edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [1,2]=>0 [2,1]=>0 [1,2,3]=>1 [1,3,2]=>0 [2,1,3]=>0 [2,3,1]=>0 [3,1,2]=>0 [3,2,1]=>0 [1,2,3,4]=>2 [1,2,4,3]=>1 [1,3,2,4]=>1 [1,3,4,2]=>1 [1,4,2,3]=>1 [1,4,3,2]=>0 [2,1,3,4]=>2 [2,1,4,3]=>0 [2,3,1,4]=>1 [2,3,4,1]=>1 [2,4,1,3]=>0 [2,4,3,1]=>0 [3,1,2,4]=>1 [3,1,4,2]=>0 [3,2,1,4]=>0 [3,2,4,1]=>0 [3,4,1,2]=>0 [3,4,2,1]=>0 [4,1,2,3]=>1 [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]=>3 [1,2,3,5,4]=>2 [1,2,4,3,5]=>2 [1,2,4,5,3]=>2 [1,2,5,3,4]=>2 [1,2,5,4,3]=>1 [1,3,2,4,5]=>3 [1,3,2,5,4]=>1 [1,3,4,2,5]=>2 [1,3,4,5,2]=>2 [1,3,5,2,4]=>1 [1,3,5,4,2]=>1 [1,4,2,3,5]=>2 [1,4,2,5,3]=>1 [1,4,3,2,5]=>1 [1,4,3,5,2]=>1 [1,4,5,2,3]=>1 [1,4,5,3,2]=>1 [1,5,2,3,4]=>2 [1,5,2,4,3]=>1 [1,5,3,2,4]=>1 [1,5,3,4,2]=>1 [1,5,4,2,3]=>1 [1,5,4,3,2]=>0 [2,1,3,4,5]=>3 [2,1,3,5,4]=>2 [2,1,4,3,5]=>2 [2,1,4,5,3]=>2 [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]=>2 [2,3,5,1,4]=>1 [2,3,5,4,1]=>1 [2,4,1,3,5]=>2 [2,4,1,5,3]=>1 [2,4,3,1,5]=>1 [2,4,3,5,1]=>1 [2,4,5,1,3]=>1 [2,4,5,3,1]=>1 [2,5,1,3,4]=>2 [2,5,1,4,3]=>0 [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]=>3 [3,1,2,5,4]=>1 [3,1,4,2,5]=>2 [3,1,4,5,2]=>2 [3,1,5,2,4]=>1 [3,1,5,4,2]=>0 [3,2,1,4,5]=>3 [3,2,1,5,4]=>0 [3,2,4,1,5]=>2 [3,2,4,5,1]=>2 [3,2,5,1,4]=>0 [3,2,5,4,1]=>0 [3,4,1,2,5]=>2 [3,4,1,5,2]=>1 [3,4,2,1,5]=>1 [3,4,2,5,1]=>1 [3,4,5,1,2]=>1 [3,4,5,2,1]=>1 [3,5,1,2,4]=>1 [3,5,1,4,2]=>0 [3,5,2,1,4]=>0 [3,5,2,4,1]=>0 [3,5,4,1,2]=>0 [3,5,4,2,1]=>0 [4,1,2,3,5]=>2 [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]=>0 [4,2,1,3,5]=>2 [4,2,1,5,3]=>0 [4,2,3,1,5]=>1 [4,2,3,5,1]=>1 [4,2,5,1,3]=>0 [4,2,5,3,1]=>0 [4,3,1,2,5]=>1 [4,3,1,5,2]=>0 [4,3,2,1,5]=>0 [4,3,2,5,1]=>0 [4,3,5,1,2]=>0 [4,3,5,2,1]=>0 [4,5,1,2,3]=>1 [4,5,1,3,2]=>0 [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]=>2 [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]=>0 [5,2,1,3,4]=>2 [5,2,1,4,3]=>0 [5,2,3,1,4]=>1 [5,2,3,4,1]=>1 [5,2,4,1,3]=>0 [5,2,4,3,1]=>0 [5,3,1,2,4]=>1 [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]=>1 [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]=>4 [1,2,3,4,6,5]=>3 [1,2,3,5,4,6]=>3 [1,2,3,5,6,4]=>3 [1,2,3,6,4,5]=>3 [1,2,3,6,5,4]=>2 [1,2,4,3,5,6]=>4 [1,2,4,3,6,5]=>2 [1,2,4,5,3,6]=>3 [1,2,4,5,6,3]=>3 [1,2,4,6,3,5]=>2 [1,2,4,6,5,3]=>2 [1,2,5,3,4,6]=>3 [1,2,5,3,6,4]=>2 [1,2,5,4,3,6]=>2 [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]=>3 [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]=>4 [1,3,2,4,6,5]=>3 [1,3,2,5,4,6]=>3 [1,3,2,5,6,4]=>3 [1,3,2,6,4,5]=>3 [1,3,2,6,5,4]=>1 [1,3,4,2,5,6]=>4 [1,3,4,2,6,5]=>2 [1,3,4,5,2,6]=>3 [1,3,4,5,6,2]=>3 [1,3,4,6,2,5]=>2 [1,3,4,6,5,2]=>2 [1,3,5,2,4,6]=>3 [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]=>3 [1,3,6,2,5,4]=>1 [1,3,6,4,2,5]=>2 [1,3,6,4,5,2]=>2 [1,3,6,5,2,4]=>1 [1,3,6,5,4,2]=>1 [1,4,2,3,5,6]=>4 [1,4,2,3,6,5]=>2 [1,4,2,5,3,6]=>3 [1,4,2,5,6,3]=>3 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>1 [1,4,3,2,5,6]=>4 [1,4,3,2,6,5]=>1 [1,4,3,5,2,6]=>3 [1,4,3,5,6,2]=>3 [1,4,3,6,2,5]=>1 [1,4,3,6,5,2]=>1 [1,4,5,2,3,6]=>3 [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]=>1 [1,4,6,3,5,2]=>1 [1,4,6,5,2,3]=>1 [1,4,6,5,3,2]=>1 [1,5,2,3,4,6]=>3 [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]=>1 [1,5,3,2,4,6]=>3 [1,5,3,2,6,4]=>1 [1,5,3,4,2,6]=>2 [1,5,3,4,6,2]=>2 [1,5,3,6,2,4]=>1 [1,5,3,6,4,2]=>1 [1,5,4,2,3,6]=>2 [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]=>1 [1,5,4,6,3,2]=>1 [1,5,6,2,3,4]=>2 [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]=>1 [1,5,6,4,3,2]=>1 [1,6,2,3,4,5]=>3 [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]=>1 [1,6,3,2,4,5]=>3 [1,6,3,2,5,4]=>1 [1,6,3,4,2,5]=>2 [1,6,3,4,5,2]=>2 [1,6,3,5,2,4]=>1 [1,6,3,5,4,2]=>1 [1,6,4,2,3,5]=>2 [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]=>1 [1,6,4,5,3,2]=>1 [1,6,5,2,3,4]=>2 [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]=>0 [2,1,3,4,5,6]=>4 [2,1,3,4,6,5]=>3 [2,1,3,5,4,6]=>3 [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]=>4 [2,1,4,3,6,5]=>2 [2,1,4,5,3,6]=>3 [2,1,4,5,6,3]=>3 [2,1,4,6,3,5]=>2 [2,1,4,6,5,3]=>2 [2,1,5,3,4,6]=>3 [2,1,5,3,6,4]=>2 [2,1,5,4,3,6]=>2 [2,1,5,4,6,3]=>2 [2,1,5,6,3,4]=>2 [2,1,5,6,4,3]=>2 [2,1,6,3,4,5]=>3 [2,1,6,3,5,4]=>2 [2,1,6,4,3,5]=>2 [2,1,6,4,5,3]=>2 [2,1,6,5,3,4]=>2 [2,1,6,5,4,3]=>0 [2,3,1,4,5,6]=>4 [2,3,1,4,6,5]=>3 [2,3,1,5,4,6]=>3 [2,3,1,5,6,4]=>3 [2,3,1,6,4,5]=>3 [2,3,1,6,5,4]=>1 [2,3,4,1,5,6]=>4 [2,3,4,1,6,5]=>2 [2,3,4,5,1,6]=>3 [2,3,4,5,6,1]=>3 [2,3,4,6,1,5]=>2 [2,3,4,6,5,1]=>2 [2,3,5,1,4,6]=>3 [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]=>3 [2,3,6,1,5,4]=>1 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>2 [2,3,6,5,1,4]=>1 [2,3,6,5,4,1]=>1 [2,4,1,3,5,6]=>4 [2,4,1,3,6,5]=>2 [2,4,1,5,3,6]=>3 [2,4,1,5,6,3]=>3 [2,4,1,6,3,5]=>2 [2,4,1,6,5,3]=>1 [2,4,3,1,5,6]=>4 [2,4,3,1,6,5]=>1 [2,4,3,5,1,6]=>3 [2,4,3,5,6,1]=>3 [2,4,3,6,1,5]=>1 [2,4,3,6,5,1]=>1 [2,4,5,1,3,6]=>3 [2,4,5,1,6,3]=>2 [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]=>2 [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]=>1 [2,4,6,5,3,1]=>1 [2,5,1,3,4,6]=>3 [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]=>1 [2,5,3,1,4,6]=>3 [2,5,3,1,6,4]=>1 [2,5,3,4,1,6]=>2 [2,5,3,4,6,1]=>2 [2,5,3,6,1,4]=>1 [2,5,3,6,4,1]=>1 [2,5,4,1,3,6]=>2 [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]=>1 [2,5,4,6,3,1]=>1 [2,5,6,1,3,4]=>2 [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]=>1 [2,5,6,4,3,1]=>1 [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]=>2 [2,6,1,5,3,4]=>2 [2,6,1,5,4,3]=>0 [2,6,3,1,4,5]=>3 [2,6,3,1,5,4]=>1 [2,6,3,4,1,5]=>2 [2,6,3,4,5,1]=>2 [2,6,3,5,1,4]=>1 [2,6,3,5,4,1]=>1 [2,6,4,1,3,5]=>2 [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]=>1 [2,6,4,5,3,1]=>1 [2,6,5,1,3,4]=>2 [2,6,5,1,4,3]=>0 [2,6,5,3,1,4]=>1 [2,6,5,3,4,1]=>1 [2,6,5,4,1,3]=>0 [2,6,5,4,3,1]=>0 [3,1,2,4,5,6]=>4 [3,1,2,4,6,5]=>3 [3,1,2,5,4,6]=>3 [3,1,2,5,6,4]=>3 [3,1,2,6,4,5]=>3 [3,1,2,6,5,4]=>1 [3,1,4,2,5,6]=>4 [3,1,4,2,6,5]=>2 [3,1,4,5,2,6]=>3 [3,1,4,5,6,2]=>3 [3,1,4,6,2,5]=>2 [3,1,4,6,5,2]=>2 [3,1,5,2,4,6]=>3 [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]=>3 [3,1,6,2,5,4]=>1 [3,1,6,4,2,5]=>2 [3,1,6,4,5,2]=>2 [3,1,6,5,2,4]=>1 [3,1,6,5,4,2]=>0 [3,2,1,4,5,6]=>4 [3,2,1,4,6,5]=>3 [3,2,1,5,4,6]=>3 [3,2,1,5,6,4]=>3 [3,2,1,6,4,5]=>3 [3,2,1,6,5,4]=>0 [3,2,4,1,5,6]=>4 [3,2,4,1,6,5]=>2 [3,2,4,5,1,6]=>3 [3,2,4,5,6,1]=>3 [3,2,4,6,1,5]=>2 [3,2,4,6,5,1]=>2 [3,2,5,1,4,6]=>3 [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]=>3 [3,2,6,1,5,4]=>0 [3,2,6,4,1,5]=>2 [3,2,6,4,5,1]=>2 [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]=>2 [3,4,1,5,2,6]=>3 [3,4,1,5,6,2]=>3 [3,4,1,6,2,5]=>2 [3,4,1,6,5,2]=>1 [3,4,2,1,5,6]=>4 [3,4,2,1,6,5]=>1 [3,4,2,5,1,6]=>3 [3,4,2,5,6,1]=>3 [3,4,2,6,1,5]=>1 [3,4,2,6,5,1]=>1 [3,4,5,1,2,6]=>3 [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]=>2 [3,4,5,6,2,1]=>2 [3,4,6,1,2,5]=>2 [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]=>1 [3,4,6,5,2,1]=>1 [3,5,1,2,4,6]=>3 [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]=>1 [3,5,2,1,4,6]=>3 [3,5,2,1,6,4]=>1 [3,5,2,4,1,6]=>2 [3,5,2,4,6,1]=>2 [3,5,2,6,1,4]=>1 [3,5,2,6,4,1]=>1 [3,5,4,1,2,6]=>2 [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]=>1 [3,5,4,6,2,1]=>1 [3,5,6,1,2,4]=>2 [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]=>1 [3,5,6,4,2,1]=>1 [3,6,1,2,4,5]=>3 [3,6,1,2,5,4]=>1 [3,6,1,4,2,5]=>2 [3,6,1,4,5,2]=>2 [3,6,1,5,2,4]=>1 [3,6,1,5,4,2]=>0 [3,6,2,1,4,5]=>3 [3,6,2,1,5,4]=>0 [3,6,2,4,1,5]=>2 [3,6,2,4,5,1]=>2 [3,6,2,5,1,4]=>0 [3,6,2,5,4,1]=>0 [3,6,4,1,2,5]=>2 [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]=>1 [3,6,4,5,2,1]=>1 [3,6,5,1,2,4]=>1 [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]=>4 [4,1,2,3,6,5]=>2 [4,1,2,5,3,6]=>3 [4,1,2,5,6,3]=>3 [4,1,2,6,3,5]=>2 [4,1,2,6,5,3]=>1 [4,1,3,2,5,6]=>4 [4,1,3,2,6,5]=>1 [4,1,3,5,2,6]=>3 [4,1,3,5,6,2]=>3 [4,1,3,6,2,5]=>1 [4,1,3,6,5,2]=>1 [4,1,5,2,3,6]=>3 [4,1,5,2,6,3]=>2 [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]=>2 [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]=>0 [4,2,1,3,5,6]=>4 [4,2,1,3,6,5]=>2 [4,2,1,5,3,6]=>3 [4,2,1,5,6,3]=>3 [4,2,1,6,3,5]=>2 [4,2,1,6,5,3]=>0 [4,2,3,1,5,6]=>4 [4,2,3,1,6,5]=>1 [4,2,3,5,1,6]=>3 [4,2,3,5,6,1]=>3 [4,2,3,6,1,5]=>1 [4,2,3,6,5,1]=>1 [4,2,5,1,3,6]=>3 [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]=>0 [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]=>4 [4,3,1,2,6,5]=>1 [4,3,1,5,2,6]=>3 [4,3,1,5,6,2]=>3 [4,3,1,6,2,5]=>1 [4,3,1,6,5,2]=>0 [4,3,2,1,5,6]=>4 [4,3,2,1,6,5]=>0 [4,3,2,5,1,6]=>3 [4,3,2,5,6,1]=>3 [4,3,2,6,1,5]=>0 [4,3,2,6,5,1]=>0 [4,3,5,1,2,6]=>3 [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]=>2 [4,3,6,1,2,5]=>1 [4,3,6,1,5,2]=>0 [4,3,6,2,1,5]=>0 [4,3,6,2,5,1]=>0 [4,3,6,5,1,2]=>0 [4,3,6,5,2,1]=>0 [4,5,1,2,3,6]=>3 [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]=>1 [4,5,2,1,3,6]=>3 [4,5,2,1,6,3]=>1 [4,5,2,3,1,6]=>2 [4,5,2,3,6,1]=>2 [4,5,2,6,1,3]=>1 [4,5,2,6,3,1]=>1 [4,5,3,1,2,6]=>2 [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]=>1 [4,5,3,6,2,1]=>1 [4,5,6,1,2,3]=>2 [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]=>1 [4,5,6,3,2,1]=>1 [4,6,1,2,3,5]=>2 [4,6,1,2,5,3]=>1 [4,6,1,3,2,5]=>1 [4,6,1,3,5,2]=>1 [4,6,1,5,2,3]=>1 [4,6,1,5,3,2]=>0 [4,6,2,1,3,5]=>2 [4,6,2,1,5,3]=>0 [4,6,2,3,1,5]=>1 [4,6,2,3,5,1]=>1 [4,6,2,5,1,3]=>0 [4,6,2,5,3,1]=>0 [4,6,3,1,2,5]=>1 [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]=>0 [4,6,3,5,2,1]=>0 [4,6,5,1,2,3]=>1 [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]=>3 [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]=>1 [5,1,3,2,4,6]=>3 [5,1,3,2,6,4]=>1 [5,1,3,4,2,6]=>2 [5,1,3,4,6,2]=>2 [5,1,3,6,2,4]=>1 [5,1,3,6,4,2]=>1 [5,1,4,2,3,6]=>2 [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]=>2 [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]=>0 [5,2,1,3,4,6]=>3 [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]=>0 [5,2,3,1,4,6]=>3 [5,2,3,1,6,4]=>1 [5,2,3,4,1,6]=>2 [5,2,3,4,6,1]=>2 [5,2,3,6,1,4]=>1 [5,2,3,6,4,1]=>1 [5,2,4,1,3,6]=>2 [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]=>1 [5,2,4,6,3,1]=>1 [5,2,6,1,3,4]=>2 [5,2,6,1,4,3]=>0 [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]=>3 [5,3,1,2,6,4]=>1 [5,3,1,4,2,6]=>2 [5,3,1,4,6,2]=>2 [5,3,1,6,2,4]=>1 [5,3,1,6,4,2]=>0 [5,3,2,1,4,6]=>3 [5,3,2,1,6,4]=>0 [5,3,2,4,1,6]=>2 [5,3,2,4,6,1]=>2 [5,3,2,6,1,4]=>0 [5,3,2,6,4,1]=>0 [5,3,4,1,2,6]=>2 [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]=>1 [5,3,4,6,2,1]=>1 [5,3,6,1,2,4]=>1 [5,3,6,1,4,2]=>0 [5,3,6,2,1,4]=>0 [5,3,6,2,4,1]=>0 [5,3,6,4,1,2]=>0 [5,3,6,4,2,1]=>0 [5,4,1,2,3,6]=>2 [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]=>1 [5,4,1,6,3,2]=>0 [5,4,2,1,3,6]=>2 [5,4,2,1,6,3]=>0 [5,4,2,3,1,6]=>1 [5,4,2,3,6,1]=>1 [5,4,2,6,1,3]=>0 [5,4,2,6,3,1]=>0 [5,4,3,1,2,6]=>1 [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]=>0 [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]=>1 [5,6,1,3,2,4]=>1 [5,6,1,3,4,2]=>1 [5,6,1,4,2,3]=>1 [5,6,1,4,3,2]=>0 [5,6,2,1,3,4]=>2 [5,6,2,1,4,3]=>0 [5,6,2,3,1,4]=>1 [5,6,2,3,4,1]=>1 [5,6,2,4,1,3]=>0 [5,6,2,4,3,1]=>0 [5,6,3,1,2,4]=>1 [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]=>0 [5,6,3,4,2,1]=>0 [5,6,4,1,2,3]=>1 [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]=>3 [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]=>1 [6,1,3,2,4,5]=>3 [6,1,3,2,5,4]=>1 [6,1,3,4,2,5]=>2 [6,1,3,4,5,2]=>2 [6,1,3,5,2,4]=>1 [6,1,3,5,4,2]=>1 [6,1,4,2,3,5]=>2 [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]=>2 [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]=>0 [6,2,1,3,4,5]=>3 [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]=>0 [6,2,3,1,4,5]=>3 [6,2,3,1,5,4]=>1 [6,2,3,4,1,5]=>2 [6,2,3,4,5,1]=>2 [6,2,3,5,1,4]=>1 [6,2,3,5,4,1]=>1 [6,2,4,1,3,5]=>2 [6,2,4,1,5,3]=>1 [6,2,4,3,1,5]=>1 [6,2,4,3,5,1]=>1 [6,2,4,5,1,3]=>1 [6,2,4,5,3,1]=>1 [6,2,5,1,3,4]=>2 [6,2,5,1,4,3]=>0 [6,2,5,3,1,4]=>1 [6,2,5,3,4,1]=>1 [6,2,5,4,1,3]=>0 [6,2,5,4,3,1]=>0 [6,3,1,2,4,5]=>3 [6,3,1,2,5,4]=>1 [6,3,1,4,2,5]=>2 [6,3,1,4,5,2]=>2 [6,3,1,5,2,4]=>1 [6,3,1,5,4,2]=>0 [6,3,2,1,4,5]=>3 [6,3,2,1,5,4]=>0 [6,3,2,4,1,5]=>2 [6,3,2,4,5,1]=>2 [6,3,2,5,1,4]=>0 [6,3,2,5,4,1]=>0 [6,3,4,1,2,5]=>2 [6,3,4,1,5,2]=>1 [6,3,4,2,1,5]=>1 [6,3,4,2,5,1]=>1 [6,3,4,5,1,2]=>1 [6,3,4,5,2,1]=>1 [6,3,5,1,2,4]=>1 [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]=>2 [6,4,1,2,5,3]=>1 [6,4,1,3,2,5]=>1 [6,4,1,3,5,2]=>1 [6,4,1,5,2,3]=>1 [6,4,1,5,3,2]=>0 [6,4,2,1,3,5]=>2 [6,4,2,1,5,3]=>0 [6,4,2,3,1,5]=>1 [6,4,2,3,5,1]=>1 [6,4,2,5,1,3]=>0 [6,4,2,5,3,1]=>0 [6,4,3,1,2,5]=>1 [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]=>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]=>2 [6,5,1,2,4,3]=>1 [6,5,1,3,2,4]=>1 [6,5,1,3,4,2]=>1 [6,5,1,4,2,3]=>1 [6,5,1,4,3,2]=>0 [6,5,2,1,3,4]=>2 [6,5,2,1,4,3]=>0 [6,5,2,3,1,4]=>1 [6,5,2,3,4,1]=>1 [6,5,2,4,1,3]=>0 [6,5,2,4,3,1]=>0 [6,5,3,1,2,4]=>1 [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]=>1 [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]=>5 [1,2,3,4,5,7,6]=>4 [1,2,3,4,6,5,7]=>4 [1,2,3,4,6,7,5]=>4 [1,2,3,4,7,5,6]=>4 [1,2,3,4,7,6,5]=>3 [1,2,3,5,4,6,7]=>5 [1,2,3,5,4,7,6]=>3 [1,2,3,5,6,4,7]=>4 [1,2,3,5,6,7,4]=>4 [1,2,3,5,7,4,6]=>3 [1,2,3,5,7,6,4]=>3 [1,2,3,6,4,5,7]=>4 [1,2,3,6,4,7,5]=>3 [1,2,3,6,5,4,7]=>3 [1,2,3,6,5,7,4]=>3 [1,2,3,6,7,4,5]=>3 [1,2,3,6,7,5,4]=>3 [1,2,3,7,4,5,6]=>4 [1,2,3,7,4,6,5]=>3 [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]=>2 [1,2,4,3,5,6,7]=>5 [1,2,4,3,5,7,6]=>4 [1,2,4,3,6,5,7]=>4 [1,2,4,3,6,7,5]=>4 [1,2,4,3,7,5,6]=>4 [1,2,4,3,7,6,5]=>2 [1,2,4,5,3,6,7]=>5 [1,2,4,5,3,7,6]=>3 [1,2,4,5,6,3,7]=>4 [1,2,4,5,6,7,3]=>4 [1,2,4,5,7,3,6]=>3 [1,2,4,5,7,6,3]=>3 [1,2,4,6,3,5,7]=>4 [1,2,4,6,3,7,5]=>3 [1,2,4,6,5,3,7]=>3 [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]=>4 [1,2,4,7,3,6,5]=>2 [1,2,4,7,5,3,6]=>3 [1,2,4,7,5,6,3]=>3 [1,2,4,7,6,3,5]=>2 [1,2,4,7,6,5,3]=>2 [1,2,5,3,4,6,7]=>5 [1,2,5,3,4,7,6]=>3 [1,2,5,3,6,4,7]=>4 [1,2,5,3,6,7,4]=>4 [1,2,5,3,7,4,6]=>3 [1,2,5,3,7,6,4]=>2 [1,2,5,4,3,6,7]=>5 [1,2,5,4,3,7,6]=>2 [1,2,5,4,6,3,7]=>4 [1,2,5,4,6,7,3]=>4 [1,2,5,4,7,3,6]=>2 [1,2,5,4,7,6,3]=>2 [1,2,5,6,3,4,7]=>4 [1,2,5,6,3,7,4]=>3 [1,2,5,6,4,3,7]=>3 [1,2,5,6,4,7,3]=>3 [1,2,5,6,7,3,4]=>3 [1,2,5,6,7,4,3]=>3 [1,2,5,7,3,4,6]=>3 [1,2,5,7,3,6,4]=>2 [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]=>4 [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]=>2 [1,2,6,4,3,5,7]=>4 [1,2,6,4,3,7,5]=>2 [1,2,6,4,5,3,7]=>3 [1,2,6,4,5,7,3]=>3 [1,2,6,4,7,3,5]=>2 [1,2,6,4,7,5,3]=>2 [1,2,6,5,3,4,7]=>3 [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]=>2 [1,2,6,5,7,4,3]=>2 [1,2,6,7,3,4,5]=>3 [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]=>2 [1,2,6,7,5,4,3]=>2 [1,2,7,3,4,5,6]=>4 [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]=>4 [1,2,7,4,3,6,5]=>2 [1,2,7,4,5,3,6]=>3 [1,2,7,4,5,6,3]=>3 [1,2,7,4,6,3,5]=>2 [1,2,7,4,6,5,3]=>2 [1,2,7,5,3,4,6]=>3 [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]=>2 [1,2,7,5,6,4,3]=>2 [1,2,7,6,3,4,5]=>3 [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]=>5 [1,3,2,4,5,7,6]=>4 [1,3,2,4,6,5,7]=>4 [1,3,2,4,6,7,5]=>4 [1,3,2,4,7,5,6]=>4 [1,3,2,4,7,6,5]=>3 [1,3,2,5,4,6,7]=>5 [1,3,2,5,4,7,6]=>3 [1,3,2,5,6,4,7]=>4 [1,3,2,5,6,7,4]=>4 [1,3,2,5,7,4,6]=>3 [1,3,2,5,7,6,4]=>3 [1,3,2,6,4,5,7]=>4 [1,3,2,6,4,7,5]=>3 [1,3,2,6,5,4,7]=>3 [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]=>4 [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]=>1 [1,3,4,2,5,6,7]=>5 [1,3,4,2,5,7,6]=>4 [1,3,4,2,6,5,7]=>4 [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]=>5 [1,3,4,5,2,7,6]=>3 [1,3,4,5,6,2,7]=>4 [1,3,4,5,6,7,2]=>4 [1,3,4,5,7,2,6]=>3 [1,3,4,5,7,6,2]=>3 [1,3,4,6,2,5,7]=>4 [1,3,4,6,2,7,5]=>3 [1,3,4,6,5,2,7]=>3 [1,3,4,6,5,7,2]=>3 [1,3,4,6,7,2,5]=>3 [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]=>3 [1,3,4,7,5,6,2]=>3 [1,3,4,7,6,2,5]=>2 [1,3,4,7,6,5,2]=>2 [1,3,5,2,4,6,7]=>5 [1,3,5,2,4,7,6]=>3 [1,3,5,2,6,4,7]=>4 [1,3,5,2,6,7,4]=>4 [1,3,5,2,7,4,6]=>3 [1,3,5,2,7,6,4]=>2 [1,3,5,4,2,6,7]=>5 [1,3,5,4,2,7,6]=>2 [1,3,5,4,6,2,7]=>4 [1,3,5,4,6,7,2]=>4 [1,3,5,4,7,2,6]=>2 [1,3,5,4,7,6,2]=>2 [1,3,5,6,2,4,7]=>4 [1,3,5,6,2,7,4]=>3 [1,3,5,6,4,2,7]=>3 [1,3,5,6,4,7,2]=>3 [1,3,5,6,7,2,4]=>3 [1,3,5,6,7,4,2]=>3 [1,3,5,7,2,4,6]=>3 [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]=>4 [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]=>2 [1,3,6,4,2,5,7]=>4 [1,3,6,4,2,7,5]=>2 [1,3,6,4,5,2,7]=>3 [1,3,6,4,5,7,2]=>3 [1,3,6,4,7,2,5]=>2 [1,3,6,4,7,5,2]=>2 [1,3,6,5,2,4,7]=>3 [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]=>2 [1,3,6,5,7,4,2]=>2 [1,3,6,7,2,4,5]=>3 [1,3,6,7,2,5,4]=>2 [1,3,6,7,4,2,5]=>2 [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]=>4 [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]=>1 [1,3,7,4,2,5,6]=>4 [1,3,7,4,2,6,5]=>2 [1,3,7,4,5,2,6]=>3 [1,3,7,4,5,6,2]=>3 [1,3,7,4,6,2,5]=>2 [1,3,7,4,6,5,2]=>2 [1,3,7,5,2,4,6]=>3 [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]=>2 [1,3,7,6,2,4,5]=>3 [1,3,7,6,2,5,4]=>1 [1,3,7,6,4,2,5]=>2 [1,3,7,6,4,5,2]=>2 [1,3,7,6,5,2,4]=>1 [1,3,7,6,5,4,2]=>1 [1,4,2,3,5,6,7]=>5 [1,4,2,3,5,7,6]=>4 [1,4,2,3,6,5,7]=>4 [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]=>5 [1,4,2,5,3,7,6]=>3 [1,4,2,5,6,3,7]=>4 [1,4,2,5,6,7,3]=>4 [1,4,2,5,7,3,6]=>3 [1,4,2,5,7,6,3]=>3 [1,4,2,6,3,5,7]=>4 [1,4,2,6,3,7,5]=>3 [1,4,2,6,5,3,7]=>3 [1,4,2,6,5,7,3]=>3 [1,4,2,6,7,3,5]=>3 [1,4,2,6,7,5,3]=>3 [1,4,2,7,3,5,6]=>4 [1,4,2,7,3,6,5]=>2 [1,4,2,7,5,3,6]=>3 [1,4,2,7,5,6,3]=>3 [1,4,2,7,6,3,5]=>2 [1,4,2,7,6,5,3]=>1 [1,4,3,2,5,6,7]=>5 [1,4,3,2,5,7,6]=>4 [1,4,3,2,6,5,7]=>4 [1,4,3,2,6,7,5]=>4 [1,4,3,2,7,5,6]=>4 [1,4,3,2,7,6,5]=>1 [1,4,3,5,2,6,7]=>5 [1,4,3,5,2,7,6]=>3 [1,4,3,5,6,2,7]=>4 [1,4,3,5,6,7,2]=>4 [1,4,3,5,7,2,6]=>3 [1,4,3,5,7,6,2]=>3 [1,4,3,6,2,5,7]=>4 [1,4,3,6,2,7,5]=>3 [1,4,3,6,5,2,7]=>3 [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]=>4 [1,4,3,7,2,6,5]=>1 [1,4,3,7,5,2,6]=>3 [1,4,3,7,5,6,2]=>3 [1,4,3,7,6,2,5]=>1 [1,4,3,7,6,5,2]=>1 [1,4,5,2,3,6,7]=>5 [1,4,5,2,3,7,6]=>3 [1,4,5,2,6,3,7]=>4 [1,4,5,2,6,7,3]=>4 [1,4,5,2,7,3,6]=>3 [1,4,5,2,7,6,3]=>2 [1,4,5,3,2,6,7]=>5 [1,4,5,3,2,7,6]=>2 [1,4,5,3,6,2,7]=>4 [1,4,5,3,6,7,2]=>4 [1,4,5,3,7,2,6]=>2 [1,4,5,3,7,6,2]=>2 [1,4,5,6,2,3,7]=>4 [1,4,5,6,2,7,3]=>3 [1,4,5,6,3,2,7]=>3 [1,4,5,6,3,7,2]=>3 [1,4,5,6,7,2,3]=>3 [1,4,5,6,7,3,2]=>3 [1,4,5,7,2,3,6]=>3 [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]=>2 [1,4,6,2,3,5,7]=>4 [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]=>2 [1,4,6,3,2,5,7]=>4 [1,4,6,3,2,7,5]=>2 [1,4,6,3,5,2,7]=>3 [1,4,6,3,5,7,2]=>3 [1,4,6,3,7,2,5]=>2 [1,4,6,3,7,5,2]=>2 [1,4,6,5,2,3,7]=>3 [1,4,6,5,2,7,3]=>2 [1,4,6,5,3,2,7]=>2
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Description
The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation.
References
[1] Thamrongpairoj, S., Remmel, J. B. Positional Marked Patterns in Permutations arXiv:2102.03867
Code
def statistic(pi, tau=[1,2,3], mark=0):
    """
    The number of positions i such that tau occurs in pi and the mark
    is at position i.

    EXAMPLES::

        sage: pi = Permutation([2,6,4,8,1,5,7,3])
        sage: tau = Permutation([1,4,3,2])
        sage: statistic(pi, tau, 1)
        2

    Table before section 3.2::

        sage: q = QQ["q"].gen()
        sage: [sum(q^statistic(pi, [1,2,3], 0) for pi in Permutations(n)) for n in range(1,7)]
        [1,
         2,
         q + 5,
         2*q^2 + 8*q + 14,
         6*q^3 + 25*q^2 + 47*q + 42,
         24*q^4 + 104*q^3 + 216*q^2 + 244*q + 132]
    """
    return len(set([pos[mark] for pos in pi.pattern_positions(tau)]))
Created
Feb 10, 2021 at 14:44 by Martin Rubey
Updated
Feb 10, 2021 at 14:44 by Martin Rubey