Identifier
- St000446: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>2
[2,3,1]=>2
[3,1,2]=>1
[3,2,1]=>3
[1,2,3,4]=>0
[1,2,4,3]=>1
[1,3,2,4]=>2
[1,3,4,2]=>2
[1,4,2,3]=>1
[1,4,3,2]=>3
[2,1,3,4]=>3
[2,1,4,3]=>4
[2,3,1,4]=>3
[2,3,4,1]=>3
[2,4,1,3]=>4
[2,4,3,1]=>4
[3,1,2,4]=>2
[3,1,4,2]=>2
[3,2,1,4]=>5
[3,2,4,1]=>5
[3,4,1,2]=>2
[3,4,2,1]=>5
[4,1,2,3]=>1
[4,1,3,2]=>3
[4,2,1,3]=>4
[4,2,3,1]=>4
[4,3,1,2]=>3
[4,3,2,1]=>6
[1,2,3,4,5]=>0
[1,2,3,5,4]=>1
[1,2,4,3,5]=>2
[1,2,4,5,3]=>2
[1,2,5,3,4]=>1
[1,2,5,4,3]=>3
[1,3,2,4,5]=>3
[1,3,2,5,4]=>4
[1,3,4,2,5]=>3
[1,3,4,5,2]=>3
[1,3,5,2,4]=>4
[1,3,5,4,2]=>4
[1,4,2,3,5]=>2
[1,4,2,5,3]=>2
[1,4,3,2,5]=>5
[1,4,3,5,2]=>5
[1,4,5,2,3]=>2
[1,4,5,3,2]=>5
[1,5,2,3,4]=>1
[1,5,2,4,3]=>3
[1,5,3,2,4]=>4
[1,5,3,4,2]=>4
[1,5,4,2,3]=>3
[1,5,4,3,2]=>6
[2,1,3,4,5]=>4
[2,1,3,5,4]=>5
[2,1,4,3,5]=>6
[2,1,4,5,3]=>6
[2,1,5,3,4]=>5
[2,1,5,4,3]=>7
[2,3,1,4,5]=>4
[2,3,1,5,4]=>5
[2,3,4,1,5]=>4
[2,3,4,5,1]=>4
[2,3,5,1,4]=>5
[2,3,5,4,1]=>5
[2,4,1,3,5]=>6
[2,4,1,5,3]=>6
[2,4,3,1,5]=>6
[2,4,3,5,1]=>6
[2,4,5,1,3]=>6
[2,4,5,3,1]=>6
[2,5,1,3,4]=>5
[2,5,1,4,3]=>7
[2,5,3,1,4]=>5
[2,5,3,4,1]=>5
[2,5,4,1,3]=>7
[2,5,4,3,1]=>7
[3,1,2,4,5]=>3
[3,1,2,5,4]=>4
[3,1,4,2,5]=>3
[3,1,4,5,2]=>3
[3,1,5,2,4]=>4
[3,1,5,4,2]=>4
[3,2,1,4,5]=>7
[3,2,1,5,4]=>8
[3,2,4,1,5]=>7
[3,2,4,5,1]=>7
[3,2,5,1,4]=>8
[3,2,5,4,1]=>8
[3,4,1,2,5]=>3
[3,4,1,5,2]=>3
[3,4,2,1,5]=>7
[3,4,2,5,1]=>7
[3,4,5,1,2]=>3
[3,4,5,2,1]=>7
[3,5,1,2,4]=>4
[3,5,1,4,2]=>4
[3,5,2,1,4]=>8
[3,5,2,4,1]=>8
[3,5,4,1,2]=>4
[3,5,4,2,1]=>8
[4,1,2,3,5]=>2
[4,1,2,5,3]=>2
[4,1,3,2,5]=>5
[4,1,3,5,2]=>5
[4,1,5,2,3]=>2
[4,1,5,3,2]=>5
[4,2,1,3,5]=>6
[4,2,1,5,3]=>6
[4,2,3,1,5]=>6
[4,2,3,5,1]=>6
[4,2,5,1,3]=>6
[4,2,5,3,1]=>6
[4,3,1,2,5]=>5
[4,3,1,5,2]=>5
[4,3,2,1,5]=>9
[4,3,2,5,1]=>9
[4,3,5,1,2]=>5
[4,3,5,2,1]=>9
[4,5,1,2,3]=>2
[4,5,1,3,2]=>5
[4,5,2,1,3]=>6
[4,5,2,3,1]=>6
[4,5,3,1,2]=>5
[4,5,3,2,1]=>9
[5,1,2,3,4]=>1
[5,1,2,4,3]=>3
[5,1,3,2,4]=>4
[5,1,3,4,2]=>4
[5,1,4,2,3]=>3
[5,1,4,3,2]=>6
[5,2,1,3,4]=>5
[5,2,1,4,3]=>7
[5,2,3,1,4]=>5
[5,2,3,4,1]=>5
[5,2,4,1,3]=>7
[5,2,4,3,1]=>7
[5,3,1,2,4]=>4
[5,3,1,4,2]=>4
[5,3,2,1,4]=>8
[5,3,2,4,1]=>8
[5,3,4,1,2]=>4
[5,3,4,2,1]=>8
[5,4,1,2,3]=>3
[5,4,1,3,2]=>6
[5,4,2,1,3]=>7
[5,4,2,3,1]=>7
[5,4,3,1,2]=>6
[5,4,3,2,1]=>10
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>2
[1,2,3,5,6,4]=>2
[1,2,3,6,4,5]=>1
[1,2,3,6,5,4]=>3
[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>4
[1,2,4,5,3,6]=>3
[1,2,4,5,6,3]=>3
[1,2,4,6,3,5]=>4
[1,2,4,6,5,3]=>4
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>2
[1,2,5,4,3,6]=>5
[1,2,5,4,6,3]=>5
[1,2,5,6,3,4]=>2
[1,2,5,6,4,3]=>5
[1,2,6,3,4,5]=>1
[1,2,6,3,5,4]=>3
[1,2,6,4,3,5]=>4
[1,2,6,4,5,3]=>4
[1,2,6,5,3,4]=>3
[1,2,6,5,4,3]=>6
[1,3,2,4,5,6]=>4
[1,3,2,4,6,5]=>5
[1,3,2,5,4,6]=>6
[1,3,2,5,6,4]=>6
[1,3,2,6,4,5]=>5
