Identifier
- St001671: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>2
[2,1,3]=>1
[2,3,1]=>3
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>0
[1,2,4,3]=>3
[1,3,2,4]=>2
[1,3,4,2]=>5
[1,4,2,3]=>3
[1,4,3,2]=>2
[2,1,3,4]=>1
[2,1,4,3]=>4
[2,3,1,4]=>3
[2,3,4,1]=>6
[2,4,1,3]=>4
[2,4,3,1]=>3
[3,1,2,4]=>2
[3,1,4,2]=>5
[3,2,1,4]=>1
[3,2,4,1]=>4
[3,4,1,2]=>4
[3,4,2,1]=>3
[4,1,2,3]=>3
[4,1,3,2]=>2
[4,2,1,3]=>2
[4,2,3,1]=>1
[4,3,1,2]=>5
[4,3,2,1]=>4
[1,2,3,4,5]=>0
[1,2,3,5,4]=>4
[1,2,4,3,5]=>3
[1,2,4,5,3]=>7
[1,2,5,3,4]=>4
[1,2,5,4,3]=>3
[1,3,2,4,5]=>2
[1,3,2,5,4]=>6
[1,3,4,2,5]=>5
[1,3,4,5,2]=>9
[1,3,5,2,4]=>6
[1,3,5,4,2]=>5
[1,4,2,3,5]=>3
[1,4,2,5,3]=>7
[1,4,3,2,5]=>2
[1,4,3,5,2]=>6
[1,4,5,2,3]=>6
[1,4,5,3,2]=>5
[1,5,2,3,4]=>4
[1,5,2,4,3]=>3
[1,5,3,2,4]=>3
[1,5,3,4,2]=>2
[1,5,4,2,3]=>7
[1,5,4,3,2]=>6
[2,1,3,4,5]=>1
[2,1,3,5,4]=>5
[2,1,4,3,5]=>4
[2,1,4,5,3]=>8
[2,1,5,3,4]=>5
[2,1,5,4,3]=>4
[2,3,1,4,5]=>3
[2,3,1,5,4]=>7
[2,3,4,1,5]=>6
[2,3,4,5,1]=>10
[2,3,5,1,4]=>7
[2,3,5,4,1]=>6
[2,4,1,3,5]=>4
[2,4,1,5,3]=>8
[2,4,3,1,5]=>3
[2,4,3,5,1]=>7
[2,4,5,1,3]=>7
[2,4,5,3,1]=>6
[2,5,1,3,4]=>5
[2,5,1,4,3]=>4
[2,5,3,1,4]=>4
[2,5,3,4,1]=>3
[2,5,4,1,3]=>8
[2,5,4,3,1]=>7
[3,1,2,4,5]=>2
[3,1,2,5,4]=>6
[3,1,4,2,5]=>5
[3,1,4,5,2]=>9
[3,1,5,2,4]=>6
[3,1,5,4,2]=>5
[3,2,1,4,5]=>1
[3,2,1,5,4]=>5
[3,2,4,1,5]=>4
[3,2,4,5,1]=>8
[3,2,5,1,4]=>5
[3,2,5,4,1]=>4
[3,4,1,2,5]=>4
[3,4,1,5,2]=>8
[3,4,2,1,5]=>3
[3,4,2,5,1]=>7
[3,4,5,1,2]=>7
[3,4,5,2,1]=>6
[3,5,1,2,4]=>5
[3,5,1,4,2]=>4
[3,5,2,1,4]=>4
[3,5,2,4,1]=>3
[3,5,4,1,2]=>8
[3,5,4,2,1]=>7
[4,1,2,3,5]=>3
[4,1,2,5,3]=>7
[4,1,3,2,5]=>2
[4,1,3,5,2]=>6
[4,1,5,2,3]=>6
[4,1,5,3,2]=>5
[4,2,1,3,5]=>2
[4,2,1,5,3]=>6
[4,2,3,1,5]=>1
[4,2,3,5,1]=>5
[4,2,5,1,3]=>5
[4,2,5,3,1]=>4
[4,3,1,2,5]=>5
[4,3,1,5,2]=>9
[4,3,2,1,5]=>4
[4,3,2,5,1]=>8
[4,3,5,1,2]=>8
[4,3,5,2,1]=>7
[4,5,1,2,3]=>6
[4,5,1,3,2]=>5
[4,5,2,1,3]=>5
[4,5,2,3,1]=>4
[4,5,3,1,2]=>4
[4,5,3,2,1]=>3
[5,1,2,3,4]=>4
[5,1,2,4,3]=>3
[5,1,3,2,4]=>3
[5,1,3,4,2]=>2
[5,1,4,2,3]=>7
[5,1,4,3,2]=>6
[5,2,1,3,4]=>3
[5,2,1,4,3]=>2
[5,2,3,1,4]=>2
[5,2,3,4,1]=>1
[5,2,4,1,3]=>6
[5,2,4,3,1]=>5
[5,3,1,2,4]=>6
[5,3,1,4,2]=>5
[5,3,2,1,4]=>5
[5,3,2,4,1]=>4
[5,3,4,1,2]=>9
[5,3,4,2,1]=>8
[5,4,1,2,3]=>7
[5,4,1,3,2]=>6
[5,4,2,1,3]=>6
[5,4,2,3,1]=>5
[5,4,3,1,2]=>5
[5,4,3,2,1]=>4
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>9
[1,2,3,6,4,5]=>5
[1,2,3,6,5,4]=>4
[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>8
[1,2,4,5,3,6]=>7
[1,2,4,5,6,3]=>12
[1,2,4,6,3,5]=>8
[1,2,4,6,5,3]=>7
[1,2,5,3,4,6]=>4
[1,2,5,3,6,4]=>9
[1,2,5,4,3,6]=>3
[1,2,5,4,6,3]=>8
[1,2,5,6,3,4]=>8
[1,2,5,6,4,3]=>7
[1,2,6,3,4,5]=>5
[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>4
[1,2,6,4,5,3]=>3
[1,2,6,5,3,4]=>9
[1,2,6,5,4,3]=>8
[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>7
[1,3,2,5,4,6]=>6
[1,3,2,5,6,4]=>11
[1,3,2,6,4,5]=>7
[1,3,2,6,5,4]=>6
[1,3,4,2,5,6]=>5
