Identifier
- St001566: Permutations ⟶ ℤ
Values
=>
[1]=>1
[1,2]=>2
[2,1]=>2
[1,2,3]=>3
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>3
[1,2,3,4]=>4
[1,2,4,3]=>3
[1,3,2,4]=>2
[1,3,4,2]=>2
[1,4,2,3]=>3
[1,4,3,2]=>3
[2,1,3,4]=>3
[2,1,4,3]=>2
[2,3,1,4]=>3
[2,3,4,1]=>3
[2,4,1,3]=>2
[2,4,3,1]=>2
[3,1,2,4]=>2
[3,1,4,2]=>2
[3,2,1,4]=>3
[3,2,4,1]=>3
[3,4,1,2]=>2
[3,4,2,1]=>3
[4,1,2,3]=>3
[4,1,3,2]=>3
[4,2,1,3]=>2
[4,2,3,1]=>2
[4,3,1,2]=>3
[4,3,2,1]=>4
[1,2,3,4,5]=>5
[1,2,3,5,4]=>4
[1,2,4,3,5]=>3
[1,2,4,5,3]=>3
[1,2,5,3,4]=>4
[1,2,5,4,3]=>3
[1,3,2,4,5]=>3
[1,3,2,5,4]=>3
[1,3,4,2,5]=>3
[1,3,4,5,2]=>3
[1,3,5,2,4]=>3
[1,3,5,4,2]=>3
[1,4,2,3,5]=>3
[1,4,2,5,3]=>3
[1,4,3,2,5]=>3
[1,4,3,5,2]=>3
[1,4,5,2,3]=>3
[1,4,5,3,2]=>3
[1,5,2,3,4]=>4
[1,5,2,4,3]=>3
[1,5,3,2,4]=>2
[1,5,3,4,2]=>2
[1,5,4,2,3]=>3
[1,5,4,3,2]=>4
[2,1,3,4,5]=>4
[2,1,3,5,4]=>3
[2,1,4,3,5]=>3
[2,1,4,5,3]=>2
[2,1,5,3,4]=>3
[2,1,5,4,3]=>3
[2,3,1,4,5]=>4
[2,3,1,5,4]=>3
[2,3,4,1,5]=>4
[2,3,4,5,1]=>4
[2,3,5,1,4]=>3
[2,3,5,4,1]=>3
[2,4,1,3,5]=>3
[2,4,1,5,3]=>2
[2,4,3,1,5]=>2
[2,4,3,5,1]=>2
[2,4,5,1,3]=>2
[2,4,5,3,1]=>3
[2,5,1,3,4]=>3
[2,5,1,4,3]=>3
[2,5,3,1,4]=>3
[2,5,3,4,1]=>3
[2,5,4,1,3]=>3
[2,5,4,3,1]=>3
[3,1,2,4,5]=>3
[3,1,2,5,4]=>2
[3,1,4,2,5]=>3
[3,1,4,5,2]=>3
[3,1,5,2,4]=>2
[3,1,5,4,2]=>2
[3,2,1,4,5]=>3
[3,2,1,5,4]=>3
[3,2,4,1,5]=>3
[3,2,4,5,1]=>3
[3,2,5,1,4]=>3
[3,2,5,4,1]=>3
[3,4,1,2,5]=>3
[3,4,1,5,2]=>3
[3,4,2,1,5]=>3
[3,4,2,5,1]=>3
[3,4,5,1,2]=>3
[3,4,5,2,1]=>3
[3,5,1,2,4]=>2
[3,5,1,4,2]=>2
[3,5,2,1,4]=>3
[3,5,2,4,1]=>3
[3,5,4,1,2]=>2
[3,5,4,2,1]=>3
[4,1,2,3,5]=>3
[4,1,2,5,3]=>3
[4,1,3,2,5]=>3
[4,1,3,5,2]=>3
[4,1,5,2,3]=>3
[4,1,5,3,2]=>3
[4,2,1,3,5]=>3
[4,2,1,5,3]=>2
[4,2,3,1,5]=>2
[4,2,3,5,1]=>2
[4,2,5,1,3]=>2
[4,2,5,3,1]=>3
[4,3,1,2,5]=>3
[4,3,1,5,2]=>3
[4,3,2,1,5]=>4
[4,3,2,5,1]=>4
[4,3,5,1,2]=>3
[4,3,5,2,1]=>4
[4,5,1,2,3]=>3
[4,5,1,3,2]=>3
[4,5,2,1,3]=>2
[4,5,2,3,1]=>3
[4,5,3,1,2]=>3
[4,5,3,2,1]=>4
[5,1,2,3,4]=>4
[5,1,2,4,3]=>3
[5,1,3,2,4]=>2
[5,1,3,4,2]=>2
[5,1,4,2,3]=>3
[5,1,4,3,2]=>4
[5,2,1,3,4]=>3
[5,2,1,4,3]=>3
[5,2,3,1,4]=>3
[5,2,3,4,1]=>3
[5,2,4,1,3]=>3
[5,2,4,3,1]=>3
[5,3,1,2,4]=>3
[5,3,1,4,2]=>3
[5,3,2,1,4]=>3
[5,3,2,4,1]=>3
[5,3,4,1,2]=>3
[5,3,4,2,1]=>3
[5,4,1,2,3]=>3
[5,4,1,3,2]=>4
[5,4,2,1,3]=>3
[5,4,2,3,1]=>3
[5,4,3,1,2]=>4
[5,4,3,2,1]=>5
[1,2,3,4,5,6]=>6
[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>4
[1,2,3,6,4,5]=>5
[1,2,3,6,5,4]=>4
[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]=>3
[1,2,4,6,3,5]=>3
[1,2,4,6,5,3]=>3
[1,2,5,3,4,6]=>4
[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]=>4
[1,2,5,6,4,3]=>3
[1,2,6,3,4,5]=>5
[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>3
[1,2,6,4,5,3]=>3
[1,2,6,5,3,4]=>4
[1,2,6,5,4,3]=>4
[1,3,2,4,5,6]=>4
[1,3,2,4,6,5]=>3
[1,3,2,5,4,6]=>3
[1,3,2,5,6,4]=>3
[1,3,2,6,4,5]=>3
[1,3,2,6,5,4]=>3
[1,3,4,2,5,6]=>4
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>4
