Identifier
- St001074: Permutations ⟶ ℤ
Values
=>
[1,2]=>2
[2,1]=>2
[1,2,3]=>3
[1,3,2]=>5
[2,1,3]=>3
[2,3,1]=>5
[3,1,2]=>3
[3,2,1]=>3
[1,2,3,4]=>4
[1,2,4,3]=>6
[1,3,2,4]=>6
[1,3,4,2]=>8
[1,4,2,3]=>8
[1,4,3,2]=>8
[2,1,3,4]=>4
[2,1,4,3]=>6
[2,3,1,4]=>6
[2,3,4,1]=>8
[2,4,1,3]=>6
[2,4,3,1]=>8
[3,1,2,4]=>4
[3,1,4,2]=>6
[3,2,1,4]=>4
[3,2,4,1]=>8
[3,4,1,2]=>6
[3,4,2,1]=>6
[4,1,2,3]=>4
[4,1,3,2]=>6
[4,2,1,3]=>4
[4,2,3,1]=>6
[4,3,1,2]=>4
[4,3,2,1]=>4
[1,2,3,4,5]=>5
[1,2,3,5,4]=>7
[1,2,4,3,5]=>7
[1,2,4,5,3]=>9
[1,2,5,3,4]=>9
[1,2,5,4,3]=>9
[1,3,2,4,5]=>7
[1,3,2,5,4]=>9
[1,3,4,2,5]=>9
[1,3,4,5,2]=>11
[1,3,5,2,4]=>9
[1,3,5,4,2]=>11
[1,4,2,3,5]=>9
[1,4,2,5,3]=>11
[1,4,3,2,5]=>9
[1,4,3,5,2]=>13
[1,4,5,2,3]=>11
[1,4,5,3,2]=>11
[1,5,2,3,4]=>11
[1,5,2,4,3]=>13
[1,5,3,2,4]=>11
[1,5,3,4,2]=>13
[1,5,4,2,3]=>11
[1,5,4,3,2]=>11
[2,1,3,4,5]=>5
[2,1,3,5,4]=>7
[2,1,4,3,5]=>7
[2,1,4,5,3]=>9
[2,1,5,3,4]=>9
[2,1,5,4,3]=>9
[2,3,1,4,5]=>7
[2,3,1,5,4]=>9
[2,3,4,1,5]=>9
[2,3,4,5,1]=>11
[2,3,5,1,4]=>9
[2,3,5,4,1]=>11
[2,4,1,3,5]=>7
[2,4,1,5,3]=>11
[2,4,3,1,5]=>9
[2,4,3,5,1]=>13
[2,4,5,1,3]=>9
[2,4,5,3,1]=>11
[2,5,1,3,4]=>9
[2,5,1,4,3]=>11
[2,5,3,1,4]=>9
[2,5,3,4,1]=>13
[2,5,4,1,3]=>9
[2,5,4,3,1]=>11
[3,1,2,4,5]=>5
[3,1,2,5,4]=>7
[3,1,4,2,5]=>7
[3,1,4,5,2]=>9
[3,1,5,2,4]=>9
[3,1,5,4,2]=>9
[3,2,1,4,5]=>5
[3,2,1,5,4]=>7
[3,2,4,1,5]=>9
[3,2,4,5,1]=>11
[3,2,5,1,4]=>9
[3,2,5,4,1]=>11
[3,4,1,2,5]=>7
[3,4,1,5,2]=>11
[3,4,2,1,5]=>7
[3,4,2,5,1]=>13
[3,4,5,1,2]=>9
[3,4,5,2,1]=>9
[3,5,1,2,4]=>7
[3,5,1,4,2]=>11
[3,5,2,1,4]=>7
[3,5,2,4,1]=>11
[3,5,4,1,2]=>9
[3,5,4,2,1]=>9
[4,1,2,3,5]=>5
[4,1,2,5,3]=>7
[4,1,3,2,5]=>7
[4,1,3,5,2]=>9
[4,1,5,2,3]=>9
[4,1,5,3,2]=>9
[4,2,1,3,5]=>5
[4,2,1,5,3]=>7
[4,2,3,1,5]=>7
[4,2,3,5,1]=>11
[4,2,5,1,3]=>9
[4,2,5,3,1]=>9
[4,3,1,2,5]=>5
[4,3,1,5,2]=>9
[4,3,2,1,5]=>5
[4,3,2,5,1]=>11
[4,3,5,1,2]=>9
[4,3,5,2,1]=>9
[4,5,1,2,3]=>7
[4,5,1,3,2]=>9
[4,5,2,1,3]=>7
[4,5,2,3,1]=>9
[4,5,3,1,2]=>7
[4,5,3,2,1]=>7
[5,1,2,3,4]=>5
[5,1,2,4,3]=>7
[5,1,3,2,4]=>7
[5,1,3,4,2]=>9
[5,1,4,2,3]=>9
[5,1,4,3,2]=>9
[5,2,1,3,4]=>5
[5,2,1,4,3]=>7
[5,2,3,1,4]=>7
[5,2,3,4,1]=>9
[5,2,4,1,3]=>7
[5,2,4,3,1]=>9
[5,3,1,2,4]=>5
[5,3,1,4,2]=>7
[5,3,2,1,4]=>5
[5,3,2,4,1]=>9
[5,3,4,1,2]=>7
[5,3,4,2,1]=>7
[5,4,1,2,3]=>5
[5,4,1,3,2]=>7
[5,4,2,1,3]=>5
[5,4,2,3,1]=>7
[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]=>8
[1,2,3,5,4,6]=>8
[1,2,3,5,6,4]=>10
[1,2,3,6,4,5]=>10
[1,2,3,6,5,4]=>10
[1,2,4,3,5,6]=>8
[1,2,4,3,6,5]=>10
[1,2,4,5,3,6]=>10
[1,2,4,5,6,3]=>12
[1,2,4,6,3,5]=>10
[1,2,4,6,5,3]=>12
[1,2,5,3,4,6]=>10
[1,2,5,3,6,4]=>12
[1,2,5,4,3,6]=>10
[1,2,5,4,6,3]=>14
[1,2,5,6,3,4]=>12
[1,2,5,6,4,3]=>12
[1,2,6,3,4,5]=>12
[1,2,6,3,5,4]=>14
[1,2,6,4,3,5]=>12
[1,2,6,4,5,3]=>14
[1,2,6,5,3,4]=>12
[1,2,6,5,4,3]=>12
[1,3,2,4,5,6]=>8
[1,3,2,4,6,5]=>10
[1,3,2,5,4,6]=>10
[1,3,2,5,6,4]=>12
[1,3,2,6,4,5]=>12
[1,3,2,6,5,4]=>12
[1,3,4,2,5,6]=>10
[1,3,4,2,6,5]=>12
[1,3,4,5,2,6]=>12
[1,3,4,5,6,2]=>14
[1,3,4,6,2,5]=>12
