Identifier
- St000246: Permutations ⟶ ℤ (values match St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.)
Values
[] => 0
[1] => 0
[1,2] => 1
[2,1] => 0
[1,2,3] => 3
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 6
[1,2,4,3] => 5
[1,3,2,4] => 5
[1,3,4,2] => 4
[1,4,2,3] => 4
[1,4,3,2] => 3
[2,1,3,4] => 5
[2,1,4,3] => 4
[2,3,1,4] => 4
[2,3,4,1] => 3
[2,4,1,3] => 3
[2,4,3,1] => 2
[3,1,2,4] => 4
[3,1,4,2] => 3
[3,2,1,4] => 3
[3,2,4,1] => 2
[3,4,1,2] => 2
[3,4,2,1] => 1
[4,1,2,3] => 3
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 1
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 10
[1,2,3,5,4] => 9
[1,2,4,3,5] => 9
[1,2,4,5,3] => 8
[1,2,5,3,4] => 8
[1,2,5,4,3] => 7
[1,3,2,4,5] => 9
[1,3,2,5,4] => 8
[1,3,4,2,5] => 8
[1,3,4,5,2] => 7
[1,3,5,2,4] => 7
[1,3,5,4,2] => 6
[1,4,2,3,5] => 8
[1,4,2,5,3] => 7
[1,4,3,2,5] => 7
[1,4,3,5,2] => 6
[1,4,5,2,3] => 6
[1,4,5,3,2] => 5
[1,5,2,3,4] => 7
[1,5,2,4,3] => 6
[1,5,3,2,4] => 6
[1,5,3,4,2] => 5
[1,5,4,2,3] => 5
[1,5,4,3,2] => 4
[2,1,3,4,5] => 9
[2,1,3,5,4] => 8
[2,1,4,3,5] => 8
[2,1,4,5,3] => 7
[2,1,5,3,4] => 7
[2,1,5,4,3] => 6
[2,3,1,4,5] => 8
[2,3,1,5,4] => 7
[2,3,4,1,5] => 7
[2,3,4,5,1] => 6
[2,3,5,1,4] => 6
[2,3,5,4,1] => 5
[2,4,1,3,5] => 7
[2,4,1,5,3] => 6
[2,4,3,1,5] => 6
[2,4,3,5,1] => 5
[2,4,5,1,3] => 5
[2,4,5,3,1] => 4
[2,5,1,3,4] => 6
[2,5,1,4,3] => 5
[2,5,3,1,4] => 5
[2,5,3,4,1] => 4
[2,5,4,1,3] => 4
[2,5,4,3,1] => 3
[3,1,2,4,5] => 8
[3,1,2,5,4] => 7
[3,1,4,2,5] => 7
[3,1,4,5,2] => 6
[3,1,5,2,4] => 6
[3,1,5,4,2] => 5
[3,2,1,4,5] => 7
[3,2,1,5,4] => 6
[3,2,4,1,5] => 6
[3,2,4,5,1] => 5
[3,2,5,1,4] => 5
[3,2,5,4,1] => 4
[3,4,1,2,5] => 6
[3,4,1,5,2] => 5
[3,4,2,1,5] => 5
[3,4,2,5,1] => 4
[3,4,5,1,2] => 4
[3,4,5,2,1] => 3
[3,5,1,2,4] => 5
>>> Load all 2680 entries. <<<[3,5,1,4,2] => 4
[3,5,2,1,4] => 4
[3,5,2,4,1] => 3
[3,5,4,1,2] => 3
[3,5,4,2,1] => 2
[4,1,2,3,5] => 7
[4,1,2,5,3] => 6
[4,1,3,2,5] => 6
[4,1,3,5,2] => 5
[4,1,5,2,3] => 5
[4,1,5,3,2] => 4
[4,2,1,3,5] => 6
[4,2,1,5,3] => 5
[4,2,3,1,5] => 5
[4,2,3,5,1] => 4
[4,2,5,1,3] => 4
[4,2,5,3,1] => 3
[4,3,1,2,5] => 5
[4,3,1,5,2] => 4
[4,3,2,1,5] => 4
[4,3,2,5,1] => 3
[4,3,5,1,2] => 3
[4,3,5,2,1] => 2
[4,5,1,2,3] => 4
[4,5,1,3,2] => 3
[4,5,2,1,3] => 3
[4,5,2,3,1] => 2
[4,5,3,1,2] => 2
[4,5,3,2,1] => 1
[5,1,2,3,4] => 6
[5,1,2,4,3] => 5
[5,1,3,2,4] => 5
[5,1,3,4,2] => 4
[5,1,4,2,3] => 4
[5,1,4,3,2] => 3
[5,2,1,3,4] => 5
[5,2,1,4,3] => 4
[5,2,3,1,4] => 4
[5,2,3,4,1] => 3
[5,2,4,1,3] => 3
[5,2,4,3,1] => 2
[5,3,1,2,4] => 4
[5,3,1,4,2] => 3
[5,3,2,1,4] => 3
[5,3,2,4,1] => 2
[5,3,4,1,2] => 2
[5,3,4,2,1] => 1
[5,4,1,2,3] => 3
[5,4,1,3,2] => 2
[5,4,2,1,3] => 2
[5,4,2,3,1] => 1
[5,4,3,1,2] => 1
[5,4,3,2,1] => 0
[1,2,3,4,5,6] => 15
[1,2,3,4,6,5] => 14
[1,2,3,5,4,6] => 14
[1,2,3,5,6,4] => 13
[1,2,3,6,4,5] => 13
[1,2,3,6,5,4] => 12
[1,2,4,3,5,6] => 14
[1,2,4,3,6,5] => 13
[1,2,4,5,3,6] => 13
[1,2,4,5,6,3] => 12
[1,2,4,6,3,5] => 12
[1,2,4,6,5,3] => 11
[1,2,5,3,4,6] => 13
[1,2,5,3,6,4] => 12
[1,2,5,4,3,6] => 12
[1,2,5,4,6,3] => 11
[1,2,5,6,3,4] => 11
[1,2,5,6,4,3] => 10
[1,2,6,3,4,5] => 12
[1,2,6,3,5,4] => 11
[1,2,6,4,3,5] => 11
[1,2,6,4,5,3] => 10
[1,2,6,5,3,4] => 10
[1,2,6,5,4,3] => 9
[1,3,2,4,5,6] => 14
[1,3,2,4,6,5] => 13
[1,3,2,5,4,6] => 13
[1,3,2,5,6,4] => 12
[1,3,2,6,4,5] => 12
[1,3,2,6,5,4] => 11
[1,3,4,2,5,6] => 13
[1,3,4,2,6,5] => 12
[1,3,4,5,2,6] => 12
[1,3,4,5,6,2] => 11
[1,3,4,6,2,5] => 11
[1,3,4,6,5,2] => 10
[1,3,5,2,4,6] => 12
[1,3,5,2,6,4] => 11
[1,3,5,4,2,6] => 11
[1,3,5,4,6,2] => 10
[1,3,5,6,2,4] => 10
[1,3,5,6,4,2] => 9
[1,3,6,2,4,5] => 11
[1,3,6,2,5,4] => 10
[1,3,6,4,2,5] => 10
[1,3,6,4,5,2] => 9
[1,3,6,5,2,4] => 9
[1,3,6,5,4,2] => 8
[1,4,2,3,5,6] => 13
[1,4,2,3,6,5] => 12
[1,4,2,5,3,6] => 12
[1,4,2,5,6,3] => 11
[1,4,2,6,3,5] => 11
[1,4,2,6,5,3] => 10
[1,4,3,2,5,6] => 12
[1,4,3,2,6,5] => 11
[1,4,3,5,2,6] => 11
[1,4,3,5,6,2] => 10
[1,4,3,6,2,5] => 10
[1,4,3,6,5,2] => 9
[1,4,5,2,3,6] => 11
[1,4,5,2,6,3] => 10
[1,4,5,3,2,6] => 10
[1,4,5,3,6,2] => 9
[1,4,5,6,2,3] => 9
[1,4,5,6,3,2] => 8
[1,4,6,2,3,5] => 10
[1,4,6,2,5,3] => 9
[1,4,6,3,2,5] => 9
[1,4,6,3,5,2] => 8
[1,4,6,5,2,3] => 8
[1,4,6,5,3,2] => 7
[1,5,2,3,4,6] => 12
[1,5,2,3,6,4] => 11
[1,5,2,4,3,6] => 11
[1,5,2,4,6,3] => 10
[1,5,2,6,3,4] => 10
[1,5,2,6,4,3] => 9
[1,5,3,2,4,6] => 11
[1,5,3,2,6,4] => 10
[1,5,3,4,2,6] => 10
[1,5,3,4,6,2] => 9
[1,5,3,6,2,4] => 9
[1,5,3,6,4,2] => 8
[1,5,4,2,3,6] => 10
[1,5,4,2,6,3] => 9
[1,5,4,3,2,6] => 9
[1,5,4,3,6,2] => 8
[1,5,4,6,2,3] => 8
[1,5,4,6,3,2] => 7
[1,5,6,2,3,4] => 9
[1,5,6,2,4,3] => 8
[1,5,6,3,2,4] => 8
[1,5,6,3,4,2] => 7
[1,5,6,4,2,3] => 7
[1,5,6,4,3,2] => 6
[1,6,2,3,4,5] => 11
[1,6,2,3,5,4] => 10
[1,6,2,4,3,5] => 10
[1,6,2,4,5,3] => 9
[1,6,2,5,3,4] => 9
[1,6,2,5,4,3] => 8
[1,6,3,2,4,5] => 10
[1,6,3,2,5,4] => 9
[1,6,3,4,2,5] => 9
[1,6,3,4,5,2] => 8
[1,6,3,5,2,4] => 8
[1,6,3,5,4,2] => 7
[1,6,4,2,3,5] => 9
[1,6,4,2,5,3] => 8
[1,6,4,3,2,5] => 8
[1,6,4,3,5,2] => 7
[1,6,4,5,2,3] => 7
[1,6,4,5,3,2] => 6
[1,6,5,2,3,4] => 8
[1,6,5,2,4,3] => 7
[1,6,5,3,2,4] => 7
[1,6,5,3,4,2] => 6
[1,6,5,4,2,3] => 6
[1,6,5,4,3,2] => 5
[2,1,3,4,5,6] => 14
[2,1,3,4,6,5] => 13
[2,1,3,5,4,6] => 13
[2,1,3,5,6,4] => 12
[2,1,3,6,4,5] => 12
[2,1,3,6,5,4] => 11
[2,1,4,3,5,6] => 13
[2,1,4,3,6,5] => 12
[2,1,4,5,3,6] => 12
[2,1,4,5,6,3] => 11
[2,1,4,6,3,5] => 11
[2,1,4,6,5,3] => 10
[2,1,5,3,4,6] => 12
[2,1,5,3,6,4] => 11
[2,1,5,4,3,6] => 11
[2,1,5,4,6,3] => 10
[2,1,5,6,3,4] => 10
[2,1,5,6,4,3] => 9
[2,1,6,3,4,5] => 11
[2,1,6,3,5,4] => 10
[2,1,6,4,3,5] => 10
[2,1,6,4,5,3] => 9
[2,1,6,5,3,4] => 9
[2,1,6,5,4,3] => 8
[2,3,1,4,5,6] => 13
[2,3,1,4,6,5] => 12
[2,3,1,5,4,6] => 12
[2,3,1,5,6,4] => 11
[2,3,1,6,4,5] => 11
[2,3,1,6,5,4] => 10
[2,3,4,1,5,6] => 12
[2,3,4,1,6,5] => 11
[2,3,4,5,1,6] => 11
[2,3,4,5,6,1] => 10
[2,3,4,6,1,5] => 10
[2,3,4,6,5,1] => 9
[2,3,5,1,4,6] => 11
[2,3,5,1,6,4] => 10
[2,3,5,4,1,6] => 10
[2,3,5,4,6,1] => 9
[2,3,5,6,1,4] => 9
[2,3,5,6,4,1] => 8
[2,3,6,1,4,5] => 10
[2,3,6,1,5,4] => 9
[2,3,6,4,1,5] => 9
[2,3,6,4,5,1] => 8
[2,3,6,5,1,4] => 8
[2,3,6,5,4,1] => 7
[2,4,1,3,5,6] => 12
[2,4,1,3,6,5] => 11
[2,4,1,5,3,6] => 11
[2,4,1,5,6,3] => 10
[2,4,1,6,3,5] => 10
[2,4,1,6,5,3] => 9
[2,4,3,1,5,6] => 11
[2,4,3,1,6,5] => 10
[2,4,3,5,1,6] => 10
[2,4,3,5,6,1] => 9
[2,4,3,6,1,5] => 9
[2,4,3,6,5,1] => 8
[2,4,5,1,3,6] => 10
[2,4,5,1,6,3] => 9
[2,4,5,3,1,6] => 9
[2,4,5,3,6,1] => 8
[2,4,5,6,1,3] => 8
[2,4,5,6,3,1] => 7
[2,4,6,1,3,5] => 9
[2,4,6,1,5,3] => 8
[2,4,6,3,1,5] => 8
[2,4,6,3,5,1] => 7
[2,4,6,5,1,3] => 7
[2,4,6,5,3,1] => 6
[2,5,1,3,4,6] => 11
[2,5,1,3,6,4] => 10
[2,5,1,4,3,6] => 10
[2,5,1,4,6,3] => 9
[2,5,1,6,3,4] => 9
[2,5,1,6,4,3] => 8
[2,5,3,1,4,6] => 10
[2,5,3,1,6,4] => 9
[2,5,3,4,1,6] => 9
[2,5,3,4,6,1] => 8
[2,5,3,6,1,4] => 8
[2,5,3,6,4,1] => 7
[2,5,4,1,3,6] => 9
[2,5,4,1,6,3] => 8
[2,5,4,3,1,6] => 8
[2,5,4,3,6,1] => 7
[2,5,4,6,1,3] => 7
[2,5,4,6,3,1] => 6
[2,5,6,1,3,4] => 8
[2,5,6,1,4,3] => 7
[2,5,6,3,1,4] => 7
[2,5,6,3,4,1] => 6
[2,5,6,4,1,3] => 6
[2,5,6,4,3,1] => 5
[2,6,1,3,4,5] => 10
[2,6,1,3,5,4] => 9
[2,6,1,4,3,5] => 9
[2,6,1,4,5,3] => 8
[2,6,1,5,3,4] => 8
[2,6,1,5,4,3] => 7
[2,6,3,1,4,5] => 9
[2,6,3,1,5,4] => 8
[2,6,3,4,1,5] => 8
[2,6,3,4,5,1] => 7
[2,6,3,5,1,4] => 7
[2,6,3,5,4,1] => 6
[2,6,4,1,3,5] => 8
[2,6,4,1,5,3] => 7
[2,6,4,3,1,5] => 7
[2,6,4,3,5,1] => 6
[2,6,4,5,1,3] => 6
[2,6,4,5,3,1] => 5
[2,6,5,1,3,4] => 7
[2,6,5,1,4,3] => 6
[2,6,5,3,1,4] => 6
[2,6,5,3,4,1] => 5
[2,6,5,4,1,3] => 5
[2,6,5,4,3,1] => 4
[3,1,2,4,5,6] => 13
[3,1,2,4,6,5] => 12
[3,1,2,5,4,6] => 12
[3,1,2,5,6,4] => 11
[3,1,2,6,4,5] => 11
[3,1,2,6,5,4] => 10
[3,1,4,2,5,6] => 12
[3,1,4,2,6,5] => 11
[3,1,4,5,2,6] => 11
[3,1,4,5,6,2] => 10
[3,1,4,6,2,5] => 10
[3,1,4,6,5,2] => 9
[3,1,5,2,4,6] => 11
[3,1,5,2,6,4] => 10
[3,1,5,4,2,6] => 10
[3,1,5,4,6,2] => 9
[3,1,5,6,2,4] => 9
[3,1,5,6,4,2] => 8
[3,1,6,2,4,5] => 10
[3,1,6,2,5,4] => 9
[3,1,6,4,2,5] => 9
[3,1,6,4,5,2] => 8
[3,1,6,5,2,4] => 8
[3,1,6,5,4,2] => 7
[3,2,1,4,5,6] => 12
[3,2,1,4,6,5] => 11
[3,2,1,5,4,6] => 11
[3,2,1,5,6,4] => 10
[3,2,1,6,4,5] => 10
[3,2,1,6,5,4] => 9
[3,2,4,1,5,6] => 11
[3,2,4,1,6,5] => 10
[3,2,4,5,1,6] => 10
[3,2,4,5,6,1] => 9
[3,2,4,6,1,5] => 9
[3,2,4,6,5,1] => 8
