edit this statistic or download as text // json
Identifier
Values
{{1}} => 0
{{1,2}} => 0
{{1},{2}} => 0
{{1,2,3}} => 0
{{1,2},{3}} => 0
{{1,3},{2}} => 1
{{1},{2,3}} => 0
{{1},{2},{3}} => 0
{{1,2,3,4}} => 0
{{1,2,3},{4}} => 0
{{1,2,4},{3}} => 0
{{1,2},{3,4}} => 0
{{1,2},{3},{4}} => 0
{{1,3,4},{2}} => 1
{{1,3},{2,4}} => 1
{{1,3},{2},{4}} => 1
{{1,4},{2,3}} => 0
{{1},{2,3,4}} => 0
{{1},{2,3},{4}} => 0
{{1,4},{2},{3}} => 2
{{1},{2,4},{3}} => 1
{{1},{2},{3,4}} => 0
{{1},{2},{3},{4}} => 0
{{1,2,3,4,5}} => 0
{{1,2,3,4},{5}} => 0
{{1,2,3,5},{4}} => 0
{{1,2,3},{4,5}} => 0
{{1,2,3},{4},{5}} => 0
{{1,2,4,5},{3}} => 0
{{1,2,4},{3,5}} => 0
{{1,2,4},{3},{5}} => 0
{{1,2,5},{3,4}} => 1
{{1,2},{3,4,5}} => 0
{{1,2},{3,4},{5}} => 0
{{1,2,5},{3},{4}} => 0
{{1,2},{3,5},{4}} => 1
{{1,2},{3},{4,5}} => 0
{{1,2},{3},{4},{5}} => 0
{{1,3,4,5},{2}} => 1
{{1,3,4},{2,5}} => 1
{{1,3,4},{2},{5}} => 1
{{1,3,5},{2,4}} => 2
{{1,3},{2,4,5}} => 1
{{1,3},{2,4},{5}} => 1
{{1,3,5},{2},{4}} => 1
{{1,3},{2,5},{4}} => 2
{{1,3},{2},{4,5}} => 1
{{1,3},{2},{4},{5}} => 1
{{1,4,5},{2,3}} => 0
{{1,4},{2,3,5}} => 1
{{1,4},{2,3},{5}} => 0
{{1,5},{2,3,4}} => 0
{{1},{2,3,4,5}} => 0
{{1},{2,3,4},{5}} => 0
{{1,5},{2,3},{4}} => 1
{{1},{2,3,5},{4}} => 0
{{1},{2,3},{4,5}} => 0
{{1},{2,3},{4},{5}} => 0
{{1,4,5},{2},{3}} => 2
{{1,4},{2,5},{3}} => 3
{{1,4},{2},{3,5}} => 2
{{1,4},{2},{3},{5}} => 2
{{1,5},{2,4},{3}} => 2
{{1},{2,4,5},{3}} => 1
{{1},{2,4},{3,5}} => 1
{{1},{2,4},{3},{5}} => 1
{{1,5},{2},{3,4}} => 1
{{1},{2,5},{3,4}} => 0
{{1},{2},{3,4,5}} => 0
{{1},{2},{3,4},{5}} => 0
{{1,5},{2},{3},{4}} => 3
{{1},{2,5},{3},{4}} => 2
{{1},{2},{3,5},{4}} => 1
{{1},{2},{3},{4,5}} => 0
{{1},{2},{3},{4},{5}} => 0
{{1,2,3,4,5,6}} => 0
{{1,2,3,4,5},{6}} => 0
{{1,2,3,4,6},{5}} => 0
{{1,2,3,4},{5,6}} => 0
{{1,2,3,4},{5},{6}} => 0
{{1,2,3,5,6},{4}} => 0
{{1,2,3,5},{4,6}} => 0
{{1,2,3,5},{4},{6}} => 0
{{1,2,3,6},{4,5}} => 0
{{1,2,3},{4,5,6}} => 0
{{1,2,3},{4,5},{6}} => 0
{{1,2,3,6},{4},{5}} => 0
{{1,2,3},{4,6},{5}} => 1
{{1,2,3},{4},{5,6}} => 0
{{1,2,3},{4},{5},{6}} => 0
{{1,2,4,5,6},{3}} => 0
{{1,2,4,5},{3,6}} => 0
{{1,2,4,5},{3},{6}} => 0
{{1,2,4,6},{3,5}} => 0
{{1,2,4},{3,5,6}} => 0
{{1,2,4},{3,5},{6}} => 0
{{1,2,4,6},{3},{5}} => 0
{{1,2,4},{3,6},{5}} => 1
{{1,2,4},{3},{5,6}} => 0
{{1,2,4},{3},{5},{6}} => 0
{{1,2,5,6},{3,4}} => 1
>>> Load all 1155 entries. <<<
{{1,2,5},{3,4,6}} => 1
{{1,2,5},{3,4},{6}} => 1
{{1,2,6},{3,4,5}} => 0
{{1,2},{3,4,5,6}} => 0
{{1,2},{3,4,5},{6}} => 0
{{1,2,6},{3,4},{5}} => 1
{{1,2},{3,4,6},{5}} => 0
{{1,2},{3,4},{5,6}} => 0
{{1,2},{3,4},{5},{6}} => 0
{{1,2,5,6},{3},{4}} => 0
{{1,2,5},{3,6},{4}} => 1
{{1,2,5},{3},{4,6}} => 0
{{1,2,5},{3},{4},{6}} => 0
{{1,2,6},{3,5},{4}} => 2
{{1,2},{3,5,6},{4}} => 1
{{1,2},{3,5},{4,6}} => 1
{{1,2},{3,5},{4},{6}} => 1
{{1,2,6},{3},{4,5}} => 1
{{1,2},{3,6},{4,5}} => 0
{{1,2},{3},{4,5,6}} => 0
{{1,2},{3},{4,5},{6}} => 0
{{1,2,6},{3},{4},{5}} => 0
{{1,2},{3,6},{4},{5}} => 2
{{1,2},{3},{4,6},{5}} => 1
{{1,2},{3},{4},{5,6}} => 0
{{1,2},{3},{4},{5},{6}} => 0
{{1,3,4,5,6},{2}} => 1
{{1,3,4,5},{2,6}} => 1
{{1,3,4,5},{2},{6}} => 1
{{1,3,4,6},{2,5}} => 1
{{1,3,4},{2,5,6}} => 1
{{1,3,4},{2,5},{6}} => 1
{{1,3,4,6},{2},{5}} => 1
{{1,3,4},{2,6},{5}} => 2
{{1,3,4},{2},{5,6}} => 1
{{1,3,4},{2},{5},{6}} => 1
{{1,3,5,6},{2,4}} => 2
{{1,3,5},{2,4,6}} => 2
{{1,3,5},{2,4},{6}} => 2
{{1,3,6},{2,4,5}} => 1
{{1,3},{2,4,5,6}} => 1
{{1,3},{2,4,5},{6}} => 1
{{1,3,6},{2,4},{5}} => 2
{{1,3},{2,4,6},{5}} => 1
{{1,3},{2,4},{5,6}} => 1
{{1,3},{2,4},{5},{6}} => 1
{{1,3,5,6},{2},{4}} => 1
{{1,3,5},{2,6},{4}} => 2
{{1,3,5},{2},{4,6}} => 1
{{1,3,5},{2},{4},{6}} => 1
{{1,3,6},{2,5},{4}} => 3
{{1,3},{2,5,6},{4}} => 2
{{1,3},{2,5},{4,6}} => 2
{{1,3},{2,5},{4},{6}} => 2
{{1,3,6},{2},{4,5}} => 2
{{1,3},{2,6},{4,5}} => 1
{{1,3},{2},{4,5,6}} => 1
{{1,3},{2},{4,5},{6}} => 1
{{1,3,6},{2},{4},{5}} => 1
{{1,3},{2,6},{4},{5}} => 3
{{1,3},{2},{4,6},{5}} => 2
{{1,3},{2},{4},{5,6}} => 1
{{1,3},{2},{4},{5},{6}} => 1
{{1,4,5,6},{2,3}} => 0
{{1,4,5},{2,3,6}} => 0
{{1,4,5},{2,3},{6}} => 0
{{1,4,6},{2,3,5}} => 1
{{1,4},{2,3,5,6}} => 1
{{1,4},{2,3,5},{6}} => 1
{{1,4,6},{2,3},{5}} => 0
{{1,4},{2,3,6},{5}} => 1
{{1,4},{2,3},{5,6}} => 0
