Identifier
-
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
St000317: Permutations ⟶ ℤ
Values
=>
[1]=>[1]=>0
[1,2]=>[1,2]=>0
[2,1]=>[2,1]=>0
[1,2,3]=>[1,2,3]=>0
[1,3,2]=>[1,3,2]=>0
[2,1,3]=>[2,1,3]=>0
[2,3,1]=>[3,2,1]=>0
[3,1,2]=>[3,2,1]=>0
[3,2,1]=>[3,2,1]=>0
[1,2,3,4]=>[1,2,3,4]=>0
[1,2,4,3]=>[1,2,4,3]=>0
[1,3,2,4]=>[1,3,2,4]=>0
[1,3,4,2]=>[1,4,3,2]=>0
[1,4,2,3]=>[1,4,3,2]=>0
[1,4,3,2]=>[1,4,3,2]=>0
[2,1,3,4]=>[2,1,3,4]=>0
[2,1,4,3]=>[2,1,4,3]=>0
[2,3,1,4]=>[3,2,1,4]=>0
[2,3,4,1]=>[4,2,3,1]=>0
[2,4,1,3]=>[3,4,1,2]=>0
[2,4,3,1]=>[4,3,2,1]=>0
[3,1,2,4]=>[3,2,1,4]=>0
[3,1,4,2]=>[4,2,3,1]=>0
[3,2,1,4]=>[3,2,1,4]=>0
[3,2,4,1]=>[4,2,3,1]=>0
[3,4,1,2]=>[4,3,2,1]=>0
[3,4,2,1]=>[4,3,2,1]=>0
[4,1,2,3]=>[4,2,3,1]=>0
[4,1,3,2]=>[4,2,3,1]=>0
[4,2,1,3]=>[4,3,2,1]=>0
[4,2,3,1]=>[4,3,2,1]=>0
[4,3,1,2]=>[4,3,2,1]=>0
[4,3,2,1]=>[4,3,2,1]=>0
[1,2,3,4,5]=>[1,2,3,4,5]=>0
[1,2,3,5,4]=>[1,2,3,5,4]=>0
[1,2,4,3,5]=>[1,2,4,3,5]=>0
[1,2,4,5,3]=>[1,2,5,4,3]=>0
[1,2,5,3,4]=>[1,2,5,4,3]=>0
[1,2,5,4,3]=>[1,2,5,4,3]=>0
[1,3,2,4,5]=>[1,3,2,4,5]=>0
[1,3,2,5,4]=>[1,3,2,5,4]=>0
[1,3,4,2,5]=>[1,4,3,2,5]=>0
[1,3,4,5,2]=>[1,5,3,4,2]=>0
[1,3,5,2,4]=>[1,4,5,2,3]=>0
[1,3,5,4,2]=>[1,5,4,3,2]=>0
[1,4,2,3,5]=>[1,4,3,2,5]=>0
[1,4,2,5,3]=>[1,5,3,4,2]=>0
[1,4,3,2,5]=>[1,4,3,2,5]=>0
[1,4,3,5,2]=>[1,5,3,4,2]=>0
[1,4,5,2,3]=>[1,5,4,3,2]=>0
[1,4,5,3,2]=>[1,5,4,3,2]=>0
[1,5,2,3,4]=>[1,5,3,4,2]=>0
[1,5,2,4,3]=>[1,5,3,4,2]=>0
[1,5,3,2,4]=>[1,5,4,3,2]=>0
[1,5,3,4,2]=>[1,5,4,3,2]=>0
[1,5,4,2,3]=>[1,5,4,3,2]=>0
[1,5,4,3,2]=>[1,5,4,3,2]=>0
[2,1,3,4,5]=>[2,1,3,4,5]=>0
[2,1,3,5,4]=>[2,1,3,5,4]=>0
[2,1,4,3,5]=>[2,1,4,3,5]=>0
[2,1,4,5,3]=>[2,1,5,4,3]=>0
[2,1,5,3,4]=>[2,1,5,4,3]=>0
[2,1,5,4,3]=>[2,1,5,4,3]=>0
[2,3,1,4,5]=>[3,2,1,4,5]=>0
[2,3,1,5,4]=>[3,2,1,5,4]=>0
[2,3,4,1,5]=>[4,2,3,1,5]=>0
[2,3,4,5,1]=>[5,2,3,4,1]=>0
[2,3,5,1,4]=>[4,2,5,1,3]=>0
[2,3,5,4,1]=>[5,2,4,3,1]=>0
[2,4,1,3,5]=>[3,4,1,2,5]=>0
[2,4,1,5,3]=>[3,5,1,4,2]=>0
[2,4,3,1,5]=>[4,3,2,1,5]=>0
[2,4,3,5,1]=>[5,3,2,4,1]=>0
[2,4,5,1,3]=>[4,5,3,1,2]=>0
[2,4,5,3,1]=>[5,4,3,2,1]=>0
[2,5,1,3,4]=>[3,5,1,4,2]=>0
[2,5,1,4,3]=>[3,5,1,4,2]=>0
[2,5,3,1,4]=>[4,5,3,1,2]=>0
[2,5,3,4,1]=>[5,4,3,2,1]=>0
[2,5,4,1,3]=>[4,5,3,1,2]=>0
[2,5,4,3,1]=>[5,4,3,2,1]=>0
[3,1,2,4,5]=>[3,2,1,4,5]=>0
[3,1,2,5,4]=>[3,2,1,5,4]=>0
[3,1,4,2,5]=>[4,2,3,1,5]=>0
[3,1,4,5,2]=>[5,2,3,4,1]=>0
[3,1,5,2,4]=>[4,2,5,1,3]=>0
[3,1,5,4,2]=>[5,2,4,3,1]=>0
[3,2,1,4,5]=>[3,2,1,4,5]=>0
[3,2,1,5,4]=>[3,2,1,5,4]=>0
[3,2,4,1,5]=>[4,2,3,1,5]=>0
[3,2,4,5,1]=>[5,2,3,4,1]=>0
[3,2,5,1,4]=>[4,2,5,1,3]=>0
[3,2,5,4,1]=>[5,2,4,3,1]=>0
[3,4,1,2,5]=>[4,3,2,1,5]=>0
[3,4,1,5,2]=>[5,3,2,4,1]=>0
[3,4,2,1,5]=>[4,3,2,1,5]=>0
[3,4,2,5,1]=>[5,3,2,4,1]=>0
[3,4,5,1,2]=>[5,4,3,2,1]=>0
[3,4,5,2,1]=>[5,4,3,2,1]=>0
[3,5,1,2,4]=>[4,5,3,1,2]=>0
[3,5,1,4,2]=>[5,4,3,2,1]=>0
[3,5,2,1,4]=>[4,5,3,1,2]=>0
[3,5,2,4,1]=>[5,4,3,2,1]=>0
[3,5,4,1,2]=>[5,4,3,2,1]=>0
[3,5,4,2,1]=>[5,4,3,2,1]=>0
[4,1,2,3,5]=>[4,2,3,1,5]=>0
[4,1,2,5,3]=>[5,2,3,4,1]=>0
[4,1,3,2,5]=>[4,2,3,1,5]=>0
[4,1,3,5,2]=>[5,2,3,4,1]=>0
[4,1,5,2,3]=>[5,2,4,3,1]=>0
[4,1,5,3,2]=>[5,2,4,3,1]=>0
[4,2,1,3,5]=>[4,3,2,1,5]=>0
[4,2,1,5,3]=>[5,3,2,4,1]=>0
[4,2,3,1,5]=>[4,3,2,1,5]=>0
[4,2,3,5,1]=>[5,3,2,4,1]=>0
[4,2,5,1,3]=>[5,4,3,2,1]=>0
[4,2,5,3,1]=>[5,4,3,2,1]=>0
[4,3,1,2,5]=>[4,3,2,1,5]=>0
[4,3,1,5,2]=>[5,3,2,4,1]=>0
[4,3,2,1,5]=>[4,3,2,1,5]=>0
[4,3,2,5,1]=>[5,3,2,4,1]=>0
[4,3,5,1,2]=>[5,4,3,2,1]=>0
[4,3,5,2,1]=>[5,4,3,2,1]=>0
[4,5,1,2,3]=>[5,4,3,2,1]=>0
[4,5,1,3,2]=>[5,4,3,2,1]=>0
[4,5,2,1,3]=>[5,4,3,2,1]=>0
[4,5,2,3,1]=>[5,4,3,2,1]=>0
[4,5,3,1,2]=>[5,4,3,2,1]=>0
[4,5,3,2,1]=>[5,4,3,2,1]=>0
[5,1,2,3,4]=>[5,2,3,4,1]=>0
[5,1,2,4,3]=>[5,2,3,4,1]=>0
[5,1,3,2,4]=>[5,2,4,3,1]=>0
[5,1,3,4,2]=>[5,2,4,3,1]=>0
[5,1,4,2,3]=>[5,2,4,3,1]=>0
[5,1,4,3,2]=>[5,2,4,3,1]=>0
[5,2,1,3,4]=>[5,3,2,4,1]=>0
[5,2,1,4,3]=>[5,3,2,4,1]=>0
[5,2,3,1,4]=>[5,4,3,2,1]=>0
