Identifier
-
Mp00087:
Permutations
—inverse first fundamental transformation⟶
Permutations
St001737: Permutations ⟶ ℤ
Values
=>
[1]=>[1]=>0
[1,2]=>[1,2]=>0
[2,1]=>[2,1]=>1
[1,2,3]=>[1,2,3]=>0
[1,3,2]=>[1,3,2]=>1
[2,1,3]=>[2,1,3]=>1
[2,3,1]=>[3,1,2]=>1
[3,1,2]=>[3,2,1]=>1
[3,2,1]=>[2,3,1]=>1
[1,2,3,4]=>[1,2,3,4]=>0
[1,2,4,3]=>[1,2,4,3]=>1
[1,3,2,4]=>[1,3,2,4]=>1
[1,3,4,2]=>[1,4,2,3]=>1
[1,4,2,3]=>[1,4,3,2]=>1
[1,4,3,2]=>[1,3,4,2]=>1
[2,1,3,4]=>[2,1,3,4]=>1
[2,1,4,3]=>[2,1,4,3]=>2
[2,3,1,4]=>[3,1,2,4]=>1
[2,3,4,1]=>[4,1,2,3]=>1
[2,4,1,3]=>[4,3,1,2]=>1
[2,4,3,1]=>[3,4,1,2]=>1
[3,1,2,4]=>[3,2,1,4]=>1
[3,1,4,2]=>[4,2,1,3]=>1
[3,2,1,4]=>[2,3,1,4]=>1
[3,2,4,1]=>[2,4,1,3]=>1
[3,4,1,2]=>[3,1,4,2]=>2
[3,4,2,1]=>[4,1,3,2]=>1
[4,1,2,3]=>[4,3,2,1]=>1
[4,1,3,2]=>[3,4,2,1]=>1
[4,2,1,3]=>[2,4,3,1]=>1
[4,2,3,1]=>[2,3,4,1]=>1
[4,3,1,2]=>[4,2,3,1]=>1
[4,3,2,1]=>[3,2,4,1]=>2
[1,2,3,4,5]=>[1,2,3,4,5]=>0
[1,2,3,5,4]=>[1,2,3,5,4]=>1
[1,2,4,3,5]=>[1,2,4,3,5]=>1
[1,2,4,5,3]=>[1,2,5,3,4]=>1
[1,2,5,3,4]=>[1,2,5,4,3]=>1
[1,2,5,4,3]=>[1,2,4,5,3]=>1
[1,3,2,4,5]=>[1,3,2,4,5]=>1
[1,3,2,5,4]=>[1,3,2,5,4]=>2
[1,3,4,2,5]=>[1,4,2,3,5]=>1
[1,3,4,5,2]=>[1,5,2,3,4]=>1
[1,3,5,2,4]=>[1,5,4,2,3]=>1
[1,3,5,4,2]=>[1,4,5,2,3]=>1
[1,4,2,3,5]=>[1,4,3,2,5]=>1
[1,4,2,5,3]=>[1,5,3,2,4]=>1
[1,4,3,2,5]=>[1,3,4,2,5]=>1
[1,4,3,5,2]=>[1,3,5,2,4]=>1
[1,4,5,2,3]=>[1,4,2,5,3]=>2
[1,4,5,3,2]=>[1,5,2,4,3]=>1
[1,5,2,3,4]=>[1,5,4,3,2]=>1
[1,5,2,4,3]=>[1,4,5,3,2]=>1
[1,5,3,2,4]=>[1,3,5,4,2]=>1
[1,5,3,4,2]=>[1,3,4,5,2]=>1
[1,5,4,2,3]=>[1,5,3,4,2]=>1
[1,5,4,3,2]=>[1,4,3,5,2]=>2
[2,1,3,4,5]=>[2,1,3,4,5]=>1
[2,1,3,5,4]=>[2,1,3,5,4]=>2
[2,1,4,3,5]=>[2,1,4,3,5]=>2
[2,1,4,5,3]=>[2,1,5,3,4]=>2
[2,1,5,3,4]=>[2,1,5,4,3]=>2
[2,1,5,4,3]=>[2,1,4,5,3]=>2
[2,3,1,4,5]=>[3,1,2,4,5]=>1
[2,3,1,5,4]=>[3,1,2,5,4]=>2
[2,3,4,1,5]=>[4,1,2,3,5]=>1
[2,3,4,5,1]=>[5,1,2,3,4]=>1
[2,3,5,1,4]=>[5,4,1,2,3]=>1
[2,3,5,4,1]=>[4,5,1,2,3]=>1
[2,4,1,3,5]=>[4,3,1,2,5]=>1
[2,4,1,5,3]=>[5,3,1,2,4]=>1
[2,4,3,1,5]=>[3,4,1,2,5]=>1
[2,4,3,5,1]=>[3,5,1,2,4]=>1
[2,4,5,1,3]=>[4,1,2,5,3]=>2
[2,4,5,3,1]=>[5,1,2,4,3]=>1
[2,5,1,3,4]=>[5,4,3,1,2]=>1
[2,5,1,4,3]=>[4,5,3,1,2]=>1
[2,5,3,1,4]=>[3,5,4,1,2]=>1
[2,5,3,4,1]=>[3,4,5,1,2]=>1
[2,5,4,1,3]=>[5,3,4,1,2]=>1
[2,5,4,3,1]=>[4,3,5,1,2]=>2
[3,1,2,4,5]=>[3,2,1,4,5]=>1
[3,1,2,5,4]=>[3,2,1,5,4]=>2
[3,1,4,2,5]=>[4,2,1,3,5]=>1
[3,1,4,5,2]=>[5,2,1,3,4]=>1
[3,1,5,2,4]=>[5,4,2,1,3]=>1
[3,1,5,4,2]=>[4,5,2,1,3]=>1
[3,2,1,4,5]=>[2,3,1,4,5]=>1
[3,2,1,5,4]=>[2,3,1,5,4]=>2
[3,2,4,1,5]=>[2,4,1,3,5]=>1
[3,2,4,5,1]=>[2,5,1,3,4]=>1
[3,2,5,1,4]=>[2,5,4,1,3]=>1
[3,2,5,4,1]=>[2,4,5,1,3]=>1
[3,4,1,2,5]=>[3,1,4,2,5]=>2
[3,4,1,5,2]=>[3,1,5,2,4]=>2
[3,4,2,1,5]=>[4,1,3,2,5]=>1
[3,4,2,5,1]=>[5,1,3,2,4]=>1
[3,4,5,1,2]=>[5,2,4,1,3]=>1
[3,4,5,2,1]=>[4,2,5,1,3]=>2
[3,5,1,2,4]=>[3,1,5,4,2]=>2
[3,5,1,4,2]=>[3,1,4,5,2]=>2
[3,5,2,1,4]=>[5,4,1,3,2]=>1
[3,5,2,4,1]=>[4,5,1,3,2]=>1
[3,5,4,1,2]=>[4,1,3,5,2]=>2
[3,5,4,2,1]=>[5,1,3,4,2]=>1
[4,1,2,3,5]=>[4,3,2,1,5]=>1
[4,1,2,5,3]=>[5,3,2,1,4]=>1
[4,1,3,2,5]=>[3,4,2,1,5]=>1
[4,1,3,5,2]=>[3,5,2,1,4]=>1
[4,1,5,2,3]=>[4,2,1,5,3]=>2
[4,1,5,3,2]=>[5,2,1,4,3]=>1
[4,2,1,3,5]=>[2,4,3,1,5]=>1
[4,2,1,5,3]=>[2,5,3,1,4]=>1
[4,2,3,1,5]=>[2,3,4,1,5]=>1
[4,2,3,5,1]=>[2,3,5,1,4]=>1
[4,2,5,1,3]=>[2,4,1,5,3]=>2
[4,2,5,3,1]=>[2,5,1,4,3]=>1
[4,3,1,2,5]=>[4,2,3,1,5]=>1
[4,3,1,5,2]=>[5,2,3,1,4]=>1
[4,3,2,1,5]=>[3,2,4,1,5]=>2
[4,3,2,5,1]=>[3,2,5,1,4]=>2
[4,3,5,1,2]=>[4,1,5,2,3]=>2
[4,3,5,2,1]=>[5,1,4,2,3]=>1
[4,5,1,2,3]=>[5,3,1,4,2]=>1
[4,5,1,3,2]=>[4,3,1,5,2]=>2
[4,5,2,1,3]=>[4,1,5,3,2]=>2
[4,5,2,3,1]=>[5,1,4,3,2]=>1
[4,5,3,1,2]=>[3,4,1,5,2]=>2
[4,5,3,2,1]=>[3,5,1,4,2]=>1
[5,1,2,3,4]=>[5,4,3,2,1]=>1
[5,1,2,4,3]=>[4,5,3,2,1]=>1
[5,1,3,2,4]=>[3,5,4,2,1]=>1
[5,1,3,4,2]=>[3,4,5,2,1]=>1
[5,1,4,2,3]=>[5,3,4,2,1]=>1
[5,1,4,3,2]=>[4,3,5,2,1]=>2
[5,2,1,3,4]=>[2,5,4,3,1]=>1
[5,2,1,4,3]=>[2,4,5,3,1]=>1
[5,2,3,1,4]=>[2,3,5,4,1]=>1
[5,2,3,4,1]=>[2,3,4,5,1]=>1
[5,2,4,1,3]=>[2,5,3,4,1]=>1
[5,2,4,3,1]=>[2,4,3,5,1]=>2
[5,3,1,2,4]=>[5,4,2,3,1]=>1
[5,3,1,4,2]=>[4,5,2,3,1]=>1
[5,3,2,1,4]=>[3,2,5,4,1]=>2
[5,3,2,4,1]=>[3,2,4,5,1]=>2
[5,3,4,1,2]=>[5,2,3,4,1]=>1
[5,3,4,2,1]=>[4,2,3,5,1]=>2
[5,4,1,2,3]=>[4,2,5,3,1]=>2
[5,4,1,3,2]=>[5,2,4,3,1]=>1
[5,4,2,1,3]=>[5,3,2,4,1]=>1
[5,4,2,3,1]=>[4,3,2,5,1]=>2
[5,4,3,1,2]=>[3,5,2,4,1]=>1
[5,4,3,2,1]=>[3,4,2,5,1]=>2
[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]=>1
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>1
[1,2,3,6,4,5]=>[1,2,3,6,5,4]=>1
[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>1
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>1
[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>1
[1,2,4,6,3,5]=>[1,2,6,5,3,4]=>1
[1,2,4,6,5,3]=>[1,2,5,6,3,4]=>1
[1,2,5,3,4,6]=>[1,2,5,4,3,6]=>1
[1,2,5,3,6,4]=>[1,2,6,4,3,5]=>1
[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>1
[1,2,5,4,6,3]=>[1,2,4,6,3,5]=>1
[1,2,5,6,3,4]=>[1,2,5,3,6,4]=>2
[1,2,5,6,4,3]=>[1,2,6,3,5,4]=>1
[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>1
[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>1
[1,2,6,4,3,5]=>[1,2,4,6,5,3]=>1
[1,2,6,4,5,3]=>[1,2,4,5,6,3]=>1
[1,2,6,5,3,4]=>[1,2,6,4,5,3]=>1
[1,2,6,5,4,3]=>[1,2,5,4,6,3]=>2
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>2
[1,3,2,6,4,5]=>[1,3,2,6,5,4]=>2
[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>2
