- FindStat

Identifier

Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00219: Set partitions —inverse Yip⟶ Set partitions

Images

[1,0] => [(1,2)] => {{1,2}} => {{1,2}}

[1,0,1,0] => [(1,2),(3,4)] => {{1,2},{3,4}} => {{1,2,4},{3}}

[1,1,0,0] => [(1,4),(2,3)] => {{1,4},{2,3}} => {{1,3},{2,4}}

[1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => {{1,2},{3,4},{5,6}} => {{1,2,4},{3,6},{5}}

[1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => {{1,2},{3,6},{4,5}} => {{1,2,5},{3,6},{4}}

[1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => {{1,4},{2,3},{5,6}} => {{1,3,6},{2,4},{5}}

[1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => {{1,6},{2,3},{4,5}} => {{1,3,6},{2,5},{4}}

[1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => {{1,6},{2,5},{3,4}} => {{1,4},{2,5},{3,6}}

[1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,8},{3,6},{5},{7}}

[1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => {{1,2},{3,4},{5,8},{6,7}} => {{1,2,4,8},{3,7},{5},{6}}

[1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => {{1,2},{3,6},{4,5},{7,8}} => {{1,2,5},{3,6},{4,8},{7}}

[1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => {{1,2},{3,8},{4,5},{6,7}} => {{1,2,5},{3,7},{4,8},{6}}

[1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => {{1,2},{3,8},{4,7},{5,6}} => {{1,2,6},{3,7},{4,8},{5}}

[1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => {{1,4},{2,3},{5,6},{7,8}} => {{1,3,6},{2,4,8},{5},{7}}

[1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => {{1,4},{2,3},{5,8},{6,7}} => {{1,3,7},{2,4,8},{5},{6}}

[1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => {{1,6},{2,3},{4,5},{7,8}} => {{1,3,6},{2,5},{4,8},{7}}

[1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => {{1,8},{2,3},{4,5},{6,7}} => {{1,3,7},{2,5},{4,8},{6}}

[1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => {{1,8},{2,3},{4,7},{5,6}} => {{1,3,7},{2,6},{4,8},{5}}

[1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => {{1,6},{2,5},{3,4},{7,8}} => {{1,4,8},{2,5},{3,6},{7}}

[1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => {{1,8},{2,5},{3,4},{6,7}} => {{1,4,8},{2,5},{3,7},{6}}

[1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => {{1,8},{2,7},{3,4},{5,6}} => {{1,4,8},{2,6},{3,7},{5}}

[1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => {{1,8},{2,7},{3,6},{4,5}} => {{1,5},{2,6},{3,7},{4,8}}

[1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,8},{3,6},{5,10},{7},{9}}

[1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => {{1,2},{3,4},{5,6},{7,10},{8,9}} => {{1,2,4,9},{3,6},{5,10},{7},{8}}

[1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => {{1,2},{3,4},{5,8},{6,7},{9,10}} => {{1,2,4,8},{3,7},{5,10},{6},{9}}

[1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => {{1,2},{3,4},{5,10},{6,7},{8,9}} => {{1,2,4,9},{3,7},{5,10},{6},{8}}

[1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => {{1,2},{3,4},{5,10},{6,9},{7,8}} => {{1,2,4,9},{3,8},{5,10},{6},{7}}

[1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => {{1,2},{3,6},{4,5},{7,8},{9,10}} => {{1,2,5,10},{3,6},{4,8},{7},{9}}

[1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => {{1,2},{3,6},{4,5},{7,10},{8,9}} => {{1,2,5,10},{3,6},{4,9},{7},{8}}

[1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => {{1,2},{3,8},{4,5},{6,7},{9,10}} => {{1,2,5,10},{3,7},{4,8},{6},{9}}

[1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => {{1,2},{3,10},{4,5},{6,7},{8,9}} => {{1,2,5,10},{3,7},{4,9},{6},{8}}

[1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => {{1,2},{3,10},{4,5},{6,9},{7,8}} => {{1,2,5,10},{3,8},{4,9},{6},{7}}

[1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => {{1,2},{3,8},{4,7},{5,6},{9,10}} => {{1,2,6},{3,7},{4,8},{5,10},{9}}

[1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => {{1,2},{3,10},{4,7},{5,6},{8,9}} => {{1,2,6},{3,7},{4,9},{5,10},{8}}

[1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => {{1,2},{3,10},{4,9},{5,6},{7,8}} => {{1,2,6},{3,8},{4,9},{5,10},{7}}

[1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => {{1,2},{3,10},{4,9},{5,8},{6,7}} => {{1,2,7},{3,8},{4,9},{5,10},{6}}

[1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => {{1,4},{2,3},{5,6},{7,8},{9,10}} => {{1,3,6},{2,4,8},{5,10},{7},{9}}

[1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => {{1,4},{2,3},{5,6},{7,10},{8,9}} => {{1,3,6},{2,4,9},{5,10},{7},{8}}

[1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => {{1,4},{2,3},{5,8},{6,7},{9,10}} => {{1,3,7},{2,4,8},{5,10},{6},{9}}

[1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => {{1,4},{2,3},{5,10},{6,7},{8,9}} => {{1,3,7},{2,4,9},{5,10},{6},{8}}

[1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => {{1,4},{2,3},{5,10},{6,9},{7,8}} => {{1,3,8},{2,4,9},{5,10},{6},{7}}

[1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => {{1,6},{2,3},{4,5},{7,8},{9,10}} => {{1,3,6},{2,5,10},{4,8},{7},{9}}

[1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => {{1,6},{2,3},{4,5},{7,10},{8,9}} => {{1,3,6},{2,5,10},{4,9},{7},{8}}

[1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => {{1,8},{2,3},{4,5},{6,7},{9,10}} => {{1,3,7},{2,5,10},{4,8},{6},{9}}

[1,1,0,1,0,1,0,1,0,0] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => {{1,10},{2,3},{4,5},{6,7},{8,9}} => {{1,3,7},{2,5,10},{4,9},{6},{8}}

[1,1,0,1,0,1,1,0,0,0] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => {{1,10},{2,3},{4,5},{6,9},{7,8}} => {{1,3,8},{2,5,10},{4,9},{6},{7}}

[1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => {{1,8},{2,3},{4,7},{5,6},{9,10}} => {{1,3,7},{2,6},{4,8},{5,10},{9}}

[1,1,0,1,1,0,0,1,0,0] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => {{1,10},{2,3},{4,7},{5,6},{8,9}} => {{1,3,7},{2,6},{4,9},{5,10},{8}}

[1,1,0,1,1,0,1,0,0,0] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => {{1,10},{2,3},{4,9},{5,6},{7,8}} => {{1,3,8},{2,6},{4,9},{5,10},{7}}

[1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => {{1,10},{2,3},{4,9},{5,8},{6,7}} => {{1,3,8},{2,7},{4,9},{5,10},{6}}

[1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => {{1,6},{2,5},{3,4},{7,8},{9,10}} => {{1,4,8},{2,5,10},{3,6},{7},{9}}

[1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => {{1,6},{2,5},{3,4},{7,10},{8,9}} => {{1,4,9},{2,5,10},{3,6},{7},{8}}

[1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => {{1,8},{2,5},{3,4},{6,7},{9,10}} => {{1,4,8},{2,5,10},{3,7},{6},{9}}

[1,1,1,0,0,1,0,1,0,0] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => {{1,10},{2,5},{3,4},{6,7},{8,9}} => {{1,4,9},{2,5,10},{3,7},{6},{8}}

[1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => {{1,10},{2,5},{3,4},{6,9},{7,8}} => {{1,4,9},{2,5,10},{3,8},{6},{7}}

[1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => {{1,8},{2,7},{3,4},{5,6},{9,10}} => {{1,4,8},{2,6},{3,7},{5,10},{9}}

[1,1,1,0,1,0,0,1,0,0] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => {{1,10},{2,7},{3,4},{5,6},{8,9}} => {{1,4,9},{2,6},{3,7},{5,10},{8}}

[1,1,1,0,1,0,1,0,0,0] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => {{1,10},{2,9},{3,4},{5,6},{7,8}} => {{1,4,9},{2,6},{3,8},{5,10},{7}}

[1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => {{1,10},{2,9},{3,4},{5,8},{6,7}} => {{1,4,9},{2,7},{3,8},{5,10},{6}}

[1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => {{1,8},{2,7},{3,6},{4,5},{9,10}} => {{1,5,10},{2,6},{3,7},{4,8},{9}}

[1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => {{1,10},{2,7},{3,6},{4,5},{8,9}} => {{1,5,10},{2,6},{3,7},{4,9},{8}}

[1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => {{1,10},{2,9},{3,6},{4,5},{7,8}} => {{1,5,10},{2,6},{3,8},{4,9},{7}}

[1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => {{1,10},{2,9},{3,8},{4,5},{6,7}} => {{1,5,10},{2,7},{3,8},{4,9},{6}}

[1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => {{1,10},{2,9},{3,8},{4,7},{5,6}} => {{1,6},{2,7},{3,8},{4,9},{5,10}}

[1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,8},{3,6,12},{5,10},{7},{9},{11}}

[1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}} => {{1,2,4,8},{3,6,12},{5,11},{7},{9},{10}}

[1,0,1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}} => {{1,2,4,9},{3,6,12},{5,10},{7},{8},{11}}

[1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}} => {{1,2,4,9},{3,6,12},{5,11},{7},{8},{10}}

[1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}} => {{1,2,4,10},{3,6,12},{5,11},{7},{8},{9}}

[1,0,1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}} => {{1,2,4,8},{3,7},{5,10},{6,12},{9},{11}}

[1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}} => {{1,2,4,8},{3,7},{5,11},{6,12},{9},{10}}

[1,0,1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}} => {{1,2,4,9},{3,7},{5,10},{6,12},{8},{11}}

[1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}} => {{1,2,4,9},{3,7},{5,11},{6,12},{8},{10}}

[1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}} => {{1,2,4,10},{3,7},{5,11},{6,12},{8},{9}}

[1,0,1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}} => {{1,2,4,9},{3,8},{5,10},{6,12},{7},{11}}

[1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}} => {{1,2,4,9},{3,8},{5,11},{6,12},{7},{10}}

[1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}} => {{1,2,4,10},{3,8},{5,11},{6,12},{7},{9}}

[1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}} => {{1,2,4,10},{3,9},{5,11},{6,12},{7},{8}}

[1,0,1,1,0,0,1,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}} => {{1,2,5,10},{3,6,12},{4,8},{7},{9},{11}}

[1,0,1,1,0,0,1,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}} => {{1,2,5,11},{3,6,12},{4,8},{7},{9},{10}}

