1,5,4,6,7] => 3
[2,5,3,4,7,1,8,6] => 3
[4,2,5,3,7,1,8,6] => 1
[4,2,5,3,1,8,6,7] => 3
[4,2,1,8,5,3,6,7] => 3
[5,1,4,8,3,2,6,7] => 3
[1,5,8,4,3,2,6,7] => 3
[4,3,6,2,8,7,5,1] => 3
[6,4,3,1,7,2,8,5] => 1
[1,7,4,3,8,5,2,6] => 3
[1,5,7,3,8,4,2,6] => 3
[5,1,4,7,8,3,2,6] => 3
[5,4,7,1,3,8,2,6] => 1
[4,8,1,5,7,3,6,2] => 1
[8,1,5,3,7,4,6,2] => 1
[1,4,3,8,7,5,6,2] => 3
[4,3,1,8,6,7,5,2] => 3
[4,3,7,1,8,6,5,2] => 1
[6,8,1,7,4,3,5,2] => 1
[6,4,8,1,7,3,5,2] => 1
[6,4,8,7,1,5,2,3] => 3
[7,6,4,1,3,8,2,5] => 1
[7,6,1,4,8,3,2,5] => 3
[7,1,6,8,4,3,2,5] => 3
[1,7,5,6,3,2,8,4] => 3
[6,1,7,5,3,2,8,4] => 1
[6,5,3,2,8,7,4,1] => 1
[5,2,6,3,8,7,4,1] => 3
[5,2,7,6,3,1,8,4] => 3
[6,5,2,1,7,3,8,4] => 1
[4,2,1,7,8,5,3,6] => 3
[2,7,4,6,3,1,8,5] => 3
[6,2,4,8,3,7,5,1] => 3
[7,2,6,3,4,1,8,5] => 3
[2,7,1,8,3,5,4,6] => 3
[2,1,7,3,5,8,4,6] => 1
[8,1,2,7,6,3,4,5] => 5
[7,8,2,6,3,1,5,4] => 3
[2,7,8,4,1,6,5,3] => 3
[2,8,1,7,5,6,3,4] => 3
[8,3,7,1,5,6,2,4] => 3
[8,6,1,2,7,5,3,4] => 3
[1,8,5,2,6,7,4,3] => 3
[5,2,1,8,6,7,4,3] => 3
[5,2,7,1,8,6,4,3] => 1
[2,8,5,7,6,4,3,1] => 1
[1,7,8,5,2,6,4,3] => 3
[7,8,1,6,4,2,5,3] => 3
[7,8,6,1,5,3,2,4] => 3
[7,3,8,6,1,5,2,4] => 3
[2,7,6,8,1,4,3,5] => 1
[8,2,5,7,6,4,3,1] => 3
[6,5,8,7,1,2,3,4] => 5
[4,1,5,3,7,2,8,6] => 1
[7,5,8,4,3,6,2,1] => 1
[4,7,3,2,1,5,8,6] => 1
[5,6,7,8,2,1,4,3] => 5
[8,5,6,7,1,3,2,4] => 5
[5,8,6,2,4,1,3,7] => 3
[5,1,6,2,7,4,8,3] => 1
[8,3,5,2,1,6,4,7] => 3
[5,7,3,8,1,4,6,2] => 1
[6,8,1,4,7,2,5,3] => 1
[3,2,1,7,8,5,6,4] => 5
[4,7,3,5,8,6,2,1] => 1
[4,3,6,5,7,1,8,2] => 1
[8,4,2,1,7,3,6,5] => 3
[3,7,5,1,4,2,8,6] => 1
[1,8,6,3,7,5,2,4] => 3
[6,2,8,1,3,4,7,5] => 3
[4,8,2,1,7,6,3,5] => 1
[2,7,4,8,1,6,5,3] => 1
[3,8,2,1,4,6,5,7] => 3
[1,4,2,8,3,6,5,7] => 3
[4,7,2,8,1,5,3,6] => 1
[5,2,1,8,3,4,7,6] => 3
[4,1,3,2,8,6,5,7] => 1
[3,1,6,7,5,8,2,4] => 3
[2,4,5,7,3,1,8,6] => 3
[4,6,8,3,2,7,5,1] => 1
[1,4,6,7,3,2,8,5] => 5
[1,7,4,8,6,3,5,2] => 3
[3,7,6,5,8,2,1,4] => 3
[2,3,5,7,6,8,1,4] => 3
[2,1,6,5,7,8,3,4] => 3
[2,1,7,8,5,6,4,3] => 3
[2,5,4,7,6,1,8,3] => 1
[3,2,5,6,1,8,7,4] => 3
[6,3,1,5,2,4,8,7] => 1
[1,3,7,4,6,8,2,5] => 3
[8,1,6,5,7,2,4,3] => 1
[7,8,1,6,2,4,5,3] => 3
[1,7,2,8,5,3,4,6] => 3
[7,6,1,8,4,3,2,5] => 3
[8,1,2,7,3,4,6,5] => 3
[1,3,8,7,5,6,2,4] => 3
[1,2,8,7,6,3,4,5] => 5
[6,3,7,5,2,8,4,1] => 1
[8,5,7,3,1,4,2,6] => 1
[2,5,7,3,8,6,4,1] => 1
[2,8,6,3,1,5,7,4] => 1
[4,8,1,2,7,6,3,5] => 3
[4,1,2,8,7,5,6,3] => 3
[8,4,2,1,7,5,3,6] => 1
[8,3,4,1,6,7,2,5] => 3
[3,1,4,8,6,5,7,2] => 1
[3,4,8,1,7,2,5,6] => 3
[2,3,8,1,4,6,7,5] => 3
[4,3,6,2,7,5,8,1] => 1
[5,3,6,4,7,2,8,1] => 1
[5,3,6,1,7,4,8,2] => 1
[5,3,6,1,7,2,8,4] => 1
[5,3,6,2,7,1,8,4] => 1
[5,3,6,2,7,4,8,1] => 1
[5,2,6,3,7,1,8,4] => 1
[5,2,6,4,7,1,8,3] => 1
[1,7,5,4,8,3,6,2] => 5
[8,1,5,4,7,6,2,3] => 3
[1,8,6,7,4,5,3,2] => 5
[7,1,6,8,4,2,5,3] => 3
[7,8,6,1,4,2,3,5] => 5
[1,7,6,8,4,3,5,2] => 3
[8,6,7,1,3,4,2,5] => 5
[7,6,8,1,3,2,4,5] => 3
[7,5,8,3,1,2,4,6] => 3
[8,6,1,7,3,5,2,4] => 1
[1,7,8,6,5,3,4,2] => 5
[7,8,1,6,5,2,3,4] => 5
[6,4,3,7,2,5,1,8] => 5
[8,4,3,6,5,1,2,7] => 3
[6,5,8,3,2,1,4,7] => 3
[1,8,2,5,3,6,4,7] => 3
[1,5,2,8,3,6,4,7] => 3
[6,7,8,1,4,3,2,5] => 5
[6,7,8,5,1,3,2,4] => 5
[5,7,6,8,2,3,4,1] => 5
[6,7,8,2,4,3,5,1] => 5
[7,8,2,1,3,4,6,5] => 3
[1,5,2,4,3,8,6,7] => 3
[3,2,7,1,8,4,6,5] => 1
[7,8,4,1,6,2,3,5] => 3
[6,1,8,4,5,2,3,7] => 3
[1,6,7,3,2,5,4,8] => 5
[7,8,3,1,2,6,4,5] => 5
[7,8,2,4,5,1,6,3] => 3
[7,8,2,3,1,5,6,4] => 5
[6,2,8,3,1,5,7,4] => 1
[6,3,8,4,5,7,1,2] => 3
[2,6,7,4,5,1,8,3] => 3
[2,6,7,3,1,5,8,4] => 3
[3,5,4,7,6,8,1,2] => 3
[5,3,4,8,6,7,1,2] => 5
[5,2,4,8,6,1,7,3] => 1