[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>1
[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>2
[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>1
[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>1
[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>1
[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>1
[1,3,5,2,4,6]=>[1,5,4,2,3,6]=>1
[1,3,5,2,6,4]=>[1,6,4,2,3,5]=>1
[1,3,5,4,2,6]=>[1,4,5,2,3,6]=>1
[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>1
[1,3,5,6,2,4]=>[1,5,2,3,6,4]=>2
[1,3,5,6,4,2]=>[1,6,2,3,5,4]=>1
[1,3,6,2,4,5]=>[1,6,5,4,2,3]=>1
[1,3,6,2,5,4]=>[1,5,6,4,2,3]=>1
[1,3,6,4,2,5]=>[1,4,6,5,2,3]=>1
[1,3,6,4,5,2]=>[1,4,5,6,2,3]=>1
[1,3,6,5,2,4]=>[1,6,4,5,2,3]=>1
[1,3,6,5,4,2]=>[1,5,4,6,2,3]=>2
[1,4,2,3,5,6]=>[1,4,3,2,5,6]=>1
[1,4,2,3,6,5]=>[1,4,3,2,6,5]=>2
[1,4,2,5,3,6]=>[1,5,3,2,4,6]=>1
[1,4,2,5,6,3]=>[1,6,3,2,4,5]=>1
[1,4,2,6,3,5]=>[1,6,5,3,2,4]=>1
[1,4,2,6,5,3]=>[1,5,6,3,2,4]=>1
[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>1
[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>2
[1,4,3,5,2,6]=>[1,3,5,2,4,6]=>1
[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>1
[1,4,3,6,2,5]=>[1,3,6,5,2,4]=>1
[1,4,3,6,5,2]=>[1,3,5,6,2,4]=>1
[1,4,5,2,3,6]=>[1,4,2,5,3,6]=>2
[1,4,5,2,6,3]=>[1,4,2,6,3,5]=>2
[1,4,5,3,2,6]=>[1,5,2,4,3,6]=>1
[1,4,5,3,6,2]=>[1,6,2,4,3,5]=>1
[1,4,5,6,2,3]=>[1,6,3,5,2,4]=>1
[1,4,5,6,3,2]=>[1,5,3,6,2,4]=>2
[1,4,6,2,3,5]=>[1,4,2,6,5,3]=>2
[1,4,6,2,5,3]=>[1,4,2,5,6,3]=>2
[1,4,6,3,2,5]=>[1,6,5,2,4,3]=>1
[1,4,6,3,5,2]=>[1,5,6,2,4,3]=>1
[1,4,6,5,2,3]=>[1,5,2,4,6,3]=>2
[1,4,6,5,3,2]=>[1,6,2,4,5,3]=>1
[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>1
[1,5,2,3,6,4]=>[1,6,4,3,2,5]=>1
[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>1
[1,5,2,4,6,3]=>[1,4,6,3,2,5]=>1
[1,5,2,6,3,4]=>[1,5,3,2,6,4]=>2
[1,5,2,6,4,3]=>[1,6,3,2,5,4]=>1
[1,5,3,2,4,6]=>[1,3,5,4,2,6]=>1
[1,5,3,2,6,4]=>[1,3,6,4,2,5]=>1
[1,5,3,4,2,6]=>[1,3,4,5,2,6]=>1
[1,5,3,4,6,2]=>[1,3,4,6,2,5]=>1
[1,5,3,6,2,4]=>[1,3,5,2,6,4]=>2
[1,5,3,6,4,2]=>[1,3,6,2,5,4]=>1
[1,5,4,2,3,6]=>[1,5,3,4,2,6]=>1
[1,5,4,2,6,3]=>[1,6,3,4,2,5]=>1
[1,5,4,3,2,6]=>[1,4,3,5,2,6]=>2
[1,5,4,3,6,2]=>[1,4,3,6,2,5]=>2
[1,5,4,6,2,3]=>[1,5,2,6,3,4]=>2
[1,5,4,6,3,2]=>[1,6,2,5,3,4]=>1
[1,5,6,2,3,4]=>[1,6,4,2,5,3]=>1
[1,5,6,2,4,3]=>[1,5,4,2,6,3]=>2
[1,5,6,3,2,4]=>[1,5,2,6,4,3]=>2
[1,5,6,3,4,2]=>[1,6,2,5,4,3]=>1
[1,5,6,4,2,3]=>[1,4,5,2,6,3]=>2
[1,5,6,4,3,2]=>[1,4,6,2,5,3]=>1
[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>1
[1,6,2,3,5,4]=>[1,5,6,4,3,2]=>1
[1,6,2,4,3,5]=>[1,4,6,5,3,2]=>1
[1,6,2,4,5,3]=>[1,4,5,6,3,2]=>1
[1,6,2,5,3,4]=>[1,6,4,5,3,2]=>1
[1,6,2,5,4,3]=>[1,5,4,6,3,2]=>2
[1,6,3,2,4,5]=>[1,3,6,5,4,2]=>1
[1,6,3,2,5,4]=>[1,3,5,6,4,2]=>1
[1,6,3,4,2,5]=>[1,3,4,6,5,2]=>1
[1,6,3,4,5,2]=>[1,3,4,5,6,2]=>1
[1,6,3,5,2,4]=>[1,3,6,4,5,2]=>1
[1,6,3,5,4,2]=>[1,3,5,4,6,2]=>2
[1,6,4,2,3,5]=>[1,6,5,3,4,2]=>1
[1,6,4,2,5,3]=>[1,5,6,3,4,2]=>1
[1,6,4,3,2,5]=>[1,4,3,6,5,2]=>2
[1,6,4,3,5,2]=>[1,4,3,5,6,2]=>2
[1,6,4,5,2,3]=>[1,6,3,4,5,2]=>1
[1,6,4,5,3,2]=>[1,5,3,4,6,2]=>2
[1,6,5,2,3,4]=>[1,5,3,6,4,2]=>2
[1,6,5,2,4,3]=>[1,6,3,5,4,2]=>1
[1,6,5,3,2,4]=>[1,6,4,3,5,2]=>1
[1,6,5,3,4,2]=>[1,5,4,3,6,2]=>2
[1,6,5,4,2,3]=>[1,4,6,3,5,2]=>1
[1,6,5,4,3,2]=>[1,4,5,3,6,2]=>2
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>2
[2,1,3,6,4,5]=>[2,1,3,6,5,4]=>2
[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>2
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>2
[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>2
[2,1,4,6,3,5]=>[2,1,6,5,3,4]=>2
[2,1,4,6,5,3]=>[2,1,5,6,3,4]=>2
[2,1,5,3,4,6]=>[2,1,5,4,3,6]=>2
[2,1,5,3,6,4]=>[2,1,6,4,3,5]=>2
[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>2
[2,1,5,4,6,3]=>[2,1,4,6,3,5]=>2
[2,1,5,6,3,4]=>[2,1,5,3,6,4]=>3
[2,1,5,6,4,3]=>[2,1,6,3,5,4]=>2
[2,1,6,3,4,5]=>[2,1,6,5,4,3]=>2
[2,1,6,3,5,4]=>[2,1,5,6,4,3]=>2
[2,1,6,4,3,5]=>[2,1,4,6,5,3]=>2
[2,1,6,4,5,3]=>[2,1,4,5,6,3]=>2
[2,1,6,5,3,4]=>[2,1,6,4,5,3]=>2
[2,1,6,5,4,3]=>[2,1,5,4,6,3]=>3
[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>1
[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>2
[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>2
[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>2
[2,3,1,6,4,5]=>[3,1,2,6,5,4]=>2
[2,3,1,6,5,4]=>[3,1,2,5,6,4]=>2
[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>1
[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>2
[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>1
[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>1
[2,3,4,6,1,5]=>[6,5,1,2,3,4]=>1
[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>1
[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>1
[2,3,5,1,6,4]=>[6,4,1,2,3,5]=>1
[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>1
[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>1
[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>2
[2,3,5,6,4,1]=>[6,1,2,3,5,4]=>1
[2,3,6,1,4,5]=>[6,5,4,1,2,3]=>1
[2,3,6,1,5,4]=>[5,6,4,1,2,3]=>1
[2,3,6,4,1,5]=>[4,6,5,1,2,3]=>1
[2,3,6,4,5,1]=>[4,5,6,1,2,3]=>1
[2,3,6,5,1,4]=>[6,4,5,1,2,3]=>1
[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>2
[2,4,1,3,5,6]=>[4,3,1,2,5,6]=>1
[2,4,1,3,6,5]=>[4,3,1,2,6,5]=>2
[2,4,1,5,3,6]=>[5,3,1,2,4,6]=>1
[2,4,1,5,6,3]=>[6,3,1,2,4,5]=>1