[1,3,4,2,6,5]=>10
[1,3,4,5,2,6]=>9
[1,3,4,5,6,2]=>14
[1,3,4,6,2,5]=>10
[1,3,4,6,5,2]=>9
[1,3,5,2,4,6]=>6
[1,3,5,2,6,4]=>11
[1,3,5,4,2,6]=>5
[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]=>7
[1,3,6,2,5,4]=>6
[1,3,6,4,2,5]=>6
[1,3,6,4,5,2]=>5
[1,3,6,5,2,4]=>11
[1,3,6,5,4,2]=>10
[1,4,2,3,5,6]=>3
[1,4,2,3,6,5]=>8
[1,4,2,5,3,6]=>7
[1,4,2,5,6,3]=>12
[1,4,2,6,3,5]=>8
[1,4,2,6,5,3]=>7
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>7
[1,4,3,5,2,6]=>6
[1,4,3,5,6,2]=>11
[1,4,3,6,2,5]=>7
[1,4,3,6,5,2]=>6
[1,4,5,2,3,6]=>6
[1,4,5,2,6,3]=>11
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>10
[1,4,5,6,2,3]=>10
[1,4,5,6,3,2]=>9
[1,4,6,2,3,5]=>7
[1,4,6,2,5,3]=>6
[1,4,6,3,2,5]=>6
[1,4,6,3,5,2]=>5
[1,4,6,5,2,3]=>11
[1,4,6,5,3,2]=>10
[1,5,2,3,4,6]=>4
[1,5,2,3,6,4]=>9
[1,5,2,4,3,6]=>3
[1,5,2,4,6,3]=>8
[1,5,2,6,3,4]=>8
[1,5,2,6,4,3]=>7
[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>8
[1,5,3,4,2,6]=>2
[1,5,3,4,6,2]=>7
[1,5,3,6,2,4]=>7
[1,5,3,6,4,2]=>6
[1,5,4,2,3,6]=>7
[1,5,4,2,6,3]=>12
[1,5,4,3,2,6]=>6
[1,5,4,3,6,2]=>11
[1,5,4,6,2,3]=>11
[1,5,4,6,3,2]=>10
[1,5,6,2,3,4]=>8
[1,5,6,2,4,3]=>7
[1,5,6,3,2,4]=>7
[1,5,6,3,4,2]=>6
[1,5,6,4,2,3]=>6
[1,5,6,4,3,2]=>5
[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>4
[1,6,2,4,3,5]=>4
[1,6,2,4,5,3]=>3
[1,6,2,5,3,4]=>9
[1,6,2,5,4,3]=>8
[1,6,3,2,4,5]=>4
[1,6,3,2,5,4]=>3
[1,6,3,4,2,5]=>3
[1,6,3,4,5,2]=>2
[1,6,3,5,2,4]=>8
[1,6,3,5,4,2]=>7
[1,6,4,2,3,5]=>8
[1,6,4,2,5,3]=>7
[1,6,4,3,2,5]=>7
[1,6,4,3,5,2]=>6
[1,6,4,5,2,3]=>12
[1,6,4,5,3,2]=>11
[1,6,5,2,3,4]=>9
[1,6,5,2,4,3]=>8
[1,6,5,3,2,4]=>8
[1,6,5,3,4,2]=>7
[1,6,5,4,2,3]=>7
[1,6,5,4,3,2]=>6
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>6
[2,1,3,5,4,6]=>5
[2,1,3,5,6,4]=>10
[2,1,3,6,4,5]=>6
[2,1,3,6,5,4]=>5
[2,1,4,3,5,6]=>4
[2,1,4,3,6,5]=>9
[2,1,4,5,3,6]=>8
[2,1,4,5,6,3]=>13
[2,1,4,6,3,5]=>9
[2,1,4,6,5,3]=>8
[2,1,5,3,4,6]=>5
[2,1,5,3,6,4]=>10
[2,1,5,4,3,6]=>4
[2,1,5,4,6,3]=>9
[2,1,5,6,3,4]=>9
[2,1,5,6,4,3]=>8
[2,1,6,3,4,5]=>6
[2,1,6,3,5,4]=>5
[2,1,6,4,3,5]=>5
[2,1,6,4,5,3]=>4
[2,1,6,5,3,4]=>10
[2,1,6,5,4,3]=>9
[2,3,1,4,5,6]=>3
[2,3,1,4,6,5]=>8
[2,3,1,5,4,6]=>7
[2,3,1,5,6,4]=>12
[2,3,1,6,4,5]=>8
[2,3,1,6,5,4]=>7
[2,3,4,1,5,6]=>6
[2,3,4,1,6,5]=>11
[2,3,4,5,1,6]=>10
[2,3,4,5,6,1]=>15
[2,3,4,6,1,5]=>11
[2,3,4,6,5,1]=>10
[2,3,5,1,4,6]=>7
[2,3,5,1,6,4]=>12
[2,3,5,4,1,6]=>6
[2,3,5,4,6,1]=>11
[2,3,5,6,1,4]=>11
[2,3,5,6,4,1]=>10
[2,3,6,1,4,5]=>8
[2,3,6,1,5,4]=>7
[2,3,6,4,1,5]=>7
[2,3,6,4,5,1]=>6
[2,3,6,5,1,4]=>12
[2,3,6,5,4,1]=>11
[2,4,1,3,5,6]=>4
[2,4,1,3,6,5]=>9
[2,4,1,5,3,6]=>8
[2,4,1,5,6,3]=>13
[2,4,1,6,3,5]=>9
[2,4,1,6,5,3]=>8
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>8
[2,4,3,5,1,6]=>7
[2,4,3,5,6,1]=>12
[2,4,3,6,1,5]=>8
[2,4,3,6,5,1]=>7
[2,4,5,1,3,6]=>7
[2,4,5,1,6,3]=>12
[2,4,5,3,1,6]=>6
[2,4,5,3,6,1]=>11
[2,4,5,6,1,3]=>11
[2,4,5,6,3,1]=>10
[2,4,6,1,3,5]=>8
[2,4,6,1,5,3]=>7
[2,4,6,3,1,5]=>7