[1,3,2,6,5,4]=>7
[1,3,4,2,5,6]=>4
[1,3,4,2,6,5]=>5
[1,3,4,5,2,6]=>4
[1,3,4,5,6,2]=>4
[1,3,4,6,2,5]=>5
[1,3,4,6,5,2]=>5
[1,3,5,2,4,6]=>6
[1,3,5,2,6,4]=>6
[1,3,5,4,2,6]=>6
[1,3,5,4,6,2]=>6
[1,3,5,6,2,4]=>6
[1,3,5,6,4,2]=>6
[1,3,6,2,4,5]=>5
[1,3,6,2,5,4]=>7
[1,3,6,4,2,5]=>5
[1,3,6,4,5,2]=>5
[1,3,6,5,2,4]=>7
[1,3,6,5,4,2]=>7
[1,4,2,3,5,6]=>3
[1,4,2,3,6,5]=>4
[1,4,2,5,3,6]=>3
[1,4,2,5,6,3]=>3
[1,4,2,6,3,5]=>4
[1,4,2,6,5,3]=>4
[1,4,3,2,5,6]=>7
[1,4,3,2,6,5]=>8
[1,4,3,5,2,6]=>7
[1,4,3,5,6,2]=>7
[1,4,3,6,2,5]=>8
[1,4,3,6,5,2]=>8
[1,4,5,2,3,6]=>3
[1,4,5,2,6,3]=>3
[1,4,5,3,2,6]=>7
[1,4,5,3,6,2]=>7
[1,4,5,6,2,3]=>3
[1,4,5,6,3,2]=>7
[1,4,6,2,3,5]=>4
[1,4,6,2,5,3]=>4
[1,4,6,3,2,5]=>8
[1,4,6,3,5,2]=>8
[1,4,6,5,2,3]=>4
[1,4,6,5,3,2]=>8
[1,5,2,3,4,6]=>2
[1,5,2,3,6,4]=>2
[1,5,2,4,3,6]=>5
[1,5,2,4,6,3]=>5
[1,5,2,6,3,4]=>2
[1,5,2,6,4,3]=>5
[1,5,3,2,4,6]=>6
[1,5,3,2,6,4]=>6
[1,5,3,4,2,6]=>6
[1,5,3,4,6,2]=>6
[1,5,3,6,2,4]=>6
[1,5,3,6,4,2]=>6
[1,5,4,2,3,6]=>5
[1,5,4,2,6,3]=>5
[1,5,4,3,2,6]=>9
[1,5,4,3,6,2]=>9
[1,5,4,6,2,3]=>5
[1,5,4,6,3,2]=>9
[1,5,6,2,3,4]=>2
[1,5,6,2,4,3]=>5
[1,5,6,3,2,4]=>6
[1,5,6,3,4,2]=>6
[1,5,6,4,2,3]=>5
[1,5,6,4,3,2]=>9
[1,6,2,3,4,5]=>1
[1,6,2,3,5,4]=>3
[1,6,2,4,3,5]=>4
[1,6,2,4,5,3]=>4
[1,6,2,5,3,4]=>3
[1,6,2,5,4,3]=>6
[1,6,3,2,4,5]=>5
[1,6,3,2,5,4]=>7
[1,6,3,4,2,5]=>5
[1,6,3,4,5,2]=>5
[1,6,3,5,2,4]=>7
[1,6,3,5,4,2]=>7
[1,6,4,2,3,5]=>4
[1,6,4,2,5,3]=>4
[1,6,4,3,2,5]=>8
[1,6,4,3,5,2]=>8
[1,6,4,5,2,3]=>4
[1,6,4,5,3,2]=>8
[1,6,5,2,3,4]=>3
[1,6,5,2,4,3]=>6
[1,6,5,3,2,4]=>7
[1,6,5,3,4,2]=>7
[1,6,5,4,2,3]=>6
[1,6,5,4,3,2]=>10
[2,1,3,4,5,6]=>5
[2,1,3,4,6,5]=>6
[2,1,3,5,4,6]=>7
[2,1,3,5,6,4]=>7
[2,1,3,6,4,5]=>6
[2,1,3,6,5,4]=>8
[2,1,4,3,5,6]=>8
[2,1,4,3,6,5]=>9
[2,1,4,5,3,6]=>8
[2,1,4,5,6,3]=>8
[2,1,4,6,3,5]=>9
[2,1,4,6,5,3]=>9
[2,1,5,3,4,6]=>7
[2,1,5,3,6,4]=>7
[2,1,5,4,3,6]=>10
[2,1,5,4,6,3]=>10
[2,1,5,6,3,4]=>7
[2,1,5,6,4,3]=>10
[2,1,6,3,4,5]=>6
[2,1,6,3,5,4]=>8
[2,1,6,4,3,5]=>9
[2,1,6,4,5,3]=>9
[2,1,6,5,3,4]=>8
[2,1,6,5,4,3]=>11
[2,3,1,4,5,6]=>5
[2,3,1,4,6,5]=>6
[2,3,1,5,4,6]=>7
[2,3,1,5,6,4]=>7
[2,3,1,6,4,5]=>6
[2,3,1,6,5,4]=>8
[2,3,4,1,5,6]=>5
[2,3,4,1,6,5]=>6
[2,3,4,5,1,6]=>5
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>6
[2,3,4,6,5,1]=>6
[2,3,5,1,4,6]=>7
[2,3,5,1,6,4]=>7
[2,3,5,4,1,6]=>7
[2,3,5,4,6,1]=>7
[2,3,5,6,1,4]=>7
[2,3,5,6,4,1]=>7
[2,3,6,1,4,5]=>6
[2,3,6,1,5,4]=>8
[2,3,6,4,1,5]=>6
[2,3,6,4,5,1]=>6
[2,3,6,5,1,4]=>8
[2,3,6,5,4,1]=>8
[2,4,1,3,5,6]=>8
[2,4,1,3,6,5]=>9
[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]=>8
[2,4,3,1,6,5]=>9
[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]=>9
[2,4,6,1,5,3]=>9
[2,4,6,3,1,5]=>9
[2,4,6,3,5,1]=>9
[2,4,6,5,1,3]=>9
[2,4,6,5,3,1]=>9
[2,5,1,3,4,6]=>7
[2,5,1,3,6,4]=>7
[2,5,1,4,3,6]=>10
[2,5,1,4,6,3]=>10
[2,5,1,6,3,4]=>7
[2,5,1,6,4,3]=>10
[2,5,3,1,4,6]=>7