[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>1
[2,4,1,6,5,3]=>[5,6,3,1,2,4]=>1
[2,4,3,1,5,6]=>[3,4,1,2,5,6]=>1
[2,4,3,1,6,5]=>[3,4,1,2,6,5]=>2
[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>1
[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>1
[2,4,3,6,1,5]=>[3,6,5,1,2,4]=>1
[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>1
[2,4,5,1,3,6]=>[4,1,2,5,3,6]=>2
[2,4,5,1,6,3]=>[4,1,2,6,3,5]=>2
[2,4,5,3,1,6]=>[5,1,2,4,3,6]=>1
[2,4,5,3,6,1]=>[6,1,2,4,3,5]=>1
[2,4,5,6,1,3]=>[6,3,5,1,2,4]=>1
[2,4,5,6,3,1]=>[5,3,6,1,2,4]=>2
[2,4,6,1,3,5]=>[4,1,2,6,5,3]=>2
[2,4,6,1,5,3]=>[4,1,2,5,6,3]=>2
[2,4,6,3,1,5]=>[6,5,1,2,4,3]=>1
[2,4,6,3,5,1]=>[5,6,1,2,4,3]=>1
[2,4,6,5,1,3]=>[5,1,2,4,6,3]=>2
[2,4,6,5,3,1]=>[6,1,2,4,5,3]=>1
[2,5,1,3,4,6]=>[5,4,3,1,2,6]=>1
[2,5,1,3,6,4]=>[6,4,3,1,2,5]=>1
[2,5,1,4,3,6]=>[4,5,3,1,2,6]=>1
[2,5,1,4,6,3]=>[4,6,3,1,2,5]=>1
[2,5,1,6,3,4]=>[5,3,1,2,6,4]=>2
[2,5,1,6,4,3]=>[6,3,1,2,5,4]=>1
[2,5,3,1,4,6]=>[3,5,4,1,2,6]=>1
[2,5,3,1,6,4]=>[3,6,4,1,2,5]=>1
[2,5,3,4,1,6]=>[3,4,5,1,2,6]=>1
[2,5,3,4,6,1]=>[3,4,6,1,2,5]=>1
[2,5,3,6,1,4]=>[3,5,1,2,6,4]=>2
[2,5,3,6,4,1]=>[3,6,1,2,5,4]=>1
[2,5,4,1,3,6]=>[5,3,4,1,2,6]=>1
[2,5,4,1,6,3]=>[6,3,4,1,2,5]=>1
[2,5,4,3,1,6]=>[4,3,5,1,2,6]=>2
[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>2
[2,5,4,6,1,3]=>[5,1,2,6,3,4]=>2
[2,5,4,6,3,1]=>[6,1,2,5,3,4]=>1
[2,5,6,1,3,4]=>[6,4,1,2,5,3]=>1
[2,5,6,1,4,3]=>[5,4,1,2,6,3]=>2
[2,5,6,3,1,4]=>[5,1,2,6,4,3]=>2
[2,5,6,3,4,1]=>[6,1,2,5,4,3]=>1
[2,5,6,4,1,3]=>[4,5,1,2,6,3]=>2
[2,5,6,4,3,1]=>[4,6,1,2,5,3]=>1
[2,6,1,3,4,5]=>[6,5,4,3,1,2]=>1
[2,6,1,3,5,4]=>[5,6,4,3,1,2]=>1
[2,6,1,4,3,5]=>[4,6,5,3,1,2]=>1
[2,6,1,4,5,3]=>[4,5,6,3,1,2]=>1
[2,6,1,5,3,4]=>[6,4,5,3,1,2]=>1
[2,6,1,5,4,3]=>[5,4,6,3,1,2]=>2
[2,6,3,1,4,5]=>[3,6,5,4,1,2]=>1
[2,6,3,1,5,4]=>[3,5,6,4,1,2]=>1
[2,6,3,4,1,5]=>[3,4,6,5,1,2]=>1
[2,6,3,4,5,1]=>[3,4,5,6,1,2]=>1
[2,6,3,5,1,4]=>[3,6,4,5,1,2]=>1
[2,6,3,5,4,1]=>[3,5,4,6,1,2]=>2
[2,6,4,1,3,5]=>[6,5,3,4,1,2]=>1
[2,6,4,1,5,3]=>[5,6,3,4,1,2]=>1
[2,6,4,3,1,5]=>[4,3,6,5,1,2]=>2
[2,6,4,3,5,1]=>[4,3,5,6,1,2]=>2
[2,6,4,5,1,3]=>[6,3,4,5,1,2]=>1
[2,6,4,5,3,1]=>[5,3,4,6,1,2]=>2
[2,6,5,1,3,4]=>[5,3,6,4,1,2]=>2
[2,6,5,1,4,3]=>[6,3,5,4,1,2]=>1
[2,6,5,3,1,4]=>[6,4,3,5,1,2]=>1
[2,6,5,3,4,1]=>[5,4,3,6,1,2]=>2
[2,6,5,4,1,3]=>[4,6,3,5,1,2]=>1
[2,6,5,4,3,1]=>[4,5,3,6,1,2]=>2
[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>1
[3,1,2,4,6,5]=>[3,2,1,4,6,5]=>2
[3,1,2,5,4,6]=>[3,2,1,5,4,6]=>2
[3,1,2,5,6,4]=>[3,2,1,6,4,5]=>2
[3,1,2,6,4,5]=>[3,2,1,6,5,4]=>2
[3,1,2,6,5,4]=>[3,2,1,5,6,4]=>2
[3,1,4,2,5,6]=>[4,2,1,3,5,6]=>1
[3,1,4,2,6,5]=>[4,2,1,3,6,5]=>2
[3,1,4,5,2,6]=>[5,2,1,3,4,6]=>1
[3,1,4,5,6,2]=>[6,2,1,3,4,5]=>1
[3,1,4,6,2,5]=>[6,5,2,1,3,4]=>1
[3,1,4,6,5,2]=>[5,6,2,1,3,4]=>1
[3,1,5,2,4,6]=>[5,4,2,1,3,6]=>1
[3,1,5,2,6,4]=>[6,4,2,1,3,5]=>1
[3,1,5,4,2,6]=>[4,5,2,1,3,6]=>1
[3,1,5,4,6,2]=>[4,6,2,1,3,5]=>1
[3,1,5,6,2,4]=>[5,2,1,3,6,4]=>2
[3,1,5,6,4,2]=>[6,2,1,3,5,4]=>1
[3,1,6,2,4,5]=>[6,5,4,2,1,3]=>1
[3,1,6,2,5,4]=>[5,6,4,2,1,3]=>1
[3,1,6,4,2,5]=>[4,6,5,2,1,3]=>1
[3,1,6,4,5,2]=>[4,5,6,2,1,3]=>1
[3,1,6,5,2,4]=>[6,4,5,2,1,3]=>1
[3,1,6,5,4,2]=>[5,4,6,2,1,3]=>2
[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>1
[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>2
[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>2
[3,2,1,5,6,4]=>[2,3,1,6,4,5]=>2
[3,2,1,6,4,5]=>[2,3,1,6,5,4]=>2
[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>2
[3,2,4,1,5,6]=>[2,4,1,3,5,6]=>1
[3,2,4,1,6,5]=>[2,4,1,3,6,5]=>2
[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>1
[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>1
[3,2,4,6,1,5]=>[2,6,5,1,3,4]=>1
[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>1
[3,2,5,1,4,6]=>[2,5,4,1,3,6]=>1
[3,2,5,1,6,4]=>[2,6,4,1,3,5]=>1
[3,2,5,4,1,6]=>[2,4,5,1,3,6]=>1
[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>1
[3,2,5,6,1,4]=>[2,5,1,3,6,4]=>2
[3,2,5,6,4,1]=>[2,6,1,3,5,4]=>1
[3,2,6,1,4,5]=>[2,6,5,4,1,3]=>1
[3,2,6,1,5,4]=>[2,5,6,4,1,3]=>1
[3,2,6,4,1,5]=>[2,4,6,5,1,3]=>1
[3,2,6,4,5,1]=>[2,4,5,6,1,3]=>1
[3,2,6,5,1,4]=>[2,6,4,5,1,3]=>1
[3,2,6,5,4,1]=>[2,5,4,6,1,3]=>2
[3,4,1,2,5,6]=>[3,1,4,2,5,6]=>2
[3,4,1,2,6,5]=>[3,1,4,2,6,5]=>3
[3,4,1,5,2,6]=>[3,1,5,2,4,6]=>2
[3,4,1,5,6,2]=>[3,1,6,2,4,5]=>2
[3,4,1,6,2,5]=>[3,1,6,5,2,4]=>2
[3,4,1,6,5,2]=>[3,1,5,6,2,4]=>2
[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>1
[3,4,2,1,6,5]=>[4,1,3,2,6,5]=>2
[3,4,2,5,1,6]=>[5,1,3,2,4,6]=>1
[3,4,2,5,6,1]=>[6,1,3,2,4,5]=>1
[3,4,2,6,1,5]=>[6,5,1,3,2,4]=>1
[3,4,2,6,5,1]=>[5,6,1,3,2,4]=>1
[3,4,5,1,2,6]=>[5,2,4,1,3,6]=>1
[3,4,5,1,6,2]=>[6,2,4,1,3,5]=>1
[3,4,5,2,1,6]=>[4,2,5,1,3,6]=>2
[3,4,5,2,6,1]=>[4,2,6,1,3,5]=>2
[3,4,5,6,1,2]=>[5,1,3,6,2,4]=>2
[3,4,5,6,2,1]=>[6,1,3,5,2,4]=>1
[3,4,6,1,2,5]=>[6,5,2,4,1,3]=>1
[3,4,6,1,5,2]=>[5,6,2,4,1,3]=>1
[3,4,6,2,1,5]=>[4,2,6,5,1,3]=>2
[3,4,6,2,5,1]=>[4,2,5,6,1,3]=>2
[3,4,6,5,1,2]=>[6,2,4,5,1,3]=>1
[3,4,6,5,2,1]=>[5,2,4,6,1,3]=>2
[3,5,1,2,4,6]=>[3,1,5,4,2,6]=>2
[3,5,1,2,6,4]=>[3,1,6,4,2,5]=>2
[3,5,1,4,2,6]=>[3,1,4,5,2,6]=>2
[3,5,1,4,6,2]=>[3,1,4,6,2,5]=>2
[3,5,1,6,2,4]=>[3,1,5,2,6,4]=>3
[3,5,1,6,4,2]=>[3,1,6,2,5,4]=>2
[3,5,2,1,4,6]=>[5,4,1,3,2,6]=>1
[3,5,2,1,6,4]=>[6,4,1,3,2,5]=>1
[3,5,2,4,1,6]=>[4,5,1,3,2,6]=>1
[3,5,2,4,6,1]=>[4,6,1,3,2,5]=>1
[3,5,2,6,1,4]=>[5,1,3,2,6,4]=>2
