Identifier
- St000234: Permutations ⟶ ℤ (values match St000056The decomposition (or block) number of a permutation.)
Values
=>
[1]=>0
[1,2]=>1
[2,1]=>0
[1,2,3]=>2
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>0
[1,2,3,4]=>3
[1,2,4,3]=>2
[1,3,2,4]=>2
[1,3,4,2]=>1
[1,4,2,3]=>1
[1,4,3,2]=>1
[2,1,3,4]=>2
[2,1,4,3]=>1
[2,3,1,4]=>1
[2,3,4,1]=>0
[2,4,1,3]=>0
[2,4,3,1]=>0
[3,1,2,4]=>1
[3,1,4,2]=>0
[3,2,1,4]=>1
[3,2,4,1]=>0
[3,4,1,2]=>0
[3,4,2,1]=>0
[4,1,2,3]=>0
[4,1,3,2]=>0
[4,2,1,3]=>0
[4,2,3,1]=>0
[4,3,1,2]=>0
[4,3,2,1]=>0
[1,2,3,4,5]=>4
[1,2,3,5,4]=>3
[1,2,4,3,5]=>3
[1,2,4,5,3]=>2
[1,2,5,3,4]=>2
[1,2,5,4,3]=>2
[1,3,2,4,5]=>3
[1,3,2,5,4]=>2
[1,3,4,2,5]=>2
[1,3,4,5,2]=>1
[1,3,5,2,4]=>1
[1,3,5,4,2]=>1
[1,4,2,3,5]=>2
[1,4,2,5,3]=>1
[1,4,3,2,5]=>2
[1,4,3,5,2]=>1
[1,4,5,2,3]=>1
[1,4,5,3,2]=>1
[1,5,2,3,4]=>1
[1,5,2,4,3]=>1
[1,5,3,2,4]=>1
[1,5,3,4,2]=>1
[1,5,4,2,3]=>1
[1,5,4,3,2]=>1
[2,1,3,4,5]=>3
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>1
[2,1,5,3,4]=>1
[2,1,5,4,3]=>1
[2,3,1,4,5]=>2
[2,3,1,5,4]=>1
[2,3,4,1,5]=>1
[2,3,4,5,1]=>0
[2,3,5,1,4]=>0
[2,3,5,4,1]=>0
[2,4,1,3,5]=>1
[2,4,1,5,3]=>0
[2,4,3,1,5]=>1
[2,4,3,5,1]=>0
[2,4,5,1,3]=>0
[2,4,5,3,1]=>0
[2,5,1,3,4]=>0
[2,5,1,4,3]=>0
[2,5,3,1,4]=>0
[2,5,3,4,1]=>0
[2,5,4,1,3]=>0
[2,5,4,3,1]=>0
[3,1,2,4,5]=>2
[3,1,2,5,4]=>1
[3,1,4,2,5]=>1
[3,1,4,5,2]=>0
[3,1,5,2,4]=>0
[3,1,5,4,2]=>0
[3,2,1,4,5]=>2
[3,2,1,5,4]=>1
[3,2,4,1,5]=>1
[3,2,4,5,1]=>0
[3,2,5,1,4]=>0
[3,2,5,4,1]=>0
[3,4,1,2,5]=>1
[3,4,1,5,2]=>0
[3,4,2,1,5]=>1
[3,4,2,5,1]=>0
[3,4,5,1,2]=>0
[3,4,5,2,1]=>0
[3,5,1,2,4]=>0
[3,5,1,4,2]=>0
[3,5,2,1,4]=>0
[3,5,2,4,1]=>0
[3,5,4,1,2]=>0
[3,5,4,2,1]=>0
[4,1,2,3,5]=>1
[4,1,2,5,3]=>0
[4,1,3,2,5]=>1
[4,1,3,5,2]=>0
[4,1,5,2,3]=>0
[4,1,5,3,2]=>0
[4,2,1,3,5]=>1
[4,2,1,5,3]=>0
[4,2,3,1,5]=>1
[4,2,3,5,1]=>0
[4,2,5,1,3]=>0
[4,2,5,3,1]=>0
[4,3,1,2,5]=>1
[4,3,1,5,2]=>0
[4,3,2,1,5]=>1
[4,3,2,5,1]=>0
[4,3,5,1,2]=>0
[4,3,5,2,1]=>0
[4,5,1,2,3]=>0
[4,5,1,3,2]=>0
[4,5,2,1,3]=>0
[4,5,2,3,1]=>0
[4,5,3,1,2]=>0
[4,5,3,2,1]=>0
[5,1,2,3,4]=>0
[5,1,2,4,3]=>0
[5,1,3,2,4]=>0
[5,1,3,4,2]=>0
[5,1,4,2,3]=>0
[5,1,4,3,2]=>0
[5,2,1,3,4]=>0
[5,2,1,4,3]=>0
[5,2,3,1,4]=>0
[5,2,3,4,1]=>0
[5,2,4,1,3]=>0
[5,2,4,3,1]=>0
[5,3,1,2,4]=>0
[5,3,1,4,2]=>0
[5,3,2,1,4]=>0
[5,3,2,4,1]=>0
[5,3,4,1,2]=>0
[5,3,4,2,1]=>0
[5,4,1,2,3]=>0
[5,4,1,3,2]=>0
[5,4,2,1,3]=>0
[5,4,2,3,1]=>0
[5,4,3,1,2]=>0
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>5
[1,2,3,4,6,5]=>4
[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>3
[1,2,3,6,4,5]=>3
[1,2,3,6,5,4]=>3
[1,2,4,3,5,6]=>4
[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]=>2
[1,2,4,6,5,3]=>2
[1,2,5,3,4,6]=>3
[1,2,5,3,6,4]=>2
[1,2,5,4,3,6]=>3
[1,2,5,4,6,3]=>2
[1,2,5,6,3,4]=>2
[1,2,5,6,4,3]=>2
[1,2,6,3,4,5]=>2
[1,2,6,3,5,4]=>2
[1,2,6,4,3,5]=>2
[1,2,6,4,5,3]=>2
[1,2,6,5,3,4]=>2
[1,2,6,5,4,3]=>2
[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]=>2
[1,3,2,6,4,5]=>2
[1,3,2,6,5,4]=>2
[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>2
[1,3,4,5,2,6]=>2
[1,3,4,5,6,2]=>1
[1,3,4,6,2,5]=>1
[1,3,4,6,5,2]=>1
[1,3,5,2,4,6]=>2
[1,3,5,2,6,4]=>1
[1,3,5,4,2,6]=>2
[1,3,5,4,6,2]=>1
[1,3,5,6,2,4]=>1
[1,3,5,6,4,2]=>1
[1,3,6,2,4,5]=>1
[1,3,6,2,5,4]=>1
[1,3,6,4,2,5]=>1
[1,3,6,4,5,2]=>1
[1,3,6,5,2,4]=>1
[1,3,6,5,4,2]=>1
[1,4,2,3,5,6]=>3
[1,4,2,3,6,5]=>2
[1,4,2,5,3,6]=>2
[1,4,2,5,6,3]=>1
[1,4,2,6,3,5]=>1
[1,4,2,6,5,3]=>1
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>2
[1,4,3,5,2,6]=>2
[1,4,3,5,6,2]=>1
[1,4,3,6,2,5]=>1
[1,4,3,6,5,2]=>1
[1,4,5,2,3,6]=>2
[1,4,5,2,6,3]=>1
[1,4,5,3,2,6]=>2
[1,4,5,3,6,2]=>1
[1,4,5,6,2,3]=>1
[1,4,5,6,3,2]=>1
[1,4,6,2,3,5]=>1
[1,4,6,2,5,3]=>1
[1,4,6,3,2,5]=>1
[1,4,6,3,5,2]=>1
[1,4,6,5,2,3]=>1
[1,4,6,5,3,2]=>1
[1,5,2,3,4,6]=>2
[1,5,2,3,6,4]=>1
[1,5,2,4,3,6]=>2
[1,5,2,4,6,3]=>1
[1,5,2,6,3,4]=>1
[1,5,2,6,4,3]=>1
[1,5,3,2,4,6]=>2
[1,5,3,2,6,4]=>1
[1,5,3,4,2,6]=>2
[1,5,3,4,6,2]=>1
[1,5,3,6,2,4]=>1
[1,5,3,6,4,2]=>1
[1,5,4,2,3,6]=>2
[1,5,4,2,6,3]=>1
[1,5,4,3,2,6]=>2
[1,5,4,3,6,2]=>1
[1,5,4,6,2,3]=>1
[1,5,4,6,3,2]=>1
[1,5,6,2,3,4]=>1
[1,5,6,2,4,3]=>1
[1,5,6,3,2,4]=>1
[1,5,6,3,4,2]=>1
[1,5,6,4,2,3]=>1
[1,5,6,4,3,2]=>1
[1,6,2,3,4,5]=>1
[1,6,2,3,5,4]=>1
[1,6,2,4,3,5]=>1
[1,6,2,4,5,3]=>1
[1,6,2,5,3,4]=>1
[1,6,2,5,4,3]=>1
[1,6,3,2,4,5]=>1
[1,6,3,2,5,4]=>1
[1,6,3,4,2,5]=>1
[1,6,3,4,5,2]=>1
[1,6,3,5,2,4]=>1
[1,6,3,5,4,2]=>1
[1,6,4,2,3,5]=>1
[1,6,4,2,5,3]=>1
[1,6,4,3,2,5]=>1
[1,6,4,3,5,2]=>1
[1,6,4,5,2,3]=>1
[1,6,4,5,3,2]=>1
[1,6,5,2,3,4]=>1
[1,6,5,2,4,3]=>1
[1,6,5,3,2,4]=>1
[1,6,5,3,4,2]=>1
[1,6,5,4,2,3]=>1
[1,6,5,4,3,2]=>1
[2,1,3,4,5,6]=>4
[2,1,3,4,6,5]=>3
[2,1,3,5,4,6]=>3
[2,1,3,5,6,4]=>2
[2,1,3,6,4,5]=>2
[2,1,3,6,5,4]=>2
[2,1,4,3,5,6]=>3
[2,1,4,3,6,5]=>2
[2,1,4,5,3,6]=>2
[2,1,4,5,6,3]=>1
[2,1,4,6,3,5]=>1
[2,1,4,6,5,3]=>1
[2,1,5,3,4,6]=>2
[2,1,5,3,6,4]=>1
[2,1,5,4,3,6]=>2
[2,1,5,4,6,3]=>1
[2,1,5,6,3,4]=>1
[2,1,5,6,4,3]=>1
[2,1,6,3,4,5]=>1
[2,1,6,3,5,4]=>1
[2,1,6,4,3,5]=>1
[2,1,6,4,5,3]=>1
[2,1,6,5,3,4]=>1
[2,1,6,5,4,3]=>1
[2,3,1,4,5,6]=>3
[2,3,1,4,6,5]=>2
[2,3,1,5,4,6]=>2
[2,3,1,5,6,4]=>1
[2,3,1,6,4,5]=>1
[2,3,1,6,5,4]=>1
[2,3,4,1,5,6]=>2
[2,3,4,1,6,5]=>1
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>0
[2,3,4,6,5,1]=>0
[2,3,5,1,4,6]=>1
[2,3,5,1,6,4]=>0
[2,3,5,4,1,6]=>1
[2,3,5,4,6,1]=>0
[2,3,5,6,1,4]=>0
[2,3,5,6,4,1]=>0
[2,3,6,1,4,5]=>0
[2,3,6,1,5,4]=>0
[2,3,6,4,1,5]=>0
[2,3,6,4,5,1]=>0
[2,3,6,5,1,4]=>0
[2,3,6,5,4,1]=>0
[2,4,1,3,5,6]=>2
[2,4,1,3,6,5]=>1
[2,4,1,5,3,6]=>1
[2,4,1,5,6,3]=>0
[2,4,1,6,3,5]=>0
[2,4,1,6,5,3]=>0
[2,4,3,1,5,6]=>2
[2,4,3,1,6,5]=>1
[2,4,3,5,1,6]=>1
[2,4,3,5,6,1]=>0
[2,4,3,6,1,5]=>0
[2,4,3,6,5,1]=>0
[2,4,5,1,3,6]=>1
[2,4,5,1,6,3]=>0
[2,4,5,3,1,6]=>1
[2,4,5,3,6,1]=>0
[2,4,5,6,1,3]=>0
[2,4,5,6,3,1]=>0
[2,4,6,1,3,5]=>0
[2,4,6,1,5,3]=>0
[2,4,6,3,1,5]=>0
[2,4,6,3,5,1]=>0
[2,4,6,5,1,3]=>0
[2,4,6,5,3,1]=>0
[2,5,1,3,4,6]=>1
[2,5,1,3,6,4]=>0
[2,5,1,4,3,6]=>1
[2,5,1,4,6,3]=>0
[2,5,1,6,3,4]=>0
[2,5,1,6,4,3]=>0
[2,5,3,1,4,6]=>1
[2,5,3,1,6,4]=>0
[2,5,3,4,1,6]=>1
[2,5,3,4,6,1]=>0
[2,5,3,6,1,4]=>0
[2,5,3,6,4,1]=>0
[2,5,4,1,3,6]=>1
[2,5,4,1,6,3]=>0
[2,5,4,3,1,6]=>1
[2,5,4,3,6,1]=>0
[2,5,4,6,1,3]=>0
[2,5,4,6,3,1]=>0
[2,5,6,1,3,4]=>0
[2,5,6,1,4,3]=>0
[2,5,6,3,1,4]=>0
[2,5,6,3,4,1]=>0
[2,5,6,4,1,3]=>0
[2,5,6,4,3,1]=>0
[2,6,1,3,4,5]=>0
[2,6,1,3,5,4]=>0
[2,6,1,4,3,5]=>0
[2,6,1,4,5,3]=>0
[2,6,1,5,3,4]=>0
[2,6,1,5,4,3]=>0
[2,6,3,1,4,5]=>0
[2,6,3,1,5,4]=>0
[2,6,3,4,1,5]=>0
[2,6,3,4,5,1]=>0
[2,6,3,5,1,4]=>0
[2,6,3,5,4,1]=>0
[2,6,4,1,3,5]=>0
[2,6,4,1,5,3]=>0
[2,6,4,3,1,5]=>0
[2,6,4,3,5,1]=>0
[2,6,4,5,1,3]=>0
[2,6,4,5,3,1]=>0
[2,6,5,1,3,4]=>0
[2,6,5,1,4,3]=>0
[2,6,5,3,1,4]=>0
[2,6,5,3,4,1]=>0
[2,6,5,4,1,3]=>0
[2,6,5,4,3,1]=>0
[3,1,2,4,5,6]=>3
[3,1,2,4,6,5]=>2
[3,1,2,5,4,6]=>2
[3,1,2,5,6,4]=>1
[3,1,2,6,4,5]=>1
[3,1,2,6,5,4]=>1
[3,1,4,2,5,6]=>2
[3,1,4,2,6,5]=>1
[3,1,4,5,2,6]=>1
[3,1,4,5,6,2]=>0
[3,1,4,6,2,5]=>0
[3,1,4,6,5,2]=>0
[3,1,5,2,4,6]=>1
[3,1,5,2,6,4]=>0
[3,1,5,4,2,6]=>1
[3,1,5,4,6,2]=>0
[3,1,5,6,2,4]=>0
[3,1,5,6,4,2]=>0
[3,1,6,2,4,5]=>0
[3,1,6,2,5,4]=>0
[3,1,6,4,2,5]=>0
[3,1,6,4,5,2]=>0
[3,1,6,5,2,4]=>0
[3,1,6,5,4,2]=>0
[3,2,1,4,5,6]=>3
[3,2,1,4,6,5]=>2
[3,2,1,5,4,6]=>2
[3,2,1,5,6,4]=>1
[3,2,1,6,4,5]=>1
[3,2,1,6,5,4]=>1
[3,2,4,1,5,6]=>2
[3,2,4,1,6,5]=>1
[3,2,4,5,1,6]=>1
[3,2,4,5,6,1]=>0
[3,2,4,6,1,5]=>0
[3,2,4,6,5,1]=>0
[3,2,5,1,4,6]=>1
[3,2,5,1,6,4]=>0
[3,2,5,4,1,6]=>1
[3,2,5,4,6,1]=>0
[3,2,5,6,1,4]=>0
[3,2,5,6,4,1]=>0
[3,2,6,1,4,5]=>0
[3,2,6,1,5,4]=>0
[3,2,6,4,1,5]=>0
[3,2,6,4,5,1]=>0
[3,2,6,5,1,4]=>0
[3,2,6,5,4,1]=>0
[3,4,1,2,5,6]=>2
[3,4,1,2,6,5]=>1
[3,4,1,5,2,6]=>1
