Identifier
- St000007: Permutations ⟶ ℤ
Values
=>
[]=>0
[1]=>1
[1,2]=>1
[2,1]=>2
[1,2,3]=>1
[1,3,2]=>2
[2,1,3]=>1
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>3
[1,2,3,4]=>1
[1,2,4,3]=>2
[1,3,2,4]=>1
[1,3,4,2]=>2
[1,4,2,3]=>2
[1,4,3,2]=>3
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>1
[2,3,4,1]=>2
[2,4,1,3]=>2
[2,4,3,1]=>3
[3,1,2,4]=>1
[3,1,4,2]=>2
[3,2,1,4]=>1
[3,2,4,1]=>2
[3,4,1,2]=>2
[3,4,2,1]=>3
[4,1,2,3]=>2
[4,1,3,2]=>3
[4,2,1,3]=>2
[4,2,3,1]=>3
[4,3,1,2]=>3
[4,3,2,1]=>4
[1,2,3,4,5]=>1
[1,2,3,5,4]=>2
[1,2,4,3,5]=>1
[1,2,4,5,3]=>2
[1,2,5,3,4]=>2
[1,2,5,4,3]=>3
[1,3,2,4,5]=>1
[1,3,2,5,4]=>2
[1,3,4,2,5]=>1
[1,3,4,5,2]=>2
[1,3,5,2,4]=>2
[1,3,5,4,2]=>3
[1,4,2,3,5]=>1
[1,4,2,5,3]=>2
[1,4,3,2,5]=>1
[1,4,3,5,2]=>2
[1,4,5,2,3]=>2
[1,4,5,3,2]=>3
[1,5,2,3,4]=>2
[1,5,2,4,3]=>3
[1,5,3,2,4]=>2
[1,5,3,4,2]=>3
[1,5,4,2,3]=>3
[1,5,4,3,2]=>4
[2,1,3,4,5]=>1
[2,1,3,5,4]=>2
[2,1,4,3,5]=>1
[2,1,4,5,3]=>2
[2,1,5,3,4]=>2
[2,1,5,4,3]=>3
[2,3,1,4,5]=>1
[2,3,1,5,4]=>2
[2,3,4,1,5]=>1
[2,3,4,5,1]=>2
[2,3,5,1,4]=>2
[2,3,5,4,1]=>3
[2,4,1,3,5]=>1
[2,4,1,5,3]=>2
[2,4,3,1,5]=>1
[2,4,3,5,1]=>2
[2,4,5,1,3]=>2
[2,4,5,3,1]=>3
[2,5,1,3,4]=>2
[2,5,1,4,3]=>3
[2,5,3,1,4]=>2
[2,5,3,4,1]=>3
[2,5,4,1,3]=>3
[2,5,4,3,1]=>4
[3,1,2,4,5]=>1
[3,1,2,5,4]=>2
[3,1,4,2,5]=>1
[3,1,4,5,2]=>2
[3,1,5,2,4]=>2
[3,1,5,4,2]=>3
[3,2,1,4,5]=>1
[3,2,1,5,4]=>2
[3,2,4,1,5]=>1
[3,2,4,5,1]=>2
[3,2,5,1,4]=>2
[3,2,5,4,1]=>3
[3,4,1,2,5]=>1
[3,4,1,5,2]=>2
[3,4,2,1,5]=>1
[3,4,2,5,1]=>2
[3,4,5,1,2]=>2
[3,4,5,2,1]=>3
[3,5,1,2,4]=>2
[3,5,1,4,2]=>3
[3,5,2,1,4]=>2
[3,5,2,4,1]=>3
[3,5,4,1,2]=>3
[3,5,4,2,1]=>4
[4,1,2,3,5]=>1
[4,1,2,5,3]=>2
[4,1,3,2,5]=>1
[4,1,3,5,2]=>2
[4,1,5,2,3]=>2
[4,1,5,3,2]=>3
[4,2,1,3,5]=>1
[4,2,1,5,3]=>2
[4,2,3,1,5]=>1
[4,2,3,5,1]=>2
[4,2,5,1,3]=>2
[4,2,5,3,1]=>3
[4,3,1,2,5]=>1
[4,3,1,5,2]=>2
[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]=>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]=>2
[5,1,2,4,3]=>3
[5,1,3,2,4]=>2
[5,1,3,4,2]=>3
[5,1,4,2,3]=>3
[5,1,4,3,2]=>4
[5,2,1,3,4]=>2
[5,2,1,4,3]=>3
[5,2,3,1,4]=>2
[5,2,3,4,1]=>3
[5,2,4,1,3]=>3
[5,2,4,3,1]=>4
[5,3,1,2,4]=>2
[5,3,1,4,2]=>3
[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]=>3
[5,4,1,3,2]=>4
[5,4,2,1,3]=>3
[5,4,2,3,1]=>4
[5,4,3,1,2]=>4
[5,4,3,2,1]=>5
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>2
[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>2
[1,2,3,6,4,5]=>2
[1,2,3,6,5,4]=>3
[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>1
[1,2,4,5,6,3]=>2
[1,2,4,6,3,5]=>2
[1,2,4,6,5,3]=>3
[1,2,5,3,4,6]=>1
[1,2,5,3,6,4]=>2
[1,2,5,4,3,6]=>1
[1,2,5,4,6,3]=>2
[1,2,5,6,3,4]=>2
[1,2,5,6,4,3]=>3
[1,2,6,3,4,5]=>2
[1,2,6,3,5,4]=>3
[1,2,6,4,3,5]=>2
[1,2,6,4,5,3]=>3
[1,2,6,5,3,4]=>3
[1,2,6,5,4,3]=>4
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>1
[1,3,2,5,6,4]=>2
[1,3,2,6,4,5]=>2
[1,3,2,6,5,4]=>3
[1,3,4,2,5,6]=>1
[1,3,4,2,6,5]=>2
[1,3,4,5,2,6]=>1
[1,3,4,5,6,2]=>2
[1,3,4,6,2,5]=>2
[1,3,4,6,5,2]=>3
[1,3,5,2,4,6]=>1
[1,3,5,2,6,4]=>2
[1,3,5,4,2,6]=>1
[1,3,5,4,6,2]=>2
[1,3,5,6,2,4]=>2
[1,3,5,6,4,2]=>3
[1,3,6,2,4,5]=>2
[1,3,6,2,5,4]=>3
[1,3,6,4,2,5]=>2
[1,3,6,4,5,2]=>3
[1,3,6,5,2,4]=>3
[1,3,6,5,4,2]=>4
[1,4,2,3,5,6]=>1
[1,4,2,3,6,5]=>2
[1,4,2,5,3,6]=>1
[1,4,2,5,6,3]=>2
[1,4,2,6,3,5]=>2
[1,4,2,6,5,3]=>3
[1,4,3,2,5,6]=>1
[1,4,3,2,6,5]=>2
[1,4,3,5,2,6]=>1
[1,4,3,5,6,2]=>2
[1,4,3,6,2,5]=>2
[1,4,3,6,5,2]=>3
[1,4,5,2,3,6]=>1
[1,4,5,2,6,3]=>2
[1,4,5,3,2,6]=>1
[1,4,5,3,6,2]=>2
[1,4,5,6,2,3]=>2
[1,4,5,6,3,2]=>3
[1,4,6,2,3,5]=>2
[1,4,6,2,5,3]=>3
[1,4,6,3,2,5]=>2
[1,4,6,3,5,2]=>3
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>1
[1,5,2,3,6,4]=>2
[1,5,2,4,3,6]=>1
[1,5,2,4,6,3]=>2
[1,5,2,6,3,4]=>2
[1,5,2,6,4,3]=>3
[1,5,3,2,4,6]=>1
[1,5,3,2,6,4]=>2
[1,5,3,4,2,6]=>1
[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]=>1
[1,5,4,2,6,3]=>2
[1,5,4,3,2,6]=>1
[1,5,4,3,6,2]=>2
[1,5,4,6,2,3]=>2
[1,5,4,6,3,2]=>3
[1,5,6,2,3,4]=>2
[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]=>2
[1,6,2,3,5,4]=>3
[1,6,2,4,3,5]=>2
[1,6,2,4,5,3]=>3
[1,6,2,5,3,4]=>3
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>2
[1,6,3,2,5,4]=>3
[1,6,3,4,2,5]=>2
[1,6,3,4,5,2]=>3
[1,6,3,5,2,4]=>3
[1,6,3,5,4,2]=>4
[1,6,4,2,3,5]=>2
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>2
[1,6,4,3,5,2]=>3
[1,6,4,5,2,3]=>3
[1,6,4,5,3,2]=>4
[1,6,5,2,3,4]=>3
[1,6,5,2,4,3]=>4
[1,6,5,3,2,4]=>3
[1,6,5,3,4,2]=>4
[1,6,5,4,2,3]=>4
[1,6,5,4,3,2]=>5
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>1
[2,1,3,5,6,4]=>2
[2,1,3,6,4,5]=>2
[2,1,3,6,5,4]=>3
[2,1,4,3,5,6]=>1
[2,1,4,3,6,5]=>2
[2,1,4,5,3,6]=>1
[2,1,4,5,6,3]=>2
[2,1,4,6,3,5]=>2
[2,1,4,6,5,3]=>3
[2,1,5,3,4,6]=>1
[2,1,5,3,6,4]=>2
[2,1,5,4,3,6]=>1
[2,1,5,4,6,3]=>2
[2,1,5,6,3,4]=>2
[2,1,5,6,4,3]=>3
[2,1,6,3,4,5]=>2
[2,1,6,3,5,4]=>3
[2,1,6,4,3,5]=>2
[2,1,6,4,5,3]=>3
[2,1,6,5,3,4]=>3
[2,1,6,5,4,3]=>4
[2,3,1,4,5,6]=>1
[2,3,1,4,6,5]=>2
[2,3,1,5,4,6]=>1
[2,3,1,5,6,4]=>2
[2,3,1,6,4,5]=>2
[2,3,1,6,5,4]=>3
[2,3,4,1,5,6]=>1
[2,3,4,1,6,5]=>2
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>2
[2,3,4,6,1,5]=>2
[2,3,4,6,5,1]=>3
[2,3,5,1,4,6]=>1
[2,3,5,1,6,4]=>2
[2,3,5,4,1,6]=>1
[2,3,5,4,6,1]=>2
[2,3,5,6,1,4]=>2
[2,3,5,6,4,1]=>3
[2,3,6,1,4,5]=>2
[2,3,6,1,5,4]=>3
[2,3,6,4,1,5]=>2
[2,3,6,4,5,1]=>3
[2,3,6,5,1,4]=>3
[2,3,6,5,4,1]=>4
[2,4,1,3,5,6]=>1
[2,4,1,3,6,5]=>2
[2,4,1,5,3,6]=>1
[2,4,1,5,6,3]=>2
[2,4,1,6,3,5]=>2
[2,4,1,6,5,3]=>3
[2,4,3,1,5,6]=>1
[2,4,3,1,6,5]=>2
[2,4,3,5,1,6]=>1
[2,4,3,5,6,1]=>2
[2,4,3,6,1,5]=>2
[2,4,3,6,5,1]=>3
[2,4,5,1,3,6]=>1
[2,4,5,1,6,3]=>2
[2,4,5,3,1,6]=>1
[2,4,5,3,6,1]=>2
[2,4,5,6,1,3]=>2
[2,4,5,6,3,1]=>3
[2,4,6,1,3,5]=>2
[2,4,6,1,5,3]=>3
[2,4,6,3,1,5]=>2
[2,4,6,3,5,1]=>3
[2,4,6,5,1,3]=>3
[2,4,6,5,3,1]=>4
[2,5,1,3,4,6]=>1
[2,5,1,3,6,4]=>2
[2,5,1,4,3,6]=>1
[2,5,1,4,6,3]=>2
[2,5,1,6,3,4]=>2
[2,5,1,6,4,3]=>3
[2,5,3,1,4,6]=>1
[2,5,3,1,6,4]=>2
[2,5,3,4,1,6]=>1
[2,5,3,4,6,1]=>2
[2,5,3,6,1,4]=>2
[2,5,3,6,4,1]=>3
[2,5,4,1,3,6]=>1
[2,5,4,1,6,3]=>2
[2,5,4,3,1,6]=>1
[2,5,4,3,6,1]=>2
[2,5,4,6,1,3]=>2
[2,5,4,6,3,1]=>3
[2,5,6,1,3,4]=>2
[2,5,6,1,4,3]=>3
[2,5,6,3,1,4]=>2
[2,5,6,3,4,1]=>3
[2,5,6,4,1,3]=>3
[2,5,6,4,3,1]=>4
[2,6,1,3,4,5]=>2
[2,6,1,3,5,4]=>3
[2,6,1,4,3,5]=>2
[2,6,1,4,5,3]=>3
[2,6,1,5,3,4]=>3
[2,6,1,5,4,3]=>4
[2,6,3,1,4,5]=>2
[2,6,3,1,5,4]=>3
[2,6,3,4,1,5]=>2
[2,6,3,4,5,1]=>3
[2,6,3,5,1,4]=>3
[2,6,3,5,4,1]=>4
[2,6,4,1,3,5]=>2
[2,6,4,1,5,3]=>3
[2,6,4,3,1,5]=>2
[2,6,4,3,5,1]=>3
[2,6,4,5,1,3]=>3
[2,6,4,5,3,1]=>4
