Identifier
-
Mp00126:
Permutations
—cactus evacuation⟶
Permutations
St000638: Permutations ⟶ ℤ
Values
=>
[1]=>[1]=>1
[1,2]=>[1,2]=>1
[2,1]=>[2,1]=>2
[1,2,3]=>[1,2,3]=>1
[1,3,2]=>[3,1,2]=>3
[2,1,3]=>[2,3,1]=>2
[2,3,1]=>[2,1,3]=>3
[3,1,2]=>[1,3,2]=>2
[3,2,1]=>[3,2,1]=>2
[1,2,3,4]=>[1,2,3,4]=>1
[1,2,4,3]=>[4,1,2,3]=>3
[1,3,2,4]=>[1,3,2,4]=>3
[1,3,4,2]=>[3,1,2,4]=>3
[1,4,2,3]=>[1,4,2,3]=>3
[1,4,3,2]=>[4,3,1,2]=>3
[2,1,3,4]=>[2,3,4,1]=>2
[2,1,4,3]=>[2,1,4,3]=>4
[2,3,1,4]=>[2,3,1,4]=>3
[2,3,4,1]=>[2,1,3,4]=>3
[2,4,1,3]=>[2,4,1,3]=>3
[2,4,3,1]=>[4,2,1,3]=>3
[3,1,2,4]=>[1,3,4,2]=>2
[3,1,4,2]=>[3,1,4,2]=>4
[3,2,1,4]=>[3,4,2,1]=>2
[3,2,4,1]=>[3,2,4,1]=>4
[3,4,1,2]=>[3,4,1,2]=>3
[3,4,2,1]=>[3,2,1,4]=>3
[4,1,2,3]=>[1,2,4,3]=>2
[4,1,3,2]=>[4,1,3,2]=>4
[4,2,1,3]=>[2,4,3,1]=>2
[4,2,3,1]=>[4,2,3,1]=>4
[4,3,1,2]=>[1,4,3,2]=>2
[4,3,2,1]=>[4,3,2,1]=>2
[1,2,3,4,5]=>[1,2,3,4,5]=>1
[1,2,3,5,4]=>[5,1,2,3,4]=>3
[1,2,4,3,5]=>[1,4,2,3,5]=>3
[1,2,4,5,3]=>[4,1,2,3,5]=>3
[1,2,5,3,4]=>[1,5,2,3,4]=>3
[1,2,5,4,3]=>[5,4,1,2,3]=>3
[1,3,2,4,5]=>[1,3,4,2,5]=>3
[1,3,2,5,4]=>[3,1,5,2,4]=>5
[1,3,4,2,5]=>[1,3,2,4,5]=>3
[1,3,4,5,2]=>[3,1,2,4,5]=>3
[1,3,5,2,4]=>[3,5,1,2,4]=>3
[1,3,5,4,2]=>[5,3,1,2,4]=>3
[1,4,2,3,5]=>[1,2,4,3,5]=>3
[1,4,2,5,3]=>[4,1,5,2,3]=>5
[1,4,3,2,5]=>[1,4,3,2,5]=>3
[1,4,3,5,2]=>[4,1,3,2,5]=>5
[1,4,5,2,3]=>[4,5,1,2,3]=>3
[1,4,5,3,2]=>[4,3,1,2,5]=>3
[1,5,2,3,4]=>[1,2,5,3,4]=>3
[1,5,2,4,3]=>[5,1,4,2,3]=>5
[1,5,3,2,4]=>[1,5,3,2,4]=>3
[1,5,3,4,2]=>[5,1,3,2,4]=>5
[1,5,4,2,3]=>[1,5,4,2,3]=>3
[1,5,4,3,2]=>[5,4,3,1,2]=>3
[2,1,3,4,5]=>[2,3,4,5,1]=>2
[2,1,3,5,4]=>[2,1,3,5,4]=>4
[2,1,4,3,5]=>[2,4,1,5,3]=>4
[2,1,4,5,3]=>[2,1,4,5,3]=>4
[2,1,5,3,4]=>[2,3,1,5,4]=>4
[2,1,5,4,3]=>[5,2,1,4,3]=>4
[2,3,1,4,5]=>[2,3,4,1,5]=>3
[2,3,1,5,4]=>[2,1,5,3,4]=>5
[2,3,4,1,5]=>[2,3,1,4,5]=>3
[2,3,4,5,1]=>[2,1,3,4,5]=>3
[2,3,5,1,4]=>[2,5,1,3,4]=>3
[2,3,5,4,1]=>[5,2,1,3,4]=>3
[2,4,1,3,5]=>[2,4,5,1,3]=>3
[2,4,1,5,3]=>[2,1,4,3,5]=>5
[2,4,3,1,5]=>[2,4,3,1,5]=>3
[2,4,3,5,1]=>[4,2,3,1,5]=>5
[2,4,5,1,3]=>[2,4,1,3,5]=>3
[2,4,5,3,1]=>[4,2,1,3,5]=>3
[2,5,1,3,4]=>[2,3,5,1,4]=>3
[2,5,1,4,3]=>[5,2,4,1,3]=>5
[2,5,3,1,4]=>[2,5,3,1,4]=>3
[2,5,3,4,1]=>[5,2,3,1,4]=>5
[2,5,4,1,3]=>[2,5,4,1,3]=>3
[2,5,4,3,1]=>[5,4,2,1,3]=>3
[3,1,2,4,5]=>[1,3,4,5,2]=>2
[3,1,2,5,4]=>[3,1,2,5,4]=>4
[3,1,4,2,5]=>[3,4,1,5,2]=>4
[3,1,4,5,2]=>[3,1,4,5,2]=>4
[3,1,5,2,4]=>[1,3,2,5,4]=>4
[3,1,5,4,2]=>[5,3,1,4,2]=>4
[3,2,1,4,5]=>[3,4,5,2,1]=>2
[3,2,1,5,4]=>[3,2,5,4,1]=>4
[3,2,4,1,5]=>[3,4,2,5,1]=>4
[3,2,4,5,1]=>[3,2,4,5,1]=>4
[3,2,5,1,4]=>[3,5,2,4,1]=>4
[3,2,5,4,1]=>[3,2,1,5,4]=>4
[3,4,1,2,5]=>[3,4,5,1,2]=>3
[3,4,1,5,2]=>[3,1,4,2,5]=>5
[3,4,2,1,5]=>[3,4,2,1,5]=>3
[3,4,2,5,1]=>[3,2,4,1,5]=>5
[3,4,5,1,2]=>[3,4,1,2,5]=>3
[3,4,5,2,1]=>[3,2,1,4,5]=>3
[3,5,1,2,4]=>[1,3,5,2,4]=>3
[3,5,1,4,2]=>[5,3,4,1,2]=>5
[3,5,2,1,4]=>[3,5,2,1,4]=>3
[3,5,2,4,1]=>[3,2,5,1,4]=>5
[3,5,4,1,2]=>[3,5,4,1,2]=>3
[3,5,4,2,1]=>[5,3,2,1,4]=>3
[4,1,2,3,5]=>[1,2,4,5,3]=>2
[4,1,2,5,3]=>[4,1,2,5,3]=>4
[4,1,3,2,5]=>[1,4,3,5,2]=>4
[4,1,3,5,2]=>[4,1,3,5,2]=>4
[4,1,5,2,3]=>[1,4,2,5,3]=>4
[4,1,5,3,2]=>[4,3,1,5,2]=>4
[4,2,1,3,5]=>[2,4,5,3,1]=>2
[4,2,1,5,3]=>[4,2,5,3,1]=>4
[4,2,3,1,5]=>[2,4,3,5,1]=>4
[4,2,3,5,1]=>[4,2,3,5,1]=>4
[4,2,5,1,3]=>[4,5,2,3,1]=>4
[4,2,5,3,1]=>[4,2,1,5,3]=>4
[4,3,1,2,5]=>[1,4,5,3,2]=>2
[4,3,1,5,2]=>[4,1,5,3,2]=>4
[4,3,2,1,5]=>[4,5,3,2,1]=>2
[4,3,2,5,1]=>[4,3,5,2,1]=>4
[4,3,5,1,2]=>[4,5,1,3,2]=>4
[4,3,5,2,1]=>[4,3,2,5,1]=>4
[4,5,1,2,3]=>[1,4,5,2,3]=>3
[4,5,1,3,2]=>[4,3,5,1,2]=>5
[4,5,2,1,3]=>[4,5,2,1,3]=>3
[4,5,2,3,1]=>[4,2,5,1,3]=>5
[4,5,3,1,2]=>[4,5,3,1,2]=>3
[4,5,3,2,1]=>[4,3,2,1,5]=>3
[5,1,2,3,4]=>[1,2,3,5,4]=>2
[5,1,2,4,3]=>[5,1,2,4,3]=>4
[5,1,3,2,4]=>[1,5,3,4,2]=>4
[5,1,3,4,2]=>[5,1,3,4,2]=>4
