Identifier
-
Mp00239:
Permutations
—Corteel⟶
Permutations
St000223: 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]=>1
[3,1,2]=>[3,1,2]=>0
[3,2,1]=>[2,3,1]=>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]=>1
[1,4,2,3]=>[1,4,2,3]=>0
[1,4,3,2]=>[1,3,4,2]=>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]=>1
[2,3,4,1]=>[4,2,3,1]=>2
[2,4,1,3]=>[4,2,1,3]=>1
[2,4,3,1]=>[3,2,4,1]=>1
[3,1,2,4]=>[3,1,2,4]=>0
[3,1,4,2]=>[4,1,3,2]=>1
[3,2,1,4]=>[2,3,1,4]=>0
[3,2,4,1]=>[2,4,3,1]=>1
[3,4,1,2]=>[4,3,2,1]=>2
[3,4,2,1]=>[4,3,1,2]=>1
[4,1,2,3]=>[4,1,2,3]=>0
[4,1,3,2]=>[3,1,4,2]=>0
[4,2,1,3]=>[2,4,1,3]=>0
[4,2,3,1]=>[2,3,4,1]=>0
[4,3,1,2]=>[3,4,2,1]=>1
[4,3,2,1]=>[3,4,1,2]=>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]=>1
[1,2,5,3,4]=>[1,2,5,3,4]=>0
[1,2,5,4,3]=>[1,2,4,5,3]=>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]=>1
[1,3,4,5,2]=>[1,5,3,4,2]=>2
[1,3,5,2,4]=>[1,5,3,2,4]=>1
[1,3,5,4,2]=>[1,4,3,5,2]=>1
[1,4,2,3,5]=>[1,4,2,3,5]=>0
[1,4,2,5,3]=>[1,5,2,4,3]=>1
[1,4,3,2,5]=>[1,3,4,2,5]=>0
[1,4,3,5,2]=>[1,3,5,4,2]=>1
[1,4,5,2,3]=>[1,5,4,3,2]=>2
[1,4,5,3,2]=>[1,5,4,2,3]=>1
[1,5,2,3,4]=>[1,5,2,3,4]=>0
[1,5,2,4,3]=>[1,4,2,5,3]=>0
[1,5,3,2,4]=>[1,3,5,2,4]=>0
[1,5,3,4,2]=>[1,3,4,5,2]=>0
[1,5,4,2,3]=>[1,4,5,3,2]=>1
[1,5,4,3,2]=>[1,4,5,2,3]=>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]=>1
[2,1,5,3,4]=>[2,1,5,3,4]=>0
[2,1,5,4,3]=>[2,1,4,5,3]=>0
[2,3,1,4,5]=>[3,2,1,4,5]=>1
[2,3,1,5,4]=>[3,2,1,5,4]=>1
[2,3,4,1,5]=>[4,2,3,1,5]=>2
[2,3,4,5,1]=>[5,2,3,4,1]=>3
[2,3,5,1,4]=>[5,2,3,1,4]=>2
[2,3,5,4,1]=>[4,2,3,5,1]=>2
[2,4,1,3,5]=>[4,2,1,3,5]=>1
[2,4,1,5,3]=>[5,2,1,4,3]=>2
[2,4,3,1,5]=>[3,2,4,1,5]=>1
[2,4,3,5,1]=>[3,2,5,4,1]=>2
[2,4,5,1,3]=>[5,2,4,3,1]=>3
[2,4,5,3,1]=>[5,2,4,1,3]=>2
[2,5,1,3,4]=>[5,2,1,3,4]=>1
[2,5,1,4,3]=>[4,2,1,5,3]=>1
[2,5,3,1,4]=>[3,2,5,1,4]=>1
[2,5,3,4,1]=>[3,2,4,5,1]=>1
[2,5,4,1,3]=>[4,2,5,3,1]=>2
[2,5,4,3,1]=>[4,2,5,1,3]=>1
[3,1,2,4,5]=>[3,1,2,4,5]=>0
[3,1,2,5,4]=>[3,1,2,5,4]=>0
[3,1,4,2,5]=>[4,1,3,2,5]=>1
[3,1,4,5,2]=>[5,1,3,4,2]=>2
[3,1,5,2,4]=>[5,1,3,2,4]=>1
[3,1,5,4,2]=>[4,1,3,5,2]=>1
[3,2,1,4,5]=>[2,3,1,4,5]=>0
[3,2,1,5,4]=>[2,3,1,5,4]=>0
[3,2,4,1,5]=>[2,4,3,1,5]=>1
[3,2,4,5,1]=>[2,5,3,4,1]=>2
[3,2,5,1,4]=>[2,5,3,1,4]=>1
[3,2,5,4,1]=>[2,4,3,5,1]=>1
[3,4,1,2,5]=>[4,3,2,1,5]=>2
[3,4,1,5,2]=>[5,3,2,4,1]=>3
[3,4,2,1,5]=>[4,3,1,2,5]=>1
[3,4,2,5,1]=>[5,3,1,4,2]=>2
[3,4,5,1,2]=>[5,4,3,2,1]=>4
[3,4,5,2,1]=>[5,4,3,1,2]=>3
[3,5,1,2,4]=>[5,3,2,1,4]=>2
[3,5,1,4,2]=>[4,3,2,5,1]=>2
[3,5,2,1,4]=>[5,3,1,2,4]=>1
[3,5,2,4,1]=>[4,3,1,5,2]=>1
[3,5,4,1,2]=>[5,3,4,2,1]=>3
[3,5,4,2,1]=>[5,3,4,1,2]=>2
[4,1,2,3,5]=>[4,1,2,3,5]=>0
[4,1,2,5,3]=>[5,1,2,4,3]=>1
[4,1,3,2,5]=>[3,1,4,2,5]=>0
[4,1,3,5,2]=>[3,1,5,4,2]=>1
[4,1,5,2,3]=>[5,1,4,3,2]=>2
[4,1,5,3,2]=>[5,1,4,2,3]=>1
[4,2,1,3,5]=>[2,4,1,3,5]=>0
[4,2,1,5,3]=>[2,5,1,4,3]=>1
[4,2,3,1,5]=>[2,3,4,1,5]=>0
[4,2,3,5,1]=>[2,3,5,4,1]=>1
[4,2,5,1,3]=>[2,5,4,3,1]=>2
[4,2,5,3,1]=>[2,5,4,1,3]=>1
[4,3,1,2,5]=>[3,4,2,1,5]=>1
[4,3,1,5,2]=>[3,5,2,4,1]=>2
[4,3,2,1,5]=>[3,4,1,2,5]=>0
[4,3,2,5,1]=>[3,5,1,4,2]=>1
[4,3,5,1,2]=>[4,5,3,2,1]=>3
[4,3,5,2,1]=>[4,5,3,1,2]=>2
[4,5,1,2,3]=>[5,4,2,3,1]=>3
[4,5,1,3,2]=>[5,4,2,1,3]=>2
[4,5,2,1,3]=>[5,4,1,3,2]=>2
[4,5,2,3,1]=>[5,4,1,2,3]=>1
[4,5,3,1,2]=>[4,3,5,2,1]=>2
[4,5,3,2,1]=>[4,3,5,1,2]=>1
[5,1,2,3,4]=>[5,1,2,3,4]=>0
[5,1,2,4,3]=>[4,1,2,5,3]=>0
[5,1,3,2,4]=>[3,1,5,2,4]=>0
[5,1,3,4,2]=>[3,1,4,5,2]=>0
[5,1,4,2,3]=>[4,1,5,3,2]=>1
[5,1,4,3,2]=>[4,1,5,2,3]=>0
[5,2,1,3,4]=>[2,5,1,3,4]=>0
[5,2,1,4,3]=>[2,4,1,5,3]=>0
[5,2,3,1,4]=>[2,3,5,1,4]=>0
[5,2,3,4,1]=>[2,3,4,5,1]=>0
[5,2,4,1,3]=>[2,4,5,3,1]=>1
[5,2,4,3,1]=>[2,4,5,1,3]=>0
[5,3,1,2,4]=>[3,5,2,1,4]=>1
[5,3,1,4,2]=>[3,4,2,5,1]=>1
[5,3,2,1,4]=>[3,5,1,2,4]=>0
[5,3,2,4,1]=>[3,4,1,5,2]=>0
[5,3,4,1,2]=>[3,5,4,2,1]=>2
[5,3,4,2,1]=>[3,5,4,1,2]=>1
[5,4,1,2,3]=>[4,5,2,3,1]=>2
[5,4,1,3,2]=>[4,5,2,1,3]=>1
[5,4,2,1,3]=>[4,5,1,3,2]=>1
[5,4,2,3,1]=>[4,5,1,2,3]=>0
[5,4,3,1,2]=>[3,4,5,2,1]=>1
[5,4,3,2,1]=>[3,4,5,1,2]=>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]=>1
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>0
[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>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]=>1
[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>2
[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>1
[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>1
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>[1,2,6,3,5,4]=>1
[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>0
[1,2,5,4,6,3]=>[1,2,4,6,5,3]=>1
[1,2,5,6,3,4]=>[1,2,6,5,4,3]=>2
[1,2,5,6,4,3]=>[1,2,6,5,3,4]=>1
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>0
[1,2,6,3,5,4]=>[1,2,5,3,6,4]=>0
[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>0
[1,2,6,4,5,3]=>[1,2,4,5,6,3]=>0
[1,2,6,5,3,4]=>[1,2,5,6,4,3]=>1
[1,2,6,5,4,3]=>[1,2,5,6,3,4]=>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]=>1
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>0
[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>0
[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>1
[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>1
[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>2
[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>3
[1,3,4,6,2,5]=>[1,6,3,4,2,5]=>2
[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>2
[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>1
[1,3,5,2,6,4]=>[1,6,3,2,5,4]=>2
[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>1
[1,3,5,4,6,2]=>[1,4,3,6,5,2]=>2
[1,3,5,6,2,4]=>[1,6,3,5,4,2]=>3
[1,3,5,6,4,2]=>[1,6,3,5,2,4]=>2
[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>1
[1,3,6,2,5,4]=>[1,5,3,2,6,4]=>1
[1,3,6,4,2,5]=>[1,4,3,6,2,5]=>1
[1,3,6,4,5,2]=>[1,4,3,5,6,2]=>1
[1,3,6,5,2,4]=>[1,5,3,6,4,2]=>2
[1,3,6,5,4,2]=>[1,5,3,6,2,4]=>1
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>0
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>0
[1,4,2,5,3,6]=>[1,5,2,4,3,6]=>1
[1,4,2,5,6,3]=>[1,6,2,4,5,3]=>2
[1,4,2,6,3,5]=>[1,6,2,4,3,5]=>1
[1,4,2,6,5,3]=>[1,5,2,4,6,3]=>1
[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>0
[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>0
[1,4,3,5,2,6]=>[1,3,5,4,2,6]=>1
[1,4,3,5,6,2]=>[1,3,6,4,5,2]=>2
[1,4,3,6,2,5]=>[1,3,6,4,2,5]=>1
[1,4,3,6,5,2]=>[1,3,5,4,6,2]=>1
[1,4,5,2,3,6]=>[1,5,4,3,2,6]=>2
[1,4,5,2,6,3]=>[1,6,4,3,5,2]=>3
[1,4,5,3,2,6]=>[1,5,4,2,3,6]=>1
[1,4,5,3,6,2]=>[1,6,4,2,5,3]=>2
[1,4,5,6,2,3]=>[1,6,5,4,3,2]=>4
[1,4,5,6,3,2]=>[1,6,5,4,2,3]=>3
[1,4,6,2,3,5]=>[1,6,4,3,2,5]=>2
[1,4,6,2,5,3]=>[1,5,4,3,6,2]=>2
[1,4,6,3,2,5]=>[1,6,4,2,3,5]=>1
[1,4,6,3,5,2]=>[1,5,4,2,6,3]=>1
[1,4,6,5,2,3]=>[1,6,4,5,3,2]=>3
[1,4,6,5,3,2]=>[1,6,4,5,2,3]=>2
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>[1,6,2,3,5,4]=>1
[1,5,2,4,3,6]=>[1,4,2,5,3,6]=>0
[1,5,2,4,6,3]=>[1,4,2,6,5,3]=>1
[1,5,2,6,3,4]=>[1,6,2,5,4,3]=>2
[1,5,2,6,4,3]=>[1,6,2,5,3,4]=>1
[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>0
[1,5,3,2,6,4]=>[1,3,6,2,5,4]=>1
[1,5,3,4,2,6]=>[1,3,4,5,2,6]=>0
[1,5,3,4,6,2]=>[1,3,4,6,5,2]=>1
[1,5,3,6,2,4]=>[1,3,6,5,4,2]=>2
[1,5,3,6,4,2]=>[1,3,6,5,2,4]=>1
[1,5,4,2,3,6]=>[1,4,5,3,2,6]=>1
[1,5,4,2,6,3]=>[1,4,6,3,5,2]=>2
[1,5,4,3,2,6]=>[1,4,5,2,3,6]=>0
[1,5,4,3,6,2]=>[1,4,6,2,5,3]=>1
[1,5,4,6,2,3]=>[1,5,6,4,3,2]=>3
[1,5,4,6,3,2]=>[1,5,6,4,2,3]=>2
[1,5,6,2,3,4]=>[1,6,5,3,4,2]=>3
[1,5,6,2,4,3]=>[1,6,5,3,2,4]=>2
[1,5,6,3,2,4]=>[1,6,5,2,4,3]=>2
[1,5,6,3,4,2]=>[1,6,5,2,3,4]=>1
[1,5,6,4,2,3]=>[1,5,4,6,3,2]=>2
[1,5,6,4,3,2]=>[1,5,4,6,2,3]=>1
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>0
[1,6,2,3,5,4]=>[1,5,2,3,6,4]=>0
[1,6,2,4,3,5]=>[1,4,2,6,3,5]=>0
[1,6,2,4,5,3]=>[1,4,2,5,6,3]=>0
[1,6,2,5,3,4]=>[1,5,2,6,4,3]=>1
[1,6,2,5,4,3]=>[1,5,2,6,3,4]=>0
[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>0
[1,6,3,2,5,4]=>[1,3,5,2,6,4]=>0
[1,6,3,4,2,5]=>[1,3,4,6,2,5]=>0
[1,6,3,4,5,2]=>[1,3,4,5,6,2]=>0
[1,6,3,5,2,4]=>[1,3,5,6,4,2]=>1
[1,6,3,5,4,2]=>[1,3,5,6,2,4]=>0
[1,6,4,2,3,5]=>[1,4,6,3,2,5]=>1
[1,6,4,2,5,3]=>[1,4,5,3,6,2]=>1
[1,6,4,3,2,5]=>[1,4,6,2,3,5]=>0
[1,6,4,3,5,2]=>[1,4,5,2,6,3]=>0
[1,6,4,5,2,3]=>[1,4,6,5,3,2]=>2
[1,6,4,5,3,2]=>[1,4,6,5,2,3]=>1
[1,6,5,2,3,4]=>[1,5,6,3,4,2]=>2
[1,6,5,2,4,3]=>[1,5,6,3,2,4]=>1
[1,6,5,3,2,4]=>[1,5,6,2,4,3]=>1
[1,6,5,3,4,2]=>[1,5,6,2,3,4]=>0
[1,6,5,4,2,3]=>[1,4,5,6,3,2]=>1
[1,6,5,4,3,2]=>[1,4,5,6,2,3]=>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]=>1
[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>0
[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>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]=>1
[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>2
[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>1
[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>1
[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>0
[2,1,5,3,6,4]=>[2,1,6,3,5,4]=>1
[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>0
[2,1,5,4,6,3]=>[2,1,4,6,5,3]=>1
[2,1,5,6,3,4]=>[2,1,6,5,4,3]=>2
[2,1,5,6,4,3]=>[2,1,6,5,3,4]=>1
[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>0
[2,1,6,3,5,4]=>[2,1,5,3,6,4]=>0
[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>0
[2,1,6,4,5,3]=>[2,1,4,5,6,3]=>0
[2,1,6,5,3,4]=>[2,1,5,6,4,3]=>1
[2,1,6,5,4,3]=>[2,1,5,6,3,4]=>0
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>1
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>1
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>1
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>2
[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>1
[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>1
[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>2
[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>2
[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>3
[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>4
[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>3
[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>3
[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>2
[2,3,5,1,6,4]=>[6,2,3,1,5,4]=>3
[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>2
[2,3,5,4,6,1]=>[4,2,3,6,5,1]=>3
[2,3,5,6,1,4]=>[6,2,3,5,4,1]=>4
[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>3
[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>2
[2,3,6,1,5,4]=>[5,2,3,1,6,4]=>2
[2,3,6,4,1,5]=>[4,2,3,6,1,5]=>2
[2,3,6,4,5,1]=>[4,2,3,5,6,1]=>2
[2,3,6,5,1,4]=>[5,2,3,6,4,1]=>3
[2,3,6,5,4,1]=>[5,2,3,6,1,4]=>2
[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>1
[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>1
[2,4,1,5,3,6]=>[5,2,1,4,3,6]=>2
[2,4,1,5,6,3]=>[6,2,1,4,5,3]=>3
[2,4,1,6,3,5]=>[6,2,1,4,3,5]=>2
[2,4,1,6,5,3]=>[5,2,1,4,6,3]=>2
[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>1
[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>1
[2,4,3,5,1,6]=>[3,2,5,4,1,6]=>2
[2,4,3,5,6,1]=>[3,2,6,4,5,1]=>3
[2,4,3,6,1,5]=>[3,2,6,4,1,5]=>2
[2,4,3,6,5,1]=>[3,2,5,4,6,1]=>2
[2,4,5,1,3,6]=>[5,2,4,3,1,6]=>3
[2,4,5,1,6,3]=>[6,2,4,3,5,1]=>4
[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>2
[2,4,5,3,6,1]=>[6,2,4,1,5,3]=>3
[2,4,5,6,1,3]=>[6,2,5,4,3,1]=>5
[2,4,5,6,3,1]=>[6,2,5,4,1,3]=>4
[2,4,6,1,3,5]=>[6,2,4,3,1,5]=>3
