Identifier
- St001639: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>0
[1,2,3,4]=>0
[1,2,4,3]=>3
[1,3,2,4]=>2
[1,3,4,2]=>3
[1,4,2,3]=>3
[1,4,3,2]=>1
[2,1,3,4]=>3
[2,1,4,3]=>2
[2,3,1,4]=>3
[2,3,4,1]=>1
[2,4,1,3]=>4
[2,4,3,1]=>3
[3,1,2,4]=>3
[3,1,4,2]=>4
[3,2,1,4]=>1
[3,2,4,1]=>3
[3,4,1,2]=>2
[3,4,2,1]=>3
[4,1,2,3]=>1
[4,1,3,2]=>3
[4,2,1,3]=>3
[4,2,3,1]=>2
[4,3,1,2]=>3
[4,3,2,1]=>0
[1,2,3,4,5]=>0
[1,2,3,5,4]=>6
[1,2,4,3,5]=>5
[1,2,4,5,3]=>7
[1,2,5,3,4]=>7
[1,2,5,4,3]=>3
[1,3,2,4,5]=>5
[1,3,2,5,4]=>6
[1,3,4,2,5]=>6
[1,3,4,5,2]=>5
[1,3,5,2,4]=>9
[1,3,5,4,2]=>7
[1,4,2,3,5]=>6
[1,4,2,5,3]=>9
[1,4,3,2,5]=>2
[1,4,3,5,2]=>7
[1,4,5,2,3]=>4
[1,4,5,3,2]=>6
[1,5,2,3,4]=>5
[1,5,2,4,3]=>7
[1,5,3,2,4]=>7
[1,5,3,4,2]=>6
[1,5,4,2,3]=>6
[1,5,4,3,2]=>3
[2,1,3,4,5]=>6
[2,1,3,5,4]=>7
[2,1,4,3,5]=>6
[2,1,4,5,3]=>6
[2,1,5,3,4]=>6
[2,1,5,4,3]=>5
[2,3,1,4,5]=>7
[2,3,1,5,4]=>6
[2,3,4,1,5]=>5
[2,3,4,5,1]=>3
[2,3,5,1,4]=>7
[2,3,5,4,1]=>6
[2,4,1,3,5]=>9
[2,4,1,5,3]=>8
[2,4,3,1,5]=>7
[2,4,3,5,1]=>6
[2,4,5,1,3]=>7
[2,4,5,3,1]=>7
[2,5,1,3,4]=>7
[2,5,1,4,3]=>7
[2,5,3,1,4]=>9
[2,5,3,4,1]=>7
[2,5,4,1,3]=>7
[2,5,4,3,1]=>5
[3,1,2,4,5]=>7
[3,1,2,5,4]=>6
[3,1,4,2,5]=>9
[3,1,4,5,2]=>7
[3,1,5,2,4]=>8
[3,1,5,4,2]=>7
[3,2,1,4,5]=>3
[3,2,1,5,4]=>5
[3,2,4,1,5]=>7
[3,2,4,5,1]=>6
[3,2,5,1,4]=>7
[3,2,5,4,1]=>4
[3,4,1,2,5]=>4
[3,4,1,5,2]=>7
[3,4,2,1,5]=>6
[3,4,2,5,1]=>7
[3,4,5,1,2]=>5
[3,4,5,2,1]=>3
[3,5,1,2,4]=>7
[3,5,1,4,2]=>8
[3,5,2,1,4]=>7
[3,5,2,4,1]=>9
[3,5,4,1,2]=>6
[3,5,4,2,1]=>7
[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]=>7
[4,1,5,3,2]=>7
[4,2,1,3,5]=>7
[4,2,1,5,3]=>7
[4,2,3,1,5]=>6
[4,2,3,5,1]=>7
[4,2,5,1,3]=>8
[4,2,5,3,1]=>9
[4,3,1,2,5]=>6
[4,3,1,5,2]=>7
[4,3,2,1,5]=>3
[4,3,2,5,1]=>5
[4,3,5,1,2]=>6
[4,3,5,2,1]=>7
[4,5,1,2,3]=>5
[4,5,1,3,2]=>6
[4,5,2,1,3]=>6
[4,5,2,3,1]=>6
[4,5,3,1,2]=>7
[4,5,3,2,1]=>6
[5,1,2,3,4]=>3
[5,1,2,4,3]=>6
[5,1,3,2,4]=>6
[5,1,3,4,2]=>7
[5,1,4,2,3]=>7
[5,1,4,3,2]=>5
[5,2,1,3,4]=>6
[5,2,1,4,3]=>4
[5,2,3,1,4]=>7
[5,2,3,4,1]=>2
[5,2,4,1,3]=>9
[5,2,4,3,1]=>6
[5,3,1,2,4]=>7
[5,3,1,4,2]=>9
[5,3,2,1,4]=>5
[5,3,2,4,1]=>6
[5,3,4,1,2]=>6
[5,3,4,2,1]=>5
[5,4,1,2,3]=>3
[5,4,1,3,2]=>7
[5,4,2,1,3]=>7
[5,4,2,3,1]=>5
[5,4,3,1,2]=>6
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>11
[1,2,3,5,4,6]=>9
[1,2,3,5,6,4]=>13
[1,2,3,6,4,5]=>13
[1,2,3,6,5,4]=>6
[1,2,4,3,5,6]=>10
[1,2,4,3,6,5]=>14
[1,2,4,5,3,6]=>12
[1,2,4,5,6,3]=>13
[1,2,4,6,3,5]=>17
[1,2,4,6,5,3]=>14
[1,2,5,3,4,6]=>12
[1,2,5,3,6,4]=>17
[1,2,5,4,3,6]=>5
[1,2,5,4,6,3]=>14
[1,2,5,6,3,4]=>8
[1,2,5,6,4,3]=>12
[1,2,6,3,4,5]=>13
[1,2,6,3,5,4]=>14
[1,2,6,4,3,5]=>14
[1,2,6,4,5,3]=>12
[1,2,6,5,3,4]=>12
[1,2,6,5,4,3]=>9
[1,3,2,4,5,6]=>9
[1,3,2,4,6,5]=>14
[1,3,2,5,4,6]=>11
[1,3,2,5,6,4]=>13
[1,3,2,6,4,5]=>13
[1,3,2,6,5,4]=>10
[1,3,4,2,5,6]=>12
[1,3,4,2,6,5]=>14
[1,3,4,5,2,6]=>10
[1,3,4,5,6,2]=>10
[1,3,4,6,2,5]=>15
[1,3,4,6,5,2]=>13
[1,3,5,2,4,6]=>17
[1,3,5,2,6,4]=>17
[1,3,5,4,2,6]=>13
[1,3,5,4,6,2]=>14