{{1,4},{2,3},{5},{6}} => 0
{{1,5,6},{2,3,4}} => 0
{{1,5},{2,3,4,6}} => 0
{{1,5},{2,3,4},{6}} => 0
{{1,6},{2,3,4,5}} => 0
{{1},{2,3,4,5,6}} => 0
{{1},{2,3,4,5},{6}} => 0
{{1,6},{2,3,4},{5}} => 1
{{1},{2,3,4,6},{5}} => 0
{{1},{2,3,4},{5,6}} => 0
{{1},{2,3,4},{5},{6}} => 0
{{1,5,6},{2,3},{4}} => 1
{{1,5},{2,3,6},{4}} => 2
{{1,5},{2,3},{4,6}} => 1
{{1,5},{2,3},{4},{6}} => 1
{{1,6},{2,3,5},{4}} => 1
{{1},{2,3,5,6},{4}} => 0
{{1},{2,3,5},{4,6}} => 0
{{1},{2,3,5},{4},{6}} => 0
{{1,6},{2,3},{4,5}} => 0
{{1},{2,3,6},{4,5}} => 1
{{1},{2,3},{4,5,6}} => 0
{{1},{2,3},{4,5},{6}} => 0
{{1,6},{2,3},{4},{5}} => 2
{{1},{2,3,6},{4},{5}} => 0
{{1},{2,3},{4,6},{5}} => 1
{{1},{2,3},{4},{5,6}} => 0
{{1},{2,3},{4},{5},{6}} => 0
{{1,4,5,6},{2},{3}} => 2
{{1,4,5},{2,6},{3}} => 3
{{1,4,5},{2},{3,6}} => 2
{{1,4,5},{2},{3},{6}} => 2
{{1,4,6},{2,5},{3}} => 4
{{1,4},{2,5,6},{3}} => 3
{{1,4},{2,5},{3,6}} => 3
{{1,4},{2,5},{3},{6}} => 3
{{1,4,6},{2},{3,5}} => 3
{{1,4},{2,6},{3,5}} => 2
{{1,4},{2},{3,5,6}} => 2
{{1,4},{2},{3,5},{6}} => 2
{{1,4,6},{2},{3},{5}} => 2
{{1,4},{2,6},{3},{5}} => 4
{{1,4},{2},{3,6},{5}} => 3
{{1,4},{2},{3},{5,6}} => 2
{{1,4},{2},{3},{5},{6}} => 2
{{1,5,6},{2,4},{3}} => 2
{{1,5},{2,4,6},{3}} => 3
{{1,5},{2,4},{3,6}} => 2
{{1,5},{2,4},{3},{6}} => 2
{{1,6},{2,4,5},{3}} => 2
{{1},{2,4,5,6},{3}} => 1
{{1},{2,4,5},{3,6}} => 1
{{1},{2,4,5},{3},{6}} => 1
{{1,6},{2,4},{3,5}} => 1
{{1},{2,4,6},{3,5}} => 2
{{1},{2,4},{3,5,6}} => 1
{{1},{2,4},{3,5},{6}} => 1
{{1,6},{2,4},{3},{5}} => 3
{{1},{2,4,6},{3},{5}} => 1
{{1},{2,4},{3,6},{5}} => 2
{{1},{2,4},{3},{5,6}} => 1
{{1},{2,4},{3},{5},{6}} => 1
{{1,5,6},{2},{3,4}} => 1
{{1,5},{2,6},{3,4}} => 1
{{1,5},{2},{3,4,6}} => 2
{{1,5},{2},{3,4},{6}} => 1
{{1,6},{2,5},{3,4}} => 0
{{1},{2,5,6},{3,4}} => 0
{{1},{2,5},{3,4,6}} => 1
{{1},{2,5},{3,4},{6}} => 0
{{1,6},{2},{3,4,5}} => 1
{{1},{2,6},{3,4,5}} => 0
{{1},{2},{3,4,5,6}} => 0
{{1},{2},{3,4,5},{6}} => 0
{{1,6},{2},{3,4},{5}} => 2
{{1},{2,6},{3,4},{5}} => 1
{{1},{2},{3,4,6},{5}} => 0
{{1},{2},{3,4},{5,6}} => 0
{{1},{2},{3,4},{5},{6}} => 0
{{1,5,6},{2},{3},{4}} => 3
{{1,5},{2,6},{3},{4}} => 5
{{1,5},{2},{3,6},{4}} => 4
{{1,5},{2},{3},{4,6}} => 3
{{1,5},{2},{3},{4},{6}} => 3
{{1,6},{2,5},{3},{4}} => 4
{{1},{2,5,6},{3},{4}} => 2
{{1},{2,5},{3,6},{4}} => 3
{{1},{2,5},{3},{4,6}} => 2
{{1},{2,5},{3},{4},{6}} => 2
{{1,6},{2},{3,5},{4}} => 3
{{1},{2,6},{3,5},{4}} => 2
{{1},{2},{3,5,6},{4}} => 1
{{1},{2},{3,5},{4,6}} => 1
{{1},{2},{3,5},{4},{6}} => 1
{{1,6},{2},{3},{4,5}} => 2
{{1},{2,6},{3},{4,5}} => 1
{{1},{2},{3,6},{4,5}} => 0
{{1},{2},{3},{4,5,6}} => 0
{{1},{2},{3},{4,5},{6}} => 0
{{1,6},{2},{3},{4},{5}} => 4
{{1},{2,6},{3},{4},{5}} => 3
{{1},{2},{3,6},{4},{5}} => 2
{{1},{2},{3},{4,6},{5}} => 1
{{1},{2},{3},{4},{5,6}} => 0
{{1},{2},{3},{4},{5},{6}} => 0
{{1,2,3,4,5,6,7}} => 0
{{1,2,3,4,5,6},{7}} => 0
{{1,2,3,4,5,7},{6}} => 0
{{1,2,3,4,5},{6,7}} => 0
{{1,2,3,4,5},{6},{7}} => 0
{{1,2,3,4,6,7},{5}} => 0
{{1,2,3,4,6},{5,7}} => 0
{{1,2,3,4,6},{5},{7}} => 0
{{1,2,3,4,7},{5,6}} => 0
{{1,2,3,4},{5,6,7}} => 0
{{1,2,3,4},{5,6},{7}} => 0
{{1,2,3,4,7},{5},{6}} => 0
{{1,2,3,4},{5,7},{6}} => 1
{{1,2,3,4},{5},{6,7}} => 0
{{1,2,3,4},{5},{6},{7}} => 0
{{1,2,3,5,6,7},{4}} => 0
{{1,2,3,5,6},{4,7}} => 0
{{1,2,3,5,6},{4},{7}} => 0
{{1,2,3,5,7},{4,6}} => 0
{{1,2,3,5},{4,6,7}} => 0
{{1,2,3,5},{4,6},{7}} => 0
{{1,2,3,5,7},{4},{6}} => 0
{{1,2,3,5},{4,7},{6}} => 1
{{1,2,3,5},{4},{6,7}} => 0
{{1,2,3,5},{4},{6},{7}} => 0
{{1,2,3,6,7},{4,5}} => 0
{{1,2,3,6},{4,5,7}} => 0
{{1,2,3,6},{4,5},{7}} => 0
{{1,2,3,7},{4,5,6}} => 1
{{1,2,3},{4,5,6,7}} => 0
{{1,2,3},{4,5,6},{7}} => 0
{{1,2,3,7},{4,5},{6}} => 0
{{1,2,3},{4,5,7},{6}} => 0
{{1,2,3},{4,5},{6,7}} => 0
{{1,2,3},{4,5},{6},{7}} => 0
{{1,2,3,6,7},{4},{5}} => 0
{{1,2,3,6},{4,7},{5}} => 1
{{1,2,3,6},{4},{5,7}} => 0
{{1,2,3,6},{4},{5},{7}} => 0
{{1,2,3,7},{4,6},{5}} => 1
{{1,2,3},{4,6,7},{5}} => 1
{{1,2,3},{4,6},{5,7}} => 1
{{1,2,3},{4,6},{5},{7}} => 1
{{1,2,3,7},{4},{5,6}} => 0
{{1,2,3},{4,7},{5,6}} => 0
{{1,2,3},{4},{5,6,7}} => 0
{{1,2,3},{4},{5,6},{7}} => 0
{{1,2,3,7},{4},{5},{6}} => 0
{{1,2,3},{4,7},{5},{6}} => 2
{{1,2,3},{4},{5,7},{6}} => 1
{{1,2,3},{4},{5},{6,7}} => 0