[5,2,3,4,1]=>[5,4,3,2,1]=>0
[5,2,4,1,3]=>[5,4,3,2,1]=>0
[5,2,4,3,1]=>[5,4,3,2,1]=>0
[5,3,1,2,4]=>[5,4,3,2,1]=>0
[5,3,1,4,2]=>[5,4,3,2,1]=>0
[5,3,2,1,4]=>[5,4,3,2,1]=>0
[5,3,2,4,1]=>[5,4,3,2,1]=>0
[5,3,4,1,2]=>[5,4,3,2,1]=>0
[5,3,4,2,1]=>[5,4,3,2,1]=>0
[5,4,1,2,3]=>[5,4,3,2,1]=>0
[5,4,1,3,2]=>[5,4,3,2,1]=>0
[5,4,2,1,3]=>[5,4,3,2,1]=>0
[5,4,2,3,1]=>[5,4,3,2,1]=>0
[5,4,3,1,2]=>[5,4,3,2,1]=>0
[5,4,3,2,1]=>[5,4,3,2,1]=>0
[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]=>0
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>0
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>0
[1,2,3,6,4,5]=>[1,2,3,6,5,4]=>0
[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>0
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>0
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>0
[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>0
[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>0
[1,2,4,6,3,5]=>[1,2,5,6,3,4]=>0
[1,2,4,6,5,3]=>[1,2,6,5,4,3]=>0
[1,2,5,3,4,6]=>[1,2,5,4,3,6]=>0
[1,2,5,3,6,4]=>[1,2,6,4,5,3]=>0
[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>0
[1,2,5,4,6,3]=>[1,2,6,4,5,3]=>0
[1,2,5,6,3,4]=>[1,2,6,5,4,3]=>0
[1,2,5,6,4,3]=>[1,2,6,5,4,3]=>0
[1,2,6,3,4,5]=>[1,2,6,4,5,3]=>0
[1,2,6,3,5,4]=>[1,2,6,4,5,3]=>0
[1,2,6,4,3,5]=>[1,2,6,5,4,3]=>0
[1,2,6,4,5,3]=>[1,2,6,5,4,3]=>0
[1,2,6,5,3,4]=>[1,2,6,5,4,3]=>0
[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>0
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>0
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>0
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>0
[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>0
[1,3,2,6,4,5]=>[1,3,2,6,5,4]=>0
[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>0
[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>0
[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>0
[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>0
[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>0
[1,3,4,6,2,5]=>[1,5,3,6,2,4]=>0
[1,3,4,6,5,2]=>[1,6,3,5,4,2]=>0
[1,3,5,2,4,6]=>[1,4,5,2,3,6]=>0
[1,3,5,2,6,4]=>[1,4,6,2,5,3]=>0
[1,3,5,4,2,6]=>[1,5,4,3,2,6]=>0
[1,3,5,4,6,2]=>[1,6,4,3,5,2]=>0
[1,3,5,6,2,4]=>[1,5,6,4,2,3]=>0
[1,3,5,6,4,2]=>[1,6,5,4,3,2]=>0
[1,3,6,2,4,5]=>[1,4,6,2,5,3]=>0
[1,3,6,2,5,4]=>[1,4,6,2,5,3]=>0
[1,3,6,4,2,5]=>[1,5,6,4,2,3]=>0
[1,3,6,4,5,2]=>[1,6,5,4,3,2]=>0
[1,3,6,5,2,4]=>[1,5,6,4,2,3]=>0
[1,3,6,5,4,2]=>[1,6,5,4,3,2]=>0
[1,4,2,3,5,6]=>[1,4,3,2,5,6]=>0
[1,4,2,3,6,5]=>[1,4,3,2,6,5]=>0
[1,4,2,5,3,6]=>[1,5,3,4,2,6]=>0
[1,4,2,5,6,3]=>[1,6,3,4,5,2]=>0
[1,4,2,6,3,5]=>[1,5,3,6,2,4]=>0
[1,4,2,6,5,3]=>[1,6,3,5,4,2]=>0
[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>0
[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>0
[1,4,3,5,2,6]=>[1,5,3,4,2,6]=>0
[1,4,3,5,6,2]=>[1,6,3,4,5,2]=>0
[1,4,3,6,2,5]=>[1,5,3,6,2,4]=>0
[1,4,3,6,5,2]=>[1,6,3,5,4,2]=>0
[1,4,5,2,3,6]=>[1,5,4,3,2,6]=>0
[1,4,5,2,6,3]=>[1,6,4,3,5,2]=>0
[1,4,5,3,2,6]=>[1,5,4,3,2,6]=>0
[1,4,5,3,6,2]=>[1,6,4,3,5,2]=>0
[1,4,5,6,2,3]=>[1,6,5,4,3,2]=>0
[1,4,5,6,3,2]=>[1,6,5,4,3,2]=>0
[1,4,6,2,3,5]=>[1,5,6,4,2,3]=>0
[1,4,6,2,5,3]=>[1,6,5,4,3,2]=>0
[1,4,6,3,2,5]=>[1,5,6,4,2,3]=>0
[1,4,6,3,5,2]=>[1,6,5,4,3,2]=>0
[1,4,6,5,2,3]=>[1,6,5,4,3,2]=>0
[1,4,6,5,3,2]=>[1,6,5,4,3,2]=>0
[1,5,2,3,4,6]=>[1,5,3,4,2,6]=>0
[1,5,2,3,6,4]=>[1,6,3,4,5,2]=>0
[1,5,2,4,3,6]=>[1,5,3,4,2,6]=>0
[1,5,2,4,6,3]=>[1,6,3,4,5,2]=>0
[1,5,2,6,3,4]=>[1,6,3,5,4,2]=>0
[1,5,2,6,4,3]=>[1,6,3,5,4,2]=>0
[1,5,3,2,4,6]=>[1,5,4,3,2,6]=>0
[1,5,3,2,6,4]=>[1,6,4,3,5,2]=>0
[1,5,3,4,2,6]=>[1,5,4,3,2,6]=>0
[1,5,3,4,6,2]=>[1,6,4,3,5,2]=>0
[1,5,3,6,2,4]=>[1,6,5,4,3,2]=>0
[1,5,3,6,4,2]=>[1,6,5,4,3,2]=>0
[1,5,4,2,3,6]=>[1,5,4,3,2,6]=>0
[1,5,4,2,6,3]=>[1,6,4,3,5,2]=>0
[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>0
[1,5,4,3,6,2]=>[1,6,4,3,5,2]=>0