[1,3,4,6,5,2]=>14
[1,3,5,2,4,6]=>10
[1,3,5,2,6,4]=>14
[1,3,5,4,2,6]=>12
[1,3,5,4,6,2]=>16
[1,3,5,6,2,4]=>12
[1,3,5,6,4,2]=>14
[1,3,6,2,4,5]=>12
[1,3,6,2,5,4]=>14
[1,3,6,4,2,5]=>12
[1,3,6,4,5,2]=>16
[1,3,6,5,2,4]=>12
[1,3,6,5,4,2]=>14
[1,4,2,3,5,6]=>10
[1,4,2,3,6,5]=>12
[1,4,2,5,3,6]=>12
[1,4,2,5,6,3]=>14
[1,4,2,6,3,5]=>14
[1,4,2,6,5,3]=>14
[1,4,3,2,5,6]=>10
[1,4,3,2,6,5]=>12
[1,4,3,5,2,6]=>14
[1,4,3,5,6,2]=>16
[1,4,3,6,2,5]=>14
[1,4,3,6,5,2]=>16
[1,4,5,2,3,6]=>12
[1,4,5,2,6,3]=>16
[1,4,5,3,2,6]=>12
[1,4,5,3,6,2]=>18
[1,4,5,6,2,3]=>14
[1,4,5,6,3,2]=>14
[1,4,6,2,3,5]=>12
[1,4,6,2,5,3]=>16
[1,4,6,3,2,5]=>12
[1,4,6,3,5,2]=>16
[1,4,6,5,2,3]=>14
[1,4,6,5,3,2]=>14
[1,5,2,3,4,6]=>12
[1,5,2,3,6,4]=>14
[1,5,2,4,3,6]=>14
[1,5,2,4,6,3]=>16
[1,5,2,6,3,4]=>16
[1,5,2,6,4,3]=>16
[1,5,3,2,4,6]=>12
[1,5,3,2,6,4]=>14
[1,5,3,4,2,6]=>14
[1,5,3,4,6,2]=>18
[1,5,3,6,2,4]=>16
[1,5,3,6,4,2]=>16
[1,5,4,2,3,6]=>12
[1,5,4,2,6,3]=>16
[1,5,4,3,2,6]=>12
[1,5,4,3,6,2]=>18
[1,5,4,6,2,3]=>16
[1,5,4,6,3,2]=>16
[1,5,6,2,3,4]=>14
[1,5,6,2,4,3]=>16
[1,5,6,3,2,4]=>14
[1,5,6,3,4,2]=>16
[1,5,6,4,2,3]=>14
[1,5,6,4,3,2]=>14
[1,6,2,3,4,5]=>14
[1,6,2,3,5,4]=>16
[1,6,2,4,3,5]=>16
[1,6,2,4,5,3]=>18
[1,6,2,5,3,4]=>18
[1,6,2,5,4,3]=>18
[1,6,3,2,4,5]=>14
[1,6,3,2,5,4]=>16
[1,6,3,4,2,5]=>16
[1,6,3,4,5,2]=>18
[1,6,3,5,2,4]=>16
[1,6,3,5,4,2]=>18
[1,6,4,2,3,5]=>14
[1,6,4,2,5,3]=>16
[1,6,4,3,2,5]=>14
[1,6,4,3,5,2]=>18
[1,6,4,5,2,3]=>16
[1,6,4,5,3,2]=>16
[1,6,5,2,3,4]=>14
[1,6,5,2,4,3]=>16
[1,6,5,3,2,4]=>14
[1,6,5,3,4,2]=>16
[1,6,5,4,2,3]=>14
[1,6,5,4,3,2]=>14
[2,1,3,4,5,6]=>6
[2,1,3,4,6,5]=>8
[2,1,3,5,4,6]=>8
[2,1,3,5,6,4]=>10
[2,1,3,6,4,5]=>10
[2,1,3,6,5,4]=>10
[2,1,4,3,5,6]=>8
[2,1,4,3,6,5]=>10
[2,1,4,5,3,6]=>10
[2,1,4,5,6,3]=>12
[2,1,4,6,3,5]=>10
[2,1,4,6,5,3]=>12
[2,1,5,3,4,6]=>10
[2,1,5,3,6,4]=>12
[2,1,5,4,3,6]=>10
[2,1,5,4,6,3]=>14
[2,1,5,6,3,4]=>12
[2,1,5,6,4,3]=>12
[2,1,6,3,4,5]=>12
[2,1,6,3,5,4]=>14
[2,1,6,4,3,5]=>12
[2,1,6,4,5,3]=>14
[2,1,6,5,3,4]=>12
[2,1,6,5,4,3]=>12
[2,3,1,4,5,6]=>8
[2,3,1,4,6,5]=>10
[2,3,1,5,4,6]=>10
[2,3,1,5,6,4]=>12
[2,3,1,6,4,5]=>12
[2,3,1,6,5,4]=>12
[2,3,4,1,5,6]=>10
[2,3,4,1,6,5]=>12
[2,3,4,5,1,6]=>12
[2,3,4,5,6,1]=>14
[2,3,4,6,1,5]=>12
[2,3,4,6,5,1]=>14
[2,3,5,1,4,6]=>10
[2,3,5,1,6,4]=>14
[2,3,5,4,1,6]=>12
[2,3,5,4,6,1]=>16
[2,3,5,6,1,4]=>12
[2,3,5,6,4,1]=>14
[2,3,6,1,4,5]=>12
[2,3,6,1,5,4]=>14
[2,3,6,4,1,5]=>12
[2,3,6,4,5,1]=>16
[2,3,6,5,1,4]=>12
[2,3,6,5,4,1]=>14
[2,4,1,3,5,6]=>8
[2,4,1,3,6,5]=>10
[2,4,1,5,3,6]=>12
[2,4,1,5,6,3]=>14
[2,4,1,6,3,5]=>14
[2,4,1,6,5,3]=>14
[2,4,3,1,5,6]=>10
[2,4,3,1,6,5]=>12
[2,4,3,5,1,6]=>14
[2,4,3,5,6,1]=>16
[2,4,3,6,1,5]=>14
[2,4,3,6,5,1]=>16
[2,4,5,1,3,6]=>10
[2,4,5,1,6,3]=>16
[2,4,5,3,1,6]=>12
[2,4,5,3,6,1]=>18
[2,4,5,6,1,3]=>12
[2,4,5,6,3,1]=>14
[2,4,6,1,3,5]=>10
[2,4,6,1,5,3]=>16
[2,4,6,3,1,5]=>12
[2,4,6,3,5,1]=>16
[2,4,6,5,1,3]=>12
[2,4,6,5,3,1]=>14
[2,5,1,3,4,6]=>10
[2,5,1,3,6,4]=>12
[2,5,1,4,3,6]=>12
[2,5,1,4,6,3]=>14
[2,5,1,6,3,4]=>16
