Identifier
Identifier
Values
[] => 0
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 1
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 2
[1,4,2,3] => 1
[1,4,3,2] => 1
[2,1,3,4] => 1
[2,1,4,3] => 1
[2,3,1,4] => 2
[2,3,4,1] => 3
[2,4,1,3] => 2
[2,4,3,1] => 2
[3,1,2,4] => 1
[3,1,4,2] => 2
[3,2,1,4] => 1
[3,2,4,1] => 3
[3,4,1,2] => 2
[3,4,2,1] => 2
[4,1,2,3] => 1
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 2
[4,3,1,2] => 1
[4,3,2,1] => 1
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 2
[1,2,5,3,4] => 1
[1,2,5,4,3] => 1
[1,3,2,4,5] => 1
[1,3,2,5,4] => 1
[1,3,4,2,5] => 2
[1,3,4,5,2] => 3
[1,3,5,2,4] => 2
[1,3,5,4,2] => 2
[1,4,2,3,5] => 1
[1,4,2,5,3] => 2
[1,4,3,2,5] => 1
[1,4,3,5,2] => 3
[1,4,5,2,3] => 2
[1,4,5,3,2] => 2
[1,5,2,3,4] => 1
[1,5,2,4,3] => 1
[1,5,3,2,4] => 1
[1,5,3,4,2] => 2
[1,5,4,2,3] => 1
[1,5,4,3,2] => 1
[2,1,3,4,5] => 1
[2,1,3,5,4] => 1
[2,1,4,3,5] => 1
[2,1,4,5,3] => 2
[2,1,5,3,4] => 1
[2,1,5,4,3] => 1
[2,3,1,4,5] => 2
[2,3,1,5,4] => 2
[2,3,4,1,5] => 3
[2,3,4,5,1] => 4
[2,3,5,1,4] => 3
[2,3,5,4,1] => 3
[2,4,1,3,5] => 2
[2,4,1,5,3] => 2
[2,4,3,1,5] => 2
[2,4,3,5,1] => 4
[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] => 2
[2,5,3,4,1] => 3
[2,5,4,1,3] => 2
[2,5,4,3,1] => 2
[3,1,2,4,5] => 1
[3,1,2,5,4] => 1
[3,1,4,2,5] => 2
[3,1,4,5,2] => 3
[3,1,5,2,4] => 2
[3,1,5,4,2] => 2
[3,2,1,4,5] => 1
[3,2,1,5,4] => 1
[3,2,4,1,5] => 3
[3,2,4,5,1] => 4
[3,2,5,1,4] => 3
[3,2,5,4,1] => 3
[3,4,1,2,5] => 2
[3,4,1,5,2] => 3
[3,4,2,1,5] => 2
[3,4,2,5,1] => 4
[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] => 2
[3,5,4,2,1] => 2
[4,1,2,3,5] => 1
[4,1,2,5,3] => 2
[4,1,3,2,5] => 1
[4,1,3,5,2] => 3
[4,1,5,2,3] => 2
[4,1,5,3,2] => 2
[4,2,1,3,5] => 1
[4,2,1,5,3] => 2
[4,2,3,1,5] => 2
[4,2,3,5,1] => 4
[4,2,5,1,3] => 3
[4,2,5,3,1] => 3
[4,3,1,2,5] => 1
[4,3,1,5,2] => 3
[4,3,2,1,5] => 1
[4,3,2,5,1] => 4
[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] => 2
[4,5,3,2,1] => 2
[5,1,2,3,4] => 1
[5,1,2,4,3] => 1
[5,1,3,2,4] => 1
[5,1,3,4,2] => 2
[5,1,4,2,3] => 1
[5,1,4,3,2] => 1
[5,2,1,3,4] => 1
[5,2,1,4,3] => 1
[5,2,3,1,4] => 2
[5,2,3,4,1] => 3
[5,2,4,1,3] => 2
[5,2,4,3,1] => 2
[5,3,1,2,4] => 1
[5,3,1,4,2] => 2
[5,3,2,1,4] => 1
[5,3,2,4,1] => 3
[5,3,4,1,2] => 2
[5,3,4,2,1] => 2
[5,4,1,2,3] => 1
[5,4,1,3,2] => 1
[5,4,2,1,3] => 1
[5,4,2,3,1] => 2
[5,4,3,1,2] => 1
[5,4,3,2,1] => 1
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => 2
[1,2,3,6,4,5] => 1
[1,2,3,6,5,4] => 1
[1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => 1
[1,2,4,5,3,6] => 2
[1,2,4,5,6,3] => 3
[1,2,4,6,3,5] => 2
[1,2,4,6,5,3] => 2
[1,2,5,3,4,6] => 1
[1,2,5,3,6,4] => 2
[1,2,5,4,3,6] => 1
[1,2,5,4,6,3] => 3
[1,2,5,6,3,4] => 2
[1,2,5,6,4,3] => 2
[1,2,6,3,4,5] => 1
[1,2,6,3,5,4] => 1
[1,2,6,4,3,5] => 1
[1,2,6,4,5,3] => 2
[1,2,6,5,3,4] => 1
[1,2,6,5,4,3] => 1
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 1
[1,3,2,5,4,6] => 1
[1,3,2,5,6,4] => 2
[1,3,2,6,4,5] => 1
[1,3,2,6,5,4] => 1
[1,3,4,2,5,6] => 2
[1,3,4,2,6,5] => 2
[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] => 3
[1,3,5,2,4,6] => 2
[1,3,5,2,6,4] => 2
[1,3,5,4,2,6] => 2
[1,3,5,4,6,2] => 4
[1,3,5,6,2,4] => 3
[1,3,5,6,4,2] => 3
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 2
[1,3,6,4,2,5] => 2
[1,3,6,4,5,2] => 3
[1,3,6,5,2,4] => 2
[1,3,6,5,4,2] => 2
[1,4,2,3,5,6] => 1
[1,4,2,3,6,5] => 1
[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] => 2
[1,4,3,2,5,6] => 1
[1,4,3,2,6,5] => 1
[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] => 3
[1,4,5,2,3,6] => 2
[1,4,5,2,6,3] => 3
[1,4,5,3,2,6] => 2
[1,4,5,3,6,2] => 4
[1,4,5,6,2,3] => 3
[1,4,5,6,3,2] => 3
[1,4,6,2,3,5] => 2
[1,4,6,2,5,3] => 2
[1,4,6,3,2,5] => 2
[1,4,6,3,5,2] => 2
[1,4,6,5,2,3] => 2
[1,4,6,5,3,2] => 2
[1,5,2,3,4,6] => 1
[1,5,2,3,6,4] => 2
[1,5,2,4,3,6] => 1
[1,5,2,4,6,3] => 3
[1,5,2,6,3,4] => 2
[1,5,2,6,4,3] => 2
[1,5,3,2,4,6] => 1
[1,5,3,2,6,4] => 2
[1,5,3,4,2,6] => 2
[1,5,3,4,6,2] => 4
[1,5,3,6,2,4] => 3
[1,5,3,6,4,2] => 3
[1,5,4,2,3,6] => 1
[1,5,4,2,6,3] => 3
[1,5,4,3,2,6] => 1
[1,5,4,3,6,2] => 4
[1,5,4,6,2,3] => 3
[1,5,4,6,3,2] => 3
[1,5,6,2,3,4] => 2
[1,5,6,2,4,3] => 2
[1,5,6,3,2,4] => 2
[1,5,6,3,4,2] => 2
[1,5,6,4,2,3] => 2
[1,5,6,4,3,2] => 2
[1,6,2,3,4,5] => 1
[1,6,2,3,5,4] => 1
[1,6,2,4,3,5] => 1
[1,6,2,4,5,3] => 2
[1,6,2,5,3,4] => 1
[1,6,2,5,4,3] => 1
[1,6,3,2,4,5] => 1
[1,6,3,2,5,4] => 1
[1,6,3,4,2,5] => 2
[1,6,3,4,5,2] => 3
[1,6,3,5,2,4] => 2
[1,6,3,5,4,2] => 2
[1,6,4,2,3,5] => 1
[1,6,4,2,5,3] => 2
[1,6,4,3,2,5] => 1
[1,6,4,3,5,2] => 3
[1,6,4,5,2,3] => 2
[1,6,4,5,3,2] => 2
[1,6,5,2,3,4] => 1
[1,6,5,2,4,3] => 1
[1,6,5,3,2,4] => 1
[1,6,5,3,4,2] => 2
[1,6,5,4,2,3] => 1
[1,6,5,4,3,2] => 1
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 1
[2,1,3,5,4,6] => 1
[2,1,3,5,6,4] => 2
[2,1,3,6,4,5] => 1
[2,1,3,6,5,4] => 1
[2,1,4,3,5,6] => 1
[2,1,4,3,6,5] => 1
[2,1,4,5,3,6] => 2
[2,1,4,5,6,3] => 3
[2,1,4,6,3,5] => 2
[2,1,4,6,5,3] => 2
[2,1,5,3,4,6] => 1
[2,1,5,3,6,4] => 2
[2,1,5,4,3,6] => 1
[2,1,5,4,6,3] => 3
[2,1,5,6,3,4] => 2
[2,1,5,6,4,3] => 2
[2,1,6,3,4,5] => 1
[2,1,6,3,5,4] => 1
[2,1,6,4,3,5] => 1
[2,1,6,4,5,3] => 2
[2,1,6,5,3,4] => 1
[2,1,6,5,4,3] => 1
[2,3,1,4,5,6] => 2
[2,3,1,4,6,5] => 2
[2,3,1,5,4,6] => 2
[2,3,1,5,6,4] => 2
[2,3,1,6,4,5] => 2
[2,3,1,6,5,4] => 2
[2,3,4,1,5,6] => 3
[2,3,4,1,6,5] => 3
[2,3,4,5,1,6] => 4
[2,3,4,5,6,1] => 5
[2,3,4,6,1,5] => 4
[2,3,4,6,5,1] => 4
[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] => 5
[2,3,5,6,1,4] => 4
[2,3,5,6,4,1] => 4
[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] => 4
[2,3,6,5,1,4] => 3
[2,3,6,5,4,1] => 3
[2,4,1,3,5,6] => 2
[2,4,1,3,6,5] => 2
[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] => 2
[2,4,3,1,5,6] => 2
[2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => 4
[2,4,3,5,6,1] => 5
[2,4,3,6,1,5] => 4
[2,4,3,6,5,1] => 4
[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] => 5
[2,4,5,6,1,3] => 4
[2,4,5,6,3,1] => 4
[2,4,6,1,3,5] => 3
[2,4,6,1,5,3] => 3
[2,4,6,3,1,5] => 3
[2,4,6,3,5,1] => 3
[2,4,6,5,1,3] => 3
[2,4,6,5,3,1] => 3
[2,5,1,3,4,6] => 2
[2,5,1,3,6,4] => 2
[2,5,1,4,3,6] => 2
[2,5,1,4,6,3] => 3
[2,5,1,6,3,4] => 2
[2,5,1,6,4,3] => 2
[2,5,3,1,4,6] => 2
[2,5,3,1,6,4] => 2
[2,5,3,4,1,6] => 3
[2,5,3,4,6,1] => 5
[2,5,3,6,1,4] => 4
[2,5,3,6,4,1] => 4
[2,5,4,1,3,6] => 2
[2,5,4,1,6,3] => 3
[2,5,4,3,1,6] => 2
[2,5,4,3,6,1] => 5
[2,5,4,6,1,3] => 4
[2,5,4,6,3,1] => 4
[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] => 2
[2,6,1,3,5,4] => 2
[2,6,1,4,3,5] => 2
[2,6,1,4,5,3] => 2
[2,6,1,5,3,4] => 2
[2,6,1,5,4,3] => 2
[2,6,3,1,4,5] => 2
[2,6,3,1,5,4] => 2
[2,6,3,4,1,5] => 3
[2,6,3,4,5,1] => 4
[2,6,3,5,1,4] => 3
[2,6,3,5,4,1] => 3
[2,6,4,1,3,5] => 2
[2,6,4,1,5,3] => 2
[2,6,4,3,1,5] => 2
[2,6,4,3,5,1] => 4
[2,6,4,5,1,3] => 3
[2,6,4,5,3,1] => 3
[2,6,5,1,3,4] => 2
[2,6,5,1,4,3] => 2
[2,6,5,3,1,4] => 2
[2,6,5,3,4,1] => 3
[2,6,5,4,1,3] => 2
[2,6,5,4,3,1] => 2
[3,1,2,4,5,6] => 1
[3,1,2,4,6,5] => 1
[3,1,2,5,4,6] => 1
[3,1,2,5,6,4] => 2
[3,1,2,6,4,5] => 1
[3,1,2,6,5,4] => 1
[3,1,4,2,5,6] => 2
[3,1,4,2,6,5] => 2
[3,1,4,5,2,6] => 3
[3,1,4,5,6,2] => 4
[3,1,4,6,2,5] => 3
[3,1,4,6,5,2] => 3
[3,1,5,2,4,6] => 2
[3,1,5,2,6,4] => 2
[3,1,5,4,2,6] => 2
[3,1,5,4,6,2] => 4
[3,1,5,6,2,4] => 3
[3,1,5,6,4,2] => 3
[3,1,6,2,4,5] => 2
[3,1,6,2,5,4] => 2
[3,1,6,4,2,5] => 2
[3,1,6,4,5,2] => 3
[3,1,6,5,2,4] => 2
[3,1,6,5,4,2] => 2
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 1
[3,2,1,5,4,6] => 1
[3,2,1,5,6,4] => 2
[3,2,1,6,4,5] => 1
[3,2,1,6,5,4] => 1
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 3
[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] => 4
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 3
[3,2,5,4,1,6] => 3
[3,2,5,4,6,1] => 5
[3,2,5,6,1,4] => 4
[3,2,5,6,4,1] => 4
[3,2,6,1,4,5] => 3
[3,2,6,1,5,4] => 3
[3,2,6,4,1,5] => 3
[3,2,6,4,5,1] => 4
[3,2,6,5,1,4] => 3
[3,2,6,5,4,1] => 3
[3,4,1,2,5,6] => 2
[3,4,1,2,6,5] => 2
[3,4,1,5,2,6] => 3