[3,5,2,6,4,1]=>[6,1,3,2,5,4]=>1
[3,5,4,1,2,6]=>[4,1,3,5,2,6]=>2
[3,5,4,1,6,2]=>[4,1,3,6,2,5]=>2
[3,5,4,2,1,6]=>[5,1,3,4,2,6]=>1
[3,5,4,2,6,1]=>[6,1,3,4,2,5]=>1
[3,5,4,6,1,2]=>[6,2,5,1,3,4]=>1
[3,5,4,6,2,1]=>[5,2,6,1,3,4]=>2
[3,5,6,1,2,4]=>[5,2,6,4,1,3]=>2
[3,5,6,1,4,2]=>[6,2,5,4,1,3]=>1
[3,5,6,2,1,4]=>[6,4,2,5,1,3]=>1
[3,5,6,2,4,1]=>[5,4,2,6,1,3]=>2
[3,5,6,4,1,2]=>[4,6,2,5,1,3]=>1
[3,5,6,4,2,1]=>[4,5,2,6,1,3]=>2
[3,6,1,2,4,5]=>[3,1,6,5,4,2]=>2
[3,6,1,2,5,4]=>[3,1,5,6,4,2]=>2
[3,6,1,4,2,5]=>[3,1,4,6,5,2]=>2
[3,6,1,4,5,2]=>[3,1,4,5,6,2]=>2
[3,6,1,5,2,4]=>[3,1,6,4,5,2]=>2
[3,6,1,5,4,2]=>[3,1,5,4,6,2]=>3
[3,6,2,1,4,5]=>[6,5,4,1,3,2]=>1
[3,6,2,1,5,4]=>[5,6,4,1,3,2]=>1
[3,6,2,4,1,5]=>[4,6,5,1,3,2]=>1
[3,6,2,4,5,1]=>[4,5,6,1,3,2]=>1
[3,6,2,5,1,4]=>[6,4,5,1,3,2]=>1
[3,6,2,5,4,1]=>[5,4,6,1,3,2]=>2
[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>2
[3,6,4,1,5,2]=>[4,1,3,5,6,2]=>2
[3,6,4,2,1,5]=>[6,5,1,3,4,2]=>1
[3,6,4,2,5,1]=>[5,6,1,3,4,2]=>1
[3,6,4,5,1,2]=>[5,1,3,4,6,2]=>2
[3,6,4,5,2,1]=>[6,1,3,4,5,2]=>1
[3,6,5,1,2,4]=>[6,4,1,3,5,2]=>1
[3,6,5,1,4,2]=>[5,4,1,3,6,2]=>2
[3,6,5,2,1,4]=>[5,1,3,6,4,2]=>2
[3,6,5,2,4,1]=>[6,1,3,5,4,2]=>1
[3,6,5,4,1,2]=>[4,5,1,3,6,2]=>2
[3,6,5,4,2,1]=>[4,6,1,3,5,2]=>1
[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>1
[4,1,2,3,6,5]=>[4,3,2,1,6,5]=>2
[4,1,2,5,3,6]=>[5,3,2,1,4,6]=>1
[4,1,2,5,6,3]=>[6,3,2,1,4,5]=>1
[4,1,2,6,3,5]=>[6,5,3,2,1,4]=>1
[4,1,2,6,5,3]=>[5,6,3,2,1,4]=>1
[4,1,3,2,5,6]=>[3,4,2,1,5,6]=>1
[4,1,3,2,6,5]=>[3,4,2,1,6,5]=>2
[4,1,3,5,2,6]=>[3,5,2,1,4,6]=>1
[4,1,3,5,6,2]=>[3,6,2,1,4,5]=>1
[4,1,3,6,2,5]=>[3,6,5,2,1,4]=>1
[4,1,3,6,5,2]=>[3,5,6,2,1,4]=>1
[4,1,5,2,3,6]=>[4,2,1,5,3,6]=>2
[4,1,5,2,6,3]=>[4,2,1,6,3,5]=>2
[4,1,5,3,2,6]=>[5,2,1,4,3,6]=>1
[4,1,5,3,6,2]=>[6,2,1,4,3,5]=>1
[4,1,5,6,2,3]=>[6,3,5,2,1,4]=>1
[4,1,5,6,3,2]=>[5,3,6,2,1,4]=>2
[4,1,6,2,3,5]=>[4,2,1,6,5,3]=>2
[4,1,6,2,5,3]=>[4,2,1,5,6,3]=>2
[4,1,6,3,2,5]=>[6,5,2,1,4,3]=>1
[4,1,6,3,5,2]=>[5,6,2,1,4,3]=>1
[4,1,6,5,2,3]=>[5,2,1,4,6,3]=>2
[4,1,6,5,3,2]=>[6,2,1,4,5,3]=>1
[4,2,1,3,5,6]=>[2,4,3,1,5,6]=>1
[4,2,1,3,6,5]=>[2,4,3,1,6,5]=>2
[4,2,1,5,3,6]=>[2,5,3,1,4,6]=>1
[4,2,1,5,6,3]=>[2,6,3,1,4,5]=>1
[4,2,1,6,3,5]=>[2,6,5,3,1,4]=>1
[4,2,1,6,5,3]=>[2,5,6,3,1,4]=>1
[4,2,3,1,5,6]=>[2,3,4,1,5,6]=>1
[4,2,3,1,6,5]=>[2,3,4,1,6,5]=>2
[4,2,3,5,1,6]=>[2,3,5,1,4,6]=>1
[4,2,3,5,6,1]=>[2,3,6,1,4,5]=>1
[4,2,3,6,1,5]=>[2,3,6,5,1,4]=>1
[4,2,3,6,5,1]=>[2,3,5,6,1,4]=>1
[4,2,5,1,3,6]=>[2,4,1,5,3,6]=>2
[4,2,5,1,6,3]=>[2,4,1,6,3,5]=>2
[4,2,5,3,1,6]=>[2,5,1,4,3,6]=>1
[4,2,5,3,6,1]=>[2,6,1,4,3,5]=>1
[4,2,5,6,1,3]=>[2,6,3,5,1,4]=>1
[4,2,5,6,3,1]=>[2,5,3,6,1,4]=>2
[4,2,6,1,3,5]=>[2,4,1,6,5,3]=>2
[4,2,6,1,5,3]=>[2,4,1,5,6,3]=>2
[4,2,6,3,1,5]=>[2,6,5,1,4,3]=>1
[4,2,6,3,5,1]=>[2,5,6,1,4,3]=>1
[4,2,6,5,1,3]=>[2,5,1,4,6,3]=>2
[4,2,6,5,3,1]=>[2,6,1,4,5,3]=>1
[4,3,1,2,5,6]=>[4,2,3,1,5,6]=>1
[4,3,1,2,6,5]=>[4,2,3,1,6,5]=>2
[4,3,1,5,2,6]=>[5,2,3,1,4,6]=>1
[4,3,1,5,6,2]=>[6,2,3,1,4,5]=>1
[4,3,1,6,2,5]=>[6,5,2,3,1,4]=>1
[4,3,1,6,5,2]=>[5,6,2,3,1,4]=>1
[4,3,2,1,5,6]=>[3,2,4,1,5,6]=>2
[4,3,2,1,6,5]=>[3,2,4,1,6,5]=>3
[4,3,2,5,1,6]=>[3,2,5,1,4,6]=>2
[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>2
[4,3,2,6,1,5]=>[3,2,6,5,1,4]=>2
[4,3,2,6,5,1]=>[3,2,5,6,1,4]=>2
[4,3,5,1,2,6]=>[4,1,5,2,3,6]=>2
[4,3,5,1,6,2]=>[4,1,6,2,3,5]=>2
[4,3,5,2,1,6]=>[5,1,4,2,3,6]=>1
[4,3,5,2,6,1]=>[6,1,4,2,3,5]=>1
[4,3,5,6,1,2]=>[6,2,3,5,1,4]=>1
[4,3,5,6,2,1]=>[5,2,3,6,1,4]=>2
[4,3,6,1,2,5]=>[4,1,6,5,2,3]=>2
[4,3,6,1,5,2]=>[4,1,5,6,2,3]=>2
[4,3,6,2,1,5]=>[6,5,1,4,2,3]=>1
[4,3,6,2,5,1]=>[5,6,1,4,2,3]=>1
[4,3,6,5,1,2]=>[5,1,4,6,2,3]=>2
[4,3,6,5,2,1]=>[6,1,4,5,2,3]=>1
[4,5,1,2,3,6]=>[5,3,1,4,2,6]=>1
[4,5,1,2,6,3]=>[6,3,1,4,2,5]=>1
[4,5,1,3,2,6]=>[4,3,1,5,2,6]=>2
[4,5,1,3,6,2]=>[4,3,1,6,2,5]=>2
[4,5,1,6,2,3]=>[5,2,6,3,1,4]=>2
[4,5,1,6,3,2]=>[6,2,5,3,1,4]=>1
[4,5,2,1,3,6]=>[4,1,5,3,2,6]=>2
[4,5,2,1,6,3]=>[4,1,6,3,2,5]=>2
[4,5,2,3,1,6]=>[5,1,4,3,2,6]=>1
[4,5,2,3,6,1]=>[6,1,4,3,2,5]=>1
[4,5,2,6,1,3]=>[6,3,2,5,1,4]=>1
[4,5,2,6,3,1]=>[5,3,2,6,1,4]=>2
[4,5,3,1,2,6]=>[3,4,1,5,2,6]=>2
[4,5,3,1,6,2]=>[3,4,1,6,2,5]=>2
[4,5,3,2,1,6]=>[3,5,1,4,2,6]=>1
[4,5,3,2,6,1]=>[3,6,1,4,2,5]=>1
[4,5,3,6,1,2]=>[3,6,2,5,1,4]=>1
[4,5,3,6,2,1]=>[3,5,2,6,1,4]=>2
[4,5,6,1,2,3]=>[4,1,5,2,6,3]=>3
[4,5,6,1,3,2]=>[4,1,6,2,5,3]=>2
[4,5,6,2,1,3]=>[5,1,4,2,6,3]=>2
[4,5,6,2,3,1]=>[6,1,4,2,5,3]=>1
[4,5,6,3,1,2]=>[6,2,5,1,4,3]=>1
[4,5,6,3,2,1]=>[5,2,6,1,4,3]=>2
[4,6,1,2,3,5]=>[6,5,3,1,4,2]=>1
[4,6,1,2,5,3]=>[5,6,3,1,4,2]=>1
[4,6,1,3,2,5]=>[4,3,1,6,5,2]=>2
[4,6,1,3,5,2]=>[4,3,1,5,6,2]=>2
[4,6,1,5,2,3]=>[6,3,1,4,5,2]=>1
[4,6,1,5,3,2]=>[5,3,1,4,6,2]=>2
[4,6,2,1,3,5]=>[4,1,6,5,3,2]=>2
[4,6,2,1,5,3]=>[4,1,5,6,3,2]=>2
[4,6,2,3,1,5]=>[6,5,1,4,3,2]=>1
[4,6,2,3,5,1]=>[5,6,1,4,3,2]=>1
[4,6,2,5,1,3]=>[5,1,4,6,3,2]=>2
[4,6,2,5,3,1]=>[6,1,4,5,3,2]=>1
[4,6,3,1,2,5]=>[3,4,1,6,5,2]=>2
[4,6,3,1,5,2]=>[3,4,1,5,6,2]=>2
[4,6,3,2,1,5]=>[3,6,5,1,4,2]=>1
[4,6,3,2,5,1]=>[3,5,6,1,4,2]=>1
[4,6,3,5,1,2]=>[3,5,1,4,6,2]=>2
[4,6,3,5,2,1]=>[3,6,1,4,5,2]=>1
[4,6,5,1,2,3]=>[4,1,6,3,5,2]=>2
[4,6,5,1,3,2]=>[4,1,5,3,6,2]=>3
[4,6,5,2,1,3]=>[6,3,5,1,4,2]=>1
[4,6,5,2,3,1]=>[5,3,6,1,4,2]=>2
[4,6,5,3,1,2]=>[5,1,4,3,6,2]=>2
[4,6,5,3,2,1]=>[6,1,4,3,5,2]=>1
[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>1
[5,1,2,3,6,4]=>[6,4,3,2,1,5]=>1
