Identifier
Values
[1,0,1,0] => {{1},{2}} => {{1},{2}} => 0
[1,1,0,0] => {{1,2}} => {{1,2}} => 0
[1,0,1,0,1,0] => {{1},{2},{3}} => {{1},{2},{3}} => 0
[1,0,1,1,0,0] => {{1},{2,3}} => {{1,2},{3}} => 0
[1,1,0,0,1,0] => {{1,2},{3}} => {{1},{2,3}} => 0
[1,1,0,1,0,0] => {{1,3},{2}} => {{1,3},{2}} => 1
[1,1,1,0,0,0] => {{1,2,3}} => {{1,2,3}} => 0
[1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}} => 0
[1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => {{1,2},{3},{4}} => 0
[1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => {{1},{2,3},{4}} => 0
[1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => {{1,3},{2},{4}} => 1
[1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => {{1,2,3},{4}} => 0
[1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => {{1},{2},{3,4}} => 0
[1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => {{1,2},{3,4}} => 0
[1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => {{1},{2,4},{3}} => 1
[1,1,0,1,0,1,0,0] => {{1,4},{2},{3}} => {{1,4},{2},{3}} => 2
[1,1,0,1,1,0,0,0] => {{1,3,4},{2}} => {{1,2,4},{3}} => 1
[1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => {{1},{2,3,4}} => 0
[1,1,1,0,0,1,0,0] => {{1,4},{2,3}} => {{1,4},{2,3}} => 1
[1,1,1,0,1,0,0,0] => {{1,2,4},{3}} => {{1,3},{2,4}} => 1
[1,1,1,1,0,0,0,0] => {{1,2,3,4}} => {{1,2,3,4}} => 0
[1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => 0
[1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => {{1,2},{3},{4},{5}} => 0
[1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => {{1},{2,3},{4},{5}} => 0
[1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => {{1,3},{2},{4},{5}} => 1
[1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => {{1,2,3},{4},{5}} => 0
[1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => {{1},{2},{3,4},{5}} => 0
[1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1,2},{3,4},{5}} => 0
[1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => {{1},{2,4},{3},{5}} => 1
[1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => {{1,4},{2},{3},{5}} => 2
[1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => {{1,2,4},{3},{5}} => 1
[1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => {{1},{2,3,4},{5}} => 0
[1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => {{1,4},{2,3},{5}} => 1
[1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => {{1,3},{2,4},{5}} => 1
[1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => {{1,2,3,4},{5}} => 0
[1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => {{1},{2},{3},{4,5}} => 0
[1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => {{1,2},{3},{4,5}} => 0
[1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => {{1},{2,3},{4,5}} => 0
[1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => {{1,3},{2},{4,5}} => 1
[1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2,3},{4,5}} => 0
[1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => {{1},{2},{3,5},{4}} => 1
[1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => {{1,2},{3,5},{4}} => 1
[1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => {{1},{2,5},{3},{4}} => 2
[1,1,0,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}} => 3
[1,1,0,1,0,1,1,0,0,0] => {{1,4,5},{2},{3}} => {{1,2,5},{3},{4}} => 2
[1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => {{1},{2,3,5},{4}} => 1
[1,1,0,1,1,0,0,1,0,0] => {{1,5},{2},{3,4}} => {{1,5},{2,3},{4}} => 2
[1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4}} => {{1,3},{2,5},{4}} => 2
[1,1,0,1,1,1,0,0,0,0] => {{1,3,4,5},{2}} => {{1,2,3,5},{4}} => 1
[1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => {{1},{2},{3,4,5}} => 0
[1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => {{1,2},{3,4,5}} => 0
[1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => {{1},{2,5},{3,4}} => 1
[1,1,1,0,0,1,0,1,0,0] => {{1,5},{2,3},{4}} => {{1,5},{2},{3,4}} => 2
[1,1,1,0,0,1,1,0,0,0] => {{1,4,5},{2,3}} => {{1,2,5},{3,4}} => 1
[1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => {{1},{2,4},{3,5}} => 1
[1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3}} => {{1,5},{2,4},{3}} => 3
[1,1,1,0,1,0,1,0,0,0] => {{1,2,5},{3},{4}} => {{1,4},{2},{3,5}} => 2
[1,1,1,0,1,1,0,0,0,0] => {{1,2,4,5},{3}} => {{1,2,4},{3,5}} => 1
[1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}} => 0
[1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3,4}} => {{1,5},{2,3,4}} => 1
[1,1,1,1,0,0,1,0,0,0] => {{1,2,5},{3,4}} => {{1,4},{2,3,5}} => 1
[1,1,1,1,0,1,0,0,0,0] => {{1,2,3,5},{4}} => {{1,3},{2,4,5}} => 1
[1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}} => {{1,2,3,4,5}} => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}} => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => {{1,2},{3},{4},{5},{6}} => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => {{1},{2,3},{4},{5},{6}} => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => {{1,3},{2},{4},{5},{6}} => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => {{1,2,3},{4},{5},{6}} => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => {{1},{2},{3,4},{5},{6}} => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => {{1,2},{3,4},{5},{6}} => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => {{1},{2,4},{3},{5},{6}} => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => {{1,4},{2},{3},{5},{6}} => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}} => {{1,2,4},{3},{5},{6}} => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => {{1},{2,3,4},{5},{6}} => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}} => {{1,4},{2,3},{5},{6}} => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => {{1,3},{2,4},{5},{6}} => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => {{1,2,3,4},{5},{6}} => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => {{1},{2},{3},{4,5},{6}} => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => {{1,2},{3},{4,5},{6}} => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1},{2,3},{4,5},{6}} => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}} => {{1,3},{2},{4,5},{6}} => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,2,3},{4,5},{6}} => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => {{1},{2},{3,5},{4},{6}} => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}} => {{1,2},{3,5},{4},{6}} => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}} => {{1},{2,5},{3},{4},{6}} => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => {{1,5},{2},{3},{4},{6}} => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => {{1,2,5},{3},{4},{6}} => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}} => {{1},{2,3,5},{4},{6}} => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => {{1,5},{2,3},{4},{6}} => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => {{1,3},{2,5},{4},{6}} => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => {{1,2,3,5},{4},{6}} => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => {{1},{2},{3,4,5},{6}} => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,2},{3,4,5},{6}} => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}} => {{1},{2,5},{3,4},{6}} => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => {{1,5},{2},{3,4},{6}} => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => {{1,2,5},{3,4},{6}} => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => {{1},{2,4},{3,5},{6}} => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => {{1,5},{2,4},{3},{6}} => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => {{1,4},{2},{3,5},{6}} => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => {{1,2,4},{3,5},{6}} => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}} => 0