[2,5,3,1,6,4]=>7
[2,5,3,4,1,6]=>7
[2,5,3,4,6,1]=>7
[2,5,3,6,1,4]=>7
[2,5,3,6,4,1]=>7
[2,5,4,1,3,6]=>10
[2,5,4,1,6,3]=>10
[2,5,4,3,1,6]=>10
[2,5,4,3,6,1]=>10
[2,5,4,6,1,3]=>10
[2,5,4,6,3,1]=>10
[2,5,6,1,3,4]=>7
[2,5,6,1,4,3]=>10
[2,5,6,3,1,4]=>7
[2,5,6,3,4,1]=>7
[2,5,6,4,1,3]=>10
[2,5,6,4,3,1]=>10
[2,6,1,3,4,5]=>6
[2,6,1,3,5,4]=>8
[2,6,1,4,3,5]=>9
[2,6,1,4,5,3]=>9
[2,6,1,5,3,4]=>8
[2,6,1,5,4,3]=>11
[2,6,3,1,4,5]=>6
[2,6,3,1,5,4]=>8
[2,6,3,4,1,5]=>6
[2,6,3,4,5,1]=>6
[2,6,3,5,1,4]=>8
[2,6,3,5,4,1]=>8
[2,6,4,1,3,5]=>9
[2,6,4,1,5,3]=>9
[2,6,4,3,1,5]=>9
[2,6,4,3,5,1]=>9
[2,6,4,5,1,3]=>9
[2,6,4,5,3,1]=>9
[2,6,5,1,3,4]=>8
[2,6,5,1,4,3]=>11
[2,6,5,3,1,4]=>8
[2,6,5,3,4,1]=>8
[2,6,5,4,1,3]=>11
[2,6,5,4,3,1]=>11
[3,1,2,4,5,6]=>4
[3,1,2,4,6,5]=>5
[3,1,2,5,4,6]=>6
[3,1,2,5,6,4]=>6
[3,1,2,6,4,5]=>5
[3,1,2,6,5,4]=>7
[3,1,4,2,5,6]=>4
[3,1,4,2,6,5]=>5
[3,1,4,5,2,6]=>4
[3,1,4,5,6,2]=>4
[3,1,4,6,2,5]=>5
[3,1,4,6,5,2]=>5
[3,1,5,2,4,6]=>6
[3,1,5,2,6,4]=>6
[3,1,5,4,2,6]=>6
[3,1,5,4,6,2]=>6
[3,1,5,6,2,4]=>6
[3,1,5,6,4,2]=>6
[3,1,6,2,4,5]=>5
[3,1,6,2,5,4]=>7
[3,1,6,4,2,5]=>5
[3,1,6,4,5,2]=>5
[3,1,6,5,2,4]=>7
[3,1,6,5,4,2]=>7
[3,2,1,4,5,6]=>9
[3,2,1,4,6,5]=>10
[3,2,1,5,4,6]=>11
[3,2,1,5,6,4]=>11
[3,2,1,6,4,5]=>10
[3,2,1,6,5,4]=>12
[3,2,4,1,5,6]=>9
[3,2,4,1,6,5]=>10
[3,2,4,5,1,6]=>9
[3,2,4,5,6,1]=>9
[3,2,4,6,1,5]=>10
[3,2,4,6,5,1]=>10
[3,2,5,1,4,6]=>11
[3,2,5,1,6,4]=>11
[3,2,5,4,1,6]=>11
[3,2,5,4,6,1]=>11
[3,2,5,6,1,4]=>11
[3,2,5,6,4,1]=>11
[3,2,6,1,4,5]=>10
[3,2,6,1,5,4]=>12
[3,2,6,4,1,5]=>10
[3,2,6,4,5,1]=>10
[3,2,6,5,1,4]=>12
[3,2,6,5,4,1]=>12
[3,4,1,2,5,6]=>4
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>4
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>5
[3,4,1,6,5,2]=>5
[3,4,2,1,5,6]=>9
[3,4,2,1,6,5]=>10
[3,4,2,5,1,6]=>9
[3,4,2,5,6,1]=>9
[3,4,2,6,1,5]=>10
[3,4,2,6,5,1]=>10
[3,4,5,1,2,6]=>4
[3,4,5,1,6,2]=>4
[3,4,5,2,1,6]=>9
[3,4,5,2,6,1]=>9
[3,4,5,6,1,2]=>4
[3,4,5,6,2,1]=>9
[3,4,6,1,2,5]=>5
[3,4,6,1,5,2]=>5
[3,4,6,2,1,5]=>10
[3,4,6,2,5,1]=>10
[3,4,6,5,1,2]=>5
[3,4,6,5,2,1]=>10
[3,5,1,2,4,6]=>6
[3,5,1,2,6,4]=>6
[3,5,1,4,2,6]=>6
[3,5,1,4,6,2]=>6
[3,5,1,6,2,4]=>6
[3,5,1,6,4,2]=>6
[3,5,2,1,4,6]=>11
[3,5,2,1,6,4]=>11
[3,5,2,4,1,6]=>11
[3,5,2,4,6,1]=>11
[3,5,2,6,1,4]=>11
[3,5,2,6,4,1]=>11
[3,5,4,1,2,6]=>6
[3,5,4,1,6,2]=>6
[3,5,4,2,1,6]=>11
[3,5,4,2,6,1]=>11
[3,5,4,6,1,2]=>6
[3,5,4,6,2,1]=>11
[3,5,6,1,2,4]=>6
[3,5,6,1,4,2]=>6
[3,5,6,2,1,4]=>11
[3,5,6,2,4,1]=>11
[3,5,6,4,1,2]=>6
[3,5,6,4,2,1]=>11
[3,6,1,2,4,5]=>5
[3,6,1,2,5,4]=>7
[3,6,1,4,2,5]=>5
[3,6,1,4,5,2]=>5
[3,6,1,5,2,4]=>7
[3,6,1,5,4,2]=>7
[3,6,2,1,4,5]=>10
[3,6,2,1,5,4]=>12
[3,6,2,4,1,5]=>10
[3,6,2,4,5,1]=>10
[3,6,2,5,1,4]=>12
[3,6,2,5,4,1]=>12
[3,6,4,1,2,5]=>5
[3,6,4,1,5,2]=>5
[3,6,4,2,1,5]=>10
[3,6,4,2,5,1]=>10
[3,6,4,5,1,2]=>5
[3,6,4,5,2,1]=>10
[3,6,5,1,2,4]=>7
[3,6,5,1,4,2]=>7
