Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St001379: Permutations ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1]=>0
[1,0,1,0]=>[1,2]=>[1,2]=>[2,1]=>2
[1,1,0,0]=>[2,1]=>[2,1]=>[1,2]=>0
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[3,2,1]=>6
[1,0,1,1,0,0]=>[1,3,2]=>[2,3,1]=>[2,1,3]=>2
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[2,3,1]=>4
[1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[1,3,2]=>3
[1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[1,2,3]=>0
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[4,3,2,1]=>12
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[2,3,4,1]=>[3,2,1,4]=>6
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[2,3,1,4]=>[3,2,4,1]=>8
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,1,3]=>[3,1,4,2]=>7
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[3,4,2,1]=>[2,1,3,4]=>2
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[3,4,2,1]=>10
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,2,4,1]=>[2,3,1,4]=>4
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[2,4,3,1]=>9
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[1,4,3,2]=>8
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>[1,3,2,4]=>3
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[2,3,4,1]=>6
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,2,1,3]=>[1,3,4,2]=>5
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,3,1,2]=>[1,2,4,3]=>4
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[1,2,3,4]=>0
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>20
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[2,3,4,5,1]=>[4,3,2,1,5]=>12
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[2,3,4,1,5]=>[4,3,2,5,1]=>14
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[2,3,5,1,4]=>[4,3,1,5,2]=>13
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[3,2,1,4,5]=>6
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[2,3,1,4,5]=>[4,3,5,2,1]=>16
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[3,4,2,5,1]=>[3,2,4,1,5]=>8
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[2,4,1,3,5]=>[4,2,5,3,1]=>15
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,5,1,3,4]=>[4,1,5,3,2]=>14
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[3,5,2,4,1]=>[3,1,4,2,5]=>7
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[3,4,2,1,5]=>[3,2,4,5,1]=>10
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[3,5,2,1,4]=>[3,1,4,5,2]=>9
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[3,5,4,1,2]=>[3,1,2,5,4]=>8
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[4,5,3,2,1]=>[2,1,3,4,5]=>2
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[4,5,3,2,1]=>18
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[3,2,4,5,1]=>[3,4,2,1,5]=>10
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[3,2,4,1,5]=>[3,4,2,5,1]=>12
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,2,5,1,4]=>[3,4,1,5,2]=>11
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[4,3,5,2,1]=>[2,3,1,4,5]=>4
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[3,5,4,2,1]=>17
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,2,3,5,1]=>[2,4,3,1,5]=>9
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[2,5,4,3,1]=>16
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,5,4,3,2]=>15
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>8
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[2,4,3,5,1]=>11
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,2,3,1,4]=>[1,4,3,5,2]=>10
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,2,4,1,3]=>[1,4,2,5,3]=>9
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,3,4,2,1]=>[1,3,2,4,5]=>3
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,4,5,2,1]=>14
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,3,2,5,1]=>[2,3,4,1,5]=>6
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[2,4,5,3,1]=>13
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[1,4,5,3,2]=>12
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[1,3,4,2,5]=>5
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[2,3,5,4,1]=>12
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,3,5,4,2]=>11
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[1,2,5,4,3]=>10
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,4,2,3,1]=>[1,2,4,3,5]=>4
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,5,1]=>8
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,3,4,5,2]=>7
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,2,4,5,3]=>6
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,2,3,5,4]=>5
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>30
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>20
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>22
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>21
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>12
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>24
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>14
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>23
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>22
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>[4,3,1,5,2,6]=>13
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>16
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>[4,3,1,5,6,2]=>15
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[3,4,6,5,1,2]=>[4,3,1,2,6,5]=>14
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>6
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>26
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>16
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>18
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>[4,3,5,1,6,2]=>17
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>8
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>25
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>[4,2,5,3,1,6]=>15
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>24
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>23
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>[4,1,5,3,2,6]=>14
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>[4,2,5,3,6,1]=>17
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>[4,1,5,3,6,2]=>16
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>15
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>[3,1,4,2,5,6]=>7
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>20
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>10
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>19
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>[4,1,5,6,3,2]=>18
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>[3,1,4,5,2,6]=>9
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>18
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>17
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[3,6,5,1,2,4]=>[4,1,2,6,5,3]=>16
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[4,6,5,2,3,1]=>[3,1,2,5,4,6]=>8
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>12
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>[3,1,4,5,6,2]=>11
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>10
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>9
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>2
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>28
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>18
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>20
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>[4,5,3,1,6,2]=>19
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>10
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>22
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>12
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>21
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>20
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>[3,4,1,5,2,6]=>11
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>14
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>[3,4,1,5,6,2]=>13
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[4,3,6,5,1,2]=>[3,4,1,2,6,5]=>12
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>4
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>27
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>17
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>19
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>[3,5,4,1,6,2]=>18
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>9
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>26
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>16
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>25
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>24
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>15
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>18
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>17