[2,4,6,3,5,1]=>6
[2,4,6,5,1,3]=>12
[2,4,6,5,3,1]=>11
[2,5,1,3,4,6]=>5
[2,5,1,3,6,4]=>10
[2,5,1,4,3,6]=>4
[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]=>4
[2,5,3,1,6,4]=>9
[2,5,3,4,1,6]=>3
[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]=>8
[2,5,4,1,6,3]=>13
[2,5,4,3,1,6]=>7
[2,5,4,3,6,1]=>12
[2,5,4,6,1,3]=>12
[2,5,4,6,3,1]=>11
[2,5,6,1,3,4]=>9
[2,5,6,1,4,3]=>8
[2,5,6,3,1,4]=>8
[2,5,6,3,4,1]=>7
[2,5,6,4,1,3]=>7
[2,5,6,4,3,1]=>6
[2,6,1,3,4,5]=>6
[2,6,1,3,5,4]=>5
[2,6,1,4,3,5]=>5
[2,6,1,4,5,3]=>4
[2,6,1,5,3,4]=>10
[2,6,1,5,4,3]=>9
[2,6,3,1,4,5]=>5
[2,6,3,1,5,4]=>4
[2,6,3,4,1,5]=>4
[2,6,3,4,5,1]=>3
[2,6,3,5,1,4]=>9
[2,6,3,5,4,1]=>8
[2,6,4,1,3,5]=>9
[2,6,4,1,5,3]=>8
[2,6,4,3,1,5]=>8
[2,6,4,3,5,1]=>7
[2,6,4,5,1,3]=>13
[2,6,4,5,3,1]=>12
[2,6,5,1,3,4]=>10
[2,6,5,1,4,3]=>9
[2,6,5,3,1,4]=>9
[2,6,5,3,4,1]=>8
[2,6,5,4,1,3]=>8
[2,6,5,4,3,1]=>7
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>7
[3,1,2,5,4,6]=>6
[3,1,2,5,6,4]=>11
[3,1,2,6,4,5]=>7
[3,1,2,6,5,4]=>6
[3,1,4,2,5,6]=>5
[3,1,4,2,6,5]=>10
[3,1,4,5,2,6]=>9
[3,1,4,5,6,2]=>14
[3,1,4,6,2,5]=>10
[3,1,4,6,5,2]=>9
[3,1,5,2,4,6]=>6
[3,1,5,2,6,4]=>11
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>10
[3,1,5,6,2,4]=>10
[3,1,5,6,4,2]=>9
[3,1,6,2,4,5]=>7
[3,1,6,2,5,4]=>6
[3,1,6,4,2,5]=>6
[3,1,6,4,5,2]=>5
[3,1,6,5,2,4]=>11
[3,1,6,5,4,2]=>10
[3,2,1,4,5,6]=>1
[3,2,1,4,6,5]=>6
[3,2,1,5,4,6]=>5
[3,2,1,5,6,4]=>10
[3,2,1,6,4,5]=>6
[3,2,1,6,5,4]=>5
[3,2,4,1,5,6]=>4
[3,2,4,1,6,5]=>9
[3,2,4,5,1,6]=>8
[3,2,4,5,6,1]=>13
[3,2,4,6,1,5]=>9
[3,2,4,6,5,1]=>8
[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>10
[3,2,5,4,1,6]=>4
[3,2,5,4,6,1]=>9
[3,2,5,6,1,4]=>9
[3,2,5,6,4,1]=>8
[3,2,6,1,4,5]=>6
[3,2,6,1,5,4]=>5
[3,2,6,4,1,5]=>5
[3,2,6,4,5,1]=>4
[3,2,6,5,1,4]=>10
[3,2,6,5,4,1]=>9
[3,4,1,2,5,6]=>4
[3,4,1,2,6,5]=>9
[3,4,1,5,2,6]=>8
[3,4,1,5,6,2]=>13
[3,4,1,6,2,5]=>9
[3,4,1,6,5,2]=>8
[3,4,2,1,5,6]=>3
[3,4,2,1,6,5]=>8
[3,4,2,5,1,6]=>7
[3,4,2,5,6,1]=>12
[3,4,2,6,1,5]=>8
[3,4,2,6,5,1]=>7
[3,4,5,1,2,6]=>7
[3,4,5,1,6,2]=>12
[3,4,5,2,1,6]=>6
[3,4,5,2,6,1]=>11
[3,4,5,6,1,2]=>11
[3,4,5,6,2,1]=>10
[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]=>12
[3,4,6,5,2,1]=>11
[3,5,1,2,4,6]=>5
[3,5,1,2,6,4]=>10
[3,5,1,4,2,6]=>4
[3,5,1,4,6,2]=>9
[3,5,1,6,2,4]=>9
[3,5,1,6,4,2]=>8
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>9
[3,5,2,4,1,6]=>3
[3,5,2,4,6,1]=>8
[3,5,2,6,1,4]=>8
[3,5,2,6,4,1]=>7
[3,5,4,1,2,6]=>8
[3,5,4,1,6,2]=>13
[3,5,4,2,1,6]=>7
[3,5,4,2,6,1]=>12
[3,5,4,6,1,2]=>12
[3,5,4,6,2,1]=>11
[3,5,6,1,2,4]=>9
[3,5,6,1,4,2]=>8
[3,5,6,2,1,4]=>8
[3,5,6,2,4,1]=>7
[3,5,6,4,1,2]=>7
[3,5,6,4,2,1]=>6
[3,6,1,2,4,5]=>6
[3,6,1,2,5,4]=>5
[3,6,1,4,2,5]=>5
[3,6,1,4,5,2]=>4
[3,6,1,5,2,4]=>10
[3,6,1,5,4,2]=>9
[3,6,2,1,4,5]=>5
[3,6,2,1,5,4]=>4
[3,6,2,4,1,5]=>4
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>9
[3,6,2,5,4,1]=>8
[3,6,4,1,2,5]=>9
[3,6,4,1,5,2]=>8