[1,3,4,5,6,2]=>4
[1,3,4,6,2,5]=>3
[1,3,4,6,5,2]=>3
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>3
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>3
[1,3,5,6,2,4]=>3
[1,3,5,6,4,2]=>3
[1,3,6,2,4,5]=>3
[1,3,6,2,5,4]=>3
[1,3,6,4,2,5]=>3
[1,3,6,4,5,2]=>3
[1,3,6,5,2,4]=>3
[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]=>3
[1,4,2,5,6,3]=>3
[1,4,2,6,3,5]=>3
[1,4,2,6,5,3]=>3
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>3
[1,4,3,5,2,6]=>3
[1,4,3,5,6,2]=>3
[1,4,3,6,2,5]=>3
[1,4,3,6,5,2]=>3
[1,4,5,2,3,6]=>3
[1,4,5,2,6,3]=>3
[1,4,5,3,2,6]=>3
[1,4,5,3,6,2]=>3
[1,4,5,6,2,3]=>3
[1,4,5,6,3,2]=>3
[1,4,6,2,3,5]=>3
[1,4,6,2,5,3]=>3
[1,4,6,3,2,5]=>3
[1,4,6,3,5,2]=>3
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>3
[1,5,2,3,4,6]=>4
[1,5,2,3,6,4]=>4
[1,5,2,4,3,6]=>3
[1,5,2,4,6,3]=>3
[1,5,2,6,3,4]=>4
[1,5,2,6,4,3]=>3
[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>2
[1,5,3,4,2,6]=>2
[1,5,3,4,6,2]=>2
[1,5,3,6,2,4]=>2
[1,5,3,6,4,2]=>3
[1,5,4,2,3,6]=>3
[1,5,4,2,6,3]=>3
[1,5,4,3,2,6]=>4
[1,5,4,3,6,2]=>4
[1,5,4,6,2,3]=>3
[1,5,4,6,3,2]=>4
[1,5,6,2,3,4]=>4
[1,5,6,2,4,3]=>3
[1,5,6,3,2,4]=>2
[1,5,6,3,4,2]=>3
[1,5,6,4,2,3]=>3
[1,5,6,4,3,2]=>4
[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>4
[1,6,2,4,3,5]=>3
[1,6,2,4,5,3]=>3
[1,6,2,5,3,4]=>4
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>3
[1,6,3,2,5,4]=>3
[1,6,3,4,2,5]=>3
[1,6,3,4,5,2]=>3
[1,6,3,5,2,4]=>3
[1,6,3,5,4,2]=>3
[1,6,4,2,3,5]=>3
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>3
[1,6,4,5,2,3]=>3
[1,6,4,5,3,2]=>3
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>4
[1,6,5,3,2,4]=>3
[1,6,5,3,4,2]=>3
[1,6,5,4,2,3]=>4
[1,6,5,4,3,2]=>5
[2,1,3,4,5,6]=>5
[2,1,3,4,6,5]=>4
[2,1,3,5,4,6]=>3
[2,1,3,5,6,4]=>3
[2,1,3,6,4,5]=>4
[2,1,3,6,5,4]=>3
[2,1,4,3,5,6]=>3
[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>3
[2,1,4,6,3,5]=>3
[2,1,4,6,5,3]=>3
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>3
[2,1,5,4,3,6]=>3
[2,1,5,4,6,3]=>3
[2,1,5,6,3,4]=>3
[2,1,5,6,4,3]=>3
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>3
[2,1,6,4,3,5]=>3
[2,1,6,4,5,3]=>2
[2,1,6,5,3,4]=>3
[2,1,6,5,4,3]=>4
[2,3,1,4,5,6]=>5
[2,3,1,4,6,5]=>4
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>3
[2,3,1,6,4,5]=>4
[2,3,1,6,5,4]=>3
[2,3,4,1,5,6]=>5
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>5
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>4
[2,3,4,6,5,1]=>4
[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>3
[2,3,5,4,1,6]=>3
[2,3,5,4,6,1]=>3
[2,3,5,6,1,4]=>3
[2,3,5,6,4,1]=>3
[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]=>3
[2,4,1,3,6,5]=>3
[2,4,1,5,3,6]=>3
[2,4,1,5,6,3]=>3
[2,4,1,6,3,5]=>3
[2,4,1,6,5,3]=>3
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>3
[2,4,3,5,1,6]=>3
[2,4,3,5,6,1]=>3
[2,4,3,6,1,5]=>3
[2,4,3,6,5,1]=>3