[2,4,6,1,5,3]=>[5,2,4,3,6,1]=>3
[2,4,6,3,1,5]=>[6,2,4,1,3,5]=>2
[2,4,6,3,5,1]=>[5,2,4,1,6,3]=>2
[2,4,6,5,1,3]=>[6,2,4,5,3,1]=>4
[2,4,6,5,3,1]=>[6,2,4,5,1,3]=>3
[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>1
[2,5,1,3,6,4]=>[6,2,1,3,5,4]=>2
[2,5,1,4,3,6]=>[4,2,1,5,3,6]=>1
[2,5,1,4,6,3]=>[4,2,1,6,5,3]=>2
[2,5,1,6,3,4]=>[6,2,1,5,4,3]=>3
[2,5,1,6,4,3]=>[6,2,1,5,3,4]=>2
[2,5,3,1,4,6]=>[3,2,5,1,4,6]=>1
[2,5,3,1,6,4]=>[3,2,6,1,5,4]=>2
[2,5,3,4,1,6]=>[3,2,4,5,1,6]=>1
[2,5,3,4,6,1]=>[3,2,4,6,5,1]=>2
[2,5,3,6,1,4]=>[3,2,6,5,4,1]=>3
[2,5,3,6,4,1]=>[3,2,6,5,1,4]=>2
[2,5,4,1,3,6]=>[4,2,5,3,1,6]=>2
[2,5,4,1,6,3]=>[4,2,6,3,5,1]=>3
[2,5,4,3,1,6]=>[4,2,5,1,3,6]=>1
[2,5,4,3,6,1]=>[4,2,6,1,5,3]=>2
[2,5,4,6,1,3]=>[5,2,6,4,3,1]=>4
[2,5,4,6,3,1]=>[5,2,6,4,1,3]=>3
[2,5,6,1,3,4]=>[6,2,5,3,4,1]=>4
[2,5,6,1,4,3]=>[6,2,5,3,1,4]=>3
[2,5,6,3,1,4]=>[6,2,5,1,4,3]=>3
[2,5,6,3,4,1]=>[6,2,5,1,3,4]=>2
[2,5,6,4,1,3]=>[5,2,4,6,3,1]=>3
[2,5,6,4,3,1]=>[5,2,4,6,1,3]=>2
[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>1
[2,6,1,3,5,4]=>[5,2,1,3,6,4]=>1
[2,6,1,4,3,5]=>[4,2,1,6,3,5]=>1
[2,6,1,4,5,3]=>[4,2,1,5,6,3]=>1
[2,6,1,5,3,4]=>[5,2,1,6,4,3]=>2
[2,6,1,5,4,3]=>[5,2,1,6,3,4]=>1
[2,6,3,1,4,5]=>[3,2,6,1,4,5]=>1
[2,6,3,1,5,4]=>[3,2,5,1,6,4]=>1
[2,6,3,4,1,5]=>[3,2,4,6,1,5]=>1
[2,6,3,4,5,1]=>[3,2,4,5,6,1]=>1
[2,6,3,5,1,4]=>[3,2,5,6,4,1]=>2
[2,6,3,5,4,1]=>[3,2,5,6,1,4]=>1
[2,6,4,1,3,5]=>[4,2,6,3,1,5]=>2
[2,6,4,1,5,3]=>[4,2,5,3,6,1]=>2
[2,6,4,3,1,5]=>[4,2,6,1,3,5]=>1
[2,6,4,3,5,1]=>[4,2,5,1,6,3]=>1
[2,6,4,5,1,3]=>[4,2,6,5,3,1]=>3
[2,6,4,5,3,1]=>[4,2,6,5,1,3]=>2
[2,6,5,1,3,4]=>[5,2,6,3,4,1]=>3
[2,6,5,1,4,3]=>[5,2,6,3,1,4]=>2
[2,6,5,3,1,4]=>[5,2,6,1,4,3]=>2
[2,6,5,3,4,1]=>[5,2,6,1,3,4]=>1
[2,6,5,4,1,3]=>[4,2,5,6,3,1]=>2
[2,6,5,4,3,1]=>[4,2,5,6,1,3]=>1
[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>0
[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>0
[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>0
[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>1
[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>0
[3,1,2,6,5,4]=>[3,1,2,5,6,4]=>0
[3,1,4,2,5,6]=>[4,1,3,2,5,6]=>1
[3,1,4,2,6,5]=>[4,1,3,2,6,5]=>1
[3,1,4,5,2,6]=>[5,1,3,4,2,6]=>2
[3,1,4,5,6,2]=>[6,1,3,4,5,2]=>3
[3,1,4,6,2,5]=>[6,1,3,4,2,5]=>2
[3,1,4,6,5,2]=>[5,1,3,4,6,2]=>2
[3,1,5,2,4,6]=>[5,1,3,2,4,6]=>1
[3,1,5,2,6,4]=>[6,1,3,2,5,4]=>2
[3,1,5,4,2,6]=>[4,1,3,5,2,6]=>1
[3,1,5,4,6,2]=>[4,1,3,6,5,2]=>2
[3,1,5,6,2,4]=>[6,1,3,5,4,2]=>3
[3,1,5,6,4,2]=>[6,1,3,5,2,4]=>2
[3,1,6,2,4,5]=>[6,1,3,2,4,5]=>1
[3,1,6,2,5,4]=>[5,1,3,2,6,4]=>1
[3,1,6,4,2,5]=>[4,1,3,6,2,5]=>1
[3,1,6,4,5,2]=>[4,1,3,5,6,2]=>1
[3,1,6,5,2,4]=>[5,1,3,6,4,2]=>2
[3,1,6,5,4,2]=>[5,1,3,6,2,4]=>1
[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>0
[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>0
[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>0
[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>1
[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>0
[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>0
[3,2,4,1,5,6]=>[2,4,3,1,5,6]=>1
[3,2,4,1,6,5]=>[2,4,3,1,6,5]=>1
[3,2,4,5,1,6]=>[2,5,3,4,1,6]=>2
[3,2,4,5,6,1]=>[2,6,3,4,5,1]=>3
[3,2,4,6,1,5]=>[2,6,3,4,1,5]=>2
[3,2,4,6,5,1]=>[2,5,3,4,6,1]=>2
[3,2,5,1,4,6]=>[2,5,3,1,4,6]=>1
[3,2,5,1,6,4]=>[2,6,3,1,5,4]=>2
[3,2,5,4,1,6]=>[2,4,3,5,1,6]=>1
[3,2,5,4,6,1]=>[2,4,3,6,5,1]=>2
[3,2,5,6,1,4]=>[2,6,3,5,4,1]=>3
[3,2,5,6,4,1]=>[2,6,3,5,1,4]=>2
[3,2,6,1,4,5]=>[2,6,3,1,4,5]=>1
[3,2,6,1,5,4]=>[2,5,3,1,6,4]=>1
[3,2,6,4,1,5]=>[2,4,3,6,1,5]=>1
[3,2,6,4,5,1]=>[2,4,3,5,6,1]=>1
[3,2,6,5,1,4]=>[2,5,3,6,4,1]=>2
[3,2,6,5,4,1]=>[2,5,3,6,1,4]=>1
[3,4,1,2,5,6]=>[4,3,2,1,5,6]=>2
[3,4,1,2,6,5]=>[4,3,2,1,6,5]=>2
[3,4,1,5,2,6]=>[5,3,2,4,1,6]=>3
[3,4,1,5,6,2]=>[6,3,2,4,5,1]=>4
[3,4,1,6,2,5]=>[6,3,2,4,1,5]=>3
[3,4,1,6,5,2]=>[5,3,2,4,6,1]=>3
[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>1
[3,4,2,1,6,5]=>[4,3,1,2,6,5]=>1
[3,4,2,5,1,6]=>[5,3,1,4,2,6]=>2
[3,4,2,5,6,1]=>[6,3,1,4,5,2]=>3
[3,4,2,6,1,5]=>[6,3,1,4,2,5]=>2
[3,4,2,6,5,1]=>[5,3,1,4,6,2]=>2
[3,4,5,1,2,6]=>[5,4,3,2,1,6]=>4
[3,4,5,1,6,2]=>[6,4,3,2,5,1]=>5
[3,4,5,2,1,6]=>[5,4,3,1,2,6]=>3
[3,4,5,2,6,1]=>[6,4,3,1,5,2]=>4
[3,4,5,6,1,2]=>[6,5,3,4,2,1]=>6
[3,4,5,6,2,1]=>[6,5,3,4,1,2]=>5
[3,4,6,1,2,5]=>[6,4,3,2,1,5]=>4
[3,4,6,1,5,2]=>[5,4,3,2,6,1]=>4
[3,4,6,2,1,5]=>[6,4,3,1,2,5]=>3
[3,4,6,2,5,1]=>[5,4,3,1,6,2]=>3
[3,4,6,5,1,2]=>[6,4,3,5,2,1]=>5
[3,4,6,5,2,1]=>[6,4,3,5,1,2]=>4
[3,5,1,2,4,6]=>[5,3,2,1,4,6]=>2
[3,5,1,2,6,4]=>[6,3,2,1,5,4]=>3
[3,5,1,4,2,6]=>[4,3,2,5,1,6]=>2
[3,5,1,4,6,2]=>[4,3,2,6,5,1]=>3
[3,5,1,6,2,4]=>[6,3,2,5,4,1]=>4
[3,5,1,6,4,2]=>[6,3,2,5,1,4]=>3
[3,5,2,1,4,6]=>[5,3,1,2,4,6]=>1
[3,5,2,1,6,4]=>[6,3,1,2,5,4]=>2
[3,5,2,4,1,6]=>[4,3,1,5,2,6]=>1
[3,5,2,4,6,1]=>[4,3,1,6,5,2]=>2
[3,5,2,6,1,4]=>[6,3,1,5,4,2]=>3
[3,5,2,6,4,1]=>[6,3,1,5,2,4]=>2
[3,5,4,1,2,6]=>[5,3,4,2,1,6]=>3
[3,5,4,1,6,2]=>[6,3,4,2,5,1]=>4
[3,5,4,2,1,6]=>[5,3,4,1,2,6]=>2
[3,5,4,2,6,1]=>[6,3,4,1,5,2]=>3
[3,5,4,6,1,2]=>[6,3,5,4,2,1]=>5
[3,5,4,6,2,1]=>[6,3,5,4,1,2]=>4
[3,5,6,1,2,4]=>[6,5,3,2,4,1]=>5
[3,5,6,1,4,2]=>[6,5,3,2,1,4]=>4
[3,5,6,2,1,4]=>[6,5,3,1,4,2]=>4
[3,5,6,2,4,1]=>[6,5,3,1,2,4]=>3
[3,5,6,4,1,2]=>[5,4,3,6,2,1]=>4
[3,5,6,4,2,1]=>[5,4,3,6,1,2]=>3
[3,6,1,2,4,5]=>[6,3,2,1,4,5]=>2
[3,6,1,2,5,4]=>[5,3,2,1,6,4]=>2
[3,6,1,4,2,5]=>[4,3,2,6,1,5]=>2
[3,6,1,4,5,2]=>[4,3,2,5,6,1]=>2
[3,6,1,5,2,4]=>[5,3,2,6,4,1]=>3
[3,6,1,5,4,2]=>[5,3,2,6,1,4]=>2
[3,6,2,1,4,5]=>[6,3,1,2,4,5]=>1
[3,6,2,1,5,4]=>[5,3,1,2,6,4]=>1
[3,6,2,4,1,5]=>[4,3,1,6,2,5]=>1
[3,6,2,4,5,1]=>[4,3,1,5,6,2]=>1
[3,6,2,5,1,4]=>[5,3,1,6,4,2]=>2
[3,6,2,5,4,1]=>[5,3,1,6,2,4]=>1
[3,6,4,1,2,5]=>[6,3,4,2,1,5]=>3
[3,6,4,1,5,2]=>[5,3,4,2,6,1]=>3
[3,6,4,2,1,5]=>[6,3,4,1,2,5]=>2
[3,6,4,2,5,1]=>[5,3,4,1,6,2]=>2
[3,6,4,5,1,2]=>[6,3,4,5,2,1]=>4
[3,6,4,5,2,1]=>[6,3,4,5,1,2]=>3
[3,6,5,1,2,4]=>[6,3,5,2,4,1]=>4
[3,6,5,1,4,2]=>[6,3,5,2,1,4]=>3
[3,6,5,2,1,4]=>[6,3,5,1,4,2]=>3
[3,6,5,2,4,1]=>[6,3,5,1,2,4]=>2
[3,6,5,4,1,2]=>[5,3,4,6,2,1]=>3
[3,6,5,4,2,1]=>[5,3,4,6,1,2]=>2
[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>0
[4,1,2,5,3,6]=>[5,1,2,4,3,6]=>1
[4,1,2,5,6,3]=>[6,1,2,4,5,3]=>2
[4,1,2,6,3,5]=>[6,1,2,4,3,5]=>1
[4,1,2,6,5,3]=>[5,1,2,4,6,3]=>1
[4,1,3,2,5,6]=>[3,1,4,2,5,6]=>0
[4,1,3,2,6,5]=>[3,1,4,2,6,5]=>0
[4,1,3,5,2,6]=>[3,1,5,4,2,6]=>1
[4,1,3,5,6,2]=>[3,1,6,4,5,2]=>2
[4,1,3,6,2,5]=>[3,1,6,4,2,5]=>1
[4,1,3,6,5,2]=>[3,1,5,4,6,2]=>1
[4,1,5,2,3,6]=>[5,1,4,3,2,6]=>2
[4,1,5,2,6,3]=>[6,1,4,3,5,2]=>3
[4,1,5,3,2,6]=>[5,1,4,2,3,6]=>1
[4,1,5,3,6,2]=>[6,1,4,2,5,3]=>2
[4,1,5,6,2,3]=>[6,1,5,4,3,2]=>4
[4,1,5,6,3,2]=>[6,1,5,4,2,3]=>3
[4,1,6,2,3,5]=>[6,1,4,3,2,5]=>2
[4,1,6,2,5,3]=>[5,1,4,3,6,2]=>2
[4,1,6,3,2,5]=>[6,1,4,2,3,5]=>1
[4,1,6,3,5,2]=>[5,1,4,2,6,3]=>1
[4,1,6,5,2,3]=>[6,1,4,5,3,2]=>3
[4,1,6,5,3,2]=>[6,1,4,5,2,3]=>2
[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>0
[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>0
[4,2,1,5,3,6]=>[2,5,1,4,3,6]=>1
[4,2,1,5,6,3]=>[2,6,1,4,5,3]=>2
[4,2,1,6,3,5]=>[2,6,1,4,3,5]=>1
[4,2,1,6,5,3]=>[2,5,1,4,6,3]=>1
[4,2,3,1,5,6]=>[2,3,4,1,5,6]=>0
[4,2,3,1,6,5]=>[2,3,4,1,6,5]=>0
[4,2,3,5,1,6]=>[2,3,5,4,1,6]=>1
[4,2,3,5,6,1]=>[2,3,6,4,5,1]=>2
[4,2,3,6,1,5]=>[2,3,6,4,1,5]=>1
[4,2,3,6,5,1]=>[2,3,5,4,6,1]=>1
[4,2,5,1,3,6]=>[2,5,4,3,1,6]=>2
[4,2,5,1,6,3]=>[2,6,4,3,5,1]=>3
[4,2,5,3,1,6]=>[2,5,4,1,3,6]=>1
[4,2,5,3,6,1]=>[2,6,4,1,5,3]=>2
[4,2,5,6,1,3]=>[2,6,5,4,3,1]=>4
[4,2,5,6,3,1]=>[2,6,5,4,1,3]=>3
[4,2,6,1,3,5]=>[2,6,4,3,1,5]=>2
[4,2,6,1,5,3]=>[2,5,4,3,6,1]=>2
[4,2,6,3,1,5]=>[2,6,4,1,3,5]=>1
[4,2,6,3,5,1]=>[2,5,4,1,6,3]=>1
[4,2,6,5,1,3]=>[2,6,4,5,3,1]=>3
[4,2,6,5,3,1]=>[2,6,4,5,1,3]=>2
[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>1
[4,3,1,2,6,5]=>[3,4,2,1,6,5]=>1
[4,3,1,5,2,6]=>[3,5,2,4,1,6]=>2
[4,3,1,5,6,2]=>[3,6,2,4,5,1]=>3
[4,3,1,6,2,5]=>[3,6,2,4,1,5]=>2
[4,3,1,6,5,2]=>[3,5,2,4,6,1]=>2
[4,3,2,1,5,6]=>[3,4,1,2,5,6]=>0
[4,3,2,1,6,5]=>[3,4,1,2,6,5]=>0
[4,3,2,5,1,6]=>[3,5,1,4,2,6]=>1
[4,3,2,5,6,1]=>[3,6,1,4,5,2]=>2
[4,3,2,6,1,5]=>[3,6,1,4,2,5]=>1
[4,3,2,6,5,1]=>[3,5,1,4,6,2]=>1
[4,3,5,1,2,6]=>[4,5,3,2,1,6]=>3
[4,3,5,1,6,2]=>[4,6,3,2,5,1]=>4
[4,3,5,2,1,6]=>[4,5,3,1,2,6]=>2
[4,3,5,2,6,1]=>[4,6,3,1,5,2]=>3
[4,3,5,6,1,2]=>[5,6,3,4,2,1]=>5
[4,3,5,6,2,1]=>[5,6,3,4,1,2]=>4
[4,3,6,1,2,5]=>[4,6,3,2,1,5]=>3
[4,3,6,1,5,2]=>[4,5,3,2,6,1]=>3
[4,3,6,2,1,5]=>[4,6,3,1,2,5]=>2
[4,3,6,2,5,1]=>[4,5,3,1,6,2]=>2
[4,3,6,5,1,2]=>[4,6,3,5,2,1]=>4
[4,3,6,5,2,1]=>[4,6,3,5,1,2]=>3
[4,5,1,2,3,6]=>[5,4,2,3,1,6]=>3
[4,5,1,2,6,3]=>[6,4,2,3,5,1]=>4
[4,5,1,3,2,6]=>[5,4,2,1,3,6]=>2
[4,5,1,3,6,2]=>[6,4,2,1,5,3]=>3
[4,5,1,6,2,3]=>[6,5,2,4,3,1]=>5
[4,5,1,6,3,2]=>[6,5,2,4,1,3]=>4
[4,5,2,1,3,6]=>[5,4,1,3,2,6]=>2
[4,5,2,1,6,3]=>[6,4,1,3,5,2]=>3
[4,5,2,3,1,6]=>[5,4,1,2,3,6]=>1
[4,5,2,3,6,1]=>[6,4,1,2,5,3]=>2
[4,5,2,6,1,3]=>[6,5,1,4,3,2]=>4
[4,5,2,6,3,1]=>[6,5,1,4,2,3]=>3
[4,5,3,1,2,6]=>[4,3,5,2,1,6]=>2
[4,5,3,1,6,2]=>[4,3,6,2,5,1]=>3
[4,5,3,2,1,6]=>[4,3,5,1,2,6]=>1
[4,5,3,2,6,1]=>[4,3,6,1,5,2]=>2
[4,5,3,6,1,2]=>[5,3,6,4,2,1]=>4
[4,5,3,6,2,1]=>[5,3,6,4,1,2]=>3
[4,5,6,1,2,3]=>[6,5,4,3,2,1]=>6
[4,5,6,1,3,2]=>[6,5,4,3,1,2]=>5
[4,5,6,2,1,3]=>[6,5,4,2,3,1]=>5
[4,5,6,2,3,1]=>[6,5,4,2,1,3]=>4
[4,5,6,3,1,2]=>[6,5,4,1,3,2]=>4
[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>3
[4,6,1,2,3,5]=>[6,4,2,3,1,5]=>3
[4,6,1,2,5,3]=>[5,4,2,3,6,1]=>3
[4,6,1,3,2,5]=>[6,4,2,1,3,5]=>2
[4,6,1,3,5,2]=>[5,4,2,1,6,3]=>2
[4,6,1,5,2,3]=>[6,4,2,5,3,1]=>4
[4,6,1,5,3,2]=>[6,4,2,5,1,3]=>3
[4,6,2,1,3,5]=>[6,4,1,3,2,5]=>2
[4,6,2,1,5,3]=>[5,4,1,3,6,2]=>2
[4,6,2,3,1,5]=>[6,4,1,2,3,5]=>1
[4,6,2,3,5,1]=>[5,4,1,2,6,3]=>1
[4,6,2,5,1,3]=>[6,4,1,5,3,2]=>3
[4,6,2,5,3,1]=>[6,4,1,5,2,3]=>2
[4,6,3,1,2,5]=>[4,3,6,2,1,5]=>2
[4,6,3,1,5,2]=>[4,3,5,2,6,1]=>2
[4,6,3,2,1,5]=>[4,3,6,1,2,5]=>1
[4,6,3,2,5,1]=>[4,3,5,1,6,2]=>1
[4,6,3,5,1,2]=>[4,3,6,5,2,1]=>3
[4,6,3,5,2,1]=>[4,3,6,5,1,2]=>2
[4,6,5,1,2,3]=>[6,4,5,3,2,1]=>5
[4,6,5,1,3,2]=>[6,4,5,3,1,2]=>4
[4,6,5,2,1,3]=>[6,4,5,2,3,1]=>4
[4,6,5,2,3,1]=>[6,4,5,2,1,3]=>3
[4,6,5,3,1,2]=>[6,4,5,1,3,2]=>3
[4,6,5,3,2,1]=>[6,4,5,1,2,3]=>2
[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>[6,1,2,3,5,4]=>1
[5,1,2,4,3,6]=>[4,1,2,5,3,6]=>0
[5,1,2,4,6,3]=>[4,1,2,6,5,3]=>1
[5,1,2,6,3,4]=>[6,1,2,5,4,3]=>2
[5,1,2,6,4,3]=>[6,1,2,5,3,4]=>1
[5,1,3,2,4,6]=>[3,1,5,2,4,6]=>0
[5,1,3,2,6,4]=>[3,1,6,2,5,4]=>1
[5,1,3,4,2,6]=>[3,1,4,5,2,6]=>0
[5,1,3,4,6,2]=>[3,1,4,6,5,2]=>1
[5,1,3,6,2,4]=>[3,1,6,5,4,2]=>2
[5,1,3,6,4,2]=>[3,1,6,5,2,4]=>1
[5,1,4,2,3,6]=>[4,1,5,3,2,6]=>1
[5,1,4,2,6,3]=>[4,1,6,3,5,2]=>2
[5,1,4,3,2,6]=>[4,1,5,2,3,6]=>0
[5,1,4,3,6,2]=>[4,1,6,2,5,3]=>1
[5,1,4,6,2,3]=>[5,1,6,4,3,2]=>3
[5,1,4,6,3,2]=>[5,1,6,4,2,3]=>2
[5,1,6,2,3,4]=>[6,1,5,3,4,2]=>3
[5,1,6,2,4,3]=>[6,1,5,3,2,4]=>2
[5,1,6,3,2,4]=>[6,1,5,2,4,3]=>2
[5,1,6,3,4,2]=>[6,1,5,2,3,4]=>1
[5,1,6,4,2,3]=>[5,1,4,6,3,2]=>2
[5,1,6,4,3,2]=>[5,1,4,6,2,3]=>1
[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>0
[5,2,1,3,6,4]=>[2,6,1,3,5,4]=>1
[5,2,1,4,3,6]=>[2,4,1,5,3,6]=>0
[5,2,1,4,6,3]=>[2,4,1,6,5,3]=>1
[5,2,1,6,3,4]=>[2,6,1,5,4,3]=>2
[5,2,1,6,4,3]=>[2,6,1,5,3,4]=>1
[5,2,3,1,4,6]=>[2,3,5,1,4,6]=>0
[5,2,3,1,6,4]=>[2,3,6,1,5,4]=>1
[5,2,3,4,1,6]=>[2,3,4,5,1,6]=>0
[5,2,3,4,6,1]=>[2,3,4,6,5,1]=>1
[5,2,3,6,1,4]=>[2,3,6,5,4,1]=>2