{{1,2,3},{4},{5},{6},{7}} => 0
{{1,2,4,5,6,7},{3}} => 0
{{1,2,4,5,6},{3,7}} => 0
{{1,2,4,5,6},{3},{7}} => 0
{{1,2,4,5,7},{3,6}} => 0
{{1,2,4,5},{3,6,7}} => 0
{{1,2,4,5},{3,6},{7}} => 0
{{1,2,4,5,7},{3},{6}} => 0
{{1,2,4,5},{3,7},{6}} => 1
{{1,2,4,5},{3},{6,7}} => 0
{{1,2,4,5},{3},{6},{7}} => 0
{{1,2,4,6,7},{3,5}} => 0
{{1,2,4,6},{3,5,7}} => 0
{{1,2,4,6},{3,5},{7}} => 0
{{1,2,4,7},{3,5,6}} => 1
{{1,2,4},{3,5,6,7}} => 0
{{1,2,4},{3,5,6},{7}} => 0
{{1,2,4,7},{3,5},{6}} => 0
{{1,2,4},{3,5,7},{6}} => 0
{{1,2,4},{3,5},{6,7}} => 0
{{1,2,4},{3,5},{6},{7}} => 0
{{1,2,4,6,7},{3},{5}} => 0
{{1,2,4,6},{3,7},{5}} => 1
{{1,2,4,6},{3},{5,7}} => 0
{{1,2,4,6},{3},{5},{7}} => 0
{{1,2,4,7},{3,6},{5}} => 1
{{1,2,4},{3,6,7},{5}} => 1
{{1,2,4},{3,6},{5,7}} => 1
{{1,2,4},{3,6},{5},{7}} => 1
{{1,2,4,7},{3},{5,6}} => 0
{{1,2,4},{3,7},{5,6}} => 0
{{1,2,4},{3},{5,6,7}} => 0
{{1,2,4},{3},{5,6},{7}} => 0
{{1,2,4,7},{3},{5},{6}} => 0
{{1,2,4},{3,7},{5},{6}} => 2
{{1,2,4},{3},{5,7},{6}} => 1
{{1,2,4},{3},{5},{6,7}} => 0
{{1,2,4},{3},{5},{6},{7}} => 0
{{1,2,5,6,7},{3,4}} => 1
{{1,2,5,6},{3,4,7}} => 1
{{1,2,5,6},{3,4},{7}} => 1
{{1,2,5,7},{3,4,6}} => 2
{{1,2,5},{3,4,6,7}} => 1
{{1,2,5},{3,4,6},{7}} => 1
{{1,2,5,7},{3,4},{6}} => 1
{{1,2,5},{3,4,7},{6}} => 1
{{1,2,5},{3,4},{6,7}} => 1
{{1,2,5},{3,4},{6},{7}} => 1
{{1,2,6,7},{3,4,5}} => 0
{{1,2,6},{3,4,5,7}} => 1
{{1,2,6},{3,4,5},{7}} => 0
{{1,2,7},{3,4,5,6}} => 0
{{1,2},{3,4,5,6,7}} => 0
{{1,2},{3,4,5,6},{7}} => 0
{{1,2,7},{3,4,5},{6}} => 0
{{1,2},{3,4,5,7},{6}} => 0
{{1,2},{3,4,5},{6,7}} => 0
{{1,2},{3,4,5},{6},{7}} => 0
{{1,2,6,7},{3,4},{5}} => 1
{{1,2,6},{3,4,7},{5}} => 1
{{1,2,6},{3,4},{5,7}} => 1
{{1,2,6},{3,4},{5},{7}} => 1
{{1,2,7},{3,4,6},{5}} => 0
{{1,2},{3,4,6,7},{5}} => 0
{{1,2},{3,4,6},{5,7}} => 0
{{1,2},{3,4,6},{5},{7}} => 0
{{1,2,7},{3,4},{5,6}} => 2
{{1,2},{3,4,7},{5,6}} => 1
{{1,2},{3,4},{5,6,7}} => 0
{{1,2},{3,4},{5,6},{7}} => 0
{{1,2,7},{3,4},{5},{6}} => 1
{{1,2},{3,4,7},{5},{6}} => 0
{{1,2},{3,4},{5,7},{6}} => 1
{{1,2},{3,4},{5},{6,7}} => 0
{{1,2},{3,4},{5},{6},{7}} => 0
{{1,2,5,6,7},{3},{4}} => 0
{{1,2,5,6},{3,7},{4}} => 1
{{1,2,5,6},{3},{4,7}} => 0
{{1,2,5,6},{3},{4},{7}} => 0
{{1,2,5,7},{3,6},{4}} => 1
{{1,2,5},{3,6,7},{4}} => 1
{{1,2,5},{3,6},{4,7}} => 1
{{1,2,5},{3,6},{4},{7}} => 1
{{1,2,5,7},{3},{4,6}} => 0
{{1,2,5},{3,7},{4,6}} => 0
{{1,2,5},{3},{4,6,7}} => 0
{{1,2,5},{3},{4,6},{7}} => 0
{{1,2,5,7},{3},{4},{6}} => 0
{{1,2,5},{3,7},{4},{6}} => 2
{{1,2,5},{3},{4,7},{6}} => 1
{{1,2,5},{3},{4},{6,7}} => 0
{{1,2,5},{3},{4},{6},{7}} => 0
{{1,2,6,7},{3,5},{4}} => 2
{{1,2,6},{3,5,7},{4}} => 2
{{1,2,6},{3,5},{4,7}} => 2
{{1,2,6},{3,5},{4},{7}} => 2
{{1,2,7},{3,5,6},{4}} => 1
{{1,2},{3,5,6,7},{4}} => 1
{{1,2},{3,5,6},{4,7}} => 1
{{1,2},{3,5,6},{4},{7}} => 1
{{1,2,7},{3,5},{4,6}} => 3
{{1,2},{3,5,7},{4,6}} => 2
{{1,2},{3,5},{4,6,7}} => 1
{{1,2},{3,5},{4,6},{7}} => 1
{{1,2,7},{3,5},{4},{6}} => 2
{{1,2},{3,5,7},{4},{6}} => 1
{{1,2},{3,5},{4,7},{6}} => 2
{{1,2},{3,5},{4},{6,7}} => 1
{{1,2},{3,5},{4},{6},{7}} => 1
{{1,2,6,7},{3},{4,5}} => 1
{{1,2,6},{3,7},{4,5}} => 1
{{1,2,6},{3},{4,5,7}} => 1
{{1,2,6},{3},{4,5},{7}} => 1
{{1,2,7},{3,6},{4,5}} => 2
{{1,2},{3,6,7},{4,5}} => 0
{{1,2},{3,6},{4,5,7}} => 1
{{1,2},{3,6},{4,5},{7}} => 0
{{1,2,7},{3},{4,5,6}} => 0
{{1,2},{3,7},{4,5,6}} => 0
{{1,2},{3},{4,5,6,7}} => 0
{{1,2},{3},{4,5,6},{7}} => 0
{{1,2,7},{3},{4,5},{6}} => 1
{{1,2},{3,7},{4,5},{6}} => 1
{{1,2},{3},{4,5,7},{6}} => 0
{{1,2},{3},{4,5},{6,7}} => 0
{{1,2},{3},{4,5},{6},{7}} => 0
{{1,2,6,7},{3},{4},{5}} => 0
{{1,2,6},{3,7},{4},{5}} => 2
{{1,2,6},{3},{4,7},{5}} => 1
{{1,2,6},{3},{4},{5,7}} => 0
{{1,2,6},{3},{4},{5},{7}} => 0
{{1,2,7},{3,6},{4},{5}} => 3
{{1,2},{3,6,7},{4},{5}} => 2
{{1,2},{3,6},{4,7},{5}} => 3
{{1,2},{3,6},{4},{5,7}} => 2
{{1,2},{3,6},{4},{5},{7}} => 2
{{1,2,7},{3},{4,6},{5}} => 2
{{1,2},{3,7},{4,6},{5}} => 2
{{1,2},{3},{4,6,7},{5}} => 1
{{1,2},{3},{4,6},{5,7}} => 1
{{1,2},{3},{4,6},{5},{7}} => 1
{{1,2,7},{3},{4},{5,6}} => 1
{{1,2},{3,7},{4},{5,6}} => 1
{{1,2},{3},{4,7},{5,6}} => 0
{{1,2},{3},{4},{5,6,7}} => 0
{{1,2},{3},{4},{5,6},{7}} => 0
{{1,2,7},{3},{4},{5},{6}} => 0
{{1,2},{3,7},{4},{5},{6}} => 3
{{1,2},{3},{4,7},{5},{6}} => 2