[3,2,5,1,4,6] => 10
[3,2,5,1,6,4] => 9
[3,2,5,4,1,6] => 9
[3,2,5,4,6,1] => 8
[3,2,5,6,1,4] => 8
[3,2,5,6,4,1] => 7
[3,2,6,1,4,5] => 9
[3,2,6,1,5,4] => 8
[3,2,6,4,1,5] => 8
[3,2,6,4,5,1] => 7
[3,2,6,5,1,4] => 7
[3,2,6,5,4,1] => 6
[3,4,1,2,5,6] => 11
[3,4,1,2,6,5] => 10
[3,4,1,5,2,6] => 10
[3,4,1,5,6,2] => 9
[3,4,1,6,2,5] => 9
[3,4,1,6,5,2] => 8
[3,4,2,1,5,6] => 10
[3,4,2,1,6,5] => 9
[3,4,2,5,1,6] => 9
[3,4,2,5,6,1] => 8
[3,4,2,6,1,5] => 8
[3,4,2,6,5,1] => 7
[3,4,5,1,2,6] => 9
[3,4,5,1,6,2] => 8
[3,4,5,2,1,6] => 8
[3,4,5,2,6,1] => 7
[3,4,5,6,1,2] => 7
[3,4,5,6,2,1] => 6
[3,4,6,1,2,5] => 8
[3,4,6,1,5,2] => 7
[3,4,6,2,1,5] => 7
[3,4,6,2,5,1] => 6
[3,4,6,5,1,2] => 6
[3,4,6,5,2,1] => 5
[3,5,1,2,4,6] => 10
[3,5,1,2,6,4] => 9
[3,5,1,4,2,6] => 9
[3,5,1,4,6,2] => 8
[3,5,1,6,2,4] => 8
[3,5,1,6,4,2] => 7
[3,5,2,1,4,6] => 9
[3,5,2,1,6,4] => 8
[3,5,2,4,1,6] => 8
[3,5,2,4,6,1] => 7
[3,5,2,6,1,4] => 7
[3,5,2,6,4,1] => 6
[3,5,4,1,2,6] => 8
[3,5,4,1,6,2] => 7
[3,5,4,2,1,6] => 7
[3,5,4,2,6,1] => 6
[3,5,4,6,1,2] => 6
[3,5,4,6,2,1] => 5
[3,5,6,1,2,4] => 7
[3,5,6,1,4,2] => 6
[3,5,6,2,1,4] => 6
[3,5,6,2,4,1] => 5
[3,5,6,4,1,2] => 5
[3,5,6,4,2,1] => 4
[3,6,1,2,4,5] => 9
[3,6,1,2,5,4] => 8
[3,6,1,4,2,5] => 8
[3,6,1,4,5,2] => 7
[3,6,1,5,2,4] => 7
[3,6,1,5,4,2] => 6
[3,6,2,1,4,5] => 8
[3,6,2,1,5,4] => 7
[3,6,2,4,1,5] => 7
[3,6,2,4,5,1] => 6
[3,6,2,5,1,4] => 6
[3,6,2,5,4,1] => 5
[3,6,4,1,2,5] => 7
[3,6,4,1,5,2] => 6
[3,6,4,2,1,5] => 6
[3,6,4,2,5,1] => 5
[3,6,4,5,1,2] => 5
[3,6,4,5,2,1] => 4
[3,6,5,1,2,4] => 6
[3,6,5,1,4,2] => 5
[3,6,5,2,1,4] => 5
[3,6,5,2,4,1] => 4
[3,6,5,4,1,2] => 4
[3,6,5,4,2,1] => 3
[4,1,2,3,5,6] => 12
[4,1,2,3,6,5] => 11
[4,1,2,5,3,6] => 11
[4,1,2,5,6,3] => 10
[4,1,2,6,3,5] => 10
[4,1,2,6,5,3] => 9
[4,1,3,2,5,6] => 11
[4,1,3,2,6,5] => 10
[4,1,3,5,2,6] => 10
[4,1,3,5,6,2] => 9
[4,1,3,6,2,5] => 9
[4,1,3,6,5,2] => 8
[4,1,5,2,3,6] => 10
[4,1,5,2,6,3] => 9
[4,1,5,3,2,6] => 9
[4,1,5,3,6,2] => 8
[4,1,5,6,2,3] => 8
[4,1,5,6,3,2] => 7
[4,1,6,2,3,5] => 9
[4,1,6,2,5,3] => 8
[4,1,6,3,2,5] => 8
[4,1,6,3,5,2] => 7
[4,1,6,5,2,3] => 7
[4,1,6,5,3,2] => 6
[4,2,1,3,5,6] => 11
[4,2,1,3,6,5] => 10
[4,2,1,5,3,6] => 10
[4,2,1,5,6,3] => 9
[4,2,1,6,3,5] => 9
[4,2,1,6,5,3] => 8
[4,2,3,1,5,6] => 10
[4,2,3,1,6,5] => 9
[4,2,3,5,1,6] => 9
[4,2,3,5,6,1] => 8
[4,2,3,6,1,5] => 8
[4,2,3,6,5,1] => 7
[4,2,5,1,3,6] => 9
[4,2,5,1,6,3] => 8
[4,2,5,3,1,6] => 8
[4,2,5,3,6,1] => 7
[4,2,5,6,1,3] => 7
[4,2,5,6,3,1] => 6
[4,2,6,1,3,5] => 8
[4,2,6,1,5,3] => 7
[4,2,6,3,1,5] => 7
[4,2,6,3,5,1] => 6
[4,2,6,5,1,3] => 6
[4,2,6,5,3,1] => 5
[4,3,1,2,5,6] => 10
[4,3,1,2,6,5] => 9
[4,3,1,5,2,6] => 9
[4,3,1,5,6,2] => 8
[4,3,1,6,2,5] => 8
[4,3,1,6,5,2] => 7
[4,3,2,1,5,6] => 9
[4,3,2,1,6,5] => 8
[4,3,2,5,1,6] => 8
[4,3,2,5,6,1] => 7
[4,3,2,6,1,5] => 7
[4,3,2,6,5,1] => 6
[4,3,5,1,2,6] => 8
[4,3,5,1,6,2] => 7
[4,3,5,2,1,6] => 7
[4,3,5,2,6,1] => 6
[4,3,5,6,1,2] => 6
[4,3,5,6,2,1] => 5
[4,3,6,1,2,5] => 7
[4,3,6,1,5,2] => 6
[4,3,6,2,1,5] => 6
[4,3,6,2,5,1] => 5
[4,3,6,5,1,2] => 5
[4,3,6,5,2,1] => 4
[4,5,1,2,3,6] => 9
[4,5,1,2,6,3] => 8
[4,5,1,3,2,6] => 8
[4,5,1,3,6,2] => 7
[4,5,1,6,2,3] => 7
[4,5,1,6,3,2] => 6
[4,5,2,1,3,6] => 8
[4,5,2,1,6,3] => 7
[4,5,2,3,1,6] => 7
[4,5,2,3,6,1] => 6
[4,5,2,6,1,3] => 6
[4,5,2,6,3,1] => 5
[4,5,3,1,2,6] => 7
[4,5,3,1,6,2] => 6
[4,5,3,2,1,6] => 6
[4,5,3,2,6,1] => 5
[4,5,3,6,1,2] => 5
[4,5,3,6,2,1] => 4
[4,5,6,1,2,3] => 6
[4,5,6,1,3,2] => 5
[4,5,6,2,1,3] => 5
[4,5,6,2,3,1] => 4
[4,5,6,3,1,2] => 4
[4,5,6,3,2,1] => 3
[4,6,1,2,3,5] => 8
[4,6,1,2,5,3] => 7
[4,6,1,3,2,5] => 7
[4,6,1,3,5,2] => 6
[4,6,1,5,2,3] => 6
[4,6,1,5,3,2] => 5
[4,6,2,1,3,5] => 7
[4,6,2,1,5,3] => 6
[4,6,2,3,1,5] => 6
[4,6,2,3,5,1] => 5
[4,6,2,5,1,3] => 5
[4,6,2,5,3,1] => 4
[4,6,3,1,2,5] => 6
[4,6,3,1,5,2] => 5
[4,6,3,2,1,5] => 5
[4,6,3,2,5,1] => 4
[4,6,3,5,1,2] => 4
[4,6,3,5,2,1] => 3
[4,6,5,1,2,3] => 5
[4,6,5,1,3,2] => 4
[4,6,5,2,1,3] => 4
[4,6,5,2,3,1] => 3
[4,6,5,3,1,2] => 3
[4,6,5,3,2,1] => 2
[5,1,2,3,4,6] => 11
[5,1,2,3,6,4] => 10
[5,1,2,4,3,6] => 10
[5,1,2,4,6,3] => 9
[5,1,2,6,3,4] => 9
[5,1,2,6,4,3] => 8
[5,1,3,2,4,6] => 10
[5,1,3,2,6,4] => 9
[5,1,3,4,2,6] => 9
[5,1,3,4,6,2] => 8
[5,1,3,6,2,4] => 8
[5,1,3,6,4,2] => 7
[5,1,4,2,3,6] => 9
[5,1,4,2,6,3] => 8
[5,1,4,3,2,6] => 8
[5,1,4,3,6,2] => 7
[5,1,4,6,2,3] => 7
[5,1,4,6,3,2] => 6
[5,1,6,2,3,4] => 8
[5,1,6,2,4,3] => 7
[5,1,6,3,2,4] => 7
[5,1,6,3,4,2] => 6
[5,1,6,4,2,3] => 6
[5,1,6,4,3,2] => 5
[5,2,1,3,4,6] => 10
[5,2,1,3,6,4] => 9
[5,2,1,4,3,6] => 9
[5,2,1,4,6,3] => 8
[5,2,1,6,3,4] => 8
[5,2,1,6,4,3] => 7
[5,2,3,1,4,6] => 9
[5,2,3,1,6,4] => 8
[5,2,3,4,1,6] => 8
[5,2,3,4,6,1] => 7
[5,2,3,6,1,4] => 7
[5,2,3,6,4,1] => 6
[5,2,4,1,3,6] => 8
[5,2,4,1,6,3] => 7
[5,2,4,3,1,6] => 7
[5,2,4,3,6,1] => 6
[5,2,4,6,1,3] => 6
[5,2,4,6,3,1] => 5
[5,2,6,1,3,4] => 7
[5,2,6,1,4,3] => 6
[5,2,6,3,1,4] => 6
[5,2,6,3,4,1] => 5
[5,2,6,4,1,3] => 5
[5,2,6,4,3,1] => 4
[5,3,1,2,4,6] => 9
[5,3,1,2,6,4] => 8
[5,3,1,4,2,6] => 8
[5,3,1,4,6,2] => 7
[5,3,1,6,2,4] => 7
[5,3,1,6,4,2] => 6
[5,3,2,1,4,6] => 8
[5,3,2,1,6,4] => 7
[5,3,2,4,1,6] => 7
[5,3,2,4,6,1] => 6
[5,3,2,6,1,4] => 6
[5,3,2,6,4,1] => 5
[5,3,4,1,2,6] => 7
[5,3,4,1,6,2] => 6
[5,3,4,2,1,6] => 6
[5,3,4,2,6,1] => 5
[5,3,4,6,1,2] => 5
[5,3,4,6,2,1] => 4
[5,3,6,1,2,4] => 6
[5,3,6,1,4,2] => 5
[5,3,6,2,1,4] => 5
[5,3,6,2,4,1] => 4
[5,3,6,4,1,2] => 4
[5,3,6,4,2,1] => 3
[5,4,1,2,3,6] => 8
[5,4,1,2,6,3] => 7
[5,4,1,3,2,6] => 7
[5,4,1,3,6,2] => 6
[5,4,1,6,2,3] => 6
[5,4,1,6,3,2] => 5
[5,4,2,1,3,6] => 7
[5,4,2,1,6,3] => 6
[5,4,2,3,1,6] => 6
[5,4,2,3,6,1] => 5
[5,4,2,6,1,3] => 5
[5,4,2,6,3,1] => 4
[5,4,3,1,2,6] => 6
[5,4,3,1,6,2] => 5
[5,4,3,2,1,6] => 5
[5,4,3,2,6,1] => 4
[5,4,3,6,1,2] => 4
[5,4,3,6,2,1] => 3
[5,4,6,1,2,3] => 5
[5,4,6,1,3,2] => 4
[5,4,6,2,1,3] => 4
[5,4,6,2,3,1] => 3
[5,4,6,3,1,2] => 3
[5,4,6,3,2,1] => 2
[5,6,1,2,3,4] => 7
[5,6,1,2,4,3] => 6
[5,6,1,3,2,4] => 6
[5,6,1,3,4,2] => 5
[5,6,1,4,2,3] => 5
[5,6,1,4,3,2] => 4
[5,6,2,1,3,4] => 6
[5,6,2,1,4,3] => 5
[5,6,2,3,1,4] => 5
[5,6,2,3,4,1] => 4
[5,6,2,4,1,3] => 4
[5,6,2,4,3,1] => 3
[5,6,3,1,2,4] => 5
[5,6,3,1,4,2] => 4
[5,6,3,2,1,4] => 4
[5,6,3,2,4,1] => 3
[5,6,3,4,1,2] => 3
[5,6,3,4,2,1] => 2
[5,6,4,1,2,3] => 4
[5,6,4,1,3,2] => 3
[5,6,4,2,1,3] => 3
[5,6,4,2,3,1] => 2
[5,6,4,3,1,2] => 2
[5,6,4,3,2,1] => 1
[6,1,2,3,4,5] => 10
[6,1,2,3,5,4] => 9
[6,1,2,4,3,5] => 9
[6,1,2,4,5,3] => 8
[6,1,2,5,3,4] => 8
[6,1,2,5,4,3] => 7
[6,1,3,2,4,5] => 9
[6,1,3,2,5,4] => 8
[6,1,3,4,2,5] => 8
[6,1,3,4,5,2] => 7
[6,1,3,5,2,4] => 7
[6,1,3,5,4,2] => 6
[6,1,4,2,3,5] => 8
[6,1,4,2,5,3] => 7
[6,1,4,3,2,5] => 7
[6,1,4,3,5,2] => 6
[6,1,4,5,2,3] => 6
[6,1,4,5,3,2] => 5
[6,1,5,2,3,4] => 7
[6,1,5,2,4,3] => 6
[6,1,5,3,2,4] => 6
[6,1,5,3,4,2] => 5
[6,1,5,4,2,3] => 5
[6,1,5,4,3,2] => 4
[6,2,1,3,4,5] => 9
[6,2,1,3,5,4] => 8
[6,2,1,4,3,5] => 8
[6,2,1,4,5,3] => 7
[6,2,1,5,3,4] => 7
[6,2,1,5,4,3] => 6
[6,2,3,1,4,5] => 8
[6,2,3,1,5,4] => 7
[6,2,3,4,1,5] => 7
[6,2,3,4,5,1] => 6
[6,2,3,5,1,4] => 6
[6,2,3,5,4,1] => 5
[6,2,4,1,3,5] => 7
[6,2,4,1,5,3] => 6
[6,2,4,3,1,5] => 6
[6,2,4,3,5,1] => 5
[6,2,4,5,1,3] => 5
[6,2,4,5,3,1] => 4
[6,2,5,1,3,4] => 6
[6,2,5,1,4,3] => 5
[6,2,5,3,1,4] => 5
[6,2,5,3,4,1] => 4
[6,2,5,4,1,3] => 4
[6,2,5,4,3,1] => 3
[6,3,1,2,4,5] => 8
[6,3,1,2,5,4] => 7
[6,3,1,4,2,5] => 7
[6,3,1,4,5,2] => 6
[6,3,1,5,2,4] => 6
[6,3,1,5,4,2] => 5
[6,3,2,1,4,5] => 7
[6,3,2,1,5,4] => 6
[6,3,2,4,1,5] => 6
[6,3,2,4,5,1] => 5
[6,3,2,5,1,4] => 5
[6,3,2,5,4,1] => 4
[6,3,4,1,2,5] => 6
[6,3,4,1,5,2] => 5
[6,3,4,2,1,5] => 5
[6,3,4,2,5,1] => 4
[6,3,4,5,1,2] => 4
[6,3,4,5,2,1] => 3
[6,3,5,1,2,4] => 5
[6,3,5,1,4,2] => 4
[6,3,5,2,1,4] => 4
[6,3,5,2,4,1] => 3
[6,3,5,4,1,2] => 3
[6,3,5,4,2,1] => 2
[6,4,1,2,3,5] => 7
[6,4,1,2,5,3] => 6
[6,4,1,3,2,5] => 6
[6,4,1,3,5,2] => 5
[6,4,1,5,2,3] => 5
[6,4,1,5,3,2] => 4
[6,4,2,1,3,5] => 6
[6,4,2,1,5,3] => 5
[6,4,2,3,1,5] => 5
[6,4,2,3,5,1] => 4
[6,4,2,5,1,3] => 4
[6,4,2,5,3,1] => 3
[6,4,3,1,2,5] => 5
[6,4,3,1,5,2] => 4
[6,4,3,2,1,5] => 4
[6,4,3,2,5,1] => 3
[6,4,3,5,1,2] => 3
[6,4,3,5,2,1] => 2
[6,4,5,1,2,3] => 4
[6,4,5,1,3,2] => 3
[6,4,5,2,1,3] => 3
[6,4,5,2,3,1] => 2
[6,4,5,3,1,2] => 2
[6,4,5,3,2,1] => 1
[6,5,1,2,3,4] => 6
