Identifier
Identifier
Values
[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] => 2
[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] => 2
[1,4,3,2] => 1
[2,1,3,4] => 1
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 2
[2,4,1,3] => 3
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 3
[3,2,1,4] => 1
[3,2,4,1] => 2
[3,4,1,2] => 2
[3,4,2,1] => 2
[4,1,2,3] => 2
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 2
[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] => 2
[1,2,5,4,3] => 1
[1,3,2,4,5] => 1
[1,3,2,5,4] => 2
[1,3,4,2,5] => 2
[1,3,4,5,2] => 2
[1,3,5,2,4] => 3
[1,3,5,4,2] => 2
[1,4,2,3,5] => 2
[1,4,2,5,3] => 3
[1,4,3,2,5] => 1
[1,4,3,5,2] => 2
[1,4,5,2,3] => 2
[1,4,5,3,2] => 2
[1,5,2,3,4] => 2
[1,5,2,4,3] => 2
[1,5,3,2,4] => 2
[1,5,3,4,2] => 2
[1,5,4,2,3] => 2
[1,5,4,3,2] => 1
[2,1,3,4,5] => 1
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 3
[2,1,5,3,4] => 3
[2,1,5,4,3] => 2
[2,3,1,4,5] => 2
[2,3,1,5,4] => 3
[2,3,4,1,5] => 2
[2,3,4,5,1] => 2
[2,3,5,1,4] => 3
[2,3,5,4,1] => 3
[2,4,1,3,5] => 3
[2,4,1,5,3] => 4
[2,4,3,1,5] => 2
[2,4,3,5,1] => 3
[2,4,5,1,3] => 3
[2,4,5,3,1] => 3
[2,5,1,3,4] => 3
[2,5,1,4,3] => 3
[2,5,3,1,4] => 3
[2,5,3,4,1] => 3
[2,5,4,1,3] => 3
[2,5,4,3,1] => 2
[3,1,2,4,5] => 2
[3,1,2,5,4] => 3
[3,1,4,2,5] => 3
[3,1,4,5,2] => 3
[3,1,5,2,4] => 4
[3,1,5,4,2] => 3
[3,2,1,4,5] => 1
[3,2,1,5,4] => 2
[3,2,4,1,5] => 2
[3,2,4,5,1] => 3
[3,2,5,1,4] => 3
[3,2,5,4,1] => 2
[3,4,1,2,5] => 2
[3,4,1,5,2] => 3
[3,4,2,1,5] => 2
[3,4,2,5,1] => 3
[3,4,5,1,2] => 2
[3,4,5,2,1] => 2
[3,5,1,2,4] => 3
[3,5,1,4,2] => 3
[3,5,2,1,4] => 3
[3,5,2,4,1] => 3
[3,5,4,1,2] => 2
[3,5,4,2,1] => 3
[4,1,2,3,5] => 2
[4,1,2,5,3] => 3
[4,1,3,2,5] => 2
[4,1,3,5,2] => 3
[4,1,5,2,3] => 3
[4,1,5,3,2] => 3
[4,2,1,3,5] => 2
[4,2,1,5,3] => 3
[4,2,3,1,5] => 2
[4,2,3,5,1] => 3
[4,2,5,1,3] => 3
[4,2,5,3,1] => 3
[4,3,1,2,5] => 2
[4,3,1,5,2] => 3
[4,3,2,1,5] => 1
[4,3,2,5,1] => 2
[4,3,5,1,2] => 2
[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] => 3
[4,5,3,1,2] => 3
[4,5,3,2,1] => 2
[5,1,2,3,4] => 2
[5,1,2,4,3] => 3
[5,1,3,2,4] => 3
[5,1,3,4,2] => 3
[5,1,4,2,3] => 3
[5,1,4,3,2] => 2
[5,2,1,3,4] => 3
[5,2,1,4,3] => 2
[5,2,3,1,4] => 3
[5,2,3,4,1] => 2
[5,2,4,1,3] => 3
[5,2,4,3,1] => 3
[5,3,1,2,4] => 3
[5,3,1,4,2] => 3
[5,3,2,1,4] => 2
[5,3,2,4,1] => 3
[5,3,4,1,2] => 3
[5,3,4,2,1] => 2
[5,4,1,2,3] => 2
[5,4,1,3,2] => 3
[5,4,2,1,3] => 3
[5,4,2,3,1] => 2
[5,4,3,1,2] => 2
[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] => 2
[1,2,3,6,5,4] => 1
[1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => 2
[1,2,4,5,6,3] => 2
[1,2,4,6,3,5] => 3
[1,2,4,6,5,3] => 2
[1,2,5,3,4,6] => 2
[1,2,5,3,6,4] => 3
[1,2,5,4,3,6] => 1
[1,2,5,4,6,3] => 2
[1,2,5,6,3,4] => 2
[1,2,5,6,4,3] => 2
[1,2,6,3,4,5] => 2
[1,2,6,3,5,4] => 2
[1,2,6,4,3,5] => 2
[1,2,6,4,5,3] => 2
[1,2,6,5,3,4] => 2
[1,2,6,5,4,3] => 1
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 3
[1,3,2,6,4,5] => 3
[1,3,2,6,5,4] => 2
[1,3,4,2,5,6] => 2
[1,3,4,2,6,5] => 3
[1,3,4,5,2,6] => 2
[1,3,4,5,6,2] => 2
[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] => 4
[1,3,5,4,2,6] => 2
[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] => 2
[1,4,2,3,5,6] => 2
[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] => 4
[1,4,2,6,5,3] => 3
[1,4,3,2,5,6] => 1
[1,4,3,2,6,5] => 2
[1,4,3,5,2,6] => 2
[1,4,3,5,6,2] => 3
[1,4,3,6,2,5] => 3
[1,4,3,6,5,2] => 2
[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] => 3
[1,4,5,6,2,3] => 2
[1,4,5,6,3,2] => 2
[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] => 2
[1,4,6,5,3,2] => 3
[1,5,2,3,4,6] => 2
[1,5,2,3,6,4] => 3
[1,5,2,4,3,6] => 2
[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] => 2
[1,5,3,2,6,4] => 3
[1,5,3,4,2,6] => 2
[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] => 2
[1,5,4,2,6,3] => 3
[1,5,4,3,2,6] => 1
[1,5,4,3,6,2] => 2
[1,5,4,6,2,3] => 2
[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] => 3
[1,5,6,4,2,3] => 3
[1,5,6,4,3,2] => 2
[1,6,2,3,4,5] => 2
[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] => 2
[1,6,3,2,4,5] => 3
[1,6,3,2,5,4] => 2
[1,6,3,4,2,5] => 3
[1,6,3,4,5,2] => 2
[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] => 2
[1,6,4,3,5,2] => 3
[1,6,4,5,2,3] => 3
[1,6,4,5,3,2] => 2
[1,6,5,2,3,4] => 2
[1,6,5,2,4,3] => 3
[1,6,5,3,2,4] => 3
[1,6,5,3,4,2] => 2
[1,6,5,4,2,3] => 2
[1,6,5,4,3,2] => 1
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => 3
[2,1,3,6,4,5] => 3