[3,6,5,2,1,4]=>12
[3,6,5,2,4,1]=>12
[3,6,5,4,1,2]=>7
[3,6,5,4,2,1]=>12
[4,1,2,3,5,6]=>3
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>3
[4,1,2,5,6,3]=>3
[4,1,2,6,3,5]=>4
[4,1,2,6,5,3]=>4
[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]=>3
[4,1,5,2,6,3]=>3
[4,1,5,3,2,6]=>7
[4,1,5,3,6,2]=>7
[4,1,5,6,2,3]=>3
[4,1,5,6,3,2]=>7
[4,1,6,2,3,5]=>4
[4,1,6,2,5,3]=>4
[4,1,6,3,2,5]=>8
[4,1,6,3,5,2]=>8
[4,1,6,5,2,3]=>4
[4,1,6,5,3,2]=>8
[4,2,1,3,5,6]=>8
[4,2,1,3,6,5]=>9
[4,2,1,5,3,6]=>8
[4,2,1,5,6,3]=>8
[4,2,1,6,3,5]=>9
[4,2,1,6,5,3]=>9
[4,2,3,1,5,6]=>8
[4,2,3,1,6,5]=>9
[4,2,3,5,1,6]=>8
[4,2,3,5,6,1]=>8
[4,2,3,6,1,5]=>9
[4,2,3,6,5,1]=>9
[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]=>9
[4,2,6,1,5,3]=>9
[4,2,6,3,1,5]=>9
[4,2,6,3,5,1]=>9
[4,2,6,5,1,3]=>9
[4,2,6,5,3,1]=>9
[4,3,1,2,5,6]=>7
[4,3,1,2,6,5]=>8
[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]=>12
[4,3,2,1,6,5]=>13
[4,3,2,5,1,6]=>12
[4,3,2,5,6,1]=>12
[4,3,2,6,1,5]=>13
[4,3,2,6,5,1]=>13
[4,3,5,1,2,6]=>7
[4,3,5,1,6,2]=>7
[4,3,5,2,1,6]=>12
[4,3,5,2,6,1]=>12
[4,3,5,6,1,2]=>7
[4,3,5,6,2,1]=>12
[4,3,6,1,2,5]=>8
[4,3,6,1,5,2]=>8
[4,3,6,2,1,5]=>13
[4,3,6,2,5,1]=>13
[4,3,6,5,1,2]=>8
[4,3,6,5,2,1]=>13
[4,5,1,2,3,6]=>3
[4,5,1,2,6,3]=>3
[4,5,1,3,2,6]=>7
[4,5,1,3,6,2]=>7
[4,5,1,6,2,3]=>3
[4,5,1,6,3,2]=>7
[4,5,2,1,3,6]=>8
[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]=>8
[4,5,2,6,3,1]=>8
[4,5,3,1,2,6]=>7
[4,5,3,1,6,2]=>7
[4,5,3,2,1,6]=>12
[4,5,3,2,6,1]=>12
[4,5,3,6,1,2]=>7
[4,5,3,6,2,1]=>12
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>7
[4,5,6,2,1,3]=>8
[4,5,6,2,3,1]=>8
[4,5,6,3,1,2]=>7
[4,5,6,3,2,1]=>12
[4,6,1,2,3,5]=>4
[4,6,1,2,5,3]=>4
[4,6,1,3,2,5]=>8
[4,6,1,3,5,2]=>8
[4,6,1,5,2,3]=>4
[4,6,1,5,3,2]=>8
[4,6,2,1,3,5]=>9
[4,6,2,1,5,3]=>9
[4,6,2,3,1,5]=>9
[4,6,2,3,5,1]=>9
[4,6,2,5,1,3]=>9
[4,6,2,5,3,1]=>9
[4,6,3,1,2,5]=>8
[4,6,3,1,5,2]=>8
[4,6,3,2,1,5]=>13
[4,6,3,2,5,1]=>13
[4,6,3,5,1,2]=>8
[4,6,3,5,2,1]=>13
[4,6,5,1,2,3]=>4
[4,6,5,1,3,2]=>8
[4,6,5,2,1,3]=>9
[4,6,5,2,3,1]=>9
[4,6,5,3,1,2]=>8
[4,6,5,3,2,1]=>13
[5,1,2,3,4,6]=>2
[5,1,2,3,6,4]=>2
[5,1,2,4,3,6]=>5
[5,1,2,4,6,3]=>5
[5,1,2,6,3,4]=>2
[5,1,2,6,4,3]=>5
[5,1,3,2,4,6]=>6
[5,1,3,2,6,4]=>6
[5,1,3,4,2,6]=>6
[5,1,3,4,6,2]=>6
[5,1,3,6,2,4]=>6
[5,1,3,6,4,2]=>6
[5,1,4,2,3,6]=>5
[5,1,4,2,6,3]=>5
[5,1,4,3,2,6]=>9
[5,1,4,3,6,2]=>9
[5,1,4,6,2,3]=>5
[5,1,4,6,3,2]=>9
[5,1,6,2,3,4]=>2
[5,1,6,2,4,3]=>5
[5,1,6,3,2,4]=>6
[5,1,6,3,4,2]=>6
[5,1,6,4,2,3]=>5
[5,1,6,4,3,2]=>9
[5,2,1,3,4,6]=>7
[5,2,1,3,6,4]=>7
[5,2,1,4,3,6]=>10
[5,2,1,4,6,3]=>10
[5,2,1,6,3,4]=>7
[5,2,1,6,4,3]=>10
[5,2,3,1,4,6]=>7
[5,2,3,1,6,4]=>7
[5,2,3,4,1,6]=>7
[5,2,3,4,6,1]=>7
[5,2,3,6,1,4]=>7
[5,2,3,6,4,1]=>7
[5,2,4,1,3,6]=>10
[5,2,4,1,6,3]=>10
[5,2,4,3,1,6]=>10
[5,2,4,3,6,1]=>10
[5,2,4,6,1,3]=>10
[5,2,4,6,3,1]=>10
[5,2,6,1,3,4]=>7