[1,0,1,1,0,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}} => {{1,2,5,10},{3,6,12},{4,9},{7},{8},{11}}

[1,0,1,1,0,0,1,1,0,1,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}} => {{1,2,5,11},{3,6,12},{4,9},{7},{8},{10}}

[1,0,1,1,0,0,1,1,1,0,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}} => {{1,2,5,11},{3,6,12},{4,10},{7},{8},{9}}

[1,0,1,1,0,1,0,0,1,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}} => {{1,2,5,10},{3,7},{4,8},{6,12},{9},{11}}

[1,0,1,1,0,1,0,0,1,1,0,0] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}} => {{1,2,5,11},{3,7},{4,8},{6,12},{9},{10}}

[1,0,1,1,0,1,0,1,0,0,1,0] => [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}} => {{1,2,5,10},{3,7},{4,9},{6,12},{8},{11}}

[1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}} => {{1,2,5,11},{3,7},{4,9},{6,12},{8},{10}}

[1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}} => {{1,2,5,11},{3,7},{4,10},{6,12},{8},{9}}

[1,0,1,1,0,1,1,0,0,0,1,0] => [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}} => {{1,2,5,10},{3,8},{4,9},{6,12},{7},{11}}

[1,0,1,1,0,1,1,0,0,1,0,0] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}} => {{1,2,5,11},{3,8},{4,9},{6,12},{7},{10}}

[1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}} => {{1,2,5,11},{3,8},{4,10},{6,12},{7},{9}}

[1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}} => {{1,2,5,11},{3,9},{4,10},{6,12},{7},{8}}

[1,0,1,1,1,0,0,0,1,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}} => {{1,2,6,12},{3,7},{4,8},{5,10},{9},{11}}

[1,0,1,1,1,0,0,0,1,1,0,0] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}} => {{1,2,6,12},{3,7},{4,8},{5,11},{9},{10}}

[1,0,1,1,1,0,0,1,0,0,1,0] => [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}} => {{1,2,6,12},{3,7},{4,9},{5,10},{8},{11}}

[1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}} => {{1,2,6,12},{3,7},{4,9},{5,11},{8},{10}}

[1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}} => {{1,2,6,12},{3,7},{4,10},{5,11},{8},{9}}

[1,0,1,1,1,0,1,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}} => {{1,2,6,12},{3,8},{4,9},{5,10},{7},{11}}

[1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}} => {{1,2,6,12},{3,8},{4,9},{5,11},{7},{10}}

[1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}} => {{1,2,6,12},{3,8},{4,10},{5,11},{7},{9}}

[1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}} => {{1,2,6,12},{3,9},{4,10},{5,11},{7},{8}}

>>> Load all 454 entries. <<<

[1,0,1,1,1,1,0,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}} => {{1,2,7},{3,8},{4,9},{5,10},{6,12},{11}}

[1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}} => {{1,2,7},{3,8},{4,9},{5,11},{6,12},{10}}

[1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}} => {{1,2,7},{3,8},{4,10},{5,11},{6,12},{9}}

[1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}} => {{1,2,7},{3,9},{4,10},{5,11},{6,12},{8}}

[1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}} => {{1,2,8},{3,9},{4,10},{5,11},{6,12},{7}}

[1,1,0,0,1,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}} => {{1,3,6,12},{2,4,8},{5,10},{7},{9},{11}}

[1,1,0,0,1,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}} => {{1,3,6,12},{2,4,8},{5,11},{7},{9},{10}}

[1,1,0,0,1,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}} => {{1,3,6,12},{2,4,9},{5,10},{7},{8},{11}}

[1,1,0,0,1,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}} => {{1,3,6,12},{2,4,9},{5,11},{7},{8},{10}}

[1,1,0,0,1,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}} => {{1,3,6,12},{2,4,10},{5,11},{7},{8},{9}}

[1,1,0,0,1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}} => {{1,3,7},{2,4,8},{5,10},{6,12},{9},{11}}

[1,1,0,0,1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}} => {{1,3,7},{2,4,8},{5,11},{6,12},{9},{10}}

[1,1,0,0,1,1,0,1,0,0,1,0] => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}} => {{1,3,7},{2,4,9},{5,10},{6,12},{8},{11}}

[1,1,0,0,1,1,0,1,0,1,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}} => {{1,3,7},{2,4,9},{5,11},{6,12},{8},{10}}

[1,1,0,0,1,1,0,1,1,0,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}} => {{1,3,7},{2,4,10},{5,11},{6,12},{8},{9}}

[1,1,0,0,1,1,1,0,0,0,1,0] => [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}} => {{1,3,8},{2,4,9},{5,10},{6,12},{7},{11}}

[1,1,0,0,1,1,1,0,0,1,0,0] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}} => {{1,3,8},{2,4,9},{5,11},{6,12},{7},{10}}

[1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}} => {{1,3,8},{2,4,10},{5,11},{6,12},{7},{9}}

[1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}} => {{1,3,9},{2,4,10},{5,11},{6,12},{7},{8}}

[1,1,0,1,0,0,1,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}} => {{1,3,6,12},{2,5,10},{4,8},{7},{9},{11}}

[1,1,0,1,0,0,1,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}} => {{1,3,6,12},{2,5,11},{4,8},{7},{9},{10}}

[1,1,0,1,0,0,1,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}} => {{1,3,6,12},{2,5,10},{4,9},{7},{8},{11}}

[1,1,0,1,0,0,1,1,0,1,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}} => {{1,3,6,12},{2,5,11},{4,9},{7},{8},{10}}

[1,1,0,1,0,0,1,1,1,0,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}} => {{1,3,6,12},{2,5,11},{4,10},{7},{8},{9}}

[1,1,0,1,0,1,0,0,1,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}} => {{1,3,7},{2,5,10},{4,8},{6,12},{9},{11}}

[1,1,0,1,0,1,0,0,1,1,0,0] => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}} => {{1,3,7},{2,5,11},{4,8},{6,12},{9},{10}}

[1,1,0,1,0,1,0,1,0,0,1,0] => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}} => {{1,3,7},{2,5,10},{4,9},{6,12},{8},{11}}

[1,1,0,1,0,1,0,1,0,1,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}} => {{1,3,7},{2,5,11},{4,9},{6,12},{8},{10}}

[1,1,0,1,0,1,0,1,1,0,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}} => {{1,3,7},{2,5,11},{4,10},{6,12},{8},{9}}

[1,1,0,1,0,1,1,0,0,0,1,0] => [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}} => {{1,3,8},{2,5,10},{4,9},{6,12},{7},{11}}

[1,1,0,1,0,1,1,0,0,1,0,0] => [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}} => {{1,3,8},{2,5,11},{4,9},{6,12},{7},{10}}

[1,1,0,1,0,1,1,0,1,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}} => {{1,3,8},{2,5,11},{4,10},{6,12},{7},{9}}

[1,1,0,1,0,1,1,1,0,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}} => {{1,3,9},{2,5,11},{4,10},{6,12},{7},{8}}

[1,1,0,1,1,0,0,0,1,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}} => {{1,3,7},{2,6,12},{4,8},{5,10},{9},{11}}

[1,1,0,1,1,0,0,0,1,1,0,0] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}} => {{1,3,7},{2,6,12},{4,8},{5,11},{9},{10}}

[1,1,0,1,1,0,0,1,0,0,1,0] => [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}} => {{1,3,7},{2,6,12},{4,9},{5,10},{8},{11}}

[1,1,0,1,1,0,0,1,0,1,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}} => {{1,3,7},{2,6,12},{4,9},{5,11},{8},{10}}

[1,1,0,1,1,0,0,1,1,0,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}} => {{1,3,7},{2,6,12},{4,10},{5,11},{8},{9}}

[1,1,0,1,1,0,1,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}} => {{1,3,8},{2,6,12},{4,9},{5,10},{7},{11}}

[1,1,0,1,1,0,1,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}} => {{1,3,8},{2,6,12},{4,9},{5,11},{7},{10}}

[1,1,0,1,1,0,1,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}} => {{1,3,8},{2,6,12},{4,10},{5,11},{7},{9}}

[1,1,0,1,1,0,1,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}} => {{1,3,9},{2,6,12},{4,10},{5,11},{7},{8}}

[1,1,0,1,1,1,0,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}} => {{1,3,8},{2,7},{4,9},{5,10},{6,12},{11}}

[1,1,0,1,1,1,0,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}} => {{1,3,8},{2,7},{4,9},{5,11},{6,12},{10}}

[1,1,0,1,1,1,0,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}} => {{1,3,8},{2,7},{4,10},{5,11},{6,12},{9}}

[1,1,0,1,1,1,0,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}} => {{1,3,9},{2,7},{4,10},{5,11},{6,12},{8}}

[1,1,0,1,1,1,1,0,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}} => {{1,3,9},{2,8},{4,10},{5,11},{6,12},{7}}

[1,1,1,0,0,0,1,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}} => {{1,4,8},{2,5,10},{3,6,12},{7},{9},{11}}

[1,1,1,0,0,0,1,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}} => {{1,4,8},{2,5,11},{3,6,12},{7},{9},{10}}

[1,1,1,0,0,0,1,1,0,0,1,0] => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}} => {{1,4,9},{2,5,10},{3,6,12},{7},{8},{11}}

[1,1,1,0,0,0,1,1,0,1,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}} => {{1,4,9},{2,5,11},{3,6,12},{7},{8},{10}}

[1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}} => {{1,4,10},{2,5,11},{3,6,12},{7},{8},{9}}

[1,1,1,0,0,1,0,0,1,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}} => {{1,4,8},{2,5,10},{3,7},{6,12},{9},{11}}

[1,1,1,0,0,1,0,0,1,1,0,0] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}} => {{1,4,8},{2,5,11},{3,7},{6,12},{9},{10}}

[1,1,1,0,0,1,0,1,0,0,1,0] => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}} => {{1,4,9},{2,5,10},{3,7},{6,12},{8},{11}}

[1,1,1,0,0,1,0,1,0,1,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}} => {{1,4,9},{2,5,11},{3,7},{6,12},{8},{10}}

[1,1,1,0,0,1,0,1,1,0,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}} => {{1,4,10},{2,5,11},{3,7},{6,12},{8},{9}}

[1,1,1,0,0,1,1,0,0,0,1,0] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}} => {{1,4,9},{2,5,10},{3,8},{6,12},{7},{11}}

[1,1,1,0,0,1,1,0,0,1,0,0] => [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}} => {{1,4,9},{2,5,11},{3,8},{6,12},{7},{10}}

[1,1,1,0,0,1,1,0,1,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}} => {{1,4,10},{2,5,11},{3,8},{6,12},{7},{9}}

[1,1,1,0,0,1,1,1,0,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}} => {{1,4,10},{2,5,11},{3,9},{6,12},{7},{8}}

[1,1,1,0,1,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}} => {{1,4,8},{2,6,12},{3,7},{5,10},{9},{11}}