[1,3,5,6,2,4]=>14
[1,3,5,6,4,2]=>15
[1,3,6,2,4,5]=>16
[1,3,6,2,5,4]=>14
[1,3,6,4,2,5]=>18
[1,3,6,4,5,2]=>14
[1,3,6,5,2,4]=>14
[1,3,6,5,4,2]=>12
[1,4,2,3,5,6]=>12
[1,4,2,3,6,5]=>14
[1,4,2,5,3,6]=>17
[1,4,2,5,6,3]=>16
[1,4,2,6,3,5]=>17
[1,4,2,6,5,3]=>14
[1,4,3,2,5,6]=>5
[1,4,3,2,6,5]=>11
[1,4,3,5,2,6]=>13
[1,4,3,5,6,2]=>13
[1,4,3,6,2,5]=>15
[1,4,3,6,5,2]=>9
[1,4,5,2,3,6]=>7
[1,4,5,2,6,3]=>14
[1,4,5,3,2,6]=>10
[1,4,5,3,6,2]=>14
[1,4,5,6,2,3]=>10
[1,4,5,6,3,2]=>7
[1,4,6,2,3,5]=>14
[1,4,6,2,5,3]=>15
[1,4,6,3,2,5]=>15
[1,4,6,3,5,2]=>17
[1,4,6,5,2,3]=>13
[1,4,6,5,3,2]=>14
[1,5,2,3,4,6]=>10
[1,5,2,3,6,4]=>15
[1,5,2,4,3,6]=>13
[1,5,2,4,6,3]=>18
[1,5,2,6,3,4]=>14
[1,5,2,6,4,3]=>14
[1,5,3,2,4,6]=>13
[1,5,3,2,6,4]=>15
[1,5,3,4,2,6]=>12
[1,5,3,4,6,2]=>15
[1,5,3,6,2,4]=>16
[1,5,3,6,4,2]=>17
[1,5,4,2,3,6]=>10
[1,5,4,2,6,3]=>15
[1,5,4,3,2,6]=>6
[1,5,4,3,6,2]=>12
[1,5,4,6,2,3]=>12
[1,5,4,6,3,2]=>13
[1,5,6,2,3,4]=>10
[1,5,6,2,4,3]=>13
[1,5,6,3,2,4]=>12
[1,5,6,3,4,2]=>13
[1,5,6,4,2,3]=>14
[1,5,6,4,3,2]=>12
[1,6,2,3,4,5]=>10
[1,6,2,3,5,4]=>13
[1,6,2,4,3,5]=>14
[1,6,2,4,5,3]=>14
[1,6,2,5,3,4]=>15
[1,6,2,5,4,3]=>12
[1,6,3,2,4,5]=>13
[1,6,3,2,5,4]=>9
[1,6,3,4,2,5]=>15
[1,6,3,4,5,2]=>7
[1,6,3,5,2,4]=>17
[1,6,3,5,4,2]=>13
[1,6,4,2,3,5]=>14
[1,6,4,2,5,3]=>17
[1,6,4,3,2,5]=>12
[1,6,4,3,5,2]=>14
[1,6,4,5,2,3]=>13
[1,6,4,5,3,2]=>12
[1,6,5,2,3,4]=>7
[1,6,5,2,4,3]=>14
[1,6,5,3,2,4]=>13
[1,6,5,3,4,2]=>12
[1,6,5,4,2,3]=>12
[1,6,5,4,3,2]=>4
[2,1,3,4,5,6]=>11
[2,1,3,4,6,5]=>15
[2,1,3,5,4,6]=>14
[2,1,3,5,6,4]=>15
[2,1,3,6,4,5]=>15
[2,1,3,6,5,4]=>12
[2,1,4,3,5,6]=>14
[2,1,4,3,6,5]=>11
[2,1,4,5,3,6]=>14
[2,1,4,5,6,3]=>9
[2,1,4,6,3,5]=>16
[2,1,4,6,5,3]=>14
[2,1,5,3,4,6]=>14
[2,1,5,3,6,4]=>16
[2,1,5,4,3,6]=>11
[2,1,5,4,6,3]=>14
[2,1,5,6,3,4]=>13
[2,1,5,6,4,3]=>14
[2,1,6,3,4,5]=>9
[2,1,6,3,5,4]=>14
[2,1,6,4,3,5]=>14
[2,1,6,4,5,3]=>13
[2,1,6,5,3,4]=>14
[2,1,6,5,4,3]=>8
[2,3,1,4,5,6]=>13
[2,3,1,4,6,5]=>15
[2,3,1,5,4,6]=>13
[2,3,1,5,6,4]=>14
[2,3,1,6,4,5]=>13
[2,3,1,6,5,4]=>12
[2,3,4,1,5,6]=>13
[2,3,4,1,6,5]=>9
[2,3,4,5,1,6]=>10
[2,3,4,5,6,1]=>4
[2,3,4,6,1,5]=>14
[2,3,4,6,5,1]=>12
[2,3,5,1,4,6]=>16
[2,3,5,1,6,4]=>16
[2,3,5,4,1,6]=>13
[2,3,5,4,6,1]=>12
[2,3,5,6,1,4]=>15
[2,3,5,6,4,1]=>14
[2,3,6,1,4,5]=>9
[2,3,6,1,5,4]=>13
[2,3,6,4,1,5]=>16
[2,3,6,4,5,1]=>13
[2,3,6,5,1,4]=>14
[2,3,6,5,4,1]=>7
[2,4,1,3,5,6]=>17
[2,4,1,3,6,5]=>16
[2,4,1,5,3,6]=>17
[2,4,1,5,6,3]=>16
[2,4,1,6,3,5]=>15
[2,4,1,6,5,3]=>15
[2,4,3,1,5,6]=>14
[2,4,3,1,6,5]=>14
[2,4,3,5,1,6]=>14
[2,4,3,5,6,1]=>12
[2,4,3,6,1,5]=>15
[2,4,3,6,5,1]=>13
[2,4,5,1,3,6]=>14
[2,4,5,1,6,3]=>15
[2,4,5,3,1,6]=>14
[2,4,5,3,6,1]=>13
[2,4,5,6,1,3]=>14
[2,4,5,6,3,1]=>12
[2,4,6,1,3,5]=>15
[2,4,6,1,5,3]=>16
[2,4,6,3,1,5]=>17
[2,4,6,3,5,1]=>17
[2,4,6,5,1,3]=>16
[2,4,6,5,3,1]=>15
[2,5,1,3,4,6]=>15
[2,5,1,3,6,4]=>15
[2,5,1,4,3,6]=>15
[2,5,1,4,6,3]=>16
[2,5,1,6,3,4]=>14
[2,5,1,6,4,3]=>15
[2,5,3,1,4,6]=>18
[2,5,3,1,6,4]=>16
[2,5,3,4,1,6]=>15
