Identifier
- St000625: Permutations ⟶ ℤ
Values
=>
[1,2]=>2
[2,1]=>2
[1,2,3]=>3
[1,3,2]=>4
[2,1,3]=>3
[2,3,1]=>4
[3,1,2]=>3
[3,2,1]=>3
[1,2,3,4]=>4
[1,2,4,3]=>5
[1,3,2,4]=>5
[1,3,4,2]=>5
[1,4,2,3]=>5
[1,4,3,2]=>5
[2,1,3,4]=>4
[2,1,4,3]=>5
[2,3,1,4]=>5
[2,3,4,1]=>5
[2,4,1,3]=>5
[2,4,3,1]=>5
[3,1,2,4]=>4
[3,1,4,2]=>5
[3,2,1,4]=>4
[3,2,4,1]=>5
[3,4,1,2]=>5
[3,4,2,1]=>5
[4,1,2,3]=>4
[4,1,3,2]=>5
[4,2,1,3]=>4
[4,2,3,1]=>5
[4,3,1,2]=>4
[4,3,2,1]=>4
[1,2,3,4,5]=>5
[1,2,3,5,4]=>6
[1,2,4,3,5]=>6
[1,2,4,5,3]=>6
[1,2,5,3,4]=>7
[1,2,5,4,3]=>7
[1,3,2,4,5]=>6
[1,3,2,5,4]=>7
[1,3,4,2,5]=>6
[1,3,4,5,2]=>6
[1,3,5,2,4]=>7
[1,3,5,4,2]=>7
[1,4,2,3,5]=>6
[1,4,2,5,3]=>7
[1,4,3,2,5]=>6
[1,4,3,5,2]=>7
[1,4,5,2,3]=>7
[1,4,5,3,2]=>7
[1,5,2,3,4]=>6
[1,5,2,4,3]=>7
[1,5,3,2,4]=>6
[1,5,3,4,2]=>7
[1,5,4,2,3]=>6
[1,5,4,3,2]=>6
[2,1,3,4,5]=>5
[2,1,3,5,4]=>6
[2,1,4,3,5]=>6
[2,1,4,5,3]=>6
[2,1,5,3,4]=>7
[2,1,5,4,3]=>7
[2,3,1,4,5]=>6
[2,3,1,5,4]=>7
[2,3,4,1,5]=>6
[2,3,4,5,1]=>6
[2,3,5,1,4]=>7
[2,3,5,4,1]=>7
[2,4,1,3,5]=>6
[2,4,1,5,3]=>7
[2,4,3,1,5]=>6
[2,4,3,5,1]=>7
[2,4,5,1,3]=>7
[2,4,5,3,1]=>7
[2,5,1,3,4]=>6
[2,5,1,4,3]=>7
[2,5,3,1,4]=>6
[2,5,3,4,1]=>7
[2,5,4,1,3]=>6
[2,5,4,3,1]=>6
[3,1,2,4,5]=>5
[3,1,2,5,4]=>6
[3,1,4,2,5]=>6
[3,1,4,5,2]=>6
[3,1,5,2,4]=>7
[3,1,5,4,2]=>7
[3,2,1,4,5]=>5
[3,2,1,5,4]=>6
[3,2,4,1,5]=>6
[3,2,4,5,1]=>6
[3,2,5,1,4]=>7
[3,2,5,4,1]=>7
[3,4,1,2,5]=>6
[3,4,1,5,2]=>7
[3,4,2,1,5]=>6
[3,4,2,5,1]=>7
[3,4,5,1,2]=>7
[3,4,5,2,1]=>7
[3,5,1,2,4]=>6
[3,5,1,4,2]=>7
[3,5,2,1,4]=>6
[3,5,2,4,1]=>7
[3,5,4,1,2]=>6
[3,5,4,2,1]=>6
[4,1,2,3,5]=>5
[4,1,2,5,3]=>6
[4,1,3,2,5]=>6
[4,1,3,5,2]=>6
[4,1,5,2,3]=>7
[4,1,5,3,2]=>7
[4,2,1,3,5]=>5
[4,2,1,5,3]=>6
[4,2,3,1,5]=>6
[4,2,3,5,1]=>6
[4,2,5,1,3]=>7
[4,2,5,3,1]=>7
[4,3,1,2,5]=>5
[4,3,1,5,2]=>6
[4,3,2,1,5]=>5
[4,3,2,5,1]=>6
[4,3,5,1,2]=>7
[4,3,5,2,1]=>7
[4,5,1,2,3]=>6
[4,5,1,3,2]=>7
[4,5,2,1,3]=>6
[4,5,2,3,1]=>7
[4,5,3,1,2]=>6
[4,5,3,2,1]=>6
[5,1,2,3,4]=>5
[5,1,2,4,3]=>6
[5,1,3,2,4]=>6
[5,1,3,4,2]=>6
[5,1,4,2,3]=>6
[5,1,4,3,2]=>6
[5,2,1,3,4]=>5
[5,2,1,4,3]=>6
[5,2,3,1,4]=>6
[5,2,3,4,1]=>6
[5,2,4,1,3]=>6
[5,2,4,3,1]=>6
[5,3,1,2,4]=>5
[5,3,1,4,2]=>6
[5,3,2,1,4]=>5
[5,3,2,4,1]=>6
[5,3,4,1,2]=>6
[5,3,4,2,1]=>6
[5,4,1,2,3]=>5
[5,4,1,3,2]=>6
[5,4,2,1,3]=>5
[5,4,2,3,1]=>6
[5,4,3,1,2]=>5
[5,4,3,2,1]=>5
[1,2,3,4,5,6]=>6
[1,2,3,4,6,5]=>7
[1,2,3,5,4,6]=>7
[1,2,3,5,6,4]=>7
[1,2,3,6,4,5]=>8
[1,2,3,6,5,4]=>8
[1,2,4,3,5,6]=>7
[1,2,4,3,6,5]=>8
[1,2,4,5,3,6]=>7
[1,2,4,5,6,3]=>7
[1,2,4,6,3,5]=>8
[1,2,4,6,5,3]=>8
[1,2,5,3,4,6]=>8
[1,2,5,3,6,4]=>8
[1,2,5,4,3,6]=>8
[1,2,5,4,6,3]=>8
[1,2,5,6,3,4]=>8
[1,2,5,6,4,3]=>8
[1,2,6,3,4,5]=>8
[1,2,6,3,5,4]=>9
[1,2,6,4,3,5]=>8
[1,2,6,4,5,3]=>9
[1,2,6,5,3,4]=>8
[1,2,6,5,4,3]=>8
[1,3,2,4,5,6]=>7
[1,3,2,4,6,5]=>8
[1,3,2,5,4,6]=>8
[1,3,2,5,6,4]=>8
[1,3,2,6,4,5]=>9
[1,3,2,6,5,4]=>9
[1,3,4,2,5,6]=>7
[1,3,4,2,6,5]=>8
[1,3,4,5,2,6]=>7