[5,1,4,2,3]=>[1,5,2,4,3]=>4
[5,1,4,3,2]=>[5,4,1,3,2]=>4
[5,2,1,3,4]=>[2,3,5,4,1]=>2
[5,2,1,4,3]=>[2,1,5,4,3]=>4
[5,2,3,1,4]=>[2,5,3,4,1]=>4
[5,2,3,4,1]=>[5,2,3,4,1]=>4
[5,2,4,1,3]=>[2,5,1,4,3]=>4
[5,2,4,3,1]=>[5,4,2,3,1]=>4
[5,3,1,2,4]=>[1,3,5,4,2]=>2
[5,3,1,4,2]=>[3,1,5,4,2]=>4
[5,3,2,1,4]=>[3,5,4,2,1]=>2
[5,3,2,4,1]=>[5,3,4,2,1]=>4
[5,3,4,1,2]=>[3,5,1,4,2]=>4
[5,3,4,2,1]=>[5,3,2,4,1]=>4
[5,4,1,2,3]=>[1,2,5,4,3]=>2
[5,4,1,3,2]=>[5,1,4,3,2]=>4
[5,4,2,1,3]=>[2,5,4,3,1]=>2
[5,4,2,3,1]=>[5,2,4,3,1]=>4
[5,4,3,1,2]=>[1,5,4,3,2]=>2
[5,4,3,2,1]=>[5,4,3,2,1]=>2
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>3
[1,2,3,5,4,6]=>[1,5,2,3,4,6]=>3
[1,2,3,5,6,4]=>[5,1,2,3,4,6]=>3
[1,2,3,6,4,5]=>[1,6,2,3,4,5]=>3
[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>3
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>[4,1,6,2,3,5]=>5
[1,2,4,5,3,6]=>[1,4,2,3,5,6]=>3
[1,2,4,5,6,3]=>[4,1,2,3,5,6]=>3
[1,2,4,6,3,5]=>[4,6,1,2,3,5]=>3
[1,2,4,6,5,3]=>[6,4,1,2,3,5]=>3
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>3
[1,2,5,3,6,4]=>[5,1,6,2,3,4]=>5
[1,2,5,4,3,6]=>[1,5,4,2,3,6]=>3
[1,2,5,4,6,3]=>[5,1,4,2,3,6]=>5
[1,2,5,6,3,4]=>[5,6,1,2,3,4]=>3
[1,2,5,6,4,3]=>[5,4,1,2,3,6]=>3
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>[6,1,5,2,3,4]=>5
[1,2,6,4,3,5]=>[1,6,4,2,3,5]=>3
[1,2,6,4,5,3]=>[6,1,4,2,3,5]=>5
[1,2,6,5,3,4]=>[1,6,5,2,3,4]=>3
[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>3
[1,3,2,4,5,6]=>[1,3,4,5,2,6]=>3
[1,3,2,4,6,5]=>[3,1,2,6,4,5]=>5
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>5
[1,3,2,5,6,4]=>[3,1,2,5,4,6]=>5
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>5
[1,3,2,6,5,4]=>[6,3,1,5,2,4]=>5
[1,3,4,2,5,6]=>[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>[3,1,6,2,4,5]=>5
[1,3,4,5,2,6]=>[1,3,2,4,5,6]=>3
[1,3,4,5,6,2]=>[3,1,2,4,5,6]=>3
[1,3,4,6,2,5]=>[3,6,1,2,4,5]=>3
[1,3,4,6,5,2]=>[6,3,1,2,4,5]=>3
[1,3,5,2,4,6]=>[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>[3,1,5,2,4,6]=>5
[1,3,5,4,2,6]=>[1,5,3,2,4,6]=>3
[1,3,5,4,6,2]=>[5,1,3,2,4,6]=>5
[1,3,5,6,2,4]=>[3,5,1,2,4,6]=>3
[1,3,5,6,4,2]=>[5,3,1,2,4,6]=>3
[1,3,6,2,4,5]=>[1,3,6,2,4,5]=>3
[1,3,6,2,5,4]=>[6,3,5,1,2,4]=>5
[1,3,6,4,2,5]=>[1,6,3,2,4,5]=>3
[1,3,6,4,5,2]=>[6,1,3,2,4,5]=>5
[1,3,6,5,2,4]=>[3,6,5,1,2,4]=>3
[1,3,6,5,4,2]=>[6,5,3,1,2,4]=>3
[1,4,2,3,5,6]=>[1,2,4,5,3,6]=>3
[1,4,2,3,6,5]=>[4,1,2,6,3,5]=>5
[1,4,2,5,3,6]=>[1,4,2,5,3,6]=>5
[1,4,2,5,6,3]=>[4,1,2,5,3,6]=>5
[1,4,2,6,3,5]=>[1,4,2,6,3,5]=>5
[1,4,2,6,5,3]=>[6,4,1,5,2,3]=>5
[1,4,3,2,5,6]=>[1,4,5,3,2,6]=>3
[1,4,3,2,6,5]=>[4,1,6,3,2,5]=>5
[1,4,3,5,2,6]=>[1,4,3,5,2,6]=>5
[1,4,3,5,6,2]=>[4,1,3,5,2,6]=>5
[1,4,3,6,2,5]=>[4,6,1,3,2,5]=>5
[1,4,3,6,5,2]=>[4,3,1,6,2,5]=>5
[1,4,5,2,3,6]=>[1,4,5,2,3,6]=>3
[1,4,5,2,6,3]=>[4,1,5,2,3,6]=>5
[1,4,5,3,2,6]=>[1,4,3,2,5,6]=>3
[1,4,5,3,6,2]=>[4,1,3,2,5,6]=>5
[1,4,5,6,2,3]=>[4,5,1,2,3,6]=>3
[1,4,5,6,3,2]=>[4,3,1,2,5,6]=>3
[1,4,6,2,3,5]=>[1,4,6,2,3,5]=>3
[1,4,6,2,5,3]=>[6,4,5,1,2,3]=>5
[1,4,6,3,2,5]=>[4,6,3,1,2,5]=>3
[1,4,6,3,5,2]=>[4,3,6,1,2,5]=>5
[1,4,6,5,2,3]=>[4,6,5,1,2,3]=>3
[1,4,6,5,3,2]=>[6,4,3,1,2,5]=>3
[1,5,2,3,4,6]=>[1,2,3,5,4,6]=>3
[1,5,2,3,6,4]=>[5,1,2,6,3,4]=>5
[1,5,2,4,3,6]=>[1,5,2,4,3,6]=>5
[1,5,2,4,6,3]=>[5,1,2,4,3,6]=>5
[1,5,2,6,3,4]=>[1,5,2,6,3,4]=>5
[1,5,2,6,4,3]=>[5,4,1,6,2,3]=>5
[1,5,3,2,4,6]=>[1,3,5,4,2,6]=>3
[1,5,3,2,6,4]=>[5,1,6,3,2,4]=>5
[1,5,3,4,2,6]=>[1,5,3,4,2,6]=>5
[1,5,3,4,6,2]=>[5,1,3,4,2,6]=>5
[1,5,3,6,2,4]=>[5,6,1,3,2,4]=>5
[1,5,3,6,4,2]=>[5,3,1,6,2,4]=>5
[1,5,4,2,3,6]=>[1,2,5,4,3,6]=>3
[1,5,4,2,6,3]=>[5,1,6,4,2,3]=>5
[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>[5,1,4,3,2,6]=>5
[1,5,4,6,2,3]=>[5,6,1,4,2,3]=>5
[1,5,4,6,3,2]=>[5,4,1,3,2,6]=>5
[1,5,6,2,3,4]=>[1,5,6,2,3,4]=>3