[2,5,3,4,6,1]=>14
[2,5,3,6,1,4]=>16
[2,5,3,6,4,1]=>17
[2,5,4,1,3,6]=>15
[2,5,4,1,6,3]=>10
[2,5,4,3,1,6]=>12
[2,5,4,3,6,1]=>7
[2,5,4,6,1,3]=>14
[2,5,4,6,3,1]=>14
[2,5,6,1,3,4]=>13
[2,5,6,1,4,3]=>10
[2,5,6,3,1,4]=>14
[2,5,6,3,4,1]=>9
[2,5,6,4,1,3]=>15
[2,5,6,4,3,1]=>13
[2,6,1,3,4,5]=>14
[2,6,1,3,5,4]=>15
[2,6,1,4,3,5]=>15
[2,6,1,4,5,3]=>14
[2,6,1,5,3,4]=>16
[2,6,1,5,4,3]=>14
[2,6,3,1,4,5]=>16
[2,6,3,1,5,4]=>14
[2,6,3,4,1,5]=>17
[2,6,3,4,5,1]=>12
[2,6,3,5,1,4]=>17
[2,6,3,5,4,1]=>14
[2,6,4,1,3,5]=>17
[2,6,4,1,5,3]=>16
[2,6,4,3,1,5]=>17
[2,6,4,3,5,1]=>15
[2,6,4,5,1,3]=>15
[2,6,4,5,3,1]=>14
[2,6,5,1,3,4]=>14
[2,6,5,1,4,3]=>15
[2,6,5,3,1,4]=>16
[2,6,5,3,4,1]=>13
[2,6,5,4,1,3]=>14
[2,6,5,4,3,1]=>10
[3,1,2,4,5,6]=>13
[3,1,2,4,6,5]=>15
[3,1,2,5,4,6]=>13
[3,1,2,5,6,4]=>13
[3,1,2,6,4,5]=>14
[3,1,2,6,5,4]=>12
[3,1,4,2,5,6]=>17
[3,1,4,2,6,5]=>16
[3,1,4,5,2,6]=>15
[3,1,4,5,6,2]=>14
[3,1,4,6,2,5]=>15
[3,1,4,6,5,2]=>15
[3,1,5,2,4,6]=>17
[3,1,5,2,6,4]=>15
[3,1,5,4,2,6]=>15
[3,1,5,4,6,2]=>15
[3,1,5,6,2,4]=>14
[3,1,5,6,4,2]=>16
[3,1,6,2,4,5]=>16
[3,1,6,2,5,4]=>15
[3,1,6,4,2,5]=>16
[3,1,6,4,5,2]=>14
[3,1,6,5,2,4]=>15
[3,1,6,5,4,2]=>14
[3,2,1,4,5,6]=>6
[3,2,1,4,6,5]=>12
[3,2,1,5,4,6]=>10
[3,2,1,5,6,4]=>12
[3,2,1,6,4,5]=>12
[3,2,1,6,5,4]=>8
[3,2,4,1,5,6]=>14
[3,2,4,1,6,5]=>14
[3,2,4,5,1,6]=>13
[3,2,4,5,6,1]=>12
[3,2,4,6,1,5]=>15
[3,2,4,6,5,1]=>14
[3,2,5,1,4,6]=>14
[3,2,5,1,6,4]=>15
[3,2,5,4,1,6]=>9
[3,2,5,4,6,1]=>13
[3,2,5,6,1,4]=>10
[3,2,5,6,4,1]=>13
[3,2,6,1,4,5]=>13
[3,2,6,1,5,4]=>14
[3,2,6,4,1,5]=>14
[3,2,6,4,5,1]=>12
[3,2,6,5,1,4]=>13
[3,2,6,5,4,1]=>10
[3,4,1,2,5,6]=>8
[3,4,1,2,6,5]=>13
[3,4,1,5,2,6]=>14
[3,4,1,5,6,2]=>15
[3,4,1,6,2,5]=>14
[3,4,1,6,5,2]=>10
[3,4,2,1,5,6]=>12
[3,4,2,1,6,5]=>14
[3,4,2,5,1,6]=>15
[3,4,2,5,6,1]=>14
[3,4,2,6,1,5]=>16
[3,4,2,6,5,1]=>13
[3,4,5,1,2,6]=>10
[3,4,5,1,6,2]=>14
[3,4,5,2,1,6]=>7
[3,4,5,2,6,1]=>12
[3,4,5,6,1,2]=>8
[3,4,5,6,2,1]=>9
[3,4,6,1,2,5]=>13
[3,4,6,1,5,2]=>15
[3,4,6,2,1,5]=>14
[3,4,6,2,5,1]=>14
[3,4,6,5,1,2]=>14
[3,4,6,5,2,1]=>12
[3,5,1,2,4,6]=>14
[3,5,1,2,6,4]=>14
[3,5,1,4,2,6]=>16
[3,5,1,4,6,2]=>16
[3,5,1,6,2,4]=>16
[3,5,1,6,4,2]=>16
[3,5,2,1,4,6]=>14
[3,5,2,1,6,4]=>15
[3,5,2,4,1,6]=>17
[3,5,2,4,6,1]=>17
[3,5,2,6,1,4]=>16
[3,5,2,6,4,1]=>15
[3,5,4,1,2,6]=>12
[3,5,4,1,6,2]=>14
[3,5,4,2,1,6]=>13
[3,5,4,2,6,1]=>14
[3,5,4,6,1,2]=>13
[3,5,4,6,2,1]=>12
[3,5,6,1,2,4]=>14
[3,5,6,1,4,2]=>15
[3,5,6,2,1,4]=>13
[3,5,6,2,4,1]=>14
[3,5,6,4,1,2]=>14
[3,5,6,4,2,1]=>14
[3,6,1,2,4,5]=>15
[3,6,1,2,5,4]=>10
[3,6,1,4,2,5]=>16
[3,6,1,4,5,2]=>10
[3,6,1,5,2,4]=>16
[3,6,1,5,4,2]=>15
[3,6,2,1,4,5]=>14
[3,6,2,1,5,4]=>13
[3,6,2,4,1,5]=>17
[3,6,2,4,5,1]=>15
[3,6,2,5,1,4]=>15
[3,6,2,5,4,1]=>14
[3,6,4,1,2,5]=>14
[3,6,4,1,5,2]=>16
[3,6,4,2,1,5]=>16
[3,6,4,2,5,1]=>18
[3,6,4,5,1,2]=>14
[3,6,4,5,2,1]=>14
[3,6,5,1,2,4]=>13
[3,6,5,1,4,2]=>16
[3,6,5,2,1,4]=>9
[3,6,5,2,4,1]=>16
[3,6,5,4,1,2]=>9
[3,6,5,4,2,1]=>13
[4,1,2,3,5,6]=>13
[4,1,2,3,6,5]=>9
[4,1,2,5,3,6]=>16