>>> Load all 641 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => {{1,5},{2,3,4},{6}} => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => {{1,4},{2,3,5},{6}} => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => {{1,3},{2,4,5},{6}} => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}} => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5,6}} => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}} => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => {{1},{2,3},{4},{5,6}} => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}} => {{1,3},{2},{4},{5,6}} => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => {{1,2,3},{4},{5,6}} => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => {{1},{2},{3,4},{5,6}} => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}} => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}} => {{1},{2,4},{3},{5,6}} => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}} => {{1,4},{2},{3},{5,6}} => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => {{1,2,4},{3},{5,6}} => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1},{2,3,4},{5,6}} => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => {{1,4},{2,3},{5,6}} => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => {{1,3},{2,4},{5,6}} => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,3,4},{5,6}} => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => {{1},{2},{3},{4,6},{5}} => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}} => {{1,2},{3},{4,6},{5}} => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}} => {{1},{2,3},{4,6},{5}} => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => {{1,3},{2},{4,6},{5}} => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => {{1,2,3},{4,6},{5}} => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => {{1},{2},{3,6},{4},{5}} => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => {{1,2},{3,6},{4},{5}} => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => {{1},{2,6},{3},{4},{5}} => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}} => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => {{1,5,6},{2},{3},{4}} => {{1,2,6},{3},{4},{5}} => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => {{1},{2,3,6},{4},{5}} => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => {{1,6},{2},{3},{4,5}} => {{1,6},{2,3},{4},{5}} => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5}} => {{1,3},{2,6},{4},{5}} => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2},{3}} => {{1,2,3,6},{4},{5}} => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}} => {{1},{2},{3,4,6},{5}} => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => {{1,2},{3,4,6},{5}} => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => {{1},{2,6},{3,4},{5}} => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => {{1,6},{2},{3,4},{5}} => {{1,6},{2},{3,4},{5}} => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4}} => {{1,2,6},{3,4},{5}} => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => {{1},{2,4},{3,6},{5}} => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => {{1,6},{2},{3,5},{4}} => {{1,6},{2,4},{3},{5}} => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => {{1,3,6},{2},{4},{5}} => {{1,4},{2},{3,6},{5}} => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4}} => {{1,2,4},{3,6},{5}} => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => {{1},{2,3,4,6},{5}} => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => {{1,6},{2},{3,4,5}} => {{1,6},{2,3,4},{5}} => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => {{1,3,6},{2},{4,5}} => {{1,4},{2,3,6},{5}} => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => {{1,3,4,6},{2},{5}} => {{1,3},{2,4,6},{5}} => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => {{1,3,4,5,6},{2}} => {{1,2,3,4,6},{5}} => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => {{1},{2},{3},{4,5,6}} => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => {{1,2},{3},{4,5,6}} => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => {{1},{2,3},{4,5,6}} => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => {{1,3},{2},{4,5,6}} => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}} => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => {{1},{2},{3,6},{4,5}} => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => {{1,2},{3,6},{4,5}} => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => {{1},{2,6},{3},{4,5}} => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => {{1,6},{2,3},{4},{5}} => {{1,6},{2},{3},{4,5}} => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => {{1,5,6},{2,3},{4}} => {{1,2,6},{3},{4,5}} => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => {{1},{2,3,6},{4,5}} => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5}} => {{1,6},{2,3},{4,5}} => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => {{1,4,6},{2,3},{5}} => {{1,3},{2,6},{4,5}} => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2,3}} => {{1,2,3,6},{4,5}} => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => {{1},{2},{3,5},{4,6}} => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => {{1,2},{3,5},{4,6}} => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => {{1},{2,6},{3,5},{4}} => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => {{1,6},{2,4},{3},{5}} => {{1,6},{2},{3,5},{4}} => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => {{1,5,6},{2,4},{3}} => {{1,2,6},{3,5},{4}} => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => {{1},{2,5},{3},{4,6}} => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => {{1,6},{2,5},{3},{4}} => {{1,6},{2,5},{3},{4}} => 5