[2,1,3,6,5,4] => 2
[2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => 3
[2,1,4,5,6,3] => 3
[2,1,4,6,3,5] => 4
[2,1,4,6,5,3] => 3
[2,1,5,3,4,6] => 3
[2,1,5,3,6,4] => 4
[2,1,5,4,3,6] => 2
[2,1,5,4,6,3] => 3
[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] => 3
[2,1,6,4,3,5] => 3
[2,1,6,4,5,3] => 3
[2,1,6,5,3,4] => 3
[2,1,6,5,4,3] => 2
[2,3,1,4,5,6] => 2
[2,3,1,4,6,5] => 3
[2,3,1,5,4,6] => 3
[2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => 4
[2,3,1,6,5,4] => 3
[2,3,4,1,5,6] => 2
[2,3,4,1,6,5] => 3
[2,3,4,5,1,6] => 2
[2,3,4,5,6,1] => 2
[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] => 4
[2,3,5,4,1,6] => 3
[2,3,5,4,6,1] => 3
[2,3,5,6,1,4] => 4
[2,3,5,6,4,1] => 4
[2,3,6,1,4,5] => 4
[2,3,6,1,5,4] => 3
[2,3,6,4,1,5] => 4
[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] => 3
[2,4,1,3,6,5] => 4
[2,4,1,5,3,6] => 4
[2,4,1,5,6,3] => 4
[2,4,1,6,3,5] => 5
[2,4,1,6,5,3] => 4
[2,4,3,1,5,6] => 2
[2,4,3,1,6,5] => 3
[2,4,3,5,1,6] => 3
[2,4,3,5,6,1] => 3
[2,4,3,6,1,5] => 4
[2,4,3,6,5,1] => 3
[2,4,5,1,3,6] => 3
[2,4,5,1,6,3] => 4
[2,4,5,3,1,6] => 3
[2,4,5,3,6,1] => 4
[2,4,5,6,1,3] => 3
[2,4,5,6,3,1] => 3
[2,4,6,1,3,5] => 4
[2,4,6,1,5,3] => 4
[2,4,6,3,1,5] => 4
[2,4,6,3,5,1] => 4
[2,4,6,5,1,3] => 3
[2,4,6,5,3,1] => 4
[2,5,1,3,4,6] => 3
[2,5,1,3,6,4] => 4
[2,5,1,4,3,6] => 3
[2,5,1,4,6,3] => 4
[2,5,1,6,3,4] => 4
[2,5,1,6,4,3] => 4
[2,5,3,1,4,6] => 3
[2,5,3,1,6,4] => 4
[2,5,3,4,1,6] => 3
[2,5,3,4,6,1] => 4
[2,5,3,6,1,4] => 4
[2,5,3,6,4,1] => 4
[2,5,4,1,3,6] => 3
[2,5,4,1,6,3] => 4
[2,5,4,3,1,6] => 2
[2,5,4,3,6,1] => 3
[2,5,4,6,1,3] => 3
[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] => 3
[2,6,1,3,5,4] => 4
[2,6,1,4,3,5] => 4
[2,6,1,4,5,3] => 4
[2,6,1,5,3,4] => 4
[2,6,1,5,4,3] => 3
[2,6,3,1,4,5] => 4
[2,6,3,1,5,4] => 3
[2,6,3,4,1,5] => 4
[2,6,3,4,5,1] => 3
[2,6,3,5,1,4] => 4
[2,6,3,5,4,1] => 4
[2,6,4,1,3,5] => 4
[2,6,4,1,5,3] => 4
[2,6,4,3,1,5] => 3
[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] => 3
[2,6,5,1,4,3] => 3
[2,6,5,3,1,4] => 4
[2,6,5,3,4,1] => 3
[2,6,5,4,1,3] => 3
[2,6,5,4,3,1] => 2
[3,1,2,4,5,6] => 2
[3,1,2,4,6,5] => 3
[3,1,2,5,4,6] => 3
[3,1,2,5,6,4] => 4
[3,1,2,6,4,5] => 4
[3,1,2,6,5,4] => 3
[3,1,4,2,5,6] => 3
[3,1,4,2,6,5] => 4
[3,1,4,5,2,6] => 3
[3,1,4,5,6,2] => 3
[3,1,4,6,2,5] => 4
[3,1,4,6,5,2] => 4
[3,1,5,2,4,6] => 4
[3,1,5,2,6,4] => 5
[3,1,5,4,2,6] => 3
[3,1,5,4,6,2] => 4
[3,1,5,6,2,4] => 4
[3,1,5,6,4,2] => 4
[3,1,6,2,4,5] => 4
[3,1,6,2,5,4] => 4
[3,1,6,4,2,5] => 4
[3,1,6,4,5,2] => 4
[3,1,6,5,2,4] => 4
[3,1,6,5,4,2] => 3
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 2
[3,2,1,5,4,6] => 2
[3,2,1,5,6,4] => 3
[3,2,1,6,4,5] => 3
[3,2,1,6,5,4] => 2
[3,2,4,1,5,6] => 2
[3,2,4,1,6,5] => 3
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 3
[3,2,4,6,1,5] => 4
[3,2,4,6,5,1] => 3
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 4
[3,2,5,4,1,6] => 2
[3,2,5,4,6,1] => 3
[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] => 3
[3,2,6,4,1,5] => 3
[3,2,6,4,5,1] => 3
[3,2,6,5,1,4] => 3
[3,2,6,5,4,1] => 2
[3,4,1,2,5,6] => 2
[3,4,1,2,6,5] => 3
[3,4,1,5,2,6] => 3
[3,4,1,5,6,2] => 4
[3,4,1,6,2,5] => 4
[3,4,1,6,5,2] => 3
[3,4,2,1,5,6] => 2
[3,4,2,1,6,5] => 3
[3,4,2,5,1,6] => 3
[3,4,2,5,6,1] => 4
[3,4,2,6,1,5] => 4
[3,4,2,6,5,1] => 3
[3,4,5,1,2,6] => 2
[3,4,5,1,6,2] => 3
[3,4,5,2,1,6] => 2
[3,4,5,2,6,1] => 3
[3,4,5,6,1,2] => 2
[3,4,5,6,2,1] => 2
[3,4,6,1,2,5] => 3
[3,4,6,1,5,2] => 4
[3,4,6,2,1,5] => 3
[3,4,6,2,5,1] => 4
[3,4,6,5,1,2] => 3
[3,4,6,5,2,1] => 3
[3,5,1,2,4,6] => 3
[3,5,1,2,6,4] => 4
[3,5,1,4,2,6] => 3
[3,5,1,4,6,2] => 4
[3,5,1,6,2,4] => 4
[3,5,1,6,4,2] => 4
[3,5,2,1,4,6] => 3
[3,5,2,1,6,4] => 4
[3,5,2,4,1,6] => 3
[3,5,2,4,6,1] => 4
[3,5,2,6,1,4] => 4
[3,5,2,6,4,1] => 4
[3,5,4,1,2,6] => 2
[3,5,4,1,6,2] => 3
[3,5,4,2,1,6] => 3
[3,5,4,2,6,1] => 4
[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] => 4
[3,6,1,2,5,4] => 3
[3,6,1,4,2,5] => 4
[3,6,1,4,5,2] => 3
[3,6,1,5,2,4] => 4
[3,6,1,5,4,2] => 4
[3,6,2,1,4,5] => 3
[3,6,2,1,5,4] => 3
[3,6,2,4,1,5] => 4
[3,6,2,4,5,1] => 4
[3,6,2,5,1,4] => 4
[3,6,2,5,4,1] => 3
[3,6,4,1,2,5] => 3
[3,6,4,1,5,2] => 4
[3,6,4,2,1,5] => 4
[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] => 3
[3,6,5,1,4,2] => 3
[3,6,5,2,1,4] => 3
[3,6,5,2,4,1] => 4
[3,6,5,4,1,2] => 2
[3,6,5,4,2,1] => 3
[4,1,2,3,5,6] => 2
[4,1,2,3,6,5] => 3
[4,1,2,5,3,6] => 3
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 4
[4,1,2,6,5,3] => 3