[2,5,1,6,4,3]=>16
[2,5,3,1,4,6]=>10
[2,5,3,1,6,4]=>14
[2,5,3,4,1,6]=>14
[2,5,3,4,6,1]=>18
[2,5,3,6,1,4]=>14
[2,5,3,6,4,1]=>16
[2,5,4,1,3,6]=>10
[2,5,4,1,6,3]=>16
[2,5,4,3,1,6]=>12
[2,5,4,3,6,1]=>18
[2,5,4,6,1,3]=>14
[2,5,4,6,3,1]=>16
[2,5,6,1,3,4]=>12
[2,5,6,1,4,3]=>14
[2,5,6,3,1,4]=>12
[2,5,6,3,4,1]=>16
[2,5,6,4,1,3]=>12
[2,5,6,4,3,1]=>14
[2,6,1,3,4,5]=>12
[2,6,1,3,5,4]=>14
[2,6,1,4,3,5]=>14
[2,6,1,4,5,3]=>16
[2,6,1,5,3,4]=>16
[2,6,1,5,4,3]=>16
[2,6,3,1,4,5]=>12
[2,6,3,1,5,4]=>14
[2,6,3,4,1,5]=>14
[2,6,3,4,5,1]=>18
[2,6,3,5,1,4]=>14
[2,6,3,5,4,1]=>18
[2,6,4,1,3,5]=>12
[2,6,4,1,5,3]=>14
[2,6,4,3,1,5]=>12
[2,6,4,3,5,1]=>18
[2,6,4,5,1,3]=>14
[2,6,4,5,3,1]=>16
[2,6,5,1,3,4]=>12
[2,6,5,1,4,3]=>14
[2,6,5,3,1,4]=>12
[2,6,5,3,4,1]=>16
[2,6,5,4,1,3]=>12
[2,6,5,4,3,1]=>14
[3,1,2,4,5,6]=>6
[3,1,2,4,6,5]=>8
[3,1,2,5,4,6]=>8
[3,1,2,5,6,4]=>10
[3,1,2,6,4,5]=>10
[3,1,2,6,5,4]=>10
[3,1,4,2,5,6]=>8
[3,1,4,2,6,5]=>10
[3,1,4,5,2,6]=>10
[3,1,4,5,6,2]=>12
[3,1,4,6,2,5]=>10
[3,1,4,6,5,2]=>12
[3,1,5,2,4,6]=>10
[3,1,5,2,6,4]=>12
[3,1,5,4,2,6]=>10
[3,1,5,4,6,2]=>14
[3,1,5,6,2,4]=>12
[3,1,5,6,4,2]=>12
[3,1,6,2,4,5]=>12
[3,1,6,2,5,4]=>14
[3,1,6,4,2,5]=>12
[3,1,6,4,5,2]=>14
[3,1,6,5,2,4]=>12
[3,1,6,5,4,2]=>12
[3,2,1,4,5,6]=>6
[3,2,1,4,6,5]=>8
[3,2,1,5,4,6]=>8
[3,2,1,5,6,4]=>10
[3,2,1,6,4,5]=>10
[3,2,1,6,5,4]=>10
[3,2,4,1,5,6]=>10
[3,2,4,1,6,5]=>12
[3,2,4,5,1,6]=>12
[3,2,4,5,6,1]=>14
[3,2,4,6,1,5]=>12
[3,2,4,6,5,1]=>14
[3,2,5,1,4,6]=>10
[3,2,5,1,6,4]=>14
[3,2,5,4,1,6]=>12
[3,2,5,4,6,1]=>16
[3,2,5,6,1,4]=>12
[3,2,5,6,4,1]=>14
[3,2,6,1,4,5]=>12
[3,2,6,1,5,4]=>14
[3,2,6,4,1,5]=>12
[3,2,6,4,5,1]=>16
[3,2,6,5,1,4]=>12
[3,2,6,5,4,1]=>14
[3,4,1,2,5,6]=>8
[3,4,1,2,6,5]=>10
[3,4,1,5,2,6]=>12
[3,4,1,5,6,2]=>14
[3,4,1,6,2,5]=>14
[3,4,1,6,5,2]=>14
[3,4,2,1,5,6]=>8
[3,4,2,1,6,5]=>10
[3,4,2,5,1,6]=>14
[3,4,2,5,6,1]=>16
[3,4,2,6,1,5]=>14
[3,4,2,6,5,1]=>16
[3,4,5,1,2,6]=>10
[3,4,5,1,6,2]=>16
[3,4,5,2,1,6]=>10
[3,4,5,2,6,1]=>18
[3,4,5,6,1,2]=>12
[3,4,5,6,2,1]=>12
[3,4,6,1,2,5]=>10
[3,4,6,1,5,2]=>16
[3,4,6,2,1,5]=>10
[3,4,6,2,5,1]=>16
[3,4,6,5,1,2]=>12
[3,4,6,5,2,1]=>12
[3,5,1,2,4,6]=>8
[3,5,1,2,6,4]=>12
[3,5,1,4,2,6]=>12
[3,5,1,4,6,2]=>14
[3,5,1,6,2,4]=>14
[3,5,1,6,4,2]=>16
[3,5,2,1,4,6]=>8
[3,5,2,1,6,4]=>12
[3,5,2,4,1,6]=>12
[3,5,2,4,6,1]=>16
[3,5,2,6,1,4]=>14
[3,5,2,6,4,1]=>16
[3,5,4,1,2,6]=>10
[3,5,4,1,6,2]=>16
[3,5,4,2,1,6]=>10
[3,5,4,2,6,1]=>18
[3,5,4,6,1,2]=>14
[3,5,4,6,2,1]=>14
[3,5,6,1,2,4]=>10
[3,5,6,1,4,2]=>14
[3,5,6,2,1,4]=>10
[3,5,6,2,4,1]=>14
[3,5,6,4,1,2]=>12
[3,5,6,4,2,1]=>12
[3,6,1,2,4,5]=>10
[3,6,1,2,5,4]=>12
[3,6,1,4,2,5]=>12
[3,6,1,4,5,2]=>16
[3,6,1,5,2,4]=>14
[3,6,1,5,4,2]=>16
[3,6,2,1,4,5]=>10
[3,6,2,1,5,4]=>12
[3,6,2,4,1,5]=>12
[3,6,2,4,5,1]=>16
[3,6,2,5,1,4]=>12
[3,6,2,5,4,1]=>16
[3,6,4,1,2,5]=>10
[3,6,4,1,5,2]=>14
[3,6,4,2,1,5]=>10
[3,6,4,2,5,1]=>16
[3,6,4,5,1,2]=>14
[3,6,4,5,2,1]=>14
[3,6,5,1,2,4]=>10
[3,6,5,1,4,2]=>14
[3,6,5,2,1,4]=>10
[3,6,5,2,4,1]=>14