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>3
[2,4,5,3,1,6]=>3
[2,4,5,3,6,1]=>3
[2,4,5,6,1,3]=>3
[2,4,5,6,3,1]=>3
[2,4,6,1,3,5]=>3
[2,4,6,1,5,3]=>3
[2,4,6,3,1,5]=>3
[2,4,6,3,5,1]=>3
[2,4,6,5,1,3]=>3
[2,4,6,5,3,1]=>3
[2,5,1,3,4,6]=>3
[2,5,1,3,6,4]=>3
[2,5,1,4,3,6]=>3
[2,5,1,4,6,3]=>3
[2,5,1,6,3,4]=>3
[2,5,1,6,4,3]=>3
[2,5,3,1,4,6]=>3
[2,5,3,1,6,4]=>3
[2,5,3,4,1,6]=>3
[2,5,3,4,6,1]=>3
[2,5,3,6,1,4]=>3
[2,5,3,6,4,1]=>3
[2,5,4,1,3,6]=>3
[2,5,4,1,6,3]=>3
[2,5,4,3,1,6]=>3
[2,5,4,3,6,1]=>3
[2,5,4,6,1,3]=>3
[2,5,4,6,3,1]=>3
[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>3
[2,5,6,3,1,4]=>3
[2,5,6,3,4,1]=>3
[2,5,6,4,1,3]=>3
[2,5,6,4,3,1]=>3
[2,6,1,3,4,5]=>4
[2,6,1,3,5,4]=>3
[2,6,1,4,3,5]=>3
[2,6,1,4,5,3]=>2
[2,6,1,5,3,4]=>3
[2,6,1,5,4,3]=>4
[2,6,3,1,4,5]=>4
[2,6,3,1,5,4]=>3
[2,6,3,4,1,5]=>4
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>3
[2,6,3,5,4,1]=>3
[2,6,4,1,3,5]=>3
[2,6,4,1,5,3]=>2
[2,6,4,3,1,5]=>2
[2,6,4,3,5,1]=>2
[2,6,4,5,1,3]=>2
[2,6,4,5,3,1]=>3
[2,6,5,1,3,4]=>3
[2,6,5,1,4,3]=>4
[2,6,5,3,1,4]=>3
[2,6,5,3,4,1]=>3
[2,6,5,4,1,3]=>4
[2,6,5,4,3,1]=>4
[3,1,2,4,5,6]=>4
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>3
[3,1,2,5,6,4]=>2
[3,1,2,6,4,5]=>3
[3,1,2,6,5,4]=>3
[3,1,4,2,5,6]=>4
[3,1,4,2,6,5]=>3
[3,1,4,5,2,6]=>4
[3,1,4,5,6,2]=>4
[3,1,4,6,2,5]=>3
[3,1,4,6,5,2]=>3
[3,1,5,2,4,6]=>3
[3,1,5,2,6,4]=>2
[3,1,5,4,2,6]=>2
[3,1,5,4,6,2]=>2
[3,1,5,6,2,4]=>2
[3,1,5,6,4,2]=>3
[3,1,6,2,4,5]=>3
[3,1,6,2,5,4]=>3
[3,1,6,4,2,5]=>3
[3,1,6,4,5,2]=>3
[3,1,6,5,2,4]=>3
[3,1,6,5,4,2]=>3
[3,2,1,4,5,6]=>4
[3,2,1,4,6,5]=>3
[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]=>3
[3,2,4,1,5,6]=>4
[3,2,4,1,6,5]=>3
[3,2,4,5,1,6]=>4
[3,2,4,5,6,1]=>4
[3,2,4,6,1,5]=>3
[3,2,4,6,5,1]=>3
[3,2,5,1,4,6]=>3
[3,2,5,1,6,4]=>3
[3,2,5,4,1,6]=>3
[3,2,5,4,6,1]=>3
[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]=>3
[3,2,6,4,1,5]=>3
[3,2,6,4,5,1]=>3
[3,2,6,5,1,4]=>3
[3,2,6,5,4,1]=>3
[3,4,1,2,5,6]=>4
[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]=>3
[3,4,1,6,5,2]=>3
[3,4,2,1,5,6]=>4
[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]=>3
[3,4,2,6,5,1]=>3
[3,4,5,1,2,6]=>4
[3,4,5,1,6,2]=>4
[3,4,5,2,1,6]=>4
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>4
[3,4,5,6,2,1]=>4
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>3
[3,4,6,2,1,5]=>3
[3,4,6,2,5,1]=>3
[3,4,6,5,1,2]=>3
[3,4,6,5,2,1]=>3
[3,5,1,2,4,6]=>3
[3,5,1,2,6,4]=>2
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>2
[3,5,1,6,2,4]=>2
[3,5,1,6,4,2]=>3
[3,5,2,1,4,6]=>3
[3,5,2,1,6,4]=>3
[3,5,2,4,1,6]=>3
[3,5,2,4,6,1]=>3
[3,5,2,6,1,4]=>3
[3,5,2,6,4,1]=>3
[3,5,4,1,2,6]=>2
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>3
[3,5,4,2,6,1]=>3
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>3
[3,5,6,1,2,4]=>2
[3,5,6,1,4,2]=>3
[3,5,6,2,1,4]=>3
[3,5,6,2,4,1]=>3
[3,5,6,4,1,2]=>3
[3,5,6,4,2,1]=>3
[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>3