[1,1,1,0,1,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}} => {{1,4,8},{2,6,12},{3,7},{5,11},{9},{10}}

[1,1,1,0,1,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}} => {{1,4,9},{2,6,12},{3,7},{5,10},{8},{11}}

[1,1,1,0,1,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}} => {{1,4,9},{2,6,12},{3,7},{5,11},{8},{10}}

[1,1,1,0,1,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}} => {{1,4,10},{2,6,12},{3,7},{5,11},{8},{9}}

[1,1,1,0,1,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}} => {{1,4,9},{2,6,12},{3,8},{5,10},{7},{11}}

[1,1,1,0,1,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}} => {{1,4,9},{2,6,12},{3,8},{5,11},{7},{10}}

[1,1,1,0,1,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}} => {{1,4,10},{2,6,12},{3,8},{5,11},{7},{9}}

[1,1,1,0,1,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}} => {{1,4,10},{2,6,12},{3,9},{5,11},{7},{8}}

[1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}} => {{1,4,9},{2,7},{3,8},{5,10},{6,12},{11}}

[1,1,1,0,1,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}} => {{1,4,9},{2,7},{3,8},{5,11},{6,12},{10}}

[1,1,1,0,1,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}} => {{1,4,10},{2,7},{3,8},{5,11},{6,12},{9}}

[1,1,1,0,1,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}} => {{1,4,10},{2,7},{3,9},{5,11},{6,12},{8}}

[1,1,1,0,1,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}} => {{1,4,10},{2,8},{3,9},{5,11},{6,12},{7}}

[1,1,1,1,0,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}} => {{1,5,10},{2,6,12},{3,7},{4,8},{9},{11}}

[1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}} => {{1,5,11},{2,6,12},{3,7},{4,8},{9},{10}}

[1,1,1,1,0,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}} => {{1,5,10},{2,6,12},{3,7},{4,9},{8},{11}}

[1,1,1,1,0,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}} => {{1,5,11},{2,6,12},{3,7},{4,9},{8},{10}}

[1,1,1,1,0,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}} => {{1,5,11},{2,6,12},{3,7},{4,10},{8},{9}}

[1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}} => {{1,5,10},{2,6,12},{3,8},{4,9},{7},{11}}

[1,1,1,1,0,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}} => {{1,5,11},{2,6,12},{3,8},{4,9},{7},{10}}

[1,1,1,1,0,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}} => {{1,5,11},{2,6,12},{3,8},{4,10},{7},{9}}

[1,1,1,1,0,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}} => {{1,5,11},{2,6,12},{3,9},{4,10},{7},{8}}

[1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}} => {{1,5,10},{2,7},{3,8},{4,9},{6,12},{11}}

[1,1,1,1,0,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}} => {{1,5,11},{2,7},{3,8},{4,9},{6,12},{10}}

[1,1,1,1,0,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}} => {{1,5,11},{2,7},{3,8},{4,10},{6,12},{9}}

[1,1,1,1,0,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}} => {{1,5,11},{2,7},{3,9},{4,10},{6,12},{8}}

[1,1,1,1,0,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}} => {{1,5,11},{2,8},{3,9},{4,10},{6,12},{7}}

[1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}} => {{1,6,12},{2,7},{3,8},{4,9},{5,10},{11}}

[1,1,1,1,1,0,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}} => {{1,6,12},{2,7},{3,8},{4,9},{5,11},{10}}

[1,1,1,1,1,0,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}} => {{1,6,12},{2,7},{3,8},{4,10},{5,11},{9}}

[1,1,1,1,1,0,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}} => {{1,6,12},{2,7},{3,9},{4,10},{5,11},{8}}

[1,1,1,1,1,0,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}} => {{1,6,12},{2,8},{3,9},{4,10},{5,11},{7}}

[1,1,1,1,1,1,0,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}} => {{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,14}} => {{1,2,4,8},{3,6,12},{5,10},{7,14},{9},{11},{13}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,14),(12,13)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,14},{12,13}} => {{1,2,4,8},{3,6,13},{5,10},{7,14},{9},{11},{12}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,14),(10,11),(12,13)] => {{1,2},{3,4},{5,6},{7,8},{9,14},{10,11},{12,13}} => {{1,2,4,8},{3,6,13},{5,11},{7,14},{9},{10},{12}}

[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,14),(10,13),(11,12)] => {{1,2},{3,4},{5,6},{7,8},{9,14},{10,13},{11,12}} => {{1,2,4,8},{3,6,13},{5,12},{7,14},{9},{10},{11}}

[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,14),(8,9),(10,11),(12,13)] => {{1,2},{3,4},{5,6},{7,14},{8,9},{10,11},{12,13}} => {{1,2,4,9},{3,6,13},{5,11},{7,14},{8},{10},{12}}

[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,6),(7,14),(8,11),(9,10),(12,13)] => {{1,2},{3,4},{5,6},{7,14},{8,11},{9,10},{12,13}} => {{1,2,4,10},{3,6,13},{5,11},{7,14},{8},{9},{12}}

[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,6),(7,14),(8,13),(9,10),(11,12)] => {{1,2},{3,4},{5,6},{7,14},{8,13},{9,10},{11,12}} => {{1,2,4,10},{3,6,13},{5,12},{7,14},{8},{9},{11}}

[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,6),(7,14),(8,13),(9,12),(10,11)] => {{1,2},{3,4},{5,6},{7,14},{8,13},{9,12},{10,11}} => {{1,2,4,11},{3,6,13},{5,12},{7,14},{8},{9},{10}}

[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,14),(6,7),(8,9),(10,11),(12,13)] => {{1,2},{3,4},{5,14},{6,7},{8,9},{10,11},{12,13}} => {{1,2,4,9},{3,7,14},{5,11},{6,13},{8},{10},{12}}

[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,4),(5,14),(6,9),(7,8),(10,11),(12,13)] => {{1,2},{3,4},{5,14},{6,9},{7,8},{10,11},{12,13}} => {{1,2,4,9},{3,8},{5,11},{6,13},{7,14},{10},{12}}

[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,4),(5,14),(6,11),(7,8),(9,10),(12,13)] => {{1,2},{3,4},{5,14},{6,11},{7,8},{9,10},{12,13}} => {{1,2,4,10},{3,8},{5,11},{6,13},{7,14},{9},{12}}

[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,4),(5,14),(6,13),(7,8),(9,10),(11,12)] => {{1,2},{3,4},{5,14},{6,13},{7,8},{9,10},{11,12}} => {{1,2,4,10},{3,8},{5,12},{6,13},{7,14},{9},{11}}

[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,4),(5,14),(6,13),(7,8),(9,12),(10,11)] => {{1,2},{3,4},{5,14},{6,13},{7,8},{9,12},{10,11}} => {{1,2,4,11},{3,8},{5,12},{6,13},{7,14},{9},{10}}

[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,4),(5,14),(6,11),(7,10),(8,9),(12,13)] => {{1,2},{3,4},{5,14},{6,11},{7,10},{8,9},{12,13}} => {{1,2,4,10},{3,9},{5,11},{6,13},{7,14},{8},{12}}

[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,4),(5,14),(6,13),(7,12),(8,9),(10,11)] => {{1,2},{3,4},{5,14},{6,13},{7,12},{8,9},{10,11}} => {{1,2,4,11},{3,9},{5,12},{6,13},{7,14},{8},{10}}

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,14),(4,5),(6,7),(8,9),(10,11),(12,13)] => {{1,2},{3,14},{4,5},{6,7},{8,9},{10,11},{12,13}} => {{1,2,5,11},{3,7,14},{4,9},{6,13},{8},{10},{12}}

[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => {{1,2},{3,14},{4,5},{6,13},{7,12},{8,11},{9,10}} => {{1,2,5,12},{3,10},{4,11},{6,13},{7,14},{8},{9}}

[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [(1,2),(3,14),(4,7),(5,6),(8,9),(10,11),(12,13)] => {{1,2},{3,14},{4,7},{5,6},{8,9},{10,11},{12,13}} => {{1,2,6,13},{3,7,14},{4,9},{5,11},{8},{10},{12}}

[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [(1,2),(3,14),(4,9),(5,6),(7,8),(10,11),(12,13)] => {{1,2},{3,14},{4,9},{5,6},{7,8},{10,11},{12,13}} => {{1,2,6,13},{3,8},{4,9},{5,11},{7,14},{10},{12}}

[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,6),(7,8),(9,10),(12,13)] => {{1,2},{3,14},{4,11},{5,6},{7,8},{9,10},{12,13}} => {{1,2,6,13},{3,8},{4,10},{5,11},{7,14},{9},{12}}

[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,6),(7,10),(8,9),(12,13)] => {{1,2},{3,14},{4,11},{5,6},{7,10},{8,9},{12,13}} => {{1,2,6,13},{3,9},{4,10},{5,11},{7,14},{8},{12}}

[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)] => {{1,2},{3,14},{4,13},{5,6},{7,12},{8,9},{10,11}} => {{1,2,6,13},{3,9},{4,11},{5,12},{7,14},{8},{10}}

[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => {{1,2},{3,14},{4,13},{5,6},{7,12},{8,11},{9,10}} => {{1,2,6,13},{3,10},{4,11},{5,12},{7,14},{8},{9}}

[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [(1,2),(3,14),(4,9),(5,8),(6,7),(10,11),(12,13)] => {{1,2},{3,14},{4,9},{5,8},{6,7},{10,11},{12,13}} => {{1,2,7,14},{3,8},{4,9},{5,11},{6,13},{10},{12}}

[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)] => {{1,2},{3,14},{4,13},{5,8},{6,7},{9,12},{10,11}} => {{1,2,7,14},{3,8},{4,11},{5,12},{6,13},{9},{10}}

[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,10),(6,7),(8,9),(12,13)] => {{1,2},{3,14},{4,11},{5,10},{6,7},{8,9},{12,13}} => {{1,2,7,14},{3,9},{4,10},{5,11},{6,13},{8},{12}}

[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)] => {{1,2},{3,14},{4,13},{5,10},{6,7},{8,9},{11,12}} => {{1,2,7,14},{3,9},{4,10},{5,12},{6,13},{8},{11}}

[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => {{1,2},{3,14},{4,13},{5,12},{6,7},{8,9},{10,11}} => {{1,2,7,14},{3,9},{4,11},{5,12},{6,13},{8},{10}}

[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => {{1,2},{3,14},{4,13},{5,12},{6,7},{8,11},{9,10}} => {{1,2,7,14},{3,10},{4,11},{5,12},{6,13},{8},{9}}

[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)] => {{1,2},{3,14},{4,11},{5,10},{6,9},{7,8},{12,13}} => {{1,2,8},{3,9},{4,10},{5,11},{6,13},{7,14},{12}}

