Identifier
- St001760: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>0
[1,2,4,3]=>1
[1,3,2,4]=>3
[1,3,4,2]=>2
[1,4,2,3]=>2
[1,4,3,2]=>1
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>2
[2,3,4,1]=>2
[2,4,1,3]=>3
[2,4,3,1]=>2
[3,1,2,4]=>2
[3,1,4,2]=>3
[3,2,1,4]=>1
[3,2,4,1]=>2
[3,4,1,2]=>2
[3,4,2,1]=>2
[4,1,2,3]=>2
[4,1,3,2]=>2
[4,2,1,3]=>2
[4,2,3,1]=>3
[4,3,1,2]=>2
[4,3,2,1]=>1
[1,2,3,4,5]=>0
[1,2,3,5,4]=>1
[1,2,4,3,5]=>3
[1,2,4,5,3]=>2
[1,2,5,3,4]=>2
[1,2,5,4,3]=>1
[1,3,2,4,5]=>3
[1,3,2,5,4]=>3
[1,3,4,2,5]=>3
[1,3,4,5,2]=>2
[1,3,5,2,4]=>4
[1,3,5,4,2]=>3
[1,4,2,3,5]=>3
[1,4,2,5,3]=>4
[1,4,3,2,5]=>3
[1,4,3,5,2]=>3
[1,4,5,2,3]=>3
[1,4,5,3,2]=>2
[1,5,2,3,4]=>2
[1,5,2,4,3]=>3
[1,5,3,2,4]=>3
[1,5,3,4,2]=>3
[1,5,4,2,3]=>2
[1,5,4,3,2]=>1
[2,1,3,4,5]=>1
[2,1,3,5,4]=>2
[2,1,4,3,5]=>3
[2,1,4,5,3]=>3
[2,1,5,3,4]=>3
[2,1,5,4,3]=>2
[2,3,1,4,5]=>2
[2,3,1,5,4]=>3
[2,3,4,1,5]=>2
[2,3,4,5,1]=>2
[2,3,5,1,4]=>3
[2,3,5,4,1]=>3
[2,4,1,3,5]=>4
[2,4,1,5,3]=>4
[2,4,3,1,5]=>3
[2,4,3,5,1]=>4
[2,4,5,1,3]=>3
[2,4,5,3,1]=>3
[2,5,1,3,4]=>3
[2,5,1,4,3]=>3
[2,5,3,1,4]=>4
[2,5,3,4,1]=>4
[2,5,4,1,3]=>3
[2,5,4,3,1]=>2
[3,1,2,4,5]=>2
[3,1,2,5,4]=>3
[3,1,4,2,5]=>4
[3,1,4,5,2]=>3
[3,1,5,2,4]=>4
[3,1,5,4,2]=>3
[3,2,1,4,5]=>1
[3,2,1,5,4]=>2
[3,2,4,1,5]=>3
[3,2,4,5,1]=>3
[3,2,5,1,4]=>3
[3,2,5,4,1]=>2
[3,4,1,2,5]=>3
[3,4,1,5,2]=>3
[3,4,2,1,5]=>2
[3,4,2,5,1]=>3
[3,4,5,1,2]=>2
[3,4,5,2,1]=>2
[3,5,1,2,4]=>3
[3,5,1,4,2]=>4
[3,5,2,1,4]=>3
[3,5,2,4,1]=>4
[3,5,4,1,2]=>2
[3,5,4,2,1]=>3
[4,1,2,3,5]=>2
[4,1,2,5,3]=>3
[4,1,3,2,5]=>3
[4,1,3,5,2]=>4
[4,1,5,2,3]=>3
[4,1,5,3,2]=>3
[4,2,1,3,5]=>3
[4,2,1,5,3]=>3
[4,2,3,1,5]=>3
[4,2,3,5,1]=>4
[4,2,5,1,3]=>4
[4,2,5,3,1]=>4
[4,3,1,2,5]=>2
[4,3,1,5,2]=>3
[4,3,2,1,5]=>1
[4,3,2,5,1]=>2
[4,3,5,1,2]=>2
[4,3,5,2,1]=>3
[4,5,1,2,3]=>2
[4,5,1,3,2]=>2
[4,5,2,1,3]=>2
[4,5,2,3,1]=>3
[4,5,3,1,2]=>3
[4,5,3,2,1]=>2
[5,1,2,3,4]=>2
[5,1,2,4,3]=>3
[5,1,3,2,4]=>4
[5,1,3,4,2]=>4
[5,1,4,2,3]=>3
[5,1,4,3,2]=>2
[5,2,1,3,4]=>3
[5,2,1,4,3]=>2
[5,2,3,1,4]=>4
[5,2,3,4,1]=>3
[5,2,4,1,3]=>4
[5,2,4,3,1]=>3
[5,3,1,2,4]=>3
[5,3,1,4,2]=>4
[5,3,2,1,4]=>2
[5,3,2,4,1]=>3
[5,3,4,1,2]=>3
[5,3,4,2,1]=>4
[5,4,1,2,3]=>2
[5,4,1,3,2]=>3
[5,4,2,1,3]=>3
[5,4,2,3,1]=>4
[5,4,3,1,2]=>2
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>3
[1,2,3,5,6,4]=>2
[1,2,3,6,4,5]=>2
[1,2,3,6,5,4]=>1
[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>3
[1,2,4,5,3,6]=>3
[1,2,4,5,6,3]=>2
[1,2,4,6,3,5]=>4
[1,2,4,6,5,3]=>3
[1,2,5,3,4,6]=>3
[1,2,5,3,6,4]=>4
[1,2,5,4,3,6]=>3
[1,2,5,4,6,3]=>3
[1,2,5,6,3,4]=>3
[1,2,5,6,4,3]=>2
[1,2,6,3,4,5]=>2
[1,2,6,3,5,4]=>3
[1,2,6,4,3,5]=>3
[1,2,6,4,5,3]=>4
[1,2,6,5,3,4]=>2
[1,2,6,5,4,3]=>1
[1,3,2,4,5,6]=>3
[1,3,2,4,6,5]=>4
[1,3,2,5,4,6]=>4
[1,3,2,5,6,4]=>4
[1,3,2,6,4,5]=>4
[1,3,2,6,5,4]=>3
[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>2
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>3
[1,3,5,2,4,6]=>5
[1,3,5,2,6,4]=>5
[1,3,5,4,2,6]=>4
[1,3,5,4,6,2]=>5
[1,3,5,6,2,4]=>4
