Identifier
-
Mp00254:
Permutations
—Inverse fireworks map⟶
Permutations
St000156: Permutations ⟶ ℤ
Values
=>
[1]=>[1]=>0
[1,2]=>[1,2]=>0
[2,1]=>[2,1]=>1
[1,2,3]=>[1,2,3]=>0
[1,3,2]=>[1,3,2]=>2
[2,1,3]=>[2,1,3]=>1
[2,3,1]=>[1,3,2]=>2
[3,1,2]=>[3,1,2]=>1
[3,2,1]=>[3,2,1]=>2
[1,2,3,4]=>[1,2,3,4]=>0
[1,2,4,3]=>[1,2,4,3]=>3
[1,3,2,4]=>[1,3,2,4]=>2
[1,3,4,2]=>[1,2,4,3]=>3
[1,4,2,3]=>[1,4,2,3]=>2
[1,4,3,2]=>[1,4,3,2]=>3
[2,1,3,4]=>[2,1,3,4]=>1
[2,1,4,3]=>[2,1,4,3]=>4
[2,3,1,4]=>[1,3,2,4]=>2
[2,3,4,1]=>[1,2,4,3]=>3
[2,4,1,3]=>[2,4,1,3]=>3
[2,4,3,1]=>[1,4,3,2]=>3
[3,1,2,4]=>[3,1,2,4]=>1
[3,1,4,2]=>[2,1,4,3]=>4
[3,2,1,4]=>[3,2,1,4]=>2
[3,2,4,1]=>[2,1,4,3]=>4
[3,4,1,2]=>[2,4,1,3]=>3
[3,4,2,1]=>[1,4,3,2]=>3
[4,1,2,3]=>[4,1,2,3]=>1
[4,1,3,2]=>[4,1,3,2]=>2
[4,2,1,3]=>[4,2,1,3]=>2
[4,2,3,1]=>[4,1,3,2]=>2
[4,3,1,2]=>[4,3,1,2]=>4
[4,3,2,1]=>[4,3,2,1]=>5
[1,2,3,4,5]=>[1,2,3,4,5]=>0
[1,2,3,5,4]=>[1,2,3,5,4]=>4
[1,2,4,3,5]=>[1,2,4,3,5]=>3
[1,2,4,5,3]=>[1,2,3,5,4]=>4
[1,2,5,3,4]=>[1,2,5,3,4]=>3
[1,2,5,4,3]=>[1,2,5,4,3]=>4
[1,3,2,4,5]=>[1,3,2,4,5]=>2
[1,3,2,5,4]=>[1,3,2,5,4]=>6
[1,3,4,2,5]=>[1,2,4,3,5]=>3
[1,3,4,5,2]=>[1,2,3,5,4]=>4
[1,3,5,2,4]=>[1,3,5,2,4]=>5
[1,3,5,4,2]=>[1,2,5,4,3]=>4
[1,4,2,3,5]=>[1,4,2,3,5]=>2
[1,4,2,5,3]=>[1,3,2,5,4]=>6
[1,4,3,2,5]=>[1,4,3,2,5]=>3
[1,4,3,5,2]=>[1,3,2,5,4]=>6
[1,4,5,2,3]=>[1,3,5,2,4]=>5
[1,4,5,3,2]=>[1,2,5,4,3]=>4
[1,5,2,3,4]=>[1,5,2,3,4]=>2
[1,5,2,4,3]=>[1,5,2,4,3]=>3
[1,5,3,2,4]=>[1,5,3,2,4]=>3
[1,5,3,4,2]=>[1,5,2,4,3]=>3
[1,5,4,2,3]=>[1,5,4,2,3]=>6
[1,5,4,3,2]=>[1,5,4,3,2]=>7
[2,1,3,4,5]=>[2,1,3,4,5]=>1
[2,1,3,5,4]=>[2,1,3,5,4]=>5
[2,1,4,3,5]=>[2,1,4,3,5]=>4
[2,1,4,5,3]=>[2,1,3,5,4]=>5
[2,1,5,3,4]=>[2,1,5,3,4]=>4
[2,1,5,4,3]=>[2,1,5,4,3]=>5
[2,3,1,4,5]=>[1,3,2,4,5]=>2
[2,3,1,5,4]=>[1,3,2,5,4]=>6
[2,3,4,1,5]=>[1,2,4,3,5]=>3
[2,3,4,5,1]=>[1,2,3,5,4]=>4
[2,3,5,1,4]=>[1,3,5,2,4]=>5
[2,3,5,4,1]=>[1,2,5,4,3]=>4
[2,4,1,3,5]=>[2,4,1,3,5]=>3
[2,4,1,5,3]=>[1,3,2,5,4]=>6
[2,4,3,1,5]=>[1,4,3,2,5]=>3
[2,4,3,5,1]=>[1,3,2,5,4]=>6
[2,4,5,1,3]=>[1,3,5,2,4]=>5
[2,4,5,3,1]=>[1,2,5,4,3]=>4
[2,5,1,3,4]=>[2,5,1,3,4]=>3
[2,5,1,4,3]=>[2,5,1,4,3]=>4
[2,5,3,1,4]=>[1,5,3,2,4]=>3
[2,5,3,4,1]=>[1,5,2,4,3]=>3
[2,5,4,1,3]=>[2,5,4,1,3]=>7
[2,5,4,3,1]=>[1,5,4,3,2]=>7
[3,1,2,4,5]=>[3,1,2,4,5]=>1
[3,1,2,5,4]=>[3,1,2,5,4]=>5
[3,1,4,2,5]=>[2,1,4,3,5]=>4
[3,1,4,5,2]=>[2,1,3,5,4]=>5
[3,1,5,2,4]=>[3,1,5,2,4]=>4
[3,1,5,4,2]=>[2,1,5,4,3]=>5
[3,2,1,4,5]=>[3,2,1,4,5]=>2
[3,2,1,5,4]=>[3,2,1,5,4]=>6
[3,2,4,1,5]=>[2,1,4,3,5]=>4
[3,2,4,5,1]=>[2,1,3,5,4]=>5
[3,2,5,1,4]=>[3,2,5,1,4]=>5
[3,2,5,4,1]=>[2,1,5,4,3]=>5
[3,4,1,2,5]=>[2,4,1,3,5]=>3
[3,4,1,5,2]=>[1,3,2,5,4]=>6
[3,4,2,1,5]=>[1,4,3,2,5]=>3
[3,4,2,5,1]=>[1,3,2,5,4]=>6
[3,4,5,1,2]=>[1,3,5,2,4]=>5
[3,4,5,2,1]=>[1,2,5,4,3]=>4
[3,5,1,2,4]=>[3,5,1,2,4]=>3
[3,5,1,4,2]=>[2,5,1,4,3]=>4
[3,5,2,1,4]=>[3,5,2,1,4]=>4
[3,5,2,4,1]=>[2,5,1,4,3]=>4
[3,5,4,1,2]=>[2,5,4,1,3]=>7
[3,5,4,2,1]=>[1,5,4,3,2]=>7
[4,1,2,3,5]=>[4,1,2,3,5]=>1
[4,1,2,5,3]=>[3,1,2,5,4]=>5
[4,1,3,2,5]=>[4,1,3,2,5]=>2
[4,1,3,5,2]=>[3,1,2,5,4]=>5
[4,1,5,2,3]=>[3,1,5,2,4]=>4
[4,1,5,3,2]=>[2,1,5,4,3]=>5
[4,2,1,3,5]=>[4,2,1,3,5]=>2
[4,2,1,5,3]=>[3,2,1,5,4]=>6
[4,2,3,1,5]=>[4,1,3,2,5]=>2
[4,2,3,5,1]=>[3,1,2,5,4]=>5
[4,2,5,1,3]=>[3,2,5,1,4]=>5
[4,2,5,3,1]=>[2,1,5,4,3]=>5
[4,3,1,2,5]=>[4,3,1,2,5]=>4
[4,3,1,5,2]=>[3,2,1,5,4]=>6
[4,3,2,1,5]=>[4,3,2,1,5]=>5
[4,3,2,5,1]=>[3,2,1,5,4]=>6
[4,3,5,1,2]=>[3,2,5,1,4]=>5
[4,3,5,2,1]=>[2,1,5,4,3]=>5
[4,5,1,2,3]=>[3,5,1,2,4]=>3
[4,5,1,3,2]=>[2,5,1,4,3]=>4
[4,5,2,1,3]=>[3,5,2,1,4]=>4
[4,5,2,3,1]=>[2,5,1,4,3]=>4
[4,5,3,1,2]=>[2,5,4,1,3]=>7
[4,5,3,2,1]=>[1,5,4,3,2]=>7
[5,1,2,3,4]=>[5,1,2,3,4]=>1
[5,1,2,4,3]=>[5,1,2,4,3]=>2
[5,1,3,2,4]=>[5,1,3,2,4]=>2
[5,1,3,4,2]=>[5,1,2,4,3]=>2
[5,1,4,2,3]=>[5,1,4,2,3]=>5
[5,1,4,3,2]=>[5,1,4,3,2]=>6