[5,1,2,4,3,6]=>[4,5,3,2,1,6]=>1
[5,1,2,4,6,3]=>[4,6,3,2,1,5]=>1
[5,1,2,6,3,4]=>[5,3,2,1,6,4]=>2
[5,1,2,6,4,3]=>[6,3,2,1,5,4]=>1
[5,1,3,2,4,6]=>[3,5,4,2,1,6]=>1
[5,1,3,2,6,4]=>[3,6,4,2,1,5]=>1
[5,1,3,4,2,6]=>[3,4,5,2,1,6]=>1
[5,1,3,4,6,2]=>[3,4,6,2,1,5]=>1
[5,1,3,6,2,4]=>[3,5,2,1,6,4]=>2
[5,1,3,6,4,2]=>[3,6,2,1,5,4]=>1
[5,1,4,2,3,6]=>[5,3,4,2,1,6]=>1
[5,1,4,2,6,3]=>[6,3,4,2,1,5]=>1
[5,1,4,3,2,6]=>[4,3,5,2,1,6]=>2
[5,1,4,3,6,2]=>[4,3,6,2,1,5]=>2
[5,1,4,6,2,3]=>[5,2,1,6,3,4]=>2
[5,1,4,6,3,2]=>[6,2,1,5,3,4]=>1
[5,1,6,2,3,4]=>[6,4,2,1,5,3]=>1
[5,1,6,2,4,3]=>[5,4,2,1,6,3]=>2
[5,1,6,3,2,4]=>[5,2,1,6,4,3]=>2
[5,1,6,3,4,2]=>[6,2,1,5,4,3]=>1
[5,1,6,4,2,3]=>[4,5,2,1,6,3]=>2
[5,1,6,4,3,2]=>[4,6,2,1,5,3]=>1
[5,2,1,3,4,6]=>[2,5,4,3,1,6]=>1
[5,2,1,3,6,4]=>[2,6,4,3,1,5]=>1
[5,2,1,4,3,6]=>[2,4,5,3,1,6]=>1
[5,2,1,4,6,3]=>[2,4,6,3,1,5]=>1
[5,2,1,6,3,4]=>[2,5,3,1,6,4]=>2
[5,2,1,6,4,3]=>[2,6,3,1,5,4]=>1
[5,2,3,1,4,6]=>[2,3,5,4,1,6]=>1
[5,2,3,1,6,4]=>[2,3,6,4,1,5]=>1
[5,2,3,4,1,6]=>[2,3,4,5,1,6]=>1
[5,2,3,4,6,1]=>[2,3,4,6,1,5]=>1
[5,2,3,6,1,4]=>[2,3,5,1,6,4]=>2
[5,2,3,6,4,1]=>[2,3,6,1,5,4]=>1
[5,2,4,1,3,6]=>[2,5,3,4,1,6]=>1
[5,2,4,1,6,3]=>[2,6,3,4,1,5]=>1
[5,2,4,3,1,6]=>[2,4,3,5,1,6]=>2
[5,2,4,3,6,1]=>[2,4,3,6,1,5]=>2
[5,2,4,6,1,3]=>[2,5,1,6,3,4]=>2
[5,2,4,6,3,1]=>[2,6,1,5,3,4]=>1
[5,2,6,1,3,4]=>[2,6,4,1,5,3]=>1
[5,2,6,1,4,3]=>[2,5,4,1,6,3]=>2
[5,2,6,3,1,4]=>[2,5,1,6,4,3]=>2
[5,2,6,3,4,1]=>[2,6,1,5,4,3]=>1
[5,2,6,4,1,3]=>[2,4,5,1,6,3]=>2
[5,2,6,4,3,1]=>[2,4,6,1,5,3]=>1
[5,3,1,2,4,6]=>[5,4,2,3,1,6]=>1
[5,3,1,2,6,4]=>[6,4,2,3,1,5]=>1
[5,3,1,4,2,6]=>[4,5,2,3,1,6]=>1
[5,3,1,4,6,2]=>[4,6,2,3,1,5]=>1
[5,3,1,6,2,4]=>[5,2,3,1,6,4]=>2
[5,3,1,6,4,2]=>[6,2,3,1,5,4]=>1
[5,3,2,1,4,6]=>[3,2,5,4,1,6]=>2
[5,3,2,1,6,4]=>[3,2,6,4,1,5]=>2
[5,3,2,4,1,6]=>[3,2,4,5,1,6]=>2
[5,3,2,4,6,1]=>[3,2,4,6,1,5]=>2
[5,3,2,6,1,4]=>[3,2,5,1,6,4]=>3
[5,3,2,6,4,1]=>[3,2,6,1,5,4]=>2
[5,3,4,1,2,6]=>[5,2,3,4,1,6]=>1
[5,3,4,1,6,2]=>[6,2,3,4,1,5]=>1
[5,3,4,2,1,6]=>[4,2,3,5,1,6]=>2
[5,3,4,2,6,1]=>[4,2,3,6,1,5]=>2
[5,3,4,6,1,2]=>[5,1,6,2,3,4]=>2
[5,3,4,6,2,1]=>[6,1,5,2,3,4]=>1
[5,3,6,1,2,4]=>[6,4,1,5,2,3]=>1
[5,3,6,1,4,2]=>[5,4,1,6,2,3]=>2
[5,3,6,2,1,4]=>[5,1,6,4,2,3]=>2
[5,3,6,2,4,1]=>[6,1,5,4,2,3]=>1
[5,3,6,4,1,2]=>[4,5,1,6,2,3]=>2
[5,3,6,4,2,1]=>[4,6,1,5,2,3]=>1
[5,4,1,2,3,6]=>[4,2,5,3,1,6]=>2
[5,4,1,2,6,3]=>[4,2,6,3,1,5]=>2
[5,4,1,3,2,6]=>[5,2,4,3,1,6]=>1
[5,4,1,3,6,2]=>[6,2,4,3,1,5]=>1
[5,4,1,6,2,3]=>[6,3,1,5,2,4]=>1
[5,4,1,6,3,2]=>[5,3,1,6,2,4]=>2
[5,4,2,1,3,6]=>[5,3,2,4,1,6]=>1
[5,4,2,1,6,3]=>[6,3,2,4,1,5]=>1
[5,4,2,3,1,6]=>[4,3,2,5,1,6]=>2
[5,4,2,3,6,1]=>[4,3,2,6,1,5]=>2
[5,4,2,6,1,3]=>[5,1,6,3,2,4]=>2
[5,4,2,6,3,1]=>[6,1,5,3,2,4]=>1
[5,4,3,1,2,6]=>[3,5,2,4,1,6]=>1
[5,4,3,1,6,2]=>[3,6,2,4,1,5]=>1
[5,4,3,2,1,6]=>[3,4,2,5,1,6]=>2
[5,4,3,2,6,1]=>[3,4,2,6,1,5]=>2
[5,4,3,6,1,2]=>[3,5,1,6,2,4]=>2
[5,4,3,6,2,1]=>[3,6,1,5,2,4]=>1
[5,4,6,1,2,3]=>[5,2,4,1,6,3]=>2
[5,4,6,1,3,2]=>[6,2,4,1,5,3]=>1
[5,4,6,2,1,3]=>[4,2,5,1,6,3]=>3
[5,4,6,2,3,1]=>[4,2,6,1,5,3]=>2
[5,4,6,3,1,2]=>[5,1,6,2,4,3]=>2
[5,4,6,3,2,1]=>[6,1,5,2,4,3]=>1
[5,6,1,2,3,4]=>[5,3,1,6,4,2]=>2
[5,6,1,2,4,3]=>[6,3,1,5,4,2]=>1
[5,6,1,3,2,4]=>[6,4,3,1,5,2]=>1
[5,6,1,3,4,2]=>[5,4,3,1,6,2]=>2
[5,6,1,4,2,3]=>[4,6,3,1,5,2]=>1
[5,6,1,4,3,2]=>[4,5,3,1,6,2]=>2
[5,6,2,1,3,4]=>[6,4,1,5,3,2]=>1
[5,6,2,1,4,3]=>[5,4,1,6,3,2]=>2
[5,6,2,3,1,4]=>[5,1,6,4,3,2]=>2
[5,6,2,3,4,1]=>[6,1,5,4,3,2]=>1
[5,6,2,4,1,3]=>[4,5,1,6,3,2]=>2
[5,6,2,4,3,1]=>[4,6,1,5,3,2]=>1
[5,6,3,1,2,4]=>[3,6,4,1,5,2]=>1
[5,6,3,1,4,2]=>[3,5,4,1,6,2]=>2
[5,6,3,2,1,4]=>[3,5,1,6,4,2]=>2
[5,6,3,2,4,1]=>[3,6,1,5,4,2]=>1
[5,6,3,4,1,2]=>[3,4,5,1,6,2]=>2
[5,6,3,4,2,1]=>[3,4,6,1,5,2]=>1
[5,6,4,1,2,3]=>[6,3,4,1,5,2]=>1
[5,6,4,1,3,2]=>[5,3,4,1,6,2]=>2
[5,6,4,2,1,3]=>[5,1,6,3,4,2]=>2
[5,6,4,2,3,1]=>[6,1,5,3,4,2]=>1
[5,6,4,3,1,2]=>[4,3,5,1,6,2]=>3
[5,6,4,3,2,1]=>[4,3,6,1,5,2]=>2
[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>1
[6,1,2,3,5,4]=>[5,6,4,3,2,1]=>1
[6,1,2,4,3,5]=>[4,6,5,3,2,1]=>1
[6,1,2,4,5,3]=>[4,5,6,3,2,1]=>1
[6,1,2,5,3,4]=>[6,4,5,3,2,1]=>1
[6,1,2,5,4,3]=>[5,4,6,3,2,1]=>2
[6,1,3,2,4,5]=>[3,6,5,4,2,1]=>1
[6,1,3,2,5,4]=>[3,5,6,4,2,1]=>1
[6,1,3,4,2,5]=>[3,4,6,5,2,1]=>1
[6,1,3,4,5,2]=>[3,4,5,6,2,1]=>1
[6,1,3,5,2,4]=>[3,6,4,5,2,1]=>1
[6,1,3,5,4,2]=>[3,5,4,6,2,1]=>2
[6,1,4,2,3,5]=>[6,5,3,4,2,1]=>1
[6,1,4,2,5,3]=>[5,6,3,4,2,1]=>1
[6,1,4,3,2,5]=>[4,3,6,5,2,1]=>2
[6,1,4,3,5,2]=>[4,3,5,6,2,1]=>2
[6,1,4,5,2,3]=>[6,3,4,5,2,1]=>1
[6,1,4,5,3,2]=>[5,3,4,6,2,1]=>2
[6,1,5,2,3,4]=>[5,3,6,4,2,1]=>2
[6,1,5,2,4,3]=>[6,3,5,4,2,1]=>1
[6,1,5,3,2,4]=>[6,4,3,5,2,1]=>1
[6,1,5,3,4,2]=>[5,4,3,6,2,1]=>2
[6,1,5,4,2,3]=>[4,6,3,5,2,1]=>1
[6,1,5,4,3,2]=>[4,5,3,6,2,1]=>2
[6,2,1,3,4,5]=>[2,6,5,4,3,1]=>1
[6,2,1,3,5,4]=>[2,5,6,4,3,1]=>1
[6,2,1,4,3,5]=>[2,4,6,5,3,1]=>1
[6,2,1,4,5,3]=>[2,4,5,6,3,1]=>1
[6,2,1,5,3,4]=>[2,6,4,5,3,1]=>1
[6,2,1,5,4,3]=>[2,5,4,6,3,1]=>2
[6,2,3,1,4,5]=>[2,3,6,5,4,1]=>1
[6,2,3,1,5,4]=>[2,3,5,6,4,1]=>1
[6,2,3,4,1,5]=>[2,3,4,6,5,1]=>1
[6,2,3,4,5,1]=>[2,3,4,5,6,1]=>1
[6,2,3,5,1,4]=>[2,3,6,4,5,1]=>1
[6,2,3,5,4,1]=>[2,3,5,4,6,1]=>2
[6,2,4,1,3,5]=>[2,6,5,3,4,1]=>1
[6,2,4,1,5,3]=>[2,5,6,3,4,1]=>1
[6,2,4,3,1,5]=>[2,4,3,6,5,1]=>2
[6,2,4,3,5,1]=>[2,4,3,5,6,1]=>2
[6,2,4,5,1,3]=>[2,6,3,4,5,1]=>1
[6,2,4,5,3,1]=>[2,5,3,4,6,1]=>2
[6,2,5,1,3,4]=>[2,5,3,6,4,1]=>2