[1,3,5,6,4,2]=>4
[1,3,6,2,4,5]=>4
[1,3,6,2,5,4]=>4
[1,3,6,4,2,5]=>5
[1,3,6,4,5,2]=>4
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>3
[1,4,2,3,5,6]=>3
[1,4,2,3,6,5]=>3
[1,4,2,5,3,6]=>5
[1,4,2,5,6,3]=>4
[1,4,2,6,3,5]=>5
[1,4,2,6,5,3]=>4
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>4
[1,4,3,5,2,6]=>4
[1,4,3,5,6,2]=>3
[1,4,3,6,2,5]=>5
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>3
[1,4,5,2,6,3]=>4
[1,4,5,3,2,6]=>4
[1,4,5,3,6,2]=>4
[1,4,5,6,2,3]=>3
[1,4,5,6,3,2]=>2
[1,4,6,2,3,5]=>4
[1,4,6,2,5,3]=>5
[1,4,6,3,2,5]=>4
[1,4,6,3,5,2]=>5
[1,4,6,5,2,3]=>4
[1,4,6,5,3,2]=>3
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>4
[1,5,2,4,3,6]=>4
[1,5,2,4,6,3]=>5
[1,5,2,6,3,4]=>4
[1,5,2,6,4,3]=>4
[1,5,3,2,4,6]=>4
[1,5,3,2,6,4]=>5
[1,5,3,4,2,6]=>5
[1,5,3,4,6,2]=>4
[1,5,3,6,2,4]=>5
[1,5,3,6,4,2]=>5
[1,5,4,2,3,6]=>4
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>3
[1,5,4,6,2,3]=>4
[1,5,4,6,3,2]=>3
[1,5,6,2,3,4]=>3
[1,5,6,2,4,3]=>4
[1,5,6,3,2,4]=>4
[1,5,6,3,4,2]=>3
[1,5,6,4,2,3]=>3
[1,5,6,4,3,2]=>2
[1,6,2,3,4,5]=>2
[1,6,2,3,5,4]=>3
[1,6,2,4,3,5]=>5
[1,6,2,4,5,3]=>4
[1,6,2,5,3,4]=>4
[1,6,2,5,4,3]=>3
[1,6,3,2,4,5]=>3
[1,6,3,2,5,4]=>4
[1,6,3,4,2,5]=>4
[1,6,3,4,5,2]=>3
[1,6,3,5,2,4]=>5
[1,6,3,5,4,2]=>4
[1,6,4,2,3,5]=>4
[1,6,4,2,5,3]=>5
[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>4
[1,6,4,5,2,3]=>3
[1,6,4,5,3,2]=>4
[1,6,5,2,3,4]=>2
[1,6,5,2,4,3]=>3
[1,6,5,3,2,4]=>3
[1,6,5,3,4,2]=>4
[1,6,5,4,2,3]=>2
[1,6,5,4,3,2]=>1
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>4
[2,1,3,5,6,4]=>3
[2,1,3,6,4,5]=>3
[2,1,3,6,5,4]=>2
[2,1,4,3,5,6]=>3
[2,1,4,3,6,5]=>4
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>3
[2,1,4,6,3,5]=>4
[2,1,4,6,5,3]=>4
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>4
[2,1,5,4,3,6]=>4
[2,1,5,4,6,3]=>4
[2,1,5,6,3,4]=>3
[2,1,5,6,4,3]=>3
[2,1,6,3,4,5]=>3
[2,1,6,3,5,4]=>4
[2,1,6,4,3,5]=>4
[2,1,6,4,5,3]=>3
[2,1,6,5,3,4]=>3
[2,1,6,5,4,3]=>2
[2,3,1,4,5,6]=>2
[2,3,1,4,6,5]=>3
[2,3,1,5,4,6]=>4
[2,3,1,5,6,4]=>4
[2,3,1,6,4,5]=>4
[2,3,1,6,5,4]=>3
[2,3,4,1,5,6]=>2
[2,3,4,1,6,5]=>3
[2,3,4,5,1,6]=>2
[2,3,4,5,6,1]=>2
[2,3,4,6,1,5]=>3
[2,3,4,6,5,1]=>3
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>4
[2,3,5,4,1,6]=>3
[2,3,5,4,6,1]=>4
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>4
[2,3,6,1,4,5]=>4
[2,3,6,1,5,4]=>3
[2,3,6,4,1,5]=>4
[2,3,6,4,5,1]=>4
[2,3,6,5,1,4]=>3
[2,3,6,5,4,1]=>3
[2,4,1,3,5,6]=>4
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>5
[2,4,1,5,6,3]=>4
[2,4,1,6,3,5]=>5
[2,4,1,6,5,3]=>4
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>5
[2,4,3,5,6,1]=>4
[2,4,3,6,1,5]=>5
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>4
[2,4,5,1,6,3]=>4
[2,4,5,3,1,6]=>4
[2,4,5,3,6,1]=>5
[2,4,5,6,1,3]=>3
[2,4,5,6,3,1]=>3
[2,4,6,1,3,5]=>5
[2,4,6,1,5,3]=>5
[2,4,6,3,1,5]=>5
[2,4,6,3,5,1]=>5
[2,4,6,5,1,3]=>4
[2,4,6,5,3,1]=>4
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>5