[5,2,3,6,4,1]=>[2,3,6,5,1,4]=>1
[5,2,4,1,3,6]=>[2,4,5,3,1,6]=>1
[5,2,4,1,6,3]=>[2,4,6,3,5,1]=>2
[5,2,4,3,1,6]=>[2,4,5,1,3,6]=>0
[5,2,4,3,6,1]=>[2,4,6,1,5,3]=>1
[5,2,4,6,1,3]=>[2,5,6,4,3,1]=>3
[5,2,4,6,3,1]=>[2,5,6,4,1,3]=>2
[5,2,6,1,3,4]=>[2,6,5,3,4,1]=>3
[5,2,6,1,4,3]=>[2,6,5,3,1,4]=>2
[5,2,6,3,1,4]=>[2,6,5,1,4,3]=>2
[5,2,6,3,4,1]=>[2,6,5,1,3,4]=>1
[5,2,6,4,1,3]=>[2,5,4,6,3,1]=>2
[5,2,6,4,3,1]=>[2,5,4,6,1,3]=>1
[5,3,1,2,4,6]=>[3,5,2,1,4,6]=>1
[5,3,1,2,6,4]=>[3,6,2,1,5,4]=>2
[5,3,1,4,2,6]=>[3,4,2,5,1,6]=>1
[5,3,1,4,6,2]=>[3,4,2,6,5,1]=>2
[5,3,1,6,2,4]=>[3,6,2,5,4,1]=>3
[5,3,1,6,4,2]=>[3,6,2,5,1,4]=>2
[5,3,2,1,4,6]=>[3,5,1,2,4,6]=>0
[5,3,2,1,6,4]=>[3,6,1,2,5,4]=>1
[5,3,2,4,1,6]=>[3,4,1,5,2,6]=>0
[5,3,2,4,6,1]=>[3,4,1,6,5,2]=>1
[5,3,2,6,1,4]=>[3,6,1,5,4,2]=>2
[5,3,2,6,4,1]=>[3,6,1,5,2,4]=>1
[5,3,4,1,2,6]=>[3,5,4,2,1,6]=>2
[5,3,4,1,6,2]=>[3,6,4,2,5,1]=>3
[5,3,4,2,1,6]=>[3,5,4,1,2,6]=>1
[5,3,4,2,6,1]=>[3,6,4,1,5,2]=>2
[5,3,4,6,1,2]=>[3,6,5,4,2,1]=>4
[5,3,4,6,2,1]=>[3,6,5,4,1,2]=>3
[5,3,6,1,2,4]=>[5,6,3,2,4,1]=>4
[5,3,6,1,4,2]=>[5,6,3,2,1,4]=>3
[5,3,6,2,1,4]=>[5,6,3,1,4,2]=>3
[5,3,6,2,4,1]=>[5,6,3,1,2,4]=>2
[5,3,6,4,1,2]=>[4,5,3,6,2,1]=>3
[5,3,6,4,2,1]=>[4,5,3,6,1,2]=>2
[5,4,1,2,3,6]=>[4,5,2,3,1,6]=>2
[5,4,1,2,6,3]=>[4,6,2,3,5,1]=>3
[5,4,1,3,2,6]=>[4,5,2,1,3,6]=>1
[5,4,1,3,6,2]=>[4,6,2,1,5,3]=>2
[5,4,1,6,2,3]=>[5,6,2,4,3,1]=>4
[5,4,1,6,3,2]=>[5,6,2,4,1,3]=>3
[5,4,2,1,3,6]=>[4,5,1,3,2,6]=>1
[5,4,2,1,6,3]=>[4,6,1,3,5,2]=>2
[5,4,2,3,1,6]=>[4,5,1,2,3,6]=>0
[5,4,2,3,6,1]=>[4,6,1,2,5,3]=>1
[5,4,2,6,1,3]=>[5,6,1,4,3,2]=>3
[5,4,2,6,3,1]=>[5,6,1,4,2,3]=>2
[5,4,3,1,2,6]=>[3,4,5,2,1,6]=>1
[5,4,3,1,6,2]=>[3,4,6,2,5,1]=>2
[5,4,3,2,1,6]=>[3,4,5,1,2,6]=>0
[5,4,3,2,6,1]=>[3,4,6,1,5,2]=>1
[5,4,3,6,1,2]=>[3,5,6,4,2,1]=>3
[5,4,3,6,2,1]=>[3,5,6,4,1,2]=>2
[5,4,6,1,2,3]=>[5,6,4,3,2,1]=>5
[5,4,6,1,3,2]=>[5,6,4,3,1,2]=>4
[5,4,6,2,1,3]=>[5,6,4,2,3,1]=>4
[5,4,6,2,3,1]=>[5,6,4,2,1,3]=>3
[5,4,6,3,1,2]=>[5,6,4,1,3,2]=>3
[5,4,6,3,2,1]=>[5,6,4,1,2,3]=>2
[5,6,1,2,3,4]=>[6,5,2,3,4,1]=>4
[5,6,1,2,4,3]=>[6,5,2,3,1,4]=>3
[5,6,1,3,2,4]=>[6,5,2,1,4,3]=>3
[5,6,1,3,4,2]=>[6,5,2,1,3,4]=>2
[5,6,1,4,2,3]=>[5,4,2,6,3,1]=>3
[5,6,1,4,3,2]=>[5,4,2,6,1,3]=>2
[5,6,2,1,3,4]=>[6,5,1,3,4,2]=>3
[5,6,2,1,4,3]=>[6,5,1,3,2,4]=>2
[5,6,2,3,1,4]=>[6,5,1,2,4,3]=>2
[5,6,2,3,4,1]=>[6,5,1,2,3,4]=>1
[5,6,2,4,1,3]=>[5,4,1,6,3,2]=>2
[5,6,2,4,3,1]=>[5,4,1,6,2,3]=>1
[5,6,3,1,2,4]=>[5,3,6,2,4,1]=>3
[5,6,3,1,4,2]=>[5,3,6,2,1,4]=>2
[5,6,3,2,1,4]=>[5,3,6,1,4,2]=>2
[5,6,3,2,4,1]=>[5,3,6,1,2,4]=>1
[5,6,3,4,1,2]=>[4,3,5,6,2,1]=>2
[5,6,3,4,2,1]=>[4,3,5,6,1,2]=>1
[5,6,4,1,2,3]=>[5,4,6,3,2,1]=>4
[5,6,4,1,3,2]=>[5,4,6,3,1,2]=>3
[5,6,4,2,1,3]=>[5,4,6,2,3,1]=>3
[5,6,4,2,3,1]=>[5,4,6,2,1,3]=>2
[5,6,4,3,1,2]=>[5,4,6,1,3,2]=>2
[5,6,4,3,2,1]=>[5,4,6,1,2,3]=>1
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>[5,1,2,3,6,4]=>0
[6,1,2,4,3,5]=>[4,1,2,6,3,5]=>0
[6,1,2,4,5,3]=>[4,1,2,5,6,3]=>0
[6,1,2,5,3,4]=>[5,1,2,6,4,3]=>1
[6,1,2,5,4,3]=>[5,1,2,6,3,4]=>0
[6,1,3,2,4,5]=>[3,1,6,2,4,5]=>0
[6,1,3,2,5,4]=>[3,1,5,2,6,4]=>0
[6,1,3,4,2,5]=>[3,1,4,6,2,5]=>0
[6,1,3,4,5,2]=>[3,1,4,5,6,2]=>0
[6,1,3,5,2,4]=>[3,1,5,6,4,2]=>1
[6,1,3,5,4,2]=>[3,1,5,6,2,4]=>0
[6,1,4,2,3,5]=>[4,1,6,3,2,5]=>1
[6,1,4,2,5,3]=>[4,1,5,3,6,2]=>1
[6,1,4,3,2,5]=>[4,1,6,2,3,5]=>0
[6,1,4,3,5,2]=>[4,1,5,2,6,3]=>0
[6,1,4,5,2,3]=>[4,1,6,5,3,2]=>2
[6,1,4,5,3,2]=>[4,1,6,5,2,3]=>1
[6,1,5,2,3,4]=>[5,1,6,3,4,2]=>2
[6,1,5,2,4,3]=>[5,1,6,3,2,4]=>1
[6,1,5,3,2,4]=>[5,1,6,2,4,3]=>1
[6,1,5,3,4,2]=>[5,1,6,2,3,4]=>0
[6,1,5,4,2,3]=>[4,1,5,6,3,2]=>1
[6,1,5,4,3,2]=>[4,1,5,6,2,3]=>0
[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>0
[6,2,1,3,5,4]=>[2,5,1,3,6,4]=>0
[6,2,1,4,3,5]=>[2,4,1,6,3,5]=>0
[6,2,1,4,5,3]=>[2,4,1,5,6,3]=>0
[6,2,1,5,3,4]=>[2,5,1,6,4,3]=>1
[6,2,1,5,4,3]=>[2,5,1,6,3,4]=>0
[6,2,3,1,4,5]=>[2,3,6,1,4,5]=>0
[6,2,3,1,5,4]=>[2,3,5,1,6,4]=>0
[6,2,3,4,1,5]=>[2,3,4,6,1,5]=>0
[6,2,3,4,5,1]=>[2,3,4,5,6,1]=>0
[6,2,3,5,1,4]=>[2,3,5,6,4,1]=>1
[6,2,3,5,4,1]=>[2,3,5,6,1,4]=>0
[6,2,4,1,3,5]=>[2,4,6,3,1,5]=>1
[6,2,4,1,5,3]=>[2,4,5,3,6,1]=>1
[6,2,4,3,1,5]=>[2,4,6,1,3,5]=>0
[6,2,4,3,5,1]=>[2,4,5,1,6,3]=>0
[6,2,4,5,1,3]=>[2,4,6,5,3,1]=>2
[6,2,4,5,3,1]=>[2,4,6,5,1,3]=>1
[6,2,5,1,3,4]=>[2,5,6,3,4,1]=>2
[6,2,5,1,4,3]=>[2,5,6,3,1,4]=>1
[6,2,5,3,1,4]=>[2,5,6,1,4,3]=>1
[6,2,5,3,4,1]=>[2,5,6,1,3,4]=>0
[6,2,5,4,1,3]=>[2,4,5,6,3,1]=>1
[6,2,5,4,3,1]=>[2,4,5,6,1,3]=>0
[6,3,1,2,4,5]=>[3,6,2,1,4,5]=>1
[6,3,1,2,5,4]=>[3,5,2,1,6,4]=>1
[6,3,1,4,2,5]=>[3,4,2,6,1,5]=>1
[6,3,1,4,5,2]=>[3,4,2,5,6,1]=>1
[6,3,1,5,2,4]=>[3,5,2,6,4,1]=>2
[6,3,1,5,4,2]=>[3,5,2,6,1,4]=>1
[6,3,2,1,4,5]=>[3,6,1,2,4,5]=>0
[6,3,2,1,5,4]=>[3,5,1,2,6,4]=>0
[6,3,2,4,1,5]=>[3,4,1,6,2,5]=>0
[6,3,2,4,5,1]=>[3,4,1,5,6,2]=>0
[6,3,2,5,1,4]=>[3,5,1,6,4,2]=>1
[6,3,2,5,4,1]=>[3,5,1,6,2,4]=>0
[6,3,4,1,2,5]=>[3,6,4,2,1,5]=>2
[6,3,4,1,5,2]=>[3,5,4,2,6,1]=>2
[6,3,4,2,1,5]=>[3,6,4,1,2,5]=>1
[6,3,4,2,5,1]=>[3,5,4,1,6,2]=>1
[6,3,4,5,1,2]=>[3,6,4,5,2,1]=>3
[6,3,4,5,2,1]=>[3,6,4,5,1,2]=>2
[6,3,5,1,2,4]=>[3,6,5,2,4,1]=>3
[6,3,5,1,4,2]=>[3,6,5,2,1,4]=>2
[6,3,5,2,1,4]=>[3,6,5,1,4,2]=>2
[6,3,5,2,4,1]=>[3,6,5,1,2,4]=>1
[6,3,5,4,1,2]=>[3,5,4,6,2,1]=>2
[6,3,5,4,2,1]=>[3,5,4,6,1,2]=>1
[6,4,1,2,3,5]=>[4,6,2,3,1,5]=>2
[6,4,1,2,5,3]=>[4,5,2,3,6,1]=>2
[6,4,1,3,2,5]=>[4,6,2,1,3,5]=>1
[6,4,1,3,5,2]=>[4,5,2,1,6,3]=>1
[6,4,1,5,2,3]=>[4,6,2,5,3,1]=>3
[6,4,1,5,3,2]=>[4,6,2,5,1,3]=>2
[6,4,2,1,3,5]=>[4,6,1,3,2,5]=>1
[6,4,2,1,5,3]=>[4,5,1,3,6,2]=>1
[6,4,2,3,1,5]=>[4,6,1,2,3,5]=>0
[6,4,2,3,5,1]=>[4,5,1,2,6,3]=>0
[6,4,2,5,1,3]=>[4,6,1,5,3,2]=>2
[6,4,2,5,3,1]=>[4,6,1,5,2,3]=>1
[6,4,3,1,2,5]=>[3,4,6,2,1,5]=>1
[6,4,3,1,5,2]=>[3,4,5,2,6,1]=>1
[6,4,3,2,1,5]=>[3,4,6,1,2,5]=>0
[6,4,3,2,5,1]=>[3,4,5,1,6,2]=>0
[6,4,3,5,1,2]=>[3,4,6,5,2,1]=>2
[6,4,3,5,2,1]=>[3,4,6,5,1,2]=>1
[6,4,5,1,2,3]=>[4,6,5,3,2,1]=>4
[6,4,5,1,3,2]=>[4,6,5,3,1,2]=>3
[6,4,5,2,1,3]=>[4,6,5,2,3,1]=>3
[6,4,5,2,3,1]=>[4,6,5,2,1,3]=>2
[6,4,5,3,1,2]=>[4,6,5,1,3,2]=>2
[6,4,5,3,2,1]=>[4,6,5,1,2,3]=>1
[6,5,1,2,3,4]=>[5,6,2,3,4,1]=>3
[6,5,1,2,4,3]=>[5,6,2,3,1,4]=>2
[6,5,1,3,2,4]=>[5,6,2,1,4,3]=>2
[6,5,1,3,4,2]=>[5,6,2,1,3,4]=>1
[6,5,1,4,2,3]=>[4,5,2,6,3,1]=>2
[6,5,1,4,3,2]=>[4,5,2,6,1,3]=>1
[6,5,2,1,3,4]=>[5,6,1,3,4,2]=>2
[6,5,2,1,4,3]=>[5,6,1,3,2,4]=>1
[6,5,2,3,1,4]=>[5,6,1,2,4,3]=>1
[6,5,2,3,4,1]=>[5,6,1,2,3,4]=>0
[6,5,2,4,1,3]=>[4,5,1,6,3,2]=>1
[6,5,2,4,3,1]=>[4,5,1,6,2,3]=>0
[6,5,3,1,2,4]=>[3,5,6,2,4,1]=>2
[6,5,3,1,4,2]=>[3,5,6,2,1,4]=>1
[6,5,3,2,1,4]=>[3,5,6,1,4,2]=>1
[6,5,3,2,4,1]=>[3,5,6,1,2,4]=>0
[6,5,3,4,1,2]=>[3,4,5,6,2,1]=>1
[6,5,3,4,2,1]=>[3,4,5,6,1,2]=>0
[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>3
[6,5,4,1,3,2]=>[4,5,6,3,1,2]=>2
[6,5,4,2,1,3]=>[4,5,6,2,3,1]=>2
[6,5,4,2,3,1]=>[4,5,6,2,1,3]=>1
[6,5,4,3,1,2]=>[4,5,6,1,3,2]=>1
[6,5,4,3,2,1]=>[4,5,6,1,2,3]=>0
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>0
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>0
[1,2,3,7,4,6,5]=>[1,2,3,6,4,7,5]=>0
[1,2,7,3,4,6,5]=>[1,2,6,3,4,7,5]=>0
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>0
[1,3,5,6,7,2,4]=>[1,7,3,6,5,4,2]=>5
[1,3,5,7,6,2,4]=>[1,7,3,5,6,4,2]=>4
[1,4,5,6,2,7,3]=>[1,7,5,4,3,6,2]=>5
[1,4,5,6,7,2,3]=>[1,7,6,4,5,3,2]=>6
[1,4,5,7,2,6,3]=>[1,6,5,4,3,7,2]=>4
[1,4,5,7,6,2,3]=>[1,7,5,4,6,3,2]=>5
[1,4,6,2,7,3,5]=>[1,7,4,3,6,5,2]=>4
[1,4,6,5,2,7,3]=>[1,7,4,5,3,6,2]=>4
[1,4,6,5,7,2,3]=>[1,7,4,6,5,3,2]=>5
[1,4,6,7,5,2,3]=>[1,6,5,4,7,3,2]=>4
[1,4,7,5,6,2,3]=>[1,7,4,5,6,3,2]=>4
[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>0
[1,5,3,6,7,2,4]=>[1,3,7,6,5,4,2]=>4
[1,5,6,7,2,3,4]=>[1,7,6,5,4,3,2]=>6
[1,5,7,4,6,2,3]=>[1,5,4,7,6,3,2]=>3
[1,6,4,5,7,2,3]=>[1,4,7,6,5,3,2]=>4
[1,6,4,7,5,2,3]=>[1,5,6,4,7,3,2]=>3
[1,6,5,4,7,2,3]=>[1,4,6,7,5,3,2]=>3
[1,6,5,7,2,3,4]=>[1,6,7,5,4,3,2]=>5
[1,6,7,5,2,3,4]=>[1,6,5,7,4,3,2]=>4
[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>0
[1,7,2,3,4,6,5]=>[1,6,2,3,4,7,5]=>0
[1,7,2,3,6,5,4]=>[1,6,2,3,7,4,5]=>0
[1,7,2,5,4,3,6]=>[1,5,2,7,3,4,6]=>0
[1,7,2,6,4,5,3]=>[1,6,2,7,3,4,5]=>0
[1,7,3,2,4,5,6]=>[1,3,7,2,4,5,6]=>0
[1,7,4,3,2,5,6]=>[1,4,7,2,3,5,6]=>0
[1,7,5,3,4,2,6]=>[1,5,7,2,3,4,6]=>0
[1,7,5,6,2,3,4]=>[1,5,7,6,4,3,2]=>4
[1,7,6,3,4,5,2]=>[1,6,7,2,3,4,5]=>0
[1,7,6,3,5,4,2]=>[1,5,6,2,7,3,4]=>0
[1,7,6,4,3,5,2]=>[1,4,6,7,2,3,5]=>0
[1,7,6,5,2,3,4]=>[1,5,6,7,4,3,2]=>3
[1,7,6,5,4,3,2]=>[1,5,6,7,2,3,4]=>0
[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>0
[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>0
[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>0
[2,1,5,6,7,3,4]=>[2,1,7,6,5,4,3]=>4
[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>0
[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>0
[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>1
[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>4
[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>4
[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>3
[2,3,4,7,5,6,1]=>[5,2,3,4,6,7,1]=>3
[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>2
[2,3,7,4,5,6,1]=>[4,2,3,5,6,7,1]=>2
[2,4,5,6,1,3,7]=>[6,2,5,4,3,1,7]=>5
[2,4,6,5,1,3,7]=>[6,2,4,5,3,1,7]=>4
[2,5,4,3,1,6,7]=>[4,2,5,1,3,6,7]=>1
[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>1
[2,7,3,4,5,6,1]=>[3,2,4,5,6,7,1]=>1
[2,7,6,5,4,3,1]=>[5,2,6,7,1,3,4]=>1
[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>0
[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>0
[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>0
[3,4,1,2,5,6,7]=>[4,3,2,1,5,6,7]=>2
[3,4,1,7,2,5,6]=>[7,3,2,4,1,5,6]=>3
[3,4,1,7,5,6,2]=>[5,3,2,4,6,7,1]=>3
[3,4,5,1,2,6,7]=>[5,4,3,2,1,6,7]=>4
[3,4,5,1,2,7,6]=>[5,4,3,2,1,7,6]=>4
[3,4,5,1,6,2,7]=>[6,4,3,2,5,1,7]=>5
[3,4,5,6,1,2,7]=>[6,5,3,4,2,1,7]=>6
[3,4,6,1,5,2,7]=>[5,4,3,2,6,1,7]=>4
[3,4,6,5,1,2,7]=>[6,4,3,5,2,1,7]=>5
[3,4,7,1,6,5,2]=>[6,4,3,2,7,1,5]=>4
[3,5,1,6,2,4,7]=>[6,3,2,5,4,1,7]=>4
[3,5,4,1,6,2,7]=>[6,3,4,2,5,1,7]=>4
[3,5,4,6,1,2,7]=>[6,3,5,4,2,1,7]=>5
[3,5,6,4,1,2,7]=>[5,4,3,6,2,1,7]=>4
[3,6,1,5,4,2,7]=>[5,3,2,6,1,4,7]=>2
[3,6,4,5,1,2,7]=>[6,3,4,5,2,1,7]=>4
[3,7,1,2,4,5,6]=>[7,3,2,1,4,5,6]=>2
[3,7,1,4,5,6,2]=>[4,3,2,5,6,7,1]=>2
[3,7,2,1,4,5,6]=>[7,3,1,2,4,5,6]=>1
[3,7,4,2,1,5,6]=>[7,3,4,1,2,5,6]=>2
[3,7,6,4,2,5,1]=>[6,3,4,7,1,2,5]=>2
[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>0
[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>0
[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>0
[4,2,3,1,5,6,7]=>[2,3,4,1,5,6,7]=>0
[4,2,3,1,5,7,6]=>[2,3,4,1,5,7,6]=>0
[4,2,5,6,1,3,7]=>[2,6,5,4,3,1,7]=>4
[4,3,2,1,5,6,7]=>[3,4,1,2,5,6,7]=>0
[4,3,5,6,2,1,7]=>[5,6,3,4,1,2,7]=>4
[4,3,6,7,2,5,1]=>[6,7,3,4,1,2,5]=>4
[4,5,6,1,2,3,7]=>[6,5,4,3,2,1,7]=>6
[4,5,6,7,1,2,3]=>[7,6,5,4,3,2,1]=>9
[4,5,6,7,1,3,2]=>[7,6,5,4,3,1,2]=>8
[4,5,6,7,3,2,1]=>[7,6,5,4,1,2,3]=>6
[4,5,7,6,3,2,1]=>[7,6,4,5,1,2,3]=>5
[4,6,3,5,1,2,7]=>[4,3,6,5,2,1,7]=>3
[4,7,1,3,2,5,6]=>[7,4,2,1,3,5,6]=>2
[4,7,2,3,1,5,6]=>[7,4,1,2,3,5,6]=>1
[4,7,3,1,5,6,2]=>[4,3,5,2,6,7,1]=>2
[4,7,6,5,3,2,1]=>[7,4,5,6,1,2,3]=>3
[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>0
[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>0
[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>0
[5,2,3,4,1,6,7]=>[2,3,4,5,1,6,7]=>0
[5,2,3,4,1,7,6]=>[2,3,4,5,1,7,6]=>0
[5,3,4,6,1,2,7]=>[3,6,5,4,2,1,7]=>4