[1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,6},{3},{4},{5}} => {{1,5},{2},{3},{4,6}} => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2,5,6},{3},{4}} => {{1,2,5},{3},{4,6}} => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => {{1},{2,3,5},{4,6}} => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => {{1,6},{2,4,5},{3}} => {{1,6},{2,3,5},{4}} => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2,6},{3},{4,5}} => {{1,5},{2,3},{4,6}} => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2,4,6},{3},{5}} => {{1,3},{2,5},{4,6}} => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,4,5,6},{3}} => {{1,2,3,5},{4,6}} => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}} => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => {{1,2},{3,4,5,6}} => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => {{1},{2,6},{3,4,5}} => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => {{1,6},{2,3,4},{5}} => {{1,6},{2},{3,4,5}} => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => {{1,5,6},{2,3,4}} => {{1,2,6},{3,4,5}} => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => {{1},{2,5},{3,4,6}} => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4}} => {{1,6},{2,5},{3,4}} => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2,6},{3,4},{5}} => {{1,5},{2},{3,4,6}} => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,5,6},{3,4}} => {{1,2,5},{3,4,6}} => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => {{1},{2,4},{3,5,6}} => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => {{1,6},{2,3,5},{4}} => {{1,6},{2,4},{3,5}} => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,6},{3,5},{4}} => {{1,5},{2,4},{3,6}} => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3,6},{4},{5}} => {{1,4},{2},{3,5,6}} => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2,3,5,6},{4}} => {{1,2,4},{3,5,6}} => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}} => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => {{1,6},{2,3,4,5}} => {{1,6},{2,3,4,5}} => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,6},{3,4,5}} => {{1,5},{2,3,4,6}} => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3,6},{4,5}} => {{1,4},{2,3,5,6}} => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3,4,6},{5}} => {{1,3},{2,4,5,6}} => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}} => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}} => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6},{7}} => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6},{7}} => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => {{1,3},{2},{4},{5},{6},{7}} => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6},{7}} => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}} => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6},{7}} => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}} => {{1},{2,4},{3},{5},{6},{7}} => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}} => {{1,4},{2},{3},{5},{6},{7}} => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}} => {{1,2,4},{3},{5},{6},{7}} => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6},{7}} => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}} => {{1,4},{2,3},{5},{6},{7}} => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}} => {{1,3},{2,4},{5},{6},{7}} => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6},{7}} => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}} => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6},{7}} => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6},{7}} => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}} => {{1,3},{2},{4,5},{6},{7}} => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6},{7}} => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6},{7}} => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6},{7}} => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}} => {{1},{2,5},{3},{4},{6},{7}} => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}} => {{1,5},{2},{3},{4},{6},{7}} => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}} => {{1,2,5},{3},{4},{6},{7}} => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}} => {{1},{2,3,5},{4},{6},{7}} => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}} => {{1,5},{2,3},{4},{6},{7}} => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}} => {{1,3},{2,5},{4},{6},{7}} => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}} => {{1,2,3,5},{4},{6},{7}} => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}} => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6},{7}} => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}} => {{1},{2,5},{3,4},{6},{7}} => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}} => {{1,5},{2},{3,4},{6},{7}} => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}} => {{1,2,5},{3,4},{6},{7}} => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}} => {{1},{2,4},{3,5},{6},{7}} => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}} => {{1,5},{2,4},{3},{6},{7}} => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => {{1,4},{2},{3,5},{6},{7}} => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}} => {{1,2,4},{3,5},{6},{7}} => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6},{7}} => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}} => {{1,5},{2,3,4},{6},{7}} => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}} => {{1,4},{2,3,5},{6},{7}} => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}} => {{1,3},{2,4,5},{6},{7}} => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}} => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6},{7}} => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6},{7}} => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6},{7}} => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}} => {{1,3},{2},{4},{5,6},{7}} => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6},{7}} => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6},{7}} => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6},{7}} => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}} => {{1},{2,4},{3},{5,6},{7}} => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}} => {{1,4},{2},{3},{5,6},{7}} => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}} => {{1,2,4},{3},{5,6},{7}} => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6},{7}} => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}} => {{1,4},{2,3},{5,6},{7}} => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}} => {{1,3},{2,4},{5,6},{7}} => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,2,3,4},{5,6},{7}} => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}} => {{1},{2},{3},{4,6},{5},{7}} => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