[3,6,4,2,1,5]=>8
[3,6,4,2,5,1]=>7
[3,6,4,5,1,2]=>13
[3,6,4,5,2,1]=>12
[3,6,5,1,2,4]=>10
[3,6,5,1,4,2]=>9
[3,6,5,2,1,4]=>9
[3,6,5,2,4,1]=>8
[3,6,5,4,1,2]=>8
[3,6,5,4,2,1]=>7
[4,1,2,3,5,6]=>3
[4,1,2,3,6,5]=>8
[4,1,2,5,3,6]=>7
[4,1,2,5,6,3]=>12
[4,1,2,6,3,5]=>8
[4,1,2,6,5,3]=>7
[4,1,3,2,5,6]=>2
[4,1,3,2,6,5]=>7
[4,1,3,5,2,6]=>6
[4,1,3,5,6,2]=>11
[4,1,3,6,2,5]=>7
[4,1,3,6,5,2]=>6
[4,1,5,2,3,6]=>6
[4,1,5,2,6,3]=>11
[4,1,5,3,2,6]=>5
[4,1,5,3,6,2]=>10
[4,1,5,6,2,3]=>10
[4,1,5,6,3,2]=>9
[4,1,6,2,3,5]=>7
[4,1,6,2,5,3]=>6
[4,1,6,3,2,5]=>6
[4,1,6,3,5,2]=>5
[4,1,6,5,2,3]=>11
[4,1,6,5,3,2]=>10
[4,2,1,3,5,6]=>2
[4,2,1,3,6,5]=>7
[4,2,1,5,3,6]=>6
[4,2,1,5,6,3]=>11
[4,2,1,6,3,5]=>7
[4,2,1,6,5,3]=>6
[4,2,3,1,5,6]=>1
[4,2,3,1,6,5]=>6
[4,2,3,5,1,6]=>5
[4,2,3,5,6,1]=>10
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>5
[4,2,5,1,3,6]=>5
[4,2,5,1,6,3]=>10
[4,2,5,3,1,6]=>4
[4,2,5,3,6,1]=>9
[4,2,5,6,1,3]=>9
[4,2,5,6,3,1]=>8
[4,2,6,1,3,5]=>6
[4,2,6,1,5,3]=>5
[4,2,6,3,1,5]=>5
[4,2,6,3,5,1]=>4
[4,2,6,5,1,3]=>10
[4,2,6,5,3,1]=>9
[4,3,1,2,5,6]=>5
[4,3,1,2,6,5]=>10
[4,3,1,5,2,6]=>9
[4,3,1,5,6,2]=>14
[4,3,1,6,2,5]=>10
[4,3,1,6,5,2]=>9
[4,3,2,1,5,6]=>4
[4,3,2,1,6,5]=>9
[4,3,2,5,1,6]=>8
[4,3,2,5,6,1]=>13
[4,3,2,6,1,5]=>9
[4,3,2,6,5,1]=>8
[4,3,5,1,2,6]=>8
[4,3,5,1,6,2]=>13
[4,3,5,2,1,6]=>7
[4,3,5,2,6,1]=>12
[4,3,5,6,1,2]=>12
[4,3,5,6,2,1]=>11
[4,3,6,1,2,5]=>9
[4,3,6,1,5,2]=>8
[4,3,6,2,1,5]=>8
[4,3,6,2,5,1]=>7
[4,3,6,5,1,2]=>13
[4,3,6,5,2,1]=>12
[4,5,1,2,3,6]=>6
[4,5,1,2,6,3]=>11
[4,5,1,3,2,6]=>5
[4,5,1,3,6,2]=>10
[4,5,1,6,2,3]=>10
[4,5,1,6,3,2]=>9
[4,5,2,1,3,6]=>5
[4,5,2,1,6,3]=>10
[4,5,2,3,1,6]=>4
[4,5,2,3,6,1]=>9
[4,5,2,6,1,3]=>9
[4,5,2,6,3,1]=>8
[4,5,3,1,2,6]=>4
[4,5,3,1,6,2]=>9
[4,5,3,2,1,6]=>3
[4,5,3,2,6,1]=>8
[4,5,3,6,1,2]=>8
[4,5,3,6,2,1]=>7
[4,5,6,1,2,3]=>9
[4,5,6,1,3,2]=>8
[4,5,6,2,1,3]=>8
[4,5,6,2,3,1]=>7
[4,5,6,3,1,2]=>7
[4,5,6,3,2,1]=>6
[4,6,1,2,3,5]=>7
[4,6,1,2,5,3]=>6
[4,6,1,3,2,5]=>6
[4,6,1,3,5,2]=>5
[4,6,1,5,2,3]=>11
[4,6,1,5,3,2]=>10
[4,6,2,1,3,5]=>6
[4,6,2,1,5,3]=>5
[4,6,2,3,1,5]=>5
[4,6,2,3,5,1]=>4
[4,6,2,5,1,3]=>10
[4,6,2,5,3,1]=>9
[4,6,3,1,2,5]=>5
[4,6,3,1,5,2]=>4
[4,6,3,2,1,5]=>4
[4,6,3,2,5,1]=>3
[4,6,3,5,1,2]=>9
[4,6,3,5,2,1]=>8
[4,6,5,1,2,3]=>10
[4,6,5,1,3,2]=>9
[4,6,5,2,1,3]=>9
[4,6,5,2,3,1]=>8
[4,6,5,3,1,2]=>8
[4,6,5,3,2,1]=>7
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>9
[5,1,2,4,3,6]=>3
[5,1,2,4,6,3]=>8
[5,1,2,6,3,4]=>8
[5,1,2,6,4,3]=>7
[5,1,3,2,4,6]=>3
[5,1,3,2,6,4]=>8
[5,1,3,4,2,6]=>2
[5,1,3,4,6,2]=>7
[5,1,3,6,2,4]=>7
[5,1,3,6,4,2]=>6
[5,1,4,2,3,6]=>7
[5,1,4,2,6,3]=>12
[5,1,4,3,2,6]=>6
[5,1,4,3,6,2]=>11
[5,1,4,6,2,3]=>11
[5,1,4,6,3,2]=>10
[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]=>3
[5,2,1,3,6,4]=>8
[5,2,1,4,3,6]=>2
[5,2,1,4,6,3]=>7
[5,2,1,6,3,4]=>7
[5,2,1,6,4,3]=>6
[5,2,3,1,4,6]=>2
[5,2,3,1,6,4]=>7
[5,2,3,4,1,6]=>1
[5,2,3,4,6,1]=>6
[5,2,3,6,1,4]=>6
[5,2,3,6,4,1]=>5
[5,2,4,1,3,6]=>6