[6,5,1,2,4,3] => 5
[6,5,1,3,2,4] => 5
[6,5,1,3,4,2] => 4
[6,5,1,4,2,3] => 4
[6,5,1,4,3,2] => 3
[6,5,2,1,3,4] => 5
[6,5,2,1,4,3] => 4
[6,5,2,3,1,4] => 4
[6,5,2,3,4,1] => 3
[6,5,2,4,1,3] => 3
[6,5,2,4,3,1] => 2
[6,5,3,1,2,4] => 4
[6,5,3,1,4,2] => 3
[6,5,3,2,1,4] => 3
[6,5,3,2,4,1] => 2
[6,5,3,4,1,2] => 2
[6,5,3,4,2,1] => 1
[6,5,4,1,2,3] => 3
[6,5,4,1,3,2] => 2
[6,5,4,2,1,3] => 2
[6,5,4,2,3,1] => 1
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 0
[1,2,3,4,5,6,7] => 21
[1,2,3,4,5,7,6] => 20
[1,2,3,4,6,5,7] => 20
[1,2,3,6,4,7,5] => 18
[1,2,6,3,4,7,5] => 17
[1,3,2,4,5,6,7] => 20
[1,3,7,2,4,5,6] => 16
[1,3,7,6,5,4,2] => 10
[1,4,6,7,2,3,5] => 13
[1,4,6,7,5,3,2] => 10
[1,4,7,2,3,5,6] => 15
[1,4,7,6,5,3,2] => 9
[1,5,2,3,4,7,6] => 17
[1,5,2,7,3,4,6] => 15
[1,5,4,7,6,3,2] => 10
[1,5,6,2,7,3,4] => 13
[1,5,6,4,7,3,2] => 10
[1,5,6,7,2,3,4] => 12
[1,5,6,7,4,3,2] => 9
[1,5,7,2,3,4,6] => 14
[1,5,7,6,4,3,2] => 8
[1,6,2,3,4,7,5] => 16
[1,6,2,3,7,4,5] => 15
[1,6,2,7,3,4,5] => 14
[1,6,5,4,3,7,2] => 10
[1,6,5,4,7,3,2] => 9
[1,6,5,7,4,3,2] => 8
[1,6,7,2,3,4,5] => 13
[1,6,7,5,4,3,2] => 7
[1,7,2,3,4,5,6] => 16
[1,7,3,5,6,4,2] => 10
[1,7,3,6,5,4,2] => 9
[1,7,4,3,6,5,2] => 10
[1,7,4,5,3,6,2] => 10
[1,7,4,5,6,3,2] => 9
[1,7,4,6,5,3,2] => 8
[1,7,5,4,3,6,2] => 9
[1,7,5,4,6,3,2] => 8
[1,7,6,4,5,3,2] => 7
[1,7,6,5,4,3,2] => 6
[2,1,3,4,5,6,7] => 20
[2,1,3,4,7,5,6] => 18
[2,1,3,7,4,5,6] => 17
[2,1,6,3,4,5,7] => 17
[2,1,7,3,4,5,6] => 16
[2,1,7,6,5,4,3] => 10
[2,3,1,4,5,6,7] => 19
[2,3,4,1,5,6,7] => 18
[2,3,4,1,5,7,6] => 17
[2,3,4,5,1,6,7] => 17
[2,3,4,5,1,7,6] => 16
[2,3,4,5,6,1,7] => 16
[2,3,4,5,6,7,1] => 15
[2,3,4,5,7,1,6] => 15
[2,3,4,6,1,7,5] => 15
[2,3,4,6,7,1,5] => 14
[2,3,4,7,1,5,6] => 15
[2,3,5,6,7,1,4] => 13
[2,4,1,3,5,6,7] => 18
[2,5,1,3,4,6,7] => 17
[2,5,7,1,3,4,6] => 13
[2,6,1,3,4,5,7] => 16
[2,6,1,7,3,4,5] => 13
[2,6,5,4,3,1,7] => 10
[2,6,7,1,3,4,5] => 12
[2,7,1,3,4,5,6] => 15
[3,1,2,4,5,6,7] => 19
[3,1,2,4,5,7,6] => 18
[3,2,1,4,5,6,7] => 18
[3,2,4,5,6,7,1] => 14
[3,4,1,2,5,6,7] => 17
[3,4,2,5,6,7,1] => 13
[3,4,5,2,6,7,1] => 12
[3,4,5,6,2,7,1] => 11
[3,4,5,6,7,1,2] => 11
[3,5,6,1,2,4,7] => 13
[3,5,6,4,2,1,7] => 10
[3,6,1,2,4,5,7] => 15
[3,6,5,4,2,1,7] => 9
[4,1,2,3,5,6,7] => 18
[4,1,2,3,5,7,6] => 17
[4,1,6,2,3,5,7] => 15
[4,2,3,5,6,7,1] => 13
[4,2,5,1,3,6,7] => 15
[4,3,2,1,5,6,7] => 15
[4,3,2,5,6,7,1] => 12
[4,3,5,2,6,7,1] => 11
[4,3,6,5,2,1,7] => 10
[4,5,1,6,2,3,7] => 13
[4,5,2,3,6,7,1] => 11
[4,5,3,6,2,1,7] => 10
[4,5,6,1,2,3,7] => 12
[4,5,6,3,2,1,7] => 9
[4,6,1,2,3,5,7] => 14
[4,6,1,2,3,7,5] => 13
[4,6,5,3,2,1,7] => 8
[5,1,2,3,4,6,7] => 17
[5,1,2,3,4,7,6] => 16
[5,1,2,3,6,4,7] => 16
[5,1,2,3,6,7,4] => 15
[5,1,2,3,7,4,6] => 15
[5,1,2,6,3,4,7] => 15
[5,1,6,2,3,4,7] => 14
[5,1,6,2,3,7,4] => 13
[5,2,3,4,6,7,1] => 12
[5,2,6,7,1,3,4] => 10
[5,3,2,4,6,7,1] => 11
[5,3,2,6,1,4,7] => 12
[5,3,6,7,1,2,4] => 9
[5,4,3,2,1,6,7] => 11
[5,4,3,2,1,7,6] => 10
[5,4,3,2,6,1,7] => 10
[5,4,3,6,2,1,7] => 9
[5,4,6,3,2,1,7] => 8
[5,4,6,7,1,2,3] => 8
[5,6,1,2,3,4,7] => 13
[5,6,1,2,3,7,4] => 12
[5,6,3,4,1,2,7] => 9
[5,6,4,3,2,1,7] => 7
[5,6,7,1,2,3,4] => 9
[6,1,2,3,4,5,7] => 16
[6,1,2,3,4,7,5] => 15
[6,1,2,3,7,4,5] => 14
[6,1,2,7,3,4,5] => 13
[6,2,3,4,5,7,1] => 11
[6,2,4,5,3,1,7] => 10
[6,2,5,4,3,1,7] => 9
[6,3,2,5,4,1,7] => 10
[6,3,4,2,5,1,7] => 10
[6,3,4,5,2,1,7] => 9
[6,3,4,7,1,2,5] => 9
[6,3,5,4,2,1,7] => 8
[6,4,3,2,5,1,7] => 9
[6,4,3,2,7,1,5] => 8
[6,4,3,5,2,1,7] => 8
[6,4,5,7,1,2,3] => 7
[6,4,7,2,5,1,3] => 6
[6,4,7,3,5,1,2] => 5
[6,5,3,4,2,1,7] => 7
[6,5,4,3,2,1,7] => 6
[6,5,7,3,4,1,2] => 4
[6,7,1,2,3,4,5] => 11
[6,7,3,4,1,2,5] => 7
[6,7,4,5,1,2,3] => 5
[7,1,2,3,4,5,6] => 15
[7,2,1,3,4,5,6] => 14
[7,2,3,1,4,5,6] => 13
[7,2,3,4,1,5,6] => 12
[7,2,3,4,5,1,6] => 11
[7,3,1,2,4,5,6] => 13
[7,3,2,1,4,5,6] => 12
[7,3,2,4,1,5,6] => 11
[7,3,4,1,2,5,6] => 11
[7,4,1,2,3,5,6] => 12
[7,4,2,1,3,5,6] => 11
[7,4,5,6,1,2,3] => 6
[7,5,1,2,3,4,6] => 11
[7,5,6,1,2,3,4] => 7
[7,5,6,3,4,1,2] => 3
[7,6,1,2,3,4,5] => 10
[7,6,4,5,1,2,3] => 4
[7,6,5,1,2,3,4] => 6
[7,6,5,3,4,1,2] => 2
[7,6,5,4,1,2,3] => 3
[7,6,5,4,3,1,2] => 1
[7,6,5,4,3,2,1] => 0
[8,7,6,5,4,3,2,1] => 0
[7,6,8,5,4,3,2,1] => 2
[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] => 4
[6,5,7,4,8,3,2,1] => 6
[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] => 6
[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] => 4
[6,7,8,5,2,3,4,1] => 6
[8,5,6,7,2,3,4,1] => 6
[7,8,3,2,4,5,6,1] => 10
[7,6,5,4,3,2,8,1] => 6
[6,5,7,4,3,2,8,1] => 8
[6,5,4,3,7,2,8,1] => 10
[5,4,6,3,7,2,8,1] => 12
[3,4,5,2,6,7,8,1] => 18
[5,2,3,4,6,7,8,1] => 18
[4,3,2,5,6,7,8,1] => 18
[3,4,2,5,6,7,8,1] => 19
[4,2,3,5,6,7,8,1] => 19
[3,2,4,5,6,7,8,1] => 20
[2,3,4,5,6,7,8,1] => 21
[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] => 3
[7,8,5,6,3,4,1,2] => 4
[5,6,7,8,3,4,1,2] => 8
[7,8,3,4,5,6,1,2] => 8
[3,4,5,6,7,8,1,2] => 16
[8,7,6,5,4,2,1,3] => 2
[7,6,8,5,4,2,1,3] => 4
[8,7,6,5,4,1,2,3] => 3
[6,7,8,5,4,1,2,3] => 6
[8,5,6,7,4,1,2,3] => 6
[8,7,6,4,5,1,2,3] => 4
[8,6,7,4,5,1,2,3] => 5
[8,7,4,5,6,1,2,3] => 6
[7,8,4,5,6,1,2,3] => 7
[6,7,4,5,8,1,2,3] => 9
[7,6,5,8,3,2,1,4] => 6
[7,5,6,8,2,3,1,4] => 8
[6,7,5,8,3,1,2,4] => 8
[6,5,7,8,2,1,3,4] => 10
[8,7,6,5,1,2,3,4] => 6
[8,7,5,6,1,2,3,4] => 7
[7,8,5,6,1,2,3,4] => 8
[8,5,6,7,1,2,3,4] => 9
[5,6,7,8,1,2,3,4] => 12
[8,7,6,4,3,2,1,5] => 4
[8,7,6,4,2,1,3,5] => 6
[8,7,6,1,2,3,4,5] => 10
[8,6,7,1,2,3,4,5] => 11
[6,7,8,1,2,3,4,5] => 13
[7,8,5,4,2,1,3,6] => 8
[7,8,5,4,1,2,3,6] => 9
[8,7,1,2,3,4,5,6] => 15
[7,8,1,2,3,4,5,6] => 16
[8,6,5,4,3,2,1,7] => 6
[8,6,5,4,3,1,2,7] => 7
[8,5,6,3,4,1,2,7] => 9
[8,6,5,4,2,1,3,7] => 8
[8,6,4,3,2,1,5,7] => 10
[8,6,4,2,1,3,5,7] => 12
[8,2,3,4,1,5,6,7] => 18
[8,4,1,2,3,5,6,7] => 18
[8,3,2,1,4,5,6,7] => 18
[8,2,3,1,4,5,6,7] => 19
[8,3,1,2,4,5,6,7] => 19
[8,2,1,3,4,5,6,7] => 20
[8,1,2,3,4,5,6,7] => 21
[7,6,5,4,3,2,1,8] => 7
[6,7,5,4,3,2,1,8] => 8
[6,5,7,4,3,2,1,8] => 9
[5,6,7,4,3,2,1,8] => 10
[7,6,4,5,3,2,1,8] => 8
[6,5,4,7,3,2,1,8] => 10
[7,5,6,3,4,2,1,8] => 9
[7,6,4,3,5,2,1,8] => 9
[7,6,3,4,5,2,1,8] => 10
[7,5,4,3,6,2,1,8] => 10
[6,7,5,4,2,3,1,8] => 9
[6,5,7,3,2,4,1,8] => 11
[5,6,7,2,3,4,1,8] => 13
[2,3,4,5,6,7,1,8] => 22
[5,6,7,1,2,3,4,8] => 16
[6,7,1,2,3,4,5,8] => 18
[7,1,2,3,4,5,6,8] => 22
[6,5,4,3,2,1,7,8] => 13
[2,3,4,5,6,1,7,8] => 23
[5,6,3,4,1,2,7,8] => 16
[4,5,6,1,2,3,7,8] => 19
[6,1,2,3,4,5,7,8] => 23
[5,4,3,2,1,6,7,8] => 18
[2,3,4,5,1,6,7,8] => 24
[5,1,2,3,4,6,7,8] => 24
[4,3,2,1,5,6,7,8] => 22
[3,4,1,2,5,6,7,8] => 24
[3,2,1,4,5,6,7,8] => 25
[2,1,3,4,5,6,7,8] => 27
[1,2,3,4,5,6,7,8] => 28
[6,5,8,7,4,3,2,1] => 4
[3,5,8,7,6,4,2,1] => 8
[4,3,6,5,8,7,2,1] => 12
[2,6,8,7,5,4,3,1] => 8
[2,3,5,6,8,7,4,1] => 16
[3,2,6,5,4,8,7,1] => 16
[4,3,6,5,7,2,8,1] => 14
[3,2,6,5,7,4,8,1] => 16
[4,3,5,2,7,6,8,1] => 16
[3,2,5,4,7,6,8,1] => 18
[1,8,7,6,5,4,3,2] => 7
[1,7,8,6,5,4,3,2] => 8
[1,6,8,7,5,4,3,2] => 9
[1,7,6,8,5,4,3,2] => 9
[1,6,7,8,5,4,3,2] => 10
[1,5,8,7,6,4,3,2] => 10
[1,7,6,5,8,4,3,2] => 10
[1,3,5,7,8,6,4,2] => 16
[1,4,3,8,7,6,5,2] => 15
[1,6,5,4,3,8,7,2] => 15
[1,4,3,6,5,8,7,2] => 19
[2,1,8,7,6,5,4,3] => 12
[2,1,6,5,7,4,8,3] => 18
[2,1,5,4,7,6,8,3] => 20
[1,2,6,7,8,5,4,3] => 16
[3,2,1,8,7,6,5,4] => 15
[3,2,1,6,5,8,7,4] => 19
[1,2,3,5,6,7,8,4] => 24
[4,3,2,1,8,7,6,5] => 16
[3,4,2,1,7,8,6,5] => 18
[2,4,3,1,6,8,7,5] => 20
[2,4,3,1,7,6,8,5] => 20
[3,2,4,1,6,8,7,5] => 20
[3,2,4,1,7,6,8,5] => 20
[2,3,4,1,6,7,8,5] => 22
[2,1,4,3,8,7,6,5] => 20
[2,1,4,3,6,8,7,5] => 22
[2,1,4,3,7,6,8,5] => 22
[5,4,3,2,1,8,7,6] => 15
[3,2,5,4,1,8,7,6] => 19
[3,2,1,4,5,8,7,6] => 22
[2,3,1,4,5,7,8,6] => 24
[6,5,4,3,2,1,8,7] => 12
[4,3,5,2,6,1,8,7] => 18
[3,2,5,4,6,1,8,7] => 20
[2,3,4,5,6,1,8,7] => 22
[2,1,6,5,4,3,8,7] => 20
[2,1,4,6,5,3,8,7] => 22
[2,1,5,4,6,3,8,7] => 22
[4,3,2,1,6,5,8,7] => 20
[2,4,3,1,6,5,8,7] => 22
[3,2,4,1,6,5,8,7] => 22
[2,1,4,3,6,5,8,7] => 24
[2,1,3,4,5,6,8,7] => 26
[1,2,3,4,5,6,8,7] => 27
[5,7,6,4,3,2,1,8] => 9
[4,7,6,5,3,2,1,8] => 10
[3,2,7,6,5,4,1,8] => 15
[5,4,3,2,7,6,1,8] => 15
[3,2,5,4,7,6,1,8] => 19
[1,4,3,2,7,6,5,8] => 22
[1,3,4,2,6,7,5,8] => 24
[1,3,2,5,4,7,6,8] => 25
[1,2,3,5,4,7,6,8] => 26
[1,3,2,4,5,7,6,8] => 26
[1,2,3,4,5,7,6,8] => 27