[3,6,1,4,2,5]=>3
[3,6,1,4,5,2]=>3
[3,6,1,5,2,4]=>3
[3,6,1,5,4,2]=>3
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>3
[3,6,2,4,1,5]=>3
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>3
[3,6,2,5,4,1]=>3
[3,6,4,1,2,5]=>3
[3,6,4,1,5,2]=>3
[3,6,4,2,1,5]=>3
[3,6,4,2,5,1]=>3
[3,6,4,5,1,2]=>3
[3,6,4,5,2,1]=>3
[3,6,5,1,2,4]=>3
[3,6,5,1,4,2]=>3
[3,6,5,2,1,4]=>3
[3,6,5,2,4,1]=>3
[3,6,5,4,1,2]=>3
[3,6,5,4,2,1]=>3
[4,1,2,3,5,6]=>3
[4,1,2,3,6,5]=>3
[4,1,2,5,3,6]=>3
[4,1,2,5,6,3]=>3
[4,1,2,6,3,5]=>3
[4,1,2,6,5,3]=>3
[4,1,3,2,5,6]=>3
[4,1,3,2,6,5]=>3
[4,1,3,5,2,6]=>3
[4,1,3,5,6,2]=>3
[4,1,3,6,2,5]=>3
[4,1,3,6,5,2]=>3
[4,1,5,2,3,6]=>3
[4,1,5,2,6,3]=>3
[4,1,5,3,2,6]=>3
[4,1,5,3,6,2]=>3
[4,1,5,6,2,3]=>3
[4,1,5,6,3,2]=>3
[4,1,6,2,3,5]=>3
[4,1,6,2,5,3]=>3
[4,1,6,3,2,5]=>3
[4,1,6,3,5,2]=>3
[4,1,6,5,2,3]=>3
[4,1,6,5,3,2]=>3
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>3
[4,2,1,5,3,6]=>3
[4,2,1,5,6,3]=>3
[4,2,1,6,3,5]=>3
[4,2,1,6,5,3]=>2
[4,2,3,1,5,6]=>3
[4,2,3,1,6,5]=>2
[4,2,3,5,1,6]=>3
[4,2,3,5,6,1]=>3
[4,2,3,6,1,5]=>2
[4,2,3,6,5,1]=>2
[4,2,5,1,3,6]=>3
[4,2,5,1,6,3]=>3
[4,2,5,3,1,6]=>3
[4,2,5,3,6,1]=>3
[4,2,5,6,1,3]=>3
[4,2,5,6,3,1]=>3
[4,2,6,1,3,5]=>3
[4,2,6,1,5,3]=>2
[4,2,6,3,1,5]=>2
[4,2,6,3,5,1]=>2
[4,2,6,5,1,3]=>2
[4,2,6,5,3,1]=>3
[4,3,1,2,5,6]=>3
[4,3,1,2,6,5]=>3
[4,3,1,5,2,6]=>3
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>3
[4,3,1,6,5,2]=>3
[4,3,2,1,5,6]=>4
[4,3,2,1,6,5]=>4
[4,3,2,5,1,6]=>4
[4,3,2,5,6,1]=>4
[4,3,2,6,1,5]=>4
[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>3
[4,3,5,1,6,2]=>3
[4,3,5,2,1,6]=>4
[4,3,5,2,6,1]=>4
[4,3,5,6,1,2]=>3
[4,3,5,6,2,1]=>4
[4,3,6,1,2,5]=>3
[4,3,6,1,5,2]=>3
[4,3,6,2,1,5]=>4
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>3
[4,3,6,5,2,1]=>4
[4,5,1,2,3,6]=>3
[4,5,1,2,6,3]=>3
[4,5,1,3,2,6]=>3
[4,5,1,3,6,2]=>3
[4,5,1,6,2,3]=>3
[4,5,1,6,3,2]=>3
[4,5,2,1,3,6]=>3
[4,5,2,1,6,3]=>3
[4,5,2,3,1,6]=>3
[4,5,2,3,6,1]=>3
[4,5,2,6,1,3]=>3
[4,5,2,6,3,1]=>3
[4,5,3,1,2,6]=>3
[4,5,3,1,6,2]=>3
[4,5,3,2,1,6]=>4
[4,5,3,2,6,1]=>4
[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]=>3
[4,5,6,2,1,3]=>3
[4,5,6,2,3,1]=>3
[4,5,6,3,1,2]=>3
[4,5,6,3,2,1]=>4
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>3
[4,6,1,3,2,5]=>3
[4,6,1,3,5,2]=>3
[4,6,1,5,2,3]=>3
[4,6,1,5,3,2]=>3
[4,6,2,1,3,5]=>3
[4,6,2,1,5,3]=>2
[4,6,2,3,1,5]=>2
[4,6,2,3,5,1]=>2
[4,6,2,5,1,3]=>2
[4,6,2,5,3,1]=>3
[4,6,3,1,2,5]=>3
[4,6,3,1,5,2]=>3
[4,6,3,2,1,5]=>4
[4,6,3,2,5,1]=>4
[4,6,3,5,1,2]=>3
[4,6,3,5,2,1]=>4
[4,6,5,1,2,3]=>3
[4,6,5,1,3,2]=>3
[4,6,5,2,1,3]=>2
[4,6,5,2,3,1]=>3
[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>4
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>3
[5,1,2,4,6,3]=>3
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>3
[5,1,3,2,4,6]=>3
[5,1,3,2,6,4]=>2
[5,1,3,4,2,6]=>2
[5,1,3,4,6,2]=>2
[5,1,3,6,2,4]=>2