[5,2,4,1,6,3]=>11
[5,2,4,3,1,6]=>5
[5,2,4,3,6,1]=>10
[5,2,4,6,1,3]=>10
[5,2,4,6,3,1]=>9
[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]=>6
[5,3,1,2,6,4]=>11
[5,3,1,4,2,6]=>5
[5,3,1,4,6,2]=>10
[5,3,1,6,2,4]=>10
[5,3,1,6,4,2]=>9
[5,3,2,1,4,6]=>5
[5,3,2,1,6,4]=>10
[5,3,2,4,1,6]=>4
[5,3,2,4,6,1]=>9
[5,3,2,6,1,4]=>9
[5,3,2,6,4,1]=>8
[5,3,4,1,2,6]=>9
[5,3,4,1,6,2]=>14
[5,3,4,2,1,6]=>8
[5,3,4,2,6,1]=>13
[5,3,4,6,1,2]=>13
[5,3,4,6,2,1]=>12
[5,3,6,1,2,4]=>10
[5,3,6,1,4,2]=>9
[5,3,6,2,1,4]=>9
[5,3,6,2,4,1]=>8
[5,3,6,4,1,2]=>8
[5,3,6,4,2,1]=>7
[5,4,1,2,3,6]=>7
[5,4,1,2,6,3]=>12
[5,4,1,3,2,6]=>6
[5,4,1,3,6,2]=>11
[5,4,1,6,2,3]=>11
[5,4,1,6,3,2]=>10
[5,4,2,1,3,6]=>6
[5,4,2,1,6,3]=>11
[5,4,2,3,1,6]=>5
[5,4,2,3,6,1]=>10
[5,4,2,6,1,3]=>10
[5,4,2,6,3,1]=>9
[5,4,3,1,2,6]=>5
[5,4,3,1,6,2]=>10
[5,4,3,2,1,6]=>4
[5,4,3,2,6,1]=>9
[5,4,3,6,1,2]=>9
[5,4,3,6,2,1]=>8
[5,4,6,1,2,3]=>10
[5,4,6,1,3,2]=>9
[5,4,6,2,1,3]=>9
[5,4,6,2,3,1]=>8
[5,4,6,3,1,2]=>8
[5,4,6,3,2,1]=>7
[5,6,1,2,3,4]=>8
[5,6,1,2,4,3]=>7
[5,6,1,3,2,4]=>7
[5,6,1,3,4,2]=>6
[5,6,1,4,2,3]=>6
[5,6,1,4,3,2]=>5
[5,6,2,1,3,4]=>7
[5,6,2,1,4,3]=>6
[5,6,2,3,1,4]=>6
[5,6,2,3,4,1]=>5
[5,6,2,4,1,3]=>5
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>6
[5,6,3,1,4,2]=>5
[5,6,3,2,1,4]=>5
[5,6,3,2,4,1]=>4
[5,6,3,4,1,2]=>4
[5,6,3,4,2,1]=>3
[5,6,4,1,2,3]=>11
[5,6,4,1,3,2]=>10
[5,6,4,2,1,3]=>10
[5,6,4,2,3,1]=>9
[5,6,4,3,1,2]=>9
[5,6,4,3,2,1]=>8
[6,1,2,3,4,5]=>5
[6,1,2,3,5,4]=>4
[6,1,2,4,3,5]=>4
[6,1,2,4,5,3]=>3
[6,1,2,5,3,4]=>9
[6,1,2,5,4,3]=>8
[6,1,3,2,4,5]=>4
[6,1,3,2,5,4]=>3
[6,1,3,4,2,5]=>3
[6,1,3,4,5,2]=>2
[6,1,3,5,2,4]=>8
[6,1,3,5,4,2]=>7
[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]=>12
[6,1,4,5,3,2]=>11
[6,1,5,2,3,4]=>9
[6,1,5,2,4,3]=>8
[6,1,5,3,2,4]=>8
[6,1,5,3,4,2]=>7
[6,1,5,4,2,3]=>7
[6,1,5,4,3,2]=>6
[6,2,1,3,4,5]=>4
[6,2,1,3,5,4]=>3
[6,2,1,4,3,5]=>3
[6,2,1,4,5,3]=>2
[6,2,1,5,3,4]=>8
[6,2,1,5,4,3]=>7
[6,2,3,1,4,5]=>3
[6,2,3,1,5,4]=>2
[6,2,3,4,1,5]=>2
[6,2,3,4,5,1]=>1
[6,2,3,5,1,4]=>7
[6,2,3,5,4,1]=>6
[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]=>11
[6,2,4,5,3,1]=>10
[6,2,5,1,3,4]=>8
[6,2,5,1,4,3]=>7
[6,2,5,3,1,4]=>7
[6,2,5,3,4,1]=>6
[6,2,5,4,1,3]=>6
[6,2,5,4,3,1]=>5
[6,3,1,2,4,5]=>7
[6,3,1,2,5,4]=>6
[6,3,1,4,2,5]=>6
[6,3,1,4,5,2]=>5
[6,3,1,5,2,4]=>11
[6,3,1,5,4,2]=>10
[6,3,2,1,4,5]=>6
[6,3,2,1,5,4]=>5
[6,3,2,4,1,5]=>5
[6,3,2,4,5,1]=>4
[6,3,2,5,1,4]=>10
[6,3,2,5,4,1]=>9
[6,3,4,1,2,5]=>10
[6,3,4,1,5,2]=>9
[6,3,4,2,1,5]=>9
[6,3,4,2,5,1]=>8
[6,3,4,5,1,2]=>14
[6,3,4,5,2,1]=>13
[6,3,5,1,2,4]=>11
[6,3,5,1,4,2]=>10
[6,3,5,2,1,4]=>10
[6,3,5,2,4,1]=>9
[6,3,5,4,1,2]=>9
[6,3,5,4,2,1]=>8
[6,4,1,2,3,5]=>8
[6,4,1,2,5,3]=>7
[6,4,1,3,2,5]=>7
[6,4,1,3,5,2]=>6
[6,4,1,5,2,3]=>12
[6,4,1,5,3,2]=>11
[6,4,2,1,3,5]=>7
[6,4,2,1,5,3]=>6
[6,4,2,3,1,5]=>6
[6,4,2,3,5,1]=>5
[6,4,2,5,1,3]=>11
[6,4,2,5,3,1]=>10
[6,4,3,1,2,5]=>6
[6,4,3,1,5,2]=>5
[6,4,3,2,1,5]=>5