[1,2,4,3,6,5,7,8] => 26
[1,3,2,5,4,6,7,8] => 26
[1,2,3,5,4,6,7,8] => 27
[1,3,2,4,5,6,7,8] => 27
[1,8,4,7,6,5,3,2] => 10
[1,8,5,4,7,6,3,2] => 11
[1,8,7,4,5,6,3,2] => 10
[1,8,7,4,6,5,3,2] => 9
[1,8,6,5,4,7,3,2] => 10
[1,8,7,5,4,6,3,2] => 9
[1,8,7,5,6,4,3,2] => 8
[2,1,4,5,8,6,7,3] => 20
[2,1,8,5,4,7,6,3] => 16
[2,3,4,8,5,6,7,1] => 18
[2,3,6,4,5,1,8,7] => 20
[2,3,7,4,5,6,8,1] => 18
[2,8,4,3,5,7,6,1] => 14
[4,2,3,1,8,6,7,5] => 18
[8,2,7,4,6,5,3,1] => 7
[4,3,2,7,5,6,8,1] => 16
[4,3,2,8,5,7,6,1] => 14
[6,3,2,5,4,1,8,7] => 16
[8,3,2,5,4,7,6,1] => 12
[8,3,2,7,6,5,4,1] => 8
[8,3,7,4,6,5,2,1] => 6
[7,3,6,5,4,2,1,8] => 10
[7,4,3,6,5,2,1,8] => 11
[7,6,3,5,4,2,1,8] => 9
[8,5,4,3,2,7,6,1] => 8
[8,7,4,3,6,5,2,1] => 4
[2,4,6,8,1,3,5,7] => 18
[2,4,6,1,7,3,8,5] => 19
[2,1,4,3,7,5,8,6] => 23
[2,4,1,3,7,5,8,6] => 22
[2,1,4,3,7,8,5,6] => 22
[2,4,7,8,1,3,5,6] => 17
[2,1,4,3,8,5,6,7] => 23
[2,4,5,6,7,1,8,3] => 18
[2,1,5,3,6,4,8,7] => 23
[2,1,5,6,3,4,8,7] => 22
[2,5,6,8,1,3,4,7] => 17
[2,1,5,3,7,4,8,6] => 22
[2,5,1,7,3,4,8,6] => 20
[2,1,5,7,3,8,4,6] => 20
[2,5,7,8,1,3,4,6] => 16
[2,3,5,6,1,7,8,4] => 20
[2,1,6,3,7,4,8,5] => 21
[2,6,7,1,3,4,8,5] => 18
[2,1,6,7,8,3,4,5] => 18
[2,6,7,8,1,3,4,5] => 15
[2,1,6,3,4,7,8,5] => 22
[2,1,6,3,4,5,8,7] => 23
[2,6,1,3,4,5,7,8] => 23
[2,7,8,1,3,4,5,6] => 17
[2,7,1,3,4,5,6,8] => 22
[2,3,4,5,7,8,1,6] => 20
[2,1,8,3,4,5,6,7] => 22
[2,8,1,3,4,5,6,7] => 21
[2,1,3,8,4,5,6,7] => 23
[2,3,4,5,6,8,1,7] => 21
[3,1,4,2,6,5,8,7] => 23
[3,4,1,2,6,5,8,7] => 22
[3,1,4,2,6,8,5,7] => 22
[3,4,6,8,1,2,5,7] => 17
[3,1,4,2,7,5,8,6] => 22
[3,4,1,2,7,8,5,6] => 20
[3,4,7,8,1,2,5,6] => 16
[3,1,5,2,6,4,8,7] => 22
[3,5,1,6,2,4,8,7] => 20
[3,1,5,6,2,8,4,7] => 20
[3,5,6,8,1,2,4,7] => 16
[3,1,5,2,7,4,8,6] => 21
[3,5,1,7,2,8,4,6] => 18
[3,5,7,8,1,2,4,6] => 15
[1,3,2,5,4,8,6,7] => 24
[1,3,5,8,2,4,6,7] => 21
[1,3,5,6,2,7,4,8] => 22
[3,1,6,2,7,4,8,5] => 20
[3,6,7,1,2,8,4,5] => 16
[3,6,1,7,8,2,4,5] => 16
[3,6,7,8,1,2,4,5] => 14
[1,3,2,6,4,7,5,8] => 24
[3,1,2,6,7,4,8,5] => 21
[1,3,2,6,4,8,5,7] => 23
[1,3,2,6,4,5,7,8] => 25
[1,3,2,7,4,8,5,6] => 22
[1,3,2,7,4,5,6,8] => 24
[1,3,2,8,4,5,6,7] => 23
[3,1,2,4,5,8,6,7] => 24
[1,3,2,4,5,8,6,7] => 25
[4,1,5,2,6,3,8,7] => 21
[4,5,6,1,2,3,8,7] => 18
[4,1,5,6,8,2,3,7] => 18
[4,5,6,8,1,2,3,7] => 15
[4,1,5,2,7,3,8,6] => 20
[4,1,5,2,7,8,3,6] => 19
[4,5,7,1,2,8,3,6] => 16
[4,5,1,7,8,2,3,6] => 16
[4,5,7,8,1,2,3,6] => 14
[1,4,2,5,3,7,6,8] => 24
[1,4,2,5,3,8,6,7] => 23
[1,4,2,5,3,6,7,8] => 25
[1,4,5,6,7,2,3,8] => 20
[4,1,6,2,7,3,8,5] => 19
[4,6,7,1,8,2,3,5] => 14
[4,6,7,8,1,2,3,5] => 13
[1,4,2,6,3,7,5,8] => 23
[1,4,2,6,7,8,3,5] => 20
[1,4,2,6,3,8,5,7] => 22
[4,1,2,3,6,5,8,7] => 23
[1,4,2,6,3,5,7,8] => 24
[1,4,2,7,3,8,5,6] => 21
[4,7,1,2,3,5,6,8] => 20
[1,4,2,7,3,5,6,8] => 23
[1,4,2,3,7,5,6,8] => 24
[1,4,2,3,5,7,6,8] => 25
[1,4,2,8,3,5,6,7] => 22
[4,1,2,3,8,5,6,7] => 22
[1,4,2,3,5,8,6,7] => 24
[1,4,2,3,5,6,7,8] => 26
[5,1,6,2,7,3,8,4] => 18
[1,5,2,6,3,7,4,8] => 22
[1,5,2,6,3,8,4,7] => 21
[1,5,2,6,3,4,7,8] => 23
[1,2,5,6,3,4,7,8] => 24
[1,5,2,7,3,8,4,6] => 20
[5,7,1,2,3,4,6,8] => 19
[1,5,2,7,3,4,6,8] => 22
[1,5,2,3,4,7,6,8] => 24
[5,1,2,8,3,4,6,7] => 20
[1,5,2,8,3,4,6,7] => 21
[1,5,8,2,3,4,6,7] => 20
[1,5,2,3,4,8,6,7] => 23
[1,2,3,5,4,8,6,7] => 25
[5,1,2,3,4,6,8,7] => 23
[1,5,2,3,4,6,7,8] => 25
[1,6,2,7,3,8,4,5] => 19
[1,6,7,8,2,3,4,5] => 16
[6,7,1,2,3,4,8,5] => 17
[6,1,7,2,3,4,5,8] => 19
[6,1,2,7,3,4,5,8] => 20
[1,6,2,7,3,4,5,8] => 21
[1,6,7,2,3,4,5,8] => 20
[1,6,2,3,4,7,5,8] => 23
[1,2,3,6,4,7,5,8] => 25
[6,1,8,2,3,4,5,7] => 18
[1,6,2,8,3,4,5,7] => 20
[1,6,8,2,3,4,5,7] => 19
[1,6,2,3,4,8,5,7] => 22
[1,2,3,6,4,8,5,7] => 24
[6,1,2,3,4,5,8,7] => 22
[1,6,2,3,4,5,7,8] => 24
[1,2,3,6,4,5,7,8] => 26
[1,7,2,8,3,4,5,6] => 19
[1,7,8,2,3,4,5,6] => 18
[1,7,2,3,8,4,5,6] => 20
[7,1,2,3,4,8,5,6] => 20
[1,7,2,3,4,8,5,6] => 21
[1,2,3,7,4,8,5,6] => 23
[7,1,2,3,4,5,8,6] => 21
[1,7,2,3,4,5,8,6] => 22
[1,2,7,3,4,5,8,6] => 23
[1,7,2,3,4,5,6,8] => 23
[1,2,3,7,4,5,6,8] => 25
[1,8,2,3,4,5,6,7] => 22
[1,2,3,8,4,5,6,7] => 24
[1,2,3,4,5,8,6,7] => 26
[5,3,2,6,1,4,8,7] => 18
[7,3,2,5,4,8,1,6] => 14
[8,4,5,2,3,7,6,1] => 10
[7,4,5,2,3,8,1,6] => 12
[6,4,5,2,3,1,8,7] => 14
[5,4,6,2,1,3,8,7] => 16
[3,6,1,5,4,2,8,7] => 18
[4,6,5,1,3,2,8,7] => 16
[5,6,4,3,1,2,8,7] => 14
[7,5,4,3,2,8,1,6] => 10
[8,6,4,3,7,2,5,1] => 6
[7,6,4,3,8,2,1,5] => 8
[6,7,4,3,8,1,2,5] => 10
[5,7,4,3,1,8,2,6] => 12
[4,7,5,1,3,8,2,6] => 14
[3,7,1,5,4,8,2,6] => 16
[2,1,7,5,4,8,3,6] => 18
[3,8,1,5,4,7,6,2] => 14
[4,8,5,1,3,7,6,2] => 12
[5,8,4,3,1,7,6,2] => 10
[6,8,4,3,7,1,5,2] => 8
[7,8,4,3,6,5,1,2] => 6
[6,8,5,7,3,1,4,2] => 6
[5,8,6,7,1,3,4,2] => 8
[4,8,6,1,7,3,5,2] => 10
[3,8,1,6,7,4,5,2] => 12
[2,1,8,6,7,4,5,3] => 14
[2,1,7,6,8,4,3,5] => 16
[3,7,1,6,8,4,2,5] => 14
[4,7,6,1,8,3,2,5] => 12
[5,7,6,8,1,3,2,4] => 10
[5,4,7,2,1,8,3,6] => 14
[6,4,7,2,8,1,3,5] => 12
[7,4,6,2,8,3,1,5] => 10
[8,4,6,2,7,3,5,1] => 8
[8,3,2,6,7,4,5,1] => 10
[7,3,2,6,8,4,1,5] => 12
[6,3,2,7,8,1,4,5] => 14
[5,3,2,7,1,8,4,6] => 16
[4,3,2,1,7,8,5,6] => 18
[3,4,1,2,8,7,6,5] => 18
[5,3,2,8,1,7,6,4] => 14
[6,3,2,8,7,1,5,4] => 12
[7,3,2,8,6,5,1,4] => 10
[8,4,7,2,6,5,3,1] => 6
[7,4,8,2,6,5,1,3] => 8
[6,4,8,2,7,1,5,3] => 10
[5,4,8,2,1,7,6,3] => 12
[4,5,8,1,2,7,6,3] => 14
[3,5,1,8,2,7,6,4] => 16
[2,1,5,8,3,7,6,4] => 18
[2,1,6,8,7,3,5,4] => 16
[3,6,1,8,7,2,5,4] => 14
[4,6,8,1,7,2,5,3] => 12
[5,6,8,7,1,2,4,3] => 10
[6,5,8,7,2,1,4,3] => 8
[7,5,8,6,2,4,1,3] => 6
[8,5,7,6,2,4,3,1] => 4
[5,7,8,6,1,4,2,3] => 8
[4,7,8,1,6,5,2,3] => 10
[3,7,1,8,6,5,2,4] => 12
[2,1,7,8,6,5,3,4] => 14
[3,8,1,7,6,5,4,2] => 10
[4,8,7,1,6,5,3,2] => 8
[5,8,7,6,1,4,3,2] => 6
[6,8,7,5,4,1,3,2] => 4
[4,2,5,1,3,6,7,8] => 22
[5,2,6,7,1,3,4,8] => 17
[3,2,7,8,1,4,5,6] => 17
[5,3,2,6,1,4,7,8] => 19
[7,4,3,8,1,2,5,6] => 13
[4,7,3,6,8,1,2,5] => 12
[6,7,3,4,8,1,2,5] => 11
[5,4,2,7,8,1,3,6] => 14
[6,4,7,2,5,1,3,8] => 13
[6,4,3,2,7,1,5,8] => 15
[5,4,3,2,8,1,6,7] => 15
[7,5,3,8,2,6,1,4] => 9
[8,5,4,7,2,6,1,3] => 7
[8,5,4,7,3,6,1,2] => 6
[8,1,2,7,6,3,4,5] => 14
[8,1,4,2,6,3,5,7] => 17
[8,3,1,2,4,7,5,6] => 17
[8,3,1,5,6,2,4,7] => 15
[6,3,8,1,2,7,4,5] => 14
[7,8,4,1,6,2,3,5] => 10
[8,3,4,1,6,7,2,5] => 13
[2,7,6,5,1,3,8,4] => 14
[8,3,6,5,1,7,2,4] => 10
[4,6,7,3,8,5,1,2] => 10
[3,5,2,7,1,8,6,4] => 16
[4,6,7,2,8,1,5,3] => 12
[5,6,7,8,2,1,4,3] => 10
[6,5,8,7,3,4,1,2] => 6
[3,6,7,4,5,8,1,2] => 12
[2,6,7,4,5,1,8,3] => 14
[1,6,7,4,5,2,3,8] => 16
[1,5,4,7,6,2,3,8] => 18
[2,5,4,7,6,1,8,3] => 16
[3,5,4,7,6,8,1,2] => 14
[4,5,3,7,8,6,1,2] => 12
[5,4,3,8,7,6,1,2] => 10
[6,4,8,3,7,5,1,2] => 8
[6,3,8,4,5,7,1,2] => 10
[5,3,4,8,6,7,1,2] => 12
[4,3,5,6,8,7,1,2] => 14
[3,2,5,6,1,8,7,4] => 18
[4,2,5,6,8,1,7,3] => 16
[5,2,4,8,6,1,7,3] => 14
[6,2,8,4,5,1,7,3] => 12
[7,8,2,4,5,1,6,3] => 10
[7,8,1,4,5,2,3,6] => 12
[6,1,8,4,5,2,3,7] => 14
[5,1,4,8,6,2,3,7] => 16
[4,1,3,2,8,6,5,7] => 20
[5,1,3,8,2,6,4,7] => 18
[6,1,8,3,2,5,4,7] => 16
[7,8,1,3,2,5,4,6] => 14
[7,8,2,3,1,5,6,4] => 12
[6,2,8,3,1,5,7,4] => 14
[5,2,3,8,1,6,7,4] => 16
[6,3,8,2,1,7,5,4] => 12
[7,8,3,2,1,6,5,4] => 10
[7,8,4,2,6,1,5,3] => 8
[5,4,2,8,7,1,6,3] => 12
[4,5,2,7,8,1,6,3] => 14
[2,5,3,7,1,6,8,4] => 18
[1,5,3,7,2,6,4,8] => 20
[1,6,7,3,2,5,4,8] => 18
[2,6,7,3,1,5,8,4] => 16
[3,6,7,2,1,8,5,4] => 14
[7,8,5,6,2,1,4,3] => 6
[6,5,8,7,1,2,3,4] => 10
[5,4,1,8,7,2,3,6] => 14
[6,4,8,1,7,2,3,5] => 12
[7,8,3,1,2,6,4,5] => 12
[5,3,1,8,2,7,4,6] => 16
[4,3,1,2,8,7,5,6] => 18
[4,2,1,3,8,5,7,6] => 20
[5,2,1,8,3,4,7,6] => 18
[6,2,8,1,3,4,7,5] => 16
[7,8,2,1,3,4,6,5] => 14
[6,3,1,5,2,4,8,7] => 18
[2,1,8,5,3,7,4,6] => 18
[8,2,6,1,4,3,7,5] => 14
[4,7,1,5,8,3,2,6] => 14
[8,6,1,3,4,2,5,7] => 14
[8,1,2,4,5,6,3,7] => 18
[8,2,5,1,3,6,4,7] => 16
[4,1,5,3,7,2,8,6] => 19
[5,2,7,1,3,8,4,6] => 17
[5,3,1,7,8,2,4,6] => 16
[1,7,3,4,2,5,8,6] => 20
[4,7,2,1,3,5,8,6] => 18
[4,5,2,3,7,6,1,8] => 17
[6,4,3,7,2,5,1,8] => 13
[8,4,3,6,5,1,2,7] => 11
[1,5,6,3,4,8,7,2] => 17
[4,6,2,7,3,5,1,8] => 15
[3,2,6,7,4,5,1,8] => 17
[4,7,2,6,5,3,1,8] => 13
[5,7,6,2,4,3,1,8] => 11
[1,7,5,4,8,3,6,2] => 13
[8,7,5,4,1,3,2,6] => 7
[6,8,5,4,2,1,3,7] => 9
[5,8,6,2,4,1,3,7] => 11
[4,8,2,6,5,1,3,7] => 13
[3,2,8,6,5,1,4,7] => 15
[4,1,2,6,5,8,7,3] => 19
[5,1,6,2,4,8,7,3] => 17