[4,1,2,5,6,3]=>9
[4,1,2,6,3,5]=>16
[4,1,2,6,5,3]=>13
[4,1,3,2,5,6]=>14
[4,1,3,2,6,5]=>14
[4,1,3,5,2,6]=>18
[4,1,3,5,6,2]=>16
[4,1,3,6,2,5]=>16
[4,1,3,6,5,2]=>14
[4,1,5,2,3,6]=>14
[4,1,5,2,6,3]=>15
[4,1,5,3,2,6]=>15
[4,1,5,3,6,2]=>17
[4,1,5,6,2,3]=>13
[4,1,5,6,3,2]=>14
[4,1,6,2,3,5]=>15
[4,1,6,2,5,3]=>16
[4,1,6,3,2,5]=>10
[4,1,6,3,5,2]=>16
[4,1,6,5,2,3]=>10
[4,1,6,5,3,2]=>15
[4,2,1,3,5,6]=>14
[4,2,1,3,6,5]=>14
[4,2,1,5,3,6]=>14
[4,2,1,5,6,3]=>13
[4,2,1,6,3,5]=>15
[4,2,1,6,5,3]=>14
[4,2,3,1,5,6]=>12
[4,2,3,1,6,5]=>13
[4,2,3,5,1,6]=>14
[4,2,3,5,6,1]=>13
[4,2,3,6,1,5]=>14
[4,2,3,6,5,1]=>12
[4,2,5,1,3,6]=>15
[4,2,5,1,6,3]=>16
[4,2,5,3,1,6]=>17
[4,2,5,3,6,1]=>17
[4,2,5,6,1,3]=>15
[4,2,5,6,3,1]=>14
[4,2,6,1,3,5]=>16
[4,2,6,1,5,3]=>16
[4,2,6,3,1,5]=>16
[4,2,6,3,5,1]=>16
[4,2,6,5,1,3]=>14
[4,2,6,5,3,1]=>14
[4,3,1,2,5,6]=>12
[4,3,1,2,6,5]=>14
[4,3,1,5,2,6]=>14
[4,3,1,5,6,2]=>14
[4,3,1,6,2,5]=>15
[4,3,1,6,5,2]=>13
[4,3,2,1,5,6]=>9
[4,3,2,1,6,5]=>8
[4,3,2,5,1,6]=>12
[4,3,2,5,6,1]=>7
[4,3,2,6,1,5]=>14
[4,3,2,6,5,1]=>10
[4,3,5,1,2,6]=>13
[4,3,5,1,6,2]=>16
[4,3,5,2,1,6]=>14
[4,3,5,2,6,1]=>15
[4,3,5,6,1,2]=>14
[4,3,5,6,2,1]=>12
[4,3,6,1,2,5]=>10
[4,3,6,1,5,2]=>14
[4,3,6,2,1,5]=>15
[4,3,6,2,5,1]=>14
[4,3,6,5,1,2]=>13
[4,3,6,5,2,1]=>8
[4,5,1,2,3,6]=>10
[4,5,1,2,6,3]=>13
[4,5,1,3,2,6]=>12
[4,5,1,3,6,2]=>14
[4,5,1,6,2,3]=>14
[4,5,1,6,3,2]=>13
[4,5,2,1,3,6]=>13
[4,5,2,1,6,3]=>10
[4,5,2,3,1,6]=>13
[4,5,2,3,6,1]=>9
[4,5,2,6,1,3]=>15
[4,5,2,6,3,1]=>14
[4,5,3,1,2,6]=>14
[4,5,3,1,6,2]=>15
[4,5,3,2,1,6]=>12
[4,5,3,2,6,1]=>13
[4,5,3,6,1,2]=>14
[4,5,3,6,2,1]=>14
[4,5,6,1,2,3]=>8
[4,5,6,1,3,2]=>12
[4,5,6,2,1,3]=>12
[4,5,6,2,3,1]=>10
[4,5,6,3,1,2]=>12
[4,5,6,3,2,1]=>6
[4,6,1,2,3,5]=>14
[4,6,1,2,5,3]=>15
[4,6,1,3,2,5]=>14
[4,6,1,3,5,2]=>16
[4,6,1,5,2,3]=>15
[4,6,1,5,3,2]=>16
[4,6,2,1,3,5]=>16
[4,6,2,1,5,3]=>14
[4,6,2,3,1,5]=>15
[4,6,2,3,5,1]=>15
[4,6,2,5,1,3]=>15
[4,6,2,5,3,1]=>17
[4,6,3,1,2,5]=>15
[4,6,3,1,5,2]=>15
[4,6,3,2,1,5]=>14
[4,6,3,2,5,1]=>15
[4,6,3,5,1,2]=>16
[4,6,3,5,2,1]=>17
[4,6,5,1,2,3]=>12
[4,6,5,1,3,2]=>14
[4,6,5,2,1,3]=>13
[4,6,5,2,3,1]=>13
[4,6,5,3,1,2]=>15
[4,6,5,3,2,1]=>13
[5,1,2,3,4,6]=>10
[5,1,2,3,6,4]=>14
[5,1,2,4,3,6]=>13
[5,1,2,4,6,3]=>16
[5,1,2,6,3,4]=>15
[5,1,2,6,4,3]=>14
[5,1,3,2,4,6]=>14
[5,1,3,2,6,4]=>15
[5,1,3,4,2,6]=>15
[5,1,3,4,6,2]=>17
[5,1,3,6,2,4]=>16
[5,1,3,6,4,2]=>17
[5,1,4,2,3,6]=>14
[5,1,4,2,6,3]=>17
[5,1,4,3,2,6]=>12
[5,1,4,3,6,2]=>17
[5,1,4,6,2,3]=>14
[5,1,4,6,3,2]=>16
[5,1,6,2,3,4]=>14
[5,1,6,2,4,3]=>16
[5,1,6,3,2,4]=>14
[5,1,6,3,4,2]=>15
[5,1,6,4,2,3]=>15
[5,1,6,4,3,2]=>14
[5,2,1,3,4,6]=>13
[5,2,1,3,6,4]=>15
[5,2,1,4,3,6]=>9
[5,2,1,4,6,3]=>14
[5,2,1,6,3,4]=>10
[5,2,1,6,4,3]=>13
[5,2,3,1,4,6]=>14
[5,2,3,1,6,4]=>14
[5,2,3,4,1,6]=>7
[5,2,3,4,6,1]=>12
[5,2,3,6,1,4]=>10
[5,2,3,6,4,1]=>15
[5,2,4,1,3,6]=>17
[5,2,4,1,6,3]=>16
[5,2,4,3,1,6]=>14
[5,2,4,3,6,1]=>15
[5,2,4,6,1,3]=>16
[5,2,4,6,3,1]=>18
[5,2,6,1,3,4]=>15
[5,2,6,1,4,3]=>14
