edit this statistic or download as text // json
Identifier
Values
=>
[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]=>2 [1,3,2,4]=>0 [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]=>3 [1,2,4,3,5]=>2 [1,2,4,5,3]=>3 [1,2,5,3,4]=>3 [1,2,5,4,3]=>3 [1,3,2,4,5]=>2 [1,3,2,5,4]=>0 [1,3,4,2,5]=>2 [1,3,4,5,2]=>2 [1,3,5,2,4]=>1 [1,3,5,4,2]=>2 [1,4,2,3,5]=>2 [1,4,2,5,3]=>1 [1,4,3,2,5]=>0 [1,4,3,5,2]=>0 [1,4,5,2,3]=>2 [1,4,5,3,2]=>1 [1,5,2,3,4]=>2 [1,5,2,4,3]=>2 [1,5,3,2,4]=>0 [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]=>4 [2,1,4,3,5]=>0 [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]=>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]=>1 [2,4,1,5,3]=>1 [2,4,3,1,5]=>0 [2,4,3,5,1]=>0 [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]=>2 [3,1,4,2,5]=>1 [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]=>2 [4,1,3,2,5]=>0 [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]=>2 [5,1,3,2,4]=>0 [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]=>4 [1,2,3,5,4,6]=>3 [1,2,3,5,6,4]=>4 [1,2,3,6,4,5]=>4 [1,2,3,6,5,4]=>4 [1,2,4,3,5,6]=>4 [1,2,4,3,6,5]=>2 [1,2,4,5,3,6]=>4 [1,2,4,5,6,3]=>4 [1,2,4,6,3,5]=>3 [1,2,4,6,5,3]=>4 [1,2,5,3,4,6]=>4 [1,2,5,3,6,4]=>3 [1,2,5,4,3,6]=>3 [1,2,5,4,6,3]=>3 [1,2,5,6,3,4]=>4 [1,2,5,6,4,3]=>4 [1,2,6,3,4,5]=>4 [1,2,6,3,5,4]=>4 [1,2,6,4,3,5]=>3 [1,2,6,4,5,3]=>4 [1,2,6,5,3,4]=>4 [1,2,6,5,4,3]=>4 [1,3,2,4,5,6]=>3 [1,3,2,4,6,5]=>4 [1,3,2,5,4,6]=>0 [1,3,2,5,6,4]=>2 [1,3,2,6,4,5]=>2 [1,3,2,6,5,4]=>0 [1,3,4,2,5,6]=>4 [1,3,4,2,6,5]=>3 [1,3,4,5,2,6]=>3 [1,3,4,5,6,2]=>3 [1,3,4,6,2,5]=>3 [1,3,4,6,5,2]=>3 [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]=>3 [1,3,6,2,4,5]=>3 [1,3,6,2,5,4]=>1 [1,3,6,4,2,5]=>3 [1,3,6,4,5,2]=>3 [1,3,6,5,2,4]=>2 [1,3,6,5,4,2]=>3 [1,4,2,3,5,6]=>4 [1,4,2,3,6,5]=>3 [1,4,2,5,3,6]=>2 [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]=>3 [1,4,3,2,6,5]=>0 [1,4,3,5,2,6]=>2 [1,4,3,5,6,2]=>2 [1,4,3,6,2,5]=>0 [1,4,3,6,5,2]=>0 [1,4,5,2,3,6]=>4 [1,4,5,2,6,3]=>3 [1,4,5,3,2,6]=>2 [1,4,5,3,6,2]=>2 [1,4,5,6,2,3]=>3 [1,4,5,6,3,2]=>2 [1,4,6,2,3,5]=>3 [1,4,6,2,5,3]=>2 [1,4,6,3,2,5]=>1 [1,4,6,3,5,2]=>1 [1,4,6,5,2,3]=>3 [1,4,6,5,3,2]=>2 [1,5,2,3,4,6]=>3 [1,5,2,3,6,4]=>3 [1,5,2,4,3,6]=>2 [1,5,2,4,6,3]=>3 [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]=>0 [1,5,3,4,2,6]=>2 [1,5,3,4,6,2]=>2 [1,5,3,6,2,4]=>0 [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]=>0 [1,5,4,3,6,2]=>0 [1,5,4,6,2,3]=>1 [1,5,4,6,3,2]=>0 [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]=>2 [1,5,6,4,2,3]=>2 [1,5,6,4,3,2]=>1 [1,6,2,3,4,5]=>3 [1,6,2,3,5,4]=>3 [1,6,2,4,3,5]=>2 [1,6,2,4,5,3]=>3 [1,6,2,5,3,4]=>3 [1,6,2,5,4,3]=>3 [1,6,3,2,4,5]=>2 [1,6,3,2,5,4]=>0 [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]=>2 [1,6,4,2,3,5]=>2 [1,6,4,2,5,3]=>1 [1,6,4,3,2,5]=>0 [1,6,4,3,5,2]=>0 [1,6,4,5,2,3]=>2 [1,6,4,5,3,2]=>1 [1,6,5,2,3,4]=>2 [1,6,5,2,4,3]=>2 [1,6,5,3,2,4]=>0 [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]=>4 [2,1,3,5,4,6]=>4 [2,1,3,5,6,4]=>5 [2,1,3,6,4,5]=>5 [2,1,3,6,5,4]=>6 [2,1,4,3,5,6]=>2 [2,1,4,3,6,5]=>0 [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]=>4 [2,1,5,3,4,6]=>3 [2,1,5,3,6,4]=>2 [2,1,5,4,3,6]=>0 [2,1,5,4,6,3]=>0 [2,1,5,6,3,4]=>4 [2,1,5,6,4,3]=>2 [2,1,6,3,4,5]=>3 [2,1,6,3,5,4]=>4 [2,1,6,4,3,5]=>0 [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]=>5 [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]=>3 [2,3,4,1,5,6]=>4 [2,3,4,1,6,5]=>3 [2,3,4,5,1,6]=>3 [2,3,4,5,6,1]=>3 [2,3,4,6,1,5]=>3 [2,3,4,6,5,1]=>3 [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]=>2 [2,3,5,6,1,4]=>3 [2,3,5,6,4,1]=>3 [2,3,6,1,4,5]=>4 [2,3,6,1,5,4]=>3 [2,3,6,4,1,5]=>3 [2,3,6,4,5,1]=>3 [2,3,6,5,1,4]=>3 [2,3,6,5,4,1]=>3 [2,4,1,3,5,6]=>3 [2,4,1,3,6,5]=>2 [2,4,1,5,3,6]=>2 [2,4,1,5,6,3]=>3 [2,4,1,6,3,5]=>2 [2,4,1,6,5,3]=>2 [2,4,3,1,5,6]=>3 [2,4,3,1,6,5]=>0 [2,4,3,5,1,6]=>2 [2,4,3,5,6,1]=>2 [2,4,3,6,1,5]=>0 [2,4,3,6,5,1]=>0 [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]=>2 [2,4,6,3,1,5]=>1 [2,4,6,3,5,1]=>1 [2,4,6,5,1,3]=>2 [2,4,6,5,3,1]=>2 [2,5,1,3,4,6]=>3 [2,5,1,3,6,4]=>3 [2,5,1,4,3,6]=>0 [2,5,1,4,6,3]=>1 [2,5,1,6,3,4]=>3 [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]=>1 [2,5,4,1,6,3]=>0 [2,5,4,3,1,6]=>0 [2,5,4,3,6,1]=>0 [2,5,4,6,1,3]=>0 [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]=>2 [2,5,6,3,4,1]=>2 [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]=>4 [2,6,1,4,3,5]=>0 [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]=>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]=>1 [2,6,4,1,5,3]=>1 [2,6,4,3,1,5]=>0 [2,6,4,3,5,1]=>0 [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]=>5 [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]=>3 [3,1,4,2,5,6]=>3 [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]=>3 [3,1,4,6,5,2]=>4 [3,1,5,2,4,6]=>2 [3,1,5,2,6,4]=>2 [3,1,5,4,2,6]=>0 [3,1,5,4,6,2]=>0 [3,1,5,6,2,4]=>3 [3,1,5,6,4,2]=>2 [3,1,6,2,4,5]=>3 [3,1,6,2,5,4]=>2 [3,1,6,4,2,5]=>1 [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]=>6 [3,2,1,5,4,6]=>0 [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]=>4 [3,2,4,5,1,6]=>3 [3,2,4,5,6,1]=>3 [3,2,4,6,1,5]=>4 [3,2,4,6,5,1]=>4 [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]=>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]=>4 [3,4,1,5,2,6]=>2 [3,4,1,5,6,2]=>3 [3,4,1,6,2,5]=>3 [3,4,1,6,5,2]=>2 [3,4,2,1,5,6]=>4 [3,4,2,1,6,5]=>2 [3,4,2,5,1,6]=>3 [3,4,2,5,6,1]=>3 [3,4,2,6,1,5]=>2 [3,4,2,6,5,1]=>2 [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]=>3 [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]=>2 [3,5,1,2,4,6]=>2 [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]=>1 [3,5,2,1,4,6]=>2 [3,5,2,1,6,4]=>1 [3,5,2,4,1,6]=>1 [3,5,2,4,6,1]=>1 [3,5,2,6,1,4]=>1 [3,5,2,6,4,1]=>1 [3,5,4,1,2,6]=>1 [3,5,4,1,6,2]=>0 [3,5,4,2,1,6]=>0 [3,5,4,2,6,1]=>0 [3,5,4,6,1,2]=>0 [3,5,4,6,2,1]=>0 [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]=>2 [3,6,1,4,2,5]=>1 [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]=>3 [4,1,2,5,3,6]=>3 [4,1,2,5,6,3]=>4 [4,1,2,6,3,5]=>3 [4,1,2,6,5,3]=>3 [4,1,3,2,5,6]=>3 [4,1,3,2,6,5]=>0 [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]=>2 [4,1,5,2,3,6]=>3 [4,1,5,2,6,3]=>2 [4,1,5,3,2,6]=>1 [4,1,5,3,6,2]=>1 [4,1,5,6,2,3]=>3 [4,1,5,6,3,2]=>2 [4,1,6,2,3,5]=>2 [4,1,6,2,5,3]=>2 [4,1,6,3,2,5]=>0 [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]=>4 [4,2,1,5,3,6]=>1 [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]=>2 [4,2,3,5,1,6]=>3 [4,2,3,5,6,1]=>3 [4,2,3,6,1,5]=>2 [4,2,3,6,5,1]=>2 [4,2,5,1,3,6]=>2 [4,2,5,1,6,3]=>2 [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]=>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]=>2 [4,3,1,5,2,6]=>2 [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]=>3 [4,5,1,3,2,6]=>1 [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]=>2 [4,6,1,3,2,5]=>0 [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]=>3 [5,1,2,4,3,6]=>2 [5,1,2,4,6,3]=>3 [5,1,2,6,3,4]=>3 [5,1,2,6,4,3]=>3 [5,1,3,2,4,6]=>2 [5,1,3,2,6,4]=>0 [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]=>2 [5,1,4,2,3,6]=>2 [5,1,4,2,6,3]=>1 [5,1,4,3,2,6]=>0 [5,1,4,3,6,2]=>0 [5,1,4,6,2,3]=>2 [5,1,4,6,3,2]=>1 [5,1,6,2,3,4]=>2 [5,1,6,2,4,3]=>2 [5,1,6,3,2,4]=>0 [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]=>4 [5,2,1,4,3,6]=>0 [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]=>2 [5,2,3,4,1,6]=>2 [5,2,3,4,6,1]=>2 [5,2,3,6,1,4]=>2 [5,2,3,6,4,1]=>2 [5,2,4,1,3,6]=>1 [5,2,4,1,6,3]=>1 [5,2,4,3,1,6]=>0 [5,2,4,3,6,1]=>0 [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]=>2 [5,3,1,4,2,6]=>1 [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]=>2 [5,4,1,3,2,6]=>0 [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]=>2 [5,6,1,3,2,4]=>0 [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]=>3 [6,1,2,4,3,5]=>2 [6,1,2,4,5,3]=>3 [6,1,2,5,3,4]=>3 [6,1,2,5,4,3]=>3 [6,1,3,2,4,5]=>2 [6,1,3,2,5,4]=>0 [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]=>2 [6,1,4,2,3,5]=>2 [6,1,4,2,5,3]=>1 [6,1,4,3,2,5]=>0 [6,1,4,3,5,2]=>0 [6,1,4,5,2,3]=>2 [6,1,4,5,3,2]=>1 [6,1,5,2,3,4]=>2 [6,1,5,2,4,3]=>2 [6,1,5,3,2,4]=>0 [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]=>4 [6,2,1,4,3,5]=>0 [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]=>2 [6,2,3,4,1,5]=>2 [6,2,3,4,5,1]=>2 [6,2,3,5,1,4]=>2 [6,2,3,5,4,1]=>2 [6,2,4,1,3,5]=>1 [6,2,4,1,5,3]=>1 [6,2,4,3,1,5]=>0 [6,2,4,3,5,1]=>0 [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]=>2 [6,3,1,4,2,5]=>1 [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]=>2 [6,4,1,3,2,5]=>0 [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]=>2 [6,5,1,3,2,4]=>0 [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]=>5 [1,2,3,4,6,5,7]=>4 [1,2,3,4,6,7,5]=>5 [1,2,3,4,7,5,6]=>5 [1,2,3,4,7,6,5]=>5 [1,2,3,5,4,6,7]=>5 [1,2,3,5,4,7,6]=>3 [1,2,3,5,6,4,7]=>5 [1,2,3,5,6,7,4]=>5 [1,2,3,5,7,4,6]=>4 [1,2,3,5,7,6,4]=>5 [1,2,3,6,4,5,7]=>5 [1,2,3,6,4,7,5]=>4 [1,2,3,6,5,4,7]=>4 [1,2,3,6,5,7,4]=>4 [1,2,3,6,7,4,5]=>5 [1,2,3,6,7,5,4]=>5 [1,2,3,7,4,5,6]=>5 [1,2,3,7,4,6,5]=>5 [1,2,3,7,5,4,6]=>4 [1,2,3,7,5,6,4]=>5 [1,2,3,7,6,4,5]=>5 [1,2,3,7,6,5,4]=>5 [1,2,4,3,5,6,7]=>5 [1,2,4,3,5,7,6]=>6 [1,2,4,3,6,5,7]=>2 [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]=>6 [1,2,4,5,3,7,6]=>5 [1,2,4,5,6,3,7]=>5 [1,2,4,5,6,7,3]=>5 [1,2,4,5,7,3,6]=>5 [1,2,4,5,7,6,3]=>5 [1,2,4,6,3,5,7]=>4 [1,2,4,6,3,7,5]=>4 [1,2,4,6,5,3,7]=>4 [1,2,4,6,5,7,3]=>4 [1,2,4,6,7,3,5]=>4 [1,2,4,6,7,5,3]=>5 [1,2,4,7,3,5,6]=>5 [1,2,4,7,3,6,5]=>3 [1,2,4,7,5,3,6]=>5 [1,2,4,7,5,6,3]=>5 [1,2,4,7,6,3,5]=>4 [1,2,4,7,6,5,3]=>5 [1,2,5,3,4,6,7]=>6 [1,2,5,3,4,7,6]=>5 [1,2,5,3,6,4,7]=>4 [1,2,5,3,6,7,4]=>5 [1,2,5,3,7,4,6]=>4 [1,2,5,3,7,6,4]=>3 [1,2,5,4,3,6,7]=>6 [1,2,5,4,3,7,6]=>3 [1,2,5,4,6,3,7]=>5 [1,2,5,4,6,7,3]=>5 [1,2,5,4,7,3,6]=>3 [1,2,5,4,7,6,3]=>3 [1,2,5,6,3,4,7]=>6 [1,2,5,6,3,7,4]=>5 [1,2,5,6,4,3,7]=>5 [1,2,5,6,4,7,3]=>5 [1,2,5,6,7,3,4]=>5 [1,2,5,6,7,4,3]=>5 [1,2,5,7,3,4,6]=>5 [1,2,5,7,3,6,4]=>4 [1,2,5,7,4,3,6]=>4 [1,2,5,7,4,6,3]=>4 [1,2,5,7,6,3,4]=>5 [1,2,5,7,6,4,3]=>5 [1,2,6,3,4,5,7]=>5 [1,2,6,3,4,7,5]=>5 [1,2,6,3,5,4,7]=>4 [1,2,6,3,5,7,4]=>5 [1,2,6,3,7,4,5]=>4 [1,2,6,3,7,5,4]=>4 [1,2,6,4,3,5,7]=>5 [1,2,6,4,3,7,5]=>3 [1,2,6,4,5,3,7]=>5 [1,2,6,4,5,7,3]=>5 [1,2,6,4,7,3,5]=>3 [1,2,6,4,7,5,3]=>4 [1,2,6,5,3,4,7]=>5 [1,2,6,5,3,7,4]=>4 [1,2,6,5,4,3,7]=>4 [1,2,6,5,4,7,3]=>4 [1,2,6,5,7,3,4]=>4 [1,2,6,5,7,4,3]=>4 [1,2,6,7,3,4,5]=>5 [1,2,6,7,3,5,4]=>5 [1,2,6,7,4,3,5]=>4 [1,2,6,7,4,5,3]=>5 [1,2,6,7,5,3,4]=>5 [1,2,6,7,5,4,3]=>5 [1,2,7,3,4,5,6]=>5 [1,2,7,3,4,6,5]=>5 [1,2,7,3,5,4,6]=>4 [1,2,7,3,5,6,4]=>5 [1,2,7,3,6,4,5]=>5 [1,2,7,3,6,5,4]=>5 [1,2,7,4,3,5,6]=>5 [1,2,7,4,3,6,5]=>3 [1,2,7,4,5,3,6]=>5 [1,2,7,4,5,6,3]=>5 [1,2,7,4,6,3,5]=>4 [1,2,7,4,6,5,3]=>5 [1,2,7,5,3,4,6]=>5 [1,2,7,5,3,6,4]=>4 [1,2,7,5,4,3,6]=>4 [1,2,7,5,4,6,3]=>4 [1,2,7,5,6,3,4]=>5 [1,2,7,5,6,4,3]=>5 [1,2,7,6,3,4,5]=>5 [1,2,7,6,3,5,4]=>5 [1,2,7,6,4,3,5]=>4 [1,2,7,6,4,5,3]=>5 [1,2,7,6,5,3,4]=>5 [1,2,7,6,5,4,3]=>5 [1,3,2,4,5,6,7]=>4 [1,3,2,4,5,7,6]=>4 [1,3,2,4,6,5,7]=>4 [1,3,2,4,6,7,5]=>5 [1,3,2,4,7,5,6]=>5 [1,3,2,4,7,6,5]=>6 [1,3,2,5,4,6,7]=>2 [1,3,2,5,4,7,6]=>0 [1,3,2,5,6,4,7]=>3 [1,3,2,5,6,7,4]=>3 [1,3,2,5,7,4,6]=>2 [1,3,2,5,7,6,4]=>4 [1,3,2,6,4,5,7]=>3 [1,3,2,6,4,7,5]=>2 [1,3,2,6,5,4,7]=>0 [1,3,2,6,5,7,4]=>0 [1,3,2,6,7,4,5]=>4 [1,3,2,6,7,5,4]=>2 [1,3,2,7,4,5,6]=>3 [1,3,2,7,4,6,5]=>4 [1,3,2,7,5,4,6]=>0 [1,3,2,7,5,6,4]=>2 [1,3,2,7,6,4,5]=>2 [1,3,2,7,6,5,4]=>0 [1,3,4,2,5,6,7]=>5 [1,3,4,2,5,7,6]=>6 [1,3,4,2,6,5,7]=>3 [1,3,4,2,6,7,5]=>5 [1,3,4,2,7,5,6]=>5 [1,3,4,2,7,6,5]=>4 [1,3,4,5,2,6,7]=>5 [1,3,4,5,2,7,6]=>4 [1,3,4,5,6,2,7]=>4 [1,3,4,5,6,7,2]=>4 [1,3,4,5,7,2,6]=>4 [1,3,4,5,7,6,2]=>4 [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]=>3 [1,3,4,6,7,2,5]=>4 [1,3,4,6,7,5,2]=>4 [1,3,4,7,2,5,6]=>5 [1,3,4,7,2,6,5]=>4 [1,3,4,7,5,2,6]=>4 [1,3,4,7,5,6,2]=>4 [1,3,4,7,6,2,5]=>4 [1,3,4,7,6,5,2]=>4 [1,3,5,2,4,6,7]=>4 [1,3,5,2,4,7,6]=>3 [1,3,5,2,6,4,7]=>3 [1,3,5,2,6,7,4]=>4 [1,3,5,2,7,4,6]=>3 [1,3,5,2,7,6,4]=>3 [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]=>4 [1,3,5,6,4,7,2]=>4 [1,3,5,6,7,2,4]=>3 [1,3,5,6,7,4,2]=>4 [1,3,5,7,2,4,6]=>3 [1,3,5,7,2,6,4]=>3 [1,3,5,7,4,2,6]=>3 [1,3,5,7,4,6,2]=>3 [1,3,5,7,6,2,4]=>3 [1,3,5,7,6,4,2]=>4 [1,3,6,2,4,5,7]=>4 [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]=>4 [1,3,6,2,7,5,4]=>2 [1,3,6,4,2,5,7]=>5 [1,3,6,4,2,7,5]=>3 [1,3,6,4,5,2,7]=>4 [1,3,6,4,5,7,2]=>4 [1,3,6,4,7,2,5]=>3 [1,3,6,4,7,5,2]=>3 [1,3,6,5,2,4,7]=>3 [1,3,6,5,2,7,4]=>2 [1,3,6,5,4,2,7]=>3 [1,3,6,5,4,7,2]=>3 [1,3,6,5,7,2,4]=>2 [1,3,6,5,7,4,2]=>3 [1,3,6,7,2,4,5]=>4 [1,3,6,7,2,5,4]=>2 [1,3,6,7,4,2,5]=>4 [1,3,6,7,4,5,2]=>4 [1,3,6,7,5,2,4]=>3 [1,3,6,7,5,4,2]=>4 [1,3,7,2,4,5,6]=>4 [1,3,7,2,4,6,5]=>5 [1,3,7,2,5,4,6]=>1 [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]=>5 [1,3,7,4,2,6,5]=>4 [1,3,7,4,5,2,6]=>4 [1,3,7,4,5,6,2]=>4 [1,3,7,4,6,2,5]=>4 [1,3,7,4,6,5,2]=>4 [1,3,7,5,2,4,6]=>3 [1,3,7,5,2,6,4]=>3 [1,3,7,5,4,2,6]=>3 [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]=>4 [1,3,7,6,2,5,4]=>2 [1,3,7,6,4,2,5]=>4 [1,3,7,6,4,5,2]=>4 [1,3,7,6,5,2,4]=>3 [1,3,7,6,5,4,2]=>4 [1,4,2,3,5,6,7]=>5 [1,4,2,3,5,7,6]=>6 [1,4,2,3,6,5,7]=>3 [1,4,2,3,6,7,5]=>5 [1,4,2,3,7,5,6]=>5 [1,4,2,3,7,6,5]=>4 [1,4,2,5,3,6,7]=>4 [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]=>4 [1,4,2,5,7,6,3]=>5 [1,4,2,6,3,5,7]=>3 [1,4,2,6,3,7,5]=>3 [1,4,2,6,5,3,7]=>1 [1,4,2,6,5,7,3]=>1 [1,4,2,6,7,3,5]=>4 [1,4,2,6,7,5,3]=>3 [1,4,2,7,3,5,6]=>4 [1,4,2,7,3,6,5]=>3 [1,4,2,7,5,3,6]=>2 [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]=>4 [1,4,3,2,5,7,6]=>6 [1,4,3,2,6,5,7]=>0 [1,4,3,2,6,7,5]=>3 [1,4,3,2,7,5,6]=>3 [1,4,3,2,7,6,5]=>0 [1,4,3,5,2,6,7]=>4 [1,4,3,5,2,7,6]=>4 [1,4,3,5,6,2,7]=>3 [1,4,3,5,6,7,2]=>3 [1,4,3,5,7,2,6]=>4 [1,4,3,5,7,6,2]=>4 [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]=>2 [1,4,3,6,7,5,2]=>2 [1,4,3,7,2,5,6]=>3 [1,4,3,7,2,6,5]=>0 [1,4,3,7,5,2,6]=>2 [1,4,3,7,5,6,2]=>2 [1,4,3,7,6,2,5]=>0 [1,4,3,7,6,5,2]=>0 [1,4,5,2,3,6,7]=>6 [1,4,5,2,3,7,6]=>6 [1,4,5,2,6,3,7]=>4 [1,4,5,2,6,7,3]=>5 [1,4,5,2,7,3,6]=>5 [1,4,5,2,7,6,3]=>4 [1,4,5,3,2,6,7]=>5 [1,4,5,3,2,7,6]=>3 [1,4,5,3,6,2,7]=>4 [1,4,5,3,6,7,2]=>4 [1,4,5,3,7,2,6]=>3 [1,4,5,3,7,6,2]=>3 [1,4,5,6,2,3,7]=>5 [1,4,5,6,2,7,3]=>4 [1,4,5,6,3,2,7]=>3 [1,4,5,6,3,7,2]=>3 [1,4,5,6,7,2,3]=>4 [1,4,5,6,7,3,2]=>3 [1,4,5,7,2,3,6]=>5 [1,4,5,7,2,6,3]=>4 [1,4,5,7,3,2,6]=>3 [1,4,5,7,3,6,2]=>3 [1,4,5,7,6,2,3]=>4 [1,4,5,7,6,3,2]=>3 [1,4,6,2,3,5,7]=>4 [1,4,6,2,3,7,5]=>5 [1,4,6,2,5,3,7]=>2 [1,4,6,2,5,7,3]=>3 [1,4,6,2,7,3,5]=>4 [1,4,6,2,7,5,3]=>3 [1,4,6,3,2,5,7]=>3 [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]=>4 [1,4,6,5,2,7,3]=>3 [1,4,6,5,3,2,7]=>2 [1,4,6,5,3,7,2]=>2
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Description
The number of boxed occurrences of 123 in a permutation.
This is the number of occurrences of the pattern $123$ such that any entry between the three matched entries is either larger than the largest matched entry or smaller than the smallest matched entry.
Code
def statistic(perm):
    pattern = [1,2,3]
    k = len(pattern)
    R = [(i, j) for i in range(1,k) for j in range(1,k)]
    return mesh_pattern_occurrences(perm, pattern, R=R)

def G(w):
    return [ (x+1,y) for (x,y) in enumerate(w) ]

def mesh_pattern_occurrences(perm, pat, R=[]):
    occs = 0
    k = len(pat)
    n = len(perm)
    pat = G(pat)
    perm = G(perm)
    for H in Subsets(perm, k):
        H = sorted(H)
        X = dict(G(sorted(i for (i,_) in H)))
        Y = dict(G(sorted(j for (_,j) in H)))
        if H == [ (X[i], Y[j]) for (i,j) in pat ]:
            X[0], X[k+1] = 0, n+1
            Y[0], Y[k+1] = 0, n+1
            shady = ( X[i] < x < X[i+1] and Y[j] < y < Y[j+1]
                      for (i,j) in R
                      for (x,y) in perm
                      )
            if not any(shady):
                occs = occs + 1
    return occs
Created
Jan 10, 2018 at 23:10 by Martin Rubey
Updated
Jan 10, 2018 at 23:10 by Martin Rubey