[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]=>4
[2,6,5,4,1,3]=>4
[2,6,5,4,3,1]=>5
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>2
[3,1,2,5,4,6]=>1
[3,1,2,5,6,4]=>2
[3,1,2,6,4,5]=>2
[3,1,2,6,5,4]=>3
[3,1,4,2,5,6]=>1
[3,1,4,2,6,5]=>2
[3,1,4,5,2,6]=>1
[3,1,4,5,6,2]=>2
[3,1,4,6,2,5]=>2
[3,1,4,6,5,2]=>3
[3,1,5,2,4,6]=>1
[3,1,5,2,6,4]=>2
[3,1,5,4,2,6]=>1
[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]=>2
[3,1,6,2,5,4]=>3
[3,1,6,4,2,5]=>2
[3,1,6,4,5,2]=>3
[3,1,6,5,2,4]=>3
[3,1,6,5,4,2]=>4
[3,2,1,4,5,6]=>1
[3,2,1,4,6,5]=>2
[3,2,1,5,4,6]=>1
[3,2,1,5,6,4]=>2
[3,2,1,6,4,5]=>2
[3,2,1,6,5,4]=>3
[3,2,4,1,5,6]=>1
[3,2,4,1,6,5]=>2
[3,2,4,5,1,6]=>1
[3,2,4,5,6,1]=>2
[3,2,4,6,1,5]=>2
[3,2,4,6,5,1]=>3
[3,2,5,1,4,6]=>1
[3,2,5,1,6,4]=>2
[3,2,5,4,1,6]=>1
[3,2,5,4,6,1]=>2
[3,2,5,6,1,4]=>2
[3,2,5,6,4,1]=>3
[3,2,6,1,4,5]=>2
[3,2,6,1,5,4]=>3
[3,2,6,4,1,5]=>2
[3,2,6,4,5,1]=>3
[3,2,6,5,1,4]=>3
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>1
[3,4,1,2,6,5]=>2
[3,4,1,5,2,6]=>1
[3,4,1,5,6,2]=>2
[3,4,1,6,2,5]=>2
[3,4,1,6,5,2]=>3
[3,4,2,1,5,6]=>1
[3,4,2,1,6,5]=>2
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>2
[3,4,2,6,1,5]=>2
[3,4,2,6,5,1]=>3
[3,4,5,1,2,6]=>1
[3,4,5,1,6,2]=>2
[3,4,5,2,1,6]=>1
[3,4,5,2,6,1]=>2
[3,4,5,6,1,2]=>2
[3,4,5,6,2,1]=>3
[3,4,6,1,2,5]=>2
[3,4,6,1,5,2]=>3
[3,4,6,2,1,5]=>2
[3,4,6,2,5,1]=>3
[3,4,6,5,1,2]=>3
[3,4,6,5,2,1]=>4
[3,5,1,2,4,6]=>1
[3,5,1,2,6,4]=>2
[3,5,1,4,2,6]=>1
[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]=>1
[3,5,2,1,6,4]=>2
[3,5,2,4,1,6]=>1
[3,5,2,4,6,1]=>2
[3,5,2,6,1,4]=>2
[3,5,2,6,4,1]=>3
[3,5,4,1,2,6]=>1
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>2
[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]=>2
[3,5,6,2,4,1]=>3
[3,5,6,4,1,2]=>3
[3,5,6,4,2,1]=>4
[3,6,1,2,4,5]=>2
[3,6,1,2,5,4]=>3
[3,6,1,4,2,5]=>2
[3,6,1,4,5,2]=>3
[3,6,1,5,2,4]=>3
[3,6,1,5,4,2]=>4
[3,6,2,1,4,5]=>2
[3,6,2,1,5,4]=>3
[3,6,2,4,1,5]=>2
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>3
[3,6,2,5,4,1]=>4
[3,6,4,1,2,5]=>2
[3,6,4,1,5,2]=>3
[3,6,4,2,1,5]=>2
[3,6,4,2,5,1]=>3
[3,6,4,5,1,2]=>3
[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]=>4
[3,6,5,4,2,1]=>5
[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>2
[4,1,2,5,3,6]=>1
[4,1,2,5,6,3]=>2
[4,1,2,6,3,5]=>2
[4,1,2,6,5,3]=>3
[4,1,3,2,5,6]=>1
[4,1,3,2,6,5]=>2
[4,1,3,5,2,6]=>1
[4,1,3,5,6,2]=>2
[4,1,3,6,2,5]=>2
[4,1,3,6,5,2]=>3
[4,1,5,2,3,6]=>1
[4,1,5,2,6,3]=>2
[4,1,5,3,2,6]=>1
[4,1,5,3,6,2]=>2
[4,1,5,6,2,3]=>2
[4,1,5,6,3,2]=>3
[4,1,6,2,3,5]=>2
[4,1,6,2,5,3]=>3
[4,1,6,3,2,5]=>2
[4,1,6,3,5,2]=>3
[4,1,6,5,2,3]=>3
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>1
[4,2,1,3,6,5]=>2
[4,2,1,5,3,6]=>1
[4,2,1,5,6,3]=>2
[4,2,1,6,3,5]=>2
[4,2,1,6,5,3]=>3
[4,2,3,1,5,6]=>1
[4,2,3,1,6,5]=>2
[4,2,3,5,1,6]=>1
[4,2,3,5,6,1]=>2
[4,2,3,6,1,5]=>2
[4,2,3,6,5,1]=>3
[4,2,5,1,3,6]=>1
[4,2,5,1,6,3]=>2
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>2
[4,2,5,6,1,3]=>2
[4,2,5,6,3,1]=>3
[4,2,6,1,3,5]=>2
[4,2,6,1,5,3]=>3
[4,2,6,3,1,5]=>2
[4,2,6,3,5,1]=>3
[4,2,6,5,1,3]=>3
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>1
[4,3,1,2,6,5]=>2
[4,3,1,5,2,6]=>1
[4,3,1,5,6,2]=>2
[4,3,1,6,2,5]=>2
[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]=>1
[4,3,2,5,6,1]=>2
[4,3,2,6,1,5]=>2
[4,3,2,6,5,1]=>3
[4,3,5,1,2,6]=>1
[4,3,5,1,6,2]=>2
[4,3,5,2,1,6]=>1
[4,3,5,2,6,1]=>2
[4,3,5,6,1,2]=>2
[4,3,5,6,2,1]=>3
[4,3,6,1,2,5]=>2
[4,3,6,1,5,2]=>3
[4,3,6,2,1,5]=>2
[4,3,6,2,5,1]=>3
[4,3,6,5,1,2]=>3
[4,3,6,5,2,1]=>4
[4,5,1,2,3,6]=>1
[4,5,1,2,6,3]=>2
[4,5,1,3,2,6]=>1
[4,5,1,3,6,2]=>2
[4,5,1,6,2,3]=>2
[4,5,1,6,3,2]=>3
[4,5,2,1,3,6]=>1
[4,5,2,1,6,3]=>2
[4,5,2,3,1,6]=>1
[4,5,2,3,6,1]=>2
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>3
[4,5,3,1,2,6]=>1
[4,5,3,1,6,2]=>2
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>2
[4,5,3,6,1,2]=>2
[4,5,3,6,2,1]=>3
[4,5,6,1,2,3]=>2
[4,5,6,1,3,2]=>3
[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]=>4
[4,6,1,2,3,5]=>2
[4,6,1,2,5,3]=>3
[4,6,1,3,2,5]=>2
[4,6,1,3,5,2]=>3
[4,6,1,5,2,3]=>3
[4,6,1,5,3,2]=>4
[4,6,2,1,3,5]=>2
[4,6,2,1,5,3]=>3
[4,6,2,3,1,5]=>2
[4,6,2,3,5,1]=>3
[4,6,2,5,1,3]=>3
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>2
[4,6,3,1,5,2]=>3
[4,6,3,2,1,5]=>2
[4,6,3,2,5,1]=>3
[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]=>4
[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]=>5
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>2
[5,1,2,4,3,6]=>1
[5,1,2,4,6,3]=>2
[5,1,2,6,3,4]=>2
[5,1,2,6,4,3]=>3
[5,1,3,2,4,6]=>1
[5,1,3,2,6,4]=>2
[5,1,3,4,2,6]=>1
[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]=>1
[5,1,4,2,6,3]=>2
[5,1,4,3,2,6]=>1
[5,1,4,3,6,2]=>2
[5,1,4,6,2,3]=>2
[5,1,4,6,3,2]=>3
[5,1,6,2,3,4]=>2
[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]=>1
[5,2,1,3,6,4]=>2
[5,2,1,4,3,6]=>1
[5,2,1,4,6,3]=>2
[5,2,1,6,3,4]=>2
[5,2,1,6,4,3]=>3
[5,2,3,1,4,6]=>1
[5,2,3,1,6,4]=>2
[5,2,3,4,1,6]=>1
[5,2,3,4,6,1]=>2
[5,2,3,6,1,4]=>2
[5,2,3,6,4,1]=>3
[5,2,4,1,3,6]=>1
[5,2,4,1,6,3]=>2
[5,2,4,3,1,6]=>1
[5,2,4,3,6,1]=>2
[5,2,4,6,1,3]=>2
[5,2,4,6,3,1]=>3
[5,2,6,1,3,4]=>2
[5,2,6,1,4,3]=>3
[5,2,6,3,1,4]=>2
[5,2,6,3,4,1]=>3
[5,2,6,4,1,3]=>3
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>1
[5,3,1,2,6,4]=>2
[5,3,1,4,2,6]=>1
[5,3,1,4,6,2]=>2
[5,3,1,6,2,4]=>2
[5,3,1,6,4,2]=>3
[5,3,2,1,4,6]=>1
[5,3,2,1,6,4]=>2
[5,3,2,4,1,6]=>1
[5,3,2,4,6,1]=>2
[5,3,2,6,1,4]=>2
[5,3,2,6,4,1]=>3
[5,3,4,1,2,6]=>1
[5,3,4,1,6,2]=>2
[5,3,4,2,1,6]=>1
[5,3,4,2,6,1]=>2
[5,3,4,6,1,2]=>2
[5,3,4,6,2,1]=>3
[5,3,6,1,2,4]=>2
[5,3,6,1,4,2]=>3
[5,3,6,2,1,4]=>2
[5,3,6,2,4,1]=>3
[5,3,6,4,1,2]=>3
[5,3,6,4,2,1]=>4
[5,4,1,2,3,6]=>1
[5,4,1,2,6,3]=>2
[5,4,1,3,2,6]=>1
[5,4,1,3,6,2]=>2
[5,4,1,6,2,3]=>2
[5,4,1,6,3,2]=>3
[5,4,2,1,3,6]=>1
[5,4,2,1,6,3]=>2
[5,4,2,3,1,6]=>1
[5,4,2,3,6,1]=>2
[5,4,2,6,1,3]=>2
[5,4,2,6,3,1]=>3
[5,4,3,1,2,6]=>1
[5,4,3,1,6,2]=>2
[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]=>2
[5,4,6,2,3,1]=>3
[5,4,6,3,1,2]=>3
[5,4,6,3,2,1]=>4
[5,6,1,2,3,4]=>2
[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]=>2
[5,6,2,1,4,3]=>3
[5,6,2,3,1,4]=>2
[5,6,2,3,4,1]=>3
[5,6,2,4,1,3]=>3
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>2
[5,6,3,1,4,2]=>3
[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]=>3
[5,6,4,2,3,1]=>4
[5,6,4,3,1,2]=>4
[5,6,4,3,2,1]=>5
[6,1,2,3,4,5]=>2
[6,1,2,3,5,4]=>3
[6,1,2,4,3,5]=>2
[6,1,2,4,5,3]=>3
[6,1,2,5,3,4]=>3
[6,1,2,5,4,3]=>4
[6,1,3,2,4,5]=>2
[6,1,3,2,5,4]=>3