[1,3,4,5,6,2]=>7
[1,3,4,6,2,5]=>8
[1,3,4,6,5,2]=>8
[1,3,5,2,4,6]=>8
[1,3,5,2,6,4]=>8
[1,3,5,4,2,6]=>8
[1,3,5,4,6,2]=>8
[1,3,5,6,2,4]=>8
[1,3,5,6,4,2]=>8
[1,3,6,2,4,5]=>8
[1,3,6,2,5,4]=>9
[1,3,6,4,2,5]=>8
[1,3,6,4,5,2]=>9
[1,3,6,5,2,4]=>8
[1,3,6,5,4,2]=>8
[1,4,2,3,5,6]=>7
[1,4,2,3,6,5]=>8
[1,4,2,5,3,6]=>8
[1,4,2,5,6,3]=>8
[1,4,2,6,3,5]=>9
[1,4,2,6,5,3]=>9
[1,4,3,2,5,6]=>7
[1,4,3,2,6,5]=>8
[1,4,3,5,2,6]=>8
[1,4,3,5,6,2]=>8
[1,4,3,6,2,5]=>9
[1,4,3,6,5,2]=>9
[1,4,5,2,3,6]=>8
[1,4,5,2,6,3]=>8
[1,4,5,3,2,6]=>8
[1,4,5,3,6,2]=>8
[1,4,5,6,2,3]=>8
[1,4,5,6,3,2]=>8
[1,4,6,2,3,5]=>8
[1,4,6,2,5,3]=>9
[1,4,6,3,2,5]=>8
[1,4,6,3,5,2]=>9
[1,4,6,5,2,3]=>8
[1,4,6,5,3,2]=>8
[1,5,2,3,4,6]=>7
[1,5,2,3,6,4]=>8
[1,5,2,4,3,6]=>8
[1,5,2,4,6,3]=>8
[1,5,2,6,3,4]=>9
[1,5,2,6,4,3]=>9
[1,5,3,2,4,6]=>7
[1,5,3,2,6,4]=>8
[1,5,3,4,2,6]=>8
[1,5,3,4,6,2]=>8
[1,5,3,6,2,4]=>9
[1,5,3,6,4,2]=>9
[1,5,4,2,3,6]=>7
[1,5,4,2,6,3]=>8
[1,5,4,3,2,6]=>7
[1,5,4,3,6,2]=>8
[1,5,4,6,2,3]=>9
[1,5,4,6,3,2]=>9
[1,5,6,2,3,4]=>8
[1,5,6,2,4,3]=>9
[1,5,6,3,2,4]=>8
[1,5,6,3,4,2]=>9
[1,5,6,4,2,3]=>8
[1,5,6,4,3,2]=>8
[1,6,2,3,4,5]=>7
[1,6,2,3,5,4]=>8
[1,6,2,4,3,5]=>8
[1,6,2,4,5,3]=>8
[1,6,2,5,3,4]=>8
[1,6,2,5,4,3]=>8
[1,6,3,2,4,5]=>7
[1,6,3,2,5,4]=>8
[1,6,3,4,2,5]=>8
[1,6,3,4,5,2]=>8
[1,6,3,5,2,4]=>8
[1,6,3,5,4,2]=>8
[1,6,4,2,3,5]=>7
[1,6,4,2,5,3]=>8
[1,6,4,3,2,5]=>7
[1,6,4,3,5,2]=>8
[1,6,4,5,2,3]=>8
[1,6,4,5,3,2]=>8
[1,6,5,2,3,4]=>7
[1,6,5,2,4,3]=>8
[1,6,5,3,2,4]=>7
[1,6,5,3,4,2]=>8
[1,6,5,4,2,3]=>7
[1,6,5,4,3,2]=>7
[2,1,3,4,5,6]=>6
[2,1,3,4,6,5]=>7
[2,1,3,5,4,6]=>7
[2,1,3,5,6,4]=>7
[2,1,3,6,4,5]=>8
[2,1,3,6,5,4]=>8
[2,1,4,3,5,6]=>7
[2,1,4,3,6,5]=>8
[2,1,4,5,3,6]=>7
[2,1,4,5,6,3]=>7
[2,1,4,6,3,5]=>8
[2,1,4,6,5,3]=>8
[2,1,5,3,4,6]=>8
[2,1,5,3,6,4]=>8
[2,1,5,4,3,6]=>8
[2,1,5,4,6,3]=>8
[2,1,5,6,3,4]=>8
[2,1,5,6,4,3]=>8
[2,1,6,3,4,5]=>8
[2,1,6,3,5,4]=>9
[2,1,6,4,3,5]=>8
[2,1,6,4,5,3]=>9
[2,1,6,5,3,4]=>8
[2,1,6,5,4,3]=>8
[2,3,1,4,5,6]=>7
[2,3,1,4,6,5]=>8
[2,3,1,5,4,6]=>8
[2,3,1,5,6,4]=>8
[2,3,1,6,4,5]=>9
[2,3,1,6,5,4]=>9
[2,3,4,1,5,6]=>7
[2,3,4,1,6,5]=>8
[2,3,4,5,1,6]=>7
[2,3,4,5,6,1]=>7
[2,3,4,6,1,5]=>8
[2,3,4,6,5,1]=>8
[2,3,5,1,4,6]=>8
[2,3,5,1,6,4]=>8
[2,3,5,4,1,6]=>8
[2,3,5,4,6,1]=>8
[2,3,5,6,1,4]=>8
[2,3,5,6,4,1]=>8
[2,3,6,1,4,5]=>8
[2,3,6,1,5,4]=>9
[2,3,6,4,1,5]=>8
[2,3,6,4,5,1]=>9
[2,3,6,5,1,4]=>8
[2,3,6,5,4,1]=>8
[2,4,1,3,5,6]=>7
[2,4,1,3,6,5]=>8
[2,4,1,5,3,6]=>8
[2,4,1,5,6,3]=>8
[2,4,1,6,3,5]=>9
[2,4,1,6,5,3]=>9
[2,4,3,1,5,6]=>7
[2,4,3,1,6,5]=>8
[2,4,3,5,1,6]=>8
[2,4,3,5,6,1]=>8
[2,4,3,6,1,5]=>9
[2,4,3,6,5,1]=>9
[2,4,5,1,3,6]=>8
[2,4,5,1,6,3]=>8
[2,4,5,3,1,6]=>8
[2,4,5,3,6,1]=>8
[2,4,5,6,1,3]=>8
[2,4,5,6,3,1]=>8
[2,4,6,1,3,5]=>8
[2,4,6,1,5,3]=>9
[2,4,6,3,1,5]=>8
[2,4,6,3,5,1]=>9
[2,4,6,5,1,3]=>8
[2,4,6,5,3,1]=>8
[2,5,1,3,4,6]=>7
[2,5,1,3,6,4]=>8
[2,5,1,4,3,6]=>8
[2,5,1,4,6,3]=>8
[2,5,1,6,3,4]=>9
[2,5,1,6,4,3]=>9