[1,5,4,6,2,3]=>[1,6,5,4,3,2]=>0
[1,5,4,6,3,2]=>[1,6,5,4,3,2]=>0
[1,5,6,2,3,4]=>[1,6,5,4,3,2]=>0
[1,5,6,2,4,3]=>[1,6,5,4,3,2]=>0
[1,5,6,3,2,4]=>[1,6,5,4,3,2]=>0
[1,5,6,3,4,2]=>[1,6,5,4,3,2]=>0
[1,5,6,4,2,3]=>[1,6,5,4,3,2]=>0
[1,5,6,4,3,2]=>[1,6,5,4,3,2]=>0
[1,6,2,3,4,5]=>[1,6,3,4,5,2]=>0
[1,6,2,3,5,4]=>[1,6,3,4,5,2]=>0
[1,6,2,4,3,5]=>[1,6,3,5,4,2]=>0
[1,6,2,4,5,3]=>[1,6,3,5,4,2]=>0
[1,6,2,5,3,4]=>[1,6,3,5,4,2]=>0
[1,6,2,5,4,3]=>[1,6,3,5,4,2]=>0
[1,6,3,2,4,5]=>[1,6,4,3,5,2]=>0
[1,6,3,2,5,4]=>[1,6,4,3,5,2]=>0
[1,6,3,4,2,5]=>[1,6,5,4,3,2]=>0
[1,6,3,4,5,2]=>[1,6,5,4,3,2]=>0
[1,6,3,5,2,4]=>[1,6,5,4,3,2]=>0
[1,6,3,5,4,2]=>[1,6,5,4,3,2]=>0
[1,6,4,2,3,5]=>[1,6,5,4,3,2]=>0
[1,6,4,2,5,3]=>[1,6,5,4,3,2]=>0
[1,6,4,3,2,5]=>[1,6,5,4,3,2]=>0
[1,6,4,3,5,2]=>[1,6,5,4,3,2]=>0
[1,6,4,5,2,3]=>[1,6,5,4,3,2]=>0
[1,6,4,5,3,2]=>[1,6,5,4,3,2]=>0
[1,6,5,2,3,4]=>[1,6,5,4,3,2]=>0
[1,6,5,2,4,3]=>[1,6,5,4,3,2]=>0
[1,6,5,3,2,4]=>[1,6,5,4,3,2]=>0
[1,6,5,3,4,2]=>[1,6,5,4,3,2]=>0
[1,6,5,4,2,3]=>[1,6,5,4,3,2]=>0
[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>0
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>0
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>0
[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>0
[2,1,3,6,4,5]=>[2,1,3,6,5,4]=>0
[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>0
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>0
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>0
[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>0
[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>0
[2,1,4,6,3,5]=>[2,1,5,6,3,4]=>0
[2,1,4,6,5,3]=>[2,1,6,5,4,3]=>0
[2,1,5,3,4,6]=>[2,1,5,4,3,6]=>0
[2,1,5,3,6,4]=>[2,1,6,4,5,3]=>0
[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>0
[2,1,5,4,6,3]=>[2,1,6,4,5,3]=>0
[2,1,5,6,3,4]=>[2,1,6,5,4,3]=>0
[2,1,5,6,4,3]=>[2,1,6,5,4,3]=>0
[2,1,6,3,4,5]=>[2,1,6,4,5,3]=>0
[2,1,6,3,5,4]=>[2,1,6,4,5,3]=>0
[2,1,6,4,3,5]=>[2,1,6,5,4,3]=>0
[2,1,6,4,5,3]=>[2,1,6,5,4,3]=>0
[2,1,6,5,3,4]=>[2,1,6,5,4,3]=>0
[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>0
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>0
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>0
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>0
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>0
[2,3,1,6,4,5]=>[3,2,1,6,5,4]=>0
[2,3,1,6,5,4]=>[3,2,1,6,5,4]=>0
[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>0
[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>0
[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>0
[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>0
[2,3,4,6,1,5]=>[5,2,3,6,1,4]=>0
[2,3,4,6,5,1]=>[6,2,3,5,4,1]=>0
[2,3,5,1,4,6]=>[4,2,5,1,3,6]=>0
[2,3,5,1,6,4]=>[4,2,6,1,5,3]=>0
[2,3,5,4,1,6]=>[5,2,4,3,1,6]=>0
[2,3,5,4,6,1]=>[6,2,4,3,5,1]=>0
[2,3,5,6,1,4]=>[5,2,6,4,1,3]=>0
[2,3,5,6,4,1]=>[6,2,5,4,3,1]=>0
[2,3,6,1,4,5]=>[4,2,6,1,5,3]=>0
[2,3,6,1,5,4]=>[4,2,6,1,5,3]=>0
[2,3,6,4,1,5]=>[5,2,6,4,1,3]=>0
[2,3,6,4,5,1]=>[6,2,5,4,3,1]=>0
[2,3,6,5,1,4]=>[5,2,6,4,1,3]=>0
[2,3,6,5,4,1]=>[6,2,5,4,3,1]=>0
[2,4,1,3,5,6]=>[3,4,1,2,5,6]=>0
[2,4,1,3,6,5]=>[3,4,1,2,6,5]=>0
[2,4,1,5,3,6]=>[3,5,1,4,2,6]=>0
[2,4,1,5,6,3]=>[3,6,1,4,5,2]=>0
[2,4,1,6,3,5]=>[3,5,1,6,2,4]=>0
[2,4,1,6,5,3]=>[3,6,1,5,4,2]=>0
[2,4,3,1,5,6]=>[4,3,2,1,5,6]=>0
[2,4,3,1,6,5]=>[4,3,2,1,6,5]=>0
[2,4,3,5,1,6]=>[5,3,2,4,1,6]=>0
[2,4,3,5,6,1]=>[6,3,2,4,5,1]=>0
[2,4,3,6,1,5]=>[5,3,2,6,1,4]=>0
[2,4,3,6,5,1]=>[6,3,2,5,4,1]=>0
[2,4,5,1,3,6]=>[4,5,3,1,2,6]=>0
[2,4,5,1,6,3]=>[4,6,3,1,5,2]=>0
[2,4,5,3,1,6]=>[5,4,3,2,1,6]=>0
[2,4,5,3,6,1]=>[6,4,3,2,5,1]=>0
[2,4,5,6,1,3]=>[5,6,3,4,1,2]=>0
[2,4,5,6,3,1]=>[6,5,3,4,2,1]=>0
[2,4,6,1,3,5]=>[4,5,6,1,2,3]=>0
[2,4,6,1,5,3]=>[4,6,5,1,3,2]=>0
[2,4,6,3,1,5]=>[5,4,6,2,1,3]=>0
[2,4,6,3,5,1]=>[6,4,5,2,3,1]=>0
[2,4,6,5,1,3]=>[5,6,4,3,1,2]=>0
[2,4,6,5,3,1]=>[6,5,4,3,2,1]=>0
[2,5,1,3,4,6]=>[3,5,1,4,2,6]=>0