[5,2,1,3,4]=>[5,2,1,3,4]=>2
[5,2,1,4,3]=>[5,2,1,4,3]=>3
[5,2,3,1,4]=>[5,1,3,2,4]=>2
[5,2,3,4,1]=>[5,1,2,4,3]=>2
[5,2,4,1,3]=>[5,2,4,1,3]=>6
[5,2,4,3,1]=>[5,1,4,3,2]=>6
[5,3,1,2,4]=>[5,3,1,2,4]=>4
[5,3,1,4,2]=>[5,2,1,4,3]=>3
[5,3,2,1,4]=>[5,3,2,1,4]=>5
[5,3,2,4,1]=>[5,2,1,4,3]=>3
[5,3,4,1,2]=>[5,2,4,1,3]=>6
[5,3,4,2,1]=>[5,1,4,3,2]=>6
[5,4,1,2,3]=>[5,4,1,2,3]=>4
[5,4,1,3,2]=>[5,4,1,3,2]=>5
[5,4,2,1,3]=>[5,4,2,1,3]=>5
[5,4,2,3,1]=>[5,4,1,3,2]=>5
[5,4,3,1,2]=>[5,4,3,1,2]=>6
[5,4,3,2,1]=>[5,4,3,2,1]=>7
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>[1,2,3,4,6,5]=>5
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>4
[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>5
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>8
[1,2,4,5,3,6]=>[1,2,3,5,4,6]=>4
[1,2,4,5,6,3]=>[1,2,3,4,6,5]=>5
[1,2,4,6,3,5]=>[1,2,4,6,3,5]=>7
[1,2,4,6,5,3]=>[1,2,3,6,5,4]=>5
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>3
[1,2,5,3,6,4]=>[1,2,4,3,6,5]=>8
[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>4
[1,2,5,4,6,3]=>[1,2,4,3,6,5]=>8
[1,2,5,6,3,4]=>[1,2,4,6,3,5]=>7
[1,2,5,6,4,3]=>[1,2,3,6,5,4]=>5
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>[1,2,6,4,3,5]=>4
[1,2,6,4,5,3]=>[1,2,6,3,5,4]=>4
[1,2,6,5,3,4]=>[1,2,6,5,3,4]=>8
[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>9
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>7
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>6
[1,3,2,5,6,4]=>[1,3,2,4,6,5]=>7
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>6
[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>7
[1,3,4,2,5,6]=>[1,2,4,3,5,6]=>3
[1,3,4,2,6,5]=>[1,2,4,3,6,5]=>8
[1,3,4,5,2,6]=>[1,2,3,5,4,6]=>4
[1,3,4,5,6,2]=>[1,2,3,4,6,5]=>5
[1,3,4,6,2,5]=>[1,2,4,6,3,5]=>7
[1,3,4,6,5,2]=>[1,2,3,6,5,4]=>5
[1,3,5,2,4,6]=>[1,3,5,2,4,6]=>5
[1,3,5,2,6,4]=>[1,2,4,3,6,5]=>8
[1,3,5,4,2,6]=>[1,2,5,4,3,6]=>4
[1,3,5,4,6,2]=>[1,2,4,3,6,5]=>8
[1,3,5,6,2,4]=>[1,2,4,6,3,5]=>7
[1,3,5,6,4,2]=>[1,2,3,6,5,4]=>5
[1,3,6,2,4,5]=>[1,3,6,2,4,5]=>5
[1,3,6,2,5,4]=>[1,3,6,2,5,4]=>6
[1,3,6,4,2,5]=>[1,2,6,4,3,5]=>4
[1,3,6,4,5,2]=>[1,2,6,3,5,4]=>4
[1,3,6,5,2,4]=>[1,3,6,5,2,4]=>10
[1,3,6,5,4,2]=>[1,2,6,5,4,3]=>9
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>7
[1,4,2,5,3,6]=>[1,3,2,5,4,6]=>6
[1,4,2,5,6,3]=>[1,3,2,4,6,5]=>7
[1,4,2,6,3,5]=>[1,4,2,6,3,5]=>6
[1,4,2,6,5,3]=>[1,3,2,6,5,4]=>7
[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>8
[1,4,3,5,2,6]=>[1,3,2,5,4,6]=>6
[1,4,3,5,6,2]=>[1,3,2,4,6,5]=>7
[1,4,3,6,2,5]=>[1,4,3,6,2,5]=>7
[1,4,3,6,5,2]=>[1,3,2,6,5,4]=>7
[1,4,5,2,3,6]=>[1,3,5,2,4,6]=>5
[1,4,5,2,6,3]=>[1,2,4,3,6,5]=>8
[1,4,5,3,2,6]=>[1,2,5,4,3,6]=>4
[1,4,5,3,6,2]=>[1,2,4,3,6,5]=>8
[1,4,5,6,2,3]=>[1,2,4,6,3,5]=>7
[1,4,5,6,3,2]=>[1,2,3,6,5,4]=>5
[1,4,6,2,3,5]=>[1,4,6,2,3,5]=>5
[1,4,6,2,5,3]=>[1,3,6,2,5,4]=>6
[1,4,6,3,2,5]=>[1,4,6,3,2,5]=>6
[1,4,6,3,5,2]=>[1,3,6,2,5,4]=>6
[1,4,6,5,2,3]=>[1,3,6,5,2,4]=>10
[1,4,6,5,3,2]=>[1,2,6,5,4,3]=>9
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>2
[1,5,2,3,6,4]=>[1,4,2,3,6,5]=>7
[1,5,2,4,3,6]=>[1,5,2,4,3,6]=>3
[1,5,2,4,6,3]=>[1,4,2,3,6,5]=>7
[1,5,2,6,3,4]=>[1,4,2,6,3,5]=>6
[1,5,2,6,4,3]=>[1,3,2,6,5,4]=>7
[1,5,3,2,4,6]=>[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>[1,4,3,2,6,5]=>8
[1,5,3,4,2,6]=>[1,5,2,4,3,6]=>3
[1,5,3,4,6,2]=>[1,4,2,3,6,5]=>7
[1,5,3,6,2,4]=>[1,4,3,6,2,5]=>7
[1,5,3,6,4,2]=>[1,3,2,6,5,4]=>7
[1,5,4,2,3,6]=>[1,5,4,2,3,6]=>6
[1,5,4,2,6,3]=>[1,4,3,2,6,5]=>8
[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>7
[1,5,4,3,6,2]=>[1,4,3,2,6,5]=>8
[1,5,4,6,2,3]=>[1,4,3,6,2,5]=>7
[1,5,4,6,3,2]=>[1,3,2,6,5,4]=>7
[1,5,6,2,3,4]=>[1,4,6,2,3,5]=>5
[1,5,6,2,4,3]=>[1,3,6,2,5,4]=>6
[1,5,6,3,2,4]=>[1,4,6,3,2,5]=>6
[1,5,6,3,4,2]=>[1,3,6,2,5,4]=>6
[1,5,6,4,2,3]=>[1,3,6,5,2,4]=>10