[2,5,3,1,4,6]=>7
[2,5,3,1,6,4]=>8
[2,5,3,4,1,6]=>8
[2,5,3,4,6,1]=>8
[2,5,3,6,1,4]=>9
[2,5,3,6,4,1]=>9
[2,5,4,1,3,6]=>7
[2,5,4,1,6,3]=>8
[2,5,4,3,1,6]=>7
[2,5,4,3,6,1]=>8
[2,5,4,6,1,3]=>9
[2,5,4,6,3,1]=>9
[2,5,6,1,3,4]=>8
[2,5,6,1,4,3]=>9
[2,5,6,3,1,4]=>8
[2,5,6,3,4,1]=>9
[2,5,6,4,1,3]=>8
[2,5,6,4,3,1]=>8
[2,6,1,3,4,5]=>7
[2,6,1,3,5,4]=>8
[2,6,1,4,3,5]=>8
[2,6,1,4,5,3]=>8
[2,6,1,5,3,4]=>8
[2,6,1,5,4,3]=>8
[2,6,3,1,4,5]=>7
[2,6,3,1,5,4]=>8
[2,6,3,4,1,5]=>8
[2,6,3,4,5,1]=>8
[2,6,3,5,1,4]=>8
[2,6,3,5,4,1]=>8
[2,6,4,1,3,5]=>7
[2,6,4,1,5,3]=>8
[2,6,4,3,1,5]=>7
[2,6,4,3,5,1]=>8
[2,6,4,5,1,3]=>8
[2,6,4,5,3,1]=>8
[2,6,5,1,3,4]=>7
[2,6,5,1,4,3]=>8
[2,6,5,3,1,4]=>7
[2,6,5,3,4,1]=>8
[2,6,5,4,1,3]=>7
[2,6,5,4,3,1]=>7
[3,1,2,4,5,6]=>6
[3,1,2,4,6,5]=>7
[3,1,2,5,4,6]=>7
[3,1,2,5,6,4]=>7
[3,1,2,6,4,5]=>8
[3,1,2,6,5,4]=>8
[3,1,4,2,5,6]=>7
[3,1,4,2,6,5]=>8
[3,1,4,5,2,6]=>7
[3,1,4,5,6,2]=>7
[3,1,4,6,2,5]=>8
[3,1,4,6,5,2]=>8
[3,1,5,2,4,6]=>8
[3,1,5,2,6,4]=>8
[3,1,5,4,2,6]=>8
[3,1,5,4,6,2]=>8
[3,1,5,6,2,4]=>8
[3,1,5,6,4,2]=>8
[3,1,6,2,4,5]=>8
[3,1,6,2,5,4]=>9
[3,1,6,4,2,5]=>8
[3,1,6,4,5,2]=>9
[3,1,6,5,2,4]=>8
[3,1,6,5,4,2]=>8
[3,2,1,4,5,6]=>6
[3,2,1,4,6,5]=>7
[3,2,1,5,4,6]=>7
[3,2,1,5,6,4]=>7
[3,2,1,6,4,5]=>8
[3,2,1,6,5,4]=>8
[3,2,4,1,5,6]=>7
[3,2,4,1,6,5]=>8
[3,2,4,5,1,6]=>7
[3,2,4,5,6,1]=>7
[3,2,4,6,1,5]=>8
[3,2,4,6,5,1]=>8
[3,2,5,1,4,6]=>8
[3,2,5,1,6,4]=>8
[3,2,5,4,1,6]=>8
[3,2,5,4,6,1]=>8
[3,2,5,6,1,4]=>8
[3,2,5,6,4,1]=>8
[3,2,6,1,4,5]=>8
[3,2,6,1,5,4]=>9
[3,2,6,4,1,5]=>8
[3,2,6,4,5,1]=>9
[3,2,6,5,1,4]=>8
[3,2,6,5,4,1]=>8
[3,4,1,2,5,6]=>7
[3,4,1,2,6,5]=>8
[3,4,1,5,2,6]=>8
[3,4,1,5,6,2]=>8
[3,4,1,6,2,5]=>9
[3,4,1,6,5,2]=>9
[3,4,2,1,5,6]=>7
[3,4,2,1,6,5]=>8
[3,4,2,5,1,6]=>8
[3,4,2,5,6,1]=>8
[3,4,2,6,1,5]=>9
[3,4,2,6,5,1]=>9
[3,4,5,1,2,6]=>8
[3,4,5,1,6,2]=>8
[3,4,5,2,1,6]=>8
[3,4,5,2,6,1]=>8
[3,4,5,6,1,2]=>8
[3,4,5,6,2,1]=>8
[3,4,6,1,2,5]=>8
[3,4,6,1,5,2]=>9
[3,4,6,2,1,5]=>8
[3,4,6,2,5,1]=>9
[3,4,6,5,1,2]=>8
[3,4,6,5,2,1]=>8
[3,5,1,2,4,6]=>7
[3,5,1,2,6,4]=>8
[3,5,1,4,2,6]=>8
[3,5,1,4,6,2]=>8
[3,5,1,6,2,4]=>9
[3,5,1,6,4,2]=>9
[3,5,2,1,4,6]=>7
[3,5,2,1,6,4]=>8
[3,5,2,4,1,6]=>8
[3,5,2,4,6,1]=>8
[3,5,2,6,1,4]=>9
[3,5,2,6,4,1]=>9
[3,5,4,1,2,6]=>7
[3,5,4,1,6,2]=>8
[3,5,4,2,1,6]=>7
[3,5,4,2,6,1]=>8
[3,5,4,6,1,2]=>9
[3,5,4,6,2,1]=>9
[3,5,6,1,2,4]=>8
[3,5,6,1,4,2]=>9
[3,5,6,2,1,4]=>8
[3,5,6,2,4,1]=>9
[3,5,6,4,1,2]=>8
[3,5,6,4,2,1]=>8
[3,6,1,2,4,5]=>7
[3,6,1,2,5,4]=>8
[3,6,1,4,2,5]=>8
[3,6,1,4,5,2]=>8
[3,6,1,5,2,4]=>8
[3,6,1,5,4,2]=>8
[3,6,2,1,4,5]=>7
[3,6,2,1,5,4]=>8
[3,6,2,4,1,5]=>8
[3,6,2,4,5,1]=>8
[3,6,2,5,1,4]=>8
[3,6,2,5,4,1]=>8
[3,6,4,1,2,5]=>7
[3,6,4,1,5,2]=>8
[3,6,4,2,1,5]=>7
[3,6,4,2,5,1]=>8
[3,6,4,5,1,2]=>8
[3,6,4,5,2,1]=>8
[3,6,5,1,2,4]=>7
[3,6,5,1,4,2]=>8
[3,6,5,2,1,4]=>7
[3,6,5,2,4,1]=>8
[3,6,5,4,1,2]=>7
[3,6,5,4,2,1]=>7
[4,1,2,3,5,6]=>6
[4,1,2,3,6,5]=>7
[4,1,2,5,3,6]=>7
[4,1,2,5,6,3]=>7