[5,1,3,6,4,2]=>3
[5,1,4,2,3,6]=>3
[5,1,4,2,6,3]=>3
[5,1,4,3,2,6]=>4
[5,1,4,3,6,2]=>4
[5,1,4,6,2,3]=>3
[5,1,4,6,3,2]=>4
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>3
[5,1,6,3,2,4]=>2
[5,1,6,3,4,2]=>3
[5,1,6,4,2,3]=>3
[5,1,6,4,3,2]=>4
[5,2,1,3,4,6]=>3
[5,2,1,3,6,4]=>3
[5,2,1,4,3,6]=>3
[5,2,1,4,6,3]=>3
[5,2,1,6,3,4]=>3
[5,2,1,6,4,3]=>3
[5,2,3,1,4,6]=>3
[5,2,3,1,6,4]=>3
[5,2,3,4,1,6]=>3
[5,2,3,4,6,1]=>3
[5,2,3,6,1,4]=>3
[5,2,3,6,4,1]=>3
[5,2,4,1,3,6]=>3
[5,2,4,1,6,3]=>3
[5,2,4,3,1,6]=>3
[5,2,4,3,6,1]=>3
[5,2,4,6,1,3]=>3
[5,2,4,6,3,1]=>3
[5,2,6,1,3,4]=>3
[5,2,6,1,4,3]=>3
[5,2,6,3,1,4]=>3
[5,2,6,3,4,1]=>3
[5,2,6,4,1,3]=>3
[5,2,6,4,3,1]=>3
[5,3,1,2,4,6]=>3
[5,3,1,2,6,4]=>3
[5,3,1,4,2,6]=>3
[5,3,1,4,6,2]=>3
[5,3,1,6,2,4]=>3
[5,3,1,6,4,2]=>3
[5,3,2,1,4,6]=>3
[5,3,2,1,6,4]=>3
[5,3,2,4,1,6]=>3
[5,3,2,4,6,1]=>3
[5,3,2,6,1,4]=>3
[5,3,2,6,4,1]=>3
[5,3,4,1,2,6]=>3
[5,3,4,1,6,2]=>3
[5,3,4,2,1,6]=>3
[5,3,4,2,6,1]=>3
[5,3,4,6,1,2]=>3
[5,3,4,6,2,1]=>3
[5,3,6,1,2,4]=>3
[5,3,6,1,4,2]=>3
[5,3,6,2,1,4]=>3
[5,3,6,2,4,1]=>3
[5,3,6,4,1,2]=>3
[5,3,6,4,2,1]=>3
[5,4,1,2,3,6]=>3
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>4
[5,4,1,3,6,2]=>4
[5,4,1,6,2,3]=>3
[5,4,1,6,3,2]=>4
[5,4,2,1,3,6]=>3
[5,4,2,1,6,3]=>3
[5,4,2,3,1,6]=>3
[5,4,2,3,6,1]=>3
[5,4,2,6,1,3]=>3
[5,4,2,6,3,1]=>3
[5,4,3,1,2,6]=>4
[5,4,3,1,6,2]=>4
[5,4,3,2,1,6]=>5
[5,4,3,2,6,1]=>5
[5,4,3,6,1,2]=>4
[5,4,3,6,2,1]=>5
[5,4,6,1,2,3]=>3
[5,4,6,1,3,2]=>4
[5,4,6,2,1,3]=>3
[5,4,6,2,3,1]=>3
[5,4,6,3,1,2]=>4
[5,4,6,3,2,1]=>5
[5,6,1,2,3,4]=>4
[5,6,1,2,4,3]=>3
[5,6,1,3,2,4]=>2
[5,6,1,3,4,2]=>3
[5,6,1,4,2,3]=>3
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>3
[5,6,2,1,4,3]=>3
[5,6,2,3,1,4]=>3
[5,6,2,3,4,1]=>3
[5,6,2,4,1,3]=>3
[5,6,2,4,3,1]=>3
[5,6,3,1,2,4]=>3
[5,6,3,1,4,2]=>3
[5,6,3,2,1,4]=>3
[5,6,3,2,4,1]=>3
[5,6,3,4,1,2]=>3
[5,6,3,4,2,1]=>3
[5,6,4,1,2,3]=>3
[5,6,4,1,3,2]=>4
[5,6,4,2,1,3]=>3
[5,6,4,2,3,1]=>3
[5,6,4,3,1,2]=>4
[5,6,4,3,2,1]=>5
[6,1,2,3,4,5]=>5
[6,1,2,3,5,4]=>4
[6,1,2,4,3,5]=>3
[6,1,2,4,5,3]=>3
[6,1,2,5,3,4]=>4
[6,1,2,5,4,3]=>4
[6,1,3,2,4,5]=>3
[6,1,3,2,5,4]=>3
[6,1,3,4,2,5]=>3
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>3
[6,1,3,5,4,2]=>3
[6,1,4,2,3,5]=>3
[6,1,4,2,5,3]=>3
[6,1,4,3,2,5]=>3
[6,1,4,3,5,2]=>3
[6,1,4,5,2,3]=>3
[6,1,4,5,3,2]=>3
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>4
[6,1,5,3,2,4]=>3
[6,1,5,3,4,2]=>3
[6,1,5,4,2,3]=>4
[6,1,5,4,3,2]=>5
[6,2,1,3,4,5]=>4
[6,2,1,3,5,4]=>3
[6,2,1,4,3,5]=>3
[6,2,1,4,5,3]=>2
[6,2,1,5,3,4]=>3
[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>4
[6,2,3,1,5,4]=>3
[6,2,3,4,1,5]=>4
[6,2,3,4,5,1]=>4
[6,2,3,5,1,4]=>3
[6,2,3,5,4,1]=>3
[6,2,4,1,3,5]=>3
[6,2,4,1,5,3]=>2
[6,2,4,3,1,5]=>2
[6,2,4,3,5,1]=>2
[6,2,4,5,1,3]=>2
[6,2,4,5,3,1]=>3
[6,2,5,1,3,4]=>3
[6,2,5,1,4,3]=>4
[6,2,5,3,1,4]=>3
[6,2,5,3,4,1]=>3
[6,2,5,4,1,3]=>4
[6,2,5,4,3,1]=>4
[6,3,1,2,4,5]=>3