}} => {{1,2},{3},{4,6},{5},{7}} => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}} => {{1},{2,3},{4,6},{5},{7}} => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}} => {{1,3},{2},{4,6},{5},{7}} => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}} => {{1,2,3},{4,6},{5},{7}} => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}} => {{1},{2},{3,6},{4},{5},{7}} => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}} => {{1,2},{3,6},{4},{5},{7}} => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}} => {{1},{2,6},{3},{4},{5},{7}} => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => {{1,6},{2},{3},{4},{5},{7}} => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}} => {{1,2,6},{3},{4},{5},{7}} => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}} => {{1},{2,3,6},{4},{5},{7}} => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}} => {{1,6},{2,3},{4},{5},{7}} => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}} => {{1,3},{2,6},{4},{5},{7}} => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}} => {{1,2,3,6},{4},{5},{7}} => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}} => {{1},{2},{3,4,6},{5},{7}} => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}} => {{1,2},{3,4,6},{5},{7}} => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}} => {{1},{2,6},{3,4},{5},{7}} => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}} => {{1,6},{2},{3,4},{5},{7}} => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}} => {{1,2,6},{3,4},{5},{7}} => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}} => {{1},{2,4},{3,6},{5},{7}} => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}} => {{1,6},{2,4},{3},{5},{7}} => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}} => {{1,4},{2},{3,6},{5},{7}} => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}} => {{1,2,4},{3,6},{5},{7}} => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}} => {{1},{2,3,4,6},{5},{7}} => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}} => {{1,6},{2,3,4},{5},{7}} => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}} => {{1,4},{2,3,6},{5},{7}} => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}} => {{1,3},{2,4,6},{5},{7}} => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}} => {{1,2,3,4,6},{5},{7}} => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6},{7}} => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6},{7}} => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6},{7}} => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}} => {{1,3},{2},{4,5,6},{7}} => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,2,3},{4,5,6},{7}} => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}} => {{1},{2},{3,6},{4,5},{7}} => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}} => {{1,2},{3,6},{4,5},{7}} => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}} => {{1},{2,6},{3},{4,5},{7}} => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}} => {{1,6},{2},{3},{4,5},{7}} => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}} => {{1,2,6},{3},{4,5},{7}} => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}} => {{1},{2,3,6},{4,5},{7}} => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}} => {{1,6},{2,3},{4,5},{7}} => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}} => {{1,3},{2,6},{4,5},{7}} => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}} => {{1,2,3,6},{4,5},{7}} => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}} => {{1},{2},{3,5},{4,6},{7}} => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}} => {{1,2},{3,5},{4,6},{7}} => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}} => {{1},{2,6},{3,5},{4},{7}} => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}} => {{1,6},{2},{3,5},{4},{7}} => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}} => {{1,2,6},{3,5},{4},{7}} => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => {{1},{2,5},{3},{4,6},{7}} => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}} => {{1,6},{2,5},{3},{4},{7}} => 5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => {{1,5},{2},{3},{4,6},{7}} => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}} => {{1,2,5},{3},{4,6},{7}} => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}} => {{1},{2,3,5},{4,6},{7}} => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}} => {{1,6},{2,3,5},{4},{7}} => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}} => {{1,5},{2,3},{4,6},{7}} => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}} => {{1,3},{2,5},{4,6},{7}} => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}} => {{1,2,3,5},{4,6},{7}} => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6},{7}} => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,2},{3,4,5,6},{7}} => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}} => {{1},{2,6},{3,4,5},{7}} => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}} => {{1,6},{2},{3,4,5},{7}} => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}} => {{1,2,6},{3,4,5},{7}} => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}} => {{1},{2,5},{3,4,6},{7}} => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}} => {{1,6},{2,5},{3,4},{7}} => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}} => {{1,5},{2},{3,4,6},{7}} => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}} => {{1,2,5},{3,4,6},{7}} => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}} => {{1},{2,4},{3,5,6},{7}} => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}} => {{1,6},{2,4},{3,5},{7}} => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}} => {{1,5},{2,4},{3,6},{7}} => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}} => {{1,4},{2},{3,5,6},{7}} => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}} => {{1,2,4},{3,5,6},{7}} => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}} => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => {{1,6},{2,3,4,5},{7}} => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => {{1,5},{2,3,4,6},{7}} => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => {{1,4},{2,3,5,6},{7}} => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => {{1,3},{2,4,5,6},{7}} => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}} => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6,7}} => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6,7}} => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6,7}} => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}} => {{1,3},{2},{4},{5},{6,7}} => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6,7}} => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6,7}} => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