[5,2,6,3,1,4]=>16
[5,2,6,3,4,1]=>15
[5,2,6,4,1,3]=>15
[5,2,6,4,3,1]=>15
[5,3,1,2,4,6]=>15
[5,3,1,2,6,4]=>16
[5,3,1,4,2,6]=>17
[5,3,1,4,6,2]=>17
[5,3,1,6,2,4]=>16
[5,3,1,6,4,2]=>15
[5,3,2,1,4,6]=>12
[5,3,2,1,6,4]=>14
[5,3,2,4,1,6]=>13
[5,3,2,4,6,1]=>14
[5,3,2,6,1,4]=>15
[5,3,2,6,4,1]=>14
[5,3,4,1,2,6]=>13
[5,3,4,1,6,2]=>15
[5,3,4,2,1,6]=>12
[5,3,4,2,6,1]=>14
[5,3,4,6,1,2]=>14
[5,3,4,6,2,1]=>14
[5,3,6,1,2,4]=>15
[5,3,6,1,4,2]=>15
[5,3,6,2,1,4]=>16
[5,3,6,2,4,1]=>17
[5,3,6,4,1,2]=>16
[5,3,6,4,2,1]=>17
[5,4,1,2,3,6]=>7
[5,4,1,2,6,3]=>14
[5,4,1,3,2,6]=>13
[5,4,1,3,6,2]=>16
[5,4,1,6,2,3]=>13
[5,4,1,6,3,2]=>9
[5,4,2,1,3,6]=>14
[5,4,2,1,6,3]=>15
[5,4,2,3,1,6]=>12
[5,4,2,3,6,1]=>13
[5,4,2,6,1,3]=>16
[5,4,2,6,3,1]=>16
[5,4,3,1,2,6]=>12
[5,4,3,1,6,2]=>14
[5,4,3,2,1,6]=>4
[5,4,3,2,6,1]=>10
[5,4,3,6,1,2]=>9
[5,4,3,6,2,1]=>13
[5,4,6,1,2,3]=>12
[5,4,6,1,3,2]=>13
[5,4,6,2,1,3]=>14
[5,4,6,2,3,1]=>13
[5,4,6,3,1,2]=>15
[5,4,6,3,2,1]=>13
[5,6,1,2,3,4]=>8
[5,6,1,2,4,3]=>14
[5,6,1,3,2,4]=>13
[5,6,1,3,4,2]=>14
[5,6,1,4,2,3]=>14
[5,6,1,4,3,2]=>9
[5,6,2,1,3,4]=>14
[5,6,2,1,4,3]=>13
[5,6,2,3,1,4]=>14
[5,6,2,3,4,1]=>11
[5,6,2,4,1,3]=>16
[5,6,2,4,3,1]=>14
[5,6,3,1,2,4]=>14
[5,6,3,1,4,2]=>16
[5,6,3,2,1,4]=>9
[5,6,3,2,4,1]=>14
[5,6,3,4,1,2]=>11
[5,6,3,4,2,1]=>14
[5,6,4,1,2,3]=>12
[5,6,4,1,3,2]=>15
[5,6,4,2,1,3]=>15
[5,6,4,2,3,1]=>14
[5,6,4,3,1,2]=>15
[5,6,4,3,2,1]=>11
[6,1,2,3,4,5]=>4
[6,1,2,3,5,4]=>12
[6,1,2,4,3,5]=>12
[6,1,2,4,5,3]=>13
[6,1,2,5,3,4]=>14
[6,1,2,5,4,3]=>7
[6,1,3,2,4,5]=>12
[6,1,3,2,5,4]=>13
[6,1,3,4,2,5]=>14
[6,1,3,4,5,2]=>12
[6,1,3,5,2,4]=>17
[6,1,3,5,4,2]=>14
[6,1,4,2,3,5]=>13
[6,1,4,2,5,3]=>17
[6,1,4,3,2,5]=>7
[6,1,4,3,5,2]=>15
[6,1,4,5,2,3]=>9
[6,1,4,5,3,2]=>13
[6,1,5,2,3,4]=>12
[6,1,5,2,4,3]=>15
[6,1,5,3,2,4]=>14
[6,1,5,3,4,2]=>14
[6,1,5,4,2,3]=>13
[6,1,5,4,3,2]=>10
[6,2,1,3,4,5]=>12
[6,2,1,3,5,4]=>14
[6,2,1,4,3,5]=>13
[6,2,1,4,5,3]=>12
[6,2,1,5,3,4]=>13
[6,2,1,5,4,3]=>10
[6,2,3,1,4,5]=>13
[6,2,3,1,5,4]=>12
[6,2,3,4,1,5]=>12
[6,2,3,4,5,1]=>6
[6,2,3,5,1,4]=>15
[6,2,3,5,4,1]=>10
[6,2,4,1,3,5]=>17
[6,2,4,1,5,3]=>16
[6,2,4,3,1,5]=>15
[6,2,4,3,5,1]=>12
[6,2,4,5,1,3]=>15
[6,2,4,5,3,1]=>13
[6,2,5,1,3,4]=>14
[6,2,5,1,4,3]=>14
[6,2,5,3,1,4]=>18
[6,2,5,3,4,1]=>13
[6,2,5,4,1,3]=>15
[6,2,5,4,3,1]=>10
[6,3,1,2,4,5]=>14
[6,3,1,2,5,4]=>13
[6,3,1,4,2,5]=>17
[6,3,1,4,5,2]=>15
[6,3,1,5,2,4]=>15
[6,3,1,5,4,2]=>14
[6,3,2,1,4,5]=>7
[6,3,2,1,5,4]=>10
[6,3,2,4,1,5]=>14
[6,3,2,4,5,1]=>10
[6,3,2,5,1,4]=>14
[6,3,2,5,4,1]=>7
[6,3,4,1,2,5]=>9
[6,3,4,1,5,2]=>15
[6,3,4,2,1,5]=>13
[6,3,4,2,5,1]=>13
[6,3,4,5,1,2]=>11
[6,3,4,5,2,1]=>5
[6,3,5,1,2,4]=>14
[6,3,5,1,4,2]=>17
[6,3,5,2,1,4]=>16
[6,3,5,2,4,1]=>17
[6,3,5,4,1,2]=>14
[6,3,5,4,2,1]=>12
[6,4,1,2,3,5]=>12
[6,4,1,2,5,3]=>14
[6,4,1,3,2,5]=>14
[6,4,1,3,5,2]=>18
[6,4,1,5,2,3]=>14
[6,4,1,5,3,2]=>16
[6,4,2,1,3,5]=>15
[6,4,2,1,5,3]=>14
[6,4,2,3,1,5]=>14
[6,4,2,3,5,1]=>13
[6,4,2,5,1,3]=>17
[6,4,2,5,3,1]=>17
[6,4,3,1,2,5]=>13
