edit this statistic or download as text // json
Identifier
Values
=>
[1,2]=>2 [2,1]=>0 [1,2,3]=>3 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>0 [3,2,1]=>0 [1,2,3,4]=>4 [1,2,4,3]=>1 [1,3,2,4]=>2 [1,3,4,2]=>1 [1,4,2,3]=>2 [1,4,3,2]=>0 [2,1,3,4]=>2 [2,1,4,3]=>1 [2,3,1,4]=>2 [2,3,4,1]=>1 [2,4,1,3]=>2 [2,4,3,1]=>0 [3,1,2,4]=>1 [3,1,4,2]=>1 [3,2,1,4]=>1 [3,2,4,1]=>1 [3,4,1,2]=>2 [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]=>5 [1,2,3,5,4]=>1 [1,2,4,3,5]=>2 [1,2,4,5,3]=>1 [1,2,5,3,4]=>2 [1,2,5,4,3]=>0 [1,3,2,4,5]=>3 [1,3,2,5,4]=>1 [1,3,4,2,5]=>2 [1,3,4,5,2]=>1 [1,3,5,2,4]=>2 [1,3,5,4,2]=>0 [1,4,2,3,5]=>3 [1,4,2,5,3]=>1 [1,4,3,2,5]=>1 [1,4,3,5,2]=>1 [1,4,5,2,3]=>2 [1,4,5,3,2]=>0 [1,5,2,3,4]=>3 [1,5,2,4,3]=>1 [1,5,3,2,4]=>1 [1,5,3,4,2]=>1 [1,5,4,2,3]=>0 [1,5,4,3,2]=>0 [2,1,3,4,5]=>3 [2,1,3,5,4]=>1 [2,1,4,3,5]=>2 [2,1,4,5,3]=>1 [2,1,5,3,4]=>2 [2,1,5,4,3]=>0 [2,3,1,4,5]=>3 [2,3,1,5,4]=>1 [2,3,4,1,5]=>2 [2,3,4,5,1]=>1 [2,3,5,1,4]=>2 [2,3,5,4,1]=>0 [2,4,1,3,5]=>3 [2,4,1,5,3]=>1 [2,4,3,1,5]=>1 [2,4,3,5,1]=>1 [2,4,5,1,3]=>2 [2,4,5,3,1]=>0 [2,5,1,3,4]=>3 [2,5,1,4,3]=>1 [2,5,3,1,4]=>1 [2,5,3,4,1]=>1 [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]=>2 [3,1,4,5,2]=>1 [3,1,5,2,4]=>2 [3,1,5,4,2]=>0 [3,2,1,4,5]=>2 [3,2,1,5,4]=>1 [3,2,4,1,5]=>2 [3,2,4,5,1]=>1 [3,2,5,1,4]=>2 [3,2,5,4,1]=>0 [3,4,1,2,5]=>3 [3,4,1,5,2]=>1 [3,4,2,1,5]=>1 [3,4,2,5,1]=>1 [3,4,5,1,2]=>2 [3,4,5,2,1]=>0 [3,5,1,2,4]=>3 [3,5,1,4,2]=>1 [3,5,2,1,4]=>1 [3,5,2,4,1]=>1 [3,5,4,1,2]=>0 [3,5,4,2,1]=>0 [4,1,2,3,5]=>1 [4,1,2,5,3]=>1 [4,1,3,2,5]=>1 [4,1,3,5,2]=>1 [4,1,5,2,3]=>2 [4,1,5,3,2]=>0 [4,2,1,3,5]=>1 [4,2,1,5,3]=>1 [4,2,3,1,5]=>1 [4,2,3,5,1]=>1 [4,2,5,1,3]=>2 [4,2,5,3,1]=>0 [4,3,1,2,5]=>1 [4,3,1,5,2]=>1 [4,3,2,1,5]=>1 [4,3,2,5,1]=>1 [4,3,5,1,2]=>2 [4,3,5,2,1]=>0 [4,5,1,2,3]=>3 [4,5,1,3,2]=>1 [4,5,2,1,3]=>1 [4,5,2,3,1]=>1 [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]=>6 [1,2,3,4,6,5]=>1 [1,2,3,5,4,6]=>2 [1,2,3,5,6,4]=>1 [1,2,3,6,4,5]=>2 [1,2,3,6,5,4]=>0 [1,2,4,3,5,6]=>3 [1,2,4,3,6,5]=>1 [1,2,4,5,3,6]=>2 [1,2,4,5,6,3]=>1 [1,2,4,6,3,5]=>2 [1,2,4,6,5,3]=>0 [1,2,5,3,4,6]=>3 [1,2,5,3,6,4]=>1 [1,2,5,4,3,6]=>1 [1,2,5,4,6,3]=>1 [1,2,5,6,3,4]=>2 [1,2,5,6,4,3]=>0 [1,2,6,3,4,5]=>3 [1,2,6,3,5,4]=>1 [1,2,6,4,3,5]=>1 [1,2,6,4,5,3]=>1 [1,2,6,5,3,4]=>0 [1,2,6,5,4,3]=>0 [1,3,2,4,5,6]=>4 [1,3,2,4,6,5]=>1 [1,3,2,5,4,6]=>2 [1,3,2,5,6,4]=>1 [1,3,2,6,4,5]=>2 [1,3,2,6,5,4]=>0 [1,3,4,2,5,6]=>3 [1,3,4,2,6,5]=>1 [1,3,4,5,2,6]=>2 [1,3,4,5,6,2]=>1 [1,3,4,6,2,5]=>2 [1,3,4,6,5,2]=>0 [1,3,5,2,4,6]=>3 [1,3,5,2,6,4]=>1 [1,3,5,4,2,6]=>1 [1,3,5,4,6,2]=>1 [1,3,5,6,2,4]=>2 [1,3,5,6,4,2]=>0 [1,3,6,2,4,5]=>3 [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]=>0 [1,3,6,5,4,2]=>0 [1,4,2,3,5,6]=>4 [1,4,2,3,6,5]=>1 [1,4,2,5,3,6]=>2 [1,4,2,5,6,3]=>1 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>0 [1,4,3,2,5,6]=>2 [1,4,3,2,6,5]=>1 [1,4,3,5,2,6]=>2 [1,4,3,5,6,2]=>1 [1,4,3,6,2,5]=>2 [1,4,3,6,5,2]=>0 [1,4,5,2,3,6]=>3 [1,4,5,2,6,3]=>1 [1,4,5,3,2,6]=>1 [1,4,5,3,6,2]=>1 [1,4,5,6,2,3]=>2 [1,4,5,6,3,2]=>0 [1,4,6,2,3,5]=>3 [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]=>0 [1,4,6,5,3,2]=>0 [1,5,2,3,4,6]=>4 [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]=>2 [1,5,2,6,4,3]=>0 [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]=>2 [1,5,3,6,4,2]=>0 [1,5,4,2,3,6]=>1 [1,5,4,2,6,3]=>1 [1,5,4,3,2,6]=>1 [1,5,4,3,6,2]=>1 [1,5,4,6,2,3]=>2 [1,5,4,6,3,2]=>0 [1,5,6,2,3,4]=>3 [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]=>0 [1,5,6,4,3,2]=>0 [1,6,2,3,4,5]=>4 [1,6,2,3,5,4]=>1 [1,6,2,4,3,5]=>2 [1,6,2,4,5,3]=>1 [1,6,2,5,3,4]=>2 [1,6,2,5,4,3]=>0 [1,6,3,2,4,5]=>2 [1,6,3,2,5,4]=>1 [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]=>0 [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]=>2 [1,6,4,5,3,2]=>0 [1,6,5,2,3,4]=>0 [1,6,5,2,4,3]=>0 [1,6,5,3,2,4]=>0 [1,6,5,3,4,2]=>0 [1,6,5,4,2,3]=>0 [1,6,5,4,3,2]=>0 [2,1,3,4,5,6]=>4 [2,1,3,4,6,5]=>1 [2,1,3,5,4,6]=>2 [2,1,3,5,6,4]=>1 [2,1,3,6,4,5]=>2 [2,1,3,6,5,4]=>0 [2,1,4,3,5,6]=>3 [2,1,4,3,6,5]=>1 [2,1,4,5,3,6]=>2 [2,1,4,5,6,3]=>1 [2,1,4,6,3,5]=>2 [2,1,4,6,5,3]=>0 [2,1,5,3,4,6]=>3 [2,1,5,3,6,4]=>1 [2,1,5,4,3,6]=>1 [2,1,5,4,6,3]=>1 [2,1,5,6,3,4]=>2 [2,1,5,6,4,3]=>0 [2,1,6,3,4,5]=>3 [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]=>0 [2,1,6,5,4,3]=>0 [2,3,1,4,5,6]=>4 [2,3,1,4,6,5]=>1 [2,3,1,5,4,6]=>2 [2,3,1,5,6,4]=>1 [2,3,1,6,4,5]=>2 [2,3,1,6,5,4]=>0 [2,3,4,1,5,6]=>3 [2,3,4,1,6,5]=>1 [2,3,4,5,1,6]=>2 [2,3,4,5,6,1]=>1 [2,3,4,6,1,5]=>2 [2,3,4,6,5,1]=>0 [2,3,5,1,4,6]=>3 [2,3,5,1,6,4]=>1 [2,3,5,4,1,6]=>1 [2,3,5,4,6,1]=>1 [2,3,5,6,1,4]=>2 [2,3,5,6,4,1]=>0 [2,3,6,1,4,5]=>3 [2,3,6,1,5,4]=>1 [2,3,6,4,1,5]=>1 [2,3,6,4,5,1]=>1 [2,3,6,5,1,4]=>0 [2,3,6,5,4,1]=>0 [2,4,1,3,5,6]=>4 [2,4,1,3,6,5]=>1 [2,4,1,5,3,6]=>2 [2,4,1,5,6,3]=>1 [2,4,1,6,3,5]=>2 [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]=>2 [2,4,3,5,6,1]=>1 [2,4,3,6,1,5]=>2 [2,4,3,6,5,1]=>0 [2,4,5,1,3,6]=>3 [2,4,5,1,6,3]=>1 [2,4,5,3,1,6]=>1 [2,4,5,3,6,1]=>1 [2,4,5,6,1,3]=>2 [2,4,5,6,3,1]=>0 [2,4,6,1,3,5]=>3 [2,4,6,1,5,3]=>1 [2,4,6,3,1,5]=>1 [2,4,6,3,5,1]=>1 [2,4,6,5,1,3]=>0 [2,4,6,5,3,1]=>0 [2,5,1,3,4,6]=>4 [2,5,1,3,6,4]=>1 [2,5,1,4,3,6]=>2 [2,5,1,4,6,3]=>1 [2,5,1,6,3,4]=>2 [2,5,1,6,4,3]=>0 [2,5,3,1,4,6]=>2 [2,5,3,1,6,4]=>1 [2,5,3,4,1,6]=>2 [2,5,3,4,6,1]=>1 [2,5,3,6,1,4]=>2 [2,5,3,6,4,1]=>0 [2,5,4,1,3,6]=>1 [2,5,4,1,6,3]=>1 [2,5,4,3,1,6]=>1 [2,5,4,3,6,1]=>1 [2,5,4,6,1,3]=>2 [2,5,4,6,3,1]=>0 [2,5,6,1,3,4]=>3 [2,5,6,1,4,3]=>1 [2,5,6,3,1,4]=>1 [2,5,6,3,4,1]=>1 [2,5,6,4,1,3]=>0 [2,5,6,4,3,1]=>0 [2,6,1,3,4,5]=>4 [2,6,1,3,5,4]=>1 [2,6,1,4,3,5]=>2 [2,6,1,4,5,3]=>1 [2,6,1,5,3,4]=>2 [2,6,1,5,4,3]=>0 [2,6,3,1,4,5]=>2 [2,6,3,1,5,4]=>1 [2,6,3,4,1,5]=>2 [2,6,3,4,5,1]=>1 [2,6,3,5,1,4]=>2 [2,6,3,5,4,1]=>0 [2,6,4,1,3,5]=>1 [2,6,4,1,5,3]=>1 [2,6,4,3,1,5]=>1 [2,6,4,3,5,1]=>1 [2,6,4,5,1,3]=>2 [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]=>1 [3,1,2,5,4,6]=>2 [3,1,2,5,6,4]=>1 [3,1,2,6,4,5]=>2 [3,1,2,6,5,4]=>0 [3,1,4,2,5,6]=>3 [3,1,4,2,6,5]=>1 [3,1,4,5,2,6]=>2 [3,1,4,5,6,2]=>1 [3,1,4,6,2,5]=>2 [3,1,4,6,5,2]=>0 [3,1,5,2,4,6]=>3 [3,1,5,2,6,4]=>1 [3,1,5,4,2,6]=>1 [3,1,5,4,6,2]=>1 [3,1,5,6,2,4]=>2 [3,1,5,6,4,2]=>0 [3,1,6,2,4,5]=>3 [3,1,6,2,5,4]=>1 [3,1,6,4,2,5]=>1 [3,1,6,4,5,2]=>1 [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]=>1 [3,2,1,5,4,6]=>2 [3,2,1,5,6,4]=>1 [3,2,1,6,4,5]=>2 [3,2,1,6,5,4]=>0 [3,2,4,1,5,6]=>3 [3,2,4,1,6,5]=>1 [3,2,4,5,1,6]=>2 [3,2,4,5,6,1]=>1 [3,2,4,6,1,5]=>2 [3,2,4,6,5,1]=>0 [3,2,5,1,4,6]=>3 [3,2,5,1,6,4]=>1 [3,2,5,4,1,6]=>1 [3,2,5,4,6,1]=>1 [3,2,5,6,1,4]=>2 [3,2,5,6,4,1]=>0 [3,2,6,1,4,5]=>3 [3,2,6,1,5,4]=>1 [3,2,6,4,1,5]=>1 [3,2,6,4,5,1]=>1 [3,2,6,5,1,4]=>0 [3,2,6,5,4,1]=>0 [3,4,1,2,5,6]=>4 [3,4,1,2,6,5]=>1 [3,4,1,5,2,6]=>2 [3,4,1,5,6,2]=>1 [3,4,1,6,2,5]=>2 [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]=>2 [3,4,2,5,6,1]=>1 [3,4,2,6,1,5]=>2 [3,4,2,6,5,1]=>0 [3,4,5,1,2,6]=>3 [3,4,5,1,6,2]=>1 [3,4,5,2,1,6]=>1 [3,4,5,2,6,1]=>1 [3,4,5,6,1,2]=>2 [3,4,5,6,2,1]=>0 [3,4,6,1,2,5]=>3 [3,4,6,1,5,2]=>1 [3,4,6,2,1,5]=>1 [3,4,6,2,5,1]=>1 [3,4,6,5,1,2]=>0 [3,4,6,5,2,1]=>0 [3,5,1,2,4,6]=>4 [3,5,1,2,6,4]=>1 [3,5,1,4,2,6]=>2 [3,5,1,4,6,2]=>1 [3,5,1,6,2,4]=>2 [3,5,1,6,4,2]=>0 [3,5,2,1,4,6]=>2 [3,5,2,1,6,4]=>1 [3,5,2,4,1,6]=>2 [3,5,2,4,6,1]=>1 [3,5,2,6,1,4]=>2 [3,5,2,6,4,1]=>0 [3,5,4,1,2,6]=>1 [3,5,4,1,6,2]=>1 [3,5,4,2,1,6]=>1 [3,5,4,2,6,1]=>1 [3,5,4,6,1,2]=>2 [3,5,4,6,2,1]=>0 [3,5,6,1,2,4]=>3 [3,5,6,1,4,2]=>1 [3,5,6,2,1,4]=>1 [3,5,6,2,4,1]=>1 [3,5,6,4,1,2]=>0 [3,5,6,4,2,1]=>0 [3,6,1,2,4,5]=>4 [3,6,1,2,5,4]=>1 [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]=>0 [3,6,2,1,4,5]=>2 [3,6,2,1,5,4]=>1 [3,6,2,4,1,5]=>2 [3,6,2,4,5,1]=>1 [3,6,2,5,1,4]=>2 [3,6,2,5,4,1]=>0 [3,6,4,1,2,5]=>1 [3,6,4,1,5,2]=>1 [3,6,4,2,1,5]=>1 [3,6,4,2,5,1]=>1 [3,6,4,5,1,2]=>2 [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]=>2 [4,1,2,5,6,3]=>1 [4,1,2,6,3,5]=>2 [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]=>2 [4,1,3,5,6,2]=>1 [4,1,3,6,2,5]=>2 [4,1,3,6,5,2]=>0 [4,1,5,2,3,6]=>3 [4,1,5,2,6,3]=>1 [4,1,5,3,2,6]=>1 [4,1,5,3,6,2]=>1 [4,1,5,6,2,3]=>2 [4,1,5,6,3,2]=>0 [4,1,6,2,3,5]=>3 [4,1,6,2,5,3]=>1 [4,1,6,3,2,5]=>1 [4,1,6,3,5,2]=>1 [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]=>2 [4,2,1,5,6,3]=>1 [4,2,1,6,3,5]=>2 [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]=>2 [4,2,3,5,6,1]=>1 [4,2,3,6,1,5]=>2 [4,2,3,6,5,1]=>0 [4,2,5,1,3,6]=>3 [4,2,5,1,6,3]=>1 [4,2,5,3,1,6]=>1 [4,2,5,3,6,1]=>1 [4,2,5,6,1,3]=>2 [4,2,5,6,3,1]=>0 [4,2,6,1,3,5]=>3 [4,2,6,1,5,3]=>1 [4,2,6,3,1,5]=>1 [4,2,6,3,5,1]=>1 [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]=>2 [4,3,1,5,6,2]=>1 [4,3,1,6,2,5]=>2 [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]=>2 [4,3,2,5,6,1]=>1 [4,3,2,6,1,5]=>2 [4,3,2,6,5,1]=>0 [4,3,5,1,2,6]=>3 [4,3,5,1,6,2]=>1 [4,3,5,2,1,6]=>1 [4,3,5,2,6,1]=>1 [4,3,5,6,1,2]=>2 [4,3,5,6,2,1]=>0 [4,3,6,1,2,5]=>3 [4,3,6,1,5,2]=>1 [4,3,6,2,1,5]=>1 [4,3,6,2,5,1]=>1 [4,3,6,5,1,2]=>0 [4,3,6,5,2,1]=>0 [4,5,1,2,3,6]=>4 [4,5,1,2,6,3]=>1 [4,5,1,3,2,6]=>2 [4,5,1,3,6,2]=>1 [4,5,1,6,2,3]=>2 [4,5,1,6,3,2]=>0 [4,5,2,1,3,6]=>2 [4,5,2,1,6,3]=>1 [4,5,2,3,1,6]=>2 [4,5,2,3,6,1]=>1 [4,5,2,6,1,3]=>2 [4,5,2,6,3,1]=>0 [4,5,3,1,2,6]=>1 [4,5,3,1,6,2]=>1 [4,5,3,2,1,6]=>1 [4,5,3,2,6,1]=>1 [4,5,3,6,1,2]=>2 [4,5,3,6,2,1]=>0 [4,5,6,1,2,3]=>3 [4,5,6,1,3,2]=>1 [4,5,6,2,1,3]=>1 [4,5,6,2,3,1]=>1 [4,5,6,3,1,2]=>0 [4,5,6,3,2,1]=>0 [4,6,1,2,3,5]=>4 [4,6,1,2,5,3]=>1 [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]=>0 [4,6,2,1,3,5]=>2 [4,6,2,1,5,3]=>1 [4,6,2,3,1,5]=>2 [4,6,2,3,5,1]=>1 [4,6,2,5,1,3]=>2 [4,6,2,5,3,1]=>0 [4,6,3,1,2,5]=>1 [4,6,3,1,5,2]=>1 [4,6,3,2,1,5]=>1 [4,6,3,2,5,1]=>1 [4,6,3,5,1,2]=>2 [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]=>1 [5,1,2,4,3,6]=>1 [5,1,2,4,6,3]=>1 [5,1,2,6,3,4]=>2 [5,1,2,6,4,3]=>0 [5,1,3,2,4,6]=>1 [5,1,3,2,6,4]=>1 [5,1,3,4,2,6]=>1 [5,1,3,4,6,2]=>1 [5,1,3,6,2,4]=>2 [5,1,3,6,4,2]=>0 [5,1,4,2,3,6]=>1 [5,1,4,2,6,3]=>1 [5,1,4,3,2,6]=>1 [5,1,4,3,6,2]=>1 [5,1,4,6,2,3]=>2 [5,1,4,6,3,2]=>0 [5,1,6,2,3,4]=>3 [5,1,6,2,4,3]=>1 [5,1,6,3,2,4]=>1 [5,1,6,3,4,2]=>1 [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]=>1 [5,2,1,4,3,6]=>1 [5,2,1,4,6,3]=>1 [5,2,1,6,3,4]=>2 [5,2,1,6,4,3]=>0 [5,2,3,1,4,6]=>1 [5,2,3,1,6,4]=>1 [5,2,3,4,1,6]=>1 [5,2,3,4,6,1]=>1 [5,2,3,6,1,4]=>2 [5,2,3,6,4,1]=>0 [5,2,4,1,3,6]=>1 [5,2,4,1,6,3]=>1 [5,2,4,3,1,6]=>1 [5,2,4,3,6,1]=>1 [5,2,4,6,1,3]=>2 [5,2,4,6,3,1]=>0 [5,2,6,1,3,4]=>3 [5,2,6,1,4,3]=>1 [5,2,6,3,1,4]=>1 [5,2,6,3,4,1]=>1 [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]=>1 [5,3,1,4,2,6]=>1 [5,3,1,4,6,2]=>1 [5,3,1,6,2,4]=>2 [5,3,1,6,4,2]=>0 [5,3,2,1,4,6]=>1 [5,3,2,1,6,4]=>1 [5,3,2,4,1,6]=>1 [5,3,2,4,6,1]=>1 [5,3,2,6,1,4]=>2 [5,3,2,6,4,1]=>0 [5,3,4,1,2,6]=>1 [5,3,4,1,6,2]=>1 [5,3,4,2,1,6]=>1 [5,3,4,2,6,1]=>1 [5,3,4,6,1,2]=>2 [5,3,4,6,2,1]=>0 [5,3,6,1,2,4]=>3 [5,3,6,1,4,2]=>1 [5,3,6,2,1,4]=>1 [5,3,6,2,4,1]=>1 [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]=>1 [5,4,1,3,2,6]=>1 [5,4,1,3,6,2]=>1 [5,4,1,6,2,3]=>2 [5,4,1,6,3,2]=>0 [5,4,2,1,3,6]=>1 [5,4,2,1,6,3]=>1 [5,4,2,3,1,6]=>1 [5,4,2,3,6,1]=>1 [5,4,2,6,1,3]=>2 [5,4,2,6,3,1]=>0 [5,4,3,1,2,6]=>1 [5,4,3,1,6,2]=>1 [5,4,3,2,1,6]=>1 [5,4,3,2,6,1]=>1 [5,4,3,6,1,2]=>2 [5,4,3,6,2,1]=>0 [5,4,6,1,2,3]=>3 [5,4,6,1,3,2]=>1 [5,4,6,2,1,3]=>1 [5,4,6,2,3,1]=>1 [5,4,6,3,1,2]=>0 [5,4,6,3,2,1]=>0 [5,6,1,2,3,4]=>4 [5,6,1,2,4,3]=>1 [5,6,1,3,2,4]=>2 [5,6,1,3,4,2]=>1 [5,6,1,4,2,3]=>2 [5,6,1,4,3,2]=>0 [5,6,2,1,3,4]=>2 [5,6,2,1,4,3]=>1 [5,6,2,3,1,4]=>2 [5,6,2,3,4,1]=>1 [5,6,2,4,1,3]=>2 [5,6,2,4,3,1]=>0 [5,6,3,1,2,4]=>1 [5,6,3,1,4,2]=>1 [5,6,3,2,1,4]=>1 [5,6,3,2,4,1]=>1 [5,6,3,4,1,2]=>2 [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]=>7 [1,2,3,4,5,7,6]=>1 [1,2,3,4,6,5,7]=>2 [1,2,3,4,6,7,5]=>1 [1,2,3,4,7,5,6]=>2 [1,2,3,4,7,6,5]=>0 [1,2,3,5,4,6,7]=>3 [1,2,3,5,4,7,6]=>1 [1,2,3,5,6,4,7]=>2 [1,2,3,5,6,7,4]=>1 [1,2,3,5,7,4,6]=>2 [1,2,3,5,7,6,4]=>0 [1,2,3,6,4,5,7]=>3 [1,2,3,6,4,7,5]=>1 [1,2,3,6,5,4,7]=>1 [1,2,3,6,5,7,4]=>1 [1,2,3,6,7,4,5]=>2 [1,2,3,6,7,5,4]=>0 [1,2,3,7,4,5,6]=>3 [1,2,3,7,4,6,5]=>1 [1,2,3,7,5,4,6]=>1 [1,2,3,7,5,6,4]=>1 [1,2,3,7,6,4,5]=>0 [1,2,3,7,6,5,4]=>0 [1,2,4,3,5,6,7]=>4 [1,2,4,3,5,7,6]=>1 [1,2,4,3,6,5,7]=>2 [1,2,4,3,6,7,5]=>1 [1,2,4,3,7,5,6]=>2 [1,2,4,3,7,6,5]=>0 [1,2,4,5,3,6,7]=>3 [1,2,4,5,3,7,6]=>1 [1,2,4,5,6,3,7]=>2 [1,2,4,5,6,7,3]=>1 [1,2,4,5,7,3,6]=>2 [1,2,4,5,7,6,3]=>0 [1,2,4,6,3,5,7]=>3 [1,2,4,6,3,7,5]=>1 [1,2,4,6,5,3,7]=>1 [1,2,4,6,5,7,3]=>1 [1,2,4,6,7,3,5]=>2 [1,2,4,6,7,5,3]=>0 [1,2,4,7,3,5,6]=>3 [1,2,4,7,3,6,5]=>1 [1,2,4,7,5,3,6]=>1 [1,2,4,7,5,6,3]=>1 [1,2,4,7,6,3,5]=>0 [1,2,4,7,6,5,3]=>0 [1,2,5,3,4,6,7]=>4 [1,2,5,3,4,7,6]=>1 [1,2,5,3,6,4,7]=>2 [1,2,5,3,6,7,4]=>1 [1,2,5,3,7,4,6]=>2 [1,2,5,3,7,6,4]=>0 [1,2,5,4,3,6,7]=>2 [1,2,5,4,3,7,6]=>1 [1,2,5,4,6,3,7]=>2 [1,2,5,4,6,7,3]=>1 [1,2,5,4,7,3,6]=>2 [1,2,5,4,7,6,3]=>0 [1,2,5,6,3,4,7]=>3 [1,2,5,6,3,7,4]=>1 [1,2,5,6,4,3,7]=>1 [1,2,5,6,4,7,3]=>1 [1,2,5,6,7,3,4]=>2 [1,2,5,6,7,4,3]=>0 [1,2,5,7,3,4,6]=>3 [1,2,5,7,3,6,4]=>1 [1,2,5,7,4,3,6]=>1 [1,2,5,7,4,6,3]=>1 [1,2,5,7,6,3,4]=>0 [1,2,5,7,6,4,3]=>0 [1,2,6,3,4,5,7]=>4 [1,2,6,3,4,7,5]=>1 [1,2,6,3,5,4,7]=>2 [1,2,6,3,5,7,4]=>1 [1,2,6,3,7,4,5]=>2 [1,2,6,3,7,5,4]=>0 [1,2,6,4,3,5,7]=>2 [1,2,6,4,3,7,5]=>1 [1,2,6,4,5,3,7]=>2 [1,2,6,4,5,7,3]=>1 [1,2,6,4,7,3,5]=>2 [1,2,6,4,7,5,3]=>0 [1,2,6,5,3,4,7]=>1 [1,2,6,5,3,7,4]=>1 [1,2,6,5,4,3,7]=>1 [1,2,6,5,4,7,3]=>1 [1,2,6,5,7,3,4]=>2 [1,2,6,5,7,4,3]=>0 [1,2,6,7,3,4,5]=>3 [1,2,6,7,3,5,4]=>1 [1,2,6,7,4,3,5]=>1 [1,2,6,7,4,5,3]=>1 [1,2,6,7,5,3,4]=>0 [1,2,6,7,5,4,3]=>0 [1,2,7,3,4,5,6]=>4 [1,2,7,3,4,6,5]=>1 [1,2,7,3,5,4,6]=>2 [1,2,7,3,5,6,4]=>1 [1,2,7,3,6,4,5]=>2 [1,2,7,3,6,5,4]=>0 [1,2,7,4,3,5,6]=>2 [1,2,7,4,3,6,5]=>1 [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]=>0 [1,2,7,5,3,4,6]=>1 [1,2,7,5,3,6,4]=>1 [1,2,7,5,4,3,6]=>1 [1,2,7,5,4,6,3]=>1 [1,2,7,5,6,3,4]=>2 [1,2,7,5,6,4,3]=>0 [1,2,7,6,3,4,5]=>0 [1,2,7,6,3,5,4]=>0 [1,2,7,6,4,3,5]=>0 [1,2,7,6,4,5,3]=>0 [1,2,7,6,5,3,4]=>0 [1,2,7,6,5,4,3]=>0 [1,3,2,4,5,6,7]=>5 [1,3,2,4,5,7,6]=>1 [1,3,2,4,6,5,7]=>2 [1,3,2,4,6,7,5]=>1 [1,3,2,4,7,5,6]=>2 [1,3,2,4,7,6,5]=>0 [1,3,2,5,4,6,7]=>3 [1,3,2,5,4,7,6]=>1 [1,3,2,5,6,4,7]=>2 [1,3,2,5,6,7,4]=>1 [1,3,2,5,7,4,6]=>2 [1,3,2,5,7,6,4]=>0 [1,3,2,6,4,5,7]=>3 [1,3,2,6,4,7,5]=>1 [1,3,2,6,5,4,7]=>1 [1,3,2,6,5,7,4]=>1 [1,3,2,6,7,4,5]=>2 [1,3,2,6,7,5,4]=>0 [1,3,2,7,4,5,6]=>3 [1,3,2,7,4,6,5]=>1 [1,3,2,7,5,4,6]=>1 [1,3,2,7,5,6,4]=>1 [1,3,2,7,6,4,5]=>0 [1,3,2,7,6,5,4]=>0 [1,3,4,2,5,6,7]=>4 [1,3,4,2,5,7,6]=>1 [1,3,4,2,6,5,7]=>2 [1,3,4,2,6,7,5]=>1 [1,3,4,2,7,5,6]=>2 [1,3,4,2,7,6,5]=>0 [1,3,4,5,2,6,7]=>3 [1,3,4,5,2,7,6]=>1 [1,3,4,5,6,2,7]=>2 [1,3,4,5,6,7,2]=>1 [1,3,4,5,7,2,6]=>2 [1,3,4,5,7,6,2]=>0 [1,3,4,6,2,5,7]=>3 [1,3,4,6,2,7,5]=>1 [1,3,4,6,5,2,7]=>1 [1,3,4,6,5,7,2]=>1 [1,3,4,6,7,2,5]=>2 [1,3,4,6,7,5,2]=>0 [1,3,4,7,2,5,6]=>3 [1,3,4,7,2,6,5]=>1 [1,3,4,7,5,2,6]=>1 [1,3,4,7,5,6,2]=>1 [1,3,4,7,6,2,5]=>0 [1,3,4,7,6,5,2]=>0 [1,3,5,2,4,6,7]=>4 [1,3,5,2,4,7,6]=>1 [1,3,5,2,6,4,7]=>2 [1,3,5,2,6,7,4]=>1 [1,3,5,2,7,4,6]=>2 [1,3,5,2,7,6,4]=>0 [1,3,5,4,2,6,7]=>2 [1,3,5,4,2,7,6]=>1 [1,3,5,4,6,2,7]=>2 [1,3,5,4,6,7,2]=>1 [1,3,5,4,7,2,6]=>2 [1,3,5,4,7,6,2]=>0 [1,3,5,6,2,4,7]=>3 [1,3,5,6,2,7,4]=>1 [1,3,5,6,4,2,7]=>1 [1,3,5,6,4,7,2]=>1 [1,3,5,6,7,2,4]=>2 [1,3,5,6,7,4,2]=>0 [1,3,5,7,2,4,6]=>3 [1,3,5,7,2,6,4]=>1 [1,3,5,7,4,2,6]=>1 [1,3,5,7,4,6,2]=>1 [1,3,5,7,6,2,4]=>0 [1,3,5,7,6,4,2]=>0 [1,3,6,2,4,5,7]=>4 [1,3,6,2,4,7,5]=>1 [1,3,6,2,5,4,7]=>2 [1,3,6,2,5,7,4]=>1 [1,3,6,2,7,4,5]=>2 [1,3,6,2,7,5,4]=>0 [1,3,6,4,2,5,7]=>2 [1,3,6,4,2,7,5]=>1 [1,3,6,4,5,2,7]=>2 [1,3,6,4,5,7,2]=>1 [1,3,6,4,7,2,5]=>2 [1,3,6,4,7,5,2]=>0 [1,3,6,5,2,4,7]=>1 [1,3,6,5,2,7,4]=>1 [1,3,6,5,4,2,7]=>1 [1,3,6,5,4,7,2]=>1 [1,3,6,5,7,2,4]=>2 [1,3,6,5,7,4,2]=>0 [1,3,6,7,2,4,5]=>3 [1,3,6,7,2,5,4]=>1 [1,3,6,7,4,2,5]=>1 [1,3,6,7,4,5,2]=>1 [1,3,6,7,5,2,4]=>0 [1,3,6,7,5,4,2]=>0 [1,3,7,2,4,5,6]=>4 [1,3,7,2,4,6,5]=>1 [1,3,7,2,5,4,6]=>2 [1,3,7,2,5,6,4]=>1 [1,3,7,2,6,4,5]=>2 [1,3,7,2,6,5,4]=>0 [1,3,7,4,2,5,6]=>2 [1,3,7,4,2,6,5]=>1 [1,3,7,4,5,2,6]=>2 [1,3,7,4,5,6,2]=>1 [1,3,7,4,6,2,5]=>2 [1,3,7,4,6,5,2]=>0 [1,3,7,5,2,4,6]=>1 [1,3,7,5,2,6,4]=>1 [1,3,7,5,4,2,6]=>1 [1,3,7,5,4,6,2]=>1 [1,3,7,5,6,2,4]=>2 [1,3,7,5,6,4,2]=>0 [1,3,7,6,2,4,5]=>0 [1,3,7,6,2,5,4]=>0 [1,3,7,6,4,2,5]=>0 [1,3,7,6,4,5,2]=>0 [1,3,7,6,5,2,4]=>0 [1,3,7,6,5,4,2]=>0 [1,4,2,3,5,6,7]=>5 [1,4,2,3,5,7,6]=>1 [1,4,2,3,6,5,7]=>2 [1,4,2,3,6,7,5]=>1 [1,4,2,3,7,5,6]=>2 [1,4,2,3,7,6,5]=>0 [1,4,2,5,3,6,7]=>3 [1,4,2,5,3,7,6]=>1 [1,4,2,5,6,3,7]=>2 [1,4,2,5,6,7,3]=>1 [1,4,2,5,7,3,6]=>2 [1,4,2,5,7,6,3]=>0 [1,4,2,6,3,5,7]=>3 [1,4,2,6,3,7,5]=>1 [1,4,2,6,5,3,7]=>1 [1,4,2,6,5,7,3]=>1 [1,4,2,6,7,3,5]=>2 [1,4,2,6,7,5,3]=>0 [1,4,2,7,3,5,6]=>3 [1,4,2,7,3,6,5]=>1 [1,4,2,7,5,3,6]=>1 [1,4,2,7,5,6,3]=>1 [1,4,2,7,6,3,5]=>0 [1,4,2,7,6,5,3]=>0 [1,4,3,2,5,6,7]=>3 [1,4,3,2,5,7,6]=>1 [1,4,3,2,6,5,7]=>2 [1,4,3,2,6,7,5]=>1 [1,4,3,2,7,5,6]=>2 [1,4,3,2,7,6,5]=>0 [1,4,3,5,2,6,7]=>3 [1,4,3,5,2,7,6]=>1 [1,4,3,5,6,2,7]=>2 [1,4,3,5,6,7,2]=>1 [1,4,3,5,7,2,6]=>2 [1,4,3,5,7,6,2]=>0 [1,4,3,6,2,5,7]=>3 [1,4,3,6,2,7,5]=>1 [1,4,3,6,5,2,7]=>1 [1,4,3,6,5,7,2]=>1 [1,4,3,6,7,2,5]=>2 [1,4,3,6,7,5,2]=>0 [1,4,3,7,2,5,6]=>3 [1,4,3,7,2,6,5]=>1 [1,4,3,7,5,2,6]=>1 [1,4,3,7,5,6,2]=>1 [1,4,3,7,6,2,5]=>0 [1,4,3,7,6,5,2]=>0 [1,4,5,2,3,6,7]=>4 [1,4,5,2,3,7,6]=>1 [1,4,5,2,6,3,7]=>2 [1,4,5,2,6,7,3]=>1 [1,4,5,2,7,3,6]=>2 [1,4,5,2,7,6,3]=>0 [1,4,5,3,2,6,7]=>2 [1,4,5,3,2,7,6]=>1 [1,4,5,3,6,2,7]=>2 [1,4,5,3,6,7,2]=>1 [1,4,5,3,7,2,6]=>2 [1,4,5,3,7,6,2]=>0 [1,4,5,6,2,3,7]=>3 [1,4,5,6,2,7,3]=>1 [1,4,5,6,3,2,7]=>1 [1,4,5,6,3,7,2]=>1 [1,4,5,6,7,2,3]=>2 [1,4,5,6,7,3,2]=>0 [1,4,5,7,2,3,6]=>3 [1,4,5,7,2,6,3]=>1 [1,4,5,7,3,2,6]=>1 [1,4,5,7,3,6,2]=>1 [1,4,5,7,6,2,3]=>0 [1,4,5,7,6,3,2]=>0 [1,4,6,2,3,5,7]=>4 [1,4,6,2,3,7,5]=>1 [1,4,6,2,5,3,7]=>2 [1,4,6,2,5,7,3]=>1 [1,4,6,2,7,3,5]=>2 [1,4,6,2,7,5,3]=>0 [1,4,6,3,2,5,7]=>2 [1,4,6,3,2,7,5]=>1 [1,4,6,3,5,2,7]=>2 [1,4,6,3,5,7,2]=>1 [1,4,6,3,7,2,5]=>2 [1,4,6,3,7,5,2]=>0 [1,4,6,5,2,3,7]=>1 [1,4,6,5,2,7,3]=>1 [1,4,6,5,3,2,7]=>1 [1,4,6,5,3,7,2]=>1
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
click to show known generating functions       
Description
The rix statistic of a permutation.
This statistic is defined recursively as follows: $rix([]) = 0$, and if $w_i = \max\{w_1, w_2,\dots, w_k\}$, then
$rix(w) := 0$ if $i = 1 < k$,
$rix(w) := 1 + rix(w_1,w_2,\dots,w_{k−1})$ if $i = k$ and
$rix(w) := rix(w_{i+1},w_{i+2},\dots,w_k)$ if $1 < i < k$.
References
[1] Lin, Z., Zeng, J. The γ-positivity of basic Eulerian polynomials via group actions arXiv:1411.3397
Code
def statistic(w):
    """
    sage: statistic([1])
    1
    sage: statistic([2,9,1,7,5,3,4,6,8])
    2

    """
    if len(w) == 0:
        return 0
    k = len(w)
    i = w.index(max(w)) + 1
    if i == 1 < k:
        return 0
    elif i == k:
        return 1 + statistic(w[:-1])
    elif 1 < i < k:
        return statistic(w[i:])
    raise ValueError
Created
Apr 07, 2016 at 11:45 by Martin Rubey
Updated
Apr 07, 2016 at 11:45 by Martin Rubey