[3,6,5,4,1,2]=>12
[3,6,5,4,2,1]=>12
[4,1,2,3,5,6]=>6
[4,1,2,3,6,5]=>8
[4,1,2,5,3,6]=>8
[4,1,2,5,6,3]=>10
[4,1,2,6,3,5]=>10
[4,1,2,6,5,3]=>10
[4,1,3,2,5,6]=>8
[4,1,3,2,6,5]=>10
[4,1,3,5,2,6]=>10
[4,1,3,5,6,2]=>12
[4,1,3,6,2,5]=>10
[4,1,3,6,5,2]=>12
[4,1,5,2,3,6]=>10
[4,1,5,2,6,3]=>12
[4,1,5,3,2,6]=>10
[4,1,5,3,6,2]=>14
[4,1,5,6,2,3]=>12
[4,1,5,6,3,2]=>12
[4,1,6,2,3,5]=>12
[4,1,6,2,5,3]=>14
[4,1,6,3,2,5]=>12
[4,1,6,3,5,2]=>14
[4,1,6,5,2,3]=>12
[4,1,6,5,3,2]=>12
[4,2,1,3,5,6]=>6
[4,2,1,3,6,5]=>8
[4,2,1,5,3,6]=>8
[4,2,1,5,6,3]=>10
[4,2,1,6,3,5]=>10
[4,2,1,6,5,3]=>10
[4,2,3,1,5,6]=>8
[4,2,3,1,6,5]=>10
[4,2,3,5,1,6]=>12
[4,2,3,5,6,1]=>14
[4,2,3,6,1,5]=>12
[4,2,3,6,5,1]=>14
[4,2,5,1,3,6]=>10
[4,2,5,1,6,3]=>14
[4,2,5,3,1,6]=>10
[4,2,5,3,6,1]=>16
[4,2,5,6,1,3]=>12
[4,2,5,6,3,1]=>12
[4,2,6,1,3,5]=>12
[4,2,6,1,5,3]=>14
[4,2,6,3,1,5]=>10
[4,2,6,3,5,1]=>16
[4,2,6,5,1,3]=>12
[4,2,6,5,3,1]=>12
[4,3,1,2,5,6]=>6
[4,3,1,2,6,5]=>8
[4,3,1,5,2,6]=>10
[4,3,1,5,6,2]=>12
[4,3,1,6,2,5]=>12
[4,3,1,6,5,2]=>12
[4,3,2,1,5,6]=>6
[4,3,2,1,6,5]=>8
[4,3,2,5,1,6]=>12
[4,3,2,5,6,1]=>14
[4,3,2,6,1,5]=>12
[4,3,2,6,5,1]=>14
[4,3,5,1,2,6]=>10
[4,3,5,1,6,2]=>16
[4,3,5,2,1,6]=>10
[4,3,5,2,6,1]=>18
[4,3,5,6,1,2]=>12
[4,3,5,6,2,1]=>12
[4,3,6,1,2,5]=>10
[4,3,6,1,5,2]=>16
[4,3,6,2,1,5]=>10
[4,3,6,2,5,1]=>16
[4,3,6,5,1,2]=>12
[4,3,6,5,2,1]=>12
[4,5,1,2,3,6]=>8
[4,5,1,2,6,3]=>12
[4,5,1,3,2,6]=>10
[4,5,1,3,6,2]=>14
[4,5,1,6,2,3]=>14
[4,5,1,6,3,2]=>14
[4,5,2,1,3,6]=>8
[4,5,2,1,6,3]=>12
[4,5,2,3,1,6]=>10
[4,5,2,3,6,1]=>16
[4,5,2,6,1,3]=>14
[4,5,2,6,3,1]=>14
[4,5,3,1,2,6]=>8
[4,5,3,1,6,2]=>14
[4,5,3,2,1,6]=>8
[4,5,3,2,6,1]=>16
[4,5,3,6,1,2]=>14
[4,5,3,6,2,1]=>14
[4,5,6,1,2,3]=>10
[4,5,6,1,3,2]=>12
[4,5,6,2,1,3]=>10
[4,5,6,2,3,1]=>12
[4,5,6,3,1,2]=>10
[4,5,6,3,2,1]=>10
[4,6,1,2,3,5]=>8
[4,6,1,2,5,3]=>12
[4,6,1,3,2,5]=>10
[4,6,1,3,5,2]=>14
[4,6,1,5,2,3]=>14
[4,6,1,5,3,2]=>14
[4,6,2,1,3,5]=>8
[4,6,2,1,5,3]=>12
[4,6,2,3,1,5]=>10
[4,6,2,3,5,1]=>14
[4,6,2,5,1,3]=>12
[4,6,2,5,3,1]=>14
[4,6,3,1,2,5]=>8
[4,6,3,1,5,2]=>12
[4,6,3,2,1,5]=>8
[4,6,3,2,5,1]=>14
[4,6,3,5,1,2]=>12
[4,6,3,5,2,1]=>12
[4,6,5,1,2,3]=>10
[4,6,5,1,3,2]=>12
[4,6,5,2,1,3]=>10
[4,6,5,2,3,1]=>12
[4,6,5,3,1,2]=>10
[4,6,5,3,2,1]=>10
[5,1,2,3,4,6]=>6
[5,1,2,3,6,4]=>8
[5,1,2,4,3,6]=>8
[5,1,2,4,6,3]=>10
[5,1,2,6,3,4]=>10
[5,1,2,6,4,3]=>10
[5,1,3,2,4,6]=>8
[5,1,3,2,6,4]=>10
[5,1,3,4,2,6]=>10
[5,1,3,4,6,2]=>12
[5,1,3,6,2,4]=>10
[5,1,3,6,4,2]=>12
[5,1,4,2,3,6]=>10
[5,1,4,2,6,3]=>12
[5,1,4,3,2,6]=>10
[5,1,4,3,6,2]=>14
[5,1,4,6,2,3]=>12
[5,1,4,6,3,2]=>12
[5,1,6,2,3,4]=>12
[5,1,6,2,4,3]=>14
[5,1,6,3,2,4]=>12
[5,1,6,3,4,2]=>14
[5,1,6,4,2,3]=>12
[5,1,6,4,3,2]=>12
[5,2,1,3,4,6]=>6
[5,2,1,3,6,4]=>8
[5,2,1,4,3,6]=>8
[5,2,1,4,6,3]=>10
[5,2,1,6,3,4]=>10
[5,2,1,6,4,3]=>10
[5,2,3,1,4,6]=>8
[5,2,3,1,6,4]=>10
[5,2,3,4,1,6]=>10
[5,2,3,4,6,1]=>14
[5,2,3,6,1,4]=>12
[5,2,3,6,4,1]=>12
[5,2,4,1,3,6]=>8
[5,2,4,1,6,3]=>12
[5,2,4,3,1,6]=>10
[5,2,4,3,6,1]=>16
[5,2,4,6,1,3]=>12