[1,5,6,2,4,3]=>[5,4,6,1,2,3]=>5
[1,5,6,3,2,4]=>[5,6,3,1,2,4]=>3
[1,5,6,3,4,2]=>[5,3,6,1,2,4]=>5
[1,5,6,4,2,3]=>[5,6,4,1,2,3]=>3
[1,5,6,4,3,2]=>[5,4,3,1,2,6]=>3
[1,6,2,3,4,5]=>[1,2,3,6,4,5]=>3
[1,6,2,3,5,4]=>[6,1,2,5,3,4]=>5
[1,6,2,4,3,5]=>[1,6,2,4,3,5]=>5
[1,6,2,4,5,3]=>[6,1,2,4,3,5]=>5
[1,6,2,5,3,4]=>[1,6,2,5,3,4]=>5
[1,6,2,5,4,3]=>[6,5,1,4,2,3]=>5
[1,6,3,2,4,5]=>[1,3,6,4,2,5]=>3
[1,6,3,2,5,4]=>[3,1,6,5,2,4]=>5
[1,6,3,4,2,5]=>[1,6,3,4,2,5]=>5
[1,6,3,4,5,2]=>[6,1,3,4,2,5]=>5
[1,6,3,5,2,4]=>[3,6,1,5,2,4]=>5
[1,6,3,5,4,2]=>[6,5,1,3,2,4]=>5
[1,6,4,2,3,5]=>[1,2,6,4,3,5]=>3
[1,6,4,2,5,3]=>[4,1,6,5,2,3]=>5
[1,6,4,3,2,5]=>[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>[6,1,4,3,2,5]=>5
[1,6,4,5,2,3]=>[4,6,1,5,2,3]=>5
[1,6,4,5,3,2]=>[6,4,1,3,2,5]=>5
[1,6,5,2,3,4]=>[1,2,6,5,3,4]=>3
[1,6,5,2,4,3]=>[6,1,5,4,2,3]=>5
[1,6,5,3,2,4]=>[1,6,5,3,2,4]=>3
[1,6,5,3,4,2]=>[6,1,5,3,2,4]=>5
[1,6,5,4,2,3]=>[1,6,5,4,2,3]=>3
[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>3
[2,1,3,4,5,6]=>[2,3,4,5,6,1]=>2
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>4
[2,1,3,5,4,6]=>[2,3,1,5,6,4]=>4
[2,1,3,5,6,4]=>[2,1,3,5,6,4]=>4
[2,1,3,6,4,5]=>[2,3,1,4,6,5]=>4
[2,1,3,6,5,4]=>[6,2,1,3,5,4]=>4
[2,1,4,3,5,6]=>[2,4,5,1,6,3]=>4
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>6
[2,1,4,5,3,6]=>[2,4,1,5,6,3]=>4
[2,1,4,5,6,3]=>[2,1,4,5,6,3]=>4
[2,1,4,6,3,5]=>[2,4,1,3,6,5]=>4
[2,1,4,6,5,3]=>[6,2,1,4,5,3]=>4
[2,1,5,3,4,6]=>[2,3,5,1,6,4]=>4
[2,1,5,3,6,4]=>[2,1,5,3,6,4]=>6
[2,1,5,4,3,6]=>[2,5,4,1,6,3]=>4
[2,1,5,4,6,3]=>[5,2,4,1,6,3]=>6
[2,1,5,6,3,4]=>[2,5,1,3,6,4]=>4
[2,1,5,6,4,3]=>[5,2,1,4,6,3]=>4
[2,1,6,3,4,5]=>[2,3,4,1,6,5]=>4
[2,1,6,3,5,4]=>[6,2,3,1,5,4]=>6
[2,1,6,4,3,5]=>[2,6,4,1,5,3]=>4
[2,1,6,4,5,3]=>[6,2,4,1,5,3]=>6
[2,1,6,5,3,4]=>[2,6,3,1,5,4]=>4
[2,1,6,5,4,3]=>[6,5,2,1,4,3]=>4
[2,3,1,4,5,6]=>[2,3,4,5,1,6]=>3
[2,3,1,4,6,5]=>[2,1,3,6,4,5]=>5
[2,3,1,5,4,6]=>[2,3,1,5,4,6]=>5
[2,3,1,5,6,4]=>[2,1,3,5,4,6]=>5
[2,3,1,6,4,5]=>[2,3,1,6,4,5]=>5
[2,3,1,6,5,4]=>[6,2,1,5,3,4]=>5
[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>3
[2,3,4,1,6,5]=>[2,1,6,3,4,5]=>5
[2,3,4,5,1,6]=>[2,3,1,4,5,6]=>3
[2,3,4,5,6,1]=>[2,1,3,4,5,6]=>3
[2,3,4,6,1,5]=>[2,6,1,3,4,5]=>3
[2,3,4,6,5,1]=>[6,2,1,3,4,5]=>3
[2,3,5,1,4,6]=>[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>[2,1,5,3,4,6]=>5
[2,3,5,4,1,6]=>[2,5,3,1,4,6]=>3
[2,3,5,4,6,1]=>[5,2,3,1,4,6]=>5
[2,3,5,6,1,4]=>[2,5,1,3,4,6]=>3
[2,3,5,6,4,1]=>[5,2,1,3,4,6]=>3
[2,3,6,1,4,5]=>[2,3,6,1,4,5]=>3
[2,3,6,1,5,4]=>[6,2,5,1,3,4]=>5
[2,3,6,4,1,5]=>[2,6,3,1,4,5]=>3
[2,3,6,4,5,1]=>[6,2,3,1,4,5]=>5
[2,3,6,5,1,4]=>[2,6,5,1,3,4]=>3
[2,3,6,5,4,1]=>[6,5,2,1,3,4]=>3
[2,4,1,3,5,6]=>[2,4,5,6,1,3]=>3
[2,4,1,3,6,5]=>[2,1,4,6,3,5]=>5
[2,4,1,5,3,6]=>[2,4,1,5,3,6]=>5
[2,4,1,5,6,3]=>[2,1,4,5,3,6]=>5
[2,4,1,6,3,5]=>[2,4,1,6,3,5]=>5
[2,4,1,6,5,3]=>[6,2,1,4,3,5]=>5
[2,4,3,1,5,6]=>[2,4,5,3,1,6]=>3
[2,4,3,1,6,5]=>[4,2,6,3,1,5]=>5
[2,4,3,5,1,6]=>[2,4,3,5,1,6]=>5
[2,4,3,5,6,1]=>[4,2,3,5,1,6]=>5
[2,4,3,6,1,5]=>[4,6,2,3,1,5]=>5
[2,4,3,6,5,1]=>[4,2,1,6,3,5]=>5
[2,4,5,1,3,6]=>[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>[2,1,4,3,5,6]=>5
[2,4,5,3,1,6]=>[2,4,3,1,5,6]=>3
[2,4,5,3,6,1]=>[4,2,3,1,5,6]=>5
[2,4,5,6,1,3]=>[2,4,1,3,5,6]=>3
[2,4,5,6,3,1]=>[4,2,1,3,5,6]=>3
[2,4,6,1,3,5]=>[2,4,6,1,3,5]=>3
[2,4,6,1,5,3]=>[6,2,4,1,3,5]=>5
[2,4,6,3,1,5]=>[4,6,2,1,3,5]=>3
[2,4,6,3,5,1]=>[4,2,6,1,3,5]=>5
[2,4,6,5,1,3]=>[2,6,4,1,3,5]=>3
[2,4,6,5,3,1]=>[6,4,2,1,3,5]=>3
[2,5,1,3,4,6]=>[2,3,5,6,1,4]=>3
[2,5,1,3,6,4]=>[2,1,5,6,3,4]=>5
[2,5,1,4,3,6]=>[2,5,4,6,1,3]=>5
[2,5,1,4,6,3]=>[5,2,4,6,1,3]=>5
[2,5,1,6,3,4]=>[2,5,1,6,3,4]=>5
[2,5,1,6,4,3]=>[5,2,1,4,3,6]=>5
[2,5,3,1,4,6]=>[2,3,5,4,1,6]=>3