[6,3,1,2,5,4]=>3
[6,3,1,4,2,5]=>3
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>3
[6,3,1,5,4,2]=>3
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>3
[6,3,2,4,1,5]=>3
[6,3,2,4,5,1]=>3
[6,3,2,5,1,4]=>3
[6,3,2,5,4,1]=>3
[6,3,4,1,2,5]=>3
[6,3,4,1,5,2]=>3
[6,3,4,2,1,5]=>3
[6,3,4,2,5,1]=>3
[6,3,4,5,1,2]=>3
[6,3,4,5,2,1]=>3
[6,3,5,1,2,4]=>3
[6,3,5,1,4,2]=>3
[6,3,5,2,1,4]=>3
[6,3,5,2,4,1]=>3
[6,3,5,4,1,2]=>3
[6,3,5,4,2,1]=>3
[6,4,1,2,3,5]=>3
[6,4,1,2,5,3]=>3
[6,4,1,3,2,5]=>3
[6,4,1,3,5,2]=>3
[6,4,1,5,2,3]=>3
[6,4,1,5,3,2]=>3
[6,4,2,1,3,5]=>3
[6,4,2,1,5,3]=>3
[6,4,2,3,1,5]=>3
[6,4,2,3,5,1]=>3
[6,4,2,5,1,3]=>3
[6,4,2,5,3,1]=>3
[6,4,3,1,2,5]=>3
[6,4,3,1,5,2]=>3
[6,4,3,2,1,5]=>4
[6,4,3,2,5,1]=>4
[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]=>3
[6,4,5,2,1,3]=>3
[6,4,5,2,3,1]=>3
[6,4,5,3,1,2]=>3
[6,4,5,3,2,1]=>4
[6,5,1,2,3,4]=>4
[6,5,1,2,4,3]=>4
[6,5,1,3,2,4]=>3
[6,5,1,3,4,2]=>3
[6,5,1,4,2,3]=>4
[6,5,1,4,3,2]=>5
[6,5,2,1,3,4]=>3
[6,5,2,1,4,3]=>4
[6,5,2,3,1,4]=>3
[6,5,2,3,4,1]=>3
[6,5,2,4,1,3]=>4
[6,5,2,4,3,1]=>4
[6,5,3,1,2,4]=>3
[6,5,3,1,4,2]=>3
[6,5,3,2,1,4]=>3
[6,5,3,2,4,1]=>3
[6,5,3,4,1,2]=>3
[6,5,3,4,2,1]=>3
[6,5,4,1,2,3]=>4
[6,5,4,1,3,2]=>5
[6,5,4,2,1,3]=>4
[6,5,4,2,3,1]=>4
[6,5,4,3,1,2]=>5
[6,5,4,3,2,1]=>6
[1,2,3,4,5,6,7]=>7
[1,2,3,4,5,7,6]=>6
[1,2,3,4,6,5,7]=>5
[1,2,3,4,6,7,5]=>5
[1,2,3,4,7,5,6]=>6
[1,2,3,4,7,6,5]=>5
[1,2,3,5,4,6,7]=>4
[1,2,3,5,4,7,6]=>4
[1,2,3,5,6,4,7]=>4
[1,2,3,5,6,7,4]=>4
[1,2,3,5,7,4,6]=>4
[1,2,3,5,7,6,4]=>4
[1,2,3,6,4,5,7]=>5
[1,2,3,6,4,7,5]=>5
[1,2,3,6,5,4,7]=>4
[1,2,3,6,5,7,4]=>4
[1,2,3,6,7,4,5]=>5
[1,2,3,6,7,5,4]=>4
[1,2,3,7,4,5,6]=>6
[1,2,3,7,4,6,5]=>5
[1,2,3,7,5,4,6]=>4
[1,2,3,7,5,6,4]=>4
[1,2,3,7,6,4,5]=>5
[1,2,3,7,6,5,4]=>4
[1,2,4,3,5,6,7]=>4
[1,2,4,3,5,7,6]=>4
[1,2,4,3,6,5,7]=>4
[1,2,4,3,6,7,5]=>3
[1,2,4,3,7,5,6]=>3
[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]=>4
[1,2,4,5,6,7,3]=>4
[1,2,4,5,7,3,6]=>3
[1,2,4,5,7,6,3]=>3
[1,2,4,6,3,5,7]=>4
[1,2,4,6,3,7,5]=>3
[1,2,4,6,5,3,7]=>3
[1,2,4,6,5,7,3]=>3
[1,2,4,6,7,3,5]=>3
[1,2,4,6,7,5,3]=>3
[1,2,4,7,3,5,6]=>3
[1,2,4,7,3,6,5]=>3
[1,2,4,7,5,3,6]=>3
[1,2,4,7,5,6,3]=>3
[1,2,4,7,6,3,5]=>3
[1,2,4,7,6,5,3]=>3
[1,2,5,3,4,6,7]=>4
[1,2,5,3,4,7,6]=>4
[1,2,5,3,6,4,7]=>4
[1,2,5,3,6,7,4]=>4
[1,2,5,3,7,4,6]=>4
[1,2,5,3,7,6,4]=>4
[1,2,5,4,3,6,7]=>3
[1,2,5,4,3,7,6]=>3
[1,2,5,4,6,3,7]=>3
[1,2,5,4,6,7,3]=>3
[1,2,5,4,7,3,6]=>3
[1,2,5,4,7,6,3]=>3
[1,2,5,6,3,4,7]=>4
[1,2,5,6,3,7,4]=>4
[1,2,5,6,4,3,7]=>3
[1,2,5,6,4,7,3]=>3
[1,2,5,6,7,3,4]=>4
[1,2,5,6,7,4,3]=>3
[1,2,5,7,3,4,6]=>4
[1,2,5,7,3,6,4]=>4
[1,2,5,7,4,3,6]=>3
[1,2,5,7,4,6,3]=>3
[1,2,5,7,6,3,4]=>4
[1,2,5,7,6,4,3]=>3
[1,2,6,3,4,5,7]=>5
[1,2,6,3,4,7,5]=>5
[1,2,6,3,5,4,7]=>4
[1,2,6,3,5,7,4]=>4
[1,2,6,3,7,4,5]=>5
[1,2,6,3,7,5,4]=>4
[1,2,6,4,3,5,7]=>4
[1,2,6,4,3,7,5]=>3
[1,2,6,4,5,3,7]=>3
[1,2,6,4,5,7,3]=>3
[1,2,6,4,7,3,5]=>3
[1,2,6,4,7,5,3]=>3