[6,1,5,4,2,8,7,3] => 15
[7,1,5,4,8,2,6,3] => 13
[8,1,5,4,7,6,2,3] => 11
[1,8,6,7,4,5,3,2] => 9
[8,1,6,7,4,5,2,3] => 9
[7,1,6,8,4,2,5,3] => 11
[6,1,7,8,2,4,5,3] => 13
[5,1,7,2,8,4,6,3] => 15
[4,1,2,7,8,5,6,3] => 17
[3,2,1,7,8,5,6,4] => 17
[3,2,8,7,1,5,4,6] => 15
[4,8,2,7,1,5,3,6] => 13
[5,8,7,2,1,4,3,6] => 11
[6,8,7,1,2,4,3,5] => 11
[7,8,6,1,4,2,3,5] => 9
[8,7,6,1,4,3,2,5] => 7
[1,7,6,8,4,3,5,2] => 11
[1,6,7,8,3,4,5,2] => 13
[8,6,7,1,3,4,2,5] => 9
[7,6,8,1,3,2,4,5] => 11
[5,7,8,2,1,3,4,6] => 13
[4,7,2,8,1,3,5,6] => 15
[3,2,6,8,4,1,5,7] => 17
[4,6,2,8,3,1,5,7] => 15
[5,6,8,2,3,1,4,7] => 13
[6,5,8,3,2,1,4,7] => 11
[7,5,8,3,1,2,4,6] => 11
[8,5,7,3,1,4,2,6] => 9
[1,5,7,3,8,4,6,2] => 15
[1,4,3,7,8,5,6,2] => 17
[8,4,3,7,1,5,2,6] => 11
[6,4,3,8,2,1,5,7] => 13
[4,5,2,3,8,1,6,7] => 17
[3,2,5,4,8,1,6,7] => 19
[4,5,2,3,1,8,7,6] => 17
[6,4,3,1,2,8,7,5] => 15
[7,4,3,1,8,2,6,5] => 13
[8,4,3,1,7,6,2,5] => 11
[1,5,8,3,7,6,4,2] => 13
[8,5,1,3,7,6,2,4] => 11
[7,5,1,3,8,2,6,4] => 13
[6,5,1,3,2,8,7,4] => 15
[5,6,1,2,3,8,7,4] => 17
[4,6,2,1,3,8,7,5] => 17
[3,2,6,1,4,8,7,5] => 19
[3,2,7,1,8,4,6,5] => 17
[4,7,2,1,8,3,6,5] => 15
[5,7,1,2,8,3,6,4] => 15
[6,7,1,8,2,3,5,4] => 13
[7,6,1,8,3,2,5,4] => 11
[8,6,1,7,3,5,2,4] => 9
[1,6,8,7,3,5,4,2] => 11
[1,7,8,6,5,3,4,2] => 9
[8,7,1,6,5,3,2,4] => 7
[7,8,1,6,5,2,3,4] => 9
[6,8,1,7,2,5,3,4] => 11
[5,8,1,2,7,6,3,4] => 13
[4,8,2,1,7,6,3,5] => 13
[3,2,8,1,7,6,4,5] => 15
[4,1,2,8,7,6,5,3] => 15
[5,1,8,2,7,6,4,3] => 13
[6,1,8,7,2,5,4,3] => 11
[7,1,8,6,5,2,4,3] => 9
[8,1,7,6,5,4,2,3] => 7
[1,4,3,8,7,5,6,2] => 16
[4,1,2,8,7,5,6,3] => 16
[3,2,5,1,6,4,8,7] => 21
[3,2,5,4,7,1,8,6] => 19
[4,2,5,3,7,6,8,1] => 17
[4,2,5,3,7,1,8,6] => 18
[4,2,5,3,6,1,8,7] => 19
[4,2,5,1,6,3,8,7] => 20
[3,1,5,4,6,2,8,7] => 21
[4,1,5,3,6,2,8,7] => 20
[4,3,5,1,6,2,8,7] => 19
[4,3,5,2,7,1,8,6] => 17
[4,3,6,2,7,5,8,1] => 15
[4,3,6,2,7,1,8,5] => 16
[4,3,6,1,7,2,8,5] => 17
[4,3,5,1,7,2,8,6] => 18
[3,1,5,4,7,2,8,6] => 20
[2,1,5,4,7,3,8,6] => 21
[3,1,5,4,7,6,8,2] => 19
[4,1,5,3,7,6,8,2] => 18
[4,3,5,1,7,6,8,2] => 17
[4,3,6,1,7,5,8,2] => 16
[4,3,6,5,7,1,8,2] => 15
[5,3,6,4,7,2,8,1] => 13
[5,3,6,4,7,1,8,2] => 14
[5,3,6,1,7,4,8,2] => 15
[5,1,6,3,7,4,8,2] => 16
[4,1,6,3,7,5,8,2] => 17
[3,1,6,4,7,5,8,2] => 18
[2,1,6,4,7,5,8,3] => 19
[2,1,6,4,7,3,8,5] => 20
[3,1,6,4,7,2,8,5] => 19
[4,1,6,3,7,2,8,5] => 18
[5,1,6,3,7,2,8,4] => 17
[5,3,6,1,7,2,8,4] => 16
[5,3,6,2,7,1,8,4] => 15
[5,3,6,2,7,4,8,1] => 14
[5,2,6,3,7,4,8,1] => 15
[5,2,6,3,7,1,8,4] => 16
[5,2,6,1,7,3,8,4] => 17
[4,2,5,1,7,3,8,6] => 19
[4,2,6,1,7,3,8,5] => 18
[4,2,6,3,7,1,8,5] => 17
[4,2,6,3,7,5,8,1] => 16
[3,2,6,4,7,5,8,1] => 17
[3,2,6,4,7,1,8,5] => 18
[3,2,6,1,7,4,8,5] => 19
[3,2,5,1,7,4,8,6] => 20
[3,2,4,1,7,5,8,6] => 21
[3,1,4,2,7,6,8,5] => 21
[3,2,5,1,7,6,8,4] => 19
[3,2,6,1,7,5,8,4] => 18
[3,2,6,5,7,1,8,4] => 17
[4,2,6,5,7,3,8,1] => 15
[4,2,6,5,7,1,8,3] => 16
[4,2,6,1,7,5,8,3] => 17
[4,2,5,1,7,6,8,3] => 18
[4,1,5,2,7,6,8,3] => 19
[3,1,5,2,7,6,8,4] => 20
[2,1,5,3,7,6,8,4] => 21
[2,1,6,3,7,5,8,4] => 20
[3,1,6,2,7,5,8,4] => 19
[4,1,6,2,7,5,8,3] => 18
[5,1,6,2,7,4,8,3] => 17
[5,2,6,1,7,4,8,3] => 16
[5,2,6,4,7,1,8,3] => 15
[5,2,6,4,7,3,8,1] => 14
[5,4,6,2,7,3,8,1] => 13
[5,4,6,2,7,1,8,3] => 14
[5,4,6,1,7,2,8,3] => 15
[5,1,6,4,7,2,8,3] => 16
[4,1,6,5,7,2,8,3] => 17
[3,1,6,5,7,2,8,4] => 18
[2,1,6,5,7,3,8,4] => 19
[3,1,6,5,7,4,8,2] => 17
[4,1,6,5,7,3,8,2] => 16
[5,1,6,4,7,3,8,2] => 15
[5,4,6,1,7,3,8,2] => 14
[5,4,6,3,7,1,8,2] => 13
[8,3,5,2,1,6,4,7] => 14
[8,6,3,5,2,4,1,7] => 9
[3,7,5,2,4,1,8,6] => 15
[8,3,7,5,2,4,6,1] => 8
[8,2,4,5,7,3,6,1] => 11
[2,4,5,7,3,1,8,6] => 18
[8,2,4,6,5,3,1,7] => 12
[8,2,5,4,6,1,3,7] => 13
[8,6,3,5,1,4,2,7] => 10
[8,6,1,4,5,3,2,7] => 11
[8,1,5,6,4,3,2,7] => 12
[5,7,4,3,2,1,8,6] => 12
[8,5,7,4,3,2,6,1] => 5
[4,6,8,3,2,7,5,1] => 10
[4,7,6,3,2,8,1,5] => 11
[1,4,6,7,3,2,8,5] => 18
[5,4,7,3,1,8,2,6] => 13
[1,7,4,5,3,2,8,6] => 17
[3,7,5,1,4,2,8,6] => 16
[5,7,4,2,1,3,8,6] => 14
[8,5,7,4,2,1,6,3] => 7
[8,3,7,5,1,4,6,2] => 9
[8,4,1,7,5,3,6,2] => 10
[4,6,3,8,7,1,5,2] => 11
[1,7,4,8,6,3,5,2] => 12
[8,4,7,6,3,5,2,1] => 4
[3,6,5,8,7,4,1,2] => 10
[3,1,5,8,6,7,4,2] => 15
[4,8,1,6,7,3,5,2] => 11
[3,6,4,1,8,7,5,2] => 14
[8,2,6,1,4,7,5,3] => 12
[2,7,6,8,1,4,3,5] => 13
[3,7,1,6,4,8,2,5] => 15
[1,7,3,5,6,8,2,4] => 16
[1,3,6,7,5,8,2,4] => 17
[3,7,6,5,8,2,1,4] => 10
[3,6,8,5,7,2,4,1] => 9
[2,3,5,7,6,8,1,4] => 17
[2,1,6,5,7,8,3,4] => 18
[4,2,7,6,8,3,1,5] => 13
[4,2,6,8,7,3,5,1] => 12
[3,8,2,4,6,7,5,1] => 13
[3,7,2,6,4,8,1,5] => 14
[3,2,6,1,4,7,8,5] => 20
[5,3,7,2,1,8,4,6] => 15
[4,7,3,2,1,5,8,6] => 16
[8,7,6,1,3,4,2,5] => 8
[8,5,7,3,2,1,6,4] => 8
[8,3,6,7,2,1,5,4] => 9
[3,7,8,6,2,1,5,4] => 10
[8,7,6,3,5,2,4,1] => 3
[2,7,4,8,1,6,5,3] => 13
[4,6,8,2,1,7,5,3] => 12
[8,4,1,5,7,2,6,3] => 12
[8,5,3,7,1,6,2,4] => 9
[8,5,7,2,1,3,6,4] => 10
[8,2,6,7,1,3,5,4] => 11
[8,3,6,1,7,5,2,4] => 10
[4,6,1,8,7,2,5,3] => 13
[8,1,2,5,6,7,4,3] => 14
[8,2,6,5,7,4,1,3] => 8
[2,1,7,8,5,6,4,3] => 14
[8,2,5,7,6,4,3,1] => 7
[2,7,6,8,5,4,1,3] => 9
[1,7,2,5,8,6,4,3] => 15
[1,7,4,8,2,6,5,3] => 14
[3,7,8,1,6,5,2,4] => 11
[2,7,8,6,1,3,5,4] => 12
[8,7,6,3,5,1,4,2] => 4
[8,4,7,6,5,1,3,2] => 5
[8,7,1,5,6,4,3,2] => 6
[8,1,6,7,5,4,3,2] => 7
[5,4,3,6,1,2,8,7] => 16
[2,7,6,4,5,8,1,3] => 12
[5,7,3,6,1,8,2,4] => 12
[2,1,7,6,5,8,3,4] => 16
[6,4,3,5,8,1,7,2] => 12
[7,3,5,4,8,6,1,2] => 10
[5,4,3,2,7,1,8,6] => 15
[4,3,6,2,8,7,5,1] => 13
[4,3,7,6,2,1,8,5] => 14
[6,4,3,1,7,2,8,5] => 15
[4,3,7,1,8,6,5,2] => 13
[5,3,8,7,6,4,2,1] => 7
[7,5,3,1,8,6,4,2] => 10
[1,8,6,5,3,7,4,2] => 11
[6,1,7,5,3,2,8,4] => 14
[7,6,5,3,2,1,8,4] => 9
[6,5,3,2,8,7,4,1] => 10
[5,2,6,3,8,7,4,1] => 13
[5,2,7,6,3,1,8,4] => 14
[6,5,2,1,7,3,8,4] => 15
[5,2,7,1,8,6,4,3] => 13
[6,2,8,7,5,4,3,1] => 7
[7,6,2,1,8,5,4,3] => 10
[6,1,7,2,8,5,4,3] => 13
[7,1,8,6,5,4,3,2] => 7
[4,5,2,6,3,1,8,7] => 17
[6,5,2,1,4,3,8,7] => 16
[6,5,2,7,4,8,3,1] => 10
[8,5,2,7,4,1,6,3] => 9
[8,3,7,5,2,1,6,4] => 9
[6,3,7,5,2,8,4,1] => 10
[3,1,6,5,4,2,8,7] => 19
[5,6,3,2,4,1,8,7] => 15
[3,6,2,4,1,5,8,7] => 19
[2,6,1,3,5,4,8,7] => 21
[6,7,2,3,4,8,5,1] => 12
[8,7,2,3,4,1,6,5] => 11
[5,1,7,3,8,4,6,2] => 14
[2,5,7,3,8,6,4,1] => 13
[7,6,1,3,5,8,4,2] => 11
[3,6,7,4,1,8,5,2] => 13
[5,6,3,7,4,8,1,2] => 11
[2,1,6,7,4,8,5,3] => 17
[2,1,8,7,4,3,6,5] => 16
[5,8,3,7,4,2,6,1] => 8
[3,8,7,4,1,2,6,5] => 12
[7,8,1,3,5,2,6,4] => 12
[5,8,7,3,2,6,1,4] => 8
[2,8,6,3,1,5,7,4] => 14
[8,1,6,3,2,5,4,7] => 15
[2,8,4,1,6,3,7,5] => 16
[4,8,1,2,7,6,3,5] => 14
[3,8,4,2,5,7,1,6] => 14
[6,8,3,5,2,7,4,1] => 8
[2,1,5,3,8,7,6,4] => 19
[6,5,3,2,8,7,1,4] => 11
[7,5,2,4,8,1,6,3] => 11
[3,4,2,8,5,7,6,1] => 15
[2,4,1,8,7,6,5,3] => 15
[8,4,2,1,7,5,3,6] => 13
[4,3,1,8,6,7,5,2] => 14
[3,1,4,8,6,5,7,2] => 17
[7,1,6,5,4,8,2,3] => 11
[3,7,5,6,8,4,2,1] => 9
[5,7,1,6,8,2,4,3] => 12
[8,6,2,5,1,7,4,3] => 9
[5,6,2,1,8,7,3,4] => 14
[4,6,2,5,8,3,7,1] => 13
[7,5,2,6,3,8,1,4] => 11
[4,1,2,3,6,8,7,5] => 21
[2,4,3,1,8,5,6,7] => 21
[7,5,2,8,3,4,6,1] => 10
[5,6,2,8,4,3,1,7] => 12
[4,7,2,8,1,5,3,6] => 14
[8,7,2,1,4,5,6,3] => 11
[3,6,8,7,1,5,4,2] => 10
[5,7,8,6,3,4,1,2] => 6
[7,1,8,5,4,3,6,2] => 10
[2,7,8,4,5,3,6,1] => 11
[5,7,3,8,1,4,6,2] => 11
[2,1,7,8,5,4,6,3] => 15
[2,1,5,8,4,6,3,7] => 19
[6,5,3,8,4,1,2,7] => 11
[7,5,8,4,3,6,2,1] => 5
[2,4,8,3,5,6,1,7] => 17
[4,1,8,3,6,5,2,7] => 16
[3,4,8,1,7,2,5,6] => 16
[8,4,1,3,7,2,6,5] => 13
[3,1,8,2,4,7,6,5] => 18
[2,3,8,1,4,6,7,5] => 19
[4,3,8,2,5,1,7,6] => 15
[6,3,8,4,2,5,7,1] => 11
[7,4,3,8,2,5,1,6] => 11
[2,1,4,8,3,5,7,6] => 21
[6,8,2,4,3,5,1,7] => 12
[4,8,2,3,5,1,6,7] => 16
[3,8,2,1,4,6,5,7] => 18
[2,8,1,3,4,5,7,6] => 20
[7,1,6,8,4,3,2,5] => 11
[7,1,6,5,8,3,2,4] => 11
[3,7,6,1,4,8,2,5] => 14
[2,7,8,4,1,6,5,3] => 12
[3,6,4,5,7,2,8,1] => 14
[1,8,2,7,3,4,5,6] => 18
[3,2,1,5,8,4,6,7] => 21
[5,4,3,2,1,8,6,7] => 16
[1,8,2,4,3,5,6,7] => 21
[1,7,2,4,3,5,6,8] => 22
[1,6,2,4,3,5,7,8] => 23
[1,5,2,4,3,6,7,8] => 24
[1,6,2,5,3,4,7,8] => 22
[1,7,2,5,3,4,6,8] => 21
[1,8,2,5,3,4,6,7] => 20
[1,8,2,6,3,4,5,7] => 19
[1,7,2,6,3,4,5,8] => 20
[1,8,2,7,3,5,4,6] => 17
[1,7,2,8,3,5,4,6] => 18
[1,6,2,8,3,5,4,7] => 19
[1,5,2,8,3,6,4,7] => 20
[1,4,2,8,3,6,5,7] => 21
[1,3,2,8,4,6,5,7] => 22