6,7}} => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}} => {{1},{2,4},{3},{5},{6,7}} => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}} => {{1,4},{2},{3},{5},{6,7}} => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}} => {{1,2,4},{3},{5},{6,7}} => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6,7}} => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}} => {{1,4},{2,3},{5},{6,7}} => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}} => {{1,3},{2,4},{5},{6,7}} => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6,7}} => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6,7}} => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6,7}} => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6,7}} => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}} => {{1,3},{2},{4,5},{6,7}} => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6,7}} => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6,7}} => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6,7}} => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}} => {{1},{2,5},{3},{4},{6,7}} => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}} => {{1,5},{2},{3},{4},{6,7}} => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}} => {{1,2,5},{3},{4},{6,7}} => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}} => {{1},{2,3,5},{4},{6,7}} => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}} => {{1,5},{2,3},{4},{6,7}} => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}} => {{1,3},{2,5},{4},{6,7}} => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}} => {{1,2,3,5},{4},{6,7}} => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6,7}} => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}} => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}} => {{1},{2,5},{3,4},{6,7}} => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}} => {{1,5},{2},{3,4},{6,7}} => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}} => {{1,2,5},{3,4},{6,7}} => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}} => {{1},{2,4},{3,5},{6,7}} => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}} => {{1,5},{2,4},{3},{6,7}} => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}} => {{1,4},{2},{3,5},{6,7}} => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}} => {{1,2,4},{3,5},{6,7}} => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6,7}} => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}} => {{1,5},{2,3,4},{6,7}} => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}} => {{1,4},{2,3,5},{6,7}} => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}} => {{1,3},{2,4,5},{6,7}} => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}} => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,7},{6}} => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}} => {{1,2},{3},{4},{5,7},{6}} => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}} => {{1},{2,3},{4},{5,7},{6}} => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}} => {{1,3},{2},{4},{5,7},{6}} => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}} => {{1,2,3},{4},{5,7},{6}} => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}} => {{1},{2},{3,4},{5,7},{6}} => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}} => {{1,2},{3,4},{5,7},{6}} => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}} => {{1},{2,4},{3},{5,7},{6}} => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}} => {{1,4},{2},{3},{5,7},{6}} => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}} => {{1,2,4},{3},{5,7},{6}} => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}} => {{1},{2,3,4},{5,7},{6}} => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}} => {{1,4},{2,3},{5,7},{6}} => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}} => {{1,3},{2,4},{5,7},{6}} => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}} => {{1,2,3,4},{5,7},{6}} => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5},{6}} => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}} => {{1,2},{3},{4,7},{5},{6}} => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}} => {{1},{2,3},{4,7},{5},{6}} => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}} => {{1,3},{2},{4,7},{5},{6}} => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}} => {{1,2,3},{4,7},{5},{6}} => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5},{6}} => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}} => {{1,2},{3,7},{4},{5},{6}} => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5},{6}} => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}} => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4},{5}} => {{1,2,7},{3},{4},{5},{6}} => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}} => {{1},{2,3,7},{4},{5},{6}} => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2},{3},{4},{5,6}} => {{1,7},{2,3},{4},{5},{6}} => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3},{4},{6}} => {{1,3},{2,7},{4},{5},{6}} => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3},{4}} => {{1,2,3,7},{4},{5},{6}} => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}} => {{1},{2},{3,4,7},{5},{6}} => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}} => {{1,2},{3,4,7},{5},{6}} => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}} => {{1},{2,7},{3,4},{5},{6}} => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2},{3},{4,5},{6}} => {{1,7},{2},{3,4},{5},{6}} => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4,5}} => {{1,2,7},{3,4},{5},{6}} => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}} => {{1},{2,4},{3,7},{5},{6}} => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2},{3},{4,6},{5}} => {{1,7},{2,4},{3},{5},{6}} => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2},{3},{5},{6}} => {{1,4},{2},{3,7},{5},{6}} => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2},{3},{5}} => {{1,2,4},{3,7},{5},{6}} => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}} => {{1},{2,3,4,7},{5},{6}} => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2},{3},{4,5,6}} => {{1,7},{2,3,4},{5},{6}} => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2},{3},{5,6}} => {{1,4},{2,3,7},{5},{6}} => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2},{3},{6}} => {{1,3},{2,4,7},{5},{6}} => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2},{3}} => {{1,2,3,4,7},{5},{6}} => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}} => {{1},{2},{3},{4,5,7},{6}} => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}} => {{1,2},{3},{4,5,7},{6}} => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}} => {{1},{2,3},{4,5,7},{6}} => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}} => {{1,3},{2},{4,5,7},{6}} => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}} => {{1,2,3},{4,5,7},{6}} => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}} => {{1},{2},{3,7},{4,5},{6}} => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}} => {{1,2},{3,7},{4,5},{6}} => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}} => {{1},{2,7},{3},{4,5},{6}} => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2},{3,4},{5},{6}} => {{1,7},{2},{3},{4,5},{6}} => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3,4},{5}} => {{1,2,7},{3},{4,5},{6}} => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}} => {{1},{2,3,7},{4,5},{6}} => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2},{3,4},{5,6}} => {{1,7},{2,3},{4,5},{6}} => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3,4},{6}} => {{1,3},{2,7},{4,5},{6}} => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3,4}} => {{1,2,3,7},{4,5},{6}} => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}} => {{1},{2},{3,5},{4,7},{6}} => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}} => {{1,2},{3,5},{4,7},{6}} => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}} => {{1},{2,7},{3,5},{4},{6}} => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2},{3,5},{4},{6}} => {{1,7},{2},{3,5},{4},{6}} => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,5},{4}} => {{1,2,7},{3,5},{4},{6}} => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}} => {{1},{2,5},{3},{4,7},{6}} => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4},{5}} => {{1,7},{2,5},{3},{4},{6}} => 6
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,3,7},{2},{4},{5},{6}} => {{1,5},{2},{3},{4,7},{6}} => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4},{5}} => {{1,2,5},{3},{4,7},{6}} => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3,5},{4,7},{6}} => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2},{3,5,6},{4}} => {{1,7},{2,3,5},{4},{6}} => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,3,7},{2},{4},{5,6}} => {{1,5},{2,3},{4,7},{6}} => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5,7},{2},{4},{6}} => {{1,3},{2,5},{4,7},{6}} => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,3,5,6,7},{2},{4}} => {{1,2,3,5},{4,7},{6}} => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}} => {{1},{2},{3,4,5,7},{6}} => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}} => {{1,2},{3,4,5,7},{6}} => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}} => {{1},{2,7},{3,4,5},{6}} => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2},{3,4,5},{6}} => {{1,7},{2},{3,4,5},{6}} => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,4,5}} => {{1,2,7},{3,4,5},{6}} => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}} => {{1},{2,5},{3,4,7},{6}} => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4,5}} => {{1,7},{2,5},{3,4},{6}} => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,3,7},{2},{4,5},{6}} => {{1,5},{2},{3,4,7},{6}} => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4,5}} => {{1,2,5},{3,4,7},{6}} => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}} => {{1},{2,4},{3,5,7},{6}} => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2},{3,4,6},{5}} => {{1,7},{2,4},{3,5},{6}} => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5}} => {{1,5},{2,4},{3,7},{6}} => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,3,4,7},{2},{5},{6}} => {{1,4},{2},{3,5,7},{6}} => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,3,4,6,7},{2},{5}} => {{1,2,4},{3,5,7},{6}} => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,7},{6}} => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2},{3,4,5,6}} => {{1,7},{2,3,4,5},{6}} => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,3,7},{2},{4,5,6}} => {{1,5},{2,3,4,7},{6}} => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,3,4,7},{2},{5,6}} => {{1,4},{2,3,5,7},{6}} => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,3,4,5,7},{2},{6}} => {{1,3},{2,4,5,7},{6}} => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,3,4,5,6,7},{2}} => {{1,2,3,4,5,7},{6}} => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6,7}} => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6,7}} => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6,7}} => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}} => {{1,3},{2},{4},{5,6,7}} => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}} => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6,7}} => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6,7}} => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4,6},{5},{7}} => {{1},{2,4},{3},{5,6,7}} => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}} => {{1,4},{2},{3},{5,6,7}} => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}} => {{1,2,4},{3},{5,6,7}} => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6,7}} => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}} => {{1,4},{2,3},{5,6,7}} => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}} => {{1,3},{2,4},{5,6,7}} => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}} => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5,6}} => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}} => {{1,2},{3},{4,7},{5,6}} => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}} => {{1},{2,3},{4,7},{5,6}} => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}} => {{1,3},{2},{4,7},{5,6}} => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}} => {{1,2,3},{4,7},{5,6}} => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5,6}} => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}} => {{1,2},{3,7},{4},{5,6}} => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5,6}} => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2,3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5,6}} => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3},{4},{5}} => {{1,2,7},{3},{4},{5,6}} => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}} => {{1},{2,3,7},{4},{5,6}} => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2,3},{4},{5,6}} => {{1,7},{2,3},{4},{5,6}} => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3},{4},{6}} => {{1,3},{2,7},{4},{5,6}} => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3},{4}} => {{1,2,3,7},{4},{5,6}} => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}} => {{1},{2},{3,4,7},{5,6}} => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}} => {{1,2},{3,4,7},{5,6}} => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}} => {{1},{2,7},{3,4},{5,6}} => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2,3},{4,5},{6}} => {{1,7},{2},{3,4},{5,6}} => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2,3},{4,5}} => {{1,2,7},{3,4},{5,6}} => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}} => {{1},{2,4},{3,7},{5,6}} => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2,3},{4,6},{5}} => {{1,7},{2,4},{3},{5,6}} => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2,3},{5},{6}} => {{1,4},{2},{3,7},{5,6}} => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2,3},{5}} => {{1,2,4},{3,7},{5,6}} => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}} => {{1},{2,3,4,7},{5,6}} => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2,3},{4,5,6}} => {{1,7},{2,3,4},{5,6}} => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2,3},{5,6}} => {{1,4},{2,3,7},{5,6}} => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2,3},{6}} => {{1,3},{2,4,7},{5,6}} => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2,3}} => {{1,2,3,4,7},{5,6}} => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}} => {{1},{2},{3},{4,6},{5,7}} => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}} => {{1,2},{3},{4,6},{5,7}} => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}} => {{1},{2,3},{4,6},{5,7}} => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}} => {{1,3},{2},{4,6},{5,7}} => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}} => {{1,2,3},{4,6},{5,7}} => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}} => {{1},{2},{3,7},{4,6},{5}} => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}} => {{1,2},{3,7},{4,6},{5}} => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}} => {{1},{2,7},{3},{4,6},{5}} => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2,4},{3},{5},{6}} => {{1,7},{2},{3},{4,6},{5}} => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,4},{3},{5}} => {{1,2,7},{3},{4,6},{5}} => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}} => {{1},{2,3,7},{4,6},{5}} => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2,4},{3},{5,6}} => {{1,7},{2,3},{4,6},{5}} => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6}} => {{1,3},{2,7},{4,6},{5}} => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,4},{3}} => {{1,2,3,7},{4,6},{5}} => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}} => {{1},{2},{3,6},{4},{5,7}} => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}} => {{1,2},{3,6},{4},{5,7}} => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}} => {{1},{2,7},{3,6},{4},{5}} => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3},{4},{6}} => {{1,7},{2},{3,6},{4},{5}} => 6
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3},{4}} => {{1,2,7},{3,6},{4},{5}} => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}} => {{1},{2,6},{3},{4},{5,7}} => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4},{5}} => {{1,7},{2,6},{3},{4},{5}} => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3},{4},{5},{6}} => {{1,6},{2},{3},{4},{5,7}} => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4},{5}} => {{1,2,6},{3},{4},{5,7}} => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}} => {{1},{2,3,6},{4},{5,7}} => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3},{4}} => {{1,7},{2,3,6},{4},{5}} => 5
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3},{4},{5,6}} => {{1,6},{2,3},{4},{5,7}} => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3},{4},{6}} => {{1,3},{2,6},{4},{5,7}} => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3},{4}} => {{1,2,3,6},{4},{5,7}} => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}} => {{1},{2},{3,4,6},{5,7}} => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}} => {{1,2},{3,4,6},{5,7}} => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}} => {{1},{2,7},{3,4,6},{5}} => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2,4,5},{3},{6}} => {{1,7},{2},{3,4,6},{5}} => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,4,5},{3}} => {{1,2,7},{3,4,6},{5}} => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}} => {{1},{2,6},{3,4},{5,7}} => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4,5}} => {{1,7},{2,6},{3,4},{5}} => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3},{4,5},{6}} => {{1,6},{2},{3,4},{5,7}} => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4,5}} => {{1,2,6},{3,4},{5,7}} => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}} => {{1},{2,4},{3,6},{5,7}} => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5}} => {{1,7},{2,4},{3,6},{5}} => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3},{4,6},{5}} => {{1,6},{2,4},{3},{5,7}} => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,4,7},{3},{5},{6}} => {{1,4},{2},{3,6},{5,7}} => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,4,6,7},{3},{5}} => {{1,2,4},{3,6},{5,7}} => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6},{5,7}} => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2,4,5,6},{3}} => {{1,7},{2,3,4,6},{5}} => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3},{4,5,6}} => {{1,6},{2,3,4},{5,7}} => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,4,7},{3},{5,6}} => {{1,4},{2,3,6},{5,7}} => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,4,5,7},{3},{6}} => {{1,3},{2,4,6},{5,7}} => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6},{5,7}} => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}} => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6,7}} => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6,7}} => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}} => {{1,3},{2},{4,5,6,7}} => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}} => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}} => {{1},{2},{3,7},{4,5,6}} => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}} => {{1,2},{3,7},{4,5,6}} => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}} => {{1},{2,7},{3},{4,5,6}} => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,7},{2,3,4},{5},{6}} => {{1,7},{2},{3},{4,5,6}} => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3,4},{5}} => {{1,2,7},{3},{4,5,6}} => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}} => {{1},{2,3,7},{4,5,6}} => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,7},{2,3,4},{5,6}} => {{1,7},{2,3},{4,5,6}} => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3,4},{6}} => {{1,3},{2,7},{4,5,6}} => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3,4}} => {{1,2,3,7},{4,5,6}} => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}} => {{1},{2},{3,6},{4,5,7}} => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}} => {{1,2},{3,6},{4,5,7}} => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}} => {{1},{2,7},{3,6},{4,5}} => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