[1,5,6,4,3,2]=>[1,2,6,5,4,3]=>9
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>2
[1,6,2,3,5,4]=>[1,6,2,3,5,4]=>3
[1,6,2,4,3,5]=>[1,6,2,4,3,5]=>3
[1,6,2,4,5,3]=>[1,6,2,3,5,4]=>3
[1,6,2,5,3,4]=>[1,6,2,5,3,4]=>7
[1,6,2,5,4,3]=>[1,6,2,5,4,3]=>8
[1,6,3,2,4,5]=>[1,6,3,2,4,5]=>3
[1,6,3,2,5,4]=>[1,6,3,2,5,4]=>4
[1,6,3,4,2,5]=>[1,6,2,4,3,5]=>3
[1,6,3,4,5,2]=>[1,6,2,3,5,4]=>3
[1,6,3,5,2,4]=>[1,6,3,5,2,4]=>8
[1,6,3,5,4,2]=>[1,6,2,5,4,3]=>8
[1,6,4,2,3,5]=>[1,6,4,2,3,5]=>6
[1,6,4,2,5,3]=>[1,6,3,2,5,4]=>4
[1,6,4,3,2,5]=>[1,6,4,3,2,5]=>7
[1,6,4,3,5,2]=>[1,6,3,2,5,4]=>4
[1,6,4,5,2,3]=>[1,6,3,5,2,4]=>8
[1,6,4,5,3,2]=>[1,6,2,5,4,3]=>8
[1,6,5,2,3,4]=>[1,6,5,2,3,4]=>6
[1,6,5,2,4,3]=>[1,6,5,2,4,3]=>7
[1,6,5,3,2,4]=>[1,6,5,3,2,4]=>7
[1,6,5,3,4,2]=>[1,6,5,2,4,3]=>7
[1,6,5,4,2,3]=>[1,6,5,4,2,3]=>8
[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>9
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>6
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>5
[2,1,3,5,6,4]=>[2,1,3,4,6,5]=>6
[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>5
[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>6
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>4
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>9
[2,1,4,5,3,6]=>[2,1,3,5,4,6]=>5
[2,1,4,5,6,3]=>[2,1,3,4,6,5]=>6
[2,1,4,6,3,5]=>[2,1,4,6,3,5]=>8
[2,1,4,6,5,3]=>[2,1,3,6,5,4]=>6
[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>4
[2,1,5,3,6,4]=>[2,1,4,3,6,5]=>9
[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>5
[2,1,5,4,6,3]=>[2,1,4,3,6,5]=>9
[2,1,5,6,3,4]=>[2,1,4,6,3,5]=>8
[2,1,5,6,4,3]=>[2,1,3,6,5,4]=>6
[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>[2,1,6,3,5,4]=>5
[2,1,6,4,3,5]=>[2,1,6,4,3,5]=>5
[2,1,6,4,5,3]=>[2,1,6,3,5,4]=>5
[2,1,6,5,3,4]=>[2,1,6,5,3,4]=>9
[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>10
[2,3,1,4,5,6]=>[1,3,2,4,5,6]=>2
[2,3,1,4,6,5]=>[1,3,2,4,6,5]=>7
[2,3,1,5,4,6]=>[1,3,2,5,4,6]=>6
[2,3,1,5,6,4]=>[1,3,2,4,6,5]=>7
[2,3,1,6,4,5]=>[1,3,2,6,4,5]=>6
[2,3,1,6,5,4]=>[1,3,2,6,5,4]=>7
[2,3,4,1,5,6]=>[1,2,4,3,5,6]=>3
[2,3,4,1,6,5]=>[1,2,4,3,6,5]=>8
[2,3,4,5,1,6]=>[1,2,3,5,4,6]=>4
[2,3,4,5,6,1]=>[1,2,3,4,6,5]=>5
[2,3,4,6,1,5]=>[1,2,4,6,3,5]=>7
[2,3,4,6,5,1]=>[1,2,3,6,5,4]=>5
[2,3,5,1,4,6]=>[1,3,5,2,4,6]=>5
[2,3,5,1,6,4]=>[1,2,4,3,6,5]=>8
[2,3,5,4,1,6]=>[1,2,5,4,3,6]=>4
[2,3,5,4,6,1]=>[1,2,4,3,6,5]=>8
[2,3,5,6,1,4]=>[1,2,4,6,3,5]=>7
[2,3,5,6,4,1]=>[1,2,3,6,5,4]=>5
[2,3,6,1,4,5]=>[1,3,6,2,4,5]=>5
[2,3,6,1,5,4]=>[1,3,6,2,5,4]=>6
[2,3,6,4,1,5]=>[1,2,6,4,3,5]=>4
[2,3,6,4,5,1]=>[1,2,6,3,5,4]=>4
[2,3,6,5,1,4]=>[1,3,6,5,2,4]=>10
[2,3,6,5,4,1]=>[1,2,6,5,4,3]=>9
[2,4,1,3,5,6]=>[2,4,1,3,5,6]=>3
[2,4,1,3,6,5]=>[2,4,1,3,6,5]=>8
[2,4,1,5,3,6]=>[1,3,2,5,4,6]=>6
[2,4,1,5,6,3]=>[1,3,2,4,6,5]=>7
[2,4,1,6,3,5]=>[2,4,1,6,3,5]=>7
[2,4,1,6,5,3]=>[1,3,2,6,5,4]=>7
[2,4,3,1,5,6]=>[1,4,3,2,5,6]=>3
[2,4,3,1,6,5]=>[1,4,3,2,6,5]=>8
[2,4,3,5,1,6]=>[1,3,2,5,4,6]=>6
[2,4,3,5,6,1]=>[1,3,2,4,6,5]=>7
[2,4,3,6,1,5]=>[1,4,3,6,2,5]=>7
[2,4,3,6,5,1]=>[1,3,2,6,5,4]=>7
[2,4,5,1,3,6]=>[1,3,5,2,4,6]=>5
[2,4,5,1,6,3]=>[1,2,4,3,6,5]=>8
[2,4,5,3,1,6]=>[1,2,5,4,3,6]=>4
[2,4,5,3,6,1]=>[1,2,4,3,6,5]=>8
[2,4,5,6,1,3]=>[1,2,4,6,3,5]=>7
[2,4,5,6,3,1]=>[1,2,3,6,5,4]=>5
[2,4,6,1,3,5]=>[2,4,6,1,3,5]=>6
[2,4,6,1,5,3]=>[1,3,6,2,5,4]=>6
[2,4,6,3,1,5]=>[1,4,6,3,2,5]=>6
[2,4,6,3,5,1]=>[1,3,6,2,5,4]=>6
[2,4,6,5,1,3]=>[1,3,6,5,2,4]=>10
[2,4,6,5,3,1]=>[1,2,6,5,4,3]=>9
[2,5,1,3,4,6]=>[2,5,1,3,4,6]=>3
[2,5,1,3,6,4]=>[2,4,1,3,6,5]=>8
[2,5,1,4,3,6]=>[2,5,1,4,3,6]=>4
[2,5,1,4,6,3]=>[2,4,1,3,6,5]=>8
[2,5,1,6,3,4]=>[2,4,1,6,3,5]=>7
[2,5,1,6,4,3]=>[1,3,2,6,5,4]=>7
[2,5,3,1,4,6]=>[1,5,3,2,4,6]=>3
[2,5,3,1,6,4]=>[1,4,3,2,6,5]=>8
[2,5,3,4,1,6]=>[1,5,2,4,3,6]=>3
[2,5,3,4,6,1]=>[1,4,2,3,6,5]=>7