[3,4,1,5,6,2]=>0
[3,4,1,6,2,5]=>0
[3,4,1,6,5,2]=>0
[3,4,2,1,5,6]=>2
[3,4,2,1,6,5]=>1
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>0
[3,4,2,6,1,5]=>0
[3,4,2,6,5,1]=>0
[3,4,5,1,2,6]=>1
[3,4,5,1,6,2]=>0
[3,4,5,2,1,6]=>1
[3,4,5,2,6,1]=>0
[3,4,5,6,1,2]=>0
[3,4,5,6,2,1]=>0
[3,4,6,1,2,5]=>0
[3,4,6,1,5,2]=>0
[3,4,6,2,1,5]=>0
[3,4,6,2,5,1]=>0
[3,4,6,5,1,2]=>0
[3,4,6,5,2,1]=>0
[3,5,1,2,4,6]=>1
[3,5,1,2,6,4]=>0
[3,5,1,4,2,6]=>1
[3,5,1,4,6,2]=>0
[3,5,1,6,2,4]=>0
[3,5,1,6,4,2]=>0
[3,5,2,1,4,6]=>1
[3,5,2,1,6,4]=>0
[3,5,2,4,1,6]=>1
[3,5,2,4,6,1]=>0
[3,5,2,6,1,4]=>0
[3,5,2,6,4,1]=>0
[3,5,4,1,2,6]=>1
[3,5,4,1,6,2]=>0
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>0
[3,5,4,6,1,2]=>0
[3,5,4,6,2,1]=>0
[3,5,6,1,2,4]=>0
[3,5,6,1,4,2]=>0
[3,5,6,2,1,4]=>0
[3,5,6,2,4,1]=>0
[3,5,6,4,1,2]=>0
[3,5,6,4,2,1]=>0
[3,6,1,2,4,5]=>0
[3,6,1,2,5,4]=>0
[3,6,1,4,2,5]=>0
[3,6,1,4,5,2]=>0
[3,6,1,5,2,4]=>0
[3,6,1,5,4,2]=>0
[3,6,2,1,4,5]=>0
[3,6,2,1,5,4]=>0
[3,6,2,4,1,5]=>0
[3,6,2,4,5,1]=>0
[3,6,2,5,1,4]=>0
[3,6,2,5,4,1]=>0
[3,6,4,1,2,5]=>0
[3,6,4,1,5,2]=>0
[3,6,4,2,1,5]=>0
[3,6,4,2,5,1]=>0
[3,6,4,5,1,2]=>0
[3,6,4,5,2,1]=>0
[3,6,5,1,2,4]=>0
[3,6,5,1,4,2]=>0
[3,6,5,2,1,4]=>0
[3,6,5,2,4,1]=>0
[3,6,5,4,1,2]=>0
[3,6,5,4,2,1]=>0
[4,1,2,3,5,6]=>2
[4,1,2,3,6,5]=>1
[4,1,2,5,3,6]=>1
[4,1,2,5,6,3]=>0
[4,1,2,6,3,5]=>0
[4,1,2,6,5,3]=>0
[4,1,3,2,5,6]=>2
[4,1,3,2,6,5]=>1
[4,1,3,5,2,6]=>1
[4,1,3,5,6,2]=>0
[4,1,3,6,2,5]=>0
[4,1,3,6,5,2]=>0
[4,1,5,2,3,6]=>1
[4,1,5,2,6,3]=>0
[4,1,5,3,2,6]=>1
[4,1,5,3,6,2]=>0
[4,1,5,6,2,3]=>0
[4,1,5,6,3,2]=>0
[4,1,6,2,3,5]=>0
[4,1,6,2,5,3]=>0
[4,1,6,3,2,5]=>0
[4,1,6,3,5,2]=>0
[4,1,6,5,2,3]=>0
[4,1,6,5,3,2]=>0
[4,2,1,3,5,6]=>2
[4,2,1,3,6,5]=>1
[4,2,1,5,3,6]=>1
[4,2,1,5,6,3]=>0
[4,2,1,6,3,5]=>0
[4,2,1,6,5,3]=>0
[4,2,3,1,5,6]=>2
[4,2,3,1,6,5]=>1
[4,2,3,5,1,6]=>1
[4,2,3,5,6,1]=>0
[4,2,3,6,1,5]=>0
[4,2,3,6,5,1]=>0
[4,2,5,1,3,6]=>1
[4,2,5,1,6,3]=>0
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>0
[4,2,5,6,1,3]=>0
[4,2,5,6,3,1]=>0
[4,2,6,1,3,5]=>0
[4,2,6,1,5,3]=>0
[4,2,6,3,1,5]=>0
[4,2,6,3,5,1]=>0
[4,2,6,5,1,3]=>0
[4,2,6,5,3,1]=>0
[4,3,1,2,5,6]=>2
[4,3,1,2,6,5]=>1
[4,3,1,5,2,6]=>1
[4,3,1,5,6,2]=>0
[4,3,1,6,2,5]=>0
[4,3,1,6,5,2]=>0
[4,3,2,1,5,6]=>2
[4,3,2,1,6,5]=>1
[4,3,2,5,1,6]=>1
[4,3,2,5,6,1]=>0
[4,3,2,6,1,5]=>0
[4,3,2,6,5,1]=>0
[4,3,5,1,2,6]=>1
[4,3,5,1,6,2]=>0
[4,3,5,2,1,6]=>1
[4,3,5,2,6,1]=>0
[4,3,5,6,1,2]=>0
[4,3,5,6,2,1]=>0
[4,3,6,1,2,5]=>0
[4,3,6,1,5,2]=>0
[4,3,6,2,1,5]=>0
[4,3,6,2,5,1]=>0
[4,3,6,5,1,2]=>0
[4,3,6,5,2,1]=>0
[4,5,1,2,3,6]=>1
[4,5,1,2,6,3]=>0
[4,5,1,3,2,6]=>1
[4,5,1,3,6,2]=>0
[4,5,1,6,2,3]=>0
[4,5,1,6,3,2]=>0
[4,5,2,1,3,6]=>1
[4,5,2,1,6,3]=>0
[4,5,2,3,1,6]=>1
[4,5,2,3,6,1]=>0
[4,5,2,6,1,3]=>0
[4,5,2,6,3,1]=>0
[4,5,3,1,2,6]=>1
[4,5,3,1,6,2]=>0
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>0
[4,5,3,6,1,2]=>0
[4,5,3,6,2,1]=>0
[4,5,6,1,2,3]=>0
[4,5,6,1,3,2]=>0
[4,5,6,2,1,3]=>0
[4,5,6,2,3,1]=>0
[4,5,6,3,1,2]=>0
[4,5,6,3,2,1]=>0
[4,6,1,2,3,5]=>0
[4,6,1,2,5,3]=>0
[4,6,1,3,2,5]=>0
[4,6,1,3,5,2]=>0
[4,6,1,5,2,3]=>0
[4,6,1,5,3,2]=>0
[4,6,2,1,3,5]=>0
[4,6,2,1,5,3]=>0
[4,6,2,3,1,5]=>0
[4,6,2,3,5,1]=>0
[4,6,2,5,1,3]=>0
[4,6,2,5,3,1]=>0
[4,6,3,1,2,5]=>0
[4,6,3,1,5,2]=>0
[4,6,3,2,1,5]=>0
[4,6,3,2,5,1]=>0
[4,6,3,5,1,2]=>0
[4,6,3,5,2,1]=>0
[4,6,5,1,2,3]=>0
[4,6,5,1,3,2]=>0
[4,6,5,2,1,3]=>0
[4,6,5,2,3,1]=>0
[4,6,5,3,1,2]=>0
[4,6,5,3,2,1]=>0
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>0
[5,1,2,4,3,6]=>1
[5,1,2,4,6,3]=>0
[5,1,2,6,3,4]=>0
[5,1,2,6,4,3]=>0
[5,1,3,2,4,6]=>1
[5,1,3,2,6,4]=>0
[5,1,3,4,2,6]=>1
[5,1,3,4,6,2]=>0
[5,1,3,6,2,4]=>0
[5,1,3,6,4,2]=>0
[5,1,4,2,3,6]=>1
[5,1,4,2,6,3]=>0
[5,1,4,3,2,6]=>1
[5,1,4,3,6,2]=>0
[5,1,4,6,2,3]=>0
[5,1,4,6,3,2]=>0
[5,1,6,2,3,4]=>0
[5,1,6,2,4,3]=>0
[5,1,6,3,2,4]=>0
[5,1,6,3,4,2]=>0
[5,1,6,4,2,3]=>0
[5,1,6,4,3,2]=>0
[5,2,1,3,4,6]=>1
[5,2,1,3,6,4]=>0
[5,2,1,4,3,6]=>1
[5,2,1,4,6,3]=>0
[5,2,1,6,3,4]=>0
[5,2,1,6,4,3]=>0
[5,2,3,1,4,6]=>1
[5,2,3,1,6,4]=>0
[5,2,3,4,1,6]=>1
[5,2,3,4,6,1]=>0
[5,2,3,6,1,4]=>0
[5,2,3,6,4,1]=>0
[5,2,4,1,3,6]=>1
[5,2,4,1,6,3]=>0
[5,2,4,3,1,6]=>1
[5,2,4,3,6,1]=>0
[5,2,4,6,1,3]=>0
[5,2,4,6,3,1]=>0
[5,2,6,1,3,4]=>0
[5,2,6,1,4,3]=>0
[5,2,6,3,1,4]=>0
[5,2,6,3,4,1]=>0
[5,2,6,4,1,3]=>0
[5,2,6,4,3,1]=>0
[5,3,1,2,4,6]=>1
[5,3,1,2,6,4]=>0
[5,3,1,4,2,6]=>1
[5,3,1,4,6,2]=>0
[5,3,1,6,2,4]=>0
[5,3,1,6,4,2]=>0
[5,3,2,1,4,6]=>1
[5,3,2,1,6,4]=>0
[5,3,2,4,1,6]=>1
[5,3,2,4,6,1]=>0
[5,3,2,6,1,4]=>0
[5,3,2,6,4,1]=>0
[5,3,4,1,2,6]=>1
[5,3,4,1,6,2]=>0
[5,3,4,2,1,6]=>1
[5,3,4,2,6,1]=>0
[5,3,4,6,1,2]=>0
[5,3,4,6,2,1]=>0
[5,3,6,1,2,4]=>0
[5,3,6,1,4,2]=>0
[5,3,6,2,1,4]=>0
[5,3,6,2,4,1]=>0
[5,3,6,4,1,2]=>0
[5,3,6,4,2,1]=>0
[5,4,1,2,3,6]=>1
[5,4,1,2,6,3]=>0
[5,4,1,3,2,6]=>1
[5,4,1,3,6,2]=>0
[5,4,1,6,2,3]=>0
[5,4,1,6,3,2]=>0
[5,4,2,1,3,6]=>1
[5,4,2,1,6,3]=>0
[5,4,2,3,1,6]=>1
[5,4,2,3,6,1]=>0
[5,4,2,6,1,3]=>0
[5,4,2,6,3,1]=>0
[5,4,3,1,2,6]=>1
[5,4,3,1,6,2]=>0
[5,4,3,2,1,6]=>1
[5,4,3,2,6,1]=>0
[5,4,3,6,1,2]=>0
[5,4,3,6,2,1]=>0
[5,4,6,1,2,3]=>0
[5,4,6,1,3,2]=>0
[5,4,6,2,1,3]=>0
[5,4,6,2,3,1]=>0
[5,4,6,3,1,2]=>0
[5,4,6,3,2,1]=>0
[5,6,1,2,3,4]=>0
[5,6,1,2,4,3]=>0
[5,6,1,3,2,4]=>0
[5,6,1,3,4,2]=>0
[5,6,1,4,2,3]=>0
[5,6,1,4,3,2]=>0
[5,6,2,1,3,4]=>0
[5,6,2,1,4,3]=>0
[5,6,2,3,1,4]=>0
[5,6,2,3,4,1]=>0
[5,6,2,4,1,3]=>0
[5,6,2,4,3,1]=>0
[5,6,3,1,2,4]=>0
[5,6,3,1,4,2]=>0
[5,6,3,2,1,4]=>0
[5,6,3,2,4,1]=>0
[5,6,3,4,1,2]=>0
[5,6,3,4,2,1]=>0
[5,6,4,1,2,3]=>0
[5,6,4,1,3,2]=>0
[5,6,4,2,1,3]=>0
[5,6,4,2,3,1]=>0
[5,6,4,3,1,2]=>0
[5,6,4,3,2,1]=>0
[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>0
[6,1,2,4,3,5]=>0
[6,1,2,4,5,3]=>0
[6,1,2,5,3,4]=>0
[6,1,2,5,4,3]=>0
[6,1,3,2,4,5]=>0
[6,1,3,2,5,4]=>0
[6,1,3,4,2,5]=>0
[6,1,3,4,5,2]=>0
[6,1,3,5,2,4]=>0
[6,1,3,5,4,2]=>0
[6,1,4,2,3,5]=>0
[6,1,4,2,5,3]=>0
[6,1,4,3,2,5]=>0
[6,1,4,3,5,2]=>0
[6,1,4,5,2,3]=>0
[6,1,4,5,3,2]=>0
[6,1,5,2,3,4]=>0
[6,1,5,2,4,3]=>0
[6,1,5,3,2,4]=>0
[6,1,5,3,4,2]=>0
[6,1,5,4,2,3]=>0
[6,1,5,4,3,2]=>0
[6,2,1,3,4,5]=>0
[6,2,1,3,5,4]=>0
[6,2,1,4,3,5]=>0
[6,2,1,4,5,3]=>0
[6,2,1,5,3,4]=>0
[6,2,1,5,4,3]=>0
[6,2,3,1,4,5]=>0
[6,2,3,1,5,4]=>0
[6,2,3,4,1,5]=>0
[6,2,3,4,5,1]=>0
[6,2,3,5,1,4]=>0
[6,2,3,5,4,1]=>0
[6,2,4,1,3,5]=>0
[6,2,4,1,5,3]=>0
[6,2,4,3,1,5]=>0
[6,2,4,3,5,1]=>0
[6,2,4,5,1,3]=>0
[6,2,4,5,3,1]=>0
[6,2,5,1,3,4]=>0
[6,2,5,1,4,3]=>0
[6,2,5,3,1,4]=>0
[6,2,5,3,4,1]=>0
[6,2,5,4,1,3]=>0
[6,2,5,4,3,1]=>0
[6,3,1,2,4,5]=>0
[6,3,1,2,5,4]=>0
[6,3,1,4,2,5]=>0
[6,3,1,4,5,2]=>0
[6,3,1,5,2,4]=>0
[6,3,1,5,4,2]=>0
[6,3,2,1,4,5]=>0
[6,3,2,1,5,4]=>0
[6,3,2,4,1,5]=>0
[6,3,2,4,5,1]=>0
[6,3,2,5,1,4]=>0
[6,3,2,5,4,1]=>0
[6,3,4,1,2,5]=>0
[6,3,4,1,5,2]=>0
[6,3,4,2,1,5]=>0
[6,3,4,2,5,1]=>0
[6,3,4,5,1,2]=>0
[6,3,4,5,2,1]=>0
[6,3,5,1,2,4]=>0
[6,3,5,1,4,2]=>0
[6,3,5,2,1,4]=>0
[6,3,5,2,4,1]=>0
[6,3,5,4,1,2]=>0
[6,3,5,4,2,1]=>0
[6,4,1,2,3,5]=>0
[6,4,1,2,5,3]=>0
[6,4,1,3,2,5]=>0
[6,4,1,3,5,2]=>0
[6,4,1,5,2,3]=>0
[6,4,1,5,3,2]=>0
[6,4,2,1,3,5]=>0
[6,4,2,1,5,3]=>0
[6,4,2,3,1,5]=>0
[6,4,2,3,5,1]=>0
[6,4,2,5,1,3]=>0
[6,4,2,5,3,1]=>0
[6,4,3,1,2,5]=>0
[6,4,3,1,5,2]=>0
[6,4,3,2,1,5]=>0
[6,4,3,2,5,1]=>0
[6,4,3,5,1,2]=>0
[6,4,3,5,2,1]=>0
[6,4,5,1,2,3]=>0
[6,4,5,1,3,2]=>0
[6,4,5,2,1,3]=>0
[6,4,5,2,3,1]=>0
[6,4,5,3,1,2]=>0
[6,4,5,3,2,1]=>0
[6,5,1,2,3,4]=>0
[6,5,1,2,4,3]=>0
[6,5,1,3,2,4]=>0
[6,5,1,3,4,2]=>0
[6,5,1,4,2,3]=>0
[6,5,1,4,3,2]=>0
[6,5,2,1,3,4]=>0
[6,5,2,1,4,3]=>0
[6,5,2,3,1,4]=>0
[6,5,2,3,4,1]=>0
[6,5,2,4,1,3]=>0
[6,5,2,4,3,1]=>0
[6,5,3,1,2,4]=>0
[6,5,3,1,4,2]=>0
[6,5,3,2,1,4]=>0
[6,5,3,2,4,1]=>0
[6,5,3,4,1,2]=>0
[6,5,3,4,2,1]=>0
[6,5,4,1,2,3]=>0
[6,5,4,1,3,2]=>0
[6,5,4,2,1,3]=>0