[2,5,3,1,6,4]=>[5,2,6,3,1,4]=>5
[2,5,3,4,1,6]=>[2,5,3,4,1,6]=>5
[2,5,3,4,6,1]=>[5,2,3,4,1,6]=>5
[2,5,3,6,1,4]=>[5,6,2,3,1,4]=>5
[2,5,3,6,4,1]=>[5,2,1,6,3,4]=>5
[2,5,4,1,3,6]=>[2,5,6,4,1,3]=>3
[2,5,4,1,6,3]=>[2,1,5,4,3,6]=>5
[2,5,4,3,1,6]=>[2,5,4,3,1,6]=>3
[2,5,4,3,6,1]=>[5,2,4,3,1,6]=>5
[2,5,4,6,1,3]=>[2,5,1,4,3,6]=>5
[2,5,4,6,3,1]=>[5,4,2,3,1,6]=>5
[2,5,6,1,3,4]=>[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>[5,2,4,1,3,6]=>5
[2,5,6,3,1,4]=>[5,6,2,1,3,4]=>3
[2,5,6,3,4,1]=>[5,2,6,1,3,4]=>5
[2,5,6,4,1,3]=>[2,5,4,1,3,6]=>3
[2,5,6,4,3,1]=>[5,4,2,1,3,6]=>3
[2,6,1,3,4,5]=>[2,3,4,6,1,5]=>3
[2,6,1,3,5,4]=>[6,2,3,5,1,4]=>5
[2,6,1,4,3,5]=>[2,6,4,5,1,3]=>5
[2,6,1,4,5,3]=>[6,2,4,5,1,3]=>5
[2,6,1,5,3,4]=>[2,6,3,5,1,4]=>5
[2,6,1,5,4,3]=>[6,5,2,4,1,3]=>5
[2,6,3,1,4,5]=>[2,3,6,4,1,5]=>3
[2,6,3,1,5,4]=>[2,1,6,5,3,4]=>5
[2,6,3,4,1,5]=>[2,6,3,4,1,5]=>5
[2,6,3,4,5,1]=>[6,2,3,4,1,5]=>5
[2,6,3,5,1,4]=>[2,6,1,5,3,4]=>5
[2,6,3,5,4,1]=>[6,5,2,3,1,4]=>5
[2,6,4,1,3,5]=>[2,4,6,5,1,3]=>3
[2,6,4,1,5,3]=>[2,1,6,4,3,5]=>5
[2,6,4,3,1,5]=>[2,6,4,3,1,5]=>3
[2,6,4,3,5,1]=>[6,2,4,3,1,5]=>5
[2,6,4,5,1,3]=>[2,6,1,4,3,5]=>5
[2,6,4,5,3,1]=>[6,4,2,3,1,5]=>5
[2,6,5,1,3,4]=>[2,3,6,5,1,4]=>3
[2,6,5,1,4,3]=>[6,2,5,4,1,3]=>5
[2,6,5,3,1,4]=>[2,6,5,3,1,4]=>3
[2,6,5,3,4,1]=>[6,2,5,3,1,4]=>5
[2,6,5,4,1,3]=>[2,6,5,4,1,3]=>3
[2,6,5,4,3,1]=>[6,5,4,2,1,3]=>3
[3,1,2,4,5,6]=>[1,3,4,5,6,2]=>2
[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>4
[3,1,2,5,4,6]=>[1,3,2,5,6,4]=>4
[3,1,2,5,6,4]=>[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>[1,3,2,4,6,5]=>4
[3,1,2,6,5,4]=>[6,3,1,2,5,4]=>4
[3,1,4,2,5,6]=>[3,4,5,1,6,2]=>4
[3,1,4,2,6,5]=>[3,1,4,2,6,5]=>6
[3,1,4,5,2,6]=>[3,4,1,5,6,2]=>4
[3,1,4,5,6,2]=>[3,1,4,5,6,2]=>4
[3,1,4,6,2,5]=>[3,4,1,2,6,5]=>4
[3,1,4,6,5,2]=>[6,3,1,4,5,2]=>4
[3,1,5,2,4,6]=>[1,3,5,2,6,4]=>4
[3,1,5,2,6,4]=>[3,1,5,2,6,4]=>6
[3,1,5,4,2,6]=>[3,5,4,1,6,2]=>4
[3,1,5,4,6,2]=>[5,3,4,1,6,2]=>6
[3,1,5,6,2,4]=>[3,5,1,2,6,4]=>4
[3,1,5,6,4,2]=>[5,3,1,4,6,2]=>4
[3,1,6,2,4,5]=>[1,3,4,2,6,5]=>4
[3,1,6,2,5,4]=>[6,1,3,2,5,4]=>6
[3,1,6,4,2,5]=>[3,6,4,1,5,2]=>4
[3,1,6,4,5,2]=>[6,3,4,1,5,2]=>6
[3,1,6,5,2,4]=>[1,6,3,2,5,4]=>4
[3,1,6,5,4,2]=>[6,5,3,1,4,2]=>4
[3,2,1,4,5,6]=>[3,4,5,6,2,1]=>2
[3,2,1,4,6,5]=>[3,2,4,6,5,1]=>4
[3,2,1,5,4,6]=>[3,5,2,6,4,1]=>4
[3,2,1,5,6,4]=>[3,2,5,6,4,1]=>4
[3,2,1,6,4,5]=>[3,4,2,6,5,1]=>4
[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>[3,4,5,2,6,1]=>4
[3,2,4,1,6,5]=>[3,2,6,4,5,1]=>6
[3,2,4,5,1,6]=>[3,4,2,5,6,1]=>4
[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>4
[3,2,4,6,1,5]=>[3,6,2,4,5,1]=>4
[3,2,4,6,5,1]=>[3,2,1,4,6,5]=>4
[3,2,5,1,4,6]=>[3,5,6,2,4,1]=>4
[3,2,5,1,6,4]=>[3,2,5,4,6,1]=>6
[3,2,5,4,1,6]=>[3,5,2,1,6,4]=>4
[3,2,5,4,6,1]=>[3,2,5,1,6,4]=>6
[3,2,5,6,1,4]=>[3,5,2,4,6,1]=>4
[3,2,5,6,4,1]=>[3,2,1,5,6,4]=>4
[3,2,6,1,4,5]=>[3,4,6,2,5,1]=>4
[3,2,6,1,5,4]=>[3,2,6,1,5,4]=>6
[3,2,6,4,1,5]=>[3,4,2,1,6,5]=>4
[3,2,6,4,5,1]=>[3,2,4,1,6,5]=>6
[3,2,6,5,1,4]=>[3,6,2,1,5,4]=>4
[3,2,6,5,4,1]=>[6,3,2,1,5,4]=>4
[3,4,1,2,5,6]=>[3,4,5,6,1,2]=>3
[3,4,1,2,6,5]=>[3,1,4,6,2,5]=>5
[3,4,1,5,2,6]=>[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>[3,1,4,5,2,6]=>5
[3,4,1,6,2,5]=>[3,4,1,6,2,5]=>5
[3,4,1,6,5,2]=>[6,3,1,4,2,5]=>5
[3,4,2,1,5,6]=>[3,4,5,2,1,6]=>3
[3,4,2,1,6,5]=>[3,2,6,4,1,5]=>5
[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>5
[3,4,2,5,6,1]=>[3,2,4,5,1,6]=>5
[3,4,2,6,1,5]=>[3,6,2,4,1,5]=>5
[3,4,2,6,5,1]=>[3,2,1,6,4,5]=>5
[3,4,5,1,2,6]=>[3,4,5,1,2,6]=>3
[3,4,5,1,6,2]=>[3,1,4,2,5,6]=>5
[3,4,5,2,1,6]=>[3,4,2,1,5,6]=>3
[3,4,5,2,6,1]=>[3,2,4,1,5,6]=>5
[3,4,5,6,1,2]=>[3,4,1,2,5,6]=>3
[3,4,5,6,2,1]=>[3,2,1,4,5,6]=>3
[3,4,6,1,2,5]=>[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>[6,3,4,1,2,5]=>5