[5,2,6,1,4,3]=>10
[5,2,6,3,1,4]=>7
[5,2,6,3,4,1]=>7
[5,2,6,4,1,3]=>10
[5,2,6,4,3,1]=>10
[5,3,1,2,4,6]=>6
[5,3,1,2,6,4]=>6
[5,3,1,4,2,6]=>6
[5,3,1,4,6,2]=>6
[5,3,1,6,2,4]=>6
[5,3,1,6,4,2]=>6
[5,3,2,1,4,6]=>11
[5,3,2,1,6,4]=>11
[5,3,2,4,1,6]=>11
[5,3,2,4,6,1]=>11
[5,3,2,6,1,4]=>11
[5,3,2,6,4,1]=>11
[5,3,4,1,2,6]=>6
[5,3,4,1,6,2]=>6
[5,3,4,2,1,6]=>11
[5,3,4,2,6,1]=>11
[5,3,4,6,1,2]=>6
[5,3,4,6,2,1]=>11
[5,3,6,1,2,4]=>6
[5,3,6,1,4,2]=>6
[5,3,6,2,1,4]=>11
[5,3,6,2,4,1]=>11
[5,3,6,4,1,2]=>6
[5,3,6,4,2,1]=>11
[5,4,1,2,3,6]=>5
[5,4,1,2,6,3]=>5
[5,4,1,3,2,6]=>9
[5,4,1,3,6,2]=>9
[5,4,1,6,2,3]=>5
[5,4,1,6,3,2]=>9
[5,4,2,1,3,6]=>10
[5,4,2,1,6,3]=>10
[5,4,2,3,1,6]=>10
[5,4,2,3,6,1]=>10
[5,4,2,6,1,3]=>10
[5,4,2,6,3,1]=>10
[5,4,3,1,2,6]=>9
[5,4,3,1,6,2]=>9
[5,4,3,2,1,6]=>14
[5,4,3,2,6,1]=>14
[5,4,3,6,1,2]=>9
[5,4,3,6,2,1]=>14
[5,4,6,1,2,3]=>5
[5,4,6,1,3,2]=>9
[5,4,6,2,1,3]=>10
[5,4,6,2,3,1]=>10
[5,4,6,3,1,2]=>9
[5,4,6,3,2,1]=>14
[5,6,1,2,3,4]=>2
[5,6,1,2,4,3]=>5
[5,6,1,3,2,4]=>6
[5,6,1,3,4,2]=>6
[5,6,1,4,2,3]=>5
[5,6,1,4,3,2]=>9
[5,6,2,1,3,4]=>7
[5,6,2,1,4,3]=>10
[5,6,2,3,1,4]=>7
[5,6,2,3,4,1]=>7
[5,6,2,4,1,3]=>10
[5,6,2,4,3,1]=>10
[5,6,3,1,2,4]=>6
[5,6,3,1,4,2]=>6
[5,6,3,2,1,4]=>11
[5,6,3,2,4,1]=>11
[5,6,3,4,1,2]=>6
[5,6,3,4,2,1]=>11
[5,6,4,1,2,3]=>5
[5,6,4,1,3,2]=>9
[5,6,4,2,1,3]=>10
[5,6,4,2,3,1]=>10
[5,6,4,3,1,2]=>9
[5,6,4,3,2,1]=>14
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>3
[6,1,2,4,3,5]=>4
[6,1,2,4,5,3]=>4
[6,1,2,5,3,4]=>3
[6,1,2,5,4,3]=>6
[6,1,3,2,4,5]=>5
[6,1,3,2,5,4]=>7
[6,1,3,4,2,5]=>5
[6,1,3,4,5,2]=>5
[6,1,3,5,2,4]=>7
[6,1,3,5,4,2]=>7
[6,1,4,2,3,5]=>4
[6,1,4,2,5,3]=>4
[6,1,4,3,2,5]=>8
[6,1,4,3,5,2]=>8
[6,1,4,5,2,3]=>4
[6,1,4,5,3,2]=>8
[6,1,5,2,3,4]=>3
[6,1,5,2,4,3]=>6
[6,1,5,3,2,4]=>7
[6,1,5,3,4,2]=>7
[6,1,5,4,2,3]=>6
[6,1,5,4,3,2]=>10
[6,2,1,3,4,5]=>6
[6,2,1,3,5,4]=>8
[6,2,1,4,3,5]=>9
[6,2,1,4,5,3]=>9
[6,2,1,5,3,4]=>8
[6,2,1,5,4,3]=>11
[6,2,3,1,4,5]=>6
[6,2,3,1,5,4]=>8
[6,2,3,4,1,5]=>6
[6,2,3,4,5,1]=>6
[6,2,3,5,1,4]=>8
[6,2,3,5,4,1]=>8
[6,2,4,1,3,5]=>9
[6,2,4,1,5,3]=>9
[6,2,4,3,1,5]=>9
[6,2,4,3,5,1]=>9
[6,2,4,5,1,3]=>9
[6,2,4,5,3,1]=>9
[6,2,5,1,3,4]=>8
[6,2,5,1,4,3]=>11
[6,2,5,3,1,4]=>8
[6,2,5,3,4,1]=>8
[6,2,5,4,1,3]=>11
[6,2,5,4,3,1]=>11
[6,3,1,2,4,5]=>5
[6,3,1,2,5,4]=>7
[6,3,1,4,2,5]=>5
[6,3,1,4,5,2]=>5
[6,3,1,5,2,4]=>7
[6,3,1,5,4,2]=>7
[6,3,2,1,4,5]=>10
[6,3,2,1,5,4]=>12
[6,3,2,4,1,5]=>10
[6,3,2,4,5,1]=>10
[6,3,2,5,1,4]=>12
[6,3,2,5,4,1]=>12
[6,3,4,1,2,5]=>5
[6,3,4,1,5,2]=>5
[6,3,4,2,1,5]=>10
[6,3,4,2,5,1]=>10
[6,3,4,5,1,2]=>5
[6,3,4,5,2,1]=>10
[6,3,5,1,2,4]=>7
[6,3,5,1,4,2]=>7
[6,3,5,2,1,4]=>12
[6,3,5,2,4,1]=>12
[6,3,5,4,1,2]=>7
[6,3,5,4,2,1]=>12
[6,4,1,2,3,5]=>4
[6,4,1,2,5,3]=>4
[6,4,1,3,2,5]=>8
[6,4,1,3,5,2]=>8
[6,4,1,5,2,3]=>4
[6,4,1,5,3,2]=>8
[6,4,2,1,3,5]=>9
[6,4,2,1,5,3]=>9
[6,4,2,3,1,5]=>9