[4,1,3,2,5,6] => 2
[4,1,3,2,6,5] => 3
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 4
[4,1,3,6,2,5] => 4
[4,1,3,6,5,2] => 3
[4,1,5,2,3,6] => 3
[4,1,5,2,6,3] => 4
[4,1,5,3,2,6] => 3
[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] => 4
[4,1,6,2,5,3] => 4
[4,1,6,3,2,5] => 4
[4,1,6,3,5,2] => 4
[4,1,6,5,2,3] => 3
[4,1,6,5,3,2] => 3
[4,2,1,3,5,6] => 2
[4,2,1,3,6,5] => 3
[4,2,1,5,3,6] => 3
[4,2,1,5,6,3] => 3
[4,2,1,6,3,5] => 4
[4,2,1,6,5,3] => 3
[4,2,3,1,5,6] => 2
[4,2,3,1,6,5] => 3
[4,2,3,5,1,6] => 3
[4,2,3,5,6,1] => 4
[4,2,3,6,1,5] => 4
[4,2,3,6,5,1] => 3
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 4
[4,2,5,3,1,6] => 3
[4,2,5,3,6,1] => 4
[4,2,5,6,1,3] => 4
[4,2,5,6,3,1] => 4
[4,2,6,1,3,5] => 4
[4,2,6,1,5,3] => 4
[4,2,6,3,1,5] => 4
[4,2,6,3,5,1] => 4
[4,2,6,5,1,3] => 3
[4,2,6,5,3,1] => 3
[4,3,1,2,5,6] => 2
[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] => 4
[4,3,1,6,5,2] => 3
[4,3,2,1,5,6] => 1
[4,3,2,1,6,5] => 2
[4,3,2,5,1,6] => 2
[4,3,2,5,6,1] => 3
[4,3,2,6,1,5] => 3
[4,3,2,6,5,1] => 2
[4,3,5,1,2,6] => 2
[4,3,5,1,6,2] => 3
[4,3,5,2,1,6] => 3
[4,3,5,2,6,1] => 4
[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] => 3
[4,3,6,2,1,5] => 3
[4,3,6,2,5,1] => 3
[4,3,6,5,1,2] => 2
[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] => 3
[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] => 3
[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] => 3
[4,5,3,1,6,2] => 3
[4,5,3,2,1,6] => 2
[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] => 3
[4,5,6,1,3,2] => 2
[4,5,6,2,1,3] => 2
[4,5,6,2,3,1] => 3
[4,5,6,3,1,2] => 3
[4,5,6,3,2,1] => 2
[4,6,1,2,3,5] => 3
[4,6,1,2,5,3] => 4
[4,6,1,3,2,5] => 3
[4,6,1,3,5,2] => 4
[4,6,1,5,2,3] => 3
[4,6,1,5,3,2] => 3
[4,6,2,1,3,5] => 3
[4,6,2,1,5,3] => 3
[4,6,2,3,1,5] => 3
[4,6,2,3,5,1] => 3
[4,6,2,5,1,3] => 4
[4,6,2,5,3,1] => 4
[4,6,3,1,2,5] => 3
[4,6,3,1,5,2] => 4
[4,6,3,2,1,5] => 3
[4,6,3,2,5,1] => 4
[4,6,3,5,1,2] => 3
[4,6,3,5,2,1] => 4
[4,6,5,1,2,3] => 2
[4,6,5,1,3,2] => 3
[4,6,5,2,1,3] => 3
[4,6,5,2,3,1] => 3
[4,6,5,3,1,2] => 3
[4,6,5,3,2,1] => 3
[5,1,2,3,4,6] => 2
[5,1,2,3,6,4] => 3
[5,1,2,4,3,6] => 3
[5,1,2,4,6,3] => 4
[5,1,2,6,3,4] => 4
[5,1,2,6,4,3] => 3
[5,1,3,2,4,6] => 3
[5,1,3,2,6,4] => 4
[5,1,3,4,2,6] => 3
[5,1,3,4,6,2] => 4
[5,1,3,6,2,4] => 4
[5,1,3,6,4,2] => 4
[5,1,4,2,3,6] => 3
[5,1,4,2,6,3] => 4
[5,1,4,3,2,6] => 2
[5,1,4,3,6,2] => 3
[5,1,4,6,2,3] => 3
[5,1,4,6,3,2] => 4
[5,1,6,2,3,4] => 3
[5,1,6,2,4,3] => 3
[5,1,6,3,2,4] => 3
[5,1,6,3,4,2] => 3
[5,1,6,4,2,3] => 3
[5,1,6,4,3,2] => 3
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 4
[5,2,1,4,3,6] => 2
[5,2,1,4,6,3] => 3
[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] => 4
[5,2,3,4,1,6] => 2
[5,2,3,4,6,1] => 3
[5,2,3,6,1,4] => 3
[5,2,3,6,4,1] => 4
[5,2,4,1,3,6] => 3
[5,2,4,1,6,3] => 4
[5,2,4,3,1,6] => 3
[5,2,4,3,6,1] => 4
[5,2,4,6,1,3] => 4
[5,2,4,6,3,1] => 4
[5,2,6,1,3,4] => 4
[5,2,6,1,4,3] => 3
[5,2,6,3,1,4] => 4
[5,2,6,3,4,1] => 3
[5,2,6,4,1,3] => 4
[5,2,6,4,3,1] => 4
[5,3,1,2,4,6] => 3
[5,3,1,2,6,4] => 4
[5,3,1,4,2,6] => 3
[5,3,1,4,6,2] => 4
[5,3,1,6,2,4] => 4
[5,3,1,6,4,2] => 4
[5,3,2,1,4,6] => 2
[5,3,2,1,6,4] => 3
[5,3,2,4,1,6] => 3
[5,3,2,4,6,1] => 4
[5,3,2,6,1,4] => 4
[5,3,2,6,4,1] => 3
[5,3,4,1,2,6] => 3
[5,3,4,1,6,2] => 3
[5,3,4,2,1,6] => 2
[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] => 4
[5,3,6,2,1,4] => 3
[5,3,6,2,4,1] => 4
[5,3,6,4,1,2] => 3
[5,3,6,4,2,1] => 4
[5,4,1,2,3,6] => 2
[5,4,1,2,6,3] => 3
[5,4,1,3,2,6] => 3
[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] => 3
[5,4,2,1,6,3] => 3
[5,4,2,3,1,6] => 2
[5,4,2,3,6,1] => 3
[5,4,2,6,1,3] => 3
[5,4,2,6,3,1] => 4
[5,4,3,1,2,6] => 2
[5,4,3,1,6,2] => 3
[5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => 2
[5,4,3,6,1,2] => 2
[5,4,3,6,2,1] => 3
[5,4,6,1,2,3] => 2
[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] => 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] => 2
[5,6,2,1,3,4] => 3
[5,6,2,1,4,3] => 2
[5,6,2,3,1,4] => 3
[5,6,2,3,4,1] => 3
[5,6,2,4,1,3] => 3
[5,6,2,4,3,1] => 3
[5,6,3,1,2,4] => 3
[5,6,3,1,4,2] => 3
[5,6,3,2,1,4] => 2
[5,6,3,2,4,1] => 3
[5,6,3,4,1,2] => 3
[5,6,3,4,2,1] => 3
[5,6,4,1,2,3] => 3
[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] => 2
[6,1,2,3,4,5] => 2
[6,1,2,3,5,4] => 3
[6,1,2,4,3,5] => 3
[6,1,2,4,5,3] => 4
[6,1,2,5,3,4] => 4
[6,1,2,5,4,3] => 3
[6,1,3,2,4,5] => 3
[6,1,3,2,5,4] => 3
[6,1,3,4,2,5] => 4
[6,1,3,4,5,2] => 3
[6,1,3,5,2,4] => 4