[2,5,3,6,1,4]=>[1,4,3,6,2,5]=>7
[2,5,3,6,4,1]=>[1,3,2,6,5,4]=>7
[2,5,4,1,3,6]=>[2,5,4,1,3,6]=>7
[2,5,4,1,6,3]=>[1,4,3,2,6,5]=>8
[2,5,4,3,1,6]=>[1,5,4,3,2,6]=>7
[2,5,4,3,6,1]=>[1,4,3,2,6,5]=>8
[2,5,4,6,1,3]=>[1,4,3,6,2,5]=>7
[2,5,4,6,3,1]=>[1,3,2,6,5,4]=>7
[2,5,6,1,3,4]=>[2,4,6,1,3,5]=>6
[2,5,6,1,4,3]=>[1,3,6,2,5,4]=>6
[2,5,6,3,1,4]=>[1,4,6,3,2,5]=>6
[2,5,6,3,4,1]=>[1,3,6,2,5,4]=>6
[2,5,6,4,1,3]=>[1,3,6,5,2,4]=>10
[2,5,6,4,3,1]=>[1,2,6,5,4,3]=>9
[2,6,1,3,4,5]=>[2,6,1,3,4,5]=>3
[2,6,1,3,5,4]=>[2,6,1,3,5,4]=>4
[2,6,1,4,3,5]=>[2,6,1,4,3,5]=>4
[2,6,1,4,5,3]=>[2,6,1,3,5,4]=>4
[2,6,1,5,3,4]=>[2,6,1,5,3,4]=>8
[2,6,1,5,4,3]=>[2,6,1,5,4,3]=>9
[2,6,3,1,4,5]=>[1,6,3,2,4,5]=>3
[2,6,3,1,5,4]=>[1,6,3,2,5,4]=>4
[2,6,3,4,1,5]=>[1,6,2,4,3,5]=>3
[2,6,3,4,5,1]=>[1,6,2,3,5,4]=>3
[2,6,3,5,1,4]=>[1,6,3,5,2,4]=>8
[2,6,3,5,4,1]=>[1,6,2,5,4,3]=>8
[2,6,4,1,3,5]=>[2,6,4,1,3,5]=>7
[2,6,4,1,5,3]=>[1,6,3,2,5,4]=>4
[2,6,4,3,1,5]=>[1,6,4,3,2,5]=>7
[2,6,4,3,5,1]=>[1,6,3,2,5,4]=>4
[2,6,4,5,1,3]=>[1,6,3,5,2,4]=>8
[2,6,4,5,3,1]=>[1,6,2,5,4,3]=>8
[2,6,5,1,3,4]=>[2,6,5,1,3,4]=>7
[2,6,5,1,4,3]=>[2,6,5,1,4,3]=>8
[2,6,5,3,1,4]=>[1,6,5,3,2,4]=>7
[2,6,5,3,4,1]=>[1,6,5,2,4,3]=>7
[2,6,5,4,1,3]=>[2,6,5,4,1,3]=>9
[2,6,5,4,3,1]=>[1,6,5,4,3,2]=>9
[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>6
[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>5
[3,1,2,5,6,4]=>[3,1,2,4,6,5]=>6
[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>5
[3,1,2,6,5,4]=>[3,1,2,6,5,4]=>6
[3,1,4,2,5,6]=>[2,1,4,3,5,6]=>4
[3,1,4,2,6,5]=>[2,1,4,3,6,5]=>9
[3,1,4,5,2,6]=>[2,1,3,5,4,6]=>5
[3,1,4,5,6,2]=>[2,1,3,4,6,5]=>6
[3,1,4,6,2,5]=>[2,1,4,6,3,5]=>8
[3,1,4,6,5,2]=>[2,1,3,6,5,4]=>6
[3,1,5,2,4,6]=>[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>[2,1,4,3,6,5]=>9
[3,1,5,4,2,6]=>[2,1,5,4,3,6]=>5
[3,1,5,4,6,2]=>[2,1,4,3,6,5]=>9
[3,1,5,6,2,4]=>[2,1,4,6,3,5]=>8
[3,1,5,6,4,2]=>[2,1,3,6,5,4]=>6
[3,1,6,2,4,5]=>[3,1,6,2,4,5]=>4
[3,1,6,2,5,4]=>[3,1,6,2,5,4]=>5
[3,1,6,4,2,5]=>[2,1,6,4,3,5]=>5
[3,1,6,4,5,2]=>[2,1,6,3,5,4]=>5
[3,1,6,5,2,4]=>[3,1,6,5,2,4]=>9
[3,1,6,5,4,2]=>[2,1,6,5,4,3]=>10
[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>2
[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>7
[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>6
[3,2,1,5,6,4]=>[3,2,1,4,6,5]=>7
[3,2,1,6,4,5]=>[3,2,1,6,4,5]=>6
[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>7
[3,2,4,1,5,6]=>[2,1,4,3,5,6]=>4
[3,2,4,1,6,5]=>[2,1,4,3,6,5]=>9
[3,2,4,5,1,6]=>[2,1,3,5,4,6]=>5
[3,2,4,5,6,1]=>[2,1,3,4,6,5]=>6
[3,2,4,6,1,5]=>[2,1,4,6,3,5]=>8
[3,2,4,6,5,1]=>[2,1,3,6,5,4]=>6
[3,2,5,1,4,6]=>[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>[2,1,4,3,6,5]=>9
[3,2,5,4,1,6]=>[2,1,5,4,3,6]=>5
[3,2,5,4,6,1]=>[2,1,4,3,6,5]=>9
[3,2,5,6,1,4]=>[2,1,4,6,3,5]=>8
[3,2,5,6,4,1]=>[2,1,3,6,5,4]=>6
[3,2,6,1,4,5]=>[3,2,6,1,4,5]=>5
[3,2,6,1,5,4]=>[3,2,6,1,5,4]=>6
[3,2,6,4,1,5]=>[2,1,6,4,3,5]=>5
[3,2,6,4,5,1]=>[2,1,6,3,5,4]=>5
[3,2,6,5,1,4]=>[3,2,6,5,1,4]=>10
[3,2,6,5,4,1]=>[2,1,6,5,4,3]=>10
[3,4,1,2,5,6]=>[2,4,1,3,5,6]=>3
[3,4,1,2,6,5]=>[2,4,1,3,6,5]=>8
[3,4,1,5,2,6]=>[1,3,2,5,4,6]=>6
[3,4,1,5,6,2]=>[1,3,2,4,6,5]=>7
[3,4,1,6,2,5]=>[2,4,1,6,3,5]=>7
[3,4,1,6,5,2]=>[1,3,2,6,5,4]=>7
[3,4,2,1,5,6]=>[1,4,3,2,5,6]=>3
[3,4,2,1,6,5]=>[1,4,3,2,6,5]=>8
[3,4,2,5,1,6]=>[1,3,2,5,4,6]=>6
[3,4,2,5,6,1]=>[1,3,2,4,6,5]=>7
[3,4,2,6,1,5]=>[1,4,3,6,2,5]=>7
[3,4,2,6,5,1]=>[1,3,2,6,5,4]=>7
[3,4,5,1,2,6]=>[1,3,5,2,4,6]=>5
[3,4,5,1,6,2]=>[1,2,4,3,6,5]=>8
[3,4,5,2,1,6]=>[1,2,5,4,3,6]=>4
[3,4,5,2,6,1]=>[1,2,4,3,6,5]=>8
[3,4,5,6,1,2]=>[1,2,4,6,3,5]=>7
[3,4,5,6,2,1]=>[1,2,3,6,5,4]=>5
[3,4,6,1,2,5]=>[2,4,6,1,3,5]=>6
[3,4,6,1,5,2]=>[1,3,6,2,5,4]=>6
[3,4,6,2,1,5]=>[1,4,6,3,2,5]=>6
[3,4,6,2,5,1]=>[1,3,6,2,5,4]=>6
[3,4,6,5,1,2]=>[1,3,6,5,2,4]=>10
[3,4,6,5,2,1]=>[1,2,6,5,4,3]=>9