[6,4,2,3,5,1]=>9
[6,4,2,5,1,3]=>9
[6,4,2,5,3,1]=>9
[6,4,3,1,2,5]=>8
[6,4,3,1,5,2]=>8
[6,4,3,2,1,5]=>13
[6,4,3,2,5,1]=>13
[6,4,3,5,1,2]=>8
[6,4,3,5,2,1]=>13
[6,4,5,1,2,3]=>4
[6,4,5,1,3,2]=>8
[6,4,5,2,1,3]=>9
[6,4,5,2,3,1]=>9
[6,4,5,3,1,2]=>8
[6,4,5,3,2,1]=>13
[6,5,1,2,3,4]=>3
[6,5,1,2,4,3]=>6
[6,5,1,3,2,4]=>7
[6,5,1,3,4,2]=>7
[6,5,1,4,2,3]=>6
[6,5,1,4,3,2]=>10
[6,5,2,1,3,4]=>8
[6,5,2,1,4,3]=>11
[6,5,2,3,1,4]=>8
[6,5,2,3,4,1]=>8
[6,5,2,4,1,3]=>11
[6,5,2,4,3,1]=>11
[6,5,3,1,2,4]=>7
[6,5,3,1,4,2]=>7
[6,5,3,2,1,4]=>12
[6,5,3,2,4,1]=>12
[6,5,3,4,1,2]=>7
[6,5,3,4,2,1]=>12
[6,5,4,1,2,3]=>6
[6,5,4,1,3,2]=>10
[6,5,4,2,1,3]=>11
[6,5,4,2,3,1]=>11
[6,5,4,3,1,2]=>10
[6,5,4,3,2,1]=>15
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>1
[1,2,3,4,6,5,7]=>2
[1,2,3,4,6,7,5]=>2
[1,2,3,4,7,5,6]=>1
[1,2,3,4,7,6,5]=>3
[1,2,3,5,4,6,7]=>3
[1,2,3,5,4,7,6]=>4
[1,2,3,5,6,4,7]=>3
[1,2,3,5,6,7,4]=>3
[1,2,3,5,7,4,6]=>4
[1,2,3,5,7,6,4]=>4
[1,2,3,6,4,5,7]=>2
[1,2,3,6,4,7,5]=>2
[1,2,3,6,5,4,7]=>5
[1,2,3,6,5,7,4]=>5
[1,2,3,6,7,4,5]=>2
[1,2,3,6,7,5,4]=>5
[1,2,3,7,4,5,6]=>1
[1,2,3,7,4,6,5]=>3
[1,2,3,7,5,4,6]=>4
[1,2,3,7,5,6,4]=>4
[1,2,3,7,6,4,5]=>3
[1,2,3,7,6,5,4]=>6
[1,2,4,3,5,6,7]=>4
[1,2,4,3,5,7,6]=>5
[1,2,4,3,6,5,7]=>6
[1,2,4,3,6,7,5]=>6
[1,2,4,3,7,5,6]=>5
[1,2,4,3,7,6,5]=>7
[1,2,4,5,3,6,7]=>4
[1,2,4,5,3,7,6]=>5
[1,2,4,5,6,3,7]=>4
[1,2,4,5,6,7,3]=>4
[1,2,4,5,7,3,6]=>5
[1,2,4,5,7,6,3]=>5
[1,2,4,6,3,5,7]=>6
[1,2,4,6,3,7,5]=>6
[1,2,4,6,5,3,7]=>6
[1,2,4,6,5,7,3]=>6
[1,2,4,6,7,3,5]=>6
[1,2,4,6,7,5,3]=>6
[1,2,4,7,3,5,6]=>5
[1,2,4,7,3,6,5]=>7
[1,2,4,7,5,3,6]=>5
[1,2,4,7,5,6,3]=>5
[1,2,4,7,6,3,5]=>7
[1,2,4,7,6,5,3]=>7
[1,2,5,3,4,6,7]=>3
[1,2,5,3,4,7,6]=>4
[1,2,5,3,6,4,7]=>3
[1,2,5,3,6,7,4]=>3
[1,2,5,3,7,4,6]=>4
[1,2,5,3,7,6,4]=>4
[1,2,5,4,3,6,7]=>7
[1,2,5,4,3,7,6]=>8
[1,2,5,4,6,3,7]=>7
[1,2,5,4,6,7,3]=>7
[1,2,5,4,7,3,6]=>8
[1,2,5,4,7,6,3]=>8
[1,2,5,6,3,4,7]=>3
[1,2,5,6,3,7,4]=>3
[1,2,5,6,4,3,7]=>7
[1,2,5,6,4,7,3]=>7
[1,2,5,6,7,3,4]=>3
[1,2,5,6,7,4,3]=>7
[1,2,5,7,3,4,6]=>4
[1,2,5,7,3,6,4]=>4
[1,2,5,7,4,3,6]=>8
[1,2,5,7,4,6,3]=>8
[1,2,5,7,6,3,4]=>4
[1,2,5,7,6,4,3]=>8
[1,2,6,3,4,5,7]=>2
[1,2,6,3,4,7,5]=>2
[1,2,6,3,5,4,7]=>5
[1,2,6,3,5,7,4]=>5
[1,2,6,3,7,4,5]=>2
[1,2,6,3,7,5,4]=>5
[1,2,6,4,3,5,7]=>6
[1,2,6,4,3,7,5]=>6
[1,2,6,4,5,3,7]=>6
[1,2,6,4,5,7,3]=>6
[1,2,6,4,7,3,5]=>6
[1,2,6,4,7,5,3]=>6
[1,2,6,5,3,4,7]=>5
[1,2,6,5,3,7,4]=>5
[1,2,6,5,4,3,7]=>9
[1,2,6,5,4,7,3]=>9
[1,2,6,5,7,3,4]=>5
[1,2,6,5,7,4,3]=>9
[1,2,6,7,3,4,5]=>2
[1,2,6,7,3,5,4]=>5
[1,2,6,7,4,3,5]=>6
[1,2,6,7,4,5,3]=>6
[1,2,6,7,5,3,4]=>5
[1,2,6,7,5,4,3]=>9
[1,2,7,3,4,5,6]=>1
[1,2,7,3,4,6,5]=>3
[1,2,7,3,5,4,6]=>4
[1,2,7,3,5,6,4]=>4
[1,2,7,3,6,4,5]=>3
[1,2,7,3,6,5,4]=>6
[1,2,7,4,3,5,6]=>5
[1,2,7,4,3,6,5]=>7
[1,2,7,4,5,3,6]=>5
[1,2,7,4,5,6,3]=>5
[1,2,7,4,6,3,5]=>7
[1,2,7,4,6,5,3]=>7
[1,2,7,5,3,4,6]=>4