[6,1,3,5,4,2] => 4
[6,1,4,2,3,5] => 4
[6,1,4,2,5,3] => 4
[6,1,4,3,2,5] => 3
[6,1,4,3,5,2] => 4
[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] => 4
[6,1,5,3,2,4] => 4
[6,1,5,3,4,2] => 3
[6,1,5,4,2,3] => 3
[6,1,5,4,3,2] => 2
[6,2,1,3,4,5] => 3
[6,2,1,3,5,4] => 3
[6,2,1,4,3,5] => 3
[6,2,1,4,5,3] => 3
[6,2,1,5,3,4] => 3
[6,2,1,5,4,3] => 2
[6,2,3,1,4,5] => 4
[6,2,3,1,5,4] => 3
[6,2,3,4,1,5] => 3
[6,2,3,4,5,1] => 2
[6,2,3,5,1,4] => 4
[6,2,3,5,4,1] => 3
[6,2,4,1,3,5] => 4
[6,2,4,1,5,3] => 4
[6,2,4,3,1,5] => 4
[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] => 4
[6,2,5,1,4,3] => 3
[6,2,5,3,1,4] => 4
[6,2,5,3,4,1] => 3
[6,2,5,4,1,3] => 4
[6,2,5,4,3,1] => 3
[6,3,1,2,4,5] => 4
[6,3,1,2,5,4] => 3
[6,3,1,4,2,5] => 4
[6,3,1,4,5,2] => 4
[6,3,1,5,2,4] => 4
[6,3,1,5,4,2] => 3
[6,3,2,1,4,5] => 3
[6,3,2,1,5,4] => 2
[6,3,2,4,1,5] => 4
[6,3,2,4,5,1] => 3
[6,3,2,5,1,4] => 3
[6,3,2,5,4,1] => 3
[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] => 3
[6,3,4,5,2,1] => 2
[6,3,5,1,2,4] => 3
[6,3,5,1,4,2] => 4
[6,3,5,2,1,4] => 4
[6,3,5,2,4,1] => 4
[6,3,5,4,1,2] => 3
[6,3,5,4,2,1] => 3
[6,4,1,2,3,5] => 3
[6,4,1,2,5,3] => 4
[6,4,1,3,2,5] => 4
[6,4,1,3,5,2] => 4
[6,4,1,5,2,3] => 3
[6,4,1,5,3,2] => 4
[6,4,2,1,3,5] => 4
[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] => 4
[6,4,2,5,3,1] => 4
[6,4,3,1,2,5] => 3
[6,4,3,1,5,2] => 4
[6,4,3,2,1,5] => 2
[6,4,3,2,5,1] => 3
[6,4,3,5,1,2] => 3
[6,4,3,5,2,1] => 3
[6,4,5,1,2,3] => 3
[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] => 2
[6,5,1,2,3,4] => 2
[6,5,1,2,4,3] => 3
[6,5,1,3,2,4] => 3
[6,5,1,3,4,2] => 3
[6,5,1,4,2,3] => 3
[6,5,1,4,3,2] => 3
[6,5,2,1,3,4] => 3
[6,5,2,1,4,3] => 3
[6,5,2,3,1,4] => 3
[6,5,2,3,4,1] => 2
[6,5,2,4,1,3] => 4
[6,5,2,4,3,1] => 3
[6,5,3,1,2,4] => 3
[6,5,3,1,4,2] => 4
[6,5,3,2,1,4] => 3
[6,5,3,2,4,1] => 3
[6,5,3,4,1,2] => 3
[6,5,3,4,2,1] => 2
[6,5,4,1,2,3] => 2
[6,5,4,1,3,2] => 3
[6,5,4,2,1,3] => 3
[6,5,4,2,3,1] => 2
[6,5,4,3,1,2] => 2
[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
[1,2,3,4,6,7,5] => 2
[1,2,3,4,7,5,6] => 2
[1,2,3,4,7,6,5] => 1
[1,2,3,5,4,6,7] => 1
[1,2,3,5,4,7,6] => 2
[1,2,3,5,6,4,7] => 2
[1,2,3,5,6,7,4] => 2
[1,2,3,5,7,4,6] => 3
[1,2,3,5,7,6,4] => 2
[1,2,3,6,4,5,7] => 2
[1,2,3,6,4,7,5] => 3
[1,2,3,6,5,4,7] => 1
[1,2,3,6,5,7,4] => 2
[1,2,3,6,7,4,5] => 2
[1,2,3,6,7,5,4] => 2
[1,2,3,7,4,5,6] => 2
[1,2,3,7,4,6,5] => 2
[1,2,3,7,5,4,6] => 2
[1,2,3,7,5,6,4] => 2
[1,2,3,7,6,4,5] => 2
[1,2,3,7,6,5,4] => 1
[1,2,4,3,5,6,7] => 1
[1,2,4,3,5,7,6] => 2
[1,2,4,3,6,5,7] => 2
[1,2,4,3,6,7,5] => 3
[1,2,4,3,7,5,6] => 3
[1,2,4,3,7,6,5] => 2
[1,2,4,5,3,6,7] => 2
[1,2,4,5,3,7,6] => 3
[1,2,4,5,6,3,7] => 2
[1,2,4,5,6,7,3] => 2
[1,2,4,5,7,3,6] => 3
[1,2,4,5,7,6,3] => 3
[1,2,4,6,3,5,7] => 3
[1,2,4,6,3,7,5] => 4
[1,2,4,6,5,3,7] => 2
[1,2,4,6,5,7,3] => 3
[1,2,4,6,7,3,5] => 3
[1,2,4,6,7,5,3] => 3
[1,2,4,7,3,5,6] => 3
[1,2,4,7,3,6,5] => 3
[1,2,4,7,5,3,6] => 3
[1,2,4,7,5,6,3] => 3
[1,2,4,7,6,3,5] => 3
[1,2,4,7,6,5,3] => 2
[1,2,5,3,4,6,7] => 2
[1,2,5,3,4,7,6] => 3
[1,2,5,3,6,4,7] => 3
[1,2,5,3,6,7,4] => 3
[1,2,5,3,7,4,6] => 4
[1,2,5,3,7,6,4] => 3
[1,2,5,4,3,6,7] => 1
[1,2,5,4,3,7,6] => 2
[1,2,5,4,6,3,7] => 2
[1,2,5,4,6,7,3] => 3
[1,2,5,4,7,3,6] => 3
[1,2,5,4,7,6,3] => 2
[1,2,5,6,3,4,7] => 2
[1,2,5,6,3,7,4] => 3
[1,2,5,6,4,3,7] => 2
[1,2,5,6,4,7,3] => 3
[1,2,5,6,7,3,4] => 2
[1,2,5,6,7,4,3] => 2
[1,2,5,7,3,4,6] => 3
[1,2,5,7,3,6,4] => 3
[1,2,5,7,4,3,6] => 3
[1,2,5,7,4,6,3] => 3
[1,2,5,7,6,3,4] => 2
[1,2,5,7,6,4,3] => 3
[1,2,6,3,4,5,7] => 2
[1,2,6,3,4,7,5] => 3
[1,2,6,3,5,4,7] => 2
[1,2,6,3,5,7,4] => 3
[1,2,6,3,7,4,5] => 3
[1,2,6,3,7,5,4] => 3
[1,2,6,4,3,5,7] => 2
[1,2,6,4,3,7,5] => 3
[1,2,6,4,5,3,7] => 2
[1,2,6,4,5,7,3] => 3
[1,2,6,4,7,3,5] => 3
[1,2,6,4,7,5,3] => 3
[1,2,6,5,3,4,7] => 2
[1,2,6,5,3,7,4] => 3
[1,2,6,5,4,3,7] => 1
[1,2,6,5,4,7,3] => 2
[1,2,6,5,7,3,4] => 2
[1,2,6,5,7,4,3] => 3
[1,2,6,7,3,4,5] => 2
[1,2,6,7,3,5,4] => 2
[1,2,6,7,4,3,5] => 2
[1,2,6,7,4,5,3] => 3
[1,2,6,7,5,3,4] => 3
[1,2,6,7,5,4,3] => 2
[1,2,7,3,4,5,6] => 2
[1,2,7,3,4,6,5] => 3
[1,2,7,3,5,4,6] => 3
[1,2,7,3,5,6,4] => 3
[1,2,7,3,6,4,5] => 3
[1,2,7,3,6,5,4] => 2
[1,2,7,4,3,5,6] => 3
[1,2,7,4,3,6,5] => 2
[1,2,7,4,5,3,6] => 3
[1,2,7,4,5,6,3] => 2
[1,2,7,4,6,3,5] => 3
[1,2,7,4,6,5,3] => 3
[1,2,7,5,3,4,6] => 3
[1,2,7,5,3,6,4] => 3
[1,2,7,5,4,3,6] => 2
[1,2,7,5,4,6,3] => 3
[1,2,7,5,6,3,4] => 3
[1,2,7,5,6,4,3] => 2
[1,2,7,6,3,4,5] => 2
[1,2,7,6,3,5,4] => 3
[1,2,7,6,4,3,5] => 3
[1,2,7,6,4,5,3] => 2