[1,2,6,5,3,4,7]=>4
[1,2,6,5,3,7,4]=>4
[1,2,6,5,4,3,7]=>4
[1,2,6,5,4,7,3]=>4
[1,2,6,5,7,3,4]=>4
[1,2,6,5,7,4,3]=>4
[1,2,6,7,3,4,5]=>5
[1,2,6,7,3,5,4]=>4
[1,2,6,7,4,3,5]=>3
[1,2,6,7,4,5,3]=>3
[1,2,6,7,5,3,4]=>4
[1,2,6,7,5,4,3]=>4
[1,2,7,3,4,5,6]=>6
[1,2,7,3,4,6,5]=>5
[1,2,7,3,5,4,6]=>4
[1,2,7,3,5,6,4]=>4
[1,2,7,3,6,4,5]=>5
[1,2,7,3,6,5,4]=>4
[1,2,7,4,3,5,6]=>3
[1,2,7,4,3,6,5]=>3
[1,2,7,4,5,3,6]=>3
[1,2,7,4,5,6,3]=>3
[1,2,7,4,6,3,5]=>3
[1,2,7,4,6,5,3]=>3
[1,2,7,5,3,4,6]=>4
[1,2,7,5,3,6,4]=>4
[1,2,7,5,4,3,6]=>3
[1,2,7,5,4,6,3]=>3
[1,2,7,5,6,3,4]=>4
[1,2,7,5,6,4,3]=>3
[1,2,7,6,3,4,5]=>5
[1,2,7,6,3,5,4]=>4
[1,2,7,6,4,3,5]=>3
[1,2,7,6,4,5,3]=>3
[1,2,7,6,5,3,4]=>4
[1,2,7,6,5,4,3]=>5
[1,3,2,4,5,6,7]=>5
[1,3,2,4,5,7,6]=>4
[1,3,2,4,6,5,7]=>4
[1,3,2,4,6,7,5]=>3
[1,3,2,4,7,5,6]=>4
[1,3,2,4,7,6,5]=>3
[1,3,2,5,4,6,7]=>4
[1,3,2,5,4,7,6]=>4
[1,3,2,5,6,4,7]=>4
[1,3,2,5,6,7,4]=>4
[1,3,2,5,7,4,6]=>4
[1,3,2,5,7,6,4]=>4
[1,3,2,6,4,5,7]=>4
[1,3,2,6,4,7,5]=>3
[1,3,2,6,5,4,7]=>4
[1,3,2,6,5,7,4]=>4
[1,3,2,6,7,4,5]=>3
[1,3,2,6,7,5,4]=>3
[1,3,2,7,4,5,6]=>4
[1,3,2,7,4,6,5]=>3
[1,3,2,7,5,4,6]=>3
[1,3,2,7,5,6,4]=>3
[1,3,2,7,6,4,5]=>3
[1,3,2,7,6,5,4]=>4
[1,3,4,2,5,6,7]=>5
[1,3,4,2,5,7,6]=>4
[1,3,4,2,6,5,7]=>4
[1,3,4,2,6,7,5]=>3
[1,3,4,2,7,5,6]=>4
[1,3,4,2,7,6,5]=>3
[1,3,4,5,2,6,7]=>5
[1,3,4,5,2,7,6]=>4
[1,3,4,5,6,2,7]=>5
[1,3,4,5,6,7,2]=>5
[1,3,4,5,7,2,6]=>4
[1,3,4,5,7,6,2]=>4
[1,3,4,6,2,5,7]=>4
[1,3,4,6,2,7,5]=>3
[1,3,4,6,5,2,7]=>4
[1,3,4,6,5,7,2]=>4
[1,3,4,6,7,2,5]=>3
[1,3,4,6,7,5,2]=>3
[1,3,4,7,2,5,6]=>4
[1,3,4,7,2,6,5]=>3
[1,3,4,7,5,2,6]=>4
[1,3,4,7,5,6,2]=>4
[1,3,4,7,6,2,5]=>3
[1,3,4,7,6,5,2]=>3
[1,3,5,2,4,6,7]=>4
[1,3,5,2,4,7,6]=>4
[1,3,5,2,6,4,7]=>4
[1,3,5,2,6,7,4]=>4
[1,3,5,2,7,4,6]=>4
[1,3,5,2,7,6,4]=>4
[1,3,5,4,2,6,7]=>4
[1,3,5,4,2,7,6]=>4
[1,3,5,4,6,2,7]=>4
[1,3,5,4,6,7,2]=>4
[1,3,5,4,7,2,6]=>4
[1,3,5,4,7,6,2]=>4
[1,3,5,6,2,4,7]=>4
[1,3,5,6,2,7,4]=>4
[1,3,5,6,4,2,7]=>4
[1,3,5,6,4,7,2]=>4
[1,3,5,6,7,2,4]=>4
[1,3,5,6,7,4,2]=>4
[1,3,5,7,2,4,6]=>4
[1,3,5,7,2,6,4]=>4
[1,3,5,7,4,2,6]=>4
[1,3,5,7,4,6,2]=>4
[1,3,5,7,6,2,4]=>4
[1,3,5,7,6,4,2]=>4
[1,3,6,2,4,5,7]=>4
[1,3,6,2,4,7,5]=>3
[1,3,6,2,5,4,7]=>4
[1,3,6,2,5,7,4]=>4
[1,3,6,2,7,4,5]=>3
[1,3,6,2,7,5,4]=>3
[1,3,6,4,2,5,7]=>4
[1,3,6,4,2,7,5]=>3
[1,3,6,4,5,2,7]=>4
[1,3,6,4,5,7,2]=>4
[1,3,6,4,7,2,5]=>3
[1,3,6,4,7,5,2]=>3
[1,3,6,5,2,4,7]=>4
[1,3,6,5,2,7,4]=>4
[1,3,6,5,4,2,7]=>4
[1,3,6,5,4,7,2]=>4
[1,3,6,5,7,2,4]=>4
[1,3,6,5,7,4,2]=>4
[1,3,6,7,2,4,5]=>3
[1,3,6,7,2,5,4]=>3
[1,3,6,7,4,2,5]=>3
[1,3,6,7,4,5,2]=>3
[1,3,6,7,5,2,4]=>3
[1,3,6,7,5,4,2]=>3
[1,3,7,2,4,5,6]=>4
[1,3,7,2,4,6,5]=>3
[1,3,7,2,5,4,6]=>3
[1,3,7,2,5,6,4]=>3
[1,3,7,2,6,4,5]=>3
[1,3,7,2,6,5,4]=>4
[1,3,7,4,2,5,6]=>4
[1,3,7,4,2,6,5]=>3
[1,3,7,4,5,2,6]=>4
[1,3,7,4,5,6,2]=>4
[1,3,7,4,6,2,5]=>3
[1,3,7,4,6,5,2]=>3
[1,3,7,5,2,4,6]=>3
[1,3,7,5,2,6,4]=>3
[1,3,7,5,4,2,6]=>3
[1,3,7,5,4,6,2]=>3
[1,3,7,5,6,2,4]=>3