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>5
[2,5,1,6,3,4]=>4
[2,5,1,6,4,3]=>4
[2,5,3,1,4,6]=>5
[2,5,3,1,6,4]=>5
[2,5,3,4,1,6]=>4
[2,5,3,4,6,1]=>5
[2,5,3,6,1,4]=>5
[2,5,3,6,4,1]=>5
[2,5,4,1,3,6]=>4
[2,5,4,1,6,3]=>5
[2,5,4,3,1,6]=>3
[2,5,4,3,6,1]=>4
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>4
[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>4
[2,5,6,3,1,4]=>4
[2,5,6,3,4,1]=>4
[2,5,6,4,1,3]=>4
[2,5,6,4,3,1]=>3
[2,6,1,3,4,5]=>3
[2,6,1,3,5,4]=>4
[2,6,1,4,3,5]=>5
[2,6,1,4,5,3]=>4
[2,6,1,5,3,4]=>4
[2,6,1,5,4,3]=>3
[2,6,3,1,4,5]=>4
[2,6,3,1,5,4]=>4
[2,6,3,4,1,5]=>4
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>5
[2,6,3,5,4,1]=>4
[2,6,4,1,3,5]=>5
[2,6,4,1,5,3]=>5
[2,6,4,3,1,5]=>4
[2,6,4,3,5,1]=>4
[2,6,4,5,1,3]=>4
[2,6,4,5,3,1]=>5
[2,6,5,1,3,4]=>3
[2,6,5,1,4,3]=>3
[2,6,5,3,1,4]=>4
[2,6,5,3,4,1]=>4
[2,6,5,4,1,3]=>3
[2,6,5,4,3,1]=>2
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>4
[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>4
[3,1,2,6,5,4]=>3
[3,1,4,2,5,6]=>4
[3,1,4,2,6,5]=>4
[3,1,4,5,2,6]=>4
[3,1,4,5,6,2]=>3
[3,1,4,6,2,5]=>5
[3,1,4,6,5,2]=>4
[3,1,5,2,4,6]=>5
[3,1,5,2,6,4]=>5
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>5
[3,1,5,6,2,4]=>4
[3,1,5,6,4,2]=>4
[3,1,6,2,4,5]=>4
[3,1,6,2,5,4]=>4
[3,1,6,4,2,5]=>5
[3,1,6,4,5,2]=>4
[3,1,6,5,2,4]=>4
[3,1,6,5,4,2]=>3
[3,2,1,4,5,6]=>1
[3,2,1,4,6,5]=>2
[3,2,1,5,4,6]=>3
[3,2,1,5,6,4]=>3
[3,2,1,6,4,5]=>3
[3,2,1,6,5,4]=>2
[3,2,4,1,5,6]=>3
[3,2,4,1,6,5]=>4
[3,2,4,5,1,6]=>3
[3,2,4,5,6,1]=>3
[3,2,4,6,1,5]=>4
[3,2,4,6,5,1]=>4
[3,2,5,1,4,6]=>4
[3,2,5,1,6,4]=>4
[3,2,5,4,1,6]=>4
[3,2,5,4,6,1]=>4
[3,2,5,6,1,4]=>3
[3,2,5,6,4,1]=>3
[3,2,6,1,4,5]=>3
[3,2,6,1,5,4]=>4
[3,2,6,4,1,5]=>4
[3,2,6,4,5,1]=>4
[3,2,6,5,1,4]=>3
[3,2,6,5,4,1]=>2
[3,4,1,2,5,6]=>3
[3,4,1,2,6,5]=>3
[3,4,1,5,2,6]=>4
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>4
[3,4,1,6,5,2]=>3
[3,4,2,1,5,6]=>2
[3,4,2,1,6,5]=>3
[3,4,2,5,1,6]=>4
[3,4,2,5,6,1]=>4
[3,4,2,6,1,5]=>4
[3,4,2,6,5,1]=>3
[3,4,5,1,2,6]=>3
[3,4,5,1,6,2]=>3
[3,4,5,2,1,6]=>2
[3,4,5,2,6,1]=>3
[3,4,5,6,1,2]=>2
[3,4,5,6,2,1]=>2
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>4
[3,4,6,2,1,5]=>3
[3,4,6,2,5,1]=>4
[3,4,6,5,1,2]=>3
[3,4,6,5,2,1]=>3
[3,5,1,2,4,6]=>4
[3,5,1,2,6,4]=>4
[3,5,1,4,2,6]=>5
[3,5,1,4,6,2]=>5
[3,5,1,6,2,4]=>5
[3,5,1,6,4,2]=>5
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>4
[3,5,2,4,1,6]=>5
[3,5,2,4,6,1]=>5
[3,5,2,6,1,4]=>5
[3,5,2,6,4,1]=>5
[3,5,4,1,2,6]=>4
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>3
[3,5,4,2,6,1]=>4
[3,5,4,6,1,2]=>4
[3,5,4,6,2,1]=>5
[3,5,6,1,2,4]=>4
[3,5,6,1,4,2]=>4
[3,5,6,2,1,4]=>3
[3,5,6,2,4,1]=>4
[3,5,6,4,1,2]=>3
[3,5,6,4,2,1]=>4
[3,6,1,2,4,5]=>4
[3,6,1,2,5,4]=>3
[3,6,1,4,2,5]=>5
[3,6,1,4,5,2]=>4
[3,6,1,5,2,4]=>5
[3,6,1,5,4,2]=>4
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>3
[3,6,2,4,1,5]=>5
[3,6,2,4,5,1]=>4
[3,6,2,5,1,4]=>5
[3,6,2,5,4,1]=>4
[3,6,4,1,2,5]=>4
[3,6,4,1,5,2]=>5
[3,6,4,2,1,5]=>4
[3,6,4,2,5,1]=>5