{{1,2},{3},{4},{5,7},{6}} => 1
{{1,2},{3},{4},{5},{6,7}} => 0
{{1,2},{3},{4},{5},{6},{7}} => 0
{{1,3,4,5,6,7},{2}} => 1
{{1,3,4,5,6},{2,7}} => 1
{{1,3,4,5,6},{2},{7}} => 1
{{1,3,4,5,7},{2,6}} => 1
{{1,3,4,5},{2,6,7}} => 1
{{1,3,4,5},{2,6},{7}} => 1
{{1,3,4,5,7},{2},{6}} => 1
{{1,3,4,5},{2,7},{6}} => 2
{{1,3,4,5},{2},{6,7}} => 1
{{1,3,4,5},{2},{6},{7}} => 1
{{1,3,4,6,7},{2,5}} => 1
{{1,3,4,6},{2,5,7}} => 1
{{1,3,4,6},{2,5},{7}} => 1
{{1,3,4,7},{2,5,6}} => 2
{{1,3,4},{2,5,6,7}} => 1
{{1,3,4},{2,5,6},{7}} => 1
{{1,3,4,7},{2,5},{6}} => 1
{{1,3,4},{2,5,7},{6}} => 1
{{1,3,4},{2,5},{6,7}} => 1
{{1,3,4},{2,5},{6},{7}} => 1
{{1,3,4,6,7},{2},{5}} => 1
{{1,3,4,6},{2,7},{5}} => 2
{{1,3,4,6},{2},{5,7}} => 1
{{1,3,4,6},{2},{5},{7}} => 1
{{1,3,4,7},{2,6},{5}} => 2
{{1,3,4},{2,6,7},{5}} => 2
{{1,3,4},{2,6},{5,7}} => 2
{{1,3,4},{2,6},{5},{7}} => 2
{{1,3,4,7},{2},{5,6}} => 1
{{1,3,4},{2,7},{5,6}} => 1
{{1,3,4},{2},{5,6,7}} => 1
{{1,3,4},{2},{5,6},{7}} => 1
{{1,3,4,7},{2},{5},{6}} => 1
{{1,3,4},{2,7},{5},{6}} => 3
{{1,3,4},{2},{5,7},{6}} => 2
{{1,3,4},{2},{5},{6,7}} => 1
{{1,3,4},{2},{5},{6},{7}} => 1
{{1,3,5,6,7},{2,4}} => 2
{{1,3,5,6},{2,4,7}} => 2
{{1,3,5,6},{2,4},{7}} => 2
{{1,3,5,7},{2,4,6}} => 3
{{1,3,5},{2,4,6,7}} => 2
{{1,3,5},{2,4,6},{7}} => 2
{{1,3,5,7},{2,4},{6}} => 2
{{1,3,5},{2,4,7},{6}} => 2
{{1,3,5},{2,4},{6,7}} => 2
{{1,3,5},{2,4},{6},{7}} => 2
{{1,3,6,7},{2,4,5}} => 1
{{1,3,6},{2,4,5,7}} => 2
{{1,3,6},{2,4,5},{7}} => 1
{{1,3,7},{2,4,5,6}} => 1
{{1,3},{2,4,5,6,7}} => 1
{{1,3},{2,4,5,6},{7}} => 1
{{1,3,7},{2,4,5},{6}} => 1
{{1,3},{2,4,5,7},{6}} => 1
{{1,3},{2,4,5},{6,7}} => 1
{{1,3},{2,4,5},{6},{7}} => 1
{{1,3,6,7},{2,4},{5}} => 2
{{1,3,6},{2,4,7},{5}} => 2
{{1,3,6},{2,4},{5,7}} => 2
{{1,3,6},{2,4},{5},{7}} => 2
{{1,3,7},{2,4,6},{5}} => 1
{{1,3},{2,4,6,7},{5}} => 1
{{1,3},{2,4,6},{5,7}} => 1
{{1,3},{2,4,6},{5},{7}} => 1
{{1,3,7},{2,4},{5,6}} => 3
{{1,3},{2,4,7},{5,6}} => 2
{{1,3},{2,4},{5,6,7}} => 1
{{1,3},{2,4},{5,6},{7}} => 1
{{1,3,7},{2,4},{5},{6}} => 2
{{1,3},{2,4,7},{5},{6}} => 1
{{1,3},{2,4},{5,7},{6}} => 2
{{1,3},{2,4},{5},{6,7}} => 1
{{1,3},{2,4},{5},{6},{7}} => 1
{{1,3,5,6,7},{2},{4}} => 1
{{1,3,5,6},{2,7},{4}} => 2
{{1,3,5,6},{2},{4,7}} => 1
{{1,3,5,6},{2},{4},{7}} => 1
{{1,3,5,7},{2,6},{4}} => 2
{{1,3,5},{2,6,7},{4}} => 2
{{1,3,5},{2,6},{4,7}} => 2
{{1,3,5},{2,6},{4},{7}} => 2
{{1,3,5,7},{2},{4,6}} => 1
{{1,3,5},{2,7},{4,6}} => 1
{{1,3,5},{2},{4,6,7}} => 1
{{1,3,5},{2},{4,6},{7}} => 1
{{1,3,5,7},{2},{4},{6}} => 1
{{1,3,5},{2,7},{4},{6}} => 3
{{1,3,5},{2},{4,7},{6}} => 2
{{1,3,5},{2},{4},{6,7}} => 1
{{1,3,5},{2},{4},{6},{7}} => 1
{{1,3,6,7},{2,5},{4}} => 3
{{1,3,6},{2,5,7},{4}} => 3
{{1,3,6},{2,5},{4,7}} => 3
{{1,3,6},{2,5},{4},{7}} => 3
{{1,3,7},{2,5,6},{4}} => 2
{{1,3},{2,5,6,7},{4}} => 2
{{1,3},{2,5,6},{4,7}} => 2
{{1,3},{2,5,6},{4},{7}} => 2
{{1,3,7},{2,5},{4,6}} => 4
{{1,3},{2,5,7},{4,6}} => 3
{{1,3},{2,5},{4,6,7}} => 2
{{1,3},{2,5},{4,6},{7}} => 2
{{1,3,7},{2,5},{4},{6}} => 3
{{1,3},{2,5,7},{4},{6}} => 2
{{1,3},{2,5},{4,7},{6}} => 3
{{1,3},{2,5},{4},{6,7}} => 2
{{1,3},{2,5},{4},{6},{7}} => 2
{{1,3,6,7},{2},{4,5}} => 2
{{1,3,6},{2,7},{4,5}} => 2
{{1,3,6},{2},{4,5,7}} => 2
{{1,3,6},{2},{4,5},{7}} => 2
{{1,3,7},{2,6},{4,5}} => 3
{{1,3},{2,6,7},{4,5}} => 1
{{1,3},{2,6},{4,5,7}} => 2
{{1,3},{2,6},{4,5},{7}} => 1
{{1,3,7},{2},{4,5,6}} => 1
{{1,3},{2,7},{4,5,6}} => 1
{{1,3},{2},{4,5,6,7}} => 1
{{1,3},{2},{4,5,6},{7}} => 1
{{1,3,7},{2},{4,5},{6}} => 2
{{1,3},{2,7},{4,5},{6}} => 2
{{1,3},{2},{4,5,7},{6}} => 1
{{1,3},{2},{4,5},{6,7}} => 1
{{1,3},{2},{4,5},{6},{7}} => 1
{{1,3,6,7},{2},{4},{5}} => 1
{{1,3,6},{2,7},{4},{5}} => 3
{{1,3,6},{2},{4,7},{5}} => 2
{{1,3,6},{2},{4},{5,7}} => 1
{{1,3,6},{2},{4},{5},{7}} => 1
{{1,3,7},{2,6},{4},{5}} => 4
{{1,3},{2,6,7},{4},{5}} => 3
{{1,3},{2,6},{4,7},{5}} => 4
{{1,3},{2,6},{4},{5,7}} => 3
{{1,3},{2,6},{4},{5},{7}} => 3
{{1,3,7},{2},{4,6},{5}} => 3
{{1,3},{2,7},{4,6},{5}} => 3
{{1,3},{2},{4,6,7},{5}} => 2
{{1,3},{2},{4,6},{5,7}} => 2
{{1,3},{2},{4,6},{5},{7}} => 2
{{1,3,7},{2},{4},{5,6}} => 2
{{1,3},{2,7},{4},{5,6}} => 2
{{1,3},{2},{4,7},{5,6}} => 1
{{1,3},{2},{4},{5,6,7}} => 1
{{1,3},{2},{4},{5,6},{7}} => 1