[3,4,1,5,6,2] => 4
[3,4,1,6,2,5] => 3
[3,4,1,6,5,2] => 3
[3,4,2,1,5,6] => 2
[3,4,2,1,6,5] => 2
[3,4,2,5,1,6] => 4
[3,4,2,5,6,1] => 5
[3,4,2,6,1,5] => 4
[3,4,2,6,5,1] => 4
[3,4,5,1,2,6] => 3
[3,4,5,1,6,2] => 4
[3,4,5,2,1,6] => 3
[3,4,5,2,6,1] => 5
[3,4,5,6,1,2] => 4
[3,4,5,6,2,1] => 4
[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] => 2
[3,5,1,2,6,4] => 2
[3,5,1,4,2,6] => 2
[3,5,1,4,6,2] => 4
[3,5,1,6,2,4] => 3
[3,5,1,6,4,2] => 3
[3,5,2,1,4,6] => 2
[3,5,2,1,6,4] => 2
[3,5,2,4,1,6] => 2
[3,5,2,4,6,1] => 5
[3,5,2,6,1,4] => 4
[3,5,2,6,4,1] => 4
[3,5,4,1,2,6] => 2
[3,5,4,1,6,2] => 4
[3,5,4,2,1,6] => 2
[3,5,4,2,6,1] => 5
[3,5,4,6,1,2] => 4
[3,5,4,6,2,1] => 4
[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] => 2
[3,6,1,2,5,4] => 2
[3,6,1,4,2,5] => 2
[3,6,1,4,5,2] => 3
[3,6,1,5,2,4] => 2
[3,6,1,5,4,2] => 2
[3,6,2,1,4,5] => 2
[3,6,2,1,5,4] => 2
[3,6,2,4,1,5] => 2
[3,6,2,4,5,1] => 4
[3,6,2,5,1,4] => 2
[3,6,2,5,4,1] => 2
[3,6,4,1,2,5] => 2
[3,6,4,1,5,2] => 3
[3,6,4,2,1,5] => 2
[3,6,4,2,5,1] => 4
[3,6,4,5,1,2] => 3
[3,6,4,5,2,1] => 3
[3,6,5,1,2,4] => 2
[3,6,5,1,4,2] => 2
[3,6,5,2,1,4] => 2
[3,6,5,2,4,1] => 2
[3,6,5,4,1,2] => 2
[3,6,5,4,2,1] => 2
[4,1,2,3,5,6] => 1
[4,1,2,3,6,5] => 1
[4,1,2,5,3,6] => 2
[4,1,2,5,6,3] => 3
[4,1,2,6,3,5] => 2
[4,1,2,6,5,3] => 2
[4,1,3,2,5,6] => 1
[4,1,3,2,6,5] => 1
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 4
[4,1,3,6,2,5] => 3
[4,1,3,6,5,2] => 3
[4,1,5,2,3,6] => 2
[4,1,5,2,6,3] => 3
[4,1,5,3,2,6] => 2
[4,1,5,3,6,2] => 4
[4,1,5,6,2,3] => 3
[4,1,5,6,3,2] => 3
[4,1,6,2,3,5] => 2
[4,1,6,2,5,3] => 2
[4,1,6,3,2,5] => 2
[4,1,6,3,5,2] => 2
[4,1,6,5,2,3] => 2
[4,1,6,5,3,2] => 2
[4,2,1,3,5,6] => 1
[4,2,1,3,6,5] => 1
[4,2,1,5,3,6] => 2
[4,2,1,5,6,3] => 3
[4,2,1,6,3,5] => 2
[4,2,1,6,5,3] => 2
[4,2,3,1,5,6] => 2
[4,2,3,1,6,5] => 2
[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] => 4
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 3
[4,2,5,3,1,6] => 3
[4,2,5,3,6,1] => 5
[4,2,5,6,1,3] => 4
[4,2,5,6,3,1] => 4
[4,2,6,1,3,5] => 3
[4,2,6,1,5,3] => 3
[4,2,6,3,1,5] => 3
[4,2,6,3,5,1] => 3
[4,2,6,5,1,3] => 3
[4,2,6,5,3,1] => 3
[4,3,1,2,5,6] => 1
[4,3,1,2,6,5] => 1
[4,3,1,5,2,6] => 3
[4,3,1,5,6,2] => 4
[4,3,1,6,2,5] => 3
[4,3,1,6,5,2] => 3
[4,3,2,1,5,6] => 1
[4,3,2,1,6,5] => 1
[4,3,2,5,1,6] => 4
[4,3,2,5,6,1] => 5
[4,3,2,6,1,5] => 4
[4,3,2,6,5,1] => 4
[4,3,5,1,2,6] => 3
[4,3,5,1,6,2] => 4
[4,3,5,2,1,6] => 3
[4,3,5,2,6,1] => 5
[4,3,5,6,1,2] => 4
[4,3,5,6,2,1] => 4
[4,3,6,1,2,5] => 3
[4,3,6,1,5,2] => 3
[4,3,6,2,1,5] => 3
[4,3,6,2,5,1] => 3
[4,3,6,5,1,2] => 3
[4,3,6,5,2,1] => 3
[4,5,1,2,3,6] => 2
[4,5,1,2,6,3] => 3
[4,5,1,3,2,6] => 2
[4,5,1,3,6,2] => 4
[4,5,1,6,2,3] => 3
[4,5,1,6,3,2] => 3
[4,5,2,1,3,6] => 2
[4,5,2,1,6,3] => 3
[4,5,2,3,1,6] => 2
[4,5,2,3,6,1] => 5
[4,5,2,6,1,3] => 4
[4,5,2,6,3,1] => 4
[4,5,3,1,2,6] => 2
[4,5,3,1,6,2] => 4
[4,5,3,2,1,6] => 2
[4,5,3,2,6,1] => 5
[4,5,3,6,1,2] => 4
[4,5,3,6,2,1] => 4
[4,5,6,1,2,3] => 3
[4,5,6,1,3,2] => 3
[4,5,6,2,1,3] => 3
[4,5,6,2,3,1] => 3
[4,5,6,3,1,2] => 3
[4,5,6,3,2,1] => 3
[4,6,1,2,3,5] => 2
[4,6,1,2,5,3] => 2
[4,6,1,3,2,5] => 2
[4,6,1,3,5,2] => 2
[4,6,1,5,2,3] => 2
[4,6,1,5,3,2] => 2
[4,6,2,1,3,5] => 2
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 2
[4,6,2,3,5,1] => 3
[4,6,2,5,1,3] => 2
[4,6,2,5,3,1] => 2
[4,6,3,1,2,5] => 2
[4,6,3,1,5,2] => 2
[4,6,3,2,1,5] => 2
[4,6,3,2,5,1] => 3
[4,6,3,5,1,2] => 2
[4,6,3,5,2,1] => 2
[4,6,5,1,2,3] => 2
[4,6,5,1,3,2] => 2
[4,6,5,2,1,3] => 2
[4,6,5,2,3,1] => 2
[4,6,5,3,1,2] => 2
[4,6,5,3,2,1] => 2
[5,1,2,3,4,6] => 1
[5,1,2,3,6,4] => 2
[5,1,2,4,3,6] => 1
[5,1,2,4,6,3] => 3
[5,1,2,6,3,4] => 2
[5,1,2,6,4,3] => 2
[5,1,3,2,4,6] => 1
[5,1,3,2,6,4] => 2
[5,1,3,4,2,6] => 2
[5,1,3,4,6,2] => 4
[5,1,3,6,2,4] => 3
[5,1,3,6,4,2] => 3
[5,1,4,2,3,6] => 1
[5,1,4,2,6,3] => 3
[5,1,4,3,2,6] => 1
[5,1,4,3,6,2] => 4
[5,1,4,6,2,3] => 3
[5,1,4,6,3,2] => 3
[5,1,6,2,3,4] => 2
[5,1,6,2,4,3] => 2
[5,1,6,3,2,4] => 2
[5,1,6,3,4,2] => 2
[5,1,6,4,2,3] => 2
[5,1,6,4,3,2] => 2
[5,2,1,3,4,6] => 1
[5,2,1,3,6,4] => 2
[5,2,1,4,3,6] => 1
[5,2,1,4,6,3] => 3
[5,2,1,6,3,4] => 2
[5,2,1,6,4,3] => 2
[5,2,3,1,4,6] => 2
[5,2,3,1,6,4] => 2
[5,2,3,4,1,6] => 3
[5,2,3,4,6,1] => 5
[5,2,3,6,1,4] => 4
[5,2,3,6,4,1] => 4
[5,2,4,1,3,6] => 2
[5,2,4,1,6,3] => 3
[5,2,4,3,1,6] => 2
[5,2,4,3,6,1] => 5
[5,2,4,6,1,3] => 4
[5,2,4,6,3,1] => 4
[5,2,6,1,3,4] => 3
[5,2,6,1,4,3] => 3
[5,2,6,3,1,4] => 3
[5,2,6,3,4,1] => 3
[5,2,6,4,1,3] => 3
[5,2,6,4,3,1] => 3
[5,3,1,2,4,6] => 1
[5,3,1,2,6,4] => 2
[5,3,1,4,2,6] => 2
[5,3,1,4,6,2] => 4
[5,3,1,6,2,4] => 3
[5,3,1,6,4,2] => 3
[5,3,2,1,4,6] => 1
[5,3,2,1,6,4] => 2
[5,3,2,4,1,6] => 3
[5,3,2,4,6,1] => 5
[5,3,2,6,1,4] => 4
[5,3,2,6,4,1] => 4
[5,3,4,1,2,6] => 2
[5,3,4,1,6,2] => 4
[5,3,4,2,1,6] => 2
[5,3,4,2,6,1] => 5
[5,3,4,6,1,2] => 4
[5,3,4,6,2,1] => 4
[5,3,6,1,2,4] => 3
[5,3,6,1,4,2] => 3
[5,3,6,2,1,4] => 3
[5,3,6,2,4,1] => 3
[5,3,6,4,1,2] => 3
[5,3,6,4,2,1] => 3
[5,4,1,2,3,6] => 1
[5,4,1,2,6,3] => 3
[5,4,1,3,2,6] => 1
[5,4,1,3,6,2] => 4
[5,4,1,6,2,3] => 3
[5,4,1,6,3,2] => 3
[5,4,2,1,3,6] => 1
[5,4,2,1,6,3] => 3
[5,4,2,3,1,6] => 2
[5,4,2,3,6,1] => 5
[5,4,2,6,1,3] => 4
[5,4,2,6,3,1] => 4
[5,4,3,1,2,6] => 1
[5,4,3,1,6,2] => 4
[5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => 5
[5,4,3,6,1,2] => 4
[5,4,3,6,2,1] => 4
[5,4,6,1,2,3] => 3
[5,4,6,1,3,2] => 3
[5,4,6,2,1,3] => 3
[5,4,6,2,3,1] => 3
[5,4,6,3,1,2] => 3
[5,4,6,3,2,1] => 3
[5,6,1,2,3,4] => 2
[5,6,1,2,4,3] => 2
[5,6,1,3,2,4] => 2
[5,6,1,3,4,2] => 2
[5,6,1,4,2,3] => 2
[5,6,1,4,3,2] => 2
[5,6,2,1,3,4] => 2
[5,6,2,1,4,3] => 2
[5,6,2,3,1,4] => 2
[5,6,2,3,4,1] => 3
[5,6,2,4,1,3] => 2
[5,6,2,4,3,1] => 2
[5,6,3,1,2,4] => 2
[5,6,3,1,4,2] => 2
[5,6,3,2,1,4] => 2
[5,6,3,2,4,1] => 3
[5,6,3,4,1,2] => 2
[5,6,3,4,2,1] => 2
[5,6,4,1,2,3] => 2
[5,6,4,1,3,2] => 2
[5,6,4,2,1,3] => 2
[5,6,4,2,3,1] => 2
[5,6,4,3,1,2] => 2
[5,6,4,3,2,1] => 2
[6,1,2,3,4,5] => 1
[6,1,2,3,5,4] => 1
[6,1,2,4,3,5] => 1
[6,1,2,4,5,3] => 2
[6,1,2,5,3,4] => 1
[6,1,2,5,4,3] => 1
[6,1,3,2,4,5] => 1
[6,1,3,2,5,4] => 1
[6,1,3,4,2,5] => 2
[6,1,3,4,5,2] => 3
[6,1,3,5,2,4] => 2
[6,1,3,5,4,2] => 2
[6,1,4,2,3,5] => 1
[6,1,4,2,5,3] => 2
[6,1,4,3,2,5] => 1
[6,1,4,3,5,2] => 3
[6,1,4,5,2,3] => 2
[6,1,4,5,3,2] => 2
[6,1,5,2,3,4] => 1
[6,1,5,2,4,3] => 1
[6,1,5,3,2,4] => 1
[6,1,5,3,4,2] => 2
[6,1,5,4,2,3] => 1
[6,1,5,4,3,2] => 1
[6,2,1,3,4,5] => 1
[6,2,1,3,5,4] => 1
[6,2,1,4,3,5] => 1
[6,2,1,4,5,3] => 2
[6,2,1,5,3,4] => 1
[6,2,1,5,4,3] => 1
[6,2,3,1,4,5] => 2
[6,2,3,1,5,4] => 2
[6,2,3,4,1,5] => 3
[6,2,3,4,5,1] => 4
[6,2,3,5,1,4] => 3
[6,2,3,5,4,1] => 3
[6,2,4,1,3,5] => 2
[6,2,4,1,5,3] => 2
[6,2,4,3,1,5] => 2
[6,2,4,3,5,1] => 4
[6,2,4,5,1,3] => 3
[6,2,4,5,3,1] => 3
[6,2,5,1,3,4] => 2
[6,2,5,1,4,3] => 2
[6,2,5,3,1,4] => 2
[6,2,5,3,4,1] => 3
[6,2,5,4,1,3] => 2
[6,2,5,4,3,1] => 2
[6,3,1,2,4,5] => 1
[6,3,1,2,5,4] => 1
[6,3,1,4,2,5] => 2
[6,3,1,4,5,2] => 3
[6,3,1,5,2,4] => 2
[6,3,1,5,4,2] => 2
[6,3,2,1,4,5] => 1
[6,3,2,1,5,4] => 1
[6,3,2,4,1,5] => 3
[6,3,2,4,5,1] => 4
[6,3,2,5,1,4] => 3
[6,3,2,5,4,1] => 3
[6,3,4,1,2,5] => 2
[6,3,4,1,5,2] => 3
[6,3,4,2,1,5] => 2
[6,3,4,2,5,1] => 4
[6,3,4,5,1,2] => 3
[6,3,4,5,2,1] => 3
[6,3,5,1,2,4] => 2
[6,3,5,1,4,2] => 2
[6,3,5,2,1,4] => 2
[6,3,5,2,4,1] => 2
[6,3,5,4,1,2] => 2
[6,3,5,4,2,1] => 2
[6,4,1,2,3,5] => 1
[6,4,1,2,5,3] => 2
[6,4,1,3,2,5] => 1
[6,4,1,3,5,2] => 3
[6,4,1,5,2,3] => 2
[6,4,1,5,3,2] => 2
[6,4,2,1,3,5] => 1
[6,4,2,1,5,3] => 2
[6,4,2,3,1,5] => 2
[6,4,2,3,5,1] => 4
[6,4,2,5,1,3] => 3
[6,4,2,5,3,1] => 3
[6,4,3,1,2,5] => 1
[6,4,3,1,5,2] => 3
[6,4,3,2,1,5] => 1
[6,4,3,2,5,1] => 4
[6,4,3,5,1,2] => 3
[6,4,3,5,2,1] => 3
[6,4,5,1,2,3] => 2
[6,4,5,1,3,2] => 2
[6,4,5,2,1,3] => 2
[6,4,5,2,3,1] => 2
[6,4,5,3,1,2] => 2
[6,4,5,3,2,1] => 2
[6,5,1,2,3,4] => 1
[6,5,1,2,4,3] => 1
[6,5,1,3,2,4] => 1
[6,5,1,3,4,2] => 2
[6,5,1,4,2,3] => 1
[6,5,1,4,3,2] => 1
[6,5,2,1,3,4] => 1
[6,5,2,1,4,3] => 1
[6,5,2,3,1,4] => 2
[6,5,2,3,4,1] => 3