[3,6,4,5,1,2]=>4
[3,6,4,5,2,1]=>4
[3,6,5,1,2,4]=>3
[3,6,5,1,4,2]=>4
[3,6,5,2,1,4]=>3
[3,6,5,2,4,1]=>4
[3,6,5,4,1,2]=>2
[3,6,5,4,2,1]=>3
[4,1,2,3,5,6]=>2
[4,1,2,3,6,5]=>3
[4,1,2,5,3,6]=>4
[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>4
[4,1,2,6,5,3]=>3
[4,1,3,2,5,6]=>3
[4,1,3,2,6,5]=>4
[4,1,3,5,2,6]=>5
[4,1,3,5,6,2]=>4
[4,1,3,6,2,5]=>5
[4,1,3,6,5,2]=>4
[4,1,5,2,3,6]=>4
[4,1,5,2,6,3]=>5
[4,1,5,3,2,6]=>4
[4,1,5,3,6,2]=>5
[4,1,5,6,2,3]=>3
[4,1,5,6,3,2]=>3
[4,1,6,2,3,5]=>4
[4,1,6,2,5,3]=>5
[4,1,6,3,2,5]=>5
[4,1,6,3,5,2]=>5
[4,1,6,5,2,3]=>4
[4,1,6,5,3,2]=>3
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>4
[4,2,1,5,3,6]=>4
[4,2,1,5,6,3]=>3
[4,2,1,6,3,5]=>4
[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>4
[4,2,3,1,6,5]=>3
[4,2,3,5,1,6]=>4
[4,2,3,5,6,1]=>4
[4,2,3,6,1,5]=>4
[4,2,3,6,5,1]=>4
[4,2,5,1,3,6]=>5
[4,2,5,1,6,3]=>5
[4,2,5,3,1,6]=>5
[4,2,5,3,6,1]=>5
[4,2,5,6,1,3]=>4
[4,2,5,6,3,1]=>4
[4,2,6,1,3,5]=>5
[4,2,6,1,5,3]=>5
[4,2,6,3,1,5]=>5
[4,2,6,3,5,1]=>5
[4,2,6,5,1,3]=>4
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>2
[4,3,1,2,6,5]=>3
[4,3,1,5,2,6]=>4
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>4
[4,3,1,6,5,2]=>3
[4,3,2,1,5,6]=>1
[4,3,2,1,6,5]=>2
[4,3,2,5,1,6]=>3
[4,3,2,5,6,1]=>3
[4,3,2,6,1,5]=>3
[4,3,2,6,5,1]=>2
[4,3,5,1,2,6]=>4
[4,3,5,1,6,2]=>4
[4,3,5,2,1,6]=>3
[4,3,5,2,6,1]=>4
[4,3,5,6,1,2]=>3
[4,3,5,6,2,1]=>3
[4,3,6,1,2,5]=>4
[4,3,6,1,5,2]=>4
[4,3,6,2,1,5]=>3
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>2
[4,3,6,5,2,1]=>3
[4,5,1,2,3,6]=>3
[4,5,1,2,6,3]=>3
[4,5,1,3,2,6]=>4
[4,5,1,3,6,2]=>4
[4,5,1,6,2,3]=>4
[4,5,1,6,3,2]=>3
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>4
[4,5,2,3,1,6]=>3
[4,5,2,3,6,1]=>4
[4,5,2,6,1,3]=>4
[4,5,2,6,3,1]=>4
[4,5,3,1,2,6]=>3
[4,5,3,1,6,2]=>4
[4,5,3,2,1,6]=>2
[4,5,3,2,6,1]=>3
[4,5,3,6,1,2]=>3
[4,5,3,6,2,1]=>4
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>2
[4,5,6,2,1,3]=>2
[4,5,6,2,3,1]=>3
[4,5,6,3,1,2]=>3
[4,5,6,3,2,1]=>2
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>4
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>5
[4,6,1,5,2,3]=>4
[4,6,1,5,3,2]=>4
[4,6,2,1,3,5]=>4
[4,6,2,1,5,3]=>4
[4,6,2,3,1,5]=>4
[4,6,2,3,5,1]=>5
[4,6,2,5,1,3]=>5
[4,6,2,5,3,1]=>5
[4,6,3,1,2,5]=>4
[4,6,3,1,5,2]=>5
[4,6,3,2,1,5]=>3
[4,6,3,2,5,1]=>4
[4,6,3,5,1,2]=>4
[4,6,3,5,2,1]=>5
[4,6,5,1,2,3]=>2
[4,6,5,1,3,2]=>3
[4,6,5,2,1,3]=>3
[4,6,5,2,3,1]=>4
[4,6,5,3,1,2]=>4
[4,6,5,3,2,1]=>3
[5,1,2,3,4,6]=>2
[5,1,2,3,6,4]=>3
[5,1,2,4,3,6]=>3
[5,1,2,4,6,3]=>4
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>3
[5,1,3,2,4,6]=>5
[5,1,3,2,6,4]=>5
[5,1,3,4,2,6]=>4
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>5
[5,1,3,6,4,2]=>5
[5,1,4,2,3,6]=>4
[5,1,4,2,6,3]=>5
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>4
[5,1,4,6,2,3]=>4
[5,1,4,6,3,2]=>4
[5,1,6,2,3,4]=>3
[5,1,6,2,4,3]=>4
[5,1,6,3,2,4]=>4
[5,1,6,3,4,2]=>4
[5,1,6,4,2,3]=>4
[5,1,6,4,3,2]=>3
[5,2,1,3,4,6]=>3
[5,2,1,3,6,4]=>4