{{1,3,7},{2},{4},{5},{6}} => 1
{{1,3},{2,7},{4},{5},{6}} => 4
{{1,3},{2},{4,7},{5},{6}} => 3
{{1,3},{2},{4},{5,7},{6}} => 2
{{1,3},{2},{4},{5},{6,7}} => 1
{{1,3},{2},{4},{5},{6},{7}} => 1
{{1,4,5,6,7},{2,3}} => 0
{{1,4,5,6},{2,3,7}} => 0
{{1,4,5,6},{2,3},{7}} => 0
{{1,4,5,7},{2,3,6}} => 1
{{1,4,5},{2,3,6,7}} => 0
{{1,4,5},{2,3,6},{7}} => 0
{{1,4,5,7},{2,3},{6}} => 0
{{1,4,5},{2,3,7},{6}} => 0
{{1,4,5},{2,3},{6,7}} => 0
{{1,4,5},{2,3},{6},{7}} => 0
{{1,4,6,7},{2,3,5}} => 1
{{1,4,6},{2,3,5,7}} => 2
{{1,4,6},{2,3,5},{7}} => 1
{{1,4,7},{2,3,5,6}} => 1
{{1,4},{2,3,5,6,7}} => 1
{{1,4},{2,3,5,6},{7}} => 1
{{1,4,7},{2,3,5},{6}} => 1
{{1,4},{2,3,5,7},{6}} => 1
{{1,4},{2,3,5},{6,7}} => 1
{{1,4},{2,3,5},{6},{7}} => 1
{{1,4,6,7},{2,3},{5}} => 0
{{1,4,6},{2,3,7},{5}} => 0
{{1,4,6},{2,3},{5,7}} => 0
{{1,4,6},{2,3},{5},{7}} => 0
{{1,4,7},{2,3,6},{5}} => 1
{{1,4},{2,3,6,7},{5}} => 1
{{1,4},{2,3,6},{5,7}} => 1
{{1,4},{2,3,6},{5},{7}} => 1
{{1,4,7},{2,3},{5,6}} => 1
{{1,4},{2,3,7},{5,6}} => 2
{{1,4},{2,3},{5,6,7}} => 0
{{1,4},{2,3},{5,6},{7}} => 0
{{1,4,7},{2,3},{5},{6}} => 0
{{1,4},{2,3,7},{5},{6}} => 1
{{1,4},{2,3},{5,7},{6}} => 1
{{1,4},{2,3},{5},{6,7}} => 0
{{1,4},{2,3},{5},{6},{7}} => 0
{{1,5,6,7},{2,3,4}} => 0
{{1,5,6},{2,3,4,7}} => 1
{{1,5,6},{2,3,4},{7}} => 0
{{1,5,7},{2,3,4,6}} => 0
{{1,5},{2,3,4,6,7}} => 0
{{1,5},{2,3,4,6},{7}} => 0
{{1,5,7},{2,3,4},{6}} => 0
{{1,5},{2,3,4,7},{6}} => 0
{{1,5},{2,3,4},{6,7}} => 0
{{1,5},{2,3,4},{6},{7}} => 0
{{1,6,7},{2,3,4,5}} => 0
{{1,6},{2,3,4,5,7}} => 0
{{1,6},{2,3,4,5},{7}} => 0
{{1,7},{2,3,4,5,6}} => 0
{{1},{2,3,4,5,6,7}} => 0
{{1},{2,3,4,5,6},{7}} => 0
{{1,7},{2,3,4,5},{6}} => 1
{{1},{2,3,4,5,7},{6}} => 0
{{1},{2,3,4,5},{6,7}} => 0
{{1},{2,3,4,5},{6},{7}} => 0
{{1,6,7},{2,3,4},{5}} => 1
{{1,6},{2,3,4,7},{5}} => 1
{{1,6},{2,3,4},{5,7}} => 1
{{1,6},{2,3,4},{5},{7}} => 1
{{1,7},{2,3,4,6},{5}} => 1
{{1},{2,3,4,6,7},{5}} => 0
{{1},{2,3,4,6},{5,7}} => 0
{{1},{2,3,4,6},{5},{7}} => 0
{{1,7},{2,3,4},{5,6}} => 0
{{1},{2,3,4,7},{5,6}} => 0
{{1},{2,3,4},{5,6,7}} => 0
{{1},{2,3,4},{5,6},{7}} => 0
{{1,7},{2,3,4},{5},{6}} => 2
{{1},{2,3,4,7},{5},{6}} => 0
{{1},{2,3,4},{5,7},{6}} => 1
{{1},{2,3,4},{5},{6,7}} => 0
{{1},{2,3,4},{5},{6},{7}} => 0
{{1,5,6,7},{2,3},{4}} => 1
{{1,5,6},{2,3,7},{4}} => 1
{{1,5,6},{2,3},{4,7}} => 1
{{1,5,6},{2,3},{4},{7}} => 1
{{1,5,7},{2,3,6},{4}} => 2
{{1,5},{2,3,6,7},{4}} => 2
{{1,5},{2,3,6},{4,7}} => 2
{{1,5},{2,3,6},{4},{7}} => 2
{{1,5,7},{2,3},{4,6}} => 2
{{1,5},{2,3,7},{4,6}} => 3
{{1,5},{2,3},{4,6,7}} => 1
{{1,5},{2,3},{4,6},{7}} => 1
{{1,5,7},{2,3},{4},{6}} => 1
{{1,5},{2,3,7},{4},{6}} => 2
{{1,5},{2,3},{4,7},{6}} => 2
{{1,5},{2,3},{4},{6,7}} => 1
{{1,5},{2,3},{4},{6},{7}} => 1
{{1,6,7},{2,3,5},{4}} => 1
{{1,6},{2,3,5,7},{4}} => 1
{{1,6},{2,3,5},{4,7}} => 1
{{1,6},{2,3,5},{4},{7}} => 1
{{1,7},{2,3,5,6},{4}} => 1
{{1},{2,3,5,6,7},{4}} => 0
{{1},{2,3,5,6},{4,7}} => 0
{{1},{2,3,5,6},{4},{7}} => 0
{{1,7},{2,3,5},{4,6}} => 0
{{1},{2,3,5,7},{4,6}} => 0
{{1},{2,3,5},{4,6,7}} => 0
{{1},{2,3,5},{4,6},{7}} => 0
{{1,7},{2,3,5},{4},{6}} => 2
{{1},{2,3,5,7},{4},{6}} => 0
{{1},{2,3,5},{4,7},{6}} => 1
{{1},{2,3,5},{4},{6,7}} => 0
{{1},{2,3,5},{4},{6},{7}} => 0
{{1,6,7},{2,3},{4,5}} => 0
{{1,6},{2,3,7},{4,5}} => 2
{{1,6},{2,3},{4,5,7}} => 1
{{1,6},{2,3},{4,5},{7}} => 0
{{1,7},{2,3,6},{4,5}} => 1
{{1},{2,3,6,7},{4,5}} => 1
{{1},{2,3,6},{4,5,7}} => 1
{{1},{2,3,6},{4,5},{7}} => 1
{{1,7},{2,3},{4,5,6}} => 0
{{1},{2,3,7},{4,5,6}} => 0
{{1},{2,3},{4,5,6,7}} => 0
{{1},{2,3},{4,5,6},{7}} => 0
{{1,7},{2,3},{4,5},{6}} => 1
{{1},{2,3,7},{4,5},{6}} => 1
{{1},{2,3},{4,5,7},{6}} => 0
{{1},{2,3},{4,5},{6,7}} => 0
{{1},{2,3},{4,5},{6},{7}} => 0
{{1,6,7},{2,3},{4},{5}} => 2
{{1,6},{2,3,7},{4},{5}} => 3
{{1,6},{2,3},{4,7},{5}} => 3
{{1,6},{2,3},{4},{5,7}} => 2
{{1,6},{2,3},{4},{5},{7}} => 2
{{1,7},{2,3,6},{4},{5}} => 2
{{1},{2,3,6,7},{4},{5}} => 0
{{1},{2,3,6},{4,7},{5}} => 1
{{1},{2,3,6},{4},{5,7}} => 0
{{1},{2,3,6},{4},{5},{7}} => 0
{{1,7},{2,3},{4,6},{5}} => 2
{{1},{2,3,7},{4,6},{5}} => 2
{{1},{2,3},{4,6,7},{5}} => 1
{{1},{2,3},{4,6},{5,7}} => 1
{{1},{2,3},{4,6},{5},{7}} => 1
{{1,7},{2,3},{4},{5,6}} => 1
{{1},{2,3,7},{4},{5,6}} => 1