[3,4,6,2,1,5]=>[3,6,2,1,4,5]=>3
[3,4,6,2,5,1]=>[3,2,6,1,4,5]=>5
[3,4,6,5,1,2]=>[3,6,4,1,2,5]=>3
[3,4,6,5,2,1]=>[6,3,2,1,4,5]=>3
[3,5,1,2,4,6]=>[1,3,5,6,2,4]=>3
[3,5,1,2,6,4]=>[3,1,5,6,2,4]=>5
[3,5,1,4,2,6]=>[3,5,4,6,1,2]=>5
[3,5,1,4,6,2]=>[5,3,4,6,1,2]=>5
[3,5,1,6,2,4]=>[3,5,1,6,2,4]=>5
[3,5,1,6,4,2]=>[5,3,1,4,2,6]=>5
[3,5,2,1,4,6]=>[3,5,6,2,1,4]=>3
[3,5,2,1,6,4]=>[3,2,5,4,1,6]=>5
[3,5,2,4,1,6]=>[3,5,2,6,1,4]=>5
[3,5,2,4,6,1]=>[3,2,5,6,1,4]=>5
[3,5,2,6,1,4]=>[3,5,2,4,1,6]=>5
[3,5,2,6,4,1]=>[3,2,1,5,4,6]=>5
[3,5,4,1,2,6]=>[3,5,6,4,1,2]=>3
[3,5,4,1,6,2]=>[3,1,5,4,2,6]=>5
[3,5,4,2,1,6]=>[3,5,4,2,1,6]=>3
[3,5,4,2,6,1]=>[5,3,4,2,1,6]=>5
[3,5,4,6,1,2]=>[3,5,1,4,2,6]=>5
[3,5,4,6,2,1]=>[5,3,2,4,1,6]=>5
[3,5,6,1,2,4]=>[3,5,6,1,2,4]=>3
[3,5,6,1,4,2]=>[5,3,4,1,2,6]=>5
[3,5,6,2,1,4]=>[3,5,2,1,4,6]=>3
[3,5,6,2,4,1]=>[3,2,5,1,4,6]=>5
[3,5,6,4,1,2]=>[3,5,4,1,2,6]=>3
[3,5,6,4,2,1]=>[5,3,2,1,4,6]=>3
[3,6,1,2,4,5]=>[1,3,4,6,2,5]=>3
[3,6,1,2,5,4]=>[6,1,3,5,2,4]=>5
[3,6,1,4,2,5]=>[3,6,4,5,1,2]=>5
[3,6,1,4,5,2]=>[6,3,4,5,1,2]=>5
[3,6,1,5,2,4]=>[1,6,3,5,2,4]=>5
[3,6,1,5,4,2]=>[6,5,3,4,1,2]=>5
[3,6,2,1,4,5]=>[3,4,6,2,1,5]=>3
[3,6,2,1,5,4]=>[3,2,6,5,1,4]=>5
[3,6,2,4,1,5]=>[3,4,2,6,1,5]=>5
[3,6,2,4,5,1]=>[3,2,4,6,1,5]=>5
[3,6,2,5,1,4]=>[3,6,2,5,1,4]=>5
[3,6,2,5,4,1]=>[6,3,2,5,1,4]=>5
[3,6,4,1,2,5]=>[3,4,6,5,1,2]=>3
[3,6,4,1,5,2]=>[3,1,6,4,2,5]=>5
[3,6,4,2,1,5]=>[3,6,4,2,1,5]=>3
[3,6,4,2,5,1]=>[6,3,4,2,1,5]=>5
[3,6,4,5,1,2]=>[3,6,1,4,2,5]=>5
[3,6,4,5,2,1]=>[6,3,2,4,1,5]=>5
[3,6,5,1,2,4]=>[1,3,6,5,2,4]=>3
[3,6,5,1,4,2]=>[6,3,5,4,1,2]=>5
[3,6,5,2,1,4]=>[3,6,5,2,1,4]=>3
[3,6,5,2,4,1]=>[6,3,5,2,1,4]=>5
[3,6,5,4,1,2]=>[3,6,5,4,1,2]=>3
[3,6,5,4,2,1]=>[6,5,3,2,1,4]=>3
[4,1,2,3,5,6]=>[1,2,4,5,6,3]=>2
[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>[1,4,2,5,6,3]=>4
[4,1,2,5,6,3]=>[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>[1,4,2,3,6,5]=>4
[4,1,2,6,5,3]=>[6,4,1,2,5,3]=>4
[4,1,3,2,5,6]=>[1,4,5,3,6,2]=>4
[4,1,3,2,6,5]=>[4,1,6,3,5,2]=>6
[4,1,3,5,2,6]=>[1,4,3,5,6,2]=>4
[4,1,3,5,6,2]=>[4,1,3,5,6,2]=>4
[4,1,3,6,2,5]=>[4,6,1,3,5,2]=>4
[4,1,3,6,5,2]=>[4,3,1,2,6,5]=>4
[4,1,5,2,3,6]=>[1,4,5,2,6,3]=>4
[4,1,5,2,6,3]=>[4,1,5,2,6,3]=>6
[4,1,5,3,2,6]=>[4,5,3,1,6,2]=>4
[4,1,5,3,6,2]=>[4,3,5,1,6,2]=>6
[4,1,5,6,2,3]=>[4,5,1,2,6,3]=>4
[4,1,5,6,3,2]=>[4,3,1,5,6,2]=>4
[4,1,6,2,3,5]=>[1,2,4,3,6,5]=>4
[4,1,6,2,5,3]=>[6,1,4,2,5,3]=>6
[4,1,6,3,2,5]=>[1,4,3,2,6,5]=>4
[4,1,6,3,5,2]=>[4,1,3,2,6,5]=>6
[4,1,6,5,2,3]=>[1,6,4,2,5,3]=>4
[4,1,6,5,3,2]=>[6,4,3,1,5,2]=>4
[4,2,1,3,5,6]=>[2,4,5,6,3,1]=>2
[4,2,1,3,6,5]=>[4,2,3,6,5,1]=>4
[4,2,1,5,3,6]=>[4,5,2,6,3,1]=>4
[4,2,1,5,6,3]=>[4,2,5,6,3,1]=>4
[4,2,1,6,3,5]=>[2,4,3,6,5,1]=>4
[4,2,1,6,5,3]=>[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>[2,4,5,3,6,1]=>4
[4,2,3,1,6,5]=>[4,2,6,3,5,1]=>6
[4,2,3,5,1,6]=>[2,4,3,5,6,1]=>4
[4,2,3,5,6,1]=>[4,2,3,5,6,1]=>4
[4,2,3,6,1,5]=>[4,6,2,3,5,1]=>4
[4,2,3,6,5,1]=>[4,2,1,3,6,5]=>4
[4,2,5,1,3,6]=>[4,5,6,2,3,1]=>4
[4,2,5,1,6,3]=>[4,2,5,3,6,1]=>6
[4,2,5,3,1,6]=>[4,5,2,1,6,3]=>4
[4,2,5,3,6,1]=>[4,2,5,1,6,3]=>6
[4,2,5,6,1,3]=>[4,5,2,3,6,1]=>4
[4,2,5,6,3,1]=>[4,2,1,5,6,3]=>4
[4,2,6,1,3,5]=>[2,4,6,3,5,1]=>4
[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>6
[4,2,6,3,1,5]=>[2,4,3,1,6,5]=>4
[4,2,6,3,5,1]=>[4,2,3,1,6,5]=>6
[4,2,6,5,1,3]=>[4,6,2,1,5,3]=>4
[4,2,6,5,3,1]=>[6,4,2,1,5,3]=>4
[4,3,1,2,5,6]=>[1,4,5,6,3,2]=>2
[4,3,1,2,6,5]=>[4,1,3,6,5,2]=>4
[4,3,1,5,2,6]=>[4,5,1,6,3,2]=>4
[4,3,1,5,6,2]=>[4,1,5,6,3,2]=>4
[4,3,1,6,2,5]=>[1,4,3,6,5,2]=>4
[4,3,1,6,5,2]=>[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>[4,5,6,3,2,1]=>2
[4,3,2,1,6,5]=>[4,3,6,5,2,1]=>4
[4,3,2,5,1,6]=>[4,5,3,6,2,1]=>4
[4,3,2,5,6,1]=>[4,3,5,6,2,1]=>4
[4,3,2,6,1,5]=>[4,6,3,5,2,1]=>4