[2,5,1,3,6,4]=>[3,6,1,4,5,2]=>0
[2,5,1,4,3,6]=>[3,5,1,4,2,6]=>0
[2,5,1,4,6,3]=>[3,6,1,4,5,2]=>0
[2,5,1,6,3,4]=>[3,6,1,5,4,2]=>0
[2,5,1,6,4,3]=>[3,6,1,5,4,2]=>0
[2,5,3,1,4,6]=>[4,5,3,1,2,6]=>0
[2,5,3,1,6,4]=>[4,6,3,1,5,2]=>0
[2,5,3,4,1,6]=>[5,4,3,2,1,6]=>0
[2,5,3,4,6,1]=>[6,4,3,2,5,1]=>0
[2,5,3,6,1,4]=>[5,6,3,4,1,2]=>0
[2,5,3,6,4,1]=>[6,5,3,4,2,1]=>0
[2,5,4,1,3,6]=>[4,5,3,1,2,6]=>0
[2,5,4,1,6,3]=>[4,6,3,1,5,2]=>0
[2,5,4,3,1,6]=>[5,4,3,2,1,6]=>0
[2,5,4,3,6,1]=>[6,4,3,2,5,1]=>0
[2,5,4,6,1,3]=>[5,6,3,4,1,2]=>0
[2,5,4,6,3,1]=>[6,5,3,4,2,1]=>0
[2,5,6,1,3,4]=>[4,6,5,1,3,2]=>0
[2,5,6,1,4,3]=>[4,6,5,1,3,2]=>0
[2,5,6,3,1,4]=>[5,6,4,3,1,2]=>0
[2,5,6,3,4,1]=>[6,5,4,3,2,1]=>0
[2,5,6,4,1,3]=>[5,6,4,3,1,2]=>0
[2,5,6,4,3,1]=>[6,5,4,3,2,1]=>0
[2,6,1,3,4,5]=>[3,6,1,4,5,2]=>0
[2,6,1,3,5,4]=>[3,6,1,4,5,2]=>0
[2,6,1,4,3,5]=>[3,6,1,5,4,2]=>0
[2,6,1,4,5,3]=>[3,6,1,5,4,2]=>0
[2,6,1,5,3,4]=>[3,6,1,5,4,2]=>0
[2,6,1,5,4,3]=>[3,6,1,5,4,2]=>0
[2,6,3,1,4,5]=>[4,6,3,1,5,2]=>0
[2,6,3,1,5,4]=>[4,6,3,1,5,2]=>0
[2,6,3,4,1,5]=>[5,6,3,4,1,2]=>0
[2,6,3,4,5,1]=>[6,5,3,4,2,1]=>0
[2,6,3,5,1,4]=>[5,6,3,4,1,2]=>0
[2,6,3,5,4,1]=>[6,5,3,4,2,1]=>0
[2,6,4,1,3,5]=>[4,6,5,1,3,2]=>0
[2,6,4,1,5,3]=>[4,6,5,1,3,2]=>0
[2,6,4,3,1,5]=>[5,6,4,3,1,2]=>0
[2,6,4,3,5,1]=>[6,5,4,3,2,1]=>0
[2,6,4,5,1,3]=>[5,6,4,3,1,2]=>0
[2,6,4,5,3,1]=>[6,5,4,3,2,1]=>0
[2,6,5,1,3,4]=>[4,6,5,1,3,2]=>0
[2,6,5,1,4,3]=>[4,6,5,1,3,2]=>0
[2,6,5,3,1,4]=>[5,6,4,3,1,2]=>0
[2,6,5,3,4,1]=>[6,5,4,3,2,1]=>0
[2,6,5,4,1,3]=>[5,6,4,3,1,2]=>0
[2,6,5,4,3,1]=>[6,5,4,3,2,1]=>0
[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>0
[3,1,2,4,6,5]=>[3,2,1,4,6,5]=>0
[3,1,2,5,4,6]=>[3,2,1,5,4,6]=>0
[3,1,2,5,6,4]=>[3,2,1,6,5,4]=>0
[3,1,2,6,4,5]=>[3,2,1,6,5,4]=>0
[3,1,2,6,5,4]=>[3,2,1,6,5,4]=>0
[3,1,4,2,5,6]=>[4,2,3,1,5,6]=>0
[3,1,4,2,6,5]=>[4,2,3,1,6,5]=>0
[3,1,4,5,2,6]=>[5,2,3,4,1,6]=>0
[3,1,4,5,6,2]=>[6,2,3,4,5,1]=>0
[3,1,4,6,2,5]=>[5,2,3,6,1,4]=>0
[3,1,4,6,5,2]=>[6,2,3,5,4,1]=>0
[3,1,5,2,4,6]=>[4,2,5,1,3,6]=>0
[3,1,5,2,6,4]=>[4,2,6,1,5,3]=>0
[3,1,5,4,2,6]=>[5,2,4,3,1,6]=>0
[3,1,5,4,6,2]=>[6,2,4,3,5,1]=>0
[3,1,5,6,2,4]=>[5,2,6,4,1,3]=>0
[3,1,5,6,4,2]=>[6,2,5,4,3,1]=>0
[3,1,6,2,4,5]=>[4,2,6,1,5,3]=>0
[3,1,6,2,5,4]=>[4,2,6,1,5,3]=>0
[3,1,6,4,2,5]=>[5,2,6,4,1,3]=>0
[3,1,6,4,5,2]=>[6,2,5,4,3,1]=>0
[3,1,6,5,2,4]=>[5,2,6,4,1,3]=>0
[3,1,6,5,4,2]=>[6,2,5,4,3,1]=>0
[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>0
[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>0
[3,2,1,5,6,4]=>[3,2,1,6,5,4]=>0
[3,2,1,6,4,5]=>[3,2,1,6,5,4]=>0
[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>0
[3,2,4,1,5,6]=>[4,2,3,1,5,6]=>0
[3,2,4,1,6,5]=>[4,2,3,1,6,5]=>0
[3,2,4,5,1,6]=>[5,2,3,4,1,6]=>0
[3,2,4,5,6,1]=>[6,2,3,4,5,1]=>0
[3,2,4,6,1,5]=>[5,2,3,6,1,4]=>0
[3,2,4,6,5,1]=>[6,2,3,5,4,1]=>0
[3,2,5,1,4,6]=>[4,2,5,1,3,6]=>0
[3,2,5,1,6,4]=>[4,2,6,1,5,3]=>0
[3,2,5,4,1,6]=>[5,2,4,3,1,6]=>0
[3,2,5,4,6,1]=>[6,2,4,3,5,1]=>0
[3,2,5,6,1,4]=>[5,2,6,4,1,3]=>0
[3,2,5,6,4,1]=>[6,2,5,4,3,1]=>0
[3,2,6,1,4,5]=>[4,2,6,1,5,3]=>0
[3,2,6,1,5,4]=>[4,2,6,1,5,3]=>0
[3,2,6,4,1,5]=>[5,2,6,4,1,3]=>0
[3,2,6,4,5,1]=>[6,2,5,4,3,1]=>0
[3,2,6,5,1,4]=>[5,2,6,4,1,3]=>0
[3,2,6,5,4,1]=>[6,2,5,4,3,1]=>0
[3,4,1,2,5,6]=>[4,3,2,1,5,6]=>0
[3,4,1,2,6,5]=>[4,3,2,1,6,5]=>0
[3,4,1,5,2,6]=>[5,3,2,4,1,6]=>0
[3,4,1,5,6,2]=>[6,3,2,4,5,1]=>0
[3,4,1,6,2,5]=>[5,3,2,6,1,4]=>0
[3,4,1,6,5,2]=>[6,3,2,5,4,1]=>0
[3,4,2,1,5,6]=>[4,3,2,1,5,6]=>0
[3,4,2,1,6,5]=>[4,3,2,1,6,5]=>0
[3,4,2,5,1,6]=>[5,3,2,4,1,6]=>0
[3,4,2,5,6,1]=>[6,3,2,4,5,1]=>0
[3,4,2,6,1,5]=>[5,3,2,6,1,4]=>0
[3,4,2,6,5,1]=>[6,3,2,5,4,1]=>0
[3,4,5,1,2,6]=>[5,4,3,2,1,6]=>0
[3,4,5,1,6,2]=>[6,4,3,2,5,1]=>0
[3,4,5,2,1,6]=>[5,4,3,2,1,6]=>0
[3,4,5,2,6,1]=>[6,4,3,2,5,1]=>0
[3,4,5,6,1,2]=>[6,5,3,4,2,1]=>0
[3,4,5,6,2,1]=>[6,5,3,4,2,1]=>0
[3,4,6,1,2,5]=>[5,4,6,2,1,3]=>0
[3,4,6,1,5,2]=>[6,4,5,2,3,1]=>0