{{1},{2,3},{4,7},{5,6}} => 0
{{1},{2,3},{4},{5,6,7}} => 0
{{1},{2,3},{4},{5,6},{7}} => 0
{{1,7},{2,3},{4},{5},{6}} => 3
{{1},{2,3,7},{4},{5},{6}} => 0
{{1},{2,3},{4,7},{5},{6}} => 2
{{1},{2,3},{4},{5,7},{6}} => 1
{{1},{2,3},{4},{5},{6,7}} => 0
{{1},{2,3},{4},{5},{6},{7}} => 0
{{1,4,5,6,7},{2},{3}} => 2
{{1,4,5,6},{2,7},{3}} => 3
{{1,4,5,6},{2},{3,7}} => 2
{{1,4,5,6},{2},{3},{7}} => 2
{{1,4,5,7},{2,6},{3}} => 3
{{1,4,5},{2,6,7},{3}} => 3
{{1,4,5},{2,6},{3,7}} => 3
{{1,4,5},{2,6},{3},{7}} => 3
{{1,4,5,7},{2},{3,6}} => 2
{{1,4,5},{2,7},{3,6}} => 2
{{1,4,5},{2},{3,6,7}} => 2
{{1,4,5},{2},{3,6},{7}} => 2
{{1,4,5,7},{2},{3},{6}} => 2
{{1,4,5},{2,7},{3},{6}} => 4
{{1,4,5},{2},{3,7},{6}} => 3
{{1,4,5},{2},{3},{6,7}} => 2
{{1,4,5},{2},{3},{6},{7}} => 2
{{1,4,6,7},{2,5},{3}} => 4
{{1,4,6},{2,5,7},{3}} => 4
{{1,4,6},{2,5},{3,7}} => 4
{{1,4,6},{2,5},{3},{7}} => 4
{{1,4,7},{2,5,6},{3}} => 3
{{1,4},{2,5,6,7},{3}} => 3
{{1,4},{2,5,6},{3,7}} => 3
{{1,4},{2,5,6},{3},{7}} => 3
{{1,4,7},{2,5},{3,6}} => 5
{{1,4},{2,5,7},{3,6}} => 4
{{1,4},{2,5},{3,6,7}} => 3
{{1,4},{2,5},{3,6},{7}} => 3
{{1,4,7},{2,5},{3},{6}} => 4
{{1,4},{2,5,7},{3},{6}} => 3
{{1,4},{2,5},{3,7},{6}} => 4
{{1,4},{2,5},{3},{6,7}} => 3
{{1,4},{2,5},{3},{6},{7}} => 3
{{1,4,6,7},{2},{3,5}} => 3
{{1,4,6},{2,7},{3,5}} => 3
{{1,4,6},{2},{3,5,7}} => 3
{{1,4,6},{2},{3,5},{7}} => 3
{{1,4,7},{2,6},{3,5}} => 4
{{1,4},{2,6,7},{3,5}} => 2
{{1,4},{2,6},{3,5,7}} => 3
{{1,4},{2,6},{3,5},{7}} => 2
{{1,4,7},{2},{3,5,6}} => 2
{{1,4},{2,7},{3,5,6}} => 2
{{1,4},{2},{3,5,6,7}} => 2
{{1,4},{2},{3,5,6},{7}} => 2
{{1,4,7},{2},{3,5},{6}} => 3
{{1,4},{2,7},{3,5},{6}} => 3
{{1,4},{2},{3,5,7},{6}} => 2
{{1,4},{2},{3,5},{6,7}} => 2
{{1,4},{2},{3,5},{6},{7}} => 2
{{1,4,6,7},{2},{3},{5}} => 2
{{1,4,6},{2,7},{3},{5}} => 4
{{1,4,6},{2},{3,7},{5}} => 3
{{1,4,6},{2},{3},{5,7}} => 2
{{1,4,6},{2},{3},{5},{7}} => 2
{{1,4,7},{2,6},{3},{5}} => 5
{{1,4},{2,6,7},{3},{5}} => 4
{{1,4},{2,6},{3,7},{5}} => 5
{{1,4},{2,6},{3},{5,7}} => 4
{{1,4},{2,6},{3},{5},{7}} => 4
{{1,4,7},{2},{3,6},{5}} => 4
{{1,4},{2,7},{3,6},{5}} => 4
{{1,4},{2},{3,6,7},{5}} => 3
{{1,4},{2},{3,6},{5,7}} => 3
{{1,4},{2},{3,6},{5},{7}} => 3
{{1,4,7},{2},{3},{5,6}} => 3
{{1,4},{2,7},{3},{5,6}} => 3
{{1,4},{2},{3,7},{5,6}} => 2
{{1,4},{2},{3},{5,6,7}} => 2
{{1,4},{2},{3},{5,6},{7}} => 2
{{1,4,7},{2},{3},{5},{6}} => 2
{{1,4},{2,7},{3},{5},{6}} => 5
{{1,4},{2},{3,7},{5},{6}} => 4
{{1,4},{2},{3},{5,7},{6}} => 3
{{1,4},{2},{3},{5},{6,7}} => 2
{{1,4},{2},{3},{5},{6},{7}} => 2
{{1,5,6,7},{2,4},{3}} => 2
{{1,5,6},{2,4,7},{3}} => 2
{{1,5,6},{2,4},{3,7}} => 2
{{1,5,6},{2,4},{3},{7}} => 2
{{1,5,7},{2,4,6},{3}} => 3
{{1,5},{2,4,6,7},{3}} => 3
{{1,5},{2,4,6},{3,7}} => 3
{{1,5},{2,4,6},{3},{7}} => 3
{{1,5,7},{2,4},{3,6}} => 3
{{1,5},{2,4,7},{3,6}} => 4
{{1,5},{2,4},{3,6,7}} => 2
{{1,5},{2,4},{3,6},{7}} => 2
{{1,5,7},{2,4},{3},{6}} => 2
{{1,5},{2,4,7},{3},{6}} => 3
{{1,5},{2,4},{3,7},{6}} => 3
{{1,5},{2,4},{3},{6,7}} => 2
{{1,5},{2,4},{3},{6},{7}} => 2
{{1,6,7},{2,4,5},{3}} => 2
{{1,6},{2,4,5,7},{3}} => 2
{{1,6},{2,4,5},{3,7}} => 2
{{1,6},{2,4,5},{3},{7}} => 2
{{1,7},{2,4,5,6},{3}} => 2
{{1},{2,4,5,6,7},{3}} => 1
{{1},{2,4,5,6},{3,7}} => 1
{{1},{2,4,5,6},{3},{7}} => 1
{{1,7},{2,4,5},{3,6}} => 1
{{1},{2,4,5,7},{3,6}} => 1
{{1},{2,4,5},{3,6,7}} => 1
{{1},{2,4,5},{3,6},{7}} => 1
{{1,7},{2,4,5},{3},{6}} => 3
{{1},{2,4,5,7},{3},{6}} => 1
{{1},{2,4,5},{3,7},{6}} => 2
{{1},{2,4,5},{3},{6,7}} => 1
{{1},{2,4,5},{3},{6},{7}} => 1
{{1,6,7},{2,4},{3,5}} => 1
{{1,6},{2,4,7},{3,5}} => 3
{{1,6},{2,4},{3,5,7}} => 2
{{1,6},{2,4},{3,5},{7}} => 1
{{1,7},{2,4,6},{3,5}} => 2
{{1},{2,4,6,7},{3,5}} => 2
{{1},{2,4,6},{3,5,7}} => 2
{{1},{2,4,6},{3,5},{7}} => 2
{{1,7},{2,4},{3,5,6}} => 1
{{1},{2,4,7},{3,5,6}} => 1
{{1},{2,4},{3,5,6,7}} => 1
{{1},{2,4},{3,5,6},{7}} => 1
{{1,7},{2,4},{3,5},{6}} => 2
{{1},{2,4,7},{3,5},{6}} => 2
{{1},{2,4},{3,5,7},{6}} => 1
{{1},{2,4},{3,5},{6,7}} => 1
{{1},{2,4},{3,5},{6},{7}} => 1
{{1,6,7},{2,4},{3},{5}} => 3
{{1,6},{2,4,7},{3},{5}} => 4
{{1,6},{2,4},{3,7},{5}} => 4
{{1,6},{2,4},{3},{5,7}} => 3
{{1,6},{2,4},{3},{5},{7}} => 3
{{1,7},{2,4,6},{3},{5}} => 3
{{1},{2,4,6,7},{3},{5}} => 1
{{1},{2,4,6},{3,7},{5}} => 2