[1,2,7,6,5,3,4] => 2
[1,2,7,6,5,4,3] => 1
[1,3,2,4,5,6,7] => 1
[1,3,2,4,5,7,6] => 2
[1,3,2,4,6,5,7] => 2
[1,3,2,4,6,7,5] => 3
[1,3,2,4,7,5,6] => 3
[1,3,2,4,7,6,5] => 2
[1,3,2,5,4,6,7] => 2
[1,3,2,5,4,7,6] => 3
[1,3,2,5,6,4,7] => 3
[1,3,2,5,6,7,4] => 3
[1,3,2,5,7,4,6] => 4
[1,3,2,5,7,6,4] => 3
[1,3,2,6,4,5,7] => 3
[1,3,2,6,4,7,5] => 4
[1,3,2,6,5,4,7] => 2
[1,3,2,6,5,7,4] => 3
[1,3,2,6,7,4,5] => 3
[1,3,2,6,7,5,4] => 3
[1,3,2,7,4,5,6] => 3
[1,3,2,7,4,6,5] => 3
[1,3,2,7,5,4,6] => 3
[1,3,2,7,5,6,4] => 3
[1,3,2,7,6,4,5] => 3
[1,3,2,7,6,5,4] => 2
[1,3,4,2,5,6,7] => 2
[1,3,4,2,5,7,6] => 3
[1,3,4,2,6,5,7] => 3
[1,3,4,2,6,7,5] => 4
[1,3,4,2,7,5,6] => 4
[1,3,4,2,7,6,5] => 3
[1,3,4,5,2,6,7] => 2
[1,3,4,5,2,7,6] => 3
[1,3,4,5,6,2,7] => 2
[1,3,4,5,6,7,2] => 2
[1,3,4,5,7,2,6] => 3
[1,3,4,5,7,6,2] => 3
[1,3,4,6,2,5,7] => 3
[1,3,4,6,2,7,5] => 4
[1,3,4,6,5,2,7] => 3
[1,3,4,6,5,7,2] => 3
[1,3,4,6,7,2,5] => 4
[1,3,4,6,7,5,2] => 4
[1,3,4,7,2,5,6] => 4
[1,3,4,7,2,6,5] => 3
[1,3,4,7,5,2,6] => 4
[1,3,4,7,5,6,2] => 4
[1,3,4,7,6,2,5] => 3
[1,3,4,7,6,5,2] => 3
[1,3,5,2,4,6,7] => 3
[1,3,5,2,4,7,6] => 4
[1,3,5,2,6,4,7] => 4
[1,3,5,2,6,7,4] => 4
[1,3,5,2,7,4,6] => 5
[1,3,5,2,7,6,4] => 4
[1,3,5,4,2,6,7] => 2
[1,3,5,4,2,7,6] => 3
[1,3,5,4,6,2,7] => 3
[1,3,5,4,6,7,2] => 3
[1,3,5,4,7,2,6] => 4
[1,3,5,4,7,6,2] => 3
[1,3,5,6,2,4,7] => 3
[1,3,5,6,2,7,4] => 4
[1,3,5,6,4,2,7] => 3
[1,3,5,6,4,7,2] => 4
[1,3,5,6,7,2,4] => 3
[1,3,5,6,7,4,2] => 3
[1,3,5,7,2,4,6] => 4
[1,3,5,7,2,6,4] => 4
[1,3,5,7,4,2,6] => 4
[1,3,5,7,4,6,2] => 4
[1,3,5,7,6,2,4] => 3
[1,3,5,7,6,4,2] => 4
[1,3,6,2,4,5,7] => 3
[1,3,6,2,4,7,5] => 4
[1,3,6,2,5,4,7] => 3
[1,3,6,2,5,7,4] => 4
[1,3,6,2,7,4,5] => 4
[1,3,6,2,7,5,4] => 4
[1,3,6,4,2,5,7] => 3
[1,3,6,4,2,7,5] => 4
[1,3,6,4,5,2,7] => 3
[1,3,6,4,5,7,2] => 4
[1,3,6,4,7,2,5] => 4
[1,3,6,4,7,5,2] => 4
[1,3,6,5,2,4,7] => 3
[1,3,6,5,2,7,4] => 4
[1,3,6,5,4,2,7] => 2
[1,3,6,5,4,7,2] => 3
[1,3,6,5,7,2,4] => 3
[1,3,6,5,7,4,2] => 4
[1,3,6,7,2,4,5] => 3
[1,3,6,7,2,5,4] => 3
[1,3,6,7,4,2,5] => 3
[1,3,6,7,4,5,2] => 3
[1,3,6,7,5,2,4] => 3
[1,3,6,7,5,4,2] => 3
[1,3,7,2,4,5,6] => 3
[1,3,7,2,4,6,5] => 4
[1,3,7,2,5,4,6] => 4
[1,3,7,2,5,6,4] => 4
[1,3,7,2,6,4,5] => 4
[1,3,7,2,6,5,4] => 3
[1,3,7,4,2,5,6] => 4
[1,3,7,4,2,6,5] => 3
[1,3,7,4,5,2,6] => 4
[1,3,7,4,5,6,2] => 3
[1,3,7,4,6,2,5] => 4
[1,3,7,4,6,5,2] => 4
[1,3,7,5,2,4,6] => 4
[1,3,7,5,2,6,4] => 4
[1,3,7,5,4,2,6] => 3
[1,3,7,5,4,6,2] => 4
[1,3,7,5,6,2,4] => 3
[1,3,7,5,6,4,2] => 3
[1,3,7,6,2,4,5] => 3
[1,3,7,6,2,5,4] => 3
[1,3,7,6,4,2,5] => 4
[1,3,7,6,4,5,2] => 3
[1,3,7,6,5,2,4] => 3
[1,3,7,6,5,4,2] => 2
[1,4,2,3,5,6,7] => 2
[1,4,2,3,5,7,6] => 3
[1,4,2,3,6,5,7] => 3
[1,4,2,3,6,7,5] => 4
[1,4,2,3,7,5,6] => 4
[1,4,2,3,7,6,5] => 3
[1,4,2,5,3,6,7] => 3
[1,4,2,5,3,7,6] => 4
[1,4,2,5,6,3,7] => 3
[1,4,2,5,6,7,3] => 3
[1,4,2,5,7,3,6] => 4
[1,4,2,5,7,6,3] => 4
[1,4,2,6,3,5,7] => 4
[1,4,2,6,3,7,5] => 5
[1,4,2,6,5,3,7] => 3
[1,4,2,6,5,7,3] => 4
[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] => 4
[1,4,2,7,5,3,6] => 4
[1,4,2,7,5,6,3] => 4
[1,4,2,7,6,3,5] => 4
[1,4,2,7,6,5,3] => 3
[1,4,3,2,5,6,7] => 1
[1,4,3,2,5,7,6] => 2
[1,4,3,2,6,5,7] => 2
[1,4,3,2,6,7,5] => 3
[1,4,3,2,7,5,6] => 3
[1,4,3,2,7,6,5] => 2
[1,4,3,5,2,6,7] => 2
[1,4,3,5,2,7,6] => 3
[1,4,3,5,6,2,7] => 3
[1,4,3,5,6,7,2] => 3
[1,4,3,5,7,2,6] => 4
[1,4,3,5,7,6,2] => 3
[1,4,3,6,2,5,7] => 3
[1,4,3,6,2,7,5] => 4
[1,4,3,6,5,2,7] => 2
[1,4,3,6,5,7,2] => 3
[1,4,3,6,7,2,5] => 3
[1,4,3,6,7,5,2] => 3
[1,4,3,7,2,5,6] => 3
[1,4,3,7,2,6,5] => 3
[1,4,3,7,5,2,6] => 3
[1,4,3,7,5,6,2] => 3
[1,4,3,7,6,2,5] => 3
[1,4,3,7,6,5,2] => 2
[1,4,5,2,3,6,7] => 2
[1,4,5,2,3,7,6] => 3
[1,4,5,2,6,3,7] => 3
[1,4,5,2,6,7,3] => 4
[1,4,5,2,7,3,6] => 4
[1,4,5,2,7,6,3] => 3
[1,4,5,3,2,6,7] => 2
[1,4,5,3,2,7,6] => 3
[1,4,5,3,6,2,7] => 3
[1,4,5,3,6,7,2] => 4
[1,4,5,3,7,2,6] => 4
[1,4,5,3,7,6,2] => 3
[1,4,5,6,2,3,7] => 2
[1,4,5,6,2,7,3] => 3
[1,4,5,6,3,2,7] => 2
[1,4,5,6,3,7,2] => 3
[1,4,5,6,7,2,3] => 2
[1,4,5,6,7,3,2] => 2
[1,4,5,7,2,3,6] => 3
[1,4,5,7,2,6,3] => 4
[1,4,5,7,3,2,6] => 3
[1,4,5,7,3,6,2] => 4
[1,4,5,7,6,2,3] => 3
[1,4,5,7,6,3,2] => 3
[1,4,6,2,3,5,7] => 3
[1,4,6,2,3,7,5] => 4
[1,4,6,2,5,3,7] => 3
[1,4,6,2,5,7,3] => 4
[1,4,6,2,7,3,5] => 4
[1,4,6,2,7,5,3] => 4
[1,4,6,3,2,5,7] => 3
[1,4,6,3,2,7,5] => 4
[1,4,6,3,5,2,7] => 3
[1,4,6,3,5,7,2] => 4
[1,4,6,3,7,2,5] => 4
[1,4,6,3,7,5,2] => 4
[1,4,6,5,2,3,7] => 2
[1,4,6,5,2,7,3] => 3
[1,4,6,5,3,2,7] => 3
[1,4,6,5,3,7,2] => 4