[1,2,3,8,4,6,5,7] => 23
[1,2,3,7,4,6,5,8] => 24
[1,3,2,7,4,6,5,8] => 23
[1,4,2,7,3,6,5,8] => 22
[1,5,2,7,3,6,4,8] => 21
[1,6,2,7,3,5,4,8] => 20
[1,7,2,6,3,5,4,8] => 19
[1,8,2,6,3,5,4,7] => 18
[1,8,2,5,3,6,4,7] => 19
[1,7,2,5,3,6,4,8] => 20
[1,6,2,5,3,7,4,8] => 21
[1,5,2,4,3,7,6,8] => 23
[1,6,2,4,3,7,5,8] => 22
[1,7,2,4,3,6,5,8] => 21
[1,8,2,4,3,6,5,7] => 20
[1,8,2,3,4,6,5,7] => 21
[1,7,2,3,4,6,5,8] => 22
[1,8,2,3,4,7,5,6] => 20
[1,8,2,4,3,7,5,6] => 19
[1,7,2,4,3,8,5,6] => 20
[1,6,2,4,3,8,5,7] => 21
[1,5,2,4,3,8,6,7] => 22
[1,6,2,5,3,8,4,7] => 20
[1,7,2,5,3,8,4,6] => 19
[1,8,2,5,3,7,4,6] => 18
[1,8,2,6,3,7,4,5] => 17
[1,7,2,6,3,8,4,5] => 18
[1,2,3,8,4,7,5,6] => 22
[1,3,2,8,4,7,5,6] => 21
[1,4,2,8,3,7,5,6] => 20
[1,5,2,8,3,7,4,6] => 19
[1,6,2,8,3,7,4,5] => 18
[1,7,2,8,3,6,4,5] => 17
[1,8,2,7,3,6,4,5] => 16
[6,7,8,1,4,3,2,5] => 10
[2,8,4,1,6,7,5,3] => 14
[4,8,5,7,1,6,2,3] => 10
[8,7,6,5,2,1,4,3] => 4
[8,3,1,5,4,7,2,6] => 14
[8,7,6,5,1,4,2,3] => 4
[7,5,1,3,8,4,2,6] => 13
[7,6,1,4,8,3,2,5] => 11
[7,1,3,5,8,2,4,6] => 16
[7,5,3,6,4,2,8,1] => 9
[8,2,6,3,4,7,5,1] => 11
[7,2,6,3,5,4,8,1] => 12
[6,2,7,4,3,5,8,1] => 13
[3,7,6,4,5,2,8,1] => 11
[2,7,6,5,3,4,8,1] => 12
[8,6,5,4,2,7,3,1] => 5
[6,5,8,4,2,7,3,1] => 7
[1,8,6,3,7,5,2,4] => 12
[8,7,5,2,6,4,3,1] => 4
[8,7,1,6,2,5,4,3] => 8
[1,7,2,8,5,3,4,6] => 17
[7,6,1,8,4,3,2,5] => 10
[8,6,1,7,4,2,5,3] => 9
[8,1,2,7,3,4,6,5] => 16
[7,1,2,8,3,5,4,6] => 17
[8,2,6,1,7,3,5,4] => 12
[4,7,5,6,8,3,2,1] => 8
[8,6,4,7,5,3,2,1] => 3
[5,4,8,1,7,2,6,3] => 12
[2,3,8,7,4,5,6,1] => 14
[7,2,8,6,4,3,5,1] => 8
[8,2,7,6,3,5,4,1] => 7
[8,1,7,6,5,2,4,3] => 8
[7,1,8,6,5,3,2,4] => 9
[1,2,8,7,6,3,4,5] => 16
[3,8,7,6,4,5,2,1] => 6
[2,8,7,6,5,3,4,1] => 7
[1,8,7,6,5,4,2,3] => 8
[3,8,6,7,1,5,2,4] => 10
[5,4,7,1,3,8,2,6] => 14
[5,6,2,1,4,8,3,7] => 16
[2,1,8,4,7,5,6,3] => 16
[4,1,3,2,8,5,6,7] => 21
[3,2,1,4,8,5,6,7] => 22
[1,8,4,2,5,3,6,7] => 19
[8,1,5,3,2,4,6,7] => 17
[3,8,1,5,2,4,6,7] => 18
[1,6,7,2,8,4,3,5] => 16
[6,7,1,4,2,8,3,5] => 14
[6,3,7,1,4,8,2,5] => 14
[3,7,8,1,5,2,4,6] => 14
[7,1,2,8,5,3,4,6] => 16
[1,7,2,8,4,5,3,6] => 17
[1,2,7,5,8,3,4,6] => 19
[2,8,1,7,4,3,6,5] => 15
[4,2,6,5,8,3,7,1] => 14
[5,2,4,7,3,6,8,1] => 15
[5,1,2,4,8,3,6,7] => 20
[4,3,6,1,5,8,2,7] => 17
[2,6,1,4,5,8,3,7] => 19
[2,5,3,4,1,8,6,7] => 20
[4,3,5,2,1,8,6,7] => 18
[3,1,6,7,5,8,2,4] => 16
[2,8,1,7,5,6,3,4] => 13
[5,3,6,8,4,7,2,1] => 10
[3,7,2,5,4,8,6,1] => 14
[8,4,2,5,7,3,6,1] => 10
[4,7,2,5,8,3,6,1] => 12
[5,2,6,8,4,3,7,1] => 12
[3,1,6,5,4,8,2,7] => 18
[4,1,6,5,8,3,2,7] => 16
[5,1,6,8,4,3,2,7] => 14
[8,5,4,7,6,3,2,1] => 4
[5,7,1,8,4,3,2,6] => 12
[2,7,1,5,4,3,8,6] => 18
[8,2,1,5,4,3,7,6] => 16
[8,4,1,5,7,3,2,6] => 12
[8,5,6,7,1,3,2,4] => 8
[8,4,6,1,7,3,2,5] => 10
[8,3,6,1,4,7,2,5] => 12
[2,7,6,1,4,3,8,5] => 16
[6,7,8,5,1,3,2,4] => 8
[5,7,6,8,2,3,4,1] => 8
[5,7,2,8,4,3,6,1] => 10
[6,7,8,2,4,3,5,1] => 8
[4,7,6,2,8,3,5,1] => 10
[8,3,6,2,4,7,5,1] => 10
[3,7,6,2,4,8,5,1] => 12
[5,7,3,8,4,6,2,1] => 8
[4,7,3,5,8,6,2,1] => 10
[8,7,2,1,4,3,6,5] => 12
[8,7,3,1,4,6,2,5] => 10
[8,7,6,3,2,5,4,1] => 4
[8,7,3,5,1,6,2,4] => 8
[8,7,2,5,1,3,6,4] => 10
[8,2,6,5,1,3,7,4] => 12
[8,4,6,5,7,1,2,3] => 8
[5,7,6,8,4,1,2,3] => 8
[4,7,6,5,8,1,2,3] => 10
[3,7,6,5,1,8,2,4] => 12
[2,6,5,7,3,4,8,1] => 14
[1,6,4,7,5,8,2,3] => 15
[8,5,3,6,2,7,4,1] => 8
[1,3,7,4,6,8,2,5] => 18
[4,7,5,6,3,2,8,1] => 10
[1,7,6,5,4,8,2,3] => 12
[8,1,6,5,7,2,4,3] => 10
[1,2,7,6,8,3,4,5] => 18
[6,1,7,5,3,8,2,4] => 13
[2,1,7,5,6,8,3,4] => 17
[5,4,1,7,6,8,2,3] => 14
[4,8,5,6,2,7,3,1] => 9
[3,8,6,4,2,7,5,1] => 10
[7,8,5,2,4,6,3,1] => 6
[2,8,6,3,7,4,5,1] => 11
[7,8,1,6,2,4,5,3] => 10
[6,8,1,4,7,2,5,3] => 11
[3,8,4,1,7,2,6,5] => 14
[5,4,7,1,8,3,2,6] => 13
[3,7,4,1,8,5,2,6] => 15
[6,7,1,4,8,3,2,5] => 12
[2,7,1,8,4,5,3,6] => 16
[6,1,2,8,4,3,5,7] => 18
[6,5,1,4,3,8,2,7] => 14
[1,6,2,5,8,3,4,7] => 19
[8,5,1,3,7,2,6,4] => 12
[8,4,2,1,7,3,6,5] => 13
[7,4,2,1,8,5,3,6] => 14
[1,5,4,2,8,3,6,7] => 20
[6,4,3,1,5,8,2,7] => 15
[3,7,6,8,4,5,2,1] => 8
[2,7,6,8,5,3,4,1] => 9
[1,7,6,8,5,4,2,3] => 10
[1,4,8,6,7,5,2,3] => 13
[2,4,8,6,7,3,5,1] => 12
[7,3,8,5,4,6,2,1] => 7
[3,4,8,5,6,7,2,1] => 12
[6,3,5,8,4,7,2,1] => 9
[5,4,3,8,6,7,2,1] => 10
[5,4,2,8,7,3,6,1] => 11
[6,2,5,8,7,3,4,1] => 10
[3,2,8,5,7,4,6,1] => 13
[1,3,8,7,5,6,2,4] => 14
[2,1,8,7,4,6,3,5] => 15
[3,1,8,5,7,6,2,4] => 14
[6,1,5,8,7,4,2,3] => 11
[5,4,1,8,7,6,2,3] => 12
[5,8,6,7,4,3,2,1] => 4
[4,8,7,5,6,3,2,1] => 5
[2,8,3,1,5,4,6,7] => 19
[2,5,3,4,7,1,8,6] => 19
[2,4,8,3,5,7,6,1] => 15
[4,2,5,3,1,8,6,7] => 19
[4,2,1,8,5,3,6,7] => 19
[5,4,1,3,8,2,6,7] => 17
[5,1,4,8,3,2,6,7] => 17
[1,5,8,4,3,2,6,7] => 17
[1,8,5,4,3,2,6,7] => 16
[1,7,4,3,8,5,2,6] => 16
[1,5,7,3,8,4,2,6] => 16
[5,1,4,7,8,3,2,6] => 15
[4,8,1,5,7,3,6,2] => 12
[8,1,5,3,7,4,6,2] => 12
[3,8,4,7,6,5,2,1] => 8
[1,6,8,5,3,7,4,2] => 12
[6,8,1,7,4,3,5,2] => 9
[6,4,8,1,7,3,5,2] => 10
[6,4,8,7,1,5,2,3] => 9
[7,6,4,1,3,8,2,5] => 11
[1,7,5,6,3,2,8,4] => 15
[4,2,1,7,8,5,3,6] => 17
[2,7,4,6,3,1,8,5] => 15
[2,6,8,4,3,7,5,1] => 12
[6,2,4,8,3,7,5,1] => 12
[7,2,6,3,4,1,8,5] => 14
[2,6,7,3,1,4,8,5] => 17
[2,7,1,8,3,5,4,6] => 17
[2,1,7,3,5,8,4,6] => 20
[8,7,1,3,6,2,4,5] => 11
[8,2,1,7,3,5,6,4] => 14
[7,8,2,6,3,1,5,4] => 9
[8,7,2,6,3,5,4,1] => 6
[1,2,8,7,4,5,6,3] => 16
[8,3,7,1,5,6,2,4] => 10
[8,6,1,2,7,5,3,4] => 11
[8,1,6,2,7,4,5,3] => 12
[1,8,5,2,6,7,4,3] => 14
[5,2,1,8,6,7,4,3] => 14
[2,8,5,7,6,4,3,1] => 8
[1,7,8,5,2,6,4,3] => 12
[7,8,1,6,4,2,5,3] => 9
[7,8,6,1,5,3,2,4] => 7
[7,3,8,6,1,5,2,4] => 9
[8,7,6,1,5,3,4,2] => 5
[8,7,1,6,4,5,3,2] => 6
[8,1,7,5,6,4,3,2] => 7
[1,8,6,7,5,4,3,2] => 8
[9,1,2,3,4,5,6,7,8] => 28
[8,1,2,3,4,5,6,9,7] => 28
[2,9,1,3,4,5,6,7,8] => 28
[9,3,1,2,4,5,6,7,8] => 26
[8,9,1,2,3,4,5,6,7] => 22
[9,7,8,1,2,3,4,5,6] => 16
[2,3,4,5,6,7,9,1,8] => 28
[2,3,4,5,6,7,8,9,1] => 28
[2,3,4,5,6,7,8,1,9] => 29
[2,3,4,5,6,7,1,8,9] => 30
[1,2,3,4,5,6,7,9,8] => 35
[2,1,3,4,5,6,7,8,9] => 35
[1,8,2,3,4,5,6,9,7] => 29
[7,1,2,3,4,5,6,9,8] => 29
[2,1,9,3,4,5,6,7,8] => 29
[2,8,1,3,4,5,6,7,9] => 29
[1,2,3,4,5,6,7,8,9] => 36
[3,2,4,5,6,7,8,9,1] => 27
[9,8,7,6,5,4,3,2,1] => 0
[8,7,6,5,4,3,2,1,9] => 8
[1,9,8,7,6,5,4,3,2] => 8
[8,7,6,4,5,3,2,1,9] => 9
[1,9,8,7,5,6,4,3,2] => 9
[8,7,5,4,6,3,2,1,9] => 10
[8,7,4,6,5,3,2,1,9] => 10
[1,9,8,6,5,7,4,3,2] => 10
[1,9,8,5,7,6,4,3,2] => 10
[9,2,1,3,4,5,6,7,8] => 27
[9,2,3,1,4,5,6,7,8] => 26
[4,2,3,5,6,7,8,9,1] => 26
[3,4,2,5,6,7,8,9,1] => 26
[9,8,1,2,3,4,5,6,7] => 21
[7,8,9,1,2,3,4,5,6] => 18
[9,8,7,1,2,3,4,5,6] => 15
[6,7,8,9,1,2,3,4,5] => 16
[9,6,7,8,1,2,3,4,5] => 13
[8,9,6,7,1,2,3,4,5] => 12
[9,8,6,7,1,2,3,4,5] => 11
[9,8,7,6,1,2,3,4,5] => 10
[9,5,6,7,8,1,2,3,4] => 12
[8,9,5,6,7,1,2,3,4] => 10
[9,8,5,6,7,1,2,3,4] => 9
[9,7,8,5,6,1,2,3,4] => 8
[9,8,7,5,6,1,2,3,4] => 7
[9,8,7,6,5,1,2,3,4] => 6
[7,8,9,4,5,6,1,2,3] => 9
[9,7,8,4,5,6,1,2,3] => 7
[9,8,7,4,5,6,1,2,3] => 6
[8,9,6,7,4,5,1,2,3] => 6
[9,8,6,7,4,5,1,2,3] => 5
[9,8,7,6,4,5,1,2,3] => 4
[9,8,7,6,5,4,1,2,3] => 3
[9,7,8,5,6,3,4,1,2] => 4
[9,8,7,5,6,3,4,1,2] => 3
[9,8,7,6,5,3,4,1,2] => 2
[9,8,7,6,5,4,3,1,2] => 1
[7,8,6,5,4,3,2,1,9] => 9
[1,8,9,7,6,5,4,3,2] => 9
[7,6,8,5,4,3,2,1,9] => 10
[6,8,7,5,4,3,2,1,9] => 10
[1,8,7,9,6,5,4,3,2] => 10
[1,7,9,8,6,5,4,3,2] => 10
[8,1,2,3,4,5,6,7,9] => 29
[1,9,2,3,4,5,6,7,8] => 29
[7,8,1,2,3,4,5,6,9] => 24
[1,8,9,2,3,4,5,6,7] => 24
[7,1,8,2,3,4,5,6,9] => 25
[6,8,1,2,3,4,5,7,9] => 25
[1,8,2,9,3,4,5,6,7] => 25
[1,7,9,2,3,4,5,6,8] => 25
[7,1,2,3,4,5,6,8,9] => 30
[3,4,1,2,5,6,7,8,9] => 32
[3,2,1,4,5,6,7,8,9] => 33
[4,5,6,1,2,3,7,8,9] => 27
[4,2,5,1,3,6,7,8,9] => 30
[4,3,2,1,5,6,7,8,9] => 30
[5,6,7,8,1,2,3,4,9] => 20
[5,2,6,7,1,3,4,8,9] => 25
[5,6,3,4,1,2,7,8,9] => 24
[5,3,2,6,1,4,7,8,9] => 27
[5,4,3,2,1,6,7,8,9] => 26
[6,2,7,8,9,1,3,4,5] => 18
[6,7,3,4,8,1,2,5,9] => 19
[6,3,2,7,8,1,4,5,9] => 22
[6,4,7,2,5,1,3,8,9] => 21
[6,4,3,2,7,1,5,8,9] => 23
[6,5,4,3,2,1,7,8,9] => 21
[7,4,8,2,5,9,1,3,6] => 16
[7,4,3,2,8,9,1,5,6] => 18
[7,8,5,6,3,4,1,2,9] => 12
[7,5,3,8,2,6,1,4,9] => 17
[7,5,4,3,2,8,1,6,9] => 18
[7,6,5,4,3,2,1,8,9] => 15
[8,6,9,4,7,2,5,1,3] => 8
[8,6,4,3,9,2,7,1,5] => 12
[8,6,5,4,3,2,9,1,7] => 12
[2,1,4,3,6,5,8,7,10,9] => 40
[4,3,2,1,6,5,8,7,10,9] => 36
[6,3,2,5,4,1,8,7,10,9] => 32