[3,4,6,2,1,5]=>[5,4,6,2,1,3]=>0
[3,4,6,2,5,1]=>[6,4,5,2,3,1]=>0
[3,4,6,5,1,2]=>[6,5,4,3,2,1]=>0
[3,4,6,5,2,1]=>[6,5,4,3,2,1]=>0
[3,5,1,2,4,6]=>[4,5,3,1,2,6]=>0
[3,5,1,2,6,4]=>[4,6,3,1,5,2]=>0
[3,5,1,4,2,6]=>[5,4,3,2,1,6]=>0
[3,5,1,4,6,2]=>[6,4,3,2,5,1]=>0
[3,5,1,6,2,4]=>[5,6,3,4,1,2]=>0
[3,5,1,6,4,2]=>[6,5,3,4,2,1]=>0
[3,5,2,1,4,6]=>[4,5,3,1,2,6]=>0
[3,5,2,1,6,4]=>[4,6,3,1,5,2]=>0
[3,5,2,4,1,6]=>[5,4,3,2,1,6]=>0
[3,5,2,4,6,1]=>[6,4,3,2,5,1]=>0
[3,5,2,6,1,4]=>[5,6,3,4,1,2]=>0
[3,5,2,6,4,1]=>[6,5,3,4,2,1]=>0
[3,5,4,1,2,6]=>[5,4,3,2,1,6]=>0
[3,5,4,1,6,2]=>[6,4,3,2,5,1]=>0
[3,5,4,2,1,6]=>[5,4,3,2,1,6]=>0
[3,5,4,2,6,1]=>[6,4,3,2,5,1]=>0
[3,5,4,6,1,2]=>[6,5,3,4,2,1]=>0
[3,5,4,6,2,1]=>[6,5,3,4,2,1]=>0
[3,5,6,1,2,4]=>[5,6,4,3,1,2]=>0
[3,5,6,1,4,2]=>[6,5,4,3,2,1]=>0
[3,5,6,2,1,4]=>[5,6,4,3,1,2]=>0
[3,5,6,2,4,1]=>[6,5,4,3,2,1]=>0
[3,5,6,4,1,2]=>[6,5,4,3,2,1]=>0
[3,5,6,4,2,1]=>[6,5,4,3,2,1]=>0
[3,6,1,2,4,5]=>[4,6,3,1,5,2]=>0
[3,6,1,2,5,4]=>[4,6,3,1,5,2]=>0
[3,6,1,4,2,5]=>[5,6,3,4,1,2]=>0
[3,6,1,4,5,2]=>[6,5,3,4,2,1]=>0
[3,6,1,5,2,4]=>[5,6,3,4,1,2]=>0
[3,6,1,5,4,2]=>[6,5,3,4,2,1]=>0
[3,6,2,1,4,5]=>[4,6,3,1,5,2]=>0
[3,6,2,1,5,4]=>[4,6,3,1,5,2]=>0
[3,6,2,4,1,5]=>[5,6,3,4,1,2]=>0
[3,6,2,4,5,1]=>[6,5,3,4,2,1]=>0
[3,6,2,5,1,4]=>[5,6,3,4,1,2]=>0
[3,6,2,5,4,1]=>[6,5,3,4,2,1]=>0
[3,6,4,1,2,5]=>[5,6,4,3,1,2]=>0
[3,6,4,1,5,2]=>[6,5,4,3,2,1]=>0
[3,6,4,2,1,5]=>[5,6,4,3,1,2]=>0
[3,6,4,2,5,1]=>[6,5,4,3,2,1]=>0
[3,6,4,5,1,2]=>[6,5,4,3,2,1]=>0
[3,6,4,5,2,1]=>[6,5,4,3,2,1]=>0
[3,6,5,1,2,4]=>[5,6,4,3,1,2]=>0
[3,6,5,1,4,2]=>[6,5,4,3,2,1]=>0
[3,6,5,2,1,4]=>[5,6,4,3,1,2]=>0
[3,6,5,2,4,1]=>[6,5,4,3,2,1]=>0
[3,6,5,4,1,2]=>[6,5,4,3,2,1]=>0
[3,6,5,4,2,1]=>[6,5,4,3,2,1]=>0
[4,1,2,3,5,6]=>[4,2,3,1,5,6]=>0
[4,1,2,3,6,5]=>[4,2,3,1,6,5]=>0
[4,1,2,5,3,6]=>[5,2,3,4,1,6]=>0
[4,1,2,5,6,3]=>[6,2,3,4,5,1]=>0
[4,1,2,6,3,5]=>[5,2,3,6,1,4]=>0
[4,1,2,6,5,3]=>[6,2,3,5,4,1]=>0
[4,1,3,2,5,6]=>[4,2,3,1,5,6]=>0
[4,1,3,2,6,5]=>[4,2,3,1,6,5]=>0
[4,1,3,5,2,6]=>[5,2,3,4,1,6]=>0
[4,1,3,5,6,2]=>[6,2,3,4,5,1]=>0
[4,1,3,6,2,5]=>[5,2,3,6,1,4]=>0
[4,1,3,6,5,2]=>[6,2,3,5,4,1]=>0
[4,1,5,2,3,6]=>[5,2,4,3,1,6]=>0
[4,1,5,2,6,3]=>[6,2,4,3,5,1]=>0
[4,1,5,3,2,6]=>[5,2,4,3,1,6]=>0
[4,1,5,3,6,2]=>[6,2,4,3,5,1]=>0
[4,1,5,6,2,3]=>[6,2,5,4,3,1]=>0
[4,1,5,6,3,2]=>[6,2,5,4,3,1]=>0
[4,1,6,2,3,5]=>[5,2,6,4,1,3]=>0
[4,1,6,2,5,3]=>[6,2,5,4,3,1]=>0
[4,1,6,3,2,5]=>[5,2,6,4,1,3]=>0
[4,1,6,3,5,2]=>[6,2,5,4,3,1]=>0
[4,1,6,5,2,3]=>[6,2,5,4,3,1]=>0
[4,1,6,5,3,2]=>[6,2,5,4,3,1]=>0
[4,2,1,3,5,6]=>[4,3,2,1,5,6]=>0
[4,2,1,3,6,5]=>[4,3,2,1,6,5]=>0
[4,2,1,5,3,6]=>[5,3,2,4,1,6]=>0
[4,2,1,5,6,3]=>[6,3,2,4,5,1]=>0
[4,2,1,6,3,5]=>[5,3,2,6,1,4]=>0
[4,2,1,6,5,3]=>[6,3,2,5,4,1]=>0
[4,2,3,1,5,6]=>[4,3,2,1,5,6]=>0
[4,2,3,1,6,5]=>[4,3,2,1,6,5]=>0
[4,2,3,5,1,6]=>[5,3,2,4,1,6]=>0
[4,2,3,5,6,1]=>[6,3,2,4,5,1]=>0
[4,2,3,6,1,5]=>[5,3,2,6,1,4]=>0
[4,2,3,6,5,1]=>[6,3,2,5,4,1]=>0
[4,2,5,1,3,6]=>[5,4,3,2,1,6]=>0
[4,2,5,1,6,3]=>[6,4,3,2,5,1]=>0
[4,2,5,3,1,6]=>[5,4,3,2,1,6]=>0
[4,2,5,3,6,1]=>[6,4,3,2,5,1]=>0
[4,2,5,6,1,3]=>[6,5,3,4,2,1]=>0
[4,2,5,6,3,1]=>[6,5,3,4,2,1]=>0
[4,2,6,1,3,5]=>[5,4,6,2,1,3]=>0
[4,2,6,1,5,3]=>[6,4,5,2,3,1]=>0
[4,2,6,3,1,5]=>[5,4,6,2,1,3]=>0
[4,2,6,3,5,1]=>[6,4,5,2,3,1]=>0
[4,2,6,5,1,3]=>[6,5,4,3,2,1]=>0
[4,2,6,5,3,1]=>[6,5,4,3,2,1]=>0
[4,3,1,2,5,6]=>[4,3,2,1,5,6]=>0
[4,3,1,2,6,5]=>[4,3,2,1,6,5]=>0
[4,3,1,5,2,6]=>[5,3,2,4,1,6]=>0
[4,3,1,5,6,2]=>[6,3,2,4,5,1]=>0
[4,3,1,6,2,5]=>[5,3,2,6,1,4]=>0
[4,3,1,6,5,2]=>[6,3,2,5,4,1]=>0
[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>0
[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>0
[4,3,2,5,1,6]=>[5,3,2,4,1,6]=>0
[4,3,2,5,6,1]=>[6,3,2,4,5,1]=>0
[4,3,2,6,1,5]=>[5,3,2,6,1,4]=>0
[4,3,2,6,5,1]=>[6,3,2,5,4,1]=>0
[4,3,5,1,2,6]=>[5,4,3,2,1,6]=>0
[4,3,5,1,6,2]=>[6,4,3,2,5,1]=>0
[4,3,5,2,1,6]=>[5,4,3,2,1,6]=>0
[4,3,5,2,6,1]=>[6,4,3,2,5,1]=>0