[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)] => {{1,2},{3,14},{4,13},{5,10},{6,9},{7,8},{11,12}} => {{1,2,8},{3,9},{4,10},{5,12},{6,13},{7,14},{11}}

[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => {{1,2},{3,14},{4,13},{5,12},{6,9},{7,8},{10,11}} => {{1,2,8},{3,9},{4,11},{5,12},{6,13},{7,14},{10}}

[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => {{1,2},{3,14},{4,13},{5,12},{6,11},{7,8},{9,10}} => {{1,2,8},{3,10},{4,11},{5,12},{6,13},{7,14},{9}}

[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => {{1,2},{3,14},{4,13},{5,12},{6,11},{7,10},{8,9}} => {{1,2,9},{3,10},{4,11},{5,12},{6,13},{7,14},{8}}

[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => {{1,4},{2,3},{5,14},{6,13},{7,12},{8,11},{9,10}} => {{1,3,10},{2,4,11},{5,12},{6,13},{7,14},{8},{9}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)] => {{1,14},{2,3},{4,5},{6,7},{8,9},{10,11},{12,13}} => {{1,3,7,14},{2,5,11},{4,9},{6,13},{8},{10},{12}}

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,9),(10,13),(11,12)] => {{1,14},{2,3},{4,5},{6,7},{8,9},{10,13},{11,12}} => {{1,3,7,14},{2,5,12},{4,9},{6,13},{8},{10},{11}}

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,11),(9,10),(12,13)] => {{1,14},{2,3},{4,5},{6,7},{8,11},{9,10},{12,13}} => {{1,3,7,14},{2,5,11},{4,10},{6,13},{8},{9},{12}}

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,13),(9,10),(11,12)] => {{1,14},{2,3},{4,5},{6,7},{8,13},{9,10},{11,12}} => {{1,3,7,14},{2,5,12},{4,10},{6,13},{8},{9},{11}}

[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,13),(9,12),(10,11)] => {{1,14},{2,3},{4,5},{6,7},{8,13},{9,12},{10,11}} => {{1,3,7,14},{2,5,12},{4,11},{6,13},{8},{9},{10}}

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [(1,14),(2,3),(4,5),(6,9),(7,8),(10,11),(12,13)] => {{1,14},{2,3},{4,5},{6,9},{7,8},{10,11},{12,13}} => {{1,3,8},{2,5,11},{4,9},{6,13},{7,14},{10},{12}}

[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [(1,14),(2,3),(4,5),(6,9),(7,8),(10,13),(11,12)] => {{1,14},{2,3},{4,5},{6,9},{7,8},{10,13},{11,12}} => {{1,3,8},{2,5,12},{4,9},{6,13},{7,14},{10},{11}}

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [(1,14),(2,3),(4,5),(6,11),(7,8),(9,10),(12,13)] => {{1,14},{2,3},{4,5},{6,11},{7,8},{9,10},{12,13}} => {{1,3,8},{2,5,11},{4,10},{6,13},{7,14},{9},{12}}

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,8),(9,10),(11,12)] => {{1,14},{2,3},{4,5},{6,13},{7,8},{9,10},{11,12}} => {{1,3,8},{2,5,12},{4,10},{6,13},{7,14},{9},{11}}

[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,8),(9,12),(10,11)] => {{1,14},{2,3},{4,5},{6,13},{7,8},{9,12},{10,11}} => {{1,3,8},{2,5,12},{4,11},{6,13},{7,14},{9},{10}}

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [(1,14),(2,3),(4,5),(6,11),(7,10),(8,9),(12,13)] => {{1,14},{2,3},{4,5},{6,11},{7,10},{8,9},{12,13}} => {{1,3,9},{2,5,11},{4,10},{6,13},{7,14},{8},{12}}

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,10),(8,9),(11,12)] => {{1,14},{2,3},{4,5},{6,13},{7,10},{8,9},{11,12}} => {{1,3,9},{2,5,12},{4,10},{6,13},{7,14},{8},{11}}

[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,12),(8,9),(10,11)] => {{1,14},{2,3},{4,5},{6,13},{7,12},{8,9},{10,11}} => {{1,3,9},{2,5,12},{4,11},{6,13},{7,14},{8},{10}}

[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,12),(8,11),(9,10)] => {{1,14},{2,3},{4,5},{6,13},{7,12},{8,11},{9,10}} => {{1,3,10},{2,5,12},{4,11},{6,13},{7,14},{8},{9}}

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,9),(10,11),(12,13)] => {{1,14},{2,3},{4,7},{5,6},{8,9},{10,11},{12,13}} => {{1,3,7,14},{2,6,13},{4,9},{5,11},{8},{10},{12}}

[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,9),(10,13),(11,12)] => {{1,14},{2,3},{4,7},{5,6},{8,9},{10,13},{11,12}} => {{1,3,7,14},{2,6,13},{4,9},{5,12},{8},{10},{11}}

[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,11),(9,10),(12,13)] => {{1,14},{2,3},{4,7},{5,6},{8,11},{9,10},{12,13}} => {{1,3,7,14},{2,6,13},{4,10},{5,11},{8},{9},{12}}

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,13),(9,10),(11,12)] => {{1,14},{2,3},{4,7},{5,6},{8,13},{9,10},{11,12}} => {{1,3,7,14},{2,6,13},{4,10},{5,12},{8},{9},{11}}

[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,13),(9,12),(10,11)] => {{1,14},{2,3},{4,7},{5,6},{8,13},{9,12},{10,11}} => {{1,3,7,14},{2,6,13},{4,11},{5,12},{8},{9},{10}}

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [(1,14),(2,3),(4,9),(5,6),(7,8),(10,11),(12,13)] => {{1,14},{2,3},{4,9},{5,6},{7,8},{10,11},{12,13}} => {{1,3,8},{2,6,13},{4,9},{5,11},{7,14},{10},{12}}

[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [(1,14),(2,3),(4,9),(5,6),(7,8),(10,13),(11,12)] => {{1,14},{2,3},{4,9},{5,6},{7,8},{10,13},{11,12}} => {{1,3,8},{2,6,13},{4,9},{5,12},{7,14},{10},{11}}

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,6),(7,8),(9,10),(12,13)] => {{1,14},{2,3},{4,11},{5,6},{7,8},{9,10},{12,13}} => {{1,3,8},{2,6,13},{4,10},{5,11},{7,14},{9},{12}}

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,8),(9,10),(11,12)] => {{1,14},{2,3},{4,13},{5,6},{7,8},{9,10},{11,12}} => {{1,3,8},{2,6,13},{4,10},{5,12},{7,14},{9},{11}}

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,8),(9,12),(10,11)] => {{1,14},{2,3},{4,13},{5,6},{7,8},{9,12},{10,11}} => {{1,3,8},{2,6,13},{4,11},{5,12},{7,14},{9},{10}}

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,6),(7,10),(8,9),(12,13)] => {{1,14},{2,3},{4,11},{5,6},{7,10},{8,9},{12,13}} => {{1,3,9},{2,6,13},{4,10},{5,11},{7,14},{8},{12}}

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,10),(8,9),(11,12)] => {{1,14},{2,3},{4,13},{5,6},{7,10},{8,9},{11,12}} => {{1,3,9},{2,6,13},{4,10},{5,12},{7,14},{8},{11}}

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,12),(8,9),(10,11)] => {{1,14},{2,3},{4,13},{5,6},{7,12},{8,9},{10,11}} => {{1,3,9},{2,6,13},{4,11},{5,12},{7,14},{8},{10}}

[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,12),(8,11),(9,10)] => {{1,14},{2,3},{4,13},{5,6},{7,12},{8,11},{9,10}} => {{1,3,10},{2,6,13},{4,11},{5,12},{7,14},{8},{9}}

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [(1,14),(2,3),(4,9),(5,8),(6,7),(10,11),(12,13)] => {{1,14},{2,3},{4,9},{5,8},{6,7},{10,11},{12,13}} => {{1,3,8},{2,7,14},{4,9},{5,11},{6,13},{10},{12}}

[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [(1,14),(2,3),(4,9),(5,8),(6,7),(10,13),(11,12)] => {{1,14},{2,3},{4,9},{5,8},{6,7},{10,13},{11,12}} => {{1,3,8},{2,7,14},{4,9},{5,12},{6,13},{10},{11}}

[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,8),(6,7),(9,10),(12,13)] => {{1,14},{2,3},{4,11},{5,8},{6,7},{9,10},{12,13}} => {{1,3,8},{2,7,14},{4,10},{5,11},{6,13},{9},{12}}

[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,8),(6,7),(9,10),(11,12)] => {{1,14},{2,3},{4,13},{5,8},{6,7},{9,10},{11,12}} => {{1,3,8},{2,7,14},{4,10},{5,12},{6,13},{9},{11}}

[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,8),(6,7),(9,12),(10,11)] => {{1,14},{2,3},{4,13},{5,8},{6,7},{9,12},{10,11}} => {{1,3,8},{2,7,14},{4,11},{5,12},{6,13},{9},{10}}

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,10),(6,7),(8,9),(12,13)] => {{1,14},{2,3},{4,11},{5,10},{6,7},{8,9},{12,13}} => {{1,3,9},{2,7,14},{4,10},{5,11},{6,13},{8},{12}}

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,10),(6,7),(8,9),(11,12)] => {{1,14},{2,3},{4,13},{5,10},{6,7},{8,9},{11,12}} => {{1,3,9},{2,7,14},{4,10},{5,12},{6,13},{8},{11}}

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,7),(8,9),(10,11)] => {{1,14},{2,3},{4,13},{5,12},{6,7},{8,9},{10,11}} => {{1,3,9},{2,7,14},{4,11},{5,12},{6,13},{8},{10}}

[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,7),(8,11),(9,10)] => {{1,14},{2,3},{4,13},{5,12},{6,7},{8,11},{9,10}} => {{1,3,10},{2,7,14},{4,11},{5,12},{6,13},{8},{9}}

[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8),(13,14)] => {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8},{13,14}} => {{1,3,9},{2,8},{4,10},{5,11},{6,12},{7,14},{13}}

[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,10),(6,9),(7,8),(12,13)] => {{1,14},{2,3},{4,11},{5,10},{6,9},{7,8},{12,13}} => {{1,3,9},{2,8},{4,10},{5,11},{6,13},{7,14},{12}}

[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,10),(6,9),(7,8),(11,12)] => {{1,14},{2,3},{4,13},{5,10},{6,9},{7,8},{11,12}} => {{1,3,9},{2,8},{4,10},{5,12},{6,13},{7,14},{11}}

[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,9),(7,8),(10,11)] => {{1,14},{2,3},{4,13},{5,12},{6,9},{7,8},{10,11}} => {{1,3,9},{2,8},{4,11},{5,12},{6,13},{7,14},{10}}