[3,5,1,2,4,6]=>[3,5,1,2,4,6]=>3
[3,5,1,2,6,4]=>[2,4,1,3,6,5]=>8
[3,5,1,4,2,6]=>[2,5,1,4,3,6]=>4
[3,5,1,4,6,2]=>[2,4,1,3,6,5]=>8
[3,5,1,6,2,4]=>[2,4,1,6,3,5]=>7
[3,5,1,6,4,2]=>[1,3,2,6,5,4]=>7
[3,5,2,1,4,6]=>[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>[1,4,3,2,6,5]=>8
[3,5,2,4,1,6]=>[2,5,1,4,3,6]=>4
[3,5,2,4,6,1]=>[2,4,1,3,6,5]=>8
[3,5,2,6,1,4]=>[1,4,3,6,2,5]=>7
[3,5,2,6,4,1]=>[1,3,2,6,5,4]=>7
[3,5,4,1,2,6]=>[2,5,4,1,3,6]=>7
[3,5,4,1,6,2]=>[1,4,3,2,6,5]=>8
[3,5,4,2,1,6]=>[1,5,4,3,2,6]=>7
[3,5,4,2,6,1]=>[1,4,3,2,6,5]=>8
[3,5,4,6,1,2]=>[1,4,3,6,2,5]=>7
[3,5,4,6,2,1]=>[1,3,2,6,5,4]=>7
[3,5,6,1,2,4]=>[2,4,6,1,3,5]=>6
[3,5,6,1,4,2]=>[1,3,6,2,5,4]=>6
[3,5,6,2,1,4]=>[1,4,6,3,2,5]=>6
[3,5,6,2,4,1]=>[1,3,6,2,5,4]=>6
[3,5,6,4,1,2]=>[1,3,6,5,2,4]=>10
[3,5,6,4,2,1]=>[1,2,6,5,4,3]=>9
[3,6,1,2,4,5]=>[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>[3,6,1,2,5,4]=>4
[3,6,1,4,2,5]=>[2,6,1,4,3,5]=>4
[3,6,1,4,5,2]=>[2,6,1,3,5,4]=>4
[3,6,1,5,2,4]=>[3,6,1,5,2,4]=>8
[3,6,1,5,4,2]=>[2,6,1,5,4,3]=>9
[3,6,2,1,4,5]=>[3,6,2,1,4,5]=>4
[3,6,2,1,5,4]=>[3,6,2,1,5,4]=>5
[3,6,2,4,1,5]=>[2,6,1,4,3,5]=>4
[3,6,2,4,5,1]=>[2,6,1,3,5,4]=>4
[3,6,2,5,1,4]=>[3,6,2,5,1,4]=>9
[3,6,2,5,4,1]=>[2,6,1,5,4,3]=>9
[3,6,4,1,2,5]=>[2,6,4,1,3,5]=>7
[3,6,4,1,5,2]=>[1,6,3,2,5,4]=>4
[3,6,4,2,1,5]=>[1,6,4,3,2,5]=>7
[3,6,4,2,5,1]=>[1,6,3,2,5,4]=>4
[3,6,4,5,1,2]=>[1,6,3,5,2,4]=>8
[3,6,4,5,2,1]=>[1,6,2,5,4,3]=>8
[3,6,5,1,2,4]=>[3,6,5,1,2,4]=>7
[3,6,5,1,4,2]=>[2,6,5,1,4,3]=>8
[3,6,5,2,1,4]=>[3,6,5,2,1,4]=>8
[3,6,5,2,4,1]=>[2,6,5,1,4,3]=>8
[3,6,5,4,1,2]=>[2,6,5,4,1,3]=>9
[3,6,5,4,2,1]=>[1,6,5,4,3,2]=>9
[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>6
[4,1,2,5,3,6]=>[3,1,2,5,4,6]=>5
[4,1,2,5,6,3]=>[3,1,2,4,6,5]=>6
[4,1,2,6,3,5]=>[4,1,2,6,3,5]=>5
[4,1,2,6,5,3]=>[3,1,2,6,5,4]=>6
[4,1,3,2,5,6]=>[4,1,3,2,5,6]=>2
[4,1,3,2,6,5]=>[4,1,3,2,6,5]=>7
[4,1,3,5,2,6]=>[3,1,2,5,4,6]=>5
[4,1,3,5,6,2]=>[3,1,2,4,6,5]=>6
[4,1,3,6,2,5]=>[4,1,3,6,2,5]=>6
[4,1,3,6,5,2]=>[3,1,2,6,5,4]=>6
[4,1,5,2,3,6]=>[3,1,5,2,4,6]=>4
[4,1,5,2,6,3]=>[2,1,4,3,6,5]=>9
[4,1,5,3,2,6]=>[2,1,5,4,3,6]=>5
[4,1,5,3,6,2]=>[2,1,4,3,6,5]=>9
[4,1,5,6,2,3]=>[2,1,4,6,3,5]=>8
[4,1,5,6,3,2]=>[2,1,3,6,5,4]=>6
[4,1,6,2,3,5]=>[4,1,6,2,3,5]=>4
[4,1,6,2,5,3]=>[3,1,6,2,5,4]=>5
[4,1,6,3,2,5]=>[4,1,6,3,2,5]=>5
[4,1,6,3,5,2]=>[3,1,6,2,5,4]=>5
[4,1,6,5,2,3]=>[3,1,6,5,2,4]=>9
[4,1,6,5,3,2]=>[2,1,6,5,4,3]=>10
[4,2,1,3,5,6]=>[4,2,1,3,5,6]=>2
[4,2,1,3,6,5]=>[4,2,1,3,6,5]=>7
[4,2,1,5,3,6]=>[3,2,1,5,4,6]=>6
[4,2,1,5,6,3]=>[3,2,1,4,6,5]=>7
[4,2,1,6,3,5]=>[4,2,1,6,3,5]=>6
[4,2,1,6,5,3]=>[3,2,1,6,5,4]=>7
[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>2
[4,2,3,1,6,5]=>[4,1,3,2,6,5]=>7
[4,2,3,5,1,6]=>[3,1,2,5,4,6]=>5
[4,2,3,5,6,1]=>[3,1,2,4,6,5]=>6
[4,2,3,6,1,5]=>[4,1,3,6,2,5]=>6
[4,2,3,6,5,1]=>[3,1,2,6,5,4]=>6
[4,2,5,1,3,6]=>[3,2,5,1,4,6]=>5
[4,2,5,1,6,3]=>[2,1,4,3,6,5]=>9
[4,2,5,3,1,6]=>[2,1,5,4,3,6]=>5
[4,2,5,3,6,1]=>[2,1,4,3,6,5]=>9
[4,2,5,6,1,3]=>[2,1,4,6,3,5]=>8
[4,2,5,6,3,1]=>[2,1,3,6,5,4]=>6
[4,2,6,1,3,5]=>[4,2,6,1,3,5]=>5
[4,2,6,1,5,3]=>[3,2,6,1,5,4]=>6
[4,2,6,3,1,5]=>[4,1,6,3,2,5]=>5
[4,2,6,3,5,1]=>[3,1,6,2,5,4]=>5
[4,2,6,5,1,3]=>[3,2,6,5,1,4]=>10
[4,2,6,5,3,1]=>[2,1,6,5,4,3]=>10
[4,3,1,2,5,6]=>[4,3,1,2,5,6]=>4
[4,3,1,2,6,5]=>[4,3,1,2,6,5]=>9
[4,3,1,5,2,6]=>[3,2,1,5,4,6]=>6
[4,3,1,5,6,2]=>[3,2,1,4,6,5]=>7
[4,3,1,6,2,5]=>[4,3,1,6,2,5]=>8
[4,3,1,6,5,2]=>[3,2,1,6,5,4]=>7
[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>5
[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>10
[4,3,2,5,1,6]=>[3,2,1,5,4,6]=>6
[4,3,2,5,6,1]=>[3,2,1,4,6,5]=>7
[4,3,2,6,1,5]=>[4,3,2,6,1,5]=>9
[4,3,2,6,5,1]=>[3,2,1,6,5,4]=>7
[4,3,5,1,2,6]=>[3,2,5,1,4,6]=>5
[4,3,5,1,6,2]=>[2,1,4,3,6,5]=>9
[4,3,5,2,1,6]=>[2,1,5,4,3,6]=>5
[4,3,5,2,6,1]=>[2,1,4,3,6,5]=>9