[5,3,6,4,1,2,7]=>[4,5,3,6,2,1,7]=>3
[5,4,3,6,1,2,7]=>[3,5,6,4,2,1,7]=>3
[5,4,6,1,2,3,7]=>[5,6,4,3,2,1,7]=>5
[5,4,7,6,3,2,1]=>[6,7,4,5,1,2,3]=>4
[5,6,4,1,2,3,7]=>[5,4,6,3,2,1,7]=>4
[5,6,4,1,7,3,2]=>[6,4,7,3,5,1,2]=>5
[5,6,4,2,7,3,1]=>[6,4,7,2,5,1,3]=>4
[5,6,7,1,2,4,3]=>[7,6,5,3,4,1,2]=>7
[5,6,7,3,4,2,1]=>[7,6,5,1,2,3,4]=>3
[5,7,2,3,4,1,6]=>[7,5,1,2,3,4,6]=>1
[5,7,6,1,2,4,3]=>[7,5,6,3,4,1,2]=>6
[5,7,6,3,4,2,1]=>[7,5,6,1,2,3,4]=>2
[5,7,6,4,3,2,1]=>[6,4,5,7,1,2,3]=>2
[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>0
[6,1,2,3,5,4,7]=>[5,1,2,3,6,4,7]=>0
[6,1,2,5,4,3,7]=>[5,1,2,6,3,4,7]=>0
[6,1,4,3,2,5,7]=>[4,1,6,2,3,5,7]=>0
[6,1,5,3,4,2,7]=>[5,1,6,2,3,4,7]=>0
[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>0
[6,2,3,4,5,1,7]=>[2,3,4,5,6,1,7]=>0
[6,3,2,1,4,5,7]=>[3,6,1,2,4,5,7]=>0
[6,4,2,3,1,5,7]=>[4,6,1,2,3,5,7]=>0
[6,4,5,1,2,3,7]=>[4,6,5,3,2,1,7]=>4
[6,5,2,3,4,1,7]=>[5,6,1,2,3,4,7]=>0
[6,5,2,4,3,1,7]=>[4,5,1,6,2,3,7]=>0
[6,5,3,2,4,1,7]=>[3,5,6,1,2,4,7]=>0
[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>3
[6,5,4,3,2,1,7]=>[4,5,6,1,2,3,7]=>0
[6,7,2,3,4,5,1]=>[7,6,1,2,3,4,5]=>1
[6,7,3,5,4,2,1]=>[5,3,6,7,1,2,4]=>1
[6,7,5,1,2,4,3]=>[6,5,7,3,4,1,2]=>5
[6,7,5,4,3,2,1]=>[5,4,6,7,1,2,3]=>1
[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>0
[7,1,2,3,4,6,5]=>[6,1,2,3,4,7,5]=>0
[7,1,2,3,5,4,6]=>[5,1,2,3,7,4,6]=>0
[7,1,2,3,5,6,4]=>[5,1,2,3,6,7,4]=>0
[7,1,2,3,6,5,4]=>[6,1,2,3,7,4,5]=>0
[7,1,2,6,4,5,3]=>[6,1,2,7,3,4,5]=>0
[7,1,5,3,4,6,2]=>[5,1,6,2,3,7,4]=>0
[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>0
[7,2,1,6,4,5,3]=>[2,6,1,7,3,4,5]=>0
[7,2,3,4,1,5,6]=>[2,3,4,7,1,5,6]=>0
[7,2,3,4,1,6,5]=>[2,3,4,6,1,7,5]=>0
[7,2,3,4,5,1,6]=>[2,3,4,5,7,1,6]=>0
[7,2,3,4,5,6,1]=>[2,3,4,5,6,7,1]=>0
[7,2,3,4,6,5,1]=>[2,3,4,6,7,1,5]=>0
[7,2,3,6,5,4,1]=>[2,3,5,6,7,1,4]=>0
[7,2,5,3,4,1,6]=>[2,5,7,1,3,4,6]=>0
[7,2,6,3,4,5,1]=>[2,6,7,1,3,4,5]=>0
[7,3,1,4,5,6,2]=>[3,4,2,5,6,7,1]=>1
[7,4,1,2,5,6,3]=>[4,5,2,3,6,7,1]=>2
[7,4,2,3,1,6,5]=>[4,6,1,2,3,7,5]=>0
[7,4,3,1,5,6,2]=>[3,4,5,2,6,7,1]=>1
[7,5,2,3,4,6,1]=>[5,6,1,2,3,7,4]=>0
[7,5,3,4,1,6,2]=>[3,4,5,6,2,7,1]=>1
[7,6,2,3,4,5,1]=>[6,7,1,2,3,4,5]=>0
[7,6,3,4,5,2,1]=>[3,4,5,6,7,1,2]=>0
[7,6,5,3,4,2,1]=>[5,6,7,1,2,3,4]=>0
[8,7,6,5,4,3,2,1]=>[5,6,7,8,1,2,3,4]=>0
[7,8,5,6,4,3,2,1]=>[6,5,8,7,1,2,3,4]=>2
[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>6
[4,5,6,7,8,3,2,1]=>[8,7,6,4,5,1,2,3]=>9
[7,8,6,5,3,4,2,1]=>[6,5,7,8,2,1,3,4]=>2
[8,7,6,4,3,5,2,1]=>[4,6,7,8,1,2,3,5]=>0
[8,7,6,3,4,5,2,1]=>[6,7,8,1,2,3,4,5]=>0
[6,7,8,3,4,5,2,1]=>[8,7,6,1,2,3,4,5]=>3
[8,7,3,4,5,6,2,1]=>[3,4,5,6,7,8,1,2]=>0
[4,3,5,6,7,8,2,1]=>[7,8,3,4,5,6,1,2]=>8
[8,6,7,5,4,2,3,1]=>[5,7,6,8,1,3,2,4]=>2
[7,6,5,8,4,2,3,1]=>[6,7,8,5,1,3,2,4]=>4
[6,7,8,5,2,3,4,1]=>[7,6,5,8,3,2,1,4]=>6
[8,6,7,3,4,2,5,1]=>[6,8,7,1,2,4,3,5]=>2
[6,7,8,3,2,4,5,1]=>[8,7,6,1,3,4,2,5]=>5
[8,7,5,4,3,2,6,1]=>[4,5,7,8,1,2,3,6]=>0
[8,7,2,3,4,5,6,1]=>[7,8,1,2,3,4,5,6]=>0
[7,8,2,3,4,5,6,1]=>[8,7,1,2,3,4,5,6]=>1
[8,6,2,3,4,5,7,1]=>[6,7,1,2,3,4,8,5]=>0
[8,2,3,4,5,6,7,1]=>[2,3,4,5,6,7,8,1]=>0
[5,2,3,4,6,7,8,1]=>[2,3,4,8,5,6,7,1]=>3
[8,7,5,6,4,3,1,2]=>[5,6,8,7,1,2,4,3]=>2
[8,7,6,5,3,4,1,2]=>[5,6,7,8,2,1,4,3]=>2
[7,8,5,6,3,4,1,2]=>[6,5,8,7,2,1,4,3]=>4
[5,6,7,8,3,4,1,2]=>[8,7,6,5,2,1,4,3]=>8
[8,4,3,5,6,7,1,2]=>[3,4,8,5,6,7,2,1]=>4
[4,5,6,7,8,2,1,3]=>[8,7,6,4,5,2,3,1]=>11
[8,5,6,7,4,1,2,3]=>[5,8,7,6,1,4,3,2]=>6
[8,4,5,6,7,1,2,3]=>[4,8,7,5,6,3,2,1]=>8
[5,4,6,7,8,1,2,3]=>[7,8,6,4,5,3,2,1]=>11
[8,6,7,5,3,2,1,4]=>[5,7,6,8,2,3,4,1]=>4
[7,6,5,8,3,2,1,4]=>[6,7,8,5,2,3,4,1]=>6
[6,5,7,8,2,1,3,4]=>[7,8,6,5,3,4,2,1]=>10
[7,8,5,6,1,2,3,4]=>[6,5,8,7,4,3,2,1]=>8
[6,7,5,8,1,2,3,4]=>[7,6,8,5,4,3,2,1]=>10
[5,6,7,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>12
[8,7,6,1,2,3,4,5]=>[6,7,8,3,4,5,2,1]=>7
[8,6,5,4,3,2,1,7]=>[4,5,6,8,1,2,3,7]=>0
[8,6,5,2,3,4,1,7]=>[5,6,8,2,3,1,4,7]=>2
[8,2,3,4,5,6,1,7]=>[2,3,4,5,6,8,1,7]=>0
[8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,7]=>0
[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,3,4,2,1,8]=>[5,6,7,1,2,3,4,8]=>0
[7,6,2,3,4,5,1,8]=>[6,7,1,2,3,4,5,8]=>0
[7,2,3,4,5,6,1,8]=>[2,3,4,5,6,7,1,8]=>0
[3,4,5,6,7,1,2,8]=>[7,6,3,4,5,2,1,8]=>8
[5,6,7,4,1,2,3,8]=>[6,5,4,7,3,2,1,8]=>6
[7,4,5,6,1,2,3,8]=>[4,7,6,5,3,2,1,8]=>6
[5,6,4,7,1,2,3,8]=>[6,5,7,4,3,2,1,8]=>7
[5,4,6,7,1,2,3,8]=>[6,7,5,4,3,2,1,8]=>8
[4,5,6,7,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>9
[7,6,5,2,3,1,4,8]=>[5,6,7,2,3,4,1,8]=>3
[7,5,2,3,4,1,6,8]=>[5,7,1,2,3,4,6,8]=>0
[7,2,1,3,4,5,6,8]=>[2,7,1,3,4,5,6,8]=>0
[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,4,3,2,1,7,8]=>[4,5,6,1,2,3,7,8]=>0
[6,2,3,4,5,1,7,8]=>[2,3,4,5,6,1,7,8]=>0
[4,5,6,1,2,3,7,8]=>[6,5,4,3,2,1,7,8]=>6
[6,2,1,3,4,5,7,8]=>[2,6,1,3,4,5,7,8]=>0
[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>0
[5,2,3,4,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>0
[3,4,5,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>4
[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[4,3,2,1,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>0
[3,4,1,2,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>2
[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1
[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>0
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0
[5,8,7,6,4,3,2,1]=>[8,5,6,7,1,2,3,4]=>3
[6,5,8,7,4,3,2,1]=>[7,8,5,6,1,2,3,4]=>4
[5,6,8,7,4,3,2,1]=>[8,7,5,6,1,2,3,4]=>5
[4,6,5,7,8,3,2,1]=>[8,6,7,4,5,1,2,3]=>8
[4,3,8,7,6,5,2,1]=>[4,7,3,6,8,1,2,5]=>3
[4,3,7,8,6,5,2,1]=>[6,7,3,4,8,1,2,5]=>4
[5,4,3,7,8,6,2,1]=>[3,6,7,4,5,8,1,2]=>4
[4,5,3,6,8,7,2,1]=>[6,3,8,4,5,7,1,2]=>6
[3,5,7,6,4,8,2,1]=>[8,5,3,7,1,6,2,4]=>6
[3,5,6,7,4,8,2,1]=>[8,7,3,5,1,6,2,4]=>7
[3,2,6,5,4,8,7,1]=>[2,5,3,7,1,6,8,4]=>2
[2,4,3,6,5,8,7,1]=>[3,2,5,4,7,6,8,1]=>3
[3,4,7,6,5,2,8,1]=>[6,4,3,5,8,1,7,2]=>5
[2,5,6,7,4,3,8,1]=>[8,2,6,5,1,3,7,4]=>5
[2,5,4,6,7,3,8,1]=>[6,2,8,4,5,1,7,3]=>6
[2,3,6,5,4,7,8,1]=>[5,2,3,8,1,6,7,4]=>4
[1,3,5,8,7,6,4,2]=>[1,7,3,5,6,8,2,4]=>3
[1,4,3,7,8,6,5,2]=>[1,3,7,4,6,8,2,5]=>2
[1,3,5,4,7,6,8,2]=>[1,4,3,6,5,8,7,2]=>3
[2,1,8,7,6,5,4,3]=>[2,1,6,7,8,3,4,5]=>0
[2,1,5,8,7,6,4,3]=>[2,1,7,5,6,8,3,4]=>2
[2,1,5,7,8,6,4,3]=>[2,1,7,6,5,8,3,4]=>3
[2,1,4,6,5,8,7,3]=>[2,1,5,4,7,6,8,3]=>2
[1,2,7,8,6,5,4,3]=>[1,2,7,6,8,3,4,5]=>1
[1,2,6,7,8,5,4,3]=>[1,2,8,7,6,3,4,5]=>3
[2,3,1,5,7,6,8,4]=>[3,2,1,6,5,8,7,4]=>3
[4,3,2,1,8,7,6,5]=>[3,4,1,2,7,8,5,6]=>0
[3,4,2,1,7,8,6,5]=>[4,3,1,2,8,7,5,6]=>2
[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]=>2
[2,4,3,1,7,6,8,5]=>[3,2,4,1,6,8,7,5]=>2
[3,2,4,1,6,8,7,5]=>[2,4,3,1,7,6,8,5]=>2
[3,2,4,1,7,6,8,5]=>[2,4,3,1,6,8,7,5]=>2
[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>4
[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,8,5,6]=>0
[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]=>1
[2,1,4,3,7,6,8,5]=>[2,1,4,3,6,8,7,5]=>1
[2,4,3,5,1,7,8,6]=>[3,2,5,4,1,8,7,6]=>3
[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>0
[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>2
[6,5,4,3,2,1,8,7]=>[4,5,6,1,2,3,8,7]=>0
[3,5,6,4,2,1,8,7]=>[5,4,3,6,1,2,8,7]=>3
[2,4,3,6,5,1,8,7]=>[3,2,5,4,6,1,8,7]=>2
[2,1,6,5,4,3,8,7]=>[2,1,5,6,3,4,8,7]=>0
[2,1,4,6,5,3,8,7]=>[2,1,5,4,6,3,8,7]=>1
[2,1,5,4,6,3,8,7]=>[2,1,4,6,5,3,8,7]=>1
[4,3,2,1,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>0
[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>1
[3,2,4,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>1
[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>0
[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>0
[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>0
[2,7,6,5,4,3,1,8]=>[5,2,6,7,1,3,4,8]=>1
[2,4,3,6,5,7,1,8]=>[3,2,5,4,7,6,1,8]=>3
[1,3,6,5,4,7,2,8]=>[1,5,3,7,2,6,4,8]=>2
[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>0
[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>2
[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>0
[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>0
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>0
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>0
[1,2,6,5,4,3,7,8]=>[1,2,5,6,3,4,7,8]=>0
[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>0
[2,5,4,3,1,6,7,8]=>[4,2,5,1,3,6,7,8]=>1
[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>0
[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0
[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0
[1,2,3,8,5,6,7,4]=>[1,2,3,5,6,7,8,4]=>0
[1,7,3,5,4,6,2,8]=>[1,3,5,6,2,7,4,8]=>0
[1,7,6,4,5,3,2,8]=>[1,4,5,6,7,2,3,8]=>0
[2,1,4,8,6,5,7,3]=>[2,1,6,4,7,3,8,5]=>1
[2,1,6,4,5,7,8,3]=>[2,1,4,5,8,6,7,3]=>2
[2,1,8,5,4,7,6,3]=>[2,1,5,7,3,8,4,6]=>0
[2,3,4,8,5,6,7,1]=>[5,2,3,4,6,7,8,1]=>3
[2,3,8,4,5,6,7,1]=>[4,2,3,5,6,7,8,1]=>2
[2,8,3,4,5,6,7,1]=>[3,2,4,5,6,7,8,1]=>1
[2,7,3,5,4,6,8,1]=>[3,2,5,6,1,8,7,4]=>2
[2,6,4,3,5,1,8,7]=>[4,2,5,1,6,3,8,7]=>1
[2,7,6,4,5,3,8,1]=>[4,2,5,6,8,1,7,3]=>2
[4,2,3,1,8,6,7,5]=>[2,3,4,1,6,7,8,5]=>0
[4,2,3,5,6,1,8,7]=>[2,3,6,4,5,1,8,7]=>2
[4,2,3,5,6,8,7,1]=>[2,3,7,4,5,6,8,1]=>3
[6,2,3,4,5,1,8,7]=>[2,3,4,5,6,1,8,7]=>0
[8,2,3,4,5,7,6,1]=>[2,3,4,5,7,8,1,6]=>0
[8,2,3,5,4,6,7,1]=>[2,3,5,6,1,7,8,4]=>0
[8,2,4,3,6,5,7,1]=>[2,4,6,1,7,3,8,5]=>0
[8,2,6,4,5,3,7,1]=>[2,4,5,6,7,1,8,3]=>0
[6,3,2,5,4,1,8,7]=>[3,5,1,6,2,4,8,7]=>0
[8,3,2,5,4,7,6,1]=>[3,5,1,7,2,8,4,6]=>0
[8,3,2,7,6,5,4,1]=>[3,6,1,7,8,2,4,5]=>0
[8,3,5,4,7,6,2,1]=>[3,5,4,7,6,8,1,2]=>2
[8,5,4,3,2,7,6,1]=>[4,5,7,1,2,8,3,6]=>0
[8,7,4,3,6,5,2,1]=>[4,6,7,1,8,2,3,5]=>0
[2,4,6,7,8,1,3,5]=>[8,2,7,4,6,5,3,1]=>9
[2,4,1,3,7,5,8,6]=>[4,2,1,3,8,5,7,6]=>2
[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,7,6,5]=>2
[2,1,4,7,8,3,5,6]=>[2,1,8,4,7,5,6,3]=>4
[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>0
[2,1,5,6,3,4,8,7]=>[2,1,6,5,4,3,8,7]=>2
[2,5,1,7,3,4,8,6]=>[8,2,1,5,4,3,7,6]=>4
[2,1,5,7,3,8,4,6]=>[2,1,8,5,4,7,6,3]=>4
[2,1,6,7,8,3,4,5]=>[2,1,8,7,6,5,4,3]=>6
[2,3,1,6,7,8,4,5]=>[3,2,1,8,7,6,5,4]=>5
[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>0
[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>0
[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]=>1
[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>0
[2,3,8,1,4,5,6,7]=>[8,2,3,1,4,5,6,7]=>2
[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>1
[2,3,4,8,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>3
[3,4,1,2,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>2
[3,1,4,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]=>2
[3,4,1,2,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>4
[3,4,5,1,2,7,8,6]=>[5,4,3,2,1,8,7,6]=>5
[3,1,4,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>1
[3,4,5,1,2,8,6,7]=>[5,4,3,2,1,8,6,7]=>4
[3,5,1,6,2,4,8,7]=>[6,3,2,5,4,1,8,7]=>4
[3,5,6,7,1,2,4,8]=>[7,6,3,5,4,2,1,8]=>8
[3,5,1,7,2,8,4,6]=>[8,3,2,5,4,7,6,1]=>6
[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>0
[3,6,1,7,8,2,4,5]=>[8,3,2,7,6,5,4,1]=>8
[1,3,2,6,4,7,5,8]=>[1,3,2,7,4,6,5,8]=>1
[1,3,2,6,4,8,5,7]=>[1,3,2,8,4,6,5,7]=>1
[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>0
[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>0
[3,8,1,2,4,5,6,7]=>[8,3,2,1,4,5,6,7]=>2
[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>0