[6,4,3,2,5,1]=>4
[6,4,3,5,1,2]=>10
[6,4,3,5,2,1]=>9
[6,4,5,1,2,3]=>11
[6,4,5,1,3,2]=>10
[6,4,5,2,1,3]=>10
[6,4,5,2,3,1]=>9
[6,4,5,3,1,2]=>9
[6,4,5,3,2,1]=>8
[6,5,1,2,3,4]=>9
[6,5,1,2,4,3]=>8
[6,5,1,3,2,4]=>8
[6,5,1,3,4,2]=>7
[6,5,1,4,2,3]=>7
[6,5,1,4,3,2]=>6
[6,5,2,1,3,4]=>8
[6,5,2,1,4,3]=>7
[6,5,2,3,1,4]=>7
[6,5,2,3,4,1]=>6
[6,5,2,4,1,3]=>6
[6,5,2,4,3,1]=>5
[6,5,3,1,2,4]=>7
[6,5,3,1,4,2]=>6
[6,5,3,2,1,4]=>6
[6,5,3,2,4,1]=>5
[6,5,3,4,1,2]=>5
[6,5,3,4,2,1]=>4
[6,5,4,1,2,3]=>12
[6,5,4,1,3,2]=>11
[6,5,4,2,1,3]=>11
[6,5,4,2,3,1]=>10
[6,5,4,3,1,2]=>10
[6,5,4,3,2,1]=>9
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>6
[1,2,3,4,6,5,7]=>5
[1,2,3,4,6,7,5]=>11
[1,2,3,4,7,5,6]=>6
[1,2,3,4,7,6,5]=>5
[1,2,3,5,4,6,7]=>4
[1,2,3,5,4,7,6]=>10
[1,2,3,5,6,4,7]=>9
[1,2,3,5,6,7,4]=>15
[1,2,3,5,7,4,6]=>10
[1,2,3,5,7,6,4]=>9
[1,2,3,6,4,5,7]=>5
[1,2,3,6,4,7,5]=>11
[1,2,3,6,5,4,7]=>4
[1,2,3,6,5,7,4]=>10
[1,2,3,6,7,4,5]=>10
[1,2,3,6,7,5,4]=>9
[1,2,3,7,4,5,6]=>6
[1,2,3,7,4,6,5]=>5
[1,2,3,7,5,4,6]=>5
[1,2,3,7,5,6,4]=>4
[1,2,3,7,6,4,5]=>11
[1,2,3,7,6,5,4]=>10
[1,2,4,3,5,6,7]=>3
[1,2,4,3,5,7,6]=>9
[1,2,4,3,6,5,7]=>8
[1,2,4,3,6,7,5]=>14
[1,2,4,3,7,5,6]=>9
[1,2,4,3,7,6,5]=>8
[1,2,4,5,3,6,7]=>7
[1,2,4,5,3,7,6]=>13
[1,2,4,5,6,3,7]=>12
[1,2,4,5,6,7,3]=>18
[1,2,4,5,7,3,6]=>13
[1,2,4,5,7,6,3]=>12
[1,2,4,6,3,5,7]=>8
[1,2,4,6,3,7,5]=>14
[1,2,4,6,5,3,7]=>7
[1,2,4,6,5,7,3]=>13
[1,2,4,6,7,3,5]=>13
[1,2,4,6,7,5,3]=>12
[1,2,4,7,3,5,6]=>9
[1,2,4,7,3,6,5]=>8
[1,2,4,7,5,3,6]=>8
[1,2,4,7,5,6,3]=>7
[1,2,4,7,6,3,5]=>14
[1,2,4,7,6,5,3]=>13
[1,2,5,3,4,6,7]=>4
[1,2,5,3,4,7,6]=>10
[1,2,5,3,6,4,7]=>9
[1,2,5,3,6,7,4]=>15
[1,2,5,3,7,4,6]=>10
[1,2,5,3,7,6,4]=>9
[1,2,5,4,3,6,7]=>3
[1,2,5,4,3,7,6]=>9
[1,2,5,4,6,3,7]=>8
[1,2,5,4,6,7,3]=>14
[1,2,5,4,7,3,6]=>9
[1,2,5,4,7,6,3]=>8
[1,2,5,6,3,4,7]=>8
[1,2,5,6,3,7,4]=>14
[1,2,5,6,4,3,7]=>7
[1,2,5,6,4,7,3]=>13
[1,2,5,6,7,3,4]=>13
[1,2,5,6,7,4,3]=>12
[1,2,5,7,3,4,6]=>9
[1,2,5,7,3,6,4]=>8
[1,2,5,7,4,3,6]=>8
[1,2,5,7,4,6,3]=>7
[1,2,5,7,6,3,4]=>14
[1,2,5,7,6,4,3]=>13
[1,2,6,3,4,5,7]=>5
[1,2,6,3,4,7,5]=>11
[1,2,6,3,5,4,7]=>4
[1,2,6,3,5,7,4]=>10
[1,2,6,3,7,4,5]=>10
[1,2,6,3,7,5,4]=>9
[1,2,6,4,3,5,7]=>4
[1,2,6,4,3,7,5]=>10
[1,2,6,4,5,3,7]=>3
[1,2,6,4,5,7,3]=>9
[1,2,6,4,7,3,5]=>9
[1,2,6,4,7,5,3]=>8
[1,2,6,5,3,4,7]=>9
[1,2,6,5,3,7,4]=>15
[1,2,6,5,4,3,7]=>8
[1,2,6,5,4,7,3]=>14
[1,2,6,5,7,3,4]=>14
[1,2,6,5,7,4,3]=>13
[1,2,6,7,3,4,5]=>10
[1,2,6,7,3,5,4]=>9
[1,2,6,7,4,3,5]=>9
[1,2,6,7,4,5,3]=>8
[1,2,6,7,5,3,4]=>8
[1,2,6,7,5,4,3]=>7
[1,2,7,3,4,5,6]=>6
[1,2,7,3,4,6,5]=>5
[1,2,7,3,5,4,6]=>5
[1,2,7,3,5,6,4]=>4
[1,2,7,3,6,4,5]=>11
[1,2,7,3,6,5,4]=>10
[1,2,7,4,3,5,6]=>5
[1,2,7,4,3,6,5]=>4
[1,2,7,4,5,3,6]=>4
[1,2,7,4,5,6,3]=>3
[1,2,7,4,6,3,5]=>10
[1,2,7,4,6,5,3]=>9
[1,2,7,5,3,4,6]=>10
[1,2,7,5,3,6,4]=>9
[1,2,7,5,4,3,6]=>9
[1,2,7,5,4,6,3]=>8
[1,2,7,5,6,3,4]=>15
[1,2,7,5,6,4,3]=>14
[1,2,7,6,3,4,5]=>11
[1,2,7,6,3,5,4]=>10