[1,3,7,5,6,4,2]=>3
[1,3,7,6,2,4,5]=>3
[1,3,7,6,2,5,4]=>4
[1,3,7,6,4,2,5]=>3
[1,3,7,6,4,5,2]=>3
[1,3,7,6,5,2,4]=>4
[1,3,7,6,5,4,2]=>4
[1,4,2,3,5,6,7]=>4
[1,4,2,3,5,7,6]=>4
[1,4,2,3,6,5,7]=>4
[1,4,2,3,6,7,5]=>3
[1,4,2,3,7,5,6]=>3
[1,4,2,3,7,6,5]=>3
[1,4,2,5,3,6,7]=>4
[1,4,2,5,3,7,6]=>3
[1,4,2,5,6,3,7]=>4
[1,4,2,5,6,7,3]=>4
[1,4,2,5,7,3,6]=>3
[1,4,2,5,7,6,3]=>3
[1,4,2,6,3,5,7]=>4
[1,4,2,6,3,7,5]=>3
[1,4,2,6,5,3,7]=>3
[1,4,2,6,5,7,3]=>3
[1,4,2,6,7,3,5]=>3
[1,4,2,6,7,5,3]=>3
[1,4,2,7,3,5,6]=>3
[1,4,2,7,3,6,5]=>3
[1,4,2,7,5,3,6]=>3
[1,4,2,7,5,6,3]=>3
[1,4,2,7,6,3,5]=>3
[1,4,2,7,6,5,3]=>3
[1,4,3,2,5,6,7]=>4
[1,4,3,2,5,7,6]=>4
[1,4,3,2,6,5,7]=>4
[1,4,3,2,6,7,5]=>3
[1,4,3,2,7,5,6]=>3
[1,4,3,2,7,6,5]=>3
[1,4,3,5,2,6,7]=>4
[1,4,3,5,2,7,6]=>4
[1,4,3,5,6,2,7]=>4
[1,4,3,5,6,7,2]=>4
[1,4,3,5,7,2,6]=>4
[1,4,3,5,7,6,2]=>4
[1,4,3,6,2,5,7]=>4
[1,4,3,6,2,7,5]=>3
[1,4,3,6,5,2,7]=>4
[1,4,3,6,5,7,2]=>4
[1,4,3,6,7,2,5]=>3
[1,4,3,6,7,5,2]=>3
[1,4,3,7,2,5,6]=>3
[1,4,3,7,2,6,5]=>3
[1,4,3,7,5,2,6]=>3
[1,4,3,7,5,6,2]=>3
[1,4,3,7,6,2,5]=>3
[1,4,3,7,6,5,2]=>3
[1,4,5,2,3,6,7]=>4
[1,4,5,2,3,7,6]=>3
[1,4,5,2,6,3,7]=>4
[1,4,5,2,6,7,3]=>4
[1,4,5,2,7,3,6]=>3
[1,4,5,2,7,6,3]=>3
[1,4,5,3,2,6,7]=>4
[1,4,5,3,2,7,6]=>3
[1,4,5,3,6,2,7]=>4
[1,4,5,3,6,7,2]=>4
[1,4,5,3,7,2,6]=>3
[1,4,5,3,7,6,2]=>3
[1,4,5,6,2,3,7]=>4
[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]=>4
[1,4,5,6,7,3,2]=>4
[1,4,5,7,2,3,6]=>3
[1,4,5,7,2,6,3]=>3
[1,4,5,7,3,2,6]=>3
[1,4,5,7,3,6,2]=>3
[1,4,5,7,6,2,3]=>3
[1,4,5,7,6,3,2]=>3
[1,4,6,2,3,5,7]=>4
[1,4,6,2,3,7,5]=>3
[1,4,6,2,5,3,7]=>3
[1,4,6,2,5,7,3]=>3
[1,4,6,2,7,3,5]=>3
[1,4,6,2,7,5,3]=>3
[1,4,6,3,2,5,7]=>4
[1,4,6,3,2,7,5]=>3
[1,4,6,3,5,2,7]=>4
[1,4,6,3,5,7,2]=>4
[1,4,6,3,7,2,5]=>3
[1,4,6,3,7,5,2]=>3
[1,4,6,5,2,3,7]=>3
[1,4,6,5,2,7,3]=>3
[1,4,6,5,3,2,7]=>3
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Description
The length of the longest arithmetic progression in a permutation.
For a permutation $\pi$ of length $n$, this is the biggest $k$ such that there exist $1 \leq i_1 < \dots < i_k \leq n$ with
$$\pi(i_2) - \pi(i_1) = \pi(i_3) - \pi(i_2) = \dots = \pi(i_k) - \pi(i_{k-1}).$$
For a permutation $\pi$ of length $n$, this is the biggest $k$ such that there exist $1 \leq i_1 < \dots < i_k \leq n$ with
$$\pi(i_2) - \pi(i_1) = \pi(i_3) - \pi(i_2) = \dots = \pi(i_k) - \pi(i_{k-1}).$$
Code
def arith_prog_next(pi,lst):
new_lst = []
for seq in lst:
for i in range(seq[-1]+1,len(pi)):
if pi[i] - pi[seq[-1]] == pi[seq[-1]] - pi[seq[-2]]:
new_lst.append(seq+[i])
return new_lst
def statistic(pi):
n = len(pi)
if n <= 2:
return n
stat = 1
lst = [[i,j] for j in range(n) for i in range(j)]
while lst:
lst = arith_prog_next(pi,lst)
stat += 1
return stat
Created
Jul 15, 2020 at 08:37 by Christian Stump
Updated
Jul 15, 2020 at 08:37 by Christian Stump
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