[6,3,8,1,2,7,4,5] => 5
[5,1,3,8,2,6,4,7] => 1
[1,5,4,7,6,2,3,8] => 5
[5,1,4,8,6,2,3,7] => 3
[4,6,7,2,8,1,5,3] => 3
[4,6,7,3,8,5,1,2] => 3
[4,5,3,7,8,6,1,2] => 5
[4,5,2,7,8,1,6,3] => 5
[4,2,5,6,8,1,7,3] => 3
[4,3,5,6,8,7,1,2] => 3
[3,7,5,2,4,1,8,6] => 1
[8,2,4,5,7,3,6,1] => 3
[8,2,4,6,5,3,1,7] => 1
[8,2,5,4,6,1,3,7] => 1
[8,6,3,5,1,4,2,7] => 3
[8,6,1,4,5,3,2,7] => 3
[8,1,5,6,4,3,2,7] => 3
[5,4,7,3,1,8,2,6] => 1
[1,7,4,5,3,2,8,6] => 3
[5,7,4,2,1,3,8,6] => 3
[8,3,7,5,1,4,6,2] => 3
[8,4,1,7,5,3,6,2] => 3
[4,6,3,8,7,1,5,2] => 3
[3,1,5,8,6,7,4,2] => 3
[4,8,1,6,7,3,5,2] => 3
[3,6,4,1,8,7,5,2] => 1
[8,2,6,1,4,7,5,3] => 3
[3,7,1,6,4,8,2,5] => 3
[1,7,3,5,6,8,2,4] => 3
[4,2,7,6,8,3,1,5] => 3
[3,8,2,4,6,7,5,1] => 3
[3,7,2,6,4,8,1,5] => 3
[5,3,7,2,1,8,4,6] => 3
[8,7,6,1,3,4,2,5] => 3
[3,7,8,6,2,1,5,4] => 3
[8,5,3,7,1,6,2,4] => 3
[8,5,7,2,1,3,6,4] => 3
[8,2,6,7,1,3,5,4] => 3
[8,3,6,1,7,5,2,4] => 1
[4,6,1,8,7,2,5,3] => 3
[8,2,6,5,7,4,1,3] => 1
[1,7,2,5,8,6,4,3] => 3
[1,7,4,8,2,6,5,3] => 3
[3,7,8,1,6,5,2,4] => 3
[2,7,8,6,1,3,5,4] => 3
[2,6,5,7,3,4,8,1] => 3
[1,6,4,7,5,8,2,3] => 3
[8,2,6,3,4,7,5,1] => 3
[7,2,6,3,5,4,8,1] => 1
[6,2,7,4,3,5,8,1] => 1
[4,7,5,6,3,2,8,1] => 3
[3,7,6,4,5,2,8,1] => 3
[6,1,7,5,3,8,2,4] => 1
[5,4,1,7,6,8,2,3] => 3
[4,8,5,6,2,7,3,1] => 3
[3,8,6,4,2,7,5,1] => 1
[7,8,5,2,4,6,3,1] => 3
[2,8,1,7,4,3,6,5] => 1
[3,8,4,1,7,2,6,5] => 1
[5,4,7,1,8,3,2,6] => 1
[6,7,1,4,8,3,2,5] => 3
[2,7,1,8,4,5,3,6] => 3
[6,5,1,4,3,8,2,7] => 3
[7,4,2,1,8,5,3,6] => 1
[6,4,3,1,5,8,2,7] => 1
[4,7,5,6,8,3,2,1] => 3
[1,4,8,6,7,5,2,3] => 5
[7,3,8,5,4,6,2,1] => 1
[6,3,5,8,4,7,2,1] => 1
[5,4,3,8,6,7,2,1] => 3
[5,4,2,8,7,3,6,1] => 3
[6,2,5,8,7,3,4,1] => 3
[7,2,8,6,4,3,5,1] => 1
[2,1,8,7,4,6,3,5] => 1
[3,1,8,5,7,6,2,4] => 3
[5,4,1,8,7,6,2,3] => 3
[4,5,2,6,3,1,8,7] => 3
[6,5,2,7,4,8,3,1] => 1
[8,3,7,5,2,1,6,4] => 3
[5,6,3,2,4,1,8,7] => 3
[3,6,2,4,1,5,8,7] => 1
[7,6,1,3,5,8,4,2] => 3
[3,6,7,4,1,8,5,2] => 3
[5,6,3,7,4,8,1,2] => 3
[2,1,6,7,4,8,5,3] => 3
[5,8,3,7,4,2,6,1] => 1
[3,8,7,4,1,2,6,5] => 3
[7,8,1,3,5,2,6,4] => 3
[3,8,4,2,5,7,1,6] => 1
[6,8,3,5,2,7,4,1] => 1
[2,1,8,5,3,7,4,6] => 1
[6,5,3,2,8,7,1,4] => 3
[7,5,2,4,8,1,6,3] => 3
[3,4,2,8,5,7,6,1] => 3
[5,7,1,6,8,2,4,3] => 1
[8,6,2,5,1,7,4,3] => 3
[5,6,2,1,8,7,3,4] => 3
[7,5,2,6,3,8,1,4] => 1
[2,4,3,1,8,5,6,7] => 3
[7,1,8,5,4,3,6,2] => 3
[2,1,7,8,5,4,6,3] => 3
[2,1,5,8,4,6,3,7] => 1
[6,5,3,8,4,1,2,7] => 3
[2,4,8,3,5,6,1,7] => 3
[4,1,8,3,6,5,2,7] => 1
[8,4,1,3,7,2,6,5] => 1
[4,3,8,2,5,1,7,6] => 3
[7,4,3,8,2,5,1,6] => 3
[2,1,4,8,3,5,7,6] => 1
[3,2,5,4,7,1,8,6] => 1
[4,2,5,3,6,1,8,7] => 1
[3,1,5,4,6,2,8,7] => 1
[4,1,5,3,6,2,8,7] => 1
[4,3,5,1,7,2,8,6] => 1
[3,1,5,4,7,2,8,6] => 1
[2,1,5,4,7,3,8,6] => 1
[4,3,5,1,7,6,8,2] => 1
[4,3,6,1,7,5,8,2] => 1
[5,1,6,3,7,4,8,2] => 1
[3,1,6,4,7,5,8,2] => 1
[2,1,6,4,7,5,8,3] => 1
[2,1,6,4,7,3,8,5] => 1
[3,1,6,4,7,2,8,5] => 1
[4,1,6,3,7,2,8,5] => 1
[5,1,6,3,7,2,8,4] => 1
[4,2,5,1,7,3,8,6] => 1
[4,2,6,3,7,1,8,5] => 1
[3,2,6,4,7,1,8,5] => 1
[3,1,4,2,7,6,8,5] => 1
[3,2,6,5,7,1,8,4] => 1
[4,2,6,5,7,3,8,1] => 1
[4,2,6,5,7,1,8,3] => 1
[3,1,5,2,7,6,8,4] => 1
[2,1,5,3,7,6,8,4] => 1
[2,1,6,3,7,5,8,4] => 1
[3,1,6,2,7,5,8,4] => 1
[5,2,6,1,7,4,8,3] => 1
[5,2,6,4,7,3,8,1] => 1
[5,1,6,4,7,2,8,3] => 1
[4,1,6,5,7,2,8,3] => 1
[3,1,6,5,7,2,8,4] => 1
[2,1,6,5,7,3,8,4] => 1
[4,7,2,6,5,3,1,8] => 5
[5,7,6,2,4,3,1,8] => 3
[4,8,2,6,5,1,3,7] => 1
[6,1,5,4,2,8,7,3] => 3
[7,1,5,4,8,2,6,3] => 1
[6,8,7,1,2,4,3,5] => 3
[8,4,3,7,1,5,2,6] => 3
[4,5,2,3,1,8,7,6] => 5
[1,5,8,3,7,6,4,2] => 5
[8,5,1,3,7,6,2,4] => 3