[6,5,2,4,1,3] => 2
[6,5,2,4,3,1] => 2
[6,5,3,1,2,4] => 1
[6,5,3,1,4,2] => 2
[6,5,3,2,1,4] => 1
[6,5,3,2,4,1] => 3
[6,5,3,4,1,2] => 2
[6,5,3,4,2,1] => 2
[6,5,4,1,2,3] => 1
[6,5,4,1,3,2] => 1
[6,5,4,2,1,3] => 1
[6,5,4,2,3,1] => 2
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 1
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 1
[1,2,3,4,6,5,7] => 1
[1,2,3,6,4,7,5] => 2
[1,2,6,3,4,7,5] => 2
[1,3,2,4,5,6,7] => 1
[1,3,7,2,4,5,6] => 2
[1,3,7,6,5,4,2] => 2
[1,4,6,7,2,3,5] => 3
[1,4,6,7,5,3,2] => 3
[1,4,7,2,3,5,6] => 2
[1,4,7,6,5,3,2] => 2
[1,5,2,3,4,7,6] => 1
[1,5,2,7,3,4,6] => 2
[1,5,4,7,6,3,2] => 3
[1,5,6,2,7,3,4] => 3
[1,5,6,4,7,3,2] => 4
[1,5,6,7,2,3,4] => 3
[1,5,6,7,4,3,2] => 3
[1,5,7,2,3,4,6] => 2
[1,5,7,6,4,3,2] => 2
[1,6,2,3,4,7,5] => 2
[1,6,2,3,7,4,5] => 2
[1,6,2,7,3,4,5] => 2
[1,6,5,4,3,7,2] => 5
[1,6,5,4,7,3,2] => 4
[1,6,5,7,4,3,2] => 3
[1,6,7,2,3,4,5] => 2
[1,6,7,5,4,3,2] => 2
[1,7,2,3,4,5,6] => 1
[1,7,3,5,6,4,2] => 3
[1,7,3,6,5,4,2] => 2
[1,7,4,3,6,5,2] => 3
[1,7,4,5,3,6,2] => 4
[1,7,4,5,6,3,2] => 3
[1,7,4,6,5,3,2] => 2
[1,7,5,4,3,6,2] => 4
[1,7,5,4,6,3,2] => 3
[1,7,6,4,5,3,2] => 2
[1,7,6,5,4,3,2] => 1
[2,1,3,4,5,6,7] => 1
[2,1,3,4,7,5,6] => 1
[2,1,3,7,4,5,6] => 1
[2,1,6,3,4,5,7] => 1
[2,1,7,3,4,5,6] => 1
[2,1,7,6,5,4,3] => 1
[2,3,1,4,5,6,7] => 2
[2,3,4,1,5,6,7] => 3
[2,3,4,1,5,7,6] => 3
[2,3,4,5,1,6,7] => 4
[2,3,4,5,1,7,6] => 4
[2,3,4,5,6,1,7] => 5
[2,3,4,5,6,7,1] => 6
[2,3,4,5,7,1,6] => 5
[2,3,4,6,1,7,5] => 4
[2,3,4,6,7,1,5] => 5
[2,3,4,7,1,5,6] => 4
[2,3,5,6,7,1,4] => 5
[2,4,1,3,5,6,7] => 2
[2,5,1,3,4,6,7] => 2
[2,5,7,1,3,4,6] => 3
[2,6,1,3,4,5,7] => 2
[2,6,1,7,3,4,5] => 2
[2,6,5,4,3,1,7] => 2
[2,6,7,1,3,4,5] => 3
[2,7,1,3,4,5,6] => 2
[3,1,2,4,5,6,7] => 1
[3,1,2,4,5,7,6] => 1
[3,2,1,4,5,6,7] => 1
[3,2,4,5,6,7,1] => 6
[3,4,1,2,5,6,7] => 2
[3,4,2,5,6,7,1] => 6
[3,4,5,2,6,7,1] => 6
[3,4,5,6,2,7,1] => 6
[3,4,5,6,7,1,2] => 5
[3,5,6,1,2,4,7] => 3
[3,5,6,4,2,1,7] => 3
[3,6,1,2,4,5,7] => 2
[3,6,5,4,2,1,7] => 2
[4,1,2,3,5,6,7] => 1
[4,1,2,3,5,7,6] => 1
[4,1,6,2,3,5,7] => 2
[4,2,3,5,6,7,1] => 6
[4,2,5,1,3,6,7] => 3
[4,3,2,1,5,6,7] => 1
[4,3,2,5,6,7,1] => 6
[4,3,5,2,6,7,1] => 6
[4,3,6,5,2,1,7] => 3
[4,5,1,6,2,3,7] => 3
[4,5,2,3,6,7,1] => 6
[4,5,3,6,2,1,7] => 4
[4,5,6,1,2,3,7] => 3
[4,5,6,3,2,1,7] => 3
[4,6,1,2,3,5,7] => 2
[4,6,1,2,3,7,5] => 2
[4,6,5,3,2,1,7] => 2
[5,1,2,3,4,6,7] => 1
[5,1,2,3,4,7,6] => 1
[5,1,2,3,6,4,7] => 2
[5,1,2,3,6,7,4] => 3
[5,1,2,3,7,4,6] => 2
[5,1,2,6,3,4,7] => 2
[5,1,6,2,3,4,7] => 2
[5,1,6,2,3,7,4] => 3
[5,2,3,4,6,7,1] => 6
[5,2,6,7,1,3,4] => 4
[5,3,2,4,6,7,1] => 6
[5,3,2,6,1,4,7] => 4
[5,3,6,7,1,2,4] => 4
[5,4,3,2,1,6,7] => 1
[5,4,3,2,1,7,6] => 1
[5,4,3,2,6,1,7] => 5
[5,4,3,6,2,1,7] => 4
[5,4,6,3,2,1,7] => 3
[5,4,6,7,1,2,3] => 4
[5,6,1,2,3,4,7] => 2
[5,6,1,2,3,7,4] => 3
[5,6,3,4,1,2,7] => 2
[5,6,4,3,2,1,7] => 2
[5,6,7,1,2,3,4] => 3
[6,1,2,3,4,5,7] => 1
[6,1,2,3,4,7,5] => 2
[6,1,2,3,7,4,5] => 2
[6,1,2,7,3,4,5] => 2
[6,2,3,4,5,7,1] => 6
[6,2,4,5,3,1,7] => 3
[6,2,5,4,3,1,7] => 2
[6,3,2,5,4,1,7] => 3
[6,3,4,2,5,1,7] => 4
[6,3,4,5,2,1,7] => 3
[6,3,4,7,1,2,5] => 4
[6,3,5,4,2,1,7] => 2
[6,4,3,2,5,1,7] => 4
[6,4,3,2,7,1,5] => 5
[6,4,3,5,2,1,7] => 3
[6,4,5,7,1,2,3] => 4
[6,4,7,2,5,1,3] => 3
[6,4,7,3,5,1,2] => 3
[6,5,3,4,2,1,7] => 2
[6,5,4,3,2,1,7] => 1
[6,5,7,3,4,1,2] => 3
[6,7,1,2,3,4,5] => 2
[6,7,3,4,1,2,5] => 2
[6,7,4,5,1,2,3] => 2
[7,1,2,3,4,5,6] => 1
[7,2,1,3,4,5,6] => 1
[7,2,3,1,4,5,6] => 2
[7,2,3,4,1,5,6] => 3
[7,2,3,4,5,1,6] => 4
[7,3,1,2,4,5,6] => 1
[7,3,2,1,4,5,6] => 1
[7,3,2,4,1,5,6] => 3
[7,3,4,1,2,5,6] => 2
[7,4,1,2,3,5,6] => 1
[7,4,2,1,3,5,6] => 1
[7,4,5,6,1,2,3] => 3
[7,5,1,2,3,4,6] => 1
[7,5,6,1,2,3,4] => 2
[7,5,6,3,4,1,2] => 2
[7,6,1,2,3,4,5] => 1
[7,6,4,5,1,2,3] => 2
[7,6,5,1,2,3,4] => 1
[7,6,5,3,4,1,2] => 2
[7,6,5,4,1,2,3] => 1
[7,6,5,4,3,1,2] => 1
[7,6,5,4,3,2,1] => 1
[8,7,6,5,4,3,2,1] => 1
[7,6,8,5,4,3,2,1] => 3
[7,8,5,6,4,3,2,1] => 2
[7,8,6,4,5,3,2,1] => 2
[8,6,7,4,5,3,2,1] => 2
[7,6,5,4,8,3,2,1] => 5
[6,5,7,4,8,3,2,1] => 5
[7,8,6,5,3,4,2,1] => 2
[8,6,7,5,3,4,2,1] => 2
[8,7,5,6,3,4,2,1] => 2
[6,7,8,3,4,5,2,1] => 3
[7,8,6,5,4,2,3,1] => 2
[8,6,7,5,4,2,3,1] => 2
[8,7,5,6,4,2,3,1] => 2
[8,7,6,4,5,2,3,1] => 2
[8,6,5,7,3,2,4,1] => 3
[6,7,8,5,2,3,4,1] => 3
[8,5,6,7,2,3,4,1] => 3
[7,8,3,2,4,5,6,1] => 5
[7,6,5,4,3,2,8,1] => 7
[6,5,7,4,3,2,8,1] => 7
[6,5,4,3,7,2,8,1] => 7
[5,4,6,3,7,2,8,1] => 7
[3,4,5,2,6,7,8,1] => 7
[5,2,3,4,6,7,8,1] => 7
[4,3,2,5,6,7,8,1] => 7
[3,4,2,5,6,7,8,1] => 7
[4,2,3,5,6,7,8,1] => 7
[3,2,4,5,6,7,8,1] => 7
[2,3,4,5,6,7,8,1] => 7
[8,7,6,5,4,3,1,2] => 1
[7,8,6,5,4,3,1,2] => 2
[8,6,7,5,4,3,1,2] => 2
[8,7,5,6,4,3,1,2] => 2
[8,7,6,4,5,3,1,2] => 2
[8,7,6,5,3,4,1,2] => 2
[8,7,5,6,3,4,1,2] => 2
[7,8,5,6,3,4,1,2] => 2
[5,6,7,8,3,4,1,2] => 4
[7,8,3,4,5,6,1,2] => 4
[3,4,5,6,7,8,1,2] => 6
[8,7,6,5,4,2,1,3] => 1
[7,6,8,5,4,2,1,3] => 3
[8,7,6,5,4,1,2,3] => 1
[6,7,8,5,4,1,2,3] => 3
[8,5,6,7,4,1,2,3] => 3
[8,7,6,4,5,1,2,3] => 2
[8,6,7,4,5,1,2,3] => 2
[8,7,4,5,6,1,2,3] => 3
[7,8,4,5,6,1,2,3] => 3
[6,7,4,5,8,1,2,3] => 5
[7,6,5,8,3,2,1,4] => 4
[7,5,6,8,2,3,1,4] => 4
[6,7,5,8,3,1,2,4] => 4
[6,5,7,8,2,1,3,4] => 4
[8,7,6,5,1,2,3,4] => 1
[8,7,5,6,1,2,3,4] => 2
[7,8,5,6,1,2,3,4] => 2
[8,5,6,7,1,2,3,4] => 3
[5,6,7,8,1,2,3,4] => 4
[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] => 1
[8,6,7,1,2,3,4,5] => 2
[6,7,8,1,2,3,4,5] => 3
[7,8,5,4,2,1,3,6] => 2
[7,8,5,4,1,2,3,6] => 2
[8,7,1,2,3,4,5,6] => 1
[7,8,1,2,3,4,5,6] => 2
[8,6,5,4,3,2,1,7] => 1
[8,6,5,4,3,1,2,7] => 1
[8,5,6,3,4,1,2,7] => 2
[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] => 3
[8,4,1,2,3,5,6,7] => 1
[8,3,2,1,4,5,6,7] => 1
[8,2,3,1,4,5,6,7] => 2
[8,3,1,2,4,5,6,7] => 1
[8,2,1,3,4,5,6,7] => 1
[8,1,2,3,4,5,6,7] => 1
[7,6,5,4,3,2,1,8] => 1
[6,7,5,4,3,2,1,8] => 2
[6,5,7,4,3,2,1,8] => 3
[5,6,7,4,3,2,1,8] => 3
[7,6,4,5,3,2,1,8] => 2
[6,5,4,7,3,2,1,8] => 4
[7,5,6,3,4,2,1,8] => 2
[7,6,4,3,5,2,1,8] => 3
[7,6,3,4,5,2,1,8] => 3
[7,5,4,3,6,2,1,8] => 4
[6,7,5,4,2,3,1,8] => 2
[6,5,7,3,2,4,1,8] => 3
[5,6,7,2,3,4,1,8] => 3
[2,3,4,5,6,7,1,8] => 6
[5,6,7,1,2,3,4,8] => 3
[6,7,1,2,3,4,5,8] => 2
[7,1,2,3,4,5,6,8] => 1
[6,5,4,3,2,1,7,8] => 1
[2,3,4,5,6,1,7,8] => 5
[5,6,3,4,1,2,7,8] => 2
[4,5,6,1,2,3,7,8] => 3
[6,1,2,3,4,5,7,8] => 1
[5,4,3,2,1,6,7,8] => 1
[2,3,4,5,1,6,7,8] => 4
[5,1,2,3,4,6,7,8] => 1
[4,3,2,1,5,6,7,8] => 1
[3,4,1,2,5,6,7,8] => 2
[3,2,1,4,5,6,7,8] => 1
[2,1,3,4,5,6,7,8] => 1
[1,2,3,4,5,6,7,8] => 0
[6,5,8,7,4,3,2,1] => 3
[3,5,8,7,6,4,2,1] => 3
[4,3,6,5,8,7,2,1] => 5
[2,6,8,7,5,4,3,1] => 3
[2,3,5,6,8,7,4,1] => 5
[3,2,6,5,4,8,7,1] => 6
[4,3,6,5,7,2,8,1] => 7
[3,2,6,5,7,4,8,1] => 7
[4,3,5,2,7,6,8,1] => 7
[3,2,5,4,7,6,8,1] => 7
[1,8,7,6,5,4,3,2] => 1
[1,7,8,6,5,4,3,2] => 2
[1,6,8,7,5,4,3,2] => 2
[1,7,6,8,5,4,3,2] => 3
[1,6,7,8,5,4,3,2] => 3
[1,5,8,7,6,4,3,2] => 2
[1,7,6,5,8,4,3,2] => 4
[1,3,5,7,8,6,4,2] => 4
[1,4,3,8,7,6,5,2] => 3
[1,6,5,4,3,8,7,2] => 5
[1,4,3,6,5,8,7,2] => 5
[2,1,8,7,6,5,4,3] => 1
[2,1,6,5,7,4,8,3] => 5
[2,1,5,4,7,6,8,3] => 5
[1,2,6,7,8,5,4,3] => 3
[3,2,1,8,7,6,5,4] => 1
[3,2,1,6,5,8,7,4] => 3
[1,2,3,5,6,7,8,4] => 4
[4,3,2,1,8,7,6,5] => 1
[3,4,2,1,7,8,6,5] => 2
[2,4,3,1,6,8,7,5] => 2
[2,4,3,1,7,6,8,5] => 3
[3,2,4,1,6,8,7,5] => 3
[3,2,4,1,7,6,8,5] => 3
[2,3,4,1,6,7,8,5] => 3
[2,1,4,3,8,7,6,5] => 1
[2,1,4,3,6,8,7,5] => 2
[2,1,4,3,7,6,8,5] => 3
[5,4,3,2,1,8,7,6] => 1
[3,2,5,4,1,8,7,6] => 3
[3,2,1,4,5,8,7,6] => 1
[2,3,1,4,5,7,8,6] => 2
[6,5,4,3,2,1,8,7] => 1
[4,3,5,2,6,1,8,7] => 5
[3,2,5,4,6,1,8,7] => 5
[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] => 2
[2,1,5,4,6,3,8,7] => 3
[4,3,2,1,6,5,8,7] => 1
[2,4,3,1,6,5,8,7] => 2
[3,2,4,1,6,5,8,7] => 3
[2,1,4,3,6,5,8,7] => 1
[2,1,3,4,5,6,8,7] => 1
[1,2,3,4,5,6,8,7] => 1
[5,7,6,4,3,2,1,8] => 2
[4,7,6,5,3,2,1,8] => 2
[3,2,7,6,5,4,1,8] => 3
[5,4,3,2,7,6,1,8] => 5
[3,2,5,4,7,6,1,8] => 5
[1,4,3,2,7,6,5,8] => 1
[1,3,4,2,6,7,5,8] => 2
[1,3,2,5,4,7,6,8] => 1
[1,2,3,5,4,7,6,8] => 1
[1,3,2,4,5,7,6,8] => 1