[4,1,2,6,3,5]=>8
[4,1,2,6,5,3]=>8
[4,1,3,2,5,6]=>7
[4,1,3,2,6,5]=>8
[4,1,3,5,2,6]=>7
[4,1,3,5,6,2]=>7
[4,1,3,6,2,5]=>8
[4,1,3,6,5,2]=>8
[4,1,5,2,3,6]=>8
[4,1,5,2,6,3]=>8
[4,1,5,3,2,6]=>8
[4,1,5,3,6,2]=>8
[4,1,5,6,2,3]=>8
[4,1,5,6,3,2]=>8
[4,1,6,2,3,5]=>8
[4,1,6,2,5,3]=>9
[4,1,6,3,2,5]=>8
[4,1,6,3,5,2]=>9
[4,1,6,5,2,3]=>8
[4,1,6,5,3,2]=>8
[4,2,1,3,5,6]=>6
[4,2,1,3,6,5]=>7
[4,2,1,5,3,6]=>7
[4,2,1,5,6,3]=>7
[4,2,1,6,3,5]=>8
[4,2,1,6,5,3]=>8
[4,2,3,1,5,6]=>7
[4,2,3,1,6,5]=>8
[4,2,3,5,1,6]=>7
[4,2,3,5,6,1]=>7
[4,2,3,6,1,5]=>8
[4,2,3,6,5,1]=>8
[4,2,5,1,3,6]=>8
[4,2,5,1,6,3]=>8
[4,2,5,3,1,6]=>8
[4,2,5,3,6,1]=>8
[4,2,5,6,1,3]=>8
[4,2,5,6,3,1]=>8
[4,2,6,1,3,5]=>8
[4,2,6,1,5,3]=>9
[4,2,6,3,1,5]=>8
[4,2,6,3,5,1]=>9
[4,2,6,5,1,3]=>8
[4,2,6,5,3,1]=>8
[4,3,1,2,5,6]=>6
[4,3,1,2,6,5]=>7
[4,3,1,5,2,6]=>7
[4,3,1,5,6,2]=>7
[4,3,1,6,2,5]=>8
[4,3,1,6,5,2]=>8
[4,3,2,1,5,6]=>6
[4,3,2,1,6,5]=>7
[4,3,2,5,1,6]=>7
[4,3,2,5,6,1]=>7
[4,3,2,6,1,5]=>8
[4,3,2,6,5,1]=>8
[4,3,5,1,2,6]=>8
[4,3,5,1,6,2]=>8
[4,3,5,2,1,6]=>8
[4,3,5,2,6,1]=>8
[4,3,5,6,1,2]=>8
[4,3,5,6,2,1]=>8
[4,3,6,1,2,5]=>8
[4,3,6,1,5,2]=>9
[4,3,6,2,1,5]=>8
[4,3,6,2,5,1]=>9
[4,3,6,5,1,2]=>8
[4,3,6,5,2,1]=>8
[4,5,1,2,3,6]=>7
[4,5,1,2,6,3]=>8
[4,5,1,3,2,6]=>8
[4,5,1,3,6,2]=>8
[4,5,1,6,2,3]=>9
[4,5,1,6,3,2]=>9
[4,5,2,1,3,6]=>7
[4,5,2,1,6,3]=>8
[4,5,2,3,1,6]=>8
[4,5,2,3,6,1]=>8
[4,5,2,6,1,3]=>9
[4,5,2,6,3,1]=>9
[4,5,3,1,2,6]=>7
[4,5,3,1,6,2]=>8
[4,5,3,2,1,6]=>7
[4,5,3,2,6,1]=>8
[4,5,3,6,1,2]=>9
[4,5,3,6,2,1]=>9
[4,5,6,1,2,3]=>8
[4,5,6,1,3,2]=>9
[4,5,6,2,1,3]=>8
[4,5,6,2,3,1]=>9
[4,5,6,3,1,2]=>8
[4,5,6,3,2,1]=>8
[4,6,1,2,3,5]=>7
[4,6,1,2,5,3]=>8
[4,6,1,3,2,5]=>8
[4,6,1,3,5,2]=>8
[4,6,1,5,2,3]=>8
[4,6,1,5,3,2]=>8
[4,6,2,1,3,5]=>7
[4,6,2,1,5,3]=>8
[4,6,2,3,1,5]=>8
[4,6,2,3,5,1]=>8
[4,6,2,5,1,3]=>8
[4,6,2,5,3,1]=>8
[4,6,3,1,2,5]=>7
[4,6,3,1,5,2]=>8
[4,6,3,2,1,5]=>7
[4,6,3,2,5,1]=>8
[4,6,3,5,1,2]=>8
[4,6,3,5,2,1]=>8
[4,6,5,1,2,3]=>7
[4,6,5,1,3,2]=>8
[4,6,5,2,1,3]=>7
[4,6,5,2,3,1]=>8
[4,6,5,3,1,2]=>7
[4,6,5,3,2,1]=>7
[5,1,2,3,4,6]=>6
[5,1,2,3,6,4]=>7
[5,1,2,4,3,6]=>7
[5,1,2,4,6,3]=>7
[5,1,2,6,3,4]=>8
[5,1,2,6,4,3]=>8
[5,1,3,2,4,6]=>7
[5,1,3,2,6,4]=>8
[5,1,3,4,2,6]=>7
[5,1,3,4,6,2]=>7
[5,1,3,6,2,4]=>8
[5,1,3,6,4,2]=>8
[5,1,4,2,3,6]=>7
[5,1,4,2,6,3]=>8
[5,1,4,3,2,6]=>7
[5,1,4,3,6,2]=>8
[5,1,4,6,2,3]=>8
[5,1,4,6,3,2]=>8
[5,1,6,2,3,4]=>8
[5,1,6,2,4,3]=>9
[5,1,6,3,2,4]=>8
[5,1,6,3,4,2]=>9
[5,1,6,4,2,3]=>8
[5,1,6,4,3,2]=>8
[5,2,1,3,4,6]=>6
[5,2,1,3,6,4]=>7
[5,2,1,4,3,6]=>7
[5,2,1,4,6,3]=>7
[5,2,1,6,3,4]=>8
[5,2,1,6,4,3]=>8
[5,2,3,1,4,6]=>7
[5,2,3,1,6,4]=>8
[5,2,3,4,1,6]=>7
[5,2,3,4,6,1]=>7
[5,2,3,6,1,4]=>8
[5,2,3,6,4,1]=>8
[5,2,4,1,3,6]=>7
[5,2,4,1,6,3]=>8
[5,2,4,3,1,6]=>7
[5,2,4,3,6,1]=>8
[5,2,4,6,1,3]=>8
[5,2,4,6,3,1]=>8
[5,2,6,1,3,4]=>8
[5,2,6,1,4,3]=>9
[5,2,6,3,1,4]=>8
[5,2,6,3,4,1]=>9
[5,2,6,4,1,3]=>8
[5,2,6,4,3,1]=>8
[5,3,1,2,4,6]=>6