[4,3,5,6,1,2]=>[2,1,4,6,3,5]=>8
[4,3,5,6,2,1]=>[2,1,3,6,5,4]=>6
[4,3,6,1,2,5]=>[4,3,6,1,2,5]=>7
[4,3,6,1,5,2]=>[3,2,6,1,5,4]=>6
[4,3,6,2,1,5]=>[4,3,6,2,1,5]=>8
[4,3,6,2,5,1]=>[3,2,6,1,5,4]=>6
[4,3,6,5,1,2]=>[3,2,6,5,1,4]=>10
[4,3,6,5,2,1]=>[2,1,6,5,4,3]=>10
[4,5,1,2,3,6]=>[3,5,1,2,4,6]=>3
[4,5,1,2,6,3]=>[2,4,1,3,6,5]=>8
[4,5,1,3,2,6]=>[2,5,1,4,3,6]=>4
[4,5,1,3,6,2]=>[2,4,1,3,6,5]=>8
[4,5,1,6,2,3]=>[2,4,1,6,3,5]=>7
[4,5,1,6,3,2]=>[1,3,2,6,5,4]=>7
[4,5,2,1,3,6]=>[3,5,2,1,4,6]=>4
[4,5,2,1,6,3]=>[1,4,3,2,6,5]=>8
[4,5,2,3,1,6]=>[2,5,1,4,3,6]=>4
[4,5,2,3,6,1]=>[2,4,1,3,6,5]=>8
[4,5,2,6,1,3]=>[1,4,3,6,2,5]=>7
[4,5,2,6,3,1]=>[1,3,2,6,5,4]=>7
[4,5,3,1,2,6]=>[2,5,4,1,3,6]=>7
[4,5,3,1,6,2]=>[1,4,3,2,6,5]=>8
[4,5,3,2,1,6]=>[1,5,4,3,2,6]=>7
[4,5,3,2,6,1]=>[1,4,3,2,6,5]=>8
[4,5,3,6,1,2]=>[1,4,3,6,2,5]=>7
[4,5,3,6,2,1]=>[1,3,2,6,5,4]=>7
[4,5,6,1,2,3]=>[2,4,6,1,3,5]=>6
[4,5,6,1,3,2]=>[1,3,6,2,5,4]=>6
[4,5,6,2,1,3]=>[1,4,6,3,2,5]=>6
[4,5,6,2,3,1]=>[1,3,6,2,5,4]=>6
[4,5,6,3,1,2]=>[1,3,6,5,2,4]=>10
[4,5,6,3,2,1]=>[1,2,6,5,4,3]=>9
[4,6,1,2,3,5]=>[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>[3,6,1,2,5,4]=>4
[4,6,1,3,2,5]=>[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>[3,6,1,2,5,4]=>4
[4,6,1,5,2,3]=>[3,6,1,5,2,4]=>8
[4,6,1,5,3,2]=>[2,6,1,5,4,3]=>9
[4,6,2,1,3,5]=>[4,6,2,1,3,5]=>4
[4,6,2,1,5,3]=>[3,6,2,1,5,4]=>5
[4,6,2,3,1,5]=>[4,6,1,3,2,5]=>4
[4,6,2,3,5,1]=>[3,6,1,2,5,4]=>4
[4,6,2,5,1,3]=>[3,6,2,5,1,4]=>9
[4,6,2,5,3,1]=>[2,6,1,5,4,3]=>9
[4,6,3,1,2,5]=>[4,6,3,1,2,5]=>5
[4,6,3,1,5,2]=>[3,6,2,1,5,4]=>5
[4,6,3,2,1,5]=>[4,6,3,2,1,5]=>6
[4,6,3,2,5,1]=>[3,6,2,1,5,4]=>5
[4,6,3,5,1,2]=>[3,6,2,5,1,4]=>9
[4,6,3,5,2,1]=>[2,6,1,5,4,3]=>9
[4,6,5,1,2,3]=>[3,6,5,1,2,4]=>7
[4,6,5,1,3,2]=>[2,6,5,1,4,3]=>8
[4,6,5,2,1,3]=>[3,6,5,2,1,4]=>8
[4,6,5,2,3,1]=>[2,6,5,1,4,3]=>8
[4,6,5,3,1,2]=>[2,6,5,4,1,3]=>9
[4,6,5,3,2,1]=>[1,6,5,4,3,2]=>9
[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>[4,1,2,3,6,5]=>6
[5,1,2,4,3,6]=>[5,1,2,4,3,6]=>2
[5,1,2,4,6,3]=>[4,1,2,3,6,5]=>6
[5,1,2,6,3,4]=>[4,1,2,6,3,5]=>5
[5,1,2,6,4,3]=>[3,1,2,6,5,4]=>6
[5,1,3,2,4,6]=>[5,1,3,2,4,6]=>2
[5,1,3,2,6,4]=>[4,1,3,2,6,5]=>7
[5,1,3,4,2,6]=>[5,1,2,4,3,6]=>2
[5,1,3,4,6,2]=>[4,1,2,3,6,5]=>6
[5,1,3,6,2,4]=>[4,1,3,6,2,5]=>6
[5,1,3,6,4,2]=>[3,1,2,6,5,4]=>6
[5,1,4,2,3,6]=>[5,1,4,2,3,6]=>5
[5,1,4,2,6,3]=>[4,1,3,2,6,5]=>7
[5,1,4,3,2,6]=>[5,1,4,3,2,6]=>6
[5,1,4,3,6,2]=>[4,1,3,2,6,5]=>7
[5,1,4,6,2,3]=>[4,1,3,6,2,5]=>6
[5,1,4,6,3,2]=>[3,1,2,6,5,4]=>6
[5,1,6,2,3,4]=>[4,1,6,2,3,5]=>4
[5,1,6,2,4,3]=>[3,1,6,2,5,4]=>5
[5,1,6,3,2,4]=>[4,1,6,3,2,5]=>5
[5,1,6,3,4,2]=>[3,1,6,2,5,4]=>5
[5,1,6,4,2,3]=>[3,1,6,5,2,4]=>9
[5,1,6,4,3,2]=>[2,1,6,5,4,3]=>10
[5,2,1,3,4,6]=>[5,2,1,3,4,6]=>2
[5,2,1,3,6,4]=>[4,2,1,3,6,5]=>7
[5,2,1,4,3,6]=>[5,2,1,4,3,6]=>3
[5,2,1,4,6,3]=>[4,2,1,3,6,5]=>7
[5,2,1,6,3,4]=>[4,2,1,6,3,5]=>6
[5,2,1,6,4,3]=>[3,2,1,6,5,4]=>7
[5,2,3,1,4,6]=>[5,1,3,2,4,6]=>2
[5,2,3,1,6,4]=>[4,1,3,2,6,5]=>7
[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>2
[5,2,3,4,6,1]=>[4,1,2,3,6,5]=>6
[5,2,3,6,1,4]=>[4,1,3,6,2,5]=>6
[5,2,3,6,4,1]=>[3,1,2,6,5,4]=>6
[5,2,4,1,3,6]=>[5,2,4,1,3,6]=>6
[5,2,4,1,6,3]=>[4,1,3,2,6,5]=>7
[5,2,4,3,1,6]=>[5,1,4,3,2,6]=>6
[5,2,4,3,6,1]=>[4,1,3,2,6,5]=>7
[5,2,4,6,1,3]=>[4,1,3,6,2,5]=>6
[5,2,4,6,3,1]=>[3,1,2,6,5,4]=>6
[5,2,6,1,3,4]=>[4,2,6,1,3,5]=>5
[5,2,6,1,4,3]=>[3,2,6,1,5,4]=>6
[5,2,6,3,1,4]=>[4,1,6,3,2,5]=>5
[5,2,6,3,4,1]=>[3,1,6,2,5,4]=>5
[5,2,6,4,1,3]=>[3,2,6,5,1,4]=>10
[5,2,6,4,3,1]=>[2,1,6,5,4,3]=>10
[5,3,1,2,4,6]=>[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>[4,3,1,2,6,5]=>9
[5,3,1,4,2,6]=>[5,2,1,4,3,6]=>3
[5,3,1,4,6,2]=>[4,2,1,3,6,5]=>7
[5,3,1,6,2,4]=>[4,3,1,6,2,5]=>8
[5,3,1,6,4,2]=>[3,2,1,6,5,4]=>7
[5,3,2,1,4,6]=>[5,3,2,1,4,6]=>5
[5,3,2,1,6,4]=>[4,3,2,1,6,5]=>10