[1,2,3,4,5,7,6,8] => 1
[1,2,4,3,6,5,7,8] => 1
[1,3,2,5,4,6,7,8] => 1
[1,2,3,5,4,6,7,8] => 1
[1,3,2,4,5,6,7,8] => 1
[1,8,4,7,6,5,3,2] => 2
[1,8,5,4,7,6,3,2] => 3
[1,8,7,4,5,6,3,2] => 3
[1,8,7,4,6,5,3,2] => 2
[1,8,6,5,4,7,3,2] => 4
[1,8,7,5,4,6,3,2] => 3
[1,8,7,5,6,4,3,2] => 2
[2,1,4,5,8,6,7,3] => 4
[2,1,8,5,4,7,6,3] => 3
[2,3,4,8,5,6,7,1] => 6
[2,3,6,4,5,1,8,7] => 4
[2,3,7,4,5,6,8,1] => 7
[2,8,4,3,5,7,6,1] => 5
[4,2,3,1,8,6,7,5] => 2
[8,2,7,4,6,5,3,1] => 3
[4,3,2,7,5,6,8,1] => 7
[4,3,2,8,5,7,6,1] => 5
[6,3,2,5,4,1,8,7] => 3
[8,3,2,5,4,7,6,1] => 5
[8,3,2,7,6,5,4,1] => 3
[8,3,7,4,6,5,2,1] => 3
[7,3,6,5,4,2,1,8] => 2
[7,4,3,6,5,2,1,8] => 3
[7,6,3,5,4,2,1,8] => 2
[8,5,4,3,2,7,6,1] => 5
[8,7,4,3,6,5,2,1] => 3
[2,4,6,8,1,3,5,7] => 4
[2,4,6,1,7,3,8,5] => 3
[2,1,4,3,7,5,8,6] => 2
[2,4,1,3,7,5,8,6] => 2
[2,1,4,3,7,8,5,6] => 2
[2,4,7,8,1,3,5,6] => 4
[2,1,4,3,8,5,6,7] => 1
[2,4,5,6,7,1,8,3] => 5
[2,1,5,3,6,4,8,7] => 2
[2,1,5,6,3,4,8,7] => 2
[2,5,6,8,1,3,4,7] => 4
[2,1,5,3,7,4,8,6] => 2
[2,5,1,7,3,4,8,6] => 2
[2,1,5,7,3,8,4,6] => 3
[2,5,7,8,1,3,4,6] => 4
[2,3,5,6,1,7,8,4] => 4
[2,1,6,3,7,4,8,5] => 3
[2,6,7,1,3,4,8,5] => 3
[2,1,6,7,8,3,4,5] => 3
[2,6,7,8,1,3,4,5] => 4
[2,1,6,3,4,7,8,5] => 3
[2,1,6,3,4,5,8,7] => 1
[2,6,1,3,4,5,7,8] => 2
[2,7,8,1,3,4,5,6] => 3
[2,7,1,3,4,5,6,8] => 2
[2,3,4,5,7,8,1,6] => 6
[2,1,8,3,4,5,6,7] => 1
[2,8,1,3,4,5,6,7] => 2
[2,1,3,8,4,5,6,7] => 1
[2,3,4,5,6,8,1,7] => 6
[3,1,4,2,6,5,8,7] => 2
[3,4,1,2,6,5,8,7] => 2
[3,1,4,2,6,8,5,7] => 2
[3,4,6,8,1,2,5,7] => 4
[3,1,4,2,7,5,8,6] => 2
[3,4,1,2,7,8,5,6] => 2
[3,4,7,8,1,2,5,6] => 4
[3,1,5,2,6,4,8,7] => 2
[3,5,1,6,2,4,8,7] => 3
[3,1,5,6,2,8,4,7] => 3
[3,5,6,8,1,2,4,7] => 4
[3,1,5,2,7,4,8,6] => 2
[3,5,1,7,2,8,4,6] => 3
[3,5,7,8,1,2,4,6] => 4
[1,3,2,5,4,8,6,7] => 1
[1,3,5,8,2,4,6,7] => 3
[1,3,5,6,2,7,4,8] => 3
[3,1,6,2,7,4,8,5] => 3
[3,6,7,1,2,8,4,5] => 3
[3,6,1,7,8,2,4,5] => 4
[3,6,7,8,1,2,4,5] => 4
[1,3,2,6,4,7,5,8] => 2
[3,1,2,6,7,4,8,5] => 3
[1,3,2,6,4,8,5,7] => 2
[1,3,2,6,4,5,7,8] => 1
[1,3,2,7,4,8,5,6] => 2
[1,3,2,7,4,5,6,8] => 1
[1,3,2,8,4,5,6,7] => 1
[3,1,2,4,5,8,6,7] => 1
[1,3,2,4,5,8,6,7] => 1
[4,1,5,2,6,3,8,7] => 3
[4,5,6,1,2,3,8,7] => 3
[4,1,5,6,8,2,3,7] => 4
[4,5,6,8,1,2,3,7] => 4
[4,1,5,2,7,3,8,6] => 3
[4,1,5,2,7,8,3,6] => 4
[4,5,7,1,2,8,3,6] => 4
[4,5,1,7,8,2,3,6] => 4
[4,5,7,8,1,2,3,6] => 4
[1,4,2,5,3,7,6,8] => 2
[1,4,2,5,3,8,6,7] => 2
[1,4,2,5,3,6,7,8] => 2
[1,4,5,6,7,2,3,8] => 4
[4,1,6,2,7,3,8,5] => 3
[4,6,7,1,8,2,3,5] => 4
[4,6,7,8,1,2,3,5] => 4
[1,4,2,6,3,7,5,8] => 2
[1,4,2,6,7,8,3,5] => 4
[1,4,2,6,3,8,5,7] => 2
[4,1,2,3,6,5,8,7] => 1
[1,4,2,6,3,5,7,8] => 2
[1,4,2,7,3,8,5,6] => 2
[4,7,1,2,3,5,6,8] => 2
[1,4,2,7,3,5,6,8] => 2
[1,4,2,3,7,5,6,8] => 1
[1,4,2,3,5,7,6,8] => 1
[1,4,2,8,3,5,6,7] => 2
[4,1,2,3,8,5,6,7] => 1
[1,4,2,3,5,8,6,7] => 1
[1,4,2,3,5,6,7,8] => 1
[5,1,6,2,7,3,8,4] => 4
[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] => 2
[1,2,5,6,3,4,7,8] => 2
[1,5,2,7,3,8,4,6] => 3
[5,7,1,2,3,4,6,8] => 2
[1,5,2,7,3,4,6,8] => 2
[1,5,2,3,4,7,6,8] => 1
[5,1,2,8,3,4,6,7] => 2
[1,5,2,8,3,4,6,7] => 2
[1,5,8,2,3,4,6,7] => 2
[1,5,2,3,4,8,6,7] => 1
[1,2,3,5,4,8,6,7] => 1
[5,1,2,3,4,6,8,7] => 1
[1,5,2,3,4,6,7,8] => 1
[1,6,2,7,3,8,4,5] => 3
[1,6,7,8,2,3,4,5] => 3
[6,7,1,2,3,4,8,5] => 3
[6,1,7,2,3,4,5,8] => 2
[6,1,2,7,3,4,5,8] => 2
[1,6,2,7,3,4,5,8] => 2
[1,6,7,2,3,4,5,8] => 2
[1,6,2,3,4,7,5,8] => 2
[1,2,3,6,4,7,5,8] => 2
[6,1,8,2,3,4,5,7] => 2
[1,6,2,8,3,4,5,7] => 2
[1,6,8,2,3,4,5,7] => 2
[1,6,2,3,4,8,5,7] => 2
[1,2,3,6,4,8,5,7] => 2
[6,1,2,3,4,5,8,7] => 1
[1,6,2,3,4,5,7,8] => 1
[1,2,3,6,4,5,7,8] => 1
[1,7,2,8,3,4,5,6] => 2
[1,7,8,2,3,4,5,6] => 2
[1,7,2,3,8,4,5,6] => 2
[7,1,2,3,4,8,5,6] => 2
[1,7,2,3,4,8,5,6] => 2
[1,2,3,7,4,8,5,6] => 2
[7,1,2,3,4,5,8,6] => 2
[1,7,2,3,4,5,8,6] => 2
[1,2,7,3,4,5,8,6] => 2
[1,7,2,3,4,5,6,8] => 1
[1,2,3,7,4,5,6,8] => 1
[1,8,2,3,4,5,6,7] => 1
[1,2,3,8,4,5,6,7] => 1
[1,2,3,4,5,8,6,7] => 1
[2,1,5,8,3,7,6,4] => 2
[2,1,6,8,7,3,5,4] => 2
[2,1,7,8,6,5,3,4] => 2
[2,1,7,6,8,4,3,5] => 3
[2,1,7,5,4,8,3,6] => 4
[2,1,8,6,7,4,5,3] => 2
[3,4,1,2,8,7,6,5] => 2
[3,5,1,8,2,7,6,4] => 3
[3,6,1,8,7,2,5,4] => 3
[3,6,1,5,4,2,8,7] => 2
[3,7,1,8,6,5,2,4] => 3
[3,7,1,6,8,4,2,5] => 4
[3,7,1,5,4,8,2,6] => 5
[3,8,1,5,4,7,6,2] => 4
[3,8,1,6,7,4,5,2] => 3
[3,8,1,7,6,5,4,2] => 2
[4,3,2,1,7,8,5,6] => 2
[4,5,8,1,2,7,6,3] => 3
[4,6,8,1,7,2,5,3] => 3
[4,6,5,1,3,2,8,7] => 2
[4,7,8,1,6,5,2,3] => 3
[4,7,6,1,8,3,2,5] => 4
[4,7,5,1,3,8,2,6] => 5
[4,8,5,1,3,7,6,2] => 4
[4,8,6,1,7,3,5,2] => 3
[4,8,7,1,6,5,3,2] => 2
[5,3,2,8,1,7,6,4] => 4
[5,3,2,7,1,8,4,6] => 4
[5,3,2,6,1,4,8,7] => 4
[5,4,8,2,1,7,6,3] => 3
[5,4,7,2,1,8,3,6] => 4
[5,4,6,2,1,3,8,7] => 3
[5,6,8,7,1,2,4,3] => 3
[5,6,4,3,1,2,8,7] => 2
[5,7,8,6,1,4,2,3] => 3
[5,7,6,8,1,3,2,4] => 4
[5,7,4,3,1,8,2,6] => 5
[5,8,4,3,1,7,6,2] => 3
[5,8,6,7,1,3,4,2] => 3
[5,8,7,6,1,4,3,2] => 2
[6,3,2,8,7,1,5,4] => 4
[6,3,2,7,8,1,4,5] => 5
[6,4,8,2,7,1,5,3] => 3
[6,4,7,2,8,1,3,5] => 5
[6,4,5,2,3,1,8,7] => 2
[6,5,8,7,2,1,4,3] => 3
[6,7,4,3,8,1,2,5] => 5
[6,8,4,3,7,1,5,2] => 3
[6,8,5,7,3,1,4,2] => 2
[6,8,7,5,4,1,3,2] => 2
[7,3,2,8,6,5,1,4] => 4
[7,3,2,6,8,4,1,5] => 5
[7,3,2,5,4,8,1,6] => 6
[7,4,8,2,6,5,1,3] => 3
[7,4,6,2,8,3,1,5] => 5
[7,4,5,2,3,8,1,6] => 6
[7,5,8,6,2,4,1,3] => 3
[7,5,4,3,2,8,1,6] => 6
[7,6,4,3,8,2,1,5] => 5
[7,8,4,3,6,5,1,2] => 3
[8,3,2,6,7,4,5,1] => 4
[8,4,5,2,3,7,6,1] => 5
[8,4,6,2,7,3,5,1] => 4
[8,4,7,2,6,5,3,1] => 2
[8,5,7,6,2,4,3,1] => 2
[8,6,4,3,7,2,5,1] => 4
[4,2,5,1,3,6,7,8] => 3
[5,2,6,7,1,3,4,8] => 4
[3,2,7,8,1,4,5,6] => 4
[5,3,2,6,1,4,7,8] => 4
[7,4,3,8,1,2,5,6] => 4
[4,7,3,6,8,1,2,5] => 5
[6,7,3,4,8,1,2,5] => 5
[5,4,2,7,8,1,3,6] => 5
[6,4,7,2,5,1,3,8] => 3
[6,4,3,2,7,1,5,8] => 5
[5,4,3,2,8,1,6,7] => 5
[7,5,3,8,2,6,1,4] => 4
[8,5,4,7,2,6,1,3] => 3
[8,5,4,7,3,6,1,2] => 3
[7,5,3,1,8,6,4,2] => 4
[8,7,1,3,6,2,4,5] => 2
[5,4,1,3,8,2,6,7] => 4
[4,8,5,7,1,6,2,3] => 3
[8,7,6,5,1,4,2,3] => 1
[3,2,1,5,8,4,6,7] => 2
[1,8,2,7,3,6,4,5] => 1
[2,5,3,4,1,8,6,7] => 3
[2,4,8,3,5,7,6,1] => 5
[8,7,2,6,3,5,4,1] => 3
[5,4,3,2,1,8,6,7] => 1
[3,8,4,7,6,5,2,1] => 3
[3,6,7,4,5,8,1,2] => 6
[7,8,1,4,5,2,3,6] => 2
[1,6,7,4,5,2,3,8] => 2
[8,5,7,4,2,1,6,3] => 2
[8,6,3,5,2,4,1,7] => 2
[8,3,7,5,2,4,6,1] => 5
[8,7,6,3,5,2,4,1] => 2
[8,5,7,4,3,2,6,1] => 4
[8,4,7,6,3,5,2,1] => 2
[6,5,8,4,2,7,3,1] => 3
[7,5,3,6,4,2,8,1] => 7
[8,5,3,6,2,7,4,1] => 5
[8,6,4,7,5,3,2,1] => 3
[8,6,5,4,2,7,3,1] => 5
[8,7,5,2,6,4,3,1] => 3
[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] => 1
[1,2,3,8,4,7,5,6] => 1
[1,8,2,3,4,7,5,6] => 1
[1,6,2,5,3,4,7,8] => 1
[1,8,2,5,3,4,6,7] => 1
[1,8,2,7,3,4,5,6] => 1
[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] => 3
[8,5,4,7,6,3,2,1] => 3
[5,4,3,8,7,6,1,2] => 4
[8,1,2,4,5,6,3,7] => 3
[1,8,2,6,3,5,4,7] => 1
[1,7,2,6,3,5,4,8] => 1
[1,7,2,6,3,4,5,8] => 1
[8,7,6,1,4,3,2,5] => 1
[7,1,8,6,5,4,3,2] => 2
[1,8,7,6,5,4,2,3] => 1
[3,2,1,4,8,5,6,7] => 1
[1,8,2,3,4,6,5,7] => 1
[1,6,2,7,3,5,4,8] => 2
[1,6,2,5,3,7,4,8] => 3
[1,5,3,7,2,6,4,8] => 3
[2,8,4,1,6,3,7,5] => 2
[5,3,6,4,7,1,8,2] => 6
[8,1,6,7,5,4,3,2] => 2
[8,1,6,7,4,5,2,3] => 2
[1,8,2,7,3,5,4,6] => 1
[1,7,2,8,3,5,4,6] => 2
[5,4,3,2,7,1,8,6] => 5
[3,5,2,7,1,8,6,4] => 4
[2,6,7,3,1,4,8,5] => 3
[5,4,1,8,7,2,3,6] => 3
[8,4,3,1,7,6,2,5] => 3
[5,7,4,3,2,1,8,6] => 2
[3,2,6,1,4,7,8,5] => 3
[3,6,7,2,1,8,5,4] => 3
[1,7,6,5,4,8,2,3] => 5
[1,5,4,2,8,3,6,7] => 3
[6,7,2,3,4,8,5,1] => 6
[4,6,2,5,8,3,7,1] => 5
[4,3,5,2,7,1,8,6] => 5
[3,2,6,1,7,4,8,5] => 3
[1,7,2,5,3,4,6,8] => 1
[1,6,2,4,3,5,7,8] => 1
[1,5,2,4,3,6,7,8] => 1
[1,6,2,4,3,7,5,8] => 2
[8,1,2,5,6,7,4,3] => 3
[7,8,3,2,1,6,5,4] => 2
[1,2,3,8,4,6,5,7] => 1
[8,7,1,6,4,5,3,2] => 2
[8,7,6,1,5,3,4,2] => 2
[4,8,7,5,6,3,2,1] => 3
[4,3,7,6,2,1,8,5] => 3
[4,7,6,3,2,8,1,5] => 6
[7,1,6,5,8,3,2,4] => 4
[7,1,6,5,4,8,2,3] => 5
[5,1,7,3,8,4,6,2] => 4
[4,3,6,2,7,1,8,5] => 5
[8,7,5,4,1,3,2,6] => 1
[6,4,3,8,2,1,5,7] => 4
[5,3,8,7,6,4,2,1] => 3
[8,4,7,6,5,1,3,2] => 2
[2,3,8,7,4,5,6,1] => 5