[5,3,1,2,6,4]=>7
[5,3,1,4,2,6]=>7
[5,3,1,4,6,2]=>7
[5,3,1,6,2,4]=>8
[5,3,1,6,4,2]=>8
[5,3,2,1,4,6]=>6
[5,3,2,1,6,4]=>7
[5,3,2,4,1,6]=>7
[5,3,2,4,6,1]=>7
[5,3,2,6,1,4]=>8
[5,3,2,6,4,1]=>8
[5,3,4,1,2,6]=>7
[5,3,4,1,6,2]=>8
[5,3,4,2,1,6]=>7
[5,3,4,2,6,1]=>8
[5,3,4,6,1,2]=>8
[5,3,4,6,2,1]=>8
[5,3,6,1,2,4]=>8
[5,3,6,1,4,2]=>9
[5,3,6,2,1,4]=>8
[5,3,6,2,4,1]=>9
[5,3,6,4,1,2]=>8
[5,3,6,4,2,1]=>8
[5,4,1,2,3,6]=>6
[5,4,1,2,6,3]=>7
[5,4,1,3,2,6]=>7
[5,4,1,3,6,2]=>7
[5,4,1,6,2,3]=>8
[5,4,1,6,3,2]=>8
[5,4,2,1,3,6]=>6
[5,4,2,1,6,3]=>7
[5,4,2,3,1,6]=>7
[5,4,2,3,6,1]=>7
[5,4,2,6,1,3]=>8
[5,4,2,6,3,1]=>8
[5,4,3,1,2,6]=>6
[5,4,3,1,6,2]=>7
[5,4,3,2,1,6]=>6
[5,4,3,2,6,1]=>7
[5,4,3,6,1,2]=>8
[5,4,3,6,2,1]=>8
[5,4,6,1,2,3]=>8
[5,4,6,1,3,2]=>9
[5,4,6,2,1,3]=>8
[5,4,6,2,3,1]=>9
[5,4,6,3,1,2]=>8
[5,4,6,3,2,1]=>8
[5,6,1,2,3,4]=>7
[5,6,1,2,4,3]=>8
[5,6,1,3,2,4]=>8
[5,6,1,3,4,2]=>8
[5,6,1,4,2,3]=>8
[5,6,1,4,3,2]=>8
[5,6,2,1,3,4]=>7
[5,6,2,1,4,3]=>8
[5,6,2,3,1,4]=>8
[5,6,2,3,4,1]=>8
[5,6,2,4,1,3]=>8
[5,6,2,4,3,1]=>8
[5,6,3,1,2,4]=>7
[5,6,3,1,4,2]=>8
[5,6,3,2,1,4]=>7
[5,6,3,2,4,1]=>8
[5,6,3,4,1,2]=>8
[5,6,3,4,2,1]=>8
[5,6,4,1,2,3]=>7
[5,6,4,1,3,2]=>8
[5,6,4,2,1,3]=>7
[5,6,4,2,3,1]=>8
[5,6,4,3,1,2]=>7
[5,6,4,3,2,1]=>7
[6,1,2,3,4,5]=>6
[6,1,2,3,5,4]=>7
[6,1,2,4,3,5]=>7
[6,1,2,4,5,3]=>7
[6,1,2,5,3,4]=>8
[6,1,2,5,4,3]=>8
[6,1,3,2,4,5]=>7
[6,1,3,2,5,4]=>8
[6,1,3,4,2,5]=>7
[6,1,3,4,5,2]=>7
[6,1,3,5,2,4]=>8
[6,1,3,5,4,2]=>8
[6,1,4,2,3,5]=>7
[6,1,4,2,5,3]=>8
[6,1,4,3,2,5]=>7
[6,1,4,3,5,2]=>8
[6,1,4,5,2,3]=>8
[6,1,4,5,3,2]=>8
[6,1,5,2,3,4]=>7
[6,1,5,2,4,3]=>8
[6,1,5,3,2,4]=>7
[6,1,5,3,4,2]=>8
[6,1,5,4,2,3]=>7
[6,1,5,4,3,2]=>7
[6,2,1,3,4,5]=>6
[6,2,1,3,5,4]=>7
[6,2,1,4,3,5]=>7
[6,2,1,4,5,3]=>7
[6,2,1,5,3,4]=>8
[6,2,1,5,4,3]=>8
[6,2,3,1,4,5]=>7
[6,2,3,1,5,4]=>8
[6,2,3,4,1,5]=>7
[6,2,3,4,5,1]=>7
[6,2,3,5,1,4]=>8
[6,2,3,5,4,1]=>8
[6,2,4,1,3,5]=>7
[6,2,4,1,5,3]=>8
[6,2,4,3,1,5]=>7
[6,2,4,3,5,1]=>8
[6,2,4,5,1,3]=>8
[6,2,4,5,3,1]=>8
[6,2,5,1,3,4]=>7
[6,2,5,1,4,3]=>8
[6,2,5,3,1,4]=>7
[6,2,5,3,4,1]=>8
[6,2,5,4,1,3]=>7
[6,2,5,4,3,1]=>7
[6,3,1,2,4,5]=>6
[6,3,1,2,5,4]=>7
[6,3,1,4,2,5]=>7
[6,3,1,4,5,2]=>7
[6,3,1,5,2,4]=>8
[6,3,1,5,4,2]=>8
[6,3,2,1,4,5]=>6
[6,3,2,1,5,4]=>7
[6,3,2,4,1,5]=>7
[6,3,2,4,5,1]=>7
[6,3,2,5,1,4]=>8
[6,3,2,5,4,1]=>8
[6,3,4,1,2,5]=>7
[6,3,4,1,5,2]=>8
[6,3,4,2,1,5]=>7
[6,3,4,2,5,1]=>8
[6,3,4,5,1,2]=>8
[6,3,4,5,2,1]=>8
[6,3,5,1,2,4]=>7
[6,3,5,1,4,2]=>8
[6,3,5,2,1,4]=>7
[6,3,5,2,4,1]=>8
[6,3,5,4,1,2]=>7
[6,3,5,4,2,1]=>7
[6,4,1,2,3,5]=>6
[6,4,1,2,5,3]=>7
[6,4,1,3,2,5]=>7
[6,4,1,3,5,2]=>7
[6,4,1,5,2,3]=>8
[6,4,1,5,3,2]=>8
[6,4,2,1,3,5]=>6
[6,4,2,1,5,3]=>7
[6,4,2,3,1,5]=>7
[6,4,2,3,5,1]=>7
[6,4,2,5,1,3]=>8
[6,4,2,5,3,1]=>8
[6,4,3,1,2,5]=>6
[6,4,3,1,5,2]=>7
[6,4,3,2,1,5]=>6
[6,4,3,2,5,1]=>7
[6,4,3,5,1,2]=>8
[6,4,3,5,2,1]=>8
[6,4,5,1,2,3]=>7
[6,4,5,1,3,2]=>8
[6,4,5,2,1,3]=>7
[6,4,5,2,3,1]=>8