[8,3,2,5,4,7,6,1,10,9] => 28
[10,3,2,5,4,7,6,9,8,1] => 24
[2,1,6,5,4,3,8,7,10,9] => 36
[6,5,4,3,2,1,8,7,10,9] => 28
[8,5,4,3,2,7,6,1,10,9] => 24
[10,5,4,3,2,7,6,9,8,1] => 20
[2,1,8,5,4,7,6,3,10,9] => 32
[8,7,4,3,6,5,2,1,10,9] => 20
[10,7,4,3,6,5,2,9,8,1] => 16
[2,1,10,5,4,7,6,9,8,3] => 28
[10,9,4,3,6,5,8,7,2,1] => 12
[8,9,5,6,3,4,10,1,2,7] => 16
[2,1,4,3,8,7,6,5,10,9] => 36
[4,3,2,1,8,7,6,5,10,9] => 32
[8,3,2,7,6,5,4,1,10,9] => 24
[10,3,2,7,6,5,4,9,8,1] => 20
[2,1,8,7,6,5,4,3,10,9] => 28
[8,7,6,5,4,3,2,1,10,9] => 16
[9,7,6,5,4,3,2,10,1,8] => 14
[10,7,6,5,4,3,2,9,8,1] => 12
[2,1,10,7,6,5,4,9,8,3] => 24
[10,9,6,5,4,3,8,7,2,1] => 8
[2,1,4,3,10,7,6,9,8,5] => 32
[4,3,2,1,10,7,6,9,8,5] => 28
[10,3,2,9,6,5,8,7,4,1] => 16
[2,1,10,9,6,5,8,7,4,3] => 20
[10,9,8,5,4,7,6,3,2,1] => 4
[6,7,8,9,10,1,2,3,4,5] => 20
[7,3,2,8,9,10,1,4,5,6] => 24
[8,5,4,3,2,9,10,1,6,7] => 22
[2,1,4,3,6,5,10,9,8,7] => 36
[4,3,2,1,6,5,10,9,8,7] => 32
[6,3,2,5,4,1,10,9,8,7] => 28
[10,3,2,5,4,9,8,7,6,1] => 20
[2,1,6,5,4,3,10,9,8,7] => 32
[6,5,4,3,2,1,10,9,8,7] => 24
[10,5,4,3,2,9,8,7,6,1] => 16
[2,1,10,5,4,9,8,7,6,3] => 24
[10,9,4,3,8,7,6,5,2,1] => 8
[9,7,5,10,3,8,2,6,1,4] => 12
[2,1,4,3,10,9,8,7,6,5] => 28
[4,3,2,1,10,9,8,7,6,5] => 24
[10,3,2,9,8,7,6,5,4,1] => 12
[2,1,10,9,8,7,6,5,4,3] => 16
[10,9,8,7,6,5,4,3,2,1] => 0
[2,3,4,5,6,7,8,9,10,1] => 36
[2,3,4,5,6,7,8,9,1,10] => 37
[10,8,9,5,6,7,1,2,3,4] => 10
[10,8,9,4,5,6,1,2,3,7] => 13
[10,7,8,5,6,9,1,2,3,4] => 12
[10,7,8,4,5,9,1,2,3,6] => 14
[10,6,7,4,5,8,1,2,3,9] => 17
[10,7,8,3,4,9,1,2,5,6] => 16
[10,6,7,3,4,8,1,2,5,9] => 19
[9,8,10,5,6,7,1,2,3,4] => 11
[9,8,10,4,5,6,1,2,3,7] => 14
[9,7,10,5,6,8,1,2,3,4] => 12
[9,7,10,4,5,8,1,2,3,6] => 14
[9,6,10,4,5,7,1,2,3,8] => 16
[9,7,10,3,4,8,1,2,5,6] => 16
[9,6,10,3,4,7,1,2,5,8] => 18
[8,7,9,5,6,10,1,2,3,4] => 14
[8,7,9,4,5,10,1,2,3,6] => 16
[8,6,9,4,5,10,1,2,3,7] => 17
[7,6,8,4,5,9,1,2,3,10] => 20
[8,7,9,3,4,10,1,2,5,6] => 18
[8,6,9,3,4,10,1,2,5,7] => 19
[7,6,8,3,4,9,1,2,5,10] => 22
[9,6,10,5,7,8,1,2,3,4] => 13
[9,6,10,4,7,8,1,2,3,5] => 14
[9,5,10,4,6,7,1,2,3,8] => 17
[9,6,10,3,7,8,1,2,4,5] => 15
[9,5,10,3,6,7,1,2,4,8] => 18
[8,6,9,5,7,10,1,2,3,4] => 15
[8,6,9,4,7,10,1,2,3,5] => 16
[8,5,9,4,6,10,1,2,3,7] => 18
[7,5,8,4,6,9,1,2,3,10] => 21
[8,6,9,3,7,10,1,2,4,5] => 17
[8,5,9,3,6,10,1,2,4,7] => 19
[7,5,8,3,6,9,1,2,4,10] => 22
[8,4,9,3,5,10,1,2,6,7] => 21
[7,4,8,3,5,9,1,2,6,10] => 24
[9,6,10,2,7,8,1,3,4,5] => 16
[9,5,10,2,6,7,1,3,4,8] => 19
[8,6,9,2,7,10,1,3,4,5] => 18
[8,5,9,2,6,10,1,3,4,7] => 20
[7,5,8,2,6,9,1,3,4,10] => 23
[8,4,9,2,5,10,1,3,6,7] => 22
[7,4,8,2,5,9,1,3,6,10] => 25
[1,2,3,4,5,6,7,8,10,9] => 44
[2,1,3,4,5,6,7,8,9,10] => 44
[9,1,2,3,4,5,6,7,10,8] => 36
[2,10,1,3,4,5,6,7,8,9] => 36
[1,2,3,4,5,6,7,8,9,10] => 45
[9,8,7,6,5,4,3,2,1,10] => 9
[10,1,2,3,4,5,6,7,8,9] => 36
[10,9,1,2,3,4,5,6,7,8] => 28
[1,10,9,8,7,6,5,4,3,2] => 9
[9,8,7,5,6,4,3,2,1,10] => 10
[1,10,9,8,6,7,5,4,3,2] => 10
[10,2,1,3,4,5,6,7,8,9] => 35
[3,2,4,5,6,7,8,9,10,1] => 35
[2,4,6,8,10,1,3,5,7,9] => 30
[2,4,6,9,10,1,3,5,7,8] => 29
[2,4,7,8,10,1,3,5,6,9] => 29
[2,4,7,9,10,1,3,5,6,8] => 28
[2,4,8,9,10,1,3,5,6,7] => 27
[2,5,6,8,10,1,3,4,7,9] => 29
[2,5,6,9,10,1,3,4,7,8] => 28
[2,5,7,8,10,1,3,4,6,9] => 28
[2,5,7,9,10,1,3,4,6,8] => 27
[2,5,8,9,10,1,3,4,6,7] => 26
[2,6,7,8,10,1,3,4,5,9] => 27
[2,6,7,9,10,1,3,4,5,8] => 26
[2,6,8,9,10,1,3,4,5,7] => 25
[2,7,8,9,10,1,3,4,5,6] => 24
[3,4,6,8,10,1,2,5,7,9] => 29
[3,4,6,9,10,1,2,5,7,8] => 28
[3,4,7,8,10,1,2,5,6,9] => 28
[3,4,7,9,10,1,2,5,6,8] => 27
[3,4,8,9,10,1,2,5,6,7] => 26
[3,5,6,8,10,1,2,4,7,9] => 28
[3,5,6,9,10,1,2,4,7,8] => 27
[3,5,7,8,10,1,2,4,6,9] => 27
[3,5,7,9,10,1,2,4,6,8] => 26
[3,5,8,9,10,1,2,4,6,7] => 25
[3,6,7,8,10,1,2,4,5,9] => 26
[3,6,7,9,10,1,2,4,5,8] => 25
[3,6,8,9,10,1,2,4,5,7] => 24
[3,7,8,9,10,1,2,4,5,6] => 23
[4,5,6,8,10,1,2,3,7,9] => 27
[4,5,6,9,10,1,2,3,7,8] => 26
[4,5,7,8,10,1,2,3,6,9] => 26
[4,5,7,9,10,1,2,3,6,8] => 25
[4,5,8,9,10,1,2,3,6,7] => 24
[4,6,7,8,10,1,2,3,5,9] => 25
[4,6,7,9,10,1,2,3,5,8] => 24
[4,6,8,9,10,1,2,3,5,7] => 23
[4,7,8,9,10,1,2,3,5,6] => 22
[5,6,7,8,10,1,2,3,4,9] => 24
[5,6,7,9,10,1,2,3,4,8] => 23
[5,6,8,9,10,1,2,3,4,7] => 22
[5,7,8,9,10,1,2,3,4,6] => 21
[9,10,1,2,3,4,5,6,7,8] => 29
[8,9,10,1,2,3,4,5,6,7] => 24
[10,8,9,1,2,3,4,5,6,7] => 22
[10,9,8,1,2,3,4,5,6,7] => 21
[7,8,9,10,1,2,3,4,5,6] => 21
[10,7,8,9,1,2,3,4,5,6] => 18
[9,10,7,8,1,2,3,4,5,6] => 17
[10,9,7,8,1,2,3,4,5,6] => 16
[10,9,8,7,1,2,3,4,5,6] => 15
[10,6,7,8,9,1,2,3,4,5] => 16
[9,10,6,7,8,1,2,3,4,5] => 14
[10,9,6,7,8,1,2,3,4,5] => 13
[10,8,9,6,7,1,2,3,4,5] => 12
[10,9,8,6,7,1,2,3,4,5] => 11
[10,9,8,7,6,1,2,3,4,5] => 10
[9,10,5,6,7,8,1,2,3,4] => 13
[10,9,5,6,7,8,1,2,3,4] => 12
[8,9,10,5,6,7,1,2,3,4] => 12
[10,9,8,5,6,7,1,2,3,4] => 9
[9,10,7,8,5,6,1,2,3,4] => 9
[10,9,7,8,5,6,1,2,3,4] => 8
[10,9,8,7,5,6,1,2,3,4] => 7
[10,9,8,7,6,5,1,2,3,4] => 6
[10,7,8,9,4,5,6,1,2,3] => 9
[9,10,7,8,4,5,6,1,2,3] => 8
[10,9,7,8,4,5,6,1,2,3] => 7
[10,9,8,7,4,5,6,1,2,3] => 6
[10,8,9,6,7,4,5,1,2,3] => 6
[10,9,8,6,7,4,5,1,2,3] => 5
[10,9,8,7,6,4,5,1,2,3] => 4
[10,9,8,7,6,5,4,1,2,3] => 3
[9,10,7,8,5,6,3,4,1,2] => 5
[10,9,7,8,5,6,3,4,1,2] => 4
[10,9,8,7,5,6,3,4,1,2] => 3
[10,9,8,7,6,5,3,4,1,2] => 2
[10,9,8,7,6,5,4,3,1,2] => 1
[8,9,7,6,5,4,3,2,1,10] => 10
[1,9,10,8,7,6,5,4,3,2] => 10
[9,1,2,3,4,5,6,7,8,10] => 37
[1,10,2,3,4,5,6,7,8,9] => 37
[8,9,1,2,3,4,5,6,7,10] => 31
[1,9,10,2,3,4,5,6,7,8] => 31
[3,4,1,2,5,6,7,8,9,10] => 41
[3,2,1,4,5,6,7,8,9,10] => 42
[4,5,6,1,2,3,7,8,9,10] => 36
[4,2,5,1,3,6,7,8,9,10] => 39
[4,3,2,1,5,6,7,8,9,10] => 39
[5,6,7,8,1,2,3,4,9,10] => 29
[5,2,6,7,1,3,4,8,9,10] => 34
[5,6,3,4,1,2,7,8,9,10] => 33
[5,3,2,6,1,4,7,8,9,10] => 36
[5,4,3,2,1,6,7,8,9,10] => 35
[6,2,7,8,9,1,3,4,5,10] => 27
[6,7,3,4,8,1,2,5,9,10] => 28
[6,3,2,7,8,1,4,5,9,10] => 31
[6,4,7,2,5,1,3,8,9,10] => 30
[6,4,3,2,7,1,5,8,9,10] => 32
[6,5,4,3,2,1,7,8,9,10] => 30
[7,8,3,4,9,10,1,2,5,6] => 21
[7,8,9,4,5,6,1,2,3,10] => 18
[7,4,3,2,8,9,1,5,6,10] => 27
[7,8,5,6,3,4,1,2,9,10] => 21
[7,5,3,8,2,6,1,4,9,10] => 26
[7,5,4,3,2,8,1,6,9,10] => 27
[7,6,5,4,3,2,1,8,9,10] => 24
[8,5,9,10,2,6,7,1,3,4] => 15
[8,5,3,9,2,6,10,1,4,7] => 21
[8,6,9,4,7,2,5,1,3,10] => 17
[8,6,4,3,9,2,7,1,5,10] => 21
[8,6,5,4,3,2,9,1,7,10] => 21
[8,7,6,5,4,3,2,1,9,10] => 17
[9,7,5,4,3,10,2,8,1,6] => 15
[1,2,3,4,5,6,7,8,9,11,10] => 54
[2,1,3,4,5,6,7,8,9,10,11] => 54
[11,1,2,3,4,5,6,7,8,9,10] => 45
[10,9,8,7,6,5,4,3,2,1,11] => 10
[1,11,10,9,8,7,6,5,4,3,2] => 10
[2,3,4,5,6,7,8,9,10,11,1] => 45
[10,1,2,3,4,5,6,7,8,9,11] => 46
[1,11,2,3,4,5,6,7,8,9,10] => 46
[2,1,4,3,6,5,8,7,12,11,10,9] => 56
[2,1,4,3,6,5,12,9,8,11,10,7] => 52
[2,1,4,3,6,5,12,11,10,9,8,7] => 48
[2,1,4,3,8,7,6,5,12,11,10,9] => 52
[2,1,4,3,12,7,6,9,8,11,10,5] => 48
[2,1,4,3,12,7,6,11,10,9,8,5] => 44
[2,1,4,3,10,9,8,7,6,5,12,11] => 48
[2,1,4,3,12,9,8,7,6,11,10,5] => 44
[2,1,4,3,12,11,8,7,10,9,6,5] => 40
[2,1,4,3,12,11,10,9,8,7,6,5] => 36
[2,1,6,5,4,3,8,7,12,11,10,9] => 52
[2,1,6,5,4,3,10,9,8,7,12,11] => 52
[2,1,6,5,4,3,12,9,8,11,10,7] => 48
[2,1,6,5,4,3,12,11,10,9,8,7] => 44
[2,1,8,5,4,7,6,3,12,11,10,9] => 48
[2,1,12,5,4,7,6,9,8,11,10,3] => 44
[2,1,12,5,4,7,6,11,10,9,8,3] => 40
[2,1,10,5,4,9,8,7,6,3,12,11] => 44
[2,1,12,5,4,9,8,7,6,11,10,3] => 40
[2,1,12,5,4,11,8,7,10,9,6,3] => 36
[2,1,12,5,4,11,10,9,8,7,6,3] => 32
[2,1,8,7,6,5,4,3,10,9,12,11] => 48
[2,1,8,7,6,5,4,3,12,11,10,9] => 44
[2,1,12,7,6,5,4,9,8,11,10,3] => 40
[2,1,12,7,6,5,4,11,10,9,8,3] => 36
[2,1,10,9,6,5,8,7,4,3,12,11] => 40
[2,1,12,9,6,5,8,7,4,11,10,3] => 36
[2,1,12,11,6,5,8,7,10,9,4,3] => 32
[2,1,12,11,6,5,10,9,8,7,4,3] => 28
[2,1,10,9,8,7,6,5,4,3,12,11] => 36
[2,1,12,9,8,7,6,5,4,11,10,3] => 32
[2,1,12,11,8,7,6,5,10,9,4,3] => 28
[2,1,12,11,10,7,6,9,8,5,4,3] => 24
[2,1,12,11,10,9,8,7,6,5,4,3] => 20
[4,3,2,1,6,5,8,7,10,9,12,11] => 56
[4,3,2,1,6,5,8,7,12,11,10,9] => 52
[4,3,2,1,6,5,10,9,8,7,12,11] => 52
[4,3,2,1,6,5,12,9,8,11,10,7] => 48
[4,3,2,1,6,5,12,11,10,9,8,7] => 44
[4,3,2,1,8,7,6,5,10,9,12,11] => 52
[4,3,2,1,8,7,6,5,12,11,10,9] => 48
[4,3,2,1,10,7,6,9,8,5,12,11] => 48
[4,3,2,1,12,7,6,9,8,11,10,5] => 44
[4,3,2,1,12,7,6,11,10,9,8,5] => 40
[4,3,2,1,10,9,8,7,6,5,12,11] => 44