[6,5,1,3,2,8,7,4] => 3
[4,6,2,1,3,8,7,5] => 1
[4,7,2,1,8,3,6,5] => 3
[7,6,1,8,3,2,5,4] => 3
[1,6,8,7,3,5,4,2] => 3
[7,1,8,6,5,2,4,3] => 1
[1,4,2,7,3,6,5,8] => 3
[1,5,2,7,3,6,4,8] => 3
[1,7,2,4,3,8,5,6] => 3
[1,6,2,5,3,8,4,7] => 3
[5,3,6,8,4,7,2,1] => 1
[3,7,2,5,4,8,6,1] => 1
[8,4,2,5,7,3,6,1] => 1
[4,2,6,5,8,3,7,1] => 1
[5,2,6,8,4,3,7,1] => 1
[3,1,6,5,4,8,2,7] => 1
[4,1,6,5,8,3,2,7] => 1
[5,1,6,8,4,3,2,7] => 1
[5,7,1,8,4,3,2,6] => 1
[4,7,1,5,8,3,2,6] => 1
[2,7,1,5,4,3,8,6] => 1
[8,3,1,5,4,7,2,6] => 1
[8,4,1,5,7,3,2,6] => 1
[8,4,6,1,7,3,2,5] => 1
[8,2,6,1,4,3,7,5] => 1
[2,7,6,1,4,3,8,5] => 1
[3,7,6,1,4,8,2,5] => 1
[4,7,6,2,8,3,5,1] => 1
[8,3,6,2,4,7,5,1] => 1
[3,7,6,2,4,8,5,1] => 1
[8,7,3,1,4,6,2,5] => 1
[8,7,2,5,1,3,6,4] => 1
[8,2,6,5,1,3,7,4] => 1
[8,3,6,5,1,7,2,4] => 1
[8,4,6,5,7,1,2,3] => 5
[5,7,6,8,4,1,2,3] => 5
[4,7,6,5,8,1,2,3] => 5
[3,7,6,5,1,8,2,4] => 1
[2,7,6,5,1,3,8,4] => 1
[9,7,8,4,5,6,1,2,3] => 6
[9,7,8,5,6,1,2,3,4] => 6
[9,8,5,6,7,1,2,3,4] => 6
[8,9,5,6,7,1,2,3,4] => 8
[7,4,8,2,5,9,1,3,6] => 2
[6,4,7,2,5,1,3,8,9] => 4
[6,3,2,7,8,1,4,5,9] => 6
[6,7,3,4,8,1,2,5,9] => 6
[8,7,6,5,4,3,2,1,9] => 2
[1,9,8,7,6,5,4,3,2] => 2
[8,7,6,4,5,3,2,1,9] => 4
[1,9,8,7,5,6,4,3,2] => 4
[8,7,5,4,6,3,2,1,9] => 2
[8,7,4,6,5,3,2,1,9] => 2
[1,9,8,6,5,7,4,3,2] => 2
[1,9,8,5,7,6,4,3,2] => 2
[9,1,2,3,4,5,6,7,8] => 8
[2,3,4,5,6,7,8,9,1] => 8
[8,1,2,3,4,5,6,7,9] => 8
[2,3,4,5,6,7,8,1,9] => 8
[8,1,2,3,4,5,6,9,7] => 6
[7,1,2,3,4,5,6,8,9] => 8
[2,3,4,5,6,7,1,8,9] => 8
[2,3,4,5,6,7,9,1,8] => 6
[9,2,1,3,4,5,6,7,8] => 6
[3,2,4,5,6,7,8,9,1] => 6
[9,3,1,2,4,5,6,7,8] => 6
[9,2,3,1,4,5,6,7,8] => 6
[4,2,3,5,6,7,8,9,1] => 6
[3,4,2,5,6,7,8,9,1] => 6
[7,8,6,5,4,3,2,1,9] => 4
[1,8,9,7,6,5,4,3,2] => 4
[7,6,8,5,4,3,2,1,9] => 2
[6,8,7,5,4,3,2,1,9] => 2
[1,8,7,9,6,5,4,3,2] => 2
[1,7,9,8,6,5,4,3,2] => 2
[1,9,2,3,4,5,6,7,8] => 8
[7,8,1,2,3,4,5,6,9] => 8
[1,8,9,2,3,4,5,6,7] => 8
[7,1,8,2,3,4,5,6,9] => 6
[6,8,1,2,3,4,5,7,9] => 6
[1,8,2,9,3,4,5,6,7] => 6
[1,7,9,2,3,4,5,6,8] => 6
[1,2,3,4,5,6,7,9,8] => 8
[2,1,3,4,5,6,7,8,9] => 8
[2,9,1,3,4,5,6,7,8] => 6
[1,8,2,3,4,5,6,9,7] => 6
[7,1,2,3,4,5,6,9,8] => 6
[2,1,9,3,4,5,6,7,8] => 6
[2,8,1,3,4,5,6,7,9] => 6
[1,2,3,4,5,6,7,8,9] => 10
[8,9,1,2,3,4,5,6,7] => 8
[9,8,1,2,3,4,5,6,7] => 8
[7,8,9,1,2,3,4,5,6] => 8
[9,7,8,1,2,3,4,5,6] => 8
[9,8,7,1,2,3,4,5,6] => 6
[6,7,8,9,1,2,3,4,5] => 8
[9,6,7,8,1,2,3,4,5] => 8
[8,9,6,7,1,2,3,4,5] => 8
[9,8,6,7,1,2,3,4,5] => 6
[9,8,7,6,1,2,3,4,5] => 6
[9,5,6,7,8,1,2,3,4] => 8
[9,8,7,5,6,1,2,3,4] => 6
[9,8,7,6,5,1,2,3,4] => 4
[7,8,9,4,5,6,1,2,3] => 8
[9,8,7,4,5,6,1,2,3] => 6
[8,9,6,7,4,5,1,2,3] => 6
[9,8,6,7,4,5,1,2,3] => 6
[9,8,7,6,4,5,1,2,3] => 4
[9,8,7,6,5,4,1,2,3] => 4
[9,7,8,5,6,3,4,1,2] => 6
[9,8,7,5,6,3,4,1,2] => 4
[9,8,7,6,5,3,4,1,2] => 4
[9,8,7,6,5,4,3,1,2] => 2
[9,8,7,6,5,4,3,2,1] => 2
[3,4,1,2,5,6,7,8,9] => 8
[3,2,1,4,5,6,7,8,9] => 8
[4,5,6,1,2,3,7,8,9] => 8
[4,2,5,1,3,6,7,8,9] => 6
[4,3,2,1,5,6,7,8,9] => 6
[5,6,7,8,1,2,3,4,9] => 8
[5,2,6,7,1,3,4,8,9] => 6
[5,6,3,4,1,2,7,8,9] => 8
[5,3,2,6,1,4,7,8,9] => 6
[5,4,3,2,1,6,7,8,9] => 6
[6,2,7,8,9,1,3,4,5] => 6
[6,4,3,2,7,1,5,8,9] => 4
[6,5,4,3,2,1,7,8,9] => 4
[7,4,3,2,8,9,1,5,6] => 4
[7,8,5,6,3,4,1,2,9] => 6
[7,5,3,8,2,6,1,4,9] => 4
[7,5,4,3,2,8,1,6,9] => 4
[7,6,5,4,3,2,1,8,9] => 4
[8,6,9,4,7,2,5,1,3] => 2
[8,6,4,3,9,2,7,1,5] => 2
[8,6,5,4,3,2,9,1,7] => 2
[2,1,4,3,6,5,8,7,10,9] => 1
[4,3,2,1,6,5,8,7,10,9] => 1
[6,3,2,5,4,1,8,7,10,9] => 1
[8,3,2,5,4,7,6,1,10,9] => 1
[10,3,2,5,4,7,6,9,8,1] => 1
[2,1,6,5,4,3,8,7,10,9] => 1
[6,5,4,3,2,1,8,7,10,9] => 1