[1,2,7,5,3,6,4]=>4
[1,2,7,5,4,3,6]=>8
[1,2,7,5,4,6,3]=>8
[1,2,7,5,6,3,4]=>4
[1,2,7,5,6,4,3]=>8
[1,2,7,6,3,4,5]=>3
[1,2,7,6,3,5,4]=>6
[1,2,7,6,4,3,5]=>7
[1,2,7,6,4,5,3]=>7
[1,2,7,6,5,3,4]=>6
[1,2,7,6,5,4,3]=>10
[1,3,2,4,5,6,7]=>5
[1,3,2,4,5,7,6]=>6
[1,3,2,4,6,5,7]=>7
[1,3,2,4,6,7,5]=>7
[1,3,2,4,7,5,6]=>6
[1,3,2,4,7,6,5]=>8
[1,3,2,5,4,6,7]=>8
[1,3,2,5,4,7,6]=>9
[1,3,2,5,6,4,7]=>8
[1,3,2,5,6,7,4]=>8
[1,3,2,5,7,4,6]=>9
[1,3,2,5,7,6,4]=>9
[1,3,2,6,4,5,7]=>7
[1,3,2,6,4,7,5]=>7
[1,3,2,6,5,4,7]=>10
[1,3,2,6,5,7,4]=>10
[1,3,2,6,7,4,5]=>7
[1,3,2,6,7,5,4]=>10
[1,3,2,7,4,5,6]=>6
[1,3,2,7,4,6,5]=>8
[1,3,2,7,5,4,6]=>9
[1,3,2,7,5,6,4]=>9
[1,3,2,7,6,4,5]=>8
[1,3,2,7,6,5,4]=>11
[1,3,4,2,5,6,7]=>5
[1,3,4,2,5,7,6]=>6
[1,3,4,2,6,5,7]=>7
[1,3,4,2,6,7,5]=>7
[1,3,4,2,7,5,6]=>6
[1,3,4,2,7,6,5]=>8
[1,3,4,5,2,6,7]=>5
[1,3,4,5,2,7,6]=>6
[1,3,4,5,6,2,7]=>5
[1,3,4,5,6,7,2]=>5
[1,3,4,5,7,2,6]=>6
[1,3,4,5,7,6,2]=>6
[1,3,4,6,2,5,7]=>7
[1,3,4,6,2,7,5]=>7
[1,3,4,6,5,2,7]=>7
[1,3,4,6,5,7,2]=>7
[1,3,4,6,7,2,5]=>7
[1,3,4,6,7,5,2]=>7
[1,3,4,7,2,5,6]=>6
[1,3,4,7,2,6,5]=>8
[1,3,4,7,5,2,6]=>6
[1,3,4,7,5,6,2]=>6
[1,3,4,7,6,2,5]=>8
[1,3,4,7,6,5,2]=>8
[1,3,5,2,4,6,7]=>8
[1,3,5,2,4,7,6]=>9
[1,3,5,2,6,4,7]=>8
[1,3,5,2,6,7,4]=>8
[1,3,5,2,7,4,6]=>9
[1,3,5,2,7,6,4]=>9
[1,3,5,4,2,6,7]=>8
[1,3,5,4,2,7,6]=>9
[1,3,5,4,6,2,7]=>8
[1,3,5,4,6,7,2]=>8
[1,3,5,4,7,2,6]=>9
[1,3,5,4,7,6,2]=>9
[1,3,5,6,2,4,7]=>8
[1,3,5,6,2,7,4]=>8
[1,3,5,6,4,2,7]=>8
[1,3,5,6,4,7,2]=>8
[1,3,5,6,7,2,4]=>8
[1,3,5,6,7,4,2]=>8
[1,3,5,7,2,4,6]=>9
[1,3,5,7,2,6,4]=>9
[1,3,5,7,4,2,6]=>9
[1,3,5,7,4,6,2]=>9
[1,3,5,7,6,2,4]=>9
[1,3,5,7,6,4,2]=>9
[1,3,6,2,4,5,7]=>7
[1,3,6,2,4,7,5]=>7
[1,3,6,2,5,4,7]=>10
[1,3,6,2,5,7,4]=>10
[1,3,6,2,7,4,5]=>7
[1,3,6,2,7,5,4]=>10
[1,3,6,4,2,5,7]=>7
[1,3,6,4,2,7,5]=>7
[1,3,6,4,5,2,7]=>7
[1,3,6,4,5,7,2]=>7
[1,3,6,4,7,2,5]=>7
[1,3,6,4,7,5,2]=>7
[1,3,6,5,2,4,7]=>10
[1,3,6,5,2,7,4]=>10
[1,3,6,5,4,2,7]=>10
[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]=>7
[1,3,6,7,2,5,4]=>10
[1,3,6,7,4,2,5]=>7
[1,3,6,7,4,5,2]=>7
[1,3,6,7,5,2,4]=>10
[1,3,6,7,5,4,2]=>10
[1,3,7,2,4,5,6]=>6
[1,3,7,2,4,6,5]=>8
[1,3,7,2,5,4,6]=>9
[1,3,7,2,5,6,4]=>9
[1,3,7,2,6,4,5]=>8
[1,3,7,2,6,5,4]=>11
[1,3,7,4,2,5,6]=>6
[1,3,7,4,2,6,5]=>8
[1,3,7,4,5,2,6]=>6
[1,3,7,4,5,6,2]=>6
[1,3,7,4,6,2,5]=>8
[1,3,7,4,6,5,2]=>8
[1,3,7,5,2,4,6]=>9
[1,3,7,5,2,6,4]=>9
[1,3,7,5,4,2,6]=>9
[1,3,7,5,4,6,2]=>9
[1,3,7,5,6,2,4]=>9
[1,3,7,5,6,4,2]=>9
[1,3,7,6,2,4,5]=>8
[1,3,7,6,2,5,4]=>11
[1,3,7,6,4,2,5]=>8
[1,3,7,6,4,5,2]=>8
[1,3,7,6,5,2,4]=>11
[1,3,7,6,5,4,2]=>11
[1,4,2,3,5,6,7]=>4
[1,4,2,3,5,7,6]=>5
[1,4,2,3,6,5,7]=>6
[1,4,2,3,6,7,5]=>6
[1,4,2,3,7,5,6]=>5
[1,4,2,3,7,6,5]=>7
[1,4,2,5,3,6,7]=>4
[1,4,2,5,3,7,6]=>5
[1,4,2,5,6,3,7]=>4
[1,4,2,5,6,7,3]=>4
[1,4,2,5,7,3,6]=>5
[1,4,2,5,7,6,3]=>5
[1,4,2,6,3,5,7]=>6
[1,4,2,6,3,7,5]=>6
[1,4,2,6,5,3,7]=>6