[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,11),(7,8),(9,10)] => {{1,14},{2,3},{4,13},{5,12},{6,11},{7,8},{9,10}} => {{1,3,10},{2,8},{4,11},{5,12},{6,13},{7,14},{9}}

[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,11),(7,10),(8,9)] => {{1,14},{2,3},{4,13},{5,12},{6,11},{7,10},{8,9}} => {{1,3,10},{2,9},{4,11},{5,12},{6,13},{7,14},{8}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13)] => {{1,14},{2,5},{3,4},{6,7},{8,9},{10,11},{12,13}} => {{1,4,9},{2,5,11},{3,7,14},{6,13},{8},{10},{12}}

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,9),(10,13),(11,12)] => {{1,14},{2,5},{3,4},{6,7},{8,9},{10,13},{11,12}} => {{1,4,9},{2,5,12},{3,7,14},{6,13},{8},{10},{11}}

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,11),(9,10),(12,13)] => {{1,14},{2,5},{3,4},{6,7},{8,11},{9,10},{12,13}} => {{1,4,10},{2,5,11},{3,7,14},{6,13},{8},{9},{12}}

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,13),(9,10),(11,12)] => {{1,14},{2,5},{3,4},{6,7},{8,13},{9,10},{11,12}} => {{1,4,10},{2,5,12},{3,7,14},{6,13},{8},{9},{11}}

[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,13),(9,12),(10,11)] => {{1,14},{2,5},{3,4},{6,7},{8,13},{9,12},{10,11}} => {{1,4,11},{2,5,12},{3,7,14},{6,13},{8},{9},{10}}

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [(1,14),(2,5),(3,4),(6,9),(7,8),(10,11),(12,13)] => {{1,14},{2,5},{3,4},{6,9},{7,8},{10,11},{12,13}} => {{1,4,9},{2,5,11},{3,8},{6,13},{7,14},{10},{12}}

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [(1,14),(2,5),(3,4),(6,9),(7,8),(10,13),(11,12)] => {{1,14},{2,5},{3,4},{6,9},{7,8},{10,13},{11,12}} => {{1,4,9},{2,5,12},{3,8},{6,13},{7,14},{10},{11}}

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [(1,14),(2,5),(3,4),(6,11),(7,8),(9,10),(12,13)] => {{1,14},{2,5},{3,4},{6,11},{7,8},{9,10},{12,13}} => {{1,4,10},{2,5,11},{3,8},{6,13},{7,14},{9},{12}}

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,8),(9,10),(11,12)] => {{1,14},{2,5},{3,4},{6,13},{7,8},{9,10},{11,12}} => {{1,4,10},{2,5,12},{3,8},{6,13},{7,14},{9},{11}}

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,8),(9,12),(10,11)] => {{1,14},{2,5},{3,4},{6,13},{7,8},{9,12},{10,11}} => {{1,4,11},{2,5,12},{3,8},{6,13},{7,14},{9},{10}}

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [(1,14),(2,5),(3,4),(6,11),(7,10),(8,9),(12,13)] => {{1,14},{2,5},{3,4},{6,11},{7,10},{8,9},{12,13}} => {{1,4,10},{2,5,11},{3,9},{6,13},{7,14},{8},{12}}

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,10),(8,9),(11,12)] => {{1,14},{2,5},{3,4},{6,13},{7,10},{8,9},{11,12}} => {{1,4,10},{2,5,12},{3,9},{6,13},{7,14},{8},{11}}

[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,12),(8,9),(10,11)] => {{1,14},{2,5},{3,4},{6,13},{7,12},{8,9},{10,11}} => {{1,4,11},{2,5,12},{3,9},{6,13},{7,14},{8},{10}}

[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,12),(8,11),(9,10)] => {{1,14},{2,5},{3,4},{6,13},{7,12},{8,11},{9,10}} => {{1,4,11},{2,5,12},{3,10},{6,13},{7,14},{8},{9}}

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,9),(10,11),(12,13)] => {{1,14},{2,7},{3,4},{5,6},{8,9},{10,11},{12,13}} => {{1,4,9},{2,6,13},{3,7,14},{5,11},{8},{10},{12}}

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,9),(10,13),(11,12)] => {{1,14},{2,7},{3,4},{5,6},{8,9},{10,13},{11,12}} => {{1,4,9},{2,6,13},{3,7,14},{5,12},{8},{10},{11}}

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,11),(9,10),(12,13)] => {{1,14},{2,7},{3,4},{5,6},{8,11},{9,10},{12,13}} => {{1,4,10},{2,6,13},{3,7,14},{5,11},{8},{9},{12}}

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,13),(9,10),(11,12)] => {{1,14},{2,7},{3,4},{5,6},{8,13},{9,10},{11,12}} => {{1,4,10},{2,6,13},{3,7,14},{5,12},{8},{9},{11}}

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,13),(9,12),(10,11)] => {{1,14},{2,7},{3,4},{5,6},{8,13},{9,12},{10,11}} => {{1,4,11},{2,6,13},{3,7,14},{5,12},{8},{9},{10}}

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,4),(5,6),(7,8),(10,11),(12,13)] => {{1,14},{2,9},{3,4},{5,6},{7,8},{10,11},{12,13}} => {{1,4,9},{2,6,13},{3,8},{5,11},{7,14},{10},{12}}

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,4),(5,6),(7,8),(10,13),(11,12)] => {{1,14},{2,9},{3,4},{5,6},{7,8},{10,13},{11,12}} => {{1,4,9},{2,6,13},{3,8},{5,12},{7,14},{10},{11}}

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,6),(7,8),(9,10),(12,13)] => {{1,14},{2,11},{3,4},{5,6},{7,8},{9,10},{12,13}} => {{1,4,10},{2,6,13},{3,8},{5,11},{7,14},{9},{12}}

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,8),(9,10),(11,12)] => {{1,14},{2,13},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,4,10},{2,6,13},{3,8},{5,12},{7,14},{9},{11}}

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,8),(9,12),(10,11)] => {{1,14},{2,13},{3,4},{5,6},{7,8},{9,12},{10,11}} => {{1,4,11},{2,6,13},{3,8},{5,12},{7,14},{9},{10}}

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,6),(7,10),(8,9),(12,13)] => {{1,14},{2,11},{3,4},{5,6},{7,10},{8,9},{12,13}} => {{1,4,10},{2,6,13},{3,9},{5,11},{7,14},{8},{12}}

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,10),(8,9),(11,12)] => {{1,14},{2,13},{3,4},{5,6},{7,10},{8,9},{11,12}} => {{1,4,10},{2,6,13},{3,9},{5,12},{7,14},{8},{11}}

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,12),(8,9),(10,11)] => {{1,14},{2,13},{3,4},{5,6},{7,12},{8,9},{10,11}} => {{1,4,11},{2,6,13},{3,9},{5,12},{7,14},{8},{10}}

[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,12),(8,11),(9,10)] => {{1,14},{2,13},{3,4},{5,6},{7,12},{8,11},{9,10}} => {{1,4,11},{2,6,13},{3,10},{5,12},{7,14},{8},{9}}

[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,4),(5,8),(6,7),(10,11),(12,13)] => {{1,14},{2,9},{3,4},{5,8},{6,7},{10,11},{12,13}} => {{1,4,9},{2,7,14},{3,8},{5,11},{6,13},{10},{12}}

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,4),(5,8),(6,7),(10,13),(11,12)] => {{1,14},{2,9},{3,4},{5,8},{6,7},{10,13},{11,12}} => {{1,4,9},{2,7,14},{3,8},{5,12},{6,13},{10},{11}}

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,8),(6,7),(9,10),(12,13)] => {{1,14},{2,11},{3,4},{5,8},{6,7},{9,10},{12,13}} => {{1,4,10},{2,7,14},{3,8},{5,11},{6,13},{9},{12}}

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,8),(6,7),(9,10),(11,12)] => {{1,14},{2,13},{3,4},{5,8},{6,7},{9,10},{11,12}} => {{1,4,10},{2,7,14},{3,8},{5,12},{6,13},{9},{11}}

[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,8),(6,7),(9,12),(10,11)] => {{1,14},{2,13},{3,4},{5,8},{6,7},{9,12},{10,11}} => {{1,4,11},{2,7,14},{3,8},{5,12},{6,13},{9},{10}}

[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9),(13,14)] => {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9},{13,14}} => {{1,4,10},{2,7,14},{3,9},{5,11},{6,12},{8},{13}}

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,10),(6,7),(8,9),(12,13)] => {{1,14},{2,11},{3,4},{5,10},{6,7},{8,9},{12,13}} => {{1,4,10},{2,7,14},{3,9},{5,11},{6,13},{8},{12}}

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,10),(6,7),(8,9),(11,12)] => {{1,14},{2,13},{3,4},{5,10},{6,7},{8,9},{11,12}} => {{1,4,10},{2,7,14},{3,9},{5,12},{6,13},{8},{11}}

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,7),(8,9),(10,11)] => {{1,14},{2,13},{3,4},{5,12},{6,7},{8,9},{10,11}} => {{1,4,11},{2,7,14},{3,9},{5,12},{6,13},{8},{10}}

[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,7),(8,11),(9,10)] => {{1,14},{2,13},{3,4},{5,12},{6,7},{8,11},{9,10}} => {{1,4,11},{2,7,14},{3,10},{5,12},{6,13},{8},{9}}

[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)] => {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8},{13,14}} => {{1,4,10},{2,8},{3,9},{5,11},{6,12},{7,14},{13}}

[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,10),(6,9),(7,8),(12,13)] => {{1,14},{2,11},{3,4},{5,10},{6,9},{7,8},{12,13}} => {{1,4,10},{2,8},{3,9},{5,11},{6,13},{7,14},{12}}

[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,10),(6,9),(7,8),(11,12)] => {{1,14},{2,13},{3,4},{5,10},{6,9},{7,8},{11,12}} => {{1,4,10},{2,8},{3,9},{5,12},{6,13},{7,14},{11}}

[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,9),(7,8),(10,11)] => {{1,14},{2,13},{3,4},{5,12},{6,9},{7,8},{10,11}} => {{1,4,11},{2,8},{3,9},{5,12},{6,13},{7,14},{10}}

[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,11),(7,8),(9,10)] => {{1,14},{2,13},{3,4},{5,12},{6,11},{7,8},{9,10}} => {{1,4,11},{2,8},{3,10},{5,12},{6,13},{7,14},{9}}

[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,11),(7,10),(8,9)] => {{1,14},{2,13},{3,4},{5,12},{6,11},{7,10},{8,9}} => {{1,4,11},{2,9},{3,10},{5,12},{6,13},{7,14},{8}}

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,9),(10,11),(12,13)] => {{1,14},{2,7},{3,6},{4,5},{8,9},{10,11},{12,13}} => {{1,5,11},{2,6,13},{3,7,14},{4,9},{8},{10},{12}}