[6,1,3,4,2,5]=>2
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>3
[6,1,3,5,4,2]=>4
[6,1,4,2,3,5]=>2
[6,1,4,2,5,3]=>3
[6,1,4,3,2,5]=>2
[6,1,4,3,5,2]=>3
[6,1,4,5,2,3]=>3
[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]=>3
[6,1,5,3,4,2]=>4
[6,1,5,4,2,3]=>4
[6,1,5,4,3,2]=>5
[6,2,1,3,4,5]=>2
[6,2,1,3,5,4]=>3
[6,2,1,4,3,5]=>2
[6,2,1,4,5,3]=>3
[6,2,1,5,3,4]=>3
[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>2
[6,2,3,1,5,4]=>3
[6,2,3,4,1,5]=>2
[6,2,3,4,5,1]=>3
[6,2,3,5,1,4]=>3
[6,2,3,5,4,1]=>4
[6,2,4,1,3,5]=>2
[6,2,4,1,5,3]=>3
[6,2,4,3,1,5]=>2
[6,2,4,3,5,1]=>3
[6,2,4,5,1,3]=>3
[6,2,4,5,3,1]=>4
[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]=>4
[6,2,5,4,1,3]=>4
[6,2,5,4,3,1]=>5
[6,3,1,2,4,5]=>2
[6,3,1,2,5,4]=>3
[6,3,1,4,2,5]=>2
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>3
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>2
[6,3,2,1,5,4]=>3
[6,3,2,4,1,5]=>2
[6,3,2,4,5,1]=>3
[6,3,2,5,1,4]=>3
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>2
[6,3,4,1,5,2]=>3
[6,3,4,2,1,5]=>2
[6,3,4,2,5,1]=>3
[6,3,4,5,1,2]=>3
[6,3,4,5,2,1]=>4
[6,3,5,1,2,4]=>3
[6,3,5,1,4,2]=>4
[6,3,5,2,1,4]=>3
[6,3,5,2,4,1]=>4
[6,3,5,4,1,2]=>4
[6,3,5,4,2,1]=>5
[6,4,1,2,3,5]=>2
[6,4,1,2,5,3]=>3
[6,4,1,3,2,5]=>2
[6,4,1,3,5,2]=>3
[6,4,1,5,2,3]=>3
[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>2
[6,4,2,1,5,3]=>3
[6,4,2,3,1,5]=>2
[6,4,2,3,5,1]=>3
[6,4,2,5,1,3]=>3
[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>2
[6,4,3,1,5,2]=>3
[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]=>3
[6,4,5,2,3,1]=>4
[6,4,5,3,1,2]=>4
[6,4,5,3,2,1]=>5
[6,5,1,2,3,4]=>3
[6,5,1,2,4,3]=>4
[6,5,1,3,2,4]=>3
[6,5,1,3,4,2]=>4
[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]=>4
[6,5,2,4,1,3]=>4
[6,5,2,4,3,1]=>5
[6,5,3,1,2,4]=>3
[6,5,3,1,4,2]=>4
[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]=>5
[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]=>5
[6,5,4,3,1,2]=>5
[6,5,4,3,2,1]=>6
[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>2
[1,2,3,4,6,5,7]=>1
[1,2,3,6,4,7,5]=>2
[1,2,6,3,4,7,5]=>2
[1,3,2,4,5,6,7]=>1
[1,3,7,2,4,5,6]=>2
[1,3,7,6,5,4,2]=>5
[1,4,6,7,2,3,5]=>2
[1,4,6,7,5,3,2]=>4
[1,4,7,2,3,5,6]=>2
[1,4,7,6,5,3,2]=>5
[1,5,2,3,4,7,6]=>2
[1,5,2,7,3,4,6]=>2
[1,5,4,7,6,3,2]=>4
[1,5,6,2,7,3,4]=>2
[1,5,6,4,7,3,2]=>3
[1,5,6,7,2,3,4]=>2
[1,5,6,7,4,3,2]=>4
[1,5,7,2,3,4,6]=>2
[1,5,7,6,4,3,2]=>5
[1,6,2,3,4,7,5]=>2
[1,6,2,3,7,4,5]=>2
[1,6,2,7,3,4,5]=>2
[1,6,5,4,3,7,2]=>2
[1,6,5,4,7,3,2]=>3
[1,6,5,7,4,3,2]=>4
[1,6,7,2,3,4,5]=>2
[1,6,7,5,4,3,2]=>5
[1,7,2,3,4,5,6]=>2
[1,7,3,5,6,4,2]=>4
[1,7,3,6,5,4,2]=>5
[1,7,4,3,6,5,2]=>4
[1,7,4,5,3,6,2]=>3
[1,7,4,5,6,3,2]=>4
[1,7,4,6,5,3,2]=>5
[1,7,5,4,3,6,2]=>3
[1,7,5,4,6,3,2]=>4
[1,7,6,4,5,3,2]=>5
[1,7,6,5,4,3,2]=>6
[2,1,3,4,5,6,7]=>1
[2,1,3,4,7,5,6]=>2
[2,1,3,7,4,5,6]=>2
[2,1,6,3,4,5,7]=>1
[2,1,7,3,4,5,6]=>2
[2,1,7,6,5,4,3]=>5
[2,3,1,4,5,6,7]=>1
[2,3,4,1,5,6,7]=>1
[2,3,4,1,5,7,6]=>2
[2,3,4,5,1,6,7]=>1
[2,3,4,5,1,7,6]=>2
[2,3,4,5,6,1,7]=>1
[2,3,4,5,6,7,1]=>2
[2,3,4,5,7,1,6]=>2
[2,3,4,6,1,7,5]=>2
[2,3,4,6,7,1,5]=>2
[2,3,4,7,1,5,6]=>2
[2,3,5,6,7,1,4]=>2
[2,4,1,3,5,6,7]=>1
[2,5,1,3,4,6,7]=>1
[2,5,7,1,3,4,6]=>2
[2,6,1,3,4,5,7]=>1
[2,6,1,7,3,4,5]=>2
[2,6,5,4,3,1,7]=>1
[2,6,7,1,3,4,5]=>2
[2,7,1,3,4,5,6]=>2
[3,1,2,4,5,6,7]=>1
[3,1,2,4,5,7,6]=>2
[3,2,1,4,5,6,7]=>1
[3,2,4,5,6,7,1]=>2
[3,4,1,2,5,6,7]=>1
[3,4,2,5,6,7,1]=>2
[3,4,5,2,6,7,1]=>2
[3,4,5,6,2,7,1]=>2
[3,4,5,6,7,1,2]=>2
[3,5,6,1,2,4,7]=>1
[3,5,6,4,2,1,7]=>1
[3,6,1,2,4,5,7]=>1
[3,6,5,4,2,1,7]=>1
[4,1,2,3,5,6,7]=>1
[4,1,2,3,5,7,6]=>2
[4,1,6,2,3,5,7]=>1
[4,2,3,5,6,7,1]=>2
[4,2,5,1,3,6,7]=>1
[4,3,2,1,5,6,7]=>1
[4,3,2,5,6,7,1]=>2
[4,3,5,2,6,7,1]=>2
[4,3,6,5,2,1,7]=>1
[4,5,1,6,2,3,7]=>1
[4,5,2,3,6,7,1]=>2
[4,5,3,6,2,1,7]=>1
[4,5,6,1,2,3,7]=>1
[4,5,6,3,2,1,7]=>1
[4,6,1,2,3,5,7]=>1
[4,6,1,2,3,7,5]=>2
[4,6,5,3,2,1,7]=>1
[5,1,2,3,4,6,7]=>1
[5,1,2,3,4,7,6]=>2
[5,1,2,3,6,4,7]=>1
[5,1,2,3,6,7,4]=>2
[5,1,2,3,7,4,6]=>2
[5,1,2,6,3,4,7]=>1
[5,1,6,2,3,4,7]=>1
[5,1,6,2,3,7,4]=>2
[5,2,3,4,6,7,1]=>2
[5,2,6,7,1,3,4]=>2
[5,3,2,4,6,7,1]=>2
[5,3,2,6,1,4,7]=>1
[5,3,6,7,1,2,4]=>2
[5,4,3,2,1,6,7]=>1
[5,4,3,2,1,7,6]=>2
[5,4,3,2,6,1,7]=>1
[5,4,3,6,2,1,7]=>1
[5,4,6,3,2,1,7]=>1
[5,4,6,7,1,2,3]=>2
[5,6,1,2,3,4,7]=>1
[5,6,1,2,3,7,4]=>2
[5,6,3,4,1,2,7]=>1
[5,6,4,3,2,1,7]=>1
[5,6,7,1,2,3,4]=>2
[6,1,2,3,4,5,7]=>1
[6,1,2,3,4,7,5]=>2
[6,1,2,3,7,4,5]=>2
[6,1,2,7,3,4,5]=>2
[6,2,3,4,5,7,1]=>2
[6,2,4,5,3,1,7]=>1
[6,2,5,4,3,1,7]=>1
[6,3,2,5,4,1,7]=>1
[6,3,4,2,5,1,7]=>1
[6,3,4,5,2,1,7]=>1
[6,3,4,7,1,2,5]=>2
[6,3,5,4,2,1,7]=>1
[6,4,3,2,5,1,7]=>1
[6,4,3,2,7,1,5]=>2
[6,4,3,5,2,1,7]=>1
[6,4,5,7,1,2,3]=>2
[6,4,7,2,5,1,3]=>3
[6,4,7,3,5,1,2]=>3
[6,5,3,4,2,1,7]=>1
[6,5,4,3,2,1,7]=>1
[6,5,7,3,4,1,2]=>3
[6,7,1,2,3,4,5]=>2
[6,7,3,4,1,2,5]=>2
[6,7,4,5,1,2,3]=>3
[7,1,2,3,4,5,6]=>2
[7,2,1,3,4,5,6]=>2
[7,2,3,1,4,5,6]=>2
[7,2,3,4,1,5,6]=>2
[7,2,3,4,5,1,6]=>2
[7,3,1,2,4,5,6]=>2
[7,3,2,1,4,5,6]=>2
[7,3,2,4,1,5,6]=>2
[7,3,4,1,2,5,6]=>2
[7,4,1,2,3,5,6]=>2
[7,4,2,1,3,5,6]=>2
[7,4,5,6,1,2,3]=>3
[7,5,1,2,3,4,6]=>2
[7,5,6,1,2,3,4]=>3
[7,5,6,3,4,1,2]=>4
[7,6,1,2,3,4,5]=>3
[7,6,4,5,1,2,3]=>4
[7,6,5,1,2,3,4]=>4
[7,6,5,3,4,1,2]=>5
[7,6,5,4,1,2,3]=>5
[7,6,5,4,3,1,2]=>6
[7,6,5,4,3,2,1]=>7
[8,7,6,5,4,3,2,1]=>8
[7,6,8,5,4,3,2,1]=>6
[7,8,5,6,4,3,2,1]=>6
[7,8,6,4,5,3,2,1]=>6
[8,6,7,4,5,3,2,1]=>6
[7,6,5,4,8,3,2,1]=>4
[6,5,7,4,8,3,2,1]=>4
[7,8,6,5,3,4,2,1]=>6
[8,6,7,5,3,4,2,1]=>6
[8,7,5,6,3,4,2,1]=>6
[6,7,8,3,4,5,2,1]=>4
[7,8,6,5,4,2,3,1]=>6
[8,6,7,5,4,2,3,1]=>6
[8,7,5,6,4,2,3,1]=>6
[8,7,6,4,5,2,3,1]=>6
[8,6,5,7,3,2,4,1]=>4
[6,7,8,5,2,3,4,1]=>4
[8,5,6,7,2,3,4,1]=>4
[7,8,3,2,4,5,6,1]=>3
[7,6,5,4,3,2,8,1]=>2
[6,5,7,4,3,2,8,1]=>2
[6,5,4,3,7,2,8,1]=>2
[5,4,6,3,7,2,8,1]=>2
[3,4,5,2,6,7,8,1]=>2
[5,2,3,4,6,7,8,1]=>2
[4,3,2,5,6,7,8,1]=>2
[3,4,2,5,6,7,8,1]=>2
[4,2,3,5,6,7,8,1]=>2
[3,2,4,5,6,7,8,1]=>2
[2,3,4,5,6,7,8,1]=>2
[8,7,6,5,4,3,1,2]=>7
[7,8,6,5,4,3,1,2]=>6
[8,6,7,5,4,3,1,2]=>6
[8,7,5,6,4,3,1,2]=>6
[8,7,6,4,5,3,1,2]=>6
[8,7,6,5,3,4,1,2]=>6
[8,7,5,6,3,4,1,2]=>5
[7,8,5,6,3,4,1,2]=>4
[5,6,7,8,3,4,1,2]=>3
[7,8,3,4,5,6,1,2]=>3
[3,4,5,6,7,8,1,2]=>2
[8,7,6,5,4,2,1,3]=>6
[7,6,8,5,4,2,1,3]=>4
[8,7,6,5,4,1,2,3]=>6
[6,7,8,5,4,1,2,3]=>4
[8,5,6,7,4,1,2,3]=>4
[8,7,6,4,5,1,2,3]=>5
[8,6,7,4,5,1,2,3]=>4
[8,7,4,5,6,1,2,3]=>4
[7,8,4,5,6,1,2,3]=>3
[6,7,4,5,8,1,2,3]=>2
[7,6,5,8,3,2,1,4]=>2
[7,5,6,8,2,3,1,4]=>2
[6,7,5,8,3,1,2,4]=>2
[6,5,7,8,2,1,3,4]=>2
[8,7,6,5,1,2,3,4]=>5
[8,7,5,6,1,2,3,4]=>4