3,4},{6}} => {{1,7},{2},{3,6},{4,5}} => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3,4}} => {{1,2,7},{3,6},{4,5}} => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}} => {{1},{2,6},{3},{4,5,7}} => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4},{5}} => {{1,7},{2,6},{3},{4,5}} => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3,4},{5},{6}} => {{1,6},{2},{3},{4,5,7}} => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4},{5}} => {{1,2,6},{3},{4,5,7}} => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => {{1},{2,3,6},{4,5,7}} => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3,4}} => {{1,7},{2,3,6},{4,5}} => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3,4},{5,6}} => {{1,6},{2,3},{4,5,7}} => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3,4},{6}} => {{1,3},{2,6},{4,5,7}} => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3,4}} => {{1,2,3,6},{4,5,7}} => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}} => {{1},{2},{3,5},{4,6,7}} => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}} => {{1,2},{3,5},{4,6,7}} => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}} => {{1},{2,7},{3,5},{4,6}} => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,7},{2,3,5},{4},{6}} => {{1,7},{2},{3,5},{4,6}} => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,5},{4}} => {{1,2,7},{3,5},{4,6}} => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => {{1},{2,6},{3,5},{4,7}} => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4}} => {{1,7},{2,6},{3,5},{4}} => 6
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3,5},{4},{6}} => {{1,6},{2},{3,5},{4,7}} => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,5},{4}} => {{1,2,6},{3,5},{4,7}} => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => {{1},{2,5},{3},{4,6,7}} => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4},{5}} => {{1,7},{2,5},{3},{4,6}} => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4},{5}} => {{1,6},{2,5},{3},{4,7}} => 5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4},{5},{6}} => {{1,5},{2},{3},{4,6,7}} => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4},{5}} => {{1,2,5},{3},{4,6,7}} => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => {{1},{2,3,5},{4,6,7}} => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,7},{2,3,5,6},{4}} => {{1,7},{2,3,5},{4,6}} => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3,5,6},{4}} => {{1,6},{2,3,5},{4,7}} => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4},{5,6}} => {{1,5},{2,3},{4,6,7}} => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,5,7},{4},{6}} => {{1,3},{2,5},{4,6,7}} => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5},{4,6,7}} => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}} => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}} => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => {{1},{2,7},{3,4,5,6}} => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,7},{2,3,4,5},{6}} => {{1,7},{2},{3,4,5,6}} => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}} => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => {{1},{2,6},{3,4,5,7}} => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4,5}} => {{1,7},{2,6},{3,4,5}} => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,7},{3,4,5},{6}} => {{1,6},{2},{3,4,5,7}} => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4,5}} => {{1,2,6},{3,4,5,7}} => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => {{1},{2,5},{3,4,6,7}} => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4,5}} => {{1,7},{2,5},{3,4,6}} => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4,5}} => {{1,6},{2,5},{3,4,7}} => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4,5},{6}} => {{1,5},{2},{3,4,6,7}} => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4,5}} => {{1,2,5},{3,4,6,7}} => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => {{1},{2,4},{3,5,6,7}} => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,7},{2,3,4,6},{5}} => {{1,7},{2,4},{3,5,6}} => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,7},{3,4,6},{5}} => {{1,6},{2,4},{3,5,7}} => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4,6},{5}} => {{1,5},{2,4},{3,6,7}} => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5},{6}} => {{1,4},{2},{3,5,6,7}} => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,6,7},{5}} => {{1,2,4},{3,5,6,7}} => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}} => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}} => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,7},{3,4,5,6}} => {{1,6},{2,3,4,5,7}} => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,7},{4,5,6}} => {{1,5},{2,3,4,6,7}} => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5,6}} => {{1,4},{2,3,5,6,7}} => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,7},{6}} => {{1,3},{2,4,5,6,7}} => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}} => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}} => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}} => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}} => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,8},{7}} => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8},{2}} => {{1,2,3,4,5,6,8},{7}} => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2,3}} => {{1,2,3,4,5,8},{6,7}} => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7},{6,8}} => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}} => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}} => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}} => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}} => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,6,7}} => {{1,7},{2,3,4,5,6,8}} => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6,7}} => {{1,6},{2,3,4,5,7,8}} => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6,7}} => {{1,5},{2,3,4,6,7,8}} => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6,7}} => {{1,4},{2,3,5,6,7,8}} => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8},{7}} => {{1,3},{2,4,5,6,7,8}} => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}} => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of occurrences of the pattern {{1,3},{2}} such that 2 is minimal, 3 is maximal, (1,3) are consecutive in a block.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
Wachs-White
Description
A transformation of set partitions due to Wachs and White.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection $\gamma$.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with $(i,j)$ to the cell in the $i$-th column from the right and the $j$-th row from the top.