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,9),(10,13),(11,12)] => {{1,14},{2,7},{3,6},{4,5},{8,9},{10,13},{11,12}} => {{1,5,12},{2,6,13},{3,7,14},{4,9},{8},{10},{11}}

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,11),(9,10),(12,13)] => {{1,14},{2,7},{3,6},{4,5},{8,11},{9,10},{12,13}} => {{1,5,11},{2,6,13},{3,7,14},{4,10},{8},{9},{12}}

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,13),(9,10),(11,12)] => {{1,14},{2,7},{3,6},{4,5},{8,13},{9,10},{11,12}} => {{1,5,12},{2,6,13},{3,7,14},{4,10},{8},{9},{11}}

[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,13),(9,12),(10,11)] => {{1,14},{2,7},{3,6},{4,5},{8,13},{9,12},{10,11}} => {{1,5,12},{2,6,13},{3,7,14},{4,11},{8},{9},{10}}

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,6),(4,5),(7,8),(10,11),(12,13)] => {{1,14},{2,9},{3,6},{4,5},{7,8},{10,11},{12,13}} => {{1,5,11},{2,6,13},{3,8},{4,9},{7,14},{10},{12}}

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,6),(4,5),(7,8),(10,13),(11,12)] => {{1,14},{2,9},{3,6},{4,5},{7,8},{10,13},{11,12}} => {{1,5,12},{2,6,13},{3,8},{4,9},{7,14},{10},{11}}

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,6),(4,5),(7,8),(9,10),(12,13)] => {{1,14},{2,11},{3,6},{4,5},{7,8},{9,10},{12,13}} => {{1,5,11},{2,6,13},{3,8},{4,10},{7,14},{9},{12}}

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,8),(9,10),(11,12)] => {{1,14},{2,13},{3,6},{4,5},{7,8},{9,10},{11,12}} => {{1,5,12},{2,6,13},{3,8},{4,10},{7,14},{9},{11}}

[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,8),(9,12),(10,11)] => {{1,14},{2,13},{3,6},{4,5},{7,8},{9,12},{10,11}} => {{1,5,12},{2,6,13},{3,8},{4,11},{7,14},{9},{10}}

[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9),(13,14)] => {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9},{13,14}} => {{1,5,11},{2,6,12},{3,9},{4,10},{7,14},{8},{13}}

[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,6),(4,5),(7,10),(8,9),(12,13)] => {{1,14},{2,11},{3,6},{4,5},{7,10},{8,9},{12,13}} => {{1,5,11},{2,6,13},{3,9},{4,10},{7,14},{8},{12}}

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,10),(8,9),(11,12)] => {{1,14},{2,13},{3,6},{4,5},{7,10},{8,9},{11,12}} => {{1,5,12},{2,6,13},{3,9},{4,10},{7,14},{8},{11}}

[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,12),(8,9),(10,11)] => {{1,14},{2,13},{3,6},{4,5},{7,12},{8,9},{10,11}} => {{1,5,12},{2,6,13},{3,9},{4,11},{7,14},{8},{10}}

[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,12),(8,11),(9,10)] => {{1,14},{2,13},{3,6},{4,5},{7,12},{8,11},{9,10}} => {{1,5,12},{2,6,13},{3,10},{4,11},{7,14},{8},{9}}

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,8),(4,5),(6,7),(10,11),(12,13)] => {{1,14},{2,9},{3,8},{4,5},{6,7},{10,11},{12,13}} => {{1,5,11},{2,7,14},{3,8},{4,9},{6,13},{10},{12}}

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,8),(4,5),(6,7),(10,13),(11,12)] => {{1,14},{2,9},{3,8},{4,5},{6,7},{10,13},{11,12}} => {{1,5,12},{2,7,14},{3,8},{4,9},{6,13},{10},{11}}

[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10),(13,14)] => {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10},{13,14}} => {{1,5,11},{2,7,14},{3,8},{4,10},{6,12},{9},{13}}

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,8),(4,5),(6,7),(9,10),(12,13)] => {{1,14},{2,11},{3,8},{4,5},{6,7},{9,10},{12,13}} => {{1,5,11},{2,7,14},{3,8},{4,10},{6,13},{9},{12}}

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,8),(4,5),(6,7),(9,10),(11,12)] => {{1,14},{2,13},{3,8},{4,5},{6,7},{9,10},{11,12}} => {{1,5,12},{2,7,14},{3,8},{4,10},{6,13},{9},{11}}

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,8),(4,5),(6,7),(9,12),(10,11)] => {{1,14},{2,13},{3,8},{4,5},{6,7},{9,12},{10,11}} => {{1,5,12},{2,7,14},{3,8},{4,11},{6,13},{9},{10}}

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)] => {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9},{13,14}} => {{1,5,11},{2,7,14},{3,9},{4,10},{6,12},{8},{13}}

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,5),(6,7),(8,9),(12,13)] => {{1,14},{2,11},{3,10},{4,5},{6,7},{8,9},{12,13}} => {{1,5,11},{2,7,14},{3,9},{4,10},{6,13},{8},{12}}

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,5),(6,7),(8,9),(11,12)] => {{1,14},{2,13},{3,10},{4,5},{6,7},{8,9},{11,12}} => {{1,5,12},{2,7,14},{3,9},{4,10},{6,13},{8},{11}}

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,7),(8,9),(10,11)] => {{1,14},{2,13},{3,12},{4,5},{6,7},{8,9},{10,11}} => {{1,5,12},{2,7,14},{3,9},{4,11},{6,13},{8},{10}}

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,7),(8,11),(9,10)] => {{1,14},{2,13},{3,12},{4,5},{6,7},{8,11},{9,10}} => {{1,5,12},{2,7,14},{3,10},{4,11},{6,13},{8},{9}}

[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)] => {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8},{13,14}} => {{1,5,11},{2,8},{3,9},{4,10},{6,12},{7,14},{13}}

[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,5),(6,9),(7,8),(12,13)] => {{1,14},{2,11},{3,10},{4,5},{6,9},{7,8},{12,13}} => {{1,5,11},{2,8},{3,9},{4,10},{6,13},{7,14},{12}}

[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,5),(6,9),(7,8),(11,12)] => {{1,14},{2,13},{3,10},{4,5},{6,9},{7,8},{11,12}} => {{1,5,12},{2,8},{3,9},{4,10},{6,13},{7,14},{11}}

[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,9),(7,8),(10,11)] => {{1,14},{2,13},{3,12},{4,5},{6,9},{7,8},{10,11}} => {{1,5,12},{2,8},{3,9},{4,11},{6,13},{7,14},{10}}

[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,8),(9,10)] => {{1,14},{2,13},{3,12},{4,5},{6,11},{7,8},{9,10}} => {{1,5,12},{2,8},{3,10},{4,11},{6,13},{7,14},{9}}

[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9)] => {{1,14},{2,13},{3,12},{4,5},{6,11},{7,10},{8,9}} => {{1,5,12},{2,9},{3,10},{4,11},{6,13},{7,14},{8}}

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)] => {{1,10},{2,9},{3,8},{4,7},{5,6},{11,14},{12,13}} => {{1,6,13},{2,7,14},{3,8},{4,9},{5,10},{11},{12}}

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)] => {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11},{13,14}} => {{1,6,12},{2,7,14},{3,8},{4,9},{5,11},{10},{13}}

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,8),(4,7),(5,6),(10,11),(12,13)] => {{1,14},{2,9},{3,8},{4,7},{5,6},{10,11},{12,13}} => {{1,6,13},{2,7,14},{3,8},{4,9},{5,11},{10},{12}}

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,8),(4,7),(5,6),(10,13),(11,12)] => {{1,14},{2,9},{3,8},{4,7},{5,6},{10,13},{11,12}} => {{1,6,13},{2,7,14},{3,8},{4,9},{5,12},{10},{11}}

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)] => {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10},{13,14}} => {{1,6,12},{2,7,14},{3,8},{4,10},{5,11},{9},{13}}

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,8),(4,7),(5,6),(9,10),(12,13)] => {{1,14},{2,11},{3,8},{4,7},{5,6},{9,10},{12,13}} => {{1,6,13},{2,7,14},{3,8},{4,10},{5,11},{9},{12}}

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,8),(4,7),(5,6),(9,10),(11,12)] => {{1,14},{2,13},{3,8},{4,7},{5,6},{9,10},{11,12}} => {{1,6,13},{2,7,14},{3,8},{4,10},{5,12},{9},{11}}

[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,8),(4,7),(5,6),(9,12),(10,11)] => {{1,14},{2,13},{3,8},{4,7},{5,6},{9,12},{10,11}} => {{1,6,13},{2,7,14},{3,8},{4,11},{5,12},{9},{10}}

[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)] => {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9},{13,14}} => {{1,6,12},{2,7,14},{3,9},{4,10},{5,11},{8},{13}}

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,7),(5,6),(8,9),(12,13)] => {{1,14},{2,11},{3,10},{4,7},{5,6},{8,9},{12,13}} => {{1,6,13},{2,7,14},{3,9},{4,10},{5,11},{8},{12}}

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,7),(5,6),(8,9),(11,12)] => {{1,14},{2,13},{3,10},{4,7},{5,6},{8,9},{11,12}} => {{1,6,13},{2,7,14},{3,9},{4,10},{5,12},{8},{11}}

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,7),(5,6),(8,9),(10,11)] => {{1,14},{2,13},{3,12},{4,7},{5,6},{8,9},{10,11}} => {{1,6,13},{2,7,14},{3,9},{4,11},{5,12},{8},{10}}

[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,7),(5,6),(8,11),(9,10)] => {{1,14},{2,13},{3,12},{4,7},{5,6},{8,11},{9,10}} => {{1,6,13},{2,7,14},{3,10},{4,11},{5,12},{8},{9}}

[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)] => {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8},{13,14}} => {{1,6,12},{2,8},{3,9},{4,10},{5,11},{7,14},{13}}

[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,9),(5,6),(7,8),(12,13)] => {{1,14},{2,11},{3,10},{4,9},{5,6},{7,8},{12,13}} => {{1,6,13},{2,8},{3,9},{4,10},{5,11},{7,14},{12}}

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,9),(5,6),(7,8),(11,12)] => {{1,14},{2,13},{3,10},{4,9},{5,6},{7,8},{11,12}} => {{1,6,13},{2,8},{3,9},{4,10},{5,12},{7,14},{11}}

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,9),(5,6),(7,8),(10,11)] => {{1,14},{2,13},{3,12},{4,9},{5,6},{7,8},{10,11}} => {{1,6,13},{2,8},{3,9},{4,11},{5,12},{7,14},{10}}

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10)] => {{1,14},{2,13},{3,12},{4,11},{5,6},{7,8},{9,10}} => {{1,6,13},{2,8},{3,10},{4,11},{5,12},{7,14},{9}}

