edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [1,2]=>0 [2,1]=>0 [1,2,3]=>0 [1,3,2]=>0 [2,1,3]=>0 [2,3,1]=>0 [3,1,2]=>0 [3,2,1]=>0 [1,2,3,4]=>0 [1,2,4,3]=>0 [1,3,2,4]=>0 [1,3,4,2]=>0 [1,4,2,3]=>0 [1,4,3,2]=>0 [2,1,3,4]=>0 [2,1,4,3]=>2 [2,3,1,4]=>0 [2,3,4,1]=>0 [2,4,1,3]=>1 [2,4,3,1]=>0 [3,1,2,4]=>0 [3,1,4,2]=>1 [3,2,1,4]=>0 [3,2,4,1]=>0 [3,4,1,2]=>0 [3,4,2,1]=>1 [4,1,2,3]=>0 [4,1,3,2]=>0 [4,2,1,3]=>0 [4,2,3,1]=>0 [4,3,1,2]=>1 [4,3,2,1]=>2 [1,2,3,4,5]=>0 [1,2,3,5,4]=>0 [1,2,4,3,5]=>0 [1,2,4,5,3]=>0 [1,2,5,3,4]=>0 [1,2,5,4,3]=>0 [1,3,2,4,5]=>0 [1,3,2,5,4]=>2 [1,3,4,2,5]=>0 [1,3,4,5,2]=>0 [1,3,5,2,4]=>1 [1,3,5,4,2]=>0 [1,4,2,3,5]=>0 [1,4,2,5,3]=>1 [1,4,3,2,5]=>0 [1,4,3,5,2]=>0 [1,4,5,2,3]=>0 [1,4,5,3,2]=>1 [1,5,2,3,4]=>0 [1,5,2,4,3]=>0 [1,5,3,2,4]=>0 [1,5,3,4,2]=>0 [1,5,4,2,3]=>1 [1,5,4,3,2]=>2 [2,1,3,4,5]=>0 [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]=>0 [2,3,1,5,4]=>3 [2,3,4,1,5]=>0 [2,3,4,5,1]=>0 [2,3,5,1,4]=>2 [2,3,5,4,1]=>0 [2,4,1,3,5]=>1 [2,4,1,5,3]=>2 [2,4,3,1,5]=>0 [2,4,3,5,1]=>0 [2,4,5,1,3]=>1 [2,4,5,3,1]=>2 [2,5,1,3,4]=>2 [2,5,1,4,3]=>1 [2,5,3,1,4]=>1 [2,5,3,4,1]=>0 [2,5,4,1,3]=>2 [2,5,4,3,1]=>3 [3,1,2,4,5]=>0 [3,1,2,5,4]=>3 [3,1,4,2,5]=>1 [3,1,4,5,2]=>2 [3,1,5,2,4]=>2 [3,1,5,4,2]=>1 [3,2,1,4,5]=>0 [3,2,1,5,4]=>2 [3,2,4,1,5]=>0 [3,2,4,5,1]=>0 [3,2,5,1,4]=>1 [3,2,5,4,1]=>0 [3,4,1,2,5]=>0 [3,4,1,5,2]=>1 [3,4,2,1,5]=>1 [3,4,2,5,1]=>2 [3,4,5,1,2]=>0 [3,4,5,2,1]=>1 [3,5,1,2,4]=>1 [3,5,1,4,2]=>0 [3,5,2,1,4]=>2 [3,5,2,4,1]=>1 [3,5,4,1,2]=>1 [3,5,4,2,1]=>2 [4,1,2,3,5]=>0 [4,1,2,5,3]=>2 [4,1,3,2,5]=>0 [4,1,3,5,2]=>1 [4,1,5,2,3]=>1 [4,1,5,3,2]=>2 [4,2,1,3,5]=>0 [4,2,1,5,3]=>1 [4,2,3,1,5]=>0 [4,2,3,5,1]=>0 [4,2,5,1,3]=>0 [4,2,5,3,1]=>1 [4,3,1,2,5]=>1 [4,3,1,5,2]=>2 [4,3,2,1,5]=>2 [4,3,2,5,1]=>3 [4,3,5,1,2]=>1 [4,3,5,2,1]=>2 [4,5,1,2,3]=>0 [4,5,1,3,2]=>1 [4,5,2,1,3]=>1 [4,5,2,3,1]=>2 [4,5,3,1,2]=>0 [4,5,3,2,1]=>1 [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]=>2 [5,1,4,3,2]=>3 [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]=>1 [5,2,4,3,1]=>2 [5,3,1,2,4]=>2 [5,3,1,4,2]=>1 [5,3,2,1,4]=>3 [5,3,2,4,1]=>2 [5,3,4,1,2]=>2 [5,3,4,2,1]=>3 [5,4,1,2,3]=>1 [5,4,1,3,2]=>2 [5,4,2,1,3]=>2 [5,4,2,3,1]=>3 [5,4,3,1,2]=>1 [5,4,3,2,1]=>2 [1,2,3,4,5,6]=>0 [1,2,3,4,6,5]=>0 [1,2,3,5,4,6]=>0 [1,2,3,5,6,4]=>0 [1,2,3,6,4,5]=>0 [1,2,3,6,5,4]=>0 [1,2,4,3,5,6]=>0 [1,2,4,3,6,5]=>2 [1,2,4,5,3,6]=>0 [1,2,4,5,6,3]=>0 [1,2,4,6,3,5]=>1 [1,2,4,6,5,3]=>0 [1,2,5,3,4,6]=>0 [1,2,5,3,6,4]=>1 [1,2,5,4,3,6]=>0 [1,2,5,4,6,3]=>0 [1,2,5,6,3,4]=>0 [1,2,5,6,4,3]=>1 [1,2,6,3,4,5]=>0 [1,2,6,3,5,4]=>0 [1,2,6,4,3,5]=>0 [1,2,6,4,5,3]=>0 [1,2,6,5,3,4]=>1 [1,2,6,5,4,3]=>2 [1,3,2,4,5,6]=>0 [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]=>0 [1,3,4,2,6,5]=>3 [1,3,4,5,2,6]=>0 [1,3,4,5,6,2]=>0 [1,3,4,6,2,5]=>2 [1,3,4,6,5,2]=>0 [1,3,5,2,4,6]=>1 [1,3,5,2,6,4]=>2 [1,3,5,4,2,6]=>0 [1,3,5,4,6,2]=>0 [1,3,5,6,2,4]=>1 [1,3,5,6,4,2]=>2 [1,3,6,2,4,5]=>2 [1,3,6,2,5,4]=>1 [1,3,6,4,2,5]=>1 [1,3,6,4,5,2]=>0 [1,3,6,5,2,4]=>2 [1,3,6,5,4,2]=>3 [1,4,2,3,5,6]=>0 [1,4,2,3,6,5]=>3 [1,4,2,5,3,6]=>1 [1,4,2,5,6,3]=>2 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>1 [1,4,3,2,5,6]=>0 [1,4,3,2,6,5]=>2 [1,4,3,5,2,6]=>0 [1,4,3,5,6,2]=>0 [1,4,3,6,2,5]=>1 [1,4,3,6,5,2]=>0 [1,4,5,2,3,6]=>0 [1,4,5,2,6,3]=>1 [1,4,5,3,2,6]=>1 [1,4,5,3,6,2]=>2 [1,4,5,6,2,3]=>0 [1,4,5,6,3,2]=>1 [1,4,6,2,3,5]=>1 [1,4,6,2,5,3]=>0 [1,4,6,3,2,5]=>2 [1,4,6,3,5,2]=>1 [1,4,6,5,2,3]=>1 [1,4,6,5,3,2]=>2 [1,5,2,3,4,6]=>0 [1,5,2,3,6,4]=>2 [1,5,2,4,3,6]=>0 [1,5,2,4,6,3]=>1 [1,5,2,6,3,4]=>1 [1,5,2,6,4,3]=>2 [1,5,3,2,4,6]=>0 [1,5,3,2,6,4]=>1 [1,5,3,4,2,6]=>0 [1,5,3,4,6,2]=>0 [1,5,3,6,2,4]=>0 [1,5,3,6,4,2]=>1 [1,5,4,2,3,6]=>1 [1,5,4,2,6,3]=>2 [1,5,4,3,2,6]=>2 [1,5,4,3,6,2]=>3 [1,5,4,6,2,3]=>1 [1,5,4,6,3,2]=>2 [1,5,6,2,3,4]=>0 [1,5,6,2,4,3]=>1 [1,5,6,3,2,4]=>1 [1,5,6,3,4,2]=>2 [1,5,6,4,2,3]=>0 [1,5,6,4,3,2]=>1 [1,6,2,3,4,5]=>0 [1,6,2,3,5,4]=>0 [1,6,2,4,3,5]=>0 [1,6,2,4,5,3]=>0 [1,6,2,5,3,4]=>2 [1,6,2,5,4,3]=>3 [1,6,3,2,4,5]=>0 [1,6,3,2,5,4]=>0 [1,6,3,4,2,5]=>0 [1,6,3,4,5,2]=>0 [1,6,3,5,2,4]=>1 [1,6,3,5,4,2]=>2 [1,6,4,2,3,5]=>2 [1,6,4,2,5,3]=>1 [1,6,4,3,2,5]=>3 [1,6,4,3,5,2]=>2 [1,6,4,5,2,3]=>2 [1,6,4,5,3,2]=>3 [1,6,5,2,3,4]=>1 [1,6,5,2,4,3]=>2 [1,6,5,3,2,4]=>2 [1,6,5,3,4,2]=>3 [1,6,5,4,2,3]=>1 [1,6,5,4,3,2]=>2 [2,1,3,4,5,6]=>0 [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]=>6 [2,1,4,5,3,6]=>3 [2,1,4,5,6,3]=>4 [2,1,4,6,3,5]=>5 [2,1,4,6,5,3]=>3 [2,1,5,3,4,6]=>3 [2,1,5,3,6,4]=>5 [2,1,5,4,3,6]=>2 [2,1,5,4,6,3]=>3 [2,1,5,6,3,4]=>4 [2,1,5,6,4,3]=>5 [2,1,6,3,4,5]=>4 [2,1,6,3,5,4]=>3 [2,1,6,4,3,5]=>3 [2,1,6,4,5,3]=>2 [2,1,6,5,3,4]=>5 [2,1,6,5,4,3]=>6 [2,3,1,4,5,6]=>0 [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]=>5 [2,3,1,6,5,4]=>3 [2,3,4,1,5,6]=>0 [2,3,4,1,6,5]=>4 [2,3,4,5,1,6]=>0 [2,3,4,5,6,1]=>0 [2,3,4,6,1,5]=>3 [2,3,4,6,5,1]=>0 [2,3,5,1,4,6]=>2 [2,3,5,1,6,4]=>3 [2,3,5,4,1,6]=>0 [2,3,5,4,6,1]=>0 [2,3,5,6,1,4]=>2 [2,3,5,6,4,1]=>3 [2,3,6,1,4,5]=>4 [2,3,6,1,5,4]=>2 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>0 [2,3,6,5,1,4]=>3 [2,3,6,5,4,1]=>4 [2,4,1,3,5,6]=>1 [2,4,1,3,6,5]=>5 [2,4,1,5,3,6]=>2 [2,4,1,5,6,3]=>3 [2,4,1,6,3,5]=>4 [2,4,1,6,5,3]=>2 [2,4,3,1,5,6]=>0 [2,4,3,1,6,5]=>3 [2,4,3,5,1,6]=>0 [2,4,3,5,6,1]=>0 [2,4,3,6,1,5]=>2 [2,4,3,6,5,1]=>0 [2,4,5,1,3,6]=>1 [2,4,5,1,6,3]=>2 [2,4,5,3,1,6]=>2 [2,4,5,3,6,1]=>3 [2,4,5,6,1,3]=>1 [2,4,5,6,3,1]=>2 [2,4,6,1,3,5]=>3 [2,4,6,1,5,3]=>1 [2,4,6,3,1,5]=>4 [2,4,6,3,5,1]=>2 [2,4,6,5,1,3]=>2 [2,4,6,5,3,1]=>3 [2,5,1,3,4,6]=>2 [2,5,1,3,6,4]=>4 [2,5,1,4,3,6]=>1 [2,5,1,4,6,3]=>2 [2,5,1,6,3,4]=>3 [2,5,1,6,4,3]=>4 [2,5,3,1,4,6]=>1 [2,5,3,1,6,4]=>2 [2,5,3,4,1,6]=>0 [2,5,3,4,6,1]=>0 [2,5,3,6,1,4]=>1 [2,5,3,6,4,1]=>2 [2,5,4,1,3,6]=>2 [2,5,4,1,6,3]=>3 [2,5,4,3,1,6]=>3 [2,5,4,3,6,1]=>4 [2,5,4,6,1,3]=>2 [2,5,4,6,3,1]=>3 [2,5,6,1,3,4]=>2 [2,5,6,1,4,3]=>3 [2,5,6,3,1,4]=>3 [2,5,6,3,4,1]=>4 [2,5,6,4,1,3]=>1 [2,5,6,4,3,1]=>2 [2,6,1,3,4,5]=>3 [2,6,1,3,5,4]=>2 [2,6,1,4,3,5]=>2 [2,6,1,4,5,3]=>1 [2,6,1,5,3,4]=>4 [2,6,1,5,4,3]=>5 [2,6,3,1,4,5]=>2 [2,6,3,1,5,4]=>1 [2,6,3,4,1,5]=>1 [2,6,3,4,5,1]=>0 [2,6,3,5,1,4]=>2 [2,6,3,5,4,1]=>3 [2,6,4,1,3,5]=>4 [2,6,4,1,5,3]=>2 [2,6,4,3,1,5]=>5 [2,6,4,3,5,1]=>3 [2,6,4,5,1,3]=>3 [2,6,4,5,3,1]=>4 [2,6,5,1,3,4]=>3 [2,6,5,1,4,3]=>4 [2,6,5,3,1,4]=>4 [2,6,5,3,4,1]=>5 [2,6,5,4,1,3]=>2 [2,6,5,4,3,1]=>3 [3,1,2,4,5,6]=>0 [3,1,2,4,6,5]=>3 [3,1,2,5,4,6]=>3 [3,1,2,5,6,4]=>5 [3,1,2,6,4,5]=>4 [3,1,2,6,5,4]=>3 [3,1,4,2,5,6]=>1 [3,1,4,2,6,5]=>5 [3,1,4,5,2,6]=>2 [3,1,4,5,6,2]=>3 [3,1,4,6,2,5]=>4 [3,1,4,6,5,2]=>2 [3,1,5,2,4,6]=>2 [3,1,5,2,6,4]=>4 [3,1,5,4,2,6]=>1 [3,1,5,4,6,2]=>2 [3,1,5,6,2,4]=>3 [3,1,5,6,4,2]=>4 [3,1,6,2,4,5]=>3 [3,1,6,2,5,4]=>2 [3,1,6,4,2,5]=>2 [3,1,6,4,5,2]=>1 [3,1,6,5,2,4]=>4 [3,1,6,5,4,2]=>5 [3,2,1,4,5,6]=>0 [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]=>0 [3,2,4,1,6,5]=>3 [3,2,4,5,1,6]=>0 [3,2,4,5,6,1]=>0 [3,2,4,6,1,5]=>2 [3,2,4,6,5,1]=>0 [3,2,5,1,4,6]=>1 [3,2,5,1,6,4]=>2 [3,2,5,4,1,6]=>0 [3,2,5,4,6,1]=>0 [3,2,5,6,1,4]=>1 [3,2,5,6,4,1]=>2 [3,2,6,1,4,5]=>2 [3,2,6,1,5,4]=>1 [3,2,6,4,1,5]=>1 [3,2,6,4,5,1]=>0 [3,2,6,5,1,4]=>2 [3,2,6,5,4,1]=>3 [3,4,1,2,5,6]=>0 [3,4,1,2,6,5]=>4 [3,4,1,5,2,6]=>1 [3,4,1,5,6,2]=>2 [3,4,1,6,2,5]=>3 [3,4,1,6,5,2]=>1 [3,4,2,1,5,6]=>1 [3,4,2,1,6,5]=>5 [3,4,2,5,1,6]=>2 [3,4,2,5,6,1]=>3 [3,4,2,6,1,5]=>4 [3,4,2,6,5,1]=>2 [3,4,5,1,2,6]=>0 [3,4,5,1,6,2]=>1 [3,4,5,2,1,6]=>1 [3,4,5,2,6,1]=>2 [3,4,5,6,1,2]=>0 [3,4,5,6,2,1]=>1 [3,4,6,1,2,5]=>2 [3,4,6,1,5,2]=>0 [3,4,6,2,1,5]=>3 [3,4,6,2,5,1]=>1 [3,4,6,5,1,2]=>1 [3,4,6,5,2,1]=>2 [3,5,1,2,4,6]=>1 [3,5,1,2,6,4]=>3 [3,5,1,4,2,6]=>0 [3,5,1,4,6,2]=>1 [3,5,1,6,2,4]=>2 [3,5,1,6,4,2]=>3 [3,5,2,1,4,6]=>2 [3,5,2,1,6,4]=>4 [3,5,2,4,1,6]=>1 [3,5,2,4,6,1]=>2 [3,5,2,6,1,4]=>3 [3,5,2,6,4,1]=>4 [3,5,4,1,2,6]=>1 [3,5,4,1,6,2]=>2 [3,5,4,2,1,6]=>2 [3,5,4,2,6,1]=>3 [3,5,4,6,1,2]=>1 [3,5,4,6,2,1]=>2 [3,5,6,1,2,4]=>1 [3,5,6,1,4,2]=>2 [3,5,6,2,1,4]=>2 [3,5,6,2,4,1]=>3 [3,5,6,4,1,2]=>0 [3,5,6,4,2,1]=>1 [3,6,1,2,4,5]=>2 [3,6,1,2,5,4]=>1 [3,6,1,4,2,5]=>1 [3,6,1,4,5,2]=>0 [3,6,1,5,2,4]=>3 [3,6,1,5,4,2]=>4 [3,6,2,1,4,5]=>3 [3,6,2,1,5,4]=>2 [3,6,2,4,1,5]=>2 [3,6,2,4,5,1]=>1 [3,6,2,5,1,4]=>4 [3,6,2,5,4,1]=>5 [3,6,4,1,2,5]=>3 [3,6,4,1,5,2]=>1 [3,6,4,2,1,5]=>4 [3,6,4,2,5,1]=>2 [3,6,4,5,1,2]=>2 [3,6,4,5,2,1]=>3 [3,6,5,1,2,4]=>2 [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]=>1 [3,6,5,4,2,1]=>2 [4,1,2,3,5,6]=>0 [4,1,2,3,6,5]=>4 [4,1,2,5,3,6]=>2 [4,1,2,5,6,3]=>4 [4,1,2,6,3,5]=>3 [4,1,2,6,5,3]=>2 [4,1,3,2,5,6]=>0 [4,1,3,2,6,5]=>3 [4,1,3,5,2,6]=>1 [4,1,3,5,6,2]=>2 [4,1,3,6,2,5]=>2 [4,1,3,6,5,2]=>1 [4,1,5,2,3,6]=>1 [4,1,5,2,6,3]=>3 [4,1,5,3,2,6]=>2 [4,1,5,3,6,2]=>4 [4,1,5,6,2,3]=>2 [4,1,5,6,3,2]=>3 [4,1,6,2,3,5]=>2 [4,1,6,2,5,3]=>1 [4,1,6,3,2,5]=>3 [4,1,6,3,5,2]=>2 [4,1,6,5,2,3]=>3 [4,1,6,5,3,2]=>4 [4,2,1,3,5,6]=>0 [4,2,1,3,6,5]=>3 [4,2,1,5,3,6]=>1 [4,2,1,5,6,3]=>2 [4,2,1,6,3,5]=>2 [4,2,1,6,5,3]=>1 [4,2,3,1,5,6]=>0 [4,2,3,1,6,5]=>2 [4,2,3,5,1,6]=>0 [4,2,3,5,6,1]=>0 [4,2,3,6,1,5]=>1 [4,2,3,6,5,1]=>0 [4,2,5,1,3,6]=>0 [4,2,5,1,6,3]=>1 [4,2,5,3,1,6]=>1 [4,2,5,3,6,1]=>2 [4,2,5,6,1,3]=>0 [4,2,5,6,3,1]=>1 [4,2,6,1,3,5]=>1 [4,2,6,1,5,3]=>0 [4,2,6,3,1,5]=>2 [4,2,6,3,5,1]=>1 [4,2,6,5,1,3]=>1 [4,2,6,5,3,1]=>2 [4,3,1,2,5,6]=>1 [4,3,1,2,6,5]=>5 [4,3,1,5,2,6]=>2 [4,3,1,5,6,2]=>3 [4,3,1,6,2,5]=>4 [4,3,1,6,5,2]=>2 [4,3,2,1,5,6]=>2 [4,3,2,1,6,5]=>6 [4,3,2,5,1,6]=>3 [4,3,2,5,6,1]=>4 [4,3,2,6,1,5]=>5 [4,3,2,6,5,1]=>3 [4,3,5,1,2,6]=>1 [4,3,5,1,6,2]=>2 [4,3,5,2,1,6]=>2 [4,3,5,2,6,1]=>3 [4,3,5,6,1,2]=>1 [4,3,5,6,2,1]=>2 [4,3,6,1,2,5]=>3 [4,3,6,1,5,2]=>1 [4,3,6,2,1,5]=>4 [4,3,6,2,5,1]=>2 [4,3,6,5,1,2]=>2 [4,3,6,5,2,1]=>3 [4,5,1,2,3,6]=>0 [4,5,1,2,6,3]=>2 [4,5,1,3,2,6]=>1 [4,5,1,3,6,2]=>3 [4,5,1,6,2,3]=>1 [4,5,1,6,3,2]=>2 [4,5,2,1,3,6]=>1 [4,5,2,1,6,3]=>3 [4,5,2,3,1,6]=>2 [4,5,2,3,6,1]=>4 [4,5,2,6,1,3]=>2 [4,5,2,6,3,1]=>3 [4,5,3,1,2,6]=>0 [4,5,3,1,6,2]=>1 [4,5,3,2,1,6]=>1 [4,5,3,2,6,1]=>2 [4,5,3,6,1,2]=>0 [4,5,3,6,2,1]=>1 [4,5,6,1,2,3]=>0 [4,5,6,1,3,2]=>1 [4,5,6,2,1,3]=>1 [4,5,6,2,3,1]=>2 [4,5,6,3,1,2]=>2 [4,5,6,3,2,1]=>3 [4,6,1,2,3,5]=>1 [4,6,1,2,5,3]=>0 [4,6,1,3,2,5]=>2 [4,6,1,3,5,2]=>1 [4,6,1,5,2,3]=>2 [4,6,1,5,3,2]=>3 [4,6,2,1,3,5]=>2 [4,6,2,1,5,3]=>1 [4,6,2,3,1,5]=>3 [4,6,2,3,5,1]=>2 [4,6,2,5,1,3]=>3 [4,6,2,5,3,1]=>4 [4,6,3,1,2,5]=>1 [4,6,3,1,5,2]=>0 [4,6,3,2,1,5]=>2 [4,6,3,2,5,1]=>1 [4,6,3,5,1,2]=>1 [4,6,3,5,2,1]=>2 [4,6,5,1,2,3]=>1 [4,6,5,1,3,2]=>2 [4,6,5,2,1,3]=>2 [4,6,5,2,3,1]=>3 [4,6,5,3,1,2]=>3 [4,6,5,3,2,1]=>4 [5,1,2,3,4,6]=>0 [5,1,2,3,6,4]=>3 [5,1,2,4,3,6]=>0 [5,1,2,4,6,3]=>2 [5,1,2,6,3,4]=>2 [5,1,2,6,4,3]=>3 [5,1,3,2,4,6]=>0 [5,1,3,2,6,4]=>2 [5,1,3,4,2,6]=>0 [5,1,3,4,6,2]=>1 [5,1,3,6,2,4]=>1 [5,1,3,6,4,2]=>2 [5,1,4,2,3,6]=>2 [5,1,4,2,6,3]=>4 [5,1,4,3,2,6]=>3 [5,1,4,3,6,2]=>5 [5,1,4,6,2,3]=>3 [5,1,4,6,3,2]=>4 [5,1,6,2,3,4]=>1 [5,1,6,2,4,3]=>2 [5,1,6,3,2,4]=>2 [5,1,6,3,4,2]=>3 [5,1,6,4,2,3]=>1 [5,1,6,4,3,2]=>2 [5,2,1,3,4,6]=>0 [5,2,1,3,6,4]=>2 [5,2,1,4,3,6]=>0 [5,2,1,4,6,3]=>1 [5,2,1,6,3,4]=>1 [5,2,1,6,4,3]=>2 [5,2,3,1,4,6]=>0 [5,2,3,1,6,4]=>1 [5,2,3,4,1,6]=>0 [5,2,3,4,6,1]=>0 [5,2,3,6,1,4]=>0 [5,2,3,6,4,1]=>1 [5,2,4,1,3,6]=>1 [5,2,4,1,6,3]=>2 [5,2,4,3,1,6]=>2 [5,2,4,3,6,1]=>3 [5,2,4,6,1,3]=>1 [5,2,4,6,3,1]=>2 [5,2,6,1,3,4]=>0 [5,2,6,1,4,3]=>1 [5,2,6,3,1,4]=>1 [5,2,6,3,4,1]=>2 [5,2,6,4,1,3]=>0 [5,2,6,4,3,1]=>1 [5,3,1,2,4,6]=>2 [5,3,1,2,6,4]=>4 [5,3,1,4,2,6]=>1 [5,3,1,4,6,2]=>2 [5,3,1,6,2,4]=>3 [5,3,1,6,4,2]=>4 [5,3,2,1,4,6]=>3 [5,3,2,1,6,4]=>5 [5,3,2,4,1,6]=>2 [5,3,2,4,6,1]=>3 [5,3,2,6,1,4]=>4 [5,3,2,6,4,1]=>5 [5,3,4,1,2,6]=>2 [5,3,4,1,6,2]=>3 [5,3,4,2,1,6]=>3 [5,3,4,2,6,1]=>4 [5,3,4,6,1,2]=>2 [5,3,4,6,2,1]=>3 [5,3,6,1,2,4]=>2 [5,3,6,1,4,2]=>3 [5,3,6,2,1,4]=>3 [5,3,6,2,4,1]=>4 [5,3,6,4,1,2]=>1 [5,3,6,4,2,1]=>2 [5,4,1,2,3,6]=>1 [5,4,1,2,6,3]=>3 [5,4,1,3,2,6]=>2 [5,4,1,3,6,2]=>4 [5,4,1,6,2,3]=>2 [5,4,1,6,3,2]=>3 [5,4,2,1,3,6]=>2 [5,4,2,1,6,3]=>4 [5,4,2,3,1,6]=>3 [5,4,2,3,6,1]=>5 [5,4,2,6,1,3]=>3 [5,4,2,6,3,1]=>4 [5,4,3,1,2,6]=>1 [5,4,3,1,6,2]=>2 [5,4,3,2,1,6]=>2 [5,4,3,2,6,1]=>3 [5,4,3,6,1,2]=>1 [5,4,3,6,2,1]=>2 [5,4,6,1,2,3]=>1 [5,4,6,1,3,2]=>2 [5,4,6,2,1,3]=>2 [5,4,6,2,3,1]=>3 [5,4,6,3,1,2]=>3 [5,4,6,3,2,1]=>4 [5,6,1,2,3,4]=>0 [5,6,1,2,4,3]=>1 [5,6,1,3,2,4]=>1 [5,6,1,3,4,2]=>2 [5,6,1,4,2,3]=>0 [5,6,1,4,3,2]=>1 [5,6,2,1,3,4]=>1 [5,6,2,1,4,3]=>2 [5,6,2,3,1,4]=>2 [5,6,2,3,4,1]=>3 [5,6,2,4,1,3]=>1 [5,6,2,4,3,1]=>2 [5,6,3,1,2,4]=>0 [5,6,3,1,4,2]=>1 [5,6,3,2,1,4]=>1 [5,6,3,2,4,1]=>2 [5,6,3,4,1,2]=>0 [5,6,3,4,2,1]=>1 [5,6,4,1,2,3]=>2 [5,6,4,1,3,2]=>3 [5,6,4,2,1,3]=>3 [5,6,4,2,3,1]=>4 [5,6,4,3,1,2]=>4 [5,6,4,3,2,1]=>5 [6,1,2,3,4,5]=>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]=>3 [6,1,2,5,4,3]=>4 [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]=>2 [6,1,3,5,4,2]=>3 [6,1,4,2,3,5]=>3 [6,1,4,2,5,3]=>2 [6,1,4,3,2,5]=>4 [6,1,4,3,5,2]=>3 [6,1,4,5,2,3]=>4 [6,1,4,5,3,2]=>5 [6,1,5,2,3,4]=>2 [6,1,5,2,4,3]=>3 [6,1,5,3,2,4]=>3 [6,1,5,3,4,2]=>4 [6,1,5,4,2,3]=>2 [6,1,5,4,3,2]=>3 [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]=>2 [6,2,1,5,4,3]=>3 [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]=>1 [6,2,3,5,4,1]=>2 [6,2,4,1,3,5]=>2 [6,2,4,1,5,3]=>1 [6,2,4,3,1,5]=>3 [6,2,4,3,5,1]=>2 [6,2,4,5,1,3]=>2 [6,2,4,5,3,1]=>3 [6,2,5,1,3,4]=>1 [6,2,5,1,4,3]=>2 [6,2,5,3,1,4]=>2 [6,2,5,3,4,1]=>3 [6,2,5,4,1,3]=>1 [6,2,5,4,3,1]=>2 [6,3,1,2,4,5]=>3 [6,3,1,2,5,4]=>2 [6,3,1,4,2,5]=>2 [6,3,1,4,5,2]=>1 [6,3,1,5,2,4]=>4 [6,3,1,5,4,2]=>5 [6,3,2,1,4,5]=>4 [6,3,2,1,5,4]=>3 [6,3,2,4,1,5]=>3 [6,3,2,4,5,1]=>2 [6,3,2,5,1,4]=>5 [6,3,2,5,4,1]=>6 [6,3,4,1,2,5]=>4 [6,3,4,1,5,2]=>2 [6,3,4,2,1,5]=>5 [6,3,4,2,5,1]=>3 [6,3,4,5,1,2]=>3 [6,3,4,5,2,1]=>4 [6,3,5,1,2,4]=>3 [6,3,5,1,4,2]=>4 [6,3,5,2,1,4]=>4 [6,3,5,2,4,1]=>5 [6,3,5,4,1,2]=>2 [6,3,5,4,2,1]=>3 [6,4,1,2,3,5]=>2 [6,4,1,2,5,3]=>1 [6,4,1,3,2,5]=>3 [6,4,1,3,5,2]=>2 [6,4,1,5,2,3]=>3 [6,4,1,5,3,2]=>4 [6,4,2,1,3,5]=>3 [6,4,2,1,5,3]=>2 [6,4,2,3,1,5]=>4 [6,4,2,3,5,1]=>3 [6,4,2,5,1,3]=>4 [6,4,2,5,3,1]=>5 [6,4,3,1,2,5]=>2 [6,4,3,1,5,2]=>1 [6,4,3,2,1,5]=>3 [6,4,3,2,5,1]=>2 [6,4,3,5,1,2]=>2 [6,4,3,5,2,1]=>3 [6,4,5,1,2,3]=>2 [6,4,5,1,3,2]=>3 [6,4,5,2,1,3]=>3 [6,4,5,2,3,1]=>4 [6,4,5,3,1,2]=>4 [6,4,5,3,2,1]=>5 [6,5,1,2,3,4]=>1 [6,5,1,2,4,3]=>2 [6,5,1,3,2,4]=>2 [6,5,1,3,4,2]=>3 [6,5,1,4,2,3]=>1 [6,5,1,4,3,2]=>2 [6,5,2,1,3,4]=>2 [6,5,2,1,4,3]=>3 [6,5,2,3,1,4]=>3 [6,5,2,3,4,1]=>4 [6,5,2,4,1,3]=>2 [6,5,2,4,3,1]=>3 [6,5,3,1,2,4]=>1 [6,5,3,1,4,2]=>2 [6,5,3,2,1,4]=>2 [6,5,3,2,4,1]=>3 [6,5,3,4,1,2]=>1 [6,5,3,4,2,1]=>2 [6,5,4,1,2,3]=>3 [6,5,4,1,3,2]=>4 [6,5,4,2,1,3]=>4 [6,5,4,2,3,1]=>5 [6,5,4,3,1,2]=>5 [6,5,4,3,2,1]=>6 [1,2,3,4,5,6,7]=>0 [1,2,3,4,5,7,6]=>0 [1,2,3,4,6,5,7]=>0 [1,2,3,4,6,7,5]=>0 [1,2,3,4,7,5,6]=>0 [1,2,3,4,7,6,5]=>0 [1,2,3,5,4,6,7]=>0 [1,2,3,5,4,7,6]=>2 [1,2,3,5,6,4,7]=>0 [1,2,3,5,6,7,4]=>0 [1,2,3,5,7,4,6]=>1 [1,2,3,5,7,6,4]=>0 [1,2,3,6,4,5,7]=>0 [1,2,3,6,4,7,5]=>1 [1,2,3,6,5,4,7]=>0 [1,2,3,6,5,7,4]=>0 [1,2,3,6,7,4,5]=>0 [1,2,3,6,7,5,4]=>1 [1,2,3,7,4,5,6]=>0 [1,2,3,7,4,6,5]=>0 [1,2,3,7,5,4,6]=>0 [1,2,3,7,5,6,4]=>0 [1,2,3,7,6,4,5]=>1 [1,2,3,7,6,5,4]=>2 [1,2,4,3,5,6,7]=>0 [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]=>0 [1,2,4,5,3,7,6]=>3 [1,2,4,5,6,3,7]=>0 [1,2,4,5,6,7,3]=>0 [1,2,4,5,7,3,6]=>2 [1,2,4,5,7,6,3]=>0 [1,2,4,6,3,5,7]=>1 [1,2,4,6,3,7,5]=>2 [1,2,4,6,5,3,7]=>0 [1,2,4,6,5,7,3]=>0 [1,2,4,6,7,3,5]=>1 [1,2,4,6,7,5,3]=>2 [1,2,4,7,3,5,6]=>2 [1,2,4,7,3,6,5]=>1 [1,2,4,7,5,3,6]=>1 [1,2,4,7,5,6,3]=>0 [1,2,4,7,6,3,5]=>2 [1,2,4,7,6,5,3]=>3 [1,2,5,3,4,6,7]=>0 [1,2,5,3,4,7,6]=>3 [1,2,5,3,6,4,7]=>1 [1,2,5,3,6,7,4]=>2 [1,2,5,3,7,4,6]=>2 [1,2,5,3,7,6,4]=>1 [1,2,5,4,3,6,7]=>0 [1,2,5,4,3,7,6]=>2 [1,2,5,4,6,3,7]=>0 [1,2,5,4,6,7,3]=>0 [1,2,5,4,7,3,6]=>1 [1,2,5,4,7,6,3]=>0 [1,2,5,6,3,4,7]=>0 [1,2,5,6,3,7,4]=>1 [1,2,5,6,4,3,7]=>1 [1,2,5,6,4,7,3]=>2 [1,2,5,6,7,3,4]=>0 [1,2,5,6,7,4,3]=>1 [1,2,5,7,3,4,6]=>1 [1,2,5,7,3,6,4]=>0 [1,2,5,7,4,3,6]=>2 [1,2,5,7,4,6,3]=>1 [1,2,5,7,6,3,4]=>1 [1,2,5,7,6,4,3]=>2 [1,2,6,3,4,5,7]=>0 [1,2,6,3,4,7,5]=>2 [1,2,6,3,5,4,7]=>0 [1,2,6,3,5,7,4]=>1 [1,2,6,3,7,4,5]=>1 [1,2,6,3,7,5,4]=>2 [1,2,6,4,3,5,7]=>0 [1,2,6,4,3,7,5]=>1 [1,2,6,4,5,3,7]=>0 [1,2,6,4,5,7,3]=>0 [1,2,6,4,7,3,5]=>0 [1,2,6,4,7,5,3]=>1 [1,2,6,5,3,4,7]=>1 [1,2,6,5,3,7,4]=>2 [1,2,6,5,4,3,7]=>2 [1,2,6,5,4,7,3]=>3 [1,2,6,5,7,3,4]=>1 [1,2,6,5,7,4,3]=>2 [1,2,6,7,3,4,5]=>0 [1,2,6,7,3,5,4]=>1 [1,2,6,7,4,3,5]=>1 [1,2,6,7,4,5,3]=>2 [1,2,6,7,5,3,4]=>0 [1,2,6,7,5,4,3]=>1 [1,2,7,3,4,5,6]=>0 [1,2,7,3,4,6,5]=>0 [1,2,7,3,5,4,6]=>0 [1,2,7,3,5,6,4]=>0 [1,2,7,3,6,4,5]=>2 [1,2,7,3,6,5,4]=>3 [1,2,7,4,3,5,6]=>0 [1,2,7,4,3,6,5]=>0 [1,2,7,4,5,3,6]=>0 [1,2,7,4,5,6,3]=>0 [1,2,7,4,6,3,5]=>1 [1,2,7,4,6,5,3]=>2 [1,2,7,5,3,4,6]=>2 [1,2,7,5,3,6,4]=>1 [1,2,7,5,4,3,6]=>3 [1,2,7,5,4,6,3]=>2 [1,2,7,5,6,3,4]=>2 [1,2,7,5,6,4,3]=>3 [1,2,7,6,3,4,5]=>1 [1,2,7,6,3,5,4]=>2 [1,2,7,6,4,3,5]=>2 [1,2,7,6,4,5,3]=>3 [1,2,7,6,5,3,4]=>1 [1,2,7,6,5,4,3]=>2 [1,3,2,4,5,6,7]=>0 [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]=>6 [1,3,2,5,6,4,7]=>3 [1,3,2,5,6,7,4]=>4 [1,3,2,5,7,4,6]=>5 [1,3,2,5,7,6,4]=>3 [1,3,2,6,4,5,7]=>3 [1,3,2,6,4,7,5]=>5 [1,3,2,6,5,4,7]=>2 [1,3,2,6,5,7,4]=>3 [1,3,2,6,7,4,5]=>4 [1,3,2,6,7,5,4]=>5 [1,3,2,7,4,5,6]=>4 [1,3,2,7,4,6,5]=>3 [1,3,2,7,5,4,6]=>3 [1,3,2,7,5,6,4]=>2 [1,3,2,7,6,4,5]=>5 [1,3,2,7,6,5,4]=>6 [1,3,4,2,5,6,7]=>0 [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]=>5 [1,3,4,2,7,6,5]=>3 [1,3,4,5,2,6,7]=>0 [1,3,4,5,2,7,6]=>4 [1,3,4,5,6,2,7]=>0 [1,3,4,5,6,7,2]=>0 [1,3,4,5,7,2,6]=>3 [1,3,4,5,7,6,2]=>0 [1,3,4,6,2,5,7]=>2 [1,3,4,6,2,7,5]=>3 [1,3,4,6,5,2,7]=>0 [1,3,4,6,5,7,2]=>0 [1,3,4,6,7,2,5]=>2 [1,3,4,6,7,5,2]=>3 [1,3,4,7,2,5,6]=>4 [1,3,4,7,2,6,5]=>2 [1,3,4,7,5,2,6]=>2 [1,3,4,7,5,6,2]=>0 [1,3,4,7,6,2,5]=>3 [1,3,4,7,6,5,2]=>4 [1,3,5,2,4,6,7]=>1 [1,3,5,2,4,7,6]=>5 [1,3,5,2,6,4,7]=>2 [1,3,5,2,6,7,4]=>3 [1,3,5,2,7,4,6]=>4 [1,3,5,2,7,6,4]=>2 [1,3,5,4,2,6,7]=>0 [1,3,5,4,2,7,6]=>3 [1,3,5,4,6,2,7]=>0 [1,3,5,4,6,7,2]=>0 [1,3,5,4,7,2,6]=>2 [1,3,5,4,7,6,2]=>0 [1,3,5,6,2,4,7]=>1 [1,3,5,6,2,7,4]=>2 [1,3,5,6,4,2,7]=>2 [1,3,5,6,4,7,2]=>3 [1,3,5,6,7,2,4]=>1 [1,3,5,6,7,4,2]=>2 [1,3,5,7,2,4,6]=>3 [1,3,5,7,2,6,4]=>1 [1,3,5,7,4,2,6]=>4 [1,3,5,7,4,6,2]=>2 [1,3,5,7,6,2,4]=>2 [1,3,5,7,6,4,2]=>3 [1,3,6,2,4,5,7]=>2 [1,3,6,2,4,7,5]=>4 [1,3,6,2,5,4,7]=>1 [1,3,6,2,5,7,4]=>2 [1,3,6,2,7,4,5]=>3 [1,3,6,2,7,5,4]=>4 [1,3,6,4,2,5,7]=>1 [1,3,6,4,2,7,5]=>2 [1,3,6,4,5,2,7]=>0 [1,3,6,4,5,7,2]=>0 [1,3,6,4,7,2,5]=>1 [1,3,6,4,7,5,2]=>2 [1,3,6,5,2,4,7]=>2 [1,3,6,5,2,7,4]=>3 [1,3,6,5,4,2,7]=>3 [1,3,6,5,4,7,2]=>4 [1,3,6,5,7,2,4]=>2 [1,3,6,5,7,4,2]=>3 [1,3,6,7,2,4,5]=>2 [1,3,6,7,2,5,4]=>3 [1,3,6,7,4,2,5]=>3 [1,3,6,7,4,5,2]=>4 [1,3,6,7,5,2,4]=>1 [1,3,6,7,5,4,2]=>2 [1,3,7,2,4,5,6]=>3 [1,3,7,2,4,6,5]=>2 [1,3,7,2,5,4,6]=>2 [1,3,7,2,5,6,4]=>1 [1,3,7,2,6,4,5]=>4 [1,3,7,2,6,5,4]=>5 [1,3,7,4,2,5,6]=>2 [1,3,7,4,2,6,5]=>1 [1,3,7,4,5,2,6]=>1 [1,3,7,4,5,6,2]=>0 [1,3,7,4,6,2,5]=>2 [1,3,7,4,6,5,2]=>3 [1,3,7,5,2,4,6]=>4 [1,3,7,5,2,6,4]=>2 [1,3,7,5,4,2,6]=>5 [1,3,7,5,4,6,2]=>3 [1,3,7,5,6,2,4]=>3 [1,3,7,5,6,4,2]=>4 [1,3,7,6,2,4,5]=>3 [1,3,7,6,2,5,4]=>4 [1,3,7,6,4,2,5]=>4 [1,3,7,6,4,5,2]=>5 [1,3,7,6,5,2,4]=>2 [1,3,7,6,5,4,2]=>3 [1,4,2,3,5,6,7]=>0 [1,4,2,3,5,7,6]=>3 [1,4,2,3,6,5,7]=>3 [1,4,2,3,6,7,5]=>5 [1,4,2,3,7,5,6]=>4 [1,4,2,3,7,6,5]=>3 [1,4,2,5,3,6,7]=>1 [1,4,2,5,3,7,6]=>5 [1,4,2,5,6,3,7]=>2 [1,4,2,5,6,7,3]=>3 [1,4,2,5,7,3,6]=>4 [1,4,2,5,7,6,3]=>2 [1,4,2,6,3,5,7]=>2 [1,4,2,6,3,7,5]=>4 [1,4,2,6,5,3,7]=>1 [1,4,2,6,5,7,3]=>2 [1,4,2,6,7,3,5]=>3 [1,4,2,6,7,5,3]=>4 [1,4,2,7,3,5,6]=>3 [1,4,2,7,3,6,5]=>2 [1,4,2,7,5,3,6]=>2 [1,4,2,7,5,6,3]=>1 [1,4,2,7,6,3,5]=>4 [1,4,2,7,6,5,3]=>5 [1,4,3,2,5,6,7]=>0 [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]=>0 [1,4,3,5,2,7,6]=>3 [1,4,3,5,6,2,7]=>0 [1,4,3,5,6,7,2]=>0 [1,4,3,5,7,2,6]=>2 [1,4,3,5,7,6,2]=>0 [1,4,3,6,2,5,7]=>1 [1,4,3,6,2,7,5]=>2 [1,4,3,6,5,2,7]=>0 [1,4,3,6,5,7,2]=>0 [1,4,3,6,7,2,5]=>1 [1,4,3,6,7,5,2]=>2 [1,4,3,7,2,5,6]=>2 [1,4,3,7,2,6,5]=>1 [1,4,3,7,5,2,6]=>1 [1,4,3,7,5,6,2]=>0 [1,4,3,7,6,2,5]=>2 [1,4,3,7,6,5,2]=>3 [1,4,5,2,3,6,7]=>0 [1,4,5,2,3,7,6]=>4 [1,4,5,2,6,3,7]=>1 [1,4,5,2,6,7,3]=>2 [1,4,5,2,7,3,6]=>3 [1,4,5,2,7,6,3]=>1 [1,4,5,3,2,6,7]=>1 [1,4,5,3,2,7,6]=>5 [1,4,5,3,6,2,7]=>2 [1,4,5,3,6,7,2]=>3 [1,4,5,3,7,2,6]=>4 [1,4,5,3,7,6,2]=>2 [1,4,5,6,2,3,7]=>0 [1,4,5,6,2,7,3]=>1 [1,4,5,6,3,2,7]=>1 [1,4,5,6,3,7,2]=>2 [1,4,5,6,7,2,3]=>0 [1,4,5,6,7,3,2]=>1 [1,4,5,7,2,3,6]=>2 [1,4,5,7,2,6,3]=>0 [1,4,5,7,3,2,6]=>3 [1,4,5,7,3,6,2]=>1 [1,4,5,7,6,2,3]=>1 [1,4,5,7,6,3,2]=>2 [1,4,6,2,3,5,7]=>1 [1,4,6,2,3,7,5]=>3 [1,4,6,2,5,3,7]=>0 [1,4,6,2,5,7,3]=>1 [1,4,6,2,7,3,5]=>2 [1,4,6,2,7,5,3]=>3 [1,4,6,3,2,5,7]=>2 [1,4,6,3,2,7,5]=>4 [1,4,6,3,5,2,7]=>1 [1,4,6,3,5,7,2]=>2 [1,4,6,3,7,2,5]=>3 [1,4,6,3,7,5,2]=>4 [1,4,6,5,2,3,7]=>1 [1,4,6,5,2,7,3]=>2 [1,4,6,5,3,2,7]=>2
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Description
The number of cyclic alignments of a permutation.
The pair $(i,j)$ is a cyclic alignment of a permutation $\pi$ if $i, j, \pi(j), \pi(i)$ are cyclically ordered and all distinct, see Section 5 of [1]
References
[1] Postnikov, A. Total positivity, Grassmannians, and networks arXiv:math/0609764
Code
def in_cyclic_order(i, j, k, l):
    return (i < j < k < l or
            j < k < l < i or
            k < l < i < j or
            l < i < j < k)

def statistic(pi):
    """
    sage: statistic(Permutation([7,6,2,1,9,5,4,3,8]))
    9

    sage: statistic(Permutation([5,4,1,6,3,2]))
    3

    sage: statistic(Permutation([4,5,6,7,8,1,2,3]))
    0
    """
    n = len(pi)
    a = 0
    for i, pi_i in enumerate(pi, 1):
        for j, pi_j in enumerate(pi, 1):
            if in_cyclic_order(i, j, pi_j, pi_i):
                a += 1
    return a
Created
May 09, 2020 at 22:00 by Martin Rubey
Updated
May 09, 2020 at 22:00 by Martin Rubey