[1,2,7,6,4,3,5]=>10
[1,2,7,6,4,5,3]=>9
[1,2,7,6,5,3,4]=>9
[1,2,7,6,5,4,3]=>8
[1,3,2,4,5,6,7]=>2
[1,3,2,4,5,7,6]=>8
[1,3,2,4,6,5,7]=>7
[1,3,2,4,6,7,5]=>13
[1,3,2,4,7,5,6]=>8
[1,3,2,4,7,6,5]=>7
[1,3,2,5,4,6,7]=>6
[1,3,2,5,4,7,6]=>12
[1,3,2,5,6,4,7]=>11
[1,3,2,5,6,7,4]=>17
[1,3,2,5,7,4,6]=>12
[1,3,2,5,7,6,4]=>11
[1,3,2,6,4,5,7]=>7
[1,3,2,6,4,7,5]=>13
[1,3,2,6,5,4,7]=>6
[1,3,2,6,5,7,4]=>12
[1,3,2,6,7,4,5]=>12
[1,3,2,6,7,5,4]=>11
[1,3,2,7,4,5,6]=>8
[1,3,2,7,4,6,5]=>7
[1,3,2,7,5,4,6]=>7
[1,3,2,7,5,6,4]=>6
[1,3,2,7,6,4,5]=>13
[1,3,2,7,6,5,4]=>12
[1,3,4,2,5,6,7]=>5
[1,3,4,2,5,7,6]=>11
[1,3,4,2,6,5,7]=>10
[1,3,4,2,6,7,5]=>16
[1,3,4,2,7,5,6]=>11
[1,3,4,2,7,6,5]=>10
[1,3,4,5,2,6,7]=>9
[1,3,4,5,2,7,6]=>15
[1,3,4,5,6,2,7]=>14
[1,3,4,5,6,7,2]=>20
[1,3,4,5,7,2,6]=>15
[1,3,4,5,7,6,2]=>14
[1,3,4,6,2,5,7]=>10
[1,3,4,6,2,7,5]=>16
[1,3,4,6,5,2,7]=>9
[1,3,4,6,5,7,2]=>15
[1,3,4,6,7,2,5]=>15
[1,3,4,6,7,5,2]=>14
[1,3,4,7,2,5,6]=>11
[1,3,4,7,2,6,5]=>10
[1,3,4,7,5,2,6]=>10
[1,3,4,7,5,6,2]=>9
[1,3,4,7,6,2,5]=>16
[1,3,4,7,6,5,2]=>15
[1,3,5,2,4,6,7]=>6
[1,3,5,2,4,7,6]=>12
[1,3,5,2,6,4,7]=>11
[1,3,5,2,6,7,4]=>17
[1,3,5,2,7,4,6]=>12
[1,3,5,2,7,6,4]=>11
[1,3,5,4,2,6,7]=>5
[1,3,5,4,2,7,6]=>11
[1,3,5,4,6,2,7]=>10
[1,3,5,4,6,7,2]=>16
[1,3,5,4,7,2,6]=>11
[1,3,5,4,7,6,2]=>10
[1,3,5,6,2,4,7]=>10
[1,3,5,6,2,7,4]=>16
[1,3,5,6,4,2,7]=>9
[1,3,5,6,4,7,2]=>15
[1,3,5,6,7,2,4]=>15
[1,3,5,6,7,4,2]=>14
[1,3,5,7,2,4,6]=>11
[1,3,5,7,2,6,4]=>10
[1,3,5,7,4,2,6]=>10
[1,3,5,7,4,6,2]=>9
[1,3,5,7,6,2,4]=>16
[1,3,5,7,6,4,2]=>15
[1,3,6,2,4,5,7]=>7
[1,3,6,2,4,7,5]=>13
[1,3,6,2,5,4,7]=>6
[1,3,6,2,5,7,4]=>12
[1,3,6,2,7,4,5]=>12
[1,3,6,2,7,5,4]=>11
[1,3,6,4,2,5,7]=>6
[1,3,6,4,2,7,5]=>12
[1,3,6,4,5,2,7]=>5
[1,3,6,4,5,7,2]=>11
[1,3,6,4,7,2,5]=>11
[1,3,6,4,7,5,2]=>10
[1,3,6,5,2,4,7]=>11
[1,3,6,5,2,7,4]=>17
[1,3,6,5,4,2,7]=>10
[1,3,6,5,4,7,2]=>16
[1,3,6,5,7,2,4]=>16
[1,3,6,5,7,4,2]=>15
[1,3,6,7,2,4,5]=>12
[1,3,6,7,2,5,4]=>11
[1,3,6,7,4,2,5]=>11
[1,3,6,7,4,5,2]=>10
[1,3,6,7,5,2,4]=>10
[1,3,6,7,5,4,2]=>9
[1,3,7,2,4,5,6]=>8
[1,3,7,2,4,6,5]=>7
[1,3,7,2,5,4,6]=>7
[1,3,7,2,5,6,4]=>6
[1,3,7,2,6,4,5]=>13
[1,3,7,2,6,5,4]=>12
[1,3,7,4,2,5,6]=>7
[1,3,7,4,2,6,5]=>6
[1,3,7,4,5,2,6]=>6
[1,3,7,4,5,6,2]=>5
[1,3,7,4,6,2,5]=>12
[1,3,7,4,6,5,2]=>11
[1,3,7,5,2,4,6]=>12
[1,3,7,5,2,6,4]=>11
[1,3,7,5,4,2,6]=>11
[1,3,7,5,4,6,2]=>10
[1,3,7,5,6,2,4]=>17
[1,3,7,5,6,4,2]=>16
[1,3,7,6,2,4,5]=>13
[1,3,7,6,2,5,4]=>12
[1,3,7,6,4,2,5]=>12
[1,3,7,6,4,5,2]=>11
[1,3,7,6,5,2,4]=>11
[1,3,7,6,5,4,2]=>10
[1,4,2,3,5,6,7]=>3
[1,4,2,3,5,7,6]=>9
[1,4,2,3,6,5,7]=>8
[1,4,2,3,6,7,5]=>14
[1,4,2,3,7,5,6]=>9
[1,4,2,3,7,6,5]=>8
[1,4,2,5,3,6,7]=>7
[1,4,2,5,3,7,6]=>13
[1,4,2,5,6,3,7]=>12
[1,4,2,5,6,7,3]=>18
[1,4,2,5,7,3,6]=>13
[1,4,2,5,7,6,3]=>12
[1,4,2,6,3,5,7]=>8
[1,4,2,6,3,7,5]=>14
[1,4,2,6,5,3,7]=>7
[1,4,2,6,5,7,3]=>13
[1,4,2,6,7,3,5]=>13
[1,4,2,6,7,5,3]=>12
[1,4,2,7,3,5,6]=>9
[1,4,2,7,3,6,5]=>8
[1,4,2,7,5,3,6]=>8