[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>0
[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>0
[4,5,6,1,2,3,8,7]=>[6,5,4,3,2,1,8,7]=>6
[4,5,6,8,1,2,3,7]=>[8,6,5,4,3,2,1,7]=>9
[4,5,6,1,7,2,3,8]=>[7,6,4,3,5,2,1,8]=>8
[4,5,7,1,2,8,3,6]=>[8,5,4,3,2,7,6,1]=>8
[1,4,2,5,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>1
[1,4,2,5,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>1
[1,4,5,8,2,3,6,7]=>[1,8,5,4,3,2,6,7]=>4
[4,1,2,5,6,8,3,7]=>[8,1,2,4,5,6,3,7]=>3
[1,4,2,5,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>1
[1,4,5,6,7,8,2,3]=>[1,8,7,4,5,6,3,2]=>8
[4,6,7,1,8,2,3,5]=>[8,7,4,3,6,5,2,1]=>10
[1,4,2,6,3,7,5,8]=>[1,7,2,4,3,6,5,8]=>2
[1,4,6,7,8,2,3,5]=>[1,8,7,4,6,5,3,2]=>8
[1,4,2,6,3,8,5,7]=>[1,8,2,4,3,6,5,7]=>2
[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>0
[1,4,2,6,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>1
[1,4,2,7,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>1
[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>0
[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>0
[1,4,2,8,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>1
[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>0
[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>0
[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>0
[1,5,6,7,2,8,3,4]=>[1,8,7,5,4,6,3,2]=>8
[1,5,6,7,8,2,3,4]=>[1,8,7,6,5,4,3,2]=>9
[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>0
[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>0
[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>0
[5,1,2,3,4,6,8,7]=>[5,1,2,3,4,6,8,7]=>0
[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>0
[1,6,2,3,4,7,5,8]=>[1,7,2,3,4,6,5,8]=>1
[1,2,3,6,4,7,5,8]=>[1,2,3,7,4,6,5,8]=>1
[1,6,2,3,4,8,5,7]=>[1,8,2,3,4,6,5,7]=>1
[1,2,3,6,4,8,5,7]=>[1,2,3,8,4,6,5,7]=>1
[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>0
[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>0
[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>0
[1,2,7,8,3,4,5,6]=>[1,2,8,7,4,5,6,3]=>4
[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>0
[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>0
[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>0
[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>0
[5,3,2,6,1,4,8,7]=>[3,6,1,5,4,2,8,7]=>2
[7,3,2,5,4,8,1,6]=>[3,5,1,8,2,7,6,4]=>2
[3,6,1,5,4,2,8,7]=>[5,3,2,6,1,4,8,7]=>2
[7,5,4,3,2,8,1,6]=>[4,5,8,1,2,7,6,3]=>2
[3,7,1,5,4,8,2,6]=>[5,3,2,8,1,7,6,4]=>4
[2,1,7,5,4,8,3,6]=>[2,1,5,8,3,7,6,4]=>2
[3,8,1,5,4,7,6,2]=>[5,3,2,7,1,8,4,6]=>2
[5,8,4,3,1,7,6,2]=>[5,4,7,1,3,8,2,6]=>2
[6,8,5,7,3,1,4,2]=>[7,5,8,6,2,4,1,3]=>6
[5,7,6,8,1,3,2,4]=>[8,6,7,5,4,2,3,1]=>10
[6,3,2,7,8,1,4,5]=>[3,8,1,7,6,5,4,2]=>6
[5,3,2,7,1,8,4,6]=>[3,8,1,5,4,7,6,2]=>4
[4,3,2,1,7,8,5,6]=>[3,4,1,2,8,7,6,5]=>2
[3,4,1,2,8,7,6,5]=>[4,3,2,1,7,8,5,6]=>2
[5,3,2,8,1,7,6,4]=>[3,7,1,5,4,8,2,6]=>2
[4,5,8,1,2,7,6,3]=>[7,5,4,3,2,8,1,6]=>6
[3,5,1,8,2,7,6,4]=>[7,3,2,5,4,8,1,6]=>4
[2,1,5,8,3,7,6,4]=>[2,1,7,5,4,8,3,6]=>2
[5,6,8,7,1,2,4,3]=>[8,7,5,6,4,3,1,2]=>10
[6,5,8,7,2,1,4,3]=>[7,8,5,6,3,4,1,2]=>8
[7,5,8,6,2,4,1,3]=>[6,8,5,7,3,1,4,2]=>6
[3,8,1,7,6,5,4,2]=>[6,3,2,7,8,1,4,5]=>2
[5,8,7,6,1,4,3,2]=>[8,5,6,7,4,1,2,3]=>6
[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>0
[3,4,1,2,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>2
[4,5,6,1,2,3,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>6
[3,5,1,6,2,4,8,7,10,9]=>[6,3,2,5,4,1,8,7,10,9]=>4
[2,1,5,6,3,4,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>2
[5,6,7,8,1,2,3,4,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>12
[4,6,7,1,8,2,3,5,10,9]=>[8,7,4,3,6,5,2,1,10,9]=>10
[3,6,1,7,8,2,4,5,10,9]=>[8,3,2,7,6,5,4,1,10,9]=>8
[2,1,6,7,8,3,4,5,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>6
[2,1,5,7,3,8,4,6,10,9]=>[2,1,8,5,4,7,6,3,10,9]=>4
[3,5,1,7,2,8,4,6,10,9]=>[8,3,2,5,4,7,6,1,10,9]=>6
[4,5,7,1,2,8,3,6,10,9]=>[8,5,4,3,2,7,6,1,10,9]=>8
[3,4,1,2,7,8,5,6,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>4
[2,1,4,3,7,8,5,6,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>2
[2,1,7,8,9,10,3,4,5,6]=>[2,1,10,9,8,7,6,5,4,3]=>12
[3,7,1,8,9,10,2,4,5,6]=>[10,3,2,9,8,7,6,5,4,1]=>14
[4,7,8,1,9,10,2,3,5,6]=>[10,9,4,3,8,7,6,5,2,1]=>16
[5,7,8,9,1,10,2,3,4,6]=>[10,9,8,5,4,7,6,3,2,1]=>18
[6,7,8,9,10,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>20
[5,6,8,9,1,2,10,3,4,7]=>[10,9,6,5,4,3,8,7,2,1]=>16
[4,6,8,1,9,2,10,3,5,7]=>[10,9,4,3,6,5,8,7,2,1]=>14
[3,6,1,8,9,2,10,4,5,7]=>[10,3,2,9,6,5,8,7,4,1]=>12
[2,1,6,8,9,3,10,4,5,7]=>[2,1,10,9,6,5,8,7,4,3]=>10
[2,1,5,8,3,9,10,4,6,7]=>[2,1,10,5,4,9,8,7,6,3]=>8
[3,5,1,8,2,9,10,4,6,7]=>[10,3,2,5,4,9,8,7,6,1]=>10
[4,5,8,1,2,9,10,3,6,7]=>[10,5,4,3,2,9,8,7,6,1]=>12
[3,4,1,2,8,9,10,5,6,7]=>[4,3,2,1,10,9,8,7,6,5]=>8
[2,1,4,3,8,9,10,5,6,7]=>[2,1,4,3,10,9,8,7,6,5]=>6
[2,1,4,3,7,9,5,10,6,8]=>[2,1,4,3,10,7,6,9,8,5]=>4
[3,4,1,2,7,9,5,10,6,8]=>[4,3,2,1,10,7,6,9,8,5]=>6
[4,5,7,1,2,9,3,10,6,8]=>[10,5,4,3,2,7,6,9,8,1]=>10
[3,5,1,7,2,9,4,10,6,8]=>[10,3,2,5,4,7,6,9,8,1]=>8
[2,1,5,7,3,9,4,10,6,8]=>[2,1,10,5,4,7,6,9,8,3]=>6
[2,1,6,7,9,3,4,10,5,8]=>[2,1,10,7,6,5,4,9,8,3]=>8
[3,6,1,7,9,2,4,10,5,8]=>[10,3,2,7,6,5,4,9,8,1]=>10
[4,6,7,1,9,2,3,10,5,8]=>[10,7,4,3,6,5,2,9,8,1]=>12
[5,6,7,9,1,2,3,10,4,8]=>[10,7,6,5,4,3,2,9,8,1]=>14
[2,1,5,6,3,4,9,10,7,8]=>[2,1,6,5,4,3,10,9,8,7]=>4
[3,5,1,6,2,4,9,10,7,8]=>[6,3,2,5,4,1,10,9,8,7]=>6
[4,5,6,1,2,3,9,10,7,8]=>[6,5,4,3,2,1,10,9,8,7]=>8
[3,4,1,2,6,5,9,10,7,8]=>[4,3,2,1,6,5,10,9,8,7]=>4
[2,1,4,3,6,5,9,10,7,8]=>[2,1,4,3,6,5,10,9,8,7]=>2
[5,6,7,10,1,2,3,9,8,4]=>[9,7,6,5,4,3,2,10,1,8]=>12
[4,5,10,1,2,9,8,7,6,3]=>[8,5,4,3,2,9,10,1,6,7]=>6
[3,10,1,9,8,7,6,5,4,2]=>[7,3,2,8,9,10,1,4,5,6]=>2
[10,9,8,7,6,5,4,3,2,1]=>[6,7,8,9,10,1,2,3,4,5]=>0
[4,7,2,5,8,1,3,6]=>[8,4,1,7,5,3,6,2]=>6
[8,4,2,5,7,1,3,6]=>[4,8,1,5,7,3,6,2]=>4
[8,5,3,6,7,1,2,4]=>[3,5,8,7,6,4,2,1]=>6
[7,4,3,8,2,6,1,5]=>[3,6,7,4,1,8,5,2]=>3
[7,6,3,8,2,5,1,4]=>[3,7,8,6,2,1,5,4]=>4
[8,1,6,5,2,3,4,7]=>[5,1,6,8,4,3,2,7]=>3
[2,8,1,5,6,7,3,4]=>[5,2,1,8,6,7,4,3]=>4
[6,3,1,2,4,8,5,7]=>[3,8,2,1,4,6,5,7]=>2
[5,4,1,2,8,3,6,7]=>[4,8,2,3,5,1,6,7]=>3
[8,7,1,5,2,3,4,6]=>[5,7,2,8,4,3,6,1]=>5
[2,6,8,1,3,7,4,5]=>[8,2,6,3,4,7,5,1]=>6
[2,7,6,5,1,3,8,4]=>[5,2,6,8,4,3,7,1]=>5
[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]=>1
[2,3,9,1,4,5,6,7,8]=>[9,2,3,1,4,5,6,7,8]=>2
[]=>[]=>0
[3,5,2,6,4,1,8,7]=>[6,3,1,5,2,4,8,7]=>2
[2,1,5,7,4,8,6,3]=>[2,1,8,5,3,7,4,6]=>2
[5,6,7,8,1,3,4,2]=>[8,7,6,5,4,2,1,3]=>10
[3,5,2,7,1,8,6,4]=>[8,3,1,5,4,7,2,6]=>4
[5,6,7,8,1,2,4,3]=>[8,7,6,5,4,3,1,2]=>11
[5,6,7,8,2,1,4,3]=>[8,7,6,5,3,4,1,2]=>10
[5,6,7,8,1,4,3,2]=>[8,7,6,5,4,1,2,3]=>9
[5,6,7,8,4,1,3,2]=>[8,7,6,5,1,4,2,3]=>8
[6,7,8,9,10,1,5,4,3,2]=>[10,9,8,7,6,5,1,2,3,4]=>14
[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>10
[6,5,8,7,3,4,1,2]=>[7,8,5,6,2,1,4,3]=>6
[4,1,3,2,8,6,5,7]=>[3,1,4,2,6,8,5,7]=>0
[5,1,3,8,2,6,4,7]=>[3,1,6,5,4,8,2,7]=>2
[7,8,1,3,2,5,4,6]=>[8,7,2,1,4,3,6,5]=>4
[6,2,8,3,1,5,7,4]=>[2,7,6,1,4,3,8,5]=>2
[7,8,3,2,1,6,5,4]=>[6,3,7,1,4,8,2,5]=>2
[2,5,3,7,1,6,8,4]=>[3,2,6,5,4,8,7,1]=>4
[2,6,7,3,1,5,8,4]=>[8,2,6,1,4,3,7,5]=>4
[3,6,7,2,1,8,5,4]=>[8,7,3,1,4,6,2,5]=>6
[7,8,5,6,2,1,4,3]=>[6,5,8,7,3,4,1,2]=>6
[6,5,8,7,1,2,3,4]=>[7,8,5,6,4,3,2,1]=>10
[5,3,1,8,2,7,4,6]=>[3,7,2,5,4,8,6,1]=>4
[4,3,1,2,8,7,5,6]=>[3,4,2,1,7,8,6,5]=>2
[4,2,1,3,8,5,7,6]=>[2,4,1,3,7,5,8,6]=>0
[5,2,1,8,3,4,7,6]=>[2,7,1,5,4,3,8,6]=>2
[8,5,7,6,1,2,3,4]=>[5,8,6,7,4,3,2,1]=>8
[6,3,8,4,7,5,1,2]=>[4,6,3,8,7,1,5,2]=>4
[5,6,8,7,2,1,4,3]=>[8,7,5,6,3,4,1,2]=>9
[4,1,3,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>0
[6,1,3,2,5,4,8,7]=>[3,1,5,2,6,4,8,7]=>0
[8,1,3,2,5,4,7,6]=>[3,1,5,2,7,4,8,6]=>0
[8,1,4,2,5,3,7,6]=>[4,1,5,3,7,2,8,6]=>1
[6,1,4,2,5,3,8,7]=>[4,1,5,3,6,2,8,7]=>1
[2,1,6,3,5,4,8,7]=>[2,1,5,3,6,4,8,7]=>0
[6,2,7,1,4,3,8,5]=>[2,8,6,3,1,5,7,4]=>4
[2,1,8,3,5,4,7,6]=>[2,1,5,3,7,4,8,6]=>0
[8,2,6,1,4,3,7,5]=>[2,6,7,3,1,5,8,4]=>2
[2,1,8,3,6,4,7,5]=>[2,1,6,3,7,5,8,4]=>1
[8,1,4,2,6,3,7,5]=>[4,1,6,3,7,5,8,2]=>2
[8,1,3,2,6,4,7,5]=>[3,1,6,2,7,5,8,4]=>1
[2,1,4,3,8,5,7,6]=>[2,1,4,3,7,5,8,6]=>0
[4,1,3,2,8,5,7,6]=>[3,1,4,2,7,5,8,6]=>0
[7,4,5,3,1,8,2,6]=>[4,8,5,1,3,7,6,2]=>4
[6,7,8,3,1,4,5,2]=>[8,7,6,1,4,3,2,5]=>6
[6,7,2,8,4,1,3,5]=>[8,7,1,6,2,5,4,3]=>6
[5,7,3,8,2,6,1,4]=>[6,3,7,5,2,8,4,1]=>5
[6,4,7,1,8,2,5,3]=>[7,8,4,3,6,5,1,2]=>8
[8,5,6,2,1,4,3,7]=>[5,8,6,2,4,1,3,7]=>4
[6,4,1,8,2,3,5,7]=>[6,8,2,4,3,5,1,7]=>5
[5,7,6,1,2,3,4,8]=>[7,5,6,3,4,2,1,8]=>7
[7,1,8,6,2,4,5,3]=>[7,1,6,8,4,3,2,5]=>4
[4,2,6,3,7,5,8,1]=>[2,8,4,1,6,3,7,5]=>3
[2,7,6,8,1,4,3,5]=>[7,2,8,6,4,3,5,1]=>7
[2,1,6,5,7,8,3,4]=>[2,1,7,8,5,6,4,3]=>5
[2,1,7,8,5,6,4,3]=>[2,1,6,5,7,8,3,4]=>1
[2,1,8,3,4,6,7,5]=>[2,1,6,3,4,7,8,5]=>0
[2,4,3,1,8,5,7,6]=>[3,2,4,1,7,5,8,6]=>1
[4,1,3,2,6,8,7,5]=>[3,1,4,2,7,6,8,5]=>1
[6,3,7,4,5,8,2,1]=>[4,5,3,7,8,6,1,2]=>4
[1,6,8,7,2,3,4,5]=>[1,8,6,7,4,5,3,2]=>7
[5,1,8,2,7,3,4,6]=>[8,1,5,3,7,4,6,2]=>5
[2,8,4,1,6,3,7,5]=>[4,2,6,3,7,5,8,1]=>3
[2,1,5,3,8,7,6,4]=>[2,1,7,3,5,8,4,6]=>1
[2,8,4,1,6,5,7,3]=>[4,2,6,3,7,1,8,5]=>2
[2,8,5,3,4,7,6,1]=>[5,2,7,1,3,8,4,6]=>1
[4,1,2,3,7,6,8,5]=>[4,1,2,3,6,8,7,5]=>1
[6,4,1,2,5,7,3,8]=>[4,5,2,3,7,6,1,8]=>3
[8,6,4,2,3,7,1,5]=>[4,6,8,2,1,7,5,3]=>3
[5,7,4,2,3,8,1,6]=>[5,4,8,2,1,7,6,3]=>4
[3,8,6,1,2,7,4,5]=>[8,3,6,2,4,7,5,1]=>6
[7,4,6,3,8,1,2,5]=>[4,8,7,1,6,5,3,2]=>6
[5,3,8,7,1,2,4,6]=>[5,8,3,7,4,2,6,1]=>7
[8,3,7,6,1,2,4,5]=>[3,7,6,8,4,5,2,1]=>6
[8,7,1,4,5,3,2,6]=>[4,5,2,7,8,1,6,3]=>2
[2,7,6,3,4,5,8,1]=>[6,2,8,1,3,4,7,5]=>2
[4,8,1,5,7,2,3,6]=>[8,4,2,5,7,3,6,1]=>6
[7,4,1,3,2,6,8,5]=>[4,6,2,1,3,8,7,5]=>2
[1,8,2,4,3,5,6,7]=>[1,4,2,8,3,5,6,7]=>0
[1,7,2,4,3,5,6,8]=>[1,4,2,7,3,5,6,8]=>0
[1,6,2,4,3,5,7,8]=>[1,4,2,6,3,5,7,8]=>0
[1,5,2,4,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>0
[1,4,2,8,3,6,5,7]=>[1,6,2,4,3,8,5,7]=>1
[1,3,2,8,4,6,5,7]=>[1,3,2,6,4,8,5,7]=>0
[1,2,3,8,4,6,5,7]=>[1,2,3,6,4,8,5,7]=>0
[1,2,3,7,4,6,5,8]=>[1,2,3,6,4,7,5,8]=>0
[1,3,2,7,4,6,5,8]=>[1,3,2,6,4,7,5,8]=>0
[1,4,2,7,3,6,5,8]=>[1,6,2,4,3,7,5,8]=>1
[1,5,2,4,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>0
[1,6,2,4,3,7,5,8]=>[1,4,2,7,3,6,5,8]=>1
[1,7,2,4,3,6,5,8]=>[1,4,2,6,3,7,5,8]=>0
[1,8,2,4,3,6,5,7]=>[1,4,2,6,3,8,5,7]=>0
[1,8,2,3,4,6,5,7]=>[1,6,2,3,4,8,5,7]=>0
[1,7,2,3,4,6,5,8]=>[1,6,2,3,4,7,5,8]=>0
[1,6,2,4,3,8,5,7]=>[1,4,2,8,3,6,5,7]=>1
[1,5,2,4,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>0
[4,6,3,8,5,1,7,2]=>[5,3,6,4,7,2,8,1]=>4
[6,7,8,1,3,2,4,5]=>[8,7,6,3,2,5,4,1]=>9
[1,5,2,7,4,6,3,8]=>[1,6,2,5,3,7,4,8]=>1
[2,5,8,6,7,1,3,4]=>[8,2,5,7,6,4,3,1]=>8
[1,8,5,6,7,2,3,4]=>[1,5,8,7,6,4,3,2]=>6
[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>0
[12,11,10,9,8,7,6,5,4,3,2,1]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>0
[8,7,6,2,1,4,3,5]=>[6,7,8,2,4,3,5,1]=>5
[1,8,7,3,4,5,6,2]=>[1,7,8,2,3,4,5,6]=>0
[8,7,4,1,6,2,5,3]=>[4,6,7,3,8,5,1,2]=>4
[8,7,6,5,2,1,4,3]=>[5,6,7,8,3,4,1,2]=>4
[8,3,1,5,4,7,2,6]=>[3,5,2,7,1,8,6,4]=>2
[8,7,4,2,6,5,1,3]=>[4,6,7,2,8,1,5,3]=>2
[8,4,7,3,6,2,5,1]=>[4,7,6,1,8,3,2,5]=>2
[1,3,8,4,7,2,5,6]=>[1,4,3,7,8,5,6,2]=>3
[1,6,7,5,8,2,4,3]=>[1,7,6,8,5,4,2,3]=>6
[4,5,7,8,3,1,6,2]=>[8,7,5,4,1,3,2,6]=>7
[2,8,3,1,7,5,4,6]=>[3,2,7,1,8,4,6,5]=>2
[6,8,2,7,1,5,3,4]=>[8,6,1,7,4,2,5,3]=>5