[6,4,3,1,5,2]=>15
[6,4,3,2,1,5]=>10
[6,4,3,2,5,1]=>10
[6,4,3,5,1,2]=>14
[6,4,3,5,2,1]=>12
[6,4,5,1,2,3]=>10
[6,4,5,1,3,2]=>13
[6,4,5,2,1,3]=>13
[6,4,5,2,3,1]=>11
[6,4,5,3,1,2]=>14
[6,4,5,3,2,1]=>9
[6,5,1,2,3,4]=>9
[6,5,1,2,4,3]=>12
[6,5,1,3,2,4]=>12
[6,5,1,3,4,2]=>14
[6,5,1,4,2,3]=>14
[6,5,1,4,3,2]=>13
[6,5,2,1,3,4]=>12
[6,5,2,1,4,3]=>8
[6,5,2,3,1,4]=>14
[6,5,2,3,4,1]=>5
[6,5,2,4,1,3]=>17
[6,5,2,4,3,1]=>12
[6,5,3,1,2,4]=>14
[6,5,3,1,4,2]=>17
[6,5,3,2,1,4]=>13
[6,5,3,2,4,1]=>12
[6,5,3,4,1,2]=>14
[6,5,3,4,2,1]=>10
[6,5,4,1,2,3]=>6
[6,5,4,1,3,2]=>13
[6,5,4,2,1,3]=>13
[6,5,4,2,3,1]=>9
[6,5,4,3,1,2]=>11
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>19
[1,2,3,4,6,5,7]=>16
[1,2,3,4,6,7,5]=>23
[1,2,3,4,7,5,6]=>23
[1,2,3,4,7,6,5]=>11
[1,2,3,5,4,6,7]=>17
[1,2,3,5,4,7,6]=>26
[1,2,3,5,6,4,7]=>21
[1,2,3,5,6,7,4]=>25
[1,2,3,5,7,4,6]=>30
[1,2,3,5,7,6,4]=>25
[1,2,3,6,4,5,7]=>21
[1,2,3,6,4,7,5]=>30
[1,2,3,6,5,4,7]=>9
[1,2,3,6,5,7,4]=>25
[1,2,3,6,7,4,5]=>14
[1,2,3,6,7,5,4]=>21
[1,2,3,7,4,5,6]=>25
[1,2,3,7,4,6,5]=>25
[1,2,3,7,5,4,6]=>25
[1,2,3,7,5,6,4]=>22
[1,2,3,7,6,4,5]=>21
[1,2,3,7,6,5,4]=>18
[1,2,4,3,5,6,7]=>17
[1,2,4,3,5,7,6]=>27
[1,2,4,3,6,5,7]=>23
[1,2,4,3,6,7,5]=>27
[1,2,4,3,7,5,6]=>27
[1,2,4,3,7,6,5]=>21
[1,2,4,5,3,6,7]=>22
[1,2,4,5,3,7,6]=>28
[1,2,4,5,6,3,7]=>22
[1,2,4,5,6,7,3]=>24
[1,2,4,5,7,3,6]=>30
[1,2,4,5,7,6,3]=>26
[1,2,4,6,3,5,7]=>30
[1,2,4,6,3,7,5]=>32
[1,2,4,6,5,3,7]=>24
[1,2,4,6,5,7,3]=>28
[1,2,4,6,7,3,5]=>26
[1,2,4,6,7,5,3]=>28
[1,2,4,7,3,5,6]=>31
[1,2,4,7,3,6,5]=>27
[1,2,4,7,5,3,6]=>33
[1,2,4,7,5,6,3]=>27
[1,2,4,7,6,3,5]=>27
[1,2,4,7,6,5,3]=>25
[1,2,5,3,4,6,7]=>22
[1,2,5,3,4,7,6]=>28
[1,2,5,3,6,4,7]=>30
[1,2,5,3,6,7,4]=>31
[1,2,5,3,7,4,6]=>32
[1,2,5,3,7,6,4]=>27
[1,2,5,4,3,6,7]=>10
[1,2,5,4,3,7,6]=>22
[1,2,5,4,6,3,7]=>24
[1,2,5,4,6,7,3]=>26
[1,2,5,4,7,3,6]=>28
[1,2,5,4,7,6,3]=>18
[1,2,5,6,3,4,7]=>13
[1,2,5,6,3,7,4]=>26
[1,2,5,6,4,3,7]=>19
[1,2,5,6,4,7,3]=>27
[1,2,5,6,7,3,4]=>20
[1,2,5,6,7,4,3]=>15
[1,2,5,7,3,4,6]=>26
[1,2,5,7,3,6,4]=>27
[1,2,5,7,4,3,6]=>28
[1,2,5,7,4,6,3]=>30
[1,2,5,7,6,3,4]=>25
[1,2,5,7,6,4,3]=>26
[1,2,6,3,4,5,7]=>22
[1,2,6,3,4,7,5]=>30
[1,2,6,3,5,4,7]=>24
[1,2,6,3,5,7,4]=>33
[1,2,6,3,7,4,5]=>26
[1,2,6,3,7,5,4]=>27
[1,2,6,4,3,5,7]=>24
[1,2,6,4,3,7,5]=>28
[1,2,6,4,5,3,7]=>22
[1,2,6,4,5,7,3]=>28
[1,2,6,4,7,3,5]=>28
[1,2,6,4,7,5,3]=>30
[1,2,6,5,3,4,7]=>19
[1,2,6,5,3,7,4]=>28
[1,2,6,5,4,3,7]=>15
[1,2,6,5,4,7,3]=>25
[1,2,6,5,7,3,4]=>24
[1,2,6,5,7,4,3]=>25
[1,2,6,7,3,4,5]=>20
[1,2,6,7,3,5,4]=>25
[1,2,6,7,4,3,5]=>24
[1,2,6,7,4,5,3]=>26
[1,2,6,7,5,3,4]=>27
[1,2,6,7,5,4,3]=>24
[1,2,7,3,4,5,6]=>24
[1,2,7,3,4,6,5]=>26
[1,2,7,3,5,4,6]=>28
[1,2,7,3,5,6,4]=>27
[1,2,7,3,6,4,5]=>28
[1,2,7,3,6,5,4]=>25
[1,2,7,4,3,5,6]=>26
[1,2,7,4,3,6,5]=>18
[1,2,7,4,5,3,6]=>28
[1,2,7,4,5,6,3]=>15
[1,2,7,4,6,3,5]=>30
[1,2,7,4,6,5,3]=>25
[1,2,7,5,3,4,6]=>27
[1,2,7,5,3,6,4]=>30
[1,2,7,5,4,3,6]=>25
[1,2,7,5,4,6,3]=>26
[1,2,7,5,6,3,4]=>26
[1,2,7,5,6,4,3]=>24