[6,4,5,3,1,2]=>7
[6,4,5,3,2,1]=>7
[6,5,1,2,3,4]=>6
[6,5,1,2,4,3]=>7
[6,5,1,3,2,4]=>7
[6,5,1,3,4,2]=>7
[6,5,1,4,2,3]=>7
[6,5,1,4,3,2]=>7
[6,5,2,1,3,4]=>6
[6,5,2,1,4,3]=>7
[6,5,2,3,1,4]=>7
[6,5,2,3,4,1]=>7
[6,5,2,4,1,3]=>7
[6,5,2,4,3,1]=>7
[6,5,3,1,2,4]=>6
[6,5,3,1,4,2]=>7
[6,5,3,2,1,4]=>6
[6,5,3,2,4,1]=>7
[6,5,3,4,1,2]=>7
[6,5,3,4,2,1]=>7
[6,5,4,1,2,3]=>6
[6,5,4,1,3,2]=>7
[6,5,4,2,1,3]=>6
[6,5,4,2,3,1]=>7
[6,5,4,3,1,2]=>6
[6,5,4,3,2,1]=>6
[1,2,3,4,5,6,7]=>7
[1,2,3,4,5,7,6]=>8
[1,2,3,4,6,5,7]=>8
[1,2,3,4,6,7,5]=>8
[1,2,3,4,7,5,6]=>9
[1,2,3,4,7,6,5]=>9
[1,2,3,5,4,6,7]=>8
[1,2,3,5,4,7,6]=>9
[1,2,3,5,6,4,7]=>8
[1,2,3,5,6,7,4]=>8
[1,2,3,5,7,4,6]=>9
[1,2,3,5,7,6,4]=>9
[1,2,3,6,4,5,7]=>9
[1,2,3,6,4,7,5]=>9
[1,2,3,6,5,4,7]=>9
[1,2,3,6,5,7,4]=>9
[1,2,3,6,7,4,5]=>9
[1,2,3,6,7,5,4]=>9
[1,2,3,7,4,5,6]=>10
[1,2,3,7,4,6,5]=>11
[1,2,3,7,5,4,6]=>10
[1,2,3,7,5,6,4]=>11
[1,2,3,7,6,4,5]=>10
[1,2,3,7,6,5,4]=>10
[1,2,4,3,5,6,7]=>8
[1,2,4,3,5,7,6]=>9
[1,2,4,3,6,5,7]=>9
[1,2,4,3,6,7,5]=>9
[1,2,4,3,7,5,6]=>10
[1,2,4,3,7,6,5]=>10
[1,2,4,5,3,6,7]=>8
[1,2,4,5,3,7,6]=>9
[1,2,4,5,6,3,7]=>8
[1,2,4,5,6,7,3]=>8
[1,2,4,5,7,3,6]=>9
[1,2,4,5,7,6,3]=>9
[1,2,4,6,3,5,7]=>9
[1,2,4,6,3,7,5]=>9
[1,2,4,6,5,3,7]=>9
[1,2,4,6,5,7,3]=>9
[1,2,4,6,7,3,5]=>9
[1,2,4,6,7,5,3]=>9
[1,2,4,7,3,5,6]=>10
[1,2,4,7,3,6,5]=>11
[1,2,4,7,5,3,6]=>10
[1,2,4,7,5,6,3]=>11
[1,2,4,7,6,3,5]=>10
[1,2,4,7,6,5,3]=>10
[1,2,5,3,4,6,7]=>9
[1,2,5,3,4,7,6]=>10
[1,2,5,3,6,4,7]=>9
[1,2,5,3,6,7,4]=>9
[1,2,5,3,7,4,6]=>10
[1,2,5,3,7,6,4]=>10
[1,2,5,4,3,6,7]=>9
[1,2,5,4,3,7,6]=>10
[1,2,5,4,6,3,7]=>9
[1,2,5,4,6,7,3]=>9
[1,2,5,4,7,3,6]=>10
[1,2,5,4,7,6,3]=>10
[1,2,5,6,3,4,7]=>9
[1,2,5,6,3,7,4]=>9
[1,2,5,6,4,3,7]=>9
[1,2,5,6,4,7,3]=>9
[1,2,5,6,7,3,4]=>9
[1,2,5,6,7,4,3]=>9
[1,2,5,7,3,4,6]=>10
[1,2,5,7,3,6,4]=>11
[1,2,5,7,4,3,6]=>10
[1,2,5,7,4,6,3]=>11
[1,2,5,7,6,3,4]=>10
[1,2,5,7,6,4,3]=>10
[1,2,6,3,4,5,7]=>9
[1,2,6,3,4,7,5]=>10
[1,2,6,3,5,4,7]=>10
[1,2,6,3,5,7,4]=>10
[1,2,6,3,7,4,5]=>10
[1,2,6,3,7,5,4]=>10
[1,2,6,4,3,5,7]=>9
[1,2,6,4,3,7,5]=>10
[1,2,6,4,5,3,7]=>10
[1,2,6,4,5,7,3]=>10
[1,2,6,4,7,3,5]=>10
[1,2,6,4,7,5,3]=>10
[1,2,6,5,3,4,7]=>9
[1,2,6,5,3,7,4]=>10
[1,2,6,5,4,3,7]=>9
[1,2,6,5,4,7,3]=>10
[1,2,6,5,7,3,4]=>10
[1,2,6,5,7,4,3]=>10
[1,2,6,7,3,4,5]=>10
[1,2,6,7,3,5,4]=>11
[1,2,6,7,4,3,5]=>10
[1,2,6,7,4,5,3]=>11
[1,2,6,7,5,3,4]=>10
[1,2,6,7,5,4,3]=>10
[1,2,7,3,4,5,6]=>9
[1,2,7,3,4,6,5]=>10
[1,2,7,3,5,4,6]=>10
[1,2,7,3,5,6,4]=>10
[1,2,7,3,6,4,5]=>10
[1,2,7,3,6,5,4]=>10
[1,2,7,4,3,5,6]=>9
[1,2,7,4,3,6,5]=>10
[1,2,7,4,5,3,6]=>10
[1,2,7,4,5,6,3]=>10
[1,2,7,4,6,3,5]=>10
[1,2,7,4,6,5,3]=>10
[1,2,7,5,3,4,6]=>9
[1,2,7,5,3,6,4]=>10
[1,2,7,5,4,3,6]=>9
[1,2,7,5,4,6,3]=>10
[1,2,7,5,6,3,4]=>10
[1,2,7,5,6,4,3]=>10
[1,2,7,6,3,4,5]=>9
[1,2,7,6,3,5,4]=>10
[1,2,7,6,4,3,5]=>9
[1,2,7,6,4,5,3]=>10
[1,2,7,6,5,3,4]=>9
[1,2,7,6,5,4,3]=>9
[1,3,2,4,5,6,7]=>8