[8,5,4,3,2,7,6,1,10,9] => 1
[10,5,4,3,2,7,6,9,8,1] => 1
[2,1,8,5,4,7,6,3,10,9] => 1
[8,7,4,3,6,5,2,1,10,9] => 1
[10,7,4,3,6,5,2,9,8,1] => 1
[2,1,10,5,4,7,6,9,8,3] => 1
[10,9,4,3,6,5,8,7,2,1] => 1
[8,9,5,6,3,4,10,1,2,7] => 7
[2,1,4,3,8,7,6,5,10,9] => 1
[4,3,2,1,8,7,6,5,10,9] => 1
[8,3,2,7,6,5,4,1,10,9] => 1
[10,3,2,7,6,5,4,9,8,1] => 1
[2,1,8,7,6,5,4,3,10,9] => 1
[8,7,6,5,4,3,2,1,10,9] => 1
[9,7,6,5,4,3,2,10,1,8] => 3
[10,7,6,5,4,3,2,9,8,1] => 1
[2,1,10,7,6,5,4,9,8,3] => 1
[10,9,6,5,4,3,8,7,2,1] => 1
[2,1,4,3,10,7,6,9,8,5] => 1
[4,3,2,1,10,7,6,9,8,5] => 1
[10,3,2,9,6,5,8,7,4,1] => 1
[2,1,10,9,6,5,8,7,4,3] => 1
[10,9,8,5,4,7,6,3,2,1] => 1
[6,7,8,9,10,1,2,3,4,5] => 9
[7,3,2,8,9,10,1,4,5,6] => 7
[8,5,4,3,2,9,10,1,6,7] => 5
[2,1,4,3,6,5,10,9,8,7] => 1
[4,3,2,1,6,5,10,9,8,7] => 1
[6,3,2,5,4,1,10,9,8,7] => 1
[10,3,2,5,4,9,8,7,6,1] => 1
[2,1,6,5,4,3,10,9,8,7] => 1
[6,5,4,3,2,1,10,9,8,7] => 1
[10,5,4,3,2,9,8,7,6,1] => 1
[2,1,10,5,4,9,8,7,6,3] => 1
[10,9,4,3,8,7,6,5,2,1] => 1
[9,7,5,10,3,8,2,6,1,4] => 1
[2,1,4,3,10,9,8,7,6,5] => 1
[4,3,2,1,10,9,8,7,6,5] => 1
[10,3,2,9,8,7,6,5,4,1] => 1
[2,1,10,9,8,7,6,5,4,3] => 1
[10,9,8,7,6,5,4,3,2,1] => 1
[2,4,6,8,10,1,3,5,7,9] => 1
[5,6,7,8,10,1,2,3,4,9] => 7
[4,7,8,9,10,1,2,3,5,6] => 7
[5,7,8,9,10,1,2,3,4,6] => 7
[4,5,6,8,10,1,2,3,7,9] => 5
[3,7,8,9,10,1,2,4,5,6] => 7
[3,6,7,8,10,1,2,4,5,9] => 5
[3,5,8,9,10,1,2,4,6,7] => 5
[3,6,8,9,10,1,2,4,5,7] => 5
[4,6,7,8,10,1,2,3,5,9] => 5
[4,5,8,9,10,1,2,3,6,7] => 7
[5,6,8,9,10,1,2,3,4,7] => 7
[4,6,8,9,10,1,2,3,5,7] => 5
[3,4,6,8,10,1,2,5,7,9] => 3
[2,7,8,9,10,1,3,4,5,6] => 7
[2,6,7,8,10,1,3,4,5,9] => 5
[2,5,8,9,10,1,3,4,6,7] => 5
[2,6,8,9,10,1,3,4,5,7] => 5
[2,5,6,8,10,1,3,4,7,9] => 3
[2,4,8,9,10,1,3,5,6,7] => 5
[2,4,7,8,10,1,3,5,6,9] => 3
[2,4,6,9,10,1,3,5,7,8] => 3
[2,4,7,9,10,1,3,5,6,8] => 3
[2,5,7,8,10,1,3,4,6,9] => 3
[4,5,6,9,10,1,2,3,7,8] => 7
[5,6,7,9,10,1,2,3,4,8] => 7
[2,5,7,9,10,1,3,4,6,8] => 3
[3,5,6,8,10,1,2,4,7,9] => 3
[3,4,8,9,10,1,2,5,6,7] => 7
[3,4,7,8,10,1,2,5,6,9] => 5
[3,4,6,9,10,1,2,5,7,8] => 5
[3,4,7,9,10,1,2,5,6,8] => 5
[4,5,7,8,10,1,2,3,6,9] => 5
[2,5,6,9,10,1,3,4,7,8] => 5
[2,6,7,9,10,1,3,4,5,8] => 5
[4,5,7,9,10,1,2,3,6,8] => 5
[3,5,7,8,10,1,2,4,6,9] => 3
[3,5,6,9,10,1,2,4,7,8] => 5
[3,6,7,9,10,1,2,4,5,8] => 5
[4,6,7,9,10,1,2,3,5,8] => 5
[3,5,7,9,10,1,2,4,6,8] => 3
[10,8,9,5,6,7,1,2,3,4] => 7
[9,6,10,2,7,8,1,3,4,5] => 5
[10,7,8,3,4,9,1,2,5,6] => 7
[9,5,10,4,6,7,1,2,3,8] => 5
[8,4,9,3,5,10,1,2,6,7] => 5
[8,4,9,2,5,10,1,3,6,7] => 3
[10,8,9,4,5,6,1,2,3,7] => 7
[9,6,10,5,7,8,1,2,3,4] => 7
[10,7,8,5,6,9,1,2,3,4] => 7
[9,8,10,5,6,7,1,2,3,4] => 7
[8,7,9,5,6,10,1,2,3,4] => 5
[8,6,9,2,7,10,1,3,4,5] => 3
[10,6,7,4,5,8,1,2,3,9] => 5
[9,5,10,2,6,7,1,3,4,8] => 3
[10,6,7,3,4,8,1,2,5,9] => 5
[9,8,10,4,5,6,1,2,3,7] => 5
[8,7,9,3,4,10,1,2,5,6] => 5
[8,6,9,5,7,10,1,2,3,4] => 5
[7,6,8,4,5,9,1,2,3,10] => 5
[7,5,8,2,6,9,1,3,4,10] => 3
[7,6,8,3,4,9,1,2,5,10] => 5
[7,5,8,4,6,9,1,2,3,10] => 5
[7,4,8,3,5,9,1,2,6,10] => 5
[7,4,8,2,5,9,1,3,6,10] => 3
[7,8,9,10,1,2,3,4,5,6] => 9
[9,10,7,8,5,6,3,4,1,2] => 7
[9,1,2,3,4,5,6,7,8,10] => 9
[1,2,3,4,5,6,7,8,9,10] => 11
[9,10,7,8,5,6,1,2,3,4] => 7
[9,10,5,6,7,8,1,2,3,4] => 9
[9,10,7,8,1,2,3,4,5,6] => 9
[9,10,1,2,3,4,5,6,7,8] => 9
[10,1,2,3,4,5,6,7,8,9] => 9
[9,8,7,6,5,4,3,2,1,10] => 3
[1,10,9,8,7,6,5,4,3,2] => 3
[1,10,2,3,4,5,6,7,8,9] => 9
[9,7,10,5,6,8,1,2,3,4] => 7
[10,7,8,4,5,9,1,2,3,6] => 7
[9,7,10,4,5,8,1,2,3,6] => 5
[8,7,9,4,5,10,1,2,3,6] => 5
[9,6,10,4,5,7,1,2,3,8] => 5
[8,6,9,4,5,10,1,2,3,7] => 5
[8,6,9,4,7,10,1,2,3,5] => 3