[1,4,2,6,5,7,3]=>6
[1,4,2,6,7,3,5]=>6
[1,4,2,6,7,5,3]=>6
[1,4,2,7,3,5,6]=>5
[1,4,2,7,3,6,5]=>7
[1,4,2,7,5,3,6]=>5
[1,4,2,7,5,6,3]=>5
[1,4,2,7,6,3,5]=>7
[1,4,2,7,6,5,3]=>7
[1,4,3,2,5,6,7]=>9
[1,4,3,2,5,7,6]=>10
[1,4,3,2,6,5,7]=>11
[1,4,3,2,6,7,5]=>11
[1,4,3,2,7,5,6]=>10
[1,4,3,2,7,6,5]=>12
[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]=>11
[1,4,3,6,2,7,5]=>11
[1,4,3,6,5,2,7]=>11
[1,4,3,6,5,7,2]=>11
[1,4,3,6,7,2,5]=>11
[1,4,3,6,7,5,2]=>11
[1,4,3,7,2,5,6]=>10
[1,4,3,7,2,6,5]=>12
[1,4,3,7,5,2,6]=>10
[1,4,3,7,5,6,2]=>10
[1,4,3,7,6,2,5]=>12
[1,4,3,7,6,5,2]=>12
[1,4,5,2,3,6,7]=>4
[1,4,5,2,3,7,6]=>5
[1,4,5,2,6,3,7]=>4
[1,4,5,2,6,7,3]=>4
[1,4,5,2,7,3,6]=>5
[1,4,5,2,7,6,3]=>5
[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]=>4
[1,4,5,6,2,7,3]=>4
[1,4,5,6,3,2,7]=>9
[1,4,5,6,3,7,2]=>9
[1,4,5,6,7,2,3]=>4
[1,4,5,6,7,3,2]=>9
[1,4,5,7,2,3,6]=>5
[1,4,5,7,2,6,3]=>5
[1,4,5,7,3,2,6]=>10
[1,4,5,7,3,6,2]=>10
[1,4,5,7,6,2,3]=>5
[1,4,5,7,6,3,2]=>10
[1,4,6,2,3,5,7]=>6
[1,4,6,2,3,7,5]=>6
[1,4,6,2,5,3,7]=>6
[1,4,6,2,5,7,3]=>6
[1,4,6,2,7,3,5]=>6
[1,4,6,2,7,5,3]=>6
[1,4,6,3,2,5,7]=>11
[1,4,6,3,2,7,5]=>11
[1,4,6,3,5,2,7]=>11
[1,4,6,3,5,7,2]=>11
[1,4,6,3,7,2,5]=>11
[1,4,6,3,7,5,2]=>11
[1,4,6,5,2,3,7]=>6
[1,4,6,5,2,7,3]=>6
[1,4,6,5,3,2,7]=>11
[1,4,6,5,3,7,2]=>11
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Description
The disorder of a permutation.
Consider a permutation $\pi = [\pi_1,\ldots,\pi_n]$ and cyclically scanning $\pi$ from left to right and remove the elements $1$ through $n$ on this order one after the other. The disorder of $\pi$ is defined to be the number of times a position was not removed in this process.
For example, the disorder of $[3,5,2,1,4]$ is $8$ since on the first scan, 3,5,2 and 4 are not removed, on the second, 3,5 and 4, and on the third and last scan, 5 is once again not removed.
Consider a permutation $\pi = [\pi_1,\ldots,\pi_n]$ and cyclically scanning $\pi$ from left to right and remove the elements $1$ through $n$ on this order one after the other. The disorder of $\pi$ is defined to be the number of times a position was not removed in this process.
For example, the disorder of $[3,5,2,1,4]$ is $8$ since on the first scan, 3,5,2 and 4 are not removed, on the second, 3,5 and 4, and on the third and last scan, 5 is once again not removed.
References
[1] Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product_i=0..n-1 (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). OEIS:A008302
Code
def statistic(pi):
i = 1
pos = 0
count = 0
while i < len(pi):
if pi[pos] == i:
i += 1
elif pi[pos] > i:
count += 1
pos = (pos+1)%len(pi)
return count
Created
Mar 15, 2016 at 22:34 by Christian Stump
Updated
May 10, 2019 at 17:35 by Henning Ulfarsson
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