[5,3,2,4,1,6]=>[5,2,1,4,3,6]=>3
[5,3,2,4,6,1]=>[4,2,1,3,6,5]=>7
[5,3,2,6,1,4]=>[4,3,2,6,1,5]=>9
[5,3,2,6,4,1]=>[3,2,1,6,5,4]=>7
[5,3,4,1,2,6]=>[5,2,4,1,3,6]=>6
[5,3,4,1,6,2]=>[4,1,3,2,6,5]=>7
[5,3,4,2,1,6]=>[5,1,4,3,2,6]=>6
[5,3,4,2,6,1]=>[4,1,3,2,6,5]=>7
[5,3,4,6,1,2]=>[4,1,3,6,2,5]=>6
[5,3,4,6,2,1]=>[3,1,2,6,5,4]=>6
[5,3,6,1,2,4]=>[4,3,6,1,2,5]=>7
[5,3,6,1,4,2]=>[3,2,6,1,5,4]=>6
[5,3,6,2,1,4]=>[4,3,6,2,1,5]=>8
[5,3,6,2,4,1]=>[3,2,6,1,5,4]=>6
[5,3,6,4,1,2]=>[3,2,6,5,1,4]=>10
[5,3,6,4,2,1]=>[2,1,6,5,4,3]=>10
[5,4,1,2,3,6]=>[5,4,1,2,3,6]=>4
[5,4,1,2,6,3]=>[4,3,1,2,6,5]=>9
[5,4,1,3,2,6]=>[5,4,1,3,2,6]=>5
[5,4,1,3,6,2]=>[4,3,1,2,6,5]=>9
[5,4,1,6,2,3]=>[4,3,1,6,2,5]=>8
[5,4,1,6,3,2]=>[3,2,1,6,5,4]=>7
[5,4,2,1,3,6]=>[5,4,2,1,3,6]=>5
[5,4,2,1,6,3]=>[4,3,2,1,6,5]=>10
[5,4,2,3,1,6]=>[5,4,1,3,2,6]=>5
[5,4,2,3,6,1]=>[4,3,1,2,6,5]=>9
[5,4,2,6,1,3]=>[4,3,2,6,1,5]=>9
[5,4,2,6,3,1]=>[3,2,1,6,5,4]=>7
[5,4,3,1,2,6]=>[5,4,3,1,2,6]=>6
[5,4,3,1,6,2]=>[4,3,2,1,6,5]=>10
[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>7
[5,4,3,2,6,1]=>[4,3,2,1,6,5]=>10
[5,4,3,6,1,2]=>[4,3,2,6,1,5]=>9
[5,4,3,6,2,1]=>[3,2,1,6,5,4]=>7
[5,4,6,1,2,3]=>[4,3,6,1,2,5]=>7
[5,4,6,1,3,2]=>[3,2,6,1,5,4]=>6
[5,4,6,2,1,3]=>[4,3,6,2,1,5]=>8
[5,4,6,2,3,1]=>[3,2,6,1,5,4]=>6
[5,4,6,3,1,2]=>[3,2,6,5,1,4]=>10
[5,4,6,3,2,1]=>[2,1,6,5,4,3]=>10
[5,6,1,2,3,4]=>[4,6,1,2,3,5]=>3
[5,6,1,2,4,3]=>[3,6,1,2,5,4]=>4
[5,6,1,3,2,4]=>[4,6,1,3,2,5]=>4
[5,6,1,3,4,2]=>[3,6,1,2,5,4]=>4
[5,6,1,4,2,3]=>[3,6,1,5,2,4]=>8
[5,6,1,4,3,2]=>[2,6,1,5,4,3]=>9
[5,6,2,1,3,4]=>[4,6,2,1,3,5]=>4
[5,6,2,1,4,3]=>[3,6,2,1,5,4]=>5
[5,6,2,3,1,4]=>[4,6,1,3,2,5]=>4
[5,6,2,3,4,1]=>[3,6,1,2,5,4]=>4
[5,6,2,4,1,3]=>[3,6,2,5,1,4]=>9
[5,6,2,4,3,1]=>[2,6,1,5,4,3]=>9
[5,6,3,1,2,4]=>[4,6,3,1,2,5]=>5
[5,6,3,1,4,2]=>[3,6,2,1,5,4]=>5
[5,6,3,2,1,4]=>[4,6,3,2,1,5]=>6
[5,6,3,2,4,1]=>[3,6,2,1,5,4]=>5
[5,6,3,4,1,2]=>[3,6,2,5,1,4]=>9
[5,6,3,4,2,1]=>[2,6,1,5,4,3]=>9
[5,6,4,1,2,3]=>[3,6,5,1,2,4]=>7
[5,6,4,1,3,2]=>[2,6,5,1,4,3]=>8
[5,6,4,2,1,3]=>[3,6,5,2,1,4]=>8
[5,6,4,2,3,1]=>[2,6,5,1,4,3]=>8
[5,6,4,3,1,2]=>[2,6,5,4,1,3]=>9
[5,6,4,3,2,1]=>[1,6,5,4,3,2]=>9
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>[6,1,2,3,5,4]=>2
[6,1,2,4,3,5]=>[6,1,2,4,3,5]=>2
[6,1,2,4,5,3]=>[6,1,2,3,5,4]=>2
[6,1,2,5,3,4]=>[6,1,2,5,3,4]=>6
[6,1,2,5,4,3]=>[6,1,2,5,4,3]=>7
[6,1,3,2,4,5]=>[6,1,3,2,4,5]=>2
[6,1,3,2,5,4]=>[6,1,3,2,5,4]=>3
[6,1,3,4,2,5]=>[6,1,2,4,3,5]=>2
[6,1,3,4,5,2]=>[6,1,2,3,5,4]=>2
[6,1,3,5,2,4]=>[6,1,3,5,2,4]=>7
[6,1,3,5,4,2]=>[6,1,2,5,4,3]=>7
[6,1,4,2,3,5]=>[6,1,4,2,3,5]=>5
[6,1,4,2,5,3]=>[6,1,3,2,5,4]=>3
[6,1,4,3,2,5]=>[6,1,4,3,2,5]=>6
[6,1,4,3,5,2]=>[6,1,3,2,5,4]=>3
[6,1,4,5,2,3]=>[6,1,3,5,2,4]=>7
[6,1,4,5,3,2]=>[6,1,2,5,4,3]=>7
[6,1,5,2,3,4]=>[6,1,5,2,3,4]=>5
[6,1,5,2,4,3]=>[6,1,5,2,4,3]=>6
[6,1,5,3,2,4]=>[6,1,5,3,2,4]=>6
[6,1,5,3,4,2]=>[6,1,5,2,4,3]=>6
[6,1,5,4,2,3]=>[6,1,5,4,2,3]=>7
[6,1,5,4,3,2]=>[6,1,5,4,3,2]=>8
[6,2,1,3,4,5]=>[6,2,1,3,4,5]=>2
[6,2,1,3,5,4]=>[6,2,1,3,5,4]=>3
[6,2,1,4,3,5]=>[6,2,1,4,3,5]=>3
[6,2,1,4,5,3]=>[6,2,1,3,5,4]=>3
[6,2,1,5,3,4]=>[6,2,1,5,3,4]=>7
[6,2,1,5,4,3]=>[6,2,1,5,4,3]=>8
[6,2,3,1,4,5]=>[6,1,3,2,4,5]=>2
[6,2,3,1,5,4]=>[6,1,3,2,5,4]=>3
[6,2,3,4,1,5]=>[6,1,2,4,3,5]=>2
[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>2
[6,2,3,5,1,4]=>[6,1,3,5,2,4]=>7
[6,2,3,5,4,1]=>[6,1,2,5,4,3]=>7
[6,2,4,1,3,5]=>[6,2,4,1,3,5]=>6
[6,2,4,1,5,3]=>[6,1,3,2,5,4]=>3
[6,2,4,3,1,5]=>[6,1,4,3,2,5]=>6
[6,2,4,3,5,1]=>[6,1,3,2,5,4]=>3
[6,2,4,5,1,3]=>[6,1,3,5,2,4]=>7
[6,2,4,5,3,1]=>[6,1,2,5,4,3]=>7
[6,2,5,1,3,4]=>[6,2,5,1,3,4]=>6
[6,2,5,1,4,3]=>[6,2,5,1,4,3]=>7
[6,2,5,3,1,4]=>[6,1,5,3,2,4]=>6
[6,2,5,3,4,1]=>[6,1,5,2,4,3]=>6
[6,2,5,4,1,3]=>[6,2,5,4,1,3]=>8
[6,2,5,4,3,1]=>[6,1,5,4,3,2]=>8
[6,3,1,2,4,5]=>[6,3,1,2,4,5]=>4