[9,6,10,3,4,7,1,2,5,8] => 3
[8,5,9,3,6,10,1,2,4,7] => 3
[9,5,10,3,6,7,1,2,4,8] => 3
[8,6,9,3,4,10,1,2,5,7] => 5
[8,6,9,3,7,10,1,2,4,5] => 3
[9,6,10,3,7,8,1,2,4,5] => 5
[9,7,10,3,4,8,1,2,5,6] => 5
[8,5,9,4,6,10,1,2,3,7] => 5
[9,6,10,4,7,8,1,2,3,5] => 5
[10,8,9,1,2,3,4,5,6,7] => 9
[9,8,7,5,6,4,3,2,1,10] => 3
[1,10,9,8,6,7,5,4,3,2] => 3
[2,3,4,5,6,7,8,9,10,1] => 9
[2,3,4,5,6,7,8,9,1,10] => 9
[10,2,1,3,4,5,6,7,8,9] => 7
[3,2,4,5,6,7,8,9,10,1] => 7
[8,9,7,6,5,4,3,2,1,10] => 3
[1,9,10,8,7,6,5,4,3,2] => 3
[8,9,1,2,3,4,5,6,7,10] => 9
[1,9,10,2,3,4,5,6,7,8] => 9
[1,2,3,4,5,6,7,8,10,9] => 9
[2,1,3,4,5,6,7,8,9,10] => 9
[9,1,2,3,4,5,6,7,10,8] => 7
[2,10,1,3,4,5,6,7,8,9] => 7
[10,9,1,2,3,4,5,6,7,8] => 9
[8,9,10,1,2,3,4,5,6,7] => 9
[10,9,8,1,2,3,4,5,6,7] => 7
[10,7,8,9,1,2,3,4,5,6] => 9
[10,9,7,8,1,2,3,4,5,6] => 7
[10,9,8,7,1,2,3,4,5,6] => 7
[10,6,7,8,9,1,2,3,4,5] => 9
[9,10,6,7,8,1,2,3,4,5] => 9
[10,9,6,7,8,1,2,3,4,5] => 7
[10,8,9,6,7,1,2,3,4,5] => 7
[10,9,8,6,7,1,2,3,4,5] => 7
[10,9,8,7,6,1,2,3,4,5] => 5
[10,9,5,6,7,8,1,2,3,4] => 7
[8,9,10,5,6,7,1,2,3,4] => 9
[10,9,8,5,6,7,1,2,3,4] => 7
[10,9,7,8,5,6,1,2,3,4] => 7
[10,9,8,7,5,6,1,2,3,4] => 5
[10,9,8,7,6,5,1,2,3,4] => 5
[10,7,8,9,4,5,6,1,2,3] => 7
[9,10,7,8,4,5,6,1,2,3] => 7
[10,9,7,8,4,5,6,1,2,3] => 7
[10,9,8,7,4,5,6,1,2,3] => 5
[10,8,9,6,7,4,5,1,2,3] => 7
[10,9,8,6,7,4,5,1,2,3] => 5
[10,9,8,7,6,4,5,1,2,3] => 5
[10,9,8,7,6,5,4,1,2,3] => 3
[10,9,7,8,5,6,3,4,1,2] => 5
[10,9,8,7,5,6,3,4,1,2] => 5
[10,9,8,7,6,5,3,4,1,2] => 3
[10,9,8,7,6,5,4,3,1,2] => 3
[3,4,1,2,5,6,7,8,9,10] => 9
[3,2,1,4,5,6,7,8,9,10] => 9
[4,5,6,1,2,3,7,8,9,10] => 9
[4,2,5,1,3,6,7,8,9,10] => 7
[4,3,2,1,5,6,7,8,9,10] => 7
[5,6,7,8,1,2,3,4,9,10] => 9
[5,2,6,7,1,3,4,8,9,10] => 7
[5,6,3,4,1,2,7,8,9,10] => 9
[5,3,2,6,1,4,7,8,9,10] => 7
[5,4,3,2,1,6,7,8,9,10] => 7
[6,2,7,8,9,1,3,4,5,10] => 7
[6,7,3,4,8,1,2,5,9,10] => 7
[6,3,2,7,8,1,4,5,9,10] => 7
[6,4,7,2,5,1,3,8,9,10] => 5
[6,4,3,2,7,1,5,8,9,10] => 5
[6,5,4,3,2,1,7,8,9,10] => 5
[7,8,3,4,9,10,1,2,5,6] => 7
[7,8,9,4,5,6,1,2,3,10] => 9
[7,4,3,2,8,9,1,5,6,10] => 5
[7,8,5,6,3,4,1,2,9,10] => 7
[7,5,3,8,2,6,1,4,9,10] => 5
[7,5,4,3,2,8,1,6,9,10] => 5
[7,6,5,4,3,2,1,8,9,10] => 5
[8,5,9,10,2,6,7,1,3,4] => 5
[8,5,3,9,2,6,10,1,4,7] => 3
[8,6,9,4,7,2,5,1,3,10] => 3
[8,6,4,3,9,2,7,1,5,10] => 3
[8,6,5,4,3,2,9,1,7,10] => 3
[8,7,6,5,4,3,2,1,9,10] => 3
[9,7,5,4,3,10,2,8,1,6] => 3
[7,5,8,3,6,9,1,2,4,10] => 3
[8,5,9,2,6,10,1,3,4,7] => 3
[10,9,8,7,6,5,4,3,2,1,11] => 2
[1,11,10,9,8,7,6,5,4,3,2] => 2
[11,1,2,3,4,5,6,7,8,9,10] => 10
[2,3,4,5,6,7,8,9,10,11,1] => 10
[10,1,2,3,4,5,6,7,8,9,11] => 10
[1,11,2,3,4,5,6,7,8,9,10] => 10
[1,2,3,4,5,6,7,8,9,11,10] => 10
[2,1,3,4,5,6,7,8,9,10,11] => 10
[6,7,8,9,10,12,1,2,3,4,5,11] => 9
[2,8,9,10,11,12,1,3,4,5,6,7] => 9
[10,9,8,7,6,5,4,3,2,1,12,11] => 1
[2,1,12,11,10,9,8,7,6,5,4,3] => 1
[2,7,9,10,11,12,1,3,4,5,6,8] => 7
[5,7,8,9,10,12,1,2,3,4,6,11] => 7
[2,6,9,10,11,12,1,3,4,5,7,8] => 7
[2,7,8,10,11,12,1,3,4,5,6,9] => 7
[4,7,8,9,10,12,1,2,3,5,6,11] => 7
[5,6,8,9,10,12,1,2,3,4,7,11] => 7
[2,5,9,10,11,12,1,3,4,6,7,8] => 7
[2,6,8,10,11,12,1,3,4,5,7,9] => 5
[2,7,8,9,11,12,1,3,4,5,6,10] => 7
[3,4,9,10,11,12,1,2,5,6,7,8] => 9
[3,7,8,9,10,12,1,2,4,5,6,11] => 7
[4,6,8,9,10,12,1,2,3,5,7,11] => 5
[5,6,7,8,11,12,1,2,3,4,9,10] => 9
[5,6,7,9,10,12,1,2,3,4,8,11] => 7
[2,4,9,10,11,12,1,3,5,6,7,8] => 7
[2,5,8,10,11,12,1,3,4,6,7,9] => 5
[2,6,7,10,11,12,1,3,4,5,8,9] => 7
[2,6,8,9,11,12,1,3,4,5,7,10] => 5
[2,7,8,9,10,12,1,3,4,5,6,11] => 7
[3,4,8,10,11,12,1,2,5,6,7,9] => 7
[3,6,8,9,10,12,1,2,4,5,7,11] => 5