[1,3,2,4,5,7,6]=>9
[1,3,2,4,6,5,7]=>9
[1,3,2,4,6,7,5]=>9
[1,3,2,4,7,5,6]=>10
[1,3,2,4,7,6,5]=>10
[1,3,2,5,4,6,7]=>9
[1,3,2,5,4,7,6]=>10
[1,3,2,5,6,4,7]=>9
[1,3,2,5,6,7,4]=>9
[1,3,2,5,7,4,6]=>10
[1,3,2,5,7,6,4]=>10
[1,3,2,6,4,5,7]=>10
[1,3,2,6,4,7,5]=>10
[1,3,2,6,5,4,7]=>10
[1,3,2,6,5,7,4]=>10
[1,3,2,6,7,4,5]=>10
[1,3,2,6,7,5,4]=>10
[1,3,2,7,4,5,6]=>11
[1,3,2,7,4,6,5]=>12
[1,3,2,7,5,4,6]=>11
[1,3,2,7,5,6,4]=>12
[1,3,2,7,6,4,5]=>11
[1,3,2,7,6,5,4]=>11
[1,3,4,2,5,6,7]=>8
[1,3,4,2,5,7,6]=>9
[1,3,4,2,6,5,7]=>9
[1,3,4,2,6,7,5]=>9
[1,3,4,2,7,5,6]=>10
[1,3,4,2,7,6,5]=>10
[1,3,4,5,2,6,7]=>8
[1,3,4,5,2,7,6]=>9
[1,3,4,5,6,2,7]=>8
[1,3,4,5,6,7,2]=>8
[1,3,4,5,7,2,6]=>9
[1,3,4,5,7,6,2]=>9
[1,3,4,6,2,5,7]=>9
[1,3,4,6,2,7,5]=>9
[1,3,4,6,5,2,7]=>9
[1,3,4,6,5,7,2]=>9
[1,3,4,6,7,2,5]=>9
[1,3,4,6,7,5,2]=>9
[1,3,4,7,2,5,6]=>10
[1,3,4,7,2,6,5]=>11
[1,3,4,7,5,2,6]=>10
[1,3,4,7,5,6,2]=>11
[1,3,4,7,6,2,5]=>10
[1,3,4,7,6,5,2]=>10
[1,3,5,2,4,6,7]=>9
[1,3,5,2,4,7,6]=>10
[1,3,5,2,6,4,7]=>9
[1,3,5,2,6,7,4]=>9
[1,3,5,2,7,4,6]=>10
[1,3,5,2,7,6,4]=>10
[1,3,5,4,2,6,7]=>9
[1,3,5,4,2,7,6]=>10
[1,3,5,4,6,2,7]=>9
[1,3,5,4,6,7,2]=>9
[1,3,5,4,7,2,6]=>10
[1,3,5,4,7,6,2]=>10
[1,3,5,6,2,4,7]=>9
[1,3,5,6,2,7,4]=>9
[1,3,5,6,4,2,7]=>9
[1,3,5,6,4,7,2]=>9
[1,3,5,6,7,2,4]=>9
[1,3,5,6,7,4,2]=>9
[1,3,5,7,2,4,6]=>10
[1,3,5,7,2,6,4]=>11
[1,3,5,7,4,2,6]=>10
[1,3,5,7,4,6,2]=>11
[1,3,5,7,6,2,4]=>10
[1,3,5,7,6,4,2]=>10
[1,3,6,2,4,5,7]=>9
[1,3,6,2,4,7,5]=>10
[1,3,6,2,5,4,7]=>10
[1,3,6,2,5,7,4]=>10
[1,3,6,2,7,4,5]=>10
[1,3,6,2,7,5,4]=>10
[1,3,6,4,2,5,7]=>9
[1,3,6,4,2,7,5]=>10
[1,3,6,4,5,2,7]=>10
[1,3,6,4,5,7,2]=>10
[1,3,6,4,7,2,5]=>10
[1,3,6,4,7,5,2]=>10
[1,3,6,5,2,4,7]=>9
[1,3,6,5,2,7,4]=>10
[1,3,6,5,4,2,7]=>9
[1,3,6,5,4,7,2]=>10
[1,3,6,5,7,2,4]=>10
[1,3,6,5,7,4,2]=>10
[1,3,6,7,2,4,5]=>10
[1,3,6,7,2,5,4]=>11
[1,3,6,7,4,2,5]=>10
[1,3,6,7,4,5,2]=>11
[1,3,6,7,5,2,4]=>10
[1,3,6,7,5,4,2]=>10
[1,3,7,2,4,5,6]=>9
[1,3,7,2,4,6,5]=>10
[1,3,7,2,5,4,6]=>10
[1,3,7,2,5,6,4]=>10
[1,3,7,2,6,4,5]=>10
[1,3,7,2,6,5,4]=>10
[1,3,7,4,2,5,6]=>9
[1,3,7,4,2,6,5]=>10
[1,3,7,4,5,2,6]=>10
[1,3,7,4,5,6,2]=>10
[1,3,7,4,6,2,5]=>10
[1,3,7,4,6,5,2]=>10
[1,3,7,5,2,4,6]=>9
[1,3,7,5,2,6,4]=>10
[1,3,7,5,4,2,6]=>9
[1,3,7,5,4,6,2]=>10
[1,3,7,5,6,2,4]=>10
[1,3,7,5,6,4,2]=>10
[1,3,7,6,2,4,5]=>9
[1,3,7,6,2,5,4]=>10
[1,3,7,6,4,2,5]=>9
[1,3,7,6,4,5,2]=>10
[1,3,7,6,5,2,4]=>9
[1,3,7,6,5,4,2]=>9
[1,4,2,3,5,6,7]=>8
[1,4,2,3,5,7,6]=>9
[1,4,2,3,6,5,7]=>9
[1,4,2,3,6,7,5]=>9
[1,4,2,3,7,5,6]=>10
[1,4,2,3,7,6,5]=>10
[1,4,2,5,3,6,7]=>9
[1,4,2,5,3,7,6]=>10
[1,4,2,5,6,3,7]=>9
[1,4,2,5,6,7,3]=>9
[1,4,2,5,7,3,6]=>10
[1,4,2,5,7,6,3]=>10
[1,4,2,6,3,5,7]=>10
[1,4,2,6,3,7,5]=>10
[1,4,2,6,5,3,7]=>10
[1,4,2,6,5,7,3]=>10
[1,4,2,6,7,3,5]=>10
[1,4,2,6,7,5,3]=>10
[1,4,2,7,3,5,6]=>11
[1,4,2,7,3,6,5]=>12
[1,4,2,7,5,3,6]=>11
[1,4,2,7,5,6,3]=>12
[1,4,2,7,6,3,5]=>11
[1,4,2,7,6,5,3]=>11