[5,2,4,6,3,1]=>12
[5,2,6,1,3,4]=>12
[5,2,6,1,4,3]=>14
[5,2,6,3,1,4]=>10
[5,2,6,3,4,1]=>14
[5,2,6,4,1,3]=>10
[5,2,6,4,3,1]=>12
[5,3,1,2,4,6]=>6
[5,3,1,2,6,4]=>8
[5,3,1,4,2,6]=>8
[5,3,1,4,6,2]=>12
[5,3,1,6,2,4]=>12
[5,3,1,6,4,2]=>10
[5,3,2,1,4,6]=>6
[5,3,2,1,6,4]=>8
[5,3,2,4,1,6]=>10
[5,3,2,4,6,1]=>14
[5,3,2,6,1,4]=>12
[5,3,2,6,4,1]=>12
[5,3,4,1,2,6]=>8
[5,3,4,1,6,2]=>14
[5,3,4,2,1,6]=>8
[5,3,4,2,6,1]=>16
[5,3,4,6,1,2]=>12
[5,3,4,6,2,1]=>12
[5,3,6,1,2,4]=>10
[5,3,6,1,4,2]=>14
[5,3,6,2,1,4]=>10
[5,3,6,2,4,1]=>14
[5,3,6,4,1,2]=>10
[5,3,6,4,2,1]=>10
[5,4,1,2,3,6]=>6
[5,4,1,2,6,3]=>10
[5,4,1,3,2,6]=>8
[5,4,1,3,6,2]=>12
[5,4,1,6,2,3]=>12
[5,4,1,6,3,2]=>12
[5,4,2,1,3,6]=>6
[5,4,2,1,6,3]=>10
[5,4,2,3,1,6]=>8
[5,4,2,3,6,1]=>14
[5,4,2,6,1,3]=>12
[5,4,2,6,3,1]=>12
[5,4,3,1,2,6]=>6
[5,4,3,1,6,2]=>12
[5,4,3,2,1,6]=>6
[5,4,3,2,6,1]=>14
[5,4,3,6,1,2]=>12
[5,4,3,6,2,1]=>12
[5,4,6,1,2,3]=>10
[5,4,6,1,3,2]=>12
[5,4,6,2,1,3]=>10
[5,4,6,2,3,1]=>12
[5,4,6,3,1,2]=>10
[5,4,6,3,2,1]=>10
[5,6,1,2,3,4]=>8
[5,6,1,2,4,3]=>10
[5,6,1,3,2,4]=>10
[5,6,1,3,4,2]=>12
[5,6,1,4,2,3]=>12
[5,6,1,4,3,2]=>12
[5,6,2,1,3,4]=>8
[5,6,2,1,4,3]=>10
[5,6,2,3,1,4]=>10
[5,6,2,3,4,1]=>12
[5,6,2,4,1,3]=>10
[5,6,2,4,3,1]=>12
[5,6,3,1,2,4]=>8
[5,6,3,1,4,2]=>10
[5,6,3,2,1,4]=>8
[5,6,3,2,4,1]=>12
[5,6,3,4,1,2]=>10
[5,6,3,4,2,1]=>10
[5,6,4,1,2,3]=>8
[5,6,4,1,3,2]=>10
[5,6,4,2,1,3]=>8
[5,6,4,2,3,1]=>10
[5,6,4,3,1,2]=>8
[5,6,4,3,2,1]=>8
[6,1,2,3,4,5]=>6
[6,1,2,3,5,4]=>8
[6,1,2,4,3,5]=>8
[6,1,2,4,5,3]=>10
[6,1,2,5,3,4]=>10
[6,1,2,5,4,3]=>10
[6,1,3,2,4,5]=>8
[6,1,3,2,5,4]=>10
[6,1,3,4,2,5]=>10
[6,1,3,4,5,2]=>12
[6,1,3,5,2,4]=>10
[6,1,3,5,4,2]=>12
[6,1,4,2,3,5]=>10
[6,1,4,2,5,3]=>12
[6,1,4,3,2,5]=>10
[6,1,4,3,5,2]=>14
[6,1,4,5,2,3]=>12
[6,1,4,5,3,2]=>12
[6,1,5,2,3,4]=>12
[6,1,5,2,4,3]=>14
[6,1,5,3,2,4]=>12
[6,1,5,3,4,2]=>14
[6,1,5,4,2,3]=>12
[6,1,5,4,3,2]=>12
[6,2,1,3,4,5]=>6
[6,2,1,3,5,4]=>8
[6,2,1,4,3,5]=>8
[6,2,1,4,5,3]=>10
[6,2,1,5,3,4]=>10
[6,2,1,5,4,3]=>10
[6,2,3,1,4,5]=>8
[6,2,3,1,5,4]=>10
[6,2,3,4,1,5]=>10
[6,2,3,4,5,1]=>12
[6,2,3,5,1,4]=>10
[6,2,3,5,4,1]=>12
[6,2,4,1,3,5]=>8
[6,2,4,1,5,3]=>12
[6,2,4,3,1,5]=>10
[6,2,4,3,5,1]=>14
[6,2,4,5,1,3]=>10
[6,2,4,5,3,1]=>12
[6,2,5,1,3,4]=>10
[6,2,5,1,4,3]=>12
[6,2,5,3,1,4]=>10
[6,2,5,3,4,1]=>14
[6,2,5,4,1,3]=>10
[6,2,5,4,3,1]=>12
[6,3,1,2,4,5]=>6
[6,3,1,2,5,4]=>8
[6,3,1,4,2,5]=>8
[6,3,1,4,5,2]=>10
[6,3,1,5,2,4]=>10
[6,3,1,5,4,2]=>10
[6,3,2,1,4,5]=>6
[6,3,2,1,5,4]=>8
[6,3,2,4,1,5]=>10
[6,3,2,4,5,1]=>12
[6,3,2,5,1,4]=>10
[6,3,2,5,4,1]=>12
[6,3,4,1,2,5]=>8
[6,3,4,1,5,2]=>12
[6,3,4,2,1,5]=>8
[6,3,4,2,5,1]=>14
[6,3,4,5,1,2]=>10
[6,3,4,5,2,1]=>10
[6,3,5,1,2,4]=>8
[6,3,5,1,4,2]=>12
[6,3,5,2,1,4]=>8
[6,3,5,2,4,1]=>12
[6,3,5,4,1,2]=>10
[6,3,5,4,2,1]=>10
[6,4,1,2,3,5]=>6
[6,4,1,2,5,3]=>8
[6,4,1,3,2,5]=>8
[6,4,1,3,5,2]=>10
[6,4,1,5,2,3]=>10
[6,4,1,5,3,2]=>10
[6,4,2,1,3,5]=>6
[6,4,2,1,5,3]=>8
[6,4,2,3,1,5]=>8
[6,4,2,3,5,1]=>12
[6,4,2,5,1,3]=>10
[6,4,2,5,3,1]=>10
[6,4,3,1,2,5]=>6