[5,2,1,4,3,6]=>4
[5,2,1,4,6,3]=>4
[5,2,1,6,3,4]=>3
[5,2,1,6,4,3]=>3
[5,2,3,1,4,6]=>4
[5,2,3,1,6,4]=>4
[5,2,3,4,1,6]=>3
[5,2,3,4,6,1]=>4
[5,2,3,6,1,4]=>4
[5,2,3,6,4,1]=>4
[5,2,4,1,3,6]=>5
[5,2,4,1,6,3]=>5
[5,2,4,3,1,6]=>4
[5,2,4,3,6,1]=>4
[5,2,4,6,1,3]=>5
[5,2,4,6,3,1]=>5
[5,2,6,1,3,4]=>4
[5,2,6,1,4,3]=>4
[5,2,6,3,1,4]=>5
[5,2,6,3,4,1]=>5
[5,2,6,4,1,3]=>5
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>4
[5,3,1,4,2,6]=>5
[5,3,1,4,6,2]=>5
[5,3,1,6,2,4]=>5
[5,3,1,6,4,2]=>5
[5,3,2,1,4,6]=>3
[5,3,2,1,6,4]=>3
[5,3,2,4,1,6]=>4
[5,3,2,4,6,1]=>4
[5,3,2,6,1,4]=>4
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>3
[5,3,4,1,6,2]=>4
[5,3,4,2,1,6]=>4
[5,3,4,2,6,1]=>5
[5,3,4,6,1,2]=>4
[5,3,4,6,2,1]=>4
[5,3,6,1,2,4]=>4
[5,3,6,1,4,2]=>5
[5,3,6,2,1,4]=>4
[5,3,6,2,4,1]=>5
[5,3,6,4,1,2]=>4
[5,3,6,4,2,1]=>5
[5,4,1,2,3,6]=>2
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>3
[5,4,1,3,6,2]=>4
[5,4,1,6,2,3]=>3
[5,4,1,6,3,2]=>3
[5,4,2,1,3,6]=>3
[5,4,2,1,6,3]=>3
[5,4,2,3,1,6]=>4
[5,4,2,3,6,1]=>4
[5,4,2,6,1,3]=>4
[5,4,2,6,3,1]=>4
[5,4,3,1,2,6]=>2
[5,4,3,1,6,2]=>3
[5,4,3,2,1,6]=>1
[5,4,3,2,6,1]=>2
[5,4,3,6,1,2]=>2
[5,4,3,6,2,1]=>3
[5,4,6,1,2,3]=>2
[5,4,6,1,3,2]=>3
[5,4,6,2,1,3]=>3
[5,4,6,2,3,1]=>4
[5,4,6,3,1,2]=>4
[5,4,6,3,2,1]=>3
[5,6,1,2,3,4]=>2
[5,6,1,2,4,3]=>3
[5,6,1,3,2,4]=>4
[5,6,1,3,4,2]=>4
[5,6,1,4,2,3]=>3
[5,6,1,4,3,2]=>2
[5,6,2,1,3,4]=>3
[5,6,2,1,4,3]=>2
[5,6,2,3,1,4]=>4
[5,6,2,3,4,1]=>3
[5,6,2,4,1,3]=>4
[5,6,2,4,3,1]=>3
[5,6,3,1,2,4]=>3
[5,6,3,1,4,2]=>4
[5,6,3,2,1,4]=>2
[5,6,3,2,4,1]=>3
[5,6,3,4,1,2]=>3
[5,6,3,4,2,1]=>4
[5,6,4,1,2,3]=>3
[5,6,4,1,3,2]=>4
[5,6,4,2,1,3]=>4
[5,6,4,2,3,1]=>5
[5,6,4,3,1,2]=>3
[5,6,4,3,2,1]=>2
[6,1,2,3,4,5]=>2
[6,1,2,3,5,4]=>3
[6,1,2,4,3,5]=>4
[6,1,2,4,5,3]=>4
[6,1,2,5,3,4]=>4
[6,1,2,5,4,3]=>3
[6,1,3,2,4,5]=>4
[6,1,3,2,5,4]=>4
[6,1,3,4,2,5]=>5
[6,1,3,4,5,2]=>4
[6,1,3,5,2,4]=>5
[6,1,3,5,4,2]=>4
[6,1,4,2,3,5]=>5
[6,1,4,2,5,3]=>5
[6,1,4,3,2,5]=>4
[6,1,4,3,5,2]=>4
[6,1,4,5,2,3]=>4
[6,1,4,5,3,2]=>4
[6,1,5,2,3,4]=>3
[6,1,5,2,4,3]=>4
[6,1,5,3,2,4]=>4
[6,1,5,3,4,2]=>5
[6,1,5,4,2,3]=>3
[6,1,5,4,3,2]=>2
[6,2,1,3,4,5]=>3
[6,2,1,3,5,4]=>4
[6,2,1,4,3,5]=>4
[6,2,1,4,5,3]=>4
[6,2,1,5,3,4]=>3
[6,2,1,5,4,3]=>2
[6,2,3,1,4,5]=>4
[6,2,3,1,5,4]=>4
[6,2,3,4,1,5]=>4
[6,2,3,4,5,1]=>3
[6,2,3,5,1,4]=>4
[6,2,3,5,4,1]=>3
[6,2,4,1,3,5]=>5
[6,2,4,1,5,3]=>5
[6,2,4,3,1,5]=>4
[6,2,4,3,5,1]=>4
[6,2,4,5,1,3]=>5
[6,2,4,5,3,1]=>5
[6,2,5,1,3,4]=>4
[6,2,5,1,4,3]=>4
[6,2,5,3,1,4]=>5
[6,2,5,3,4,1]=>5
[6,2,5,4,1,3]=>4
[6,2,5,4,3,1]=>3
[6,3,1,2,4,5]=>4
[6,3,1,2,5,4]=>3
[6,3,1,4,2,5]=>5
[6,3,1,4,5,2]=>4
[6,3,1,5,2,4]=>5
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>2
[6,3,2,4,1,5]=>4
[6,3,2,4,5,1]=>3
[6,3,2,5,1,4]=>4
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>4
[6,3,4,1,5,2]=>5
[6,3,4,2,1,5]=>4
[6,3,4,2,5,1]=>5
[6,3,4,5,1,2]=>3
[6,3,4,5,2,1]=>4
[6,3,5,1,2,4]=>4
[6,3,5,1,4,2]=>5
[6,3,5,2,1,4]=>4
[6,3,5,2,4,1]=>5
[6,3,5,4,1,2]=>3
[6,3,5,4,2,1]=>4
[6,4,1,2,3,5]=>3