[6,2,5,1,4,3]=>[2,6,3,5,4,1]=>1
[6,2,5,3,1,4]=>[2,6,4,3,5,1]=>1
[6,2,5,3,4,1]=>[2,5,4,3,6,1]=>2
[6,2,5,4,1,3]=>[2,4,6,3,5,1]=>1
[6,2,5,4,3,1]=>[2,4,5,3,6,1]=>2
[6,3,1,2,4,5]=>[6,5,4,2,3,1]=>1
[6,3,1,2,5,4]=>[5,6,4,2,3,1]=>1
[6,3,1,4,2,5]=>[4,6,5,2,3,1]=>1
[6,3,1,4,5,2]=>[4,5,6,2,3,1]=>1
[6,3,1,5,2,4]=>[6,4,5,2,3,1]=>1
[6,3,1,5,4,2]=>[5,4,6,2,3,1]=>2
[6,3,2,1,4,5]=>[3,2,6,5,4,1]=>2
[6,3,2,1,5,4]=>[3,2,5,6,4,1]=>2
[6,3,2,4,1,5]=>[3,2,4,6,5,1]=>2
[6,3,2,4,5,1]=>[3,2,4,5,6,1]=>2
[6,3,2,5,1,4]=>[3,2,6,4,5,1]=>2
[6,3,2,5,4,1]=>[3,2,5,4,6,1]=>3
[6,3,4,1,2,5]=>[6,5,2,3,4,1]=>1
[6,3,4,1,5,2]=>[5,6,2,3,4,1]=>1
[6,3,4,2,1,5]=>[4,2,3,6,5,1]=>2
[6,3,4,2,5,1]=>[4,2,3,5,6,1]=>2
[6,3,4,5,1,2]=>[6,2,3,4,5,1]=>1
[6,3,4,5,2,1]=>[5,2,3,4,6,1]=>2
[6,3,5,1,2,4]=>[5,2,3,6,4,1]=>2
[6,3,5,1,4,2]=>[6,2,3,5,4,1]=>1
[6,3,5,2,1,4]=>[6,4,2,3,5,1]=>1
[6,3,5,2,4,1]=>[5,4,2,3,6,1]=>2
[6,3,5,4,1,2]=>[4,6,2,3,5,1]=>1
[6,3,5,4,2,1]=>[4,5,2,3,6,1]=>2
[6,4,1,2,3,5]=>[4,2,6,5,3,1]=>2
[6,4,1,2,5,3]=>[4,2,5,6,3,1]=>2
[6,4,1,3,2,5]=>[6,5,2,4,3,1]=>1
[6,4,1,3,5,2]=>[5,6,2,4,3,1]=>1
[6,4,1,5,2,3]=>[5,2,4,6,3,1]=>2
[6,4,1,5,3,2]=>[6,2,4,5,3,1]=>1
[6,4,2,1,3,5]=>[6,5,3,2,4,1]=>1
[6,4,2,1,5,3]=>[5,6,3,2,4,1]=>1
[6,4,2,3,1,5]=>[4,3,2,6,5,1]=>2
[6,4,2,3,5,1]=>[4,3,2,5,6,1]=>2
[6,4,2,5,1,3]=>[6,3,2,4,5,1]=>1
[6,4,2,5,3,1]=>[5,3,2,4,6,1]=>2
[6,4,3,1,2,5]=>[3,6,5,2,4,1]=>1
[6,4,3,1,5,2]=>[3,5,6,2,4,1]=>1
[6,4,3,2,1,5]=>[3,4,2,6,5,1]=>2
[6,4,3,2,5,1]=>[3,4,2,5,6,1]=>2
[6,4,3,5,1,2]=>[3,6,2,4,5,1]=>1
[6,4,3,5,2,1]=>[3,5,2,4,6,1]=>2
[6,4,5,1,2,3]=>[6,3,5,2,4,1]=>1
[6,4,5,1,3,2]=>[5,3,6,2,4,1]=>2
[6,4,5,2,1,3]=>[4,2,6,3,5,1]=>2
[6,4,5,2,3,1]=>[4,2,5,3,6,1]=>3
[6,4,5,3,1,2]=>[6,2,4,3,5,1]=>1
[6,4,5,3,2,1]=>[5,2,4,3,6,1]=>2
[6,5,1,2,3,4]=>[6,4,2,5,3,1]=>1
[6,5,1,2,4,3]=>[5,4,2,6,3,1]=>2
[6,5,1,3,2,4]=>[5,2,6,4,3,1]=>2
[6,5,1,3,4,2]=>[6,2,5,4,3,1]=>1
[6,5,1,4,2,3]=>[4,5,2,6,3,1]=>2
[6,5,1,4,3,2]=>[4,6,2,5,3,1]=>1
[6,5,2,1,3,4]=>[5,3,2,6,4,1]=>2
[6,5,2,1,4,3]=>[6,3,2,5,4,1]=>1
[6,5,2,3,1,4]=>[6,4,3,2,5,1]=>1
[6,5,2,3,4,1]=>[5,4,3,2,6,1]=>2
[6,5,2,4,1,3]=>[4,6,3,2,5,1]=>1
[6,5,2,4,3,1]=>[4,5,3,2,6,1]=>2
[6,5,3,1,2,4]=>[3,5,2,6,4,1]=>2
[6,5,3,1,4,2]=>[3,6,2,5,4,1]=>1
[6,5,3,2,1,4]=>[3,6,4,2,5,1]=>1
[6,5,3,2,4,1]=>[3,5,4,2,6,1]=>2
[6,5,3,4,1,2]=>[3,4,6,2,5,1]=>1
[6,5,3,4,2,1]=>[3,4,5,2,6,1]=>2
[6,5,4,1,2,3]=>[5,2,6,3,4,1]=>2
[6,5,4,1,3,2]=>[6,2,5,3,4,1]=>1
[6,5,4,2,1,3]=>[6,3,4,2,5,1]=>1
[6,5,4,2,3,1]=>[5,3,4,2,6,1]=>2
[6,5,4,3,1,2]=>[4,3,6,2,5,1]=>2
[6,5,4,3,2,1]=>[4,3,5,2,6,1]=>3
[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]=>1
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>1
[1,2,3,4,6,7,5]=>[1,2,3,4,7,5,6]=>1
[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]=>1
[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>1
[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>1
[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>2
[1,2,3,5,6,4,7]=>[1,2,3,6,4,5,7]=>1
[1,2,3,5,6,7,4]=>[1,2,3,7,4,5,6]=>1
[1,2,3,5,7,4,6]=>[1,2,3,7,6,4,5]=>1
[1,2,3,5,7,6,4]=>[1,2,3,6,7,4,5]=>1
[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]=>1
[1,2,3,6,4,7,5]=>[1,2,3,7,5,4,6]=>1
[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>1
[1,2,3,6,5,7,4]=>[1,2,3,5,7,4,6]=>1
[1,2,3,6,7,4,5]=>[1,2,3,6,4,7,5]=>2
[1,2,3,6,7,5,4]=>[1,2,3,7,4,6,5]=>1
[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]=>1
[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>1
[1,2,3,7,5,4,6]=>[1,2,3,5,7,6,4]=>1
[1,2,3,7,5,6,4]=>[1,2,3,5,6,7,4]=>1
[1,2,3,7,6,4,5]=>[1,2,3,7,5,6,4]=>1
[1,2,3,7,6,5,4]=>[1,2,3,6,5,7,4]=>2
[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>1
[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>2
[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>2
[1,2,4,3,6,7,5]=>[1,2,4,3,7,5,6]=>2
[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]=>2
[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>2
[1,2,4,5,3,6,7]=>[1,2,5,3,4,6,7]=>1
[1,2,4,5,3,7,6]=>[1,2,5,3,4,7,6]=>2
[1,2,4,5,6,3,7]=>[1,2,6,3,4,5,7]=>1
[1,2,4,5,6,7,3]=>[1,2,7,3,4,5,6]=>1
[1,2,4,5,7,3,6]=>[1,2,7,6,3,4,5]=>1
[1,2,4,5,7,6,3]=>[1,2,6,7,3,4,5]=>1
[1,2,4,6,3,5,7]=>[1,2,6,5,3,4,7]=>1
[1,2,4,6,3,7,5]=>[1,2,7,5,3,4,6]=>1
[1,2,4,6,5,3,7]=>[1,2,5,6,3,4,7]=>1
[1,2,4,6,5,7,3]=>[1,2,5,7,3,4,6]=>1
[1,2,4,6,7,3,5]=>[1,2,6,3,4,7,5]=>2
[1,2,4,6,7,5,3]=>[1,2,7,3,4,6,5]=>1
[1,2,4,7,3,5,6]=>[1,2,7,6,5,3,4]=>1
[1,2,4,7,3,6,5]=>[1,2,6,7,5,3,4]=>1
[1,2,4,7,5,3,6]=>[1,2,5,7,6,3,4]=>1
[1,2,4,7,5,6,3]=>[1,2,5,6,7,3,4]=>1
[1,2,4,7,6,3,5]=>[1,2,7,5,6,3,4]=>1
[1,2,4,7,6,5,3]=>[1,2,6,5,7,3,4]=>2
[1,2,5,3,4,6,7]=>[1,2,5,4,3,6,7]=>1
[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]=>2
[1,2,5,3,6,4,7]=>[1,2,6,4,3,5,7]=>1
[1,2,5,3,6,7,4]=>[1,2,7,4,3,5,6]=>1
[1,2,5,3,7,4,6]=>[1,2,7,6,4,3,5]=>1
[1,2,5,3,7,6,4]=>[1,2,6,7,4,3,5]=>1
[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>1
[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>2
[1,2,5,4,6,3,7]=>[1,2,4,6,3,5,7]=>1
[1,2,5,4,6,7,3]=>[1,2,4,7,3,5,6]=>1
[1,2,5,4,7,3,6]=>[1,2,4,7,6,3,5]=>1
[1,2,5,4,7,6,3]=>[1,2,4,6,7,3,5]=>1
[1,2,5,6,3,4,7]=>[1,2,5,3,6,4,7]=>2
[1,2,5,6,3,7,4]=>[1,2,5,3,7,4,6]=>2
[1,2,5,6,4,3,7]=>[1,2,6,3,5,4,7]=>1
[1,2,5,6,4,7,3]=>[1,2,7,3,5,4,6]=>1
[1,2,5,6,7,3,4]=>[1,2,7,4,6,3,5]=>1
[1,2,5,6,7,4,3]=>[1,2,6,4,7,3,5]=>2