[6,4,3,1,5,2]=>10
[6,4,3,2,1,5]=>6
[6,4,3,2,5,1]=>12
[6,4,3,5,1,2]=>10
[6,4,3,5,2,1]=>10
[6,4,5,1,2,3]=>8
[6,4,5,1,3,2]=>10
[6,4,5,2,1,3]=>8
[6,4,5,2,3,1]=>10
[6,4,5,3,1,2]=>8
[6,4,5,3,2,1]=>8
[6,5,1,2,3,4]=>6
[6,5,1,2,4,3]=>8
[6,5,1,3,2,4]=>8
[6,5,1,3,4,2]=>10
[6,5,1,4,2,3]=>10
[6,5,1,4,3,2]=>10
[6,5,2,1,3,4]=>6
[6,5,2,1,4,3]=>8
[6,5,2,3,1,4]=>8
[6,5,2,3,4,1]=>10
[6,5,2,4,1,3]=>8
[6,5,2,4,3,1]=>10
[6,5,3,1,2,4]=>6
[6,5,3,1,4,2]=>8
[6,5,3,2,1,4]=>6
[6,5,3,2,4,1]=>10
[6,5,3,4,1,2]=>8
[6,5,3,4,2,1]=>8
[6,5,4,1,2,3]=>6
[6,5,4,1,3,2]=>8
[6,5,4,2,1,3]=>6
[6,5,4,2,3,1]=>8
[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]=>9
[1,2,3,4,6,5,7]=>9
[1,2,3,4,6,7,5]=>11
[1,2,3,4,7,5,6]=>11
[1,2,3,4,7,6,5]=>11
[1,2,3,5,4,6,7]=>9
[1,2,3,5,4,7,6]=>11
[1,2,3,5,6,4,7]=>11
[1,2,3,5,6,7,4]=>13
[1,2,3,5,7,4,6]=>11
[1,2,3,5,7,6,4]=>13
[1,2,3,6,4,5,7]=>11
[1,2,3,6,4,7,5]=>13
[1,2,3,6,5,4,7]=>11
[1,2,3,6,5,7,4]=>15
[1,2,3,6,7,4,5]=>13
[1,2,3,6,7,5,4]=>13
[1,2,3,7,4,5,6]=>13
[1,2,3,7,4,6,5]=>15
[1,2,3,7,5,4,6]=>13
[1,2,3,7,5,6,4]=>15
[1,2,3,7,6,4,5]=>13
[1,2,3,7,6,5,4]=>13
[1,2,4,3,5,6,7]=>9
[1,2,4,3,5,7,6]=>11
[1,2,4,3,6,5,7]=>11
[1,2,4,3,6,7,5]=>13
[1,2,4,3,7,5,6]=>13
[1,2,4,3,7,6,5]=>13
[1,2,4,5,3,6,7]=>11
[1,2,4,5,3,7,6]=>13
[1,2,4,5,6,3,7]=>13
[1,2,4,5,6,7,3]=>15
[1,2,4,5,7,3,6]=>13
[1,2,4,5,7,6,3]=>15
[1,2,4,6,3,5,7]=>11
[1,2,4,6,3,7,5]=>15
[1,2,4,6,5,3,7]=>13
[1,2,4,6,5,7,3]=>17
[1,2,4,6,7,3,5]=>13
[1,2,4,6,7,5,3]=>15
[1,2,4,7,3,5,6]=>13
[1,2,4,7,3,6,5]=>15
[1,2,4,7,5,3,6]=>13
[1,2,4,7,5,6,3]=>17
[1,2,4,7,6,3,5]=>13
[1,2,4,7,6,5,3]=>15
[1,2,5,3,4,6,7]=>11
[1,2,5,3,4,7,6]=>13
[1,2,5,3,6,4,7]=>13
[1,2,5,3,6,7,4]=>15
[1,2,5,3,7,4,6]=>15
[1,2,5,3,7,6,4]=>15
[1,2,5,4,3,6,7]=>11
[1,2,5,4,3,7,6]=>13
[1,2,5,4,6,3,7]=>15
[1,2,5,4,6,7,3]=>17
[1,2,5,4,7,3,6]=>15
[1,2,5,4,7,6,3]=>17
[1,2,5,6,3,4,7]=>13
[1,2,5,6,3,7,4]=>17
[1,2,5,6,4,3,7]=>13
[1,2,5,6,4,7,3]=>19
[1,2,5,6,7,3,4]=>15
[1,2,5,6,7,4,3]=>15
[1,2,5,7,3,4,6]=>13
[1,2,5,7,3,6,4]=>17
[1,2,5,7,4,3,6]=>13
[1,2,5,7,4,6,3]=>17
[1,2,5,7,6,3,4]=>15
[1,2,5,7,6,4,3]=>15
[1,2,6,3,4,5,7]=>13
[1,2,6,3,4,7,5]=>15
[1,2,6,3,5,4,7]=>15
[1,2,6,3,5,7,4]=>17
[1,2,6,3,7,4,5]=>17
[1,2,6,3,7,5,4]=>17
[1,2,6,4,3,5,7]=>13
[1,2,6,4,3,7,5]=>15
[1,2,6,4,5,3,7]=>15
[1,2,6,4,5,7,3]=>19
[1,2,6,4,7,3,5]=>17
[1,2,6,4,7,5,3]=>17
[1,2,6,5,3,4,7]=>13
[1,2,6,5,3,7,4]=>17
[1,2,6,5,4,3,7]=>13
[1,2,6,5,4,7,3]=>19
[1,2,6,5,7,3,4]=>17
[1,2,6,5,7,4,3]=>17
[1,2,6,7,3,4,5]=>15
[1,2,6,7,3,5,4]=>17
[1,2,6,7,4,3,5]=>15
[1,2,6,7,4,5,3]=>17
[1,2,6,7,5,3,4]=>15
[1,2,6,7,5,4,3]=>15
[1,2,7,3,4,5,6]=>15
[1,2,7,3,4,6,5]=>17
[1,2,7,3,5,4,6]=>17
[1,2,7,3,5,6,4]=>19
[1,2,7,3,6,4,5]=>19
[1,2,7,3,6,5,4]=>19
[1,2,7,4,3,5,6]=>15
[1,2,7,4,3,6,5]=>17
[1,2,7,4,5,3,6]=>17
[1,2,7,4,5,6,3]=>19
[1,2,7,4,6,3,5]=>17
[1,2,7,4,6,5,3]=>19
[1,2,7,5,3,4,6]=>15
[1,2,7,5,3,6,4]=>17
[1,2,7,5,4,3,6]=>15
[1,2,7,5,4,6,3]=>19
[1,2,7,5,6,3,4]=>17
[1,2,7,5,6,4,3]=>17
[1,2,7,6,3,4,5]=>15