[6,5,4,2,3,1]=>0
[6,5,4,3,1,2]=>0
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>6
[1,2,3,4,5,7,6]=>5
[1,2,3,4,6,5,7]=>5
[1,2,3,4,6,7,5]=>4
[1,2,3,4,7,5,6]=>4
[1,2,3,4,7,6,5]=>4
[1,2,3,5,4,6,7]=>5
[1,2,3,5,4,7,6]=>4
[1,2,3,5,6,4,7]=>4
[1,2,3,5,6,7,4]=>3
[1,2,3,5,7,4,6]=>3
[1,2,3,5,7,6,4]=>3
[1,2,3,6,4,5,7]=>4
[1,2,3,6,4,7,5]=>3
[1,2,3,6,5,4,7]=>4
[1,2,3,6,5,7,4]=>3
[1,2,3,6,7,4,5]=>3
[1,2,3,6,7,5,4]=>3
[1,2,3,7,4,5,6]=>3
[1,2,3,7,4,6,5]=>3
[1,2,3,7,5,4,6]=>3
[1,2,3,7,5,6,4]=>3
[1,2,3,7,6,4,5]=>3
[1,2,3,7,6,5,4]=>3
[1,2,4,3,5,6,7]=>5
[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]=>3
[1,2,4,5,6,7,3]=>2
[1,2,4,5,7,3,6]=>2
[1,2,4,5,7,6,3]=>2
[1,2,4,6,3,5,7]=>3
[1,2,4,6,3,7,5]=>2
[1,2,4,6,7,3,5]=>2
[1,2,4,6,7,5,3]=>2
[1,2,4,7,3,5,6]=>2
[1,2,4,7,5,6,3]=>2
[1,2,4,7,6,5,3]=>2
[1,2,5,3,4,6,7]=>4
[1,2,5,3,4,7,6]=>3
[1,2,5,3,6,4,7]=>3
[1,2,5,3,6,7,4]=>2
[1,2,5,3,7,4,6]=>2
[1,2,5,4,3,6,7]=>4
[1,2,5,4,3,7,6]=>3
[1,2,5,4,6,7,3]=>2
[1,2,5,6,3,4,7]=>3
[1,2,5,6,3,7,4]=>2
[1,2,5,6,4,7,3]=>2
[1,2,5,6,7,3,4]=>2
[1,2,5,6,7,4,3]=>2
[1,2,5,7,3,4,6]=>2
[1,2,5,7,3,6,4]=>2
[1,2,5,7,4,3,6]=>2
[1,2,5,7,6,3,4]=>2
[1,2,5,7,6,4,3]=>2
[1,2,6,3,4,5,7]=>3
[1,2,6,3,4,7,5]=>2
[1,2,6,3,5,4,7]=>3
[1,2,6,3,5,7,4]=>2
[1,2,6,3,7,4,5]=>2
[1,2,6,3,7,5,4]=>2
[1,2,6,4,3,7,5]=>2
[1,2,6,4,5,7,3]=>2
[1,2,6,4,7,3,5]=>2
[1,2,6,5,3,7,4]=>2
[1,2,6,5,4,3,7]=>3
[1,2,6,5,4,7,3]=>2
[1,2,6,5,7,3,4]=>2
[1,2,6,7,3,4,5]=>2
[1,2,6,7,4,3,5]=>2
[1,2,6,7,4,5,3]=>2
[1,2,6,7,5,3,4]=>2
[1,2,6,7,5,4,3]=>2
[1,2,7,3,4,5,6]=>2
[1,2,7,3,4,6,5]=>2
[1,2,7,3,5,4,6]=>2
[1,2,7,3,5,6,4]=>2
[1,2,7,3,6,4,5]=>2
[1,2,7,3,6,5,4]=>2
[1,2,7,4,3,5,6]=>2
[1,2,7,4,3,6,5]=>2
[1,2,7,4,5,3,6]=>2
[1,2,7,4,5,6,3]=>2
[1,2,7,4,6,5,3]=>2
[1,2,7,5,3,4,6]=>2
[1,2,7,5,6,3,4]=>2
[1,2,7,5,6,4,3]=>2
[1,2,7,6,3,4,5]=>2
[1,2,7,6,3,5,4]=>2
[1,2,7,6,4,3,5]=>2
[1,2,7,6,4,5,3]=>2
[1,2,7,6,5,3,4]=>2
[1,2,7,6,5,4,3]=>2
[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]=>3
[1,3,2,4,7,6,5]=>3
[1,3,2,5,4,6,7]=>4
[1,3,2,5,4,7,6]=>3
[1,3,2,5,6,4,7]=>3
[1,3,2,5,6,7,4]=>2
[1,3,2,5,7,4,6]=>2
[1,3,2,6,4,5,7]=>3
[1,3,2,6,4,7,5]=>2
[1,3,2,6,5,4,7]=>3
[1,3,2,6,7,4,5]=>2
[1,3,2,7,4,5,6]=>2
[1,3,2,7,6,5,4]=>2
[1,3,4,2,5,6,7]=>4
[1,3,4,2,5,7,6]=>3
[1,3,4,2,6,5,7]=>3
[1,3,4,2,6,7,5]=>2
[1,3,4,2,7,5,6]=>2
[1,3,4,2,7,6,5]=>2
[1,3,4,5,2,6,7]=>3
[1,3,4,5,2,7,6]=>2
[1,3,4,5,6,2,7]=>2
[1,3,4,5,6,7,2]=>1
[1,3,4,5,7,2,6]=>1
[1,3,4,5,7,6,2]=>1
[1,3,4,6,2,5,7]=>2
[1,3,4,6,2,7,5]=>1
[1,3,4,6,7,2,5]=>1
[1,3,4,6,7,5,2]=>1
[1,3,4,7,2,5,6]=>1
[1,3,4,7,2,6,5]=>1
[1,3,4,7,5,6,2]=>1
[1,3,4,7,6,5,2]=>1
[1,3,5,2,4,6,7]=>3
[1,3,5,2,4,7,6]=>2
[1,3,5,2,6,4,7]=>2
[1,3,5,2,6,7,4]=>1
[1,3,5,2,7,4,6]=>1
[1,3,5,2,7,6,4]=>1
[1,3,5,6,2,4,7]=>2
[1,3,5,6,2,7,4]=>1
[1,3,5,6,7,2,4]=>1
[1,3,5,6,7,4,2]=>1
[1,3,5,7,2,4,6]=>1
[1,3,5,7,2,6,4]=>1
[1,3,5,7,6,4,2]=>1
[1,3,6,2,4,5,7]=>2
[1,3,6,2,4,7,5]=>1
[1,3,6,2,5,7,4]=>1
[1,3,6,2,7,4,5]=>1
[1,3,6,4,2,7,5]=>1
[1,3,6,4,5,7,2]=>1
[1,3,6,7,2,4,5]=>1
[1,3,6,7,2,5,4]=>1
[1,3,6,7,4,5,2]=>1
[1,3,6,7,5,4,2]=>1
[1,3,7,2,4,5,6]=>1
[1,3,7,2,5,4,6]=>1
[1,3,7,2,6,4,5]=>1
[1,3,7,2,6,5,4]=>1
[1,3,7,4,2,6,5]=>1
[1,3,7,4,5,6,2]=>1
[1,3,7,5,2,4,6]=>1
[1,3,7,5,2,6,4]=>1
[1,3,7,5,6,4,2]=>1
[1,3,7,6,2,5,4]=>1
[1,3,7,6,4,5,2]=>1
[1,3,7,6,5,4,2]=>1
[1,4,2,3,5,6,7]=>4
[1,4,2,3,5,7,6]=>3
[1,4,2,3,6,5,7]=>3
[1,4,2,3,6,7,5]=>2
[1,4,2,3,7,5,6]=>2
[1,4,2,3,7,6,5]=>2
[1,4,2,5,3,6,7]=>3
[1,4,2,5,3,7,6]=>2
[1,4,2,5,6,3,7]=>2
[1,4,2,5,6,7,3]=>1
[1,4,2,5,7,3,6]=>1
[1,4,2,5,7,6,3]=>1
[1,4,2,6,3,5,7]=>2
[1,4,2,6,3,7,5]=>1
[1,4,2,6,7,3,5]=>1
[1,4,2,7,3,5,6]=>1
[1,4,2,7,3,6,5]=>1
[1,4,2,7,6,3,5]=>1
[1,4,2,7,6,5,3]=>1
[1,4,3,2,5,6,7]=>4
[1,4,3,2,5,7,6]=>3
[1,4,3,2,6,5,7]=>3
[1,4,3,2,7,6,5]=>2
[1,4,3,5,6,7,2]=>1
[1,4,5,2,3,6,7]=>3
[1,4,5,2,3,7,6]=>2
[1,4,5,2,6,3,7]=>2
[1,4,5,2,6,7,3]=>1
[1,4,5,2,7,3,6]=>1
[1,4,5,2,7,6,3]=>1
[1,4,5,3,6,7,2]=>1
[1,4,5,3,7,6,2]=>1
[1,4,5,6,2,3,7]=>2
[1,4,5,6,2,7,3]=>1
[1,4,5,6,3,7,2]=>1
[1,4,5,6,7,2,3]=>1
[1,4,5,6,7,3,2]=>1
[1,4,5,7,2,3,6]=>1
[1,4,5,7,2,6,3]=>1
[1,4,5,7,6,2,3]=>1
[1,4,5,7,6,3,2]=>1
[1,4,6,2,3,5,7]=>2
[1,4,6,2,3,7,5]=>1
[1,4,6,2,7,3,5]=>1
[1,4,6,2,7,5,3]=>1
[1,4,6,5,3,7,2]=>1
[1,4,6,7,2,3,5]=>1
[1,4,6,7,5,2,3]=>1
[1,4,6,7,5,3,2]=>1
[1,4,7,2,3,5,6]=>1
[1,4,7,2,3,6,5]=>1
[1,4,7,2,5,3,6]=>1
[1,4,7,2,5,6,3]=>1
[1,4,7,2,6,5,3]=>1
[1,4,7,3,2,6,5]=>1
[1,4,7,3,5,2,6]=>1
[1,4,7,3,6,5,2]=>1
[1,4,7,5,6,2,3]=>1
[1,4,7,5,6,3,2]=>1
[1,4,7,6,2,5,3]=>1
[1,4,7,6,5,2,3]=>1
[1,4,7,6,5,3,2]=>1
[1,5,2,3,4,6,7]=>3
[1,5,2,3,4,7,6]=>2
[1,5,2,3,6,4,7]=>2
[1,5,2,3,6,7,4]=>1
[1,5,2,3,7,4,6]=>1
[1,5,2,3,7,6,4]=>1
[1,5,2,4,6,3,7]=>2
[1,5,2,4,6,7,3]=>1
[1,5,2,4,7,6,3]=>1
[1,5,2,6,3,4,7]=>2
[1,5,2,6,3,7,4]=>1
[1,5,2,6,7,3,4]=>1
[1,5,2,6,7,4,3]=>1
[1,5,2,7,3,4,6]=>1
[1,5,2,7,3,6,4]=>1
[1,5,2,7,4,6,3]=>1
[1,5,2,7,6,4,3]=>1
[1,5,3,2,4,7,6]=>2
[1,5,3,2,6,7,4]=>1
[1,5,3,2,7,6,4]=>1
[1,5,3,4,2,7,6]=>2
[1,5,3,4,6,7,2]=>1
[1,5,3,4,7,6,2]=>1
[1,5,3,6,7,2,4]=>1
[1,5,3,7,2,4,6]=>1
[1,5,3,7,2,6,4]=>1
[1,5,3,7,4,6,2]=>1
[1,5,3,7,6,4,2]=>1
[1,5,4,2,7,6,3]=>1
[1,5,4,3,2,6,7]=>3
[1,5,4,3,2,7,6]=>2
[1,5,4,3,6,7,2]=>1
[1,5,4,3,7,6,2]=>1
[1,5,4,7,2,6,3]=>1
[1,5,4,7,6,3,2]=>1
[1,5,6,2,3,4,7]=>2
[1,5,6,2,3,7,4]=>1
[1,5,6,2,4,3,7]=>2
[1,5,6,2,4,7,3]=>1
[1,5,6,2,7,3,4]=>1
[1,5,6,3,2,7,4]=>1
[1,5,6,3,4,7,2]=>1
[1,5,6,3,7,2,4]=>1
[1,5,6,4,3,7,2]=>1
[1,5,6,4,7,2,3]=>1
[1,5,6,4,7,3,2]=>1
[1,5,6,7,2,3,4]=>1
[1,5,6,7,2,4,3]=>1
[1,5,6,7,3,2,4]=>1
[1,5,6,7,3,4,2]=>1
[1,5,6,7,4,2,3]=>1
[1,5,6,7,4,3,2]=>1
[1,5,7,2,3,4,6]=>1
[1,5,7,2,4,3,6]=>1
[1,5,7,2,6,3,4]=>1
[1,5,7,2,6,4,3]=>1
[1,5,7,3,2,6,4]=>1
[1,5,7,3,4,6,2]=>1
[1,5,7,3,6,4,2]=>1
[1,5,7,4,2,6,3]=>1
[1,5,7,4,6,2,3]=>1
[1,5,7,6,2,3,4]=>1
[1,5,7,6,2,4,3]=>1
[1,5,7,6,3,2,4]=>1
[1,5,7,6,3,4,2]=>1
[1,5,7,6,4,2,3]=>1
[1,5,7,6,4,3,2]=>1
[1,6,2,3,4,5,7]=>2
[1,6,2,3,4,7,5]=>1
[1,6,2,3,5,4,7]=>2
[1,6,2,3,5,7,4]=>1
[1,6,2,3,7,4,5]=>1
[1,6,2,3,7,5,4]=>1
[1,6,2,4,3,5,7]=>2
[1,6,2,4,3,7,5]=>1
[1,6,2,4,5,3,7]=>2
[1,6,2,4,7,3,5]=>1
[1,6,2,4,7,5,3]=>1
[1,6,2,5,3,4,7]=>2
[1,6,2,7,3,4,5]=>1
[1,6,2,7,3,5,4]=>1
[1,6,2,7,5,4,3]=>1
[1,6,3,2,4,7,5]=>1
[1,6,3,2,5,7,4]=>1
[1,6,3,2,7,4,5]=>1
[1,6,3,2,7,5,4]=>1
[1,6,3,4,2,7,5]=>1
[1,6,3,4,5,7,2]=>1
[1,6,3,4,7,2,5]=>1
[1,6,3,5,2,7,4]=>1
[1,6,3,5,4,7,2]=>1
[1,6,3,7,2,4,5]=>1
[1,6,3,7,2,5,4]=>1
[1,6,3,7,4,2,5]=>1
[1,6,3,7,4,5,2]=>1
[1,6,3,7,5,2,4]=>1
[1,6,4,2,3,7,5]=>1
[1,6,4,5,3,7,2]=>1
[1,6,5,4,3,2,7]=>2
[1,6,5,4,3,7,2]=>1
[1,6,5,4,7,3,2]=>1
[1,6,5,7,4,3,2]=>1
[1,6,7,2,3,4,5]=>1
[1,6,7,2,3,5,4]=>1
[1,6,7,2,5,3,4]=>1
[1,6,7,3,2,4,5]=>1
[1,6,7,3,4,2,5]=>1
[1,6,7,3,4,5,2]=>1
[1,6,7,3,5,2,4]=>1
[1,6,7,4,2,3,5]=>1
[1,6,7,4,3,2,5]=>1
[1,6,7,4,5,2,3]=>1
[1,6,7,4,5,3,2]=>1
[1,6,7,5,2,3,4]=>1
[1,6,7,5,3,2,4]=>1
[1,6,7,5,3,4,2]=>1
[1,6,7,5,4,2,3]=>1
[1,6,7,5,4,3,2]=>1
[1,7,2,3,4,5,6]=>1
[1,7,2,3,4,6,5]=>1
[1,7,2,3,5,4,6]=>1
[1,7,2,3,6,4,5]=>1
[1,7,2,3,6,5,4]=>1
[1,7,2,4,3,5,6]=>1
[1,7,2,4,5,3,6]=>1
[1,7,2,4,5,6,3]=>1
[1,7,2,4,6,3,5]=>1
[1,7,2,5,3,4,6]=>1
[1,7,2,5,3,6,4]=>1
[1,7,2,5,6,3,4]=>1
[1,7,2,6,3,4,5]=>1
[1,7,3,2,4,5,6]=>1
[1,7,3,2,4,6,5]=>1
[1,7,3,2,5,6,4]=>1
[1,7,3,2,6,4,5]=>1
[1,7,3,4,2,5,6]=>1
[1,7,3,4,2,6,5]=>1
[1,7,3,4,5,2,6]=>1
[1,7,3,4,5,6,2]=>1
[1,7,3,5,2,4,6]=>1
[1,7,3,5,6,4,2]=>1
[1,7,3,6,2,5,4]=>1
[1,7,3,6,5,4,2]=>1
[1,7,4,2,3,5,6]=>1
[1,7,4,2,3,6,5]=>1
[1,7,4,2,6,3,5]=>1
[1,7,4,2,6,5,3]=>1
[1,7,4,3,2,6,5]=>1
[1,7,4,3,6,5,2]=>1
[1,7,4,5,2,3,6]=>1
[1,7,4,5,2,6,3]=>1
[1,7,4,5,3,6,2]=>1
[1,7,4,5,6,2,3]=>1
[1,7,4,5,6,3,2]=>1
[1,7,4,6,2,5,3]=>1
[1,7,4,6,5,3,2]=>1
[1,7,5,2,3,4,6]=>1
[1,7,5,2,4,6,3]=>1