[7,6,5,3,2,1,8,4] => 4
[1,7,2,8,3,6,4,5] => 2
[1,5,2,8,3,7,4,6] => 2
[3,2,4,1,7,5,8,6] => 3
[4,3,6,1,7,2,8,5] => 4
[3,7,5,6,8,4,2,1] => 5
[5,4,6,3,7,1,8,2] => 6
[1,2,8,7,4,5,6,3] => 3
[2,8,6,3,7,4,5,1] => 4
[5,4,6,1,7,3,8,2] => 6
[1,8,2,6,3,4,5,7] => 1
[6,3,8,4,2,5,7,1] => 5
[8,7,1,6,2,5,4,3] => 1
[8,2,7,6,3,5,4,1] => 3
[1,2,3,7,4,6,5,8] => 1
[4,5,2,3,8,1,6,7] => 5
[8,1,7,6,5,4,2,3] => 1
[1,8,6,7,5,4,3,2] => 2
[6,2,8,7,5,4,3,1] => 3
[7,1,3,5,8,2,4,6] => 4
[4,6,2,7,3,5,1,8] => 4
[1,5,7,3,8,4,6,2] => 4
[8,1,7,6,5,2,4,3] => 1
[1,3,2,8,4,7,5,6] => 1
[5,2,3,8,1,6,7,4] => 4
[1,8,2,4,3,5,6,7] => 1
[2,4,1,8,7,6,5,3] => 2
[1,8,5,4,3,2,6,7] => 1
[8,2,6,1,7,3,5,4] => 2
[7,1,8,6,5,3,2,4] => 2
[1,7,2,5,3,6,4,8] => 2
[1,8,2,6,3,7,4,5] => 2
[5,1,2,4,8,3,6,7] => 3
[1,6,2,8,3,7,4,5] => 2
[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] => 4
[8,7,3,5,1,6,2,4] => 3
[6,4,8,1,7,2,3,5] => 3
[6,1,7,2,8,5,4,3] => 3
[7,1,2,8,3,5,4,6] => 2
[1,6,2,5,8,3,4,7] => 3
[8,1,7,5,6,4,3,2] => 2
[1,7,2,8,4,5,3,6] => 2
[1,7,3,4,2,5,8,6] => 2
[8,2,5,1,3,6,4,7] => 2
[7,1,2,8,5,3,4,6] => 2
[5,2,6,3,7,4,8,1] => 7
[1,6,2,8,3,5,4,7] => 2
[8,1,5,3,2,4,6,7] => 1
[7,8,5,6,2,1,4,3] => 2
[7,8,4,2,6,1,5,3] => 3
[8,6,1,3,4,2,5,7] => 2
[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] => 3
[3,6,4,5,7,2,8,1] => 7
[5,2,4,7,3,6,8,1] => 7
[4,2,5,1,6,3,8,7] => 3
[5,4,3,6,1,2,8,7] => 4
[4,5,2,3,7,6,1,8] => 5
[4,1,2,6,5,8,7,3] => 4
[5,1,6,2,4,8,7,3] => 4
[7,6,2,1,8,5,4,3] => 3
[2,7,6,8,5,4,1,3] => 4
[8,7,1,6,5,3,2,4] => 1
[2,8,1,3,4,5,7,6] => 2
[3,1,8,2,4,7,6,5] => 2
[5,4,8,1,7,2,6,3] => 3
[5,4,6,2,7,1,8,3] => 5
[1,7,6,8,5,4,2,3] => 3
[6,8,5,4,2,1,3,7] => 2
[1,7,2,6,3,8,4,5] => 3
[8,5,7,3,2,1,6,4] => 2
[4,2,5,3,7,6,8,1] => 7
[3,2,6,4,7,5,8,1] => 7
[4,2,6,3,7,5,8,1] => 7
[2,7,6,5,3,4,8,1] => 7
[5,8,6,7,4,3,2,1] => 3
[4,2,5,1,7,6,8,3] => 5
[4,2,6,1,7,3,8,5] => 3
[4,3,1,2,8,7,5,6] => 1
[4,1,5,2,7,6,8,3] => 5
[4,1,6,2,7,5,8,3] => 5
[1,7,2,4,3,5,6,8] => 1
[6,2,8,4,5,1,7,3] => 3
[8,1,4,2,6,3,5,7] => 2
[4,3,5,1,6,2,8,7] => 4
[3,1,5,4,7,6,8,2] => 6
[4,1,5,3,7,6,8,2] => 6
[4,1,6,3,7,5,8,2] => 6
[8,3,6,1,4,7,2,5] => 4
[1,7,2,3,4,6,5,8] => 1
[6,3,7,1,4,8,2,5] => 5
[2,1,7,5,6,8,3,4] => 4
[2,1,5,3,8,7,6,4] => 2
[1,6,7,8,3,4,5,2] => 3
[1,8,4,2,5,3,6,7] => 2
[3,1,6,5,4,2,8,7] => 2
[5,6,1,2,3,8,7,4] => 3
[1,3,2,7,4,6,5,8] => 1
[1,2,7,6,8,3,4,5] => 3
[8,7,1,5,6,4,3,2] => 2
[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] => 6
[6,1,8,7,2,5,4,3] => 2
[1,8,2,5,3,7,4,6] => 2
[2,6,8,4,3,7,5,1] => 4
[4,2,6,8,7,3,5,1] => 4
[8,5,1,3,7,2,6,4] => 3
[8,3,1,2,4,7,5,6] => 1
[1,8,2,4,3,7,5,6] => 1
[1,8,2,4,3,6,5,7] => 1
[4,7,2,5,8,3,6,1] => 5
[5,4,6,2,7,3,8,1] => 7
[6,1,8,3,2,5,4,7] => 2
[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] => 2
[3,4,8,5,6,7,2,1] => 5
[2,7,8,4,5,3,6,1] => 5
[3,1,6,5,7,4,8,2] => 6
[4,1,2,8,7,6,5,3] => 2
[5,8,1,2,7,6,3,4] => 2
[5,3,1,8,2,7,4,6] => 3
[4,1,2,3,6,8,7,5] => 2
[7,5,1,3,8,2,6,4] => 4
[3,6,8,5,7,2,4,1] => 3
[8,2,1,7,3,5,6,4] => 2
[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] => 3
[3,7,6,8,4,5,2,1] => 4
[2,7,6,8,5,3,4,1] => 4
[2,4,8,6,7,3,5,1] => 4
[6,8,2,4,3,5,1,7] => 4
[7,5,2,8,3,4,6,1] => 4
[5,6,2,8,4,3,1,7] => 4
[5,7,8,6,3,4,1,2] => 3
[4,1,6,5,7,3,8,2] => 6
[3,2,5,1,7,6,8,4] => 4
[3,2,6,1,7,5,8,4] => 4
[4,2,6,1,7,5,8,3] => 5
[5,1,8,2,7,6,4,3] => 2
[6,4,3,1,2,8,7,5] => 2
[7,4,3,1,8,2,6,5] => 4
[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] => 2
[1,4,2,8,3,7,5,6] => 2
[1,6,2,4,3,8,5,7] => 2
[6,3,8,2,1,7,5,4] => 3
[7,5,1,3,8,4,2,6] => 4
[8,1,6,2,7,4,5,3] => 2
[6,8,1,7,2,5,3,4] => 2
[4,2,1,3,8,5,7,6] => 1
[3,2,5,1,6,4,8,7] => 3
[5,8,7,2,1,4,3,6] => 2
[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] => 4
[3,7,4,1,8,5,2,6] => 4
[5,2,6,1,7,3,8,4] => 4
[7,8,1,3,2,5,4,6] => 2
[6,1,2,8,4,3,5,7] => 2
[3,2,5,1,7,4,8,6] => 3
[5,4,6,1,7,2,8,3] => 5
[1,6,8,5,3,7,4,2] => 3
[8,6,1,7,4,2,5,3] => 2
[3,2,8,5,7,4,6,1] => 4
[3,6,5,8,7,4,1,2] => 4
[4,3,6,1,5,8,2,7] => 5
[1,3,6,7,5,8,2,4] => 5
[3,8,1,5,2,4,6,7] => 2
[3,7,8,1,5,2,4,6] => 3
[1,2,7,5,8,3,4,6] => 3
[6,7,1,4,2,8,3,5] => 4
[1,6,7,2,8,4,3,5] => 3
[5,4,2,8,7,1,6,3] => 4
[4,7,2,1,3,5,8,6] => 2
[5,2,7,1,3,8,4,6] => 3
[5,3,1,7,8,2,4,6] => 4
[4,3,5,2,1,8,6,7] => 3
[5,6,2,1,4,8,3,7] => 4
[4,1,3,2,8,5,6,7] => 1
[2,6,1,4,5,8,3,7] => 4
[2,1,7,6,5,8,3,4] => 4
[5,7,3,6,1,8,2,4] => 5
[6,4,3,5,8,1,7,2] => 5
[2,7,6,4,5,8,1,3] => 6
[7,3,5,4,8,6,1,2] => 5
[3,2,5,4,8,1,6,7] => 5
[3,2,6,7,4,5,1,8] => 4
[3,2,6,8,4,1,5,7] => 4
[4,6,2,8,3,1,5,7] => 4
[4,7,2,8,1,3,5,6] => 4
[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] => 4
[1,5,6,3,4,8,7,2] => 5
[4,1,2,7,8,5,6,3] => 3
[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] => 4
[5,8,7,3,2,6,1,4] => 3
[2,5,3,7,1,6,8,4] => 4
[2,6,1,3,5,4,8,7] => 2
[1,5,2,4,3,7,6,8] => 1
[1,3,2,8,4,6,5,7] => 1
[1,7,2,4,3,6,5,8] => 1
[8,3,7,1,5,6,2,4] => 3
[7,3,8,6,1,5,2,4] => 3
[7,6,4,1,3,8,2,5] => 5
[5,4,7,1,3,8,2,6] => 5
[6,4,8,7,1,5,2,3] => 3
[8,1,2,7,6,3,4,5] => 1
[2,8,1,7,5,6,3,4] => 2
[8,6,1,2,7,5,3,4] => 2
[5,1,4,8,3,2,6,7] => 3
[7,8,6,1,5,3,2,4] => 2
[7,6,1,4,8,3,2,5] => 4
[5,1,4,7,8,3,2,6] => 4
[4,8,1,5,7,3,6,2] => 3
[6,4,8,1,7,3,5,2] => 3
[2,1,7,3,5,8,4,6] => 3
[1,5,8,4,3,2,6,7] => 2
[7,8,1,6,4,2,5,3] => 2
[7,1,6,8,4,3,2,5] => 3
[1,5,7,3,8,4,2,6] => 4
[8,1,5,3,7,4,6,2] => 3
[6,8,1,7,4,3,5,2] => 3
[2,7,1,8,3,5,4,6] => 2
[2,8,3,1,5,4,6,7] => 2
[4,2,1,7,8,5,3,6] => 3
[4,2,1,8,5,3,6,7] => 2
[1,8,5,2,6,7,4,3] => 3
[1,7,8,5,2,6,4,3] => 2
[1,7,5,6,3,2,8,4] => 4
[1,7,4,3,8,5,2,6] => 4
[1,4,3,8,7,5,6,2] => 4
[4,2,5,3,1,8,6,7] => 3
[5,2,1,8,6,7,4,3] => 3
[6,5,2,1,7,3,8,4] => 4
[6,1,7,5,3,2,8,4] => 4
[6,4,3,1,7,2,8,5] => 4
[4,3,1,8,6,7,5,2] => 4
[7,8,2,6,3,1,5,4] => 2
[7,2,6,3,4,1,8,5] => 3
[2,5,3,4,7,1,8,6] => 5
[2,7,8,4,1,6,5,3] => 3
[2,7,4,6,3,1,8,5] => 3
[4,2,5,3,7,1,8,6] => 5
[5,2,7,1,8,6,4,3] => 3
[5,2,7,6,3,1,8,4] => 4
[4,3,7,1,8,6,5,2] => 4
[6,2,4,8,3,7,5,1] => 4
[5,2,6,3,8,7,4,1] => 5
[2,8,5,7,6,4,3,1] => 3
[4,3,6,2,8,7,5,1] => 5
[6,5,3,2,8,7,4,1] => 5
[2,7,6,8,1,4,3,5] => 4
[8,2,5,7,6,4,3,1] => 3
[4,1,5,3,7,2,8,6] => 4
[6,5,8,7,1,2,3,4] => 3
[7,5,8,4,3,6,2,1] => 3
[4,7,3,2,1,5,8,6] => 2
[5,6,7,8,2,1,4,3] => 4
[8,3,5,2,1,6,4,7] => 2
[8,5,6,7,1,3,2,4] => 3
[5,1,6,2,7,4,8,3] => 5
[5,8,6,2,4,1,3,7] => 2
[5,7,3,8,1,4,6,2] => 4
[6,8,1,4,7,2,5,3] => 2
[3,2,1,7,8,5,6,4] => 2
[4,7,3,5,8,6,2,1] => 5
[4,3,6,5,7,1,8,2] => 6
[8,4,2,1,7,3,6,5] => 2
[3,7,5,1,4,2,8,6] => 2
[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] => 2
[2,7,4,8,1,6,5,3] => 4
[3,8,2,1,4,6,5,7] => 2
[1,4,2,8,3,6,5,7] => 2
[4,7,2,8,1,5,3,6] => 4
[5,2,1,8,3,4,7,6] => 2
[4,1,3,2,8,6,5,7] => 1
[3,1,6,7,5,8,2,4] => 5
[2,1,6,5,7,8,3,4] => 4
[1,4,6,7,3,2,8,5] => 3
[2,4,5,7,3,1,8,6] => 4
[2,1,7,8,5,6,4,3] => 2
[2,3,5,7,6,8,1,4] => 6
[3,7,6,5,8,2,1,4] => 5
[1,7,4,8,6,3,5,2] => 3
[4,6,8,3,2,7,5,1] => 3
[3,2,5,6,1,8,7,4] => 4
[2,5,4,7,6,1,8,3] => 5
[6,3,1,5,2,4,8,7] => 2
[1,2,8,7,6,3,4,5] => 1
[1,7,2,8,5,3,4,6] => 2
[7,8,1,6,2,4,5,3] => 2
[1,3,7,4,6,8,2,5] => 5
[1,3,8,7,5,6,2,4] => 3
[7,6,1,8,4,3,2,5] => 3
[8,1,2,7,3,4,6,5] => 1
[8,1,6,5,7,2,4,3] => 3
[3,1,4,8,6,5,7,2] => 5
[2,3,8,1,4,6,7,5] => 3
[2,5,7,3,8,6,4,1] => 5
[4,8,1,2,7,6,3,5] => 2
[6,3,7,5,2,8,4,1] => 6
[3,4,8,1,7,2,5,6] => 3
[4,1,2,8,7,5,6,3] => 3
[2,8,6,3,1,5,7,4] => 3
[8,3,4,1,6,7,2,5] => 4
[8,5,7,3,1,4,2,6] => 2
[8,4,2,1,7,5,3,6] => 2
[5,3,6,1,7,2,8,4] => 4
[5,3,6,1,7,4,8,2] => 6
[5,2,6,4,7,1,8,3] => 5
[5,2,6,3,7,1,8,4] => 5
[5,3,6,2,7,1,8,4] => 5
[4,3,6,2,7,5,8,1] => 7
[5,3,6,2,7,4,8,1] => 7
[5,3,6,4,7,2,8,1] => 7
[7,5,8,3,1,2,4,6] => 3
[7,6,8,1,3,2,4,5] => 3
[7,8,1,6,5,2,3,4] => 2
[7,8,6,1,4,2,3,5] => 2
[7,1,6,8,4,2,5,3] => 3
[8,6,1,7,3,5,2,4] => 2
[8,6,7,1,3,4,2,5] => 2
[8,1,5,4,7,6,2,3] => 3
[1,7,5,4,8,3,6,2] => 4
[1,7,6,8,4,3,5,2] => 3
[1,7,8,6,5,3,4,2] => 2
[1,8,6,7,4,5,3,2] => 2
[6,5,8,3,2,1,4,7] => 3
[8,4,3,6,5,1,2,7] => 3
[6,4,3,7,2,5,1,8] => 4
[1,5,2,8,3,6,4,7] => 2