[1,2,7,6,3,5,4]=>17
[1,2,7,6,4,3,5]=>15
[1,2,7,6,4,5,3]=>17
[1,2,7,6,5,3,4]=>15
[1,2,7,6,5,4,3]=>15
[1,3,2,4,5,6,7]=>9
[1,3,2,4,5,7,6]=>11
[1,3,2,4,6,5,7]=>11
[1,3,2,4,6,7,5]=>13
[1,3,2,4,7,5,6]=>13
[1,3,2,4,7,6,5]=>13
[1,3,2,5,4,6,7]=>11
[1,3,2,5,4,7,6]=>13
[1,3,2,5,6,4,7]=>13
[1,3,2,5,6,7,4]=>15
[1,3,2,5,7,4,6]=>13
[1,3,2,5,7,6,4]=>15
[1,3,2,6,4,5,7]=>13
[1,3,2,6,4,7,5]=>15
[1,3,2,6,5,4,7]=>13
[1,3,2,6,5,7,4]=>17
[1,3,2,6,7,4,5]=>15
[1,3,2,6,7,5,4]=>15
[1,3,2,7,4,5,6]=>15
[1,3,2,7,4,6,5]=>17
[1,3,2,7,5,4,6]=>15
[1,3,2,7,5,6,4]=>17
[1,3,2,7,6,4,5]=>15
[1,3,2,7,6,5,4]=>15
[1,3,4,2,5,6,7]=>11
[1,3,4,2,5,7,6]=>13
[1,3,4,2,6,5,7]=>13
[1,3,4,2,6,7,5]=>15
[1,3,4,2,7,5,6]=>15
[1,3,4,2,7,6,5]=>15
[1,3,4,5,2,6,7]=>13
[1,3,4,5,2,7,6]=>15
[1,3,4,5,6,2,7]=>15
[1,3,4,5,6,7,2]=>17
[1,3,4,5,7,2,6]=>15
[1,3,4,5,7,6,2]=>17
[1,3,4,6,2,5,7]=>13
[1,3,4,6,2,7,5]=>17
[1,3,4,6,5,2,7]=>15
[1,3,4,6,5,7,2]=>19
[1,3,4,6,7,2,5]=>15
[1,3,4,6,7,5,2]=>17
[1,3,4,7,2,5,6]=>15
[1,3,4,7,2,6,5]=>17
[1,3,4,7,5,2,6]=>15
[1,3,4,7,5,6,2]=>19
[1,3,4,7,6,2,5]=>15
[1,3,4,7,6,5,2]=>17
[1,3,5,2,4,6,7]=>11
[1,3,5,2,4,7,6]=>13
[1,3,5,2,6,4,7]=>15
[1,3,5,2,6,7,4]=>17
[1,3,5,2,7,4,6]=>17
[1,3,5,2,7,6,4]=>17
[1,3,5,4,2,6,7]=>13
[1,3,5,4,2,7,6]=>15
[1,3,5,4,6,2,7]=>17
[1,3,5,4,6,7,2]=>19
[1,3,5,4,7,2,6]=>17
[1,3,5,4,7,6,2]=>19
[1,3,5,6,2,4,7]=>13
[1,3,5,6,2,7,4]=>19
[1,3,5,6,4,2,7]=>15
[1,3,5,6,4,7,2]=>21
[1,3,5,6,7,2,4]=>15
[1,3,5,6,7,4,2]=>17
[1,3,5,7,2,4,6]=>13
[1,3,5,7,2,6,4]=>19
[1,3,5,7,4,2,6]=>15
[1,3,5,7,4,6,2]=>19
[1,3,5,7,6,2,4]=>15
[1,3,5,7,6,4,2]=>17
[1,3,6,2,4,5,7]=>13
[1,3,6,2,4,7,5]=>15
[1,3,6,2,5,4,7]=>15
[1,3,6,2,5,7,4]=>17
[1,3,6,2,7,4,5]=>19
[1,3,6,2,7,5,4]=>19
[1,3,6,4,2,5,7]=>13
[1,3,6,4,2,7,5]=>17
[1,3,6,4,5,2,7]=>17
[1,3,6,4,5,7,2]=>21
[1,3,6,4,7,2,5]=>17
[1,3,6,4,7,5,2]=>19
[1,3,6,5,2,4,7]=>13
[1,3,6,5,2,7,4]=>19
[1,3,6,5,4,2,7]=>15
[1,3,6,5,4,7,2]=>21
[1,3,6,5,7,2,4]=>17
[1,3,6,5,7,4,2]=>19
[1,3,6,7,2,4,5]=>15
[1,3,6,7,2,5,4]=>17
[1,3,6,7,4,2,5]=>15
[1,3,6,7,4,5,2]=>19
[1,3,6,7,5,2,4]=>15
[1,3,6,7,5,4,2]=>17
[1,3,7,2,4,5,6]=>15
[1,3,7,2,4,6,5]=>17
[1,3,7,2,5,4,6]=>17
[1,3,7,2,5,6,4]=>19
[1,3,7,2,6,4,5]=>19
[1,3,7,2,6,5,4]=>19
[1,3,7,4,2,5,6]=>15
[1,3,7,4,2,6,5]=>17
[1,3,7,4,5,2,6]=>17
[1,3,7,4,5,6,2]=>21
[1,3,7,4,6,2,5]=>17
[1,3,7,4,6,5,2]=>21
[1,3,7,5,2,4,6]=>15
[1,3,7,5,2,6,4]=>17
[1,3,7,5,4,2,6]=>15
[1,3,7,5,4,6,2]=>21
[1,3,7,5,6,2,4]=>17
[1,3,7,5,6,4,2]=>19
[1,3,7,6,2,4,5]=>15
[1,3,7,6,2,5,4]=>17
[1,3,7,6,4,2,5]=>15
[1,3,7,6,4,5,2]=>19
[1,3,7,6,5,2,4]=>15
[1,3,7,6,5,4,2]=>17
[1,4,2,3,5,6,7]=>11
[1,4,2,3,5,7,6]=>13
[1,4,2,3,6,5,7]=>13
[1,4,2,3,6,7,5]=>15
[1,4,2,3,7,5,6]=>15
[1,4,2,3,7,6,5]=>15
[1,4,2,5,3,6,7]=>13
[1,4,2,5,3,7,6]=>15
[1,4,2,5,6,3,7]=>15
[1,4,2,5,6,7,3]=>17
[1,4,2,5,7,3,6]=>15
[1,4,2,5,7,6,3]=>17
[1,4,2,6,3,5,7]=>15
[1,4,2,6,3,7,5]=>17
[1,4,2,6,5,3,7]=>15
[1,4,2,6,5,7,3]=>19
[1,4,2,6,7,3,5]=>17
[1,4,2,6,7,5,3]=>17
[1,4,2,7,3,5,6]=>17
[1,4,2,7,3,6,5]=>19
