edit this statistic or download as text // json
Identifier
Values
=>
[{1}]=>0 [{1},{2}]=>0 [{2},{1}]=>0 [{1,2}]=>0 [{1},{2},{3}]=>0 [{1},{3},{2}]=>1 [{2},{1},{3}]=>0 [{3},{1},{2}]=>0 [{2},{3},{1}]=>0 [{3},{2},{1}]=>0 [{1},{2,3}]=>0 [{2},{1,3}]=>0 [{3},{1,2}]=>0 [{1,2},{3}]=>0 [{1,3},{2}]=>0 [{2,3},{1}]=>0 [{1,2,3}]=>0 [{1},{2},{3},{4}]=>0 [{1},{2},{4},{3}]=>2 [{1},{3},{2},{4}]=>1 [{1},{4},{2},{3}]=>2 [{1},{3},{4},{2}]=>2 [{1},{4},{3},{2}]=>3 [{2},{1},{3},{4}]=>0 [{2},{1},{4},{3}]=>2 [{3},{1},{2},{4}]=>0 [{4},{1},{2},{3}]=>0 [{3},{1},{4},{2}]=>1 [{4},{1},{3},{2}]=>1 [{2},{3},{1},{4}]=>0 [{2},{4},{1},{3}]=>1 [{3},{2},{1},{4}]=>0 [{4},{2},{1},{3}]=>0 [{3},{4},{1},{2}]=>0 [{4},{3},{1},{2}]=>0 [{2},{3},{4},{1}]=>0 [{2},{4},{3},{1}]=>1 [{3},{2},{4},{1}]=>0 [{4},{2},{3},{1}]=>0 [{3},{4},{2},{1}]=>0 [{4},{3},{2},{1}]=>0 [{1},{2},{3,4}]=>0 [{1},{3},{2,4}]=>1 [{1},{4},{2,3}]=>2 [{2},{1},{3,4}]=>0 [{3},{1},{2,4}]=>0 [{4},{1},{2,3}]=>0 [{2},{3},{1,4}]=>0 [{2},{4},{1,3}]=>1 [{3},{2},{1,4}]=>0 [{4},{2},{1,3}]=>0 [{3},{4},{1,2}]=>0 [{4},{3},{1,2}]=>0 [{1},{2,3},{4}]=>0 [{1},{2,4},{3}]=>1 [{1},{3,4},{2}]=>2 [{2},{1,3},{4}]=>0 [{2},{1,4},{3}]=>1 [{3},{1,2},{4}]=>0 [{4},{1,2},{3}]=>0 [{3},{1,4},{2}]=>0 [{4},{1,3},{2}]=>0 [{2},{3,4},{1}]=>0 [{3},{2,4},{1}]=>0 [{4},{2,3},{1}]=>0 [{1},{2,3,4}]=>0 [{2},{1,3,4}]=>0 [{3},{1,2,4}]=>0 [{4},{1,2,3}]=>0 [{1,2},{3},{4}]=>0 [{1,2},{4},{3}]=>2 [{1,3},{2},{4}]=>0 [{1,4},{2},{3}]=>0 [{1,3},{4},{2}]=>1 [{1,4},{3},{2}]=>1 [{2,3},{1},{4}]=>0 [{2,4},{1},{3}]=>0 [{3,4},{1},{2}]=>0 [{2,3},{4},{1}]=>0 [{2,4},{3},{1}]=>0 [{3,4},{2},{1}]=>0 [{1,2},{3,4}]=>0 [{1,3},{2,4}]=>0 [{1,4},{2,3}]=>0 [{2,3},{1,4}]=>0 [{2,4},{1,3}]=>0 [{3,4},{1,2}]=>0 [{1,2,3},{4}]=>0 [{1,2,4},{3}]=>0 [{1,3,4},{2}]=>0 [{2,3,4},{1}]=>0 [{1,2,3,4}]=>0 [{1},{2},{3},{4},{5}]=>0 [{1},{2},{3},{5},{4}]=>3 [{1},{2},{4},{3},{5}]=>2 [{1},{2},{5},{3},{4}]=>4 [{1},{2},{4},{5},{3}]=>4 [{1},{2},{5},{4},{3}]=>6 [{1},{3},{2},{4},{5}]=>1 [{1},{3},{2},{5},{4}]=>4 [{1},{4},{2},{3},{5}]=>2 [{1},{5},{2},{3},{4}]=>3 [{1},{4},{2},{5},{3}]=>4 [{1},{5},{2},{4},{3}]=>5 [{1},{3},{4},{2},{5}]=>2 [{1},{3},{5},{2},{4}]=>4 [{1},{4},{3},{2},{5}]=>3 [{1},{5},{3},{2},{4}]=>4 [{1},{4},{5},{2},{3}]=>4 [{1},{5},{4},{2},{3}]=>5 [{1},{3},{4},{5},{2}]=>3 [{1},{3},{5},{4},{2}]=>5 [{1},{4},{3},{5},{2}]=>4 [{1},{5},{3},{4},{2}]=>5 [{1},{4},{5},{3},{2}]=>5 [{1},{5},{4},{3},{2}]=>6 [{2},{1},{3},{4},{5}]=>0 [{2},{1},{3},{5},{4}]=>3 [{2},{1},{4},{3},{5}]=>2 [{2},{1},{5},{3},{4}]=>4 [{2},{1},{4},{5},{3}]=>4 [{2},{1},{5},{4},{3}]=>6 [{3},{1},{2},{4},{5}]=>0 [{3},{1},{2},{5},{4}]=>3 [{4},{1},{2},{3},{5}]=>0 [{5},{1},{2},{3},{4}]=>0 [{4},{1},{2},{5},{3}]=>2 [{5},{1},{2},{4},{3}]=>2 [{3},{1},{4},{2},{5}]=>1 [{3},{1},{5},{2},{4}]=>3 [{4},{1},{3},{2},{5}]=>1 [{5},{1},{3},{2},{4}]=>1 [{4},{1},{5},{2},{3}]=>2 [{5},{1},{4},{2},{3}]=>2 [{3},{1},{4},{5},{2}]=>2 [{3},{1},{5},{4},{2}]=>4 [{4},{1},{3},{5},{2}]=>2 [{5},{1},{3},{4},{2}]=>2 [{4},{1},{5},{3},{2}]=>3 [{5},{1},{4},{3},{2}]=>3 [{2},{3},{1},{4},{5}]=>0 [{2},{3},{1},{5},{4}]=>3 [{2},{4},{1},{3},{5}]=>1 [{2},{5},{1},{3},{4}]=>2 [{2},{4},{1},{5},{3}]=>3 [{2},{5},{1},{4},{3}]=>4 [{3},{2},{1},{4},{5}]=>0 [{3},{2},{1},{5},{4}]=>3 [{4},{2},{1},{3},{5}]=>0 [{5},{2},{1},{3},{4}]=>0 [{4},{2},{1},{5},{3}]=>2 [{5},{2},{1},{4},{3}]=>2 [{3},{4},{1},{2},{5}]=>0 [{3},{5},{1},{2},{4}]=>1 [{4},{3},{1},{2},{5}]=>0 [{5},{3},{1},{2},{4}]=>0 [{4},{5},{1},{2},{3}]=>0 [{5},{4},{1},{2},{3}]=>0 [{3},{4},{1},{5},{2}]=>1 [{3},{5},{1},{4},{2}]=>2 [{4},{3},{1},{5},{2}]=>1 [{5},{3},{1},{4},{2}]=>1 [{4},{5},{1},{3},{2}]=>1 [{5},{4},{1},{3},{2}]=>1 [{2},{3},{4},{1},{5}]=>0 [{2},{3},{5},{1},{4}]=>2 [{2},{4},{3},{1},{5}]=>1 [{2},{5},{3},{1},{4}]=>2 [{2},{4},{5},{1},{3}]=>2 [{2},{5},{4},{1},{3}]=>3 [{3},{2},{4},{1},{5}]=>0 [{3},{2},{5},{1},{4}]=>2 [{4},{2},{3},{1},{5}]=>0 [{5},{2},{3},{1},{4}]=>0 [{4},{2},{5},{1},{3}]=>1 [{5},{2},{4},{1},{3}]=>1 [{3},{4},{2},{1},{5}]=>0 [{3},{5},{2},{1},{4}]=>1 [{4},{3},{2},{1},{5}]=>0 [{5},{3},{2},{1},{4}]=>0 [{4},{5},{2},{1},{3}]=>0 [{5},{4},{2},{1},{3}]=>0 [{3},{4},{5},{1},{2}]=>0 [{3},{5},{4},{1},{2}]=>1 [{4},{3},{5},{1},{2}]=>0 [{5},{3},{4},{1},{2}]=>0 [{4},{5},{3},{1},{2}]=>0 [{5},{4},{3},{1},{2}]=>0 [{2},{3},{4},{5},{1}]=>0 [{2},{3},{5},{4},{1}]=>2 [{2},{4},{3},{5},{1}]=>1 [{2},{5},{3},{4},{1}]=>2 [{2},{4},{5},{3},{1}]=>2 [{2},{5},{4},{3},{1}]=>3 [{3},{2},{4},{5},{1}]=>0 [{3},{2},{5},{4},{1}]=>2 [{4},{2},{3},{5},{1}]=>0 [{5},{2},{3},{4},{1}]=>0 [{4},{2},{5},{3},{1}]=>1 [{5},{2},{4},{3},{1}]=>1 [{3},{4},{2},{5},{1}]=>0 [{3},{5},{2},{4},{1}]=>1 [{4},{3},{2},{5},{1}]=>0 [{5},{3},{2},{4},{1}]=>0 [{4},{5},{2},{3},{1}]=>0 [{5},{4},{2},{3},{1}]=>0 [{3},{4},{5},{2},{1}]=>0 [{3},{5},{4},{2},{1}]=>1 [{4},{3},{5},{2},{1}]=>0 [{5},{3},{4},{2},{1}]=>0 [{4},{5},{3},{2},{1}]=>0 [{5},{4},{3},{2},{1}]=>0 [{1},{2},{3},{4,5}]=>0 [{1},{2},{4},{3,5}]=>2 [{1},{2},{5},{3,4}]=>4 [{1},{3},{2},{4,5}]=>1 [{1},{4},{2},{3,5}]=>2 [{1},{5},{2},{3,4}]=>3 [{1},{3},{4},{2,5}]=>2 [{1},{3},{5},{2,4}]=>4 [{1},{4},{3},{2,5}]=>3 [{1},{5},{3},{2,4}]=>4 [{1},{4},{5},{2,3}]=>4 [{1},{5},{4},{2,3}]=>5 [{2},{1},{3},{4,5}]=>0 [{2},{1},{4},{3,5}]=>2 [{2},{1},{5},{3,4}]=>4 [{3},{1},{2},{4,5}]=>0 [{4},{1},{2},{3,5}]=>0 [{5},{1},{2},{3,4}]=>0 [{3},{1},{4},{2,5}]=>1 [{3},{1},{5},{2,4}]=>3 [{4},{1},{3},{2,5}]=>1 [{5},{1},{3},{2,4}]=>1 [{4},{1},{5},{2,3}]=>2 [{5},{1},{4},{2,3}]=>2 [{2},{3},{1},{4,5}]=>0 [{2},{4},{1},{3,5}]=>1 [{2},{5},{1},{3,4}]=>2 [{3},{2},{1},{4,5}]=>0 [{4},{2},{1},{3,5}]=>0 [{5},{2},{1},{3,4}]=>0 [{3},{4},{1},{2,5}]=>0 [{3},{5},{1},{2,4}]=>1 [{4},{3},{1},{2,5}]=>0 [{5},{3},{1},{2,4}]=>0 [{4},{5},{1},{2,3}]=>0 [{5},{4},{1},{2,3}]=>0 [{2},{3},{4},{1,5}]=>0 [{2},{3},{5},{1,4}]=>2 [{2},{4},{3},{1,5}]=>1 [{2},{5},{3},{1,4}]=>2 [{2},{4},{5},{1,3}]=>2 [{2},{5},{4},{1,3}]=>3 [{3},{2},{4},{1,5}]=>0 [{3},{2},{5},{1,4}]=>2 [{4},{2},{3},{1,5}]=>0 [{5},{2},{3},{1,4}]=>0 [{4},{2},{5},{1,3}]=>1 [{5},{2},{4},{1,3}]=>1 [{3},{4},{2},{1,5}]=>0 [{3},{5},{2},{1,4}]=>1 [{4},{3},{2},{1,5}]=>0 [{5},{3},{2},{1,4}]=>0 [{4},{5},{2},{1,3}]=>0 [{5},{4},{2},{1,3}]=>0 [{3},{4},{5},{1,2}]=>0 [{3},{5},{4},{1,2}]=>1 [{4},{3},{5},{1,2}]=>0 [{5},{3},{4},{1,2}]=>0 [{4},{5},{3},{1,2}]=>0 [{5},{4},{3},{1,2}]=>0 [{1},{2},{3,4},{5}]=>0 [{1},{2},{3,5},{4}]=>2 [{1},{2},{4,5},{3}]=>4 [{1},{3},{2,4},{5}]=>1 [{1},{3},{2,5},{4}]=>3 [{1},{4},{2,3},{5}]=>2 [{1},{5},{2,3},{4}]=>3 [{1},{4},{2,5},{3}]=>3 [{1},{5},{2,4},{3}]=>4 [{1},{3},{4,5},{2}]=>3 [{1},{4},{3,5},{2}]=>4 [{1},{5},{3,4},{2}]=>5 [{2},{1},{3,4},{5}]=>0 [{2},{1},{3,5},{4}]=>2 [{2},{1},{4,5},{3}]=>4 [{3},{1},{2,4},{5}]=>0 [{3},{1},{2,5},{4}]=>2 [{4},{1},{2,3},{5}]=>0 [{5},{1},{2,3},{4}]=>0 [{4},{1},{2,5},{3}]=>1 [{5},{1},{2,4},{3}]=>1 [{3},{1},{4,5},{2}]=>2 [{4},{1},{3,5},{2}]=>2 [{5},{1},{3,4},{2}]=>2 [{2},{3},{1,4},{5}]=>0 [{2},{3},{1,5},{4}]=>2 [{2},{4},{1,3},{5}]=>1 [{2},{5},{1,3},{4}]=>2 [{2},{4},{1,5},{3}]=>2 [{2},{5},{1,4},{3}]=>3 [{3},{2},{1,4},{5}]=>0 [{3},{2},{1,5},{4}]=>2 [{4},{2},{1,3},{5}]=>0 [{5},{2},{1,3},{4}]=>0 [{4},{2},{1,5},{3}]=>1 [{5},{2},{1,4},{3}]=>1 [{3},{4},{1,2},{5}]=>0 [{3},{5},{1,2},{4}]=>1 [{4},{3},{1,2},{5}]=>0 [{5},{3},{1,2},{4}]=>0 [{4},{5},{1,2},{3}]=>0 [{5},{4},{1,2},{3}]=>0 [{3},{4},{1,5},{2}]=>0 [{3},{5},{1,4},{2}]=>1 [{4},{3},{1,5},{2}]=>0 [{5},{3},{1,4},{2}]=>0 [{4},{5},{1,3},{2}]=>0 [{5},{4},{1,3},{2}]=>0 [{2},{3},{4,5},{1}]=>0 [{2},{4},{3,5},{1}]=>1 [{2},{5},{3,4},{1}]=>2 [{3},{2},{4,5},{1}]=>0 [{4},{2},{3,5},{1}]=>0 [{5},{2},{3,4},{1}]=>0 [{3},{4},{2,5},{1}]=>0 [{3},{5},{2,4},{1}]=>1 [{4},{3},{2,5},{1}]=>0 [{5},{3},{2,4},{1}]=>0 [{4},{5},{2,3},{1}]=>0 [{5},{4},{2,3},{1}]=>0 [{1},{2},{3,4,5}]=>0 [{1},{3},{2,4,5}]=>1 [{1},{4},{2,3,5}]=>2 [{1},{5},{2,3,4}]=>3 [{2},{1},{3,4,5}]=>0 [{3},{1},{2,4,5}]=>0 [{4},{1},{2,3,5}]=>0 [{5},{1},{2,3,4}]=>0 [{2},{3},{1,4,5}]=>0 [{2},{4},{1,3,5}]=>1 [{2},{5},{1,3,4}]=>2 [{3},{2},{1,4,5}]=>0 [{4},{2},{1,3,5}]=>0 [{5},{2},{1,3,4}]=>0 [{3},{4},{1,2,5}]=>0 [{3},{5},{1,2,4}]=>1 [{4},{3},{1,2,5}]=>0 [{5},{3},{1,2,4}]=>0 [{4},{5},{1,2,3}]=>0 [{5},{4},{1,2,3}]=>0 [{1},{2,3},{4},{5}]=>0 [{1},{2,3},{5},{4}]=>3 [{1},{2,4},{3},{5}]=>1 [{1},{2,5},{3},{4}]=>2 [{1},{2,4},{5},{3}]=>3 [{1},{2,5},{4},{3}]=>4 [{1},{3,4},{2},{5}]=>2 [{1},{3,5},{2},{4}]=>3 [{1},{4,5},{2},{3}]=>4 [{1},{3,4},{5},{2}]=>3 [{1},{3,5},{4},{2}]=>4 [{1},{4,5},{3},{2}]=>5 [{2},{1,3},{4},{5}]=>0 [{2},{1,3},{5},{4}]=>3 [{2},{1,4},{3},{5}]=>1 [{2},{1,5},{3},{4}]=>2 [{2},{1,4},{5},{3}]=>3 [{2},{1,5},{4},{3}]=>4 [{3},{1,2},{4},{5}]=>0 [{3},{1,2},{5},{4}]=>3 [{4},{1,2},{3},{5}]=>0 [{5},{1,2},{3},{4}]=>0 [{4},{1,2},{5},{3}]=>2 [{5},{1,2},{4},{3}]=>2 [{3},{1,4},{2},{5}]=>0 [{3},{1,5},{2},{4}]=>1 [{4},{1,3},{2},{5}]=>0 [{5},{1,3},{2},{4}]=>0 [{4},{1,5},{2},{3}]=>0 [{5},{1,4},{2},{3}]=>0 [{3},{1,4},{5},{2}]=>1 [{3},{1,5},{4},{2}]=>2 [{4},{1,3},{5},{2}]=>1 [{5},{1,3},{4},{2}]=>1 [{4},{1,5},{3},{2}]=>1 [{5},{1,4},{3},{2}]=>1 [{2},{3,4},{1},{5}]=>0 [{2},{3,5},{1},{4}]=>1 [{2},{4,5},{1},{3}]=>2 [{3},{2,4},{1},{5}]=>0 [{3},{2,5},{1},{4}]=>1 [{4},{2,3},{1},{5}]=>0 [{5},{2,3},{1},{4}]=>0 [{4},{2,5},{1},{3}]=>0 [{5},{2,4},{1},{3}]=>0 [{3},{4,5},{1},{2}]=>0 [{4},{3,5},{1},{2}]=>0 [{5},{3,4},{1},{2}]=>0 [{2},{3,4},{5},{1}]=>0 [{2},{3,5},{4},{1}]=>1 [{2},{4,5},{3},{1}]=>2 [{3},{2,4},{5},{1}]=>0 [{3},{2,5},{4},{1}]=>1 [{4},{2,3},{5},{1}]=>0 [{5},{2,3},{4},{1}]=>0 [{4},{2,5},{3},{1}]=>0 [{5},{2,4},{3},{1}]=>0 [{3},{4,5},{2},{1}]=>0 [{4},{3,5},{2},{1}]=>0 [{5},{3,4},{2},{1}]=>0 [{1},{2,3},{4,5}]=>0 [{1},{2,4},{3,5}]=>1 [{1},{2,5},{3,4}]=>2 [{1},{3,4},{2,5}]=>2 [{1},{3,5},{2,4}]=>3 [{1},{4,5},{2,3}]=>4 [{2},{1,3},{4,5}]=>0 [{2},{1,4},{3,5}]=>1 [{2},{1,5},{3,4}]=>2 [{3},{1,2},{4,5}]=>0 [{4},{1,2},{3,5}]=>0 [{5},{1,2},{3,4}]=>0 [{3},{1,4},{2,5}]=>0 [{3},{1,5},{2,4}]=>1 [{4},{1,3},{2,5}]=>0 [{5},{1,3},{2,4}]=>0 [{4},{1,5},{2,3}]=>0 [{5},{1,4},{2,3}]=>0 [{2},{3,4},{1,5}]=>0 [{2},{3,5},{1,4}]=>1 [{2},{4,5},{1,3}]=>2 [{3},{2,4},{1,5}]=>0 [{3},{2,5},{1,4}]=>1 [{4},{2,3},{1,5}]=>0 [{5},{2,3},{1,4}]=>0 [{4},{2,5},{1,3}]=>0 [{5},{2,4},{1,3}]=>0 [{3},{4,5},{1,2}]=>0 [{4},{3,5},{1,2}]=>0 [{5},{3,4},{1,2}]=>0 [{1},{2,3,4},{5}]=>0 [{1},{2,3,5},{4}]=>1 [{1},{2,4,5},{3}]=>2 [{1},{3,4,5},{2}]=>3 [{2},{1,3,4},{5}]=>0 [{2},{1,3,5},{4}]=>1 [{2},{1,4,5},{3}]=>2 [{3},{1,2,4},{5}]=>0 [{3},{1,2,5},{4}]=>1 [{4},{1,2,3},{5}]=>0 [{5},{1,2,3},{4}]=>0 [{4},{1,2,5},{3}]=>0 [{5},{1,2,4},{3}]=>0 [{3},{1,4,5},{2}]=>0 [{4},{1,3,5},{2}]=>0 [{5},{1,3,4},{2}]=>0 [{2},{3,4,5},{1}]=>0 [{3},{2,4,5},{1}]=>0 [{4},{2,3,5},{1}]=>0 [{5},{2,3,4},{1}]=>0 [{1},{2,3,4,5}]=>0 [{2},{1,3,4,5}]=>0 [{3},{1,2,4,5}]=>0 [{4},{1,2,3,5}]=>0 [{5},{1,2,3,4}]=>0 [{1,2},{3},{4},{5}]=>0 [{1,2},{3},{5},{4}]=>3 [{1,2},{4},{3},{5}]=>2 [{1,2},{5},{3},{4}]=>4 [{1,2},{4},{5},{3}]=>4 [{1,2},{5},{4},{3}]=>6 [{1,3},{2},{4},{5}]=>0 [{1,3},{2},{5},{4}]=>3 [{1,4},{2},{3},{5}]=>0 [{1,5},{2},{3},{4}]=>0 [{1,4},{2},{5},{3}]=>2 [{1,5},{2},{4},{3}]=>2 [{1,3},{4},{2},{5}]=>1 [{1,3},{5},{2},{4}]=>3 [{1,4},{3},{2},{5}]=>1 [{1,5},{3},{2},{4}]=>1 [{1,4},{5},{2},{3}]=>2 [{1,5},{4},{2},{3}]=>2 [{1,3},{4},{5},{2}]=>2 [{1,3},{5},{4},{2}]=>4 [{1,4},{3},{5},{2}]=>2 [{1,5},{3},{4},{2}]=>2 [{1,4},{5},{3},{2}]=>3 [{1,5},{4},{3},{2}]=>3 [{2,3},{1},{4},{5}]=>0 [{2,3},{1},{5},{4}]=>3 [{2,4},{1},{3},{5}]=>0 [{2,5},{1},{3},{4}]=>0 [{2,4},{1},{5},{3}]=>2 [{2,5},{1},{4},{3}]=>2 [{3,4},{1},{2},{5}]=>0 [{3,5},{1},{2},{4}]=>0 [{4,5},{1},{2},{3}]=>0 [{3,4},{1},{5},{2}]=>1 [{3,5},{1},{4},{2}]=>1 [{4,5},{1},{3},{2}]=>1 [{2,3},{4},{1},{5}]=>0 [{2,3},{5},{1},{4}]=>2 [{2,4},{3},{1},{5}]=>0 [{2,5},{3},{1},{4}]=>0 [{2,4},{5},{1},{3}]=>1 [{2,5},{4},{1},{3}]=>1 [{3,4},{2},{1},{5}]=>0 [{3,5},{2},{1},{4}]=>0 [{4,5},{2},{1},{3}]=>0 [{3,4},{5},{1},{2}]=>0 [{3,5},{4},{1},{2}]=>0 [{4,5},{3},{1},{2}]=>0 [{2,3},{4},{5},{1}]=>0 [{2,3},{5},{4},{1}]=>2 [{2,4},{3},{5},{1}]=>0 [{2,5},{3},{4},{1}]=>0 [{2,4},{5},{3},{1}]=>1 [{2,5},{4},{3},{1}]=>1 [{3,4},{2},{5},{1}]=>0 [{3,5},{2},{4},{1}]=>0 [{4,5},{2},{3},{1}]=>0 [{3,4},{5},{2},{1}]=>0 [{3,5},{4},{2},{1}]=>0 [{4,5},{3},{2},{1}]=>0 [{1,2},{3},{4,5}]=>0 [{1,2},{4},{3,5}]=>2 [{1,2},{5},{3,4}]=>4 [{1,3},{2},{4,5}]=>0 [{1,4},{2},{3,5}]=>0 [{1,5},{2},{3,4}]=>0 [{1,3},{4},{2,5}]=>1 [{1,3},{5},{2,4}]=>3 [{1,4},{3},{2,5}]=>1 [{1,5},{3},{2,4}]=>1 [{1,4},{5},{2,3}]=>2 [{1,5},{4},{2,3}]=>2 [{2,3},{1},{4,5}]=>0 [{2,4},{1},{3,5}]=>0 [{2,5},{1},{3,4}]=>0 [{3,4},{1},{2,5}]=>0 [{3,5},{1},{2,4}]=>0 [{4,5},{1},{2,3}]=>0 [{2,3},{4},{1,5}]=>0 [{2,3},{5},{1,4}]=>2 [{2,4},{3},{1,5}]=>0 [{2,5},{3},{1,4}]=>0 [{2,4},{5},{1,3}]=>1 [{2,5},{4},{1,3}]=>1 [{3,4},{2},{1,5}]=>0 [{3,5},{2},{1,4}]=>0 [{4,5},{2},{1,3}]=>0 [{3,4},{5},{1,2}]=>0 [{3,5},{4},{1,2}]=>0 [{4,5},{3},{1,2}]=>0 [{1,2},{3,4},{5}]=>0 [{1,2},{3,5},{4}]=>2 [{1,2},{4,5},{3}]=>4 [{1,3},{2,4},{5}]=>0 [{1,3},{2,5},{4}]=>2 [{1,4},{2,3},{5}]=>0 [{1,5},{2,3},{4}]=>0 [{1,4},{2,5},{3}]=>1 [{1,5},{2,4},{3}]=>1 [{1,3},{4,5},{2}]=>2 [{1,4},{3,5},{2}]=>2 [{1,5},{3,4},{2}]=>2 [{2,3},{1,4},{5}]=>0 [{2,3},{1,5},{4}]=>2 [{2,4},{1,3},{5}]=>0 [{2,5},{1,3},{4}]=>0 [{2,4},{1,5},{3}]=>1 [{2,5},{1,4},{3}]=>1 [{3,4},{1,2},{5}]=>0 [{3,5},{1,2},{4}]=>0 [{4,5},{1,2},{3}]=>0 [{3,4},{1,5},{2}]=>0 [{3,5},{1,4},{2}]=>0 [{4,5},{1,3},{2}]=>0 [{2,3},{4,5},{1}]=>0 [{2,4},{3,5},{1}]=>0 [{2,5},{3,4},{1}]=>0 [{3,4},{2,5},{1}]=>0 [{3,5},{2,4},{1}]=>0 [{4,5},{2,3},{1}]=>0 [{1,2},{3,4,5}]=>0 [{1,3},{2,4,5}]=>0 [{1,4},{2,3,5}]=>0 [{1,5},{2,3,4}]=>0 [{2,3},{1,4,5}]=>0 [{2,4},{1,3,5}]=>0 [{2,5},{1,3,4}]=>0 [{3,4},{1,2,5}]=>0 [{3,5},{1,2,4}]=>0 [{4,5},{1,2,3}]=>0 [{1,2,3},{4},{5}]=>0 [{1,2,3},{5},{4}]=>3 [{1,2,4},{3},{5}]=>0 [{1,2,5},{3},{4}]=>0 [{1,2,4},{5},{3}]=>2 [{1,2,5},{4},{3}]=>2 [{1,3,4},{2},{5}]=>0 [{1,3,5},{2},{4}]=>0 [{1,4,5},{2},{3}]=>0 [{1,3,4},{5},{2}]=>1 [{1,3,5},{4},{2}]=>1 [{1,4,5},{3},{2}]=>1 [{2,3,4},{1},{5}]=>0 [{2,3,5},{1},{4}]=>0 [{2,4,5},{1},{3}]=>0 [{3,4,5},{1},{2}]=>0 [{2,3,4},{5},{1}]=>0 [{2,3,5},{4},{1}]=>0 [{2,4,5},{3},{1}]=>0 [{3,4,5},{2},{1}]=>0 [{1,2,3},{4,5}]=>0 [{1,2,4},{3,5}]=>0 [{1,2,5},{3,4}]=>0 [{1,3,4},{2,5}]=>0 [{1,3,5},{2,4}]=>0 [{1,4,5},{2,3}]=>0 [{2,3,4},{1,5}]=>0 [{2,3,5},{1,4}]=>0 [{2,4,5},{1,3}]=>0 [{3,4,5},{1,2}]=>0 [{1,2,3,4},{5}]=>0 [{1,2,3,5},{4}]=>0 [{1,2,4,5},{3}]=>0 [{1,3,4,5},{2}]=>0 [{2,3,4,5},{1}]=>0 [{1,2,3,4,5}]=>0 [{1},{2},{3},{4},{5},{6}]=>0 [{1},{2},{3},{4},{6},{5}]=>4 [{1},{2},{3},{5},{4},{6}]=>3 [{1},{2},{3},{6},{4},{5}]=>6 [{1},{2},{3},{5},{6},{4}]=>6 [{1},{2},{3},{6},{5},{4}]=>9 [{1},{2},{4},{3},{5},{6}]=>2 [{1},{2},{4},{3},{6},{5}]=>6 [{1},{2},{5},{3},{4},{6}]=>4 [{1},{2},{6},{3},{4},{5}]=>6 [{1},{2},{5},{3},{6},{4}]=>7 [{1},{2},{6},{3},{5},{4}]=>9 [{1},{2},{4},{5},{3},{6}]=>4 [{1},{2},{4},{6},{3},{5}]=>7 [{1},{2},{5},{4},{3},{6}]=>6 [{1},{2},{6},{4},{3},{5}]=>8 [{1},{2},{5},{6},{3},{4}]=>8 [{1},{2},{6},{5},{3},{4}]=>10 [{1},{2},{4},{5},{6},{3}]=>6 [{1},{2},{4},{6},{5},{3}]=>9 [{1},{2},{5},{4},{6},{3}]=>8 [{1},{2},{6},{4},{5},{3}]=>10 [{1},{2},{5},{6},{4},{3}]=>10 [{1},{2},{6},{5},{4},{3}]=>12 [{1},{3},{2},{4},{5},{6}]=>1 [{1},{3},{2},{4},{6},{5}]=>5 [{1},{3},{2},{5},{4},{6}]=>4 [{1},{3},{2},{6},{4},{5}]=>7 [{1},{3},{2},{5},{6},{4}]=>7 [{1},{3},{2},{6},{5},{4}]=>10 [{1},{4},{2},{3},{5},{6}]=>2 [{1},{4},{2},{3},{6},{5}]=>6 [{1},{5},{2},{3},{4},{6}]=>3 [{1},{6},{2},{3},{4},{5}]=>4 [{1},{5},{2},{3},{6},{4}]=>6 [{1},{6},{2},{3},{5},{4}]=>7 [{1},{4},{2},{5},{3},{6}]=>4 [{1},{4},{2},{6},{3},{5}]=>7 [{1},{5},{2},{4},{3},{6}]=>5 [{1},{6},{2},{4},{3},{5}]=>6 [{1},{5},{2},{6},{3},{4}]=>7 [{1},{6},{2},{5},{3},{4}]=>8 [{1},{4},{2},{5},{6},{3}]=>6 [{1},{4},{2},{6},{5},{3}]=>9 [{1},{5},{2},{4},{6},{3}]=>7 [{1},{6},{2},{4},{5},{3}]=>8 [{1},{5},{2},{6},{4},{3}]=>9 [{1},{6},{2},{5},{4},{3}]=>10 [{1},{3},{4},{2},{5},{6}]=>2 [{1},{3},{4},{2},{6},{5}]=>6 [{1},{3},{5},{2},{4},{6}]=>4 [{1},{3},{6},{2},{4},{5}]=>6 [{1},{3},{5},{2},{6},{4}]=>7 [{1},{3},{6},{2},{5},{4}]=>9 [{1},{4},{3},{2},{5},{6}]=>3 [{1},{4},{3},{2},{6},{5}]=>7 [{1},{5},{3},{2},{4},{6}]=>4 [{1},{6},{3},{2},{4},{5}]=>5 [{1},{5},{3},{2},{6},{4}]=>7 [{1},{6},{3},{2},{5},{4}]=>8 [{1},{4},{5},{2},{3},{6}]=>4 [{1},{4},{6},{2},{3},{5}]=>6 [{1},{5},{4},{2},{3},{6}]=>5 [{1},{6},{4},{2},{3},{5}]=>6 [{1},{5},{6},{2},{3},{4}]=>6 [{1},{6},{5},{2},{3},{4}]=>7 [{1},{4},{5},{2},{6},{3}]=>6 [{1},{4},{6},{2},{5},{3}]=>8 [{1},{5},{4},{2},{6},{3}]=>7 [{1},{6},{4},{2},{5},{3}]=>8 [{1},{5},{6},{2},{4},{3}]=>8 [{1},{6},{5},{2},{4},{3}]=>9 [{1},{3},{4},{5},{2},{6}]=>3 [{1},{3},{4},{6},{2},{5}]=>6 [{1},{3},{5},{4},{2},{6}]=>5 [{1},{3},{6},{4},{2},{5}]=>7 [{1},{3},{5},{6},{2},{4}]=>7 [{1},{3},{6},{5},{2},{4}]=>9 [{1},{4},{3},{5},{2},{6}]=>4 [{1},{4},{3},{6},{2},{5}]=>7 [{1},{5},{3},{4},{2},{6}]=>5 [{1},{6},{3},{4},{2},{5}]=>6 [{1},{5},{3},{6},{2},{4}]=>7 [{1},{6},{3},{5},{2},{4}]=>8 [{1},{4},{5},{3},{2},{6}]=>5 [{1},{4},{6},{3},{2},{5}]=>7 [{1},{5},{4},{3},{2},{6}]=>6 [{1},{6},{4},{3},{2},{5}]=>7 [{1},{5},{6},{3},{2},{4}]=>7 [{1},{6},{5},{3},{2},{4}]=>8 [{1},{4},{5},{6},{2},{3}]=>6 [{1},{4},{6},{5},{2},{3}]=>8 [{1},{5},{4},{6},{2},{3}]=>7 [{1},{6},{4},{5},{2},{3}]=>8 [{1},{5},{6},{4},{2},{3}]=>8 [{1},{6},{5},{4},{2},{3}]=>9 [{1},{3},{4},{5},{6},{2}]=>4 [{1},{3},{4},{6},{5},{2}]=>7 [{1},{3},{5},{4},{6},{2}]=>6 [{1},{3},{6},{4},{5},{2}]=>8 [{1},{3},{5},{6},{4},{2}]=>8 [{1},{3},{6},{5},{4},{2}]=>10 [{1},{4},{3},{5},{6},{2}]=>5 [{1},{4},{3},{6},{5},{2}]=>8 [{1},{5},{3},{4},{6},{2}]=>6 [{1},{6},{3},{4},{5},{2}]=>7 [{1},{5},{3},{6},{4},{2}]=>8 [{1},{6},{3},{5},{4},{2}]=>9 [{1},{4},{5},{3},{6},{2}]=>6 [{1},{4},{6},{3},{5},{2}]=>8 [{1},{5},{4},{3},{6},{2}]=>7 [{1},{6},{4},{3},{5},{2}]=>8 [{1},{5},{6},{3},{4},{2}]=>8 [{1},{6},{5},{3},{4},{2}]=>9 [{1},{4},{5},{6},{3},{2}]=>7 [{1},{4},{6},{5},{3},{2}]=>9 [{1},{5},{4},{6},{3},{2}]=>8 [{1},{6},{4},{5},{3},{2}]=>9 [{1},{5},{6},{4},{3},{2}]=>9 [{1},{6},{5},{4},{3},{2}]=>10 [{2},{1},{3},{4},{5},{6}]=>0 [{2},{1},{3},{4},{6},{5}]=>4 [{2},{1},{3},{5},{4},{6}]=>3 [{2},{1},{3},{6},{4},{5}]=>6 [{2},{1},{3},{5},{6},{4}]=>6 [{2},{1},{3},{6},{5},{4}]=>9 [{2},{1},{4},{3},{5},{6}]=>2 [{2},{1},{4},{3},{6},{5}]=>6 [{2},{1},{5},{3},{4},{6}]=>4 [{2},{1},{6},{3},{4},{5}]=>6 [{2},{1},{5},{3},{6},{4}]=>7 [{2},{1},{6},{3},{5},{4}]=>9 [{2},{1},{4},{5},{3},{6}]=>4 [{2},{1},{4},{6},{3},{5}]=>7 [{2},{1},{5},{4},{3},{6}]=>6 [{2},{1},{6},{4},{3},{5}]=>8 [{2},{1},{5},{6},{3},{4}]=>8 [{2},{1},{6},{5},{3},{4}]=>10 [{2},{1},{4},{5},{6},{3}]=>6 [{2},{1},{4},{6},{5},{3}]=>9 [{2},{1},{5},{4},{6},{3}]=>8 [{2},{1},{6},{4},{5},{3}]=>10 [{2},{1},{5},{6},{4},{3}]=>10 [{2},{1},{6},{5},{4},{3}]=>12 [{3},{1},{2},{4},{5},{6}]=>0 [{3},{1},{2},{4},{6},{5}]=>4 [{3},{1},{2},{5},{4},{6}]=>3 [{3},{1},{2},{6},{4},{5}]=>6 [{3},{1},{2},{5},{6},{4}]=>6 [{3},{1},{2},{6},{5},{4}]=>9 [{4},{1},{2},{3},{5},{6}]=>0 [{4},{1},{2},{3},{6},{5}]=>4 [{5},{1},{2},{3},{4},{6}]=>0 [{6},{1},{2},{3},{4},{5}]=>0 [{5},{1},{2},{3},{6},{4}]=>3 [{6},{1},{2},{3},{5},{4}]=>3 [{4},{1},{2},{5},{3},{6}]=>2 [{4},{1},{2},{6},{3},{5}]=>5 [{5},{1},{2},{4},{3},{6}]=>2 [{6},{1},{2},{4},{3},{5}]=>2 [{5},{1},{2},{6},{3},{4}]=>4 [{6},{1},{2},{5},{3},{4}]=>4 [{4},{1},{2},{5},{6},{3}]=>4 [{4},{1},{2},{6},{5},{3}]=>7 [{5},{1},{2},{4},{6},{3}]=>4 [{6},{1},{2},{4},{5},{3}]=>4 [{5},{1},{2},{6},{4},{3}]=>6 [{6},{1},{2},{5},{4},{3}]=>6 [{3},{1},{4},{2},{5},{6}]=>1 [{3},{1},{4},{2},{6},{5}]=>5 [{3},{1},{5},{2},{4},{6}]=>3 [{3},{1},{6},{2},{4},{5}]=>5 [{3},{1},{5},{2},{6},{4}]=>6 [{3},{1},{6},{2},{5},{4}]=>8 [{4},{1},{3},{2},{5},{6}]=>1 [{4},{1},{3},{2},{6},{5}]=>5 [{5},{1},{3},{2},{4},{6}]=>1 [{6},{1},{3},{2},{4},{5}]=>1 [{5},{1},{3},{2},{6},{4}]=>4 [{6},{1},{3},{2},{5},{4}]=>4 [{4},{1},{5},{2},{3},{6}]=>2 [{4},{1},{6},{2},{3},{5}]=>4 [{5},{1},{4},{2},{3},{6}]=>2 [{6},{1},{4},{2},{3},{5}]=>2 [{5},{1},{6},{2},{3},{4}]=>3 [{6},{1},{5},{2},{3},{4}]=>3 [{4},{1},{5},{2},{6},{3}]=>4 [{4},{1},{6},{2},{5},{3}]=>6 [{5},{1},{4},{2},{6},{3}]=>4 [{6},{1},{4},{2},{5},{3}]=>4 [{5},{1},{6},{2},{4},{3}]=>5 [{6},{1},{5},{2},{4},{3}]=>5 [{3},{1},{4},{5},{2},{6}]=>2 [{3},{1},{4},{6},{2},{5}]=>5 [{3},{1},{5},{4},{2},{6}]=>4 [{3},{1},{6},{4},{2},{5}]=>6 [{3},{1},{5},{6},{2},{4}]=>6 [{3},{1},{6},{5},{2},{4}]=>8 [{4},{1},{3},{5},{2},{6}]=>2 [{4},{1},{3},{6},{2},{5}]=>5 [{5},{1},{3},{4},{2},{6}]=>2 [{6},{1},{3},{4},{2},{5}]=>2 [{5},{1},{3},{6},{2},{4}]=>4 [{6},{1},{3},{5},{2},{4}]=>4 [{4},{1},{5},{3},{2},{6}]=>3 [{4},{1},{6},{3},{2},{5}]=>5 [{5},{1},{4},{3},{2},{6}]=>3 [{6},{1},{4},{3},{2},{5}]=>3 [{5},{1},{6},{3},{2},{4}]=>4 [{6},{1},{5},{3},{2},{4}]=>4 [{4},{1},{5},{6},{2},{3}]=>4 [{4},{1},{6},{5},{2},{3}]=>6 [{5},{1},{4},{6},{2},{3}]=>4 [{6},{1},{4},{5},{2},{3}]=>4 [{5},{1},{6},{4},{2},{3}]=>5 [{6},{1},{5},{4},{2},{3}]=>5 [{3},{1},{4},{5},{6},{2}]=>3 [{3},{1},{4},{6},{5},{2}]=>6 [{3},{1},{5},{4},{6},{2}]=>5 [{3},{1},{6},{4},{5},{2}]=>7 [{3},{1},{5},{6},{4},{2}]=>7 [{3},{1},{6},{5},{4},{2}]=>9 [{4},{1},{3},{5},{6},{2}]=>3 [{4},{1},{3},{6},{5},{2}]=>6 [{5},{1},{3},{4},{6},{2}]=>3 [{6},{1},{3},{4},{5},{2}]=>3 [{5},{1},{3},{6},{4},{2}]=>5 [{6},{1},{3},{5},{4},{2}]=>5 [{4},{1},{5},{3},{6},{2}]=>4 [{4},{1},{6},{3},{5},{2}]=>6 [{5},{1},{4},{3},{6},{2}]=>4 [{6},{1},{4},{3},{5},{2}]=>4 [{5},{1},{6},{3},{4},{2}]=>5 [{6},{1},{5},{3},{4},{2}]=>5 [{4},{1},{5},{6},{3},{2}]=>5 [{4},{1},{6},{5},{3},{2}]=>7 [{5},{1},{4},{6},{3},{2}]=>5 [{6},{1},{4},{5},{3},{2}]=>5 [{5},{1},{6},{4},{3},{2}]=>6 [{6},{1},{5},{4},{3},{2}]=>6 [{2},{3},{1},{4},{5},{6}]=>0 [{2},{3},{1},{4},{6},{5}]=>4 [{2},{3},{1},{5},{4},{6}]=>3 [{2},{3},{1},{6},{4},{5}]=>6 [{2},{3},{1},{5},{6},{4}]=>6 [{2},{3},{1},{6},{5},{4}]=>9 [{2},{4},{1},{3},{5},{6}]=>1 [{2},{4},{1},{3},{6},{5}]=>5 [{2},{5},{1},{3},{4},{6}]=>2 [{2},{6},{1},{3},{4},{5}]=>3 [{2},{5},{1},{3},{6},{4}]=>5 [{2},{6},{1},{3},{5},{4}]=>6 [{2},{4},{1},{5},{3},{6}]=>3 [{2},{4},{1},{6},{3},{5}]=>6 [{2},{5},{1},{4},{3},{6}]=>4 [{2},{6},{1},{4},{3},{5}]=>5 [{2},{5},{1},{6},{3},{4}]=>6 [{2},{6},{1},{5},{3},{4}]=>7 [{2},{4},{1},{5},{6},{3}]=>5 [{2},{4},{1},{6},{5},{3}]=>8 [{2},{5},{1},{4},{6},{3}]=>6 [{2},{6},{1},{4},{5},{3}]=>7 [{2},{5},{1},{6},{4},{3}]=>8 [{2},{6},{1},{5},{4},{3}]=>9 [{3},{2},{1},{4},{5},{6}]=>0 [{3},{2},{1},{4},{6},{5}]=>4 [{3},{2},{1},{5},{4},{6}]=>3 [{3},{2},{1},{6},{4},{5}]=>6 [{3},{2},{1},{5},{6},{4}]=>6 [{3},{2},{1},{6},{5},{4}]=>9 [{4},{2},{1},{3},{5},{6}]=>0 [{4},{2},{1},{3},{6},{5}]=>4 [{5},{2},{1},{3},{4},{6}]=>0 [{6},{2},{1},{3},{4},{5}]=>0 [{5},{2},{1},{3},{6},{4}]=>3 [{6},{2},{1},{3},{5},{4}]=>3 [{4},{2},{1},{5},{3},{6}]=>2 [{4},{2},{1},{6},{3},{5}]=>5 [{5},{2},{1},{4},{3},{6}]=>2 [{6},{2},{1},{4},{3},{5}]=>2 [{5},{2},{1},{6},{3},{4}]=>4 [{6},{2},{1},{5},{3},{4}]=>4 [{4},{2},{1},{5},{6},{3}]=>4 [{4},{2},{1},{6},{5},{3}]=>7 [{5},{2},{1},{4},{6},{3}]=>4 [{6},{2},{1},{4},{5},{3}]=>4 [{5},{2},{1},{6},{4},{3}]=>6 [{6},{2},{1},{5},{4},{3}]=>6 [{3},{4},{1},{2},{5},{6}]=>0 [{3},{4},{1},{2},{6},{5}]=>4 [{3},{5},{1},{2},{4},{6}]=>1 [{3},{6},{1},{2},{4},{5}]=>2 [{3},{5},{1},{2},{6},{4}]=>4 [{3},{6},{1},{2},{5},{4}]=>5 [{4},{3},{1},{2},{5},{6}]=>0 [{4},{3},{1},{2},{6},{5}]=>4 [{5},{3},{1},{2},{4},{6}]=>0 [{6},{3},{1},{2},{4},{5}]=>0 [{5},{3},{1},{2},{6},{4}]=>3 [{6},{3},{1},{2},{5},{4}]=>3 [{4},{5},{1},{2},{3},{6}]=>0 [{4},{6},{1},{2},{3},{5}]=>1 [{5},{4},{1},{2},{3},{6}]=>0 [{6},{4},{1},{2},{3},{5}]=>0 [{5},{6},{1},{2},{3},{4}]=>0 [{6},{5},{1},{2},{3},{4}]=>0 [{4},{5},{1},{2},{6},{3}]=>2 [{4},{6},{1},{2},{5},{3}]=>3 [{5},{4},{1},{2},{6},{3}]=>2 [{6},{4},{1},{2},{5},{3}]=>2 [{5},{6},{1},{2},{4},{3}]=>2 [{6},{5},{1},{2},{4},{3}]=>2 [{3},{4},{1},{5},{2},{6}]=>1 [{3},{4},{1},{6},{2},{5}]=>4 [{3},{5},{1},{4},{2},{6}]=>2 [{3},{6},{1},{4},{2},{5}]=>3 [{3},{5},{1},{6},{2},{4}]=>4 [{3},{6},{1},{5},{2},{4}]=>5 [{4},{3},{1},{5},{2},{6}]=>1 [{4},{3},{1},{6},{2},{5}]=>4 [{5},{3},{1},{4},{2},{6}]=>1 [{6},{3},{1},{4},{2},{5}]=>1 [{5},{3},{1},{6},{2},{4}]=>3 [{6},{3},{1},{5},{2},{4}]=>3 [{4},{5},{1},{3},{2},{6}]=>1 [{4},{6},{1},{3},{2},{5}]=>2 [{5},{4},{1},{3},{2},{6}]=>1 [{6},{4},{1},{3},{2},{5}]=>1 [{5},{6},{1},{3},{2},{4}]=>1 [{6},{5},{1},{3},{2},{4}]=>1 [{4},{5},{1},{6},{2},{3}]=>2 [{4},{6},{1},{5},{2},{3}]=>3 [{5},{4},{1},{6},{2},{3}]=>2 [{6},{4},{1},{5},{2},{3}]=>2 [{5},{6},{1},{4},{2},{3}]=>2 [{6},{5},{1},{4},{2},{3}]=>2 [{3},{4},{1},{5},{6},{2}]=>2 [{3},{4},{1},{6},{5},{2}]=>5 [{3},{5},{1},{4},{6},{2}]=>3 [{3},{6},{1},{4},{5},{2}]=>4 [{3},{5},{1},{6},{4},{2}]=>5 [{3},{6},{1},{5},{4},{2}]=>6 [{4},{3},{1},{5},{6},{2}]=>2 [{4},{3},{1},{6},{5},{2}]=>5 [{5},{3},{1},{4},{6},{2}]=>2 [{6},{3},{1},{4},{5},{2}]=>2 [{5},{3},{1},{6},{4},{2}]=>4 [{6},{3},{1},{5},{4},{2}]=>4 [{4},{5},{1},{3},{6},{2}]=>2 [{4},{6},{1},{3},{5},{2}]=>3 [{5},{4},{1},{3},{6},{2}]=>2 [{6},{4},{1},{3},{5},{2}]=>2 [{5},{6},{1},{3},{4},{2}]=>2 [{6},{5},{1},{3},{4},{2}]=>2 [{4},{5},{1},{6},{3},{2}]=>3 [{4},{6},{1},{5},{3},{2}]=>4 [{5},{4},{1},{6},{3},{2}]=>3 [{6},{4},{1},{5},{3},{2}]=>3 [{5},{6},{1},{4},{3},{2}]=>3 [{6},{5},{1},{4},{3},{2}]=>3 [{2},{3},{4},{1},{5},{6}]=>0 [{2},{3},{4},{1},{6},{5}]=>4 [{2},{3},{5},{1},{4},{6}]=>2 [{2},{3},{6},{1},{4},{5}]=>4 [{2},{3},{5},{1},{6},{4}]=>5 [{2},{3},{6},{1},{5},{4}]=>7 [{2},{4},{3},{1},{5},{6}]=>1 [{2},{4},{3},{1},{6},{5}]=>5 [{2},{5},{3},{1},{4},{6}]=>2 [{2},{6},{3},{1},{4},{5}]=>3 [{2},{5},{3},{1},{6},{4}]=>5 [{2},{6},{3},{1},{5},{4}]=>6 [{2},{4},{5},{1},{3},{6}]=>2 [{2},{4},{6},{1},{3},{5}]=>4 [{2},{5},{4},{1},{3},{6}]=>3 [{2},{6},{4},{1},{3},{5}]=>4 [{2},{5},{6},{1},{3},{4}]=>4 [{2},{6},{5},{1},{3},{4}]=>5 [{2},{4},{5},{1},{6},{3}]=>4 [{2},{4},{6},{1},{5},{3}]=>6 [{2},{5},{4},{1},{6},{3}]=>5 [{2},{6},{4},{1},{5},{3}]=>6 [{2},{5},{6},{1},{4},{3}]=>6 [{2},{6},{5},{1},{4},{3}]=>7 [{3},{2},{4},{1},{5},{6}]=>0 [{3},{2},{4},{1},{6},{5}]=>4 [{3},{2},{5},{1},{4},{6}]=>2 [{3},{2},{6},{1},{4},{5}]=>4 [{3},{2},{5},{1},{6},{4}]=>5 [{3},{2},{6},{1},{5},{4}]=>7 [{4},{2},{3},{1},{5},{6}]=>0 [{4},{2},{3},{1},{6},{5}]=>4 [{5},{2},{3},{1},{4},{6}]=>0 [{6},{2},{3},{1},{4},{5}]=>0 [{5},{2},{3},{1},{6},{4}]=>3 [{6},{2},{3},{1},{5},{4}]=>3 [{4},{2},{5},{1},{3},{6}]=>1 [{4},{2},{6},{1},{3},{5}]=>3 [{5},{2},{4},{1},{3},{6}]=>1 [{6},{2},{4},{1},{3},{5}]=>1 [{5},{2},{6},{1},{3},{4}]=>2 [{6},{2},{5},{1},{3},{4}]=>2 [{4},{2},{5},{1},{6},{3}]=>3 [{4},{2},{6},{1},{5},{3}]=>5 [{5},{2},{4},{1},{6},{3}]=>3 [{6},{2},{4},{1},{5},{3}]=>3 [{5},{2},{6},{1},{4},{3}]=>4 [{6},{2},{5},{1},{4},{3}]=>4 [{3},{4},{2},{1},{5},{6}]=>0 [{3},{4},{2},{1},{6},{5}]=>4 [{3},{5},{2},{1},{4},{6}]=>1 [{3},{6},{2},{1},{4},{5}]=>2 [{3},{5},{2},{1},{6},{4}]=>4 [{3},{6},{2},{1},{5},{4}]=>5 [{4},{3},{2},{1},{5},{6}]=>0 [{4},{3},{2},{1},{6},{5}]=>4 [{5},{3},{2},{1},{4},{6}]=>0 [{6},{3},{2},{1},{4},{5}]=>0 [{5},{3},{2},{1},{6},{4}]=>3 [{6},{3},{2},{1},{5},{4}]=>3 [{4},{5},{2},{1},{3},{6}]=>0 [{4},{6},{2},{1},{3},{5}]=>1 [{5},{4},{2},{1},{3},{6}]=>0 [{6},{4},{2},{1},{3},{5}]=>0 [{5},{6},{2},{1},{3},{4}]=>0 [{6},{5},{2},{1},{3},{4}]=>0 [{4},{5},{2},{1},{6},{3}]=>2 [{4},{6},{2},{1},{5},{3}]=>3 [{5},{4},{2},{1},{6},{3}]=>2 [{6},{4},{2},{1},{5},{3}]=>2 [{5},{6},{2},{1},{4},{3}]=>2 [{6},{5},{2},{1},{4},{3}]=>2 [{3},{4},{5},{1},{2},{6}]=>0 [{3},{4},{6},{1},{2},{5}]=>2 [{3},{5},{4},{1},{2},{6}]=>1 [{3},{6},{4},{1},{2},{5}]=>2 [{3},{5},{6},{1},{2},{4}]=>2 [{3},{6},{5},{1},{2},{4}]=>3 [{4},{3},{5},{1},{2},{6}]=>0 [{4},{3},{6},{1},{2},{5}]=>2 [{5},{3},{4},{1},{2},{6}]=>0 [{6},{3},{4},{1},{2},{5}]=>0 [{5},{3},{6},{1},{2},{4}]=>1 [{6},{3},{5},{1},{2},{4}]=>1 [{4},{5},{3},{1},{2},{6}]=>0 [{4},{6},{3},{1},{2},{5}]=>1 [{5},{4},{3},{1},{2},{6}]=>0 [{6},{4},{3},{1},{2},{5}]=>0 [{5},{6},{3},{1},{2},{4}]=>0 [{6},{5},{3},{1},{2},{4}]=>0 [{4},{5},{6},{1},{2},{3}]=>0 [{4},{6},{5},{1},{2},{3}]=>1 [{5},{4},{6},{1},{2},{3}]=>0 [{6},{4},{5},{1},{2},{3}]=>0 [{5},{6},{4},{1},{2},{3}]=>0 [{6},{5},{4},{1},{2},{3}]=>0 [{3},{4},{5},{1},{6},{2}]=>1 [{3},{4},{6},{1},{5},{2}]=>3 [{3},{5},{4},{1},{6},{2}]=>2 [{3},{6},{4},{1},{5},{2}]=>3 [{3},{5},{6},{1},{4},{2}]=>3 [{3},{6},{5},{1},{4},{2}]=>4 [{4},{3},{5},{1},{6},{2}]=>1 [{4},{3},{6},{1},{5},{2}]=>3 [{5},{3},{4},{1},{6},{2}]=>1 [{6},{3},{4},{1},{5},{2}]=>1 [{5},{3},{6},{1},{4},{2}]=>2 [{6},{3},{5},{1},{4},{2}]=>2 [{4},{5},{3},{1},{6},{2}]=>1 [{4},{6},{3},{1},{5},{2}]=>2 [{5},{4},{3},{1},{6},{2}]=>1 [{6},{4},{3},{1},{5},{2}]=>1 [{5},{6},{3},{1},{4},{2}]=>1 [{6},{5},{3},{1},{4},{2}]=>1 [{4},{5},{6},{1},{3},{2}]=>1 [{4},{6},{5},{1},{3},{2}]=>2 [{5},{4},{6},{1},{3},{2}]=>1 [{6},{4},{5},{1},{3},{2}]=>1 [{5},{6},{4},{1},{3},{2}]=>1 [{6},{5},{4},{1},{3},{2}]=>1 [{2},{3},{4},{5},{1},{6}]=>0 [{2},{3},{4},{6},{1},{5}]=>3 [{2},{3},{5},{4},{1},{6}]=>2 [{2},{3},{6},{4},{1},{5}]=>4 [{2},{3},{5},{6},{1},{4}]=>4 [{2},{3},{6},{5},{1},{4}]=>6 [{2},{4},{3},{5},{1},{6}]=>1 [{2},{4},{3},{6},{1},{5}]=>4 [{2},{5},{3},{4},{1},{6}]=>2 [{2},{6},{3},{4},{1},{5}]=>3 [{2},{5},{3},{6},{1},{4}]=>4 [{2},{6},{3},{5},{1},{4}]=>5 [{2},{4},{5},{3},{1},{6}]=>2 [{2},{4},{6},{3},{1},{5}]=>4 [{2},{5},{4},{3},{1},{6}]=>3 [{2},{6},{4},{3},{1},{5}]=>4 [{2},{5},{6},{3},{1},{4}]=>4 [{2},{6},{5},{3},{1},{4}]=>5 [{2},{4},{5},{6},{1},{3}]=>3 [{2},{4},{6},{5},{1},{3}]=>5 [{2},{5},{4},{6},{1},{3}]=>4 [{2},{6},{4},{5},{1},{3}]=>5 [{2},{5},{6},{4},{1},{3}]=>5 [{2},{6},{5},{4},{1},{3}]=>6 [{3},{2},{4},{5},{1},{6}]=>0 [{3},{2},{4},{6},{1},{5}]=>3 [{3},{2},{5},{4},{1},{6}]=>2 [{3},{2},{6},{4},{1},{5}]=>4 [{3},{2},{5},{6},{1},{4}]=>4 [{3},{2},{6},{5},{1},{4}]=>6 [{4},{2},{3},{5},{1},{6}]=>0 [{4},{2},{3},{6},{1},{5}]=>3 [{5},{2},{3},{4},{1},{6}]=>0 [{6},{2},{3},{4},{1},{5}]=>0 [{5},{2},{3},{6},{1},{4}]=>2 [{6},{2},{3},{5},{1},{4}]=>2 [{4},{2},{5},{3},{1},{6}]=>1 [{4},{2},{6},{3},{1},{5}]=>3 [{5},{2},{4},{3},{1},{6}]=>1 [{6},{2},{4},{3},{1},{5}]=>1 [{5},{2},{6},{3},{1},{4}]=>2 [{6},{2},{5},{3},{1},{4}]=>2 [{4},{2},{5},{6},{1},{3}]=>2 [{4},{2},{6},{5},{1},{3}]=>4 [{5},{2},{4},{6},{1},{3}]=>2 [{6},{2},{4},{5},{1},{3}]=>2 [{5},{2},{6},{4},{1},{3}]=>3 [{6},{2},{5},{4},{1},{3}]=>3 [{3},{4},{2},{5},{1},{6}]=>0 [{3},{4},{2},{6},{1},{5}]=>3 [{3},{5},{2},{4},{1},{6}]=>1 [{3},{6},{2},{4},{1},{5}]=>2 [{3},{5},{2},{6},{1},{4}]=>3 [{3},{6},{2},{5},{1},{4}]=>4 [{4},{3},{2},{5},{1},{6}]=>0 [{4},{3},{2},{6},{1},{5}]=>3 [{5},{3},{2},{4},{1},{6}]=>0 [{6},{3},{2},{4},{1},{5}]=>0 [{5},{3},{2},{6},{1},{4}]=>2 [{6},{3},{2},{5},{1},{4}]=>2 [{4},{5},{2},{3},{1},{6}]=>0 [{4},{6},{2},{3},{1},{5}]=>1 [{5},{4},{2},{3},{1},{6}]=>0 [{6},{4},{2},{3},{1},{5}]=>0 [{5},{6},{2},{3},{1},{4}]=>0 [{6},{5},{2},{3},{1},{4}]=>0 [{4},{5},{2},{6},{1},{3}]=>1 [{4},{6},{2},{5},{1},{3}]=>2 [{5},{4},{2},{6},{1},{3}]=>1 [{6},{4},{2},{5},{1},{3}]=>1 [{5},{6},{2},{4},{1},{3}]=>1 [{6},{5},{2},{4},{1},{3}]=>1 [{3},{4},{5},{2},{1},{6}]=>0 [{3},{4},{6},{2},{1},{5}]=>2 [{3},{5},{4},{2},{1},{6}]=>1 [{3},{6},{4},{2},{1},{5}]=>2 [{3},{5},{6},{2},{1},{4}]=>2 [{3},{6},{5},{2},{1},{4}]=>3 [{4},{3},{5},{2},{1},{6}]=>0 [{4},{3},{6},{2},{1},{5}]=>2 [{5},{3},{4},{2},{1},{6}]=>0 [{6},{3},{4},{2},{1},{5}]=>0 [{5},{3},{6},{2},{1},{4}]=>1 [{6},{3},{5},{2},{1},{4}]=>1 [{4},{5},{3},{2},{1},{6}]=>0 [{4},{6},{3},{2},{1},{5}]=>1 [{5},{4},{3},{2},{1},{6}]=>0
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Description
The number of occurrences of an 132 pattern in an ordered set partition.
An occurrence of a pattern $\pi\in\mathfrak S_k$ ordered set partition with blocks $B_1|\dots|B_\ell$ is a sequence of elements $e_1,\dots,e_k$ with $e_i\in B_{j_i}$ and $j_1 < \dots < j_k$ order-isomorphic to $\pi$.
References
[1] Godbole, A., Goyt, A., Herdan, J., Pudwell, L. Pattern avoidance in ordered set partitions MathSciNet:3245891
Code
from sage.combinat.permutation import to_standard

def occurrences(p, pattern):
    """
    Return elements in sequences of distinct blocks order isomorphic
    to `pattern`.
    """
    o = []
    for i, b in enumerate(p):
        q = p[i+1:]
        for e in b:
            o.extend(occurrences_aux(q, [e], pattern))
    return o
            

def occurrences_aux(p, prefix, pattern):
    """
    Return all occurrences of the form `(prefix, suffix)` order
    isomorphic to `pattern`, where `suffix` are elements in sequences
    of distinct blocks of `p`.
    """
    # TODO: we could do better, probably
    if len(pattern) == len(prefix):
        yield prefix
    else:
        pattern_prefix = to_standard(pattern[:len(prefix)+1])
        for i, b in enumerate(p):
            q = p[i+1:]
            for e in b:
                new_prefix = prefix + [e]
                if to_standard(new_prefix) == pattern_prefix:
                    yield from occurrences_aux(q, new_prefix, pattern)

def statistic(p):
    return len(occurrences(p, [1,3,2]))
Created
May 25, 2023 at 11:08 by Martin Rubey
Updated
May 25, 2023 at 11:08 by Martin Rubey