edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [1,2]=>0 [2,1]=>1 [1,2,3]=>0 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>2 [3,1,2]=>2 [3,2,1]=>1 [1,2,3,4]=>0 [1,2,4,3]=>1 [1,3,2,4]=>1 [1,3,4,2]=>2 [1,4,2,3]=>2 [1,4,3,2]=>1 [2,1,3,4]=>1 [2,1,4,3]=>2 [2,3,1,4]=>2 [2,3,4,1]=>2 [2,4,1,3]=>3 [2,4,3,1]=>2 [3,1,2,4]=>2 [3,1,4,2]=>3 [3,2,1,4]=>1 [3,2,4,1]=>2 [3,4,1,2]=>2 [3,4,2,1]=>2 [4,1,2,3]=>2 [4,1,3,2]=>2 [4,2,1,3]=>2 [4,2,3,1]=>2 [4,3,1,2]=>2 [4,3,2,1]=>1 [1,2,3,4,5]=>0 [1,2,3,5,4]=>1 [1,2,4,3,5]=>1 [1,2,4,5,3]=>2 [1,2,5,3,4]=>2 [1,2,5,4,3]=>1 [1,3,2,4,5]=>1 [1,3,2,5,4]=>2 [1,3,4,2,5]=>2 [1,3,4,5,2]=>2 [1,3,5,2,4]=>3 [1,3,5,4,2]=>2 [1,4,2,3,5]=>2 [1,4,2,5,3]=>3 [1,4,3,2,5]=>1 [1,4,3,5,2]=>2 [1,4,5,2,3]=>2 [1,4,5,3,2]=>2 [1,5,2,3,4]=>2 [1,5,2,4,3]=>2 [1,5,3,2,4]=>2 [1,5,3,4,2]=>2 [1,5,4,2,3]=>2 [1,5,4,3,2]=>1 [2,1,3,4,5]=>1 [2,1,3,5,4]=>2 [2,1,4,3,5]=>2 [2,1,4,5,3]=>3 [2,1,5,3,4]=>3 [2,1,5,4,3]=>2 [2,3,1,4,5]=>2 [2,3,1,5,4]=>3 [2,3,4,1,5]=>2 [2,3,4,5,1]=>2 [2,3,5,1,4]=>3 [2,3,5,4,1]=>3 [2,4,1,3,5]=>3 [2,4,1,5,3]=>4 [2,4,3,1,5]=>2 [2,4,3,5,1]=>3 [2,4,5,1,3]=>3 [2,4,5,3,1]=>3 [2,5,1,3,4]=>3 [2,5,1,4,3]=>3 [2,5,3,1,4]=>3 [2,5,3,4,1]=>3 [2,5,4,1,3]=>3 [2,5,4,3,1]=>2 [3,1,2,4,5]=>2 [3,1,2,5,4]=>3 [3,1,4,2,5]=>3 [3,1,4,5,2]=>3 [3,1,5,2,4]=>4 [3,1,5,4,2]=>3 [3,2,1,4,5]=>1 [3,2,1,5,4]=>2 [3,2,4,1,5]=>2 [3,2,4,5,1]=>3 [3,2,5,1,4]=>3 [3,2,5,4,1]=>2 [3,4,1,2,5]=>2 [3,4,1,5,2]=>3 [3,4,2,1,5]=>2 [3,4,2,5,1]=>3 [3,4,5,1,2]=>2 [3,4,5,2,1]=>2 [3,5,1,2,4]=>3 [3,5,1,4,2]=>3 [3,5,2,1,4]=>3 [3,5,2,4,1]=>3 [3,5,4,1,2]=>2 [3,5,4,2,1]=>3 [4,1,2,3,5]=>2 [4,1,2,5,3]=>3 [4,1,3,2,5]=>2 [4,1,3,5,2]=>3 [4,1,5,2,3]=>3 [4,1,5,3,2]=>3 [4,2,1,3,5]=>2 [4,2,1,5,3]=>3 [4,2,3,1,5]=>2 [4,2,3,5,1]=>3 [4,2,5,1,3]=>3 [4,2,5,3,1]=>3 [4,3,1,2,5]=>2 [4,3,1,5,2]=>3 [4,3,2,1,5]=>1 [4,3,2,5,1]=>2 [4,3,5,1,2]=>2 [4,3,5,2,1]=>3 [4,5,1,2,3]=>2 [4,5,1,3,2]=>2 [4,5,2,1,3]=>2 [4,5,2,3,1]=>3 [4,5,3,1,2]=>3 [4,5,3,2,1]=>2 [5,1,2,3,4]=>2 [5,1,2,4,3]=>3 [5,1,3,2,4]=>3 [5,1,3,4,2]=>3 [5,1,4,2,3]=>3 [5,1,4,3,2]=>2 [5,2,1,3,4]=>3 [5,2,1,4,3]=>2 [5,2,3,1,4]=>3 [5,2,3,4,1]=>2 [5,2,4,1,3]=>3 [5,2,4,3,1]=>3 [5,3,1,2,4]=>3 [5,3,1,4,2]=>3 [5,3,2,1,4]=>2 [5,3,2,4,1]=>3 [5,3,4,1,2]=>3 [5,3,4,2,1]=>2 [5,4,1,2,3]=>2 [5,4,1,3,2]=>3 [5,4,2,1,3]=>3 [5,4,2,3,1]=>2 [5,4,3,1,2]=>2 [5,4,3,2,1]=>1 [1,2,3,4,5,6]=>0 [1,2,3,4,6,5]=>1 [1,2,3,5,4,6]=>1 [1,2,3,5,6,4]=>2 [1,2,3,6,4,5]=>2 [1,2,3,6,5,4]=>1 [1,2,4,3,5,6]=>1 [1,2,4,3,6,5]=>2 [1,2,4,5,3,6]=>2 [1,2,4,5,6,3]=>2 [1,2,4,6,3,5]=>3 [1,2,4,6,5,3]=>2 [1,2,5,3,4,6]=>2 [1,2,5,3,6,4]=>3 [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]=>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]=>1 [1,3,2,4,5,6]=>1 [1,3,2,4,6,5]=>2 [1,3,2,5,4,6]=>2 [1,3,2,5,6,4]=>3 [1,3,2,6,4,5]=>3 [1,3,2,6,5,4]=>2 [1,3,4,2,5,6]=>2 [1,3,4,2,6,5]=>3 [1,3,4,5,2,6]=>2 [1,3,4,5,6,2]=>2 [1,3,4,6,2,5]=>3 [1,3,4,6,5,2]=>3 [1,3,5,2,4,6]=>3 [1,3,5,2,6,4]=>4 [1,3,5,4,2,6]=>2 [1,3,5,4,6,2]=>3 [1,3,5,6,2,4]=>3 [1,3,5,6,4,2]=>3 [1,3,6,2,4,5]=>3 [1,3,6,2,5,4]=>3 [1,3,6,4,2,5]=>3 [1,3,6,4,5,2]=>3 [1,3,6,5,2,4]=>3 [1,3,6,5,4,2]=>2 [1,4,2,3,5,6]=>2 [1,4,2,3,6,5]=>3 [1,4,2,5,3,6]=>3 [1,4,2,5,6,3]=>3 [1,4,2,6,3,5]=>4 [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]=>2 [1,4,3,5,6,2]=>3 [1,4,3,6,2,5]=>3 [1,4,3,6,5,2]=>2 [1,4,5,2,3,6]=>2 [1,4,5,2,6,3]=>3 [1,4,5,3,2,6]=>2 [1,4,5,3,6,2]=>3 [1,4,5,6,2,3]=>2 [1,4,5,6,3,2]=>2 [1,4,6,2,3,5]=>3 [1,4,6,2,5,3]=>3 [1,4,6,3,2,5]=>3 [1,4,6,3,5,2]=>3 [1,4,6,5,2,3]=>2 [1,4,6,5,3,2]=>3 [1,5,2,3,4,6]=>2 [1,5,2,3,6,4]=>3 [1,5,2,4,3,6]=>2 [1,5,2,4,6,3]=>3 [1,5,2,6,3,4]=>3 [1,5,2,6,4,3]=>3 [1,5,3,2,4,6]=>2 [1,5,3,2,6,4]=>3 [1,5,3,4,2,6]=>2 [1,5,3,4,6,2]=>3 [1,5,3,6,2,4]=>3 [1,5,3,6,4,2]=>3 [1,5,4,2,3,6]=>2 [1,5,4,2,6,3]=>3 [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]=>2 [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]=>2 [1,6,2,3,4,5]=>2 [1,6,2,3,5,4]=>3 [1,6,2,4,3,5]=>3 [1,6,2,4,5,3]=>3 [1,6,2,5,3,4]=>3 [1,6,2,5,4,3]=>2 [1,6,3,2,4,5]=>3 [1,6,3,2,5,4]=>2 [1,6,3,4,2,5]=>3 [1,6,3,4,5,2]=>2 [1,6,3,5,2,4]=>3 [1,6,3,5,4,2]=>3 [1,6,4,2,3,5]=>3 [1,6,4,2,5,3]=>3 [1,6,4,3,2,5]=>2 [1,6,4,3,5,2]=>3 [1,6,4,5,2,3]=>3 [1,6,4,5,3,2]=>2 [1,6,5,2,3,4]=>2 [1,6,5,2,4,3]=>3 [1,6,5,3,2,4]=>3 [1,6,5,3,4,2]=>2 [1,6,5,4,2,3]=>2 [1,6,5,4,3,2]=>1 [2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>2 [2,1,3,5,4,6]=>2 [2,1,3,5,6,4]=>3 [2,1,3,6,4,5]=>3 [2,1,3,6,5,4]=>2 [2,1,4,3,5,6]=>2 [2,1,4,3,6,5]=>3 [2,1,4,5,3,6]=>3 [2,1,4,5,6,3]=>3 [2,1,4,6,3,5]=>4 [2,1,4,6,5,3]=>3 [2,1,5,3,4,6]=>3 [2,1,5,3,6,4]=>4 [2,1,5,4,3,6]=>2 [2,1,5,4,6,3]=>3 [2,1,5,6,3,4]=>3 [2,1,5,6,4,3]=>3 [2,1,6,3,4,5]=>3 [2,1,6,3,5,4]=>3 [2,1,6,4,3,5]=>3 [2,1,6,4,5,3]=>3 [2,1,6,5,3,4]=>3 [2,1,6,5,4,3]=>2 [2,3,1,4,5,6]=>2 [2,3,1,4,6,5]=>3 [2,3,1,5,4,6]=>3 [2,3,1,5,6,4]=>4 [2,3,1,6,4,5]=>4 [2,3,1,6,5,4]=>3 [2,3,4,1,5,6]=>2 [2,3,4,1,6,5]=>3 [2,3,4,5,1,6]=>2 [2,3,4,5,6,1]=>2 [2,3,4,6,1,5]=>3 [2,3,4,6,5,1]=>3 [2,3,5,1,4,6]=>3 [2,3,5,1,6,4]=>4 [2,3,5,4,1,6]=>3 [2,3,5,4,6,1]=>3 [2,3,5,6,1,4]=>4 [2,3,5,6,4,1]=>4 [2,3,6,1,4,5]=>4 [2,3,6,1,5,4]=>3 [2,3,6,4,1,5]=>4 [2,3,6,4,5,1]=>4 [2,3,6,5,1,4]=>3 [2,3,6,5,4,1]=>3 [2,4,1,3,5,6]=>3 [2,4,1,3,6,5]=>4 [2,4,1,5,3,6]=>4 [2,4,1,5,6,3]=>4 [2,4,1,6,3,5]=>5 [2,4,1,6,5,3]=>4 [2,4,3,1,5,6]=>2 [2,4,3,1,6,5]=>3 [2,4,3,5,1,6]=>3 [2,4,3,5,6,1]=>3 [2,4,3,6,1,5]=>4 [2,4,3,6,5,1]=>3 [2,4,5,1,3,6]=>3 [2,4,5,1,6,3]=>4 [2,4,5,3,1,6]=>3 [2,4,5,3,6,1]=>4 [2,4,5,6,1,3]=>3 [2,4,5,6,3,1]=>3 [2,4,6,1,3,5]=>4 [2,4,6,1,5,3]=>4 [2,4,6,3,1,5]=>4 [2,4,6,3,5,1]=>4 [2,4,6,5,1,3]=>3 [2,4,6,5,3,1]=>4 [2,5,1,3,4,6]=>3 [2,5,1,3,6,4]=>4 [2,5,1,4,3,6]=>3 [2,5,1,4,6,3]=>4 [2,5,1,6,3,4]=>4 [2,5,1,6,4,3]=>4 [2,5,3,1,4,6]=>3 [2,5,3,1,6,4]=>4 [2,5,3,4,1,6]=>3 [2,5,3,4,6,1]=>4 [2,5,3,6,1,4]=>4 [2,5,3,6,4,1]=>4 [2,5,4,1,3,6]=>3 [2,5,4,1,6,3]=>4 [2,5,4,3,1,6]=>2 [2,5,4,3,6,1]=>3 [2,5,4,6,1,3]=>3 [2,5,4,6,3,1]=>4 [2,5,6,1,3,4]=>3 [2,5,6,1,4,3]=>3 [2,5,6,3,1,4]=>3 [2,5,6,3,4,1]=>3 [2,5,6,4,1,3]=>3 [2,5,6,4,3,1]=>3 [2,6,1,3,4,5]=>3 [2,6,1,3,5,4]=>4 [2,6,1,4,3,5]=>4 [2,6,1,4,5,3]=>4 [2,6,1,5,3,4]=>4 [2,6,1,5,4,3]=>3 [2,6,3,1,4,5]=>4 [2,6,3,1,5,4]=>3 [2,6,3,4,1,5]=>4 [2,6,3,4,5,1]=>3 [2,6,3,5,1,4]=>4 [2,6,3,5,4,1]=>4 [2,6,4,1,3,5]=>4 [2,6,4,1,5,3]=>4 [2,6,4,3,1,5]=>3 [2,6,4,3,5,1]=>4 [2,6,4,5,1,3]=>3 [2,6,4,5,3,1]=>3 [2,6,5,1,3,4]=>3 [2,6,5,1,4,3]=>3 [2,6,5,3,1,4]=>4 [2,6,5,3,4,1]=>3 [2,6,5,4,1,3]=>3 [2,6,5,4,3,1]=>2 [3,1,2,4,5,6]=>2 [3,1,2,4,6,5]=>3 [3,1,2,5,4,6]=>3 [3,1,2,5,6,4]=>4 [3,1,2,6,4,5]=>4 [3,1,2,6,5,4]=>3 [3,1,4,2,5,6]=>3 [3,1,4,2,6,5]=>4 [3,1,4,5,2,6]=>3 [3,1,4,5,6,2]=>3 [3,1,4,6,2,5]=>4 [3,1,4,6,5,2]=>4 [3,1,5,2,4,6]=>4 [3,1,5,2,6,4]=>5 [3,1,5,4,2,6]=>3 [3,1,5,4,6,2]=>4 [3,1,5,6,2,4]=>4 [3,1,5,6,4,2]=>4 [3,1,6,2,4,5]=>4 [3,1,6,2,5,4]=>4 [3,1,6,4,2,5]=>4 [3,1,6,4,5,2]=>4 [3,1,6,5,2,4]=>4 [3,1,6,5,4,2]=>3 [3,2,1,4,5,6]=>1 [3,2,1,4,6,5]=>2 [3,2,1,5,4,6]=>2 [3,2,1,5,6,4]=>3 [3,2,1,6,4,5]=>3 [3,2,1,6,5,4]=>2 [3,2,4,1,5,6]=>2 [3,2,4,1,6,5]=>3 [3,2,4,5,1,6]=>3 [3,2,4,5,6,1]=>3 [3,2,4,6,1,5]=>4 [3,2,4,6,5,1]=>3 [3,2,5,1,4,6]=>3 [3,2,5,1,6,4]=>4 [3,2,5,4,1,6]=>2 [3,2,5,4,6,1]=>3 [3,2,5,6,1,4]=>3 [3,2,5,6,4,1]=>3 [3,2,6,1,4,5]=>3 [3,2,6,1,5,4]=>3 [3,2,6,4,1,5]=>3 [3,2,6,4,5,1]=>3 [3,2,6,5,1,4]=>3 [3,2,6,5,4,1]=>2 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>3 [3,4,1,5,2,6]=>3 [3,4,1,5,6,2]=>4 [3,4,1,6,2,5]=>4 [3,4,1,6,5,2]=>3 [3,4,2,1,5,6]=>2 [3,4,2,1,6,5]=>3 [3,4,2,5,1,6]=>3 [3,4,2,5,6,1]=>4 [3,4,2,6,1,5]=>4 [3,4,2,6,5,1]=>3 [3,4,5,1,2,6]=>2 [3,4,5,1,6,2]=>3 [3,4,5,2,1,6]=>2 [3,4,5,2,6,1]=>3 [3,4,5,6,1,2]=>2 [3,4,5,6,2,1]=>2 [3,4,6,1,2,5]=>3 [3,4,6,1,5,2]=>4 [3,4,6,2,1,5]=>3 [3,4,6,2,5,1]=>4 [3,4,6,5,1,2]=>3 [3,4,6,5,2,1]=>3 [3,5,1,2,4,6]=>3 [3,5,1,2,6,4]=>4 [3,5,1,4,2,6]=>3 [3,5,1,4,6,2]=>4 [3,5,1,6,2,4]=>4 [3,5,1,6,4,2]=>4 [3,5,2,1,4,6]=>3 [3,5,2,1,6,4]=>4 [3,5,2,4,1,6]=>3 [3,5,2,4,6,1]=>4 [3,5,2,6,1,4]=>4 [3,5,2,6,4,1]=>4 [3,5,4,1,2,6]=>2 [3,5,4,1,6,2]=>3 [3,5,4,2,1,6]=>3 [3,5,4,2,6,1]=>4 [3,5,4,6,1,2]=>3 [3,5,4,6,2,1]=>3 [3,5,6,1,2,4]=>3 [3,5,6,1,4,2]=>3 [3,5,6,2,1,4]=>3 [3,5,6,2,4,1]=>3 [3,5,6,4,1,2]=>3 [3,5,6,4,2,1]=>3 [3,6,1,2,4,5]=>4 [3,6,1,2,5,4]=>3 [3,6,1,4,2,5]=>4 [3,6,1,4,5,2]=>3 [3,6,1,5,2,4]=>4 [3,6,1,5,4,2]=>4 [3,6,2,1,4,5]=>3 [3,6,2,1,5,4]=>3 [3,6,2,4,1,5]=>4 [3,6,2,4,5,1]=>4 [3,6,2,5,1,4]=>4 [3,6,2,5,4,1]=>3 [3,6,4,1,2,5]=>3 [3,6,4,1,5,2]=>4 [3,6,4,2,1,5]=>4 [3,6,4,2,5,1]=>4 [3,6,4,5,1,2]=>3 [3,6,4,5,2,1]=>3 [3,6,5,1,2,4]=>3 [3,6,5,1,4,2]=>3 [3,6,5,2,1,4]=>3 [3,6,5,2,4,1]=>4 [3,6,5,4,1,2]=>2 [3,6,5,4,2,1]=>3 [4,1,2,3,5,6]=>2 [4,1,2,3,6,5]=>3 [4,1,2,5,3,6]=>3 [4,1,2,5,6,3]=>4 [4,1,2,6,3,5]=>4 [4,1,2,6,5,3]=>3 [4,1,3,2,5,6]=>2 [4,1,3,2,6,5]=>3 [4,1,3,5,2,6]=>3 [4,1,3,5,6,2]=>4 [4,1,3,6,2,5]=>4 [4,1,3,6,5,2]=>3 [4,1,5,2,3,6]=>3 [4,1,5,2,6,3]=>4 [4,1,5,3,2,6]=>3 [4,1,5,3,6,2]=>4 [4,1,5,6,2,3]=>3 [4,1,5,6,3,2]=>3 [4,1,6,2,3,5]=>4 [4,1,6,2,5,3]=>4 [4,1,6,3,2,5]=>4 [4,1,6,3,5,2]=>4 [4,1,6,5,2,3]=>3 [4,1,6,5,3,2]=>3 [4,2,1,3,5,6]=>2 [4,2,1,3,6,5]=>3 [4,2,1,5,3,6]=>3 [4,2,1,5,6,3]=>3 [4,2,1,6,3,5]=>4 [4,2,1,6,5,3]=>3 [4,2,3,1,5,6]=>2 [4,2,3,1,6,5]=>3 [4,2,3,5,1,6]=>3 [4,2,3,5,6,1]=>4 [4,2,3,6,1,5]=>4 [4,2,3,6,5,1]=>3 [4,2,5,1,3,6]=>3 [4,2,5,1,6,3]=>4 [4,2,5,3,1,6]=>3 [4,2,5,3,6,1]=>4 [4,2,5,6,1,3]=>4 [4,2,5,6,3,1]=>4 [4,2,6,1,3,5]=>4 [4,2,6,1,5,3]=>4 [4,2,6,3,1,5]=>4 [4,2,6,3,5,1]=>4 [4,2,6,5,1,3]=>3 [4,2,6,5,3,1]=>3 [4,3,1,2,5,6]=>2 [4,3,1,2,6,5]=>3 [4,3,1,5,2,6]=>3 [4,3,1,5,6,2]=>3 [4,3,1,6,2,5]=>4 [4,3,1,6,5,2]=>3 [4,3,2,1,5,6]=>1 [4,3,2,1,6,5]=>2 [4,3,2,5,1,6]=>2 [4,3,2,5,6,1]=>3 [4,3,2,6,1,5]=>3 [4,3,2,6,5,1]=>2 [4,3,5,1,2,6]=>2 [4,3,5,1,6,2]=>3 [4,3,5,2,1,6]=>3 [4,3,5,2,6,1]=>4 [4,3,5,6,1,2]=>3 [4,3,5,6,2,1]=>3 [4,3,6,1,2,5]=>3 [4,3,6,1,5,2]=>3 [4,3,6,2,1,5]=>3 [4,3,6,2,5,1]=>3 [4,3,6,5,1,2]=>2 [4,3,6,5,2,1]=>3 [4,5,1,2,3,6]=>2 [4,5,1,2,6,3]=>3 [4,5,1,3,2,6]=>2 [4,5,1,3,6,2]=>3 [4,5,1,6,2,3]=>3 [4,5,1,6,3,2]=>3 [4,5,2,1,3,6]=>2 [4,5,2,1,6,3]=>3 [4,5,2,3,1,6]=>3 [4,5,2,3,6,1]=>3 [4,5,2,6,1,3]=>3 [4,5,2,6,3,1]=>3 [4,5,3,1,2,6]=>3 [4,5,3,1,6,2]=>3 [4,5,3,2,1,6]=>2 [4,5,3,2,6,1]=>3 [4,5,3,6,1,2]=>3 [4,5,3,6,2,1]=>3 [4,5,6,1,2,3]=>3 [4,5,6,1,3,2]=>2 [4,5,6,2,1,3]=>2 [4,5,6,2,3,1]=>3 [4,5,6,3,1,2]=>3 [4,5,6,3,2,1]=>2 [4,6,1,2,3,5]=>3 [4,6,1,2,5,3]=>4 [4,6,1,3,2,5]=>3 [4,6,1,3,5,2]=>4 [4,6,1,5,2,3]=>3 [4,6,1,5,3,2]=>3 [4,6,2,1,3,5]=>3 [4,6,2,1,5,3]=>3 [4,6,2,3,1,5]=>3 [4,6,2,3,5,1]=>3 [4,6,2,5,1,3]=>4 [4,6,2,5,3,1]=>4 [4,6,3,1,2,5]=>3 [4,6,3,1,5,2]=>4 [4,6,3,2,1,5]=>3 [4,6,3,2,5,1]=>4 [4,6,3,5,1,2]=>3 [4,6,3,5,2,1]=>4 [4,6,5,1,2,3]=>2 [4,6,5,1,3,2]=>3 [4,6,5,2,1,3]=>3 [4,6,5,2,3,1]=>3 [4,6,5,3,1,2]=>3 [4,6,5,3,2,1]=>3 [5,1,2,3,4,6]=>2 [5,1,2,3,6,4]=>3 [5,1,2,4,3,6]=>3 [5,1,2,4,6,3]=>4 [5,1,2,6,3,4]=>4 [5,1,2,6,4,3]=>3 [5,1,3,2,4,6]=>3 [5,1,3,2,6,4]=>4 [5,1,3,4,2,6]=>3 [5,1,3,4,6,2]=>4 [5,1,3,6,2,4]=>4 [5,1,3,6,4,2]=>4 [5,1,4,2,3,6]=>3 [5,1,4,2,6,3]=>4 [5,1,4,3,2,6]=>2 [5,1,4,3,6,2]=>3 [5,1,4,6,2,3]=>3 [5,1,4,6,3,2]=>4 [5,1,6,2,3,4]=>3 [5,1,6,2,4,3]=>3 [5,1,6,3,2,4]=>3 [5,1,6,3,4,2]=>3 [5,1,6,4,2,3]=>3 [5,1,6,4,3,2]=>3 [5,2,1,3,4,6]=>3 [5,2,1,3,6,4]=>4 [5,2,1,4,3,6]=>2 [5,2,1,4,6,3]=>3 [5,2,1,6,3,4]=>3 [5,2,1,6,4,3]=>3 [5,2,3,1,4,6]=>3 [5,2,3,1,6,4]=>4 [5,2,3,4,1,6]=>2 [5,2,3,4,6,1]=>3 [5,2,3,6,1,4]=>3 [5,2,3,6,4,1]=>4 [5,2,4,1,3,6]=>3 [5,2,4,1,6,3]=>4 [5,2,4,3,1,6]=>3 [5,2,4,3,6,1]=>4 [5,2,4,6,1,3]=>4 [5,2,4,6,3,1]=>4 [5,2,6,1,3,4]=>4 [5,2,6,1,4,3]=>3 [5,2,6,3,1,4]=>4 [5,2,6,3,4,1]=>3 [5,2,6,4,1,3]=>4 [5,2,6,4,3,1]=>4 [5,3,1,2,4,6]=>3 [5,3,1,2,6,4]=>4 [5,3,1,4,2,6]=>3 [5,3,1,4,6,2]=>4 [5,3,1,6,2,4]=>4 [5,3,1,6,4,2]=>4 [5,3,2,1,4,6]=>2 [5,3,2,1,6,4]=>3 [5,3,2,4,1,6]=>3 [5,3,2,4,6,1]=>4 [5,3,2,6,1,4]=>4 [5,3,2,6,4,1]=>3 [5,3,4,1,2,6]=>3 [5,3,4,1,6,2]=>3 [5,3,4,2,1,6]=>2 [5,3,4,2,6,1]=>3 [5,3,4,6,1,2]=>3 [5,3,4,6,2,1]=>3 [5,3,6,1,2,4]=>3 [5,3,6,1,4,2]=>4 [5,3,6,2,1,4]=>3 [5,3,6,2,4,1]=>4 [5,3,6,4,1,2]=>3 [5,3,6,4,2,1]=>4 [5,4,1,2,3,6]=>2 [5,4,1,2,6,3]=>3 [5,4,1,3,2,6]=>3 [5,4,1,3,6,2]=>4 [5,4,1,6,2,3]=>3 [5,4,1,6,3,2]=>3 [5,4,2,1,3,6]=>3 [5,4,2,1,6,3]=>3 [5,4,2,3,1,6]=>2 [5,4,2,3,6,1]=>3 [5,4,2,6,1,3]=>3 [5,4,2,6,3,1]=>4 [5,4,3,1,2,6]=>2 [5,4,3,1,6,2]=>3 [5,4,3,2,1,6]=>1 [5,4,3,2,6,1]=>2 [5,4,3,6,1,2]=>2 [5,4,3,6,2,1]=>3 [5,4,6,1,2,3]=>2 [5,4,6,1,3,2]=>3 [5,4,6,2,1,3]=>3 [5,4,6,2,3,1]=>3 [5,4,6,3,1,2]=>3 [5,4,6,3,2,1]=>3 [5,6,1,2,3,4]=>2 [5,6,1,2,4,3]=>3 [5,6,1,3,2,4]=>3 [5,6,1,3,4,2]=>3 [5,6,1,4,2,3]=>3 [5,6,1,4,3,2]=>2 [5,6,2,1,3,4]=>3 [5,6,2,1,4,3]=>2 [5,6,2,3,1,4]=>3 [5,6,2,3,4,1]=>3 [5,6,2,4,1,3]=>3 [5,6,2,4,3,1]=>3 [5,6,3,1,2,4]=>3 [5,6,3,1,4,2]=>3 [5,6,3,2,1,4]=>2 [5,6,3,2,4,1]=>3 [5,6,3,4,1,2]=>3 [5,6,3,4,2,1]=>3 [5,6,4,1,2,3]=>3 [5,6,4,1,3,2]=>3 [5,6,4,2,1,3]=>3 [5,6,4,2,3,1]=>3 [5,6,4,3,1,2]=>3 [5,6,4,3,2,1]=>2 [6,1,2,3,4,5]=>2 [6,1,2,3,5,4]=>3 [6,1,2,4,3,5]=>3 [6,1,2,4,5,3]=>4 [6,1,2,5,3,4]=>4 [6,1,2,5,4,3]=>3 [6,1,3,2,4,5]=>3 [6,1,3,2,5,4]=>3 [6,1,3,4,2,5]=>4 [6,1,3,4,5,2]=>3 [6,1,3,5,2,4]=>4 [6,1,3,5,4,2]=>4 [6,1,4,2,3,5]=>4 [6,1,4,2,5,3]=>4 [6,1,4,3,2,5]=>3 [6,1,4,3,5,2]=>4 [6,1,4,5,2,3]=>3 [6,1,4,5,3,2]=>3 [6,1,5,2,3,4]=>3 [6,1,5,2,4,3]=>4 [6,1,5,3,2,4]=>4 [6,1,5,3,4,2]=>3 [6,1,5,4,2,3]=>3 [6,1,5,4,3,2]=>2 [6,2,1,3,4,5]=>3 [6,2,1,3,5,4]=>3 [6,2,1,4,3,5]=>3 [6,2,1,4,5,3]=>3 [6,2,1,5,3,4]=>3 [6,2,1,5,4,3]=>2 [6,2,3,1,4,5]=>4 [6,2,3,1,5,4]=>3 [6,2,3,4,1,5]=>3 [6,2,3,4,5,1]=>2 [6,2,3,5,1,4]=>4 [6,2,3,5,4,1]=>3 [6,2,4,1,3,5]=>4 [6,2,4,1,5,3]=>4 [6,2,4,3,1,5]=>4 [6,2,4,3,5,1]=>3 [6,2,4,5,1,3]=>3 [6,2,4,5,3,1]=>3 [6,2,5,1,3,4]=>4 [6,2,5,1,4,3]=>3 [6,2,5,3,1,4]=>4 [6,2,5,3,4,1]=>3 [6,2,5,4,1,3]=>4 [6,2,5,4,3,1]=>3 [6,3,1,2,4,5]=>4 [6,3,1,2,5,4]=>3 [6,3,1,4,2,5]=>4 [6,3,1,4,5,2]=>4 [6,3,1,5,2,4]=>4 [6,3,1,5,4,2]=>3 [6,3,2,1,4,5]=>3 [6,3,2,1,5,4]=>2 [6,3,2,4,1,5]=>4 [6,3,2,4,5,1]=>3 [6,3,2,5,1,4]=>3 [6,3,2,5,4,1]=>3 [6,3,4,1,2,5]=>3 [6,3,4,1,5,2]=>3 [6,3,4,2,1,5]=>3 [6,3,4,2,5,1]=>3 [6,3,4,5,1,2]=>3 [6,3,4,5,2,1]=>2 [6,3,5,1,2,4]=>3 [6,3,5,1,4,2]=>4 [6,3,5,2,1,4]=>4 [6,3,5,2,4,1]=>4 [6,3,5,4,1,2]=>3 [6,3,5,4,2,1]=>3 [6,4,1,2,3,5]=>3 [6,4,1,2,5,3]=>4 [6,4,1,3,2,5]=>4 [6,4,1,3,5,2]=>4 [6,4,1,5,2,3]=>3 [6,4,1,5,3,2]=>4 [6,4,2,1,3,5]=>4 [6,4,2,1,5,3]=>3 [6,4,2,3,1,5]=>3 [6,4,2,3,5,1]=>3 [6,4,2,5,1,3]=>4 [6,4,2,5,3,1]=>4 [6,4,3,1,2,5]=>3 [6,4,3,1,5,2]=>4 [6,4,3,2,1,5]=>2 [6,4,3,2,5,1]=>3 [6,4,3,5,1,2]=>3 [6,4,3,5,2,1]=>3 [6,4,5,1,2,3]=>3 [6,4,5,1,3,2]=>3 [6,4,5,2,1,3]=>3 [6,4,5,2,3,1]=>3 [6,4,5,3,1,2]=>3 [6,4,5,3,2,1]=>2 [6,5,1,2,3,4]=>2 [6,5,1,2,4,3]=>3 [6,5,1,3,2,4]=>3 [6,5,1,3,4,2]=>3 [6,5,1,4,2,3]=>3 [6,5,1,4,3,2]=>3 [6,5,2,1,3,4]=>3 [6,5,2,1,4,3]=>3 [6,5,2,3,1,4]=>3 [6,5,2,3,4,1]=>2 [6,5,2,4,1,3]=>4 [6,5,2,4,3,1]=>3 [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]=>3 [6,5,3,4,1,2]=>3 [6,5,3,4,2,1]=>2 [6,5,4,1,2,3]=>2 [6,5,4,1,3,2]=>3 [6,5,4,2,1,3]=>3 [6,5,4,2,3,1]=>2 [6,5,4,3,1,2]=>2 [6,5,4,3,2,1]=>1 [1,2,3,4,5,6,7]=>0 [1,2,3,4,5,7,6]=>1 [1,2,3,4,6,5,7]=>1 [1,2,3,4,6,7,5]=>2 [1,2,3,4,7,5,6]=>2 [1,2,3,4,7,6,5]=>1 [1,2,3,5,4,6,7]=>1 [1,2,3,5,4,7,6]=>2 [1,2,3,5,6,4,7]=>2 [1,2,3,5,6,7,4]=>2 [1,2,3,5,7,4,6]=>3 [1,2,3,5,7,6,4]=>2 [1,2,3,6,4,5,7]=>2 [1,2,3,6,4,7,5]=>3 [1,2,3,6,5,4,7]=>1 [1,2,3,6,5,7,4]=>2 [1,2,3,6,7,4,5]=>2 [1,2,3,6,7,5,4]=>2 [1,2,3,7,4,5,6]=>2 [1,2,3,7,4,6,5]=>2 [1,2,3,7,5,4,6]=>2 [1,2,3,7,5,6,4]=>2 [1,2,3,7,6,4,5]=>2 [1,2,3,7,6,5,4]=>1 [1,2,4,3,5,6,7]=>1 [1,2,4,3,5,7,6]=>2 [1,2,4,3,6,5,7]=>2 [1,2,4,3,6,7,5]=>3 [1,2,4,3,7,5,6]=>3 [1,2,4,3,7,6,5]=>2 [1,2,4,5,3,6,7]=>2 [1,2,4,5,3,7,6]=>3 [1,2,4,5,6,3,7]=>2 [1,2,4,5,6,7,3]=>2 [1,2,4,5,7,3,6]=>3 [1,2,4,5,7,6,3]=>3 [1,2,4,6,3,5,7]=>3 [1,2,4,6,3,7,5]=>4 [1,2,4,6,5,3,7]=>2 [1,2,4,6,5,7,3]=>3 [1,2,4,6,7,3,5]=>3 [1,2,4,6,7,5,3]=>3 [1,2,4,7,3,5,6]=>3 [1,2,4,7,3,6,5]=>3 [1,2,4,7,5,3,6]=>3 [1,2,4,7,5,6,3]=>3 [1,2,4,7,6,3,5]=>3 [1,2,4,7,6,5,3]=>2 [1,2,5,3,4,6,7]=>2 [1,2,5,3,4,7,6]=>3 [1,2,5,3,6,4,7]=>3 [1,2,5,3,6,7,4]=>3 [1,2,5,3,7,4,6]=>4 [1,2,5,3,7,6,4]=>3 [1,2,5,4,3,6,7]=>1 [1,2,5,4,3,7,6]=>2 [1,2,5,4,6,3,7]=>2 [1,2,5,4,6,7,3]=>3 [1,2,5,4,7,3,6]=>3 [1,2,5,4,7,6,3]=>2 [1,2,5,6,3,4,7]=>2 [1,2,5,6,3,7,4]=>3 [1,2,5,6,4,3,7]=>2 [1,2,5,6,4,7,3]=>3 [1,2,5,6,7,3,4]=>2 [1,2,5,6,7,4,3]=>2 [1,2,5,7,3,4,6]=>3 [1,2,5,7,3,6,4]=>3 [1,2,5,7,4,3,6]=>3 [1,2,5,7,4,6,3]=>3 [1,2,5,7,6,3,4]=>2 [1,2,5,7,6,4,3]=>3 [1,2,6,3,4,5,7]=>2 [1,2,6,3,4,7,5]=>3 [1,2,6,3,5,4,7]=>2 [1,2,6,3,5,7,4]=>3 [1,2,6,3,7,4,5]=>3 [1,2,6,3,7,5,4]=>3 [1,2,6,4,3,5,7]=>2 [1,2,6,4,3,7,5]=>3 [1,2,6,4,5,3,7]=>2 [1,2,6,4,5,7,3]=>3 [1,2,6,4,7,3,5]=>3 [1,2,6,4,7,5,3]=>3 [1,2,6,5,3,4,7]=>2 [1,2,6,5,3,7,4]=>3 [1,2,6,5,4,3,7]=>1 [1,2,6,5,4,7,3]=>2 [1,2,6,5,7,3,4]=>2 [1,2,6,5,7,4,3]=>3 [1,2,6,7,3,4,5]=>2 [1,2,6,7,3,5,4]=>2 [1,2,6,7,4,3,5]=>2 [1,2,6,7,4,5,3]=>3 [1,2,6,7,5,3,4]=>3 [1,2,6,7,5,4,3]=>2 [1,2,7,3,4,5,6]=>2 [1,2,7,3,4,6,5]=>3 [1,2,7,3,5,4,6]=>3 [1,2,7,3,5,6,4]=>3 [1,2,7,3,6,4,5]=>3 [1,2,7,3,6,5,4]=>2 [1,2,7,4,3,5,6]=>3 [1,2,7,4,3,6,5]=>2 [1,2,7,4,5,3,6]=>3 [1,2,7,4,5,6,3]=>2 [1,2,7,4,6,3,5]=>3 [1,2,7,4,6,5,3]=>3 [1,2,7,5,3,4,6]=>3 [1,2,7,5,3,6,4]=>3 [1,2,7,5,4,3,6]=>2 [1,2,7,5,4,6,3]=>3 [1,2,7,5,6,3,4]=>3 [1,2,7,5,6,4,3]=>2 [1,2,7,6,3,4,5]=>2 [1,2,7,6,3,5,4]=>3 [1,2,7,6,4,3,5]=>3 [1,2,7,6,4,5,3]=>2 [1,2,7,6,5,3,4]=>2 [1,2,7,6,5,4,3]=>1 [1,3,2,4,5,6,7]=>1 [1,3,2,4,5,7,6]=>2 [1,3,2,4,6,5,7]=>2 [1,3,2,4,6,7,5]=>3 [1,3,2,4,7,5,6]=>3 [1,3,2,4,7,6,5]=>2 [1,3,2,5,4,6,7]=>2 [1,3,2,5,4,7,6]=>3 [1,3,2,5,6,4,7]=>3 [1,3,2,5,6,7,4]=>3 [1,3,2,5,7,4,6]=>4 [1,3,2,5,7,6,4]=>3 [1,3,2,6,4,5,7]=>3 [1,3,2,6,4,7,5]=>4 [1,3,2,6,5,4,7]=>2 [1,3,2,6,5,7,4]=>3 [1,3,2,6,7,4,5]=>3 [1,3,2,6,7,5,4]=>3 [1,3,2,7,4,5,6]=>3 [1,3,2,7,4,6,5]=>3 [1,3,2,7,5,4,6]=>3 [1,3,2,7,5,6,4]=>3 [1,3,2,7,6,4,5]=>3 [1,3,2,7,6,5,4]=>2 [1,3,4,2,5,6,7]=>2 [1,3,4,2,5,7,6]=>3 [1,3,4,2,6,5,7]=>3 [1,3,4,2,6,7,5]=>4 [1,3,4,2,7,5,6]=>4 [1,3,4,2,7,6,5]=>3 [1,3,4,5,2,6,7]=>2 [1,3,4,5,2,7,6]=>3 [1,3,4,5,6,2,7]=>2 [1,3,4,5,6,7,2]=>2 [1,3,4,5,7,2,6]=>3 [1,3,4,5,7,6,2]=>3 [1,3,4,6,2,5,7]=>3 [1,3,4,6,2,7,5]=>4 [1,3,4,6,5,2,7]=>3 [1,3,4,6,5,7,2]=>3 [1,3,4,6,7,2,5]=>4 [1,3,4,6,7,5,2]=>4 [1,3,4,7,2,5,6]=>4 [1,3,4,7,2,6,5]=>3 [1,3,4,7,5,2,6]=>4 [1,3,4,7,5,6,2]=>4 [1,3,4,7,6,2,5]=>3 [1,3,4,7,6,5,2]=>3 [1,3,5,2,4,6,7]=>3 [1,3,5,2,4,7,6]=>4 [1,3,5,2,6,4,7]=>4 [1,3,5,2,6,7,4]=>4 [1,3,5,2,7,4,6]=>5 [1,3,5,2,7,6,4]=>4 [1,3,5,4,2,6,7]=>2 [1,3,5,4,2,7,6]=>3 [1,3,5,4,6,2,7]=>3 [1,3,5,4,6,7,2]=>3 [1,3,5,4,7,2,6]=>4 [1,3,5,4,7,6,2]=>3 [1,3,5,6,2,4,7]=>3 [1,3,5,6,2,7,4]=>4 [1,3,5,6,4,2,7]=>3 [1,3,5,6,4,7,2]=>4 [1,3,5,6,7,2,4]=>3 [1,3,5,6,7,4,2]=>3 [1,3,5,7,2,4,6]=>4 [1,3,5,7,2,6,4]=>4 [1,3,5,7,4,2,6]=>4 [1,3,5,7,4,6,2]=>4 [1,3,5,7,6,2,4]=>3 [1,3,5,7,6,4,2]=>4 [1,3,6,2,4,5,7]=>3 [1,3,6,2,4,7,5]=>4 [1,3,6,2,5,4,7]=>3 [1,3,6,2,5,7,4]=>4 [1,3,6,2,7,4,5]=>4 [1,3,6,2,7,5,4]=>4 [1,3,6,4,2,5,7]=>3 [1,3,6,4,2,7,5]=>4 [1,3,6,4,5,2,7]=>3 [1,3,6,4,5,7,2]=>4 [1,3,6,4,7,2,5]=>4 [1,3,6,4,7,5,2]=>4 [1,3,6,5,2,4,7]=>3 [1,3,6,5,2,7,4]=>4 [1,3,6,5,4,2,7]=>2 [1,3,6,5,4,7,2]=>3 [1,3,6,5,7,2,4]=>3 [1,3,6,5,7,4,2]=>4 [1,3,6,7,2,4,5]=>3 [1,3,6,7,2,5,4]=>3 [1,3,6,7,4,2,5]=>3 [1,3,6,7,4,5,2]=>3 [1,3,6,7,5,2,4]=>3 [1,3,6,7,5,4,2]=>3 [1,3,7,2,4,5,6]=>3 [1,3,7,2,4,6,5]=>4 [1,3,7,2,5,4,6]=>4 [1,3,7,2,5,6,4]=>4 [1,3,7,2,6,4,5]=>4 [1,3,7,2,6,5,4]=>3 [1,3,7,4,2,5,6]=>4 [1,3,7,4,2,6,5]=>3 [1,3,7,4,5,2,6]=>4 [1,3,7,4,5,6,2]=>3 [1,3,7,4,6,2,5]=>4 [1,3,7,4,6,5,2]=>4 [1,3,7,5,2,4,6]=>4 [1,3,7,5,2,6,4]=>4 [1,3,7,5,4,2,6]=>3 [1,3,7,5,4,6,2]=>4 [1,3,7,5,6,2,4]=>3 [1,3,7,5,6,4,2]=>3 [1,3,7,6,2,4,5]=>3 [1,3,7,6,2,5,4]=>3 [1,3,7,6,4,2,5]=>4 [1,3,7,6,4,5,2]=>3 [1,3,7,6,5,2,4]=>3 [1,3,7,6,5,4,2]=>2 [1,4,2,3,5,6,7]=>2 [1,4,2,3,5,7,6]=>3 [1,4,2,3,6,5,7]=>3 [1,4,2,3,6,7,5]=>4 [1,4,2,3,7,5,6]=>4 [1,4,2,3,7,6,5]=>3 [1,4,2,5,3,6,7]=>3 [1,4,2,5,3,7,6]=>4 [1,4,2,5,6,3,7]=>3 [1,4,2,5,6,7,3]=>3 [1,4,2,5,7,3,6]=>4 [1,4,2,5,7,6,3]=>4 [1,4,2,6,3,5,7]=>4 [1,4,2,6,3,7,5]=>5 [1,4,2,6,5,3,7]=>3 [1,4,2,6,5,7,3]=>4 [1,4,2,6,7,3,5]=>4 [1,4,2,6,7,5,3]=>4 [1,4,2,7,3,5,6]=>4 [1,4,2,7,3,6,5]=>4 [1,4,2,7,5,3,6]=>4 [1,4,2,7,5,6,3]=>4 [1,4,2,7,6,3,5]=>4 [1,4,2,7,6,5,3]=>3 [1,4,3,2,5,6,7]=>1 [1,4,3,2,5,7,6]=>2 [1,4,3,2,6,5,7]=>2 [1,4,3,2,6,7,5]=>3 [1,4,3,2,7,5,6]=>3 [1,4,3,2,7,6,5]=>2 [1,4,3,5,2,6,7]=>2 [1,4,3,5,2,7,6]=>3 [1,4,3,5,6,2,7]=>3 [1,4,3,5,6,7,2]=>3 [1,4,3,5,7,2,6]=>4 [1,4,3,5,7,6,2]=>3 [1,4,3,6,2,5,7]=>3 [1,4,3,6,2,7,5]=>4 [1,4,3,6,5,2,7]=>2 [1,4,3,6,5,7,2]=>3 [1,4,3,6,7,2,5]=>3 [1,4,3,6,7,5,2]=>3 [1,4,3,7,2,5,6]=>3 [1,4,3,7,2,6,5]=>3 [1,4,3,7,5,2,6]=>3 [1,4,3,7,5,6,2]=>3 [1,4,3,7,6,2,5]=>3 [1,4,3,7,6,5,2]=>2 [1,4,5,2,3,6,7]=>2 [1,4,5,2,3,7,6]=>3 [1,4,5,2,6,3,7]=>3 [1,4,5,2,6,7,3]=>4 [1,4,5,2,7,3,6]=>4 [1,4,5,2,7,6,3]=>3 [1,4,5,3,2,6,7]=>2 [1,4,5,3,2,7,6]=>3 [1,4,5,3,6,2,7]=>3 [1,4,5,3,6,7,2]=>4 [1,4,5,3,7,2,6]=>4 [1,4,5,3,7,6,2]=>3 [1,4,5,6,2,3,7]=>2 [1,4,5,6,2,7,3]=>3 [1,4,5,6,3,2,7]=>2 [1,4,5,6,3,7,2]=>3 [1,4,5,6,7,2,3]=>2 [1,4,5,6,7,3,2]=>2 [1,4,5,7,2,3,6]=>3 [1,4,5,7,2,6,3]=>4 [1,4,5,7,3,2,6]=>3 [1,4,5,7,3,6,2]=>4 [1,4,5,7,6,2,3]=>3 [1,4,5,7,6,3,2]=>3 [1,4,6,2,3,5,7]=>3 [1,4,6,2,3,7,5]=>4 [1,4,6,2,5,3,7]=>3 [1,4,6,2,5,7,3]=>4 [1,4,6,2,7,3,5]=>4 [1,4,6,2,7,5,3]=>4 [1,4,6,3,2,5,7]=>3 [1,4,6,3,2,7,5]=>4 [1,4,6,3,5,2,7]=>3 [1,4,6,3,5,7,2]=>4 [1,4,6,3,7,2,5]=>4 [1,4,6,3,7,5,2]=>4 [1,4,6,5,2,3,7]=>2 [1,4,6,5,2,7,3]=>3 [1,4,6,5,3,2,7]=>3 [1,4,6,5,3,7,2]=>4 [1,4,6,7,2,3,5]=>3 [1,4,6,7,5,3,2]=>3 [1,4,7,2,3,5,6]=>4 [1,4,7,6,5,3,2]=>3 [1,5,2,3,4,7,6]=>3 [1,5,2,7,3,4,6]=>4 [1,5,4,7,6,3,2]=>3 [1,5,6,2,7,3,4]=>3 [1,5,6,4,7,3,2]=>3 [1,5,6,7,2,3,4]=>3 [1,5,6,7,4,3,2]=>2 [1,5,7,2,3,4,6]=>3 [1,5,7,6,4,3,2]=>3 [1,6,2,3,4,7,5]=>3 [1,6,2,3,7,4,5]=>4 [1,6,2,7,3,4,5]=>3 [1,6,5,4,3,7,2]=>2 [1,6,5,4,7,3,2]=>3 [1,6,5,7,4,3,2]=>3 [1,6,7,2,3,4,5]=>2 [1,6,7,5,4,3,2]=>2 [1,7,2,3,4,5,6]=>2 [1,7,3,5,6,4,2]=>3 [1,7,3,6,5,4,2]=>3 [1,7,4,3,6,5,2]=>3 [1,7,4,5,3,6,2]=>3 [1,7,4,5,6,3,2]=>2 [1,7,4,6,5,3,2]=>3 [1,7,5,4,3,6,2]=>3 [1,7,5,4,6,3,2]=>3 [1,7,6,4,5,3,2]=>2 [1,7,6,5,4,3,2]=>1 [2,1,3,4,5,6,7]=>1 [2,1,3,4,7,5,6]=>3 [2,1,3,7,4,5,6]=>3 [2,1,6,3,4,5,7]=>3 [2,1,7,3,4,5,6]=>3 [2,1,7,6,5,4,3]=>2 [2,3,1,4,5,6,7]=>2 [2,3,4,1,5,6,7]=>2 [2,3,4,1,5,7,6]=>3 [2,3,4,5,1,6,7]=>2 [2,3,4,5,1,7,6]=>3 [2,3,4,5,6,1,7]=>2 [2,3,4,5,6,7,1]=>2 [2,3,4,5,7,1,6]=>3 [2,3,4,6,1,7,5]=>4 [2,3,4,6,7,1,5]=>4 [2,3,4,7,1,5,6]=>4 [2,3,5,6,7,1,4]=>4 [2,4,1,3,5,6,7]=>3 [2,5,1,3,4,6,7]=>3 [2,5,7,1,3,4,6]=>4 [2,6,1,3,4,5,7]=>3 [2,6,1,7,3,4,5]=>4 [2,6,5,4,3,1,7]=>2 [2,6,7,1,3,4,5]=>3 [2,7,1,3,4,5,6]=>3 [3,1,2,4,5,6,7]=>2 [3,1,2,4,5,7,6]=>3 [3,2,1,4,5,6,7]=>1 [3,2,4,5,6,7,1]=>3 [3,4,1,2,5,6,7]=>2 [3,4,2,5,6,7,1]=>4 [3,4,5,2,6,7,1]=>4 [3,4,5,6,2,7,1]=>3 [3,4,5,6,7,1,2]=>2 [3,5,6,1,2,4,7]=>3 [3,5,6,4,2,1,7]=>3 [3,6,1,2,4,5,7]=>4 [3,6,5,4,2,1,7]=>3 [4,1,2,3,5,6,7]=>2 [4,1,2,3,5,7,6]=>3 [4,1,6,2,3,5,7]=>4 [4,2,3,5,6,7,1]=>4 [4,2,5,1,3,6,7]=>3 [4,3,2,1,5,6,7]=>1 [4,3,2,5,6,7,1]=>3 [4,3,5,2,6,7,1]=>4 [4,3,6,5,2,1,7]=>3 [4,5,1,6,2,3,7]=>3 [4,5,2,3,6,7,1]=>4 [4,5,3,6,2,1,7]=>3 [4,5,6,1,2,3,7]=>3 [4,5,6,3,2,1,7]=>2 [4,6,1,2,3,5,7]=>3 [4,6,1,2,3,7,5]=>4 [4,6,5,3,2,1,7]=>3 [5,1,2,3,4,6,7]=>2 [5,1,2,3,4,7,6]=>3 [5,1,2,3,6,4,7]=>3 [5,1,2,3,6,7,4]=>4 [5,1,2,3,7,4,6]=>4 [5,1,2,6,3,4,7]=>4 [5,1,6,2,3,4,7]=>3 [5,1,6,2,3,7,4]=>4 [5,2,3,4,6,7,1]=>4 [5,2,6,7,1,3,4]=>4 [5,3,2,4,6,7,1]=>4 [5,3,2,6,1,4,7]=>4 [5,3,6,7,1,2,4]=>4 [5,4,3,2,1,6,7]=>1 [5,4,3,2,1,7,6]=>2 [5,4,3,2,6,1,7]=>2 [5,4,3,6,2,1,7]=>3 [5,4,6,3,2,1,7]=>3 [5,4,6,7,1,2,3]=>3 [5,6,1,2,3,4,7]=>2 [5,6,1,2,3,7,4]=>3 [5,6,3,4,1,2,7]=>3 [5,6,4,3,2,1,7]=>2 [5,6,7,1,2,3,4]=>3 [6,1,2,3,4,5,7]=>2 [6,1,2,3,4,7,5]=>3 [6,1,2,3,7,4,5]=>4 [6,1,2,7,3,4,5]=>4 [6,2,3,4,5,7,1]=>3 [6,2,4,5,3,1,7]=>3 [6,2,5,4,3,1,7]=>3 [6,3,2,5,4,1,7]=>3 [6,3,4,2,5,1,7]=>3 [6,3,4,5,2,1,7]=>2 [6,3,4,7,1,2,5]=>3 [6,3,5,4,2,1,7]=>3 [6,4,3,2,5,1,7]=>3 [6,4,3,2,7,1,5]=>4 [6,4,3,5,2,1,7]=>3 [6,4,5,7,1,2,3]=>3 [6,4,7,2,5,1,3]=>5 [6,4,7,3,5,1,2]=>4 [6,5,3,4,2,1,7]=>2 [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]=>4 [6,7,4,5,1,2,3]=>3 [7,1,2,3,4,5,6]=>2 [7,2,1,3,4,5,6]=>3 [7,2,3,1,4,5,6]=>4 [7,2,3,4,1,5,6]=>4 [7,2,3,4,5,1,6]=>3 [7,3,1,2,4,5,6]=>4 [7,3,2,1,4,5,6]=>3 [7,3,2,4,1,5,6]=>4 [7,3,4,1,2,5,6]=>4 [7,4,1,2,3,5,6]=>4 [7,4,2,1,3,5,6]=>4 [7,4,5,6,1,2,3]=>3 [7,5,1,2,3,4,6]=>3 [7,5,6,1,2,3,4]=>3 [7,5,6,3,4,1,2]=>4 [7,6,1,2,3,4,5]=>2 [7,6,4,5,1,2,3]=>3 [7,6,5,1,2,3,4]=>2 [7,6,5,3,4,1,2]=>3 [7,6,5,4,1,2,3]=>2 [7,6,5,4,3,1,2]=>2 [7,6,5,4,3,2,1]=>1 [8,7,6,5,4,3,2,1]=>1 [7,6,8,5,4,3,2,1]=>3 [7,8,5,6,4,3,2,1]=>3 [7,8,6,4,5,3,2,1]=>3 [8,6,7,4,5,3,2,1]=>3 [7,6,5,4,8,3,2,1]=>3 [6,5,7,4,8,3,2,1]=>4 [7,8,6,5,3,4,2,1]=>3 [8,6,7,5,3,4,2,1]=>3 [8,7,5,6,3,4,2,1]=>3 [6,7,8,3,4,5,2,1]=>3 [7,8,6,5,4,2,3,1]=>3 [8,6,7,5,4,2,3,1]=>3 [8,7,5,6,4,2,3,1]=>3 [8,7,6,4,5,2,3,1]=>3 [8,6,5,7,3,2,4,1]=>5 [6,7,8,5,2,3,4,1]=>3 [8,5,6,7,2,3,4,1]=>3 [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]=>4 [6,5,4,3,7,2,8,1]=>4 [5,4,6,3,7,2,8,1]=>5 [3,4,5,2,6,7,8,1]=>4 [5,2,3,4,6,7,8,1]=>4 [4,3,2,5,6,7,8,1]=>3 [3,4,2,5,6,7,8,1]=>4 [4,2,3,5,6,7,8,1]=>4 [3,2,4,5,6,7,8,1]=>3 [2,3,4,5,6,7,8,1]=>2 [8,7,6,5,4,3,1,2]=>2 [7,8,6,5,4,3,1,2]=>3 [8,6,7,5,4,3,1,2]=>3 [8,7,5,6,4,3,1,2]=>3 [8,7,6,4,5,3,1,2]=>3 [8,7,6,5,3,4,1,2]=>3 [8,7,5,6,3,4,1,2]=>4 [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]=>3 [7,6,8,5,4,2,1,3]=>5 [8,7,6,5,4,1,2,3]=>2 [6,7,8,5,4,1,2,3]=>3 [8,5,6,7,4,1,2,3]=>3 [8,7,6,4,5,1,2,3]=>3 [8,6,7,4,5,1,2,3]=>4 [8,7,4,5,6,1,2,3]=>3 [7,8,4,5,6,1,2,3]=>3 [6,7,4,5,8,1,2,3]=>4 [7,6,5,8,3,2,1,4]=>3 [7,5,6,8,2,3,1,4]=>5 [6,7,5,8,3,1,2,4]=>5 [6,5,7,8,2,1,3,4]=>4 [8,7,6,5,1,2,3,4]=>2 [8,7,5,6,1,2,3,4]=>3 [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]=>3 [8,7,6,4,3,2,1,5]=>3 [8,7,6,4,2,1,3,5]=>4 [8,7,6,1,2,3,4,5]=>2 [8,6,7,1,2,3,4,5]=>3 [6,7,8,1,2,3,4,5]=>3 [7,8,5,4,2,1,3,6]=>4 [7,8,5,4,1,2,3,6]=>3 [8,7,1,2,3,4,5,6]=>2 [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]=>3 [8,5,6,3,4,1,2,7]=>4 [8,6,5,4,2,1,3,7]=>4 [8,6,4,3,2,1,5,7]=>4 [8,6,4,2,1,3,5,7]=>5 [8,2,3,4,1,5,6,7]=>4 [8,4,1,2,3,5,6,7]=>4 [8,3,2,1,4,5,6,7]=>3 [8,2,3,1,4,5,6,7]=>4 [8,3,1,2,4,5,6,7]=>4 [8,2,1,3,4,5,6,7]=>3 [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]=>2 [6,5,7,4,3,2,1,8]=>3 [5,6,7,4,3,2,1,8]=>2 [7,6,4,5,3,2,1,8]=>2 [6,5,4,7,3,2,1,8]=>3 [7,5,6,3,4,2,1,8]=>3 [7,6,4,3,5,2,1,8]=>3 [7,6,3,4,5,2,1,8]=>2 [7,5,4,3,6,2,1,8]=>3 [6,7,5,4,2,3,1,8]=>3 [6,5,7,3,2,4,1,8]=>4 [5,6,7,2,3,4,1,8]=>3 [2,3,4,5,6,7,1,8]=>2 [5,6,7,1,2,3,4,8]=>3 [6,7,1,2,3,4,5,8]=>2 [7,1,2,3,4,5,6,8]=>2 [6,5,4,3,2,1,7,8]=>1 [2,3,4,5,6,1,7,8]=>2 [5,6,3,4,1,2,7,8]=>3 [4,5,6,1,2,3,7,8]=>3 [6,1,2,3,4,5,7,8]=>2 [5,4,3,2,1,6,7,8]=>1 [2,3,4,5,1,6,7,8]=>2 [5,1,2,3,4,6,7,8]=>2 [4,3,2,1,5,6,7,8]=>1 [3,4,1,2,5,6,7,8]=>2 [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]=>0 [6,5,8,7,4,3,2,1]=>3 [3,5,8,7,6,4,2,1]=>4 [4,3,6,5,8,7,2,1]=>3 [2,6,8,7,5,4,3,1]=>4 [2,3,5,6,8,7,4,1]=>5 [3,2,6,5,4,8,7,1]=>3 [4,3,6,5,7,2,8,1]=>4 [3,2,6,5,7,4,8,1]=>5 [4,3,5,2,7,6,8,1]=>5 [3,2,5,4,7,6,8,1]=>4 [1,8,7,6,5,4,3,2]=>1 [1,7,8,6,5,4,3,2]=>2 [1,6,8,7,5,4,3,2]=>3 [1,7,6,8,5,4,3,2]=>3 [1,6,7,8,5,4,3,2]=>2 [1,5,8,7,6,4,3,2]=>3 [1,7,6,5,8,4,3,2]=>3 [1,3,5,7,8,6,4,2]=>4 [1,4,3,8,7,6,5,2]=>2 [1,6,5,4,3,8,7,2]=>2 [1,4,3,6,5,8,7,2]=>3 [2,1,8,7,6,5,4,3]=>2 [2,1,6,5,7,4,8,3]=>5 [2,1,5,4,7,6,8,3]=>4 [1,2,6,7,8,5,4,3]=>2 [3,2,1,8,7,6,5,4]=>2 [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]=>2 [3,4,2,1,7,8,6,5]=>4 [2,4,3,1,6,8,7,5]=>4 [2,4,3,1,7,6,8,5]=>4 [3,2,4,1,6,8,7,5]=>4 [3,2,4,1,7,6,8,5]=>4 [2,3,4,1,6,7,8,5]=>4 [2,1,4,3,8,7,6,5]=>3 [2,1,4,3,6,8,7,5]=>4 [2,1,4,3,7,6,8,5]=>4 [5,4,3,2,1,8,7,6]=>2 [3,2,5,4,1,8,7,6]=>3 [3,2,1,4,5,8,7,6]=>2 [2,3,1,4,5,7,8,6]=>4 [6,5,4,3,2,1,8,7]=>2 [4,3,5,2,6,1,8,7]=>5 [3,2,5,4,6,1,8,7]=>4 [2,3,4,5,6,1,8,7]=>3 [2,1,6,5,4,3,8,7]=>3 [2,1,4,6,5,3,8,7]=>4 [2,1,5,4,6,3,8,7]=>4 [4,3,2,1,6,5,8,7]=>3 [2,4,3,1,6,5,8,7]=>4 [3,2,4,1,6,5,8,7]=>4 [2,1,4,3,6,5,8,7]=>4 [2,1,3,4,5,6,8,7]=>2 [1,2,3,4,5,6,8,7]=>1 [5,7,6,4,3,2,1,8]=>3 [4,7,6,5,3,2,1,8]=>3 [3,2,7,6,5,4,1,8]=>2 [5,4,3,2,7,6,1,8]=>2 [3,2,5,4,7,6,1,8]=>3 [1,4,3,2,7,6,5,8]=>2 [1,3,4,2,6,7,5,8]=>4 [1,3,2,5,4,7,6,8]=>3 [1,2,3,5,4,7,6,8]=>2 [1,3,2,4,5,7,6,8]=>2 [1,2,3,4,5,7,6,8]=>1 [1,2,4,3,6,5,7,8]=>2 [1,3,2,5,4,6,7,8]=>2 [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]=>3 [1,8,5,4,7,6,3,2]=>3 [1,8,7,4,5,6,3,2]=>2 [1,8,7,4,6,5,3,2]=>3 [1,8,6,5,4,7,3,2]=>3 [1,8,7,5,4,6,3,2]=>3 [1,8,7,5,6,4,3,2]=>2 [2,1,4,5,8,6,7,3]=>5 [2,1,8,5,4,7,6,3]=>4 [2,3,4,8,5,6,7,1]=>4 [2,3,6,4,5,1,8,7]=>5 [2,3,7,4,5,6,8,1]=>4 [2,8,4,3,5,7,6,1]=>4 [4,2,3,1,8,6,7,5]=>4 [8,2,7,4,6,5,3,1]=>5 [4,3,2,7,5,6,8,1]=>4 [4,3,2,8,5,7,6,1]=>4 [6,3,2,5,4,1,8,7]=>4 [8,3,2,5,4,7,6,1]=>4 [8,3,2,7,6,5,4,1]=>3 [8,3,7,4,6,5,2,1]=>4 [7,3,6,5,4,2,1,8]=>3 [7,4,3,6,5,2,1,8]=>3 [7,6,3,5,4,2,1,8]=>3 [8,5,4,3,2,7,6,1]=>3 [8,7,4,3,6,5,2,1]=>3 [2,4,6,8,1,3,5,7]=>5 [2,4,6,1,7,3,8,5]=>6 [2,1,4,3,7,5,8,6]=>5 [2,4,1,3,7,5,8,6]=>6 [2,1,4,3,7,8,5,6]=>4 [2,4,7,8,1,3,5,6]=>5 [2,1,4,3,8,5,6,7]=>4 [2,4,5,6,7,1,8,3]=>4 [2,1,5,3,6,4,8,7]=>5 [2,1,5,6,3,4,8,7]=>4 [2,5,6,8,1,3,4,7]=>4 [2,1,5,3,7,4,8,6]=>6 [2,5,1,7,3,4,8,6]=>6 [2,1,5,7,3,8,4,6]=>5 [2,5,7,8,1,3,4,6]=>4 [2,3,5,6,1,7,8,4]=>4 [2,1,6,3,7,4,8,5]=>5 [2,6,7,1,3,4,8,5]=>4 [2,1,6,7,8,3,4,5]=>3 [2,6,7,8,1,3,4,5]=>3 [2,1,6,3,4,7,8,5]=>5 [2,1,6,3,4,5,8,7]=>4 [2,6,1,3,4,5,7,8]=>3 [2,7,8,1,3,4,5,6]=>3 [2,7,1,3,4,5,6,8]=>3 [2,3,4,5,7,8,1,6]=>4 [2,1,8,3,4,5,6,7]=>3 [2,8,1,3,4,5,6,7]=>3 [2,1,3,8,4,5,6,7]=>3 [2,3,4,5,6,8,1,7]=>3 [3,1,4,2,6,5,8,7]=>5 [3,4,1,2,6,5,8,7]=>4 [3,1,4,2,6,8,5,7]=>6 [3,4,6,8,1,2,5,7]=>5 [3,1,4,2,7,5,8,6]=>6 [3,4,1,2,7,8,5,6]=>4 [3,4,7,8,1,2,5,6]=>4 [3,1,5,2,6,4,8,7]=>6 [3,5,1,6,2,4,8,7]=>5 [3,1,5,6,2,8,4,7]=>6 [3,5,6,8,1,2,4,7]=>4 [3,1,5,2,7,4,8,6]=>7 [3,5,1,7,2,8,4,6]=>6 [3,5,7,8,1,2,4,6]=>5 [1,3,2,5,4,8,6,7]=>4 [1,3,5,8,2,4,6,7]=>5 [1,3,5,6,2,7,4,8]=>4 [3,1,6,2,7,4,8,5]=>6 [3,6,7,1,2,8,4,5]=>4 [3,6,1,7,8,2,4,5]=>5 [3,6,7,8,1,2,4,5]=>4 [1,3,2,6,4,7,5,8]=>4 [3,1,2,6,7,4,8,5]=>5 [1,3,2,6,4,8,5,7]=>5 [1,3,2,6,4,5,7,8]=>3 [1,3,2,7,4,8,5,6]=>4 [1,3,2,7,4,5,6,8]=>3 [1,3,2,8,4,5,6,7]=>3 [3,1,2,4,5,8,6,7]=>4 [1,3,2,4,5,8,6,7]=>3 [4,1,5,2,6,3,8,7]=>5 [4,5,6,1,2,3,8,7]=>3 [4,1,5,6,8,2,3,7]=>4 [4,5,6,8,1,2,3,7]=>3 [4,1,5,2,7,3,8,6]=>6 [4,1,5,2,7,8,3,6]=>5 [4,5,7,1,2,8,3,6]=>5 [4,5,1,7,8,2,3,6]=>4 [4,5,7,8,1,2,3,6]=>4 [1,4,2,5,3,7,6,8]=>4 [1,4,2,5,3,8,6,7]=>5 [1,4,2,5,3,6,7,8]=>3 [1,4,5,6,7,2,3,8]=>2 [4,1,6,2,7,3,8,5]=>6 [4,6,7,1,8,2,3,5]=>4 [4,6,7,8,1,2,3,5]=>3 [1,4,2,6,3,7,5,8]=>5 [1,4,2,6,7,8,3,5]=>4 [1,4,2,6,3,8,5,7]=>6 [4,1,2,3,6,5,8,7]=>4 [1,4,2,6,3,5,7,8]=>4 [1,4,2,7,3,8,5,6]=>5 [4,7,1,2,3,5,6,8]=>4 [1,4,2,7,3,5,6,8]=>4 [1,4,2,3,7,5,6,8]=>4 [1,4,2,3,5,7,6,8]=>3 [1,4,2,8,3,5,6,7]=>4 [4,1,2,3,8,5,6,7]=>4 [1,4,2,3,5,8,6,7]=>4 [1,4,2,3,5,6,7,8]=>2 [5,1,6,2,7,3,8,4]=>5 [1,5,2,6,3,7,4,8]=>4 [1,5,2,6,3,8,4,7]=>5 [1,5,2,6,3,4,7,8]=>3 [1,2,5,6,3,4,7,8]=>2 [1,5,2,7,3,8,4,6]=>5 [5,7,1,2,3,4,6,8]=>3 [1,5,2,7,3,4,6,8]=>4 [1,5,2,3,4,7,6,8]=>3 [5,1,2,8,3,4,6,7]=>4 [1,5,2,8,3,4,6,7]=>4 [1,5,8,2,3,4,6,7]=>4 [1,5,2,3,4,8,6,7]=>4 [1,2,3,5,4,8,6,7]=>3 [5,1,2,3,4,6,8,7]=>3 [1,5,2,3,4,6,7,8]=>2 [1,6,2,7,3,8,4,5]=>4 [1,6,7,8,2,3,4,5]=>3 [6,7,1,2,3,4,8,5]=>3 [6,1,7,2,3,4,5,8]=>3 [6,1,2,7,3,4,5,8]=>4 [1,6,2,7,3,4,5,8]=>3 [1,6,7,2,3,4,5,8]=>2 [1,6,2,3,4,7,5,8]=>3 [1,2,3,6,4,7,5,8]=>3 [6,1,8,2,3,4,5,7]=>4 [1,6,2,8,3,4,5,7]=>4 [1,6,8,2,3,4,5,7]=>3 [1,6,2,3,4,8,5,7]=>4 [1,2,3,6,4,8,5,7]=>4 [6,1,2,3,4,5,8,7]=>3 [1,6,2,3,4,5,7,8]=>2 [1,2,3,6,4,5,7,8]=>2 [1,7,2,8,3,4,5,6]=>3 [1,7,8,2,3,4,5,6]=>2 [1,7,2,3,8,4,5,6]=>4 [7,1,2,3,4,8,5,6]=>4 [1,7,2,3,4,8,5,6]=>4 [1,2,3,7,4,8,5,6]=>3 [7,1,2,3,4,5,8,6]=>3 [1,7,2,3,4,5,8,6]=>3 [1,2,7,3,4,5,8,6]=>3 [1,7,2,3,4,5,6,8]=>2 [1,2,3,7,4,5,6,8]=>2 [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]=>5 [7,3,2,5,4,8,1,6]=>4 [8,4,5,2,3,7,6,1]=>3 [7,4,5,2,3,8,1,6]=>4 [6,4,5,2,3,1,8,7]=>4 [5,4,6,2,1,3,8,7]=>4 [3,6,1,5,4,2,8,7]=>5 [4,6,5,1,3,2,8,7]=>4 [5,6,4,3,1,2,8,7]=>4 [7,5,4,3,2,8,1,6]=>4 [8,6,4,3,7,2,5,1]=>5 [7,6,4,3,8,2,1,5]=>5 [6,7,4,3,8,1,2,5]=>4 [5,7,4,3,1,8,2,6]=>6 [4,7,5,1,3,8,2,6]=>6 [3,7,1,5,4,8,2,6]=>5 [2,1,7,5,4,8,3,6]=>5 [3,8,1,5,4,7,6,2]=>4 [4,8,5,1,3,7,6,2]=>5 [5,8,4,3,1,7,6,2]=>5 [6,8,4,3,7,1,5,2]=>5 [7,8,4,3,6,5,1,2]=>4 [6,8,5,7,3,1,4,2]=>6 [5,8,6,7,1,3,4,2]=>5 [4,8,6,1,7,3,5,2]=>6 [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]=>4 [3,7,1,6,8,4,2,5]=>6 [4,7,6,1,8,3,2,5]=>4 [5,7,6,8,1,3,2,4]=>5 [5,4,7,2,1,8,3,6]=>4 [6,4,7,2,8,1,3,5]=>6 [7,4,6,2,8,3,1,5]=>6 [8,4,6,2,7,3,5,1]=>5 [8,3,2,6,7,4,5,1]=>3 [7,3,2,6,8,4,1,5]=>5 [6,3,2,7,8,1,4,5]=>4 [5,3,2,7,1,8,4,6]=>5 [4,3,2,1,7,8,5,6]=>3 [3,4,1,2,8,7,6,5]=>3 [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]=>5 [8,4,7,2,6,5,3,1]=>5 [7,4,8,2,6,5,1,3]=>5 [6,4,8,2,7,1,5,3]=>5 [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]=>5 [2,1,5,8,3,7,6,4]=>5 [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]=>6 [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]=>6 [8,5,7,6,2,4,3,1]=>5 [5,7,8,6,1,4,2,3]=>5 [4,7,8,1,6,5,2,3]=>4 [3,7,1,8,6,5,2,4]=>6 [2,1,7,8,6,5,3,4]=>4 [3,8,1,7,6,5,4,2]=>4 [4,8,7,1,6,5,3,2]=>5 [5,8,7,6,1,4,3,2]=>3 [6,8,7,5,4,1,3,2]=>5
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Description
The reversal length of a permutation.
A reversal in a permutation $\pi = [\pi_1,\ldots,\pi_n]$ is a reversal of a subsequence of the form $\operatorname{reversal}_{i,j}(\pi) = [\pi_1,\ldots,\pi_{i-1},\pi_j,\pi_{j-1},\ldots,\pi_{i+1},\pi_i,\pi_{j+1},\ldots,\pi_n]$ for $1 \leq i < j \leq n$.
This statistic is then given by the minimal number of reversals needed to sort a permutation.
The reversal distance between two permutations plays an important role in studying DNA structures.
Code
def children(pi):
    pi = list(pi)
    n = len(pi)
    for j in range(n):
        for i in range(j):
            yield Permutation(pi[:i]+list(reversed(pi[i:j+1]))+pi[j+1:])

@cached_function
def statistic_classes(n):
    A = RecursivelyEnumeratedSet([Permutation([1..n])], children,structure='symmetric')
    return list(A.graded_component_iterator())

def statistic(pi):
    comps = statistic_classes(len(pi))
    for rank,comp in enumerate(comps):
        if pi in comp:
            return rank
Created
Dec 15, 2016 at 17:57 by Christian Stump
Updated
Jun 21, 2018 at 09:53 by Martin Rubey