[4,3,5,6,1,2]=>[6,5,3,4,2,1]=>0
[4,3,5,6,2,1]=>[6,5,3,4,2,1]=>0
[4,3,6,1,2,5]=>[5,4,6,2,1,3]=>0
[4,3,6,1,5,2]=>[6,4,5,2,3,1]=>0
[4,3,6,2,1,5]=>[5,4,6,2,1,3]=>0
[4,3,6,2,5,1]=>[6,4,5,2,3,1]=>0
[4,3,6,5,1,2]=>[6,5,4,3,2,1]=>0
[4,3,6,5,2,1]=>[6,5,4,3,2,1]=>0
[4,5,1,2,3,6]=>[5,4,3,2,1,6]=>0
[4,5,1,2,6,3]=>[6,4,3,2,5,1]=>0
[4,5,1,3,2,6]=>[5,4,3,2,1,6]=>0
[4,5,1,3,6,2]=>[6,4,3,2,5,1]=>0
[4,5,1,6,2,3]=>[6,5,3,4,2,1]=>0
[4,5,1,6,3,2]=>[6,5,3,4,2,1]=>0
[4,5,2,1,3,6]=>[5,4,3,2,1,6]=>0
[4,5,2,1,6,3]=>[6,4,3,2,5,1]=>0
[4,5,2,3,1,6]=>[5,4,3,2,1,6]=>0
[4,5,2,3,6,1]=>[6,4,3,2,5,1]=>0
[4,5,2,6,1,3]=>[6,5,3,4,2,1]=>0
[4,5,2,6,3,1]=>[6,5,3,4,2,1]=>0
[4,5,3,1,2,6]=>[5,4,3,2,1,6]=>0
[4,5,3,1,6,2]=>[6,4,3,2,5,1]=>0
[4,5,3,2,1,6]=>[5,4,3,2,1,6]=>0
[4,5,3,2,6,1]=>[6,4,3,2,5,1]=>0
[4,5,3,6,1,2]=>[6,5,3,4,2,1]=>0
[4,5,3,6,2,1]=>[6,5,3,4,2,1]=>0
[4,5,6,1,2,3]=>[6,5,4,3,2,1]=>0
[4,5,6,1,3,2]=>[6,5,4,3,2,1]=>0
[4,5,6,2,1,3]=>[6,5,4,3,2,1]=>0
[4,5,6,2,3,1]=>[6,5,4,3,2,1]=>0
[4,5,6,3,1,2]=>[6,5,4,3,2,1]=>0
[4,5,6,3,2,1]=>[6,5,4,3,2,1]=>0
[4,6,1,2,3,5]=>[5,6,3,4,1,2]=>0
[4,6,1,2,5,3]=>[6,5,3,4,2,1]=>0
[4,6,1,3,2,5]=>[5,6,3,4,1,2]=>0
[4,6,1,3,5,2]=>[6,5,3,4,2,1]=>0
[4,6,1,5,2,3]=>[6,5,3,4,2,1]=>0
[4,6,1,5,3,2]=>[6,5,3,4,2,1]=>0
[4,6,2,1,3,5]=>[5,6,4,3,1,2]=>0
[4,6,2,1,5,3]=>[6,5,4,3,2,1]=>0
[4,6,2,3,1,5]=>[5,6,4,3,1,2]=>0
[4,6,2,3,5,1]=>[6,5,4,3,2,1]=>0
[4,6,2,5,1,3]=>[6,5,4,3,2,1]=>0
[4,6,2,5,3,1]=>[6,5,4,3,2,1]=>0
[4,6,3,1,2,5]=>[5,6,4,3,1,2]=>0
[4,6,3,1,5,2]=>[6,5,4,3,2,1]=>0
[4,6,3,2,1,5]=>[5,6,4,3,1,2]=>0
[4,6,3,2,5,1]=>[6,5,4,3,2,1]=>0
[4,6,3,5,1,2]=>[6,5,4,3,2,1]=>0
[4,6,3,5,2,1]=>[6,5,4,3,2,1]=>0
[4,6,5,1,2,3]=>[6,5,4,3,2,1]=>0
[4,6,5,1,3,2]=>[6,5,4,3,2,1]=>0
[4,6,5,2,1,3]=>[6,5,4,3,2,1]=>0
[4,6,5,2,3,1]=>[6,5,4,3,2,1]=>0
[4,6,5,3,1,2]=>[6,5,4,3,2,1]=>0
[4,6,5,3,2,1]=>[6,5,4,3,2,1]=>0
[5,1,2,3,4,6]=>[5,2,3,4,1,6]=>0
[5,1,2,3,6,4]=>[6,2,3,4,5,1]=>0
[5,1,2,4,3,6]=>[5,2,3,4,1,6]=>0
[5,1,2,4,6,3]=>[6,2,3,4,5,1]=>0
[5,1,2,6,3,4]=>[6,2,3,5,4,1]=>0
[5,1,2,6,4,3]=>[6,2,3,5,4,1]=>0
[5,1,3,2,4,6]=>[5,2,4,3,1,6]=>0
[5,1,3,2,6,4]=>[6,2,4,3,5,1]=>0
[5,1,3,4,2,6]=>[5,2,4,3,1,6]=>0
[5,1,3,4,6,2]=>[6,2,4,3,5,1]=>0
[5,1,3,6,2,4]=>[6,2,5,4,3,1]=>0
[5,1,3,6,4,2]=>[6,2,5,4,3,1]=>0
[5,1,4,2,3,6]=>[5,2,4,3,1,6]=>0
[5,1,4,2,6,3]=>[6,2,4,3,5,1]=>0
[5,1,4,3,2,6]=>[5,2,4,3,1,6]=>0
[5,1,4,3,6,2]=>[6,2,4,3,5,1]=>0
[5,1,4,6,2,3]=>[6,2,5,4,3,1]=>0
[5,1,4,6,3,2]=>[6,2,5,4,3,1]=>0
[5,1,6,2,3,4]=>[6,2,5,4,3,1]=>0
[5,1,6,2,4,3]=>[6,2,5,4,3,1]=>0
[5,1,6,3,2,4]=>[6,2,5,4,3,1]=>0
[5,1,6,3,4,2]=>[6,2,5,4,3,1]=>0
[5,1,6,4,2,3]=>[6,2,5,4,3,1]=>0
[5,1,6,4,3,2]=>[6,2,5,4,3,1]=>0
[5,2,1,3,4,6]=>[5,3,2,4,1,6]=>0
[5,2,1,3,6,4]=>[6,3,2,4,5,1]=>0
[5,2,1,4,3,6]=>[5,3,2,4,1,6]=>0
[5,2,1,4,6,3]=>[6,3,2,4,5,1]=>0
[5,2,1,6,3,4]=>[6,3,2,5,4,1]=>0
[5,2,1,6,4,3]=>[6,3,2,5,4,1]=>0
[5,2,3,1,4,6]=>[5,4,3,2,1,6]=>0
[5,2,3,1,6,4]=>[6,4,3,2,5,1]=>0
[5,2,3,4,1,6]=>[5,4,3,2,1,6]=>0
[5,2,3,4,6,1]=>[6,4,3,2,5,1]=>0
[5,2,3,6,1,4]=>[6,5,3,4,2,1]=>0
[5,2,3,6,4,1]=>[6,5,3,4,2,1]=>0
[5,2,4,1,3,6]=>[5,4,3,2,1,6]=>0
[5,2,4,1,6,3]=>[6,4,3,2,5,1]=>0
[5,2,4,3,1,6]=>[5,4,3,2,1,6]=>0
[5,2,4,3,6,1]=>[6,4,3,2,5,1]=>0
[5,2,4,6,1,3]=>[6,5,3,4,2,1]=>0
[5,2,4,6,3,1]=>[6,5,3,4,2,1]=>0
[5,2,6,1,3,4]=>[6,4,5,2,3,1]=>0
[5,2,6,1,4,3]=>[6,4,5,2,3,1]=>0
[5,2,6,3,1,4]=>[6,5,4,3,2,1]=>0
[5,2,6,3,4,1]=>[6,5,4,3,2,1]=>0
[5,2,6,4,1,3]=>[6,5,4,3,2,1]=>0
[5,2,6,4,3,1]=>[6,5,4,3,2,1]=>0
[5,3,1,2,4,6]=>[5,4,3,2,1,6]=>0
[5,3,1,2,6,4]=>[6,4,3,2,5,1]=>0
[5,3,1,4,2,6]=>[5,4,3,2,1,6]=>0
[5,3,1,4,6,2]=>[6,4,3,2,5,1]=>0
[5,3,1,6,2,4]=>[6,5,3,4,2,1]=>0
[5,3,1,6,4,2]=>[6,5,3,4,2,1]=>0
[5,3,2,1,4,6]=>[5,4,3,2,1,6]=>0
[5,3,2,1,6,4]=>[6,4,3,2,5,1]=>0
[5,3,2,4,1,6]=>[5,4,3,2,1,6]=>0
[5,3,2,4,6,1]=>[6,4,3,2,5,1]=>0
[5,3,2,6,1,4]=>[6,5,3,4,2,1]=>0
[5,3,2,6,4,1]=>[6,5,3,4,2,1]=>0
[5,3,4,1,2,6]=>[5,4,3,2,1,6]=>0
[5,3,4,1,6,2]=>[6,4,3,2,5,1]=>0