[4,3,2,6,5,1]=>[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>[4,5,6,1,3,2]=>4
[4,3,5,1,6,2]=>[4,1,5,3,6,2]=>6
[4,3,5,2,1,6]=>[4,5,3,2,6,1]=>4
[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>6
[4,3,5,6,1,2]=>[4,5,1,3,6,2]=>4
[4,3,5,6,2,1]=>[4,3,2,5,6,1]=>4
[4,3,6,1,2,5]=>[1,4,6,3,5,2]=>4
[4,3,6,1,5,2]=>[4,3,6,1,5,2]=>6
[4,3,6,2,1,5]=>[4,6,3,2,5,1]=>4
[4,3,6,2,5,1]=>[4,3,6,2,5,1]=>6
[4,3,6,5,1,2]=>[4,6,3,1,5,2]=>4
[4,3,6,5,2,1]=>[4,3,2,1,6,5]=>4
[4,5,1,2,3,6]=>[1,4,5,6,2,3]=>3
[4,5,1,2,6,3]=>[4,1,5,6,2,3]=>5
[4,5,1,3,2,6]=>[4,5,3,6,1,2]=>5
[4,5,1,3,6,2]=>[4,3,5,6,1,2]=>5
[4,5,1,6,2,3]=>[4,5,1,6,2,3]=>5
[4,5,1,6,3,2]=>[4,3,1,5,2,6]=>5
[4,5,2,1,3,6]=>[4,5,6,2,1,3]=>3
[4,5,2,1,6,3]=>[4,2,5,3,1,6]=>5
[4,5,2,3,1,6]=>[4,5,2,6,1,3]=>5
[4,5,2,3,6,1]=>[4,2,5,6,1,3]=>5
[4,5,2,6,1,3]=>[4,5,2,3,1,6]=>5
[4,5,2,6,3,1]=>[4,2,1,5,3,6]=>5
[4,5,3,1,2,6]=>[4,5,6,3,1,2]=>3
[4,5,3,1,6,2]=>[4,1,5,3,2,6]=>5
[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>3
[4,5,3,2,6,1]=>[4,3,5,2,1,6]=>5
[4,5,3,6,1,2]=>[4,5,1,3,2,6]=>5
[4,5,3,6,2,1]=>[4,3,2,5,1,6]=>5
[4,5,6,1,2,3]=>[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>[4,3,5,1,2,6]=>5
[4,5,6,2,1,3]=>[4,5,2,1,3,6]=>3
[4,5,6,2,3,1]=>[4,2,5,1,3,6]=>5
[4,5,6,3,1,2]=>[4,5,3,1,2,6]=>3
[4,5,6,3,2,1]=>[4,3,2,1,5,6]=>3
[4,6,1,2,3,5]=>[1,2,4,6,3,5]=>3
[4,6,1,2,5,3]=>[6,1,4,5,2,3]=>5
[4,6,1,3,2,5]=>[1,4,3,6,2,5]=>5
[4,6,1,3,5,2]=>[4,1,3,6,2,5]=>5
[4,6,1,5,2,3]=>[1,6,4,5,2,3]=>5
[4,6,1,5,3,2]=>[6,4,3,5,1,2]=>5
[4,6,2,1,3,5]=>[2,4,6,3,1,5]=>3
[4,6,2,1,5,3]=>[4,2,6,5,1,3]=>5
[4,6,2,3,1,5]=>[2,4,3,6,1,5]=>5
[4,6,2,3,5,1]=>[4,2,3,6,1,5]=>5
[4,6,2,5,1,3]=>[4,6,2,5,1,3]=>5
[4,6,2,5,3,1]=>[6,4,2,5,1,3]=>5
[4,6,3,1,2,5]=>[1,4,6,3,2,5]=>3
[4,6,3,1,5,2]=>[4,3,6,5,1,2]=>5
[4,6,3,2,1,5]=>[4,6,3,2,1,5]=>3
[4,6,3,2,5,1]=>[4,3,6,2,1,5]=>5
[4,6,3,5,1,2]=>[4,6,3,5,1,2]=>5
[4,6,3,5,2,1]=>[4,3,2,6,1,5]=>5
[4,6,5,1,2,3]=>[1,4,6,5,2,3]=>3
[4,6,5,1,3,2]=>[6,4,5,3,1,2]=>5
[4,6,5,2,1,3]=>[4,6,5,2,1,3]=>3
[4,6,5,2,3,1]=>[6,4,5,2,1,3]=>5
[4,6,5,3,1,2]=>[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>[6,4,3,2,1,5]=>3
[5,1,2,3,4,6]=>[1,2,3,5,6,4]=>2
[5,1,2,3,6,4]=>[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>[1,5,2,4,6,3]=>4
[5,1,2,4,6,3]=>[5,1,2,4,6,3]=>4
[5,1,2,6,3,4]=>[1,5,2,3,6,4]=>4
[5,1,2,6,4,3]=>[5,4,1,2,6,3]=>4
[5,1,3,2,4,6]=>[1,3,5,4,6,2]=>4
[5,1,3,2,6,4]=>[5,1,6,3,4,2]=>6
[5,1,3,4,2,6]=>[1,5,3,4,6,2]=>4
[5,1,3,4,6,2]=>[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>[5,6,1,3,4,2]=>4
[5,1,3,6,4,2]=>[5,3,1,2,6,4]=>4
[5,1,4,2,3,6]=>[1,2,5,4,6,3]=>4
[5,1,4,2,6,3]=>[5,1,6,2,4,3]=>6
[5,1,4,3,2,6]=>[1,5,4,3,6,2]=>4
[5,1,4,3,6,2]=>[5,1,4,3,6,2]=>6
[5,1,4,6,2,3]=>[5,6,1,2,4,3]=>4
[5,1,4,6,3,2]=>[5,4,1,3,6,2]=>4
[5,1,6,2,3,4]=>[1,2,5,3,6,4]=>4
[5,1,6,2,4,3]=>[5,1,4,2,6,3]=>6
[5,1,6,3,2,4]=>[1,5,3,2,6,4]=>4
[5,1,6,3,4,2]=>[5,1,3,2,6,4]=>6
[5,1,6,4,2,3]=>[1,5,4,2,6,3]=>4
[5,1,6,4,3,2]=>[5,4,3,1,6,2]=>4
[5,2,1,3,4,6]=>[2,3,5,6,4,1]=>2
[5,2,1,3,6,4]=>[5,2,3,6,4,1]=>4
[5,2,1,4,3,6]=>[2,5,1,6,4,3]=>4
[5,2,1,4,6,3]=>[2,1,5,6,4,3]=>4
[5,2,1,6,3,4]=>[2,5,3,6,4,1]=>4
[5,2,1,6,4,3]=>[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>[2,3,5,4,6,1]=>4
[5,2,3,1,6,4]=>[5,2,6,3,4,1]=>6
[5,2,3,4,1,6]=>[2,5,3,4,6,1]=>4
[5,2,3,4,6,1]=>[5,2,3,4,6,1]=>4
[5,2,3,6,1,4]=>[5,6,2,3,4,1]=>4
[5,2,3,6,4,1]=>[5,2,1,3,6,4]=>4
[5,2,4,1,3,6]=>[2,5,6,1,4,3]=>4
[5,2,4,1,6,3]=>[2,1,5,4,6,3]=>6
[5,2,4,3,1,6]=>[2,5,4,3,6,1]=>4
[5,2,4,3,6,1]=>[5,2,4,3,6,1]=>6
[5,2,4,6,1,3]=>[2,5,1,4,6,3]=>4
[5,2,4,6,3,1]=>[5,4,2,3,6,1]=>4
[5,2,6,1,3,4]=>[2,5,6,3,4,1]=>4
[5,2,6,1,4,3]=>[5,2,6,1,4,3]=>6
[5,2,6,3,1,4]=>[2,5,3,1,6,4]=>4
[5,2,6,3,4,1]=>[5,2,3,1,6,4]=>6
[5,2,6,4,1,3]=>[5,6,2,1,4,3]=>4