[6,4,1,2,5,3]=>4
[6,4,1,3,2,5]=>4
[6,4,1,3,5,2]=>5
[6,4,1,5,2,3]=>4
[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>4
[6,4,2,1,5,3]=>4
[6,4,2,3,1,5]=>5
[6,4,2,3,5,1]=>5
[6,4,2,5,1,3]=>5
[6,4,2,5,3,1]=>5
[6,4,3,1,2,5]=>3
[6,4,3,1,5,2]=>4
[6,4,3,2,1,5]=>2
[6,4,3,2,5,1]=>3
[6,4,3,5,1,2]=>3
[6,4,3,5,2,1]=>4
[6,4,5,1,2,3]=>3
[6,4,5,1,3,2]=>4
[6,4,5,2,1,3]=>4
[6,4,5,2,3,1]=>5
[6,4,5,3,1,2]=>5
[6,4,5,3,2,1]=>4
[6,5,1,2,3,4]=>2
[6,5,1,2,4,3]=>3
[6,5,1,3,2,4]=>5
[6,5,1,3,4,2]=>4
[6,5,1,4,2,3]=>4
[6,5,1,4,3,2]=>3
[6,5,2,1,3,4]=>3
[6,5,2,1,4,3]=>3
[6,5,2,3,1,4]=>4
[6,5,2,3,4,1]=>4
[6,5,2,4,1,3]=>5
[6,5,2,4,3,1]=>4
[6,5,3,1,2,4]=>4
[6,5,3,1,4,2]=>5
[6,5,3,2,1,4]=>3
[6,5,3,2,4,1]=>4
[6,5,3,4,1,2]=>4
[6,5,3,4,2,1]=>4
[6,5,4,1,2,3]=>2
[6,5,4,1,3,2]=>3
[6,5,4,2,1,3]=>3
[6,5,4,2,3,1]=>4
[6,5,4,3,1,2]=>2
[6,5,4,3,2,1]=>1
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>1
[1,2,3,4,6,5,7]=>3
[1,2,3,4,6,7,5]=>2
[1,2,3,4,7,5,6]=>2
[1,2,3,4,7,6,5]=>1
[1,2,3,5,4,6,7]=>3
[1,2,3,5,4,7,6]=>3
[1,2,3,5,6,4,7]=>3
[1,2,3,5,6,7,4]=>2
[1,2,3,5,7,4,6]=>4
[1,2,3,5,7,6,4]=>3
[1,2,3,6,4,5,7]=>3
[1,2,3,6,4,7,5]=>4
[1,2,3,6,5,4,7]=>3
[1,2,3,6,5,7,4]=>3
[1,2,3,6,7,4,5]=>3
[1,2,3,6,7,5,4]=>2
[1,2,3,7,4,5,6]=>2
[1,2,3,7,4,6,5]=>3
[1,2,3,7,5,4,6]=>3
[1,2,3,7,5,6,4]=>4
[1,2,3,7,6,4,5]=>2
[1,2,3,7,6,5,4]=>1
[1,2,4,3,5,6,7]=>3
[1,2,4,3,5,7,6]=>4
[1,2,4,3,6,5,7]=>5
[1,2,4,3,6,7,5]=>4
[1,2,4,3,7,5,6]=>4
[1,2,4,3,7,6,5]=>3
[1,2,4,5,3,6,7]=>4
[1,2,4,5,3,7,6]=>3
[1,2,4,5,6,3,7]=>3
[1,2,4,5,6,7,3]=>2
[1,2,4,5,7,3,6]=>4
[1,2,4,5,7,6,3]=>3
[1,2,4,6,3,5,7]=>5
[1,2,4,6,3,7,5]=>5
[1,2,4,6,5,3,7]=>5
[1,2,4,6,5,7,3]=>5
[1,2,4,6,7,3,5]=>4
[1,2,4,6,7,5,3]=>4
[1,2,4,7,3,5,6]=>4
[1,2,4,7,3,6,5]=>4
[1,2,4,7,5,3,6]=>5
[1,2,4,7,5,6,3]=>4
[1,2,4,7,6,3,5]=>4
[1,2,4,7,6,5,3]=>3
[1,2,5,3,4,6,7]=>4
[1,2,5,3,4,7,6]=>3
[1,2,5,3,6,4,7]=>5
[1,2,5,3,6,7,4]=>4
[1,2,5,3,7,4,6]=>5
[1,2,5,3,7,6,4]=>4
[1,2,5,4,3,6,7]=>3
[1,2,5,4,3,7,6]=>4
[1,2,5,4,6,3,7]=>4
[1,2,5,4,6,7,3]=>3
[1,2,5,4,7,3,6]=>5
[1,2,5,4,7,6,3]=>4
[1,2,5,6,3,4,7]=>3
[1,2,5,6,3,7,4]=>4
[1,2,5,6,4,3,7]=>4
[1,2,5,6,4,7,3]=>4
[1,2,5,6,7,3,4]=>3
[1,2,5,6,7,4,3]=>2
[1,2,5,7,3,4,6]=>4
[1,2,5,7,3,6,4]=>5
[1,2,5,7,4,3,6]=>4
[1,2,5,7,4,6,3]=>5
[1,2,5,7,6,3,4]=>4
[1,2,5,7,6,4,3]=>3
[1,2,6,3,4,5,7]=>3
[1,2,6,3,4,7,5]=>4
[1,2,6,3,5,4,7]=>5
[1,2,6,3,5,7,4]=>5
[1,2,6,3,7,4,5]=>4
[1,2,6,3,7,5,4]=>4
[1,2,6,4,3,5,7]=>4
[1,2,6,4,3,7,5]=>5
[1,2,6,4,5,3,7]=>5
[1,2,6,4,5,7,3]=>4
[1,2,6,4,7,3,5]=>5
[1,2,6,4,7,5,3]=>5
[1,2,6,5,3,4,7]=>4
[1,2,6,5,3,7,4]=>4
[1,2,6,5,4,3,7]=>3
[1,2,6,5,4,7,3]=>3
[1,2,6,5,7,3,4]=>4
[1,2,6,5,7,4,3]=>3
[1,2,6,7,3,4,5]=>3
[1,2,6,7,3,5,4]=>4
[1,2,6,7,4,3,5]=>4
[1,2,6,7,4,5,3]=>4
[1,2,6,7,5,3,4]=>3
[1,2,6,7,5,4,3]=>2
[1,2,7,3,4,5,6]=>2
[1,2,7,3,4,6,5]=>3
[1,2,7,3,5,4,6]=>5
[1,2,7,3,5,6,4]=>4
[1,2,7,3,6,4,5]=>4
[1,2,7,3,6,5,4]=>3
[1,2,7,4,3,5,6]=>3
[1,2,7,4,3,6,5]=>4
[1,2,7,4,5,3,6]=>4
[1,2,7,4,5,6,3]=>4
[1,2,7,4,6,3,5]=>5
[1,2,7,4,6,5,3]=>4
[1,2,7,5,3,4,6]=>4