[1,5,2,6,4,8,3,7]=>[1,8,2,5,3,6,4,7]=>2
[1,4,2,8,3,7,6,5]=>[1,7,2,4,3,8,5,6]=>1
[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>0
[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>0
[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>0
[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>0
[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>0
[7,1,2,3,4,5,6,9,8]=>[7,1,2,3,4,5,6,9,8]=>0
[2,1,9,3,4,5,6,7,8]=>[2,1,9,3,4,5,6,7,8]=>0
[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]=>1
[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>0
[8,1,2,3,4,5,7,6]=>[7,1,2,3,4,5,8,6]=>0
[6,7,2,1,8,5,4,3]=>[8,7,1,3,6,2,4,5]=>4
[1,8,2,3,4,5,7,6]=>[1,7,2,3,4,5,8,6]=>0
[1,5,7,4,8,6,3,2]=>[1,6,4,7,5,8,2,3]=>3
[5,7,2,1,8,6,3,4]=>[7,6,1,3,5,8,4,2]=>5
[5,8,1,4,7,2,3,6]=>[5,4,2,8,7,3,6,1]=>5
[3,6,4,2,8,7,5,1]=>[8,3,4,1,6,7,2,5]=>4
[4,8,1,3,7,2,6,5]=>[7,4,2,1,8,5,3,6]=>3
[4,7,2,8,6,3,5,1]=>[7,6,1,4,8,3,2,5]=>4
[7,2,8,6,4,3,5,1]=>[2,7,6,8,1,4,3,5]=>2
[1,2,8,7,6,3,4,5]=>[1,2,6,7,8,5,4,3]=>3
[7,8,2,6,3,5,1,4]=>[7,6,1,8,3,2,5,4]=>3
[3,8,6,7,2,5,1,4]=>[8,3,6,7,2,1,5,4]=>5
[7,8,1,5,2,6,3,4]=>[6,5,2,7,4,8,3,1]=>5
[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>0
[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>0
[5,6,4,8,2,7,1,3]=>[6,5,8,4,2,7,3,1]=>7
[4,7,5,2,1,8,3,6]=>[8,4,5,2,3,7,6,1]=>6
[4,8,5,2,1,7,6,3]=>[7,4,5,2,3,8,1,6]=>4
[4,6,5,2,1,3,8,7]=>[6,4,5,2,3,1,8,7]=>4
[5,6,4,2,3,1,8,7]=>[5,4,6,2,1,3,8,7]=>2
[6,4,5,3,1,2,8,7]=>[4,6,5,1,3,2,8,7]=>2
[5,4,6,1,3,2,8,7]=>[5,6,4,3,1,2,8,7]=>4
[4,6,8,1,7,3,2,5]=>[8,6,4,3,7,2,5,1]=>8
[4,7,8,1,6,3,5,2]=>[7,6,4,3,8,2,1,5]=>6
[7,4,8,1,6,5,3,2]=>[6,7,4,3,8,1,2,5]=>4
[5,4,8,1,3,7,6,2]=>[5,7,4,3,1,8,2,6]=>4
[8,4,5,3,1,7,6,2]=>[4,7,5,1,3,8,2,6]=>2
[5,4,7,1,3,8,2,6]=>[5,8,4,3,1,7,6,2]=>6
[6,4,8,1,7,5,2,3]=>[6,8,4,3,7,1,5,2]=>6
[5,6,8,7,2,1,3,4]=>[8,7,5,6,3,4,2,1]=>10
[8,5,7,6,4,2,1,3]=>[5,8,6,7,1,3,4,2]=>4
[6,3,2,8,7,4,1,5]=>[3,8,1,6,7,4,5,2]=>4
[2,1,6,8,7,4,3,5]=>[2,1,8,6,7,4,5,3]=>4
[2,1,7,8,6,4,5,3]=>[2,1,7,6,8,4,3,5]=>2
[7,3,2,8,6,4,5,1]=>[3,7,1,6,8,4,2,5]=>2
[7,6,8,5,2,4,3,1]=>[6,7,5,8,3,1,2,4]=>4
[5,7,8,6,2,3,1,4]=>[8,6,5,7,3,2,4,1]=>8
[5,8,7,6,3,2,1,4]=>[8,5,6,7,2,3,4,1]=>6
[6,8,7,5,3,2,4,1]=>[7,5,6,8,2,3,1,4]=>4
[5,8,4,2,3,7,6,1]=>[5,4,7,2,1,8,3,6]=>2
[4,8,6,2,7,3,1,5]=>[8,4,6,2,7,3,5,1]=>6
[3,6,1,8,7,4,2,5]=>[8,3,2,6,7,4,5,1]=>6
[3,7,1,8,6,4,5,2]=>[7,3,2,6,8,4,1,5]=>4
[3,8,1,6,7,5,2,4]=>[6,3,2,8,7,1,5,4]=>4
[3,7,1,6,8,2,5,4]=>[7,3,2,8,6,5,1,4]=>6
[4,7,6,2,8,1,3,5]=>[8,4,7,2,6,5,3,1]=>8
[6,7,4,2,8,1,5,3]=>[7,4,8,2,6,5,1,3]=>6
[6,8,4,2,7,5,1,3]=>[6,4,8,2,7,1,5,3]=>4
[2,1,8,6,7,5,3,4]=>[2,1,6,8,7,3,5,4]=>2
[8,3,2,6,7,5,1,4]=>[3,6,1,8,7,2,5,4]=>2
[5,8,6,7,3,1,2,4]=>[8,5,7,6,2,4,3,1]=>8
[6,7,5,8,1,3,4,2]=>[7,6,8,5,4,2,1,3]=>8
[7,6,5,8,1,4,3,2]=>[6,7,8,5,4,1,2,3]=>6
[8,6,5,7,4,1,3,2]=>[5,7,8,6,1,4,2,3]=>4
[7,6,4,3,8,1,5,2]=>[4,7,8,1,6,5,2,3]=>4
[7,3,2,6,8,1,5,4]=>[3,7,1,8,6,5,2,4]=>4
[2,1,7,6,8,3,5,4]=>[2,1,7,8,6,5,3,4]=>4
[7,5,6,8,1,4,2,3]=>[6,8,7,5,4,1,3,2]=>8
[6,5,7,8,1,2,4,3]=>[7,8,6,5,4,3,1,2]=>10
[1,6,2,5,4,7,3,8]=>[1,5,2,7,3,6,4,8]=>1
[8,7,6,5,4,3,2,1,9]=>[5,6,7,8,1,2,3,4,9]=>0
[1,4,2,7,3,8,6,5]=>[1,8,2,4,3,7,5,6]=>2
[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>0
[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>0
[4,5,6,7,8,1,3,2]=>[8,7,6,4,5,3,1,2]=>11
[3,2,5,1,8,4,6,7]=>[2,8,3,1,5,4,6,7]=>2
[3,2,4,1,8,5,6,7]=>[2,4,3,1,8,5,6,7]=>1
[8,3,7,5,6,1,4,2]=>[3,6,5,8,7,4,1,2]=>4
[1,7,2,8,4,6,5,3]=>[1,7,2,6,3,8,4,5]=>1
[1,2,7,8,5,4,6,3]=>[1,2,7,5,8,3,4,6]=>1
[1,5,2,8,4,3,6,7]=>[1,8,2,5,3,4,6,7]=>1
[6,3,7,1,4,8,2,5]=>[7,8,3,2,1,6,5,4]=>6
[9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,8]=>0
[10,2,1,3,4,5,6,7,8,9]=>[2,10,1,3,4,5,6,7,8,9]=>0
[6,8,3,5,1,7,2,4]=>[5,3,6,8,4,7,2,1]=>5
[7,8,9,10,11,12,1,2,3,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>30
[1,5,7,8,2,6,4,3]=>[1,7,6,5,4,8,2,3]=>5
[5,1,7,8,2,6,4,3]=>[7,1,6,5,4,8,2,3]=>5
[2,5,6,1,8,3,7,4]=>[7,2,6,3,5,4,8,1]=>6
[8,1,2,3,4,7,6,5]=>[7,1,2,3,4,8,5,6]=>0
[6,4,2,8,7,5,1,3]=>[6,8,1,4,7,2,5,3]=>4
[3,7,5,8,2,1,4,6]=>[8,3,7,5,2,4,6,1]=>7
[8,3,5,2,1,4,7,6]=>[3,7,5,1,4,2,8,6]=>2
[6,4,1,5,8,3,2,7]=>[4,8,2,6,5,1,3,7]=>4
[7,1,8,4,5,2,6,3]=>[5,1,4,7,8,3,2,6]=>2
[3,7,2,5,4,8,6,1]=>[5,3,1,8,2,7,4,6]=>2
[5,2,6,8,4,3,7,1]=>[2,7,6,5,1,3,8,4]=>3
[3,1,6,5,4,8,2,7]=>[5,1,3,8,2,6,4,7]=>2
[5,7,1,8,4,3,2,6]=>[8,7,2,5,1,3,6,4]=>5
[2,7,1,5,4,3,8,6]=>[5,2,1,8,3,4,7,6]=>2
[8,2,1,5,4,3,7,6]=>[2,5,1,7,3,4,8,6]=>0
[2,7,6,1,4,3,8,5]=>[6,2,8,3,1,5,7,4]=>4
[8,7,2,1,4,3,6,5]=>[7,8,1,3,2,5,4,6]=>2
[8,7,3,1,4,6,2,5]=>[3,6,7,2,1,8,5,4]=>2
[8,7,2,5,1,3,6,4]=>[5,7,1,8,4,3,2,6]=>3
[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>0
[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>0
[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]=>0
[10,1,2,3,4,5,6,7,8,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>0
[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,2,3,4,5,6,7,8,9,10]=>0
[3,5,8,6,2,7,1,4]=>[8,5,3,6,2,7,4,1]=>7
[8,2,3,6,5,7,1,4]=>[2,3,5,6,8,7,4,1]=>2
[6,8,5,1,3,4,2,7]=>[6,5,8,3,2,1,4,7]=>4
[1,3,7,4,8,2,5,6]=>[1,4,3,8,7,5,6,2]=>4
[6,1,7,8,5,3,4,2]=>[7,1,6,5,8,3,2,4]=>4
[7,1,8,5,6,2,4,3]=>[6,1,5,8,7,4,2,3]=>4
[2,1,7,3,5,8,4,6]=>[2,1,5,3,8,7,6,4]=>2
[3,4,6,2,7,8,5,1]=>[8,4,3,1,7,6,2,5]=>6
[5,8,7,6,4,2,3,1]=>[8,5,6,7,1,3,2,4]=>4
[5,2,1,6,7,8,4,3]=>[2,8,1,7,5,6,3,4]=>5
[1,5,6,7,8,2,4,3]=>[1,8,7,6,5,4,2,3]=>8
[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[7,8,1,4,5,3,6,2]=>[5,4,2,7,8,1,3,6]=>2
[4,8,3,6,1,5,7,2]=>[4,3,7,6,2,1,8,5]=>3
[7,8,2,1,5,3,6,4]=>[7,5,1,3,8,4,2,6]=>3
[6,1,4,2,8,3,5,7]=>[4,1,8,3,6,5,2,7]=>3
[3,4,1,2,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>2
[4,5,6,1,2,3,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>6
[4,3,2,1,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>0
[5,6,7,8,1,2,3,4,9]=>[8,7,6,5,4,3,2,1,9]=>12
[6,5,4,3,2,1,7,8,9]=>[4,5,6,1,2,3,7,8,9]=>0
[3,4,1,2,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>2
[4,5,6,1,2,3,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>6
[4,3,2,1,5,6,7,8,9,10]=>[3,4,1,2,5,6,7,8,9,10]=>0
[5,6,7,8,1,2,3,4,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>12
[6,5,4,3,2,1,7,8,9,10]=>[4,5,6,1,2,3,7,8,9,10]=>0
[8,7,6,5,4,3,2,1,9,10]=>[5,6,7,8,1,2,3,4,9,10]=>0
[3,7,5,8,2,4,1,6]=>[8,3,7,5,2,1,6,4]=>6
[2,6,8,3,7,5,1,4]=>[8,2,6,1,7,3,5,4]=>4
[4,3,1,6,8,7,2,5]=>[3,8,2,4,6,7,5,1]=>5
[8,3,7,1,2,6,4,5]=>[3,7,6,2,4,8,5,1]=>4
[6,4,7,3,8,5,2,1]=>[7,8,4,1,6,2,3,5]=>4
[6,8,4,3,7,5,2,1]=>[6,4,8,1,7,2,3,5]=>2
[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>1
[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>1
[5,8,7,1,4,2,6,3]=>[8,5,7,3,1,4,2,6]=>5
[4,6,3,1,5,2,8,7]=>[4,3,5,2,6,1,8,7]=>2
[1,7,2,4,3,8,6,5]=>[1,4,2,8,3,7,5,6]=>1
[2,8,6,1,5,3,7,4]=>[5,2,6,3,7,4,8,1]=>3
[1,6,2,7,5,8,3,4]=>[1,7,2,5,8,6,4,3]=>4
[1,8,2,4,3,7,6,5]=>[1,4,2,7,3,8,5,6]=>0
[6,3,7,2,4,8,5,1]=>[7,8,3,1,2,6,4,5]=>4
[7,4,3,2,8,5,6,1]=>[3,4,8,1,7,2,5,6]=>1
[2,6,4,8,5,3,7,1]=>[5,2,6,4,7,1,8,3]=>3
[1,5,8,6,3,4,7,2]=>[1,7,5,6,3,2,8,4]=>3
[4,8,3,6,5,7,1,2]=>[4,3,6,5,8,7,2,1]=>4
[5,6,4,7,1,8,2,3]=>[7,5,8,4,3,6,2,1]=>9
[5,6,1,8,4,7,2,3]=>[8,6,2,5,1,7,4,3]=>6
[2,8,3,6,1,5,4,7]=>[3,2,6,8,4,1,5,7]=>2
[4,5,2,8,1,6,3,7]=>[6,5,1,4,3,8,2,7]=>4
[7,6,1,8,3,5,2,4]=>[7,8,2,6,3,1,5,4]=>5
[2,4,8,5,7,1,3,6]=>[8,2,4,5,7,3,6,1]=>6
[1,2,8,3,4,5,7,6]=>[1,2,7,3,4,5,8,6]=>0
[6,8,3,1,5,2,7,4]=>[5,3,6,2,7,4,8,1]=>3
[4,6,8,5,7,1,2,3]=>[8,5,4,7,6,3,2,1]=>9
[4,6,7,5,8,1,2,3]=>[8,6,4,7,5,3,2,1]=>10
[4,6,5,7,8,1,2,3]=>[8,6,7,4,5,3,2,1]=>11
[4,6,7,8,5,1,2,3]=>[7,6,5,4,8,3,2,1]=>9
[1,2,3,7,4,8,6,5]=>[1,2,3,8,4,7,5,6]=>1
[1,2,3,8,4,7,6,5]=>[1,2,3,7,4,8,5,6]=>0
[4,8,6,7,1,2,3,5]=>[8,4,7,6,3,5,2,1]=>9
[8,7,3,6,4,5,2,1]=>[3,6,7,8,1,2,4,5]=>0
[8,2,7,5,4,3,6,1]=>[2,5,7,8,1,3,4,6]=>0
[3,6,8,1,5,7,2,4]=>[6,5,3,2,8,7,4,1]=>6
[5,6,4,8,1,2,7,3]=>[6,5,7,4,3,2,8,1]=>7
[5,1,8,4,2,3,6,7]=>[5,1,4,8,3,2,6,7]=>2
[5,8,7,1,3,4,2,6]=>[8,5,7,3,2,1,6,4]=>6
[4,1,7,8,5,3,2,6]=>[7,1,5,4,8,2,6,3]=>4
[8,6,2,7,4,1,5,3]=>[6,8,1,7,2,5,3,4]=>3
[7,3,2,8,1,6,5,4]=>[3,7,1,6,4,8,2,5]=>2
[8,6,7,5,1,4,3,2]=>[5,7,6,8,4,1,2,3]=>4
[4,8,3,2,5,1,7,6]=>[4,3,5,1,7,2,8,6]=>1
[6,3,7,5,1,8,2,4]=>[5,7,3,8,4,6,2,1]=>7
[2,1,6,7,3,8,5,4]=>[2,1,8,7,4,6,3,5]=>4
[7,5,3,2,8,4,6,1]=>[3,7,8,1,5,2,4,6]=>2
[4,5,6,8,1,3,2,7]=>[8,6,5,4,3,1,2,7]=>8
[5,1,6,7,8,2,4,3]=>[8,1,7,6,5,4,2,3]=>8
[2,4,6,5,8,1,3,7]=>[8,2,4,6,5,3,1,7]=>6
[3,4,8,7,2,1,6,5]=>[8,4,3,7,1,5,2,6]=>5
[3,8,1,4,5,6,7,2]=>[4,3,2,5,6,7,8,1]=>2
[3,5,6,8,4,1,2,7]=>[8,6,3,5,1,4,2,7]=>6
[3,7,2,1,4,8,6,5]=>[8,3,1,2,4,7,5,6]=>2
[3,8,2,1,4,5,6,7]=>[8,3,1,2,4,5,6,7]=>1
[4,1,6,3,8,5,2,7]=>[8,1,4,2,6,3,5,7]=>2
[4,5,2,6,8,1,3,7]=>[8,6,1,4,5,3,2,7]=>6
[4,8,2,3,1,5,6,7]=>[8,4,1,2,3,5,6,7]=>1
[5,1,6,7,8,4,2,3]=>[8,1,7,6,5,2,4,3]=>7
[6,1,2,7,8,5,4,3]=>[8,1,2,7,6,3,4,5]=>3
[5,9,8,7,6,4,3,2,1]=>[9,5,6,7,8,1,2,3,4]=>4
[2,9,8,7,6,5,4,3,1]=>[6,2,7,8,9,1,3,4,5]=>1
[6,10,9,8,7,5,4,3,2,1]=>[10,6,7,8,9,1,2,3,4,5]=>4
[2,8,6,1,5,7,3,4]=>[5,2,6,3,8,7,4,1]=>4
[1,5,6,8,2,7,3,4]=>[1,8,6,5,4,7,3,2]=>7
[2,8,4,1,5,3,7,6]=>[4,2,5,3,7,1,8,6]=>2
[1,5,6,8,7,2,3,4]=>[1,8,7,5,6,4,3,2]=>8
[1,6,7,8,5,2,3,4]=>[1,7,6,5,8,4,3,2]=>6
[1,4,7,6,8,2,3,5]=>[1,8,4,7,6,5,3,2]=>7
[6,8,4,3,7,2,1,5]=>[6,4,8,1,7,3,5,2]=>4
[5,6,3,7,1,8,2,4]=>[7,3,8,5,4,6,2,1]=>8
[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>10
[4,5,6,7,8,9,3,2,1]=>[9,8,7,4,5,6,1,2,3]=>12
[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,5,6,1,2,3,4]=>14
[1,8,2,7,3,4,6,5]=>[1,7,2,8,4,5,3,6]=>2
[5,3,6,1,2,4,8,7]=>[5,6,3,2,4,1,8,7]=>4
[2,1,7,5,8,3,4,6]=>[2,1,7,8,5,4,6,3]=>4
[4,8,2,5,7,1,6,3]=>[8,4,1,5,7,3,2,6]=>4
[5,8,2,4,7,6,3,1]=>[5,4,1,7,6,8,2,3]=>2
[6,2,7,5,8,3,1,4]=>[2,7,6,8,5,3,4,1]=>6
[8,2,7,3,4,5,6,1]=>[2,7,8,1,3,4,5,6]=>0
[7,8,10,9,1,2,3,6,5,4]=>[10,9,7,8,4,5,6,1,2,3]=>14
[1,3,2,7,4,8,6,5]=>[1,3,2,8,4,7,5,6]=>1
[6,8,3,2,5,4,7,1]=>[5,3,6,1,7,2,8,4]=>1
[8,1,6,2,5,3,7,4]=>[5,1,6,3,7,4,8,2]=>2
[7,8,1,3,2,4,5,6]=>[8,7,2,1,4,5,6,3]=>5
[1,6,2,8,4,3,5,7]=>[1,8,2,6,3,5,4,7]=>2
[1,8,6,3,4,5,2,7]=>[1,6,8,2,3,4,5,7]=>0
[1,8,2,7,4,3,6,5]=>[1,7,2,8,3,5,4,6]=>1
[4,5,6,8,2,3,1,7]=>[8,6,5,4,2,1,3,7]=>7
[4,6,7,8,1,3,5,2]=>[8,7,6,4,3,2,1,5]=>9
[4,8,3,6,5,1,7,2]=>[4,3,6,5,7,2,8,1]=>3
[2,7,3,6,1,4,5,8]=>[3,2,6,7,4,5,1,8]=>3
[6,7,3,8,4,1,5,2]=>[7,3,8,6,1,5,2,4]=>5
[2,6,4,8,1,3,7,5]=>[6,2,7,4,3,5,8,1]=>5
[7,2,5,6,8,1,3,4]=>[2,6,8,7,5,4,3,1]=>7
[6,7,4,8,5,1,2,3]=>[6,5,7,4,8,3,2,1]=>7
[6,1,4,8,5,3,7,2]=>[5,1,6,4,7,2,8,3]=>2
[8,6,3,7,4,1,2,5]=>[3,6,8,7,1,5,4,2]=>4
[5,6,7,8,9,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>16
[6,7,8,9,4,5,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>6
[7,8,9,10,4,5,6,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>6
[1,8,2,5,4,7,6,3]=>[1,5,2,7,3,8,4,6]=>0
[4,6,3,7,1,2,8,5]=>[6,3,8,4,2,5,7,1]=>6
[4,2,6,3,8,7,1,5]=>[2,8,4,1,6,7,5,3]=>4
[4,1,3,6,5,8,7,2]=>[3,1,5,4,7,6,8,2]=>2
[2,1,6,3,5,8,7,4]=>[2,1,5,3,7,6,8,4]=>1
[6,1,4,3,5,8,7,2]=>[4,1,5,2,7,6,8,3]=>1
[8,1,4,3,6,5,7,2]=>[4,1,6,2,7,3,8,5]=>0
[2,6,8,1,3,5,7,4]=>[7,2,6,3,4,1,8,5]=>4
[4,1,3,8,6,5,7,2]=>[3,1,6,4,7,2,8,5]=>1
[2,1,8,3,6,5,7,4]=>[2,1,6,3,7,4,8,5]=>0
[5,6,4,2,7,3,1,8]=>[6,4,7,2,5,1,3,8]=>4