[1,4,2,7,5,3,6]=>17
[1,4,2,7,5,6,3]=>19
[1,4,2,7,6,3,5]=>17
[1,4,2,7,6,5,3]=>17
[1,4,3,2,5,6,7]=>11
[1,4,3,2,5,7,6]=>13
[1,4,3,2,6,5,7]=>13
[1,4,3,2,6,7,5]=>15
[1,4,3,2,7,5,6]=>15
[1,4,3,2,7,6,5]=>15
[1,4,3,5,2,6,7]=>15
[1,4,3,5,2,7,6]=>17
[1,4,3,5,6,2,7]=>17
[1,4,3,5,6,7,2]=>19
[1,4,3,5,7,2,6]=>17
[1,4,3,5,7,6,2]=>19
[1,4,3,6,2,5,7]=>15
[1,4,3,6,2,7,5]=>19
[1,4,3,6,5,2,7]=>17
[1,4,3,6,5,7,2]=>21
[1,4,3,6,7,2,5]=>17
[1,4,3,6,7,5,2]=>19
[1,4,3,7,2,5,6]=>17
[1,4,3,7,2,6,5]=>19
[1,4,3,7,5,2,6]=>17
[1,4,3,7,5,6,2]=>21
[1,4,3,7,6,2,5]=>17
[1,4,3,7,6,5,2]=>19
[1,4,5,2,3,6,7]=>13
[1,4,5,2,3,7,6]=>15
[1,4,5,2,6,3,7]=>17
[1,4,5,2,6,7,3]=>19
[1,4,5,2,7,3,6]=>19
[1,4,5,2,7,6,3]=>19
[1,4,5,3,2,6,7]=>13
[1,4,5,3,2,7,6]=>15
[1,4,5,3,6,2,7]=>19
[1,4,5,3,6,7,2]=>21
[1,4,5,3,7,2,6]=>19
[1,4,5,3,7,6,2]=>21
[1,4,5,6,2,3,7]=>15
[1,4,5,6,2,7,3]=>21
[1,4,5,6,3,2,7]=>15
[1,4,5,6,3,7,2]=>23
[1,4,5,6,7,2,3]=>17
[1,4,5,6,7,3,2]=>17
[1,4,5,7,2,3,6]=>15
[1,4,5,7,2,6,3]=>21
[1,4,5,7,3,2,6]=>15
[1,4,5,7,3,6,2]=>21
[1,4,5,7,6,2,3]=>17
[1,4,5,7,6,3,2]=>17
[1,4,6,2,3,5,7]=>13
[1,4,6,2,3,7,5]=>17
[1,4,6,2,5,3,7]=>17
[1,4,6,2,5,7,3]=>19
[1,4,6,2,7,3,5]=>19
[1,4,6,2,7,5,3]=>21
[1,4,6,3,2,5,7]=>13
[1,4,6,3,2,7,5]=>17
[1,4,6,3,5,2,7]=>17
[1,4,6,3,5,7,2]=>21
[1,4,6,3,7,2,5]=>19
[1,4,6,3,7,5,2]=>21
[1,4,6,5,2,3,7]=>15
[1,4,6,5,2,7,3]=>21
[1,4,6,5,3,2,7]=>15
[1,4,6,5,3,7,2]=>23
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Description
The number of inversions of the cyclic embedding of a permutation.
The cyclic embedding of a permutation $\pi$ of length $n$ is given by the permutation of length $n+1$ represented in cycle notation by $(\pi_1,\ldots,\pi_n,n+1)$.
This reflects in particular the fact that the number of long cycles of length $n+1$ equals $n!$.
This statistic counts the number of inversions of this embedding, see [1]. As shown in [2], the sum of this statistic on all permutations of length $n$ equals $n!\cdot(3n-1)/12$.
The cyclic embedding of a permutation $\pi$ of length $n$ is given by the permutation of length $n+1$ represented in cycle notation by $(\pi_1,\ldots,\pi_n,n+1)$.
This reflects in particular the fact that the number of long cycles of length $n+1$ equals $n!$.
This statistic counts the number of inversions of this embedding, see [1]. As shown in [2], the sum of this statistic on all permutations of length $n$ equals $n!\cdot(3n-1)/12$.
References
[1] The number of inversions over all n-permutations consisting only of a single cycle. OEIS:A227404
[2] Palcoux, S. Examples of integer sequences coincidences MathOverflow:289976
[2] Palcoux, S. Examples of integer sequences coincidences MathOverflow:289976
Code
def statistic(pi):
n = len(pi)+Integer(1)
pi = tuple(list(pi)+[n])
return Permutation(pi).number_of_inversions()
Created
Jan 05, 2018 at 15:58 by Christian Stump
Updated
Jan 05, 2018 at 18:38 by Christian Stump
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