[1,4,6,7,2,3,5] => 3
[1,4,6,7,5,3,2] => 3
[1,4,7,2,3,5,6] => 4
[1,4,7,6,5,3,2] => 3
[1,5,2,3,4,7,6] => 3
[1,5,2,7,3,4,6] => 4
[1,5,4,7,6,3,2] => 3
[1,5,6,2,7,3,4] => 3
[1,5,6,4,7,3,2] => 3
[1,5,6,7,2,3,4] => 3
[1,5,6,7,4,3,2] => 2
[1,5,7,2,3,4,6] => 3
[1,5,7,6,4,3,2] => 3
[1,6,2,3,4,7,5] => 3
[1,6,2,3,7,4,5] => 4
[1,6,2,7,3,4,5] => 3
[1,6,5,4,3,7,2] => 2
[1,6,5,4,7,3,2] => 3
[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] => 2
[1,7,3,5,6,4,2] => 3
[1,7,3,6,5,4,2] => 3
[1,7,4,3,6,5,2] => 3
[1,7,4,5,3,6,2] => 3
[1,7,4,5,6,3,2] => 2
[1,7,4,6,5,3,2] => 3
[1,7,5,4,3,6,2] => 3
[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] => 3
[2,1,3,7,4,5,6] => 3
[2,1,6,3,4,5,7] => 3
[2,1,7,3,4,5,6] => 3
[2,1,7,6,5,4,3] => 2
[2,3,1,4,5,6,7] => 2
[2,3,4,1,5,6,7] => 2
[2,3,4,1,5,7,6] => 3
[2,3,4,5,1,6,7] => 2
[2,3,4,5,1,7,6] => 3
[2,3,4,5,6,1,7] => 2
[2,3,4,5,6,7,1] => 2
[2,3,4,5,7,1,6] => 3
[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] => 3
[2,5,1,3,4,6,7] => 3
[2,5,7,1,3,4,6] => 4
[2,6,1,3,4,5,7] => 3
[2,6,1,7,3,4,5] => 4
[2,6,5,4,3,1,7] => 2
[2,6,7,1,3,4,5] => 3
[2,7,1,3,4,5,6] => 3
[3,1,2,4,5,6,7] => 2
[3,1,2,4,5,7,6] => 3
[3,2,1,4,5,6,7] => 1
[3,2,4,5,6,7,1] => 3
[3,4,1,2,5,6,7] => 2
[3,4,2,5,6,7,1] => 4
[3,4,5,2,6,7,1] => 4
[3,4,5,6,2,7,1] => 3
[3,4,5,6,7,1,2] => 2
[3,5,6,1,2,4,7] => 3
[3,5,6,4,2,1,7] => 3
[3,6,1,2,4,5,7] => 4
[3,6,5,4,2,1,7] => 3
[4,1,2,3,5,6,7] => 2
[4,1,2,3,5,7,6] => 3
[4,1,6,2,3,5,7] => 4
[4,2,3,5,6,7,1] => 4
[4,2,5,1,3,6,7] => 3
[4,3,2,1,5,6,7] => 1
[4,3,2,5,6,7,1] => 3
[4,3,5,2,6,7,1] => 4
[4,3,6,5,2,1,7] => 3
[4,5,1,6,2,3,7] => 3
[4,5,2,3,6,7,1] => 4
[4,5,3,6,2,1,7] => 3
[4,5,6,1,2,3,7] => 3
[4,5,6,3,2,1,7] => 2
[4,6,1,2,3,5,7] => 3
[4,6,1,2,3,7,5] => 4
[4,6,5,3,2,1,7] => 3
[5,1,2,3,4,6,7] => 2
[5,1,2,3,4,7,6] => 3
[5,1,2,3,6,4,7] => 3
[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] => 3
[5,1,6,2,3,7,4] => 4
[5,2,3,4,6,7,1] => 4
[5,2,6,7,1,3,4] => 4
[5,3,2,4,6,7,1] => 4
[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] => 2
[5,4,3,2,6,1,7] => 2
[5,4,3,6,2,1,7] => 3
[5,4,6,3,2,1,7] => 3
[5,4,6,7,1,2,3] => 3
[5,6,1,2,3,4,7] => 2
[5,6,1,2,3,7,4] => 3
[5,6,3,4,1,2,7] => 3
[5,6,4,3,2,1,7] => 2
[5,6,7,1,2,3,4] => 3
[6,1,2,3,4,5,7] => 2
[6,1,2,3,4,7,5] => 3
[6,1,2,3,7,4,5] => 4
[6,1,2,7,3,4,5] => 4
[6,2,3,4,5,7,1] => 3
[6,2,4,5,3,1,7] => 3
[6,2,5,4,3,1,7] => 3
[6,3,2,5,4,1,7] => 3
[6,3,4,2,5,1,7] => 3
[6,3,4,5,2,1,7] => 2
[6,3,4,7,1,2,5] => 3
[6,3,5,4,2,1,7] => 3
[6,4,3,2,5,1,7] => 3
[6,4,3,2,7,1,5] => 4
[6,4,3,5,2,1,7] => 3
[6,4,5,7,1,2,3] => 3
[6,4,7,2,5,1,3] => 5
[6,4,7,3,5,1,2] => 4
[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] => 4
[6,7,4,5,1,2,3] => 3
[7,1,2,3,4,5,6] => 2
[7,2,1,3,4,5,6] => 3
[7,2,3,1,4,5,6] => 4
[7,2,3,4,1,5,6] => 4
[7,2,3,4,5,1,6] => 3
[7,3,1,2,4,5,6] => 4
[7,3,2,1,4,5,6] => 3
[7,3,2,4,1,5,6] => 4
[7,3,4,1,2,5,6] => 4
[7,4,1,2,3,5,6] => 4
[7,4,2,1,3,5,6] => 4
[7,4,5,6,1,2,3] => 3
[7,5,1,2,3,4,6] => 3
[7,5,6,1,2,3,4] => 3
[7,5,6,3,4,1,2] => 4
[7,6,1,2,3,4,5] => 2
[7,6,4,5,1,2,3] => 3
[7,6,5,1,2,3,4] => 2
[7,6,5,3,4,1,2] => 3
[7,6,5,4,1,2,3] => 2
[7,6,5,4,3,1,2] => 2
[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] => 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] => 3
[6,5,7,4,8,3,2,1] => 4
[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] => 3
[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] => 5
[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] => 3
[7,6,5,4,3,2,8,1] => 2
[6,5,7,4,3,2,8,1] => 4
[6,5,4,3,7,2,8,1] => 4
[5,4,6,3,7,2,8,1] => 5
[3,4,5,2,6,7,8,1] => 4
[5,2,3,4,6,7,8,1] => 4
[4,3,2,5,6,7,8,1] => 3
[3,4,2,5,6,7,8,1] => 4
[4,2,3,5,6,7,8,1] => 4
[3,2,4,5,6,7,8,1] => 3
[2,3,4,5,6,7,8,1] => 2
[8,7,6,5,4,3,1,2] => 2
[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] => 4
[7,8,5,6,3,4,1,2] => 4
[5,6,7,8,3,4,1,2] => 3
[7,8,3,4,5,6,1,2] => 3
[3,4,5,6,7,8,1,2] => 2
[8,7,6,5,4,2,1,3] => 3
[7,6,8,5,4,2,1,3] => 5
[8,7,6,5,4,1,2,3] => 2
[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] => 3
[8,6,7,4,5,1,2,3] => 4
[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] => 4
[7,6,5,8,3,2,1,4] => 3
[7,5,6,8,2,3,1,4] => 5
[6,7,5,8,3,1,2,4] => 5
[6,5,7,8,2,1,3,4] => 4
[8,7,6,5,1,2,3,4] => 2
[8,7,5,6,1,2,3,4] => 3
[7,8,5,6,1,2,3,4] => 3
[8,5,6,7,1,2,3,4] => 3
[5,6,7,8,1,2,3,4] => 3
[8,7,6,4,3,2,1,5] => 3
[8,7,6,4,2,1,3,5] => 4
[8,7,6,1,2,3,4,5] => 2
[8,6,7,1,2,3,4,5] => 3
[6,7,8,1,2,3,4,5] => 3
[7,8,5,4,2,1,3,6] => 4