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>[1,5,4,2,6,3]=>16
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>8
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>21
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>11
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>20
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>19
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>10
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>[2,5,3,6,4,1]=>19
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>18
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>17
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>9
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>13
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>12
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,3,5,2,1,4]=>[1,4,2,5,6,3]=>11
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[6,3,5,4,1,2]=>[1,4,2,3,6,5]=>10
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>3
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>24
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>14
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>16
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>[3,4,5,1,6,2]=>15
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>6
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>23
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>13
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>22
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>21
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>12
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>15
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>14
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[6,3,2,5,1,4]=>[1,4,5,2,6,3]=>13
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>5
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>22
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>12
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>21
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>20
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>11
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>20
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>19
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>18
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>10
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>14
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>13
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>12
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[6,5,2,4,1,3]=>[1,2,5,3,6,4]=>11
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>4
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>18
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>8
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>17
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>16
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>7
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>16
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>15
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>14
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>6
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>15
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>14
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>13
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>12
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>5
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>10
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>9
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>8
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>7
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>6
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>10
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,4,6,3,5,2,1]=>[1,4,2,5,3,6,7]=>9
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>12
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,4,6,3,2,5,1]=>[1,4,2,5,6,3,7]=>11
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,4,6,5,2,3,1]=>[1,4,2,3,6,5,7]=>10
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>14
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[7,4,6,3,2,1,5]=>[1,4,2,5,6,7,3]=>13
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[7,4,6,5,2,1,3]=>[1,4,2,3,6,7,5]=>12
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[7,4,6,5,3,1,2]=>[1,4,2,3,5,7,6]=>11
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>12
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>14
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,4,3,6,2,5,1]=>[1,4,5,2,6,3,7]=>13
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>16
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[7,4,3,6,2,1,5]=>[1,4,5,2,6,7,3]=>15
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[7,4,3,6,5,1,2]=>[1,4,5,2,3,7,6]=>14
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>20
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[7,4,2,3,6,1,5]=>[1,4,6,5,2,7,3]=>21
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>11
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>19
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>29
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>28
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>18
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>21
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>20
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[7,6,2,3,5,1,4]=>[1,2,6,5,3,7,4]=>19
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>13
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>23
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>22
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>12
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,3,6,4,7,5,2]=>22
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[7,6,2,4,1,3,5]=>[1,2,6,4,7,5,3]=>21
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[7,6,2,5,1,3,4]=>[1,2,6,3,7,5,4]=>20
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,2,5,3,6,4,7]=>11
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>15
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>14
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,2,5,3,6,7,4]=>13
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,2,5,3,4,7,6]=>12
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>16
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>18
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[7,4,3,2,6,1,5]=>[1,4,5,6,2,7,3]=>17
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>15
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>25
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>24
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>14
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>17
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>16
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,2,5,6,3,7,4]=>15
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>25
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>24
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>23
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>13
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>23
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>22
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>21
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>12
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>16
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>15
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>14
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,2,3,6,4,7,5]=>13
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>20
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>9
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>19
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>18
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>8
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>18
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>17
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>16
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>7
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>17
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>16
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>15
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>14
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>11
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>10
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>0
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Description
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
to 312-avoiding permutation
Description
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
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