[7,8,5,6,1,2,3,4]=>3
[8,5,6,7,1,2,3,4]=>3
[5,6,7,8,1,2,3,4]=>2
[8,7,6,4,3,2,1,5]=>4
[8,7,6,4,2,1,3,5]=>4
[8,7,6,1,2,3,4,5]=>4
[8,6,7,1,2,3,4,5]=>3
[6,7,8,1,2,3,4,5]=>2
[7,8,5,4,2,1,3,6]=>2
[7,8,5,4,1,2,3,6]=>2
[8,7,1,2,3,4,5,6]=>3
[7,8,1,2,3,4,5,6]=>2
[8,6,5,4,3,2,1,7]=>2
[8,6,5,4,3,1,2,7]=>2
[8,5,6,3,4,1,2,7]=>2
[8,6,5,4,2,1,3,7]=>2
[8,6,4,3,2,1,5,7]=>2
[8,6,4,2,1,3,5,7]=>2
[8,2,3,4,1,5,6,7]=>2
[8,4,1,2,3,5,6,7]=>2
[8,3,2,1,4,5,6,7]=>2
[8,2,3,1,4,5,6,7]=>2
[8,3,1,2,4,5,6,7]=>2
[8,2,1,3,4,5,6,7]=>2
[8,1,2,3,4,5,6,7]=>2
[7,6,5,4,3,2,1,8]=>1
[6,7,5,4,3,2,1,8]=>1
[6,5,7,4,3,2,1,8]=>1
[5,6,7,4,3,2,1,8]=>1
[7,6,4,5,3,2,1,8]=>1
[6,5,4,7,3,2,1,8]=>1
[7,5,6,3,4,2,1,8]=>1
[7,6,4,3,5,2,1,8]=>1
[7,6,3,4,5,2,1,8]=>1
[7,5,4,3,6,2,1,8]=>1
[6,7,5,4,2,3,1,8]=>1
[6,5,7,3,2,4,1,8]=>1
[5,6,7,2,3,4,1,8]=>1
[2,3,4,5,6,7,1,8]=>1
[5,6,7,1,2,3,4,8]=>1
[6,7,1,2,3,4,5,8]=>1
[7,1,2,3,4,5,6,8]=>1
[6,5,4,3,2,1,7,8]=>1
[2,3,4,5,6,1,7,8]=>1
[5,6,3,4,1,2,7,8]=>1
[4,5,6,1,2,3,7,8]=>1
[6,1,2,3,4,5,7,8]=>1
[5,4,3,2,1,6,7,8]=>1
[2,3,4,5,1,6,7,8]=>1
[5,1,2,3,4,6,7,8]=>1
[4,3,2,1,5,6,7,8]=>1
[3,4,1,2,5,6,7,8]=>1
[3,2,1,4,5,6,7,8]=>1
[2,1,3,4,5,6,7,8]=>1
[1,2,3,4,5,6,7,8]=>1
[6,5,8,7,4,3,2,1]=>6
[3,5,8,7,6,4,2,1]=>6
[4,3,6,5,8,7,2,1]=>4
[2,6,8,7,5,4,3,1]=>6
[2,3,5,6,8,7,4,1]=>4
[3,2,6,5,4,8,7,1]=>3
[4,3,6,5,7,2,8,1]=>2
[3,2,6,5,7,4,8,1]=>2
[4,3,5,2,7,6,8,1]=>2
[3,2,5,4,7,6,8,1]=>2
[1,8,7,6,5,4,3,2]=>7
[1,7,8,6,5,4,3,2]=>6
[1,6,8,7,5,4,3,2]=>6
[1,7,6,8,5,4,3,2]=>5
[1,6,7,8,5,4,3,2]=>5
[1,5,8,7,6,4,3,2]=>6
[1,7,6,5,8,4,3,2]=>4
[1,3,5,7,8,6,4,2]=>4
[1,4,3,8,7,6,5,2]=>5
[1,6,5,4,3,8,7,2]=>3
[1,4,3,6,5,8,7,2]=>3
[2,1,8,7,6,5,4,3]=>6
[2,1,6,5,7,4,8,3]=>2
[2,1,5,4,7,6,8,3]=>2
[1,2,6,7,8,5,4,3]=>4
[3,2,1,8,7,6,5,4]=>5
[3,2,1,6,5,8,7,4]=>3
[1,2,3,5,6,7,8,4]=>2
[4,3,2,1,8,7,6,5]=>4
[3,4,2,1,7,8,6,5]=>3
[2,4,3,1,6,8,7,5]=>3
[2,4,3,1,7,6,8,5]=>2
[3,2,4,1,6,8,7,5]=>3
[3,2,4,1,7,6,8,5]=>2
[2,3,4,1,6,7,8,5]=>2
[2,1,4,3,8,7,6,5]=>4
[2,1,4,3,6,8,7,5]=>3
[2,1,4,3,7,6,8,5]=>2
[5,4,3,2,1,8,7,6]=>3
[3,2,5,4,1,8,7,6]=>3
[3,2,1,4,5,8,7,6]=>3
[2,3,1,4,5,7,8,6]=>2
[6,5,4,3,2,1,8,7]=>2
[4,3,5,2,6,1,8,7]=>2
[3,2,5,4,6,1,8,7]=>2
[2,3,4,5,6,1,8,7]=>2
[2,1,6,5,4,3,8,7]=>2
[2,1,4,6,5,3,8,7]=>2
[2,1,5,4,6,3,8,7]=>2
[4,3,2,1,6,5,8,7]=>2
[2,4,3,1,6,5,8,7]=>2
[3,2,4,1,6,5,8,7]=>2
[2,1,4,3,6,5,8,7]=>2
[2,1,3,4,5,6,8,7]=>2
[1,2,3,4,5,6,8,7]=>2
[5,7,6,4,3,2,1,8]=>1
[4,7,6,5,3,2,1,8]=>1
[3,2,7,6,5,4,1,8]=>1
[5,4,3,2,7,6,1,8]=>1
[3,2,5,4,7,6,1,8]=>1
[1,4,3,2,7,6,5,8]=>1
[1,3,4,2,6,7,5,8]=>1
[1,3,2,5,4,7,6,8]=>1
[1,2,3,5,4,7,6,8]=>1
[1,3,2,4,5,7,6,8]=>1
[1,2,3,4,5,7,6,8]=>1
[1,2,4,3,6,5,7,8]=>1
[1,3,2,5,4,6,7,8]=>1
[1,2,3,5,4,6,7,8]=>1
[1,3,2,4,5,6,7,8]=>1
[1,8,4,7,6,5,3,2]=>6
[1,8,5,4,7,6,3,2]=>5
[1,8,7,4,5,6,3,2]=>5
[1,8,7,4,6,5,3,2]=>6
[1,8,6,5,4,7,3,2]=>4
[1,8,7,5,4,6,3,2]=>5
[1,8,7,5,6,4,3,2]=>6
[2,1,4,5,8,6,7,3]=>3
[2,1,8,5,4,7,6,3]=>4
[2,3,4,8,5,6,7,1]=>3
[2,3,6,4,5,1,8,7]=>2
[2,3,7,4,5,6,8,1]=>2
[2,8,4,3,5,7,6,1]=>4
[4,2,3,1,8,6,7,5]=>3
[8,2,7,4,6,5,3,1]=>6
[4,3,2,7,5,6,8,1]=>2
[4,3,2,8,5,7,6,1]=>4
[6,3,2,5,4,1,8,7]=>2
[8,3,2,5,4,7,6,1]=>4
[8,3,2,7,6,5,4,1]=>6
[8,3,7,4,6,5,2,1]=>6
[7,3,6,5,4,2,1,8]=>1
[7,4,3,6,5,2,1,8]=>1
[7,6,3,5,4,2,1,8]=>1
[8,5,4,3,2,7,6,1]=>4
[8,7,4,3,6,5,2,1]=>6
[2,4,6,8,1,3,5,7]=>2
[2,4,6,1,7,3,8,5]=>2
[2,1,4,3,7,5,8,6]=>2
[2,4,1,3,7,5,8,6]=>2
[2,1,4,3,7,8,5,6]=>2
[2,4,7,8,1,3,5,6]=>2
[2,1,4,3,8,5,6,7]=>2
[2,4,5,6,7,1,8,3]=>2
[2,1,5,3,6,4,8,7]=>2
[2,1,5,6,3,4,8,7]=>2
[2,5,6,8,1,3,4,7]=>2
[2,1,5,3,7,4,8,6]=>2
[2,5,1,7,3,4,8,6]=>2
[2,1,5,7,3,8,4,6]=>2
[2,5,7,8,1,3,4,6]=>2
[2,3,5,6,1,7,8,4]=>2
[2,1,6,3,7,4,8,5]=>2
[2,6,7,1,3,4,8,5]=>2
[2,1,6,7,8,3,4,5]=>2
[2,6,7,8,1,3,4,5]=>2
[2,1,6,3,4,7,8,5]=>2
[2,1,6,3,4,5,8,7]=>2
[2,6,1,3,4,5,7,8]=>1
[2,7,8,1,3,4,5,6]=>2
[2,7,1,3,4,5,6,8]=>1
[2,3,4,5,7,8,1,6]=>2
[2,1,8,3,4,5,6,7]=>2
[2,8,1,3,4,5,6,7]=>2
[2,1,3,8,4,5,6,7]=>2
[2,3,4,5,6,8,1,7]=>2
[3,1,4,2,6,5,8,7]=>2
[3,4,1,2,6,5,8,7]=>2
[3,1,4,2,6,8,5,7]=>2
[3,4,6,8,1,2,5,7]=>2
[3,1,4,2,7,5,8,6]=>2
[3,4,1,2,7,8,5,6]=>2
[3,4,7,8,1,2,5,6]=>2
[3,1,5,2,6,4,8,7]=>2
[3,5,1,6,2,4,8,7]=>2
[3,1,5,6,2,8,4,7]=>2
[3,5,6,8,1,2,4,7]=>2
[3,1,5,2,7,4,8,6]=>2
[3,5,1,7,2,8,4,6]=>2
[3,5,7,8,1,2,4,6]=>2
[1,3,2,5,4,8,6,7]=>2
[1,3,5,8,2,4,6,7]=>2
[1,3,5,6,2,7,4,8]=>1
[3,1,6,2,7,4,8,5]=>2
[3,6,7,1,2,8,4,5]=>2
[3,6,1,7,8,2,4,5]=>2
[3,6,7,8,1,2,4,5]=>2
[1,3,2,6,4,7,5,8]=>1
[3,1,2,6,7,4,8,5]=>2
[1,3,2,6,4,8,5,7]=>2
[1,3,2,6,4,5,7,8]=>1
[1,3,2,7,4,8,5,6]=>2
[1,3,2,7,4,5,6,8]=>1
[1,3,2,8,4,5,6,7]=>2
[3,1,2,4,5,8,6,7]=>2
[1,3,2,4,5,8,6,7]=>2
[4,1,5,2,6,3,8,7]=>2
[4,5,6,1,2,3,8,7]=>2
[4,1,5,6,8,2,3,7]=>2
[4,5,6,8,1,2,3,7]=>2
[4,1,5,2,7,3,8,6]=>2
[4,1,5,2,7,8,3,6]=>2
[4,5,7,1,2,8,3,6]=>2
[4,5,1,7,8,2,3,6]=>2
[4,5,7,8,1,2,3,6]=>2
[1,4,2,5,3,7,6,8]=>1
[1,4,2,5,3,8,6,7]=>2
[1,4,2,5,3,6,7,8]=>1
[1,4,5,6,7,2,3,8]=>1
[4,1,6,2,7,3,8,5]=>2
[4,6,7,1,8,2,3,5]=>2
[4,6,7,8,1,2,3,5]=>2
[1,4,2,6,3,7,5,8]=>1
[1,4,2,6,7,8,3,5]=>2
[1,4,2,6,3,8,5,7]=>2
[4,1,2,3,6,5,8,7]=>2
[1,4,2,6,3,5,7,8]=>1
[1,4,2,7,3,8,5,6]=>2
[4,7,1,2,3,5,6,8]=>1
[1,4,2,7,3,5,6,8]=>1
[1,4,2,3,7,5,6,8]=>1
[1,4,2,3,5,7,6,8]=>1
[1,4,2,8,3,5,6,7]=>2
[4,1,2,3,8,5,6,7]=>2
[1,4,2,3,5,8,6,7]=>2
[1,4,2,3,5,6,7,8]=>1
[5,1,6,2,7,3,8,4]=>2
[1,5,2,6,3,7,4,8]=>1
[1,5,2,6,3,8,4,7]=>2
[1,5,2,6,3,4,7,8]=>1
[1,2,5,6,3,4,7,8]=>1
[1,5,2,7,3,8,4,6]=>2
[5,7,1,2,3,4,6,8]=>1
[1,5,2,7,3,4,6,8]=>1
[1,5,2,3,4,7,6,8]=>1
[5,1,2,8,3,4,6,7]=>2
[1,5,2,8,3,4,6,7]=>2
[1,5,8,2,3,4,6,7]=>2
[1,5,2,3,4,8,6,7]=>2
[1,2,3,5,4,8,6,7]=>2
[5,1,2,3,4,6,8,7]=>2
[1,5,2,3,4,6,7,8]=>1
[1,6,2,7,3,8,4,5]=>2
[1,6,7,8,2,3,4,5]=>2
[6,7,1,2,3,4,8,5]=>2
[6,1,7,2,3,4,5,8]=>1
[6,1,2,7,3,4,5,8]=>1
[1,6,2,7,3,4,5,8]=>1
[1,6,7,2,3,4,5,8]=>1
[1,6,2,3,4,7,5,8]=>1
[1,2,3,6,4,7,5,8]=>1
[6,1,8,2,3,4,5,7]=>2
[1,6,2,8,3,4,5,7]=>2
[1,6,8,2,3,4,5,7]=>2
[1,6,2,3,4,8,5,7]=>2
[1,2,3,6,4,8,5,7]=>2
[6,1,2,3,4,5,8,7]=>2
[1,6,2,3,4,5,7,8]=>1
[1,2,3,6,4,5,7,8]=>1
[1,7,2,8,3,4,5,6]=>2
[1,7,8,2,3,4,5,6]=>2
[1,7,2,3,8,4,5,6]=>2
[7,1,2,3,4,8,5,6]=>2
[1,7,2,3,4,8,5,6]=>2
[1,2,3,7,4,8,5,6]=>2
[7,1,2,3,4,5,8,6]=>2
[1,7,2,3,4,5,8,6]=>2
[1,2,7,3,4,5,8,6]=>2
[1,7,2,3,4,5,6,8]=>1
[1,2,3,7,4,5,6,8]=>1
[1,8,2,3,4,5,6,7]=>2
[1,2,3,8,4,5,6,7]=>2
[1,2,3,4,5,8,6,7]=>2
[5,3,2,6,1,4,8,7]=>2
[7,3,2,5,4,8,1,6]=>2
[8,4,5,2,3,7,6,1]=>4
[7,4,5,2,3,8,1,6]=>2
[6,4,5,2,3,1,8,7]=>2
[5,4,6,2,1,3,8,7]=>2
[3,6,1,5,4,2,8,7]=>2
[4,6,5,1,3,2,8,7]=>2
[5,6,4,3,1,2,8,7]=>2
[7,5,4,3,2,8,1,6]=>2
[8,6,4,3,7,2,5,1]=>4
[7,6,4,3,8,2,1,5]=>2
[6,7,4,3,8,1,2,5]=>2