[7,8,5,4,1,2,3,6] => 3
[8,7,1,2,3,4,5,6] => 2
[7,8,1,2,3,4,5,6] => 2
[8,6,5,4,3,2,1,7] => 2
[8,6,5,4,3,1,2,7] => 3
[8,5,6,3,4,1,2,7] => 4
[8,6,5,4,2,1,3,7] => 4
[8,6,4,3,2,1,5,7] => 4
[8,6,4,2,1,3,5,7] => 5
[8,2,3,4,1,5,6,7] => 4
[8,4,1,2,3,5,6,7] => 4
[8,3,2,1,4,5,6,7] => 3
[8,2,3,1,4,5,6,7] => 4
[8,3,1,2,4,5,6,7] => 4
[8,2,1,3,4,5,6,7] => 3
[8,1,2,3,4,5,6,7] => 2
[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] => 2
[7,6,4,5,3,2,1,8] => 2
[6,5,4,7,3,2,1,8] => 3
[7,5,6,3,4,2,1,8] => 3
[7,6,4,3,5,2,1,8] => 3
[7,6,3,4,5,2,1,8] => 2
[7,5,4,3,6,2,1,8] => 3
[6,7,5,4,2,3,1,8] => 3
[6,5,7,3,2,4,1,8] => 4
[5,6,7,2,3,4,1,8] => 3
[2,3,4,5,6,7,1,8] => 2
[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] => 2
[6,5,4,3,2,1,7,8] => 1
[2,3,4,5,6,1,7,8] => 2
[5,6,3,4,1,2,7,8] => 3
[4,5,6,1,2,3,7,8] => 3
[6,1,2,3,4,5,7,8] => 2
[5,4,3,2,1,6,7,8] => 1
[2,3,4,5,1,6,7,8] => 2
[5,1,2,3,4,6,7,8] => 2
[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] => 4
[4,3,6,5,8,7,2,1] => 3
[2,6,8,7,5,4,3,1] => 4
[2,3,5,6,8,7,4,1] => 5
[3,2,6,5,4,8,7,1] => 3
[4,3,6,5,7,2,8,1] => 4
[3,2,6,5,7,4,8,1] => 5
[4,3,5,2,7,6,8,1] => 5
[3,2,5,4,7,6,8,1] => 4
[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] => 3
[1,7,6,8,5,4,3,2] => 3
[1,6,7,8,5,4,3,2] => 2
[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] => 4
[1,4,3,8,7,6,5,2] => 2
[1,6,5,4,3,8,7,2] => 2
[1,4,3,6,5,8,7,2] => 3
[2,1,8,7,6,5,4,3] => 2
[2,1,6,5,7,4,8,3] => 5
[2,1,5,4,7,6,8,3] => 4
[1,2,6,7,8,5,4,3] => 2
[3,2,1,8,7,6,5,4] => 2
[3,2,1,6,5,8,7,4] => 3
[1,2,3,5,6,7,8,4] => 2
[4,3,2,1,8,7,6,5] => 2
[3,4,2,1,7,8,6,5] => 4
[2,4,3,1,6,8,7,5] => 4
[2,4,3,1,7,6,8,5] => 4
[3,2,4,1,6,8,7,5] => 4
[3,2,4,1,7,6,8,5] => 4
[2,3,4,1,6,7,8,5] => 4
[2,1,4,3,8,7,6,5] => 3
[2,1,4,3,6,8,7,5] => 4
[2,1,4,3,7,6,8,5] => 4
[5,4,3,2,1,8,7,6] => 2
[3,2,5,4,1,8,7,6] => 3
[3,2,1,4,5,8,7,6] => 2
[2,3,1,4,5,7,8,6] => 4
[6,5,4,3,2,1,8,7] => 2
[4,3,5,2,6,1,8,7] => 5
[3,2,5,4,6,1,8,7] => 4
[2,3,4,5,6,1,8,7] => 3
[2,1,6,5,4,3,8,7] => 3
[2,1,4,6,5,3,8,7] => 4
[2,1,5,4,6,3,8,7] => 4
[4,3,2,1,6,5,8,7] => 3
[2,4,3,1,6,5,8,7] => 4
[3,2,4,1,6,5,8,7] => 4
[2,1,4,3,6,5,8,7] => 4
[2,1,3,4,5,6,8,7] => 2
[1,2,3,4,5,6,8,7] => 1
[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] => 2
[5,4,3,2,7,6,1,8] => 2
[3,2,5,4,7,6,1,8] => 3
[1,4,3,2,7,6,5,8] => 2
[1,3,4,2,6,7,5,8] => 4
[1,3,2,5,4,7,6,8] => 3
[1,2,3,5,4,7,6,8] => 2
[1,3,2,4,5,7,6,8] => 2
[1,2,3,4,5,7,6,8] => 1
[1,2,4,3,6,5,7,8] => 2
[1,3,2,5,4,6,7,8] => 2
[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] => 3
[1,8,5,4,7,6,3,2] => 3
[1,8,7,4,5,6,3,2] => 2
[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] => 2
[2,1,4,5,8,6,7,3] => 5
[2,1,8,5,4,7,6,3] => 4
[2,3,4,8,5,6,7,1] => 4
[2,3,6,4,5,1,8,7] => 5
[2,3,7,4,5,6,8,1] => 4
[2,8,4,3,5,7,6,1] => 4
[4,2,3,1,8,6,7,5] => 4
[8,2,7,4,6,5,3,1] => 5
[4,3,2,7,5,6,8,1] => 4
[4,3,2,8,5,7,6,1] => 4
[6,3,2,5,4,1,8,7] => 4
[8,3,2,5,4,7,6,1] => 4
[8,3,2,7,6,5,4,1] => 3
[8,3,7,4,6,5,2,1] => 4
[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] => 3
[8,7,4,3,6,5,2,1] => 3
[2,4,6,8,1,3,5,7] => 5
[2,4,6,1,7,3,8,5] => 6
[2,1,4,3,7,5,8,6] => 5
[2,4,1,3,7,5,8,6] => 6
[2,1,4,3,7,8,5,6] => 4
[2,4,7,8,1,3,5,6] => 5
[2,1,4,3,8,5,6,7] => 4
[2,4,5,6,7,1,8,3] => 4
[2,1,5,3,6,4,8,7] => 5
[2,1,5,6,3,4,8,7] => 4
[2,5,6,8,1,3,4,7] => 4
[2,1,5,3,7,4,8,6] => 6
[2,5,1,7,3,4,8,6] => 6
[2,1,5,7,3,8,4,6] => 5
[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] => 5
[2,6,7,1,3,4,8,5] => 4
[2,1,6,7,8,3,4,5] => 3
[2,6,7,8,1,3,4,5] => 3
[2,1,6,3,4,7,8,5] => 5
[2,1,6,3,4,5,8,7] => 4
[2,6,1,3,4,5,7,8] => 3
[2,7,8,1,3,4,5,6] => 3
[2,7,1,3,4,5,6,8] => 3
[2,3,4,5,7,8,1,6] => 4
[2,1,8,3,4,5,6,7] => 3
[2,8,1,3,4,5,6,7] => 3
[2,1,3,8,4,5,6,7] => 3
[2,3,4,5,6,8,1,7] => 3
[3,1,4,2,6,5,8,7] => 5
[3,4,1,2,6,5,8,7] => 4
[3,1,4,2,6,8,5,7] => 6
[3,4,6,8,1,2,5,7] => 5
[3,1,4,2,7,5,8,6] => 6
[3,4,1,2,7,8,5,6] => 4
[3,4,7,8,1,2,5,6] => 4
[3,1,5,2,6,4,8,7] => 6
[3,5,1,6,2,4,8,7] => 5
[3,1,5,6,2,8,4,7] => 6
[3,5,6,8,1,2,4,7] => 4
[3,1,5,2,7,4,8,6] => 7
[3,5,1,7,2,8,4,6] => 6
[3,5,7,8,1,2,4,6] => 5
[1,3,2,5,4,8,6,7] => 4
[1,3,5,8,2,4,6,7] => 5
[1,3,5,6,2,7,4,8] => 4
[3,1,6,2,7,4,8,5] => 6
[3,6,7,1,2,8,4,5] => 4
[3,6,1,7,8,2,4,5] => 5
[3,6,7,8,1,2,4,5] => 4
[1,3,2,6,4,7,5,8] => 4
[3,1,2,6,7,4,8,5] => 5
[1,3,2,6,4,8,5,7] => 5
[1,3,2,6,4,5,7,8] => 3
[1,3,2,7,4,8,5,6] => 4
[1,3,2,7,4,5,6,8] => 3
[1,3,2,8,4,5,6,7] => 3
[3,1,2,4,5,8,6,7] => 4
[1,3,2,4,5,8,6,7] => 3