{{1},{2,4,6},{3},{5,7}} => 1
{{1},{2,4,6},{3},{5},{7}} => 1
{{1,7},{2,4},{3,6},{5}} => 3
{{1},{2,4,7},{3,6},{5}} => 3
{{1},{2,4},{3,6,7},{5}} => 2
{{1},{2,4},{3,6},{5,7}} => 2
{{1},{2,4},{3,6},{5},{7}} => 2
{{1,7},{2,4},{3},{5,6}} => 2
{{1},{2,4,7},{3},{5,6}} => 2
{{1},{2,4},{3,7},{5,6}} => 1
{{1},{2,4},{3},{5,6,7}} => 1
{{1},{2,4},{3},{5,6},{7}} => 1
{{1,7},{2,4},{3},{5},{6}} => 4
{{1},{2,4,7},{3},{5},{6}} => 1
{{1},{2,4},{3,7},{5},{6}} => 3
{{1},{2,4},{3},{5,7},{6}} => 2
{{1},{2,4},{3},{5},{6,7}} => 1
{{1},{2,4},{3},{5},{6},{7}} => 1
{{1,5,6,7},{2},{3,4}} => 1
{{1,5,6},{2,7},{3,4}} => 1
{{1,5,6},{2},{3,4,7}} => 1
{{1,5,6},{2},{3,4},{7}} => 1
{{1,5,7},{2,6},{3,4}} => 2
{{1,5},{2,6,7},{3,4}} => 1
{{1,5},{2,6},{3,4,7}} => 3
{{1,5},{2,6},{3,4},{7}} => 1
{{1,5,7},{2},{3,4,6}} => 2
{{1,5},{2,7},{3,4,6}} => 2
{{1,5},{2},{3,4,6,7}} => 2
{{1,5},{2},{3,4,6},{7}} => 2
{{1,5,7},{2},{3,4},{6}} => 1
{{1,5},{2,7},{3,4},{6}} => 2
{{1,5},{2},{3,4,7},{6}} => 2
{{1,5},{2},{3,4},{6,7}} => 1
{{1,5},{2},{3,4},{6},{7}} => 1
{{1,6,7},{2,5},{3,4}} => 0
{{1,6},{2,5,7},{3,4}} => 1
{{1,6},{2,5},{3,4,7}} => 2
{{1,6},{2,5},{3,4},{7}} => 0
{{1,7},{2,5,6},{3,4}} => 0
{{1},{2,5,6,7},{3,4}} => 0
{{1},{2,5,6},{3,4,7}} => 0
{{1},{2,5,6},{3,4},{7}} => 0
{{1,7},{2,5},{3,4,6}} => 1
{{1},{2,5,7},{3,4,6}} => 1
{{1},{2,5},{3,4,6,7}} => 1
{{1},{2,5},{3,4,6},{7}} => 1
{{1,7},{2,5},{3,4},{6}} => 1
{{1},{2,5,7},{3,4},{6}} => 0
{{1},{2,5},{3,4,7},{6}} => 1
{{1},{2,5},{3,4},{6,7}} => 0
{{1},{2,5},{3,4},{6},{7}} => 0
{{1,6,7},{2},{3,4,5}} => 1
{{1,6},{2,7},{3,4,5}} => 1
{{1,6},{2},{3,4,5,7}} => 1
{{1,6},{2},{3,4,5},{7}} => 1
{{1,7},{2,6},{3,4,5}} => 0
{{1},{2,6,7},{3,4,5}} => 0
{{1},{2,6},{3,4,5,7}} => 0
{{1},{2,6},{3,4,5},{7}} => 0
{{1,7},{2},{3,4,5,6}} => 1
{{1},{2,7},{3,4,5,6}} => 0
{{1},{2},{3,4,5,6,7}} => 0
{{1},{2},{3,4,5,6},{7}} => 0
{{1,7},{2},{3,4,5},{6}} => 2
{{1},{2,7},{3,4,5},{6}} => 1
{{1},{2},{3,4,5,7},{6}} => 0
{{1},{2},{3,4,5},{6,7}} => 0
{{1},{2},{3,4,5},{6},{7}} => 0
{{1,6,7},{2},{3,4},{5}} => 2
{{1,6},{2,7},{3,4},{5}} => 3
{{1,6},{2},{3,4,7},{5}} => 3
{{1,6},{2},{3,4},{5,7}} => 2
{{1,6},{2},{3,4},{5},{7}} => 2
{{1,7},{2,6},{3,4},{5}} => 2
{{1},{2,6,7},{3,4},{5}} => 1
{{1},{2,6},{3,4,7},{5}} => 2
{{1},{2,6},{3,4},{5,7}} => 1
{{1},{2,6},{3,4},{5},{7}} => 1
{{1,7},{2},{3,4,6},{5}} => 2
{{1},{2,7},{3,4,6},{5}} => 1
{{1},{2},{3,4,6,7},{5}} => 0
{{1},{2},{3,4,6},{5,7}} => 0
{{1},{2},{3,4,6},{5},{7}} => 0
{{1,7},{2},{3,4},{5,6}} => 1
{{1},{2,7},{3,4},{5,6}} => 0
{{1},{2},{3,4,7},{5,6}} => 1
{{1},{2},{3,4},{5,6,7}} => 0
{{1},{2},{3,4},{5,6},{7}} => 0
{{1,7},{2},{3,4},{5},{6}} => 3
{{1},{2,7},{3,4},{5},{6}} => 2
{{1},{2},{3,4,7},{5},{6}} => 0
{{1},{2},{3,4},{5,7},{6}} => 1
{{1},{2},{3,4},{5},{6,7}} => 0
{{1},{2},{3,4},{5},{6},{7}} => 0
{{1,5,6,7},{2},{3},{4}} => 3
{{1,5,6},{2,7},{3},{4}} => 5
{{1,5,6},{2},{3,7},{4}} => 4
{{1,5,6},{2},{3},{4,7}} => 3
{{1,5,6},{2},{3},{4},{7}} => 3
{{1,5,7},{2,6},{3},{4}} => 6
{{1,5},{2,6,7},{3},{4}} => 5
{{1,5},{2,6},{3,7},{4}} => 6
{{1,5},{2,6},{3},{4,7}} => 5
{{1,5},{2,6},{3},{4},{7}} => 5
{{1,5,7},{2},{3,6},{4}} => 5
{{1,5},{2,7},{3,6},{4}} => 5
{{1,5},{2},{3,6,7},{4}} => 4
{{1,5},{2},{3,6},{4,7}} => 4
{{1,5},{2},{3,6},{4},{7}} => 4
{{1,5,7},{2},{3},{4,6}} => 4
{{1,5},{2,7},{3},{4,6}} => 4
{{1,5},{2},{3,7},{4,6}} => 3
{{1,5},{2},{3},{4,6,7}} => 3
{{1,5},{2},{3},{4,6},{7}} => 3
{{1,5,7},{2},{3},{4},{6}} => 3
{{1,5},{2,7},{3},{4},{6}} => 6
{{1,5},{2},{3,7},{4},{6}} => 5
{{1,5},{2},{3},{4,7},{6}} => 4
{{1,5},{2},{3},{4},{6,7}} => 3
{{1,5},{2},{3},{4},{6},{7}} => 3
{{1,6,7},{2,5},{3},{4}} => 4
{{1,6},{2,5,7},{3},{4}} => 5
{{1,6},{2,5},{3,7},{4}} => 5
{{1,6},{2,5},{3},{4,7}} => 4
{{1,6},{2,5},{3},{4},{7}} => 4
{{1,7},{2,5,6},{3},{4}} => 4
{{1},{2,5,6,7},{3},{4}} => 2
{{1},{2,5,6},{3,7},{4}} => 3
{{1},{2,5,6},{3},{4,7}} => 2
{{1},{2,5,6},{3},{4},{7}} => 2
{{1,7},{2,5},{3,6},{4}} => 4
{{1},{2,5,7},{3,6},{4}} => 4
{{1},{2,5},{3,6,7},{4}} => 3
{{1},{2,5},{3,6},{4,7}} => 3
{{1},{2,5},{3,6},{4},{7}} => 3
{{1,7},{2,5},{3},{4,6}} => 3
{{1},{2,5,7},{3},{4,6}} => 3
{{1},{2,5},{3,7},{4,6}} => 2
{{1},{2,5},{3},{4,6,7}} => 2
{{1},{2,5},{3},{4,6},{7}} => 2
{{1,7},{2,5},{3},{4},{6}} => 5