[1,4,3,2,5,6,7]=>8
[1,4,3,2,5,7,6]=>9
[1,4,3,2,6,5,7]=>9
[1,4,3,2,6,7,5]=>9
[1,4,3,2,7,5,6]=>10
[1,4,3,2,7,6,5]=>10
[1,4,3,5,2,6,7]=>9
[1,4,3,5,2,7,6]=>10
[1,4,3,5,6,2,7]=>9
[1,4,3,5,6,7,2]=>9
[1,4,3,5,7,2,6]=>10
[1,4,3,5,7,6,2]=>10
[1,4,3,6,2,5,7]=>10
[1,4,3,6,2,7,5]=>10
[1,4,3,6,5,2,7]=>10
[1,4,3,6,5,7,2]=>10
[1,4,3,6,7,2,5]=>10
[1,4,3,6,7,5,2]=>10
[1,4,3,7,2,5,6]=>11
[1,4,3,7,2,6,5]=>12
[1,4,3,7,5,2,6]=>11
[1,4,3,7,5,6,2]=>12
[1,4,3,7,6,2,5]=>11
[1,4,3,7,6,5,2]=>11
[1,4,5,2,3,6,7]=>9
[1,4,5,2,3,7,6]=>10
[1,4,5,2,6,3,7]=>9
[1,4,5,2,6,7,3]=>9
[1,4,5,2,7,3,6]=>10
[1,4,5,2,7,6,3]=>10
[1,4,5,3,2,6,7]=>9
[1,4,5,3,2,7,6]=>10
[1,4,5,3,6,2,7]=>9
[1,4,5,3,6,7,2]=>9
[1,4,5,3,7,2,6]=>10
[1,4,5,3,7,6,2]=>10
[1,4,5,6,2,3,7]=>9
[1,4,5,6,2,7,3]=>9
[1,4,5,6,3,2,7]=>9
[1,4,5,6,3,7,2]=>9
[1,4,5,6,7,2,3]=>9
[1,4,5,6,7,3,2]=>9
[1,4,5,7,2,3,6]=>10
[1,4,5,7,2,6,3]=>11
[1,4,5,7,3,2,6]=>10
[1,4,5,7,3,6,2]=>11
[1,4,5,7,6,2,3]=>10
[1,4,5,7,6,3,2]=>10
[1,4,6,2,3,5,7]=>9
[1,4,6,2,3,7,5]=>10
[1,4,6,2,5,3,7]=>10
[1,4,6,2,5,7,3]=>10
[1,4,6,2,7,3,5]=>10
[1,4,6,2,7,5,3]=>10
[1,4,6,3,2,5,7]=>9
[1,4,6,3,2,7,5]=>10
[1,4,6,3,5,2,7]=>10
[1,4,6,3,5,7,2]=>10
[1,4,6,3,7,2,5]=>10
[1,4,6,3,7,5,2]=>10
[1,4,6,5,2,3,7]=>9
[1,4,6,5,2,7,3]=>10
[1,4,6,5,3,2,7]=>9
[1,4,6,5,3,7,2]=>10
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Description
The sum of the minimal distances to a greater element.
Set $\pi_0 = \pi_{n+1} = n+1$, then this statistic is
$$ \sum_{i=1}^n \min_d(\pi_{i-d}>\pi_i\text{ or }\pi_{i+d}>\pi_i) $$
This statistic appears in [1].
The generating function for the sequence of maximal values attained on $\mathfrak S_r$, $r\geq 0$ apparently coincides with [2], which satisfies the functional equation
$$ (x-1)^2 (x+1)^3 f(x^2) - (x-1)^2 (x+1) f(x) + x = 0. $$
Set $\pi_0 = \pi_{n+1} = n+1$, then this statistic is
$$ \sum_{i=1}^n \min_d(\pi_{i-d}>\pi_i\text{ or }\pi_{i+d}>\pi_i) $$
This statistic appears in [1].
The generating function for the sequence of maximal values attained on $\mathfrak S_r$, $r\geq 0$ apparently coincides with [2], which satisfies the functional equation
$$ (x-1)^2 (x+1)^3 f(x^2) - (x-1)^2 (x+1) f(x) + x = 0. $$
References
[1] newbie How to find a permutation of [n] so that $\sum \{\min (i-l[i],r[i]-i)\}$ is maximized? MathOverflow:251968
[2] Total number of 1's in binary expansions of 0, ..., n. OEIS:A000788
[2] Total number of 1's in binary expansions of 0, ..., n. OEIS:A000788
Code
def statistic(pi):
n = len(pi)
def closest_major(i):
ai = pi[i]
distance = 1
while True:
if (i-distance < 0 or pi[i-distance] >= ai or
i+distance >= n or pi[i+distance] >= ai):
return distance
distance += 1
return sum(closest_major(i) for i in range(n))
Created
Oct 15, 2016 at 21:57 by Martin Rubey
Updated
Oct 15, 2016 at 21:57 by Martin Rubey
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