[4,5,6,10,11,12,1,2,3,7,8,9] => 9
[4,5,8,9,10,12,1,2,3,6,7,11] => 7
[4,6,7,8,11,12,1,2,3,5,9,10] => 7
[4,6,7,9,10,12,1,2,3,5,8,11] => 5
[5,6,7,8,10,12,1,2,3,4,9,11] => 7
[2,4,8,10,11,12,1,3,5,6,7,9] => 5
[2,5,7,10,11,12,1,3,4,6,8,9] => 5
[2,5,8,9,11,12,1,3,4,6,7,10] => 5
[2,6,7,9,11,12,1,3,4,5,8,10] => 5
[2,6,8,9,10,12,1,3,4,5,7,11] => 5
[3,4,7,10,11,12,1,2,5,6,8,9] => 7
[3,4,8,9,11,12,1,2,5,6,7,10] => 7
[3,5,6,10,11,12,1,2,4,7,8,9] => 7
[3,5,8,9,10,12,1,2,4,6,7,11] => 5
[3,6,7,8,11,12,1,2,4,5,9,10] => 7
[3,6,7,9,10,12,1,2,4,5,8,11] => 5
[4,5,6,9,11,12,1,2,3,7,8,10] => 7
[4,5,7,8,11,12,1,2,3,6,9,10] => 7
[4,5,7,9,10,12,1,2,3,6,8,11] => 5
[4,6,7,8,10,12,1,2,3,5,9,11] => 5
[2,1,12,11,10,7,6,9,8,5,4,3] => 1
[10,9,8,5,4,7,6,3,2,1,12,11] => 1
[2,1,12,11,6,5,10,9,8,7,4,3] => 1
[2,1,12,11,8,7,6,5,10,9,4,3] => 1
[10,9,4,3,8,7,6,5,2,1,12,11] => 1
[10,9,6,5,4,3,8,7,2,1,12,11] => 1
[2,1,12,5,4,11,10,9,8,7,6,3] => 1
[2,1,12,11,6,5,8,7,10,9,4,3] => 1
[2,1,12,9,8,7,6,5,4,11,10,3] => 1
[4,3,2,1,12,11,10,9,8,7,6,5] => 1
[10,3,2,9,8,7,6,5,4,1,12,11] => 1
[10,9,4,3,6,5,8,7,2,1,12,11] => 1
[8,7,6,5,4,3,2,1,12,11,10,9] => 1
[10,7,6,5,4,3,2,9,8,1,12,11] => 1
[2,1,4,3,12,11,10,9,8,7,6,5] => 1
[2,1,12,5,4,11,8,7,10,9,6,3] => 1
[2,1,12,7,6,5,4,11,10,9,8,3] => 1
[2,1,12,9,6,5,8,7,4,11,10,3] => 1
[2,1,10,9,8,7,6,5,4,3,12,11] => 1
[4,3,2,1,12,11,8,7,10,9,6,5] => 1
[10,3,2,9,6,5,8,7,4,1,12,11] => 1
[6,5,4,3,2,1,12,11,10,9,8,7] => 1
[10,5,4,3,2,9,8,7,6,1,12,11] => 1
[8,7,4,3,6,5,2,1,12,11,10,9] => 1
[10,7,4,3,6,5,2,9,8,1,12,11] => 1
[8,7,6,5,4,3,2,1,10,9,12,11] => 1
[2,1,4,3,12,11,8,7,10,9,6,5] => 1
[2,1,12,5,4,7,6,11,10,9,8,3] => 1
[2,1,12,5,4,9,8,7,6,11,10,3] => 1
[2,1,12,7,6,5,4,9,8,11,10,3] => 1
[2,1,10,9,6,5,8,7,4,3,12,11] => 1
[4,3,2,1,12,7,6,11,10,9,8,5] => 1
[4,3,2,1,12,9,8,7,6,11,10,5] => 1
[6,3,2,5,4,1,12,11,10,9,8,7] => 1
[10,3,2,5,4,9,8,7,6,1,12,11] => 1
[8,3,2,7,6,5,4,1,12,11,10,9] => 1
[10,3,2,7,6,5,4,9,8,1,12,11] => 1
[6,5,4,3,2,1,12,9,8,11,10,7] => 1
[8,5,4,3,2,7,6,1,12,11,10,9] => 1
[10,5,4,3,2,7,6,9,8,1,12,11] => 1
[8,7,4,3,6,5,2,1,10,9,12,11] => 1
[2,4,6,9,11,12,1,3,5,7,8,10] => 3
[2,4,6,8,11,12,1,3,5,7,9,10] => 3
[3,4,6,9,11,12,1,2,5,7,8,10] => 5
[3,4,6,8,11,12,1,2,5,7,9,10] => 5
[3,5,6,9,11,12,1,2,4,7,8,10] => 5
[2,5,6,9,11,12,1,3,4,7,8,10] => 5
[3,5,6,8,11,12,1,2,4,7,9,10] => 5
[2,5,6,8,11,12,1,3,4,7,9,10] => 5
[2,4,8,9,11,12,1,3,5,6,7,10] => 5
[2,5,7,9,11,12,1,3,4,6,8,10] => 3
[2,5,7,8,11,12,1,3,4,6,9,10] => 5
[4,5,6,8,11,12,1,2,3,7,9,10] => 7
[2,4,7,9,11,12,1,3,5,6,8,10] => 3
[2,4,7,8,11,12,1,3,5,6,9,10] => 5
[4,5,8,9,11,12,1,2,3,6,7,10] => 7
[3,5,8,9,11,12,1,2,4,6,7,10] => 5
[2,4,7,10,11,12,1,3,5,6,8,9] => 5
[4,5,7,9,11,12,1,2,3,6,8,10] => 5
[3,5,7,9,11,12,1,2,4,6,8,10] => 3
[3,5,7,8,11,12,1,2,4,6,9,10] => 5
[3,4,7,9,11,12,1,2,5,6,8,10] => 5
[3,4,7,8,11,12,1,2,5,6,9,10] => 7
[2,4,6,10,11,12,1,3,5,7,8,9] => 5
[4,7,8,9,11,12,1,2,3,5,6,10] => 7
[3,7,8,9,11,12,1,2,4,5,6,10] => 7
[4,6,8,9,11,12,1,2,3,5,7,10] => 5
[3,6,8,9,11,12,1,2,4,5,7,10] => 5
[4,6,7,9,11,12,1,2,3,5,8,10] => 5
[3,6,7,9,11,12,1,2,4,5,8,10] => 5
[2,6,7,8,11,12,1,3,4,5,9,10] => 7
[3,4,6,10,11,12,1,2,5,7,8,9] => 7
[4,5,6,8,10,12,1,2,3,7,9,11] => 5
[3,6,7,8,10,12,1,2,4,5,9,11] => 5
[2,6,7,8,10,12,1,3,4,5,9,11] => 5
[3,4,8,9,10,12,1,2,5,6,7,11] => 7
[2,4,8,9,10,12,1,3,5,6,7,11] => 5
[4,6,8,10,11,12,1,2,3,5,7,9] => 5
[4,6,7,10,11,12,1,2,3,5,8,9] => 7
[4,5,7,10,11,12,1,2,3,6,8,9] => 7
[3,5,7,10,11,12,1,2,4,6,8,9] => 5
[2,5,8,9,10,12,1,3,4,6,7,11] => 5
[5,6,8,10,11,12,1,2,3,4,7,9] => 7