[1,8,2,5,3,6,4,7] => 2
[6,7,8,2,4,3,5,1] => 4
[6,7,8,5,1,3,2,4] => 3
[6,7,8,1,4,3,2,5] => 3
[5,7,6,8,2,3,4,1] => 4
[7,8,2,1,3,4,6,5] => 2
[1,5,2,4,3,8,6,7] => 1
[3,2,7,1,8,4,6,5] => 3
[4,6,7,3,8,5,1,2] => 5
[4,5,3,7,8,6,1,2] => 5
[4,3,5,6,8,7,1,2] => 5
[5,3,4,8,6,7,1,2] => 5
[6,3,8,4,5,7,1,2] => 4
[3,5,4,7,6,8,1,2] => 6
[4,6,7,2,8,1,5,3] => 5
[4,5,2,7,8,1,6,3] => 5
[7,8,2,4,5,1,6,3] => 3
[4,2,5,6,8,1,7,3] => 5
[5,2,4,8,6,1,7,3] => 4
[2,6,7,4,5,1,8,3] => 5
[7,8,2,3,1,5,6,4] => 2
[6,2,8,3,1,5,7,4] => 3
[2,6,7,3,1,5,8,4] => 4
[7,8,4,1,6,2,3,5] => 2
[6,3,8,1,2,7,4,5] => 3
[7,8,3,1,2,6,4,5] => 2
[5,1,4,8,6,2,3,7] => 3
[6,1,8,4,5,2,3,7] => 2
[5,1,3,8,2,6,4,7] => 3
[1,5,4,7,6,2,3,8] => 3
[1,6,7,3,2,5,4,8] => 2
[8,5,7,2,1,3,6,4] => 2
[8,2,6,7,1,3,5,4] => 3
[2,7,8,6,1,3,5,4] => 3
[5,7,4,2,1,3,8,6] => 2
[8,2,6,1,4,7,5,3] => 3
[8,7,6,1,3,4,2,5] => 2
[8,5,3,7,1,6,2,4] => 3
[8,3,6,1,7,5,2,4] => 3
[8,6,3,5,1,4,2,7] => 2
[3,7,8,1,6,5,2,4] => 3
[3,7,1,6,4,8,2,5] => 5
[8,3,7,5,1,4,6,2] => 4
[3,6,4,1,8,7,5,2] => 4
[4,6,1,8,7,2,5,3] => 3
[8,6,1,4,5,3,2,7] => 2
[1,7,4,8,2,6,5,3] => 3
[1,7,4,5,3,2,8,6] => 2
[8,4,1,7,5,3,6,2] => 4
[4,8,1,6,7,3,5,2] => 3
[5,3,7,2,1,8,4,6] => 3
[8,2,5,4,6,1,3,7] => 4
[8,1,5,6,4,3,2,7] => 2
[1,7,2,5,8,6,4,3] => 3
[1,7,3,5,6,8,2,4] => 5
[5,4,7,3,1,8,2,6] => 5
[3,1,5,8,6,7,4,2] => 4
[8,2,4,6,5,3,1,7] => 3
[8,2,6,5,7,4,1,3] => 4
[4,6,3,8,7,1,5,2] => 4
[3,7,8,6,2,1,5,4] => 3
[3,7,2,6,4,8,1,5] => 6
[3,7,5,2,4,1,8,6] => 2
[4,2,7,6,8,3,1,5] => 5
[3,8,2,4,6,7,5,1] => 5
[8,2,4,5,7,3,6,1] => 4
[5,4,3,8,6,7,2,1] => 5
[5,4,2,8,7,3,6,1] => 4
[5,4,1,8,7,6,2,3] => 3
[5,4,7,1,8,3,2,6] => 4
[5,4,1,7,6,8,2,3] => 5
[4,7,5,6,8,3,2,1] => 5
[6,3,5,8,4,7,2,1] => 4
[6,2,5,8,7,3,4,1] => 4
[4,7,5,6,3,2,8,1] => 7
[4,8,5,6,2,7,3,1] => 5
[3,8,4,1,7,2,6,5] => 3
[3,7,6,4,5,2,8,1] => 7
[3,1,8,5,7,6,2,4] => 3
[6,7,1,4,8,3,2,5] => 4
[3,8,6,4,2,7,5,1] => 5
[6,4,3,1,5,8,2,7] => 5
[2,6,5,7,3,4,8,1] => 7
[7,3,8,5,4,6,2,1] => 4
[6,5,1,4,3,8,2,7] => 5
[6,2,7,4,3,5,8,1] => 7
[2,1,8,7,4,6,3,5] => 2
[2,7,1,8,4,5,3,6] => 2
[6,1,7,5,3,8,2,4] => 5
[7,8,5,2,4,6,3,1] => 4
[2,8,1,7,4,3,6,5] => 2
[7,2,6,3,5,4,8,1] => 7
[7,2,8,6,4,3,5,1] => 4
[7,4,2,1,8,5,3,6] => 3
[1,6,4,7,5,8,2,3] => 5
[1,4,8,6,7,5,2,3] => 3
[8,2,6,3,4,7,5,1] => 5
[2,1,7,8,5,4,6,3] => 3
[2,1,5,8,4,6,3,7] => 2
[2,1,4,8,3,5,7,6] => 2
[2,1,6,7,4,8,5,3] => 4
[2,1,8,5,3,7,4,6] => 2
[2,4,3,1,8,5,6,7] => 2
[6,5,3,8,4,1,2,7] => 4
[5,6,3,2,4,1,8,7] => 3
[7,4,3,8,2,5,1,6] => 4
[6,5,3,2,8,7,1,4] => 5
[5,6,3,7,4,8,1,2] => 6
[5,8,3,7,4,2,6,1] => 4
[6,8,3,5,2,7,4,1] => 4
[3,6,2,4,1,5,8,7] => 2
[7,5,2,4,8,1,6,3] => 5
[3,6,7,4,1,8,5,2] => 5
[3,8,7,4,1,2,6,5] => 2
[7,5,2,6,3,8,1,4] => 6
[4,5,2,6,3,1,8,7] => 4
[7,1,8,5,4,3,6,2] => 4
[2,4,8,3,5,6,1,7] => 5
[4,3,8,2,5,1,7,6] => 3
[3,4,2,8,5,7,6,1] => 5
[7,6,1,3,5,8,4,2] => 5
[7,8,1,3,5,2,6,4] => 2
[3,8,4,2,5,7,1,6] => 5
[4,1,8,3,6,5,2,7] => 2
[5,6,2,1,8,7,3,4] => 3
[6,5,2,7,4,8,3,1] => 6
[5,7,1,6,8,2,4,3] => 4
[8,6,2,5,1,7,4,3] => 3
[8,3,7,5,2,1,6,4] => 2
[8,4,1,3,7,2,6,5] => 3
[2,1,5,3,7,6,8,4] => 4
[2,1,6,3,7,5,8,4] => 4
[2,1,6,5,7,3,8,4] => 4
[2,1,6,4,7,3,8,5] => 3
[2,1,5,4,7,3,8,6] => 3
[2,1,6,4,7,5,8,3] => 5
[3,1,4,2,7,6,8,5] => 3
[3,1,5,2,7,6,8,4] => 4
[3,1,6,2,7,5,8,4] => 4
[3,1,5,4,6,2,8,7] => 4
[3,1,6,5,7,2,8,4] => 4
[3,1,6,4,7,2,8,5] => 4
[3,1,5,4,7,2,8,6] => 4
[3,1,6,4,7,5,8,2] => 6
[4,1,5,3,6,2,8,7] => 4
[4,1,6,5,7,2,8,3] => 5
[4,1,6,3,7,2,8,5] => 4
[4,2,5,1,7,3,8,6] => 3
[5,1,6,4,7,2,8,3] => 5
[5,1,6,3,7,2,8,4] => 4
[4,3,5,1,7,2,8,6] => 4
[4,3,5,1,7,6,8,2] => 6
[5,1,6,3,7,4,8,2] => 6
[4,2,5,3,6,1,8,7] => 5
[5,2,6,1,7,4,8,3] => 5
[4,3,6,1,7,5,8,2] => 6
[3,2,6,5,7,1,8,4] => 5
[3,2,6,4,7,1,8,5] => 5
[3,2,5,4,7,1,8,6] => 5
[4,2,6,5,7,1,8,3] => 5
[4,2,6,3,7,1,8,5] => 5
[4,2,6,5,7,3,8,1] => 7
[5,2,6,4,7,3,8,1] => 7
[4,5,2,3,1,8,7,6] => 2
[4,6,2,1,3,8,7,5] => 2
[4,7,2,1,8,3,6,5] => 3
[4,7,2,6,5,3,1,8] => 2
[4,8,2,6,5,1,3,7] => 2
[5,7,6,2,4,3,1,8] => 2
[6,5,1,3,2,8,7,4] => 3
[6,8,7,1,2,4,3,5] => 2
[6,1,5,4,2,8,7,3] => 4
[7,6,1,8,3,2,5,4] => 3
[7,1,5,4,8,2,6,3] => 4
[7,1,8,6,5,2,4,3] => 2
[8,4,3,7,1,5,2,6] => 3
[8,5,1,3,7,6,2,4] => 3
[1,5,8,3,7,6,4,2] => 2
[1,6,8,7,3,5,4,2] => 2
[1,4,2,7,3,6,5,8] => 2
[1,5,2,7,3,6,4,8] => 2
[1,6,2,5,3,8,4,7] => 3
[1,7,2,4,3,8,5,6] => 2
[8,7,2,5,1,3,6,4] => 2
[8,2,6,5,1,3,7,4] => 3
[2,7,6,5,1,3,8,4] => 4
[2,7,6,1,4,3,8,5] => 3
[2,7,1,5,4,3,8,6] => 2
[8,2,6,1,4,3,7,5] => 2
[8,7,3,1,4,6,2,5] => 3
[8,3,6,5,1,7,2,4] => 4
[3,1,6,5,4,8,2,7] => 5
[3,7,6,5,1,8,2,4] => 5
[3,7,6,1,4,8,2,5] => 5
[8,3,1,5,4,7,2,6] => 4
[8,4,6,5,7,1,2,3] => 4
[4,1,6,5,8,3,2,7] => 4
[4,7,6,5,8,1,2,3] => 5
[4,7,1,5,8,3,2,6] => 4
[8,4,1,5,7,3,2,6] => 3
[8,4,6,1,7,3,2,5] => 3
[5,3,6,8,4,7,2,1] => 4
[5,2,6,8,4,3,7,1] => 4
[5,1,6,8,4,3,2,7] => 3
[5,7,6,8,4,1,2,3] => 4
[5,7,1,8,4,3,2,6] => 3
[4,2,6,5,8,3,7,1] => 5
[3,7,6,2,4,8,5,1] => 6
[3,7,2,5,4,8,6,1] => 6
[4,7,6,2,8,3,5,1] => 5
[8,3,6,2,4,7,5,1] => 5
[8,4,2,5,7,3,6,1] => 4
[9,7,8,4,5,6,1,2,3] => 3
[9,7,8,5,6,1,2,3,4] => 2
[9,8,5,6,7,1,2,3,4] => 3
[8,9,5,6,7,1,2,3,4] => 3
[7,4,8,2,5,9,1,3,6] => 6
[6,4,7,2,5,1,3,8,9] => 3
[6,3,2,7,8,1,4,5,9] => 5
[6,7,3,4,8,1,2,5,9] => 5
[8,7,6,5,4,3,2,1,9] => 1
[1,9,8,7,6,5,4,3,2] => 1
[8,7,6,4,5,3,2,1,9] => 2
[1,9,8,7,5,6,4,3,2] => 2
[8,7,5,4,6,3,2,1,9] => 3
[8,7,4,6,5,3,2,1,9] => 2
[1,9,8,6,5,7,4,3,2] => 3
[1,9,8,5,7,6,4,3,2] => 2
[9,1,2,3,4,5,6,7,8] => 1
[2,3,4,5,6,7,8,9,1] => 8
[8,1,2,3,4,5,6,7,9] => 1
[2,3,4,5,6,7,8,1,9] => 7
[8,1,2,3,4,5,6,9,7] => 2
[7,1,2,3,4,5,6,8,9] => 1
[2,3,4,5,6,7,1,8,9] => 6
[2,3,4,5,6,7,9,1,8] => 7
[9,2,1,3,4,5,6,7,8] => 1
[3,2,4,5,6,7,8,9,1] => 8
[9,3,1,2,4,5,6,7,8] => 1
[9,2,3,1,4,5,6,7,8] => 2
[4,2,3,5,6,7,8,9,1] => 8
[3,4,2,5,6,7,8,9,1] => 8
[7,8,6,5,4,3,2,1,9] => 2
[1,8,9,7,6,5,4,3,2] => 2
[7,6,8,5,4,3,2,1,9] => 3
[6,8,7,5,4,3,2,1,9] => 2
[1,8,7,9,6,5,4,3,2] => 3
[1,7,9,8,6,5,4,3,2] => 2
[1,9,2,3,4,5,6,7,8] => 1
[7,8,1,2,3,4,5,6,9] => 2
[1,8,9,2,3,4,5,6,7] => 2
[7,1,8,2,3,4,5,6,9] => 2
[6,8,1,2,3,4,5,7,9] => 2
[1,8,2,9,3,4,5,6,7] => 2
[1,7,9,2,3,4,5,6,8] => 2
[1,2,3,4,5,6,7,9,8] => 1
[2,1,3,4,5,6,7,8,9] => 1
[2,9,1,3,4,5,6,7,8] => 2
[1,8,2,3,4,5,6,9,7] => 2
[7,1,2,3,4,5,6,9,8] => 1
[2,1,9,3,4,5,6,7,8] => 1
[2,8,1,3,4,5,6,7,9] => 2
[1,2,3,4,5,6,7,8,9] => 0
[8,9,1,2,3,4,5,6,7] => 2
[9,8,1,2,3,4,5,6,7] => 1
[7,8,9,1,2,3,4,5,6] => 3
[9,7,8,1,2,3,4,5,6] => 2
[9,8,7,1,2,3,4,5,6] => 1
[6,7,8,9,1,2,3,4,5] => 4
[9,6,7,8,1,2,3,4,5] => 3
[8,9,6,7,1,2,3,4,5] => 2
[9,8,6,7,1,2,3,4,5] => 2
[9,8,7,6,1,2,3,4,5] => 1
[9,5,6,7,8,1,2,3,4] => 4
[9,8,7,5,6,1,2,3,4] => 2
[9,8,7,6,5,1,2,3,4] => 1
[7,8,9,4,5,6,1,2,3] => 3
[9,8,7,4,5,6,1,2,3] => 3
[8,9,6,7,4,5,1,2,3] => 2
[9,8,6,7,4,5,1,2,3] => 2
[9,8,7,6,4,5,1,2,3] => 2
[9,8,7,6,5,4,1,2,3] => 1
[9,7,8,5,6,3,4,1,2] => 2
[9,8,7,5,6,3,4,1,2] => 2
[9,8,7,6,5,3,4,1,2] => 2
[9,8,7,6,5,4,3,1,2] => 1
[9,8,7,6,5,4,3,2,1] => 1
[3,4,1,2,5,6,7,8,9] => 2
[3,2,1,4,5,6,7,8,9] => 1
[4,5,6,1,2,3,7,8,9] => 3
[4,2,5,1,3,6,7,8,9] => 3
[4,3,2,1,5,6,7,8,9] => 1
[5,6,7,8,1,2,3,4,9] => 4
[5,2,6,7,1,3,4,8,9] => 4
[5,6,3,4,1,2,7,8,9] => 2
[5,3,2,6,1,4,7,8,9] => 4
[5,4,3,2,1,6,7,8,9] => 1
[6,2,7,8,9,1,3,4,5] => 5
[6,4,3,2,7,1,5,8,9] => 5
[6,5,4,3,2,1,7,8,9] => 1
[7,4,3,2,8,9,1,5,6] => 6
[7,8,5,6,3,4,1,2,9] => 2
[7,5,3,8,2,6,1,4,9] => 4
[7,5,4,3,2,8,1,6,9] => 6
[7,6,5,4,3,2,1,8,9] => 1
[8,6,9,4,7,2,5,1,3] => 3
[8,6,4,3,9,2,7,1,5] => 5
[8,6,5,4,3,2,9,1,7] => 7
[2,1,4,3,6,5,10,9,8,7] => 1
[2,1,4,3,6,5,8,7,10,9] => 1
[2,1,4,3,8,7,6,5,10,9] => 1
[2,1,4,3,10,7,6,9,8,5] => 3
[2,1,4,3,10,9,8,7,6,5] => 1
[2,1,6,5,4,3,10,9,8,7] => 1
[2,1,6,5,4,3,8,7,10,9] => 1
[2,1,8,5,4,7,6,3,10,9] => 3
[2,1,8,7,6,5,4,3,10,9] => 1
[2,1,10,5,4,7,6,9,8,3] => 5
[2,1,10,5,4,9,8,7,6,3] => 3
[2,1,10,7,6,5,4,9,8,3] => 5
[2,1,10,9,8,7,6,5,4,3] => 1
[2,1,10,9,6,5,8,7,4,3] => 3
[4,3,2,1,6,5,10,9,8,7] => 1
[4,3,2,1,6,5,8,7,10,9] => 1
[4,3,2,1,8,7,6,5,10,9] => 1
[4,3,2,1,10,7,6,9,8,5] => 3
[4,3,2,1,10,9,8,7,6,5] => 1