[1,7,5,3,2,4,6]=>1
[1,7,5,3,2,6,4]=>1
[1,7,5,4,3,6,2]=>1
[1,7,5,4,6,3,2]=>1
[1,7,5,6,2,3,4]=>1
[1,7,5,6,3,2,4]=>1
[1,7,5,6,3,4,2]=>1
[1,7,5,6,4,2,3]=>1
[1,7,5,6,4,3,2]=>1
[1,7,6,2,3,4,5]=>1
[1,7,6,2,5,4,3]=>1
[1,7,6,3,2,4,5]=>1
[1,7,6,3,2,5,4]=>1
[1,7,6,3,4,2,5]=>1
[1,7,6,3,4,5,2]=>1
[1,7,6,3,5,4,2]=>1
[1,7,6,4,2,3,5]=>1
[1,7,6,4,5,2,3]=>1
[1,7,6,4,5,3,2]=>1
[1,7,6,5,2,3,4]=>1
[1,7,6,5,2,4,3]=>1
[1,7,6,5,3,2,4]=>1
[1,7,6,5,3,4,2]=>1
[1,7,6,5,4,2,3]=>1
[1,7,6,5,4,3,2]=>1
[2,1,3,4,5,6,7]=>5
[2,1,3,4,5,7,6]=>4
[2,1,3,4,6,5,7]=>4
[2,1,3,4,6,7,5]=>3
[2,1,3,4,7,5,6]=>3
[2,1,3,4,7,6,5]=>3
[2,1,3,5,4,6,7]=>4
[2,1,3,5,4,7,6]=>3
[2,1,3,5,6,4,7]=>3
[2,1,3,5,6,7,4]=>2
[2,1,3,5,7,6,4]=>2
[2,1,3,6,4,5,7]=>3
[2,1,3,6,4,7,5]=>2
[2,1,3,6,5,4,7]=>3
[2,1,3,6,7,4,5]=>2
[2,1,3,7,4,5,6]=>2
[2,1,3,7,5,4,6]=>2
[2,1,3,7,6,4,5]=>2
[2,1,3,7,6,5,4]=>2
[2,1,4,3,5,6,7]=>4
[2,1,4,3,5,7,6]=>3
[2,1,4,3,6,5,7]=>3
[2,1,4,3,6,7,5]=>2
[2,1,4,3,7,5,6]=>2
[2,1,4,3,7,6,5]=>2
[2,1,4,5,3,6,7]=>3
[2,1,4,5,3,7,6]=>2
[2,1,4,5,6,3,7]=>2
[2,1,4,5,6,7,3]=>1
[2,1,4,6,3,5,7]=>2
[2,1,4,6,7,3,5]=>1
[2,1,4,7,3,5,6]=>1
[2,1,4,7,3,6,5]=>1
[2,1,4,7,5,3,6]=>1
[2,1,4,7,5,6,3]=>1
[2,1,4,7,6,5,3]=>1
[2,1,5,3,4,6,7]=>3
[2,1,5,3,4,7,6]=>2
[2,1,5,3,6,4,7]=>2
[2,1,5,3,6,7,4]=>1
[2,1,5,4,3,6,7]=>3
[2,1,5,4,3,7,6]=>2
[2,1,5,6,3,4,7]=>2
[2,1,5,6,4,3,7]=>2
[2,1,5,6,7,3,4]=>1
[2,1,6,3,4,5,7]=>2
[2,1,6,3,4,7,5]=>1
[2,1,6,3,7,4,5]=>1
[2,1,6,4,5,3,7]=>2
[2,1,6,5,3,4,7]=>2
[2,1,6,5,4,3,7]=>2
[2,1,6,5,7,3,4]=>1
[2,1,6,7,3,4,5]=>1
[2,1,6,7,4,3,5]=>1
[2,1,6,7,5,3,4]=>1
[2,1,7,3,4,5,6]=>1
[2,1,7,3,4,6,5]=>1
[2,1,7,3,5,4,6]=>1
[2,1,7,3,6,4,5]=>1
[2,1,7,3,6,5,4]=>1
[2,1,7,5,3,4,6]=>1
[2,1,7,6,3,5,4]=>1
[2,1,7,6,5,3,4]=>1
[2,1,7,6,5,4,3]=>1
[2,3,1,4,5,6,7]=>4
[2,3,1,4,5,7,6]=>3
[2,3,1,4,6,5,7]=>3
[2,3,1,4,6,7,5]=>2
[2,3,1,4,7,5,6]=>2
[2,3,1,4,7,6,5]=>2
[2,3,1,5,4,6,7]=>3
[2,3,1,5,4,7,6]=>2
[2,3,1,5,6,4,7]=>2
[2,3,1,5,6,7,4]=>1
[2,3,1,5,7,4,6]=>1
[2,3,1,6,4,5,7]=>2
[2,3,1,6,4,7,5]=>1
[2,3,1,6,7,4,5]=>1
[2,3,1,7,4,5,6]=>1
[2,3,1,7,4,6,5]=>1
[2,3,1,7,5,6,4]=>1
[2,3,4,1,5,6,7]=>3
[2,3,4,1,5,7,6]=>2
[2,3,4,1,6,5,7]=>2
[2,3,4,1,6,7,5]=>1
[2,3,4,1,7,5,6]=>1
[2,3,4,1,7,6,5]=>1
[2,3,4,5,1,6,7]=>2
[2,3,4,5,1,7,6]=>1
[2,3,4,5,6,1,7]=>1
[2,3,4,5,6,7,1]=>0
[2,3,4,5,7,1,6]=>0
[2,3,4,5,7,6,1]=>0
[2,3,4,6,1,7,5]=>0
[2,3,4,6,5,7,1]=>0
[2,3,4,6,7,1,5]=>0
[2,3,4,6,7,5,1]=>0
[2,3,4,7,1,5,6]=>0
[2,3,4,7,1,6,5]=>0
[2,3,4,7,5,6,1]=>0
[2,3,4,7,6,1,5]=>0
[2,3,4,7,6,5,1]=>0
[2,3,5,1,6,7,4]=>0
[2,3,5,1,7,4,6]=>0
[2,3,5,1,7,6,4]=>0
[2,3,5,4,6,7,1]=>0
[2,3,5,4,7,6,1]=>0
[2,3,5,6,1,7,4]=>0
[2,3,5,6,4,7,1]=>0
[2,3,5,6,7,1,4]=>0
[2,3,5,6,7,4,1]=>0
[2,3,5,7,1,4,6]=>0
[2,3,5,7,1,6,4]=>0
[2,3,5,7,4,1,6]=>0
[2,3,5,7,6,1,4]=>0
[2,3,5,7,6,4,1]=>0
[2,3,6,1,4,5,7]=>1
[2,3,6,1,4,7,5]=>0
[2,3,6,1,7,4,5]=>0
[2,3,6,1,7,5,4]=>0
[2,3,6,4,5,7,1]=>0
[2,3,6,4,7,5,1]=>0
[2,3,6,5,1,7,4]=>0
[2,3,6,5,4,7,1]=>0
[2,3,6,5,7,1,4]=>0
[2,3,6,5,7,4,1]=>0
[2,3,6,7,1,4,5]=>0
[2,3,6,7,4,5,1]=>0
[2,3,6,7,5,1,4]=>0
[2,3,6,7,5,4,1]=>0
[2,3,7,1,4,5,6]=>0
[2,3,7,1,4,6,5]=>0
[2,3,7,1,5,4,6]=>0
[2,3,7,1,5,6,4]=>0
[2,3,7,1,6,4,5]=>0
[2,3,7,4,5,6,1]=>0
[2,3,7,4,6,1,5]=>0
[2,3,7,4,6,5,1]=>0
[2,3,7,5,1,4,6]=>0
[2,3,7,5,4,1,6]=>0
[2,3,7,5,4,6,1]=>0
[2,3,7,5,6,1,4]=>0
[2,3,7,5,6,4,1]=>0
[2,3,7,6,1,4,5]=>0
[2,3,7,6,5,1,4]=>0
[2,3,7,6,5,4,1]=>0
[2,4,1,3,5,6,7]=>3
[2,4,1,3,6,5,7]=>2
[2,4,1,3,6,7,5]=>1
[2,4,1,3,7,5,6]=>1
[2,4,1,3,7,6,5]=>1
[2,4,1,5,3,6,7]=>2
[2,4,1,5,3,7,6]=>1
[2,4,1,5,6,3,7]=>1
[2,4,1,5,6,7,3]=>0
[2,4,1,5,7,3,6]=>0
[2,4,1,6,3,5,7]=>1
[2,4,1,6,3,7,5]=>0
[2,4,1,6,7,3,5]=>0
[2,4,1,6,7,5,3]=>0
[2,4,1,7,3,5,6]=>0
[2,4,1,7,3,6,5]=>0
[2,4,1,7,6,3,5]=>0
[2,4,3,1,7,6,5]=>1
[2,4,3,5,6,7,1]=>0
[2,4,3,5,7,6,1]=>0
[2,4,3,6,5,7,1]=>0
[2,4,3,6,7,1,5]=>0
[2,4,3,6,7,5,1]=>0
[2,4,3,7,5,6,1]=>0
[2,4,3,7,6,5,1]=>0
[2,4,5,1,6,3,7]=>1
[2,4,5,1,6,7,3]=>0
[2,4,5,1,7,3,6]=>0
[2,4,5,1,7,6,3]=>0
[2,4,5,3,6,7,1]=>0
[2,4,5,3,7,1,6]=>0
[2,4,5,3,7,6,1]=>0
[2,4,5,6,1,3,7]=>1
[2,4,5,6,1,7,3]=>0
[2,4,5,6,3,7,1]=>0
[2,4,5,6,7,1,3]=>0
[2,4,5,6,7,3,1]=>0
[2,4,5,7,1,3,6]=>0
[2,4,5,7,3,1,6]=>0
[2,4,5,7,6,1,3]=>0
[2,4,5,7,6,3,1]=>0
[2,4,6,1,3,5,7]=>1
[2,4,6,1,3,7,5]=>0
[2,4,6,1,5,7,3]=>0
[2,4,6,1,7,3,5]=>0
[2,4,6,3,1,7,5]=>0
[2,4,6,3,7,5,1]=>0
[2,4,6,5,3,7,1]=>0
[2,4,6,5,7,3,1]=>0
[2,4,6,7,1,3,5]=>0
[2,4,6,7,1,5,3]=>0
[2,4,6,7,3,5,1]=>0
[2,4,6,7,5,3,1]=>0
[2,4,7,1,3,5,6]=>0
[2,4,7,1,5,3,6]=>0
[2,4,7,1,5,6,3]=>0
[2,4,7,1,6,3,5]=>0
[2,4,7,3,1,5,6]=>0
[2,4,7,3,6,1,5]=>0
[2,4,7,6,5,1,3]=>0
[2,4,7,6,5,3,1]=>0
[2,5,1,3,4,6,7]=>2
[2,5,1,3,6,4,7]=>1
[2,5,1,3,6,7,4]=>0
[2,5,1,3,7,4,6]=>0
[2,5,1,3,7,6,4]=>0
[2,5,1,4,7,6,3]=>0
[2,5,1,6,3,7,4]=>0
[2,5,1,6,4,7,3]=>0
[2,5,1,6,7,3,4]=>0
[2,5,1,6,7,4,3]=>0
[2,5,1,7,3,4,6]=>0
[2,5,1,7,3,6,4]=>0
[2,5,1,7,4,3,6]=>0
[2,5,1,7,6,3,4]=>0
[2,5,1,7,6,4,3]=>0
[2,5,3,1,7,4,6]=>0
[2,5,3,1,7,6,4]=>0
[2,5,3,4,6,7,1]=>0
[2,5,3,4,7,6,1]=>0
[2,5,3,6,4,7,1]=>0
[2,5,3,6,7,1,4]=>0
[2,5,3,6,7,4,1]=>0
[2,5,3,7,6,1,4]=>0
[2,5,4,1,6,7,3]=>0
[2,5,4,1,7,3,6]=>0
[2,5,4,3,6,7,1]=>0
[2,5,4,3,7,1,6]=>0
[2,5,4,3,7,6,1]=>0
[2,5,4,6,3,7,1]=>0
[2,5,4,6,7,1,3]=>0
[2,5,4,6,7,3,1]=>0
[2,5,4,7,1,3,6]=>0
[2,5,4,7,6,1,3]=>0
[2,5,4,7,6,3,1]=>0
[2,5,6,1,3,4,7]=>1
[2,5,6,1,3,7,4]=>0
[2,5,6,1,4,7,3]=>0
[2,5,6,1,7,3,4]=>0
[2,5,6,3,4,7,1]=>0
[2,5,6,3,7,4,1]=>0
[2,5,6,4,3,7,1]=>0
[2,5,6,4,7,1,3]=>0
[2,5,6,4,7,3,1]=>0
[2,5,6,7,1,3,4]=>0
[2,5,6,7,3,1,4]=>0
[2,5,6,7,4,3,1]=>0
[2,5,7,1,3,4,6]=>0
[2,5,7,1,4,6,3]=>0
[2,5,7,3,1,4,6]=>0
[2,5,7,3,4,1,6]=>0
[2,5,7,3,6,1,4]=>0
[2,5,7,6,4,1,3]=>0
[2,5,7,6,4,3,1]=>0
[2,6,1,3,4,5,7]=>1
[2,6,1,3,4,7,5]=>0
[2,6,1,3,7,4,5]=>0
[2,6,1,3,7,5,4]=>0
[2,6,1,5,3,7,4]=>0
[2,6,1,5,7,4,3]=>0
[2,6,1,7,3,4,5]=>0
[2,6,1,7,4,5,3]=>0
[2,6,3,1,7,4,5]=>0
[2,6,3,4,5,7,1]=>0
[2,6,3,5,4,7,1]=>0
[2,6,3,5,7,1,4]=>0
[2,6,3,7,1,4,5]=>0
[2,6,3,7,4,1,5]=>0
[2,6,3,7,4,5,1]=>0
[2,6,4,1,3,7,5]=>0
[2,6,4,1,7,3,5]=>0
[2,6,4,3,5,7,1]=>0
[2,6,4,5,1,7,3]=>0
[2,6,4,5,3,7,1]=>0
[2,6,4,5,7,3,1]=>0
[2,6,4,7,3,5,1]=>0
[2,6,4,7,5,3,1]=>0
[2,6,5,1,3,7,4]=>0
[2,6,5,1,7,3,4]=>0
[2,6,5,4,3,1,7]=>1
[2,6,5,4,3,7,1]=>0
[2,6,5,4,7,3,1]=>0
[2,6,5,7,1,3,4]=>0
[2,6,5,7,4,3,1]=>0
[2,6,7,1,3,4,5]=>0
[2,6,7,1,4,5,3]=>0
[2,6,7,1,5,3,4]=>0
[2,6,7,3,4,5,1]=>0
[2,6,7,4,3,1,5]=>0
[2,6,7,4,3,5,1]=>0
[2,6,7,5,4,3,1]=>0
[2,7,1,3,4,5,6]=>0
[2,7,1,3,4,6,5]=>0
[2,7,1,3,6,4,5]=>0
[2,7,1,4,5,3,6]=>0
[2,7,1,5,3,4,6]=>0
[2,7,1,5,4,3,6]=>0
[2,7,1,5,6,3,4]=>0
[2,7,1,6,3,4,5]=>0
[2,7,1,6,5,4,3]=>0
[2,7,3,1,4,6,5]=>0
[2,7,3,4,1,5,6]=>0
[2,7,3,4,1,6,5]=>0
[2,7,3,4,5,6,1]=>0
[2,7,3,4,6,1,5]=>0
[2,7,3,4,6,5,1]=>0
[2,7,3,5,4,6,1]=>0
[2,7,3,5,6,4,1]=>0
[2,7,3,6,1,4,5]=>0
[2,7,3,6,5,1,4]=>0
[2,7,3,6,5,4,1]=>0
[2,7,4,1,3,5,6]=>0
[2,7,4,1,5,3,6]=>0
[2,7,4,1,6,3,5]=>0
[2,7,4,3,5,1,6]=>0
[2,7,4,3,5,6,1]=>0
[2,7,4,3,6,1,5]=>0
[2,7,4,3,6,5,1]=>0
[2,7,4,5,1,3,6]=>0
[2,7,4,5,3,1,6]=>0
[2,7,4,5,3,6,1]=>0
[2,7,4,5,6,1,3]=>0
[2,7,4,5,6,3,1]=>0
[2,7,4,6,1,3,5]=>0
[2,7,4,6,5,1,3]=>0
[2,7,4,6,5,3,1]=>0
[2,7,5,1,3,4,6]=>0
[2,7,5,1,6,3,4]=>0
[2,7,5,3,4,1,6]=>0
[2,7,5,4,3,6,1]=>0
[2,7,5,4,6,3,1]=>0
[2,7,6,1,3,4,5]=>0
[2,7,6,1,4,3,5]=>0
[2,7,6,1,5,4,3]=>0
[2,7,6,3,1,4,5]=>0
[2,7,6,3,5,1,4]=>0
[2,7,6,4,5,3,1]=>0
[2,7,6,5,1,3,4]=>0
[2,7,6,5,1,4,3]=>0
[2,7,6,5,4,1,3]=>0
[2,7,6,5,4,3,1]=>0
[3,1,2,4,5,6,7]=>4
[3,1,2,4,5,7,6]=>3
[3,1,2,4,6,5,7]=>3
[3,1,2,4,6,7,5]=>2
[3,1,2,4,7,5,6]=>2
[3,1,2,5,4,6,7]=>3
[3,1,2,5,4,7,6]=>2
[3,1,2,6,4,5,7]=>2
[3,1,2,6,4,7,5]=>1
[3,1,2,6,7,4,5]=>1
[3,1,2,7,4,5,6]=>1
[3,1,2,7,6,4,5]=>1
[3,1,2,7,6,5,4]=>1
[3,1,4,2,5,6,7]=>3
[3,1,4,2,5,7,6]=>2
[3,1,4,2,6,5,7]=>2