[1,2,7,6,3,4,5]=>15
[1,2,7,6,3,5,4]=>26
[1,2,7,6,4,3,5]=>25
[1,2,7,6,4,5,3]=>24
[1,2,7,6,5,3,4]=>24
[1,2,7,6,5,4,3]=>12
[1,3,2,4,5,6,7]=>16
[1,3,2,4,5,7,6]=>26
[1,3,2,4,6,5,7]=>25
[1,3,2,4,6,7,5]=>28
[1,3,2,4,7,5,6]=>28
[1,3,2,4,7,6,5]=>21
[1,3,2,5,4,6,7]=>23
[1,3,2,5,4,7,6]=>24
[1,3,2,5,6,4,7]=>25
[1,3,2,5,6,7,4]=>22
[1,3,2,5,7,4,6]=>31
[1,3,2,5,7,6,4]=>27
[1,3,2,6,4,5,7]=>25
[1,3,2,6,4,7,5]=>31
[1,3,2,6,5,4,7]=>18
[1,3,2,6,5,7,4]=>27
[1,3,2,6,7,4,5]=>22
[1,3,2,6,7,5,4]=>25
[1,3,2,7,4,5,6]=>22
[1,3,2,7,4,6,5]=>27
[1,3,2,7,5,4,6]=>27
[1,3,2,7,5,6,4]=>26
[1,3,2,7,6,4,5]=>25
[1,3,2,7,6,5,4]=>19
[1,3,4,2,5,6,7]=>21
[1,3,4,2,5,7,6]=>28
[1,3,4,2,6,5,7]=>25
[1,3,4,2,6,7,5]=>28
[1,3,4,2,7,5,6]=>27
[1,3,4,2,7,6,5]=>23
[1,3,4,5,2,6,7]=>22
[1,3,4,5,2,7,6]=>22
[1,3,4,5,6,2,7]=>20
[1,3,4,5,6,7,2]=>16
[1,3,4,5,7,2,6]=>29
[1,3,4,5,7,6,2]=>25
[1,3,4,6,2,5,7]=>29
[1,3,4,6,2,7,5]=>32
[1,3,4,6,5,2,7]=>23
[1,3,4,6,5,7,2]=>26
[1,3,4,6,7,2,5]=>27
[1,3,4,6,7,5,2]=>27
[1,3,4,7,2,5,6]=>23
[1,3,4,7,2,6,5]=>26
[1,3,4,7,5,2,6]=>31
[1,3,4,7,5,6,2]=>27
[1,3,4,7,6,2,5]=>26
[1,3,4,7,6,5,2]=>19
[1,3,5,2,4,6,7]=>30
[1,3,5,2,4,7,6]=>32
[1,3,5,2,6,4,7]=>31
[1,3,5,2,6,7,4]=>32
[1,3,5,2,7,4,6]=>31
[1,3,5,2,7,6,4]=>30
[1,3,5,4,2,6,7]=>24
[1,3,5,4,2,7,6]=>28
[1,3,5,4,6,2,7]=>26
[1,3,5,4,6,7,2]=>26
[1,3,5,4,7,2,6]=>30
[1,3,5,4,7,6,2]=>26
[1,3,5,6,2,4,7]=>25
[1,3,5,6,2,7,4]=>30
[1,3,5,6,4,2,7]=>26
[1,3,5,6,4,7,2]=>28
[1,3,5,6,7,2,4]=>28
[1,3,5,6,7,4,2]=>25
[1,3,5,7,2,4,6]=>29
[1,3,5,7,2,6,4]=>30
[1,3,5,7,4,2,6]=>32
[1,3,5,7,4,6,2]=>32
[1,3,5,7,6,2,4]=>30
[1,3,5,7,6,4,2]=>29
[1,3,6,2,4,5,7]=>29
[1,3,6,2,4,7,5]=>31
[1,3,6,2,5,4,7]=>26
[1,3,6,2,5,7,4]=>31
[1,3,6,2,7,4,5]=>26
[1,3,6,2,7,5,4]=>29
[1,3,6,4,2,5,7]=>33
[1,3,6,4,2,7,5]=>32
[1,3,6,4,5,2,7]=>26
[1,3,6,4,5,7,2]=>28
[1,3,6,4,7,2,5]=>29
[1,3,6,4,7,5,2]=>32
[1,3,6,5,2,4,7]=>27
[1,3,6,5,2,7,4]=>24
[1,3,6,5,4,2,7]=>23
[1,3,6,5,4,7,2]=>20
[1,3,6,5,7,2,4]=>29
[1,3,6,5,7,4,2]=>29
[1,3,6,7,2,4,5]=>25
[1,3,6,7,2,5,4]=>23
[1,3,6,7,4,2,5]=>27
[1,3,6,7,4,5,2]=>22
[1,3,6,7,5,2,4]=>30
[1,3,6,7,5,4,2]=>27
[1,3,7,2,4,5,6]=>30
[1,3,7,2,4,6,5]=>30
[1,3,7,2,5,4,6]=>30
[1,3,7,2,5,6,4]=>28
[1,3,7,2,6,4,5]=>30
[1,3,7,2,6,5,4]=>28
[1,3,7,4,2,5,6]=>32
[1,3,7,4,2,6,5]=>27
[1,3,7,4,5,2,6]=>32
[1,3,7,4,5,6,2]=>24
[1,3,7,4,6,2,5]=>31
[1,3,7,4,6,5,2]=>28
[1,3,7,5,2,4,6]=>32
[1,3,7,5,2,6,4]=>29
[1,3,7,5,4,2,6]=>32
[1,3,7,5,4,6,2]=>28
[1,3,7,5,6,2,4]=>29
[1,3,7,5,6,4,2]=>28
[1,3,7,6,2,4,5]=>26
[1,3,7,6,2,5,4]=>28
[1,3,7,6,4,2,5]=>30
[1,3,7,6,4,5,2]=>26
[1,3,7,6,5,2,4]=>28
[1,3,7,6,5,4,2]=>22
[1,4,2,3,5,6,7]=>21
[1,4,2,3,5,7,6]=>28
[1,4,2,3,6,5,7]=>25
[1,4,2,3,6,7,5]=>27
[1,4,2,3,7,5,6]=>28
[1,4,2,3,7,6,5]=>23
[1,4,2,5,3,6,7]=>30
[1,4,2,5,3,7,6]=>32
[1,4,2,5,6,3,7]=>29
[1,4,2,5,6,7,3]=>30
[1,4,2,5,7,3,6]=>31
[1,4,2,5,7,6,3]=>30
[1,4,2,6,3,5,7]=>31
[1,4,2,6,3,7,5]=>31
[1,4,2,6,5,3,7]=>26
[1,4,2,6,5,7,3]=>30
[1,4,2,6,7,3,5]=>26
[1,4,2,6,7,5,3]=>30