[1,2,7,5,3,6,4]=>5
[1,2,7,5,4,3,6]=>3
[1,2,7,5,4,6,3]=>4
[1,2,7,5,6,3,4]=>4
[1,2,7,5,6,4,3]=>4
[1,2,7,6,3,4,5]=>2
[1,2,7,6,3,5,4]=>3
[1,2,7,6,4,3,5]=>3
[1,2,7,6,4,5,3]=>4
[1,2,7,6,5,3,4]=>2
[1,2,7,6,5,4,3]=>1
[1,3,2,4,5,6,7]=>3
[1,3,2,4,5,7,6]=>4
[1,3,2,4,6,5,7]=>6
[1,3,2,4,6,7,5]=>5
[1,3,2,4,7,5,6]=>5
[1,3,2,4,7,6,5]=>4
[1,3,2,5,4,6,7]=>5
[1,3,2,5,4,7,6]=>4
[1,3,2,5,6,4,7]=>5
[1,3,2,5,6,7,4]=>4
[1,3,2,5,7,4,6]=>6
[1,3,2,5,7,6,4]=>5
[1,3,2,6,4,5,7]=>5
[1,3,2,6,4,7,5]=>6
[1,3,2,6,5,4,7]=>4
[1,3,2,6,5,7,4]=>5
[1,3,2,6,7,4,5]=>5
[1,3,2,6,7,5,4]=>4
[1,3,2,7,4,5,6]=>4
[1,3,2,7,4,6,5]=>5
[1,3,2,7,5,4,6]=>5
[1,3,2,7,5,6,4]=>5
[1,3,2,7,6,4,5]=>4
[1,3,2,7,6,5,4]=>3
[1,3,4,2,5,6,7]=>3
[1,3,4,2,5,7,6]=>4
[1,3,4,2,6,5,7]=>5
[1,3,4,2,6,7,5]=>4
[1,3,4,2,7,5,6]=>4
[1,3,4,2,7,6,5]=>3
[1,3,4,5,2,6,7]=>3
[1,3,4,5,2,7,6]=>3
[1,3,4,5,6,2,7]=>3
[1,3,4,5,6,7,2]=>2
[1,3,4,5,7,2,6]=>4
[1,3,4,5,7,6,2]=>3
[1,3,4,6,2,5,7]=>5
[1,3,4,6,2,7,5]=>5
[1,3,4,6,5,2,7]=>4
[1,3,4,6,5,7,2]=>5
[1,3,4,6,7,2,5]=>4
[1,3,4,6,7,5,2]=>4
[1,3,4,7,2,5,6]=>4
[1,3,4,7,2,6,5]=>4
[1,3,4,7,5,2,6]=>5
[1,3,4,7,5,6,2]=>4
[1,3,4,7,6,2,5]=>4
[1,3,4,7,6,5,2]=>3
[1,3,5,2,4,6,7]=>5
[1,3,5,2,4,7,6]=>5
[1,3,5,2,6,4,7]=>6
[1,3,5,2,6,7,4]=>5
[1,3,5,2,7,4,6]=>6
[1,3,5,2,7,6,4]=>5
[1,3,5,4,2,6,7]=>4
[1,3,5,4,2,7,6]=>4
[1,3,5,4,6,2,7]=>6
[1,3,5,4,6,7,2]=>5
[1,3,5,4,7,2,6]=>6
[1,3,5,4,7,6,2]=>5
[1,3,5,6,2,4,7]=>5
[1,3,5,6,2,7,4]=>5
[1,3,5,6,4,2,7]=>5
[1,3,5,6,4,7,2]=>5
[1,3,5,6,7,2,4]=>4
[1,3,5,6,7,4,2]=>4
[1,3,5,7,2,4,6]=>6
[1,3,5,7,2,6,4]=>6
[1,3,5,7,4,2,6]=>6
[1,3,5,7,4,6,2]=>6
[1,3,5,7,6,2,4]=>5
[1,3,5,7,6,4,2]=>5
[1,3,6,2,4,5,7]=>5
[1,3,6,2,4,7,5]=>6
[1,3,6,2,5,4,7]=>6
[1,3,6,2,5,7,4]=>6
[1,3,6,2,7,4,5]=>5
[1,3,6,2,7,5,4]=>5
[1,3,6,4,2,5,7]=>6
[1,3,6,4,2,7,5]=>6
[1,3,6,4,5,2,7]=>5
[1,3,6,4,5,7,2]=>5
[1,3,6,4,7,2,5]=>6
[1,3,6,4,7,5,2]=>6
[1,3,6,5,2,4,7]=>6
[1,3,6,5,2,7,4]=>5
[1,3,6,5,4,2,7]=>4
[1,3,6,5,4,7,2]=>5
[1,3,6,5,7,2,4]=>5
[1,3,6,5,7,4,2]=>5
[1,3,6,7,2,4,5]=>5
[1,3,6,7,2,5,4]=>4
[1,3,6,7,4,2,5]=>5
[1,3,6,7,4,5,2]=>5
[1,3,6,7,5,2,4]=>5
[1,3,6,7,5,4,2]=>4
[1,3,7,2,4,5,6]=>4
[1,3,7,2,4,6,5]=>5
[1,3,7,2,5,4,6]=>5
[1,3,7,2,5,6,4]=>5
[1,3,7,2,6,4,5]=>5
[1,3,7,2,6,5,4]=>4
[1,3,7,4,2,5,6]=>5
[1,3,7,4,2,6,5]=>5
[1,3,7,4,5,2,6]=>5
[1,3,7,4,5,6,2]=>4
[1,3,7,4,6,2,5]=>6
[1,3,7,4,6,5,2]=>5
[1,3,7,5,2,4,6]=>6
[1,3,7,5,2,6,4]=>6
[1,3,7,5,4,2,6]=>5
[1,3,7,5,4,6,2]=>5
[1,3,7,5,6,2,4]=>5
[1,3,7,5,6,4,2]=>6
[1,3,7,6,2,4,5]=>4
[1,3,7,6,2,5,4]=>4
[1,3,7,6,4,2,5]=>5
[1,3,7,6,4,5,2]=>4
[1,3,7,6,5,2,4]=>4
[1,3,7,6,5,4,2]=>3
[1,4,2,3,5,6,7]=>3
[1,4,2,3,5,7,6]=>4
[1,4,2,3,6,5,7]=>5
[1,4,2,3,6,7,5]=>4
[1,4,2,3,7,5,6]=>4
[1,4,2,3,7,6,5]=>3
[1,4,2,5,3,6,7]=>5
[1,4,2,5,3,7,6]=>5
[1,4,2,5,6,3,7]=>5
[1,4,2,5,6,7,3]=>4
[1,4,2,5,7,3,6]=>6
[1,4,2,5,7,6,3]=>5
[1,4,2,6,3,5,7]=>6
[1,4,2,6,3,7,5]=>6
[1,4,2,6,5,3,7]=>6
[1,4,2,6,5,7,3]=>5
[1,4,2,6,7,3,5]=>5
[1,4,2,6,7,5,3]=>5
[1,4,2,7,3,5,6]=>5
[1,4,2,7,3,6,5]=>5
[1,4,2,7,5,3,6]=>6
[1,4,2,7,5,6,3]=>5