[4,3,2,1,12,9,8,7,6,11,10,5] => 40
[4,3,2,1,12,11,8,7,10,9,6,5] => 36
[4,3,2,1,12,11,10,9,8,7,6,5] => 32
[6,3,2,5,4,1,8,7,10,9,12,11] => 52
[6,3,2,5,4,1,8,7,12,11,10,9] => 48
[6,3,2,5,4,1,10,9,8,7,12,11] => 48
[6,3,2,5,4,1,12,9,8,11,10,7] => 44
[6,3,2,5,4,1,12,11,10,9,8,7] => 40
[8,3,2,5,4,7,6,1,10,9,12,11] => 48
[8,3,2,5,4,7,6,1,12,11,10,9] => 44
[10,3,2,5,4,7,6,9,8,1,12,11] => 44
[12,3,2,5,4,7,6,9,8,11,10,1] => 40
[12,3,2,5,4,7,6,11,10,9,8,1] => 36
[10,3,2,5,4,9,8,7,6,1,12,11] => 40
[12,3,2,5,4,9,8,7,6,11,10,1] => 36
[12,3,2,5,4,11,8,7,10,9,6,1] => 32
[12,3,2,5,4,11,10,9,8,7,6,1] => 28
[8,3,2,7,6,5,4,1,10,9,12,11] => 44
[8,3,2,7,6,5,4,1,12,11,10,9] => 40
[10,3,2,7,6,5,4,9,8,1,12,11] => 40
[12,3,2,7,6,5,4,9,8,11,10,1] => 36
[12,3,2,7,6,5,4,11,10,9,8,1] => 32
[10,3,2,9,6,5,8,7,4,1,12,11] => 36
[12,3,2,9,6,5,8,7,4,11,10,1] => 32
[12,3,2,11,6,5,8,7,10,9,4,1] => 28
[12,3,2,11,6,5,10,9,8,7,4,1] => 24
[10,3,2,9,8,7,6,5,4,1,12,11] => 32
[12,3,2,9,8,7,6,5,4,11,10,1] => 28
[12,3,2,11,8,7,6,5,10,9,4,1] => 24
[6,5,4,3,2,1,8,7,10,9,12,11] => 48
[6,5,4,3,2,1,8,7,12,11,10,9] => 44
[6,5,4,3,2,1,10,9,8,7,12,11] => 44
[6,5,4,3,2,1,12,9,8,11,10,7] => 40
[6,5,4,3,2,1,12,11,10,9,8,7] => 36
[8,5,4,3,2,7,6,1,12,11,10,9] => 40
[10,5,4,3,2,7,6,9,8,1,12,11] => 40
[12,5,4,3,2,7,6,9,8,11,10,1] => 36
[12,5,4,3,2,7,6,11,10,9,8,1] => 32
[10,5,4,3,2,9,8,7,6,1,12,11] => 36
[12,5,4,3,2,9,8,7,6,11,10,1] => 32
[12,5,4,3,2,11,8,7,10,9,6,1] => 28
[8,7,4,3,6,5,2,1,10,9,12,11] => 40
[8,7,4,3,6,5,2,1,12,11,10,9] => 36
[10,7,4,3,6,5,2,9,8,1,12,11] => 36
[12,7,4,3,6,5,2,9,8,11,10,1] => 32
[12,7,4,3,6,5,2,11,10,9,8,1] => 28
[10,9,4,3,6,5,8,7,2,1,12,11] => 32
[12,9,4,3,6,5,8,7,2,11,10,1] => 28
[12,11,4,3,6,5,8,7,10,9,2,1] => 24
[10,9,4,3,8,7,6,5,2,1,12,11] => 28
[12,9,4,3,8,7,6,5,2,11,10,1] => 24
[8,7,6,5,4,3,2,1,10,9,12,11] => 36
[8,7,6,5,4,3,2,1,12,11,10,9] => 32
[10,7,6,5,4,3,2,9,8,1,12,11] => 32
[12,7,6,5,4,3,2,9,8,11,10,1] => 28
[10,9,6,5,4,3,8,7,2,1,12,11] => 28
[12,9,6,5,4,3,8,7,2,11,10,1] => 24
[12,11,6,5,4,3,8,7,10,9,2,1] => 20
[10,9,8,5,4,7,6,3,2,1,12,11] => 24
[10,9,8,7,6,5,4,3,2,1,12,11] => 20
[2,4,6,8,10,12,1,3,5,7,9,11] => 45
[2,4,6,8,11,12,1,3,5,7,9,10] => 44
[2,4,6,9,10,12,1,3,5,7,8,11] => 44
[2,4,6,9,11,12,1,3,5,7,8,10] => 43
[2,4,6,10,11,12,1,3,5,7,8,9] => 42
[2,4,7,8,10,12,1,3,5,6,9,11] => 44
[2,4,7,8,11,12,1,3,5,6,9,10] => 43
[2,4,7,9,10,12,1,3,5,6,8,11] => 43
[2,4,7,9,11,12,1,3,5,6,8,10] => 42
[2,4,7,10,11,12,1,3,5,6,8,9] => 41
[2,4,8,9,10,12,1,3,5,6,7,11] => 42
[2,4,8,9,11,12,1,3,5,6,7,10] => 41
[2,4,8,10,11,12,1,3,5,6,7,9] => 40
[2,4,9,10,11,12,1,3,5,6,7,8] => 39
[2,5,6,8,10,12,1,3,4,7,9,11] => 44
[2,5,6,8,11,12,1,3,4,7,9,10] => 43
[2,5,6,9,10,12,1,3,4,7,8,11] => 43
[2,5,6,9,11,12,1,3,4,7,8,10] => 42
[2,5,6,10,11,12,1,3,4,7,8,9] => 41
[2,5,7,8,10,12,1,3,4,6,9,11] => 43
[2,5,7,8,11,12,1,3,4,6,9,10] => 42
[2,5,7,9,11,12,1,3,4,6,8,10] => 41
[2,5,7,10,11,12,1,3,4,6,8,9] => 40
[2,5,8,9,10,12,1,3,4,6,7,11] => 41
[2,5,8,9,11,12,1,3,4,6,7,10] => 40
[2,5,8,10,11,12,1,3,4,6,7,9] => 39
[2,5,9,10,11,12,1,3,4,6,7,8] => 38
[2,6,7,8,10,12,1,3,4,5,9,11] => 42
[2,6,7,8,11,12,1,3,4,5,9,10] => 41
[2,6,7,9,10,12,1,3,4,5,8,11] => 41
[2,6,7,9,11,12,1,3,4,5,8,10] => 40
[2,6,7,10,11,12,1,3,4,5,8,9] => 39
[2,6,8,9,10,12,1,3,4,5,7,11] => 40
[2,6,8,9,11,12,1,3,4,5,7,10] => 39
[2,6,8,10,11,12,1,3,4,5,7,9] => 38
[2,6,9,10,11,12,1,3,4,5,7,8] => 37
[2,7,8,9,10,12,1,3,4,5,6,11] => 39
[2,7,8,9,11,12,1,3,4,5,6,10] => 38
[2,7,8,10,11,12,1,3,4,5,6,9] => 37
[2,7,9,10,11,12,1,3,4,5,6,8] => 36
[2,8,9,10,11,12,1,3,4,5,6,7] => 35
[3,4,6,8,10,12,1,2,5,7,9,11] => 44
[3,4,6,8,11,12,1,2,5,7,9,10] => 43
[3,4,6,9,10,12,1,2,5,7,8,11] => 43
[3,4,6,9,11,12,1,2,5,7,8,10] => 42
[3,4,6,10,11,12,1,2,5,7,8,9] => 41
[3,4,7,8,10,12,1,2,5,6,9,11] => 43
[3,4,7,8,11,12,1,2,5,6,9,10] => 42
[3,4,7,9,10,12,1,2,5,6,8,11] => 42
[3,4,7,9,11,12,1,2,5,6,8,10] => 41
[3,4,7,10,11,12,1,2,5,6,8,9] => 40
[3,4,8,9,10,12,1,2,5,6,7,11] => 41
[3,4,8,9,11,12,1,2,5,6,7,10] => 40
[3,4,8,10,11,12,1,2,5,6,7,9] => 39
[3,4,9,10,11,12,1,2,5,6,7,8] => 38
[3,5,6,8,10,12,1,2,4,7,9,11] => 43
[3,5,6,8,11,12,1,2,4,7,9,10] => 42
[3,5,6,9,10,12,1,2,4,7,8,11] => 42
[3,5,6,9,11,12,1,2,4,7,8,10] => 41
[3,5,6,10,11,12,1,2,4,7,8,9] => 40
[3,5,7,8,10,12,1,2,4,6,9,11] => 42
[3,5,7,8,11,12,1,2,4,6,9,10] => 41
[3,5,7,9,10,12,1,2,4,6,8,11] => 41
[3,5,7,9,11,12,1,2,4,6,8,10] => 40
[3,5,7,10,11,12,1,2,4,6,8,9] => 39
[3,5,8,9,10,12,1,2,4,6,7,11] => 40
[3,5,8,9,11,12,1,2,4,6,7,10] => 39
[3,5,8,10,11,12,1,2,4,6,7,9] => 38
[3,5,9,10,11,12,1,2,4,6,7,8] => 37
[3,6,7,8,10,12,1,2,4,5,9,11] => 41
[3,6,7,8,11,12,1,2,4,5,9,10] => 40
[3,6,7,9,10,12,1,2,4,5,8,11] => 40
[3,6,7,9,11,12,1,2,4,5,8,10] => 39
[3,6,7,10,11,12,1,2,4,5,8,9] => 38
[3,6,8,9,10,12,1,2,4,5,7,11] => 39
[3,6,8,9,11,12,1,2,4,5,7,10] => 38
[3,6,8,10,11,12,1,2,4,5,7,9] => 37
[3,6,9,10,11,12,1,2,4,5,7,8] => 36
[3,7,8,9,10,12,1,2,4,5,6,11] => 38
[3,7,8,9,11,12,1,2,4,5,6,10] => 37
[3,7,8,10,11,12,1,2,4,5,6,9] => 36
[3,7,9,10,11,12,1,2,4,5,6,8] => 35
[3,8,9,10,11,12,1,2,4,5,6,7] => 34
[4,5,6,8,10,12,1,2,3,7,9,11] => 42
[4,5,6,8,11,12,1,2,3,7,9,10] => 41
[4,5,6,9,10,12,1,2,3,7,8,11] => 41
[4,5,6,9,11,12,1,2,3,7,8,10] => 40
[4,5,6,10,11,12,1,2,3,7,8,9] => 39
[4,5,7,8,10,12,1,2,3,6,9,11] => 41
[4,5,7,8,11,12,1,2,3,6,9,10] => 40
[4,5,7,9,10,12,1,2,3,6,8,11] => 40
[4,5,7,9,11,12,1,2,3,6,8,10] => 39
[4,5,7,10,11,12,1,2,3,6,8,9] => 38
[4,5,8,9,10,12,1,2,3,6,7,11] => 39
[4,5,8,9,11,12,1,2,3,6,7,10] => 38
[4,5,8,10,11,12,1,2,3,6,7,9] => 37
[4,5,9,10,11,12,1,2,3,6,7,8] => 36
[4,6,7,8,10,12,1,2,3,5,9,11] => 40
[4,6,7,8,11,12,1,2,3,5,9,10] => 39
[4,6,7,9,10,12,1,2,3,5,8,11] => 39
[4,6,7,9,11,12,1,2,3,5,8,10] => 38
[4,6,7,10,11,12,1,2,3,5,8,9] => 37
[4,6,8,9,10,12,1,2,3,5,7,11] => 38
[4,6,8,9,11,12,1,2,3,5,7,10] => 37
[4,6,8,10,11,12,1,2,3,5,7,9] => 36
[4,6,9,10,11,12,1,2,3,5,7,8] => 35
[4,7,8,9,10,12,1,2,3,5,6,11] => 37
[4,7,8,9,11,12,1,2,3,5,6,10] => 36
[4,7,8,10,11,12,1,2,3,5,6,9] => 35
[4,7,9,10,11,12,1,2,3,5,6,8] => 34
[4,8,9,10,11,12,1,2,3,5,6,7] => 33
[5,6,7,8,10,12,1,2,3,4,9,11] => 39
[5,6,7,8,11,12,1,2,3,4,9,10] => 38
[5,6,7,9,10,12,1,2,3,4,8,11] => 38
[5,6,7,9,11,12,1,2,3,4,8,10] => 37
[5,6,7,10,11,12,1,2,3,4,8,9] => 36
[5,6,8,9,10,12,1,2,3,4,7,11] => 37
[5,6,8,9,11,12,1,2,3,4,7,10] => 36
[5,6,8,10,11,12,1,2,3,4,7,9] => 35
[5,6,9,10,11,12,1,2,3,4,7,8] => 34
[5,7,8,9,10,12,1,2,3,4,6,11] => 36
[5,7,8,9,11,12,1,2,3,4,6,10] => 35
[5,7,8,10,11,12,1,2,3,4,6,9] => 34
[5,7,9,10,11,12,1,2,3,4,6,8] => 33
[5,8,9,10,11,12,1,2,3,4,6,7] => 32
[6,7,8,9,10,12,1,2,3,4,5,11] => 35
[6,7,8,9,11,12,1,2,3,4,5,10] => 34
[6,7,8,10,11,12,1,2,3,4,5,9] => 33
[6,7,9,10,11,12,1,2,3,4,5,8] => 32
[6,8,9,10,11,12,1,2,3,4,5,7] => 31
[7,8,9,10,11,12,1,2,3,4,5,6] => 30
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,2,1 1,3,5,6,5,3,1 1,4,9,15,20,22,20,15,9,4,1 1,5,14,29,49,71,90,101,101,90,71,49,29,14,5,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + 2\ q^{2} + q^{3}$
$F_{4} = 1 + 3\ q + 5\ q^{2} + 6\ q^{3} + 5\ q^{4} + 3\ q^{5} + q^{6}$
$F_{5} = 1 + 4\ q + 9\ q^{2} + 15\ q^{3} + 20\ q^{4} + 22\ q^{5} + 20\ q^{6} + 15\ q^{7} + 9\ q^{8} + 4\ q^{9} + q^{10}$
$F_{6} = 1 + 5\ q + 14\ q^{2} + 29\ q^{3} + 49\ q^{4} + 71\ q^{5} + 90\ q^{6} + 101\ q^{7} + 101\ q^{8} + 90\ q^{9} + 71\ q^{10} + 49\ q^{11} + 29\ q^{12} + 14\ q^{13} + 5\ q^{14} + q^{15}$
Description
The number of non-inversions of a permutation.
For a permutation of $\{1,\ldots,n\}$, this is given by $\operatorname{noninv}(\pi) = \binom{n}{2}-\operatorname{inv}(\pi)$.
For a permutation of $\{1,\ldots,n\}$, this is given by $\operatorname{noninv}(\pi) = \binom{n}{2}-\operatorname{inv}(\pi)$.
References
[1] Reiner, V., Saliola, F., Welker, V. Spectra of Symmetrized Shuffling Operators arXiv:1102.2460
[2] The number of inversions of a permutation. St000018
[2] The number of inversions of a permutation. St000018
Code
def statistic(pi):
return binomial(len(pi),2)-pi.number_of_inversions()
Created
Feb 27, 2015 at 10:43 by Christian Stump
Updated
Jan 11, 2018 at 21:35 by Martin Rubey
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