[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9)] => {{1,14},{2,13},{3,12},{4,11},{5,6},{7,10},{8,9}} => {{1,6,13},{2,9},{3,10},{4,11},{5,12},{7,14},{8}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7},{13,14}} => {{1,7,14},{2,8},{3,9},{4,10},{5,11},{6,12},{13}}

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,9),(5,8),(6,7),(12,13)] => {{1,14},{2,11},{3,10},{4,9},{5,8},{6,7},{12,13}} => {{1,7,14},{2,8},{3,9},{4,10},{5,11},{6,13},{12}}

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,9),(5,8),(6,7),(11,12)] => {{1,14},{2,13},{3,10},{4,9},{5,8},{6,7},{11,12}} => {{1,7,14},{2,8},{3,9},{4,10},{5,12},{6,13},{11}}

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11)] => {{1,14},{2,13},{3,12},{4,9},{5,8},{6,7},{10,11}} => {{1,7,14},{2,8},{3,9},{4,11},{5,12},{6,13},{10}}

[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10)] => {{1,14},{2,13},{3,12},{4,11},{5,8},{6,7},{9,10}} => {{1,7,14},{2,8},{3,10},{4,11},{5,12},{6,13},{9}}

[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9)] => {{1,14},{2,13},{3,12},{4,11},{5,10},{6,7},{8,9}} => {{1,7,14},{2,9},{3,10},{4,11},{5,12},{6,13},{8}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8)] => {{1,14},{2,13},{3,12},{4,11},{5,10},{6,9},{7,8}} => {{1,8},{2,9},{3,10},{4,11},{5,12},{6,13},{7,14}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,14},{15,16}} => {{1,2,4,8,16},{3,6,12},{5,10},{7,14},{9},{11},{13},{15}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,16),(14,15)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,16},{14,15}} => {{1,2,4,8,16},{3,6,12},{5,10},{7,15},{9},{11},{13},{14}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,16),(12,13),(14,15)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,16},{12,13},{14,15}} => {{1,2,4,8,16},{3,6,13},{5,10},{7,15},{9},{11},{12},{14}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,16),(12,15),(13,14)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,16},{12,15},{13,14}} => {{1,2,4,8,16},{3,6,14},{5,10},{7,15},{9},{11},{12},{13}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,16),(10,11),(12,13),(14,15)] => {{1,2},{3,4},{5,6},{7,8},{9,16},{10,11},{12,13},{14,15}} => {{1,2,4,8,16},{3,6,13},{5,11},{7,15},{9},{10},{12},{14}}

[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,16),(10,13),(11,12),(14,15)] => {{1,2},{3,4},{5,6},{7,8},{9,16},{10,13},{11,12},{14,15}} => {{1,2,4,8,16},{3,6,13},{5,12},{7,15},{9},{10},{11},{14}}

[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,16),(10,15),(11,12),(13,14)] => {{1,2},{3,4},{5,6},{7,8},{9,16},{10,15},{11,12},{13,14}} => {{1,2,4,8,16},{3,6,14},{5,12},{7,15},{9},{10},{11},{13}}

[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,16),(10,15),(11,14),(12,13)] => {{1,2},{3,4},{5,6},{7,8},{9,16},{10,15},{11,14},{12,13}} => {{1,2,4,8,16},{3,6,14},{5,13},{7,15},{9},{10},{11},{12}}

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,16),(8,9),(10,11),(12,13),(14,15)] => {{1,2},{3,4},{5,6},{7,16},{8,9},{10,11},{12,13},{14,15}} => {{1,2,4,9},{3,6,13},{5,11},{7,15},{8,16},{10},{12},{14}}

[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,16),(8,11),(9,10),(12,13),(14,15)] => {{1,2},{3,4},{5,6},{7,16},{8,11},{9,10},{12,13},{14,15}} => {{1,2,4,10},{3,6,13},{5,11},{7,15},{8,16},{9},{12},{14}}

[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,4),(5,6),(7,16),(8,13),(9,10),(11,12),(14,15)] => {{1,2},{3,4},{5,6},{7,16},{8,13},{9,10},{11,12},{14,15}} => {{1,2,4,10},{3,6,13},{5,12},{7,15},{8,16},{9},{11},{14}}

[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,4),(5,6),(7,16),(8,13),(9,12),(10,11),(14,15)] => {{1,2},{3,4},{5,6},{7,16},{8,13},{9,12},{10,11},{14,15}} => {{1,2,4,11},{3,6,13},{5,12},{7,15},{8,16},{9},{10},{14}}

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,16),(6,7),(8,9),(10,11),(12,13),(14,15)] => {{1,2},{3,4},{5,16},{6,7},{8,9},{10,11},{12,13},{14,15}} => {{1,2,4,9},{3,7,15},{5,11},{6,13},{8,16},{10},{12},{14}}

[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,16),(6,9),(7,8),(10,11),(12,13),(14,15)] => {{1,2},{3,4},{5,16},{6,9},{7,8},{10,11},{12,13},{14,15}} => {{1,2,4,9},{3,8,16},{5,11},{6,13},{7,15},{10},{12},{14}}

[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [(1,2),(3,4),(5,16),(6,11),(7,8),(9,10),(12,13),(14,15)] => {{1,2},{3,4},{5,16},{6,11},{7,8},{9,10},{12,13},{14,15}} => {{1,2,4,10},{3,8,16},{5,11},{6,13},{7,15},{9},{12},{14}}

[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [(1,2),(3,4),(5,16),(6,11),(7,10),(8,9),(12,13),(14,15)] => {{1,2},{3,4},{5,16},{6,11},{7,10},{8,9},{12,13},{14,15}} => {{1,2,4,10},{3,9},{5,11},{6,13},{7,15},{8,16},{12},{14}}

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,16),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15)] => {{1,2},{3,16},{4,5},{6,7},{8,9},{10,11},{12,13},{14,15}} => {{1,2,5,11},{3,7,15},{4,9},{6,13},{8,16},{10},{12},{14}}

[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,16),(4,7),(5,6),(8,9),(10,11),(12,13),(14,15)] => {{1,2},{3,16},{4,7},{5,6},{8,9},{10,11},{12,13},{14,15}} => {{1,2,6,13},{3,7,15},{4,9},{5,11},{8,16},{10},{12},{14}}

[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [(1,2),(3,16),(4,9),(5,6),(7,8),(10,11),(12,13),(14,15)] => {{1,2},{3,16},{4,9},{5,6},{7,8},{10,11},{12,13},{14,15}} => {{1,2,6,13},{3,8,16},{4,9},{5,11},{7,15},{10},{12},{14}}

[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [(1,2),(3,16),(4,9),(5,8),(6,7),(10,11),(12,13),(14,15)] => {{1,2},{3,16},{4,9},{5,8},{6,7},{10,11},{12,13},{14,15}} => {{1,2,7,15},{3,8,16},{4,9},{5,11},{6,13},{10},{12},{14}}

[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => {{1,2},{3,16},{4,15},{5,14},{6,7},{8,13},{9,12},{10,11}} => {{1,2,7,15},{3,11},{4,12},{5,13},{6,14},{8,16},{9},{10}}

[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)] => {{1,2},{3,16},{4,15},{5,14},{6,13},{7,8},{9,10},{11,12}} => {{1,2,8,16},{3,10},{4,12},{5,13},{6,14},{7,15},{9},{11}}

[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => {{1,2},{3,16},{4,15},{5,14},{6,13},{7,8},{9,12},{10,11}} => {{1,2,8,16},{3,11},{4,12},{5,13},{6,14},{7,15},{9},{10}}

[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)] => {{1,2},{3,16},{4,15},{5,14},{6,11},{7,10},{8,9},{12,13}} => {{1,2,9},{3,10},{4,11},{5,13},{6,14},{7,15},{8,16},{12}}

[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => {{1,2},{3,16},{4,15},{5,14},{6,13},{7,10},{8,9},{11,12}} => {{1,2,9},{3,10},{4,12},{5,13},{6,14},{7,15},{8,16},{11}}

[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => {{1,2},{3,16},{4,15},{5,14},{6,13},{7,12},{8,9},{10,11}} => {{1,2,9},{3,11},{4,12},{5,13},{6,14},{7,15},{8,16},{10}}

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => {{1,2},{3,16},{4,15},{5,14},{6,13},{7,12},{8,11},{9,10}} => {{1,2,10},{3,11},{4,12},{5,13},{6,14},{7,15},{8,16},{9}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15)] => {{1,16},{2,3},{4,5},{6,7},{8,9},{10,11},{12,13},{14,15}} => {{1,3,7,15},{2,5,11},{4,9},{6,13},{8,16},{10},{12},{14}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13),(14,15)] => {{1,16},{2,5},{3,4},{6,7},{8,9},{10,11},{12,13},{14,15}} => {{1,4,9},{2,5,11},{3,7,15},{6,13},{8,16},{10},{12},{14}}

[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,7),(3,4),(5,6),(8,9),(10,11),(12,13),(14,15)] => {{1,16},{2,7},{3,4},{5,6},{8,9},{10,11},{12,13},{14,15}} => {{1,4,9},{2,6,13},{3,7,15},{5,11},{8,16},{10},{12},{14}}

[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,7),(3,6),(4,5),(8,9),(10,11),(12,13),(14,15)] => {{1,16},{2,7},{3,6},{4,5},{8,9},{10,11},{12,13},{14,15}} => {{1,5,11},{2,6,13},{3,7,15},{4,9},{8,16},{10},{12},{14}}

[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9),(15,16)] => {{1,14},{2,13},{3,12},{4,5},{6,11},{7,10},{8,9},{15,16}} => {{1,5,12},{2,9},{3,10},{4,11},{6,13},{7,14},{8,16},{15}}

[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10),(15,16)] => {{1,14},{2,13},{3,12},{4,11},{5,6},{7,8},{9,10},{15,16}} => {{1,6,13},{2,8,16},{3,10},{4,11},{5,12},{7,14},{9},{15}}

[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9),(15,16)] => {{1,14},{2,13},{3,12},{4,11},{5,6},{7,10},{8,9},{15,16}} => {{1,6,13},{2,9},{3,10},{4,11},{5,12},{7,14},{8,16},{15}}

[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)] => {{1,14},{2,13},{3,12},{4,9},{5,8},{6,7},{10,11},{15,16}} => {{1,7,14},{2,8,16},{3,9},{4,11},{5,12},{6,13},{10},{15}}

[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10),(15,16)] => {{1,14},{2,13},{3,12},{4,11},{5,8},{6,7},{9,10},{15,16}} => {{1,7,14},{2,8,16},{3,10},{4,11},{5,12},{6,13},{9},{15}}

