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]=>0 [3,1,2]=>1 [3,2,1]=>0 [1,2,3,4]=>4 [1,2,4,3]=>2 [1,3,2,4]=>2 [1,3,4,2]=>1 [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]=>0 [2,4,1,3]=>2 [2,4,3,1]=>0 [3,1,2,4]=>1 [3,1,4,2]=>1 [3,2,1,4]=>0 [3,2,4,1]=>0 [3,4,1,2]=>2 [3,4,2,1]=>0 [4,1,2,3]=>1 [4,1,3,2]=>1 [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]=>3 [1,2,4,3,5]=>3 [1,2,4,5,3]=>2 [1,2,5,3,4]=>3 [1,2,5,4,3]=>2 [1,3,2,4,5]=>2 [1,3,2,5,4]=>2 [1,3,4,2,5]=>3 [1,3,4,5,2]=>1 [1,3,5,2,4]=>3 [1,3,5,4,2]=>1 [1,4,2,3,5]=>2 [1,4,2,5,3]=>2 [1,4,3,2,5]=>1 [1,4,3,5,2]=>1 [1,4,5,2,3]=>3 [1,4,5,3,2]=>1 [1,5,2,3,4]=>2 [1,5,2,4,3]=>2 [1,5,3,2,4]=>1 [1,5,3,4,2]=>1 [1,5,4,2,3]=>1 [1,5,4,3,2]=>1 [2,1,3,4,5]=>1 [2,1,3,5,4]=>1 [2,1,4,3,5]=>1 [2,1,4,5,3]=>1 [2,1,5,3,4]=>1 [2,1,5,4,3]=>1 [2,3,1,4,5]=>2 [2,3,1,5,4]=>2 [2,3,4,1,5]=>3 [2,3,4,5,1]=>0 [2,3,5,1,4]=>3 [2,3,5,4,1]=>0 [2,4,1,3,5]=>2 [2,4,1,5,3]=>2 [2,4,3,1,5]=>1 [2,4,3,5,1]=>0 [2,4,5,1,3]=>3 [2,4,5,3,1]=>0 [2,5,1,3,4]=>2 [2,5,1,4,3]=>2 [2,5,3,1,4]=>1 [2,5,3,4,1]=>0 [2,5,4,1,3]=>1 [2,5,4,3,1]=>0 [3,1,2,4,5]=>1 [3,1,2,5,4]=>1 [3,1,4,2,5]=>1 [3,1,4,5,2]=>1 [3,1,5,2,4]=>1 [3,1,5,4,2]=>1 [3,2,1,4,5]=>0 [3,2,1,5,4]=>0 [3,2,4,1,5]=>1 [3,2,4,5,1]=>0 [3,2,5,1,4]=>1 [3,2,5,4,1]=>0 [3,4,1,2,5]=>2 [3,4,1,5,2]=>2 [3,4,2,1,5]=>0 [3,4,2,5,1]=>0 [3,4,5,1,2]=>3 [3,4,5,2,1]=>0 [3,5,1,2,4]=>2 [3,5,1,4,2]=>2 [3,5,2,1,4]=>0 [3,5,2,4,1]=>0 [3,5,4,1,2]=>1 [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]=>1 [4,1,5,3,2]=>1 [4,2,1,3,5]=>0 [4,2,1,5,3]=>0 [4,2,3,1,5]=>1 [4,2,3,5,1]=>0 [4,2,5,1,3]=>1 [4,2,5,3,1]=>0 [4,3,1,2,5]=>0 [4,3,1,5,2]=>0 [4,3,2,1,5]=>0 [4,3,2,5,1]=>0 [4,3,5,1,2]=>1 [4,3,5,2,1]=>0 [4,5,1,2,3]=>2 [4,5,1,3,2]=>2 [4,5,2,1,3]=>0 [4,5,2,3,1]=>0 [4,5,3,1,2]=>0 [4,5,3,2,1]=>0 [5,1,2,3,4]=>1 [5,1,2,4,3]=>1 [5,1,3,2,4]=>1 [5,1,3,4,2]=>1 [5,1,4,2,3]=>1 [5,1,4,3,2]=>1 [5,2,1,3,4]=>0 [5,2,1,4,3]=>0 [5,2,3,1,4]=>1 [5,2,3,4,1]=>0 [5,2,4,1,3]=>1 [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]=>1 [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]=>4 [1,2,3,5,4,6]=>4 [1,2,3,5,6,4]=>3 [1,2,3,6,4,5]=>4 [1,2,3,6,5,4]=>3 [1,2,4,3,5,6]=>3 [1,2,4,3,6,5]=>3 [1,2,4,5,3,6]=>4 [1,2,4,5,6,3]=>2 [1,2,4,6,3,5]=>4 [1,2,4,6,5,3]=>2 [1,2,5,3,4,6]=>3 [1,2,5,3,6,4]=>3 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>2 [1,2,5,6,3,4]=>4 [1,2,5,6,4,3]=>2 [1,2,6,3,4,5]=>3 [1,2,6,3,5,4]=>3 [1,2,6,4,3,5]=>2 [1,2,6,4,5,3]=>2 [1,2,6,5,3,4]=>2 [1,2,6,5,4,3]=>2 [1,3,2,4,5,6]=>2 [1,3,2,4,6,5]=>2 [1,3,2,5,4,6]=>2 [1,3,2,5,6,4]=>2 [1,3,2,6,4,5]=>2 [1,3,2,6,5,4]=>2 [1,3,4,2,5,6]=>3 [1,3,4,2,6,5]=>3 [1,3,4,5,2,6]=>4 [1,3,4,5,6,2]=>1 [1,3,4,6,2,5]=>4 [1,3,4,6,5,2]=>1 [1,3,5,2,4,6]=>3 [1,3,5,2,6,4]=>3 [1,3,5,4,2,6]=>2 [1,3,5,4,6,2]=>1 [1,3,5,6,2,4]=>4 [1,3,5,6,4,2]=>1 [1,3,6,2,4,5]=>3 [1,3,6,2,5,4]=>3 [1,3,6,4,2,5]=>2 [1,3,6,4,5,2]=>1 [1,3,6,5,2,4]=>2 [1,3,6,5,4,2]=>1 [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]=>1 [1,4,3,6,2,5]=>2 [1,4,3,6,5,2]=>1 [1,4,5,2,3,6]=>3 [1,4,5,2,6,3]=>3 [1,4,5,3,2,6]=>1 [1,4,5,3,6,2]=>1 [1,4,5,6,2,3]=>4 [1,4,5,6,3,2]=>1 [1,4,6,2,3,5]=>3 [1,4,6,2,5,3]=>3 [1,4,6,3,2,5]=>1 [1,4,6,3,5,2]=>1 [1,4,6,5,2,3]=>2 [1,4,6,5,3,2]=>1 [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]=>1 [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]=>1 [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]=>1 [1,5,6,2,3,4]=>3 [1,5,6,2,4,3]=>3 [1,5,6,3,2,4]=>1 [1,5,6,3,4,2]=>1 [1,5,6,4,2,3]=>1 [1,5,6,4,3,2]=>1 [1,6,2,3,4,5]=>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]=>1 [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]=>1 [1,6,4,2,3,5]=>1 [1,6,4,2,5,3]=>1 [1,6,4,3,2,5]=>1 [1,6,4,3,5,2]=>1 [1,6,4,5,2,3]=>2 [1,6,4,5,3,2]=>1 [1,6,5,2,3,4]=>1 [1,6,5,2,4,3]=>1 [1,6,5,3,2,4]=>1 [1,6,5,3,4,2]=>1 [1,6,5,4,2,3]=>1 [1,6,5,4,3,2]=>1 [2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>1 [2,1,3,5,4,6]=>1 [2,1,3,5,6,4]=>1 [2,1,3,6,4,5]=>1 [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]=>1 [2,1,4,5,6,3]=>1 [2,1,4,6,3,5]=>1 [2,1,4,6,5,3]=>1 [2,1,5,3,4,6]=>1 [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]=>1 [2,1,5,6,4,3]=>1 [2,1,6,3,4,5]=>1 [2,1,6,3,5,4]=>1 [2,1,6,4,3,5]=>1 [2,1,6,4,5,3]=>1 [2,1,6,5,3,4]=>1 [2,1,6,5,4,3]=>1 [2,3,1,4,5,6]=>2 [2,3,1,4,6,5]=>2 [2,3,1,5,4,6]=>2 [2,3,1,5,6,4]=>2 [2,3,1,6,4,5]=>2 [2,3,1,6,5,4]=>2 [2,3,4,1,5,6]=>3 [2,3,4,1,6,5]=>3 [2,3,4,5,1,6]=>4 [2,3,4,5,6,1]=>0 [2,3,4,6,1,5]=>4 [2,3,4,6,5,1]=>0 [2,3,5,1,4,6]=>3 [2,3,5,1,6,4]=>3 [2,3,5,4,1,6]=>2 [2,3,5,4,6,1]=>0 [2,3,5,6,1,4]=>4 [2,3,5,6,4,1]=>0 [2,3,6,1,4,5]=>3 [2,3,6,1,5,4]=>3 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>0 [2,3,6,5,1,4]=>2 [2,3,6,5,4,1]=>0 [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]=>1 [2,4,3,1,6,5]=>1 [2,4,3,5,1,6]=>2 [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]=>3 [2,4,5,1,6,3]=>3 [2,4,5,3,1,6]=>1 [2,4,5,3,6,1]=>0 [2,4,5,6,1,3]=>4 [2,4,5,6,3,1]=>0 [2,4,6,1,3,5]=>3 [2,4,6,1,5,3]=>3 [2,4,6,3,1,5]=>1 [2,4,6,3,5,1]=>0 [2,4,6,5,1,3]=>2 [2,4,6,5,3,1]=>0 [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]=>1 [2,5,3,1,6,4]=>1 [2,5,3,4,1,6]=>2 [2,5,3,4,6,1]=>0 [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]=>0 [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]=>3 [2,5,6,3,1,4]=>1 [2,5,6,3,4,1]=>0 [2,5,6,4,1,3]=>1 [2,5,6,4,3,1]=>0 [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]=>1 [2,6,3,1,5,4]=>1 [2,6,3,4,1,5]=>2 [2,6,3,4,5,1]=>0 [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]=>0 [2,6,4,5,1,3]=>2 [2,6,4,5,3,1]=>0 [2,6,5,1,3,4]=>1 [2,6,5,1,4,3]=>1 [2,6,5,3,1,4]=>1 [2,6,5,3,4,1]=>0 [2,6,5,4,1,3]=>1 [2,6,5,4,3,1]=>0 [3,1,2,4,5,6]=>1 [3,1,2,4,6,5]=>1 [3,1,2,5,4,6]=>1 [3,1,2,5,6,4]=>1 [3,1,2,6,4,5]=>1 [3,1,2,6,5,4]=>1 [3,1,4,2,5,6]=>1 [3,1,4,2,6,5]=>1 [3,1,4,5,2,6]=>1 [3,1,4,5,6,2]=>1 [3,1,4,6,2,5]=>1 [3,1,4,6,5,2]=>1 [3,1,5,2,4,6]=>1 [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]=>1 [3,1,5,6,4,2]=>1 [3,1,6,2,4,5]=>1 [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]=>1 [3,1,6,5,4,2]=>1 [3,2,1,4,5,6]=>0 [3,2,1,4,6,5]=>0 [3,2,1,5,4,6]=>0 [3,2,1,5,6,4]=>0 [3,2,1,6,4,5]=>0 [3,2,1,6,5,4]=>0 [3,2,4,1,5,6]=>1 [3,2,4,1,6,5]=>1 [3,2,4,5,1,6]=>1 [3,2,4,5,6,1]=>0 [3,2,4,6,1,5]=>1 [3,2,4,6,5,1]=>0 [3,2,5,1,4,6]=>1 [3,2,5,1,6,4]=>1 [3,2,5,4,1,6]=>1 [3,2,5,4,6,1]=>0 [3,2,5,6,1,4]=>1 [3,2,5,6,4,1]=>0 [3,2,6,1,4,5]=>1 [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]=>1 [3,2,6,5,4,1]=>0 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>2 [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]=>0 [3,4,2,1,6,5]=>0 [3,4,2,5,1,6]=>2 [3,4,2,5,6,1]=>0 [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]=>3 [3,4,5,2,1,6]=>0 [3,4,5,2,6,1]=>0 [3,4,5,6,1,2]=>4 [3,4,5,6,2,1]=>0 [3,4,6,1,2,5]=>3 [3,4,6,1,5,2]=>3 [3,4,6,2,1,5]=>0 [3,4,6,2,5,1]=>0 [3,4,6,5,1,2]=>2 [3,4,6,5,2,1]=>0 [3,5,1,2,4,6]=>2 [3,5,1,2,6,4]=>2 [3,5,1,4,2,6]=>2 [3,5,1,4,6,2]=>2 [3,5,1,6,2,4]=>2 [3,5,1,6,4,2]=>2 [3,5,2,1,4,6]=>0 [3,5,2,1,6,4]=>0 [3,5,2,4,1,6]=>2 [3,5,2,4,6,1]=>0 [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]=>0 [3,5,4,2,6,1]=>0 [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]=>3 [3,5,6,2,1,4]=>0 [3,5,6,2,4,1]=>0 [3,5,6,4,1,2]=>1 [3,5,6,4,2,1]=>0 [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]=>2 [3,6,1,5,2,4]=>2 [3,6,1,5,4,2]=>2 [3,6,2,1,4,5]=>0 [3,6,2,1,5,4]=>0 [3,6,2,4,1,5]=>2 [3,6,2,4,5,1]=>0 [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]=>0 [3,6,4,2,5,1]=>0 [3,6,4,5,1,2]=>2 [3,6,4,5,2,1]=>0 [3,6,5,1,2,4]=>1 [3,6,5,1,4,2]=>1 [3,6,5,2,1,4]=>0 [3,6,5,2,4,1]=>0 [3,6,5,4,1,2]=>1 [3,6,5,4,2,1]=>0 [4,1,2,3,5,6]=>1 [4,1,2,3,6,5]=>1 [4,1,2,5,3,6]=>1 [4,1,2,5,6,3]=>1 [4,1,2,6,3,5]=>1 [4,1,2,6,5,3]=>1 [4,1,3,2,5,6]=>1 [4,1,3,2,6,5]=>1 [4,1,3,5,2,6]=>1 [4,1,3,5,6,2]=>1 [4,1,3,6,2,5]=>1 [4,1,3,6,5,2]=>1 [4,1,5,2,3,6]=>1 [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]=>1 [4,1,5,6,3,2]=>1 [4,1,6,2,3,5]=>1 [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]=>1 [4,1,6,5,3,2]=>1 [4,2,1,3,5,6]=>0 [4,2,1,3,6,5]=>0 [4,2,1,5,3,6]=>0 [4,2,1,5,6,3]=>0 [4,2,1,6,3,5]=>0 [4,2,1,6,5,3]=>0 [4,2,3,1,5,6]=>1 [4,2,3,1,6,5]=>1 [4,2,3,5,1,6]=>1 [4,2,3,5,6,1]=>0 [4,2,3,6,1,5]=>1 [4,2,3,6,5,1]=>0 [4,2,5,1,3,6]=>1 [4,2,5,1,6,3]=>1 [4,2,5,3,1,6]=>1 [4,2,5,3,6,1]=>0 [4,2,5,6,1,3]=>1 [4,2,5,6,3,1]=>0 [4,2,6,1,3,5]=>1 [4,2,6,1,5,3]=>1 [4,2,6,3,1,5]=>1 [4,2,6,3,5,1]=>0 [4,2,6,5,1,3]=>1 [4,2,6,5,3,1]=>0 [4,3,1,2,5,6]=>0 [4,3,1,2,6,5]=>0 [4,3,1,5,2,6]=>0 [4,3,1,5,6,2]=>0 [4,3,1,6,2,5]=>0 [4,3,1,6,5,2]=>0 [4,3,2,1,5,6]=>0 [4,3,2,1,6,5]=>0 [4,3,2,5,1,6]=>0 [4,3,2,5,6,1]=>0 [4,3,2,6,1,5]=>0 [4,3,2,6,5,1]=>0 [4,3,5,1,2,6]=>1 [4,3,5,1,6,2]=>1 [4,3,5,2,1,6]=>0 [4,3,5,2,6,1]=>0 [4,3,5,6,1,2]=>1 [4,3,5,6,2,1]=>0 [4,3,6,1,2,5]=>1 [4,3,6,1,5,2]=>1 [4,3,6,2,1,5]=>0 [4,3,6,2,5,1]=>0 [4,3,6,5,1,2]=>1 [4,3,6,5,2,1]=>0 [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]=>2 [4,5,1,6,2,3]=>2 [4,5,1,6,3,2]=>2 [4,5,2,1,3,6]=>0 [4,5,2,1,6,3]=>0 [4,5,2,3,1,6]=>2 [4,5,2,3,6,1]=>0 [4,5,2,6,1,3]=>2 [4,5,2,6,3,1]=>0 [4,5,3,1,2,6]=>0 [4,5,3,1,6,2]=>0 [4,5,3,2,1,6]=>0 [4,5,3,2,6,1]=>0 [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]=>3 [4,5,6,2,1,3]=>0 [4,5,6,2,3,1]=>0 [4,5,6,3,1,2]=>0 [4,5,6,3,2,1]=>0 [4,6,1,2,3,5]=>2 [4,6,1,2,5,3]=>2 [4,6,1,3,2,5]=>2 [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]=>0 [4,6,2,1,5,3]=>0 [4,6,2,3,1,5]=>2 [4,6,2,3,5,1]=>0 [4,6,2,5,1,3]=>2 [4,6,2,5,3,1]=>0 [4,6,3,1,2,5]=>0 [4,6,3,1,5,2]=>0 [4,6,3,2,1,5]=>0 [4,6,3,2,5,1]=>0 [4,6,3,5,1,2]=>2 [4,6,3,5,2,1]=>0 [4,6,5,1,2,3]=>1 [4,6,5,1,3,2]=>1 [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]=>1 [5,1,2,6,4,3]=>1 [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]=>1 [5,1,3,6,4,2]=>1 [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]=>1 [5,1,4,6,3,2]=>1 [5,1,6,2,3,4]=>1 [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]=>1 [5,1,6,4,3,2]=>1 [5,2,1,3,4,6]=>0 [5,2,1,3,6,4]=>0 [5,2,1,4,3,6]=>0 [5,2,1,4,6,3]=>0 [5,2,1,6,3,4]=>0 [5,2,1,6,4,3]=>0 [5,2,3,1,4,6]=>1 [5,2,3,1,6,4]=>1 [5,2,3,4,1,6]=>1 [5,2,3,4,6,1]=>0 [5,2,3,6,1,4]=>1 [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]=>0 [5,2,4,6,1,3]=>1 [5,2,4,6,3,1]=>0 [5,2,6,1,3,4]=>1 [5,2,6,1,4,3]=>1 [5,2,6,3,1,4]=>1 [5,2,6,3,4,1]=>0 [5,2,6,4,1,3]=>1 [5,2,6,4,3,1]=>0 [5,3,1,2,4,6]=>0 [5,3,1,2,6,4]=>0 [5,3,1,4,2,6]=>0 [5,3,1,4,6,2]=>0 [5,3,1,6,2,4]=>0 [5,3,1,6,4,2]=>0 [5,3,2,1,4,6]=>0 [5,3,2,1,6,4]=>0 [5,3,2,4,1,6]=>0 [5,3,2,4,6,1]=>0 [5,3,2,6,1,4]=>0 [5,3,2,6,4,1]=>0 [5,3,4,1,2,6]=>1 [5,3,4,1,6,2]=>1 [5,3,4,2,1,6]=>0 [5,3,4,2,6,1]=>0 [5,3,4,6,1,2]=>1 [5,3,4,6,2,1]=>0 [5,3,6,1,2,4]=>1 [5,3,6,1,4,2]=>1 [5,3,6,2,1,4]=>0 [5,3,6,2,4,1]=>0 [5,3,6,4,1,2]=>1 [5,3,6,4,2,1]=>0 [5,4,1,2,3,6]=>0 [5,4,1,2,6,3]=>0 [5,4,1,3,2,6]=>0 [5,4,1,3,6,2]=>0 [5,4,1,6,2,3]=>0 [5,4,1,6,3,2]=>0 [5,4,2,1,3,6]=>0 [5,4,2,1,6,3]=>0 [5,4,2,3,1,6]=>0 [5,4,2,3,6,1]=>0 [5,4,2,6,1,3]=>0 [5,4,2,6,3,1]=>0 [5,4,3,1,2,6]=>0 [5,4,3,1,6,2]=>0 [5,4,3,2,1,6]=>0 [5,4,3,2,6,1]=>0 [5,4,3,6,1,2]=>0 [5,4,3,6,2,1]=>0 [5,4,6,1,2,3]=>1 [5,4,6,1,3,2]=>1 [5,4,6,2,1,3]=>0 [5,4,6,2,3,1]=>0 [5,4,6,3,1,2]=>0 [5,4,6,3,2,1]=>0 [5,6,1,2,3,4]=>2 [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]=>0 [5,6,2,1,4,3]=>0 [5,6,2,3,1,4]=>2 [5,6,2,3,4,1]=>0 [5,6,2,4,1,3]=>2 [5,6,2,4,3,1]=>0 [5,6,3,1,2,4]=>0 [5,6,3,1,4,2]=>0 [5,6,3,2,1,4]=>0 [5,6,3,2,4,1]=>0 [5,6,3,4,1,2]=>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]=>1 [6,1,2,3,5,4]=>1 [6,1,2,4,3,5]=>1 [6,1,2,4,5,3]=>1 [6,1,2,5,3,4]=>1 [6,1,2,5,4,3]=>1 [6,1,3,2,4,5]=>1 [6,1,3,2,5,4]=>1 [6,1,3,4,2,5]=>1 [6,1,3,4,5,2]=>1 [6,1,3,5,2,4]=>1 [6,1,3,5,4,2]=>1 [6,1,4,2,3,5]=>1 [6,1,4,2,5,3]=>1 [6,1,4,3,2,5]=>1 [6,1,4,3,5,2]=>1 [6,1,4,5,2,3]=>1 [6,1,4,5,3,2]=>1 [6,1,5,2,3,4]=>1 [6,1,5,2,4,3]=>1 [6,1,5,3,2,4]=>1 [6,1,5,3,4,2]=>1 [6,1,5,4,2,3]=>1 [6,1,5,4,3,2]=>1 [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]=>1 [6,2,3,1,5,4]=>1 [6,2,3,4,1,5]=>1 [6,2,3,4,5,1]=>0 [6,2,3,5,1,4]=>1 [6,2,3,5,4,1]=>0 [6,2,4,1,3,5]=>1 [6,2,4,1,5,3]=>1 [6,2,4,3,1,5]=>1 [6,2,4,3,5,1]=>0 [6,2,4,5,1,3]=>1 [6,2,4,5,3,1]=>0 [6,2,5,1,3,4]=>1 [6,2,5,1,4,3]=>1 [6,2,5,3,1,4]=>1 [6,2,5,3,4,1]=>0 [6,2,5,4,1,3]=>1 [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]=>1 [6,3,4,1,5,2]=>1 [6,3,4,2,1,5]=>0 [6,3,4,2,5,1]=>0 [6,3,4,5,1,2]=>1 [6,3,4,5,2,1]=>0 [6,3,5,1,2,4]=>1 [6,3,5,1,4,2]=>1 [6,3,5,2,1,4]=>0 [6,3,5,2,4,1]=>0 [6,3,5,4,1,2]=>1 [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]=>1 [6,4,5,1,3,2]=>1 [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]=>5 [1,2,3,4,6,5,7]=>5 [1,2,3,4,6,7,5]=>4 [1,2,3,4,7,5,6]=>5 [1,2,3,4,7,6,5]=>4 [1,2,3,5,4,6,7]=>4 [1,2,3,5,4,7,6]=>4 [1,2,3,5,6,4,7]=>5 [1,2,3,5,6,7,4]=>3 [1,2,3,5,7,4,6]=>5 [1,2,3,5,7,6,4]=>3 [1,2,3,6,4,5,7]=>4 [1,2,3,6,4,7,5]=>4 [1,2,3,6,5,4,7]=>3 [1,2,3,6,5,7,4]=>3 [1,2,3,6,7,4,5]=>5 [1,2,3,6,7,5,4]=>3 [1,2,3,7,4,5,6]=>4 [1,2,3,7,4,6,5]=>4 [1,2,3,7,5,4,6]=>3 [1,2,3,7,5,6,4]=>3 [1,2,3,7,6,4,5]=>3 [1,2,3,7,6,5,4]=>3 [1,2,4,3,5,6,7]=>3 [1,2,4,3,5,7,6]=>3 [1,2,4,3,6,5,7]=>3 [1,2,4,3,6,7,5]=>3 [1,2,4,3,7,5,6]=>3 [1,2,4,3,7,6,5]=>3 [1,2,4,5,3,6,7]=>4 [1,2,4,5,3,7,6]=>4 [1,2,4,5,6,3,7]=>5 [1,2,4,5,6,7,3]=>2 [1,2,4,5,7,3,6]=>5 [1,2,4,5,7,6,3]=>2 [1,2,4,6,3,5,7]=>4 [1,2,4,6,3,7,5]=>4 [1,2,4,6,5,3,7]=>3 [1,2,4,6,5,7,3]=>2 [1,2,4,6,7,3,5]=>5 [1,2,4,6,7,5,3]=>2 [1,2,4,7,3,5,6]=>4 [1,2,4,7,3,6,5]=>4 [1,2,4,7,5,3,6]=>3 [1,2,4,7,5,6,3]=>2 [1,2,4,7,6,3,5]=>3 [1,2,4,7,6,5,3]=>2 [1,2,5,3,4,6,7]=>3 [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]=>3 [1,2,5,3,7,6,4]=>3 [1,2,5,4,3,6,7]=>2 [1,2,5,4,3,7,6]=>2 [1,2,5,4,6,3,7]=>3 [1,2,5,4,6,7,3]=>2 [1,2,5,4,7,3,6]=>3 [1,2,5,4,7,6,3]=>2 [1,2,5,6,3,4,7]=>4 [1,2,5,6,3,7,4]=>4 [1,2,5,6,4,3,7]=>2 [1,2,5,6,4,7,3]=>2 [1,2,5,6,7,3,4]=>5 [1,2,5,6,7,4,3]=>2 [1,2,5,7,3,4,6]=>4 [1,2,5,7,3,6,4]=>4 [1,2,5,7,4,3,6]=>2 [1,2,5,7,4,6,3]=>2 [1,2,5,7,6,3,4]=>3 [1,2,5,7,6,4,3]=>2 [1,2,6,3,4,5,7]=>3 [1,2,6,3,4,7,5]=>3 [1,2,6,3,5,4,7]=>3 [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]=>2 [1,2,6,4,5,3,7]=>3 [1,2,6,4,5,7,3]=>2 [1,2,6,4,7,3,5]=>3 [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]=>2 [1,2,6,5,4,7,3]=>2 [1,2,6,5,7,3,4]=>3 [1,2,6,5,7,4,3]=>2 [1,2,6,7,3,4,5]=>4 [1,2,6,7,3,5,4]=>4 [1,2,6,7,4,3,5]=>2 [1,2,6,7,4,5,3]=>2 [1,2,6,7,5,3,4]=>2 [1,2,6,7,5,4,3]=>2 [1,2,7,3,4,5,6]=>3 [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]=>3 [1,2,7,4,3,5,6]=>2 [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]=>2 [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]=>2 [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]=>2 [1,2,7,6,4,3,5]=>2 [1,2,7,6,4,5,3]=>2 [1,2,7,6,5,3,4]=>2 [1,2,7,6,5,4,3]=>2 [1,3,2,4,5,6,7]=>2 [1,3,2,4,5,7,6]=>2 [1,3,2,4,6,5,7]=>2 [1,3,2,4,6,7,5]=>2 [1,3,2,4,7,5,6]=>2 [1,3,2,4,7,6,5]=>2 [1,3,2,5,4,6,7]=>2 [1,3,2,5,4,7,6]=>2 [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]=>2 [1,3,2,6,5,7,4]=>2 [1,3,2,6,7,4,5]=>2 [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]=>2 [1,3,2,7,6,4,5]=>2 [1,3,2,7,6,5,4]=>2 [1,3,4,2,5,6,7]=>3 [1,3,4,2,5,7,6]=>3 [1,3,4,2,6,5,7]=>3 [1,3,4,2,6,7,5]=>3 [1,3,4,2,7,5,6]=>3 [1,3,4,2,7,6,5]=>3 [1,3,4,5,2,6,7]=>4 [1,3,4,5,2,7,6]=>4 [1,3,4,5,6,2,7]=>5 [1,3,4,5,6,7,2]=>1 [1,3,4,5,7,2,6]=>5 [1,3,4,5,7,6,2]=>1 [1,3,4,6,2,5,7]=>4 [1,3,4,6,2,7,5]=>4 [1,3,4,6,5,2,7]=>3 [1,3,4,6,5,7,2]=>1 [1,3,4,6,7,2,5]=>5 [1,3,4,6,7,5,2]=>1 [1,3,4,7,2,5,6]=>4 [1,3,4,7,2,6,5]=>4 [1,3,4,7,5,2,6]=>3 [1,3,4,7,5,6,2]=>1 [1,3,4,7,6,2,5]=>3 [1,3,4,7,6,5,2]=>1 [1,3,5,2,4,6,7]=>3 [1,3,5,2,4,7,6]=>3 [1,3,5,2,6,4,7]=>3 [1,3,5,2,6,7,4]=>3 [1,3,5,2,7,4,6]=>3 [1,3,5,2,7,6,4]=>3 [1,3,5,4,2,6,7]=>2 [1,3,5,4,2,7,6]=>2 [1,3,5,4,6,2,7]=>3 [1,3,5,4,6,7,2]=>1 [1,3,5,4,7,2,6]=>3 [1,3,5,4,7,6,2]=>1 [1,3,5,6,2,4,7]=>4 [1,3,5,6,2,7,4]=>4 [1,3,5,6,4,2,7]=>2 [1,3,5,6,4,7,2]=>1 [1,3,5,6,7,2,4]=>5 [1,3,5,6,7,4,2]=>1 [1,3,5,7,2,4,6]=>4 [1,3,5,7,2,6,4]=>4 [1,3,5,7,4,2,6]=>2 [1,3,5,7,4,6,2]=>1 [1,3,5,7,6,2,4]=>3 [1,3,5,7,6,4,2]=>1 [1,3,6,2,4,5,7]=>3 [1,3,6,2,4,7,5]=>3 [1,3,6,2,5,4,7]=>3 [1,3,6,2,5,7,4]=>3 [1,3,6,2,7,4,5]=>3 [1,3,6,2,7,5,4]=>3 [1,3,6,4,2,5,7]=>2 [1,3,6,4,2,7,5]=>2 [1,3,6,4,5,2,7]=>3 [1,3,6,4,5,7,2]=>1 [1,3,6,4,7,2,5]=>3 [1,3,6,4,7,5,2]=>1 [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]=>1 [1,3,6,5,7,2,4]=>3 [1,3,6,5,7,4,2]=>1 [1,3,6,7,2,4,5]=>4 [1,3,6,7,2,5,4]=>4 [1,3,6,7,4,2,5]=>2 [1,3,6,7,4,5,2]=>1 [1,3,6,7,5,2,4]=>2 [1,3,6,7,5,4,2]=>1 [1,3,7,2,4,5,6]=>3 [1,3,7,2,4,6,5]=>3 [1,3,7,2,5,4,6]=>3 [1,3,7,2,5,6,4]=>3 [1,3,7,2,6,4,5]=>3 [1,3,7,2,6,5,4]=>3 [1,3,7,4,2,5,6]=>2 [1,3,7,4,2,6,5]=>2 [1,3,7,4,5,2,6]=>3 [1,3,7,4,5,6,2]=>1 [1,3,7,4,6,2,5]=>3 [1,3,7,4,6,5,2]=>1 [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]=>1 [1,3,7,5,6,2,4]=>3 [1,3,7,5,6,4,2]=>1 [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]=>1 [1,3,7,6,5,2,4]=>2 [1,3,7,6,5,4,2]=>1 [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]=>2 [1,4,2,3,7,5,6]=>2 [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]=>1 [1,4,3,2,7,5,6]=>1 [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]=>1 [1,4,3,5,7,2,6]=>2 [1,4,3,5,7,6,2]=>1 [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]=>1 [1,4,3,6,7,2,5]=>2 [1,4,3,6,7,5,2]=>1 [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]=>1 [1,4,3,7,6,2,5]=>2 [1,4,3,7,6,5,2]=>1 [1,4,5,2,3,6,7]=>3 [1,4,5,2,3,7,6]=>3 [1,4,5,2,6,3,7]=>3 [1,4,5,2,6,7,3]=>3 [1,4,5,2,7,3,6]=>3 [1,4,5,2,7,6,3]=>3 [1,4,5,3,2,6,7]=>1 [1,4,5,3,2,7,6]=>1 [1,4,5,3,6,2,7]=>3 [1,4,5,3,6,7,2]=>1 [1,4,5,3,7,2,6]=>3 [1,4,5,3,7,6,2]=>1 [1,4,5,6,2,3,7]=>4 [1,4,5,6,2,7,3]=>4 [1,4,5,6,3,2,7]=>1 [1,4,5,6,3,7,2]=>1 [1,4,5,6,7,2,3]=>5 [1,4,5,6,7,3,2]=>1 [1,4,5,7,2,3,6]=>4 [1,4,5,7,2,6,3]=>4 [1,4,5,7,3,2,6]=>1 [1,4,5,7,3,6,2]=>1 [1,4,5,7,6,2,3]=>3 [1,4,5,7,6,3,2]=>1 [1,4,6,2,3,5,7]=>3 [1,4,6,2,3,7,5]=>3 [1,4,6,2,5,3,7]=>3 [1,4,6,2,5,7,3]=>3 [1,4,6,2,7,3,5]=>3 [1,4,6,2,7,5,3]=>3 [1,4,6,3,2,5,7]=>1 [1,4,6,3,2,7,5]=>1 [1,4,6,3,5,2,7]=>3 [1,4,6,3,5,7,2]=>1 [1,4,6,3,7,2,5]=>3 [1,4,6,3,7,5,2]=>1 [1,4,6,5,2,3,7]=>2 [1,4,6,5,2,7,3]=>2 [1,4,6,5,3,2,7]=>1 [1,4,6,5,3,7,2]=>1
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Description
The aix statistic of a permutation.
According to [1], this statistic on finite strings $\pi$ of integers is given as follows: let $m$ be the leftmost occurrence of the minimal entry and let $\pi = \alpha\ m\ \beta$. Then
$$ \operatorname{aix}\pi = \begin{cases} \operatorname{aix}\alpha & \text{ if } \alpha,\beta \neq \emptyset \\ 1 + \operatorname{aix}\beta & \text{ if } \alpha = \emptyset \\ 0 & \text{ if } \beta = \emptyset \end{cases}\ . $$
References
[1] Burstein, A. On the distribution of some Euler-Mahonian statistics MathSciNet:3357124
Code
def statistic(pi):
    pi = list(pi)
    if not pi:
        return 0
    i = min(pi)
    j = pi.index(i)
    alpha = pi[:j]
    beta = pi[j+1:]
    if alpha and beta:
        return statistic(alpha)
    elif alpha == []:
        return 1 + statistic(beta)
    else:
        return 0
Created
Jun 27, 2017 at 11:42 by Christian Stump
Updated
Jun 27, 2017 at 11:42 by Christian Stump