[5,3,4,2,1,6]=>[5,4,3,2,1,6]=>0
[5,3,4,2,6,1]=>[6,4,3,2,5,1]=>0
[5,3,4,6,1,2]=>[6,5,3,4,2,1]=>0
[5,3,4,6,2,1]=>[6,5,3,4,2,1]=>0
[5,3,6,1,2,4]=>[6,5,4,3,2,1]=>0
[5,3,6,1,4,2]=>[6,5,4,3,2,1]=>0
[5,3,6,2,1,4]=>[6,5,4,3,2,1]=>0
[5,3,6,2,4,1]=>[6,5,4,3,2,1]=>0
[5,3,6,4,1,2]=>[6,5,4,3,2,1]=>0
[5,3,6,4,2,1]=>[6,5,4,3,2,1]=>0
[5,4,1,2,3,6]=>[5,4,3,2,1,6]=>0
[5,4,1,2,6,3]=>[6,4,3,2,5,1]=>0
[5,4,1,3,2,6]=>[5,4,3,2,1,6]=>0
[5,4,1,3,6,2]=>[6,4,3,2,5,1]=>0
[5,4,1,6,2,3]=>[6,5,3,4,2,1]=>0
[5,4,1,6,3,2]=>[6,5,3,4,2,1]=>0
[5,4,2,1,3,6]=>[5,4,3,2,1,6]=>0
[5,4,2,1,6,3]=>[6,4,3,2,5,1]=>0
[5,4,2,3,1,6]=>[5,4,3,2,1,6]=>0
[5,4,2,3,6,1]=>[6,4,3,2,5,1]=>0
[5,4,2,6,1,3]=>[6,5,3,4,2,1]=>0
[5,4,2,6,3,1]=>[6,5,3,4,2,1]=>0
[5,4,3,1,2,6]=>[5,4,3,2,1,6]=>0
[5,4,3,1,6,2]=>[6,4,3,2,5,1]=>0
[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>[6,4,3,2,5,1]=>0
[5,4,3,6,1,2]=>[6,5,3,4,2,1]=>0
[5,4,3,6,2,1]=>[6,5,3,4,2,1]=>0
[5,4,6,1,2,3]=>[6,5,4,3,2,1]=>0
[5,4,6,1,3,2]=>[6,5,4,3,2,1]=>0
[5,4,6,2,1,3]=>[6,5,4,3,2,1]=>0
[5,4,6,2,3,1]=>[6,5,4,3,2,1]=>0
[5,4,6,3,1,2]=>[6,5,4,3,2,1]=>0
[5,4,6,3,2,1]=>[6,5,4,3,2,1]=>0
[5,6,1,2,3,4]=>[6,5,3,4,2,1]=>0
[5,6,1,2,4,3]=>[6,5,3,4,2,1]=>0
[5,6,1,3,2,4]=>[6,5,3,4,2,1]=>0
[5,6,1,3,4,2]=>[6,5,3,4,2,1]=>0
[5,6,1,4,2,3]=>[6,5,3,4,2,1]=>0
[5,6,1,4,3,2]=>[6,5,3,4,2,1]=>0
[5,6,2,1,3,4]=>[6,5,4,3,2,1]=>0
[5,6,2,1,4,3]=>[6,5,4,3,2,1]=>0
[5,6,2,3,1,4]=>[6,5,4,3,2,1]=>0
[5,6,2,3,4,1]=>[6,5,4,3,2,1]=>0
[5,6,2,4,1,3]=>[6,5,4,3,2,1]=>0
[5,6,2,4,3,1]=>[6,5,4,3,2,1]=>0
[5,6,3,1,2,4]=>[6,5,4,3,2,1]=>0
[5,6,3,1,4,2]=>[6,5,4,3,2,1]=>0
[5,6,3,2,1,4]=>[6,5,4,3,2,1]=>0
[5,6,3,2,4,1]=>[6,5,4,3,2,1]=>0
[5,6,3,4,1,2]=>[6,5,4,3,2,1]=>0
[5,6,3,4,2,1]=>[6,5,4,3,2,1]=>0
[5,6,4,1,2,3]=>[6,5,4,3,2,1]=>0
[5,6,4,1,3,2]=>[6,5,4,3,2,1]=>0
[5,6,4,2,1,3]=>[6,5,4,3,2,1]=>0
[5,6,4,2,3,1]=>[6,5,4,3,2,1]=>0
[5,6,4,3,1,2]=>[6,5,4,3,2,1]=>0
[5,6,4,3,2,1]=>[6,5,4,3,2,1]=>0
[6,1,2,3,4,5]=>[6,2,3,4,5,1]=>0
[6,1,2,3,5,4]=>[6,2,3,4,5,1]=>0
[6,1,2,4,3,5]=>[6,2,3,5,4,1]=>0
[6,1,2,4,5,3]=>[6,2,3,5,4,1]=>0
[6,1,2,5,3,4]=>[6,2,3,5,4,1]=>0
[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>0
[6,1,3,2,4,5]=>[6,2,4,3,5,1]=>0
[6,1,3,2,5,4]=>[6,2,4,3,5,1]=>0
[6,1,3,4,2,5]=>[6,2,5,4,3,1]=>0
[6,1,3,4,5,2]=>[6,2,5,4,3,1]=>0
[6,1,3,5,2,4]=>[6,2,5,4,3,1]=>0
[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>0
[6,1,4,2,3,5]=>[6,2,5,4,3,1]=>0
[6,1,4,2,5,3]=>[6,2,5,4,3,1]=>0
[6,1,4,3,2,5]=>[6,2,5,4,3,1]=>0
[6,1,4,3,5,2]=>[6,2,5,4,3,1]=>0
[6,1,4,5,2,3]=>[6,2,5,4,3,1]=>0
[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>0
[6,1,5,2,3,4]=>[6,2,5,4,3,1]=>0
[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>0
[6,1,5,3,2,4]=>[6,2,5,4,3,1]=>0
[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>0
[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>0
[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>0
[6,2,1,3,4,5]=>[6,3,2,4,5,1]=>0
[6,2,1,3,5,4]=>[6,3,2,4,5,1]=>0
[6,2,1,4,3,5]=>[6,3,2,5,4,1]=>0
[6,2,1,4,5,3]=>[6,3,2,5,4,1]=>0
[6,2,1,5,3,4]=>[6,3,2,5,4,1]=>0
[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>0
[6,2,3,1,4,5]=>[6,4,3,2,5,1]=>0
[6,2,3,1,5,4]=>[6,4,3,2,5,1]=>0
[6,2,3,4,1,5]=>[6,5,3,4,2,1]=>0
[6,2,3,4,5,1]=>[6,5,3,4,2,1]=>0
[6,2,3,5,1,4]=>[6,5,3,4,2,1]=>0
[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>0
[6,2,4,1,3,5]=>[6,4,5,2,3,1]=>0
[6,2,4,1,5,3]=>[6,4,5,2,3,1]=>0
[6,2,4,3,1,5]=>[6,5,4,3,2,1]=>0
[6,2,4,3,5,1]=>[6,5,4,3,2,1]=>0
[6,2,4,5,1,3]=>[6,5,4,3,2,1]=>0
[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>0
[6,2,5,1,3,4]=>[6,4,5,2,3,1]=>0
[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>0
[6,2,5,3,1,4]=>[6,5,4,3,2,1]=>0
[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>0
[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>0
[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>0
[6,3,1,2,4,5]=>[6,4,3,2,5,1]=>0