[5,7,4,3,1,8,2,6]=>2
[4,7,5,1,3,8,2,6]=>2
[3,7,1,5,4,8,2,6]=>2
[2,1,7,5,4,8,3,6]=>2
[3,8,1,5,4,7,6,2]=>4
[4,8,5,1,3,7,6,2]=>4
[5,8,4,3,1,7,6,2]=>4
[6,8,4,3,7,1,5,2]=>4
[7,8,4,3,6,5,1,2]=>4
[6,8,5,7,3,1,4,2]=>4
[5,8,6,7,1,3,4,2]=>4
[4,8,6,1,7,3,5,2]=>4
[3,8,1,6,7,4,5,2]=>4
[2,1,8,6,7,4,5,3]=>4
[2,1,7,6,8,4,3,5]=>2
[3,7,1,6,8,4,2,5]=>2
[4,7,6,1,8,3,2,5]=>2
[5,7,6,8,1,3,2,4]=>2
[5,4,7,2,1,8,3,6]=>2
[6,4,7,2,8,1,3,5]=>2
[7,4,6,2,8,3,1,5]=>2
[8,4,6,2,7,3,5,1]=>4
[8,3,2,6,7,4,5,1]=>4
[7,3,2,6,8,4,1,5]=>2
[6,3,2,7,8,1,4,5]=>2
[5,3,2,7,1,8,4,6]=>2
[4,3,2,1,7,8,5,6]=>2
[3,4,1,2,8,7,6,5]=>4
[5,3,2,8,1,7,6,4]=>4
[6,3,2,8,7,1,5,4]=>4
[7,3,2,8,6,5,1,4]=>4
[8,4,7,2,6,5,3,1]=>6
[7,4,8,2,6,5,1,3]=>4
[6,4,8,2,7,1,5,3]=>4
[5,4,8,2,1,7,6,3]=>4
[4,5,8,1,2,7,6,3]=>4
[3,5,1,8,2,7,6,4]=>4
[2,1,5,8,3,7,6,4]=>4
[2,1,6,8,7,3,5,4]=>4
[3,6,1,8,7,2,5,4]=>4
[4,6,8,1,7,2,5,3]=>4
[5,6,8,7,1,2,4,3]=>4
[6,5,8,7,2,1,4,3]=>4
[7,5,8,6,2,4,1,3]=>4
[8,5,7,6,2,4,3,1]=>6
[5,7,8,6,1,4,2,3]=>4
[4,7,8,1,6,5,2,3]=>4
[3,7,1,8,6,5,2,4]=>4
[2,1,7,8,6,5,3,4]=>4
[3,8,1,7,6,5,4,2]=>6
[4,8,7,1,6,5,3,2]=>6
[5,8,7,6,1,4,3,2]=>6
[6,8,7,5,4,1,3,2]=>6
[4,2,5,1,3,6,7,8]=>1
[5,2,6,7,1,3,4,8]=>1
[3,2,7,8,1,4,5,6]=>2
[5,3,2,6,1,4,7,8]=>1
[7,4,3,8,1,2,5,6]=>2
[4,7,3,6,8,1,2,5]=>2
[6,7,3,4,8,1,2,5]=>2
[5,4,2,7,8,1,3,6]=>2
[6,4,7,2,5,1,3,8]=>1
[6,4,3,2,7,1,5,8]=>1
[5,4,3,2,8,1,6,7]=>2
[7,5,3,8,2,6,1,4]=>3
[8,5,4,7,2,6,1,3]=>4
[8,5,4,7,3,6,1,2]=>4
[8,1,4,2,6,3,5,7]=>2
[8,3,1,2,4,7,5,6]=>3
[8,3,1,5,6,2,4,7]=>2
[3,5,2,7,1,8,6,4]=>3
[6,5,8,7,3,4,1,2]=>4
[3,6,7,4,5,8,1,2]=>2
[1,6,7,4,5,2,3,8]=>1
[5,4,3,8,7,6,1,2]=>4
[6,4,8,3,7,5,1,2]=>4
[6,2,8,4,5,1,7,3]=>3
[7,8,1,4,5,2,3,6]=>2
[6,1,8,3,2,5,4,7]=>2
[7,8,1,3,2,5,4,6]=>2
[5,2,3,8,1,6,7,4]=>3
[6,3,8,2,1,7,5,4]=>4
[7,8,3,2,1,6,5,4]=>4
[7,8,4,2,6,1,5,3]=>4
[5,4,2,8,7,1,6,3]=>4
[2,5,3,7,1,6,8,4]=>2
[1,5,3,7,2,6,4,8]=>1
[3,6,7,2,1,8,5,4]=>3
[7,8,5,6,2,1,4,3]=>4
[5,4,1,8,7,2,3,6]=>3
[6,4,8,1,7,2,3,5]=>3
[5,3,1,8,2,7,4,6]=>3
[4,3,1,2,8,7,5,6]=>3
[4,2,1,3,8,5,7,6]=>3
[8,6,1,3,4,2,5,7]=>2
[8,1,2,4,5,6,3,7]=>2
[8,2,5,1,3,6,4,7]=>2
[5,2,7,1,3,8,4,6]=>2
[5,3,1,7,8,2,4,6]=>2
[1,7,3,4,2,5,8,6]=>2
[4,7,2,1,3,5,8,6]=>2
[4,5,2,3,7,6,1,8]=>1
[1,5,6,3,4,8,7,2]=>3
[4,6,2,7,3,5,1,8]=>1
[3,2,6,7,4,5,1,8]=>1
[8,7,5,4,1,3,2,6]=>3
[6,8,5,4,2,1,3,7]=>2
[3,2,8,6,5,1,4,7]=>2
[4,1,2,6,5,8,7,3]=>3
[5,1,6,2,4,8,7,3]=>3
[8,1,6,7,4,5,2,3]=>4
[6,1,7,8,2,4,5,3]=>3
[5,1,7,2,8,4,6,3]=>3
[4,1,2,7,8,5,6,3]=>3
[3,2,8,7,1,5,4,6]=>3
[4,8,2,7,1,5,3,6]=>3
[5,8,7,2,1,4,3,6]=>3
[8,7,6,1,4,3,2,5]=>4
[1,6,7,8,3,4,5,2]=>3
[5,7,8,2,1,3,4,6]=>2
[4,7,2,8,1,3,5,6]=>2
[3,2,6,8,4,1,5,7]=>2
[4,6,2,8,3,1,5,7]=>2
[5,6,8,2,3,1,4,7]=>2
[1,5,7,3,8,4,6,2]=>3
[1,4,3,7,8,5,6,2]=>3
[6,4,3,8,2,1,5,7]=>2
[4,5,2,3,8,1,6,7]=>2
[3,2,5,4,8,1,6,7]=>2
[6,4,3,1,2,8,7,5]=>3
[7,4,3,1,8,2,6,5]=>3
[8,4,3,1,7,6,2,5]=>4
[7,5,1,3,8,2,6,4]=>3
[5,6,1,2,3,8,7,4]=>3
[3,2,6,1,4,8,7,5]=>3
[5,7,1,2,8,3,6,4]=>3
[6,7,1,8,2,3,5,4]=>3
[8,7,1,6,5,3,2,4]=>5
[6,8,1,7,2,5,3,4]=>4
[5,8,1,2,7,6,3,4]=>4
[3,2,8,1,7,6,4,5]=>4
[4,1,2,8,7,6,5,3]=>5
[5,1,8,2,7,6,4,3]=>5
[6,1,8,7,2,5,4,3]=>5
[8,1,7,6,5,4,2,3]=>6
[3,2,5,1,6,4,8,7]=>2
[4,2,5,3,7,6,8,1]=>2
[4,2,5,1,6,3,8,7]=>2
[4,3,5,1,6,2,8,7]=>2
[4,3,5,2,7,1,8,6]=>2
[4,3,6,2,7,1,8,5]=>2
[4,3,6,1,7,2,8,5]=>2
[3,1,5,4,7,6,8,2]=>2
[4,1,5,3,7,6,8,2]=>2
[5,3,6,4,7,1,8,2]=>2
[4,1,6,3,7,5,8,2]=>2
[5,2,6,3,7,4,8,1]=>2
[5,2,6,1,7,3,8,4]=>2
[4,2,6,1,7,3,8,5]=>2
[4,2,6,3,7,5,8,1]=>2
[3,2,6,4,7,5,8,1]=>2
[3,2,6,1,7,4,8,5]=>2
[3,2,5,1,7,4,8,6]=>2
[3,2,4,1,7,5,8,6]=>2
[3,2,5,1,7,6,8,4]=>2
[3,2,6,1,7,5,8,4]=>2
[4,2,6,1,7,5,8,3]=>2
[4,2,5,1,7,6,8,3]=>2
[4,1,5,2,7,6,8,3]=>2
[4,1,6,2,7,5,8,3]=>2
[5,4,6,2,7,3,8,1]=>2
[5,4,6,2,7,1,8,3]=>2
[5,4,6,1,7,2,8,3]=>2
[3,1,6,5,7,4,8,2]=>2
[4,1,6,5,7,3,8,2]=>2
[5,1,6,4,7,3,8,2]=>2
[5,4,6,1,7,3,8,2]=>2
[5,4,6,3,7,1,8,2]=>2
[8,6,3,5,2,4,1,7]=>2
[8,3,7,5,2,4,6,1]=>4
[5,7,4,3,2,1,8,6]=>2
[8,5,7,4,3,2,6,1]=>4
[4,7,6,3,2,8,1,5]=>2
[8,5,7,4,2,1,6,3]=>4
[8,4,7,6,3,5,2,1]=>6
[3,6,5,8,7,4,1,2]=>4
[1,3,6,7,5,8,2,4]=>2
[3,6,8,5,7,2,4,1]=>4
[4,2,6,8,7,3,5,1]=>4
[3,2,6,1,4,7,8,5]=>2
[8,5,7,3,2,1,6,4]=>4
[8,3,6,7,2,1,5,4]=>4
[8,7,6,3,5,2,4,1]=>6
[4,6,8,2,1,7,5,3]=>4
[8,4,1,5,7,2,6,3]=>4
[8,1,2,5,6,7,4,3]=>4
[2,7,6,8,5,4,1,3]=>4
[8,7,6,3,5,1,4,2]=>6
[8,4,7,6,5,1,3,2]=>6
[8,7,1,5,6,4,3,2]=>6
[8,1,6,7,5,4,3,2]=>6
[5,4,3,6,1,2,8,7]=>2
[2,7,6,4,5,8,1,3]=>2
[5,7,3,6,1,8,2,4]=>2
[2,1,7,6,5,8,3,4]=>2
[6,4,3,5,8,1,7,2]=>3
[7,3,5,4,8,6,1,2]=>3
[5,4,3,2,7,1,8,6]=>2
[4,3,7,6,2,1,8,5]=>2
[5,3,8,7,6,4,2,1]=>6
[7,5,3,1,8,6,4,2]=>4
[1,8,6,5,3,7,4,2]=>4
[7,6,5,3,2,1,8,4]=>2
[6,2,8,7,5,4,3,1]=>6
[7,6,2,1,8,5,4,3]=>4
[6,1,7,2,8,5,4,3]=>4
[7,1,8,6,5,4,3,2]=>6
[6,5,2,1,4,3,8,7]=>2
[8,5,2,7,4,1,6,3]=>4
[3,1,6,5,4,2,8,7]=>2
[6,7,2,3,4,8,5,1]=>3
[8,7,2,3,4,1,6,5]=>4
[5,1,7,3,8,4,6,2]=>3
[2,1,8,7,4,3,6,5]=>4
[5,8,7,3,2,6,1,4]=>4
[8,1,6,3,2,5,4,7]=>2
[2,8,4,1,6,3,7,5]=>3
[2,1,5,3,8,7,6,4]=>4
[2,4,1,8,7,6,5,3]=>5
[7,1,6,5,4,8,2,3]=>2
[3,7,5,6,8,4,2,1]=>4
[4,6,2,5,8,3,7,1]=>3
[4,1,2,3,6,8,7,5]=>3
[7,5,2,8,3,4,6,1]=>3
[5,6,2,8,4,3,1,7]=>2
[8,7,2,1,4,5,6,3]=>4
[3,6,8,7,1,5,4,2]=>5
[5,7,8,6,3,4,1,2]=>4
[2,7,8,4,5,3,6,1]=>3
[3,1,8,2,4,7,6,5]=>4
[6,3,8,4,2,5,7,1]=>3
[6,8,2,4,3,5,1,7]=>2
[4,8,2,3,5,1,6,7]=>2
[2,8,1,3,4,5,7,6]=>3
[7,1,6,5,8,3,2,4]=>2
[3,6,4,5,7,2,8,1]=>2
[1,8,2,7,3,4,5,6]=>3
[3,2,1,5,8,4,6,7]=>2
[5,4,3,2,1,8,6,7]=>2
[1,8,2,4,3,5,6,7]=>2
[1,7,2,4,3,5,6,8]=>1
[1,6,2,4,3,5,7,8]=>1
[1,5,2,4,3,6,7,8]=>1
[1,6,2,5,3,4,7,8]=>1
[1,7,2,5,3,4,6,8]=>1
[1,8,2,5,3,4,6,7]=>2
[1,8,2,6,3,4,5,7]=>2
[1,7,2,6,3,4,5,8]=>1
[1,8,2,7,3,5,4,6]=>3
[1,7,2,8,3,5,4,6]=>2
[1,6,2,8,3,5,4,7]=>2
[1,2,3,8,4,6,5,7]=>2
[1,2,3,7,4,6,5,8]=>1
[1,3,2,7,4,6,5,8]=>1
[1,6,2,7,3,5,4,8]=>1
[1,7,2,6,3,5,4,8]=>1
[1,8,2,6,3,5,4,7]=>2
[1,7,2,5,3,6,4,8]=>1
[1,6,2,5,3,7,4,8]=>1
[1,6,2,4,3,7,5,8]=>1
[1,8,2,4,3,6,5,7]=>2
[1,8,2,3,4,6,5,7]=>2
[1,7,2,3,4,6,5,8]=>1
[1,8,2,3,4,7,5,6]=>3
[1,8,2,4,3,7,5,6]=>3
[1,6,2,4,3,8,5,7]=>2
[1,7,2,5,3,8,4,6]=>2
[1,8,2,5,3,7,4,6]=>3
[1,8,2,6,3,7,4,5]=>3
[1,7,2,6,3,8,4,5]=>2
[1,2,3,8,4,7,5,6]=>3
[1,3,2,8,4,7,5,6]=>3
[1,4,2,8,3,7,5,6]=>3
[1,5,2,8,3,7,4,6]=>3
[1,6,2,8,3,7,4,5]=>3
[1,7,2,8,3,6,4,5]=>3
[1,8,2,7,3,6,4,5]=>4
[2,8,4,1,6,7,5,3]=>4
[4,8,5,7,1,6,2,3]=>4
[8,7,6,5,2,1,4,3]=>6
[8,7,6,5,1,4,2,3]=>6
[7,5,1,3,8,4,2,6]=>2
[7,1,3,5,8,2,4,6]=>2
[7,5,3,6,4,2,8,1]=>2
[2,7,6,5,3,4,8,1]=>2
[8,6,5,4,2,7,3,1]=>4
[6,5,8,4,2,7,3,1]=>4
[8,7,5,2,6,4,3,1]=>6
[8,7,1,6,2,5,4,3]=>6
[8,6,1,7,4,2,5,3]=>4