[6,3,1,2,5,4]=>[6,3,1,2,5,4]=>5
[6,3,1,4,2,5]=>[6,2,1,4,3,5]=>3
[6,3,1,4,5,2]=>[6,2,1,3,5,4]=>3
[6,3,1,5,2,4]=>[6,3,1,5,2,4]=>9
[6,3,1,5,4,2]=>[6,2,1,5,4,3]=>8
[6,3,2,1,4,5]=>[6,3,2,1,4,5]=>5
[6,3,2,1,5,4]=>[6,3,2,1,5,4]=>6
[6,3,2,4,1,5]=>[6,2,1,4,3,5]=>3
[6,3,2,4,5,1]=>[6,2,1,3,5,4]=>3
[6,3,2,5,1,4]=>[6,3,2,5,1,4]=>10
[6,3,2,5,4,1]=>[6,2,1,5,4,3]=>8
[6,3,4,1,2,5]=>[6,2,4,1,3,5]=>6
[6,3,4,1,5,2]=>[6,1,3,2,5,4]=>3
[6,3,4,2,1,5]=>[6,1,4,3,2,5]=>6
[6,3,4,2,5,1]=>[6,1,3,2,5,4]=>3
[6,3,4,5,1,2]=>[6,1,3,5,2,4]=>7
[6,3,4,5,2,1]=>[6,1,2,5,4,3]=>7
[6,3,5,1,2,4]=>[6,3,5,1,2,4]=>8
[6,3,5,1,4,2]=>[6,2,5,1,4,3]=>7
[6,3,5,2,1,4]=>[6,3,5,2,1,4]=>9
[6,3,5,2,4,1]=>[6,2,5,1,4,3]=>7
[6,3,5,4,1,2]=>[6,2,5,4,1,3]=>8
[6,3,5,4,2,1]=>[6,1,5,4,3,2]=>8
[6,4,1,2,3,5]=>[6,4,1,2,3,5]=>4
[6,4,1,2,5,3]=>[6,3,1,2,5,4]=>5
[6,4,1,3,2,5]=>[6,4,1,3,2,5]=>5
[6,4,1,3,5,2]=>[6,3,1,2,5,4]=>5
[6,4,1,5,2,3]=>[6,3,1,5,2,4]=>9
[6,4,1,5,3,2]=>[6,2,1,5,4,3]=>8
[6,4,2,1,3,5]=>[6,4,2,1,3,5]=>5
[6,4,2,1,5,3]=>[6,3,2,1,5,4]=>6
[6,4,2,3,1,5]=>[6,4,1,3,2,5]=>5
[6,4,2,3,5,1]=>[6,3,1,2,5,4]=>5
[6,4,2,5,1,3]=>[6,3,2,5,1,4]=>10
[6,4,2,5,3,1]=>[6,2,1,5,4,3]=>8
[6,4,3,1,2,5]=>[6,4,3,1,2,5]=>6
[6,4,3,1,5,2]=>[6,3,2,1,5,4]=>6
[6,4,3,2,1,5]=>[6,4,3,2,1,5]=>7
[6,4,3,2,5,1]=>[6,3,2,1,5,4]=>6
[6,4,3,5,1,2]=>[6,3,2,5,1,4]=>10
[6,4,3,5,2,1]=>[6,2,1,5,4,3]=>8
[6,4,5,1,2,3]=>[6,3,5,1,2,4]=>8
[6,4,5,1,3,2]=>[6,2,5,1,4,3]=>7
[6,4,5,2,1,3]=>[6,3,5,2,1,4]=>9
[6,4,5,2,3,1]=>[6,2,5,1,4,3]=>7
[6,4,5,3,1,2]=>[6,2,5,4,1,3]=>8
[6,4,5,3,2,1]=>[6,1,5,4,3,2]=>8
[6,5,1,2,3,4]=>[6,5,1,2,3,4]=>4
[6,5,1,2,4,3]=>[6,5,1,2,4,3]=>5
[6,5,1,3,2,4]=>[6,5,1,3,2,4]=>5
[6,5,1,3,4,2]=>[6,5,1,2,4,3]=>5
[6,5,1,4,2,3]=>[6,5,1,4,2,3]=>6
[6,5,1,4,3,2]=>[6,5,1,4,3,2]=>7
[6,5,2,1,3,4]=>[6,5,2,1,3,4]=>5
[6,5,2,1,4,3]=>[6,5,2,1,4,3]=>6
[6,5,2,3,1,4]=>[6,5,1,3,2,4]=>5
[6,5,2,3,4,1]=>[6,5,1,2,4,3]=>5
[6,5,2,4,1,3]=>[6,5,2,4,1,3]=>7
[6,5,2,4,3,1]=>[6,5,1,4,3,2]=>7
[6,5,3,1,2,4]=>[6,5,3,1,2,4]=>6
[6,5,3,1,4,2]=>[6,5,2,1,4,3]=>6
[6,5,3,2,1,4]=>[6,5,3,2,1,4]=>7
[6,5,3,2,4,1]=>[6,5,2,1,4,3]=>6
[6,5,3,4,1,2]=>[6,5,2,4,1,3]=>7
[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>7
[6,5,4,1,2,3]=>[6,5,4,1,2,3]=>9
[6,5,4,1,3,2]=>[6,5,4,1,3,2]=>10
[6,5,4,2,1,3]=>[6,5,4,2,1,3]=>10
[6,5,4,2,3,1]=>[6,5,4,1,3,2]=>10
[6,5,4,3,1,2]=>[6,5,4,3,1,2]=>11
[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>12
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Description
The Denert index of a permutation.
It is defined as
$$ \begin{align*} den(\sigma) &= \#\{ 1\leq l < k \leq n : \sigma(k) < \sigma(l) \leq k \} \\ &+ \#\{ 1\leq l < k \leq n : \sigma(l) \leq k < \sigma(k) \} \\ &+ \#\{ 1\leq l < k \leq n : k < \sigma(k) < \sigma(l) \} \end{align*} $$
where $n$ is the size of $\sigma$. It was studied by Denert in [1], and it was shown by Foata and Zeilberger in [2] that the bistatistic $(exc,den)$ is Euler-Mahonian. Here, $exc$ is the number of weak exceedences, see St000155The number of exceedances (also excedences) of a permutation..
It is defined as
$$ \begin{align*} den(\sigma) &= \#\{ 1\leq l < k \leq n : \sigma(k) < \sigma(l) \leq k \} \\ &+ \#\{ 1\leq l < k \leq n : \sigma(l) \leq k < \sigma(k) \} \\ &+ \#\{ 1\leq l < k \leq n : k < \sigma(k) < \sigma(l) \} \end{align*} $$
where $n$ is the size of $\sigma$. It was studied by Denert in [1], and it was shown by Foata and Zeilberger in [2] that the bistatistic $(exc,den)$ is Euler-Mahonian. Here, $exc$ is the number of weak exceedences, see St000155The number of exceedances (also excedences) of a permutation..
Map
Inverse fireworks map
Description
Sends a permutation to an inverse fireworks permutation.
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..
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