[4,5,8,10,11,12,1,2,3,6,7,9] => 7
[5,6,8,9,11,12,1,2,3,4,7,10] => 7
[3,6,7,10,11,12,1,2,4,5,8,9] => 7
[5,6,7,9,11,12,1,2,3,4,8,10] => 7
[2,5,6,10,11,12,1,3,4,7,8,9] => 7
[4,5,6,9,10,12,1,2,3,7,8,11] => 7
[2,5,6,9,10,12,1,3,4,7,8,11] => 5
[3,4,6,8,10,12,1,2,5,7,9,11] => 3
[3,4,6,9,10,12,1,2,5,7,8,11] => 5
[3,5,8,10,11,12,1,2,4,6,7,9] => 5
[3,4,7,8,10,12,1,2,5,6,9,11] => 5
[3,5,6,8,10,12,1,2,4,7,9,11] => 3
[3,5,9,10,11,12,1,2,4,6,7,8] => 7
[3,5,7,9,10,12,1,2,4,6,8,11] => 3
[3,6,8,10,11,12,1,2,4,5,7,9] => 5
[3,4,7,9,10,12,1,2,5,6,8,11] => 5
[3,5,7,8,10,12,1,2,4,6,9,11] => 3
[3,6,9,10,11,12,1,2,4,5,7,8] => 7
[3,5,6,9,10,12,1,2,4,7,8,11] => 5
[3,7,8,10,11,12,1,2,4,5,6,9] => 7
[3,7,9,10,11,12,1,2,4,5,6,8] => 7
[4,6,9,10,11,12,1,2,3,5,7,8] => 7
[2,5,7,8,10,12,1,3,4,6,9,11] => 3
[2,4,7,9,10,12,1,3,5,6,8,11] => 3
[2,5,6,8,10,12,1,3,4,7,9,11] => 3
[2,4,7,8,10,12,1,3,5,6,9,11] => 3
[2,4,6,9,10,12,1,3,5,7,8,11] => 3
[2,4,6,8,10,12,1,3,5,7,9,11] => 1
[6,7,8,9,11,12,1,2,3,4,5,10] => 9
[5,7,8,9,11,12,1,2,3,4,6,10] => 7
[5,6,7,10,11,12,1,2,3,4,8,9] => 9
[6,7,8,10,11,12,1,2,3,4,5,9] => 9
[5,7,8,10,11,12,1,2,3,4,6,9] => 7
[4,5,7,8,10,12,1,2,3,6,9,11] => 5
[2,6,7,9,10,12,1,3,4,5,8,11] => 5
[6,7,9,10,11,12,1,2,3,4,5,8] => 9
[6,8,9,10,11,12,1,2,3,4,5,7] => 9
[4,7,8,10,11,12,1,2,3,5,6,9] => 7
[5,6,9,10,11,12,1,2,3,4,7,8] => 9
[4,7,9,10,11,12,1,2,3,5,6,8] => 7
[5,7,9,10,11,12,1,2,3,4,6,8] => 7
[4,8,9,10,11,12,1,2,3,5,6,7] => 9
[7,8,9,10,11,12,1,2,3,4,5,6] => 11
[5,8,9,10,11,12,1,2,3,4,6,7] => 9
[3,8,9,10,11,12,1,2,4,5,6,7] => 9
[4,5,9,10,11,12,1,2,3,6,7,8] => 9
[2,1,4,3,6,5,12,9,8,11,10,7] => 1
[2,1,4,3,6,5,8,7,12,11,10,9] => 1
[4,3,2,1,6,5,12,9,8,11,10,7] => 1
[4,3,2,1,6,5,8,7,12,11,10,9] => 1
[6,3,2,5,4,1,12,9,8,11,10,7] => 1
[2,1,6,5,4,3,12,9,8,11,10,7] => 1
[6,3,2,5,4,1,8,7,12,11,10,9] => 1
[2,1,6,5,4,3,8,7,12,11,10,9] => 1
[2,1,4,3,12,9,8,7,6,11,10,5] => 1
[2,1,12,5,4,7,6,9,8,11,10,3] => 1
[2,1,8,5,4,7,6,3,12,11,10,9] => 1
[6,5,4,3,2,1,8,7,12,11,10,9] => 1
[2,1,4,3,12,7,6,9,8,11,10,5] => 1
[2,1,4,3,8,7,6,5,12,11,10,9] => 1
[12,5,4,3,2,9,8,7,6,11,10,1] => 1
[12,3,2,5,4,9,8,7,6,11,10,1] => 1
[2,1,4,3,12,7,6,11,10,9,8,5] => 1
[12,5,4,3,2,7,6,9,8,11,10,1] => 1
[12,3,2,5,4,7,6,9,8,11,10,1] => 1
[8,3,2,5,4,7,6,1,12,11,10,9] => 1
[4,3,2,1,12,7,6,9,8,11,10,5] => 1
[4,3,2,1,8,7,6,5,12,11,10,9] => 1
[2,1,4,3,6,5,12,11,10,9,8,7] => 1
[12,9,4,3,8,7,6,5,2,11,10,1] => 1
[12,3,2,9,8,7,6,5,4,11,10,1] => 1
[12,9,4,3,6,5,8,7,2,11,10,1] => 1
[12,3,2,9,6,5,8,7,4,11,10,1] => 1
[12,7,4,3,6,5,2,9,8,11,10,1] => 1
[12,3,2,7,6,5,4,9,8,11,10,1] => 1
[2,1,8,7,6,5,4,3,12,11,10,9] => 1
[4,3,2,1,6,5,12,11,10,9,8,7] => 1
[6,5,4,3,2,1,8,7,10,9,12,11] => 1
[8,3,2,7,6,5,4,1,10,9,12,11] => 1
[2,1,8,7,6,5,4,3,10,9,12,11] => 1
[4,3,2,1,10,9,8,7,6,5,12,11] => 1
[2,1,4,3,10,9,8,7,6,5,12,11] => 1
[12,11,4,3,6,5,8,7,10,9,2,1] => 1
[12,7,4,3,6,5,2,11,10,9,8,1] => 1
[12,5,4,3,2,7,6,11,10,9,8,1] => 1
[12,3,2,5,4,7,6,11,10,9,8,1] => 1
[2,1,10,5,4,9,8,7,6,3,12,11] => 1
[12,11,6,5,4,3,8,7,10,9,2,1] => 1
[12,5,4,3,2,11,8,7,10,9,6,1] => 1
[12,9,6,5,4,3,8,7,2,11,10,1] => 1
[12,3,2,7,6,5,4,11,10,9,8,1] => 1
[12,7,6,5,4,3,2,9,8,11,10,1] => 1
[2,1,6,5,4,3,12,11,10,9,8,7] => 1
[6,5,4,3,2,1,10,9,8,7,12,11] => 1
[2,1,6,5,4,3,10,9,8,7,12,11] => 1
[4,3,2,1,6,5,8,7,10,9,12,11] => 1
[4,3,2,1,6,5,10,9,8,7,12,11] => 1
[12,3,2,5,4,11,8,7,10,9,6,1] => 1
[4,3,2,1,8,7,6,5,10,9,12,11] => 1
[6,3,2,5,4,1,8,7,10,9,12,11] => 1
[12,3,2,5,4,11,10,9,8,7,6,1] => 1
[10,3,2,5,4,7,6,9,8,1,12,11] => 1
[12,3,2,11,6,5,8,7,10,9,4,1] => 1