[5,2,6,4,3,1]=>[5,4,2,1,6,3]=>4
[5,3,1,2,4,6]=>[1,3,5,6,4,2]=>2
[5,3,1,2,6,4]=>[5,1,3,6,4,2]=>4
[5,3,1,4,2,6]=>[3,5,1,6,4,2]=>4
[5,3,1,4,6,2]=>[3,1,5,6,4,2]=>4
[5,3,1,6,2,4]=>[1,5,3,6,4,2]=>4
[5,3,1,6,4,2]=>[5,3,1,6,4,2]=>4
[5,3,2,1,4,6]=>[3,5,6,4,2,1]=>2
[5,3,2,1,6,4]=>[5,3,6,4,2,1]=>4
[5,3,2,4,1,6]=>[3,5,4,6,2,1]=>4
[5,3,2,4,6,1]=>[5,3,4,6,2,1]=>4
[5,3,2,6,1,4]=>[5,6,3,4,2,1]=>4
[5,3,2,6,4,1]=>[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>[3,5,6,1,4,2]=>4
[5,3,4,1,6,2]=>[3,1,5,4,6,2]=>6
[5,3,4,2,1,6]=>[3,5,4,2,6,1]=>4
[5,3,4,2,6,1]=>[5,3,4,2,6,1]=>6
[5,3,4,6,1,2]=>[3,5,1,4,6,2]=>4
[5,3,4,6,2,1]=>[5,3,2,4,6,1]=>4
[5,3,6,1,2,4]=>[1,5,6,3,4,2]=>4
[5,3,6,1,4,2]=>[5,3,6,1,4,2]=>6
[5,3,6,2,1,4]=>[5,6,3,2,4,1]=>4
[5,3,6,2,4,1]=>[5,3,6,2,4,1]=>6
[5,3,6,4,1,2]=>[5,6,3,1,4,2]=>4
[5,3,6,4,2,1]=>[5,3,2,1,6,4]=>4
[5,4,1,2,3,6]=>[1,2,5,6,4,3]=>2
[5,4,1,2,6,3]=>[5,1,2,6,4,3]=>4
[5,4,1,3,2,6]=>[1,5,4,6,3,2]=>4
[5,4,1,3,6,2]=>[5,1,4,6,3,2]=>4
[5,4,1,6,2,3]=>[1,5,2,6,4,3]=>4
[5,4,1,6,3,2]=>[5,4,1,6,3,2]=>4
[5,4,2,1,3,6]=>[2,5,6,4,3,1]=>2
[5,4,2,1,6,3]=>[5,2,6,4,3,1]=>4
[5,4,2,3,1,6]=>[2,5,4,6,3,1]=>4
[5,4,2,3,6,1]=>[5,2,4,6,3,1]=>4
[5,4,2,6,1,3]=>[5,6,2,4,3,1]=>4
[5,4,2,6,3,1]=>[5,4,2,6,3,1]=>4
[5,4,3,1,2,6]=>[1,5,6,4,3,2]=>2
[5,4,3,1,6,2]=>[5,1,6,4,3,2]=>4
[5,4,3,2,1,6]=>[5,6,4,3,2,1]=>2
[5,4,3,2,6,1]=>[5,4,6,3,2,1]=>4
[5,4,3,6,1,2]=>[5,6,1,4,3,2]=>4
[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>4
[5,4,6,1,2,3]=>[1,5,6,2,4,3]=>4
[5,4,6,1,3,2]=>[5,4,6,1,3,2]=>6
[5,4,6,2,1,3]=>[5,6,4,2,3,1]=>4
[5,4,6,2,3,1]=>[5,4,6,2,3,1]=>6
[5,4,6,3,1,2]=>[5,6,4,1,3,2]=>4
[5,4,6,3,2,1]=>[5,4,3,2,6,1]=>4
[5,6,1,2,3,4]=>[1,2,5,6,3,4]=>3
[5,6,1,2,4,3]=>[5,1,4,6,2,3]=>5
[5,6,1,3,2,4]=>[1,5,3,6,2,4]=>5
[5,6,1,3,4,2]=>[5,1,3,6,2,4]=>5
[5,6,1,4,2,3]=>[1,5,4,6,2,3]=>5
[5,6,1,4,3,2]=>[5,4,3,6,1,2]=>5
[5,6,2,1,3,4]=>[2,5,6,3,1,4]=>3
[5,6,2,1,4,3]=>[5,2,6,4,1,3]=>5
[5,6,2,3,1,4]=>[2,5,3,6,1,4]=>5
[5,6,2,3,4,1]=>[5,2,3,6,1,4]=>5
[5,6,2,4,1,3]=>[5,6,2,4,1,3]=>5
[5,6,2,4,3,1]=>[5,4,2,6,1,3]=>5
[5,6,3,1,2,4]=>[1,5,6,3,2,4]=>3
[5,6,3,1,4,2]=>[5,3,6,4,1,2]=>5
[5,6,3,2,1,4]=>[5,6,3,2,1,4]=>3
[5,6,3,2,4,1]=>[5,3,6,2,1,4]=>5
[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>5
[5,6,3,4,2,1]=>[5,3,2,6,1,4]=>5
[5,6,4,1,2,3]=>[1,5,6,4,2,3]=>3
[5,6,4,1,3,2]=>[5,4,6,3,1,2]=>5
[5,6,4,2,1,3]=>[5,6,4,2,1,3]=>3
[5,6,4,2,3,1]=>[5,4,6,2,1,3]=>5
[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>3
[5,6,4,3,2,1]=>[5,4,3,2,1,6]=>3
[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>2
[6,1,2,3,5,4]=>[6,1,2,3,5,4]=>4
[6,1,2,4,3,5]=>[1,6,2,4,5,3]=>4
[6,1,2,4,5,3]=>[6,1,2,4,5,3]=>4
[6,1,2,5,3,4]=>[1,6,2,3,5,4]=>4
[6,1,2,5,4,3]=>[6,5,1,2,4,3]=>4
[6,1,3,2,4,5]=>[1,3,6,4,5,2]=>4
[6,1,3,2,5,4]=>[3,1,6,2,5,4]=>6
[6,1,3,4,2,5]=>[1,6,3,4,5,2]=>4
[6,1,3,4,5,2]=>[6,1,3,4,5,2]=>4
[6,1,3,5,2,4]=>[3,6,1,2,5,4]=>4
[6,1,3,5,4,2]=>[6,5,1,3,4,2]=>4
[6,1,4,2,3,5]=>[1,2,6,4,5,3]=>4
[6,1,4,2,5,3]=>[4,1,6,2,5,3]=>6
[6,1,4,3,2,5]=>[1,6,4,3,5,2]=>4
[6,1,4,3,5,2]=>[6,1,4,3,5,2]=>6
[6,1,4,5,2,3]=>[4,6,1,2,5,3]=>4
[6,1,4,5,3,2]=>[6,4,1,3,5,2]=>4
[6,1,5,2,3,4]=>[1,2,6,3,5,4]=>4
[6,1,5,2,4,3]=>[6,1,5,2,4,3]=>6
[6,1,5,3,2,4]=>[1,6,5,3,4,2]=>4
[6,1,5,3,4,2]=>[6,1,5,3,4,2]=>6
[6,1,5,4,2,3]=>[1,6,5,2,4,3]=>4
[6,1,5,4,3,2]=>[6,5,4,1,3,2]=>4
[6,2,1,3,4,5]=>[2,3,4,6,5,1]=>2
[6,2,1,3,5,4]=>[2,1,3,6,5,4]=>4
[6,2,1,4,3,5]=>[2,4,1,6,5,3]=>4
[6,2,1,4,5,3]=>[2,1,4,6,5,3]=>4
[6,2,1,5,3,4]=>[2,3,1,6,5,4]=>4
[6,2,1,5,4,3]=>[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>[2,3,6,4,5,1]=>4
[6,2,3,1,5,4]=>[2,1,6,3,5,4]=>6
[6,2,3,4,1,5]=>[2,6,3,4,5,1]=>4
[6,2,3,4,5,1]=>[6,2,3,4,5,1]=>4
[6,2,3,5,1,4]=>[2,6,1,3,5,4]=>4
[6,2,3,5,4,1]=>[6,5,2,3,4,1]=>4