[1,4,2,7,5,6,3]=>7
[1,4,2,7,6,3,5]=>14
[1,4,2,7,6,5,3]=>13
[1,4,3,2,5,6,7]=>2
[1,4,3,2,5,7,6]=>8
[1,4,3,2,6,5,7]=>7
[1,4,3,2,6,7,5]=>13
[1,4,3,2,7,5,6]=>8
[1,4,3,2,7,6,5]=>7
[1,4,3,5,2,6,7]=>6
[1,4,3,5,2,7,6]=>12
[1,4,3,5,6,2,7]=>11
[1,4,3,5,6,7,2]=>17
[1,4,3,5,7,2,6]=>12
[1,4,3,5,7,6,2]=>11
[1,4,3,6,2,5,7]=>7
[1,4,3,6,2,7,5]=>13
[1,4,3,6,5,2,7]=>6
[1,4,3,6,5,7,2]=>12
[1,4,3,6,7,2,5]=>12
[1,4,3,6,7,5,2]=>11
[1,4,3,7,2,5,6]=>8
[1,4,3,7,2,6,5]=>7
[1,4,3,7,5,2,6]=>7
[1,4,3,7,5,6,2]=>6
[1,4,3,7,6,2,5]=>13
[1,4,3,7,6,5,2]=>12
[1,4,5,2,3,6,7]=>6
[1,4,5,2,3,7,6]=>12
[1,4,5,2,6,3,7]=>11
[1,4,5,2,6,7,3]=>17
[1,4,5,2,7,3,6]=>12
[1,4,5,2,7,6,3]=>11
[1,4,5,3,2,6,7]=>5
[1,4,5,3,2,7,6]=>11
[1,4,5,3,6,2,7]=>10
[1,4,5,3,6,7,2]=>16
[1,4,5,3,7,2,6]=>11
[1,4,5,3,7,6,2]=>10
[1,4,5,6,2,3,7]=>10
[1,4,5,6,2,7,3]=>16
[1,4,5,6,3,2,7]=>9
[1,4,5,6,3,7,2]=>15
[1,4,5,6,7,2,3]=>15
[1,4,5,6,7,3,2]=>14
[1,4,5,7,2,3,6]=>11
[1,4,5,7,2,6,3]=>10
[1,4,5,7,3,2,6]=>10
[1,4,5,7,3,6,2]=>9
[1,4,5,7,6,2,3]=>16
[1,4,5,7,6,3,2]=>15
[1,4,6,2,3,5,7]=>7
[1,4,6,2,3,7,5]=>13
[1,4,6,2,5,3,7]=>6
[1,4,6,2,5,7,3]=>12
[1,4,6,2,7,3,5]=>12
[1,4,6,2,7,5,3]=>11
[1,4,6,3,2,5,7]=>6
[1,4,6,3,2,7,5]=>12
[1,4,6,3,5,2,7]=>5
[1,4,6,3,5,7,2]=>11
[1,4,6,3,7,2,5]=>11
[1,4,6,3,7,5,2]=>10
[1,4,6,5,2,3,7]=>11
[1,4,6,5,2,7,3]=>17
[1,4,6,5,3,2,7]=>10
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Description
Haglund's hag of a permutation.
Let $edif$ be the sum of the differences of exceedence tops and bottoms, let $\pi_E$ the subsequence of exceedence tops and let $\pi_N$ be the subsequence of non-exceedence tops. Finally, let $L$ be the number of pairs of indices $k < i$ such that $\pi_k \leq i < \pi_i$.
Then $hag(\pi) = edif + inv(\pi_E) - inv(\pi_N) + L$, where $inv$ denotes the number of inversions of a word.
Let $edif$ be the sum of the differences of exceedence tops and bottoms, let $\pi_E$ the subsequence of exceedence tops and let $\pi_N$ be the subsequence of non-exceedence tops. Finally, let $L$ be the number of pairs of indices $k < i$ such that $\pi_k \leq i < \pi_i$.
Then $hag(\pi) = edif + inv(\pi_E) - inv(\pi_N) + L$, where $inv$ denotes the number of inversions of a word.
References
[1] Wilson, M. C. An interesting new Mahonian permutation statistic MathSciNet:2745700
Code
def statistic(pi):
standard = sage.combinat.permutation.to_standard
pi_E = standard([pi_i for i, pi_i in enumerate(pi, 1) if i < pi_i])
pi_N = standard([pi_i for i, pi_i in enumerate(pi, 1) if i >= pi_i])
edif = sum(pi_i - i for i, pi_i in enumerate(pi, 1) if i < pi_i)
L = sum(sum(1 for k in range(1, i) if pi(k) <= i)
for i, pi_i in enumerate(pi, 1) if i < pi_i)
return edif + pi_E.number_of_inversions() - pi_N.number_of_inversions() + L
Created
Jan 18, 2021 at 19:10 by Martin Rubey
Updated
Jan 18, 2021 at 19:10 by Martin Rubey
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