[7,1,2,8,3,5,4,6]=>2
[8,2,6,1,7,3,5,4]=>4
[8,6,4,7,5,3,2,1]=>6
[5,4,8,1,7,2,6,3]=>4
[2,3,8,7,4,5,6,1]=>4
[8,2,7,6,3,5,4,1]=>6
[8,1,7,6,5,2,4,3]=>6
[7,1,8,6,5,3,2,4]=>4
[3,8,7,6,4,5,2,1]=>6
[2,8,7,6,5,3,4,1]=>6
[1,8,7,6,5,4,2,3]=>6
[3,8,6,7,1,5,2,4]=>4
[5,6,2,1,4,8,3,7]=>2
[2,1,8,4,7,5,6,3]=>4
[4,1,3,2,8,5,6,7]=>2
[3,2,1,4,8,5,6,7]=>2
[1,8,4,2,5,3,6,7]=>2
[8,1,5,3,2,4,6,7]=>2
[3,8,1,5,2,4,6,7]=>2
[1,6,7,2,8,4,3,5]=>2
[6,7,1,4,2,8,3,5]=>2
[6,3,7,1,4,8,2,5]=>2
[3,7,8,1,5,2,4,6]=>2
[7,1,2,8,5,3,4,6]=>2
[1,7,2,8,4,5,3,6]=>2
[1,2,7,5,8,3,4,6]=>2
[5,2,4,7,3,6,8,1]=>2
[5,1,2,4,8,3,6,7]=>2
[4,3,6,1,5,8,2,7]=>2
[2,6,1,4,5,8,3,7]=>2
[2,5,3,4,1,8,6,7]=>2
[4,3,5,2,1,8,6,7]=>2
[4,7,2,5,8,3,6,1]=>3
[8,5,4,7,6,3,2,1]=>6
[8,2,1,5,4,3,7,6]=>3
[8,3,6,1,4,7,2,5]=>3
[5,7,2,8,4,3,6,1]=>3
[5,7,3,8,4,6,2,1]=>4
[8,7,2,1,4,3,6,5]=>4
[8,7,6,3,2,5,4,1]=>6
[8,7,3,5,1,6,2,4]=>4
[8,5,3,6,2,7,4,1]=>4
[1,7,6,5,4,8,2,3]=>2
[1,2,7,6,8,3,4,5]=>2
[2,1,7,5,6,8,3,4]=>2
[2,8,6,3,7,4,5,1]=>4
[3,7,4,1,8,5,2,6]=>2
[6,1,2,8,4,3,5,7]=>2
[1,6,2,5,8,3,4,7]=>2
[8,5,1,3,7,2,6,4]=>4
[1,5,4,2,8,3,6,7]=>2
[3,7,6,8,4,5,2,1]=>4
[2,7,6,8,5,3,4,1]=>4
[1,7,6,8,5,4,2,3]=>4
[2,4,8,6,7,3,5,1]=>4
[3,4,8,5,6,7,2,1]=>4
[3,2,8,5,7,4,6,1]=>4
[6,1,5,8,7,4,2,3]=>4
[5,8,6,7,4,3,2,1]=>6
[4,8,7,5,6,3,2,1]=>6
[2,4,8,3,5,7,6,1]=>4
[5,4,1,3,8,2,6,7]=>2
[1,8,5,4,3,2,6,7]=>2
[3,8,4,7,6,5,2,1]=>6
[1,6,8,5,3,7,4,2]=>4
[2,6,8,4,3,7,5,1]=>4
[2,6,7,3,1,4,8,5]=>2
[8,7,1,3,6,2,4,5]=>4
[8,2,1,7,3,5,6,4]=>4
[8,7,2,6,3,5,4,1]=>6
[1,2,8,7,4,5,6,3]=>4
[8,1,6,2,7,4,5,3]=>4
[8,7,6,1,5,3,4,2]=>6
[8,7,1,6,4,5,3,2]=>6
[8,1,7,5,6,4,3,2]=>6
[1,8,6,7,5,4,3,2]=>6
[9,1,2,3,4,5,6,7,8]=>2
[8,1,2,3,4,5,6,9,7]=>2
[2,9,1,3,4,5,6,7,8]=>2
[9,3,1,2,4,5,6,7,8]=>2
[8,9,1,2,3,4,5,6,7]=>2
[9,7,8,1,2,3,4,5,6]=>3
[2,3,4,5,6,7,9,1,8]=>2
[2,3,4,5,6,7,8,9,1]=>2
[2,3,4,5,6,7,8,1,9]=>1
[2,3,4,5,6,7,1,8,9]=>1
[1,2,3,4,5,6,7,9,8]=>2
[2,1,3,4,5,6,7,8,9]=>1
[1,8,2,3,4,5,6,9,7]=>2
[7,1,2,3,4,5,6,9,8]=>2
[2,1,9,3,4,5,6,7,8]=>2
[2,8,1,3,4,5,6,7,9]=>1
[1,2,3,4,5,6,7,8,9]=>1
[3,2,4,5,6,7,8,9,1]=>2
[9,8,7,6,5,4,3,2,1]=>9
[8,7,6,5,4,3,2,1,9]=>1
[1,9,8,7,6,5,4,3,2]=>8
[8,7,6,4,5,3,2,1,9]=>1
[1,9,8,7,5,6,4,3,2]=>7
[8,7,5,4,6,3,2,1,9]=>1
[8,7,4,6,5,3,2,1,9]=>1
[1,9,8,6,5,7,4,3,2]=>6
[1,9,8,5,7,6,4,3,2]=>7
[9,2,1,3,4,5,6,7,8]=>2
[9,2,3,1,4,5,6,7,8]=>2
[4,2,3,5,6,7,8,9,1]=>2
[3,4,2,5,6,7,8,9,1]=>2
[9,8,1,2,3,4,5,6,7]=>3
[7,8,9,1,2,3,4,5,6]=>2
[9,8,7,1,2,3,4,5,6]=>4
[6,7,8,9,1,2,3,4,5]=>2
[9,6,7,8,1,2,3,4,5]=>3
[8,9,6,7,1,2,3,4,5]=>3
[9,8,6,7,1,2,3,4,5]=>4
[9,8,7,6,1,2,3,4,5]=>5
[9,5,6,7,8,1,2,3,4]=>3
[8,9,5,6,7,1,2,3,4]=>3
[9,8,5,6,7,1,2,3,4]=>4
[9,7,8,5,6,1,2,3,4]=>4
[9,8,7,5,6,1,2,3,4]=>5
[9,8,7,6,5,1,2,3,4]=>6
[7,8,9,4,5,6,1,2,3]=>3
[9,7,8,4,5,6,1,2,3]=>4
[9,8,7,4,5,6,1,2,3]=>5
[8,9,6,7,4,5,1,2,3]=>4
[9,8,6,7,4,5,1,2,3]=>5
[9,8,7,6,4,5,1,2,3]=>6
[9,8,7,6,5,4,1,2,3]=>7
[9,7,8,5,6,3,4,1,2]=>5
[9,8,7,5,6,3,4,1,2]=>6
[9,8,7,6,5,3,4,1,2]=>7
[9,8,7,6,5,4,3,1,2]=>8
[7,8,6,5,4,3,2,1,9]=>1
[1,8,9,7,6,5,4,3,2]=>7
[7,6,8,5,4,3,2,1,9]=>1
[6,8,7,5,4,3,2,1,9]=>1
[1,8,7,9,6,5,4,3,2]=>6
[1,7,9,8,6,5,4,3,2]=>7
[8,1,2,3,4,5,6,7,9]=>1
[1,9,2,3,4,5,6,7,8]=>2
[7,8,1,2,3,4,5,6,9]=>1
[1,8,9,2,3,4,5,6,7]=>2
[7,1,8,2,3,4,5,6,9]=>1
[6,8,1,2,3,4,5,7,9]=>1
[1,8,2,9,3,4,5,6,7]=>2
[1,7,9,2,3,4,5,6,8]=>2
[7,1,2,3,4,5,6,8,9]=>1
[3,4,1,2,5,6,7,8,9]=>1
[3,2,1,4,5,6,7,8,9]=>1
[4,5,6,1,2,3,7,8,9]=>1
[4,2,5,1,3,6,7,8,9]=>1
[4,3,2,1,5,6,7,8,9]=>1
[5,6,7,8,1,2,3,4,9]=>1
[5,2,6,7,1,3,4,8,9]=>1
[5,6,3,4,1,2,7,8,9]=>1
[5,3,2,6,1,4,7,8,9]=>1
[5,4,3,2,1,6,7,8,9]=>1
[6,2,7,8,9,1,3,4,5]=>2
[6,7,3,4,8,1,2,5,9]=>1
[6,3,2,7,8,1,4,5,9]=>1
[6,4,7,2,5,1,3,8,9]=>1
[6,4,3,2,7,1,5,8,9]=>1
[6,5,4,3,2,1,7,8,9]=>1
[7,4,8,2,5,9,1,3,6]=>2
[7,4,3,2,8,9,1,5,6]=>2
[7,8,5,6,3,4,1,2,9]=>1
[7,5,3,8,2,6,1,4,9]=>1
[7,5,4,3,2,8,1,6,9]=>1
[7,6,5,4,3,2,1,8,9]=>1
[8,6,9,4,7,2,5,1,3]=>4
[8,6,4,3,9,2,7,1,5]=>3
[8,6,5,4,3,2,9,1,7]=>2
[2,1,4,3,6,5,8,7,10,9]=>2
[4,3,2,1,6,5,8,7,10,9]=>2
[6,3,2,5,4,1,8,7,10,9]=>2
[8,3,2,5,4,7,6,1,10,9]=>2
[10,3,2,5,4,7,6,9,8,1]=>4
[2,1,6,5,4,3,8,7,10,9]=>2
[6,5,4,3,2,1,8,7,10,9]=>2
[8,5,4,3,2,7,6,1,10,9]=>2
[10,5,4,3,2,7,6,9,8,1]=>4
[2,1,8,5,4,7,6,3,10,9]=>2
[8,7,4,3,6,5,2,1,10,9]=>2
[10,7,4,3,6,5,2,9,8,1]=>4
[2,1,10,5,4,7,6,9,8,3]=>4
[10,9,4,3,6,5,8,7,2,1]=>6
[8,9,5,6,3,4,10,1,2,7]=>2
[2,1,4,3,8,7,6,5,10,9]=>2
[4,3,2,1,8,7,6,5,10,9]=>2
[8,3,2,7,6,5,4,1,10,9]=>2
[10,3,2,7,6,5,4,9,8,1]=>4
[2,1,8,7,6,5,4,3,10,9]=>2
[8,7,6,5,4,3,2,1,10,9]=>2
[9,7,6,5,4,3,2,10,1,8]=>2
[10,7,6,5,4,3,2,9,8,1]=>4
[2,1,10,7,6,5,4,9,8,3]=>4
[10,9,6,5,4,3,8,7,2,1]=>6
[2,1,4,3,10,7,6,9,8,5]=>4
[4,3,2,1,10,7,6,9,8,5]=>4
[10,3,2,9,6,5,8,7,4,1]=>6
[2,1,10,9,6,5,8,7,4,3]=>6
[10,9,8,5,4,7,6,3,2,1]=>8
[6,7,8,9,10,1,2,3,4,5]=>2
[7,3,2,8,9,10,1,4,5,6]=>2
[8,5,4,3,2,9,10,1,6,7]=>2
[2,1,4,3,6,5,10,9,8,7]=>4
[4,3,2,1,6,5,10,9,8,7]=>4
[6,3,2,5,4,1,10,9,8,7]=>4
[10,3,2,5,4,9,8,7,6,1]=>6
[2,1,6,5,4,3,10,9,8,7]=>4
[6,5,4,3,2,1,10,9,8,7]=>4
[10,5,4,3,2,9,8,7,6,1]=>6
[2,1,10,5,4,9,8,7,6,3]=>6
[10,9,4,3,8,7,6,5,2,1]=>8
[9,7,5,10,3,8,2,6,1,4]=>4
[2,1,4,3,10,9,8,7,6,5]=>6
[4,3,2,1,10,9,8,7,6,5]=>6
[10,3,2,9,8,7,6,5,4,1]=>8
[2,1,10,9,8,7,6,5,4,3]=>8
[10,9,8,7,6,5,4,3,2,1]=>10
[2,3,4,5,6,7,8,9,10,1]=>2
[2,3,4,5,6,7,8,9,1,10]=>1
[10,8,9,5,6,7,1,2,3,4]=>4
[10,8,9,4,5,6,1,2,3,7]=>3
[10,7,8,5,6,9,1,2,3,4]=>3
[10,7,8,4,5,9,1,2,3,6]=>3
[10,6,7,4,5,8,1,2,3,9]=>2
[10,7,8,3,4,9,1,2,5,6]=>3
[10,6,7,3,4,8,1,2,5,9]=>2
[9,8,10,5,6,7,1,2,3,4]=>3
[9,8,10,4,5,6,1,2,3,7]=>2
[9,7,10,5,6,8,1,2,3,4]=>3
[9,7,10,4,5,8,1,2,3,6]=>3
[9,6,10,4,5,7,1,2,3,8]=>2
[9,7,10,3,4,8,1,2,5,6]=>3
[9,6,10,3,4,7,1,2,5,8]=>2
[8,7,9,5,6,10,1,2,3,4]=>2
[8,7,9,4,5,10,1,2,3,6]=>2
[8,6,9,4,5,10,1,2,3,7]=>2
[7,6,8,4,5,9,1,2,3,10]=>1
[8,7,9,3,4,10,1,2,5,6]=>2
[8,6,9,3,4,10,1,2,5,7]=>2
[7,6,8,3,4,9,1,2,5,10]=>1
[9,6,10,5,7,8,1,2,3,4]=>3
[9,6,10,4,7,8,1,2,3,5]=>3
[9,5,10,4,6,7,1,2,3,8]=>2
[9,6,10,3,7,8,1,2,4,5]=>3
[9,5,10,3,6,7,1,2,4,8]=>2
[8,6,9,5,7,10,1,2,3,4]=>2
[8,6,9,4,7,10,1,2,3,5]=>2
[8,5,9,4,6,10,1,2,3,7]=>2
[7,5,8,4,6,9,1,2,3,10]=>1
[8,6,9,3,7,10,1,2,4,5]=>2
[8,5,9,3,6,10,1,2,4,7]=>2
[7,5,8,3,6,9,1,2,4,10]=>1
[8,4,9,3,5,10,1,2,6,7]=>2
[7,4,8,3,5,9,1,2,6,10]=>1
[9,6,10,2,7,8,1,3,4,5]=>3
[9,5,10,2,6,7,1,3,4,8]=>2
[8,6,9,2,7,10,1,3,4,5]=>2
[8,5,9,2,6,10,1,3,4,7]=>2
[7,5,8,2,6,9,1,3,4,10]=>1
[8,4,9,2,5,10,1,3,6,7]=>2
[7,4,8,2,5,9,1,3,6,10]=>1
[1,2,3,4,5,6,7,8,10,9]=>2
[2,1,3,4,5,6,7,8,9,10]=>1
[9,1,2,3,4,5,6,7,10,8]=>2
[2,10,1,3,4,5,6,7,8,9]=>2