[3,1,4,2,6,7,5]=>1
[3,1,4,2,7,5,6]=>1
[3,1,4,5,2,7,6]=>1
[3,1,4,5,6,7,2]=>0
[3,1,4,5,7,2,6]=>0
[3,1,4,6,2,5,7]=>1
[3,1,4,6,2,7,5]=>0
[3,1,4,6,7,2,5]=>0
[3,1,4,6,7,5,2]=>0
[3,1,4,7,2,5,6]=>0
[3,1,4,7,2,6,5]=>0
[3,1,4,7,5,6,2]=>0
[3,1,4,7,6,2,5]=>0
[3,1,5,2,4,6,7]=>2
[3,1,5,2,4,7,6]=>1
[3,1,5,2,6,7,4]=>0
[3,1,5,2,7,4,6]=>0
[3,1,5,4,6,7,2]=>0
[3,1,5,6,2,4,7]=>1
[3,1,5,6,2,7,4]=>0
[3,1,5,6,4,7,2]=>0
[3,1,5,6,7,2,4]=>0
[3,1,5,6,7,4,2]=>0
[3,1,5,7,2,4,6]=>0
[3,1,5,7,2,6,4]=>0
[3,1,5,7,4,2,6]=>0
[3,1,5,7,6,2,4]=>0
[3,1,6,2,4,5,7]=>1
[3,1,6,2,4,7,5]=>0
[3,1,6,2,5,7,4]=>0
[3,1,6,2,7,4,5]=>0
[3,1,6,2,7,5,4]=>0
[3,1,6,4,2,7,5]=>0
[3,1,6,4,5,7,2]=>0
[3,1,6,5,2,7,4]=>0
[3,1,6,5,4,7,2]=>0
[3,1,6,7,2,4,5]=>0
[3,1,6,7,2,5,4]=>0
[3,1,6,7,4,5,2]=>0
[3,1,7,2,4,5,6]=>0
[3,1,7,2,4,6,5]=>0
[3,1,7,2,5,6,4]=>0
[3,1,7,2,6,4,5]=>0
[3,1,7,4,2,6,5]=>0
[3,1,7,4,5,6,2]=>0
[3,1,7,5,2,4,6]=>0
[3,1,7,5,2,6,4]=>0
[3,1,7,5,6,2,4]=>0
[3,1,7,6,2,4,5]=>0
[3,1,7,6,2,5,4]=>0
[3,1,7,6,4,2,5]=>0
[3,1,7,6,5,4,2]=>0
[3,2,1,4,5,6,7]=>4
[3,2,1,4,5,7,6]=>3
[3,2,1,4,6,5,7]=>3
[3,2,1,4,7,6,5]=>2
[3,2,1,5,4,6,7]=>3
[3,2,1,5,4,7,6]=>2
[3,2,1,6,5,4,7]=>2
[3,2,1,7,6,5,4]=>1
[3,2,4,1,5,6,7]=>3
[3,2,4,5,1,6,7]=>2
[3,2,4,5,6,1,7]=>1
[3,2,4,5,6,7,1]=>0
[3,2,4,5,7,6,1]=>0
[3,2,4,6,1,7,5]=>0
[3,2,4,6,5,7,1]=>0
[3,2,4,6,7,1,5]=>0
[3,2,4,6,7,5,1]=>0
[3,2,4,7,1,5,6]=>0
[3,2,4,7,5,6,1]=>0
[3,2,4,7,6,5,1]=>0
[3,2,5,1,6,7,4]=>0
[3,2,5,4,6,7,1]=>0
[3,2,5,4,7,6,1]=>0
[3,2,5,6,1,7,4]=>0
[3,2,5,6,4,7,1]=>0
[3,2,5,6,7,1,4]=>0
[3,2,5,6,7,4,1]=>0
[3,2,5,7,1,6,4]=>0
[3,2,5,7,6,4,1]=>0
[3,2,6,1,4,5,7]=>1
[3,2,6,1,7,4,5]=>0
[3,2,6,4,5,7,1]=>0
[3,2,6,5,1,4,7]=>1
[3,2,6,5,1,7,4]=>0
[3,2,6,5,4,1,7]=>1
[3,2,6,5,4,7,1]=>0
[3,2,6,5,7,1,4]=>0
[3,2,6,5,7,4,1]=>0
[3,2,6,7,1,5,4]=>0
[3,2,6,7,4,1,5]=>0
[3,2,6,7,5,4,1]=>0
[3,2,7,4,5,6,1]=>0
[3,2,7,4,6,5,1]=>0
[3,2,7,5,4,6,1]=>0
[3,2,7,5,6,1,4]=>0
[3,2,7,5,6,4,1]=>0
[3,2,7,6,5,1,4]=>0
[3,2,7,6,5,4,1]=>0
[3,4,1,2,5,6,7]=>3
[3,4,1,2,5,7,6]=>2
[3,4,1,2,6,5,7]=>2
[3,4,1,2,6,7,5]=>1
[3,4,1,2,7,5,6]=>1
[3,4,1,5,2,7,6]=>1
[3,4,1,5,6,7,2]=>0
[3,4,1,5,7,2,6]=>0
[3,4,1,6,2,5,7]=>1
[3,4,1,6,2,7,5]=>0
[3,4,1,6,5,7,2]=>0
[3,4,1,6,7,2,5]=>0
[3,4,1,7,2,5,6]=>0
[3,4,1,7,2,6,5]=>0
[3,4,1,7,5,6,2]=>0
[3,4,1,7,6,2,5]=>0
[3,4,2,1,5,6,7]=>3
[3,4,2,5,1,6,7]=>2
[3,4,2,5,6,1,7]=>1
[3,4,2,5,6,7,1]=>0
[3,4,2,5,7,1,6]=>0
[3,4,2,5,7,6,1]=>0
[3,4,2,6,1,7,5]=>0
[3,4,2,6,5,7,1]=>0
[3,4,2,6,7,5,1]=>0
[3,4,2,7,1,5,6]=>0
[3,4,2,7,6,5,1]=>0
[3,4,5,1,2,6,7]=>2
[3,4,5,1,2,7,6]=>1
[3,4,5,1,6,7,2]=>0
[3,4,5,1,7,2,6]=>0
[3,4,5,1,7,6,2]=>0
[3,4,5,2,1,6,7]=>2
[3,4,5,2,6,1,7]=>1
[3,4,5,2,6,7,1]=>0
[3,4,5,2,7,1,6]=>0
[3,4,5,2,7,6,1]=>0
[3,4,5,6,1,2,7]=>1
[3,4,5,6,1,7,2]=>0
[3,4,5,6,2,1,7]=>1
[3,4,5,6,2,7,1]=>0
[3,4,5,6,7,1,2]=>0
[3,4,5,6,7,2,1]=>0
[3,4,5,7,1,2,6]=>0
[3,4,5,7,1,6,2]=>0
[3,4,5,7,2,1,6]=>0
[3,4,5,7,6,2,1]=>0
[3,4,6,1,2,5,7]=>1
[3,4,6,1,2,7,5]=>0
[3,4,6,1,5,2,7]=>1
[3,4,6,1,7,2,5]=>0
[3,4,6,1,7,5,2]=>0
[3,4,6,2,1,5,7]=>1
[3,4,6,2,1,7,5]=>0
[3,4,6,2,7,1,5]=>0
[3,4,6,2,7,5,1]=>0
[3,4,6,5,2,7,1]=>0
[3,4,6,5,7,1,2]=>0
[3,4,6,5,7,2,1]=>0
[3,4,6,7,1,2,5]=>0
[3,4,6,7,1,5,2]=>0
[3,4,6,7,2,1,5]=>0
[3,4,6,7,2,5,1]=>0
[3,4,6,7,5,1,2]=>0
[3,4,6,7,5,2,1]=>0
[3,4,7,1,2,5,6]=>0
[3,4,7,1,2,6,5]=>0
[3,4,7,1,5,6,2]=>0
[3,4,7,2,1,5,6]=>0
[3,4,7,2,1,6,5]=>0
[3,4,7,2,5,1,6]=>0
[3,4,7,2,5,6,1]=>0
[3,4,7,6,1,5,2]=>0
[3,4,7,6,2,1,5]=>0
[3,4,7,6,5,2,1]=>0
[3,5,1,2,4,6,7]=>2
[3,5,1,2,6,7,4]=>0
[3,5,1,2,7,4,6]=>0
[3,5,1,2,7,6,4]=>0
[3,5,1,4,2,6,7]=>2
[3,5,1,4,6,7,2]=>0
[3,5,1,4,7,2,6]=>0
[3,5,1,4,7,6,2]=>0
[3,5,1,6,2,4,7]=>1
[3,5,1,6,2,7,4]=>0
[3,5,1,6,4,7,2]=>0
[3,5,1,6,7,2,4]=>0
[3,5,1,6,7,4,2]=>0
[3,5,1,7,2,4,6]=>0
[3,5,1,7,2,6,4]=>0
[3,5,1,7,4,6,2]=>0
[3,5,2,1,4,6,7]=>2
[3,5,2,1,4,7,6]=>1
[3,5,2,1,6,7,4]=>0
[3,5,2,1,7,4,6]=>0
[3,5,2,6,1,4,7]=>1
[3,5,2,6,1,7,4]=>0
[3,5,2,6,4,7,1]=>0
[3,5,2,6,7,1,4]=>0
[3,5,2,6,7,4,1]=>0
[3,5,2,7,1,6,4]=>0
[3,5,2,7,4,1,6]=>0
[3,5,4,1,7,2,6]=>0
[3,5,4,2,6,7,1]=>0
[3,5,4,2,7,6,1]=>0
[3,5,4,6,1,7,2]=>0
[3,5,4,6,2,7,1]=>0
[3,5,4,6,7,2,1]=>0
[3,5,4,7,1,6,2]=>0
[3,5,4,7,2,1,6]=>0
[3,5,4,7,6,2,1]=>0
[3,5,6,1,2,4,7]=>1
[3,5,6,1,2,7,4]=>0
[3,5,6,1,4,2,7]=>1
[3,5,6,1,7,2,4]=>0
[3,5,6,2,4,7,1]=>0
[3,5,6,2,7,1,4]=>0
[3,5,6,2,7,4,1]=>0
[3,5,6,4,1,2,7]=>1
[3,5,6,4,2,1,7]=>1
[3,5,6,4,2,7,1]=>0
[3,5,6,4,7,1,2]=>0
[3,5,6,4,7,2,1]=>0
[3,5,6,7,1,2,4]=>0
[3,5,6,7,2,1,4]=>0
[3,5,6,7,4,1,2]=>0
[3,5,6,7,4,2,1]=>0
[3,5,7,1,2,4,6]=>0
[3,5,7,1,4,6,2]=>0
[3,5,7,2,1,4,6]=>0
[3,5,7,2,4,1,6]=>0
[3,5,7,2,6,1,4]=>0
[3,5,7,4,1,6,2]=>0
[3,5,7,4,2,1,6]=>0
[3,5,7,6,1,4,2]=>0
[3,5,7,6,2,1,4]=>0
[3,5,7,6,4,2,1]=>0
[3,6,1,2,4,5,7]=>1
[3,6,1,2,4,7,5]=>0
[3,6,1,2,7,4,5]=>0
[3,6,1,2,7,5,4]=>0
[3,6,1,4,2,7,5]=>0
[3,6,1,4,5,2,7]=>1
[3,6,1,4,5,7,2]=>0
[3,6,1,4,7,2,5]=>0
[3,6,1,4,7,5,2]=>0
[3,6,1,5,7,4,2]=>0
[3,6,1,7,2,4,5]=>0
[3,6,1,7,2,5,4]=>0
[3,6,1,7,5,4,2]=>0
[3,6,2,1,4,7,5]=>0
[3,6,2,1,5,4,7]=>1
[3,6,2,1,7,5,4]=>0
[3,6,2,4,1,5,7]=>1
[3,6,2,4,1,7,5]=>0
[3,6,2,4,7,1,5]=>0
[3,6,2,7,1,5,4]=>0
[3,6,2,7,4,5,1]=>0
[3,6,2,7,5,1,4]=>0
[3,6,4,7,1,5,2]=>0
[3,6,4,7,2,5,1]=>0
[3,6,5,2,1,7,4]=>0
[3,6,5,2,7,1,4]=>0
[3,6,5,4,2,1,7]=>1
[3,6,5,4,2,7,1]=>0
[3,6,5,4,7,2,1]=>0
[3,6,5,7,2,1,4]=>0
[3,6,5,7,4,2,1]=>0
[3,6,7,1,2,4,5]=>0
[3,6,7,1,4,2,5]=>0
[3,6,7,1,5,4,2]=>0
[3,6,7,2,1,5,4]=>0
[3,6,7,2,4,5,1]=>0
[3,6,7,2,5,4,1]=>0
[3,6,7,4,1,5,2]=>0
[3,6,7,4,5,1,2]=>0
[3,6,7,5,4,2,1]=>0
[3,7,1,2,4,5,6]=>0
[3,7,1,2,6,4,5]=>0
[3,7,1,4,2,5,6]=>0
[3,7,1,4,5,2,6]=>0
[3,7,1,4,5,6,2]=>0
[3,7,1,5,2,6,4]=>0
[3,7,1,5,4,6,2]=>0
[3,7,1,6,4,2,5]=>0
[3,7,2,1,4,5,6]=>0
[3,7,2,1,5,6,4]=>0
[3,7,2,4,1,6,5]=>0
[3,7,2,4,5,1,6]=>0
[3,7,2,5,1,4,6]=>0
[3,7,2,5,4,1,6]=>0
[3,7,2,6,4,1,5]=>0
[3,7,4,1,2,6,5]=>0
[3,7,4,6,1,5,2]=>0
[3,7,4,6,2,1,5]=>0
[3,7,5,1,2,4,6]=>0
[3,7,5,1,4,2,6]=>0
[3,7,5,1,6,2,4]=>0
[3,7,5,2,4,1,6]=>0
[3,7,5,6,2,1,4]=>0
[3,7,6,1,2,5,4]=>0
[3,7,6,1,4,2,5]=>0
[3,7,6,1,4,5,2]=>0
[3,7,6,2,1,4,5]=>0
[3,7,6,2,4,1,5]=>0
[3,7,6,5,1,4,2]=>0
[3,7,6,5,2,1,4]=>0
[3,7,6,5,4,2,1]=>0
[4,1,2,3,5,6,7]=>3
[4,1,2,3,5,7,6]=>2
[4,1,2,3,6,5,7]=>2
[4,1,2,3,7,5,6]=>1
[4,1,2,5,3,7,6]=>1
[4,1,2,5,6,7,3]=>0
[4,1,2,5,7,3,6]=>0
[4,1,2,5,7,6,3]=>0
[4,1,2,6,3,5,7]=>1
[4,1,2,6,3,7,5]=>0
[4,1,2,6,5,7,3]=>0
[4,1,2,6,7,3,5]=>0
[4,1,2,6,7,5,3]=>0
[4,1,2,7,3,5,6]=>0
[4,1,2,7,3,6,5]=>0
[4,1,2,7,6,3,5]=>0
[4,1,3,2,5,6,7]=>3
[4,1,3,2,7,6,5]=>1
[4,1,3,6,2,7,5]=>0
[4,1,3,7,2,6,5]=>0
[4,1,5,2,3,6,7]=>2
[4,1,5,2,3,7,6]=>1
[4,1,5,2,6,3,7]=>1
[4,1,5,2,6,7,3]=>0
[4,1,5,2,7,3,6]=>0
[4,1,5,2,7,6,3]=>0
[4,1,5,3,2,7,6]=>1
[4,1,5,3,6,7,2]=>0
[4,1,5,3,7,2,6]=>0
[4,1,5,6,2,3,7]=>1
[4,1,5,6,2,7,3]=>0
[4,1,5,6,3,7,2]=>0
[4,1,5,6,7,2,3]=>0
[4,1,5,6,7,3,2]=>0
[4,1,5,7,2,3,6]=>0
[4,1,5,7,2,6,3]=>0
[4,1,5,7,3,2,6]=>0
[4,1,5,7,3,6,2]=>0
[4,1,6,2,3,5,7]=>1
[4,1,6,2,3,7,5]=>0
[4,1,6,2,5,7,3]=>0
[4,1,6,2,7,3,5]=>0
[4,1,6,2,7,5,3]=>0
[4,1,6,3,2,7,5]=>0
[4,1,6,3,7,2,5]=>0
[4,1,6,3,7,5,2]=>0
[4,1,6,5,7,3,2]=>0
[4,1,6,7,2,3,5]=>0
[4,1,6,7,3,5,2]=>0
[4,1,6,7,5,3,2]=>0
[4,1,7,2,3,5,6]=>0
[4,1,7,2,3,6,5]=>0
[4,1,7,2,5,3,6]=>0
[4,1,7,2,5,6,3]=>0
[4,1,7,3,2,5,6]=>0
[4,1,7,3,5,6,2]=>0
[4,1,7,6,2,3,5]=>0
[4,1,7,6,5,3,2]=>0
[4,2,1,3,5,6,7]=>3
[4,2,1,3,6,7,5]=>1
[4,2,1,3,7,5,6]=>1
[4,2,1,5,3,7,6]=>1
[4,2,1,5,6,3,7]=>1
[4,2,1,5,6,7,3]=>0
[4,2,1,5,7,3,6]=>0
[4,2,1,6,7,3,5]=>0
[4,2,1,7,3,5,6]=>0
[4,2,1,7,3,6,5]=>0
[4,2,1,7,5,6,3]=>0
[4,2,3,1,5,6,7]=>3
[4,2,3,5,1,6,7]=>2
[4,2,3,5,6,1,7]=>1
[4,2,3,5,6,7,1]=>0
[4,2,3,5,7,1,6]=>0
[4,2,3,5,7,6,1]=>0
[4,2,3,6,1,7,5]=>0
[4,2,3,6,5,7,1]=>0
[4,2,3,6,7,1,5]=>0
[4,2,3,7,5,6,1]=>0
[4,2,3,7,6,1,5]=>0