[6,3,2,5,4,1,10,9,8,7] => 3
[6,3,2,5,4,1,8,7,10,9] => 3
[6,5,4,3,2,1,10,9,8,7] => 1
[6,5,4,3,2,1,8,7,10,9] => 1
[6,7,8,9,10,1,2,3,4,5] => 5
[7,3,2,8,9,10,1,4,5,6] => 6
[8,3,2,5,4,7,6,1,10,9] => 5
[8,3,2,7,6,5,4,1,10,9] => 3
[8,5,4,3,2,7,6,1,10,9] => 5
[8,5,4,3,2,9,10,1,6,7] => 7
[8,7,4,3,6,5,2,1,10,9] => 3
[8,7,6,5,4,3,2,1,10,9] => 1
[8,9,5,6,3,4,10,1,2,7] => 7
[9,7,5,10,3,8,2,6,1,4] => 4
[9,7,6,5,4,3,2,10,1,8] => 8
[10,3,2,5,4,7,6,9,8,1] => 7
[10,3,2,5,4,9,8,7,6,1] => 5
[10,3,2,7,6,5,4,9,8,1] => 7
[10,3,2,9,8,7,6,5,4,1] => 3
[10,3,2,9,6,5,8,7,4,1] => 5
[10,5,4,3,2,7,6,9,8,1] => 7
[10,5,4,3,2,9,8,7,6,1] => 5
[10,7,4,3,6,5,2,9,8,1] => 7
[10,7,6,5,4,3,2,9,8,1] => 7
[10,9,4,3,8,7,6,5,2,1] => 3
[10,9,4,3,6,5,8,7,2,1] => 5
[10,9,6,5,4,3,8,7,2,1] => 5
[10,9,8,5,4,7,6,3,2,1] => 3
[10,9,8,7,6,5,4,3,2,1] => 1
[2,4,6,8,10,1,3,5,7,9] => 5
[5,6,7,8,10,1,2,3,4,9] => 5
[4,7,8,9,10,1,2,3,5,6] => 5
[5,7,8,9,10,1,2,3,4,6] => 5
[4,5,6,8,10,1,2,3,7,9] => 5
[3,7,8,9,10,1,2,4,5,6] => 5
[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] => 5
[5,6,8,9,10,1,2,3,4,7] => 5
[4,6,8,9,10,1,2,3,5,7] => 5
[3,4,6,8,10,1,2,5,7,9] => 5
[2,7,8,9,10,1,3,4,5,6] => 5
[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] => 5
[2,4,8,9,10,1,3,5,6,7] => 5
[2,4,7,8,10,1,3,5,6,9] => 5
[2,4,6,9,10,1,3,5,7,8] => 5
[2,4,7,9,10,1,3,5,6,8] => 5
[2,5,7,8,10,1,3,4,6,9] => 5
[4,5,6,9,10,1,2,3,7,8] => 5
[5,6,7,9,10,1,2,3,4,8] => 5
[2,5,7,9,10,1,3,4,6,8] => 5
[3,5,6,8,10,1,2,4,7,9] => 5
[3,4,8,9,10,1,2,5,6,7] => 5
[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] => 5
[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] => 5
[10,8,9,5,6,7,1,2,3,4] => 3
[9,6,10,2,7,8,1,3,4,5] => 3
[10,7,8,3,4,9,1,2,5,6] => 5
[9,5,10,4,6,7,1,2,3,8] => 3
[8,4,9,3,5,10,1,2,6,7] => 6
[8,4,9,2,5,10,1,3,6,7] => 6
[10,8,9,4,5,6,1,2,3,7] => 3
[9,6,10,5,7,8,1,2,3,4] => 3
[10,7,8,5,6,9,1,2,3,4] => 5
[9,8,10,5,6,7,1,2,3,4] => 3
[8,7,9,5,6,10,1,2,3,4] => 6
[8,6,9,2,7,10,1,3,4,5] => 6
[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] => 3
[8,7,9,3,4,10,1,2,5,6] => 6
[8,6,9,5,7,10,1,2,3,4] => 6
[7,6,8,4,5,9,1,2,3,10] => 6
[7,5,8,2,6,9,1,3,4,10] => 6
[7,6,8,3,4,9,1,2,5,10] => 6
[7,5,8,4,6,9,1,2,3,10] => 6
[7,4,8,3,5,9,1,2,6,10] => 6
[7,4,8,2,5,9,1,3,6,10] => 6
[7,8,9,10,1,2,3,4,5,6] => 4
[9,10,7,8,5,6,3,4,1,2] => 2
[9,1,2,3,4,5,6,7,8,10] => 1
[1,2,3,4,5,6,7,8,9,10] => 0
[9,10,7,8,5,6,1,2,3,4] => 2
[9,10,5,6,7,8,1,2,3,4] => 4
[9,10,7,8,1,2,3,4,5,6] => 2
[9,10,1,2,3,4,5,6,7,8] => 2
[10,1,2,3,4,5,6,7,8,9] => 1
[9,8,7,6,5,4,3,2,1,10] => 1
[1,10,9,8,7,6,5,4,3,2] => 1
[1,10,2,3,4,5,6,7,8,9] => 1
[9,7,10,5,6,8,1,2,3,4] => 3
[10,7,8,4,5,9,1,2,3,6] => 5
[9,7,10,4,5,8,1,2,3,6] => 3
[8,7,9,4,5,10,1,2,3,6] => 6
[9,6,10,4,5,7,1,2,3,8] => 3
[8,6,9,4,5,10,1,2,3,7] => 6
[8,6,9,4,7,10,1,2,3,5] => 6
[9,6,10,3,4,7,1,2,5,8] => 3
[8,5,9,3,6,10,1,2,4,7] => 6
[9,5,10,3,6,7,1,2,4,8] => 3
[8,6,9,3,4,10,1,2,5,7] => 6
[8,6,9,3,7,10,1,2,4,5] => 6
[9,6,10,3,7,8,1,2,4,5] => 3
[9,7,10,3,4,8,1,2,5,6] => 3
[8,5,9,4,6,10,1,2,3,7] => 6
[9,6,10,4,7,8,1,2,3,5] => 3
[10,8,9,1,2,3,4,5,6,7] => 2
[9,8,7,5,6,4,3,2,1,10] => 2
[1,10,9,8,6,7,5,4,3,2] => 2
[2,3,4,5,6,7,8,9,10,1] => 9
[2,3,4,5,6,7,8,9,1,10] => 8
[10,2,1,3,4,5,6,7,8,9] => 1
[3,2,4,5,6,7,8,9,10,1] => 9
[8,9,7,6,5,4,3,2,1,10] => 2
[1,9,10,8,7,6,5,4,3,2] => 2
[8,9,1,2,3,4,5,6,7,10] => 2
[1,9,10,2,3,4,5,6,7,8] => 2
[1,2,3,4,5,6,7,8,10,9] => 1
[2,1,3,4,5,6,7,8,9,10] => 1
[9,1,2,3,4,5,6,7,10,8] => 2
[2,10,1,3,4,5,6,7,8,9] => 2
[10,9,1,2,3,4,5,6,7,8] => 1
[8,9,10,1,2,3,4,5,6,7] => 3
[10,9,8,1,2,3,4,5,6,7] => 1
[10,7,8,9,1,2,3,4,5,6] => 3
[10,9,7,8,1,2,3,4,5,6] => 2
[10,9,8,7,1,2,3,4,5,6] => 1
[10,6,7,8,9,1,2,3,4,5] => 4
[9,10,6,7,8,1,2,3,4,5] => 3
[10,9,6,7,8,1,2,3,4,5] => 3
[10,8,9,6,7,1,2,3,4,5] => 2
[10,9,8,6,7,1,2,3,4,5] => 2
[10,9,8,7,6,1,2,3,4,5] => 1
[10,9,5,6,7,8,1,2,3,4] => 4
[8,9,10,5,6,7,1,2,3,4] => 3
[10,9,8,5,6,7,1,2,3,4] => 3
[10,9,7,8,5,6,1,2,3,4] => 2
[10,9,8,7,5,6,1,2,3,4] => 2
[10,9,8,7,6,5,1,2,3,4] => 1
[10,7,8,9,4,5,6,1,2,3] => 3
[9,10,7,8,4,5,6,1,2,3] => 3
[10,9,7,8,4,5,6,1,2,3] => 3
[10,9,8,7,4,5,6,1,2,3] => 3
[10,8,9,6,7,4,5,1,2,3] => 2
[10,9,8,6,7,4,5,1,2,3] => 2
[10,9,8,7,6,4,5,1,2,3] => 2
[10,9,8,7,6,5,4,1,2,3] => 1
[10,9,7,8,5,6,3,4,1,2] => 2
[10,9,8,7,5,6,3,4,1,2] => 2
[10,9,8,7,6,5,3,4,1,2] => 2
[10,9,8,7,6,5,4,3,1,2] => 1
[3,4,1,2,5,6,7,8,9,10] => 2
[3,2,1,4,5,6,7,8,9,10] => 1
[4,5,6,1,2,3,7,8,9,10] => 3
[4,2,5,1,3,6,7,8,9,10] => 3
[4,3,2,1,5,6,7,8,9,10] => 1
[5,6,7,8,1,2,3,4,9,10] => 4
[5,2,6,7,1,3,4,8,9,10] => 4
[5,6,3,4,1,2,7,8,9,10] => 2
[5,3,2,6,1,4,7,8,9,10] => 4
[5,4,3,2,1,6,7,8,9,10] => 1
[6,2,7,8,9,1,3,4,5,10] => 5
[6,7,3,4,8,1,2,5,9,10] => 5
[6,3,2,7,8,1,4,5,9,10] => 5
[6,4,7,2,5,1,3,8,9,10] => 3
[6,4,3,2,7,1,5,8,9,10] => 5
[6,5,4,3,2,1,7,8,9,10] => 1
[7,8,3,4,9,10,1,2,5,6] => 6
[7,8,9,4,5,6,1,2,3,10] => 3
[7,4,3,2,8,9,1,5,6,10] => 6
[7,8,5,6,3,4,1,2,9,10] => 2
[7,5,3,8,2,6,1,4,9,10] => 4
[7,5,4,3,2,8,1,6,9,10] => 6
[7,6,5,4,3,2,1,8,9,10] => 1
[8,5,9,10,2,6,7,1,3,4] => 4
[8,5,3,9,2,6,10,1,4,7] => 7
[8,6,9,4,7,2,5,1,3,10] => 3
[8,6,4,3,9,2,7,1,5,10] => 5
[8,6,5,4,3,2,9,1,7,10] => 7
[8,7,6,5,4,3,2,1,9,10] => 1
[9,7,5,4,3,10,2,8,1,6] => 6
[7,5,8,3,6,9,1,2,4,10] => 6
[8,5,9,2,6,10,1,3,4,7] => 6
[10,9,8,7,6,5,4,3,2,1,11] => 1
[1,11,10,9,8,7,6,5,4,3,2] => 1
[11,1,2,3,4,5,6,7,8,9,10] => 1
[2,3,4,5,6,7,8,9,10,11,1] => 10
[10,1,2,3,4,5,6,7,8,9,11] => 1
[1,11,2,3,4,5,6,7,8,9,10] => 1
[1,2,3,4,5,6,7,8,9,11,10] => 1
[2,1,3,4,5,6,7,8,9,10,11] => 1
[6,7,8,9,10,12,1,2,3,4,5,11] => 6
[2,8,9,10,11,12,1,3,4,5,6,7] => 6
[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] => 6
[5,7,8,9,10,12,1,2,3,4,6,11] => 6
[2,6,9,10,11,12,1,3,4,5,7,8] => 6
[2,7,8,10,11,12,1,3,4,5,6,9] => 6
[4,7,8,9,10,12,1,2,3,5,6,11] => 6
[5,6,8,9,10,12,1,2,3,4,7,11] => 6
[2,5,9,10,11,12,1,3,4,6,7,8] => 6
[2,6,8,10,11,12,1,3,4,5,7,9] => 6
[2,7,8,9,11,12,1,3,4,5,6,10] => 6
[3,4,9,10,11,12,1,2,5,6,7,8] => 6
[3,7,8,9,10,12,1,2,4,5,6,11] => 6
[4,6,8,9,10,12,1,2,3,5,7,11] => 6
[5,6,7,8,11,12,1,2,3,4,9,10] => 6
[5,6,7,9,10,12,1,2,3,4,8,11] => 6
[2,4,9,10,11,12,1,3,5,6,7,8] => 6
[2,5,8,10,11,12,1,3,4,6,7,9] => 6
[2,6,7,10,11,12,1,3,4,5,8,9] => 6
[2,6,8,9,11,12,1,3,4,5,7,10] => 6
[2,7,8,9,10,12,1,3,4,5,6,11] => 6
[3,4,8,10,11,12,1,2,5,6,7,9] => 6
[3,6,8,9,10,12,1,2,4,5,7,11] => 6
[4,5,6,10,11,12,1,2,3,7,8,9] => 6
[4,5,8,9,10,12,1,2,3,6,7,11] => 6
[4,6,7,8,11,12,1,2,3,5,9,10] => 6
[4,6,7,9,10,12,1,2,3,5,8,11] => 6
[5,6,7,8,10,12,1,2,3,4,9,11] => 6
[2,4,8,10,11,12,1,3,5,6,7,9] => 6
[2,5,7,10,11,12,1,3,4,6,8,9] => 6
[2,5,8,9,11,12,1,3,4,6,7,10] => 6
[2,6,7,9,11,12,1,3,4,5,8,10] => 6
[2,6,8,9,10,12,1,3,4,5,7,11] => 6
[3,4,7,10,11,12,1,2,5,6,8,9] => 6
[3,4,8,9,11,12,1,2,5,6,7,10] => 6
[3,5,6,10,11,12,1,2,4,7,8,9] => 6
[3,5,8,9,10,12,1,2,4,6,7,11] => 6
[3,6,7,8,11,12,1,2,4,5,9,10] => 6
[3,6,7,9,10,12,1,2,4,5,8,11] => 6
[4,5,6,9,11,12,1,2,3,7,8,10] => 6
[4,5,7,8,11,12,1,2,3,6,9,10] => 6
[4,5,7,9,10,12,1,2,3,6,8,11] => 6
[4,6,7,8,10,12,1,2,3,5,9,11] => 6
[2,1,12,11,10,7,6,9,8,5,4,3] => 3
[10,9,8,5,4,7,6,3,2,1,12,11] => 3
[2,1,12,11,6,5,10,9,8,7,4,3] => 3
[2,1,12,11,8,7,6,5,10,9,4,3] => 5
[10,9,4,3,8,7,6,5,2,1,12,11] => 3
[10,9,6,5,4,3,8,7,2,1,12,11] => 5
[2,1,12,5,4,11,10,9,8,7,6,3] => 3
[2,1,12,11,6,5,8,7,10,9,4,3] => 5
[2,1,12,9,8,7,6,5,4,11,10,3] => 7
[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] => 3
[10,9,4,3,6,5,8,7,2,1,12,11] => 5
[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] => 7
[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] => 5
[2,1,12,7,6,5,4,11,10,9,8,3] => 5
[2,1,12,9,6,5,8,7,4,11,10,3] => 7
[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] => 3
[10,3,2,9,6,5,8,7,4,1,12,11] => 5
[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] => 5
[8,7,4,3,6,5,2,1,12,11,10,9] => 3
[10,7,4,3,6,5,2,9,8,1,12,11] => 7
[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] => 3
[2,1,12,5,4,7,6,11,10,9,8,3] => 5