[1,2,5,7,3,4,6]=>[1,2,5,3,7,6,4]=>2
[1,2,5,7,3,6,4]=>[1,2,5,3,6,7,4]=>2
[1,2,5,7,4,3,6]=>[1,2,7,6,3,5,4]=>1
[1,2,5,7,4,6,3]=>[1,2,6,7,3,5,4]=>1
[1,2,5,7,6,3,4]=>[1,2,6,3,5,7,4]=>2
[1,2,5,7,6,4,3]=>[1,2,7,3,5,6,4]=>1
[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]=>1
[1,2,6,3,4,7,5]=>[1,2,7,5,4,3,6]=>1
[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>1
[1,2,6,3,5,7,4]=>[1,2,5,7,4,3,6]=>1
[1,2,6,3,7,4,5]=>[1,2,6,4,3,7,5]=>2
[1,2,6,3,7,5,4]=>[1,2,7,4,3,6,5]=>1
[1,2,6,4,3,5,7]=>[1,2,4,6,5,3,7]=>1
[1,2,6,4,3,7,5]=>[1,2,4,7,5,3,6]=>1
[1,2,6,4,5,3,7]=>[1,2,4,5,6,3,7]=>1
[1,2,6,4,5,7,3]=>[1,2,4,5,7,3,6]=>1
[1,2,6,4,7,3,5]=>[1,2,4,6,3,7,5]=>2
[1,2,6,4,7,5,3]=>[1,2,4,7,3,6,5]=>1
[1,2,6,5,3,4,7]=>[1,2,6,4,5,3,7]=>1
[1,2,6,5,3,7,4]=>[1,2,7,4,5,3,6]=>1
[1,2,6,5,4,3,7]=>[1,2,5,4,6,3,7]=>2
[1,2,6,5,4,7,3]=>[1,2,5,4,7,3,6]=>2
[1,2,6,5,7,3,4]=>[1,2,6,3,7,4,5]=>2
[1,2,6,5,7,4,3]=>[1,2,7,3,6,4,5]=>1
[1,2,6,7,3,4,5]=>[1,2,7,5,3,6,4]=>1
[1,2,6,7,3,5,4]=>[1,2,6,5,3,7,4]=>2
[1,2,6,7,4,3,5]=>[1,2,6,3,7,5,4]=>2
[1,2,6,7,4,5,3]=>[1,2,7,3,6,5,4]=>1
[1,2,6,7,5,3,4]=>[1,2,5,6,3,7,4]=>2
[1,2,6,7,5,4,3]=>[1,2,5,7,3,6,4]=>1
[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]=>1
[1,2,7,3,4,6,5]=>[1,2,6,7,5,4,3]=>1
[1,2,7,3,5,4,6]=>[1,2,5,7,6,4,3]=>1
[1,2,7,3,5,6,4]=>[1,2,5,6,7,4,3]=>1
[1,2,7,3,6,4,5]=>[1,2,7,5,6,4,3]=>1
[1,2,7,3,6,5,4]=>[1,2,6,5,7,4,3]=>2
[1,2,7,4,3,5,6]=>[1,2,4,7,6,5,3]=>1
[1,2,7,4,3,6,5]=>[1,2,4,6,7,5,3]=>1
[1,2,7,4,5,3,6]=>[1,2,4,5,7,6,3]=>1
[1,2,7,4,5,6,3]=>[1,2,4,5,6,7,3]=>1
[1,2,7,4,6,3,5]=>[1,2,4,7,5,6,3]=>1
[1,2,7,4,6,5,3]=>[1,2,4,6,5,7,3]=>2
[1,2,7,5,3,4,6]=>[1,2,7,6,4,5,3]=>1
[1,2,7,5,3,6,4]=>[1,2,6,7,4,5,3]=>1
[1,2,7,5,4,3,6]=>[1,2,5,4,7,6,3]=>2
[1,2,7,5,4,6,3]=>[1,2,5,4,6,7,3]=>2
[1,2,7,5,6,3,4]=>[1,2,7,4,5,6,3]=>1
[1,2,7,5,6,4,3]=>[1,2,6,4,5,7,3]=>2
[1,2,7,6,3,4,5]=>[1,2,6,4,7,5,3]=>2
[1,2,7,6,3,5,4]=>[1,2,7,4,6,5,3]=>1
[1,2,7,6,4,3,5]=>[1,2,7,5,4,6,3]=>1
[1,2,7,6,4,5,3]=>[1,2,6,5,4,7,3]=>2
[1,2,7,6,5,3,4]=>[1,2,5,7,4,6,3]=>1
[1,2,7,6,5,4,3]=>[1,2,5,6,4,7,3]=>2
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>1
[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>2
[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>2
[1,3,2,4,6,7,5]=>[1,3,2,4,7,5,6]=>2
[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]=>2
[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>2
[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>2
[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>3
[1,3,2,5,6,4,7]=>[1,3,2,6,4,5,7]=>2
[1,3,2,5,6,7,4]=>[1,3,2,7,4,5,6]=>2
[1,3,2,5,7,4,6]=>[1,3,2,7,6,4,5]=>2
[1,3,2,5,7,6,4]=>[1,3,2,6,7,4,5]=>2
[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]=>2
[1,3,2,6,4,7,5]=>[1,3,2,7,5,4,6]=>2
[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>2
[1,3,2,6,5,7,4]=>[1,3,2,5,7,4,6]=>2
[1,3,2,6,7,4,5]=>[1,3,2,6,4,7,5]=>3
[1,3,2,6,7,5,4]=>[1,3,2,7,4,6,5]=>2
[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]=>2
[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>2
[1,3,2,7,5,4,6]=>[1,3,2,5,7,6,4]=>2
[1,3,2,7,5,6,4]=>[1,3,2,5,6,7,4]=>2
[1,3,2,7,6,4,5]=>[1,3,2,7,5,6,4]=>2
[1,3,2,7,6,5,4]=>[1,3,2,6,5,7,4]=>3
[1,3,4,2,5,6,7]=>[1,4,2,3,5,6,7]=>1
[1,3,4,2,5,7,6]=>[1,4,2,3,5,7,6]=>2
[1,3,4,2,6,5,7]=>[1,4,2,3,6,5,7]=>2
[1,3,4,2,6,7,5]=>[1,4,2,3,7,5,6]=>2
[1,3,4,2,7,5,6]=>[1,4,2,3,7,6,5]=>2
[1,3,4,2,7,6,5]=>[1,4,2,3,6,7,5]=>2
[1,3,5,4,2,6,7]=>[1,4,5,2,3,6,7]=>1
[1,3,5,4,2,7,6]=>[1,4,5,2,3,7,6]=>2
[1,3,5,4,6,2,7]=>[1,4,6,2,3,5,7]=>1
[1,3,6,4,2,5,7]=>[1,4,6,5,2,3,7]=>1
[1,3,6,4,5,2,7]=>[1,4,5,6,2,3,7]=>1
[1,3,6,4,5,7,2]=>[1,4,5,7,2,3,6]=>1
[1,3,6,4,7,2,5]=>[1,4,6,2,3,7,5]=>2
[1,3,7,4,5,2,6]=>[1,4,5,7,6,2,3]=>1
[1,3,7,4,5,6,2]=>[1,4,5,6,7,2,3]=>1
[1,4,2,3,5,6,7]=>[1,4,3,2,5,6,7]=>1
[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]=>2
[1,4,2,3,6,5,7]=>[1,4,3,2,6,5,7]=>2
[1,4,2,3,6,7,5]=>[1,4,3,2,7,5,6]=>2
[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]=>2
[1,4,2,3,7,6,5]=>[1,4,3,2,6,7,5]=>2
[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>1
[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>2
[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>2
[1,4,3,2,6,7,5]=>[1,3,4,2,7,5,6]=>2
[1,4,3,2,7,5,6]=>[1,3,4,2,7,6,5]=>2
[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>2
[1,4,3,5,2,6,7]=>[1,3,5,2,4,6,7]=>1
[1,4,3,5,2,7,6]=>[1,3,5,2,4,7,6]=>2
[1,4,3,5,6,2,7]=>[1,3,6,2,4,5,7]=>1
[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>1
[1,4,3,5,7,2,6]=>[1,3,7,6,2,4,5]=>1
[1,4,3,5,7,6,2]=>[1,3,6,7,2,4,5]=>1
[1,4,3,6,2,5,7]=>[1,3,6,5,2,4,7]=>1
[1,4,3,6,2,7,5]=>[1,3,7,5,2,4,6]=>1
[1,4,3,6,5,2,7]=>[1,3,5,6,2,4,7]=>1
[1,4,3,6,5,7,2]=>[1,3,5,7,2,4,6]=>1
[1,4,3,6,7,2,5]=>[1,3,6,2,4,7,5]=>2
[1,4,3,6,7,5,2]=>[1,3,7,2,4,6,5]=>1
[1,4,3,7,2,5,6]=>[1,3,7,6,5,2,4]=>1
[1,4,3,7,2,6,5]=>[1,3,6,7,5,2,4]=>1
[1,4,3,7,5,2,6]=>[1,3,5,7,6,2,4]=>1
[1,4,3,7,5,6,2]=>[1,3,5,6,7,2,4]=>1
[1,4,3,7,6,2,5]=>[1,3,7,5,6,2,4]=>1
[1,4,3,7,6,5,2]=>[1,3,6,5,7,2,4]=>2
[1,4,5,2,3,6,7]=>[1,4,2,5,3,6,7]=>2
[1,4,5,2,3,7,6]=>[1,4,2,5,3,7,6]=>3
[1,4,5,2,6,3,7]=>[1,4,2,6,3,5,7]=>2
[1,4,5,2,6,7,3]=>[1,4,2,7,3,5,6]=>2
[1,4,5,2,7,3,6]=>[1,4,2,7,6,3,5]=>2
[1,4,5,2,7,6,3]=>[1,4,2,6,7,3,5]=>2
[1,4,6,2,3,5,7]=>[1,4,2,6,5,3,7]=>2
[1,4,6,2,3,7,5]=>[1,4,2,7,5,3,6]=>2
[1,4,6,2,5,3,7]=>[1,4,2,5,6,3,7]=>2