[1,4,2,7,3,5,6]=>32
[1,4,2,7,3,6,5]=>30
[1,4,2,7,5,3,6]=>31
[1,4,2,7,5,6,3]=>28
[1,4,2,7,6,3,5]=>29
[1,4,2,7,6,5,3]=>28
[1,4,3,2,5,6,7]=>9
[1,4,3,2,5,7,6]=>22
[1,4,3,2,6,5,7]=>18
[1,4,3,2,6,7,5]=>23
[1,4,3,2,7,5,6]=>23
[1,4,3,2,7,6,5]=>15
[1,4,3,5,2,6,7]=>24
[1,4,3,5,2,7,6]=>28
[1,4,3,5,6,2,7]=>23
[1,4,3,5,6,7,2]=>25
[1,4,3,5,7,2,6]=>29
[1,4,3,5,7,6,2]=>27
[1,4,3,6,2,5,7]=>26
[1,4,3,6,2,7,5]=>30
[1,4,3,6,5,2,7]=>16
[1,4,3,6,5,7,2]=>26
[1,4,3,6,7,2,5]=>19
[1,4,3,6,7,5,2]=>25
[1,4,3,7,2,5,6]=>27
[1,4,3,7,2,6,5]=>27
[1,4,3,7,5,2,6]=>27
[1,4,3,7,5,6,2]=>24
[1,4,3,7,6,2,5]=>24
[1,4,3,7,6,5,2]=>21
[1,4,5,2,3,6,7]=>13
[1,4,5,2,3,7,6]=>24
[1,4,5,2,6,3,7]=>25
[1,4,5,2,6,7,3]=>28
[1,4,5,2,7,3,6]=>27
[1,4,5,2,7,6,3]=>19
[1,4,5,3,2,6,7]=>19
[1,4,5,3,2,7,6]=>26
[1,4,5,3,6,2,7]=>26
[1,4,5,3,6,7,2]=>27
[1,4,5,3,7,2,6]=>30
[1,4,5,3,7,6,2]=>24
[1,4,5,6,2,3,7]=>17
[1,4,5,6,2,7,3]=>27
[1,4,5,6,3,2,7]=>12
[1,4,5,6,3,7,2]=>24
[1,4,5,6,7,2,3]=>15
[1,4,5,6,7,3,2]=>17
[1,4,5,7,2,3,6]=>25
[1,4,5,7,2,6,3]=>28
[1,4,5,7,3,2,6]=>26
[1,4,5,7,3,6,2]=>27
[1,4,5,7,6,2,3]=>25
[1,4,5,7,6,3,2]=>23
[1,4,6,2,3,5,7]=>25
[1,4,6,2,3,7,5]=>27
[1,4,6,2,5,3,7]=>28
[1,4,6,2,5,7,3]=>30
[1,4,6,2,7,3,5]=>29
[1,4,6,2,7,5,3]=>29
[1,4,6,3,2,5,7]=>27
[1,4,6,3,2,7,5]=>30
[1,4,6,3,5,2,7]=>30
[1,4,6,3,5,7,2]=>32
[1,4,6,3,7,2,5]=>30
[1,4,6,3,7,5,2]=>29
[1,4,6,5,2,3,7]=>23
[1,4,6,5,2,7,3]=>29
[1,4,6,5,3,2,7]=>23
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Description
The number of alternating subsets such that applying the permutation does not yield an alternating subset.
A subset of $[n]=\{1,\dots,n\}$ is alternating if any two successive elements have different parity. This statistic records for each permutation $\pi\in\mathfrak S_n$ the number of alternating subsets $S\subseteq [n]$ such that $\pi(S)$ is not alternating.
Note that the number of alternating subsets of $[n]$ is $F(n+3)-1$, where $F(n)$ is the $n$-th Fibonacci number.
A subset of $[n]=\{1,\dots,n\}$ is alternating if any two successive elements have different parity. This statistic records for each permutation $\pi\in\mathfrak S_n$ the number of alternating subsets $S\subseteq [n]$ such that $\pi(S)$ is not alternating.
Note that the number of alternating subsets of $[n]$ is $F(n+3)-1$, where $F(n)$ is the $n$-th Fibonacci number.
References
[1] Dawar, A. Counting sets whose alternation is preserved by a permutation MathOverflow:375868
Code
def is_alternating(S):
return all(is_odd(s + t) for s, t in zip(S, S[1:]))
@cached_function
def alternating_subsets(n):
return [S for S in Subsets(n) if (is_alternating(sorted(S)))]
def statistic(pi):
pi = Permutation(pi)
n = len(pi)
good = 0
for S in alternating_subsets(n):
if not is_alternating(sorted(pi(s) for s in S)):
good += 1
return good
Created
Nov 07, 2020 at 18:04 by Martin Rubey
Updated
Nov 07, 2020 at 18:04 by Martin Rubey
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