[1,2,3,4,5,6,7,8,9,10]=>1
[9,8,7,6,5,4,3,2,1,10]=>1
[10,1,2,3,4,5,6,7,8,9]=>2
[10,9,1,2,3,4,5,6,7,8]=>3
[1,10,9,8,7,6,5,4,3,2]=>9
[9,8,7,5,6,4,3,2,1,10]=>1
[1,10,9,8,6,7,5,4,3,2]=>8
[10,2,1,3,4,5,6,7,8,9]=>2
[3,2,4,5,6,7,8,9,10,1]=>2
[2,4,6,8,10,1,3,5,7,9]=>2
[2,4,6,9,10,1,3,5,7,8]=>2
[2,4,7,8,10,1,3,5,6,9]=>2
[2,4,7,9,10,1,3,5,6,8]=>2
[2,4,8,9,10,1,3,5,6,7]=>2
[2,5,6,8,10,1,3,4,7,9]=>2
[2,5,6,9,10,1,3,4,7,8]=>2
[2,5,7,8,10,1,3,4,6,9]=>2
[2,5,7,9,10,1,3,4,6,8]=>2
[2,5,8,9,10,1,3,4,6,7]=>2
[2,6,7,8,10,1,3,4,5,9]=>2
[2,6,7,9,10,1,3,4,5,8]=>2
[2,6,8,9,10,1,3,4,5,7]=>2
[2,7,8,9,10,1,3,4,5,6]=>2
[3,4,6,8,10,1,2,5,7,9]=>2
[3,4,6,9,10,1,2,5,7,8]=>2
[3,4,7,8,10,1,2,5,6,9]=>2
[3,4,7,9,10,1,2,5,6,8]=>2
[3,4,8,9,10,1,2,5,6,7]=>2
[3,5,6,8,10,1,2,4,7,9]=>2
[3,5,6,9,10,1,2,4,7,8]=>2
[3,5,7,8,10,1,2,4,6,9]=>2
[3,5,7,9,10,1,2,4,6,8]=>2
[3,5,8,9,10,1,2,4,6,7]=>2
[3,6,7,8,10,1,2,4,5,9]=>2
[3,6,7,9,10,1,2,4,5,8]=>2
[3,6,8,9,10,1,2,4,5,7]=>2
[3,7,8,9,10,1,2,4,5,6]=>2
[4,5,6,8,10,1,2,3,7,9]=>2
[4,5,6,9,10,1,2,3,7,8]=>2
[4,5,7,8,10,1,2,3,6,9]=>2
[4,5,7,9,10,1,2,3,6,8]=>2
[4,5,8,9,10,1,2,3,6,7]=>2
[4,6,7,8,10,1,2,3,5,9]=>2
[4,6,7,9,10,1,2,3,5,8]=>2
[4,6,8,9,10,1,2,3,5,7]=>2
[4,7,8,9,10,1,2,3,5,6]=>2
[5,6,7,8,10,1,2,3,4,9]=>2
[5,6,7,9,10,1,2,3,4,8]=>2
[5,6,8,9,10,1,2,3,4,7]=>2
[5,7,8,9,10,1,2,3,4,6]=>2
[9,10,1,2,3,4,5,6,7,8]=>2
[8,9,10,1,2,3,4,5,6,7]=>2
[10,8,9,1,2,3,4,5,6,7]=>3
[10,9,8,1,2,3,4,5,6,7]=>4
[7,8,9,10,1,2,3,4,5,6]=>2
[10,7,8,9,1,2,3,4,5,6]=>3
[9,10,7,8,1,2,3,4,5,6]=>3
[10,9,7,8,1,2,3,4,5,6]=>4
[10,9,8,7,1,2,3,4,5,6]=>5
[10,6,7,8,9,1,2,3,4,5]=>3
[9,10,6,7,8,1,2,3,4,5]=>3
[10,9,6,7,8,1,2,3,4,5]=>4
[10,8,9,6,7,1,2,3,4,5]=>4
[10,9,8,6,7,1,2,3,4,5]=>5
[10,9,8,7,6,1,2,3,4,5]=>6
[9,10,5,6,7,8,1,2,3,4]=>3
[10,9,5,6,7,8,1,2,3,4]=>4
[8,9,10,5,6,7,1,2,3,4]=>3
[10,9,8,5,6,7,1,2,3,4]=>5
[9,10,7,8,5,6,1,2,3,4]=>4
[10,9,7,8,5,6,1,2,3,4]=>5
[10,9,8,7,5,6,1,2,3,4]=>6
[10,9,8,7,6,5,1,2,3,4]=>7
[10,7,8,9,4,5,6,1,2,3]=>4
[9,10,7,8,4,5,6,1,2,3]=>4
[10,9,7,8,4,5,6,1,2,3]=>5
[10,9,8,7,4,5,6,1,2,3]=>6
[10,8,9,6,7,4,5,1,2,3]=>5
[10,9,8,6,7,4,5,1,2,3]=>6
[10,9,8,7,6,4,5,1,2,3]=>7
[10,9,8,7,6,5,4,1,2,3]=>8
[9,10,7,8,5,6,3,4,1,2]=>5
[10,9,7,8,5,6,3,4,1,2]=>6
[10,9,8,7,5,6,3,4,1,2]=>7
[10,9,8,7,6,5,3,4,1,2]=>8
[10,9,8,7,6,5,4,3,1,2]=>9
[8,9,7,6,5,4,3,2,1,10]=>1
[1,9,10,8,7,6,5,4,3,2]=>8
[9,1,2,3,4,5,6,7,8,10]=>1
[1,10,2,3,4,5,6,7,8,9]=>2
[8,9,1,2,3,4,5,6,7,10]=>1
[1,9,10,2,3,4,5,6,7,8]=>2
[3,4,1,2,5,6,7,8,9,10]=>1
[3,2,1,4,5,6,7,8,9,10]=>1
[4,5,6,1,2,3,7,8,9,10]=>1
[4,2,5,1,3,6,7,8,9,10]=>1
[4,3,2,1,5,6,7,8,9,10]=>1
[5,6,7,8,1,2,3,4,9,10]=>1
[5,2,6,7,1,3,4,8,9,10]=>1
[5,6,3,4,1,2,7,8,9,10]=>1
[5,3,2,6,1,4,7,8,9,10]=>1
[5,4,3,2,1,6,7,8,9,10]=>1
[6,2,7,8,9,1,3,4,5,10]=>1
[6,7,3,4,8,1,2,5,9,10]=>1
[6,3,2,7,8,1,4,5,9,10]=>1
[6,4,7,2,5,1,3,8,9,10]=>1
[6,4,3,2,7,1,5,8,9,10]=>1
[6,5,4,3,2,1,7,8,9,10]=>1
[7,8,3,4,9,10,1,2,5,6]=>2
[7,8,9,4,5,6,1,2,3,10]=>1
[7,4,3,2,8,9,1,5,6,10]=>1
[7,8,5,6,3,4,1,2,9,10]=>1
[7,5,3,8,2,6,1,4,9,10]=>1
[7,5,4,3,2,8,1,6,9,10]=>1
[7,6,5,4,3,2,1,8,9,10]=>1
[8,5,9,10,2,6,7,1,3,4]=>3
[8,5,3,9,2,6,10,1,4,7]=>2
[8,6,9,4,7,2,5,1,3,10]=>1
[8,6,4,3,9,2,7,1,5,10]=>1
[8,6,5,4,3,2,9,1,7,10]=>1
[8,7,6,5,4,3,2,1,9,10]=>1
[9,7,5,4,3,10,2,8,1,6]=>3
[1,2,3,4,5,6,7,8,9,11,10]=>2
[2,1,3,4,5,6,7,8,9,10,11]=>1
[11,1,2,3,4,5,6,7,8,9,10]=>2
[10,9,8,7,6,5,4,3,2,1,11]=>1
[1,11,10,9,8,7,6,5,4,3,2]=>10
[2,3,4,5,6,7,8,9,10,11,1]=>2
[10,1,2,3,4,5,6,7,8,9,11]=>1
[1,11,2,3,4,5,6,7,8,9,10]=>2
[2,1,4,3,6,5,8,7,10,9,12,11]=>2
[2,1,4,3,6,5,8,7,12,11,10,9]=>4
[2,1,4,3,6,5,10,9,8,7,12,11]=>2
[2,1,4,3,6,5,12,9,8,11,10,7]=>4
[2,1,4,3,6,5,12,11,10,9,8,7]=>6
[2,1,4,3,8,7,6,5,10,9,12,11]=>2
[2,1,4,3,8,7,6,5,12,11,10,9]=>4
[2,1,4,3,10,7,6,9,8,5,12,11]=>2
[2,1,4,3,12,7,6,9,8,11,10,5]=>4
[2,1,4,3,12,7,6,11,10,9,8,5]=>6
[2,1,4,3,10,9,8,7,6,5,12,11]=>2
[2,1,4,3,12,9,8,7,6,11,10,5]=>4
[2,1,4,3,12,11,8,7,10,9,6,5]=>6
[2,1,4,3,12,11,10,9,8,7,6,5]=>8
[2,1,6,5,4,3,8,7,10,9,12,11]=>2
[2,1,6,5,4,3,8,7,12,11,10,9]=>4
[2,1,6,5,4,3,10,9,8,7,12,11]=>2
[2,1,6,5,4,3,12,9,8,11,10,7]=>4
[2,1,6,5,4,3,12,11,10,9,8,7]=>6
[2,1,8,5,4,7,6,3,10,9,12,11]=>2
[2,1,8,5,4,7,6,3,12,11,10,9]=>4
[2,1,10,5,4,7,6,9,8,3,12,11]=>2
[2,1,12,5,4,7,6,9,8,11,10,3]=>4
[2,1,12,5,4,7,6,11,10,9,8,3]=>6
[2,1,10,5,4,9,8,7,6,3,12,11]=>2
[2,1,12,5,4,9,8,7,6,11,10,3]=>4
[2,1,12,5,4,11,8,7,10,9,6,3]=>6
[2,1,12,5,4,11,10,9,8,7,6,3]=>8
[2,1,8,7,6,5,4,3,10,9,12,11]=>2
[2,1,8,7,6,5,4,3,12,11,10,9]=>4
[2,1,10,7,6,5,4,9,8,3,12,11]=>2
[2,1,12,7,6,5,4,9,8,11,10,3]=>4
[2,1,12,7,6,5,4,11,10,9,8,3]=>6
[2,1,10,9,6,5,8,7,4,3,12,11]=>2
[2,1,12,9,6,5,8,7,4,11,10,3]=>4
[2,1,12,11,6,5,8,7,10,9,4,3]=>6
[2,1,12,11,6,5,10,9,8,7,4,3]=>8
[2,1,10,9,8,7,6,5,4,3,12,11]=>2
[2,1,12,9,8,7,6,5,4,11,10,3]=>4
[2,1,12,11,8,7,6,5,10,9,4,3]=>6
[2,1,12,11,10,7,6,9,8,5,4,3]=>8
[2,1,12,11,10,9,8,7,6,5,4,3]=>10
[4,3,2,1,6,5,8,7,10,9,12,11]=>2
[4,3,2,1,6,5,8,7,12,11,10,9]=>4
[4,3,2,1,6,5,10,9,8,7,12,11]=>2
[4,3,2,1,6,5,12,9,8,11,10,7]=>4
[4,3,2,1,6,5,12,11,10,9,8,7]=>6
[4,3,2,1,8,7,6,5,10,9,12,11]=>2
[4,3,2,1,8,7,6,5,12,11,10,9]=>4
[4,3,2,1,10,7,6,9,8,5,12,11]=>2
[4,3,2,1,12,7,6,9,8,11,10,5]=>4
[4,3,2,1,12,7,6,11,10,9,8,5]=>6
[4,3,2,1,10,9,8,7,6,5,12,11]=>2
[4,3,2,1,12,9,8,7,6,11,10,5]=>4
[4,3,2,1,12,11,8,7,10,9,6,5]=>6
[4,3,2,1,12,11,10,9,8,7,6,5]=>8
[6,3,2,5,4,1,8,7,10,9,12,11]=>2
[6,3,2,5,4,1,8,7,12,11,10,9]=>4
[6,3,2,5,4,1,10,9,8,7,12,11]=>2
[6,3,2,5,4,1,12,9,8,11,10,7]=>4
[6,3,2,5,4,1,12,11,10,9,8,7]=>6
[8,3,2,5,4,7,6,1,10,9,12,11]=>2
[8,3,2,5,4,7,6,1,12,11,10,9]=>4
[10,3,2,5,4,7,6,9,8,1,12,11]=>2
[12,3,2,5,4,7,6,9,8,11,10,1]=>4
[12,3,2,5,4,7,6,11,10,9,8,1]=>6
[10,3,2,5,4,9,8,7,6,1,12,11]=>2
[12,3,2,5,4,9,8,7,6,11,10,1]=>4
[12,3,2,5,4,11,8,7,10,9,6,1]=>6
[12,3,2,5,4,11,10,9,8,7,6,1]=>8
[8,3,2,7,6,5,4,1,10,9,12,11]=>2
[8,3,2,7,6,5,4,1,12,11,10,9]=>4
[10,3,2,7,6,5,4,9,8,1,12,11]=>2
[12,3,2,7,6,5,4,9,8,11,10,1]=>4
[12,3,2,7,6,5,4,11,10,9,8,1]=>6
[10,3,2,9,6,5,8,7,4,1,12,11]=>2
[12,3,2,9,6,5,8,7,4,11,10,1]=>4
[12,3,2,11,6,5,8,7,10,9,4,1]=>6
[12,3,2,11,6,5,10,9,8,7,4,1]=>8
[10,3,2,9,8,7,6,5,4,1,12,11]=>2
[12,3,2,9,8,7,6,5,4,11,10,1]=>4
[12,3,2,11,8,7,6,5,10,9,4,1]=>6
[12,3,2,11,10,7,6,9,8,5,4,1]=>8
[12,3,2,11,10,9,8,7,6,5,4,1]=>10
[6,5,4,3,2,1,8,7,10,9,12,11]=>2
[6,5,4,3,2,1,8,7,12,11,10,9]=>4
[6,5,4,3,2,1,10,9,8,7,12,11]=>2
[6,5,4,3,2,1,12,9,8,11,10,7]=>4
[6,5,4,3,2,1,12,11,10,9,8,7]=>6
[8,5,4,3,2,7,6,1,10,9,12,11]=>2
[8,5,4,3,2,7,6,1,12,11,10,9]=>4