[2,1,12,5,4,9,8,7,6,11,10,3] => 7
[2,1,12,7,6,5,4,9,8,11,10,3] => 7
[2,1,10,9,6,5,8,7,4,3,12,11] => 3
[4,3,2,1,12,7,6,11,10,9,8,5] => 3
[4,3,2,1,12,9,8,7,6,11,10,5] => 5
[6,3,2,5,4,1,12,11,10,9,8,7] => 3
[10,3,2,5,4,9,8,7,6,1,12,11] => 5
[8,3,2,7,6,5,4,1,12,11,10,9] => 3
[10,3,2,7,6,5,4,9,8,1,12,11] => 7
[6,5,4,3,2,1,12,9,8,11,10,7] => 3
[8,5,4,3,2,7,6,1,12,11,10,9] => 5
[10,5,4,3,2,7,6,9,8,1,12,11] => 7
[8,7,4,3,6,5,2,1,10,9,12,11] => 3
[2,4,6,9,11,12,1,3,5,7,8,10] => 6
[2,4,6,8,11,12,1,3,5,7,9,10] => 6
[3,4,6,9,11,12,1,2,5,7,8,10] => 6
[3,4,6,8,11,12,1,2,5,7,9,10] => 6
[3,5,6,9,11,12,1,2,4,7,8,10] => 6
[2,5,6,9,11,12,1,3,4,7,8,10] => 6
[3,5,6,8,11,12,1,2,4,7,9,10] => 6
[2,5,6,8,11,12,1,3,4,7,9,10] => 6
[2,4,8,9,11,12,1,3,5,6,7,10] => 6
[2,5,7,9,11,12,1,3,4,6,8,10] => 6
[2,5,7,8,11,12,1,3,4,6,9,10] => 6
[4,5,6,8,11,12,1,2,3,7,9,10] => 6
[2,4,7,9,11,12,1,3,5,6,8,10] => 6
[2,4,7,8,11,12,1,3,5,6,9,10] => 6
[4,5,8,9,11,12,1,2,3,6,7,10] => 6
[3,5,8,9,11,12,1,2,4,6,7,10] => 6
[2,4,7,10,11,12,1,3,5,6,8,9] => 6
[4,5,7,9,11,12,1,2,3,6,8,10] => 6
[3,5,7,9,11,12,1,2,4,6,8,10] => 6
[3,5,7,8,11,12,1,2,4,6,9,10] => 6
[3,4,7,9,11,12,1,2,5,6,8,10] => 6
[3,4,7,8,11,12,1,2,5,6,9,10] => 6
[2,4,6,10,11,12,1,3,5,7,8,9] => 6
[4,7,8,9,11,12,1,2,3,5,6,10] => 6
[3,7,8,9,11,12,1,2,4,5,6,10] => 6
[4,6,8,9,11,12,1,2,3,5,7,10] => 6
[3,6,8,9,11,12,1,2,4,5,7,10] => 6
[4,6,7,9,11,12,1,2,3,5,8,10] => 6
[3,6,7,9,11,12,1,2,4,5,8,10] => 6
[2,6,7,8,11,12,1,3,4,5,9,10] => 6
[3,4,6,10,11,12,1,2,5,7,8,9] => 6
[4,5,6,8,10,12,1,2,3,7,9,11] => 6
[3,6,7,8,10,12,1,2,4,5,9,11] => 6
[2,6,7,8,10,12,1,3,4,5,9,11] => 6
[3,4,8,9,10,12,1,2,5,6,7,11] => 6
[2,4,8,9,10,12,1,3,5,6,7,11] => 6
[4,6,8,10,11,12,1,2,3,5,7,9] => 6
[4,6,7,10,11,12,1,2,3,5,8,9] => 6
[4,5,7,10,11,12,1,2,3,6,8,9] => 6
[3,5,7,10,11,12,1,2,4,6,8,9] => 6
[2,5,8,9,10,12,1,3,4,6,7,11] => 6
[5,6,8,10,11,12,1,2,3,4,7,9] => 6
[4,5,8,10,11,12,1,2,3,6,7,9] => 6
[5,6,8,9,11,12,1,2,3,4,7,10] => 6
[3,6,7,10,11,12,1,2,4,5,8,9] => 6
[5,6,7,9,11,12,1,2,3,4,8,10] => 6
[2,5,6,10,11,12,1,3,4,7,8,9] => 6
[4,5,6,9,10,12,1,2,3,7,8,11] => 6
[2,5,6,9,10,12,1,3,4,7,8,11] => 6
[3,4,6,8,10,12,1,2,5,7,9,11] => 6
[3,4,6,9,10,12,1,2,5,7,8,11] => 6
[3,5,8,10,11,12,1,2,4,6,7,9] => 6
[3,4,7,8,10,12,1,2,5,6,9,11] => 6
[3,5,6,8,10,12,1,2,4,7,9,11] => 6
[3,5,9,10,11,12,1,2,4,6,7,8] => 6
[3,5,7,9,10,12,1,2,4,6,8,11] => 6
[3,6,8,10,11,12,1,2,4,5,7,9] => 6
[3,4,7,9,10,12,1,2,5,6,8,11] => 6
[3,5,7,8,10,12,1,2,4,6,9,11] => 6
[3,6,9,10,11,12,1,2,4,5,7,8] => 6
[3,5,6,9,10,12,1,2,4,7,8,11] => 6
[3,7,8,10,11,12,1,2,4,5,6,9] => 6
[3,7,9,10,11,12,1,2,4,5,6,8] => 6
[4,6,9,10,11,12,1,2,3,5,7,8] => 6
[2,5,7,8,10,12,1,3,4,6,9,11] => 6
[2,4,7,9,10,12,1,3,5,6,8,11] => 6
[2,5,6,8,10,12,1,3,4,7,9,11] => 6
[2,4,7,8,10,12,1,3,5,6,9,11] => 6
[2,4,6,9,10,12,1,3,5,7,8,11] => 6
[2,4,6,8,10,12,1,3,5,7,9,11] => 6
[6,7,8,9,11,12,1,2,3,4,5,10] => 6
[5,7,8,9,11,12,1,2,3,4,6,10] => 6
[5,6,7,10,11,12,1,2,3,4,8,9] => 6
[6,7,8,10,11,12,1,2,3,4,5,9] => 6
[5,7,8,10,11,12,1,2,3,4,6,9] => 6
[4,5,7,8,10,12,1,2,3,6,9,11] => 6
[2,6,7,9,10,12,1,3,4,5,8,11] => 6
[6,7,9,10,11,12,1,2,3,4,5,8] => 6
[6,8,9,10,11,12,1,2,3,4,5,7] => 6
[4,7,8,10,11,12,1,2,3,5,6,9] => 6
[5,6,9,10,11,12,1,2,3,4,7,8] => 6
[4,7,9,10,11,12,1,2,3,5,6,8] => 6
[5,7,9,10,11,12,1,2,3,4,6,8] => 6
[4,8,9,10,11,12,1,2,3,5,6,7] => 6
[7,8,9,10,11,12,1,2,3,4,5,6] => 6
[5,8,9,10,11,12,1,2,3,4,6,7] => 6
[3,8,9,10,11,12,1,2,4,5,6,7] => 6
[4,5,9,10,11,12,1,2,3,6,7,8] => 6
[2,1,4,3,6,5,12,9,8,11,10,7] => 3
[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] => 3
[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] => 3
[2,1,6,5,4,3,12,9,8,11,10,7] => 3
[6,3,2,5,4,1,8,7,12,11,10,9] => 3
[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] => 5
[2,1,12,5,4,7,6,9,8,11,10,3] => 7
[2,1,8,5,4,7,6,3,12,11,10,9] => 3
[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] => 5
[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] => 9
[12,3,2,5,4,9,8,7,6,11,10,1] => 9
[2,1,4,3,12,7,6,11,10,9,8,5] => 3
[12,5,4,3,2,7,6,9,8,11,10,1] => 9
[12,3,2,5,4,7,6,9,8,11,10,1] => 9
[8,3,2,5,4,7,6,1,12,11,10,9] => 5
[4,3,2,1,12,7,6,9,8,11,10,5] => 5
[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] => 9
[12,3,2,9,8,7,6,5,4,11,10,1] => 9
[12,9,4,3,6,5,8,7,2,11,10,1] => 9
[12,3,2,9,6,5,8,7,4,11,10,1] => 9
[12,7,4,3,6,5,2,9,8,11,10,1] => 9
[12,3,2,7,6,5,4,9,8,11,10,1] => 9
[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] => 3
[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] => 7
[12,7,4,3,6,5,2,11,10,9,8,1] => 7
[12,5,4,3,2,7,6,11,10,9,8,1] => 7
[12,3,2,5,4,7,6,11,10,9,8,1] => 7
[2,1,10,5,4,9,8,7,6,3,12,11] => 3
[12,11,6,5,4,3,8,7,10,9,2,1] => 7
[12,5,4,3,2,11,8,7,10,9,6,1] => 7
[12,9,6,5,4,3,8,7,2,11,10,1] => 9
[12,3,2,7,6,5,4,11,10,9,8,1] => 7
[12,7,6,5,4,3,2,9,8,11,10,1] => 9
[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] => 7
[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] => 3
[12,3,2,5,4,11,10,9,8,7,6,1] => 5
[10,3,2,5,4,7,6,9,8,1,12,11] => 7
[12,3,2,11,6,5,8,7,10,9,4,1] => 7
[4,3,2,1,10,7,6,9,8,5,12,11] => 3
[8,3,2,5,4,7,6,1,10,9,12,11] => 5
[12,3,2,11,6,5,10,9,8,7,4,1] => 5
[6,3,2,5,4,1,10,9,8,7,12,11] => 3
[12,3,2,11,8,7,6,5,10,9,4,1] => 7
[12,3,2,11,10,7,6,9,8,5,4,1] => 5
[12,11,4,3,6,5,10,9,8,7,2,1] => 5
[2,1,8,5,4,7,6,3,10,9,12,11] => 3
[2,1,4,3,10,7,6,9,8,5,12,11] => 3
[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] => 9
[12,9,8,5,4,7,6,3,2,11,10,1] => 9
[12,7,6,5,4,3,2,11,10,9,8,1] => 7
[12,11,8,7,6,5,4,3,10,9,2,1] => 7
[12,11,8,5,4,7,6,3,10,9,2,1] => 7
[8,5,4,3,2,7,6,1,10,9,12,11] => 5
[2,1,10,7,6,5,4,9,8,3,12,11] => 5
[12,11,10,7,6,5,4,9,8,3,2,1] => 5
[12,11,10,9,6,5,8,7,4,3,2,1] => 3
[12,11,4,3,8,7,6,5,10,9,2,1] => 7
[12,11,6,5,4,3,10,9,8,7,2,1] => 5
[12,11,4,3,10,7,6,9,8,5,2,1] => 5
[12,11,10,5,4,7,6,9,8,3,2,1] => 5
[12,11,4,3,10,9,8,7,6,5,2,1] => 3
[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] => 3
[12,3,2,11,10,9,8,7,6,5,4,1] => 3
[12,5,4,3,2,11,10,9,8,7,6,1] => 5
[2,1,10,5,4,7,6,9,8,3,12,11] => 5
[2,5,7,9,10,12,1,3,4,6,8,11] => 6
click to show generating function       
Description
The number of stack-sorts needed to sort a permutation.
A permutation is (West) $t$-stack sortable if it is sortable using $t$ stacks in series.
Let $W_t(n,k)$ be the number of permutations of size $n$
with $k$ descents which are $t$-stack sortable. Then the polynomials $W_{n,t}(x) = \sum_{k=0}^n W_t(n,k)x^k$
are symmetric and unimodal.
We have $W_{n,1}(x) = A_n(x)$, the Eulerian polynomials. One can show that $W_{n,1}(x)$ and $W_{n,2}(x)$ are real-rooted.
Precisely the permutations that avoid the pattern $231$ have statistic at most $1$, see [3]. These are counted by $\frac{1}{n+1}\binom{2n}{n}$ (OEIS:A000108). Precisely the permutations that avoid the pattern $2341$ and the barred pattern $3\bar 5241$ have statistic at most $2$, see [4]. These are counted by $\frac{2(3n)!}{(n+1)!(2n+1)!}$ (OEIS:A000139).
References
[1] Bóna, Miklós A survey of stack-sorting disciplines MathSciNet:2028290
[2] Úlfarsson, H. Describing West-3-stack-sortable permutations with permutation patterns arXiv:1110.1219
[3] Knuth, D. E. The art of computer programming. Volume 3 MathSciNet:0445948
[4] Zeilberger, D. A proof of Julian West's conjecture that the number of two-stack-sortable permutations of length $n$ is $2(3n)!/((n+1)!(2n+1)!)$ MathSciNet:1168135
Code
def stack_sort(x):
    stack = []
    result = []
    for e in x:
        while stack and e > stack[-1]:
            result += [stack.pop()]
        stack.append(e)
    while stack:
        result += [stack.pop()]
    return Permutation(result)

def statistic(x):
    i = 0
    id = Permutations(x.size()).identity()
    while x != id:
        x = stack_sort(x)
        i += 1
    return i

Created
Aug 05, 2012 at 10:27 by Per Alexandersson
Updated
Jan 17, 2018 at 08:56 by Martin Rubey