{{1},{2,5,7},{3},{4},{6}} => 2
{{1},{2,5},{3,7},{4},{6}} => 4
{{1},{2,5},{3},{4,7},{6}} => 3
{{1},{2,5},{3},{4},{6,7}} => 2
{{1},{2,5},{3},{4},{6},{7}} => 2
{{1,6,7},{2},{3,5},{4}} => 3
{{1,6},{2,7},{3,5},{4}} => 4
{{1,6},{2},{3,5,7},{4}} => 4
{{1,6},{2},{3,5},{4,7}} => 3
{{1,6},{2},{3,5},{4},{7}} => 3
{{1,7},{2,6},{3,5},{4}} => 3
{{1},{2,6,7},{3,5},{4}} => 2
{{1},{2,6},{3,5,7},{4}} => 3
{{1},{2,6},{3,5},{4,7}} => 2
{{1},{2,6},{3,5},{4},{7}} => 2
{{1,7},{2},{3,5,6},{4}} => 3
{{1},{2,7},{3,5,6},{4}} => 2
{{1},{2},{3,5,6,7},{4}} => 1
{{1},{2},{3,5,6},{4,7}} => 1
{{1},{2},{3,5,6},{4},{7}} => 1
{{1,7},{2},{3,5},{4,6}} => 2
{{1},{2,7},{3,5},{4,6}} => 1
{{1},{2},{3,5,7},{4,6}} => 2
{{1},{2},{3,5},{4,6,7}} => 1
{{1},{2},{3,5},{4,6},{7}} => 1
{{1,7},{2},{3,5},{4},{6}} => 4
{{1},{2,7},{3,5},{4},{6}} => 3
{{1},{2},{3,5,7},{4},{6}} => 1
{{1},{2},{3,5},{4,7},{6}} => 2
{{1},{2},{3,5},{4},{6,7}} => 1
{{1},{2},{3,5},{4},{6},{7}} => 1
{{1,6,7},{2},{3},{4,5}} => 2
{{1,6},{2,7},{3},{4,5}} => 3
{{1,6},{2},{3,7},{4,5}} => 2
{{1,6},{2},{3},{4,5,7}} => 3
{{1,6},{2},{3},{4,5},{7}} => 2
{{1,7},{2,6},{3},{4,5}} => 2
{{1},{2,6,7},{3},{4,5}} => 1
{{1},{2,6},{3,7},{4,5}} => 1
{{1},{2,6},{3},{4,5,7}} => 2
{{1},{2,6},{3},{4,5},{7}} => 1
{{1,7},{2},{3,6},{4,5}} => 1
{{1},{2,7},{3,6},{4,5}} => 0
{{1},{2},{3,6,7},{4,5}} => 0
{{1},{2},{3,6},{4,5,7}} => 1
{{1},{2},{3,6},{4,5},{7}} => 0
{{1,7},{2},{3},{4,5,6}} => 2
{{1},{2,7},{3},{4,5,6}} => 1
{{1},{2},{3,7},{4,5,6}} => 0
{{1},{2},{3},{4,5,6,7}} => 0
{{1},{2},{3},{4,5,6},{7}} => 0
{{1,7},{2},{3},{4,5},{6}} => 3
{{1},{2,7},{3},{4,5},{6}} => 2
{{1},{2},{3,7},{4,5},{6}} => 1
{{1},{2},{3},{4,5,7},{6}} => 0
{{1},{2},{3},{4,5},{6,7}} => 0
{{1},{2},{3},{4,5},{6},{7}} => 0
{{1,6,7},{2},{3},{4},{5}} => 4
{{1,6},{2,7},{3},{4},{5}} => 7
{{1,6},{2},{3,7},{4},{5}} => 6
{{1,6},{2},{3},{4,7},{5}} => 5
{{1,6},{2},{3},{4},{5,7}} => 4
{{1,6},{2},{3},{4},{5},{7}} => 4
{{1,7},{2,6},{3},{4},{5}} => 6
{{1},{2,6,7},{3},{4},{5}} => 3
{{1},{2,6},{3,7},{4},{5}} => 5
{{1},{2,6},{3},{4,7},{5}} => 4
{{1},{2,6},{3},{4},{5,7}} => 3
{{1},{2,6},{3},{4},{5},{7}} => 3
{{1,7},{2},{3,6},{4},{5}} => 5
{{1},{2,7},{3,6},{4},{5}} => 4
{{1},{2},{3,6,7},{4},{5}} => 2
{{1},{2},{3,6},{4,7},{5}} => 3
{{1},{2},{3,6},{4},{5,7}} => 2
{{1},{2},{3,6},{4},{5},{7}} => 2
{{1,7},{2},{3},{4,6},{5}} => 4
{{1},{2,7},{3},{4,6},{5}} => 3
{{1},{2},{3,7},{4,6},{5}} => 2
{{1},{2},{3},{4,6,7},{5}} => 1
{{1},{2},{3},{4,6},{5,7}} => 1
{{1},{2},{3},{4,6},{5},{7}} => 1
{{1,7},{2},{3},{4},{5,6}} => 3
{{1},{2,7},{3},{4},{5,6}} => 2
{{1},{2},{3,7},{4},{5,6}} => 1
{{1},{2},{3},{4,7},{5,6}} => 0
{{1},{2},{3},{4},{5,6,7}} => 0
{{1},{2},{3},{4},{5,6},{7}} => 0
{{1,7},{2},{3},{4},{5},{6}} => 5
{{1},{2,7},{3},{4},{5},{6}} => 4
{{1},{2},{3,7},{4},{5},{6}} => 3
{{1},{2},{3},{4,7},{5},{6}} => 2
{{1},{2},{3},{4},{5,7},{6}} => 1
{{1},{2},{3},{4},{5},{6,7}} => 0
{{1},{2},{3},{4},{5},{6},{7}} => 0
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Description
The interlacing number of a set partition.
Let $\pi$ be a set partition of $\{1,\dots,n\}$ with $k$ blocks. To each block of $\pi$ we add the element $\infty$, which is larger than $n$. Then, an interlacing of $\pi$ is a pair of blocks $B=(B_1 < \dots < B_b < B_{b+1} = \infty)$ and $C=(C_1 < \dots < C_c < C_{c+1} = \infty)$ together with an index $1\leq i\leq \min(b, c)$, such that $B_i < C_i < B_{i+1} < C_{i+1}$.
References
[1] Prasad, A., Ram, S. Set partitions, tableaux, and subspace profiles under regular split semisimple matrices arXiv:2112.00479
Code
def statistic(self):
    self = SetPartition(self)
    arcs = []
    for j, p in enumerate(sorted(self)):
        p = sorted(p)
        arcs.append([])
        for i in range(len(p)-1):
            arcs[j].append((p[i], p[i+1]))
        arcs[j].append((p[-1], Infinity))

    interlacings = 0
    for i in range(len(arcs)):
        for j in range(i+1, len(arcs)):
            for (a,b), (c,d) in zip(arcs[i], arcs[j]):
                if a < c < b < d or c < a < d < b:
                    interlacings += 1
    return interlacings
Created
Mar 28, 2022 at 11:14 by Martin Rubey
Updated
Mar 28, 2022 at 11:14 by Martin Rubey