[1,4,2,7,6,3,5]=>5
[1,4,2,7,6,5,3]=>4
[1,4,3,2,5,6,7]=>3
[1,4,3,2,5,7,6]=>4
[1,4,3,2,6,5,7]=>4
[1,4,3,2,6,7,5]=>5
[1,4,3,2,7,5,6]=>5
[1,4,3,2,7,6,5]=>4
[1,4,3,5,2,6,7]=>5
[1,4,3,5,2,7,6]=>4
[1,4,3,5,6,2,7]=>4
[1,4,3,5,6,7,2]=>3
[1,4,3,5,7,2,6]=>5
[1,4,3,5,7,6,2]=>4
[1,4,3,6,2,5,7]=>6
[1,4,3,6,2,7,5]=>5
[1,4,3,6,5,2,7]=>4
[1,4,3,6,5,7,2]=>5
[1,4,3,6,7,2,5]=>5
[1,4,3,6,7,5,2]=>5
[1,4,3,7,2,5,6]=>5
[1,4,3,7,2,6,5]=>5
[1,4,3,7,5,2,6]=>5
[1,4,3,7,5,6,2]=>5
[1,4,3,7,6,2,5]=>5
[1,4,3,7,6,5,2]=>4
[1,4,5,2,3,6,7]=>3
[1,4,5,2,3,7,6]=>3
[1,4,5,2,6,3,7]=>5
[1,4,5,2,6,7,3]=>4
[1,4,5,2,7,3,6]=>5
[1,4,5,2,7,6,3]=>4
[1,4,5,3,2,6,7]=>4
[1,4,5,3,2,7,6]=>4
[1,4,5,3,6,2,7]=>5
[1,4,5,3,6,7,2]=>4
[1,4,5,3,7,2,6]=>5
[1,4,5,3,7,6,2]=>4
[1,4,5,6,2,3,7]=>3
[1,4,5,6,2,7,3]=>4
[1,4,5,6,3,2,7]=>4
[1,4,5,6,3,7,2]=>4
[1,4,5,6,7,2,3]=>3
[1,4,5,6,7,3,2]=>2
[1,4,5,7,2,3,6]=>4
[1,4,5,7,2,6,3]=>5
[1,4,5,7,3,2,6]=>4
[1,4,5,7,3,6,2]=>5
[1,4,5,7,6,2,3]=>4
[1,4,5,7,6,3,2]=>3
[1,4,6,2,3,5,7]=>5
[1,4,6,2,3,7,5]=>5
[1,4,6,2,5,3,7]=>6
[1,4,6,2,5,7,3]=>6
[1,4,6,2,7,3,5]=>6
[1,4,6,2,7,5,3]=>6
[1,4,6,3,2,5,7]=>6
[1,4,6,3,2,7,5]=>5
[1,4,6,3,5,2,7]=>6
[1,4,6,3,5,7,2]=>6
[1,4,6,3,7,2,5]=>6
[1,4,6,3,7,5,2]=>6
[1,4,6,5,2,3,7]=>4
[1,4,6,5,2,7,3]=>5
[1,4,6,5,3,2,7]=>5
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Description
The number of prefix or suffix reversals needed to sort a permutation.
A prefix reversal in a permutation $\pi = [\pi_1,\ldots,\pi_n]$ is a reversal of an initial subsequence of the form $\operatorname{reversal}_{j}(\pi) = [\pi_j,\ldots,\pi_{1},\pi_{j+1},\ldots,\pi_n]$ for $1 < j \leq n$. Final reversals are defined analogously.
This statistic is then given by the minimal number of initial or final reversals needed to sort a permutation.
A prefix reversal in a permutation $\pi = [\pi_1,\ldots,\pi_n]$ is a reversal of an initial subsequence of the form $\operatorname{reversal}_{j}(\pi) = [\pi_j,\ldots,\pi_{1},\pi_{j+1},\ldots,\pi_n]$ for $1 < j \leq n$. Final reversals are defined analogously.
This statistic is then given by the minimal number of initial or final reversals needed to sort a permutation.
References
[1] The reversal length of a permutation. St000670
[2] Hunter, Z. Variant of the pancake problem MathOverflow:413359
[2] Hunter, Z. Variant of the pancake problem MathOverflow:413359
Code
def children(pi):
pi = list(pi)
n = len(pi)
for j in range(n):
for i in range(j):
if i == 0 or j == n-1:
yield Permutation(pi[:i]+list(reversed(pi[i:j+1]))+pi[j+1:])
@cached_function
def statistic_classes(n):
A = RecursivelyEnumeratedSet([Permutation([1..n])], children,structure='symmetric')
return list(A.graded_component_iterator())
def statistic(pi):
comps = statistic_classes(len(pi))
for rank,comp in enumerate(comps):
if pi in comp:
return rank
Created
Jan 08, 2022 at 08:48 by Christian Stump
Updated
Jan 08, 2022 at 08:48 by Christian Stump
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