[3,5,7,4,6,8,2,1]=>[5,4,3,8,7,6,1,2]=>6
[3,6,1,5,4,2,7,8]=>[5,3,2,6,1,4,7,8]=>2
[6,4,7,2,8,5,1,3]=>[7,8,4,2,6,1,5,3]=>6
[5,8,1,4,7,3,2,6]=>[5,4,2,8,7,1,6,3]=>4
[10,8,7,6,5,4,3,2,1,9]=>[5,6,7,8,10,1,2,3,4,9]=>0
[3,7,8,4,1,2,6,5]=>[7,4,3,8,2,5,1,6]=>5
[7,3,5,8,4,6,2,1]=>[3,7,6,5,1,8,2,4]=>3
[5,2,8,4,6,3,7,1]=>[2,5,4,7,6,1,8,3]=>2
[3,8,5,4,6,7,2,1]=>[5,3,4,8,6,7,1,2]=>4
[6,8,3,4,5,7,2,1]=>[4,3,5,6,8,7,1,2]=>2
[2,5,7,4,6,3,8,1]=>[5,2,4,8,6,1,7,3]=>4
[5,1,4,6,8,3,2,7]=>[6,1,8,4,5,2,3,7]=>4
[8,1,6,4,5,3,2,7]=>[4,1,5,6,8,2,3,7]=>0
[8,1,3,5,4,6,2,7]=>[3,1,5,6,2,8,4,7]=>0
[8,1,6,2,4,3,5,7]=>[6,1,8,3,2,5,4,7]=>2
[8,7,1,2,4,3,5,6]=>[7,8,2,3,1,5,6,4]=>4
[1,7,6,2,4,3,5,8]=>[1,6,7,3,2,5,4,8]=>2
[8,7,3,2,4,6,5,1]=>[3,6,7,1,2,8,4,5]=>0
[1,7,2,5,4,3,6,8]=>[1,5,2,7,3,4,6,8]=>0
[8,7,1,3,4,5,2,6]=>[7,8,2,1,3,4,6,5]=>2
[8,1,2,5,4,3,6,7]=>[5,1,2,8,3,4,6,7]=>0
[5,1,8,6,2,3,4,7]=>[8,1,5,6,4,3,2,7]=>5
[7,3,8,5,4,1,2,6]=>[5,7,3,8,1,4,6,2]=>4
[2,3,1,8,5,4,6,7]=>[3,2,1,5,8,4,6,7]=>1
[6,8,4,2,5,1,7,3]=>[5,4,6,2,7,3,8,1]=>3
[4,7,2,1,8,5,3,6]=>[8,4,1,3,7,2,6,5]=>4
[8,3,1,4,5,6,7,2]=>[3,4,2,5,6,7,8,1]=>1
[7,3,8,5,1,6,4,2]=>[5,6,3,7,4,8,1,2]=>4
[1,3,4,8,2,5,7,6]=>[1,7,3,4,2,5,8,6]=>2
[6,5,7,3,8,2,4,1]=>[7,8,6,1,5,3,2,4]=>6
[3,5,2,8,6,4,1,7]=>[8,3,1,5,6,2,4,7]=>3
[1,5,3,6,7,8,4,2]=>[1,3,8,7,5,6,2,4]=>5
[3,4,8,2,7,5,1,6]=>[7,4,3,1,8,2,6,5]=>4
[6,2,8,5,3,1,7,4]=>[2,6,5,7,3,4,8,1]=>3
[4,7,8,3,1,6,5,2]=>[7,6,4,1,3,8,2,5]=>4
[1,8,7,2,5,3,4,6]=>[1,5,7,3,8,4,6,2]=>3
[8,1,6,3,5,2,7,4]=>[5,1,6,2,7,4,8,3]=>1
[2,1,6,8,5,4,7,3]=>[2,1,6,5,7,3,8,4]=>1
[1,5,2,8,4,6,3,7]=>[1,6,2,5,3,8,4,7]=>1
[1,6,2,8,4,5,3,7]=>[1,8,2,6,3,4,5,7]=>1
[6,1,5,7,8,2,3,4]=>[7,1,8,6,5,4,3,2]=>8
[8,6,4,1,2,7,3,5]=>[4,6,8,3,2,7,5,1]=>5
[1,8,7,6,4,5,3,2]=>[1,6,7,8,2,3,4,5]=>0
[4,2,1,5,8,6,3,7]=>[2,6,1,4,5,8,3,7]=>2
[2,8,4,3,6,1,7,5]=>[4,2,6,1,7,5,8,3]=>2
[5,4,8,1,2,3,7,6]=>[5,7,4,3,2,1,8,6]=>5
[4,6,3,1,5,8,7,2]=>[4,3,5,2,7,6,8,1]=>3
[1,7,2,3,4,8,6,5]=>[1,8,2,3,4,7,5,6]=>1
[1,8,2,3,4,7,6,5]=>[1,7,2,3,4,8,5,6]=>0
[1,8,7,6,3,4,2,5]=>[1,6,7,8,3,4,5,2]=>3
[6,1,3,8,5,2,7,4]=>[3,1,6,5,7,4,8,2]=>2
[3,4,6,1,5,7,2,8]=>[5,4,3,2,7,6,1,8]=>5
[1,4,5,7,2,6,8,3]=>[1,6,5,4,3,8,7,2]=>5
[8,4,3,1,5,6,7,2]=>[3,4,5,2,6,7,8,1]=>1
[4,8,5,7,6,3,2,1]=>[8,4,6,5,7,1,2,3]=>5
[7,8,1,5,3,2,4,6]=>[7,5,2,8,3,4,6,1]=>5
[7,8,2,1,5,4,3,6]=>[7,5,1,3,8,2,6,4]=>3
[8,4,1,7,5,2,3,6]=>[4,7,2,5,8,3,6,1]=>4
[8,4,1,7,3,2,6,5]=>[4,8,2,7,1,5,3,6]=>3
[6,5,7,2,1,8,3,4]=>[7,8,5,2,4,6,3,1]=>8
[7,1,5,8,3,6,4,2]=>[6,1,7,5,3,8,2,4]=>3
[1,7,3,5,8,6,4,2]=>[1,3,6,7,5,8,2,4]=>2
[7,1,3,5,8,6,4,2]=>[3,1,6,7,5,8,2,4]=>2
[6,1,4,3,5,2,8,7]=>[4,1,5,2,6,3,8,7]=>0
[4,7,5,6,8,3,1,2]=>[8,4,7,6,5,1,3,2]=>8
[8,1,2,7,4,3,6,5]=>[7,1,2,8,3,5,4,6]=>1
[2,3,1,8,7,4,5,6]=>[3,2,1,7,8,5,6,4]=>3
[5,8,1,7,3,6,4,2]=>[7,5,2,6,3,8,1,4]=>4
[1,6,2,8,4,7,5,3]=>[1,8,2,6,3,7,4,5]=>2
[8,1,7,3,6,2,4,5]=>[6,1,7,2,8,5,4,3]=>3
[8,7,1,2,3,6,4,5]=>[6,7,2,3,4,8,5,1]=>4
[4,5,8,6,7,3,2,1]=>[8,7,4,5,6,1,2,3]=>7
[1,5,2,6,4,7,3,8]=>[1,7,2,5,3,6,4,8]=>2
[3,6,5,2,7,8,4,1]=>[8,3,7,1,5,6,2,4]=>6
[4,6,7,8,2,5,3,1]=>[8,7,6,4,2,1,3,5]=>7
[7,8,1,2,3,5,4,6]=>[8,7,2,3,4,1,6,5]=>5
[2,6,8,7,4,5,1,3]=>[8,2,6,7,1,3,5,4]=>4
[7,8,1,3,6,2,4,5]=>[7,6,2,1,8,5,4,3]=>5
[1,7,2,8,4,5,6,3]=>[1,8,2,7,3,4,5,6]=>1
[1,8,2,4,7,6,5,3]=>[1,4,2,6,7,8,3,5]=>0
[7,3,6,8,5,2,4,1]=>[3,7,6,5,8,2,1,4]=>4
[2,6,4,1,5,3,8,7]=>[4,2,5,3,6,1,8,7]=>2
[6,2,1,4,7,8,3,5]=>[2,4,1,8,7,6,5,3]=>4
[6,8,3,2,5,1,7,4]=>[5,3,6,1,7,4,8,2]=>2
[7,6,2,8,4,3,1,5]=>[7,8,1,6,2,4,5,3]=>4
[6,5,1,4,2,3,8,7]=>[4,5,2,6,3,1,8,7]=>2
[2,1,8,7,3,6,4,5]=>[2,1,6,7,4,8,5,3]=>2
[3,6,4,7,8,1,2,5]=>[8,3,7,4,6,5,2,1]=>9
[2,6,4,8,5,1,7,3]=>[5,2,6,4,7,3,8,1]=>4
[2,1,7,4,3,5,8,6]=>[2,1,4,8,3,5,7,6]=>1
[6,2,3,1,4,7,8,5]=>[2,3,8,1,4,6,7,5]=>2
[5,2,1,3,6,4,8,7]=>[2,6,1,3,5,4,8,7]=>1
[7,2,1,3,4,5,8,6]=>[2,8,1,3,4,5,7,6]=>1
[5,6,7,1,8,3,2,4]=>[8,7,6,3,5,2,4,1]=>10
[5,6,7,3,8,2,1,4]=>[8,7,6,1,5,3,4,2]=>8
[8,2,1,7,4,3,6,5]=>[2,7,1,8,3,5,4,6]=>1
[5,1,7,8,6,4,2,3]=>[8,1,6,5,7,2,4,3]=>5
[7,1,2,8,4,5,3,6]=>[8,1,2,7,3,4,6,5]=>2
[7,4,2,8,6,3,5,1]=>[6,7,1,4,8,3,2,5]=>3
[6,3,4,8,1,7,2,5]=>[3,8,6,4,2,7,5,1]=>6
[2,6,8,4,1,7,3,5]=>[6,2,4,8,3,7,5,1]=>5
[5,2,8,6,7,1,3,4]=>[2,8,5,7,6,4,3,1]=>7
[8,7,2,3,5,4,1,6]=>[5,7,1,2,8,3,6,4]=>1
[5,2,6,8,3,1,7,4]=>[2,7,6,5,3,4,8,1]=>5
[7,3,4,2,8,5,1,6]=>[3,8,4,1,7,2,6,5]=>3
[7,1,8,6,2,5,3,4]=>[7,1,6,8,4,2,5,3]=>4
[9,1,2,3,4,5,6,8,7]=>[8,1,2,3,4,5,6,9,7]=>0
[10,1,2,3,4,5,6,7,9,8]=>[9,1,2,3,4,5,6,7,10,8]=>0
[1,8,2,7,4,5,6,3]=>[1,7,2,8,3,4,5,6]=>0
[3,6,5,8,4,7,2,1]=>[8,3,6,5,1,7,2,4]=>5
[5,1,2,4,7,6,8,3]=>[4,1,2,6,5,8,7,3]=>2
[4,7,1,3,8,2,6,5]=>[8,4,2,1,7,5,3,6]=>4
[8,1,4,3,6,2,7,5]=>[4,1,6,2,7,5,8,3]=>1
[3,4,8,1,5,2,7,6]=>[5,4,3,2,7,1,8,6]=>4
[7,10,9,1,2,8,6,5,4,3]=>[10,7,8,3,4,9,1,2,5,6]=>7
[7,1,3,2,4,8,5,6]=>[3,1,8,2,4,7,6,5]=>2
[4,5,3,1,7,2,8,6]=>[4,3,8,2,5,1,7,6]=>4
[2,1,4,8,6,3,7,5]=>[2,1,6,4,7,5,8,3]=>2
[8,6,2,4,7,5,1,3]=>[4,6,1,8,7,2,5,3]=>2
[8,4,2,6,7,3,1,5]=>[4,8,1,6,7,3,5,2]=>4
[1,6,7,5,8,2,3,4]=>[1,7,6,8,5,4,3,2]=>7
[5,8,4,1,3,7,6,2]=>[5,4,7,3,1,8,2,6]=>3
[1,8,4,6,7,2,5,3]=>[1,4,8,6,7,5,2,3]=>4
[1,8,2,6,4,7,5,3]=>[1,6,2,8,3,7,4,5]=>1
[8,3,4,6,5,1,7,2]=>[3,6,4,5,7,2,8,1]=>3
[7,6,8,3,1,5,4,2]=>[7,8,6,1,4,2,3,5]=>4
[8,1,4,3,5,7,6,2]=>[4,1,5,2,7,8,3,6]=>0
[6,8,4,1,5,3,7,2]=>[5,4,6,3,7,1,8,2]=>3
[1,8,2,7,4,6,5,3]=>[1,6,2,7,3,8,4,5]=>0
[6,8,7,3,4,5,2,1]=>[8,6,7,1,2,3,4,5]=>2
[1,6,7,8,9,2,3,4,5]=>[1,9,8,7,6,5,4,3,2]=>12
[6,7,8,9,10,1,2,3,4,5,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>20
[5,6,7,8,9,1,2,3,4,10]=>[9,8,7,6,5,4,3,2,1,10]=>16
[1,6,7,8,9,10,2,3,4,5]=>[1,10,9,8,7,6,5,4,3,2]=>16
[1,7,8,9,10,11,2,3,4,5,6]=>[1,11,10,9,8,7,6,5,4,3,2]=>20
[4,1,2,8,5,3,6,7]=>[5,1,2,4,8,3,6,7]=>1
[9,2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,9,1]=>0
[8,2,3,4,5,6,7,1,9]=>[2,3,4,5,6,7,8,1,9]=>0
[7,2,3,4,5,6,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>0
[3,2,4,5,1,8,6,7]=>[2,5,3,4,1,8,6,7]=>2
[4,2,5,1,7,8,3,6]=>[2,8,4,3,5,7,6,1]=>5
[2,5,4,1,3,8,6,7]=>[4,2,5,3,1,8,6,7]=>2
[1,4,5,3,8,2,6,7]=>[1,8,4,2,5,3,6,7]=>2
[5,1,8,2,4,3,6,7]=>[8,1,5,3,2,4,6,7]=>2
[1,5,4,8,2,3,6,7]=>[1,5,8,4,3,2,6,7]=>3
[3,5,1,4,7,8,2,6]=>[4,3,2,8,5,7,6,1]=>5
[4,8,3,1,6,7,2,5]=>[4,3,6,2,8,7,5,1]=>4
[3,6,2,4,8,7,1,5]=>[4,3,1,8,6,7,5,2]=>4
[7,3,4,6,8,1,2,5]=>[3,8,4,7,6,5,2,1]=>7
[3,6,7,2,5,8,1,4]=>[7,5,3,1,8,6,4,2]=>6
[1,5,6,8,3,7,2,4]=>[1,8,6,5,3,7,4,2]=>6
[6,1,5,8,3,4,7,2]=>[6,1,7,5,3,2,8,4]=>3
[5,6,8,1,3,4,7,2]=>[7,6,5,3,2,1,8,4]=>6
[1,8,7,3,6,4,5,2]=>[1,6,7,2,8,4,3,5]=>1
[7,1,2,5,8,4,6,3]=>[7,1,2,8,5,3,4,6]=>2
[6,2,4,8,1,7,3,5]=>[2,6,8,4,3,7,5,1]=>5
[3,1,7,8,5,4,6,2]=>[7,1,3,5,8,2,4,6]=>2
[1,6,2,7,4,8,5,3]=>[1,8,2,7,3,6,4,5]=>3
[2,7,1,8,4,3,5,6]=>[8,2,1,7,3,5,6,4]=>4
[6,7,1,8,3,2,4,5]=>[8,7,2,6,3,5,4,1]=>8
[6,7,2,8,1,3,4,5]=>[8,7,1,6,4,5,3,2]=>8
[5,1,6,8,7,2,3,4]=>[8,1,7,5,6,4,3,2]=>8
[1,5,7,6,8,2,3,4]=>[1,8,6,7,5,4,3,2]=>8
[8,2,1,3,4,5,6,7,9]=>[2,8,1,3,4,5,6,7,9]=>0
[2,7,3,1,4,6,8,5]=>[3,2,6,1,4,8,7,5]=>2
[2,1,6,5,3,8,4,7]=>[2,1,5,8,4,6,3,7]=>2
[1,7,6,5,8,2,3,4]=>[1,6,7,8,5,4,3,2]=>6
[9,2,3,4,5,6,7,8,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>0
[8,7,1,4,3,5,6,2]=>[4,7,2,8,1,3,5,6]=>1
[4,5,6,8,1,2,7,3]=>[7,6,5,4,3,2,8,1]=>9
[3,5,8,6,1,2,7,4]=>[7,5,3,6,4,2,8,1]=>7
[1,7,2,6,4,8,5,3]=>[1,7,2,8,3,6,4,5]=>2
[1,5,2,7,4,8,6,3]=>[1,8,2,5,3,7,4,6]=>2
[5,3,8,7,4,6,2,1]=>[5,7,3,6,1,8,2,4]=>3
[6,8,4,1,5,2,7,3]=>[5,4,6,3,7,2,8,1]=>4
[10,2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,9,10,1]=>0
[5,7,6,8,1,2,4,3]=>[8,6,7,5,4,3,1,2]=>10
[4,8,2,5,7,3,1,6]=>[8,4,1,5,7,2,6,3]=>4
[6,4,2,3,7,8,5,1]=>[4,8,1,2,7,6,3,5]=>3
[5,3,6,8,2,7,1,4]=>[6,8,3,5,2,7,4,1]=>7
[3,8,6,5,1,7,2,4]=>[6,3,5,8,4,7,2,1]=>6
[1,6,2,5,4,8,3,7]=>[1,5,2,8,3,6,4,7]=>1
[8,4,2,7,5,1,6,3]=>[4,7,1,5,8,3,2,6]=>2
[8,4,7,6,5,1,2,3]=>[4,7,5,6,8,3,2,1]=>5
[2,4,3,8,5,1,6,7]=>[3,2,5,4,8,1,6,7]=>2
[1,4,7,8,5,2,3,6]=>[1,7,5,4,8,3,6,2]=>5
[8,1,4,6,5,2,7,3]=>[4,1,6,5,7,3,8,2]=>2
[1,3,6,4,7,8,2,5]=>[1,4,3,8,7,6,5,2]=>5
[8,4,6,5,1,2,7,3]=>[4,7,5,6,3,2,8,1]=>5
[8,6,5,7,2,1,4,3]=>[5,7,8,6,3,4,1,2]=>6
[4,5,3,2,8,6,1,7]=>[4,3,6,1,5,8,2,7]=>2
[8,2,6,5,4,3,1,7]=>[2,5,6,8,1,3,4,7]=>0
[8,2,7,6,4,5,3,1]=>[2,6,7,8,1,3,4,5]=>0
[8,7,3,5,4,2,6,1]=>[3,5,7,8,1,2,4,6]=>0
[12,10,9,8,7,6,5,4,3,2,1,11]=>[6,7,8,9,10,12,1,2,3,4,5,11]=>0
[9,2,3,4,5,6,7,1,8]=>[2,3,4,5,6,7,9,1,8]=>0
[1,8,2,3,7,5,6,4]=>[1,7,2,3,8,4,5,6]=>0
[1,5,2,7,4,3,6,8]=>[1,7,2,5,3,4,6,8]=>1
[2,8,6,4,7,3,1,5]=>[4,2,6,8,7,3,5,1]=>4
[1,5,2,6,4,3,7,8]=>[1,6,2,5,3,4,7,8]=>1
[1,6,2,8,5,4,3,7]=>[1,6,2,5,8,3,4,7]=>1
[2,9,3,4,5,6,7,8,1]=>[3,2,4,5,6,7,8,9,1]=>1
[2,10,3,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,9,10,1]=>1
[8,4,6,7,5,3,2,1]=>[4,7,6,5,8,1,2,3]=>3
[1,6,2,7,4,5,3,8]=>[1,7,2,6,3,4,5,8]=>1
[1,8,2,6,4,3,5,7]=>[1,6,2,8,3,5,4,7]=>1
[1,7,2,6,4,3,5,8]=>[1,6,2,7,3,5,4,8]=>1
[1,7,2,5,4,6,3,8]=>[1,5,2,6,3,7,4,8]=>0
[11,2,3,4,5,6,7,8,9,10,1]=>[2,3,4,5,6,7,8,9,10,11,1]=>0
[1,9,2,3,4,5,6,8,7]=>[1,8,2,3,4,5,6,9,7]=>0
[7,1,2,6,4,5,3,8]=>[6,1,2,7,3,4,5,8]=>0
[8,1,7,6,4,3,2,5]=>[6,1,7,8,2,4,5,3]=>2
[1,7,8,6,2,4,3,5]=>[1,7,6,8,4,3,5,2]=>5
[7,5,6,1,3,8,4,2]=>[5,8,7,3,2,6,1,4]=>6
[2,6,3,8,5,1,7,4]=>[3,2,6,5,7,4,8,1]=>3
[5,8,4,3,7,2,1,6]=>[5,4,8,1,7,2,6,3]=>3
[3,4,8,1,5,2,6,7]=>[5,4,3,2,8,1,6,7]=>4
[1,6,7,4,8,3,2,5]=>[1,7,4,8,6,3,5,2]=>5
[6,1,8,7,2,3,5,4]=>[8,1,6,7,4,5,2,3]=>6
[6,2,7,4,3,8,1,5]=>[2,7,4,8,1,6,5,3]=>4
[3,7,5,8,4,1,2,6]=>[8,3,7,5,1,4,6,2]=>6
[6,1,4,8,5,2,7,3]=>[5,1,6,4,7,3,8,2]=>3
[2,1,4,3,6,5,8,7,11,12,9,10]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>2
[2,1,4,3,6,5,9,10,7,8,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>2
[2,1,4,3,6,5,9,11,7,12,8,10]=>[2,1,4,3,6,5,12,9,8,11,10,7]=>4
[2,1,4,3,6,5,10,11,12,7,8,9]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>6
[2,1,4,3,7,8,5,6,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>2
[2,1,4,3,7,8,5,6,11,12,9,10]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>4
[2,1,4,3,7,9,5,10,6,8,12,11]=>[2,1,4,3,10,7,6,9,8,5,12,11]=>4
[2,1,4,3,7,9,5,11,6,12,8,10]=>[2,1,4,3,12,7,6,9,8,11,10,5]=>6
[2,1,4,3,7,10,5,11,12,6,8,9]=>[2,1,4,3,12,7,6,11,10,9,8,5]=>8
[2,1,4,3,8,9,10,5,6,7,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>6
[2,1,4,3,8,9,11,5,6,12,7,10]=>[2,1,4,3,12,9,8,7,6,11,10,5]=>8
[2,1,4,3,8,10,11,5,12,6,7,9]=>[2,1,4,3,12,11,8,7,10,9,6,5]=>10
[2,1,4,3,9,10,11,12,5,6,7,8]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>12
[2,1,5,6,3,4,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>2
[2,1,5,6,3,4,8,7,11,12,9,10]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>4
[2,1,5,6,3,4,9,10,7,8,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>4
[2,1,5,6,3,4,9,11,7,12,8,10]=>[2,1,6,5,4,3,12,9,8,11,10,7]=>6
[2,1,5,6,3,4,10,11,12,7,8,9]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>8
[2,1,5,7,3,8,4,6,10,9,12,11]=>[2,1,8,5,4,7,6,3,10,9,12,11]=>4
[2,1,5,7,3,8,4,6,11,12,9,10]=>[2,1,8,5,4,7,6,3,12,11,10,9]=>6
[2,1,5,7,3,9,4,10,6,8,12,11]=>[2,1,10,5,4,7,6,9,8,3,12,11]=>6
[2,1,5,7,3,9,4,11,6,12,8,10]=>[2,1,12,5,4,7,6,9,8,11,10,3]=>8
[2,1,5,7,3,10,4,11,12,6,8,9]=>[2,1,12,5,4,7,6,11,10,9,8,3]=>10
[2,1,5,8,3,9,10,4,6,7,12,11]=>[2,1,10,5,4,9,8,7,6,3,12,11]=>8
[2,1,5,8,3,9,11,4,6,12,7,10]=>[2,1,12,5,4,9,8,7,6,11,10,3]=>10