[4,3,2,1,10,7,6,9,8,5,12,11] => 1
[8,3,2,5,4,7,6,1,10,9,12,11] => 1
[12,3,2,11,6,5,10,9,8,7,4,1] => 1
[6,3,2,5,4,1,10,9,8,7,12,11] => 1
[12,3,2,11,8,7,6,5,10,9,4,1] => 1
[12,3,2,11,10,7,6,9,8,5,4,1] => 1
[12,11,4,3,6,5,10,9,8,7,2,1] => 1
[2,1,8,5,4,7,6,3,10,9,12,11] => 1
[2,1,4,3,10,7,6,9,8,5,12,11] => 1
[2,1,6,5,4,3,8,7,10,9,12,11] => 1
[2,1,4,3,8,7,6,5,10,9,12,11] => 1
[2,1,4,3,6,5,10,9,8,7,12,11] => 1
[2,1,4,3,6,5,8,7,10,9,12,11] => 1
[12,9,8,7,6,5,4,3,2,11,10,1] => 1
[12,9,8,5,4,7,6,3,2,11,10,1] => 1
[12,7,6,5,4,3,2,11,10,9,8,1] => 1
[12,11,8,7,6,5,4,3,10,9,2,1] => 1
[12,11,8,5,4,7,6,3,10,9,2,1] => 1
[8,5,4,3,2,7,6,1,10,9,12,11] => 1
[2,1,10,7,6,5,4,9,8,3,12,11] => 1
[12,11,10,7,6,5,4,9,8,3,2,1] => 1
[12,11,10,9,6,5,8,7,4,3,2,1] => 1
[12,11,4,3,8,7,6,5,10,9,2,1] => 1
[12,11,6,5,4,3,10,9,8,7,2,1] => 1
[12,11,4,3,10,7,6,9,8,5,2,1] => 1
[12,11,10,5,4,7,6,9,8,3,2,1] => 1
[12,11,4,3,10,9,8,7,6,5,2,1] => 1
[12,11,10,9,8,7,6,5,4,3,2,1] => 1
[12,11,10,5,4,9,8,7,6,3,2,1] => 1
[12,3,2,11,10,9,8,7,6,5,4,1] => 1
[12,5,4,3,2,11,10,9,8,7,6,1] => 1
[2,1,10,5,4,7,6,9,8,3,12,11] => 1
[2,5,7,9,10,12,1,3,4,6,8,11] => 3
click to show generating function       
Description
The number of cycles in the breakpoint graph of a permutation.
The breakpoint graph of a permutation $\pi_1,\dots,\pi_n$ is the directed, bicoloured graph with vertices $0,\dots,n$, a grey edge from $i$ to $i+1$ and a black edge from $\pi_i$ to $\pi_{i-1}$ for $0\leq i\leq n$, all indices taken modulo $n+1$.
This graph decomposes into alternating cycles, which this statistic counts.
The distribution of this statistic on permutations of $n-1$ is, according to [cor.1, 5] and [eq.6, 6], given by
$$ \frac{1}{n(n+1)}((q+n)_{n+1}-(q)_{n+1}), $$
where $(x)_n=x(x-1)\dots(x-n+1)$.
References
[1] Grusea, S., Labarre, A. The distribution of cycles in breakpoint graphs of signed permutations arXiv:1104.3353
[2] Alexeev, N., Zograf, P. Hultman numbers, polygon gluings and matrix integrals arXiv:1111.3061
[3] Doignon, J.-P., Labarre, A. On Hultman numbers MathSciNet:2312248
[4] Alexeev, N., Pologova, A., Alekseyev, M. A. Generalized Hultman Numbers and Cycle Structures of Breakpoint Graphs arXiv:1503.05285
[5] Bona, M., Flynn, R. The Average Number of Block Interchanges Needed to Sort A Permutation and a recent result of Stanley arXiv:0811.0740
[6] Stanley, R. P. Two Enumerative Results on Cycles of Permutations arXiv:0901.2008
Code
def statistic(pi):
    return len(Hultman_class(pi))

def Hultman_class(pi):
    """
    sage: Hultman_class([1,2])
    [1, 1, 1]
    sage: Hultman_class([2,1])
    [3]

    sage: Hultman_class([2,3,1,4])
    [3, 1, 1]

    sage: Hultman_class([4,1,6,2,5,7,3])
    [5, 3]

    sage: [len(set([Hultman_class(pi) for pi in Permutations(r)])) for r in range(10)]
    [1, 1, 2, 3, 4, 6, 8, 12, 16, 22]
    """
    n = len(pi)
    grey  = {i: (i+1) % (n+1) for i in range(n+1)}
    pi_list = [0] + list(pi)
    black = {pi_list[i]: pi_list[(i-1) % (n+1)] for i in range(n+1)}

    blocks = []
    size = 0
    start = 0
    odd = 0
    for i in range(n+1):
        even = grey.pop(odd)
        odd = black.pop(even)
        size += 1
        if start == odd:
            blocks.append(size)
            size = 0
            try:
                start = odd = grey.iterkeys().next()
            except StopIteration:
                return Partition(sorted(blocks, reverse=True))
    raise ValueError

Created
Feb 14, 2017 at 17:21 by Martin Rubey
Updated
Oct 11, 2019 at 14:55 by Martin Rubey