[4,1,5,2,6,3,8,7] => 5
[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] => 3
[4,1,5,2,7,3,8,6] => 6
[4,1,5,2,7,8,3,6] => 5
[4,5,7,1,2,8,3,6] => 5
[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] => 4
[1,4,2,5,3,8,6,7] => 5
[1,4,2,5,3,6,7,8] => 3
[1,4,5,6,7,2,3,8] => 2
[4,1,6,2,7,3,8,5] => 6
[4,6,7,1,8,2,3,5] => 4
[4,6,7,8,1,2,3,5] => 3
[1,4,2,6,3,7,5,8] => 5
[1,4,2,6,7,8,3,5] => 4
[1,4,2,6,3,8,5,7] => 6
[4,1,2,3,6,5,8,7] => 4
[1,4,2,6,3,5,7,8] => 4
[1,4,2,7,3,8,5,6] => 5
[4,7,1,2,3,5,6,8] => 4
[1,4,2,7,3,5,6,8] => 4
[1,4,2,3,7,5,6,8] => 4
[1,4,2,3,5,7,6,8] => 3
[1,4,2,8,3,5,6,7] => 4
[4,1,2,3,8,5,6,7] => 4
[1,4,2,3,5,8,6,7] => 4
[1,4,2,3,5,6,7,8] => 2
[5,1,6,2,7,3,8,4] => 5
[1,5,2,6,3,7,4,8] => 4
[1,5,2,6,3,8,4,7] => 5
[1,5,2,6,3,4,7,8] => 3
[1,2,5,6,3,4,7,8] => 2
[1,5,2,7,3,8,4,6] => 5
[5,7,1,2,3,4,6,8] => 3
[1,5,2,7,3,4,6,8] => 4
[1,5,2,3,4,7,6,8] => 3
[5,1,2,8,3,4,6,7] => 4
[1,5,2,8,3,4,6,7] => 4
[1,5,8,2,3,4,6,7] => 4
[1,5,2,3,4,8,6,7] => 4
[1,2,3,5,4,8,6,7] => 3
[5,1,2,3,4,6,8,7] => 3
[1,5,2,3,4,6,7,8] => 2
[1,6,2,7,3,8,4,5] => 4
[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] => 3
[6,1,2,7,3,4,5,8] => 4
[1,6,2,7,3,4,5,8] => 3
[1,6,7,2,3,4,5,8] => 2
[1,6,2,3,4,7,5,8] => 3
[1,2,3,6,4,7,5,8] => 3
[6,1,8,2,3,4,5,7] => 4
[1,6,2,8,3,4,5,7] => 4
[1,6,8,2,3,4,5,7] => 3
[1,6,2,3,4,8,5,7] => 4
[1,2,3,6,4,8,5,7] => 4
[6,1,2,3,4,5,8,7] => 3
[1,6,2,3,4,5,7,8] => 2
[1,2,3,6,4,5,7,8] => 2
[1,7,2,8,3,4,5,6] => 3
[1,7,8,2,3,4,5,6] => 2
[1,7,2,3,8,4,5,6] => 4
[7,1,2,3,4,8,5,6] => 4
[1,7,2,3,4,8,5,6] => 4
[1,2,3,7,4,8,5,6] => 3
[7,1,2,3,4,5,8,6] => 3
[1,7,2,3,4,5,8,6] => 3
[1,2,7,3,4,5,8,6] => 3
[1,7,2,3,4,5,6,8] => 2
[1,2,3,7,4,5,6,8] => 2
[1,8,2,3,4,5,6,7] => 2
[1,2,3,8,4,5,6,7] => 2
[1,2,3,4,5,8,6,7] => 2
[2,1,5,8,3,7,6,4] => 5
[2,1,6,8,7,3,5,4] => 4
[2,1,7,8,6,5,3,4] => 4
[2,1,7,6,8,4,3,5] => 4
[2,1,7,5,4,8,3,6] => 5
[2,1,8,6,7,4,5,3] => 4
[3,4,1,2,8,7,6,5] => 3
[3,5,1,8,2,7,6,4] => 5
[3,6,1,8,7,2,5,4] => 4
[3,6,1,5,4,2,8,7] => 5
[3,7,1,8,6,5,2,4] => 6
[3,7,1,6,8,4,2,5] => 6
[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] => 4
[3,8,1,7,6,5,4,2] => 4
[4,3,2,1,7,8,5,6] => 3
[4,5,8,1,2,7,6,3] => 4
[4,6,8,1,7,2,5,3] => 6
[4,6,5,1,3,2,8,7] => 4
[4,7,8,1,6,5,2,3] => 4
[4,7,6,1,8,3,2,5] => 4
[4,7,5,1,3,8,2,6] => 6
[4,8,5,1,3,7,6,2] => 5
[4,8,6,1,7,3,5,2] => 6
[4,8,7,1,6,5,3,2] => 5
[5,3,2,8,1,7,6,4] => 4
[5,3,2,7,1,8,4,6] => 5
[5,3,2,6,1,4,8,7] => 5
[5,4,8,2,1,7,6,3] => 4
[5,4,7,2,1,8,3,6] => 4
[5,4,6,2,1,3,8,7] => 4
[5,6,8,7,1,2,4,3] => 4
[5,6,4,3,1,2,8,7] => 4
[5,7,8,6,1,4,2,3] => 5
[5,7,6,8,1,3,2,4] => 5
[5,7,4,3,1,8,2,6] => 6
[5,8,4,3,1,7,6,2] => 5
[5,8,6,7,1,3,4,2] => 5
[5,8,7,6,1,4,3,2] => 3
[6,3,2,8,7,1,5,4] => 4
[6,3,2,7,8,1,4,5] => 4
[6,4,8,2,7,1,5,3] => 5
[6,4,7,2,8,1,3,5] => 6
[6,4,5,2,3,1,8,7] => 4
[6,5,8,7,2,1,4,3] => 4
[6,7,4,3,8,1,2,5] => 4
[6,8,4,3,7,1,5,2] => 5
[6,8,5,7,3,1,4,2] => 6
[6,8,7,5,4,1,3,2] => 5
[7,3,2,8,6,5,1,4] => 5
[7,3,2,6,8,4,1,5] => 5
[7,3,2,5,4,8,1,6] => 4
[7,4,8,2,6,5,1,3] => 5
[7,4,6,2,8,3,1,5] => 6
[7,4,5,2,3,8,1,6] => 4
[7,5,8,6,2,4,1,3] => 6
[7,5,4,3,2,8,1,6] => 4
[7,6,4,3,8,2,1,5] => 5
[7,8,4,3,6,5,1,2] => 4
[8,3,2,6,7,4,5,1] => 3
[8,4,5,2,3,7,6,1] => 3
[8,4,6,2,7,3,5,1] => 5
[8,4,7,2,6,5,3,1] => 5
[8,5,7,6,2,4,3,1] => 5
[8,6,4,3,7,2,5,1] => 5
click to show generating function       
Description
The reversal length of a permutation.
A reversal in a permutation $\pi = [\pi_1,\ldots,\pi_n]$ is a reversal of a subsequence of the form $\operatorname{reversal}_{i,j}(\pi) = [\pi_1,\ldots,\pi_{i-1},\pi_j,\pi_{j-1},\ldots,\pi_{i+1},\pi_i,\pi_{j+1},\ldots,\pi_n]$ for $1 \leq i < j \leq n$.
This statistic is then given by the minimal number of reversals needed to sort a permutation.
The reversal distance between two permutations plays an important role in studying DNA structures.
Code
def children(pi):
    pi = list(pi)
    n = len(pi)
    for j in range(n):
        for i in range(j):
            yield Permutation(pi[:i]+list(reversed(pi[i:j+1]))+pi[j+1:])

@cached_function
def statistic_classes(n):
    A = RecursivelyEnumeratedSet([Permutation([1..n])], children,structure='symmetric')
    return list(A.graded_component_iterator())

def statistic(pi):
    comps = statistic_classes(len(pi))
    for rank,comp in enumerate(comps):
        if pi in comp:
            return rank

Created
Dec 15, 2016 at 17:57 by Christian Stump
Updated
Jun 21, 2018 at 09:53 by Martin Rubey