[2,1,5,8,3,10,11,4,12,6,7,9]=>[2,1,12,5,4,11,8,7,10,9,6,3]=>12
[2,1,5,9,3,10,11,12,4,6,7,8]=>[2,1,12,5,4,11,10,9,8,7,6,3]=>14
[2,1,6,7,8,3,4,5,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>6
[2,1,6,7,8,3,4,5,11,12,9,10]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>8
[2,1,6,7,9,3,4,10,5,8,12,11]=>[2,1,10,7,6,5,4,9,8,3,12,11]=>8
[2,1,6,7,9,3,4,11,5,12,8,10]=>[2,1,12,7,6,5,4,9,8,11,10,3]=>10
[2,1,6,7,10,3,4,11,12,5,8,9]=>[2,1,12,7,6,5,4,11,10,9,8,3]=>12
[2,1,6,8,9,3,10,4,5,7,12,11]=>[2,1,10,9,6,5,8,7,4,3,12,11]=>10
[2,1,6,8,9,3,11,4,5,12,7,10]=>[2,1,12,9,6,5,8,7,4,11,10,3]=>12
[2,1,6,8,10,3,11,4,12,5,7,9]=>[2,1,12,11,6,5,8,7,10,9,4,3]=>14
[2,1,6,9,10,3,11,12,4,5,7,8]=>[2,1,12,11,6,5,10,9,8,7,4,3]=>16
[2,1,7,8,9,10,3,4,5,6,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>12
[2,1,7,8,9,11,3,4,5,12,6,10]=>[2,1,12,9,8,7,6,5,4,11,10,3]=>14
[2,1,7,8,10,11,3,4,12,5,6,9]=>[2,1,12,11,8,7,6,5,10,9,4,3]=>16
[2,1,7,9,10,11,3,12,4,5,6,8]=>[2,1,12,11,10,7,6,9,8,5,4,3]=>18
[2,1,8,9,10,11,12,3,4,5,6,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>20
[3,4,1,2,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>2
[3,4,1,2,6,5,8,7,11,12,9,10]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>4
[3,4,1,2,6,5,9,10,7,8,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>4
[3,4,1,2,6,5,9,11,7,12,8,10]=>[4,3,2,1,6,5,12,9,8,11,10,7]=>6
[3,4,1,2,6,5,10,11,12,7,8,9]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>8
[3,4,1,2,7,8,5,6,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>4
[3,4,1,2,7,8,5,6,11,12,9,10]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>6
[3,4,1,2,7,9,5,10,6,8,12,11]=>[4,3,2,1,10,7,6,9,8,5,12,11]=>6
[3,4,1,2,7,9,5,11,6,12,8,10]=>[4,3,2,1,12,7,6,9,8,11,10,5]=>8
[3,4,1,2,7,10,5,11,12,6,8,9]=>[4,3,2,1,12,7,6,11,10,9,8,5]=>10
[3,4,1,2,8,9,10,5,6,7,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>8
[3,4,1,2,8,9,11,5,6,12,7,10]=>[4,3,2,1,12,9,8,7,6,11,10,5]=>10
[3,4,1,2,8,10,11,5,12,6,7,9]=>[4,3,2,1,12,11,8,7,10,9,6,5]=>12
[3,4,1,2,9,10,11,12,5,6,7,8]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>14
[3,5,1,6,2,4,8,7,10,9,12,11]=>[6,3,2,5,4,1,8,7,10,9,12,11]=>4
[3,5,1,6,2,4,8,7,11,12,9,10]=>[6,3,2,5,4,1,8,7,12,11,10,9]=>6
[3,5,1,6,2,4,9,10,7,8,12,11]=>[6,3,2,5,4,1,10,9,8,7,12,11]=>6
[3,5,1,6,2,4,9,11,7,12,8,10]=>[6,3,2,5,4,1,12,9,8,11,10,7]=>8
[3,5,1,6,2,4,10,11,12,7,8,9]=>[6,3,2,5,4,1,12,11,10,9,8,7]=>10
[3,5,1,7,2,8,4,6,10,9,12,11]=>[8,3,2,5,4,7,6,1,10,9,12,11]=>6
[3,5,1,7,2,8,4,6,11,12,9,10]=>[8,3,2,5,4,7,6,1,12,11,10,9]=>8
[3,5,1,7,2,9,4,10,6,8,12,11]=>[10,3,2,5,4,7,6,9,8,1,12,11]=>8
[3,5,1,7,2,9,4,11,6,12,8,10]=>[12,3,2,5,4,7,6,9,8,11,10,1]=>10
[3,5,1,7,2,10,4,11,12,6,8,9]=>[12,3,2,5,4,7,6,11,10,9,8,1]=>12
[3,5,1,8,2,9,10,4,6,7,12,11]=>[10,3,2,5,4,9,8,7,6,1,12,11]=>10
[3,5,1,8,2,9,11,4,6,12,7,10]=>[12,3,2,5,4,9,8,7,6,11,10,1]=>12
[3,5,1,8,2,10,11,4,12,6,7,9]=>[12,3,2,5,4,11,8,7,10,9,6,1]=>14
[3,5,1,9,2,10,11,12,4,6,7,8]=>[12,3,2,5,4,11,10,9,8,7,6,1]=>16
[3,6,1,7,8,2,4,5,10,9,12,11]=>[8,3,2,7,6,5,4,1,10,9,12,11]=>8
[3,6,1,7,8,2,4,5,11,12,9,10]=>[8,3,2,7,6,5,4,1,12,11,10,9]=>10
[3,6,1,7,9,2,4,10,5,8,12,11]=>[10,3,2,7,6,5,4,9,8,1,12,11]=>10
[3,6,1,7,9,2,4,11,5,12,8,10]=>[12,3,2,7,6,5,4,9,8,11,10,1]=>12
[3,6,1,7,10,2,4,11,12,5,8,9]=>[12,3,2,7,6,5,4,11,10,9,8,1]=>14
[3,6,1,8,9,2,10,4,5,7,12,11]=>[10,3,2,9,6,5,8,7,4,1,12,11]=>12
[3,6,1,8,9,2,11,4,5,12,7,10]=>[12,3,2,9,6,5,8,7,4,11,10,1]=>14
[3,6,1,8,10,2,11,4,12,5,7,9]=>[12,3,2,11,6,5,8,7,10,9,4,1]=>16
[3,6,1,9,10,2,11,12,4,5,7,8]=>[12,3,2,11,6,5,10,9,8,7,4,1]=>18
[3,7,1,8,9,10,2,4,5,6,12,11]=>[10,3,2,9,8,7,6,5,4,1,12,11]=>14
[3,7,1,8,9,11,2,4,5,12,6,10]=>[12,3,2,9,8,7,6,5,4,11,10,1]=>16
[3,7,1,8,10,11,2,4,12,5,6,9]=>[12,3,2,11,8,7,6,5,10,9,4,1]=>18
[3,7,1,9,10,11,2,12,4,5,6,8]=>[12,3,2,11,10,7,6,9,8,5,4,1]=>20
[3,8,1,9,10,11,12,2,4,5,6,7]=>[12,3,2,11,10,9,8,7,6,5,4,1]=>22
[4,5,6,1,2,3,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>6
[4,5,6,1,2,3,8,7,11,12,9,10]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>8
[4,5,6,1,2,3,9,10,7,8,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>8
[4,5,6,1,2,3,9,11,7,12,8,10]=>[6,5,4,3,2,1,12,9,8,11,10,7]=>10
[4,5,6,1,2,3,10,11,12,7,8,9]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>12
[4,5,7,1,2,8,3,6,10,9,12,11]=>[8,5,4,3,2,7,6,1,10,9,12,11]=>8
[4,5,7,1,2,8,3,6,11,12,9,10]=>[8,5,4,3,2,7,6,1,12,11,10,9]=>10
[4,5,7,1,2,9,3,10,6,8,12,11]=>[10,5,4,3,2,7,6,9,8,1,12,11]=>10
[4,5,7,1,2,9,3,11,6,12,8,10]=>[12,5,4,3,2,7,6,9,8,11,10,1]=>12
[4,5,7,1,2,10,3,11,12,6,8,9]=>[12,5,4,3,2,7,6,11,10,9,8,1]=>14
[4,5,8,1,2,9,10,3,6,7,12,11]=>[10,5,4,3,2,9,8,7,6,1,12,11]=>12
[4,5,8,1,2,9,11,3,6,12,7,10]=>[12,5,4,3,2,9,8,7,6,11,10,1]=>14
[4,5,8,1,2,10,11,3,12,6,7,9]=>[12,5,4,3,2,11,8,7,10,9,6,1]=>16
[4,5,9,1,2,10,11,12,3,6,7,8]=>[12,5,4,3,2,11,10,9,8,7,6,1]=>18
[4,6,7,1,8,2,3,5,10,9,12,11]=>[8,7,4,3,6,5,2,1,10,9,12,11]=>10
[4,6,7,1,8,2,3,5,11,12,9,10]=>[8,7,4,3,6,5,2,1,12,11,10,9]=>12
[4,6,7,1,9,2,3,10,5,8,12,11]=>[10,7,4,3,6,5,2,9,8,1,12,11]=>12
[4,6,7,1,9,2,3,11,5,12,8,10]=>[12,7,4,3,6,5,2,9,8,11,10,1]=>14
[4,6,7,1,10,2,3,11,12,5,8,9]=>[12,7,4,3,6,5,2,11,10,9,8,1]=>16
[4,6,8,1,9,2,10,3,5,7,12,11]=>[10,9,4,3,6,5,8,7,2,1,12,11]=>14
[4,6,8,1,9,2,11,3,5,12,7,10]=>[12,9,4,3,6,5,8,7,2,11,10,1]=>16
[4,6,8,1,10,2,11,3,12,5,7,9]=>[12,11,4,3,6,5,8,7,10,9,2,1]=>18
[4,6,9,1,10,2,11,12,3,5,7,8]=>[12,11,4,3,6,5,10,9,8,7,2,1]=>20
[4,7,8,1,9,10,2,3,5,6,12,11]=>[10,9,4,3,8,7,6,5,2,1,12,11]=>16
[4,7,8,1,9,11,2,3,5,12,6,10]=>[12,9,4,3,8,7,6,5,2,11,10,1]=>18
[4,7,8,1,10,11,2,3,12,5,6,9]=>[12,11,4,3,8,7,6,5,10,9,2,1]=>20
[4,7,9,1,10,11,2,12,3,5,6,8]=>[12,11,4,3,10,7,6,9,8,5,2,1]=>22
[4,8,9,1,10,11,12,2,3,5,6,7]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>24
[5,6,7,8,1,2,3,4,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>12
[5,6,7,8,1,2,3,4,11,12,9,10]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>14
[5,6,7,9,1,2,3,10,4,8,12,11]=>[10,7,6,5,4,3,2,9,8,1,12,11]=>14
[5,6,7,9,1,2,3,11,4,12,8,10]=>[12,7,6,5,4,3,2,9,8,11,10,1]=>16
[5,6,7,10,1,2,3,11,12,4,8,9]=>[12,7,6,5,4,3,2,11,10,9,8,1]=>18
[5,6,8,9,1,2,10,3,4,7,12,11]=>[10,9,6,5,4,3,8,7,2,1,12,11]=>16
[5,6,8,9,1,2,11,3,4,12,7,10]=>[12,9,6,5,4,3,8,7,2,11,10,1]=>18
[5,6,8,10,1,2,11,3,12,4,7,9]=>[12,11,6,5,4,3,8,7,10,9,2,1]=>20
[5,6,9,10,1,2,11,12,3,4,7,8]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>22
[5,7,8,9,1,10,2,3,4,6,12,11]=>[10,9,8,5,4,7,6,3,2,1,12,11]=>18
[5,7,8,9,1,11,2,3,4,12,6,10]=>[12,9,8,5,4,7,6,3,2,11,10,1]=>20
[5,7,8,10,1,11,2,3,12,4,6,9]=>[12,11,8,5,4,7,6,3,10,9,2,1]=>22
[5,7,9,10,1,11,2,12,3,4,6,8]=>[12,11,10,5,4,7,6,9,8,3,2,1]=>24
[5,8,9,10,1,11,12,2,3,4,6,7]=>[12,11,10,5,4,9,8,7,6,3,2,1]=>26
[6,7,8,9,10,1,2,3,4,5,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>20
[6,7,8,9,11,1,2,3,4,12,5,10]=>[12,9,8,7,6,5,4,3,2,11,10,1]=>22
[6,7,8,10,11,1,2,3,12,4,5,9]=>[12,11,8,7,6,5,4,3,10,9,2,1]=>24
[6,7,9,10,11,1,2,12,3,4,5,8]=>[12,11,10,7,6,5,4,9,8,3,2,1]=>26
[6,8,9,10,11,1,12,2,3,4,5,7]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>28
[8,4,1,3,7,5,2,6]=>[4,7,2,1,8,3,6,5]=>2
[7,1,5,3,2,6,8,4]=>[5,1,6,2,4,8,7,3]=>2
[5,6,2,7,8,3,4,1]=>[8,7,1,6,5,3,2,4]=>7
[5,4,7,8,2,3,6,1]=>[7,8,5,4,2,1,3,6]=>6
[6,1,5,7,8,3,4,2]=>[7,1,8,6,5,3,2,4]=>6
[6,1,4,2,5,8,7,3]=>[4,1,5,3,7,6,8,2]=>2
[6,7,5,1,3,2,4,8]=>[6,5,7,3,2,4,1,8]=>5
[5,4,6,8,2,3,1,7]=>[6,8,5,4,2,1,3,7]=>6
[6,8,2,7,3,1,5,4]=>[8,6,1,7,3,5,2,4]=>5
[6,1,3,4,7,2,8,5]=>[3,1,4,8,6,5,7,2]=>3
[8,1,7,2,5,3,4,6]=>[5,1,7,3,8,4,6,2]=>3
[3,4,7,2,1,6,8,5]=>[6,4,3,1,2,8,7,5]=>4
[7,6,1,4,2,3,5,8]=>[4,6,2,7,3,5,1,8]=>3
[2,8,3,7,4,5,6,1]=>[3,2,7,8,1,4,5,6]=>1
[8,7,5,2,4,3,6,1]=>[5,7,8,2,1,3,4,6]=>1
[8,1,6,7,4,2,3,5]=>[6,1,8,7,2,5,4,3]=>4
[9,8,2,3,4,5,6,7,1]=>[8,9,1,2,3,4,5,6,7]=>0
[8,9,2,3,4,5,6,7,1]=>[9,8,1,2,3,4,5,6,7]=>1
[9,8,7,6,4,5,3,2,1]=>[6,7,8,9,1,2,3,4,5]=>0
[5,6,7,9,8,4,3,2,1]=>[9,8,7,5,6,1,2,3,4]=>9
[5,6,7,8,9,1,4,3,2]=>[9,8,7,6,5,4,1,2,3]=>13
[10,9,2,3,4,5,6,7,8,1]=>[9,10,1,2,3,4,5,6,7,8]=>0
[5,4,7,8,3,2,6,1]=>[7,8,5,4,1,2,3,6]=>5
[3,4,6,5,8,2,1,7]=>[8,4,3,6,5,1,2,7]=>6
[2,8,3,1,4,6,7,5]=>[3,2,6,1,4,7,8,5]=>1
[3,6,8,4,1,5,2,7]=>[6,4,3,8,2,1,5,7]=>4
[8,3,7,2,1,6,5,4]=>[3,7,6,1,4,8,2,5]=>2
[5,8,3,1,4,7,6,2]=>[5,3,7,2,1,8,4,6]=>2
[2,1,6,8,5,3,7,4]=>[2,1,6,5,7,4,8,3]=>2
[3,7,8,4,2,5,6,1]=>[7,4,3,8,1,2,5,6]=>3
[5,7,6,8,2,1,3,4]=>[8,6,7,5,3,4,2,1]=>10
[7,6,3,2,8,1,5,4]=>[3,7,8,1,6,5,2,4]=>4
[8,1,3,2,6,5,7,4]=>[3,1,6,2,7,4,8,5]=>0
[8,1,4,3,5,2,7,6]=>[4,1,5,2,7,3,8,6]=>0
[5,1,3,6,2,4,8,7]=>[3,1,6,5,4,2,8,7]=>2
[2,3,9,4,5,6,7,8,1]=>[4,2,3,5,6,7,8,9,1]=>2
[8,6,1,5,2,3,4,7]=>[5,6,2,8,4,3,1,7]=>4
[8,1,3,5,6,7,2,4]=>[3,1,5,8,6,7,4,2]=>3
[2,7,4,6,5,1,8,3]=>[4,2,6,5,8,3,7,1]=>4
[4,1,5,7,6,8,3,2]=>[8,1,5,4,7,6,2,3]=>6
[1,5,6,7,8,9,2,3,4]=>[1,9,8,7,5,6,4,3,2]=>12
[4,5,3,1,2,8,6,7]=>[4,3,5,2,1,8,6,7]=>2
[8,3,6,7,5,1,2,4]=>[3,7,5,6,8,4,2,1]=>5
[4,6,8,2,3,5,1,7]=>[8,6,4,2,1,3,5,7]=>4
[6,8,2,1,3,5,4,7]=>[8,6,1,3,4,2,5,7]=>3
[6,4,8,7,5,3,2,1]=>[6,7,4,5,8,1,2,3]=>4
[4,2,5,7,8,6,3,1]=>[2,7,6,4,5,8,1,3]=>5
[8,3,5,1,2,4,7,6]=>[3,7,5,2,4,1,8,6]=>3
[8,4,7,2,6,3,1,5]=>[4,7,6,2,8,3,5,1]=>4
[3,6,5,1,4,8,2,7]=>[8,3,5,2,1,6,4,7]=>4
[8,1,4,2,6,5,7,3]=>[4,1,6,3,7,2,8,5]=>1
[5,8,2,1,7,4,3,6]=>[8,5,1,3,7,2,6,4]=>4
[6,8,3,1,5,4,7,2]=>[5,3,6,2,7,1,8,4]=>2
[2,6,7,8,3,1,4,5]=>[8,2,7,6,3,5,4,1]=>8
[5,6,7,1,8,4,2,3]=>[8,7,6,3,5,1,4,2]=>9
[5,7,2,1,4,6,8,3]=>[6,5,1,3,2,8,7,4]=>3
[2,8,6,1,5,4,7,3]=>[5,2,6,3,7,1,8,4]=>2
[2,8,4,6,5,1,7,3]=>[4,2,6,5,7,3,8,1]=>3
[4,7,5,8,1,2,3,6]=>[8,5,7,4,3,2,6,1]=>9
[1,6,7,4,3,8,2,5]=>[1,7,4,8,2,6,5,3]=>4
[4,5,6,7,8,1,2,3,9]=>[8,7,6,4,5,3,2,1,9]=>12
[6,1,8,2,4,3,5,7]=>[8,1,6,3,2,5,4,7]=>3
[1,4,8,5,2,3,7,6]=>[1,7,4,5,3,2,8,6]=>3
[6,8,4,3,5,1,7,2]=>[5,4,6,1,7,3,8,2]=>2
[3,6,7,4,1,2,5,8]=>[6,4,3,7,2,5,1,8]=>5
[8,2,5,4,1,3,7,6]=>[2,4,5,7,3,1,8,6]=>1
[2,4,5,8,6,3,1,7]=>[8,2,5,4,6,1,3,7]=>5
[4,6,7,5,1,8,3,2]=>[8,5,4,7,3,6,1,2]=>8
[4,6,7,5,2,8,3,1]=>[8,5,4,7,2,6,1,3]=>7
[2,5,7,8,6,1,4,3]=>[8,2,6,5,7,4,1,3]=>7
[5,1,7,6,8,2,3,4]=>[8,1,6,7,5,4,3,2]=>8
[5,6,8,7,1,3,2,4]=>[8,7,5,6,4,2,3,1]=>10
[6,1,5,7,8,4,2,3]=>[7,1,8,6,5,2,4,3]=>6
[5,2,6,7,8,3,1,4]=>[2,8,7,6,5,3,4,1]=>8
[3,4,5,1,2,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>4
[5,3,4,1,7,8,6,2]=>[3,8,4,2,5,7,1,6]=>4
[2,8,6,3,5,1,7,4]=>[5,2,6,1,7,4,8,3]=>2
[5,2,4,7,8,1,3,6]=>[2,7,8,4,5,3,6,1]=>6
[4,6,8,1,5,2,7,3]=>[6,5,4,3,7,2,8,1]=>6
[3,9,2,1,4,5,6,7,8]=>[9,3,1,2,4,5,6,7,8]=>1
[7,1,5,3,6,8,2,4]=>[5,1,8,2,7,6,4,3]=>4
[7,4,1,6,5,2,8,3]=>[4,6,2,5,8,3,7,1]=>4
[2,1,7,8,3,5,4,6]=>[2,1,8,7,4,3,6,5]=>3
[5,4,1,2,3,7,8,6]=>[4,5,2,3,1,8,7,6]=>3
[4,8,3,2,6,1,7,5]=>[4,3,6,1,7,5,8,2]=>2
[3,5,8,4,6,7,1,2]=>[5,4,3,8,6,7,2,1]=>6
[6,4,1,3,7,8,5,2]=>[4,8,2,1,7,6,3,5]=>4
[4,3,1,6,2,5,8,7]=>[3,6,2,4,1,5,8,7]=>2
[5,3,1,4,7,8,2,6]=>[3,4,2,8,5,7,6,1]=>4
[7,1,2,4,8,3,5,6]=>[4,1,2,8,7,5,6,3]=>3
[5,2,4,1,6,8,3,7]=>[2,4,8,3,5,6,1,7]=>3
[4,6,3,2,5,1,8,7]=>[4,3,5,1,6,2,8,7]=>1
[4,8,3,2,6,5,7,1]=>[4,3,6,1,7,2,8,5]=>1
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Description
The number of nestings in the permutation.
Map
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
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