[4,2,3,7,6,5,1]=>0
[4,2,5,1,3,6,7]=>2
[4,2,5,1,3,7,6]=>1
[4,2,5,1,6,7,3]=>0
[4,2,5,1,7,3,6]=>0
[4,2,5,1,7,6,3]=>0
[4,2,5,3,6,7,1]=>0
[4,2,5,6,1,3,7]=>1
[4,2,5,6,1,7,3]=>0
[4,2,5,6,3,7,1]=>0
[4,2,5,6,7,1,3]=>0
[4,2,5,7,1,6,3]=>0
[4,2,5,7,3,1,6]=>0
[4,2,5,7,3,6,1]=>0
[4,2,6,1,3,7,5]=>0
[4,2,6,1,5,3,7]=>1
[4,2,6,1,5,7,3]=>0
[4,2,6,1,7,3,5]=>0
[4,2,6,1,7,5,3]=>0
[4,2,6,3,1,5,7]=>1
[4,2,6,3,1,7,5]=>0
[4,2,6,3,7,1,5]=>0
[4,2,6,5,1,3,7]=>1
[4,2,6,5,7,1,3]=>0
[4,2,6,7,1,5,3]=>0
[4,2,6,7,5,1,3]=>0
[4,2,7,1,3,5,6]=>0
[4,2,7,1,5,3,6]=>0
[4,2,7,1,5,6,3]=>0
[4,2,7,3,1,5,6]=>0
[4,2,7,3,1,6,5]=>0
[4,2,7,3,5,1,6]=>0
[4,2,7,5,3,1,6]=>0
[4,2,7,5,6,3,1]=>0
[4,2,7,6,1,3,5]=>0
[4,2,7,6,3,1,5]=>0
[4,2,7,6,5,3,1]=>0
[4,3,1,2,5,6,7]=>3
[4,3,1,2,7,5,6]=>1
[4,3,1,5,6,7,2]=>0
[4,3,1,5,7,2,6]=>0
[4,3,1,6,2,7,5]=>0
[4,3,1,6,7,2,5]=>0
[4,3,1,7,2,5,6]=>0
[4,3,1,7,6,2,5]=>0
[4,3,1,7,6,5,2]=>0
[4,3,2,1,5,6,7]=>3
[4,3,2,1,5,7,6]=>2
[4,3,2,1,6,5,7]=>2
[4,3,2,1,7,6,5]=>1
[4,3,2,5,1,6,7]=>2
[4,3,2,5,1,7,6]=>1
[4,3,2,5,6,1,7]=>1
[4,3,2,5,6,7,1]=>0
[4,3,2,5,7,6,1]=>0
[4,3,2,6,5,7,1]=>0
[4,3,2,6,7,5,1]=>0
[4,3,2,7,5,6,1]=>0
[4,3,2,7,6,5,1]=>0
[4,3,5,1,2,6,7]=>2
[4,3,5,1,2,7,6]=>1
[4,3,5,1,6,7,2]=>0
[4,3,5,2,1,6,7]=>2
[4,3,5,2,6,1,7]=>1
[4,3,5,2,6,7,1]=>0
[4,3,5,2,7,6,1]=>0
[4,3,5,6,1,2,7]=>1
[4,3,5,6,2,1,7]=>1
[4,3,5,6,2,7,1]=>0
[4,3,5,6,7,2,1]=>0
[4,3,5,7,6,1,2]=>0
[4,3,5,7,6,2,1]=>0
[4,3,6,1,5,7,2]=>0
[4,3,6,2,1,7,5]=>0
[4,3,6,2,5,1,7]=>1
[4,3,6,2,7,1,5]=>0
[4,3,6,5,1,7,2]=>0
[4,3,6,5,2,1,7]=>1
[4,3,6,5,2,7,1]=>0
[4,3,6,5,7,2,1]=>0
[4,3,6,7,1,5,2]=>0
[4,3,6,7,5,2,1]=>0
[4,3,7,5,6,2,1]=>0
[4,3,7,6,1,2,5]=>0
[4,3,7,6,5,2,1]=>0
[4,5,1,2,3,6,7]=>2
[4,5,1,2,3,7,6]=>1
[4,5,1,2,6,3,7]=>1
[4,5,1,2,6,7,3]=>0
[4,5,1,2,7,3,6]=>0
[4,5,1,2,7,6,3]=>0
[4,5,1,3,2,6,7]=>2
[4,5,1,3,6,7,2]=>0
[4,5,1,3,7,2,6]=>0
[4,5,1,3,7,6,2]=>0
[4,5,1,6,2,3,7]=>1
[4,5,1,6,2,7,3]=>0
[4,5,1,6,7,2,3]=>0
[4,5,1,7,2,3,6]=>0
[4,5,2,1,3,6,7]=>2
[4,5,2,1,6,7,3]=>0
[4,5,2,3,1,6,7]=>2
[4,5,2,3,6,1,7]=>1
[4,5,2,3,6,7,1]=>0
[4,5,2,3,7,1,6]=>0
[4,5,2,6,3,7,1]=>0
[4,5,2,6,7,1,3]=>0
[4,5,2,6,7,3,1]=>0
[4,5,2,7,1,3,6]=>0
[4,5,2,7,1,6,3]=>0
[4,5,2,7,3,1,6]=>0
[4,5,2,7,6,1,3]=>0
[4,5,3,1,2,6,7]=>2
[4,5,3,2,1,6,7]=>2
[4,5,3,2,6,1,7]=>1
[4,5,3,2,6,7,1]=>0
[4,5,3,2,7,6,1]=>0
[4,5,3,6,1,2,7]=>1
[4,5,3,6,2,1,7]=>1
[4,5,3,6,2,7,1]=>0
[4,5,3,6,7,1,2]=>0
[4,5,3,6,7,2,1]=>0
[4,5,3,7,1,6,2]=>0
[4,5,3,7,2,1,6]=>0
[4,5,3,7,6,2,1]=>0
[4,5,6,1,2,3,7]=>1
[4,5,6,1,2,7,3]=>0
[4,5,6,1,3,7,2]=>0
[4,5,6,1,7,2,3]=>0
[4,5,6,1,7,3,2]=>0
[4,5,6,2,1,3,7]=>1
[4,5,6,2,1,7,3]=>0
[4,5,6,2,3,1,7]=>1
[4,5,6,2,3,7,1]=>0
[4,5,6,3,1,2,7]=>1
[4,5,6,3,1,7,2]=>0
[4,5,6,3,2,1,7]=>1
[4,5,6,3,2,7,1]=>0
[4,5,6,3,7,1,2]=>0
[4,5,6,3,7,2,1]=>0
[4,5,6,7,1,2,3]=>0
[4,5,6,7,1,3,2]=>0
[4,5,6,7,2,1,3]=>0
[4,5,6,7,2,3,1]=>0
[4,5,6,7,3,1,2]=>0
[4,5,6,7,3,2,1]=>0
[4,5,7,1,2,3,6]=>0
[4,5,7,1,2,6,3]=>0
[4,5,7,1,6,3,2]=>0
[4,5,7,2,1,6,3]=>0
[4,5,7,2,6,1,3]=>0
[4,5,7,3,1,6,2]=>0
[4,5,7,3,2,1,6]=>0
[4,5,7,3,6,2,1]=>0
[4,5,7,6,2,1,3]=>0
[4,5,7,6,3,2,1]=>0
[4,6,1,2,3,5,7]=>1
[4,6,1,2,3,7,5]=>0
[4,6,1,2,7,3,5]=>0
[4,6,1,3,5,2,7]=>1
[4,6,1,3,5,7,2]=>0
[4,6,1,3,7,2,5]=>0
[4,6,1,5,7,2,3]=>0
[4,6,1,7,2,3,5]=>0
[4,6,2,1,7,5,3]=>0
[4,6,2,3,1,7,5]=>0
[4,6,2,3,7,1,5]=>0
[4,6,2,3,7,5,1]=>0
[4,6,2,7,1,3,5]=>0
[4,6,2,7,1,5,3]=>0
[4,6,2,7,3,5,1]=>0
[4,6,2,7,5,1,3]=>0
[4,6,2,7,5,3,1]=>0
[4,6,3,1,5,2,7]=>1
[4,6,3,1,7,5,2]=>0
[4,6,3,2,1,5,7]=>1
[4,6,3,2,7,1,5]=>0
[4,6,3,7,1,5,2]=>0
[4,6,3,7,2,5,1]=>0
[4,6,3,7,5,1,2]=>0
[4,6,3,7,5,2,1]=>0
[4,6,5,2,7,1,3]=>0
[4,6,5,2,7,3,1]=>0
[4,6,5,3,2,1,7]=>1
[4,6,5,3,2,7,1]=>0
[4,6,5,3,7,2,1]=>0
[4,6,5,7,1,2,3]=>0
[4,6,5,7,2,3,1]=>0
[4,6,5,7,3,2,1]=>0
[4,6,7,1,2,3,5]=>0
[4,6,7,1,5,2,3]=>0
[4,6,7,3,1,5,2]=>0
[4,6,7,3,2,1,5]=>0
[4,6,7,3,2,5,1]=>0
[4,6,7,3,5,1,2]=>0
[4,6,7,3,5,2,1]=>0
[4,6,7,5,2,1,3]=>0
[4,6,7,5,3,2,1]=>0
[4,7,1,2,3,5,6]=>0
[4,7,1,2,5,6,3]=>0
[4,7,1,2,6,3,5]=>0
[4,7,1,3,5,6,2]=>0
[4,7,1,5,2,3,6]=>0
[4,7,1,5,6,3,2]=>0
[4,7,1,6,2,5,3]=>0
[4,7,1,6,3,2,5]=>0
[4,7,2,1,3,5,6]=>0
[4,7,2,1,5,3,6]=>0
[4,7,2,1,5,6,3]=>0
[4,7,2,1,6,3,5]=>0
[4,7,2,3,1,5,6]=>0
[4,7,2,5,1,3,6]=>0
[4,7,2,5,6,1,3]=>0
[4,7,2,6,1,3,5]=>0
[4,7,3,1,5,6,2]=>0
[4,7,3,1,6,2,5]=>0
[4,7,3,2,1,6,5]=>0
[4,7,3,2,5,1,6]=>0
[4,7,3,5,1,6,2]=>0
[4,7,3,5,2,1,6]=>0
[4,7,3,6,2,1,5]=>0
[4,7,5,3,1,2,6]=>0
[4,7,5,3,1,6,2]=>0
[4,7,5,6,3,2,1]=>0
[4,7,6,1,2,5,3]=>0
[4,7,6,1,5,3,2]=>0
[4,7,6,2,1,3,5]=>0
[4,7,6,2,5,1,3]=>0
[4,7,6,3,1,5,2]=>0
[4,7,6,3,2,1,5]=>0
[4,7,6,5,3,2,1]=>0
[5,1,2,3,4,6,7]=>2
[5,1,2,3,4,7,6]=>1
[5,1,2,3,6,4,7]=>1
[5,1,2,3,6,7,4]=>0
[5,1,2,3,7,4,6]=>0
[5,1,2,3,7,6,4]=>0
[5,1,2,6,3,4,7]=>1
[5,1,2,6,3,7,4]=>0
[5,1,2,6,4,7,3]=>0
[5,1,2,6,7,3,4]=>0
[5,1,2,6,7,4,3]=>0
[5,1,2,7,3,4,6]=>0
[5,1,2,7,3,6,4]=>0
[5,1,2,7,4,3,6]=>0
[5,1,3,4,2,6,7]=>2
[5,1,3,4,7,6,2]=>0
[5,1,3,6,4,7,2]=>0
[5,1,3,6,7,4,2]=>0
[5,1,3,7,2,4,6]=>0
[5,1,3,7,2,6,4]=>0
[5,1,3,7,4,6,2]=>0
[5,1,4,2,6,7,3]=>0
[5,1,4,2,7,3,6]=>0
[5,1,4,2,7,6,3]=>0
[5,1,4,6,2,7,3]=>0
[5,1,6,2,3,4,7]=>1
[5,1,6,2,3,7,4]=>0
[5,1,6,2,7,3,4]=>0
[5,1,6,3,2,7,4]=>0
[5,1,6,3,4,7,2]=>0
[5,1,6,3,7,2,4]=>0
[5,1,6,3,7,4,2]=>0
[5,1,6,4,7,3,2]=>0
[5,1,6,7,2,3,4]=>0
[5,1,6,7,3,2,4]=>0
[5,1,6,7,4,3,2]=>0
[5,1,7,2,3,4,6]=>0
[5,1,7,3,4,2,6]=>0
[5,1,7,4,2,6,3]=>0
[5,1,7,4,3,6,2]=>0
[5,1,7,6,4,3,2]=>0
[5,2,1,3,4,6,7]=>2
[5,2,1,3,6,7,4]=>0
[5,2,1,3,7,4,6]=>0
[5,2,1,4,3,6,7]=>2
[5,2,1,6,3,7,4]=>0
[5,2,1,6,4,3,7]=>1
[5,2,1,6,7,3,4]=>0
[5,2,1,6,7,4,3]=>0
[5,2,1,7,3,4,6]=>0
[5,2,1,7,3,6,4]=>0
[5,2,1,7,4,3,6]=>0
[5,2,1,7,4,6,3]=>0
[5,2,3,1,4,6,7]=>2
[5,2,3,1,4,7,6]=>1
[5,2,3,1,6,7,4]=>0
[5,2,3,1,7,4,6]=>0
[5,2,3,4,1,6,7]=>2
[5,2,3,4,6,1,7]=>1
[5,2,3,4,6,7,1]=>0
[5,2,3,4,7,1,6]=>0
[5,2,3,4,7,6,1]=>0
[5,2,3,6,1,4,7]=>1
[5,2,3,6,1,7,4]=>0
[5,2,3,6,7,1,4]=>0
[5,2,3,6,7,4,1]=>0
[5,2,3,7,1,4,6]=>0
[5,2,3,7,1,6,4]=>0
[5,2,3,7,4,1,6]=>0
[5,2,3,7,6,4,1]=>0
[5,2,4,3,6,7,1]=>0
[5,2,4,3,7,6,1]=>0
[5,2,4,6,3,7,1]=>0
[5,2,4,7,3,1,6]=>0
[5,2,4,7,6,3,1]=>0
[5,2,6,1,4,3,7]=>1
[5,2,6,1,4,7,3]=>0
[5,2,6,3,4,7,1]=>0
[5,2,6,3,7,1,4]=>0
[5,2,6,4,1,3,7]=>1
[5,2,6,4,7,1,3]=>0
[5,2,6,7,1,3,4]=>0
[5,2,6,7,3,1,4]=>0
[5,2,6,7,3,4,1]=>0
[5,2,6,7,4,1,3]=>0
[5,2,7,1,4,6,3]=>0
[5,2,7,1,6,3,4]=>0
[5,2,7,3,1,4,6]=>0
[5,2,7,3,1,6,4]=>0
[5,2,7,3,4,1,6]=>0
[5,2,7,4,1,6,3]=>0
[5,2,7,4,3,1,6]=>0
[5,2,7,6,3,4,1]=>0
[5,2,7,6,4,1,3]=>0
[5,3,1,2,4,6,7]=>2
[5,3,1,2,6,7,4]=>0
[5,3,1,2,7,4,6]=>0
[5,3,1,4,7,6,2]=>0
[5,3,1,6,4,7,2]=>0
[5,3,1,6,7,4,2]=>0
[5,3,1,7,2,4,6]=>0
[5,3,1,7,2,6,4]=>0
[5,3,1,7,4,2,6]=>0
[5,3,1,7,6,4,2]=>0
[5,3,2,1,4,6,7]=>2
[5,3,2,1,4,7,6]=>1
[5,3,2,4,1,6,7]=>2
[5,3,2,4,6,1,7]=>1
[5,3,2,4,6,7,1]=>0
[5,3,2,4,7,6,1]=>0
[5,3,2,6,1,4,7]=>1
[5,3,2,6,4,1,7]=>1
[5,3,4,1,2,6,7]=>2
[5,3,4,1,6,7,2]=>0
[5,3,4,1,7,2,6]=>0
[5,3,4,2,1,6,7]=>2
[5,3,4,2,6,1,7]=>1
[5,3,4,2,6,7,1]=>0
[5,3,4,2,7,6,1]=>0
[5,3,4,6,1,2,7]=>1
[5,3,4,6,2,1,7]=>1
[5,3,4,6,2,7,1]=>0
[5,3,4,7,2,6,1]=>0
[5,3,6,1,2,7,4]=>0
[5,3,6,1,4,7,2]=>0
[5,3,6,1,7,4,2]=>0
[5,3,6,2,1,4,7]=>1
[5,3,6,2,4,1,7]=>1
[5,3,6,2,4,7,1]=>0
[5,3,6,2,7,1,4]=>0
[5,3,6,7,1,4,2]=>0
[5,3,6,7,2,1,4]=>0
[5,3,6,7,2,4,1]=>0
[5,3,6,7,4,2,1]=>0
[5,3,7,1,6,2,4]=>0
[5,3,7,1,6,4,2]=>0
[5,3,7,2,1,4,6]=>0
[5,3,7,4,1,2,6]=>0
[5,3,7,4,2,1,6]=>0
[5,3,7,6,4,1,2]=>0
[5,3,7,6,4,2,1]=>0
[5,4,1,2,3,6,7]=>2
[5,4,1,2,6,7,3]=>0
[5,4,1,2,7,3,6]=>0
[5,4,1,6,2,7,3]=>0
[5,4,1,6,7,3,2]=>0
[5,4,1,7,6,2,3]=>0
[5,4,1,7,6,3,2]=>0
[5,4,2,1,3,6,7]=>2
[5,4,2,1,3,7,6]=>1
[5,4,2,1,6,7,3]=>0
[5,4,2,1,7,3,6]=>0
[5,4,2,3,1,6,7]=>2
[5,4,2,3,6,1,7]=>1
[5,4,2,6,1,3,7]=>1
[5,4,2,6,1,7,3]=>0
[5,4,2,6,7,1,3]=>0