[10,5,4,3,2,7,6,9,8,1,12,11]=>2
[12,5,4,3,2,7,6,9,8,11,10,1]=>4
[12,5,4,3,2,7,6,11,10,9,8,1]=>6
[10,5,4,3,2,9,8,7,6,1,12,11]=>2
[12,5,4,3,2,9,8,7,6,11,10,1]=>4
[12,5,4,3,2,11,8,7,10,9,6,1]=>6
[12,5,4,3,2,11,10,9,8,7,6,1]=>8
[8,7,4,3,6,5,2,1,10,9,12,11]=>2
[8,7,4,3,6,5,2,1,12,11,10,9]=>4
[10,7,4,3,6,5,2,9,8,1,12,11]=>2
[12,7,4,3,6,5,2,9,8,11,10,1]=>4
[12,7,4,3,6,5,2,11,10,9,8,1]=>6
[10,9,4,3,6,5,8,7,2,1,12,11]=>2
[12,9,4,3,6,5,8,7,2,11,10,1]=>4
[12,11,4,3,6,5,8,7,10,9,2,1]=>6
[12,11,4,3,6,5,10,9,8,7,2,1]=>8
[10,9,4,3,8,7,6,5,2,1,12,11]=>2
[12,9,4,3,8,7,6,5,2,11,10,1]=>4
[12,11,4,3,8,7,6,5,10,9,2,1]=>6
[12,11,4,3,10,7,6,9,8,5,2,1]=>8
[12,11,4,3,10,9,8,7,6,5,2,1]=>10
[8,7,6,5,4,3,2,1,10,9,12,11]=>2
[8,7,6,5,4,3,2,1,12,11,10,9]=>4
[10,7,6,5,4,3,2,9,8,1,12,11]=>2
[12,7,6,5,4,3,2,9,8,11,10,1]=>4
[12,7,6,5,4,3,2,11,10,9,8,1]=>6
[10,9,6,5,4,3,8,7,2,1,12,11]=>2
[12,9,6,5,4,3,8,7,2,11,10,1]=>4
[12,11,6,5,4,3,8,7,10,9,2,1]=>6
[12,11,6,5,4,3,10,9,8,7,2,1]=>8
[10,9,8,5,4,7,6,3,2,1,12,11]=>2
[12,9,8,5,4,7,6,3,2,11,10,1]=>4
[12,11,8,5,4,7,6,3,10,9,2,1]=>6
[12,11,10,5,4,7,6,9,8,3,2,1]=>8
[12,11,10,5,4,9,8,7,6,3,2,1]=>10
[10,9,8,7,6,5,4,3,2,1,12,11]=>2
[12,9,8,7,6,5,4,3,2,11,10,1]=>4
[12,11,8,7,6,5,4,3,10,9,2,1]=>6
[12,11,10,7,6,5,4,9,8,3,2,1]=>8
[12,11,10,9,6,5,8,7,4,3,2,1]=>10
[12,11,10,9,8,7,6,5,4,3,2,1]=>12
[2,4,6,8,10,12,1,3,5,7,9,11]=>2
[2,4,6,8,11,12,1,3,5,7,9,10]=>2
[2,4,6,9,10,12,1,3,5,7,8,11]=>2
[2,4,6,9,11,12,1,3,5,7,8,10]=>2
[2,4,6,10,11,12,1,3,5,7,8,9]=>2
[2,4,7,8,10,12,1,3,5,6,9,11]=>2
[2,4,7,8,11,12,1,3,5,6,9,10]=>2
[2,4,7,9,10,12,1,3,5,6,8,11]=>2
[2,4,7,9,11,12,1,3,5,6,8,10]=>2
[2,4,7,10,11,12,1,3,5,6,8,9]=>2
[2,4,8,9,10,12,1,3,5,6,7,11]=>2
[2,4,8,9,11,12,1,3,5,6,7,10]=>2
[2,4,8,10,11,12,1,3,5,6,7,9]=>2
[2,4,9,10,11,12,1,3,5,6,7,8]=>2
[2,5,6,8,10,12,1,3,4,7,9,11]=>2
[2,5,6,8,11,12,1,3,4,7,9,10]=>2
[2,5,6,9,10,12,1,3,4,7,8,11]=>2
[2,5,6,9,11,12,1,3,4,7,8,10]=>2
[2,5,6,10,11,12,1,3,4,7,8,9]=>2
[2,5,7,8,10,12,1,3,4,6,9,11]=>2
[2,5,7,8,11,12,1,3,4,6,9,10]=>2
[2,5,7,9,10,12,1,3,4,6,8,11]=>2
[2,5,7,9,11,12,1,3,4,6,8,10]=>2
[2,5,7,10,11,12,1,3,4,6,8,9]=>2
[2,5,8,9,10,12,1,3,4,6,7,11]=>2
[2,5,8,9,11,12,1,3,4,6,7,10]=>2
[2,5,8,10,11,12,1,3,4,6,7,9]=>2
[2,5,9,10,11,12,1,3,4,6,7,8]=>2
[2,6,7,8,10,12,1,3,4,5,9,11]=>2
[2,6,7,8,11,12,1,3,4,5,9,10]=>2
[2,6,7,9,10,12,1,3,4,5,8,11]=>2
[2,6,7,9,11,12,1,3,4,5,8,10]=>2
[2,6,7,10,11,12,1,3,4,5,8,9]=>2
[2,6,8,9,10,12,1,3,4,5,7,11]=>2
[2,6,8,9,11,12,1,3,4,5,7,10]=>2
[2,6,8,10,11,12,1,3,4,5,7,9]=>2
[2,6,9,10,11,12,1,3,4,5,7,8]=>2
[2,7,8,9,10,12,1,3,4,5,6,11]=>2
[2,7,8,9,11,12,1,3,4,5,6,10]=>2
[2,7,8,10,11,12,1,3,4,5,6,9]=>2
[2,7,9,10,11,12,1,3,4,5,6,8]=>2
[2,8,9,10,11,12,1,3,4,5,6,7]=>2
[3,4,6,8,10,12,1,2,5,7,9,11]=>2
[3,4,6,8,11,12,1,2,5,7,9,10]=>2
[3,4,6,9,10,12,1,2,5,7,8,11]=>2
[3,4,6,9,11,12,1,2,5,7,8,10]=>2
[3,4,6,10,11,12,1,2,5,7,8,9]=>2
[3,4,7,8,10,12,1,2,5,6,9,11]=>2
[3,4,7,8,11,12,1,2,5,6,9,10]=>2
[3,4,7,9,10,12,1,2,5,6,8,11]=>2
[3,4,7,9,11,12,1,2,5,6,8,10]=>2
[3,4,7,10,11,12,1,2,5,6,8,9]=>2
[3,4,8,9,10,12,1,2,5,6,7,11]=>2
[3,4,8,9,11,12,1,2,5,6,7,10]=>2
[3,4,8,10,11,12,1,2,5,6,7,9]=>2
[3,4,9,10,11,12,1,2,5,6,7,8]=>2
[3,5,6,8,10,12,1,2,4,7,9,11]=>2
[3,5,6,8,11,12,1,2,4,7,9,10]=>2
[3,5,6,9,10,12,1,2,4,7,8,11]=>2
[3,5,6,9,11,12,1,2,4,7,8,10]=>2
[3,5,6,10,11,12,1,2,4,7,8,9]=>2
[3,5,7,8,10,12,1,2,4,6,9,11]=>2
[3,5,7,8,11,12,1,2,4,6,9,10]=>2
[3,5,7,9,10,12,1,2,4,6,8,11]=>2
[3,5,7,9,11,12,1,2,4,6,8,10]=>2
[3,5,7,10,11,12,1,2,4,6,8,9]=>2
[3,5,8,9,10,12,1,2,4,6,7,11]=>2
[3,5,8,9,11,12,1,2,4,6,7,10]=>2
[3,5,8,10,11,12,1,2,4,6,7,9]=>2
[3,5,9,10,11,12,1,2,4,6,7,8]=>2
[3,6,7,8,10,12,1,2,4,5,9,11]=>2
[3,6,7,8,11,12,1,2,4,5,9,10]=>2
[3,6,7,9,10,12,1,2,4,5,8,11]=>2
[3,6,7,9,11,12,1,2,4,5,8,10]=>2
[3,6,7,10,11,12,1,2,4,5,8,9]=>2
[3,6,8,9,10,12,1,2,4,5,7,11]=>2
[3,6,8,9,11,12,1,2,4,5,7,10]=>2
[3,6,8,10,11,12,1,2,4,5,7,9]=>2
[3,6,9,10,11,12,1,2,4,5,7,8]=>2
[3,7,8,9,10,12,1,2,4,5,6,11]=>2
[3,7,8,9,11,12,1,2,4,5,6,10]=>2
[3,7,8,10,11,12,1,2,4,5,6,9]=>2
[3,7,9,10,11,12,1,2,4,5,6,8]=>2
[3,8,9,10,11,12,1,2,4,5,6,7]=>2
[4,5,6,8,10,12,1,2,3,7,9,11]=>2
[4,5,6,8,11,12,1,2,3,7,9,10]=>2
[4,5,6,9,10,12,1,2,3,7,8,11]=>2
[4,5,6,9,11,12,1,2,3,7,8,10]=>2
[4,5,6,10,11,12,1,2,3,7,8,9]=>2
[4,5,7,8,10,12,1,2,3,6,9,11]=>2
[4,5,7,8,11,12,1,2,3,6,9,10]=>2
[4,5,7,9,10,12,1,2,3,6,8,11]=>2
[4,5,7,9,11,12,1,2,3,6,8,10]=>2
[4,5,7,10,11,12,1,2,3,6,8,9]=>2
[4,5,8,9,10,12,1,2,3,6,7,11]=>2
[4,5,8,9,11,12,1,2,3,6,7,10]=>2
[4,5,8,10,11,12,1,2,3,6,7,9]=>2
[4,5,9,10,11,12,1,2,3,6,7,8]=>2
[4,6,7,8,10,12,1,2,3,5,9,11]=>2
[4,6,7,8,11,12,1,2,3,5,9,10]=>2
[4,6,7,9,10,12,1,2,3,5,8,11]=>2
[4,6,7,9,11,12,1,2,3,5,8,10]=>2
[4,6,7,10,11,12,1,2,3,5,8,9]=>2
[4,6,8,9,10,12,1,2,3,5,7,11]=>2
[4,6,8,9,11,12,1,2,3,5,7,10]=>2
[4,6,8,10,11,12,1,2,3,5,7,9]=>2
[4,6,9,10,11,12,1,2,3,5,7,8]=>2
[4,7,8,9,10,12,1,2,3,5,6,11]=>2
[4,7,8,9,11,12,1,2,3,5,6,10]=>2
[4,7,8,10,11,12,1,2,3,5,6,9]=>2
[4,7,9,10,11,12,1,2,3,5,6,8]=>2
[4,8,9,10,11,12,1,2,3,5,6,7]=>2
[5,6,7,8,10,12,1,2,3,4,9,11]=>2
[5,6,7,8,11,12,1,2,3,4,9,10]=>2
[5,6,7,9,10,12,1,2,3,4,8,11]=>2
[5,6,7,9,11,12,1,2,3,4,8,10]=>2
[5,6,7,10,11,12,1,2,3,4,8,9]=>2
[5,6,8,9,10,12,1,2,3,4,7,11]=>2
[5,6,8,9,11,12,1,2,3,4,7,10]=>2
[5,6,8,10,11,12,1,2,3,4,7,9]=>2
[5,6,9,10,11,12,1,2,3,4,7,8]=>2
[5,7,8,9,10,12,1,2,3,4,6,11]=>2
[5,7,8,9,11,12,1,2,3,4,6,10]=>2
[5,7,8,10,11,12,1,2,3,4,6,9]=>2
[5,7,9,10,11,12,1,2,3,4,6,8]=>2
[5,8,9,10,11,12,1,2,3,4,6,7]=>2
[6,7,8,9,10,12,1,2,3,4,5,11]=>2
[6,7,8,9,11,12,1,2,3,4,5,10]=>2
[6,7,8,10,11,12,1,2,3,4,5,9]=>2
[6,7,9,10,11,12,1,2,3,4,5,8]=>2
[6,8,9,10,11,12,1,2,3,4,5,7]=>2
[7,8,9,10,11,12,1,2,3,4,5,6]=>2
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Description
The number of saliances of the permutation.
A saliance is a right-to-left maximum. This can be described as an occurrence of the mesh pattern $([1], {(1,1)})$, i.e., the upper right quadrant is shaded, see [1].
A saliance is a right-to-left maximum. This can be described as an occurrence of the mesh pattern $([1], {(1,1)})$, i.e., the upper right quadrant is shaded, see [1].
References
[1] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns MathSciNet:2795782 arXiv:1102.4226
Code
def statistic(x):
return x.number_of_saliances()
Created
Sep 21, 2011 at 03:51 by Christian Stump
Updated
Sep 27, 2018 at 11:04 by Martin Rubey
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