[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)] => {{1,14},{2,13},{3,12},{4,11},{5,10},{6,7},{8,9},{15,16}} => {{1,7,14},{2,9},{3,10},{4,11},{5,12},{6,13},{8,16},{15}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)] => {{1,14},{2,13},{3,12},{4,11},{5,10},{6,9},{7,8},{15,16}} => {{1,8,16},{2,9},{3,10},{4,11},{5,12},{6,13},{7,14},{15}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9),(17,18)] => {{1,16},{2,15},{3,14},{4,13},{5,12},{6,11},{7,10},{8,9},{17,18}} => {{1,9,18},{2,10},{3,11},{4,12},{5,13},{6,14},{7,15},{8,16},{17}}

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => {{1,2},{3,18},{4,17},{5,16},{6,15},{7,14},{8,13},{9,12},{10,11}} => {{1,2,11},{3,12},{4,13},{5,14},{6,15},{7,16},{8,17},{9,18},{10}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10),(19,20)] => {{1,18},{2,17},{3,16},{4,15},{5,14},{6,13},{7,12},{8,11},{9,10},{19,20}} => {{1,10,20},{2,11},{3,12},{4,13},{5,14},{6,15},{7,16},{8,17},{9,18},{19}}

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10),(17,18)] => {{1,16},{2,15},{3,14},{4,13},{5,12},{6,11},{7,8},{9,10},{17,18}} => {{1,8,16},{2,10},{3,11},{4,12},{5,13},{6,14},{7,15},{9,18},{17}}

[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => {{1,2},{3,18},{4,17},{5,16},{6,15},{7,14},{8,13},{9,10},{11,12}} => {{1,2,10},{3,12},{4,13},{5,14},{6,15},{7,16},{8,17},{9,18},{11}}

[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => {{1,2},{3,20},{4,19},{5,18},{6,17},{7,16},{8,15},{9,14},{10,13},{11,12}} => {{1,2,12},{3,13},{4,14},{5,15},{6,16},{7,17},{8,18},{9,19},{10,20},{11}}

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [(1,20),(2,19),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11),(21,22)] => {{1,20},{2,19},{3,18},{4,17},{5,16},{6,15},{7,14},{8,13},{9,12},{10,11},{21,22}} => {{1,11,22},{2,12},{3,13},{4,14},{5,15},{6,16},{7,17},{8,18},{9,19},{10,20},{21}}

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11),(19,20)] => {{1,18},{2,17},{3,16},{4,15},{5,14},{6,13},{7,12},{8,9},{10,11},{19,20}} => {{1,9,18},{2,11},{3,12},{4,13},{5,14},{6,15},{7,16},{8,17},{10,20},{19}}

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11),(17,18)] => {{1,16},{2,15},{3,14},{4,13},{5,12},{6,9},{7,8},{10,11},{17,18}} => {{1,8,16},{2,9,18},{3,11},{4,12},{5,13},{6,14},{7,15},{10},{17}}

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10),(17,18)] => {{1,16},{2,15},{3,14},{4,13},{5,12},{6,7},{8,11},{9,10},{17,18}} => {{1,7,15},{2,10},{3,11},{4,12},{5,13},{6,14},{8,16},{9,18},{17}}

[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)] => {{1,2},{3,18},{4,17},{5,16},{6,15},{7,14},{8,11},{9,10},{12,13}} => {{1,2,10},{3,11},{4,13},{5,14},{6,15},{7,16},{8,17},{9,18},{12}}

[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)] => {{1,2},{3,18},{4,17},{5,16},{6,15},{7,14},{8,9},{10,13},{11,12}} => {{1,2,9,18},{3,12},{4,13},{5,14},{6,15},{7,16},{8,17},{10},{11}}

[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)] => {{1,2},{3,20},{4,19},{5,18},{6,17},{7,16},{8,15},{9,14},{10,11},{12,13}} => {{1,2,11},{3,13},{4,14},{5,15},{6,16},{7,17},{8,18},{9,19},{10,20},{12}}

[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => {{1,2},{3,22},{4,21},{5,20},{6,19},{7,18},{8,17},{9,16},{10,15},{11,14},{12,13}} => {{1,2,13},{3,14},{4,15},{5,16},{6,17},{7,18},{8,19},{9,20},{10,21},{11,22},{12}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,18),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)] => {{1,18},{2,3},{4,5},{6,7},{8,9},{10,11},{12,13},{14,15},{16,17}} => {{1,3,7,15},{2,5,11},{4,9,18},{6,13},{8,17},{10},{12},{14},{16}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,18),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)] => {{1,18},{2,5},{3,4},{6,7},{8,9},{10,11},{12,13},{14,15},{16,17}} => {{1,4,9,18},{2,5,11},{3,7,15},{6,13},{8,17},{10},{12},{14},{16}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,14},{15,16},{17,18}} => {{1,2,4,8,16},{3,6,12},{5,10},{7,14},{9,18},{11},{13},{15},{17}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,18),(16,17)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,14},{15,18},{16,17}} => {{1,2,4,8,17},{3,6,12},{5,10},{7,14},{9,18},{11},{13},{15},{16}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,18),(14,15),(16,17)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,18},{14,15},{16,17}} => {{1,2,4,8,17},{3,6,12},{5,10},{7,15},{9,18},{11},{13},{14},{16}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,18),(12,13),(14,15),(16,17)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,18},{12,13},{14,15},{16,17}} => {{1,2,4,8,17},{3,6,13},{5,10},{7,15},{9,18},{11},{12},{14},{16}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,18),(10,11),(12,13),(14,15),(16,17)] => {{1,2},{3,4},{5,6},{7,8},{9,18},{10,11},{12,13},{14,15},{16,17}} => {{1,2,4,8,17},{3,6,13},{5,11},{7,15},{9,18},{10},{12},{14},{16}}

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,18),(8,9),(10,11),(12,13),(14,15),(16,17)] => {{1,2},{3,4},{5,6},{7,18},{8,9},{10,11},{12,13},{14,15},{16,17}} => {{1,2,4,9,18},{3,6,13},{5,11},{7,15},{8,17},{10},{12},{14},{16}}

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,18),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)] => {{1,2},{3,4},{5,18},{6,7},{8,9},{10,11},{12,13},{14,15},{16,17}} => {{1,2,4,9,18},{3,7,15},{5,11},{6,13},{8,17},{10},{12},{14},{16}}

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,18),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)] => {{1,2},{3,18},{4,5},{6,7},{8,9},{10,11},{12,13},{14,15},{16,17}} => {{1,2,5,11},{3,7,15},{4,9,18},{6,13},{8,17},{10},{12},{14},{16}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,14},{15,16},{17,18},{19,20}} => {{1,2,4,8,16},{3,6,12},{5,10,20},{7,14},{9,18},{11},{13},{15},{17},{19}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,20),(18,19)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,14},{15,16},{17,20},{18,19}} => {{1,2,4,8,16},{3,6,12},{5,10,20},{7,14},{9,19},{11},{13},{15},{17},{18}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,18),(14,17),(15,16)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,18},{14,17},{15,16}} => {{1,2,4,8,17},{3,6,12},{5,10},{7,16},{9,18},{11},{13},{14},{15}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,20),(16,17),(18,19)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,14},{15,20},{16,17},{18,19}} => {{1,2,4,8,17},{3,6,12},{5,10,20},{7,14},{9,19},{11},{13},{15},{16},{18}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,18),(12,15),(13,14),(16,17)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,18},{12,15},{13,14},{16,17}} => {{1,2,4,8,17},{3,6,14},{5,10},{7,15},{9,18},{11},{12},{13},{16}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,20),(14,15),(16,17),(18,19)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,20},{14,15},{16,17},{18,19}} => {{1,2,4,8,17},{3,6,12},{5,10,20},{7,15},{9,19},{11},{13},{14},{16},{18}}

[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,18),(10,13),(11,12),(14,15),(16,17)] => {{1,2},{3,4},{5,6},{7,8},{9,18},{10,13},{11,12},{14,15},{16,17}} => {{1,2,4,8,17},{3,6,13},{5,12},{7,15},{9,18},{10},{11},{14},{16}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,20),(12,13),(14,15),(16,17),(18,19)] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,20},{12,13},{14,15},{16,17},{18,19}} => {{1,2,4,8,17},{3,6,13},{5,10,20},{7,15},{9,19},{11},{12},{14},{16},{18}}

[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,18),(8,11),(9,10),(12,13),(14,15),(16,17)] => {{1,2},{3,4},{5,6},{7,18},{8,11},{9,10},{12,13},{14,15},{16,17}} => {{1,2,4,10},{3,6,13},{5,11},{7,15},{8,17},{9,18},{12},{14},{16}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,20),(10,11),(12,13),(14,15),(16,17),(18,19)] => {{1,2},{3,4},{5,6},{7,8},{9,20},{10,11},{12,13},{14,15},{16,17},{18,19}} => {{1,2,4,8,17},{3,6,13},{5,11},{7,15},{9,19},{10,20},{12},{14},{16},{18}}

[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,18),(6,9),(7,8),(10,11),(12,13),(14,15),(16,17)] => {{1,2},{3,4},{5,18},{6,9},{7,8},{10,11},{12,13},{14,15},{16,17}} => {{1,2,4,9,18},{3,8,17},{5,11},{6,13},{7,15},{10},{12},{14},{16}}

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,20),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)] => {{1,2},{3,4},{5,6},{7,20},{8,9},{10,11},{12,13},{14,15},{16,17},{18,19}} => {{1,2,4,9,19},{3,6,13},{5,11},{7,15},{8,17},{10,20},{12},{14},{16},{18}}

[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,18),(4,7),(5,6),(8,9),(10,11),(12,13),(14,15),(16,17)] => {{1,2},{3,18},{4,7},{5,6},{8,9},{10,11},{12,13},{14,15},{16,17}} => {{1,2,6,13},{3,7,15},{4,9,18},{5,11},{8,17},{10},{12},{14},{16}}

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,20),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)] => {{1,2},{3,4},{5,20},{6,7},{8,9},{10,11},{12,13},{14,15},{16,17},{18,19}} => {{1,2,4,9,19},{3,7,15},{5,11},{6,13},{8,17},{10,20},{12},{14},{16},{18}}

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,20),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)] => {{1,2},{3,20},{4,5},{6,7},{8,9},{10,11},{12,13},{14,15},{16,17},{18,19}} => {{1,2,5,11},{3,7,15},{4,9,19},{6,13},{8,17},{10,20},{12},{14},{16},{18}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,20),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)] => {{1,20},{2,3},{4,5},{6,7},{8,9},{10,11},{12,13},{14,15},{16,17},{18,19}} => {{1,3,7,15},{2,5,11},{4,9,19},{6,13},{8,17},{10,20},{12},{14},{16},{18}}

Map

to tunnel matching

Description

Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.

Map

to set partition

Description

Return the set partition corresponding to the perfect matching.

Map

inverse Yip

Description

The inverse of a transformation of set partitions due to Yip.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Yip's bijection $\psi^{-1}$.