[5,4,2,7,3,1,6]=>0
[5,4,3,1,2,6,7]=>2
[5,4,3,1,7,6,2]=>0
[5,4,3,2,1,6,7]=>2
[5,4,3,2,1,7,6]=>1
[5,4,3,2,6,1,7]=>1
[5,4,3,2,6,7,1]=>0
[5,4,3,2,7,1,6]=>0
[5,4,3,2,7,6,1]=>0
[5,4,3,6,1,2,7]=>1
[5,4,3,6,1,7,2]=>0
[5,4,3,6,2,1,7]=>1
[5,4,3,6,2,7,1]=>0
[5,4,3,6,7,2,1]=>0
[5,4,3,7,6,2,1]=>0
[5,4,6,1,2,3,7]=>1
[5,4,6,1,7,3,2]=>0
[5,4,6,2,1,3,7]=>1
[5,4,6,2,3,1,7]=>1
[5,4,6,2,7,1,3]=>0
[5,4,6,3,1,2,7]=>1
[5,4,6,3,1,7,2]=>0
[5,4,6,3,2,1,7]=>1
[5,4,6,3,2,7,1]=>0
[5,4,6,3,7,2,1]=>0
[5,4,6,7,3,2,1]=>0
[5,4,7,1,2,3,6]=>0
[5,4,7,1,2,6,3]=>0
[5,4,7,2,1,3,6]=>0
[5,4,7,3,6,1,2]=>0
[5,4,7,3,6,2,1]=>0
[5,4,7,6,3,2,1]=>0
[5,6,1,2,3,4,7]=>1
[5,6,1,2,3,7,4]=>0
[5,6,1,2,4,7,3]=>0
[5,6,1,2,7,3,4]=>0
[5,6,1,3,4,7,2]=>0
[5,6,1,4,3,2,7]=>1
[5,6,1,7,2,3,4]=>0
[5,6,2,1,3,4,7]=>1
[5,6,2,1,7,4,3]=>0
[5,6,2,3,1,4,7]=>1
[5,6,2,3,4,1,7]=>1
[5,6,2,3,4,7,1]=>0
[5,6,2,3,7,4,1]=>0
[5,6,2,4,7,1,3]=>0
[5,6,2,7,3,1,4]=>0
[5,6,2,7,3,4,1]=>0
[5,6,2,7,4,1,3]=>0
[5,6,2,7,4,3,1]=>0
[5,6,3,1,2,4,7]=>1
[5,6,3,1,4,2,7]=>1
[5,6,3,2,1,4,7]=>1
[5,6,3,2,4,1,7]=>1
[5,6,3,2,4,7,1]=>0
[5,6,3,2,7,1,4]=>0
[5,6,3,2,7,4,1]=>0
[5,6,3,4,1,2,7]=>1
[5,6,3,4,2,1,7]=>1
[5,6,3,4,7,1,2]=>0
[5,6,3,7,1,2,4]=>0
[5,6,3,7,2,1,4]=>0
[5,6,3,7,4,1,2]=>0
[5,6,3,7,4,2,1]=>0
[5,6,4,1,2,3,7]=>1
[5,6,4,1,3,7,2]=>0
[5,6,4,2,1,3,7]=>1
[5,6,4,2,3,1,7]=>1
[5,6,4,3,1,2,7]=>1
[5,6,4,3,2,1,7]=>1
[5,6,4,3,2,7,1]=>0
[5,6,4,3,7,2,1]=>0
[5,6,4,7,2,3,1]=>0
[5,6,4,7,3,2,1]=>0
[5,6,7,1,2,3,4]=>0
[5,6,7,1,2,4,3]=>0
[5,6,7,1,3,2,4]=>0
[5,6,7,1,3,4,2]=>0
[5,6,7,1,4,2,3]=>0
[5,6,7,2,3,1,4]=>0
[5,6,7,2,3,4,1]=>0
[5,6,7,3,1,2,4]=>0
[5,6,7,3,1,4,2]=>0
[5,6,7,3,4,1,2]=>0
[5,6,7,3,4,2,1]=>0
[5,6,7,4,1,2,3]=>0
[5,6,7,4,1,3,2]=>0
[5,6,7,4,2,3,1]=>0
[5,6,7,4,3,1,2]=>0
[5,6,7,4,3,2,1]=>0
[5,7,1,2,3,4,6]=>0
[5,7,1,2,3,6,4]=>0
[5,7,1,2,6,3,4]=>0
[5,7,1,2,6,4,3]=>0
[5,7,1,3,2,4,6]=>0
[5,7,1,3,2,6,4]=>0
[5,7,1,3,6,4,2]=>0
[5,7,1,4,3,6,2]=>0
[5,7,1,6,2,4,3]=>0
[5,7,1,6,4,3,2]=>0
[5,7,2,1,4,3,6]=>0
[5,7,2,1,6,3,4]=>0
[5,7,2,3,1,4,6]=>0
[5,7,2,3,4,1,6]=>0
[5,7,2,3,6,1,4]=>0
[5,7,2,4,1,6,3]=>0
[5,7,2,6,1,3,4]=>0
[5,7,2,6,4,1,3]=>0
[5,7,2,6,4,3,1]=>0
[5,7,3,1,4,6,2]=>0
[5,7,3,2,1,4,6]=>0
[5,7,3,2,1,6,4]=>0
[5,7,3,2,4,1,6]=>0
[5,7,3,2,6,1,4]=>0
[5,7,3,4,1,6,2]=>0
[5,7,3,4,2,1,6]=>0
[5,7,3,6,1,4,2]=>0
[5,7,3,6,2,1,4]=>0
[5,7,3,6,4,2,1]=>0
[5,7,4,1,2,6,3]=>0
[5,7,4,1,3,6,2]=>0
[5,7,4,1,6,3,2]=>0
[5,7,4,2,1,3,6]=>0
[5,7,4,2,6,1,3]=>0
[5,7,4,3,1,6,2]=>0
[5,7,4,3,2,1,6]=>0
[5,7,4,3,6,2,1]=>0
[5,7,4,6,3,1,2]=>0
[5,7,6,2,3,1,4]=>0
[5,7,6,3,4,1,2]=>0
[5,7,6,4,3,2,1]=>0
[6,1,2,3,4,5,7]=>1
[6,1,2,3,4,7,5]=>0
[6,1,2,3,7,4,5]=>0
[6,1,2,3,7,5,4]=>0
[6,1,2,4,7,5,3]=>0
[6,1,2,5,3,7,4]=>0
[6,1,2,7,3,4,5]=>0
[6,1,2,7,3,5,4]=>0
[6,1,2,7,4,3,5]=>0
[6,1,2,7,4,5,3]=>0
[6,1,2,7,5,3,4]=>0
[6,1,2,7,5,4,3]=>0
[6,1,3,4,2,7,5]=>0
[6,1,3,4,5,2,7]=>1
[6,1,3,4,5,7,2]=>0
[6,1,3,4,7,2,5]=>0
[6,1,3,4,7,5,2]=>0
[6,1,3,5,7,2,4]=>0
[6,1,3,7,2,4,5]=>0
[6,1,3,7,2,5,4]=>0
[6,1,3,7,4,2,5]=>0
[6,1,3,7,5,4,2]=>0
[6,1,4,2,3,7,5]=>0
[6,1,4,2,5,7,3]=>0
[6,1,4,2,7,5,3]=>0
[6,1,4,3,2,7,5]=>0
[6,1,4,3,7,5,2]=>0
[6,1,4,5,2,7,3]=>0
[6,1,4,7,2,5,3]=>0
[6,1,4,7,5,2,3]=>0
[6,1,4,7,5,3,2]=>0
[6,1,5,2,3,7,4]=>0
[6,1,5,2,7,3,4]=>0
[6,1,5,4,7,2,3]=>0
[6,1,5,7,2,3,4]=>0
[6,1,7,2,3,4,5]=>0
[6,1,7,2,3,5,4]=>0
[6,1,7,2,4,3,5]=>0
[6,1,7,2,5,4,3]=>0
[6,1,7,3,2,4,5]=>0
[6,1,7,3,2,5,4]=>0
[6,1,7,3,4,5,2]=>0
[6,1,7,3,5,4,2]=>0
[6,1,7,4,5,3,2]=>0
[6,1,7,5,2,3,4]=>0
[6,1,7,5,2,4,3]=>0
[6,1,7,5,4,3,2]=>0
[6,2,1,3,4,5,7]=>1
[6,2,1,3,7,4,5]=>0
[6,2,1,4,5,3,7]=>1
[6,2,1,4,7,3,5]=>0
[6,2,1,4,7,5,3]=>0
[6,2,1,5,4,3,7]=>1
[6,2,1,5,7,3,4]=>0
[6,2,1,7,3,4,5]=>0
[6,2,1,7,4,5,3]=>0
[6,2,1,7,5,4,3]=>0
[6,2,3,1,4,5,7]=>1
[6,2,3,1,4,7,5]=>0
[6,2,3,1,5,4,7]=>1
[6,2,3,1,7,4,5]=>0
[6,2,3,1,7,5,4]=>0
[6,2,3,4,1,5,7]=>1
[6,2,3,4,1,7,5]=>0
[6,2,3,4,5,1,7]=>1
[6,2,3,4,5,7,1]=>0
[6,2,3,4,7,1,5]=>0
[6,2,3,4,7,5,1]=>0
[6,2,3,5,4,7,1]=>0
[6,2,3,5,7,4,1]=>0
[6,2,3,7,1,5,4]=>0
[6,2,3,7,4,1,5]=>0
[6,2,3,7,4,5,1]=>0
[6,2,3,7,5,1,4]=>0
[6,2,4,3,5,7,1]=>0
[6,2,4,3,7,1,5]=>0
[6,2,4,5,3,1,7]=>1
[6,2,4,5,3,7,1]=>0
[6,2,4,5,7,1,3]=>0
[6,2,4,5,7,3,1]=>0
[6,2,4,7,1,3,5]=>0
[6,2,4,7,5,1,3]=>0
[6,2,5,1,7,3,4]=>0
[6,2,5,3,1,7,4]=>0
[6,2,5,3,7,1,4]=>0
[6,2,5,4,3,1,7]=>1
[6,2,5,4,3,7,1]=>0
[6,2,5,7,1,3,4]=>0
[6,2,5,7,3,4,1]=>0
[6,2,7,1,4,3,5]=>0
[6,2,7,1,5,4,3]=>0
[6,2,7,3,1,4,5]=>0
[6,2,7,3,4,5,1]=>0
[6,2,7,3,5,1,4]=>0
[6,2,7,4,1,5,3]=>0
[6,2,7,4,3,1,5]=>0
[6,2,7,4,5,1,3]=>0
[6,2,7,5,1,3,4]=>0
[6,2,7,5,1,4,3]=>0
[6,2,7,5,4,1,3]=>0
[6,3,1,2,4,5,7]=>1
[6,3,1,2,4,7,5]=>0
[6,3,1,2,7,4,5]=>0
[6,3,1,5,2,7,4]=>0
[6,3,1,5,4,7,2]=>0
[6,3,1,5,7,2,4]=>0
[6,3,1,5,7,4,2]=>0
[6,3,1,7,2,4,5]=>0
[6,3,1,7,4,5,2]=>0
[6,3,1,7,5,4,2]=>0
[6,3,2,1,4,5,7]=>1
[6,3,2,4,1,5,7]=>1
[6,3,2,4,5,1,7]=>1
[6,3,2,4,5,7,1]=>0
[6,3,2,5,1,4,7]=>1
[6,3,2,5,4,1,7]=>1
[6,3,2,5,4,7,1]=>0
[6,3,4,1,2,5,7]=>1
[6,3,4,1,2,7,5]=>0
[6,3,4,1,7,2,5]=>0
[6,3,4,1,7,5,2]=>0
[6,3,4,2,1,5,7]=>1
[6,3,4,2,5,1,7]=>1
[6,3,4,2,5,7,1]=>0
[6,3,4,5,1,2,7]=>1
[6,3,4,5,1,7,2]=>0
[6,3,4,5,2,1,7]=>1
[6,3,4,5,2,7,1]=>0
[6,3,4,5,7,1,2]=>0
[6,3,4,5,7,2,1]=>0
[6,3,4,7,1,5,2]=>0
[6,3,4,7,2,1,5]=>0
[6,3,4,7,2,5,1]=>0
[6,3,4,7,5,1,2]=>0
[6,3,4,7,5,2,1]=>0
[6,3,5,1,2,7,4]=>0
[6,3,5,1,7,2,4]=>0
[6,3,5,4,2,1,7]=>1
[6,3,5,4,2,7,1]=>0
[6,3,5,7,1,2,4]=>0
[6,3,5,7,4,1,2]=>0
[6,3,5,7,4,2,1]=>0
[6,3,7,1,2,4,5]=>0
[6,3,7,1,2,5,4]=>0
[6,3,7,1,4,2,5]=>0
[6,3,7,1,4,5,2]=>0
[6,3,7,1,5,4,2]=>0
[6,3,7,2,1,4,5]=>0
[6,3,7,2,4,1,5]=>0
[6,3,7,2,4,5,1]=>0
[6,3,7,4,5,1,2]=>0
[6,3,7,4,5,2,1]=>0
[6,3,7,5,1,4,2]=>0
[6,3,7,5,2,1,4]=>0
[6,3,7,5,4,2,1]=>0
[6,4,1,2,3,5,7]=>1
[6,4,1,2,3,7,5]=>0
[6,4,1,2,7,5,3]=>0
[6,4,1,5,2,7,3]=>0
[6,4,1,5,7,2,3]=>0
[6,4,1,5,7,3,2]=>0
[6,4,1,7,2,3,5]=>0
[6,4,1,7,2,5,3]=>0
[6,4,1,7,5,2,3]=>0
[6,4,1,7,5,3,2]=>0
[6,4,2,1,3,5,7]=>1
[6,4,2,1,5,3,7]=>1
[6,4,2,1,7,3,5]=>0
[6,4,2,1,7,5,3]=>0
[6,4,2,3,1,5,7]=>1
[6,4,2,3,1,7,5]=>0
[6,4,2,3,5,1,7]=>1
[6,4,2,3,7,1,5]=>0
[6,4,2,5,1,3,7]=>1
[6,4,2,5,7,1,3]=>0
[6,4,2,7,1,3,5]=>0
[6,4,2,7,3,5,1]=>0
[6,4,2,7,5,3,1]=>0
[6,4,3,1,2,5,7]=>1
[6,4,3,1,5,7,2]=>0
[6,4,3,2,1,5,7]=>1
[6,4,3,2,1,7,5]=>0
[6,4,3,2,5,1,7]=>1
[6,4,3,2,5,7,1]=>0
[6,4,3,2,7,1,5]=>0
[6,4,3,5,1,2,7]=>1
[6,4,3,5,1,7,2]=>0
[6,4,3,5,2,1,7]=>1
[6,4,3,5,2,7,1]=>0
[6,4,3,5,7,2,1]=>0
[6,4,3,7,1,2,5]=>0
[6,4,5,1,2,3,7]=>1
[6,4,5,2,1,3,7]=>1
[6,4,5,2,1,7,3]=>0
[6,4,5,2,3,1,7]=>1
[6,4,5,2,7,1,3]=>0
[6,4,5,3,1,2,7]=>1
[6,4,5,3,2,1,7]=>1
[6,4,5,7,1,2,3]=>0
[6,4,5,7,3,2,1]=>0
[6,4,7,1,2,5,3]=>0
[6,4,7,1,3,5,2]=>0
[6,4,7,1,5,3,2]=>0
[6,4,7,2,1,3,5]=>0
[6,4,7,2,3,5,1]=>0
[6,4,7,2,5,1,3]=>0
[6,4,7,3,1,5,2]=>0
[6,4,7,3,2,1,5]=>0
[6,4,7,3,2,5,1]=>0
[6,4,7,3,5,2,1]=>0
[6,4,7,5,1,2,3]=>0
[6,4,7,5,2,1,3]=>0
[6,4,7,5,2,3,1]=>0
[6,4,7,5,3,1,2]=>0
[6,4,7,5,3,2,1]=>0
[6,5,1,2,3,4,7]=>1
[6,5,1,2,7,3,4]=>0
[6,5,1,2,7,4,3]=>0
[6,5,1,3,2,7,4]=>0
[6,5,1,3,7,4,2]=>0
[6,5,1,7,2,4,3]=>0
[6,5,1,7,4,3,2]=>0
[6,5,2,1,3,4,7]=>1
[6,5,2,1,4,3,7]=>1
[6,5,2,1,7,3,4]=>0
[6,5,2,3,1,4,7]=>1
[6,5,2,3,1,7,4]=>0
[6,5,2,3,4,1,7]=>1
[6,5,2,3,4,7,1]=>0
[6,5,2,3,7,1,4]=>0
[6,5,2,7,1,3,4]=>0
[6,5,2,7,4,1,3]=>0
[6,5,3,1,2,4,7]=>1
[6,5,3,1,4,7,2]=>0
[6,5,3,2,1,4,7]=>1
[6,5,3,2,4,1,7]=>1
[6,5,3,2,4,7,1]=>0
[6,5,3,4,1,2,7]=>1
[6,5,3,4,2,1,7]=>1
[6,5,3,4,2,7,1]=>0
[6,5,3,4,7,2,1]=>0
[6,5,3,7,1,2,4]=>0
[6,5,3,7,1,4,2]=>0
[6,5,3,7,2,1,4]=>0
[6,5,4,1,2,3,7]=>1
[6,5,4,1,2,7,3]=>0
[6,5,4,1,7,2,3]=>0
[6,5,4,1,7,3,2]=>0
[6,5,4,2,1,3,7]=>1
[6,5,4,2,3,1,7]=>1
[6,5,4,2,3,7,1]=>0
[6,5,4,2,7,1,3]=>0
[6,5,4,3,1,2,7]=>1
[6,5,4,3,1,7,2]=>0
[6,5,4,3,2,1,7]=>1
[6,5,4,3,2,7,1]=>0
[6,5,4,3,7,2,1]=>0