[6,2,4,1,3,5]=>[2,4,6,1,5,3]=>4
[6,2,4,1,5,3]=>[2,1,6,4,5,3]=>6
[6,2,4,3,1,5]=>[2,6,4,3,5,1]=>4
[6,2,4,3,5,1]=>[6,2,4,3,5,1]=>6
[6,2,4,5,1,3]=>[2,6,1,4,5,3]=>4
[6,2,4,5,3,1]=>[6,4,2,3,5,1]=>4
[6,2,5,1,3,4]=>[2,3,6,1,5,4]=>4
[6,2,5,1,4,3]=>[6,2,5,1,4,3]=>6
[6,2,5,3,1,4]=>[2,6,5,3,4,1]=>4
[6,2,5,3,4,1]=>[6,2,5,3,4,1]=>6
[6,2,5,4,1,3]=>[2,6,5,1,4,3]=>4
[6,2,5,4,3,1]=>[6,5,4,2,3,1]=>4
[6,3,1,2,4,5]=>[1,3,4,6,5,2]=>2
[6,3,1,2,5,4]=>[3,1,2,6,5,4]=>4
[6,3,1,4,2,5]=>[3,4,1,6,5,2]=>4
[6,3,1,4,5,2]=>[3,1,4,6,5,2]=>4
[6,3,1,5,2,4]=>[1,3,2,6,5,4]=>4
[6,3,1,5,4,2]=>[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>[3,4,6,5,2,1]=>2
[6,3,2,1,5,4]=>[3,2,6,5,4,1]=>4
[6,3,2,4,1,5]=>[3,6,4,5,2,1]=>4
[6,3,2,4,5,1]=>[6,3,4,5,2,1]=>4
[6,3,2,5,1,4]=>[3,6,2,5,4,1]=>4
[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>[3,4,6,1,5,2]=>4
[6,3,4,1,5,2]=>[3,1,6,4,5,2]=>6
[6,3,4,2,1,5]=>[3,6,4,2,5,1]=>4
[6,3,4,2,5,1]=>[6,3,4,2,5,1]=>6
[6,3,4,5,1,2]=>[3,6,1,4,5,2]=>4
[6,3,4,5,2,1]=>[6,3,2,4,5,1]=>4
[6,3,5,1,2,4]=>[1,3,6,2,5,4]=>4
[6,3,5,1,4,2]=>[6,3,5,1,4,2]=>6
[6,3,5,2,1,4]=>[3,6,5,2,4,1]=>4
[6,3,5,2,4,1]=>[6,3,5,2,4,1]=>6
[6,3,5,4,1,2]=>[3,6,5,1,4,2]=>4
[6,3,5,4,2,1]=>[6,5,3,2,4,1]=>4
[6,4,1,2,3,5]=>[1,2,4,6,5,3]=>2
[6,4,1,2,5,3]=>[4,1,2,6,5,3]=>4
[6,4,1,3,2,5]=>[1,6,4,5,3,2]=>4
[6,4,1,3,5,2]=>[6,1,4,5,3,2]=>4
[6,4,1,5,2,3]=>[1,4,2,6,5,3]=>4
[6,4,1,5,3,2]=>[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>[2,4,6,5,3,1]=>2
[6,4,2,1,5,3]=>[4,2,6,5,3,1]=>4
[6,4,2,3,1,5]=>[2,6,4,5,3,1]=>4
[6,4,2,3,5,1]=>[6,2,4,5,3,1]=>4
[6,4,2,5,1,3]=>[4,6,2,5,3,1]=>4
[6,4,2,5,3,1]=>[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>[1,4,6,5,3,2]=>2
[6,4,3,1,5,2]=>[4,1,6,5,3,2]=>4
[6,4,3,2,1,5]=>[4,6,5,3,2,1]=>2
[6,4,3,2,5,1]=>[6,4,5,3,2,1]=>4
[6,4,3,5,1,2]=>[4,6,1,5,3,2]=>4
[6,4,3,5,2,1]=>[6,4,3,5,2,1]=>4
[6,4,5,1,2,3]=>[1,4,6,2,5,3]=>4
[6,4,5,1,3,2]=>[6,4,5,1,3,2]=>6
[6,4,5,2,1,3]=>[4,6,5,2,3,1]=>4
[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>6
[6,4,5,3,1,2]=>[4,6,5,1,3,2]=>4
[6,4,5,3,2,1]=>[6,4,3,2,5,1]=>4
[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>2
[6,5,1,2,4,3]=>[6,1,2,5,4,3]=>4
[6,5,1,3,2,4]=>[1,6,3,5,4,2]=>4
[6,5,1,3,4,2]=>[6,1,3,5,4,2]=>4
[6,5,1,4,2,3]=>[1,6,2,5,4,3]=>4
[6,5,1,4,3,2]=>[6,5,1,4,3,2]=>4
[6,5,2,1,3,4]=>[2,3,6,5,4,1]=>2
[6,5,2,1,4,3]=>[2,1,6,5,4,3]=>4
[6,5,2,3,1,4]=>[2,6,3,5,4,1]=>4
[6,5,2,3,4,1]=>[6,2,3,5,4,1]=>4
[6,5,2,4,1,3]=>[2,6,1,5,4,3]=>4
[6,5,2,4,3,1]=>[6,5,2,4,3,1]=>4
[6,5,3,1,2,4]=>[1,3,6,5,4,2]=>2
[6,5,3,1,4,2]=>[3,1,6,5,4,2]=>4
[6,5,3,2,1,4]=>[3,6,5,4,2,1]=>2
[6,5,3,2,4,1]=>[6,3,5,4,2,1]=>4
[6,5,3,4,1,2]=>[3,6,1,5,4,2]=>4
[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>4
[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>2
[6,5,4,1,3,2]=>[6,1,5,4,3,2]=>4
[6,5,4,2,1,3]=>[2,6,5,4,3,1]=>2
[6,5,4,2,3,1]=>[6,2,5,4,3,1]=>4
[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>2
[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>2
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Description
The number of up-down runs of a permutation.
An up-down run of a permutation $\pi=\pi_{1}\pi_{2}\cdots\pi_{n}$ is either a maximal monotone consecutive subsequence or $\pi_{1}$ if 1 is a descent of $\pi$.
For example, the up-down runs of $\pi=85712643$ are $8$, $85$, $57$, $71$, $126$, and
$643$.
An up-down run of a permutation $\pi=\pi_{1}\pi_{2}\cdots\pi_{n}$ is either a maximal monotone consecutive subsequence or $\pi_{1}$ if 1 is a descent of $\pi$.
For example, the up-down runs of $\pi=85712643$ are $8$, $85$, $57$, $71$, $126$, and
$643$.
Map
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
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