edit this statistic or download as text // json
Identifier
Values
=>
[1]=>1 [1,2]=>1 [2,1]=>1 [1,2,3]=>1 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>2 [3,1,2]=>2 [3,2,1]=>1 [1,2,3,4]=>1 [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]=>1 [2,3,1,4]=>2 [2,3,4,1]=>2 [2,4,1,3]=>2 [2,4,3,1]=>2 [3,1,2,4]=>2 [3,1,4,2]=>2 [3,2,1,4]=>1 [3,2,4,1]=>2 [3,4,1,2]=>1 [3,4,2,1]=>2 [4,1,2,3]=>2 [4,1,3,2]=>2 [4,2,1,3]=>2 [4,2,3,1]=>1 [4,3,1,2]=>2 [4,3,2,1]=>1 [1,2,3,4,5]=>1 [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]=>1 [1,3,4,2,5]=>2 [1,3,4,5,2]=>2 [1,3,5,2,4]=>2 [1,3,5,4,2]=>2 [1,4,2,3,5]=>2 [1,4,2,5,3]=>2 [1,4,3,2,5]=>1 [1,4,3,5,2]=>2 [1,4,5,2,3]=>1 [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]=>1 [1,5,4,2,3]=>2 [1,5,4,3,2]=>1 [2,1,3,4,5]=>1 [2,1,3,5,4]=>1 [2,1,4,3,5]=>1 [2,1,4,5,3]=>2 [2,1,5,3,4]=>2 [2,1,5,4,3]=>1 [2,3,1,4,5]=>2 [2,3,1,5,4]=>2 [2,3,4,1,5]=>2 [2,3,4,5,1]=>2 [2,3,5,1,4]=>2 [2,3,5,4,1]=>2 [2,4,1,3,5]=>2 [2,4,1,5,3]=>2 [2,4,3,1,5]=>2 [2,4,3,5,1]=>2 [2,4,5,1,3]=>2 [2,4,5,3,1]=>2 [2,5,1,3,4]=>2 [2,5,1,4,3]=>2 [2,5,3,1,4]=>2 [2,5,3,4,1]=>2 [2,5,4,1,3]=>2 [2,5,4,3,1]=>2 [3,1,2,4,5]=>2 [3,1,2,5,4]=>2 [3,1,4,2,5]=>2 [3,1,4,5,2]=>2 [3,1,5,2,4]=>2 [3,1,5,4,2]=>2 [3,2,1,4,5]=>1 [3,2,1,5,4]=>1 [3,2,4,1,5]=>2 [3,2,4,5,1]=>2 [3,2,5,1,4]=>2 [3,2,5,4,1]=>2 [3,4,1,2,5]=>1 [3,4,1,5,2]=>2 [3,4,2,1,5]=>2 [3,4,2,5,1]=>2 [3,4,5,1,2]=>2 [3,4,5,2,1]=>2 [3,5,1,2,4]=>2 [3,5,1,4,2]=>1 [3,5,2,1,4]=>2 [3,5,2,4,1]=>2 [3,5,4,1,2]=>2 [3,5,4,2,1]=>2 [4,1,2,3,5]=>2 [4,1,2,5,3]=>2 [4,1,3,2,5]=>2 [4,1,3,5,2]=>2 [4,1,5,2,3]=>2 [4,1,5,3,2]=>2 [4,2,1,3,5]=>2 [4,2,1,5,3]=>2 [4,2,3,1,5]=>1 [4,2,3,5,1]=>2 [4,2,5,1,3]=>1 [4,2,5,3,1]=>2 [4,3,1,2,5]=>2 [4,3,1,5,2]=>2 [4,3,2,1,5]=>1 [4,3,2,5,1]=>2 [4,3,5,1,2]=>2 [4,3,5,2,1]=>2 [4,5,1,2,3]=>2 [4,5,1,3,2]=>2 [4,5,2,1,3]=>2 [4,5,2,3,1]=>2 [4,5,3,1,2]=>1 [4,5,3,2,1]=>2 [5,1,2,3,4]=>2 [5,1,2,4,3]=>2 [5,1,3,2,4]=>2 [5,1,3,4,2]=>2 [5,1,4,2,3]=>2 [5,1,4,3,2]=>2 [5,2,1,3,4]=>2 [5,2,1,4,3]=>2 [5,2,3,1,4]=>2 [5,2,3,4,1]=>1 [5,2,4,1,3]=>2 [5,2,4,3,1]=>1 [5,3,1,2,4]=>2 [5,3,1,4,2]=>2 [5,3,2,1,4]=>2 [5,3,2,4,1]=>1 [5,3,4,1,2]=>2 [5,3,4,2,1]=>2 [5,4,1,2,3]=>2 [5,4,1,3,2]=>2 [5,4,2,1,3]=>2 [5,4,2,3,1]=>2 [5,4,3,1,2]=>2 [5,4,3,2,1]=>1 [1,2,3,4,5,6]=>1 [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]=>1 [1,2,4,5,3,6]=>2 [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]=>2 [1,2,5,3,6,4]=>2 [1,2,5,4,3,6]=>1 [1,2,5,4,6,3]=>2 [1,2,5,6,3,4]=>1 [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]=>1 [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]=>1 [1,3,2,5,4,6]=>1 [1,3,2,5,6,4]=>2 [1,3,2,6,4,5]=>2 [1,3,2,6,5,4]=>1 [1,3,4,2,5,6]=>2 [1,3,4,2,6,5]=>2 [1,3,4,5,2,6]=>2 [1,3,4,5,6,2]=>2 [1,3,4,6,2,5]=>2 [1,3,4,6,5,2]=>2 [1,3,5,2,4,6]=>2 [1,3,5,2,6,4]=>2 [1,3,5,4,2,6]=>2 [1,3,5,4,6,2]=>2 [1,3,5,6,2,4]=>2 [1,3,5,6,4,2]=>2 [1,3,6,2,4,5]=>2 [1,3,6,2,5,4]=>2 [1,3,6,4,2,5]=>2 [1,3,6,4,5,2]=>2 [1,3,6,5,2,4]=>2 [1,3,6,5,4,2]=>2 [1,4,2,3,5,6]=>2 [1,4,2,3,6,5]=>2 [1,4,2,5,3,6]=>2 [1,4,2,5,6,3]=>2 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>2 [1,4,3,2,5,6]=>1 [1,4,3,2,6,5]=>1 [1,4,3,5,2,6]=>2 [1,4,3,5,6,2]=>2 [1,4,3,6,2,5]=>2 [1,4,3,6,5,2]=>2 [1,4,5,2,3,6]=>1 [1,4,5,2,6,3]=>2 [1,4,5,3,2,6]=>2 [1,4,5,3,6,2]=>2 [1,4,5,6,2,3]=>2 [1,4,5,6,3,2]=>2 [1,4,6,2,3,5]=>2 [1,4,6,2,5,3]=>1 [1,4,6,3,2,5]=>2 [1,4,6,3,5,2]=>2 [1,4,6,5,2,3]=>2 [1,4,6,5,3,2]=>2 [1,5,2,3,4,6]=>2 [1,5,2,3,6,4]=>2 [1,5,2,4,3,6]=>2 [1,5,2,4,6,3]=>2 [1,5,2,6,3,4]=>2 [1,5,2,6,4,3]=>2 [1,5,3,2,4,6]=>2 [1,5,3,2,6,4]=>2 [1,5,3,4,2,6]=>1 [1,5,3,4,6,2]=>2 [1,5,3,6,2,4]=>1 [1,5,3,6,4,2]=>2 [1,5,4,2,3,6]=>2 [1,5,4,2,6,3]=>2 [1,5,4,3,2,6]=>1 [1,5,4,3,6,2]=>2 [1,5,4,6,2,3]=>2 [1,5,4,6,3,2]=>2 [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]=>2 [1,5,6,4,2,3]=>1 [1,5,6,4,3,2]=>2 [1,6,2,3,4,5]=>2 [1,6,2,3,5,4]=>2 [1,6,2,4,3,5]=>2 [1,6,2,4,5,3]=>2 [1,6,2,5,3,4]=>2 [1,6,2,5,4,3]=>2 [1,6,3,2,4,5]=>2 [1,6,3,2,5,4]=>2 [1,6,3,4,2,5]=>2 [1,6,3,4,5,2]=>1 [1,6,3,5,2,4]=>2 [1,6,3,5,4,2]=>1 [1,6,4,2,3,5]=>2 [1,6,4,2,5,3]=>2 [1,6,4,3,2,5]=>2 [1,6,4,3,5,2]=>1 [1,6,4,5,2,3]=>2 [1,6,4,5,3,2]=>2 [1,6,5,2,3,4]=>2 [1,6,5,2,4,3]=>2 [1,6,5,3,2,4]=>2 [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]=>1 [2,1,3,5,4,6]=>1 [2,1,3,5,6,4]=>2 [2,1,3,6,4,5]=>2 [2,1,3,6,5,4]=>1 [2,1,4,3,5,6]=>1 [2,1,4,3,6,5]=>1 [2,1,4,5,3,6]=>2 [2,1,4,5,6,3]=>2 [2,1,4,6,3,5]=>2 [2,1,4,6,5,3]=>2 [2,1,5,3,4,6]=>2 [2,1,5,3,6,4]=>2 [2,1,5,4,3,6]=>1 [2,1,5,4,6,3]=>2 [2,1,5,6,3,4]=>1 [2,1,5,6,4,3]=>2 [2,1,6,3,4,5]=>2 [2,1,6,3,5,4]=>2 [2,1,6,4,3,5]=>2 [2,1,6,4,5,3]=>1 [2,1,6,5,3,4]=>2 [2,1,6,5,4,3]=>1 [2,3,1,4,5,6]=>2 [2,3,1,4,6,5]=>2 [2,3,1,5,4,6]=>2 [2,3,1,5,6,4]=>4 [2,3,1,6,4,5]=>4 [2,3,1,6,5,4]=>2 [2,3,4,1,5,6]=>2 [2,3,4,1,6,5]=>2 [2,3,4,5,1,6]=>2 [2,3,4,5,6,1]=>2 [2,3,4,6,1,5]=>2 [2,3,4,6,5,1]=>2 [2,3,5,1,4,6]=>2 [2,3,5,1,6,4]=>2 [2,3,5,4,1,6]=>2 [2,3,5,4,6,1]=>2 [2,3,5,6,1,4]=>2 [2,3,5,6,4,1]=>2 [2,3,6,1,4,5]=>2 [2,3,6,1,5,4]=>2 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>2 [2,3,6,5,1,4]=>2 [2,3,6,5,4,1]=>2 [2,4,1,3,5,6]=>2 [2,4,1,3,6,5]=>2 [2,4,1,5,3,6]=>2 [2,4,1,5,6,3]=>2 [2,4,1,6,3,5]=>2 [2,4,1,6,5,3]=>2 [2,4,3,1,5,6]=>2 [2,4,3,1,6,5]=>2 [2,4,3,5,1,6]=>2 [2,4,3,5,6,1]=>2 [2,4,3,6,1,5]=>2 [2,4,3,6,5,1]=>2 [2,4,5,1,3,6]=>2 [2,4,5,1,6,3]=>4 [2,4,5,3,1,6]=>2 [2,4,5,3,6,1]=>2 [2,4,5,6,1,3]=>2 [2,4,5,6,3,1]=>2 [2,4,6,1,3,5]=>4 [2,4,6,1,5,3]=>2 [2,4,6,3,1,5]=>2 [2,4,6,3,5,1]=>2 [2,4,6,5,1,3]=>2 [2,4,6,5,3,1]=>2 [2,5,1,3,4,6]=>2 [2,5,1,3,6,4]=>2 [2,5,1,4,3,6]=>2 [2,5,1,4,6,3]=>2 [2,5,1,6,3,4]=>2 [2,5,1,6,4,3]=>2 [2,5,3,1,4,6]=>2 [2,5,3,1,6,4]=>2 [2,5,3,4,1,6]=>2 [2,5,3,4,6,1]=>2 [2,5,3,6,1,4]=>2 [2,5,3,6,4,1]=>2 [2,5,4,1,3,6]=>2 [2,5,4,1,6,3]=>2 [2,5,4,3,1,6]=>2 [2,5,4,3,6,1]=>2 [2,5,4,6,1,3]=>4 [2,5,4,6,3,1]=>2 [2,5,6,1,3,4]=>2 [2,5,6,1,4,3]=>2 [2,5,6,3,1,4]=>4 [2,5,6,3,4,1]=>2 [2,5,6,4,1,3]=>2 [2,5,6,4,3,1]=>2 [2,6,1,3,4,5]=>2 [2,6,1,3,5,4]=>2 [2,6,1,4,3,5]=>2 [2,6,1,4,5,3]=>2 [2,6,1,5,3,4]=>2 [2,6,1,5,4,3]=>2 [2,6,3,1,4,5]=>2 [2,6,3,1,5,4]=>2 [2,6,3,4,1,5]=>2 [2,6,3,4,5,1]=>2 [2,6,3,5,1,4]=>2 [2,6,3,5,4,1]=>2 [2,6,4,1,3,5]=>2 [2,6,4,1,5,3]=>2 [2,6,4,3,1,5]=>2 [2,6,4,3,5,1]=>2 [2,6,4,5,1,3]=>2 [2,6,4,5,3,1]=>4 [2,6,5,1,3,4]=>2 [2,6,5,1,4,3]=>2 [2,6,5,3,1,4]=>2 [2,6,5,3,4,1]=>4 [2,6,5,4,1,3]=>2 [2,6,5,4,3,1]=>2 [3,1,2,4,5,6]=>2 [3,1,2,4,6,5]=>2 [3,1,2,5,4,6]=>2 [3,1,2,5,6,4]=>4 [3,1,2,6,4,5]=>4 [3,1,2,6,5,4]=>2 [3,1,4,2,5,6]=>2 [3,1,4,2,6,5]=>2 [3,1,4,5,2,6]=>2 [3,1,4,5,6,2]=>2 [3,1,4,6,2,5]=>2 [3,1,4,6,5,2]=>2 [3,1,5,2,4,6]=>2 [3,1,5,2,6,4]=>2 [3,1,5,4,2,6]=>2 [3,1,5,4,6,2]=>2 [3,1,5,6,2,4]=>2 [3,1,5,6,4,2]=>2 [3,1,6,2,4,5]=>2 [3,1,6,2,5,4]=>2 [3,1,6,4,2,5]=>2 [3,1,6,4,5,2]=>2 [3,1,6,5,2,4]=>2 [3,1,6,5,4,2]=>2 [3,2,1,4,5,6]=>1 [3,2,1,4,6,5]=>1 [3,2,1,5,4,6]=>1 [3,2,1,5,6,4]=>2 [3,2,1,6,4,5]=>2 [3,2,1,6,5,4]=>1 [3,2,4,1,5,6]=>2 [3,2,4,1,6,5]=>2 [3,2,4,5,1,6]=>2 [3,2,4,5,6,1]=>2 [3,2,4,6,1,5]=>2 [3,2,4,6,5,1]=>2 [3,2,5,1,4,6]=>2 [3,2,5,1,6,4]=>2 [3,2,5,4,1,6]=>2 [3,2,5,4,6,1]=>2 [3,2,5,6,1,4]=>2 [3,2,5,6,4,1]=>2 [3,2,6,1,4,5]=>2 [3,2,6,1,5,4]=>2 [3,2,6,4,1,5]=>2 [3,2,6,4,5,1]=>2 [3,2,6,5,1,4]=>2 [3,2,6,5,4,1]=>2 [3,4,1,2,5,6]=>1 [3,4,1,2,6,5]=>1 [3,4,1,5,2,6]=>2 [3,4,1,5,6,2]=>2 [3,4,1,6,2,5]=>2 [3,4,1,6,5,2]=>2 [3,4,2,1,5,6]=>2 [3,4,2,1,6,5]=>2 [3,4,2,5,1,6]=>2 [3,4,2,5,6,1]=>2 [3,4,2,6,1,5]=>2 [3,4,2,6,5,1]=>2 [3,4,5,1,2,6]=>2 [3,4,5,1,6,2]=>2 [3,4,5,2,1,6]=>2 [3,4,5,2,6,1]=>2 [3,4,5,6,1,2]=>4 [3,4,5,6,2,1]=>2 [3,4,6,1,2,5]=>2 [3,4,6,1,5,2]=>2 [3,4,6,2,1,5]=>2 [3,4,6,2,5,1]=>2 [3,4,6,5,1,2]=>2 [3,4,6,5,2,1]=>4 [3,5,1,2,4,6]=>2 [3,5,1,2,6,4]=>2 [3,5,1,4,2,6]=>1 [3,5,1,4,6,2]=>2 [3,5,1,6,2,4]=>1 [3,5,1,6,4,2]=>2 [3,5,2,1,4,6]=>2 [3,5,2,1,6,4]=>2 [3,5,2,4,1,6]=>2 [3,5,2,4,6,1]=>2 [3,5,2,6,1,4]=>2 [3,5,2,6,4,1]=>2 [3,5,4,1,2,6]=>2 [3,5,4,1,6,2]=>4 [3,5,4,2,1,6]=>2 [3,5,4,2,6,1]=>2 [3,5,4,6,1,2]=>2 [3,5,4,6,2,1]=>2 [3,5,6,1,2,4]=>2 [3,5,6,1,4,2]=>2 [3,5,6,2,1,4]=>2 [3,5,6,2,4,1]=>4 [3,5,6,4,1,2]=>2 [3,5,6,4,2,1]=>2 [3,6,1,2,4,5]=>2 [3,6,1,2,5,4]=>2 [3,6,1,4,2,5]=>2 [3,6,1,4,5,2]=>1 [3,6,1,5,2,4]=>2 [3,6,1,5,4,2]=>1 [3,6,2,1,4,5]=>2 [3,6,2,1,5,4]=>2 [3,6,2,4,1,5]=>2 [3,6,2,4,5,1]=>2 [3,6,2,5,1,4]=>2 [3,6,2,5,4,1]=>2 [3,6,4,1,2,5]=>4 [3,6,4,1,5,2]=>2 [3,6,4,2,1,5]=>2 [3,6,4,2,5,1]=>2 [3,6,4,5,1,2]=>2 [3,6,4,5,2,1]=>2 [3,6,5,1,2,4]=>2 [3,6,5,1,4,2]=>2 [3,6,5,2,1,4]=>4 [3,6,5,2,4,1]=>2 [3,6,5,4,1,2]=>2 [3,6,5,4,2,1]=>2 [4,1,2,3,5,6]=>2 [4,1,2,3,6,5]=>2 [4,1,2,5,3,6]=>2 [4,1,2,5,6,3]=>2 [4,1,2,6,3,5]=>2 [4,1,2,6,5,3]=>2 [4,1,3,2,5,6]=>2 [4,1,3,2,6,5]=>2 [4,1,3,5,2,6]=>2 [4,1,3,5,6,2]=>2 [4,1,3,6,2,5]=>2 [4,1,3,6,5,2]=>2 [4,1,5,2,3,6]=>2 [4,1,5,2,6,3]=>4 [4,1,5,3,2,6]=>2 [4,1,5,3,6,2]=>2 [4,1,5,6,2,3]=>2 [4,1,5,6,3,2]=>2 [4,1,6,2,3,5]=>4 [4,1,6,2,5,3]=>2 [4,1,6,3,2,5]=>2 [4,1,6,3,5,2]=>2 [4,1,6,5,2,3]=>2 [4,1,6,5,3,2]=>2 [4,2,1,3,5,6]=>2 [4,2,1,3,6,5]=>2 [4,2,1,5,3,6]=>2 [4,2,1,5,6,3]=>2 [4,2,1,6,3,5]=>2 [4,2,1,6,5,3]=>2 [4,2,3,1,5,6]=>1 [4,2,3,1,6,5]=>1 [4,2,3,5,1,6]=>2 [4,2,3,5,6,1]=>2 [4,2,3,6,1,5]=>2 [4,2,3,6,5,1]=>2 [4,2,5,1,3,6]=>1 [4,2,5,1,6,3]=>2 [4,2,5,3,1,6]=>2 [4,2,5,3,6,1]=>2 [4,2,5,6,1,3]=>2 [4,2,5,6,3,1]=>2 [4,2,6,1,3,5]=>2 [4,2,6,1,5,3]=>1 [4,2,6,3,1,5]=>2 [4,2,6,3,5,1]=>2 [4,2,6,5,1,3]=>2 [4,2,6,5,3,1]=>2 [4,3,1,2,5,6]=>2 [4,3,1,2,6,5]=>2 [4,3,1,5,2,6]=>2 [4,3,1,5,6,2]=>2 [4,3,1,6,2,5]=>2 [4,3,1,6,5,2]=>2 [4,3,2,1,5,6]=>1 [4,3,2,1,6,5]=>1 [4,3,2,5,1,6]=>2 [4,3,2,5,6,1]=>2 [4,3,2,6,1,5]=>2 [4,3,2,6,5,1]=>2 [4,3,5,1,2,6]=>2 [4,3,5,1,6,2]=>2 [4,3,5,2,1,6]=>2 [4,3,5,2,6,1]=>2 [4,3,5,6,1,2]=>2 [4,3,5,6,2,1]=>4 [4,3,6,1,2,5]=>2 [4,3,6,1,5,2]=>2 [4,3,6,2,1,5]=>2 [4,3,6,2,5,1]=>2 [4,3,6,5,1,2]=>4 [4,3,6,5,2,1]=>2 [4,5,1,2,3,6]=>2 [4,5,1,2,6,3]=>2 [4,5,1,3,2,6]=>2 [4,5,1,3,6,2]=>4 [4,5,1,6,2,3]=>2 [4,5,1,6,3,2]=>2 [4,5,2,1,3,6]=>2 [4,5,2,1,6,3]=>2 [4,5,2,3,1,6]=>2 [4,5,2,3,6,1]=>2 [4,5,2,6,1,3]=>2 [4,5,2,6,3,1]=>4 [4,5,3,1,2,6]=>1 [4,5,3,1,6,2]=>2 [4,5,3,2,1,6]=>2 [4,5,3,2,6,1]=>2 [4,5,3,6,1,2]=>2 [4,5,3,6,2,1]=>2 [4,5,6,1,2,3]=>1 [4,5,6,1,3,2]=>2 [4,5,6,2,1,3]=>2 [4,5,6,2,3,1]=>2 [4,5,6,3,1,2]=>2 [4,5,6,3,2,1]=>2 [4,6,1,2,3,5]=>2 [4,6,1,2,5,3]=>2 [4,6,1,3,2,5]=>4 [4,6,1,3,5,2]=>2 [4,6,1,5,2,3]=>2 [4,6,1,5,3,2]=>2 [4,6,2,1,3,5]=>2 [4,6,2,1,5,3]=>2 [4,6,2,3,1,5]=>2 [4,6,2,3,5,1]=>2 [4,6,2,5,1,3]=>4 [4,6,2,5,3,1]=>2 [4,6,3,1,2,5]=>2 [4,6,3,1,5,2]=>1 [4,6,3,2,1,5]=>2 [4,6,3,2,5,1]=>2 [4,6,3,5,1,2]=>2 [4,6,3,5,2,1]=>2 [4,6,5,1,2,3]=>2 [4,6,5,1,3,2]=>1 [4,6,5,2,1,3]=>2 [4,6,5,2,3,1]=>2 [4,6,5,3,1,2]=>2 [4,6,5,3,2,1]=>2 [5,1,2,3,4,6]=>2 [5,1,2,3,6,4]=>2 [5,1,2,4,3,6]=>2 [5,1,2,4,6,3]=>2 [5,1,2,6,3,4]=>2 [5,1,2,6,4,3]=>2 [5,1,3,2,4,6]=>2 [5,1,3,2,6,4]=>2 [5,1,3,4,2,6]=>2 [5,1,3,4,6,2]=>2 [5,1,3,6,2,4]=>2 [5,1,3,6,4,2]=>2 [5,1,4,2,3,6]=>2 [5,1,4,2,6,3]=>2 [5,1,4,3,2,6]=>2 [5,1,4,3,6,2]=>2 [5,1,4,6,2,3]=>4 [5,1,4,6,3,2]=>2 [5,1,6,2,3,4]=>2 [5,1,6,2,4,3]=>2 [5,1,6,3,2,4]=>4 [5,1,6,3,4,2]=>2 [5,1,6,4,2,3]=>2 [5,1,6,4,3,2]=>2 [5,2,1,3,4,6]=>2 [5,2,1,3,6,4]=>2 [5,2,1,4,3,6]=>2 [5,2,1,4,6,3]=>2 [5,2,1,6,3,4]=>2 [5,2,1,6,4,3]=>2 [5,2,3,1,4,6]=>2 [5,2,3,1,6,4]=>2 [5,2,3,4,1,6]=>1 [5,2,3,4,6,1]=>2 [5,2,3,6,1,4]=>1 [5,2,3,6,4,1]=>2 [5,2,4,1,3,6]=>2 [5,2,4,1,6,3]=>2 [5,2,4,3,1,6]=>1 [5,2,4,3,6,1]=>2 [5,2,4,6,1,3]=>2 [5,2,4,6,3,1]=>2 [5,2,6,1,3,4]=>2 [5,2,6,1,4,3]=>2 [5,2,6,3,1,4]=>2 [5,2,6,3,4,1]=>2 [5,2,6,4,1,3]=>1 [5,2,6,4,3,1]=>2 [5,3,1,2,4,6]=>2 [5,3,1,2,6,4]=>2 [5,3,1,4,2,6]=>2 [5,3,1,4,6,2]=>2 [5,3,1,6,2,4]=>2 [5,3,1,6,4,2]=>2 [5,3,2,1,4,6]=>2 [5,3,2,1,6,4]=>2 [5,3,2,4,1,6]=>1 [5,3,2,4,6,1]=>2 [5,3,2,6,1,4]=>1 [5,3,2,6,4,1]=>2 [5,3,4,1,2,6]=>2 [5,3,4,1,6,2]=>2 [5,3,4,2,1,6]=>2 [5,3,4,2,6,1]=>4 [5,3,4,6,1,2]=>2 [5,3,4,6,2,1]=>2 [5,3,6,1,2,4]=>2 [5,3,6,1,4,2]=>4 [5,3,6,2,1,4]=>2 [5,3,6,2,4,1]=>2 [5,3,6,4,1,2]=>2 [5,3,6,4,2,1]=>2 [5,4,1,2,3,6]=>2 [5,4,1,2,6,3]=>2 [5,4,1,3,2,6]=>2 [5,4,1,3,6,2]=>2 [5,4,1,6,2,3]=>2 [5,4,1,6,3,2]=>4 [5,4,2,1,3,6]=>2 [5,4,2,1,6,3]=>2 [5,4,2,3,1,6]=>2 [5,4,2,3,6,1]=>4 [5,4,2,6,1,3]=>2 [5,4,2,6,3,1]=>2 [5,4,3,1,2,6]=>2 [5,4,3,1,6,2]=>2 [5,4,3,2,1,6]=>1 [5,4,3,2,6,1]=>2 [5,4,3,6,1,2]=>2 [5,4,3,6,2,1]=>2 [5,4,6,1,2,3]=>2 [5,4,6,1,3,2]=>2 [5,4,6,2,1,3]=>1 [5,4,6,2,3,1]=>2 [5,4,6,3,1,2]=>2 [5,4,6,3,2,1]=>2 [5,6,1,2,3,4]=>4 [5,6,1,2,4,3]=>2 [5,6,1,3,2,4]=>2 [5,6,1,3,4,2]=>2 [5,6,1,4,2,3]=>2 [5,6,1,4,3,2]=>2 [5,6,2,1,3,4]=>2 [5,6,2,1,4,3]=>4 [5,6,2,3,1,4]=>2 [5,6,2,3,4,1]=>2 [5,6,2,4,1,3]=>2 [5,6,2,4,3,1]=>2 [5,6,3,1,2,4]=>2 [5,6,3,1,4,2]=>2 [5,6,3,2,1,4]=>2 [5,6,3,2,4,1]=>2 [5,6,3,4,1,2]=>1 [5,6,3,4,2,1]=>2 [5,6,4,1,2,3]=>2 [5,6,4,1,3,2]=>2 [5,6,4,2,1,3]=>2 [5,6,4,2,3,1]=>2 [5,6,4,3,1,2]=>1 [5,6,4,3,2,1]=>2 [6,1,2,3,4,5]=>2 [6,1,2,3,5,4]=>2 [6,1,2,4,3,5]=>2 [6,1,2,4,5,3]=>2 [6,1,2,5,3,4]=>2 [6,1,2,5,4,3]=>2 [6,1,3,2,4,5]=>2 [6,1,3,2,5,4]=>2 [6,1,3,4,2,5]=>2 [6,1,3,4,5,2]=>2 [6,1,3,5,2,4]=>2 [6,1,3,5,4,2]=>2 [6,1,4,2,3,5]=>2 [6,1,4,2,5,3]=>2 [6,1,4,3,2,5]=>2 [6,1,4,3,5,2]=>2 [6,1,4,5,2,3]=>2 [6,1,4,5,3,2]=>4 [6,1,5,2,3,4]=>2 [6,1,5,2,4,3]=>2 [6,1,5,3,2,4]=>2 [6,1,5,3,4,2]=>4 [6,1,5,4,2,3]=>2 [6,1,5,4,3,2]=>2 [6,2,1,3,4,5]=>2 [6,2,1,3,5,4]=>2 [6,2,1,4,3,5]=>2 [6,2,1,4,5,3]=>2 [6,2,1,5,3,4]=>2 [6,2,1,5,4,3]=>2 [6,2,3,1,4,5]=>2 [6,2,3,1,5,4]=>2 [6,2,3,4,1,5]=>2 [6,2,3,4,5,1]=>1 [6,2,3,5,1,4]=>2 [6,2,3,5,4,1]=>1 [6,2,4,1,3,5]=>2 [6,2,4,1,5,3]=>2 [6,2,4,3,1,5]=>2 [6,2,4,3,5,1]=>1 [6,2,4,5,1,3]=>2 [6,2,4,5,3,1]=>2 [6,2,5,1,3,4]=>2 [6,2,5,1,4,3]=>2 [6,2,5,3,1,4]=>2 [6,2,5,3,4,1]=>2 [6,2,5,4,1,3]=>2 [6,2,5,4,3,1]=>1 [6,3,1,2,4,5]=>2 [6,3,1,2,5,4]=>2 [6,3,1,4,2,5]=>2 [6,3,1,4,5,2]=>2 [6,3,1,5,2,4]=>2 [6,3,1,5,4,2]=>2 [6,3,2,1,4,5]=>2 [6,3,2,1,5,4]=>2 [6,3,2,4,1,5]=>2 [6,3,2,4,5,1]=>1 [6,3,2,5,1,4]=>2 [6,3,2,5,4,1]=>1 [6,3,4,1,2,5]=>2 [6,3,4,1,5,2]=>2 [6,3,4,2,1,5]=>4 [6,3,4,2,5,1]=>2 [6,3,4,5,1,2]=>2 [6,3,4,5,2,1]=>2 [6,3,5,1,2,4]=>4 [6,3,5,1,4,2]=>2 [6,3,5,2,1,4]=>2 [6,3,5,2,4,1]=>2 [6,3,5,4,1,2]=>2 [6,3,5,4,2,1]=>2 [6,4,1,2,3,5]=>2 [6,4,1,2,5,3]=>2 [6,4,1,3,2,5]=>2 [6,4,1,3,5,2]=>2 [6,4,1,5,2,3]=>4 [6,4,1,5,3,2]=>2 [6,4,2,1,3,5]=>2 [6,4,2,1,5,3]=>2 [6,4,2,3,1,5]=>4 [6,4,2,3,5,1]=>2 [6,4,2,5,1,3]=>2 [6,4,2,5,3,1]=>2 [6,4,3,1,2,5]=>2 [6,4,3,1,5,2]=>2 [6,4,3,2,1,5]=>2 [6,4,3,2,5,1]=>1 [6,4,3,5,1,2]=>2 [6,4,3,5,2,1]=>2 [6,4,5,1,2,3]=>2 [6,4,5,1,3,2]=>2 [6,4,5,2,1,3]=>2 [6,4,5,2,3,1]=>1 [6,4,5,3,1,2]=>2 [6,4,5,3,2,1]=>2 [6,5,1,2,3,4]=>2 [6,5,1,2,4,3]=>4 [6,5,1,3,2,4]=>2 [6,5,1,3,4,2]=>2 [6,5,1,4,2,3]=>2 [6,5,1,4,3,2]=>2 [6,5,2,1,3,4]=>4 [6,5,2,1,4,3]=>2 [6,5,2,3,1,4]=>2 [6,5,2,3,4,1]=>2 [6,5,2,4,1,3]=>2 [6,5,2,4,3,1]=>2 [6,5,3,1,2,4]=>2 [6,5,3,1,4,2]=>2 [6,5,3,2,1,4]=>2 [6,5,3,2,4,1]=>2 [6,5,3,4,1,2]=>2 [6,5,3,4,2,1]=>1 [6,5,4,1,2,3]=>2 [6,5,4,1,3,2]=>2 [6,5,4,2,1,3]=>2 [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]=>1 [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]=>1 [1,2,3,5,6,4,7]=>2 [1,2,3,5,6,7,4]=>2 [1,2,3,5,7,4,6]=>2 [1,2,3,5,7,6,4]=>2 [1,2,3,6,4,5,7]=>2 [1,2,3,6,4,7,5]=>2 [1,2,3,6,5,4,7]=>1 [1,2,3,6,5,7,4]=>2 [1,2,3,6,7,4,5]=>1 [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]=>1 [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]=>1 [1,2,4,3,6,5,7]=>1 [1,2,4,3,6,7,5]=>2 [1,2,4,3,7,5,6]=>2 [1,2,4,3,7,6,5]=>1 [1,2,4,5,3,6,7]=>2 [1,2,4,5,3,7,6]=>2 [1,2,4,5,6,3,7]=>2 [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]=>2 [1,2,4,6,3,7,5]=>2 [1,2,4,6,5,3,7]=>2 [1,2,4,6,5,7,3]=>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 [1,2,4,7,3,6,5]=>2 [1,2,4,7,5,3,6]=>2 [1,2,4,7,5,6,3]=>2 [1,2,4,7,6,3,5]=>2 [1,2,4,7,6,5,3]=>2 [1,2,5,3,4,6,7]=>2 [1,2,5,3,4,7,6]=>2 [1,2,5,3,6,4,7]=>2 [1,2,5,3,6,7,4]=>2 [1,2,5,3,7,4,6]=>2 [1,2,5,3,7,6,4]=>2 [1,2,5,4,3,6,7]=>1 [1,2,5,4,3,7,6]=>1 [1,2,5,4,6,3,7]=>2 [1,2,5,4,6,7,3]=>2 [1,2,5,4,7,3,6]=>2 [1,2,5,4,7,6,3]=>2 [1,2,5,6,3,4,7]=>1 [1,2,5,6,3,7,4]=>2 [1,2,5,6,4,3,7]=>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]=>1 [1,2,5,7,4,3,6]=>2 [1,2,5,7,4,6,3]=>2 [1,2,5,7,6,3,4]=>2 [1,2,5,7,6,4,3]=>2 [1,2,6,3,4,5,7]=>2 [1,2,6,3,4,7,5]=>2 [1,2,6,3,5,4,7]=>2 [1,2,6,3,5,7,4]=>2 [1,2,6,3,7,4,5]=>2 [1,2,6,3,7,5,4]=>2 [1,2,6,4,3,5,7]=>2 [1,2,6,4,3,7,5]=>2 [1,2,6,4,5,3,7]=>1 [1,2,6,4,5,7,3]=>2 [1,2,6,4,7,3,5]=>1 [1,2,6,4,7,5,3]=>2 [1,2,6,5,3,4,7]=>2 [1,2,6,5,3,7,4]=>2 [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]=>2 [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]=>2 [1,2,6,7,5,3,4]=>1 [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]=>1 [1,2,7,4,6,3,5]=>2 [1,2,7,4,6,5,3]=>1 [1,2,7,5,3,4,6]=>2 [1,2,7,5,3,6,4]=>2 [1,2,7,5,4,3,6]=>2 [1,2,7,5,4,6,3]=>1 [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]=>1 [1,3,2,4,5,6,7]=>1 [1,3,2,4,5,7,6]=>1 [1,3,2,4,6,5,7]=>1 [1,3,2,4,6,7,5]=>2 [1,3,2,4,7,5,6]=>2 [1,3,2,4,7,6,5]=>1 [1,3,2,5,4,6,7]=>1 [1,3,2,5,4,7,6]=>1 [1,3,2,5,6,4,7]=>2 [1,3,2,5,6,7,4]=>2 [1,3,2,5,7,4,6]=>2 [1,3,2,5,7,6,4]=>2 [1,3,2,6,4,5,7]=>2 [1,3,2,6,4,7,5]=>2 [1,3,2,6,5,4,7]=>1 [1,3,2,6,5,7,4]=>2 [1,3,2,6,7,4,5]=>1 [1,3,2,6,7,5,4]=>2 [1,3,2,7,4,5,6]=>2 [1,3,2,7,4,6,5]=>2 [1,3,2,7,5,4,6]=>2 [1,3,2,7,5,6,4]=>1 [1,3,2,7,6,4,5]=>2 [1,3,2,7,6,5,4]=>1 [1,3,4,2,5,6,7]=>2 [1,3,4,2,5,7,6]=>2 [1,3,4,2,6,5,7]=>2 [1,3,4,2,6,7,5]=>4 [1,3,4,2,7,5,6]=>4 [1,3,4,2,7,6,5]=>2 [1,3,4,5,2,6,7]=>2 [1,3,4,5,2,7,6]=>2 [1,3,4,5,6,2,7]=>2 [1,3,4,5,6,7,2]=>2 [1,3,4,5,7,2,6]=>2 [1,3,4,5,7,6,2]=>2 [1,3,4,6,2,5,7]=>2 [1,3,4,6,2,7,5]=>2 [1,3,4,6,5,2,7]=>2 [1,3,4,6,5,7,2]=>2 [1,3,4,6,7,2,5]=>2 [1,3,4,6,7,5,2]=>2 [1,3,4,7,2,5,6]=>2 [1,3,4,7,2,6,5]=>2 [1,3,4,7,5,2,6]=>2 [1,3,4,7,5,6,2]=>2 [1,3,4,7,6,2,5]=>2 [1,3,4,7,6,5,2]=>2 [1,3,5,2,4,6,7]=>2 [1,3,5,2,4,7,6]=>2 [1,3,5,2,6,4,7]=>2 [1,3,5,2,6,7,4]=>2 [1,3,5,2,7,4,6]=>2 [1,3,5,2,7,6,4]=>2 [1,3,5,4,2,6,7]=>2 [1,3,5,4,2,7,6]=>2 [1,3,5,4,6,2,7]=>2 [1,3,5,4,6,7,2]=>2 [1,3,5,4,7,2,6]=>2 [1,3,5,4,7,6,2]=>2 [1,3,5,6,2,4,7]=>2 [1,3,5,6,2,7,4]=>4 [1,3,5,6,4,2,7]=>2 [1,3,5,6,4,7,2]=>2 [1,3,5,6,7,2,4]=>2 [1,3,5,6,7,4,2]=>2 [1,3,5,7,2,4,6]=>4 [1,3,5,7,2,6,4]=>2 [1,3,5,7,4,2,6]=>2 [1,3,5,7,4,6,2]=>2 [1,3,5,7,6,2,4]=>2 [1,3,5,7,6,4,2]=>2 [1,3,6,2,4,5,7]=>2 [1,3,6,2,4,7,5]=>2 [1,3,6,2,5,4,7]=>2 [1,3,6,2,5,7,4]=>2 [1,3,6,2,7,4,5]=>2 [1,3,6,2,7,5,4]=>2 [1,3,6,4,2,5,7]=>2 [1,3,6,4,2,7,5]=>2 [1,3,6,4,5,2,7]=>2 [1,3,6,4,5,7,2]=>2 [1,3,6,4,7,2,5]=>2 [1,3,6,4,7,5,2]=>2 [1,3,6,5,2,4,7]=>2 [1,3,6,5,2,7,4]=>2 [1,3,6,5,4,2,7]=>2 [1,3,6,5,4,7,2]=>2 [1,3,6,5,7,2,4]=>4 [1,3,6,5,7,4,2]=>2 [1,3,6,7,2,4,5]=>2 [1,3,6,7,2,5,4]=>2 [1,3,6,7,4,2,5]=>4 [1,3,6,7,4,5,2]=>2 [1,3,6,7,5,2,4]=>2 [1,3,6,7,5,4,2]=>2 [1,3,7,2,4,5,6]=>2 [1,3,7,2,4,6,5]=>2 [1,3,7,2,5,4,6]=>2 [1,3,7,2,5,6,4]=>2 [1,3,7,2,6,4,5]=>2 [1,3,7,2,6,5,4]=>2 [1,3,7,4,2,5,6]=>2 [1,3,7,4,2,6,5]=>2 [1,3,7,4,5,2,6]=>2 [1,3,7,4,5,6,2]=>2 [1,3,7,4,6,2,5]=>2 [1,3,7,4,6,5,2]=>2 [1,3,7,5,2,4,6]=>2 [1,3,7,5,2,6,4]=>2 [1,3,7,5,4,2,6]=>2 [1,3,7,5,4,6,2]=>2 [1,3,7,5,6,2,4]=>2 [1,3,7,5,6,4,2]=>4 [1,3,7,6,2,4,5]=>2 [1,3,7,6,2,5,4]=>2 [1,3,7,6,4,2,5]=>2 [1,3,7,6,4,5,2]=>4 [1,3,7,6,5,2,4]=>2 [1,3,7,6,5,4,2]=>2 [1,4,2,3,5,6,7]=>2 [1,4,2,3,5,7,6]=>2 [1,4,2,3,6,5,7]=>2 [1,4,2,3,6,7,5]=>4 [1,4,2,3,7,5,6]=>4 [1,4,2,3,7,6,5]=>2 [1,4,2,5,3,6,7]=>2 [1,4,2,5,3,7,6]=>2 [1,4,2,5,6,3,7]=>2 [1,4,2,5,6,7,3]=>2 [1,4,2,5,7,3,6]=>2 [1,4,2,5,7,6,3]=>2 [1,4,2,6,3,5,7]=>2 [1,4,2,6,3,7,5]=>2 [1,4,2,6,5,3,7]=>2 [1,4,2,6,5,7,3]=>2 [1,4,2,6,7,3,5]=>2 [1,4,2,6,7,5,3]=>2 [1,4,2,7,3,5,6]=>2 [1,4,2,7,3,6,5]=>2 [1,4,2,7,5,3,6]=>2 [1,4,2,7,5,6,3]=>2 [1,4,2,7,6,3,5]=>2 [1,4,2,7,6,5,3]=>2 [1,4,3,2,5,6,7]=>1 [1,4,3,2,5,7,6]=>1 [1,4,3,2,6,5,7]=>1 [1,4,3,2,6,7,5]=>2 [1,4,3,2,7,5,6]=>2 [1,4,3,2,7,6,5]=>1 [1,4,3,5,2,6,7]=>2 [1,4,3,5,2,7,6]=>2 [1,4,3,5,6,2,7]=>2 [1,4,3,5,6,7,2]=>2 [1,4,3,5,7,2,6]=>2 [1,4,3,5,7,6,2]=>2 [1,4,3,6,2,5,7]=>2 [1,4,3,6,2,7,5]=>2 [1,4,3,6,5,2,7]=>2 [1,4,3,6,5,7,2]=>2 [1,4,3,6,7,2,5]=>2 [1,4,3,6,7,5,2]=>2 [1,4,3,7,2,5,6]=>2 [1,4,3,7,2,6,5]=>2 [1,4,3,7,5,2,6]=>2 [1,4,3,7,5,6,2]=>2 [1,4,3,7,6,2,5]=>2 [1,4,3,7,6,5,2]=>2 [1,4,5,2,3,6,7]=>1 [1,4,5,2,3,7,6]=>1 [1,4,5,2,6,3,7]=>2 [1,4,5,2,6,7,3]=>2 [1,4,5,2,7,3,6]=>2 [1,4,5,2,7,6,3]=>2 [1,4,5,3,2,6,7]=>2 [1,4,5,3,2,7,6]=>2 [1,4,5,3,6,2,7]=>2 [1,4,5,3,6,7,2]=>2 [1,4,5,3,7,2,6]=>2 [1,4,5,3,7,6,2]=>2 [1,4,5,6,2,3,7]=>2 [1,4,5,6,2,7,3]=>2 [1,4,5,6,3,2,7]=>2 [1,4,5,6,3,7,2]=>2 [1,4,5,6,7,2,3]=>4 [1,4,5,6,7,3,2]=>2 [1,4,5,7,2,3,6]=>2 [1,4,5,7,2,6,3]=>2 [1,4,5,7,3,2,6]=>2 [1,4,5,7,3,6,2]=>2 [1,4,5,7,6,2,3]=>2 [1,4,5,7,6,3,2]=>4 [1,4,6,2,3,5,7]=>2 [1,4,6,2,3,7,5]=>2 [1,4,6,2,5,3,7]=>1 [1,4,6,2,5,7,3]=>2 [1,4,6,2,7,3,5]=>1 [1,4,6,2,7,5,3]=>2 [1,4,6,3,2,5,7]=>2 [1,4,6,3,2,7,5]=>2 [1,4,6,3,5,2,7]=>2 [1,4,6,3,5,7,2]=>2 [1,4,6,3,7,2,5]=>2 [1,4,6,3,7,5,2]=>2 [1,4,6,5,2,3,7]=>2 [1,4,6,5,2,7,3]=>4 [1,4,6,5,3,2,7]=>2
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Description
The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles.
In other words, this is $2^k$ where $k$ is the number of cycles of length at least three (St000486The number of cycles of length at least 3 of a permutation.) in its cycle decomposition.
The generating function for the number of equivalence classes, $f(n)$, is
$$\sum_{n\geq 0} f(n)\frac{x^n}{n!} = \frac{e(\frac{x}{2} + \frac{x^2}{4})}{\sqrt{1-x}}.$$
References
[1] Zwick, D. Equivalence class of permutations based on cycle decomposition and their inverses MathOverflow:324510
[2] Example 5.2.9. and Exercise 5.18. Stanley, R. P. Enumerative combinatorics. Vol. 2 MathSciNet:1676282
Code
def statistic(sigma):
    return 2^sum(1 for c in sigma.cycle_tuples() if len(c) > 2)
Created
Mar 03, 2019 at 17:09 by Christian Stump
Updated
Mar 03, 2019 at 17:09 by Christian Stump