[6,5,4,7,3,2,1]=>0
[6,5,7,1,4,2,3]=>0
[6,5,7,4,3,2,1]=>0
[6,7,1,2,3,4,5]=>0
[6,7,1,2,3,5,4]=>0
[6,7,1,2,4,3,5]=>0
[6,7,1,2,4,5,3]=>0
[6,7,1,3,2,4,5]=>0
[6,7,1,3,4,5,2]=>0
[6,7,1,4,5,3,2]=>0
[6,7,1,5,2,3,4]=>0
[6,7,1,5,4,3,2]=>0
[6,7,2,1,3,5,4]=>0
[6,7,2,1,5,4,3]=>0
[6,7,2,3,1,4,5]=>0
[6,7,2,3,4,1,5]=>0
[6,7,2,3,4,5,1]=>0
[6,7,2,4,5,1,3]=>0
[6,7,2,5,4,3,1]=>0
[6,7,3,1,4,5,2]=>0
[6,7,3,1,5,4,2]=>0
[6,7,3,2,1,4,5]=>0
[6,7,3,2,1,5,4]=>0
[6,7,3,2,4,5,1]=>0
[6,7,3,2,5,1,4]=>0
[6,7,3,2,5,4,1]=>0
[6,7,3,4,1,5,2]=>0
[6,7,3,4,2,1,5]=>0
[6,7,3,4,5,1,2]=>0
[6,7,3,4,5,2,1]=>0
[6,7,3,5,4,2,1]=>0
[6,7,4,1,2,3,5]=>0
[6,7,4,1,3,5,2]=>0
[6,7,4,1,5,3,2]=>0
[6,7,4,2,3,5,1]=>0
[6,7,4,3,2,5,1]=>0
[6,7,4,3,5,2,1]=>0
[6,7,4,5,1,2,3]=>0
[6,7,4,5,1,3,2]=>0
[6,7,4,5,2,3,1]=>0
[6,7,4,5,3,1,2]=>0
[6,7,4,5,3,2,1]=>0
[6,7,5,1,2,3,4]=>0
[6,7,5,1,4,3,2]=>0
[6,7,5,2,3,4,1]=>0
[6,7,5,3,4,1,2]=>0
[6,7,5,3,4,2,1]=>0
[6,7,5,4,1,2,3]=>0
[6,7,5,4,2,3,1]=>0
[6,7,5,4,3,1,2]=>0
[6,7,5,4,3,2,1]=>0
[7,1,2,3,4,5,6]=>0
[7,1,2,3,5,4,6]=>0
[7,1,2,3,6,4,5]=>0
[7,1,2,4,5,3,6]=>0
[7,1,2,4,5,6,3]=>0
[7,1,2,5,3,4,6]=>0
[7,1,2,5,3,6,4]=>0
[7,1,2,5,6,3,4]=>0
[7,1,2,6,3,4,5]=>0
[7,1,2,6,4,3,5]=>0
[7,1,3,2,5,6,4]=>0
[7,1,3,4,5,2,6]=>0
[7,1,3,4,5,6,2]=>0
[7,1,4,2,3,5,6]=>0
[7,1,4,2,6,3,5]=>0
[7,1,4,5,2,3,6]=>0
[7,1,4,5,6,2,3]=>0
[7,1,4,6,2,3,5]=>0
[7,1,5,2,3,4,6]=>0
[7,1,5,2,3,6,4]=>0
[7,1,5,2,6,3,4]=>0
[7,1,5,3,2,4,6]=>0
[7,1,5,4,2,3,6]=>0
[7,1,6,2,4,3,5]=>0
[7,1,6,3,2,5,4]=>0
[7,1,6,3,4,2,5]=>0
[7,1,6,3,4,5,2]=>0
[7,1,6,3,5,2,4]=>0
[7,1,6,5,2,3,4]=>0
[7,1,6,5,4,3,2]=>0
[7,2,1,3,4,5,6]=>0
[7,2,1,3,4,6,5]=>0
[7,2,1,3,5,4,6]=>0
[7,2,1,3,6,4,5]=>0
[7,2,1,4,5,6,3]=>0
[7,2,1,6,4,3,5]=>0
[7,2,3,1,4,5,6]=>0
[7,2,3,1,5,6,4]=>0
[7,2,3,4,1,5,6]=>0
[7,2,3,4,1,6,5]=>0
[7,2,3,4,5,1,6]=>0
[7,2,3,4,5,6,1]=>0
[7,2,3,4,6,5,1]=>0
[7,2,3,5,4,6,1]=>0
[7,2,3,5,6,4,1]=>0
[7,2,3,6,4,1,5]=>0
[7,2,3,6,5,4,1]=>0
[7,2,4,3,5,6,1]=>0
[7,2,4,3,6,5,1]=>0
[7,2,4,5,3,6,1]=>0
[7,2,4,5,6,3,1]=>0
[7,2,4,6,5,3,1]=>0
[7,2,5,3,1,4,6]=>0
[7,2,5,3,4,1,6]=>0
[7,2,5,4,3,6,1]=>0
[7,2,5,4,6,3,1]=>0
[7,2,5,6,3,1,4]=>0
[7,2,6,3,1,4,5]=>0
[7,2,6,3,1,5,4]=>0
[7,2,6,3,4,1,5]=>0
[7,2,6,4,5,3,1]=>0
[7,2,6,5,4,3,1]=>0
[7,3,1,2,4,5,6]=>0
[7,3,1,2,6,4,5]=>0
[7,3,1,4,2,6,5]=>0
[7,3,1,5,2,4,6]=>0
[7,3,1,5,6,2,4]=>0
[7,3,1,6,2,4,5]=>0
[7,3,1,6,5,4,2]=>0
[7,3,2,1,4,5,6]=>0
[7,3,2,4,1,5,6]=>0
[7,3,2,4,5,1,6]=>0
[7,3,2,4,5,6,1]=>0
[7,3,2,4,6,5,1]=>0
[7,3,2,5,4,6,1]=>0
[7,3,2,5,6,4,1]=>0
[7,3,2,6,5,4,1]=>0
[7,3,4,1,2,5,6]=>0
[7,3,4,1,5,2,6]=>0
[7,3,4,1,6,2,5]=>0
[7,3,4,2,1,5,6]=>0
[7,3,4,2,5,1,6]=>0
[7,3,4,2,5,6,1]=>0
[7,3,4,2,6,5,1]=>0
[7,3,4,5,1,2,6]=>0
[7,3,4,5,2,1,6]=>0
[7,3,4,5,2,6,1]=>0
[7,3,4,5,6,1,2]=>0
[7,3,4,5,6,2,1]=>0
[7,3,4,6,1,2,5]=>0
[7,3,4,6,5,2,1]=>0
[7,3,5,1,2,4,6]=>0
[7,3,5,1,6,2,4]=>0
[7,3,5,4,2,6,1]=>0
[7,3,5,4,6,2,1]=>0
[7,3,6,1,2,4,5]=>0
[7,3,6,1,5,4,2]=>0
[7,3,6,4,5,2,1]=>0
[7,3,6,5,1,2,4]=>0
[7,3,6,5,1,4,2]=>0
[7,3,6,5,4,1,2]=>0
[7,3,6,5,4,2,1]=>0
[7,4,1,2,3,5,6]=>0
[7,4,1,2,6,3,5]=>0
[7,4,1,3,5,2,6]=>0
[7,4,1,3,5,6,2]=>0
[7,4,1,5,2,3,6]=>0
[7,4,1,5,6,2,3]=>0
[7,4,1,6,2,3,5]=>0
[7,4,1,6,3,5,2]=>0
[7,4,1,6,5,3,2]=>0
[7,4,2,1,3,5,6]=>0
[7,4,2,3,1,5,6]=>0
[7,4,2,3,5,1,6]=>0
[7,4,2,6,3,1,5]=>0
[7,4,3,1,2,5,6]=>0
[7,4,3,2,1,5,6]=>0
[7,4,3,2,5,6,1]=>0
[7,4,3,2,6,5,1]=>0
[7,4,3,5,2,6,1]=>0
[7,4,3,5,6,2,1]=>0
[7,4,3,6,5,2,1]=>0
[7,4,5,1,2,3,6]=>0
[7,4,5,1,3,2,6]=>0
[7,4,5,2,1,3,6]=>0
[7,4,5,2,3,1,6]=>0
[7,4,5,3,1,2,6]=>0
[7,4,5,3,2,1,6]=>0
[7,4,5,6,1,2,3]=>0
[7,4,5,6,2,1,3]=>0
[7,4,5,6,2,3,1]=>0
[7,4,5,6,3,1,2]=>0
[7,4,5,6,3,2,1]=>0
[7,4,6,1,3,2,5]=>0
[7,4,6,2,1,3,5]=>0
[7,4,6,2,3,1,5]=>0
[7,4,6,3,1,2,5]=>0
[7,4,6,3,2,1,5]=>0
[7,4,6,5,3,2,1]=>0
[7,5,1,2,3,4,6]=>0
[7,5,1,2,4,3,6]=>0
[7,5,1,2,6,3,4]=>0
[7,5,1,3,4,2,6]=>0
[7,5,1,6,4,2,3]=>0
[7,5,1,6,4,3,2]=>0
[7,5,2,1,3,4,6]=>0
[7,5,2,1,4,3,6]=>0
[7,5,2,3,1,4,6]=>0
[7,5,2,3,1,6,4]=>0
[7,5,2,3,4,1,6]=>0
[7,5,2,3,6,1,4]=>0
[7,5,2,4,6,3,1]=>0
[7,5,2,6,3,1,4]=>0
[7,5,3,1,2,4,6]=>0
[7,5,3,2,1,4,6]=>0
[7,5,3,2,4,1,6]=>0
[7,5,3,4,1,2,6]=>0
[7,5,3,4,2,1,6]=>0
[7,5,3,4,2,6,1]=>0
[7,5,3,4,6,2,1]=>0
[7,5,4,1,2,3,6]=>0
[7,5,4,1,6,2,3]=>0
[7,5,4,1,6,3,2]=>0
[7,5,4,2,1,3,6]=>0
[7,5,4,2,3,1,6]=>0
[7,5,4,3,1,2,6]=>0
[7,5,4,3,2,1,6]=>0
[7,5,4,3,2,6,1]=>0
[7,5,4,3,6,2,1]=>0
[7,5,4,6,3,2,1]=>0
[7,5,6,1,2,3,4]=>0
[7,5,6,2,1,3,4]=>0
[7,5,6,2,3,1,4]=>0
[7,5,6,2,3,4,1]=>0
[7,5,6,3,1,2,4]=>0
[7,5,6,3,2,1,4]=>0
[7,5,6,3,4,1,2]=>0
[7,5,6,3,4,2,1]=>0
[7,5,6,4,1,2,3]=>0
[7,5,6,4,2,1,3]=>0
[7,5,6,4,2,3,1]=>0
[7,5,6,4,3,1,2]=>0
[7,5,6,4,3,2,1]=>0
[7,6,1,2,3,4,5]=>0
[7,6,1,2,3,5,4]=>0
[7,6,1,2,5,4,3]=>0
[7,6,1,3,4,2,5]=>0
[7,6,1,5,4,3,2]=>0
[7,6,2,1,3,4,5]=>0
[7,6,2,1,4,3,5]=>0
[7,6,2,1,4,5,3]=>0
[7,6,2,3,1,4,5]=>0
[7,6,2,3,4,1,5]=>0
[7,6,2,3,4,5,1]=>0
[7,6,3,1,2,4,5]=>0
[7,6,3,2,1,4,5]=>0
[7,6,3,4,1,2,5]=>0
[7,6,3,4,2,1,5]=>0
[7,6,3,4,5,1,2]=>0
[7,6,3,4,5,2,1]=>0
[7,6,3,5,4,2,1]=>0
[7,6,4,1,2,3,5]=>0
[7,6,4,2,1,3,5]=>0
[7,6,4,2,3,1,5]=>0
[7,6,4,3,1,2,5]=>0
[7,6,4,3,2,1,5]=>0
[7,6,4,3,5,2,1]=>0
[7,6,4,5,1,2,3]=>0
[7,6,4,5,1,3,2]=>0
[7,6,4,5,2,1,3]=>0
[7,6,4,5,2,3,1]=>0
[7,6,4,5,3,1,2]=>0
[7,6,4,5,3,2,1]=>0
[7,6,5,1,2,3,4]=>0
[7,6,5,2,1,3,4]=>0
[7,6,5,2,3,1,4]=>0
[7,6,5,2,3,4,1]=>0
[7,6,5,3,1,2,4]=>0
[7,6,5,3,2,1,4]=>0
[7,6,5,3,4,1,2]=>0
[7,6,5,3,4,2,1]=>0
[7,6,5,4,1,2,3]=>0
[7,6,5,4,2,1,3]=>0
[7,6,5,4,2,3,1]=>0
[7,6,5,4,3,1,2]=>0
[7,6,5,4,3,2,1]=>0
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of global ascents of a permutation.
The global ascents are the integers $i$ such that
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i < k \leq n: \pi(j) < \pi(k)\}.$$
Equivalently, by the pigeonhole principle,
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i: \pi(j) \leq i \}.$$
For $n > 1$ it can also be described as an occurrence of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
According to [2], this is also the cardinality of the connectivity set of a permutation. The permutation is connected, when the connectivity set is empty. This gives oeis:A003319.
The global ascents are the integers $i$ such that
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i < k \leq n: \pi(j) < \pi(k)\}.$$
Equivalently, by the pigeonhole principle,
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i: \pi(j) \leq i \}.$$
For $n > 1$ it can also be described as an occurrence of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
According to [2], this is also the cardinality of the connectivity set of a permutation. The permutation is connected, when the connectivity set is empty. This gives oeis:A003319.
References
[1] Stanley, R. P. The descent set and connectivity set of a permutation MathSciNet:2167418 arXiv:math/0507224
[2] Bergeron, N., Hohlweg, C., Zabrocki, M. Posets related to the connectivity set of Coxeter groups MathSciNet:2255139 arXiv:math/0509271
[3] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns arXiv:1102.4226
[2] Bergeron, N., Hohlweg, C., Zabrocki, M. Posets related to the connectivity set of Coxeter groups MathSciNet:2255139 arXiv:math/0509271
[3] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns arXiv:1102.4226
Code
def statistic(pi):
return len([i for i in range(1, pi.size()) if all(pi(j) < pi(k) for j in range(1, i+1) for k in range(i+1, pi.size()+1))])
def statistic(pi):
return sum(1 for i in range(1, len(pi)) if max(pi[:i]) <= i)
Created
Feb 17, 2015 at 20:44 by Martin Rubey
Updated
Aug 24, 2021 at 08:25 by Martin Rubey
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