[6,3,1,2,5,4]=>[6,4,3,2,5,1]=>0
[6,3,1,4,2,5]=>[6,5,3,4,2,1]=>0
[6,3,1,4,5,2]=>[6,5,3,4,2,1]=>0
[6,3,1,5,2,4]=>[6,5,3,4,2,1]=>0
[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>0
[6,3,2,1,4,5]=>[6,4,3,2,5,1]=>0
[6,3,2,1,5,4]=>[6,4,3,2,5,1]=>0
[6,3,2,4,1,5]=>[6,5,3,4,2,1]=>0
[6,3,2,4,5,1]=>[6,5,3,4,2,1]=>0
[6,3,2,5,1,4]=>[6,5,3,4,2,1]=>0
[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>0
[6,3,4,1,2,5]=>[6,5,4,3,2,1]=>0
[6,3,4,1,5,2]=>[6,5,4,3,2,1]=>0
[6,3,4,2,1,5]=>[6,5,4,3,2,1]=>0
[6,3,4,2,5,1]=>[6,5,4,3,2,1]=>0
[6,3,4,5,1,2]=>[6,5,4,3,2,1]=>0
[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>0
[6,3,5,1,2,4]=>[6,5,4,3,2,1]=>0
[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>0
[6,3,5,2,1,4]=>[6,5,4,3,2,1]=>0
[6,3,5,2,4,1]=>[6,5,4,3,2,1]=>0
[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>0
[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>0
[6,4,1,2,3,5]=>[6,5,3,4,2,1]=>0
[6,4,1,2,5,3]=>[6,5,3,4,2,1]=>0
[6,4,1,3,2,5]=>[6,5,3,4,2,1]=>0
[6,4,1,3,5,2]=>[6,5,3,4,2,1]=>0
[6,4,1,5,2,3]=>[6,5,3,4,2,1]=>0
[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>0
[6,4,2,1,3,5]=>[6,5,4,3,2,1]=>0
[6,4,2,1,5,3]=>[6,5,4,3,2,1]=>0
[6,4,2,3,1,5]=>[6,5,4,3,2,1]=>0
[6,4,2,3,5,1]=>[6,5,4,3,2,1]=>0
[6,4,2,5,1,3]=>[6,5,4,3,2,1]=>0
[6,4,2,5,3,1]=>[6,5,4,3,2,1]=>0
[6,4,3,1,2,5]=>[6,5,4,3,2,1]=>0
[6,4,3,1,5,2]=>[6,5,4,3,2,1]=>0
[6,4,3,2,1,5]=>[6,5,4,3,2,1]=>0
[6,4,3,2,5,1]=>[6,5,4,3,2,1]=>0
[6,4,3,5,1,2]=>[6,5,4,3,2,1]=>0
[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>0
[6,4,5,1,2,3]=>[6,5,4,3,2,1]=>0
[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>0
[6,4,5,2,1,3]=>[6,5,4,3,2,1]=>0
[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>0
[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>0
[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>0
[6,5,1,2,3,4]=>[6,5,3,4,2,1]=>0
[6,5,1,2,4,3]=>[6,5,3,4,2,1]=>0
[6,5,1,3,2,4]=>[6,5,3,4,2,1]=>0
[6,5,1,3,4,2]=>[6,5,3,4,2,1]=>0
[6,5,1,4,2,3]=>[6,5,3,4,2,1]=>0
[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>0
[6,5,2,1,3,4]=>[6,5,4,3,2,1]=>0
[6,5,2,1,4,3]=>[6,5,4,3,2,1]=>0
[6,5,2,3,1,4]=>[6,5,4,3,2,1]=>0
[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>0
[6,5,2,4,1,3]=>[6,5,4,3,2,1]=>0
[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>0
[6,5,3,1,2,4]=>[6,5,4,3,2,1]=>0
[6,5,3,1,4,2]=>[6,5,4,3,2,1]=>0
[6,5,3,2,1,4]=>[6,5,4,3,2,1]=>0
[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>0
[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>0
[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>0
[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>0
[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>0
[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>0
[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>0
[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>0
[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>0
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Description
The cycle descent number of a permutation.
Let $(i_1,\ldots,i_k)$ be a cycle of a permutation $\pi$ such that $i_1$ is its smallest element. A **cycle descent** of $(i_1,\ldots,i_k)$ is an $i_a$ for $1 \leq a < k$ such that $i_a > i_{a+1}$. The **cycle descent set** of $\pi$ is then the set of descents in all the cycles of $\pi$, and the **cycle descent number** is its cardinality.
Let $(i_1,\ldots,i_k)$ be a cycle of a permutation $\pi$ such that $i_1$ is its smallest element. A **cycle descent** of $(i_1,\ldots,i_k)$ is an $i_a$ for $1 \leq a < k$ such that $i_a > i_{a+1}$. The **cycle descent set** of $\pi$ is then the set of descents in all the cycles of $\pi$, and the **cycle descent number** is its cardinality.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
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