[1,4,6,2,5,7,3]=>[1,4,2,5,7,3,6]=>2
[1,4,6,2,7,3,5]=>[1,4,2,6,3,7,5]=>3
[1,4,6,2,7,5,3]=>[1,4,2,7,3,6,5]=>2
[1,4,7,2,3,5,6]=>[1,4,2,7,6,5,3]=>2
[1,4,7,2,3,6,5]=>[1,4,2,6,7,5,3]=>2
[1,4,7,2,5,3,6]=>[1,4,2,5,7,6,3]=>2
[1,4,7,2,5,6,3]=>[1,4,2,5,6,7,3]=>2
[1,4,7,2,6,3,5]=>[1,4,2,7,5,6,3]=>2
[1,4,7,2,6,5,3]=>[1,4,2,6,5,7,3]=>3
[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>1
[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>2
[1,5,2,4,6,3,7]=>[1,4,6,3,2,5,7]=>1
[1,5,3,2,4,6,7]=>[1,3,5,4,2,6,7]=>1
[1,5,3,2,4,7,6]=>[1,3,5,4,2,7,6]=>2
[1,5,3,2,6,4,7]=>[1,3,6,4,2,5,7]=>1
[1,5,3,2,6,7,4]=>[1,3,7,4,2,5,6]=>1
[1,5,3,2,7,4,6]=>[1,3,7,6,4,2,5]=>1
[1,5,3,2,7,6,4]=>[1,3,6,7,4,2,5]=>1
[1,5,3,4,2,6,7]=>[1,3,4,5,2,6,7]=>1
[1,5,3,4,2,7,6]=>[1,3,4,5,2,7,6]=>2
[1,5,3,4,6,2,7]=>[1,3,4,6,2,5,7]=>1
[1,5,3,4,6,7,2]=>[1,3,4,7,2,5,6]=>1
[1,5,3,4,7,2,6]=>[1,3,4,7,6,2,5]=>1
[1,5,3,4,7,6,2]=>[1,3,4,6,7,2,5]=>1
[1,5,3,6,2,4,7]=>[1,3,5,2,6,4,7]=>2
[1,5,3,6,2,7,4]=>[1,3,5,2,7,4,6]=>2
[1,5,3,6,4,2,7]=>[1,3,6,2,5,4,7]=>1
[1,5,3,6,4,7,2]=>[1,3,7,2,5,4,6]=>1
[1,5,3,6,7,2,4]=>[1,3,7,4,6,2,5]=>1
[1,5,3,6,7,4,2]=>[1,3,6,4,7,2,5]=>2
[1,5,3,7,2,4,6]=>[1,3,5,2,7,6,4]=>2
[1,5,3,7,2,6,4]=>[1,3,5,2,6,7,4]=>2
[1,5,3,7,4,2,6]=>[1,3,7,6,2,5,4]=>1
[1,5,3,7,4,6,2]=>[1,3,6,7,2,5,4]=>1
[1,5,3,7,6,2,4]=>[1,3,6,2,5,7,4]=>2
[1,5,3,7,6,4,2]=>[1,3,7,2,5,6,4]=>1
[1,5,4,3,2,6,7]=>[1,4,3,5,2,6,7]=>2
[1,5,4,3,2,7,6]=>[1,4,3,5,2,7,6]=>3
[1,5,4,3,6,2,7]=>[1,4,3,6,2,5,7]=>2
[1,5,4,3,6,7,2]=>[1,4,3,7,2,5,6]=>2
[1,5,4,3,7,2,6]=>[1,4,3,7,6,2,5]=>2
[1,5,4,3,7,6,2]=>[1,4,3,6,7,2,5]=>2
[1,5,6,4,2,3,7]=>[1,4,5,2,6,3,7]=>2
[1,5,6,4,2,7,3]=>[1,4,5,2,7,3,6]=>2
[1,5,6,4,3,2,7]=>[1,4,6,2,5,3,7]=>1
[1,5,6,4,7,3,2]=>[1,4,6,3,7,2,5]=>2
[1,5,7,4,2,3,6]=>[1,4,5,2,7,6,3]=>2
[1,5,7,4,2,6,3]=>[1,4,5,2,6,7,3]=>2
[1,5,7,4,6,2,3]=>[1,4,6,2,5,7,3]=>2
[1,6,2,4,3,5,7]=>[1,4,6,5,3,2,7]=>1
[1,6,2,4,5,3,7]=>[1,4,5,6,3,2,7]=>1
[1,6,2,4,5,7,3]=>[1,4,5,7,3,2,6]=>1
[1,6,2,4,7,3,5]=>[1,4,6,3,2,7,5]=>2
[1,6,3,2,4,5,7]=>[1,3,6,5,4,2,7]=>1
[1,6,3,2,4,7,5]=>[1,3,7,5,4,2,6]=>1
[1,6,3,2,5,4,7]=>[1,3,5,6,4,2,7]=>1
[1,6,3,2,5,7,4]=>[1,3,5,7,4,2,6]=>1
[1,6,3,2,7,4,5]=>[1,3,6,4,2,7,5]=>2
[1,6,3,2,7,5,4]=>[1,3,7,4,2,6,5]=>1
[1,6,3,4,2,5,7]=>[1,3,4,6,5,2,7]=>1
[1,6,3,4,2,7,5]=>[1,3,4,7,5,2,6]=>1
[1,6,3,4,5,2,7]=>[1,3,4,5,6,2,7]=>1
[1,6,3,4,5,7,2]=>[1,3,4,5,7,2,6]=>1
[1,6,3,4,7,2,5]=>[1,3,4,6,2,7,5]=>2
[1,6,3,4,7,5,2]=>[1,3,4,7,2,6,5]=>1
[1,6,3,5,2,4,7]=>[1,3,6,4,5,2,7]=>1
[1,6,3,5,2,7,4]=>[1,3,7,4,5,2,6]=>1
[1,6,3,5,4,2,7]=>[1,3,5,4,6,2,7]=>2
[1,6,3,5,4,7,2]=>[1,3,5,4,7,2,6]=>2
[1,6,3,5,7,2,4]=>[1,3,6,2,7,4,5]=>2
[1,6,3,5,7,4,2]=>[1,3,7,2,6,4,5]=>1
[1,6,3,7,2,4,5]=>[1,3,7,5,2,6,4]=>1
[1,6,3,7,2,5,4]=>[1,3,6,5,2,7,4]=>2
[1,6,3,7,4,2,5]=>[1,3,6,2,7,5,4]=>2
[1,6,3,7,4,5,2]=>[1,3,7,2,6,5,4]=>1
[1,6,3,7,5,2,4]=>[1,3,5,6,2,7,4]=>2
[1,6,3,7,5,4,2]=>[1,3,5,7,2,6,4]=>1
[1,6,4,3,2,5,7]=>[1,4,3,6,5,2,7]=>2
[1,6,4,3,2,7,5]=>[1,4,3,7,5,2,6]=>2
[1,6,4,3,5,2,7]=>[1,4,3,5,6,2,7]=>2
[1,6,4,3,5,7,2]=>[1,4,3,5,7,2,6]=>2
[1,6,4,3,7,2,5]=>[1,4,3,6,2,7,5]=>3
[1,6,4,3,7,5,2]=>[1,4,3,7,2,6,5]=>2
[1,6,5,4,2,3,7]=>[1,4,6,3,5,2,7]=>1
[1,6,5,4,3,2,7]=>[1,4,5,3,6,2,7]=>2
[1,6,5,4,3,7,2]=>[1,4,5,3,7,2,6]=>2
[1,6,5,4,7,2,3]=>[1,4,6,2,7,3,5]=>2
[1,6,7,4,2,5,3]=>[1,4,6,5,2,7,3]=>2
[1,6,7,4,3,2,5]=>[1,4,6,2,7,5,3]=>2
[1,6,7,4,5,2,3]=>[1,4,5,6,2,7,3]=>2
[1,6,7,4,5,3,2]=>[1,4,5,7,2,6,3]=>1
[1,7,2,4,5,3,6]=>[1,4,5,7,6,3,2]=>1
[1,7,2,4,5,6,3]=>[1,4,5,6,7,3,2]=>1
[1,7,3,2,4,5,6]=>[1,3,7,6,5,4,2]=>1
[1,7,3,2,4,6,5]=>[1,3,6,7,5,4,2]=>1
[1,7,3,2,5,4,6]=>[1,3,5,7,6,4,2]=>1
[1,7,3,2,5,6,4]=>[1,3,5,6,7,4,2]=>1
[1,7,3,2,6,4,5]=>[1,3,7,5,6,4,2]=>1
[1,7,3,2,6,5,4]=>[1,3,6,5,7,4,2]=>2
[1,7,3,4,2,5,6]=>[1,3,4,7,6,5,2]=>1
[1,7,3,4,2,6,5]=>[1,3,4,6,7,5,2]=>1
[1,7,3,4,5,2,6]=>[1,3,4,5,7,6,2]=>1
[1,7,3,4,5,6,2]=>[1,3,4,5,6,7,2]=>1
[1,7,3,4,6,2,5]=>[1,3,4,7,5,6,2]=>1
[1,7,3,4,6,5,2]=>[1,3,4,6,5,7,2]=>2
[1,7,3,5,2,4,6]=>[1,3,7,6,4,5,2]=>1
[1,7,3,5,2,6,4]=>[1,3,6,7,4,5,2]=>1
[1,7,3,5,4,2,6]=>[1,3,5,4,7,6,2]=>2
[1,7,3,5,4,6,2]=>[1,3,5,4,6,7,2]=>2
[1,7,3,5,6,2,4]=>[1,3,7,4,5,6,2]=>1
[1,7,3,5,6,4,2]=>[1,3,6,4,5,7,2]=>2
[1,7,3,6,2,4,5]=>[1,3,6,4,7,5,2]=>2
[1,7,3,6,2,5,4]=>[1,3,7,4,6,5,2]=>1
[1,7,3,6,4,2,5]=>[1,3,7,5,4,6,2]=>1
[1,7,3,6,4,5,2]=>[1,3,6,5,4,7,2]=>2
[1,7,3,6,5,2,4]=>[1,3,5,7,4,6,2]=>1
[1,7,3,6,5,4,2]=>[1,3,5,6,4,7,2]=>2
[1,7,4,3,2,5,6]=>[1,4,3,7,6,5,2]=>2
[1,7,4,3,2,6,5]=>[1,4,3,6,7,5,2]=>2
[1,7,4,3,5,2,6]=>[1,4,3,5,7,6,2]=>2
[1,7,4,3,5,6,2]=>[1,4,3,5,6,7,2]=>2
[1,7,4,3,6,2,5]=>[1,4,3,7,5,6,2]=>2
[1,7,4,3,6,5,2]=>[1,4,3,6,5,7,2]=>3
[1,7,5,4,3,2,6]=>[1,4,5,3,7,6,2]=>2
[1,7,5,4,3,6,2]=>[1,4,5,3,6,7,2]=>2
[1,7,5,4,6,3,2]=>[1,4,6,3,5,7,2]=>2
[1,7,6,4,2,3,5]=>[1,4,6,3,7,5,2]=>2
[1,7,6,4,5,2,3]=>[1,4,5,7,3,6,2]=>1
[1,7,6,4,5,3,2]=>[1,4,5,6,3,7,2]=>2
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Description
The number of descents of type 2 in a permutation.
A position $i\in[1,n-1]$ is a descent of type 2 of a permutation $\pi$ of $n$ letters, if it is a descent and if $\pi(j) < \pi(i)$ for all $j < i$.
A position $i\in[1,n-1]$ is a descent of type 2 of a permutation $\pi$ of $n$ letters, if it is a descent and if $\pi(j) < \pi(i)$ for all $j < i$.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
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